LMFDB - Embedded newform 390.2.bh.c.71.6

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			71.6
Character	$\chi$	$=$	390.71
Dual form			390.2.bh.c.11.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965926 - 0.258819i) q^{2} +(-1.73185 - 0.0263575i) q^{3} +(0.866025 - 0.500000i) q^{4} +(0.707107 + 0.707107i) q^{5} +(-1.67966 + 0.422776i) q^{6} +(0.431103 - 1.60890i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.99861 + 0.0912946i) q^{9} +O(q^{10})$	\(q+(0.965926 - 0.258819i) q^{2} +(-1.73185 - 0.0263575i) q^{3} +(0.866025 - 0.500000i) q^{4} +(0.707107 + 0.707107i) q^{5} +(-1.67966 + 0.422776i) q^{6} +(0.431103 - 1.60890i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.99861 + 0.0912946i) 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} +(-1.20597 - 1.24324i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-0.660987 - 1.14486i) q^{17} +(2.92006 - 0.687914i) q^{18} +(5.54438 + 1.48561i) q^{19} +(0.965926 + 0.258819i) q^{20} +(-0.789012 + 2.77501i) q^{21} +(-1.90406 - 3.29793i) q^{22} +(3.32990 - 5.76756i) q^{23} +(-1.24324 + 1.20597i) 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} +(-1.48665 - 0.888751i) q^{30} +(5.84819 - 5.84819i) q^{31} +(0.258819 - 0.965926i) q^{32} +(1.60998 + 6.39635i) q^{33} +(-0.934777 - 0.934777i) q^{34} +(1.44250 - 0.832827i) q^{35} +(2.64252 - 1.42024i) q^{36} +(-9.72471 + 2.60573i) q^{37} +5.73996 q^{38} +(-4.85204 - 3.93163i) q^{39} +1.00000 q^{40} +(-4.33407 + 1.16131i) q^{41} +(-0.0439025 + 2.88466i) q^{42} +(-6.30456 + 3.63994i) q^{43} +(-2.69275 - 2.69275i) q^{44} +(2.05578 + 2.18489i) q^{45} +(1.72368 - 6.43288i) q^{46} +(-9.18700 + 9.18700i) q^{47} +(-0.888751 + 1.48665i) 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} +(-5.07525 + 1.11440i) q^{54} +(1.90406 - 3.29793i) q^{55} +(-0.832827 - 1.44250i) q^{56} +(-9.56288 - 2.71899i) q^{57} +(1.48163 + 0.397002i) q^{58} +(3.71613 + 0.995733i) q^{59} +(-1.66602 - 0.473695i) q^{60} +(2.23843 + 3.87708i) q^{61} +(4.13529 - 7.16254i) q^{62} +(1.43959 - 4.78510i) 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} +(-5.91891 + 9.90078i) q^{69} +(1.17780 - 1.17780i) q^{70} +(-3.95652 + 14.7659i) q^{71} +(2.18489 - 2.05578i) q^{72} +(-0.682227 - 0.682227i) q^{73} +(-8.71894 + 5.03388i) q^{74} +(0.0263575 - 1.73185i) q^{75} +(5.54438 - 1.48561i) q^{76} -6.34302 q^{77} +(-5.70429 - 2.54186i) q^{78} -8.02282 q^{79} +(0.965926 - 0.258819i) q^{80} +(8.98333 + 0.547514i) q^{81} +(-3.88582 + 2.24348i) q^{82} +(8.80953 + 8.80953i) q^{83} +(0.704199 + 2.79773i) q^{84} +(0.342152 - 1.27693i) q^{85} +(-5.14765 + 5.14765i) q^{86} +(-2.28036 - 1.36325i) 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} +(-10.2823 + 9.97404i) q^{93} +(-6.49619 + 11.2517i) q^{94} +(2.86998 + 4.97095i) q^{95} +(-0.473695 + 1.66602i) q^{96} +(-1.63135 - 0.437120i) q^{97} +(4.08161 + 1.09366i) q^{98} +(-2.61966 - 11.1200i) 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
$3$	−1.73185	−	0.0263575i	−0.999884	−	0.0152175i
$3$	−1.73185	−	0.0263575i	−0.999884	−	0.0152175i
$4$	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
$6$	−1.67966	+	0.422776i	−0.685719	+	0.172598i
$7$	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
$9$	2.99861	+	0.0912946i	0.999537	+	0.0304315i
$10$	0.866025	+	0.500000i	0.273861	+	0.158114i
$11$	−0.985615	−	3.67836i	−0.297174	−	1.10907i	−0.939475	−	0.342616i	$-0.888687\pi$
$11$	−0.985615	−	3.67836i	−0.297174	−	1.10907i	0.642301	−	0.766452i	$-0.277980\pi$
$12$	−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
$15$	−1.20597	−	1.24324i	−0.311379	−	0.321003i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−0.660987	−	1.14486i	−0.160313	−	0.277670i	0.774668	−	0.632368i	$-0.217917\pi$
$17$	−0.660987	−	1.14486i	−0.160313	−	0.277670i	−0.934981	+	0.354698i	$0.884584\pi$
$18$	2.92006	−	0.687914i	0.688266	−	0.162143i
$19$	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
$21$	−0.789012	+	2.77501i	−0.172177	+	0.605556i
$22$	−1.90406	−	3.29793i	−0.405947	−	0.703121i
$23$	3.32990	−	5.76756i	0.694333	−	1.20262i	−0.276073	−	0.961137i	$-0.589033\pi$
$23$	3.32990	−	5.76756i	0.694333	−	1.20262i	0.970405	−	0.241482i	$-0.0776336\pi$
$24$	−1.24324	+	1.20597i	−0.253775	+	0.246167i
$25$			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	0.618242	−	0.785988i	$-0.287845\pi$
$29$	1.32839	+	0.766948i	0.246677	+	0.142419i	−0.371565	+	0.928407i	$0.621179\pi$
$30$	−1.48665	−	0.888751i	−0.271423	−	0.162263i
$31$	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
$33$	1.60998	+	6.39635i	0.280262	+	1.11346i
$34$	−0.934777	−	0.934777i	−0.160313	−	0.160313i
$35$	1.44250	−	0.832827i	0.243827	−	0.140773i
$36$	2.64252	−	1.42024i	0.440420	−	0.236707i
$37$	−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
$39$	−4.85204	−	3.93163i	−0.776948	−	0.629564i
$40$	1.00000			0.158114
$41$	−4.33407	+	1.16131i	−0.676868	+	0.181366i	−0.580847	−	0.814013i	$-0.697278\pi$
$41$	−4.33407	+	1.16131i	−0.676868	+	0.181366i	−0.0960213	+	0.995379i	$0.530612\pi$
$42$	−0.0439025	+	2.88466i	−0.00677431	+	0.445113i
$43$	−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
$45$	2.05578	+	2.18489i	0.306458	+	0.325705i
$46$	1.72368	−	6.43288i	0.254143	−	0.948476i
$47$	−9.18700	+	9.18700i	−1.34006	+	1.34006i	−0.444070	+	0.895992i	$0.646466\pi$
$47$	−9.18700	+	9.18700i	−1.34006	+	1.34006i	−0.895992	+	0.444070i	$0.853534\pi$
$48$	−0.888751	+	1.48665i	−0.128280	+	0.214579i
$49$	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	$-0.993387\pi$
$53$		−	0.302458i		−	0.0415458i	0.999784	−	0.0207729i	$-0.00661269\pi$
$54$	−5.07525	+	1.11440i	−0.690653	+	0.151650i
$55$	1.90406	−	3.29793i	0.256744	−	0.444693i
$56$	−0.832827	−	1.44250i	−0.111291	−	0.192762i
$57$	−9.56288	−	2.71899i	−1.26663	−	0.360140i
$58$	1.48163	+	0.397002i	0.194548	+	0.0521289i
$59$	3.71613	+	0.995733i	0.483798	+	0.129633i	0.492471	−	0.870329i	$-0.336094\pi$
$59$	3.71613	+	0.995733i	0.483798	+	0.129633i	−0.00867240	+	0.999962i	$0.502761\pi$
$60$	−1.66602	−	0.473695i	−0.215082	−	0.0611538i
$61$	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
$63$	1.43959	−	4.78510i	0.181372	−	0.602866i
$64$		−	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
$69$	−5.91891	+	9.90078i	−0.712553	+	1.19191i
$70$	1.17780	−	1.17780i	0.140773	−	0.140773i
$71$	−3.95652	+	14.7659i	−0.469553	+	1.75240i	0.171782	+	0.985135i	$0.445047\pi$
$71$	−3.95652	+	14.7659i	−0.469553	+	1.75240i	−0.641335	+	0.767261i	$0.721619\pi$
$72$	2.18489	−	2.05578i	0.257492	−	0.242276i
$73$	−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
$75$	0.0263575	−	1.73185i	0.00304351	−	0.199977i
$76$	5.54438	−	1.48561i	0.635984	−	0.170411i
$77$	−6.34302			−0.722854
$78$	−5.70429	−	2.54186i	−0.645884	−	0.287809i
$79$	−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
$81$	8.98333	+	0.547514i	0.998148	+	0.0608349i
$82$	−3.88582	+	2.24348i	−0.429117	+	0.247751i
$83$	8.80953	+	8.80953i	0.966972	+	0.966972i	0.999472	−	0.0324997i	$-0.0103468\pi$
$83$	8.80953	+	8.80953i	0.966972	+	0.966972i	−0.0324997	+	0.999472i	$0.510347\pi$
$84$	0.704199	+	2.79773i	0.0768344	+	0.305258i
$85$	0.342152	−	1.27693i	0.0371116	−	0.138502i
$86$	−5.14765	+	5.14765i	−0.555085	+	0.555085i
$87$	−2.28036	−	1.36325i	−0.244481	−	0.146156i
$88$	−3.29793	−	1.90406i	−0.351561	−	0.202974i
$89$	−2.31981	−	8.65764i	−0.245899	−	0.917708i	−0.972929	−	0.231103i	$-0.925767\pi$
$89$	−2.31981	−	8.65764i	−0.245899	−	0.917708i	0.727030	−	0.686606i	$-0.240900\pi$
$90$	2.55123	+	1.57837i	0.268923	+	0.166375i
$91$	4.80548	−	3.60202i	0.503752	−	0.377595i
$92$		−	6.65980i		−	0.694333i
$93$	−10.2823	+	9.97404i	−1.06623	+	1.03426i
$94$	−6.49619	+	11.2517i	−0.670031	+	1.16053i
$95$	2.86998	+	4.97095i	0.294454	+	0.510009i
$96$	−0.473695	+	1.66602i	−0.0483463	+	0.170037i
$97$	−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
$99$	−2.61966	−	11.1200i	−0.263286	−	1.11760i
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$	−3.60713	+	6.24773i	−0.358923	+	0.621672i	−0.987781	−	0.155848i	$-0.950189\pi$
$101$	−3.60713	+	6.24773i	−0.358923	+	0.621672i	0.628859	+	0.777520i	$0.283522\pi$
$102$	1.59425	+	1.64353i	0.157855	+	0.162734i
$103$		−	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	0.232668	−	0.972556i	$-0.425254\pi$
$107$	−5.10228	−	2.94580i	−0.493256	−	0.284781i	−0.725924	+	0.687775i	$0.758588\pi$
$108$	−4.61388	+	2.39000i	−0.443971	+	0.229977i
$109$	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
$111$	16.9104	−	4.25641i	1.60507	−	0.404001i
$112$	−1.17780	−	1.17780i	−0.111291	−	0.111291i
$113$	−9.89888	+	5.71512i	−0.931208	+	0.537633i	−0.887194	−	0.461398i	$-0.847348\pi$
$113$	−9.89888	+	5.71512i	−0.931208	+	0.537633i	−0.0440148	+	0.999031i	$0.514015\pi$
$114$	−9.94076	−	0.151291i	−0.931037	−	0.0141697i
$115$	6.43288	−	1.72368i	0.599869	−	0.160734i
$116$	1.53390			0.142419
$117$	8.29938	+	6.93688i	0.767278	+	0.641315i
$118$	3.84722			0.354165
$119$	−2.12692	+	0.569907i	−0.194975	+	0.0522433i
$120$	−1.73185	−	0.0263575i	−0.158096	−	0.00240610i
$121$	−3.03264	+	1.75090i	−0.275695	+	0.159173i
$122$	3.16562	+	3.16562i	0.286602	+	0.286602i
$123$	7.53657	−	1.89698i	0.679549	−	0.171045i
$124$	2.14059	−	7.98877i	0.192230	−	0.717413i
$125$	−0.707107	+	0.707107i	−0.0632456	+	0.0632456i
$126$	0.152065	−	4.99465i	0.0135470	−	0.444959i
$127$	−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	$-0.941440\pi$
$131$		−	4.18756i		−	0.365869i	0.983125	−	0.182935i	$-0.0585597\pi$
$132$	4.59246	+	4.73441i	0.399723	+	0.412078i
$133$	4.78040	−	8.27989i	0.414513	−	0.717958i
$134$	−0.113303	−	0.196246i	−0.00978785	−	0.0169531i
$135$	−3.50272	−	3.83809i	−0.301466	−	0.330330i
$136$	−1.27693	−	0.342152i	−0.109496	−	0.0293393i
$137$	11.6063	+	3.10990i	0.991593	+	0.265697i	0.717920	−	0.696126i	$-0.245094\pi$
$137$	11.6063	+	3.10990i	0.991593	+	0.265697i	0.273674	+	0.961823i	$0.411761\pi$
$138$	−3.15472	+	11.0953i	−0.268547	+	0.944499i
$139$	−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
$141$	16.1527	−	15.6684i	1.36030	−	1.31951i
$142$			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
$147$	−6.28197	−	3.75550i	−0.518128	−	0.309749i
$148$	−7.11898	+	7.11898i	−0.585177	+	0.585177i
$149$	0.101260	−	0.377907i	0.00829554	−	0.0309594i	−0.961654	−	0.274265i	$-0.911565\pi$
$149$	0.101260	−	0.377907i	0.00829554	−	0.0309594i	0.969950	+	0.243306i	$0.0782320\pi$
$150$	−0.422776	−	1.67966i	−0.0345195	−	0.137144i
$151$	−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
$153$	−1.87752	−	3.49334i	−0.151789	−	0.282420i
$154$	−6.12688	+	1.64169i	−0.493718	+	0.132291i
$155$	8.27059			0.664310
$156$	−6.16780	−	0.978869i	−0.493820	−	0.0783723i
$157$	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
$159$	−0.00797204	+	0.523812i	−0.000632224	+	0.0415410i
$160$	0.866025	−	0.500000i	0.0684653	−	0.0395285i
$161$	−7.84389	−	7.84389i	−0.618185	−	0.618185i
$162$	8.81894	−	1.79620i	0.692881	−	0.141123i
$163$	−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
$165$	−3.38447	+	5.66134i	−0.263481	+	0.440734i
$166$	10.7894	+	6.22928i	0.837422	+	0.483486i
$167$	−2.70988	−	10.1134i	−0.209697	−	0.782599i	−0.987966	−	0.154669i	$-0.950569\pi$
$167$	−2.70988	−	10.1134i	−0.209697	−	0.782599i	0.778270	−	0.627930i	$-0.216098\pi$
$168$	1.40431	+	2.52014i	0.108345	+	0.194433i
$169$	3.08064	+	12.6297i	0.236972	+	0.971516i
$170$		−	1.32197i		−	0.101391i
$171$	16.4898	+	4.96094i	1.26101	+	0.379373i
$172$	−3.63994	+	6.30456i	−0.277543	+	0.480718i
$173$	4.64852	+	8.05147i	0.353420	+	0.612142i	0.986846	−	0.161661i	$-0.0516852\pi$
$173$	4.64852	+	8.05147i	0.353420	+	0.612142i	−0.633426	+	0.773803i	$0.718352\pi$
$174$	−2.55550	−	0.726600i	−0.193732	−	0.0550834i
$175$	1.60890	+	0.431103i	0.121621	+	0.0325883i
$176$	−3.67836	−	0.985615i	−0.277267	−	0.0742935i
$177$	−6.40953	−	1.82241i	−0.481770	−	0.136981i
$178$	−4.48153	−	7.76223i	−0.335905	−	0.581804i
$179$	−7.73613	+	13.3994i	−0.578226	+	1.00152i	0.417457	+	0.908697i	$0.362921\pi$
$179$	−7.73613	+	13.3994i	−0.578226	+	1.00152i	−0.995683	+	0.0928197i	$0.970412\pi$
$180$	2.87281	+	0.864281i	0.214126	+	0.0644197i
$181$			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
$186$	−7.35050	+	12.2954i	−0.538965	+	0.901546i
$187$	−3.55974	+	3.55974i	−0.260314	+	0.260314i
$188$	−3.36268	+	12.5497i	−0.245248	+	0.915280i
$189$	−2.61928	+	8.24914i	−0.190525	+	0.600036i
$190$	4.05877	+	4.05877i	0.294454	+	0.294454i
$191$	6.68706	−	3.86078i	0.483859	−	0.279356i	−0.238164	−	0.971225i	$-0.576546\pi$
$191$	6.68706	−	3.86078i	0.483859	−	0.279356i	0.722023	+	0.691869i	$0.243212\pi$
$192$	−0.0263575	+	1.73185i	−0.00190219	+	0.124986i
$193$	−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
$195$	−0.650830	−	6.21099i	−0.0466069	−	0.444778i
$196$	4.22560			0.301828
$197$	−14.1811	+	3.79982i	−1.01036	+	0.270726i	−0.725781	−	0.687925i	$-0.758522\pi$
$197$	−14.1811	+	3.79982i	−1.01036	+	0.270726i	−0.284582	+	0.958652i	$0.591855\pi$
$198$	−5.40845	−	10.0630i	−0.384362	−	0.715149i
$199$	−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
$201$	0.0958033	+	0.380620i	0.00675744	+	0.0268468i
$202$	−1.86719	+	6.96843i	−0.131375	+	0.490297i
$203$	1.80662	−	1.80662i	0.126800	−	0.126800i
$204$	1.96531	+	1.17491i	0.137599	+	0.0822599i
$205$	−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
$210$	−2.07081	+	2.00872i	−0.142899	+	0.138615i
$211$	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
$213$	7.24130	−	25.4681i	0.496166	−	1.74505i
$214$	−5.69085	−	1.52486i	−0.389019	−	0.104237i
$215$	−7.03182	−	1.88417i	−0.479566	−	0.128499i
$216$	−3.83809	+	3.50272i	−0.261149	+	0.238330i
$217$	−6.88797	−	11.9303i	−0.467586	−	0.809882i
$218$	5.23392	−	9.06541i	0.354486	−	0.613987i
$219$	1.16353	+	1.19950i	0.0786243	+	0.0810545i
$220$		−	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
$225$	−0.0912946	+	2.99861i	−0.00608631	+	0.199907i
$226$	−8.08240	+	8.08240i	−0.537633	+	0.537633i
$227$	−1.72914	+	6.45324i	−0.114767	+	0.428317i	−0.999269	−	0.0382192i	$-0.987831\pi$
$227$	−1.72914	+	6.45324i	−0.114767	+	0.428317i	0.884502	+	0.466536i	$0.154498\pi$
$228$	−9.64119	+	2.42672i	−0.638504	+	0.160714i
$229$	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
$231$	10.9852	+	0.167186i	0.722770	+	0.0110000i
$232$	1.48163	−	0.397002i	0.0972738	−	0.0260644i
$233$	20.9127			1.37004			0.685018	−	0.728526i	$-0.259794\pi$
$233$	20.9127			1.37004			0.685018	+	0.728526i	$0.259794\pi$
$234$	9.81198	+	4.55247i	0.641429	+	0.297604i
$235$	−12.9924			−0.847530
$236$	3.71613	−	0.995733i	0.241899	−	0.0648167i
$237$	13.8943	+	0.211462i	0.902533	+	0.0137359i
$238$	−1.90695	+	1.10098i	−0.123609	+	0.0713657i
$239$	−2.33729	−	2.33729i	−0.151186	−	0.151186i	0.627461	−	0.778648i	$-0.284094\pi$
$239$	−2.33729	−	2.33729i	−0.151186	−	0.151186i	−0.778648	+	0.627461i	$0.784094\pi$
$240$	−1.67966	+	0.422776i	−0.108422	+	0.0272901i
$241$	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
$243$	−15.5434	−	1.18499i	−0.997107	−	0.0760172i
$244$	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
$249$	−15.0246	−	15.4890i	−0.952145	−	0.981575i
$250$	−0.500000	+	0.866025i	−0.0316228	+	0.0547723i
$251$	11.4780	+	19.8805i	0.724485	+	1.25485i	0.959186	+	0.282777i	$0.0912558\pi$
$251$	11.4780	+	19.8805i	0.724485	+	1.25485i	−0.234700	+	0.972068i	$0.575411\pi$
$252$	−1.14583	−	4.86382i	−0.0721803	−	0.306392i
$253$	−24.4972	−	6.56400i	−1.54012	−	0.412675i
$254$	−3.99758	−	1.07115i	−0.250831	−	0.0672098i
$255$	−0.626213	+	2.20243i	−0.0392150	+	0.137922i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	2.27804	−	3.94568i	0.142100	−	0.246125i	−0.786187	−	0.617989i	$-0.787948\pi$
$257$	2.27804	−	3.94568i	0.142100	−	0.246125i	0.928287	+	0.371864i	$0.121281\pi$
$258$	9.05064	−	8.77928i	0.563468	−	0.546574i
$259$			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	0.830217	−	0.557441i	$-0.188217\pi$
$263$	12.3668	+	7.13996i	0.762568	+	0.440269i	−0.0676492	+	0.997709i	$0.521550\pi$
$264$	5.66134	+	3.38447i	0.348431	+	0.208300i
$265$	0.213870	−	0.213870i	0.0131379	−	0.0131379i
$266$	2.47452	−	9.23502i	0.151722	−	0.566235i
$267$	3.78937	+	15.0549i	0.231905	+	0.921344i
$268$	−0.160234	−	0.160234i	−0.00978785	−	0.00978785i
$269$	15.2218	−	8.78829i	0.928087	−	0.535831i	0.0418811	−	0.999123i	$-0.486665\pi$
$269$	15.2218	−	8.78829i	0.928087	−	0.535831i	0.886206	+	0.463291i	$0.153332\pi$
$270$	−4.37674	−	2.80074i	−0.266360	−	0.170448i
$271$	−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
$273$	−8.41732	+	6.11150i	−0.509439	+	0.369885i
$274$	12.0157			0.725897
$275$	3.67836	−	0.985615i	0.221814	−	0.0594348i
$276$	−0.175536	+	11.5338i	−0.0105660	+	0.694252i
$277$	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
$279$	18.0703	−	17.0025i	1.08184	−	1.01791i
$280$	0.431103	−	1.60890i	0.0257633	−	0.0961501i
$281$	4.41645	−	4.41645i	0.263463	−	0.263463i	−0.562996	−	0.826460i	$-0.690351\pi$
$281$	4.41645	−	4.41645i	0.263463	−	0.263463i	0.826460	+	0.562996i	$0.190351\pi$
$282$	11.5470	−	19.3151i	0.687614	−	1.15020i
$283$	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
$288$	0.864281	−	2.87281i	0.0509283	−	0.169282i
$289$	7.62619	−	13.2090i	0.448600	−	0.776997i
$290$	0.766948	+	1.32839i	0.0450368	+	0.0780060i
$291$	2.81374	+	0.800025i	0.164944	+	0.0468983i
$292$	−0.931940	−	0.249713i	−0.0545377	−	0.0146133i
$293$	10.8549	+	2.90856i	0.634149	+	0.169920i	0.561552	−	0.827442i	$-0.310205\pi$
$293$	10.8549	+	2.90856i	0.634149	+	0.169920i	0.0725974	+	0.997361i	$0.476871\pi$
$294$	−7.03992	−	2.00164i	−0.410576	−	0.116738i
$295$	1.92361	+	3.33179i	0.111997	+	0.193984i
$296$	−5.03388	+	8.71894i	−0.292588	+	0.506778i
$297$	4.24376	+	19.3272i	0.246248	+	1.12148i
$298$		−	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
$303$	6.41168	−	10.7251i	0.368341	−	0.616138i
$304$	4.05877	−	4.05877i	0.232786	−	0.232786i
$305$	−1.15870	+	4.32432i	−0.0663469	+	0.247610i
$306$	−2.71769	−	2.88837i	−0.155360	−	0.165117i
$307$	−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
$309$	−0.372169	+	24.4538i	−0.0211719	+	1.39113i
$310$	7.98877	−	2.14059i	0.453732	−	0.121577i
$311$	−8.83372			−0.500914			−0.250457	−	0.968128i	$-0.580581\pi$
$311$	−8.83372			−0.500914			−0.250457	+	0.968128i	$0.580581\pi$
$312$	−6.21099	+	0.650830i	−0.351628	+	0.0368460i
$313$	−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
$315$	4.40152	−	2.36563i	0.247998	−	0.133288i
$316$	−6.94796	+	4.01141i	−0.390854	+	0.225659i
$317$	−14.7971	−	14.7971i	−0.831089	−	0.831089i	0.156577	−	0.987666i	$-0.449954\pi$
$317$	−14.7971	−	14.7971i	−0.831089	−	0.831089i	−0.987666	+	0.156577i	$0.949954\pi$
$318$	0.127872	+	0.508026i	0.00717071	+	0.0284887i
$319$	1.51183	−	5.64223i	0.0846463	−	0.315904i
$320$	0.707107	−	0.707107i	0.0395285	−	0.0395285i
$321$	8.75874	+	5.23617i	0.488865	+	0.292255i
$322$	−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
$327$	−13.0140	+	12.6239i	−0.719678	+	0.698101i
$328$	−2.24348	+	3.88582i	−0.123875	+	0.214559i
$329$	10.8204	+	18.7415i	0.596549	+	1.03325i
$330$	−1.80389	+	6.34440i	−0.0993009	+	0.349248i
$331$	−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
$333$	−29.3985	+	6.92575i	−1.61103	+	0.379529i
$334$	−5.23508	−	9.06743i	−0.286451	−	0.496148i
$335$	0.113303	−	0.196246i	0.00619038	−	0.0107221i
$336$	2.00872	+	2.07081i	0.109585	+	0.112972i
$337$			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
$342$	17.2119	+	0.524028i	0.930714	+	0.0283362i
$343$	13.2215	−	13.2215i	0.713891	−	0.713891i
$344$	−1.88417	+	7.03182i	−0.101588	+	0.379130i
$345$	−11.1862	+	2.81561i	−0.602245	+	0.151587i
$346$	6.57400	+	6.57400i	0.353420	+	0.353420i
$347$	−29.8164	+	17.2145i	−1.60063	+	0.924122i	−0.609264	+	0.792967i	$0.708535\pi$
$347$	−29.8164	+	17.2145i	−1.60063	+	0.924122i	−0.991362	+	0.131154i	$0.958132\pi$
$348$	−2.65648	−	0.0404297i	−0.142402	−	0.00216726i
$349$	−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
$351$	−14.1904	−	12.2324i	−0.757430	−	0.652916i
$352$	−3.80812			−0.202974
$353$	9.59155	−	2.57005i	0.510507	−	0.136790i	0.00563473	−	0.999984i	$-0.498206\pi$
$353$	9.59155	−	2.57005i	0.510507	−	0.136790i	0.504872	+	0.863194i	$0.331540\pi$
$354$	−6.66280	−	0.101403i	−0.354124	−	0.00538952i
$355$	−13.2388	+	7.64342i	−0.702642	+	0.405670i
$356$	−6.33783	−	6.33783i	−0.335905	−	0.335905i
$357$	3.69853	−	0.930933i	0.195747	−	0.0492702i
$358$	−4.00452	+	14.9451i	−0.211645	+	0.789871i
$359$	−11.6427	+	11.6427i	−0.614477	+	0.614477i	−0.944109	−	0.329632i	$-0.893075\pi$
$359$	−11.6427	+	11.6427i	−0.614477	+	0.614477i	0.329632	+	0.944109i	$0.393075\pi$
$360$	2.99861	+	0.0912946i	0.158041	+	0.00481165i
$361$	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
$366$	−5.39895	−	5.56582i	−0.282207	−	0.290930i
$367$	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
$369$	−13.1022	+	3.08664i	−0.682074	+	0.160684i
$370$	−9.72471	−	2.60573i	−0.505564	−	0.135465i
$371$	−0.486624	−	0.130390i	−0.0252642	−	0.00676954i
$372$	−3.91774	+	13.7789i	−0.203125	+	0.714405i
$373$	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
$375$	1.24324	−	1.20597i	0.0642007	−	0.0622758i
$376$			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
$381$	6.15264	+	3.67819i	0.315209	+	0.188439i
$382$	5.45996	−	5.45996i	0.279356	−	0.279356i
$383$	−1.94574	+	7.26162i	−0.0994229	+	0.371051i	−0.997653	−	0.0684745i	$-0.978187\pi$
$383$	−1.94574	+	7.26162i	−0.0994229	+	0.371051i	0.898230	+	0.439526i	$0.144853\pi$
$384$	0.422776	+	1.67966i	0.0215747	+	0.0857148i
$385$	−4.48519	−	4.48519i	−0.228586	−	0.228586i
$386$	−5.53616	+	3.19630i	−0.281783	+	0.162688i
$387$	−19.2372	+	10.3392i	−0.977883	+	0.525570i
$388$	−1.63135	+	0.437120i	−0.0828195	+	0.0221914i
$389$	−3.37539			−0.171139			−0.0855694	−	0.996332i	$-0.527271\pi$
$389$	−3.37539			−0.171139			−0.0855694	+	0.996332i	$0.527271\pi$
$390$	−2.23618	−	5.83091i	−0.113233	−	0.295260i
$391$	−8.80409			−0.445242
$392$	4.08161	−	1.09366i	0.206153	−	0.0552384i
$393$	−0.110374	+	7.25224i	−0.00556763	+	0.365827i
$394$	−12.7145	+	7.34069i	−0.640545	+	0.369819i
$395$	−5.67299	−	5.67299i	−0.285439	−	0.285439i
$396$	−7.82867	−	8.32034i	−0.393406	−	0.418113i
$397$	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
$399$	−8.49717	+	14.2135i	−0.425391	+	0.711567i
$400$	0.866025	+	0.500000i	0.0433013	+	0.0250000i
$401$	−8.32881	−	31.0836i	−0.415921	−	1.55224i	−0.782984	−	0.622042i	$-0.786303\pi$
$401$	−8.32881	−	31.0836i	−0.415921	−	1.55224i	0.367062	−	0.930196i	$-0.380364\pi$
$402$	0.191051	+	0.342855i	0.00952873	+	0.0171000i
$403$	29.6069	−	3.55869i	1.47483	−	0.177271i
$404$			7.21425i			0.358923i
$405$	5.96502	+	6.73932i	0.296404	+	0.334880i
$406$	1.27747	−	2.21264i	0.0633998	−	0.109812i
$407$	19.1696	+	33.2028i	0.950203	+	1.64580i
$408$	2.20243	+	0.626213i	0.109037	+	0.0310022i
$409$	−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
$411$	−20.0184	−	5.69179i	−0.987435	−	0.280755i
$412$	−7.06001	−	12.2283i	−0.347822	−	0.602445i
$413$	3.20407	−	5.54960i	0.157662	−	0.273078i
$414$	5.75594	−	19.1323i	0.282889	−	0.940303i
$415$			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	0.166884	−	0.985977i	$-0.446629\pi$
$419$	−12.3545	−	7.13285i	−0.603555	−	0.348463i	−0.770439	+	0.637514i	$0.779963\pi$
$420$	−1.48035	+	2.47624i	−0.0722338	+	0.120828i
$421$	−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
$423$	−28.3870	+	26.7095i	−1.38022	+	1.29866i
$424$	−0.213870	−	0.213870i	−0.0103864	−	0.0103864i
$425$	1.14486	−	0.660987i	0.0555340	−	0.0320626i
$426$	0.402923	−	26.4745i	0.0195217	−	1.28269i
$427$	7.20282	−	1.92999i	0.348569	−	0.0933988i
$428$	−5.89160			−0.284781
$429$	−9.67972	+	21.7226i	−0.467341	+	1.04878i
$430$	−7.27987			−0.351067
$431$	−26.6309	+	7.13573i	−1.28277	+	0.343716i	−0.834909	−	0.550389i	$-0.814480\pi$
$431$	−26.6309	+	7.13573i	−1.28277	+	0.343716i	−0.447858	+	0.894105i	$0.647813\pi$
$432$	−2.80074	+	4.37674i	−0.134751	+	0.210576i
$433$	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
$435$	−0.648495	−	2.57643i	−0.0310930	−	0.123530i
$436$	2.70928	−	10.1112i	0.129751	−	0.484236i
$437$	27.0306	−	27.0306i	1.29305	−	1.29305i
$438$	1.43434	+	0.857481i	0.0685354	+	0.0409720i
$439$	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	$-0.762815\pi$
$443$		−	28.5436i		−	1.35615i	0.734994	−	0.678074i	$-0.237185\pi$
$444$	12.5166	−	12.1414i	0.594014	−	0.576204i
$445$	4.48153	−	7.76223i	0.212445	−	0.367965i
$446$	0.789946	+	1.36823i	0.0374050	+	0.0647874i
$447$	−0.185328	+	0.651810i	−0.00876571	+	0.0308296i
$448$	−1.60890	−	0.431103i	−0.0760133	−	0.0203677i
$449$	−28.8338	−	7.72600i	−1.36075	−	0.364612i	−0.496659	−	0.867946i	$-0.665440\pi$
$449$	−28.8338	−	7.72600i	−1.36075	−	0.364612i	−0.864092	+	0.503333i	$0.832107\pi$
$450$	0.687914	+	2.92006i	0.0324286	+	0.137653i
$451$	8.54344	+	14.7977i	0.402295	+	0.696795i
$452$	−5.71512	+	9.89888i	−0.268817	+	0.465604i
$453$	23.2592	+	23.9781i	1.09281	+	1.12659i
$454$			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
$459$	3.15951	+	6.09943i	0.147473	+	0.284697i
$460$	4.70919	−	4.70919i	0.219567	−	0.219567i
$461$	−2.90972	+	10.8592i	−0.135519	+	0.505764i	0.864476	+	0.502674i	$0.167650\pi$
$461$	−2.90972	+	10.8592i	−0.135519	+	0.505764i	−0.999995	+	0.00309039i	$0.999016\pi$
$462$	10.6541	−	2.68168i	0.495674	−	0.124763i
$463$	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
$465$	−14.3234	−	0.217992i	−0.664233	−	0.0101092i
$466$	20.2001	−	5.41260i	0.935752	−	0.250734i
$467$	−13.7987			−0.638528			−0.319264	−	0.947666i	$-0.603436\pi$
$467$	−13.7987			−0.638528			−0.319264	+	0.947666i	$0.603436\pi$
$468$	10.6559	+	1.85782i	0.492570	+	0.0858779i
$469$	−0.377446			−0.0174288
$470$	−12.5497	+	3.36268i	−0.578874	+	0.155109i
$471$	−27.5669	−	0.419548i	−1.27021	−	0.0193318i
$472$	3.33179	−	1.92361i	0.153358	−	0.0885412i
$473$	19.6029	+	19.6029i	0.901341	+	0.901341i
$474$	13.4756	−	3.39186i	0.618955	−	0.155793i
$475$	−1.48561	+	5.54438i	−0.0681646	+	0.254394i
$476$	−1.55701	+	1.55701i	−0.0713657	+	0.0713657i
$477$	0.0276128	−	0.906953i	0.00126430	−	0.0415265i
$478$	−2.86258	−	1.65271i	−0.130931	−	0.0755932i
$479$	8.00989	+	29.8933i	0.365981	+	1.36586i	0.866086	+	0.499895i	$0.166628\pi$
$479$	8.00989	+	29.8933i	0.365981	+	1.36586i	−0.500105	+	0.865965i	$0.666705\pi$
$480$	−1.51301	+	0.843099i	−0.0690589	+	0.0384820i
$481$	−33.3779	−	14.2686i	−1.52190	−	0.650592i
$482$		−	10.2894i		−	0.468669i
$483$	13.3777	+	13.7912i	0.608706	+	0.627520i
$484$	−1.75090	+	3.03264i	−0.0795863	+	0.137847i
$485$	−0.844451	−	1.46263i	−0.0383445	−	0.0664147i
$486$	−15.3204	+	2.87830i	−0.694949	+	0.130562i
$487$	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
$489$	6.32194	−	22.2347i	0.285888	−	1.00549i
$490$	2.11280	+	3.65947i	0.0954465	+	0.165318i
$491$	3.99952	−	6.92737i	0.180496	−	0.312628i	−0.761554	−	0.648102i	$-0.775563\pi$
$491$	3.99952	−	6.92737i	0.180496	−	0.312628i	0.942049	+	0.335474i	$0.108896\pi$
$492$	5.57837	−	5.41112i	0.251492	−	0.243952i
$493$		−	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
$498$	−18.5215	−	11.0726i	−0.829968	−	0.496174i
$499$	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
$501$	4.42654	+	17.5863i	0.197763	+	0.785699i
$502$	16.2323	+	16.2323i	0.724485	+	0.724485i
$503$	21.5869	−	12.4632i	0.962513	−	0.555707i	0.0655671	−	0.997848i	$-0.479114\pi$
$503$	21.5869	−	12.4632i	0.962513	−	0.555707i	0.896945	+	0.442141i	$0.145781\pi$
$504$	−2.36563	−	4.40152i	−0.105374	−	0.196059i
$505$	−6.96843	+	1.86719i	−0.310091	+	0.0830887i
$506$	−25.3613			−1.12745
$507$	−5.00231	−	21.9540i	−0.222160	−	0.975010i
$508$	−4.13860			−0.183621
$509$	−5.42645	+	1.45401i	−0.240523	+	0.0644479i	−0.377067	−	0.926186i	$-0.623067\pi$
$509$	−5.42645	+	1.45401i	−0.240523	+	0.0644479i	0.136544	+	0.990634i	$0.456401\pi$
$510$	−0.0348440	+	2.28946i	−0.00154292	+	0.101379i
$511$	−1.39174	+	0.803524i	−0.0615672	+	0.0355458i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−28.4271	−	9.02624i	−1.25509	−	0.398518i
$514$	1.17920	−	4.40083i	0.0520123	−	0.194112i
$515$	9.98436	−	9.98436i	0.439963	−	0.439963i
$516$	6.47000	−	10.8226i	0.284826	−	0.476439i
$517$	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	$-0.909122\pi$
$521$		−	12.8570i		−	0.563275i	0.959521	−	0.281637i	$-0.0908775\pi$
$522$	4.40659	+	1.32572i	0.192871	+	0.0580251i
$523$	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
$525$	−2.77501	−	0.789012i	−0.121111	−	0.0344353i
$526$	13.7933	+	3.69591i	0.601418	+	0.161150i
$527$	−10.5610	−	2.82980i	−0.460042	−	0.123268i
$528$	6.34440	+	1.80389i	0.276104	+	0.0785042i
$529$	−10.6765	−	18.4922i	−0.464195	−	0.804010i
$530$	0.151229	−	0.261936i	0.00656896	−	0.0113778i
$531$	11.0523	+	3.32508i	0.479629	+	0.144296i
$532$		−	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
$537$	13.7510	−	23.0018i	0.593399	−	0.992601i
$538$	12.4285	−	12.4285i	0.535831	−	0.535831i
$539$	4.16481	−	15.5433i	0.179391	−	0.669496i
$540$	−4.95249	−	1.57253i	−0.213121	−	0.0676707i
$541$	−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
$543$	0.603533	−	39.6558i	0.0259001	−	1.70179i
$544$	−1.27693	+	0.342152i	−0.0547479	+	0.0146696i
$545$	10.4678			0.448393
$546$	−6.54873	+	8.08182i	−0.280260	+	0.345870i
$547$	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
$549$	6.35823	+	11.8302i	0.271363	+	0.504901i
$550$	3.29793	−	1.90406i	0.140624	−	0.0811894i
$551$	6.22573	+	6.22573i	0.265225	+	0.265225i
$552$	2.81561	+	11.1862i	0.119840	+	0.476117i
$553$	−3.45866	+	12.9079i	−0.147077	+	0.548900i
$554$	10.0410	−	10.0410i	0.426600	−	0.426600i
$555$	14.9672	+	8.94774i	0.635323	+	0.379810i
$556$	−3.25411	−	1.87876i	−0.138005	−	0.0796772i
$557$	−6.52205	−	24.3406i	−0.276348	−	1.03135i	−0.954933	−	0.296823i	$-0.904073\pi$
$557$	−6.52205	−	24.3406i	−0.276348	−	1.03135i	0.678584	−	0.734523i	$-0.262594\pi$
$558$	13.0540	−	21.1001i	0.552621	−	0.893240i
$559$	−25.9831	−	3.71926i	−1.09897	−	0.157308i
$560$		−	1.66565i		−	0.0703867i
$561$	6.25877	−	6.07112i	0.264245	−	0.256323i
$562$	3.12290	−	5.40903i	0.131732	−	0.228166i
$563$	3.12854	+	5.41879i	0.131852	+	0.228375i	0.924391	−	0.381447i	$-0.124574\pi$
$563$	3.12854	+	5.41879i	0.131852	+	0.228375i	−0.792538	+	0.609822i	$0.791241\pi$
$564$	6.15443	−	21.6455i	0.259148	−	0.911442i
$565$	−11.0408	−	2.95836i	−0.464489	−	0.124459i
$566$	16.3514	+	4.38134i	0.687300	+	0.184162i
$567$	4.75364	−	14.2172i	0.199634	−	0.597068i
$568$	7.64342	+	13.2388i	0.320711	+	0.555487i
$569$	9.18102	−	15.9020i	0.384889	−	0.666647i	−0.606865	−	0.794805i	$-0.707573\pi$
$569$	9.18102	−	15.9020i	0.384889	−	0.666647i	0.991754	+	0.128158i	$0.0409065\pi$
$570$	−6.92220	−	7.13616i	−0.289939	−	0.298901i
$571$			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
$576$	0.0912946	−	2.99861i	0.00380394	−	0.124942i
$577$	−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
$579$	10.7374	−	2.70264i	0.446232	−	0.112318i
$580$	1.08463	+	1.08463i	0.0450368	+	0.0450368i
$581$	17.9715	−	10.3758i	0.745582	−	0.430462i
$582$	2.92493	+	0.0445153i	0.121242	+	0.00184522i
$583$	−1.11255	+	0.298107i	−0.0460771	+	0.0123463i
$584$	−0.964815			−0.0399243
$585$	0.963434	+	10.7737i	0.0398331	+	0.445436i
$586$	11.2378			0.464229
$587$	6.45368	−	1.72926i	0.266372	−	0.0713741i	−0.123161	−	0.992387i	$-0.539303\pi$
$587$	6.45368	−	1.72926i	0.266372	−	0.0713741i	0.389533	+	0.921013i	$0.372637\pi$
$588$	−7.31810	−	0.111376i	−0.301793	−	0.00459308i
$589$	41.1127	−	23.7364i	1.69402	−	0.978043i
$590$	2.72039	+	2.72039i	0.111997	+	0.111997i
$591$	24.6597	−	6.20694i	1.01437	−	0.255320i
$592$	−2.60573	+	9.72471i	−0.107095	+	0.399683i
$593$	−26.8093	+	26.8093i	−1.10092	+	1.10092i	−0.106625	+	0.994299i	$0.534004\pi$
$593$	−26.8093	+	26.8093i	−1.10092	+	1.10092i	−0.994299	+	0.106625i	$0.965996\pi$
$594$	9.10140	+	17.5702i	0.373435	+	0.720915i
$595$	−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	$0.176129\pi$
$599$			25.7236i			1.05104i	−0.850781	+	0.525520i	$0.823871\pi$
$600$	−1.20597	−	1.24324i	−0.0492333	−	0.0507551i
$601$	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
$603$	−0.155885	−	0.661702i	−0.00634812	−	0.0269466i
$604$	−18.6296	−	4.99178i	−0.758026	−	0.203113i
$605$	−3.38248	−	0.906332i	−0.137517	−	0.0368476i
$606$	3.41736	−	12.0191i	0.138821	−	0.488241i
$607$	−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
$609$	−3.17641	+	3.08117i	−0.128715	+	0.124855i
$610$			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
$615$	6.67053	+	3.98779i	0.268982	+	0.160803i
$616$	−4.48519	+	4.48519i	−0.180713	+	0.180713i
$617$	6.01064	−	22.4320i	0.241979	−	0.903078i	−0.732899	−	0.680338i	$-0.761833\pi$
$617$	6.01064	−	22.4320i	0.241979	−	0.903078i	0.974878	−	0.222740i	$-0.0715003\pi$
$618$	5.96961	+	23.7168i	0.240133	+	0.954031i
$619$	−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
$621$	−18.6524	+	29.1482i	−0.748495	+	1.16968i
$622$	−8.53272	+	2.28634i	−0.342131	+	0.0916737i
$623$	−14.9293			−0.598132
$624$	−5.83091	+	2.23618i	−0.233423	+	0.0895187i
$625$	−1.00000			−0.0400000
$626$	−19.7595	+	5.29453i	−0.789747	+	0.211612i
$627$	−0.576136	+	37.8556i	−0.0230087	+	1.51181i
$628$	13.7850	−	7.95879i	0.550082	−	0.317590i
$629$	9.41111	+	9.41111i	0.375245	+	0.375245i
$630$	3.63928	−	3.42422i	0.144992	−	0.136424i
$631$	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
$633$	−6.10856	+	10.2180i	−0.242794	+	0.406130i
$634$	−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
$639$	−13.2121	+	43.9161i	−0.522664	+	1.73729i
$640$	0.500000	−	0.866025i	0.0197642	−	0.0342327i
$641$	−14.2640	−	24.7060i	−0.563394	−	0.975828i	−0.997197	−	0.0748198i	$-0.976162\pi$
$641$	−14.2640	−	24.7060i	−0.563394	−	0.975828i	0.433803	−	0.901008i	$-0.357171\pi$
$642$	9.81551	+	2.79082i	0.387387	+	0.110145i
$643$	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
$645$	12.1284	+	3.44844i	0.477555	+	0.135782i
$646$	−3.79404	−	6.57147i	−0.149275	−	0.258551i
$647$	9.53414	−	16.5136i	0.374826	−	0.649217i	−0.615475	−	0.788156i	$-0.711036\pi$
$647$	9.53414	−	16.5136i	0.374826	−	0.649217i	0.990301	+	0.138939i	$0.0443692\pi$
$648$	6.73932	−	5.96502i	0.264746	−	0.234328i
$649$		−	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	0.941300	−	0.337571i	$-0.109605\pi$
$653$	28.6102	+	16.5181i	1.11961	+	0.646404i	0.178305	+	0.983975i	$0.442939\pi$
$654$	−9.30331	+	15.5620i	−0.363788	+	0.608522i
$655$	2.96106	−	2.96106i	0.115698	−	0.115698i
$656$	−1.16131	+	4.33407i	−0.0453415	+	0.169217i
$657$	−1.98345	−	2.10802i	−0.0773818	−	0.0822416i
$658$	15.3024	+	15.3024i	0.596549	+	0.596549i
$659$	16.8251	−	9.71399i	0.655414	−	0.378403i	−0.135113	−	0.990830i	$-0.543140\pi$
$659$	16.8251	−	9.71399i	0.655414	−	0.378403i	0.790527	+	0.612427i	$0.209807\pi$
$660$	−0.100373	+	6.59510i	−0.00390700	+	0.256714i
$661$	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
$663$	−1.29404	+	8.15368i	−0.0502563	+	0.316663i
$664$	12.4586			0.483486
$665$	9.23502	−	2.47452i	0.358119	−	0.0959576i
$666$	−26.6043	+	14.2987i	−1.03089	+	0.554062i
$667$	8.84684	−	5.10773i	0.342551	−	0.197772i
$668$	−7.40353	−	7.40353i	−0.286451	−	0.286451i
$669$	−0.667941	−	2.65368i	−0.0258241	−	0.102597i
$670$	0.0586497	−	0.218884i	0.00226584	−	0.00845622i
$671$	12.0551	−	12.0551i	0.465381	−	0.465381i
$672$	2.47624	+	1.48035i	0.0955231	+	0.0571058i
$673$	−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	$0.164332\pi$
$677$			25.6880i			0.987270i	−0.869669	+	0.493635i	$0.835668\pi$
$678$	14.2105	−	13.7845i	0.545753	−	0.529390i
$679$	−1.40656	+	2.43624i	−0.0539789	+	0.0934943i
$680$	−0.660987	−	1.14486i	−0.0253477	−	0.0439035i
$681$	3.16470	−	11.1305i	0.121272	−	0.426521i
$682$	−30.4222	−	8.15161i	−1.16493	−	0.312141i
$683$	−46.1988	−	12.3789i	−1.76775	−	0.473667i	−0.779485	−	0.626421i	$-0.784519\pi$
$683$	−46.1988	−	12.3789i	−1.76775	−	0.473667i	−0.988264	+	0.152754i	$0.951186\pi$
$684$	16.7611	−	3.94860i	0.640875	−	0.150978i
$685$	6.00786	+	10.4059i	0.229549	+	0.397590i
$686$	9.34898	−	16.1929i	0.356946	−	0.618248i
$687$	−27.4168	−	28.2642i	−1.04602	−	1.07835i
$688$			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
$693$	−19.0202	−	0.579083i	−0.722519	−	0.0219975i
$694$	−24.3450	+	24.3450i	−0.924122	+	0.924122i
$695$	0.972518	−	3.62949i	0.0368897	−	0.137674i
$696$	−2.57643	+	0.648495i	−0.0976592	+	0.0245812i
$697$	4.19430	+	4.19430i	0.158871	+	0.158871i
$698$	−12.5831	+	7.26485i	−0.476277	+	0.274979i
$699$	−36.2177	−	0.551207i	−1.36988	−	0.0208486i
$700$	1.60890	−	0.431103i	0.0608106	−	0.0162942i
$701$	33.1881			1.25350			0.626748	−	0.779222i	$-0.284386\pi$
$701$	33.1881			1.25350			0.626748	+	0.779222i	$0.284386\pi$
$702$	−16.8729	−	8.14282i	−0.636826	−	0.307331i
$703$	−57.7886			−2.17954
$704$	−3.67836	+	0.985615i	−0.138634	+	0.0371467i
$705$	22.5009	+	0.342447i	0.847432	+	0.0128973i
$706$	8.59955	−	4.96495i	0.323648	−	0.186858i
$707$	8.49692	+	8.49692i	0.319559	+	0.319559i
$708$	−6.46202	+	1.62651i	−0.242857	+	0.0611281i
$709$	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
$711$	−24.0573	−	0.732440i	−0.902219	−	0.0274686i
$712$	−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
$717$	3.98622	+	4.10943i	0.148868	+	0.153470i
$718$	−8.23262	+	14.2593i	−0.307239	+	0.532153i
$719$	3.79520	+	6.57348i	0.141537	+	0.245150i	0.928076	−	0.372392i	$-0.121462\pi$
$719$	3.79520	+	6.57348i	0.141537	+	0.245150i	−0.786539	+	0.617541i	$0.788129\pi$
$720$	2.92006	−	0.687914i	0.108824	−	0.0256370i
$721$	−22.7177	−	6.08718i	−0.846050	−	0.226699i
$722$	13.4719	+	3.60980i	0.501374	+	0.134343i
$723$	−4.87404	+	17.1423i	−0.181267	+	0.637529i
$724$	11.4490	+	19.8302i	0.425498	+	0.736984i
$725$	−0.766948	+	1.32839i	−0.0284838	+	0.0493353i
$726$	4.35358	−	4.22305i	0.161576	−	0.156732i
$727$			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
$732$	−6.65552	−	3.97882i	−0.245995	−	0.147061i
$733$	−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
$735$	−1.78648	−	7.09757i	−0.0658954	−	0.261798i
$736$	−4.70919	−	4.70919i	−0.173583	−	0.173583i
$737$	−0.747328	+	0.431470i	−0.0275282	+	0.0158934i
$738$	−11.8569	+	6.37257i	−0.436458	+	0.234577i
$739$	−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
$741$	−21.0607	−	29.0067i	−0.773684	−	1.06559i
$742$	−0.503790			−0.0184947
$743$	27.9882	−	7.49941i	1.02679	−	0.275127i	0.294159	−	0.955756i	$-0.404960\pi$
$743$	27.9882	−	7.49941i	1.02679	−	0.275127i	0.732627	+	0.680630i	$0.238294\pi$
$744$	−0.217992	+	14.3234i	−0.00799199	+	0.525122i
$745$	0.338823	−	0.195619i	0.0124135	−	0.00716694i
$746$	25.8663	+	25.8663i	0.947031	+	0.947031i
$747$	25.6121	+	27.2206i	0.937098	+	0.995951i
$748$	−1.30296	+	4.86270i	−0.0476408	+	0.177798i
$749$	−6.93910	+	6.93910i	−0.253549	+	0.253549i
$750$	0.888751	−	1.48665i	0.0324526	−	0.0542847i
$751$	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
$756$	1.85620	+	8.45360i	0.0675094	+	0.307455i
$757$	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
$759$	42.2524	+	12.0136i	1.53367	+	0.436064i
$760$	5.54438	+	1.48561i	0.201116	+	0.0538888i
$761$	33.5908	+	9.00062i	1.21766	+	0.326272i	0.809765	−	0.586755i	$-0.199595\pi$
$761$	33.5908	+	9.00062i	1.21766	+	0.326272i	0.407900	+	0.913027i	$0.366261\pi$
$762$	6.89498	+	1.96044i	0.249779	+	0.0710191i
$763$	−8.71790	−	15.0998i	−0.315609	−	0.546651i
$764$	3.86078	−	6.68706i	0.139678	−	0.241929i
$765$	1.14256	−	3.79778i	0.0413093	−	0.137309i
$766$			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
$771$	−4.04922	+	6.77328i	−0.145829	+	0.243934i
$772$	−4.52026	+	4.52026i	−0.162688	+	0.162688i
$773$	−9.35460	+	34.9119i	−0.336462	+	1.25569i	0.565814	+	0.824533i	$0.308562\pi$
$773$	−9.35460	+	34.9119i	−0.336462	+	1.25569i	−0.902276	+	0.431159i	$0.858105\pi$
$774$	−15.9057	+	14.9658i	−0.571720	+	0.537936i
$775$	5.84819	+	5.84819i	0.210073	+	0.210073i
$776$	−1.46263	+	0.844451i	−0.0525054	+	0.0303140i
$777$	0.442000	−	29.0421i	0.0158567	−	1.04188i
$778$	−3.26037	+	0.873614i	−0.116890	+	0.0313206i
$779$	−25.7550			−0.922768
$780$	−3.66913	−	5.05346i	−0.131376	−	0.180943i
$781$	58.2141			2.08307
$782$	−8.50410	+	2.27867i	−0.304106	+	0.0814849i
$783$	−6.71347	−	4.29605i	−0.239920	−	0.153528i
$784$	3.65947	−	2.11280i	0.130695	−	0.0754571i
$785$	11.2554	+	11.2554i	0.401723	+	0.401723i
$786$	1.77040	+	7.03369i	0.0631482	+	0.250883i
$787$	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
$789$	−21.2292	−	12.6913i	−0.755780	−	0.451822i
$790$	−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
$795$	−0.376028	+	0.364754i	−0.0133363	+	0.0129365i
$796$	−1.45610	+	2.52204i	−0.0516100	+	0.0893912i
$797$	−16.8835	−	29.2431i	−0.598045	−	1.03584i	−0.993109	−	0.117191i	$-0.962611\pi$
$797$	−16.8835	−	29.2431i	−0.598045	−	1.03584i	0.395065	−	0.918653i	$-0.370722\pi$
$798$	−4.52890	+	15.9284i	−0.160321	+	0.563861i
$799$	16.5904	+	4.44537i	0.586924	+	0.157266i
$800$	0.965926	+	0.258819i	0.0341506	+	0.00915064i
$801$	−6.16581	−	26.1727i	−0.217858	−	0.924766i
$802$	−16.0900	−	27.8688i	−0.568159	−	0.984080i
$803$	−1.83707	+	3.18189i	−0.0648287	+	0.112287i
$804$	0.273278	+	0.281725i	0.00963777	+	0.00993566i
$805$		−	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	0.370475	−	0.928842i	$-0.379195\pi$
$809$	−7.07341	−	4.08384i	−0.248688	−	0.143580i	−0.619163	+	0.785262i	$0.712528\pi$
$810$	7.50604	+	4.96583i	0.263735	+	0.174481i
$811$	−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
$813$	48.2761	−	12.1513i	1.69312	−	0.426164i
$814$	27.1100	+	27.1100i	0.950203	+	0.950203i
$815$	−11.5580	+	6.67301i	−0.404859	+	0.233745i
$816$	2.28946	+	0.0348440i	0.0801472	+	0.00121978i
$817$	−40.3624	+	10.8151i	−1.41210	+	0.378371i
$818$	−2.74748			−0.0960635
$819$	14.7386	−	10.3623i	0.515009	−	0.362090i
$820$	−4.48696			−0.156691
$821$	40.7978	−	10.9318i	1.42385	−	0.381521i	0.537005	−	0.843579i	$-0.319556\pi$
$821$	40.7978	−	10.9318i	1.42385	−	0.381521i	0.886850	+	0.462058i	$0.152889\pi$
$822$	−20.8094	−	0.316705i	−0.725813	−	0.0110464i
$823$	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
$825$	−6.39635	+	1.60998i	−0.222692	+	0.0560525i
$826$	1.65855	−	6.18978i	0.0577082	−	0.215370i
$827$	35.9420	−	35.9420i	1.24982	−	1.24982i	0.294028	−	0.955797i	$-0.405004\pi$
$827$	35.9420	−	35.9420i	1.24982	−	1.24982i	0.955797	−	0.294028i	$-0.0949959\pi$
$828$	0.608004	−	19.9702i	0.0211296	−	0.694011i
$829$	−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
$834$	4.53144	+	4.67150i	0.156911	+	0.161761i
$835$	5.23508	−	9.06743i	0.181168	−	0.313791i
$836$	−10.9292	−	18.9300i	−0.377996	−	0.654708i
$837$	−31.7433	+	28.9695i	−1.09721	+	1.00133i
$838$	−13.7796	−	3.69224i	−0.476009	−	0.127546i
$839$	−30.3149	−	8.12286i	−1.04659	−	0.280432i	−0.305746	−	0.952113i	$-0.598906\pi$
$839$	−30.3149	−	8.12286i	−1.04659	−	0.280432i	−0.740841	+	0.671681i	$0.765573\pi$
$840$	−0.789012	+	2.77501i	−0.0272235	+	0.0957469i
$841$	−13.3236	−	23.0771i	−0.459434	−	0.795763i
$842$	−16.4580	+	28.5061i	−0.567180	+	0.982385i
$843$	−7.76504	+	7.53223i	−0.267442	+	0.259424i
$844$		−	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
$849$	−25.1663	−	15.0450i	−0.863704	−	0.516342i
$850$	0.934777	−	0.934777i	0.0320626	−	0.0320626i
$851$	−17.3536	+	64.7647i	−0.594875	+	2.22010i
$852$	−6.46291	−	25.6767i	−0.221416	−	0.879669i
$853$	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
$855$	8.15214	+	15.1680i	0.278797	+	0.518734i
$856$	−5.69085	+	1.52486i	−0.194509	+	0.0521186i
$857$	28.3530			0.968520			0.484260	−	0.874924i	$-0.339089\pi$
$857$	28.3530			0.968520			0.484260	+	0.874924i	$0.339089\pi$
$858$	−3.72765	+	23.4878i	−0.127260	+	0.801859i
$859$	−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
$861$	0.196989	−	12.9434i	0.00671336	−	0.441109i
$862$	−23.8766	+	13.7852i	−0.813241	+	0.469525i
$863$	16.5706	+	16.5706i	0.564068	+	0.564068i	0.930461	−	0.366392i	$-0.119407\pi$
$863$	16.5706	+	16.5706i	0.564068	+	0.564068i	−0.366392	+	0.930461i	$0.619407\pi$
$864$	−1.57253	+	4.95249i	−0.0534984	+	0.168487i
$865$	−2.40625	+	8.98025i	−0.0818150	+	0.305338i
$866$	5.97890	−	5.97890i	0.203171	−	0.203171i
$867$	−13.5556	+	22.6749i	−0.460372	+	0.770081i
$868$	−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
$873$	−4.85189	−	1.45969i	−0.164212	−	0.0494029i
$874$	19.1135	−	33.1056i	0.646524	−	1.11981i
$875$	0.832827	+	1.44250i	0.0281547	+	0.0487654i
$876$	1.60740	+	0.457028i	0.0543090	+	0.0154416i
$877$	−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
$879$	−18.7224	−	5.32330i	−0.631490	−	0.179550i
$880$	−1.90406	−	3.29793i	−0.0641859	−	0.111173i
$881$	−2.39325	+	4.14523i	−0.0806306	+	0.139656i	−0.903521	−	0.428544i	$-0.859027\pi$
$881$	−2.39325	+	4.14523i	−0.0806306	+	0.139656i	0.822890	+	0.568200i	$0.192360\pi$
$882$	12.1393	+	3.65210i	0.408752	+	0.122973i
$883$		−	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	0.761585	−	0.648066i	$-0.224422\pi$
$887$	17.3077	+	9.99260i	0.581136	+	0.335519i	−0.180449	+	0.983584i	$0.557755\pi$
$888$	8.94774	−	14.9672i	0.300266	−	0.502267i
$889$	−4.87442	+	4.87442i	−0.163483	+	0.163483i
$890$	2.31981	−	8.65764i	0.0777602	−	0.290205i
$891$	−6.84015	−	33.5836i	−0.229154	−	1.12509i
$892$	1.11715	+	1.11715i	0.0374050	+	0.0374050i
$893$	−64.5846	+	37.2879i	−2.16124	+	1.24779i
$894$	−0.0103121	+	0.677567i	−0.000344888	+	0.0226612i
$895$	−14.9451	+	4.00452i	−0.499558	+	0.133856i
$896$	−1.66565			−0.0556456
$897$	−38.8327	+	14.8925i	−1.29659	+	0.497246i
$898$	−29.8510			−0.996139
$899$	12.2540	−	3.28344i	0.408692	−	0.109509i
$900$	1.42024	+	2.64252i	0.0473414	+	0.0880840i
$901$	−0.346273	+	0.199921i	−0.0115360	+	0.00666032i
$902$	12.0823	+	12.0823i	0.402295	+	0.402295i
$903$	−5.12648	−	20.3672i	−0.170599	−	0.677776i
$904$	−2.95836	+	11.0408i	−0.0983937	+	0.367210i
$905$	−16.1913	+	16.1913i	−0.538217	+	0.538217i
$906$	28.6726	+	17.1411i	0.952583	+	0.569476i
$907$	−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	$0.150862\pi$
$911$			27.5510i			0.912806i	−0.889773	+	0.456403i	$0.849138\pi$
$912$	−7.13616	+	6.92220i	−0.236302	+	0.229217i
$913$	23.7219	−	41.0875i	0.785079	−	1.35980i
$914$	−15.9522	−	27.6301i	−0.527653	−	0.913923i
$915$	2.12067	−	7.45854i	0.0701072	−	0.246572i
$916$	21.9597	+	5.88407i	0.725567	+	0.194415i
$917$	−6.73737	−	1.80527i	−0.222487	−	0.0596153i
$918$	4.63050	+	5.07386i	0.152829	+	0.167462i
$919$	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
$921$	34.9362	+	36.0160i	1.15119	+	1.18677i
$922$			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
$927$	1.28908	−	42.3404i	0.0423390	−	1.39064i
$928$	1.08463	−	1.08463i	0.0356047	−	0.0356047i
$929$	6.22343	−	23.2262i	0.204184	−	0.762026i	−0.785512	−	0.618846i	$-0.787601\pi$
$929$	6.22343	−	23.2262i	0.204184	−	0.762026i	0.989697	−	0.143180i	$-0.0457328\pi$
$930$	−13.8918	+	3.49661i	−0.455529	+	0.114658i
$931$	17.1507	+	17.1507i	0.562092	+	0.562092i
$932$	18.1109	−	10.4563i	0.593243	−	0.342509i
$933$	15.2987	+	0.232835i	0.500856	+	0.00762268i
$934$	−13.3285	+	3.57137i	−0.436123	+	0.116859i
$935$	−5.03424			−0.164637
$936$	10.7737	−	0.963434i	0.352148	−	0.0314908i
$937$	−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
$939$	35.4276	+	0.539183i	1.15614	+	0.0175956i
$940$	−11.2517	+	6.49619i	−0.366991	+	0.211882i
$941$	2.48077	+	2.48077i	0.0808706	+	0.0808706i	0.746385	−	0.665514i	$-0.231788\pi$
$941$	2.48077	+	2.48077i	0.0808706	+	0.0808706i	−0.665514	+	0.746385i	$0.731788\pi$
$942$	−26.7361	+	6.72958i	−0.871110	+	0.219261i
$943$	−7.73410	+	28.8640i	−0.251857	+	0.939943i
$944$	2.72039	−	2.72039i	0.0885412	−	0.0885412i
$945$	−7.68513	+	3.98091i	−0.249997	+	0.129499i
$946$	24.0085	+	13.8613i	0.780584	+	0.450671i
$947$	3.58159	+	13.3667i	0.116386	+	0.434359i	0.999387	−	0.0350128i	$-0.0111472\pi$
$947$	3.58159	+	13.3667i	0.116386	+	0.434359i	−0.883001	+	0.469371i	$0.844481\pi$
$948$	12.1386	−	6.76403i	0.394242	−	0.219685i
$949$	−0.415143	−	3.45383i	−0.0134761	−	0.112116i
$950$			5.73996i			0.186229i
$951$	25.2364	+	26.0164i	0.818345	+	0.843640i
$952$	−1.10098	+	1.90695i	−0.0356828	+	0.0618045i
$953$	−23.6090	−	40.8920i	−0.764770	−	1.32462i	−0.940368	−	0.340159i	$-0.889519\pi$
$953$	−23.6090	−	40.8920i	−0.764770	−	1.32462i	0.175598	−	0.984462i	$-0.443814\pi$
$954$	−0.208065	−	0.883196i	−0.00673635	−	0.0285945i
$955$	7.45845	+	1.99848i	0.241350	+	0.0646695i
$956$	−3.19279	−	0.855506i	−0.103262	−	0.0276690i
$957$	−2.76698	+	9.73165i	−0.0894438	+	0.314580i
$958$	15.4739	+	26.8016i	0.499940	+	0.865921i
$959$	10.0070	−	17.3327i	0.323144	−	0.559701i
$960$	−1.24324	+	1.20597i	−0.0401254	+	0.0389224i
$961$		−	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
$966$	16.4913	+	9.85886i	0.530598	+	0.317204i
$967$	−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
$969$	3.20806	+	12.7454i	0.103058	+	0.409441i
$970$	−1.19423	−	1.19423i	−0.0383445	−	0.0383445i
$971$	7.70575	−	4.44892i	0.247289	−	0.142773i	−0.371233	−	0.928540i	$-0.621065\pi$
$971$	7.70575	−	4.44892i	0.247289	−	0.142773i	0.618522	+	0.785767i	$0.287732\pi$
$972$	−14.0534	+	6.74544i	−0.450764	+	0.216360i
$973$	−6.04547	+	1.61988i	−0.193809	+	0.0519309i
$974$	28.8687			0.925014
$975$	3.93163	−	4.85204i	0.125913	−	0.155390i
$976$	4.47687			0.143301
$977$	6.37132	−	1.70719i	0.203837	−	0.0546178i	−0.155456	−	0.987843i	$-0.549685\pi$
$977$	6.37132	−	1.70719i	0.203837	−	0.0546178i	0.359293	+	0.933225i	$0.383018\pi$
$978$	0.351768	−	23.1133i	0.0112483	−	0.739082i
$979$	−29.5595	+	17.0662i	−0.944726	+	0.545438i
$980$	2.98795	+	2.98795i	0.0954465	+	0.0954465i
$981$	22.8711	−	21.5196i	0.730218	−	0.687068i
$982$	2.07030	−	7.72647i	0.0660660	−	0.246562i
$983$	17.6609	−	17.6609i	0.563294	−	0.563294i	−0.366947	−	0.930242i	$-0.619597\pi$
$983$	17.6609	−	17.6609i	0.563294	−	0.563294i	0.930242	+	0.366947i	$0.119597\pi$
$984$	3.98779	−	6.67053i	0.127126	−	0.212649i
$985$	−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
$990$	3.29129	−	10.9400i	0.104604	−	0.347696i
$991$	−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
$993$	46.3420	+	13.1763i	1.47062	+	0.418138i
$994$	24.5950	+	6.59020i	0.780105	+	0.209028i
$995$	−2.81296	−	0.753732i	−0.0891770	−	0.0238949i
$996$	−20.7562	−	5.90156i	−0.657685	−	0.186998i
$997$	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
$999$	51.0964	−	11.2195i	1.61662	−	0.354969i

Twists

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

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

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)

\(f(q)\)	\(=\)	\(q+(0.965926 - 0.258819i) q^{2} +(-1.73185 - 0.0263575i) q^{3} +(0.866025 - 0.500000i) q^{4} +(0.707107 + 0.707107i) q^{5} +(-1.67966 + 0.422776i) q^{6} +(0.431103 - 1.60890i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.99861 + 0.0912946i) q^{9} +O(q^{10})\)	\(q+(0.965926 - 0.258819i) q^{2} +(-1.73185 - 0.0263575i) q^{3} +(0.866025 - 0.500000i) q^{4} +(0.707107 + 0.707107i) q^{5} +(-1.67966 + 0.422776i) q^{6} +(0.431103 - 1.60890i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.99861 + 0.0912946i) 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} +(-1.20597 - 1.24324i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-0.660987 - 1.14486i) q^{17} +(2.92006 - 0.687914i) q^{18} +(5.54438 + 1.48561i) q^{19} +(0.965926 + 0.258819i) q^{20} +(-0.789012 + 2.77501i) q^{21} +(-1.90406 - 3.29793i) q^{22} +(3.32990 - 5.76756i) q^{23} +(-1.24324 + 1.20597i) 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} +(-1.48665 - 0.888751i) q^{30} +(5.84819 - 5.84819i) q^{31} +(0.258819 - 0.965926i) q^{32} +(1.60998 + 6.39635i) q^{33} +(-0.934777 - 0.934777i) q^{34} +(1.44250 - 0.832827i) q^{35} +(2.64252 - 1.42024i) q^{36} +(-9.72471 + 2.60573i) q^{37} +5.73996 q^{38} +(-4.85204 - 3.93163i) q^{39} +1.00000 q^{40} +(-4.33407 + 1.16131i) q^{41} +(-0.0439025 + 2.88466i) q^{42} +(-6.30456 + 3.63994i) q^{43} +(-2.69275 - 2.69275i) q^{44} +(2.05578 + 2.18489i) q^{45} +(1.72368 - 6.43288i) q^{46} +(-9.18700 + 9.18700i) q^{47} +(-0.888751 + 1.48665i) 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} +(-5.07525 + 1.11440i) q^{54} +(1.90406 - 3.29793i) q^{55} +(-0.832827 - 1.44250i) q^{56} +(-9.56288 - 2.71899i) q^{57} +(1.48163 + 0.397002i) q^{58} +(3.71613 + 0.995733i) q^{59} +(-1.66602 - 0.473695i) q^{60} +(2.23843 + 3.87708i) q^{61} +(4.13529 - 7.16254i) q^{62} +(1.43959 - 4.78510i) 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} +(-5.91891 + 9.90078i) q^{69} +(1.17780 - 1.17780i) q^{70} +(-3.95652 + 14.7659i) q^{71} +(2.18489 - 2.05578i) q^{72} +(-0.682227 - 0.682227i) q^{73} +(-8.71894 + 5.03388i) q^{74} +(0.0263575 - 1.73185i) q^{75} +(5.54438 - 1.48561i) q^{76} -6.34302 q^{77} +(-5.70429 - 2.54186i) q^{78} -8.02282 q^{79} +(0.965926 - 0.258819i) q^{80} +(8.98333 + 0.547514i) q^{81} +(-3.88582 + 2.24348i) q^{82} +(8.80953 + 8.80953i) q^{83} +(0.704199 + 2.79773i) q^{84} +(0.342152 - 1.27693i) q^{85} +(-5.14765 + 5.14765i) q^{86} +(-2.28036 - 1.36325i) 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} +(-10.2823 + 9.97404i) q^{93} +(-6.49619 + 11.2517i) q^{94} +(2.86998 + 4.97095i) q^{95} +(-0.473695 + 1.66602i) q^{96} +(-1.63135 - 0.437120i) q^{97} +(4.08161 + 1.09366i) q^{98} +(-2.61966 - 11.1200i) 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

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more