LMFDB - Embedded newform 61.7.j.a.23.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [61,7,Mod(8,61)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(61, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 7, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("61.8");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 61 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	61.j (of order $20$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$14.0332991008$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			23.4
Character	$\chi$	$=$	61.23
Dual form			61.7.j.a.8.4

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-12.0990 + 1.91629i) q^{2} +(10.2537 - 14.1131i) q^{3} +(81.8450 - 26.5930i) q^{4} +(10.5714 - 3.43485i) q^{5} +(-97.0148 + 190.402i) q^{6} +(-33.3080 + 210.298i) q^{7} +(-240.743 + 122.664i) q^{8} +(131.234 + 403.897i) q^{9} +O(q^{10})$	\(q+(-12.0990 + 1.91629i) q^{2} +(10.2537 - 14.1131i) q^{3} +(81.8450 - 26.5930i) q^{4} +(10.5714 - 3.43485i) q^{5} +(-97.0148 + 190.402i) q^{6} +(-33.3080 + 210.298i) q^{7} +(-240.743 + 122.664i) q^{8} +(131.234 + 403.897i) q^{9} +(-121.321 + 61.8159i) q^{10} +(-1774.53 - 1774.53i) q^{11} +(463.908 - 1427.76i) q^{12} +1268.39 q^{13} -2608.22i q^{14} +(59.9200 - 184.415i) q^{15} +(-1778.10 + 1291.87i) q^{16} +(210.353 - 412.841i) q^{17} +(-2361.78 - 4635.25i) q^{18} +(-1492.28 + 2053.95i) q^{19} +(773.872 - 562.251i) q^{20} +(2626.42 + 2626.42i) q^{21} +(24870.4 + 18069.4i) q^{22} +(18876.1 + 9617.85i) q^{23} +(-737.340 + 4655.38i) q^{24} +(-12540.9 + 9111.52i) q^{25} +(-15346.2 + 2430.61i) q^{26} +(19140.6 + 6219.17i) q^{27} +(2866.38 + 18097.6i) q^{28} +(23267.1 + 23267.1i) q^{29} +(-371.578 + 2346.05i) q^{30} +(20503.5 + 3247.43i) q^{31} +(31265.1 - 31265.1i) q^{32} +(-43239.6 + 6848.47i) q^{33} +(-1753.93 + 5398.05i) q^{34} +(370.232 + 2337.56i) q^{35} +(21481.7 + 29567.0i) q^{36} +(-31409.6 - 4974.80i) q^{37} +(14119.1 - 27710.3i) q^{38} +(13005.8 - 17900.9i) q^{39} +(-2123.65 + 2123.65i) q^{40} +(28107.5 + 38686.6i) q^{41} +(-36810.0 - 26744.0i) q^{42} +(37117.0 - 18912.1i) q^{43} +(-192426. - 98046.1i) q^{44} +(2774.65 + 3818.98i) q^{45} +(-246811. - 80193.9i) q^{46} +130556. q^{47} +38340.9i q^{48} +(68774.8 + 22346.3i) q^{49} +(134272. - 134272. i) q^{50} +(-3669.55 - 7201.90i) q^{51} +(103812. - 33730.5i) q^{52} +(-18127.4 - 35577.0i) q^{53} +(-243499. - 38566.5i) q^{54} +(-24854.5 - 12664.0i) q^{55} +(-17777.5 - 54713.5i) q^{56} +(13686.1 + 42121.3i) q^{57} +(-326094. - 236921. i) q^{58} +(-3793.24 - 23949.6i) q^{59} -16686.9i q^{60} +(209531. + 87275.9i) q^{61} -254294. q^{62} +(-89310.1 + 14145.3i) q^{63} +(-235682. + 324389. i) q^{64} +(13408.7 - 4356.75i) q^{65} +(510030. - 165719. i) q^{66} +(-230354. + 452095. i) q^{67} +(6237.64 - 39382.9i) q^{68} +(329288. - 167780. i) q^{69} +(-8958.85 - 27572.5i) q^{70} +(327937. - 167092. i) q^{71} +(-81137.4 - 81137.4i) q^{72} +(-164195. + 505341. i) q^{73} +389557. q^{74} +270418. i q^{75} +(-67515.0 + 207790. i) q^{76} +(432287. - 314075. i) q^{77} +(-123053. + 241505. i) q^{78} +(249483. + 489639. i) q^{79} +(-14359.6 + 19764.3i) q^{80} +(33567.9 - 24388.5i) q^{81} +(-414206. - 414206. i) q^{82} +(-678519. - 492973. i) q^{83} +(284804. + 145115. i) q^{84} +(805.676 - 5086.84i) q^{85} +(-412836. + 299943. i) q^{86} +(566945. - 89795.3i) q^{87} +(644876. + 209533. i) q^{88} +(-111706. - 705283. i) q^{89} +(-40888.7 - 40888.7i) q^{90} +(-42247.7 + 266741. i) q^{91} +(1.80068e6 + 285200. i) q^{92} +(256069. - 256069. i) q^{93} +(-1.57959e6 + 250183. i) q^{94} +(-8720.48 + 26838.9i) q^{95} +(-120662. - 761829. i) q^{96} +(151346. + 208311. i) q^{97} +(-874925. - 138575. i) q^{98} +(483848. - 949605. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 16 q^{2} - 10 q^{3} - 10 q^{4} - 230 q^{5} + 1384 q^{6} + 248 q^{7} + 632 q^{8} + 13602 q^{9}+O(q^{10}) $ 240 * q - 16 * q^2 - 10 * q^3 - 10 * q^4 - 230 * q^5 + 1384 * q^6 + 248 * q^7 + 632 * q^8 + 13602 * q^9	\( 240 q - 16 q^{2} - 10 q^{3} - 10 q^{4} - 230 q^{5} + 1384 q^{6} + 248 q^{7} + 632 q^{8} + 13602 q^{9} + 1256 q^{10} - 1128 q^{11} - 2922 q^{12} - 2500 q^{13} + 18726 q^{15} + 70002 q^{16} - 4010 q^{17} + 51414 q^{18} - 10 q^{19} - 69254 q^{20} - 47962 q^{21} - 6 q^{22} + 1888 q^{23} - 177422 q^{24} + 228644 q^{25} + 117514 q^{26} - 62410 q^{27} - 60166 q^{28} + 154546 q^{29} - 132584 q^{30} - 17928 q^{31} - 428258 q^{32} + 44454 q^{33} - 167910 q^{34} - 101034 q^{35} + 641510 q^{36} + 116574 q^{37} - 262448 q^{38} - 329300 q^{39} - 524818 q^{40} + 519110 q^{41} - 82532 q^{42} + 745560 q^{43} + 1335810 q^{44} - 120410 q^{45} - 10 q^{46} + 588192 q^{47} + 5710 q^{49} + 97068 q^{50} + 297094 q^{51} - 1682120 q^{52} - 1503774 q^{53} - 1126786 q^{54} + 564038 q^{55} + 1572190 q^{56} + 555510 q^{57} + 937506 q^{58} - 48960 q^{59} + 42668 q^{61} - 2163580 q^{62} + 2141384 q^{63} - 2703370 q^{64} - 836260 q^{65} - 6744010 q^{66} - 1823136 q^{67} - 787264 q^{68} - 810946 q^{69} + 2027862 q^{70} + 4427536 q^{71} + 2755822 q^{72} + 455594 q^{73} + 1925380 q^{74} - 1199542 q^{76} - 3436182 q^{77} + 2415212 q^{78} - 2921256 q^{79} - 5044870 q^{80} - 7581422 q^{81} + 480560 q^{82} + 2764914 q^{83} + 5311480 q^{84} + 7048220 q^{85} - 2426786 q^{86} + 5291070 q^{87} - 3660970 q^{88} - 2695354 q^{89} + 8317796 q^{90} - 681472 q^{91} - 3392292 q^{92} + 4964430 q^{93} + 2757602 q^{94} + 5554934 q^{95} + 14100214 q^{96} + 2233430 q^{97} + 7768418 q^{98} + 7983712 q^{99}+O(q^{100}) \) 240 * q - 16 * q^2 - 10 * q^3 - 10 * q^4 - 230 * q^5 + 1384 * q^6 + 248 * q^7 + 632 * q^8 + 13602 * q^9 + 1256 * q^10 - 1128 * q^11 - 2922 * q^12 - 2500 * q^13 + 18726 * q^15 + 70002 * q^16 - 4010 * q^17 + 51414 * q^18 - 10 * q^19 - 69254 * q^20 - 47962 * q^21 - 6 * q^22 + 1888 * q^23 - 177422 * q^24 + 228644 * q^25 + 117514 * q^26 - 62410 * q^27 - 60166 * q^28 + 154546 * q^29 - 132584 * q^30 - 17928 * q^31 - 428258 * q^32 + 44454 * q^33 - 167910 * q^34 - 101034 * q^35 + 641510 * q^36 + 116574 * q^37 - 262448 * q^38 - 329300 * q^39 - 524818 * q^40 + 519110 * q^41 - 82532 * q^42 + 745560 * q^43 + 1335810 * q^44 - 120410 * q^45 - 10 * q^46 + 588192 * q^47 + 5710 * q^49 + 97068 * q^50 + 297094 * q^51 - 1682120 * q^52 - 1503774 * q^53 - 1126786 * q^54 + 564038 * q^55 + 1572190 * q^56 + 555510 * q^57 + 937506 * q^58 - 48960 * q^59 + 42668 * q^61 - 2163580 * q^62 + 2141384 * q^63 - 2703370 * q^64 - 836260 * q^65 - 6744010 * q^66 - 1823136 * q^67 - 787264 * q^68 - 810946 * q^69 + 2027862 * q^70 + 4427536 * q^71 + 2755822 * q^72 + 455594 * q^73 + 1925380 * q^74 - 1199542 * q^76 - 3436182 * q^77 + 2415212 * q^78 - 2921256 * q^79 - 5044870 * q^80 - 7581422 * q^81 + 480560 * q^82 + 2764914 * q^83 + 5311480 * q^84 + 7048220 * q^85 - 2426786 * q^86 + 5291070 * q^87 - 3660970 * q^88 - 2695354 * q^89 + 8317796 * q^90 - 681472 * q^91 - 3392292 * q^92 + 4964430 * q^93 + 2757602 * q^94 + 5554934 * q^95 + 14100214 * q^96 + 2233430 * q^97 + 7768418 * q^98 + 7983712 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/61\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{19}{20}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−12.0990	+	1.91629i	−1.51237	+	0.239536i	−0.856820	−	0.515616i	$-0.827563\pi$
$2$	−12.0990	+	1.91629i	−1.51237	+	0.239536i	−0.655550	+	0.755152i	$0.727563\pi$
$3$	10.2537	−	14.1131i	0.379768	−	0.522706i	−0.575755	−	0.817622i	$-0.695292\pi$
$3$	10.2537	−	14.1131i	0.379768	−	0.522706i	0.955523	+	0.294916i	$0.0952918\pi$
$4$	81.8450	−	26.5930i	1.27883	−	0.415516i
$5$	10.5714	−	3.43485i	0.0845711	−	0.0274788i	−0.266426	−	0.963855i	$-0.585843\pi$
$5$	10.5714	−	3.43485i	0.0845711	−	0.0274788i	0.350997	+	0.936377i	$0.385843\pi$
$6$	−97.0148	+	190.402i	−0.449143	+	0.881492i
$7$	−33.3080	+	210.298i	−0.0971079	+	0.613115i	0.890355	+	0.455266i	$0.150456\pi$
$7$	−33.3080	+	210.298i	−0.0971079	+	0.613115i	−0.987463	+	0.157849i	$0.949544\pi$
$8$	−240.743	+	122.664i	−0.470200	+	0.239579i
$9$	131.234	+	403.897i	0.180019	+	0.554043i
$10$	−121.321	+	61.8159i	−0.121321	+	0.0618159i
$11$	−1774.53	−	1774.53i	−1.33323	−	1.33323i	−0.902464	−	0.430765i	$-0.858244\pi$
$11$	−1774.53	−	1774.53i	−1.33323	−	1.33323i	−0.430765	−	0.902464i	$-0.641756\pi$
$12$	463.908	−	1427.76i	0.268465	−	0.826250i
$13$	1268.39			0.577330			0.288665	−	0.957430i	$-0.406789\pi$
$13$	1268.39			0.577330			0.288665	+	0.957430i	$0.406789\pi$
$14$		−	2608.22i		−	0.950517i
$15$	59.9200	−	184.415i	0.0177541	−	0.0546414i
$16$	−1778.10	+	1291.87i	−0.434107	+	0.315397i
$17$	210.353	−	412.841i	0.0428156	−	0.0840304i	−0.868608	−	0.495501i	$-0.834985\pi$
$17$	210.353	−	412.841i	0.0428156	−	0.0840304i	0.911423	+	0.411470i	$0.134985\pi$
$18$	−2361.78	−	4635.25i	−0.404969	−	0.794796i
$19$	−1492.28	+	2053.95i	−0.217566	+	0.299453i	−0.903824	−	0.427905i	$-0.859252\pi$
$19$	−1492.28	+	2053.95i	−0.217566	+	0.299453i	0.686258	+	0.727358i	$0.259252\pi$
$20$	773.872	−	562.251i	0.0967340	−	0.0702813i
$21$	2626.42	+	2626.42i	0.283600	+	0.283600i
$22$	24870.4	+	18069.4i	2.33569	+	1.69698i
$23$	18876.1	+	9617.85i	1.55142	+	0.790486i	0.999070	−	0.0431279i	$-0.0137323\pi$
$23$	18876.1	+	9617.85i	1.55142	+	0.790486i	0.552347	+	0.833614i	$0.313732\pi$
$24$	−737.340	+	4655.38i	−0.0533377	+	0.336761i
$25$	−12540.9	+	9111.52i	−0.802620	+	0.583137i
$26$	−15346.2	+	2430.61i	−0.873136	+	0.138291i
$27$	19140.6	+	6219.17i	0.972444	+	0.315966i
$28$	2866.38	+	18097.6i	0.130575	+	0.824418i
$29$	23267.1	+	23267.1i	0.954001	+	0.954001i	0.998988	−	0.0449868i	$-0.0143246\pi$
$29$	23267.1	+	23267.1i	0.954001	+	0.954001i	−0.0449868	+	0.998988i	$0.514325\pi$
$30$	−371.578	+	2346.05i	−0.0137621	+	0.0868907i
$31$	20503.5	+	3247.43i	0.688244	+	0.109007i	0.490755	−	0.871298i	$-0.336721\pi$
$31$	20503.5	+	3247.43i	0.688244	+	0.109007i	0.197490	+	0.980305i	$0.436721\pi$
$32$	31265.1	−	31265.1i	0.954134	−	0.954134i
$33$	−43239.6	+	6848.47i	−1.20320	+	0.190569i
$34$	−1753.93	+	5398.05i	−0.0446248	+	0.137341i
$35$	370.232	+	2337.56i	0.00863516	+	0.0545202i
$36$	21481.7	+	29567.0i	0.460427	+	0.633724i
$37$	−31409.6	−	4974.80i	−0.620095	−	0.0982133i	−0.161520	−	0.986869i	$-0.551640\pi$
$37$	−31409.6	−	4974.80i	−0.620095	−	0.0982133i	−0.458574	+	0.888656i	$0.651640\pi$
$38$	14119.1	−	27710.3i	0.257310	−	0.504999i
$39$	13005.8	−	17900.9i	0.219252	−	0.301774i
$40$	−2123.65	+	2123.65i	−0.0331820	+	0.0331820i
$41$	28107.5	+	38686.6i	0.407822	+	0.561319i	0.962685	−	0.270623i	$-0.0872296\pi$
$41$	28107.5	+	38686.6i	0.407822	+	0.561319i	−0.554864	+	0.831941i	$0.687230\pi$
$42$	−36810.0	−	26744.0i	−0.496841	−	0.360976i
$43$	37117.0	−	18912.1i	0.466839	−	0.237867i	−0.204715	−	0.978822i	$-0.565627\pi$
$43$	37117.0	−	18912.1i	0.466839	−	0.237867i	0.671555	+	0.740955i	$0.265627\pi$
$44$	−192426.	−	98046.1i	−2.25895	−	1.15099i
$45$	2774.65	+	3818.98i	0.0304489	+	0.0419093i
$46$	−246811.	−	80193.9i	−2.53567	−	0.823888i
$47$	130556.			1.25749			0.628743	−	0.777613i	$-0.283570\pi$
$47$	130556.			1.25749			0.628743	+	0.777613i	$0.283570\pi$
$48$			38340.9i			0.346688i
$49$	68774.8	+	22346.3i	0.584576	+	0.189940i
$50$	134272.	−	134272.i	1.07418	−	1.07418i
$51$	−3669.55	−	7201.90i	−0.0276632	−	0.0542921i
$52$	103812.	−	33730.5i	0.738306	−	0.239890i
$53$	−18127.4	−	35577.0i	−0.121761	−	0.238969i	0.822078	−	0.569375i	$-0.192815\pi$
$53$	−18127.4	−	35577.0i	−0.121761	−	0.238969i	−0.943839	+	0.330405i	$0.892815\pi$
$54$	−243499.	−	38566.5i	−1.54638	−	0.244923i
$55$	−24854.5	−	12664.0i	−0.149388	−	0.0761171i
$56$	−17777.5	−	54713.5i	−0.101229	−	0.311552i
$57$	13686.1	+	42121.3i	0.0739016	+	0.227446i
$58$	−326094.	−	236921.i	−1.67132	−	1.21428i
$59$	−3793.24	−	23949.6i	−0.0184695	−	0.116612i	0.976731	−	0.214467i	$-0.0688016\pi$
$59$	−3793.24	−	23949.6i	−0.0184695	−	0.116612i	−0.995201	+	0.0978559i	$0.968802\pi$
$60$		−	16686.9i		−	0.0772540i
$61$	209531.	+	87275.9i	0.923122	+	0.384507i
$61$	209531.	+	87275.9i	0.923122	+	0.384507i
$62$	−254294.			−1.06699
$63$	−89310.1	+	14145.3i	−0.357173	+	0.0565707i
$64$	−235682.	+	324389.i	−0.899057	+	1.23745i
$65$	13408.7	−	4356.75i	0.0488255	−	0.0158644i
$66$	510030.	−	165719.i	1.77404	−	0.576421i
$67$	−230354.	+	452095.i	−0.765898	+	1.50316i	0.0956123	+	0.995419i	$0.469519\pi$
$67$	−230354.	+	452095.i	−0.765898	+	1.50316i	−0.861510	+	0.507740i	$0.830481\pi$
$68$	6237.64	−	39382.9i	0.0198378	−	0.125251i
$69$	329288.	−	167780.i	1.00237	−	0.510733i
$70$	−8958.85	−	27572.5i	−0.0261191	−	0.0803863i
$71$	327937.	−	167092.i	0.916252	−	0.466854i	0.0687429	−	0.997634i	$-0.478101\pi$
$71$	327937.	−	167092.i	0.916252	−	0.466854i	0.847509	+	0.530781i	$0.178101\pi$
$72$	−81137.4	−	81137.4i	−0.217382	−	0.217382i
$73$	−164195.	+	505341.i	−0.422077	+	1.29902i	0.483688	+	0.875240i	$0.339297\pi$
$73$	−164195.	+	505341.i	−0.422077	+	1.29902i	−0.905765	+	0.423780i	$0.860703\pi$
$74$	389557.			0.961338
$75$			270418.i			0.640991i
$76$	−67515.0	+	207790.i	−0.153801	+	0.473351i
$77$	432287.	−	314075.i	0.946890	−	0.687956i
$78$	−123053.	+	241505.i	−0.259304	+	0.508912i
$79$	249483.	+	489639.i	0.506011	+	0.993103i	0.992823	+	0.119596i	$0.0381599\pi$
$79$	249483.	+	489639.i	0.506011	+	0.993103i	−0.486811	+	0.873507i	$0.661840\pi$
$80$	−14359.6	+	19764.3i	−0.0280462	+	0.0386022i
$81$	33567.9	−	24388.5i	0.0631640	−	0.0458913i
$82$	−414206.	−	414206.i	−0.751233	−	0.751233i
$83$	−678519.	−	492973.i	−1.18666	−	0.862162i	−0.193756	−	0.981050i	$-0.562067\pi$
$83$	−678519.	−	492973.i	−1.18666	−	0.862162i	−0.992908	+	0.118888i	$0.962067\pi$
$84$	284804.	+	145115.i	0.480516	+	0.244835i
$85$	805.676	−	5086.84i	0.00131191	−	0.00828307i
$86$	−412836.	+	299943.i	−0.649056	+	0.471567i
$87$	566945.	−	89795.3i	0.860961	−	0.136363i
$88$	644876.	+	209533.i	0.946298	+	0.307471i
$89$	−111706.	−	705283.i	−0.158455	−	1.00045i	−0.930876	−	0.365335i	$-0.880954\pi$
$89$	−111706.	−	705283.i	−0.158455	−	1.00045i	0.772421	−	0.635111i	$-0.219046\pi$
$90$	−40888.7	−	40888.7i	−0.0560887	−	0.0560887i
$91$	−42247.7	+	266741.i	−0.0560633	+	0.353970i
$92$	1.80068e6	+	285200.i	2.31245	+	0.366257i
$93$	256069.	−	256069.i	0.318352	−	0.318352i
$94$	−1.57959e6	+	250183.i	−1.90178	+	0.301213i
$95$	−8720.48	+	26838.9i	−0.0101711	+	0.0313036i
$96$	−120662.	−	761829.i	−0.136382	−	0.861081i
$97$	151346.	+	208311.i	0.165828	+	0.228242i	0.883841	−	0.467787i	$-0.154948\pi$
$97$	151346.	+	208311.i	0.165828	+	0.228242i	−0.718014	+	0.696029i	$0.754948\pi$
$98$	−874925.	−	138575.i	−0.929593	−	0.147233i
$99$	483848.	−	949605.i	0.498659	−	0.978673i
$100$	−784109.	+	1.07923e6i	−0.784109	+	1.07923i
$101$	−101866.	+	101866.i	−0.0988703	+	0.0988703i	−0.754812	−	0.655941i	$-0.772272\pi$
$101$	−101866.	+	101866.i	−0.0988703	+	0.0988703i	0.655941	+	0.754812i	$0.272272\pi$
$102$	58198.6	+	80103.5i	0.0548418	+	0.0754833i
$103$	−851593.	−	618718.i	−0.779328	−	0.566215i	0.125449	−	0.992100i	$-0.459963\pi$
$103$	−851593.	−	618718.i	−0.779328	−	0.566215i	−0.904777	+	0.425885i	$0.859963\pi$
$104$	−305356.	+	155587.i	−0.271461	+	0.138316i
$105$	36786.3	+	18743.6i	0.0317774	+	0.0161914i
$106$	287498.	+	395707.i	0.241389	+	0.332244i
$107$	128244.	+	41669.0i	0.104685	+	0.0340143i	0.360891	−	0.932608i	$-0.382473\pi$
$107$	128244.	+	41669.0i	0.104685	+	0.0340143i	−0.256206	+	0.966622i	$0.582473\pi$
$108$	1.73195e6			1.37488
$109$		−	533857.i		−	0.412235i	−0.978527	−	0.206118i	$-0.933917\pi$
$109$		−	533857.i		−	0.412235i	0.978527	−	0.206118i	$-0.0660830\pi$
$110$	324981.	+	105593.i	0.244163	+	0.0793334i
$111$	−392276.	+	392276.i	−0.286829	+	0.286829i
$112$	−212453.	−	416962.i	−0.151220	−	0.296785i
$113$	−670227.	+	217770.i	−0.464501	+	0.150925i	−0.531912	−	0.846800i	$-0.678526\pi$
$113$	−670227.	+	217770.i	−0.464501	+	0.150925i	0.0674110	+	0.997725i	$0.478526\pi$
$114$	−246303.	−	483398.i	−0.166248	−	0.326280i
$115$	232582.	+	36837.4i	0.152927	+	0.0242212i
$116$	2.52304e6	+	1.28555e6i	1.61641	+	0.823600i
$117$	166457.	+	512301.i	0.103931	+	0.319865i
$118$	91788.4	+	282496.i	0.0558653	+	0.171936i
$119$	79813.5	+	57987.9i	0.0473626	+	0.0344109i
$120$	8195.84	+	51746.5i	0.00474296	+	0.0299459i
$121$			4.52634e6i			2.55500i
$122$	−2.70235e6	−	654425.i	−1.48820	−	0.360397i
$123$	834194.			0.448282
$124$	1.76447e6	−	279464.i	0.925440	−	0.146575i
$125$	−203364.	+	279907.i	−0.104122	+	0.143312i
$126$	1.05345e6	−	342287.i	0.526627	−	0.171112i
$127$	−468008.	+	152065.i	−0.228477	+	0.0742366i	−0.421018	−	0.907052i	$-0.638327\pi$
$127$	−468008.	+	152065.i	−0.228477	+	0.0742366i	0.192541	+	0.981289i	$0.438327\pi$
$128$	945190.	−	1.85504e6i	0.450702	−	0.884552i
$129$	113681.	−	717754.i	0.0529564	−	0.334354i
$130$	−153882.	+	78407.0i	−0.0700420	+	0.0356882i
$131$	358838.	+	1.10439e6i	0.159619	+	0.491256i	0.998600	−	0.0529050i	$-0.0168480\pi$
$131$	358838.	+	1.10439e6i	0.159619	+	0.491256i	−0.838981	+	0.544161i	$0.816848\pi$
$132$	−3.35682e6	+	1.71038e6i	−1.45951	+	0.743656i
$133$	−382238.	−	382238.i	−0.162472	−	0.162472i
$134$	1.92070e6	−	5.91130e6i	0.798260	−	2.45679i
$135$	223705.			0.0909231
$136$			125191.i			0.0497689i
$137$	−725877.	+	2.23402e6i	−0.282294	+	0.868811i	0.704903	+	0.709304i	$0.250991\pi$
$137$	−725877.	+	2.23402e6i	−0.282294	+	0.868811i	−0.987197	+	0.159507i	$0.949009\pi$
$138$	−3.66252e6	+	2.66098e6i	−1.39362	+	1.01252i
$139$	2.09873e6	−	4.11899e6i	0.781471	−	1.53372i	−0.0629350	−	0.998018i	$-0.520046\pi$
$139$	2.09873e6	−	4.11899e6i	0.781471	−	1.53372i	0.844405	−	0.535705i	$-0.179954\pi$
$140$	92464.3	+	181472.i	0.0336969	+	0.0661339i
$141$	1.33869e6	−	1.84254e6i	0.477553	−	0.657295i
$142$	−3.64750e6	+	2.65006e6i	−1.27388	+	0.925531i
$143$	−2.25080e6	−	2.25080e6i	−0.769713	−	0.769713i
$144$	−755129.	−	548633.i	−0.252891	−	0.183736i
$145$	325885.	+	166047.i	0.106896	+	0.0544661i
$146$	1.01821e6	−	6.42874e6i	0.327175	−	2.06570i
$147$	1.02057e6	−	741490.i	0.321286	−	0.233428i
$148$	−2.70302e6	+	428116.i	−0.833803	+	0.132061i
$149$	443475.	+	144094.i	0.134064	+	0.0435599i	0.375280	−	0.926911i	$-0.377546\pi$
$149$	443475.	+	144094.i	0.134064	+	0.0435599i	−0.241217	+	0.970471i	$0.577546\pi$
$150$	−518198.	−	3.27178e6i	−0.153540	−	0.969415i
$151$	988651.	+	988651.i	0.287152	+	0.287152i	0.835953	−	0.548801i	$-0.184916\pi$
$151$	988651.	+	988651.i	0.287152	+	0.287152i	−0.548801	+	0.835953i	$0.684916\pi$
$152$	107309.	−	677523.i	0.0305567	−	0.192927i
$153$	194351.	+	30782.2i	0.0542641	+	0.00859459i
$154$	−4.62836e6	+	4.62836e6i	−1.26726	+	1.26726i
$155$	227905.	−	36096.6i	0.0612010	−	0.00969329i
$156$	588418.	−	1.81096e6i	0.154993	−	0.477019i
$157$	−235842.	−	1.48905e6i	−0.0609429	−	0.384778i	−0.999241	−	0.0389511i	$-0.987598\pi$
$157$	−235842.	−	1.48905e6i	−0.0609429	−	0.384778i	0.938298	−	0.345827i	$-0.112402\pi$
$158$	−3.95678e6	−	5.44603e6i	−1.00316	−	1.38073i
$159$	−687974.	−	108964.i	−0.171151	−	0.0271077i
$160$	223124.	−	437906.i	0.0544737	−	0.106911i
$161$	−2.65134e6	+	3.64926e6i	−0.635314	+	0.874435i
$162$	−359402.	+	359402.i	−0.0845347	+	0.0845347i
$163$	−1.88516e6	−	2.59470e6i	−0.435297	−	0.599135i	0.533862	−	0.845572i	$-0.320740\pi$
$163$	−1.88516e6	−	2.59470e6i	−0.435297	−	0.599135i	−0.969159	+	0.246437i	$0.920740\pi$
$164$	3.32925e6	+	2.41884e6i	0.754771	+	0.548373i
$165$	−433579.	+	220919.i	−0.0965197	+	0.0491793i
$166$	9.15405e6	+	4.66422e6i	2.00119	+	1.01966i
$167$	4.75486e6	+	6.54450e6i	1.02091	+	1.40516i	0.911563	+	0.411160i	$0.134876\pi$
$167$	4.75486e6	+	6.54450e6i	1.02091	+	1.40516i	0.109348	+	0.994003i	$0.465124\pi$
$168$	−954460.	−	310123.i	−0.201294	−	0.0654043i
$169$	−3.21799e6			−0.666690
$170$			63089.4i			0.0128413i
$171$	−1.02542e6	−	333180.i	−0.205076	−	0.0666332i
$172$	2.53491e6	−	2.53491e6i	0.498170	−	0.498170i
$173$	−334452.	−	656399.i	−0.0645945	−	0.126774i	0.856452	−	0.516227i	$-0.172664\pi$
$173$	−334452.	−	656399.i	−0.0645945	−	0.126774i	−0.921046	+	0.389453i	$0.872664\pi$
$174$	−6.68737e6	+	2.17286e6i	−1.26943	+	0.412462i
$175$	−1.49843e6	−	2.94083e6i	−0.279590	−	0.548726i
$176$	5.44774e6	+	862838.i	0.999260	+	0.158267i
$177$	−376896.	−	192038.i	−0.0679676	−	0.0346312i
$178$	2.70305e6	+	8.31913e6i	0.479285	+	1.47509i
$179$	−531479.	−	1.63572e6i	−0.0926674	−	0.285201i	0.893971	−	0.448124i	$-0.147908\pi$
$179$	−531479.	−	1.63572e6i	−0.0926674	−	0.285201i	−0.986639	+	0.162923i	$0.947908\pi$
$180$	328650.	+	238778.i	0.0563528	+	0.0409427i
$181$	328609.	+	2.07476e6i	0.0554172	+	0.349890i	0.999780	+	0.0209841i	$0.00667994\pi$
$181$	328609.	+	2.07476e6i	0.0554172	+	0.349890i	−0.944363	+	0.328906i	$0.893320\pi$
$182$		−	3.30825e6i		−	0.548762i
$183$	3.38021e6	−	2.06222e6i	0.551556	−	0.336498i
$184$	−5.72404e6			−0.918860
$185$	−349131.	+	55297.0i	−0.0551409	+	0.00873346i
$186$	−2.60746e6	+	3.58886e6i	−0.405209	+	0.557722i
$187$	−1.10588e6	+	359321.i	−0.169115	+	0.0549488i
$188$	1.06853e7	−	3.47188e6i	1.60811	−	0.522506i
$189$	−1.94542e6	+	3.81810e6i	−0.288156	+	0.565538i
$190$	54077.7	−	341433.i	0.00788420	−	0.0497789i
$191$	8.46358e6	−	4.31241e6i	1.21466	−	0.618899i	0.275141	−	0.961404i	$-0.411275\pi$
$191$	8.46358e6	−	4.31241e6i	1.21466	−	0.618899i	0.939516	+	0.342505i	$0.111275\pi$
$192$	2.16149e6	+	6.65240e6i	0.305387	+	0.939884i
$193$	9.87426e6	−	5.03119e6i	1.37351	−	0.699839i	0.397510	−	0.917598i	$-0.369875\pi$
$193$	9.87426e6	−	5.03119e6i	1.37351	−	0.699839i	0.976003	+	0.217758i	$0.0698745\pi$
$194$	−2.23032e6	−	2.23032e6i	−0.305465	−	0.305465i
$195$	76002.2	−	233911.i	0.0102500	−	0.0315461i
$196$	6.22313e6			0.826496
$197$		−	9.46668e6i		−	1.23822i	−0.785303	−	0.619112i	$-0.787493\pi$
$197$		−	9.46668e6i		−	1.23822i	0.785303	−	0.619112i	$-0.212507\pi$
$198$	−4.03434e6	+	1.24164e7i	−0.519729	+	1.59956i
$199$	−3.98313e6	+	2.89391e6i	−0.505434	+	0.367220i	−0.811089	−	0.584923i	$-0.801125\pi$
$199$	−3.98313e6	+	2.89391e6i	−0.505434	+	0.367220i	0.305654	+	0.952142i	$0.401125\pi$
$200$	1.90148e6	−	3.73186e6i	0.237685	−	0.466482i
$201$	4.01845e6	+	7.88665e6i	0.494847	+	0.971191i
$202$	1.03727e6	−	1.42768e6i	0.125845	−	0.173211i
$203$	−5.66802e6	+	4.11806e6i	−0.677553	+	0.492271i
$204$	−491854.	−	491854.i	−0.0579357	−	0.0579357i
$205$	430018.	+	312426.i	0.0499143	+	0.0362649i
$206$	1.14890e7	+	5.85395e6i	1.31426	+	0.669649i
$207$	−1.40743e6	+	8.88619e6i	−0.158678	+	1.00185i
$208$	−2.25533e6	+	1.63860e6i	−0.250623	+	0.182088i
$209$	6.29289e6	−	996696.i	0.689305	−	0.109175i
$210$	−480994.	−	156284.i	−0.0519376	−	0.0168755i
$211$	1.27233e6	+	8.03316e6i	0.135441	+	0.855143i	0.958064	+	0.286555i	$0.0925101\pi$
$211$	1.27233e6	+	8.03316e6i	0.135441	+	0.855143i	−0.822622	+	0.568588i	$0.807490\pi$
$212$	−2.42974e6	−	2.42974e6i	−0.255007	−	0.255007i
$213$	1.00440e6	−	6.34151e6i	0.103936	−	0.656227i
$214$	−1.63147e6	−	258399.i	−0.166470	−	0.0263663i
$215$	327418.	−	327418.i	0.0329448	−	0.0329448i
$216$	−5.37083e6	+	850656.i	−0.532943	+	0.0844098i
$217$	−1.36586e6	+	4.20369e6i	−0.133668	+	0.411388i
$218$	1.02302e6	+	6.45911e6i	0.0987451	+	0.623452i
$219$	5.44829e6	+	7.49893e6i	0.518714	+	0.713948i
$220$	−2.37099e6	−	375527.i	−0.222670	−	0.0352674i
$221$	266811.	−	523646.i	0.0247188	−	0.0485133i
$222$	3.99442e6	−	5.49784e6i	0.365085	−	0.502497i
$223$	−5.67424e6	+	5.67424e6i	−0.511673	+	0.511673i	−0.915039	−	0.403366i	$-0.867840\pi$
$223$	−5.67424e6	+	5.67424e6i	−0.511673	+	0.511673i	0.403366	+	0.915039i	$0.367840\pi$
$224$	5.53362e6	+	7.61637e6i	0.492340	+	0.677648i
$225$	−5.32592e6	−	3.86950e6i	−0.467570	−	0.339710i
$226$	7.69173e6	−	3.91913e6i	0.666344	−	0.339519i
$227$	−9.52738e6	−	4.85444e6i	−0.814509	−	0.415013i	−0.00346199	−	0.999994i	$-0.501102\pi$
$227$	−9.52738e6	−	4.85444e6i	−0.814509	−	0.415013i	−0.811047	+	0.584981i	$0.801102\pi$
$228$	2.24027e6	+	3.08346e6i	0.189015	+	0.260156i
$229$	−1.79686e7	−	5.83837e6i	−1.49627	−	0.486166i	−0.557340	−	0.830284i	$-0.688178\pi$
$229$	−1.79686e7	−	5.83837e6i	−1.49627	−	0.486166i	−0.938926	+	0.344118i	$0.888178\pi$
$230$	−2.88459e6			−0.237083
$231$		−	9.32132e6i		−	0.756209i
$232$	−8.45544e6	−	2.74734e6i	−0.677130	−	0.220013i
$233$	−1.90259e6	+	1.90259e6i	−0.150410	+	0.150410i	−0.778301	−	0.627891i	$-0.783918\pi$
$233$	−1.90259e6	+	1.90259e6i	−0.150410	+	0.150410i	0.627891	+	0.778301i	$0.283918\pi$
$234$	−2.99567e6	−	5.87932e6i	−0.233801	−	0.458860i
$235$	1.38016e6	−	448441.i	0.106347	−	0.0345542i
$236$	−947349.	−	1.85928e6i	−0.0720732	−	0.141452i
$237$	9.46843e6	+	1.49965e6i	0.711268	+	0.112654i
$238$	−1.07678e6	−	548647.i	−0.0798724	−	0.0406970i
$239$	−1.93344e6	−	5.95051e6i	−0.141624	−	0.435873i	0.854938	−	0.518731i	$-0.173595\pi$
$239$	−1.93344e6	−	5.95051e6i	−0.141624	−	0.435873i	−0.996561	+	0.0828576i	$0.973595\pi$
$240$	131695.	+	405317.i	0.00952658	+	0.0293198i
$241$	−4.00773e6	−	2.91179e6i	−0.286317	−	0.208022i	0.435351	−	0.900261i	$-0.356624\pi$
$241$	−4.00773e6	−	2.91179e6i	−0.286317	−	0.208022i	−0.721668	+	0.692239i	$0.756624\pi$
$242$	−8.67376e6	−	5.47640e7i	−0.612014	−	3.86410i
$243$			1.39478e7i			0.972044i
$244$	1.94700e7	+	1.57102e6i	1.34028	+	0.108147i
$245$	803802.			0.0546576
$246$	−1.00929e7	+	1.59855e6i	−0.677968	+	0.107380i
$247$	−1.89280e6	+	2.60522e6i	−0.125607	+	0.172883i
$248$	−5.33441e6	+	1.73325e6i	−0.349729	+	0.113634i
$249$	−1.39147e7	+	4.52116e6i	−0.901314	+	0.292855i
$250$	1.92411e6	−	3.77628e6i	0.123143	−	0.241682i
$251$	3.67792e6	−	2.32215e7i	0.232585	−	1.46848i	−0.544328	−	0.838873i	$-0.683215\pi$
$251$	3.67792e6	−	2.32215e7i	0.232585	−	1.46848i	0.776912	−	0.629609i	$-0.216785\pi$
$252$	−6.93341e6	+	3.53275e6i	−0.433257	+	0.220755i
$253$	−1.64290e7	−	5.05633e7i	−1.01449	−	3.12229i
$254$	5.37101e6	−	2.73666e6i	0.327759	−	0.167001i
$255$	−63529.7	−	63529.7i	−0.00383139	−	0.00383139i
$256$	48929.2	−	150589.i	0.00291641	−	0.00897579i
$257$	−2.97789e7			−1.75432			−0.877162	−	0.480195i	$-0.840566\pi$
$257$	−2.97789e7			−1.75432			−0.877162	+	0.480195i	$0.840566\pi$
$258$			8.90191e6i			0.518351i
$259$	2.09239e6	−	6.43970e6i	0.120432	−	0.370652i
$260$	981574.	−	713156.i	0.0558474	−	0.0405755i
$261$	−6.34408e6	+	1.24510e7i	−0.356818	+	0.700296i
$262$	−6.45788e6	−	1.26743e7i	−0.359076	−	0.704726i
$263$	−1.64827e6	+	2.26865e6i	−0.0906069	+	0.124710i	−0.851914	−	0.523682i	$-0.824558\pi$
$263$	−1.64827e6	+	2.26865e6i	−0.0906069	+	0.124710i	0.761307	+	0.648392i	$0.224558\pi$
$264$	9.56954e6	−	6.95268e6i	0.520091	−	0.377868i
$265$	−313834.	−	313834.i	−0.0168640	−	0.0168640i
$266$	5.35715e6	+	3.89220e6i	0.284636	+	0.206800i
$267$	−1.10991e7	−	5.65528e6i	−0.583115	−	0.297112i
$268$	−6.83072e6	+	4.31275e7i	−0.354864	+	2.24052i
$269$	−2.15223e7	+	1.56369e7i	−1.10569	+	0.803328i	−0.981979	−	0.188990i	$-0.939479\pi$
$269$	−2.15223e7	+	1.56369e7i	−1.10569	+	0.803328i	−0.123708	+	0.992319i	$0.539479\pi$
$270$	−2.70660e6	+	428683.i	−0.137509	+	0.0217793i
$271$	3.49365e7	+	1.13516e7i	1.75538	+	0.570358i	0.996705	−	0.0811081i	$-0.0258459\pi$
$271$	3.49365e7	+	1.13516e7i	1.75538	+	0.570358i	0.758677	+	0.651466i	$0.225846\pi$
$272$	159307.	+	1.00582e6i	0.00791639	+	0.0499821i
$273$	3.33134e6	+	3.33134e6i	0.163731	+	0.163731i
$274$	4.50133e6	−	2.84203e7i	0.218821	−	1.38158i
$275$	3.84229e7	+	6.08559e6i	1.84753	+	0.292620i
$276$	2.24887e7	−	2.24887e7i	1.06964	−	1.06964i
$277$	−2.01230e6	+	318716.i	−0.0946787	+	0.0149956i	−0.203594	−	0.979055i	$-0.565262\pi$
$277$	−2.01230e6	+	318716.i	−0.0946787	+	0.0149956i	0.108915	+	0.994051i	$0.465262\pi$
$278$	−1.74993e7	+	5.38573e7i	−0.814491	+	2.50674i
$279$	1.37913e6	+	8.70747e6i	0.0635027	+	0.400940i
$280$	−375866.	−	517335.i	−0.0171222	−	0.0235666i
$281$	−9.53283e6	−	1.50985e6i	−0.429638	−	0.0680480i	−0.0621296	−	0.998068i	$-0.519789\pi$
$281$	−9.53283e6	−	1.50985e6i	−0.429638	−	0.0680480i	−0.367509	+	0.930020i	$0.619789\pi$
$282$	−1.26659e7	+	2.48582e7i	−0.564791	+	1.10846i
$283$	1.63842e7	−	2.25509e7i	0.722878	−	0.994956i	−0.276545	−	0.961001i	$-0.589190\pi$
$283$	1.63842e7	−	2.25509e7i	0.722878	−	0.994956i	0.999423	−	0.0339555i	$-0.0108105\pi$
$284$	2.23965e7	−	2.23965e7i	0.977743	−	0.977743i
$285$	289361.	+	398271.i	0.0124999	+	0.0172046i
$286$	3.15455e7	+	2.29192e7i	1.34846	+	0.979717i
$287$	−9.07195e6	+	4.62239e6i	−0.383756	+	0.195533i
$288$	1.67309e7	+	8.52482e6i	0.700393	+	0.356868i
$289$	1.40615e7	+	1.93540e7i	0.582557	+	0.801821i
$290$	−4.26106e6	−	1.38450e6i	−0.174712	−	0.0567675i
$291$	4.49177e6			0.182280
$292$			4.57260e7i			1.83660i
$293$	−4.30147e6	−	1.39763e6i	−0.171007	−	0.0555636i	0.222262	−	0.974987i	$-0.428656\pi$
$293$	−4.30147e6	−	1.39763e6i	−0.171007	−	0.0555636i	−0.393269	+	0.919423i	$0.628656\pi$
$294$	−1.09270e7	+	1.09270e7i	−0.429989	+	0.429989i
$295$	−122363.	−	240151.i	−0.00476633	−	0.00935445i
$296$	8.17187e6	−	2.65520e6i	0.315098	−	0.102382i
$297$	−2.29295e7	−	4.50017e7i	−0.875236	−	1.71775i
$298$	−5.64171e6	−	893560.i	−0.213188	−	0.0337656i
$299$	2.39423e7	+	1.21992e7i	0.895680	+	0.456372i
$300$	7.19124e6	+	2.21324e7i	0.266342	+	0.819717i
$301$	2.74088e6	+	8.43557e6i	0.100506	+	0.309325i
$302$	−1.38562e7	−	1.00671e7i	−0.503063	−	0.365497i
$303$	393134.	+	2.48215e6i	0.0141323	+	0.0892279i
$304$		−	5.57996e6i		−	0.198614i
$305$	2.51482e6	+	202919.i	0.0886353	+	0.00715192i
$306$	−2.41043e6			−0.0841260
$307$	−4.66460e7	+	7.38800e6i	−1.61213	+	0.255336i	−0.896466	−	0.443113i	$-0.853874\pi$
$307$	−4.66460e7	+	7.38800e6i	−1.61213	+	0.255336i	−0.715661	+	0.698448i	$0.753874\pi$
$308$	2.70283e7	−	3.72012e7i	0.925052	−	1.27322i
$309$	−1.74640e7	+	5.67440e6i	−0.591928	+	0.192329i
$310$	−2.68824e6	+	873462.i	−0.0902366	+	0.0293197i
$311$	−1.63909e7	+	3.21690e7i	−0.544906	+	1.06944i	0.440266	+	0.897868i	$0.354884\pi$
$311$	−1.63909e7	+	3.21690e7i	−0.544906	+	1.06944i	−0.985172	+	0.171571i	$0.945116\pi$
$312$	−935238.	+	5.90486e6i	−0.0307934	+	0.194422i
$313$	3.78164e7	−	1.92684e7i	1.23324	−	0.628366i	0.288905	−	0.957358i	$-0.406709\pi$
$313$	3.78164e7	−	1.92684e7i	1.23324	−	0.628366i	0.944333	+	0.328991i	$0.106709\pi$
$314$	5.70690e6	+	1.75640e7i	0.184336	+	0.567329i
$315$	−895545.	+	456303.i	−0.0286520	+	0.0145989i
$316$	3.34399e7	+	3.34399e7i	1.05975	+	1.05975i
$317$	−1.13711e7	+	3.49966e7i	−0.356964	+	1.09862i	0.597898	+	0.801572i	$0.296003\pi$
$317$	−1.13711e7	+	3.49966e7i	−0.356964	+	1.09862i	−0.954862	+	0.297050i	$0.903997\pi$
$318$	8.53257e6			0.265338
$319$		−	8.25763e7i		−	2.54380i
$320$	−1.37726e6	+	4.23878e6i	−0.0420307	+	0.129357i
$321$	1.90306e6	−	1.38265e6i	0.0575356	−	0.0418020i
$322$	2.50855e7	−	4.92330e7i	0.751371	−	1.47465i
$323$	534050.	+	1.04813e6i	0.0158480	+	0.0311034i
$324$	2.09880e6	−	2.88875e6i	0.0617073	−	0.0849328i
$325$	−1.59068e7	+	1.15570e7i	−0.463377	+	0.336663i
$326$	2.77807e7	+	2.77807e7i	0.801844	+	0.801844i
$327$	−7.53435e6	−	5.47403e6i	−0.215478	−	0.156554i
$328$	−1.15121e7	−	5.86573e6i	−0.326238	−	0.166227i
$329$	−4.34856e6	+	2.74557e7i	−0.122112	+	0.770984i
$330$	4.82251e6	−	3.50376e6i	0.134193	−	0.0974972i
$331$	3.82786e7	−	6.06274e6i	1.05553	−	0.167180i	0.395538	−	0.918450i	$-0.370558\pi$
$331$	3.82786e7	−	6.06274e6i	1.05553	−	0.167180i	0.659996	+	0.751269i	$0.270558\pi$
$332$	−6.86430e7	−	2.23035e7i	−1.87578	−	0.609478i
$333$	−2.11271e6	−	1.33391e7i	−0.0572146	−	0.361239i
$334$	−7.00699e7	−	7.00699e7i	−1.88058	−	1.88058i
$335$	−882281.	+	5.57050e6i	−0.0234678	+	0.148170i
$336$	−8.06303e6	−	1.27706e6i	−0.212560	−	0.0336661i
$337$	850223.	−	850223.i	0.0222148	−	0.0222148i	−0.695912	−	0.718127i	$-0.745000\pi$
$337$	850223.	−	850223.i	0.0222148	−	0.0222148i	0.718127	+	0.695912i	$0.245000\pi$
$338$	3.89343e7	−	6.16658e6i	1.00828	−	0.159696i
$339$	−3.79893e6	+	1.16919e7i	−0.0975129	+	0.300114i
$340$	−69334.0	−	437758.i	−0.00176404	−	0.0111377i
$341$	−3.06214e7	−	4.21467e7i	−0.772256	−	1.06292i
$342$	1.30450e7	+	2.06613e6i	0.326112	+	0.0516510i
$343$	−1.83625e7	+	3.60385e7i	−0.455040	+	0.893067i
$344$	−6.61580e6	+	9.10587e6i	−0.162520	+	0.223690i
$345$	2.90473e6	−	2.90473e6i	0.0707372	−	0.0707372i
$346$	5.30437e6	+	7.30084e6i	0.128058	+	0.176256i
$347$	2.73922e7	+	1.99016e7i	0.655600	+	0.476321i	0.865174	−	0.501471i	$-0.167208\pi$
$347$	2.73922e7	+	1.99016e7i	0.655600	+	0.476321i	−0.209574	+	0.977793i	$0.567208\pi$
$348$	4.40137e7	−	2.24261e7i	1.04436	−	0.532128i
$349$	2.67352e7	+	1.36223e7i	0.628937	+	0.320459i	0.739244	−	0.673438i	$-0.235183\pi$
$349$	2.67352e7	+	1.36223e7i	0.628937	+	0.320459i	−0.110307	+	0.993898i	$0.535183\pi$
$350$	2.37649e7	+	3.27095e7i	0.554282	+	0.762904i
$351$	2.42779e7	+	7.88835e6i	0.561421	+	0.182417i
$352$	−1.10961e8			−2.54416
$353$		−	7.17775e7i		−	1.63179i	−0.578201	−	0.815894i	$-0.696245\pi$
$353$		−	7.17775e7i		−	1.63179i	0.578201	−	0.815894i	$-0.303755\pi$
$354$	4.92805e6	+	1.60122e6i	0.111088	+	0.0360946i
$355$	2.89281e6	−	2.89281e6i	0.0646599	−	0.0646599i
$356$	−2.78982e7	−	5.47533e7i	−0.618338	−	1.21356i
$357$	1.63677e6	−	531820.i	0.0359736	−	0.0116885i
$358$	9.56486e6	+	1.87721e7i	0.208463	+	0.409132i
$359$	7.55788e7	+	1.19705e7i	1.63349	+	0.258719i	0.904710	−	0.426028i	$-0.140087\pi$
$359$	7.55788e7	+	1.19705e7i	1.63349	+	0.258719i	0.728781	+	0.684747i	$0.240087\pi$
$360$	−1.13643e6	−	579040.i	−0.0243577	−	0.0124108i
$361$	1.25462e7	+	3.86131e7i	0.266679	+	0.820755i
$362$	−7.95166e6	−	2.44727e7i	−0.167622	−	0.515889i
$363$	6.38805e7	+	4.64119e7i	1.33551	+	0.970307i
$364$	3.63570e6	+	2.29549e7i	0.0753849	+	0.475961i
$365$			5.90614e6i			0.121458i
$366$	−3.69452e7	+	3.14282e7i	−0.753554	+	0.641026i
$367$	1.71586e7			0.347124			0.173562	−	0.984823i	$-0.444472\pi$
$367$	1.71586e7			0.347124			0.173562	+	0.984823i	$0.444472\pi$
$368$	−4.59886e7	+	7.28387e6i	−0.922798	+	0.146157i
$369$	−1.19368e7	+	1.64295e7i	−0.237579	+	0.326999i
$370$	4.11816e6	−	1.33807e6i	0.0813014	−	0.0264164i
$371$	8.08558e6	−	2.62716e6i	0.158340	−	0.0514476i
$372$	1.41483e7	−	2.77676e7i	0.274837	−	0.539398i
$373$	−5.85488e6	+	3.69663e7i	−0.112821	+	0.712326i	0.864825	+	0.502073i	$0.167429\pi$
$373$	−5.85488e6	+	3.69663e7i	−0.112821	+	0.712326i	−0.977647	+	0.210254i	$0.932571\pi$
$374$	1.26914e7	−	6.46659e6i	0.242602	−	0.123612i
$375$	1.86510e6	+	5.74018e6i	0.0353677	+	0.108851i
$376$	−3.14304e7	+	1.60146e7i	−0.591270	+	0.301267i
$377$	2.95119e7	+	2.95119e7i	0.550773	+	0.550773i
$378$	1.62209e7	−	4.99230e7i	0.300331	−	0.924325i
$379$	−1.67013e7			−0.306784			−0.153392	−	0.988165i	$-0.549020\pi$
$379$	−1.67013e7			−0.306784			−0.153392	+	0.988165i	$0.549020\pi$
$380$			2.42853e6i			0.0442581i
$381$	−2.65273e6	+	8.16425e6i	−0.0479642	+	0.147619i
$382$	−9.41366e7	+	6.83943e7i	−1.68876	+	1.22696i
$383$	3.34982e7	−	6.57439e7i	0.596245	−	1.17020i	−0.373854	−	0.927488i	$-0.621964\pi$
$383$	3.34982e7	−	6.57439e7i	0.596245	−	1.17020i	0.970099	−	0.242710i	$-0.0780363\pi$
$384$	−1.64886e7	−	3.23606e7i	−0.291198	−	0.571509i
$385$	3.49107e6	−	4.80505e6i	0.0611753	−	0.0842006i
$386$	−1.09827e8	+	7.97940e7i	−1.90962	+	1.38742i
$387$	1.25095e7	+	1.25095e7i	0.215828	+	0.215828i
$388$	1.79266e7	+	1.30244e7i	0.306903	+	0.222978i
$389$	−7.34974e7	−	3.74488e7i	−1.24860	−	0.636193i	−0.300384	−	0.953818i	$-0.597115\pi$
$389$	−7.34974e7	−	3.74488e7i	−1.24860	−	0.636193i	−0.948216	+	0.317625i	$0.897115\pi$
$390$	−471307.	+	2.97572e6i	−0.00794530	+	0.0501646i
$391$	7.94129e6	−	5.76969e6i	0.132850	−	0.0965210i
$392$	−1.92981e7	+	3.05652e6i	−0.320374	+	0.0507422i
$393$	1.92657e7	+	6.25981e6i	0.317401	+	0.103130i
$394$	1.81409e7	+	1.14537e8i	0.296599	+	1.87265i
$395$	4.31922e6	+	4.31922e6i	0.0700833	+	0.0700833i
$396$	1.43476e7	−	9.05874e7i	0.231044	−	1.45875i
$397$	−8.81142e6	−	1.39559e6i	−0.140823	−	0.0223042i	0.0856248	−	0.996327i	$-0.472711\pi$
$397$	−8.81142e6	−	1.39559e6i	−0.140823	−	0.0223042i	−0.226448	+	0.974023i	$0.572711\pi$
$398$	4.26461e7	−	4.26461e7i	0.676441	−	0.676441i
$399$	−9.31391e6	+	1.47518e6i	−0.146627	+	0.0232234i
$400$	1.05282e7	−	3.24024e7i	0.164503	−	0.506288i
$401$	−4.97517e6	−	3.14120e7i	−0.0771569	−	0.487150i	−0.995762	−	0.0919719i	$-0.970683\pi$
$401$	−4.97517e6	−	3.14120e7i	−0.0771569	−	0.487150i	0.918605	−	0.395178i	$-0.129317\pi$
$402$	−6.37321e7	−	8.77198e7i	−0.981026	−	1.35027i
$403$	2.60065e7	+	4.11903e6i	0.397344	+	0.0629331i
$404$	−5.62830e6	+	1.10462e7i	−0.0853559	+	0.167520i
$405$	271089.	−	373122.i	0.00408081	−	0.00561676i
$406$	6.06858e7	−	6.06858e7i	0.906794	−	0.906794i
$407$	4.69094e7	+	6.45652e7i	0.695787	+	0.957669i
$408$	1.76683e6	+	1.28368e6i	0.0260145	+	0.0189006i
$409$	7.61996e7	−	3.88256e7i	1.11374	−	0.567477i	0.202468	−	0.979289i	$-0.435104\pi$
$409$	7.61996e7	−	3.88256e7i	1.11374	−	0.567477i	0.911269	+	0.411812i	$0.135104\pi$
$410$	−5.80147e6	−	2.95600e6i	−0.0841756	−	0.0428896i
$411$	2.40859e7	+	3.31514e7i	0.346927	+	0.477504i
$412$	−8.61522e7	−	2.79925e7i	−1.23190	−	0.400268i
$413$	5.16290e6			0.0732898
$414$		−	1.10211e8i		−	1.55318i
$415$	−8.86618e6	−	2.88080e6i	−0.124049	−	0.0403059i
$416$	3.96564e7	−	3.96564e7i	0.550850	−	0.550850i
$417$	−3.66117e7	−	7.18546e7i	−0.504908	−	0.990938i
$418$	−7.42274e7	+	2.41180e7i	−1.01633	+	0.330226i
$419$	6.47088e6	+	1.26998e7i	0.0879674	+	0.172646i	0.930799	−	0.365532i	$-0.119113\pi$
$419$	6.47088e6	+	1.26998e7i	0.0879674	+	0.172646i	−0.842831	+	0.538178i	$0.819113\pi$
$420$	3.50922e6	+	555806.i	0.0473656	+	0.00750197i
$421$	4.30957e7	+	2.19583e7i	0.577547	+	0.294275i	0.718259	−	0.695776i	$-0.244939\pi$
$421$	4.30957e7	+	2.19583e7i	0.577547	+	0.294275i	−0.140712	+	0.990051i	$0.544939\pi$
$422$	−3.07876e7	−	9.47546e7i	−0.409675	−	1.26085i
$423$	1.71334e7	+	5.27312e7i	0.226372	+	0.696701i
$424$	8.72807e6	+	6.34131e6i	0.114504	+	0.0831920i
$425$	1.12359e6	+	7.09406e6i	0.0146366	+	0.0924119i
$426$			7.86503e7i			1.01735i
$427$	−2.53331e7	+	4.11571e7i	−0.325390	+	0.528641i
$428$	1.16042e7			0.148008
$429$	−5.48448e7	+	8.68656e6i	−0.694646	+	0.110021i
$430$	−3.33399e6	+	4.58884e6i	−0.0419333	+	0.0577162i
$431$	9.22989e7	−	2.99897e7i	1.15283	−	0.374577i	0.330620	−	0.943764i	$-0.392742\pi$
$431$	9.22989e7	−	2.99897e7i	1.15283	−	0.374577i	0.822208	+	0.569187i	$0.192742\pi$
$432$	−4.20683e7	+	1.36688e7i	−0.521800	+	0.169543i
$433$	−6.10826e7	+	1.19881e8i	−0.752409	+	1.47669i	0.122536	+	0.992464i	$0.460897\pi$
$433$	−6.10826e7	+	1.19881e8i	−0.752409	+	1.47669i	−0.874945	+	0.484222i	$0.839103\pi$
$434$	8.47002e6	−	5.34776e7i	0.103613	−	0.654188i
$435$	5.68497e6	−	2.89663e6i	0.0690653	−	0.0351905i
$436$	−1.41969e7	−	4.36935e7i	−0.171290	−	0.527178i
$437$	−4.79230e7	+	2.44180e7i	−0.574249	+	0.292594i
$438$	−8.02887e7	−	8.02887e7i	−0.955503	−	0.955503i
$439$	−1.06805e7	+	3.28714e7i	−0.126241	+	0.388530i	−0.994125	−	0.108237i	$-0.965479\pi$
$439$	−1.06805e7	+	3.28714e7i	−0.126241	+	0.388530i	0.867884	+	0.496767i	$0.165479\pi$
$440$	7.53695e6			0.0884785
$441$			3.07105e7i			0.358073i
$442$	−2.22468e6	+	6.84685e6i	−0.0257632	+	0.0792911i
$443$	−1.36178e8	+	9.89389e7i	−1.56637	+	1.13804i	−0.635842	+	0.771819i	$0.719347\pi$
$443$	−1.36178e8	+	9.89389e7i	−1.56637	+	1.13804i	−0.930530	+	0.366217i	$0.880653\pi$
$444$	−2.16740e7	+	4.25376e7i	−0.247622	+	0.485986i
$445$	−3.60343e6	−	7.07213e6i	−0.0408918	−	0.0802547i
$446$	5.77789e7	−	7.95258e7i	0.651275	−	0.896403i
$447$	6.58089e6	−	4.78129e6i	0.0736821	−	0.0535332i
$448$	−6.03684e7	−	6.03684e7i	−0.671391	−	0.671391i
$449$	3.61612e7	+	2.62726e7i	0.399488	+	0.290245i	0.769332	−	0.638849i	$-0.220589\pi$
$449$	3.61612e7	+	2.62726e7i	0.399488	+	0.290245i	−0.369844	+	0.929094i	$0.620589\pi$
$450$	7.18531e7	+	3.66110e7i	0.788511	+	0.401767i
$451$	1.87730e7	−	1.18528e8i	0.204646	−	1.29209i
$452$	−4.90635e7	+	3.56467e7i	−0.531304	+	0.386015i
$453$	2.40902e7	−	3.81552e6i	0.259147	−	0.0410449i
$454$	1.24574e8	+	4.04765e7i	1.33125	+	0.432549i
$455$	469601.	+	2.96494e6i	0.00498534	+	0.0314762i
$456$	−8.46160e6	−	8.46160e6i	−0.0892397	−	0.0892397i
$457$	9.56346e6	−	6.03813e7i	0.100200	−	0.632636i	−0.885566	−	0.464513i	$-0.846229\pi$
$457$	9.56346e6	−	6.03813e7i	0.100200	−	0.632636i	0.985766	−	0.168123i	$-0.0537706\pi$
$458$	2.28590e8	+	3.62051e7i	2.37936	+	0.376854i
$459$	6.59382e6	−	6.59382e6i	0.0681866	−	0.0681866i
$460$	2.00153e7	−	3.17011e6i	0.205631	−	0.0325688i
$461$	−2.18361e7	+	6.72047e7i	−0.222881	+	0.685957i	0.775619	+	0.631202i	$0.217438\pi$
$461$	−2.18361e7	+	6.72047e7i	−0.222881	+	0.685957i	−0.998500	+	0.0547556i	$0.982562\pi$
$462$	1.78623e7	+	1.12778e8i	0.181139	+	1.14367i
$463$	−6.11021e7	−	8.40998e7i	−0.615621	−	0.847329i	0.381404	−	0.924408i	$-0.375441\pi$
$463$	−6.11021e7	−	8.40998e7i	−0.615621	−	0.847329i	−0.997025	+	0.0770793i	$0.975441\pi$
$464$	−7.14293e7	−	1.13133e7i	−0.715027	−	0.113249i
$465$	1.82744e6	−	3.58656e6i	0.0181754	−	0.0356713i
$466$	1.93734e7	−	2.66652e7i	0.191447	−	0.263504i
$467$	1.30075e8	−	1.30075e8i	1.27715	−	1.27715i	0.334895	−	0.942255i	$-0.391299\pi$
$467$	1.30075e8	−	1.30075e8i	1.27715	−	1.27715i	0.942255	−	0.334895i	$-0.108701\pi$
$468$	2.72473e7	+	3.75026e7i	0.265819	+	0.365868i
$469$	−8.74022e7	−	6.35014e7i	−0.847235	−	0.615552i
$470$	−1.58391e7	+	8.07044e6i	−0.152559	+	0.0777327i
$471$	−2.34333e7	−	1.19399e7i	−0.224270	−	0.114271i
$472$	3.85095e6	+	5.30038e6i	0.0366220	+	0.0504059i
$473$	−9.94251e7	−	3.23052e7i	−0.939534	−	0.305273i
$474$	−1.17432e8			−1.10268
$475$		−	3.93554e7i		−	0.367218i
$476$	8.07441e6	+	2.62353e6i	0.0748669	+	0.0243257i
$477$	1.19905e7	−	1.19905e7i	0.110480	−	0.110480i
$478$	3.47954e7	+	6.82899e7i	0.318595	+	0.625278i
$479$	1.10986e8	−	3.60615e7i	1.00986	−	0.328124i	0.243062	−	0.970011i	$-0.421848\pi$
$479$	1.10986e8	−	3.60615e7i	1.00986	−	0.328124i	0.766799	+	0.641887i	$0.221848\pi$
$480$	−3.89234e6	−	7.63914e6i	−0.0351955	−	0.0690750i
$481$	−3.98398e7	−	6.31001e6i	−0.357999	−	0.0567015i
$482$	5.40692e7	+	2.75496e7i	0.482846	+	0.246023i
$483$	2.43161e7	+	7.48371e7i	0.215800	+	0.664165i
$484$	1.20369e8	+	3.70458e8i	1.06164	+	3.26740i
$485$	2.31546e6	+	1.68228e6i	0.0202961	+	0.0147460i
$486$	−2.67279e7	−	1.68753e8i	−0.232839	−	1.47009i
$487$		−	2.20368e7i		−	0.190793i	−0.995439	−	0.0953963i	$-0.969588\pi$
$487$		−	2.20368e7i		−	0.190793i	0.995439	−	0.0953963i	$-0.0304118\pi$
$488$	−6.11487e7	+	4.69100e6i	−0.526172	+	0.0403651i
$489$	−5.59491e7			−0.478483
$490$	−9.72516e6	+	1.54031e6i	−0.0826625	+	0.0130925i
$491$	−5.42667e7	+	7.46917e7i	−0.458447	+	0.630998i	−0.974186	−	0.225748i	$-0.927517\pi$
$491$	−5.42667e7	+	7.46917e7i	−0.458447	+	0.630998i	0.515739	+	0.856746i	$0.327517\pi$
$492$	6.82745e7	−	2.21837e7i	0.573276	−	0.186269i
$493$	1.45000e7	−	4.71132e6i	0.121011	−	0.0393189i
$494$	1.79086e7	−	3.51476e7i	0.148553	−	0.291551i
$495$	1.85319e6	−	1.17006e7i	0.0152793	−	0.0964700i
$496$	−4.06525e7	+	2.07135e7i	−0.333152	+	0.169750i
$497$	2.42163e7	+	7.45301e7i	0.197260	+	0.607103i
$498$	1.59690e8	−	8.13659e7i	1.29297	−	0.658801i
$499$	8.73388e7	+	8.73388e7i	0.702920	+	0.702920i	0.965036	−	0.262116i	$-0.0844204\pi$
$499$	8.73388e7	+	8.73388e7i	0.702920	+	0.702920i	−0.262116	+	0.965036i	$0.584420\pi$
$500$	−9.20075e6	+	2.83170e7i	−0.0736060	+	0.226536i
$501$	1.41118e8			1.12220
$502$			2.88003e8i			2.27660i
$503$	2.59498e6	−	7.98654e6i	0.0203906	−	0.0627559i	−0.940343	−	0.340227i	$-0.889496\pi$
$503$	2.59498e6	−	7.98654e6i	0.0203906	−	0.0627559i	0.960734	+	0.277471i	$0.0894962\pi$
$504$	1.97656e7	−	1.43606e7i	0.154390	−	0.112171i
$505$	−726972.	+	1.42676e6i	−0.00564473	+	0.0110784i
$506$	2.95668e8	+	5.80280e8i	2.28219	+	4.47905i
$507$	−3.29964e7	+	4.54156e7i	−0.253188	+	0.348483i
$508$	−3.42602e7	+	2.48915e7i	−0.261336	+	0.189872i
$509$	−8.27271e7	−	8.27271e7i	−0.627327	−	0.627327i	0.320067	−	0.947395i	$-0.396294\pi$
$509$	−8.27271e7	−	8.27271e7i	−0.627327	−	0.627327i	−0.947395	+	0.320067i	$0.896294\pi$
$510$	890384.	+	646902.i	0.00671223	+	0.00487672i
$511$	−1.00803e8	−	5.13619e7i	−0.755462	−	0.384927i
$512$	−2.11476e7	+	1.33521e8i	−0.157562	+	0.994807i
$513$	−4.13371e7	+	3.00331e7i	−0.306188	+	0.222458i
$514$	3.60294e8	−	5.70650e7i	2.65319	−	0.420223i
$515$	−1.11277e7	−	3.61562e6i	−0.0814676	−	0.0264704i
$516$	−9.78303e6	−	6.17676e7i	−0.0712073	−	0.449585i
$517$	−2.31675e8	−	2.31675e8i	−1.67652	−	1.67652i
$518$	−1.29754e7	+	8.19233e7i	−0.0933535	+	0.589411i
$519$	−1.26932e7	−	2.01040e6i	−0.0907964	−	0.0143807i
$520$	−2.69362e6	+	2.69362e6i	−0.0191570	+	0.0191570i
$521$	−1.61017e8	+	2.55025e7i	−1.13856	+	0.180331i	−0.697118	−	0.716956i	$-0.745535\pi$
$521$	−1.61017e8	+	2.55025e7i	−1.13856	+	0.180331i	−0.441447	+	0.897287i	$0.645535\pi$
$522$	5.28972e7	−	1.62801e8i	0.371895	−	1.14458i
$523$	−3.41094e7	−	2.15358e8i	−0.238434	−	1.50541i	−0.758717	−	0.651420i	$-0.774174\pi$
$523$	−3.41094e7	−	2.15358e8i	−0.238434	−	1.50541i	0.520283	−	0.853994i	$-0.325826\pi$
$524$	5.87381e7	+	8.08460e7i	0.408250	+	0.561908i
$525$	−5.68685e7	−	9.00709e6i	−0.393001	−	0.0622453i
$526$	1.55950e7	−	3.06068e7i	0.107159	−	0.210311i
$527$	5.65365e6	−	7.78158e6i	0.0386275	−	0.0531663i
$528$	6.80370e7	−	6.80370e7i	0.462214	−	0.462214i
$529$	1.76790e8	+	2.43331e8i	1.19424	+	1.64373i
$530$	4.39845e6	+	3.19566e6i	0.0295442	+	0.0214651i
$531$	9.17536e6	−	4.67508e6i	0.0612829	−	0.0312252i
$532$	−4.14491e7	−	2.11194e7i	−0.275283	−	0.140264i
$533$	3.56514e7	+	4.90699e7i	0.235448	+	0.324066i
$534$	1.45125e8	+	4.71539e7i	0.953054	+	0.309666i
$535$	1.49884e6			0.00978802
$536$		−	1.37095e8i		−	0.890279i
$537$	−2.85347e7	−	9.27149e6i	−0.184268	−	0.0598724i
$538$	2.30433e8	−	2.30433e8i	1.47978	−	1.47978i
$539$	−8.23887e7	−	1.61697e8i	−0.526140	−	1.03261i
$540$	1.83091e7	−	5.94899e6i	0.116275	−	0.0377800i
$541$	−7.48758e7	−	1.46952e8i	−0.472879	−	0.928077i	−0.997071	−	0.0764769i	$-0.975633\pi$
$541$	−7.48758e7	−	1.46952e8i	−0.472879	−	0.928077i	0.524193	−	0.851600i	$-0.324367\pi$
$542$	−4.44448e8	−	7.03937e7i	−2.79141	−	0.442116i
$543$	3.26507e7	+	1.66363e7i	0.203935	+	0.103910i
$544$	−6.33081e6	−	1.94842e7i	−0.0393244	−	0.121028i
$545$	−1.83372e6	−	5.64361e6i	−0.0113277	−	0.0348632i
$546$	−4.66895e7	−	3.39219e7i	−0.286841	−	0.208402i
$547$	−3.10923e7	−	1.96309e8i	−0.189973	−	1.19944i	−0.879756	−	0.475425i	$-0.842294\pi$
$547$	−3.10923e7	−	1.96309e8i	−0.189973	−	1.19944i	0.689784	−	0.724015i	$-0.257706\pi$
$548$			2.02147e8i			1.22836i
$549$	−7.75284e6	+	9.60826e7i	−0.0468537	+	0.580668i
$550$	−4.76539e8			−2.86424
$551$	−8.25106e7	+	1.30684e7i	−0.493236	+	0.0781210i
$552$	−5.86928e7	+	8.07838e7i	−0.348954	+	0.480294i
$553$	−1.11280e8	+	3.61571e7i	−0.658024	+	0.213805i
$554$	2.37359e7	−	7.71227e6i	0.139597	−	0.0453579i
$555$	−2.79949e6	+	5.49431e6i	−0.0163757	+	0.0321391i
$556$	6.22341e7	−	3.92930e8i	0.362079	−	2.28608i
$557$	1.28887e8	−	6.56710e7i	0.745834	−	0.380021i	−0.0393976	−	0.999224i	$-0.512544\pi$
$557$	1.28887e8	−	6.56710e7i	0.745834	−	0.380021i	0.785232	+	0.619202i	$0.212544\pi$
$558$	−3.33720e7	−	1.02709e8i	−0.192079	−	0.591158i
$559$	4.70790e7	−	2.39879e7i	0.269520	−	0.137328i
$560$	−3.67812e6	−	3.67812e6i	−0.0209441	−	0.0209441i
$561$	−6.26825e6	+	1.92917e7i	−0.0355024	+	0.109265i
$562$	1.18231e8			0.666072
$563$		−	1.22711e8i		−	0.687637i	−0.939036	−	0.343819i	$-0.888279\pi$
$563$		−	1.22711e8i		−	0.687637i	0.939036	−	0.343819i	$-0.111721\pi$
$564$	6.05659e7	−	1.86403e8i	0.337591	−	1.03900i
$565$	−6.33722e6	+	4.60426e6i	−0.0351361	+	0.0255279i
$566$	−1.55017e8	+	3.04239e8i	−0.854931	+	1.67790i
$567$	4.01079e6	+	7.87162e6i	0.0220030	+	0.0431832i
$568$	−5.84521e7	+	8.04524e7i	−0.318974	+	0.439030i
$569$	−7.31745e7	+	5.31644e7i	−0.397213	+	0.288592i	−0.768405	−	0.639964i	$-0.778949\pi$
$569$	−7.31745e7	+	5.31644e7i	−0.397213	+	0.288592i	0.371192	+	0.928556i	$0.378949\pi$
$570$	−4.26417e6	−	4.26417e6i	−0.0230255	−	0.0230255i
$571$	2.41972e8	+	1.75803e8i	1.29974	+	0.944316i	0.999953	−	0.00969105i	$-0.00308481\pi$
$571$	2.41972e8	+	1.75803e8i	1.29974	+	0.944316i	0.299786	+	0.954007i	$0.403085\pi$
$572$	−2.44072e8	−	1.24361e8i	−1.30416	−	0.664502i
$573$	2.59220e7	−	1.63665e8i	0.137786	−	0.869946i
$574$	1.00903e8	−	7.33105e7i	0.533543	−	0.387642i
$575$	−3.24357e8	+	5.13731e7i	−1.70616	+	0.270229i
$576$	−1.61949e8	−	5.26205e7i	−0.847445	−	0.275352i
$577$	−1.57550e7	−	9.94730e7i	−0.0820144	−	0.517819i	−0.994157	−	0.107945i	$-0.965573\pi$
$577$	−1.57550e7	−	9.94730e7i	−0.0820144	−	0.517819i	0.912142	−	0.409873i	$-0.134427\pi$
$578$	−2.07218e8	−	2.07218e8i	−1.07311	−	1.07311i
$579$	3.02426e7	−	1.90944e8i	0.155806	−	0.983720i
$580$	3.10877e7	+	4.92381e6i	0.159333	+	0.0252358i
$581$	1.26272e8	−	1.26272e8i	0.643839	−	0.643839i
$582$	−5.43457e7	+	8.60751e6i	−0.275674	+	0.0436625i
$583$	−3.09648e7	+	9.53000e7i	−0.156266	+	0.480936i
$584$	−2.24586e7	−	1.41798e8i	−0.112757	−	0.711920i
$585$	3.51935e6	+	4.84398e6i	0.0175791	+	0.0241955i
$586$	5.47216e7	+	8.66705e6i	0.271936	+	0.0430704i
$587$	−1.45754e8	+	2.86058e8i	−0.720618	+	1.41429i	0.181758	+	0.983343i	$0.441821\pi$
$587$	−1.45754e8	+	2.86058e8i	−0.720618	+	1.41429i	−0.902376	+	0.430949i	$0.858179\pi$
$588$	6.38103e7	−	8.78274e7i	0.313877	−	0.432014i
$589$	−3.72671e7	+	3.72671e7i	−0.182381	+	0.182381i
$590$	1.94066e6	+	2.67109e6i	0.00944918	+	0.0130057i
$591$	−1.33604e8	−	9.70688e7i	−0.647227	−	0.470238i
$592$	6.22763e7	−	3.17314e7i	0.300163	−	0.152941i
$593$	−2.23636e8	−	1.13948e8i	−1.07245	−	0.546441i	−0.173654	−	0.984807i	$-0.555557\pi$
$593$	−2.23636e8	−	1.13948e8i	−1.07245	−	0.546441i	−0.898797	+	0.438366i	$0.855557\pi$
$594$	3.63659e8	+	5.00534e8i	1.73514	+	2.38822i
$595$	1.04292e6	+	338865.i	0.00495108	+	0.00160870i
$596$	4.01281e7			0.189544
$597$			8.58875e7i			0.403652i
$598$	−3.13054e8	−	1.01717e8i	−1.46392	−	0.475655i
$599$	−9.92529e7	+	9.92529e7i	−0.461809	+	0.461809i	−0.899248	−	0.437439i	$-0.855886\pi$
$599$	−9.92529e7	+	9.92529e7i	−0.461809	+	0.461809i	0.437439	+	0.899248i	$0.355886\pi$
$600$	−3.31707e7	−	6.51011e7i	−0.153568	−	0.301394i
$601$	9.45764e7	−	3.07297e7i	0.435672	−	0.141558i	−0.0829661	−	0.996552i	$-0.526439\pi$
$601$	9.45764e7	−	3.07297e7i	0.435672	−	0.141558i	0.518638	+	0.854994i	$0.326439\pi$
$602$	−4.93268e7	−	9.68093e7i	−0.226096	−	0.443739i
$603$	−2.12830e8	−	3.37090e7i	−0.970691	−	0.153742i
$604$	1.07207e8	+	5.46248e7i	0.486534	+	0.247902i
$605$	1.55473e7	+	4.78497e7i	0.0702084	+	0.216079i
$606$	−9.51303e6	−	2.92781e7i	−0.0427465	−	0.131560i
$607$	2.32240e8	+	1.68732e8i	1.03841	+	0.754452i	0.969975	−	0.243204i	$-0.0781983\pi$
$607$	2.32240e8	+	1.68732e8i	1.03841	+	0.754452i	0.0684385	+	0.997655i	$0.478198\pi$
$608$	1.75606e7	+	1.10873e8i	0.0781319	+	0.493305i
$609$			1.22219e8i			0.541110i
$610$	−3.08155e7	+	2.36400e6i	−0.135762	+	0.0104150i
$611$	1.65596e8			0.725985
$612$	1.67252e7	−	2.64902e6i	0.0729656	−	0.0115566i
$613$	3.89971e7	−	5.36749e7i	0.169298	−	0.233018i	−0.715935	−	0.698167i	$-0.753999\pi$
$613$	3.89971e7	−	5.36749e7i	0.169298	−	0.233018i	0.885232	+	0.465149i	$0.153999\pi$
$614$	5.50210e8	−	1.78774e8i	2.37697	−	0.772324i
$615$	8.81859e6	−	2.86533e6i	0.0379117	−	0.0123183i
$616$	−6.55440e7	+	1.28637e8i	−0.280408	+	0.550332i
$617$	−5.48445e7	+	3.46275e8i	−0.233495	+	1.47423i	0.540664	+	0.841238i	$0.318173\pi$
$617$	−5.48445e7	+	3.46275e8i	−0.233495	+	1.47423i	−0.774159	+	0.632991i	$0.781827\pi$
$618$	2.00423e8	−	1.02120e8i	0.849144	−	0.432660i
$619$	5.24028e6	+	1.61279e7i	0.0220944	+	0.0679996i	0.961496	−	0.274820i	$-0.0886181\pi$
$619$	5.24028e6	+	1.61279e7i	0.0220944	+	0.0679996i	−0.939401	+	0.342819i	$0.888618\pi$
$620$	1.76929e7	−	9.01501e6i	0.0742378	−	0.0378260i
$621$	3.01485e8	+	3.01485e8i	1.25890	+	1.25890i
$622$	1.36668e8	−	4.20620e8i	0.567931	−	1.74791i
$623$	1.52041e8			0.628776
$624$			4.86314e7i			0.200153i
$625$	7.36586e7	−	2.26698e8i	0.301706	−	0.928555i
$626$	−4.20615e8	+	3.05595e8i	−1.71460	+	1.24573i
$627$	5.04592e7	−	9.90318e7i	0.204709	−	0.401765i
$628$	−5.89009e7	−	1.15600e8i	−0.237817	−	0.466742i
$629$	−8.66092e6	+	1.19207e7i	−0.0348027	+	0.0479017i
$630$	9.96075e6	−	7.23691e6i	0.0398355	−	0.0289422i
$631$	−2.75294e7	−	2.75294e7i	−0.109574	−	0.109574i	0.650194	−	0.759768i	$-0.274688\pi$
$631$	−2.75294e7	−	2.75294e7i	−0.109574	−	0.109574i	−0.759768	+	0.650194i	$0.774688\pi$
$632$	−1.20122e8	−	8.72741e7i	−0.475853	−	0.345728i
$633$	1.26418e8	+	6.44134e7i	0.498425	+	0.253960i
$634$	7.05147e7	−	4.45213e8i	0.276702	−	1.74703i
$635$	−4.42517e6	+	3.21508e6i	−0.0172826	+	0.0125565i
$636$	−5.92049e7	+	9.37713e6i	−0.230137	+	0.0364501i
$637$	8.72336e7	+	2.83439e7i	0.337494	+	0.109658i
$638$	1.58240e8	+	9.99087e8i	0.609332	+	3.84717i
$639$	1.10524e8	+	1.10524e8i	0.423600	+	0.423600i
$640$	3.62018e6	−	2.28569e7i	0.0138099	−	0.0871923i
$641$	−1.59893e7	−	2.53245e6i	−0.0607092	−	0.00961540i	0.126006	−	0.992029i	$-0.459784\pi$
$641$	−1.59893e7	−	2.53245e6i	−0.0607092	−	0.00961540i	−0.186715	+	0.982414i	$0.559784\pi$
$642$	−2.03754e7	+	2.03754e7i	−0.0770020	+	0.0770020i
$643$	2.06708e8	−	3.27393e7i	0.777542	−	0.123151i	0.244965	−	0.969532i	$-0.421224\pi$
$643$	2.06708e8	−	3.27393e7i	0.777542	−	0.123151i	0.532577	+	0.846381i	$0.321224\pi$
$644$	−1.19954e8	+	3.69181e8i	−0.449115	+	1.38223i
$645$	−1.26361e6	−	7.97813e6i	−0.00470906	−	0.0297319i
$646$	−8.46996e6	−	1.16579e7i	−0.0314184	−	0.0432437i
$647$	2.07204e8	+	3.28179e7i	0.765043	+	0.121171i	0.526747	−	0.850022i	$-0.323411\pi$
$647$	2.07204e8	+	3.28179e7i	0.765043	+	0.121171i	0.238295	+	0.971193i	$0.423411\pi$
$648$	−5.08963e6	+	9.98895e6i	−0.0187051	+	0.0367109i
$649$	−3.57680e7	+	4.92304e7i	−0.130846	+	0.180094i
$650$	1.70310e8	−	1.70310e8i	0.620154	−	0.620154i
$651$	4.53217e7	+	6.23800e7i	0.164272	+	0.226101i
$652$	−2.23292e8	−	1.62231e8i	−0.805620	−	0.585317i
$653$	−2.22151e8	+	1.13192e8i	−0.797827	+	0.406513i	−0.804862	−	0.593462i	$-0.797761\pi$
$653$	−2.22151e8	+	1.13192e8i	−0.797827	+	0.406513i	0.00703470	+	0.999975i	$0.497761\pi$
$654$	1.01648e8	+	5.17920e7i	0.363382	+	0.185153i
$655$	7.58682e6	+	1.04424e7i	0.0269983	+	0.0371599i
$656$	−9.99559e7	−	3.24777e7i	−0.354076	−	0.115046i
$657$	−2.25654e8			−0.795694
$658$		−	3.40519e8i		−	1.19526i
$659$	2.04386e8	+	6.64090e7i	0.714158	+	0.232044i	0.643489	−	0.765456i	$-0.277486\pi$
$659$	2.04386e8	+	6.64090e7i	0.714158	+	0.232044i	0.0706697	+	0.997500i	$0.477486\pi$
$660$	−2.96113e7	+	2.96113e7i	−0.102997	+	0.102997i
$661$	−1.50201e8	−	2.94787e8i	−0.520079	−	1.02071i	−0.990402	−	0.138219i	$-0.955862\pi$
$661$	−1.50201e8	−	2.94787e8i	−0.520079	−	1.02071i	0.470322	−	0.882495i	$-0.344138\pi$
$662$	−4.51513e8	+	1.46706e8i	−1.55631	+	0.505676i
$663$	−4.65443e6	−	9.13484e6i	−0.0159708	−	0.0313444i
$664$	2.23819e8	+	3.54494e7i	0.764525	+	0.121089i
$665$	−5.35371e6	−	2.72785e6i	−0.0182050	−	0.00927590i
$666$	5.11232e7	+	1.57341e8i	0.173059	+	0.532622i
$667$	2.15413e8	+	6.62972e8i	0.725928	+	2.23418i
$668$	5.63199e8	+	4.09188e8i	1.88944	+	1.37276i
$669$	2.18987e7	+	1.38263e8i	0.0731375	+	0.461772i
$670$		−	6.90879e7i		−	0.229709i
$671$	−2.16945e8	−	5.26692e8i	−0.718096	−	1.74337i
$672$	1.64231e8			0.541186
$673$	3.57038e8	−	5.65492e7i	1.17130	−	0.185516i	0.459684	−	0.888082i	$-0.347963\pi$
$673$	3.57038e8	−	5.65492e7i	1.17130	−	0.185516i	0.711618	+	0.702566i	$0.247963\pi$
$674$	−8.65754e6	+	1.19161e7i	−0.0282758	+	0.0389183i
$675$	−2.96707e8	+	9.64061e7i	−0.964755	+	0.313468i
$676$	−2.63376e8	+	8.55760e7i	−0.852581	+	0.277020i
$677$	2.36892e8	−	4.64927e8i	0.763458	−	1.49837i	−0.100572	−	0.994930i	$-0.532067\pi$
$677$	2.36892e8	−	4.64927e8i	0.763458	−	1.49837i	0.864030	−	0.503440i	$-0.167933\pi$
$678$	2.35580e7	−	1.48740e8i	0.0755875	−	0.477241i
$679$	−4.88484e7	+	2.48895e7i	−0.156042	+	0.0795073i
$680$	430014.	+	1.32345e6i	0.00136759	+	0.00420901i
$681$	−1.66202e8	+	8.46843e7i	−0.526254	+	0.268140i
$682$	4.51252e8	+	4.51252e8i	1.42254	+	1.42254i
$683$	4.67578e7	−	1.43906e8i	0.146755	−	0.451664i	−0.850478	−	0.526011i	$-0.823687\pi$
$683$	4.67578e7	−	1.43906e8i	0.146755	−	0.451664i	0.997232	+	0.0743465i	$0.0236871\pi$
$684$	−9.27860e7			−0.289944
$685$			2.61100e7i			0.0812335i
$686$	1.53107e8	−	4.71216e8i	0.474268	−	1.45965i
$687$	−2.66643e8	+	1.93727e8i	−0.822356	+	0.597477i
$688$	−4.15659e7	+	8.15777e7i	−0.127636	+	0.250499i
$689$	−2.29927e7	−	4.51257e7i	−0.0702962	−	0.137964i
$690$	−2.95779e7	+	4.07105e7i	−0.0900367	+	0.123925i
$691$	3.67175e8	−	2.66768e8i	1.11286	−	0.808537i	0.129745	−	0.991547i	$-0.458584\pi$
$691$	3.67175e8	−	2.66768e8i	1.11286	−	0.808537i	0.983111	+	0.183010i	$0.0585842\pi$
$692$	−4.48289e7	−	4.48289e7i	−0.135282	−	0.135282i
$693$	1.83585e8	+	1.33382e8i	0.551615	+	0.400772i
$694$	−3.69555e8	−	1.88298e8i	−1.10561	−	0.563334i
$695$	8.03838e6	−	5.07523e7i	0.0239450	−	0.151183i
$696$	−1.25473e8	+	9.11616e7i	−0.372154	+	0.270386i
$697$	2.18840e7	−	3.46608e6i	0.0646290	−	0.0102362i
$698$	−3.49572e8	−	1.13583e8i	−1.02795	−	0.334000i
$699$	7.34270e6	+	4.63600e7i	0.0214993	+	0.135741i
$700$	−2.00844e8	−	2.00844e8i	−0.585551	−	0.585551i
$701$	−5.89297e6	+	3.72067e7i	−0.0171072	+	0.108011i	−0.994764	−	0.102195i	$-0.967413\pi$
$701$	−5.89297e6	+	3.72067e7i	−0.0171072	+	0.108011i	0.977657	+	0.210206i	$0.0674134\pi$
$702$	−3.08853e8	−	4.89175e7i	−0.892772	−	0.141401i
$703$	5.70901e7	−	5.70901e7i	0.164322	−	0.164322i
$704$	9.93862e8	−	1.57412e8i	2.84845	−	0.451150i
$705$	7.82291e6	−	2.40764e7i	0.0223255	−	0.0687108i
$706$	1.37546e8	+	8.68432e8i	0.390872	+	2.46787i
$707$	−1.80293e7	−	2.48153e7i	−0.0510178	−	0.0702200i
$708$	−3.59540e7	−	5.69455e6i	−0.101309	−	0.0160457i
$709$	−1.30012e8	+	2.55163e8i	−0.364791	+	0.715943i	−0.998330	−	0.0577680i	$-0.981602\pi$
$709$	−1.30012e8	+	2.55163e8i	−0.364791	+	0.715943i	0.633539	+	0.773711i	$0.281602\pi$
$710$	−2.94565e7	+	4.05434e7i	−0.0823013	+	0.113278i
$711$	−1.65023e8	+	1.65023e8i	−0.459130	+	0.459130i
$712$	1.13406e8	+	1.56089e8i	0.314191	+	0.432447i
$713$	3.55792e8	+	2.58498e8i	0.981585	+	0.713163i
$714$	−1.87841e7	+	9.57099e6i	−0.0516055	+	0.0262943i
$715$	−3.15253e7	−	1.60629e7i	−0.0862463	−	0.0439447i
$716$	−8.69977e7	−	1.19742e8i	−0.237011	−	0.326218i
$717$	−1.03805e8	−	3.37282e7i	−0.281618	−	0.0915032i
$718$	−9.37363e8			−2.53241
$719$		−	4.29621e8i		−	1.15584i	−0.816093	−	0.577921i	$-0.803864\pi$
$719$		−	4.29621e8i		−	1.15584i	0.816093	−	0.577921i	$-0.196136\pi$
$720$	−9.86723e6	−	3.20606e6i	−0.0264361	−	0.00858962i
$721$	1.58480e8	−	1.58480e8i	0.422834	−	0.422834i
$722$	−2.25789e8	−	4.43137e8i	−0.599918	−	1.17741i
$723$	−8.21885e7	+	2.67047e7i	−0.217468	+	0.0706598i
$724$	8.20691e7	+	1.61070e8i	0.216254	+	0.424422i
$725$	−5.03790e8	−	7.97926e7i	−1.32201	−	0.209386i
$726$	−8.61825e8	−	4.39122e8i	−2.25221	−	1.14756i
$727$	1.03032e8	+	3.17099e8i	0.268144	+	0.825261i	0.990953	+	0.134213i	$0.0428506\pi$
$727$	1.03032e8	+	3.17099e8i	0.268144	+	0.825261i	−0.722809	+	0.691048i	$0.757149\pi$
$728$	−2.25489e7	−	6.93983e7i	−0.0584427	−	0.179868i
$729$	2.21317e8	+	1.60796e8i	0.571257	+	0.415043i
$730$	−1.13179e7	−	7.14581e7i	−0.0290935	−	0.183689i
$731$		−	1.93016e7i		−	0.0494131i
$732$	2.21812e8	−	2.58672e8i	0.565525	−	0.659503i
$733$	−4.82287e8			−1.22460			−0.612300	−	0.790626i	$-0.709755\pi$
$733$	−4.82287e8			−1.22460			−0.612300	+	0.790626i	$0.709755\pi$
$734$	−2.07602e8	+	3.28809e7i	−0.524980	+	0.0831486i
$735$	8.24197e6	−	1.13441e7i	0.0207572	−	0.0285699i
$736$	8.90865e8	−	2.89459e8i	2.23449	−	0.726030i
$737$	1.21102e9	−	3.93485e8i	3.02517	−	0.982938i
$738$	1.12939e8	−	2.21654e8i	0.280979	−	0.551452i
$739$	7.66393e6	−	4.83881e7i	0.0189897	−	0.119896i	−0.976373	−	0.216094i	$-0.930668\pi$
$739$	7.66393e6	−	4.83881e7i	0.0189897	−	0.119896i	0.995362	+	0.0961979i	$0.0306682\pi$
$740$	−2.71041e7	+	1.38102e7i	−0.0668868	+	0.0340805i
$741$	1.73593e7	+	5.34265e7i	0.0426656	+	0.131311i
$742$	−9.27927e7	+	4.72802e7i	−0.227144	+	0.115736i
$743$	4.04430e8	+	4.04430e8i	0.986000	+	0.986000i	0.999903	−	0.0139029i	$-0.00442558\pi$
$743$	4.04430e8	+	4.04430e8i	0.986000	+	0.986000i	−0.0139029	+	0.999903i	$0.504426\pi$
$744$	−3.02361e7	+	9.30571e7i	−0.0734187	+	0.225960i
$745$	5.18309e6			0.0125349
$746$		−	4.58473e8i		−	1.10433i
$747$	1.10065e8	−	3.38747e8i	0.264052	−	0.812668i
$748$	−8.09550e7	+	5.88172e7i	−0.193437	+	0.140540i
$749$	−1.30345e7	+	2.55816e7i	−0.0310204	+	0.0608810i
$750$	−3.35655e7	−	6.58761e7i	−0.0795627	−	0.156151i
$751$	−2.80855e8	+	3.86564e8i	−0.663076	+	0.912645i	−0.999578	−	0.0290371i	$-0.990756\pi$
$751$	−2.80855e8	+	3.86564e8i	−0.663076	+	0.912645i	0.336503	+	0.941683i	$0.390756\pi$
$752$	−2.32142e8	+	1.68661e8i	−0.545883	+	0.396607i
$753$	−2.90014e8	−	2.90014e8i	−0.679256	−	0.679256i
$754$	−4.13616e8	−	3.00510e8i	−0.964903	−	0.701043i
$755$	1.38473e7	+	7.05554e6i	0.0321754	+	0.0163942i
$756$	−5.76878e7	+	3.64226e8i	−0.133511	+	0.842958i
$757$	−8.25686e7	+	5.99896e7i	−0.190339	+	0.138289i	−0.678874	−	0.734255i	$-0.737532\pi$
$757$	−8.25686e7	+	5.99896e7i	−0.190339	+	0.138289i	0.488535	+	0.872544i	$0.337532\pi$
$758$	2.02069e8	−	3.20045e7i	0.463971	−	0.0734859i
$759$	−8.82061e8	−	2.86599e8i	−2.01731	−	0.655465i
$760$	−1.19279e6	−	7.53095e6i	−0.00271720	−	0.0171557i
$761$	−3.64602e8	−	3.64602e8i	−0.827305	−	0.827305i	0.159839	−	0.987143i	$-0.448903\pi$
$761$	−3.64602e8	−	3.64602e8i	−0.827305	−	0.827305i	−0.987143	+	0.159839i	$0.948903\pi$
$762$	1.64502e7	−	1.03862e8i	0.0371797	−	0.234743i
$763$	1.12269e8	+	1.77817e7i	0.252748	+	0.0400313i
$764$	5.78021e8	−	5.78021e8i	1.29617	−	1.29617i
$765$	2.16029e6	−	342157.i	0.00482534	−	0.000764259i
$766$	−2.79309e8	+	8.59625e8i	−0.621439	+	1.91259i
$767$	−4.81132e6	−	3.03775e7i	−0.0106630	−	0.0673234i
$768$	−1.62356e6	−	2.23464e6i	−0.00358414	−	0.00493314i
$769$	1.54494e8	+	2.44694e7i	0.339728	+	0.0538076i	0.323968	−	0.946068i	$-0.394983\pi$
$769$	1.54494e8	+	2.44694e7i	0.339728	+	0.0538076i	0.0157604	+	0.999876i	$0.494983\pi$
$770$	−3.30305e7	+	6.48259e7i	−0.0723506	+	0.141996i
$771$	−3.05345e8	+	4.20272e8i	−0.666236	+	0.916995i
$772$	6.74364e8	−	6.74364e8i	1.46569	−	1.46569i
$773$	1.39106e8	+	1.91463e8i	0.301168	+	0.414522i	0.932601	−	0.360908i	$-0.117533\pi$
$773$	1.39106e8	+	1.91463e8i	0.301168	+	0.414522i	−0.631434	+	0.775430i	$0.717533\pi$
$774$	−1.75324e8	−	1.27380e8i	−0.378111	−	0.274714i
$775$	−2.86722e8	+	1.46092e8i	−0.615965	+	0.313850i
$776$	−6.19878e7	−	3.15844e7i	−0.132654	−	0.0675907i
$777$	−6.94291e7	−	9.55609e7i	−0.148006	−	0.203712i
$778$	9.61005e8	+	3.12249e8i	2.04074	+	0.663075i
$779$	−1.21405e8			−0.256817
$780$		−	2.11655e7i		−	0.0446011i
$781$	−8.78443e8	−	2.85423e8i	−1.84400	−	0.599151i
$782$	−8.50250e7	+	8.50250e7i	−0.177798	+	0.177798i
$783$	3.00645e8	+	5.90049e8i	0.626281	+	1.22914i
$784$	−1.51157e8	+	4.91139e7i	−0.313675	+	0.101919i
$785$	−7.60785e6	−	1.49313e7i	−0.0157273	−	0.0308665i
$786$	−2.45091e8	−	3.88186e7i	−0.504730	−	0.0799414i
$787$	−1.82427e8	−	9.29513e7i	−0.374253	−	0.190692i	0.256739	−	0.966481i	$-0.417352\pi$
$787$	−1.82427e8	−	9.29513e7i	−0.374253	−	0.190692i	−0.630992	+	0.775789i	$0.717352\pi$
$788$	−2.51748e8	−	7.74800e8i	−0.514502	−	1.58347i
$789$	1.51167e7	+	4.65243e7i	0.0307769	+	0.0947215i
$790$	−6.05349e7	−	4.39812e7i	−0.122779	−	0.0892043i
$791$	−2.34727e7	−	1.48201e8i	−0.0474280	−	0.299448i
$792$			2.87961e8i			0.579640i
$793$	2.65768e8	+	1.10700e8i	0.532946	+	0.221988i
$794$	1.09283e8			0.218319
$795$	−7.64712e6	+	1.21118e6i	−0.0152194	+	0.00241051i
$796$	−2.49041e8	+	3.42775e8i	−0.493778	+	0.679627i
$797$	5.44904e8	−	1.77050e8i	1.07633	−	0.349721i	0.283380	−	0.959008i	$-0.408544\pi$
$797$	5.44904e8	−	1.77050e8i	1.07633	−	0.349721i	0.792950	+	0.609287i	$0.208544\pi$
$798$	1.09862e8	−	3.56962e7i	0.216191	−	0.0702447i
$799$	2.74629e7	−	5.38989e7i	0.0538401	−	0.105667i
$800$	−1.07221e8	+	6.76965e8i	−0.209416	+	1.32220i
$801$	2.70202e8	−	1.37675e8i	0.525765	−	0.267890i
$802$	1.20389e8	+	3.70518e8i	0.233380	+	0.718268i
$803$	1.18811e9	−	6.05373e8i	2.29462	−	1.16917i
$804$	5.38620e8	+	5.38620e8i	1.03637	+	1.03637i
$805$	−1.54937e7	+	4.76847e7i	−0.0297008	+	0.0914096i
$806$	−3.22545e8			−0.616006
$807$			4.64082e8i			0.883027i
$808$	1.20282e7	−	3.70189e7i	0.0228016	−	0.0701761i
$809$	3.06835e8	−	2.22928e8i	0.579507	−	0.421037i	−0.259039	−	0.965867i	$-0.583406\pi$
$809$	3.06835e8	−	2.22928e8i	0.579507	−	0.421037i	0.838546	+	0.544830i	$0.183406\pi$
$810$	−2.56488e6	+	5.03387e6i	−0.00482628	+	0.00947211i
$811$	−2.55054e8	−	5.00572e8i	−0.478156	−	0.938434i	−0.996526	−	0.0832777i	$-0.973461\pi$
$811$	−2.55054e8	−	5.00572e8i	−0.478156	−	0.938434i	0.518370	−	0.855156i	$-0.326539\pi$
$812$	−3.54387e8	+	4.87772e8i	−0.661927	+	0.911064i
$813$	5.18435e8	−	3.76665e8i	0.964768	−	0.700945i
$814$	−6.91280e8	−	6.91280e8i	−1.28168	−	1.28168i
$815$	−2.88412e7	−	2.09544e7i	−0.0532771	−	0.0387081i
$816$	1.58287e7	+	8.06513e6i	0.0291323	+	0.0148437i
$817$	−1.65446e7	+	1.04459e8i	−0.0303382	+	0.191548i
$818$	−8.47534e8	+	6.15769e8i	−1.54845	+	1.12501i
$819$	−1.13280e8	+	1.79419e7i	−0.206207	+	0.0326600i
$820$	4.35032e7	+	1.41350e7i	0.0789005	+	0.0256363i
$821$	1.02699e8	+	6.48417e8i	0.185583	+	1.17172i	0.887961	+	0.459919i	$0.152121\pi$
$821$	1.02699e8	+	6.48417e8i	0.185583	+	1.17172i	−0.702379	+	0.711804i	$0.747879\pi$
$822$	−3.54942e8	−	3.54942e8i	−0.639060	−	0.639060i
$823$	3.07578e7	−	1.94197e8i	0.0551767	−	0.348372i	−0.944619	−	0.328169i	$-0.893569\pi$
$823$	3.07578e7	−	1.94197e8i	0.0551767	−	0.348372i	0.999796	−	0.0202036i	$-0.00643144\pi$
$824$	2.80909e8	+	4.44917e7i	0.502093	+	0.0795238i
$825$	4.79864e8	−	4.79864e8i	0.854588	−	0.854588i
$826$	−6.24657e7	+	9.89360e6i	−0.110841	+	0.0175555i
$827$	−1.59920e8	+	4.92184e8i	−0.282740	+	0.870184i	0.704327	+	0.709876i	$0.251249\pi$
$827$	−1.59920e8	+	4.92184e8i	−0.282740	+	0.870184i	−0.987067	+	0.160308i	$0.948751\pi$
$828$	1.21119e8	+	7.64717e8i	0.213365	+	1.34713i
$829$	2.97762e7	+	4.09834e7i	0.0522643	+	0.0719356i	0.834349	−	0.551236i	$-0.185844\pi$
$829$	2.97762e7	+	4.09834e7i	0.0522643	+	0.0719356i	−0.782085	+	0.623172i	$0.785844\pi$
$830$	1.12792e8	+	1.78645e7i	0.197262	+	0.0312432i
$831$	−1.61355e7	+	3.16677e7i	−0.0281177	+	0.0551840i
$832$	−2.98938e8	+	4.11453e8i	−0.519053	+	0.714415i
$833$	2.36925e7	−	2.36925e7i	0.0409898	−	0.0409898i
$834$	5.80658e8	+	7.99207e8i	1.00097	+	1.37772i
$835$	7.27448e7	+	5.28522e7i	0.124952	+	0.0907828i
$836$	4.88536e8	−	2.48922e8i	0.836138	−	0.426033i
$837$	3.72253e8	+	1.89673e8i	0.634837	+	0.323466i
$838$	−1.02627e8	−	1.41255e8i	−0.174394	−	0.240033i
$839$	−3.89128e8	−	1.26435e8i	−0.658880	−	0.214083i	−0.0395545	−	0.999217i	$-0.512594\pi$
$839$	−3.89128e8	−	1.26435e8i	−0.658880	−	0.214083i	−0.619326	+	0.785134i	$0.712594\pi$
$840$	−1.11552e7			−0.0188209
$841$			4.87895e8i			0.820235i
$842$	−5.63491e8	−	1.83089e8i	−0.943954	−	0.306709i
$843$	−1.19056e8	+	1.19056e8i	−0.198732	+	0.198732i
$844$	3.17760e8	+	6.23638e8i	0.528532	+	1.03730i
$845$	−3.40186e7	+	1.10533e7i	−0.0563827	+	0.0183199i
$846$	−3.08344e8	−	6.05160e8i	−0.509243	−	0.999445i
$847$	−9.51882e8	−	1.50763e8i	−1.56651	−	0.248111i
$848$	7.81931e7	+	3.98414e7i	0.128227	+	0.0653351i
$849$	−1.50263e8	−	4.62461e8i	−0.245544	−	0.755705i
$850$	−2.71885e7	−	8.36776e7i	−0.0442719	−	0.136255i
$851$	−5.45044e8	−	3.95998e8i	−0.884389	−	0.642546i
$852$	−8.64352e7	−	5.45730e8i	−0.139756	−	0.882388i
$853$			5.26757e8i			0.848718i	0.905494	+	0.424359i	$0.139501\pi$
$853$			5.26757e8i			0.848718i	−0.905494	+	0.424359i	$0.860499\pi$
$854$	2.27635e8	−	5.46503e8i	0.365481	−	0.877443i
$855$	−1.19846e7			−0.0191745
$856$	−3.59851e7	+	5.69947e6i	−0.0573721	+	0.00908685i
$857$	−1.46301e8	+	2.01366e8i	−0.232436	+	0.319921i	−0.909264	−	0.416221i	$-0.863354\pi$
$857$	−1.46301e8	+	2.01366e8i	−0.232436	+	0.319921i	0.676827	+	0.736142i	$0.263354\pi$
$858$	6.46919e8	−	2.10197e8i	1.02421	−	0.332785i
$859$	−4.52690e8	+	1.47088e8i	−0.714202	+	0.232058i	−0.643508	−	0.765440i	$-0.722521\pi$
$859$	−4.52690e8	+	1.47088e8i	−0.714202	+	0.232058i	−0.0706944	+	0.997498i	$0.522521\pi$
$860$	1.80905e7	−	3.55046e7i	0.0284416	−	0.0558199i
$861$	−2.77853e7	+	1.75430e8i	−0.0435317	+	0.274849i
$862$	−1.05925e9	+	5.39715e8i	−1.65378	+	0.842642i
$863$	−3.14020e8	−	9.66453e8i	−0.488567	−	1.50366i	−0.826747	−	0.562574i	$-0.809811\pi$
$863$	−3.14020e8	−	9.66453e8i	−0.488567	−	1.50366i	0.338179	−	0.941082i	$-0.390189\pi$
$864$	7.92875e8	−	4.03990e8i	1.22932	−	0.626368i
$865$	−5.79026e6	−	5.79026e6i	−0.00894643	−	0.00894643i
$866$	5.09309e8	−	1.56749e9i	0.784201	−	2.41352i
$867$	4.17327e8			0.640353
$868$			3.80373e8i			0.581635i
$869$	4.26162e8	−	1.31159e9i	0.649405	−	1.99866i
$870$	−6.32314e7	+	4.59403e7i	−0.0960229	+	0.0697647i
$871$	−2.92179e8	+	5.73434e8i	−0.442176	+	0.867819i
$872$	6.54852e7	+	1.28522e8i	0.0987629	+	0.193833i
$873$	−6.42742e7	+	8.84658e7i	−0.0966037	+	0.132964i
$874$	5.33027e8	−	3.87267e8i	0.798389	−	0.580064i
$875$	−5.20903e7	−	5.20903e7i	−0.0777557	−	0.0777557i
$876$	6.45334e8	+	4.68863e8i	0.960003	+	0.697483i
$877$	4.10270e8	+	2.09043e8i	0.608234	+	0.309911i	0.730844	−	0.682544i	$-0.239126\pi$
$877$	4.10270e8	+	2.09043e8i	0.608234	+	0.309911i	−0.122610	+	0.992455i	$0.539126\pi$
$878$	6.62326e7	−	4.18176e8i	0.0978561	−	0.617839i
$879$	−6.38311e7	+	4.63760e7i	−0.0939865	+	0.0682852i
$880$	6.05540e7	−	9.59080e6i	0.0888576	−	0.0140737i
$881$	−6.25155e8	−	2.03125e8i	−0.914239	−	0.297054i	−0.186138	−	0.982524i	$-0.559597\pi$
$881$	−6.25155e8	−	2.03125e8i	−0.914239	−	0.297054i	−0.728101	+	0.685469i	$0.759597\pi$
$882$	−5.88502e7	−	3.71565e8i	−0.0857713	−	0.541539i
$883$	3.19565e8	+	3.19565e8i	0.464171	+	0.464171i	0.900020	−	0.435849i	$-0.143552\pi$
$883$	3.19565e8	+	3.19565e8i	0.464171	+	0.464171i	−0.435849	+	0.900020i	$0.643552\pi$
$884$	7.91179e6	−	4.99531e7i	0.0114530	−	0.0723112i
$885$	−4.64394e6	−	735528.i	−0.00669973	−	0.00106113i
$886$	1.45801e9	−	1.45801e9i	2.09633	−	2.09633i
$887$	−6.33592e8	+	1.00351e8i	−0.907902	+	0.143798i	−0.592884	−	0.805288i	$-0.702011\pi$
$887$	−6.33592e8	+	1.00351e8i	−0.907902	+	0.143798i	−0.315018	+	0.949086i	$0.602011\pi$
$888$	4.63192e7	−	1.42556e8i	0.0661488	−	0.203585i
$889$	−1.63906e7	−	1.03486e8i	−0.0233287	−	0.147291i
$890$	5.71500e7	+	7.86602e7i	0.0810674	+	0.111580i
$891$	−1.02845e8	−	1.62891e7i	−0.145396	−	0.0230284i
$892$	−3.13512e8	+	6.15303e8i	−0.441733	+	0.866950i
$893$	−1.94826e8	+	2.68156e8i	−0.273586	+	0.376558i
$894$	−7.04595e7	+	7.04595e7i	−0.0986114	+	0.0986114i
$895$	−1.12369e7	−	1.54663e7i	−0.0156740	−	0.0215734i
$896$	3.58630e8	+	2.60560e8i	0.498566	+	0.362229i
$897$	4.17667e8	−	2.12812e8i	0.578699	−	0.294862i
$898$	−4.87858e8	−	2.48576e8i	−0.673697	−	0.343266i
$899$	4.01499e8	+	5.52616e8i	0.552593	+	0.760579i
$900$	−5.38801e8	−	1.75067e8i	−0.739096	−	0.240147i
$901$	−1.85008e7			−0.0252940
$902$			1.47004e9i			2.00313i
$903$	1.47156e8	+	4.78139e7i	0.199855	+	0.0649368i
$904$	1.34639e8	−	1.34639e8i	0.182250	−	0.182250i
$905$	1.06003e7	+	2.08044e7i	0.0143013	+	0.0280678i
$906$	−2.84155e8	+	9.23276e7i	−0.382095	+	0.124150i
$907$	−2.62867e8	−	5.15905e8i	−0.352301	−	0.691430i	0.645052	−	0.764139i	$-0.276836\pi$
$907$	−2.62867e8	−	5.15905e8i	−0.352301	−	0.691430i	−0.997353	+	0.0727087i	$0.976836\pi$
$908$	−9.08862e8	−	1.43950e8i	−1.21406	−	0.192288i
$909$	−5.45118e7	−	2.77751e7i	−0.0725769	−	0.0369798i
$910$	−1.13634e7	−	3.49728e7i	−0.0150793	−	0.0464094i
$911$	−7.20314e7	−	2.21690e8i	−0.0952723	−	0.293218i	0.892052	−	0.451932i	$-0.149265\pi$
$911$	−7.20314e7	−	2.21690e8i	−0.0952723	−	0.293218i	−0.987325	+	0.158714i	$0.949265\pi$
$912$	−7.87503e7	−	5.72155e7i	−0.103817	−	0.0754274i
$913$	3.29257e8	+	2.07884e9i	0.432636	+	2.73155i
$914$			7.48877e8i			0.980781i
$915$	2.86501e7	−	3.34111e7i	0.0373992	−	0.0436141i
$916$	−1.62590e9			−2.11548
$917$	−2.44203e8	+	3.86780e7i	−0.316697	+	0.0501598i
$918$	−6.71427e7	+	9.24140e7i	−0.0867902	+	0.119456i
$919$	1.43229e9	−	4.65381e8i	1.84538	−	0.599600i	0.847780	−	0.530348i	$-0.177939\pi$
$919$	1.43229e9	−	4.65381e8i	1.84538	−	0.599600i	0.997599	−	0.0692526i	$-0.0220614\pi$
$920$	−6.05111e7	+	1.96613e7i	−0.0777091	+	0.0252492i
$921$	−3.74028e8	+	7.34072e8i	−0.478769	+	0.939636i
$922$	1.35411e8	−	8.54951e8i	0.172767	−	1.09081i
$923$	4.15953e8	−	2.11939e8i	0.528980	−	0.269529i
$924$	−2.47882e8	−	7.62903e8i	−0.314217	−	0.967060i
$925$	4.39234e8	−	2.23801e8i	0.554972	−	0.282772i
$926$	9.00431e8	+	9.00431e8i	1.13401	+	1.13401i
$927$	1.38140e8	−	4.25153e8i	0.173413	−	0.533710i
$928$	1.45490e9			1.82049
$929$			5.89234e8i			0.734920i	0.930039	+	0.367460i	$0.119773\pi$
$929$			5.89234e8i			0.734920i	−0.930039	+	0.367460i	$0.880227\pi$
$930$	−1.52373e7	+	4.68955e7i	−0.0189434	+	0.0583019i
$931$	−1.48530e8	+	1.07913e8i	−0.184062	+	0.133729i
$932$	−1.05122e8	+	2.06313e8i	−0.129851	+	0.254846i
$933$	2.85934e8	+	5.61178e8i	0.352064	+	0.690964i
$934$	−1.32451e9	+	1.82303e9i	−1.62560	+	2.23745i
$935$	−1.04564e7	+	7.59705e6i	−0.0127923	+	0.00929416i
$936$	−1.02914e8	−	1.02914e8i	−0.125501	−	0.125501i
$937$	1.13898e9	+	8.27516e8i	1.38451	+	1.00591i	0.996442	+	0.0842755i	$0.0268576\pi$
$937$	1.13898e9	+	8.27516e8i	1.38451	+	1.00591i	0.388068	+	0.921631i	$0.373142\pi$
$938$	1.17916e9	+	6.00813e8i	1.42878	+	0.727999i
$939$	1.15823e8	−	7.31278e8i	0.139894	−	0.883254i
$940$	1.01034e8	−	7.34052e7i	0.121642	−	0.0883778i
$941$	1.36634e9	−	2.16407e8i	1.63979	−	0.259718i	0.732671	−	0.680583i	$-0.238273\pi$
$941$	1.36634e9	−	2.16407e8i	1.63979	−	0.259718i	0.907123	+	0.420865i	$0.138273\pi$
$942$	3.06399e8	+	9.95551e7i	0.366551	+	0.119100i
$943$	1.58477e8	+	1.00059e9i	0.188987	+	1.19322i
$944$	3.76844e7	+	3.76844e7i	0.0447967	+	0.0447967i
$945$	−7.45117e6	+	4.70448e7i	−0.00882935	+	0.0557463i
$946$	1.26485e9	+	2.00332e8i	1.49405	+	0.236634i
$947$	−4.05342e8	+	4.05342e8i	−0.477279	+	0.477279i	−0.904260	−	0.426981i	$-0.859577\pi$
$947$	−4.05342e8	+	4.05342e8i	−0.477279	+	0.477279i	0.426981	+	0.904260i	$0.359577\pi$
$948$	8.14824e8	−	1.29055e8i	0.956398	−	0.151479i
$949$	−2.08264e8	+	6.40971e8i	−0.243678	+	0.749963i
$950$	7.54163e7	+	4.76159e8i	0.0879618	+	0.555369i
$951$	3.77313e8	+	5.19327e8i	0.438692	+	0.603808i
$952$	−2.63276e7	−	4.16987e6i	−0.0305140	−	0.00483295i
$953$	1.23223e7	−	2.41839e7i	0.0142369	−	0.0279414i	−0.883779	−	0.467905i	$-0.845009\pi$
$953$	1.23223e7	−	2.41839e7i	0.0142369	−	0.0279414i	0.898015	+	0.439964i	$0.145009\pi$
$954$	−1.22095e8	+	1.68050e8i	−0.140622	+	0.193550i
$955$	7.46593e7	−	7.46593e7i	0.0857183	−	0.0857183i
$956$	−3.16484e8	−	4.35603e8i	−0.362225	−	0.498560i
$957$	−1.16540e9	−	8.46716e8i	−1.32966	−	0.966055i
$958$	−1.27371e9	+	6.48987e8i	−1.44868	+	0.738142i
$959$	−4.45634e8	−	2.27062e8i	−0.505268	−	0.257447i
$960$	4.57000e7	+	6.29007e7i	0.0516538	+	0.0710954i
$961$	−4.34219e8	−	1.41086e8i	−0.489259	−	0.158970i
$962$	4.94112e8			0.555009
$963$			5.72657e7i			0.0641233i
$964$	−4.05446e8	−	1.31737e8i	−0.452587	−	0.147054i
$965$	8.71033e7	−	8.71033e7i	0.0969287	−	0.0969287i
$966$	−4.37608e8	−	8.58855e8i	−0.485461	−	0.952770i
$967$	−7.79549e8	+	2.53291e8i	−0.862113	+	0.280117i	−0.706511	−	0.707702i	$-0.749732\pi$
$967$	−7.79549e8	+	2.53291e8i	−0.862113	+	0.280117i	−0.155602	+	0.987820i	$0.549732\pi$
$968$	−5.55221e8	−	1.08968e9i	−0.612124	−	1.20136i
$969$	2.02683e7	+	3.21019e6i	0.0222765	+	0.00352825i
$970$	−3.12384e7	−	1.59167e7i	−0.0342273	−	0.0174397i
$971$	−4.12196e8	−	1.26861e9i	−0.450242	−	1.38570i	−0.876631	−	0.481163i	$-0.840214\pi$
$971$	−4.12196e8	−	1.26861e9i	−0.450242	−	1.38570i	0.426389	−	0.904540i	$-0.359786\pi$
$972$	3.70914e8	+	1.14155e9i	0.403900	+	1.24308i
$973$	7.96313e8	+	5.78556e8i	0.864461	+	0.628068i
$974$	4.22288e7	+	2.66622e8i	0.0457017	+	0.288549i
$975$			3.42997e8i			0.370063i
$976$	−4.85316e8	+	1.15501e8i	−0.522006	+	0.124233i
$977$	−7.07375e8			−0.758518			−0.379259	−	0.925290i	$-0.623821\pi$
$977$	−7.07375e8			−0.758518			−0.379259	+	0.925290i	$0.623821\pi$
$978$	6.76926e8	−	1.07215e8i	0.723644	−	0.114614i
$979$	−1.05332e9	+	1.44977e9i	−1.12257	+	1.54508i
$980$	6.57871e7	−	2.13755e7i	0.0698977	−	0.0227111i
$981$	2.15623e8	−	7.00602e7i	0.228396	−	0.0742103i
$982$	5.13440e8	−	1.00768e9i	0.542195	−	1.06412i
$983$	2.92929e8	−	1.84948e9i	0.308391	−	1.94710i	−0.0123178	−	0.999924i	$-0.503921\pi$
$983$	2.92929e8	−	1.84948e9i	0.308391	−	1.94710i	0.320708	−	0.947178i	$-0.396079\pi$
$984$	−2.00826e8	+	1.02326e8i	−0.210782	+	0.107399i
$985$	−3.25167e7	−	1.00076e8i	−0.0340249	−	0.104718i
$986$	−1.66406e8	+	8.47881e7i	−0.173595	+	0.0884513i
$987$	3.42895e8	+	3.42895e8i	0.356624	+	0.356624i
$988$	−8.56356e7	+	2.63559e8i	−0.0887940	+	0.273280i
$989$	8.82517e8			0.912293
$990$			1.45116e8i			0.149558i
$991$	2.35426e8	−	7.24568e8i	0.241899	−	0.744488i	−0.754232	−	0.656608i	$-0.771991\pi$
$991$	2.35426e8	−	7.24568e8i	0.241899	−	0.744488i	0.996131	−	0.0878805i	$-0.0280094\pi$
$992$	7.42574e8	−	5.39512e8i	0.760685	−	0.552670i
$993$	3.06935e8	−	6.02394e8i	0.313472	−	0.615223i
$994$	−4.35813e8	−	8.55331e8i	−0.443753	−	0.870914i
$995$	−3.21670e7	+	4.42741e7i	−0.0326544	+	0.0449449i
$996$	−1.01862e9	+	7.40069e8i	−1.03094	+	0.749021i
$997$	−1.11284e9	−	1.11284e9i	−1.12291	−	1.12291i	−0.991301	−	0.131612i	$-0.957985\pi$
$997$	−1.11284e9	−	1.11284e9i	−1.12291	−	1.12291i	−0.131612	−	0.991301i	$-0.542015\pi$
$998$	−1.22408e9	−	8.89343e8i	−1.23145	−	0.894700i
$999$	−5.70261e8	−	2.90563e8i	−0.571975	−	0.291436i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	61.7.j.a.23.4	yes	240
61.8	odd	20	inner	61.7.j.a.8.4	✓	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
61.7.j.a.8.4	✓	240	61.8	odd	20	inner
61.7.j.a.23.4	yes	240	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 61 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	61.j (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-12.0990 + 1.91629i) q^{2} +(10.2537 - 14.1131i) q^{3} +(81.8450 - 26.5930i) q^{4} +(10.5714 - 3.43485i) q^{5} +(-97.0148 + 190.402i) q^{6} +(-33.3080 + 210.298i) q^{7} +(-240.743 + 122.664i) q^{8} +(131.234 + 403.897i) q^{9} +O(q^{10})\)	\(q+(-12.0990 + 1.91629i) q^{2} +(10.2537 - 14.1131i) q^{3} +(81.8450 - 26.5930i) q^{4} +(10.5714 - 3.43485i) q^{5} +(-97.0148 + 190.402i) q^{6} +(-33.3080 + 210.298i) q^{7} +(-240.743 + 122.664i) q^{8} +(131.234 + 403.897i) q^{9} +(-121.321 + 61.8159i) q^{10} +(-1774.53 - 1774.53i) q^{11} +(463.908 - 1427.76i) q^{12} +1268.39 q^{13} -2608.22i q^{14} +(59.9200 - 184.415i) q^{15} +(-1778.10 + 1291.87i) q^{16} +(210.353 - 412.841i) q^{17} +(-2361.78 - 4635.25i) q^{18} +(-1492.28 + 2053.95i) q^{19} +(773.872 - 562.251i) q^{20} +(2626.42 + 2626.42i) q^{21} +(24870.4 + 18069.4i) q^{22} +(18876.1 + 9617.85i) q^{23} +(-737.340 + 4655.38i) q^{24} +(-12540.9 + 9111.52i) q^{25} +(-15346.2 + 2430.61i) q^{26} +(19140.6 + 6219.17i) q^{27} +(2866.38 + 18097.6i) q^{28} +(23267.1 + 23267.1i) q^{29} +(-371.578 + 2346.05i) q^{30} +(20503.5 + 3247.43i) q^{31} +(31265.1 - 31265.1i) q^{32} +(-43239.6 + 6848.47i) q^{33} +(-1753.93 + 5398.05i) q^{34} +(370.232 + 2337.56i) q^{35} +(21481.7 + 29567.0i) q^{36} +(-31409.6 - 4974.80i) q^{37} +(14119.1 - 27710.3i) q^{38} +(13005.8 - 17900.9i) q^{39} +(-2123.65 + 2123.65i) q^{40} +(28107.5 + 38686.6i) q^{41} +(-36810.0 - 26744.0i) q^{42} +(37117.0 - 18912.1i) q^{43} +(-192426. - 98046.1i) q^{44} +(2774.65 + 3818.98i) q^{45} +(-246811. - 80193.9i) q^{46} +130556. q^{47} +38340.9i q^{48} +(68774.8 + 22346.3i) q^{49} +(134272. - 134272. i) q^{50} +(-3669.55 - 7201.90i) q^{51} +(103812. - 33730.5i) q^{52} +(-18127.4 - 35577.0i) q^{53} +(-243499. - 38566.5i) q^{54} +(-24854.5 - 12664.0i) q^{55} +(-17777.5 - 54713.5i) q^{56} +(13686.1 + 42121.3i) q^{57} +(-326094. - 236921. i) q^{58} +(-3793.24 - 23949.6i) q^{59} -16686.9i q^{60} +(209531. + 87275.9i) q^{61} -254294. q^{62} +(-89310.1 + 14145.3i) q^{63} +(-235682. + 324389. i) q^{64} +(13408.7 - 4356.75i) q^{65} +(510030. - 165719. i) q^{66} +(-230354. + 452095. i) q^{67} +(6237.64 - 39382.9i) q^{68} +(329288. - 167780. i) q^{69} +(-8958.85 - 27572.5i) q^{70} +(327937. - 167092. i) q^{71} +(-81137.4 - 81137.4i) q^{72} +(-164195. + 505341. i) q^{73} +389557. q^{74} +270418. i q^{75} +(-67515.0 + 207790. i) q^{76} +(432287. - 314075. i) q^{77} +(-123053. + 241505. i) q^{78} +(249483. + 489639. i) q^{79} +(-14359.6 + 19764.3i) q^{80} +(33567.9 - 24388.5i) q^{81} +(-414206. - 414206. i) q^{82} +(-678519. - 492973. i) q^{83} +(284804. + 145115. i) q^{84} +(805.676 - 5086.84i) q^{85} +(-412836. + 299943. i) q^{86} +(566945. - 89795.3i) q^{87} +(644876. + 209533. i) q^{88} +(-111706. - 705283. i) q^{89} +(-40888.7 - 40888.7i) q^{90} +(-42247.7 + 266741. i) q^{91} +(1.80068e6 + 285200. i) q^{92} +(256069. - 256069. i) q^{93} +(-1.57959e6 + 250183. i) q^{94} +(-8720.48 + 26838.9i) q^{95} +(-120662. - 761829. i) q^{96} +(151346. + 208311. i) q^{97} +(-874925. - 138575. i) q^{98} +(483848. - 949605. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 16 q^{2} - 10 q^{3} - 10 q^{4} - 230 q^{5} + 1384 q^{6} + 248 q^{7} + 632 q^{8} + 13602 q^{9}+O(q^{10}) \) 240 * q - 16 * q^2 - 10 * q^3 - 10 * q^4 - 230 * q^5 + 1384 * q^6 + 248 * q^7 + 632 * q^8 + 13602 * q^9	\( 240 q - 16 q^{2} - 10 q^{3} - 10 q^{4} - 230 q^{5} + 1384 q^{6} + 248 q^{7} + 632 q^{8} + 13602 q^{9} + 1256 q^{10} - 1128 q^{11} - 2922 q^{12} - 2500 q^{13} + 18726 q^{15} + 70002 q^{16} - 4010 q^{17} + 51414 q^{18} - 10 q^{19} - 69254 q^{20} - 47962 q^{21} - 6 q^{22} + 1888 q^{23} - 177422 q^{24} + 228644 q^{25} + 117514 q^{26} - 62410 q^{27} - 60166 q^{28} + 154546 q^{29} - 132584 q^{30} - 17928 q^{31} - 428258 q^{32} + 44454 q^{33} - 167910 q^{34} - 101034 q^{35} + 641510 q^{36} + 116574 q^{37} - 262448 q^{38} - 329300 q^{39} - 524818 q^{40} + 519110 q^{41} - 82532 q^{42} + 745560 q^{43} + 1335810 q^{44} - 120410 q^{45} - 10 q^{46} + 588192 q^{47} + 5710 q^{49} + 97068 q^{50} + 297094 q^{51} - 1682120 q^{52} - 1503774 q^{53} - 1126786 q^{54} + 564038 q^{55} + 1572190 q^{56} + 555510 q^{57} + 937506 q^{58} - 48960 q^{59} + 42668 q^{61} - 2163580 q^{62} + 2141384 q^{63} - 2703370 q^{64} - 836260 q^{65} - 6744010 q^{66} - 1823136 q^{67} - 787264 q^{68} - 810946 q^{69} + 2027862 q^{70} + 4427536 q^{71} + 2755822 q^{72} + 455594 q^{73} + 1925380 q^{74} - 1199542 q^{76} - 3436182 q^{77} + 2415212 q^{78} - 2921256 q^{79} - 5044870 q^{80} - 7581422 q^{81} + 480560 q^{82} + 2764914 q^{83} + 5311480 q^{84} + 7048220 q^{85} - 2426786 q^{86} + 5291070 q^{87} - 3660970 q^{88} - 2695354 q^{89} + 8317796 q^{90} - 681472 q^{91} - 3392292 q^{92} + 4964430 q^{93} + 2757602 q^{94} + 5554934 q^{95} + 14100214 q^{96} + 2233430 q^{97} + 7768418 q^{98} + 7983712 q^{99}+O(q^{100}) \) 240 * q - 16 * q^2 - 10 * q^3 - 10 * q^4 - 230 * q^5 + 1384 * q^6 + 248 * q^7 + 632 * q^8 + 13602 * q^9 + 1256 * q^10 - 1128 * q^11 - 2922 * q^12 - 2500 * q^13 + 18726 * q^15 + 70002 * q^16 - 4010 * q^17 + 51414 * q^18 - 10 * q^19 - 69254 * q^20 - 47962 * q^21 - 6 * q^22 + 1888 * q^23 - 177422 * q^24 + 228644 * q^25 + 117514 * q^26 - 62410 * q^27 - 60166 * q^28 + 154546 * q^29 - 132584 * q^30 - 17928 * q^31 - 428258 * q^32 + 44454 * q^33 - 167910 * q^34 - 101034 * q^35 + 641510 * q^36 + 116574 * q^37 - 262448 * q^38 - 329300 * q^39 - 524818 * q^40 + 519110 * q^41 - 82532 * q^42 + 745560 * q^43 + 1335810 * q^44 - 120410 * q^45 - 10 * q^46 + 588192 * q^47 + 5710 * q^49 + 97068 * q^50 + 297094 * q^51 - 1682120 * q^52 - 1503774 * q^53 - 1126786 * q^54 + 564038 * q^55 + 1572190 * q^56 + 555510 * q^57 + 937506 * q^58 - 48960 * q^59 + 42668 * q^61 - 2163580 * q^62 + 2141384 * q^63 - 2703370 * q^64 - 836260 * q^65 - 6744010 * q^66 - 1823136 * q^67 - 787264 * q^68 - 810946 * q^69 + 2027862 * q^70 + 4427536 * q^71 + 2755822 * q^72 + 455594 * q^73 + 1925380 * q^74 - 1199542 * q^76 - 3436182 * q^77 + 2415212 * q^78 - 2921256 * q^79 - 5044870 * q^80 - 7581422 * q^81 + 480560 * q^82 + 2764914 * q^83 + 5311480 * q^84 + 7048220 * q^85 - 2426786 * q^86 + 5291070 * q^87 - 3660970 * q^88 - 2695354 * q^89 + 8317796 * q^90 - 681472 * q^91 - 3392292 * q^92 + 4964430 * q^93 + 2757602 * q^94 + 5554934 * q^95 + 14100214 * q^96 + 2233430 * q^97 + 7768418 * q^98 + 7983712 * q^99

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