LMFDB - Embedded newform 189.2.ba.a.101.16

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			101.16
Character	$\chi$	$=$	189.101
Dual form			189.2.ba.a.131.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.905074 - 1.07862i) q^{2} +(-1.67571 + 0.438172i) q^{3} +(0.00302336 + 0.0171463i) q^{4} +(1.61655 - 1.35644i) q^{5} +(-1.04402 + 2.20404i) q^{6} +(1.08812 - 2.41164i) q^{7} +(2.46004 + 1.42030i) q^{8} +(2.61601 - 1.46850i) q^{9} +O(q^{10})$	\(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}+O(q^{10}) $ 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	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} - 18 q^{6} - 6 q^{7} - 18 q^{8} + 3 q^{9} - 9 q^{11} - 9 q^{12} + 3 q^{14} - 24 q^{15} + 3 q^{16} - 18 q^{17} - 3 q^{18} + 18 q^{20} - 21 q^{21} - 12 q^{22} - 6 q^{23} - 9 q^{24} - 3 q^{25} - 12 q^{28} + 6 q^{29} + 51 q^{30} - 9 q^{31} + 3 q^{32} - 9 q^{33} - 18 q^{34} + 18 q^{35} + 3 q^{37} - 99 q^{38} - 36 q^{39} - 54 q^{40} - 45 q^{42} - 12 q^{43} - 9 q^{44} - 9 q^{45} + 3 q^{46} + 45 q^{47} - 24 q^{49} - 9 q^{50} - 48 q^{51} - 9 q^{52} - 45 q^{53} + 171 q^{54} + 3 q^{56} - 3 q^{58} + 36 q^{59} + 57 q^{60} - 9 q^{61} - 99 q^{62} - 33 q^{63} + 18 q^{64} + 69 q^{65} - 9 q^{66} - 3 q^{67} + 36 q^{68} + 108 q^{69} + 66 q^{70} + 18 q^{71} - 129 q^{72} - 9 q^{73} + 75 q^{74} + 36 q^{75} + 36 q^{76} + 15 q^{77} + 66 q^{78} - 21 q^{79} + 72 q^{80} - 33 q^{81} - 18 q^{82} - 90 q^{83} - 120 q^{84} + 9 q^{85} - 105 q^{86} - 54 q^{87} - 63 q^{88} - 18 q^{89} + 81 q^{90} + 6 q^{91} + 150 q^{92} + 21 q^{93} - 9 q^{94} + 45 q^{95} - 81 q^{96} + 27 q^{98} + 96 q^{99}+O(q^{100}) \) 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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{1}{6}\right)$

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	−0.344384	−	0.938829i	$-0.611912\pi$
$2$	0.905074	−	1.07862i	0.639984	−	0.762703i	0.984368	+	0.176126i	$0.0563566\pi$
$3$	−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	−0.205256	−	0.978708i	$-0.565803\pi$
$5$	1.61655	−	1.35644i	0.722942	−	0.606620i	0.928197	+	0.372088i	$0.121358\pi$
$6$	−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	−0.994410	−	0.105586i	$-0.966328\pi$
$11$	−2.38051	+	2.83698i	−0.717751	+	0.855382i	0.276659	+	0.960968i	$0.410773\pi$
$12$	−0.0125793	−	0.0274075i	−0.00363133	−	0.00791187i
$13$	2.27684	−	6.25557i	0.631482	−	1.73498i	−0.0454806	−	0.998965i	$-0.514482\pi$
$13$	2.27684	−	6.25557i	0.631482	−	1.73498i	0.676963	−	0.736017i	$-0.263296\pi$
$14$	−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	$0.209281\pi$
$19$			5.32762i			1.22224i	−0.791538	+	0.611120i	$0.790719\pi$
$20$	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	−0.962160	−	0.272487i	$-0.912154\pi$
$23$	−0.239559	+	0.658182i	−0.0499514	+	0.137240i	0.912208	+	0.409727i	$0.134376\pi$
$24$	−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	0.997511	+	0.0705128i	$0.0224636\pi$
$29$	1.50083	+	4.12351i	0.278698	+	0.765716i	−0.718813	+	0.695204i	$0.755314\pi$
$30$	1.30195	+	4.97909i	0.237703	+	0.909052i
$31$	−1.47986	+	0.260940i	−0.265791	+	0.0468662i	−0.304955	−	0.952367i	$-0.598642\pi$
$31$	−1.47986	+	0.260940i	−0.265791	+	0.0468662i	0.0391641	+	0.999233i	$0.487530\pi$
$32$	−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	0.465191	+	0.885210i	$0.345985\pi$
$37$	−3.24831	+	5.62624i	−0.534019	+	0.924947i	−0.999210	+	0.0397374i	$0.987348\pi$
$38$	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	−0.650871	−	0.759188i	$-0.725596\pi$
$41$	−10.4849	−	3.81619i	−1.63746	−	0.595988i	−0.986593	+	0.163200i	$0.947818\pi$
$42$	4.17932	+	4.91606i	0.644883	+	0.758565i
$43$	1.29121	−	7.32280i	0.196907	−	1.11672i	−0.712769	−	0.701399i	$-0.752559\pi$
$43$	1.29121	−	7.32280i	0.196907	−	1.11672i	0.909676	−	0.415318i	$-0.136330\pi$
$44$	−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	0.809728	+	0.586805i	$0.199614\pi$
$47$	−1.04114	+	5.90462i	−0.151866	+	0.861278i	−0.961595	+	0.274473i	$0.911497\pi$
$48$	−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	0.446443	−	0.894812i	$-0.352691\pi$
$53$	−0.766350	−	0.442452i	−0.105266	−	0.0607755i	−0.551709	+	0.834037i	$0.686024\pi$
$54$	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	0.693954	−	0.720019i	$-0.255867\pi$
$59$	5.85868	+	2.13238i	0.762735	+	0.277613i	0.0687807	+	0.997632i	$0.478089\pi$
$60$	−0.0575118	−	0.0272424i	−0.00742474	−	0.00351698i
$61$	7.32422	+	1.29146i	0.937771	+	0.165354i	0.621588	−	0.783344i	$-0.286488\pi$
$61$	7.32422	+	1.29146i	0.937771	+	0.165354i	0.316183	+	0.948698i	$0.397599\pi$
$62$	−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	−0.000302478	−	1.00000i	$-0.500096\pi$
$67$	8.05809	−	6.76154i	0.984453	−	0.826054i	0.984755	+	0.173946i	$0.0556518\pi$
$68$	−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	−0.709869	−	0.704334i	$-0.751246\pi$
$71$	−3.83248	+	2.21268i	−0.454832	+	0.262597i	0.255037	+	0.966931i	$0.417912\pi$
$72$	8.52119	+	0.102968i	1.00423	+	0.0121349i
$73$	−2.65123	+	1.53069i	−0.310303	+	0.179154i	−0.647062	−	0.762437i	$-0.724003\pi$
$73$	−2.65123	+	1.53069i	−0.310303	+	0.179154i	0.336759	+	0.941591i	$0.390669\pi$
$74$	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	0.132612	−	0.991168i	$-0.457664\pi$
$79$	−7.29250	−	6.11913i	−0.820470	−	0.688456i	−0.953082	+	0.302712i	$0.902108\pi$
$80$	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	−0.882241	−	0.470799i	$-0.843966\pi$
$83$	−11.4377	+	4.16299i	−1.25545	+	0.456947i	−0.373212	+	0.927746i	$0.621744\pi$
$84$	−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	0.510629	−	0.859801i	$-0.329413\pi$
$97$	6.85869	+	1.20937i	0.696394	+	0.122793i	0.185765	+	0.982594i	$0.440524\pi$
$98$	−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	−0.162290	−	0.986743i	$-0.551888\pi$
$101$	3.49388	−	1.27167i	0.347654	−	0.126536i	0.509945	+	0.860207i	$0.329666\pi$
$102$	3.38027	−	7.13613i	0.334697	−	0.706582i
$103$	3.98929	+	4.75425i	0.393076	+	0.468450i	0.925896	−	0.377779i	$-0.123312\pi$
$103$	3.98929	+	4.75425i	0.393076	+	0.468450i	−0.532820	+	0.846229i	$0.678868\pi$
$104$	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	−0.614823	−	0.788665i	$-0.710772\pi$
$107$	−2.47461	+	1.42872i	−0.239230	+	0.138119i	0.375593	+	0.926785i	$0.377439\pi$
$108$	−0.0731555	−	0.0532257i	−0.00703939	−	0.00512164i
$109$	2.81692	−	4.87905i	0.269812	−	0.467328i	−0.699001	−	0.715121i	$-0.746372\pi$
$109$	2.81692	−	4.87905i	0.269812	−	0.467328i	0.968813	+	0.247792i	$0.0797051\pi$
$110$	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	0.268765	−	0.963206i	$-0.413385\pi$
$113$	9.04367	−	1.59464i	0.850757	−	0.150011i	0.581992	+	0.813194i	$0.302273\pi$
$114$	−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	−0.905406	−	0.424547i	$-0.860433\pi$
$127$	−0.958294	+	1.65981i	−0.0850349	+	0.147285i	0.820371	+	0.571831i	$0.193767\pi$
$128$	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	−0.0411416	−	0.999153i	$-0.513099\pi$
$131$	−8.18242	−	2.97816i	−0.714901	−	0.260203i	−0.673760	+	0.738951i	$0.735322\pi$
$132$	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	0.459274	−	0.888295i	$-0.348110\pi$
$137$	6.87107	+	1.21155i	0.587035	+	0.103510i	0.127761	+	0.991805i	$0.459221\pi$
$138$	−1.20056	−	1.21515i	−0.102198	−	0.103441i
$139$	6.76177	+	8.05836i	0.573526	+	0.683501i	0.972351	−	0.233526i	$-0.0750263\pi$
$139$	6.76177	+	8.05836i	0.573526	+	0.683501i	−0.398825	+	0.917027i	$0.630582\pi$
$140$	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	0.294314	−	0.955709i	$-0.404909\pi$
$149$	10.9584	−	1.93227i	0.897750	−	0.158298i	0.603436	+	0.797411i	$0.293798\pi$
$150$	−1.08781	−	0.771526i	−0.0888189	−	0.0629948i
$151$	−15.4692	−	12.9802i	−1.25887	−	1.05632i	−0.995802	−	0.0915375i	$-0.970822\pi$
$151$	−15.4692	−	12.9802i	−1.25887	−	1.05632i	−0.263066	−	0.964778i	$-0.584734\pi$
$152$	−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	−0.854838	−	0.518895i	$-0.826344\pi$
$157$	1.67332	−	4.59740i	0.133545	−	0.366912i	0.988383	+	0.151983i	$0.0485658\pi$
$158$	−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	0.622051	−	0.782977i	$-0.286300\pi$
$163$	−4.68621	−	8.11676i	−0.367053	−	0.635754i	−0.989103	+	0.147223i	$0.952966\pi$
$164$	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	−0.986382	−	0.164468i	$-0.947409\pi$
$167$	−1.49566	−	8.48231i	−0.115738	−	0.656381i	0.870645	−	0.491912i	$-0.163702\pi$
$168$	−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	−0.0210995	−	0.999777i	$-0.506717\pi$
$173$	7.96256	−	2.89813i	0.605382	−	0.220341i	0.626481	+	0.779436i	$0.284494\pi$
$174$	−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	$0.0578433\pi$
$179$			4.83578i			0.361443i	−0.983534	+	0.180722i	$0.942157\pi$
$180$	0.108310	+	0.0204503i	0.00807295	+	0.00152428i
$181$	−3.95269	−	2.28209i	−0.293801	−	0.169626i	0.345854	−	0.938288i	$-0.387589\pi$
$181$	−3.95269	−	2.28209i	−0.293801	−	0.169626i	−0.639655	+	0.768662i	$0.720923\pi$
$182$	−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	−0.469902	−	0.882718i	$-0.655711\pi$
$191$	6.64760	−	7.92230i	0.481003	−	0.573237i	0.950906	+	0.309481i	$0.100155\pi$
$192$	−9.82188	−	9.94128i	−0.708833	−	0.717450i
$193$	1.80685	+	10.2471i	0.130060	+	0.737605i	0.978173	+	0.207791i	$0.0666273\pi$
$193$	1.80685	+	10.2471i	0.130060	+	0.737605i	−0.848114	+	0.529814i	$0.822262\pi$
$194$	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	0.868967	−	0.494870i	$-0.164784\pi$
$197$	12.2795	+	7.08959i	0.874880	+	0.505112i	0.00591309	+	0.999983i	$0.498118\pi$
$198$	9.91006	+	12.1044i	0.704277	+	0.860223i
$199$			20.1176i			1.42610i	0.701113	+	0.713050i	$0.252687\pi$
$199$			20.1176i			1.42610i	−0.701113	+	0.713050i	$0.747313\pi$
$200$	−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	0.998275	−	0.0587176i	$-0.0187011\pi$
$211$	0.582787	+	3.30515i	0.0401207	+	0.227536i	−0.958154	+	0.286254i	$0.907590\pi$
$212$	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	−0.505506	−	0.862823i	$-0.668694\pi$
$223$	6.45098	−	7.68798i	0.431990	−	0.514825i	0.937495	+	0.347998i	$0.113138\pi$
$224$	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	0.0682365	−	0.997669i	$-0.478263\pi$
$227$	−13.5964	−	11.4088i	−0.902427	−	0.757226i	−0.970663	+	0.240443i	$0.922707\pi$
$228$	0.146017	−	0.0670178i	0.00967020	−	0.00443836i
$229$	−12.8653	+	2.26849i	−0.850160	+	0.149906i	−0.581719	−	0.813390i	$-0.697620\pi$
$229$	−12.8653	+	2.26849i	−0.850160	+	0.149906i	−0.268441	+	0.963296i	$0.586509\pi$
$230$	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	−0.146460	−	0.989217i	$-0.546788\pi$
$233$	−16.4302	−	9.48596i	−1.07638	−	0.621446i	−0.929917	+	0.367771i	$0.880121\pi$
$234$	−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	−0.998244	−	0.0592349i	$-0.981134\pi$
$239$	−13.6545	−	16.2728i	−0.883236	−	1.05260i	0.115008	−	0.993365i	$-0.463311\pi$
$240$	−3.83527	+	13.9752i	−0.247566	+	0.902092i
$241$	−11.6046	−	2.04621i	−0.747519	−	0.131808i	−0.213103	−	0.977030i	$-0.568357\pi$
$241$	−11.6046	−	2.04621i	−0.747519	−	0.131808i	−0.534415	+	0.845222i	$0.679468\pi$
$242$	−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	−0.00354445	−	0.999994i	$-0.501128\pi$
$251$	13.6923	−	23.7157i	0.864248	−	1.49692i	0.867792	−	0.496927i	$-0.165538\pi$
$252$	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	−0.940426	−	0.339999i	$-0.889573\pi$
$257$	−2.77342	−	15.7288i	−0.173001	−	0.981138i	0.767425	−	0.641139i	$-0.221538\pi$
$258$	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	−0.733592	−	0.679590i	$-0.762158\pi$
$263$	−9.86756	−	27.1109i	−0.608460	−	1.67173i	0.125132	−	0.992140i	$-0.460065\pi$
$264$	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	−0.714374	−	0.699764i	$-0.753289\pi$
$269$	4.08105	−	7.06859i	0.248826	−	0.430979i	0.963200	+	0.268784i	$0.0866219\pi$
$270$	10.7177	+	11.1134i	0.652258	+	0.676342i
$271$	10.1461	−	5.85783i	0.616329	−	0.355838i	−0.159109	−	0.987261i	$-0.550862\pi$
$271$	10.1461	−	5.85783i	0.616329	−	0.355838i	0.775438	+	0.631423i	$0.217529\pi$
$272$	−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	−0.0590684	−	0.998254i	$-0.518813\pi$
$277$	8.94325	−	3.25508i	0.537348	−	0.195579i	0.596416	+	0.802675i	$0.296591\pi$
$278$	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	0.748426	−	0.663218i	$-0.230810\pi$
$281$	20.5328	+	3.62048i	1.22488	+	0.215980i	0.476457	+	0.879198i	$0.341921\pi$
$282$	−11.9271	−	8.45926i	−0.710246	−	0.503741i
$283$	0.946510	+	1.12801i	0.0562642	+	0.0670531i	0.793443	−	0.608645i	$-0.208287\pi$
$283$	0.946510	+	1.12801i	0.0562642	+	0.0670531i	−0.737178	+	0.675698i	$0.763842\pi$
$284$	−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	−0.755120	−	0.655586i	$-0.772422\pi$
$293$	−4.11874	+	3.45603i	−0.240619	+	0.201904i	0.514501	+	0.857490i	$0.327977\pi$
$294$	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	−0.294227	−	0.955736i	$-0.595062\pi$
$307$	6.76941	−	3.90832i	0.386351	−	0.223060i	0.680578	+	0.732676i	$0.261729\pi$
$308$	−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	−0.871113	−	0.491083i	$-0.836601\pi$
$311$	−9.50108	+	7.97235i	−0.538757	+	0.452071i	0.332356	+	0.943154i	$0.392157\pi$
$312$	−18.9482	+	26.7158i	−1.07273	+	1.51248i
$313$	2.42423	+	6.66051i	0.137026	+	0.376474i	0.989159	−	0.146850i	$-0.0469136\pi$
$313$	2.42423	+	6.66051i	0.137026	+	0.376474i	−0.852133	+	0.523325i	$0.824691\pi$
$314$	−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	0.620887	−	0.783900i	$-0.286772\pi$
$317$	16.6689	+	2.93919i	0.936221	+	0.165081i	0.315334	+	0.948981i	$0.397883\pi$
$318$	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	−0.834674	−	0.550745i	$-0.814344\pi$
$331$	2.51122	−	14.2418i	0.138029	−	0.782801i	0.972702	−	0.232056i	$-0.0745452\pi$
$332$	−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	−0.0978073	−	0.995205i	$-0.531183\pi$
$337$	−14.9144	−	5.42839i	−0.812438	−	0.295703i	−0.714630	+	0.699502i	$0.753405\pi$
$338$	−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	−0.307874	−	0.951427i	$-0.599617\pi$
$347$	−5.06257	+	0.892668i	−0.271773	+	0.0479209i	0.0361006	+	0.999348i	$0.488506\pi$
$348$	0.0941357	−	0.0930050i	0.00504620	−	0.00498559i
$349$	3.81124	+	10.4713i	0.204011	+	0.560516i	0.998932	−	0.0461967i	$-0.0147101\pi$
$349$	3.81124	+	10.4713i	0.204011	+	0.560516i	−0.794921	+	0.606713i	$0.792488\pi$
$350$	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	−0.995728	−	0.0923333i	$-0.970567\pi$
$353$	−0.534901	+	3.03357i	−0.0284699	+	0.161461i	0.967258	+	0.253794i	$0.0816786\pi$
$354$	−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	$0.196205\pi$
$359$			21.9068i			1.15620i	−0.815967	+	0.578099i	$0.803795\pi$
$360$	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	−0.865499	−	0.500912i	$-0.832998\pi$
$367$	−4.25108	+	5.06624i	−0.221905	+	0.264456i	0.643594	+	0.765367i	$0.277443\pi$
$368$			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	−0.00664425	−	0.999978i	$-0.502115\pi$
$373$	18.8688	−	15.8328i	0.976988	−	0.819790i	0.983632	+	0.180188i	$0.0576705\pi$
$374$	−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	−0.497334	−	0.867559i	$-0.665687\pi$
$383$	5.29740	−	4.44505i	0.270685	−	0.227131i	0.768018	+	0.640428i	$0.221243\pi$
$384$	−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	−0.939880	−	0.341505i	$-0.889063\pi$
$389$	−8.68514	+	10.3505i	−0.440354	+	0.524794i	0.499526	+	0.866299i	$0.333508\pi$
$390$	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	$-0.818287\pi$
$397$		−	21.5333i		−	1.08072i	0.841433	−	0.540362i	$-0.181713\pi$
$398$	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	0.479537	+	0.877522i	$0.340805\pi$
$401$	−9.04869	+	24.8611i	−0.451870	+	1.24150i	−0.931407	+	0.363981i	$0.881417\pi$
$402$	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	−0.746897	−	0.664939i	$-0.768457\pi$
$409$	−24.6998	+	4.35525i	−1.22133	+	0.215353i	−0.474431	+	0.880293i	$0.657346\pi$
$410$	−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	0.824880	−	0.565307i	$-0.191242\pi$
$419$	22.3814	+	8.14616i	1.09340	+	0.397966i	0.268522	+	0.963273i	$0.413465\pi$
$420$	−0.128279	+	0.109054i	−0.00625936	+	0.00532131i
$421$	−1.34235	+	7.61285i	−0.0654222	+	0.371027i	0.934466	+	0.356053i	$0.115878\pi$
$421$	−1.34235	+	7.61285i	−0.0654222	+	0.371027i	−0.999888	+	0.0149744i	$0.995233\pi$
$422$	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	0.609630	−	0.792686i	$-0.291318\pi$
$431$	4.73254	+	2.73233i	0.227959	+	0.131612i	−0.381671	+	0.924298i	$0.624651\pi$
$432$	−9.04380	+	18.5110i	−0.435120	+	0.890610i
$433$			35.5423i			1.70805i	0.520229	+	0.854027i	$0.325846\pi$
$433$			35.5423i			1.70805i	−0.520229	+	0.854027i	$0.674154\pi$
$434$	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	0.0774513	−	0.996996i	$-0.475322\pi$
$439$	−3.99689	−	0.704759i	−0.190761	−	0.0336363i	−0.268212	+	0.963360i	$0.586433\pi$
$440$	−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	0.988640	−	0.150303i	$-0.0480250\pi$
$443$	2.83479	+	7.78852i	0.134685	+	0.370044i	−0.853955	+	0.520347i	$0.825803\pi$
$444$	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	0.228486	−	0.973547i	$-0.426623\pi$
$449$	25.1276	−	14.5074i	1.18585	−	0.684648i	0.957359	+	0.288899i	$0.0932893\pi$
$450$	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	0.517647	−	0.855594i	$-0.326808\pi$
$457$	−5.02502	−	4.21649i	−0.235061	−	0.197239i	−0.752708	+	0.658355i	$0.771253\pi$
$458$	−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	−0.777263	−	0.629176i	$-0.783393\pi$
$461$	−20.7893	+	7.56669i	−0.968255	+	0.352416i	−0.190992	+	0.981592i	$0.561170\pi$
$462$	−23.8957	+	0.153915i	−1.11173	+	0.00716076i
$463$	12.6417	−	10.6077i	0.587511	−	0.492980i	−0.299893	−	0.953973i	$-0.596951\pi$
$463$	12.6417	−	10.6077i	0.587511	−	0.492980i	0.887404	+	0.460993i	$0.152507\pi$
$464$	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	0.230144	−	0.973157i	$-0.426080\pi$
$479$	22.5859	−	8.22061i	1.03198	−	0.375609i	0.801834	+	0.597547i	$0.203858\pi$
$480$	−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	−0.111501	−	0.993764i	$-0.535566\pi$
$487$	17.7620	−	30.7647i	0.804874	−	1.39408i	0.916376	−	0.400319i	$-0.131101\pi$
$488$	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	−0.813360	−	0.581761i	$-0.802364\pi$
$491$	−30.5498	+	5.38675i	−1.37869	+	0.243101i	−0.565334	+	0.824862i	$0.691253\pi$
$492$	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	0.712012	+	0.702167i	$0.247784\pi$
$499$	6.32386	+	35.8644i	0.283095	+	1.60551i	−0.428917	+	0.903344i	$0.641105\pi$
$500$	−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	0.580681	−	0.814131i	$-0.302787\pi$
$503$	−9.30116	−	16.1101i	−0.414718	−	0.718313i	−0.995399	+	0.0958185i	$0.969453\pi$
$504$	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	0.433441	−	0.901182i	$-0.357299\pi$
$509$	4.20101	+	1.52904i	0.186207	+	0.0677737i	−0.247234	+	0.968956i	$0.579522\pi$
$510$	−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	−0.943149	−	0.332369i	$-0.892152\pi$
$521$	−17.3340	−	30.0233i	−0.759415	−	1.31535i	0.183735	−	0.982976i	$-0.441181\pi$
$522$	18.2921	−	2.99796i	0.800622	−	0.131217i
$523$	−22.2749	−	12.8604i	−0.974015	−	0.562348i	−0.0735572	−	0.997291i	$-0.523435\pi$
$523$	−22.2749	−	12.8604i	−0.974015	−	0.562348i	−0.900458	+	0.434943i	$0.856768\pi$
$524$	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	0.996952	+	0.0780204i	$0.0248599\pi$
$541$	13.1658	+	22.8039i	0.566044	+	0.980416i	−0.430908	+	0.902396i	$0.641807\pi$
$542$	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	0.887387	−	0.461025i	$-0.152518\pi$
$547$	13.7395	+	11.5288i	0.587459	+	0.492937i	−0.299928	+	0.953962i	$0.596963\pi$
$548$			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	$-0.992265\pi$
$557$		−	1.14693i		−	0.0485968i	0.999705	−	0.0242984i	$-0.00773518\pi$
$558$	−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	−0.999856	−	0.0169880i	$-0.994592\pi$
$563$	−1.56861	−	8.89601i	−0.0661089	−	0.374922i	0.933747	−	0.357934i	$-0.116519\pi$
$564$	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	0.242178	−	0.970232i	$-0.422138\pi$
$569$	27.5657	−	32.8516i	1.15562	−	1.37721i	0.913438	−	0.406978i	$-0.133417\pi$
$570$	−26.5267	+	6.93631i	−1.11108	+	0.290530i
$571$	−5.74972	−	32.6083i	−0.240618	−	1.36461i	−0.830453	−	0.557089i	$-0.811918\pi$
$571$	−5.74972	−	32.6083i	−0.240618	−	1.36461i	0.589834	−	0.807524i	$-0.299193\pi$
$572$	−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	$0.336388\pi$
$577$			41.8339i			1.74157i	−0.491665	+	0.870784i	$0.663612\pi$
$578$	−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	0.828228	−	0.560391i	$-0.189349\pi$
$587$	10.1800	+	8.54200i	0.420172	+	0.352566i	−0.408057	+	0.912957i	$0.633793\pi$
$588$	−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	0.963393	−	0.268093i	$-0.0863933\pi$
$593$	6.07625	+	10.5244i	0.249522	+	0.432184i	−0.713872	+	0.700277i	$0.753060\pi$
$594$	−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	−0.518749	−	0.854927i	$-0.673602\pi$
$599$	10.4793	−	28.7916i	0.428172	−	1.17639i	0.946921	−	0.321466i	$-0.104176\pi$
$600$	1.15176	−	2.43149i	0.0470203	−	0.0992652i
$601$	0.739101	−	0.880827i	0.0301486	−	0.0359297i	−0.750759	−	0.660576i	$-0.770312\pi$
$601$	0.739101	−	0.880827i	0.0301486	−	0.0359297i	0.780908	+	0.624646i	$0.214757\pi$
$602$	−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	−0.113047	−	0.993590i	$-0.536061\pi$
$607$	2.97007	−	0.523704i	0.120552	−	0.0212565i	0.233598	+	0.972333i	$0.424950\pi$
$608$	−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	0.913119	+	0.407694i	$0.133667\pi$
$613$	20.0456	+	34.7199i	0.809633	+	1.40232i	−0.103486	+	0.994631i	$0.533000\pi$
$614$	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	0.881942	−	0.471357i	$-0.156236\pi$
$617$	6.57249	+	7.83278i	0.264598	+	0.315336i	−0.617344	+	0.786693i	$0.711791\pi$
$618$	−14.6435	+	3.82903i	−0.589046	+	0.154026i
$619$	38.3209	+	6.75702i	1.54025	+	0.271587i	0.878354	−	0.478010i	$-0.158642\pi$
$619$	38.3209	+	6.75702i	1.54025	+	0.271587i	0.661894	+	0.749597i	$0.269753\pi$
$620$	−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	0.959748	−	0.280864i	$-0.0906210\pi$
$631$	5.94429	+	10.2958i	0.236639	+	0.409870i	−0.723109	+	0.690734i	$0.757288\pi$
$632$	−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	−0.490509	−	0.871436i	$-0.663189\pi$
$641$	−17.0872	−	46.9468i	−0.674906	−	1.85429i	−0.184396	−	0.982852i	$-0.559033\pi$
$642$	−0.565412	−	6.94575i	−0.0223150	−	0.274127i
$643$	−7.32572	+	1.29172i	−0.288898	+	0.0509406i	−0.316219	−	0.948686i	$-0.602414\pi$
$643$	−7.32572	+	1.29172i	−0.288898	+	0.0509406i	0.0273209	+	0.999627i	$0.491302\pi$
$644$	−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	−0.987382	−	0.158354i	$-0.949381\pi$
$647$	−9.06934	+	15.7086i	−0.356553	+	0.617567i	0.630830	+	0.775921i	$0.282715\pi$
$648$	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	0.410392	−	0.911909i	$-0.365392\pi$
$653$	−14.2828	−	17.0215i	−0.558928	−	0.666104i	−0.969319	+	0.245805i	$0.920948\pi$
$654$	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	0.572167	−	0.820137i	$-0.306103\pi$
$659$	21.2896	+	3.75393i	0.829324	+	0.146232i	0.257157	+	0.966370i	$0.417214\pi$
$660$	0.214194	−	0.0983091i	0.00833748	−	0.00382668i
$661$	3.08248	+	3.67356i	0.119895	+	0.142885i	0.822653	−	0.568544i	$-0.192493\pi$
$661$	3.08248	+	3.67356i	0.119895	+	0.142885i	−0.702758	+	0.711428i	$0.748049\pi$
$662$	−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	−0.981941	−	0.189186i	$-0.939415\pi$
$673$	−41.8330	+	15.2260i	−1.61255	+	0.586918i	−0.630604	+	0.776105i	$0.717193\pi$
$674$	−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	0.999970	+	0.00770076i	$0.00245125\pi$
$677$	30.7338	+	25.7887i	1.18120	+	0.991142i	0.181227	+	0.983441i	$0.441993\pi$
$678$	−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	−0.934606	−	0.355685i	$-0.884248\pi$
$683$	−28.5877	+	16.5051i	−1.09388	+	0.631550i	−0.159271	+	0.987235i	$0.550914\pi$
$684$	−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	0.957279	−	0.289165i	$-0.0933778\pi$
$691$	1.00124	+	2.75087i	0.0380888	+	0.104648i	−0.919190	+	0.393814i	$0.871156\pi$
$692$	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	$-0.961471\pi$
$701$		−	6.39386i		−	0.241493i	0.992683	−	0.120746i	$-0.0385288\pi$
$702$	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	0.611287	+	0.791409i	$0.290652\pi$
$709$	−6.22575	+	35.3080i	−0.233813	+	1.32602i	−0.845099	+	0.534609i	$0.820459\pi$
$710$	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	0.313890	+	0.949459i	$0.398368\pi$
$719$	−17.8398	+	30.8994i	−0.665311	+	1.15235i	−0.979201	+	0.202893i	$0.934966\pi$
$720$	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	0.924520	−	0.381135i	$-0.124467\pi$
$727$	−0.773622	−	2.12551i	−0.0286921	−	0.0788308i	−0.953212	+	0.302304i	$0.902244\pi$
$728$	−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	−0.795210	−	0.606334i	$-0.792640\pi$
$733$	5.51496	−	15.1522i	0.203700	−	0.559661i	0.998910	+	0.0466729i	$0.0148618\pi$
$734$	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	−0.684307	−	0.729194i	$-0.739895\pi$
$743$	8.41237	−	23.1128i	0.308620	−	0.847926i	0.992926	−	0.118732i	$-0.0378828\pi$
$744$	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	−0.990029	−	0.140865i	$-0.955012\pi$
$751$	−28.0407	+	23.5290i	−1.02322	+	0.858584i	−0.0331922	+	0.999449i	$0.510567\pi$
$752$	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	0.358765	−	0.933428i	$-0.383198\pi$
$761$	36.9741	−	31.0250i	1.34031	−	1.12465i	0.981546	−	0.191226i	$-0.0612464\pi$
$762$	−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	0.189264	+	0.981926i	$0.439390\pi$
$769$	−16.2750	+	44.7151i	−0.586891	+	1.61247i	−0.776155	+	0.630543i	$0.782832\pi$
$770$	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	0.399286	−	0.916827i	$-0.369258\pi$
$787$	30.5240	−	5.38221i	1.08806	−	0.191855i	0.688779	+	0.724971i	$0.258147\pi$
$788$	−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	0.642147	−	0.766582i	$-0.278044\pi$
$797$	18.1049	+	6.58966i	0.641310	+	0.233418i	−0.000836476		1.00000i	$0.500266\pi$
$798$	−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	0.295558	−	0.955325i	$-0.404494\pi$
$809$	−10.9220	−	6.30585i	−0.383999	−	0.221702i	−0.679557	+	0.733623i	$0.737828\pi$
$810$	−22.8294	−	13.9267i	−0.802142	−	0.489334i
$811$		−	43.6085i		−	1.53130i	−0.643256	−	0.765652i	$-0.722417\pi$
$811$		−	43.6085i		−	1.53130i	0.643256	−	0.765652i	$-0.277583\pi$
$812$	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	0.988605	+	0.150532i	$0.0480988\pi$
$821$	9.39965	+	25.8253i	0.328050	+	0.901310i	−0.660555	+	0.750778i	$0.729679\pi$
$822$	−9.84384	+	13.8792i	−0.343343	+	0.484094i
$823$	−3.92941	+	3.29717i	−0.136971	+	0.114932i	−0.708699	−	0.705511i	$-0.750718\pi$
$823$	−3.92941	+	3.29717i	−0.136971	+	0.114932i	0.571728	+	0.820443i	$0.306273\pi$
$824$	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	−0.0499094	−	0.998754i	$-0.515893\pi$
$827$	22.7209	−	13.1179i	0.790082	−	0.456154i	0.839991	+	0.542600i	$0.182560\pi$
$828$	−0.0345272	+	0.0120964i	−0.00119990	+	0.000420380i
$829$	13.7370	−	7.93108i	0.477107	−	0.275458i	−0.242103	−	0.970251i	$-0.577837\pi$
$829$	13.7370	−	7.93108i	0.477107	−	0.275458i	0.719210	+	0.694793i	$0.244504\pi$
$830$	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	−0.959113	−	0.283023i	$-0.908663\pi$
$839$	−43.7933	+	15.9395i	−1.51191	+	0.550291i	−0.552800	+	0.833314i	$0.686440\pi$
$840$	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	−0.428708	−	0.903443i	$-0.641031\pi$
$853$	−33.3113	−	5.87368i	−1.14056	−	0.201111i	−0.711850	+	0.702332i	$0.752142\pi$
$854$	−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	−0.931973	−	0.362527i	$-0.881914\pi$
$857$	−41.3614	+	15.0543i	−1.41288	+	0.514246i	−0.480905	+	0.876773i	$0.659692\pi$
$858$	−59.9275	+	4.87834i	−2.04589	+	0.166544i
$859$	29.8856	+	35.6162i	1.01968	+	1.21521i	0.976360	+	0.216149i	$0.0693496\pi$
$859$	29.8856	+	35.6162i	1.01968	+	1.21521i	0.0433218	+	0.999061i	$0.486206\pi$
$860$	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	−0.602513	−	0.798109i	$-0.705834\pi$
$863$	−6.24515	+	3.60564i	−0.212587	+	0.122737i	0.389926	+	0.920846i	$0.372501\pi$
$864$	−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	−0.771005	−	0.636829i	$-0.780246\pi$
$877$	−7.82720	−	44.3903i	−0.264306	−	1.49895i	0.506699	−	0.862123i	$-0.330866\pi$
$878$	−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	0.995330	+	0.0965261i	$0.0307731\pi$
$881$	17.2527	+	29.8826i	0.581259	+	1.00677i	−0.414071	+	0.910245i	$0.635894\pi$
$882$	−25.4149	+	15.1131i	−0.855763	+	0.508885i
$883$	−19.2076	+	33.2686i	−0.646388	+	1.11958i	0.337591	+	0.941293i	$0.390388\pi$
$883$	−19.2076	+	33.2686i	−0.646388	+	1.11958i	−0.983979	+	0.178284i	$0.942945\pi$
$884$	−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	−0.120871	−	0.992668i	$-0.538569\pi$
$887$	−25.3610	−	9.23065i	−0.851539	−	0.309935i	−0.730668	+	0.682733i	$0.760791\pi$
$888$	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	0.0491052	−	0.998794i	$-0.484363\pi$
$907$	−27.8874	−	23.4003i	−0.925987	−	0.776996i	−0.975093	+	0.221798i	$0.928807\pi$
$908$	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	−0.382873	−	0.923801i	$-0.625065\pi$
$911$	17.9098	−	21.3441i	0.593378	−	0.707160i	0.976251	+	0.216640i	$0.0695099\pi$
$912$	−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	0.908607	+	0.417653i	$0.137147\pi$
$919$	24.7371	+	42.8459i	0.816001	+	1.41336i	−0.0926055	+	0.995703i	$0.529520\pi$
$920$	−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	−0.774630	−	0.632415i	$-0.782064\pi$
$929$	−29.3067	+	10.6668i	−0.961522	+	0.349966i	−0.186892	+	0.982380i	$0.559842\pi$
$930$	−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	0.737548	−	0.675294i	$-0.235983\pi$
$937$	15.9634	+	9.21646i	0.521501	+	0.301089i	−0.216048	+	0.976383i	$0.569317\pi$
$938$	−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	−0.978091	−	0.208180i	$-0.933246\pi$
$941$	−3.99360	−	22.6488i	−0.130188	−	0.738331i	0.847903	−	0.530152i	$-0.177865\pi$
$942$	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	−0.921924	−	0.387370i	$-0.873384\pi$
$947$	−11.7046	+	13.9490i	−0.380349	+	0.453282i	0.541575	+	0.840652i	$0.317828\pi$
$948$	−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	0.131301	−	0.991343i	$-0.458085\pi$
$953$	−20.4233	−	11.7914i	−0.661576	−	0.381961i	−0.792877	+	0.609381i	$0.791418\pi$
$954$	−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	−0.896120	−	0.443811i	$-0.853626\pi$
$967$	−6.40078	−	36.3006i	−0.205835	−	1.16735i	0.690285	−	0.723537i	$-0.257485\pi$
$968$	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	0.747426	−	0.664345i	$-0.231289\pi$
$971$	−6.28287	−	10.8822i	−0.201627	−	0.349228i	−0.949053	+	0.315117i	$0.897956\pi$
$972$	−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	−0.818996	−	0.573799i	$-0.805469\pi$
$977$	5.53944	−	15.2195i	0.177222	−	0.486914i	0.996218	+	0.0868850i	$0.0276913\pi$
$978$	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	0.627947	−	0.778256i	$-0.283895\pi$
$983$	−0.923122	−	0.774591i	−0.0294430	−	0.0247056i	−0.657390	+	0.753550i	$0.728340\pi$
$984$	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	0.880636	+	0.473793i	$0.157115\pi$
$991$	26.7781	+	46.3810i	0.850635	+	1.47334i	−0.0300019	+	0.999550i	$0.509551\pi$
$992$	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	0.131021	−	0.991380i	$-0.458174\pi$
$997$	−2.68170	−	0.472857i	−0.0849304	−	0.0149755i	−0.215952	+	0.976404i	$0.569285\pi$
$998$	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.101.16	✓	132
3.2	odd	2		567.2.ba.a.143.7		132
7.5	odd	6		189.2.bd.a.47.7	yes	132
21.5	even	6		567.2.bd.a.467.16		132
27.4	even	9		567.2.bd.a.17.16		132
27.23	odd	18		189.2.bd.a.185.7	yes	132
189.131	even	18	inner	189.2.ba.a.131.16	yes	132
189.166	odd	18		567.2.ba.a.341.7		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.ba.a.101.16	✓	132	1.1	even	1	trivial
189.2.ba.a.131.16	yes	132	189.131	even	18	inner
189.2.bd.a.47.7	yes	132	7.5	odd	6
189.2.bd.a.185.7	yes	132	27.23	odd	18
567.2.ba.a.143.7		132	3.2	odd	2
567.2.ba.a.341.7		132	189.166	odd	18
567.2.bd.a.17.16		132	27.4	even	9
567.2.bd.a.467.16		132	21.5	even	6

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)

\(f(q)\)	\(=\)	\(q+(0.905074 - 1.07862i) q^{2} +(-1.67571 + 0.438172i) q^{3} +(0.00302336 + 0.0171463i) q^{4} +(1.61655 - 1.35644i) q^{5} +(-1.04402 + 2.20404i) q^{6} +(1.08812 - 2.41164i) q^{7} +(2.46004 + 1.42030i) q^{8} +(2.61601 - 1.46850i) q^{9} +O(q^{10})\)	\(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} - 18 q^{6} - 6 q^{7} - 18 q^{8} + 3 q^{9}+O(q^{10}) \) 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	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} - 18 q^{6} - 6 q^{7} - 18 q^{8} + 3 q^{9} - 9 q^{11} - 9 q^{12} + 3 q^{14} - 24 q^{15} + 3 q^{16} - 18 q^{17} - 3 q^{18} + 18 q^{20} - 21 q^{21} - 12 q^{22} - 6 q^{23} - 9 q^{24} - 3 q^{25} - 12 q^{28} + 6 q^{29} + 51 q^{30} - 9 q^{31} + 3 q^{32} - 9 q^{33} - 18 q^{34} + 18 q^{35} + 3 q^{37} - 99 q^{38} - 36 q^{39} - 54 q^{40} - 45 q^{42} - 12 q^{43} - 9 q^{44} - 9 q^{45} + 3 q^{46} + 45 q^{47} - 24 q^{49} - 9 q^{50} - 48 q^{51} - 9 q^{52} - 45 q^{53} + 171 q^{54} + 3 q^{56} - 3 q^{58} + 36 q^{59} + 57 q^{60} - 9 q^{61} - 99 q^{62} - 33 q^{63} + 18 q^{64} + 69 q^{65} - 9 q^{66} - 3 q^{67} + 36 q^{68} + 108 q^{69} + 66 q^{70} + 18 q^{71} - 129 q^{72} - 9 q^{73} + 75 q^{74} + 36 q^{75} + 36 q^{76} + 15 q^{77} + 66 q^{78} - 21 q^{79} + 72 q^{80} - 33 q^{81} - 18 q^{82} - 90 q^{83} - 120 q^{84} + 9 q^{85} - 105 q^{86} - 54 q^{87} - 63 q^{88} - 18 q^{89} + 81 q^{90} + 6 q^{91} + 150 q^{92} + 21 q^{93} - 9 q^{94} + 45 q^{95} - 81 q^{96} + 27 q^{98} + 96 q^{99}+O(q^{100}) \) 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

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