LMFDB - Embedded newform 370.2.r.c.23.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(23,370)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([9, 5]))

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

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

chi := DirichletCharacter("370.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.r (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:	$2.95446487479$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			23.1
Root			$0.965926 - 0.258819i$ of defining polynomial
Character	$\chi$	$=$	370.23
Dual form			370.2.r.c.177.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.900100 + 0.241181i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-2.22474 + 0.224745i) q^{5} +(-0.658919 - 0.658919i) q^{6} +(-0.0999004 - 0.0267682i) q^{7} -1.00000i q^{8} +(-1.84607 - 1.06583i) q^{9} +(2.03906 + 0.917738i) q^{10} -5.56048i q^{11} +(0.241181 + 0.900100i) q^{12} +(1.48735 - 0.858719i) q^{13} +(0.0731322 + 0.0731322i) q^{14} +(-2.05670 - 0.334273i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.57313 - 6.18885i) q^{17} +(1.06583 + 1.84607i) q^{18} +(1.98004 + 0.530550i) q^{19} +(-1.30701 - 1.81431i) q^{20} +(-0.0834643 - 0.0481882i) q^{21} +(-2.78024 + 4.81552i) q^{22} -3.96713i q^{23} +(0.241181 - 0.900100i) q^{24} +(4.89898 - 1.00000i) q^{25} -1.71744 q^{26} +(-3.38134 - 3.38134i) q^{27} +(-0.0267682 - 0.0999004i) q^{28} +(5.95680 + 5.95680i) q^{29} +(1.61401 + 1.31784i) q^{30} +(-5.87832 + 5.87832i) q^{31} +(0.866025 - 0.500000i) q^{32} +(1.34108 - 5.00498i) q^{33} +(-6.18885 + 3.57313i) q^{34} +(0.228269 + 0.0371004i) q^{35} -2.13165i q^{36} +(-2.05197 - 5.72620i) q^{37} +(-1.44949 - 1.44949i) q^{38} +(1.54587 - 0.414214i) q^{39} +(0.224745 + 2.22474i) q^{40} +(-8.14893 + 4.70478i) q^{41} +(0.0481882 + 0.0834643i) q^{42} +1.18519i q^{43} +(4.81552 - 2.78024i) q^{44} +(4.34656 + 1.95630i) q^{45} +(-1.98356 + 3.43563i) q^{46} +(4.09878 - 4.09878i) q^{47} +(-0.658919 + 0.658919i) q^{48} +(-6.05291 - 3.49465i) q^{49} +(-4.74264 - 1.58346i) q^{50} +(4.70881 - 4.70881i) q^{51} +(1.48735 + 0.858719i) q^{52} +(-3.44949 + 0.924288i) q^{53} +(1.23766 + 4.61900i) q^{54} +(1.24969 + 12.3706i) q^{55} +(-0.0267682 + 0.0999004i) q^{56} +(1.65427 + 0.955096i) q^{57} +(-2.18034 - 8.13713i) q^{58} +(-1.94646 - 7.26430i) q^{59} +(-0.738859 - 1.94829i) q^{60} +(-6.44364 - 1.72657i) q^{61} +(8.02993 - 2.15161i) q^{62} +(0.155892 + 0.155892i) q^{63} -1.00000 q^{64} +(-3.11597 + 2.24471i) q^{65} +(-3.66390 + 3.66390i) q^{66} +(-0.154193 + 0.575454i) q^{67} +7.14626 q^{68} +(0.956796 - 3.57081i) q^{69} +(-0.179137 - 0.146264i) q^{70} +(3.42272 + 5.92833i) q^{71} +(-1.06583 + 1.84607i) q^{72} +(-2.83548 + 2.83548i) q^{73} +(-1.08604 + 5.98502i) q^{74} +(4.65075 + 0.281441i) q^{75} +(0.530550 + 1.98004i) q^{76} +(-0.148844 + 0.555494i) q^{77} +(-1.54587 - 0.414214i) q^{78} +(12.0349 + 3.22474i) q^{79} +(0.917738 - 2.03906i) q^{80} +(0.969450 + 1.67914i) q^{81} +9.40957 q^{82} +(-6.98784 + 1.87239i) q^{83} -0.0963763i q^{84} +(-6.55840 + 14.5716i) q^{85} +(0.592594 - 1.02640i) q^{86} +(3.92504 + 6.79837i) q^{87} -5.56048 q^{88} +(0.962402 - 0.257875i) q^{89} +(-2.78609 - 3.86749i) q^{90} +(-0.171573 + 0.0459728i) q^{91} +(3.43563 - 1.98356i) q^{92} +(-6.70881 + 3.87333i) q^{93} +(-5.59904 + 1.50026i) q^{94} +(-4.52432 - 0.735335i) q^{95} +(0.900100 - 0.241181i) q^{96} +16.0652 q^{97} +(3.49465 + 6.05291i) q^{98} +(-5.92650 + 10.2650i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{3} + 4 q^{4} - 8 q^{5} - 4 q^{6} + 12 q^{9} - 4 q^{10} + 4 q^{12} - 12 q^{13} - 12 q^{14} + 8 q^{15} - 4 q^{16} + 16 q^{17} - 4 q^{19} - 4 q^{20} + 12 q^{21} - 4 q^{22} + 4 q^{24} - 8 q^{26}+ \cdots - 4 q^{99}+O(q^{100}) $ 8 * q + 8 * q^3 + 4 * q^4 - 8 * q^5 - 4 * q^6 + 12 * q^9 - 4 * q^10 + 4 * q^12 - 12 * q^13 - 12 * q^14 + 8 * q^15 - 4 * q^16 + 16 * q^17 - 4 * q^19 - 4 * q^20 + 12 * q^21 - 4 * q^22 + 4 * q^24 - 8 * q^26 + 8 * q^27 - 12 * q^28 + 24 * q^29 - 8 * q^31 + 12 * q^33 - 12 * q^34 + 8 * q^38 - 16 * q^39 - 8 * q^40 + 12 * q^41 - 4 * q^42 + 12 * q^44 + 12 * q^45 - 4 * q^46 - 8 * q^47 - 4 * q^48 - 36 * q^49 - 4 * q^50 + 20 * q^51 - 12 * q^52 - 8 * q^53 + 4 * q^54 - 8 * q^55 - 12 * q^56 - 36 * q^57 + 8 * q^59 + 16 * q^60 + 28 * q^62 - 4 * q^63 - 8 * q^64 + 20 * q^65 - 8 * q^67 + 32 * q^68 - 16 * q^69 - 4 * q^71 - 16 * q^73 - 20 * q^75 + 4 * q^76 + 20 * q^77 + 16 * q^78 + 32 * q^79 + 4 * q^80 + 8 * q^81 + 16 * q^82 - 36 * q^83 - 16 * q^85 + 8 * q^86 + 24 * q^87 - 8 * q^88 - 8 * q^89 - 36 * q^90 - 24 * q^91 - 36 * q^93 + 16 * q^94 + 8 * q^95 + 8 * q^96 - 48 * q^97 - 4 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	0.900100	+	0.241181i	0.519673	+	0.139246i	0.509115	−	0.860698i	$-0.329973\pi$
$3$	0.900100	+	0.241181i	0.519673	+	0.139246i	0.0105575	+	0.999944i	$0.496639\pi$
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−2.22474	+	0.224745i	−0.994936	+	0.100509i
$5$	−2.22474	+	0.224745i	−0.994936	+	0.100509i
$6$	−0.658919	−	0.658919i	−0.269002	−	0.269002i
$7$	−0.0999004	−	0.0267682i	−0.0377588	−	0.0101174i	0.239890	−	0.970800i	$-0.422889\pi$
$7$	−0.0999004	−	0.0267682i	−0.0377588	−	0.0101174i	−0.277649	+	0.960683i	$0.589555\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−1.84607	−	1.06583i	−0.615355	−	0.355275i
$10$	2.03906	+	0.917738i	0.644807	+	0.290214i
$11$		−	5.56048i		−	1.67655i	−0.545250	−	0.838274i	$-0.683565\pi$
$11$		−	5.56048i		−	1.67655i	0.545250	−	0.838274i	$-0.316435\pi$
$12$	0.241181	+	0.900100i	0.0696229	+	0.259836i
$13$	1.48735	−	0.858719i	0.412515	−	0.238166i	−0.279354	−	0.960188i	$-0.590120\pi$
$13$	1.48735	−	0.858719i	0.412515	−	0.238166i	0.691870	+	0.722022i	$0.256787\pi$
$14$	0.0731322	+	0.0731322i	0.0195454	+	0.0195454i
$15$	−2.05670	−	0.334273i	−0.531037	−	0.0863090i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	3.57313	−	6.18885i	0.866612	−	1.50102i	0.00117408	−	0.999999i	$-0.499626\pi$
$17$	3.57313	−	6.18885i	0.866612	−	1.50102i	0.865438	−	0.501016i	$-0.167040\pi$
$18$	1.06583	+	1.84607i	0.251218	+	0.435122i
$19$	1.98004	+	0.530550i	0.454252	+	0.121717i	0.478688	−	0.877985i	$-0.341112\pi$
$19$	1.98004	+	0.530550i	0.454252	+	0.121717i	−0.0244361	+	0.999701i	$0.507779\pi$
$20$	−1.30701	−	1.81431i	−0.292256	−	0.405693i
$21$	−0.0834643	−	0.0481882i	−0.0182134	−	0.0105155i
$22$	−2.78024	+	4.81552i	−0.592749	+	1.02667i
$23$		−	3.96713i		−	0.827203i	−0.910458	−	0.413602i	$-0.864271\pi$
$23$		−	3.96713i		−	0.827203i	0.910458	−	0.413602i	$-0.135729\pi$
$24$	0.241181	−	0.900100i	0.0492309	−	0.183732i
$25$	4.89898	−	1.00000i	0.979796	−	0.200000i
$26$	−1.71744			−0.336817
$27$	−3.38134	−	3.38134i	−0.650739	−	0.650739i
$28$	−0.0267682	−	0.0999004i	−0.00505872	−	0.0188794i
$29$	5.95680	+	5.95680i	1.10615	+	1.10615i	0.993652	+	0.112497i	$0.0358849\pi$
$29$	5.95680	+	5.95680i	1.10615	+	1.10615i	0.112497	+	0.993652i	$0.464115\pi$
$30$	1.61401	+	1.31784i	0.294677	+	0.240603i
$31$	−5.87832	+	5.87832i	−1.05578	+	1.05578i	−0.0574269	+	0.998350i	$0.518290\pi$
$31$	−5.87832	+	5.87832i	−1.05578	+	1.05578i	−0.998350	+	0.0574269i	$0.981710\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	1.34108	−	5.00498i	0.233452	−	0.871256i
$34$	−6.18885	+	3.57313i	−1.06138	+	0.612787i
$35$	0.228269	+	0.0371004i	0.0385845	+	0.00627111i
$36$		−	2.13165i		−	0.355275i
$37$	−2.05197	−	5.72620i	−0.337342	−	0.941382i
$37$	−2.05197	−	5.72620i	−0.337342	−	0.941382i
$38$	−1.44949	−	1.44949i	−0.235138	−	0.235138i
$39$	1.54587	−	0.414214i	0.247537	−	0.0663273i
$40$	0.224745	+	2.22474i	0.0355353	+	0.351763i
$41$	−8.14893	+	4.70478i	−1.27265	+	0.734764i	−0.975486	−	0.220063i	$-0.929374\pi$
$41$	−8.14893	+	4.70478i	−1.27265	+	0.734764i	−0.297163	+	0.954827i	$0.596040\pi$
$42$	0.0481882	+	0.0834643i	0.00743559	+	0.0128788i
$43$			1.18519i			0.180740i	0.995908	+	0.0903698i	$0.0288049\pi$
$43$			1.18519i			0.180740i	−0.995908	+	0.0903698i	$0.971195\pi$
$44$	4.81552	−	2.78024i	0.725966	−	0.419137i
$45$	4.34656	+	1.95630i	0.647947	+	0.291628i
$46$	−1.98356	+	3.43563i	−0.292461	+	0.506557i
$47$	4.09878	−	4.09878i	0.597869	−	0.597869i	−0.341876	−	0.939745i	$-0.611062\pi$
$47$	4.09878	−	4.09878i	0.597869	−	0.597869i	0.939745	+	0.341876i	$0.111062\pi$
$48$	−0.658919	+	0.658919i	−0.0951067	+	0.0951067i
$49$	−6.05291	−	3.49465i	−0.864702	−	0.499236i
$50$	−4.74264	−	1.58346i	−0.670711	−	0.223936i
$51$	4.70881	−	4.70881i	0.659365	−	0.659365i
$52$	1.48735	+	0.858719i	0.206258	+	0.119083i
$53$	−3.44949	+	0.924288i	−0.473824	+	0.126961i	−0.487825	−	0.872941i	$-0.662210\pi$
$53$	−3.44949	+	0.924288i	−0.473824	+	0.126961i	0.0140015	+	0.999902i	$0.495543\pi$
$54$	1.23766	+	4.61900i	0.168424	+	0.628566i
$55$	1.24969	+	12.3706i	0.168508	+	1.66806i
$56$	−0.0267682	+	0.0999004i	−0.00357706	+	0.0133498i
$57$	1.65427	+	0.955096i	0.219114	+	0.126506i
$58$	−2.18034	−	8.13713i	−0.286292	−	1.06846i
$59$	−1.94646	−	7.26430i	−0.253408	−	0.945731i	−0.968969	−	0.247181i	$-0.920496\pi$
$59$	−1.94646	−	7.26430i	−0.253408	−	0.945731i	0.715561	−	0.698550i	$-0.246171\pi$
$60$	−0.738859	−	1.94829i	−0.0953863	−	0.251523i
$61$	−6.44364	−	1.72657i	−0.825024	−	0.221065i	−0.178482	−	0.983943i	$-0.557119\pi$
$61$	−6.44364	−	1.72657i	−0.825024	−	0.221065i	−0.646542	+	0.762879i	$0.723785\pi$
$62$	8.02993	−	2.15161i	1.01980	−	0.273255i
$63$	0.155892	+	0.155892i	0.0196406	+	0.0196406i
$64$	−1.00000			−0.125000
$65$	−3.11597	+	2.24471i	−0.386489	+	0.278421i
$66$	−3.66390	+	3.66390i	−0.450995	+	0.450995i
$67$	−0.154193	+	0.575454i	−0.0188376	+	0.0703029i	−0.974705	−	0.223496i	$-0.928253\pi$
$67$	−0.154193	+	0.575454i	−0.0188376	+	0.0703029i	0.955867	+	0.293799i	$0.0949197\pi$
$68$	7.14626			0.866612
$69$	0.956796	−	3.57081i	0.115185	−	0.429875i
$70$	−0.179137	−	0.146264i	−0.0214109	−	0.0174819i
$71$	3.42272	+	5.92833i	0.406202	+	0.703563i	0.994461	−	0.105110i	$-0.0335195\pi$
$71$	3.42272	+	5.92833i	0.406202	+	0.703563i	−0.588258	+	0.808673i	$0.700186\pi$
$72$	−1.06583	+	1.84607i	−0.125609	+	0.217561i
$73$	−2.83548	+	2.83548i	−0.331867	+	0.331867i	−0.853295	−	0.521428i	$-0.825400\pi$
$73$	−2.83548	+	2.83548i	−0.331867	+	0.331867i	0.521428	+	0.853295i	$0.325400\pi$
$74$	−1.08604	+	5.98502i	−0.126250	+	0.695745i
$75$	4.65075	+	0.281441i	0.537022	+	0.0324980i
$76$	0.530550	+	1.98004i	0.0608583	+	0.227126i
$77$	−0.148844	+	0.555494i	−0.0169624	+	0.0633044i
$78$	−1.54587	−	0.414214i	−0.175035	−	0.0469005i
$79$	12.0349	+	3.22474i	1.35403	+	0.362812i	0.861622	−	0.507550i	$-0.169449\pi$
$79$	12.0349	+	3.22474i	1.35403	+	0.362812i	0.492411	+	0.870363i	$0.336116\pi$
$80$	0.917738	−	2.03906i	0.102606	−	0.227974i
$81$	0.969450	+	1.67914i	0.107717	+	0.186571i
$82$	9.40957			1.03911
$83$	−6.98784	+	1.87239i	−0.767015	+	0.205521i	−0.621053	−	0.783769i	$-0.713295\pi$
$83$	−6.98784	+	1.87239i	−0.767015	+	0.205521i	−0.145963	+	0.989290i	$0.546628\pi$
$84$		−	0.0963763i		−	0.0105155i
$85$	−6.55840	+	14.5716i	−0.711358	+	1.58052i
$86$	0.592594	−	1.02640i	0.0639011	−	0.110680i
$87$	3.92504	+	6.79837i	0.420809	+	0.728862i
$88$	−5.56048			−0.592749
$89$	0.962402	−	0.257875i	0.102014	−	0.0273347i	−0.207451	−	0.978245i	$-0.566517\pi$
$89$	0.962402	−	0.257875i	0.102014	−	0.0273347i	0.309465	+	0.950911i	$0.399850\pi$
$90$	−2.78609	−	3.86749i	−0.293679	−	0.407669i
$91$	−0.171573	+	0.0459728i	−0.0179857	+	0.00481926i
$92$	3.43563	−	1.98356i	0.358190	−	0.206801i
$93$	−6.70881	+	3.87333i	−0.695671	+	0.401646i
$94$	−5.59904	+	1.50026i	−0.577497	+	0.154740i
$95$	−4.52432	−	0.735335i	−0.464186	−	0.0754438i
$96$	0.900100	−	0.241181i	0.0918660	−	0.0246154i
$97$	16.0652			1.63117			0.815586	−	0.578636i	$-0.196415\pi$
$97$	16.0652			1.63117			0.815586	+	0.578636i	$0.196415\pi$
$98$	3.49465	+	6.05291i	0.353013	+	0.611437i
$99$	−5.92650	+	10.2650i	−0.595636	+	1.03167i
$100$	3.31552	+	3.74264i	0.331552	+	0.374264i
$101$		−	10.2850i		−	1.02339i	−0.859166	−	0.511696i	$-0.829017\pi$
$101$		−	10.2850i		−	1.02339i	0.859166	−	0.511696i	$-0.170983\pi$
$102$	−6.43235	+	1.72354i	−0.636898	+	0.170656i
$103$	18.9019			1.86246			0.931230	−	0.364433i	$-0.118737\pi$
$103$	18.9019			1.86246			0.931230	+	0.364433i	$0.118737\pi$
$104$	−0.858719	−	1.48735i	−0.0842044	−	0.145846i
$105$	0.196517	+	0.0884482i	0.0191781	+	0.00863166i
$106$	3.44949	+	0.924288i	0.335044	+	0.0897748i
$107$	14.2176	+	3.80959i	1.37446	+	0.368287i	0.869107	−	0.494624i	$-0.164694\pi$
$107$	14.2176	+	3.80959i	1.37446	+	0.368287i	0.505357	+	0.862910i	$0.331361\pi$
$108$	1.23766	−	4.61900i	0.119094	−	0.444463i
$109$	5.10684	+	19.0590i	0.489147	+	1.82552i	0.560614	+	0.828078i	$0.310565\pi$
$109$	5.10684	+	19.0590i	0.489147	+	1.82552i	−0.0714669	+	0.997443i	$0.522768\pi$
$110$	5.10306	−	11.3381i	0.486558	−	1.08105i
$111$	−0.465926	−	5.64905i	−0.0442237	−	0.536184i
$112$	0.0731322	−	0.0731322i	0.00691034	−	0.00691034i
$113$	0.968008	−	1.67664i	0.0910625	−	0.157725i	−0.816896	−	0.576785i	$-0.804307\pi$
$113$	0.968008	−	1.67664i	0.0910625	−	0.157725i	0.907958	+	0.419060i	$0.137640\pi$
$114$	−0.955096	−	1.65427i	−0.0894529	−	0.154937i
$115$	0.891592	+	8.82585i	0.0831413	+	0.823015i
$116$	−2.18034	+	8.13713i	−0.202439	+	0.755514i
$117$	−3.66098			−0.338458
$118$	−1.94646	+	7.26430i	−0.179186	+	0.668733i
$119$	−0.522622	+	0.522622i	−0.0479087	+	0.0479087i
$120$	−0.334273	+	2.05670i	−0.0305148	+	0.187750i
$121$	−19.9189			−1.81081
$122$	4.71707	+	4.71707i	0.427064	+	0.427064i
$123$	−8.46955	+	2.26941i	−0.763674	+	0.204626i
$124$	−8.02993	−	2.15161i	−0.721109	−	0.193221i
$125$	−10.6742	+	3.32577i	−0.954733	+	0.297465i
$126$	−0.0570606	−	0.212953i	−0.00508336	−	0.0189714i
$127$	−1.98490	−	7.40775i	−0.176131	−	0.657331i	−0.996356	−	0.0852898i	$-0.972818\pi$
$127$	−1.98490	−	7.40775i	−0.176131	−	0.657331i	0.820225	−	0.572041i	$-0.193848\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	−0.285845	+	1.06679i	−0.0251672	+	0.0939255i
$130$	3.82086	−	0.385986i	0.335112	−	0.0338532i
$131$	1.24483	+	4.64577i	0.108761	+	0.405903i	0.998745	−	0.0500903i	$-0.0159509\pi$
$131$	1.24483	+	4.64577i	0.108761	+	0.405903i	−0.889983	+	0.455993i	$0.849284\pi$
$132$	5.00498	−	1.34108i	0.435628	−	0.116726i
$133$	−0.183605	−	0.106004i	−0.0159206	−	0.00919174i
$134$	0.421262	−	0.421262i	0.0363915	−	0.0363915i
$135$	8.28256	+	6.76268i	0.712849	+	0.582039i
$136$	−6.18885	−	3.57313i	−0.530689	−	0.306394i
$137$	−5.06937	+	5.06937i	−0.433105	+	0.433105i	−0.889683	−	0.456578i	$-0.849075\pi$
$137$	−5.06937	+	5.06937i	−0.433105	+	0.433105i	0.456578	+	0.889683i	$0.349075\pi$
$138$	−2.61401	+	2.61401i	−0.222520	+	0.222520i
$139$	5.01349	−	8.68362i	0.425239	−	0.736535i	−0.571204	−	0.820808i	$-0.693523\pi$
$139$	5.01349	−	8.68362i	0.425239	−	0.736535i	0.996443	+	0.0842730i	$0.0268568\pi$
$140$	0.0820046	+	0.216237i	0.00693065	+	0.0182754i
$141$	4.67786	−	2.70076i	0.393947	−	0.227445i
$142$		−	6.84544i		−	0.574457i
$143$	−4.77489	−	8.27035i	−0.399296	−	0.691602i
$144$	1.84607	−	1.06583i	0.153839	−	0.0888189i
$145$	−14.5911	−	11.9136i	−1.21173	−	0.989370i
$146$	3.87333	−	1.03786i	0.320559	−	0.0858936i
$147$	−4.60538	−	4.60538i	−0.379846	−	0.379846i
$148$	3.93305	−	4.64016i	0.323295	−	0.381419i
$149$		−	11.5581i		−	0.946874i	−0.880828	−	0.473437i	$-0.843013\pi$
$149$		−	11.5581i		−	0.946874i	0.880828	−	0.473437i	$-0.156987\pi$
$150$	−3.88695	−	2.56911i	−0.317368	−	0.209767i
$151$	14.2396	−	8.22122i	1.15880	−	0.669033i	0.207784	−	0.978175i	$-0.433375\pi$
$151$	14.2396	−	8.22122i	1.15880	−	0.669033i	0.951016	+	0.309141i	$0.100042\pi$
$152$	0.530550	−	1.98004i	0.0430333	−	0.160602i
$153$	−13.1925	+	7.61668i	−1.06655	+	0.615772i
$154$	0.406650	−	0.406650i	0.0327688	−	0.0327688i
$155$	11.7566	−	14.3989i	0.944315	−	1.15655i
$156$	1.13165	+	1.13165i	0.0906047	+	0.0906047i
$157$	−0.708309	−	2.64344i	−0.0565292	−	0.210970i	0.931884	−	0.362756i	$-0.118164\pi$
$157$	−0.708309	−	2.64344i	−0.0565292	−	0.210970i	−0.988413	+	0.151786i	$0.951497\pi$
$158$	−8.81017	−	8.81017i	−0.700899	−	0.700899i
$159$	−3.32780			−0.263912
$160$	−1.81431	+	1.30701i	−0.143434	+	0.103328i
$161$	−0.106193	+	0.396318i	−0.00836918	+	0.0312342i
$162$		−	1.93890i		−	0.152334i
$163$	9.70492	−	16.8094i	0.760148	−	1.31661i	−0.182626	−	0.983182i	$-0.558460\pi$
$163$	9.70492	−	16.8094i	0.760148	−	1.31661i	0.942774	−	0.333432i	$-0.108207\pi$
$164$	−8.14893	−	4.70478i	−0.636324	−	0.367382i
$165$	−1.85872	+	11.4362i	−0.144701	+	0.890308i
$166$	6.98784	+	1.87239i	0.542362	+	0.145325i
$167$	−1.35311	−	2.34366i	−0.104707	−	0.181358i	0.808911	−	0.587931i	$-0.200057\pi$
$167$	−1.35311	−	2.34366i	−0.104707	−	0.181358i	−0.913618	+	0.406573i	$0.866724\pi$
$168$	−0.0481882	+	0.0834643i	−0.00371780	+	0.00643941i
$169$	−5.02520	+	8.70390i	−0.386554	+	0.669531i
$170$	12.9656	−	9.34022i	0.994413	−	0.716362i
$171$	−3.08981	−	3.08981i	−0.236284	−	0.236284i
$172$	−1.02640	+	0.592594i	−0.0782626	+	0.0451849i
$173$	−4.25970	−	15.8974i	−0.323859	−	1.20866i	−0.915454	−	0.402423i	$-0.868168\pi$
$173$	−4.25970	−	15.8974i	−0.323859	−	1.20866i	0.591595	−	0.806235i	$-0.298498\pi$
$174$		−	7.85009i		−	0.595114i
$175$	−0.516178	−	0.0312366i	−0.0390194	−	0.00236127i
$176$	4.81552	+	2.78024i	0.362983	+	0.209568i
$177$		−	7.00804i		−	0.526757i
$178$	−0.962402	−	0.257875i	−0.0721351	−	0.0193285i
$179$	−0.100025	−	0.100025i	−0.00747620	−	0.00747620i	0.703359	−	0.710835i	$-0.251683\pi$
$179$	−0.100025	−	0.100025i	−0.00747620	−	0.00747620i	−0.710835	+	0.703359i	$0.751683\pi$
$180$	0.479078	+	4.74238i	0.0357084	+	0.353476i
$181$	−3.50352	−	6.06828i	−0.260415	−	0.451052i	0.705937	−	0.708274i	$-0.250526\pi$
$181$	−3.50352	−	6.06828i	−0.260415	−	0.451052i	−0.966352	+	0.257222i	$0.917193\pi$
$182$	0.171573	+	0.0459728i	0.0127178	+	0.00340773i
$183$	−5.38351	−	3.10817i	−0.397960	−	0.229762i
$184$	−3.96713			−0.292461
$185$	5.85204	+	12.2782i	0.430251	+	0.902709i
$186$	7.74666			0.568013
$187$	−34.4129	−	19.8683i	−2.51652	−	1.45292i
$188$	5.59904	+	1.50026i	0.408352	+	0.109418i
$189$	0.247285	+	0.428310i	0.0179873	+	0.0311550i
$190$	3.55051	+	2.89898i	0.257581	+	0.210314i
$191$	−0.807587	−	0.807587i	−0.0584349	−	0.0584349i	0.677285	−	0.735720i	$-0.263156\pi$
$191$	−0.807587	−	0.807587i	−0.0584349	−	0.0584349i	−0.735720	+	0.677285i	$0.763156\pi$
$192$	−0.900100	−	0.241181i	−0.0649591	−	0.0174057i
$193$			9.84320i			0.708529i	0.935145	+	0.354265i	$0.115269\pi$
$193$			9.84320i			0.708529i	−0.935145	+	0.354265i	$0.884731\pi$
$194$	−13.9129	−	8.03259i	−0.998885	−	0.576706i
$195$	−3.34607	+	1.26894i	−0.239617	+	0.0908710i
$196$		−	6.98930i		−	0.499236i
$197$	4.03390	+	15.0547i	0.287403	+	1.07260i	0.947065	+	0.321041i	$0.104033\pi$
$197$	4.03390	+	15.0547i	0.287403	+	1.07260i	−0.659662	+	0.751563i	$0.729300\pi$
$198$	10.2650	−	5.92650i	0.729502	−	0.421178i
$199$	15.2717	+	15.2717i	1.08258	+	1.08258i	0.996268	+	0.0863133i	$0.0275086\pi$
$199$	15.2717	+	15.2717i	1.08258	+	1.08258i	0.0863133	+	0.996268i	$0.472491\pi$
$200$	−1.00000	−	4.89898i	−0.0707107	−	0.346410i
$201$	−0.277577	+	0.480778i	−0.0195788	+	0.0339115i
$202$	−5.14248	+	8.90704i	−0.361824	+	0.626697i
$203$	−0.435633	−	0.754539i	−0.0305755	−	0.0529583i
$204$	6.43235	+	1.72354i	0.450355	+	0.120672i
$205$	17.0719	−	12.2984i	1.19235	−	0.858956i
$206$	−16.3695	−	9.45095i	−1.14052	−	0.658479i
$207$	−4.22827	+	7.32358i	−0.293885	+	0.509024i
$208$			1.71744i			0.119083i
$209$	2.95011	−	11.0100i	0.204064	−	0.761575i
$210$	−0.125965	−	0.174857i	−0.00869238	−	0.0120663i
$211$	10.0377			0.691022			0.345511	−	0.938415i	$-0.387706\pi$
$211$	10.0377			0.691022			0.345511	+	0.938415i	$0.387706\pi$
$212$	−2.52520	−	2.52520i	−0.173432	−	0.173432i
$213$	1.65099	+	6.16158i	0.113124	+	0.422185i
$214$	−10.4080	−	10.4080i	−0.711475	−	0.711475i
$215$	−0.266365	−	2.63674i	−0.0181660	−	0.179824i
$216$	−3.38134	+	3.38134i	−0.230071	+	0.230071i
$217$	0.744598	−	0.429894i	0.0505466	−	0.0291831i
$218$	5.10684	−	19.0590i	0.345879	−	1.29084i
$219$	−3.23607	+	1.86835i	−0.218674	+	0.126251i
$220$	−10.0884	+	7.26758i	−0.680163	+	0.489980i
$221$		−	12.2733i		−	0.825590i
$222$	−2.42102	+	5.12518i	−0.162488	+	0.343980i
$223$	15.3605	+	15.3605i	1.02862	+	1.02862i	0.999578	+	0.0290369i	$0.00924403\pi$
$223$	15.3605	+	15.3605i	1.02862	+	1.02862i	0.0290369	+	0.999578i	$0.490756\pi$
$224$	−0.0999004	+	0.0267682i	−0.00667488	+	0.00178853i
$225$	−10.1097	−	3.37540i	−0.673977	−	0.225026i
$226$	−1.67664	+	0.968008i	−0.111528	+	0.0643909i
$227$	−3.64893	−	6.32013i	−0.242188	−	0.419481i	0.719149	−	0.694855i	$-0.244532\pi$
$227$	−3.64893	−	6.32013i	−0.242188	−	0.419481i	−0.961337	+	0.275374i	$0.911198\pi$
$228$			1.91019i			0.126506i
$229$	−13.6418	+	7.87612i	−0.901478	+	0.520468i	−0.877679	−	0.479248i	$-0.840909\pi$
$229$	−13.6418	+	7.87612i	−0.901478	+	0.520468i	−0.0237985	+	0.999717i	$0.507576\pi$
$230$	3.64078	−	8.08920i	0.240066	−	0.533386i
$231$	−0.267949	+	0.464102i	−0.0176298	+	0.0305356i
$232$	5.95680	−	5.95680i	0.391083	−	0.391083i
$233$	1.56317	−	1.56317i	0.102407	−	0.102407i	−0.654047	−	0.756454i	$-0.726930\pi$
$233$	1.56317	−	1.56317i	0.102407	−	0.102407i	0.756454	+	0.654047i	$0.226930\pi$
$234$	3.17050	+	1.83049i	0.207262	+	0.119663i
$235$	−8.19756	+	10.0399i	−0.534750	+	0.654932i
$236$	5.31784	−	5.31784i	0.346162	−	0.346162i
$237$	10.0549	+	5.80518i	0.653134	+	0.377087i
$238$	0.713915	−	0.191293i	0.0462762	−	0.0123997i
$239$	6.10746	+	22.7934i	0.395059	+	1.47438i	0.821680	+	0.569950i	$0.193037\pi$
$239$	6.10746	+	22.7934i	0.395059	+	1.47438i	−0.426621	+	0.904431i	$0.640296\pi$
$240$	1.31784	−	1.61401i	0.0850660	−	0.104184i
$241$	5.03837	−	18.8035i	0.324550	−	1.21124i	−0.590213	−	0.807247i	$-0.700956\pi$
$241$	5.03837	−	18.8035i	0.324550	−	1.21124i	0.914763	−	0.403990i	$-0.132377\pi$
$242$	17.2503	+	9.95946i	1.10889	+	0.640218i
$243$	4.18060	+	15.6022i	0.268185	+	1.00088i
$244$	−1.72657	−	6.44364i	−0.110532	−	0.412512i
$245$	14.2516	+	6.41435i	0.910501	+	0.409798i
$246$	8.46955	+	2.26941i	0.539999	+	0.144692i
$247$	3.40060	−	0.911187i	0.216375	−	0.0579775i
$248$	5.87832	+	5.87832i	0.373273	+	0.373273i
$249$	−6.74134			−0.427215
$250$	10.9070	+	2.45692i	0.689822	+	0.155389i
$251$	0.577154	−	0.577154i	0.0364296	−	0.0364296i	−0.688657	−	0.725087i	$-0.741800\pi$
$251$	0.577154	−	0.577154i	0.0364296	−	0.0364296i	0.725087	+	0.688657i	$0.241800\pi$
$252$	−0.0570606	+	0.212953i	−0.00359448	+	0.0134148i
$253$	−22.0591			−1.38685
$254$	−1.98490	+	7.40775i	−0.124544	+	0.464803i
$255$	−9.41761	+	11.5342i	−0.589754	+	0.722298i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−12.5313	+	21.7048i	−0.781679	+	1.35391i	0.149284	+	0.988794i	$0.452303\pi$
$257$	−12.5313	+	21.7048i	−0.781679	+	1.35391i	−0.930963	+	0.365113i	$0.881030\pi$
$258$	0.780943	−	0.780943i	0.0486194	−	0.0486194i
$259$	0.0517123	+	0.626978i	0.00321324	+	0.0389585i
$260$	−3.50196	−	1.57616i	−0.217182	−	0.0977492i
$261$	−4.64772	−	17.3455i	−0.287687	−	1.07366i
$262$	1.24483	−	4.64577i	0.0769058	−	0.287016i
$263$	−5.50901	−	1.47613i	−0.339700	−	0.0910223i	0.0849363	−	0.996386i	$-0.472931\pi$
$263$	−5.50901	−	1.47613i	−0.339700	−	0.0910223i	−0.424636	+	0.905364i	$0.639598\pi$
$264$	−5.00498	−	1.34108i	−0.308035	−	0.0825379i
$265$	7.46651	−	2.83156i	0.458664	−	0.173941i
$266$	0.106004	+	0.183605i	0.00649954	+	0.0112575i
$267$	0.928452			0.0568203
$268$	−0.575454	+	0.154193i	−0.0351515	+	0.00941881i
$269$		−	8.45805i		−	0.515696i	−0.966185	−	0.257848i	$-0.916987\pi$
$269$		−	8.45805i		−	0.515696i	0.966185	−	0.257848i	$-0.0830134\pi$
$270$	−3.79157	−	9.99794i	−0.230747	−	0.608455i
$271$	−7.60110	+	13.1655i	−0.461734	+	0.799747i	−0.999048	−	0.0436357i	$-0.986106\pi$
$271$	−7.60110	+	13.1655i	−0.461734	+	0.799747i	0.537313	+	0.843383i	$0.319439\pi$
$272$	3.57313	+	6.18885i	0.216653	+	0.375254i
$273$	−0.165520			−0.0100178
$274$	6.92489	−	1.85552i	0.418348	−	0.112096i
$275$	−5.56048	−	27.2407i	−0.335309	−	1.64267i
$276$	3.57081	−	0.956796i	0.214938	−	0.0575923i
$277$	13.3828	−	7.72657i	0.804095	−	0.464245i	−0.0408060	−	0.999167i	$-0.512993\pi$
$277$	13.3828	−	7.72657i	0.804095	−	0.464245i	0.844901	+	0.534923i	$0.179659\pi$
$278$	−8.68362	+	5.01349i	−0.520809	+	0.300689i
$279$	17.1170	−	4.58649i	1.02477	−	0.274586i
$280$	0.0371004	−	0.228269i	0.00221717	−	0.0136417i
$281$	4.29157	−	1.14992i	0.256013	−	0.0685986i	−0.128530	−	0.991706i	$-0.541026\pi$
$281$	4.29157	−	1.14992i	0.256013	−	0.0685986i	0.384543	+	0.923107i	$0.374359\pi$
$282$	−5.40153			−0.321656
$283$	4.18230	+	7.24395i	0.248612	+	0.430608i	0.963141	−	0.268998i	$-0.0866924\pi$
$283$	4.18230	+	7.24395i	0.248612	+	0.430608i	−0.714529	+	0.699606i	$0.753359\pi$
$284$	−3.42272	+	5.92833i	−0.203101	+	0.351782i
$285$	−3.89499	−	1.75305i	−0.230719	−	0.103842i
$286$			9.54978i			0.564690i
$287$	0.940020	−	0.251878i	0.0554876	−	0.0148679i
$288$	−2.13165			−0.125609
$289$	−17.0345	−	29.5047i	−1.00203	−	1.73557i
$290$	6.67948	+	17.6130i	0.392232	+	1.03427i
$291$	14.4603	+	3.87462i	0.847676	+	0.227134i
$292$	−3.87333	−	1.03786i	−0.226670	−	0.0607359i
$293$	−2.18960	+	8.17171i	−0.127918	+	0.477396i	−0.999927	−	0.0120938i	$-0.996150\pi$
$293$	−2.18960	+	8.17171i	−0.127918	+	0.477396i	0.872009	+	0.489490i	$0.162817\pi$
$294$	1.68569	+	6.29107i	0.0983113	+	0.366903i
$295$	5.96300	+	15.7238i	0.347179	+	0.915473i
$296$	−5.72620	+	2.05197i	−0.332829	+	0.119268i
$297$	−18.8019	+	18.8019i	−1.09100	+	1.09100i
$298$	−5.77904	+	10.0096i	−0.334771	+	0.579840i
$299$	−3.40665	−	5.90049i	−0.197012	−	0.341234i
$300$	2.08164	+	4.16839i	0.120184	+	0.240662i
$301$	0.0317254	−	0.118401i	0.00182862	−	0.00682451i
$302$	−16.4424			−0.946156
$303$	2.48054	−	9.25749i	0.142503	−	0.531829i
$304$	−1.44949	+	1.44949i	−0.0831339	+	0.0831339i
$305$	14.7235	+	2.39300i	0.843065	+	0.137023i
$306$	15.2334			0.870833
$307$	−8.70076	−	8.70076i	−0.496579	−	0.496579i	0.413792	−	0.910371i	$-0.364204\pi$
$307$	−8.70076	−	8.70076i	−0.496579	−	0.496579i	−0.910371	+	0.413792i	$0.864204\pi$
$308$	−0.555494	+	0.148844i	−0.0316522	+	0.00848119i
$309$	17.0136	+	4.55878i	0.967869	+	0.259340i
$310$	−17.3810	+	6.59147i	−0.987173	+	0.374371i
$311$	7.18747	+	26.8240i	0.407564	+	1.52105i	0.799277	+	0.600962i	$0.205216\pi$
$311$	7.18747	+	26.8240i	0.407564	+	1.52105i	−0.391714	+	0.920087i	$0.628118\pi$
$312$	−0.414214	−	1.54587i	−0.0234502	−	0.0875174i
$313$	−1.62078	−	0.935758i	−0.0916119	−	0.0528922i	0.453494	−	0.891259i	$-0.350177\pi$
$313$	−1.62078	−	0.935758i	−0.0916119	−	0.0528922i	−0.545106	+	0.838367i	$0.683511\pi$
$314$	−0.708309	+	2.64344i	−0.0399722	+	0.149178i
$315$	−0.381857	−	0.311785i	−0.0215152	−	0.0175671i
$316$	3.22474	+	12.0349i	0.181406	+	0.677017i
$317$	−6.16108	+	1.65086i	−0.346041	+	0.0927214i	−0.427653	−	0.903943i	$-0.640660\pi$
$317$	−6.16108	+	1.65086i	−0.346041	+	0.0927214i	0.0816126	+	0.996664i	$0.473993\pi$
$318$	2.88196	+	1.66390i	0.161612	+	0.0933070i
$319$	33.1226	−	33.1226i	1.85451	−	1.85451i
$320$	2.22474	−	0.224745i	0.124367	−	0.0125636i
$321$	11.8784	+	6.85802i	0.662989	+	0.382777i
$322$	0.290125	−	0.290125i	0.0161680	−	0.0161680i
$323$	10.3584	−	10.3584i	0.576359	−	0.576359i
$324$	−0.969450	+	1.67914i	−0.0538583	+	0.0932854i
$325$	6.42776	−	5.69419i	0.356548	−	0.315857i
$326$	−16.8094	+	9.70492i	−0.930987	+	0.537506i
$327$			18.3867i			1.01678i
$328$	4.70478	+	8.14893i	0.259778	+	0.449949i
$329$	−0.519187	+	0.299753i	−0.0286237	+	0.0165259i
$330$	7.32780	−	8.97469i	0.403382	−	0.494041i
$331$	−6.22338	+	1.66755i	−0.342068	+	0.0916569i	−0.425763	−	0.904835i	$-0.639994\pi$
$331$	−6.22338	+	1.66755i	−0.342068	+	0.0916569i	0.0836953	+	0.996491i	$0.473328\pi$
$332$	−5.11546	−	5.11546i	−0.280747	−	0.280747i
$333$	−2.31507	+	12.7580i	−0.126865	+	0.699134i
$334$			2.70623i			0.148078i
$335$	0.213709	−	1.31489i	0.0116761	−	0.0718403i
$336$	0.0834643	−	0.0481882i	0.00455335	−	0.00262888i
$337$	−3.20711	+	11.9691i	−0.174702	+	0.651998i	0.821900	+	0.569632i	$0.192914\pi$
$337$	−3.20711	+	11.9691i	−0.174702	+	0.651998i	−0.996602	+	0.0823657i	$0.973752\pi$
$338$	8.70390	−	5.02520i	0.473430	−	0.273335i
$339$	1.27568	−	1.27568i	0.0692852	−	0.0692852i
$340$	−15.8986	+	1.60609i	−0.862223	+	0.0871023i
$341$	32.6862	+	32.6862i	1.77006	+	1.77006i
$342$	1.13095	+	4.22076i	0.0611547	+	0.228232i
$343$	1.02307	+	1.02307i	0.0552405	+	0.0552405i
$344$	1.18519			0.0639011
$345$	−1.32611	+	8.15918i	−0.0713951	+	0.439275i
$346$	−4.25970	+	15.8974i	−0.229003	+	0.854650i
$347$		−	28.4004i		−	1.52461i	−0.647216	−	0.762306i	$-0.724067\pi$
$347$		−	28.4004i		−	1.52461i	0.647216	−	0.762306i	$-0.275933\pi$
$348$	−3.92504	+	6.79837i	−0.210404	+	0.364431i
$349$	−8.00242	−	4.62020i	−0.428360	−	0.247314i	0.270288	−	0.962780i	$-0.412881\pi$
$349$	−8.00242	−	4.62020i	−0.428360	−	0.247314i	−0.698648	+	0.715466i	$0.746214\pi$
$350$	0.431405	+	0.285141i	0.0230596	+	0.0152414i
$351$	−7.93285	−	2.12560i	−0.423424	−	0.113456i
$352$	−2.78024	−	4.81552i	−0.148187	−	0.256668i
$353$	−5.13859	+	8.90031i	−0.273500	+	0.473715i	−0.969756	−	0.244078i	$-0.921515\pi$
$353$	−5.13859	+	8.90031i	−0.273500	+	0.473715i	0.696256	+	0.717794i	$0.254848\pi$
$354$	−3.50402	+	6.06914i	−0.186237	+	0.322571i
$355$	−8.94704	−	12.4198i	−0.474860	−	0.659173i
$356$	0.704527	+	0.704527i	0.0373399	+	0.0373399i
$357$	−0.596458	+	0.344365i	−0.0315679	+	0.0182257i
$358$	0.0366116	+	0.136636i	0.00193498	+	0.00722145i
$359$		−	12.2560i		−	0.646847i	−0.946254	−	0.323424i	$-0.895166\pi$
$359$		−	12.2560i		−	0.646847i	0.946254	−	0.323424i	$-0.104834\pi$
$360$	1.95630	−	4.34656i	0.103106	−	0.229084i
$361$	−12.8154	−	7.39898i	−0.674495	−	0.389420i
$362$			7.00705i			0.368282i
$363$	−17.9290	−	4.80406i	−0.941029	−	0.252148i
$364$	−0.125600	−	0.125600i	−0.00658323	−	0.00658323i
$365$	5.67095	−	6.94547i	0.296831	−	0.363542i
$366$	3.10817	+	5.38351i	0.162467	+	0.281400i
$367$	5.09944	+	1.36639i	0.266188	+	0.0713250i	0.389445	−	0.921050i	$-0.372667\pi$
$367$	5.09944	+	1.36639i	0.266188	+	0.0713250i	−0.123256	+	0.992375i	$0.539334\pi$
$368$	3.43563	+	1.98356i	0.179095	+	0.103400i
$369$	20.0579			1.04417
$370$	1.07107	−	13.5592i	0.0556822	−	0.704911i
$371$	0.369347			0.0191755
$372$	−6.70881	−	3.87333i	−0.347835	−	0.200823i
$373$	12.3227	+	3.30185i	0.638043	+	0.170963i	0.563317	−	0.826241i	$-0.309525\pi$
$373$	12.3227	+	3.30185i	0.638043	+	0.170963i	0.0747263	+	0.997204i	$0.476192\pi$
$374$	19.8683	+	34.4129i	1.02737	+	1.77945i
$375$	−10.4100	+	0.419098i	−0.537569	+	0.0216421i
$376$	−4.09878	−	4.09878i	−0.211378	−	0.211378i
$377$	13.9750	+	3.74460i	0.719751	+	0.192857i
$378$		−	0.494570i		−	0.0254379i
$379$	5.52269	+	3.18852i	0.283681	+	0.163783i	0.635089	−	0.772439i	$-0.280963\pi$
$379$	5.52269	+	3.18852i	0.283681	+	0.163783i	−0.351407	+	0.936223i	$0.614297\pi$
$380$	−1.62534	−	4.28585i	−0.0833783	−	0.219859i
$381$		−	7.14643i		−	0.366123i
$382$	0.295597	+	1.10318i	0.0151241	+	0.0564438i
$383$	−10.2601	+	5.92368i	−0.524268	+	0.302686i	−0.738679	−	0.674057i	$-0.764550\pi$
$383$	−10.2601	+	5.92368i	−0.524268	+	0.302686i	0.214411	+	0.976743i	$0.431217\pi$
$384$	0.658919	+	0.658919i	0.0336253	+	0.0336253i
$385$	0.206296	−	1.26928i	0.0105138	−	0.0646887i
$386$	4.92160	−	8.52446i	0.250503	−	0.433884i
$387$	1.26321	−	2.18794i	0.0642123	−	0.111219i
$388$	8.03259	+	13.9129i	0.407793	+	0.706318i
$389$	3.59492	+	0.963255i	0.182270	+	0.0488390i	0.348799	−	0.937197i	$-0.386590\pi$
$389$	3.59492	+	0.963255i	0.182270	+	0.0488390i	−0.166530	+	0.986036i	$0.553256\pi$
$390$	3.53225	+	0.574094i	0.178862	+	0.0290704i
$391$	−24.5519	−	14.1751i	−1.24165	−	0.716864i
$392$	−3.49465	+	6.05291i	−0.176507	+	0.305718i
$393$			4.48188i			0.226081i
$394$	4.03390	−	15.0547i	0.203225	−	0.758446i
$395$	−27.4994	−	4.46945i	−1.38364	−	0.224882i
$396$	−11.8530			−0.595636
$397$	−5.68644	−	5.68644i	−0.285394	−	0.285394i	0.549861	−	0.835256i	$-0.314680\pi$
$397$	−5.68644	−	5.68644i	−0.285394	−	0.285394i	−0.835256	+	0.549861i	$0.814680\pi$
$398$	−5.58983	−	20.8615i	−0.280193	−	1.04569i
$399$	−0.139696	−	0.139696i	−0.00699357	−	0.00699357i
$400$	−1.58346	+	4.74264i	−0.0791732	+	0.237132i
$401$	10.6700	−	10.6700i	0.532832	−	0.532832i	−0.388582	−	0.921414i	$-0.627035\pi$
$401$	10.6700	−	10.6700i	0.532832	−	0.532832i	0.921414	+	0.388582i	$0.127035\pi$
$402$	0.480778	−	0.277577i	0.0239790	−	0.0138443i
$403$	−3.69526	+	13.7909i	−0.184074	+	0.686974i
$404$	8.90704	−	5.14248i	0.443142	−	0.255848i
$405$	−2.53416	−	3.51777i	−0.125923	−	0.174799i
$406$			0.871267i			0.0432403i
$407$	−31.8404	+	11.4099i	−1.57827	+	0.565569i
$408$	−4.70881	−	4.70881i	−0.233121	−	0.233121i
$409$	−21.4831	+	5.75637i	−1.06227	+	0.284634i	−0.747313	−	0.664472i	$-0.768657\pi$
$409$	−21.4831	+	5.75637i	−1.06227	+	0.284634i	−0.314956	+	0.949106i	$0.601990\pi$
$410$	−20.9339	+	2.11475i	−1.03385	+	0.104440i
$411$	−5.78557	+	3.34030i	−0.285381	+	0.164765i
$412$	9.45095	+	16.3695i	0.465615	+	0.806469i
$413$			0.777810i			0.0382735i
$414$	7.32358	−	4.22827i	0.359934	−	0.207808i
$415$	15.1254	−	5.73607i	0.742475	−	0.281572i
$416$	0.858719	−	1.48735i	0.0421022	−	0.0729231i
$417$	6.60697	−	6.60697i	0.323545	−	0.323545i
$418$	−8.05986	+	8.05986i	−0.394220	+	0.394220i
$419$	4.02283	+	2.32258i	0.196528	+	0.113466i	0.595035	−	0.803700i	$-0.297138\pi$
$419$	4.02283	+	2.32258i	0.196528	+	0.113466i	−0.398507	+	0.917165i	$0.630472\pi$
$420$	0.0216601	+	0.214413i	0.00105690	+	0.0104623i
$421$	4.93926	−	4.93926i	0.240725	−	0.240725i	−0.576425	−	0.817150i	$-0.695553\pi$
$421$	4.93926	−	4.93926i	0.240725	−	0.240725i	0.817150	+	0.576425i	$0.195553\pi$
$422$	−8.69289	−	5.01884i	−0.423163	−	0.244313i
$423$	−11.9352	+	3.19803i	−0.580309	+	0.155493i
$424$	0.924288	+	3.44949i	0.0448874	+	0.167522i
$425$	11.3159	−	33.8922i	0.548900	−	1.64401i
$426$	1.65099	−	6.16158i	0.0799908	−	0.298530i
$427$	0.597506	+	0.344970i	0.0289153	+	0.0166943i
$428$	3.80959	+	14.2176i	0.184143	+	0.687232i
$429$	−2.30323	−	8.59575i	−0.111201	−	0.415007i
$430$	−1.08769	+	2.41667i	−0.0524532	+	0.116542i
$431$	2.02030	+	0.541338i	0.0973144	+	0.0260753i	0.307148	−	0.951662i	$-0.400625\pi$
$431$	2.02030	+	0.541338i	0.0973144	+	0.0260753i	−0.209833	+	0.977737i	$0.567292\pi$
$432$	4.61900	−	1.23766i	0.222232	−	0.0595468i
$433$	15.5293	+	15.5293i	0.746291	+	0.746291i	0.973780	−	0.227490i	$-0.0730518\pi$
$433$	15.5293	+	15.5293i	0.746291	+	0.746291i	−0.227490	+	0.973780i	$0.573052\pi$
$434$	−0.859788			−0.0412711
$435$	−10.2601	−	14.2425i	−0.491935	−	0.682876i
$436$	−13.9522	+	13.9522i	−0.668187	+	0.668187i
$437$	2.10476	−	7.85507i	0.100684	−	0.375759i
$438$	3.73670			0.178546
$439$	2.43746	−	9.09672i	0.116334	−	0.434163i	−0.883050	−	0.469279i	$-0.844514\pi$
$439$	2.43746	−	9.09672i	0.116334	−	0.434163i	0.999383	+	0.0351169i	$0.0111804\pi$
$440$	12.3706	−	1.24969i	0.589747	−	0.0595766i
$441$	7.44938	+	12.9027i	0.354733	+	0.614415i
$442$	−6.13664	+	10.6290i	−0.291890	+	0.505568i
$443$	−1.60697	+	1.60697i	−0.0763493	+	0.0763493i	−0.744250	−	0.667901i	$-0.767193\pi$
$443$	−1.60697	+	1.60697i	−0.0763493	+	0.0763493i	0.667901	+	0.744250i	$0.267193\pi$
$444$	4.65926	−	3.22803i	0.221119	−	0.153195i
$445$	−2.08314	+	0.790000i	−0.0987504	+	0.0374496i
$446$	−5.62233	−	20.9828i	−0.266225	−	0.993566i
$447$	2.78759	−	10.4034i	0.131848	−	0.492065i
$448$	0.0999004	+	0.0267682i	0.00471985	+	0.00126468i
$449$	−2.87798	−	0.771151i	−0.135820	−	0.0363929i	0.190269	−	0.981732i	$-0.439064\pi$
$449$	−2.87798	−	0.771151i	−0.135820	−	0.0363929i	−0.326089	+	0.945339i	$0.605731\pi$
$450$	7.06753	+	7.97801i	0.333166	+	0.376087i
$451$	26.1609	+	45.3119i	1.23187	+	2.13366i
$452$	1.93602			0.0910625
$453$	14.7998	−	3.96560i	0.695357	−	0.186320i
$454$			7.29785i			0.342505i
$455$	0.371374	−	0.140838i	0.0174103	−	0.00660258i
$456$	0.955096	−	1.65427i	0.0447265	−	0.0774685i
$457$	−3.99197	−	6.91429i	−0.186736	−	0.323437i	0.757424	−	0.652923i	$-0.226458\pi$
$457$	−3.99197	−	6.91429i	−0.186736	−	0.323437i	−0.944160	+	0.329487i	$0.893124\pi$
$458$	15.7522			0.736054
$459$	−33.0086	+	8.84462i	−1.54071	+	0.412832i
$460$	−7.19761	+	5.18506i	−0.335590	+	0.241755i
$461$	−7.44879	+	1.99590i	−0.346925	+	0.0929581i	−0.428074	−	0.903744i	$-0.640808\pi$
$461$	−7.44879	+	1.99590i	−0.346925	+	0.0929581i	0.0811492	+	0.996702i	$0.474141\pi$
$462$	0.464102	−	0.267949i	0.0215920	−	0.0124661i
$463$	4.63923	−	2.67846i	0.215603	−	0.124479i	−0.388309	−	0.921529i	$-0.626941\pi$
$463$	4.63923	−	2.67846i	0.215603	−	0.124479i	0.603913	+	0.797050i	$0.293607\pi$
$464$	−8.13713	+	2.18034i	−0.377757	+	0.101220i
$465$	14.0549	−	10.1249i	0.651779	−	0.469533i
$466$	−2.13533	+	0.572161i	−0.0989175	+	0.0265049i
$467$	−1.68754			−0.0780898			−0.0390449	−	0.999237i	$-0.512432\pi$
$467$	−1.68754			−0.0780898			−0.0390449	+	0.999237i	$0.512432\pi$
$468$	−1.83049	−	3.17050i	−0.0846145	−	0.146557i
$469$	0.0308078	−	0.0533607i	0.00142257	−	0.00246397i
$470$	12.1193	−	4.59605i	0.559020	−	0.212000i
$471$		−	2.55019i		−	0.117507i
$472$	−7.26430	+	1.94646i	−0.334367	+	0.0895932i
$473$	6.59022			0.303019
$474$	−5.80518	−	10.0549i	−0.266641	−	0.461836i
$475$	10.2307	+	0.619114i	0.469418	+	0.0284069i
$476$	−0.713915	−	0.191293i	−0.0327222	−	0.00876790i
$477$	7.35311	+	1.97026i	0.336676	+	0.0902120i
$478$	6.10746	−	22.7934i	0.279349	−	1.04254i
$479$	1.22580	+	4.57475i	0.0560083	+	0.209026i	0.988259	−	0.152787i	$-0.0488248\pi$
$479$	1.22580	+	4.57475i	0.0560083	+	0.209026i	−0.932251	+	0.361812i	$0.882158\pi$
$480$	−1.94829	+	0.738859i	−0.0889268	+	0.0337241i
$481$	−7.96919	−	6.75478i	−0.363364	−	0.307991i
$482$	−13.7651	+	13.7651i	−0.626983	+	0.626983i
$483$	−0.191169	+	0.331114i	−0.00869847	+	0.0150662i
$484$	−9.95946	−	17.2503i	−0.452703	−	0.784104i
$485$	−35.7409	+	3.61057i	−1.62291	+	0.163947i
$486$	4.18060	−	15.6022i	0.189636	−	0.707730i
$487$	5.21509			0.236318			0.118159	−	0.992995i	$-0.462301\pi$
$487$	5.21509			0.236318			0.118159	+	0.992995i	$0.462301\pi$
$488$	−1.72657	+	6.44364i	−0.0781581	+	0.291690i
$489$	12.7895	−	12.7895i	0.578361	−	0.578361i
$490$	−9.13507	−	12.6808i	−0.412680	−	0.572859i
$491$	11.4803			0.518098			0.259049	−	0.965864i	$-0.416591\pi$
$491$	11.4803			0.518098			0.259049	+	0.965864i	$0.416591\pi$
$492$	−6.20014	−	6.20014i	−0.279524	−	0.279524i
$493$	58.1501	−	15.5813i	2.61895	−	0.701745i
$494$	−3.40060	−	0.911187i	−0.153000	−	0.0409963i
$495$	10.8780	−	24.1690i	0.488928	−	1.08631i
$496$	−2.15161	−	8.02993i	−0.0966103	−	0.360554i
$497$	−0.183240	−	0.683863i	−0.00821946	−	0.0306754i
$498$	5.83817	+	3.37067i	0.261615	+	0.151043i
$499$	9.13764	−	34.1022i	0.409057	−	1.52662i	−0.387391	−	0.921915i	$-0.626624\pi$
$499$	9.13764	−	34.1022i	0.409057	−	1.52662i	0.796448	−	0.604707i	$-0.206710\pi$
$500$	−8.21731	−	7.58128i	−0.367489	−	0.339045i
$501$	−0.652690	−	2.43587i	−0.0291601	−	0.108827i
$502$	−0.788407	+	0.211253i	−0.0351883	+	0.00942869i
$503$	−10.6996	−	6.17744i	−0.477073	−	0.275438i	0.242123	−	0.970246i	$-0.422156\pi$
$503$	−10.6996	−	6.17744i	−0.477073	−	0.275438i	−0.719196	+	0.694807i	$0.755490\pi$
$504$	0.155892	−	0.155892i	0.00694400	−	0.00694400i
$505$	2.31149	+	22.8814i	0.102860	+	1.01821i
$506$	19.1038	+	11.0296i	0.849266	+	0.490324i
$507$	−6.62240	+	6.62240i	−0.294111	+	0.294111i
$508$	5.42285	−	5.42285i	0.240600	−	0.240600i
$509$	−20.5218	+	35.5447i	−0.909611	+	1.57549i	−0.0950057	+	0.995477i	$0.530287\pi$
$509$	−20.5218	+	35.5447i	−0.909611	+	1.57549i	−0.814605	+	0.580016i	$0.803046\pi$
$510$	13.9230	−	5.28008i	0.616520	−	0.233806i
$511$	0.359166	−	0.207365i	0.0158886	−	0.00917327i
$512$			1.00000i			0.0441942i
$513$	−4.90122	−	8.48916i	−0.216394	−	0.374806i
$514$	21.7048	−	12.5313i	0.957357	−	0.552730i
$515$	−42.0519	+	4.24810i	−1.85303	+	0.187194i
$516$	−1.06679	+	0.285845i	−0.0469627	+	0.0125836i
$517$	−22.7912	−	22.7912i	−1.00235	−	1.00235i
$518$	0.268705	−	0.568835i	0.0118062	−	0.0249932i
$519$		−	15.3366i		−	0.673203i
$520$	2.24471	+	3.11597i	0.0984368	+	0.136644i
$521$	8.38514	−	4.84116i	0.367360	−	0.212095i	−0.304945	−	0.952370i	$-0.598638\pi$
$521$	8.38514	−	4.84116i	0.367360	−	0.212095i	0.672304	+	0.740275i	$0.265305\pi$
$522$	−4.64772	+	17.3455i	−0.203425	+	0.759194i
$523$	34.6083	−	19.9811i	1.51332	−	0.873714i	0.513439	−	0.858126i	$-0.328371\pi$
$523$	34.6083	−	19.9811i	1.51332	−	0.873714i	0.999879	−	0.0155877i	$-0.00496192\pi$
$524$	−3.40094	+	3.40094i	−0.148571	+	0.148571i
$525$	−0.457078	−	0.152608i	−0.0199485	−	0.00666038i
$526$	4.03287	+	4.03287i	0.175842	+	0.175842i
$527$	15.3760	+	57.3840i	0.669789	+	2.49969i
$528$	3.66390	+	3.66390i	0.159451	+	0.159451i
$529$	7.26190			0.315735
$530$	−7.88196	−	1.28105i	−0.342371	−	0.0556452i
$531$	−4.14918	+	15.4850i	−0.180059	+	0.671990i
$532$		−	0.212009i		−	0.00919174i
$533$	−8.08018	+	13.9953i	−0.349991	+	0.606203i
$534$	−0.804063	−	0.464226i	−0.0347952	−	0.0200890i
$535$	−32.4867	−	5.28003i	−1.40452	−	0.228276i
$536$	0.575454	+	0.154193i	0.0248558	+	0.00666010i
$537$	−0.0659082	−	0.114156i	−0.00284415	−	0.00492621i
$538$	−4.22902	+	7.32489i	−0.182326	+	0.315798i
$539$	−19.4319	+	33.6571i	−0.836993	+	1.44971i
$540$	−1.71537	+	10.5542i	−0.0738180	+	0.454183i
$541$	7.18294	+	7.18294i	0.308819	+	0.308819i	0.844451	−	0.535633i	$-0.179927\pi$
$541$	7.18294	+	7.18294i	0.308819	+	0.308819i	−0.535633	+	0.844451i	$0.679927\pi$
$542$	13.1655	−	7.60110i	0.565506	−	0.326495i
$543$	−1.68997	−	6.30704i	−0.0725234	−	0.270661i
$544$		−	7.14626i		−	0.306394i
$545$	−15.6448	−	41.2537i	−0.670151	−	1.76711i
$546$	0.143345	+	0.0827602i	0.00613460	+	0.00354181i
$547$			25.9211i			1.10830i	0.832415	+	0.554152i	$0.186958\pi$
$547$			25.9211i			1.10830i	−0.832415	+	0.554152i	$0.813042\pi$
$548$	−6.92489	−	1.85552i	−0.295816	−	0.0792638i
$549$	10.0552	+	10.0552i	0.429144	+	0.429144i
$550$	−8.80482	+	26.3713i	−0.375439	+	1.12448i
$551$	8.63431	+	14.9551i	0.367834	+	0.637107i
$552$	−3.57081	−	0.956796i	−0.151984	−	0.0407239i
$553$	−1.11597	−	0.644307i	−0.0474560	−	0.0273987i
$554$	−15.4531			−0.656541
$555$	2.30616	+	12.4630i	0.0978911	+	0.529024i
$556$	10.0270			0.425239
$557$	−34.7420	−	20.0583i	−1.47206	−	0.849897i	−0.472558	−	0.881300i	$-0.656669\pi$
$557$	−34.7420	−	20.0583i	−1.47206	−	0.849897i	−0.999507	+	0.0314026i	$0.990003\pi$
$558$	−17.1170	−	4.58649i	−0.724621	−	0.194162i
$559$	1.01774	+	1.76279i	0.0430460	+	0.0745579i
$560$	−0.146264	+	0.179137i	−0.00618080	+	0.00756990i
$561$	−26.1832	−	26.1832i	−1.10546	−	1.10546i
$562$	−4.29157	−	1.14992i	−0.181029	−	0.0485065i
$563$		−	10.1495i		−	0.427752i	−0.976861	−	0.213876i	$-0.931391\pi$
$563$		−	10.1495i		−	0.427752i	0.976861	−	0.213876i	$-0.0686088\pi$
$564$	4.67786	+	2.70076i	0.196973	+	0.113723i
$565$	−1.77675	+	3.94765i	−0.0747486	+	0.166079i
$566$		−	8.36459i		−	0.351590i
$567$	−0.0519009	−	0.193697i	−0.00217963	−	0.00813451i
$568$	5.92833	−	3.42272i	0.248747	−	0.143614i
$569$	27.5816	+	27.5816i	1.15628	+	1.15628i	0.985269	+	0.171012i	$0.0547036\pi$
$569$	27.5816	+	27.5816i	1.15628	+	1.15628i	0.171012	+	0.985269i	$0.445296\pi$
$570$	2.49663	+	3.46569i	0.104572	+	0.145162i
$571$	19.0735	−	33.0363i	0.798202	−	1.38253i	−0.122584	−	0.992458i	$-0.539118\pi$
$571$	19.0735	−	33.0363i	0.798202	−	1.38253i	0.920786	−	0.390068i	$-0.127549\pi$
$572$	4.77489	−	8.27035i	0.199648	−	0.345801i
$573$	−0.532134	−	0.921683i	−0.0222302	−	0.0385039i
$574$	−0.940020	−	0.251878i	−0.0392357	−	0.0105132i
$575$	−3.96713	−	19.4349i	−0.165441	−	0.810490i
$576$	1.84607	+	1.06583i	0.0769194	+	0.0444094i
$577$	21.7350	−	37.6461i	0.904839	−	1.56723i	0.0837050	−	0.996491i	$-0.473325\pi$
$577$	21.7350	−	37.6461i	0.904839	−	1.56723i	0.821134	−	0.570736i	$-0.193342\pi$
$578$			34.0691i			1.41709i
$579$	−2.37399	+	8.85986i	−0.0986598	+	0.368203i
$580$	3.02192	−	18.5931i	0.125478	−	0.772035i
$581$	0.748209			0.0310409
$582$	−10.5856	−	10.5856i	−0.438789	−	0.438789i
$583$	5.13948	+	19.1808i	0.212856	+	0.794388i
$584$	2.83548	+	2.83548i	0.117333	+	0.117333i
$585$	8.14475	−	0.822787i	0.336744	−	0.0340181i
$586$	5.98210	−	5.98210i	0.247118	−	0.247118i
$587$	9.49194	−	5.48017i	0.391774	−	0.226191i	−0.291154	−	0.956676i	$-0.594039\pi$
$587$	9.49194	−	5.48017i	0.391774	−	0.226191i	0.682929	+	0.730485i	$0.260706\pi$
$588$	1.68569	−	6.29107i	0.0695166	−	0.259439i
$589$	−14.7580	+	8.52056i	−0.608094	+	0.351083i
$590$	2.69777	−	16.5987i	0.111065	−	0.683357i
$591$			14.5236i			0.597423i
$592$	5.98502	+	1.08604i	0.245983	+	0.0446361i
$593$	21.7960	+	21.7960i	0.895055	+	0.895055i	0.994994	−	0.0999387i	$-0.0318647\pi$
$593$	21.7960	+	21.7960i	0.895055	+	0.895055i	−0.0999387	+	0.994994i	$0.531865\pi$
$594$	25.6838	−	6.88196i	1.05382	−	0.282370i
$595$	1.04524	−	1.28016i	0.0428508	−	0.0524813i
$596$	10.0096	−	5.77904i	0.410009	−	0.236719i
$597$	10.0628	+	17.4293i	0.411843	+	0.713333i
$598$			6.81330i			0.278617i
$599$	21.0451	−	12.1504i	0.859878	−	0.496451i	−0.00409367	−	0.999992i	$-0.501303\pi$
$599$	21.0451	−	12.1504i	0.859878	−	0.496451i	0.863971	+	0.503541i	$0.167970\pi$
$600$	0.281441	−	4.65075i	0.0114898	−	0.189866i
$601$	9.26404	−	16.0458i	0.377888	−	0.654522i	−0.612867	−	0.790186i	$-0.709984\pi$
$601$	9.26404	−	16.0458i	0.377888	−	0.654522i	0.990755	+	0.135665i	$0.0433170\pi$
$602$	−0.0866755	+	0.0866755i	−0.00353263	+	0.00353263i
$603$	0.897984	−	0.897984i	0.0365687	−	0.0365687i
$604$	14.2396	+	8.22122i	0.579400	+	0.334517i
$605$	44.3145	−	4.47667i	1.80164	−	0.182003i
$606$	−6.77696	+	6.77696i	−0.275295	+	0.275295i
$607$	−25.9002	−	14.9535i	−1.05126	−	0.606943i	−0.128256	−	0.991741i	$-0.540938\pi$
$607$	−25.9002	−	14.9535i	−1.05126	−	0.606943i	−0.923001	+	0.384798i	$0.874271\pi$
$608$	1.98004	−	0.530550i	0.0803012	−	0.0215166i
$609$	−0.210133	−	0.784227i	−0.00851502	−	0.0317785i
$610$	−11.5544	−	9.43415i	−0.467825	−	0.381978i
$611$	2.57660	−	9.61601i	0.104238	−	0.389022i
$612$	−13.1925	−	7.61668i	−0.533274	−	0.307886i
$613$	−2.36036	−	8.80896i	−0.0953338	−	0.355791i	0.901736	−	0.432287i	$-0.142293\pi$
$613$	−2.36036	−	8.80896i	−0.0953338	−	0.355791i	−0.997070	+	0.0764964i	$0.975627\pi$
$614$	3.18470	+	11.8855i	0.128524	+	0.479658i
$615$	18.3325	−	6.95234i	0.739240	−	0.280346i
$616$	0.555494	+	0.148844i	0.0223815	+	0.00599710i
$617$	35.9026	−	9.62007i	1.44538	−	0.387289i	0.550968	−	0.834526i	$-0.314259\pi$
$617$	35.9026	−	9.62007i	1.44538	−	0.387289i	0.894415	+	0.447237i	$0.147592\pi$
$618$	−12.4548	−	12.4548i	−0.501006	−	0.501006i
$619$	−34.2163			−1.37527			−0.687635	−	0.726056i	$-0.741351\pi$
$619$	−34.2163			−1.37527			−0.687635	+	0.726056i	$0.741351\pi$
$620$	18.3481	+	2.98210i	0.736878	+	0.119764i
$621$	−13.4142	+	13.4142i	−0.538294	+	0.538294i
$622$	7.18747	−	26.8240i	0.288191	−	1.07554i
$623$	−0.103047			−0.00412850
$624$	−0.414214	+	1.54587i	−0.0165818	+	0.0618842i
$625$	23.0000	−	9.79796i	0.920000	−	0.391918i
$626$	0.935758	+	1.62078i	0.0374004	+	0.0647794i
$627$	5.31079	−	9.19856i	0.212092	−	0.367355i
$628$	1.93514	−	1.93514i	0.0772203	−	0.0772203i
$629$	−42.7706	−	7.76116i	−1.70537	−	0.309458i
$630$	0.174805	+	0.460942i	0.00696441	+	0.0183644i
$631$	7.88594	+	29.4307i	0.313934	+	1.17162i	0.924977	+	0.380022i	$0.124084\pi$
$631$	7.88594	+	29.4307i	0.313934	+	1.17162i	−0.611043	+	0.791597i	$0.709250\pi$
$632$	3.22474	−	12.0349i	0.128273	−	0.478723i
$633$	9.03491	+	2.42090i	0.359106	+	0.0962220i
$634$	6.16108	+	1.65086i	0.244688	+	0.0655639i
$635$	6.08075	+	16.0342i	0.241307	+	0.636300i
$636$	−1.66390	−	2.88196i	−0.0659780	−	0.114277i
$637$	−12.0037			−0.475604
$638$	−45.2464	+	12.1237i	−1.79132	+	0.479983i
$639$		−	14.5921i		−	0.577255i
$640$	−2.03906	−	0.917738i	−0.0806008	−	0.0362768i
$641$	−0.400224	+	0.693208i	−0.0158079	+	0.0273801i	−0.873821	−	0.486247i	$-0.838365\pi$
$641$	−0.400224	+	0.693208i	−0.0158079	+	0.0273801i	0.858013	+	0.513628i	$0.171699\pi$
$642$	−6.85802	−	11.8784i	−0.270664	−	0.468804i
$643$	−40.2835			−1.58863			−0.794313	−	0.607509i	$-0.792169\pi$
$643$	−40.2835			−1.58863			−0.794313	+	0.607509i	$0.792169\pi$
$644$	−0.396318	+	0.106193i	−0.0156171	+	0.00418459i
$645$	0.396177	−	2.43757i	0.0155995	−	0.0959794i
$646$	−14.1499	+	3.79145i	−0.556720	+	0.149173i
$647$	−34.5740	+	19.9613i	−1.35924	+	0.784759i	−0.989522	−	0.144383i	$-0.953880\pi$
$647$	−34.5740	+	19.9613i	−1.35924	+	0.784759i	−0.369721	+	0.929143i	$0.620547\pi$
$648$	1.67914	−	0.969450i	0.0659627	−	0.0380836i
$649$	−40.3930	+	10.8233i	−1.58556	+	0.424850i
$650$	−8.41370	+	1.71744i	−0.330012	+	0.0673635i
$651$	0.773895	−	0.207365i	0.0303313	−	0.00812726i
$652$	19.4098			0.760148
$653$	−11.8499	−	20.5247i	−0.463724	−	0.803193i	0.535419	−	0.844586i	$-0.320154\pi$
$653$	−11.8499	−	20.5247i	−0.463724	−	0.803193i	−0.999143	+	0.0413936i	$0.986820\pi$
$654$	9.19333	−	15.9233i	0.359488	−	0.622651i
$655$	−3.81354	−	10.0559i	−0.149007	−	0.392916i
$656$		−	9.40957i		−	0.367382i
$657$	8.25660	−	2.21235i	0.322121	−	0.0863119i
$658$	0.599506			0.0233712
$659$	−3.68216	−	6.37769i	−0.143437	−	0.248440i	0.785352	−	0.619050i	$-0.212482\pi$
$659$	−3.68216	−	6.37769i	−0.143437	−	0.248440i	−0.928789	+	0.370610i	$0.879149\pi$
$660$	−10.8334	+	4.10841i	−0.421690	+	0.159920i
$661$	−35.4174	−	9.49007i	−1.37758	−	0.369121i	−0.507337	−	0.861747i	$-0.669370\pi$
$661$	−35.4174	−	9.49007i	−1.37758	−	0.369121i	−0.870241	+	0.492626i	$0.836037\pi$
$662$	6.22338	+	1.66755i	0.241879	+	0.0648112i
$663$	2.96008	−	11.0472i	0.114960	−	0.429036i
$664$	1.87239	+	6.98784i	0.0726627	+	0.271181i
$665$	0.432298	+	0.194568i	0.0167638	+	0.00754504i
$666$	8.38390	−	9.89121i	0.324870	−	0.383277i
$667$	23.6314	−	23.6314i	0.915010	−	0.915010i
$668$	1.35311	−	2.34366i	0.0523535	−	0.0906790i
$669$	10.1213	+	17.5306i	0.391313	+	0.677774i
$670$	−0.842524	+	1.03188i	−0.0325495	+	0.0398649i
$671$	−9.60055	+	35.8297i	−0.370625	+	1.38319i
$672$	−0.0963763			−0.00371780
$673$	6.20302	−	23.1500i	0.239109	−	0.892367i	−0.737144	−	0.675735i	$-0.763826\pi$
$673$	6.20302	−	23.1500i	0.239109	−	0.892367i	0.976253	−	0.216632i	$-0.0695071\pi$
$674$	8.76198	−	8.76198i	0.337499	−	0.337499i
$675$	−19.9465	−	13.1838i	−0.767740	−	0.507444i
$676$	−10.0504			−0.386554
$677$	−5.42867	−	5.42867i	−0.208641	−	0.208641i	0.595049	−	0.803690i	$-0.297133\pi$
$677$	−5.42867	−	5.42867i	−0.208641	−	0.208641i	−0.803690	+	0.595049i	$0.797133\pi$
$678$	−1.74261	+	0.466930i	−0.0669244	+	0.0179323i
$679$	−1.60492	−	0.430037i	−0.0615911	−	0.0165033i
$680$	14.5716	+	6.55840i	0.558797	+	0.251503i
$681$	−1.76010	−	6.56879i	−0.0674473	−	0.251717i
$682$	−11.9640	−	44.6502i	−0.458125	−	1.70975i
$683$	−15.3520	−	8.86346i	−0.587427	−	0.339151i	0.176653	−	0.984273i	$-0.443473\pi$
$683$	−15.3520	−	8.86346i	−0.587427	−	0.339151i	−0.764079	+	0.645122i	$0.776806\pi$
$684$	1.13095	−	4.22076i	0.0432429	−	0.161385i
$685$	10.1387	−	12.4174i	0.387381	−	0.474443i
$686$	−0.374469	−	1.39754i	−0.0142973	−	0.0533582i
$687$	−14.1786	+	3.79914i	−0.540947	+	0.144946i
$688$	−1.02640	−	0.592594i	−0.0391313	−	0.0225925i
$689$	−4.33688	+	4.33688i	−0.165222	+	0.165222i
$690$	5.22803	−	6.40300i	0.199028	−	0.243758i
$691$	0.382057	+	0.220581i	0.0145342	+	0.00839130i	0.507249	−	0.861799i	$-0.330662\pi$
$691$	0.382057	+	0.220581i	0.0145342	+	0.00839130i	−0.492715	+	0.870191i	$0.663996\pi$
$692$	11.6377	−	11.6377i	0.442400	−	0.442400i
$693$	0.866836	−	0.866836i	0.0329284	−	0.0329284i
$694$	−14.2002	+	24.5955i	−0.539032	+	0.933631i
$695$	−9.20214	+	20.4456i	−0.349057	+	0.775546i
$696$	6.79837	−	3.92504i	0.257692	−	0.148778i
$697$			67.2433i			2.54702i
$698$	4.62020	+	8.00242i	0.174877	+	0.302896i
$699$	1.78402	−	1.03000i	0.0674778	−	0.0389583i
$700$	−0.231037	−	0.462642i	−0.00873240	−	0.0174862i
$701$	−38.1400	+	10.2196i	−1.44053	+	0.385988i	−0.892719	−	0.450615i	$-0.851205\pi$
$701$	−38.1400	+	10.2196i	−1.44053	+	0.385988i	−0.547810	+	0.836603i	$0.684538\pi$
$702$	5.80725	+	5.80725i	0.219180	+	0.219180i
$703$	−1.02494	−	12.4268i	−0.0386565	−	0.468685i
$704$			5.56048i			0.209568i
$705$	−9.80006	+	7.05983i	−0.369092	+	0.265889i
$706$	8.90031	−	5.13859i	0.334967	−	0.193394i
$707$	−0.275310	+	1.02747i	−0.0103541	+	0.0386421i
$708$	6.06914	−	3.50402i	0.228092	−	0.131689i
$709$	13.8629	−	13.8629i	0.520634	−	0.520634i	−0.397129	−	0.917763i	$-0.629993\pi$
$709$	13.8629	−	13.8629i	0.520634	−	0.520634i	0.917763	+	0.397129i	$0.129993\pi$
$710$	1.53848	+	15.2294i	0.0577381	+	0.571548i
$711$	−18.7802	−	18.7802i	−0.704313	−	0.704313i
$712$	−0.257875	−	0.962402i	−0.00966427	−	0.0360675i
$713$	23.3200	+	23.3200i	0.873342	+	0.873342i
$714$	0.688731			0.0257751
$715$	12.4816	+	17.3263i	0.466787	+	0.647967i
$716$	0.0366116	−	0.136636i	0.00136824	−	0.00510634i
$717$			21.9893i			0.821206i
$718$	−6.12800	+	10.6140i	−0.228695	+	0.396111i
$719$	12.5516	+	7.24669i	0.468097	+	0.270256i	0.715443	−	0.698671i	$-0.246225\pi$
$719$	12.5516	+	7.24669i	0.468097	+	0.270256i	−0.247346	+	0.968927i	$0.579558\pi$
$720$	−3.86749	+	2.78609i	−0.144133	+	0.103831i
$721$	−1.88831	−	0.505971i	−0.0703243	−	0.0188433i
$722$	7.39898	+	12.8154i	0.275362	+	0.476940i
$723$	9.07007	−	15.7098i	0.337320	−	0.584255i
$724$	3.50352	−	6.06828i	0.130207	−	0.225526i
$725$	35.1390	+	23.2254i	1.30503	+	0.862571i
$726$	13.1249	+	13.1249i	0.487112	+	0.487112i
$727$	28.9864	−	16.7353i	1.07505	−	0.620678i	0.145490	−	0.989360i	$-0.453524\pi$
$727$	28.9864	−	16.7353i	1.07505	−	0.620678i	0.929556	+	0.368681i	$0.120191\pi$
$728$	0.0459728	+	0.171573i	0.00170387	+	0.00635891i
$729$			9.23511i			0.342041i
$730$	−8.38392	+	3.17948i	−0.310303	+	0.117678i
$731$	7.33495	+	4.23484i	0.271293	+	0.156631i
$732$		−	6.21634i		−	0.229762i
$733$	0.195861	+	0.0524807i	0.00723428	+	0.00193842i	0.262434	−	0.964950i	$-0.415475\pi$
$733$	0.195861	+	0.0524807i	0.00723428	+	0.00193842i	−0.255200	+	0.966888i	$0.582141\pi$
$734$	−3.73305	−	3.73305i	−0.137789	−	0.137789i
$735$	11.2808	+	9.21076i	0.416100	+	0.339744i
$736$	−1.98356	−	3.43563i	−0.0731151	−	0.126639i
$737$	3.19980	+	0.857384i	0.117866	+	0.0315821i
$738$	−17.3707	−	10.0290i	−0.639424	−	0.369171i
$739$	34.4241			1.26631			0.633155	−	0.774025i	$-0.281759\pi$
$739$	34.4241			1.26631			0.633155	+	0.774025i	$0.281759\pi$
$740$	−7.70719	+	11.2071i	−0.283322	+	0.411981i
$741$	3.28064			0.120517
$742$	−0.319864	−	0.184674i	−0.0117426	−	0.00677958i
$743$	−24.8398	−	6.65580i	−0.911283	−	0.244178i	−0.227428	−	0.973795i	$-0.573031\pi$
$743$	−24.8398	−	6.65580i	−0.911283	−	0.244178i	−0.683856	+	0.729617i	$0.739698\pi$
$744$	3.87333	+	6.70881i	0.142003	+	0.245957i
$745$	2.59762	+	25.7138i	0.0951694	+	0.942079i
$746$	−9.02082	−	9.02082i	−0.330276	−	0.330276i
$747$	14.8957	+	3.99128i	0.545003	+	0.146033i
$748$		−	39.7366i		−	1.45292i
$749$	−1.31837	−	0.761159i	−0.0481720	−	0.0278121i
$750$	9.22486	+	4.84204i	0.336844	+	0.176806i
$751$			46.7091i			1.70444i	0.523183	+	0.852220i	$0.324744\pi$
$751$			46.7091i			1.70444i	−0.523183	+	0.852220i	$0.675256\pi$
$752$	1.50026	+	5.59904i	0.0547088	+	0.204176i
$753$	0.658695	−	0.380298i	0.0240042	−	0.0138588i
$754$	−10.2304	−	10.2304i	−0.372570	−	0.372570i
$755$	−29.8317	+	21.4904i	−1.08569	+	0.782115i
$756$	−0.247285	+	0.428310i	−0.00899366	+	0.0155775i
$757$	−1.06570	+	1.84585i	−0.0387336	+	0.0670886i	−0.884742	−	0.466081i	$-0.845666\pi$
$757$	−1.06570	+	1.84585i	−0.0387336	+	0.0670886i	0.846009	+	0.533169i	$0.178999\pi$
$758$	−3.18852	−	5.52269i	−0.115812	−	0.200593i
$759$	−19.8554	−	5.32024i	−0.720706	−	0.193113i
$760$	−0.735335	+	4.52432i	−0.0266734	+	0.164114i
$761$	2.82489	+	1.63095i	0.102402	+	0.0591218i	0.550326	−	0.834950i	$-0.314503\pi$
$761$	2.82489	+	1.63095i	0.102402	+	0.0591218i	−0.447924	+	0.894071i	$0.647837\pi$
$762$	−3.57321	+	6.18899i	−0.129444	+	0.224203i
$763$		−	2.04070i		−	0.0738784i
$764$	0.295597	−	1.10318i	0.0106943	−	0.0399118i
$765$	27.6381	−	19.9101i	0.999257	−	0.719851i
$766$	11.8474			0.428063
$767$	−9.13306	−	9.13306i	−0.329776	−	0.329776i
$768$	−0.241181	−	0.900100i	−0.00870287	−	0.0324795i
$769$	11.7676	+	11.7676i	0.424350	+	0.424350i	0.886698	−	0.462349i	$-0.152993\pi$
$769$	11.7676	+	11.7676i	0.424350	+	0.424350i	−0.462349	+	0.886698i	$0.652993\pi$
$770$	−0.813300	+	0.996085i	−0.0293093	+	0.0358964i
$771$	−16.5142	+	16.5142i	−0.594743	+	0.594743i
$772$	−8.52446	+	4.92160i	−0.306802	+	0.177132i
$773$	−10.4016	+	38.8194i	−0.374120	+	1.39624i	0.480505	+	0.876992i	$0.340453\pi$
$773$	−10.4016	+	38.8194i	−0.374120	+	1.39624i	−0.854626	+	0.519245i	$0.826213\pi$
$774$	−2.18794	+	1.26321i	−0.0786437	+	0.0454050i
$775$	−22.9194	+	34.6761i	−0.823290	+	1.24560i
$776$		−	16.0652i		−	0.576706i
$777$	−0.104669	+	0.576815i	−0.00375498	+	0.0206931i
$778$	−2.63166	−	2.63166i	−0.0943496	−	0.0943496i
$779$	−18.6313	+	4.99225i	−0.667536	+	0.178866i
$780$	−2.77197	−	2.26330i	−0.0992525	−	0.0810393i
$781$	32.9643	−	19.0320i	1.17956	−	0.681017i
$782$	14.1751	+	24.5519i	0.506900	+	0.877976i
$783$		−	40.2839i		−	1.43963i
$784$	6.05291	−	3.49465i	0.216176	−	0.124809i
$785$	2.16991	+	5.72180i	0.0774473	+	0.204220i
$786$	2.24094	−	3.88142i	0.0799317	−	0.138446i
$787$	−30.9931	+	30.9931i	−1.10479	+	1.10479i	−0.110960	+	0.993825i	$0.535393\pi$
$787$	−30.9931	+	30.9931i	−1.10479	+	1.10479i	−0.993825	+	0.110960i	$0.964607\pi$
$788$	−11.0208	+	11.0208i	−0.392600	+	0.392600i
$789$	−4.60264	−	2.65733i	−0.163858	−	0.0946036i
$790$	21.5804	+	17.6203i	0.767797	+	0.626903i
$791$	−0.141585	+	0.141585i	−0.00503418	+	0.00503418i
$792$	10.2650	+	5.92650i	0.364751	+	0.210589i
$793$	−11.0666	+	2.96528i	−0.392985	+	0.105300i
$794$	2.08138	+	7.76782i	0.0738655	+	0.275670i
$795$	7.40352	−	0.747907i	0.262576	−	0.0265255i
$796$	−5.58983	+	20.8615i	−0.198126	+	0.739417i
$797$	29.9995	+	17.3202i	1.06264	+	0.613514i	0.926161	−	0.377129i	$-0.123089\pi$
$797$	29.9995	+	17.3202i	1.06264	+	0.613514i	0.136477	+	0.990643i	$0.456422\pi$
$798$	0.0511325	+	0.190829i	0.00181007	+	0.00675527i
$799$	−10.7212	−	40.0122i	−0.379290	−	1.41553i
$800$	3.74264	−	3.31552i	0.132322	−	0.117221i
$801$	−2.05151	−	0.549699i	−0.0724864	−	0.0194227i
$802$	−14.5754	+	3.90547i	−0.514676	+	0.137907i
$803$	15.7666	+	15.7666i	0.556391	+	0.556391i
$804$	−0.555154			−0.0195788
$805$	0.147182	−	0.905572i	0.00518748	−	0.0319172i
$806$	10.0956	−	10.0956i	0.355604	−	0.355604i
$807$	2.03992	−	7.61309i	0.0718086	−	0.267993i
$808$	−10.2850			−0.361824
$809$	−8.37202	+	31.2448i	−0.294344	+	1.09851i	0.647392	+	0.762157i	$0.275860\pi$
$809$	−8.37202	+	31.2448i	−0.294344	+	1.09851i	−0.941737	+	0.336351i	$0.890807\pi$
$810$	0.435758	+	4.31356i	0.0153110	+	0.151563i
$811$	−18.5340	−	32.1018i	−0.650817	−	1.12725i	−0.982925	−	0.184006i	$-0.941093\pi$
$811$	−18.5340	−	32.1018i	−0.650817	−	1.12725i	0.332108	−	0.943241i	$-0.392240\pi$
$812$	0.435633	−	0.754539i	0.0152877	−	0.0264791i
$813$	−10.0170	+	10.0170i	−0.351312	+	0.351312i
$814$	33.2796	+	6.03892i	1.16645	+	0.211664i
$815$	−17.8131	+	39.5778i	−0.623967	+	1.38635i
$816$	1.72354	+	6.43235i	0.0603361	+	0.225177i
$817$	−0.628802	+	2.34672i	−0.0219990	+	0.0821014i
$818$	21.4831	+	5.75637i	0.751138	+	0.201267i
$819$	0.365734	+	0.0979981i	0.0127798	+	0.00342433i
$820$	19.1867	+	8.63552i	0.670027	+	0.301565i
$821$	−13.6420	−	23.6286i	−0.476109	−	0.824645i	0.523516	−	0.852016i	$-0.324620\pi$
$821$	−13.6420	−	23.6286i	−0.476109	−	0.824645i	−0.999625	+	0.0273708i	$0.991287\pi$
$822$	6.68060			0.233013
$823$	42.9224	−	11.5010i	1.49618	−	0.400901i	0.584362	−	0.811493i	$-0.301345\pi$
$823$	42.9224	−	11.5010i	1.49618	−	0.400901i	0.911819	+	0.410592i	$0.134678\pi$
$824$		−	18.9019i		−	0.658479i
$825$	1.56495	−	25.8604i	0.0544844	−	0.900343i
$826$	0.388905	−	0.673603i	0.0135317	−	0.0234377i
$827$	13.1602	+	22.7942i	0.457626	+	0.792631i	0.998835	−	0.0482570i	$-0.0153666\pi$
$827$	13.1602	+	22.7942i	0.457626	+	0.792631i	−0.541209	+	0.840888i	$0.682033\pi$
$828$	−8.45654			−0.293885
$829$	−15.2862	+	4.09592i	−0.530911	+	0.142257i	−0.514309	−	0.857605i	$-0.671952\pi$
$829$	−15.2862	+	4.09592i	−0.530911	+	0.142257i	−0.0166022	+	0.999862i	$0.505285\pi$
$830$	−15.9670	−	2.59510i	−0.554222	−	0.0900773i
$831$	13.9094	−	3.72700i	0.482510	−	0.129288i
$832$	−1.48735	+	0.858719i	−0.0515644	+	0.0297707i
$833$	−43.2557	+	24.9737i	−1.49872	+	0.865288i
$834$	−9.02528	+	2.41832i	−0.312520	+	0.0837395i
$835$	3.53706	+	4.90994i	0.122405	+	0.169916i
$836$	11.0100	−	2.95011i	0.380788	−	0.102032i
$837$	39.7532			1.37407
$838$	−2.32258	−	4.02283i	−0.0802322	−	0.138966i
$839$	6.91184	−	11.9717i	0.238623	−	0.413308i	−0.721696	−	0.692210i	$-0.756637\pi$
$839$	6.91184	−	11.9717i	0.238623	−	0.413308i	0.960319	+	0.278902i	$0.0899706\pi$
$840$	0.0884482	−	0.196517i	0.00305175	−	0.00678048i
$841$			41.9668i			1.44713i
$842$	−6.74716	+	1.80790i	−0.232523	+	0.0623042i
$843$	4.14018			0.142595
$844$	5.01884	+	8.69289i	0.172756	+	0.299221i
$845$	9.22363	−	20.4934i	0.317303	−	0.704993i
$846$	11.9352	+	3.19803i	0.410341	+	0.109950i
$847$	1.98991	+	0.533194i	0.0683740	+	0.0183208i
$848$	0.924288	−	3.44949i	0.0317402	−	0.118456i
$849$	2.01738	+	7.52897i	0.0692363	+	0.258393i
$850$	−26.7459	+	23.6935i	−0.917377	+	0.812682i
$851$	−22.7166	+	8.14043i	−0.778715	+	0.279050i
$852$	−4.51059	+	4.51059i	−0.154530	+	0.154530i
$853$	4.13643	−	7.16451i	0.141629	−	0.245308i	−0.786481	−	0.617614i	$-0.788099\pi$
$853$	4.13643	−	7.16451i	0.141629	−	0.245308i	0.928110	+	0.372306i	$0.121433\pi$
$854$	−0.344970	−	0.597506i	−0.0118046	−	0.0204462i
$855$	7.56845	+	6.17962i	0.258836	+	0.211338i
$856$	3.80959	−	14.2176i	0.130209	−	0.485947i
$857$	14.1078			0.481914			0.240957	−	0.970536i	$-0.422539\pi$
$857$	14.1078			0.481914			0.240957	+	0.970536i	$0.422539\pi$
$858$	−2.30323	+	8.59575i	−0.0786308	+	0.293454i
$859$	−12.6794	+	12.6794i	−0.432615	+	0.432615i	−0.889517	−	0.456902i	$-0.848959\pi$
$859$	−12.6794	+	12.6794i	−0.432615	+	0.432615i	0.456902	+	0.889517i	$0.348959\pi$
$860$	2.15030	−	1.54905i	0.0733248	−	0.0528222i
$861$	0.906860			0.0309057
$862$	−1.47896	−	1.47896i	−0.0503736	−	0.0503736i
$863$	7.54779	−	2.02242i	0.256930	−	0.0688441i	−0.128055	−	0.991767i	$-0.540873\pi$
$863$	7.54779	−	2.02242i	0.256930	−	0.0688441i	0.384985	+	0.922923i	$0.374207\pi$
$864$	−4.61900	−	1.23766i	−0.157142	−	0.0421059i
$865$	13.0496	+	34.4103i	0.443700	+	1.16999i
$866$	−5.68412	−	21.2134i	−0.193154	−	0.720862i
$867$	−8.21682	−	30.6656i	−0.279058	−	1.04146i
$868$	0.744598	+	0.429894i	0.0252733	+	0.0145916i
$869$	17.9311	−	66.9199i	0.608272	−	2.27010i
$870$	1.76427	+	17.4644i	0.0598142	+	0.592100i
$871$	0.264816	+	0.988308i	0.00897296	+	0.0334875i
$872$	19.0590	−	5.10684i	0.645419	−	0.172939i
$873$	−29.6574	−	17.1227i	−1.00375	−	0.579515i
$874$	−5.75031	+	5.75031i	−0.194507	+	0.194507i
$875$	1.15539	−	0.0465149i	0.0390592	−	0.00157249i
$876$	−3.23607	−	1.86835i	−0.109337	−	0.0631256i
$877$	19.8334	−	19.8334i	0.669725	−	0.669725i	−0.287928	−	0.957652i	$-0.592966\pi$
$877$	19.8334	−	19.8334i	0.669725	−	0.669725i	0.957652	+	0.287928i	$0.0929662\pi$
$878$	−6.65926	+	6.65926i	−0.224739	+	0.224739i
$879$	−3.94172	+	6.82726i	−0.132951	+	0.230278i
$880$	−11.3381	−	5.10306i	−0.382209	−	0.172024i
$881$	14.2562	−	8.23081i	0.480303	−	0.277303i	−0.240240	−	0.970714i	$-0.577226\pi$
$881$	14.2562	−	8.23081i	0.480303	−	0.277303i	0.720543	+	0.693411i	$0.243893\pi$
$882$		−	14.8988i		−	0.501668i
$883$	−23.5281	−	40.7518i	−0.791783	−	1.37141i	−0.924862	−	0.380302i	$-0.875820\pi$
$883$	−23.5281	−	40.7518i	−0.791783	−	1.37141i	0.133080	−	0.991105i	$-0.457513\pi$
$884$	10.6290	−	6.13664i	0.357491	−	0.206397i
$885$	1.57502	+	15.5911i	0.0529438	+	0.524089i
$886$	2.19516	−	0.588190i	0.0737477	−	0.0197606i
$887$	24.1505	+	24.1505i	0.810895	+	0.810895i	0.984768	−	0.173873i	$-0.0556282\pi$
$887$	24.1505	+	24.1505i	0.810895	+	0.810895i	−0.173873	+	0.984768i	$0.555628\pi$
$888$	−5.64905	+	0.465926i	−0.189570	+	0.0156354i
$889$			0.793169i			0.0266020i
$890$	2.19905	+	0.357411i	0.0737125	+	0.0119804i
$891$	9.33680	−	5.39060i	0.312795	−	0.180592i
$892$	−5.62233	+	20.9828i	−0.188250	+	0.702557i
$893$	10.2904	−	5.94114i	0.344354	−	0.198813i
$894$	−7.61583	+	7.61583i	−0.254711	+	0.254711i
$895$	0.245010	+	0.200049i	0.00818977	+	0.00668692i
$896$	−0.0731322	−	0.0731322i	−0.00244317	−	0.00244317i
$897$	−1.64324	−	6.13265i	−0.0548661	−	0.204763i
$898$	2.10682	+	2.10682i	0.0703056	+	0.0703056i
$899$	−70.0318			−2.33569
$900$	−2.13165	−	10.4429i	−0.0710551	−	0.348097i
$901$	−6.60521	+	24.6510i	−0.220051	+	0.821243i
$902$		−	52.3217i		−	1.74212i
$903$	0.0571121	−	0.0989210i	0.00190057	−	0.00329189i
$904$	−1.67664	−	0.968008i	−0.0557642	−	0.0321955i
$905$	9.15826	+	12.7130i	0.304431	+	0.422594i
$906$	−14.7998	−	3.96560i	−0.491692	−	0.131748i
$907$	28.1724	+	48.7960i	0.935448	+	1.62024i	0.773833	+	0.633390i	$0.218337\pi$
$907$	28.1724	+	48.7960i	0.935448	+	1.62024i	0.161615	+	0.986854i	$0.448330\pi$
$908$	3.64893	−	6.32013i	0.121094	−	0.209741i
$909$	−10.9620	+	18.9867i	−0.363586	+	0.629750i
$910$	−0.392038	−	0.0637177i	−0.0129959	−	0.00211222i
$911$	17.0931	+	17.0931i	0.566319	+	0.566319i	0.931095	−	0.364777i	$-0.118855\pi$
$911$	17.0931	+	17.0931i	0.566319	+	0.566319i	−0.364777	+	0.931095i	$0.618855\pi$
$912$	−1.65427	+	0.955096i	−0.0547785	+	0.0316264i
$913$	10.4114	+	38.8558i	0.344566	+	1.28594i
$914$			7.98393i			0.264085i
$915$	12.6755	+	5.70497i	0.419038	+	0.188600i
$916$	−13.6418	−	7.87612i	−0.450739	−	0.260234i
$917$		−	0.497436i		−	0.0164268i
$918$	33.0086	+	8.84462i	1.08945	+	0.291916i
$919$	−0.483267	−	0.483267i	−0.0159415	−	0.0159415i	0.699091	−	0.715033i	$-0.253588\pi$
$919$	−0.483267	−	0.483267i	−0.0159415	−	0.0159415i	−0.715033	+	0.699091i	$0.753588\pi$
$920$	8.82585	−	0.891592i	0.290980	−	0.0293949i
$921$	−5.73309	−	9.93001i	−0.188912	−	0.327205i
$922$	7.44879	+	1.99590i	0.245313	+	0.0657313i
$923$	10.1815	+	5.87832i	0.335129	+	0.193487i
$924$	−0.535898			−0.0176298
$925$	−15.7788	−	26.0006i	−0.518803	−	0.854894i
$926$	−5.35693			−0.176040
$927$	−34.8941	−	20.1461i	−1.14607	−	0.661686i
$928$	8.13713	+	2.18034i	0.267115	+	0.0715731i
$929$	5.20264	+	9.01123i	0.170693	+	0.295649i	0.938662	−	0.344838i	$-0.112066\pi$
$929$	5.20264	+	9.01123i	0.170693	+	0.295649i	−0.767969	+	0.640487i	$0.778733\pi$
$930$	−17.2343	+	1.74102i	−0.565137	+	0.0570904i
$931$	−10.1309	−	10.1309i	−0.332028	−	0.332028i
$932$	2.13533	+	0.572161i	0.0699452	+	0.0187418i
$933$			25.8778i			0.847200i
$934$	1.46145	+	0.843768i	0.0478201	+	0.0276089i
$935$	81.0253	+	36.4678i	2.64981	+	1.19263i
$936$			3.66098i			0.119663i
$937$	−3.06093	−	11.4236i	−0.0999963	−	0.373191i	0.897733	−	0.440540i	$-0.145213\pi$
$937$	−3.06093	−	11.4236i	−0.0999963	−	0.373191i	−0.997730	+	0.0673482i	$0.978546\pi$
$938$	−0.0533607	+	0.0308078i	−0.00174229	+	0.00100591i
$939$	−1.23318	−	1.23318i	−0.0402432	−	0.0402432i
$940$	−12.7936	−	2.07934i	−0.417281	−	0.0678204i
$941$	−3.01224	+	5.21735i	−0.0981962	+	0.170081i	−0.910938	−	0.412543i	$-0.864641\pi$
$941$	−3.01224	+	5.21735i	−0.0981962	+	0.170081i	0.812742	+	0.582624i	$0.197974\pi$
$942$	−1.27510	+	2.20853i	−0.0415449	+	0.0719579i
$943$	18.6645	+	32.3278i	0.607799	+	1.05274i
$944$	7.26430	+	1.94646i	0.236433	+	0.0633520i
$945$	−0.646406	−	0.897304i	−0.0210276	−	0.0291893i
$946$	−5.70730	−	3.29511i	−0.185560	−	0.107133i
$947$	21.4522	−	37.1564i	0.697104	−	1.20742i	−0.272362	−	0.962195i	$-0.587805\pi$
$947$	21.4522	−	37.1564i	0.697104	−	1.20742i	0.969466	−	0.245225i	$-0.0788617\pi$
$948$			11.6104i			0.377087i
$949$	−1.78245	+	6.65221i	−0.0578609	+	0.215940i
$950$	−8.55051	−	5.65153i	−0.277415	−	0.183360i
$951$	−5.94374			−0.192739
$952$	0.522622	+	0.522622i	0.0169383	+	0.0169383i
$953$	−9.17111	−	34.2271i	−0.297081	−	1.10872i	−0.939550	−	0.342411i	$-0.888756\pi$
$953$	−9.17111	−	34.2271i	−0.297081	−	1.10872i	0.642469	−	0.766312i	$-0.277910\pi$
$954$	−5.38285	−	5.38285i	−0.174276	−	0.174276i
$955$	1.97818	+	1.61517i	0.0640123	+	0.0522658i
$956$	−16.6859	+	16.6859i	−0.539661	+	0.539661i
$957$	37.8022	−	21.8251i	1.22197	−	0.705506i
$958$	1.22580	−	4.57475i	0.0396038	−	0.147803i
$959$	0.642130	−	0.370734i	0.0207355	−	0.0119716i
$960$	2.05670	+	0.334273i	0.0663796	+	0.0107886i
$961$		−	38.1092i		−	1.22933i
$962$	3.52413	+	9.83441i	0.113623	+	0.317074i
$963$	−22.1862	−	22.1862i	−0.714941	−	0.714941i
$964$	18.8035	−	5.03837i	0.605619	−	0.162275i
$965$	−2.21221	−	21.8986i	−0.0712135	−	0.704941i
$966$	0.331114	−	0.191169i	0.0106534	−	0.00615075i
$967$	20.4256	+	35.3782i	0.656843	+	1.13768i	0.981428	+	0.191829i	$0.0614418\pi$
$967$	20.4256	+	35.3782i	0.656843	+	1.13768i	−0.324586	+	0.945856i	$0.605225\pi$
$968$			19.9189i			0.640218i
$969$	11.8219	−	6.82537i	0.379774	−	0.219262i
$970$	32.7578	+	14.7436i	1.05179	+	0.473389i
$971$	23.2903	−	40.3401i	0.747423	−	1.29457i	−0.201632	−	0.979461i	$-0.564624\pi$
$971$	23.2903	−	40.3401i	0.747423	−	1.29457i	0.949054	−	0.315112i	$-0.102042\pi$
$972$	−11.4216	+	11.4216i	−0.366348	+	0.366348i
$973$	−0.733295	+	0.733295i	−0.0235084	+	0.0235084i
$974$	−4.51640	−	2.60755i	−0.144715	−	0.0835512i
$975$	7.15895	−	3.57509i	0.229270	−	0.114495i
$976$	4.71707	−	4.71707i	0.150990	−	0.150990i
$977$	−25.5703	−	14.7630i	−0.818068	−	0.472312i	0.0316818	−	0.999498i	$-0.489914\pi$
$977$	−25.5703	−	14.7630i	−0.818068	−	0.472312i	−0.849750	+	0.527186i	$0.823247\pi$
$978$	−17.4708	+	4.68128i	−0.558654	+	0.149691i
$979$	−1.43391	−	5.35141i	−0.0458279	−	0.171032i
$980$	1.57081	+	15.5494i	0.0501777	+	0.496708i
$981$	10.8860	−	40.6272i	0.347564	−	1.29713i
$982$	−9.94222	−	5.74014i	−0.317269	−	0.183175i
$983$	−8.04703	−	30.0319i	−0.256661	−	0.957870i	−0.967159	−	0.254172i	$-0.918197\pi$
$983$	−8.04703	−	30.0319i	−0.256661	−	0.957870i	0.710499	−	0.703699i	$-0.248469\pi$
$984$	2.26941	+	8.46955i	0.0723461	+	0.269999i
$985$	−12.3579	−	32.5863i	−0.393754	−	1.03829i
$986$	−58.1501	−	15.5813i	−1.85188	−	0.496209i
$987$	−0.539615	+	0.144589i	−0.0171761	+	0.00460233i
$988$	2.48941	+	2.48941i	0.0791987	+	0.0791987i
$989$	4.70180			0.149508
$990$	−21.5051	+	15.4920i	−0.683476	+	0.492367i
$991$	8.42577	−	8.42577i	0.267653	−	0.267653i	−0.560501	−	0.828154i	$-0.689391\pi$
$991$	8.42577	−	8.42577i	0.267653	−	0.267653i	0.828154	+	0.560501i	$0.189391\pi$
$992$	−2.15161	+	8.02993i	−0.0683138	+	0.254950i
$993$	−6.00385			−0.190526
$994$	−0.183240	+	0.683863i	−0.00581203	+	0.0216908i
$995$	−37.4078	−	30.5434i	−1.18591	−	0.968290i
$996$	−3.37067	−	5.83817i	−0.106804	−	0.184990i
$997$	−0.0537123	+	0.0930324i	−0.00170109	+	0.00294637i	−0.866875	−	0.498526i	$-0.833875\pi$
$997$	−0.0537123	+	0.0930324i	−0.00170109	+	0.00294637i	0.865174	+	0.501472i	$0.167208\pi$
$998$	−24.9645	+	24.9645i	−0.790238	+	0.790238i
$999$	−12.4238	+	26.3007i	−0.393073	+	0.832116i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.r.c.23.1	yes	8
5.2	odd	4		370.2.q.c.97.1	✓	8
37.29	odd	12		370.2.q.c.103.1	yes	8
185.177	even	12	inner	370.2.r.c.177.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.q.c.97.1	✓	8	5.2	odd	4
370.2.q.c.103.1	yes	8	37.29	odd	12
370.2.r.c.23.1	yes	8	1.1	even	1	trivial
370.2.r.c.177.1	yes	8	185.177	even	12	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:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.r (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.900100 + 0.241181i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-2.22474 + 0.224745i) q^{5} +(-0.658919 - 0.658919i) q^{6} +(-0.0999004 - 0.0267682i) q^{7} -1.00000i q^{8} +(-1.84607 - 1.06583i) q^{9} +(2.03906 + 0.917738i) q^{10} -5.56048i q^{11} +(0.241181 + 0.900100i) q^{12} +(1.48735 - 0.858719i) q^{13} +(0.0731322 + 0.0731322i) q^{14} +(-2.05670 - 0.334273i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.57313 - 6.18885i) q^{17} +(1.06583 + 1.84607i) q^{18} +(1.98004 + 0.530550i) q^{19} +(-1.30701 - 1.81431i) q^{20} +(-0.0834643 - 0.0481882i) q^{21} +(-2.78024 + 4.81552i) q^{22} -3.96713i q^{23} +(0.241181 - 0.900100i) q^{24} +(4.89898 - 1.00000i) q^{25} -1.71744 q^{26} +(-3.38134 - 3.38134i) q^{27} +(-0.0267682 - 0.0999004i) q^{28} +(5.95680 + 5.95680i) q^{29} +(1.61401 + 1.31784i) q^{30} +(-5.87832 + 5.87832i) q^{31} +(0.866025 - 0.500000i) q^{32} +(1.34108 - 5.00498i) q^{33} +(-6.18885 + 3.57313i) q^{34} +(0.228269 + 0.0371004i) q^{35} -2.13165i q^{36} +(-2.05197 - 5.72620i) q^{37} +(-1.44949 - 1.44949i) q^{38} +(1.54587 - 0.414214i) q^{39} +(0.224745 + 2.22474i) q^{40} +(-8.14893 + 4.70478i) q^{41} +(0.0481882 + 0.0834643i) q^{42} +1.18519i q^{43} +(4.81552 - 2.78024i) q^{44} +(4.34656 + 1.95630i) q^{45} +(-1.98356 + 3.43563i) q^{46} +(4.09878 - 4.09878i) q^{47} +(-0.658919 + 0.658919i) q^{48} +(-6.05291 - 3.49465i) q^{49} +(-4.74264 - 1.58346i) q^{50} +(4.70881 - 4.70881i) q^{51} +(1.48735 + 0.858719i) q^{52} +(-3.44949 + 0.924288i) q^{53} +(1.23766 + 4.61900i) q^{54} +(1.24969 + 12.3706i) q^{55} +(-0.0267682 + 0.0999004i) q^{56} +(1.65427 + 0.955096i) q^{57} +(-2.18034 - 8.13713i) q^{58} +(-1.94646 - 7.26430i) q^{59} +(-0.738859 - 1.94829i) q^{60} +(-6.44364 - 1.72657i) q^{61} +(8.02993 - 2.15161i) q^{62} +(0.155892 + 0.155892i) q^{63} -1.00000 q^{64} +(-3.11597 + 2.24471i) q^{65} +(-3.66390 + 3.66390i) q^{66} +(-0.154193 + 0.575454i) q^{67} +7.14626 q^{68} +(0.956796 - 3.57081i) q^{69} +(-0.179137 - 0.146264i) q^{70} +(3.42272 + 5.92833i) q^{71} +(-1.06583 + 1.84607i) q^{72} +(-2.83548 + 2.83548i) q^{73} +(-1.08604 + 5.98502i) q^{74} +(4.65075 + 0.281441i) q^{75} +(0.530550 + 1.98004i) q^{76} +(-0.148844 + 0.555494i) q^{77} +(-1.54587 - 0.414214i) q^{78} +(12.0349 + 3.22474i) q^{79} +(0.917738 - 2.03906i) q^{80} +(0.969450 + 1.67914i) q^{81} +9.40957 q^{82} +(-6.98784 + 1.87239i) q^{83} -0.0963763i q^{84} +(-6.55840 + 14.5716i) q^{85} +(0.592594 - 1.02640i) q^{86} +(3.92504 + 6.79837i) q^{87} -5.56048 q^{88} +(0.962402 - 0.257875i) q^{89} +(-2.78609 - 3.86749i) q^{90} +(-0.171573 + 0.0459728i) q^{91} +(3.43563 - 1.98356i) q^{92} +(-6.70881 + 3.87333i) q^{93} +(-5.59904 + 1.50026i) q^{94} +(-4.52432 - 0.735335i) q^{95} +(0.900100 - 0.241181i) q^{96} +16.0652 q^{97} +(3.49465 + 6.05291i) q^{98} +(-5.92650 + 10.2650i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{3} + 4 q^{4} - 8 q^{5} - 4 q^{6} + 12 q^{9} - 4 q^{10} + 4 q^{12} - 12 q^{13} - 12 q^{14} + 8 q^{15} - 4 q^{16} + 16 q^{17} - 4 q^{19} - 4 q^{20} + 12 q^{21} - 4 q^{22} + 4 q^{24} - 8 q^{26}+ \cdots - 4 q^{99}+O(q^{100}) \) 8 * q + 8 * q^3 + 4 * q^4 - 8 * q^5 - 4 * q^6 + 12 * q^9 - 4 * q^10 + 4 * q^12 - 12 * q^13 - 12 * q^14 + 8 * q^15 - 4 * q^16 + 16 * q^17 - 4 * q^19 - 4 * q^20 + 12 * q^21 - 4 * q^22 + 4 * q^24 - 8 * q^26 + 8 * q^27 - 12 * q^28 + 24 * q^29 - 8 * q^31 + 12 * q^33 - 12 * q^34 + 8 * q^38 - 16 * q^39 - 8 * q^40 + 12 * q^41 - 4 * q^42 + 12 * q^44 + 12 * q^45 - 4 * q^46 - 8 * q^47 - 4 * q^48 - 36 * q^49 - 4 * q^50 + 20 * q^51 - 12 * q^52 - 8 * q^53 + 4 * q^54 - 8 * q^55 - 12 * q^56 - 36 * q^57 + 8 * q^59 + 16 * q^60 + 28 * q^62 - 4 * q^63 - 8 * q^64 + 20 * q^65 - 8 * q^67 + 32 * q^68 - 16 * q^69 - 4 * q^71 - 16 * q^73 - 20 * q^75 + 4 * q^76 + 20 * q^77 + 16 * q^78 + 32 * q^79 + 4 * q^80 + 8 * q^81 + 16 * q^82 - 36 * q^83 - 16 * q^85 + 8 * q^86 + 24 * q^87 - 8 * q^88 - 8 * q^89 - 36 * q^90 - 24 * q^91 - 36 * q^93 + 16 * q^94 + 8 * q^95 + 8 * q^96 - 48 * q^97 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more