LMFDB - Embedded newform 390.2.bh.c.71.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [390,2,Mod(11,390)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(390, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 0, 7]))

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

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

chi := DirichletCharacter("390.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 390 = 2 \cdot 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	390.bh (of order $12$, degree $4$, 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:	$3.11416567883$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			71.4
Character	$\chi$	$=$	390.71
Dual form			390.2.bh.c.11.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 + 0.258819i) q^{2} +(0.888751 + 1.48665i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-0.707107 - 0.707107i) q^{5} +(-1.24324 - 1.20597i) q^{6} +(0.431103 - 1.60890i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-1.42024 + 2.64252i) q^{9} +O(q^{10})$	\(q+(-0.965926 + 0.258819i) q^{2} +(0.888751 + 1.48665i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-0.707107 - 0.707107i) q^{5} +(-1.24324 - 1.20597i) q^{6} +(0.431103 - 1.60890i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-1.42024 + 2.64252i) q^{9} +(0.866025 + 0.500000i) q^{10} +(0.985615 + 3.67836i) q^{11} +(1.51301 + 0.843099i) q^{12} +(2.83555 + 2.22703i) q^{13} +1.66565i q^{14} +(0.422776 - 1.67966i) q^{15} +(0.500000 - 0.866025i) q^{16} +(0.660987 + 1.14486i) q^{17} +(0.687914 - 2.92006i) q^{18} +(5.54438 + 1.48561i) q^{19} +(-0.965926 - 0.258819i) q^{20} +(2.77501 - 0.789012i) q^{21} +(-1.90406 - 3.29793i) q^{22} +(-3.32990 + 5.76756i) q^{23} +(-1.67966 - 0.422776i) q^{24} +1.00000i q^{25} +(-3.31533 - 1.41726i) q^{26} +(-5.19074 + 0.237145i) q^{27} +(-0.431103 - 1.60890i) q^{28} +(-1.32839 - 0.766948i) q^{29} +(0.0263575 + 1.73185i) q^{30} +(5.84819 - 5.84819i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(-4.59246 + 4.73441i) q^{33} +(-0.934777 - 0.934777i) q^{34} +(-1.44250 + 0.832827i) q^{35} +(0.0912946 + 2.99861i) q^{36} +(-9.72471 + 2.60573i) q^{37} -5.73996 q^{38} +(-0.790720 + 6.19474i) q^{39} +1.00000 q^{40} +(4.33407 - 1.16131i) q^{41} +(-2.47624 + 1.48035i) q^{42} +(-6.30456 + 3.63994i) q^{43} +(2.69275 + 2.69275i) q^{44} +(2.87281 - 0.864281i) q^{45} +(1.72368 - 6.43288i) q^{46} +(9.18700 - 9.18700i) q^{47} +(1.73185 - 0.0263575i) q^{48} +(3.65947 + 2.11280i) q^{49} +(-0.258819 - 0.965926i) q^{50} +(-1.11455 + 2.00015i) q^{51} +(3.56917 + 0.510896i) q^{52} +0.302458i q^{53} +(4.95249 - 1.57253i) q^{54} +(1.90406 - 3.29793i) q^{55} +(0.832827 + 1.44250i) q^{56} +(2.71899 + 9.56288i) q^{57} +(1.48163 + 0.397002i) q^{58} +(-3.71613 - 0.995733i) q^{59} +(-0.473695 - 1.66602i) q^{60} +(2.23843 + 3.87708i) q^{61} +(-4.13529 + 7.16254i) q^{62} +(3.63928 + 3.42422i) q^{63} -1.00000i q^{64} +(-0.430282 - 3.57978i) q^{65} +(3.21062 - 5.76171i) q^{66} +(-0.0586497 - 0.218884i) q^{67} +(1.14486 + 0.660987i) q^{68} +(-11.5338 + 0.175536i) q^{69} +(1.17780 - 1.17780i) q^{70} +(3.95652 - 14.7659i) q^{71} +(-0.864281 - 2.87281i) q^{72} +(-0.682227 - 0.682227i) q^{73} +(8.71894 - 5.03388i) q^{74} +(-1.48665 + 0.888751i) q^{75} +(5.54438 - 1.48561i) q^{76} +6.34302 q^{77} +(-0.839539 - 6.18831i) q^{78} -8.02282 q^{79} +(-0.965926 + 0.258819i) q^{80} +(-4.96583 - 7.50604i) q^{81} +(-3.88582 + 2.24348i) q^{82} +(-8.80953 - 8.80953i) q^{83} +(2.00872 - 2.07081i) q^{84} +(0.342152 - 1.27693i) q^{85} +(5.14765 - 5.14765i) q^{86} +(-0.0404297 - 2.65648i) q^{87} +(-3.29793 - 1.90406i) q^{88} +(2.31981 + 8.65764i) q^{89} +(-2.55123 + 1.57837i) q^{90} +(4.80548 - 3.60202i) q^{91} +6.65980i q^{92} +(13.8918 + 3.49661i) q^{93} +(-6.49619 + 11.2517i) q^{94} +(-2.86998 - 4.97095i) q^{95} +(-1.66602 + 0.473695i) q^{96} +(-1.63135 - 0.437120i) q^{97} +(-4.08161 - 1.09366i) q^{98} +(-11.1200 - 2.61966i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 8 q^{6} - 8 q^{7} + 8 q^{9}+O(q^{10}) $ 40 * q + 8 * q^6 - 8 * q^7 + 8 * q^9	$ 40 q + 8 q^{6} - 8 q^{7} + 8 q^{9} + 8 q^{13} + 4 q^{15} + 20 q^{16} - 8 q^{18} - 16 q^{19} + 4 q^{21} - 8 q^{22} + 8 q^{24} - 48 q^{27} + 8 q^{28} + 36 q^{31} + 12 q^{33} + 16 q^{34} - 12 q^{36} - 64 q^{37} - 60 q^{39} + 40 q^{40} - 12 q^{42} + 8 q^{45} - 32 q^{46} + 48 q^{49} + 24 q^{52} - 28 q^{54} + 8 q^{55} - 76 q^{57} - 28 q^{58} + 4 q^{60} - 40 q^{61} + 80 q^{63} + 40 q^{66} - 28 q^{67} - 36 q^{69} + 16 q^{70} + 16 q^{72} + 8 q^{73} - 16 q^{76} - 28 q^{78} + 40 q^{79} + 12 q^{81} + 20 q^{84} + 44 q^{85} + 40 q^{87} + 12 q^{88} + 120 q^{91} - 8 q^{93} - 16 q^{94} + 4 q^{96} - 160 q^{97} - 96 q^{99}+O(q^{100}) $ 40 * q + 8 * q^6 - 8 * q^7 + 8 * q^9 + 8 * q^13 + 4 * q^15 + 20 * q^16 - 8 * q^18 - 16 * q^19 + 4 * q^21 - 8 * q^22 + 8 * q^24 - 48 * q^27 + 8 * q^28 + 36 * q^31 + 12 * q^33 + 16 * q^34 - 12 * q^36 - 64 * q^37 - 60 * q^39 + 40 * q^40 - 12 * q^42 + 8 * q^45 - 32 * q^46 + 48 * q^49 + 24 * q^52 - 28 * q^54 + 8 * q^55 - 76 * q^57 - 28 * q^58 + 4 * q^60 - 40 * q^61 + 80 * q^63 + 40 * q^66 - 28 * q^67 - 36 * q^69 + 16 * q^70 + 16 * q^72 + 8 * q^73 - 16 * q^76 - 28 * q^78 + 40 * q^79 + 12 * q^81 + 20 * q^84 + 44 * q^85 + 40 * q^87 + 12 * q^88 + 120 * q^91 - 8 * q^93 - 16 * q^94 + 4 * q^96 - 160 * q^97 - 96 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/390\mathbb{Z}\right)^\times$.

$n$	$131$	$157$	$301$
$\chi(n)$	$-1$	$1$	$e\left(\frac{5}{12}\right)$

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 $

$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$3$	0.888751	+	1.48665i	0.513121	+	0.858316i
$3$	0.888751	+	1.48665i	0.513121	+	0.858316i
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$	−0.707107	−	0.707107i	−0.316228	−	0.316228i
$5$	−0.707107	−	0.707107i	−0.316228	−	0.316228i
$6$	−1.24324	−	1.20597i	−0.507551	−	0.492333i
$7$	0.431103	−	1.60890i	0.162942	−	0.608106i	−0.835352	−	0.549715i	$-0.814736\pi$
$7$	0.431103	−	1.60890i	0.162942	−	0.608106i	0.998294	−	0.0583912i	$-0.0185971\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	−1.42024	+	2.64252i	−0.473414	+	0.880840i
$10$	0.866025	+	0.500000i	0.273861	+	0.158114i
$11$	0.985615	+	3.67836i	0.297174	+	1.10907i	0.939475	+	0.342616i	$0.111313\pi$
$11$	0.985615	+	3.67836i	0.297174	+	1.10907i	−0.642301	+	0.766452i	$0.722020\pi$
$12$	1.51301	+	0.843099i	0.436767	+	0.243382i
$13$	2.83555	+	2.22703i	0.786439	+	0.617668i
$13$	2.83555	+	2.22703i	0.786439	+	0.617668i
$14$			1.66565i			0.445165i
$15$	0.422776	−	1.67966i	0.109160	−	0.433687i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	0.660987	+	1.14486i	0.160313	+	0.277670i	0.934981	−	0.354698i	$-0.115416\pi$
$17$	0.660987	+	1.14486i	0.160313	+	0.277670i	−0.774668	+	0.632368i	$0.782083\pi$
$18$	0.687914	−	2.92006i	0.162143	−	0.688266i
$19$	5.54438	+	1.48561i	1.27197	+	0.340823i	0.830785	−	0.556594i	$-0.187892\pi$
$19$	5.54438	+	1.48561i	1.27197	+	0.340823i	0.441183	+	0.897417i	$0.354559\pi$
$20$	−0.965926	−	0.258819i	−0.215988	−	0.0578737i
$21$	2.77501	−	0.789012i	0.605556	−	0.172177i
$22$	−1.90406	−	3.29793i	−0.405947	−	0.703121i
$23$	−3.32990	+	5.76756i	−0.694333	+	1.20262i	0.276073	+	0.961137i	$0.410967\pi$
$23$	−3.32990	+	5.76756i	−0.694333	+	1.20262i	−0.970405	+	0.241482i	$0.922366\pi$
$24$	−1.67966	−	0.422776i	−0.342859	−	0.0862989i
$25$			1.00000i			0.200000i
$26$	−3.31533	−	1.41726i	−0.650189	−	0.277947i
$27$	−5.19074	+	0.237145i	−0.998958	+	0.0456385i
$28$	−0.431103	−	1.60890i	−0.0814708	−	0.304053i
$29$	−1.32839	−	0.766948i	−0.246677	−	0.142419i	0.371565	−	0.928407i	$-0.378821\pi$
$29$	−1.32839	−	0.766948i	−0.246677	−	0.142419i	−0.618242	+	0.785988i	$0.712155\pi$
$30$	0.0263575	+	1.73185i	0.00481221	+	0.316191i
$31$	5.84819	−	5.84819i	1.05037	−	1.05037i	0.0517031	−	0.998662i	$-0.483535\pi$
$31$	5.84819	−	5.84819i	1.05037	−	1.05037i	0.998662	−	0.0517031i	$-0.0164650\pi$
$32$	−0.258819	+	0.965926i	−0.0457532	+	0.170753i
$33$	−4.59246	+	4.73441i	−0.799445	+	0.824155i
$34$	−0.934777	−	0.934777i	−0.160313	−	0.160313i
$35$	−1.44250	+	0.832827i	−0.243827	+	0.140773i
$36$	0.0912946	+	2.99861i	0.0152158	+	0.499768i
$37$	−9.72471	+	2.60573i	−1.59873	+	0.428379i	−0.944659	−	0.328052i	$-0.893608\pi$
$37$	−9.72471	+	2.60573i	−1.59873	+	0.428379i	−0.654073	+	0.756432i	$0.726941\pi$
$38$	−5.73996			−0.931145
$39$	−0.790720	+	6.19474i	−0.126617	+	0.991952i
$40$	1.00000			0.158114
$41$	4.33407	−	1.16131i	0.676868	−	0.181366i	0.0960213	−	0.995379i	$-0.469388\pi$
$41$	4.33407	−	1.16131i	0.676868	−	0.181366i	0.580847	+	0.814013i	$0.302722\pi$
$42$	−2.47624	+	1.48035i	−0.382092	+	0.228423i
$43$	−6.30456	+	3.63994i	−0.961436	+	0.555085i	−0.896615	−	0.442812i	$-0.853981\pi$
$43$	−6.30456	+	3.63994i	−0.961436	+	0.555085i	−0.0648212	+	0.997897i	$0.520648\pi$
$44$	2.69275	+	2.69275i	0.405947	+	0.405947i
$45$	2.87281	−	0.864281i	0.428253	−	0.128839i
$46$	1.72368	−	6.43288i	0.254143	−	0.948476i
$47$	9.18700	−	9.18700i	1.34006	−	1.34006i	0.444070	−	0.895992i	$-0.353534\pi$
$47$	9.18700	−	9.18700i	1.34006	−	1.34006i	0.895992	−	0.444070i	$-0.146466\pi$
$48$	1.73185	−	0.0263575i	0.249971	−	0.00380438i
$49$	3.65947	+	2.11280i	0.522782	+	0.301828i
$50$	−0.258819	−	0.965926i	−0.0366025	−	0.136603i
$51$	−1.11455	+	2.00015i	−0.156069	+	0.280077i
$52$	3.56917	+	0.510896i	0.494955	+	0.0708485i
$53$			0.302458i			0.0415458i	0.999784	+	0.0207729i	$0.00661269\pi$
$53$			0.302458i			0.0415458i	−0.999784	+	0.0207729i	$0.993387\pi$
$54$	4.95249	−	1.57253i	0.673949	−	0.213994i
$55$	1.90406	−	3.29793i	0.256744	−	0.444693i
$56$	0.832827	+	1.44250i	0.111291	+	0.192762i
$57$	2.71899	+	9.56288i	0.360140	+	1.26663i
$58$	1.48163	+	0.397002i	0.194548	+	0.0521289i
$59$	−3.71613	−	0.995733i	−0.483798	−	0.129633i	0.00867240	−	0.999962i	$-0.497239\pi$
$59$	−3.71613	−	0.995733i	−0.483798	−	0.129633i	−0.492471	+	0.870329i	$0.663906\pi$
$60$	−0.473695	−	1.66602i	−0.0611538	−	0.215082i
$61$	2.23843	+	3.87708i	0.286602	+	0.496409i	0.972996	−	0.230820i	$-0.0741409\pi$
$61$	2.23843	+	3.87708i	0.286602	+	0.496409i	−0.686394	+	0.727229i	$0.740808\pi$
$62$	−4.13529	+	7.16254i	−0.525183	+	0.909643i
$63$	3.63928	+	3.42422i	0.458506	+	0.431412i
$64$		−	1.00000i		−	0.125000i
$65$	−0.430282	−	3.57978i	−0.0533699	−	0.444018i
$66$	3.21062	−	5.76171i	0.395200	−	0.709217i
$67$	−0.0586497	−	0.218884i	−0.00716520	−	0.0267409i	0.962251	−	0.272165i	$-0.0877396\pi$
$67$	−0.0586497	−	0.218884i	−0.00716520	−	0.0267409i	−0.969416	+	0.245424i	$0.921073\pi$
$68$	1.14486	+	0.660987i	0.138835	+	0.0801564i
$69$	−11.5338	+	0.175536i	−1.38850	+	0.0211321i
$70$	1.17780	−	1.17780i	0.140773	−	0.140773i
$71$	3.95652	−	14.7659i	0.469553	−	1.75240i	−0.171782	−	0.985135i	$-0.554953\pi$
$71$	3.95652	−	14.7659i	0.469553	−	1.75240i	0.641335	−	0.767261i	$-0.278381\pi$
$72$	−0.864281	−	2.87281i	−0.101857	−	0.338564i
$73$	−0.682227	−	0.682227i	−0.0798487	−	0.0798487i	0.666054	−	0.745903i	$-0.267982\pi$
$73$	−0.682227	−	0.682227i	−0.0798487	−	0.0798487i	−0.745903	+	0.666054i	$0.767982\pi$
$74$	8.71894	−	5.03388i	1.01356	−	0.585177i
$75$	−1.48665	+	0.888751i	−0.171663	+	0.102624i
$76$	5.54438	−	1.48561i	0.635984	−	0.170411i
$77$	6.34302			0.722854
$78$	−0.839539	−	6.18831i	−0.0950590	−	0.700688i
$79$	−8.02282			−0.902638			−0.451319	−	0.892363i	$-0.649046\pi$
$79$	−8.02282			−0.902638			−0.451319	+	0.892363i	$0.649046\pi$
$80$	−0.965926	+	0.258819i	−0.107994	+	0.0289368i
$81$	−4.96583	−	7.50604i	−0.551758	−	0.834004i
$82$	−3.88582	+	2.24348i	−0.429117	+	0.247751i
$83$	−8.80953	−	8.80953i	−0.966972	−	0.966972i	0.0324997	−	0.999472i	$-0.489653\pi$
$83$	−8.80953	−	8.80953i	−0.966972	−	0.966972i	−0.999472	+	0.0324997i	$0.989653\pi$
$84$	2.00872	−	2.07081i	0.219169	−	0.225944i
$85$	0.342152	−	1.27693i	0.0371116	−	0.138502i
$86$	5.14765	−	5.14765i	0.555085	−	0.555085i
$87$	−0.0404297	−	2.65648i	−0.00433452	−	0.284805i
$88$	−3.29793	−	1.90406i	−0.351561	−	0.202974i
$89$	2.31981	+	8.65764i	0.245899	+	0.917708i	0.972929	+	0.231103i	$0.0742334\pi$
$89$	2.31981	+	8.65764i	0.245899	+	0.917708i	−0.727030	+	0.686606i	$0.759100\pi$
$90$	−2.55123	+	1.57837i	−0.268923	+	0.166375i
$91$	4.80548	−	3.60202i	0.503752	−	0.377595i
$92$			6.65980i			0.694333i
$93$	13.8918	+	3.49661i	1.44051	+	0.362581i
$94$	−6.49619	+	11.2517i	−0.670031	+	1.16053i
$95$	−2.86998	−	4.97095i	−0.294454	−	0.510009i
$96$	−1.66602	+	0.473695i	−0.170037	+	0.0483463i
$97$	−1.63135	−	0.437120i	−0.165639	−	0.0443828i	0.175046	−	0.984560i	$-0.443992\pi$
$97$	−1.63135	−	0.437120i	−0.165639	−	0.0443828i	−0.340685	+	0.940177i	$0.610659\pi$
$98$	−4.08161	−	1.09366i	−0.412305	−	0.110477i
$99$	−11.1200	−	2.61966i	−1.11760	−	0.263286i
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$	3.60713	−	6.24773i	0.358923	−	0.621672i	−0.628859	−	0.777520i	$-0.716478\pi$
$101$	3.60713	−	6.24773i	0.358923	−	0.621672i	0.987781	+	0.155848i	$0.0498109\pi$
$102$	0.558899	−	2.22047i	0.0553393	−	0.219859i
$103$		−	14.1200i		−	1.39129i	−0.718387	−	0.695643i	$-0.755119\pi$
$103$		−	14.1200i		−	1.39129i	0.718387	−	0.695643i	$-0.244881\pi$
$104$	−3.57978	+	0.430282i	−0.351027	+	0.0421926i
$105$	−2.52014	−	1.40431i	−0.245941	−	0.137047i
$106$	−0.0782818	−	0.292152i	−0.00760340	−	0.0283763i
$107$	5.10228	+	2.94580i	0.493256	+	0.284781i	0.725924	−	0.687775i	$-0.241412\pi$
$107$	5.10228	+	2.94580i	0.493256	+	0.284781i	−0.232668	+	0.972556i	$0.574746\pi$
$108$	−4.37674	+	2.80074i	−0.421152	+	0.269502i
$109$	7.40188	−	7.40188i	0.708971	−	0.708971i	−0.257348	−	0.966319i	$-0.582849\pi$
$109$	7.40188	−	7.40188i	0.708971	−	0.708971i	0.966319	+	0.257348i	$0.0828485\pi$
$110$	−0.985615	+	3.67836i	−0.0939747	+	0.350718i
$111$	−12.5166	−	12.1414i	−1.18803	−	1.15241i
$112$	−1.17780	−	1.17780i	−0.111291	−	0.111291i
$113$	9.89888	−	5.71512i	0.931208	−	0.537633i	0.0440148	−	0.999031i	$-0.485985\pi$
$113$	9.89888	−	5.71512i	0.931208	−	0.537633i	0.887194	+	0.461398i	$0.152652\pi$
$114$	−5.10140	−	8.53330i	−0.477790	−	0.799217i
$115$	6.43288	−	1.72368i	0.599869	−	0.160734i
$116$	−1.53390			−0.142419
$117$	−9.91214	+	4.33006i	−0.916378	+	0.400314i
$118$	3.84722			0.354165
$119$	2.12692	−	0.569907i	0.194975	−	0.0522433i
$120$	0.888751	+	1.48665i	0.0811315	+	0.135712i
$121$	−3.03264	+	1.75090i	−0.275695	+	0.159173i
$122$	−3.16562	−	3.16562i	−0.286602	−	0.286602i
$123$	5.57837	+	5.41112i	0.502985	+	0.487904i
$124$	2.14059	−	7.98877i	0.192230	−	0.717413i
$125$	0.707107	−	0.707107i	0.0632456	−	0.0632456i
$126$	−4.40152	−	2.36563i	−0.392119	−	0.210747i
$127$	−3.58413	−	2.06930i	−0.318040	−	0.183621i	0.332478	−	0.943111i	$-0.392115\pi$
$127$	−3.58413	−	2.06930i	−0.318040	−	0.183621i	−0.650519	+	0.759490i	$0.725448\pi$
$128$	0.258819	+	0.965926i	0.0228766	+	0.0853766i
$129$	−11.0145	−	6.13765i	−0.969772	−	0.540390i
$130$	1.34214	+	3.34644i	0.117713	+	0.293502i
$131$			4.18756i			0.365869i	0.983125	+	0.182935i	$0.0585597\pi$
$131$			4.18756i			0.365869i	−0.983125	+	0.182935i	$0.941440\pi$
$132$	−1.60998	+	6.39635i	−0.140131	+	0.556731i
$133$	4.78040	−	8.27989i	0.414513	−	0.717958i
$134$	0.113303	+	0.196246i	0.00978785	+	0.0169531i
$135$	3.83809	+	3.50272i	0.330330	+	0.301466i
$136$	−1.27693	−	0.342152i	−0.109496	−	0.0293393i
$137$	−11.6063	−	3.10990i	−0.991593	−	0.265697i	−0.273674	−	0.961823i	$-0.588239\pi$
$137$	−11.6063	−	3.10990i	−0.991593	−	0.265697i	−0.717920	+	0.696126i	$0.754906\pi$
$138$	11.0953	−	3.15472i	0.944499	−	0.268547i
$139$	−1.87876	−	3.25411i	−0.159354	−	0.276010i	0.775282	−	0.631616i	$-0.217608\pi$
$139$	−1.87876	−	3.25411i	−0.159354	−	0.276010i	−0.934636	+	0.355606i	$0.884275\pi$
$140$	−0.832827	+	1.44250i	−0.0703867	+	0.121913i
$141$	21.8228	+	5.49287i	1.83781	+	0.462583i
$142$			15.2868i			1.28284i
$143$	−5.39709	+	12.6252i	−0.451327	+	1.05577i
$144$	1.57837	+	2.55123i	0.131531	+	0.212602i
$145$	0.397002	+	1.48163i	0.0329692	+	0.123043i
$146$	0.835555	+	0.482408i	0.0691510	+	0.0399243i
$147$	0.111376	+	7.31810i	0.00918616	+	0.603587i
$148$	−7.11898	+	7.11898i	−0.585177	+	0.585177i
$149$	−0.101260	+	0.377907i	−0.00829554	+	0.0309594i	−0.969950	−	0.243306i	$-0.921768\pi$
$149$	−0.101260	+	0.377907i	−0.00829554	+	0.0309594i	0.961654	+	0.274265i	$0.0884347\pi$
$150$	1.20597	−	1.24324i	0.0984667	−	0.101510i
$151$	−13.6378	−	13.6378i	−1.10983	−	1.10983i	−0.993172	−	0.116655i	$-0.962783\pi$
$151$	−13.6378	−	13.6378i	−1.10983	−	1.10983i	−0.116655	−	0.993172i	$-0.537217\pi$
$152$	−4.97095	+	2.86998i	−0.403198	+	0.232786i
$153$	−3.96409	+	0.120689i	−0.320477	+	0.00975714i
$154$	−6.12688	+	1.64169i	−0.493718	+	0.132291i
$155$	−8.27059			−0.664310
$156$	2.41258	+	5.76016i	0.193161	+	0.461182i
$157$	15.9176			1.27036			0.635180	−	0.772364i	$-0.280926\pi$
$157$	15.9176			1.27036			0.635180	+	0.772364i	$0.280926\pi$
$158$	7.74945	−	2.07646i	0.616513	−	0.165194i
$159$	−0.449648	+	0.268810i	−0.0356594	+	0.0213180i
$160$	0.866025	−	0.500000i	0.0684653	−	0.0395285i
$161$	7.84389	+	7.84389i	0.618185	+	0.618185i
$162$	6.73932	+	5.96502i	0.529491	+	0.468656i
$163$	−3.45420	+	12.8913i	−0.270554	+	1.00972i	0.688208	+	0.725513i	$0.258397\pi$
$163$	−3.45420	+	12.8913i	−0.270554	+	1.00972i	−0.958762	+	0.284209i	$0.908269\pi$
$164$	3.17276	−	3.17276i	0.247751	−	0.247751i
$165$	6.59510	−	0.100373i	0.513428	−	0.00781401i
$166$	10.7894	+	6.22928i	0.837422	+	0.483486i
$167$	2.70988	+	10.1134i	0.209697	+	0.782599i	0.987966	+	0.154669i	$0.0494310\pi$
$167$	2.70988	+	10.1134i	0.209697	+	0.782599i	−0.778270	+	0.627930i	$0.783902\pi$
$168$	−1.40431	+	2.52014i	−0.108345	+	0.194433i
$169$	3.08064	+	12.6297i	0.236972	+	0.971516i
$170$			1.32197i			0.101391i
$171$	−11.8001	+	12.5412i	−0.902378	+	0.959050i
$172$	−3.63994	+	6.30456i	−0.277543	+	0.480718i
$173$	−4.64852	−	8.05147i	−0.353420	−	0.612142i	0.633426	−	0.773803i	$-0.281648\pi$
$173$	−4.64852	−	8.05147i	−0.353420	−	0.612142i	−0.986846	+	0.161661i	$0.948315\pi$
$174$	0.726600	+	2.55550i	0.0550834	+	0.193732i
$175$	1.60890	+	0.431103i	0.121621	+	0.0325883i
$176$	3.67836	+	0.985615i	0.277267	+	0.0742935i
$177$	−1.82241	−	6.40953i	−0.136981	−	0.481770i
$178$	−4.48153	−	7.76223i	−0.335905	−	0.581804i
$179$	7.73613	−	13.3994i	0.578226	−	1.00152i	−0.417457	−	0.908697i	$-0.637079\pi$
$179$	7.73613	−	13.3994i	0.578226	−	1.00152i	0.995683	−	0.0928197i	$-0.0295880\pi$
$180$	2.05578	−	2.18489i	0.153229	−	0.162852i
$181$			22.8979i			1.70199i	0.525173	+	0.850995i	$0.324000\pi$
$181$			22.8979i			1.70199i	−0.525173	+	0.850995i	$0.676000\pi$
$182$	−3.70947	+	4.72304i	−0.274964	+	0.350095i
$183$	−3.77444	+	6.77352i	−0.279015	+	0.500713i
$184$	−1.72368	−	6.43288i	−0.127072	−	0.474238i
$185$	8.71894	+	5.03388i	0.641029	+	0.370098i
$186$	−14.3234	+	0.217992i	−1.05024	+	0.0159840i
$187$	−3.55974	+	3.55974i	−0.260314	+	0.260314i
$188$	3.36268	−	12.5497i	0.245248	−	0.915280i
$189$	−1.85620	+	8.45360i	−0.135019	+	0.614909i
$190$	4.05877	+	4.05877i	0.294454	+	0.294454i
$191$	−6.68706	+	3.86078i	−0.483859	+	0.279356i	−0.722023	−	0.691869i	$-0.756788\pi$
$191$	−6.68706	+	3.86078i	−0.483859	+	0.279356i	0.238164	+	0.971225i	$0.423454\pi$
$192$	1.48665	−	0.888751i	0.107290	−	0.0641401i
$193$	−6.17479	+	1.65453i	−0.444471	+	0.119096i	−0.474111	−	0.880465i	$-0.657230\pi$
$193$	−6.17479	+	1.65453i	−0.444471	+	0.119096i	0.0296403	+	0.999561i	$0.490564\pi$
$194$	1.68890			0.121256
$195$	4.93946	−	3.82122i	0.353722	−	0.273643i
$196$	4.22560			0.301828
$197$	14.1811	−	3.79982i	1.01036	−	0.270726i	0.284582	−	0.958652i	$-0.408145\pi$
$197$	14.1811	−	3.79982i	1.01036	−	0.270726i	0.725781	+	0.687925i	$0.241478\pi$
$198$	11.4191	−	0.347661i	0.811518	−	0.0247072i
$199$	−2.52204	+	1.45610i	−0.178782	+	0.103220i	−0.586720	−	0.809790i	$-0.699581\pi$
$199$	−2.52204	+	1.45610i	−0.178782	+	0.103220i	0.407938	+	0.913010i	$0.366248\pi$
$200$	−0.707107	−	0.707107i	−0.0500000	−	0.0500000i
$201$	0.273278	−	0.281725i	0.0192755	−	0.0198713i
$202$	−1.86719	+	6.96843i	−0.131375	+	0.490297i
$203$	−1.80662	+	1.80662i	−0.126800	+	0.126800i
$204$	0.0348440	+	2.28946i	0.00243957	+	0.160294i
$205$	−3.88582	−	2.24348i	−0.271397	−	0.156691i
$206$	3.65453	+	13.6389i	0.254623	+	0.950266i
$207$	−10.5116	−	16.9907i	−0.730609	−	1.18093i
$208$	3.34644	−	1.34214i	0.232034	−	0.0930605i
$209$			21.8585i			1.51198i
$210$	2.79773	+	0.704199i	0.193062	+	0.0485944i
$211$	3.43660	−	5.95236i	0.236585	−	0.409777i	−0.723147	−	0.690694i	$-0.757305\pi$
$211$	3.43660	−	5.95236i	0.236585	−	0.409777i	0.959732	+	0.280917i	$0.0906384\pi$
$212$	0.151229	+	0.261936i	0.0103864	+	0.0179898i
$213$	25.4681	−	7.24130i	1.74505	−	0.496166i
$214$	−5.69085	−	1.52486i	−0.389019	−	0.104237i
$215$	7.03182	+	1.88417i	0.479566	+	0.128499i
$216$	3.50272	−	3.83809i	0.238330	−	0.261149i
$217$	−6.88797	−	11.9303i	−0.467586	−	0.809882i
$218$	−5.23392	+	9.06541i	−0.354486	+	0.613987i
$219$	0.407901	−	1.62056i	0.0275634	−	0.109507i
$220$		−	3.80812i		−	0.256744i
$221$	−0.675391	+	4.71835i	−0.0454317	+	0.317391i
$222$	15.2326	+	8.48812i	1.02234	+	0.569685i
$223$	0.408906	+	1.52606i	0.0273824	+	0.102192i	0.978265	−	0.207360i	$-0.0664873\pi$
$223$	0.408906	+	1.52606i	0.0273824	+	0.102192i	−0.950882	+	0.309553i	$0.899821\pi$
$224$	1.44250	+	0.832827i	0.0963810	+	0.0556456i
$225$	−2.64252	−	1.42024i	−0.176168	−	0.0946828i
$226$	−8.08240	+	8.08240i	−0.537633	+	0.537633i
$227$	1.72914	−	6.45324i	0.114767	−	0.428317i	−0.884502	−	0.466536i	$-0.845502\pi$
$227$	1.72914	−	6.45324i	0.114767	−	0.428317i	0.999269	+	0.0382192i	$0.0121685\pi$
$228$	7.13616	+	6.92220i	0.472604	+	0.458434i
$229$	16.0756	+	16.0756i	1.06230	+	1.06230i	0.997926	+	0.0643787i	$0.0205066\pi$
$229$	16.0756	+	16.0756i	1.06230	+	1.06230i	0.0643787	+	0.997926i	$0.479493\pi$
$230$	−5.76756	+	3.32990i	−0.380302	+	0.219567i
$231$	5.63736	+	9.42983i	0.370911	+	0.620437i
$232$	1.48163	−	0.397002i	0.0972738	−	0.0260644i
$233$	−20.9127			−1.37004			−0.685018	−	0.728526i	$-0.740206\pi$
$233$	−20.9127			−1.37004			−0.685018	+	0.728526i	$0.740206\pi$
$234$	8.45369	−	6.74797i	0.552635	−	0.441128i
$235$	−12.9924			−0.847530
$236$	−3.71613	+	0.995733i	−0.241899	+	0.0648167i
$237$	−7.13029	−	11.9271i	−0.463162	−	0.774749i
$238$	−1.90695	+	1.10098i	−0.123609	+	0.0713657i
$239$	2.33729	+	2.33729i	0.151186	+	0.151186i	0.778648	−	0.627461i	$-0.215906\pi$
$239$	2.33729	+	2.33729i	0.151186	+	0.151186i	−0.627461	+	0.778648i	$0.715906\pi$
$240$	−1.24324	−	1.20597i	−0.0802508	−	0.0778447i
$241$	2.66309	−	9.93879i	0.171545	−	0.640214i	−0.825570	−	0.564300i	$-0.809146\pi$
$241$	2.66309	−	9.93879i	0.171545	−	0.640214i	0.997114	−	0.0759136i	$-0.0241873\pi$
$242$	2.47614	−	2.47614i	0.159173	−	0.159173i
$243$	6.74544	−	14.0534i	0.432720	−	0.901528i
$244$	3.87708	+	2.23843i	0.248205	+	0.143301i
$245$	−1.09366	−	4.08161i	−0.0698717	−	0.260765i
$246$	−6.78879	−	3.78295i	−0.432837	−	0.241192i
$247$	12.4128	+	16.5600i	0.789810	+	1.05369i
$248$			8.27059i			0.525183i
$249$	5.26719	−	20.9262i	0.333794	−	1.32614i
$250$	−0.500000	+	0.866025i	−0.0316228	+	0.0547723i
$251$	−11.4780	−	19.8805i	−0.724485	−	1.25485i	−0.959186	−	0.282777i	$-0.908744\pi$
$251$	−11.4780	−	19.8805i	−0.724485	−	1.25485i	0.234700	−	0.972068i	$-0.424589\pi$
$252$	4.86382	+	1.14583i	0.306392	+	0.0721803i
$253$	−24.4972	−	6.56400i	−1.54012	−	0.412675i
$254$	3.99758	+	1.07115i	0.250831	+	0.0672098i
$255$	2.20243	−	0.626213i	0.137922	−	0.0392150i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−2.27804	+	3.94568i	−0.142100	+	0.246125i	−0.928287	−	0.371864i	$-0.878719\pi$
$257$	−2.27804	+	3.94568i	−0.142100	+	0.246125i	0.786187	+	0.617989i	$0.212052\pi$
$258$	12.2277	+	3.07776i	0.761265	+	0.191613i
$259$			16.7694i			1.04200i
$260$	−2.16253	−	2.88504i	−0.134114	−	0.178923i
$261$	3.91332	−	2.42106i	0.242228	−	0.149860i
$262$	−1.08382	−	4.04488i	−0.0669587	−	0.249893i
$263$	−12.3668	−	7.13996i	−0.762568	−	0.440269i	0.0676492	−	0.997709i	$-0.478450\pi$
$263$	−12.3668	−	7.13996i	−0.762568	−	0.440269i	−0.830217	+	0.557441i	$0.811783\pi$
$264$	−0.100373	−	6.59510i	−0.00617751	−	0.405900i
$265$	0.213870	−	0.213870i	0.0131379	−	0.0131379i
$266$	−2.47452	+	9.23502i	−0.151722	+	0.566235i
$267$	−10.8091	+	11.1432i	−0.661508	+	0.681955i
$268$	−0.160234	−	0.160234i	−0.00978785	−	0.00978785i
$269$	−15.2218	+	8.78829i	−0.928087	+	0.535831i	−0.886206	−	0.463291i	$-0.846668\pi$
$269$	−15.2218	+	8.78829i	−0.928087	+	0.535831i	−0.0418811	+	0.999123i	$0.513335\pi$
$270$	−4.61388	−	2.39000i	−0.280792	−	0.145451i
$271$	−27.7623	+	7.43888i	−1.68644	+	0.451879i	−0.969467	−	0.245224i	$-0.921139\pi$
$271$	−27.7623	+	7.43888i	−1.68644	+	0.451879i	−0.716971	+	0.697103i	$0.754472\pi$
$272$	1.32197			0.0801564
$273$	9.62582	+	3.94276i	0.582581	+	0.238627i
$274$	12.0157			0.725897
$275$	−3.67836	+	0.985615i	−0.221814	+	0.0594348i
$276$	−9.90078	+	5.91891i	−0.595957	+	0.356277i
$277$	12.2976	−	7.10003i	0.738892	−	0.426600i	−0.0827742	−	0.996568i	$-0.526378\pi$
$277$	12.2976	−	7.10003i	0.738892	−	0.426600i	0.821666	+	0.569969i	$0.193045\pi$
$278$	2.65697	+	2.65697i	0.159354	+	0.159354i
$279$	7.14811	+	23.7598i	0.427946	+	1.42246i
$280$	0.431103	−	1.60890i	0.0257633	−	0.0961501i
$281$	−4.41645	+	4.41645i	−0.263463	+	0.263463i	−0.826460	−	0.562996i	$-0.809649\pi$
$281$	−4.41645	+	4.41645i	−0.263463	+	0.263463i	0.562996	+	0.826460i	$0.309649\pi$
$282$	−22.5009	+	0.342447i	−1.33991	+	0.0203924i
$283$	14.6603	+	8.46410i	0.871462	+	0.503139i	0.867834	−	0.496855i	$-0.165512\pi$
$283$	14.6603	+	8.46410i	0.871462	+	0.503139i	0.00362808	+	0.999993i	$0.498845\pi$
$284$	−3.95652	−	14.7659i	−0.234777	−	0.876198i
$285$	4.83936	−	8.68459i	0.286659	−	0.514431i
$286$	1.94555	−	13.5918i	0.115043	−	0.803702i
$287$		−	7.47372i		−	0.441160i
$288$	−2.18489	−	2.05578i	−0.128746	−	0.121138i
$289$	7.62619	−	13.2090i	0.448600	−	0.776997i
$290$	−0.766948	−	1.32839i	−0.0450368	−	0.0780060i
$291$	−0.800025	−	2.81374i	−0.0468983	−	0.164944i
$292$	−0.931940	−	0.249713i	−0.0545377	−	0.0146133i
$293$	−10.8549	−	2.90856i	−0.634149	−	0.169920i	−0.0725974	−	0.997361i	$-0.523129\pi$
$293$	−10.8549	−	2.90856i	−0.634149	−	0.169920i	−0.561552	+	0.827442i	$0.689795\pi$
$294$	−2.00164	−	7.03992i	−0.116738	−	0.410576i
$295$	1.92361	+	3.33179i	0.111997	+	0.193984i
$296$	5.03388	−	8.71894i	0.292588	−	0.506778i
$297$	−5.98837	−	18.8597i	−0.347481	−	1.09435i
$298$		−	0.391239i		−	0.0226638i
$299$	−22.2866	+	8.93837i	−1.28887	+	0.516919i
$300$	−0.843099	+	1.51301i	−0.0486763	+	0.0873534i
$301$	3.13838	+	11.7126i	0.180893	+	0.675102i
$302$	16.7028	+	9.64337i	0.961139	+	0.554914i
$303$	12.4940	−	0.190150i	0.717762	−	0.0109238i
$304$	4.05877	−	4.05877i	0.232786	−	0.232786i
$305$	1.15870	−	4.32432i	0.0663469	−	0.247610i
$306$	3.79778	−	1.14256i	0.217104	−	0.0653157i
$307$	−20.4845	−	20.4845i	−1.16911	−	1.16911i	−0.982418	−	0.186694i	$-0.940223\pi$
$307$	−20.4845	−	20.4845i	−1.16911	−	1.16911i	−0.186694	−	0.982418i	$-0.559777\pi$
$308$	5.49321	−	3.17151i	0.313005	−	0.180713i
$309$	20.9915	−	12.5492i	1.19416	−	0.713898i
$310$	7.98877	−	2.14059i	0.453732	−	0.121577i
$311$	8.83372			0.500914			0.250457	−	0.968128i	$-0.419419\pi$
$311$	8.83372			0.500914			0.250457	+	0.968128i	$0.419419\pi$
$312$	−3.82122	−	4.93946i	−0.216334	−	0.279642i
$313$	−20.4565			−1.15627			−0.578135	−	0.815941i	$-0.696219\pi$
$313$	−20.4565			−1.15627			−0.578135	+	0.815941i	$0.696219\pi$
$314$	−15.3752	+	4.11977i	−0.867673	+	0.232492i
$315$	−0.152065	−	4.99465i	−0.00856791	−	0.281417i
$316$	−6.94796	+	4.01141i	−0.390854	+	0.225659i
$317$	14.7971	+	14.7971i	0.831089	+	0.831089i	0.987666	−	0.156577i	$-0.0500460\pi$
$317$	14.7971	+	14.7971i	0.831089	+	0.831089i	−0.156577	+	0.987666i	$0.550046\pi$
$318$	0.364754	−	0.376028i	0.0204544	−	0.0210866i
$319$	1.51183	−	5.64223i	0.0846463	−	0.315904i
$320$	−0.707107	+	0.707107i	−0.0395285	+	0.0395285i
$321$	0.155288	+	10.2034i	0.00866734	+	0.569497i
$322$	−9.60676	−	5.54646i	−0.535364	−	0.309092i
$323$	1.96394	+	7.32953i	0.109277	+	0.407826i
$324$	−8.05355	−	4.01750i	−0.447419	−	0.223195i
$325$	−2.22703	+	2.83555i	−0.123534	+	0.157288i
$326$		−	13.3460i		−	0.739168i
$327$	17.5824	+	4.42555i	0.972310	+	0.244734i
$328$	−2.24348	+	3.88582i	−0.123875	+	0.214559i
$329$	−10.8204	−	18.7415i	−0.596549	−	1.03325i
$330$	−6.34440	+	1.80389i	−0.349248	+	0.0993009i
$331$	−26.8683	−	7.19933i	−1.47681	−	0.395711i	−0.571551	−	0.820566i	$-0.693658\pi$
$331$	−26.8683	−	7.19933i	−1.47681	−	0.395711i	−0.905261	+	0.424855i	$0.860325\pi$
$332$	−12.0340	−	3.22451i	−0.660454	−	0.176968i
$333$	6.92575	−	29.3985i	0.379529	−	1.61103i
$334$	−5.23508	−	9.06743i	−0.286451	−	0.496148i
$335$	−0.113303	+	0.196246i	−0.00619038	+	0.0107221i
$336$	0.704199	−	2.79773i	0.0384172	−	0.152629i
$337$			5.59425i			0.304738i	0.988324	+	0.152369i	$0.0486903\pi$
$337$			5.59425i			0.304738i	−0.988324	+	0.152369i	$0.951310\pi$
$338$	−6.24448	−	11.4020i	−0.339655	−	0.620189i
$339$	17.2940	+	9.63682i	0.939282	+	0.523400i
$340$	−0.342152	−	1.27693i	−0.0185558	−	0.0692512i
$341$	27.2758	+	15.7477i	1.47707	+	0.852786i
$342$	8.15214	−	15.1680i	0.440817	−	0.820190i
$343$	13.2215	−	13.2215i	0.713891	−	0.713891i
$344$	1.88417	−	7.03182i	0.101588	−	0.379130i
$345$	8.27974	+	8.03149i	0.445766	+	0.432401i
$346$	6.57400	+	6.57400i	0.353420	+	0.353420i
$347$	29.8164	−	17.2145i	1.60063	−	0.924122i	0.609264	−	0.792967i	$-0.291465\pi$
$347$	29.8164	−	17.2145i	1.60063	−	0.924122i	0.991362	−	0.131154i	$-0.0418683\pi$
$348$	−1.36325	−	2.28036i	−0.0730780	−	0.122240i
$349$	−14.0346	+	3.76057i	−0.751256	+	0.201298i	−0.614075	−	0.789248i	$-0.710471\pi$
$349$	−14.0346	+	3.76057i	−0.751256	+	0.201298i	−0.137181	+	0.990546i	$0.543804\pi$
$350$	−1.66565			−0.0890330
$351$	−15.2467	−	10.8875i	−0.813809	−	0.581133i
$352$	−3.80812			−0.202974
$353$	−9.59155	+	2.57005i	−0.510507	+	0.136790i	−0.504872	−	0.863194i	$-0.668460\pi$
$353$	−9.59155	+	2.57005i	−0.510507	+	0.136790i	−0.00563473	+	0.999984i	$0.501794\pi$
$354$	3.41922	+	5.71945i	0.181729	+	0.303986i
$355$	−13.2388	+	7.64342i	−0.702642	+	0.405670i
$356$	6.33783	+	6.33783i	0.335905	+	0.335905i
$357$	2.73756	+	2.65548i	0.144887	+	0.140543i
$358$	−4.00452	+	14.9451i	−0.211645	+	0.789871i
$359$	11.6427	−	11.6427i	0.614477	−	0.614477i	−0.329632	−	0.944109i	$-0.606925\pi$
$359$	11.6427	−	11.6427i	0.614477	−	0.614477i	0.944109	+	0.329632i	$0.106925\pi$
$360$	−1.42024	+	2.64252i	−0.0748533	+	0.139273i
$361$	12.0786	+	6.97359i	0.635717	+	0.367031i
$362$	−5.92642	−	22.1177i	−0.311486	−	1.16248i
$363$	−5.29824	−	2.95236i	−0.278085	−	0.154959i
$364$	2.36066	−	5.52219i	0.123732	−	0.289441i
$365$			0.964815i			0.0505007i
$366$	1.89271	−	7.51962i	0.0989337	−	0.393057i
$367$	2.43188	−	4.21213i	0.126943	−	0.219872i	−0.795548	−	0.605891i	$-0.792817\pi$
$367$	2.43188	−	4.21213i	0.126943	−	0.219872i	0.922491	+	0.386019i	$0.126150\pi$
$368$	3.32990	+	5.76756i	0.173583	+	0.300655i
$369$	−3.08664	+	13.1022i	−0.160684	+	0.682074i
$370$	−9.72471	−	2.60573i	−0.505564	−	0.135465i
$371$	0.486624	+	0.130390i	0.0252642	+	0.00676954i
$372$	13.7789	−	3.91774i	0.714405	−	0.203125i
$373$	18.2902	+	31.6796i	0.947031	+	1.64031i	0.751632	+	0.659582i	$0.229267\pi$
$373$	18.2902	+	31.6796i	0.947031	+	1.64031i	0.195399	+	0.980724i	$0.437400\pi$
$374$	2.51712	−	4.35978i	0.130157	−	0.225439i
$375$	1.67966	+	0.422776i	0.0867373	+	0.0218321i
$376$			12.9924i			0.670031i
$377$	−2.05870	−	5.13310i	−0.106028	−	0.264368i
$378$	−0.395001	−	8.64597i	−0.0203167	−	0.444701i
$379$	−0.672900	−	2.51130i	−0.0345646	−	0.128997i	0.946488	−	0.322740i	$-0.104604\pi$
$379$	−0.672900	−	2.51130i	−0.0345646	−	0.128997i	−0.981052	+	0.193743i	$0.937937\pi$
$380$	−4.97095	−	2.86998i	−0.255005	−	0.147227i
$381$	−0.109083	−	7.16744i	−0.00558851	−	0.367199i
$382$	5.45996	−	5.45996i	0.279356	−	0.279356i
$383$	1.94574	−	7.26162i	0.0994229	−	0.371051i	−0.898230	−	0.439526i	$-0.855147\pi$
$383$	1.94574	−	7.26162i	0.0994229	−	0.371051i	0.997653	+	0.0684745i	$0.0218132\pi$
$384$	−1.20597	+	1.24324i	−0.0615417	+	0.0634439i
$385$	−4.48519	−	4.48519i	−0.228586	−	0.228586i
$386$	5.53616	−	3.19630i	0.281783	−	0.162688i
$387$	−0.664613	−	21.8295i	−0.0337842	−	1.10966i
$388$	−1.63135	+	0.437120i	−0.0828195	+	0.0221914i
$389$	3.37539			0.171139			0.0855694	−	0.996332i	$-0.472729\pi$
$389$	3.37539			0.171139			0.0855694	+	0.996332i	$0.472729\pi$
$390$	−3.78215	+	4.96944i	−0.191517	+	0.251637i
$391$	−8.80409			−0.445242
$392$	−4.08161	+	1.09366i	−0.206153	+	0.0552384i
$393$	−6.22543	+	3.72170i	−0.314032	+	0.187735i
$394$	−12.7145	+	7.34069i	−0.640545	+	0.369819i
$395$	5.67299	+	5.67299i	0.285439	+	0.285439i
$396$	−10.9400	+	3.29129i	−0.549756	+	0.165394i
$397$	0.728848	−	2.72010i	0.0365798	−	0.136518i	−0.945221	−	0.326431i	$-0.894154\pi$
$397$	0.728848	−	2.72010i	0.0365798	−	0.136518i	0.981801	+	0.189913i	$0.0608206\pi$
$398$	2.05923	−	2.05923i	0.103220	−	0.103220i
$399$	16.5579	−	0.251999i	0.828930	−	0.0126157i
$400$	0.866025	+	0.500000i	0.0433013	+	0.0250000i
$401$	8.32881	+	31.0836i	0.415921	+	1.55224i	0.782984	+	0.622042i	$0.213697\pi$
$401$	8.32881	+	31.0836i	0.415921	+	1.55224i	−0.367062	+	0.930196i	$0.619636\pi$
$402$	−0.191051	+	0.342855i	−0.00952873	+	0.0171000i
$403$	29.6069	−	3.55869i	1.47483	−	0.177271i
$404$		−	7.21425i		−	0.358923i
$405$	−1.79620	+	8.81894i	−0.0892539	+	0.438217i
$406$	1.27747	−	2.21264i	0.0633998	−	0.109812i
$407$	−19.1696	−	33.2028i	−0.950203	−	1.64580i
$408$	−0.626213	−	2.20243i	−0.0310022	−	0.109037i
$409$	−2.65386	−	0.711101i	−0.131225	−	0.0351617i	0.192609	−	0.981276i	$-0.438305\pi$
$409$	−2.65386	−	0.711101i	−0.131225	−	0.0351617i	−0.323834	+	0.946114i	$0.604972\pi$
$410$	4.33407	+	1.16131i	0.214044	+	0.0573530i
$411$	−5.69179	−	20.0184i	−0.280755	−	0.987435i
$412$	−7.06001	−	12.2283i	−0.347822	−	0.602445i
$413$	−3.20407	+	5.54960i	−0.157662	+	0.273078i
$414$	14.5510	+	13.6911i	0.715141	+	0.672881i
$415$			12.4586i			0.611567i
$416$	−2.88504	+	2.16253i	−0.141451	+	0.106027i
$417$	3.16796	−	5.68515i	0.155136	−	0.278403i
$418$	−5.65739	−	21.1137i	−0.276712	−	1.03270i
$419$	12.3545	+	7.13285i	0.603555	+	0.348463i	0.770439	−	0.637514i	$-0.220037\pi$
$419$	12.3545	+	7.13285i	0.603555	+	0.348463i	−0.166884	+	0.985977i	$0.553371\pi$
$420$	−2.88466	+	0.0439025i	−0.140757	+	0.00214222i
$421$	−23.2751	+	23.2751i	−1.13436	+	1.13436i	−0.144916	+	0.989444i	$0.546291\pi$
$421$	−23.2751	+	23.2751i	−1.13436	+	1.13436i	−0.989444	+	0.144916i	$0.953709\pi$
$422$	−1.77891	+	6.63900i	−0.0865962	+	0.323181i
$423$	11.2291	+	37.3246i	0.545976	+	1.81478i
$424$	−0.213870	−	0.213870i	−0.0103864	−	0.0103864i
$425$	−1.14486	+	0.660987i	−0.0555340	+	0.0320626i
$426$	−22.7261	+	13.5862i	−1.10108	+	0.658253i
$427$	7.20282	−	1.92999i	0.348569	−	0.0933988i
$428$	5.89160			0.284781
$429$	−23.5658	+	3.19707i	−1.13777	+	0.154356i
$430$	−7.27987			−0.351067
$431$	26.6309	−	7.13573i	1.28277	−	0.343716i	0.447858	−	0.894105i	$-0.352187\pi$
$431$	26.6309	−	7.13573i	1.28277	−	0.343716i	0.834909	+	0.550389i	$0.185520\pi$
$432$	−2.39000	+	4.61388i	−0.114989	+	0.221986i
$433$	7.32263	−	4.22772i	0.351903	−	0.203171i	−0.313620	−	0.949549i	$-0.601542\pi$
$433$	7.32263	−	4.22772i	0.351903	−	0.203171i	0.665523	+	0.746377i	$0.268208\pi$
$434$	9.74106	+	9.74106i	0.467586	+	0.467586i
$435$	−1.84983	+	1.90700i	−0.0886924	+	0.0914338i
$436$	2.70928	−	10.1112i	0.129751	−	0.484236i
$437$	−27.0306	+	27.0306i	−1.29305	+	1.29305i
$438$	0.0254302	+	1.67092i	0.00121510	+	0.0798394i
$439$	10.9300	+	6.31042i	0.521659	+	0.301180i	0.737613	−	0.675224i	$-0.235953\pi$
$439$	10.9300	+	6.31042i	0.521659	+	0.301180i	−0.215954	+	0.976404i	$0.569286\pi$
$440$	0.985615	+	3.67836i	0.0469873	+	0.175359i
$441$	−10.7804	+	6.66955i	−0.513355	+	0.317598i
$442$	−0.568822	−	4.73238i	−0.0270561	−	0.225096i
$443$			28.5436i			1.35615i	0.734994	+	0.678074i	$0.237185\pi$
$443$			28.5436i			1.35615i	−0.734994	+	0.678074i	$0.762815\pi$
$444$	−16.9104	−	4.25641i	−0.802533	−	0.202000i
$445$	4.48153	−	7.76223i	0.212445	−	0.367965i
$446$	−0.789946	−	1.36823i	−0.0374050	−	0.0647874i
$447$	−0.651810	+	0.185328i	−0.0308296	+	0.00876571i
$448$	−1.60890	−	0.431103i	−0.0760133	−	0.0203677i
$449$	28.8338	+	7.72600i	1.36075	+	0.364612i	0.864092	−	0.503333i	$-0.167893\pi$
$449$	28.8338	+	7.72600i	1.36075	+	0.364612i	0.496659	+	0.867946i	$0.334560\pi$
$450$	2.92006	+	0.687914i	0.137653	+	0.0324286i
$451$	8.54344	+	14.7977i	0.402295	+	0.696795i
$452$	5.71512	−	9.89888i	0.268817	−	0.465604i
$453$	8.15398	−	32.3952i	0.383107	−	1.52206i
$454$			6.68089i			0.313550i
$455$	−5.94501	−	0.850975i	−0.278706	−	0.0398943i
$456$	−8.68459	−	4.83936i	−0.406693	−	0.226624i
$457$	−8.25749	−	30.8174i	−0.386269	−	1.44158i	−0.836157	−	0.548491i	$-0.815203\pi$
$457$	−8.25749	−	30.8174i	−0.386269	−	1.44158i	0.449887	−	0.893085i	$-0.351464\pi$
$458$	−19.6885	−	11.3672i	−0.919982	−	0.531152i
$459$	−3.70251	−	5.78593i	−0.172818	−	0.270064i
$460$	4.70919	−	4.70919i	0.219567	−	0.219567i
$461$	2.90972	−	10.8592i	0.135519	−	0.505764i	−0.864476	−	0.502674i	$-0.832350\pi$
$461$	2.90972	−	10.8592i	0.135519	−	0.505764i	0.999995	−	0.00309039i	$-0.000983704\pi$
$462$	−7.88589	−	7.64946i	−0.366885	−	0.355885i
$463$	9.47819	+	9.47819i	0.440489	+	0.440489i	0.892176	−	0.451687i	$-0.149178\pi$
$463$	9.47819	+	9.47819i	0.440489	+	0.440489i	−0.451687	+	0.892176i	$0.649178\pi$
$464$	−1.32839	+	0.766948i	−0.0616691	+	0.0356047i
$465$	−7.35050	−	12.2954i	−0.340871	−	0.570188i
$466$	20.2001	−	5.41260i	0.935752	−	0.250734i
$467$	13.7987			0.638528			0.319264	−	0.947666i	$-0.396564\pi$
$467$	13.7987			0.638528			0.319264	+	0.947666i	$0.396564\pi$
$468$	−6.41914	+	8.70601i	−0.296725	+	0.402436i
$469$	−0.377446			−0.0174288
$470$	12.5497	−	3.36268i	0.578874	−	0.155109i
$471$	14.1468	+	23.6638i	0.651849	+	1.09037i
$472$	3.33179	−	1.92361i	0.153358	−	0.0885412i
$473$	−19.6029	−	19.6029i	−0.901341	−	0.901341i
$474$	9.97429	+	9.67524i	0.458134	+	0.444399i
$475$	−1.48561	+	5.54438i	−0.0681646	+	0.254394i
$476$	1.55701	−	1.55701i	0.0713657	−	0.0713657i
$477$	−0.799251	−	0.429563i	−0.0365952	−	0.0196683i
$478$	−2.86258	−	1.65271i	−0.130931	−	0.0755932i
$479$	−8.00989	−	29.8933i	−0.365981	−	1.36586i	−0.866086	−	0.499895i	$-0.833372\pi$
$479$	−8.00989	−	29.8933i	−0.365981	−	1.36586i	0.500105	−	0.865965i	$-0.333295\pi$
$480$	1.51301	+	0.843099i	0.0690589	+	0.0384820i
$481$	−33.3779	−	14.2686i	−1.52190	−	0.650592i
$482$			10.2894i			0.468669i
$483$	−4.68983	+	18.6324i	−0.213395	+	0.847802i
$484$	−1.75090	+	3.03264i	−0.0795863	+	0.137847i
$485$	0.844451	+	1.46263i	0.0383445	+	0.0664147i
$486$	−2.87830	+	15.3204i	−0.130562	+	0.694949i
$487$	27.8851	+	7.47178i	1.26359	+	0.338579i	0.827573	−	0.561358i	$-0.189721\pi$
$487$	27.8851	+	7.47178i	1.26359	+	0.338579i	0.436020	+	0.899937i	$0.356388\pi$
$488$	−4.32432	−	1.15870i	−0.195753	−	0.0524518i
$489$	−22.2347	+	6.32194i	−1.00549	+	0.285888i
$490$	2.11280	+	3.65947i	0.0954465	+	0.165318i
$491$	−3.99952	+	6.92737i	−0.180496	+	0.312628i	−0.942049	−	0.335474i	$-0.891104\pi$
$491$	−3.99952	+	6.92737i	−0.180496	+	0.312628i	0.761554	+	0.648102i	$0.224437\pi$
$492$	7.53657	+	1.89698i	0.339775	+	0.0855225i
$493$		−	2.02777i		−	0.0913263i
$494$	−16.2759	−	12.7831i	−0.732289	−	0.575139i
$495$	6.01062	+	9.71538i	0.270157	+	0.436674i
$496$	−2.14059	−	7.98877i	−0.0961151	−	0.358707i
$497$	−22.0512	−	12.7313i	−0.989133	−	0.571076i
$498$	0.328377	+	21.5764i	0.0147149	+	0.966860i
$499$	15.4167	−	15.4167i	0.690144	−	0.690144i	−0.272119	−	0.962264i	$-0.587725\pi$
$499$	15.4167	−	15.4167i	0.690144	−	0.690144i	0.962264	+	0.272119i	$0.0877246\pi$
$500$	0.258819	−	0.965926i	0.0115747	−	0.0431975i
$501$	−12.6267	+	13.0169i	−0.564118	+	0.581554i
$502$	16.2323	+	16.2323i	0.724485	+	0.724485i
$503$	−21.5869	+	12.4632i	−0.962513	+	0.555707i	−0.896945	−	0.442141i	$-0.854219\pi$
$503$	−21.5869	+	12.4632i	−0.962513	+	0.555707i	−0.0655671	+	0.997848i	$0.520886\pi$
$504$	−4.99465	+	0.152065i	−0.222479	+	0.00677352i
$505$	−6.96843	+	1.86719i	−0.310091	+	0.0830887i
$506$	25.3613			1.12745
$507$	−16.0380	+	15.8045i	−0.712273	+	0.701902i
$508$	−4.13860			−0.183621
$509$	5.42645	−	1.45401i	0.240523	−	0.0644479i	−0.136544	−	0.990634i	$-0.543599\pi$
$509$	5.42645	−	1.45401i	0.240523	−	0.0644479i	0.377067	+	0.926186i	$0.376933\pi$
$510$	−1.96531	+	1.17491i	−0.0870254	+	0.0520257i
$511$	−1.39174	+	0.803524i	−0.0615672	+	0.0355458i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−29.1317	−	6.39660i	−1.28620	−	0.282417i
$514$	1.17920	−	4.40083i	0.0520123	−	0.194112i
$515$	−9.98436	+	9.98436i	−0.439963	+	0.439963i
$516$	−12.6077	+	0.191880i	−0.555021	+	0.00844703i
$517$	42.8480	+	24.7383i	1.88445	+	1.08799i
$518$	−4.34024	−	16.1980i	−0.190699	−	0.711699i
$519$	7.83832	−	14.0665i	0.344064	−	0.617449i
$520$	2.83555	+	2.22703i	0.124347	+	0.0976619i
$521$			12.8570i			0.563275i	0.959521	+	0.281637i	$0.0908775\pi$
$521$			12.8570i			0.563275i	−0.959521	+	0.281637i	$0.909122\pi$
$522$	−3.15336	+	3.35140i	−0.138019	+	0.146687i
$523$	7.21582	−	12.4982i	0.315526	−	0.546507i	−0.664023	−	0.747712i	$-0.731152\pi$
$523$	7.21582	−	12.4982i	0.315526	−	0.546507i	0.979549	+	0.201205i	$0.0644858\pi$
$524$	2.09378	+	3.62654i	0.0914673	+	0.158426i
$525$	0.789012	+	2.77501i	0.0344353	+	0.121111i
$526$	13.7933	+	3.69591i	0.601418	+	0.161150i
$527$	10.5610	+	2.82980i	0.460042	+	0.123268i
$528$	1.80389	+	6.34440i	0.0785042	+	0.276104i
$529$	−10.6765	−	18.4922i	−0.464195	−	0.804010i
$530$	−0.151229	+	0.261936i	−0.00656896	+	0.0113778i
$531$	7.90904	−	8.40575i	0.343223	−	0.364779i
$532$		−	9.56080i		−	0.414513i
$533$	14.8757	+	6.35917i	0.644339	+	0.275446i
$534$	7.55674	−	13.5611i	0.327012	−	0.586848i
$535$	−1.52486	−	5.69085i	−0.0659254	−	0.246037i
$536$	0.196246	+	0.113303i	0.00847653	+	0.00489393i
$537$	26.7956	−	0.407811i	1.15632	−	0.0175983i
$538$	12.4285	−	12.4285i	0.535831	−	0.535831i
$539$	−4.16481	+	15.5433i	−0.179391	+	0.669496i
$540$	5.07525	+	1.11440i	0.218404	+	0.0479560i
$541$	−15.6462	−	15.6462i	−0.672681	−	0.672681i	0.285652	−	0.958333i	$-0.407790\pi$
$541$	−15.6462	−	15.6462i	−0.672681	−	0.672681i	−0.958333	+	0.285652i	$0.907790\pi$
$542$	24.8910	−	14.3708i	1.06916	−	0.617279i
$543$	−34.0412	+	20.3506i	−1.46085	+	0.873327i
$544$	−1.27693	+	0.342152i	−0.0547479	+	0.0146696i
$545$	−10.4678			−0.448393
$546$	−10.3183	−	1.31707i	−0.441582	−	0.0563652i
$547$	39.1213			1.67271			0.836354	−	0.548190i	$-0.184683\pi$
$547$	39.1213			1.67271			0.836354	+	0.548190i	$0.184683\pi$
$548$	−11.6063	+	3.10990i	−0.495797	+	0.132848i
$549$	−13.4244	+	0.408714i	−0.572939	+	0.0174435i
$550$	3.29793	−	1.90406i	0.140624	−	0.0811894i
$551$	−6.22573	−	6.22573i	−0.265225	−	0.265225i
$552$	8.03149	−	8.27974i	0.341843	−	0.352409i
$553$	−3.45866	+	12.9079i	−0.147077	+	0.548900i
$554$	−10.0410	+	10.0410i	−0.426600	+	0.426600i
$555$	0.265361	+	17.4359i	0.0112640	+	0.740111i
$556$	−3.25411	−	1.87876i	−0.138005	−	0.0796772i
$557$	6.52205	+	24.3406i	0.276348	+	1.03135i	0.954933	+	0.296823i	$0.0959271\pi$
$557$	6.52205	+	24.3406i	0.276348	+	1.03135i	−0.678584	+	0.734523i	$0.737406\pi$
$558$	−13.0540	−	21.1001i	−0.552621	−	0.893240i
$559$	−25.9831	−	3.71926i	−1.09897	−	0.157308i
$560$			1.66565i			0.0703867i
$561$	−8.45581	−	2.12836i	−0.357005	−	0.0898593i
$562$	3.12290	−	5.40903i	0.131732	−	0.228166i
$563$	−3.12854	−	5.41879i	−0.131852	−	0.228375i	0.792538	−	0.609822i	$-0.208759\pi$
$563$	−3.12854	−	5.41879i	−0.131852	−	0.228375i	−0.924391	+	0.381447i	$0.875426\pi$
$564$	21.6455	−	6.15443i	0.911442	−	0.259148i
$565$	−11.0408	−	2.95836i	−0.464489	−	0.124459i
$566$	−16.3514	−	4.38134i	−0.687300	−	0.184162i
$567$	−14.2172	+	4.75364i	−0.597068	+	0.199634i
$568$	7.64342	+	13.2388i	0.320711	+	0.555487i
$569$	−9.18102	+	15.9020i	−0.384889	+	0.666647i	−0.991754	−	0.128158i	$-0.959093\pi$
$569$	−9.18102	+	15.9020i	−0.384889	+	0.666647i	0.606865	+	0.794805i	$0.292427\pi$
$570$	−2.42672	+	9.64119i	−0.101644	+	0.403825i
$571$			37.1767i			1.55580i	0.628391	+	0.777898i	$0.283714\pi$
$571$			37.1767i			1.55580i	−0.628391	+	0.777898i	$0.716286\pi$
$572$	1.63857	+	13.6323i	0.0685120	+	0.569993i
$573$	−11.6827	−	6.51003i	−0.488054	−	0.271960i
$574$	1.93434	+	7.21906i	0.0807378	+	0.301318i
$575$	−5.76756	−	3.32990i	−0.240524	−	0.138867i
$576$	2.64252	+	1.42024i	0.110105	+	0.0591767i
$577$	−2.97894	+	2.97894i	−0.124015	+	0.124015i	−0.766390	−	0.642375i	$-0.777949\pi$
$577$	−2.97894	+	2.97894i	−0.124015	+	0.124015i	0.642375	+	0.766390i	$0.277949\pi$
$578$	−3.94761	+	14.7327i	−0.164199	+	0.612798i
$579$	−7.94755	−	7.70927i	−0.330289	−	0.320386i
$580$	1.08463	+	1.08463i	0.0450368	+	0.0450368i
$581$	−17.9715	+	10.3758i	−0.745582	+	0.430462i
$582$	1.50101	+	2.51080i	0.0622190	+	0.104076i
$583$	−1.11255	+	0.298107i	−0.0460771	+	0.0123463i
$584$	0.964815			0.0399243
$585$	10.0708	+	3.94713i	0.416375	+	0.163194i
$586$	11.2378			0.464229
$587$	−6.45368	+	1.72926i	−0.266372	+	0.0713741i	−0.389533	−	0.921013i	$-0.627363\pi$
$587$	−6.45368	+	1.72926i	−0.266372	+	0.0713741i	0.123161	+	0.992387i	$0.460697\pi$
$588$	3.75550	+	6.28197i	0.154874	+	0.259064i
$589$	41.1127	−	23.7364i	1.69402	−	0.978043i
$590$	−2.72039	−	2.72039i	−0.111997	−	0.111997i
$591$	18.2525	+	17.7052i	0.750807	+	0.728296i
$592$	−2.60573	+	9.72471i	−0.107095	+	0.399683i
$593$	26.8093	−	26.8093i	1.10092	−	1.10092i	0.106625	−	0.994299i	$-0.465996\pi$
$593$	26.8093	−	26.8093i	1.10092	−	1.10092i	0.994299	−	0.106625i	$-0.0340045\pi$
$594$	10.6656	+	16.6672i	0.437614	+	0.683862i
$595$	−1.90695	−	1.10098i	−0.0781772	−	0.0451356i
$596$	0.101260	+	0.377907i	0.00414777	+	0.0154797i
$597$	−4.40617	−	2.45527i	−0.180332	−	0.100487i
$598$	19.2138	−	14.4020i	0.785712	−	0.588942i
$599$		−	25.7236i		−	1.05104i	−0.850781	−	0.525520i	$-0.823871\pi$
$599$		−	25.7236i		−	1.05104i	0.850781	−	0.525520i	$-0.176129\pi$
$600$	0.422776	−	1.67966i	0.0172598	−	0.0685719i
$601$	4.01013	−	6.94574i	0.163577	−	0.283323i	−0.772572	−	0.634927i	$-0.781030\pi$
$601$	4.01013	−	6.94574i	0.163577	−	0.283323i	0.936149	+	0.351604i	$0.114364\pi$
$602$	−6.06288	−	10.5012i	−0.247104	−	0.427997i
$603$	0.661702	+	0.155885i	0.0269466	+	0.00634812i
$604$	−18.6296	−	4.99178i	−0.758026	−	0.203113i
$605$	3.38248	+	0.906332i	0.137517	+	0.0368476i
$606$	−12.0191	+	3.41736i	−0.488241	+	0.138821i
$607$	−5.80367	−	10.0522i	−0.235564	−	0.408008i	0.723873	−	0.689933i	$-0.242360\pi$
$607$	−5.80367	−	10.0522i	−0.235564	−	0.408008i	−0.959436	+	0.281925i	$0.909027\pi$
$608$	−2.86998	+	4.97095i	−0.116393	+	0.201599i
$609$	−4.29144	−	1.08017i	−0.173898	−	0.0437707i
$610$			4.47687i			0.181263i
$611$	46.5099	−	5.59039i	1.88159	−	0.226163i
$612$	−3.37265	+	2.08656i	−0.136331	+	0.0843443i
$613$	−9.32778	−	34.8117i	−0.376745	−	1.40603i	−0.850778	−	0.525525i	$-0.823869\pi$
$613$	−9.32778	−	34.8117i	−0.376745	−	1.40603i	0.474033	−	0.880507i	$-0.342798\pi$
$614$	25.0883	+	14.4847i	1.01248	+	0.584556i
$615$	−0.118265	−	7.77074i	−0.00476891	−	0.313346i
$616$	−4.48519	+	4.48519i	−0.180713	+	0.180713i
$617$	−6.01064	+	22.4320i	−0.241979	+	0.903078i	0.732899	+	0.680338i	$0.238167\pi$
$617$	−6.01064	+	22.4320i	−0.241979	+	0.903078i	−0.974878	+	0.222740i	$0.928500\pi$
$618$	−17.0283	+	17.5546i	−0.684977	+	0.706149i
$619$	−2.30174	−	2.30174i	−0.0925149	−	0.0925149i	0.659335	−	0.751850i	$-0.270838\pi$
$619$	−2.30174	−	2.30174i	−0.0925149	−	0.0925149i	−0.751850	+	0.659335i	$0.770838\pi$
$620$	−7.16254	+	4.13529i	−0.287654	+	0.166077i
$621$	15.9169	−	30.7276i	0.638723	−	1.23305i
$622$	−8.53272	+	2.28634i	−0.342131	+	0.0916737i
$623$	14.9293			0.598132
$624$	4.96944	+	3.78215i	0.198937	+	0.151407i
$625$	−1.00000			−0.0400000
$626$	19.7595	−	5.29453i	0.789747	−	0.211612i
$627$	−32.4959	+	19.4268i	−1.29776	+	0.775830i
$628$	13.7850	−	7.95879i	0.550082	−	0.317590i
$629$	−9.41111	−	9.41111i	−0.375245	−	0.375245i
$630$	1.43959	+	4.78510i	0.0573548	+	0.190643i
$631$	9.17574	−	34.2443i	0.365281	−	1.36325i	−0.501759	−	0.865007i	$-0.667314\pi$
$631$	9.17574	−	34.2443i	0.365281	−	1.36325i	0.867040	−	0.498239i	$-0.166020\pi$
$632$	5.67299	−	5.67299i	0.225659	−	0.225659i
$633$	11.9033	−	0.181160i	0.473115	−	0.00720048i
$634$	−18.1227	−	10.4631i	−0.719744	−	0.415544i
$635$	1.07115	+	3.99758i	0.0425072	+	0.158639i
$636$	−0.255002	+	0.457620i	−0.0101115	+	0.0181458i
$637$	5.67133	+	14.1407i	0.224706	+	0.560275i
$638$			5.84127i			0.231258i
$639$	33.4001	+	31.4264i	1.32129	+	1.24321i
$640$	0.500000	−	0.866025i	0.0197642	−	0.0342327i
$641$	14.2640	+	24.7060i	0.563394	+	0.975828i	0.997197	+	0.0748198i	$0.0238381\pi$
$641$	14.2640	+	24.7060i	0.563394	+	0.975828i	−0.433803	+	0.901008i	$0.642829\pi$
$642$	−2.79082	−	9.81551i	−0.110145	−	0.387387i
$643$	37.0551	+	9.92889i	1.46131	+	0.391557i	0.899943	−	0.436009i	$-0.143608\pi$
$643$	37.0551	+	9.92889i	1.46131	+	0.391557i	0.561369	+	0.827566i	$0.310275\pi$
$644$	10.7149	+	2.87106i	0.422228	+	0.113136i
$645$	3.44844	+	12.1284i	0.135782	+	0.477555i
$646$	−3.79404	−	6.57147i	−0.149275	−	0.258551i
$647$	−9.53414	+	16.5136i	−0.374826	+	0.649217i	−0.990301	−	0.138939i	$-0.955631\pi$
$647$	−9.53414	+	16.5136i	−0.374826	+	0.649217i	0.615475	+	0.788156i	$0.288964\pi$
$648$	8.81894	+	1.79620i	0.346441	+	0.0705614i
$649$		−	14.6507i		−	0.575089i
$650$	1.41726	−	3.31533i	0.0555894	−	0.130038i
$651$	11.6145	−	20.8431i	0.455207	−	0.816904i
$652$	3.45420	+	12.8913i	0.135277	+	0.504861i
$653$	−28.6102	−	16.5181i	−1.11961	−	0.646404i	−0.178305	−	0.983975i	$-0.557061\pi$
$653$	−28.6102	−	16.5181i	−1.11961	−	0.646404i	−0.941300	+	0.337571i	$0.890395\pi$
$654$	−18.1287	+	0.275906i	−0.708889	+	0.0107888i
$655$	2.96106	−	2.96106i	0.115698	−	0.115698i
$656$	1.16131	−	4.33407i	0.0453415	−	0.169217i
$657$	2.77173	−	0.833872i	0.108135	−	0.0325324i
$658$	15.3024	+	15.3024i	0.596549	+	0.596549i
$659$	−16.8251	+	9.71399i	−0.655414	+	0.378403i	−0.790527	−	0.612427i	$-0.790193\pi$
$659$	−16.8251	+	9.71399i	−0.655414	+	0.378403i	0.135113	+	0.990830i	$0.456860\pi$
$660$	5.66134	−	3.38447i	0.220367	−	0.131740i
$661$	23.4203	−	6.27544i	0.910942	−	0.244086i	0.227233	−	0.973840i	$-0.427032\pi$
$661$	23.4203	−	6.27544i	0.910942	−	0.244086i	0.683710	+	0.729754i	$0.260365\pi$
$662$	27.8161			1.08110
$663$	−7.61478	+	3.18937i	−0.295734	+	0.123865i
$664$	12.4586			0.483486
$665$	−9.23502	+	2.47452i	−0.358119	+	0.0959576i
$666$	0.919132	+	30.1893i	0.0356157	+	1.16981i
$667$	8.84684	−	5.10773i	0.342551	−	0.197772i
$668$	7.40353	+	7.40353i	0.286451	+	0.286451i
$669$	−1.90530	+	1.96419i	−0.0736630	+	0.0759398i
$670$	0.0586497	−	0.218884i	0.00226584	−	0.00845622i
$671$	−12.0551	+	12.0551i	−0.465381	+	0.465381i
$672$	0.0439025	+	2.88466i	0.00169358	+	0.111278i
$673$	−9.78648	−	5.65023i	−0.377241	−	0.217800i	0.299376	−	0.954135i	$-0.403221\pi$
$673$	−9.78648	−	5.65023i	−0.377241	−	0.217800i	−0.676617	+	0.736335i	$0.736555\pi$
$674$	−1.44790	−	5.40363i	−0.0557710	−	0.208140i
$675$	−0.237145	−	5.19074i	−0.00912770	−	0.199792i
$676$	8.98277	+	9.39734i	0.345491	+	0.361436i
$677$		−	25.6880i		−	0.987270i	−0.869669	−	0.493635i	$-0.835668\pi$
$677$		−	25.6880i		−	0.987270i	0.869669	−	0.493635i	$-0.164332\pi$
$678$	−19.1989	−	4.83244i	−0.737330	−	0.185589i
$679$	−1.40656	+	2.43624i	−0.0539789	+	0.0934943i
$680$	0.660987	+	1.14486i	0.0253477	+	0.0439035i
$681$	11.1305	−	3.16470i	0.426521	−	0.121272i
$682$	−30.4222	−	8.15161i	−1.16493	−	0.312141i
$683$	46.1988	+	12.3789i	1.76775	+	0.473667i	0.988264	−	0.152754i	$-0.0488141\pi$
$683$	46.1988	+	12.3789i	1.76775	+	0.473667i	0.779485	+	0.626421i	$0.215481\pi$
$684$	−3.94860	+	16.7611i	−0.150978	+	0.640875i
$685$	6.00786	+	10.4059i	0.229549	+	0.397590i
$686$	−9.34898	+	16.1929i	−0.356946	+	0.618248i
$687$	−9.61153	+	38.1859i	−0.366703	+	1.45688i
$688$			7.27987i			0.277543i
$689$	−0.673584	+	0.857633i	−0.0256615	+	0.0326732i
$690$	−10.0763	−	5.61487i	−0.383599	−	0.213755i
$691$	−3.41753	−	12.7544i	−0.130009	−	0.485200i	0.869960	−	0.493123i	$-0.164145\pi$
$691$	−3.41753	−	12.7544i	−0.130009	−	0.485200i	−0.999969	+	0.00792315i	$0.997478\pi$
$692$	−8.05147	−	4.64852i	−0.306071	−	0.176710i
$693$	−9.00862	+	16.7615i	−0.342209	+	0.636718i
$694$	−24.3450	+	24.3450i	−0.924122	+	0.924122i
$695$	−0.972518	+	3.62949i	−0.0368897	+	0.137674i
$696$	1.90700	+	1.84983i	0.0722848	+	0.0701175i
$697$	4.19430	+	4.19430i	0.158871	+	0.158871i
$698$	12.5831	−	7.26485i	0.476277	−	0.274979i
$699$	−18.5862	−	31.0898i	−0.702994	−	1.17592i
$700$	1.60890	−	0.431103i	0.0608106	−	0.0162942i
$701$	−33.1881			−1.25350			−0.626748	−	0.779222i	$-0.715614\pi$
$701$	−33.1881			−1.25350			−0.626748	+	0.779222i	$0.715614\pi$
$702$	17.5451	+	6.57040i	0.662196	+	0.247984i
$703$	−57.7886			−2.17954
$704$	3.67836	−	0.985615i	0.138634	−	0.0371467i
$705$	−11.5470	−	19.3151i	−0.434885	−	0.727449i
$706$	8.59955	−	4.96495i	0.323648	−	0.186858i
$707$	−8.49692	−	8.49692i	−0.319559	−	0.319559i
$708$	−4.78302	−	4.63961i	−0.179757	−	0.174367i
$709$	6.64653	−	24.8052i	0.249616	−	0.931578i	−0.721392	−	0.692527i	$-0.756497\pi$
$709$	6.64653	−	24.8052i	0.249616	−	0.931578i	0.971007	−	0.239050i	$-0.0768361\pi$
$710$	10.8094	−	10.8094i	0.405670	−	0.405670i
$711$	11.3943	−	21.2005i	0.427321	−	0.795079i
$712$	−7.76223	−	4.48153i	−0.290902	−	0.167952i
$713$	14.2559	+	53.2037i	0.533887	+	1.99249i
$714$	−3.33156	−	1.85646i	−0.124681	−	0.0694764i
$715$	12.7437	−	5.11102i	0.476586	−	0.191141i
$716$		−	15.4723i		−	0.578226i
$717$	−1.39745	+	5.55198i	−0.0521889	+	0.207343i
$718$	−8.23262	+	14.2593i	−0.307239	+	0.532153i
$719$	−3.79520	−	6.57348i	−0.141537	−	0.245150i	0.786539	−	0.617541i	$-0.211871\pi$
$719$	−3.79520	−	6.57348i	−0.141537	−	0.245150i	−0.928076	+	0.372392i	$0.878538\pi$
$720$	0.687914	−	2.92006i	0.0256370	−	0.108824i
$721$	−22.7177	−	6.08718i	−0.846050	−	0.226699i
$722$	−13.4719	−	3.60980i	−0.501374	−	0.134343i
$723$	17.1423	−	4.87404i	0.637529	−	0.181267i
$724$	11.4490	+	19.8302i	0.425498	+	0.736984i
$725$	0.766948	−	1.32839i	0.0284838	−	0.0493353i
$726$	5.88183	+	1.48048i	0.218295	+	0.0549457i
$727$			51.1962i			1.89876i	0.314129	+	0.949380i	$0.398288\pi$
$727$			51.1962i			1.89876i	−0.314129	+	0.949380i	$0.601712\pi$
$728$	−0.850975	+	5.94501i	−0.0315392	+	0.220337i
$729$	26.8875	−	2.46191i	0.995834	−	0.0911819i
$730$	−0.249713	−	0.931940i	−0.00924228	−	0.0344926i
$731$	−8.33446	−	4.81190i	−0.308261	−	0.177975i
$732$	0.117999	+	7.75326i	0.00436138	+	0.286569i
$733$	−19.8432	+	19.8432i	−0.732925	+	0.732925i	−0.971198	−	0.238273i	$-0.923419\pi$
$733$	−19.8432	+	19.8432i	−0.732925	+	0.732925i	0.238273	+	0.971198i	$0.423419\pi$
$734$	−1.25883	+	4.69802i	−0.0464643	+	0.173407i
$735$	5.09592	−	5.25343i	0.187966	−	0.193776i
$736$	−4.70919	−	4.70919i	−0.173583	−	0.173583i
$737$	0.747328	−	0.431470i	0.0275282	−	0.0158934i
$738$	−0.409635	−	13.4546i	−0.0150789	−	0.495272i
$739$	−33.6777	+	9.02391i	−1.23885	+	0.331950i	−0.818021	−	0.575189i	$-0.804929\pi$
$739$	−33.6777	+	9.02391i	−1.23885	+	0.331950i	−0.420832	+	0.907138i	$0.638262\pi$
$740$	10.0678			0.370098
$741$	−13.5870	+	33.1713i	−0.499132	+	1.21858i
$742$	−0.503790			−0.0184947
$743$	−27.9882	+	7.49941i	−1.02679	+	0.275127i	−0.732627	−	0.680630i	$-0.761706\pi$
$743$	−27.9882	+	7.49941i	−1.02679	+	0.275127i	−0.294159	+	0.955756i	$0.595040\pi$
$744$	−12.2954	+	7.35050i	−0.450773	+	0.269482i
$745$	0.338823	−	0.195619i	0.0124135	−	0.00716694i
$746$	−25.8663	−	25.8663i	−0.947031	−	0.947031i
$747$	35.7910	−	10.7677i	1.30953	−	0.393970i
$748$	−1.30296	+	4.86270i	−0.0476408	+	0.177798i
$749$	6.93910	−	6.93910i	0.253549	−	0.253549i
$750$	−1.73185	+	0.0263575i	−0.0632382	+	0.000962441i
$751$	23.9936	+	13.8527i	0.875537	+	0.505492i	0.869184	−	0.494488i	$-0.164644\pi$
$751$	23.9936	+	13.8527i	0.875537	+	0.505492i	0.00635294	+	0.999980i	$0.497978\pi$
$752$	−3.36268	−	12.5497i	−0.122624	−	0.457640i
$753$	19.3542	−	34.7326i	0.705306	−	1.26572i
$754$	3.31709	+	4.42536i	0.120801	+	0.161162i
$755$			19.2867i			0.701917i
$756$	2.61928	+	8.24914i	0.0952625	+	0.300018i
$757$	15.6835	−	27.1647i	0.570027	−	0.987316i	−0.426535	−	0.904471i	$-0.640266\pi$
$757$	15.6835	−	27.1647i	0.570027	−	0.987316i	0.996562	−	0.0828451i	$-0.0264007\pi$
$758$	1.29994	+	2.25157i	0.0472161	+	0.0817806i
$759$	−12.0136	−	42.2524i	−0.436064	−	1.53367i
$760$	5.54438	+	1.48561i	0.201116	+	0.0538888i
$761$	−33.5908	−	9.00062i	−1.21766	−	0.326272i	−0.407900	−	0.913027i	$-0.633739\pi$
$761$	−33.5908	−	9.00062i	−1.21766	−	0.326272i	−0.809765	+	0.586755i	$0.800405\pi$
$762$	1.96044	+	6.89498i	0.0710191	+	0.249779i
$763$	−8.71790	−	15.0998i	−0.315609	−	0.546651i
$764$	−3.86078	+	6.68706i	−0.139678	+	0.241929i
$765$	2.88837	+	2.71769i	0.104429	+	0.0982583i
$766$			7.51778i			0.271628i
$767$	−8.31971	−	11.0994i	−0.300407	−	0.400776i
$768$	0.843099	−	1.51301i	0.0304227	−	0.0545959i
$769$	−3.20108	−	11.9466i	−0.115434	−	0.430805i	0.883885	−	0.467704i	$-0.154919\pi$
$769$	−3.20108	−	11.9466i	−0.115434	−	0.430805i	−0.999319	+	0.0368988i	$0.988252\pi$
$770$	5.49321	+	3.17151i	0.197962	+	0.114293i
$771$	−7.89045	+	0.120087i	−0.284167	+	0.00432483i
$772$	−4.52026	+	4.52026i	−0.162688	+	0.162688i
$773$	9.35460	−	34.9119i	0.336462	−	1.25569i	−0.565814	−	0.824533i	$-0.691438\pi$
$773$	9.35460	−	34.9119i	0.336462	−	1.25569i	0.902276	−	0.431159i	$-0.141895\pi$
$774$	6.29186	+	20.9137i	0.226156	+	0.751726i
$775$	5.84819	+	5.84819i	0.210073	+	0.210073i
$776$	1.46263	−	0.844451i	0.0525054	−	0.0303140i
$777$	−24.9302	+	14.9038i	−0.894366	+	0.534672i
$778$	−3.26037	+	0.873614i	−0.116890	+	0.0313206i
$779$	25.7550			0.922768
$780$	2.36709	−	5.77900i	0.0847555	−	0.206921i
$781$	58.2141			2.08307
$782$	8.50410	−	2.27867i	0.304106	−	0.0814849i
$783$	7.07722	+	3.66601i	0.252919	+	0.131012i
$784$	3.65947	−	2.11280i	0.130695	−	0.0754571i
$785$	−11.2554	−	11.2554i	−0.401723	−	0.401723i
$786$	5.05006	−	5.20615i	0.180130	−	0.185697i
$787$	9.31123	−	34.7500i	0.331910	−	1.23870i	−0.575271	−	0.817963i	$-0.695104\pi$
$787$	9.31123	−	34.7500i	0.331910	−	1.23870i	0.907181	−	0.420741i	$-0.138230\pi$
$788$	10.3813	−	10.3813i	0.369819	−	0.369819i
$789$	−0.376383	−	24.7307i	−0.0133996	−	0.880435i
$790$	−6.94796	−	4.01141i	−0.247197	−	0.142720i
$791$	−4.92761	−	18.3901i	−0.175206	−	0.653877i
$792$	9.71538	−	6.01062i	0.345221	−	0.213578i
$793$	−2.28721	+	15.9787i	−0.0812213	+	0.567420i
$794$			2.81605i			0.0999380i
$795$	0.508026	+	0.127872i	0.0180178	+	0.00453515i
$796$	−1.45610	+	2.52204i	−0.0516100	+	0.0893912i
$797$	16.8835	+	29.2431i	0.598045	+	1.03584i	0.993109	+	0.117191i	$0.0373888\pi$
$797$	16.8835	+	29.2431i	0.598045	+	1.03584i	−0.395065	+	0.918653i	$0.629278\pi$
$798$	−15.9284	+	4.52890i	−0.563861	+	0.160321i
$799$	16.5904	+	4.44537i	0.586924	+	0.157266i
$800$	−0.965926	−	0.258819i	−0.0341506	−	0.00915064i
$801$	−26.1727	−	6.16581i	−0.924766	−	0.217858i
$802$	−16.0900	−	27.8688i	−0.568159	−	0.984080i
$803$	1.83707	−	3.18189i	0.0648287	−	0.112287i
$804$	0.0958033	−	0.380620i	0.00337872	−	0.0134234i
$805$		−	11.0929i		−	0.390974i
$806$	−27.6770	+	11.1003i	−0.974882	+	0.390990i
$807$	−26.5934	−	14.8188i	−0.936134	−	0.521646i
$808$	1.86719	+	6.96843i	0.0656874	+	0.245149i
$809$	7.07341	+	4.08384i	0.248688	+	0.143580i	0.619163	−	0.785262i	$-0.287472\pi$
$809$	7.07341	+	4.08384i	0.248688	+	0.143580i	−0.370475	+	0.928842i	$0.620805\pi$
$810$	−0.547514	−	8.98333i	−0.0192377	−	0.315642i
$811$	−18.2887	+	18.2887i	−0.642205	+	0.642205i	−0.951097	−	0.308892i	$-0.900042\pi$
$811$	−18.2887	+	18.2887i	−0.642205	+	0.642205i	0.308892	+	0.951097i	$0.400042\pi$
$812$	−0.661268	+	2.46788i	−0.0232059	+	0.0866058i
$813$	−35.7327	−	34.6614i	−1.25320	−	1.21563i
$814$	27.1100	+	27.1100i	0.950203	+	0.950203i
$815$	11.5580	−	6.67301i	0.404859	−	0.233745i
$816$	1.17491	+	1.96531i	0.0411299	+	0.0687996i
$817$	−40.3624	+	10.8151i	−1.41210	+	0.378371i
$818$	2.74748			0.0960635
$819$	2.69347	+	17.8143i	0.0941174	+	0.622483i
$820$	−4.48696			−0.156691
$821$	−40.7978	+	10.9318i	−1.42385	+	0.381521i	−0.886850	−	0.462058i	$-0.847111\pi$
$821$	−40.7978	+	10.9318i	−1.42385	+	0.381521i	−0.537005	+	0.843579i	$0.680444\pi$
$822$	10.6790	+	17.8632i	0.372473	+	0.623049i
$823$	38.7259	−	22.3584i	1.34990	−	0.779365i	0.361664	−	0.932308i	$-0.382209\pi$
$823$	38.7259	−	22.3584i	1.34990	−	0.779365i	0.988235	+	0.152944i	$0.0488753\pi$
$824$	9.98436	+	9.98436i	0.347822	+	0.347822i
$825$	−4.73441	−	4.59246i	−0.164831	−	0.159889i
$826$	1.65855	−	6.18978i	0.0577082	−	0.215370i
$827$	−35.9420	+	35.9420i	−1.24982	+	1.24982i	−0.294028	+	0.955797i	$0.594996\pi$
$827$	−35.9420	+	35.9420i	−1.24982	+	1.24982i	−0.955797	+	0.294028i	$0.905004\pi$
$828$	−17.5987	−	9.45853i	−0.611596	−	0.328707i
$829$	−21.1423	−	12.2065i	−0.734301	−	0.423949i	0.0856926	−	0.996322i	$-0.472690\pi$
$829$	−21.1423	−	12.2065i	−0.734301	−	0.423949i	−0.819994	+	0.572373i	$0.806023\pi$
$830$	−3.22451	−	12.0340i	−0.111924	−	0.417708i
$831$	21.4848	+	11.9721i	0.745298	+	0.415306i
$832$	2.22703	−	2.83555i	0.0772085	−	0.0983048i
$833$			5.58613i			0.193548i
$834$	−1.58859	+	6.31136i	−0.0550084	+	0.218545i
$835$	5.23508	−	9.06743i	0.181168	−	0.313791i
$836$	10.9292	+	18.9300i	0.377996	+	0.654708i
$837$	−28.9695	+	31.7433i	−1.00133	+	1.09721i
$838$	−13.7796	−	3.69224i	−0.476009	−	0.127546i
$839$	30.3149	+	8.12286i	1.04659	+	0.280432i	0.740841	−	0.671681i	$-0.234427\pi$
$839$	30.3149	+	8.12286i	1.04659	+	0.280432i	0.305746	+	0.952113i	$0.401094\pi$
$840$	2.77501	−	0.789012i	0.0957469	−	0.0272235i
$841$	−13.3236	−	23.0771i	−0.459434	−	0.795763i
$842$	16.4580	−	28.5061i	0.567180	−	0.982385i
$843$	−10.4908	−	2.64058i	−0.361324	−	0.0909464i
$844$		−	6.87320i		−	0.236585i
$845$	6.75222	−	11.1089i	0.232283	−	0.382158i
$846$	−20.5068	−	33.1465i	−0.705038	−	1.13960i
$847$	1.50964	+	5.63404i	0.0518717	+	0.193588i
$848$	0.261936	+	0.151229i	0.00899492	+	0.00519322i
$849$	0.446186	+	29.3171i	0.0153131	+	1.00616i
$850$	0.934777	−	0.934777i	0.0320626	−	0.0320626i
$851$	17.3536	−	64.7647i	0.594875	−	2.22010i
$852$	18.4354	−	19.0052i	0.631586	−	0.651108i
$853$	30.7798	+	30.7798i	1.05388	+	1.05388i	0.998463	+	0.0554178i	$0.0176491\pi$
$853$	30.7798	+	30.7798i	1.05388	+	1.05388i	0.0554178	+	0.998463i	$0.482351\pi$
$854$	−6.45787	+	3.72846i	−0.220984	+	0.127585i
$855$	17.2119	−	0.524028i	0.588635	−	0.0179214i
$856$	−5.69085	+	1.52486i	−0.194509	+	0.0521186i
$857$	−28.3530			−0.968520			−0.484260	−	0.874924i	$-0.660911\pi$
$857$	−28.3530			−0.968520			−0.484260	+	0.874924i	$0.660911\pi$
$858$	21.9354	−	9.18742i	0.748862	−	0.313653i
$859$	−42.4132			−1.44712			−0.723559	−	0.690262i	$-0.757495\pi$
$859$	−42.4132			−1.44712			−0.723559	+	0.690262i	$0.757495\pi$
$860$	7.03182	−	1.88417i	0.239783	−	0.0642497i
$861$	11.1108	−	6.64228i	0.378655	−	0.226368i
$862$	−23.8766	+	13.7852i	−0.813241	+	0.469525i
$863$	−16.5706	−	16.5706i	−0.564068	−	0.564068i	0.366392	−	0.930461i	$-0.380593\pi$
$863$	−16.5706	−	16.5706i	−0.564068	−	0.564068i	−0.930461	+	0.366392i	$0.880593\pi$
$864$	1.11440	−	5.07525i	0.0379126	−	0.172663i
$865$	−2.40625	+	8.98025i	−0.0818150	+	0.305338i
$866$	−5.97890	+	5.97890i	−0.203171	+	0.203171i
$867$	26.4148	−	0.402015i	0.897095	−	0.0136532i
$868$	−11.9303	−	6.88797i	−0.404941	−	0.233793i
$869$	−7.90741	−	29.5108i	−0.268240	−	1.00109i
$870$	1.29323	−	2.32079i	0.0438445	−	0.0786823i
$871$	0.321158	−	0.751270i	0.0108820	−	0.0254558i
$872$			10.4678i			0.354486i
$873$	3.47202	−	3.69007i	0.117510	−	0.124890i
$874$	19.1135	−	33.1056i	0.646524	−	1.11981i
$875$	−0.832827	−	1.44250i	−0.0281547	−	0.0487654i
$876$	−0.457028	−	1.60740i	−0.0154416	−	0.0543090i
$877$	−22.4068	−	6.00390i	−0.756625	−	0.202737i	−0.140170	−	0.990127i	$-0.544765\pi$
$877$	−22.4068	−	6.00390i	−0.756625	−	0.202737i	−0.616455	+	0.787390i	$0.711432\pi$
$878$	−12.1908	−	3.26651i	−0.411419	−	0.110240i
$879$	−5.32330	−	18.7224i	−0.179550	−	0.631490i
$880$	−1.90406	−	3.29793i	−0.0641859	−	0.111173i
$881$	2.39325	−	4.14523i	0.0806306	−	0.139656i	−0.822890	−	0.568200i	$-0.807640\pi$
$881$	2.39325	−	4.14523i	0.0806306	−	0.139656i	0.903521	+	0.428544i	$0.140973\pi$
$882$	8.68691	−	9.23248i	0.292503	−	0.310874i
$883$		−	10.5075i		−	0.353606i	−0.984246	−	0.176803i	$-0.943424\pi$
$883$		−	10.5075i		−	0.353606i	0.984246	−	0.176803i	$-0.0565756\pi$
$884$	1.77427	+	4.42391i	0.0596752	+	0.148792i
$885$	−3.24358	+	5.82086i	−0.109032	+	0.195666i
$886$	−7.38763	−	27.5710i	−0.248192	−	0.926266i
$887$	−17.3077	−	9.99260i	−0.581136	−	0.335519i	0.180449	−	0.983584i	$-0.442245\pi$
$887$	−17.3077	−	9.99260i	−0.581136	−	0.335519i	−0.761585	+	0.648066i	$0.775578\pi$
$888$	17.4359	−	0.265361i	0.585109	−	0.00890494i
$889$	−4.87442	+	4.87442i	−0.163483	+	0.163483i
$890$	−2.31981	+	8.65764i	−0.0777602	+	0.290205i
$891$	22.7155	−	25.6642i	0.760999	−	0.859782i
$892$	1.11715	+	1.11715i	0.0374050	+	0.0374050i
$893$	64.5846	−	37.2879i	2.16124	−	1.24779i
$894$	0.581634	−	0.347714i	0.0194527	−	0.0116293i
$895$	−14.9451	+	4.00452i	−0.499558	+	0.133856i
$896$	1.66565			0.0556456
$897$	−33.0955	−	25.1884i	−1.10503	−	0.841016i
$898$	−29.8510			−0.996139
$899$	−12.2540	+	3.28344i	−0.408692	+	0.109509i
$900$	−2.99861	+	0.0912946i	−0.0999537	+	0.00304315i
$901$	−0.346273	+	0.199921i	−0.0115360	+	0.00666032i
$902$	−12.0823	−	12.0823i	−0.402295	−	0.402295i
$903$	−14.6232	+	15.0752i	−0.486631	+	0.501672i
$904$	−2.95836	+	11.0408i	−0.0983937	+	0.367210i
$905$	16.1913	−	16.1913i	0.538217	−	0.538217i
$906$	0.508351	+	33.4018i	0.0168888	+	1.10970i
$907$	−5.19882	−	3.00154i	−0.172624	−	0.0996644i	0.411199	−	0.911546i	$-0.365110\pi$
$907$	−5.19882	−	3.00154i	−0.172624	−	0.0996644i	−0.583822	+	0.811881i	$0.698444\pi$
$908$	−1.72914	−	6.45324i	−0.0573835	−	0.214158i
$909$	11.3868	+	18.4052i	0.377675	+	0.610462i
$910$	5.96268	−	0.716701i	0.197661	−	0.0237584i
$911$		−	27.5510i		−	0.912806i	−0.889773	−	0.456403i	$-0.849138\pi$
$911$		−	27.5510i		−	0.912806i	0.889773	−	0.456403i	$-0.150862\pi$
$912$	9.64119	+	2.42672i	0.319252	+	0.0803568i
$913$	23.7219	−	41.0875i	0.785079	−	1.35980i
$914$	15.9522	+	27.6301i	0.527653	+	0.913923i
$915$	7.45854	−	2.12067i	0.246572	−	0.0701072i
$916$	21.9597	+	5.88407i	0.725567	+	0.194415i
$917$	6.73737	+	1.80527i	0.222487	+	0.0596153i
$918$	5.07386	+	4.63050i	0.167462	+	0.152829i
$919$	16.2627	+	28.1677i	0.536456	+	0.929168i	0.999091	+	0.0426199i	$0.0135704\pi$
$919$	16.2627	+	28.1677i	0.536456	+	0.929168i	−0.462636	+	0.886548i	$0.653096\pi$
$920$	−3.32990	+	5.76756i	−0.109784	+	0.190151i
$921$	12.2476	−	48.6589i	0.403572	−	1.60336i
$922$			11.2423i			0.370245i
$923$	44.1032	−	33.0582i	1.45167	−	1.08812i
$924$	9.59701	+	5.34779i	0.315719	+	0.175929i
$925$	−2.60573	−	9.72471i	−0.0856758	−	0.319746i
$926$	−11.6084	−	6.70209i	−0.381475	−	0.220244i
$927$	37.3124	+	20.0538i	1.22550	+	0.658655i
$928$	1.08463	−	1.08463i	0.0356047	−	0.0356047i
$929$	−6.22343	+	23.2262i	−0.204184	+	0.762026i	0.785512	+	0.618846i	$0.212399\pi$
$929$	−6.22343	+	23.2262i	−0.204184	+	0.762026i	−0.989697	+	0.143180i	$0.954267\pi$
$930$	10.2823	+	9.97404i	0.337171	+	0.327062i
$931$	17.1507	+	17.1507i	0.562092	+	0.562092i
$932$	−18.1109	+	10.4563i	−0.593243	+	0.342509i
$933$	7.85098	+	13.1326i	0.257030	+	0.429943i
$934$	−13.3285	+	3.57137i	−0.436123	+	0.116859i
$935$	5.03424			0.164637
$936$	3.94713	−	10.0708i	0.129016	−	0.329173i
$937$	−4.78415			−0.156292			−0.0781458	−	0.996942i	$-0.524900\pi$
$937$	−4.78415			−0.156292			−0.0781458	+	0.996942i	$0.524900\pi$
$938$	0.364585	−	0.0976902i	0.0119041	−	0.00318970i
$939$	−18.1808	−	30.4116i	−0.593306	−	0.992446i
$940$	−11.2517	+	6.49619i	−0.366991	+	0.211882i
$941$	−2.48077	−	2.48077i	−0.0808706	−	0.0808706i	0.665514	−	0.746385i	$-0.268212\pi$
$941$	−2.48077	−	2.48077i	−0.0808706	−	0.0808706i	−0.746385	+	0.665514i	$0.768212\pi$
$942$	−19.7894	−	19.1960i	−0.644773	−	0.625441i
$943$	−7.73410	+	28.8640i	−0.251857	+	0.939943i
$944$	−2.72039	+	2.72039i	−0.0885412	+	0.0885412i
$945$	7.29013	−	4.66507i	0.237148	−	0.151755i
$946$	24.0085	+	13.8613i	0.780584	+	0.450671i
$947$	−3.58159	−	13.3667i	−0.116386	−	0.434359i	0.883001	−	0.469371i	$-0.155519\pi$
$947$	−3.58159	−	13.3667i	−0.116386	−	0.434359i	−0.999387	+	0.0350128i	$0.988853\pi$
$948$	−12.1386	−	6.76403i	−0.394242	−	0.219685i
$949$	−0.415143	−	3.45383i	−0.0134761	−	0.112116i
$950$		−	5.73996i		−	0.186229i
$951$	−8.84714	+	35.1490i	−0.286888	+	1.13979i
$952$	−1.10098	+	1.90695i	−0.0356828	+	0.0618045i
$953$	23.6090	+	40.8920i	0.764770	+	1.32462i	0.940368	+	0.340159i	$0.110481\pi$
$953$	23.6090	+	40.8920i	0.764770	+	1.32462i	−0.175598	+	0.984462i	$0.556186\pi$
$954$	0.883196	+	0.208065i	0.0285945	+	0.00673635i
$955$	7.45845	+	1.99848i	0.241350	+	0.0646695i
$956$	3.19279	+	0.855506i	0.103262	+	0.0276690i
$957$	9.73165	−	2.76698i	0.314580	−	0.0894438i
$958$	15.4739	+	26.8016i	0.499940	+	0.865921i
$959$	−10.0070	+	17.3327i	−0.323144	+	0.559701i
$960$	−1.67966	−	0.422776i	−0.0542108	−	0.0136450i
$961$		−	37.4026i		−	1.20654i
$962$	35.9336	+	5.14357i	1.15854	+	0.165836i
$963$	−15.0308	+	9.29912i	−0.484361	+	0.299660i
$964$	−2.66309	−	9.93879i	−0.0857724	−	0.320107i
$965$	5.53616	+	3.19630i	0.178215	+	0.102893i
$966$	−0.292382	−	19.2113i	−0.00940725	−	0.618113i
$967$	−12.9619	+	12.9619i	−0.416828	+	0.416828i	−0.884109	−	0.467281i	$-0.845234\pi$
$967$	−12.9619	+	12.9619i	−0.416828	+	0.416828i	0.467281	+	0.884109i	$0.345234\pi$
$968$	0.906332	−	3.38248i	0.0291306	−	0.108717i
$969$	−9.15097	+	9.43381i	−0.293971	+	0.303058i
$970$	−1.19423	−	1.19423i	−0.0383445	−	0.0383445i
$971$	−7.70575	+	4.44892i	−0.247289	+	0.142773i	−0.618522	−	0.785767i	$-0.712268\pi$
$971$	−7.70575	+	4.44892i	−0.247289	+	0.142773i	0.371233	+	0.928540i	$0.378935\pi$
$972$	−1.18499	−	15.5434i	−0.0380086	−	0.498553i
$973$	−6.04547	+	1.61988i	−0.193809	+	0.0519309i
$974$	−28.8687			−0.925014
$975$	−6.19474	−	0.790720i	−0.198390	−	0.0253233i
$976$	4.47687			0.143301
$977$	−6.37132	+	1.70719i	−0.203837	+	0.0546178i	−0.359293	−	0.933225i	$-0.616982\pi$
$977$	−6.37132	+	1.70719i	−0.203837	+	0.0546178i	0.155456	+	0.987843i	$0.450315\pi$
$978$	19.8408	−	11.8613i	0.634440	−	0.379282i
$979$	−29.5595	+	17.0662i	−0.944726	+	0.545438i
$980$	−2.98795	−	2.98795i	−0.0954465	−	0.0954465i
$981$	9.04716	+	30.0721i	0.288853	+	0.960127i
$982$	2.07030	−	7.72647i	0.0660660	−	0.246562i
$983$	−17.6609	+	17.6609i	−0.563294	+	0.563294i	−0.930242	−	0.366947i	$-0.880403\pi$
$983$	−17.6609	+	17.6609i	−0.563294	+	0.563294i	0.366947	+	0.930242i	$0.380403\pi$
$984$	−7.77074	+	0.118265i	−0.247722	+	0.00377016i
$985$	−12.7145	−	7.34069i	−0.405116	−	0.233894i
$986$	0.524826	+	1.95868i	0.0167139	+	0.0623770i
$987$	18.2454	−	32.7427i	0.580756	−	1.04221i
$988$	19.0298	+	8.13500i	0.605420	+	0.258809i
$989$		−	48.4825i		−	1.54165i
$990$	−8.32034	−	7.82867i	−0.264438	−	0.248812i
$991$	−8.86830	+	15.3603i	−0.281711	+	0.487937i	−0.971806	−	0.235781i	$-0.924235\pi$
$991$	−8.86830	+	15.3603i	−0.281711	+	0.487937i	0.690095	+	0.723718i	$0.257569\pi$
$992$	4.13529	+	7.16254i	0.131296	+	0.227411i
$993$	−13.1763	−	46.3420i	−0.418138	−	1.47062i
$994$	24.5950	+	6.59020i	0.780105	+	0.209028i
$995$	2.81296	+	0.753732i	0.0891770	+	0.0238949i
$996$	−5.90156	−	20.7562i	−0.186998	−	0.657685i
$997$	20.3319	+	35.2159i	0.643918	+	1.11530i	0.984550	+	0.175102i	$0.0560257\pi$
$997$	20.3319	+	35.2159i	0.643918	+	1.11530i	−0.340632	+	0.940197i	$0.610641\pi$
$998$	−10.9012	+	18.8815i	−0.345072	+	0.597682i
$999$	49.8605	−	15.8318i	1.57752	−	0.500896i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	390.2.bh.c.71.4	yes	40
3.2	odd	2	inner	390.2.bh.c.71.6	yes	40
13.11	odd	12	inner	390.2.bh.c.11.6	yes	40
39.11	even	12	inner	390.2.bh.c.11.4	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.bh.c.11.4	✓	40	39.11	even	12	inner
390.2.bh.c.11.6	yes	40	13.11	odd	12	inner
390.2.bh.c.71.4	yes	40	1.1	even	1	trivial
390.2.bh.c.71.6	yes	40	3.2	odd	2	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:	\( N \)	\(=\)	\( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	390.bh (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.965926 + 0.258819i) q^{2} +(0.888751 + 1.48665i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-0.707107 - 0.707107i) q^{5} +(-1.24324 - 1.20597i) q^{6} +(0.431103 - 1.60890i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-1.42024 + 2.64252i) q^{9} +O(q^{10})\)	\(q+(-0.965926 + 0.258819i) q^{2} +(0.888751 + 1.48665i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-0.707107 - 0.707107i) q^{5} +(-1.24324 - 1.20597i) q^{6} +(0.431103 - 1.60890i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-1.42024 + 2.64252i) q^{9} +(0.866025 + 0.500000i) q^{10} +(0.985615 + 3.67836i) q^{11} +(1.51301 + 0.843099i) q^{12} +(2.83555 + 2.22703i) q^{13} +1.66565i q^{14} +(0.422776 - 1.67966i) q^{15} +(0.500000 - 0.866025i) q^{16} +(0.660987 + 1.14486i) q^{17} +(0.687914 - 2.92006i) q^{18} +(5.54438 + 1.48561i) q^{19} +(-0.965926 - 0.258819i) q^{20} +(2.77501 - 0.789012i) q^{21} +(-1.90406 - 3.29793i) q^{22} +(-3.32990 + 5.76756i) q^{23} +(-1.67966 - 0.422776i) q^{24} +1.00000i q^{25} +(-3.31533 - 1.41726i) q^{26} +(-5.19074 + 0.237145i) q^{27} +(-0.431103 - 1.60890i) q^{28} +(-1.32839 - 0.766948i) q^{29} +(0.0263575 + 1.73185i) q^{30} +(5.84819 - 5.84819i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(-4.59246 + 4.73441i) q^{33} +(-0.934777 - 0.934777i) q^{34} +(-1.44250 + 0.832827i) q^{35} +(0.0912946 + 2.99861i) q^{36} +(-9.72471 + 2.60573i) q^{37} -5.73996 q^{38} +(-0.790720 + 6.19474i) q^{39} +1.00000 q^{40} +(4.33407 - 1.16131i) q^{41} +(-2.47624 + 1.48035i) q^{42} +(-6.30456 + 3.63994i) q^{43} +(2.69275 + 2.69275i) q^{44} +(2.87281 - 0.864281i) q^{45} +(1.72368 - 6.43288i) q^{46} +(9.18700 - 9.18700i) q^{47} +(1.73185 - 0.0263575i) q^{48} +(3.65947 + 2.11280i) q^{49} +(-0.258819 - 0.965926i) q^{50} +(-1.11455 + 2.00015i) q^{51} +(3.56917 + 0.510896i) q^{52} +0.302458i q^{53} +(4.95249 - 1.57253i) q^{54} +(1.90406 - 3.29793i) q^{55} +(0.832827 + 1.44250i) q^{56} +(2.71899 + 9.56288i) q^{57} +(1.48163 + 0.397002i) q^{58} +(-3.71613 - 0.995733i) q^{59} +(-0.473695 - 1.66602i) q^{60} +(2.23843 + 3.87708i) q^{61} +(-4.13529 + 7.16254i) q^{62} +(3.63928 + 3.42422i) q^{63} -1.00000i q^{64} +(-0.430282 - 3.57978i) q^{65} +(3.21062 - 5.76171i) q^{66} +(-0.0586497 - 0.218884i) q^{67} +(1.14486 + 0.660987i) q^{68} +(-11.5338 + 0.175536i) q^{69} +(1.17780 - 1.17780i) q^{70} +(3.95652 - 14.7659i) q^{71} +(-0.864281 - 2.87281i) q^{72} +(-0.682227 - 0.682227i) q^{73} +(8.71894 - 5.03388i) q^{74} +(-1.48665 + 0.888751i) q^{75} +(5.54438 - 1.48561i) q^{76} +6.34302 q^{77} +(-0.839539 - 6.18831i) q^{78} -8.02282 q^{79} +(-0.965926 + 0.258819i) q^{80} +(-4.96583 - 7.50604i) q^{81} +(-3.88582 + 2.24348i) q^{82} +(-8.80953 - 8.80953i) q^{83} +(2.00872 - 2.07081i) q^{84} +(0.342152 - 1.27693i) q^{85} +(5.14765 - 5.14765i) q^{86} +(-0.0404297 - 2.65648i) q^{87} +(-3.29793 - 1.90406i) q^{88} +(2.31981 + 8.65764i) q^{89} +(-2.55123 + 1.57837i) q^{90} +(4.80548 - 3.60202i) q^{91} +6.65980i q^{92} +(13.8918 + 3.49661i) q^{93} +(-6.49619 + 11.2517i) q^{94} +(-2.86998 - 4.97095i) q^{95} +(-1.66602 + 0.473695i) q^{96} +(-1.63135 - 0.437120i) q^{97} +(-4.08161 - 1.09366i) q^{98} +(-11.1200 - 2.61966i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 8 q^{6} - 8 q^{7} + 8 q^{9}+O(q^{10}) \) 40 * q + 8 * q^6 - 8 * q^7 + 8 * q^9	\( 40 q + 8 q^{6} - 8 q^{7} + 8 q^{9} + 8 q^{13} + 4 q^{15} + 20 q^{16} - 8 q^{18} - 16 q^{19} + 4 q^{21} - 8 q^{22} + 8 q^{24} - 48 q^{27} + 8 q^{28} + 36 q^{31} + 12 q^{33} + 16 q^{34} - 12 q^{36} - 64 q^{37} - 60 q^{39} + 40 q^{40} - 12 q^{42} + 8 q^{45} - 32 q^{46} + 48 q^{49} + 24 q^{52} - 28 q^{54} + 8 q^{55} - 76 q^{57} - 28 q^{58} + 4 q^{60} - 40 q^{61} + 80 q^{63} + 40 q^{66} - 28 q^{67} - 36 q^{69} + 16 q^{70} + 16 q^{72} + 8 q^{73} - 16 q^{76} - 28 q^{78} + 40 q^{79} + 12 q^{81} + 20 q^{84} + 44 q^{85} + 40 q^{87} + 12 q^{88} + 120 q^{91} - 8 q^{93} - 16 q^{94} + 4 q^{96} - 160 q^{97} - 96 q^{99}+O(q^{100}) \) 40 * q + 8 * q^6 - 8 * q^7 + 8 * q^9 + 8 * q^13 + 4 * q^15 + 20 * q^16 - 8 * q^18 - 16 * q^19 + 4 * q^21 - 8 * q^22 + 8 * q^24 - 48 * q^27 + 8 * q^28 + 36 * q^31 + 12 * q^33 + 16 * q^34 - 12 * q^36 - 64 * q^37 - 60 * q^39 + 40 * q^40 - 12 * q^42 + 8 * q^45 - 32 * q^46 + 48 * q^49 + 24 * q^52 - 28 * q^54 + 8 * q^55 - 76 * q^57 - 28 * q^58 + 4 * q^60 - 40 * q^61 + 80 * q^63 + 40 * q^66 - 28 * q^67 - 36 * q^69 + 16 * q^70 + 16 * q^72 + 8 * q^73 - 16 * q^76 - 28 * q^78 + 40 * q^79 + 12 * q^81 + 20 * q^84 + 44 * q^85 + 40 * q^87 + 12 * q^88 + 120 * q^91 - 8 * q^93 - 16 * q^94 + 4 * q^96 - 160 * q^97 - 96 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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