LMFDB - Embedded newform 370.2.q.c.97.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(97,370)]

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([3, 5]))

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

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

chi := DirichletCharacter("370.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.q (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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			97.1
Root			$-0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	370.97
Dual form			370.2.q.c.103.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 - 0.866025i) q^{2} +(0.241181 - 0.900100i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.81431 + 1.30701i) q^{5} +(-0.658919 - 0.658919i) q^{6} +(0.0267682 - 0.0999004i) q^{7} -1.00000 q^{8} +(1.84607 + 1.06583i) q^{9} +(2.03906 - 0.917738i) q^{10} -5.56048i q^{11} +(-0.900100 + 0.241181i) q^{12} +(-0.858719 - 1.48735i) q^{13} +(-0.0731322 - 0.0731322i) q^{14} +(1.61401 - 1.31784i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(6.18885 + 3.57313i) q^{17} +(1.84607 - 1.06583i) q^{18} +(-1.98004 - 0.530550i) q^{19} +(0.224745 - 2.22474i) q^{20} +(-0.0834643 - 0.0481882i) q^{21} +(-4.81552 - 2.78024i) q^{22} -3.96713 q^{23} +(-0.241181 + 0.900100i) q^{24} +(1.58346 + 4.74264i) q^{25} -1.71744 q^{26} +(3.38134 - 3.38134i) q^{27} +(-0.0999004 + 0.0267682i) q^{28} +(-5.95680 - 5.95680i) q^{29} +(-0.334273 - 2.05670i) q^{30} +(-5.87832 + 5.87832i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-5.00498 - 1.34108i) q^{33} +(6.18885 - 3.57313i) q^{34} +(0.179137 - 0.146264i) q^{35} -2.13165i q^{36} +(5.72620 - 2.05197i) q^{37} +(-1.44949 + 1.44949i) q^{38} +(-1.54587 + 0.414214i) q^{39} +(-1.81431 - 1.30701i) q^{40} +(-8.14893 + 4.70478i) q^{41} +(-0.0834643 + 0.0481882i) q^{42} +1.18519 q^{43} +(-4.81552 + 2.78024i) q^{44} +(1.95630 + 4.34656i) 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} +(4.89898 + 1.00000i) q^{50} +(4.70881 - 4.70881i) q^{51} +(-0.858719 + 1.48735i) q^{52} +(0.924288 + 3.44949i) q^{53} +(-1.23766 - 4.61900i) q^{54} +(7.26758 - 10.0884i) q^{55} +(-0.0267682 + 0.0999004i) q^{56} +(-0.955096 + 1.65427i) q^{57} +(-8.13713 + 2.18034i) q^{58} +(1.94646 + 7.26430i) q^{59} +(-1.94829 - 0.738859i) q^{60} +(-6.44364 - 1.72657i) q^{61} +(2.15161 + 8.02993i) q^{62} +(0.155892 - 0.155892i) q^{63} +1.00000 q^{64} +(0.385986 - 3.82086i) q^{65} +(-3.66390 + 3.66390i) q^{66} +(-0.575454 - 0.154193i) q^{67} -7.14626i q^{68} +(-0.956796 + 3.57081i) q^{69} +(-0.0371004 - 0.228269i) q^{70} +(3.42272 + 5.92833i) q^{71} +(-1.84607 - 1.06583i) 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} +(-0.555494 - 0.148844i) q^{77} +(-0.414214 + 1.54587i) q^{78} +(-12.0349 - 3.22474i) q^{79} +(-2.03906 + 0.917738i) q^{80} +(0.969450 + 1.67914i) q^{81} +9.40957i q^{82} +(1.87239 + 6.98784i) q^{83} +0.0963763i q^{84} +(6.55840 + 14.5716i) q^{85} +(0.592594 - 1.02640i) q^{86} +(-6.79837 + 3.92504i) q^{87} +5.56048i q^{88} +(-0.962402 + 0.257875i) q^{89} +(4.74238 + 0.479078i) q^{90} +(-0.171573 + 0.0459728i) q^{91} +(1.98356 + 3.43563i) q^{92} +(3.87333 + 6.70881i) q^{93} +(5.59904 - 1.50026i) q^{94} +(-2.89898 - 3.55051i) q^{95} +(0.900100 - 0.241181i) q^{96} +16.0652i q^{97} +(6.05291 - 3.49465i) q^{98} +(5.92650 - 10.2650i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} + 4 q^{3} - 4 q^{4} + 4 q^{5} - 4 q^{6} + 12 q^{7} - 8 q^{8} - 12 q^{9} - 4 q^{10} - 8 q^{12} - 4 q^{13} + 12 q^{14} - 4 q^{16} + 12 q^{17} - 12 q^{18} + 4 q^{19} - 8 q^{20} + 12 q^{21} - 12 q^{22}+ \cdots + 4 q^{99}+O(q^{100}) $ 8 * q + 4 * q^2 + 4 * q^3 - 4 * q^4 + 4 * q^5 - 4 * q^6 + 12 * q^7 - 8 * q^8 - 12 * q^9 - 4 * q^10 - 8 * q^12 - 4 * q^13 + 12 * q^14 - 4 * q^16 + 12 * q^17 - 12 * q^18 + 4 * q^19 - 8 * q^20 + 12 * q^21 - 12 * q^22 - 8 * q^23 - 4 * q^24 - 8 * q^26 - 8 * q^27 - 24 * q^29 - 12 * q^30 - 8 * q^31 + 4 * q^32 - 12 * q^33 + 12 * q^34 + 8 * q^38 + 16 * q^39 - 4 * q^40 + 12 * q^41 + 12 * q^42 + 16 * q^43 - 12 * q^44 - 12 * q^45 - 4 * q^46 - 8 * q^47 + 4 * q^48 + 36 * q^49 + 20 * q^51 - 4 * q^52 + 16 * q^53 - 4 * q^54 + 16 * q^55 - 12 * q^56 + 4 * q^57 - 24 * q^58 - 8 * q^59 - 12 * q^60 + 20 * q^62 - 4 * q^63 + 8 * q^64 + 16 * q^65 - 16 * q^67 + 16 * q^69 - 12 * q^70 - 4 * q^71 + 12 * q^72 + 16 * q^73 - 20 * q^75 + 4 * q^76 + 4 * q^77 + 8 * q^78 - 32 * q^79 + 4 * q^80 + 8 * q^81 + 16 * q^85 + 8 * q^86 - 36 * q^87 + 8 * q^89 + 24 * q^90 - 24 * q^91 + 4 * q^92 + 20 * q^93 - 16 * q^94 + 16 * q^95 + 8 * q^96 + 36 * q^98 + 4 * q^99

Character values

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

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	0.241181	−	0.900100i	0.139246	−	0.519673i	−0.860698	−	0.509115i	$-0.829973\pi$
$3$	0.241181	−	0.900100i	0.139246	−	0.519673i	0.999944	−	0.0105575i	$-0.00336063\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	1.81431	+	1.30701i	0.811386	+	0.584511i
$5$	1.81431	+	1.30701i	0.811386	+	0.584511i
$6$	−0.658919	−	0.658919i	−0.269002	−	0.269002i
$7$	0.0267682	−	0.0999004i	0.0101174	−	0.0377588i	−0.960683	−	0.277649i	$-0.910445\pi$
$7$	0.0267682	−	0.0999004i	0.0101174	−	0.0377588i	0.970800	+	0.239890i	$0.0771114\pi$
$8$	−1.00000			−0.353553
$9$	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	$-0.316435\pi$
$12$	−0.900100	+	0.241181i	−0.259836	+	0.0696229i
$13$	−0.858719	−	1.48735i	−0.238166	−	0.412515i	0.722022	−	0.691870i	$-0.243213\pi$
$13$	−0.858719	−	1.48735i	−0.238166	−	0.412515i	−0.960188	+	0.279354i	$0.909880\pi$
$14$	−0.0731322	−	0.0731322i	−0.0195454	−	0.0195454i
$15$	1.61401	−	1.31784i	0.416737	−	0.340264i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	6.18885	+	3.57313i	1.50102	+	0.866612i	0.999999	+	0.00117408i	$0.000373722\pi$
$17$	6.18885	+	3.57313i	1.50102	+	0.866612i	0.501016	+	0.865438i	$0.332960\pi$
$18$	1.84607	−	1.06583i	0.435122	−	0.251218i
$19$	−1.98004	−	0.530550i	−0.454252	−	0.121717i	0.0244361	−	0.999701i	$-0.492221\pi$
$19$	−1.98004	−	0.530550i	−0.454252	−	0.121717i	−0.478688	+	0.877985i	$0.658888\pi$
$20$	0.224745	−	2.22474i	0.0502545	−	0.497468i
$21$	−0.0834643	−	0.0481882i	−0.0182134	−	0.0105155i
$22$	−4.81552	−	2.78024i	−1.02667	−	0.592749i
$23$	−3.96713			−0.827203			−0.413602	−	0.910458i	$-0.635729\pi$
$23$	−3.96713			−0.827203			−0.413602	+	0.910458i	$0.635729\pi$
$24$	−0.241181	+	0.900100i	−0.0492309	+	0.183732i
$25$	1.58346	+	4.74264i	0.316693	+	0.948528i
$26$	−1.71744			−0.336817
$27$	3.38134	−	3.38134i	0.650739	−	0.650739i
$28$	−0.0999004	+	0.0267682i	−0.0188794	+	0.00505872i
$29$	−5.95680	−	5.95680i	−1.10615	−	1.10615i	−0.993652	−	0.112497i	$-0.964115\pi$
$29$	−5.95680	−	5.95680i	−1.10615	−	1.10615i	−0.112497	−	0.993652i	$-0.535885\pi$
$30$	−0.334273	−	2.05670i	−0.0610297	−	0.375500i
$31$	−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	$0.981710\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−5.00498	−	1.34108i	−0.871256	−	0.233452i
$34$	6.18885	−	3.57313i	1.06138	−	0.612787i
$35$	0.179137	−	0.146264i	0.0302796	−	0.0247232i
$36$		−	2.13165i		−	0.355275i
$37$	5.72620	−	2.05197i	0.941382	−	0.337342i
$37$	5.72620	−	2.05197i	0.941382	−	0.337342i
$38$	−1.44949	+	1.44949i	−0.235138	+	0.235138i
$39$	−1.54587	+	0.414214i	−0.247537	+	0.0663273i
$40$	−1.81431	−	1.30701i	−0.286868	−	0.206656i
$41$	−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	$0.596040\pi$
$42$	−0.0834643	+	0.0481882i	−0.0128788	+	0.00743559i
$43$	1.18519			0.180740			0.0903698	−	0.995908i	$-0.471195\pi$
$43$	1.18519			0.180740			0.0903698	+	0.995908i	$0.471195\pi$
$44$	−4.81552	+	2.78024i	−0.725966	+	0.419137i
$45$	1.95630	+	4.34656i	0.291628	+	0.647947i
$46$	−1.98356	+	3.43563i	−0.292461	+	0.506557i
$47$	4.09878	+	4.09878i	0.597869	+	0.597869i	0.939745	−	0.341876i	$-0.111062\pi$
$47$	4.09878	+	4.09878i	0.597869	+	0.597869i	−0.341876	+	0.939745i	$0.611062\pi$
$48$	0.658919	+	0.658919i	0.0951067	+	0.0951067i
$49$	6.05291	+	3.49465i	0.864702	+	0.499236i
$50$	4.89898	+	1.00000i	0.692820	+	0.141421i
$51$	4.70881	−	4.70881i	0.659365	−	0.659365i
$52$	−0.858719	+	1.48735i	−0.119083	+	0.206258i
$53$	0.924288	+	3.44949i	0.126961	+	0.473824i	0.999902	−	0.0140015i	$-0.00445696\pi$
$53$	0.924288	+	3.44949i	0.126961	+	0.473824i	−0.872941	+	0.487825i	$0.837790\pi$
$54$	−1.23766	−	4.61900i	−0.168424	−	0.628566i
$55$	7.26758	−	10.0884i	0.979961	−	1.36033i
$56$	−0.0267682	+	0.0999004i	−0.00357706	+	0.0133498i
$57$	−0.955096	+	1.65427i	−0.126506	+	0.219114i
$58$	−8.13713	+	2.18034i	−1.06846	+	0.286292i
$59$	1.94646	+	7.26430i	0.253408	+	0.945731i	0.968969	+	0.247181i	$0.0795044\pi$
$59$	1.94646	+	7.26430i	0.253408	+	0.945731i	−0.715561	+	0.698550i	$0.753829\pi$
$60$	−1.94829	−	0.738859i	−0.251523	−	0.0953863i
$61$	−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	$0.723785\pi$
$62$	2.15161	+	8.02993i	0.273255	+	1.01980i
$63$	0.155892	−	0.155892i	0.0196406	−	0.0196406i
$64$	1.00000			0.125000
$65$	0.385986	−	3.82086i	0.0478756	−	0.473920i
$66$	−3.66390	+	3.66390i	−0.450995	+	0.450995i
$67$	−0.575454	−	0.154193i	−0.0703029	−	0.0188376i	0.223496	−	0.974705i	$-0.428253\pi$
$67$	−0.575454	−	0.154193i	−0.0703029	−	0.0188376i	−0.293799	+	0.955867i	$0.594920\pi$
$68$		−	7.14626i		−	0.866612i
$69$	−0.956796	+	3.57081i	−0.115185	+	0.429875i
$70$	−0.0371004	−	0.228269i	−0.00443434	−	0.0272834i
$71$	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	$0.700186\pi$
$72$	−1.84607	−	1.06583i	−0.217561	−	0.125609i
$73$	2.83548	+	2.83548i	0.331867	+	0.331867i	0.853295	−	0.521428i	$-0.174600\pi$
$73$	2.83548	+	2.83548i	0.331867	+	0.331867i	−0.521428	+	0.853295i	$0.674600\pi$
$74$	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
$77$	−0.555494	−	0.148844i	−0.0633044	−	0.0169624i
$78$	−0.414214	+	1.54587i	−0.0469005	+	0.175035i
$79$	−12.0349	−	3.22474i	−1.35403	−	0.362812i	−0.492411	−	0.870363i	$-0.663884\pi$
$79$	−12.0349	−	3.22474i	−1.35403	−	0.362812i	−0.861622	+	0.507550i	$0.830551\pi$
$80$	−2.03906	+	0.917738i	−0.227974	+	0.102606i
$81$	0.969450	+	1.67914i	0.107717	+	0.186571i
$82$			9.40957i			1.03911i
$83$	1.87239	+	6.98784i	0.205521	+	0.767015i	0.989290	+	0.145963i	$0.0466280\pi$
$83$	1.87239	+	6.98784i	0.205521	+	0.767015i	−0.783769	+	0.621053i	$0.786705\pi$
$84$			0.0963763i			0.0105155i
$85$	6.55840	+	14.5716i	0.711358	+	1.58052i
$86$	0.592594	−	1.02640i	0.0639011	−	0.110680i
$87$	−6.79837	+	3.92504i	−0.728862	+	0.420809i
$88$			5.56048i			0.592749i
$89$	−0.962402	+	0.257875i	−0.102014	+	0.0273347i	−0.309465	−	0.950911i	$-0.600150\pi$
$89$	−0.962402	+	0.257875i	−0.102014	+	0.0273347i	0.207451	+	0.978245i	$0.433483\pi$
$90$	4.74238	+	0.479078i	0.499891	+	0.0504993i
$91$	−0.171573	+	0.0459728i	−0.0179857	+	0.00481926i
$92$	1.98356	+	3.43563i	0.206801	+	0.358190i
$93$	3.87333	+	6.70881i	0.401646	+	0.695671i
$94$	5.59904	−	1.50026i	0.577497	−	0.154740i
$95$	−2.89898	−	3.55051i	−0.297429	−	0.364275i
$96$	0.900100	−	0.241181i	0.0918660	−	0.0246154i
$97$			16.0652i			1.63117i	0.578636	+	0.815586i	$0.303585\pi$
$97$			16.0652i			1.63117i	−0.578636	+	0.815586i	$0.696415\pi$
$98$	6.05291	−	3.49465i	0.611437	−	0.353013i
$99$	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	$-0.170983\pi$
$102$	−1.72354	−	6.43235i	−0.170656	−	0.636898i
$103$		−	18.9019i		−	1.86246i	−0.364433	−	0.931230i	$-0.618737\pi$
$103$		−	18.9019i		−	1.86246i	0.364433	−	0.931230i	$-0.381263\pi$
$104$	0.858719	+	1.48735i	0.0842044	+	0.145846i
$105$	−0.0884482	−	0.196517i	−0.00863166	−	0.0191781i
$106$	3.44949	+	0.924288i	0.335044	+	0.0897748i
$107$	−3.80959	+	14.2176i	−0.368287	+	1.37446i	0.494624	+	0.869107i	$0.335306\pi$
$107$	−3.80959	+	14.2176i	−0.368287	+	1.37446i	−0.862910	+	0.505357i	$0.831361\pi$
$108$	−4.61900	−	1.23766i	−0.444463	−	0.119094i
$109$	−5.10684	−	19.0590i	−0.489147	−	1.82552i	−0.560614	−	0.828078i	$-0.689435\pi$
$109$	−5.10684	−	19.0590i	−0.489147	−	1.82552i	0.0714669	−	0.997443i	$-0.477232\pi$
$110$	−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
$113$	−1.67664	−	0.968008i	−0.157725	−	0.0910625i	0.419060	−	0.907958i	$-0.362360\pi$
$113$	−1.67664	−	0.968008i	−0.157725	−	0.0910625i	−0.576785	+	0.816896i	$0.695693\pi$
$114$	0.955096	+	1.65427i	0.0894529	+	0.154937i
$115$	−7.19761	−	5.18506i	−0.671181	−	0.483510i
$116$	−2.18034	+	8.13713i	−0.202439	+	0.755514i
$117$		−	3.66098i		−	0.338458i
$118$	7.26430	+	1.94646i	0.668733	+	0.179186i
$119$	0.522622	−	0.522622i	0.0479087	−	0.0479087i
$120$	−1.61401	+	1.31784i	−0.147339	+	0.120302i
$121$	−19.9189			−1.81081
$122$	−4.71707	+	4.71707i	−0.427064	+	0.427064i
$123$	2.26941	+	8.46955i	0.204626	+	0.763674i
$124$	8.02993	+	2.15161i	0.721109	+	0.193221i
$125$	−3.32577	+	10.6742i	−0.297465	+	0.954733i
$126$	−0.0570606	−	0.212953i	−0.00508336	−	0.0189714i
$127$	7.40775	−	1.98490i	0.657331	−	0.176131i	0.0852898	−	0.996356i	$-0.472818\pi$
$127$	7.40775	−	1.98490i	0.657331	−	0.176131i	0.572041	+	0.820225i	$0.306152\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	0.285845	−	1.06679i	0.0251672	−	0.0939255i
$130$	−3.11597	−	2.24471i	−0.273289	−	0.196874i
$131$	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	$0.849284\pi$
$132$	1.34108	+	5.00498i	0.116726	+	0.435628i
$133$	−0.106004	+	0.183605i	−0.00919174	+	0.0159206i
$134$	−0.421262	+	0.421262i	−0.0363915	+	0.0363915i
$135$	10.5542	−	1.71537i	0.908365	−	0.147636i
$136$	−6.18885	−	3.57313i	−0.530689	−	0.306394i
$137$	−5.06937	−	5.06937i	−0.433105	−	0.433105i	0.456578	−	0.889683i	$-0.349075\pi$
$137$	−5.06937	−	5.06937i	−0.433105	−	0.433105i	−0.889683	+	0.456578i	$0.849075\pi$
$138$	2.61401	+	2.61401i	0.222520	+	0.222520i
$139$	−5.01349	+	8.68362i	−0.425239	+	0.736535i	−0.996443	−	0.0842730i	$-0.973143\pi$
$139$	−5.01349	+	8.68362i	−0.425239	+	0.736535i	0.571204	+	0.820808i	$0.306477\pi$
$140$	−0.216237	−	0.0820046i	−0.0182754	−	0.00693065i
$141$	4.67786	−	2.70076i	0.393947	−	0.227445i
$142$	6.84544			0.574457
$143$	−8.27035	+	4.77489i	−0.691602	+	0.399296i
$144$	−1.84607	+	1.06583i	−0.153839	+	0.0888189i
$145$	−3.02192	−	18.5931i	−0.250957	−	1.54407i
$146$	3.87333	−	1.03786i	0.320559	−	0.0858936i
$147$	4.60538	−	4.60538i	0.379846	−	0.379846i
$148$	−4.64016	−	3.93305i	−0.381419	−	0.323295i
$149$			11.5581i			0.946874i	0.880828	+	0.473437i	$0.156987\pi$
$149$			11.5581i			0.946874i	−0.880828	+	0.473437i	$0.843013\pi$
$150$	2.08164	−	4.16839i	0.169965	−	0.340347i
$151$	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	$0.100042\pi$
$152$	1.98004	+	0.530550i	0.160602	+	0.0430333i
$153$	7.61668	+	13.1925i	0.615772	+	1.06655i
$154$	−0.406650	+	0.406650i	−0.0327688	+	0.0327688i
$155$	−18.3481	+	2.98210i	−1.47376	+	0.239528i
$156$	1.13165	+	1.13165i	0.0906047	+	0.0906047i
$157$	2.64344	−	0.708309i	0.210970	−	0.0565292i	−0.151786	−	0.988413i	$-0.548503\pi$
$157$	2.64344	−	0.708309i	0.210970	−	0.0565292i	0.362756	+	0.931884i	$0.381836\pi$
$158$	−8.81017	+	8.81017i	−0.700899	+	0.700899i
$159$	3.32780			0.263912
$160$	−0.224745	+	2.22474i	−0.0177676	+	0.175882i
$161$	−0.106193	+	0.396318i	−0.00836918	+	0.0312342i
$162$	1.93890			0.152334
$163$	−16.8094	−	9.70492i	−1.31661	−	0.760148i	−0.333432	−	0.942774i	$-0.608207\pi$
$163$	−16.8094	−	9.70492i	−1.31661	−	0.760148i	−0.983182	+	0.182626i	$0.941540\pi$
$164$	8.14893	+	4.70478i	0.636324	+	0.367382i
$165$	−7.32780	−	8.97469i	−0.570469	−	0.698679i
$166$	6.98784	+	1.87239i	0.542362	+	0.145325i
$167$	2.34366	−	1.35311i	0.181358	−	0.104707i	−0.406573	−	0.913618i	$-0.633276\pi$
$167$	2.34366	−	1.35311i	0.181358	−	0.104707i	0.587931	+	0.808911i	$0.299943\pi$
$168$	0.0834643	+	0.0481882i	0.00643941	+	0.00371780i
$169$	5.02520	−	8.70390i	0.386554	−	0.669531i
$170$	15.8986	+	1.60609i	1.21937	+	0.123181i
$171$	−3.08981	−	3.08981i	−0.236284	−	0.236284i
$172$	−0.592594	−	1.02640i	−0.0451849	−	0.0782626i
$173$	−15.8974	+	4.25970i	−1.20866	+	0.323859i	−0.806235	−	0.591595i	$-0.798498\pi$
$173$	−15.8974	+	4.25970i	−1.20866	+	0.323859i	−0.402423	+	0.915454i	$0.631832\pi$
$174$			7.85009i			0.595114i
$175$	0.516178	−	0.0312366i	0.0390194	−	0.00236127i
$176$	4.81552	+	2.78024i	0.362983	+	0.209568i
$177$	7.00804			0.526757
$178$	−0.257875	+	0.962402i	−0.0193285	+	0.0721351i
$179$	0.100025	+	0.100025i	0.00747620	+	0.00747620i	0.710835	−	0.703359i	$-0.248317\pi$
$179$	0.100025	+	0.100025i	0.00747620	+	0.00747620i	−0.703359	+	0.710835i	$0.748317\pi$
$180$	2.78609	−	3.86749i	0.207663	−	0.288265i
$181$	−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	$0.917193\pi$
$182$	−0.0459728	+	0.171573i	−0.00340773	+	0.0127178i
$183$	−3.10817	+	5.38351i	−0.229762	+	0.397960i
$184$	3.96713			0.292461
$185$	13.0711	+	3.76127i	0.961004	+	0.276534i
$186$	7.74666			0.568013
$187$	19.8683	−	34.4129i	1.45292	−	2.51652i
$188$	1.50026	−	5.59904i	0.109418	−	0.408352i
$189$	−0.247285	−	0.428310i	−0.0179873	−	0.0311550i
$190$	−4.52432	+	0.735335i	−0.328229	+	0.0533468i
$191$	−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	$0.763156\pi$
$192$	0.241181	−	0.900100i	0.0174057	−	0.0649591i
$193$	9.84320			0.708529			0.354265	−	0.935145i	$-0.384731\pi$
$193$	9.84320			0.708529			0.354265	+	0.935145i	$0.384731\pi$
$194$	13.9129	+	8.03259i	0.998885	+	0.576706i
$195$	−3.34607	−	1.26894i	−0.239617	−	0.0908710i
$196$		−	6.98930i		−	0.499236i
$197$	−15.0547	+	4.03390i	−1.07260	+	0.287403i	−0.751563	−	0.659662i	$-0.770700\pi$
$197$	−15.0547	+	4.03390i	−1.07260	+	0.287403i	−0.321041	+	0.947065i	$0.604033\pi$
$198$	−5.92650	−	10.2650i	−0.421178	−	0.729502i
$199$	−15.2717	−	15.2717i	−1.08258	−	1.08258i	−0.996268	−	0.0863133i	$-0.972491\pi$
$199$	−15.2717	−	15.2717i	−1.08258	−	1.08258i	−0.0863133	−	0.996268i	$-0.527509\pi$
$200$	−1.58346	−	4.74264i	−0.111968	−	0.335355i
$201$	−0.277577	+	0.480778i	−0.0195788	+	0.0339115i
$202$	−8.90704	−	5.14248i	−0.626697	−	0.361824i
$203$	−0.754539	+	0.435633i	−0.0529583	+	0.0305755i
$204$	−6.43235	−	1.72354i	−0.450355	−	0.120672i
$205$	−20.9339	−	2.11475i	−1.46209	−	0.147701i
$206$	−16.3695	−	9.45095i	−1.14052	−	0.658479i
$207$	−7.32358	−	4.22827i	−0.509024	−	0.293885i
$208$	1.71744			0.119083
$209$	−2.95011	+	11.0100i	−0.204064	+	0.761575i
$210$	−0.214413	−	0.0216601i	−0.0147959	−	0.00149469i
$211$	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
$213$	6.16158	−	1.65099i	0.422185	−	0.113124i
$214$	10.4080	+	10.4080i	0.711475	+	0.711475i
$215$	2.15030	+	1.54905i	0.146650	+	0.105644i
$216$	−3.38134	+	3.38134i	−0.230071	+	0.230071i
$217$	0.429894	+	0.744598i	0.0291831	+	0.0505466i
$218$	−19.0590	−	5.10684i	−1.29084	−	0.345879i
$219$	3.23607	−	1.86835i	0.218674	−	0.126251i
$220$	−12.3706	−	1.24969i	−0.834029	−	0.0842540i
$221$		−	12.2733i		−	0.825590i
$222$	−5.12518	−	2.42102i	−0.343980	−	0.162488i
$223$	15.3605	−	15.3605i	1.02862	−	1.02862i	0.0290369	−	0.999578i	$-0.490756\pi$
$223$	15.3605	−	15.3605i	1.02862	−	1.02862i	0.999578	−	0.0290369i	$-0.00924403\pi$
$224$	0.0999004	−	0.0267682i	0.00667488	−	0.00178853i
$225$	−2.13165	+	10.4429i	−0.142110	+	0.696195i
$226$	−1.67664	+	0.968008i	−0.111528	+	0.0643909i
$227$	6.32013	−	3.64893i	0.419481	−	0.242188i	−0.275374	−	0.961337i	$-0.588802\pi$
$227$	6.32013	−	3.64893i	0.419481	−	0.242188i	0.694855	+	0.719149i	$0.255468\pi$
$228$	1.91019			0.126506
$229$	13.6418	−	7.87612i	0.901478	−	0.520468i	0.0237985	−	0.999717i	$-0.492424\pi$
$229$	13.6418	−	7.87612i	0.901478	−	0.520468i	0.877679	+	0.479248i	$0.159091\pi$
$230$	−8.08920	+	3.64078i	−0.533386	+	0.240066i
$231$	−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	$-0.273070\pi$
$233$	−1.56317	−	1.56317i	−0.102407	−	0.102407i	−0.756454	+	0.654047i	$0.773070\pi$
$234$	−3.17050	−	1.83049i	−0.207262	−	0.119663i
$235$	2.07934	+	12.7936i	0.135641	+	0.834563i
$236$	5.31784	−	5.31784i	0.346162	−	0.346162i
$237$	−5.80518	+	10.0549i	−0.377087	+	0.653134i
$238$	−0.191293	−	0.713915i	−0.0123997	−	0.0462762i
$239$	−6.10746	−	22.7934i	−0.395059	−	1.47438i	−0.821680	−	0.569950i	$-0.806963\pi$
$239$	−6.10746	−	22.7934i	−0.395059	−	1.47438i	0.426621	−	0.904431i	$-0.359704\pi$
$240$	0.334273	+	2.05670i	0.0215773	+	0.132759i
$241$	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	$-0.132377\pi$
$242$	−9.95946	+	17.2503i	−0.640218	+	1.10889i
$243$	15.6022	−	4.18060i	1.00088	−	0.268185i
$244$	1.72657	+	6.44364i	0.110532	+	0.412512i
$245$	6.41435	+	14.2516i	0.409798	+	0.910501i
$246$	8.46955	+	2.26941i	0.539999	+	0.144692i
$247$	0.911187	+	3.40060i	0.0579775	+	0.216375i
$248$	5.87832	−	5.87832i	0.373273	−	0.373273i
$249$	6.74134			0.427215
$250$	7.58128	+	8.21731i	0.479482	+	0.519709i
$251$	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	$0.241800\pi$
$252$	−0.212953	−	0.0570606i	−0.0134148	−	0.00359448i
$253$			22.0591i			1.38685i
$254$	1.98490	−	7.40775i	0.124544	−	0.464803i
$255$	14.6977	−	2.38881i	0.920405	−	0.149593i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−21.7048	−	12.5313i	−1.35391	−	0.781679i	−0.365113	−	0.930963i	$-0.618970\pi$
$257$	−21.7048	−	12.5313i	−1.35391	−	0.781679i	−0.988794	+	0.149284i	$0.952303\pi$
$258$	−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
$262$	4.64577	+	1.24483i	0.287016	+	0.0769058i
$263$	−1.47613	+	5.50901i	−0.0910223	+	0.339700i	−0.996386	−	0.0849363i	$-0.972931\pi$
$263$	−1.47613	+	5.50901i	−0.0910223	+	0.339700i	0.905364	+	0.424636i	$0.139598\pi$
$264$	5.00498	+	1.34108i	0.308035	+	0.0825379i
$265$	−2.83156	+	7.46651i	−0.173941	+	0.458664i
$266$	0.106004	+	0.183605i	0.00649954	+	0.0112575i
$267$			0.928452i			0.0568203i
$268$	0.154193	+	0.575454i	0.00941881	+	0.0351515i
$269$			8.45805i			0.515696i	0.966185	+	0.257848i	$0.0830134\pi$
$269$			8.45805i			0.515696i	−0.966185	+	0.257848i	$0.916987\pi$
$270$	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	$0.319439\pi$
$272$	−6.18885	+	3.57313i	−0.375254	+	0.216653i
$273$			0.165520i			0.0100178i
$274$	−6.92489	+	1.85552i	−0.418348	+	0.112096i
$275$	26.3713	−	8.80482i	1.59025	−	0.530951i
$276$	3.57081	−	0.956796i	0.214938	−	0.0575923i
$277$	7.72657	+	13.3828i	0.464245	+	0.804095i	0.999167	−	0.0408060i	$-0.0129925\pi$
$277$	7.72657	+	13.3828i	0.464245	+	0.804095i	−0.534923	+	0.844901i	$0.679659\pi$
$278$	5.01349	+	8.68362i	0.300689	+	0.520809i
$279$	−17.1170	+	4.58649i	−1.02477	+	0.274586i
$280$	−0.179137	+	0.146264i	−0.0107055	+	0.00874097i
$281$	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	$0.374359\pi$
$282$		−	5.40153i		−	0.321656i
$283$	7.24395	−	4.18230i	0.430608	−	0.248612i	−0.268998	−	0.963141i	$-0.586692\pi$
$283$	7.24395	−	4.18230i	0.430608	−	0.248612i	0.699606	+	0.714529i	$0.253359\pi$
$284$	3.42272	−	5.92833i	0.203101	−	0.351782i
$285$	−3.89499	+	1.75305i	−0.230719	+	0.103842i
$286$			9.54978i			0.564690i
$287$	0.251878	+	0.940020i	0.0148679	+	0.0554876i
$288$			2.13165i			0.125609i
$289$	17.0345	+	29.5047i	1.00203	+	1.73557i
$290$	−17.6130	−	6.67948i	−1.03427	−	0.392232i
$291$	14.4603	+	3.87462i	0.847676	+	0.227134i
$292$	1.03786	−	3.87333i	0.0607359	−	0.226670i
$293$	8.17171	+	2.18960i	0.477396	+	0.127918i	0.489490	−	0.872009i	$-0.337183\pi$
$293$	8.17171	+	2.18960i	0.477396	+	0.127918i	−0.0120938	+	0.999927i	$0.503850\pi$
$294$	−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
$298$	10.0096	+	5.77904i	0.579840	+	0.334771i
$299$	3.40665	+	5.90049i	0.197012	+	0.341234i
$300$	−2.56911	−	3.88695i	−0.148328	−	0.224413i
$301$	0.0317254	−	0.118401i	0.00182862	−	0.00682451i
$302$		−	16.4424i		−	0.946156i
$303$	−9.25749	−	2.48054i	−0.531829	−	0.142503i
$304$	1.44949	−	1.44949i	0.0831339	−	0.0831339i
$305$	−9.43415	−	11.5544i	−0.540198	−	0.661604i
$306$	15.2334			0.870833
$307$	8.70076	−	8.70076i	0.496579	−	0.496579i	−0.413792	−	0.910371i	$-0.635796\pi$
$307$	8.70076	−	8.70076i	0.496579	−	0.496579i	0.910371	+	0.413792i	$0.135796\pi$
$308$	0.148844	+	0.555494i	0.00848119	+	0.0316522i
$309$	−17.0136	−	4.55878i	−0.967869	−	0.259340i
$310$	−6.59147	+	17.3810i	−0.374371	+	0.987173i
$311$	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	$0.628118\pi$
$312$	1.54587	−	0.414214i	0.0875174	−	0.0234502i
$313$	−0.935758	+	1.62078i	−0.0528922	+	0.0916119i	−0.891259	−	0.453494i	$-0.850177\pi$
$313$	−0.935758	+	1.62078i	−0.0528922	+	0.0916119i	0.838367	+	0.545106i	$0.183511\pi$
$314$	0.708309	−	2.64344i	0.0399722	−	0.149178i
$315$	0.486590	−	0.0790851i	0.0274162	−	0.00445594i
$316$	3.22474	+	12.0349i	0.181406	+	0.677017i
$317$	−1.65086	−	6.16108i	−0.0927214	−	0.346041i	0.903943	−	0.427653i	$-0.140660\pi$
$317$	−1.65086	−	6.16108i	−0.0927214	−	0.346041i	−0.996664	+	0.0816126i	$0.973993\pi$
$318$	1.66390	−	2.88196i	0.0933070	−	0.161612i
$319$	−33.1226	+	33.1226i	−1.85451	+	1.85451i
$320$	1.81431	+	1.30701i	0.101423	+	0.0730639i
$321$	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
$325$	5.69419	−	6.42776i	0.315857	−	0.356548i
$326$	−16.8094	+	9.70492i	−0.930987	+	0.537506i
$327$	−18.3867			−1.01678
$328$	8.14893	−	4.70478i	0.449949	−	0.259778i
$329$	0.519187	−	0.299753i	0.0286237	−	0.0165259i
$330$	−11.4362	+	1.85872i	−0.629543	+	0.102319i
$331$	−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
$333$	12.7580	+	2.31507i	0.699134	+	0.126865i
$334$		−	2.70623i		−	0.148078i
$335$	−0.842524	−	1.03188i	−0.0460320	−	0.0563774i
$336$	0.0834643	−	0.0481882i	0.00455335	−	0.00262888i
$337$	−11.9691	−	3.20711i	−0.651998	−	0.174702i	−0.0823657	−	0.996602i	$-0.526248\pi$
$337$	−11.9691	−	3.20711i	−0.651998	−	0.174702i	−0.569632	+	0.821900i	$0.692914\pi$
$338$	−5.02520	−	8.70390i	−0.273335	−	0.473430i
$339$	−1.27568	+	1.27568i	−0.0692852	+	0.0692852i
$340$	9.34022	−	12.9656i	0.506544	−	0.703156i
$341$	32.6862	+	32.6862i	1.77006	+	1.77006i
$342$	−4.22076	+	1.13095i	−0.228232	+	0.0611547i
$343$	1.02307	−	1.02307i	0.0552405	−	0.0552405i
$344$	−1.18519			−0.0639011
$345$	−6.40300	+	5.22803i	−0.344726	+	0.281468i
$346$	−4.25970	+	15.8974i	−0.229003	+	0.854650i
$347$	28.4004			1.52461			0.762306	−	0.647216i	$-0.224067\pi$
$347$	28.4004			1.52461			0.762306	+	0.647216i	$0.224067\pi$
$348$	6.79837	+	3.92504i	0.364431	+	0.210404i
$349$	8.00242	+	4.62020i	0.428360	+	0.247314i	0.698648	−	0.715466i	$-0.253786\pi$
$349$	8.00242	+	4.62020i	0.428360	+	0.247314i	−0.270288	+	0.962780i	$0.587119\pi$
$350$	0.231037	−	0.462642i	0.0123495	−	0.0247292i
$351$	−7.93285	−	2.12560i	−0.423424	−	0.113456i
$352$	4.81552	−	2.78024i	0.256668	−	0.148187i
$353$	8.90031	+	5.13859i	0.473715	+	0.273500i	0.717794	−	0.696256i	$-0.245152\pi$
$353$	8.90031	+	5.13859i	0.473715	+	0.273500i	−0.244078	+	0.969756i	$0.578485\pi$
$354$	3.50402	−	6.06914i	0.186237	−	0.322571i
$355$	−1.53848	+	15.2294i	−0.0816539	+	0.808291i
$356$	0.704527	+	0.704527i	0.0373399	+	0.0373399i
$357$	−0.344365	−	0.596458i	−0.0182257	−	0.0315679i
$358$	0.136636	−	0.0366116i	0.00722145	−	0.00193498i
$359$			12.2560i			0.646847i	0.946254	+	0.323424i	$0.104834\pi$
$359$			12.2560i			0.646847i	−0.946254	+	0.323424i	$0.895166\pi$
$360$	−1.95630	−	4.34656i	−0.103106	−	0.229084i
$361$	−12.8154	−	7.39898i	−0.674495	−	0.389420i
$362$	−7.00705			−0.368282
$363$	−4.80406	+	17.9290i	−0.252148	+	0.941029i
$364$	0.125600	+	0.125600i	0.00658323	+	0.00658323i
$365$	1.43845	+	8.85043i	0.0752921	+	0.463253i
$366$	3.10817	+	5.38351i	0.162467	+	0.281400i
$367$	−1.36639	+	5.09944i	−0.0713250	+	0.266188i	−0.992375	−	0.123256i	$-0.960666\pi$
$367$	−1.36639	+	5.09944i	−0.0713250	+	0.266188i	0.921050	+	0.389445i	$0.127333\pi$
$368$	1.98356	−	3.43563i	0.103400	−	0.179095i
$369$	−20.0579			−1.04417
$370$	9.79289	−	9.43924i	0.509108	−	0.490723i
$371$	0.369347			0.0191755
$372$	3.87333	−	6.70881i	0.200823	−	0.347835i
$373$	3.30185	−	12.3227i	0.170963	−	0.638043i	−0.826241	−	0.563317i	$-0.809525\pi$
$373$	3.30185	−	12.3227i	0.170963	−	0.638043i	0.997204	−	0.0747263i	$-0.0238083\pi$
$374$	−19.8683	−	34.4129i	−1.02737	−	1.77945i
$375$	8.80576	+	5.56794i	0.454728	+	0.287527i
$376$	−4.09878	−	4.09878i	−0.211378	−	0.211378i
$377$	−3.74460	+	13.9750i	−0.192857	+	0.719751i
$378$	−0.494570			−0.0254379
$379$	−5.52269	−	3.18852i	−0.283681	−	0.163783i	0.351407	−	0.936223i	$-0.385703\pi$
$379$	−5.52269	−	3.18852i	−0.283681	−	0.163783i	−0.635089	+	0.772439i	$0.719037\pi$
$380$	−1.62534	+	4.28585i	−0.0833783	+	0.219859i
$381$		−	7.14643i		−	0.366123i
$382$	−1.10318	+	0.295597i	−0.0564438	+	0.0151241i
$383$	5.92368	+	10.2601i	0.302686	+	0.524268i	0.976743	−	0.214411i	$-0.0687833\pi$
$383$	5.92368	+	10.2601i	0.302686	+	0.524268i	−0.674057	+	0.738679i	$0.735450\pi$
$384$	−0.658919	−	0.658919i	−0.0336253	−	0.0336253i
$385$	−0.813300	−	0.996085i	−0.0414496	−	0.0507652i
$386$	4.92160	−	8.52446i	0.250503	−	0.433884i
$387$	2.18794	+	1.26321i	0.111219	+	0.0642123i
$388$	13.9129	−	8.03259i	0.706318	−	0.407793i
$389$	−3.59492	−	0.963255i	−0.182270	−	0.0488390i	0.166530	−	0.986036i	$-0.446744\pi$
$389$	−3.59492	−	0.963255i	−0.182270	−	0.0488390i	−0.348799	+	0.937197i	$0.613410\pi$
$390$	−2.77197	+	2.26330i	−0.140364	+	0.114607i
$391$	−24.5519	−	14.1751i	−1.24165	−	0.716864i
$392$	−6.05291	−	3.49465i	−0.305718	−	0.176507i
$393$	4.48188			0.226081
$394$	−4.03390	+	15.0547i	−0.203225	+	0.758446i
$395$	−17.6203	−	21.5804i	−0.886575	−	1.08583i
$396$	−11.8530			−0.595636
$397$	5.68644	−	5.68644i	0.285394	−	0.285394i	−0.549861	−	0.835256i	$-0.685320\pi$
$397$	5.68644	−	5.68644i	0.285394	−	0.285394i	0.835256	+	0.549861i	$0.185320\pi$
$398$	−20.8615	+	5.58983i	−1.04569	+	0.280193i
$399$	0.139696	+	0.139696i	0.00699357	+	0.00699357i
$400$	−4.89898	−	1.00000i	−0.244949	−	0.0500000i
$401$	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	$0.127035\pi$
$402$	0.277577	+	0.480778i	0.0138443	+	0.0239790i
$403$	13.7909	+	3.69526i	0.686974	+	0.184074i
$404$	−8.90704	+	5.14248i	−0.443142	+	0.255848i
$405$	−0.435758	+	4.31356i	−0.0216530	+	0.214342i
$406$			0.871267i			0.0432403i
$407$	−11.4099	−	31.8404i	−0.565569	−	1.57827i
$408$	−4.70881	+	4.70881i	−0.233121	+	0.233121i
$409$	21.4831	−	5.75637i	1.06227	−	0.284634i	0.314956	−	0.949106i	$-0.398010\pi$
$409$	21.4831	−	5.75637i	1.06227	−	0.284634i	0.747313	+	0.664472i	$0.231343\pi$
$410$	−12.2984	+	17.0719i	−0.607373	+	0.843121i
$411$	−5.78557	+	3.34030i	−0.285381	+	0.164765i
$412$	−16.3695	+	9.45095i	−0.806469	+	0.465615i
$413$	0.777810			0.0382735
$414$	−7.32358	+	4.22827i	−0.359934	+	0.207808i
$415$	−5.73607	+	15.1254i	−0.281572	+	0.742475i
$416$	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	0.398507	−	0.917165i	$-0.369528\pi$
$419$	−4.02283	−	2.32258i	−0.196528	−	0.113466i	−0.595035	+	0.803700i	$0.702862\pi$
$420$	−0.125965	+	0.174857i	−0.00614644	+	0.00853214i
$421$	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	$0.195553\pi$
$422$	5.01884	−	8.69289i	0.244313	−	0.423163i
$423$	3.19803	+	11.9352i	0.155493	+	0.580309i
$424$	−0.924288	−	3.44949i	−0.0448874	−	0.167522i
$425$	−7.14626	+	35.0094i	−0.346645	+	1.69821i
$426$	1.65099	−	6.16158i	0.0799908	−	0.298530i
$427$	−0.344970	+	0.597506i	−0.0166943	+	0.0289153i
$428$	14.2176	−	3.80959i	0.687232	−	0.184143i
$429$	2.30323	+	8.59575i	0.111201	+	0.415007i
$430$	2.41667	−	1.08769i	0.116542	−	0.0524532i
$431$	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	$0.567292\pi$
$432$	1.23766	+	4.61900i	0.0595468	+	0.222232i
$433$	15.5293	−	15.5293i	0.746291	−	0.746291i	−0.227490	−	0.973780i	$-0.573052\pi$
$433$	15.5293	−	15.5293i	0.746291	−	0.746291i	0.973780	+	0.227490i	$0.0730518\pi$
$434$	0.859788			0.0412711
$435$	−17.4644	−	1.76427i	−0.837356	−	0.0845901i
$436$	−13.9522	+	13.9522i	−0.668187	+	0.668187i
$437$	7.85507	+	2.10476i	0.375759	+	0.100684i
$438$		−	3.73670i		−	0.178546i
$439$	−2.43746	+	9.09672i	−0.116334	+	0.434163i	−0.999383	−	0.0351169i	$-0.988820\pi$
$439$	−2.43746	+	9.09672i	−0.116334	+	0.434163i	0.883050	+	0.469279i	$0.155486\pi$
$440$	−7.26758	+	10.0884i	−0.346469	+	0.480948i
$441$	7.44938	+	12.9027i	0.354733	+	0.614415i
$442$	−10.6290	−	6.13664i	−0.505568	−	0.291890i
$443$	1.60697	+	1.60697i	0.0763493	+	0.0763493i	0.744250	−	0.667901i	$-0.232807\pi$
$443$	1.60697	+	1.60697i	0.0763493	+	0.0763493i	−0.667901	+	0.744250i	$0.732807\pi$
$444$	−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
$447$	10.4034	+	2.78759i	0.492065	+	0.131848i
$448$	0.0267682	−	0.0999004i	0.00126468	−	0.00471985i
$449$	2.87798	+	0.771151i	0.135820	+	0.0363929i	0.326089	−	0.945339i	$-0.394269\pi$
$449$	2.87798	+	0.771151i	0.135820	+	0.0363929i	−0.190269	+	0.981732i	$0.560936\pi$
$450$	7.97801	+	7.06753i	0.376087	+	0.333166i
$451$	26.1609	+	45.3119i	1.23187	+	2.13366i
$452$			1.93602i			0.0910625i
$453$	−3.96560	−	14.7998i	−0.186320	−	0.695357i
$454$		−	7.29785i		−	0.342505i
$455$	−0.371374	−	0.140838i	−0.0174103	−	0.00660258i
$456$	0.955096	−	1.65427i	0.0447265	−	0.0774685i
$457$	6.91429	−	3.99197i	0.323437	−	0.186736i	−0.329487	−	0.944160i	$-0.606876\pi$
$457$	6.91429	−	3.99197i	0.323437	−	0.186736i	0.652923	+	0.757424i	$0.273542\pi$
$458$		−	15.7522i		−	0.736054i
$459$	33.0086	−	8.84462i	1.54071	−	0.412832i
$460$	−0.891592	+	8.82585i	−0.0415707	+	0.411507i
$461$	−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	$0.474141\pi$
$462$	0.267949	+	0.464102i	0.0124661	+	0.0215920i
$463$	−2.67846	−	4.63923i	−0.124479	−	0.215603i	0.797050	−	0.603913i	$-0.206393\pi$
$463$	−2.67846	−	4.63923i	−0.124479	−	0.215603i	−0.921529	+	0.388309i	$0.873059\pi$
$464$	8.13713	−	2.18034i	0.377757	−	0.101220i
$465$	−1.74102	+	17.2343i	−0.0807380	+	0.799224i
$466$	−2.13533	+	0.572161i	−0.0989175	+	0.0265049i
$467$		−	1.68754i		−	0.0780898i	−0.999237	−	0.0390449i	$-0.987568\pi$
$467$		−	1.68754i		−	0.0780898i	0.999237	−	0.0390449i	$-0.0124315\pi$
$468$	−3.17050	+	1.83049i	−0.146557	+	0.0846145i
$469$	−0.0308078	+	0.0533607i	−0.00142257	+	0.00246397i
$470$	12.1193	+	4.59605i	0.559020	+	0.212000i
$471$		−	2.55019i		−	0.117507i
$472$	−1.94646	−	7.26430i	−0.0895932	−	0.334367i
$473$		−	6.59022i		−	0.303019i
$474$	5.80518	+	10.0549i	0.266641	+	0.461836i
$475$	−0.619114	−	10.2307i	−0.0284069	−	0.469418i
$476$	−0.713915	−	0.191293i	−0.0327222	−	0.00876790i
$477$	−1.97026	+	7.35311i	−0.0902120	+	0.336676i
$478$	−22.7934	−	6.10746i	−1.04254	−	0.279349i
$479$	−1.22580	−	4.57475i	−0.0560083	−	0.209026i	0.932251	−	0.361812i	$-0.117842\pi$
$479$	−1.22580	−	4.57475i	−0.0560083	−	0.209026i	−0.988259	+	0.152787i	$0.951175\pi$
$480$	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
$483$	0.331114	+	0.191169i	0.0150662	+	0.00869847i
$484$	9.95946	+	17.2503i	0.452703	+	0.784104i
$485$	−20.9973	+	29.1473i	−0.953439	+	1.32351i
$486$	4.18060	−	15.6022i	0.189636	−	0.707730i
$487$			5.21509i			0.236318i	0.992995	+	0.118159i	$0.0376993\pi$
$487$			5.21509i			0.236318i	−0.992995	+	0.118159i	$0.962301\pi$
$488$	6.44364	+	1.72657i	0.291690	+	0.0781581i
$489$	−12.7895	+	12.7895i	−0.578361	+	0.578361i
$490$	15.5494	+	1.57081i	0.702451	+	0.0709620i
$491$	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
$493$	−15.5813	−	58.1501i	−0.701745	−	2.61895i
$494$	3.40060	+	0.911187i	0.153000	+	0.0409963i
$495$	24.1690	−	10.8780i	1.08631	−	0.488928i
$496$	−2.15161	−	8.02993i	−0.0966103	−	0.360554i
$497$	0.683863	−	0.183240i	0.0306754	−	0.00821946i
$498$	3.37067	−	5.83817i	0.151043	−	0.261615i
$499$	−9.13764	+	34.1022i	−0.409057	+	1.52662i	0.387391	+	0.921915i	$0.373376\pi$
$499$	−9.13764	+	34.1022i	−0.409057	+	1.52662i	−0.796448	+	0.604707i	$0.793290\pi$
$500$	10.9070	−	2.45692i	0.487778	−	0.109877i
$501$	−0.652690	−	2.43587i	−0.0291601	−	0.108827i
$502$	−0.211253	−	0.788407i	−0.00942869	−	0.0351883i
$503$	−6.17744	+	10.6996i	−0.275438	+	0.477073i	−0.970246	−	0.242123i	$-0.922156\pi$
$503$	−6.17744	+	10.6996i	−0.275438	+	0.477073i	0.694807	+	0.719196i	$0.255490\pi$
$504$	−0.155892	+	0.155892i	−0.00694400	+	0.00694400i
$505$	13.4425	−	18.6601i	0.598184	−	0.830366i
$506$	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	$-0.469713\pi$
$509$	20.5218	−	35.5447i	0.909611	−	1.57549i	0.814605	−	0.580016i	$-0.196954\pi$
$510$	5.28008	−	13.9230i	0.233806	−	0.616520i
$511$	0.359166	−	0.207365i	0.0158886	−	0.00917327i
$512$	−1.00000			−0.0441942
$513$	−8.48916	+	4.90122i	−0.374806	+	0.216394i
$514$	−21.7048	+	12.5313i	−0.957357	+	0.552730i
$515$	24.7049	−	34.2940i	1.08863	−	1.51117i
$516$	−1.06679	+	0.285845i	−0.0469627	+	0.0125836i
$517$	22.7912	−	22.7912i	1.00235	−	1.00235i
$518$	−0.568835	−	0.268705i	−0.0249932	−	0.0118062i
$519$			15.3366i			0.673203i
$520$	−0.385986	+	3.82086i	−0.0169266	+	0.167556i
$521$	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	$0.265305\pi$
$522$	−17.3455	−	4.64772i	−0.759194	−	0.203425i
$523$	−19.9811	−	34.6083i	−0.873714	−	1.51332i	−0.858126	−	0.513439i	$-0.828371\pi$
$523$	−19.9811	−	34.6083i	−0.873714	−	1.51332i	−0.0155877	−	0.999879i	$-0.504962\pi$
$524$	3.40094	−	3.40094i	0.148571	−	0.148571i
$525$	0.0963763	−	0.472146i	0.00420621	−	0.0206061i
$526$	4.03287	+	4.03287i	0.175842	+	0.175842i
$527$	−57.3840	+	15.3760i	−2.49969	+	0.669789i
$528$	3.66390	−	3.66390i	0.159451	−	0.159451i
$529$	−7.26190			−0.315735
$530$	5.05040	+	6.18546i	0.219376	+	0.268679i
$531$	−4.14918	+	15.4850i	−0.180059	+	0.671990i
$532$	0.212009			0.00919174
$533$	13.9953	+	8.08018i	0.606203	+	0.349991i
$534$	0.804063	+	0.464226i	0.0347952	+	0.0200890i
$535$	−25.4943	+	20.8160i	−1.10221	+	0.899953i
$536$	0.575454	+	0.154193i	0.0248558	+	0.00666010i
$537$	0.114156	−	0.0659082i	0.00492621	−	0.00284415i
$538$	7.32489	+	4.22902i	0.315798	+	0.182326i
$539$	19.4319	−	33.6571i	0.836993	−	1.44971i
$540$	−6.76268	−	8.28256i	−0.291020	−	0.356425i
$541$	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	$0.679927\pi$
$542$	7.60110	+	13.1655i	0.326495	+	0.565506i
$543$	−6.30704	+	1.68997i	−0.270661	+	0.0725234i
$544$			7.14626i			0.306394i
$545$	15.6448	−	41.2537i	0.670151	−	1.76711i
$546$	0.143345	+	0.0827602i	0.00613460	+	0.00354181i
$547$	−25.9211			−1.10830			−0.554152	−	0.832415i	$-0.686958\pi$
$547$	−25.9211			−1.10830			−0.554152	+	0.832415i	$0.686958\pi$
$548$	−1.85552	+	6.92489i	−0.0792638	+	0.295816i
$549$	−10.0552	−	10.0552i	−0.429144	−	0.429144i
$550$	5.56048	−	27.2407i	0.237100	−	1.16155i
$551$	8.63431	+	14.9551i	0.367834	+	0.637107i
$552$	0.956796	−	3.57081i	0.0407239	−	0.151984i
$553$	−0.644307	+	1.11597i	−0.0273987	+	0.0474560i
$554$	15.4531			0.656541
$555$	6.53801	−	10.8581i	0.277523	−	0.460901i
$556$	10.0270			0.425239
$557$	20.0583	−	34.7420i	0.849897	−	1.47206i	−0.0314026	−	0.999507i	$-0.509997\pi$
$557$	20.0583	−	34.7420i	0.849897	−	1.47206i	0.881300	−	0.472558i	$-0.156669\pi$
$558$	−4.58649	+	17.1170i	−0.194162	+	0.724621i
$559$	−1.01774	−	1.76279i	−0.0430460	−	0.0745579i
$560$	0.0371004	+	0.228269i	0.00156778	+	0.00964612i
$561$	−26.1832	−	26.1832i	−1.10546	−	1.10546i
$562$	1.14992	−	4.29157i	0.0485065	−	0.181029i
$563$	−10.1495			−0.427752			−0.213876	−	0.976861i	$-0.568609\pi$
$563$	−10.1495			−0.427752			−0.213876	+	0.976861i	$0.568609\pi$
$564$	−4.67786	−	2.70076i	−0.196973	−	0.113723i
$565$	−1.77675	−	3.94765i	−0.0747486	−	0.166079i
$566$		−	8.36459i		−	0.351590i
$567$	0.193697	−	0.0519009i	0.00813451	−	0.00217963i
$568$	−3.42272	−	5.92833i	−0.143614	−	0.248747i
$569$	−27.5816	−	27.5816i	−1.15628	−	1.15628i	−0.985269	−	0.171012i	$-0.945296\pi$
$569$	−27.5816	−	27.5816i	−1.15628	−	1.15628i	−0.171012	−	0.985269i	$-0.554704\pi$
$570$	−0.429306	+	4.24969i	−0.0179816	+	0.178000i
$571$	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	$-0.127549\pi$
$572$	8.27035	+	4.77489i	0.345801	+	0.199648i
$573$	−0.921683	+	0.532134i	−0.0385039	+	0.0222302i
$574$	0.940020	+	0.251878i	0.0392357	+	0.0105132i
$575$	−6.28181	−	18.8147i	−0.261969	−	0.784626i
$576$	1.84607	+	1.06583i	0.0769194	+	0.0444094i
$577$	37.6461	+	21.7350i	1.56723	+	0.904839i	0.996491	+	0.0837050i	$0.0266753\pi$
$577$	37.6461	+	21.7350i	1.56723	+	0.904839i	0.570736	+	0.821134i	$0.306658\pi$
$578$	34.0691			1.41709
$579$	2.37399	−	8.85986i	0.0986598	−	0.368203i
$580$	−14.5911	+	11.9136i	−0.605863	+	0.494685i
$581$	0.748209			0.0310409
$582$	10.5856	−	10.5856i	0.438789	−	0.438789i
$583$	19.1808	−	5.13948i	0.794388	−	0.212856i
$584$	−2.83548	−	2.83548i	−0.117333	−	0.117333i
$585$	4.78493	−	6.64217i	0.197833	−	0.274620i
$586$	5.98210	−	5.98210i	0.247118	−	0.247118i
$587$	5.48017	+	9.49194i	0.226191	+	0.391774i	0.956676	−	0.291154i	$-0.0940393\pi$
$587$	5.48017	+	9.49194i	0.226191	+	0.391774i	−0.730485	+	0.682929i	$0.760706\pi$
$588$	−6.29107	−	1.68569i	−0.259439	−	0.0695166i
$589$	14.7580	−	8.52056i	0.608094	−	0.351083i
$590$	10.6357	+	13.0260i	0.437864	+	0.536271i
$591$			14.5236i			0.597423i
$592$	−1.08604	+	5.98502i	−0.0446361	+	0.245983i
$593$	21.7960	−	21.7960i	0.895055	−	0.895055i	−0.0999387	−	0.994994i	$-0.531865\pi$
$593$	21.7960	−	21.7960i	0.895055	−	0.895055i	0.994994	+	0.0999387i	$0.0318647\pi$
$594$	−25.6838	+	6.88196i	−1.05382	+	0.282370i
$595$	1.63127	−	0.265129i	0.0668756	−	0.0108692i
$596$	10.0096	−	5.77904i	0.410009	−	0.236719i
$597$	−17.4293	+	10.0628i	−0.713333	+	0.411843i
$598$	6.81330			0.278617
$599$	−21.0451	+	12.1504i	−0.859878	+	0.496451i	−0.863971	−	0.503541i	$-0.832030\pi$
$599$	−21.0451	+	12.1504i	−0.859878	+	0.496451i	0.00409367	+	0.999992i	$0.498697\pi$
$600$	−4.65075	+	0.281441i	−0.189866	+	0.0114898i
$601$	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
$605$	−36.1391	−	26.0342i	−1.46927	−	1.05844i
$606$	−6.77696	+	6.77696i	−0.275295	+	0.275295i
$607$	14.9535	−	25.9002i	0.606943	−	1.05126i	−0.384798	−	0.923001i	$-0.625729\pi$
$607$	14.9535	−	25.9002i	0.606943	−	1.05126i	0.991741	−	0.128256i	$-0.0409378\pi$
$608$	−0.530550	−	1.98004i	−0.0215166	−	0.0803012i
$609$	0.210133	+	0.784227i	0.00851502	+	0.0317785i
$610$	−14.7235	+	2.39300i	−0.596137	+	0.0968897i
$611$	2.57660	−	9.61601i	0.104238	−	0.389022i
$612$	7.61668	−	13.1925i	0.307886	−	0.533274i
$613$	−8.80896	+	2.36036i	−0.355791	+	0.0953338i	−0.432287	−	0.901736i	$-0.642293\pi$
$613$	−8.80896	+	2.36036i	−0.355791	+	0.0953338i	0.0764964	+	0.997070i	$0.475627\pi$
$614$	−3.18470	−	11.8855i	−0.128524	−	0.479658i
$615$	−6.95234	+	18.3325i	−0.280346	+	0.739240i
$616$	0.555494	+	0.148844i	0.0223815	+	0.00599710i
$617$	9.62007	+	35.9026i	0.387289	+	1.44538i	0.834526	+	0.550968i	$0.185741\pi$
$617$	9.62007	+	35.9026i	0.387289	+	1.44538i	−0.447237	+	0.894415i	$0.647592\pi$
$618$	−12.4548	+	12.4548i	−0.501006	+	0.501006i
$619$	34.2163			1.37527			0.687635	−	0.726056i	$-0.258649\pi$
$619$	34.2163			1.37527			0.687635	+	0.726056i	$0.258649\pi$
$620$	11.7566	+	14.3989i	0.472158	+	0.578273i
$621$	−13.4142	+	13.4142i	−0.538294	+	0.538294i
$622$	26.8240	+	7.18747i	1.07554	+	0.288191i
$623$			0.103047i			0.00412850i
$624$	0.414214	−	1.54587i	0.0165818	−	0.0618842i
$625$	−19.9853	+	15.0196i	−0.799411	+	0.600784i
$626$	0.935758	+	1.62078i	0.0374004	+	0.0647794i
$627$	9.19856	+	5.31079i	0.367355	+	0.212092i
$628$	−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	$0.709250\pi$
$632$	12.0349	+	3.22474i	0.478723	+	0.128273i
$633$	2.42090	−	9.03491i	0.0962220	−	0.359106i
$634$	−6.16108	−	1.65086i	−0.244688	−	0.0655639i
$635$	16.0342	+	6.08075i	0.636300	+	0.241307i
$636$	−1.66390	−	2.88196i	−0.0659780	−	0.114277i
$637$		−	12.0037i		−	0.475604i
$638$	12.1237	+	45.2464i	0.479983	+	1.79132i
$639$			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	$0.171699\pi$
$642$	11.8784	−	6.85802i	0.468804	−	0.270664i
$643$			40.2835i			1.58863i	0.607509	+	0.794313i	$0.292169\pi$
$643$			40.2835i			1.58863i	−0.607509	+	0.794313i	$0.707831\pi$
$644$	0.396318	−	0.106193i	0.0156171	−	0.00418459i
$645$	1.91291	−	1.56189i	0.0753208	−	0.0614992i
$646$	−14.1499	+	3.79145i	−0.556720	+	0.149173i
$647$	−19.9613	−	34.5740i	−0.784759	−	1.35924i	−0.929143	−	0.369721i	$-0.879453\pi$
$647$	−19.9613	−	34.5740i	−0.784759	−	1.35924i	0.144383	−	0.989522i	$-0.453880\pi$
$648$	−0.969450	−	1.67914i	−0.0380836	−	0.0659627i
$649$	40.3930	−	10.8233i	1.58556	−	0.424850i
$650$	−2.71950	−	8.14520i	−0.106668	−	0.319481i
$651$	0.773895	−	0.207365i	0.0303313	−	0.00812726i
$652$			19.4098i			0.760148i
$653$	−20.5247	+	11.8499i	−0.803193	+	0.463724i	−0.844586	−	0.535419i	$-0.820154\pi$
$653$	−20.5247	+	11.8499i	−0.803193	+	0.463724i	0.0413936	+	0.999143i	$0.486820\pi$
$654$	−9.19333	+	15.9233i	−0.359488	+	0.622651i
$655$	−3.81354	+	10.0559i	−0.149007	+	0.392916i
$656$		−	9.40957i		−	0.367382i
$657$	2.21235	+	8.25660i	0.0863119	+	0.322121i
$658$		−	0.599506i		−	0.0233712i
$659$	3.68216	+	6.37769i	0.143437	+	0.248440i	0.928789	−	0.370610i	$-0.120851\pi$
$659$	3.68216	+	6.37769i	0.143437	+	0.248440i	−0.785352	+	0.619050i	$0.787518\pi$
$660$	−4.10841	+	10.8334i	−0.159920	+	0.421690i
$661$	−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	$0.836037\pi$
$662$	−1.66755	+	6.22338i	−0.0648112	+	0.241879i
$663$	−11.0472	−	2.96008i	−0.429036	−	0.114960i
$664$	−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
$668$	−2.34366	−	1.35311i	−0.0906790	−	0.0523535i
$669$	−10.1213	−	17.5306i	−0.391313	−	0.677774i
$670$	−1.31489	+	0.213709i	−0.0507987	+	0.00825628i
$671$	−9.60055	+	35.8297i	−0.370625	+	1.38319i
$672$		−	0.0963763i		−	0.00371780i
$673$	−23.1500	−	6.20302i	−0.892367	−	0.239109i	−0.216632	−	0.976253i	$-0.569507\pi$
$673$	−23.1500	−	6.20302i	−0.892367	−	0.239109i	−0.675735	+	0.737144i	$0.736174\pi$
$674$	−8.76198	+	8.76198i	−0.337499	+	0.337499i
$675$	21.3907	+	10.6823i	0.823329	+	0.411160i
$676$	−10.0504			−0.386554
$677$	5.42867	−	5.42867i	0.208641	−	0.208641i	−0.595049	−	0.803690i	$-0.702867\pi$
$677$	5.42867	−	5.42867i	0.208641	−	0.208641i	0.803690	+	0.595049i	$0.202867\pi$
$678$	0.466930	+	1.74261i	0.0179323	+	0.0669244i
$679$	1.60492	+	0.430037i	0.0615911	+	0.0165033i
$680$	−6.55840	−	14.5716i	−0.251503	−	0.558797i
$681$	−1.76010	−	6.56879i	−0.0674473	−	0.251717i
$682$	44.6502	−	11.9640i	1.70975	−	0.458125i
$683$	−8.86346	+	15.3520i	−0.339151	+	0.587427i	−0.984273	−	0.176653i	$-0.943473\pi$
$683$	−8.86346	+	15.3520i	−0.339151	+	0.587427i	0.645122	+	0.764079i	$0.276806\pi$
$684$	−1.13095	+	4.22076i	−0.0432429	+	0.161385i
$685$	−2.57172	−	15.8231i	−0.0982604	−	0.604570i
$686$	−0.374469	−	1.39754i	−0.0142973	−	0.0533582i
$687$	−3.79914	−	14.1786i	−0.144946	−	0.540947i
$688$	−0.592594	+	1.02640i	−0.0225925	+	0.0391313i
$689$	4.33688	−	4.33688i	0.165222	−	0.165222i
$690$	1.32611	+	8.15918i	0.0504840	+	0.310615i
$691$	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
$695$	−20.4456	+	9.20214i	−0.775546	+	0.349057i
$696$	6.79837	−	3.92504i	0.257692	−	0.148778i
$697$	−67.2433			−2.54702
$698$	8.00242	−	4.62020i	0.302896	−	0.174877i
$699$	−1.78402	+	1.03000i	−0.0674778	+	0.0389583i
$700$	−0.285141	−	0.431405i	−0.0107773	−	0.0163056i
$701$	−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
$703$	−12.4268	+	1.02494i	−0.468685	+	0.0386565i
$704$		−	5.56048i		−	0.209568i
$705$	12.0170	+	1.21397i	0.452587	+	0.0457206i
$706$	8.90031	−	5.13859i	0.334967	−	0.193394i
$707$	−1.02747	−	0.275310i	−0.0386421	−	0.0103541i
$708$	−3.50402	−	6.06914i	−0.131689	−	0.228092i
$709$	−13.8629	+	13.8629i	−0.520634	+	0.520634i	−0.917763	−	0.397129i	$-0.870007\pi$
$709$	−13.8629	+	13.8629i	−0.520634	+	0.520634i	0.397129	+	0.917763i	$0.370007\pi$
$710$	12.4198	+	8.94704i	0.466106	+	0.335777i
$711$	−18.7802	−	18.7802i	−0.704313	−	0.704313i
$712$	0.962402	−	0.257875i	0.0360675	−	0.00966427i
$713$	23.3200	−	23.3200i	0.873342	−	0.873342i
$714$	−0.688731			−0.0257751
$715$	−21.2458	−	2.14626i	−0.794549	−	0.0802657i
$716$	0.0366116	−	0.136636i	0.00136824	−	0.00510634i
$717$	−21.9893			−0.821206
$718$	10.6140	+	6.12800i	0.396111	+	0.228695i
$719$	−12.5516	−	7.24669i	−0.468097	−	0.270256i	0.247346	−	0.968927i	$-0.420442\pi$
$719$	−12.5516	−	7.24669i	−0.468097	−	0.270256i	−0.715443	+	0.698671i	$0.753775\pi$
$720$	−4.74238	−	0.479078i	−0.176738	−	0.0178542i
$721$	−1.88831	−	0.505971i	−0.0703243	−	0.0188433i
$722$	−12.8154	+	7.39898i	−0.476940	+	0.275362i
$723$	−15.7098	−	9.07007i	−0.584255	−	0.337320i
$724$	−3.50352	+	6.06828i	−0.130207	+	0.225526i
$725$	18.8186	−	37.6833i	0.698904	−	1.39952i
$726$	13.1249	+	13.1249i	0.487112	+	0.487112i
$727$	16.7353	+	28.9864i	0.620678	+	1.07505i	0.989360	+	0.145490i	$0.0464760\pi$
$727$	16.7353	+	28.9864i	0.620678	+	1.07505i	−0.368681	+	0.929556i	$0.620191\pi$
$728$	0.171573	−	0.0459728i	0.00635891	−	0.00170387i
$729$		−	9.23511i		−	0.342041i
$730$	8.38392	+	3.17948i	0.310303	+	0.117678i
$731$	7.33495	+	4.23484i	0.271293	+	0.156631i
$732$	6.21634			0.229762
$733$	0.0524807	−	0.195861i	0.00193842	−	0.00723428i	−0.964950	−	0.262434i	$-0.915475\pi$
$733$	0.0524807	−	0.195861i	0.00193842	−	0.00723428i	0.966888	+	0.255200i	$0.0821413\pi$
$734$	3.73305	+	3.73305i	0.137789	+	0.137789i
$735$	14.3749	−	2.33634i	0.530225	−	0.0861771i
$736$	−1.98356	−	3.43563i	−0.0731151	−	0.126639i
$737$	−0.857384	+	3.19980i	−0.0315821	+	0.117866i
$738$	−10.0290	+	17.3707i	−0.369171	+	0.639424i
$739$	−34.4241			−1.26631			−0.633155	−	0.774025i	$-0.718241\pi$
$739$	−34.4241			−1.26631			−0.633155	+	0.774025i	$0.718241\pi$
$740$	−3.27817	−	13.2005i	−0.120508	−	0.485261i
$741$	3.28064			0.120517
$742$	0.184674	−	0.319864i	0.00677958	−	0.0117426i
$743$	−6.65580	+	24.8398i	−0.244178	+	0.911283i	0.729617	+	0.683856i	$0.239698\pi$
$743$	−6.65580	+	24.8398i	−0.244178	+	0.911283i	−0.973795	+	0.227428i	$0.926969\pi$
$744$	−3.87333	−	6.70881i	−0.142003	−	0.245957i
$745$	−15.1065	+	20.9700i	−0.553459	+	0.768280i
$746$	−9.02082	−	9.02082i	−0.330276	−	0.330276i
$747$	−3.99128	+	14.8957i	−0.146033	+	0.545003i
$748$	−39.7366			−1.45292
$749$	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	$0.675256\pi$
$752$	−5.59904	+	1.50026i	−0.204176	+	0.0547088i
$753$	−0.380298	−	0.658695i	−0.0138588	−	0.0240042i
$754$	10.2304	+	10.2304i	0.372570	+	0.372570i
$755$	36.5802	+	3.69535i	1.33129	+	0.134488i
$756$	−0.247285	+	0.428310i	−0.00899366	+	0.0155775i
$757$	−1.84585	−	1.06570i	−0.0670886	−	0.0387336i	0.466081	−	0.884742i	$-0.345666\pi$
$757$	−1.84585	−	1.06570i	−0.0670886	−	0.0387336i	−0.533169	+	0.846009i	$0.678999\pi$
$758$	−5.52269	+	3.18852i	−0.200593	+	0.115812i
$759$	19.8554	+	5.32024i	0.720706	+	0.193113i
$760$	2.89898	+	3.55051i	0.105157	+	0.128791i
$761$	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	$0.647837\pi$
$762$	−6.18899	−	3.57321i	−0.224203	−	0.129444i
$763$	−2.04070			−0.0738784
$764$	−0.295597	+	1.10318i	−0.0106943	+	0.0399118i
$765$	−3.42362	+	33.8903i	−0.123781	+	1.22531i
$766$	11.8474			0.428063
$767$	9.13306	−	9.13306i	0.329776	−	0.329776i
$768$	−0.900100	+	0.241181i	−0.0324795	+	0.00870287i
$769$	−11.7676	−	11.7676i	−0.424350	−	0.424350i	0.462349	−	0.886698i	$-0.347007\pi$
$769$	−11.7676	−	11.7676i	−0.424350	−	0.424350i	−0.886698	+	0.462349i	$0.847007\pi$
$770$	−1.26928	+	0.206296i	−0.0457418	+	0.00743439i
$771$	−16.5142	+	16.5142i	−0.594743	+	0.594743i
$772$	−4.92160	−	8.52446i	−0.177132	−	0.306802i
$773$	38.8194	+	10.4016i	1.39624	+	0.374120i	0.876992	−	0.480505i	$-0.159547\pi$
$773$	38.8194	+	10.4016i	1.39624	+	0.374120i	0.519245	+	0.854626i	$0.326213\pi$
$774$	2.18794	−	1.26321i	0.0786437	−	0.0454050i
$775$	−37.1868	−	18.5706i	−1.33579	−	0.667077i
$776$		−	16.0652i		−	0.576706i
$777$	−0.576815	−	0.104669i	−0.0206931	−	0.00375498i
$778$	−2.63166	+	2.63166i	−0.0943496	+	0.0943496i
$779$	18.6313	−	4.99225i	0.667536	−	0.178866i
$780$	0.574094	+	3.53225i	0.0205559	+	0.126475i
$781$	32.9643	−	19.0320i	1.17956	−	0.681017i
$782$	−24.5519	+	14.1751i	−0.877976	+	0.506900i
$783$	−40.2839			−1.43963
$784$	−6.05291	+	3.49465i	−0.216176	+	0.124809i
$785$	5.72180	+	2.16991i	0.204220	+	0.0774473i
$786$	2.24094	−	3.88142i	0.0799317	−	0.138446i
$787$	−30.9931	−	30.9931i	−1.10479	−	1.10479i	−0.993825	−	0.110960i	$-0.964607\pi$
$787$	−30.9931	−	30.9931i	−1.10479	−	1.10479i	−0.110960	−	0.993825i	$-0.535393\pi$
$788$	11.0208	+	11.0208i	0.392600	+	0.392600i
$789$	4.60264	+	2.65733i	0.163858	+	0.0946036i
$790$	−27.4994	+	4.46945i	−0.978383	+	0.159016i
$791$	−0.141585	+	0.141585i	−0.00503418	+	0.00503418i
$792$	−5.92650	+	10.2650i	−0.210589	+	0.364751i
$793$	2.96528	+	11.0666i	0.105300	+	0.392985i
$794$	−2.08138	−	7.76782i	−0.0738655	−	0.275670i
$795$	6.03768	+	4.34947i	0.214134	+	0.154260i
$796$	−5.58983	+	20.8615i	−0.198126	+	0.739417i
$797$	−17.3202	+	29.9995i	−0.613514	+	1.06264i	0.377129	+	0.926161i	$0.376911\pi$
$797$	−17.3202	+	29.9995i	−0.613514	+	1.06264i	−0.990643	+	0.136477i	$0.956422\pi$
$798$	0.190829	−	0.0511325i	0.00675527	−	0.00181007i
$799$	10.7212	+	40.0122i	0.379290	+	1.41553i
$800$	−3.31552	+	3.74264i	−0.117221	+	0.132322i
$801$	−2.05151	−	0.549699i	−0.0724864	−	0.0194227i
$802$	−3.90547	−	14.5754i	−0.137907	−	0.514676i
$803$	15.7666	−	15.7666i	0.556391	−	0.556391i
$804$	0.555154			0.0195788
$805$	−0.710658	+	0.580249i	−0.0250474	+	0.0204511i
$806$	10.0956	−	10.0956i	0.355604	−	0.355604i
$807$	7.61309	+	2.03992i	0.267993	+	0.0718086i
$808$			10.2850i			0.361824i
$809$	8.37202	−	31.2448i	0.294344	−	1.09851i	−0.647392	−	0.762157i	$-0.724140\pi$
$809$	8.37202	−	31.2448i	0.294344	−	1.09851i	0.941737	−	0.336351i	$-0.109193\pi$
$810$	3.51777	+	2.53416i	0.123602	+	0.0890412i
$811$	−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	$-0.392240\pi$
$812$	0.754539	+	0.435633i	0.0264791	+	0.0152877i
$813$	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
$817$	−2.34672	−	0.628802i	−0.0821014	−	0.0219990i
$818$	5.75637	−	21.4831i	0.201267	−	0.751138i
$819$	−0.365734	−	0.0979981i	−0.0127798	−	0.00342433i
$820$	8.63552	+	19.1867i	0.301565	+	0.670027i
$821$	−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	$0.991287\pi$
$822$			6.68060i			0.233013i
$823$	−11.5010	−	42.9224i	−0.400901	−	1.49618i	−0.811493	−	0.584362i	$-0.801345\pi$
$823$	−11.5010	−	42.9224i	−0.400901	−	1.49618i	0.410592	−	0.911819i	$-0.365322\pi$
$824$			18.9019i			0.658479i
$825$	−1.56495	−	25.8604i	−0.0544844	−	0.900343i
$826$	0.388905	−	0.673603i	0.0135317	−	0.0234377i
$827$	−22.7942	+	13.1602i	−0.792631	+	0.457626i	−0.840888	−	0.541209i	$-0.817967\pi$
$827$	−22.7942	+	13.1602i	−0.792631	+	0.457626i	0.0482570	+	0.998835i	$0.484633\pi$
$828$			8.45654i			0.293885i
$829$	15.2862	−	4.09592i	0.530911	−	0.142257i	0.0166022	−	0.999862i	$-0.494715\pi$
$829$	15.2862	−	4.09592i	0.530911	−	0.142257i	0.514309	+	0.857605i	$0.328048\pi$
$830$	10.2309	+	12.5303i	0.355120	+	0.434932i
$831$	13.9094	−	3.72700i	0.482510	−	0.129288i
$832$	−0.858719	−	1.48735i	−0.0297707	−	0.0515644i
$833$	24.9737	+	43.2557i	0.865288	+	1.49872i
$834$	9.02528	−	2.41832i	0.312520	−	0.0837395i
$835$	6.02066	+	0.608211i	0.208354	+	0.0210480i
$836$	11.0100	−	2.95011i	0.380788	−	0.102032i
$837$			39.7532i			1.37407i
$838$	−4.02283	+	2.32258i	−0.138966	+	0.0802322i
$839$	−6.91184	+	11.9717i	−0.238623	+	0.413308i	−0.960319	−	0.278902i	$-0.910029\pi$
$839$	−6.91184	+	11.9717i	−0.238623	+	0.413308i	0.721696	+	0.692210i	$0.243363\pi$
$840$	0.0884482	+	0.196517i	0.00305175	+	0.00678048i
$841$			41.9668i			1.44713i
$842$	−1.80790	−	6.74716i	−0.0623042	−	0.232523i
$843$		−	4.14018i		−	0.142595i
$844$	−5.01884	−	8.69289i	−0.172756	−	0.299221i
$845$	20.4934	−	9.22363i	0.704993	−	0.317303i
$846$	11.9352	+	3.19803i	0.410341	+	0.109950i
$847$	−0.533194	+	1.98991i	−0.0183208	+	0.0683740i
$848$	−3.44949	−	0.924288i	−0.118456	−	0.0317402i
$849$	−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
$853$	−7.16451	−	4.13643i	−0.245308	−	0.141629i	0.372306	−	0.928110i	$-0.378567\pi$
$853$	−7.16451	−	4.13643i	−0.245308	−	0.141629i	−0.617614	+	0.786481i	$0.711901\pi$
$854$	0.344970	+	0.597506i	0.0118046	+	0.0204462i
$855$	−1.56748	−	9.64428i	−0.0536066	−	0.329827i
$856$	3.80959	−	14.2176i	0.130209	−	0.485947i
$857$			14.1078i			0.481914i	0.970536	+	0.240957i	$0.0774613\pi$
$857$			14.1078i			0.481914i	−0.970536	+	0.240957i	$0.922539\pi$
$858$	8.59575	+	2.30323i	0.293454	+	0.0786308i
$859$	12.6794	−	12.6794i	0.432615	−	0.432615i	−0.456902	−	0.889517i	$-0.651041\pi$
$859$	12.6794	−	12.6794i	0.432615	−	0.432615i	0.889517	+	0.456902i	$0.151041\pi$
$860$	0.266365	−	2.63674i	0.00908298	−	0.0899122i
$861$	0.906860			0.0309057
$862$	1.47896	−	1.47896i	0.0503736	−	0.0503736i
$863$	−2.02242	−	7.54779i	−0.0688441	−	0.256930i	0.922923	−	0.384985i	$-0.125793\pi$
$863$	−2.02242	−	7.54779i	−0.0688441	−	0.256930i	−0.991767	+	0.128055i	$0.959127\pi$
$864$	4.61900	+	1.23766i	0.157142	+	0.0421059i
$865$	−34.4103	−	13.0496i	−1.16999	−	0.443700i
$866$	−5.68412	−	21.2134i	−0.193154	−	0.720862i
$867$	30.6656	−	8.21682i	1.04146	−	0.279058i
$868$	0.429894	−	0.744598i	0.0145916	−	0.0252733i
$869$	−17.9311	+	66.9199i	−0.608272	+	2.27010i
$870$	−10.2601	+	14.2425i	−0.347851	+	0.482867i
$871$	0.264816	+	0.988308i	0.00897296	+	0.0334875i
$872$	5.10684	+	19.0590i	0.172939	+	0.645419i
$873$	−17.1227	+	29.6574i	−0.579515	+	1.00375i
$874$	5.75031	−	5.75031i	0.194507	−	0.194507i
$875$	0.977336	+	0.617976i	0.0330400	+	0.0208914i
$876$	−3.23607	−	1.86835i	−0.109337	−	0.0631256i
$877$	19.8334	+	19.8334i	0.669725	+	0.669725i	0.957652	−	0.287928i	$-0.0929662\pi$
$877$	19.8334	+	19.8334i	0.669725	+	0.669725i	−0.287928	+	0.957652i	$0.592966\pi$
$878$	6.65926	+	6.65926i	0.224739	+	0.224739i
$879$	3.94172	−	6.82726i	0.132951	−	0.230278i
$880$	5.10306	+	11.3381i	0.172024	+	0.382209i
$881$	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	$0.243893\pi$
$882$	14.8988			0.501668
$883$	−40.7518	+	23.5281i	−1.37141	+	0.791783i	−0.991105	−	0.133080i	$-0.957513\pi$
$883$	−40.7518	+	23.5281i	−1.37141	+	0.791783i	−0.380302	+	0.924862i	$0.624180\pi$
$884$	−10.6290	+	6.13664i	−0.357491	+	0.206397i
$885$	12.7148	+	9.15956i	0.427403	+	0.307895i
$886$	2.19516	−	0.588190i	0.0737477	−	0.0197606i
$887$	−24.1505	+	24.1505i	−0.810895	+	0.810895i	−0.984768	−	0.173873i	$-0.944372\pi$
$887$	−24.1505	+	24.1505i	−0.810895	+	0.810895i	0.173873	+	0.984768i	$0.444372\pi$
$888$	0.465926	+	5.64905i	0.0156354	+	0.189570i
$889$		−	0.793169i		−	0.0266020i
$890$	−1.72573	+	1.40905i	−0.0578467	+	0.0472316i
$891$	9.33680	−	5.39060i	0.312795	−	0.180592i
$892$	−20.9828	−	5.62233i	−0.702557	−	0.188250i
$893$	−5.94114	−	10.2904i	−0.198813	−	0.344354i
$894$	7.61583	−	7.61583i	0.254711	−	0.254711i
$895$	0.0507431	+	0.312209i	0.00169616	+	0.0104360i
$896$	−0.0731322	−	0.0731322i	−0.00244317	−	0.00244317i
$897$	6.13265	−	1.64324i	0.204763	−	0.0548661i
$898$	2.10682	−	2.10682i	0.0703056	−	0.0703056i
$899$	70.0318			2.33569
$900$	10.1097	−	3.37540i	0.336989	−	0.112513i
$901$	−6.60521	+	24.6510i	−0.220051	+	0.821243i
$902$	52.3217			1.74212
$903$	−0.0989210	−	0.0571121i	−0.00329189	−	0.00190057i
$904$	1.67664	+	0.968008i	0.0557642	+	0.0321955i
$905$	1.57480	−	15.5889i	0.0523481	−	0.518192i
$906$	−14.7998	−	3.96560i	−0.491692	−	0.131748i
$907$	−48.7960	+	28.1724i	−1.62024	+	0.935448i	−0.633390	+	0.773833i	$0.718337\pi$
$907$	−48.7960	+	28.1724i	−1.62024	+	0.935448i	−0.986854	+	0.161615i	$0.948330\pi$
$908$	−6.32013	−	3.64893i	−0.209741	−	0.121094i
$909$	10.9620	−	18.9867i	0.363586	−	0.629750i
$910$	−0.307656	+	0.251200i	−0.0101987	+	0.00832720i
$911$	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	$0.618855\pi$
$912$	−0.955096	−	1.65427i	−0.0316264	−	0.0547785i
$913$	38.8558	−	10.4114i	1.28594	−	0.344566i
$914$		−	7.98393i		−	0.264085i
$915$	−12.6755	+	5.70497i	−0.419038	+	0.188600i
$916$	−13.6418	−	7.87612i	−0.450739	−	0.260234i
$917$	0.497436			0.0164268
$918$	8.84462	−	33.0086i	0.291916	−	1.08945i
$919$	0.483267	+	0.483267i	0.0159415	+	0.0159415i	0.715033	−	0.699091i	$-0.246412\pi$
$919$	0.483267	+	0.483267i	0.0159415	+	0.0159415i	−0.699091	+	0.715033i	$0.746412\pi$
$920$	7.19761	+	5.18506i	0.237298	+	0.170947i
$921$	−5.73309	−	9.93001i	−0.188912	−	0.327205i
$922$	−1.99590	+	7.44879i	−0.0657313	+	0.245313i
$923$	5.87832	−	10.1815i	0.193487	−	0.335129i
$924$	0.535898			0.0176298
$925$	18.7990	+	23.9081i	0.618107	+	0.786094i
$926$	−5.35693			−0.176040
$927$	20.1461	−	34.8941i	0.661686	−	1.14607i
$928$	2.18034	−	8.13713i	0.0715731	−	0.267115i
$929$	−5.20264	−	9.01123i	−0.170693	−	0.295649i	0.767969	−	0.640487i	$-0.221267\pi$
$929$	−5.20264	−	9.01123i	−0.170693	−	0.295649i	−0.938662	+	0.344838i	$0.887934\pi$
$930$	14.0549	+	10.1249i	0.460877	+	0.332010i
$931$	−10.1309	−	10.1309i	−0.332028	−	0.332028i
$932$	−0.572161	+	2.13533i	−0.0187418	+	0.0699452i
$933$	25.8778			0.847200
$934$	−1.46145	−	0.843768i	−0.0478201	−	0.0276089i
$935$	81.0253	−	36.4678i	2.64981	−	1.19263i
$936$			3.66098i			0.119663i
$937$	11.4236	−	3.06093i	0.373191	−	0.0999963i	−0.0673482	−	0.997730i	$-0.521454\pi$
$937$	11.4236	−	3.06093i	0.373191	−	0.0999963i	0.440540	+	0.897733i	$0.354787\pi$
$938$	0.0308078	+	0.0533607i	0.00100591	+	0.00174229i
$939$	1.23318	+	1.23318i	0.0402432	+	0.0402432i
$940$	10.0399	−	8.19756i	0.327466	−	0.267375i
$941$	−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	$0.197974\pi$
$942$	−2.20853	−	1.27510i	−0.0719579	−	0.0415449i
$943$	32.3278	−	18.6645i	1.05274	−	0.607799i
$944$	−7.26430	−	1.94646i	−0.236433	−	0.0633520i
$945$	0.111152	−	1.10029i	0.00361578	−	0.0357925i
$946$	−5.70730	−	3.29511i	−0.185560	−	0.107133i
$947$	37.1564	+	21.4522i	1.20742	+	0.697104i	0.962195	−	0.272362i	$-0.0878049\pi$
$947$	37.1564	+	21.4522i	1.20742	+	0.697104i	0.245225	+	0.969466i	$0.421138\pi$
$948$	11.6104			0.377087
$949$	1.78245	−	6.65221i	0.0578609	−	0.215940i
$950$	−9.16962	−	4.57919i	−0.297502	−	0.148569i
$951$	−5.94374			−0.192739
$952$	−0.522622	+	0.522622i	−0.0169383	+	0.0169383i
$953$	−34.2271	+	9.17111i	−1.10872	+	0.297081i	−0.766312	−	0.642469i	$-0.777910\pi$
$953$	−34.2271	+	9.17111i	−1.10872	+	0.297081i	−0.342411	+	0.939550i	$0.611244\pi$
$954$	5.38285	+	5.38285i	0.174276	+	0.174276i
$955$	−0.409694	−	2.52074i	−0.0132574	−	0.0815692i
$956$	−16.6859	+	16.6859i	−0.539661	+	0.539661i
$957$	21.8251	+	37.8022i	0.705506	+	1.22197i
$958$	−4.57475	−	1.22580i	−0.147803	−	0.0396038i
$959$	−0.642130	+	0.370734i	−0.0207355	+	0.0119716i
$960$	1.61401	−	1.31784i	0.0520921	−	0.0425330i
$961$		−	38.1092i		−	1.22933i
$962$	−9.83441	+	3.52413i	−0.317074	+	0.113623i
$963$	−22.1862	+	22.1862i	−0.714941	+	0.714941i
$964$	−18.8035	+	5.03837i	−0.605619	+	0.162275i
$965$	17.8587	+	12.8651i	0.574890	+	0.414143i
$966$	0.331114	−	0.191169i	0.0106534	−	0.00615075i
$967$	−35.3782	+	20.4256i	−1.13768	+	0.656843i	−0.945856	−	0.324586i	$-0.894775\pi$
$967$	−35.3782	+	20.4256i	−1.13768	+	0.656843i	−0.191829	+	0.981428i	$0.561442\pi$
$968$	19.9189			0.640218
$969$	−11.8219	+	6.82537i	−0.379774	+	0.219262i
$970$	14.7436	+	32.7578i	0.473389	+	1.05179i
$971$	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
$975$	−4.41229	−	6.67559i	−0.141306	−	0.213790i
$976$	4.71707	−	4.71707i	0.150990	−	0.150990i
$977$	14.7630	−	25.5703i	0.472312	−	0.818068i	−0.527186	−	0.849750i	$-0.676753\pi$
$977$	14.7630	−	25.5703i	0.472312	−	0.818068i	0.999498	+	0.0316818i	$0.0100863\pi$
$978$	4.68128	+	17.4708i	0.149691	+	0.558654i
$979$	1.43391	+	5.35141i	0.0458279	+	0.171032i
$980$	9.13507	−	12.6808i	0.291809	−	0.405073i
$981$	10.8860	−	40.6272i	0.347564	−	1.29713i
$982$	5.74014	−	9.94222i	0.183175	−	0.317269i
$983$	−30.0319	+	8.04703i	−0.957870	+	0.256661i	−0.703699	−	0.710499i	$-0.748469\pi$
$983$	−30.0319	+	8.04703i	−0.957870	+	0.256661i	−0.254172	+	0.967159i	$0.581803\pi$
$984$	−2.26941	−	8.46955i	−0.0723461	−	0.269999i
$985$	−32.5863	−	12.3579i	−1.03829	−	0.393754i
$986$	−58.1501	−	15.5813i	−1.85188	−	0.496209i
$987$	−0.144589	−	0.539615i	−0.00460233	−	0.0171761i
$988$	2.48941	−	2.48941i	0.0791987	−	0.0791987i
$989$	−4.70180			−0.149508
$990$	2.66390	−	26.3699i	0.0846644	−	0.838091i
$991$	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	$0.189391\pi$
$992$	−8.02993	−	2.15161i	−0.254950	−	0.0683138i
$993$			6.00385i			0.190526i
$994$	0.183240	−	0.683863i	0.00581203	−	0.0216908i
$995$	−7.74742	−	47.6678i	−0.245610	−	1.51117i
$996$	−3.37067	−	5.83817i	−0.106804	−	0.184990i
$997$	−0.0930324	−	0.0537123i	−0.00294637	−	0.00170109i	0.498526	−	0.866875i	$-0.333875\pi$
$997$	−0.0930324	−	0.0537123i	−0.00294637	−	0.00170109i	−0.501472	+	0.865174i	$0.667208\pi$
$998$	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.q.c.97.1	✓	8
5.3	odd	4		370.2.r.c.23.1	yes	8
37.29	odd	12		370.2.r.c.177.1	yes	8
185.103	even	12	inner	370.2.q.c.103.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.q.c.97.1	✓	8	1.1	even	1	trivial
370.2.q.c.103.1	yes	8	185.103	even	12	inner
370.2.r.c.23.1	yes	8	5.3	odd	4
370.2.r.c.177.1	yes	8	37.29	odd	12

Overview	Random
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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.q (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.241181 - 0.900100i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.81431 + 1.30701i) q^{5} +(-0.658919 - 0.658919i) q^{6} +(0.0267682 - 0.0999004i) q^{7} -1.00000 q^{8} +(1.84607 + 1.06583i) q^{9} +(2.03906 - 0.917738i) q^{10} -5.56048i q^{11} +(-0.900100 + 0.241181i) q^{12} +(-0.858719 - 1.48735i) q^{13} +(-0.0731322 - 0.0731322i) q^{14} +(1.61401 - 1.31784i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(6.18885 + 3.57313i) q^{17} +(1.84607 - 1.06583i) q^{18} +(-1.98004 - 0.530550i) q^{19} +(0.224745 - 2.22474i) q^{20} +(-0.0834643 - 0.0481882i) q^{21} +(-4.81552 - 2.78024i) q^{22} -3.96713 q^{23} +(-0.241181 + 0.900100i) q^{24} +(1.58346 + 4.74264i) q^{25} -1.71744 q^{26} +(3.38134 - 3.38134i) q^{27} +(-0.0999004 + 0.0267682i) q^{28} +(-5.95680 - 5.95680i) q^{29} +(-0.334273 - 2.05670i) q^{30} +(-5.87832 + 5.87832i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-5.00498 - 1.34108i) q^{33} +(6.18885 - 3.57313i) q^{34} +(0.179137 - 0.146264i) q^{35} -2.13165i q^{36} +(5.72620 - 2.05197i) q^{37} +(-1.44949 + 1.44949i) q^{38} +(-1.54587 + 0.414214i) q^{39} +(-1.81431 - 1.30701i) q^{40} +(-8.14893 + 4.70478i) q^{41} +(-0.0834643 + 0.0481882i) q^{42} +1.18519 q^{43} +(-4.81552 + 2.78024i) q^{44} +(1.95630 + 4.34656i) 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} +(4.89898 + 1.00000i) q^{50} +(4.70881 - 4.70881i) q^{51} +(-0.858719 + 1.48735i) q^{52} +(0.924288 + 3.44949i) q^{53} +(-1.23766 - 4.61900i) q^{54} +(7.26758 - 10.0884i) q^{55} +(-0.0267682 + 0.0999004i) q^{56} +(-0.955096 + 1.65427i) q^{57} +(-8.13713 + 2.18034i) q^{58} +(1.94646 + 7.26430i) q^{59} +(-1.94829 - 0.738859i) q^{60} +(-6.44364 - 1.72657i) q^{61} +(2.15161 + 8.02993i) q^{62} +(0.155892 - 0.155892i) q^{63} +1.00000 q^{64} +(0.385986 - 3.82086i) q^{65} +(-3.66390 + 3.66390i) q^{66} +(-0.575454 - 0.154193i) q^{67} -7.14626i q^{68} +(-0.956796 + 3.57081i) q^{69} +(-0.0371004 - 0.228269i) q^{70} +(3.42272 + 5.92833i) q^{71} +(-1.84607 - 1.06583i) 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} +(-0.555494 - 0.148844i) q^{77} +(-0.414214 + 1.54587i) q^{78} +(-12.0349 - 3.22474i) q^{79} +(-2.03906 + 0.917738i) q^{80} +(0.969450 + 1.67914i) q^{81} +9.40957i q^{82} +(1.87239 + 6.98784i) q^{83} +0.0963763i q^{84} +(6.55840 + 14.5716i) q^{85} +(0.592594 - 1.02640i) q^{86} +(-6.79837 + 3.92504i) q^{87} +5.56048i q^{88} +(-0.962402 + 0.257875i) q^{89} +(4.74238 + 0.479078i) q^{90} +(-0.171573 + 0.0459728i) q^{91} +(1.98356 + 3.43563i) q^{92} +(3.87333 + 6.70881i) q^{93} +(5.59904 - 1.50026i) q^{94} +(-2.89898 - 3.55051i) q^{95} +(0.900100 - 0.241181i) q^{96} +16.0652i q^{97} +(6.05291 - 3.49465i) q^{98} +(5.92650 - 10.2650i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} + 4 q^{3} - 4 q^{4} + 4 q^{5} - 4 q^{6} + 12 q^{7} - 8 q^{8} - 12 q^{9} - 4 q^{10} - 8 q^{12} - 4 q^{13} + 12 q^{14} - 4 q^{16} + 12 q^{17} - 12 q^{18} + 4 q^{19} - 8 q^{20} + 12 q^{21} - 12 q^{22}+ \cdots + 4 q^{99}+O(q^{100}) \) 8 * q + 4 * q^2 + 4 * q^3 - 4 * q^4 + 4 * q^5 - 4 * q^6 + 12 * q^7 - 8 * q^8 - 12 * q^9 - 4 * q^10 - 8 * q^12 - 4 * q^13 + 12 * q^14 - 4 * q^16 + 12 * q^17 - 12 * q^18 + 4 * q^19 - 8 * q^20 + 12 * q^21 - 12 * q^22 - 8 * q^23 - 4 * q^24 - 8 * q^26 - 8 * q^27 - 24 * q^29 - 12 * q^30 - 8 * q^31 + 4 * q^32 - 12 * q^33 + 12 * q^34 + 8 * q^38 + 16 * q^39 - 4 * q^40 + 12 * q^41 + 12 * q^42 + 16 * q^43 - 12 * q^44 - 12 * q^45 - 4 * q^46 - 8 * q^47 + 4 * q^48 + 36 * q^49 + 20 * q^51 - 4 * q^52 + 16 * q^53 - 4 * q^54 + 16 * q^55 - 12 * q^56 + 4 * q^57 - 24 * q^58 - 8 * q^59 - 12 * q^60 + 20 * q^62 - 4 * q^63 + 8 * q^64 + 16 * q^65 - 16 * q^67 + 16 * q^69 - 12 * q^70 - 4 * q^71 + 12 * q^72 + 16 * q^73 - 20 * q^75 + 4 * q^76 + 4 * q^77 + 8 * q^78 - 32 * q^79 + 4 * q^80 + 8 * q^81 + 16 * q^85 + 8 * q^86 - 36 * q^87 + 8 * q^89 + 24 * q^90 - 24 * q^91 + 4 * q^92 + 20 * q^93 - 16 * q^94 + 16 * q^95 + 8 * q^96 + 36 * q^98 + 4 * q^99

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