LMFDB - Embedded newform 456.2.bk.a.253.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [456,2,Mod(61,456)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(456, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 9, 0, 2]))

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

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

chi := DirichletCharacter("456.61");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 456 = 2^{3} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	456.bk (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.64117833217$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$40$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			253.2
Character	$\chi$	$=$	456.253
Dual form			456.2.bk.a.301.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40819 - 0.130418i) q^{2} +(0.342020 - 0.939693i) q^{3} +(1.96598 + 0.367306i) q^{4} +(-0.0410365 + 0.00723583i) q^{5} +(-0.604181 + 1.27866i) q^{6} +(-1.18673 + 2.05547i) q^{7} +(-2.72057 - 0.773635i) q^{8} +(-0.766044 - 0.642788i) q^{9} +O(q^{10})$	\(q+(-1.40819 - 0.130418i) q^{2} +(0.342020 - 0.939693i) q^{3} +(1.96598 + 0.367306i) q^{4} +(-0.0410365 + 0.00723583i) q^{5} +(-0.604181 + 1.27866i) q^{6} +(-1.18673 + 2.05547i) q^{7} +(-2.72057 - 0.773635i) q^{8} +(-0.766044 - 0.642788i) q^{9} +(0.0587307 - 0.00483752i) q^{10} +(4.23984 - 2.44787i) q^{11} +(1.01756 - 1.72179i) q^{12} +(1.16739 + 3.20738i) q^{13} +(1.93920 - 2.73972i) q^{14} +(-0.00723583 + 0.0410365i) q^{15} +(3.73017 + 1.44423i) q^{16} +(2.30287 - 1.93233i) q^{17} +(0.994903 + 1.00507i) q^{18} +(4.20938 + 1.13188i) q^{19} +(-0.0833347 - 0.000847406i) q^{20} +(1.52563 + 1.81817i) q^{21} +(-6.28973 + 2.89411i) q^{22} +(-0.281659 + 1.59737i) q^{23} +(-1.65747 + 2.29190i) q^{24} +(-4.69683 + 1.70951i) q^{25} +(-1.22560 - 4.66884i) q^{26} +(-0.866025 + 0.500000i) q^{27} +(-3.08807 + 3.60513i) q^{28} +(3.88126 - 4.62551i) q^{29} +(0.0155413 - 0.0568433i) q^{30} +(4.72736 - 8.18803i) q^{31} +(-5.06443 - 2.52023i) q^{32} +(-0.850137 - 4.82137i) q^{33} +(-3.49488 + 2.42075i) q^{34} +(0.0338260 - 0.0929361i) q^{35} +(-1.26993 - 1.54508i) q^{36} +5.19065i q^{37} +(-5.77997 - 2.14287i) q^{38} +3.41322 q^{39} +(0.117240 + 0.0120616i) q^{40} +(-0.487044 - 0.177269i) q^{41} +(-1.91124 - 2.75929i) q^{42} +(10.2230 - 1.80259i) q^{43} +(9.23457 - 3.25516i) q^{44} +(0.0360869 + 0.0208348i) q^{45} +(0.604954 - 2.21266i) q^{46} +(4.77903 + 4.01008i) q^{47} +(2.63293 - 3.01126i) q^{48} +(0.683363 + 1.18362i) q^{49} +(6.83697 - 1.79475i) q^{50} +(-1.02817 - 2.82488i) q^{51} +(1.11698 + 6.73444i) q^{52} +(-2.10907 - 0.371886i) q^{53} +(1.28473 - 0.591148i) q^{54} +(-0.156276 + 0.131131i) q^{55} +(4.81875 - 4.67395i) q^{56} +(2.50331 - 3.56840i) q^{57} +(-6.06880 + 6.00740i) q^{58} +(-8.37755 - 9.98398i) q^{59} +(-0.0292984 + 0.0780192i) q^{60} +(0.262558 + 0.0462961i) q^{61} +(-7.72488 + 10.9137i) q^{62} +(2.23032 - 0.811768i) q^{63} +(6.80298 + 4.20945i) q^{64} +(-0.0711136 - 0.123172i) q^{65} +(0.568359 + 6.90026i) q^{66} +(8.74062 - 10.4167i) q^{67} +(5.23715 - 2.95308i) q^{68} +(1.40470 + 0.811005i) q^{69} +(-0.0597539 + 0.126460i) q^{70} +(1.81482 + 10.2924i) q^{71} +(1.58679 + 2.34139i) q^{72} +(-2.97798 - 1.08389i) q^{73} +(0.676954 - 7.30941i) q^{74} +4.99826i q^{75} +(7.85982 + 3.77138i) q^{76} +11.6198i q^{77} +(-4.80646 - 0.445145i) q^{78} +(-10.9766 - 3.99514i) q^{79} +(-0.163523 - 0.0322753i) q^{80} +(0.173648 + 0.984808i) q^{81} +(0.662730 + 0.313148i) q^{82} +(7.53195 + 4.34857i) q^{83} +(2.33153 + 4.13486i) q^{84} +(-0.0805194 + 0.0959593i) q^{85} +(-14.6310 + 1.20512i) q^{86} +(-3.01909 - 5.22921i) q^{87} +(-13.4285 + 3.37952i) q^{88} +(-14.5178 + 5.28404i) q^{89} +(-0.0480998 - 0.0340456i) q^{90} +(-7.97804 - 1.40674i) q^{91} +(-1.14046 + 3.03694i) q^{92} +(-6.07738 - 7.24274i) q^{93} +(-6.20679 - 6.27022i) q^{94} +(-0.180928 - 0.0159899i) q^{95} +(-4.10038 + 3.89704i) q^{96} +(-4.09249 + 3.43400i) q^{97} +(-0.807937 - 1.75588i) q^{98} +(-4.82137 - 0.850137i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 6 q^{4} + 6 q^{6}+O(q^{10}) $ 240 * q + 6 * q^4 + 6 * q^6	$ 240 q + 6 q^{4} + 6 q^{6} - 24 q^{10} + 18 q^{14} - 6 q^{16} + 60 q^{20} - 36 q^{28} - 72 q^{31} - 90 q^{32} + 66 q^{34} - 6 q^{36} + 72 q^{38} - 114 q^{40} - 60 q^{44} + 30 q^{46} + 72 q^{47} + 24 q^{48} - 120 q^{49} + 18 q^{50} + 6 q^{52} - 6 q^{54} + 72 q^{58} - 12 q^{60} + 12 q^{62} + 30 q^{64} - 48 q^{66} - 78 q^{68} - 108 q^{70} - 36 q^{72} - 24 q^{73} - 96 q^{74} - 48 q^{76} - 96 q^{78} - 114 q^{80} - 66 q^{82} - 36 q^{84} - 24 q^{86} - 24 q^{88} + 6 q^{90} - 108 q^{94} + 120 q^{95} - 12 q^{98}+O(q^{100}) $ 240 * q + 6 * q^4 + 6 * q^6 - 24 * q^10 + 18 * q^14 - 6 * q^16 + 60 * q^20 - 36 * q^28 - 72 * q^31 - 90 * q^32 + 66 * q^34 - 6 * q^36 + 72 * q^38 - 114 * q^40 - 60 * q^44 + 30 * q^46 + 72 * q^47 + 24 * q^48 - 120 * q^49 + 18 * q^50 + 6 * q^52 - 6 * q^54 + 72 * q^58 - 12 * q^60 + 12 * q^62 + 30 * q^64 - 48 * q^66 - 78 * q^68 - 108 * q^70 - 36 * q^72 - 24 * q^73 - 96 * q^74 - 48 * q^76 - 96 * q^78 - 114 * q^80 - 66 * q^82 - 36 * q^84 - 24 * q^86 - 24 * q^88 + 6 * q^90 - 108 * q^94 + 120 * q^95 - 12 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/456\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$343$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$-1$	$1$	$1$

Coefficient data

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

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

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

$2$	−1.40819	−	0.130418i	−0.995739	−	0.0922194i
$2$	−1.40819	−	0.130418i	−0.995739	−	0.0922194i
$3$	0.342020	−	0.939693i	0.197465	−	0.542532i
$3$	0.342020	−	0.939693i	0.197465	−	0.542532i
$4$	1.96598	+	0.367306i	0.982991	+	0.183653i
$5$	−0.0410365	+	0.00723583i	−0.0183521	+	0.00323596i	−0.182817	−	0.983147i	$-0.558521\pi$
$5$	−0.0410365	+	0.00723583i	−0.0183521	+	0.00323596i	0.164465	+	0.986383i	$0.447410\pi$
$6$	−0.604181	+	1.27866i	−0.246656	+	0.522010i
$7$	−1.18673	+	2.05547i	−0.448540	+	0.776895i	−0.998291	−	0.0584340i	$-0.981389\pi$
$7$	−1.18673	+	2.05547i	−0.448540	+	0.776895i	0.549751	+	0.835329i	$0.314723\pi$
$8$	−2.72057	−	0.773635i	−0.961866	−	0.273521i
$9$	−0.766044	−	0.642788i	−0.255348	−	0.214263i
$10$	0.0587307	−	0.00483752i	0.0185723	−	0.00152976i
$11$	4.23984	−	2.44787i	1.27836	−	0.738061i	0.301813	−	0.953367i	$-0.402408\pi$
$11$	4.23984	−	2.44787i	1.27836	−	0.738061i	0.976547	+	0.215306i	$0.0690749\pi$
$12$	1.01756	−	1.72179i	0.293744	−	0.497039i
$13$	1.16739	+	3.20738i	0.323776	+	0.889567i	0.989650	+	0.143503i	$0.0458366\pi$
$13$	1.16739	+	3.20738i	0.323776	+	0.889567i	−0.665874	+	0.746064i	$0.731941\pi$
$14$	1.93920	−	2.73972i	0.518274	−	0.732220i
$15$	−0.00723583	+	0.0410365i	−0.00186828	+	0.0105956i
$16$	3.73017	+	1.44423i	0.932543	+	0.361058i
$17$	2.30287	−	1.93233i	0.558527	−	0.468660i	−0.319289	−	0.947657i	$-0.603444\pi$
$17$	2.30287	−	1.93233i	0.558527	−	0.468660i	0.877816	+	0.478997i	$0.159000\pi$
$18$	0.994903	+	1.00507i	0.234501	+	0.236898i
$19$	4.20938	+	1.13188i	0.965697	+	0.259670i
$19$	4.20938	+	1.13188i	0.965697	+	0.259670i
$20$	−0.0833347		0.000847406i	−0.0186342		0.000189486i
$21$	1.52563	+	1.81817i	0.332919	+	0.396757i
$22$	−6.28973	+	2.89411i	−1.34098	+	0.617026i
$23$	−0.281659	+	1.59737i	−0.0587300	+	0.333074i	−0.999989	−	0.00461020i	$-0.998533\pi$
$23$	−0.281659	+	1.59737i	−0.0587300	+	0.333074i	0.941259	+	0.337684i	$0.109644\pi$
$24$	−1.65747	+	2.29190i	−0.338329	+	0.467832i
$25$	−4.69683	+	1.70951i	−0.939366	+	0.341901i
$26$	−1.22560	−	4.66884i	−0.240361	−	0.915635i
$27$	−0.866025	+	0.500000i	−0.166667	+	0.0962250i
$28$	−3.08807	+	3.60513i	−0.583590	+	0.681305i
$29$	3.88126	−	4.62551i	0.720733	−	0.858936i	−0.273969	−	0.961738i	$-0.588337\pi$
$29$	3.88126	−	4.62551i	0.720733	−	0.858936i	0.994702	+	0.102803i	$0.0327811\pi$
$30$	0.0155413	−	0.0568433i	0.00283744	−	0.0103781i
$31$	4.72736	−	8.18803i	0.849059	−	1.47061i	−0.0329892	−	0.999456i	$-0.510503\pi$
$31$	4.72736	−	8.18803i	0.849059	−	1.47061i	0.882049	−	0.471158i	$-0.156164\pi$
$32$	−5.06443	−	2.52023i	−0.895273	−	0.445518i
$33$	−0.850137	−	4.82137i	−0.147990	−	0.839292i
$34$	−3.49488	+	2.42075i	−0.599367	+	0.415156i
$35$	0.0338260	−	0.0929361i	0.00571764	−	0.0157091i
$36$	−1.26993	−	1.54508i	−0.211655	−	0.257514i
$37$			5.19065i			0.853338i	0.904408	+	0.426669i	$0.140313\pi$
$37$			5.19065i			0.853338i	−0.904408	+	0.426669i	$0.859687\pi$
$38$	−5.77997	−	2.14287i	−0.937636	−	0.347620i
$39$	3.41322			0.546553
$40$	0.117240	+	0.0120616i	0.0185373	+	0.00190711i
$41$	−0.487044	−	0.177269i	−0.0760635	−	0.0276848i	0.303708	−	0.952765i	$-0.401775\pi$
$41$	−0.487044	−	0.177269i	−0.0760635	−	0.0276848i	−0.379772	+	0.925080i	$0.623997\pi$
$42$	−1.91124	−	2.75929i	−0.294911	−	0.425768i
$43$	10.2230	−	1.80259i	1.55900	−	0.274893i	0.673375	−	0.739302i	$-0.264844\pi$
$43$	10.2230	−	1.80259i	1.55900	−	0.274893i	0.885621	+	0.464409i	$0.153733\pi$
$44$	9.23457	−	3.25516i	1.39216	−	0.490733i
$45$	0.0360869	+	0.0208348i	0.00537951	+	0.00310586i
$46$	0.604954	−	2.21266i	0.0891956	−	0.326239i
$47$	4.77903	+	4.01008i	0.697094	+	0.584931i	0.920945	−	0.389692i	$-0.127419\pi$
$47$	4.77903	+	4.01008i	0.697094	+	0.584931i	−0.223852	+	0.974623i	$0.571863\pi$
$48$	2.63293	−	3.01126i	0.380031	−	0.434638i
$49$	0.683363	+	1.18362i	0.0976232	+	0.169088i
$50$	6.83697	−	1.79475i	0.966893	−	0.253817i
$51$	−1.02817	−	2.82488i	−0.143973	−	0.395563i
$52$	1.11698	+	6.73444i	0.154897	+	0.933899i
$53$	−2.10907	−	0.371886i	−0.289703	−	0.0510825i	0.0269080	−	0.999638i	$-0.491434\pi$
$53$	−2.10907	−	0.371886i	−0.289703	−	0.0510825i	−0.316611	+	0.948555i	$0.602545\pi$
$54$	1.28473	−	0.591148i	0.174830	−	0.0804451i
$55$	−0.156276	+	0.131131i	−0.0210722	+	0.0176817i
$56$	4.81875	−	4.67395i	0.643933	−	0.624583i
$57$	2.50331	−	3.56840i	0.331571	−	0.472646i
$58$	−6.06880	+	6.00740i	−0.796872	+	0.788810i
$59$	−8.37755	−	9.98398i	−1.09066	−	1.29980i	−0.950859	−	0.309624i	$-0.899797\pi$
$59$	−8.37755	−	9.98398i	−1.09066	−	1.29980i	−0.139806	−	0.990179i	$-0.544648\pi$
$60$	−0.0292984	+	0.0780192i	−0.00378241	+	0.0100722i
$61$	0.262558	+	0.0462961i	0.0336172	+	0.00592761i	0.190431	−	0.981700i	$-0.439011\pi$
$61$	0.262558	+	0.0462961i	0.0336172	+	0.00592761i	−0.156814	+	0.987628i	$0.550122\pi$
$62$	−7.72488	+	10.9137i	−0.981061	+	1.38605i
$63$	2.23032	−	0.811768i	0.280993	−	0.102273i
$64$	6.80298	+	4.20945i	0.850372	+	0.526181i
$65$	−0.0711136	−	0.123172i	−0.00882056	−	0.0152777i
$66$	0.568359	+	6.90026i	0.0699602	+	0.849363i
$67$	8.74062	−	10.4167i	1.06784	−	1.27260i	0.107365	−	0.994220i	$-0.465759\pi$
$67$	8.74062	−	10.4167i	1.06784	−	1.27260i	0.960472	−	0.278378i	$-0.0897969\pi$
$68$	5.23715	−	2.95308i	0.635098	−	0.358113i
$69$	1.40470	+	0.811005i	0.169106	+	0.0976335i
$70$	−0.0597539	+	0.126460i	−0.00714195	+	0.0151149i
$71$	1.81482	+	10.2924i	0.215380	+	1.22148i	0.880246	+	0.474517i	$0.157377\pi$
$71$	1.81482	+	10.2924i	0.215380	+	1.22148i	−0.664867	+	0.746962i	$0.731512\pi$
$72$	1.58679	+	2.34139i	0.187005	+	0.275935i
$73$	−2.97798	−	1.08389i	−0.348546	−	0.126860i	0.161814	−	0.986821i	$-0.448266\pi$
$73$	−2.97798	−	1.08389i	−0.348546	−	0.126860i	−0.510360	+	0.859961i	$0.670488\pi$
$74$	0.676954	−	7.30941i	0.0786943	−	0.849701i
$75$			4.99826i			0.577150i
$76$	7.85982	+	3.77138i	0.901583	+	0.432607i
$77$			11.6198i			1.32420i
$78$	−4.80646	−	0.445145i	−0.544224	−	0.0504028i
$79$	−10.9766	−	3.99514i	−1.23496	−	0.449488i	−0.359666	−	0.933081i	$-0.617109\pi$
$79$	−10.9766	−	3.99514i	−1.23496	−	0.449488i	−0.875293	+	0.483593i	$0.839332\pi$
$80$	−0.163523	−	0.0322753i	−0.0182825	−	0.00360849i
$81$	0.173648	+	0.984808i	0.0192942	+	0.109423i
$82$	0.662730	+	0.313148i	0.0731862	+	0.0345814i
$83$	7.53195	+	4.34857i	0.826739	+	0.477318i	0.852735	−	0.522344i	$-0.174942\pi$
$83$	7.53195	+	4.34857i	0.826739	+	0.477318i	−0.0259957	+	0.999662i	$0.508276\pi$
$84$	2.33153	+	4.13486i	0.254391	+	0.451150i
$85$	−0.0805194	+	0.0959593i	−0.00873356	+	0.0104082i
$86$	−14.6310	+	1.20512i	−1.57770	+	0.129952i
$87$	−3.01909	−	5.22921i	−0.323680	−	0.560630i
$88$	−13.4285	+	3.37952i	−1.43149	+	0.360258i
$89$	−14.5178	+	5.28404i	−1.53888	+	0.560107i	−0.965777	−	0.259375i	$-0.916484\pi$
$89$	−14.5178	+	5.28404i	−1.53888	+	0.560107i	−0.573105	+	0.819482i	$0.694261\pi$
$90$	−0.0480998	−	0.0340456i	−0.00507017	−	0.00358872i
$91$	−7.97804	−	1.40674i	−0.836326	−	0.147467i
$92$	−1.14046	+	3.03694i	−0.118901	+	0.316623i
$93$	−6.07738	−	7.24274i	−0.630195	−	0.751037i
$94$	−6.20679	−	6.27022i	−0.640181	−	0.646724i
$95$	−0.180928	−	0.0159899i	−0.0185628	−	0.00164053i
$96$	−4.10038	+	3.89704i	−0.418493	+	0.397739i
$97$	−4.09249	+	3.43400i	−0.415529	+	0.348670i	−0.826459	−	0.562997i	$-0.809648\pi$
$97$	−4.09249	+	3.43400i	−0.415529	+	0.348670i	0.410930	+	0.911667i	$0.365204\pi$
$98$	−0.807937	−	1.75588i	−0.0816140	−	0.177371i
$99$	−4.82137	−	0.850137i	−0.484566	−	0.0854420i
$100$	−9.86180	+	1.63569i	−0.986180	+	0.163569i
$101$	−0.821669	−	2.25752i	−0.0817591	−	0.224631i	0.892077	−	0.451884i	$-0.149248\pi$
$101$	−0.821669	−	2.25752i	−0.0817591	−	0.224631i	−0.973836	+	0.227253i	$0.927026\pi$
$102$	1.07945	+	4.11206i	0.106881	+	0.407154i
$103$	6.33502	+	10.9726i	0.624208	+	1.08116i	0.988693	+	0.149951i	$0.0479116\pi$
$103$	6.33502	+	10.9726i	0.624208	+	1.08116i	−0.364485	+	0.931209i	$0.618755\pi$
$104$	−0.694625	−	9.62903i	−0.0681136	−	0.944204i
$105$	−0.0757622	−	0.0635721i	−0.00739364	−	0.00620400i
$106$	2.92146	+	0.798746i	0.283758	+	0.0775810i
$107$	−3.50225	−	2.02202i	−0.338575	−	0.195476i	0.321067	−	0.947057i	$-0.395959\pi$
$107$	−3.50225	−	2.02202i	−0.338575	−	0.195476i	−0.659642	+	0.751580i	$0.729292\pi$
$108$	−1.88624	+	0.664895i	−0.181504	+	0.0639796i
$109$	−8.18094	+	1.44252i	−0.783592	+	0.138168i	−0.551110	−	0.834432i	$-0.685796\pi$
$109$	−8.18094	+	1.44252i	−0.783592	+	0.138168i	−0.232481	+	0.972601i	$0.574684\pi$
$110$	0.237167	−	0.164276i	0.0226130	−	0.0156631i
$111$	4.87762	+	1.77531i	0.462963	+	0.168505i
$112$	−7.39527	+	5.95335i	−0.698787	+	0.562539i
$113$	−8.06543			−0.758732			−0.379366	−	0.925247i	$-0.623858\pi$
$113$	−8.06543			−0.758732			−0.379366	+	0.925247i	$0.623858\pi$
$114$	−3.99051	+	4.69849i	−0.373745	+	0.440054i
$115$		−	0.0675883i		−	0.00630264i
$116$	9.32947	−	7.66806i	0.866220	−	0.711961i
$117$	1.16739	−	3.20738i	0.107925	−	0.296522i
$118$	10.4951	+	15.1519i	0.966150	+	1.39484i
$119$	1.23898	+	7.02662i	0.113577	+	0.644130i
$120$	0.0514328	−	0.106045i	0.00469515	−	0.00968050i
$121$	6.48415	−	11.2309i	0.589469	−	1.02099i
$122$	−0.363694	−	0.0994360i	−0.0329273	−	0.00900251i
$123$	−0.333158	+	0.397042i	−0.0300398	+	0.0358000i
$124$	12.3014	−	14.3611i	1.10470	−	1.28967i
$125$	0.360806	−	0.208311i	0.0322715	−	0.0186319i
$126$	−3.24657	+	0.852249i	−0.289228	+	0.0759243i
$127$	−12.4309	+	4.52448i	−1.10307	+	0.401483i	−0.828445	−	0.560070i	$-0.810774\pi$
$127$	−12.4309	+	4.52448i	−1.10307	+	0.401483i	−0.274620	+	0.961553i	$0.588552\pi$
$128$	−9.03088	−	6.81493i	−0.798224	−	0.602360i
$129$	1.80259	−	10.2230i	0.158710	−	0.900087i
$130$	0.0840774	+	0.182724i	0.00737408	+	0.0160260i
$131$	2.41434	+	2.87730i	0.210942	+	0.251391i	0.861133	−	0.508380i	$-0.169755\pi$
$131$	2.41434	+	2.87730i	0.210942	+	0.251391i	−0.650191	+	0.759771i	$0.725311\pi$
$132$	0.0995616	−	9.79098i	0.00866572	−	0.852196i
$133$	−7.32192	+	7.30902i	−0.634891	+	0.633772i
$134$	−13.6669	+	13.5287i	−1.18064	+	1.16870i
$135$	0.0319207	−	0.0267846i	0.00274730	−	0.00230525i
$136$	−7.76003	+	3.47547i	−0.665417	+	0.298019i
$137$	−2.02646	+	11.4926i	−0.173132	+	0.981882i	0.767145	+	0.641473i	$0.221677\pi$
$137$	−2.02646	+	11.4926i	−0.173132	+	0.981882i	−0.940278	+	0.340409i	$0.889435\pi$
$138$	−1.87231	−	1.32524i	−0.159382	−	0.112812i
$139$	3.35011	+	9.20436i	0.284153	+	0.780704i	0.996856	+	0.0792377i	$0.0252486\pi$
$139$	3.35011	+	9.20436i	0.284153	+	0.780704i	−0.712703	+	0.701466i	$0.752529\pi$
$140$	0.100637	−	0.170286i	0.00850540	−	0.0143918i
$141$	5.40277	−	3.11929i	0.454996	−	0.262692i
$142$	−1.21330	−	14.7303i	−0.101818	−	1.23614i
$143$	12.8008	+	10.7411i	1.07046	+	0.898220i
$144$	−1.92914	−	3.50406i	−0.160762	−	0.292005i
$145$	−0.125804	+	0.217899i	−0.0104474	+	0.0180955i
$146$	4.05219	+	1.91471i	0.335362	+	0.158462i
$147$	1.34596	−	0.237329i	0.111013	−	0.0195746i
$148$	−1.90656	+	10.2047i	−0.156718	+	0.838823i
$149$	−2.96694	+	8.15160i	−0.243061	+	0.667805i	0.756838	+	0.653603i	$0.226743\pi$
$149$	−2.96694	+	8.15160i	−0.243061	+	0.667805i	−0.999899	+	0.0142026i	$0.995479\pi$
$150$	0.651863	−	7.03849i	0.0532244	−	0.574690i
$151$	18.4553			1.50187			0.750937	−	0.660374i	$-0.229602\pi$
$151$	18.4553			1.50187			0.750937	+	0.660374i	$0.229602\pi$
$152$	−10.5762	−	6.33587i	−0.857846	−	0.513907i
$153$	−3.00618			−0.243035
$154$	1.51543	−	16.3629i	0.122117	−	1.31856i
$155$	−0.134747	+	0.370214i	−0.0108231	+	0.0297363i
$156$	6.71033	+	1.25370i	0.537257	+	0.100376i
$157$	−17.6276	+	3.10823i	−1.40684	+	0.248064i	−0.824951	−	0.565205i	$-0.808797\pi$
$157$	−17.6276	+	3.10823i	−1.40684	+	0.248064i	−0.581889	+	0.813269i	$0.697686\pi$
$158$	14.9360	+	7.05744i	1.18824	+	0.561460i
$159$	−1.07080	+	1.85469i	−0.0849202	+	0.147086i
$160$	0.226062	+	0.0667760i	0.0178718	+	0.00527911i
$161$	−2.94909	−	2.47458i	−0.232421	−	0.195024i
$162$	−0.116093	−	1.40944i	−0.00912109	−	0.110736i
$163$	−4.14121	+	2.39093i	−0.324364	+	0.187272i	−0.653336	−	0.757068i	$-0.726631\pi$
$163$	−4.14121	+	2.39093i	−0.324364	+	0.187272i	0.328972	+	0.944340i	$0.393298\pi$
$164$	−0.892407	−	0.527403i	−0.0696853	−	0.0411832i
$165$	0.0697732	+	0.191700i	0.00543184	+	0.0149239i
$166$	−10.0393	−	7.10591i	−0.779198	−	0.551526i
$167$	−0.355724	+	2.01741i	−0.0275267	+	0.156112i	−0.995473	−	0.0950460i	$-0.969700\pi$
$167$	−0.355724	+	2.01741i	−0.0275267	+	0.156112i	0.967946	+	0.251158i	$0.0808113\pi$
$168$	−2.74397	−	6.12673i	−0.211702	−	0.472688i
$169$	1.03410	−	0.867710i	0.0795459	−	0.0667470i
$170$	0.125901	−	0.124628i	0.00965618	−	0.00955849i
$171$	−2.49701	−	3.57280i	−0.190951	−	0.273219i
$172$	20.7604	+	0.211106i	1.58296	+	0.0160967i
$173$	−11.6498	−	13.8837i	−0.885721	−	1.05556i	−0.998083	−	0.0618942i	$-0.980286\pi$
$173$	−11.6498	−	13.8837i	−0.885721	−	1.05556i	0.112361	−	0.993667i	$-0.464159\pi$
$174$	3.56946	+	7.75745i	0.270600	+	0.588091i
$175$	2.06001	−	11.6829i	0.155722	−	0.883145i
$176$	19.3506	−	3.00767i	1.45861	−	0.226712i
$177$	−12.2472	+	4.45760i	−0.920553	+	0.335054i
$178$	21.1329	−	5.54754i	1.58398	−	0.415806i
$179$	−17.7790	+	10.2647i	−1.32886	+	0.767219i	−0.985124	−	0.171847i	$-0.945027\pi$
$179$	−17.7790	+	10.2647i	−1.32886	+	0.767219i	−0.343738	+	0.939066i	$0.611693\pi$
$180$	0.0632934	+	0.0542157i	0.00471761	+	0.00404100i
$181$	2.62332	−	3.12636i	0.194990	−	0.232380i	−0.659686	−	0.751541i	$-0.729311\pi$
$181$	2.62332	−	3.12636i	0.194990	−	0.232380i	0.854677	+	0.519161i	$0.173755\pi$
$182$	11.0511	+	3.02144i	0.819163	+	0.223964i
$183$	0.133304	−	0.230890i	0.00985415	−	0.0170679i
$184$	2.00205	−	4.12785i	0.147593	−	0.304309i
$185$	−0.0375587	−	0.213006i	−0.00276137	−	0.0156605i
$186$	7.61351	+	10.9917i	0.558249	+	0.805953i
$187$	5.03368	−	13.8299i	0.368099	−	1.01134i
$188$	7.92257	+	9.63912i	0.577813	+	0.703005i
$189$		−	2.37345i		−	0.172643i
$190$	0.252695	+	0.0461130i	0.0183324	+	0.00334539i
$191$	8.73762			0.632232			0.316116	−	0.948721i	$-0.397621\pi$
$191$	8.73762			0.632232			0.316116	+	0.948721i	$0.397621\pi$
$192$	6.28235	−	4.95299i	0.453389	−	0.357451i
$193$	3.11206	+	1.13270i	0.224011	+	0.0815335i	0.451588	−	0.892227i	$-0.350858\pi$
$193$	3.11206	+	1.13270i	0.224011	+	0.0815335i	−0.227576	+	0.973760i	$0.573080\pi$
$194$	6.21084	−	4.30199i	0.445913	−	0.308865i
$195$	−0.140067	+	0.0246975i	−0.0100304	+	0.00176863i
$196$	0.908729	+	2.57798i	0.0649092	+	0.184141i
$197$	2.18078	+	1.25908i	0.155374	+	0.0897054i	0.575671	−	0.817681i	$-0.304741\pi$
$197$	2.18078	+	1.25908i	0.155374	+	0.0897054i	−0.420297	+	0.907387i	$0.638074\pi$
$198$	6.67851	+	1.82594i	0.474621	+	0.129764i
$199$	−13.9606	−	11.7143i	−0.989640	−	0.830406i	−0.00412434	−	0.999991i	$-0.501313\pi$
$199$	−13.9606	−	11.7143i	−0.989640	−	0.830406i	−0.985516	+	0.169585i	$0.945757\pi$
$200$	14.1006	−	1.01720i	0.997062	−	0.0719267i
$201$	−6.79899	−	11.7762i	−0.479564	−	0.830629i
$202$	0.862643	+	3.28617i	0.0606953	+	0.231214i
$203$	4.90160	+	13.4670i	0.344025	+	0.945200i
$204$	−0.983775	−	5.93133i	−0.0688780	−	0.415276i
$205$	0.0212692	+	0.00375034i	0.00148551	+	0.000261935i
$206$	−7.48987	−	16.2776i	−0.521844	−	1.13412i
$207$	1.24253	−	1.04261i	0.0863619	−	0.0724662i
$208$	−0.277636	+	13.6501i	−0.0192506	+	0.946462i
$209$	20.6178	−	5.50504i	1.42616	−	0.380792i
$210$	0.0983965	+	0.0994021i	0.00679000	+	0.00685940i
$211$	−7.89687	−	9.41113i	−0.543643	−	0.647889i	0.422357	−	0.906430i	$-0.361203\pi$
$211$	−7.89687	−	9.41113i	−0.543643	−	0.647889i	−0.966000	+	0.258541i	$0.916758\pi$
$212$	−4.00980	−	1.50579i	−0.275394	−	0.103418i
$213$	10.2924	+	1.81482i	0.705221	+	0.124350i
$214$	4.66811	+	3.30414i	0.319106	+	0.225867i
$215$	−0.406473	+	0.147944i	−0.0277212	+	0.0100897i
$216$	2.74290	−	0.690297i	0.186631	−	0.0469687i
$217$	11.2202	+	19.4339i	0.761675	+	1.31926i
$218$	11.7084	−	0.964397i	0.792994	−	0.0653172i
$219$	−2.03706	+	2.42767i	−0.137652	+	0.164047i
$220$	−0.355400	+	0.200400i	−0.0239611	+	0.0135110i
$221$	8.88607	+	5.13038i	0.597742	+	0.345107i
$222$	−6.63706	−	3.13609i	−0.445451	−	0.210481i
$223$	−5.00455	−	28.3822i	−0.335130	−	1.90061i	−0.425950	−	0.904747i	$-0.640060\pi$
$223$	−5.00455	−	28.3822i	−0.335130	−	1.90061i	0.0908204	−	0.995867i	$-0.471051\pi$
$224$	11.1903	−	7.41895i	0.747687	−	0.495700i
$225$	4.69683	+	1.70951i	0.313122	+	0.113967i
$226$	11.3576	+	1.05188i	0.755499	+	0.0699698i
$227$		−	6.23350i		−	0.413732i	−0.978369	−	0.206866i	$-0.933674\pi$
$227$		−	6.23350i		−	0.413732i	0.978369	−	0.206866i	$-0.0663264\pi$
$228$	6.23215	−	6.09592i	0.412734	−	0.403712i
$229$			3.97342i			0.262571i	0.991345	+	0.131285i	$0.0419104\pi$
$229$			3.97342i			0.262571i	−0.991345	+	0.131285i	$0.958090\pi$
$230$	−0.00881473	+	0.0951770i	−0.000581226	+	0.00627579i
$231$	10.9191	+	3.97421i	0.718421	+	0.261484i
$232$	−14.1377	+	9.58133i	−0.928185	+	0.629045i
$233$	0.542503	+	3.07669i	0.0355405	+	0.201560i	0.997408	−	0.0719563i	$-0.0229242\pi$
$233$	0.542503	+	3.07669i	0.0355405	+	0.201560i	−0.961867	+	0.273517i	$0.911813\pi$
$234$	−2.06220	+	4.36434i	−0.134811	+	0.285306i
$235$	−0.225131	−	0.129979i	−0.0146859	−	0.00847892i
$236$	−12.8029	−	22.7054i	−0.833401	−	1.47800i
$237$	−7.50841	+	8.94817i	−0.487723	+	0.581246i
$238$	−0.828323	−	10.0564i	−0.0536922	−	0.651859i
$239$	−3.72390	−	6.44998i	−0.240879	−	0.417214i	0.720086	−	0.693885i	$-0.244102\pi$
$239$	−3.72390	−	6.44998i	−0.240879	−	0.417214i	−0.960965	+	0.276670i	$0.910769\pi$
$240$	−0.0862571	+	0.142623i	−0.00556787	+	0.00920626i
$241$	18.7705	−	6.83191i	1.20912	−	0.440082i	0.342719	−	0.939438i	$-0.388652\pi$
$241$	18.7705	−	6.83191i	1.20912	−	0.440082i	0.866397	+	0.499356i	$0.166430\pi$
$242$	−10.5956	+	14.9695i	−0.681112	+	0.962278i
$243$	0.984808	+	0.173648i	0.0631754	+	0.0111395i
$244$	0.499180	+	0.187457i	0.0319568	+	0.0120007i
$245$	−0.0366073	−	0.0436268i	−0.00233875	−	0.00278722i
$246$	0.520930	−	0.515659i	0.0332133	−	0.0328772i
$247$	1.28363	+	14.8224i	0.0816753	+	0.943127i
$248$	−19.1957	+	18.6188i	−1.21893	+	1.18230i
$249$	6.66240	−	5.59042i	0.422213	−	0.354278i
$250$	−0.535250	+	0.246286i	−0.0338522	+	0.0155765i
$251$	7.23276	+	1.27533i	0.456528	+	0.0804982i	0.397183	−	0.917739i	$-0.369988\pi$
$251$	7.23276	+	1.27533i	0.456528	+	0.0804982i	0.0593446	+	0.998238i	$0.481099\pi$
$252$	4.68293	−	0.776715i	0.294997	−	0.0489284i
$253$	2.71596	+	7.46205i	0.170751	+	0.469135i
$254$	18.0951	−	4.75010i	1.13539	−	0.298048i
$255$	0.0626330	+	0.108484i	0.00392223	+	0.00679350i
$256$	11.8284	+	10.7745i	0.739274	+	0.673405i
$257$	1.92782	+	1.61764i	0.120254	+	0.100905i	0.700932	−	0.713228i	$-0.252768\pi$
$257$	1.92782	+	1.61764i	0.120254	+	0.100905i	−0.580677	+	0.814134i	$0.697212\pi$
$258$	−3.87165	+	14.1608i	−0.241039	+	0.881615i
$259$	−10.6692	−	6.15988i	−0.662953	−	0.382756i
$260$	−0.0945662	−	0.268275i	−0.00586475	−	0.0166377i
$261$	−5.94644	+	1.04852i	−0.368075	+	0.0649016i
$262$	−3.02460	−	4.36666i	−0.186860	−	0.269773i
$263$	−25.7079	−	9.35691i	−1.58522	−	0.576972i	−0.608887	−	0.793257i	$-0.708384\pi$
$263$	−25.7079	−	9.35691i	−1.58522	−	0.576972i	−0.976330	+	0.216285i	$0.930606\pi$
$264$	−1.41712	+	13.7746i	−0.0872178	+	0.847765i
$265$	0.0892397			0.00548195
$266$	11.2639	−	9.33756i	0.690631	−	0.572522i
$267$			15.4495i			0.945494i
$268$	21.0100	−	17.2685i	1.28339	−	1.05484i
$269$	−5.31229	+	14.5954i	−0.323896	+	0.889897i	0.665725	+	0.746197i	$0.268122\pi$
$269$	−5.31229	+	14.5954i	−0.323896	+	0.889897i	−0.989621	+	0.143700i	$0.954100\pi$
$270$	−0.0484435	+	0.0335548i	−0.00294818	+	0.00204208i
$271$	−1.78542	−	10.1256i	−0.108457	−	0.615088i	−0.989783	−	0.142581i	$-0.954460\pi$
$271$	−1.78542	−	10.1256i	−0.108457	−	0.615088i	0.881327	−	0.472508i	$-0.156651\pi$
$272$	11.3808	−	3.88207i	0.690064	−	0.235385i
$273$	−4.05056	+	7.01577i	−0.245151	+	0.424614i
$274$	4.35248	−	15.9195i	0.262943	−	0.961732i
$275$	−15.7292	+	18.7453i	−0.948504	+	1.13038i
$276$	2.46373	+	2.11038i	0.148299	+	0.127030i
$277$	18.5627	−	10.7172i	1.11533	−	0.643935i	0.175123	−	0.984546i	$-0.443968\pi$
$277$	18.5627	−	10.7172i	1.11533	−	0.643935i	0.940204	+	0.340612i	$0.110634\pi$
$278$	−3.51717	−	13.3984i	−0.210946	−	0.803581i
$279$	−8.88454	+	3.23371i	−0.531903	+	0.193597i
$280$	−0.163925	+	0.226670i	−0.00979636	+	0.0135461i
$281$	3.25039	−	18.4339i	0.193902	−	1.09967i	−0.720071	−	0.693900i	$-0.755891\pi$
$281$	3.25039	−	18.4339i	0.193902	−	1.09967i	0.913974	−	0.405774i	$-0.132998\pi$
$282$	−8.01493	+	3.68793i	−0.477282	+	0.219613i
$283$	−2.71913	−	3.24053i	−0.161635	−	0.192629i	0.679148	−	0.734001i	$-0.262349\pi$
$283$	−2.71913	−	3.24053i	−0.161635	−	0.192629i	−0.840783	+	0.541372i	$0.817905\pi$
$284$	−0.212538	+	20.9012i	−0.0126118	+	1.24026i
$285$	−0.0769066	+	0.164548i	−0.00455555	+	0.00974697i
$286$	−16.6251	−	16.7950i	−0.983062	−	0.993109i
$287$	0.942359	−	0.790733i	0.0556257	−	0.0466755i
$288$	2.25960	+	5.18596i	0.133148	+	0.305586i
$289$	−1.38274	+	7.84191i	−0.0813377	+	0.461289i
$290$	0.205573	−	0.290435i	0.0120717	−	0.0170549i
$291$	1.82720	+	5.02018i	0.107112	+	0.294288i
$292$	−5.45653	−	3.22475i	−0.319319	−	0.188714i
$293$	28.1669	−	16.2621i	1.64553	−	0.950045i	0.666706	−	0.745321i	$-0.267704\pi$
$293$	28.1669	−	16.2621i	1.64553	−	0.950045i	0.978820	−	0.204723i	$-0.0656295\pi$
$294$	−1.92632	+	0.158667i	−0.112345	+	0.00925362i
$295$	0.416027	+	0.349088i	0.0242221	+	0.0203247i
$296$	4.01567	−	14.1215i	0.233406	−	0.820796i
$297$	−2.44787	+	4.23984i	−0.142040	+	0.246020i
$298$	5.24112	−	11.0920i	0.303610	−	0.642545i
$299$	−5.45217	+	0.961365i	−0.315307	+	0.0555971i
$300$	−1.83589	+	9.82650i	−0.105995	+	0.567333i
$301$	−8.42674	+	23.1523i	−0.485709	+	1.33448i
$302$	−25.9886	−	2.40691i	−1.49547	−	0.138502i
$303$	−2.40240			−0.138014
$304$	14.0670	+	10.3014i	0.806798	+	0.590827i
$305$	−0.0111095			−0.000636126
$306$	4.23326	+	0.392060i	0.242000	+	0.0224126i
$307$	−1.48742	+	4.08666i	−0.0848917	+	0.233238i	−0.974874	−	0.222757i	$-0.928494\pi$
$307$	−1.48742	+	4.08666i	−0.0848917	+	0.233238i	0.889982	+	0.455995i	$0.150717\pi$
$308$	−4.26802	+	22.8443i	−0.243193	+	1.30168i
$309$	12.4776	−	2.20013i	0.709823	−	0.125161i
$310$	0.238032	−	0.503758i	0.0135193	−	0.0286115i
$311$	−14.0839	+	24.3940i	−0.798623	+	1.38326i	0.121889	+	0.992544i	$0.461105\pi$
$311$	−14.0839	+	24.3940i	−0.798623	+	1.38326i	−0.920513	+	0.390712i	$0.872229\pi$
$312$	−9.28590	−	2.64059i	−0.525711	−	0.149494i
$313$	−7.36582	−	6.18066i	−0.416341	−	0.349352i	0.410428	−	0.911893i	$-0.365379\pi$
$313$	−7.36582	−	6.18066i	−0.416341	−	0.349352i	−0.826769	+	0.562541i	$0.809824\pi$
$314$	25.2284	−	2.07801i	1.42372	−	0.117269i
$315$	−0.0856504	+	0.0494503i	−0.00482585	+	0.00278621i
$316$	−20.1123	−	11.8861i	−1.13140	−	0.668647i
$317$	−0.0166987	−	0.0458793i	−0.000937893	−	0.00257684i	0.939223	−	0.343308i	$-0.111548\pi$
$317$	−0.0166987	−	0.0458793i	−0.000937893	−	0.00257684i	−0.940161	+	0.340731i	$0.889325\pi$
$318$	1.74978	−	2.47209i	0.0981225	−	0.138628i
$319$	5.13328	−	29.1123i	0.287408	−	1.62997i
$320$	−0.309629	−	0.123516i	−0.0173088	−	0.00690474i
$321$	−3.09792	+	2.59946i	−0.172909	+	0.145088i
$322$	3.83014	+	3.86928i	0.213445	+	0.215627i
$323$	11.8808	−	5.52736i	0.661065	−	0.307551i
$324$	−0.0203364	+	1.99990i	−0.00112980	+	0.111105i
$325$	−10.9661	−	13.0689i	−0.608288	−	0.724930i
$326$	6.14342	−	2.82679i	0.340252	−	0.156561i
$327$	−1.44252	+	8.18094i	−0.0797715	+	0.452407i
$328$	1.18789	+	0.859067i	0.0655905	+	0.0474341i
$329$	−13.9140	+	5.06429i	−0.767104	+	0.279203i
$330$	−0.0732526	−	0.279050i	−0.00403242	−	0.0153612i
$331$	18.5772	−	10.7255i	1.02109	−	0.589529i	0.106673	−	0.994294i	$-0.465980\pi$
$331$	18.5772	−	10.7255i	1.02109	−	0.589529i	0.914420	+	0.404766i	$0.132647\pi$
$332$	13.2104	+	11.3158i	0.725016	+	0.621033i
$333$	3.33649	−	3.97627i	0.182838	−	0.217898i
$334$	0.764032	−	2.79450i	0.0418060	−	0.152908i
$335$	−0.283311	+	0.490709i	−0.0154789	+	0.0268103i
$336$	3.06499	+	8.98545i	0.167209	+	0.490196i
$337$	−0.765660	−	4.34228i	−0.0417082	−	0.236539i	0.956826	−	0.290661i	$-0.0938751\pi$
$337$	−0.765660	−	4.34228i	−0.0417082	−	0.236539i	−0.998534	+	0.0541220i	$0.982764\pi$
$338$	−1.56937	+	1.08703i	−0.0853623	+	0.0591268i
$339$	−2.75854	+	7.57903i	−0.149823	+	0.411636i
$340$	−0.193546	+	0.159079i	−0.0104965	+	0.00862727i
$341$		−	46.2879i		−	2.50663i
$342$	3.05030	+	5.35683i	0.164942	+	0.289664i
$343$	−19.8580			−1.07223
$344$	−29.2070	−	3.00480i	−1.57473	−	0.162008i
$345$	−0.0635123	−	0.0231166i	−0.00341938	−	0.00124455i
$346$	14.5945	+	21.0703i	0.784604	+	1.13274i
$347$	−10.9964	+	1.93896i	−0.590316	+	0.104089i	−0.460823	−	0.887492i	$-0.652446\pi$
$347$	−10.9964	+	1.93896i	−0.590316	+	0.104089i	−0.129492	+	0.991580i	$0.541335\pi$
$348$	−4.01475	−	11.3895i	−0.215213	−	0.610540i
$349$	−20.5782	−	11.8808i	−1.10153	−	0.635966i	−0.164905	−	0.986310i	$-0.552732\pi$
$349$	−20.5782	−	11.8808i	−1.10153	−	0.635966i	−0.936621	+	0.350343i	$0.886065\pi$
$350$	−4.42454	+	16.1831i	−0.236502	+	0.865021i
$351$	−2.61468	−	2.19398i	−0.139561	−	0.117106i
$352$	−27.6416	+	1.71169i	−1.47330	+	0.0912335i
$353$	0.773591	+	1.33990i	0.0411741	+	0.0713156i	0.885878	−	0.463918i	$-0.153557\pi$
$353$	0.773591	+	1.33990i	0.0411741	+	0.0713156i	−0.844704	+	0.535234i	$0.820224\pi$
$354$	17.8276	−	4.67989i	0.947529	−	0.248733i
$355$	−0.148948	−	0.409230i	−0.00790532	−	0.0217197i
$356$	−30.4826	+	5.05587i	−1.61557	+	0.267960i
$357$	7.02662	+	1.23898i	0.371888	+	0.0655740i
$358$	26.3748	−	12.1359i	1.39395	−	0.641402i
$359$	17.1627	−	14.4012i	0.905812	−	0.760066i	−0.0655058	−	0.997852i	$-0.520866\pi$
$359$	17.1627	−	14.4012i	0.905812	−	0.760066i	0.971318	+	0.237786i	$0.0764216\pi$
$360$	−0.0820582	−	0.0846004i	−0.00432485	−	0.00445883i
$361$	16.4377	+	9.52899i	0.865143	+	0.501526i
$362$	−4.10187	+	4.06037i	−0.215589	+	0.213408i
$363$	−8.33587	−	9.93430i	−0.437520	−	0.521416i
$364$	−15.1680	−	5.69602i	−0.795019	−	0.298552i
$365$	0.130048	+	0.0229311i	0.00680705	+	0.00120027i
$366$	−0.217830	+	0.307751i	−0.0113861	+	0.0160864i
$367$	−3.97914	+	1.44829i	−0.207709	+	0.0756001i	−0.443780	−	0.896136i	$-0.646363\pi$
$367$	−3.97914	+	1.44829i	−0.207709	+	0.0756001i	0.236070	+	0.971736i	$0.424140\pi$
$368$	−3.35761	+	5.55168i	−0.175027	+	0.289401i
$369$	0.259151	+	0.448862i	0.0134908	+	0.0233668i
$370$	0.0251099	+	0.304850i	0.00130540	+	0.0158484i
$371$	3.26729	−	3.89380i	0.169629	−	0.202156i
$372$	−9.28772	−	16.4714i	−0.481546	−	0.854000i
$373$	−13.1922	−	7.61650i	−0.683064	−	0.394367i	0.117944	−	0.993020i	$-0.462370\pi$
$373$	−13.1922	−	7.61650i	−0.683064	−	0.394367i	−0.801009	+	0.598653i	$0.795703\pi$
$374$	−8.89203	+	18.8186i	−0.459796	+	0.973088i
$375$	−0.0723458	−	0.410293i	−0.00373592	−	0.0211875i
$376$	−9.89934	−	14.6069i	−0.510520	−	0.753295i
$377$	19.3667	+	7.04891i	0.997437	+	0.363037i
$378$	−0.309541	+	3.34226i	−0.0159211	+	0.171908i
$379$			26.5582i			1.36420i	0.731259	+	0.682100i	$0.238933\pi$
$379$			26.5582i			1.36420i	−0.731259	+	0.682100i	$0.761067\pi$
$380$	−0.349828	−	0.0978917i	−0.0179458	−	0.00502174i
$381$			13.2287i			0.677727i
$382$	−12.3042	−	1.13954i	−0.629538	−	0.0583040i
$383$	−29.7738	−	10.8368i	−1.52137	−	0.553734i	−0.559882	−	0.828573i	$-0.689153\pi$
$383$	−29.7738	−	10.8368i	−1.52137	−	0.553734i	−0.961490	+	0.274838i	$0.911376\pi$
$384$	−9.49268	+	6.15541i	−0.484421	+	0.314117i
$385$	−0.0840790	−	0.476836i	−0.00428506	−	0.0243018i
$386$	−4.23465	−	2.00092i	−0.215538	−	0.101844i
$387$	−8.98997	−	5.19036i	−0.456986	−	0.263841i
$388$	−9.30709	+	5.24800i	−0.472496	+	0.266427i
$389$	−10.5963	+	12.6282i	−0.537253	+	0.640274i	−0.964570	−	0.263829i	$-0.915015\pi$
$389$	−10.5963	+	12.6282i	−0.537253	+	0.640274i	0.427316	+	0.904102i	$0.359459\pi$
$390$	0.200461	−	0.0165115i	0.0101507	−	0.000836093i
$391$	2.43803	+	4.22278i	0.123296	+	0.213555i
$392$	−0.943446	−	3.74879i	−0.0476512	−	0.189342i
$393$	3.52954	−	1.28465i	0.178042	−	0.0648018i
$394$	−2.90674	−	2.05743i	−0.146440	−	0.103652i
$395$	0.479347	+	0.0845218i	0.0241186	+	0.00425275i
$396$	−9.16646	−	3.44227i	−0.460632	−	0.172981i
$397$	−6.90727	−	8.23176i	−0.346666	−	0.413140i	0.564334	−	0.825546i	$-0.309133\pi$
$397$	−6.90727	−	8.23176i	−0.346666	−	0.413140i	−0.911000	+	0.412406i	$0.864688\pi$
$398$	18.1314	+	18.3167i	0.908843	+	0.918132i
$399$	4.36399	+	9.38018i	0.218473	+	0.469596i
$400$	−19.9889	−	0.406565i	−0.999446	−	0.0203282i
$401$	−18.2141	+	15.2835i	−0.909570	+	0.763220i	−0.972037	−	0.234827i	$-0.924547\pi$
$401$	−18.2141	+	15.2835i	−0.909570	+	0.763220i	0.0624675	+	0.998047i	$0.480103\pi$
$402$	8.03843	+	17.4698i	0.400920	+	0.871315i
$403$	31.7808	+	5.60381i	1.58311	+	0.279146i
$404$	−0.786188	−	4.74004i	−0.0391143	−	0.235826i
$405$	−0.0142518	−	0.0391565i	−0.000708178	−	0.00194570i
$406$	−5.14603	−	19.6034i	−0.255393	−	0.972898i
$407$	12.7060	+	22.0075i	0.629815	+	1.09087i
$408$	0.611788	+	8.48072i	0.0302880	+	0.419858i
$409$	23.5162	+	19.7324i	1.16280	+	0.975707i	0.999940	−	0.0109421i	$-0.00348306\pi$
$409$	23.5162	+	19.7324i	1.16280	+	0.975707i	0.162862	+	0.986649i	$0.447928\pi$
$410$	−0.0294620	−	0.00805507i	−0.00145502	−	0.000397812i
$411$	10.1065	+	5.83496i	0.498515	+	0.287818i
$412$	8.42425	+	23.8988i	0.415033	+	1.17741i
$413$	30.4636	−	5.37156i	1.49902	−	0.264317i
$414$	−1.88569	+	1.30614i	−0.0926767	+	0.0641932i
$415$	−0.340550	−	0.123950i	−0.0167170	−	0.00608447i
$416$	2.17118	−	19.1856i	0.106451	−	0.940653i
$417$	9.79508			0.479667
$418$	−29.7516	+	5.06320i	−1.45520	+	0.247649i
$419$		−	18.9017i		−	0.923410i	−0.887034	−	0.461705i	$-0.847238\pi$
$419$		−	18.9017i		−	0.923410i	0.887034	−	0.461705i	$-0.152762\pi$
$420$	−0.125597	−	0.152809i	−0.00612850	−	0.00745634i
$421$	3.17715	−	8.72915i	0.154845	−	0.425433i	−0.837877	−	0.545858i	$-0.816204\pi$
$421$	3.17715	−	8.72915i	0.154845	−	0.425433i	0.992722	+	0.120425i	$0.0384259\pi$
$422$	9.89290	+	14.2825i	0.481579	+	0.695262i
$423$	−1.08332	−	6.14381i	−0.0526728	−	0.298722i
$424$	5.45016	+	2.64339i	0.264683	+	0.128374i
$425$	−7.51284	+	13.0126i	−0.364426	+	0.631205i
$426$	−14.2569	−	3.89792i	−0.690749	−	0.188855i
$427$	−0.406745	+	0.484740i	−0.0196838	+	0.0234582i
$428$	−6.14266	−	5.26166i	−0.296916	−	0.254332i
$429$	14.4715	−	8.35513i	0.698691	−	0.403389i
$430$	0.591685	−	0.155322i	0.0285336	−	0.00749027i
$431$	−5.14174	+	1.87144i	−0.247669	+	0.0901441i	−0.462872	−	0.886425i	$-0.653181\pi$
$431$	−5.14174	+	1.87144i	−0.247669	+	0.0901441i	0.215203	+	0.976569i	$0.430959\pi$
$432$	−3.95254	+	0.614344i	−0.190167	+	0.0295576i
$433$	−4.13052	+	23.4254i	−0.198500	+	1.12575i	0.708845	+	0.705364i	$0.249217\pi$
$433$	−4.13052	+	23.4254i	−0.198500	+	1.12575i	−0.907345	+	0.420386i	$0.861895\pi$
$434$	−13.2656	−	28.8299i	−0.636768	−	1.38388i
$435$	0.161730	+	0.192743i	0.00775438	+	0.00924131i
$436$	−16.6134	−	0.168937i	−0.795639	−	0.00809061i
$437$	−2.99363	+	6.40512i	−0.143205	+	0.306398i
$438$	3.18517	−	3.15294i	0.152193	−	0.150653i
$439$	−15.2565	+	12.8017i	−0.728153	+	0.610993i	−0.929627	−	0.368501i	$-0.879871\pi$
$439$	−15.2565	+	12.8017i	−0.728153	+	0.610993i	0.201475	+	0.979494i	$0.435427\pi$
$440$	0.526606	−	0.235850i	0.0251049	−	0.0112437i
$441$	0.237329	−	1.34596i	0.0113014	−	0.0640934i
$442$	−11.8442	−	8.38344i	−0.563369	−	0.398759i
$443$	−2.54487	−	6.99196i	−0.120910	−	0.332198i	0.864441	−	0.502734i	$-0.167672\pi$
$443$	−2.54487	−	6.99196i	−0.120910	−	0.332198i	−0.985352	+	0.170536i	$0.945450\pi$
$444$	8.93723	+	5.28180i	0.424142	+	0.250663i
$445$	0.557524	−	0.321887i	0.0264292	−	0.0152589i
$446$	3.34579	+	40.6202i	0.158428	+	1.92342i
$447$	6.64525	+	5.57602i	0.314309	+	0.263737i
$448$	−16.7257	+	8.98785i	−0.790214	+	0.424636i
$449$	1.87400	−	3.24586i	0.0884395	−	0.153182i	−0.818412	−	0.574632i	$-0.805145\pi$
$449$	1.87400	−	3.24586i	0.0884395	−	0.153182i	0.906852	+	0.421450i	$0.138479\pi$
$450$	−6.39107	−	3.01986i	−0.301278	−	0.142357i
$451$	−2.49892	+	0.440627i	−0.117670	+	0.0207483i
$452$	−15.8565	−	2.96248i	−0.745827	−	0.139343i
$453$	6.31210	−	17.3423i	0.296568	−	0.814814i
$454$	−0.812960	+	8.77793i	−0.0381541	+	0.411969i
$455$	0.337570			0.0158255
$456$	−9.57105	+	7.77142i	−0.448206	+	0.363930i
$457$	4.64905			0.217473			0.108737	−	0.994071i	$-0.465319\pi$
$457$	4.64905			0.217473			0.108737	+	0.994071i	$0.465319\pi$
$458$	0.518205	−	5.59532i	0.0242141	−	0.261452i
$459$	−1.02817	+	2.82488i	−0.0479910	+	0.131854i
$460$	0.0248256	−	0.132877i	0.00115750	−	0.00619544i
$461$	6.86149	−	1.20987i	0.319571	−	0.0563491i	−0.0115616	−	0.999933i	$-0.503680\pi$
$461$	6.86149	−	1.20987i	0.319571	−	0.0563491i	0.331133	+	0.943584i	$0.392569\pi$
$462$	−14.8578	−	7.02047i	−0.691246	−	0.326622i
$463$	5.36310	−	9.28916i	0.249244	−	0.431704i	−0.714072	−	0.700072i	$-0.753151\pi$
$463$	5.36310	−	9.28916i	0.249244	−	0.431704i	0.963316	+	0.268368i	$0.0864845\pi$
$464$	21.1581	−	11.6485i	0.982240	−	0.540768i
$465$	0.301801	+	0.253241i	0.0139957	+	0.0117438i
$466$	−0.362690	−	4.40330i	−0.0168013	−	0.203979i
$467$	−16.7166	+	9.65131i	−0.773550	+	0.446609i	−0.834139	−	0.551554i	$-0.814035\pi$
$467$	−16.7166	+	9.65131i	−0.773550	+	0.446609i	0.0605896	+	0.998163i	$0.480702\pi$
$468$	3.47316	−	5.87686i	0.160547	−	0.271658i
$469$	11.0384	+	30.3278i	0.509707	+	1.40041i
$470$	0.300075	+	0.212396i	0.0138414	+	0.00979711i
$471$	−3.10823	+	17.6276i	−0.143220	+	0.812239i
$472$	15.0677	+	33.6433i	0.693549	+	1.54856i
$473$	38.9314	−	32.6673i	1.79007	−	1.50205i
$474$	11.7402	−	11.6215i	0.539247	−	0.533792i
$475$	−21.7057	+	1.87972i	−0.995925	+	0.0862476i
$476$	−0.145100	+	14.2693i	−0.00665066	+	0.654033i
$477$	1.37660	+	1.64057i	0.0630301	+	0.0751163i
$478$	4.40275	+	9.56844i	0.201377	+	0.437650i
$479$	6.41906	−	36.4043i	0.293294	−	1.66335i	−0.380761	−	0.924673i	$-0.624338\pi$
$479$	6.41906	−	36.4043i	0.293294	−	1.66335i	0.674055	−	0.738681i	$-0.264551\pi$
$480$	0.140067	−	0.189590i	0.00639314	−	0.00865357i
$481$	−16.6484	+	6.05952i	−0.759101	+	0.276290i
$482$	−27.3234	+	7.17260i	−1.24455	+	0.326703i
$483$	−3.33399	+	1.92488i	−0.151702	+	0.0875851i
$484$	16.8729	−	19.6981i	0.766950	−	0.895366i
$485$	0.143093	−	0.170532i	0.00649753	−	0.00774345i
$486$	−1.36415	−	0.372966i	−0.0618790	−	0.0169181i
$487$	−12.4068	+	21.4892i	−0.562204	+	0.973767i	0.435099	+	0.900382i	$0.356713\pi$
$487$	−12.4068	+	21.4892i	−0.562204	+	0.973767i	−0.997304	+	0.0733842i	$0.976620\pi$
$488$	−0.678492	−	0.329076i	−0.0307139	−	0.0148966i
$489$	0.830361	+	4.70921i	0.0375502	+	0.212958i
$490$	0.0458601	+	0.0662090i	0.00207175	+	0.00299102i
$491$	1.44697	−	3.97552i	0.0653008	−	0.179413i	−0.902751	−	0.430164i	$-0.858456\pi$
$491$	1.44697	−	3.97552i	0.0653008	−	0.179413i	0.968051	+	0.250752i	$0.0806778\pi$
$492$	−0.800818	+	0.658206i	−0.0361036	+	0.0296742i
$493$		−	18.1518i		−	0.817517i
$494$	0.125520	−	21.0401i	0.00564743	−	0.946641i
$495$	0.204003			0.00916926
$496$	29.4593	−	23.7154i	1.32276	−	1.06485i
$497$	−23.3093	−	8.48391i	−1.04557	−	0.380555i
$498$	−10.1110	+	7.00346i	−0.453085	+	0.313833i
$499$	34.1670	−	6.02457i	1.52953	−	0.269697i	0.655357	−	0.755319i	$-0.272518\pi$
$499$	34.1670	−	6.02457i	1.52953	−	0.269697i	0.874169	+	0.485622i	$0.161407\pi$
$500$	0.785852	−	0.277010i	0.0351444	−	0.0123883i
$501$	1.77408	+	1.02427i	0.0792600	+	0.0457608i
$502$	−10.0188	−	2.73919i	−0.447159	−	0.122256i
$503$	4.28289	+	3.59378i	0.190965	+	0.160239i	0.733257	−	0.679951i	$-0.237999\pi$
$503$	4.28289	+	3.59378i	0.190965	+	0.160239i	−0.542292	+	0.840190i	$0.682444\pi$
$504$	−6.69574	+	0.483022i	−0.298252	+	0.0215155i
$505$	0.0500534	+	0.0866950i	0.00222735	+	0.00385788i
$506$	−2.85140	−	10.8622i	−0.126760	−	0.482882i
$507$	−0.461699	−	1.26851i	−0.0205048	−	0.0563364i
$508$	−26.1008	+	4.32911i	−1.15804	+	0.192073i
$509$	24.8024	+	4.37333i	1.09935	+	0.193844i	0.693756	−	0.720210i	$-0.255955\pi$
$509$	24.8024	+	4.37333i	1.09935	+	0.193844i	0.405591	+	0.914055i	$0.367066\pi$
$510$	−0.0740508	−	0.160934i	−0.00327902	−	0.00712626i
$511$	5.76196	−	4.83486i	0.254894	−	0.213881i
$512$	−15.2514	−	16.7151i	−0.674022	−	0.738711i
$513$	−4.21137	+	1.12445i	−0.185936	+	0.0496459i
$514$	−2.50377	−	2.52936i	−0.110437	−	0.111565i
$515$	−0.339362	−	0.404436i	−0.0149541	−	0.0178216i
$516$	7.29884	−	19.4362i	0.321314	−	0.855630i
$517$	30.0785	+	5.30365i	1.32285	+	0.233254i
$518$	14.2209	+	10.0657i	0.624831	+	0.442262i
$519$	−17.0309	+	6.19875i	−0.747575	+	0.272095i
$520$	0.0981790	+	0.390115i	0.00430543	+	0.0171077i
$521$	−12.5151	−	21.6768i	−0.548298	−	0.949680i	−0.998391	−	0.0566984i	$-0.981943\pi$
$521$	−12.5151	−	21.6768i	−0.548298	−	0.949680i	0.450093	−	0.892981i	$-0.351391\pi$
$522$	8.51045	−	0.700987i	0.372492	−	0.0306814i
$523$	2.06651	−	2.46277i	0.0903621	−	0.107689i	−0.718969	−	0.695042i	$-0.755386\pi$
$523$	2.06651	−	2.46277i	0.0903621	−	0.107689i	0.809331	+	0.587353i	$0.199830\pi$
$524$	3.68971	+	6.54353i	0.161186	+	0.285856i
$525$	−10.2738	−	5.93157i	−0.448385	−	0.258875i
$526$	34.9812	+	16.5291i	1.52525	+	0.720701i
$527$	−4.93553	−	27.9908i	−0.214995	−	1.21930i
$528$	3.79202	−	19.2123i	0.165027	−	0.836109i
$529$	19.1407	+	6.96664i	0.832203	+	0.302897i
$530$	−0.125666	−	0.0116385i	−0.00545859	−	0.000505542i
$531$			13.0332i			0.565591i
$532$	−17.0794	+	11.6800i	−0.740486	+	0.506393i
$533$		−	1.76908i		−	0.0766272i
$534$	2.01489	−	21.7558i	0.0871929	−	0.941465i
$535$	0.158351	+	0.0576350i	0.00684610	+	0.00249178i
$536$	−31.8381	+	21.5772i	−1.37520	+	0.931993i
$537$	3.56489	+	20.2175i	0.153836	+	0.872449i
$538$	9.38421	−	19.8602i	0.404582	−	0.856236i
$539$	5.79469	+	3.34557i	0.249595	+	0.144104i
$540$	0.0725937	−	0.0409335i	0.00312393	−	0.00176150i
$541$	10.0026	−	11.9206i	0.430045	−	0.512508i	−0.506890	−	0.862011i	$-0.669205\pi$
$541$	10.0026	−	11.9206i	0.430045	−	0.512508i	0.936935	+	0.349503i	$0.113650\pi$
$542$	1.19364	+	14.4916i	0.0512714	+	0.622469i
$543$	−2.04058	−	3.53440i	−0.0875699	−	0.151675i
$544$	−16.5326	+	3.98241i	−0.708831	+	0.170744i
$545$	0.325279	−	0.118392i	0.0139334	−	0.00507135i
$546$	6.61893	−	9.35126i	0.283264	−	0.400197i
$547$	−25.1223	−	4.42973i	−1.07415	−	0.189402i	−0.391523	−	0.920168i	$-0.628052\pi$
$547$	−25.1223	−	4.42973i	−1.07415	−	0.189402i	−0.682628	+	0.730767i	$0.739163\pi$
$548$	−8.20530	+	21.8500i	−0.350513	+	0.933385i
$549$	−0.171373	−	0.204234i	−0.00731402	−	0.00871650i
$550$	24.5943	−	24.3455i	1.04871	−	1.03810i
$551$	21.5732	−	15.0774i	0.919050	−	0.642319i
$552$	−3.19416	−	3.29312i	−0.135953	−	0.140164i
$553$	21.2381	−	17.8208i	0.903134	−	0.757819i
$554$	−27.5375	+	12.6709i	−1.16996	+	0.538336i
$555$	−0.213006	−	0.0375587i	−0.00904160	−	0.00159428i
$556$	3.20545	+	19.3261i	0.135941	+	0.819610i
$557$	−6.93736	−	19.0603i	−0.293946	−	0.807609i	−0.995480	−	0.0949731i	$-0.969723\pi$
$557$	−6.93736	−	19.0603i	−0.293946	−	0.807609i	0.701534	−	0.712636i	$-0.252499\pi$
$558$	12.9328	−	3.39496i	0.547490	−	0.143720i
$559$	17.7159	+	30.6848i	0.749301	+	1.29783i
$560$	0.260398	−	0.297815i	0.0110038	−	0.0125850i
$561$	−11.2742	−	9.46022i	−0.475999	−	0.399411i
$562$	−6.98127	+	25.5345i	−0.294487	+	1.07711i
$563$	37.4015	+	21.5938i	1.57629	+	0.910069i	0.995371	+	0.0961056i	$0.0306386\pi$
$563$	37.4015	+	21.5938i	1.57629	+	0.910069i	0.580915	+	0.813964i	$0.302695\pi$
$564$	11.7675	−	4.14800i	0.495501	−	0.174662i
$565$	0.330977	−	0.0583601i	0.0139243	−	0.00245523i
$566$	3.40642	+	4.91789i	0.143182	+	0.206714i
$567$	−2.23032	−	0.811768i	−0.0936644	−	0.0340911i
$568$	3.02519	−	29.4051i	0.126934	−	1.23381i
$569$	33.3043			1.39619			0.698095	−	0.716005i	$-0.254031\pi$
$569$	33.3043			1.39619			0.698095	+	0.716005i	$0.254031\pi$
$570$	0.129759	−	0.221684i	0.00543500	−	0.00928533i
$571$			12.1571i			0.508757i	0.967105	+	0.254378i	$0.0818709\pi$
$571$			12.1571i			0.508757i	−0.967105	+	0.254378i	$0.918129\pi$
$572$	21.2209	+	25.8187i	0.887289	+	1.07953i
$573$	2.98844	−	8.21067i	0.124844	−	0.343006i
$574$	−1.43014	+	0.990600i	−0.0596931	+	0.0413468i
$575$	−1.40781	−	7.98406i	−0.0587096	−	0.332958i
$576$	−2.50560	−	7.59750i	−0.104400	−	0.316562i
$577$	−10.7070	+	18.5451i	−0.445740	+	0.772044i	−0.998103	−	0.0615590i	$-0.980393\pi$
$577$	−10.7070	+	18.5451i	−0.445740	+	0.772044i	0.552363	+	0.833603i	$0.313726\pi$
$578$	2.96988	−	10.8625i	0.123531	−	0.451822i
$579$	2.12878	−	2.53698i	0.0884690	−	0.105433i
$580$	−0.327364	+	0.382176i	−0.0135930	+	0.0158690i
$581$	−17.8767	+	10.3211i	−0.741652	+	0.428193i
$582$	−1.91831	−	7.30765i	−0.0795166	−	0.302912i
$583$	−9.85245	+	3.58600i	−0.408047	+	0.148517i
$584$	7.26325	+	5.25268i	0.300555	+	0.217357i
$585$	−0.0246975	+	0.140067i	−0.00102112	+	0.00579104i
$586$	−41.7851	+	19.2267i	−1.72613	+	0.794247i
$587$	−18.8965	−	22.5199i	−0.779941	−	0.929497i	0.218990	−	0.975727i	$-0.429724\pi$
$587$	−18.8965	−	22.5199i	−0.779941	−	0.929497i	−0.998931	+	0.0462300i	$0.985279\pi$
$588$	2.73331	+	0.0277942i	0.112720	+	0.00114621i
$589$	29.1671	−	29.1157i	1.20181	−	1.19969i
$590$	−0.540317	−	0.545839i	−0.0222445	−	0.0224719i
$591$	1.92902	−	1.61864i	0.0793491	−	0.0665818i
$592$	−7.49651	+	19.3620i	−0.308105	+	0.795774i
$593$	2.44482	−	13.8653i	0.100397	−	0.569378i	−0.892563	−	0.450923i	$-0.851095\pi$
$593$	2.44482	−	13.8653i	0.100397	−	0.569378i	0.992959	−	0.118455i	$-0.0377940\pi$
$594$	4.00001	−	5.65124i	0.164123	−	0.231873i
$595$	−0.101687	−	0.279383i	−0.00416876	−	0.0114536i
$596$	−8.82708	+	14.9361i	−0.361571	+	0.611808i
$597$	−15.7827	+	9.11213i	−0.645942	+	0.372935i
$598$	7.80305	−	0.642720i	0.319091	−	0.0262828i
$599$	33.8902	+	28.4372i	1.38472	+	1.16191i	0.967430	+	0.253139i	$0.0814629\pi$
$599$	33.8902	+	28.4372i	1.38472	+	1.16191i	0.417285	+	0.908775i	$0.362982\pi$
$600$	3.86683	−	13.5981i	0.157863	−	0.555141i
$601$	−21.0133	+	36.3961i	−0.857151	+	1.48463i	0.0174834	+	0.999847i	$0.494435\pi$
$601$	−21.0133	+	36.3961i	−0.857151	+	1.48463i	−0.874635	+	0.484783i	$0.838899\pi$
$602$	14.8859	−	31.5038i	0.606704	−	1.28400i
$603$	−13.3914	+	2.36127i	−0.545340	+	0.0961582i
$604$	36.2829	+	6.77875i	1.47633	+	0.275824i
$605$	−0.184822	+	0.507794i	−0.00751408	+	0.0206448i
$606$	3.38303	+	0.313316i	0.137426	+	0.0127276i
$607$	−6.29523			−0.255515			−0.127758	−	0.991805i	$-0.540778\pi$
$607$	−6.29523			−0.255515			−0.127758	+	0.991805i	$0.540778\pi$
$608$	−18.4655	−	16.3409i	−0.748875	−	0.662712i
$609$	14.3313			0.580734
$610$	0.0156442	+	0.00144887i	0.000633415	+	5.86632e-5i
$611$	−7.28286	+	20.0095i	−0.294633	+	0.809498i
$612$	−5.91009	−	1.10419i	−0.238901	−	0.0446341i
$613$	14.6790	−	2.58830i	0.592879	−	0.104541i	0.130845	−	0.991403i	$-0.458231\pi$
$613$	14.6790	−	2.58830i	0.592879	−	0.104541i	0.462034	+	0.886862i	$0.347120\pi$
$614$	2.62754	−	5.56079i	0.106039	−	0.224415i
$615$	0.0107987	−	0.0187039i	0.000435445	−	0.000754212i
$616$	8.98949	−	31.6125i	0.362197	−	1.27370i
$617$	−36.4509	−	30.5860i	−1.46746	−	1.23134i	−0.918455	−	0.395526i	$-0.870562\pi$
$617$	−36.4509	−	30.5860i	−1.46746	−	1.23134i	−0.549005	−	0.835819i	$-0.684993\pi$
$618$	−17.8577	+	1.47090i	−0.718341	+	0.0591681i
$619$	−7.05628	+	4.07394i	−0.283616	+	0.163746i	−0.635059	−	0.772463i	$-0.719024\pi$
$619$	−7.05628	+	4.07394i	−0.283616	+	0.163746i	0.351443	+	0.936209i	$0.385691\pi$
$620$	−0.400892	+	0.678341i	−0.0161002	+	0.0272428i
$621$	−0.554760	−	1.52419i	−0.0222617	−	0.0611636i
$622$	23.0141	−	32.5145i	0.922783	−	1.30371i
$623$	6.36745	−	36.1116i	0.255106	−	1.44678i
$624$	12.7319	+	4.92949i	0.509684	+	0.197337i
$625$	19.1312	−	16.0530i	0.765246	−	0.642118i
$626$	9.56639	+	9.66416i	0.382350	+	0.386258i
$627$	1.87865	−	21.2572i	0.0750260	−	0.848931i
$628$	−35.7973	−	0.364012i	−1.42847	−	0.0145257i
$629$	10.0301	+	11.9534i	0.399925	+	0.476612i
$630$	0.127061	−	0.0584649i	0.00506223	−	0.00232930i
$631$	7.38602	−	41.8882i	0.294033	−	1.66754i	−0.377074	−	0.926183i	$-0.623070\pi$
$631$	7.38602	−	41.8882i	0.294033	−	1.66754i	0.671107	−	0.741361i	$-0.265819\pi$
$632$	26.7717	+	19.3609i	1.06492	+	0.770135i
$633$	−11.5445	+	4.20184i	−0.458851	+	0.167008i
$634$	0.0175314	+	0.0667845i	0.000696262	+	0.00265235i
$635$	0.477382	−	0.275617i	0.0189443	−	0.0109375i
$636$	−2.78642	+	3.25297i	−0.110489	+	0.128988i
$637$	−2.99856	+	3.57355i	−0.118807	+	0.141589i
$638$	−11.0254	+	40.3260i	−0.436499	+	1.59652i
$639$	5.22557	−	9.05095i	0.206720	−	0.358050i
$640$	0.419907	+	0.214314i	0.0165983	+	0.00847152i
$641$	6.68302	+	37.9013i	0.263963	+	1.49701i	0.771971	+	0.635658i	$0.219271\pi$
$641$	6.68302	+	37.9013i	0.263963	+	1.49701i	−0.508008	+	0.861352i	$0.669618\pi$
$642$	4.70147	−	3.25651i	0.185552	−	0.128524i
$643$	0.989671	−	2.71910i	0.0390288	−	0.107231i	−0.918647	−	0.395078i	$-0.870717\pi$
$643$	0.989671	−	2.71910i	0.0390288	−	0.107231i	0.957676	+	0.287848i	$0.0929397\pi$
$644$	−4.88893	−	5.94820i	−0.192651	−	0.234392i
$645$			0.432560i			0.0170320i
$646$	−17.4513	+	6.23409i	−0.686611	+	0.245277i
$647$	−25.3253			−0.995639			−0.497820	−	0.867281i	$-0.665866\pi$
$647$	−25.3253			−0.995639			−0.497820	+	0.867281i	$0.665866\pi$
$648$	0.289460	−	2.81358i	0.0113711	−	0.110528i
$649$	−59.9590	−	21.8233i	−2.35360	−	0.856639i
$650$	13.7379	+	19.8336i	0.538844	+	0.777937i
$651$	22.0994	−	3.89672i	0.866145	−	0.152725i
$652$	−9.01974	+	3.17943i	−0.353240	+	0.124516i
$653$	6.13708	+	3.54324i	0.240162	+	0.138658i	0.615251	−	0.788331i	$-0.289055\pi$
$653$	6.13708	+	3.54324i	0.240162	+	0.138658i	−0.375089	+	0.926989i	$0.622388\pi$
$654$	3.09828	−	11.3322i	0.121152	−	0.443123i
$655$	−0.119896	−	0.100605i	−0.00468472	−	0.00393095i
$656$	−1.56074	−	1.36465i	−0.0609366	−	0.0532806i
$657$	1.58455	+	2.74452i	0.0618191	+	0.107074i
$658$	20.2540	−	5.31683i	0.789583	−	0.207271i
$659$	7.50469	+	20.6190i	0.292341	+	0.803201i	0.995723	+	0.0923886i	$0.0294502\pi$
$659$	7.50469	+	20.6190i	0.292341	+	0.803201i	−0.703382	+	0.710812i	$0.748328\pi$
$660$	0.0667603	+	0.402508i	0.00259864	+	0.0156676i
$661$	−16.6606	−	2.93772i	−0.648023	−	0.114264i	−0.160031	−	0.987112i	$-0.551159\pi$
$661$	−16.6606	−	2.93772i	−0.648023	−	0.114264i	−0.487992	+	0.872848i	$0.662271\pi$
$662$	−27.5589	+	12.6808i	−1.07111	+	0.492852i
$663$	7.86019	−	6.59549i	0.305265	−	0.256147i
$664$	−17.1270	−	17.6576i	−0.664656	−	0.685247i
$665$	0.247579	−	0.352916i	0.00960069	−	0.0136855i
$666$	−5.21697	+	5.16419i	−0.202154	+	0.200108i
$667$	6.29545	+	7.50262i	0.243761	+	0.290503i
$668$	−1.44035	+	3.83553i	−0.0557289	+	0.148401i
$669$	−28.3822	−	5.00455i	−1.09732	−	0.193487i
$670$	0.462952	−	0.654061i	0.0178854	−	0.0252686i
$671$	1.22653	−	0.446421i	0.0473498	−	0.0172339i
$672$	−3.14421	−	13.0529i	−0.121291	−	0.503527i
$673$	0.240496	+	0.416552i	0.00927045	+	0.0160569i	0.870623	−	0.491950i	$-0.163716\pi$
$673$	0.240496	+	0.416552i	0.00927045	+	0.0160569i	−0.861353	+	0.508007i	$0.830382\pi$
$674$	0.511882	+	6.21459i	0.0197170	+	0.239377i
$675$	3.21282	−	3.82889i	0.123662	−	0.147374i
$676$	2.35173	−	1.32607i	0.0904512	−	0.0510028i
$677$	−39.8407	−	23.0020i	−1.53120	−	0.884040i	−0.999307	−	0.0372297i	$-0.988147\pi$
$677$	−39.8407	−	23.0020i	−1.53120	−	0.884040i	−0.531895	−	0.846810i	$-0.678520\pi$
$678$	4.87298	−	10.3129i	0.187146	−	0.396065i
$679$	−2.20183	−	12.4872i	−0.0844985	−	0.479215i
$680$	0.293296	−	0.198771i	0.0112474	−	0.00762253i
$681$	−5.85757	−	2.13198i	−0.224463	−	0.0816977i
$682$	−6.03678	+	65.1820i	−0.231160	+	2.49595i
$683$			24.6012i			0.941339i	0.882310	+	0.470669i	$0.155988\pi$
$683$			24.6012i			0.941339i	−0.882310	+	0.470669i	$0.844012\pi$
$684$	−3.59677	−	7.94124i	−0.137526	−	0.303641i
$685$		−	0.486280i		−	0.0185798i
$686$	27.9638	+	2.58984i	1.06766	+	0.0988807i
$687$	3.73379	+	1.35899i	0.142453	+	0.0518487i
$688$	40.7370	+	8.04044i	1.55308	+	0.306539i
$689$	−1.26933	−	7.19872i	−0.0483576	−	0.274250i
$690$	0.0864223	+	0.0408356i	0.00329004	+	0.00155458i
$691$	−1.35596	−	0.782865i	−0.0515832	−	0.0297816i	0.473987	−	0.880532i	$-0.342815\pi$
$691$	−1.35596	−	0.782865i	−0.0515832	−	0.0297816i	−0.525570	+	0.850750i	$0.676148\pi$
$692$	−17.8038	−	31.5743i	−0.676799	−	1.20027i
$693$	7.46907	−	8.90129i	0.283727	−	0.338132i
$694$	15.7378	−	1.29629i	0.597399	−	0.0492065i
$695$	−0.204078	−	0.353473i	−0.00774112	−	0.0134080i
$696$	4.16813	+	16.5621i	0.157993	+	0.627785i
$697$	−1.46414	+	0.532904i	−0.0554583	+	0.0201852i
$698$	27.4285	+	19.4142i	1.03818	+	0.734838i
$699$	3.07669	+	0.542503i	0.116371	+	0.0205193i
$700$	8.34115	−	22.2117i	0.315266	−	0.839525i
$701$	15.8308	+	18.8665i	0.597922	+	0.712576i	0.977108	−	0.212744i	$-0.0682402\pi$
$701$	15.8308	+	18.8665i	0.597922	+	0.712576i	−0.379185	+	0.925321i	$0.623796\pi$
$702$	3.39582	+	3.43053i	0.128167	+	0.129477i
$703$	−5.87518	+	21.8494i	−0.221587	+	0.824066i
$704$	39.1477	+	1.19457i	1.47544	+	0.0450222i
$705$	−0.199140	+	0.167098i	−0.00750004	+	0.00629328i
$706$	−0.914614	−	1.98772i	−0.0344220	−	0.0748088i
$707$	5.61535	+	0.990138i	0.211187	+	0.0372380i
$708$	−25.7150	+	4.26511i	−0.966429	+	0.160293i
$709$	9.53648	+	26.2013i	0.358150	+	0.984009i	0.979671	+	0.200611i	$0.0642929\pi$
$709$	9.53648	+	26.2013i	0.358150	+	0.984009i	−0.621521	+	0.783398i	$0.713485\pi$
$710$	0.156375	+	0.595698i	0.00586866	+	0.0223562i
$711$	5.84050	+	10.1160i	0.219036	+	0.379381i
$712$	43.5845	−	3.14413i	1.63340	−	0.117831i
$713$	11.7478	+	9.85757i	0.439958	+	0.369169i
$714$	−9.73322	−	2.66112i	−0.364256	−	0.0995899i
$715$	−0.603021	−	0.348154i	−0.0225517	−	0.0130202i
$716$	−38.7234	+	13.6499i	−1.44716	+	0.510120i
$717$	−7.33465	+	1.29330i	−0.273917	+	0.0482990i
$718$	−26.0464	+	18.0413i	−0.972045	+	0.673294i
$719$	−25.7009	−	9.35436i	−0.958482	−	0.348859i	−0.185043	−	0.982730i	$-0.559243\pi$
$719$	−25.7009	−	9.35436i	−0.958482	−	0.348859i	−0.773438	+	0.633871i	$0.781465\pi$
$720$	0.104520	+	0.129835i	0.00389523	+	0.00483867i
$721$	−30.0717			−1.11993
$722$	−21.9046	−	15.5624i	−0.815205	−	0.579172i
$723$		−	19.9752i		−	0.742885i
$724$	6.30574	−	5.18280i	0.234351	−	0.192617i
$725$	−10.3223	+	28.3603i	−0.383361	+	1.05327i
$726$	10.4429	+	15.0765i	0.387571	+	0.559541i
$727$	6.55780	+	37.1911i	0.243215	+	1.37934i	0.824601	+	0.565715i	$0.191400\pi$
$727$	6.55780	+	37.1911i	0.243215	+	1.37934i	−0.581386	+	0.813628i	$0.697489\pi$
$728$	20.6165	+	9.99924i	0.764098	+	0.370596i
$729$	0.500000	−	0.866025i	0.0185185	−	0.0320750i
$730$	−0.180142	−	0.0492519i	−0.00666735	−	0.00182289i
$731$	20.0590	−	23.9054i	0.741910	−	0.884174i
$732$	0.346881	−	0.404962i	0.0128211	−	0.0149678i
$733$	−7.47397	+	4.31510i	−0.276057	+	0.159382i	−0.631637	−	0.775264i	$-0.717617\pi$
$733$	−7.47397	+	4.31510i	−0.276057	+	0.159382i	0.355580	+	0.934646i	$0.384283\pi$
$734$	5.79226	−	1.52051i	0.213796	−	0.0561231i
$735$	−0.0535162	+	0.0194783i	−0.00197398	+	0.000718468i
$736$	5.45218	−	7.37991i	0.200970	−	0.272027i
$737$	11.5602	−	65.5609i	0.425824	−	2.41497i
$738$	−0.306393	−	0.665880i	−0.0112785	−	0.0245114i
$739$	5.65966	+	6.74492i	0.208194	+	0.248116i	0.860029	−	0.510245i	$-0.170445\pi$
$739$	5.65966	+	6.74492i	0.208194	+	0.248116i	−0.651835	+	0.758360i	$0.726001\pi$
$740$	0.00439859	−	0.432561i	0.000161695	−	0.0159013i
$741$	14.3675	+	3.86335i	0.527805	+	0.141924i
$742$	−5.10878	+	5.05709i	−0.187549	+	0.185652i
$743$	−35.4297	+	29.7290i	−1.29979	+	1.09065i	−0.309607	+	0.950865i	$0.600197\pi$
$743$	−35.4297	+	29.7290i	−1.29979	+	1.09065i	−0.990182	+	0.139787i	$0.955358\pi$
$744$	10.9307	+	24.4060i	0.400739	+	0.894769i
$745$	0.0627691	−	0.355981i	0.00229968	−	0.0130421i
$746$	17.5837	+	12.4459i	0.643785	+	0.455679i
$747$	−2.97460	−	8.17265i	−0.108835	−	0.299022i
$748$	14.9759	−	25.3405i	0.547574	−	0.926539i
$749$	8.31242	−	4.79918i	0.303729	−	0.175358i
$750$	0.0483668	+	0.587205i	0.00176611	+	0.0214417i
$751$	−12.9771	−	10.8891i	−0.473542	−	0.397349i	0.374542	−	0.927210i	$-0.377800\pi$
$751$	−12.9771	−	10.8891i	−0.473542	−	0.397349i	−0.848085	+	0.529861i	$0.822244\pi$
$752$	12.0351	+	21.8603i	0.438876	+	0.797165i
$753$	3.67217	−	6.36038i	0.133821	−	0.231785i
$754$	−26.3527	−	12.4519i	−0.959707	−	0.453473i
$755$	−0.757342	+	0.133540i	−0.0275625	+	0.00486001i
$756$	0.871783	−	4.66616i	0.0317064	−	0.169707i
$757$	−15.6394	+	42.9689i	−0.568424	+	1.56173i	0.238540	+	0.971133i	$0.423331\pi$
$757$	−15.6394	+	42.9689i	−0.568424	+	1.56173i	−0.806964	+	0.590600i	$0.798891\pi$
$758$	3.46366	−	37.3989i	0.125806	−	1.35839i
$759$	7.94094			0.288238
$760$	0.479857	+	0.183474i	0.0174062	+	0.00665529i
$761$	22.3198			0.809093			0.404547	−	0.914517i	$-0.367429\pi$
$761$	22.3198			0.809093			0.404547	+	0.914517i	$0.367429\pi$
$762$	1.72526	−	18.6285i	0.0624996	−	0.674839i
$763$	6.74347	−	18.5275i	0.244130	−	0.670742i
$764$	17.1780	+	3.20938i	0.621478	+	0.116111i
$765$	0.123363	−	0.0217522i	0.00446020	−	0.000786453i
$766$	40.5138	+	19.1433i	1.46382	+	0.691675i
$767$	22.2425	−	38.5252i	0.803131	−	1.39106i
$768$	14.1702	−	7.42995i	0.511325	−	0.268105i
$769$	−38.4981	−	32.3038i	−1.38828	−	1.16490i	−0.966032	−	0.258423i	$-0.916797\pi$
$769$	−38.4981	−	32.3038i	−1.38828	−	1.16490i	−0.422246	−	0.906481i	$-0.638758\pi$
$770$	0.0562111	+	0.682440i	0.00202571	+	0.0245934i
$771$	2.17944	−	1.25830i	0.0784905	−	0.0453165i
$772$	5.70222	+	3.36995i	0.205227	+	0.121287i
$773$	−6.87035	−	18.8761i	−0.247109	−	0.678927i	−0.999789	−	0.0205405i	$-0.993461\pi$
$773$	−6.87035	−	18.8761i	−0.247109	−	0.678927i	0.752680	−	0.658387i	$-0.228761\pi$
$774$	11.9826	+	8.48146i	0.430707	+	0.304860i
$775$	−8.20613	+	46.5393i	−0.294773	+	1.67174i
$776$	13.7906	−	6.17635i	0.495052	−	0.221718i
$777$	−9.43748	+	7.91899i	−0.338568	+	0.284092i
$778$	16.5685	−	16.4009i	0.594010	−	0.588000i
$779$	−1.84950	−	1.29747i	−0.0662653	−	0.0464866i
$780$	−0.284440	−	0.00289238i	−0.0101846	−	0.000103564i
$781$	32.8889	+	39.1955i	1.17686	+	1.40253i
$782$	−2.88247	−	6.26443i	−0.103077	−	0.224016i
$783$	−1.04852	+	5.94644i	−0.0374710	+	0.212508i
$784$	0.839639	+	5.40204i	0.0299871	+	0.192930i
$785$	0.700885	−	0.255101i	0.0250157	−	0.00910496i
$786$	−5.13779	+	1.34871i	−0.183259	+	0.0481068i
$787$	−39.5505	+	22.8345i	−1.40982	+	0.813961i	−0.995371	−	0.0961103i	$-0.969360\pi$
$787$	−39.5505	+	22.8345i	−1.40982	+	0.813961i	−0.414451	+	0.910071i	$0.636026\pi$
$788$	3.82491	+	3.27633i	0.136257	+	0.116715i
$789$	−17.5852	+	20.9573i	−0.626051	+	0.746099i
$790$	−0.663987	−	0.181538i	−0.0236236	−	0.00645883i
$791$	9.57146	−	16.5782i	0.340322	−	0.589455i
$792$	12.4592	+	6.04283i	0.442717	+	0.214723i
$793$	0.158019	+	0.896170i	0.00561142	+	0.0318239i
$794$	8.65315	+	12.4927i	0.307089	+	0.443349i
$795$	0.0305218	−	0.0838578i	0.00108250	−	0.00297413i
$796$	−23.1435	−	28.1580i	−0.820301	−	0.998032i
$797$			6.54154i			0.231713i	0.993266	+	0.115857i	$0.0369613\pi$
$797$			6.54154i			0.231713i	−0.993266	+	0.115857i	$0.963039\pi$
$798$	−4.92197	−	13.7782i	−0.174236	−	0.487743i
$799$	18.7543			0.663479
$800$	28.0951	+	3.17943i	0.993312	+	0.112410i
$801$	14.5178	+	5.28404i	0.512961	+	0.186702i
$802$	27.6421	−	19.1465i	0.976077	−	0.676087i
$803$	−15.2794	+	2.69417i	−0.539198	+	0.0950751i
$804$	−9.04123	−	25.6491i	−0.318860	−	0.904575i
$805$	0.138926	+	0.0802088i	0.00489649	+	0.00282699i
$806$	−44.0225	−	12.0360i	−1.55063	−	0.423950i
$807$	11.8983	+	9.98384i	0.418839	+	0.351448i
$808$	0.488913	+	6.77740i	0.0171999	+	0.238428i
$809$	−3.48724	−	6.04008i	−0.122605	−	0.212358i	0.798189	−	0.602407i	$-0.205791\pi$
$809$	−3.48724	−	6.04008i	−0.122605	−	0.212358i	−0.920794	+	0.390049i	$0.872458\pi$
$810$	0.0149625	+	0.0569984i	0.000525729	+	0.00200272i
$811$	−2.75035	−	7.55654i	−0.0965780	−	0.265346i	0.881991	−	0.471267i	$-0.156203\pi$
$811$	−2.75035	−	7.55654i	−0.0965780	−	0.265346i	−0.978569	+	0.205921i	$0.933981\pi$
$812$	4.68994	+	28.2763i	0.164585	+	0.992305i
$813$	−10.1256	−	1.78542i	−0.355121	−	0.0626175i
$814$	−15.0223	−	32.6478i	−0.526532	−	1.14430i
$815$	0.152640	−	0.128080i	0.00534675	−	0.00448646i
$816$	0.244526	−	12.0222i	0.00856013	−	0.420862i
$817$	45.0729	+	3.98340i	1.57690	+	0.139362i
$818$	−30.5418	−	30.8539i	−1.06787	−	1.07878i
$819$	5.20730	+	6.20582i	0.181958	+	0.216849i
$820$	0.0404374	+	0.0151854i	0.00141214	+	0.000530298i
$821$	−46.3693	−	8.17616i	−1.61830	−	0.285350i	−0.710168	−	0.704032i	$-0.751381\pi$
$821$	−46.3693	−	8.17616i	−1.61830	−	0.285350i	−0.908133	+	0.418682i	$0.862492\pi$
$822$	−13.4708	−	9.53478i	−0.469848	−	0.332564i
$823$	−3.65233	+	1.32934i	−0.127312	+	0.0463379i	−0.404891	−	0.914365i	$-0.632690\pi$
$823$	−3.65233	+	1.32934i	−0.127312	+	0.0463379i	0.277578	+	0.960703i	$0.410468\pi$
$824$	−8.74609	−	34.7526i	−0.304684	−	1.21067i
$825$	12.2351	+	21.1918i	0.425972	+	0.737805i
$826$	−43.5990	+	3.59116i	−1.51700	+	0.124952i
$827$	16.3014	−	19.4273i	0.566855	−	0.675552i	−0.404127	−	0.914703i	$-0.632425\pi$
$827$	16.3014	−	19.4273i	0.566855	−	0.675552i	0.970982	+	0.239151i	$0.0768691\pi$
$828$	2.82575	−	1.59336i	0.0982016	−	0.0553731i
$829$	−32.7764	−	18.9235i	−1.13837	−	0.657240i	−0.192345	−	0.981327i	$-0.561609\pi$
$829$	−32.7764	−	18.9235i	−1.13837	−	0.657240i	−0.946027	+	0.324088i	$0.894943\pi$
$830$	0.463393	+	0.218959i	0.0160846	+	0.00760017i
$831$	−3.72205	−	21.1088i	−0.129116	−	0.732255i
$832$	−5.55957	+	26.7338i	−0.192744	+	0.926828i
$833$	3.86084	+	1.40523i	0.133770	+	0.0486884i
$834$	−13.7933	−	1.27745i	−0.477623	−	0.0442346i
$835$		−	0.0853613i		−	0.00295405i
$836$	42.5562	−	3.24978i	1.47184	−	0.112396i
$837$			9.45473i			0.326803i
$838$	−2.46512	+	26.6172i	−0.0851563	+	0.919475i
$839$	30.7140	+	11.1790i	1.06037	+	0.385941i	0.812565	−	0.582870i	$-0.198070\pi$
$839$	30.7140	+	11.1790i	1.06037	+	0.385941i	0.247800	+	0.968811i	$0.420293\pi$
$840$	0.156935	+	0.231564i	0.00541476	+	0.00798973i
$841$	−1.29534	−	7.34622i	−0.0446668	−	0.253318i
$842$	−5.61246	+	11.8779i	−0.193418	+	0.409340i
$843$	−16.2105	−	9.35913i	−0.558319	−	0.322346i
$844$	−12.0684	−	21.4027i	−0.415410	−	0.736711i
$845$	−0.0361571	+	0.0430903i	−0.00124384	+	0.00148235i
$846$	0.724253	+	8.79291i	0.0249003	+	0.302307i
$847$	15.3898	+	26.6560i	0.528801	+	0.915910i
$848$	−7.33011	−	4.43319i	−0.251717	−	0.152236i
$849$	−3.97510	+	1.44682i	−0.136425	+	0.0496546i
$850$	12.2766	−	17.3444i	0.421083	−	0.594908i
$851$	−8.29138	−	1.46199i	−0.284225	−	0.0501165i
$852$	19.5680	+	7.34835i	0.670389	+	0.251750i
$853$	8.36191	+	9.96534i	0.286306	+	0.341207i	0.889959	−	0.456041i	$-0.150733\pi$
$853$	8.36191	+	9.96534i	0.286306	+	0.341207i	−0.603652	+	0.797248i	$0.706289\pi$
$854$	0.635992	−	0.629558i	0.0217632	−	0.0215430i
$855$	0.128321	+	0.128547i	0.00438848	+	0.00439622i
$856$	7.96379	+	8.21051i	0.272197	+	0.280630i
$857$	−6.87693	+	5.77043i	−0.234911	+	0.197114i	−0.752643	−	0.658429i	$-0.771221\pi$
$857$	−6.87693	+	5.77043i	−0.234911	+	0.197114i	0.517731	+	0.855543i	$0.326777\pi$
$858$	−21.4683	+	9.87824i	−0.732914	+	0.337238i
$859$	−5.81563	−	1.02545i	−0.198427	−	0.0349880i	0.0735514	−	0.997291i	$-0.476567\pi$
$859$	−5.81563	−	1.02545i	−0.198427	−	0.0349880i	−0.271978	+	0.962303i	$0.587678\pi$
$860$	−0.853460	+	0.141556i	−0.0291027	+	0.00482701i
$861$	−0.420740	−	1.15597i	−0.0143388	−	0.0393955i
$862$	7.48460	−	1.96476i	0.254927	−	0.0669201i
$863$	18.3058	+	31.7067i	0.623138	+	1.07931i	0.988898	+	0.148598i	$0.0474759\pi$
$863$	18.3058	+	31.7067i	0.623138	+	1.07931i	−0.365760	+	0.930709i	$0.619191\pi$
$864$	5.64604	−	0.349628i	0.192082	−	0.0118946i
$865$	0.578529	+	0.485443i	0.0196706	+	0.0165056i
$866$	8.87164	−	32.4486i	0.301470	−	1.10265i
$867$	6.89606	+	3.98144i	0.234203	+	0.135217i
$868$	14.9205	+	42.3279i	0.506434	+	1.43670i
$869$	−56.3184	+	9.93046i	−1.91047	+	0.336868i
$870$	−0.202609	−	0.292510i	−0.00686910	−	0.00991703i
$871$	43.6139	+	15.8742i	1.47780	+	0.537875i
$872$	23.3728	+	2.40458i	0.791502	+	0.0814295i
$873$	5.34236			0.180812
$874$	5.05094	−	8.62918i	0.170851	−	0.291886i
$875$			0.988834i			0.0334287i
$876$	−4.89651	+	4.02453i	−0.165438	+	0.135976i
$877$	2.42046	−	6.65016i	0.0817332	−	0.224560i	−0.892094	−	0.451850i	$-0.850764\pi$
$877$	2.42046	−	6.65016i	0.0817332	−	0.224560i	0.973827	+	0.227290i	$0.0729865\pi$
$878$	23.1536	−	16.0375i	0.781395	−	0.541239i
$879$	−5.64778	−	32.0302i	−0.190495	−	1.08035i
$880$	−0.772318	+	0.263442i	−0.0260348	+	0.00888063i
$881$	−13.1328	+	22.7467i	−0.442457	+	0.766357i	−0.997871	−	0.0652164i	$-0.979226\pi$
$881$	−13.1328	+	22.7467i	−0.442457	+	0.766357i	0.555415	+	0.831574i	$0.312560\pi$
$882$	−0.509742	+	1.86441i	−0.0171639	+	0.0627781i
$883$	34.0089	−	40.5302i	1.14449	−	1.36395i	0.223342	−	0.974740i	$-0.428303\pi$
$883$	34.0089	−	40.5302i	1.14449	−	1.36395i	0.921149	−	0.389211i	$-0.127252\pi$
$884$	15.5854	+	13.3501i	0.524195	+	0.449014i
$885$	0.470326	−	0.271543i	0.0158098	−	0.00912781i
$886$	2.67177	+	10.1779i	0.0897599	+	0.341933i
$887$	−10.3417	+	3.76406i	−0.347240	+	0.126385i	−0.509751	−	0.860322i	$-0.670263\pi$
$887$	−10.3417	+	3.76406i	−0.347240	+	0.126385i	0.162512	+	0.986707i	$0.448040\pi$
$888$	−11.8964	−	8.60334i	−0.399219	−	0.288709i
$889$	5.45215	−	30.9207i	0.182859	−	1.03705i
$890$	−0.827078	+	0.380565i	−0.0277237	+	0.0127566i
$891$	3.14692	+	3.75036i	0.105426	+	0.125642i
$892$	0.586095	−	57.6371i	0.0196239	−	1.92983i
$893$	15.5778	+	22.2892i	0.521292	+	0.745881i
$894$	−8.63054	−	8.71874i	−0.288648	−	0.291598i
$895$	0.655312	−	0.549872i	0.0219047	−	0.0183802i
$896$	24.7251	−	10.4752i	0.826006	−	0.349954i
$897$	−0.961365	+	5.45217i	−0.0320990	+	0.182043i
$898$	−3.06226	+	4.32638i	−0.102189	+	0.144373i
$899$	−19.5257	−	53.6464i	−0.651218	−	1.78921i
$900$	8.60598	+	5.08603i	0.286866	+	0.169534i
$901$	−5.57552	+	3.21903i	−0.185747	+	0.107241i
$902$	3.57641	−	0.294581i	0.119082	−	0.00980848i
$903$	18.8739	+	15.8371i	0.628085	+	0.527026i
$904$	21.9426	+	6.23970i	0.729798	+	0.207529i
$905$	−0.0850301	+	0.147277i	−0.00282650	+	0.00489564i
$906$	−11.1504	+	23.5981i	−0.370446	+	0.783993i
$907$	8.54250	−	1.50627i	0.283649	−	0.0500150i	−0.0300135	−	0.999549i	$-0.509555\pi$
$907$	8.54250	−	1.50627i	0.283649	−	0.0500150i	0.313663	+	0.949535i	$0.398444\pi$
$908$	2.28960	−	12.2549i	0.0759830	−	0.406695i
$909$	−0.821669	+	2.25752i	−0.0272530	+	0.0748771i
$910$	−0.475361	−	0.0440251i	−0.0157581	−	0.00145942i
$911$	2.69710			0.0893589			0.0446795	−	0.999001i	$-0.485773\pi$
$911$	2.69710			0.0893589			0.0446795	+	0.999001i	$0.485773\pi$
$912$	14.4914	−	9.69537i	0.479857	−	0.321046i
$913$	42.5790			1.40916
$914$	−6.54673	−	0.606320i	−0.216547	−	0.0200553i
$915$	−0.00379966	+	0.0104395i	−0.000125613	+	0.000345118i
$916$	−1.45946	+	7.81167i	−0.0482219	+	0.258105i
$917$	−8.77938	+	1.54804i	−0.289921	+	0.0511208i
$918$	1.81628	−	3.84387i	0.0599461	−	0.126867i
$919$	−22.6602	+	39.2487i	−0.747492	+	1.29469i	0.201529	+	0.979483i	$0.435409\pi$
$919$	−22.6602	+	39.2487i	−0.747492	+	1.29469i	−0.949021	+	0.315212i	$0.897924\pi$
$920$	−0.0522887	+	0.183879i	−0.00172391	+	0.00606230i
$921$	3.33147	+	2.79544i	0.109776	+	0.0921128i
$922$	−9.82005	+	0.808856i	−0.323406	+	0.0266382i
$923$	−30.8929	+	17.8360i	−1.01685	+	0.587080i
$924$	20.0069	+	11.8239i	0.658179	+	0.388976i
$925$	−8.87345	−	24.3796i	−0.291757	−	0.801597i
$926$	−8.76372	+	12.3814i	−0.287994	+	0.406879i
$927$	2.20013	−	12.4776i	0.0722617	−	0.409817i
$928$	−31.3137	+	13.6439i	−1.02792	+	0.447882i
$929$	−28.0919	+	23.5719i	−0.921665	+	0.773369i	−0.974302	−	0.225245i	$-0.927682\pi$
$929$	−28.0919	+	23.5719i	−0.921665	+	0.773369i	0.0526369	+	0.998614i	$0.483237\pi$
$930$	−0.391966	−	0.395972i	−0.0128531	−	0.0129844i
$931$	1.53682	+	5.75578i	0.0503672	+	0.188638i
$932$	−0.0635338	+	6.24797i	−0.00208112	+	0.204659i
$933$	18.1059	+	21.5777i	0.592760	+	0.706424i
$934$	24.7987	−	11.4107i	0.811440	−	0.373370i
$935$	−0.106493	+	0.603953i	−0.00348270	+	0.0197514i
$936$	−5.65731	+	7.82276i	−0.184915	+	0.255695i
$937$	−26.9092	+	9.79413i	−0.879084	+	0.319960i	−0.741840	−	0.670577i	$-0.766047\pi$
$937$	−26.9092	+	9.79413i	−0.879084	+	0.319960i	−0.137244	+	0.990537i	$0.543824\pi$
$938$	−11.5889	−	44.1468i	−0.378390	−	1.44145i
$939$	−8.32718	+	4.80770i	−0.271747	+	0.156893i
$940$	−0.394861	−	0.338229i	−0.0128789	−	0.0110318i
$941$	−7.24233	+	8.63107i	−0.236093	+	0.281365i	−0.871062	−	0.491173i	$-0.836568\pi$
$941$	−7.24233	+	8.63107i	−0.236093	+	0.281365i	0.634969	+	0.772538i	$0.281013\pi$
$942$	6.67593	−	24.4177i	0.217514	−	0.795570i
$943$	0.420345	−	0.728058i	0.0136883	−	0.0237088i
$944$	−16.8305	−	49.3411i	−0.547787	−	1.60592i
$945$	0.0171739	+	0.0973981i	0.000558667	+	0.00316836i
$946$	−59.0831	+	40.9244i	−1.92096	+	1.33057i
$947$	13.8572	−	38.0724i	0.450300	−	1.23719i	−0.482214	−	0.876053i	$-0.660167\pi$
$947$	13.8572	−	38.0724i	0.450300	−	1.23719i	0.932514	−	0.361134i	$-0.117610\pi$
$948$	−18.0481	+	14.8341i	−0.586175	+	0.481788i
$949$		−	10.8168i		−	0.351129i
$950$	30.8108	+	0.183810i	0.999635	+	0.00596358i
$951$	−0.0488238			−0.00158322
$952$	2.06530	−	20.0749i	0.0669368	−	0.650632i
$953$	−0.176120	−	0.0641025i	−0.00570510	−	0.00207648i	0.339166	−	0.940727i	$-0.389855\pi$
$953$	−0.176120	−	0.0641025i	−0.00570510	−	0.00207648i	−0.344871	+	0.938650i	$0.612077\pi$
$954$	−1.72455	−	2.48976i	−0.0558343	−	0.0806088i
$955$	−0.358561	+	0.0632239i	−0.0116028	+	0.00204588i
$956$	−4.95200	−	14.0484i	−0.160159	−	0.454356i
$957$	−25.6009	−	14.7807i	−0.827559	−	0.477791i
$958$	−13.7870	+	50.4269i	−0.445438	+	1.62922i
$959$	−21.2179	−	17.8039i	−0.685162	−	0.574919i
$960$	−0.221966	+	0.248711i	−0.00716393	+	0.00802712i
$961$	−29.1959	−	50.5688i	−0.941804	−	1.63125i
$962$	24.2343	−	6.36168i	0.781346	−	0.205109i
$963$	1.38315	+	3.80016i	0.0445712	+	0.122458i
$964$	39.4119	−	6.53690i	1.26937	−	0.210539i
$965$	−0.135904	−	0.0239636i	−0.00437491	−	0.000771414i
$966$	4.94592	−	2.27578i	0.159132	−	0.0732220i
$967$	14.0998	−	11.8311i	0.453419	−	0.380464i	−0.387284	−	0.921961i	$-0.626587\pi$
$967$	14.0998	−	11.8311i	0.453419	−	0.380464i	0.840703	+	0.541497i	$0.182142\pi$
$968$	−26.3292	+	25.5380i	−0.846252	+	0.820823i
$969$	−1.13055	−	13.0548i	−0.0363185	−	0.419380i
$970$	−0.223743	+	0.221479i	−0.00718394	+	0.00711126i
$971$	−28.0168	−	33.3891i	−0.899103	−	1.07151i	−0.997083	−	0.0763204i	$-0.975683\pi$
$971$	−28.0168	−	33.3891i	−0.899103	−	1.07151i	0.0979807	−	0.995188i	$-0.468762\pi$
$972$	1.87233	+	0.703115i	0.0600551	+	0.0225524i
$973$	−22.8950	−	4.03700i	−0.733979	−	0.129420i
$974$	20.2736	−	28.6427i	0.649609	−	0.917771i
$975$	−16.0313	+	5.83493i	−0.513413	+	0.186867i
$976$	0.912526	+	0.551888i	0.0292092	+	0.0176655i
$977$	14.0117	+	24.2690i	0.448275	+	0.776435i	0.998274	−	0.0587302i	$-0.0187052\pi$
$977$	14.0117	+	24.2690i	0.448275	+	0.776435i	−0.549999	+	0.835165i	$0.685372\pi$
$978$	−0.555138	−	6.73974i	−0.0177513	−	0.215513i
$979$	−48.6184	+	57.9412i	−1.55385	+	1.85181i
$980$	−0.0559448	−	0.0992156i	−0.00178709	−	0.00316933i
$981$	7.19419	+	4.15357i	0.229693	+	0.132613i
$982$	−2.55608	+	5.40956i	−0.0815679	+	0.172626i
$983$	−4.89803	−	27.7781i	−0.156223	−	0.885984i	−0.957659	−	0.287904i	$-0.907042\pi$
$983$	−4.89803	−	27.7781i	−0.156223	−	0.885984i	0.801436	−	0.598080i	$-0.204070\pi$
$984$	1.21354	−	0.822437i	0.0386863	−	0.0262183i
$985$	−0.0986020	−	0.0358882i	−0.00314172	−	0.00114349i
$986$	−2.36732	+	25.5612i	−0.0753910	+	0.814034i
$987$			14.8070i			0.471311i
$988$	−2.92077	+	29.6121i	−0.0929220	+	0.942086i
$989$			16.8376i			0.535406i
$990$	−0.287275	−	0.0266057i	−0.00913019	−	0.000845584i
$991$	8.86842	+	3.22784i	0.281715	+	0.102536i	0.479013	−	0.877808i	$-0.340995\pi$
$991$	8.86842	+	3.22784i	0.281715	+	0.102536i	−0.197299	+	0.980343i	$0.563217\pi$
$992$	−44.5771	+	29.5536i	−1.41533	+	0.938329i
$993$	−3.72494	−	21.1252i	−0.118207	−	0.670387i
$994$	31.7175	+	14.9869i	1.00602	+	0.475355i
$995$	0.657656	+	0.379698i	0.0208491	+	0.0120372i
$996$	15.1516	−	8.54353i	0.480096	−	0.270712i
$997$	−9.76136	+	11.6331i	−0.309145	+	0.368425i	−0.898138	−	0.439713i	$-0.855080\pi$
$997$	−9.76136	+	11.6331i	−0.309145	+	0.368425i	0.588993	+	0.808138i	$0.299525\pi$
$998$	−48.8993	+	4.02773i	−1.54788	+	0.127495i
$999$	−2.59533	−	4.49523i	−0.0821125	−	0.142223i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	456.2.bk.a.253.2	✓	240
8.5	even	2	inner	456.2.bk.a.253.20	yes	240
19.16	even	9	inner	456.2.bk.a.301.20	yes	240
152.149	even	18	inner	456.2.bk.a.301.2	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
456.2.bk.a.253.2	✓	240	1.1	even	1	trivial
456.2.bk.a.253.20	yes	240	8.5	even	2	inner
456.2.bk.a.301.2	yes	240	152.149	even	18	inner
456.2.bk.a.301.20	yes	240	19.16	even	9	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:	\( N \)	\(=\)	\( 456 = 2^{3} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	456.bk (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40819 - 0.130418i) q^{2} +(0.342020 - 0.939693i) q^{3} +(1.96598 + 0.367306i) q^{4} +(-0.0410365 + 0.00723583i) q^{5} +(-0.604181 + 1.27866i) q^{6} +(-1.18673 + 2.05547i) q^{7} +(-2.72057 - 0.773635i) q^{8} +(-0.766044 - 0.642788i) q^{9} +O(q^{10})\)	\(q+(-1.40819 - 0.130418i) q^{2} +(0.342020 - 0.939693i) q^{3} +(1.96598 + 0.367306i) q^{4} +(-0.0410365 + 0.00723583i) q^{5} +(-0.604181 + 1.27866i) q^{6} +(-1.18673 + 2.05547i) q^{7} +(-2.72057 - 0.773635i) q^{8} +(-0.766044 - 0.642788i) q^{9} +(0.0587307 - 0.00483752i) q^{10} +(4.23984 - 2.44787i) q^{11} +(1.01756 - 1.72179i) q^{12} +(1.16739 + 3.20738i) q^{13} +(1.93920 - 2.73972i) q^{14} +(-0.00723583 + 0.0410365i) q^{15} +(3.73017 + 1.44423i) q^{16} +(2.30287 - 1.93233i) q^{17} +(0.994903 + 1.00507i) q^{18} +(4.20938 + 1.13188i) q^{19} +(-0.0833347 - 0.000847406i) q^{20} +(1.52563 + 1.81817i) q^{21} +(-6.28973 + 2.89411i) q^{22} +(-0.281659 + 1.59737i) q^{23} +(-1.65747 + 2.29190i) q^{24} +(-4.69683 + 1.70951i) q^{25} +(-1.22560 - 4.66884i) q^{26} +(-0.866025 + 0.500000i) q^{27} +(-3.08807 + 3.60513i) q^{28} +(3.88126 - 4.62551i) q^{29} +(0.0155413 - 0.0568433i) q^{30} +(4.72736 - 8.18803i) q^{31} +(-5.06443 - 2.52023i) q^{32} +(-0.850137 - 4.82137i) q^{33} +(-3.49488 + 2.42075i) q^{34} +(0.0338260 - 0.0929361i) q^{35} +(-1.26993 - 1.54508i) q^{36} +5.19065i q^{37} +(-5.77997 - 2.14287i) q^{38} +3.41322 q^{39} +(0.117240 + 0.0120616i) q^{40} +(-0.487044 - 0.177269i) q^{41} +(-1.91124 - 2.75929i) q^{42} +(10.2230 - 1.80259i) q^{43} +(9.23457 - 3.25516i) q^{44} +(0.0360869 + 0.0208348i) q^{45} +(0.604954 - 2.21266i) q^{46} +(4.77903 + 4.01008i) q^{47} +(2.63293 - 3.01126i) q^{48} +(0.683363 + 1.18362i) q^{49} +(6.83697 - 1.79475i) q^{50} +(-1.02817 - 2.82488i) q^{51} +(1.11698 + 6.73444i) q^{52} +(-2.10907 - 0.371886i) q^{53} +(1.28473 - 0.591148i) q^{54} +(-0.156276 + 0.131131i) q^{55} +(4.81875 - 4.67395i) q^{56} +(2.50331 - 3.56840i) q^{57} +(-6.06880 + 6.00740i) q^{58} +(-8.37755 - 9.98398i) q^{59} +(-0.0292984 + 0.0780192i) q^{60} +(0.262558 + 0.0462961i) q^{61} +(-7.72488 + 10.9137i) q^{62} +(2.23032 - 0.811768i) q^{63} +(6.80298 + 4.20945i) q^{64} +(-0.0711136 - 0.123172i) q^{65} +(0.568359 + 6.90026i) q^{66} +(8.74062 - 10.4167i) q^{67} +(5.23715 - 2.95308i) q^{68} +(1.40470 + 0.811005i) q^{69} +(-0.0597539 + 0.126460i) q^{70} +(1.81482 + 10.2924i) q^{71} +(1.58679 + 2.34139i) q^{72} +(-2.97798 - 1.08389i) q^{73} +(0.676954 - 7.30941i) q^{74} +4.99826i q^{75} +(7.85982 + 3.77138i) q^{76} +11.6198i q^{77} +(-4.80646 - 0.445145i) q^{78} +(-10.9766 - 3.99514i) q^{79} +(-0.163523 - 0.0322753i) q^{80} +(0.173648 + 0.984808i) q^{81} +(0.662730 + 0.313148i) q^{82} +(7.53195 + 4.34857i) q^{83} +(2.33153 + 4.13486i) q^{84} +(-0.0805194 + 0.0959593i) q^{85} +(-14.6310 + 1.20512i) q^{86} +(-3.01909 - 5.22921i) q^{87} +(-13.4285 + 3.37952i) q^{88} +(-14.5178 + 5.28404i) q^{89} +(-0.0480998 - 0.0340456i) q^{90} +(-7.97804 - 1.40674i) q^{91} +(-1.14046 + 3.03694i) q^{92} +(-6.07738 - 7.24274i) q^{93} +(-6.20679 - 6.27022i) q^{94} +(-0.180928 - 0.0159899i) q^{95} +(-4.10038 + 3.89704i) q^{96} +(-4.09249 + 3.43400i) q^{97} +(-0.807937 - 1.75588i) q^{98} +(-4.82137 - 0.850137i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 6 q^{4} + 6 q^{6}+O(q^{10}) \) 240 * q + 6 * q^4 + 6 * q^6	\( 240 q + 6 q^{4} + 6 q^{6} - 24 q^{10} + 18 q^{14} - 6 q^{16} + 60 q^{20} - 36 q^{28} - 72 q^{31} - 90 q^{32} + 66 q^{34} - 6 q^{36} + 72 q^{38} - 114 q^{40} - 60 q^{44} + 30 q^{46} + 72 q^{47} + 24 q^{48} - 120 q^{49} + 18 q^{50} + 6 q^{52} - 6 q^{54} + 72 q^{58} - 12 q^{60} + 12 q^{62} + 30 q^{64} - 48 q^{66} - 78 q^{68} - 108 q^{70} - 36 q^{72} - 24 q^{73} - 96 q^{74} - 48 q^{76} - 96 q^{78} - 114 q^{80} - 66 q^{82} - 36 q^{84} - 24 q^{86} - 24 q^{88} + 6 q^{90} - 108 q^{94} + 120 q^{95} - 12 q^{98}+O(q^{100}) \) 240 * q + 6 * q^4 + 6 * q^6 - 24 * q^10 + 18 * q^14 - 6 * q^16 + 60 * q^20 - 36 * q^28 - 72 * q^31 - 90 * q^32 + 66 * q^34 - 6 * q^36 + 72 * q^38 - 114 * q^40 - 60 * q^44 + 30 * q^46 + 72 * q^47 + 24 * q^48 - 120 * q^49 + 18 * q^50 + 6 * q^52 - 6 * q^54 + 72 * q^58 - 12 * q^60 + 12 * q^62 + 30 * q^64 - 48 * q^66 - 78 * q^68 - 108 * q^70 - 36 * q^72 - 24 * q^73 - 96 * q^74 - 48 * q^76 - 96 * q^78 - 114 * q^80 - 66 * q^82 - 36 * q^84 - 24 * q^86 - 24 * q^88 + 6 * q^90 - 108 * q^94 + 120 * q^95 - 12 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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