LMFDB - Embedded newform 414.2.p.a.5.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [414,2,Mod(5,414)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(414, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([55, 3]))

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

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

chi := DirichletCharacter("414.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 414 = 2 \cdot 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	414.p (of order $66$, degree $20$, 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:	$3.30580664368$
Analytic rank:	$0$
Dimension:	$480$
Relative dimension:	$24$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			5.2
Character	$\chi$	$=$	414.5
Dual form			414.2.p.a.83.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.971812 + 0.235759i) q^{2} +(-1.53348 - 0.805250i) q^{3} +(0.888835 - 0.458227i) q^{4} +(-2.29731 - 1.80663i) q^{5} +(1.68010 + 0.421018i) q^{6} +(-1.55923 - 1.11032i) q^{7} +(-0.755750 + 0.654861i) q^{8} +(1.70315 + 2.46967i) q^{9} +O(q^{10})$	\(q+(-0.971812 + 0.235759i) q^{2} +(-1.53348 - 0.805250i) q^{3} +(0.888835 - 0.458227i) q^{4} +(-2.29731 - 1.80663i) q^{5} +(1.68010 + 0.421018i) q^{6} +(-1.55923 - 1.11032i) q^{7} +(-0.755750 + 0.654861i) q^{8} +(1.70315 + 2.46967i) q^{9} +(2.65848 + 1.21409i) q^{10} +(-3.80440 - 3.62748i) q^{11} +(-1.73200 - 0.0130514i) q^{12} +(2.22667 + 3.12692i) q^{13} +(1.77704 + 0.711421i) q^{14} +(2.06811 + 4.62034i) q^{15} +(0.580057 - 0.814576i) q^{16} +(2.98061 - 1.91552i) q^{17} +(-2.23738 - 1.99853i) q^{18} +(-3.40935 + 5.30505i) q^{19} +(-2.86978 - 0.553104i) q^{20} +(1.49697 + 2.95823i) q^{21} +(4.55237 + 2.62831i) q^{22} +(4.58640 + 1.40176i) q^{23} +(1.68626 - 0.395651i) q^{24} +(0.834951 + 3.44172i) q^{25} +(-2.90110 - 2.51382i) q^{26} +(-0.623042 - 5.15866i) q^{27} +(-1.89468 - 0.272413i) q^{28} +(-4.24570 + 8.23550i) q^{29} +(-3.09910 - 4.00253i) q^{30} +(2.08951 - 0.402720i) q^{31} +(-0.371662 + 0.928368i) q^{32} +(2.91295 + 8.62618i) q^{33} +(-2.44499 + 2.56423i) q^{34} +(1.57610 + 5.36770i) q^{35} +(2.64549 + 1.41471i) q^{36} +(2.38003 - 0.342197i) q^{37} +(2.06253 - 5.95930i) q^{38} +(-0.896611 - 6.58811i) q^{39} +(2.91928 - 0.139063i) q^{40} +(-4.87371 + 6.19742i) q^{41} +(-2.15220 - 2.52192i) q^{42} +(-1.18798 + 6.16381i) q^{43} +(-5.04369 - 1.48096i) q^{44} +(0.549121 - 8.75056i) q^{45} +(-4.78759 - 0.280957i) q^{46} +(-2.26865 + 1.30981i) q^{47} +(-1.54544 + 0.782049i) q^{48} +(-1.09110 - 3.15252i) q^{49} +(-1.62283 - 3.14785i) q^{50} +(-6.11319 + 0.537286i) q^{51} +(3.41198 + 1.75900i) q^{52} +(-0.0652286 - 0.142831i) q^{53} +(1.82168 + 4.86636i) q^{54} +(2.18638 + 15.2066i) q^{55} +(1.90549 - 0.181952i) q^{56} +(9.50007 - 5.38983i) q^{57} +(2.18442 - 9.00431i) q^{58} +(-4.50084 + 3.20503i) q^{59} +(3.95537 + 3.15906i) q^{60} +(-2.59949 - 0.899693i) q^{61} +(-1.93566 + 0.883988i) q^{62} +(0.0865394 - 5.74183i) q^{63} +(0.142315 - 0.989821i) q^{64} +(0.533821 - 11.2063i) q^{65} +(-4.86454 - 7.69627i) q^{66} +(-0.359054 - 0.376565i) q^{67} +(1.77153 - 3.06838i) q^{68} +(-5.90441 - 5.84277i) q^{69} +(-2.79715 - 4.84481i) q^{70} +(3.32190 - 11.3133i) q^{71} +(-2.90444 - 0.751132i) q^{72} +(13.9071 + 8.93755i) q^{73} +(-2.23227 + 0.893664i) q^{74} +(1.49106 - 5.95016i) q^{75} +(-0.599436 + 6.27757i) q^{76} +(1.90425 + 9.88018i) q^{77} +(2.42454 + 6.19102i) q^{78} +(-0.676914 - 7.08896i) q^{79} +(-2.80421 + 0.823389i) q^{80} +(-3.19859 + 8.41243i) q^{81} +(3.27523 - 7.17175i) q^{82} +(-1.18934 + 0.935307i) q^{83} +(2.68609 + 1.94343i) q^{84} +(-10.3080 - 0.984296i) q^{85} +(-0.298684 - 6.27014i) q^{86} +(13.1423 - 9.21016i) q^{87} +(5.25067 + 0.250120i) q^{88} +(-6.59187 + 7.60742i) q^{89} +(1.52938 + 8.63336i) q^{90} -7.34790i q^{91} +(4.71888 - 0.855681i) q^{92} +(-3.52852 - 1.06501i) q^{93} +(1.89590 - 1.80774i) q^{94} +(17.4166 - 6.02794i) q^{95} +(1.31751 - 1.12436i) q^{96} +(-0.863748 - 2.15754i) q^{97} +(1.80357 + 2.80642i) q^{98} +(2.47926 - 15.5738i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 480 q - 4 q^{3} - 24 q^{4} + 8 q^{6}+O(q^{10}) $ 480 * q - 4 * q^3 - 24 * q^4 + 8 * q^6	$ 480 q - 4 q^{3} - 24 q^{4} + 8 q^{6} + 4 q^{12} - 44 q^{15} + 24 q^{16} + 28 q^{18} + 66 q^{21} + 6 q^{23} + 4 q^{24} + 12 q^{25} + 86 q^{27} - 48 q^{29} + 44 q^{30} - 12 q^{31} - 44 q^{33} + 24 q^{39} - 60 q^{41} + 12 q^{46} + 48 q^{47} + 8 q^{48} - 78 q^{49} + 24 q^{50} - 30 q^{54} - 24 q^{55} - 66 q^{56} - 66 q^{57} - 72 q^{59} - 22 q^{60} - 110 q^{63} + 48 q^{64} - 462 q^{65} - 88 q^{66} - 70 q^{69} + 12 q^{70} - 52 q^{72} - 264 q^{74} - 76 q^{75} - 12 q^{77} - 58 q^{78} - 96 q^{81} - 198 q^{83} - 22 q^{84} + 178 q^{87} + 6 q^{92} - 20 q^{93} - 12 q^{94} + 12 q^{95} - 4 q^{96} - 66 q^{97} - 132 q^{99}+O(q^{100}) $ 480 * q - 4 * q^3 - 24 * q^4 + 8 * q^6 + 4 * q^12 - 44 * q^15 + 24 * q^16 + 28 * q^18 + 66 * q^21 + 6 * q^23 + 4 * q^24 + 12 * q^25 + 86 * q^27 - 48 * q^29 + 44 * q^30 - 12 * q^31 - 44 * q^33 + 24 * q^39 - 60 * q^41 + 12 * q^46 + 48 * q^47 + 8 * q^48 - 78 * q^49 + 24 * q^50 - 30 * q^54 - 24 * q^55 - 66 * q^56 - 66 * q^57 - 72 * q^59 - 22 * q^60 - 110 * q^63 + 48 * q^64 - 462 * q^65 - 88 * q^66 - 70 * q^69 + 12 * q^70 - 52 * q^72 - 264 * q^74 - 76 * q^75 - 12 * q^77 - 58 * q^78 - 96 * q^81 - 198 * q^83 - 22 * q^84 + 178 * q^87 + 6 * q^92 - 20 * q^93 - 12 * q^94 + 12 * q^95 - 4 * q^96 - 66 * q^97 - 132 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/414\mathbb{Z}\right)^\times$.

$n$	$47$	$235$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{22}\right)$

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 $

$2$	−0.971812	+	0.235759i	−0.687175	+	0.166707i
$2$	−0.971812	+	0.235759i	−0.687175	+	0.166707i
$3$	−1.53348	−	0.805250i	−0.885357	−	0.464911i
$3$	−1.53348	−	0.805250i	−0.885357	−	0.464911i
$4$	0.888835	−	0.458227i	0.444418	−	0.229113i
$5$	−2.29731	−	1.80663i	−1.02739	−	0.807948i	−0.0458000	−	0.998951i	$-0.514584\pi$
$5$	−2.29731	−	1.80663i	−1.02739	−	0.807948i	−0.981590	+	0.191003i	$0.938826\pi$
$6$	1.68010	+	0.421018i	0.685899	+	0.171880i
$7$	−1.55923	−	1.11032i	−0.589333	−	0.419662i	0.246108	−	0.969242i	$-0.420848\pi$
$7$	−1.55923	−	1.11032i	−0.589333	−	0.419662i	−0.835441	+	0.549580i	$0.814788\pi$
$8$	−0.755750	+	0.654861i	−0.267198	+	0.231528i
$9$	1.70315	+	2.46967i	0.567715	+	0.823225i
$10$	2.65848	+	1.21409i	0.840686	+	0.383929i
$11$	−3.80440	−	3.62748i	−1.14707	−	1.09373i	−0.994425	−	0.105446i	$-0.966373\pi$
$11$	−3.80440	−	3.62748i	−1.14707	−	1.09373i	−0.152644	−	0.988281i	$-0.548779\pi$
$12$	−1.73200	−	0.0130514i	−0.499986	−	0.00376762i
$13$	2.22667	+	3.12692i	0.617567	+	0.867252i	0.998351	−	0.0574125i	$-0.0182850\pi$
$13$	2.22667	+	3.12692i	0.617567	+	0.867252i	−0.380783	+	0.924664i	$0.624346\pi$
$14$	1.77704	+	0.711421i	0.474935	+	0.190135i
$15$	2.06811	+	4.62034i	0.533983	+	1.19297i
$16$	0.580057	−	0.814576i	0.145014	−	0.203644i
$17$	2.98061	−	1.91552i	0.722903	−	0.464582i	−0.126742	−	0.991936i	$-0.540452\pi$
$17$	2.98061	−	1.91552i	0.722903	−	0.464582i	0.849646	+	0.527354i	$0.176816\pi$
$18$	−2.23738	−	1.99853i	−0.527357	−	0.471057i
$19$	−3.40935	+	5.30505i	−0.782158	+	1.21706i	0.189780	+	0.981827i	$0.439223\pi$
$19$	−3.40935	+	5.30505i	−0.782158	+	1.21706i	−0.971938	+	0.235236i	$0.924414\pi$
$20$	−2.86978	−	0.553104i	−0.641702	−	0.123678i
$21$	1.49697	+	2.95823i	0.326665	+	0.645538i
$22$	4.55237	+	2.62831i	0.970568	+	0.560358i
$23$	4.58640	+	1.40176i	0.956331	+	0.292286i
$23$	4.58640	+	1.40176i	0.956331	+	0.292286i
$24$	1.68626	−	0.395651i	0.344206	−	0.0807620i
$25$	0.834951	+	3.44172i	0.166990	+	0.688343i
$26$	−2.90110	−	2.51382i	−0.568953	−	0.493001i
$27$	−0.623042	−	5.15866i	−0.119905	−	0.992785i
$28$	−1.89468	−	0.272413i	−0.358060	−	0.0514813i
$29$	−4.24570	+	8.23550i	−0.788406	+	1.52929i	0.0589455	+	0.998261i	$0.481226\pi$
$29$	−4.24570	+	8.23550i	−0.788406	+	1.52929i	−0.847351	+	0.531033i	$0.821804\pi$
$30$	−3.09910	−	4.00253i	−0.565815	−	0.730758i
$31$	2.08951	−	0.402720i	0.375287	−	0.0723306i	0.00187974	−	0.999998i	$-0.499402\pi$
$31$	2.08951	−	0.402720i	0.375287	−	0.0723306i	0.373407	+	0.927668i	$0.378190\pi$
$32$	−0.371662	+	0.928368i	−0.0657013	+	0.164114i
$33$	2.91295	+	8.62618i	0.507079	+	1.50162i
$34$	−2.44499	+	2.56423i	−0.419312	+	0.439762i
$35$	1.57610	+	5.36770i	0.266409	+	0.907307i
$36$	2.64549	+	1.41471i	0.440915	+	0.235785i
$37$	2.38003	−	0.342197i	0.391275	−	0.0562568i	0.0561299	−	0.998423i	$-0.482124\pi$
$37$	2.38003	−	0.342197i	0.391275	−	0.0562568i	0.335145	+	0.942167i	$0.391215\pi$
$38$	2.06253	−	5.95930i	0.334587	−	0.966725i
$39$	−0.896611	−	6.58811i	−0.143573	−	1.05494i
$40$	2.91928	−	0.139063i	0.461579	−	0.0219877i
$41$	−4.87371	+	6.19742i	−0.761145	+	0.967875i	−0.999995	−	0.00318193i	$-0.998987\pi$
$41$	−4.87371	+	6.19742i	−0.761145	+	0.967875i	0.238850	+	0.971056i	$0.423230\pi$
$42$	−2.15220	−	2.52192i	−0.332091	−	0.389140i
$43$	−1.18798	+	6.16381i	−0.181165	+	0.939973i	0.771564	+	0.636151i	$0.219475\pi$
$43$	−1.18798	+	6.16381i	−0.181165	+	0.939973i	−0.952729	+	0.303821i	$0.901737\pi$
$44$	−5.04369	−	1.48096i	−0.760365	−	0.223263i
$45$	0.549121	−	8.75056i	0.0818582	−	1.30446i
$46$	−4.78759	−	0.280957i	−0.705892	−	0.0414248i
$47$	−2.26865	+	1.30981i	−0.330917	+	0.191055i	−0.656248	−	0.754545i	$-0.727858\pi$
$47$	−2.26865	+	1.30981i	−0.330917	+	0.191055i	0.325331	+	0.945600i	$0.394524\pi$
$48$	−1.54544	+	0.782049i	−0.223066	+	0.112879i
$49$	−1.09110	−	3.15252i	−0.155871	−	0.450360i
$50$	−1.62283	−	3.14785i	−0.229503	−	0.445174i
$51$	−6.11319	+	0.537286i	−0.856017	+	0.0752351i
$52$	3.41198	+	1.75900i	0.473157	+	0.243929i
$53$	−0.0652286	−	0.142831i	−0.00895984	−	0.0196193i	0.905099	−	0.425201i	$-0.139796\pi$
$53$	−0.0652286	−	0.142831i	−0.00895984	−	0.0196193i	−0.914059	+	0.405581i	$0.867069\pi$
$54$	1.82168	+	4.86636i	0.247899	+	0.662228i
$55$	2.18638	+	15.2066i	0.294811	+	2.05046i
$56$	1.90549	−	0.181952i	0.254632	−	0.0243144i
$57$	9.50007	−	5.38983i	1.25832	−	0.713901i
$58$	2.18442	−	9.00431i	0.286829	−	1.18232i
$59$	−4.50084	+	3.20503i	−0.585959	+	0.417260i	−0.834218	−	0.551434i	$-0.814081\pi$
$59$	−4.50084	+	3.20503i	−0.585959	+	0.417260i	0.248259	+	0.968694i	$0.420141\pi$
$60$	3.95537	+	3.15906i	0.510636	+	0.407833i
$61$	−2.59949	−	0.899693i	−0.332831	−	0.115194i	0.155541	−	0.987829i	$-0.450288\pi$
$61$	−2.59949	−	0.899693i	−0.332831	−	0.115194i	−0.488372	+	0.872635i	$0.662409\pi$
$62$	−1.93566	+	0.883988i	−0.245829	+	0.112267i
$63$	0.0865394	−	5.74183i	0.0109029	−	0.723402i
$64$	0.142315	−	0.989821i	0.0177894	−	0.123728i
$65$	0.533821	−	11.2063i	0.0662123	−	1.38997i
$66$	−4.86454	−	7.69627i	−0.598783	−	0.947345i
$67$	−0.359054	−	0.376565i	−0.0438655	−	0.0460048i	0.701436	−	0.712733i	$-0.252543\pi$
$67$	−0.359054	−	0.376565i	−0.0438655	−	0.0460048i	−0.745301	+	0.666728i	$0.767694\pi$
$68$	1.77153	−	3.06838i	0.214829	−	0.372095i
$69$	−5.90441	−	5.84277i	−0.710807	−	0.703387i
$70$	−2.79715	−	4.84481i	−0.334324	−	0.579066i
$71$	3.32190	−	11.3133i	0.394237	−	1.34265i	−0.488412	−	0.872613i	$-0.662424\pi$
$71$	3.32190	−	11.3133i	0.394237	−	1.34265i	0.882649	−	0.470033i	$-0.155758\pi$
$72$	−2.90444	−	0.751132i	−0.342292	−	0.0885218i
$73$	13.9071	+	8.93755i	1.62770	+	1.04606i	0.950714	+	0.310068i	$0.100352\pi$
$73$	13.9071	+	8.93755i	1.62770	+	1.04606i	0.676989	+	0.735993i	$0.263284\pi$
$74$	−2.23227	+	0.893664i	−0.259496	+	0.103886i
$75$	1.49106	−	5.95016i	0.172172	−	0.687065i
$76$	−0.599436	+	6.27757i	−0.0687600	+	0.720087i
$77$	1.90425	+	9.88018i	0.217009	+	1.12595i
$78$	2.42454	+	6.19102i	0.274525	+	0.700994i
$79$	−0.676914	−	7.08896i	−0.0761588	−	0.797571i	−0.950184	−	0.311690i	$-0.899105\pi$
$79$	−0.676914	−	7.08896i	−0.0761588	−	0.797571i	0.874025	−	0.485881i	$-0.161501\pi$
$80$	−2.80421	+	0.823389i	−0.313520	+	0.0920577i
$81$	−3.19859	+	8.41243i	−0.355399	+	0.934715i
$82$	3.27523	−	7.17175i	0.361688	−	0.791987i
$83$	−1.18934	+	0.935307i	−0.130547	+	0.102663i	−0.681298	−	0.732007i	$-0.738584\pi$
$83$	−1.18934	+	0.935307i	−0.130547	+	0.102663i	0.550751	+	0.834670i	$0.314342\pi$
$84$	2.68609	+	1.94343i	0.293077	+	0.212045i
$85$	−10.3080	−	0.984296i	−1.11806	−	0.106762i
$86$	−0.298684	−	6.27014i	−0.0322079	−	0.676127i
$87$	13.1423	−	9.21016i	1.40901	−	0.987433i
$88$	5.25067	+	0.250120i	0.559723	+	0.0266629i
$89$	−6.59187	+	7.60742i	−0.698737	+	0.806385i	−0.988581	−	0.150689i	$-0.951851\pi$
$89$	−6.59187	+	7.60742i	−0.698737	+	0.806385i	0.289845	+	0.957074i	$0.406396\pi$
$90$	1.52938	+	8.63336i	0.161211	+	0.910036i
$91$		−	7.34790i		−	0.770269i
$92$	4.71888	−	0.855681i	0.491977	−	0.0892109i
$93$	−3.52852	−	1.06501i	−0.365890	−	0.110437i
$94$	1.89590	−	1.80774i	0.195548	−	0.186454i
$95$	17.4166	−	6.02794i	1.78690	−	0.618454i
$96$	1.31751	−	1.12436i	0.134467	−	0.114754i
$97$	−0.863748	−	2.15754i	−0.0877003	−	0.219065i	0.878034	−	0.478599i	$-0.158855\pi$
$97$	−0.863748	−	2.15754i	−0.0877003	−	0.219065i	−0.965734	+	0.259534i	$0.916431\pi$
$98$	1.80357	+	2.80642i	0.182189	+	0.283491i
$99$	2.47926	−	15.5738i	0.249175	−	1.56522i
$100$	2.31922	+	2.67652i	0.231922	+	0.267652i
$101$	1.85482	+	2.35860i	0.184562	+	0.234689i	0.869526	−	0.493888i	$-0.164425\pi$
$101$	1.85482	+	2.35860i	0.184562	+	0.234689i	−0.684964	+	0.728577i	$0.740182\pi$
$102$	5.81419	−	1.96338i	0.575691	−	0.194403i
$103$	−14.2690	−	3.46161i	−1.40596	−	0.341083i	−0.540200	−	0.841537i	$-0.681651\pi$
$103$	−14.2690	−	3.46161i	−1.40596	−	0.341083i	−0.865763	+	0.500454i	$0.833167\pi$
$104$	−3.73050	−	0.905010i	−0.365806	−	0.0887435i
$105$	1.90542	−	9.50043i	0.185950	−	0.927147i
$106$	0.0970636	+	0.123426i	0.00942765	+	0.0119882i
$107$	−5.46710	−	6.30937i	−0.528525	−	0.609950i	0.427220	−	0.904148i	$-0.359493\pi$
$107$	−5.46710	−	6.30937i	−0.528525	−	0.609950i	−0.955745	+	0.294198i	$0.904948\pi$
$108$	−2.91762	−	4.29971i	−0.280748	−	0.413740i
$109$	−8.07194	−	12.5602i	−0.773151	−	1.20305i	−0.974689	−	0.223566i	$-0.928230\pi$
$109$	−8.07194	−	12.5602i	−0.773151	−	1.20305i	0.201537	−	0.979481i	$-0.435406\pi$
$110$	−5.70984	−	14.2625i	−0.544412	−	1.35987i
$111$	−3.92529	−	1.39177i	−0.372572	−	0.132101i
$112$	−1.80888	+	0.626060i	−0.170923	+	0.0591571i
$113$	11.1858	−	10.6657i	1.05227	−	1.00334i	0.0522842	−	0.998632i	$-0.483350\pi$
$113$	11.1858	−	10.6657i	1.05227	−	1.00334i	0.999989	−	0.00470816i	$-0.00149866\pi$
$114$	−7.96158	+	7.47763i	−0.745670	+	0.700344i
$115$	−8.00395	−	11.5062i	−0.746372	−	1.07296i
$116$			9.26549i			0.860280i
$117$	−3.93013	+	10.8248i	−0.363341	+	1.00075i
$118$	3.61835	−	4.17580i	0.333096	−	0.384413i
$119$	−6.77429	−	0.322699i	−0.620998	−	0.0295818i
$120$	−4.58865	−	2.13750i	−0.418885	−	0.195126i
$121$	0.791386	+	16.6132i	0.0719442	+	1.51029i
$122$	2.73833	+	0.261479i	0.247917	+	0.0236732i
$123$	12.4642	−	5.57910i	1.12386	−	0.503050i
$124$	1.67269	−	1.31542i	0.150212	−	0.118128i
$125$	−1.77069	+	3.87727i	−0.158375	+	0.346794i
$126$	1.26959	+	5.60037i	0.113104	+	0.498921i
$127$	−7.20314	+	2.11503i	−0.639175	+	0.187679i	−0.585233	−	0.810865i	$-0.698997\pi$
$127$	−7.20314	+	2.11503i	−0.639175	+	0.187679i	−0.0539423	+	0.998544i	$0.517179\pi$
$128$	0.0950560	+	0.995472i	0.00840185	+	0.0879881i
$129$	6.78515	−	8.49549i	0.597399	−	0.747986i
$130$	2.12321	+	11.0162i	0.186218	+	0.966188i
$131$	−1.84723	+	19.3451i	−0.161393	+	1.69019i	0.445405	+	0.895329i	$0.353060\pi$
$131$	−1.84723	+	19.3451i	−0.161393	+	1.69019i	−0.606798	+	0.794856i	$0.707546\pi$
$132$	6.54188	+	6.33246i	0.569397	+	0.551170i
$133$	11.2063	−	4.48631i	0.971706	−	0.389013i
$134$	0.437712	+	0.281300i	0.0378125	+	0.0243006i
$135$	−7.88846	+	12.9767i	−0.678930	+	1.11685i
$136$	−0.998194	+	3.39954i	−0.0855944	+	0.291508i
$137$	5.31197	+	9.20060i	0.453832	+	0.786060i	0.998620	−	0.0525133i	$-0.0167232\pi$
$137$	5.31197	+	9.20060i	0.453832	+	0.786060i	−0.544788	+	0.838574i	$0.683390\pi$
$138$	7.11546	+	4.28605i	0.605708	+	0.364853i
$139$	0.566521	−	0.981243i	0.0480517	−	0.0832279i	−0.840999	−	0.541036i	$-0.818032\pi$
$139$	0.566521	−	0.981243i	0.0480517	−	0.0832279i	0.889051	+	0.457808i	$0.151365\pi$
$140$	3.86051	+	4.04879i	0.326273	+	0.342185i
$141$	4.53366	−	0.181737i	0.381803	−	0.0153050i
$142$	−0.561036	+	11.7776i	−0.0470811	+	0.988354i
$143$	2.87172	−	19.9733i	0.240145	−	1.67025i
$144$	2.99966	+	0.0452101i	0.249972	+	0.00376751i
$145$	24.6322	−	11.2491i	2.04559	−	0.934190i
$146$	−15.6222	−	5.40689i	−1.29290	−	0.447478i
$147$	−0.865384	+	5.71294i	−0.0713757	+	0.471195i
$148$	1.95865	−	1.39475i	0.161000	−	0.114648i
$149$	−4.18720	+	17.2599i	−0.343029	+	1.41399i	0.495253	+	0.868749i	$0.335075\pi$
$149$	−4.18720	+	17.2599i	−0.343029	+	1.41399i	−0.838282	+	0.545236i	$0.816440\pi$
$150$	−0.0462222	+	6.13396i	−0.00377403	+	0.500836i
$151$	−17.7356	+	1.69354i	−1.44330	+	0.137818i	−0.787126	−	0.616792i	$-0.788432\pi$
$151$	−17.7356	+	1.69354i	−1.44330	+	0.137818i	−0.656173	+	0.754610i	$0.727826\pi$
$152$	−0.897455	−	6.24194i	−0.0727933	−	0.506288i
$153$	9.80712	+	4.09872i	0.792859	+	0.331362i
$154$	−4.17991	−	9.15273i	−0.336827	−	0.737548i
$155$	−5.52782	−	2.84979i	−0.444005	−	0.228900i
$156$	−3.81579	−	5.44489i	−0.305507	−	0.435940i
$157$	4.52296	+	8.77333i	0.360972	+	0.700188i	0.997470	−	0.0710906i	$-0.0226479\pi$
$157$	4.52296	+	8.77333i	0.360972	+	0.700188i	−0.636498	+	0.771278i	$0.719618\pi$
$158$	2.32912	+	6.72955i	0.185295	+	0.535374i
$159$	−0.0149874	+	0.271554i	−0.00118858	+	0.0215356i
$160$	2.53104	−	1.46130i	0.200096	−	0.115526i
$161$	−5.59485	−	7.27804i	−0.440936	−	0.573590i
$162$	1.12512	−	8.92940i	0.0883976	−	0.701560i
$163$	7.61775	+	2.23677i	0.596668	+	0.175198i	0.566102	−	0.824335i	$-0.308451\pi$
$163$	7.61775	+	2.23677i	0.596668	+	0.175198i	0.0305662	+	0.999533i	$0.490269\pi$
$164$	−1.49210	+	7.74175i	−0.116513	+	0.604529i
$165$	8.89233	−	25.0796i	0.692267	−	1.95245i
$166$	0.935307	−	1.18934i	0.0725939	−	0.0923107i
$167$	−13.8884	+	0.661587i	−1.07472	+	0.0511951i	−0.577469	−	0.816413i	$-0.695960\pi$
$167$	−13.8884	+	0.661587i	−1.07472	+	0.0511951i	−0.497249	+	0.867608i	$0.665657\pi$
$168$	−3.06856	−	1.25538i	−0.236744	−	0.0968543i
$169$	−0.567690	+	1.64023i	−0.0436684	+	0.126172i
$170$	10.2495	−	1.47366i	0.786101	−	0.113024i
$171$	−18.9084	+	0.615293i	−1.44596	+	0.0470526i
$172$	1.76851	+	6.02298i	0.134847	+	0.459248i
$173$	−15.7443	+	16.5122i	−1.19702	+	1.25540i	−0.238254	+	0.971203i	$0.576575\pi$
$173$	−15.7443	+	16.5122i	−1.19702	+	1.25540i	−0.958766	+	0.284196i	$0.908273\pi$
$174$	−10.6005	+	12.0490i	−0.803622	+	0.913430i
$175$	2.51953	−	6.29348i	0.190459	−	0.475743i
$176$	−5.16163	+	0.994822i	−0.389072	+	0.0749875i
$177$	9.48281	−	1.29057i	0.712772	−	0.0970049i
$178$	4.61254	−	8.94707i	0.345724	−	0.670611i
$179$	19.5594	+	2.81222i	1.46194	+	0.210195i	0.826928	−	0.562308i	$-0.190087\pi$
$179$	19.5594	+	2.81222i	1.46194	+	0.210195i	0.635011	+	0.772503i	$0.280996\pi$
$180$	−3.52166	−	8.02943i	−0.262489	−	0.598479i
$181$	3.25449	+	2.82003i	0.241905	+	0.209612i	0.767372	−	0.641202i	$-0.221564\pi$
$181$	3.25449	+	2.82003i	0.241905	+	0.209612i	−0.525467	+	0.850814i	$0.676109\pi$
$182$	1.73233	+	7.14078i	0.128409	+	0.529309i
$183$	3.26180	+	3.47291i	0.241119	+	0.256725i
$184$	−4.38413	+	1.94408i	−0.323202	+	0.143319i
$185$	−6.08590	−	3.51369i	−0.447444	−	0.258332i
$186$	3.68014	+	0.203111i	0.269841	+	0.0148928i
$187$	−18.2879	−	3.52471i	−1.33735	−	0.257752i
$188$	−1.41627	+	2.20376i	−0.103292	+	0.160726i
$189$	−4.75631	+	8.73531i	−0.345971	+	0.635400i
$190$	−15.5045	+	9.96414i	−1.12481	+	0.722875i
$191$	−10.4990	+	14.7438i	−0.759680	+	1.06682i	0.235796	+	0.971803i	$0.424230\pi$
$191$	−10.4990	+	14.7438i	−0.759680	+	1.06682i	−0.995476	+	0.0950186i	$0.969709\pi$
$192$	−1.01529	+	1.40328i	−0.0732723	+	0.101273i
$193$	−3.71460	−	1.48710i	−0.267383	−	0.107044i	0.234097	−	0.972213i	$-0.424787\pi$
$193$	−3.71460	−	1.48710i	−0.267383	−	0.107044i	−0.501480	+	0.865169i	$0.667211\pi$
$194$	1.34806	+	1.89308i	0.0967850	+	0.135916i
$195$	−9.84246	+	16.7548i	−0.704833	+	1.19984i
$196$	−2.41437	−	2.30210i	−0.172455	−	0.164436i
$197$	−14.1978	−	6.48392i	−1.01155	−	0.461960i	−0.160497	−	0.987036i	$-0.551310\pi$
$197$	−14.1978	−	6.48392i	−1.01155	−	0.461960i	−0.851055	+	0.525076i	$0.824037\pi$
$198$	1.26227	+	15.7193i	0.0897059	+	1.11712i
$199$	−7.18478	+	6.22565i	−0.509316	+	0.441325i	−0.871222	−	0.490890i	$-0.836672\pi$
$199$	−7.18478	+	6.22565i	−0.509316	+	0.441325i	0.361906	+	0.932215i	$0.382126\pi$
$200$	−2.88486	−	2.05430i	−0.203990	−	0.145261i
$201$	0.247375	+	0.866585i	0.0174485	+	0.0611242i
$202$	−2.35860	−	1.85482i	−0.165950	−	0.130505i
$203$	15.7641	−	8.12694i	1.10642	−	0.570399i
$204$	−5.18742	+	3.27878i	−0.363192	+	0.229561i
$205$	22.3929	−	5.43245i	1.56398	−	0.379419i
$206$	14.6829			1.02300
$207$	4.34943	+	13.7143i	0.302306	+	0.953211i
$208$	3.83871			0.266167
$209$	32.2145	−	7.81516i	2.22832	−	0.540586i
$210$	0.388107	+	9.68185i	0.0267819	+	0.668111i
$211$	−10.7719	+	5.55328i	−0.741565	+	0.382303i	−0.787235	−	0.616653i	$-0.788488\pi$
$211$	−10.7719	+	5.55328i	−0.741565	+	0.382303i	0.0456699	+	0.998957i	$0.485458\pi$
$212$	−0.123426	−	0.0970636i	−0.00847696	−	0.00666636i
$213$	−14.2041	+	14.6739i	−0.973252	+	1.00544i
$214$	6.80049	+	4.84260i	0.464872	+	0.331034i
$215$	13.8649	−	12.0140i	0.945576	−	0.819346i
$216$	3.84907	+	3.49065i	0.261896	+	0.237509i
$217$	−3.70517	−	1.69209i	−0.251523	−	0.114867i
$218$	10.8056	+	10.3031i	0.731846	+	0.697814i
$219$	−14.1294	−	24.9043i	−0.954774	−	1.68288i
$220$	8.91139	+	12.5143i	0.600806	+	0.843714i
$221$	12.6265	+	5.05489i	0.849351	+	0.340029i
$222$	4.14277	+	0.427111i	0.278044	+	0.0286658i
$223$	0.569778	−	0.800142i	0.0381552	−	0.0535815i	−0.795058	−	0.606534i	$-0.792559\pi$
$223$	0.569778	−	0.800142i	0.0381552	−	0.0535815i	0.833213	+	0.552952i	$0.186499\pi$
$224$	1.61029	−	1.03487i	0.107592	−	0.0691453i
$225$	−7.07788	+	7.92380i	−0.471858	+	0.528254i
$226$	−8.35598	+	13.0022i	−0.555832	+	0.864891i
$227$	−7.59434	−	1.46369i	−0.504054	−	0.0971484i	−0.0691156	−	0.997609i	$-0.522018\pi$
$227$	−7.59434	−	1.46369i	−0.504054	−	0.0971484i	−0.434938	+	0.900460i	$0.643230\pi$
$228$	5.97424	−	9.14386i	0.395654	−	0.605567i
$229$	−19.8147	−	11.4400i	−1.30939	−	0.755978i	−0.327398	−	0.944887i	$-0.606172\pi$
$229$	−19.8147	−	11.4400i	−1.30939	−	0.755978i	−0.981995	+	0.188909i	$0.939505\pi$
$230$	10.4910	+	9.29484i	0.691757	+	0.612884i
$231$	5.03588	−	16.6845i	0.331336	−	1.09776i
$232$	−2.18442	−	9.00431i	−0.143414	−	0.591162i
$233$	1.44596	+	1.25293i	0.0947282	+	0.0820825i	0.700938	−	0.713223i	$-0.252765\pi$
$233$	1.44596	+	1.25293i	0.0947282	+	0.0820825i	−0.606209	+	0.795305i	$0.707311\pi$
$234$	1.26732	−	11.4462i	0.0828470	−	0.748261i
$235$	7.57814	+	1.08957i	0.494343	+	0.0710758i
$236$	−2.53187	+	4.91115i	−0.164811	+	0.319689i
$237$	−4.67035	+	11.4159i	−0.303372	+	0.741542i
$238$	6.65941	−	1.28350i	0.431666	−	0.0831967i
$239$	−6.66769	+	16.6551i	−0.431297	+	1.07733i	0.540466	+	0.841366i	$0.318248\pi$
$239$	−6.66769	+	16.6551i	−0.431297	+	1.07733i	−0.971763	+	0.235961i	$0.924176\pi$
$240$	4.96324	+	0.995432i	0.320376	+	0.0642549i
$241$	−14.1116	+	14.7998i	−0.909006	+	0.953338i	−0.999092	−	0.0425960i	$-0.986437\pi$
$241$	−14.1116	+	14.7998i	−0.909006	+	0.953338i	0.0900865	+	0.995934i	$0.471286\pi$
$242$	−4.68580	−	15.9584i	−0.301214	−	1.02584i
$243$	11.6791	−	10.3247i	0.749214	−	0.662328i
$244$	−2.72279	+	0.391477i	−0.174308	+	0.0250618i
$245$	−3.18883	+	9.21353i	−0.203727	+	0.588631i
$246$	−10.7976	+	8.36038i	−0.688427	+	0.533038i
$247$	−24.1800	+	1.15183i	−1.53853	+	0.0732894i
$248$	−1.31542	+	1.67269i	−0.0835292	+	0.106216i
$249$	2.57699	−	0.476563i	0.163310	−	0.0302010i
$250$	0.806677	−	4.18544i	0.0510187	−	0.264710i
$251$	20.4593	+	6.00740i	1.29138	+	0.379184i	0.854085	−	0.520134i	$-0.174118\pi$
$251$	20.4593	+	6.00740i	1.29138	+	0.379184i	0.437296	+	0.899318i	$0.355936\pi$
$252$	−2.55414	−	5.14319i	−0.160896	−	0.323991i
$253$	−12.3636	−	21.9699i	−0.777296	−	1.38124i
$254$	6.50146	−	3.75362i	0.407938	−	0.235523i
$255$	15.0146	+	9.80993i	0.940249	+	0.614322i
$256$	−0.327068	−	0.945001i	−0.0204417	−	0.0590626i
$257$	0.297607	+	0.577276i	0.0185642	+	0.0360095i	0.897935	−	0.440128i	$-0.145067\pi$
$257$	0.297607	+	0.577276i	0.0185642	+	0.0360095i	−0.879371	+	0.476137i	$0.842037\pi$
$258$	−4.59100	+	9.85568i	−0.285823	+	0.613588i
$259$	−4.09096	−	2.10904i	−0.254200	−	0.131049i
$260$	−4.66053	−	10.2051i	−0.289034	−	0.632896i
$261$	−27.5700	+	3.54077i	−1.70654	+	0.219168i
$262$	−2.76561	−	19.2353i	−0.170860	−	1.18836i
$263$	15.6372	−	1.49317i	0.964229	−	0.0920727i	0.398950	−	0.916973i	$-0.369375\pi$
$263$	15.6372	−	1.49317i	0.964229	−	0.0920727i	0.565279	+	0.824900i	$0.308769\pi$
$264$	−7.85041	−	4.61165i	−0.483159	−	0.283828i
$265$	−0.108191	+	0.445971i	−0.00664614	+	0.0273958i
$266$	−9.83269	+	7.00183i	−0.602881	+	0.429310i
$267$	16.2344	−	6.35776i	0.993529	−	0.389089i
$268$	−0.491692	−	0.170176i	−0.0300349	−	0.0103952i
$269$	21.2010	−	9.68217i	1.29265	−	0.590332i	0.354011	−	0.935241i	$-0.384817\pi$
$269$	21.2010	−	9.68217i	1.29265	−	0.590332i	0.938636	+	0.344909i	$0.112090\pi$
$270$	4.60673	−	14.4707i	0.280357	−	0.880656i
$271$	0.0905077	−	0.629495i	0.00549795	−	0.0382391i	−0.986888	−	0.161408i	$-0.948397\pi$
$271$	0.0905077	−	0.629495i	0.00549795	−	0.0382391i	0.992386	+	0.123169i	$0.0393056\pi$
$272$	0.168585	−	3.53904i	0.0102220	−	0.214586i
$273$	−5.91689	+	11.2679i	−0.358107	+	0.681964i
$274$	−7.33136	−	7.68891i	−0.442904	−	0.464504i
$275$	9.30829	−	16.1224i	0.561311	−	0.972219i
$276$	−7.92536	−	2.48770i	−0.477051	−	0.149742i
$277$	−0.193544	−	0.335228i	−0.0116289	−	0.0201419i	0.860152	−	0.510037i	$-0.170368\pi$
$277$	−0.193544	−	0.335228i	−0.0116289	−	0.0201419i	−0.871781	+	0.489895i	$0.837035\pi$
$278$	−0.319215	+	1.08715i	−0.0191452	+	0.0652026i
$279$	4.55332	+	4.47451i	0.272600	+	0.267882i
$280$	−4.70623	−	3.02451i	−0.281251	−	0.180749i
$281$	6.34872	−	2.54164i	0.378733	−	0.151622i	−0.174482	−	0.984660i	$-0.555825\pi$
$281$	6.34872	−	2.54164i	0.378733	−	0.151622i	0.553215	+	0.833039i	$0.313401\pi$
$282$	−4.36302	+	1.24547i	−0.259814	+	0.0741664i
$283$	0.263198	−	2.75634i	0.0156455	−	0.163847i	−0.984272	−	0.176657i	$-0.943472\pi$
$283$	0.263198	−	2.75634i	0.0156455	−	0.163847i	0.999918	+	0.0128100i	$0.00407767\pi$
$284$	−2.23145	−	11.5779i	−0.132412	−	0.687021i
$285$	−31.5621	−	4.78095i	−1.86958	−	0.283199i
$286$	1.91810	+	20.0873i	0.113420	+	1.18779i
$287$	14.4803	−	4.25181i	0.854748	−	0.250977i
$288$	−2.92576	+	0.663261i	−0.172402	+	0.0390830i
$289$	−1.84725	+	4.04492i	−0.108662	+	0.237936i
$290$	−21.2857	+	16.7393i	−1.24994	+	0.982965i
$291$	−0.412813	+	4.00408i	−0.0241995	+	0.234724i
$292$	16.4565	+	1.57141i	0.963047	+	0.0919598i
$293$	−0.783430	−	16.4462i	−0.0457685	−	0.960799i	−0.898642	−	0.438682i	$-0.855446\pi$
$293$	−0.783430	−	16.4462i	−0.0457685	−	0.960799i	0.852874	−	0.522117i	$-0.174858\pi$
$294$	−0.505887	−	5.75592i	−0.0295039	−	0.335692i
$295$	16.1301	+	0.768373i	0.939132	+	0.0447364i
$296$	−1.57462	+	1.81720i	−0.0915227	+	0.105623i
$297$	−16.3427	+	21.8857i	−0.948298	+	1.26994i
$298$		−	17.7605i		−	1.02884i
$299$	5.82923	+	17.4626i	0.337113	+	1.00989i
$300$	−1.40122	−	5.97196i	−0.0808993	−	0.344791i
$301$	8.69614	−	8.29175i	0.501237	−	0.477929i
$302$	16.8364	−	5.82712i	0.968823	−	0.335313i
$303$	−0.945080	−	5.11047i	−0.0542934	−	0.293589i
$304$	2.34375	+	5.85441i	0.134423	+	0.335773i
$305$	4.34644	+	6.76319i	0.248876	+	0.387259i
$306$	−10.4970	−	1.67107i	−0.600073	−	0.0955286i
$307$	−10.1844	−	11.7535i	−0.581257	−	0.670806i	0.386618	−	0.922240i	$-0.373643\pi$
$307$	−10.1844	−	11.7535i	−0.581257	−	0.670806i	−0.967874	+	0.251434i	$0.919098\pi$
$308$	6.21992	+	7.90927i	0.354413	+	0.450673i
$309$	19.0938	+	16.7984i	1.08621	+	0.955628i
$310$	6.04386	+	1.46622i	0.343268	+	0.0832759i
$311$	−8.18127	−	1.98475i	−0.463917	−	0.112545i	−0.00301387	−	0.999995i	$-0.500959\pi$
$311$	−8.18127	−	1.98475i	−0.463917	−	0.112545i	−0.460903	+	0.887450i	$0.652474\pi$
$312$	4.99191	+	4.39180i	0.282611	+	0.248637i
$313$	15.9755	+	20.3145i	0.902987	+	1.14824i	0.988397	+	0.151895i	$0.0485375\pi$
$313$	15.9755	+	20.3145i	0.902987	+	1.14824i	−0.0854101	+	0.996346i	$0.527220\pi$
$314$	−6.46386	−	7.45969i	−0.364777	−	0.420975i
$315$	−10.5721	+	13.0344i	−0.595673	+	0.734407i
$316$	−3.85002	−	5.99074i	−0.216580	−	0.337006i
$317$	−8.44643	−	21.0982i	−0.474399	−	1.18499i	−0.951913	−	0.306367i	$-0.900886\pi$
$317$	−8.44643	−	21.0982i	−0.474399	−	1.18499i	0.477515	−	0.878624i	$-0.341538\pi$
$318$	−0.0494564	−	0.267433i	−0.00277338	−	0.0149969i
$319$	46.0265	−	15.9299i	2.57699	−	0.891904i
$320$	−2.11518	+	2.01682i	−0.118242	+	0.112744i
$321$	3.30309	+	14.0777i	0.184361	+	0.785741i
$322$	7.15300	+	5.75384i	0.398621	+	0.320649i
$323$			22.3430i			1.24320i
$324$	1.01178	+	8.94295i	0.0562101	+	0.496830i
$325$	−8.90281	+	10.2744i	−0.493839	+	0.569921i
$326$	−7.93036	−	0.377770i	−0.439222	−	0.0209227i
$327$	2.26411	+	25.7608i	0.125205	+	1.42457i
$328$	−0.375147	−	7.87530i	−0.0207140	−	0.434841i
$329$	4.99165	+	0.476645i	0.275199	+	0.0262783i
$330$	−2.72892	+	26.4691i	−0.150222	+	1.45708i
$331$	22.5627	−	17.7435i	1.24016	−	0.975269i	0.240166	−	0.970732i	$-0.422798\pi$
$331$	22.5627	−	17.7435i	1.24016	−	0.975269i	0.999990	−	0.00453773i	$-0.00144441\pi$
$332$	−0.628545	+	1.37632i	−0.0344959	+	0.0755354i
$333$	4.89865	+	5.29509i	0.268445	+	0.290169i
$334$	13.3410	−	3.91726i	0.729985	−	0.214343i
$335$	0.144547	+	1.51377i	0.00789745	+	0.0827058i
$336$	3.27803	+	0.496548i	0.178831	+	0.0270889i
$337$	−0.960789	−	4.98505i	−0.0523375	−	0.271553i	0.946327	−	0.323210i	$-0.104762\pi$
$337$	−0.960789	−	4.98505i	−0.0523375	−	0.271553i	−0.998665	+	0.0516568i	$0.983550\pi$
$338$	0.164988	−	1.72783i	0.00897417	−	0.0939818i
$339$	−25.7418	+	7.34824i	−1.39810	+	0.399101i
$340$	−9.61316	+	3.84853i	−0.521347	+	0.208716i
$341$	−9.41017	−	6.04755i	−0.509589	−	0.327493i
$342$	18.2303	−	5.05577i	0.985783	−	0.273385i
$343$	−5.57401	+	18.9833i	−0.300968	+	1.02500i
$344$	−3.13863	−	5.43626i	−0.169223	−	0.293103i
$345$	3.00858	+	24.0897i	0.161976	+	1.29695i
$346$	11.4076	−	19.7586i	0.613278	−	1.06223i
$347$	14.3674	+	15.0681i	0.771283	+	0.808898i	0.985818	−	0.167818i	$-0.0536721\pi$
$347$	14.3674	+	15.0681i	0.771283	+	0.808898i	−0.214535	+	0.976716i	$0.568824\pi$
$348$	7.46104	−	14.2085i	0.399954	−	0.761655i
$349$	1.09092	−	22.9013i	0.0583958	−	1.22588i	−0.759498	−	0.650509i	$-0.774555\pi$
$349$	1.09092	−	22.9013i	0.0583958	−	1.22588i	0.817894	−	0.575369i	$-0.195142\pi$
$350$	−0.964764	+	6.71008i	−0.0515688	+	0.358669i
$351$	14.7434	−	13.4348i	0.786946	−	0.717099i
$352$	4.78159	−	2.18368i	0.254860	−	0.116391i
$353$	−13.3314	−	4.61405i	−0.709560	−	0.245581i	−0.0516367	−	0.998666i	$-0.516444\pi$
$353$	−13.3314	−	4.61405i	−0.709560	−	0.245581i	−0.657924	+	0.753085i	$0.728565\pi$
$354$	−8.91124	+	3.48985i	−0.473627	+	0.185483i
$355$	−28.0704	+	19.9889i	−1.48982	+	1.06090i
$356$	−2.37316	+	9.78232i	−0.125777	+	0.518462i
$357$	10.1284	+	5.94985i	0.536052	+	0.314899i
$358$	−19.6711	+	1.87836i	−1.03965	+	0.0992743i
$359$	−2.57212	−	17.8895i	−0.135751	−	0.944170i	−0.937865	−	0.346999i	$-0.887201\pi$
$359$	−2.57212	−	17.8895i	−0.135751	−	0.944170i	0.802114	−	0.597171i	$-0.203709\pi$
$360$	5.31540	+	6.97283i	0.280146	+	0.367501i
$361$	−8.62702	−	18.8905i	−0.454054	−	0.994239i
$362$	−3.82760	−	1.97327i	−0.201174	−	0.103713i
$363$	12.1642	−	26.1134i	0.638456	−	1.37060i
$364$	−3.36700	−	6.53108i	−0.176479	−	0.342321i
$365$	−15.8021	−	45.6573i	−0.827122	−	2.38981i
$366$	−3.98863	−	2.60601i	−0.208489	−	0.136218i
$367$	9.57238	−	5.52662i	0.499674	−	0.288487i	−0.228905	−	0.973449i	$-0.573514\pi$
$367$	9.57238	−	5.52662i	0.499674	−	0.288487i	0.728579	+	0.684962i	$0.240181\pi$
$368$	3.80221	−	2.92287i	0.198204	−	0.152365i
$369$	−23.6062	−	1.48136i	−1.22889	−	0.0771163i
$370$	6.74273	+	1.97984i	0.350538	+	0.102927i
$371$	−0.0568818	+	0.295131i	−0.00295315	+	0.0153224i
$372$	−3.62429	+	0.670240i	−0.187911	+	0.0347503i
$373$	6.04226	−	7.68335i	0.312856	−	0.397829i	−0.604041	−	0.796954i	$-0.706444\pi$
$373$	6.04226	−	7.68335i	0.312856	−	0.397829i	0.916897	+	0.399125i	$0.130686\pi$
$374$	18.6034	−	0.886189i	0.961959	−	0.0458238i
$375$	5.83750	−	4.51989i	0.301447	−	0.233406i
$376$	0.856792	−	2.47554i	0.0441857	−	0.127666i
$377$	−35.2055	+	5.06179i	−1.81318	+	0.260695i
$378$	2.56281	−	9.61042i	0.131817	−	0.494307i
$379$	1.45464	+	4.95403i	0.0747196	+	0.254472i	0.988379	−	0.152009i	$-0.0485742\pi$
$379$	1.45464	+	4.95403i	0.0747196	+	0.254472i	−0.913660	+	0.406480i	$0.866756\pi$
$380$	12.7183	−	13.3386i	0.652436	−	0.684255i
$381$	12.7490	+	2.55696i	0.653152	+	0.130997i
$382$	6.72706	−	16.8034i	0.344186	−	0.859736i
$383$	4.03427	−	0.777541i	0.206141	−	0.0397305i	−0.0851351	−	0.996369i	$-0.527132\pi$
$383$	4.03427	−	0.777541i	0.206141	−	0.0397305i	0.291276	+	0.956639i	$0.405920\pi$
$384$	0.655836	−	1.60308i	0.0334680	−	0.0818070i
$385$	13.4751	−	26.1381i	0.686757	−	1.33212i
$386$	3.96049	+	0.569432i	0.201583	+	0.0289833i
$387$	−17.2459	+	7.56396i	−0.876659	+	0.384497i
$388$	−1.75637	−	1.52190i	−0.0891663	−	0.0772630i
$389$	−7.64113	−	31.4972i	−0.387421	−	1.59697i	−0.747642	−	0.664102i	$-0.768814\pi$
$389$	−7.64113	−	31.4972i	−0.387421	−	1.59697i	0.360221	−	0.932867i	$-0.382701\pi$
$390$	5.61492	−	18.6029i	0.284323	−	0.941997i
$391$	16.3554	−	4.60726i	0.827126	−	0.232999i
$392$	2.88906	+	1.66800i	0.145919	+	0.0842466i
$393$	18.4103	−	28.1779i	0.928677	−	1.42138i
$394$	15.3262	+	2.95389i	0.772125	+	0.148815i
$395$	−11.2520	+	17.5085i	−0.566151	+	0.880948i
$396$	−4.93265	−	14.9786i	−0.247875	−	0.752702i
$397$	−4.94641	+	3.17886i	−0.248253	+	0.159543i	−0.658850	−	0.752274i	$-0.728957\pi$
$397$	−4.94641	+	3.17886i	−0.248253	+	0.159543i	0.410597	+	0.911817i	$0.365320\pi$
$398$	5.51450	−	7.74404i	0.276417	−	0.388173i
$399$	−20.7972	−	2.14415i	−1.04116	−	0.107342i
$400$	3.28786	+	1.31626i	0.164393	+	0.0658130i
$401$	−0.627552	−	0.881273i	−0.0313384	−	0.0440087i	0.798609	−	0.601850i	$-0.205569\pi$
$401$	−0.627552	−	0.881273i	−0.0313384	−	0.0440087i	−0.829948	+	0.557841i	$0.811630\pi$
$402$	−0.444707	−	0.783837i	−0.0221800	−	0.0390942i
$403$	5.91192	+	5.63700i	0.294494	+	0.280799i
$404$	2.72940	+	1.24648i	0.135793	+	0.0620146i
$405$	22.5463	−	13.5473i	1.12033	−	0.673173i
$406$	−13.4037	+	11.6144i	−0.665214	+	0.576411i
$407$	−10.2959	−	7.33167i	−0.510348	−	0.363417i
$408$	4.26819	−	4.40934i	0.211307	−	0.218295i
$409$	−15.2912	−	12.0252i	−0.756104	−	0.594606i	0.163918	−	0.986474i	$-0.447587\pi$
$409$	−15.2912	−	12.0252i	−0.756104	−	0.594606i	−0.920022	+	0.391868i	$0.871829\pi$
$410$	−20.4809	+	10.5586i	−1.01148	+	0.521454i
$411$	−0.737039	−	18.3864i	−0.0363555	−	0.906936i
$412$	−14.2690	+	3.46161i	−0.702982	+	0.170542i
$413$	10.5764			0.520433
$414$	−7.46010	−	12.3023i	−0.366644	−	0.604626i
$415$	4.42204			0.217069
$416$	−3.73050	+	0.905010i	−0.182903	+	0.0443718i
$417$	−1.65890	+	1.04853i	−0.0812365	+	0.0513467i
$418$	−29.4639	+	15.1897i	−1.44113	+	0.742953i
$419$	−22.2328	−	17.4841i	−1.08614	−	0.854152i	−0.0961636	−	0.995366i	$-0.530657\pi$
$419$	−22.2328	−	17.4841i	−1.08614	−	0.854152i	−0.989979	+	0.141213i	$0.954900\pi$
$420$	−2.65975	−	9.31743i	−0.129782	−	0.454644i
$421$	−5.75539	−	4.09840i	−0.280501	−	0.199744i	0.431144	−	0.902283i	$-0.358110\pi$
$421$	−5.75539	−	4.09840i	−0.280501	−	0.199744i	−0.711645	+	0.702539i	$0.752049\pi$
$422$	9.15898	−	7.93630i	0.445852	−	0.386333i
$423$	−7.09864	−	3.37204i	−0.345148	−	0.163954i
$424$	0.142831	+	0.0652286i	0.00693648	+	0.00316778i
$425$	9.08134	+	8.65904i	0.440510	+	0.420025i
$426$	10.3443	−	17.6090i	0.501181	−	0.853158i
$427$	3.05425	+	4.28910i	0.147806	+	0.207564i
$428$	−7.75048	−	3.10282i	−0.374633	−	0.149981i
$429$	−20.4872	+	28.3162i	−0.989131	+	1.36712i
$430$	−10.6416	+	14.9441i	−0.513185	+	0.720668i
$431$	3.72048	−	2.39100i	0.179209	−	0.115171i	−0.447961	−	0.894053i	$-0.647850\pi$
$431$	3.72048	−	2.39100i	0.179209	−	0.115171i	0.627170	+	0.778883i	$0.284213\pi$
$432$	−4.56352	−	2.48480i	−0.219563	−	0.119550i
$433$	−11.8328	+	18.4122i	−0.568649	+	0.884835i	−0.999848	−	0.0174214i	$-0.994454\pi$
$433$	−11.8328	+	18.4122i	−0.568649	+	0.884835i	0.431199	+	0.902257i	$0.358091\pi$
$434$	3.99965	+	0.770869i	0.191989	+	0.0370029i
$435$	−46.8314	−	2.58468i	−2.24539	−	0.123926i
$436$	−12.9300	−	7.46516i	−0.619236	−	0.357516i
$437$	−23.0730	+	19.5520i	−1.10373	+	0.935300i
$438$	19.6025	+	20.8711i	0.936643	+	0.997262i
$439$	8.08728	+	33.3362i	0.385985	+	1.59105i	0.751165	+	0.660114i	$0.229492\pi$
$439$	8.08728	+	33.3362i	0.385985	+	1.59105i	−0.365181	+	0.930937i	$0.618993\pi$
$440$	−11.6106	−	10.0606i	−0.553511	−	0.479620i
$441$	5.92740	−	8.06385i	0.282257	−	0.383993i
$442$	−13.4623	−	1.93559i	−0.640337	−	0.0920666i
$443$	15.3118	−	29.7008i	0.727486	−	1.41113i	−0.176821	−	0.984243i	$-0.556581\pi$
$443$	15.3118	−	29.7008i	0.727486	−	1.41113i	0.904307	−	0.426883i	$-0.140388\pi$
$444$	−4.12668	+	0.561623i	−0.195844	+	0.0266534i
$445$	28.8874	−	5.56758i	1.36939	−	0.263929i
$446$	−0.365077	+	0.911917i	−0.0172869	+	0.0431805i
$447$	20.3195	−	23.0960i	0.961081	−	1.09240i
$448$	−1.32092	+	1.38534i	−0.0624077	+	0.0654513i
$449$	0.969303	+	3.30114i	0.0457442	+	0.155791i	0.979198	−	0.202907i	$-0.0650390\pi$
$449$	0.969303	+	3.30114i	0.0457442	+	0.155791i	−0.933454	+	0.358698i	$0.883221\pi$
$450$	5.01025	−	9.36912i	0.236186	−	0.441664i
$451$	41.0226	−	5.89815i	1.93168	−	0.277733i
$452$	5.05506	−	14.6057i	0.237770	−	0.686992i
$453$	28.5609	+	11.6845i	1.34191	+	0.548987i
$454$	7.72534	−	0.368003i	0.362568	−	0.0172713i
$455$	−13.2749	+	16.8804i	−0.622338	+	0.791367i
$456$	−3.65009	+	10.2946i	−0.170931	+	0.482088i
$457$	−2.39150	+	12.4083i	−0.111870	+	0.580436i	0.882126	+	0.471014i	$0.156112\pi$
$457$	−2.39150	+	12.4083i	−0.111870	+	0.580436i	−0.993995	+	0.109422i	$0.965100\pi$
$458$	21.9532	+	6.44605i	1.02581	+	0.301204i
$459$	−11.7386	−	14.1825i	−0.547910	−	0.661983i
$460$	−12.3866	−	6.55948i	−0.577530	−	0.305838i
$461$	18.2647	−	10.5451i	0.850673	−	0.491136i	−0.0102050	−	0.999948i	$-0.503248\pi$
$461$	18.2647	−	10.5451i	0.850673	−	0.491136i	0.860878	+	0.508812i	$0.169915\pi$
$462$	−0.960405	+	17.4014i	−0.0446821	+	0.809588i
$463$	7.42357	+	21.4490i	0.345003	+	0.996820i	0.975380	+	0.220531i	$0.0707790\pi$
$463$	7.42357	+	21.4490i	0.345003	+	0.996820i	−0.630377	+	0.776289i	$0.717100\pi$
$464$	4.24570	+	8.23550i	0.197101	+	0.382323i
$465$	6.18203	+	8.82138i	0.286685	+	0.409081i
$466$	−1.70059	−	0.876718i	−0.0787785	−	0.0406132i
$467$	7.08985	+	15.5246i	0.328079	+	0.718394i	0.999748	−	0.0224583i	$-0.00714931\pi$
$467$	7.08985	+	15.5246i	0.328079	+	0.718394i	−0.671668	+	0.740852i	$0.734422\pi$
$468$	1.46695	+	11.4223i	0.0678097	+	0.527997i
$469$	0.141739	+	0.985817i	0.00654490	+	0.0455208i
$470$	−7.62140	+	0.727755i	−0.351549	+	0.0335688i
$471$	0.128825	−	17.0959i	0.00593595	−	0.787736i
$472$	1.30266	−	5.36962i	0.0599596	−	0.247157i
$473$	26.8787	−	19.1402i	1.23588	−	0.880068i
$474$	1.84730	−	12.1952i	0.0848493	−	0.560143i
$475$	−21.1051	−	7.30455i	−0.968369	−	0.335156i
$476$	−6.16910	+	2.81733i	−0.282760	+	0.129132i
$477$	0.241652	−	0.404355i	0.0110645	−	0.0185142i
$478$	2.55315	−	17.7576i	0.116778	−	0.812212i
$479$	−1.47674	+	31.0005i	−0.0674738	+	1.41645i	0.670645	+	0.741779i	$0.266018\pi$
$479$	−1.47674	+	31.0005i	−0.0674738	+	1.41645i	−0.738118	+	0.674671i	$0.764285\pi$
$480$	−5.05802	+	0.202756i	−0.230866	+	0.00925449i
$481$	6.36956	+	6.68021i	0.290427	+	0.304591i
$482$	10.2246	−	17.7095i	0.465718	−	0.806647i
$483$	2.71897	+	15.6660i	0.123718	+	0.712828i
$484$	8.31604	+	14.4038i	0.378002	+	0.654718i
$485$	−1.91357	+	6.51701i	−0.0868906	+	0.295922i
$486$	−8.91574	+	12.7871i	−0.404426	+	0.580034i
$487$	−6.05717	−	3.89271i	−0.274477	−	0.176395i	0.396160	−	0.918182i	$-0.370343\pi$
$487$	−6.05717	−	3.89271i	−0.274477	−	0.176395i	−0.670637	+	0.741786i	$0.733979\pi$
$488$	2.55374	−	1.02236i	0.115602	−	0.0462802i
$489$	−9.88054	−	9.56425i	−0.446813	−	0.432510i
$490$	0.926773	−	9.70561i	0.0418673	−	0.438455i
$491$	1.57434	+	8.16843i	0.0710488	+	0.368636i	0.999999	−	0.00156915i	$-0.000499477\pi$
$491$	1.57434	+	8.16843i	0.0710488	+	0.368636i	−0.928950	+	0.370205i	$0.879287\pi$
$492$	8.52215	−	10.6703i	0.384208	−	0.481056i
$493$	3.12051	+	32.6795i	0.140541	+	1.47181i
$494$	23.2268	−	6.82001i	1.04502	−	0.306847i
$495$	−33.8316	+	31.2987i	−1.52062	+	1.40677i
$496$	0.883988	−	1.93566i	0.0396922	−	0.0869138i
$497$	−17.7410	+	13.9517i	−0.795794	+	0.625820i
$498$	−2.39199	+	1.07068i	−0.107188	+	0.0479782i
$499$	−9.82741	−	0.938404i	−0.439935	−	0.0420087i	−0.127261	−	0.991869i	$-0.540619\pi$
$499$	−9.82741	−	0.938404i	−0.439935	−	0.0420087i	−0.312674	+	0.949861i	$0.601225\pi$
$500$	0.202816	+	4.25764i	0.00907022	+	0.190407i
$501$	21.8304	+	10.1691i	0.975311	+	0.454323i
$502$	−21.2989	−	1.01459i	−0.950616	−	0.0452834i
$503$	−27.4999	+	31.7366i	−1.22616	+	1.41506i	−0.347455	+	0.937697i	$0.612954\pi$
$503$	−27.4999	+	31.7366i	−1.22616	+	1.41506i	−0.878704	+	0.477367i	$0.841591\pi$
$504$	3.69469	+	4.39605i	0.164575	+	0.195816i
$505$		−	8.76941i		−	0.390234i
$506$	17.1947	+	18.4358i	0.764399	+	0.819571i
$507$	2.19134	−	2.05814i	0.0973208	−	0.0914050i
$508$	−5.43324	+	5.18058i	−0.241061	+	0.229851i
$509$	−19.7896	+	6.84926i	−0.877160	+	0.303588i	−0.728290	−	0.685269i	$-0.759685\pi$
$509$	−19.7896	+	6.84926i	−0.877160	+	0.303588i	−0.148870	+	0.988857i	$0.547564\pi$
$510$	−16.9041	−	5.99358i	−0.748527	−	0.265400i
$511$	−11.7608	−	29.3770i	−0.520267	−	1.29956i
$512$	0.540641	+	0.841254i	0.0238932	+	0.0371785i
$513$	29.4912	+	14.2824i	1.30207	+	0.630584i
$514$	−0.425316	−	0.490840i	−0.0187599	−	0.0216500i
$515$	26.5264	+	33.7311i	1.16889	+	1.48637i
$516$	2.13803	−	10.6602i	0.0941213	−	0.469290i
$517$	13.3822	+	3.24648i	0.588547	+	0.142780i
$518$	4.47286	+	1.08511i	0.196526	+	0.0476768i
$519$	37.4401	−	12.6431i	1.64344	−	0.554969i
$520$	6.93512	+	8.81872i	0.304125	+	0.386726i
$521$	−18.1377	−	20.9321i	−0.794629	−	0.917050i	0.203445	−	0.979086i	$-0.434786\pi$
$521$	−18.1377	−	20.9321i	−0.794629	−	0.917050i	−0.998074	+	0.0620359i	$0.980241\pi$
$522$	25.9581	−	9.94085i	1.13616	−	0.435099i
$523$	4.31686	+	6.71717i	0.188763	+	0.293721i	0.922717	−	0.385478i	$-0.125963\pi$
$523$	4.31686	+	6.71717i	0.188763	+	0.293721i	−0.733954	+	0.679199i	$0.762327\pi$
$524$	7.22254	+	18.0410i	0.315518	+	0.788126i
$525$	−8.93149	+	7.62211i	−0.389802	+	0.332656i
$526$	−14.8443	+	5.13768i	−0.647244	+	0.224013i
$527$	5.45658	−	5.20284i	0.237693	−	0.226639i
$528$	8.71635	+	2.63086i	0.379331	+	0.114493i
$529$	19.0702	+	12.8580i	0.829138	+	0.559045i
$530$		−	0.458907i		−	0.0199336i
$531$	−15.5810	−	5.65697i	−0.676156	−	0.245491i
$532$	7.90478	−	9.12260i	0.342716	−	0.395515i
$533$	−30.2310	−	1.44008i	−1.30945	−	0.0623767i
$534$	−14.2779	+	10.0059i	−0.617864	+	0.433000i
$535$	1.16096	+	24.3716i	0.0501928	+	1.05368i
$536$	0.517953	+	0.0494585i	0.0223722	+	0.00213628i
$537$	−27.7295	−	20.0627i	−1.19662	−	0.865769i
$538$	−18.3207	+	14.4076i	−0.789862	+	0.621154i
$539$	−7.28474	+	15.9514i	−0.313776	+	0.687074i
$540$	−1.06529	+	15.1488i	−0.0458426	+	0.651902i
$541$	−3.96349	+	1.16378i	−0.170404	+	0.0500350i	−0.365821	−	0.930685i	$-0.619212\pi$
$541$	−3.96349	+	1.16378i	−0.170404	+	0.0500350i	0.195418	+	0.980720i	$0.437394\pi$
$542$	0.0604526	+	0.633088i	0.00259666	+	0.0271935i
$543$	−2.71988	−	6.94516i	−0.116721	−	0.298045i
$544$	0.670528	+	3.47903i	0.0287486	+	0.149162i
$545$	−4.14779	+	43.4376i	−0.177672	+	1.86066i
$546$	3.09360	−	12.3452i	0.132394	−	0.528327i
$547$	18.1421	−	7.26300i	0.775700	−	0.310543i	0.0501760	−	0.998740i	$-0.484022\pi$
$547$	18.1421	−	7.26300i	0.775700	−	0.310543i	0.725524	+	0.688197i	$0.241598\pi$
$548$	8.93743	+	5.74374i	0.381788	+	0.245360i
$549$	−2.20537	−	7.95221i	−0.0941228	−	0.339392i
$550$	−5.24489	+	17.8625i	−0.223643	+	0.761658i
$551$	−29.2147	−	50.6013i	−1.24459	−	2.15569i
$552$	8.28845	+	0.549103i	0.352780	+	0.0233714i
$553$	−6.81556	+	11.8049i	−0.289827	+	0.501996i
$554$	0.267121	+	0.280149i	0.0113489	+	0.0119024i
$555$	6.50322	+	10.2889i	0.276046	+	0.436738i
$556$	0.0539123	−	1.13176i	0.00228639	−	0.0479972i
$557$	−0.252666	+	1.75733i	−0.0107058	+	0.0744604i	−0.994474	−	0.104984i	$-0.966521\pi$
$557$	−0.252666	+	1.75733i	−0.0107058	+	0.0744604i	0.983768	+	0.179444i	$0.0574300\pi$
$558$	−5.47988	−	3.27490i	−0.231982	−	0.138637i
$559$	−21.9190	+	10.0101i	−0.927074	+	0.423381i
$560$	5.28662	+	1.82972i	0.223401	+	0.0773197i
$561$	25.2060	+	20.1314i	1.06420	+	0.849950i
$562$	−5.57054	+	3.96677i	−0.234979	+	0.167328i
$563$	7.57245	−	31.2141i	0.319141	−	1.31552i	−0.555812	−	0.831308i	$-0.687593\pi$
$563$	7.57245	−	31.2141i	0.319141	−	1.31552i	0.874953	−	0.484208i	$-0.160892\pi$
$564$	3.94640	−	2.23898i	0.166174	−	0.0942780i
$565$	−44.9662	+	4.29375i	−1.89174	+	0.180639i
$566$	0.394052	+	2.74069i	0.0165632	+	0.115200i
$567$	14.3278	−	9.56544i	0.601712	−	0.401711i
$568$	4.89814	+	10.7254i	0.205521	+	0.450029i
$569$	23.4021	+	12.0646i	0.981069	+	0.505776i	0.872659	−	0.488330i	$-0.162394\pi$
$569$	23.4021	+	12.0646i	0.981069	+	0.505776i	0.108410	+	0.994106i	$0.465424\pi$
$570$	31.7995	−	2.79485i	1.33194	−	0.117063i
$571$	2.78954	+	5.41096i	0.116739	+	0.226442i	0.939964	−	0.341273i	$-0.110858\pi$
$571$	2.78954	+	5.41096i	0.116739	+	0.226442i	−0.823225	+	0.567715i	$0.807828\pi$
$572$	−6.59979	−	19.0688i	−0.275951	−	0.797308i
$573$	27.9724	−	14.1550i	1.16857	−	0.591334i
$574$	−13.0698	+	7.54583i	−0.545521	+	0.314957i
$575$	−0.995022	+	16.9555i	−0.0414953	+	0.707093i
$576$	2.68692	−	1.33434i	0.111955	−	0.0555975i
$577$	2.10819	+	0.619020i	0.0877651	+	0.0257702i	0.325320	−	0.945604i	$-0.394528\pi$
$577$	2.10819	+	0.619020i	0.0877651	+	0.0257702i	−0.237555	+	0.971374i	$0.576346\pi$
$578$	0.841555	−	4.36640i	0.0350041	−	0.181618i
$579$	4.49879	+	5.27162i	0.186963	+	0.219081i
$580$	16.7393	−	21.2857i	0.695061	−	0.883842i
$581$	2.89294	−	0.137808i	0.120020	−	0.00571723i
$582$	−0.542822	−	3.98854i	−0.0225007	−	0.165330i
$583$	−0.269961	+	0.780001i	−0.0111806	+	0.0323043i
$584$	−16.3631	+	2.35266i	−0.677111	+	0.0973539i
$585$	28.5850	−	17.7676i	1.18185	−	0.734598i
$586$	4.63869	+	15.7979i	0.191623	+	0.652607i
$587$	−12.2715	+	12.8699i	−0.506498	+	0.531200i	−0.926486	−	0.376330i	$-0.877186\pi$
$587$	−12.2715	+	12.8699i	−0.506498	+	0.531200i	0.419988	+	0.907530i	$0.362034\pi$
$588$	1.84864	+	5.47441i	0.0762365	+	0.225761i
$589$	−4.98741	+	12.4580i	−0.205503	+	0.513321i
$590$	−15.8566	+	3.05611i	−0.652806	+	0.125818i
$591$	16.5509	+	21.3758i	0.680815	+	0.879282i
$592$	1.10181	−	2.13721i	0.0452840	−	0.0878388i
$593$	−31.4394	−	4.52031i	−1.29106	−	0.185627i	−0.537647	−	0.843170i	$-0.680687\pi$
$593$	−31.4394	−	4.52031i	−1.29106	−	0.185627i	−0.753417	+	0.657543i	$0.771596\pi$
$594$	10.7223	−	25.1217i	0.439939	−	1.03076i
$595$	14.9797	+	12.9800i	0.614106	+	0.532126i
$596$	4.18720	+	17.2599i	0.171515	+	0.706993i
$597$	16.0310	−	3.76139i	0.656103	−	0.153943i
$598$	−9.78186	−	15.5960i	−0.400010	−	0.637769i
$599$	1.51754	+	0.876151i	0.0620049	+	0.0357986i	0.530682	−	0.847571i	$-0.321936\pi$
$599$	1.51754	+	0.876151i	0.0620049	+	0.0357986i	−0.468677	+	0.883370i	$0.655269\pi$
$600$	2.76966	+	5.47327i	0.113071	+	0.223445i
$601$	11.8878	+	2.29118i	0.484912	+	0.0934591i	0.425847	−	0.904795i	$-0.359976\pi$
$601$	11.8878	+	2.29118i	0.484912	+	0.0934591i	0.0590647	+	0.998254i	$0.481188\pi$
$602$	−6.49615	+	10.1082i	−0.264764	+	0.411980i
$603$	0.318472	−	1.52809i	0.0129692	−	0.0622288i
$604$	−14.9880	+	9.63218i	−0.609852	+	0.391928i
$605$	28.1959	−	39.5955i	1.14632	−	1.60979i
$606$	2.12328	+	4.74360i	0.0862523	+	0.192696i
$607$	−31.1728	−	12.4797i	−1.26526	−	0.506535i	−0.360623	−	0.932712i	$-0.617436\pi$
$607$	−31.1728	−	12.4797i	−1.26526	−	0.506535i	−0.904640	+	0.426176i	$0.859860\pi$
$608$	−3.65791	−	5.13682i	−0.148348	−	0.208326i
$609$	−30.7181	−	0.231475i	−1.24476	−	0.00937984i
$610$	−5.81840	−	5.54784i	−0.235580	−	0.224625i
$611$	−9.14720	−	4.17739i	−0.370056	−	0.168999i
$612$	10.5951	−	0.850795i	0.428280	−	0.0343913i
$613$	12.2931	−	10.6520i	0.496512	−	0.430230i	−0.370265	−	0.928926i	$-0.620733\pi$
$613$	12.2931	−	10.6520i	0.496512	−	0.430230i	0.866777	+	0.498696i	$0.166188\pi$
$614$	12.6683	+	9.02109i	0.511253	+	0.364061i
$615$	−38.7136	−	9.70127i	−1.56108	−	0.391193i
$616$	−7.90927	−	6.21992i	−0.318674	−	0.250608i
$617$	10.3119	−	5.31618i	0.415143	−	0.214021i	−0.237984	−	0.971269i	$-0.576487\pi$
$617$	10.3119	−	5.31618i	0.415143	−	0.214021i	0.653128	+	0.757248i	$0.273456\pi$
$618$	−22.5159	−	11.8234i	−0.905723	−	0.475605i
$619$	−19.9137	+	4.83101i	−0.800399	+	0.194175i	−0.615040	−	0.788496i	$-0.710860\pi$
$619$	−19.9137	+	4.83101i	−0.800399	+	0.194175i	−0.185359	+	0.982671i	$0.559345\pi$
$620$	−6.21917			−0.249768
$621$	4.37366	−	24.5331i	0.175509	−	0.984478i
$622$	8.41857			0.337554
$623$	18.7249	−	4.54261i	0.750198	−	0.181996i
$624$	−5.88660	−	3.09112i	−0.235653	−	0.123744i
$625$	26.8119	−	13.8225i	1.07248	−	0.552899i
$626$	−20.3145	−	15.9755i	−0.811929	−	0.638508i
$627$	−55.6936	−	13.9563i	−2.22419	−	0.557361i
$628$	8.04034	+	5.72550i	0.320845	+	0.228472i
$629$	6.43845	−	5.57895i	0.256718	−	0.222447i
$630$	7.20115	−	15.1595i	0.286901	−	0.603968i
$631$	16.8776	+	7.70775i	0.671888	+	0.306841i	0.721990	−	0.691903i	$-0.243228\pi$
$631$	16.8776	+	7.70775i	0.671888	+	0.306841i	−0.0501025	+	0.998744i	$0.515955\pi$
$632$	5.15386	+	4.91420i	0.205010	+	0.195476i
$633$	20.9902	+	0.158171i	0.834287	+	0.00628673i
$634$	13.1824	+	18.5121i	0.523541	+	0.735210i
$635$	20.3689	+	8.15449i	0.808317	+	0.323601i
$636$	0.111112	+	0.248235i	0.00440588	+	0.00984314i
$637$	7.42816	−	10.4314i	0.294314	−	0.413307i
$638$	−40.9734	+	26.3320i	−1.62215	+	1.04249i
$639$	33.5979	−	11.0643i	1.32911	−	0.437696i
$640$	1.58007	−	2.45864i	0.0624579	−	0.0971863i
$641$	−5.52193	−	1.06426i	−0.218103	−	0.0420359i	0.0790290	−	0.996872i	$-0.474818\pi$
$641$	−5.52193	−	1.06426i	−0.218103	−	0.0420359i	−0.297132	+	0.954836i	$0.596030\pi$
$642$	−6.52893	−	12.9021i	−0.257676	−	0.509207i
$643$	30.5879	+	17.6599i	1.20627	+	0.696439i	0.961942	−	0.273254i	$-0.0880999\pi$
$643$	30.5879	+	17.6599i	1.20627	+	0.696439i	0.244326	+	0.969693i	$0.421433\pi$
$644$	−8.30789	−	3.90527i	−0.327377	−	0.153889i
$645$	−30.9358	+	7.25856i	−1.21810	+	0.285805i
$646$	−5.26755	−	21.7131i	−0.207249	−	0.854292i
$647$	3.13589	+	2.71726i	0.123284	+	0.106827i	0.714321	−	0.699818i	$-0.246736\pi$
$647$	3.13589	+	2.71726i	0.123284	+	0.106827i	−0.591037	+	0.806645i	$0.701281\pi$
$648$	−3.09164	−	8.45232i	−0.121451	−	0.332039i
$649$	28.7492	+	4.13351i	1.12850	+	0.162254i
$650$	6.22958	−	12.0837i	0.244344	−	0.473961i
$651$	4.31926	+	5.57838i	0.169285	+	0.218634i
$652$	7.79588	−	1.50253i	0.305310	−	0.0588437i
$653$	5.46924	−	13.6615i	0.214028	−	0.534616i	−0.782038	−	0.623231i	$-0.785820\pi$
$653$	5.46924	−	13.6615i	0.214028	−	0.534616i	0.996066	+	0.0886150i	$0.0282441\pi$
$654$	−8.27361	−	24.5008i	−0.323524	−	0.958058i
$655$	39.1930	−	41.1044i	1.53140	−	1.60608i
$656$	2.22124	+	7.56486i	0.0867250	+	0.295358i
$657$	1.61298	+	49.5680i	0.0629283	+	1.93383i
$658$	−4.96332	+	0.713618i	−0.193490	+	0.0278197i
$659$	−3.17584	+	9.17599i	−0.123713	+	0.357446i	−0.989803	−	0.142442i	$-0.954504\pi$
$659$	−3.17584	+	9.17599i	−0.123713	+	0.357446i	0.866090	+	0.499888i	$0.166626\pi$
$660$	−3.58834	−	26.3664i	−0.139676	−	1.02631i
$661$	−25.3500	+	1.20757i	−0.986002	+	0.0469691i	−0.534384	−	0.845242i	$-0.679456\pi$
$661$	−25.3500	+	1.20757i	−0.986002	+	0.0469691i	−0.451619	+	0.892211i	$0.649153\pi$
$662$	−17.7435	+	22.5627i	−0.689620	+	0.876923i
$663$	−15.2921	−	17.9191i	−0.593896	−	0.695920i
$664$	0.286347	−	1.48571i	0.0111124	−	0.0576567i
$665$	−33.8494	−	9.93908i	−1.31262	−	0.385421i
$666$	−6.00893	−	3.99093i	−0.232841	−	0.154645i
$667$	−31.0166	+	31.8199i	−1.20097	+	1.23207i
$668$	−12.0414	+	6.95209i	−0.465894	+	0.268984i
$669$	−1.51806	+	0.768191i	−0.0586916	+	0.0297000i
$670$	−0.497356	−	1.43702i	−0.0192145	−	0.0555168i
$671$	6.62588	+	12.8524i	0.255789	+	0.496162i
$672$	−3.30269	+	0.290272i	−0.127404	+	0.0111975i
$673$	−25.2752	−	13.0303i	−0.974289	−	0.502281i	−0.103869	−	0.994591i	$-0.533122\pi$
$673$	−25.2752	−	13.0303i	−0.974289	−	0.502281i	−0.870420	+	0.492310i	$0.836153\pi$
$674$	2.10898	+	4.61801i	0.0812347	+	0.177879i
$675$	17.2344	−	6.45157i	0.663354	−	0.248321i
$676$	0.247015	+	1.71803i	0.00950057	+	0.0660779i
$677$	−25.0222	+	2.38933i	−0.961680	+	0.0918293i	−0.564071	−	0.825726i	$-0.690766\pi$
$677$	−25.0222	+	2.38933i	−0.961680	+	0.0918293i	−0.397608	+	0.917555i	$0.630160\pi$
$678$	23.2838	−	13.2100i	0.894207	−	0.507325i
$679$	−1.04878	+	4.32313i	−0.0402485	+	0.165907i
$680$	8.43486	−	6.00643i	0.323462	−	0.230336i
$681$	10.4672	+	8.35988i	0.401103	+	0.320351i
$682$	10.5707	+	3.65855i	0.404772	+	0.140093i
$683$	14.9816	−	6.84185i	0.573253	−	0.261796i	−0.107626	−	0.994191i	$-0.534325\pi$
$683$	14.9816	−	6.84185i	0.573253	−	0.261796i	0.680880	+	0.732395i	$0.261598\pi$
$684$	−16.5245	+	9.21121i	−0.631830	+	0.352199i
$685$	4.41880	−	30.7334i	0.168834	−	1.17426i
$686$	0.941396	−	19.7623i	0.0359427	−	0.754529i
$687$	21.1735	+	33.4989i	0.807818	+	1.27806i
$688$	4.33180	+	4.54306i	0.165148	+	0.173203i
$689$	0.301378	−	0.522002i	0.0114816	−	0.0198867i
$690$	−8.60314	−	22.7014i	−0.327516	−	0.864227i
$691$	−4.09026	−	7.08455i	−0.155601	−	0.269509i	0.777677	−	0.628664i	$-0.216398\pi$
$691$	−4.09026	−	7.08455i	−0.155601	−	0.269509i	−0.933278	+	0.359156i	$0.883065\pi$
$692$	−6.42781	+	21.8911i	−0.244349	+	0.832175i
$693$	−21.1576	+	21.5303i	−0.803711	+	0.817867i
$694$	−17.5149	−	11.2561i	−0.664855	−	0.427276i
$695$	−3.07421	+	1.23073i	−0.116612	+	0.0466842i
$696$	−3.90094	+	15.5670i	−0.147865	+	0.590065i
$697$	−2.65532	+	27.8078i	−0.100577	+	1.05329i
$698$	4.33901	+	22.5129i	0.164234	+	0.852127i
$699$	−1.20844	−	3.08572i	−0.0457073	−	0.116713i
$700$	−0.644393	−	6.74839i	−0.0243558	−	0.255065i
$701$	−35.4086	+	10.3969i	−1.33736	+	0.392686i	−0.870729	−	0.491764i	$-0.836352\pi$
$701$	−35.4086	+	10.3969i	−1.33736	+	0.392686i	−0.466636	+	0.884449i	$0.654534\pi$
$702$	−11.1604	+	16.5320i	−0.421224	+	0.623961i
$703$	−6.29899	+	13.7929i	−0.237571	+	0.520207i
$704$	−4.13198	+	3.24943i	−0.155730	+	0.122467i
$705$	−10.7436	−	7.77313i	−0.404626	−	0.292753i
$706$	14.0434	+	1.34099i	0.528532	+	0.0504687i
$707$	−0.273289	−	5.73704i	−0.0102781	−	0.215764i
$708$	7.83729	−	5.49238i	0.294543	−	0.206416i
$709$	25.5139	+	1.21538i	0.958195	+	0.0456445i	0.520849	−	0.853649i	$-0.325615\pi$
$709$	25.5139	+	1.21538i	0.958195	+	0.0456445i	0.437346	+	0.899293i	$0.355918\pi$
$710$	22.5666	−	26.0433i	0.846910	−	0.977386i
$711$	16.3546	−	13.7453i	0.613344	−	0.515489i
$712$		−	10.0661i		−	0.377242i
$713$	10.1478	+	1.08194i	0.380039	+	0.0405191i
$714$	−11.2456	−	3.39427i	−0.420857	−	0.127027i
$715$	−42.6815	+	40.6967i	−1.59620	+	1.52197i
$716$	18.6737	−	6.46304i	0.697870	−	0.241535i
$717$	23.6363	−	20.1711i	0.882713	−	0.753305i
$718$	6.71722	+	16.7788i	0.250684	+	0.626179i
$719$	−1.88833	−	2.93829i	−0.0704226	−	0.109580i	0.804256	−	0.594283i	$-0.202564\pi$
$719$	−1.88833	−	2.93829i	−0.0704226	−	0.109580i	−0.874679	+	0.484703i	$0.838928\pi$
$720$	−6.80948	−	5.52313i	−0.253774	−	0.205835i
$721$	18.4051	+	21.2406i	0.685441	+	0.791041i
$722$	12.8375	+	16.3242i	0.477761	+	0.607522i
$723$	33.5574	−	11.3319i	1.24801	−	0.421438i
$724$	4.18492	+	1.01525i	0.155531	+	0.0377315i
$725$	−31.8892	−	7.73624i	−1.18434	−	0.287317i
$726$	−5.66487	+	28.2451i	−0.210243	+	1.04827i
$727$	−11.8156	−	15.0247i	−0.438215	−	0.557235i	0.515911	−	0.856642i	$-0.327454\pi$
$727$	−11.8156	−	15.0247i	−0.438215	−	0.557235i	−0.954126	+	0.299407i	$0.903211\pi$
$728$	4.81185	+	5.55317i	0.178339	+	0.205814i
$729$	−26.2236	+	6.42813i	−0.971246	+	0.238079i
$730$	26.1208	+	40.6448i	0.966775	+	1.50433i
$731$	8.26601	+	20.6475i	0.305730	+	0.763675i
$732$	4.49058	+	1.59220i	0.165977	+	0.0588493i
$733$	39.3353	−	13.6141i	1.45288	−	0.502848i	0.517254	−	0.855832i	$-0.326954\pi$
$733$	39.3353	−	13.6141i	1.45288	−	0.502848i	0.935629	+	0.352984i	$0.114833\pi$
$734$	−7.99960	+	7.62761i	−0.295271	+	0.281540i
$735$	12.3092	−	11.5610i	0.454032	−	0.426433i
$736$	−3.00594	+	3.73689i	−0.110800	+	0.137744i
$737$			2.73507i			0.100747i
$738$	23.2901	−	4.12579i	0.857319	−	0.151872i
$739$	−16.8475	+	19.4431i	−0.619747	+	0.715226i	−0.975659	−	0.219293i	$-0.929625\pi$
$739$	−16.8475	+	19.4431i	−0.619747	+	0.715226i	0.355912	+	0.934519i	$0.384170\pi$
$740$	−7.01943	−	0.334377i	−0.258039	−	0.0122919i
$741$	38.0071	+	17.7046i	1.39623	+	0.650395i
$742$	−0.0143013	−	0.300222i	−0.000525018	−	0.0110215i
$743$	−0.934767	−	0.0892594i	−0.0342933	−	0.00327461i	0.0778953	−	0.996962i	$-0.475180\pi$
$743$	−0.934767	−	0.0892594i	−0.0342933	−	0.00327461i	−0.112189	+	0.993687i	$0.535786\pi$
$744$	3.36411	−	1.50580i	0.123334	−	0.0552055i
$745$	40.8015	−	32.0866i	1.49485	−	1.17556i
$746$	−4.06051	+	8.89129i	−0.148666	+	0.325533i
$747$	−4.33552	−	1.34432i	−0.158629	−	0.0491860i
$748$	−17.8701	+	5.24713i	−0.653395	+	0.191854i
$749$	1.51903	+	15.9080i	0.0555041	+	0.581265i
$750$	−4.60735	+	5.76872i	−0.168237	+	0.210644i
$751$	−8.11399	−	42.0994i	−0.296084	−	1.53623i	−0.759748	−	0.650217i	$-0.774678\pi$
$751$	−8.11399	−	42.0994i	−0.296084	−	1.53623i	0.463665	−	0.886011i	$-0.346534\pi$
$752$	−0.249010	+	2.60775i	−0.00908047	+	0.0950949i
$753$	−26.5366	−	25.6871i	−0.967047	−	0.936090i
$754$	33.0198	−	13.2191i	1.20251	−	0.481412i
$755$	43.8037	+	28.1509i	1.59418	+	1.02452i
$756$	−0.224825	+	9.94372i	−0.00817682	+	0.361650i
$757$	−0.210864	+	0.718136i	−0.00766397	+	0.0261011i	−0.963236	−	0.268656i	$-0.913421\pi$
$757$	−0.210864	+	0.718136i	−0.00766397	+	0.0261011i	0.955572	+	0.294757i	$0.0952387\pi$
$758$	−2.58159	−	4.47144i	−0.0937675	−	0.162410i
$759$	1.26817	+	43.6464i	0.0460316	+	1.58426i
$760$	−9.21512	+	15.9611i	−0.334268	+	0.578968i
$761$	13.5277	+	14.1875i	0.490380	+	0.514296i	0.921700	−	0.387903i	$-0.126800\pi$
$761$	13.5277	+	14.1875i	0.490380	+	0.514296i	−0.431320	+	0.902199i	$0.641952\pi$
$762$	−12.9925	+	0.520817i	−0.470668	+	0.0188672i
$763$	−1.35984	+	28.5466i	−0.0492296	+	1.03346i
$764$	−2.57589	+	17.9157i	−0.0931923	+	0.648167i
$765$	−15.1252	−	27.1339i	−0.546852	−	0.981026i
$766$	−3.73723	+	1.70674i	−0.135032	+	0.0616669i
$767$	−20.0438	−	6.93721i	−0.723738	−	0.250488i
$768$	−0.259408	+	1.71251i	−0.00936058	+	0.0617951i
$769$	26.9524	−	19.1927i	0.971928	−	0.692107i	0.0204394	−	0.999791i	$-0.493493\pi$
$769$	26.9524	−	19.1927i	0.971928	−	0.692107i	0.951488	+	0.307684i	$0.0995541\pi$
$770$	−6.93300	+	28.5782i	−0.249848	+	1.02989i
$771$	0.00847656	−	1.12489i	0.000305276	−	0.0405120i
$772$	−3.98309	+	0.380339i	−0.143355	+	0.0136887i
$773$	−2.84188	−	19.7657i	−0.102215	−	0.710924i	−0.974901	−	0.222640i	$-0.928532\pi$
$773$	−2.84188	−	19.7657i	−0.102215	−	0.710924i	0.872685	−	0.488283i	$-0.162377\pi$
$774$	14.9765	−	11.4166i	0.538319	−	0.410362i
$775$	3.13068	+	6.85524i	0.112457	+	0.246248i
$776$	2.06566	+	1.06492i	0.0741530	+	0.0382286i
$777$	4.57512	+	6.52842i	0.164131	+	0.234206i
$778$	14.8515	+	28.8078i	0.532451	+	1.03281i
$779$	−16.2615	−	46.9844i	−0.582628	−	1.68339i
$780$	−1.07084	+	19.4023i	−0.0383421	+	0.694715i
$781$	−53.6768	+	30.9903i	−1.92071	+	1.10892i
$782$	−14.8081	+	8.33331i	−0.529537	+	0.297999i
$783$	45.1294	+	16.7711i	1.61279	+	0.599348i
$784$	−3.20086	−	0.939858i	−0.114317	−	0.0335664i
$785$	5.45946	−	28.3264i	0.194857	−	1.01101i
$786$	−11.2482	+	31.7240i	−0.401209	+	1.13156i
$787$	13.0249	−	16.5625i	0.464287	−	0.590389i	−0.496375	−	0.868108i	$-0.665336\pi$
$787$	13.0249	−	16.5625i	0.464287	−	0.590389i	0.960662	+	0.277719i	$0.0895784\pi$
$788$	−15.5906	+	0.742673i	−0.555393	+	0.0264566i
$789$	−25.1817	−	10.3021i	−0.896493	−	0.366763i
$790$	6.80707	−	19.6677i	0.242185	−	0.699746i
$791$	−29.2835	+	4.21034i	−1.04120	+	0.149702i
$792$	8.32494	+	13.3934i	0.295814	+	0.475915i
$793$	−2.97494	−	10.1317i	−0.105643	−	0.359788i
$794$	4.05753	−	4.25542i	0.143996	−	0.151019i
$795$	0.525028	−	0.596768i	0.0186208	−	0.0211652i
$796$	−3.53333	+	8.82584i	−0.125236	+	0.312824i
$797$	−11.2413	+	2.16659i	−0.398188	+	0.0767444i	−0.384414	−	0.923161i	$-0.625597\pi$
$797$	−11.2413	+	2.16659i	−0.398188	+	0.0767444i	−0.0137736	+	0.999905i	$0.504384\pi$
$798$	20.7165	−	2.81942i	0.733356	−	0.0998064i
$799$	−4.25300	+	8.24967i	−0.150460	+	0.291852i
$800$	−3.50550	−	0.504015i	−0.123938	−	0.0178196i
$801$	−30.0148	−	3.32322i	−1.06052	−	0.117420i
$802$	0.817630	+	0.708481i	0.0288715	+	0.0250173i
$803$	−20.4873	−	84.4498i	−0.722981	−	2.98017i
$804$	0.616968	+	0.656898i	0.0217588	+	0.0231670i
$805$	−0.295580	+	26.8277i	−0.0104178	+	0.945553i
$806$	−7.07424	−	4.08432i	−0.249180	−	0.143864i
$807$	−40.3080	−	2.22464i	−1.41891	−	0.0783111i
$808$	−2.94633	−	0.567860i	−0.103652	−	0.0199772i
$809$	23.2181	−	36.1281i	0.816306	−	1.27020i	−0.143533	−	0.989646i	$-0.545846\pi$
$809$	23.2181	−	36.1281i	0.816306	−	1.27020i	0.959839	−	0.280552i	$-0.0905175\pi$
$810$	−18.7168	+	18.4809i	−0.657642	+	0.649354i
$811$	−41.4103	+	26.6128i	−1.45411	+	0.934501i	−0.455083	+	0.890449i	$0.650391\pi$
$811$	−41.4103	+	26.6128i	−1.45411	+	0.934501i	−0.999029	+	0.0440526i	$0.985973\pi$
$812$	10.2877	−	14.4470i	0.361027	−	0.506991i
$813$	−0.645693	+	0.892439i	−0.0226454	+	0.0312992i
$814$	11.7342	+	4.69765i	0.411283	+	0.164653i
$815$	−13.4593	−	18.9010i	−0.471460	−	0.662073i
$816$	−3.10834	+	5.29131i	−0.108813	+	0.185233i
$817$	−28.6491	−	27.3169i	−1.00231	−	0.955697i
$818$	17.6953	+	8.08115i	0.618700	+	0.282551i
$819$	18.1469	−	12.5145i	0.634105	−	0.437294i
$820$	17.4143	−	15.0896i	0.608133	−	0.526950i
$821$	−13.5097	−	9.62020i	−0.471491	−	0.335747i	0.319488	−	0.947590i	$-0.396489\pi$
$821$	−13.5097	−	9.62020i	−0.471491	−	0.335747i	−0.790979	+	0.611843i	$0.790428\pi$
$822$	5.05103	+	17.6944i	0.176175	+	0.617163i
$823$	−35.8111	−	28.1621i	−1.24830	−	0.981670i	−0.999915	−	0.0130078i	$-0.995859\pi$
$823$	−35.8111	−	28.1621i	−1.24830	−	0.981670i	−0.248380	−	0.968663i	$-0.579898\pi$
$824$	13.0506	−	6.72807i	0.454641	−	0.234384i
$825$	−27.2567	+	17.2280i	−0.948956	+	0.599801i
$826$	−10.2783	+	2.49349i	−0.357628	+	0.0867597i
$827$	−24.6229			−0.856223			−0.428112	−	0.903726i	$-0.640821\pi$
$827$	−24.6229			−0.856223			−0.428112	+	0.903726i	$0.640821\pi$
$828$	10.1502	+	10.1967i	0.352744	+	0.354361i
$829$	33.9207			1.17811			0.589056	−	0.808092i	$-0.299500\pi$
$829$	33.9207			1.17811			0.589056	+	0.808092i	$0.299500\pi$
$830$	−4.29739	+	1.04253i	−0.149164	+	0.0361869i
$831$	0.0268543	+	0.669917i	0.000931566	+	0.0232392i
$832$	3.41198	−	1.75900i	0.118289	−	0.0609823i
$833$	−9.29084	−	7.30640i	−0.321909	−	0.253152i
$834$	1.36493	−	1.41007i	0.0472638	−	0.0488268i
$835$	33.1013	+	23.5713i	1.14552	+	0.815719i
$836$	25.0523	−	21.7079i	0.866451	−	0.750784i
$837$	−3.37935	−	10.5282i	−0.116807	−	0.363906i
$838$	25.7281	+	11.7496i	0.888763	+	0.405884i
$839$	−11.7425	−	11.1964i	−0.405396	−	0.386544i	0.459763	−	0.888041i	$-0.347934\pi$
$839$	−11.7425	−	11.1964i	−0.405396	−	0.386544i	−0.865159	+	0.501497i	$0.832783\pi$
$840$	4.78144	+	8.42773i	0.164975	+	0.290784i
$841$	−32.9759	−	46.3081i	−1.13710	−	1.59683i
$842$	6.55939	+	2.62598i	0.226052	+	0.0904974i
$843$	−11.7823	−	1.21473i	−0.405804	−	0.0418376i
$844$	−7.02975	+	9.87190i	−0.241974	+	0.339805i
$845$	4.26745	−	2.74252i	0.146805	−	0.0943456i
$846$	7.69353	+	1.60342i	0.264509	+	0.0551267i
$847$	17.2121	−	26.7825i	0.591414	−	0.920258i
$848$	−0.154183	−	0.0297163i	−0.00529466	−	0.00102046i
$849$	−2.62315	+	4.01486i	−0.0900262	+	0.137790i
$850$	−10.8668	−	6.27395i	−0.372728	−	0.215195i
$851$	11.3955	+	1.76677i	0.390631	+	0.0605641i
$852$	−5.90119	+	19.5514i	−0.202171	+	0.669819i
$853$	−9.68001	−	39.9015i	−0.331437	−	1.36620i	−0.856942	−	0.515412i	$-0.827639\pi$
$853$	−9.68001	−	39.9015i	−0.331437	−	1.36620i	0.525505	−	0.850791i	$-0.323876\pi$
$854$	−3.97935	−	3.44813i	−0.136171	−	0.117993i
$855$	44.5501	+	32.7469i	1.52358	+	1.11992i
$856$	8.26352	+	1.18812i	0.282441	+	0.0406089i
$857$	−2.45647	+	4.76489i	−0.0839114	+	0.162765i	−0.927058	−	0.374919i	$-0.877671\pi$
$857$	−2.45647	+	4.76489i	−0.0839114	+	0.162765i	0.843146	+	0.537684i	$0.180701\pi$
$858$	13.2339	−	32.3481i	0.451798	−	1.10434i
$859$	25.1135	−	4.84023i	0.856862	−	0.165147i	0.258144	−	0.966107i	$-0.416889\pi$
$859$	25.1135	−	4.84023i	0.856862	−	0.165147i	0.598718	+	0.800960i	$0.295677\pi$
$860$	6.81846	−	17.0317i	0.232508	−	0.580776i
$861$	−25.6291	−	5.14021i	−0.873439	−	0.175178i
$862$	−3.05190	+	3.20074i	−0.103948	+	0.109018i
$863$	0.772662	+	2.63145i	0.0263017	+	0.0895755i	0.971598	−	0.236638i	$-0.0760454\pi$
$863$	0.772662	+	2.63145i	0.0263017	+	0.0895755i	−0.945296	+	0.326213i	$0.894227\pi$
$864$	5.02070	+	1.33887i	0.170808	+	0.0455493i
$865$	66.0011	−	9.48952i	2.24410	−	0.322653i
$866$	7.15843	−	20.6829i	0.243253	−	0.702834i
$867$	6.08990	−	4.71532i	0.206824	−	0.160141i
$868$	−4.06865	+	0.193813i	−0.138099	+	0.00657846i
$869$	−23.1399	+	29.4247i	−0.784966	+	0.998165i
$870$	46.1206	−	8.52910i	1.56364	−	0.289164i
$871$	0.377994	−	1.96122i	0.0128078	−	0.0664534i
$872$	14.3255	+	4.20636i	0.485124	+	0.142445i
$873$	3.85733	−	5.80778i	0.130551	−	0.196564i
$874$	17.8131	−	24.4406i	0.602536	−	0.826714i
$875$	7.06593	−	4.07952i	0.238872	−	0.137913i
$876$	−23.9705	−	15.6614i	−0.809887	−	0.529148i
$877$	−9.48354	−	27.4009i	−0.320236	−	0.925262i	−0.984132	−	0.177437i	$-0.943219\pi$
$877$	−9.48354	−	27.4009i	−0.320236	−	0.925262i	0.663896	−	0.747825i	$-0.268902\pi$
$878$	−15.7186	−	30.4899i	−0.530478	−	1.02898i
$879$	−12.0419	+	25.8509i	−0.406165	+	0.871929i
$880$	13.6551	+	7.03972i	0.460315	+	0.237309i
$881$	18.1886	+	39.8275i	0.612790	+	1.34182i	0.920649	+	0.390391i	$0.127660\pi$
$881$	18.1886	+	39.8275i	0.612790	+	1.34182i	−0.307859	+	0.951432i	$0.599613\pi$
$882$	−3.85919	+	9.23398i	−0.129946	+	0.310924i
$883$	3.63144	+	25.2573i	0.122208	+	0.849974i	0.955046	+	0.296458i	$0.0958054\pi$
$883$	3.63144	+	25.2573i	0.122208	+	0.849974i	−0.832838	+	0.553517i	$0.813286\pi$
$884$	13.5392	−	1.29283i	0.455372	−	0.0434827i
$885$	−24.1166	−	14.1671i	−0.810669	−	0.476221i
$886$	−7.87797	+	32.4734i	−0.264666	+	1.09097i
$887$	−11.5580	+	8.23038i	−0.388078	+	0.276349i	−0.757398	−	0.652953i	$-0.773530\pi$
$887$	−11.5580	+	8.23038i	−0.388078	+	0.276349i	0.369320	+	0.929302i	$0.379591\pi$
$888$	3.87795	−	1.51869i	0.130136	−	0.0509640i
$889$	13.5797	+	4.69998i	0.455449	+	0.157632i
$890$	−26.7605	+	12.2211i	−0.897013	+	0.409652i
$891$	42.6847	−	20.4014i	1.42999	−	0.683473i
$892$	0.139793	−	0.972282i	0.00468062	−	0.0325544i
$893$	0.786035	−	16.5009i	0.0263037	−	0.552182i
$894$	−14.3017	+	27.2355i	−0.478319	+	0.910891i
$895$	−39.8534	−	41.7971i	−1.33215	−	1.39712i
$896$	0.957080	−	1.65771i	0.0319738	−	0.0553802i
$897$	5.12270	−	31.4725i	0.171042	−	1.05084i
$898$	−1.72025	−	2.97957i	−0.0574056	−	0.0994294i
$899$	−5.55482	+	18.9180i	−0.185263	+	0.630949i
$900$	−2.66017	+	10.2862i	−0.0886723	+	0.342874i
$901$	−0.468016	−	0.300776i	−0.0155919	−	0.0100203i
$902$	−38.4757	+	15.4033i	−1.28110	+	0.512875i
$903$	−20.0123	+	5.71271i	−0.665968	+	0.190107i
$904$	−1.46916	+	15.3857i	−0.0488635	+	0.511721i
$905$	−2.38184	−	12.3582i	−0.0791750	−	0.410799i
$906$	−30.5106	−	4.62168i	−1.01365	−	0.153545i
$907$	0.261815	+	2.74185i	0.00869341	+	0.0910415i	0.998777	−	0.0494358i	$-0.0157423\pi$
$907$	0.261815	+	2.74185i	0.00869341	+	0.0910415i	−0.990084	+	0.140477i	$0.955136\pi$
$908$	−7.42082	+	2.17895i	−0.246269	+	0.0723110i
$909$	−2.66594	+	8.59785i	−0.0884236	+	0.285173i
$910$	8.92100	−	19.5343i	0.295728	−	0.647555i
$911$	−13.8371	+	10.8816i	−0.458442	+	0.360523i	−0.820513	−	0.571627i	$-0.806312\pi$
$911$	−13.8371	+	10.8816i	−0.458442	+	0.360523i	0.362071	+	0.932151i	$0.382070\pi$
$912$	1.12015	−	10.8649i	0.0370920	−	0.359774i
$913$	7.91753	+	0.756033i	0.262032	+	0.0250210i
$914$	−0.601277	−	12.6223i	−0.0198885	−	0.417510i
$915$	−1.21914	−	13.8712i	−0.0403034	−	0.458568i
$916$	−22.8541	−	1.08868i	−0.755122	−	0.0359709i
$917$	24.3595	−	28.1123i	0.804421	−	0.928351i
$918$	14.7513	+	11.0152i	0.486866	+	0.363557i
$919$			19.6238i			0.647328i	0.946172	+	0.323664i	$0.104915\pi$
$919$			19.6238i			0.647328i	−0.946172	+	0.323664i	$0.895085\pi$
$920$	13.5839	+	3.45432i	0.447849	+	0.113886i
$921$	6.15320	+	26.2248i	0.202755	+	0.864136i
$922$	−15.2638	+	14.5540i	−0.502685	+	0.479309i
$923$	42.7727	−	14.8038i	1.40788	−	0.487272i
$924$	−3.16921	−	17.1373i	−0.104259	−	0.563777i
$925$	3.16495	+	7.90567i	0.104063	+	0.259937i
$926$	−12.2711	−	19.0942i	−0.403254	−	0.627475i
$927$	−15.7531	−	41.1353i	−0.517399	−	1.35106i
$928$	−6.06761	−	7.00239i	−0.199179	−	0.229865i
$929$	23.3583	+	29.7025i	0.766361	+	0.974507i	0.999998	+	0.00218283i	$0.000694817\pi$
$929$	23.3583	+	29.7025i	0.766361	+	0.974507i	−0.233637	+	0.972324i	$0.575063\pi$
$930$	−8.08748	−	7.11525i	−0.265199	−	0.233318i
$931$	20.4442	+	4.95971i	0.670032	+	0.162548i
$932$	1.85935	+	0.451074i	0.0609051	+	0.0147754i
$933$	10.9476	+	9.63155i	0.358409	+	0.315323i
$934$	−10.5501	−	13.4155i	−0.345209	−	0.438969i
$935$	35.6453	+	41.1368i	1.16572	+	1.34532i
$936$	−4.11851	−	10.7545i	−0.134618	−	0.351522i
$937$	−29.7916	−	46.3566i	−0.973249	−	1.51440i	−0.853165	−	0.521641i	$-0.825320\pi$
$937$	−29.7916	−	46.3566i	−0.973249	−	1.51440i	−0.120083	−	0.992764i	$-0.538316\pi$
$938$	−0.370159	−	0.924612i	−0.0120861	−	0.0301896i
$939$	−8.13991	−	44.0161i	−0.265636	−	1.43641i
$940$	7.23499	−	2.50405i	0.235979	−	0.0816732i
$941$	26.3050	−	25.0817i	0.857517	−	0.817641i	−0.127186	−	0.991879i	$-0.540595\pi$
$941$	26.3050	−	25.0817i	0.857517	−	0.817641i	0.984704	+	0.174238i	$0.0557461\pi$
$942$	3.90531	+	16.6443i	0.127242	+	0.542302i
$943$	−31.0400	+	21.5921i	−1.01080	+	0.703136i
$944$			5.52537i			0.179836i
$945$	26.7082	−	11.4749i	0.868817	−	0.373277i
$946$	−21.6085	+	24.9376i	−0.702554	+	0.810790i
$947$	46.2589	+	2.20358i	1.50321	+	0.0716069i	0.782946	−	0.622090i	$-0.213716\pi$
$947$	46.2589	+	2.20358i	1.50321	+	0.0716069i	0.720267	+	0.693697i	$0.244019\pi$
$948$	1.07990	+	12.2869i	0.0350734	+	0.399061i
$949$	3.01951	+	63.3874i	0.0980176	+	2.05764i
$950$	22.2323	+	2.12293i	0.721312	+	0.0688769i
$951$	−4.03682	+	39.1552i	−0.130903	+	1.26969i
$952$	5.33099	−	4.19234i	0.172778	−	0.135874i
$953$	15.0336	−	32.9190i	0.486986	−	1.06635i	−0.493497	−	0.869747i	$-0.664282\pi$
$953$	15.0336	−	32.9190i	0.486986	−	1.06635i	0.980483	−	0.196603i	$-0.0629910\pi$
$954$	−0.139510	+	0.449929i	−0.00451679	+	0.0145670i
$955$	50.7559	−	14.9033i	1.64242	−	0.482259i
$956$	1.70532	+	17.8589i	0.0551540	+	0.577599i
$957$	−83.4084	−	12.6345i	−2.69621	−	0.408416i
$958$	−5.87354	−	30.4748i	−0.189765	−	0.984597i
$959$	1.93305	−	20.2438i	0.0624215	−	0.653707i
$960$	4.86764	−	1.38951i	0.157102	−	0.0448463i
$961$	−24.5755	+	9.83856i	−0.792760	+	0.317373i
$962$	−7.76494	−	4.99022i	−0.250352	−	0.160891i
$963$	6.27083	−	24.2478i	0.202075	−	0.781373i
$964$	−5.76121	+	19.6209i	−0.185556	+	0.631946i
$965$	5.84696	+	10.1272i	0.188220	+	0.326007i
$966$	−6.33573	−	14.5834i	−0.203849	−	0.469212i
$967$	−14.6753	+	25.4183i	−0.471925	+	0.817399i	−0.999484	−	0.0321199i	$-0.989774\pi$
$967$	−14.6753	+	25.4183i	−0.471925	+	0.817399i	0.527559	+	0.849519i	$0.323108\pi$
$968$	−11.4774	−	12.0372i	−0.368899	−	0.386890i
$969$	17.9917	−	34.2626i	0.577975	−	1.10067i
$970$	0.323183	−	6.78445i	0.0103768	−	0.217836i
$971$	1.10071	−	7.65562i	0.0353235	−	0.245681i	−0.964508	−	0.264055i	$-0.914940\pi$
$971$	1.10071	−	7.65562i	0.0353235	−	0.245681i	0.999831	+	0.0183743i	$0.00584906\pi$
$972$	5.64975	−	14.5286i	0.181216	−	0.466005i
$973$	−1.97283	+	0.900961i	−0.0632460	+	0.0288835i
$974$	6.80417	+	2.35495i	0.218020	+	0.0754573i
$975$	21.9258	−	8.58663i	0.702187	−	0.274992i
$976$	−2.24072	+	1.59561i	−0.0717238	+	0.0510743i
$977$	−4.34499	+	17.9103i	−0.139009	+	0.573001i	0.859116	+	0.511781i	$0.171014\pi$
$977$	−4.34499	+	17.9103i	−0.139009	+	0.573001i	−0.998124	+	0.0612199i	$0.980501\pi$
$978$	11.8569	+	6.96522i	0.379141	+	0.222723i
$979$	52.6739	−	5.02975i	1.68346	−	0.160751i
$980$	1.38753	+	9.65052i	0.0443232	+	0.308274i
$981$	17.2719	−	41.3269i	0.551448	−	1.31947i
$982$	−3.45574	−	7.56701i	−0.110277	−	0.241473i
$983$	32.4850	+	16.7472i	1.03611	+	0.534153i	0.890402	−	0.455175i	$-0.150423\pi$
$983$	32.4850	+	16.7472i	1.03611	+	0.534153i	0.145709	+	0.989327i	$0.453454\pi$
$984$	−5.76630	+	12.3787i	−0.183823	+	0.394619i
$985$	20.9028	+	40.5458i	0.666018	+	1.29190i
$986$	−10.7370	−	31.0226i	−0.341937	−	0.987962i
$987$	−7.27080	−	4.75045i	−0.231432	−	0.151209i
$988$	−20.9642	+	12.1037i	−0.666961	+	0.385070i
$989$	−14.0887	+	26.6045i	−0.447995	+	0.845973i
$990$	25.4990	−	38.3925i	0.810412	−	1.22019i
$991$	10.0760	+	2.95857i	0.320074	+	0.0939821i	0.437823	−	0.899061i	$-0.355750\pi$
$991$	10.0760	+	2.95857i	0.320074	+	0.0939821i	−0.117749	+	0.993043i	$0.537568\pi$
$992$	−0.402720	+	2.08951i	−0.0127864	+	0.0663419i
$993$	−48.8874	+	9.04076i	−1.55139	+	0.286900i
$994$	13.9517	−	17.7410i	0.442521	−	0.562712i
$995$	27.7531	−	1.32204i	0.879833	−	0.0419116i
$996$	2.07215	−	1.60443i	0.0656584	−	0.0508383i
$997$	−16.2386	+	46.9184i	−0.514283	+	1.48592i	0.326841	+	0.945079i	$0.394016\pi$
$997$	−16.2386	+	46.9184i	−0.514283	+	1.48592i	−0.841124	+	0.540843i	$0.818105\pi$
$998$	9.77162	−	1.40495i	0.309315	−	0.0444728i
$999$	−3.24814	−	12.0646i	−0.102767	−	0.381706i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	414.2.p.a.5.2	✓	480
9.2	odd	6	inner	414.2.p.a.281.9	yes	480
23.14	odd	22	inner	414.2.p.a.221.9	yes	480
207.83	even	66	inner	414.2.p.a.83.2	yes	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
414.2.p.a.5.2	✓	480	1.1	even	1	trivial
414.2.p.a.83.2	yes	480	207.83	even	66	inner
414.2.p.a.221.9	yes	480	23.14	odd	22	inner
414.2.p.a.281.9	yes	480	9.2	odd	6	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:	\( N \)	\(=\)	\( 414 = 2 \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	414.p (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.971812 + 0.235759i) q^{2} +(-1.53348 - 0.805250i) q^{3} +(0.888835 - 0.458227i) q^{4} +(-2.29731 - 1.80663i) q^{5} +(1.68010 + 0.421018i) q^{6} +(-1.55923 - 1.11032i) q^{7} +(-0.755750 + 0.654861i) q^{8} +(1.70315 + 2.46967i) q^{9} +O(q^{10})\)	\(q+(-0.971812 + 0.235759i) q^{2} +(-1.53348 - 0.805250i) q^{3} +(0.888835 - 0.458227i) q^{4} +(-2.29731 - 1.80663i) q^{5} +(1.68010 + 0.421018i) q^{6} +(-1.55923 - 1.11032i) q^{7} +(-0.755750 + 0.654861i) q^{8} +(1.70315 + 2.46967i) q^{9} +(2.65848 + 1.21409i) q^{10} +(-3.80440 - 3.62748i) q^{11} +(-1.73200 - 0.0130514i) q^{12} +(2.22667 + 3.12692i) q^{13} +(1.77704 + 0.711421i) q^{14} +(2.06811 + 4.62034i) q^{15} +(0.580057 - 0.814576i) q^{16} +(2.98061 - 1.91552i) q^{17} +(-2.23738 - 1.99853i) q^{18} +(-3.40935 + 5.30505i) q^{19} +(-2.86978 - 0.553104i) q^{20} +(1.49697 + 2.95823i) q^{21} +(4.55237 + 2.62831i) q^{22} +(4.58640 + 1.40176i) q^{23} +(1.68626 - 0.395651i) q^{24} +(0.834951 + 3.44172i) q^{25} +(-2.90110 - 2.51382i) q^{26} +(-0.623042 - 5.15866i) q^{27} +(-1.89468 - 0.272413i) q^{28} +(-4.24570 + 8.23550i) q^{29} +(-3.09910 - 4.00253i) q^{30} +(2.08951 - 0.402720i) q^{31} +(-0.371662 + 0.928368i) q^{32} +(2.91295 + 8.62618i) q^{33} +(-2.44499 + 2.56423i) q^{34} +(1.57610 + 5.36770i) q^{35} +(2.64549 + 1.41471i) q^{36} +(2.38003 - 0.342197i) q^{37} +(2.06253 - 5.95930i) q^{38} +(-0.896611 - 6.58811i) q^{39} +(2.91928 - 0.139063i) q^{40} +(-4.87371 + 6.19742i) q^{41} +(-2.15220 - 2.52192i) q^{42} +(-1.18798 + 6.16381i) q^{43} +(-5.04369 - 1.48096i) q^{44} +(0.549121 - 8.75056i) q^{45} +(-4.78759 - 0.280957i) q^{46} +(-2.26865 + 1.30981i) q^{47} +(-1.54544 + 0.782049i) q^{48} +(-1.09110 - 3.15252i) q^{49} +(-1.62283 - 3.14785i) q^{50} +(-6.11319 + 0.537286i) q^{51} +(3.41198 + 1.75900i) q^{52} +(-0.0652286 - 0.142831i) q^{53} +(1.82168 + 4.86636i) q^{54} +(2.18638 + 15.2066i) q^{55} +(1.90549 - 0.181952i) q^{56} +(9.50007 - 5.38983i) q^{57} +(2.18442 - 9.00431i) q^{58} +(-4.50084 + 3.20503i) q^{59} +(3.95537 + 3.15906i) q^{60} +(-2.59949 - 0.899693i) q^{61} +(-1.93566 + 0.883988i) q^{62} +(0.0865394 - 5.74183i) q^{63} +(0.142315 - 0.989821i) q^{64} +(0.533821 - 11.2063i) q^{65} +(-4.86454 - 7.69627i) q^{66} +(-0.359054 - 0.376565i) q^{67} +(1.77153 - 3.06838i) q^{68} +(-5.90441 - 5.84277i) q^{69} +(-2.79715 - 4.84481i) q^{70} +(3.32190 - 11.3133i) q^{71} +(-2.90444 - 0.751132i) q^{72} +(13.9071 + 8.93755i) q^{73} +(-2.23227 + 0.893664i) q^{74} +(1.49106 - 5.95016i) q^{75} +(-0.599436 + 6.27757i) q^{76} +(1.90425 + 9.88018i) q^{77} +(2.42454 + 6.19102i) q^{78} +(-0.676914 - 7.08896i) q^{79} +(-2.80421 + 0.823389i) q^{80} +(-3.19859 + 8.41243i) q^{81} +(3.27523 - 7.17175i) q^{82} +(-1.18934 + 0.935307i) q^{83} +(2.68609 + 1.94343i) q^{84} +(-10.3080 - 0.984296i) q^{85} +(-0.298684 - 6.27014i) q^{86} +(13.1423 - 9.21016i) q^{87} +(5.25067 + 0.250120i) q^{88} +(-6.59187 + 7.60742i) q^{89} +(1.52938 + 8.63336i) q^{90} -7.34790i q^{91} +(4.71888 - 0.855681i) q^{92} +(-3.52852 - 1.06501i) q^{93} +(1.89590 - 1.80774i) q^{94} +(17.4166 - 6.02794i) q^{95} +(1.31751 - 1.12436i) q^{96} +(-0.863748 - 2.15754i) q^{97} +(1.80357 + 2.80642i) q^{98} +(2.47926 - 15.5738i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 480 q - 4 q^{3} - 24 q^{4} + 8 q^{6}+O(q^{10}) \) 480 * q - 4 * q^3 - 24 * q^4 + 8 * q^6	\( 480 q - 4 q^{3} - 24 q^{4} + 8 q^{6} + 4 q^{12} - 44 q^{15} + 24 q^{16} + 28 q^{18} + 66 q^{21} + 6 q^{23} + 4 q^{24} + 12 q^{25} + 86 q^{27} - 48 q^{29} + 44 q^{30} - 12 q^{31} - 44 q^{33} + 24 q^{39} - 60 q^{41} + 12 q^{46} + 48 q^{47} + 8 q^{48} - 78 q^{49} + 24 q^{50} - 30 q^{54} - 24 q^{55} - 66 q^{56} - 66 q^{57} - 72 q^{59} - 22 q^{60} - 110 q^{63} + 48 q^{64} - 462 q^{65} - 88 q^{66} - 70 q^{69} + 12 q^{70} - 52 q^{72} - 264 q^{74} - 76 q^{75} - 12 q^{77} - 58 q^{78} - 96 q^{81} - 198 q^{83} - 22 q^{84} + 178 q^{87} + 6 q^{92} - 20 q^{93} - 12 q^{94} + 12 q^{95} - 4 q^{96} - 66 q^{97} - 132 q^{99}+O(q^{100}) \) 480 * q - 4 * q^3 - 24 * q^4 + 8 * q^6 + 4 * q^12 - 44 * q^15 + 24 * q^16 + 28 * q^18 + 66 * q^21 + 6 * q^23 + 4 * q^24 + 12 * q^25 + 86 * q^27 - 48 * q^29 + 44 * q^30 - 12 * q^31 - 44 * q^33 + 24 * q^39 - 60 * q^41 + 12 * q^46 + 48 * q^47 + 8 * q^48 - 78 * q^49 + 24 * q^50 - 30 * q^54 - 24 * q^55 - 66 * q^56 - 66 * q^57 - 72 * q^59 - 22 * q^60 - 110 * q^63 + 48 * q^64 - 462 * q^65 - 88 * q^66 - 70 * q^69 + 12 * q^70 - 52 * q^72 - 264 * q^74 - 76 * q^75 - 12 * q^77 - 58 * q^78 - 96 * q^81 - 198 * q^83 - 22 * q^84 + 178 * q^87 + 6 * q^92 - 20 * q^93 - 12 * q^94 + 12 * q^95 - 4 * q^96 - 66 * q^97 - 132 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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