LMFDB - Embedded newform 69.7.f.a.7.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [69,7,Mod(7,69)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(69, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 19]))

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

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

chi := DirichletCharacter("69.7");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 69 = 3 \cdot 23 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	69.f (of order $22$, degree $10$, 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:	$15.8737317698$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$24$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			7.20
Character	$\chi$	$=$	69.7
Dual form			69.7.f.a.10.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(6.34640 - 7.32413i) q^{2} +(13.1138 - 8.42776i) q^{3} +(-4.25801 - 29.6151i) q^{4} +(79.9255 - 36.5007i) q^{5} +(21.4997 - 149.533i) q^{6} +(-34.3232 - 116.894i) q^{7} +(277.849 + 178.563i) q^{8} +(100.946 - 221.041i) q^{9} +O(q^{10})$	\(q+(6.34640 - 7.32413i) q^{2} +(13.1138 - 8.42776i) q^{3} +(-4.25801 - 29.6151i) q^{4} +(79.9255 - 36.5007i) q^{5} +(21.4997 - 149.533i) q^{6} +(-34.3232 - 116.894i) q^{7} +(277.849 + 178.563i) q^{8} +(100.946 - 221.041i) q^{9} +(239.903 - 817.033i) q^{10} +(1331.17 - 1153.47i) q^{11} +(-305.428 - 352.483i) q^{12} +(-2552.02 - 749.340i) q^{13} +(-1073.98 - 490.468i) q^{14} +(740.511 - 1152.26i) q^{15} +(4908.45 - 1441.25i) q^{16} +(2066.67 + 297.142i) q^{17} +(-978.288 - 2142.15i) q^{18} +(-2203.06 + 316.753i) q^{19} +(-1421.30 - 2211.58i) q^{20} +(-1435.26 - 1243.66i) q^{21} -17070.1i q^{22} +(4268.24 - 11393.8i) q^{23} +5148.55 q^{24} +(-5176.42 + 5973.91i) q^{25} +(-21684.4 + 13935.7i) q^{26} +(-539.088 - 3749.44i) q^{27} +(-3315.68 + 1514.22i) q^{28} +(-5683.62 + 39530.4i) q^{29} +(-3739.71 - 12736.3i) q^{30} +(-20746.6 - 13333.0i) q^{31} +(11814.1 - 25869.2i) q^{32} +(7735.66 - 26345.2i) q^{33} +(15292.2 - 13250.8i) q^{34} +(-7010.01 - 8089.99i) q^{35} +(-6975.97 - 2048.33i) q^{36} +(8549.41 + 3904.38i) q^{37} +(-11661.6 + 18145.8i) q^{38} +(-39782.0 + 11681.1i) q^{39} +(28724.9 + 4130.02i) q^{40} +(-7153.06 - 15663.0i) q^{41} +(-18217.5 + 2619.28i) q^{42} +(32938.7 + 51253.7i) q^{43} +(-39828.3 - 34511.4i) q^{44} -21351.4i q^{45} +(-56361.6 - 103571. i) q^{46} -27056.0 q^{47} +(52222.2 - 60267.6i) q^{48} +(86486.5 - 55581.5i) q^{49} +(10902.1 + 75825.6i) q^{50} +(29606.2 - 13520.7i) q^{51} +(-11325.3 + 78769.0i) q^{52} +(69929.4 + 238158. i) q^{53} +(-30882.7 - 19847.1i) q^{54} +(64292.3 - 140780. i) q^{55} +(11336.3 - 38607.7i) q^{56} +(-26221.1 + 22720.7i) q^{57} +(253456. + 292503. i) q^{58} +(247140. + 72566.9i) q^{59} +(-37277.4 - 17024.0i) q^{60} +(8137.85 - 12662.7i) q^{61} +(-229319. + 67334.1i) q^{62} +(-29303.1 - 4213.15i) q^{63} +(21515.5 + 47112.4i) q^{64} +(-231323. + 33259.2i) q^{65} +(-143862. - 223854. i) q^{66} +(240994. + 208822. i) q^{67} -62469.9i q^{68} +(-40050.9 - 185388. i) q^{69} -103740. q^{70} +(-38509.2 + 44442.0i) q^{71} +(67517.3 - 43390.8i) q^{72} +(70725.9 + 491909. i) q^{73} +(82854.2 - 37838.2i) q^{74} +(-17536.1 + 121967. i) q^{75} +(18761.3 + 63895.3i) q^{76} +(-180524. - 116016. i) q^{77} +(-166919. + 365501. i) q^{78} +(-244482. + 832629. i) q^{79} +(339704. - 294355. i) q^{80} +(-38668.9 - 44626.3i) q^{81} +(-160114. - 47013.7i) q^{82} +(-660482. - 301632. i) q^{83} +(-30719.9 + 47801.0i) q^{84} +(176025. - 51685.7i) q^{85} +(584431. + 84028.5i) q^{86} +(258619. + 566296. i) q^{87} +(575832. - 82792.2i) q^{88} +(-301763. - 469553. i) q^{89} +(-156380. - 135504. i) q^{90} +324035. i q^{91} +(-355602. - 77889.6i) q^{92} -384435. q^{93} +(-171708. + 198162. i) q^{94} +(-164519. + 105730. i) q^{95} +(-63091.4 - 438810. i) q^{96} +(234785. - 107223. i) q^{97} +(141791. - 986181. i) q^{98} +(-120587. - 410681. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 20 q^{2} - 816 q^{4} + 324 q^{6} + 940 q^{8} - 5832 q^{9}+O(q^{10}) $ 240 * q + 20 * q^2 - 816 * q^4 + 324 * q^6 + 940 * q^8 - 5832 * q^9	\( 240 q + 20 q^{2} - 816 q^{4} + 324 q^{6} + 940 q^{8} - 5832 q^{9} - 384 q^{13} + 33816 q^{16} + 22880 q^{17} + 4860 q^{18} - 31680 q^{19} - 157696 q^{20} + 36488 q^{23} + 39204 q^{24} + 200664 q^{25} + 99032 q^{26} - 202752 q^{28} - 181712 q^{29} - 128496 q^{31} + 439300 q^{32} - 400026 q^{34} + 368744 q^{35} + 42282 q^{36} + 446688 q^{37} + 550550 q^{38} - 52488 q^{39} - 156750 q^{40} - 606080 q^{41} - 1274130 q^{42} - 429000 q^{43} - 867482 q^{44} + 309288 q^{46} + 1111152 q^{47} + 837864 q^{48} + 722136 q^{49} + 1786926 q^{50} + 463320 q^{51} - 812550 q^{52} - 367840 q^{53} - 354294 q^{54} - 398088 q^{55} - 3696550 q^{56} - 1240272 q^{57} + 1903134 q^{58} + 545800 q^{59} + 2450250 q^{60} - 495264 q^{61} + 488776 q^{62} - 2699808 q^{64} - 290400 q^{67} + 23328 q^{69} - 392616 q^{70} + 255392 q^{71} + 228420 q^{72} + 1346880 q^{73} - 5387470 q^{74} + 365472 q^{75} + 2123022 q^{76} + 6134240 q^{77} + 171072 q^{78} + 4025472 q^{79} + 10626462 q^{80} - 1417176 q^{81} + 2025492 q^{82} - 2474560 q^{83} - 8866152 q^{85} - 15634300 q^{86} - 611712 q^{87} - 10636560 q^{88} - 5901720 q^{89} + 6566394 q^{92} - 2484432 q^{93} + 13931490 q^{94} + 8183072 q^{95} - 4682124 q^{96} + 12319560 q^{97} + 14139580 q^{98} + 2993760 q^{99}+O(q^{100}) \) 240 * q + 20 * q^2 - 816 * q^4 + 324 * q^6 + 940 * q^8 - 5832 * q^9 - 384 * q^13 + 33816 * q^16 + 22880 * q^17 + 4860 * q^18 - 31680 * q^19 - 157696 * q^20 + 36488 * q^23 + 39204 * q^24 + 200664 * q^25 + 99032 * q^26 - 202752 * q^28 - 181712 * q^29 - 128496 * q^31 + 439300 * q^32 - 400026 * q^34 + 368744 * q^35 + 42282 * q^36 + 446688 * q^37 + 550550 * q^38 - 52488 * q^39 - 156750 * q^40 - 606080 * q^41 - 1274130 * q^42 - 429000 * q^43 - 867482 * q^44 + 309288 * q^46 + 1111152 * q^47 + 837864 * q^48 + 722136 * q^49 + 1786926 * q^50 + 463320 * q^51 - 812550 * q^52 - 367840 * q^53 - 354294 * q^54 - 398088 * q^55 - 3696550 * q^56 - 1240272 * q^57 + 1903134 * q^58 + 545800 * q^59 + 2450250 * q^60 - 495264 * q^61 + 488776 * q^62 - 2699808 * q^64 - 290400 * q^67 + 23328 * q^69 - 392616 * q^70 + 255392 * q^71 + 228420 * q^72 + 1346880 * q^73 - 5387470 * q^74 + 365472 * q^75 + 2123022 * q^76 + 6134240 * q^77 + 171072 * q^78 + 4025472 * q^79 + 10626462 * q^80 - 1417176 * q^81 + 2025492 * q^82 - 2474560 * q^83 - 8866152 * q^85 - 15634300 * q^86 - 611712 * q^87 - 10636560 * q^88 - 5901720 * q^89 + 6566394 * q^92 - 2484432 * q^93 + 13931490 * q^94 + 8183072 * q^95 - 4682124 * q^96 + 12319560 * q^97 + 14139580 * q^98 + 2993760 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/69\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{19}{22}\right)$	$1$

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 $

$2$	6.34640	−	7.32413i	0.793300	−	0.915517i	−0.204694	−	0.978826i	$-0.565620\pi$
$2$	6.34640	−	7.32413i	0.793300	−	0.915517i	0.997994	+	0.0633094i	$0.0201655\pi$
$3$	13.1138	−	8.42776i	0.485698	−	0.312139i
$3$	13.1138	−	8.42776i	0.485698	−	0.312139i
$4$	−4.25801	−	29.6151i	−0.0665315	−	0.462736i
$5$	79.9255	−	36.5007i	0.639404	−	0.292006i	−0.0692104	−	0.997602i	$-0.522048\pi$
$5$	79.9255	−	36.5007i	0.639404	−	0.292006i	0.708614	+	0.705596i	$0.249321\pi$
$6$	21.4997	−	149.533i	0.0995355	−	0.692284i
$7$	−34.3232	−	116.894i	−0.100068	−	0.340799i	0.894207	−	0.447654i	$-0.147740\pi$
$7$	−34.3232	−	116.894i	−0.100068	−	0.340799i	−0.994275	+	0.106855i	$0.965922\pi$
$8$	277.849	+	178.563i	0.542674	+	0.348755i
$9$	100.946	−	221.041i	0.138472	−	0.303211i
$10$	239.903	−	817.033i	0.239903	−	0.817033i
$11$	1331.17	−	1153.47i	1.00013	−	0.866618i	0.00906057	−	0.999959i	$-0.497116\pi$
$11$	1331.17	−	1153.47i	1.00013	−	0.866618i	0.991070	+	0.133341i	$0.0425704\pi$
$12$	−305.428	−	352.483i	−0.176752	−	0.203983i
$13$	−2552.02	−	749.340i	−1.16159	−	0.341074i	−0.356541	−	0.934280i	$-0.616044\pi$
$13$	−2552.02	−	749.340i	−1.16159	−	0.341074i	−0.805051	+	0.593206i	$0.797862\pi$
$14$	−1073.98	−	490.468i	−0.391390	−	0.178742i
$15$	740.511	−	1152.26i	0.219411	−	0.341410i
$16$	4908.45	−	1441.25i	1.19835	−	0.351868i
$17$	2066.67	+	297.142i	0.420653	+	0.0604808i	0.349391	−	0.936977i	$-0.386388\pi$
$17$	2066.67	+	297.142i	0.420653	+	0.0604808i	0.0712618	+	0.997458i	$0.477297\pi$
$18$	−978.288	−	2142.15i	−0.167745	−	0.367310i
$19$	−2203.06	+	316.753i	−0.321193	+	0.0461806i	−0.301026	−	0.953616i	$-0.597329\pi$
$19$	−2203.06	+	316.753i	−0.321193	+	0.0461806i	−0.0201674	+	0.999797i	$0.506420\pi$
$20$	−1421.30	−	2211.58i	−0.177662	−	0.276448i
$21$	−1435.26	−	1243.66i	−0.154979	−	0.134290i
$22$		−	17070.1i		−	1.60312i
$23$	4268.24	−	11393.8i	0.350804	−	0.936449i
$23$	4268.24	−	11393.8i	0.350804	−	0.936449i
$24$	5148.55			0.372436
$25$	−5176.42	+	5973.91i	−0.331291	+	0.382330i
$26$	−21684.4	+	13935.7i	−1.23375	+	0.792883i
$27$	−539.088	−	3749.44i	−0.0273885	−	0.190491i
$28$	−3315.68	+	1514.22i	−0.151042	+	0.0689787i
$29$	−5683.62	+	39530.4i	−0.233040	+	1.62083i	0.451788	+	0.892126i	$0.350787\pi$
$29$	−5683.62	+	39530.4i	−0.233040	+	1.62083i	−0.684828	+	0.728705i	$0.740123\pi$
$30$	−3739.71	−	12736.3i	−0.138508	−	0.471714i
$31$	−20746.6	−	13333.0i	−0.696404	−	0.447552i	0.143953	−	0.989585i	$-0.454019\pi$
$31$	−20746.6	−	13333.0i	−0.696404	−	0.447552i	−0.840357	+	0.542033i	$0.817655\pi$
$32$	11814.1	−	25869.2i	0.360537	−	0.789465i
$33$	7735.66	−	26345.2i	0.215256	−	0.733095i
$34$	15292.2	−	13250.8i	0.389075	−	0.337136i
$35$	−7010.01	−	8089.99i	−0.163499	−	0.188688i
$36$	−6975.97	−	2048.33i	−0.149519	−	0.0439028i
$37$	8549.41	+	3904.38i	0.168784	+	0.0770810i	0.498015	−	0.867168i	$-0.334062\pi$
$37$	8549.41	+	3904.38i	0.168784	+	0.0770810i	−0.329231	+	0.944249i	$0.606790\pi$
$38$	−11661.6	+	18145.8i	−0.212523	+	0.330693i
$39$	−39782.0	+	11681.1i	−0.670645	+	0.196919i
$40$	28724.9	+	4130.02i	0.448826	+	0.0645315i
$41$	−7153.06	−	15663.0i	−0.103786	−	0.227260i	0.850614	−	0.525791i	$-0.176231\pi$
$41$	−7153.06	−	15663.0i	−0.103786	−	0.227260i	−0.954400	+	0.298531i	$0.903503\pi$
$42$	−18217.5	+	2619.28i	−0.245890	+	0.0353536i
$43$	32938.7	+	51253.7i	0.414287	+	0.644643i	0.984200	−	0.177062i	$-0.0566593\pi$
$43$	32938.7	+	51253.7i	0.414287	+	0.644643i	−0.569912	+	0.821705i	$0.693023\pi$
$44$	−39828.3	−	34511.4i	−0.467556	−	0.405140i
$45$		−	21351.4i		−	0.234309i
$46$	−56361.6	−	103571.i	−0.579041	−	1.06405i
$47$	−27056.0			−0.260598			−0.130299	−	0.991475i	$-0.541594\pi$
$47$	−27056.0			−0.260598			−0.130299	+	0.991475i	$0.541594\pi$
$48$	52222.2	−	60267.6i	0.472206	−	0.544954i
$49$	86486.5	−	55581.5i	0.735123	−	0.472435i
$50$	10902.1	+	75825.6i	0.0872166	+	0.606605i
$51$	29606.2	−	13520.7i	0.223189	−	0.101927i
$52$	−11325.3	+	78769.0i	−0.0805450	+	0.560203i
$53$	69929.4	+	238158.i	0.469712	+	1.59969i	0.764830	+	0.644233i	$0.222823\pi$
$53$	69929.4	+	238158.i	0.469712	+	1.59969i	−0.295117	+	0.955461i	$0.595359\pi$
$54$	−30882.7	−	19847.1i	−0.196125	−	0.126042i
$55$	64292.3	−	140780.i	0.386430	−	0.846163i
$56$	11336.3	−	38607.7i	0.0645514	−	0.219842i
$57$	−26221.1	+	22720.7i	−0.141588	+	0.122687i
$58$	253456.	+	292503.i	1.29903	+	1.49916i
$59$	247140.	+	72566.9i	1.20334	+	0.353332i	0.821128	−	0.570744i	$-0.193345\pi$
$59$	247140.	+	72566.9i	1.20334	+	0.353332i	0.382209	+	0.924076i	$0.375163\pi$
$60$	−37277.4	−	17024.0i	−0.172580	−	0.0788148i
$61$	8137.85	−	12662.7i	0.0358525	−	0.0557876i	−0.822865	−	0.568237i	$-0.807626\pi$
$61$	8137.85	−	12662.7i	0.0358525	−	0.0557876i	0.858717	+	0.512450i	$0.171262\pi$
$62$	−229319.	+	67334.1i	−0.962199	+	0.282527i
$63$	−29303.1	−	4213.15i	−0.117190	−	0.0168494i
$64$	21515.5	+	47112.4i	0.0820752	+	0.179720i
$65$	−231323.	+	33259.2i	−0.842322	+	0.121108i
$66$	−143862.	−	223854.i	−0.500398	−	0.778634i
$67$	240994.	+	208822.i	0.801274	+	0.694308i	0.955909	−	0.293663i	$-0.0948745\pi$
$67$	240994.	+	208822.i	0.801274	+	0.694308i	−0.154634	+	0.987972i	$0.549420\pi$
$68$		−	62469.9i		−	0.198675i
$69$	−40050.9	−	185388.i	−0.121917	−	0.564331i
$70$	−103740.			−0.302450
$71$	−38509.2	+	44442.0i	−0.107594	+	0.124171i	−0.806992	−	0.590562i	$-0.798906\pi$
$71$	−38509.2	+	44442.0i	−0.107594	+	0.124171i	0.699398	+	0.714733i	$0.253452\pi$
$72$	67517.3	−	43390.8i	0.180891	−	0.116252i
$73$	70725.9	+	491909.i	0.181807	+	1.26449i	0.852488	+	0.522747i	$0.175093\pi$
$73$	70725.9	+	491909.i	0.181807	+	1.26449i	−0.670681	+	0.741746i	$0.733998\pi$
$74$	82854.2	−	37838.2i	0.204465	−	0.0933761i
$75$	−17536.1	+	121967.i	−0.0415672	+	0.289106i
$76$	18761.3	+	63895.3i	0.0427389	+	0.145555i
$77$	−180524.	−	116016.i	−0.395423	−	0.254123i
$78$	−166919.	+	365501.i	−0.351740	+	0.770203i
$79$	−244482.	+	832629.i	−0.495868	+	1.68877i	0.207743	+	0.978184i	$0.433388\pi$
$79$	−244482.	+	832629.i	−0.495868	+	1.68877i	−0.703610	+	0.710586i	$0.748430\pi$
$80$	339704.	−	294355.i	0.663484	−	0.574912i
$81$	−38668.9	−	44626.3i	−0.0727623	−	0.0839722i
$82$	−160114.	−	47013.7i	−0.290394	−	0.0852674i
$83$	−660482.	−	301632.i	−1.15512	−	0.527525i	−0.256625	−	0.966511i	$-0.582611\pi$
$83$	−660482.	−	301632.i	−1.15512	−	0.527525i	−0.898494	+	0.438985i	$0.855338\pi$
$84$	−30719.9	+	47801.0i	−0.0518300	+	0.0806491i
$85$	176025.	−	51685.7i	0.286628	−	0.0841616i
$86$	584431.	+	84028.5i	0.918836	+	0.132109i
$87$	258619.	+	566296.i	0.392737	+	0.859975i
$88$	575832.	−	82792.2i	0.844983	−	0.121490i
$89$	−301763.	−	469553.i	−0.428052	−	0.666062i	0.558501	−	0.829504i	$-0.311377\pi$
$89$	−301763.	−	469553.i	−0.428052	−	0.666062i	−0.986553	+	0.163442i	$0.947740\pi$
$90$	−156380.	−	135504.i	−0.214513	−	0.185877i
$91$			324035.i			0.429999i
$92$	−355602.	−	77889.6i	−0.456668	−	0.100027i
$93$	−384435.			−0.477941
$94$	−171708.	+	198162.i	−0.206732	+	0.238582i
$95$	−164519.	+	105730.i	−0.191887	+	0.123318i
$96$	−63091.4	−	438810.i	−0.0713110	−	0.495979i
$97$	234785.	−	107223.i	0.257249	−	0.117482i	−0.282616	−	0.959233i	$-0.591202\pi$
$97$	234785.	−	107223.i	0.257249	−	0.117482i	0.539866	+	0.841751i	$0.318475\pi$
$98$	141791.	−	986181.i	0.150651	−	1.04780i
$99$	−120587.	−	410681.i	−0.124278	−	0.423252i
$100$	198959.	+	127863.i	0.198959	+	0.127863i
$101$	372064.	−	814707.i	0.361122	−	0.790747i	−0.638652	−	0.769495i	$-0.720508\pi$
$101$	372064.	−	814707.i	0.361122	−	0.790747i	0.999774	−	0.0212512i	$-0.00676497\pi$
$102$	88865.4	−	302648.i	0.0837398	−	0.285192i
$103$	−307574.	+	266514.i	−0.281473	+	0.243898i	−0.784142	−	0.620581i	$-0.786897\pi$
$103$	−307574.	+	266514.i	−0.281473	+	0.243898i	0.502669	+	0.864479i	$0.332351\pi$
$104$	−575271.	−	663899.i	−0.511414	−	0.590203i
$105$	−160109.	−	47012.1i	−0.138308	−	0.0406109i
$106$	2.18810e6	+	999271.i	1.83717	+	0.839007i
$107$	506641.	−	788349.i	0.413570	−	0.643528i	−0.570502	−	0.821296i	$-0.693251\pi$
$107$	506641.	−	788349.i	0.413570	−	0.643528i	0.984072	+	0.177768i	$0.0568878\pi$
$108$	−108745.	+	31930.3i	−0.0863250	+	0.0253473i
$109$	−583658.	−	83917.4i	−0.450691	−	0.0647996i	−0.0867680	−	0.996229i	$-0.527654\pi$
$109$	−583658.	−	83917.4i	−0.450691	−	0.0647996i	−0.363923	+	0.931429i	$0.618563\pi$
$110$	−623070.	−	1.36433e6i	−0.468122	−	1.02504i
$111$	145021.	−	20850.8i	0.106038	−	0.0152460i
$112$	−336947.	−	524300.i	−0.239832	−	0.373186i
$113$	−2.06372e6	−	1.78822e6i	−1.43026	−	1.23933i	−0.926931	−	0.375232i	$-0.877563\pi$
$113$	−2.06372e6	−	1.78822e6i	−1.43026	−	1.23933i	−0.503328	−	0.864095i	$-0.667891\pi$
$114$			336242.i			0.226954i
$115$	−74740.2	−	1.06645e6i	−0.0491429	−	0.701206i
$116$	1.19490e6			0.765522
$117$	−423250.	+	488457.i	−0.264265	+	0.304978i
$118$	2.09994e6	−	1.34955e6i	1.27809	−	0.821377i
$119$	−36200.5	−	251780.i	−0.0214820	−	0.149410i
$120$	411501.	−	187926.i	0.238137	−	0.108753i
$121$	189415.	−	1.31741e6i	0.106920	−	0.743642i
$122$	−41097.6	−	139965.i	−0.0226327	−	0.0770799i
$123$	−225808.	−	145118.i	−0.121346	−	0.0779841i
$124$	−306520.	+	671185.i	−0.160766	+	0.352028i
$125$	−582467.	+	1.98370e6i	−0.298223	+	1.01565i
$126$	−216827.	+	187881.i	−0.108393	+	0.0939231i
$127$	−1.45659e6	−	1.68100e6i	−0.711093	−	0.820645i	0.279113	−	0.960258i	$-0.409960\pi$
$127$	−1.45659e6	−	1.68100e6i	−0.711093	−	0.820645i	−0.990206	+	0.139613i	$0.955414\pi$
$128$	2.22798e6	+	654195.i	1.06239	+	0.311944i
$129$	863907.	+	394533.i	0.402437	+	0.183787i
$130$	−1.22447e6	+	1.90531e6i	−0.557338	+	0.867234i
$131$	−1.53309e6	+	450155.i	−0.681950	+	0.200239i	−0.604318	−	0.796743i	$-0.706554\pi$
$131$	−1.53309e6	+	450155.i	−0.681950	+	0.200239i	−0.0776323	+	0.996982i	$0.524736\pi$
$132$	−813156.	−	116914.i	−0.353551	−	0.0508329i
$133$	112643.	+	246653.i	0.0478793	+	0.104841i
$134$	3.05888e6	−	439801.i	1.27130	−	0.182786i
$135$	−179944.	−	279999.i	−0.0731369	−	0.113803i
$136$	521164.	+	451591.i	0.207185	+	0.179526i
$137$			4.63498e6i			1.80255i	0.433251	+	0.901273i	$0.357366\pi$
$137$			4.63498e6i			1.80255i	−0.433251	+	0.901273i	$0.642634\pi$
$138$	−1.61198e6	−	883206.i	−0.613371	−	0.336066i
$139$	−103335.			−0.0384773			−0.0192386	−	0.999815i	$-0.506124\pi$
$139$	−103335.			−0.0384773			−0.0192386	+	0.999815i	$0.506124\pi$
$140$	−209737.	+	242050.i	−0.0764349	+	0.0882105i
$141$	−354809.	+	228022.i	−0.126572	+	0.0813428i
$142$	81104.3	+	564093.i	0.0283256	+	0.197009i
$143$	−4.26152e6	+	1.94617e6i	−1.45732	+	0.665538i
$144$	176913.	−	1.23046e6i	0.0592477	−	0.412077i
$145$	988624.	+	3.36695e6i	0.324285	+	1.10441i
$146$	4.05166e6	+	2.60385e6i	1.30189	+	0.836675i
$147$	665743.	−	1.45777e6i	0.209582	−	0.458921i
$148$	79225.3	−	269817.i	0.0244387	−	0.0832307i
$149$	−2.16399e6	+	1.87511e6i	−0.654179	+	0.566849i	−0.917439	−	0.397876i	$-0.869748\pi$
$149$	−2.16399e6	+	1.87511e6i	−0.654179	+	0.566849i	0.263261	+	0.964725i	$0.415202\pi$
$150$	782008.	+	902485.i	0.231706	+	0.267403i
$151$	−1.04975e6	−	308234.i	−0.304898	−	0.0895260i	0.125705	−	0.992068i	$-0.459881\pi$
$151$	−1.04975e6	−	308234.i	−0.304898	−	0.0895260i	−0.430603	+	0.902542i	$0.641699\pi$
$152$	−668679.	−	305376.i	−0.190409	−	0.0869568i
$153$	274302.	−	426823.i	0.0765870	−	0.119172i
$154$	−1.99539e6	+	585899.i	−0.546343	+	0.160421i
$155$	−2.14485e6	−	308382.i	−0.575971	−	0.0828122i
$156$	515328.	+	1.12841e6i	0.135741	+	0.297231i
$157$	−2.99973e6	+	431296.i	−0.775146	+	0.111449i	−0.518524	−	0.855063i	$-0.673518\pi$
$157$	−2.99973e6	+	431296.i	−0.775146	+	0.111449i	−0.256621	+	0.966512i	$0.582609\pi$
$158$	4.54671e6	+	7.07482e6i	1.15273	+	1.79368i
$159$	2.92418e6	+	2.53381e6i	0.727465	+	0.630352i
$160$		−	2.49883e6i		−	0.610066i
$161$	−1.47836e6	−	107861.i	−0.354245	−	0.0258456i
$162$	−572257.			−0.134600
$163$	3.14968e6	−	3.63492e6i	0.727283	−	0.839329i	−0.264880	−	0.964281i	$-0.585332\pi$
$163$	3.14968e6	−	3.63492e6i	0.727283	−	0.839329i	0.992163	+	0.124952i	$0.0398777\pi$
$164$	−433404.	+	278532.i	−0.0982566	+	0.0631457i
$165$	−343344.	−	2.38801e6i	−0.0764325	−	0.531600i
$166$	−6.40088e6	+	2.92318e6i	−1.39931	+	0.639045i
$167$	−103111.	+	717153.i	−0.0221389	+	0.153979i	−0.997892	−	0.0648940i	$-0.979329\pi$
$167$	−103111.	+	717153.i	−0.0221389	+	0.153979i	0.975753	+	0.218873i	$0.0702381\pi$
$168$	−176715.	−	601835.i	−0.0372687	−	0.126926i
$169$	1.89071e6	+	1.21509e6i	0.391710	+	0.251737i
$170$	738574.	−	1.61725e6i	0.150331	−	0.329178i
$171$	−152375.	+	518941.i	−0.0304737	+	0.103784i
$172$	1.37763e6	−	1.19372e6i	0.270737	−	0.234595i
$173$	1.89219e6	+	2.18370e6i	0.365448	+	0.421750i	0.908458	−	0.417977i	$-0.137261\pi$
$173$	1.89219e6	+	2.18370e6i	0.365448	+	0.421750i	−0.543009	+	0.839727i	$0.682715\pi$
$174$	5.78893e6	+	1.69978e6i	1.09888	+	0.322660i
$175$	875985.	+	400049.i	0.163449	+	0.0746447i
$176$	4.87157e6	−	7.58030e6i	0.893574	−	1.39043i
$177$	3.85253e6	−	1.13121e6i	0.694747	−	0.203996i
$178$	−5.35418e6	−	769815.i	−0.949364	−	0.136498i
$179$	217144.	+	475479.i	0.0378607	+	0.0829035i	0.927617	−	0.373532i	$-0.121853\pi$
$179$	217144.	+	475479.i	0.0378607	+	0.0829035i	−0.889757	+	0.456435i	$0.849126\pi$
$180$	−632324.	+	90914.4i	−0.108423	+	0.0155889i
$181$	−2.24627e6	−	3.49526e6i	−0.378813	−	0.589445i	0.598531	−	0.801100i	$-0.295751\pi$
$181$	−2.24627e6	−	3.49526e6i	−0.378813	−	0.589445i	−0.977345	+	0.211654i	$0.932115\pi$
$182$	2.37328e6	+	2.05646e6i	0.393672	+	0.341118i
$183$		−	234641.i		−	0.0382869i
$184$	3.22043e6	−	2.40360e6i	0.516964	−	0.385841i
$185$	825828.			0.130429
$186$	−2.43978e6	+	2.81565e6i	−0.379150	+	0.437563i
$187$	3.09384e6	−	1.98829e6i	0.473122	−	0.304057i
$188$	115205.	+	801268.i	0.0173380	+	0.120588i
$189$	−419784.	+	191709.i	−0.0621785	+	0.0283960i
$190$	−269723.	+	1.87597e6i	−0.0393240	+	0.273504i
$191$	84455.1	+	287628.i	0.0121206	+	0.0412791i	0.965331	−	0.261028i	$-0.0840614\pi$
$191$	84455.1	+	287628.i	0.0121206	+	0.0412791i	−0.953211	+	0.302307i	$0.902243\pi$
$192$	679203.	+	436497.i	0.0959613	+	0.0616706i
$193$	4.71202e6	−	1.03179e7i	0.655444	−	1.43522i	−0.231264	−	0.972891i	$-0.574286\pi$
$193$	4.71202e6	−	1.03179e7i	0.655444	−	1.43522i	0.886708	−	0.462330i	$-0.152987\pi$
$194$	704724.	−	2.40007e6i	0.0965193	−	0.328714i
$195$	−2.75323e6	+	2.38569e6i	−0.371312	+	0.321743i
$196$	−2.01431e6	−	2.32464e6i	−0.267522	−	0.308737i
$197$	−5.43399e6	−	1.59556e6i	−0.710755	−	0.208697i	−0.0936819	−	0.995602i	$-0.529864\pi$
$197$	−5.43399e6	−	1.59556e6i	−0.710755	−	0.208697i	−0.617073	+	0.786906i	$0.711682\pi$
$198$	−3.77318e6	−	1.72315e6i	−0.486084	−	0.221987i
$199$	2.41966e6	−	3.76506e6i	0.307040	−	0.477763i	−0.653105	−	0.757268i	$-0.726534\pi$
$199$	2.41966e6	−	3.76506e6i	0.307040	−	0.477763i	0.960144	+	0.279504i	$0.0901701\pi$
$200$	−2.50498e6	+	735529.i	−0.313123	+	0.0919411i
$201$	4.92026e6	+	707426.i	0.605898	+	0.0871150i
$202$	−3.60575e6	−	7.89550e6i	−0.437464	−	0.957912i
$203$	4.81595e6	−	692429.i	0.575697	−	0.0827727i
$204$	−526481.	−	819221.i	−0.0620144	−	0.0964963i
$205$	−1.14342e6	−	990781.i	−0.132723	−	0.115005i
$206$			3.94411e6i			0.451178i
$207$	−2.08762e6	−	2.09361e6i	−0.235365	−	0.236039i
$208$	−1.36064e7			−1.51201
$209$	−2.56730e6	+	2.96282e6i	−0.281214	+	0.324538i
$210$	−1.36044e6	+	874299.i	−0.146899	+	0.0944066i
$211$	951540.	+	6.61811e6i	0.101293	+	0.704509i	0.975667	+	0.219257i	$0.0703632\pi$
$211$	951540.	+	6.61811e6i	0.101293	+	0.704509i	−0.874374	+	0.485252i	$0.838728\pi$
$212$	6.75531e6	−	3.08505e6i	0.708986	−	0.323783i
$213$	−130457.	+	907352.i	−0.0134999	+	0.0938938i
$214$	−2.55863e6	−	8.71389e6i	−0.261075	−	0.889141i
$215$	4.50344e6	+	2.89419e6i	0.453137	+	0.291213i
$216$	519725.	−	1.13804e6i	0.0515718	−	0.112927i
$217$	−846461.	+	2.88278e6i	−0.0828377	+	0.282119i
$218$	−4.31875e6	+	3.74222e6i	−0.416858	+	0.361210i
$219$	5.07318e6	+	5.85476e6i	0.483001	+	0.557413i
$220$	−4.44299e6	−	1.30458e6i	−0.417260	−	0.122519i
$221$	−5.05152e6	−	2.30695e6i	−0.467999	−	0.213728i
$222$	767645.	−	1.19448e6i	0.0701619	−	0.109174i
$223$	1.58647e7	−	4.65831e6i	1.43060	−	0.420062i	0.527523	−	0.849541i	$-0.323121\pi$
$223$	1.58647e7	−	4.65831e6i	1.43060	−	0.420062i	0.903077	+	0.429479i	$0.141303\pi$
$224$	−3.42945e6	−	493080.i	−0.305127	−	0.0438706i
$225$	797938.	+	1.74724e6i	0.0700522	+	0.153393i
$226$	−2.61943e7	+	3.76618e6i	−2.26925	+	0.326269i
$227$	−173617.	−	270154.i	−0.0148428	−	0.0230958i	0.833753	−	0.552138i	$-0.186188\pi$
$227$	−173617.	−	270154.i	−0.0148428	−	0.0230958i	−0.848596	+	0.529042i	$0.822551\pi$
$228$	784527.	+	679797.i	0.0661917	+	0.0573554i
$229$			1.47003e7i			1.22411i	0.790817	+	0.612053i	$0.209656\pi$
$229$			1.47003e7i			1.22411i	−0.790817	+	0.612053i	$0.790344\pi$
$230$	−8.28513e6	−	6.22069e6i	−0.680951	−	0.511275i
$231$	−3.34511e6			−0.271378
$232$	−8.63785e6	+	9.96861e6i	−0.691738	+	0.798309i
$233$	1.14793e7	−	7.37733e6i	0.907506	−	0.583219i	−0.00150145	−	0.999999i	$-0.500478\pi$
$233$	1.14793e7	−	7.37733e6i	0.907506	−	0.583219i	0.909007	+	0.416780i	$0.136842\pi$
$234$	891408.	+	6.19988e6i	0.0695711	+	0.483878i
$235$	−2.16247e6	+	987566.i	−0.166627	+	0.0760961i
$236$	1.09675e6	−	7.62808e6i	0.0834397	−	0.580336i
$237$	3.81110e6	+	1.29794e7i	0.286289	+	0.975012i
$238$	−2.07381e6	−	1.33276e6i	−0.153829	−	0.0988600i
$239$	944182.	−	2.06747e6i	0.0691611	−	0.151442i	−0.871894	−	0.489694i	$-0.837108\pi$
$239$	944182.	−	2.06747e6i	0.0691611	−	0.151442i	0.941055	+	0.338252i	$0.109836\pi$
$240$	1.97407e6	−	6.72306e6i	0.142800	−	0.486333i
$241$	1.01306e7	−	8.77824e6i	0.723745	−	0.627129i	−0.213036	−	0.977044i	$-0.568335\pi$
$241$	1.01306e7	−	8.77824e6i	0.723745	−	0.627129i	0.936781	+	0.349916i	$0.113790\pi$
$242$	−8.44676e6	−	9.74809e6i	−0.595997	−	0.687817i
$243$	−883197.	−	259330.i	−0.0615515	−	0.0180732i
$244$	−409660.	−	187085.i	−0.0282003	−	0.0128786i
$245$	4.88371e6	−	7.59920e6i	0.332087	−	0.516737i
$246$	−2.49593e6	+	732872.i	−0.167659	+	0.0492292i
$247$	5.85961e6	+	842485.i	0.388846	+	0.0559077i
$248$	−3.38364e6	−	7.40913e6i	−0.221834	−	0.485750i
$249$	−1.12035e7	+	1.61083e6i	−0.725701	+	0.104340i
$250$	1.08323e7	+	1.68554e7i	0.693268	+	1.07875i
$251$	1.45158e7	+	1.25780e7i	0.917951	+	0.795409i	0.979239	−	0.202711i	$-0.0649752\pi$
$251$	1.45158e7	+	1.25780e7i	0.917951	+	0.795409i	−0.0612875	+	0.998120i	$0.519521\pi$
$252$			885755.i			0.0553493i
$253$	−7.46059e6	−	2.00904e7i	−0.460693	−	1.24058i
$254$	−2.15559e7			−1.31542
$255$	1.87278e6	−	2.16130e6i	0.112945	−	0.130345i
$256$	1.61425e7	−	1.03742e7i	0.962170	−	0.618349i
$257$	−3.69408e6	−	2.56929e7i	−0.217624	−	1.51361i	−0.746772	−	0.665080i	$-0.768397\pi$
$257$	−3.69408e6	−	2.56929e7i	−0.217624	−	1.51361i	0.529148	−	0.848530i	$-0.322512\pi$
$258$	8.37231e6	−	3.82351e6i	0.487513	−	0.222640i
$259$	162956.	−	1.13338e6i	0.00937932	−	0.0652346i
$260$	1.96995e6	+	6.70903e6i	0.112082	+	0.381716i
$261$	8.16409e6	+	5.24674e6i	0.459184	+	0.295099i
$262$	−6.43258e6	+	1.40854e7i	−0.357669	+	0.783186i
$263$	676282.	−	2.30320e6i	0.0371758	−	0.126609i	−0.938814	−	0.344423i	$-0.888074\pi$
$263$	676282.	−	2.30320e6i	0.0371758	−	0.126609i	0.975990	+	0.217814i	$0.0698926\pi$
$264$	6.85362e6	−	5.93870e6i	0.372485	−	0.322760i
$265$	1.42821e7	+	1.64824e7i	0.767456	+	0.885691i
$266$	2.52139e6	+	740348.i	0.133966	+	0.0393361i
$267$	−7.91456e6	−	3.61446e6i	−0.415808	−	0.189893i
$268$	5.15814e6	−	8.02623e6i	0.267972	−	0.416972i
$269$	2.88708e7	−	8.47723e6i	1.48321	−	0.435509i	0.562840	−	0.826566i	$-0.309709\pi$
$269$	2.88708e7	−	8.47723e6i	1.48321	−	0.435509i	0.920367	+	0.391057i	$0.127890\pi$
$270$	−3.19274e6	−	459047.i	−0.162208	−	0.0233220i
$271$	−1.17377e7	−	2.57020e7i	−0.589760	−	1.29139i	−0.935587	−	0.353096i	$-0.885129\pi$
$271$	−1.17377e7	−	2.57020e7i	−0.589760	−	1.29139i	0.345827	−	0.938298i	$-0.387599\pi$
$272$	1.05724e7	−	1.52008e6i	0.525372	−	0.0755371i
$273$	2.73089e6	+	4.24935e6i	0.134220	+	0.208850i
$274$	3.39472e7	+	2.94154e7i	1.65026	+	1.42996i
$275$			1.39232e7i			0.669483i
$276$	−5.31975e6	+	1.97550e6i	−0.253025	+	0.0939613i
$277$	−6.72173e6			−0.316258			−0.158129	−	0.987418i	$-0.550546\pi$
$277$	−6.72173e6			−0.316258			−0.158129	+	0.987418i	$0.550546\pi$
$278$	−655807.	+	756841.i	−0.0305240	+	0.0352266i
$279$	−5.04142e6	+	3.23992e6i	−0.232135	+	0.149184i
$280$	−503155.	−	3.49952e6i	−0.0229207	−	0.159417i
$281$	−2.41113e7	+	1.10113e7i	−1.08668	+	0.496270i	−0.876505	−	0.481393i	$-0.840131\pi$
$281$	−2.41113e7	+	1.10113e7i	−1.08668	+	0.496270i	−0.210176	+	0.977664i	$0.567404\pi$
$282$	−581696.	+	4.04578e6i	−0.0259387	+	0.180408i
$283$	2.42094e6	+	8.24497e6i	0.106813	+	0.363773i	0.995502	−	0.0947380i	$-0.0302013\pi$
$283$	2.42094e6	+	8.24497e6i	0.106813	+	0.363773i	−0.888689	+	0.458510i	$0.848383\pi$
$284$	1.48013e6	+	951221.i	0.0646166	+	0.0415266i
$285$	−1.26641e6	+	2.77306e6i	−0.0547067	+	0.119791i
$286$	−1.27913e7	+	4.35631e7i	−0.546784	+	1.86218i
$287$	−1.58540e6	+	1.37375e6i	−0.0670644	+	0.0581116i
$288$	−4.52556e6	−	5.22277e6i	−0.189450	−	0.218637i
$289$	−1.89770e7	−	5.57215e6i	−0.786202	−	0.230850i
$290$	3.09342e7	+	1.41272e7i	1.26836	+	0.579243i
$291$	2.17528e6	−	3.38481e6i	0.0882748	−	0.137358i
$292$	1.42668e7	−	4.18911e6i	0.573031	−	0.168257i
$293$	−2.67614e7	−	3.84770e6i	−1.06391	−	0.152967i	−0.411940	−	0.911211i	$-0.635149\pi$
$293$	−2.67614e7	−	3.84770e6i	−1.06391	−	0.152967i	−0.651971	+	0.758244i	$0.726058\pi$
$294$	−6.45186e6	−	1.41276e7i	−0.253889	−	0.555938i
$295$	2.24015e7	−	3.22086e6i	0.872593	−	0.125460i
$296$	1.67827e6	+	2.61144e6i	0.0647122	+	0.100694i
$297$	−5.04248e6	−	4.36933e6i	−0.192475	−	0.166781i
$298$			2.77495e7i			1.04859i
$299$	−1.94304e7	+	2.58787e7i	−0.726890	+	0.968121i
$300$	3.68672e6			0.136545
$301$	4.86068e6	−	5.60953e6i	0.178237	−	0.205696i
$302$	−8.91966e6	+	5.73232e6i	−0.323838	+	0.208118i
$303$	−1.98696e6	−	1.38196e7i	−0.0714268	−	0.496784i
$304$	−1.03571e7	+	4.72993e6i	−0.368653	+	0.168358i
$305$	188222.	−	1.30911e6i	0.00663393	−	0.0461400i
$306$	−1.38527e6	−	4.71781e6i	−0.0483472	−	0.164656i
$307$	−9.91119e6	−	6.36953e6i	−0.342539	−	0.220137i	0.358048	−	0.933703i	$-0.383442\pi$
$307$	−9.91119e6	−	6.36953e6i	−0.342539	−	0.220137i	−0.700588	+	0.713566i	$0.747079\pi$
$308$	−2.66714e6	+	5.84023e6i	−0.0912839	+	0.199884i
$309$	−1.78736e6	+	6.08718e6i	−0.0605809	+	0.206320i
$310$	−1.58707e7	+	1.37520e7i	−0.532734	+	0.461616i
$311$	2.45610e7	+	2.83449e7i	0.816515	+	0.942309i	0.999165	−	0.0408692i	$-0.0130127\pi$
$311$	2.45610e7	+	2.83449e7i	0.816515	+	0.942309i	−0.182649	+	0.983178i	$0.558467\pi$
$312$	−1.31392e7	−	3.85802e6i	−0.432618	−	0.127028i
$313$	−1.31356e7	−	5.99881e6i	−0.428367	−	0.195629i	0.189552	−	0.981871i	$-0.439297\pi$
$313$	−1.31356e7	−	5.99881e6i	−0.428367	−	0.195629i	−0.617918	+	0.786242i	$0.712024\pi$
$314$	−1.58786e7	+	2.47076e7i	−0.512889	+	0.798071i
$315$	−2.49585e6	+	732847.i	−0.0798521	+	0.0234467i
$316$	2.56994e7	+	3.69502e6i	0.814446	+	0.117100i
$317$	−1.32376e7	−	2.89864e7i	−0.415559	−	0.909947i	−0.995453	−	0.0952552i	$-0.969633\pi$
$317$	−1.32376e7	−	2.89864e7i	−0.415559	−	0.909947i	0.579894	−	0.814692i	$-0.303094\pi$
$318$	3.71160e7	−	5.33647e6i	1.15420	−	0.165948i
$319$	3.80312e7	+	5.91778e7i	1.17157	+	1.82300i
$320$	3.43928e6	+	2.98015e6i	0.104958	+	0.0909469i
$321$		−	1.46081e7i		−	0.441652i
$322$	−1.01723e7	+	1.01432e7i	−0.304684	+	0.303814i
$323$	−4.64713e6			−0.137904
$324$	−1.15696e6	+	1.33520e6i	−0.0340160	+	0.0392566i
$325$	1.76868e7	−	1.13666e7i	0.515228	−	0.331117i
$326$	−6.63355e6	−	4.61373e7i	−0.191467	−	1.33168i
$327$	−8.36124e6	+	3.81845e6i	−0.239126	+	0.109205i
$328$	809360.	−	5.62922e6i	0.0229361	−	0.159524i
$329$	928649.	+	3.16269e6i	0.0260774	+	0.0888114i
$330$	−1.96691e7	−	1.26406e7i	−0.547322	−	0.351743i
$331$	1.62597e7	−	3.56038e7i	0.448362	−	0.981776i	−0.541625	−	0.840620i	$-0.682191\pi$
$331$	1.62597e7	−	3.56038e7i	0.448362	−	0.981776i	0.989987	−	0.141156i	$-0.0450819\pi$
$332$	−6.12053e6	+	2.08446e7i	−0.167253	+	0.569613i
$333$	1.72605e6	−	1.49563e6i	0.0467436	−	0.0405035i
$334$	4.59814e6	+	5.30653e6i	0.123408	+	0.142420i
$335$	2.68837e7	+	7.89377e6i	0.715080	+	0.209966i
$336$	−8.83735e6	−	4.03588e6i	−0.232972	−	0.106395i
$337$	3.20187e7	−	4.98220e7i	0.836592	−	1.30176i	−0.114678	−	0.993403i	$-0.536584\pi$
$337$	3.20187e7	−	4.98220e7i	0.836592	−	1.30176i	0.951270	−	0.308360i	$-0.0997801\pi$
$338$	2.08987e7	−	6.13640e6i	0.541213	−	0.158914i
$339$	−4.21340e7	−	6.05795e6i	−1.08152	−	0.155499i
$340$	−2.28020e6	−	4.99294e6i	−0.0580144	−	0.127034i
$341$	−4.29965e7	+	6.18197e6i	−1.08435	+	0.155906i
$342$	2.83376e6	+	4.40942e6i	0.0708411	+	0.110231i
$343$	−2.02978e7	−	1.75882e7i	−0.502999	−	0.435851i
$344$			2.01224e7i			0.494316i
$345$	−9.96788e6	−	1.33553e7i	−0.242742	−	0.325235i
$346$	2.80023e7			0.676029
$347$	−5.23332e7	+	6.03958e7i	−1.25253	+	1.44550i	−0.405383	+	0.914147i	$0.632862\pi$
$347$	−5.23332e7	+	6.03958e7i	−1.25253	+	1.44550i	−0.847150	+	0.531353i	$0.821684\pi$
$348$	1.56697e7	−	1.00703e7i	0.371812	−	0.238949i
$349$	−3.32773e6	−	2.31449e7i	−0.0782837	−	0.544475i	−0.990789	−	0.135411i	$-0.956764\pi$
$349$	−3.32773e6	−	2.31449e7i	−0.0782837	−	0.544475i	0.912506	−	0.409064i	$-0.134145\pi$
$350$	8.48936e6	−	3.87696e6i	0.198003	−	0.0904248i
$351$	−1.43384e6	+	9.97259e6i	−0.0331574	+	0.230615i
$352$	−1.41127e7	−	4.80635e7i	−0.323581	−	1.10202i
$353$	−5.47643e7	−	3.51949e7i	−1.24501	−	0.800121i	−0.258852	−	0.965917i	$-0.583344\pi$
$353$	−5.47643e7	−	3.51949e7i	−1.24501	−	0.800121i	−0.986160	+	0.165796i	$0.946981\pi$
$354$	1.61646e7	−	3.53956e7i	0.364381	−	0.797883i
$355$	−1.45570e6	+	4.95766e6i	−0.0325377	+	0.110813i
$356$	−1.26210e7	+	1.09361e7i	−0.279732	+	0.242389i
$357$	−2.59667e6	−	2.99672e6i	−0.0570705	−	0.0658629i
$358$	4.86056e6	+	1.42719e6i	0.105934	+	0.0311051i
$359$	4.43930e7	+	2.02736e7i	0.959469	+	0.438175i	0.832680	−	0.553755i	$-0.186805\pi$
$359$	4.43930e7	+	2.02736e7i	0.959469	+	0.438175i	0.126790	+	0.991930i	$0.459533\pi$
$360$	3.81256e6	−	5.93246e6i	0.0817164	−	0.127153i
$361$	−4.03870e7	+	1.18587e7i	−0.858461	+	0.252067i
$362$	−3.98554e7	−	5.73035e6i	−0.840160	−	0.120797i
$363$	−8.61883e6	−	1.88726e7i	−0.180189	−	0.394559i
$364$	9.59634e6	−	1.37975e6i	0.198976	−	0.0286085i
$365$	2.36079e7	+	3.67345e7i	0.485487	+	0.755433i
$366$	−1.71854e6	−	1.48912e6i	−0.0350523	−	0.0303730i
$367$			6.16261e7i			1.24671i	0.781937	+	0.623357i	$0.214232\pi$
$367$			6.16261e7i			1.24671i	−0.781937	+	0.623357i	$0.785768\pi$
$368$	4.52915e6	−	6.20774e7i	0.0908810	−	1.24563i
$369$	−4.18423e6			−0.0832792
$370$	5.24103e6	−	6.04848e6i	0.103469	−	0.119410i
$371$	2.54390e7	−	1.63486e7i	0.498171	−	0.320155i
$372$	1.63693e6	+	1.13851e7i	0.0317981	+	0.221161i
$373$	5.41095e7	−	2.47110e7i	1.04267	−	0.476171i	0.180916	−	0.983498i	$-0.442094\pi$
$373$	5.41095e7	−	2.47110e7i	1.04267	−	0.476171i	0.861754	+	0.507327i	$0.169366\pi$
$374$	5.07224e6	−	3.52782e7i	0.0969583	−	0.674359i
$375$	9.07976e6	+	3.09228e7i	0.172179	+	0.586388i
$376$	−7.51750e6	−	4.83120e6i	−0.141420	−	0.0908849i
$377$	4.41264e7	−	9.66234e7i	0.823521	−	1.80326i
$378$	−1.26001e6	+	4.29121e6i	−0.0233292	+	0.0794519i
$379$	−2.18345e7	+	1.89197e7i	−0.401076	+	0.347534i	−0.831923	−	0.554891i	$-0.812760\pi$
$379$	−2.18345e7	+	1.89197e7i	−0.401076	+	0.347534i	0.430847	+	0.902425i	$0.358215\pi$
$380$	3.83173e6	+	4.42206e6i	0.0698304	+	0.0805886i
$381$	−3.32685e7	−	9.76852e6i	−0.601532	−	0.176626i
$382$	2.64261e6	+	1.20684e6i	0.0474070	+	0.0216501i
$383$	4.08128e7	−	6.35060e7i	0.726441	−	1.13036i	−0.259898	−	0.965636i	$-0.583689\pi$
$383$	4.08128e7	−	6.35060e7i	0.726441	−	1.13036i	0.986339	−	0.164729i	$-0.0526748\pi$
$384$	3.47308e7	−	1.01979e7i	0.613368	−	0.180101i
$385$	−1.86631e7	−	2.68335e6i	−0.327040	−	0.0470213i
$386$	−4.56652e7	−	9.99929e7i	−0.794006	−	1.73863i
$387$	1.46542e7	−	2.10695e6i	0.252830	−	0.0363514i
$388$	−4.17513e6	−	6.49662e6i	−0.0714783	−	0.111222i
$389$	1.59812e7	+	1.38478e7i	0.271494	+	0.235251i	0.779957	−	0.625833i	$-0.215241\pi$
$389$	1.59812e7	+	1.38478e7i	0.271494	+	0.235251i	−0.508463	+	0.861084i	$0.669786\pi$
$390$			3.53055e7i			0.595181i
$391$	1.22066e7	−	2.22789e7i	0.204204	−	0.372703i
$392$	3.39550e7			0.563697
$393$	−1.63109e7	+	1.88237e7i	−0.268719	+	0.310119i
$394$	−4.61724e7	+	2.96732e7i	−0.754907	+	0.485149i
$395$	1.08512e7	+	7.54721e7i	0.176071	+	1.22460i
$396$	−1.16489e7	+	5.31988e6i	−0.187586	+	0.0856676i
$397$	1.29963e7	−	9.03910e7i	0.207705	−	1.44462i	−0.572915	−	0.819614i	$-0.694188\pi$
$397$	1.29963e7	−	9.03910e7i	0.207705	−	1.44462i	0.780620	−	0.625005i	$-0.214903\pi$
$398$	−1.22197e7	−	4.16165e7i	−0.193826	−	0.660110i
$399$	3.55591e6	+	2.28524e6i	0.0559799	+	0.0359761i
$400$	−1.67983e7	+	3.67832e7i	−0.262474	+	0.574737i
$401$	713969.	−	2.43155e6i	0.0110725	−	0.0377095i	−0.953771	−	0.300533i	$-0.902835\pi$
$401$	713969.	−	2.43155e6i	0.0110725	−	0.0377095i	0.964844	+	0.262823i	$0.0846537\pi$
$402$	3.64072e7	−	3.15470e7i	0.560414	−	0.485601i
$403$	4.29547e7	+	4.95723e7i	0.656289	+	0.757398i
$404$	−2.57119e7	−	7.54970e6i	−0.389933	−	0.114495i
$405$	−4.71952e6	−	2.15533e6i	−0.0710449	−	0.0324451i
$406$	2.54925e7	−	3.96671e7i	0.380920	−	0.592724i
$407$	1.58843e7	−	4.66406e6i	0.235606	−	0.0691801i
$408$	1.06404e7	+	1.52985e6i	0.156666	+	0.0225252i
$409$	2.58150e7	+	5.65269e7i	0.377313	+	0.826201i	0.999075	+	0.0429944i	$0.0136898\pi$
$409$	2.58150e7	+	5.65269e7i	0.377313	+	0.826201i	−0.621762	+	0.783206i	$0.713583\pi$
$410$	−1.45132e7	+	2.08669e6i	−0.210578	+	0.0302765i
$411$	3.90625e7	+	6.07824e7i	0.562645	+	0.875493i
$412$	9.20250e6	+	7.97401e6i	0.131587	+	0.114021i
$413$		−	3.13799e7i		−	0.445453i
$414$	−2.85828e7	+	2.00318e6i	−0.402813	+	0.0282305i
$415$	−6.37992e7			−0.892628
$416$	−4.95345e7	+	5.71659e7i	−0.688062	+	0.794066i
$417$	−1.35512e6	+	870885.i	−0.0186883	+	0.0120103i
$418$	5.40699e6	+	3.76064e7i	0.0740332	+	0.514913i
$419$	−1.32467e7	+	6.04955e6i	−0.180080	+	0.0822397i	−0.503415	−	0.864045i	$-0.667923\pi$
$419$	−1.32467e7	+	6.04955e6i	−0.180080	+	0.0822397i	0.323335	+	0.946285i	$0.395196\pi$
$420$	−710526.	+	4.94182e6i	−0.00959030	+	0.0667020i
$421$	−1.13368e7	−	3.86098e7i	−0.151931	−	0.517429i	0.847990	−	0.530012i	$-0.177813\pi$
$421$	−1.13368e7	−	3.86098e7i	−0.151931	−	0.517429i	−0.999921	+	0.0125833i	$0.995995\pi$
$422$	5.45107e7	+	3.50319e7i	0.725345	+	0.466151i
$423$	−2.73120e6	+	5.98048e6i	−0.0360854	+	0.0790160i
$424$	−2.30963e7	+	7.86587e7i	−0.303001	+	1.03193i
$425$	−1.24731e7	+	1.08080e7i	−0.162482	+	0.140792i
$426$	5.81763e6	+	6.71390e6i	0.0752519	+	0.0868453i
$427$	−1.75951e6	−	516640.i	−0.0226000	−	0.00663597i
$428$	−2.55044e7	−	1.16474e7i	−0.325299	−	0.148559i
$429$	−3.94831e7	+	6.14368e7i	−0.500079	+	0.778139i
$430$	4.97780e7	−	1.46161e7i	0.626084	−	0.183835i
$431$	−4.22386e7	−	6.07300e6i	−0.527568	−	0.0758528i	−0.126616	−	0.991952i	$-0.540411\pi$
$431$	−4.22386e7	−	6.07300e6i	−0.527568	−	0.0758528i	−0.400952	+	0.916099i	$0.631321\pi$
$432$	−8.04997e6	−	1.76270e7i	−0.0998489	−	0.218638i
$433$	−6.45818e7	+	9.28546e6i	−0.795511	+	0.114377i	−0.528074	−	0.849198i	$-0.677086\pi$
$433$	−6.45818e7	+	9.28546e6i	−0.795511	+	0.114377i	−0.267437	+	0.963575i	$0.586177\pi$
$434$	1.57419e7	+	2.44949e7i	0.192570	+	0.299644i
$435$	4.13405e7	+	3.58217e7i	0.502236	+	0.435190i
$436$			1.76424e7i			0.212862i
$437$	−5.79419e6	+	2.64532e7i	−0.0694302	+	0.316981i
$438$	7.50775e7			0.893485
$439$	−8.53076e7	+	9.84502e7i	−1.00831	+	1.16365i	−0.0218310	+	0.999762i	$0.506950\pi$
$439$	−8.53076e7	+	9.84502e7i	−1.00831	+	1.16365i	−0.986479	+	0.163890i	$0.947596\pi$
$440$	4.30017e7	−	2.76355e7i	0.504809	−	0.324421i
$441$	−3.55531e6	−	2.47278e7i	−0.0414536	−	0.288316i
$442$	−4.89553e7	+	2.23571e7i	−0.566935	+	0.258910i
$443$	−1.79956e7	+	1.25162e8i	−0.206992	+	1.43966i	0.575908	+	0.817515i	$0.304649\pi$
$443$	−1.79956e7	+	1.25162e8i	−0.206992	+	1.43966i	−0.782900	+	0.622148i	$0.786260\pi$
$444$	−1.23500e6	−	4.20603e6i	−0.0141097	−	0.0480533i
$445$	−4.12576e7	−	2.65147e7i	−0.468192	−	0.300889i
$446$	6.65658e7	−	1.45759e8i	0.750321	−	1.64297i
$447$	−1.25753e7	+	4.28274e7i	−0.140797	+	0.479512i
$448$	4.76868e6	−	4.13208e6i	0.0530352	−	0.0459552i
$449$	6.34026e7	+	7.31705e7i	0.700435	+	0.808345i	0.988811	−	0.149172i	$-0.0476607\pi$
$449$	6.34026e7	+	7.31705e7i	0.700435	+	0.808345i	−0.288376	+	0.957517i	$0.593115\pi$
$450$	1.78611e7	+	5.24448e6i	0.196006	+	0.0575526i
$451$	−2.75888e7	−	1.25994e7i	−0.300748	−	0.137347i
$452$	−4.41711e7	+	6.87315e7i	−0.478324	+	0.744287i
$453$	−1.63639e7	+	4.80489e6i	−0.176033	+	0.0516879i
$454$	−3.08049e6	−	442907.i	−0.0329194	−	0.00473309i
$455$	1.18275e7	+	2.58987e7i	0.125562	+	0.274943i
$456$	−1.13426e7	+	1.63082e6i	−0.119624	+	0.0171993i
$457$	−1.42499e7	−	2.21733e7i	−0.149301	−	0.232318i	0.758545	−	0.651621i	$-0.225911\pi$
$457$	−1.42499e7	−	2.21733e7i	−0.149301	−	0.232318i	−0.907846	+	0.419303i	$0.862274\pi$
$458$	1.07667e8	+	9.32938e7i	1.12069	+	0.971083i
$459$		−	7.90904e6i		−	0.0817872i
$460$	−3.12647e7	+	6.75438e6i	−0.321204	+	0.0693924i
$461$	−1.10666e8			−1.12956			−0.564782	−	0.825240i	$-0.691040\pi$
$461$	−1.10666e8			−1.12956			−0.564782	+	0.825240i	$0.691040\pi$
$462$	−2.12294e7	+	2.45000e7i	−0.215284	+	0.248451i
$463$	1.48647e7	−	9.55298e6i	0.149766	−	0.0962490i	−0.463612	−	0.886039i	$-0.653447\pi$
$463$	1.48647e7	−	9.55298e6i	0.149766	−	0.0962490i	0.613378	+	0.789790i	$0.289810\pi$
$464$	2.90755e7	+	2.02225e8i	0.291054	+	2.02433i
$465$	−3.07261e7	+	1.40322e7i	−0.305597	+	0.139561i
$466$	1.88200e7	−	1.30896e8i	0.185978	−	1.29350i
$467$	−5.37019e7	−	1.82892e8i	−0.527277	−	1.79574i	−0.601952	−	0.798532i	$-0.705610\pi$
$467$	−5.37019e7	−	1.82892e8i	−0.527277	−	1.79574i	0.0746754	−	0.997208i	$-0.476208\pi$
$468$	1.62679e7	+	1.04548e7i	0.158706	+	0.101994i
$469$	1.61384e7	−	3.53382e7i	0.156438	−	0.342551i
$470$	−6.49081e6	+	2.21057e7i	−0.0625181	+	0.212917i
$471$	−3.57032e7	+	3.09370e7i	−0.341699	+	0.296084i
$472$	5.57099e7	+	6.42927e7i	0.529794	+	0.611414i
$473$	1.02967e8	+	3.02338e7i	0.973001	+	0.285699i
$474$	1.19250e8	+	5.44595e7i	1.11975	+	0.511374i
$475$	9.51174e6	−	1.48005e7i	0.0887522	−	0.138101i
$476$	−7.30236e6	+	2.14417e6i	−0.0677084	+	0.0198810i
$477$	5.97016e7	+	8.58379e6i	0.550086	+	0.0790904i
$478$	−9.15027e6	−	2.00363e7i	−0.0837819	−	0.183457i
$479$	9.70494e7	−	1.39536e7i	0.883052	−	0.126964i	0.314154	−	0.949372i	$-0.398279\pi$
$479$	9.70494e7	−	1.39536e7i	0.883052	−	0.126964i	0.568898	+	0.822408i	$0.307370\pi$
$480$	−2.10595e7	−	3.27693e7i	−0.190425	−	0.296308i
$481$	−1.88925e7	−	1.63705e7i	−0.169768	−	0.147104i
$482$		−	1.29908e8i		−	1.16010i
$483$	−2.02960e7	+	1.10448e7i	−0.180123	+	0.0980205i
$484$	−3.98217e7			−0.351224
$485$	1.48516e7	−	1.71396e7i	0.130181	−	0.150237i
$486$	−7.50448e6	+	4.82284e6i	−0.0653751	+	0.0420140i
$487$	5.58802e6	+	3.88655e7i	0.0483806	+	0.336494i	0.999608	+	0.0280032i	$0.00891486\pi$
$487$	5.58802e6	+	3.88655e7i	0.0483806	+	0.336494i	−0.951227	+	0.308491i	$0.900176\pi$
$488$	4.52219e6	−	2.06521e6i	0.0389125	−	0.0177707i
$489$	1.06702e7	−	7.42125e7i	0.0912523	−	0.634674i
$490$	−2.46636e7	−	8.39965e7i	−0.209637	−	0.713958i
$491$	−4.17787e7	−	2.68496e7i	−0.352948	−	0.226826i	0.352137	−	0.935948i	$-0.385455\pi$
$491$	−4.17787e7	−	2.68496e7i	−0.352948	−	0.226826i	−0.705085	+	0.709122i	$0.749091\pi$
$492$	−3.33620e6	+	7.30525e6i	−0.0280128	+	0.0613394i
$493$	−2.34923e7	+	8.00075e7i	−0.196058	+	0.667713i
$494$	4.33579e7	−	3.75698e7i	0.359656	−	0.311644i
$495$	−2.46281e7	−	2.84224e7i	−0.203056	−	0.234339i
$496$	−1.21050e8	−	3.55434e7i	−0.992017	−	0.291282i
$497$	6.51676e6	+	2.97610e6i	0.0530839	+	0.0242426i
$498$	−5.93042e7	+	9.22792e7i	−0.480173	+	0.747164i
$499$	1.70431e8	−	5.00430e7i	1.37166	−	0.402756i	0.488802	−	0.872395i	$-0.337434\pi$
$499$	1.70431e8	−	5.00430e7i	1.37166	−	0.402756i	0.882859	+	0.469639i	$0.155616\pi$
$500$	6.12277e7	+	8.80321e6i	0.489822	+	0.0704257i
$501$	4.69181e6	+	1.02736e7i	0.0373101	+	0.0816978i
$502$	1.84246e8	−	2.64906e7i	1.45642	−	0.209402i
$503$	7.55858e7	+	1.17614e8i	0.593931	+	0.924175i	0.999947	+	0.0103089i	$0.00328148\pi$
$503$	7.55858e7	+	1.17614e8i	0.593931	+	0.924175i	−0.406016	+	0.913866i	$0.633082\pi$
$504$	−7.38953e6	−	6.40306e6i	−0.0577198	−	0.0500145i
$505$		−	7.86965e7i		−	0.611056i
$506$	−1.94492e8	−	7.28591e7i	−1.50124	−	0.562383i
$507$	3.50349e7			0.268830
$508$	−4.35807e7	+	5.02948e7i	−0.332432	+	0.383647i
$509$	−6.64985e7	+	4.27360e7i	−0.504265	+	0.324071i	−0.767920	−	0.640546i	$-0.778708\pi$
$509$	−6.64985e7	+	4.27360e7i	−0.504265	+	0.324071i	0.263655	+	0.964617i	$0.415072\pi$
$510$	−3.94426e6	−	2.74329e7i	−0.0297341	−	0.206805i
$511$	5.50737e7	−	2.51513e7i	0.412745	−	0.188494i
$512$	5.31558e6	−	3.69707e7i	0.0396042	−	0.275453i
$513$	2.37529e6	+	8.08950e6i	0.0175940	+	0.0599197i
$514$	−2.11622e8	−	1.36001e8i	−1.55838	−	1.00151i
$515$	−1.48550e7	+	3.25279e7i	−0.108755	+	0.238141i
$516$	8.00562e6	−	2.72646e7i	0.0582701	−	0.198450i
$517$	−3.60163e7	+	3.12083e7i	−0.260632	+	0.225839i
$518$	−7.26688e6	−	8.38642e6i	−0.0522828	−	0.0603375i
$519$	4.32176e7	+	1.26898e7i	0.309142	+	0.0907723i
$520$	−7.02116e7	−	3.20646e7i	−0.499343	−	0.228042i
$521$	−2.40324e7	+	3.73951e7i	−0.169935	+	0.264425i	−0.915767	−	0.401710i	$-0.868416\pi$
$521$	−2.40324e7	+	3.73951e7i	−0.169935	+	0.264425i	0.745832	+	0.666135i	$0.232052\pi$
$522$	9.02404e7	−	2.64970e7i	0.634439	−	0.186288i
$523$	1.44397e8	+	2.07612e7i	1.00938	+	0.145126i	0.627114	−	0.778927i	$-0.284236\pi$
$523$	1.44397e8	+	2.07612e7i	1.00938	+	0.145126i	0.382262	+	0.924054i	$0.375145\pi$
$524$	1.98593e7	+	4.34858e7i	0.138029	+	0.302241i
$525$	1.48591e7	−	2.13641e6i	0.102686	−	0.0147641i
$526$	−1.25770e7	−	1.95702e7i	−0.0864213	−	0.134474i
$527$	−3.89145e7	−	3.37196e7i	−0.265876	−	0.230383i
$528$		−	1.40463e8i		−	0.954248i
$529$	−1.11600e8	−	9.72627e7i	−0.753872	−	0.657021i
$530$	2.11359e8			1.41969
$531$	4.09880e7	−	4.73027e7i	0.273762	−	0.315938i
$532$	6.82502e6	−	4.38618e6i	0.0453283	−	0.0291307i
$533$	6.51781e6	+	4.53323e7i	0.0430447	+	0.299383i
$534$	−7.67017e7	+	3.50285e7i	−0.503711	+	0.230037i
$535$	1.17182e7	−	8.15020e7i	0.0765244	−	0.532239i
$536$	2.96720e7	+	1.01054e8i	0.192687	+	0.656232i
$537$	6.85482e6	+	4.40533e6i	0.0442663	+	0.0284482i
$538$	1.21137e8	−	2.65253e8i	0.777912	−	1.70339i
$539$	5.10171e7	−	1.73748e8i	0.325799	−	1.10957i
$540$	−7.52599e6	+	6.52131e6i	−0.0477950	+	0.0414146i
$541$	−1.88511e8	−	2.17554e8i	−1.19055	−	1.37396i	−0.910256	−	0.414047i	$-0.864115\pi$
$541$	−1.88511e8	−	2.17554e8i	−1.19055	−	1.37396i	−0.280289	−	0.959916i	$-0.590430\pi$
$542$	−2.62737e8	−	7.71465e7i	−1.65015	−	0.484528i
$543$	−5.89144e7	−	2.69053e7i	−0.367978	−	0.168050i
$544$	3.21026e7	−	4.99526e7i	0.199408	−	0.310285i
$545$	−4.97122e7	+	1.45968e7i	−0.307096	+	0.0901714i
$546$	4.84541e7	+	6.96665e6i	0.297682	+	0.0428002i
$547$	3.28184e7	+	7.18622e7i	0.200519	+	0.439075i	0.983002	−	0.183597i	$-0.0587743\pi$
$547$	3.28184e7	+	7.18622e7i	0.200519	+	0.439075i	−0.782483	+	0.622672i	$0.786047\pi$
$548$	1.37266e8	−	1.97358e7i	0.834104	−	0.119926i
$549$	−1.97750e6	−	3.07704e6i	−0.0119508	−	0.0185959i
$550$	1.01975e8	+	8.83619e7i	0.612923	+	0.531101i
$551$		−	8.88884e7i		−	0.531362i
$552$	2.19752e7	−	5.86614e7i	0.130652	−	0.348767i
$553$	1.05721e8			0.625151
$554$	−4.26588e7	+	4.92309e7i	−0.250888	+	0.289540i
$555$	1.08298e7	−	6.95988e6i	0.0633492	−	0.0407120i
$556$	440003.	+	3.06029e6i	0.00255995	+	0.0178048i
$557$	−1.84590e8	+	8.42993e7i	−1.06817	+	0.487819i	−0.870357	−	0.492421i	$-0.836112\pi$
$557$	−1.84590e8	+	8.42993e7i	−1.06817	+	0.487819i	−0.197816	+	0.980239i	$0.563385\pi$
$558$	−8.26522e6	+	5.74859e7i	−0.0475720	+	0.330871i
$559$	−4.56538e7	−	1.55483e8i	−0.261361	−	0.890115i
$560$	−4.60680e7	−	2.96061e7i	−0.262322	−	0.168584i
$561$	2.38153e7	−	5.21483e7i	0.134886	−	0.295360i
$562$	−7.23720e7	+	2.46476e8i	−0.407720	+	1.38857i
$563$	−1.19736e8	+	1.03752e8i	−0.670965	+	0.581395i	−0.922286	−	0.386509i	$-0.873681\pi$
$563$	−1.19736e8	+	1.03752e8i	−0.670965	+	0.581395i	0.251320	+	0.967904i	$0.419135\pi$
$564$	8.26368e6	+	9.53679e6i	0.0460613	+	0.0531575i
$565$	−2.30215e8	−	6.75972e7i	−1.27640	−	0.374786i
$566$	7.57515e7	+	3.45946e7i	0.417775	+	0.190791i
$567$	−3.88930e6	+	6.05187e6i	−0.0213365	+	0.0332002i
$568$	−1.86354e7	+	5.47186e6i	−0.101694	+	0.0298600i
$569$	2.09264e8	+	3.00877e7i	1.13595	+	0.163325i	0.684528	−	0.728987i	$-0.260008\pi$
$569$	2.09264e8	+	3.00877e7i	1.13595	+	0.163325i	0.451420	+	0.892311i	$0.350918\pi$
$570$	1.22731e7	+	2.68743e7i	0.0662718	+	0.145115i
$571$	−2.48380e8	+	3.57116e7i	−1.33416	+	0.191823i	−0.772220	−	0.635355i	$-0.780854\pi$
$571$	−2.48380e8	+	3.57116e7i	−1.33416	+	0.191823i	−0.561939	+	0.827178i	$0.689945\pi$
$572$	7.57817e7	+	1.17919e8i	0.404927	+	0.630078i
$573$	3.53159e6	+	3.06014e6i	0.0187718	+	0.0162659i
$574$			2.03300e7i			0.107498i
$575$	4.59712e7	+	8.44770e7i	0.241814	+	0.444360i
$576$	1.25857e7			0.0658580
$577$	−2.43805e8	+	2.81366e8i	−1.26916	+	1.46469i	−0.447947	+	0.894060i	$0.647845\pi$
$577$	−2.43805e8	+	2.81366e8i	−1.26916	+	1.46469i	−0.821211	+	0.570625i	$0.806701\pi$
$578$	−1.61247e8	+	1.03627e8i	−0.835040	+	0.536648i
$579$	−2.51639e7	−	1.75019e8i	−0.129641	−	0.901674i
$580$	9.55029e7	−	4.36147e7i	0.489478	−	0.223537i
$581$	−1.25891e7	+	8.75594e7i	−0.0641900	+	0.446452i
$582$	−1.09856e7	−	3.74134e7i	−0.0557254	−	0.189783i
$583$	3.67796e8	+	2.36368e8i	1.85610	+	1.19284i
$584$	−6.81856e7	+	1.49306e8i	−0.342337	+	0.749614i
$585$	−1.59994e7	+	5.44891e7i	−0.0799166	+	0.272171i
$586$	−1.98019e8	+	1.71585e8i	−0.984045	+	0.852679i
$587$	−1.50475e8	−	1.73658e8i	−0.743962	−	0.858578i	0.250007	−	0.968244i	$-0.419567\pi$
$587$	−1.50475e8	−	1.73658e8i	−0.743962	−	0.858578i	−0.993968	+	0.109667i	$0.965022\pi$
$588$	−4.60069e7	−	1.35089e7i	−0.226303	−	0.0664487i
$589$	4.99293e7	+	2.28020e7i	0.244349	+	0.111590i
$590$	1.18579e8	−	1.84513e8i	0.577367	−	0.898401i
$591$	−8.47075e7	+	2.48724e7i	−0.410355	+	0.120491i
$592$	4.75915e7	+	6.84263e6i	0.229385	+	0.0329806i
$593$	−6.59779e7	−	1.44472e8i	−0.316399	−	0.692816i	0.682890	−	0.730521i	$-0.260723\pi$
$593$	−6.59779e7	−	1.44472e8i	−0.316399	−	0.692816i	−0.999289	+	0.0377046i	$0.987995\pi$
$594$	−6.40032e7	+	9.20227e6i	−0.305381	+	0.0439072i
$595$	−1.20835e7	−	1.88023e7i	−0.0573643	−	0.0892606i
$596$	6.47458e7	+	5.61026e7i	0.305825	+	0.264999i
$597$		−	6.97667e7i		−	0.327888i
$598$	6.62261e7	+	3.06548e8i	0.309689	+	1.43349i
$599$	7.44894e7			0.346588			0.173294	−	0.984870i	$-0.444559\pi$
$599$	7.44894e7			0.346588			0.173294	+	0.984870i	$0.444559\pi$
$600$	−2.66511e7	+	3.07570e7i	−0.123385	+	0.142393i
$601$	2.87485e8	−	1.84756e8i	1.32432	−	0.851088i	0.328686	−	0.944439i	$-0.393394\pi$
$601$	2.87485e8	−	1.84756e8i	1.32432	−	0.851088i	0.995633	+	0.0933514i	$0.0297580\pi$
$602$	−1.02371e7	−	7.12006e7i	−0.0469232	−	0.326358i
$603$	7.04855e7	−	3.21897e7i	0.321475	−	0.146813i
$604$	−4.65854e6	+	3.24009e7i	−0.0211417	+	0.147043i
$605$	−3.29473e7	−	1.12208e8i	−0.148783	−	0.506709i
$606$	−1.13827e8	−	7.31520e7i	−0.511477	−	0.328706i
$607$	9.50577e6	−	2.08147e7i	0.0425032	−	0.0930689i	−0.887189	−	0.461406i	$-0.847345\pi$
$607$	9.50577e6	−	2.08147e7i	0.0425032	−	0.0930689i	0.929692	+	0.368337i	$0.120073\pi$
$608$	−1.78330e7	+	6.07336e7i	−0.0793439	+	0.270220i
$609$	5.73200e7	−	4.96681e7i	0.253778	−	0.219900i
$610$	−8.39358e6	−	9.68671e6i	−0.0369792	−	0.0426763i
$611$	6.90475e7	+	2.02742e7i	0.302708	+	0.0888832i
$612$	−1.38084e7	−	6.30608e6i	−0.0602405	−	0.0275109i
$613$	1.31805e8	−	2.05093e8i	0.572205	−	0.890368i	−0.427704	−	0.903919i	$-0.640677\pi$
$613$	1.31805e8	−	2.05093e8i	0.572205	−	0.890368i	0.999908	+	0.0135513i	$0.00431363\pi$
$614$	−1.09552e8	+	3.21673e7i	−0.473275	+	0.138966i
$615$	−2.33447e7	−	3.35647e6i	−0.100361	−	0.0144297i
$616$	−2.94423e7	−	6.44696e7i	−0.125959	−	0.275812i
$617$	2.65119e8	−	3.81183e7i	1.12872	−	0.162285i	0.447442	−	0.894313i	$-0.352335\pi$
$617$	2.65119e8	−	3.81183e7i	1.12872	−	0.162285i	0.681274	+	0.732028i	$0.261426\pi$
$618$	3.32400e7	+	5.17225e7i	0.140830	+	0.219136i
$619$	2.72501e8	+	2.36124e8i	1.14894	+	0.995561i	0.999977	+	0.00671739i	$0.00213823\pi$
$619$	2.72501e8	+	2.36124e8i	1.14894	+	0.995561i	0.148961	+	0.988843i	$0.452407\pi$
$620$			6.48330e7i			0.272033i
$621$	−4.50212e7	−	9.86125e6i	−0.187993	−	0.0411772i
$622$	3.63475e8			1.51044
$623$	−4.45304e7	+	5.13909e7i	−0.184159	+	0.212531i
$624$	−1.78433e8	+	1.14672e8i	−0.734380	+	0.471957i
$625$	8.27533e6	+	5.75562e7i	0.0338958	+	0.235750i
$626$	−1.27300e8	+	5.81358e7i	−0.518924	+	0.236985i
$627$	−8.69722e6	+	6.04905e7i	−0.0352840	+	0.245406i
$628$	2.55458e7	+	8.70010e7i	0.103143	+	0.351273i
$629$	1.65086e7	+	1.06095e7i	0.0663375	+	0.0426326i
$630$	−1.04722e7	+	2.29308e7i	−0.0418808	+	0.0917061i
$631$	−7.20782e7	+	2.45476e8i	−0.286890	+	0.977059i	0.682367	+	0.731010i	$0.260951\pi$
$631$	−7.20782e7	+	2.45476e8i	−0.286890	+	0.977059i	−0.969257	+	0.246049i	$0.920868\pi$
$632$	−2.16606e8	+	1.87690e8i	−0.858062	+	0.743515i
$633$	6.82541e7	+	7.87695e7i	0.269103	+	0.310561i
$634$	−2.96311e8	−	8.70049e7i	−1.16273	−	0.341410i
$635$	−1.77776e8	−	8.11877e7i	−0.694309	−	0.317080i
$636$	6.25880e7	−	9.73889e7i	0.243288	−	0.378563i
$637$	−2.62365e8	+	7.70372e7i	−1.01505	+	0.298045i
$638$	6.74787e8	+	9.70198e7i	2.59839	+	0.373592i
$639$	5.93614e6	+	1.29983e7i	0.0227511	+	0.0498179i
$640$	2.01951e8	−	2.90362e7i	0.770383	−	0.110764i
$641$	−7.57453e7	−	1.17862e8i	−0.287595	−	0.447507i	0.667154	−	0.744920i	$-0.267512\pi$
$641$	−7.57453e7	−	1.17862e8i	−0.287595	−	0.447507i	−0.954749	+	0.297413i	$0.903876\pi$
$642$	−1.06992e8	−	9.27090e7i	−0.404339	−	0.350362i
$643$		−	2.63018e8i		−	0.989357i	−0.869076	−	0.494679i	$-0.835286\pi$
$643$		−	2.63018e8i		−	0.989357i	0.869076	−	0.494679i	$-0.164714\pi$
$644$	3.10057e6	+	4.42412e7i	0.0116087	+	0.165641i
$645$	8.34489e7			0.310987
$646$	−2.94925e7	+	3.40362e7i	−0.109399	+	0.126253i
$647$	−1.07603e8	+	6.91520e7i	−0.397292	+	0.255324i	−0.723998	−	0.689802i	$-0.757698\pi$
$647$	−1.07603e8	+	6.91520e7i	−0.397292	+	0.255324i	0.326706	+	0.945126i	$0.394061\pi$
$648$	−2.77552e6	−	1.93042e7i	−0.0102005	−	0.0709458i
$649$	4.12690e8	−	1.88469e8i	1.50970	−	0.689456i
$650$	2.89969e7	−	2.01678e8i	0.105587	−	0.734374i
$651$	1.31950e7	+	4.49381e7i	0.0478263	+	0.162882i
$652$	−1.21060e8	−	7.78006e7i	−0.436775	−	0.280699i
$653$	2.20421e8	−	4.82656e8i	0.791615	−	1.73340i	0.119646	−	0.992817i	$-0.461824\pi$
$653$	2.20421e8	−	4.82656e8i	0.791615	−	1.73340i	0.671969	−	0.740579i	$-0.265449\pi$
$654$	−2.50969e7	+	8.54722e7i	−0.0897195	+	0.305557i
$655$	−1.06102e8	+	9.19376e7i	−0.377571	+	0.327167i
$656$	−5.76848e7	−	6.65718e7i	−0.204338	−	0.235819i
$657$	1.15871e8	+	3.40229e7i	0.408583	+	0.119971i
$658$	2.90575e7	+	1.32701e7i	0.101996	+	0.0465798i
$659$	−2.37506e8	+	3.69567e8i	−0.829888	+	1.29133i	0.124337	+	0.992240i	$0.460320\pi$
$659$	−2.37506e8	+	3.69567e8i	−0.829888	+	1.29133i	−0.954225	+	0.299090i	$0.903317\pi$
$660$	−6.92593e7	+	2.03364e7i	−0.240905	+	0.0707362i
$661$	1.39729e8	+	2.00900e7i	0.483818	+	0.0695625i	0.379908	−	0.925024i	$-0.375956\pi$
$661$	1.39729e8	+	2.00900e7i	0.483818	+	0.0695625i	0.103910	+	0.994587i	$0.466865\pi$
$662$	−1.57576e8	−	3.45044e8i	−0.543147	−	1.18933i
$663$	−8.56872e7	+	1.23200e7i	−0.294019	+	0.0422735i
$664$	−1.29654e8	−	2.01746e8i	−0.442876	−	0.689129i
$665$	1.80060e7	+	1.56023e7i	0.0612284	+	0.0530547i
$666$		−	2.21337e7i		−	0.0749259i
$667$	4.26142e8	+	2.33483e8i	1.43607	+	0.786825i
$668$	2.16776e7			0.0727248
$669$	1.68789e8	−	1.94792e8i	0.563722	−	0.650569i
$670$	2.28430e8	−	1.46803e8i	0.759500	−	0.488101i
$671$	−3.77318e6	−	2.62431e7i	−0.0124894	−	0.0868654i
$672$	−4.91288e7	+	2.24364e7i	−0.161893	+	0.0739341i
$673$	−8.04689e7	+	5.59673e8i	−0.263987	+	1.83607i	0.238085	+	0.971244i	$0.423480\pi$
$673$	−8.04689e7	+	5.59673e8i	−0.263987	+	1.83607i	−0.502072	+	0.864826i	$0.667429\pi$
$674$	−1.61700e8	−	5.50700e8i	−0.528117	−	1.79860i
$675$	2.51894e7	+	1.61882e7i	0.0819041	+	0.0526366i
$676$	2.79343e7	−	6.11675e7i	0.0904268	−	0.198007i
$677$	−6.06142e7	+	2.06433e8i	−0.195348	+	0.665293i	0.802311	+	0.596906i	$0.203603\pi$
$677$	−6.06142e7	+	2.06433e8i	−0.195348	+	0.665293i	−0.997659	+	0.0683869i	$0.978215\pi$
$678$	−3.11768e8	+	2.70149e8i	−1.00033	+	0.866789i
$679$	−2.05922e7	−	2.37647e7i	−0.0657800	−	0.0759142i
$680$	5.81377e7	+	1.70708e7i	0.184897	+	0.0542908i
$681$	−4.55358e6	−	2.07955e6i	−0.0144182	−	0.00658458i
$682$	−2.27596e8	+	3.54146e8i	−0.717481	+	1.11642i
$683$	4.02450e8	−	1.18170e8i	1.26314	−	0.370890i	0.419475	−	0.907767i	$-0.362214\pi$
$683$	4.02450e8	−	1.18170e8i	1.26314	−	0.370890i	0.843661	+	0.536877i	$0.180396\pi$
$684$	1.60173e7	+	2.30294e6i	0.0500520	+	0.00719640i
$685$	1.69180e8	+	3.70453e8i	0.526354	+	1.15255i
$686$	−2.57636e8	+	3.70425e7i	−0.798058	+	0.114743i
$687$	1.23890e8	+	1.92777e8i	0.382092	+	0.594546i
$688$	2.35548e8	+	2.04103e8i	0.723292	+	0.626736i
$689$		−	6.60183e8i		−	2.01840i
$690$	−1.61076e8	−	1.17521e7i	−0.490325	−	0.0357740i
$691$	5.67214e8			1.71915			0.859573	−	0.511013i	$-0.170729\pi$
$691$	5.67214e8			1.71915			0.859573	+	0.511013i	$0.170729\pi$
$692$	5.66136e7	−	6.53356e7i	0.170845	−	0.197166i
$693$	−4.38673e7	+	2.81918e7i	−0.131808	+	0.0847077i
$694$	1.10219e8	+	7.66591e8i	0.329745	+	2.29343i
$695$	−8.25912e6	+	3.77182e6i	−0.0246025	+	0.0112356i
$696$	−2.92624e7	+	2.03525e8i	−0.0867925	+	0.603655i
$697$	−1.01289e7	−	3.44957e7i	−0.0299132	−	0.101875i
$698$	−1.90635e8	−	1.22514e8i	−0.560579	−	0.360262i
$699$	8.83640e7	−	1.93490e8i	0.258728	−	0.566536i
$700$	8.11755e6	−	2.76458e7i	0.0236663	−	0.0806001i
$701$	−3.71993e8	+	3.22334e8i	−1.07989	+	0.935733i	−0.998143	−	0.0609196i	$-0.980597\pi$
$701$	−3.71993e8	+	3.22334e8i	−1.07989	+	0.935733i	−0.0817510	+	0.996653i	$0.526051\pi$
$702$	6.39409e7	+	7.37917e7i	0.184828	+	0.213303i
$703$	−2.00716e7	−	5.89356e6i	−0.0577719	−	0.0169633i
$704$	8.29836e7	+	3.78973e7i	0.237834	+	0.108615i
$705$	−2.00353e7	+	3.11755e7i	−0.0571779	+	0.0889706i
$706$	−6.05328e8	+	1.77740e8i	−1.72019	+	0.505094i
$707$	−1.08005e8	−	1.55287e7i	−0.305622	−	0.0439418i
$708$	−4.99050e7	−	1.09277e8i	−0.140619	−	0.307913i
$709$	−2.57988e8	+	3.70931e7i	−0.723870	+	0.104077i	−0.494395	−	0.869238i	$-0.664610\pi$
$709$	−2.57988e8	+	3.70931e7i	−0.723870	+	0.104077i	−0.229476	+	0.973314i	$0.573701\pi$
$710$	2.70721e7	+	4.21250e7i	0.0756392	+	0.117697i
$711$	1.59365e8	+	1.38091e8i	0.443389	+	0.384199i
$712$		−	1.84349e8i		−	0.510740i
$713$	−2.40465e8	+	1.79473e8i	−0.663411	+	0.495144i
$714$	−3.84278e7			−0.105573
$715$	−2.69567e8	+	3.11097e8i	−0.737478	+	0.851095i
$716$	1.31568e7	−	8.45535e6i	0.0358435	−	0.0230352i
$717$	−5.04228e6	−	3.50698e7i	−0.0136795	−	0.0951428i
$718$	4.30222e8	−	1.96476e8i	1.16230	−	0.530806i
$719$	9.55636e7	−	6.64659e8i	0.257102	−	1.78818i	−0.296120	−	0.955151i	$-0.595693\pi$
$719$	9.55636e7	−	6.64659e8i	0.257102	−	1.78818i	0.553222	−	0.833034i	$-0.313398\pi$
$720$	−3.07727e7	−	1.04802e8i	−0.0824457	−	0.280784i
$721$	4.17108e7	+	2.68059e7i	0.111287	+	0.0715195i
$722$	−1.69457e8	+	3.71060e8i	−0.450245	+	0.985899i
$723$	5.88707e7	−	2.00495e8i	0.155770	−	0.530504i
$724$	−9.39479e7	+	8.14063e7i	−0.247555	+	0.214507i
$725$	−2.06730e8	−	2.38580e8i	−0.542488	−	0.626065i
$726$	−1.92924e8	−	5.66476e7i	−0.504169	−	0.148037i
$727$	−5.20709e8	−	2.37800e8i	−1.35516	−	0.618882i	−0.400425	−	0.916330i	$-0.631137\pi$
$727$	−5.20709e8	−	2.37800e8i	−1.35516	−	0.618882i	−0.954738	+	0.297448i	$0.903865\pi$
$728$	−5.78606e7	+	9.00329e7i	−0.149965	+	0.233350i
$729$	−1.37677e7	+	4.04255e6i	−0.0355368	+	0.0104345i
$730$	4.18873e8	+	6.02249e7i	1.07675	+	0.154813i
$731$	5.28438e7	+	1.15712e8i	0.135283	+	0.296228i
$732$	−6.94892e6	+	999104.i	−0.0177168	+	0.00254728i
$733$	−2.89650e8	−	4.50704e8i	−0.735464	−	1.14440i	−0.984410	−	0.175887i	$-0.943721\pi$
$733$	−2.89650e8	−	4.50704e8i	−0.735464	−	1.14440i	0.248946	−	0.968517i	$-0.419916\pi$
$734$	4.51358e8	+	3.91104e8i	1.14139	+	0.989018i
$735$		−	1.40813e8i		−	0.354635i
$736$	−2.44322e8	−	2.45023e8i	−0.612816	−	0.614572i
$737$	5.61675e8			1.40308
$738$	−2.65548e7	+	3.06459e7i	−0.0660654	+	0.0762435i
$739$	−1.00847e8	+	6.48101e7i	−0.249878	+	0.160587i	−0.659584	−	0.751631i	$-0.729268\pi$
$739$	−1.00847e8	+	6.48101e7i	−0.249878	+	0.160587i	0.409706	+	0.912217i	$0.365631\pi$
$740$	−3.51639e6	−	2.44570e7i	−0.00867764	−	0.0603543i
$741$	8.39423e7	−	3.83352e7i	0.206313	−	0.0942199i
$742$	4.17063e7	−	2.90074e8i	0.102092	−	0.710062i
$743$	1.66958e8	+	5.68606e8i	0.407043	+	1.38626i	0.866995	+	0.498317i	$0.166048\pi$
$743$	1.66958e8	+	5.68606e8i	0.407043	+	1.38626i	−0.459952	+	0.887944i	$0.652133\pi$
$744$	−1.06815e8	−	6.86458e7i	−0.259366	−	0.166684i
$745$	−1.04515e8	+	2.28856e8i	−0.252761	+	0.553469i
$746$	1.62414e8	−	5.53131e8i	0.391207	−	1.33233i
$747$	−1.33346e8	+	1.15545e8i	−0.319903	+	0.277197i
$748$	−7.20571e7	−	8.31583e7i	−0.172176	−	0.198701i
$749$	−1.09543e8	−	3.21647e7i	−0.260698	−	0.0765480i
$750$	2.84107e8	+	1.29747e8i	0.673438	+	0.307549i
$751$	−1.72085e8	+	2.67770e8i	−0.406279	+	0.632182i	−0.982751	−	0.184935i	$-0.940793\pi$
$751$	−1.72085e8	+	2.67770e8i	−0.406279	+	0.632182i	0.576472	+	0.817117i	$0.304429\pi$
$752$	−1.32803e8	+	3.89946e7i	−0.312288	+	0.0916960i
$753$	2.96362e8	+	4.26105e7i	0.694125	+	0.0998002i
$754$	−4.27639e8	−	9.36398e8i	−0.997615	−	2.18447i
$755$	−9.51523e7	+	1.36808e7i	−0.221095	+	0.0317886i
$756$	7.46492e6	+	1.16156e7i	0.0172767	+	0.0268830i
$757$	7.71696e7	+	6.68678e7i	0.177893	+	0.154145i	0.739256	−	0.673425i	$-0.235177\pi$
$757$	7.71696e7	+	6.68678e7i	0.177893	+	0.154145i	−0.561363	+	0.827570i	$0.689723\pi$
$758$			2.79991e8i			0.642890i
$759$	−2.67154e8	−	2.00586e8i	−0.610993	−	0.458749i
$760$	−6.45910e7			−0.147140
$761$	−4.11853e7	+	4.75304e7i	−0.0934519	+	0.107849i	−0.800549	−	0.599267i	$-0.795459\pi$
$761$	−4.11853e7	+	4.75304e7i	−0.0934519	+	0.107849i	0.707097	+	0.707116i	$0.250004\pi$
$762$	−2.82681e8	+	1.81668e8i	−0.638899	+	0.410595i
$763$	1.02236e7	+	7.11065e7i	0.0230159	+	0.160079i
$764$	8.15852e6	−	3.72587e6i	0.0182949	−	0.00835502i
$765$	6.34439e6	−	4.41262e7i	0.0141712	−	0.0985627i
$766$	−2.06112e8	−	7.01953e8i	−0.458582	−	1.56179i
$767$	−5.76329e8	−	3.70384e8i	−1.27727	−	0.820854i
$768$	1.24260e8	−	2.72091e8i	0.274313	−	0.600662i
$769$	1.58737e8	−	5.40607e8i	0.349058	−	1.18878i	−0.578681	−	0.815554i	$-0.696432\pi$
$769$	1.58737e8	−	5.40607e8i	0.349058	−	1.18878i	0.927739	−	0.373229i	$-0.121749\pi$
$770$	−1.38097e8	+	1.19661e8i	−0.302490	+	0.262109i
$771$	−2.64977e8	−	3.05800e8i	−0.578156	−	0.667228i
$772$	−3.25629e8	−	9.56134e7i	−0.707737	−	0.207810i
$773$	6.26313e8	+	2.86028e8i	1.35598	+	0.619255i	0.954938	−	0.296805i	$-0.0959212\pi$
$773$	6.26313e8	+	2.86028e8i	1.35598	+	0.619255i	0.401041	+	0.916060i	$0.368648\pi$
$774$	7.75696e7	−	1.20701e8i	0.167289	−	0.260307i
$775$	1.87043e8	−	5.49209e7i	0.401825	−	0.117987i
$776$	8.43806e7	+	1.21321e7i	0.180575	+	0.0259628i
$777$	−7.41491e6	−	1.62364e7i	−0.0158068	−	0.0346120i
$778$	2.02846e8	−	2.91648e7i	0.430752	−	0.0619328i
$779$	2.07199e7	+	3.22409e7i	0.0438305	+	0.0682015i
$780$	8.23757e7	+	7.13790e7i	0.173586	+	0.150413i
$781$			1.03579e8i			0.217430i
$782$	−8.57055e7	−	2.30793e8i	−0.179221	−	0.482618i
$783$	1.51281e8			0.315137
$784$	3.44408e8	−	3.97468e8i	0.714702	−	0.824810i
$785$	−2.24012e8	+	1.43964e8i	−0.463087	+	0.297608i
$786$	3.43523e7	+	2.38926e8i	0.0707438	+	0.492034i
$787$	4.74399e8	−	2.16651e8i	0.973240	−	0.444464i	0.135646	−	0.990757i	$-0.456689\pi$
$787$	4.74399e8	−	2.16651e8i	0.973240	−	0.444464i	0.837594	+	0.546293i	$0.183962\pi$
$788$	−2.41148e7	+	1.67722e8i	−0.0492839	+	0.342777i
$789$	−1.05422e7	−	3.59034e7i	−0.0214635	−	0.0730979i
$790$	6.21634e8	+	3.99500e8i	1.26082	+	0.810280i
$791$	−1.38199e8	+	3.02614e8i	−0.279239	+	0.611447i
$792$	3.98274e7	−	1.35640e8i	0.0801691	−	0.273031i
$793$	−3.02566e7	+	2.62175e7i	−0.0606737	+	0.0525741i
$794$	−5.79556e8	−	6.68843e8i	−1.15780	−	1.33617i
$795$	3.26202e8	+	9.57816e7i	0.649211	+	0.190625i
$796$	−1.21806e8	−	5.56268e7i	−0.241506	−	0.110292i
$797$	1.46595e8	−	2.28107e8i	0.289564	−	0.450571i	−0.665745	−	0.746179i	$-0.731886\pi$
$797$	1.46595e8	−	2.28107e8i	0.289564	−	0.450571i	0.955309	+	0.295609i	$0.0955225\pi$
$798$	3.93046e7	−	1.15409e7i	0.0773455	−	0.0227107i
$799$	−5.59159e7	−	8.03949e6i	−0.109621	−	0.0157612i
$800$	9.33856e7	+	2.04486e8i	0.182394	+	0.399387i
$801$	−1.34252e8	+	1.93025e7i	−0.261230	+	0.0375592i
$802$	−1.32779e7	−	2.06608e7i	−0.0257399	−	0.0400520i
$803$	6.61551e8	+	5.73237e8i	1.27766	+	1.10710i
$804$		−	1.48726e8i		−	0.286167i
$805$	−1.22096e8	+	4.53405e7i	−0.234052	+	0.0869158i
$806$	6.35682e8			1.21404
$807$	3.07163e8	−	3.54485e8i	0.584451	−	0.674493i
$808$	2.48854e8	−	1.59929e8i	0.471749	−	0.303174i
$809$	3.42558e7	+	2.38254e8i	0.0646976	+	0.449982i	0.996260	+	0.0864013i	$0.0275367\pi$
$809$	3.42558e7	+	2.38254e8i	0.0646976	+	0.449982i	−0.931563	+	0.363580i	$0.881554\pi$
$810$	−4.57379e7	+	2.08878e7i	−0.0860639	+	0.0393041i
$811$	3.83844e7	−	2.66969e8i	0.0719601	−	0.500494i	−0.921685	−	0.387938i	$-0.873187\pi$
$811$	3.83844e7	−	2.66969e8i	0.0719601	−	0.500494i	0.993645	−	0.112555i	$-0.0359035\pi$
$812$	−4.10128e7	−	1.39677e8i	−0.0766039	−	0.260889i
$813$	−3.70537e8	−	2.38129e8i	−0.689540	−	0.443141i
$814$	6.66481e7	−	1.45939e8i	0.123570	−	0.270581i
$815$	1.19062e8	−	4.05489e8i	0.219938	−	0.749041i
$816$	1.25834e8	−	1.09036e8i	0.231594	−	0.200677i
$817$	−8.88009e7	−	1.02482e8i	−0.162836	−	0.187923i
$818$	5.77843e8	+	1.69670e8i	1.05572	+	0.309988i
$819$	7.16249e7	+	3.27100e7i	0.130380	+	0.0595427i
$820$	−2.44734e7	+	3.80814e7i	−0.0443867	+	0.0690671i
$821$	−2.49988e8	+	7.34031e7i	−0.451741	+	0.132643i	−0.499686	−	0.866207i	$-0.666551\pi$
$821$	−2.49988e8	+	7.34031e7i	−0.451741	+	0.132643i	0.0479446	+	0.998850i	$0.484733\pi$
$822$	6.93085e8	+	9.96505e7i	1.24787	+	0.179417i
$823$	6.06401e7	+	1.32783e8i	0.108783	+	0.238201i	0.956193	−	0.292738i	$-0.0945664\pi$
$823$	6.06401e7	+	1.32783e8i	0.108783	+	0.238201i	−0.847410	+	0.530939i	$0.821839\pi$
$824$	−1.33049e8	+	1.91295e7i	−0.237809	+	0.0341918i
$825$	1.17341e8	+	1.82586e8i	0.208972	+	0.325167i
$826$	−2.29831e8	−	1.99149e8i	−0.407820	−	0.353378i
$827$		−	8.29335e8i		−	1.46627i	−0.680084	−	0.733134i	$-0.738057\pi$
$827$		−	8.29335e8i		−	1.46627i	0.680084	−	0.733134i	$-0.261943\pi$
$828$	−5.31133e7	+	7.07399e7i	−0.0935648	+	0.124616i
$829$	−5.18280e8			−0.909705			−0.454853	−	0.890567i	$-0.650308\pi$
$829$	−5.18280e8			−0.909705			−0.454853	+	0.890567i	$0.650308\pi$
$830$	−4.04895e8	+	4.67274e8i	−0.708122	+	0.817216i
$831$	−8.81478e7	+	5.66491e7i	−0.153606	+	0.0987166i
$832$	−1.96048e7	−	1.36354e8i	−0.0340402	−	0.236755i
$833$	1.95255e8	−	8.91698e7i	0.337805	−	0.154270i
$834$	−2.22167e6	+	1.54521e7i	−0.00382985	+	0.0266372i
$835$	1.79354e7	+	6.10824e7i	0.0308072	+	0.104920i
$836$	9.86758e7	+	6.34151e7i	0.168885	+	0.108536i
$837$	−3.88071e7	+	8.49757e7i	−0.0661812	+	0.144917i
$838$	−3.97609e7	+	1.35413e8i	−0.0675654	+	0.230107i
$839$	−7.22763e8	+	6.26278e8i	−1.22380	+	1.06043i	−0.227561	+	0.973764i	$0.573075\pi$
$839$	−7.22763e8	+	6.26278e8i	−1.22380	+	1.06043i	−0.996238	+	0.0866640i	$0.972379\pi$
$840$	−3.60914e7	−	4.16517e7i	−0.0608928	−	0.0702741i
$841$	−9.59623e8	−	2.81771e8i	−1.61329	−	0.473705i
$842$	−3.54731e8	−	1.62000e8i	−0.594242	−	0.271381i
$843$	−2.23392e8	+	3.47604e8i	−0.372893	+	0.580233i
$844$	1.91944e8	−	5.63600e7i	0.319263	−	0.0937440i
$845$	1.95468e8	+	2.81040e7i	0.323970	+	0.0465798i
$846$	2.64686e7	+	5.79582e7i	0.0437139	+	0.0957202i
$847$	−1.60498e8	+	2.30762e7i	−0.264131	+	0.0379764i
$848$	6.86490e8	+	1.06820e9i	1.12576	+	1.75172i
$849$	1.01234e8	+	8.77202e7i	0.165427	+	0.143343i
$850$			1.59946e8i			0.260445i
$851$	8.09766e7	−	8.07452e7i	0.131393	−	0.131017i
$852$	2.74268e7			0.0443462
$853$	−7.83148e8	+	9.03801e8i	−1.26182	+	1.45622i	−0.428383	+	0.903597i	$0.640916\pi$
$853$	−7.83148e8	+	9.03801e8i	−1.26182	+	1.45622i	−0.833435	+	0.552618i	$0.813629\pi$
$854$	−1.49505e7	+	9.60811e6i	−0.0240039	+	0.0154264i
$855$	6.76311e6	+	4.70384e7i	0.0108205	+	0.0752583i
$856$	2.81540e8	−	1.28575e8i	0.448868	−	0.204991i
$857$	−9.52592e6	+	6.62543e7i	−0.0151344	+	0.105262i	−0.995988	−	0.0894825i	$-0.971479\pi$
$857$	−9.52592e6	+	6.62543e7i	−0.0151344	+	0.105262i	0.980854	+	0.194744i	$0.0623878\pi$
$858$	1.99396e8	+	6.79082e8i	0.315686	+	1.07513i
$859$	−6.92903e8	−	4.45302e8i	−1.09318	−	0.702546i	−0.135617	−	0.990761i	$-0.543302\pi$
$859$	−6.92903e8	−	4.45302e8i	−1.09318	−	0.702546i	−0.957566	+	0.288215i	$0.906938\pi$
$860$	6.65360e7	−	1.45693e8i	0.104607	−	0.229058i
$861$	−9.21298e6	+	3.13765e7i	−0.0144341	+	0.0491581i
$862$	−3.12543e8	+	2.70820e8i	−0.487964	+	0.422823i
$863$	1.88050e8	+	2.17021e8i	0.292577	+	0.337652i	0.882940	−	0.469486i	$-0.155561\pi$
$863$	1.88050e8	+	2.17021e8i	0.292577	+	0.337652i	−0.590363	+	0.807138i	$0.701015\pi$
$864$	−1.03364e8	−	3.03503e7i	−0.160261	−	0.0470568i
$865$	2.30941e8	+	1.05467e8i	0.356822	+	0.162955i
$866$	−3.41854e8	+	5.31935e8i	−0.526364	+	0.819039i
$867$	−2.95822e8	+	8.68612e7i	−0.453914	+	0.133281i
$868$	8.89782e7	+	1.27931e7i	0.136058	+	0.0195622i
$869$	6.34964e8	+	1.39038e9i	0.967586	+	2.11872i
$870$	5.24726e8	−	7.54442e7i	0.796847	−	0.114569i
$871$	−4.58541e8	−	7.13504e8i	−0.693943	−	1.07980i
$872$	−1.47184e8	−	1.27536e8i	−0.221979	−	0.192346i
$873$		−	6.27206e7i		−	0.0942687i
$874$	1.56974e8	+	2.10320e8i	0.235123	+	0.315026i
$875$	2.51875e8			0.375976
$876$	1.51788e8	−	1.75173e8i	0.225800	−	0.260588i
$877$	6.83001e8	−	4.38938e8i	1.01256	−	0.650736i	0.0745091	−	0.997220i	$-0.476261\pi$
$877$	6.83001e8	−	4.38938e8i	1.01256	−	0.650736i	0.938056	+	0.346484i	$0.112625\pi$
$878$	1.79666e8	+	1.24961e9i	0.265450	+	1.84625i
$879$	−3.83372e8	+	1.75080e8i	−0.564487	+	0.257792i
$880$	1.12675e8	−	7.83675e8i	0.165341	−	1.14997i
$881$	1.08215e8	+	3.68547e8i	0.158256	+	0.538971i	1.00000		0.000906760i	$-0.000288631\pi$
$881$	1.08215e8	+	3.68547e8i	0.158256	+	0.538971i	−0.841743	+	0.539878i	$0.818470\pi$
$882$	−2.03673e8	−	1.30893e8i	−0.296843	−	0.190770i
$883$	−2.57326e8	+	5.63466e8i	−0.373768	+	0.818437i	0.625502	+	0.780223i	$0.284894\pi$
$883$	−2.57326e8	+	5.63466e8i	−0.373768	+	0.818437i	−0.999270	+	0.0382145i	$0.987833\pi$
$884$	−4.68112e7	+	1.59424e8i	−0.0677631	+	0.230780i
$885$	2.66626e8	−	2.31033e8i	0.384656	−	0.333306i
$886$	8.02495e8	+	9.26129e8i	1.15383	+	1.33159i
$887$	−6.23127e8	−	1.82967e8i	−0.892906	−	0.262181i	−0.197077	−	0.980388i	$-0.563145\pi$
$887$	−6.23127e8	−	1.82967e8i	−0.892906	−	0.262181i	−0.695829	+	0.718207i	$0.744963\pi$
$888$	4.40171e7	+	2.01019e7i	0.0628611	+	0.0287077i
$889$	−1.46503e8	+	2.27964e8i	−0.208518	+	0.324460i
$890$	−4.56034e8	+	1.33904e8i	−0.646885	+	0.189943i
$891$	−1.02950e8	−	1.48020e7i	−0.145544	−	0.0209260i
$892$	−2.05509e8	−	4.50001e8i	−0.289558	−	0.634043i
$893$	5.96062e7	−	8.57008e6i	0.0837022	−	0.0120346i
$894$	2.33866e8	+	3.63903e8i	0.327307	+	0.509299i
$895$	3.47107e7	+	3.00770e7i	0.0484166	+	0.0419532i
$896$		−	2.82892e8i		−	0.393275i
$897$	−3.67078e7	+	5.03125e8i	−0.0508606	+	0.697105i
$898$	9.38288e8			1.29571
$899$	6.44976e8	−	7.44342e8i	0.887696	−	1.02446i
$900$	4.83471e7	−	3.10708e7i	0.0663198	−	0.0426211i
$901$	7.37542e7	+	5.12972e8i	0.100835	+	0.701325i
$902$	−2.67369e8	+	1.22103e8i	−0.364327	+	0.166382i
$903$	1.64665e7	−	1.14527e8i	0.0223634	−	0.155541i
$904$	−2.54092e8	−	8.65359e8i	−0.343943	−	1.17136i
$905$	−3.07113e8	−	1.97370e8i	−0.414336	−	0.266278i
$906$	−6.86604e7	+	1.50345e8i	−0.0923256	+	0.202165i
$907$	−1.25685e8	+	4.28042e8i	−0.168446	+	0.573674i	0.831392	+	0.555686i	$0.187544\pi$
$907$	−1.25685e8	+	4.28042e8i	−0.168446	+	0.573674i	−0.999838	+	0.0179880i	$0.994274\pi$
$908$	−7.26138e6	+	6.29202e6i	−0.00969977	+	0.00840490i
$909$	−1.42525e8	−	1.64483e8i	−0.189758	−	0.218992i
$910$	2.64747e8	+	7.77368e7i	0.351324	+	0.103158i
$911$	−3.09376e8	−	1.41288e8i	−0.409197	−	0.186874i	0.200172	−	0.979761i	$-0.435850\pi$
$911$	−3.09376e8	−	1.41288e8i	−0.409197	−	0.186874i	−0.609369	+	0.792887i	$0.708577\pi$
$912$	−9.59588e7	+	1.49315e8i	−0.126503	+	0.196842i
$913$	−1.22714e9	+	3.60321e8i	−1.61243	+	0.473453i
$914$	−2.52836e8	−	3.63523e7i	−0.331131	−	0.0476095i
$915$	−8.56457e6	−	1.87538e7i	−0.0111800	−	0.0244808i
$916$	4.35351e8	−	6.25940e7i	0.566439	−	0.0814416i
$917$	1.05241e8	+	1.63758e8i	0.136482	+	0.212370i
$918$	−5.79268e7	−	5.01939e7i	−0.0748776	−	0.0648818i
$919$			9.28925e8i			1.19683i	0.801185	+	0.598417i	$0.204203\pi$
$919$			9.28925e8i			1.19683i	−0.801185	+	0.598417i	$0.795797\pi$
$920$	1.69661e8	−	3.09657e8i	0.217881	−	0.397665i
$921$	−1.83655e8			−0.235084
$922$	−7.02330e8	+	8.10532e8i	−0.896083	+	1.03414i
$923$	1.31578e8	−	8.45603e7i	0.167332	−	0.107538i
$924$	1.42435e7	+	9.90659e7i	0.0180552	+	0.125576i
$925$	−6.75798e7	+	3.08626e7i	−0.0853870	+	0.0389949i
$926$	2.43702e7	−	1.69498e8i	0.0306920	−	0.213468i
$927$	2.78621e7	+	9.48897e7i	0.0349764	+	0.119119i
$928$	9.55474e8	+	6.14046e8i	1.19557	+	0.768346i
$929$	2.42910e8	−	5.31898e8i	0.302969	−	0.663409i	−0.695512	−	0.718515i	$-0.744822\pi$
$929$	2.42910e8	−	5.31898e8i	0.302969	−	0.663409i	0.998481	+	0.0551058i	$0.0175496\pi$
$930$	−9.22269e7	+	3.14096e8i	−0.114659	+	0.390493i
$931$	−1.72930e8	+	1.49844e8i	−0.214299	+	0.185691i
$932$	−2.67360e8	−	3.08550e8i	−0.330254	−	0.381134i
$933$	5.60972e8	+	1.64716e8i	0.690711	+	0.202811i
$934$	−1.68034e9	−	7.67384e8i	−2.06232	−	0.941829i
$935$	1.74703e8	−	2.71843e8i	0.213730	−	0.332570i
$936$	−2.04820e8	+	6.01405e7i	−0.249772	+	0.0733398i
$937$	5.81767e8	+	8.36454e7i	0.707180	+	0.101677i	0.486515	−	0.873672i	$-0.338268\pi$
$937$	5.81767e8	+	8.36454e7i	0.707180	+	0.101677i	0.220666	+	0.975350i	$0.429177\pi$
$938$	−1.56401e8	−	3.42470e8i	−0.189509	−	0.414967i
$939$	−2.22814e8	+	3.20359e7i	−0.269120	+	0.0386936i
$940$	3.84547e7	+	5.98367e7i	0.0462984	+	0.0720417i
$941$	−1.42220e7	−	1.23234e7i	−0.0170683	−	0.0147898i	0.646285	−	0.763096i	$-0.276322\pi$
$941$	−1.42220e7	−	1.23234e7i	−0.0170683	−	0.0147898i	−0.663353	+	0.748306i	$0.730867\pi$
$942$			4.57833e8i			0.547715i
$943$	−2.08992e8	+	1.46468e7i	−0.249226	+	0.0174666i
$944$	1.31766e9			1.56635
$945$	−2.65539e7	+	3.06448e7i	−0.0314654	+	0.0363130i
$946$	8.74904e8	−	5.62266e8i	1.03344	−	0.664154i
$947$	−1.73159e8	−	1.20434e9i	−0.203889	−	1.41808i	−0.792603	−	0.609739i	$-0.791274\pi$
$947$	−1.73159e8	−	1.20434e9i	−0.203889	−	1.41808i	0.588713	−	0.808342i	$-0.299635\pi$
$948$	3.68159e8	−	1.68133e8i	0.432126	−	0.197345i
$949$	1.88114e8	−	1.30836e9i	0.220101	−	1.53083i
$950$	−4.80359e7	−	1.63595e8i	−0.0560267	−	0.190810i
$951$	−4.17886e8	−	2.68559e8i	−0.485866	−	0.312247i
$952$	3.49003e7	−	7.64209e7i	0.0404499	−	0.0885730i
$953$	−1.33447e8	+	4.54477e8i	−0.154180	+	0.525089i	−0.999964	−	0.00843563i	$-0.997315\pi$
$953$	−1.33447e8	+	4.54477e8i	−0.154180	+	0.525089i	0.845784	+	0.533525i	$0.179133\pi$
$954$	4.41759e8	−	3.82786e8i	0.508792	−	0.440870i
$955$	1.72487e7	+	1.99061e7i	0.0198037	+	0.0228547i
$956$	−6.52487e7	−	1.91588e7i	−0.0746790	−	0.0219277i
$957$	9.97472e8	+	4.55530e8i	1.13806	+	0.519734i
$958$	5.13716e8	−	7.99358e8i	0.584288	−	0.909169i
$959$	5.41802e8	−	1.59087e8i	0.614306	−	0.180376i
$960$	7.02181e7	+	1.00958e7i	0.0793662	+	0.0114111i
$961$	−1.16031e8	−	2.54073e8i	−0.130739	−	0.286278i
$962$	−2.39799e8	+	3.44779e7i	−0.269353	+	0.0387271i
$963$	−1.23114e8	−	1.91569e8i	−0.137857	−	0.214509i
$964$	−3.03105e8	−	2.62642e8i	−0.338347	−	0.293179i
$965$		−	9.96654e8i		−	1.10908i
$966$	−4.79131e7	+	2.18746e8i	−0.0531524	+	0.242666i
$967$	6.25260e8			0.691483			0.345741	−	0.938330i	$-0.387627\pi$
$967$	6.25260e8			0.691483			0.345741	+	0.938330i	$0.387627\pi$
$968$	2.87868e8	−	3.32218e8i	0.317372	−	0.366266i
$969$	−6.09417e7	+	3.91648e7i	−0.0669797	+	0.0430452i
$970$	−3.12789e7	−	2.17550e8i	−0.0342718	−	0.238365i
$971$	−4.54993e8	+	2.07789e8i	−0.496990	+	0.226968i	−0.648109	−	0.761548i	$-0.724440\pi$
$971$	−4.54993e8	+	2.07789e8i	−0.496990	+	0.226968i	0.151119	+	0.988516i	$0.451712\pi$
$972$	−3.91943e6	+	2.72602e7i	−0.00426799	+	0.0296846i
$973$	3.54680e6	+	1.20793e7i	0.00385033	+	0.0131130i
$974$	3.20120e8	+	2.05729e8i	0.346446	+	0.222647i
$975$	1.36147e8	−	2.98120e8i	0.146891	−	0.321646i
$976$	2.16940e7	−	7.38831e7i	0.0233341	−	0.0794686i
$977$	7.12372e8	−	6.17274e8i	0.763876	−	0.661903i	−0.183140	−	0.983087i	$-0.558626\pi$
$977$	7.12372e8	−	6.17274e8i	0.763876	−	0.661903i	0.947017	+	0.321184i	$0.104081\pi$
$978$	−4.75825e8	−	5.49132e8i	−0.508664	−	0.587030i
$979$	−9.43314e8	−	2.76982e8i	−1.00533	−	0.295191i
$980$	−2.45846e8	−	1.12274e8i	−0.261207	−	0.119289i
$981$	−7.74670e7	+	1.20541e8i	−0.0820559	+	0.127681i
$982$	−4.61794e8	+	1.35595e8i	−0.487657	+	0.143189i
$983$	−1.57124e9	−	2.25910e8i	−1.65417	−	0.237834i	−0.748905	−	0.662677i	$-0.769420\pi$
$983$	−1.57124e9	−	2.25910e8i	−1.65417	−	0.237834i	−0.905267	+	0.424843i	$0.860329\pi$
$984$	−3.68279e7	−	8.06418e7i	−0.0386537	−	0.0846399i
$985$	−4.92553e8	+	7.08185e7i	−0.515400	+	0.0741034i
$986$	4.36894e8	+	6.79820e8i	0.455770	+	0.709191i
$987$	3.88325e7	+	3.36486e7i	0.0403872	+	0.0349958i
$988$		−	1.77120e8i		−	0.183653i
$989$	7.24563e8	−	1.56534e8i	0.749009	−	0.161815i
$990$	−3.64469e8			−0.375626
$991$	−1.03394e9	+	1.19323e9i	−1.06237	+	1.22604i	−0.0891809	+	0.996015i	$0.528425\pi$
$991$	−1.03394e9	+	1.19323e9i	−1.06237	+	1.22604i	−0.973186	+	0.230021i	$0.926121\pi$
$992$	−5.90016e8	+	3.79180e8i	−0.604406	+	0.388428i
$993$	−8.68328e7	−	6.03936e8i	−0.0886822	−	0.616798i
$994$	6.31553e7	−	2.88421e7i	0.0643059	−	0.0293675i
$995$	5.59648e7	−	3.89244e8i	0.0568127	−	0.395141i
$996$	9.54097e7	+	3.24936e8i	0.0965638	+	0.328866i
$997$	9.31942e8	+	5.98923e8i	0.940380	+	0.604345i	0.918502	−	0.395415i	$-0.129399\pi$
$997$	9.31942e8	+	5.98923e8i	0.940380	+	0.604345i	0.0218772	+	0.999761i	$0.493036\pi$
$998$	7.15100e8	−	1.56585e9i	0.719408	−	1.57528i
$999$	1.00304e7	−	3.41603e7i	0.0100605	−	0.0342630i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	69.7.f.a.7.20	✓	240
23.10	odd	22	inner	69.7.f.a.10.20	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.7.f.a.7.20	✓	240	1.1	even	1	trivial
69.7.f.a.10.20	yes	240	23.10	odd	22	inner

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:	\( N \)	\(=\)	\( 69 = 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	69.f (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(6.34640 - 7.32413i) q^{2} +(13.1138 - 8.42776i) q^{3} +(-4.25801 - 29.6151i) q^{4} +(79.9255 - 36.5007i) q^{5} +(21.4997 - 149.533i) q^{6} +(-34.3232 - 116.894i) q^{7} +(277.849 + 178.563i) q^{8} +(100.946 - 221.041i) q^{9} +O(q^{10})\)	\(q+(6.34640 - 7.32413i) q^{2} +(13.1138 - 8.42776i) q^{3} +(-4.25801 - 29.6151i) q^{4} +(79.9255 - 36.5007i) q^{5} +(21.4997 - 149.533i) q^{6} +(-34.3232 - 116.894i) q^{7} +(277.849 + 178.563i) q^{8} +(100.946 - 221.041i) q^{9} +(239.903 - 817.033i) q^{10} +(1331.17 - 1153.47i) q^{11} +(-305.428 - 352.483i) q^{12} +(-2552.02 - 749.340i) q^{13} +(-1073.98 - 490.468i) q^{14} +(740.511 - 1152.26i) q^{15} +(4908.45 - 1441.25i) q^{16} +(2066.67 + 297.142i) q^{17} +(-978.288 - 2142.15i) q^{18} +(-2203.06 + 316.753i) q^{19} +(-1421.30 - 2211.58i) q^{20} +(-1435.26 - 1243.66i) q^{21} -17070.1i q^{22} +(4268.24 - 11393.8i) q^{23} +5148.55 q^{24} +(-5176.42 + 5973.91i) q^{25} +(-21684.4 + 13935.7i) q^{26} +(-539.088 - 3749.44i) q^{27} +(-3315.68 + 1514.22i) q^{28} +(-5683.62 + 39530.4i) q^{29} +(-3739.71 - 12736.3i) q^{30} +(-20746.6 - 13333.0i) q^{31} +(11814.1 - 25869.2i) q^{32} +(7735.66 - 26345.2i) q^{33} +(15292.2 - 13250.8i) q^{34} +(-7010.01 - 8089.99i) q^{35} +(-6975.97 - 2048.33i) q^{36} +(8549.41 + 3904.38i) q^{37} +(-11661.6 + 18145.8i) q^{38} +(-39782.0 + 11681.1i) q^{39} +(28724.9 + 4130.02i) q^{40} +(-7153.06 - 15663.0i) q^{41} +(-18217.5 + 2619.28i) q^{42} +(32938.7 + 51253.7i) q^{43} +(-39828.3 - 34511.4i) q^{44} -21351.4i q^{45} +(-56361.6 - 103571. i) q^{46} -27056.0 q^{47} +(52222.2 - 60267.6i) q^{48} +(86486.5 - 55581.5i) q^{49} +(10902.1 + 75825.6i) q^{50} +(29606.2 - 13520.7i) q^{51} +(-11325.3 + 78769.0i) q^{52} +(69929.4 + 238158. i) q^{53} +(-30882.7 - 19847.1i) q^{54} +(64292.3 - 140780. i) q^{55} +(11336.3 - 38607.7i) q^{56} +(-26221.1 + 22720.7i) q^{57} +(253456. + 292503. i) q^{58} +(247140. + 72566.9i) q^{59} +(-37277.4 - 17024.0i) q^{60} +(8137.85 - 12662.7i) q^{61} +(-229319. + 67334.1i) q^{62} +(-29303.1 - 4213.15i) q^{63} +(21515.5 + 47112.4i) q^{64} +(-231323. + 33259.2i) q^{65} +(-143862. - 223854. i) q^{66} +(240994. + 208822. i) q^{67} -62469.9i q^{68} +(-40050.9 - 185388. i) q^{69} -103740. q^{70} +(-38509.2 + 44442.0i) q^{71} +(67517.3 - 43390.8i) q^{72} +(70725.9 + 491909. i) q^{73} +(82854.2 - 37838.2i) q^{74} +(-17536.1 + 121967. i) q^{75} +(18761.3 + 63895.3i) q^{76} +(-180524. - 116016. i) q^{77} +(-166919. + 365501. i) q^{78} +(-244482. + 832629. i) q^{79} +(339704. - 294355. i) q^{80} +(-38668.9 - 44626.3i) q^{81} +(-160114. - 47013.7i) q^{82} +(-660482. - 301632. i) q^{83} +(-30719.9 + 47801.0i) q^{84} +(176025. - 51685.7i) q^{85} +(584431. + 84028.5i) q^{86} +(258619. + 566296. i) q^{87} +(575832. - 82792.2i) q^{88} +(-301763. - 469553. i) q^{89} +(-156380. - 135504. i) q^{90} +324035. i q^{91} +(-355602. - 77889.6i) q^{92} -384435. q^{93} +(-171708. + 198162. i) q^{94} +(-164519. + 105730. i) q^{95} +(-63091.4 - 438810. i) q^{96} +(234785. - 107223. i) q^{97} +(141791. - 986181. i) q^{98} +(-120587. - 410681. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 20 q^{2} - 816 q^{4} + 324 q^{6} + 940 q^{8} - 5832 q^{9}+O(q^{10}) \) 240 * q + 20 * q^2 - 816 * q^4 + 324 * q^6 + 940 * q^8 - 5832 * q^9	\( 240 q + 20 q^{2} - 816 q^{4} + 324 q^{6} + 940 q^{8} - 5832 q^{9} - 384 q^{13} + 33816 q^{16} + 22880 q^{17} + 4860 q^{18} - 31680 q^{19} - 157696 q^{20} + 36488 q^{23} + 39204 q^{24} + 200664 q^{25} + 99032 q^{26} - 202752 q^{28} - 181712 q^{29} - 128496 q^{31} + 439300 q^{32} - 400026 q^{34} + 368744 q^{35} + 42282 q^{36} + 446688 q^{37} + 550550 q^{38} - 52488 q^{39} - 156750 q^{40} - 606080 q^{41} - 1274130 q^{42} - 429000 q^{43} - 867482 q^{44} + 309288 q^{46} + 1111152 q^{47} + 837864 q^{48} + 722136 q^{49} + 1786926 q^{50} + 463320 q^{51} - 812550 q^{52} - 367840 q^{53} - 354294 q^{54} - 398088 q^{55} - 3696550 q^{56} - 1240272 q^{57} + 1903134 q^{58} + 545800 q^{59} + 2450250 q^{60} - 495264 q^{61} + 488776 q^{62} - 2699808 q^{64} - 290400 q^{67} + 23328 q^{69} - 392616 q^{70} + 255392 q^{71} + 228420 q^{72} + 1346880 q^{73} - 5387470 q^{74} + 365472 q^{75} + 2123022 q^{76} + 6134240 q^{77} + 171072 q^{78} + 4025472 q^{79} + 10626462 q^{80} - 1417176 q^{81} + 2025492 q^{82} - 2474560 q^{83} - 8866152 q^{85} - 15634300 q^{86} - 611712 q^{87} - 10636560 q^{88} - 5901720 q^{89} + 6566394 q^{92} - 2484432 q^{93} + 13931490 q^{94} + 8183072 q^{95} - 4682124 q^{96} + 12319560 q^{97} + 14139580 q^{98} + 2993760 q^{99}+O(q^{100}) \) 240 * q + 20 * q^2 - 816 * q^4 + 324 * q^6 + 940 * q^8 - 5832 * q^9 - 384 * q^13 + 33816 * q^16 + 22880 * q^17 + 4860 * q^18 - 31680 * q^19 - 157696 * q^20 + 36488 * q^23 + 39204 * q^24 + 200664 * q^25 + 99032 * q^26 - 202752 * q^28 - 181712 * q^29 - 128496 * q^31 + 439300 * q^32 - 400026 * q^34 + 368744 * q^35 + 42282 * q^36 + 446688 * q^37 + 550550 * q^38 - 52488 * q^39 - 156750 * q^40 - 606080 * q^41 - 1274130 * q^42 - 429000 * q^43 - 867482 * q^44 + 309288 * q^46 + 1111152 * q^47 + 837864 * q^48 + 722136 * q^49 + 1786926 * q^50 + 463320 * q^51 - 812550 * q^52 - 367840 * q^53 - 354294 * q^54 - 398088 * q^55 - 3696550 * q^56 - 1240272 * q^57 + 1903134 * q^58 + 545800 * q^59 + 2450250 * q^60 - 495264 * q^61 + 488776 * q^62 - 2699808 * q^64 - 290400 * q^67 + 23328 * q^69 - 392616 * q^70 + 255392 * q^71 + 228420 * q^72 + 1346880 * q^73 - 5387470 * q^74 + 365472 * q^75 + 2123022 * q^76 + 6134240 * q^77 + 171072 * q^78 + 4025472 * q^79 + 10626462 * q^80 - 1417176 * q^81 + 2025492 * q^82 - 2474560 * q^83 - 8866152 * q^85 - 15634300 * q^86 - 611712 * q^87 - 10636560 * q^88 - 5901720 * q^89 + 6566394 * q^92 - 2484432 * q^93 + 13931490 * q^94 + 8183072 * q^95 - 4682124 * q^96 + 12319560 * q^97 + 14139580 * q^98 + 2993760 * q^99

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