LMFDB - Embedded newform 95.4.e.c.11.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [95,4,Mod(11,95)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(95, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("95.11");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 95 = 5 \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	95.e (of order $3$, degree $2$, 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:	$5.60518145055$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 3 x^{19} + 66 x^{18} - 125 x^{17} + 2555 x^{16} - 3995 x^{15} + 60229 x^{14} + \cdots + 2336368896 $ x^20 - 3x^19 + 66x^18 - 125x^17 + 2555x^16 - 3995x^15 + 60229x^14 - 60298x^13 + 973502x^12 - 718952x^11 + 10405341x^10 - 2780554x^9 + 75565678x^8 - 3086948x^7 + 383106268x^6 + 101986984x^5 + 1262984080x^4 + 373132800x^3 + 2532879168x^2 + 1338713856*x + 2336368896
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			11.6
Root			$-0.575519 - 0.996828i$ of defining polynomial
Character	$\chi$	$=$	95.11
Dual form			95.4.e.c.26.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.575519 - 0.996828i) q^{2} +(-0.184280 + 0.319183i) q^{3} +(3.33756 + 5.78082i) q^{4} +(2.50000 - 4.33013i) q^{5} +(0.212114 + 0.367391i) q^{6} -2.58808 q^{7} +16.8916 q^{8} +(13.4321 + 23.2650i) q^{9} +O(q^{10})$	\(q+(0.575519 - 0.996828i) q^{2} +(-0.184280 + 0.319183i) q^{3} +(3.33756 + 5.78082i) q^{4} +(2.50000 - 4.33013i) q^{5} +(0.212114 + 0.367391i) q^{6} -2.58808 q^{7} +16.8916 q^{8} +(13.4321 + 23.2650i) q^{9} +(-2.87759 - 4.98414i) q^{10} +25.8086 q^{11} -2.46018 q^{12} +(11.0911 + 19.2104i) q^{13} +(-1.48949 + 2.57987i) q^{14} +(0.921402 + 1.59591i) q^{15} +(-16.9790 + 29.4085i) q^{16} +(22.9903 - 39.8204i) q^{17} +30.9217 q^{18} +(82.8087 + 1.31075i) q^{19} +33.3756 q^{20} +(0.476932 - 0.826071i) q^{21} +(14.8533 - 25.7267i) q^{22} +(-49.4507 - 85.6511i) q^{23} +(-3.11279 + 5.39151i) q^{24} +(-12.5000 - 21.6506i) q^{25} +25.5326 q^{26} -19.8522 q^{27} +(-8.63787 - 14.9612i) q^{28} +(2.52693 + 4.37677i) q^{29} +2.12114 q^{30} -239.400 q^{31} +(87.1099 + 150.879i) q^{32} +(-4.75602 + 8.23766i) q^{33} +(-26.4627 - 45.8348i) q^{34} +(-6.47020 + 11.2067i) q^{35} +(-89.6607 + 155.297i) q^{36} -352.236 q^{37} +(48.9646 - 81.7917i) q^{38} -8.17552 q^{39} +(42.2290 - 73.1428i) q^{40} +(-70.6255 + 122.327i) q^{41} +(-0.548967 - 0.950839i) q^{42} +(143.336 - 248.265i) q^{43} +(86.1376 + 149.195i) q^{44} +134.321 q^{45} -113.839 q^{46} +(-4.83575 - 8.37576i) q^{47} +(-6.25779 - 10.8388i) q^{48} -336.302 q^{49} -28.7759 q^{50} +(8.47332 + 14.6762i) q^{51} +(-74.0346 + 128.232i) q^{52} +(-139.106 - 240.939i) q^{53} +(-11.4253 + 19.7892i) q^{54} +(64.5215 - 111.754i) q^{55} -43.7168 q^{56} +(-15.6784 + 26.1896i) q^{57} +5.81718 q^{58} +(198.616 - 344.013i) q^{59} +(-6.15046 + 10.6529i) q^{60} +(-76.2027 - 131.987i) q^{61} +(-137.779 + 238.641i) q^{62} +(-34.7633 - 60.2118i) q^{63} -71.1306 q^{64} +110.911 q^{65} +(5.47435 + 9.48186i) q^{66} +(78.5416 + 136.038i) q^{67} +306.926 q^{68} +36.4511 q^{69} +(7.44745 + 12.8994i) q^{70} +(-204.728 + 354.599i) q^{71} +(226.889 + 392.984i) q^{72} +(566.525 - 981.249i) q^{73} +(-202.719 + 351.119i) q^{74} +9.21402 q^{75} +(268.802 + 483.077i) q^{76} -66.7947 q^{77} +(-4.70516 + 8.14958i) q^{78} +(255.014 - 441.698i) q^{79} +(84.8951 + 147.043i) q^{80} +(-359.008 + 621.820i) q^{81} +(81.2926 + 140.803i) q^{82} +943.890 q^{83} +6.36715 q^{84} +(-114.952 - 199.102i) q^{85} +(-164.985 - 285.762i) q^{86} -1.86265 q^{87} +435.949 q^{88} +(-22.4593 - 38.9007i) q^{89} +(77.3042 - 133.895i) q^{90} +(-28.7048 - 49.7181i) q^{91} +(330.089 - 571.731i) q^{92} +(44.1168 - 76.4125i) q^{93} -11.1323 q^{94} +(212.697 - 355.295i) q^{95} -64.2106 q^{96} +(302.447 - 523.853i) q^{97} +(-193.548 + 335.235i) q^{98} +(346.663 + 600.438i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 3 q^{2} - 5 q^{3} - 43 q^{4} + 50 q^{5} + 9 q^{6} + 6 q^{7} + 96 q^{8} - 97 q^{9}+O(q^{10}) $ 20 * q - 3 * q^2 - 5 * q^3 - 43 * q^4 + 50 * q^5 + 9 * q^6 + 6 * q^7 + 96 * q^8 - 97 * q^9	\( 20 q - 3 q^{2} - 5 q^{3} - 43 q^{4} + 50 q^{5} + 9 q^{6} + 6 q^{7} + 96 q^{8} - 97 q^{9} + 15 q^{10} - 36 q^{11} + 186 q^{12} + 14 q^{13} + 68 q^{14} + 25 q^{15} + 9 q^{16} - 144 q^{17} - 22 q^{18} + 96 q^{19} - 430 q^{20} + 46 q^{21} - 136 q^{22} + 321 q^{23} - 416 q^{24} - 250 q^{25} - 46 q^{26} + 1006 q^{27} + 130 q^{28} - 178 q^{29} + 90 q^{30} + 604 q^{31} - 202 q^{32} + 1099 q^{33} - 751 q^{34} + 15 q^{35} - 526 q^{36} - 774 q^{37} - 12 q^{38} - 1216 q^{39} + 240 q^{40} - 388 q^{41} + 143 q^{42} - 514 q^{43} - 1246 q^{44} - 970 q^{45} + 3650 q^{46} + 522 q^{47} + 4 q^{48} + 1582 q^{49} + 150 q^{50} - 1080 q^{51} + 569 q^{52} - 681 q^{53} - 321 q^{54} - 90 q^{55} - 3184 q^{56} + 514 q^{57} + 1198 q^{58} - 891 q^{59} + 465 q^{60} + 1110 q^{61} - 1921 q^{62} - 727 q^{63} + 952 q^{64} + 140 q^{65} + 3312 q^{66} - 691 q^{67} - 228 q^{68} + 172 q^{69} - 340 q^{70} + 382 q^{71} - 2678 q^{72} - 797 q^{73} + 404 q^{74} + 250 q^{75} + 462 q^{76} + 2390 q^{77} + 1000 q^{78} - 660 q^{79} - 45 q^{80} - 2454 q^{81} - 1155 q^{82} - 2026 q^{83} + 10756 q^{84} + 720 q^{85} + 858 q^{86} + 312 q^{87} - 98 q^{88} - 2957 q^{89} - 55 q^{90} - 3110 q^{91} + 98 q^{92} + 1500 q^{93} - 6374 q^{94} + 945 q^{95} - 584 q^{96} - 2881 q^{97} + 4062 q^{98} + 2723 q^{99}+O(q^{100}) \) 20 * q - 3 * q^2 - 5 * q^3 - 43 * q^4 + 50 * q^5 + 9 * q^6 + 6 * q^7 + 96 * q^8 - 97 * q^9 + 15 * q^10 - 36 * q^11 + 186 * q^12 + 14 * q^13 + 68 * q^14 + 25 * q^15 + 9 * q^16 - 144 * q^17 - 22 * q^18 + 96 * q^19 - 430 * q^20 + 46 * q^21 - 136 * q^22 + 321 * q^23 - 416 * q^24 - 250 * q^25 - 46 * q^26 + 1006 * q^27 + 130 * q^28 - 178 * q^29 + 90 * q^30 + 604 * q^31 - 202 * q^32 + 1099 * q^33 - 751 * q^34 + 15 * q^35 - 526 * q^36 - 774 * q^37 - 12 * q^38 - 1216 * q^39 + 240 * q^40 - 388 * q^41 + 143 * q^42 - 514 * q^43 - 1246 * q^44 - 970 * q^45 + 3650 * q^46 + 522 * q^47 + 4 * q^48 + 1582 * q^49 + 150 * q^50 - 1080 * q^51 + 569 * q^52 - 681 * q^53 - 321 * q^54 - 90 * q^55 - 3184 * q^56 + 514 * q^57 + 1198 * q^58 - 891 * q^59 + 465 * q^60 + 1110 * q^61 - 1921 * q^62 - 727 * q^63 + 952 * q^64 + 140 * q^65 + 3312 * q^66 - 691 * q^67 - 228 * q^68 + 172 * q^69 - 340 * q^70 + 382 * q^71 - 2678 * q^72 - 797 * q^73 + 404 * q^74 + 250 * q^75 + 462 * q^76 + 2390 * q^77 + 1000 * q^78 - 660 * q^79 - 45 * q^80 - 2454 * q^81 - 1155 * q^82 - 2026 * q^83 + 10756 * q^84 + 720 * q^85 + 858 * q^86 + 312 * q^87 - 98 * q^88 - 2957 * q^89 - 55 * q^90 - 3110 * q^91 + 98 * q^92 + 1500 * q^93 - 6374 * q^94 + 945 * q^95 - 584 * q^96 - 2881 * q^97 + 4062 * q^98 + 2723 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/95\mathbb{Z}\right)^\times$.

$n$	$21$	$77$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	0.575519	−	0.996828i	0.203477	−	0.352432i	−0.746170	−	0.665756i	$-0.768109\pi$
$2$	0.575519	−	0.996828i	0.203477	−	0.352432i	0.949646	+	0.313324i	$0.101443\pi$
$3$	−0.184280	+	0.319183i	−0.0354648	+	0.0614268i	−0.883213	−	0.468972i	$-0.844624\pi$
$3$	−0.184280	+	0.319183i	−0.0354648	+	0.0614268i	0.847748	+	0.530399i	$0.177958\pi$
$4$	3.33756	+	5.78082i	0.417195	+	0.722602i
$5$	2.50000	−	4.33013i	0.223607	−	0.387298i
$5$	2.50000	−	4.33013i	0.223607	−	0.387298i
$6$	0.212114	+	0.367391i	0.0144325	+	0.0249978i
$7$	−2.58808			−0.139743			−0.0698716	−	0.997556i	$-0.522259\pi$
$7$	−2.58808			−0.139743			−0.0698716	+	0.997556i	$0.522259\pi$
$8$	16.8916			0.746511
$9$	13.4321	+	23.2650i	0.497485	+	0.861668i
$10$	−2.87759	−	4.98414i	−0.0909975	−	0.157612i
$11$	25.8086			0.707417			0.353708	−	0.935356i	$-0.384921\pi$
$11$	25.8086			0.707417			0.353708	+	0.935356i	$0.384921\pi$
$12$	−2.46018			−0.0591828
$13$	11.0911	+	19.2104i	0.236625	+	0.409847i	0.959744	−	0.280877i	$-0.0906253\pi$
$13$	11.0911	+	19.2104i	0.236625	+	0.409847i	−0.723118	+	0.690724i	$0.757292\pi$
$14$	−1.48949	+	2.57987i	−0.0284345	+	0.0492500i
$15$	0.921402	+	1.59591i	0.0158603	+	0.0274709i
$16$	−16.9790	+	29.4085i	−0.265297	+	0.459508i
$17$	22.9903	−	39.8204i	0.327998	−	0.568109i	−0.654116	−	0.756394i	$-0.726959\pi$
$17$	22.9903	−	39.8204i	0.327998	−	0.568109i	0.982115	+	0.188284i	$0.0602927\pi$
$18$	30.9217			0.404906
$19$	82.8087	+	1.31075i	0.999875	+	0.0158266i
$19$	82.8087	+	1.31075i	0.999875	+	0.0158266i
$20$	33.3756			0.373150
$21$	0.476932	−	0.826071i	0.00495596	−	0.00858398i
$22$	14.8533	−	25.7267i	0.143943	−	0.249316i
$23$	−49.4507	−	85.6511i	−0.448312	−	0.776499i	0.549964	−	0.835188i	$-0.314641\pi$
$23$	−49.4507	−	85.6511i	−0.448312	−	0.776499i	−0.998276	+	0.0586889i	$0.981308\pi$
$24$	−3.11279	+	5.39151i	−0.0264748	+	0.0458557i
$25$	−12.5000	−	21.6506i	−0.100000	−	0.173205i
$26$	25.5326			0.192591
$27$	−19.8522			−0.141502
$28$	−8.63787	−	14.9612i	−0.0583001	−	0.100979i
$29$	2.52693	+	4.37677i	0.0161806	+	0.0280257i	0.874002	−	0.485922i	$-0.161516\pi$
$29$	2.52693	+	4.37677i	0.0161806	+	0.0280257i	−0.857822	+	0.513947i	$0.828183\pi$
$30$	2.12114			0.0129088
$31$	−239.400			−1.38702			−0.693509	−	0.720448i	$-0.743936\pi$
$31$	−239.400			−1.38702			−0.693509	+	0.720448i	$0.743936\pi$
$32$	87.1099	+	150.879i	0.481219	+	0.833495i
$33$	−4.75602	+	8.23766i	−0.0250884	+	0.0434543i
$34$	−26.4627	−	45.8348i	−0.133480	−	0.231194i
$35$	−6.47020	+	11.2067i	−0.0312475	+	0.0541223i
$36$	−89.6607	+	155.297i	−0.415096	+	0.718967i
$37$	−352.236			−1.56506			−0.782531	−	0.622611i	$-0.786072\pi$
$37$	−352.236			−1.56506			−0.782531	+	0.622611i	$0.786072\pi$
$38$	48.9646	−	81.7917i	0.209029	−	0.349167i
$39$	−8.17552			−0.0335674
$40$	42.2290	−	73.1428i	0.166925	−	0.289122i
$41$	−70.6255	+	122.327i	−0.269021	+	0.465958i	−0.968609	−	0.248588i	$-0.920033\pi$
$41$	−70.6255	+	122.327i	−0.269021	+	0.465958i	0.699588	+	0.714546i	$0.253367\pi$
$42$	−0.548967	−	0.950839i	−0.00201684	−	0.00349328i
$43$	143.336	−	248.265i	0.508337	−	0.880465i	−0.491616	−	0.870812i	$-0.663594\pi$
$43$	143.336	−	248.265i	0.508337	−	0.880465i	0.999953	−	0.00965358i	$-0.00307288\pi$
$44$	86.1376	+	149.195i	0.295130	+	0.511181i
$45$	134.321			0.444964
$46$	−113.839			−0.364884
$47$	−4.83575	−	8.37576i	−0.0150078	−	0.0259943i	0.858424	−	0.512941i	$-0.171444\pi$
$47$	−4.83575	−	8.37576i	−0.0150078	−	0.0259943i	−0.873432	+	0.486947i	$0.838111\pi$
$48$	−6.25779	−	10.8388i	−0.0188174	−	0.0325927i
$49$	−336.302			−0.980472
$50$	−28.7759			−0.0813907
$51$	8.47332	+	14.6762i	0.0232648	+	0.0402957i
$52$	−74.0346	+	128.232i	−0.197438	+	0.341972i
$53$	−139.106	−	240.939i	−0.360522	−	0.624442i	0.627525	−	0.778597i	$-0.284068\pi$
$53$	−139.106	−	240.939i	−0.360522	−	0.624442i	−0.988047	+	0.154154i	$0.950735\pi$
$54$	−11.4253	+	19.7892i	−0.0287924	+	0.0498699i
$55$	64.5215	−	111.754i	0.158183	−	0.273981i
$56$	−43.7168			−0.104320
$57$	−15.6784	+	26.1896i	−0.0364325	+	0.0608578i
$58$	5.81718			0.0131695
$59$	198.616	−	344.013i	0.438265	−	0.759097i	−0.559291	−	0.828971i	$-0.688927\pi$
$59$	198.616	−	344.013i	0.438265	−	0.759097i	0.997556	+	0.0698746i	$0.0222599\pi$
$60$	−6.15046	+	10.6529i	−0.0132337	+	0.0229214i
$61$	−76.2027	−	131.987i	−0.159947	−	0.277036i	0.774902	−	0.632081i	$-0.217799\pi$
$61$	−76.2027	−	131.987i	−0.159947	−	0.277036i	−0.934849	+	0.355045i	$0.884466\pi$
$62$	−137.779	+	238.641i	−0.282226	+	0.488830i
$63$	−34.7633	−	60.2118i	−0.0695201	−	0.120412i
$64$	−71.1306			−0.138927
$65$	110.911			0.211644
$66$	5.47435	+	9.48186i	0.0102098	+	0.0176839i
$67$	78.5416	+	136.038i	0.143215	+	0.248055i	0.928705	−	0.370818i	$-0.120923\pi$
$67$	78.5416	+	136.038i	0.143215	+	0.248055i	−0.785491	+	0.618873i	$0.787589\pi$
$68$	306.926			0.547356
$69$	36.4511			0.0635971
$70$	7.44745	+	12.8994i	0.0127163	+	0.0220253i
$71$	−204.728	+	354.599i	−0.342207	+	0.592720i	−0.984842	−	0.173452i	$-0.944508\pi$
$71$	−204.728	+	354.599i	−0.342207	+	0.592720i	0.642635	+	0.766172i	$0.277841\pi$
$72$	226.889	+	392.984i	0.371377	+	0.643245i
$73$	566.525	−	981.249i	0.908311	−	1.57324i	0.0919001	−	0.995768i	$-0.470706\pi$
$73$	566.525	−	981.249i	0.908311	−	1.57324i	0.816411	−	0.577472i	$-0.195961\pi$
$74$	−202.719	+	351.119i	−0.318454	+	0.551578i
$75$	9.21402			0.0141859
$76$	268.802	+	483.077i	0.405706	+	0.729114i
$77$	−66.7947			−0.0988567
$78$	−4.70516	+	8.14958i	−0.00683019	+	0.0118302i
$79$	255.014	−	441.698i	0.363182	−	0.629049i	−0.625301	−	0.780384i	$-0.715024\pi$
$79$	255.014	−	441.698i	0.363182	−	0.629049i	0.988483	+	0.151335i	$0.0483571\pi$
$80$	84.8951	+	147.043i	0.118644	+	0.205498i
$81$	−359.008	+	621.820i	−0.492466	+	0.852976i
$82$	81.2926	+	140.803i	0.109479	+	0.189623i
$83$	943.890			1.24826			0.624129	−	0.781321i	$-0.285454\pi$
$83$	943.890			1.24826			0.624129	+	0.781321i	$0.285454\pi$
$84$	6.36715			0.00827040
$85$	−114.952	−	199.102i	−0.146685	−	0.254066i
$86$	−164.985	−	285.762i	−0.206869	−	0.358308i
$87$	−1.86265			−0.00229537
$88$	435.949			0.528094
$89$	−22.4593	−	38.9007i	−0.0267493	−	0.0463311i	0.852341	−	0.522987i	$-0.175182\pi$
$89$	−22.4593	−	38.9007i	−0.0267493	−	0.0463311i	−0.879090	+	0.476656i	$0.841849\pi$
$90$	77.3042	−	133.895i	0.0905397	−	0.156819i
$91$	−28.7048	−	49.7181i	−0.0330668	−	0.0572734i
$92$	330.089	−	571.731i	0.374067	−	0.647902i
$93$	44.1168	−	76.4125i	0.0491903	−	0.0852001i
$94$	−11.1323			−0.0122149
$95$	212.697	−	355.295i	0.229708	−	0.383711i
$96$	−64.2106			−0.0682652
$97$	302.447	−	523.853i	0.316586	−	0.548342i	−0.663188	−	0.748453i	$-0.730797\pi$
$97$	302.447	−	523.853i	0.316586	−	0.548342i	0.979773	+	0.200111i	$0.0641302\pi$
$98$	−193.548	+	335.235i	−0.199503	+	0.345550i
$99$	346.663	+	600.438i	0.351929	+	0.609559i
$100$	83.4389	−	144.520i	0.0834389	−	0.144520i
$101$	627.023	+	1086.04i	0.617734	+	1.06995i	0.989898	+	0.141779i	$0.0452823\pi$
$101$	627.023	+	1086.04i	0.617734	+	1.06995i	−0.372165	+	0.928167i	$0.621384\pi$
$102$	19.5062			0.0189353
$103$	1031.27			0.986542			0.493271	−	0.869876i	$-0.335801\pi$
$103$	1031.27			0.986542			0.493271	+	0.869876i	$0.335801\pi$
$104$	187.347	+	324.495i	0.176643	+	0.305955i
$105$	−2.38466	−	4.13036i	−0.00221637	−	0.00383887i
$106$	−320.232			−0.293431
$107$	−1294.29			−1.16938			−0.584688	−	0.811258i	$-0.698783\pi$
$107$	−1294.29			−1.16938			−0.584688	+	0.811258i	$0.698783\pi$
$108$	−66.2579	−	114.762i	−0.0590339	−	0.102250i
$109$	−722.620	+	1251.61i	−0.634995	+	1.09984i	0.351521	+	0.936180i	$0.385664\pi$
$109$	−722.620	+	1251.61i	−0.634995	+	1.09984i	−0.986516	+	0.163664i	$0.947669\pi$
$110$	−74.2667	−	128.634i	−0.0643732	−	0.111498i
$111$	64.9102	−	112.428i	0.0555046	−	0.0961367i
$112$	43.9431	−	76.1116i	0.0370735	−	0.0642131i
$113$	−407.535			−0.339272			−0.169636	−	0.985507i	$-0.554259\pi$
$113$	−407.535			−0.339272			−0.169636	+	0.985507i	$0.554259\pi$
$114$	17.0833	+	30.7012i	0.0140351	+	0.0252231i
$115$	−494.507			−0.400983
$116$	−16.8675	+	29.2154i	−0.0135010	+	0.0233843i
$117$	−297.954	+	516.072i	−0.235435	+	0.407785i
$118$	−228.615	−	395.972i	−0.178353	−	0.308917i
$119$	−59.5008	+	103.058i	−0.0458355	+	0.0793895i
$120$	15.5640	+	26.9576i	0.0118399	+	0.0205073i
$121$	−664.917			−0.499562
$122$	−175.424			−0.130182
$123$	−26.0298	−	45.0849i	−0.0190815	−	0.0330502i
$124$	−799.012	−	1383.93i	−0.578657	−	1.00226i
$125$	−125.000			−0.0894427
$126$	−80.0278			−0.0565829
$127$	−813.325	−	1408.72i	−0.568275	−	0.984282i	−0.996737	−	0.0807216i	$-0.974278\pi$
$127$	−813.325	−	1408.72i	−0.568275	−	0.984282i	0.428461	−	0.903560i	$-0.359056\pi$
$128$	−737.816	+	1277.94i	−0.509487	+	0.882458i
$129$	52.8279	+	91.5006i	0.0360561	+	0.0624510i
$130$	63.8316	−	110.560i	0.0430646	−	0.0745901i
$131$	601.176	−	1041.27i	0.400954	−	0.694473i	−0.592887	−	0.805285i	$-0.702012\pi$
$131$	601.176	−	1041.27i	0.400954	−	0.694473i	0.993841	+	0.110813i	$0.0353454\pi$
$132$	−63.4939			−0.0418669
$133$	−214.316	−	3.39232i	−0.139726	−	0.00221166i
$134$	180.809			0.116563
$135$	−49.6305	+	85.9626i	−0.0316409	+	0.0548036i
$136$	388.343	−	672.630i	0.244854	−	0.424100i
$137$	330.071	+	571.699i	0.205838	+	0.356522i	0.950400	−	0.311032i	$-0.100675\pi$
$137$	330.071	+	571.699i	0.205838	+	0.356522i	−0.744561	+	0.667554i	$0.767341\pi$
$138$	20.9783	−	36.3355i	0.0129405	−	0.0224137i
$139$	−710.930	−	1231.37i	−0.433815	−	0.751390i	0.563383	−	0.826196i	$-0.309500\pi$
$139$	−710.930	−	1231.37i	−0.433815	−	0.751390i	−0.997198	+	0.0748058i	$0.976166\pi$
$140$	−86.3787			−0.0521452
$141$	3.56453			0.00212899
$142$	235.649	+	408.156i	0.139262	+	0.241209i
$143$	286.247	+	495.794i	0.167393	+	0.289933i
$144$	−912.254			−0.527925
$145$	25.2693			0.0144724
$146$	−652.091	−	1129.45i	−0.369640	−	0.640235i
$147$	61.9738	−	107.342i	0.0347722	−	0.0602272i
$148$	−1175.61	−	2036.21i	−0.652935	−	1.13092i
$149$	−180.283	+	312.259i	−0.0991232	+	0.171686i	−0.911322	−	0.411694i	$-0.864937\pi$
$149$	−180.283	+	312.259i	−0.0991232	+	0.171686i	0.812199	+	0.583381i	$0.198270\pi$
$150$	5.30284	−	9.18479i	0.00288650	−	0.00499956i
$151$	−1232.33			−0.664143			−0.332072	−	0.943254i	$-0.607748\pi$
$151$	−1232.33			−0.664143			−0.332072	+	0.943254i	$0.607748\pi$
$152$	1398.77	+	22.1406i	0.746417	+	0.0118147i
$153$	1235.23			0.652696
$154$	−38.4416	+	66.5828i	−0.0201150	+	0.0348402i
$155$	−598.501	+	1036.63i	−0.310147	+	0.537190i
$156$	−27.2862	−	47.2612i	−0.0140042	−	0.0242559i
$157$	−948.462	+	1642.78i	−0.482137	+	0.835085i	−0.999790	−	0.0205053i	$-0.993473\pi$
$157$	−948.462	+	1642.78i	−0.482137	+	0.835085i	0.517653	+	0.855591i	$0.326806\pi$
$158$	−293.531	−	508.411i	−0.147798	−	0.255994i
$159$	102.538			0.0511433
$160$	871.099			0.430415
$161$	127.982	+	221.672i	0.0626486	+	0.108511i
$162$	413.232	+	715.738i	0.200411	+	0.347122i
$163$	−1294.60			−0.622090			−0.311045	−	0.950395i	$-0.600679\pi$
$163$	−1294.60			−0.622090			−0.311045	+	0.950395i	$0.600679\pi$
$164$	−942.867			−0.448936
$165$	23.7801	+	41.1883i	0.0112199	+	0.0194334i
$166$	543.226	−	940.896i	0.253991	−	0.439926i
$167$	−298.795	−	517.528i	−0.138452	−	0.239805i	0.788459	−	0.615087i	$-0.210879\pi$
$167$	−298.795	−	517.528i	−0.138452	−	0.239805i	−0.926911	+	0.375282i	$0.877546\pi$
$168$	8.05615	−	13.9537i	0.00369968	−	0.00640803i
$169$	852.473	−	1476.53i	0.388017	−	0.672065i
$170$	−264.627			−0.119388
$171$	1081.80	+	1944.15i	0.483785	+	0.869434i
$172$	1913.56			0.848302
$173$	−1834.67	+	3177.74i	−0.806284	+	1.39652i	0.109137	+	0.994027i	$0.465191\pi$
$173$	−1834.67	+	3177.74i	−0.806284	+	1.39652i	−0.915421	+	0.402498i	$0.868142\pi$
$174$	−1.07199	+	1.85674i	−0.000467054	+	0.000808962i
$175$	32.3510	+	56.0336i	0.0139743	+	0.0242042i
$176$	−438.204	+	758.992i	−0.187676	+	0.325064i
$177$	73.2021	+	126.790i	0.0310859	+	0.0538424i
$178$	−51.7031			−0.0217714
$179$	4658.93			1.94539			0.972694	−	0.232091i	$-0.0745566\pi$
$179$	4658.93			1.94539			0.972694	+	0.232091i	$0.0745566\pi$
$180$	448.303	+	776.484i	0.185636	+	0.321532i
$181$	36.6402	+	63.4628i	0.0150467	+	0.0260616i	0.873451	−	0.486913i	$-0.161877\pi$
$181$	36.6402	+	63.4628i	0.0150467	+	0.0260616i	−0.858404	+	0.512974i	$0.828544\pi$
$182$	−66.0806			−0.0269133
$183$	56.1707			0.0226899
$184$	−835.301	−	1446.78i	−0.334670	−	0.579665i
$185$	−880.591	+	1525.23i	−0.349959	+	0.606146i
$186$	−50.7801	−	87.9537i	−0.0200181	−	0.0346724i
$187$	593.347	−	1027.71i	0.232031	−	0.401890i
$188$	32.2792	−	55.9091i	0.0125223	−	0.0216893i
$189$	51.3791			0.0197740
$190$	−231.757	−	416.502i	−0.0884916	−	0.159033i
$191$	4596.51			1.74132			0.870660	−	0.491885i	$-0.163692\pi$
$191$	4596.51			1.74132			0.870660	+	0.491885i	$0.163692\pi$
$192$	13.1080	−	22.7037i	0.00492701	−	0.00853384i
$193$	−1681.09	+	2911.74i	−0.626984	+	1.08597i	0.361170	+	0.932500i	$0.382377\pi$
$193$	−1681.09	+	2911.74i	−0.626984	+	1.08597i	−0.988154	+	0.153468i	$0.950956\pi$
$194$	−348.127	−	602.974i	−0.128836	−	0.223150i
$195$	−20.4388	+	35.4010i	−0.00750591	+	0.0130006i
$196$	−1122.43	−	1944.10i	−0.409047	−	0.708491i
$197$	−413.750			−0.149637			−0.0748184	−	0.997197i	$-0.523838\pi$
$197$	−413.750			−0.149637			−0.0748184	+	0.997197i	$0.523838\pi$
$198$	798.045			0.286437
$199$	1791.27	+	3102.58i	0.638091	+	1.10521i	0.985851	+	0.167623i	$0.0536090\pi$
$199$	1791.27	+	3102.58i	0.638091	+	1.10521i	−0.347760	+	0.937584i	$0.613058\pi$
$200$	−211.145	−	365.714i	−0.0746511	−	0.129299i
$201$	−57.8947			−0.0203163
$202$	1443.45			0.502777
$203$	−6.53989	−	11.3274i	−0.00226114	−	0.00391640i
$204$	−56.5604	+	97.9654i	−0.0194119	+	0.0336223i
$205$	353.128	+	611.635i	0.120310	+	0.208383i
$206$	593.514	−	1028.00i	0.200738	−	0.347689i
$207$	1328.45	−	2300.94i	0.446057	−	0.772593i
$208$	−753.267			−0.251104
$209$	2137.18	+	33.8285i	0.707328	+	0.0111960i
$210$	−5.48967			−0.00180392
$211$	2699.91	−	4676.39i	0.880899	−	1.52576i	0.0305553	−	0.999533i	$-0.490272\pi$
$211$	2699.91	−	4676.39i	0.880899	−	1.52576i	0.850343	−	0.526228i	$-0.176394\pi$
$212$	928.548	−	1608.29i	0.300816	−	0.521028i
$213$	−75.4545	−	130.691i	−0.0242726	−	0.0420413i
$214$	−744.886	+	1290.18i	−0.237941	+	0.412126i
$215$	−716.678	−	1241.32i	−0.227335	−	0.393756i
$216$	−335.336			−0.105633
$217$	619.588			0.193826
$218$	831.763	+	1440.66i	0.258413	+	0.447585i
$219$	208.799	+	361.650i	0.0644260	+	0.111589i
$220$	861.376			0.263973
$221$	1019.96			0.310451
$222$	−74.7141	−	129.409i	−0.0225878	−	0.0391231i
$223$	−882.469	+	1528.48i	−0.264998	+	0.458989i	−0.967563	−	0.252630i	$-0.918705\pi$
$223$	−882.469	+	1528.48i	−0.264998	+	0.458989i	0.702565	+	0.711619i	$0.252038\pi$
$224$	−225.447	−	390.487i	−0.0672471	−	0.116475i
$225$	335.802	−	581.626i	0.0994969	−	0.172334i
$226$	−234.544	+	406.243i	−0.0690338	+	0.119570i
$227$	−3359.57			−0.982303			−0.491151	−	0.871074i	$-0.663424\pi$
$227$	−3359.57			−0.982303			−0.491151	+	0.871074i	$0.663424\pi$
$228$	−203.725	−	3.22468i	−0.0591754	−	0.000936664i
$229$	−124.494			−0.0359249			−0.0179624	−	0.999839i	$-0.505718\pi$
$229$	−124.494			−0.0359249			−0.0179624	+	0.999839i	$0.505718\pi$
$230$	−284.598	+	492.938i	−0.0815906	+	0.141319i
$231$	12.3090	−	21.3197i	0.00350593	−	0.00607245i
$232$	42.6839	+	73.9306i	0.0120790	+	0.0209215i
$233$	−3181.79	+	5511.01i	−0.894617	+	1.54952i	−0.0603387	+	0.998178i	$0.519218\pi$
$233$	−3181.79	+	5511.01i	−0.894617	+	1.54952i	−0.834278	+	0.551344i	$0.814115\pi$
$234$	342.957	+	594.018i	0.0958110	+	0.165950i
$235$	−48.3575			−0.0134234
$236$	2651.57			0.731367
$237$	93.9882	+	162.792i	0.0257603	+	0.0446182i
$238$	68.4876	+	118.624i	0.0186529	+	0.0323078i
$239$	258.817			0.0700479			0.0350240	−	0.999386i	$-0.488849\pi$
$239$	258.817			0.0700479			0.0350240	+	0.999386i	$0.488849\pi$
$240$	−62.5779			−0.0168308
$241$	−1832.67	−	3174.28i	−0.489845	−	0.848436i	0.510087	−	0.860123i	$-0.329613\pi$
$241$	−1832.67	−	3174.28i	−0.489845	−	0.848436i	−0.999932	+	0.0116868i	$0.996280\pi$
$242$	−382.672	+	662.807i	−0.101649	+	0.176061i
$243$	−400.321	−	693.376i	−0.105681	−	0.183046i
$244$	508.662	−	881.028i	0.133458	−	0.231156i
$245$	−840.755	+	1456.23i	−0.219240	+	0.379735i
$246$	−59.9225			−0.0155306
$247$	893.263	+	1605.33i	0.230109	+	0.413541i
$248$	−4043.86			−1.03542
$249$	−173.940	+	301.274i	−0.0442692	+	0.0766764i
$250$	−71.9399	+	124.603i	−0.0181995	+	0.0315225i
$251$	−486.649	−	842.901i	−0.122379	−	0.211966i	0.798327	−	0.602225i	$-0.205719\pi$
$251$	−486.649	−	842.901i	−0.122379	−	0.211966i	−0.920705	+	0.390259i	$0.872386\pi$
$252$	232.049	−	401.921i	0.0580068	−	0.100471i
$253$	−1276.25	−	2210.53i	−0.317143	−	0.549309i
$254$	−1872.34			−0.462523
$255$	84.7332			0.0208086
$256$	564.732	+	978.144i	0.137874	+	0.238805i
$257$	−2817.77	−	4880.53i	−0.683922	−	1.18459i	−0.973774	−	0.227516i	$-0.926940\pi$
$257$	−2817.77	−	4880.53i	−0.683922	−	1.18459i	0.289853	−	0.957071i	$-0.406394\pi$
$258$	121.614			0.0293463
$259$	911.616			0.218707
$260$	370.173	+	641.159i	0.0882968	+	0.152935i
$261$	−67.8838	+	117.578i	−0.0160992	+	0.0278847i
$262$	−691.976	−	1198.54i	−0.163170	−	0.282618i
$263$	2323.30	−	4024.07i	0.544718	−	0.943479i	−0.453907	−	0.891049i	$-0.649970\pi$
$263$	2323.30	−	4024.07i	0.544718	−	0.943479i	0.998625	−	0.0524301i	$-0.0166967\pi$
$264$	−80.3367	+	139.147i	−0.0187287	+	0.0324391i
$265$	−1391.06			−0.322461
$266$	−126.724	+	211.683i	−0.0292104	+	0.0487938i
$267$	16.5553			0.00379463
$268$	−524.274	+	908.069i	−0.119497	+	0.206974i
$269$	−884.075	+	1531.26i	−0.200383	+	0.347073i	−0.948652	−	0.316322i	$-0.897552\pi$
$269$	−884.075	+	1531.26i	−0.200383	+	0.347073i	0.748269	+	0.663396i	$0.230885\pi$
$270$	57.1266	+	98.9462i	0.0128763	+	0.0223025i
$271$	−2245.70	+	3889.67i	−0.503383	+	0.871885i	0.496609	+	0.867974i	$0.334578\pi$
$271$	−2245.70	+	3889.67i	−0.503383	+	0.871885i	−0.999992	+	0.00391063i	$0.998755\pi$
$272$	780.705	+	1352.22i	0.174034	+	0.301436i
$273$	21.1589			0.00469082
$274$	759.848			0.167533
$275$	−322.607	−	558.772i	−0.0707417	−	0.122528i
$276$	121.658	+	210.717i	0.0265324	+	0.0459554i
$277$	−3462.25			−0.750999			−0.375499	−	0.926823i	$-0.622529\pi$
$277$	−3462.25			−0.750999			−0.375499	+	0.926823i	$0.622529\pi$
$278$	−1636.62			−0.353085
$279$	−3215.65	−	5569.66i	−0.690020	−	1.19515i
$280$	−109.292	+	189.299i	−0.0233266	+	0.0404029i
$281$	−981.589	−	1700.16i	−0.208387	−	0.360937i	0.742820	−	0.669492i	$-0.233488\pi$
$281$	−981.589	−	1700.16i	−0.208387	−	0.360937i	−0.951207	+	0.308555i	$0.900155\pi$
$282$	2.05145	−	3.55322i	0.000433200	−	0.000750324i
$283$	−46.2075	+	80.0338i	−0.00970584	+	0.0168110i	−0.870838	−	0.491571i	$-0.836423\pi$
$283$	−46.2075	+	80.0338i	−0.00970584	+	0.0168110i	0.861132	+	0.508382i	$0.169756\pi$
$284$	−2733.16			−0.571067
$285$	74.2082	+	133.363i	0.0154236	+	0.0277185i
$286$	658.962			0.136242
$287$	182.785	−	316.592i	0.0375938	−	0.0651144i
$288$	−2340.13	+	4053.23i	−0.478798	+	0.829302i
$289$	1399.39	+	2423.82i	0.284834	+	0.493348i
$290$	14.5429	−	25.1891i	0.00294480	−	0.00510054i
$291$	111.470	+	193.072i	0.0224553	+	0.0388937i
$292$	7563.23			1.51577
$293$	5135.22			1.02390			0.511950	−	0.859015i	$-0.328923\pi$
$293$	5135.22			1.02390			0.511950	+	0.859015i	$0.328923\pi$
$294$	−71.3342	−	123.554i	−0.0141507	−	0.0245097i
$295$	−993.081	−	1720.07i	−0.195998	−	0.339478i
$296$	−5949.84			−1.16834
$297$	−512.358			−0.100101
$298$	207.512	+	359.422i	0.0403385	+	0.0698683i
$299$	1096.93	−	1899.94i	0.212164	−	0.367479i
$300$	30.7523	+	53.2645i	0.00591828	+	0.0102508i
$301$	−370.964	+	642.529i	−0.0710367	+	0.123039i
$302$	−709.230	+	1228.42i	−0.135138	+	0.234065i
$303$	−462.192			−0.0876311
$304$	−1444.56	+	2413.03i	−0.272536	+	0.455252i
$305$	−762.027			−0.143061
$306$	710.899	−	1231.31i	0.132808	−	0.230031i
$307$	237.795	−	411.874i	0.0442075	−	0.0765696i	−0.843075	−	0.537796i	$-0.819257\pi$
$307$	237.795	−	411.874i	0.0442075	−	0.0765696i	0.887283	+	0.461226i	$0.152590\pi$
$308$	−222.931	−	386.128i	−0.0412425	−	0.0714341i
$309$	−190.042	+	329.163i	−0.0349875	+	0.0606001i
$310$	688.897	+	1193.20i	0.126215	+	0.218611i
$311$	4440.53			0.809645			0.404822	−	0.914395i	$-0.367333\pi$
$311$	4440.53			0.809645			0.404822	+	0.914395i	$0.367333\pi$
$312$	−138.098			−0.0250585
$313$	2981.16	+	5163.53i	0.538356	+	0.932460i	0.998993	+	0.0448711i	$0.0142877\pi$
$313$	2981.16	+	5163.53i	0.538356	+	0.932460i	−0.460637	+	0.887589i	$0.652379\pi$
$314$	1091.71	+	1890.91i	0.196207	+	0.339841i
$315$	−347.633			−0.0621807
$316$	3404.50			0.606070
$317$	−4195.06	−	7266.05i	−0.743274	−	1.28739i	−0.950997	−	0.309201i	$-0.899938\pi$
$317$	−4195.06	−	7266.05i	−0.743274	−	1.28739i	0.207722	−	0.978188i	$-0.433395\pi$
$318$	59.0125	−	102.213i	0.0104065	−	0.0180245i
$319$	65.2164	+	112.958i	0.0114465	+	0.0198258i
$320$	−177.827	+	308.005i	−0.0310650	+	0.0538062i
$321$	238.511	−	413.114i	0.0414717	−	0.0718310i
$322$	294.625			0.0509901
$323$	1955.99	−	3267.34i	0.336948	−	0.562847i
$324$	−4792.84			−0.821817
$325$	277.279	−	480.261i	0.0473251	−	0.0819694i
$326$	−745.065	+	1290.49i	−0.126581	+	0.219244i
$327$	−266.329	−	461.296i	−0.0450399	−	0.0780114i
$328$	−1192.98	+	2066.30i	−0.200827	+	0.347842i
$329$	12.5153	+	21.6771i	0.00209724	+	0.00363252i
$330$	54.7435			0.00913191
$331$	−1839.59			−0.305477			−0.152739	−	0.988267i	$-0.548809\pi$
$331$	−1839.59			−0.305477			−0.152739	+	0.988267i	$0.548809\pi$
$332$	3150.29	+	5456.46i	0.520766	+	0.901994i
$333$	−4731.27	−	8194.80i	−0.778594	−	1.34856i
$334$	−687.848			−0.112687
$335$	785.416			0.128095
$336$	16.1957	+	28.0517i	0.00262960	+	0.00455461i
$337$	−4543.75	+	7870.00i	−0.734462	+	1.27213i	0.220497	+	0.975388i	$0.429232\pi$
$337$	−4543.75	+	7870.00i	−0.734462	+	1.27213i	−0.954959	+	0.296738i	$0.904101\pi$
$338$	−981.229	−	1699.54i	−0.157905	−	0.273499i
$339$	75.1007	−	130.078i	0.0120322	−	0.0208404i
$340$	767.314	−	1329.03i	0.122393	−	0.211990i
$341$	−6178.59			−0.981200
$342$	2560.58	+	40.5305i	0.404855	+	0.00640829i
$343$	1758.09			0.276758
$344$	2421.17	−	4193.59i	0.379479	−	0.657277i
$345$	91.1278	−	157.838i	0.0142207	−	0.0246311i
$346$	2111.77	+	3657.69i	0.328120	+	0.568320i
$347$	−897.204	+	1554.00i	−0.138802	+	0.240413i	−0.927044	−	0.374954i	$-0.877659\pi$
$347$	−897.204	+	1554.00i	−0.138802	+	0.240413i	0.788241	+	0.615366i	$0.210992\pi$
$348$	−6.21671	−	10.7676i	−0.000957616	−	0.00165864i
$349$	4962.78			0.761179			0.380590	−	0.924744i	$-0.375721\pi$
$349$	4962.78			0.761179			0.380590	+	0.924744i	$0.375721\pi$
$350$	74.4745			0.0113738
$351$	−220.184	−	381.369i	−0.0334830	−	0.0579943i
$352$	2248.18	+	3893.97i	0.340422	+	0.589629i
$353$	12867.5			1.94013			0.970067	−	0.242837i	$-0.0780780\pi$
$353$	12867.5			1.94013			0.970067	+	0.242837i	$0.0780780\pi$
$354$	168.517			0.0253010
$355$	1023.64	+	1772.99i	0.153040	+	0.265072i
$356$	149.919	−	259.667i	0.0223193	−	0.0386582i
$357$	−21.9296	−	37.9833i	−0.00325109	−	0.00563106i
$358$	2681.30	−	4644.15i	0.395841	−	0.685617i
$359$	2890.84	−	5007.08i	0.424994	−	0.736111i	−0.571426	−	0.820654i	$-0.693610\pi$
$359$	2890.84	−	5007.08i	0.424994	−	0.736111i	0.996420	+	0.0845427i	$0.0269429\pi$
$360$	2268.89			0.332170
$361$	6855.56	+	217.082i	0.999499	+	0.0316493i
$362$	84.3486			0.0122466
$363$	122.531	−	212.230i	0.0177168	−	0.0306865i
$364$	191.608	−	331.874i	0.0275906	−	0.0477883i
$365$	−2832.62	−	4906.25i	−0.406209	−	0.703574i
$366$	32.3273	−	55.9925i	0.00461687	−	0.00799665i
$367$	3096.84	+	5363.89i	0.440474	+	0.762923i	0.997725	−	0.0674214i	$-0.0214772\pi$
$367$	3096.84	+	5363.89i	0.440474	+	0.762923i	−0.557251	+	0.830344i	$0.688144\pi$
$368$	3358.49			0.475743
$369$	−3794.59			−0.535335
$370$	1013.59	+	1755.60i	0.142417	+	0.246673i
$371$	360.017	+	623.568i	0.0503805	+	0.0872616i
$372$	588.969			0.0820877
$373$	−422.558			−0.0586574			−0.0293287	−	0.999570i	$-0.509337\pi$
$373$	−422.558			−0.0586574			−0.0293287	+	0.999570i	$0.509337\pi$
$374$	−682.965	−	1182.93i	−0.0944259	−	0.163550i
$375$	23.0350	−	39.8979i	0.00317206	−	0.00549418i
$376$	−81.6835	−	141.480i	−0.0112035	−	0.0194050i
$377$	−56.0530	+	97.0867i	−0.00765750	+	0.0132632i
$378$	29.5697	−	51.2161i	0.00402354	−	0.00696898i
$379$	−8681.99			−1.17669			−0.588343	−	0.808611i	$-0.700220\pi$
$379$	−8681.99			−1.17669			−0.588343	+	0.808611i	$0.700220\pi$
$380$	2763.79	+	43.7469i	0.373103	+	0.00590571i
$381$	599.519			0.0806150
$382$	2645.38	−	4581.93i	0.354318	−	0.613697i
$383$	5189.90	−	8989.17i	0.692406	−	1.19928i	−0.278641	−	0.960395i	$-0.589884\pi$
$383$	5189.90	−	8989.17i	0.692406	−	1.19928i	0.971047	−	0.238887i	$-0.0767827\pi$
$384$	−271.930	−	470.997i	−0.0361377	−	0.0625923i
$385$	−166.987	+	289.230i	−0.0221050	+	0.0382870i
$386$	1935.00	+	3351.52i	0.255153	+	0.441938i
$387$	7701.19			1.01156
$388$	4037.73			0.528311
$389$	2069.41	+	3584.32i	0.269726	+	0.467179i	0.968791	−	0.247879i	$-0.0797336\pi$
$389$	2069.41	+	3584.32i	0.269726	+	0.467179i	−0.699065	+	0.715058i	$0.746400\pi$
$390$	23.5258	+	40.7479i	0.00305455	+	0.00529064i
$391$	−4547.54			−0.588182
$392$	−5680.68			−0.731933
$393$	221.570	+	383.770i	0.0284395	+	0.0492586i
$394$	−238.121	+	412.437i	−0.0304476	+	0.0527368i
$395$	−1275.07	−	2208.49i	−0.162420	−	0.281319i
$396$	−2314.02	+	4007.99i	−0.293646	+	0.508609i
$397$	−3297.75	+	5711.87i	−0.416900	+	0.722092i	−0.995626	−	0.0934299i	$-0.970217\pi$
$397$	−3297.75	+	5711.87i	−0.416900	+	0.722092i	0.578726	+	0.815522i	$0.303550\pi$
$398$	4123.65			0.519346
$399$	40.5769	−	67.7807i	0.00509120	−	0.00850446i
$400$	848.951			0.106119
$401$	−1960.14	+	3395.06i	−0.244101	+	0.422796i	−0.961879	−	0.273477i	$-0.911826\pi$
$401$	−1960.14	+	3395.06i	−0.244101	+	0.422796i	0.717777	+	0.696273i	$0.245160\pi$
$402$	−33.3195	+	57.7110i	−0.00413389	+	0.00716011i
$403$	−2655.22	−	4598.98i	−0.328204	−	0.568466i
$404$	−4185.45	+	7249.41i	−0.515430	+	0.892751i
$405$	1795.04	+	3109.10i	0.220238	+	0.381463i
$406$	−15.0553			−0.00184035
$407$	−9090.72			−1.10715
$408$	143.128	+	247.905i	0.0173674	+	0.0300812i
$409$	−207.335	−	359.115i	−0.0250661	−	0.0434158i	0.853220	−	0.521551i	$-0.174646\pi$
$409$	−207.335	−	359.115i	−0.0250661	−	0.0434158i	−0.878286	+	0.478135i	$0.841313\pi$
$410$	812.926			0.0979209
$411$	−243.302			−0.0292000
$412$	3441.91	+	5961.57i	0.411580	+	0.712877i
$413$	−514.035	+	890.334i	−0.0612445	+	0.106079i
$414$	−1529.10	−	2648.47i	−0.181524	−	0.314409i
$415$	2359.73	−	4087.16i	0.279119	−	0.483448i
$416$	−1932.30	+	3346.84i	−0.227737	+	0.394452i
$417$	524.042			0.0615406
$418$	1263.71	−	2110.93i	0.147871	−	0.247007i
$419$	15070.1			1.75710			0.878549	−	0.477653i	$-0.158512\pi$
$419$	15070.1			1.75710			0.878549	+	0.477653i	$0.158512\pi$
$420$	15.9179	−	27.5706i	0.00184932	−	0.00320311i
$421$	−5971.55	+	10343.0i	−0.691296	+	1.19736i	0.280118	+	0.959966i	$0.409627\pi$
$421$	−5971.55	+	10343.0i	−0.691296	+	1.19736i	−0.971413	+	0.237394i	$0.923707\pi$
$422$	−3107.70	−	5382.70i	−0.358485	−	0.620914i
$423$	129.908	−	225.008i	0.0149323	−	0.0258635i
$424$	−2349.72	−	4069.84i	−0.269134	−	0.466153i
$425$	−1149.52			−0.131199
$426$	−173.702			−0.0197556
$427$	197.219	+	341.593i	0.0223515	+	0.0387139i
$428$	−4319.75	−	7482.03i	−0.487858	−	0.844994i
$429$	−210.999			−0.0237462
$430$	−1649.85			−0.185030
$431$	−473.209	−	819.621i	−0.0528855	−	0.0916004i	0.838371	−	0.545100i	$-0.183509\pi$
$431$	−473.209	−	819.621i	−0.0528855	−	0.0916004i	−0.891256	+	0.453500i	$0.850175\pi$
$432$	337.071	−	583.824i	0.0375401	−	0.0650214i
$433$	6940.19	+	12020.8i	0.770264	+	1.33414i	0.937418	+	0.348206i	$0.113209\pi$
$433$	6940.19	+	12020.8i	0.770264	+	1.33414i	−0.167154	+	0.985931i	$0.553458\pi$
$434$	356.584	−	617.622i	0.0394392	−	0.0683106i
$435$	−4.65663	+	8.06552i	−0.000513260	+	0.000888993i
$436$	−9647.14			−1.05967
$437$	−3982.68	−	7157.47i	−0.435967	−	0.783497i
$438$	480.670			0.0524368
$439$	−6876.88	+	11911.1i	−0.747644	+	1.29496i	0.201305	+	0.979529i	$0.435482\pi$
$439$	−6876.88	+	11911.1i	−0.747644	+	1.29496i	−0.948949	+	0.315429i	$0.897852\pi$
$440$	1089.87	−	1887.71i	0.118085	−	0.204530i
$441$	−4517.23	−	7824.08i	−0.487770	−	0.844842i
$442$	587.003	−	1016.72i	0.0631695	−	0.109413i
$443$	−2893.97	−	5012.50i	−0.310376	−	0.537587i	0.668068	−	0.744101i	$-0.267122\pi$
$443$	−2893.97	−	5012.50i	−0.310376	−	0.537587i	−0.978444	+	0.206513i	$0.933788\pi$
$444$	866.566			0.0926248
$445$	−224.593			−0.0239253
$446$	1015.75	+	1759.34i	0.107842	+	0.186787i
$447$	−66.4452	−	115.086i	−0.00703076	−	0.0121776i
$448$	184.092			0.0194141
$449$	6435.59			0.676424			0.338212	−	0.941070i	$-0.390178\pi$
$449$	6435.59			0.676424			0.338212	+	0.941070i	$0.390178\pi$
$450$	−386.521	−	669.474i	−0.0404906	−	0.0701318i
$451$	−1822.75	+	3157.09i	−0.190310	+	0.329626i
$452$	−1360.17	−	2355.89i	−0.141542	−	0.245158i
$453$	227.094	−	393.339i	0.0235537	−	0.0407962i
$454$	−1933.50	+	3348.92i	−0.199876	+	0.346195i
$455$	−287.048			−0.0295758
$456$	−264.833	+	442.384i	−0.0271972	+	0.0454310i
$457$	−5341.33			−0.546733			−0.273366	−	0.961910i	$-0.588137\pi$
$457$	−5341.33			−0.546733			−0.273366	+	0.961910i	$0.588137\pi$
$458$	−71.6487	+	124.099i	−0.00730987	+	0.0126611i
$459$	−456.408	+	790.523i	−0.0464125	+	0.0803887i
$460$	−1650.44	−	2858.65i	−0.167288	−	0.289751i
$461$	3386.25	−	5865.17i	0.342112	−	0.592555i	−0.642713	−	0.766107i	$-0.722191\pi$
$461$	3386.25	−	5865.17i	0.342112	−	0.592555i	0.984825	+	0.173552i	$0.0555245\pi$
$462$	−14.1681	−	24.5398i	−0.00142675	−	0.00247120i
$463$	−10076.8			−1.01146			−0.505731	−	0.862691i	$-0.668777\pi$
$463$	−10076.8			−1.01146			−0.505731	+	0.862691i	$0.668777\pi$
$464$	−171.619			−0.0171707
$465$	−220.584	−	382.062i	−0.0219986	−	0.0381026i
$466$	3662.36	+	6343.39i	0.364067	+	0.630583i
$467$	−14220.5			−1.40909			−0.704546	−	0.709658i	$-0.748849\pi$
$467$	−14220.5			−1.40909			−0.704546	+	0.709658i	$0.748849\pi$
$468$	−3977.76			−0.392889
$469$	−203.272	−	352.077i	−0.0200133	−	0.0346640i
$470$	−27.8306	+	48.2041i	−0.00273134	+	0.00473083i
$471$	−349.566	−	605.465i	−0.0341977	−	0.0592322i
$472$	3354.95	−	5810.94i	0.327169	−	0.566674i
$473$	3699.29	−	6407.36i	0.359606	−	0.622856i
$474$	216.368			0.0209665
$475$	−1006.73	−	1809.25i	−0.0972462	−	0.174766i
$476$	−794.349			−0.0764893
$477$	3736.96	−	6472.61i	0.358708	−	0.621301i
$478$	148.954	−	257.996i	0.0142531	−	0.0246871i
$479$	3710.05	+	6425.99i	0.353896	+	0.612967i	0.986928	−	0.161159i	$-0.0515232\pi$
$479$	3710.05	+	6425.99i	0.353896	+	0.612967i	−0.633032	+	0.774126i	$0.718190\pi$
$480$	−160.526	+	278.040i	−0.0152646	+	0.0264390i
$481$	−3906.70	−	6766.61i	−0.370333	−	0.641436i
$482$	−4218.94			−0.398688
$483$	−94.3385			−0.00888727
$484$	−2219.20	−	3843.76i	−0.208414	−	0.360984i
$485$	−1512.23	−	2619.26i	−0.141581	−	0.245226i
$486$	−921.569			−0.0860149
$487$	8547.96			0.795370			0.397685	−	0.917522i	$-0.369814\pi$
$487$	8547.96			0.795370			0.397685	+	0.917522i	$0.369814\pi$
$488$	−1287.19	−	2229.47i	−0.119402	−	0.206810i
$489$	238.569	−	413.213i	0.0220623	−	0.0382130i
$490$	967.740	+	1676.18i	0.0892205	+	0.154534i
$491$	−10470.8	+	18136.0i	−0.962406	+	1.66694i	−0.245978	+	0.969276i	$0.579109\pi$
$491$	−10470.8	+	18136.0i	−0.962406	+	1.66694i	−0.716428	+	0.697661i	$0.754224\pi$
$492$	173.752	−	300.947i	0.0159214	−	0.0275767i
$493$	232.379			0.0212289
$494$	2114.33	+	33.4668i	0.192567	+	0.00304806i
$495$	3466.63			0.314775
$496$	4064.78	−	7040.41i	0.367972	−	0.637346i
$497$	529.851	−	917.730i	0.0478211	−	0.0828286i
$498$	200.212	+	346.777i	0.0180155	+	0.0312037i
$499$	−1953.51	+	3383.58i	−0.175253	+	0.303547i	−0.940249	−	0.340488i	$-0.889408\pi$
$499$	−1953.51	+	3383.58i	−0.175253	+	0.303547i	0.764996	+	0.644035i	$0.222741\pi$
$500$	−417.195	−	722.602i	−0.0373150	−	0.0646315i
$501$	220.248			0.0196406
$502$	−1120.30			−0.0996047
$503$	2160.78	+	3742.58i	0.191540	+	0.331756i	0.945761	−	0.324864i	$-0.105319\pi$
$503$	2160.78	+	3742.58i	0.191540	+	0.331756i	−0.754221	+	0.656621i	$0.771985\pi$
$504$	−587.208	−	1017.07i	−0.0518975	−	0.0898891i
$505$	6270.23			0.552518
$506$	−2938.03			−0.258125
$507$	314.188	+	544.190i	0.0275219	+	0.0476692i
$508$	5429.04	−	9403.37i	0.474163	−	0.821274i
$509$	−3872.55	−	6707.45i	−0.337225	−	0.584091i	0.646685	−	0.762758i	$-0.276155\pi$
$509$	−3872.55	−	6707.45i	−0.337225	−	0.584091i	−0.983910	+	0.178666i	$0.942822\pi$
$510$	48.7656	−	84.4644i	0.00423407	−	0.00733362i
$511$	−1466.21	+	2539.55i	−0.126930	+	0.219850i
$512$	−10505.0			−0.906758
$513$	−1643.94	−	26.0212i	−0.141484	−	0.00223950i
$514$	−6486.72			−0.556648
$515$	2578.17	−	4465.52i	0.220597	−	0.382086i
$516$	−352.632	+	610.777i	−0.0300848	+	0.0521084i
$517$	−124.804	−	216.167i	−0.0106168	−	0.0183888i
$518$	524.652	−	908.724i	0.0445017	−	0.0770793i
$519$	−676.186	−	1171.19i	−0.0571893	−	0.0990548i
$520$	1873.47			0.157995
$521$	5276.05			0.443662			0.221831	−	0.975085i	$-0.428797\pi$
$521$	5276.05			0.443662			0.221831	+	0.975085i	$0.428797\pi$
$522$	78.1368	+	135.337i	0.00655164	+	0.0113478i
$523$	398.642	+	690.469i	0.0333297	+	0.0577287i	0.882209	−	0.470858i	$-0.156056\pi$
$523$	398.642	+	690.469i	0.0333297	+	0.0577287i	−0.848879	+	0.528587i	$0.822722\pi$
$524$	8025.83			0.669103
$525$	−23.8466			−0.00198238
$526$	−2674.21	−	4631.86i	−0.221675	−	0.383952i
$527$	−5503.89	+	9533.01i	−0.454940	+	0.787978i
$528$	−161.505	−	279.735i	−0.0133117	−	0.0230566i
$529$	1192.76	−	2065.93i	0.0980326	−	0.169797i
$530$	−800.581	+	1386.65i	−0.0656132	+	0.113645i
$531$	10671.3			0.872120
$532$	−695.680	−	1250.24i	−0.0566947	−	0.101889i
$533$	−3133.27			−0.254629
$534$	9.52786	−	16.5027i	0.000772118	−	0.00133735i
$535$	−3235.71	+	5604.42i	−0.261481	+	0.452898i
$536$	1326.69	+	2297.90i	0.106911	+	0.185176i
$537$	−858.548	+	1487.05i	−0.0689927	+	0.119499i
$538$	1017.60	+	1762.54i	0.0815465	+	0.141243i
$539$	−8679.48			−0.693602
$540$	−662.579			−0.0528016
$541$	−4311.17	−	7467.17i	−0.342609	−	0.593417i	0.642307	−	0.766447i	$-0.277977\pi$
$541$	−4311.17	−	7467.17i	−0.342609	−	0.593417i	−0.984916	+	0.173031i	$0.944644\pi$
$542$	2584.89	+	4477.16i	0.204853	+	0.354816i
$543$	−27.0083			−0.00213451
$544$	8010.73			0.631356
$545$	3613.10	+	6258.07i	0.283978	+	0.491865i
$546$	12.1773	−	21.0918i	0.000954473	−	0.00165320i
$547$	9656.70	+	16725.9i	0.754828	+	1.30740i	0.945460	+	0.325739i	$0.105613\pi$
$547$	9656.70	+	16725.9i	0.754828	+	1.30740i	−0.190632	+	0.981662i	$0.561054\pi$
$548$	−2203.26	+	3816.16i	−0.171749	+	0.297478i
$549$	2047.12	−	3545.72i	0.159142	−	0.275642i
$550$	−742.667			−0.0575771
$551$	203.515	+	365.747i	0.0157351	+	0.0282783i
$552$	615.718			0.0474759
$553$	−659.998	+	1143.15i	−0.0507522	+	0.0879054i
$554$	−1992.59	+	3451.27i	−0.152811	+	0.264676i
$555$	−324.551	−	562.139i	−0.0248224	−	0.0429936i
$556$	4745.54	−	8219.52i	0.361971	−	0.626952i
$557$	10048.8	+	17405.0i	0.764419	+	1.32401i	0.940553	+	0.339646i	$0.110307\pi$
$557$	10048.8	+	17405.0i	0.764419	+	1.32401i	−0.176134	+	0.984366i	$0.556359\pi$
$558$	−7402.66			−0.561612
$559$	6359.03			0.481142
$560$	−219.715	−	380.558i	−0.0165798	−	0.0287170i
$561$	218.685	+	378.773i	0.0164579	+	0.0285059i
$562$	−2259.69			−0.169607
$563$	5824.27			0.435993			0.217996	−	0.975950i	$-0.430048\pi$
$563$	5824.27			0.435993			0.217996	+	0.975950i	$0.430048\pi$
$564$	11.8968	+	20.6059i	0.000888203	+	0.00153841i
$565$	−1018.84	+	1764.68i	−0.0758634	+	0.131399i
$566$	53.1866	+	92.1219i	0.00394982	+	0.00684129i
$567$	929.141	−	1609.32i	0.0688188	−	0.119198i
$568$	−3458.18	+	5989.74i	−0.255461	+	0.442472i
$569$	24499.0			1.80501			0.902505	−	0.430679i	$-0.141726\pi$
$569$	24499.0			1.80501			0.902505	+	0.430679i	$0.141726\pi$
$570$	175.649	+	2.78027i	0.0129072	+	0.000204303i
$571$	13632.0			0.999091			0.499545	−	0.866288i	$-0.333500\pi$
$571$	13632.0			0.999091			0.499545	+	0.866288i	$0.333500\pi$
$572$	−1910.73	+	3309.48i	−0.139671	+	0.241917i
$573$	−847.047	+	1467.13i	−0.0617555	+	0.106964i
$574$	−210.392	−	364.409i	−0.0152989	−	0.0264985i
$575$	−1236.27	+	2141.28i	−0.0896624	+	0.155300i
$576$	−955.432	−	1654.86i	−0.0691140	−	0.119709i
$577$	24088.5			1.73798			0.868991	−	0.494828i	$-0.164769\pi$
$577$	24088.5			1.73798			0.868991	+	0.494828i	$0.164769\pi$
$578$	3221.50			0.231829
$579$	−619.585	−	1073.15i	−0.0444717	−	0.0770272i
$580$	84.3376	+	146.077i	0.00603781	+	0.0104578i
$581$	−2442.86			−0.174436
$582$	256.612			0.0182765
$583$	−3590.13	−	6218.28i	−0.255039	−	0.441741i
$584$	9569.51	−	16574.9i	0.678064	−	1.17444i
$585$	1489.77	+	2580.36i	0.105290	+	0.182367i
$586$	2955.41	−	5118.93i	0.208340	−	0.360855i
$587$	5259.46	−	9109.66i	0.369815	−	0.640538i	−0.619722	−	0.784822i	$-0.712754\pi$
$587$	5259.46	−	9109.66i	0.369815	−	0.640538i	0.989536	+	0.144284i	$0.0460878\pi$
$588$	827.364			0.0580271
$589$	−19824.4	−	313.793i	−1.38684	−	0.0219518i
$590$	−2286.15			−0.159524
$591$	76.2459	−	132.062i	0.00530683	−	0.00919171i
$592$	5980.63	−	10358.7i	0.415206	−	0.719159i
$593$	4775.75	+	8271.83i	0.330719	+	0.572822i	0.982653	−	0.185454i	$-0.0593754\pi$
$593$	4775.75	+	8271.83i	0.330719	+	0.572822i	−0.651934	+	0.758276i	$0.726042\pi$
$594$	−294.871	+	510.732i	−0.0203682	+	0.0352788i
$595$	297.504	+	515.292i	0.0204983	+	0.0355040i
$596$	−2406.82			−0.165415
$597$	−1320.39			−0.0905190
$598$	−1262.61	−	2186.90i	−0.0863408	−	0.149547i
$599$	5624.85	+	9742.53i	0.383682	+	0.664556i	0.991585	−	0.129455i	$-0.0413226\pi$
$599$	5624.85	+	9742.53i	0.383682	+	0.664556i	−0.607904	+	0.794011i	$0.707989\pi$
$600$	155.640			0.0105899
$601$	13628.9			0.925017			0.462509	−	0.886615i	$-0.346949\pi$
$601$	13628.9			0.925017			0.462509	+	0.886615i	$0.346949\pi$
$602$	426.994	+	739.575i	0.0289086	+	0.0500712i
$603$	−2109.95	+	3654.55i	−0.142494	+	0.246807i
$604$	−4112.97	−	7123.88i	−0.277077	−	0.479911i
$605$	−1662.29	+	2879.17i	−0.111705	+	0.193479i
$606$	−266.000	+	460.726i	−0.0178309	+	0.0308840i
$607$	4894.09			0.327257			0.163628	−	0.986522i	$-0.447680\pi$
$607$	4894.09			0.327257			0.163628	+	0.986522i	$0.447680\pi$
$608$	7015.70	+	12608.3i	0.467967	+	0.841007i
$609$	4.82069			0.000320763
$610$	−438.561	+	759.610i	−0.0291095	+	0.0504192i
$611$	107.268	−	185.793i	0.00710245	−	0.0123018i
$612$	4122.65	+	7140.64i	0.272301	+	0.471639i
$613$	−268.211	+	464.555i	−0.0176720	+	0.0306088i	−0.874726	−	0.484617i	$-0.838959\pi$
$613$	−268.211	+	464.555i	−0.0176720	+	0.0306088i	0.857054	+	0.515226i	$0.172292\pi$
$614$	−273.711	−	474.082i	−0.0179904	−	0.0311603i
$615$	−260.298			−0.0170670
$616$	−1128.27			−0.0737976
$617$	−12322.5	−	21343.2i	−0.804029	−	1.39262i	−0.916945	−	0.399014i	$-0.869352\pi$
$617$	−12322.5	−	21343.2i	−0.804029	−	1.39262i	0.112916	−	0.993605i	$-0.463981\pi$
$618$	218.746	+	378.879i	0.0142383	+	0.0246614i
$619$	806.607			0.0523752			0.0261876	−	0.999657i	$-0.491663\pi$
$619$	806.607			0.0523752			0.0261876	+	0.999657i	$0.491663\pi$
$620$	−7990.12			−0.517566
$621$	981.705	+	1700.36i	0.0634371	+	0.109876i
$622$	2555.61	−	4426.45i	0.164744	−	0.285345i
$623$	58.1266	+	100.678i	0.00373803	+	0.00647446i
$624$	138.812	−	240.430i	0.00890534	−	0.0154245i
$625$	−312.500	+	541.266i	−0.0200000	+	0.0346410i
$626$	6862.87			0.438171
$627$	−404.637	+	675.916i	−0.0257730	+	0.0430518i
$628$	−12662.2			−0.804579
$629$	−8098.02	+	14026.2i	−0.513338	+	0.889127i
$630$	−200.069	+	346.530i	−0.0126523	+	0.0219144i
$631$	2705.38	+	4685.85i	0.170680	+	0.295627i	0.938658	−	0.344850i	$-0.112070\pi$
$631$	2705.38	+	4685.85i	0.170680	+	0.295627i	−0.767977	+	0.640477i	$0.778737\pi$
$632$	4307.60	−	7460.99i	0.271119	−	0.469592i
$633$	995.081	+	1723.53i	0.0624817	+	0.108222i
$634$	−9657.34			−0.604956
$635$	−8133.25			−0.508281
$636$	342.226	+	592.753i	0.0213367	+	0.0369563i
$637$	−3729.97	−	6460.50i	−0.232004	−	0.401844i
$638$	150.133			0.00931635
$639$	−10999.7			−0.680970
$640$	3689.08	+	6389.68i	0.227850	+	0.394647i
$641$	7052.62	−	12215.5i	0.434574	−	0.752704i	−0.562687	−	0.826670i	$-0.690232\pi$
$641$	7052.62	−	12215.5i	0.434574	−	0.752704i	0.997261	+	0.0739662i	$0.0235657\pi$
$642$	−274.536	−	475.510i	−0.0168770	−	0.0292319i
$643$	−8387.65	+	14527.8i	−0.514427	+	0.891014i	0.485433	+	0.874274i	$0.338662\pi$
$643$	−8387.65	+	14527.8i	−0.514427	+	0.891014i	−0.999860	+	0.0167402i	$0.994671\pi$
$644$	−854.296	+	1479.68i	−0.0522733	+	0.0905400i
$645$	528.279			0.0322496
$646$	−2131.27	−	3830.20i	−0.129804	−	0.233278i
$647$	−17101.5			−1.03915			−0.519574	−	0.854425i	$-0.673909\pi$
$647$	−17101.5			−1.03915			−0.519574	+	0.854425i	$0.673909\pi$
$648$	−6064.22	+	10503.5i	−0.367631	+	0.636756i
$649$	5126.00	−	8878.50i	0.310036	−	0.536998i
$650$	−319.158	−	552.798i	−0.0192591	−	0.0333577i
$651$	−114.178	+	197.762i	−0.00687401	+	0.0119061i
$652$	−4320.79	−	7483.83i	−0.259533	−	0.449524i
$653$	−14235.5			−0.853107			−0.426553	−	0.904462i	$-0.640272\pi$
$653$	−14235.5			−0.853107			−0.426553	+	0.904462i	$0.640272\pi$
$654$	−613.110			−0.0366583
$655$	−3005.88	−	5206.34i	−0.179312	−	0.310578i
$656$	−2398.30	−	4153.98i	−0.142741	−	0.247234i
$657$	30438.4			1.80748
$658$	28.8112			0.00170696
$659$	−5313.77	−	9203.72i	−0.314105	−	0.544046i	0.665142	−	0.746717i	$-0.268371\pi$
$659$	−5313.77	−	9203.72i	−0.314105	−	0.544046i	−0.979247	+	0.202671i	$0.935038\pi$
$660$	−158.735	+	274.937i	−0.00936173	+	0.0162150i
$661$	−2831.74	−	4904.72i	−0.166629	−	0.288611i	0.770603	−	0.637315i	$-0.219955\pi$
$661$	−2831.74	−	4904.72i	−0.166629	−	0.288611i	−0.937233	+	0.348705i	$0.886622\pi$
$662$	−1058.72	+	1833.75i	−0.0621575	+	0.107660i
$663$	−187.958	+	325.552i	−0.0110101	+	0.0190700i
$664$	15943.8			0.931838
$665$	−550.478	+	919.533i	−0.0321002	+	0.0536210i
$666$	−10891.7			−0.633703
$667$	249.917	−	432.868i	0.0145080	−	0.0251285i
$668$	1994.49	−	3454.56i	0.115523	−	0.200091i
$669$	−325.243	−	563.338i	−0.0187962	−	0.0325559i
$670$	452.022	−	782.924i	0.0260644	−	0.0451448i
$671$	−1966.69	−	3406.40i	−0.113149	−	0.195980i
$672$	166.182			0.00953961
$673$	3143.18			0.180031			0.0900155	−	0.995940i	$-0.471308\pi$
$673$	3143.18			0.180031			0.0900155	+	0.995940i	$0.471308\pi$
$674$	5230.02	+	9058.67i	0.298892	+	0.517696i
$675$	248.153	+	429.813i	0.0141502	+	0.0245089i
$676$	11380.7			0.647514
$677$	−22858.3			−1.29766			−0.648831	−	0.760933i	$-0.724742\pi$
$677$	−22858.3			−1.29766			−0.648831	+	0.760933i	$0.724742\pi$
$678$	−86.4438	−	149.725i	−0.00489654	−	0.00848105i
$679$	−782.756	+	1355.77i	−0.0442407	+	0.0766271i
$680$	−1941.72	−	3363.15i	−0.109502	−	0.189663i
$681$	619.103	−	1072.32i	0.0348371	−	0.0603397i
$682$	−3555.89	+	6158.99i	−0.199651	+	0.345806i
$683$	6550.06			0.366956			0.183478	−	0.983024i	$-0.441264\pi$
$683$	6550.06			0.366956			0.183478	+	0.983024i	$0.441264\pi$
$684$	−7628.24	+	12742.4i	−0.426422	+	0.712307i
$685$	3300.71			0.184107
$686$	1011.81	−	1752.51i	0.0563137	−	0.0975382i
$687$	22.9418	−	39.7364i	0.00127407	−	0.00220675i
$688$	4867.40	+	8430.58i	0.269721	+	0.467170i
$689$	3085.69	−	5344.57i	0.170617	−	0.295518i
$690$	−104.892	−	181.678i	−0.00578718	−	0.0100237i
$691$	−26440.9			−1.45566			−0.727828	−	0.685760i	$-0.759470\pi$
$691$	−26440.9			−1.45566			−0.727828	+	0.685760i	$0.759470\pi$
$692$	−24493.2			−1.34551
$693$	−897.192	−	1553.98i	−0.0491797	−	0.0851817i
$694$	1032.72	+	1788.72i	0.0564861	+	0.0978368i
$695$	−7109.30			−0.388016
$696$	−31.4632			−0.00171352
$697$	3247.40	+	5624.67i	0.176477	+	0.305667i
$698$	2856.17	−	4947.04i	0.154882	−	0.268264i
$699$	−1172.68	−	2031.14i	−0.0634547	−	0.109907i
$700$	−215.947	+	374.031i	−0.0116600	+	0.0201958i
$701$	11619.5	−	20125.6i	0.626053	−	1.08436i	−0.362283	−	0.932068i	$-0.618003\pi$
$701$	11619.5	−	20125.6i	0.626053	−	1.08436i	0.988336	−	0.152287i	$-0.0486639\pi$
$702$	−506.879			−0.0272520
$703$	−29168.2	−	461.693i	−1.56487	−	0.0247696i
$704$	−1835.78			−0.0982793
$705$	8.91133	−	15.4349i	0.000476057	−	0.000824555i
$706$	7405.48	−	12826.7i	0.394772	−	0.683765i
$707$	−1622.79	−	2810.75i	−0.0863241	−	0.149518i
$708$	−488.632	+	846.336i	−0.0259377	+	0.0449255i
$709$	−15782.9	−	27336.7i	−0.836020	−	1.44803i	−0.893198	−	0.449664i	$-0.851544\pi$
$709$	−15782.9	−	27336.7i	−0.836020	−	1.44803i	0.0571780	−	0.998364i	$-0.481790\pi$
$710$	2356.49			0.124560
$711$	13701.5			0.722709
$712$	−379.374	−	657.096i	−0.0199686	−	0.0345867i
$713$	11838.5	+	20504.9i	0.621817	+	1.07702i
$714$	−50.4837			−0.00264608
$715$	2862.47			0.149721
$716$	15549.4	+	26932.4i	0.811605	+	1.40574i
$717$	−47.6948	+	82.6098i	−0.00248423	+	0.00430282i
$718$	−3327.47	−	5763.34i	−0.172953	−	0.299563i
$719$	−8762.16	+	15176.5i	−0.454483	+	0.787188i	−0.998658	−	0.0517836i	$-0.983509\pi$
$719$	−8762.16	+	15176.5i	−0.454483	+	0.787188i	0.544175	+	0.838972i	$0.316843\pi$
$720$	−2280.63	+	3950.18i	−0.118048	+	0.204464i
$721$	−2669.00			−0.137863
$722$	4161.90	−	6708.88i	0.214529	−	0.345815i
$723$	1350.90			0.0694889
$724$	−244.578	+	423.621i	−0.0125548	+	0.0217455i
$725$	63.1732	−	109.419i	0.00323613	−	0.00560514i
$726$	−141.038	−	244.285i	−0.00720992	−	0.0124880i
$727$	14565.2	−	25227.7i	0.743047	−	1.28699i	−0.208055	−	0.978117i	$-0.566713\pi$
$727$	14565.2	−	25227.7i	0.743047	−	1.28699i	0.951102	−	0.308878i	$-0.0999533\pi$
$728$	−484.870	−	839.819i	−0.0246847	−	0.0427552i
$729$	−19091.3			−0.969940
$730$	−6520.91			−0.330616
$731$	−6590.66	−	11415.4i	−0.333467	−	0.577582i
$732$	187.473	+	324.712i	0.00946611	+	0.0163958i
$733$	−30764.9			−1.55024			−0.775120	−	0.631814i	$-0.782311\pi$
$733$	−30764.9			−1.55024			−0.775120	+	0.631814i	$0.782311\pi$
$734$	7129.16			0.358504
$735$	−309.869	−	536.709i	−0.0155506	−	0.0269344i
$736$	8615.29	−	14922.1i	0.431472	−	0.747332i
$737$	2027.05	+	3510.95i	0.101312	+	0.175478i
$738$	−2183.86	+	3782.55i	−0.108928	+	0.188669i
$739$	−440.776	+	763.447i	−0.0219408	+	0.0380025i	−0.876787	−	0.480878i	$-0.840318\pi$
$739$	−440.776	+	763.447i	−0.0219408	+	0.0380025i	0.854847	+	0.518881i	$0.173651\pi$
$740$	−11756.1			−0.584003
$741$	−677.004	−	10.7160i	−0.0335632	−	0.000531259i
$742$	828.787			0.0410050
$743$	−11087.4	+	19203.9i	−0.547452	+	0.948214i	0.450996	+	0.892526i	$0.351069\pi$
$743$	−11087.4	+	19203.9i	−0.547452	+	0.948214i	−0.998448	+	0.0556885i	$0.982265\pi$
$744$	745.203	−	1290.73i	0.0367211	−	0.0636028i
$745$	901.415	+	1561.30i	0.0443292	+	0.0767805i
$746$	−243.190	+	421.217i	−0.0119354	+	0.0206727i
$747$	12678.4	+	21959.6i	0.620989	+	1.07558i
$748$	7921.32			0.387209
$749$	3349.72			0.163413
$750$	−26.5142	−	45.9239i	−0.00129088	−	0.00223587i
$751$	2070.76	+	3586.65i	0.100616	+	0.174273i	0.911939	−	0.410326i	$-0.134585\pi$
$751$	2070.76	+	3586.65i	0.100616	+	0.174273i	−0.811322	+	0.584599i	$0.801252\pi$
$752$	328.425			0.0159261
$753$	358.719			0.0173605
$754$	64.5191	+	111.750i	0.00311624	+	0.00539749i
$755$	−3080.83	+	5336.15i	−0.148507	+	0.257222i
$756$	171.481	+	297.013i	0.00824959	+	0.0142887i
$757$	11286.5	−	19548.8i	0.541895	−	0.938590i	−0.456900	−	0.889518i	$-0.651040\pi$
$757$	11286.5	−	19548.8i	0.541895	−	0.938590i	0.998795	−	0.0490720i	$-0.0156264\pi$
$758$	−4996.65	+	8654.45i	−0.239428	+	0.414702i
$759$	940.753			0.0449897
$760$	3592.80	−	6001.51i	0.171480	−	0.286444i
$761$	17386.0			0.828175			0.414088	−	0.910237i	$-0.364101\pi$
$761$	17386.0			0.828175			0.414088	+	0.910237i	$0.364101\pi$
$762$	345.035	−	597.618i	0.0164033	−	0.0284113i
$763$	1870.20	−	3239.28i	0.0887362	−	0.153696i
$764$	15341.1	+	26571.6i	0.726469	+	1.25828i
$765$	3088.08	−	5348.71i	0.145947	−	0.252788i
$766$	−5973.77	−	10346.9i	−0.281777	−	0.488052i
$767$	8811.52			0.414818
$768$	−416.276			−0.0195587
$769$	−5968.85	−	10338.3i	−0.279899	−	0.484799i	0.691461	−	0.722414i	$-0.256968\pi$
$769$	−5968.85	−	10338.3i	−0.279899	−	0.484799i	−0.971359	+	0.237615i	$0.923634\pi$
$770$	192.208	+	332.914i	0.00899571	+	0.0155810i
$771$	2077.04			0.0970205
$772$	−22443.0			−1.04630
$773$	11520.8	+	19954.6i	0.536060	+	0.928484i	0.999111	+	0.0421522i	$0.0134214\pi$
$773$	11520.8	+	19954.6i	0.536060	+	0.928484i	−0.463051	+	0.886332i	$0.653245\pi$
$774$	4432.18	−	7676.76i	0.205829	−	0.356506i
$775$	2992.50	+	5183.17i	0.138702	+	0.240239i
$776$	5108.81	−	8848.72i	0.236334	−	0.409343i
$777$	−167.993	+	290.972i	−0.00775639	+	0.0134345i
$778$	4763.94			0.219531
$779$	−6008.75	+	10037.2i	−0.276362	+	0.461642i
$780$	−272.862			−0.0125257
$781$	−5283.73	+	9151.69i	−0.242083	+	0.419300i
$782$	−2617.20	+	4533.12i	−0.119681	+	0.207294i
$783$	−50.1651	−	86.8885i	−0.00228960	−	0.00396570i
$784$	5710.07	−	9890.14i	0.260116	−	0.450535i
$785$	4742.31	+	8213.92i	0.215618	+	0.373462i
$786$	510.070			0.0231471
$787$	−31761.0			−1.43857			−0.719287	−	0.694713i	$-0.755531\pi$
$787$	−31761.0			−1.43857			−0.719287	+	0.694713i	$0.755531\pi$
$788$	−1380.91	−	2391.81i	−0.0624277	−	0.108128i
$789$	856.277	+	1483.12i	0.0386366	+	0.0669205i
$790$	−2935.31			−0.132195
$791$	1054.73			0.0474109
$792$	5855.70	+	10142.4i	0.262719	+	0.455042i
$793$	1690.35	−	2927.77i	0.0756950	−	0.131108i
$794$	3795.84	+	6574.58i	0.169659	+	0.293858i
$795$	256.345	−	444.002i	0.0114360	−	0.0198077i
$796$	−11957.0	+	20710.1i	−0.532416	+	0.922172i
$797$	20214.7			0.898421			0.449211	−	0.893426i	$-0.351705\pi$
$797$	20214.7			0.898421			0.449211	+	0.893426i	$0.351705\pi$
$798$	−44.2129	−	79.4573i	−0.00196130	−	0.00352476i
$799$	−444.701			−0.0196901
$800$	2177.75	−	3771.97i	0.0962438	−	0.166699i
$801$	603.351	−	1045.04i	0.0266147	−	0.0460980i
$802$	2256.19	+	3907.84i	0.0993378	+	0.172058i
$803$	14621.2	−	25324.7i	0.642554	−	1.11294i
$804$	−193.227	−	334.678i	−0.00847585	−	0.0146806i
$805$	1279.82			0.0560346
$806$	−6112.52			−0.267127
$807$	−325.835	−	564.363i	−0.0142131	−	0.0246178i
$808$	10591.4	+	18344.9i	0.461145	+	0.798726i
$809$	−3305.76			−0.143664			−0.0718321	−	0.997417i	$-0.522885\pi$
$809$	−3305.76			−0.143664			−0.0718321	+	0.997417i	$0.522885\pi$
$810$	4132.32			0.179253
$811$	15626.0	+	27065.0i	0.676575	+	1.17186i	0.976006	+	0.217744i	$0.0698699\pi$
$811$	15626.0	+	27065.0i	0.676575	+	1.17186i	−0.299431	+	0.954118i	$0.596797\pi$
$812$	43.6545	−	75.6118i	0.00188667	−	0.00326780i
$813$	−827.678	−	1433.58i	−0.0357047	−	0.0618424i
$814$	−5231.88	+	9061.89i	−0.225279	+	0.390195i
$815$	−3236.49	+	5605.77i	−0.139104	+	0.240934i
$816$	−575.475			−0.0246883
$817$	12194.9	−	20370.6i	0.522208	−	0.872310i
$818$	−477.301			−0.0204015
$819$	771.130	−	1335.64i	0.0329004	−	0.0569852i
$820$	−2357.17	+	4082.73i	−0.100385	+	0.173872i
$821$	−16763.3	−	29035.0i	−0.712600	−	1.23426i	−0.963878	−	0.266345i	$-0.914184\pi$
$821$	−16763.3	−	29035.0i	−0.712600	−	1.23426i	0.251278	−	0.967915i	$-0.419149\pi$
$822$	−140.025	+	242.530i	−0.00594152	+	0.0102910i
$823$	−11619.8	−	20126.1i	−0.492152	−	0.852432i	0.507807	−	0.861471i	$-0.330456\pi$
$823$	−11619.8	−	20126.1i	−0.492152	−	0.852432i	−0.999959	+	0.00903875i	$0.997123\pi$
$824$	17419.8			0.736464
$825$	237.801			0.0100353
$826$	591.673	+	1024.81i	0.0249237	+	0.0431690i
$827$	501.659	+	868.899i	0.0210936	+	0.0365352i	0.876380	−	0.481621i	$-0.159952\pi$
$827$	501.659	+	868.899i	0.0210936	+	0.0365352i	−0.855286	+	0.518156i	$0.826619\pi$
$828$	17735.1			0.744369
$829$	−2688.58			−0.112639			−0.0563197	−	0.998413i	$-0.517937\pi$
$829$	−2688.58			−0.112639			−0.0563197	+	0.998413i	$0.517937\pi$
$830$	−2716.13	−	4704.48i	−0.113588	−	0.196741i
$831$	638.025	−	1105.09i	0.0266340	−	0.0461314i
$832$	−788.920	−	1366.45i	−0.0328736	−	0.0569388i
$833$	−7731.68	+	13391.7i	−0.321593	+	0.557015i
$834$	301.596	−	522.380i	0.0125221	−	0.0216889i
$835$	−2987.95			−0.123835
$836$	6937.39	+	12467.5i	0.287003	+	0.515788i
$837$	4752.63			0.196266
$838$	8673.14	−	15022.3i	0.357528	−	0.619257i
$839$	15168.0	−	26271.7i	0.624144	−	1.08105i	−0.364562	−	0.931179i	$-0.618781\pi$
$839$	15168.0	−	26271.7i	0.624144	−	1.08105i	0.988706	−	0.149870i	$-0.0478854\pi$
$840$	−40.2808	−	69.7683i	−0.00165455	−	0.00286576i
$841$	12181.7	−	21099.4i	0.499476	−	0.865118i
$842$	6873.48	+	11905.2i	0.281325	+	0.487269i
$843$	723.550			0.0295616
$844$	36044.4			1.47002
$845$	−4262.37	−	7382.63i	−0.173526	−	0.300557i
$846$	−149.529	−	258.992i	−0.00607674	−	0.0105252i
$847$	1720.86			0.0698104
$848$	9447.52			0.382582
$849$	−17.0303	−	29.4973i	−0.000688431	−	0.00119240i
$850$	−661.568	+	1145.87i	−0.0266960	+	0.0462388i
$851$	17418.3	+	30169.4i	0.701636	+	1.21527i
$852$	503.667	−	872.377i	0.0202528	−	0.0350788i
$853$	10145.8	−	17573.1i	0.407253	−	0.705383i	−0.587328	−	0.809349i	$-0.699820\pi$
$853$	10145.8	−	17573.1i	0.407253	−	0.705383i	0.994581	+	0.103966i	$0.0331534\pi$
$854$	454.013			0.0181920
$855$	11122.9	+	176.061i	0.444908	+	0.00704227i
$856$	−21862.6			−0.872952
$857$	16899.9	−	29271.5i	0.673618	−	1.16674i	−0.303253	−	0.952910i	$-0.598073\pi$
$857$	16899.9	−	29271.5i	0.673618	−	1.16674i	0.976871	−	0.213831i	$-0.0685941\pi$
$858$	−121.434	+	210.329i	−0.00483179	+	0.00836891i
$859$	−1209.64	−	2095.15i	−0.0480468	−	0.0832196i	0.841002	−	0.541032i	$-0.181966\pi$
$859$	−1209.64	−	2095.15i	−0.0480468	−	0.0832196i	−0.889049	+	0.457813i	$0.848633\pi$
$860$	4783.91	−	8285.97i	0.189686	−	0.328546i
$861$	67.3672	+	116.683i	0.00266651	+	0.00461854i
$862$	−1089.36			−0.0430439
$863$	−20162.4			−0.795290			−0.397645	−	0.917539i	$-0.630172\pi$
$863$	−20162.4			−0.795290			−0.397645	+	0.917539i	$0.630172\pi$
$864$	−1729.32	−	2995.28i	−0.0680935	−	0.117941i
$865$	9173.33	+	15888.7i	0.360581	+	0.624545i
$866$	15976.8			0.626923
$867$	−1031.52			−0.0404063
$868$	2067.91	+	3581.72i	0.0808633	+	0.140059i
$869$	6581.56	−	11399.6i	0.256921	−	0.445000i
$870$	5.35996	+	9.28372i	0.000208873	+	0.000361779i
$871$	−1742.23	+	3017.63i	−0.0677764	+	0.117392i
$872$	−12206.2	+	21141.8i	−0.474030	+	0.821045i
$873$	16249.9			0.629986
$874$	−9426.87	−	149.214i	−0.364838	−	0.00577488i
$875$	323.510			0.0124990
$876$	−1393.75	+	2414.05i	−0.0537564	+	0.0931088i
$877$	7410.30	−	12835.0i	0.285323	−	0.494193i	−0.687365	−	0.726312i	$-0.741233\pi$
$877$	7410.30	−	12835.0i	0.285323	−	0.494193i	0.972687	+	0.232119i	$0.0745659\pi$
$878$	7915.55	+	13710.1i	0.304256	+	0.526987i
$879$	−946.319	+	1639.07i	−0.0363124	+	0.0628948i
$880$	2191.02	+	3794.96i	0.0839311	+	0.145373i
$881$	−38578.1			−1.47529			−0.737644	−	0.675190i	$-0.764062\pi$
$881$	−38578.1			−1.47529			−0.737644	+	0.675190i	$0.764062\pi$
$882$	−10399.0			−0.396999
$883$	−24494.8	−	42426.3i	−0.933541	−	1.61694i	−0.777215	−	0.629236i	$-0.783368\pi$
$883$	−24494.8	−	42426.3i	−0.933541	−	1.61694i	−0.156327	−	0.987705i	$-0.549965\pi$
$884$	3404.16	+	5896.17i	0.129518	+	0.224332i
$885$	732.021			0.0278041
$886$	−6662.14			−0.252617
$887$	20603.2	+	35685.9i	0.779920	+	1.35086i	0.931987	+	0.362492i	$0.118074\pi$
$887$	20603.2	+	35685.9i	0.779920	+	1.35086i	−0.152067	+	0.988370i	$0.548593\pi$
$888$	1096.44	−	1899.09i	0.0414347	−	0.0717671i
$889$	2104.95	+	3645.88i	0.0794126	+	0.137547i
$890$	−129.258	+	223.881i	−0.00486823	+	0.00843203i
$891$	−9265.49	+	16048.3i	−0.348379	+	0.603410i
$892$	−11781.2			−0.442222
$893$	−389.463	−	699.924i	−0.0145945	−	0.0262285i
$894$	−152.962			−0.00572238
$895$	11647.3	−	20173.7i	0.435002	−	0.753446i
$896$	1909.53	−	3307.40i	0.0711974	−	0.123317i
$897$	404.285	+	700.242i	0.0150487	+	0.0260651i
$898$	3703.80	−	6415.18i	0.137636	−	0.238393i
$899$	−604.947	−	1047.80i	−0.0224429	−	0.0388722i
$900$	4483.03			0.166038
$901$	−12792.4			−0.473002
$902$	2098.05	+	3633.93i	0.0774472	+	0.134142i
$903$	−136.723	−	236.811i	−0.00503860	−	0.00872710i
$904$	−6883.93			−0.253270
$905$	366.402			0.0134582
$906$	−261.394	−	452.748i	−0.00958525	−	0.0166021i
$907$	−22275.7	+	38582.7i	−0.815495	+	1.41248i	0.0934769	+	0.995621i	$0.470202\pi$
$907$	−22275.7	+	38582.7i	−0.815495	+	1.41248i	−0.908972	+	0.416857i	$0.863131\pi$
$908$	−11212.8	−	19421.1i	−0.409811	−	0.709814i
$909$	−16844.4	+	29175.4i	−0.614626	+	1.06456i
$910$	−165.201	+	286.137i	−0.00601799	+	0.0104235i
$911$	31428.8			1.14301			0.571506	−	0.820598i	$-0.306359\pi$
$911$	31428.8			1.14301			0.571506	+	0.820598i	$0.306359\pi$
$912$	−503.993	−	905.751i	−0.0182992	−	0.0328864i
$913$	24360.5			0.883038
$914$	−3074.04	+	5324.39i	−0.111247	+	0.192686i
$915$	140.427	−	243.226i	0.00507362	−	0.00878777i
$916$	−415.506	−	719.677i	−0.0149877	−	0.0259594i
$917$	−1555.89	+	2694.88i	−0.0560306	+	0.0970479i
$918$	525.343	+	909.921i	0.0188877	+	0.0327145i
$919$	−45902.9			−1.64766			−0.823829	−	0.566838i	$-0.808166\pi$
$919$	−45902.9			−1.64766			−0.823829	+	0.566838i	$0.808166\pi$
$920$	−8353.01			−0.299338
$921$	87.6420	+	151.800i	0.00313562	+	0.00543105i
$922$	−3897.71	−	6751.03i	−0.139224	−	0.241142i
$923$	−9082.65			−0.323899
$924$	164.327			0.00585062
$925$	4402.95	+	7626.14i	0.156506	+	0.271077i
$926$	−5799.37	+	10044.8i	−0.205809	+	0.356472i
$927$	13852.1	+	23992.5i	0.490789	+	0.850072i
$928$	−440.241	+	762.520i	−0.0155729	+	0.0269730i
$929$	22839.3	−	39558.8i	0.806601	−	1.39707i	−0.108604	−	0.994085i	$-0.534638\pi$
$929$	22839.3	−	39558.8i	0.806601	−	1.39707i	0.915205	−	0.402989i	$-0.132029\pi$
$930$	−507.801			−0.0179048
$931$	−27848.7	−	440.806i	−0.980349	−	0.0155176i
$932$	−42477.6			−1.49292
$933$	−818.303	+	1417.34i	−0.0287138	+	0.0497338i
$934$	−8184.16	+	14175.4i	−0.286717	+	0.496609i
$935$	−2966.74	−	5138.54i	−0.103768	−	0.179731i
$936$	−5032.93	+	8717.28i	−0.175755	+	0.304416i
$937$	26754.6	+	46340.4i	0.932802	+	1.61566i	0.778507	+	0.627636i	$0.215977\pi$
$937$	26754.6	+	46340.4i	0.932802	+	1.61566i	0.154295	+	0.988025i	$0.450689\pi$
$938$	−467.947			−0.0162889
$939$	−2197.48			−0.0763707
$940$	−161.396	−	279.546i	−0.00560016	−	0.00969976i
$941$	−15739.6	−	27261.7i	−0.545265	−	0.944427i	−0.998590	−	0.0530820i	$-0.983096\pi$
$941$	−15739.6	−	27261.7i	−0.545265	−	0.944427i	0.453325	−	0.891345i	$-0.350238\pi$
$942$	−804.726			−0.0278338
$943$	13969.9			0.482421
$944$	6744.61	+	11682.0i	0.232541	+	0.402772i
$945$	128.448	−	222.478i	0.00442160	−	0.00765843i
$946$	−4258.03	−	7375.12i	−0.146343	−	0.253473i
$947$	13928.9	−	24125.5i	0.477960	−	0.827851i	−0.521721	−	0.853116i	$-0.674710\pi$
$947$	13928.9	−	24125.5i	0.477960	−	0.827851i	0.999681	+	0.0252654i	$0.00804307\pi$
$948$	−627.382	+	1086.66i	−0.0214941	+	0.0372289i
$949$	25133.6			0.859717
$950$	−2382.90	−	37.7180i	−0.0813805	−	0.00128814i
$951$	3092.27			0.105440
$952$	−1005.06	+	1740.82i	−0.0342167	+	0.0592651i
$953$	−11581.9	+	20060.5i	−0.393679	+	0.681871i	−0.992932	−	0.118689i	$-0.962131\pi$
$953$	−11581.9	+	20060.5i	−0.393679	+	0.681871i	0.599253	+	0.800560i	$0.295464\pi$
$954$	−4301.39	−	7450.22i	−0.145977	−	0.252840i
$955$	11491.3	−	19903.5i	0.389371	−	0.674410i
$956$	863.815	+	1496.17i	0.0292236	+	0.0506168i
$957$	−48.0724			−0.00162378
$958$	8540.81			0.288039
$959$	−854.250	−	1479.60i	−0.0287645	−	0.0498216i
$960$	−65.5399	−	113.518i	−0.00220343	−	0.00381645i
$961$	27521.5			0.923821
$962$	−8993.53			−0.301417
$963$	−17385.0	−	30111.6i	−0.581747	−	1.00762i
$964$	12233.3	−	21188.7i	0.408721	−	0.707926i
$965$	8405.47	+	14558.7i	0.280396	+	0.485660i
$966$	−54.2936	+	94.0392i	−0.00180835	+	0.00313216i
$967$	−6757.44	+	11704.2i	−0.224721	+	0.389227i	−0.956236	−	0.292598i	$-0.905480\pi$
$967$	−6757.44	+	11704.2i	−0.224721	+	0.389227i	0.731515	+	0.681825i	$0.238814\pi$
$968$	−11231.5			−0.372928
$969$	682.428	+	1226.43i	0.0226241	+	0.0406589i
$970$	−3481.27			−0.115234
$971$	−4945.90	+	8566.55i	−0.163462	+	0.283124i	−0.936108	−	0.351713i	$-0.885599\pi$
$971$	−4945.90	+	8566.55i	−0.163462	+	0.283124i	0.772646	+	0.634837i	$0.218933\pi$
$972$	2672.19	−	4628.36i	0.0881795	−	0.152731i
$973$	1839.95	+	3186.88i	0.0606228	+	0.105002i
$974$	4919.51	−	8520.85i	0.161839	−	0.280314i
$975$	102.194	+	177.005i	0.00335674	+	0.00581405i
$976$	5175.39			0.169734
$977$	−51946.1			−1.70102			−0.850512	−	0.525955i	$-0.823708\pi$
$977$	−51946.1			−1.70102			−0.850512	+	0.525955i	$0.823708\pi$
$978$	−274.602	−	475.624i	−0.00897832	−	0.0155509i
$979$	−579.644	−	1003.97i	−0.0189229	−	0.0327754i
$980$	−11224.3			−0.365863
$981$	−38825.2			−1.26360
$982$	12052.3	+	20875.2i	0.391654	+	0.678365i
$983$	26362.4	−	45661.0i	0.855371	−	1.48155i	−0.0209301	−	0.999781i	$-0.506663\pi$
$983$	26362.4	−	45661.0i	0.855371	−	1.48155i	0.876301	−	0.481764i	$-0.160004\pi$
$984$	−439.685	−	761.557i	−0.0142446	−	0.0246723i
$985$	−1034.37	+	1791.59i	−0.0334598	+	0.0579541i
$986$	133.739	−	231.642i	0.00431958	−	0.00748174i
$987$	−9.22530			−0.000297512
$988$	−6298.79	+	10521.7i	−0.202825	+	0.338804i
$989$	−28352.2			−0.911574
$990$	1995.11	−	3455.63i	0.0640493	−	0.110937i
$991$	−26779.5	+	46383.5i	−0.858405	+	1.48680i	0.0150451	+	0.999887i	$0.495211\pi$
$991$	−26779.5	+	46383.5i	−0.858405	+	1.48680i	−0.873450	+	0.486914i	$0.838123\pi$
$992$	−20854.1	−	36120.4i	−0.667459	−	1.15607i
$993$	339.000	−	587.166i	0.0108337	−	0.0187645i
$994$	−609.879	−	1056.34i	−0.0194610	−	0.0337074i
$995$	17912.7			0.570726
$996$	−2322.14			−0.0738754
$997$	−20636.2	−	35742.9i	−0.655521	−	1.13540i	−0.981763	−	0.190110i	$-0.939116\pi$
$997$	−20636.2	−	35742.9i	−0.655521	−	1.13540i	0.326242	−	0.945286i	$-0.394218\pi$
$998$	2248.57	+	3894.63i	0.0713198	+	0.123529i
$999$	6992.67			0.221460

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	95.4.e.c.11.6	✓	20
19.7	even	3	inner	95.4.e.c.26.6	yes	20
19.8	odd	6		1805.4.a.p.1.6		10
19.11	even	3		1805.4.a.r.1.5		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.4.e.c.11.6	✓	20	1.1	even	1	trivial
95.4.e.c.26.6	yes	20	19.7	even	3	inner
1805.4.a.p.1.6		10	19.8	odd	6
1805.4.a.r.1.5		10	19.11	even	3

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:	\( N \)	\(=\)	\( 95 = 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	95.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.575519 - 0.996828i) q^{2} +(-0.184280 + 0.319183i) q^{3} +(3.33756 + 5.78082i) q^{4} +(2.50000 - 4.33013i) q^{5} +(0.212114 + 0.367391i) q^{6} -2.58808 q^{7} +16.8916 q^{8} +(13.4321 + 23.2650i) q^{9} +O(q^{10})\)	\(q+(0.575519 - 0.996828i) q^{2} +(-0.184280 + 0.319183i) q^{3} +(3.33756 + 5.78082i) q^{4} +(2.50000 - 4.33013i) q^{5} +(0.212114 + 0.367391i) q^{6} -2.58808 q^{7} +16.8916 q^{8} +(13.4321 + 23.2650i) q^{9} +(-2.87759 - 4.98414i) q^{10} +25.8086 q^{11} -2.46018 q^{12} +(11.0911 + 19.2104i) q^{13} +(-1.48949 + 2.57987i) q^{14} +(0.921402 + 1.59591i) q^{15} +(-16.9790 + 29.4085i) q^{16} +(22.9903 - 39.8204i) q^{17} +30.9217 q^{18} +(82.8087 + 1.31075i) q^{19} +33.3756 q^{20} +(0.476932 - 0.826071i) q^{21} +(14.8533 - 25.7267i) q^{22} +(-49.4507 - 85.6511i) q^{23} +(-3.11279 + 5.39151i) q^{24} +(-12.5000 - 21.6506i) q^{25} +25.5326 q^{26} -19.8522 q^{27} +(-8.63787 - 14.9612i) q^{28} +(2.52693 + 4.37677i) q^{29} +2.12114 q^{30} -239.400 q^{31} +(87.1099 + 150.879i) q^{32} +(-4.75602 + 8.23766i) q^{33} +(-26.4627 - 45.8348i) q^{34} +(-6.47020 + 11.2067i) q^{35} +(-89.6607 + 155.297i) q^{36} -352.236 q^{37} +(48.9646 - 81.7917i) q^{38} -8.17552 q^{39} +(42.2290 - 73.1428i) q^{40} +(-70.6255 + 122.327i) q^{41} +(-0.548967 - 0.950839i) q^{42} +(143.336 - 248.265i) q^{43} +(86.1376 + 149.195i) q^{44} +134.321 q^{45} -113.839 q^{46} +(-4.83575 - 8.37576i) q^{47} +(-6.25779 - 10.8388i) q^{48} -336.302 q^{49} -28.7759 q^{50} +(8.47332 + 14.6762i) q^{51} +(-74.0346 + 128.232i) q^{52} +(-139.106 - 240.939i) q^{53} +(-11.4253 + 19.7892i) q^{54} +(64.5215 - 111.754i) q^{55} -43.7168 q^{56} +(-15.6784 + 26.1896i) q^{57} +5.81718 q^{58} +(198.616 - 344.013i) q^{59} +(-6.15046 + 10.6529i) q^{60} +(-76.2027 - 131.987i) q^{61} +(-137.779 + 238.641i) q^{62} +(-34.7633 - 60.2118i) q^{63} -71.1306 q^{64} +110.911 q^{65} +(5.47435 + 9.48186i) q^{66} +(78.5416 + 136.038i) q^{67} +306.926 q^{68} +36.4511 q^{69} +(7.44745 + 12.8994i) q^{70} +(-204.728 + 354.599i) q^{71} +(226.889 + 392.984i) q^{72} +(566.525 - 981.249i) q^{73} +(-202.719 + 351.119i) q^{74} +9.21402 q^{75} +(268.802 + 483.077i) q^{76} -66.7947 q^{77} +(-4.70516 + 8.14958i) q^{78} +(255.014 - 441.698i) q^{79} +(84.8951 + 147.043i) q^{80} +(-359.008 + 621.820i) q^{81} +(81.2926 + 140.803i) q^{82} +943.890 q^{83} +6.36715 q^{84} +(-114.952 - 199.102i) q^{85} +(-164.985 - 285.762i) q^{86} -1.86265 q^{87} +435.949 q^{88} +(-22.4593 - 38.9007i) q^{89} +(77.3042 - 133.895i) q^{90} +(-28.7048 - 49.7181i) q^{91} +(330.089 - 571.731i) q^{92} +(44.1168 - 76.4125i) q^{93} -11.1323 q^{94} +(212.697 - 355.295i) q^{95} -64.2106 q^{96} +(302.447 - 523.853i) q^{97} +(-193.548 + 335.235i) q^{98} +(346.663 + 600.438i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 3 q^{2} - 5 q^{3} - 43 q^{4} + 50 q^{5} + 9 q^{6} + 6 q^{7} + 96 q^{8} - 97 q^{9}+O(q^{10}) \) 20 * q - 3 * q^2 - 5 * q^3 - 43 * q^4 + 50 * q^5 + 9 * q^6 + 6 * q^7 + 96 * q^8 - 97 * q^9	\( 20 q - 3 q^{2} - 5 q^{3} - 43 q^{4} + 50 q^{5} + 9 q^{6} + 6 q^{7} + 96 q^{8} - 97 q^{9} + 15 q^{10} - 36 q^{11} + 186 q^{12} + 14 q^{13} + 68 q^{14} + 25 q^{15} + 9 q^{16} - 144 q^{17} - 22 q^{18} + 96 q^{19} - 430 q^{20} + 46 q^{21} - 136 q^{22} + 321 q^{23} - 416 q^{24} - 250 q^{25} - 46 q^{26} + 1006 q^{27} + 130 q^{28} - 178 q^{29} + 90 q^{30} + 604 q^{31} - 202 q^{32} + 1099 q^{33} - 751 q^{34} + 15 q^{35} - 526 q^{36} - 774 q^{37} - 12 q^{38} - 1216 q^{39} + 240 q^{40} - 388 q^{41} + 143 q^{42} - 514 q^{43} - 1246 q^{44} - 970 q^{45} + 3650 q^{46} + 522 q^{47} + 4 q^{48} + 1582 q^{49} + 150 q^{50} - 1080 q^{51} + 569 q^{52} - 681 q^{53} - 321 q^{54} - 90 q^{55} - 3184 q^{56} + 514 q^{57} + 1198 q^{58} - 891 q^{59} + 465 q^{60} + 1110 q^{61} - 1921 q^{62} - 727 q^{63} + 952 q^{64} + 140 q^{65} + 3312 q^{66} - 691 q^{67} - 228 q^{68} + 172 q^{69} - 340 q^{70} + 382 q^{71} - 2678 q^{72} - 797 q^{73} + 404 q^{74} + 250 q^{75} + 462 q^{76} + 2390 q^{77} + 1000 q^{78} - 660 q^{79} - 45 q^{80} - 2454 q^{81} - 1155 q^{82} - 2026 q^{83} + 10756 q^{84} + 720 q^{85} + 858 q^{86} + 312 q^{87} - 98 q^{88} - 2957 q^{89} - 55 q^{90} - 3110 q^{91} + 98 q^{92} + 1500 q^{93} - 6374 q^{94} + 945 q^{95} - 584 q^{96} - 2881 q^{97} + 4062 q^{98} + 2723 q^{99}+O(q^{100}) \) 20 * q - 3 * q^2 - 5 * q^3 - 43 * q^4 + 50 * q^5 + 9 * q^6 + 6 * q^7 + 96 * q^8 - 97 * q^9 + 15 * q^10 - 36 * q^11 + 186 * q^12 + 14 * q^13 + 68 * q^14 + 25 * q^15 + 9 * q^16 - 144 * q^17 - 22 * q^18 + 96 * q^19 - 430 * q^20 + 46 * q^21 - 136 * q^22 + 321 * q^23 - 416 * q^24 - 250 * q^25 - 46 * q^26 + 1006 * q^27 + 130 * q^28 - 178 * q^29 + 90 * q^30 + 604 * q^31 - 202 * q^32 + 1099 * q^33 - 751 * q^34 + 15 * q^35 - 526 * q^36 - 774 * q^37 - 12 * q^38 - 1216 * q^39 + 240 * q^40 - 388 * q^41 + 143 * q^42 - 514 * q^43 - 1246 * q^44 - 970 * q^45 + 3650 * q^46 + 522 * q^47 + 4 * q^48 + 1582 * q^49 + 150 * q^50 - 1080 * q^51 + 569 * q^52 - 681 * q^53 - 321 * q^54 - 90 * q^55 - 3184 * q^56 + 514 * q^57 + 1198 * q^58 - 891 * q^59 + 465 * q^60 + 1110 * q^61 - 1921 * q^62 - 727 * q^63 + 952 * q^64 + 140 * q^65 + 3312 * q^66 - 691 * q^67 - 228 * q^68 + 172 * q^69 - 340 * q^70 + 382 * q^71 - 2678 * q^72 - 797 * q^73 + 404 * q^74 + 250 * q^75 + 462 * q^76 + 2390 * q^77 + 1000 * q^78 - 660 * q^79 - 45 * q^80 - 2454 * q^81 - 1155 * q^82 - 2026 * q^83 + 10756 * q^84 + 720 * q^85 + 858 * q^86 + 312 * q^87 - 98 * q^88 - 2957 * q^89 - 55 * q^90 - 3110 * q^91 + 98 * q^92 + 1500 * q^93 - 6374 * q^94 + 945 * q^95 - 584 * q^96 - 2881 * q^97 + 4062 * q^98 + 2723 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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