LMFDB - Embedded newform 189.2.ba.a.131.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(5,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([5, 15]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("189.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.ba (of order $18$, degree $6$, 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:	$1.50917259820$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			131.16
Character	$\chi$	$=$	189.131
Dual form			189.2.ba.a.101.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.905074 + 1.07862i) q^{2} +(-1.67571 - 0.438172i) q^{3} +(0.00302336 - 0.0171463i) q^{4} +(1.61655 + 1.35644i) q^{5} +(-1.04402 - 2.20404i) q^{6} +(1.08812 + 2.41164i) q^{7} +(2.46004 - 1.42030i) q^{8} +(2.61601 + 1.46850i) q^{9} +2.97133i q^{10} +(-2.38051 - 2.83698i) q^{11} +(-0.0125793 + 0.0274075i) q^{12} +(2.27684 + 6.25557i) q^{13} +(-1.61642 + 3.35639i) q^{14} +(-2.11451 - 2.98133i) q^{15} +(3.72576 + 1.35607i) q^{16} -3.23775 q^{17} +(0.783724 + 4.15079i) q^{18} -5.32762i q^{19} +(0.0281454 - 0.0236168i) q^{20} +(-0.766672 - 4.51799i) q^{21} +(0.905502 - 5.13536i) q^{22} +(-0.239559 - 0.658182i) q^{23} +(-4.74464 + 1.30210i) q^{24} +(-0.0949575 - 0.538530i) q^{25} +(-4.68670 + 8.11761i) q^{26} +(-3.74022 - 3.60704i) q^{27} +(0.0446405 - 0.0113661i) q^{28} +(1.50083 - 4.12351i) q^{29} +(1.30195 - 4.97909i) q^{30} +(-1.47986 - 0.260940i) q^{31} +(-0.0336848 - 0.0925482i) q^{32} +(2.74596 + 5.79703i) q^{33} +(-2.93040 - 3.49232i) q^{34} +(-1.51224 + 5.37450i) q^{35} +(0.0330885 - 0.0404152i) q^{36} +(-3.24831 - 5.62624i) q^{37} +(5.74650 - 4.82189i) q^{38} +(-1.07431 - 11.4802i) q^{39} +(5.90332 + 1.04091i) q^{40} +(-10.4849 + 3.81619i) q^{41} +(4.17932 - 4.91606i) q^{42} +(1.29121 + 7.32280i) q^{43} +(-0.0558409 + 0.0322398i) q^{44} +(2.23697 + 5.92237i) q^{45} +(0.493113 - 0.854097i) q^{46} +(-1.04114 - 5.90462i) q^{47} +(-5.64911 - 3.90490i) q^{48} +(-4.63197 + 5.24832i) q^{49} +(0.494929 - 0.589833i) q^{50} +(5.42553 + 1.41869i) q^{51} +(0.114144 - 0.0201266i) q^{52} +(-0.766350 + 0.442452i) q^{53} +(0.505466 - 7.29893i) q^{54} -7.81514i q^{55} +(6.10208 + 4.38724i) q^{56} +(-2.33441 + 8.92755i) q^{57} +(5.80608 - 2.11324i) q^{58} +(5.85868 - 2.13238i) q^{59} +(-0.0575118 + 0.0272424i) q^{60} +(7.32422 - 1.29146i) q^{61} +(-1.05793 - 1.83239i) q^{62} +(-0.694936 + 7.90677i) q^{63} +(4.03421 - 6.98746i) q^{64} +(-4.80471 + 13.2008i) q^{65} +(-3.76753 + 8.20860i) q^{66} +(8.05809 + 6.76154i) q^{67} +(-0.00978888 + 0.0555155i) q^{68} +(0.113034 + 1.20789i) q^{69} +(-7.16576 + 3.23318i) q^{70} +(-3.83248 - 2.21268i) q^{71} +(8.52119 - 0.102968i) q^{72} +(-2.65123 - 1.53069i) q^{73} +(3.12864 - 8.59586i) q^{74} +(-0.0768477 + 0.944029i) q^{75} +(-0.0913491 - 0.0161073i) q^{76} +(4.25147 - 8.82791i) q^{77} +(11.4105 - 11.5492i) q^{78} +(-7.29250 + 6.11913i) q^{79} +(4.18344 + 7.24593i) q^{80} +(4.68703 + 7.68321i) q^{81} +(-13.6058 - 7.85533i) q^{82} +(-11.4377 - 4.16299i) q^{83} +(-0.0797848 - 0.000513902i) q^{84} +(-5.23397 - 4.39182i) q^{85} +(-6.72991 + 8.02040i) q^{86} +(-4.32177 + 6.25218i) q^{87} +(-9.88551 - 3.59803i) q^{88} -4.35832 q^{89} +(-4.36339 + 7.77303i) q^{90} +(-12.6087 + 12.2977i) q^{91} +(-0.0120097 + 0.00211763i) q^{92} +(2.36549 + 1.08569i) q^{93} +(5.42656 - 6.46712i) q^{94} +(7.22662 - 8.61234i) q^{95} +(0.0158939 + 0.169844i) q^{96} +(6.85869 - 1.20937i) q^{97} +(-9.85324 - 0.246039i) q^{98} +(-2.06134 - 10.9174i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} - 18 q^{6} - 6 q^{7} - 18 q^{8} + 3 q^{9} - 9 q^{11} - 9 q^{12} + 3 q^{14} - 24 q^{15} + 3 q^{16} - 18 q^{17} - 3 q^{18} + 18 q^{20} - 21 q^{21} - 12 q^{22}+ \cdots + 96 q^{99}+O(q^{100}) $ 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 - 18 * q^6 - 6 * q^7 - 18 * q^8 + 3 * q^9 - 9 * q^11 - 9 * q^12 + 3 * q^14 - 24 * q^15 + 3 * q^16 - 18 * q^17 - 3 * q^18 + 18 * q^20 - 21 * q^21 - 12 * q^22 - 6 * q^23 - 9 * q^24 - 3 * q^25 - 12 * q^28 + 6 * q^29 + 51 * q^30 - 9 * q^31 + 3 * q^32 - 9 * q^33 - 18 * q^34 + 18 * q^35 + 3 * q^37 - 99 * q^38 - 36 * q^39 - 54 * q^40 - 45 * q^42 - 12 * q^43 - 9 * q^44 - 9 * q^45 + 3 * q^46 + 45 * q^47 - 24 * q^49 - 9 * q^50 - 48 * q^51 - 9 * q^52 - 45 * q^53 + 171 * q^54 + 3 * q^56 - 3 * q^58 + 36 * q^59 + 57 * q^60 - 9 * q^61 - 99 * q^62 - 33 * q^63 + 18 * q^64 + 69 * q^65 - 9 * q^66 - 3 * q^67 + 36 * q^68 + 108 * q^69 + 66 * q^70 + 18 * q^71 - 129 * q^72 - 9 * q^73 + 75 * q^74 + 36 * q^75 + 36 * q^76 + 15 * q^77 + 66 * q^78 - 21 * q^79 + 72 * q^80 - 33 * q^81 - 18 * q^82 - 90 * q^83 - 120 * q^84 + 9 * q^85 - 105 * q^86 - 54 * q^87 - 63 * q^88 - 18 * q^89 + 81 * q^90 + 6 * q^91 + 150 * q^92 + 21 * q^93 - 9 * q^94 + 45 * q^95 - 81 * q^96 + 27 * q^98 + 96 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	0.905074	+	1.07862i	0.639984	+	0.762703i	0.984368	−	0.176126i	$-0.0563566\pi$
$2$	0.905074	+	1.07862i	0.639984	+	0.762703i	−0.344384	+	0.938829i	$0.611912\pi$
$3$	−1.67571	−	0.438172i	−0.967472	−	0.252979i
$3$	−1.67571	−	0.438172i	−0.967472	−	0.252979i
$4$	0.00302336	−	0.0171463i	0.00151168	−	0.00857316i
$5$	1.61655	+	1.35644i	0.722942	+	0.606620i	0.928197	−	0.372088i	$-0.121358\pi$
$5$	1.61655	+	1.35644i	0.722942	+	0.606620i	−0.205256	+	0.978708i	$0.565803\pi$
$6$	−1.04402	−	2.20404i	−0.426219	−	0.899796i
$7$	1.08812	+	2.41164i	0.411273	+	0.911512i
$7$	1.08812	+	2.41164i	0.411273	+	0.911512i
$8$	2.46004	−	1.42030i	0.869754	−	0.502153i
$9$	2.61601	+	1.46850i	0.872004	+	0.489499i
$10$			2.97133i			0.939616i
$11$	−2.38051	−	2.83698i	−0.717751	−	0.855382i	0.276659	−	0.960968i	$-0.410773\pi$
$11$	−2.38051	−	2.83698i	−0.717751	−	0.855382i	−0.994410	+	0.105586i	$0.966328\pi$
$12$	−0.0125793	+	0.0274075i	−0.00363133	+	0.00791187i
$13$	2.27684	+	6.25557i	0.631482	+	1.73498i	0.676963	+	0.736017i	$0.263296\pi$
$13$	2.27684	+	6.25557i	0.631482	+	1.73498i	−0.0454806	+	0.998965i	$0.514482\pi$
$14$	−1.61642	+	3.35639i	−0.432005	+	0.897032i
$15$	−2.11451	−	2.98133i	−0.545964	−	0.769777i
$16$	3.72576	+	1.35607i	0.931441	+	0.339017i
$17$	−3.23775			−0.785270			−0.392635	−	0.919694i	$-0.628436\pi$
$17$	−3.23775			−0.785270			−0.392635	+	0.919694i	$0.628436\pi$
$18$	0.783724	+	4.15079i	0.184725	+	0.978351i
$19$		−	5.32762i		−	1.22224i	−0.791538	−	0.611120i	$-0.790719\pi$
$19$		−	5.32762i		−	1.22224i	0.791538	−	0.611120i	$-0.209281\pi$
$20$	0.0281454	−	0.0236168i	0.00629351	−	0.00528088i
$21$	−0.766672	−	4.51799i	−0.167301	−	0.985906i
$22$	0.905502	−	5.13536i	0.193054	−	1.09486i
$23$	−0.239559	−	0.658182i	−0.0499514	−	0.137240i	0.912208	−	0.409727i	$-0.134376\pi$
$23$	−0.239559	−	0.658182i	−0.0499514	−	0.137240i	−0.962160	+	0.272487i	$0.912154\pi$
$24$	−4.74464	+	1.30210i	−0.968496	+	0.265789i
$25$	−0.0949575	−	0.538530i	−0.0189915	−	0.107706i
$26$	−4.68670	+	8.11761i	−0.919138	+	1.59199i
$27$	−3.74022	−	3.60704i	−0.719806	−	0.694175i
$28$	0.0446405	−	0.0113661i	0.00843625	−	0.00214799i
$29$	1.50083	−	4.12351i	0.278698	−	0.765716i	−0.718813	−	0.695204i	$-0.755314\pi$
$29$	1.50083	−	4.12351i	0.278698	−	0.765716i	0.997511	−	0.0705128i	$-0.0224636\pi$
$30$	1.30195	−	4.97909i	0.237703	−	0.909052i
$31$	−1.47986	−	0.260940i	−0.265791	−	0.0468662i	0.0391641	−	0.999233i	$-0.487530\pi$
$31$	−1.47986	−	0.260940i	−0.265791	−	0.0468662i	−0.304955	+	0.952367i	$0.598642\pi$
$32$	−0.0336848	−	0.0925482i	−0.00595468	−	0.0163604i
$33$	2.74596	+	5.79703i	0.478010	+	1.00913i
$34$	−2.93040	−	3.49232i	−0.502560	−	0.598927i
$35$	−1.51224	+	5.37450i	−0.255616	+	0.908456i
$36$	0.0330885	−	0.0404152i	0.00551475	−	0.00673586i
$37$	−3.24831	−	5.62624i	−0.534019	−	0.924947i	−0.999210	−	0.0397374i	$-0.987348\pi$
$37$	−3.24831	−	5.62624i	−0.534019	−	0.924947i	0.465191	−	0.885210i	$-0.345985\pi$
$38$	5.74650	−	4.82189i	0.932206	−	0.782213i
$39$	−1.07431	−	11.4802i	−0.172028	−	1.83830i
$40$	5.90332	+	1.04091i	0.933397	+	0.164583i
$41$	−10.4849	+	3.81619i	−1.63746	+	0.595988i	−0.986593	−	0.163200i	$-0.947818\pi$
$41$	−10.4849	+	3.81619i	−1.63746	+	0.595988i	−0.650871	+	0.759188i	$0.725596\pi$
$42$	4.17932	−	4.91606i	0.644883	−	0.758565i
$43$	1.29121	+	7.32280i	0.196907	+	1.11672i	0.909676	+	0.415318i	$0.136330\pi$
$43$	1.29121	+	7.32280i	0.196907	+	1.11672i	−0.712769	+	0.701399i	$0.752559\pi$
$44$	−0.0558409	+	0.0322398i	−0.00841834	+	0.00486033i
$45$	2.23697	+	5.92237i	0.333468	+	0.882854i
$46$	0.493113	−	0.854097i	0.0727056	−	0.125930i
$47$	−1.04114	−	5.90462i	−0.151866	−	0.861278i	−0.961595	−	0.274473i	$-0.911497\pi$
$47$	−1.04114	−	5.90462i	−0.151866	−	0.861278i	0.809728	−	0.586805i	$-0.199614\pi$
$48$	−5.64911	−	3.90490i	−0.815379	−	0.563624i
$49$	−4.63197	+	5.24832i	−0.661710	+	0.749760i
$50$	0.494929	−	0.589833i	0.0699935	−	0.0834150i
$51$	5.42553	+	1.41869i	0.759726	+	0.198656i
$52$	0.114144	−	0.0201266i	0.0158289	−	0.00279106i
$53$	−0.766350	+	0.442452i	−0.105266	+	0.0607755i	−0.551709	−	0.834037i	$-0.686024\pi$
$53$	−0.766350	+	0.442452i	−0.105266	+	0.0607755i	0.446443	+	0.894812i	$0.352691\pi$
$54$	0.505466	−	7.29893i	0.0687853	−	0.993259i
$55$		−	7.81514i		−	1.05379i
$56$	6.10208	+	4.38724i	0.815424	+	0.586270i
$57$	−2.33441	+	8.92755i	−0.309201	+	1.18248i
$58$	5.80608	−	2.11324i	0.762376	−	0.277482i
$59$	5.85868	−	2.13238i	0.762735	−	0.277613i	0.0687807	−	0.997632i	$-0.478089\pi$
$59$	5.85868	−	2.13238i	0.762735	−	0.277613i	0.693954	+	0.720019i	$0.255867\pi$
$60$	−0.0575118	+	0.0272424i	−0.00742474	+	0.00351698i
$61$	7.32422	−	1.29146i	0.937771	−	0.165354i	0.316183	−	0.948698i	$-0.397599\pi$
$61$	7.32422	−	1.29146i	0.937771	−	0.165354i	0.621588	+	0.783344i	$0.286488\pi$
$62$	−1.05793	−	1.83239i	−0.134357	−	0.232713i
$63$	−0.694936	+	7.90677i	−0.0875537	+	0.996160i
$64$	4.03421	−	6.98746i	0.504277	−	0.873433i
$65$	−4.80471	+	13.2008i	−0.595951	+	1.63736i
$66$	−3.76753	+	8.20860i	−0.463750	+	1.01041i
$67$	8.05809	+	6.76154i	0.984453	+	0.826054i	0.984755	−	0.173946i	$-0.0556518\pi$
$67$	8.05809	+	6.76154i	0.984453	+	0.826054i	−0.000302478		1.00000i	$0.500096\pi$
$68$	−0.00978888	+	0.0555155i	−0.00118708	+	0.00673224i
$69$	0.113034	+	1.20789i	0.0136077	+	0.145413i
$70$	−7.16576	+	3.23318i	−0.856472	+	0.386438i
$71$	−3.83248	−	2.21268i	−0.454832	−	0.262597i	0.255037	−	0.966931i	$-0.417912\pi$
$71$	−3.83248	−	2.21268i	−0.454832	−	0.262597i	−0.709869	+	0.704334i	$0.751246\pi$
$72$	8.52119	−	0.102968i	1.00423	−	0.0121349i
$73$	−2.65123	−	1.53069i	−0.310303	−	0.179154i	0.336759	−	0.941591i	$-0.390669\pi$
$73$	−2.65123	−	1.53069i	−0.310303	−	0.179154i	−0.647062	+	0.762437i	$0.724003\pi$
$74$	3.12864	−	8.59586i	0.363697	−	0.999249i
$75$	−0.0768477	+	0.944029i	−0.00887361	+	0.109007i
$76$	−0.0913491	−	0.0161073i	−0.0104785	−	0.00184763i
$77$	4.25147	−	8.82791i	0.484500	−	1.00603i
$78$	11.4105	−	11.5492i	1.29198	−	1.30769i
$79$	−7.29250	+	6.11913i	−0.820470	+	0.688456i	−0.953082	−	0.302712i	$-0.902108\pi$
$79$	−7.29250	+	6.11913i	−0.820470	+	0.688456i	0.132612	+	0.991168i	$0.457664\pi$
$80$	4.18344	+	7.24593i	0.467723	+	0.810120i
$81$	4.68703	+	7.68321i	0.520781	+	0.853691i
$82$	−13.6058	−	7.85533i	−1.50251	−	0.867476i
$83$	−11.4377	−	4.16299i	−1.25545	−	0.456947i	−0.373212	−	0.927746i	$-0.621744\pi$
$83$	−11.4377	−	4.16299i	−1.25545	−	0.456947i	−0.882241	+	0.470799i	$0.843966\pi$
$84$	−0.0797848		0.000513902i	−0.00870523		5.60713e-5i
$85$	−5.23397	−	4.39182i	−0.567704	−	0.476360i
$86$	−6.72991	+	8.02040i	−0.725705	+	0.864862i
$87$	−4.32177	+	6.25218i	−0.463342	+	0.670304i
$88$	−9.88551	−	3.59803i	−1.05380	−	0.383552i
$89$	−4.35832			−0.461982			−0.230991	−	0.972956i	$-0.574197\pi$
$89$	−4.35832			−0.461982			−0.230991	+	0.972956i	$0.574197\pi$
$90$	−4.36339	+	7.77303i	−0.459942	+	0.819349i
$91$	−12.6087	+	12.2977i	−1.32175	+	1.28915i
$92$	−0.0120097	+	0.00211763i	−0.00125210	+	0.000220778i
$93$	2.36549	+	1.08569i	0.245289	+	0.112581i
$94$	5.42656	−	6.46712i	0.559707	−	0.667033i
$95$	7.22662	−	8.61234i	0.741435	−	0.883608i
$96$	0.0158939	+	0.169844i	0.00162217	+	0.0173346i
$97$	6.85869	−	1.20937i	0.696394	−	0.122793i	0.185765	−	0.982594i	$-0.440524\pi$
$97$	6.85869	−	1.20937i	0.696394	−	0.122793i	0.510629	+	0.859801i	$0.329413\pi$
$98$	−9.85324	−	0.246039i	−0.995328	−	0.0248537i
$99$	−2.06134	−	10.9174i	−0.207172	−	1.09724i
$100$	−0.00952091			−0.000952091
$101$	3.49388	+	1.27167i	0.347654	+	0.126536i	0.509945	−	0.860207i	$-0.329666\pi$
$101$	3.49388	+	1.27167i	0.347654	+	0.126536i	−0.162290	+	0.986743i	$0.551888\pi$
$102$	3.38027	+	7.13613i	0.334697	+	0.706582i
$103$	3.98929	−	4.75425i	0.393076	−	0.468450i	−0.532820	−	0.846229i	$-0.678868\pi$
$103$	3.98929	−	4.75425i	0.393076	−	0.468450i	0.925896	+	0.377779i	$0.123312\pi$
$104$	14.4859	+	12.1551i	1.42046	+	1.19191i
$105$	4.88904	−	8.34348i	0.477121	−	0.814241i
$106$	−1.17084	−	0.426152i	−0.113722	−	0.0413915i
$107$	−2.47461	−	1.42872i	−0.239230	−	0.138119i	0.375593	−	0.926785i	$-0.377439\pi$
$107$	−2.47461	−	1.42872i	−0.239230	−	0.138119i	−0.614823	+	0.788665i	$0.710772\pi$
$108$	−0.0731555	+	0.0532257i	−0.00703939	+	0.00512164i
$109$	2.81692	+	4.87905i	0.269812	+	0.467328i	0.968813	−	0.247792i	$-0.0797051\pi$
$109$	2.81692	+	4.87905i	0.269812	+	0.467328i	−0.699001	+	0.715121i	$0.746372\pi$
$110$	8.42961	−	7.07328i	0.803731	−	0.674411i
$111$	2.97797	+	10.8513i	0.282656	+	1.02996i
$112$	0.783757	+	10.4608i	0.0740581	+	0.988448i
$113$	9.04367	+	1.59464i	0.850757	+	0.150011i	0.581992	−	0.813194i	$-0.302273\pi$
$113$	9.04367	+	1.59464i	0.850757	+	0.150011i	0.268765	+	0.963206i	$0.413385\pi$
$114$	−11.7423	+	5.56213i	−1.09977	+	0.520941i
$115$	0.505529	−	1.38893i	0.0471408	−	0.129518i
$116$	−0.0661654	−	0.0382006i	−0.00614331	−	0.00354684i
$117$	−3.23005	+	19.7082i	−0.298618	+	1.82202i
$118$	7.60258	+	4.38935i	0.699874	+	0.404073i
$119$	−3.52308	−	7.80827i	−0.322960	−	0.715783i
$120$	−9.43616	−	4.33094i	−0.861399	−	0.395359i
$121$	−0.471507	+	2.67405i	−0.0428643	+	0.243095i
$122$	8.02196	+	6.73122i	0.726274	+	0.609416i
$123$	19.2418	−	1.80064i	1.73497	−	0.162358i
$124$	−0.00894832	+	0.0245853i	−0.000803582	+	0.00220782i
$125$	5.85261	−	10.1370i	0.523474	−	0.906683i
$126$	−9.15741	+	6.40664i	−0.815807	+	0.570749i
$127$	−0.958294	−	1.65981i	−0.0850349	−	0.147285i	0.820371	−	0.571831i	$-0.193767\pi$
$127$	−0.958294	−	1.65981i	−0.0850349	−	0.147285i	−0.905406	+	0.424547i	$0.860433\pi$
$128$	10.9941	−	1.93856i	0.971752	−	0.171346i
$129$	1.04496	−	12.8367i	0.0920032	−	1.13020i
$130$	−18.5873	+	6.76524i	−1.63022	+	0.593351i
$131$	−8.18242	+	2.97816i	−0.714901	+	0.260203i	−0.673760	−	0.738951i	$-0.735322\pi$
$131$	−8.18242	+	2.97816i	−0.714901	+	0.260203i	−0.0411416	+	0.999153i	$0.513099\pi$
$132$	0.107700	−	0.0295566i	0.00937407	−	0.00257257i
$133$	12.8483	−	5.79712i	1.11409	−	0.502674i
$134$			14.8114i			1.27951i
$135$	−1.15350	−	10.9043i	−0.0992772	−	0.938497i
$136$	−7.96498	+	4.59858i	−0.682991	+	0.394325i
$137$	6.87107	−	1.21155i	0.587035	−	0.103510i	0.127761	−	0.991805i	$-0.459221\pi$
$137$	6.87107	−	1.21155i	0.587035	−	0.103510i	0.459274	+	0.888295i	$0.348110\pi$
$138$	−1.20056	+	1.21515i	−0.102198	+	0.103441i
$139$	6.76177	−	8.05836i	0.573526	−	0.683501i	−0.398825	−	0.917027i	$-0.630582\pi$
$139$	6.76177	−	8.05836i	0.573526	−	0.683501i	0.972351	+	0.233526i	$0.0750263\pi$
$140$	0.0875808	+	0.0421784i	0.00740193	+	0.00356473i
$141$	−0.842583	+	10.3506i	−0.0709583	+	0.871681i
$142$	−1.08202	−	6.13645i	−0.0908012	−	0.514959i
$143$	12.3269	−	21.3508i	1.03083	−	1.78544i
$144$	7.75526	+	9.01876i	0.646271	+	0.751564i
$145$	8.01948	−	4.63005i	0.665981	−	0.384504i
$146$	−0.748521	−	4.24507i	−0.0619480	−	0.351325i
$147$	10.0615	−	6.76507i	0.829859	−	0.557973i
$148$	−0.106290	+	0.0386864i	−0.00873699	+	0.00318000i
$149$	10.9584	+	1.93227i	0.897750	+	0.158298i	0.603436	−	0.797411i	$-0.293798\pi$
$149$	10.9584	+	1.93227i	0.897750	+	0.158298i	0.294314	+	0.955709i	$0.404909\pi$
$150$	−1.08781	+	0.771526i	−0.0888189	+	0.0629948i
$151$	−15.4692	+	12.9802i	−1.25887	+	1.05632i	−0.263066	+	0.964778i	$0.584734\pi$
$151$	−15.4692	+	12.9802i	−1.25887	+	1.05632i	−0.995802	+	0.0915375i	$0.970822\pi$
$152$	−7.56683	−	13.1061i	−0.613751	−	1.06305i
$153$	−8.46999	−	4.75463i	−0.684758	−	0.384389i
$154$	13.3699	−	3.40417i	1.07738	−	0.274316i
$155$	−2.03832	−	2.42917i	−0.163722	−	0.195116i
$156$	−0.200091	−	0.0162882i	−0.0160201	−	0.00130410i
$157$	1.67332	+	4.59740i	0.133545	+	0.366912i	0.988383	−	0.151983i	$-0.0485658\pi$
$157$	1.67332	+	4.59740i	0.133545	+	0.366912i	−0.854838	+	0.518895i	$0.826344\pi$
$158$	−13.2005	−	2.32760i	−1.05017	−	0.185174i
$159$	1.47805	−	0.405629i	0.117217	−	0.0321685i
$160$	0.0710834	−	0.195300i	0.00561963	−	0.0154398i
$161$	1.32663	−	1.29391i	0.104553	−	0.101975i
$162$	−4.04520	+	12.0094i	−0.317821	+	0.943549i
$163$	−4.68621	+	8.11676i	−0.367053	+	0.635754i	−0.989103	−	0.147223i	$-0.952966\pi$
$163$	−4.68621	+	8.11676i	−0.367053	+	0.635754i	0.622051	+	0.782977i	$0.286300\pi$
$164$	0.0337340	+	0.191315i	0.00263418	+	0.0149392i
$165$	−3.42438	+	13.0959i	−0.266587	+	1.01952i
$166$	−5.86167	−	16.1048i	−0.454954	−	1.24998i
$167$	−1.49566	+	8.48231i	−0.115738	+	0.656381i	0.870645	+	0.491912i	$0.163702\pi$
$167$	−1.49566	+	8.48231i	−0.115738	+	0.656381i	−0.986382	+	0.164468i	$0.947409\pi$
$168$	−8.30295	−	10.0255i	−0.640586	−	0.773484i
$169$	−23.9896	+	20.1296i	−1.84535	+	1.54843i
$170$		−	9.62042i		−	0.737852i
$171$	7.82360	−	13.9371i	0.598286	−	1.06580i
$172$	0.129463			0.00987145
$173$	7.96256	+	2.89813i	0.605382	+	0.220341i	0.626481	−	0.779436i	$-0.284494\pi$
$173$	7.96256	+	2.89813i	0.605382	+	0.220341i	−0.0210995	+	0.999777i	$0.506717\pi$
$174$	−10.6553	+	0.997119i	−0.807775	+	0.0755914i
$175$	1.19541	−	0.814991i	0.0903648	−	0.0616075i
$176$	−5.02208	−	13.7981i	−0.378554	−	1.04007i
$177$	−10.7518	+	1.00615i	−0.808155	+	0.0756270i
$178$	−3.94460	−	4.70100i	−0.295661	−	0.352355i
$179$		−	4.83578i		−	0.361443i	−0.983534	−	0.180722i	$-0.942157\pi$
$179$		−	4.83578i		−	0.361443i	0.983534	−	0.180722i	$-0.0578433\pi$
$180$	0.108310	−	0.0204503i	0.00807295	−	0.00152428i
$181$	−3.95269	+	2.28209i	−0.293801	+	0.169626i	−0.639655	−	0.768662i	$-0.720923\pi$
$181$	−3.95269	+	2.28209i	−0.293801	+	0.169626i	0.345854	+	0.938288i	$0.387589\pi$
$182$	−24.6764	−	2.46965i	−1.82914	−	0.183062i
$183$	−12.8392	−	1.04516i	−0.949098	−	0.0772604i
$184$	−1.52414	−	1.27891i	−0.112361	−	0.0942822i
$185$	2.38063	−	13.5012i	0.175027	−	0.992629i
$186$	0.969882	+	3.53410i	0.0711152	+	0.259133i
$187$	7.70750	+	9.18544i	0.563628	+	0.671706i
$188$	−0.104390			−0.00761344
$189$	4.62904	−	12.9450i	0.336713	−	0.941607i
$190$	15.8301			1.14844
$191$	6.64760	+	7.92230i	0.481003	+	0.573237i	0.950906	−	0.309481i	$-0.100155\pi$
$191$	6.64760	+	7.92230i	0.481003	+	0.573237i	−0.469902	+	0.882718i	$0.655711\pi$
$192$	−9.82188	+	9.94128i	−0.708833	+	0.717450i
$193$	1.80685	−	10.2471i	0.130060	−	0.737605i	−0.848114	−	0.529814i	$-0.822262\pi$
$193$	1.80685	−	10.2471i	0.130060	−	0.737605i	0.978173	−	0.207791i	$-0.0666273\pi$
$194$	7.51207	+	6.30338i	0.539335	+	0.452556i
$195$	13.8355	−	20.0155i	0.990783	−	1.43334i
$196$	0.0759853	+	0.0952888i	0.00542752	+	0.00680634i
$197$	12.2795	−	7.08959i	0.874880	−	0.505112i	0.00591309	−	0.999983i	$-0.498118\pi$
$197$	12.2795	−	7.08959i	0.874880	−	0.505112i	0.868967	+	0.494870i	$0.164784\pi$
$198$	9.91006	−	12.1044i	0.704277	−	0.860223i
$199$		−	20.1176i		−	1.42610i	−0.701113	−	0.713050i	$-0.747313\pi$
$199$		−	20.1176i		−	1.42610i	0.701113	−	0.713050i	$-0.252687\pi$
$200$	−0.998475	−	1.18994i	−0.0706028	−	0.0841412i
$201$	−10.5403	−	14.8612i	−0.743456	−	1.04823i
$202$	1.79057	+	4.91954i	0.125984	+	0.346138i
$203$	11.5775	−	0.867427i	0.812581	−	0.0608815i
$204$	0.0407286	−	0.0887387i	0.00285158	−	0.00621295i
$205$	−22.1257	−	8.05311i	−1.54533	−	0.562454i
$206$	8.73865			0.608851
$207$	0.339851	−	2.07360i	0.0236213	−	0.144125i
$208$			26.3943i			1.83012i
$209$	−15.1144	+	12.6825i	−1.04548	+	0.877264i
$210$	13.4244	−	2.27803i	0.926373	−	0.157199i
$211$	0.582787	−	3.30515i	0.0401207	−	0.227536i	−0.958154	−	0.286254i	$-0.907590\pi$
$211$	0.582787	−	3.30515i	0.0401207	−	0.227536i	0.998275	+	0.0587176i	$0.0187011\pi$
$212$	0.00526948	+	0.0144778i	0.000361909	+	0.000994338i
$213$	5.45259	+	5.38710i	0.373605	+	0.369118i
$214$	−0.698655	−	3.96227i	−0.0477591	−	0.270855i
$215$	−7.84567	+	13.5891i	−0.535070	+	0.926768i
$216$	−14.3242	−	3.56120i	−0.974636	−	0.242309i
$217$	−0.980985	−	3.85283i	−0.0665936	−	0.261547i
$218$	−2.71314	+	7.45430i	−0.183757	+	0.504869i
$219$	3.77199	+	3.72669i	0.254888	+	0.251826i
$220$	−0.134001	−	0.0236280i	−0.00903434	−	0.00159300i
$221$	−7.37184	−	20.2540i	−0.495884	−	1.36243i
$222$	−9.00916	+	13.0333i	−0.604655	+	0.874738i
$223$	6.45098	+	7.68798i	0.431990	+	0.514825i	0.937495	−	0.347998i	$-0.113138\pi$
$223$	6.45098	+	7.68798i	0.431990	+	0.514825i	−0.505506	+	0.862823i	$0.668694\pi$
$224$	0.186539	−	0.181939i	0.0124637	−	0.0121563i
$225$	0.542421	−	1.54825i	0.0361614	−	0.103216i
$226$	6.46517	+	11.1980i	0.430056	+	0.744880i
$227$	−13.5964	+	11.4088i	−0.902427	+	0.757226i	−0.970663	−	0.240443i	$-0.922707\pi$
$227$	−13.5964	+	11.4088i	−0.902427	+	0.757226i	0.0682365	+	0.997669i	$0.478263\pi$
$228$	0.146017	+	0.0670178i	0.00967020	+	0.00443836i
$229$	−12.8653	−	2.26849i	−0.850160	−	0.149906i	−0.268441	−	0.963296i	$-0.586509\pi$
$229$	−12.8653	−	2.26849i	−0.850160	−	0.149906i	−0.581719	+	0.813390i	$0.697620\pi$
$230$	1.95568	−	0.711808i	0.128953	−	0.0469352i
$231$	−10.9924	+	12.9302i	−0.723246	+	0.850742i
$232$	−2.16452	−	12.2756i	−0.142108	−	0.805934i
$233$	−16.4302	+	9.48596i	−1.07638	+	0.621446i	−0.929917	−	0.367771i	$-0.880121\pi$
$233$	−16.4302	+	9.48596i	−1.07638	+	0.621446i	−0.146460	+	0.989217i	$0.546788\pi$
$234$	−24.1812	+	14.3533i	−1.58077	+	0.938307i
$235$	6.32623	−	10.9573i	0.412678	−	0.714779i
$236$	−0.0188497	−	0.106902i	−0.00122701	−	0.00695871i
$237$	14.9013	−	7.05853i	0.967946	−	0.458501i
$238$	5.23355	−	10.8671i	0.339241	−	0.704412i
$239$	−13.6545	+	16.2728i	−0.883236	+	1.05260i	0.115008	+	0.993365i	$0.463311\pi$
$239$	−13.6545	+	16.2728i	−0.883236	+	1.05260i	−0.998244	+	0.0592349i	$0.981134\pi$
$240$	−3.83527	−	13.9752i	−0.247566	−	0.902092i
$241$	−11.6046	+	2.04621i	−0.747519	+	0.131808i	−0.534415	−	0.845222i	$-0.679468\pi$
$241$	−11.6046	+	2.04621i	−0.747519	+	0.131808i	−0.213103	+	0.977030i	$0.568357\pi$
$242$	−3.31104	+	1.91163i	−0.212842	+	0.122884i
$243$	−4.48753	−	14.9286i	−0.287875	−	0.957668i
$244$		−	0.129488i		−	0.00828962i
$245$	−14.6068	+	2.20115i	−0.933197	+	0.140626i
$246$	19.3574	+	19.1249i	1.23419	+	1.21936i
$247$	33.3273	−	12.1301i	2.12056	−	0.771822i
$248$	−4.01113	+	1.45993i	−0.254707	+	0.0927058i
$249$	17.3422	+	11.9877i	1.09902	+	0.759686i
$250$	16.2311	−	2.86198i	1.02654	−	0.181007i
$251$	13.6923	+	23.7157i	0.864248	+	1.49692i	0.867792	+	0.496927i	$0.165538\pi$
$251$	13.6923	+	23.7157i	0.864248	+	1.49692i	−0.00354445	+	0.999994i	$0.501128\pi$
$252$	0.133471	+	0.0358206i	0.00840788	+	0.00225649i
$253$	−1.29698	+	2.24643i	−0.0815404	+	0.141232i
$254$	0.922990	−	2.53589i	0.0579135	−	0.159116i
$255$	6.84625	+	9.65280i	0.428729	+	0.604482i
$256$	−0.320075	−	0.268575i	−0.0200047	−	0.0167859i
$257$	−2.77342	+	15.7288i	−0.173001	+	0.981138i	0.767425	+	0.641139i	$0.221538\pi$
$257$	−2.77342	+	15.7288i	−0.173001	+	0.981138i	−0.940426	+	0.339999i	$0.889573\pi$
$258$	14.7917	−	10.4910i	0.920891	−	0.653141i
$259$	10.0339	−	13.9558i	0.623474	−	0.867170i
$260$	0.211819	+	0.122294i	0.0131365	+	0.00758434i
$261$	9.98156	−	8.58317i	0.617843	−	0.531285i
$262$	−10.6180	−	6.13031i	−0.655983	−	0.378732i
$263$	−9.86756	+	27.1109i	−0.608460	+	1.67173i	0.125132	+	0.992140i	$0.460065\pi$
$263$	−9.86756	+	27.1109i	−0.608460	+	1.67173i	−0.733592	+	0.679590i	$0.762158\pi$
$264$	14.9887	+	10.3608i	0.922491	+	0.637664i
$265$	−1.83900	−	0.324266i	−0.112969	−	0.0199195i
$266$	17.8815	+	8.61165i	1.09639	+	0.528014i
$267$	7.30329	+	1.90970i	0.446954	+	0.116871i
$268$	0.140298	−	0.117724i	0.00857007	−	0.00719114i
$269$	4.08105	+	7.06859i	0.248826	+	0.430979i	0.963200	−	0.268784i	$-0.0866219\pi$
$269$	4.08105	+	7.06859i	0.248826	+	0.430979i	−0.714374	+	0.699764i	$0.753289\pi$
$270$	10.7177	−	11.1134i	0.652258	−	0.676342i
$271$	10.1461	+	5.85783i	0.616329	+	0.355838i	0.775438	−	0.631423i	$-0.217529\pi$
$271$	10.1461	+	5.85783i	0.616329	+	0.355838i	−0.159109	+	0.987261i	$0.550862\pi$
$272$	−12.0631	−	4.39061i	−0.731432	−	0.266220i
$273$	26.5170	−	15.0827i	1.60488	−	0.912847i
$274$	7.52564	+	6.31476i	0.454640	+	0.381488i
$275$	−1.30175	+	1.55137i	−0.0784987	+	0.0935511i
$276$	0.0210526	+	0.00171377i	0.00126722	+	0.000103157i
$277$	8.94325	+	3.25508i	0.537348	+	0.195579i	0.596416	−	0.802675i	$-0.296591\pi$
$277$	8.94325	+	3.25508i	0.537348	+	0.195579i	−0.0590684	+	0.998254i	$0.518813\pi$
$278$	14.8118			0.888356
$279$	−3.48815	−	2.85580i	−0.208830	−	0.170972i
$280$	3.91324	+	15.3693i	0.233861	+	0.918491i
$281$	20.5328	−	3.62048i	1.22488	−	0.215980i	0.476457	−	0.879198i	$-0.341921\pi$
$281$	20.5328	−	3.62048i	1.22488	−	0.215980i	0.748426	+	0.663218i	$0.230810\pi$
$282$	−11.9271	+	8.45926i	−0.710246	+	0.503741i
$283$	0.946510	−	1.12801i	0.0562642	−	0.0670531i	−0.737178	−	0.675698i	$-0.763842\pi$
$283$	0.946510	−	1.12801i	0.0562642	−	0.0670531i	0.793443	+	0.608645i	$0.208287\pi$
$284$	−0.0495263	+	0.0590232i	−0.00293885	+	0.00350238i
$285$	−15.8834	+	11.2653i	−0.940852	+	0.667299i
$286$	34.1863	−	6.02796i	2.02148	−	0.356441i
$287$	−20.6121	−	21.1332i	−1.21669	−	1.24746i
$288$	0.0477871	−	0.291573i	0.00281588	−	0.0171811i
$289$	−6.51698			−0.383352
$290$	12.2523	+	4.45947i	0.719480	+	0.261869i
$291$	−12.0231	−	0.978727i	−0.704806	−	0.0573740i
$292$	−0.0342613	+	0.0408310i	−0.00200499	+	0.00238946i
$293$	−4.11874	−	3.45603i	−0.240619	−	0.201904i	0.514501	−	0.857490i	$-0.327977\pi$
$293$	−4.11874	−	3.45603i	−0.240619	−	0.201904i	−0.755120	+	0.655586i	$0.772422\pi$
$294$	16.4034	+	4.72970i	0.956664	+	0.275842i
$295$	12.3633	+	4.49987i	0.719818	+	0.261992i
$296$	−15.9819	−	9.22716i	−0.928930	−	0.536318i
$297$	−1.32947	+	19.1975i	−0.0771437	+	1.11395i
$298$	7.83400	+	13.5689i	0.453811	+	0.786024i
$299$	3.57187	−	2.99715i	0.206566	−	0.173330i
$300$	0.0159543	+	0.00417179i	0.000921121	+	0.000240859i
$301$	−16.2549	+	11.0820i	−0.936918	+	0.638758i
$302$	−28.0016	−	4.93743i	−1.61131	−	0.284117i
$303$	−5.29753	−	3.66187i	−0.304335	−	0.210369i
$304$	7.22461	−	19.8495i	0.414360	−	1.13844i
$305$	13.5917	+	7.84719i	0.778261	+	0.449329i
$306$	−2.53750	−	13.4392i	−0.145059	−	0.768269i
$307$	6.76941	+	3.90832i	0.386351	+	0.223060i	0.680578	−	0.732676i	$-0.261729\pi$
$307$	6.76941	+	3.90832i	0.386351	+	0.223060i	−0.294227	+	0.955736i	$0.595062\pi$
$308$	−0.138513	−	0.0995871i	−0.00789248	−	0.00567450i
$309$	−8.76807	+	6.21875i	−0.498798	+	0.353772i
$310$	0.775338	−	4.39716i	0.0440362	−	0.249742i
$311$	−9.50108	−	7.97235i	−0.538757	−	0.452071i	0.332356	−	0.943154i	$-0.392157\pi$
$311$	−9.50108	−	7.97235i	−0.538757	−	0.452071i	−0.871113	+	0.491083i	$0.836601\pi$
$312$	−18.9482	−	26.7158i	−1.07273	−	1.51248i
$313$	2.42423	−	6.66051i	0.137026	−	0.376474i	−0.852133	−	0.523325i	$-0.824691\pi$
$313$	2.42423	−	6.66051i	0.137026	−	0.376474i	0.989159	+	0.146850i	$0.0469136\pi$
$314$	−3.44439	+	5.96587i	−0.194378	+	0.336673i
$315$	−11.8485	+	11.8390i	−0.667587	+	0.667054i
$316$	0.0828727	+	0.143540i	0.00466196	+	0.00807475i
$317$	16.6689	−	2.93919i	0.936221	−	0.165081i	0.315334	−	0.948981i	$-0.397883\pi$
$317$	16.6689	−	2.93919i	0.936221	−	0.165081i	0.620887	+	0.783900i	$0.286772\pi$
$318$	1.77527	+	1.22714i	0.0995520	+	0.0688145i
$319$	−15.2711	+	5.55822i	−0.855016	+	0.311200i
$320$	15.9996	−	5.82337i	0.894404	−	0.325537i
$321$	3.52071	+	3.47842i	0.196507	+	0.194147i
$322$	2.59634	+	0.259845i	0.144688	+	0.0144806i
$323$			17.2495i			0.959788i
$324$	0.145909	−	0.0571361i	0.00810608	−	0.00317423i
$325$	3.15261	−	1.82016i	0.174875	−	0.100964i
$326$	−12.9963	+	2.29160i	−0.719799	+	0.126920i
$327$	−2.58248	−	9.41017i	−0.142812	−	0.520383i
$328$	−20.3730	+	24.2797i	−1.12491	+	1.34062i
$329$	13.1069	−	8.93583i	0.722607	−	0.492648i
$330$	−17.2249	+	8.15915i	−0.948199	+	0.449146i
$331$	2.51122	+	14.2418i	0.138029	+	0.782801i	0.972702	+	0.232056i	$0.0745452\pi$
$331$	2.51122	+	14.2418i	0.138029	+	0.782801i	−0.834674	+	0.550745i	$0.814344\pi$
$332$	−0.105960	+	0.183529i	−0.00581532	+	0.0100724i
$333$	−0.235493	−	19.4884i	−0.0129050	−	1.06796i
$334$	−10.5029	+	6.06386i	−0.574694	+	0.331799i
$335$	3.85463	+	21.8607i	0.210601	+	1.19438i
$336$	3.27026	−	17.8726i	0.178407	−	0.975031i
$337$	−14.9144	+	5.42839i	−0.812438	+	0.295703i	−0.714630	−	0.699502i	$-0.753405\pi$
$337$	−14.9144	+	5.42839i	−0.812438	+	0.295703i	−0.0978073	+	0.995205i	$0.531183\pi$
$338$	−43.4246	−	7.65693i	−2.36199	−	0.416482i
$339$	−14.4558	−	6.63484i	−0.785134	−	0.360355i
$340$	−0.0911278	+	0.0764653i	−0.00494210	+	0.00414691i
$341$	2.78255	+	4.81952i	0.150683	+	0.260991i
$342$	22.1138	−	4.17538i	1.19578	−	0.225779i
$343$	−17.6972	−	5.45979i	−0.955559	−	0.294801i
$344$	13.5770	+	16.1804i	0.732023	+	0.872391i
$345$	−1.45571	+	2.10594i	−0.0783728	+	0.113380i
$346$	4.08070	+	11.2116i	0.219380	+	0.602741i
$347$	−5.06257	−	0.892668i	−0.271773	−	0.0479209i	0.0361006	−	0.999348i	$-0.488506\pi$
$347$	−5.06257	−	0.892668i	−0.271773	−	0.0479209i	−0.307874	+	0.951427i	$0.599617\pi$
$348$	0.0941357	+	0.0930050i	0.00504620	+	0.00498559i
$349$	3.81124	−	10.4713i	0.204011	−	0.560516i	−0.794921	−	0.606713i	$-0.792488\pi$
$349$	3.81124	−	10.4713i	0.204011	−	0.560516i	0.998932	+	0.0461967i	$0.0147101\pi$
$350$	1.96101	+	0.551775i	0.104820	+	0.0294936i
$351$	14.0482	−	31.6099i	0.749837	−	1.68721i
$352$	−0.182371	+	0.315875i	−0.00972038	+	0.0168362i
$353$	−0.534901	−	3.03357i	−0.0284699	−	0.161461i	0.967258	−	0.253794i	$-0.0816786\pi$
$353$	−0.534901	−	3.03357i	−0.0284699	−	0.161461i	−0.995728	+	0.0923333i	$0.970567\pi$
$354$	−10.8164	−	10.6865i	−0.574887	−	0.567982i
$355$	−3.19400	−	8.77545i	−0.169520	−	0.465752i
$356$	−0.0131768	+	0.0747292i	−0.000698368	+	0.00396064i
$357$	2.48229	+	14.6281i	0.131377	+	0.774202i
$358$	5.21599	−	4.37674i	0.275674	−	0.231318i
$359$		−	21.9068i		−	1.15620i	−0.815967	−	0.578099i	$-0.803795\pi$
$359$		−	21.9068i		−	1.15620i	0.815967	−	0.578099i	$-0.196205\pi$
$360$	13.9146	+	11.3921i	0.733362	+	0.600414i
$361$	−9.38353			−0.493870
$362$	−6.03899	−	2.19801i	−0.317402	−	0.115525i
$363$	1.96180	−	4.27433i	0.102968	−	0.224344i
$364$	0.172741	+	0.253373i	0.00905407	+	0.0132803i
$365$	−2.20955	−	6.07068i	−0.115653	−	0.317754i
$366$	−10.4931	−	14.7946i	−0.548481	−	0.773325i
$367$	−4.25108	−	5.06624i	−0.221905	−	0.264456i	0.643594	−	0.765367i	$-0.277443\pi$
$367$	−4.25108	−	5.06624i	−0.221905	−	0.264456i	−0.865499	+	0.500912i	$0.832998\pi$
$368$		−	2.77709i		−	0.144766i
$369$	−33.0326	−	5.41385i	−1.71961	−	0.281834i
$370$	16.7174	−	9.65179i	0.869096	−	0.501773i
$371$	−1.90092	−	1.36671i	−0.0986908	−	0.0709562i
$372$	0.0257674	−	0.0372769i	0.00133598	−	0.00193272i
$373$	18.8688	+	15.8328i	0.976988	+	0.819790i	0.983632	−	0.180188i	$-0.0576705\pi$
$373$	18.8688	+	15.8328i	0.976988	+	0.819790i	−0.00664425	+	0.999978i	$0.502115\pi$
$374$	−2.93179	+	16.6270i	−0.151599	+	0.859761i
$375$	−14.2490	+	14.4223i	−0.735817	+	0.744762i
$376$	−10.9476	−	13.0468i	−0.564579	−	0.672839i
$377$	29.2121			1.50450
$378$	18.1524	−	6.72315i	0.933657	−	0.345801i
$379$	2.06704			0.106176			0.0530882	−	0.998590i	$-0.483094\pi$
$379$	2.06704			0.106176			0.0530882	+	0.998590i	$0.483094\pi$
$380$	−0.125821	−	0.149948i	−0.00645450	−	0.00769217i
$381$	0.878540	+	3.20127i	0.0450089	+	0.164006i
$382$	−2.52862	+	14.3405i	−0.129376	+	0.733725i
$383$	5.29740	+	4.44505i	0.270685	+	0.227131i	0.768018	−	0.640428i	$-0.221243\pi$
$383$	5.29740	+	4.44505i	0.270685	+	0.227131i	−0.497334	+	0.867559i	$0.665687\pi$
$384$	−19.2724	−	1.56885i	−0.983490	−	0.0800600i
$385$	18.8473	−	8.50385i	0.960546	−	0.433396i
$386$	12.6881	−	7.32550i	0.645810	−	0.372858i
$387$	−7.37570	+	21.0527i	−0.374928	+	1.07017i
$388$		−	0.121258i		−	0.00615592i
$389$	−8.68514	−	10.3505i	−0.440354	−	0.524794i	0.499526	−	0.866299i	$-0.333508\pi$
$389$	−8.68514	−	10.3505i	−0.440354	−	0.524794i	−0.939880	+	0.341505i	$0.889063\pi$
$390$	34.1113	−	3.19213i	1.72730	−	0.161640i
$391$	0.775631	+	2.13103i	0.0392254	+	0.107771i
$392$	−3.94061	+	19.4898i	−0.199031	+	0.984386i
$393$	15.0163	−	1.40522i	0.757473	−	0.0708841i
$394$	18.7609	+	6.82840i	0.945159	+	0.344010i
$395$	−20.0889			−1.01078
$396$	−0.193425	+	0.00233729i	−0.00971995	+	0.000117453i
$397$			21.5333i			1.08072i	0.841433	+	0.540362i	$0.181713\pi$
$397$			21.5333i			1.08072i	−0.841433	+	0.540362i	$0.818287\pi$
$398$	21.6994	−	18.2079i	1.08769	−	0.912681i
$399$	−24.0701	+	4.08453i	−1.20501	+	0.204482i
$400$	0.376494	−	2.13521i	0.0188247	−	0.106760i
$401$	−9.04869	−	24.8611i	−0.451870	−	1.24150i	−0.931407	−	0.363981i	$-0.881417\pi$
$401$	−9.04869	−	24.8611i	−0.451870	−	1.24150i	0.479537	−	0.877522i	$-0.340805\pi$
$402$	6.48992	−	24.8195i	0.323688	−	1.23789i
$403$	−1.73709	−	9.85151i	−0.0865304	−	0.490738i
$404$	0.0323677	−	0.0560625i	0.00161035	−	0.00278921i
$405$	−2.84505	+	18.7780i	−0.141372	+	0.933084i
$406$	11.4141	+	11.7027i	0.566473	+	0.580794i
$407$	−8.22890	+	22.6087i	−0.407891	+	1.12067i
$408$	15.3620	−	4.21586i	0.760531	−	0.208716i
$409$	−24.6998	−	4.35525i	−1.22133	−	0.215353i	−0.474431	−	0.880293i	$-0.657346\pi$
$409$	−24.6998	−	4.35525i	−1.22133	−	0.215353i	−0.746897	+	0.664939i	$0.768457\pi$
$410$	−11.3391	−	31.1540i	−0.560000	−	1.53859i
$411$	−12.0448	−	0.980494i	−0.594126	−	0.0483642i
$412$	−0.0694568	−	0.0827754i	−0.00342189	−	0.00407805i
$413$	11.5175	+	11.8087i	0.566740	+	0.581068i
$414$	2.54423	−	1.51019i	0.125042	−	0.0742219i
$415$	−12.8427	−	22.2443i	−0.630426	−	1.09193i
$416$	0.502247	−	0.421435i	0.0246247	−	0.0206625i
$417$	−14.8617	+	10.5407i	−0.727781	+	0.516179i
$418$	−27.3592	−	4.82417i	−1.33818	−	0.235958i
$419$	22.3814	−	8.14616i	1.09340	−	0.397966i	0.268522	−	0.963273i	$-0.413465\pi$
$419$	22.3814	−	8.14616i	1.09340	−	0.397966i	0.824880	+	0.565307i	$0.191242\pi$
$420$	−0.128279	−	0.109054i	−0.00625936	−	0.00532131i
$421$	−1.34235	−	7.61285i	−0.0654222	−	0.371027i	−0.999888	−	0.0149744i	$-0.995233\pi$
$421$	−1.34235	−	7.61285i	−0.0654222	−	0.371027i	0.934466	−	0.356053i	$-0.115878\pi$
$422$	4.09248	−	2.36280i	0.199219	−	0.115019i
$423$	5.94728	−	16.9755i	0.289167	−	0.825376i
$424$	−1.25683	+	2.17690i	−0.0610372	+	0.105719i
$425$	0.307448	+	1.74363i	0.0149134	+	0.0845783i
$426$	−0.875664	+	10.7570i	−0.0424261	+	0.521179i
$427$	11.0842	+	16.2581i	0.536402	+	0.786784i
$428$	−0.0319789	+	0.0381110i	−0.00154576	+	0.00184216i
$429$	−30.0116	+	30.3765i	−1.44898	+	1.46659i
$430$	−21.7584	+	3.83660i	−1.04928	+	0.185017i
$431$	4.73254	−	2.73233i	0.227959	−	0.131612i	−0.381671	−	0.924298i	$-0.624651\pi$
$431$	4.73254	−	2.73233i	0.227959	−	0.131612i	0.609630	+	0.792686i	$0.291318\pi$
$432$	−9.04380	−	18.5110i	−0.435120	−	0.890610i
$433$		−	35.5423i		−	1.70805i	−0.520229	−	0.854027i	$-0.674154\pi$
$433$		−	35.5423i		−	1.70805i	0.520229	−	0.854027i	$-0.325846\pi$
$434$	3.26789	−	4.54521i	0.156864	−	0.218177i
$435$	−15.4671	+	4.24471i	−0.741589	+	0.203518i
$436$	0.0921743	−	0.0335487i	0.00441435	−	0.00160669i
$437$	−3.50654	+	1.27628i	−0.167741	+	0.0610526i
$438$	−0.605767	+	7.44149i	−0.0289447	+	0.355568i
$439$	−3.99689	+	0.704759i	−0.190761	+	0.0336363i	−0.268212	−	0.963360i	$-0.586433\pi$
$439$	−3.99689	+	0.704759i	−0.190761	+	0.0336363i	0.0774513	+	0.996996i	$0.475322\pi$
$440$	−11.0999	−	19.2255i	−0.529165	−	0.916541i
$441$	−19.8244	+	6.92763i	−0.944020	+	0.329887i
$442$	15.1744	−	26.2828i	0.721771	−	1.25014i
$443$	2.83479	−	7.78852i	0.134685	−	0.370044i	−0.853955	−	0.520347i	$-0.825803\pi$
$443$	2.83479	−	7.78852i	0.134685	−	0.370044i	0.988640	+	0.150303i	$0.0480250\pi$
$444$	0.195063	−	0.0182539i	0.00925726	−	0.000866293i
$445$	−7.04544	−	5.91182i	−0.333986	−	0.280247i
$446$	−2.45383	+	13.9164i	−0.116192	+	0.658960i
$447$	−17.5165	−	8.03960i	−0.828502	−	0.380260i
$448$	21.2409	+	2.12582i	1.00354	+	0.100435i
$449$	25.1276	+	14.5074i	1.18585	+	0.684648i	0.957359	−	0.288899i	$-0.0932893\pi$
$449$	25.1276	+	14.5074i	1.18585	+	0.684648i	0.228486	+	0.973547i	$0.426623\pi$
$450$	2.16091	−	0.816208i	0.101866	−	0.0384764i
$451$	35.7858	+	20.6610i	1.68509	+	0.972887i
$452$	0.0546845	−	0.150244i	0.00257214	−	0.00706691i
$453$	31.6095	−	14.9729i	1.48514	−	0.703489i
$454$	−24.6115	−	4.33968i	−1.15508	−	0.203671i
$455$	−37.0637	+	2.77695i	−1.73757	+	0.130185i
$456$	6.93708	+	25.2777i	0.324858	+	1.18373i
$457$	−5.02502	+	4.21649i	−0.235061	+	0.197239i	−0.752708	−	0.658355i	$-0.771253\pi$
$457$	−5.02502	+	4.21649i	−0.235061	+	0.197239i	0.517647	+	0.855594i	$0.326808\pi$
$458$	−9.19715	−	15.9299i	−0.429755	−	0.744357i
$459$	12.1099	+	11.6787i	0.565242	+	0.545115i
$460$	−0.0222866	−	0.0128672i	−0.00103912	−	0.000599936i
$461$	−20.7893	−	7.56669i	−0.968255	−	0.352416i	−0.190992	−	0.981592i	$-0.561170\pi$
$461$	−20.7893	−	7.56669i	−0.968255	−	0.352416i	−0.777263	+	0.629176i	$0.783393\pi$
$462$	−23.8957	−	0.153915i	−1.11173	−	0.00716076i
$463$	12.6417	+	10.6077i	0.587511	+	0.492980i	0.887404	−	0.460993i	$-0.152507\pi$
$463$	12.6417	+	10.6077i	0.587511	+	0.492980i	−0.299893	+	0.953973i	$0.596951\pi$
$464$	11.1835	−	13.3280i	0.519181	−	0.618736i
$465$	2.35124	+	4.96372i	0.109036	+	0.230187i
$466$	−25.1023	−	9.13649i	−1.16284	−	0.423240i
$467$	1.42626			0.0659994			0.0329997	−	0.999455i	$-0.489494\pi$
$467$	1.42626			0.0659994			0.0329997	+	0.999455i	$0.489494\pi$
$468$	0.328157	+	0.114968i	0.0151691	+	0.00531441i
$469$	−7.53816	+	26.7906i	−0.348080	+	1.23707i
$470$	17.5446	−	3.09358i	0.809271	−	0.142696i
$471$	−0.789543	−	8.43711i	−0.0363802	−	0.388762i
$472$	11.3839	−	13.5668i	0.523988	−	0.624464i
$473$	17.7009	−	21.0951i	0.813889	−	0.969955i
$474$	21.1003	+	9.68447i	0.969169	+	0.444823i
$475$	−2.86909	+	0.505897i	−0.131643	+	0.0232122i
$476$	−0.144535	+	0.0368006i	−0.00662473	+	0.00168675i
$477$	−2.65452	+	0.0320766i	−0.121542	+	0.00146868i
$478$	−29.9106			−1.36808
$479$	22.5859	+	8.22061i	1.03198	+	0.375609i	0.801834	−	0.597547i	$-0.203858\pi$
$479$	22.5859	+	8.22061i	1.03198	+	0.375609i	0.230144	+	0.973157i	$0.426080\pi$
$480$	−0.204690	+	0.296119i	−0.00934278	+	0.0135159i
$481$	27.7994	−	33.1301i	1.26754	−	1.51060i
$482$	−12.7101	−	10.6651i	−0.578930	−	0.485780i
$483$	−2.79000	+	1.58693i	−0.126949	+	0.0722080i
$484$	0.0444246	+	0.0161692i	0.00201930	+	0.000734965i
$485$	12.7278	+	7.34842i	0.577941	+	0.333674i
$486$	12.0408	−	18.3518i	0.546181	−	0.832455i
$487$	17.7620	+	30.7647i	0.804874	+	1.39408i	0.916376	+	0.400319i	$0.131101\pi$
$487$	17.7620	+	30.7647i	0.804874	+	1.39408i	−0.111501	+	0.993764i	$0.535566\pi$
$488$	16.1836	−	13.5796i	0.732597	−	0.614722i
$489$	11.4093	−	11.5480i	0.515945	−	0.522217i
$490$	−15.5945	−	13.7631i	−0.704487	−	0.621753i
$491$	−30.5498	−	5.38675i	−1.37869	−	0.243101i	−0.565334	−	0.824862i	$-0.691253\pi$
$491$	−30.5498	−	5.38675i	−1.37869	−	0.243101i	−0.813360	+	0.581761i	$0.802364\pi$
$492$	0.0273004	−	0.335370i	0.00123080	−	0.0151196i
$493$	−4.85933	+	13.3509i	−0.218853	+	0.601294i
$494$	43.2475	+	24.9690i	1.94580	+	1.12341i
$495$	11.4765	−	20.4445i	0.515831	−	0.918912i
$496$	−5.15977	−	2.97899i	−0.231681	−	0.133761i
$497$	1.16597	−	11.6502i	0.0523008	−	0.522584i
$498$	2.76579	+	29.5554i	0.123938	+	1.32441i
$499$	6.32386	−	35.8644i	0.283095	−	1.60551i	−0.428917	−	0.903344i	$-0.641105\pi$
$499$	6.32386	−	35.8644i	0.283095	−	1.60551i	0.712012	−	0.702167i	$-0.247784\pi$
$500$	−0.156118	−	0.130999i	−0.00698181	−	0.00585844i
$501$	6.22300	−	13.5585i	0.278023	−	0.605751i
$502$	−13.1878	+	36.2332i	−0.588601	+	1.61717i
$503$	−9.30116	+	16.1101i	−0.414718	+	0.718313i	−0.995399	−	0.0958185i	$-0.969453\pi$
$503$	−9.30116	+	16.1101i	−0.414718	+	0.718313i	0.580681	+	0.814131i	$0.302787\pi$
$504$	9.52044	+	20.4380i	0.424074	+	0.910379i
$505$	3.92308	+	6.79497i	0.174575	+	0.302372i
$506$	−3.59692	+	0.634234i	−0.159903	+	0.0281951i
$507$	49.0198	−	23.2199i	2.17705	−	1.03123i
$508$	−0.0313570	+	0.0114130i	−0.00139124	+	0.000506370i
$509$	4.20101	−	1.52904i	0.186207	−	0.0677737i	−0.247234	−	0.968956i	$-0.579522\pi$
$509$	4.20101	−	1.52904i	0.186207	−	0.0677737i	0.433441	+	0.901182i	$0.357299\pi$
$510$	−4.21540	+	16.1210i	−0.186661	+	0.713851i
$511$	0.806593	−	8.05939i	0.0356816	−	0.356526i
$512$		−	22.9158i		−	1.01274i
$513$	−19.2169	+	19.9265i	−0.848449	+	0.879776i
$514$	−19.4757	+	11.2443i	−0.859034	+	0.495964i
$515$	12.8977	−	2.27422i	0.568343	−	0.100214i
$516$	−0.216942	−	0.0567270i	−0.00955035	−	0.00249726i
$517$	−14.2729	+	17.0097i	−0.627719	+	0.748087i
$518$	24.1344	−	1.80824i	1.06041	−	0.0794494i
$519$	−12.0731	−	8.34540i	−0.529948	−	0.366322i
$520$	6.92941	+	39.2986i	0.303875	+	1.72336i
$521$	−17.3340	+	30.0233i	−0.759415	+	1.31535i	0.183735	+	0.982976i	$0.441181\pi$
$521$	−17.3340	+	30.0233i	−0.759415	+	1.31535i	−0.943149	+	0.332369i	$0.892152\pi$
$522$	18.2921	+	2.99796i	0.800622	+	0.131217i
$523$	−22.2749	+	12.8604i	−0.974015	+	0.562348i	−0.900458	−	0.434943i	$-0.856768\pi$
$523$	−22.2749	+	12.8604i	−0.974015	+	0.562348i	−0.0735572	+	0.997291i	$0.523435\pi$
$524$	0.0263260	+	0.149302i	0.00115006	+	0.00652231i
$525$	−2.36027	+	0.841893i	−0.103011	+	0.0367432i
$526$	−38.1734	+	13.8940i	−1.66444	+	0.605806i
$527$	4.79143	+	0.844858i	0.208718	+	0.0368026i
$528$	2.36964	+	25.3221i	0.103125	+	1.10200i
$529$	17.2432	−	14.4688i	0.749705	−	0.629077i
$530$	−1.31467	−	2.27708i	−0.0571057	−	0.0989099i
$531$	18.4578	+	3.02512i	0.800999	+	0.131279i
$532$	−0.0605542	−	0.237827i	−0.00262536	−	0.0103111i
$533$	−47.7448	−	56.9001i	−2.06806	−	2.46462i
$534$	4.55017	+	9.60592i	0.196905	+	0.415689i
$535$	−2.06235	−	5.66626i	−0.0891632	−	0.244974i
$536$	29.4266	+	5.18871i	1.27104	+	0.224118i
$537$	−2.11890	+	8.10337i	−0.0914374	+	0.349686i
$538$	−3.93070	+	10.7995i	−0.169465	+	0.465600i
$539$	25.9158	+	0.647128i	1.11627	+	0.0278738i
$540$	−0.190457	−	0.0131895i	−0.00819596	−	0.000567587i
$541$	13.1658	−	22.8039i	0.566044	−	0.980416i	−0.430908	−	0.902396i	$-0.641807\pi$
$541$	13.1658	−	22.8039i	0.566044	−	0.980416i	0.996952	−	0.0780204i	$-0.0248599\pi$
$542$	2.86453	+	16.2455i	0.123042	+	0.697806i
$543$	7.62351	−	2.09216i	0.327156	−	0.0897831i
$544$	0.109063	+	0.299648i	0.00467603	+	0.0128473i
$545$	−2.06447	+	11.7082i	−0.0884323	+	0.501524i
$546$	40.2684	+	14.9509i	1.72333	+	0.639841i
$547$	13.7395	−	11.5288i	0.587459	−	0.492937i	−0.299928	−	0.953962i	$-0.596963\pi$
$547$	13.7395	−	11.5288i	0.587459	−	0.492937i	0.887387	+	0.461025i	$0.152518\pi$
$548$		−	0.121477i		−	0.00518922i
$549$	21.0568	+	7.37714i	0.898680	+	0.314849i
$550$	−2.85153			−0.121590
$551$	−21.9685	−	7.99587i	−0.935889	−	0.340636i
$552$	1.99364	+	2.81091i	0.0848549	+	0.119640i
$553$	−22.6923	−	10.9285i	−0.964973	−	0.464726i
$554$	4.58329	+	12.5925i	0.194725	+	0.535004i
$555$	−9.90510	+	21.5810i	−0.420448	+	0.916063i
$556$	−0.117728	−	0.140303i	−0.00499278	−	0.00595016i
$557$			1.14693i			0.0485968i	0.999705	+	0.0242984i	$0.00773518\pi$
$557$			1.14693i			0.0485968i	−0.999705	+	0.0242984i	$0.992265\pi$
$558$	−0.0766969	−	6.34711i	−0.00324684	−	0.268695i
$559$	−42.8684	+	24.7501i	−1.81314	+	1.04682i
$560$	−12.9224	+	17.9734i	−0.546073	+	0.759516i
$561$	−8.89073	−	18.7693i	−0.375367	−	0.792442i
$562$	22.4888	+	18.8704i	0.948634	+	0.795998i
$563$	−1.56861	+	8.89601i	−0.0661089	+	0.374922i	0.933747	+	0.357934i	$0.116519\pi$
$563$	−1.56861	+	8.89601i	−0.0661089	+	0.374922i	−0.999856	+	0.0169880i	$0.994592\pi$
$564$	0.174928	+	0.0457409i	0.00736579	+	0.00192604i
$565$	12.4565	+	14.8450i	0.524048	+	0.624536i
$566$	2.07336			0.0871497
$567$	−13.4290	+	19.6637i	−0.563967	+	0.825797i
$568$	−12.5707			−0.527455
$569$	27.5657	+	32.8516i	1.15562	+	1.37721i	0.913438	+	0.406978i	$0.133417\pi$
$569$	27.5657	+	32.8516i	1.15562	+	1.37721i	0.242178	+	0.970232i	$0.422138\pi$
$570$	−26.5267	−	6.93631i	−1.11108	−	0.290530i
$571$	−5.74972	+	32.6083i	−0.240618	+	1.36461i	0.589834	+	0.807524i	$0.299193\pi$
$571$	−5.74972	+	32.6083i	−0.240618	+	1.36461i	−0.830453	+	0.557089i	$0.811918\pi$
$572$	−0.328819	−	0.275912i	−0.0137486	−	0.0115365i
$573$	−7.66812	−	16.1883i	−0.320340	−	0.676275i
$574$	4.13934	−	41.3599i	0.172773	−	1.72633i
$575$	−0.331703	+	0.191509i	−0.0138330	+	0.00798648i
$576$	20.8146	−	12.3550i	0.867276	−	0.514793i
$577$		−	41.8339i		−	1.74157i	−0.491665	−	0.870784i	$-0.663612\pi$
$577$		−	41.8339i		−	1.74157i	0.491665	−	0.870784i	$-0.336388\pi$
$578$	−5.89835	−	7.02938i	−0.245339	−	0.292383i
$579$	−7.51776	+	16.3795i	−0.312427	+	0.680710i
$580$	−0.0551425	−	0.151503i	−0.00228967	−	0.00629081i
$581$	−2.40606	−	32.1135i	−0.0998200	−	1.33229i
$582$	−9.82610	−	13.8542i	−0.407305	−	0.574276i
$583$	3.07953	+	1.12086i	0.127541	+	0.0464212i
$584$	−8.69617			−0.359850
$585$	−31.9546	+	27.4778i	−1.32116	+	1.13607i
$586$		−	7.57054i		−	0.312736i
$587$	10.1800	−	8.54200i	0.420172	−	0.352566i	−0.408057	−	0.912957i	$-0.633793\pi$
$587$	10.1800	−	8.54200i	0.420172	−	0.352566i	0.828228	+	0.560391i	$0.189349\pi$
$588$	−0.0855765	−	0.192971i	−0.00352911	−	0.00795799i
$589$	−1.39019	+	7.88415i	−0.0572817	+	0.324861i
$590$	6.33602	+	17.4081i	0.260850	+	0.716678i
$591$	−23.6834	+	6.49955i	−0.974204	+	0.267356i
$592$	−4.47288	−	25.3670i	−0.183834	−	1.04258i
$593$	6.07625	−	10.5244i	0.249522	−	0.432184i	−0.713872	−	0.700277i	$-0.753060\pi$
$593$	6.07625	−	10.5244i	0.249522	−	0.432184i	0.963393	+	0.268093i	$0.0863933\pi$
$594$	−21.9102	+	15.9412i	−0.898987	+	0.654075i
$595$	4.89626	−	17.4013i	0.200727	−	0.713383i
$596$	0.0662626	−	0.182055i	0.00271422	−	0.00745726i
$597$	−8.81497	+	33.7113i	−0.360773	+	1.37971i
$598$	6.46560	+	1.14006i	0.264398	+	0.0466205i
$599$	10.4793	+	28.7916i	0.428172	+	1.17639i	0.946921	+	0.321466i	$0.104176\pi$
$599$	10.4793	+	28.7916i	0.428172	+	1.17639i	−0.518749	+	0.854927i	$0.673602\pi$
$600$	1.15176	+	2.43149i	0.0470203	+	0.0992652i
$601$	0.739101	+	0.880827i	0.0301486	+	0.0359297i	0.780908	−	0.624646i	$-0.214757\pi$
$601$	0.739101	+	0.880827i	0.0301486	+	0.0359297i	−0.750759	+	0.660576i	$0.770312\pi$
$602$	−26.6653	−	7.50290i	−1.08679	−	0.305795i
$603$	11.1507	+	29.5216i	0.454093	+	1.20221i
$604$	0.175794	+	0.304484i	0.00715296	+	0.0123893i
$605$	−4.38941	+	3.68315i	−0.178455	+	0.149741i
$606$	−0.844867	−	9.02830i	−0.0343204	−	0.366750i
$607$	2.97007	+	0.523704i	0.120552	+	0.0212565i	0.233598	−	0.972333i	$-0.424950\pi$
$607$	2.97007	+	0.523704i	0.120552	+	0.0212565i	−0.113047	+	0.993590i	$0.536061\pi$
$608$	−0.493061	+	0.179460i	−0.0199963	+	0.00727805i
$609$	−19.7806	−	3.61937i	−0.801551	−	0.146664i
$610$	3.83735	+	21.7627i	0.155370	+	0.881145i
$611$	34.5662	−	19.9568i	1.39840	−	0.807367i
$612$	−0.107132	+	0.130854i	−0.00433056	+	0.00528947i
$613$	20.0456	−	34.7199i	0.809633	−	1.40232i	−0.103486	−	0.994631i	$-0.533000\pi$
$613$	20.0456	−	34.7199i	0.809633	−	1.40232i	0.913119	−	0.407694i	$-0.133667\pi$
$614$	1.91120	+	10.8390i	0.0771299	+	0.437425i
$615$	33.5477	+	23.1896i	1.35277	+	0.935093i
$616$	−2.07953	−	27.7554i	−0.0837867	−	1.11830i
$617$	6.57249	−	7.83278i	0.264598	−	0.315336i	−0.617344	−	0.786693i	$-0.711791\pi$
$617$	6.57249	−	7.83278i	0.264598	−	0.315336i	0.881942	+	0.471357i	$0.156236\pi$
$618$	−14.6435	−	3.82903i	−0.589046	−	0.154026i
$619$	38.3209	−	6.75702i	1.54025	−	0.271587i	0.661894	−	0.749597i	$-0.269753\pi$
$619$	38.3209	−	6.75702i	1.54025	−	0.271587i	0.878354	+	0.478010i	$0.158642\pi$
$620$	−0.0478139	+	0.0276054i	−0.00192025	+	0.00110866i
$621$	−1.47809	+	3.32585i	−0.0593136	+	0.133462i
$622$		−	17.4637i		−	0.700229i
$623$	−4.74240	−	10.5107i	−0.190000	−	0.421102i
$624$	11.5652	−	44.2292i	0.462980	−	1.77059i
$625$	20.6420	−	7.51308i	0.825681	−	0.300523i
$626$	9.37830	−	3.41342i	0.374832	−	0.136428i
$627$	30.8844	−	14.6294i	1.23340	−	0.584243i
$628$	0.0838875	−	0.0147916i	0.00334748	−	0.000590250i
$629$	10.5172	+	18.2163i	0.419349	+	0.726333i
$630$	−23.4936	−	2.06488i	−0.936008	−	0.0822668i
$631$	5.94429	−	10.2958i	0.236639	−	0.409870i	−0.723109	−	0.690734i	$-0.757288\pi$
$631$	5.94429	−	10.2958i	0.236639	−	0.409870i	0.959748	+	0.280864i	$0.0906210\pi$
$632$	−9.24879	+	25.4108i	−0.367897	+	1.01079i
$633$	−2.42481	+	5.28311i	−0.0963774	+	0.209985i
$634$	18.2569	+	15.3194i	0.725074	+	0.608409i
$635$	0.702317	−	3.98304i	0.0278706	−	0.158062i
$636$	−0.00248637	−	0.0265695i	−9.85909e−5	−	0.00105355i
$637$	−43.3775	−	17.0260i	−1.71868	−	0.674595i
$638$	−19.8167	−	11.4412i	−0.784550	−	0.452960i
$639$	−6.77649	−	11.4164i	−0.268074	−	0.451626i
$640$	20.4021	+	11.7791i	0.806462	+	0.465611i
$641$	−17.0872	+	46.9468i	−0.674906	+	1.85429i	−0.184396	+	0.982852i	$0.559033\pi$
$641$	−17.0872	+	46.9468i	−0.674906	+	1.85429i	−0.490509	+	0.871436i	$0.663189\pi$
$642$	−0.565412	+	6.94575i	−0.0223150	+	0.274127i
$643$	−7.32572	−	1.29172i	−0.288898	−	0.0509406i	0.0273209	−	0.999627i	$-0.491302\pi$
$643$	−7.32572	−	1.29172i	−0.288898	−	0.0509406i	−0.316219	+	0.948686i	$0.602414\pi$
$644$	−0.0181750	−	0.0266587i	−0.000716194	−	0.00105050i
$645$	19.1014	−	19.3336i	0.752118	−	0.761261i
$646$	−18.6057	+	15.6121i	−0.732033	+	0.614248i
$647$	−9.06934	−	15.7086i	−0.356553	−	0.617567i	0.630830	−	0.775921i	$-0.282715\pi$
$647$	−9.06934	−	15.7086i	−0.356553	−	0.617567i	−0.987382	+	0.158354i	$0.949381\pi$
$648$	22.4427	+	12.2440i	0.881634	+	0.480989i
$649$	−19.9962	−	11.5448i	−0.784919	−	0.453173i
$650$	4.81662	+	1.75310i	0.188923	+	0.0687624i
$651$	−0.0443538	+	6.88606i	−0.00173836	+	0.269886i
$652$	0.125004	+	0.104891i	0.00489555	+	0.00410786i
$653$	−14.2828	+	17.0215i	−0.558928	+	0.666104i	−0.969319	−	0.245805i	$-0.920948\pi$
$653$	−14.2828	+	17.0215i	−0.558928	+	0.666104i	0.410392	+	0.911909i	$0.365392\pi$
$654$	7.81270	−	11.3024i	0.305501	−	0.441960i
$655$	−17.2670	−	6.28466i	−0.674676	−	0.245562i
$656$	−44.2392			−1.72725
$657$	−4.68784	−	7.89763i	−0.182890	−	0.308116i
$658$	21.5011	+	6.04984i	0.838200	+	0.235847i
$659$	21.2896	−	3.75393i	0.829324	−	0.146232i	0.257157	−	0.966370i	$-0.417214\pi$
$659$	21.2896	−	3.75393i	0.829324	−	0.146232i	0.572167	+	0.820137i	$0.306103\pi$
$660$	0.214194	+	0.0983091i	0.00833748	+	0.00382668i
$661$	3.08248	−	3.67356i	0.119895	−	0.142885i	−0.702758	−	0.711428i	$-0.748049\pi$
$661$	3.08248	−	3.67356i	0.119895	−	0.142885i	0.822653	+	0.568544i	$0.192493\pi$
$662$	−13.0887	+	15.5986i	−0.508708	+	0.606255i
$663$	3.47835	+	37.1699i	0.135088	+	1.44356i
$664$	−34.0499	+	6.00391i	−1.32139	+	0.232997i
$665$	28.6333	+	8.05665i	1.11035	+	0.312424i
$666$	20.8076	−	17.8925i	0.806277	−	0.693319i
$667$	−3.07356			−0.119009
$668$	0.140918	+	0.0512901i	0.00545230	+	0.00198447i
$669$	−7.44132	−	15.7095i	−0.287698	−	0.607363i
$670$	−20.0908	+	23.9432i	−0.776174	+	0.925008i
$671$	−21.0992	−	17.7044i	−0.814527	−	0.683469i
$672$	−0.392306	+	0.223141i	−0.0151335	+	0.00860787i
$673$	−41.8330	−	15.2260i	−1.61255	−	0.586918i	−0.630604	−	0.776105i	$-0.717193\pi$
$673$	−41.8330	−	15.2260i	−1.61255	−	0.586918i	−0.981941	+	0.189186i	$0.939415\pi$
$674$	−19.3538	−	11.1739i	−0.745480	−	0.430403i
$675$	−1.58734	+	2.35674i	−0.0610967	+	0.0907109i
$676$	0.272620	+	0.472192i	0.0104854	+	0.0181612i
$677$	30.7338	−	25.7887i	1.18120	−	0.991142i	0.181227	−	0.983441i	$-0.441993\pi$
$677$	30.7338	−	25.7887i	1.18120	−	0.991142i	0.999970	−	0.00770076i	$-0.00245125\pi$
$678$	−5.92710	−	21.5975i	−0.227629	−	0.829445i
$679$	10.3797	+	15.2247i	0.398335	+	0.584270i
$680$	−19.1135	−	3.37022i	−0.732968	−	0.129242i
$681$	27.7827	−	13.1602i	1.06463	−	0.504300i
$682$	−2.68004	+	7.36334i	−0.102624	+	0.281957i
$683$	−28.5877	−	16.5051i	−1.09388	−	0.631550i	−0.159271	−	0.987235i	$-0.550914\pi$
$683$	−28.5877	−	16.5051i	−1.09388	−	0.631550i	−0.934606	+	0.355685i	$0.884248\pi$
$684$	−0.215317	−	0.176283i	−0.00823284	−	0.00674034i
$685$	12.7508	+	7.36168i	0.487183	+	0.281275i
$686$	−10.1282	−	24.0301i	−0.386696	−	0.917475i
$687$	20.5645	+	9.43853i	0.784583	+	0.360102i
$688$	−5.11947	+	29.0340i	−0.195178	+	1.10691i
$689$	−4.51265	−	3.78656i	−0.171918	−	0.144257i
$690$	−3.58904	+	0.335862i	−0.136632	+	0.0127860i
$691$	1.00124	−	2.75087i	0.0380888	−	0.104648i	−0.919190	−	0.393814i	$-0.871156\pi$
$691$	1.00124	−	2.75087i	0.0380888	−	0.104648i	0.957279	+	0.289165i	$0.0933778\pi$
$692$	0.0737660	−	0.127766i	0.00280416	−	0.00485695i
$693$	24.0857	−	16.8506i	0.914939	−	0.640103i
$694$	−3.61915	−	6.26854i	−0.137381	−	0.237951i
$695$	21.8614	−	3.85476i	0.829251	−	0.146219i
$696$	−1.75172	+	21.5188i	−0.0663987	+	0.815668i
$697$	33.9474	−	12.3559i	1.28585	−	0.468011i
$698$	14.7441	−	5.36640i	0.558071	−	0.203121i
$699$	31.6887	−	8.69649i	1.19858	−	0.328931i
$700$	−0.0103599	−	0.0229609i	−0.000391569	−	0.000867842i
$701$			6.39386i			0.241493i	0.992683	+	0.120746i	$0.0385288\pi$
$701$			6.39386i			0.241493i	−0.992683	+	0.120746i	$0.961471\pi$
$702$	46.8098	−	13.4565i	1.76672	−	0.507884i
$703$	−29.9744	+	17.3058i	−1.13051	+	0.652699i
$704$	−29.4268	+	5.18874i	−1.10906	+	0.195558i
$705$	−15.4021	+	15.5894i	−0.580078	+	0.587130i
$706$	2.78796	−	3.32257i	0.104926	−	0.125046i
$707$	0.734978	+	9.80970i	0.0276417	+	0.368932i
$708$	−0.0152548	+	0.187396i	−0.000573309	+	0.00704276i
$709$	−6.22575	−	35.3080i	−0.233813	−	1.32602i	−0.845099	−	0.534609i	$-0.820459\pi$
$709$	−6.22575	−	35.3080i	−0.233813	−	1.32602i	0.611287	−	0.791409i	$-0.290652\pi$
$710$	6.57461	−	11.3876i	0.246741	−	0.427367i
$711$	−28.0632	+	5.29870i	−1.05245	+	0.198717i
$712$	−10.7216	+	6.19014i	−0.401810	+	0.231985i
$713$	0.182768	+	1.03653i	0.00684472	+	0.0388184i
$714$	−13.5316	+	15.9170i	−0.506407	+	0.595678i
$715$	48.8882	−	17.7938i	1.82831	−	0.665452i
$716$	−0.0829158	−	0.0146203i	−0.00309871	−	0.000546386i
$717$	30.0113	−	21.2855i	1.12079	−	0.794921i
$718$	23.6292	−	19.8273i	0.881836	−	0.739948i
$719$	−17.8398	−	30.8994i	−0.665311	−	1.15235i	−0.979201	−	0.202893i	$-0.934966\pi$
$719$	−17.8398	−	30.8994i	−0.665311	−	1.15235i	0.313890	−	0.949459i	$-0.398368\pi$
$720$	0.303288	+	25.0988i	0.0113029	+	0.935378i
$721$	15.8064	+	4.44749i	0.588660	+	0.165633i
$722$	−8.49278	−	10.1213i	−0.316069	−	0.376676i
$723$	20.3426	+	1.65597i	0.756548	+	0.0615860i
$724$	0.0271790	+	0.0746736i	0.00101010	+	0.00277522i
$725$	−2.36315	−	0.416687i	−0.0877652	−	0.0154754i
$726$	6.38597	−	1.75254i	0.237006	−	0.0650427i
$727$	−0.773622	+	2.12551i	−0.0286921	+	0.0788308i	−0.953212	−	0.302304i	$-0.902244\pi$
$727$	−0.773622	+	2.12551i	−0.0286921	+	0.0788308i	0.924520	+	0.381135i	$0.124467\pi$
$728$	−13.5512	+	48.1610i	−0.502242	+	1.78497i
$729$	0.978522	+	26.9823i	0.0362415	+	0.999343i
$730$	4.54818	−	7.87768i	0.168336	−	0.291566i
$731$	−4.18060	−	23.7094i	−0.154625	−	0.876923i
$732$	−0.0567380	+	0.216984i	−0.00209710	+	0.00801998i
$733$	5.51496	+	15.1522i	0.203700	+	0.559661i	0.998910	−	0.0466729i	$-0.0148618\pi$
$733$	5.51496	+	15.1522i	0.203700	+	0.559661i	−0.795210	+	0.606334i	$0.792640\pi$
$734$	1.61703	−	9.17065i	0.0596858	−	0.338495i
$735$	25.4413	+	2.71182i	0.938417	+	0.100027i
$736$	−0.0528441	+	0.0443414i	−0.00194786	+	0.00163445i
$737$		−	38.9566i		−	1.43498i
$738$	−24.0574	−	40.5297i	−0.885567	−	1.49192i
$739$	24.5989			0.904884			0.452442	−	0.891794i	$-0.350553\pi$
$739$	24.5989			0.904884			0.452442	+	0.891794i	$0.350553\pi$
$740$	−0.224299	−	0.0816381i	−0.00824538	−	0.00300107i
$741$	−61.1620	+	5.72352i	−2.24684	+	0.210259i
$742$	−0.246300	−	3.28735i	−0.00904197	−	0.120683i
$743$	8.41237	+	23.1128i	0.308620	+	0.847926i	0.992926	+	0.118732i	$0.0378828\pi$
$743$	8.41237	+	23.1128i	0.308620	+	0.847926i	−0.684307	+	0.729194i	$0.739895\pi$
$744$	7.36119	−	0.688859i	0.269874	−	0.0252548i
$745$	15.0938	+	17.9881i	0.552994	+	0.659033i
$746$			34.6822i			1.26980i
$747$	−23.8079	−	27.6867i	−0.871084	−	1.01300i
$748$	0.180799	−	0.104384i	0.00661066	−	0.00381667i
$749$	0.752859	−	7.52248i	0.0275089	−	0.274866i
$750$	−28.4526	−	2.31616i	−1.03894	−	0.0845741i
$751$	−28.0407	−	23.5290i	−1.02322	−	0.858584i	−0.0331922	−	0.999449i	$-0.510567\pi$
$751$	−28.0407	−	23.5290i	−1.02322	−	0.858584i	−0.990029	+	0.140865i	$0.955012\pi$
$752$	4.12801	−	23.4111i	0.150533	−	0.853715i
$753$	−12.5527	−	45.7402i	−0.457446	−	1.66687i
$754$	26.4391	+	31.5088i	0.962854	+	1.14748i
$755$	−42.6137			−1.55087
$756$	−0.207963	−	0.118508i	−0.00756355	−	0.00431010i
$757$	−38.6682			−1.40542			−0.702709	−	0.711477i	$-0.748027\pi$
$757$	−38.6682			−1.40542			−0.702709	+	0.711477i	$0.748027\pi$
$758$	1.87082	+	2.22956i	0.0679512	+	0.0809811i
$759$	3.15769	−	3.19607i	0.114617	−	0.116010i
$760$	5.54560	−	31.4506i	0.201160	−	1.14083i
$761$	36.9741	+	31.0250i	1.34031	+	1.12465i	0.981546	+	0.191226i	$0.0612464\pi$
$761$	36.9741	+	31.0250i	1.34031	+	1.12465i	0.358765	+	0.933428i	$0.383198\pi$
$762$	−2.65782	+	3.84499i	−0.0962827	+	0.139289i
$763$	−8.70132	+	12.1024i	−0.315009	+	0.438136i
$764$	0.155936	−	0.0900299i	0.00564158	−	0.00325717i
$765$	−7.24274	−	19.1751i	−0.261862	−	0.693279i
$766$			9.73700i			0.351812i
$767$	26.6786	+	31.7943i	0.963307	+	1.14802i
$768$	0.418671	+	0.590301i	0.0151075	+	0.0213007i
$769$	−16.2750	−	44.7151i	−0.586891	−	1.61247i	−0.776155	−	0.630543i	$-0.782832\pi$
$769$	−16.2750	−	44.7151i	−0.586891	−	1.61247i	0.189264	−	0.981926i	$-0.439390\pi$
$770$	26.2306	+	12.6325i	0.945286	+	0.455244i
$771$	11.5394	−	25.1417i	0.415580	−	0.905457i
$772$	−0.170238	−	0.0619615i	−0.00612700	−	0.00223004i
$773$	3.58933			0.129099			0.0645496	−	0.997914i	$-0.479439\pi$
$773$	3.58933			0.129099			0.0645496	+	0.997914i	$0.479439\pi$
$774$	−29.3835	+	11.0986i	−1.05617	+	0.398930i
$775$			0.821730i			0.0295174i
$776$	15.1549	−	12.7165i	0.544031	−	0.456496i
$777$	−22.9289	+	18.9893i	−0.822569	+	0.681237i
$778$	3.30367	−	18.7360i	0.118442	−	0.671719i
$779$	20.3312	+	55.8595i	0.728440	+	2.00137i
$780$	−0.301362	−	0.297742i	−0.0107905	−	0.0106609i
$781$	2.84592	+	16.1400i	0.101835	+	0.577534i
$782$	−1.59658	+	2.76535i	−0.0570935	+	0.0988888i
$783$	−20.4871	+	10.0093i	−0.732150	+	0.357702i
$784$	−24.3747	+	13.2727i	−0.870525	+	0.474027i
$785$	−3.53112	+	9.70167i	−0.126031	+	0.346267i
$786$	15.1066	+	14.9251i	0.538834	+	0.532362i
$787$	30.5240	+	5.38221i	1.08806	+	0.191855i	0.688779	−	0.724971i	$-0.258147\pi$
$787$	30.5240	+	5.38221i	1.08806	+	0.191855i	0.399286	+	0.916827i	$0.369258\pi$
$788$	−0.0844349	−	0.231983i	−0.00300787	−	0.00826405i
$789$	28.4144	−	41.1063i	1.01158	−	1.46342i
$790$	−18.1819	−	21.6684i	−0.646885	−	0.770927i
$791$	5.99495	+	23.5452i	0.213156	+	0.837171i
$792$	−20.5769	−	23.9294i	−0.731168	−	0.850292i
$793$	24.7549	+	42.8767i	0.879072	+	1.52260i
$794$	−23.2263	+	19.4892i	−0.824271	+	0.691645i
$795$	2.93955	+	1.34917i	0.104255	+	0.0478503i
$796$	−0.344943	−	0.0608228i	−0.0122262	−	0.00215581i
$797$	18.1049	−	6.58966i	0.641310	−	0.233418i	−0.000836476	−	1.00000i	$-0.500266\pi$
$797$	18.1049	−	6.58966i	0.641310	−	0.233418i	0.642147	+	0.766582i	$0.278044\pi$
$798$	−26.1909	−	22.2658i	−0.927148	−	0.788202i
$799$	3.37096	+	19.1177i	0.119256	+	0.676335i
$800$	−0.0466414	+	0.0269284i	−0.00164902	+	0.000952063i
$801$	−11.4014	−	6.40019i	−0.402850	−	0.226140i
$802$	18.6260	−	32.2612i	0.657708	−	1.13918i
$803$	1.96875	+	11.1653i	0.0694756	+	0.394016i
$804$	−0.286682	+	0.135797i	−0.0101105	+	0.00478918i
$805$	3.89967	−	0.292177i	0.137445	−	0.0102979i
$806$	9.05389	−	10.7900i	0.318910	−	0.380062i
$807$	−3.74140	−	13.6331i	−0.131704	−	0.479908i
$808$	10.4012	−	1.83402i	0.365914	−	0.0645205i
$809$	−10.9220	+	6.30585i	−0.383999	+	0.221702i	−0.679557	−	0.733623i	$-0.737828\pi$
$809$	−10.9220	+	6.30585i	−0.383999	+	0.221702i	0.295558	+	0.955325i	$0.404494\pi$
$810$	−22.8294	+	13.9267i	−0.802142	+	0.489334i
$811$			43.6085i			1.53130i	0.643256	+	0.765652i	$0.277583\pi$
$811$			43.6085i			1.53130i	−0.643256	+	0.765652i	$0.722417\pi$
$812$	0.0201297	−	0.201134i	0.000706415	−	0.00705842i
$813$	−14.4351	−	14.2617i	−0.506262	−	0.500181i
$814$	−31.8341	+	11.5867i	−1.11578	+	0.406112i
$815$	−18.5854	+	6.76454i	−0.651019	+	0.236951i
$816$	18.2904	+	12.6431i	0.640292	+	0.442597i
$817$	39.0131	−	6.87906i	1.36489	−	0.240668i
$818$	−17.6575	−	30.5837i	−0.617380	−	1.06933i
$819$	−51.0436	+	13.6552i	−1.78361	+	0.477153i
$820$	−0.204975	+	0.355028i	−0.00715805	+	0.0123981i
$821$	9.39965	−	25.8253i	0.328050	−	0.901310i	−0.660555	−	0.750778i	$-0.729679\pi$
$821$	9.39965	−	25.8253i	0.328050	−	0.901310i	0.988605	−	0.150532i	$-0.0480988\pi$
$822$	−9.84384	−	13.8792i	−0.343343	−	0.484094i
$823$	−3.92941	−	3.29717i	−0.136971	−	0.114932i	0.571728	−	0.820443i	$-0.306273\pi$
$823$	−3.92941	−	3.29717i	−0.136971	−	0.114932i	−0.708699	+	0.705511i	$0.750718\pi$
$824$	3.06132	−	17.3616i	0.106646	−	0.604821i
$825$	2.86113	−	2.02926i	0.0996118	−	0.0706496i
$826$	−2.31296	+	23.1108i	−0.0804781	+	0.804128i
$827$	22.7209	+	13.1179i	0.790082	+	0.456154i	0.839991	−	0.542600i	$-0.182560\pi$
$827$	22.7209	+	13.1179i	0.790082	+	0.456154i	−0.0499094	+	0.998754i	$0.515893\pi$
$828$	−0.0345272	−	0.0120964i	−0.00119990	−	0.000420380i
$829$	13.7370	+	7.93108i	0.477107	+	0.275458i	0.719210	−	0.694793i	$-0.244504\pi$
$829$	13.7370	+	7.93108i	0.477107	+	0.275458i	−0.242103	+	0.970251i	$0.577837\pi$
$830$	12.3696	−	33.9852i	0.429355	−	1.17964i
$831$	−13.5600	−	9.37325i	−0.470392	−	0.325154i
$832$	52.8958	+	9.32696i	1.83383	+	0.323354i
$833$	14.9972	−	16.9927i	0.519621	−	0.588764i
$834$	−24.8204	−	6.49013i	−0.859459	−	0.224735i
$835$	−13.9236	+	11.6833i	−0.481845	+	0.404316i
$836$	0.171761	+	0.297499i	0.00594049	+	0.0102892i
$837$	4.59380	+	6.31390i	0.158785	+	0.218240i
$838$	29.0435	+	16.7682i	1.00329	+	0.579249i
$839$	−43.7933	−	15.9395i	−1.51191	−	0.550291i	−0.552800	−	0.833314i	$-0.686440\pi$
$839$	−43.7933	−	15.9395i	−1.51191	−	0.550291i	−0.959113	+	0.283023i	$0.908663\pi$
$840$	0.176932	−	27.4692i	0.00610473	−	0.947777i
$841$	7.46447	+	6.26343i	0.257395	+	0.215980i
$842$	6.99648	−	8.33808i	0.241115	−	0.287349i
$843$	−35.9934	−	2.93001i	−1.23968	−	0.100915i
$844$	−0.0549092	−	0.0199853i	−0.00189005	−	0.000687923i
$845$	−66.0849			−2.27339
$846$	23.6929	−	8.94917i	0.814578	−	0.307679i
$847$	−6.96189	+	1.77260i	−0.239213	+	0.0609071i
$848$	−3.45523	+	0.609251i	−0.118653	+	0.0209218i
$849$	−2.08034	+	1.47548i	−0.0713970	+	0.0506383i
$850$	−1.60246	+	1.90973i	−0.0549638	+	0.0655033i
$851$	−2.92493	+	3.48579i	−0.100265	+	0.119491i
$852$	0.108854	−	0.0772047i	0.00372928	−	0.00264499i
$853$	−33.3113	+	5.87368i	−1.14056	+	0.201111i	−0.711850	−	0.702332i	$-0.752142\pi$
$853$	−33.3113	+	5.87368i	−1.14056	+	0.201111i	−0.428708	+	0.903443i	$0.641031\pi$
$854$	−7.50436	+	26.6705i	−0.256794	+	0.912644i
$855$	31.5521	−	11.9177i	1.07906	−	0.407577i
$856$	−8.11684			−0.277428
$857$	−41.3614	−	15.0543i	−1.41288	−	0.514246i	−0.480905	−	0.876773i	$-0.659692\pi$
$857$	−41.3614	−	15.0543i	−1.41288	−	0.514246i	−0.931973	+	0.362527i	$0.881914\pi$
$858$	−59.9275	−	4.87834i	−2.04589	−	0.166544i
$859$	29.8856	−	35.6162i	1.01968	−	1.21521i	0.0433218	−	0.999061i	$-0.486206\pi$
$859$	29.8856	−	35.6162i	1.01968	−	1.21521i	0.976360	−	0.216149i	$-0.0693496\pi$
$860$	0.209283	+	0.175609i	0.00713648	+	0.00598822i
$861$	25.2799	+	44.4448i	0.861538	+	1.51468i
$862$	7.23046	+	2.63167i	0.246271	+	0.0896351i
$863$	−6.24515	−	3.60564i	−0.212587	−	0.122737i	0.389926	−	0.920846i	$-0.372501\pi$
$863$	−6.24515	−	3.60564i	−0.212587	−	0.122737i	−0.602513	+	0.798109i	$0.705834\pi$
$864$	−0.207836	+	0.467653i	−0.00707074	+	0.0159099i
$865$	8.94069	+	15.4857i	0.303992	+	0.526530i
$866$	38.3368	−	32.1684i	1.30274	−	1.09313i
$867$	10.9206	+	2.85556i	0.370882	+	0.0969798i
$868$	−0.0690276	+	0.00517180i	−0.00234295	+	0.000175542i
$869$	34.7197	+	6.12203i	1.17779	+	0.207676i
$870$	−18.5773	−	12.8414i	−0.629829	−	0.435364i
$871$	−23.9503	+	65.8029i	−0.811525	+	2.22965i
$872$	13.8594	+	8.00176i	0.469340	+	0.270974i
$873$	19.7184	+	6.90824i	0.667365	+	0.233809i
$874$	−4.55031	−	2.62712i	−0.153916	−	0.0888637i
$875$	30.8152	+	3.08402i	1.04174	+	0.104259i
$876$	0.0753031	−	0.0534087i	0.00254425	−	0.00180451i
$877$	−7.82720	+	44.3903i	−0.264306	+	1.49895i	0.506699	+	0.862123i	$0.330866\pi$
$877$	−7.82720	+	44.3903i	−0.264306	+	1.49895i	−0.771005	+	0.636829i	$0.780246\pi$
$878$	−4.37765	−	3.67328i	−0.147739	−	0.123967i
$879$	5.38748	+	7.59603i	0.181715	+	0.256208i
$880$	10.5979	−	29.1174i	0.357254	−	0.981547i
$881$	17.2527	−	29.8826i	0.581259	−	1.00677i	−0.414071	−	0.910245i	$-0.635894\pi$
$881$	17.2527	−	29.8826i	0.581259	−	1.00677i	0.995330	−	0.0965261i	$-0.0307731\pi$
$882$	−25.4149	−	15.1131i	−0.855763	−	0.508885i
$883$	−19.2076	−	33.2686i	−0.646388	−	1.11958i	−0.983979	−	0.178284i	$-0.942945\pi$
$883$	−19.2076	−	33.2686i	−0.646388	−	1.11958i	0.337591	−	0.941293i	$-0.390388\pi$
$884$	−0.369569	+	0.0651649i	−0.0124299	+	0.00219173i
$885$	−18.7456	−	12.9577i	−0.630126	−	0.435569i
$886$	10.9666	−	3.99151i	0.368429	−	0.134097i
$887$	−25.3610	+	9.23065i	−0.851539	+	0.309935i	−0.730668	−	0.682733i	$-0.760791\pi$
$887$	−25.3610	+	9.23065i	−0.851539	+	0.309935i	−0.120871	+	0.992668i	$0.538569\pi$
$888$	22.7380	+	22.4649i	0.763036	+	0.753872i
$889$	2.96012	−	4.11714i	0.0992793	−	0.138084i
$890$		−	12.9500i		−	0.434085i
$891$	10.6396	−	31.5870i	0.356441	−	1.05820i
$892$	0.151324	−	0.0873671i	0.00506671	−	0.00292527i
$893$	−31.4576	+	5.54682i	−1.05269	+	0.185617i
$894$	−7.18201	−	26.1702i	−0.240202	−	0.875261i
$895$	6.55946	−	7.81726i	0.219259	−	0.261302i
$896$	16.6381	+	24.4044i	0.555839	+	0.815294i
$897$	−7.29868	+	3.45727i	−0.243696	+	0.115435i
$898$	7.09426	+	40.2335i	0.236739	+	1.34261i
$899$	−3.29702	+	5.71060i	−0.109962	+	0.190459i
$900$	−0.0249068	−	0.0139814i	−0.000830226	−	0.000466048i
$901$	2.48125	−	1.43255i	0.0826624	−	0.0477252i
$902$	10.1034	+	57.2992i	0.336406	+	1.90785i
$903$	32.0944	−	11.4478i	1.06803	−	0.380960i
$904$	24.5126	−	8.92187i	0.815278	−	0.296737i
$905$	−9.48522	−	1.67250i	−0.315299	−	0.0555958i
$906$	44.7591	+	20.5432i	1.48702	+	0.682502i
$907$	−27.8874	+	23.4003i	−0.925987	+	0.776996i	−0.975093	−	0.221798i	$-0.928807\pi$
$907$	−27.8874	+	23.4003i	−0.925987	+	0.776996i	0.0491052	+	0.998794i	$0.484363\pi$
$908$	0.154511	+	0.267621i	0.00512764	+	0.00888133i
$909$	7.27259	+	8.45746i	0.241217	+	0.280516i
$910$	−36.5406	−	37.4645i	−1.21131	−	1.24194i
$911$	17.9098	+	21.3441i	0.593378	+	0.707160i	0.976251	−	0.216640i	$-0.0695099\pi$
$911$	17.9098	+	21.3441i	0.593378	+	0.707160i	−0.382873	+	0.923801i	$0.625065\pi$
$912$	−20.8038	+	30.0963i	−0.688884	+	0.996589i
$913$	15.4173	+	42.3586i	0.510238	+	1.40187i
$914$	−9.09603	−	1.60388i	−0.300870	−	0.0530515i
$915$	−19.3374	−	19.1051i	−0.639275	−	0.631597i
$916$	−0.0777926	+	0.213733i	−0.00257034	+	0.00706195i
$917$	−16.0857	−	16.4924i	−0.531197	−	0.544627i
$918$	−1.63657	+	23.6321i	−0.0540150	+	0.779976i
$919$	24.7371	−	42.8459i	0.816001	−	1.41336i	−0.0926055	−	0.995703i	$-0.529520\pi$
$919$	24.7371	−	42.8459i	0.816001	−	1.41336i	0.908607	−	0.417653i	$-0.137147\pi$
$920$	−0.729081	−	4.13482i	−0.0240371	−	0.136321i
$921$	−9.63105	−	9.51538i	−0.317354	−	0.313542i
$922$	−10.6542	−	29.2723i	−0.350879	−	0.964031i
$923$	5.11565	−	29.0123i	0.168384	−	0.954950i
$924$	0.188471	+	0.227571i	0.00620023	+	0.00748655i
$925$	−2.72145	+	2.28357i	−0.0894807	+	0.0750832i
$926$			23.2364i			0.763595i
$927$	17.4176	−	6.57891i	0.572070	−	0.216080i
$928$	−0.432178			−0.0141870
$929$	−29.3067	−	10.6668i	−0.961522	−	0.349966i	−0.186892	−	0.982380i	$-0.559842\pi$
$929$	−29.3067	−	10.6668i	−0.961522	−	0.349966i	−0.774630	+	0.632415i	$0.782064\pi$
$930$	−3.22595	+	7.02864i	−0.105783	+	0.230478i
$931$	27.9611	+	24.6774i	0.916387	+	0.808768i
$932$	0.112975	+	0.310396i	0.00370062	+	0.0101674i
$933$	12.4278	+	17.5225i	0.406868	+	0.573660i
$934$	1.29087	+	1.53840i	0.0422386	+	0.0503380i
$935$			25.3035i			0.827512i
$936$	20.0455	+	53.0704i	0.655208	+	1.73466i
$937$	15.9634	−	9.21646i	0.521501	−	0.301089i	−0.216048	−	0.976383i	$-0.569317\pi$
$937$	15.9634	−	9.21646i	0.521501	−	0.301089i	0.737548	+	0.675294i	$0.235983\pi$
$938$	−35.7196	+	16.1166i	−1.16629	+	0.526226i
$939$	−6.98076	+	10.0989i	−0.227808	+	0.329564i
$940$	−0.168752	−	0.141600i	−0.00550407	−	0.00461847i
$941$	−3.99360	+	22.6488i	−0.130188	+	0.738331i	0.847903	+	0.530152i	$0.177865\pi$
$941$	−3.99360	+	22.6488i	−0.130188	+	0.738331i	−0.978091	+	0.208180i	$0.933246\pi$
$942$	8.38588	−	8.48783i	0.273227	−	0.276548i
$943$	5.02349	+	5.98676i	0.163587	+	0.194956i
$944$	24.7197			0.804558
$945$	25.0422	−	14.6471i	0.814622	−	0.476470i
$946$	38.7744			1.26066
$947$	−11.7046	−	13.9490i	−0.380349	−	0.453282i	0.541575	−	0.840652i	$-0.317828\pi$
$947$	−11.7046	−	13.9490i	−0.380349	−	0.453282i	−0.921924	+	0.387370i	$0.873384\pi$
$948$	−0.0759756	−	0.276844i	−0.00246757	−	0.00899146i
$949$	3.53890	−	20.0701i	0.114878	−	0.651503i
$950$	−3.14241	−	2.63679i	−0.101953	−	0.0855488i
$951$	−29.2202	−	2.37864i	−0.947530	−	0.0771327i
$952$	−19.7570	−	14.2048i	−0.640328	−	0.460380i
$953$	−20.4233	+	11.7914i	−0.661576	+	0.381961i	−0.792877	−	0.609381i	$-0.791418\pi$
$953$	−20.4233	+	11.7914i	−0.661576	+	0.381961i	0.131301	+	0.991343i	$0.458085\pi$
$954$	−2.43713	−	2.83420i	−0.0789052	−	0.0917606i
$955$			21.8239i			0.706203i
$956$	0.237736	+	0.283323i	0.00768893	+	0.00916331i
$957$	28.0254	−	2.62261i	0.905931	−	0.0847768i
$958$	11.5750	+	31.8020i	0.373971	+	1.02748i
$959$	10.3984	+	15.2522i	0.335782	+	0.492519i
$960$	−29.3623	+	2.74772i	−0.947665	+	0.0886823i
$961$	−27.0086	−	9.83031i	−0.871244	−	0.317107i
$962$	60.8954			1.96335
$963$	−4.37554	−	7.37150i	−0.141000	−	0.237543i
$964$			0.205163i			0.00660785i
$965$	16.8205	−	14.1141i	0.541472	−	0.454349i
$966$	−4.23686	−	1.57307i	−0.136319	−	0.0506126i
$967$	−6.40078	+	36.3006i	−0.205835	+	1.16735i	0.690285	+	0.723537i	$0.257485\pi$
$967$	−6.40078	+	36.3006i	−0.205835	+	1.16735i	−0.896120	+	0.443811i	$0.853626\pi$
$968$	2.63803	+	7.24794i	0.0847896	+	0.232958i
$969$	7.55824	−	28.9052i	0.242806	−	0.928568i
$970$	3.59344	+	20.3794i	0.115378	+	0.654343i
$971$	−6.28287	+	10.8822i	−0.201627	+	0.349228i	−0.949053	−	0.315117i	$-0.897956\pi$
$971$	−6.28287	+	10.8822i	−0.201627	+	0.349228i	0.747426	+	0.664345i	$0.231289\pi$
$972$	−0.269537	+	0.0318102i	−0.00864541	+	0.00102031i
$973$	26.7915	+	7.53842i	0.858895	+	0.241671i
$974$	−17.1077	+	47.0029i	−0.548165	+	1.50607i
$975$	−6.08041	+	1.66868i	−0.194729	+	0.0534404i
$976$	29.0396	+	5.12047i	0.929536	+	0.163902i
$977$	5.53944	+	15.2195i	0.177222	+	0.486914i	0.996218	−	0.0868850i	$-0.0276913\pi$
$977$	5.53944	+	15.2195i	0.177222	+	0.486914i	−0.818996	+	0.573799i	$0.805469\pi$
$978$	22.7822	+	1.85456i	0.728493	+	0.0593022i
$979$	10.3750	+	12.3645i	0.331588	+	0.395171i
$980$	−0.00642009	+	0.257108i	−0.000205082	+	0.00821303i
$981$	0.204219	+	16.9003i	0.00652020	+	0.539585i
$982$	−21.8395	−	37.8272i	−0.696927	−	1.20711i
$983$	−0.923122	+	0.774591i	−0.0294430	+	0.0247056i	−0.657390	−	0.753550i	$-0.728340\pi$
$983$	−0.923122	+	0.774591i	−0.0294430	+	0.0247056i	0.627947	+	0.778256i	$0.283895\pi$
$984$	44.7780	−	31.7588i	1.42747	−	1.01243i
$985$	29.4670	+	5.19584i	0.938898	+	0.165553i
$986$	−18.7986	+	6.84215i	−0.598671	+	0.217898i
$987$	−25.8788	+	9.23078i	−0.823731	+	0.293819i
$988$	−0.107227	−	0.608114i	−0.00341134	−	0.0193467i
$989$	4.51042	−	2.60409i	0.143423	−	0.0828052i
$990$	32.4390	−	6.12491i	1.03098	−	0.194663i
$991$	26.7781	−	46.3810i	0.850635	−	1.47334i	−0.0300019	−	0.999550i	$-0.509551\pi$
$991$	26.7781	−	46.3810i	0.850635	−	1.47334i	0.880636	−	0.473793i	$-0.157115\pi$
$992$	0.0256994	+	0.145748i	0.000815956	+	0.00462752i
$993$	2.03229	−	24.9655i	0.0644928	−	0.792256i
$994$	13.6215	−	9.28666i	0.432048	−	0.294555i
$995$	27.2884	−	32.5211i	0.865101	−	1.03099i
$996$	0.257976	−	0.261112i	0.00817427	−	0.00827365i
$997$	−2.68170	+	0.472857i	−0.0849304	+	0.0149755i	−0.215952	−	0.976404i	$-0.569285\pi$
$997$	−2.68170	+	0.472857i	−0.0849304	+	0.0149755i	0.131021	+	0.991380i	$0.458174\pi$
$998$	44.4078	−	25.6388i	1.40570	−	0.811584i
$999$	−8.14466	+	32.7602i	−0.257686	+	1.03649i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.ba.a.131.16	yes	132
3.2	odd	2		567.2.ba.a.341.7		132
7.3	odd	6		189.2.bd.a.185.7	yes	132
21.17	even	6		567.2.bd.a.17.16		132
27.7	even	9		567.2.bd.a.467.16		132
27.20	odd	18		189.2.bd.a.47.7	yes	132
189.101	even	18	inner	189.2.ba.a.101.16	✓	132
189.115	odd	18		567.2.ba.a.143.7		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.ba.a.101.16	✓	132	189.101	even	18	inner
189.2.ba.a.131.16	yes	132	1.1	even	1	trivial
189.2.bd.a.47.7	yes	132	27.20	odd	18
189.2.bd.a.185.7	yes	132	7.3	odd	6
567.2.ba.a.143.7		132	189.115	odd	18
567.2.ba.a.341.7		132	3.2	odd	2
567.2.bd.a.17.16		132	21.17	even	6
567.2.bd.a.467.16		132	27.7	even	9

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:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.ba (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.905074 + 1.07862i) q^{2} +(-1.67571 - 0.438172i) q^{3} +(0.00302336 - 0.0171463i) q^{4} +(1.61655 + 1.35644i) q^{5} +(-1.04402 - 2.20404i) q^{6} +(1.08812 + 2.41164i) q^{7} +(2.46004 - 1.42030i) q^{8} +(2.61601 + 1.46850i) q^{9} +2.97133i q^{10} +(-2.38051 - 2.83698i) q^{11} +(-0.0125793 + 0.0274075i) q^{12} +(2.27684 + 6.25557i) q^{13} +(-1.61642 + 3.35639i) q^{14} +(-2.11451 - 2.98133i) q^{15} +(3.72576 + 1.35607i) q^{16} -3.23775 q^{17} +(0.783724 + 4.15079i) q^{18} -5.32762i q^{19} +(0.0281454 - 0.0236168i) q^{20} +(-0.766672 - 4.51799i) q^{21} +(0.905502 - 5.13536i) q^{22} +(-0.239559 - 0.658182i) q^{23} +(-4.74464 + 1.30210i) q^{24} +(-0.0949575 - 0.538530i) q^{25} +(-4.68670 + 8.11761i) q^{26} +(-3.74022 - 3.60704i) q^{27} +(0.0446405 - 0.0113661i) q^{28} +(1.50083 - 4.12351i) q^{29} +(1.30195 - 4.97909i) q^{30} +(-1.47986 - 0.260940i) q^{31} +(-0.0336848 - 0.0925482i) q^{32} +(2.74596 + 5.79703i) q^{33} +(-2.93040 - 3.49232i) q^{34} +(-1.51224 + 5.37450i) q^{35} +(0.0330885 - 0.0404152i) q^{36} +(-3.24831 - 5.62624i) q^{37} +(5.74650 - 4.82189i) q^{38} +(-1.07431 - 11.4802i) q^{39} +(5.90332 + 1.04091i) q^{40} +(-10.4849 + 3.81619i) q^{41} +(4.17932 - 4.91606i) q^{42} +(1.29121 + 7.32280i) q^{43} +(-0.0558409 + 0.0322398i) q^{44} +(2.23697 + 5.92237i) q^{45} +(0.493113 - 0.854097i) q^{46} +(-1.04114 - 5.90462i) q^{47} +(-5.64911 - 3.90490i) q^{48} +(-4.63197 + 5.24832i) q^{49} +(0.494929 - 0.589833i) q^{50} +(5.42553 + 1.41869i) q^{51} +(0.114144 - 0.0201266i) q^{52} +(-0.766350 + 0.442452i) q^{53} +(0.505466 - 7.29893i) q^{54} -7.81514i q^{55} +(6.10208 + 4.38724i) q^{56} +(-2.33441 + 8.92755i) q^{57} +(5.80608 - 2.11324i) q^{58} +(5.85868 - 2.13238i) q^{59} +(-0.0575118 + 0.0272424i) q^{60} +(7.32422 - 1.29146i) q^{61} +(-1.05793 - 1.83239i) q^{62} +(-0.694936 + 7.90677i) q^{63} +(4.03421 - 6.98746i) q^{64} +(-4.80471 + 13.2008i) q^{65} +(-3.76753 + 8.20860i) q^{66} +(8.05809 + 6.76154i) q^{67} +(-0.00978888 + 0.0555155i) q^{68} +(0.113034 + 1.20789i) q^{69} +(-7.16576 + 3.23318i) q^{70} +(-3.83248 - 2.21268i) q^{71} +(8.52119 - 0.102968i) q^{72} +(-2.65123 - 1.53069i) q^{73} +(3.12864 - 8.59586i) q^{74} +(-0.0768477 + 0.944029i) q^{75} +(-0.0913491 - 0.0161073i) q^{76} +(4.25147 - 8.82791i) q^{77} +(11.4105 - 11.5492i) q^{78} +(-7.29250 + 6.11913i) q^{79} +(4.18344 + 7.24593i) q^{80} +(4.68703 + 7.68321i) q^{81} +(-13.6058 - 7.85533i) q^{82} +(-11.4377 - 4.16299i) q^{83} +(-0.0797848 - 0.000513902i) q^{84} +(-5.23397 - 4.39182i) q^{85} +(-6.72991 + 8.02040i) q^{86} +(-4.32177 + 6.25218i) q^{87} +(-9.88551 - 3.59803i) q^{88} -4.35832 q^{89} +(-4.36339 + 7.77303i) q^{90} +(-12.6087 + 12.2977i) q^{91} +(-0.0120097 + 0.00211763i) q^{92} +(2.36549 + 1.08569i) q^{93} +(5.42656 - 6.46712i) q^{94} +(7.22662 - 8.61234i) q^{95} +(0.0158939 + 0.169844i) q^{96} +(6.85869 - 1.20937i) q^{97} +(-9.85324 - 0.246039i) q^{98} +(-2.06134 - 10.9174i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} - 18 q^{6} - 6 q^{7} - 18 q^{8} + 3 q^{9} - 9 q^{11} - 9 q^{12} + 3 q^{14} - 24 q^{15} + 3 q^{16} - 18 q^{17} - 3 q^{18} + 18 q^{20} - 21 q^{21} - 12 q^{22}+ \cdots + 96 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 - 18 * q^6 - 6 * q^7 - 18 * q^8 + 3 * q^9 - 9 * q^11 - 9 * q^12 + 3 * q^14 - 24 * q^15 + 3 * q^16 - 18 * q^17 - 3 * q^18 + 18 * q^20 - 21 * q^21 - 12 * q^22 - 6 * q^23 - 9 * q^24 - 3 * q^25 - 12 * q^28 + 6 * q^29 + 51 * q^30 - 9 * q^31 + 3 * q^32 - 9 * q^33 - 18 * q^34 + 18 * q^35 + 3 * q^37 - 99 * q^38 - 36 * q^39 - 54 * q^40 - 45 * q^42 - 12 * q^43 - 9 * q^44 - 9 * q^45 + 3 * q^46 + 45 * q^47 - 24 * q^49 - 9 * q^50 - 48 * q^51 - 9 * q^52 - 45 * q^53 + 171 * q^54 + 3 * q^56 - 3 * q^58 + 36 * q^59 + 57 * q^60 - 9 * q^61 - 99 * q^62 - 33 * q^63 + 18 * q^64 + 69 * q^65 - 9 * q^66 - 3 * q^67 + 36 * q^68 + 108 * q^69 + 66 * q^70 + 18 * q^71 - 129 * q^72 - 9 * q^73 + 75 * q^74 + 36 * q^75 + 36 * q^76 + 15 * q^77 + 66 * q^78 - 21 * q^79 + 72 * q^80 - 33 * q^81 - 18 * q^82 - 90 * q^83 - 120 * q^84 + 9 * q^85 - 105 * q^86 - 54 * q^87 - 63 * q^88 - 18 * q^89 + 81 * q^90 + 6 * q^91 + 150 * q^92 + 21 * q^93 - 9 * q^94 + 45 * q^95 - 81 * q^96 + 27 * q^98 + 96 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more