LMFDB - Embedded newform 87.2.k.a.2.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [87,2,Mod(2,87)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("87.2"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(87, base_ring=CyclotomicField(28)) chi = DirichletCharacter(H, H._module([14, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 87 = 3 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	87.k (of order $28$, degree $12$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$0.694698497585$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$8$ over $\Q(\zeta_{28})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{28}]$

Embedding invariants

Embedding label			2.2
Character	$\chi$	$=$	87.2
Dual form			87.2.k.a.44.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.255714 + 2.26953i) q^{2} +(-1.44205 + 0.959421i) q^{3} +(-3.13550 - 0.715657i) q^{4} +(-1.22248 - 1.53294i) q^{5} +(-1.80868 - 3.51811i) q^{6} +(0.968527 + 4.24339i) q^{7} +(0.917355 - 2.62165i) q^{8} +(1.15902 - 2.76707i) q^{9} +(3.79166 - 2.38246i) q^{10} +(0.304506 + 0.870228i) q^{11} +(5.20817 - 1.97625i) q^{12} +(-0.526689 + 1.09368i) q^{13} +(-9.87816 + 1.11300i) q^{14} +(3.23362 + 1.03771i) q^{15} +(-0.0799573 - 0.0385054i) q^{16} +(4.38493 + 4.38493i) q^{17} +(5.98355 + 3.33801i) q^{18} +(0.885852 + 1.40983i) q^{19} +(2.73603 + 5.68142i) q^{20} +(-5.46787 - 5.18996i) q^{21} +(-2.05287 + 0.468555i) q^{22} +(-2.41688 - 1.92740i) q^{23} +(1.19239 + 4.66068i) q^{24} +(0.257151 - 1.12665i) q^{25} +(-2.34745 - 1.47500i) q^{26} +(0.983418 + 5.10224i) q^{27} -13.9983i q^{28} +(4.21298 - 3.35422i) q^{29} +(-3.18198 + 7.07342i) q^{30} +(10.4895 + 1.18188i) q^{31} +(3.06329 - 4.87519i) q^{32} +(-1.27403 - 0.962764i) q^{33} +(-11.0730 + 8.83042i) q^{34} +(5.32087 - 6.67217i) q^{35} +(-5.61438 + 7.84668i) q^{36} +(-5.88562 - 2.05947i) q^{37} +(-3.42616 + 1.64995i) q^{38} +(-0.289789 - 2.08246i) q^{39} +(-5.14029 + 1.79866i) q^{40} +(-2.44440 + 2.44440i) q^{41} +(13.1770 - 11.0823i) q^{42} +(-0.647855 - 5.74987i) q^{43} +(-0.331993 - 2.94652i) q^{44} +(-5.65864 + 1.60598i) q^{45} +(4.99231 - 4.99231i) q^{46} +(2.99334 - 1.04741i) q^{47} +(0.152245 - 0.0211860i) q^{48} +(-10.7616 + 5.18250i) q^{49} +(2.49121 + 0.871712i) q^{50} +(-10.5303 - 2.11630i) q^{51} +(2.43413 - 3.05231i) q^{52} +(-1.71289 + 1.36599i) q^{53} +(-11.8311 + 0.927176i) q^{54} +(0.961757 - 1.53063i) q^{55} +(12.0132 + 1.35356i) q^{56} +(-2.63006 - 1.18313i) q^{57} +(6.53516 + 10.4192i) q^{58} +4.23167i q^{59} +(-9.39637 - 5.56789i) q^{60} +(-3.53348 - 2.22023i) q^{61} +(-5.36462 + 23.5040i) q^{62} +(12.8643 + 2.23820i) q^{63} +(10.1423 + 8.08820i) q^{64} +(2.32042 - 0.529620i) q^{65} +(2.51080 - 2.64525i) q^{66} +(0.236814 + 0.491748i) q^{67} +(-10.6108 - 16.8871i) q^{68} +(5.33445 + 0.460599i) q^{69} +(13.7820 + 13.7820i) q^{70} +(-6.12060 - 2.94753i) q^{71} +(-6.19105 - 5.57693i) q^{72} +(8.47945 - 0.955405i) q^{73} +(6.17905 - 12.8309i) q^{74} +(0.710109 + 1.87141i) q^{75} +(-1.76864 - 5.05447i) q^{76} +(-3.39780 + 2.13498i) q^{77} +(4.80030 - 0.125168i) q^{78} +(-3.08062 + 8.80389i) q^{79} +(0.0387197 + 0.169642i) q^{80} +(-6.31334 - 6.41418i) q^{81} +(-4.92257 - 6.17270i) q^{82} +(4.18332 + 0.954815i) q^{83} +(13.4303 + 20.1863i) q^{84} +(1.36135 - 12.0823i) q^{85} +13.2151 q^{86} +(-2.85723 + 8.87898i) q^{87} +2.56077 q^{88} +(0.344100 - 3.05397i) q^{89} +(-2.19781 - 13.2531i) q^{90} +(-5.15103 - 1.17569i) q^{91} +(6.19877 + 7.77301i) q^{92} +(-16.2603 + 8.35951i) q^{93} +(1.61169 + 7.06129i) q^{94} +(1.07824 - 3.08145i) q^{95} +(0.259949 + 9.96926i) q^{96} +(4.21195 - 2.64655i) q^{97} +(-9.00992 - 25.7489i) q^{98} +(2.76091 + 0.166024i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 12 q^{3} - 28 q^{4} - 14 q^{6} - 20 q^{7} - 14 q^{9} - 4 q^{10} - 8 q^{12} - 28 q^{13} - 16 q^{15} - 48 q^{16} - 28 q^{18} - 20 q^{19} + 26 q^{21} - 28 q^{22} + 58 q^{24} - 20 q^{25} + 36 q^{27}+ \cdots + 82 q^{99}+O(q^{100}) $ 96 * q - 12 * q^3 - 28 * q^4 - 14 * q^6 - 20 * q^7 - 14 * q^9 - 4 * q^10 - 8 * q^12 - 28 * q^13 - 16 * q^15 - 48 * q^16 - 28 * q^18 - 20 * q^19 + 26 * q^21 - 28 * q^22 + 58 * q^24 - 20 * q^25 + 36 * q^27 + 96 * q^30 - 32 * q^31 + 28 * q^33 - 28 * q^34 + 22 * q^36 - 4 * q^37 - 40 * q^39 - 48 * q^40 - 14 * q^42 - 32 * q^43 + 42 * q^45 + 120 * q^46 - 20 * q^48 + 4 * q^49 - 14 * q^51 + 72 * q^52 - 30 * q^54 + 148 * q^55 + 112 * q^58 + 20 * q^60 + 12 * q^61 - 14 * q^63 + 224 * q^64 - 32 * q^66 + 28 * q^67 + 10 * q^69 + 52 * q^70 - 44 * q^72 + 16 * q^73 - 144 * q^75 - 100 * q^76 - 102 * q^78 - 60 * q^79 - 146 * q^81 - 108 * q^82 - 64 * q^84 - 104 * q^85 - 70 * q^87 - 312 * q^88 - 96 * q^90 - 112 * q^91 - 70 * q^93 + 56 * q^94 - 168 * q^96 + 32 * q^97 + 82 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/87\mathbb{Z}\right)^\times$.

$n$	$31$	$59$
$\chi(n)$	$e\left(\frac{1}{28}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.255714	+	2.26953i	−0.180817	+	1.60480i	0.495783	+	0.868446i	$0.334881\pi$
$2$	−0.255714	+	2.26953i	−0.180817	+	1.60480i	−0.676600	+	0.736350i	$0.736548\pi$
$3$	−1.44205	+	0.959421i	−0.832568	+	0.553922i
$3$	−1.44205	+	0.959421i	−0.832568	+	0.553922i
$4$	−3.13550	−	0.715657i	−1.56775	−	0.357829i
$5$	−1.22248	−	1.53294i	−0.546710	−	0.685553i	0.429329	−	0.903148i	$-0.358750\pi$
$5$	−1.22248	−	1.53294i	−0.546710	−	0.685553i	−0.976039	+	0.217595i	$0.930179\pi$
$6$	−1.80868	−	3.51811i	−0.738390	−	1.43626i
$7$	0.968527	+	4.24339i	0.366069	+	1.60385i	0.737470	+	0.675380i	$0.236020\pi$
$7$	0.968527	+	4.24339i	0.366069	+	1.60385i	−0.371401	+	0.928472i	$0.621123\pi$
$8$	0.917355	−	2.62165i	0.324334	−	0.926893i
$9$	1.15902	−	2.76707i	0.386340	−	0.922356i
$10$	3.79166	−	2.38246i	1.19903	−	0.753399i
$11$	0.304506	+	0.870228i	0.0918120	+	0.262384i	0.980628	−	0.195881i	$-0.0627568\pi$
$11$	0.304506	+	0.870228i	0.0918120	+	0.262384i	−0.888816	+	0.458265i	$0.848471\pi$
$12$	5.20817	−	1.97625i	1.50347	−	0.570495i
$13$	−0.526689	+	1.09368i	−0.146077	+	0.303332i	−0.961150	−	0.276026i	$-0.910982\pi$
$13$	−0.526689	+	1.09368i	−0.146077	+	0.303332i	0.815073	+	0.579358i	$0.196697\pi$
$14$	−9.87816	+	1.11300i	−2.64005	+	0.297462i
$15$	3.23362	+	1.03771i	0.834917	+	0.267935i
$16$	−0.0799573	−	0.0385054i	−0.0199893	−	0.00962635i
$17$	4.38493	+	4.38493i	1.06350	+	1.06350i	0.997842	+	0.0656596i	$0.0209151\pi$
$17$	4.38493	+	4.38493i	1.06350	+	1.06350i	0.0656596	+	0.997842i	$0.479085\pi$
$18$	5.98355	+	3.33801i	1.41034	+	0.786776i
$19$	0.885852	+	1.40983i	0.203228	+	0.323436i	0.932751	−	0.360520i	$-0.117401\pi$
$19$	0.885852	+	1.40983i	0.203228	+	0.323436i	−0.729523	+	0.683956i	$0.760258\pi$
$20$	2.73603	+	5.68142i	0.611794	+	1.27040i
$21$	−5.46787	−	5.18996i	−1.19319	−	1.13254i
$22$	−2.05287	+	0.468555i	−0.437674	+	0.0998962i
$23$	−2.41688	−	1.92740i	−0.503954	−	0.401890i	0.338244	−	0.941059i	$-0.390167\pi$
$23$	−2.41688	−	1.92740i	−0.503954	−	0.401890i	−0.842198	+	0.539168i	$0.818739\pi$
$24$	1.19239	+	4.66068i	0.243396	+	0.951357i
$25$	0.257151	−	1.12665i	0.0514302	−	0.225330i
$26$	−2.34745	−	1.47500i	−0.460374	−	0.289272i
$27$	0.983418	+	5.10224i	0.189259	+	0.981927i
$28$		−	13.9983i		−	2.64543i
$29$	4.21298	−	3.35422i	0.782332	−	0.622862i
$29$	4.21298	−	3.35422i	0.782332	−	0.622862i
$30$	−3.18198	+	7.07342i	−0.580948	+	1.29142i
$31$	10.4895	+	1.18188i	1.88397	+	0.212272i	0.977638	−	0.210295i	$-0.0674425\pi$
$31$	10.4895	+	1.18188i	1.88397	+	0.212272i	0.906331	+	0.422567i	$0.138871\pi$
$32$	3.06329	−	4.87519i	0.541518	−	0.861821i
$33$	−1.27403	−	0.962764i	−0.221780	−	0.167596i
$34$	−11.0730	+	8.83042i	−1.89900	+	1.51440i
$35$	5.32087	−	6.67217i	0.899392	−	1.12780i
$36$	−5.61438	+	7.84668i	−0.935731	+	1.30778i
$37$	−5.88562	−	2.05947i	−0.967590	−	0.338574i	−0.200200	−	0.979755i	$-0.564159\pi$
$37$	−5.88562	−	2.05947i	−0.967590	−	0.338574i	−0.767390	+	0.641181i	$0.778445\pi$
$38$	−3.42616	+	1.64995i	−0.555796	+	0.267657i
$39$	−0.289789	−	2.08246i	−0.0464033	−	0.333460i
$40$	−5.14029	+	1.79866i	−0.812751	+	0.284394i
$41$	−2.44440	+	2.44440i	−0.381752	+	0.381752i	−0.871733	−	0.489981i	$-0.837004\pi$
$41$	−2.44440	+	2.44440i	−0.381752	+	0.381752i	0.489981	+	0.871733i	$0.337004\pi$
$42$	13.1770	−	11.0823i	2.03325	−	1.71004i
$43$	−0.647855	−	5.74987i	−0.0987970	−	0.876847i	−0.941166	−	0.337946i	$-0.890268\pi$
$43$	−0.647855	−	5.74987i	−0.0987970	−	0.876847i	0.842369	−	0.538902i	$-0.181161\pi$
$44$	−0.331993	−	2.94652i	−0.0500499	−	0.444205i
$45$	−5.65864	+	1.60598i	−0.843540	+	0.239405i
$46$	4.99231	−	4.99231i	0.736076	−	0.736076i
$47$	2.99334	−	1.04741i	0.436623	−	0.152781i	−0.103012	−	0.994680i	$-0.532848\pi$
$47$	2.99334	−	1.04741i	0.436623	−	0.152781i	0.539635	+	0.841899i	$0.318562\pi$
$48$	0.152245	−	0.0211860i	0.0219747	−	0.00305793i
$49$	−10.7616	+	5.18250i	−1.53737	+	0.740357i
$50$	2.49121	+	0.871712i	0.352310	+	0.123279i
$51$	−10.5303	−	2.11630i	−1.47454	−	0.296341i
$52$	2.43413	−	3.05231i	0.337554	−	0.423279i
$53$	−1.71289	+	1.36599i	−0.235284	+	0.187633i	−0.734033	−	0.679114i	$-0.762364\pi$
$53$	−1.71289	+	1.36599i	−0.235284	+	0.187633i	0.498749	+	0.866746i	$0.333793\pi$
$54$	−11.8311	+	0.927176i	−1.61001	+	0.126173i
$55$	0.961757	−	1.53063i	0.129683	−	0.206390i
$56$	12.0132	+	1.35356i	1.60533	+	0.180877i
$57$	−2.63006	−	1.18313i	−0.348360	−	0.156710i
$58$	6.53516	+	10.4192i	0.858108	+	1.36811i
$59$			4.23167i			0.550917i	0.961313	+	0.275458i	$0.0888297\pi$
$59$			4.23167i			0.550917i	−0.961313	+	0.275458i	$0.911170\pi$
$60$	−9.39637	−	5.56789i	−1.21307	−	0.718812i
$61$	−3.53348	−	2.22023i	−0.452416	−	0.284272i	0.286487	−	0.958084i	$-0.407513\pi$
$61$	−3.53348	−	2.22023i	−0.452416	−	0.284272i	−0.738902	+	0.673813i	$0.764655\pi$
$62$	−5.36462	+	23.5040i	−0.681308	+	2.98501i
$63$	12.8643	+	2.23820i	1.62075	+	0.281987i
$64$	10.1423	+	8.08820i	1.26779	+	1.01103i
$65$	2.32042	−	0.529620i	0.287812	−	0.0656913i
$66$	2.51080	−	2.64525i	0.309059	−	0.325608i
$67$	0.236814	+	0.491748i	0.0289314	+	0.0600766i	0.914934	−	0.403604i	$-0.132243\pi$
$67$	0.236814	+	0.491748i	0.0289314	+	0.0600766i	−0.886002	+	0.463681i	$0.846528\pi$
$68$	−10.6108	−	16.8871i	−1.28675	−	2.04786i
$69$	5.33445	+	0.460599i	0.642192	+	0.0554496i
$70$	13.7820	+	13.7820i	1.64727	+	1.64727i
$71$	−6.12060	−	2.94753i	−0.726382	−	0.349807i	0.0338783	−	0.999426i	$-0.489214\pi$
$71$	−6.12060	−	2.94753i	−0.726382	−	0.349807i	−0.760260	+	0.649619i	$0.774928\pi$
$72$	−6.19105	−	5.57693i	−0.729622	−	0.657247i
$73$	8.47945	−	0.955405i	0.992445	−	0.111822i	0.399217	−	0.916856i	$-0.369282\pi$
$73$	8.47945	−	0.955405i	0.992445	−	0.111822i	0.593228	+	0.805035i	$0.297853\pi$
$74$	6.17905	−	12.8309i	0.718300	−	1.49157i
$75$	0.710109	+	1.87141i	0.0819964	+	0.216091i
$76$	−1.76864	−	5.05447i	−0.202877	−	0.579788i
$77$	−3.39780	+	2.13498i	−0.387215	+	0.243303i
$78$	4.80030	−	0.125168i	0.543527	−	0.0141725i
$79$	−3.08062	+	8.80389i	−0.346596	+	0.990515i	0.630216	+	0.776420i	$0.282966\pi$
$79$	−3.08062	+	8.80389i	−0.346596	+	0.990515i	−0.976813	+	0.214096i	$0.931320\pi$
$80$	0.0387197	+	0.169642i	0.00432899	+	0.0189666i
$81$	−6.31334	−	6.41418i	−0.701482	−	0.712687i
$82$	−4.92257	−	6.17270i	−0.543606	−	0.681661i
$83$	4.18332	+	0.954815i	0.459179	+	0.104805i	0.445852	−	0.895107i	$-0.352901\pi$
$83$	4.18332	+	0.954815i	0.459179	+	0.104805i	0.0133267	+	0.999911i	$0.495758\pi$
$84$	13.4303	+	20.1863i	1.46536	+	2.20250i
$85$	1.36135	−	12.0823i	0.147659	−	1.31051i
$86$	13.2151			1.42503
$87$	−2.85723	+	8.87898i	−0.306327	+	0.951926i
$88$	2.56077			0.272979
$89$	0.344100	−	3.05397i	0.0364745	−	0.323720i	−0.962204	−	0.272329i	$-0.912206\pi$
$89$	0.344100	−	3.05397i	0.0364745	−	0.323720i	0.998679	−	0.0513908i	$-0.0163654\pi$
$90$	−2.19781	−	13.2531i	−0.231670	−	1.39700i
$91$	−5.15103	−	1.17569i	−0.539975	−	0.123246i
$92$	6.19877	+	7.77301i	0.646266	+	0.810392i
$93$	−16.2603	+	8.35951i	−1.68612	+	0.866841i
$94$	1.61169	+	7.06129i	0.166234	+	0.728317i
$95$	1.07824	−	3.08145i	0.110626	−	0.316150i
$96$	0.259949	+	9.96926i	0.0265310	+	1.01748i
$97$	4.21195	−	2.64655i	0.427659	−	0.268716i	−0.300958	−	0.953637i	$-0.597306\pi$
$97$	4.21195	−	2.64655i	0.427659	−	0.268716i	0.728617	+	0.684921i	$0.240164\pi$
$98$	−9.00992	−	25.7489i	−0.910140	−	2.60103i
$99$	2.76091	+	0.166024i	0.277482	+	0.0166860i
$100$	−1.61259	+	3.34859i	−0.161259	+	0.334859i
$101$	3.60138	−	0.405778i	0.358351	−	0.0403764i	0.0690460	−	0.997613i	$-0.478004\pi$
$101$	3.60138	−	0.405778i	0.358351	−	0.0403764i	0.289305	+	0.957237i	$0.406576\pi$
$102$	7.49573	−	23.3576i	0.742188	−	2.31275i
$103$	−8.82327	−	4.24906i	−0.869382	−	0.418672i	−0.0546471	−	0.998506i	$-0.517403\pi$
$103$	−8.82327	−	4.24906i	−0.869382	−	0.418672i	−0.814735	+	0.579833i	$0.803118\pi$
$104$	2.38409	+	2.38409i	0.233779	+	0.233779i
$105$	−1.27155	+	14.7266i	−0.124091	+	1.43717i
$106$	−2.66213	−	4.23675i	−0.258569	−	0.411510i
$107$	−1.05757	−	2.19606i	−0.102239	−	0.212301i	0.843574	−	0.537012i	$-0.180447\pi$
$107$	−1.05757	−	2.19606i	−0.102239	−	0.212301i	−0.945813	+	0.324711i	$0.894733\pi$
$108$	0.567952	−	16.7019i	0.0546512	−	1.60714i
$109$	5.21028	−	1.18921i	0.499055	−	0.113906i	0.0344182	−	0.999408i	$-0.489042\pi$
$109$	5.21028	−	1.18921i	0.499055	−	0.113906i	0.464636	+	0.885502i	$0.346185\pi$
$110$	3.22786	+	2.57414i	0.307765	+	0.245434i
$111$	10.4633	−	2.67693i	0.993129	−	0.254083i
$112$	0.0859528	−	0.376584i	0.00812177	−	0.0355838i
$113$	7.53601	+	4.73519i	0.708928	+	0.445449i	0.837633	−	0.546234i	$-0.183939\pi$
$113$	7.53601	+	4.73519i	0.708928	+	0.445449i	−0.128705	+	0.991683i	$0.541082\pi$
$114$	3.35770	−	5.66644i	0.314477	−	0.530711i
$115$			6.06115i			0.565205i
$116$	−15.6103	+	7.50209i	−1.44938	+	0.696552i
$117$	2.41585	+	2.72498i	0.223345	+	0.251925i
$118$	−9.60389	−	1.08210i	−0.884110	−	0.0996152i
$119$	−14.3601	+	22.8539i	−1.31638	+	2.09501i
$120$	5.68688	−	7.52547i	0.519138	−	0.686978i
$121$	7.93557	−	6.32841i	0.721416	−	0.575310i
$122$	5.94243	−	7.45158i	0.538003	−	0.674634i
$123$	1.17974	−	5.87016i	0.106374	−	0.529295i
$124$	−32.0440	−	11.2127i	−2.87764	−	1.00693i
$125$	−10.8741	+	5.23671i	−0.972612	+	0.468385i
$126$	−8.36924	+	28.6235i	−0.745591	+	2.54999i
$127$	−14.2831	+	4.99786i	−1.26742	+	0.443488i	−0.878481	−	0.477776i	$-0.841443\pi$
$127$	−14.2831	+	4.99786i	−1.26742	+	0.443488i	−0.388936	+	0.921265i	$0.627157\pi$
$128$	−12.8073	+	12.8073i	−1.13201	+	1.13201i
$129$	6.45079	+	7.67004i	0.567960	+	0.675310i
$130$	0.608623	+	5.40168i	0.0533798	+	0.473758i
$131$	0.560570	+	4.97520i	0.0489772	+	0.434685i	0.994141	+	0.108089i	$0.0344731\pi$
$131$	0.560570	+	4.97520i	0.0489772	+	0.434685i	−0.945164	+	0.326596i	$0.894098\pi$
$132$	3.30571	+	3.93051i	0.287725	+	0.342107i
$133$	−5.12447	+	5.12447i	−0.444348	+	0.444348i
$134$	−1.17659	+	0.411707i	−0.101642	+	0.0355661i
$135$	6.61924	−	7.74492i	0.569693	−	0.666577i
$136$	15.5183	−	7.47321i	1.33068	−	0.640822i
$137$	7.12142	+	2.49189i	0.608424	+	0.212897i	0.616867	−	0.787068i	$-0.288402\pi$
$137$	7.12142	+	2.49189i	0.608424	+	0.212897i	−0.00844278	+	0.999964i	$0.502687\pi$
$138$	−2.40943	+	11.9889i	−0.205105	+	1.02056i
$139$	11.9796	−	15.0219i	1.01609	−	1.27414i	0.0548353	−	0.998495i	$-0.482537\pi$
$139$	11.9796	−	15.0219i	1.01609	−	1.27414i	0.961259	−	0.275647i	$-0.0888920\pi$
$140$	−21.4586	+	17.1126i	−1.81358	+	1.44628i
$141$	−3.31163	+	4.38230i	−0.278890	+	0.369056i
$142$	8.25461	−	13.1371i	0.692711	−	1.10244i
$143$	−1.11213	−	0.125307i	−0.0930011	−	0.0104787i
$144$	−0.199219	+	0.176619i	−0.0166016	+	0.0147182i
$145$	−10.2921	−	2.35780i	−0.854714	−	0.195805i
$146$			19.4886i			1.61289i
$147$	10.5465	−	17.7983i	0.869863	−	1.46798i
$148$	16.9805	+	10.6695i	1.39579	+	0.877032i
$149$	3.80232	−	16.6591i	0.311498	−	1.36476i	−0.540555	−	0.841308i	$-0.681786\pi$
$149$	3.80232	−	16.6591i	0.311498	−	1.36476i	0.852054	−	0.523455i	$-0.175357\pi$
$150$	−4.42879	+	1.13307i	−0.361609	+	0.0925145i
$151$	3.51415	+	2.80244i	0.285977	+	0.228059i	0.755962	−	0.654615i	$-0.227169\pi$
$151$	3.51415	+	2.80244i	0.285977	+	0.228059i	−0.469985	+	0.882674i	$0.655741\pi$
$152$	4.50871	−	1.02908i	0.365704	−	0.0834697i
$153$	17.2156	−	7.05118i	1.39180	−	0.570054i
$154$	−3.97652	−	8.25734i	−0.320437	−	0.665395i
$155$	−11.0115	−	17.5246i	−0.884461	−	1.40761i
$156$	−0.581696	+	6.73694i	−0.0465729	+	0.539387i
$157$	−9.97951	−	9.97951i	−0.796451	−	0.796451i	0.186083	−	0.982534i	$-0.440421\pi$
$157$	−9.97951	−	9.97951i	−0.796451	−	0.796451i	−0.982534	+	0.186083i	$0.940421\pi$
$158$	−19.1929	−	9.24282i	−1.52691	−	0.735319i
$159$	1.15952	−	3.61321i	0.0919560	−	0.286546i
$160$	−11.2182	+	1.26399i	−0.886877	+	0.0999270i
$161$	5.83789	−	12.1225i	0.460090	−	0.955388i
$162$	16.1716	−	12.6881i	1.27056	−	0.996870i
$163$	2.13312	+	6.09610i	0.167079	+	0.477483i	0.996731	−	0.0807978i	$-0.0257468\pi$
$163$	2.13312	+	6.09610i	0.167079	+	0.477483i	−0.829652	+	0.558281i	$0.811461\pi$
$164$	9.41378	−	5.91507i	0.735093	−	0.461889i
$165$	0.0816144	+	3.12997i	0.00635367	+	0.243668i
$166$	−3.23671	+	9.24999i	−0.251217	+	0.717938i
$167$	−0.00133704	−	0.00585796i	−0.000103463	−	0.000453303i	0.974876	−	0.222748i	$-0.0715026\pi$
$167$	−0.00133704	−	0.00585796i	−0.000103463	−	0.000453303i	−0.974980	+	0.222294i	$0.928645\pi$
$168$	−18.6222	+	9.57379i	−1.43674	+	0.738634i
$169$	7.18663	+	9.01175i	0.552818	+	0.693212i
$170$	27.0731	+	6.17925i	2.07641	+	0.473927i
$171$	4.92781	−	0.817196i	0.376839	−	0.0624926i
$172$	−2.08359	+	18.4924i	−0.158872	+	1.41003i
$173$	20.1966			1.53552			0.767758	−	0.640740i	$-0.221372\pi$
$173$	20.1966			1.53552			0.767758	+	0.640740i	$0.221372\pi$
$174$	−19.4204	−	8.75504i	−1.47226	−	0.663718i
$175$	5.02989			0.380224
$176$	0.00916101	−	0.0813062i	0.000690537	−	0.00612869i
$177$	−4.05996	−	6.10229i	−0.305165	−	0.458676i
$178$	6.84307	+	1.56189i	0.512910	+	0.117068i
$179$	−7.25204	−	9.09377i	−0.542043	−	0.679700i	0.433083	−	0.901354i	$-0.357426\pi$
$179$	−7.25204	−	9.09377i	−0.542043	−	0.679700i	−0.975125	+	0.221654i	$0.928854\pi$
$180$	18.8920	−	0.985891i	1.40813	−	0.0734840i
$181$	−1.34322	−	5.88504i	−0.0998409	−	0.437432i	−0.999998	−	0.00186673i	$-0.999406\pi$
$181$	−1.34322	−	5.88504i	−0.0998409	−	0.437432i	0.900157	−	0.435565i	$-0.143451\pi$
$182$	3.98545	−	11.3898i	0.295421	−	0.844265i
$183$	7.22560	−	0.188408i	0.534131	−	0.0139275i
$184$	−7.27009	+	4.56810i	−0.535958	+	0.336765i
$185$	4.03801	+	11.5400i	0.296881	+	0.848436i
$186$	−14.8141	−	39.0408i	−1.08623	−	2.86261i
$187$	−2.48065	+	5.15113i	−0.181403	+	0.376688i
$188$	−10.1352	+	1.14196i	−0.739185	+	0.0832862i
$189$	−20.6984	+	9.11469i	−1.50558	+	0.662996i
$190$	6.71770	+	3.23507i	0.487353	+	0.234697i
$191$	−9.46401	−	9.46401i	−0.684792	−	0.684792i	0.276284	−	0.961076i	$-0.410897\pi$
$191$	−9.46401	−	9.46401i	−0.684792	−	0.684792i	−0.961076	+	0.276284i	$0.910897\pi$
$192$	−22.3857	−	1.93287i	−1.61555	−	0.139493i
$193$	2.46006	+	3.91517i	0.177079	+	0.281820i	0.923457	−	0.383703i	$-0.125351\pi$
$193$	2.46006	+	3.91517i	0.177079	+	0.281820i	−0.746377	+	0.665523i	$0.768209\pi$
$194$	4.92935	+	10.2359i	0.353906	+	0.734894i
$195$	−2.83803	+	2.99000i	−0.203236	+	0.214118i
$196$	37.4518	−	8.54812i	2.67513	−	0.610580i
$197$	−11.0474	−	8.81001i	−0.787094	−	0.627687i	0.145194	−	0.989403i	$-0.453619\pi$
$197$	−11.0474	−	8.81001i	−0.787094	−	0.627687i	−0.932288	+	0.361716i	$0.882191\pi$
$198$	−1.08280	+	6.22350i	−0.0769512	+	0.442285i
$199$	0.625226	−	2.73929i	0.0443211	−	0.194183i	−0.947921	−	0.318506i	$-0.896819\pi$
$199$	0.625226	−	2.73929i	0.0443211	−	0.194183i	0.992242	+	0.124323i	$0.0396759\pi$
$200$	−2.71779	−	1.70770i	−0.192177	−	0.120753i
$201$	−0.813291	−	0.481922i	−0.0573651	−	0.0339922i
$202$			8.27719i			0.582381i
$203$	18.3136	+	14.6287i	1.28537	+	1.02673i
$204$	31.5032	+	14.1717i	2.20566	+	0.992219i
$205$	6.73536	+	0.758893i	0.470418	+	0.0530034i
$206$	11.8996	−	18.9381i	0.829083	−	1.31948i
$207$	−8.13446	+	4.45378i	−0.565384	+	0.309559i
$208$	0.0842252	−	0.0671674i	0.00583997	−	0.00465722i
$209$	−0.957123	+	1.20019i	−0.0662056	+	0.0830192i
$210$	−33.0972	−	6.65161i	−2.28392	−	0.459005i
$211$	13.9685	+	4.88779i	0.961631	+	0.336489i	0.765030	−	0.643994i	$-0.222724\pi$
$211$	13.9685	+	4.88779i	0.961631	+	0.336489i	0.196601	+	0.980484i	$0.437010\pi$
$212$	6.34835	−	3.05720i	0.436006	−	0.209970i
$213$	11.6541	−	1.62175i	0.798528	−	0.111121i
$214$	5.25445	−	1.83861i	0.359187	−	0.125685i
$215$	−8.02224	+	8.02224i	−0.547112	+	0.547112i
$216$	14.2784	+	2.10239i	0.971524	+	0.143050i
$217$	5.14417	+	45.6558i	0.349209	+	3.09931i
$218$	1.36661	+	12.1290i	0.0925583	+	0.821477i
$219$	−11.3112	+	9.51311i	−0.764338	+	0.642836i
$220$	−4.11100	+	4.11100i	−0.277163	+	0.277163i
$221$	−7.10521	+	2.48622i	−0.477948	+	0.167241i
$222$	3.39976	+	24.4312i	0.228177	+	1.63971i
$223$	7.63961	−	3.67904i	0.511586	−	0.246367i	−0.160237	−	0.987079i	$-0.551226\pi$
$223$	7.63961	−	3.67904i	0.511586	−	0.246367i	0.671823	+	0.740712i	$0.265512\pi$
$224$	23.6542	+	8.27698i	1.58047	+	0.553029i
$225$	−2.81948	−	2.01737i	−0.187965	−	0.134491i
$226$	−12.6737	+	15.8923i	−0.843041	+	1.05714i
$227$	−18.0225	+	14.3725i	−1.19620	+	0.953935i	−0.999647	−	0.0265586i	$-0.991545\pi$
$227$	−18.0225	+	14.3725i	−1.19620	+	0.953935i	−0.196550	+	0.980494i	$0.562974\pi$
$228$	7.39984	+	5.59194i	0.490066	+	0.370335i
$229$	6.64157	−	10.5700i	0.438887	−	0.698485i	−0.551900	−	0.833910i	$-0.686097\pi$
$229$	6.64157	−	10.5700i	0.438887	−	0.698485i	0.990788	+	0.135425i	$0.0432399\pi$
$230$	−13.7559	−	1.54992i	−0.907039	−	0.102199i
$231$	2.85145	−	6.33867i	0.187612	−	0.417054i
$232$	−4.92877	−	14.1220i	−0.323590	−	0.927153i
$233$		−	17.4712i		−	1.14457i	−0.820053	−	0.572287i	$-0.806056\pi$
$233$		−	17.4712i		−	1.14457i	0.820053	−	0.572287i	$-0.193944\pi$
$234$	−6.80218	+	4.78601i	−0.444673	+	0.312871i
$235$	−5.26492	−	3.30817i	−0.343446	−	0.215801i
$236$	3.02843	−	13.2684i	0.197134	−	0.863700i
$237$	−4.00424	−	15.6513i	−0.260103	−	1.01666i
$238$	−48.1954	−	38.4346i	−3.12405	−	2.49134i
$239$	7.31189	−	1.66889i	0.472967	−	0.107952i	0.0206079	−	0.999788i	$-0.493440\pi$
$239$	7.31189	−	1.66889i	0.472967	−	0.107952i	0.452359	+	0.891836i	$0.350583\pi$
$240$	−0.218594	−	0.207484i	−0.0141102	−	0.0133930i
$241$	0.500275	+	1.03883i	0.0322256	+	0.0669171i	0.916460	−	0.400126i	$-0.131034\pi$
$241$	0.500275	+	1.03883i	0.0322256	+	0.0669171i	−0.884235	+	0.467043i	$0.845319\pi$
$242$	12.3332	+	19.6282i	0.792811	+	1.26175i
$243$	15.2581	+	3.19242i	0.978805	+	0.204794i
$244$	9.49030	+	9.49030i	0.607554	+	0.607554i
$245$	21.1003	+	10.1614i	1.34805	+	0.649185i
$246$	13.0208	+	4.17853i	0.830177	+	0.266414i
$247$	−2.00847	+	0.226300i	−0.127796	+	0.0143991i
$248$	12.7211	−	26.4156i	0.807789	−	1.67739i
$249$	−6.94863	+	2.63667i	−0.440351	+	0.167092i
$250$	−9.10417	−	26.0182i	−0.575798	−	1.64554i
$251$	−3.03879	+	1.90940i	−0.191807	+	0.120520i	−0.624512	−	0.781015i	$-0.714702\pi$
$251$	−3.03879	+	1.90940i	−0.191807	+	0.120520i	0.432705	+	0.901536i	$0.357559\pi$
$252$	−38.7342	−	16.2243i	−2.44003	−	1.02204i
$253$	0.941321	−	2.69014i	0.0591804	−	0.169128i
$254$	−7.69039	−	33.6938i	−0.482538	−	2.11414i
$255$	9.62892	+	18.7295i	0.602986	+	1.17288i
$256$	−9.61502	−	12.0568i	−0.600938	−	0.753553i
$257$	−28.3839	−	6.47844i	−1.77054	−	0.404114i	−0.792056	−	0.610448i	$-0.790989\pi$
$257$	−28.3839	−	6.47844i	−1.77054	−	0.404114i	−0.978482	+	0.206334i	$0.933847\pi$
$258$	−19.0569	+	12.6789i	−1.18643	+	0.789354i
$259$	3.03875	−	26.9697i	0.188819	−	1.67581i
$260$	−7.65469			−0.474724
$261$	−4.39841	−	15.5452i	−0.272255	−	0.962225i
$262$	−11.4347			−0.706437
$263$	−2.13091	+	18.9124i	−0.131398	+	1.16619i	0.738954	+	0.673756i	$0.235320\pi$
$263$	−2.13091	+	18.9124i	−0.131398	+	1.16619i	−0.870352	+	0.492431i	$0.836108\pi$
$264$	−3.69276	+	2.45686i	−0.227274	+	0.151209i
$265$	4.18796	+	0.955873i	0.257264	+	0.0587188i
$266$	−10.3197	−	12.9405i	−0.632743	−	0.793434i
$267$	2.43383	+	4.73411i	0.148948	+	0.289723i
$268$	−0.390605	−	1.71135i	−0.0238600	−	0.104538i
$269$	−4.65375	+	13.2997i	−0.283744	+	0.810895i	0.710494	+	0.703703i	$0.248471\pi$
$269$	−4.65375	+	13.2997i	−0.283744	+	0.810895i	−0.994238	+	0.107191i	$0.965814\pi$
$270$	15.8847	+	17.0030i	0.966710	+	1.03477i
$271$	−17.1301	+	10.7636i	−1.04058	+	0.653841i	−0.940030	−	0.341091i	$-0.889203\pi$
$271$	−17.1301	+	10.7636i	−1.04058	+	0.653841i	−0.100551	+	0.994932i	$0.532061\pi$
$272$	−0.181764	−	0.519450i	−0.0110210	−	0.0314963i
$273$	8.55603	−	3.24661i	0.517834	−	0.196493i
$274$	−7.47646	+	15.5250i	−0.451670	+	0.937901i
$275$	1.05875	−	0.119292i	0.0638450	−	0.00719360i
$276$	−16.3965	−	5.26184i	−0.986955	−	0.316726i
$277$	−10.5176	−	5.06501i	−0.631942	−	0.304327i	0.0903559	−	0.995910i	$-0.471200\pi$
$277$	−10.5176	−	5.06501i	−0.631942	−	0.304327i	−0.722297	+	0.691583i	$0.756914\pi$
$278$	31.0293	+	31.0293i	1.86101	+	1.86101i
$279$	15.4279	−	27.6553i	0.923644	−	1.65568i
$280$	−12.6109	−	20.0702i	−0.753648	−	1.19942i
$281$	2.12781	+	4.41844i	0.126935	+	0.263582i	0.954745	−	0.297426i	$-0.0961280\pi$
$281$	2.12781	+	4.41844i	0.126935	+	0.263582i	−0.827810	+	0.561008i	$0.810414\pi$
$282$	−9.09890	−	8.63645i	−0.541832	−	0.514293i
$283$	−7.85956	+	1.79389i	−0.467202	+	0.106636i	−0.449640	−	0.893210i	$-0.648448\pi$
$283$	−7.85956	+	1.79389i	−0.467202	+	0.106636i	−0.0175624	+	0.999846i	$0.505591\pi$
$284$	17.0817	+	13.6222i	1.01361	+	0.808330i
$285$	1.40152	+	5.47809i	0.0830190	+	0.324494i
$286$	0.568776	−	2.49197i	0.0336324	−	0.147353i
$287$	−12.7400	−	8.00509i	−0.752020	−	0.472526i
$288$	−9.93958	−	14.1268i	−0.585696	−	0.832429i
$289$			21.4552i			1.26207i
$290$	7.98292	−	22.7553i	0.468773	−	1.33624i
$291$	−3.53470	+	7.85749i	−0.207208	+	0.460614i
$292$	−27.2711	−	3.07271i	−1.59592	−	0.179817i
$293$	5.38901	−	8.57656i	0.314829	−	0.501048i	−0.651399	−	0.758735i	$-0.725818\pi$
$293$	5.38901	−	8.57656i	0.314829	−	0.501048i	0.966228	+	0.257687i	$0.0829605\pi$
$294$	37.6968	+	28.4869i	2.19852	+	1.66139i
$295$	6.48691	−	5.17314i	0.377683	−	0.301192i
$296$	−10.7984	+	13.5408i	−0.627644	+	0.787041i
$297$	−4.14066	+	2.40946i	−0.240265	+	0.139811i
$298$	36.8358	+	12.8894i	2.13384	+	0.746664i
$299$	3.38090	−	1.62816i	0.195523	−	0.0941587i
$300$	−0.887263	−	6.37599i	−0.0512261	−	0.368118i
$301$	23.7715	−	8.31801i	1.37017	−	0.479442i
$302$	−7.25883	+	7.25883i	−0.417699	+	0.417699i
$303$	−4.80406	+	4.04039i	−0.275986	+	0.232115i
$304$	−0.0165444	−	0.146836i	−0.000948888	−	0.00842161i
$305$	0.916123	+	8.13081i	0.0524570	+	0.465569i
$306$	11.6005	+	40.8744i	0.663159	+	2.33663i
$307$	−19.9438	+	19.9438i	−1.13825	+	1.13825i	−0.149489	+	0.988763i	$0.547763\pi$
$307$	−19.9438	+	19.9438i	−1.13825	+	1.13825i	−0.988763	+	0.149489i	$0.952237\pi$
$308$	12.1817	−	4.26257i	0.694117	−	0.242882i
$309$	16.8002	−	2.33787i	0.955732	−	0.132997i
$310$	42.5884	−	20.5095i	2.41886	−	1.16486i
$311$	−28.2925	−	9.89997i	−1.60432	−	0.561376i	−0.628096	−	0.778136i	$-0.716165\pi$
$311$	−28.2925	−	9.89997i	−1.60432	−	0.561376i	−0.976225	+	0.216760i	$0.930451\pi$
$312$	−5.72532	−	1.15063i	−0.324132	−	0.0651416i
$313$	−2.90318	+	3.64047i	−0.164097	+	0.205772i	−0.857081	−	0.515182i	$-0.827724\pi$
$313$	−2.90318	+	3.64047i	−0.164097	+	0.205772i	0.692984	+	0.720953i	$0.256296\pi$
$314$	25.2006	−	20.0968i	1.42215	−	1.13413i
$315$	−12.2953	−	22.4564i	−0.692764	−	1.26528i
$316$	15.9598	−	25.3999i	0.897811	−	1.42886i
$317$	23.2288	+	2.61725i	1.30466	+	0.147000i	0.736791	−	0.676121i	$-0.236340\pi$
$317$	23.2288	+	2.61725i	1.30466	+	0.147000i	0.567867	+	0.823120i	$0.307769\pi$
$318$	7.90376	+	3.55551i	0.443221	+	0.199383i
$319$	4.20181	+	2.64488i	0.235256	+	0.148085i
$320$		−	25.4352i		−	1.42187i
$321$	3.63201	+	2.15218i	0.202719	+	0.120123i
$322$	26.0195	+	16.3491i	1.45001	+	0.911102i
$323$	−2.29759	+	10.0664i	−0.127841	+	0.560109i
$324$	15.2051	+	24.6299i	0.844729	+	1.36833i
$325$	1.09676	+	0.874636i	0.0608373	+	0.0485161i
$326$	−14.3807	+	3.28230i	−0.796474	+	0.181790i
$327$	−6.37254	+	6.71376i	−0.352402	+	0.371272i
$328$	4.16598	+	8.65075i	0.230028	+	0.477658i
$329$	7.34372	+	11.6875i	0.404872	+	0.644351i
$330$	−7.12443	−	0.615153i	−0.392187	−	0.0338630i
$331$	−11.5323	−	11.5323i	−0.633875	−	0.633875i	0.315163	−	0.949038i	$-0.397941\pi$
$331$	−11.5323	−	11.5323i	−0.633875	−	0.633875i	−0.949038	+	0.315163i	$0.897941\pi$
$332$	−12.4335	−	5.98764i	−0.682375	−	0.328615i
$333$	−12.5202	+	13.8990i	−0.686105	+	0.761658i
$334$	0.0136367	−	0.00153649i	0.000746167	−	8.40728e-5i
$335$	0.464322	−	0.964175i	0.0253686	−	0.0526785i
$336$	0.237354	+	0.625518i	0.0129487	+	0.0341248i
$337$	−2.05189	−	5.86397i	−0.111774	−	0.319431i	0.874386	−	0.485232i	$-0.161265\pi$
$337$	−2.05189	−	5.86397i	−0.111774	−	0.319431i	−0.986159	+	0.165801i	$0.946979\pi$
$338$	−22.2901	+	14.0058i	−1.21242	+	0.761816i
$339$	−15.4103	+	0.401826i	−0.836975	+	0.0218242i
$340$	−12.9153	+	36.9099i	−0.700432	+	2.00172i
$341$	2.16561	+	9.48815i	0.117274	+	0.513812i
$342$	0.594538	+	11.3927i	0.0321489	+	0.616049i
$343$	−13.4180	−	16.8256i	−0.724502	−	0.908497i
$344$	−15.6685	−	3.57622i	−0.844787	−	0.192817i
$345$	−5.81519	−	8.74048i	−0.313079	−	0.470572i
$346$	−5.16454	+	45.8366i	−0.277648	+	2.46419i
$347$	21.7588			1.16807			0.584037	−	0.811727i	$-0.301472\pi$
$347$	21.7588			1.16807			0.584037	+	0.811727i	$0.301472\pi$
$348$	15.3132	−	25.7952i	0.820871	−	1.38277i
$349$	−27.3902			−1.46616			−0.733081	−	0.680142i	$-0.761918\pi$
$349$	−27.3902			−1.46616			−0.733081	+	0.680142i	$0.761918\pi$
$350$	−1.28621	+	11.4155i	−0.0687510	+	0.610182i
$351$	−6.09818	−	1.61175i	−0.325497	−	0.0860288i
$352$	5.17532	+	1.18123i	0.275846	+	0.0629600i
$353$	−1.83355	−	2.29920i	−0.0975900	−	0.122374i	0.730639	−	0.682764i	$-0.239222\pi$
$353$	−1.83355	−	2.29920i	−0.0975900	−	0.122374i	−0.828229	+	0.560390i	$0.810651\pi$
$354$	14.8875	−	7.65374i	0.791261	−	0.406791i
$355$	2.96393	+	12.9858i	0.157309	+	0.689216i
$356$	−3.26452	+	9.32946i	−0.173019	+	0.494460i
$357$	−1.21859	−	46.7338i	−0.0644946	−	2.47342i
$358$	22.4930	−	14.1333i	1.18879	−	0.746967i
$359$	−11.1483	−	31.8601i	−0.588387	−	1.68151i	−0.723197	−	0.690641i	$-0.757328\pi$
$359$	−11.1483	−	31.8601i	−0.588387	−	1.68151i	0.134811	−	0.990871i	$-0.456957\pi$
$360$	−0.980673	+	16.3082i	−0.0516860	+	0.859518i
$361$	7.04092	−	14.6206i	0.370575	−	0.769506i
$362$	13.6997	−	1.54359i	0.720042	−	0.0811292i
$363$	−5.37189	+	16.7394i	−0.281951	+	0.878593i
$364$	15.3097	+	7.37275i	0.802444	+	0.386437i
$365$	−11.8306	−	11.8306i	−0.619239	−	0.619239i
$366$	−1.42009	+	16.4468i	−0.0742293	+	0.859691i
$367$	−2.28042	−	3.62926i	−0.119037	−	0.189446i	0.781891	−	0.623415i	$-0.214255\pi$
$367$	−2.28042	−	3.62926i	−0.119037	−	0.189446i	−0.900928	+	0.433969i	$0.857113\pi$
$368$	0.119032	+	0.247172i	0.00620497	+	0.0128847i
$369$	3.93072	+	9.59694i	0.204625	+	0.499597i
$370$	−27.2229	+	6.21344i	−1.41525	+	0.323021i
$371$	−7.45540	−	5.94548i	−0.387065	−	0.308674i
$372$	56.9668	−	14.5744i	2.95359	−	0.755650i
$373$	−4.09626	+	17.9469i	−0.212096	+	0.929255i	0.751043	+	0.660253i	$0.229551\pi$
$373$	−4.09626	+	17.9469i	−0.212096	+	0.929255i	−0.963140	+	0.269002i	$0.913306\pi$
$374$	−11.0563	−	6.94712i	−0.571706	−	0.359227i
$375$	10.6568	−	17.9845i	0.550317	−	0.928715i
$376$		−	8.80833i		−	0.454255i
$377$	1.44951	+	6.37429i	0.0746535	+	0.328293i
$378$	−15.3932	−	49.3062i	−0.791738	−	2.53604i
$379$	21.1100	+	2.37852i	1.08435	+	0.122176i	0.636004	−	0.771686i	$-0.280586\pi$
$379$	21.1100	+	2.37852i	1.08435	+	0.122176i	0.448342	+	0.893862i	$0.352015\pi$
$380$	−5.58609	+	8.89022i	−0.286561	+	0.456059i
$381$	15.8019	−	20.9106i	0.809553	−	1.07128i
$382$	23.8989	−	19.0587i	1.22277	−	0.975130i
$383$	1.11105	−	1.39321i	0.0567718	−	0.0711896i	−0.752635	−	0.658438i	$-0.771217\pi$
$383$	1.11105	−	1.39321i	0.0567718	−	0.0711896i	0.809407	+	0.587248i	$0.199789\pi$
$384$	6.18116	−	30.7563i	0.315431	−	1.56953i
$385$	7.42655	+	2.59866i	0.378492	+	0.132440i
$386$	−9.51464	+	4.58201i	−0.484283	+	0.233218i
$387$	−16.6612	−	4.87156i	−0.846935	−	0.247636i
$388$	−15.1006	+	5.28393i	−0.766617	+	0.268251i
$389$	−18.1731	+	18.1731i	−0.921411	+	0.921411i	−0.997129	−	0.0757178i	$-0.975875\pi$
$389$	−18.1731	+	18.1731i	−0.921411	+	0.921411i	0.0757178	+	0.997129i	$0.475875\pi$
$390$	−6.06015	−	7.20557i	−0.306868	−	0.364868i
$391$	−2.14635	−	19.0493i	−0.108545	−	0.963367i
$392$	3.71451	+	32.9672i	0.187611	+	1.66510i
$393$	−5.58168	−	6.63666i	−0.281559	−	0.334775i
$394$	22.8195	−	22.8195i	1.14963	−	1.14963i
$395$	17.2619	−	6.04019i	0.868538	−	0.303915i
$396$	−8.53802	−	2.49643i	−0.429052	−	0.125451i
$397$	18.9892	−	9.14473i	0.953042	−	0.458961i	0.108290	−	0.994119i	$-0.465462\pi$
$397$	18.9892	−	9.14473i	0.953042	−	0.458961i	0.844752	+	0.535159i	$0.179748\pi$
$398$	6.05702	+	2.11944i	0.303611	+	0.106238i
$399$	2.47322	−	12.3063i	0.123816	−	0.616085i
$400$	−0.0639433	+	0.0801823i	−0.00319716	+	0.00400912i
$401$	28.3608	−	22.6170i	1.41627	−	1.12944i	0.443878	−	0.896087i	$-0.353603\pi$
$401$	28.3608	−	22.6170i	1.41627	−	1.12944i	0.972393	−	0.233350i	$-0.0749689\pi$
$402$	1.30170	−	1.72255i	0.0649231	−	0.0859130i
$403$	−6.81730	+	10.8497i	−0.339594	+	0.540461i
$404$	−11.5825	−	1.30504i	−0.576252	−	0.0649280i
$405$	−2.11464	+	17.5192i	−0.105077	+	0.870536i
$406$	−37.8833	+	37.8225i	−1.88012	+	1.87710i
$407$		−	5.74895i		−	0.284965i
$408$	−15.2082	+	25.6653i	−0.752918	+	1.27062i
$409$	23.8836	+	15.0071i	1.18097	+	0.742052i	0.971795	−	0.235826i	$-0.0757796\pi$
$409$	23.8836	+	15.0071i	1.18097	+	0.742052i	0.209174	+	0.977878i	$0.432922\pi$
$410$	−3.44466	+	15.0920i	−0.170119	+	0.745342i
$411$	−12.6602	+	3.23901i	−0.624483	+	0.159768i
$412$	24.6245	+	19.6374i	1.21316	+	0.967464i
$413$	−17.9567	+	4.09849i	−0.883589	+	0.201673i
$414$	−8.02787	−	19.6002i	−0.394548	−	0.963300i
$415$	−3.65035	−	7.58003i	−0.179189	−	0.372089i
$416$	3.71851	+	5.91797i	0.182315	+	0.290152i
$417$	−2.86281	+	33.1558i	−0.140193	+	1.62365i
$418$	−2.47912	−	2.47912i	−0.121258	−	0.121258i
$419$	14.1065	+	6.79335i	0.689149	+	0.331877i	0.745473	−	0.666536i	$-0.232224\pi$
$419$	14.1065	+	6.79335i	0.689149	+	0.331877i	−0.0563240	+	0.998413i	$0.517938\pi$
$420$	14.5261	−	45.2651i	0.708802	−	2.20871i
$421$	−30.8054	+	3.47094i	−1.50137	+	0.169163i	−0.824045	−	0.566525i	$-0.808288\pi$
$421$	−30.8054	+	3.47094i	−1.50137	+	0.169163i	−0.677321	+	0.735688i	$0.736859\pi$
$422$	−14.6649	+	30.4520i	−0.713876	+	1.48238i
$423$	0.571074	−	9.49675i	0.0277666	−	0.461748i
$424$	2.00981	+	5.74369i	0.0976048	+	0.278938i
$425$	6.06788	−	3.81270i	0.294335	−	0.184943i
$426$	0.700483	+	26.8641i	0.0339385	+	1.30157i
$427$	5.99905	−	17.1443i	0.290314	−	0.829671i
$428$	1.74437	+	7.64260i	0.0843175	+	0.369419i
$429$	1.72397	−	0.886304i	0.0832342	−	0.0427912i
$430$	−16.1553	−	20.2581i	−0.779076	−	0.976931i
$431$	12.2814	+	2.80314i	0.591573	+	0.135023i	0.507819	−	0.861464i	$-0.330452\pi$
$431$	12.2814	+	2.80314i	0.591573	+	0.135023i	0.0837541	+	0.996486i	$0.473309\pi$
$432$	0.117832	−	0.445828i	0.00566922	−	0.0214499i
$433$	0.0498950	−	0.442830i	0.00239780	−	0.0212811i	−0.992456	−	0.122599i	$-0.960877\pi$
$433$	0.0498950	−	0.442830i	0.00239780	−	0.0212811i	0.994854	+	0.101318i	$0.0323058\pi$
$434$	−104.932			−5.03691
$435$	17.1039	−	6.47441i	0.820068	−	0.310424i
$436$	−17.1879			−0.823152
$437$	0.576296	−	5.11477i	0.0275680	−	0.244673i
$438$	−18.6978	−	28.1036i	−0.893416	−	1.34284i
$439$	−4.58884	−	1.04737i	−0.219013	−	0.0499883i	0.111606	−	0.993753i	$-0.464400\pi$
$439$	−4.58884	−	1.04737i	−0.219013	−	0.0499883i	−0.330619	+	0.943764i	$0.607258\pi$
$440$	−3.13050	−	3.92552i	−0.149241	−	0.187142i
$441$	1.86744	+	35.7846i	0.0889259	+	1.70403i
$442$	−3.82564	−	16.7612i	−0.181967	−	0.797249i
$443$	−4.46740	+	12.7671i	−0.212253	+	0.606583i	−0.999955	−	0.00947284i	$-0.996985\pi$
$443$	−4.46740	+	12.7671i	−0.212253	+	0.606583i	0.787703	+	0.616056i	$0.211270\pi$
$444$	−34.7233	+	0.905414i	−1.64790	+	0.0429690i
$445$	−5.10221	+	3.20593i	−0.241868	+	0.151976i
$446$	6.39613	+	18.2791i	0.302865	+	0.865539i
$447$	10.4999	+	27.6712i	0.496629	+	1.30880i
$448$	−24.4983	+	50.8713i	−1.15744	+	2.40344i
$449$	26.9196	−	3.03311i	1.27042	−	0.143142i	0.549105	−	0.835753i	$-0.314969\pi$
$449$	26.9196	−	3.03311i	1.27042	−	0.143142i	0.721311	+	0.692612i	$0.243540\pi$
$450$	5.29945	−	5.88301i	0.249818	−	0.277328i
$451$	−2.87152	−	1.38285i	−0.135215	−	0.0651160i
$452$	−20.2404	−	20.2404i	−0.952027	−	0.952027i
$453$	−7.75630	−	0.669712i	−0.364423	−	0.0314658i
$454$	−28.0101	−	44.5778i	−1.31458	−	2.09214i
$455$	4.49477	+	9.33349i	0.210718	+	0.437561i
$456$	−5.51446	+	5.80974i	−0.258238	+	0.272066i
$457$	−10.7710	+	2.45840i	−0.503845	+	0.114999i	−0.466886	−	0.884318i	$-0.654624\pi$
$457$	−10.7710	+	2.45840i	−0.503845	+	0.114999i	−0.0369587	+	0.999317i	$0.511767\pi$
$458$	22.2905	+	17.7761i	1.04157	+	0.830623i
$459$	−18.0608	+	26.6852i	−0.843004	+	1.24556i
$460$	4.33770	−	19.0047i	0.202246	−	0.886100i
$461$	−0.0837455	−	0.0526208i	−0.00390042	−	0.00245079i	0.530080	−	0.847947i	$-0.322162\pi$
$461$	−0.0837455	−	0.0526208i	−0.00390042	−	0.00245079i	−0.533981	+	0.845497i	$0.679305\pi$
$462$	13.6566	+	8.09234i	0.635363	+	0.376490i
$463$		−	23.8232i		−	1.10716i	−0.832796	−	0.553580i	$-0.813261\pi$
$463$		−	23.8232i		−	1.10716i	0.832796	−	0.553580i	$-0.186739\pi$
$464$	−0.466014	+	0.105971i	−0.0216342	+	0.00491959i
$465$	32.6926	+	14.7068i	1.51608	+	0.682011i
$466$	39.6513	+	4.46763i	1.83681	+	0.206959i
$467$	−12.6736	+	20.1700i	−0.586466	+	0.933355i	0.413275	+	0.910606i	$0.364385\pi$
$467$	−12.6736	+	20.1700i	−0.586466	+	0.933355i	−0.999741	+	0.0227488i	$0.992758\pi$
$468$	−5.62473	−	10.2731i	−0.260003	−	0.474874i
$469$	−1.85732	+	1.48116i	−0.0857632	+	0.0683938i
$470$	8.85429	−	11.1029i	0.408418	−	0.512140i
$471$	23.9655	+	4.81640i	1.10427	+	0.221928i
$472$	11.0940	+	3.88194i	0.510641	+	0.178681i
$473$	4.80643	−	2.31465i	0.221000	−	0.106428i
$474$	36.5449	−	5.08547i	1.67856	−	0.233584i
$475$	1.81618	−	0.635509i	0.0833321	−	0.0291592i
$476$	61.3815	−	61.3815i	2.81342	−	2.81342i
$477$	1.79450	+	6.32289i	0.0821644	+	0.289505i
$478$	1.91784	+	17.0213i	0.0877198	+	0.778535i
$479$	−3.60700	−	32.0131i	−0.164808	−	1.46271i	−0.755146	−	0.655557i	$-0.772434\pi$
$479$	−3.60700	−	32.0131i	−0.164808	−	1.46271i	0.590337	−	0.807157i	$-0.298995\pi$
$480$	14.9645	−	12.5857i	0.683034	−	0.574457i
$481$	5.35229	−	5.35229i	0.244043	−	0.244043i
$482$	−2.48558	+	0.869743i	−0.113215	+	0.0396157i
$483$	3.21206	+	23.0823i	0.146154	+	1.05028i
$484$	−29.4110	+	14.1636i	−1.33686	+	0.643799i
$485$	−9.20603	−	3.22133i	−0.418025	−	0.146273i
$486$	−11.1470	+	33.8122i	−0.505638	+	1.53375i
$487$	13.2800	−	16.6526i	0.601775	−	0.754602i	−0.383878	−	0.923384i	$-0.625412\pi$
$487$	13.2800	−	16.6526i	0.601775	−	0.754602i	0.985654	+	0.168781i	$0.0539832\pi$
$488$	−9.06212	+	7.22680i	−0.410223	+	0.327142i
$489$	−8.92479	−	6.74432i	−0.403593	−	0.304989i
$490$	−28.4571	+	45.2892i	−1.28556	+	2.04596i
$491$	−22.6585	−	2.55300i	−1.02256	−	0.115215i	−0.415274	−	0.909696i	$-0.636314\pi$
$491$	−22.6585	−	2.55300i	−1.02256	−	0.115215i	−0.607289	+	0.794481i	$0.707743\pi$
$492$	−7.90010	+	17.5616i	−0.356164	+	0.791738i
$493$	33.1816	+	3.76564i	1.49443	+	0.169596i
$494$		−	4.61614i		−	0.207690i
$495$	−3.12066	−	4.43528i	−0.140263	−	0.199351i
$496$	−0.793203	−	0.498402i	−0.0356159	−	0.0223789i
$497$	6.57955	−	28.8269i	0.295133	−	1.29306i
$498$	−4.20713	−	16.4443i	−0.188526	−	0.736888i
$499$	−14.9065	−	11.8876i	−0.667308	−	0.532160i	0.230209	−	0.973141i	$-0.426059\pi$
$499$	−14.9065	−	11.8876i	−0.667308	−	0.532160i	−0.897516	+	0.440981i	$0.854631\pi$
$500$	37.8435	−	8.63754i	1.69241	−	0.386283i
$501$	0.00754834	+	0.00716470i	0.000337235	+	0.000320095i
$502$	−3.55637	−	7.38487i	−0.158728	−	0.329603i
$503$	−15.6116	−	24.8457i	−0.696085	−	1.10781i	−0.988456	−	0.151508i	$-0.951587\pi$
$503$	−15.6116	−	24.8457i	−0.696085	−	1.10781i	0.292371	−	0.956305i	$-0.405556\pi$
$504$	17.6689	−	31.6725i	0.787036	−	1.41080i
$505$	−5.02465	−	5.02465i	−0.223594	−	0.223594i
$506$	5.86463	+	2.82426i	0.260715	+	0.125554i
$507$	−19.0096	−	6.10039i	−0.844244	−	0.270928i
$508$	48.3613	−	5.44901i	2.14569	−	0.241761i
$509$	−13.5768	+	28.1924i	−0.601779	+	1.24961i	0.348237	+	0.937406i	$0.386780\pi$
$509$	−13.5768	+	28.1924i	−0.601779	+	1.24961i	−0.950016	+	0.312200i	$0.898934\pi$
$510$	−44.9692	+	17.0637i	−1.99127	+	0.755593i
$511$	12.2667	+	35.0563i	0.542649	+	1.55080i
$512$	−0.850076	+	0.534138i	−0.0375684	+	0.0236058i
$513$	−6.32211	+	5.90628i	−0.279128	+	0.260769i
$514$	21.9611	−	62.7613i	0.968664	−	2.76828i
$515$	4.27271	+	18.7200i	0.188278	+	0.824900i
$516$	−14.7373	−	28.6660i	−0.648775	−	1.26195i
$517$	1.82298	+	2.28594i	0.0801745	+	0.100536i
$518$	60.4313	+	13.7930i	2.65520	+	0.606032i
$519$	−29.1245	+	19.3770i	−1.27842	+	0.850556i
$520$	0.740167	−	6.56917i	0.0324585	−	0.288077i
$521$	15.7366			0.689434			0.344717	−	0.938707i	$-0.387975\pi$
$521$	15.7366			0.689434			0.344717	+	0.938707i	$0.387975\pi$
$522$	36.4050	−	6.00717i	1.59340	−	0.262926i
$523$	8.79883			0.384746			0.192373	−	0.981322i	$-0.438382\pi$
$523$	8.79883			0.384746			0.192373	+	0.981322i	$0.438382\pi$
$524$	1.80287	−	16.0009i	0.0787587	−	0.699003i
$525$	−7.25335	+	4.82578i	−0.316562	+	0.210614i
$526$	−42.3772	−	9.67232i	−1.84773	−	0.421733i
$527$	40.8132	+	51.1782i	1.77785	+	2.22936i
$528$	0.0647963	+	0.126037i	0.00281990	+	0.00548505i
$529$	−2.99153	−	13.1068i	−0.130067	−	0.569859i
$530$	−3.24030	+	9.26024i	−0.140750	+	0.402239i
$531$	11.7093	+	4.90460i	0.508142	+	0.212841i
$532$	19.7352	−	12.4004i	0.855627	−	0.537626i
$533$	−1.38596	−	3.96084i	−0.0600324	−	0.171563i
$534$	−11.3666	+	4.31307i	−0.491879	+	0.186645i
$535$	−2.07358	+	4.30583i	−0.0896486	+	0.186157i
$536$	1.50643	−	0.169734i	0.0650680	−	0.00733141i
$537$	19.1826	+	6.15591i	0.827789	+	0.265647i
$538$	−28.9939	−	13.9627i	−1.25002	−	0.601976i
$539$	−7.78692	−	7.78692i	−0.335406	−	0.335406i
$540$	−26.2973	+	19.5471i	−1.13166	+	0.841173i
$541$	7.17314	+	11.4160i	0.308398	+	0.490812i	0.964580	−	0.263790i	$-0.0849727\pi$
$541$	7.17314	+	11.4160i	0.308398	+	0.490812i	−0.656182	+	0.754602i	$0.727830\pi$
$542$	−20.0478	−	41.6297i	−0.861126	−	1.78815i
$543$	7.58323	+	7.19781i	0.325427	+	0.308888i
$544$	34.8097	−	7.94508i	1.49245	−	0.340643i
$545$	−8.19247	−	6.53328i	−0.350927	−	0.279855i
$546$	5.18036	+	20.2483i	0.221699	+	0.866548i
$547$	−3.44838	+	15.1083i	−0.147442	+	0.645985i	0.846149	+	0.532947i	$0.178915\pi$
$547$	−3.44838	+	15.1083i	−0.147442	+	0.645985i	−0.993591	+	0.113039i	$0.963942\pi$
$548$	−20.5459	−	12.9098i	−0.877676	−	0.551480i
$549$	−10.2389	+	7.20408i	−0.436986	+	0.307463i
$550$			2.43336i			0.103759i
$551$	8.46094	+	2.96823i	0.360448	+	0.126451i
$552$	6.10111	−	13.5625i	0.259680	−	0.577259i
$553$	−40.3420	−	4.54546i	−1.71552	−	0.193293i
$554$	14.1847	−	22.5748i	0.602649	−	0.959110i
$555$	−16.8947	−	12.7671i	−0.717141	−	0.541932i
$556$	−48.3125	+	38.5279i	−2.04891	+	1.63395i
$557$	−4.04179	+	5.06825i	−0.171256	+	0.214748i	−0.860051	−	0.510208i	$-0.829569\pi$
$557$	−4.04179	+	5.06825i	−0.171256	+	0.214748i	0.688795	+	0.724956i	$0.258140\pi$
$558$	58.8194	+	42.0859i	2.49002	+	1.78164i
$559$	6.62974	+	2.31985i	0.280408	+	0.0981191i
$560$	−0.682357	+	0.328606i	−0.0288348	+	0.0138861i
$561$	−1.36488	−	9.80818i	−0.0576251	−	0.414102i
$562$	−10.5719	+	3.69926i	−0.445948	+	0.156044i
$563$	25.9488	−	25.9488i	1.09361	−	1.09361i	0.0984717	−	0.995140i	$-0.468605\pi$
$563$	25.9488	−	25.9488i	1.09361	−	1.09361i	0.995140	−	0.0984717i	$-0.0313954\pi$
$564$	13.5198	−	11.3707i	0.569288	−	0.478793i
$565$	−1.95386	−	17.3409i	−0.0821993	−	0.729539i
$566$	−2.06149	−	18.2962i	−0.0866507	−	0.769047i
$567$	21.1033	−	33.0023i	0.886254	−	1.38597i
$568$	−13.3421	+	13.3421i	−0.559824	+	0.559824i
$569$	−11.3456	+	3.97000i	−0.475632	+	0.166431i	−0.557440	−	0.830217i	$-0.688216\pi$
$569$	−11.3456	+	3.97000i	−0.475632	+	0.166431i	0.0818078	+	0.996648i	$0.473931\pi$
$570$	−12.7911	+	1.77996i	−0.535758	+	0.0745545i
$571$	−7.18785	+	3.46149i	−0.300802	+	0.144859i	−0.578197	−	0.815897i	$-0.696243\pi$
$571$	−7.18785	+	3.46149i	−0.300802	+	0.144859i	0.277395	+	0.960756i	$0.410529\pi$
$572$	3.39741	+	1.18881i	0.142053	+	0.0497065i
$573$	22.7276	+	4.56761i	0.949458	+	0.190815i
$574$	21.4256	−	26.8668i	0.894286	−	1.12140i
$575$	−2.79301	+	2.22735i	−0.116477	+	0.0928870i
$576$	34.1357	−	18.6900i	1.42232	−	0.778750i
$577$	18.2757	−	29.0856i	0.760828	−	1.21085i	−0.211534	−	0.977371i	$-0.567846\pi$
$577$	18.2757	−	29.0856i	0.760828	−	1.21085i	0.972362	−	0.233480i	$-0.0750112\pi$
$578$	−48.6932	−	5.48640i	−2.02537	−	0.228204i
$579$	−7.30383	−	3.28563i	−0.303537	−	0.136546i
$580$	30.5835	+	14.7585i	1.26991	+	0.612814i
$581$			18.6762i			0.774821i
$582$	−16.9289	−	10.0314i	−0.701726	−	0.415813i
$583$	−1.71031	−	1.07466i	−0.0708336	−	0.0445077i
$584$	5.27393	−	23.1066i	0.218237	−	0.956158i
$585$	1.22392	−	7.03459i	0.0506028	−	0.290845i
$586$	18.0867	+	14.4236i	0.747153	+	0.595835i
$587$	26.4964	−	6.04763i	1.09362	−	0.249613i	0.362587	−	0.931950i	$-0.381894\pi$
$587$	26.4964	−	6.04763i	1.09362	−	0.249613i	0.731037	+	0.682338i	$0.239037\pi$
$588$	−45.8061	+	48.2589i	−1.88901	+	1.99016i
$589$	7.62590	+	15.8353i	0.314220	+	0.652484i
$590$	10.0818	+	16.0451i	0.415060	+	0.660565i
$591$	24.3834	+	2.10537i	1.00300	+	0.0866032i
$592$	0.391298	+	0.391298i	0.0160822	+	0.0160822i
$593$	−13.5958	−	6.54740i	−0.558313	−	0.268869i	0.133375	−	0.991066i	$-0.457418\pi$
$593$	−13.5958	−	6.54740i	−0.558313	−	0.268869i	−0.691688	+	0.722196i	$0.743133\pi$
$594$	−4.40951	−	10.0135i	−0.180924	−	0.410858i
$595$	52.5886	−	5.92532i	2.15592	−	0.242914i
$596$	−23.8444	+	49.5133i	−0.976703	+	2.02814i
$597$	1.72653	+	4.55006i	0.0706622	+	0.186221i
$598$	2.83060	+	8.08938i	0.115752	+	0.330799i
$599$	−8.47719	+	5.32657i	−0.346369	+	0.217638i	−0.693969	−	0.720005i	$-0.744139\pi$
$599$	−8.47719	+	5.32657i	−0.346369	+	0.217638i	0.347600	+	0.937643i	$0.386997\pi$
$600$	5.55759	−	0.144915i	0.226888	−	0.00591612i
$601$	−9.04221	+	25.8412i	−0.368840	+	1.05408i	0.598615	+	0.801037i	$0.295718\pi$
$601$	−9.04221	+	25.8412i	−0.368840	+	1.05408i	−0.967454	+	0.253046i	$0.918568\pi$
$602$	12.7992	+	56.0771i	0.521658	+	2.28553i
$603$	1.63517	−	0.0853326i	0.0665894	−	0.00347501i
$604$	−9.01303	−	11.3020i	−0.366735	−	0.459871i
$605$	−19.4022	−	4.42842i	−0.788811	−	0.180041i
$606$	−7.94131	−	11.9361i	−0.322594	−	0.484872i
$607$	−2.92661	+	25.9744i	−0.118788	+	1.05427i	0.782980	+	0.622047i	$0.213699\pi$
$607$	−2.92661	+	25.9744i	−0.118788	+	1.05427i	−0.901767	+	0.432222i	$0.857730\pi$
$608$	9.58679			0.388796
$609$	−40.4443	−	3.52483i	−1.63889	−	0.142833i
$610$	−18.6874			−0.756629
$611$	−0.431021	+	3.82542i	−0.0174372	+	0.154760i
$612$	−59.0258	+	9.78847i	−2.38598	+	0.395675i
$613$	−39.7512	−	9.07296i	−1.60554	−	0.366453i	−0.676501	−	0.736442i	$-0.736504\pi$
$613$	−39.7512	−	9.07296i	−1.60554	−	0.366453i	−0.929036	+	0.369989i	$0.879362\pi$
$614$	−40.1630	−	50.3628i	−1.62085	−	2.03248i
$615$	−10.4408	+	5.36769i	−0.421015	+	0.216446i
$616$	2.48018	+	10.8664i	0.0999292	+	0.437818i
$617$	5.38521	−	15.3901i	0.216801	−	0.619580i	−0.783197	−	0.621774i	$-0.786412\pi$
$617$	5.38521	−	15.3901i	0.216801	−	0.619580i	0.999998	+	0.00219326i	$0.000698137\pi$
$618$	1.00979	+	38.7264i	0.0406199	+	1.55780i
$619$	11.7667	−	7.39350i	0.472943	−	0.297170i	−0.274391	−	0.961618i	$-0.588476\pi$
$619$	11.7667	−	7.39350i	0.472943	−	0.297170i	0.747334	+	0.664448i	$0.231333\pi$
$620$	21.9848	+	62.8289i	0.882930	+	2.52327i
$621$	7.45725	−	14.2269i	0.299249	−	0.570908i
$622$	29.7030	−	61.6790i	1.19098	−	2.47310i
$623$	13.2925	−	1.49770i	0.532551	−	0.0600041i
$624$	−0.0570152	+	0.177666i	−0.00228244	+	0.00711234i
$625$	16.1151	+	7.76062i	0.644603	+	0.310425i
$626$	−7.51976	−	7.51976i	−0.300550	−	0.300550i
$627$	0.228728	−	2.64902i	0.00913451	−	0.105792i
$628$	24.1488	+	38.4327i	0.963644	+	1.53363i
$629$	−16.7774	−	34.8387i	−0.668959	−	1.38911i
$630$	54.1095	−	22.1622i	2.15577	−	0.882961i
$631$	−26.7244	+	6.09968i	−1.06388	+	0.242824i	−0.718421	−	0.695608i	$-0.755135\pi$
$631$	−26.7244	+	6.09968i	−1.06388	+	0.242824i	−0.345462	+	0.938433i	$0.612278\pi$
$632$	20.2547	+	16.1526i	0.805689	+	0.642515i
$633$	−24.8327	+	6.35323i	−0.987012	+	0.252518i
$634$	−11.8798	+	52.0490i	−0.471809	+	2.06713i
$635$	25.1222	+	15.7853i	0.996945	+	0.626422i
$636$	−6.22149	+	10.4994i	−0.246698	+	0.416328i
$637$		−	14.4993i		−	0.574482i
$638$	−7.07708	+	8.85979i	−0.280184	+	0.350762i
$639$	−15.2499	+	13.5199i	−0.603277	+	0.534838i
$640$	35.2894	+	3.97617i	1.39494	+	0.157172i
$641$	−3.31074	+	5.26902i	−0.130767	+	0.208114i	−0.905689	−	0.423942i	$-0.860646\pi$
$641$	−3.31074	+	5.26902i	−0.130767	+	0.208114i	0.774923	+	0.632056i	$0.217789\pi$
$642$	−5.81318	+	7.69260i	−0.229428	+	0.303603i
$643$	−24.5458	+	19.5746i	−0.967990	+	0.771947i	−0.973652	−	0.228037i	$-0.926769\pi$
$643$	−24.5458	+	19.5746i	−0.967990	+	0.771947i	0.00566202	+	0.999984i	$0.498198\pi$
$644$	−26.9803	+	33.8322i	−1.06317	+	1.33318i
$645$	3.87177	−	19.2652i	0.152451	−	0.758566i
$646$	−22.2584	−	7.78855i	−0.875745	−	0.306436i
$647$	11.9368	−	5.74846i	0.469284	−	0.225995i	−0.184269	−	0.982876i	$-0.558992\pi$
$647$	11.9368	−	5.74846i	0.469284	−	0.225995i	0.653553	+	0.756881i	$0.273278\pi$
$648$	−22.6073	+	10.6673i	−0.888099	+	0.419050i
$649$	−3.68252	+	1.28857i	−0.144552	+	0.0505808i
$650$	−2.26547	+	2.26547i	−0.0888589	+	0.0888589i
$651$	−51.2213	−	60.9025i	−2.00752	−	2.38696i
$652$	−2.32567	−	20.6409i	−0.0910803	−	0.808360i
$653$	−2.23808	−	19.8635i	−0.0875829	−	0.777320i	−0.958345	−	0.285614i	$-0.907802\pi$
$653$	−2.23808	−	19.8635i	−0.0875829	−	0.777320i	0.870762	−	0.491705i	$-0.163626\pi$
$654$	−13.6075	−	16.1794i	−0.532096	−	0.632666i
$655$	6.94141	−	6.94141i	0.271223	−	0.271223i
$656$	0.289570	−	0.101325i	0.0113058	−	0.00395608i
$657$	7.18419	−	24.5706i	0.280282	−	0.958589i
$658$	−28.4029	+	13.6781i	−1.10726	+	0.533228i
$659$	42.3962	+	14.8351i	1.65152	+	0.577893i	0.985743	−	0.168257i	$-0.0538137\pi$
$659$	42.3962	+	14.8351i	1.65152	+	0.577893i	0.665779	+	0.746149i	$0.268099\pi$
$660$	1.98409	−	9.87244i	0.0772305	−	0.384284i
$661$	2.32376	−	2.91390i	0.0903837	−	0.113338i	−0.734583	−	0.678519i	$-0.762622\pi$
$661$	2.32376	−	2.91390i	0.0903837	−	0.113338i	0.824967	+	0.565181i	$0.191194\pi$
$662$	29.1219	−	23.2240i	1.13186	−	0.902625i
$663$	7.86074	−	10.4021i	0.305286	−	0.403986i
$664$	6.34078	−	10.0913i	0.246070	−	0.391618i
$665$	14.1201	+	1.59095i	0.547554	+	0.0616945i
$666$	−28.3424	−	31.9692i	−1.09825	−	1.23878i
$667$	−16.6472	−	0.0133585i	−0.644581	−	0.000517242i
$668$			0.0193245i			0.000747688i
$669$	−7.48696	+	12.6350i	−0.289462	+	0.488496i
$670$	2.06949	+	1.30034i	0.0799512	+	0.0502367i
$671$	0.856143	−	3.75101i	0.0330510	−	0.144806i
$672$	−42.0517	+	10.7586i	−1.62218	+	0.415021i
$673$	4.00224	+	3.19168i	0.154275	+	0.123030i	0.697585	−	0.716502i	$-0.254258\pi$
$673$	4.00224	+	3.19168i	0.154275	+	0.123030i	−0.543310	+	0.839532i	$0.682829\pi$
$674$	13.8331	−	3.15732i	0.532832	−	0.121616i
$675$	6.00134	+	0.204077i	0.230992	+	0.00785494i
$676$	−16.0844	−	33.3995i	−0.618629	−	1.28460i
$677$	17.3756	+	27.6531i	0.667799	+	1.06280i	0.993110	+	0.117188i	$0.0373881\pi$
$677$	17.3756	+	27.6531i	0.667799	+	1.06280i	−0.325311	+	0.945607i	$0.605469\pi$
$678$	3.02869	−	35.0769i	0.116316	−	1.34712i
$679$	15.3097	+	15.3097i	0.587533	+	0.587533i
$680$	−30.4268	−	14.6528i	−1.16681	−	0.561908i
$681$	12.2001	−	38.0170i	0.467510	−	1.45682i
$682$	−22.0874	+	2.48865i	−0.845769	+	0.0952953i
$683$	13.3272	−	27.6741i	0.509950	−	1.05892i	−0.474008	−	0.880520i	$-0.657193\pi$
$683$	13.3272	−	27.6741i	0.509950	−	1.05892i	0.983958	−	0.178401i	$-0.0570924\pi$
$684$	−16.0360	−	0.964302i	−0.613150	−	0.0368710i
$685$	−4.88587	−	13.9630i	−0.186680	−	0.533500i
$686$	41.6173	−	26.1499i	1.58896	−	0.998407i
$687$	0.563601	+	21.6145i	0.0215027	+	0.824646i
$688$	−0.169600	+	0.484690i	−0.00646595	+	0.0184786i
$689$	−0.591791	−	2.59281i	−0.0225454	−	0.0987780i
$690$	21.3238	−	10.9627i	0.811782	−	0.417341i
$691$	21.6766	+	27.1816i	0.824617	+	1.03404i	0.998783	+	0.0493209i	$0.0157057\pi$
$691$	21.6766	+	27.1816i	0.824617	+	1.03404i	−0.174166	+	0.984716i	$0.555723\pi$
$692$	−63.3263	−	14.4538i	−2.40730	−	0.549451i
$693$	1.96951	+	11.8764i	0.0748156	+	0.451148i
$694$	−5.56403	+	49.3822i	−0.211208	+	1.87452i
$695$	−37.6725			−1.42900
$696$	20.6565	+	15.6358i	0.782981	+	0.592674i
$697$	−21.4371			−0.811987
$698$	7.00405	−	62.1627i	0.265107	−	2.35289i
$699$	16.7622	+	25.1943i	0.634006	+	0.952937i
$700$	−15.7712	−	3.59968i	−0.596096	−	0.136055i
$701$	19.0197	+	23.8500i	0.718366	+	0.900802i	0.998244	−	0.0592332i	$-0.0188656\pi$
$701$	19.0197	+	23.8500i	0.718366	+	0.900802i	−0.279878	+	0.960035i	$0.590294\pi$
$702$	5.21730	−	13.4278i	0.196914	−	0.506801i
$703$	−2.31030	−	10.1221i	−0.0871346	−	0.381762i
$704$	−3.95019	+	11.2890i	−0.148879	+	0.425471i
$705$	10.7662	−	0.280730i	0.405479	−	0.0105729i
$706$	5.68695	−	3.57335i	0.214031	−	0.134485i
$707$	5.20991	+	14.8891i	0.195939	+	0.559961i
$708$	8.36285	+	22.0393i	0.314295	+	0.828286i
$709$	9.99034	−	20.7451i	0.375195	−	0.779100i	−0.624804	−	0.780782i	$-0.714821\pi$
$709$	9.99034	−	20.7451i	0.375195	−	0.779100i	0.999999	+	0.00168159i	$0.000535266\pi$
$710$	−30.2296	+	3.40606i	−1.13450	+	0.127827i
$711$	20.7905	+	18.7282i	0.779704	+	0.702361i
$712$	−7.69077	−	3.70368i	−0.288224	−	0.138801i
$713$	−23.0739	−	23.0739i	−0.864124	−	0.864124i
$714$	106.375	+	9.18488i	3.98099	+	0.343736i
$715$	1.16747	+	1.85802i	0.0436610	+	0.0694860i
$716$	16.2307	+	33.7035i	0.606571	+	1.25956i
$717$	−8.94294	+	9.42180i	−0.333980	+	0.351864i
$718$	75.1581	−	17.1544i	2.80488	−	0.640195i
$719$	−23.5343	−	18.7679i	−0.877679	−	0.699926i	0.0771694	−	0.997018i	$-0.475412\pi$
$719$	−23.5343	−	18.7679i	−0.877679	−	0.699926i	−0.954849	+	0.297092i	$0.903983\pi$
$720$	0.514288	+	0.0894787i	0.0191664	+	0.00333467i
$721$	9.48487	−	41.5559i	0.353235	−	1.54762i
$722$	31.3814	+	19.7182i	1.16789	+	0.733837i
$723$	−1.71810	−	1.01807i	−0.0638968	−	0.0378626i
$724$			19.4138i			0.721509i
$725$	−2.69566	−	5.60911i	−0.100114	−	0.208317i
$726$	−36.6169	−	16.4722i	−1.35898	−	0.611339i
$727$	1.74604	+	0.196731i	0.0647569	+	0.00729635i	0.144283	−	0.989536i	$-0.453912\pi$
$727$	1.74604	+	0.196731i	0.0647569	+	0.00729635i	−0.0795266	+	0.996833i	$0.525341\pi$
$728$	−7.80756	+	12.4257i	−0.289368	+	0.460526i
$729$	−25.0658	+	10.0353i	−0.928362	+	0.371677i
$730$	29.8750	−	23.8245i	1.10572	−	0.881784i
$731$	22.3720	−	28.0536i	0.827458	−	1.03760i
$732$	−22.7907	−	4.58030i	−0.842368	−	0.169293i
$733$	−33.5056	−	11.7241i	−1.23756	−	0.433040i	−0.369373	−	0.929281i	$-0.620428\pi$
$733$	−33.5056	−	11.7241i	−1.23756	−	0.433040i	−0.868185	+	0.496241i	$0.834713\pi$
$734$	8.81984	−	4.24741i	0.325546	−	0.156775i
$735$	−40.1767	+	5.59086i	−1.48194	+	0.206222i
$736$	−16.8000	+	5.87859i	−0.619257	+	0.216688i
$737$	−0.355822	+	0.355822i	−0.0131069	+	0.0131069i
$738$	−22.7856	+	6.46679i	−0.838751	+	0.238046i
$739$	2.01850	+	17.9146i	0.0742516	+	0.659001i	0.974619	+	0.223870i	$0.0718692\pi$
$739$	2.01850	+	17.9146i	0.0742516	+	0.659001i	−0.900367	+	0.435131i	$0.856702\pi$
$740$	−4.40252	−	39.0734i	−0.161840	−	1.43637i
$741$	2.67920	−	2.25330i	0.0984227	−	0.0827771i
$742$	15.3999	−	15.3999i	0.565347	−	0.565347i
$743$	−46.8311	+	16.3869i	−1.71807	+	0.601178i	−0.995893	−	0.0905344i	$-0.971142\pi$
$743$	−46.8311	+	16.3869i	−1.71807	+	0.601178i	−0.722173	+	0.691712i	$0.756857\pi$
$744$	6.99924	+	50.2975i	0.256604	+	1.84399i
$745$	−30.1856	+	14.5366i	−1.10592	+	0.532581i
$746$	−39.6835	−	13.8858i	−1.45291	−	0.508397i
$747$	7.49059	−	10.4689i	0.274066	−	0.383036i
$748$	11.4645	−	14.3761i	0.419185	−	0.525641i
$749$	8.29447	−	6.61462i	0.303073	−	0.241693i
$750$	38.0911	+	28.7849i	1.39089	+	1.05107i
$751$	−5.16453	+	8.21930i	−0.188456	+	0.299926i	−0.927567	−	0.373658i	$-0.878103\pi$
$751$	−5.16453	+	8.21930i	−0.188456	+	0.299926i	0.739110	+	0.673584i	$0.235246\pi$
$752$	−0.279670	−	0.0315113i	−0.0101985	−	0.00114910i
$753$	2.55017	−	5.66893i	0.0929334	−	0.206587i
$754$	−14.8373	+	1.65970i	−0.540341	+	0.0604428i
$755$		−	8.81292i		−	0.320735i
$756$	71.4227	−	13.7662i	2.59762	−	0.500671i
$757$	25.8506	+	16.2430i	0.939556	+	0.590362i	0.912414	−	0.409269i	$-0.134216\pi$
$757$	25.8506	+	16.2430i	0.939556	+	0.590362i	0.0271425	+	0.999632i	$0.491359\pi$
$758$	−10.7962	+	47.3014i	−0.392137	+	1.71806i
$759$	1.22355	+	4.78244i	0.0444119	+	0.173592i
$760$	−7.08934	−	5.65356i	−0.257157	−	0.205076i
$761$	−44.6863	+	10.1994i	−1.61988	+	0.369726i	−0.933798	−	0.357801i	$-0.883527\pi$
$761$	−44.6863	+	10.1994i	−1.61988	+	0.369726i	−0.686079	+	0.727527i	$0.740669\pi$
$762$	43.4165	+	41.2099i	1.57281	+	1.49288i
$763$	10.0926	+	20.9575i	0.365377	+	0.758712i
$764$	22.9014	+	36.4474i	0.828544	+	1.31862i
$765$	−31.8548	−	17.7706i	−1.15171	−	0.642499i
$766$	2.87781	+	2.87781i	0.103980	+	0.103980i
$767$	−4.62810	−	2.22878i	−0.167111	−	0.0804764i
$768$	25.4329	+	8.16174i	0.917732	+	0.294511i
$769$	11.9833	−	1.35019i	0.432127	−	0.0486890i	0.106778	−	0.994283i	$-0.465947\pi$
$769$	11.9833	−	1.35019i	0.432127	−	0.0486890i	0.325349	+	0.945594i	$0.394518\pi$
$770$	−7.79680	+	16.1902i	−0.280977	+	0.583455i
$771$	47.1465	−	17.8899i	1.69794	−	0.644288i
$772$	−4.91161	−	14.0366i	−0.176773	−	0.505187i
$773$	−19.6078	+	12.3204i	−0.705242	+	0.443133i	−0.836322	−	0.548239i	$-0.815298\pi$
$773$	−19.6078	+	12.3204i	−0.705242	+	0.443133i	0.131080	+	0.991372i	$0.458156\pi$
$774$	15.3166	−	36.5672i	0.550545	−	1.31438i
$775$	4.02896	−	11.5141i	0.144724	−	0.413598i
$776$	−3.07446	−	13.4701i	−0.110367	−	0.483548i
$777$	21.4932	+	41.8071i	0.771065	+	1.49982i
$778$	−36.5971	−	45.8914i	−1.31207	−	1.64529i
$779$	−5.61156	−	1.28080i	−0.201055	−	0.0458895i
$780$	11.0385	−	7.34408i	0.395240	−	0.262960i
$781$	0.701261	−	6.22386i	0.0250931	−	0.222707i
$782$	43.7818			1.56564
$783$	21.2571	+	18.1971i	0.759669	+	0.650310i
$784$	1.06002			0.0378578
$785$	−3.09826	+	27.4978i	−0.110581	+	0.981438i
$786$	16.4894	−	10.9707i	0.588157	−	0.391311i
$787$	6.47817	+	1.47860i	0.230922	+	0.0527064i	0.336416	−	0.941714i	$-0.390785\pi$
$787$	6.47817	+	1.47860i	0.230922	+	0.0527064i	−0.105494	+	0.994420i	$0.533642\pi$
$788$	28.3342	+	35.5299i	1.00936	+	1.26570i
$789$	−15.0721	−	29.3170i	−0.536579	−	1.04371i
$790$	9.29426	+	40.7208i	0.330675	+	1.44878i
$791$	−12.7944	+	36.5644i	−0.454918	+	1.30008i
$792$	2.96799	−	7.08584i	0.105463	−	0.251784i
$793$	4.28927	−	2.69513i	0.152316	−	0.0957067i
$794$	15.8984	+	45.4350i	0.564212	+	1.61243i
$795$	−6.95633	+	2.63960i	−0.246716	+	0.0936168i
$796$	−3.92079	+	8.14161i	−0.138969	+	0.288572i
$797$	0.273912	−	0.0308625i	0.00970248	−	0.00109321i	−0.107112	−	0.994247i	$-0.534160\pi$
$797$	0.273912	−	0.0308625i	0.00970248	−	0.00109321i	0.116814	+	0.993154i	$0.462732\pi$
$798$	27.2970	+	8.75993i	0.966303	+	0.310098i
$799$	17.7184	+	8.53274i	0.626832	+	0.301867i
$800$	−4.70492	−	4.70492i	−0.166344	−	0.166344i
$801$	−8.05172	−	4.49176i	−0.284494	−	0.158709i
$802$	44.0775	+	70.1490i	1.55643	+	2.47705i
$803$	3.41347	+	7.08813i	0.120459	+	0.250135i
$804$	2.20518	+	2.09310i	0.0777708	+	0.0738181i
$805$	−25.7198	+	5.87038i	−0.906505	+	0.206904i
$806$	−22.8803	−	18.2465i	−0.805925	−	0.642704i
$807$	−6.04903	−	23.6437i	−0.212936	−	0.832297i
$808$	2.23993	−	9.81380i	0.0788006	−	0.345248i
$809$	36.3670	+	22.8509i	1.27860	+	0.803395i	0.988149	−	0.153496i	$-0.0490532\pi$
$809$	36.3670	+	22.8509i	1.27860	+	0.803395i	0.290447	+	0.956891i	$0.406196\pi$
$810$	−39.2195	−	9.27913i	−1.37803	−	0.326035i
$811$		−	50.3099i		−	1.76662i	−0.468790	−	0.883310i	$-0.655310\pi$
$811$		−	50.3099i		−	1.76662i	0.468790	−	0.883310i	$-0.344690\pi$
$812$	−46.9533	−	58.9746i	−1.64774	−	2.06960i
$813$	14.3757	−	31.9566i	0.504178	−	1.12077i
$814$	13.0474	+	1.47009i	0.457311	+	0.0515266i
$815$	6.73727	−	10.7223i	0.235996	−	0.375586i
$816$	0.760484	+	0.574686i	0.0266223	+	0.0201180i
$817$	7.53241	−	6.00690i	0.263526	−	0.210155i
$818$	−40.1663	+	50.3670i	−1.40438	+	1.76104i
$819$	−9.22337	+	12.8906i	−0.322290	+	0.450434i
$820$	−20.5756	−	7.19972i	−0.718532	−	0.251425i
$821$	5.26094	−	2.53354i	0.183608	−	0.0884210i	−0.339821	−	0.940490i	$-0.610367\pi$
$821$	5.26094	−	2.53354i	0.183608	−	0.0884210i	0.523430	+	0.852069i	$0.324652\pi$
$822$	−4.11361	−	29.5610i	−0.143479	−	1.03106i
$823$	−9.37832	+	3.28162i	−0.326908	+	0.114390i	−0.488743	−	0.872428i	$-0.662544\pi$
$823$	−9.37832	+	3.28162i	−0.326908	+	0.114390i	0.161835	+	0.986818i	$0.448259\pi$
$824$	−19.2336	+	19.2336i	−0.670034	+	0.670034i
$825$	−1.41232	+	1.18781i	−0.0491706	+	0.0413543i
$826$	−4.70986	−	41.8011i	−0.163877	−	1.45445i
$827$	1.83444	+	16.2811i	0.0637897	+	0.566150i	0.984435	+	0.175749i	$0.0562348\pi$
$827$	1.83444	+	16.2811i	0.0637897	+	0.566150i	−0.920645	+	0.390400i	$0.872337\pi$
$828$	28.6930	−	8.14334i	0.997149	−	0.283001i
$829$	−8.35437	+	8.35437i	−0.290159	+	0.290159i	−0.837143	−	0.546984i	$-0.815776\pi$
$829$	−8.35437	+	8.35437i	−0.290159	+	0.290159i	0.546984	+	0.837143i	$0.315776\pi$
$830$	18.1365	−	6.34624i	0.629528	−	0.220281i
$831$	20.0264	−	2.78681i	0.694708	−	0.0966734i
$832$	−14.1877	+	6.83245i	−0.491871	+	0.236873i
$833$	−69.9136	−	24.4638i	−2.42236	−	0.847621i
$834$	−74.5159	−	14.9756i	−2.58028	−	0.518564i
$835$	−0.00734542	+	0.00921086i	−0.000254199	+	0.000318755i
$836$	3.85999	−	3.07824i	0.133500	−	0.106463i
$837$	4.28531	+	54.6823i	0.148122	+	1.89010i
$838$	−19.0249	+	30.2780i	−0.657205	+	1.04594i
$839$	47.2967	+	5.32906i	1.63286	+	0.183979i	0.880259	−	0.474494i	$-0.157369\pi$
$839$	47.2967	+	5.32906i	1.63286	+	0.183979i	0.752604	+	0.658473i	$0.228797\pi$
$840$	37.4414	+	16.8430i	1.29185	+	0.581140i
$841$	6.49847	−	28.2625i	0.224085	−	0.974570i
$842$		−	70.8013i		−	2.43997i
$843$	−7.30756	−	4.33015i	−0.251686	−	0.149138i
$844$	−40.3002	−	25.3223i	−1.38719	−	0.871630i
$845$	5.02898	−	22.0334i	0.173002	−	0.757972i
$846$	21.4071	+	3.72452i	0.735990	+	0.128052i
$847$	34.5397	+	27.5445i	1.18680	+	0.946441i
$848$	0.189556	−	0.0432649i	0.00650938	−	0.00148572i
$849$	9.61279	−	10.1275i	0.329910	−	0.347576i
$850$	7.10138	+	14.7462i	0.243575	+	0.505789i
$851$	10.2554	+	16.3214i	0.351551	+	0.559491i
$852$	−37.7022	−	3.25536i	−1.29165	−	0.111527i
$853$	26.7792	+	26.7792i	0.916904	+	0.916904i	0.996803	−	0.0798992i	$-0.0254599\pi$
$853$	26.7792	+	26.7792i	0.916904	+	0.916904i	−0.0798992	+	0.996803i	$0.525460\pi$
$854$	37.3754	+	17.9990i	1.27896	+	0.615914i
$855$	−7.27686	−	6.55504i	−0.248864	−	0.224178i
$856$	−6.72746	+	0.758003i	−0.229940	+	0.0259080i
$857$	−21.2466	+	44.1191i	−0.725771	+	1.50708i	0.131000	+	0.991382i	$0.458181\pi$
$857$	−21.2466	+	44.1191i	−0.725771	+	1.50708i	−0.856771	+	0.515697i	$0.827533\pi$
$858$	1.57064	+	4.13924i	0.0536209	+	0.141311i
$859$	4.15623	+	11.8778i	0.141809	+	0.405266i	0.992780	−	0.119945i	$-0.0382720\pi$
$859$	4.15623	+	11.8778i	0.141809	+	0.405266i	−0.850972	+	0.525211i	$0.823986\pi$
$860$	30.8949	−	19.4125i	1.05351	−	0.661962i
$861$	26.0520	−	0.679309i	0.887851	−	0.0231508i
$862$	−9.50233	+	27.1561i	−0.323651	+	0.924940i
$863$	−11.1910	−	49.0310i	−0.380946	−	1.66903i	−0.694522	−	0.719471i	$-0.744384\pi$
$863$	−11.1910	−	49.0310i	−0.380946	−	1.66903i	0.313576	−	0.949563i	$-0.398473\pi$
$864$	27.8869	+	10.8353i	0.948732	+	0.368624i
$865$	−24.6899	−	30.9602i	−0.839482	−	1.05268i
$866$	0.992256	+	0.226476i	0.0337182	+	0.00769596i
$867$	−20.5846	−	30.9395i	−0.699089	−	1.05076i
$868$	16.5443	−	146.835i	0.561551	−	4.98391i
$869$	−8.59946			−0.291717
$870$	10.3201	+	40.4733i	0.349885	+	1.37217i
$871$	−0.662543			−0.0224494
$872$	1.66198	−	14.7505i	0.0562817	−	0.499514i
$873$	−2.44143	−	14.7222i	−0.0826299	−	0.498270i
$874$	11.4607	+	2.61584i	0.387665	+	0.0884820i
$875$	−32.7533	−	41.0714i	−1.10726	−	1.38847i
$876$	42.2743	−	21.7334i	1.42832	−	0.734305i
$877$	4.63487	+	20.3067i	0.156509	+	0.685709i	0.990907	+	0.134547i	$0.0429581\pi$
$877$	4.63487	+	20.3067i	0.156509	+	0.685709i	−0.834399	+	0.551162i	$0.814185\pi$
$878$	3.55047	−	10.1467i	0.119822	−	0.342433i
$879$	0.457309	+	17.5382i	0.0154247	+	0.591547i
$880$	−0.135837	+	0.0853520i	−0.00457906	+	0.00287722i
$881$	7.03466	+	20.1039i	0.237004	+	0.677317i	0.999539	+	0.0303706i	$0.00966874\pi$
$881$	7.03466	+	20.1039i	0.237004	+	0.677317i	−0.762535	+	0.646947i	$0.776046\pi$
$882$	−81.6916	−	4.91242i	−2.75070	−	0.165410i
$883$	−19.3867	+	40.2568i	−0.652413	+	1.35475i	0.267854	+	0.963460i	$0.413686\pi$
$883$	−19.3867	+	40.2568i	−0.652413	+	1.35475i	−0.920267	+	0.391291i	$0.872029\pi$
$884$	24.0577	−	2.71065i	0.809146	−	0.0911689i
$885$	−4.39124	+	13.6836i	−0.147610	+	0.459970i
$886$	−27.8329	−	13.4036i	−0.935063	−	0.450303i
$887$	7.23403	+	7.23403i	0.242895	+	0.242895i	0.818047	−	0.575152i	$-0.195057\pi$
$887$	7.23403	+	7.23403i	0.242895	+	0.242895i	−0.575152	+	0.818047i	$0.695057\pi$
$888$	2.58054	−	29.8867i	0.0865973	−	1.00293i
$889$	−35.0414	−	55.7681i	−1.17525	−	1.87040i
$890$	−5.97124	−	12.3994i	−0.200156	−	0.415629i
$891$	3.65935	−	7.44721i	0.122593	−	0.249491i
$892$	−26.5869	+	6.06829i	−0.890196	+	0.203182i
$893$	4.12833	+	3.29223i	0.138149	+	0.110170i
$894$	−65.4855	+	16.7539i	−2.19016	+	0.560334i
$895$	−5.07475	+	22.2339i	−0.169630	+	0.743198i
$896$	−66.7505	−	41.9421i	−2.22998	−	1.40119i
$897$	−3.31334	+	5.59159i	−0.110629	+	0.186698i
$898$			61.8704i			2.06464i
$899$	48.1564	−	30.2048i	1.60611	−	1.00739i
$900$	7.39674	+	8.34324i	0.246558	+	0.278108i
$901$	−13.5007	−	1.52116i	−0.449772	−	0.0506772i
$902$	3.87271	−	6.16338i	0.128947	−	0.205218i
$903$	−26.2992	+	34.8019i	−0.875184	+	1.15813i
$904$	19.3272	−	15.4129i	0.642813	−	0.512626i
$905$	−7.37937	+	9.25343i	−0.245298	+	0.307595i
$906$	3.50332	−	17.4319i	0.116390	−	0.579135i
$907$	−48.7098	−	17.0443i	−1.61738	−	0.565946i	−0.638366	−	0.769733i	$-0.720390\pi$
$907$	−48.7098	−	17.0443i	−1.61738	−	0.565946i	−0.979015	+	0.203786i	$0.934675\pi$
$908$	66.7954	−	32.1670i	2.21668	−	1.06750i
$909$	3.05126	−	10.4356i	0.101204	−	0.346126i
$910$	−22.3320	+	7.81430i	−0.740298	+	0.259041i
$911$	−20.6095	+	20.6095i	−0.682822	+	0.682822i	−0.960635	−	0.277813i	$-0.910390\pi$
$911$	−20.6095	+	20.6095i	−0.682822	+	0.682822i	0.277813	+	0.960635i	$0.410390\pi$
$912$	0.164735	+	0.195872i	0.00545493	+	0.00648596i
$913$	0.442939	+	3.93119i	0.0146591	+	0.130103i
$914$	−2.82512	−	25.0736i	−0.0934467	−	0.829362i
$915$	−9.12197	−	10.8461i	−0.301563	−	0.358561i
$916$	−28.3891	+	28.3891i	−0.938004	+	0.938004i
$917$	−20.5688	+	7.19733i	−0.679241	+	0.237677i
$918$	−55.9443	−	47.8131i	−1.84644	−	1.57807i
$919$	22.1518	−	10.6677i	0.730720	−	0.351896i	−0.0312473	−	0.999512i	$-0.509948\pi$
$919$	22.1518	−	10.6677i	0.730720	−	0.351896i	0.761967	+	0.647615i	$0.224234\pi$
$920$	15.8902	+	5.56022i	0.523884	+	0.183315i
$921$	9.62546	−	47.8945i	0.317170	−	1.57818i
$922$	0.140839	−	0.176607i	0.00463829	−	0.00581623i
$923$	6.44730	−	5.14155i	0.212216	−	0.169236i
$924$	−13.4771	+	17.8342i	−0.443362	+	0.586703i
$925$	−3.83380	+	6.10145i	−0.126054	+	0.200615i
$926$	54.0675	+	6.09194i	1.77677	+	0.200194i
$927$	−21.9838	+	19.4898i	−0.722043	+	0.640130i
$928$	−3.44687	−	30.8140i	−0.113149	−	1.01152i
$929$			57.3986i			1.88319i	0.336754	+	0.941593i	$0.390671\pi$
$929$			57.3986i			1.88319i	−0.336754	+	0.941593i	$0.609329\pi$
$930$	−41.7374	+	70.4359i	−1.36862	+	2.30968i
$931$	−16.8396	−	10.5810i	−0.551895	−	0.346778i
$932$	−12.5034	+	54.7809i	−0.409562	+	1.79441i
$933$	50.2975	−	12.8682i	1.64667	−	0.421285i
$934$	−42.5354	−	33.9209i	−1.39180	−	1.10992i
$935$	10.9289	−	2.49446i	0.357414	−	0.0815775i
$936$	9.36014	−	3.83372i	0.305946	−	0.125309i
$937$	−3.97769	−	8.25977i	−0.129946	−	0.269835i	0.825837	−	0.563909i	$-0.190703\pi$
$937$	−3.97769	−	8.25977i	−0.129946	−	0.269835i	−0.955783	+	0.294074i	$0.904989\pi$
$938$	−2.88660	−	4.59399i	−0.0942508	−	0.149999i
$939$	0.693786	−	8.03512i	0.0226408	−	0.262216i
$940$	14.1407	+	14.1407i	0.461217	+	0.461217i
$941$	47.6168	+	22.9310i	1.55226	+	0.747530i	0.996483	−	0.0838000i	$-0.0267057\pi$
$941$	47.6168	+	22.9310i	1.55226	+	0.747530i	0.555779	+	0.831330i	$0.312420\pi$
$942$	−17.0593	+	53.1587i	−0.555821	+	1.73200i
$943$	10.6192	−	1.19649i	0.345807	−	0.0389631i
$944$	0.162942	−	0.338353i	0.00530332	−	0.0110125i
$945$	39.2757	+	20.5869i	1.27764	+	0.669691i
$946$	4.02409	+	11.5002i	0.130835	+	0.373904i
$947$	11.8423	−	7.44101i	0.384823	−	0.241800i	−0.325702	−	0.945473i	$-0.605601\pi$
$947$	11.8423	−	7.44101i	0.384823	−	0.241800i	0.710525	+	0.703672i	$0.248458\pi$
$948$	1.35435	+	51.9402i	0.0439871	+	1.68694i
$949$	−3.42113	+	9.77701i	−0.111054	+	0.317375i
$950$	0.977881	+	4.28438i	0.0317267	+	0.139004i
$951$	−36.0081	+	18.5120i	−1.16764	+	0.600292i
$952$	46.7416	+	58.6122i	1.51491	+	1.89963i
$953$	−18.1576	−	4.14436i	−0.588183	−	0.134249i	−0.0819364	−	0.996638i	$-0.526110\pi$
$953$	−18.1576	−	4.14436i	−0.588183	−	0.134249i	−0.506247	+	0.862389i	$0.668968\pi$
$954$	−14.8088	+	2.45581i	−0.479454	+	0.0795097i
$955$	−2.93821	+	26.0774i	−0.0950784	+	0.843844i
$956$	−24.1208			−0.780121
$957$	−8.59678	+	0.217259i	−0.277894	+	0.00702298i
$958$	73.5768			2.37716
$959$	−3.67679	+	32.6325i	−0.118730	+	1.05376i
$960$	24.4031	+	36.6789i	0.787606	+	1.18381i
$961$	78.4100	+	17.8966i	2.52935	+	0.577308i
$962$	10.7785	+	13.5158i	0.347513	+	0.435767i
$963$	−7.30239	+	0.381080i	−0.235316	+	0.0122801i
$964$	−0.825165	−	3.61528i	−0.0265768	−	0.116440i
$965$	2.99435	−	8.55735i	0.0963914	−	0.275471i
$966$	−53.2072	+	1.38738i	−1.71191	+	0.0446383i
$967$	38.1798	−	23.9900i	1.22778	−	0.771465i	0.247463	−	0.968897i	$-0.420403\pi$
$967$	38.1798	−	23.9900i	1.22778	−	0.771465i	0.980316	+	0.197433i	$0.0632603\pi$
$968$	−9.31113	−	26.6097i	−0.299271	−	0.855267i
$969$	−6.34467	−	16.7206i	−0.203820	−	0.537143i
$970$	9.66500	−	20.0696i	0.310325	−	0.644396i
$971$	−49.5958	+	5.58810i	−1.59160	+	0.179331i	−0.862855	−	0.505451i	$-0.831326\pi$
$971$	−49.5958	+	5.58810i	−1.59160	+	0.179331i	−0.728748	+	0.684782i	$0.759898\pi$
$972$	−45.5570	−	20.9294i	−1.46124	−	0.671310i
$973$	75.3464	+	36.2849i	2.41550	+	1.16324i
$974$	34.3977	+	34.3977i	1.10217	+	1.10217i
$975$	−2.42073	−	0.209016i	−0.0775253	−	0.00669386i
$976$	0.197036	+	0.313582i	0.00630698	+	0.0100375i
$977$	−19.9205	−	41.3653i	−0.637313	−	1.32339i	−0.930132	−	0.367226i	$-0.880308\pi$
$977$	−19.9205	−	41.3653i	−0.637313	−	1.32339i	0.292819	−	0.956168i	$-0.405407\pi$
$978$	17.5886	−	18.5304i	0.562422	−	0.592537i
$979$	2.76243	−	0.630507i	0.0882877	−	0.0201511i
$980$	−58.8879	−	46.9615i	−1.88110	−	1.50013i
$981$	2.74819	−	15.7955i	0.0877431	−	0.504313i
$982$	11.5882	−	50.7712i	0.369794	−	1.62017i
$983$	12.8754	+	8.09013i	0.410661	+	0.258035i	0.721482	−	0.692433i	$-0.243461\pi$
$983$	12.8754	+	8.09013i	0.410661	+	0.258035i	−0.310821	+	0.950468i	$0.600604\pi$
$984$	−14.3073	−	8.47789i	−0.456099	−	0.270265i
$985$			27.7051i			0.882758i
$986$	−17.0312	+	74.3436i	−0.542385	+	2.36758i
$987$	−21.8032	−	9.80819i	−0.694004	−	0.312198i
$988$	6.45950	+	0.727811i	0.205504	+	0.0231548i
$989$	−9.51650	+	15.1454i	−0.302607	+	0.481596i
$990$	10.8640	−	5.94825i	0.345280	−	0.189048i
$991$	−43.3214	+	34.5476i	−1.37615	+	1.09744i	−0.392025	+	0.919955i	$0.628225\pi$
$991$	−43.3214	+	34.5476i	−1.37615	+	1.09744i	−0.984123	+	0.177487i	$0.943203\pi$
$992$	37.8943	−	47.5179i	1.20314	−	1.50869i
$993$	27.6946	+	5.56585i	0.878862	+	0.176627i
$994$	63.7408	+	22.3039i	2.02174	+	0.707436i
$995$	−4.96351	+	2.39030i	−0.157354	+	0.0757776i
$996$	23.6744	−	3.29445i	0.750151	−	0.104389i
$997$	29.9398	−	10.4764i	0.948204	−	0.331791i	0.188510	−	0.982071i	$-0.439634\pi$
$997$	29.9398	−	10.4764i	0.948204	−	0.331791i	0.759694	+	0.650280i	$0.225349\pi$
$998$	30.7909	−	30.7909i	0.974670	−	0.974670i
$999$	4.71988	−	32.0552i	0.149330	−	1.01418i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	87.2.k.a.2.2	✓	96
3.2	odd	2	inner	87.2.k.a.2.7	yes	96
29.15	odd	28	inner	87.2.k.a.44.7	yes	96
87.44	even	28	inner	87.2.k.a.44.2	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
87.2.k.a.2.2	✓	96	1.1	even	1	trivial
87.2.k.a.2.7	yes	96	3.2	odd	2	inner
87.2.k.a.44.2	yes	96	87.44	even	28	inner
87.2.k.a.44.7	yes	96	29.15	odd	28	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 87 = 3 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	87.k (of order \(28\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.255714 + 2.26953i) q^{2} +(-1.44205 + 0.959421i) q^{3} +(-3.13550 - 0.715657i) q^{4} +(-1.22248 - 1.53294i) q^{5} +(-1.80868 - 3.51811i) q^{6} +(0.968527 + 4.24339i) q^{7} +(0.917355 - 2.62165i) q^{8} +(1.15902 - 2.76707i) q^{9} +(3.79166 - 2.38246i) q^{10} +(0.304506 + 0.870228i) q^{11} +(5.20817 - 1.97625i) q^{12} +(-0.526689 + 1.09368i) q^{13} +(-9.87816 + 1.11300i) q^{14} +(3.23362 + 1.03771i) q^{15} +(-0.0799573 - 0.0385054i) q^{16} +(4.38493 + 4.38493i) q^{17} +(5.98355 + 3.33801i) q^{18} +(0.885852 + 1.40983i) q^{19} +(2.73603 + 5.68142i) q^{20} +(-5.46787 - 5.18996i) q^{21} +(-2.05287 + 0.468555i) q^{22} +(-2.41688 - 1.92740i) q^{23} +(1.19239 + 4.66068i) q^{24} +(0.257151 - 1.12665i) q^{25} +(-2.34745 - 1.47500i) q^{26} +(0.983418 + 5.10224i) q^{27} -13.9983i q^{28} +(4.21298 - 3.35422i) q^{29} +(-3.18198 + 7.07342i) q^{30} +(10.4895 + 1.18188i) q^{31} +(3.06329 - 4.87519i) q^{32} +(-1.27403 - 0.962764i) q^{33} +(-11.0730 + 8.83042i) q^{34} +(5.32087 - 6.67217i) q^{35} +(-5.61438 + 7.84668i) q^{36} +(-5.88562 - 2.05947i) q^{37} +(-3.42616 + 1.64995i) q^{38} +(-0.289789 - 2.08246i) q^{39} +(-5.14029 + 1.79866i) q^{40} +(-2.44440 + 2.44440i) q^{41} +(13.1770 - 11.0823i) q^{42} +(-0.647855 - 5.74987i) q^{43} +(-0.331993 - 2.94652i) q^{44} +(-5.65864 + 1.60598i) q^{45} +(4.99231 - 4.99231i) q^{46} +(2.99334 - 1.04741i) q^{47} +(0.152245 - 0.0211860i) q^{48} +(-10.7616 + 5.18250i) q^{49} +(2.49121 + 0.871712i) q^{50} +(-10.5303 - 2.11630i) q^{51} +(2.43413 - 3.05231i) q^{52} +(-1.71289 + 1.36599i) q^{53} +(-11.8311 + 0.927176i) q^{54} +(0.961757 - 1.53063i) q^{55} +(12.0132 + 1.35356i) q^{56} +(-2.63006 - 1.18313i) q^{57} +(6.53516 + 10.4192i) q^{58} +4.23167i q^{59} +(-9.39637 - 5.56789i) q^{60} +(-3.53348 - 2.22023i) q^{61} +(-5.36462 + 23.5040i) q^{62} +(12.8643 + 2.23820i) q^{63} +(10.1423 + 8.08820i) q^{64} +(2.32042 - 0.529620i) q^{65} +(2.51080 - 2.64525i) q^{66} +(0.236814 + 0.491748i) q^{67} +(-10.6108 - 16.8871i) q^{68} +(5.33445 + 0.460599i) q^{69} +(13.7820 + 13.7820i) q^{70} +(-6.12060 - 2.94753i) q^{71} +(-6.19105 - 5.57693i) q^{72} +(8.47945 - 0.955405i) q^{73} +(6.17905 - 12.8309i) q^{74} +(0.710109 + 1.87141i) q^{75} +(-1.76864 - 5.05447i) q^{76} +(-3.39780 + 2.13498i) q^{77} +(4.80030 - 0.125168i) q^{78} +(-3.08062 + 8.80389i) q^{79} +(0.0387197 + 0.169642i) q^{80} +(-6.31334 - 6.41418i) q^{81} +(-4.92257 - 6.17270i) q^{82} +(4.18332 + 0.954815i) q^{83} +(13.4303 + 20.1863i) q^{84} +(1.36135 - 12.0823i) q^{85} +13.2151 q^{86} +(-2.85723 + 8.87898i) q^{87} +2.56077 q^{88} +(0.344100 - 3.05397i) q^{89} +(-2.19781 - 13.2531i) q^{90} +(-5.15103 - 1.17569i) q^{91} +(6.19877 + 7.77301i) q^{92} +(-16.2603 + 8.35951i) q^{93} +(1.61169 + 7.06129i) q^{94} +(1.07824 - 3.08145i) q^{95} +(0.259949 + 9.96926i) q^{96} +(4.21195 - 2.64655i) q^{97} +(-9.00992 - 25.7489i) q^{98} +(2.76091 + 0.166024i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 12 q^{3} - 28 q^{4} - 14 q^{6} - 20 q^{7} - 14 q^{9} - 4 q^{10} - 8 q^{12} - 28 q^{13} - 16 q^{15} - 48 q^{16} - 28 q^{18} - 20 q^{19} + 26 q^{21} - 28 q^{22} + 58 q^{24} - 20 q^{25} + 36 q^{27}+ \cdots + 82 q^{99}+O(q^{100}) \) 96 * q - 12 * q^3 - 28 * q^4 - 14 * q^6 - 20 * q^7 - 14 * q^9 - 4 * q^10 - 8 * q^12 - 28 * q^13 - 16 * q^15 - 48 * q^16 - 28 * q^18 - 20 * q^19 + 26 * q^21 - 28 * q^22 + 58 * q^24 - 20 * q^25 + 36 * q^27 + 96 * q^30 - 32 * q^31 + 28 * q^33 - 28 * q^34 + 22 * q^36 - 4 * q^37 - 40 * q^39 - 48 * q^40 - 14 * q^42 - 32 * q^43 + 42 * q^45 + 120 * q^46 - 20 * q^48 + 4 * q^49 - 14 * q^51 + 72 * q^52 - 30 * q^54 + 148 * q^55 + 112 * q^58 + 20 * q^60 + 12 * q^61 - 14 * q^63 + 224 * q^64 - 32 * q^66 + 28 * q^67 + 10 * q^69 + 52 * q^70 - 44 * q^72 + 16 * q^73 - 144 * q^75 - 100 * q^76 - 102 * q^78 - 60 * q^79 - 146 * q^81 - 108 * q^82 - 64 * q^84 - 104 * q^85 - 70 * q^87 - 312 * q^88 - 96 * q^90 - 112 * q^91 - 70 * q^93 + 56 * q^94 - 168 * q^96 + 32 * q^97 + 82 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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