LMFDB - Embedded newform 460.2.o.b.19.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [460,2,Mod(19,460)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(460, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 11, 15]))

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

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

chi := DirichletCharacter("460.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	460.o (of order $22$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.67311849298$
Analytic rank:	$0$
Dimension:	$640$
Relative dimension:	$64$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			19.9
Character	$\chi$	$=$	460.19
Dual form			460.2.o.b.339.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.27975 - 0.601871i) q^{2} +(-2.51556 + 0.738636i) q^{3} +(1.27550 + 1.54049i) q^{4} +(2.08492 + 0.808149i) q^{5} +(3.66385 + 0.568779i) q^{6} +(-0.0121874 + 0.00175228i) q^{7} +(-0.705145 - 2.73912i) q^{8} +(3.25872 - 2.09425i) q^{9} +O(q^{10})$	\(q+(-1.27975 - 0.601871i) q^{2} +(-2.51556 + 0.738636i) q^{3} +(1.27550 + 1.54049i) q^{4} +(2.08492 + 0.808149i) q^{5} +(3.66385 + 0.568779i) q^{6} +(-0.0121874 + 0.00175228i) q^{7} +(-0.705145 - 2.73912i) q^{8} +(3.25872 - 2.09425i) q^{9} +(-2.18177 - 2.28908i) q^{10} +(0.836058 - 1.83071i) q^{11} +(-4.34647 - 2.93306i) q^{12} +(1.12708 + 0.162050i) q^{13} +(0.0166514 + 0.00509277i) q^{14} +(-5.84168 - 0.492954i) q^{15} +(-0.746191 + 3.92978i) q^{16} +(-1.57639 - 1.81925i) q^{17} +(-5.43081 + 0.718782i) q^{18} +(-1.81730 + 2.09728i) q^{19} +(1.41438 + 4.24259i) q^{20} +(0.0293639 - 0.0134100i) q^{21} +(-2.17179 + 1.83965i) q^{22} +(4.45408 + 1.77797i) q^{23} +(3.79705 + 6.36958i) q^{24} +(3.69379 + 3.36985i) q^{25} +(-1.34485 - 0.885744i) q^{26} +(-1.49996 + 1.73105i) q^{27} +(-0.0182444 - 0.0165395i) q^{28} +(2.12136 + 2.44818i) q^{29} +(7.17918 + 4.14680i) q^{30} +(0.635355 - 2.16382i) q^{31} +(3.32016 - 4.58002i) q^{32} +(-0.750927 + 5.22282i) q^{33} +(0.922424 + 3.27696i) q^{34} +(-0.0268259 - 0.00619587i) q^{35} +(7.38267 + 2.34879i) q^{36} +(5.87561 - 3.77602i) q^{37} +(3.58798 - 1.59020i) q^{38} +(-2.95495 + 0.424858i) q^{39} +(0.743446 - 6.28071i) q^{40} +(1.30295 + 0.837356i) q^{41} +(-0.0456495 - 0.000511836i) q^{42} +(3.34730 + 11.3998i) q^{43} +(3.88658 - 1.04714i) q^{44} +(8.48664 - 1.73282i) q^{45} +(-4.62999 - 4.95613i) q^{46} +4.57330 q^{47} +(-1.02559 - 10.4368i) q^{48} +(-6.71631 + 1.97209i) q^{49} +(-2.69889 - 6.53575i) q^{50} +(5.30927 + 3.41206i) q^{51} +(1.18796 + 1.94295i) q^{52} +(1.60246 + 11.1454i) q^{53} +(2.96144 - 1.31252i) q^{54} +(3.22260 - 3.14123i) q^{55} +(0.0133936 + 0.0321471i) q^{56} +(3.02241 - 6.61816i) q^{57} +(-1.24132 - 4.40984i) q^{58} +(12.9845 + 1.86689i) q^{59} +(-6.69169 - 9.62779i) q^{60} +(-2.83682 + 9.66133i) q^{61} +(-2.11543 + 2.38674i) q^{62} +(-0.0360456 + 0.0312337i) q^{63} +(-7.00554 + 3.86295i) q^{64} +(2.21892 + 1.24872i) q^{65} +(4.10446 - 6.23192i) q^{66} +(-7.40739 + 3.38284i) q^{67} +(0.791841 - 4.74886i) q^{68} +(-12.5178 - 1.18264i) q^{69} +(0.0306012 + 0.0240749i) q^{70} +(5.31808 - 2.42869i) q^{71} +(-8.03428 - 7.44927i) q^{72} +(-2.59413 - 2.24783i) q^{73} +(-9.79197 + 1.29599i) q^{74} +(-11.7811 - 5.74872i) q^{75} +(-5.54880 - 0.124445i) q^{76} +(-0.00698145 + 0.0237766i) q^{77} +(4.03730 + 1.23479i) q^{78} +(-0.0753216 + 0.523873i) q^{79} +(-4.73160 + 7.59025i) q^{80} +(-2.33288 + 5.10830i) q^{81} +(-1.16347 - 1.85581i) q^{82} +(-0.607844 - 0.945824i) q^{83} +(0.0581117 + 0.0281301i) q^{84} +(-1.81642 - 5.06695i) q^{85} +(2.57755 - 16.6036i) q^{86} +(-7.14475 - 4.59165i) q^{87} +(-5.60408 - 0.999145i) q^{88} +(-2.72204 - 9.27042i) q^{89} +(-11.9037 - 2.89030i) q^{90} -0.0140202 q^{91} +(2.94226 + 9.12925i) q^{92} +5.91252i q^{93} +(-5.85267 - 2.75254i) q^{94} +(-5.48384 + 2.90401i) q^{95} +(-4.96911 + 13.9737i) q^{96} +(-11.6232 - 7.46978i) q^{97} +(9.78211 + 1.51858i) q^{98} +(-1.10949 - 7.71669i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 640 q - 6 q^{4} - 22 q^{5} + 2 q^{6} - 100 q^{9}+O(q^{10}) $ 640 * q - 6 * q^4 - 22 * q^5 + 2 * q^6 - 100 * q^9	$ 640 q - 6 q^{4} - 22 q^{5} + 2 q^{6} - 100 q^{9} - 11 q^{10} - 22 q^{14} + 2 q^{16} - 11 q^{20} - 44 q^{21} - 8 q^{24} - 38 q^{25} - 46 q^{26} - 52 q^{29} - 11 q^{30} - 44 q^{34} + 18 q^{36} - 11 q^{40} - 76 q^{41} - 154 q^{44} - 30 q^{46} - 100 q^{49} + 21 q^{50} + 178 q^{54} + 242 q^{56} - 11 q^{60} - 44 q^{61} + 6 q^{64} - 22 q^{65} + 44 q^{66} - 12 q^{69} + 22 q^{70} - 22 q^{74} + 88 q^{76} - 110 q^{80} - 252 q^{81} - 374 q^{84} + 94 q^{85} - 198 q^{86} - 44 q^{89} - 242 q^{90} - 62 q^{94} + 372 q^{96}+O(q^{100}) $ 640 * q - 6 * q^4 - 22 * q^5 + 2 * q^6 - 100 * q^9 - 11 * q^10 - 22 * q^14 + 2 * q^16 - 11 * q^20 - 44 * q^21 - 8 * q^24 - 38 * q^25 - 46 * q^26 - 52 * q^29 - 11 * q^30 - 44 * q^34 + 18 * q^36 - 11 * q^40 - 76 * q^41 - 154 * q^44 - 30 * q^46 - 100 * q^49 + 21 * q^50 + 178 * q^54 + 242 * q^56 - 11 * q^60 - 44 * q^61 + 6 * q^64 - 22 * q^65 + 44 * q^66 - 12 * q^69 + 22 * q^70 - 22 * q^74 + 88 * q^76 - 110 * q^80 - 252 * q^81 - 374 * q^84 + 94 * q^85 - 198 * q^86 - 44 * q^89 - 242 * q^90 - 62 * q^94 + 372 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

$n$	$231$	$277$	$281$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{15}{22}\right)$

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 $

$2$	−1.27975	−	0.601871i	−0.904917	−	0.425587i
$2$	−1.27975	−	0.601871i	−0.904917	−	0.425587i
$3$	−2.51556	+	0.738636i	−1.45236	+	0.426452i	−0.910322	−	0.413901i	$-0.864166\pi$
$3$	−2.51556	+	0.738636i	−1.45236	+	0.426452i	−0.542040	+	0.840353i	$0.682348\pi$
$4$	1.27550	+	1.54049i	0.637751	+	0.770243i
$5$	2.08492	+	0.808149i	0.932405	+	0.361415i
$5$	2.08492	+	0.808149i	0.932405	+	0.361415i
$6$	3.66385	+	0.568779i	1.49576	+	0.232203i
$7$	−0.0121874	+	0.00175228i	−0.00460641	+	0.000662301i	−0.144618	−	0.989488i	$-0.546195\pi$
$7$	−0.0121874	+	0.00175228i	−0.00460641	+	0.000662301i	0.140011	+	0.990150i	$0.455286\pi$
$8$	−0.705145	−	2.73912i	−0.249306	−	0.968425i
$9$	3.25872	−	2.09425i	1.08624	−	0.698084i
$10$	−2.18177	−	2.28908i	−0.689936	−	0.723871i
$11$	0.836058	−	1.83071i	0.252081	−	0.551980i	−0.740712	−	0.671823i	$-0.765512\pi$
$11$	0.836058	−	1.83071i	0.252081	−	0.551980i	0.992793	+	0.119842i	$0.0382390\pi$
$12$	−4.34647	−	2.93306i	−1.25472	−	0.846701i
$13$	1.12708	+	0.162050i	0.312597	+	0.0449447i	0.296828	−	0.954931i	$-0.404071\pi$
$13$	1.12708	+	0.162050i	0.312597	+	0.0449447i	0.0157692	+	0.999876i	$0.494980\pi$
$14$	0.0166514	+	0.00509277i	0.00445028	+	0.00136110i
$15$	−5.84168	−	0.492954i	−1.50832	−	0.127280i
$16$	−0.746191	+	3.92978i	−0.186548	+	0.982446i
$17$	−1.57639	−	1.81925i	−0.382330	−	0.441233i	0.531667	−	0.846954i	$-0.321566\pi$
$17$	−1.57639	−	1.81925i	−0.382330	−	0.441233i	−0.913997	+	0.405721i	$0.867021\pi$
$18$	−5.43081	+	0.718782i	−1.28005	+	0.169418i
$19$	−1.81730	+	2.09728i	−0.416918	+	0.481149i	−0.924895	−	0.380222i	$-0.875848\pi$
$19$	−1.81730	+	2.09728i	−0.416918	+	0.481149i	0.507978	+	0.861370i	$0.330393\pi$
$20$	1.41438	+	4.24259i	0.316264	+	0.948671i
$21$	0.0293639	−	0.0134100i	0.00640773	−	0.00292631i
$22$	−2.17179	+	1.83965i	−0.463028	+	0.392214i
$23$	4.45408	+	1.77797i	0.928740	+	0.370732i
$23$	4.45408	+	1.77797i	0.928740	+	0.370732i
$24$	3.79705	+	6.36958i	0.775070	+	1.30019i
$25$	3.69379	+	3.36985i	0.738758	+	0.673971i
$26$	−1.34485	−	0.885744i	−0.263747	−	0.173709i
$27$	−1.49996	+	1.73105i	−0.288667	+	0.333140i
$28$	−0.0182444	−	0.0165395i	−0.00344787	−	0.00312567i
$29$	2.12136	+	2.44818i	0.393927	+	0.454616i	0.917719	−	0.397230i	$-0.130028\pi$
$29$	2.12136	+	2.44818i	0.393927	+	0.454616i	−0.523792	+	0.851846i	$0.675483\pi$
$30$	7.17918	+	4.14680i	1.31073	+	0.757098i
$31$	0.635355	−	2.16382i	0.114113	−	0.388633i	−0.882554	−	0.470211i	$-0.844178\pi$
$31$	0.635355	−	2.16382i	0.114113	−	0.388633i	0.996667	+	0.0815778i	$0.0259959\pi$
$32$	3.32016	−	4.58002i	0.586927	−	0.809640i
$33$	−0.750927	+	5.22282i	−0.130720	+	0.909175i
$34$	0.922424	+	3.27696i	0.158194	+	0.561994i
$35$	−0.0268259	−	0.00619587i	−0.00453440	−	0.00104729i
$36$	7.38267	+	2.34879i	1.23045	+	0.391465i
$37$	5.87561	−	3.77602i	0.965944	−	0.620774i	0.0403069	−	0.999187i	$-0.487166\pi$
$37$	5.87561	−	3.77602i	0.965944	−	0.620774i	0.925637	+	0.378413i	$0.123530\pi$
$38$	3.58798	−	1.59020i	0.582047	−	0.257965i
$39$	−2.95495	+	0.424858i	−0.473171	+	0.0680317i
$40$	0.743446	−	6.28071i	0.117549	−	0.993067i
$41$	1.30295	+	0.837356i	0.203487	+	0.130773i	0.638416	−	0.769692i	$-0.279590\pi$
$41$	1.30295	+	0.837356i	0.203487	+	0.130773i	−0.434929	+	0.900465i	$0.643226\pi$
$42$	−0.0456495		0.000511836i	−0.00704387		7.89779e-5i
$43$	3.34730	+	11.3998i	0.510458	+	1.73846i	0.661512	+	0.749934i	$0.269915\pi$
$43$	3.34730	+	11.3998i	0.510458	+	1.73846i	−0.151054	+	0.988525i	$0.548267\pi$
$44$	3.88658	−	1.04714i	0.585924	−	0.157862i
$45$	8.48664	−	1.73282i	1.26511	−	0.258313i
$46$	−4.62999	−	4.95613i	−0.682654	−	0.730741i
$47$	4.57330			0.667085			0.333542	−	0.942735i	$-0.391756\pi$
$47$	4.57330			0.667085			0.333542	+	0.942735i	$0.391756\pi$
$48$	−1.02559	−	10.4368i	−0.148031	−	1.50642i
$49$	−6.71631	+	1.97209i	−0.959472	+	0.281726i
$50$	−2.69889	−	6.53575i	−0.381681	−	0.924294i
$51$	5.30927	+	3.41206i	0.743447	+	0.477784i
$52$	1.18796	+	1.94295i	0.164741	+	0.269439i
$53$	1.60246	+	11.1454i	0.220115	+	1.53093i	0.737597	+	0.675241i	$0.235960\pi$
$53$	1.60246	+	11.1454i	0.220115	+	1.53093i	−0.517482	+	0.855694i	$0.673131\pi$
$54$	2.96144	−	1.31252i	0.403000	−	0.178611i
$55$	3.22260	−	3.14123i	0.434536	−	0.423563i
$56$	0.0133936	+	0.0321471i	0.00178979	+	0.00429584i
$57$	3.02241	−	6.61816i	0.400328	−	0.876597i
$58$	−1.24132	−	4.40984i	−0.162993	−	0.579041i
$59$	12.9845	+	1.86689i	1.69043	+	0.243048i	0.919281	−	0.393602i	$-0.128771\pi$
$59$	12.9845	+	1.86689i	1.69043	+	0.243048i	0.771153	+	0.636650i	$0.219680\pi$
$60$	−6.69169	−	9.62779i	−0.863893	−	1.24294i
$61$	−2.83682	+	9.66133i	−0.363218	+	1.23701i	0.551931	+	0.833890i	$0.313891\pi$
$61$	−2.83682	+	9.66133i	−0.363218	+	1.23701i	−0.915149	+	0.403116i	$0.867927\pi$
$62$	−2.11543	+	2.38674i	−0.268660	+	0.303116i
$63$	−0.0360456	+	0.0312337i	−0.00454132	+	0.00393508i
$64$	−7.00554	+	3.86295i	−0.875693	+	0.482869i
$65$	2.21892	+	1.24872i	0.275223	+	0.154884i
$66$	4.10446	−	6.23192i	0.505224	−	0.767096i
$67$	−7.40739	+	3.38284i	−0.904957	+	0.413280i	−0.812853	−	0.582469i	$-0.802087\pi$
$67$	−7.40739	+	3.38284i	−0.904957	+	0.413280i	−0.0921045	+	0.995749i	$0.529359\pi$
$68$	0.791841	−	4.74886i	0.0960248	−	0.575884i
$69$	−12.5178	−	1.18264i	−1.50697	−	0.142373i
$70$	0.0306012	+	0.0240749i	0.00365754	+	0.00287750i
$71$	5.31808	−	2.42869i	0.631141	−	0.288232i	−0.0740451	−	0.997255i	$-0.523591\pi$
$71$	5.31808	−	2.42869i	0.631141	−	0.288232i	0.705186	+	0.709023i	$0.250864\pi$
$72$	−8.03428	−	7.44927i	−0.946849	−	0.877905i
$73$	−2.59413	−	2.24783i	−0.303620	−	0.263088i	0.489703	−	0.871889i	$-0.337105\pi$
$73$	−2.59413	−	2.24783i	−0.303620	−	0.263088i	−0.793323	+	0.608801i	$0.791651\pi$
$74$	−9.79197	+	1.29599i	−1.13829	+	0.150656i
$75$	−11.7811	−	5.74872i	−1.36036	−	0.663805i
$76$	−5.54880	−	0.124445i	−0.636491	−	0.0142748i
$77$	−0.00698145	+	0.0237766i	−0.000795610	+	0.00270960i
$78$	4.03730	+	1.23479i	0.457134	+	0.139812i
$79$	−0.0753216	+	0.523873i	−0.00847434	+	0.0589403i	−0.993620	−	0.112782i	$-0.964024\pi$
$79$	−0.0753216	+	0.523873i	−0.00847434	+	0.0589403i	0.985145	+	0.171722i	$0.0549331\pi$
$80$	−4.73160	+	7.59025i	−0.529009	+	0.848616i
$81$	−2.33288	+	5.10830i	−0.259209	+	0.567589i
$82$	−1.16347	−	1.85581i	−0.128483	−	0.204940i
$83$	−0.607844	−	0.945824i	−0.0667196	−	0.103818i	0.806291	−	0.591519i	$-0.201472\pi$
$83$	−0.607844	−	0.945824i	−0.0667196	−	0.103818i	−0.873010	+	0.487702i	$0.837835\pi$
$84$	0.0581117	+	0.0281301i	0.00634051	+	0.00306925i
$85$	−1.81642	−	5.06695i	−0.197018	−	0.549588i
$86$	2.57755	−	16.6036i	0.277944	−	1.79041i
$87$	−7.14475	−	4.59165i	−0.765997	−	0.492276i
$88$	−5.60408	−	0.999145i	−0.597397	−	0.106509i
$89$	−2.72204	−	9.27042i	−0.288536	−	0.982663i	−0.968416	−	0.249340i	$-0.919786\pi$
$89$	−2.72204	−	9.27042i	−0.288536	−	0.982663i	0.679880	−	0.733323i	$-0.262032\pi$
$90$	−11.9037	−	2.89030i	−1.25476	−	0.304664i
$91$	−0.0140202			−0.00146972
$92$	2.94226	+	9.12925i	0.306751	+	0.951790i
$93$			5.91252i			0.613100i
$94$	−5.85267	−	2.75254i	−0.603657	−	0.283903i
$95$	−5.48384	+	2.90401i	−0.562630	+	0.297945i
$96$	−4.96911	+	13.9737i	−0.507158	+	1.42619i
$97$	−11.6232	−	7.46978i	−1.18016	−	0.758442i	−0.204743	−	0.978816i	$-0.565636\pi$
$97$	−11.6232	−	7.46978i	−1.18016	−	0.758442i	−0.975415	+	0.220374i	$0.929272\pi$
$98$	9.78211	+	1.51858i	0.988142	+	0.153400i
$99$	−1.10949	−	7.71669i	−0.111508	−	0.775557i
$100$	−0.479778	+	9.98848i	−0.0479778	+	0.998848i
$101$	11.7789	−	7.56981i	1.17204	−	0.753224i	0.198133	−	0.980175i	$-0.436512\pi$
$101$	11.7789	−	7.56981i	1.17204	−	0.753224i	0.973906	+	0.226951i	$0.0728758\pi$
$102$	−4.74090	−	7.56207i	−0.469419	−	0.748757i
$103$	11.2874	+	5.15477i	1.11218	+	0.507915i	0.884837	−	0.465900i	$-0.154269\pi$
$103$	11.2874	+	5.15477i	1.11218	+	0.507915i	0.227341	+	0.973815i	$0.426997\pi$
$104$	−0.350883	−	3.20149i	−0.0344069	−	0.313932i
$105$	0.0720587	−	0.00422846i	0.00703221	−	0.000412655i
$106$	4.65734	−	15.2277i	0.452360	−	1.47905i
$107$	−0.305391	+	1.04007i	−0.0295233	+	0.100547i	−0.972937	−	0.231072i	$-0.925777\pi$
$107$	−0.305391	+	1.04007i	−0.0295233	+	0.100547i	0.943413	+	0.331619i	$0.107595\pi$
$108$	−4.57985	−	0.102714i	−0.440697	−	0.00988368i
$109$	−0.0519940	+	0.0450530i	−0.00498012	+	0.00431530i	−0.657347	−	0.753588i	$-0.728322\pi$
$109$	−0.0519940	+	0.0450530i	−0.00498012	+	0.00431530i	0.652367	+	0.757903i	$0.273776\pi$
$110$	−6.01473	+	2.08038i	−0.573482	+	0.198357i
$111$	−11.9914	+	13.8388i	−1.13817	+	1.31352i
$112$	0.00220803	−	0.0492014i	0.000208639	−	0.00464910i
$113$	−5.97945	−	13.0932i	−0.562499	−	1.23170i	−0.950696	−	0.310125i	$-0.899629\pi$
$113$	−5.97945	−	13.0932i	−0.562499	−	1.23170i	0.388196	−	0.921577i	$-0.373098\pi$
$114$	−7.85121	+	6.65047i	−0.735333	+	0.622873i
$115$	7.84954	+	7.30648i	0.731974	+	0.681333i
$116$	−1.06559	+	6.39059i	−0.0989375	+	0.593352i
$117$	4.01223	−	1.83232i	0.370931	−	0.169398i
$118$	−15.4932	−	10.2041i	−1.42627	−	0.939365i
$119$	0.0223999	+	0.0194097i	0.00205340	+	0.00177928i
$120$	2.76897	+	16.3487i	0.252771	+	1.49242i
$121$	4.55096	+	5.25208i	0.413723	+	0.477462i
$122$	9.44529	−	10.6566i	0.855136	−	0.964807i
$123$	−3.89616	−	1.14402i	−0.351305	−	0.103152i
$124$	4.14373	−	1.78120i	0.372118	−	0.159957i
$125$	4.97791	+	10.0110i	0.445238	+	0.895412i
$126$	0.0649279	−	0.0182764i	0.00578424	−	0.00162819i
$127$	−4.38633	+	9.60472i	−0.389224	+	0.852281i	0.609026	+	0.793150i	$0.291560\pi$
$127$	−4.38633	+	9.60472i	−0.389224	+	0.852281i	−0.998250	+	0.0591312i	$0.981167\pi$
$128$	11.2903	−	0.727161i	0.997932	−	0.0642725i
$129$	−16.8407	−	26.2046i	−1.48274	−	2.30719i
$130$	−2.08809	−	2.93354i	−0.183138	−	0.257289i
$131$	−3.71771	+	0.534525i	−0.324817	+	0.0467017i	−0.302795	−	0.953056i	$-0.597920\pi$
$131$	−3.71771	+	0.534525i	−0.324817	+	0.0467017i	−0.0220226	+	0.999757i	$0.507011\pi$
$132$	−9.00348	+	5.50492i	−0.783652	+	0.479142i
$133$	0.0184732	−	0.0287448i	0.00160183	−	0.00249249i
$134$	11.5156	+	0.129117i	0.994798	+	0.0111540i
$135$	−4.52624	+	2.39690i	−0.389557	+	0.206292i
$136$	−3.87156	+	5.60075i	−0.331983	+	0.480260i
$137$	6.23594			0.532773			0.266386	−	0.963866i	$-0.414170\pi$
$137$	6.23594			0.532773			0.266386	+	0.963866i	$0.414170\pi$
$138$	15.3078	+	9.04759i	1.30309	+	0.770182i
$139$		−	9.88439i		−	0.838383i	−0.907898	−	0.419192i	$-0.862314\pi$
$139$		−	9.88439i		−	0.838383i	0.907898	−	0.419192i	$-0.137686\pi$
$140$	−0.0246718	−	0.0492277i	−0.00208515	−	0.00416050i
$141$	−11.5044	+	3.37801i	−0.968849	+	0.284480i
$142$	−8.26756	−	0.0926983i	−0.693798	−	0.00777907i
$143$	1.23898	−	1.92788i	0.103608	−	0.161218i
$144$	5.79833	+	14.3688i	0.483194	+	1.19740i
$145$	2.44438	+	6.81865i	0.202994	+	0.566258i
$146$	1.96693	+	4.43798i	0.162784	+	0.367290i
$147$	15.4386	−	9.92182i	1.27336	−	0.818338i
$148$	13.3113	+	4.23496i	1.09418	+	0.348112i
$149$	13.0627	+	5.96552i	1.07014	+	0.488714i	0.871013	−	0.491260i	$-0.163464\pi$
$149$	13.0627	+	5.96552i	1.07014	+	0.488714i	0.199122	+	0.979975i	$0.436191\pi$
$150$	11.6168	+	14.4476i	0.948506	+	1.17964i
$151$	−9.24107	−	1.32866i	−0.752027	−	0.108125i	−0.244367	−	0.969683i	$-0.578580\pi$
$151$	−9.24107	−	1.32866i	−0.752027	−	0.108125i	−0.507660	+	0.861557i	$0.669489\pi$
$152$	7.02615	+	3.49892i	0.569896	+	0.283800i
$153$	−8.94698	−	2.62707i	−0.723321	−	0.212386i
$154$	0.0232450	−	0.0262261i	0.00187313	−	0.00211336i
$155$	3.07335	−	3.99793i	0.246858	−	0.321122i
$156$	−4.42353	−	4.01015i	−0.354166	−	0.321069i
$157$	9.35532	−	10.7966i	0.746636	−	0.861663i	−0.247602	−	0.968862i	$-0.579643\pi$
$157$	9.35532	−	10.7966i	0.746636	−	0.861663i	0.994238	+	0.107198i	$0.0341880\pi$
$158$	0.411697	−	0.625091i	0.0327528	−	0.0497296i
$159$	−12.2635	−	26.8533i	−0.972557	−	2.12960i
$160$	10.6236	−	6.86578i	0.839870	−	0.542788i
$161$	−0.0573992	−	0.0138640i	−0.00452369	−	0.00109263i
$162$	6.06004	−	5.13324i	0.476122	−	0.403305i
$163$	8.80113	+	19.2718i	0.689358	+	1.50948i	0.852415	+	0.522866i	$0.175137\pi$
$163$	8.80113	+	19.2718i	0.689358	+	1.50948i	−0.163057	+	0.986617i	$0.552136\pi$
$164$	0.371982	+	3.07523i	0.0290469	+	0.240135i
$165$	−5.78644	+	10.2823i	−0.450474	+	0.800476i
$166$	0.208622	+	1.57626i	0.0161922	+	0.122341i
$167$	−11.3320	−	13.0778i	−0.876896	−	1.01199i	−0.999808	−	0.0195741i	$-0.993769\pi$
$167$	−11.3320	−	13.0778i	−0.876896	−	1.01199i	0.122913	−	0.992417i	$-0.460776\pi$
$168$	−0.0574375	−	0.0709752i	−0.00443140	−	0.00547586i
$169$	−11.2293	−	3.29723i	−0.863796	−	0.253633i
$170$	−0.725094	+	7.57766i	−0.0556122	+	0.581180i
$171$	−1.52985	+	10.6403i	−0.116990	+	0.813687i
$172$	−13.2918	+	19.6970i	−1.01349	+	1.50188i
$173$	14.2284	+	6.49789i	1.08177	+	0.494026i	0.874880	−	0.484340i	$-0.160940\pi$
$173$	14.2284	+	6.49789i	1.08177	+	0.494026i	0.206885	+	0.978365i	$0.433667\pi$
$174$	6.37988	+	10.1764i	0.483657	+	0.771468i
$175$	−0.0509226	−	0.0345972i	−0.00384939	−	0.00261530i
$176$	6.57044	+	4.65159i	0.495266	+	0.350626i
$177$	−34.0422	+	4.89453i	−2.55877	+	0.367896i
$178$	−2.09608	+	13.5021i	−0.157108	+	1.01203i
$179$	11.0240	−	17.1537i	0.823971	−	1.28212i	−0.132759	−	0.991148i	$-0.542384\pi$
$179$	11.0240	−	17.1537i	0.823971	−	1.28212i	0.956730	−	0.290976i	$-0.0939800\pi$
$180$	13.4941	+	10.8633i	1.00579	+	0.809706i
$181$	−3.33988	−	11.3746i	−0.248251	−	0.845467i	−0.985475	−	0.169818i	$-0.945682\pi$
$181$	−3.33988	−	11.3746i	−0.248251	−	0.845467i	0.737224	−	0.675649i	$-0.236136\pi$
$182$	0.0179423	+	0.00843836i	0.00132997	+	0.000625493i
$183$		−	26.3991i		−	1.95148i
$184$	1.72929	−	13.4540i	0.127485	−	0.991841i
$185$	15.3018	−	3.12434i	1.12501	−	0.229706i
$186$	3.55858	−	7.56653i	0.260928	−	0.554805i
$187$	−4.64847	+	1.36491i	−0.339930	+	0.0998125i
$188$	5.83326	+	7.04511i	0.425434	+	0.513817i
$189$	0.0152473	−	0.0237253i	0.00110908	−	0.00172576i
$190$	8.76577	−	0.415824i	0.635936	−	0.0301670i
$191$	−0.635485	−	4.41989i	−0.0459821	−	0.319812i	−0.999811	−	0.0194607i	$-0.993805\pi$
$191$	−0.635485	−	4.41989i	−0.0459821	−	0.319812i	0.953829	−	0.300352i	$-0.0971040\pi$
$192$	14.7696	−	14.8920i	1.06590	−	1.07474i
$193$	−5.05996	−	7.87345i	−0.364224	−	0.566744i	0.609979	−	0.792418i	$-0.291178\pi$
$193$	−5.05996	−	7.87345i	−0.364224	−	0.566744i	−0.974203	+	0.225674i	$0.927542\pi$
$194$	10.3789	+	16.5551i	0.745162	+	1.18859i
$195$	−6.50419	−	1.50225i	−0.465775	−	0.107578i
$196$	−11.6046	−	7.83097i	−0.828902	−	0.559355i
$197$	−22.8774	−	3.28927i	−1.62995	−	0.234351i	−0.734205	−	0.678928i	$-0.762445\pi$
$197$	−22.8774	−	3.28927i	−1.62995	−	0.234351i	−0.895740	+	0.444577i	$0.853354\pi$
$198$	−3.22459	+	10.5432i	−0.229161	+	0.749271i
$199$	16.9156	+	4.96686i	1.19911	+	0.352091i	0.819514	−	0.573060i	$-0.194244\pi$
$199$	16.9156	+	4.96686i	1.19911	+	0.352091i	0.379599	+	0.925151i	$0.376062\pi$
$200$	6.62578	−	12.4940i	0.468513	−	0.883456i
$201$	16.1351	−	13.9811i	1.13808	−	0.986153i
$202$	−19.6300	+	2.59808i	−1.38116	+	0.182800i
$203$	−0.0301438	−	0.0261198i	−0.00211568	−	0.00183325i
$204$	1.51575	+	12.5309i	0.106124	+	0.877342i
$205$	2.03984	+	2.79880i	0.142469	+	0.195477i
$206$	−11.3425	−	13.3904i	−0.790268	−	0.932950i
$207$	18.2381	−	3.53408i	1.26764	−	0.245635i
$208$	−1.47784	+	4.30828i	−0.102470	+	0.298725i
$209$	2.32014	+	5.08040i	0.160488	+	0.351419i
$210$	−0.0947619	−	0.0379587i	−0.00653919	−	0.00261940i
$211$	−6.34906	−	5.50149i	−0.437087	−	0.378738i	0.408339	−	0.912830i	$-0.366108\pi$
$211$	−6.34906	−	5.50149i	−0.437087	−	0.378738i	−0.845426	+	0.534092i	$0.820654\pi$
$212$	−15.1253	+	16.6845i	−1.03881	+	1.14590i
$213$	−11.5841	+	10.0377i	−0.793727	+	0.687769i
$214$	1.01681	−	1.14722i	0.0695077	−	0.0784220i
$215$	−2.23393	+	26.4729i	−0.152353	+	1.80544i
$216$	5.79923	+	2.88793i	0.394588	+	0.196499i
$217$	−0.00395170	+	0.0274847i	−0.000268259	+	0.00186578i
$218$	0.0936553	−	0.0263628i	0.00634313	−	0.00178551i
$219$	8.18603	+	3.73844i	0.553161	+	0.252620i
$220$	8.94945	+	0.957730i	0.603372	+	0.0645702i
$221$	−1.48191	−	2.30590i	−0.0996843	−	0.155112i
$222$	23.6751	−	10.4929i	1.58897	−	0.704234i
$223$	−3.60966	−	25.1058i	−0.241721	−	1.68121i	−0.643482	−	0.765461i	$-0.722511\pi$
$223$	−3.60966	−	25.1058i	−0.241721	−	1.68121i	0.401761	−	0.915745i	$-0.368398\pi$
$224$	−0.0324386	+	0.0616364i	−0.00216740	+	0.00411825i
$225$	19.0944	+	3.24569i	1.27296	+	0.216379i
$226$	−0.228224	+	20.3548i	−0.0151812	+	1.35398i
$227$	−5.35532	−	18.2386i	−0.355445	−	1.21054i	−0.922221	−	0.386663i	$-0.873628\pi$
$227$	−5.35532	−	18.2386i	−0.355445	−	1.21054i	0.566776	−	0.823872i	$-0.308191\pi$
$228$	14.0503	−	3.78549i	0.930502	−	0.250700i
$229$			2.16214i			0.142878i	0.997445	+	0.0714391i	$0.0227592\pi$
$229$			2.16214i			0.142878i	−0.997445	+	0.0714391i	$0.977241\pi$
$230$	−5.64786	−	14.0749i	−0.372409	−	0.928069i
$231$		−	0.0649684i		−	0.00427461i
$232$	5.21000	−	7.53699i	0.342053	−	0.494828i
$233$	6.57398	+	22.3889i	0.430675	+	1.46675i	0.834039	+	0.551706i	$0.186023\pi$
$233$	6.57398	+	22.3889i	0.430675	+	1.46675i	−0.403363	+	0.915040i	$0.632159\pi$
$234$	−6.23746	−	0.0699363i	−0.407756	−	0.00457188i
$235$	9.53497	+	3.69591i	0.621993	+	0.241095i
$236$	13.6858	+	22.3836i	0.890870	+	1.45705i
$237$	−0.197475	−	1.37347i	−0.0128274	−	0.0892166i
$238$	−0.0169841	−	0.0383213i	−0.00110092	−	0.00248400i
$239$	−2.55908	−	3.98201i	−0.165533	−	0.257575i	0.748570	−	0.663055i	$-0.230741\pi$
$239$	−2.55908	−	3.98201i	−0.165533	−	0.257575i	−0.914104	+	0.405480i	$0.867104\pi$
$240$	6.29621	−	22.5887i	0.406419	−	1.45809i
$241$	9.69110	+	4.42578i	0.624259	+	0.285089i	0.702322	−	0.711859i	$-0.252146\pi$
$241$	9.69110	+	4.42578i	0.624259	+	0.285089i	−0.0780637	+	0.996948i	$0.524874\pi$
$242$	−2.66299	−	9.46043i	−0.171184	−	0.608139i
$243$	3.07326	−	21.3750i	0.197150	−	1.37121i
$244$	−18.5015	+	7.95296i	−1.18444	+	0.509136i
$245$	−15.5967	−	1.31614i	−0.996437	−	0.0840849i
$246$	4.29755	+	3.80904i	0.274002	+	0.242855i
$247$	−2.38812	+	2.06932i	−0.151952	+	0.131667i
$248$	−6.37498	−	0.214506i	−0.404811	−	0.0136212i
$249$	2.22769	+	1.93031i	0.141174	+	0.122328i
$250$	−0.345121	−	15.8076i	−0.0218274	−	0.999762i
$251$	3.91172	+	8.56546i	0.246905	+	0.540647i	0.991989	−	0.126324i	$-0.0403178\pi$
$251$	3.91172	+	8.56546i	0.246905	+	0.540647i	−0.745084	+	0.666971i	$0.767591\pi$
$252$	−0.0940913	−	0.0156891i	−0.00592720	−	0.000988321i
$253$	6.97881	−	6.66765i	0.438754	−	0.419192i
$254$	11.3942	−	9.65160i	0.714935	−	0.605595i
$255$	8.31196	+	11.4046i	0.520515	+	0.714182i
$256$	−14.8864	−	5.86474i	−0.930400	−	0.366546i
$257$	−1.24118	−	1.07548i	−0.0774224	−	0.0670869i	0.615290	−	0.788301i	$-0.289039\pi$
$257$	−1.24118	−	1.07548i	−0.0774224	−	0.0670869i	−0.692712	+	0.721214i	$0.743584\pi$
$258$	5.78000	+	43.6712i	0.359847	+	2.71885i
$259$	−0.0649917	+	0.0563157i	−0.00403839	+	0.00349928i
$260$	0.906611	+	5.01096i	0.0562256	+	0.310766i
$261$	12.0400	+	3.53528i	0.745260	+	0.218828i
$262$	5.07944	+	1.55352i	0.313809	+	0.0959770i
$263$	−22.2026	−	3.19226i	−1.36907	−	0.196843i	−0.581742	−	0.813373i	$-0.697629\pi$
$263$	−22.2026	−	3.19226i	−1.36907	−	0.196843i	−0.787331	+	0.616530i	$0.788538\pi$
$264$	14.8354	−	1.62596i	0.913057	−	0.100071i
$265$	−5.66612	+	24.5322i	−0.348067	+	1.50700i
$266$	−0.0409416	+	0.0256676i	−0.00251029	+	0.00157378i
$267$	13.6949	+	21.3098i	0.838117	+	1.30414i
$268$	−14.6594	−	7.09616i	−0.895463	−	0.433467i
$269$	2.71850	+	18.9076i	0.165750	+	1.15282i	0.887549	+	0.460714i	$0.152407\pi$
$269$	2.71850	+	18.9076i	0.165750	+	1.15282i	−0.721798	+	0.692103i	$0.756684\pi$
$270$	7.23507	−	0.343212i	0.440312	−	0.0208872i
$271$	0.469306	−	0.730254i	0.0285083	−	0.0443598i	−0.826707	−	0.562633i	$-0.809789\pi$
$271$	0.469306	−	0.730254i	0.0285083	−	0.0443598i	0.855215	+	0.518273i	$0.173425\pi$
$272$	8.32555	−	4.83736i	0.504810	−	0.293308i
$273$	0.0352687	−	0.0103558i	0.00213456	−	0.000626763i
$274$	−7.98043	−	3.75324i	−0.482115	−	0.226741i
$275$	9.25745	−	3.94487i	0.558245	−	0.237884i
$276$	−14.1446	−	20.7919i	−0.851407	−	1.25153i
$277$			24.5706i			1.47630i	0.674634	+	0.738152i	$0.264301\pi$
$277$			24.5706i			1.47630i	−0.674634	+	0.738152i	$0.735699\pi$
$278$	−5.94913	+	12.6495i	−0.356805	+	0.758668i
$279$	−2.46114	−	8.38188i	−0.147345	−	0.501810i
$280$	0.00194490	+	0.0778483i	0.000116230	+	0.00465232i
$281$	−6.98653	+	10.8713i	−0.416781	+	0.648524i	−0.984639	−	0.174602i	$-0.944136\pi$
$281$	−6.98653	+	10.8713i	−0.416781	+	0.648524i	0.567858	+	0.823127i	$0.307772\pi$
$282$	16.7559	+	2.60120i	0.997799	+	0.154899i
$283$	−13.2771	+	1.90896i	−0.789240	+	0.113476i	−0.525136	−	0.851018i	$-0.675985\pi$
$283$	−13.2771	+	1.90896i	−0.789240	+	0.113476i	−0.264105	+	0.964494i	$0.585076\pi$
$284$	10.5246	+	5.09464i	0.624519	+	0.302311i
$285$	11.6500	−	11.3558i	0.690084	−	0.672659i
$286$	−2.74591	+	1.72150i	−0.162369	+	0.101794i
$287$	−0.0173469	−	0.00792206i	−0.00102395	−	0.000467624i
$288$	1.22776	−	21.8782i	0.0723466	−	1.28919i
$289$	1.59468	−	11.0913i	0.0938050	−	0.652428i
$290$	0.975768	−	10.1973i	0.0572990	−	0.598809i
$291$	34.7564	+	10.2054i	2.03746	+	0.598251i
$292$	0.153927	−	6.86333i	0.00900788	−	0.401646i
$293$	−14.2073	−	16.3961i	−0.830001	−	0.957872i	0.169617	−	0.985510i	$-0.445747\pi$
$293$	−14.2073	−	16.3961i	−0.830001	−	0.957872i	−0.999618	+	0.0276378i	$0.991201\pi$
$294$	−25.7292	+	3.40533i	−1.50056	+	0.198603i
$295$	25.5629	+	14.3857i	1.48833	+	0.837568i
$296$	−14.4861	−	13.4313i	−0.841989	−	0.780681i
$297$	1.91499	+	4.19325i	0.111119	+	0.243317i
$298$	−13.1264	−	15.4964i	−0.760393	−	0.897682i
$299$	4.73201	+	2.72570i	0.273659	+	0.157632i
$300$	−6.17094	−	25.4811i	−0.356280	−	1.47115i
$301$	−0.0607706	−	0.133069i	−0.00350276	−	0.00766998i
$302$	11.0265	+	7.26229i	0.634506	+	0.417898i
$303$	−24.0391	+	27.7426i	−1.38101	+	1.59377i
$304$	−6.88579	−	8.70657i	−0.394927	−	0.499356i
$305$	−13.7223	+	17.8505i	−0.785739	+	1.02212i
$306$	9.86871	+	8.74692i	0.564156	+	0.500028i
$307$	−12.0555	−	3.53982i	−0.688044	−	0.202028i	−0.0810213	−	0.996712i	$-0.525818\pi$
$307$	−12.0555	−	3.53982i	−0.688044	−	0.202028i	−0.607023	+	0.794684i	$0.707636\pi$
$308$	−0.0455324	+	0.0195723i	−0.00259445	+	0.00111524i
$309$	−32.2016	−	4.62990i	−1.83189	−	0.263386i
$310$	−6.33935	+	3.26657i	−0.360051	+	0.185529i
$311$	−28.5791	−	13.0517i	−1.62057	−	0.740092i	−0.621513	−	0.783404i	$-0.713482\pi$
$311$	−28.5791	−	13.0517i	−1.62057	−	0.740092i	−0.999062	+	0.0433124i	$0.986209\pi$
$312$	3.24740	+	7.79438i	0.183848	+	0.441270i
$313$	27.9405	−	17.9563i	1.57929	−	1.01495i	0.603200	−	0.797590i	$-0.293892\pi$
$313$	27.9405	−	17.9563i	1.57929	−	1.01495i	0.976092	−	0.217360i	$-0.0697445\pi$
$314$	−18.4706	+	8.18623i	−1.04236	+	0.461976i
$315$	−0.100394	+	0.0359896i	−0.00565655	+	0.00202778i
$316$	−0.903092	+	0.552169i	−0.0508029	+	0.0310619i
$317$	3.27265	−	5.09235i	0.183811	−	0.286015i	−0.737104	−	0.675779i	$-0.763807\pi$
$317$	3.27265	−	5.09235i	0.183811	−	0.286015i	0.920915	+	0.389765i	$0.127444\pi$
$318$	−0.468073	+	41.7464i	−0.0262482	+	2.34102i
$319$	6.25550	−	1.83678i	0.350241	−	0.102840i
$320$	−17.7278	+	2.39242i	−0.991016	+	0.133740i
$321$		−	2.84193i		−	0.158621i
$322$	0.0651121	+	0.0522893i	0.00362855	+	0.00291397i
$323$	6.68025			0.371699
$324$	−10.8449	+	2.92188i	−0.602492	+	0.162326i
$325$	3.61713	+	4.39669i	0.200642	+	0.243885i
$326$	0.335922	−	29.9601i	0.0186050	−	1.65934i
$327$	0.0975164	−	0.151739i	0.00539267	−	0.00839116i
$328$	1.37485	−	4.15940i	0.0759133	−	0.229664i
$329$	−0.0557367	+	0.00801373i	−0.00307286	+	0.000441811i
$330$	13.5938	−	9.67604i	0.748314	−	0.532648i
$331$	2.90425	+	4.51909i	0.159632	+	0.248392i	0.911851	−	0.410521i	$-0.134653\pi$
$331$	2.90425	+	4.51909i	0.159632	+	0.248392i	−0.752220	+	0.658913i	$0.771017\pi$
$332$	0.681722	−	2.14278i	0.0374144	−	0.117600i
$333$	11.2390	−	24.6100i	0.615894	−	1.34862i
$334$	6.63091	+	23.5567i	0.362827	+	1.28896i
$335$	−18.1777	+	1.06668i	−0.993152	+	0.0582789i
$336$	0.0307875	+	0.125400i	0.00167960	+	0.00684114i
$337$	29.2151	+	8.57833i	1.59145	+	0.467291i	0.953150	−	0.302498i	$-0.0978205\pi$
$337$	29.2151	+	8.57833i	1.59145	+	0.467291i	0.638298	+	0.769789i	$0.279639\pi$
$338$	12.3862	+	10.9782i	0.673721	+	0.597138i
$339$	24.7128	+	28.5201i	1.34221	+	1.54900i
$340$	5.48871	−	9.26107i	0.297667	−	0.502252i
$341$	−3.43014	−	2.97223i	−0.185752	−	0.160955i
$342$	8.36193	−	12.6962i	0.452161	−	0.686529i
$343$	0.156799	−	0.0716077i	0.00846635	−	0.00386645i
$344$	28.8652	−	17.2072i	1.55631	−	0.927749i
$345$	−25.1429	−	12.5820i	−1.35365	−	0.677390i
$346$	−14.2978	−	16.8793i	−0.768657	−	0.907438i
$347$	11.4454	+	25.0619i	0.614421	+	1.34539i	0.919509	+	0.393070i	$0.128587\pi$
$347$	11.4454	+	25.0619i	0.614421	+	1.34539i	−0.305088	+	0.952324i	$0.598686\pi$
$348$	−2.03977	−	16.8630i	−0.109343	−	0.903953i
$349$	0.0748555	−	0.0863878i	0.00400692	−	0.00462423i	−0.753743	−	0.657170i	$-0.771753\pi$
$349$	0.0748555	−	0.0863878i	0.00400692	−	0.00462423i	0.757749	+	0.652546i	$0.226299\pi$
$350$	0.0443450	+	0.0749245i	0.00237034	+	0.00400489i
$351$	−1.97110	+	1.70797i	−0.105209	+	0.0911645i
$352$	−5.60884	−	9.90741i	−0.298952	−	0.528067i
$353$	−3.53470	+	12.0381i	−0.188133	+	0.640723i	0.810364	+	0.585926i	$0.199269\pi$
$353$	−3.53470	+	12.0381i	−0.188133	+	0.640723i	−0.998498	+	0.0547964i	$0.982549\pi$
$354$	46.5113	+	14.2253i	2.47205	+	0.756065i
$355$	13.0505	−	0.765815i	0.692650	−	0.0406452i
$356$	10.8090	−	16.0177i	0.572875	−	0.848937i
$357$	−0.0706852	−	0.0322808i	−0.00374106	−	0.00170848i
$358$	−24.4322	+	15.3173i	−1.29128	+	0.809545i
$359$	1.90711	−	1.22562i	0.100653	−	0.0646859i	−0.489346	−	0.872090i	$-0.662764\pi$
$359$	1.90711	−	1.22562i	0.100653	−	0.0646859i	0.589999	+	0.807404i	$0.299128\pi$
$360$	−10.7307	−	22.0240i	−0.565558	−	1.16077i
$361$	1.60799	+	11.1838i	0.0846312	+	0.588623i
$362$	−2.57184	+	16.5668i	−0.135173	+	0.870730i
$363$	−15.3276	−	9.85046i	−0.804491	−	0.517015i
$364$	−0.0178828	−	0.0215979i	−0.000937313	−	0.00113204i
$365$	−3.59198	−	6.78299i	−0.188013	−	0.355038i
$366$	−15.8888	+	33.7841i	−0.830523	+	1.76592i
$367$			4.24377i			0.221523i	0.993847	+	0.110761i	$0.0353289\pi$
$367$			4.24377i			0.221523i	−0.993847	+	0.110761i	$0.964671\pi$
$368$	−10.3106	+	16.1769i	−0.537478	+	0.843278i
$369$	5.99959			0.312326
$370$	−21.4628	−	5.21133i	−1.11580	−	0.270924i
$371$	−0.0390597	−	0.133025i	−0.00202788	−	0.00690632i
$372$	−9.10816	+	7.54143i	−0.472236	+	0.391005i
$373$	−16.1950	−	10.4079i	−0.838545	−	0.538900i	0.0494373	−	0.998777i	$-0.484257\pi$
$373$	−16.1950	−	10.4079i	−0.838545	−	0.538900i	−0.887983	+	0.459877i	$0.847894\pi$
$374$	6.77037	+	1.05104i	0.350088	+	0.0543479i
$375$	−19.9168	−	21.5065i	−1.02850	−	1.11059i
$376$	−3.22484	−	12.5268i	−0.166308	−	0.646021i
$377$	1.99423	+	3.10308i	0.102708	+	0.159817i
$378$	−0.0337923	+	0.0211855i	−0.00173809	+	0.00108966i
$379$	−7.26990	+	15.9189i	−0.373430	+	0.817697i	0.625857	+	0.779938i	$0.284749\pi$
$379$	−7.26990	+	15.9189i	−0.373430	+	0.817697i	−0.999287	+	0.0377590i	$0.987978\pi$
$380$	−11.4682	−	4.74372i	−0.588308	−	0.243347i
$381$	3.93970	−	27.4012i	0.201837	−	1.40381i
$382$	−1.84695	+	6.03882i	−0.0944981	+	0.308973i
$383$	2.78332	−	9.47912i	0.142221	−	0.484360i	−0.857316	−	0.514791i	$-0.827870\pi$
$383$	2.78332	−	9.47912i	0.142221	−	0.484360i	0.999537	+	0.0304305i	$0.00968783\pi$
$384$	−27.8644	+	10.1687i	−1.42195	+	0.518917i
$385$	−0.0337708	+	0.0439303i	−0.00172112	+	0.00223890i
$386$	1.73666	+	13.1215i	0.0883937	+	0.667865i
$387$	34.7821	+	30.1388i	1.76807	+	1.53204i
$388$	−3.31833	−	27.4331i	−0.168463	−	1.39270i
$389$	3.34399	−	1.52715i	0.169547	−	0.0774295i	−0.328834	−	0.944388i	$-0.606656\pi$
$389$	3.34399	−	1.52715i	0.169547	−	0.0774295i	0.498381	+	0.866958i	$0.333928\pi$
$390$	7.41955	+	5.83718i	0.375704	+	0.295577i
$391$	−3.78680	−	10.9059i	−0.191507	−	0.551533i
$392$	10.1377	+	17.0062i	0.512033	+	0.858940i
$393$	8.95731	−	4.09067i	0.451836	−	0.206347i
$394$	27.2975	+	17.9787i	1.37523	+	0.905752i
$395$	−0.580407	+	1.03136i	−0.0292035	+	0.0518935i
$396$	10.4723	−	11.5518i	0.526253	−	0.580500i
$397$	7.18703	−	6.22760i	0.360707	−	0.312554i	−0.455587	−	0.890191i	$-0.650571\pi$
$397$	7.18703	−	6.22760i	0.360707	−	0.312554i	0.816294	+	0.577637i	$0.196025\pi$
$398$	−18.6582	−	16.5373i	−0.935253	−	0.828941i
$399$	−0.0252385	+	0.0859544i	−0.00126350	+	0.00430310i
$400$	−15.9991	+	12.0012i	−0.799954	+	0.600062i
$401$	−24.4943	−	3.52175i	−1.22319	−	0.175868i	−0.499695	−	0.866201i	$-0.666555\pi$
$401$	−24.4943	−	3.52175i	−1.22319	−	0.175868i	−0.723491	+	0.690333i	$0.757464\pi$
$402$	−29.0637	+	8.18106i	−1.44956	+	0.408034i
$403$	1.06675	−	2.33585i	0.0531384	−	0.116357i
$404$	26.6851	+	8.48985i	1.32763	+	0.422386i
$405$	−8.99215	+	8.76509i	−0.446823	+	0.435541i
$406$	0.0228557	+	0.0515694i	0.00113431	+	0.00255935i
$407$	−2.00046	−	13.9135i	−0.0991592	−	0.689667i
$408$	5.60224	−	16.9487i	0.277352	−	0.839087i
$409$	−14.3475	−	9.22058i	−0.709438	−	0.455928i	0.135510	−	0.990776i	$-0.456733\pi$
$409$	−14.3475	−	9.22058i	−0.709438	−	0.455928i	−0.844948	+	0.534848i	$0.820369\pi$
$410$	−0.925963	−	4.80948i	−0.0457300	−	0.237523i
$411$	−15.6869	+	4.60609i	−0.773779	+	0.227202i
$412$	6.45622	+	23.9630i	0.318075	+	1.18057i
$413$	−0.161518			−0.00794780
$414$	−25.4672	−	6.45428i	−1.25165	−	0.317211i
$415$	−0.502940	−	2.46320i	−0.0246884	−	0.120914i
$416$	4.48429	−	4.62403i	0.219861	−	0.226712i
$417$	7.30097	+	24.8648i	0.357530	+	1.21764i
$418$	0.0885553	−	7.89805i	0.00433138	−	0.386306i
$419$	−2.45502	−	1.57775i	−0.119936	−	0.0770779i	0.479298	−	0.877652i	$-0.340891\pi$
$419$	−2.45502	−	1.57775i	−0.119936	−	0.0770779i	−0.599233	+	0.800574i	$0.704528\pi$
$420$	0.0984249	+	0.105612i	0.00480264	+	0.00515334i
$421$	−2.84774	+	0.409443i	−0.138790	+	0.0199550i	−0.211360	−	0.977408i	$-0.567789\pi$
$421$	−2.84774	+	0.409443i	−0.138790	+	0.0199550i	0.0725695	+	0.997363i	$0.476880\pi$
$422$	4.81399	+	10.8618i	0.234342	+	0.528745i
$423$	14.9031	−	9.57765i	0.724614	−	0.465681i
$424$	29.3985	−	12.2484i	1.42772	−	0.594837i
$425$	0.307760	−	12.0321i	0.0149285	−	0.583644i
$426$	20.8660	−	5.87353i	1.01096	−	0.284573i
$427$	0.0176441	−	0.122717i	0.000853858	−	0.00593871i
$428$	−1.99173	+	0.856156i	−0.0962741	+	0.0413839i
$429$	−1.69272	+	5.76487i	−0.0817252	+	0.278330i
$430$	18.7921	−	32.5340i	0.906237	−	1.56893i
$431$	−25.8761	−	29.8626i	−1.24641	−	1.43843i	−0.855336	−	0.518073i	$-0.826649\pi$
$431$	−25.8761	−	29.8626i	−1.24641	−	1.43843i	−0.391073	−	0.920360i	$-0.627896\pi$
$432$	−5.68338	−	7.18621i	−0.273442	−	0.345747i
$433$	−1.33972	+	1.54612i	−0.0643828	+	0.0743017i	−0.787027	−	0.616918i	$-0.788381\pi$
$433$	−1.33972	+	1.54612i	−0.0643828	+	0.0743017i	0.722645	+	0.691220i	$0.242926\pi$
$434$	0.0215994	−	0.0327950i	0.00103680	−	0.00157421i
$435$	−11.1855	−	15.3472i	−0.536303	−	0.735844i
$436$	−0.135722	−	0.0226307i	−0.00649990	−	0.00108382i
$437$	−11.8233	+	6.11034i	−0.565585	+	0.292297i
$438$	−8.22599	−	9.71119i	−0.393053	−	0.464019i
$439$	−37.2226	+	16.9990i	−1.77654	+	0.811317i	−0.798763	+	0.601645i	$0.794512\pi$
$439$	−37.2226	+	16.9990i	−1.77654	+	0.811317i	−0.977772	+	0.209671i	$0.932761\pi$
$440$	−10.8766	−	6.61207i	−0.518521	−	0.315218i
$441$	−17.7565	+	20.4921i	−0.845549	+	0.975815i
$442$	0.508617	+	3.84289i	0.0241924	+	0.182788i
$443$	−8.73880	−	10.0851i	−0.415193	−	0.479158i	0.509174	−	0.860664i	$-0.329951\pi$
$443$	−8.73880	−	10.0851i	−0.415193	−	0.479158i	−0.924367	+	0.381506i	$0.875406\pi$
$444$	−36.6134	−	0.821144i	−1.73760	−	0.0389698i
$445$	1.81665	−	21.5279i	0.0861173	−	1.02052i
$446$	−10.4910	+	34.3016i	−0.496762	+	1.62423i
$447$	−37.2663	−	5.35809i	−1.76264	−	0.253429i
$448$	0.0786104	−	0.0593550i	0.00371399	−	0.00280426i
$449$	12.6869	−	27.7804i	0.598730	−	1.31104i	−0.331290	−	0.943529i	$-0.607484\pi$
$449$	12.6869	−	27.7804i	0.598730	−	1.31104i	0.930021	−	0.367508i	$-0.119789\pi$
$450$	−22.4824	−	15.6460i	−1.05983	−	0.737560i
$451$	2.62230	−	1.68525i	0.123479	−	0.0793553i
$452$	12.5430	−	25.9116i	0.589975	−	1.21878i
$453$	24.2279	−	3.48345i	1.13833	−	0.163667i
$454$	−4.12381	+	26.5639i	−0.193540	+	1.24671i
$455$	−0.0292310	−	0.0113304i	−0.00137037	−	0.000531178i
$456$	−20.2592	−	3.61199i	−0.948723	−	0.169147i
$457$	34.5593	−	10.1475i	1.61662	−	0.474682i	0.656510	−	0.754317i	$-0.272032\pi$
$457$	34.5593	−	10.1475i	1.61662	−	0.474682i	0.960106	+	0.279635i	$0.0902136\pi$
$458$	1.30133	−	2.76699i	0.0608072	−	0.129293i
$459$	5.51373			0.257359
$460$	−1.24342	+	21.4115i	−0.0579748	+	0.998318i
$461$	−14.3080			−0.666388			−0.333194	−	0.942858i	$-0.608126\pi$
$461$	−14.3080			−0.666388			−0.333194	+	0.942858i	$0.608126\pi$
$462$	−0.0391026	+	0.0831431i	−0.00181922	+	0.00386817i
$463$	−1.70451	+	0.500488i	−0.0792151	+	0.0232597i	−0.321100	−	0.947045i	$-0.604053\pi$
$463$	−1.70451	+	0.500488i	−0.0792151	+	0.0232597i	0.241885	+	0.970305i	$0.422234\pi$
$464$	−11.2038	+	6.50969i	−0.520122	+	0.302205i
$465$	−4.77820	+	12.3271i	−0.221584	+	0.571658i
$466$	5.06222	−	32.6088i	0.234503	−	1.51057i
$467$	−28.2836	+	4.06657i	−1.30881	+	0.188178i	−0.761179	−	0.648542i	$-0.775379\pi$
$467$	−28.2836	+	4.06657i	−1.30881	+	0.188178i	−0.547630	+	0.836720i	$0.684470\pi$
$468$	7.94027	+	3.84365i	0.367039	+	0.177673i
$469$	0.0843492	−	0.0542079i	0.00389488	−	0.00250309i
$470$	−9.97788	−	10.4687i	−0.460246	−	0.482883i
$471$	−15.5591	+	34.0697i	−0.716927	+	1.56985i
$472$	−4.04231	−	36.8824i	−0.186062	−	1.69765i
$473$	23.6684	+	3.40300i	1.08827	+	0.156470i
$474$	−0.573935	+	1.87655i	−0.0263617	+	0.0861928i
$475$	−13.7803	+	1.62286i	−0.632281	+	0.0744619i
$476$	−0.00132913	+	0.0592638i	−6.09208e−5	+	0.00271635i
$477$	28.5632	+	32.9637i	1.30782	+	1.50930i
$478$	0.878319	+	6.63620i	0.0401734	+	0.303533i
$479$	14.3983	−	16.6165i	0.657875	−	0.759228i	−0.324554	−	0.945867i	$-0.605214\pi$
$479$	14.3983	−	16.6165i	0.657875	−	0.759228i	0.982429	+	0.186639i	$0.0597595\pi$
$480$	−21.6530	+	25.1183i	−0.988322	+	1.14649i
$481$	7.23421	−	3.30375i	0.329852	−	0.150638i
$482$	−9.73840	−	11.4967i	−0.443572	−	0.523659i
$483$	0.154632	−	0.00752140i	0.00703599	−	0.000342236i
$484$	−2.28601	+	13.7097i	−0.103909	+	0.623169i
$485$	−18.1968	−	24.9672i	−0.826273	−	1.13370i
$486$	−16.7980	+	25.5048i	−0.761972	+	1.15692i
$487$	8.56499	−	9.88452i	0.388117	−	0.447910i	−0.527746	−	0.849402i	$-0.676963\pi$
$487$	8.56499	−	9.88452i	0.388117	−	0.447910i	0.915863	+	0.401492i	$0.131508\pi$
$488$	28.4639	+	0.957758i	1.28850	+	0.0433557i
$489$	−36.3746	−	41.9786i	−1.64492	−	1.89834i
$490$	19.1677	+	11.0715i	0.865908	+	0.500161i
$491$	1.83307	−	6.24285i	0.0827251	−	0.281736i	−0.907733	−	0.419548i	$-0.862189\pi$
$491$	1.83307	−	6.24285i	0.0827251	−	0.281736i	0.990458	+	0.137812i	$0.0440069\pi$
$492$	−3.20722	−	7.46118i	−0.144593	−	0.336376i
$493$	1.10976	−	7.71858i	0.0499813	−	0.347627i
$494$	4.30165	−	1.21086i	0.193540	−	0.0544792i
$495$	3.92304	−	16.9853i	0.176327	−	0.763434i
$496$	8.02925	+	4.11143i	0.360524	+	0.184609i
$497$	−0.0605579	+	0.0389182i	−0.00271639	+	0.00174572i
$498$	−1.68908	−	3.81109i	−0.0756897	−	0.170779i
$499$	8.30194	−	1.19364i	0.371646	−	0.0534346i	0.0460385	−	0.998940i	$-0.485340\pi$
$499$	8.30194	−	1.19364i	0.371646	−	0.0534346i	0.325607	+	0.945505i	$0.394431\pi$
$500$	−9.07249	+	20.4375i	−0.405734	+	0.913991i
$501$	38.1661	+	24.5279i	1.70514	+	1.09582i
$502$	0.149303	−	13.3160i	0.00666370	−	0.594321i
$503$	6.83294	+	23.2708i	0.304666	+	1.03760i	0.959473	+	0.281800i	$0.0909314\pi$
$503$	6.83294	+	23.2708i	0.304666	+	1.03760i	−0.654808	+	0.755796i	$0.727250\pi$
$504$	0.110970	+	0.0767090i	0.00494301	+	0.00341689i
$505$	30.6755	−	6.26338i	1.36504	−	0.278717i
$506$	−12.9442	+	4.33256i	−0.575439	+	0.192606i
$507$	30.6836			1.36271
$508$	−20.3907	+	5.49376i	−0.904691	+	0.243746i
$509$	22.0335	−	6.46962i	0.976618	−	0.286761i	0.245790	−	0.969323i	$-0.420953\pi$
$509$	22.0335	−	6.46962i	0.976618	−	0.286761i	0.730827	+	0.682562i	$0.239134\pi$
$510$	−3.77312	−	19.5977i	−0.167076	−	0.867800i
$511$	0.0355546	+	0.0228495i	0.00157284	+	0.00101080i
$512$	15.5210	+	16.4651i	0.685938	+	0.727660i
$513$	−0.904605	−	6.29167i	−0.0399393	−	0.277784i
$514$	0.941086	+	2.12338i	0.0415095	+	0.0936581i
$515$	19.3675	+	19.8692i	0.853433	+	0.875541i
$516$	18.8875	−	59.3668i	0.831476	−	2.61348i
$517$	3.82355	−	8.37240i	0.168159	−	0.368218i
$518$	0.117068	−	0.0329531i	0.00514366	−	0.00144788i
$519$	−40.5920	−	5.83625i	−1.78179	−	0.256183i
$520$	1.85572	−	6.95842i	0.0813786	−	0.305147i
$521$	−6.62671	+	22.5685i	−0.290321	+	0.988744i	0.677167	+	0.735829i	$0.263207\pi$
$521$	−6.62671	+	22.5685i	−0.290321	+	0.988744i	−0.967489	+	0.252915i	$0.918611\pi$
$522$	−13.2804	−	11.7708i	−0.581269	−	0.515195i
$523$	1.20024	−	1.04001i	0.0524828	−	0.0454766i	−0.628224	−	0.778032i	$-0.716218\pi$
$523$	1.20024	−	1.04001i	0.0524828	−	0.0454766i	0.680707	+	0.732556i	$0.261673\pi$
$524$	−5.56537	−	5.04528i	−0.243124	−	0.220404i
$525$	0.153654	+	0.0494182i	0.00670601	+	0.00215679i
$526$	26.4924	+	17.4484i	1.15512	+	0.760787i
$527$	−4.93809	+	2.25515i	−0.215107	+	0.0982360i
$528$	−19.9642	−	6.84820i	−0.868830	−	0.298030i
$529$	16.6777	+	15.8384i	0.725116	+	0.688626i
$530$	22.0165	−	27.9848i	0.956334	−	1.21558i
$531$	46.2225	−	21.1091i	2.00589	−	0.916057i
$532$	0.0678435	−	0.00820641i	0.00294139	−	0.000355793i
$533$	1.33284	+	1.15492i	0.0577319	+	0.0500250i
$534$	−4.70033	−	35.5137i	−0.203403	−	1.53683i
$535$	−1.47725	+	1.92166i	−0.0638669	+	0.0830804i
$536$	14.4893	+	17.9043i	0.625842	+	0.773350i
$537$	−15.0612	+	51.2939i	−0.649940	+	2.21349i
$538$	7.90095	−	25.8331i	0.340634	−	1.11375i
$539$	−2.00490	+	13.9444i	−0.0863572	+	0.600628i
$540$	−9.46562	−	3.91536i	−0.407335	−	0.168490i
$541$	5.11848	−	11.2079i	0.220061	−	0.481866i	−0.767114	−	0.641511i	$-0.778308\pi$
$541$	5.11848	−	11.2079i	0.220061	−	0.481866i	0.987174	+	0.159646i	$0.0510351\pi$
$542$	−1.04011	+	0.652078i	−0.0446766	+	0.0280092i
$543$	16.8034	+	26.1466i	0.721102	+	1.12206i
$544$	−13.5661	+	1.17969i	−0.581640	+	0.0505787i
$545$	−0.144813	+	0.0519131i	−0.00620311	+	0.00222371i
$546$	−0.0513679	−	0.00797440i	−0.00219834	−	0.000341273i
$547$	4.15136	+	2.66792i	0.177499	+	0.114072i	0.626373	−	0.779523i	$-0.284539\pi$
$547$	4.15136	+	2.66792i	0.177499	+	0.114072i	−0.448874	+	0.893595i	$0.648175\pi$
$548$	7.95396	+	9.60638i	0.339776	+	0.410364i
$549$	10.9889	+	37.4246i	0.468993	+	1.59724i
$550$	−14.2215	−	0.523366i	−0.606407	−	0.0223164i
$551$	−8.98968			−0.382973
$552$	5.58746	+	35.1217i	0.237818	+	1.49488i
$553$		−	0.00651664i		−	0.000277116i
$554$	14.7883	−	31.4441i	0.628296	−	1.33593i
$555$	−36.1848	+	19.1619i	−1.53596	+	0.813378i
$556$	15.2268	−	12.6076i	0.645759	−	0.534680i
$557$	−11.9890	−	7.70487i	−0.507991	−	0.326466i	0.261415	−	0.965227i	$-0.415811\pi$
$557$	−11.9890	−	7.70487i	−0.507991	−	0.326466i	−0.769405	+	0.638761i	$0.779447\pi$
$558$	−1.89518	+	12.2080i	−0.0802292	+	0.516805i
$559$	1.92534	+	13.3910i	0.0814331	+	0.566380i
$560$	0.0443657	−	0.100797i	0.00187479	−	0.00425943i
$561$	10.6854	−	6.86706i	0.451136	−	0.289928i
$562$	15.4841	−	9.70745i	0.653156	−	0.409484i
$563$	19.9542	+	9.11276i	0.840967	+	0.384057i	0.788851	−	0.614584i	$-0.210676\pi$
$563$	19.9542	+	9.11276i	0.840967	+	0.384057i	0.0521161	+	0.998641i	$0.483403\pi$
$564$	−19.8777	−	13.4138i	−0.837002	−	0.564821i
$565$	−1.88544	−	32.1305i	−0.0793212	−	1.35174i
$566$	18.1402	+	5.54811i	0.762491	+	0.233205i
$567$	0.0194806	−	0.0663448i	0.000818108	−	0.00278622i
$568$	−10.4025	−	12.8543i	−0.436479	−	0.539354i
$569$	−10.6002	+	9.18517i	−0.444386	+	0.385062i	−0.848112	−	0.529818i	$-0.822260\pi$
$569$	−10.6002	+	9.18517i	−0.444386	+	0.385062i	0.403726	+	0.914880i	$0.367715\pi$
$570$	−21.7437	+	7.52075i	−0.910744	+	0.315009i
$571$	−14.0079	+	16.1660i	−0.586211	+	0.676524i	−0.968928	−	0.247342i	$-0.920443\pi$
$571$	−14.0079	+	16.1660i	−0.586211	+	0.676524i	0.382717	+	0.923866i	$0.374988\pi$
$572$	4.55019	−	0.550395i	0.190253	−	0.0230132i
$573$	4.86330	+	10.6491i	0.203167	+	0.444874i
$574$	0.0174316	+	0.0205788i	0.000727579	+	0.000858944i
$575$	10.4609	+	21.5770i	0.436252	+	0.899825i
$576$	−14.7391	+	27.2597i	−0.614130	+	1.13582i
$577$	31.5353	−	14.4017i	1.31283	−	0.599551i	0.368833	−	0.929496i	$-0.379757\pi$
$577$	31.5353	−	14.4017i	1.31283	−	0.599551i	0.944000	+	0.329945i	$0.107030\pi$
$578$	−8.71631	+	13.2342i	−0.362551	+	0.550471i
$579$	18.5443	+	16.0687i	0.770674	+	0.667793i
$580$	−7.38622	+	12.4627i	−0.306696	+	0.517486i
$581$	0.00906540	+	0.0104620i	0.000376096	+	0.000434038i
$582$	−38.3370	−	33.9792i	−1.58912	−	1.40848i
$583$	21.7437	+	6.38453i	0.900533	+	0.264420i
$584$	−4.32783	+	8.69068i	−0.179087	+	0.359623i
$585$	9.84597	−	0.577769i	0.407081	−	0.0238878i
$586$	8.31342	+	29.5339i	0.343424	+	1.22003i
$587$	3.12434	−	6.84136i	0.128955	−	0.282373i	−0.834130	−	0.551567i	$-0.814030\pi$
$587$	3.12434	−	6.84136i	0.128955	−	0.282373i	0.963086	+	0.269194i	$0.0867573\pi$
$588$	34.9764	+	11.1277i	1.44240	+	0.458899i
$589$	3.38350	+	5.26483i	0.139415	+	0.216933i
$590$	−24.0557	−	33.7956i	−0.990356	−	1.39134i
$591$	59.9791	−	8.62369i	2.46721	−	0.354731i
$592$	10.4546	+	25.9075i	0.429683	+	1.06479i
$593$	−10.8129	+	16.8252i	−0.444033	+	0.690929i	−0.989064	−	0.147487i	$-0.952882\pi$
$593$	−10.8129	+	16.8252i	−0.444033	+	0.690929i	0.545031	+	0.838416i	$0.316518\pi$
$594$	0.0730915	−	6.51887i	0.00299898	−	0.267473i
$595$	0.0310162	+	0.0585701i	0.00127154	+	0.00240114i
$596$	7.47165	+	27.7319i	0.306051	+	1.13594i
$597$	−46.2209			−1.89170
$598$	−4.41525	−	6.33627i	−0.180553	−	0.259109i
$599$		−	5.34259i		−	0.218292i	−0.994026	−	0.109146i	$-0.965188\pi$
$599$		−	5.34259i		−	0.218292i	0.994026	−	0.109146i	$-0.0348117\pi$
$600$	−7.43908	+	36.3234i	−0.303699	+	1.48290i
$601$	27.1835	−	7.98180i	1.10884	−	0.325584i	0.324480	−	0.945892i	$-0.394811\pi$
$601$	27.1835	−	7.98180i	1.10884	−	0.325584i	0.784358	+	0.620308i	$0.212992\pi$
$602$	−0.00231950	+	0.206871i	−9.45356e−5	+	0.00843142i
$603$	−17.0541	+	26.5367i	−0.694497	+	1.08066i
$604$	−9.74021	−	15.9304i	−0.396323	−	0.648201i
$605$	5.24392	+	14.6280i	0.213195	+	0.594714i
$606$	47.4615	−	21.0351i	1.92799	−	0.854491i
$607$	25.3575	−	16.2963i	1.02923	−	0.661445i	0.0869286	−	0.996215i	$-0.472295\pi$
$607$	25.3575	−	16.2963i	1.02923	−	0.661445i	0.942300	+	0.334769i	$0.108658\pi$
$608$	3.57183	+	15.2866i	0.144857	+	0.619952i
$609$	0.0951218	+	0.0434407i	0.00385453	+	0.00176030i
$610$	28.3048	−	14.5851i	1.14603	−	0.590532i
$611$	5.15450	+	0.741105i	0.208529	+	0.0299819i
$612$	−7.36493	−	17.1335i	−0.297709	−	0.692582i
$613$	−22.5918	−	6.63356i	−0.912475	−	0.267927i	−0.208393	−	0.978045i	$-0.566823\pi$
$613$	−22.5918	−	6.63356i	−0.912475	−	0.267927i	−0.704082	+	0.710118i	$0.748641\pi$
$614$	13.2975	+	11.7859i	0.536643	+	0.475641i
$615$	−7.19865	−	5.53386i	−0.290278	−	0.223147i
$616$	0.0700499	+	0.00235705i	0.00282239	+	9.49684e-5i
$617$	17.9025	−	20.6605i	0.720726	−	0.831762i	−0.270669	−	0.962673i	$-0.587245\pi$
$617$	17.9025	−	20.6605i	0.720726	−	0.831762i	0.991394	+	0.130911i	$0.0417902\pi$
$618$	38.4233	+	25.3063i	1.54561	+	1.01797i
$619$	−10.8854	−	23.8356i	−0.437519	−	0.958034i	−0.992047	−	0.125869i	$-0.959828\pi$
$619$	−10.8854	−	23.8356i	−0.437519	−	0.958034i	0.554527	−	0.832165i	$-0.312899\pi$
$620$	10.0788	−	0.364911i	0.404775	−	0.0146552i
$621$	−9.75868	+	5.04334i	−0.391602	+	0.202382i
$622$	28.7186	+	33.9038i	1.15151	+	1.35942i
$623$	0.0494190	+	0.108213i	0.00197993	+	0.00433545i
$624$	0.535358	−	11.9293i	0.0214315	−	0.477556i
$625$	2.28815	+	24.8951i	0.0915262	+	0.995803i
$626$	−46.5642	+	6.16289i	−1.86108	+	0.246319i
$627$	−9.58903	−	11.0663i	−0.382949	−	0.441947i
$628$	28.5647	+	0.640633i	1.13986	+	0.0255641i
$629$	−16.1318	−	4.73672i	−0.643216	−	0.188865i
$630$	0.150140	+	0.0143666i	0.00598171	+	0.000572380i
$631$	−3.35827	+	23.3573i	−0.133690	+	0.929838i	0.806995	+	0.590558i	$0.201092\pi$
$631$	−3.35827	+	23.3573i	−0.133690	+	0.929838i	−0.940686	+	0.339280i	$0.889817\pi$
$632$	1.48806	−	0.163092i	0.0591920	−	0.00648743i
$633$	20.0351	+	9.14971i	0.796322	+	0.363668i
$634$	−7.25311	+	4.54720i	−0.288058	+	0.180592i
$635$	−16.9072	+	16.4803i	−0.670942	+	0.654000i
$636$	25.7250	−	53.1431i	1.02006	−	2.10726i
$637$	−7.88942	+	1.13433i	−0.312590	+	0.0449437i
$638$	−9.11096	−	1.41439i	−0.360706	−	0.0559964i
$639$	12.2439	−	19.0518i	0.484360	−	0.753679i
$640$	24.1271	+	7.60819i	0.953706	+	0.300740i
$641$	−0.133734	−	0.455455i	−0.00528216	−	0.0179894i	0.956810	−	0.290715i	$-0.0938931\pi$
$641$	−0.133734	−	0.455455i	−0.00528216	−	0.0179894i	−0.962092	+	0.272725i	$0.912075\pi$
$642$	−1.71048	+	3.63695i	−0.0675071	+	0.143539i
$643$			14.6041i			0.575930i	0.957641	+	0.287965i	$0.0929787\pi$
$643$			14.6041i			0.575930i	−0.957641	+	0.287965i	$0.907021\pi$
$644$	−0.0518555	−	0.106106i	−0.00204339	−	0.00418117i
$645$	−13.9342	−	68.2443i	−0.548660	−	2.68712i
$646$	−8.54902	−	4.02065i	−0.336357	−	0.158190i
$647$	−23.2993	+	6.84130i	−0.915991	+	0.268959i	−0.705561	−	0.708650i	$-0.749305\pi$
$647$	−23.2993	+	6.84130i	−0.915991	+	0.268959i	−0.210430	+	0.977609i	$0.567487\pi$
$648$	15.6373	+	2.78795i	0.614290	+	0.109521i
$649$	14.2735	−	22.2100i	0.560284	−	0.871819i
$650$	−1.98276	−	7.80370i	−0.0777704	−	0.306086i
$651$	−0.0103604	−	0.0720583i	−0.000406057	−	0.00282419i
$652$	−18.4620	+	38.1392i	−0.723030	+	1.49365i
$653$	−18.5726	−	28.8996i	−0.726804	−	1.13093i	−0.986264	−	0.165175i	$-0.947181\pi$
$653$	−18.5726	−	28.8996i	−0.726804	−	1.13093i	0.259460	−	0.965754i	$-0.416455\pi$
$654$	−0.216123	+	0.135494i	−0.00845109	+	0.00529825i
$655$	−8.18310	−	1.89002i	−0.319740	−	0.0738491i
$656$	−4.26288	+	4.49549i	−0.166438	+	0.175519i
$657$	−13.1611	−	1.89228i	−0.513462	−	0.0738247i
$658$	0.0761521	+	0.0232908i	0.00296872	+	0.000907969i
$659$	13.5184	+	3.96935i	0.526601	+	0.154624i	0.534218	−	0.845347i	$-0.320606\pi$
$659$	13.5184	+	3.96935i	0.526601	+	0.154624i	−0.00761676	+	0.999971i	$0.502425\pi$
$660$	−23.2203	+	4.20116i	−0.903850	+	0.163530i
$661$	−24.0844	+	20.8692i	−0.936773	+	0.811719i	−0.982313	−	0.187244i	$-0.940045\pi$
$661$	−24.0844	+	20.8692i	−0.936773	+	0.811719i	0.0455402	+	0.998963i	$0.485499\pi$
$662$	−0.996784	−	7.53128i	−0.0387411	−	0.292711i
$663$	5.43108	+	4.70605i	0.210925	+	0.182768i
$664$	−2.16211	+	2.33190i	−0.0839060	+	0.0904953i
$665$	0.0617452	−	0.0450016i	0.00239438	−	0.00174509i
$666$	−29.1952	+	24.7301i	−1.13129	+	0.958273i
$667$	5.09594	+	14.6761i	0.197315	+	0.568262i
$668$	5.69221	−	34.1375i	0.220238	−	1.32082i
$669$	27.6244	+	60.4889i	1.06802	+	2.33864i
$670$	23.9048	+	9.57554i	0.923524	+	0.369935i
$671$	15.3154	+	13.2708i	0.591243	+	0.512315i
$672$	0.0360746	−	0.179011i	0.00139161	−	0.00690548i
$673$	−28.6353	+	24.8127i	−1.10381	+	0.956458i	−0.999275	−	0.0380629i	$-0.987881\pi$
$673$	−28.6353	+	24.8127i	−1.10381	+	0.956458i	−0.104536	+	0.994521i	$0.533336\pi$
$674$	−32.2249	−	28.5618i	−1.24126	−	1.10016i
$675$	−11.3739	+	1.33947i	−0.437782	+	0.0515563i
$676$	−9.24371	−	21.5043i	−0.355527	−	0.827088i
$677$	1.48682	−	10.3411i	0.0571432	−	0.397440i	−0.941097	−	0.338137i	$-0.890203\pi$
$677$	1.48682	−	10.3411i	0.0571432	−	0.397440i	0.998240	−	0.0593027i	$-0.0188877\pi$
$678$	−14.4607	−	51.3724i	−0.555359	−	1.97294i
$679$	0.154746	+	0.0706701i	0.00593860	+	0.00271207i
$680$	−12.5981	+	8.54832i	−0.483117	+	0.327813i
$681$	26.9433	+	41.9246i	1.03247	+	1.60656i
$682$	2.60080	+	5.86820i	0.0995899	+	0.224705i
$683$	−4.69919	−	32.6836i	−0.179809	−	1.25060i	−0.857202	−	0.514980i	$-0.827799\pi$
$683$	−4.69919	−	32.6836i	−0.179809	−	1.25060i	0.677392	−	0.735622i	$-0.263110\pi$
$684$	−18.3426	+	11.2151i	−0.701347	+	0.428818i
$685$	13.0014	+	5.03957i	0.496760	+	0.192552i
$686$	−0.243762	−	0.00273313i	−0.00930686	−	0.000104351i
$687$	−1.59704	−	5.43900i	−0.0609307	−	0.207511i
$688$	−47.2966	+	4.64769i	−1.80317	+	0.177192i
$689$			12.8215i			0.488459i
$690$	24.6038	+	31.2345i	0.936649	+	1.18908i
$691$		−	13.3134i		−	0.506465i	−0.967405	−	0.253232i	$-0.918506\pi$
$691$		−	13.3134i		−	0.506465i	0.967405	−	0.253232i	$-0.0814937\pi$
$692$	8.13844	+	30.2067i	0.309377	+	1.14829i
$693$	0.0270437	+	0.0921023i	0.00102730	+	0.00349868i
$694$	0.436848	−	38.9615i	0.0165825	−	1.47896i
$695$	7.98807	−	20.6082i	0.303005	−	0.781713i
$696$	−7.53899	+	22.8081i	−0.285765	+	0.864538i
$697$	−0.530599	−	3.69039i	−0.0200979	−	0.139784i
$698$	−0.147790	+	0.0655011i	−0.00559395	+	0.00247925i
$699$	−33.0745	−	51.4650i	−1.25099	−	1.94658i
$700$	−0.0116554	−	0.122574i	−0.000440533	−	0.00463288i
$701$	−37.8820	−	17.3001i	−1.43078	−	0.653416i	−0.458815	−	0.888532i	$-0.651726\pi$
$701$	−37.8820	−	17.3001i	−1.43078	−	0.653416i	−0.971967	+	0.235115i	$0.924453\pi$
$702$	3.55048	−	0.999416i	0.134004	−	0.0377205i
$703$	−2.75838	+	19.1850i	−0.104034	+	0.723574i
$704$	1.21491	+	16.0548i	0.0457885	+	0.605087i
$705$	−26.7158	−	2.25443i	−1.00617	−	0.0849066i
$706$	11.7689	−	13.2783i	0.442928	−	0.499734i
$707$	−0.130289	+	0.112896i	−0.00490003	+	0.00424590i
$708$	−50.9609	−	46.1986i	−1.91523	−	1.73625i
$709$	23.2200	+	20.1202i	0.872045	+	0.755631i	0.970904	−	0.239471i	$-0.0769738\pi$
$709$	23.2200	+	20.1202i	0.872045	+	0.755631i	−0.0988590	+	0.995101i	$0.531519\pi$
$710$	−17.1623	−	6.87469i	−0.644089	−	0.258003i
$711$	0.851671	+	1.86490i	0.0319401	+	0.0699392i
$712$	−23.4734	+	13.9930i	−0.879701	+	0.524409i
$713$	6.67712	−	8.50819i	0.250060	−	0.318634i
$714$	0.0710302	+	0.0838546i	0.00265824	+	0.00313818i
$715$	4.14118	−	3.01821i	0.154872	−	0.112875i
$716$	40.4861	−	4.89723i	1.51304	−	0.183018i
$717$	9.37879	+	8.12677i	0.350258	+	0.303500i
$718$	−3.17828	+	0.420654i	−0.118612	+	0.0156987i
$719$	−20.8455	+	18.0628i	−0.777407	+	0.673627i	−0.950308	−	0.311312i	$-0.899232\pi$
$719$	−20.8455	+	18.0628i	−0.777407	+	0.673627i	0.172901	+	0.984939i	$0.444686\pi$
$720$	0.476943	+	34.6437i	0.0177746	+	1.29109i
$721$	−0.146597	−	0.0430446i	−0.00545954	−	0.00160307i
$722$	4.67341	−	15.2803i	0.173926	−	0.568673i
$723$	−27.6476	−	3.97513i	−1.02823	−	0.147837i
$724$	13.2624	−	19.6534i	0.492892	−	0.730411i
$725$	−0.414156	+	16.1918i	−0.0153814	+	0.601347i
$726$	13.6867	+	21.8313i	0.507963	+	0.810237i
$727$	−19.2548	−	29.9610i	−0.714121	−	1.11119i	−0.988740	−	0.149640i	$-0.952188\pi$
$727$	−19.2548	−	29.9610i	−0.714121	−	1.11119i	0.274620	−	0.961553i	$-0.411448\pi$
$728$	0.00988627	+	0.0384030i	0.000366409	+	0.00142331i
$729$	5.65973	+	39.3643i	0.209620	+	1.45794i
$730$	0.514334	+	10.8424i	0.0190364	+	0.401296i
$731$	15.4625	−	24.0602i	0.571902	−	0.889897i
$732$	40.6674	−	33.6721i	1.50311	−	1.24456i
$733$	−24.7709	+	7.27339i	−0.914934	+	0.268649i	−0.705116	−	0.709092i	$-0.749105\pi$
$733$	−24.7709	+	7.27339i	−0.914934	+	0.268649i	−0.209818	+	0.977740i	$0.567287\pi$
$734$	2.55420	−	5.43095i	0.0942773	−	0.200460i
$735$	40.2067	−	8.20947i	1.48305	−	0.302811i
$736$	22.9314	−	14.4966i	0.845262	−	0.534353i
$737$			16.3891i			0.603699i
$738$	−7.67796	−	3.61098i	−0.282630	−	0.132922i
$739$	−4.10926	−	13.9949i	−0.151162	−	0.514809i	0.848740	−	0.528810i	$-0.177361\pi$
$739$	−4.10926	−	13.9949i	−0.151162	−	0.514809i	−0.999902	+	0.0140007i	$0.995543\pi$
$740$	24.3304	+	19.5870i	0.894404	+	0.720034i
$741$	4.47899	−	6.96945i	0.164540	−	0.256029i
$742$	−0.0300775	+	0.193747i	−0.00110418	+	0.00711269i
$743$	23.7076	−	3.40864i	0.869748	−	0.125051i	0.307030	−	0.951700i	$-0.400665\pi$
$743$	23.7076	−	3.40864i	0.869748	−	0.125051i	0.562718	+	0.826649i	$0.309756\pi$
$744$	16.1951	−	4.16918i	0.593741	−	0.152850i
$745$	22.4136	+	22.9942i	0.821170	+	0.842443i
$746$	14.4613	+	23.0668i	0.529465	+	0.844535i
$747$	−3.96159	−	1.80920i	−0.144947	−	0.0661951i
$748$	−8.03177	−	5.41995i	−0.293671	−	0.198173i
$749$	0.00189943	−	0.0132108i	6.94038e−5	−	0.000482714i
$750$	12.5443	+	39.5102i	0.458052	+	1.44271i
$751$	40.7797	+	11.9740i	1.48807	+	0.436937i	0.921925	−	0.387368i	$-0.126616\pi$
$751$	40.7797	+	11.9740i	1.48807	+	0.436937i	0.566146	+	0.824305i	$0.308434\pi$
$752$	−3.41256	+	17.9721i	−0.124443	+	0.655375i
$753$	−16.1669	−	18.6576i	−0.589156	−	0.679922i
$754$	−0.684452	−	5.17142i	−0.0249263	−	0.188332i
$755$	−18.1931	−	10.2383i	−0.662116	−	0.372611i
$756$	0.0559965	−	0.00677338i	0.00203657	−	0.000246346i
$757$	11.2752	+	24.6891i	0.409802	+	0.897342i	0.996182	+	0.0873055i	$0.0278256\pi$
$757$	11.2752	+	24.6891i	0.409802	+	0.897342i	−0.586379	+	0.810037i	$0.699447\pi$
$758$	18.8847	−	15.9966i	0.685924	−	0.581021i
$759$	−12.6307	+	21.9277i	−0.458465	+	0.795926i
$760$	11.8213	+	12.9732i	0.428804	+	0.470586i
$761$	−7.19066	−	15.7453i	−0.260661	−	0.570768i	0.733374	−	0.679825i	$-0.237944\pi$
$761$	−7.19066	−	15.7453i	−0.260661	−	0.570768i	−0.994036	+	0.109057i	$0.965217\pi$
$762$	−21.5338	+	32.6954i	−0.780088	+	1.18443i
$763$	0.000554726	0	0.000640188i	2.00824e−5	0	2.31764e-5i
$764$	5.99822	−	6.61654i	0.217008	−	0.239378i
$765$	−16.5307	−	12.7077i	−0.597668	−	0.459449i
$766$	−9.26715	+	10.4557i	−0.334836	+	0.377778i
$767$	14.3321	+	4.20828i	0.517501	+	0.151952i
$768$	41.7796	+	3.75749i	1.50759	+	0.135587i
$769$	−40.7743	−	5.86246i	−1.47036	−	0.211406i	−0.639889	−	0.768468i	$-0.721019\pi$
$769$	−40.7743	−	5.86246i	−1.47036	−	0.211406i	−0.830471	+	0.557062i	$0.811929\pi$
$770$	0.0696585	−	0.0358940i	0.00251032	−	0.00129353i
$771$	3.91665	+	1.78867i	0.141055	+	0.0644175i
$772$	5.67495	−	17.8374i	0.204246	−	0.641982i
$773$	−20.5022	+	13.1760i	−0.737414	+	0.473907i	−0.854655	−	0.519196i	$-0.826231\pi$
$773$	−20.5022	+	13.1760i	−0.737414	+	0.473907i	0.117241	+	0.993103i	$0.462595\pi$
$774$	−26.3725	−	59.5044i	−0.947941	−	2.13884i
$775$	9.63862	−	5.85164i	0.346230	−	0.210197i
$776$	−12.2646	+	37.1046i	−0.440273	+	1.33198i
$777$	0.121894	−	0.189671i	0.00437293	−	0.00680441i
$778$	−5.19861	−	0.0582883i	−0.186379	−	0.00208974i
$779$	−4.12403	+	1.21092i	−0.147759	+	0.0433858i
$780$	−5.98191	−	11.9357i	−0.214187	−	0.427368i
$781$		−	11.7664i		−	0.421035i
$782$	−1.71778	+	16.2359i	−0.0614276	+	0.580594i
$783$	−7.41988			−0.265165
$784$	−2.73822	−	27.8652i	−0.0977937	−	0.995185i
$785$	28.2304	−	14.9496i	1.00759	−	0.533574i
$786$	−13.9251	−	0.156133i	−0.496693	−	0.00556907i
$787$	−20.7098	+	32.2250i	−0.738223	+	1.14870i	0.245568	+	0.969379i	$0.421026\pi$
$787$	−20.7098	+	32.2250i	−0.738223	+	1.14870i	−0.983791	+	0.179319i	$0.942611\pi$
$788$	−24.1131	−	39.4377i	−0.858992	−	1.40491i
$789$	58.2101	−	8.36935i	2.07233	−	0.297957i
$790$	1.36352	−	0.970552i	0.0485119	−	0.0345307i
$791$	0.0958170	+	0.149094i	0.00340686	+	0.00530118i
$792$	−20.3546	+	8.48042i	−0.723269	+	0.301339i
$793$	−4.76296	+	10.4294i	−0.169138	+	0.370360i
$794$	−12.9458	+	3.64408i	−0.459429	+	0.129323i
$795$	−3.86692	−	65.8977i	−0.137146	−	2.33715i
$796$	13.9245	+	32.3934i	0.493540	+	1.14815i
$797$	14.5789	+	4.28076i	0.516412	+	0.151632i	0.529546	−	0.848281i	$-0.322362\pi$
$797$	14.5789	+	4.28076i	0.516412	+	0.151632i	−0.0131335	+	0.999914i	$0.504181\pi$
$798$	0.0840323	−	0.0948095i	0.00297471	−	0.00335622i
$799$	−7.20930	−	8.31998i	−0.255047	−	0.294340i
$800$	27.6980	−	5.72916i	0.979271	−	0.202556i
$801$	−28.2850	−	24.5091i	−0.999401	−	0.865986i
$802$	29.2268	+	19.2494i	1.03204	+	0.679719i
$803$	−6.28397	+	2.86979i	−0.221756	+	0.101273i
$804$	42.1181	+	7.02291i	1.48539	+	0.247679i
$805$	−0.108469	−	0.0752924i	−0.00382302	−	0.00265371i
$806$	−2.77105	+	2.34725i	−0.0976059	+	0.0826784i
$807$	−20.8044	−	45.5553i	−0.732350	−	1.60362i
$808$	−29.0404	−	26.9259i	−1.02164	−	0.947248i
$809$	27.3043	−	31.5108i	0.959967	−	1.10786i	−0.0341359	−	0.999417i	$-0.510868\pi$
$809$	27.3043	−	31.5108i	0.959967	−	1.10786i	0.994103	−	0.108443i	$-0.0345866\pi$
$810$	16.7831	−	5.80497i	0.589699	−	0.203966i
$811$	−37.3542	+	32.3676i	−1.31168	+	1.13658i	−0.330437	+	0.943828i	$0.607196\pi$
$811$	−37.3542	+	32.3676i	−1.31168	+	1.13658i	−0.981247	+	0.192753i	$0.938258\pi$
$812$	0.00178863	−	0.0797520i	6.27686e−5	−	0.00279875i
$813$	−0.641177	+	2.18365i	−0.0224870	+	0.0765838i
$814$	−5.81406	+	19.0098i	−0.203783	+	0.666293i
$815$	2.77517	+	47.2928i	0.0972101	+	1.65659i
$816$	−17.3704	+	18.3182i	−0.608086	+	0.641267i
$817$	−29.9917	−	13.6967i	−1.04928	−	0.479188i
$818$	12.8116	+	20.4353i	0.447946	+	0.714505i
$819$	−0.0456879	+	0.0293618i	−0.00159647	+	0.00102599i
$820$	−1.70969	+	6.71222i	−0.0597050	+	0.234401i
$821$	−4.28445	−	29.7990i	−0.149528	−	1.03999i	−0.916994	−	0.398902i	$-0.869391\pi$
$821$	−4.28445	−	29.7990i	−0.149528	−	1.03999i	0.767465	−	0.641090i	$-0.221518\pi$
$822$	22.8476	+	3.54687i	0.796900	+	0.123711i
$823$	17.7248	+	11.3910i	0.617846	+	0.397066i	0.811792	−	0.583947i	$-0.198492\pi$
$823$	17.7248	+	11.3910i	0.617846	+	0.397066i	−0.193946	+	0.981012i	$0.562129\pi$
$824$	6.16030	−	34.5523i	0.214604	−	1.20369i
$825$	−20.3739	+	16.7615i	−0.709328	+	0.583559i
$826$	0.206702	+	0.0972133i	0.00719210	+	0.00338248i
$827$			8.00791i			0.278462i	0.990260	+	0.139231i	$0.0444631\pi$
$827$			8.00791i			0.278462i	−0.990260	+	0.139231i	$0.955537\pi$
$828$	28.7069	+	23.5878i	0.997635	+	0.819734i
$829$	−22.3968			−0.777874			−0.388937	−	0.921264i	$-0.627158\pi$
$829$	−22.3968			−0.777874			−0.388937	+	0.921264i	$0.627158\pi$
$830$	−0.838893	+	3.45497i	−0.0291184	+	0.119924i
$831$	−18.1487	−	61.8089i	−0.629573	−	2.14413i
$832$	−8.52183	+	3.21862i	−0.295441	+	0.111586i
$833$	14.1752	+	9.10986i	0.491142	+	0.315638i
$834$	5.62204	−	36.2149i	0.194675	−	1.25402i
$835$	−13.0575	−	36.4241i	−0.451872	−	1.26051i
$836$	−4.86694	+	10.0542i	−0.168327	+	0.347732i
$837$	2.79266	+	4.34547i	0.0965286	+	0.150201i
$838$	2.19220	+	3.49672i	0.0757284	+	0.120792i
$839$	−3.54475	+	7.76193i	−0.122379	+	0.267972i	−0.960899	−	0.276898i	$-0.910694\pi$
$839$	−3.54475	+	7.76193i	−0.122379	+	0.267972i	0.838521	+	0.544870i	$0.183421\pi$
$840$	−0.0623941	−	0.194396i	−0.00215280	−	0.00670729i
$841$	2.63371	−	18.3178i	0.0908175	−	0.631650i
$842$	3.89081	+	1.18999i	0.134086	+	0.0410097i
$843$	9.54516	−	32.5078i	0.328753	−	1.11963i
$844$	0.376731	−	16.7978i	0.0129676	−	0.578204i
$845$	−20.7476	−	15.9495i	−0.713741	−	0.548678i
$846$	−24.8367	+	3.28721i	−0.853904	+	0.113016i
$847$	−0.0646675	−	0.0560347i	−0.00222200	−	0.00192538i
$848$	−44.9946	−	2.01924i	−1.54512	−	0.0693411i
$849$	31.9893	−	14.6090i	1.09787	−	0.501381i
$850$	−7.63565	+	15.2128i	−0.261901	+	0.521796i
$851$	32.8841	−	6.37208i	1.12725	−	0.218432i
$852$	−30.2384	−	5.04205i	−1.03595	−	0.172738i
$853$	−45.9804	+	20.9986i	−1.57434	+	0.718977i	−0.995347	−	0.0963563i	$-0.969281\pi$
$853$	−45.9804	+	20.9986i	−1.57434	+	0.718977i	−0.578992	+	0.815333i	$0.696554\pi$
$854$	−0.0964401	+	0.146428i	−0.00330011	+	0.00501065i
$855$	−11.7886	+	20.9479i	−0.403161	+	0.716403i
$856$	3.06421	+	0.103105i	0.104733	+	0.00352406i
$857$	42.9807	−	37.2430i	1.46819	−	1.27220i	0.578460	−	0.815711i	$-0.303654\pi$
$857$	42.9807	−	37.2430i	1.46819	−	1.27220i	0.889731	−	0.456484i	$-0.150892\pi$
$858$	5.63596	−	6.35877i	0.192408	−	0.217085i
$859$	−2.05068	+	6.98398i	−0.0699683	+	0.238290i	−0.987051	−	0.160407i	$-0.948719\pi$
$859$	−2.05068	+	6.98398i	−0.0699683	+	0.238290i	0.917083	+	0.398697i	$0.130538\pi$
$860$	−43.6305	+	30.3249i	−1.48779	+	1.03407i
$861$	0.0494887	+	0.00711541i	0.00168657	+	0.000242492i
$862$	15.1414	+	53.7907i	0.515718	+	1.83212i
$863$	−3.25885	+	7.13590i	−0.110933	+	0.242909i	−0.956954	−	0.290241i	$-0.906265\pi$
$863$	−3.25885	+	7.13590i	−0.110933	+	0.242909i	0.846021	+	0.533150i	$0.178992\pi$
$864$	2.94811	+	12.6172i	0.100297	+	0.429245i
$865$	24.4138	+	25.0463i	0.830095	+	0.851598i
$866$	2.64506	−	1.17230i	0.0898829	−	0.0398364i
$867$	4.18089	+	29.0787i	0.141990	+	0.987565i
$868$	−0.0473801	+	0.0289692i	−0.00160819	+	0.000983279i
$869$	0.896087	+	0.575880i	0.0303977	+	0.0195354i
$870$	5.07752	+	26.3728i	0.172144	+	0.894122i
$871$	−8.89695	+	2.61238i	−0.301462	+	0.0885172i
$872$	0.160069	+	0.110649i	0.00542062	+	0.00374704i
$873$	−53.5204			−1.81139
$874$	18.8085	−	0.703587i	0.636206	−	0.0237992i
$875$	−0.0782100	−	0.113286i	−0.00264398	−	0.00382975i
$876$	4.68229	+	17.3788i	0.158200	+	0.587177i
$877$	−9.91590	−	33.7704i	−0.334836	−	1.14035i	−0.939123	−	0.343580i	$-0.888360\pi$
$877$	−9.91590	−	33.7704i	−0.334836	−	1.14035i	0.604287	−	0.796767i	$-0.293458\pi$
$878$	57.8666	+	0.648818i	1.95290	+	0.0218965i
$879$	47.8502	+	30.7515i	1.61395	+	1.03722i
$880$	9.93967	+	15.0081i	0.335066	+	0.505922i
$881$	−22.2068	+	3.19285i	−0.748165	+	0.107570i	−0.505842	−	0.862626i	$-0.668818\pi$
$881$	−22.2068	+	3.19285i	−0.748165	+	0.107570i	−0.242322	+	0.970196i	$0.577909\pi$
$882$	35.0575	−	15.5376i	1.18045	−	0.523177i
$883$	29.0578	−	18.6743i	0.977874	−	0.628441i	0.0489847	−	0.998800i	$-0.484401\pi$
$883$	29.0578	−	18.6743i	0.977874	−	0.628441i	0.928889	+	0.370358i	$0.120765\pi$
$884$	1.66203	−	5.22405i	0.0559000	−	0.175704i
$885$	−74.9309	−	17.3065i	−2.51877	−	0.581751i
$886$	5.11351	+	18.1660i	0.171792	+	0.610299i
$887$	4.78725	−	33.2961i	0.160740	−	1.11797i	−0.736502	−	0.676435i	$-0.763524\pi$
$887$	4.78725	−	33.2961i	0.160740	−	1.11797i	0.897243	−	0.441538i	$-0.145567\pi$
$888$	46.3617	+	23.0874i	1.55580	+	0.774763i
$889$	0.0366278	−	0.124743i	0.00122846	−	0.00418374i
$890$	−15.2819	+	26.4569i	−0.512250	+	0.886837i
$891$	7.40140	+	8.54167i	0.247956	+	0.286157i
$892$	34.0709	−	37.5831i	1.14078	−	1.25837i
$893$	−8.31107	+	9.59149i	−0.278119	+	0.320967i
$894$	44.4666	+	29.2865i	1.48718	+	0.979488i
$895$	36.8469	−	26.8550i	1.23165	−	0.897663i
$896$	−0.136325	+	0.0286460i	−0.00455431	+	0.000956997i
$897$	−13.9170	−	3.36145i	−0.464674	−	0.112236i
$898$	−32.9562	+	27.9160i	−1.09976	+	0.931568i
$899$	6.64525	−	3.03478i	0.221631	−	0.101216i
$900$	19.3549	+	33.5545i	0.645165	+	1.11848i
$901$	17.7501	−	20.4847i	0.591342	−	0.682445i
$902$	−4.37018	+	0.578405i	−0.145511	+	0.0192588i
$903$	0.251162	+	0.289857i	0.00835815	+	0.00964582i
$904$	−31.6474	+	25.6110i	−1.05258	+	0.851809i
$905$	2.22898	−	26.4143i	0.0740939	−	0.878039i
$906$	−33.1022	−	10.1242i	−1.09975	−	0.336352i
$907$	30.7872	+	4.42652i	1.02227	+	0.146980i	0.633007	−	0.774146i	$-0.281820\pi$
$907$	30.7872	+	4.42652i	1.02227	+	0.146980i	0.389264	+	0.921126i	$0.372730\pi$
$908$	21.2655	−	31.5131i	0.705720	−	1.04580i
$909$	22.5309	−	49.3358i	0.747303	−	1.63636i
$910$	0.0305888	+	0.0320934i	0.00101401	+	0.00106388i
$911$	−21.1721	+	13.6065i	−0.701463	+	0.450803i	−0.842144	−	0.539252i	$-0.818707\pi$
$911$	−21.1721	+	13.6065i	−0.701463	+	0.450803i	0.140681	+	0.990055i	$0.455071\pi$
$912$	23.7527	+	16.8158i	0.786529	+	0.556828i
$913$	−2.23972	+	0.322024i	−0.0741241	+	0.0106574i
$914$	−50.3347	−	7.81400i	−1.66492	−	0.258464i
$915$	21.3344	−	55.0400i	0.705293	−	1.81957i
$916$	−3.33075	+	2.75781i	−0.110051	+	0.0911207i
$917$	0.0443725	−	0.0130290i	0.00146531	−	0.000430254i
$918$	−7.05617	−	3.31855i	−0.232888	−	0.109529i
$919$	−17.8150			−0.587664			−0.293832	−	0.955857i	$-0.594931\pi$
$919$	−17.8150			−0.587664			−0.293832	+	0.955857i	$0.594931\pi$
$920$	14.4783	−	26.6530i	0.477334	−	0.878722i
$921$	32.9410			1.08544
$922$	18.3105	+	8.61155i	0.603026	+	0.283606i
$923$	6.38750	−	1.87554i	0.210247	−	0.0617342i
$924$	0.100083	−	0.0828673i	0.00329248	−	0.00272613i
$925$	34.4279	+	5.85211i	1.13198	+	0.192416i
$926$	2.48256	+	0.385395i	0.0815821	+	0.0126649i
$927$	47.5778	−	6.84066i	1.56266	−	0.224677i
$928$	18.2560	−	1.58752i	0.599282	−	0.0521128i
$929$	−32.6220	+	20.9649i	−1.07029	+	0.687836i	−0.952296	−	0.305177i	$-0.901284\pi$
$929$	−32.6220	+	20.9649i	−1.07029	+	0.687836i	−0.117999	+	0.993014i	$0.537648\pi$
$930$	13.5342	−	12.8998i	0.443805	−	0.423000i
$931$	8.06954	−	17.6698i	0.264469	−	0.579105i
$932$	−26.1047	+	38.6842i	−0.855087	+	1.26714i
$933$	81.5331	+	11.7227i	2.66927	+	0.383784i
$934$	38.6434	+	11.8189i	1.26445	+	0.386727i
$935$	−10.7948	−	0.910922i	−0.353026	−	0.0297903i
$936$	−7.84816	−	9.69792i	−0.256525	−	0.316986i
$937$	−0.610415	−	0.704457i	−0.0199414	−	0.0230136i	0.745691	−	0.666292i	$-0.232119\pi$
$937$	−0.610415	−	0.704457i	−0.0199414	−	0.0230136i	−0.765633	+	0.643278i	$0.777574\pi$
$938$	−0.140572	+	0.0186050i	−0.00458983	+	0.000607476i
$939$	−57.0230	+	65.8081i	−1.86088	+	2.14757i
$940$	6.46838	+	19.4026i	0.210975	+	0.632844i
$941$	−8.95480	+	4.08952i	−0.291918	+	0.133315i	−0.555991	−	0.831188i	$-0.687661\pi$
$941$	−8.95480	+	4.08952i	−0.291918	+	0.133315i	0.264073	+	0.964503i	$0.414934\pi$
$942$	40.4174	−	34.2360i	1.31687	−	1.11547i
$943$	4.31466	+	6.04626i	0.140505	+	0.196893i
$944$	−17.0253	+	49.6331i	−0.554128	+	1.61542i
$945$	0.0509631	−	0.0371433i	0.00165783	−	0.00120827i
$946$	−28.2413	−	18.6003i	−0.918205	−	0.604747i
$947$	18.5830	−	21.4459i	0.603866	−	0.696899i	−0.368694	−	0.929551i	$-0.620195\pi$
$947$	18.5830	−	21.4459i	0.603866	−	0.696899i	0.972560	+	0.232652i	$0.0747404\pi$
$948$	1.86393	−	2.05607i	0.0605377	−	0.0667782i
$949$	−2.55955	−	2.95387i	−0.0830864	−	0.0958868i
$950$	18.6120	+	6.21709i	0.603852	+	0.201709i
$951$	−4.47118	+	15.2274i	−0.144988	+	0.493783i
$952$	0.0373702	−	0.0750427i	0.00121117	−	0.00243215i
$953$	−3.05576	+	21.2533i	−0.0989857	+	0.688461i	0.878544	+	0.477662i	$0.158516\pi$
$953$	−3.05576	+	21.2533i	−0.0989857	+	0.688461i	−0.977529	+	0.210799i	$0.932394\pi$
$954$	−16.7138	−	59.3766i	−0.541128	−	1.92239i
$955$	2.24700	−	9.72869i	0.0727112	−	0.314813i
$956$	2.87011	−	9.02129i	0.0928261	−	0.291769i
$957$	−14.3794	+	9.24108i	−0.464820	+	0.298722i
$958$	−28.4272	+	12.5990i	−0.918440	+	0.407055i
$959$	−0.0760000	+	0.0109271i	−0.00245417	+	0.000352856i
$960$	42.8284	−	19.1127i	1.38228	−	0.616860i
$961$	21.8004	+	14.0103i	0.703239	+	0.451944i
$962$	−11.2464	−	0.126098i	−0.362598	−	0.00406556i
$963$	1.18298	+	4.02885i	0.0381209	+	0.129828i
$964$	5.54317	+	20.5741i	0.178534	+	0.662647i
$965$	−4.18669	−	20.5047i	−0.134774	−	0.660071i
$966$	−0.202416	−	0.0834430i	−0.00651264	−	0.00268473i
$967$	−24.4501			−0.786264			−0.393132	−	0.919482i	$-0.628608\pi$
$967$	−24.4501			−0.786264			−0.393132	+	0.919482i	$0.628608\pi$
$968$	11.1770	−	16.1691i	0.359242	−	0.519694i
$969$	−16.8046	+	4.93427i	−0.539841	+	0.158512i
$970$	8.26021	+	42.9038i	0.265219	+	1.37756i
$971$	−30.5341	−	19.6231i	−0.979885	−	0.629734i	−0.0504526	−	0.998726i	$-0.516066\pi$
$971$	−30.5341	−	19.6231i	−0.979885	−	0.629734i	−0.929432	+	0.368993i	$0.879703\pi$
$972$	36.8478	−	22.5295i	1.18189	−	0.722635i
$973$	0.0173203	+	0.120465i	0.000555262	+	0.00386193i
$974$	−16.9102	+	7.49466i	−0.541839	+	0.240144i
$975$	−12.3467	−	8.38842i	−0.395410	−	0.268645i
$976$	−35.8501	−	18.3573i	−1.14753	−	0.587602i
$977$	−9.80542	+	21.4709i	−0.313703	+	0.686914i	−0.999151	−	0.0412079i	$-0.986879\pi$
$977$	−9.80542	+	21.4709i	−0.313703	+	0.686914i	0.685447	+	0.728122i	$0.259607\pi$
$978$	21.2846	+	75.6148i	0.680607	+	2.41789i
$979$	−19.2473	−	2.76734i	−0.615145	−	0.0884445i
$980$	−17.8661	−	25.7052i	−0.570713	−	0.821123i
$981$	−0.0750814	+	0.255704i	−0.00239717	+	0.00816400i
$982$	−6.10325	+	6.88600i	−0.194763	+	0.219741i
$983$	−1.38225	+	1.19773i	−0.0440871	+	0.0382017i	−0.676626	−	0.736327i	$-0.736558\pi$
$983$	−1.38225	+	1.19773i	−0.0440871	+	0.0382017i	0.632539	+	0.774529i	$0.282013\pi$
$984$	−0.386239	+	11.4787i	−0.0123128	+	0.365929i
$985$	−45.0393	−	25.3462i	−1.43507	−	0.807597i
$986$	−6.06581	+	9.20989i	−0.193175	+	0.293303i
$987$	0.134290	−	0.0613282i	0.00427450	−	0.00195210i
$988$	−6.23380	−	1.03944i	−0.198324	−	0.0330691i
$989$	−5.35941	+	56.7272i	−0.170419	+	1.80382i
$990$	−15.2435	+	19.3758i	−0.484469	+	0.615802i
$991$	20.9297	−	9.55825i	0.664852	−	0.303628i	−0.0542547	−	0.998527i	$-0.517278\pi$
$991$	20.9297	−	9.55825i	0.664852	−	0.303628i	0.719107	+	0.694899i	$0.244551\pi$
$992$	−7.80085	−	10.0942i	−0.247677	−	0.320490i
$993$	−10.6438	−	9.22289i	−0.337770	−	0.292680i
$994$	0.100923	−	0.0133574i	0.00320107	−	0.000423670i
$995$	31.2537	+	24.0258i	0.990808	+	0.761670i
$996$	−0.132184	+	5.89384i	−0.00418840	+	0.186753i
$997$	11.8221	−	40.2623i	0.374409	−	1.27512i	−0.529834	−	0.848101i	$-0.677746\pi$
$997$	11.8221	−	40.2623i	0.374409	−	1.27512i	0.904243	−	0.427018i	$-0.140436\pi$
$998$	−11.3428	−	3.46915i	−0.359050	−	0.109814i
$999$	−2.27670	+	15.8348i	−0.0720317	+	0.500992i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.o.b.19.9	✓	640
4.3	odd	2	inner	460.2.o.b.19.26	yes	640
5.4	even	2	inner	460.2.o.b.19.56	yes	640
20.19	odd	2	inner	460.2.o.b.19.39	yes	640
23.17	odd	22	inner	460.2.o.b.339.39	yes	640
92.63	even	22	inner	460.2.o.b.339.56	yes	640
115.109	odd	22	inner	460.2.o.b.339.26	yes	640
460.339	even	22	inner	460.2.o.b.339.9	yes	640

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.o.b.19.9	✓	640	1.1	even	1	trivial
460.2.o.b.19.26	yes	640	4.3	odd	2	inner
460.2.o.b.19.39	yes	640	20.19	odd	2	inner
460.2.o.b.19.56	yes	640	5.4	even	2	inner
460.2.o.b.339.9	yes	640	460.339	even	22	inner
460.2.o.b.339.26	yes	640	115.109	odd	22	inner
460.2.o.b.339.39	yes	640	23.17	odd	22	inner
460.2.o.b.339.56	yes	640	92.63	even	22	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.o (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.27975 - 0.601871i) q^{2} +(-2.51556 + 0.738636i) q^{3} +(1.27550 + 1.54049i) q^{4} +(2.08492 + 0.808149i) q^{5} +(3.66385 + 0.568779i) q^{6} +(-0.0121874 + 0.00175228i) q^{7} +(-0.705145 - 2.73912i) q^{8} +(3.25872 - 2.09425i) q^{9} +O(q^{10})\)	\(q+(-1.27975 - 0.601871i) q^{2} +(-2.51556 + 0.738636i) q^{3} +(1.27550 + 1.54049i) q^{4} +(2.08492 + 0.808149i) q^{5} +(3.66385 + 0.568779i) q^{6} +(-0.0121874 + 0.00175228i) q^{7} +(-0.705145 - 2.73912i) q^{8} +(3.25872 - 2.09425i) q^{9} +(-2.18177 - 2.28908i) q^{10} +(0.836058 - 1.83071i) q^{11} +(-4.34647 - 2.93306i) q^{12} +(1.12708 + 0.162050i) q^{13} +(0.0166514 + 0.00509277i) q^{14} +(-5.84168 - 0.492954i) q^{15} +(-0.746191 + 3.92978i) q^{16} +(-1.57639 - 1.81925i) q^{17} +(-5.43081 + 0.718782i) q^{18} +(-1.81730 + 2.09728i) q^{19} +(1.41438 + 4.24259i) q^{20} +(0.0293639 - 0.0134100i) q^{21} +(-2.17179 + 1.83965i) q^{22} +(4.45408 + 1.77797i) q^{23} +(3.79705 + 6.36958i) q^{24} +(3.69379 + 3.36985i) q^{25} +(-1.34485 - 0.885744i) q^{26} +(-1.49996 + 1.73105i) q^{27} +(-0.0182444 - 0.0165395i) q^{28} +(2.12136 + 2.44818i) q^{29} +(7.17918 + 4.14680i) q^{30} +(0.635355 - 2.16382i) q^{31} +(3.32016 - 4.58002i) q^{32} +(-0.750927 + 5.22282i) q^{33} +(0.922424 + 3.27696i) q^{34} +(-0.0268259 - 0.00619587i) q^{35} +(7.38267 + 2.34879i) q^{36} +(5.87561 - 3.77602i) q^{37} +(3.58798 - 1.59020i) q^{38} +(-2.95495 + 0.424858i) q^{39} +(0.743446 - 6.28071i) q^{40} +(1.30295 + 0.837356i) q^{41} +(-0.0456495 - 0.000511836i) q^{42} +(3.34730 + 11.3998i) q^{43} +(3.88658 - 1.04714i) q^{44} +(8.48664 - 1.73282i) q^{45} +(-4.62999 - 4.95613i) q^{46} +4.57330 q^{47} +(-1.02559 - 10.4368i) q^{48} +(-6.71631 + 1.97209i) q^{49} +(-2.69889 - 6.53575i) q^{50} +(5.30927 + 3.41206i) q^{51} +(1.18796 + 1.94295i) q^{52} +(1.60246 + 11.1454i) q^{53} +(2.96144 - 1.31252i) q^{54} +(3.22260 - 3.14123i) q^{55} +(0.0133936 + 0.0321471i) q^{56} +(3.02241 - 6.61816i) q^{57} +(-1.24132 - 4.40984i) q^{58} +(12.9845 + 1.86689i) q^{59} +(-6.69169 - 9.62779i) q^{60} +(-2.83682 + 9.66133i) q^{61} +(-2.11543 + 2.38674i) q^{62} +(-0.0360456 + 0.0312337i) q^{63} +(-7.00554 + 3.86295i) q^{64} +(2.21892 + 1.24872i) q^{65} +(4.10446 - 6.23192i) q^{66} +(-7.40739 + 3.38284i) q^{67} +(0.791841 - 4.74886i) q^{68} +(-12.5178 - 1.18264i) q^{69} +(0.0306012 + 0.0240749i) q^{70} +(5.31808 - 2.42869i) q^{71} +(-8.03428 - 7.44927i) q^{72} +(-2.59413 - 2.24783i) q^{73} +(-9.79197 + 1.29599i) q^{74} +(-11.7811 - 5.74872i) q^{75} +(-5.54880 - 0.124445i) q^{76} +(-0.00698145 + 0.0237766i) q^{77} +(4.03730 + 1.23479i) q^{78} +(-0.0753216 + 0.523873i) q^{79} +(-4.73160 + 7.59025i) q^{80} +(-2.33288 + 5.10830i) q^{81} +(-1.16347 - 1.85581i) q^{82} +(-0.607844 - 0.945824i) q^{83} +(0.0581117 + 0.0281301i) q^{84} +(-1.81642 - 5.06695i) q^{85} +(2.57755 - 16.6036i) q^{86} +(-7.14475 - 4.59165i) q^{87} +(-5.60408 - 0.999145i) q^{88} +(-2.72204 - 9.27042i) q^{89} +(-11.9037 - 2.89030i) q^{90} -0.0140202 q^{91} +(2.94226 + 9.12925i) q^{92} +5.91252i q^{93} +(-5.85267 - 2.75254i) q^{94} +(-5.48384 + 2.90401i) q^{95} +(-4.96911 + 13.9737i) q^{96} +(-11.6232 - 7.46978i) q^{97} +(9.78211 + 1.51858i) q^{98} +(-1.10949 - 7.71669i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 640 q - 6 q^{4} - 22 q^{5} + 2 q^{6} - 100 q^{9}+O(q^{10}) \) 640 * q - 6 * q^4 - 22 * q^5 + 2 * q^6 - 100 * q^9	\( 640 q - 6 q^{4} - 22 q^{5} + 2 q^{6} - 100 q^{9} - 11 q^{10} - 22 q^{14} + 2 q^{16} - 11 q^{20} - 44 q^{21} - 8 q^{24} - 38 q^{25} - 46 q^{26} - 52 q^{29} - 11 q^{30} - 44 q^{34} + 18 q^{36} - 11 q^{40} - 76 q^{41} - 154 q^{44} - 30 q^{46} - 100 q^{49} + 21 q^{50} + 178 q^{54} + 242 q^{56} - 11 q^{60} - 44 q^{61} + 6 q^{64} - 22 q^{65} + 44 q^{66} - 12 q^{69} + 22 q^{70} - 22 q^{74} + 88 q^{76} - 110 q^{80} - 252 q^{81} - 374 q^{84} + 94 q^{85} - 198 q^{86} - 44 q^{89} - 242 q^{90} - 62 q^{94} + 372 q^{96}+O(q^{100}) \) 640 * q - 6 * q^4 - 22 * q^5 + 2 * q^6 - 100 * q^9 - 11 * q^10 - 22 * q^14 + 2 * q^16 - 11 * q^20 - 44 * q^21 - 8 * q^24 - 38 * q^25 - 46 * q^26 - 52 * q^29 - 11 * q^30 - 44 * q^34 + 18 * q^36 - 11 * q^40 - 76 * q^41 - 154 * q^44 - 30 * q^46 - 100 * q^49 + 21 * q^50 + 178 * q^54 + 242 * q^56 - 11 * q^60 - 44 * q^61 + 6 * q^64 - 22 * q^65 + 44 * q^66 - 12 * q^69 + 22 * q^70 - 22 * q^74 + 88 * q^76 - 110 * q^80 - 252 * q^81 - 374 * q^84 + 94 * q^85 - 198 * q^86 - 44 * q^89 - 242 * q^90 - 62 * q^94 + 372 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more