LMFDB - Embedded newform 370.2.l.a.11.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(11,370)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5]))

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

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

chi := DirichletCharacter("370.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.l (of order $6$, degree $2$, 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:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.2
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	370.11
Dual form			370.2.l.a.101.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{5} +1.73205i q^{6} +(1.36603 - 2.36603i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{5} +1.73205i q^{6} +(1.36603 - 2.36603i) q^{7} -1.00000i q^{8} -1.00000 q^{10} +4.73205 q^{11} +(0.866025 + 1.50000i) q^{12} +(2.76795 + 1.59808i) q^{13} -2.73205i q^{14} +(1.50000 - 0.866025i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.633975 - 0.366025i) q^{17} +(0.464102 + 0.267949i) q^{19} +(-0.866025 + 0.500000i) q^{20} +(2.36603 + 4.09808i) q^{21} +(4.09808 - 2.36603i) q^{22} +1.26795i q^{23} +(1.50000 + 0.866025i) q^{24} +(0.500000 + 0.866025i) q^{25} +3.19615 q^{26} -5.19615 q^{27} +(-1.36603 - 2.36603i) q^{28} -4.92820i q^{29} +(0.866025 - 1.50000i) q^{30} +7.92820i q^{31} +(-0.866025 - 0.500000i) q^{32} +(-4.09808 + 7.09808i) q^{33} +(0.366025 - 0.633975i) q^{34} +(-2.36603 + 1.36603i) q^{35} +(-0.500000 - 6.06218i) q^{37} +0.535898 q^{38} +(-4.79423 + 2.76795i) q^{39} +(-0.500000 + 0.866025i) q^{40} +(2.23205 - 3.86603i) q^{41} +(4.09808 + 2.36603i) q^{42} -1.53590i q^{43} +(2.36603 - 4.09808i) q^{44} +(0.633975 + 1.09808i) q^{46} -6.73205 q^{47} +1.73205 q^{48} +(-0.232051 - 0.401924i) q^{49} +(0.866025 + 0.500000i) q^{50} +1.26795i q^{51} +(2.76795 - 1.59808i) q^{52} +(-6.69615 - 11.5981i) q^{53} +(-4.50000 + 2.59808i) q^{54} +(-4.09808 - 2.36603i) q^{55} +(-2.36603 - 1.36603i) q^{56} +(-0.803848 + 0.464102i) q^{57} +(-2.46410 - 4.26795i) q^{58} +(-4.90192 + 2.83013i) q^{59} -1.73205i q^{60} +(0.464102 + 0.267949i) q^{61} +(3.96410 + 6.86603i) q^{62} -1.00000 q^{64} +(-1.59808 - 2.76795i) q^{65} +8.19615i q^{66} +(-4.00000 + 6.92820i) q^{67} -0.732051i q^{68} +(-1.90192 - 1.09808i) q^{69} +(-1.36603 + 2.36603i) q^{70} +(-6.19615 + 10.7321i) q^{71} -5.66025 q^{73} +(-3.46410 - 5.00000i) q^{74} -1.73205 q^{75} +(0.464102 - 0.267949i) q^{76} +(6.46410 - 11.1962i) q^{77} +(-2.76795 + 4.79423i) q^{78} +(10.3923 + 6.00000i) q^{79} +1.00000i q^{80} +(4.50000 - 7.79423i) q^{81} -4.46410i q^{82} +(-4.26795 - 7.39230i) q^{83} +4.73205 q^{84} -0.732051 q^{85} +(-0.767949 - 1.33013i) q^{86} +(7.39230 + 4.26795i) q^{87} -4.73205i q^{88} +(-7.73205 + 4.46410i) q^{89} +(7.56218 - 4.36603i) q^{91} +(1.09808 + 0.633975i) q^{92} +(-11.8923 - 6.86603i) q^{93} +(-5.83013 + 3.36603i) q^{94} +(-0.267949 - 0.464102i) q^{95} +(1.50000 - 0.866025i) q^{96} +14.3923i q^{97} +(-0.401924 - 0.232051i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4} + 2 q^{7}+O(q^{10}) $ 4 * q + 2 * q^4 + 2 * q^7	$ 4 q + 2 q^{4} + 2 q^{7} - 4 q^{10} + 12 q^{11} + 18 q^{13} + 6 q^{15} - 2 q^{16} + 6 q^{17} - 12 q^{19} + 6 q^{21} + 6 q^{22} + 6 q^{24} + 2 q^{25} - 8 q^{26} - 2 q^{28} - 6 q^{33} - 2 q^{34} - 6 q^{35} - 2 q^{37} + 16 q^{38} + 12 q^{39} - 2 q^{40} + 2 q^{41} + 6 q^{42} + 6 q^{44} + 6 q^{46} - 20 q^{47} + 6 q^{49} + 18 q^{52} - 6 q^{53} - 18 q^{54} - 6 q^{55} - 6 q^{56} - 24 q^{57} + 4 q^{58} - 30 q^{59} - 12 q^{61} + 2 q^{62} - 4 q^{64} + 4 q^{65} - 16 q^{67} - 18 q^{69} - 2 q^{70} - 4 q^{71} + 12 q^{73} - 12 q^{76} + 12 q^{77} - 18 q^{78} + 18 q^{81} - 24 q^{83} + 12 q^{84} + 4 q^{85} - 10 q^{86} - 12 q^{87} - 24 q^{89} + 6 q^{91} - 6 q^{92} - 6 q^{93} - 6 q^{94} - 8 q^{95} + 6 q^{96} - 12 q^{98}+O(q^{100}) $ 4 * q + 2 * q^4 + 2 * q^7 - 4 * q^10 + 12 * q^11 + 18 * q^13 + 6 * q^15 - 2 * q^16 + 6 * q^17 - 12 * q^19 + 6 * q^21 + 6 * q^22 + 6 * q^24 + 2 * q^25 - 8 * q^26 - 2 * q^28 - 6 * q^33 - 2 * q^34 - 6 * q^35 - 2 * q^37 + 16 * q^38 + 12 * q^39 - 2 * q^40 + 2 * q^41 + 6 * q^42 + 6 * q^44 + 6 * q^46 - 20 * q^47 + 6 * q^49 + 18 * q^52 - 6 * q^53 - 18 * q^54 - 6 * q^55 - 6 * q^56 - 24 * q^57 + 4 * q^58 - 30 * q^59 - 12 * q^61 + 2 * q^62 - 4 * q^64 + 4 * q^65 - 16 * q^67 - 18 * q^69 - 2 * q^70 - 4 * q^71 + 12 * q^73 - 12 * q^76 + 12 * q^77 - 18 * q^78 + 18 * q^81 - 24 * q^83 + 12 * q^84 + 4 * q^85 - 10 * q^86 - 12 * q^87 - 24 * q^89 + 6 * q^91 - 6 * q^92 - 6 * q^93 - 6 * q^94 - 8 * q^95 + 6 * q^96 - 12 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$	−0.866025	+	1.50000i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$3$	−0.866025	+	1.50000i	−0.500000	+	0.866025i	−1.00000			$\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−0.866025	−	0.500000i	−0.387298	−	0.223607i
$5$	−0.866025	−	0.500000i	−0.387298	−	0.223607i
$6$			1.73205i			0.707107i
$7$	1.36603	−	2.36603i	0.516309	−	0.894274i	−0.483512	−	0.875338i	$-0.660639\pi$
$7$	1.36603	−	2.36603i	0.516309	−	0.894274i	0.999821	−	0.0189356i	$-0.00602775\pi$
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	−1.00000			−0.316228
$11$	4.73205			1.42677			0.713384	−	0.700774i	$-0.247162\pi$
$11$	4.73205			1.42677			0.713384	+	0.700774i	$0.247162\pi$
$12$	0.866025	+	1.50000i	0.250000	+	0.433013i
$13$	2.76795	+	1.59808i	0.767691	+	0.443227i	0.832050	−	0.554700i	$-0.187167\pi$
$13$	2.76795	+	1.59808i	0.767691	+	0.443227i	−0.0643593	+	0.997927i	$0.520500\pi$
$14$		−	2.73205i		−	0.730171i
$15$	1.50000	−	0.866025i	0.387298	−	0.223607i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	0.633975	−	0.366025i	0.153761	−	0.0887742i	−0.421145	−	0.906993i	$-0.638372\pi$
$17$	0.633975	−	0.366025i	0.153761	−	0.0887742i	0.574907	+	0.818219i	$0.305038\pi$
$18$		0			0
$19$	0.464102	+	0.267949i	0.106472	+	0.0614718i	0.552291	−	0.833652i	$-0.313754\pi$
$19$	0.464102	+	0.267949i	0.106472	+	0.0614718i	−0.445818	+	0.895123i	$0.647087\pi$
$20$	−0.866025	+	0.500000i	−0.193649	+	0.111803i
$21$	2.36603	+	4.09808i	0.516309	+	0.894274i
$22$	4.09808	−	2.36603i	0.873713	−	0.504438i
$23$			1.26795i			0.264386i	0.991224	+	0.132193i	$0.0422018\pi$
$23$			1.26795i			0.264386i	−0.991224	+	0.132193i	$0.957798\pi$
$24$	1.50000	+	0.866025i	0.306186	+	0.176777i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	3.19615			0.626817
$27$	−5.19615			−1.00000
$28$	−1.36603	−	2.36603i	−0.258155	−	0.447137i
$29$		−	4.92820i		−	0.915144i	−0.889172	−	0.457572i	$-0.848719\pi$
$29$		−	4.92820i		−	0.915144i	0.889172	−	0.457572i	$-0.151281\pi$
$30$	0.866025	−	1.50000i	0.158114	−	0.273861i
$31$			7.92820i			1.42395i	0.702206	+	0.711974i	$0.252198\pi$
$31$			7.92820i			1.42395i	−0.702206	+	0.711974i	$0.747802\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	−4.09808	+	7.09808i	−0.713384	+	1.23562i
$34$	0.366025	−	0.633975i	0.0627728	−	0.108726i
$35$	−2.36603	+	1.36603i	−0.399931	+	0.230900i
$36$		0			0
$37$	−0.500000	−	6.06218i	−0.0821995	−	0.996616i
$37$	−0.500000	−	6.06218i	−0.0821995	−	0.996616i
$38$	0.535898			0.0869342
$39$	−4.79423	+	2.76795i	−0.767691	+	0.443227i
$40$	−0.500000	+	0.866025i	−0.0790569	+	0.136931i
$41$	2.23205	−	3.86603i	0.348588	−	0.603772i	−0.637411	−	0.770524i	$-0.719995\pi$
$41$	2.23205	−	3.86603i	0.348588	−	0.603772i	0.985999	+	0.166752i	$0.0533280\pi$
$42$	4.09808	+	2.36603i	0.632347	+	0.365086i
$43$		−	1.53590i		−	0.234222i	−0.993119	−	0.117111i	$-0.962637\pi$
$43$		−	1.53590i		−	0.234222i	0.993119	−	0.117111i	$-0.0373634\pi$
$44$	2.36603	−	4.09808i	0.356692	−	0.617808i
$45$		0			0
$46$	0.633975	+	1.09808i	0.0934745	+	0.161903i
$47$	−6.73205			−0.981971			−0.490985	−	0.871168i	$-0.663363\pi$
$47$	−6.73205			−0.981971			−0.490985	+	0.871168i	$0.663363\pi$
$48$	1.73205			0.250000
$49$	−0.232051	−	0.401924i	−0.0331501	−	0.0574177i
$50$	0.866025	+	0.500000i	0.122474	+	0.0707107i
$51$			1.26795i			0.177548i
$52$	2.76795	−	1.59808i	0.383845	−	0.221613i
$53$	−6.69615	−	11.5981i	−0.919787	−	1.59312i	−0.799737	−	0.600350i	$-0.795028\pi$
$53$	−6.69615	−	11.5981i	−0.919787	−	1.59312i	−0.120050	−	0.992768i	$-0.538306\pi$
$54$	−4.50000	+	2.59808i	−0.612372	+	0.353553i
$55$	−4.09808	−	2.36603i	−0.552584	−	0.319035i
$56$	−2.36603	−	1.36603i	−0.316173	−	0.182543i
$57$	−0.803848	+	0.464102i	−0.106472	+	0.0614718i
$58$	−2.46410	−	4.26795i	−0.323552	−	0.560409i
$59$	−4.90192	+	2.83013i	−0.638176	+	0.368451i	−0.783912	−	0.620872i	$-0.786778\pi$
$59$	−4.90192	+	2.83013i	−0.638176	+	0.368451i	0.145735	+	0.989324i	$0.453445\pi$
$60$		−	1.73205i		−	0.223607i
$61$	0.464102	+	0.267949i	0.0594221	+	0.0343074i	0.529417	−	0.848362i	$-0.322411\pi$
$61$	0.464102	+	0.267949i	0.0594221	+	0.0343074i	−0.469995	+	0.882669i	$0.655744\pi$
$62$	3.96410	+	6.86603i	0.503441	+	0.871986i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−1.59808	−	2.76795i	−0.198217	−	0.343322i
$66$			8.19615i			1.00888i
$67$	−4.00000	+	6.92820i	−0.488678	+	0.846415i	−0.999915	−	0.0130248i	$-0.995854\pi$
$67$	−4.00000	+	6.92820i	−0.488678	+	0.846415i	0.511237	+	0.859440i	$0.329187\pi$
$68$		−	0.732051i		−	0.0887742i
$69$	−1.90192	−	1.09808i	−0.228965	−	0.132193i
$70$	−1.36603	+	2.36603i	−0.163271	+	0.282794i
$71$	−6.19615	+	10.7321i	−0.735348	+	1.27366i	0.219222	+	0.975675i	$0.429648\pi$
$71$	−6.19615	+	10.7321i	−0.735348	+	1.27366i	−0.954570	+	0.297985i	$0.903685\pi$
$72$		0			0
$73$	−5.66025			−0.662483			−0.331241	−	0.943546i	$-0.607467\pi$
$73$	−5.66025			−0.662483			−0.331241	+	0.943546i	$0.607467\pi$
$74$	−3.46410	−	5.00000i	−0.402694	−	0.581238i
$75$	−1.73205			−0.200000
$76$	0.464102	−	0.267949i	0.0532361	−	0.0307359i
$77$	6.46410	−	11.1962i	0.736653	−	1.27592i
$78$	−2.76795	+	4.79423i	−0.313409	+	0.542839i
$79$	10.3923	+	6.00000i	1.16923	+	0.675053i	0.953498	−	0.301401i	$-0.0974542\pi$
$79$	10.3923	+	6.00000i	1.16923	+	0.675053i	0.215728	+	0.976453i	$0.430788\pi$
$80$			1.00000i			0.111803i
$81$	4.50000	−	7.79423i	0.500000	−	0.866025i
$82$		−	4.46410i		−	0.492978i
$83$	−4.26795	−	7.39230i	−0.468468	−	0.811411i	0.530882	−	0.847446i	$-0.321861\pi$
$83$	−4.26795	−	7.39230i	−0.468468	−	0.811411i	−0.999351	+	0.0360347i	$0.988527\pi$
$84$	4.73205			0.516309
$85$	−0.732051			−0.0794021
$86$	−0.767949	−	1.33013i	−0.0828101	−	0.143431i
$87$	7.39230	+	4.26795i	0.792538	+	0.457572i
$88$		−	4.73205i		−	0.504438i
$89$	−7.73205	+	4.46410i	−0.819596	+	0.473194i	−0.850277	−	0.526335i	$-0.823566\pi$
$89$	−7.73205	+	4.46410i	−0.819596	+	0.473194i	0.0306813	+	0.999529i	$0.490232\pi$
$90$		0			0
$91$	7.56218	−	4.36603i	0.792732	−	0.457684i
$92$	1.09808	+	0.633975i	0.114482	+	0.0660964i
$93$	−11.8923	−	6.86603i	−1.23317	−	0.711974i
$94$	−5.83013	+	3.36603i	−0.601332	+	0.347179i
$95$	−0.267949	−	0.464102i	−0.0274910	−	0.0476158i
$96$	1.50000	−	0.866025i	0.153093	−	0.0883883i
$97$			14.3923i			1.46132i	0.682743	+	0.730659i	$0.260787\pi$
$97$			14.3923i			1.46132i	−0.682743	+	0.730659i	$0.739213\pi$
$98$	−0.401924	−	0.232051i	−0.0406004	−	0.0234407i
$99$		0			0
$100$	1.00000			0.100000
$101$	13.6603			1.35925			0.679623	−	0.733562i	$-0.262143\pi$
$101$	13.6603			1.35925			0.679623	+	0.733562i	$0.262143\pi$
$102$	0.633975	+	1.09808i	0.0627728	+	0.108726i
$103$			0.196152i			0.0193275i	0.999953	+	0.00966374i	$0.00307611\pi$
$103$			0.196152i			0.0193275i	−0.999953	+	0.00966374i	$0.996924\pi$
$104$	1.59808	−	2.76795i	0.156704	−	0.271420i
$105$		−	4.73205i		−	0.461801i
$106$	−11.5981	−	6.69615i	−1.12650	−	0.650388i
$107$	−8.06218	+	13.9641i	−0.779400	+	1.34996i	0.152888	+	0.988244i	$0.451143\pi$
$107$	−8.06218	+	13.9641i	−0.779400	+	1.34996i	−0.932288	+	0.361717i	$0.882191\pi$
$108$	−2.59808	+	4.50000i	−0.250000	+	0.433013i
$109$	8.66025	−	5.00000i	0.829502	−	0.478913i	−0.0241802	−	0.999708i	$-0.507698\pi$
$109$	8.66025	−	5.00000i	0.829502	−	0.478913i	0.853682	+	0.520794i	$0.174364\pi$
$110$	−4.73205			−0.451183
$111$	9.52628	+	4.50000i	0.904194	+	0.427121i
$112$	−2.73205			−0.258155
$113$	−7.26795	+	4.19615i	−0.683711	+	0.394741i	−0.801252	−	0.598327i	$-0.795832\pi$
$113$	−7.26795	+	4.19615i	−0.683711	+	0.394741i	0.117541	+	0.993068i	$0.462499\pi$
$114$	−0.464102	+	0.803848i	−0.0434671	+	0.0752872i
$115$	0.633975	−	1.09808i	0.0591184	−	0.102396i
$116$	−4.26795	−	2.46410i	−0.396269	−	0.228786i
$117$		0			0
$118$	−2.83013	+	4.90192i	−0.260534	+	0.451259i
$119$		−	2.00000i		−	0.183340i
$120$	−0.866025	−	1.50000i	−0.0790569	−	0.136931i
$121$	11.3923			1.03566
$122$	0.535898			0.0485180
$123$	3.86603	+	6.69615i	0.348588	+	0.603772i
$124$	6.86603	+	3.96410i	0.616587	+	0.355987i
$125$		−	1.00000i		−	0.0894427i
$126$		0			0
$127$	1.26795	+	2.19615i	0.112512	+	0.194877i	0.916783	−	0.399387i	$-0.130777\pi$
$127$	1.26795	+	2.19615i	0.112512	+	0.194877i	−0.804270	+	0.594264i	$0.797444\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	2.30385	+	1.33013i	0.202842	+	0.117111i
$130$	−2.76795	−	1.59808i	−0.242765	−	0.140161i
$131$	−8.66025	+	5.00000i	−0.756650	+	0.436852i	−0.828092	−	0.560593i	$-0.810573\pi$
$131$	−8.66025	+	5.00000i	−0.756650	+	0.436852i	0.0714417	+	0.997445i	$0.477240\pi$
$132$	4.09808	+	7.09808i	0.356692	+	0.617808i
$133$	1.26795	−	0.732051i	0.109945	−	0.0634769i
$134$			8.00000i			0.691095i
$135$	4.50000	+	2.59808i	0.387298	+	0.223607i
$136$	−0.366025	−	0.633975i	−0.0313864	−	0.0543629i
$137$	5.66025			0.483588			0.241794	−	0.970328i	$-0.422264\pi$
$137$	5.66025			0.483588			0.241794	+	0.970328i	$0.422264\pi$
$138$	−2.19615			−0.186949
$139$	−5.83013	−	10.0981i	−0.494505	−	0.856508i	0.505475	−	0.862841i	$-0.331317\pi$
$139$	−5.83013	−	10.0981i	−0.494505	−	0.856508i	−0.999980	+	0.00633359i	$0.997984\pi$
$140$			2.73205i			0.230900i
$141$	5.83013	−	10.0981i	0.490985	−	0.850411i
$142$			12.3923i			1.03994i
$143$	13.0981	+	7.56218i	1.09532	+	0.632381i
$144$		0			0
$145$	−2.46410	+	4.26795i	−0.204633	+	0.354434i
$146$	−4.90192	+	2.83013i	−0.405686	+	0.234223i
$147$	0.803848			0.0663002
$148$	−5.50000	−	2.59808i	−0.452097	−	0.213561i
$149$	−12.0000			−0.983078			−0.491539	−	0.870855i	$-0.663566\pi$
$149$	−12.0000			−0.983078			−0.491539	+	0.870855i	$0.663566\pi$
$150$	−1.50000	+	0.866025i	−0.122474	+	0.0707107i
$151$	11.3301	−	19.6244i	0.922033	−	1.59701i	0.125767	−	0.992060i	$-0.459861\pi$
$151$	11.3301	−	19.6244i	0.922033	−	1.59701i	0.796265	−	0.604948i	$-0.206806\pi$
$152$	0.267949	−	0.464102i	0.0217335	−	0.0376436i
$153$		0			0
$154$		−	12.9282i		−	1.04178i
$155$	3.96410	−	6.86603i	0.318404	−	0.551492i
$156$			5.53590i			0.443227i
$157$	2.23205	+	3.86603i	0.178137	+	0.308542i	0.941242	−	0.337732i	$-0.109660\pi$
$157$	2.23205	+	3.86603i	0.178137	+	0.308542i	−0.763105	+	0.646274i	$0.776326\pi$
$158$	12.0000			0.954669
$159$	23.1962			1.83957
$160$	0.500000	+	0.866025i	0.0395285	+	0.0684653i
$161$	3.00000	+	1.73205i	0.236433	+	0.136505i
$162$		−	9.00000i		−	0.707107i
$163$	−4.33013	+	2.50000i	−0.339162	+	0.195815i	−0.659901	−	0.751352i	$-0.729402\pi$
$163$	−4.33013	+	2.50000i	−0.339162	+	0.195815i	0.320740	+	0.947167i	$0.396069\pi$
$164$	−2.23205	−	3.86603i	−0.174294	−	0.301886i
$165$	7.09808	−	4.09808i	0.552584	−	0.319035i
$166$	−7.39230	−	4.26795i	−0.573754	−	0.331257i
$167$	−10.2679	−	5.92820i	−0.794558	−	0.458738i	0.0470069	−	0.998895i	$-0.485032\pi$
$167$	−10.2679	−	5.92820i	−0.794558	−	0.458738i	−0.841565	+	0.540156i	$0.818365\pi$
$168$	4.09808	−	2.36603i	0.316173	−	0.182543i
$169$	−1.39230	−	2.41154i	−0.107100	−	0.185503i
$170$	−0.633975	+	0.366025i	−0.0486236	+	0.0280729i
$171$		0			0
$172$	−1.33013	−	0.767949i	−0.101421	−	0.0585556i
$173$	−3.00000	−	5.19615i	−0.228086	−	0.395056i	0.729155	−	0.684349i	$-0.239913\pi$
$173$	−3.00000	−	5.19615i	−0.228086	−	0.395056i	−0.957241	+	0.289292i	$0.906580\pi$
$174$	8.53590			0.647105
$175$	2.73205			0.206524
$176$	−2.36603	−	4.09808i	−0.178346	−	0.308904i
$177$		−	9.80385i		−	0.736902i
$178$	−4.46410	+	7.73205i	−0.334599	+	0.579542i
$179$			12.0000i			0.896922i	0.893802	+	0.448461i	$0.148028\pi$
$179$			12.0000i			0.896922i	−0.893802	+	0.448461i	$0.851972\pi$
$180$		0			0
$181$	−1.83013	+	3.16987i	−0.136032	+	0.235615i	−0.925991	−	0.377545i	$-0.876768\pi$
$181$	−1.83013	+	3.16987i	−0.136032	+	0.235615i	0.789959	+	0.613160i	$0.210102\pi$
$182$	4.36603	−	7.56218i	0.323631	−	0.560546i
$183$	−0.803848	+	0.464102i	−0.0594221	+	0.0343074i
$184$	1.26795			0.0934745
$185$	−2.59808	+	5.50000i	−0.191014	+	0.404368i
$186$	−13.7321			−1.00688
$187$	3.00000	−	1.73205i	0.219382	−	0.126660i
$188$	−3.36603	+	5.83013i	−0.245493	+	0.425206i
$189$	−7.09808	+	12.2942i	−0.516309	+	0.894274i
$190$	−0.464102	−	0.267949i	−0.0336695	−	0.0194391i
$191$		−	21.3923i		−	1.54789i	−0.633251	−	0.773946i	$-0.718280\pi$
$191$		−	21.3923i		−	1.54789i	0.633251	−	0.773946i	$-0.281720\pi$
$192$	0.866025	−	1.50000i	0.0625000	−	0.108253i
$193$		−	14.5885i		−	1.05010i	−0.851071	−	0.525050i	$-0.824047\pi$
$193$		−	14.5885i		−	1.05010i	0.851071	−	0.525050i	$-0.175953\pi$
$194$	7.19615	+	12.4641i	0.516654	+	0.894870i
$195$	5.53590			0.396434
$196$	−0.464102			−0.0331501
$197$	−13.1603	−	22.7942i	−0.937629	−	1.62402i	−0.769877	−	0.638192i	$-0.779682\pi$
$197$	−13.1603	−	22.7942i	−0.937629	−	1.62402i	−0.167752	−	0.985829i	$-0.553651\pi$
$198$		0			0
$199$			1.00000i			0.0708881i	0.999372	+	0.0354441i	$0.0112846\pi$
$199$			1.00000i			0.0708881i	−0.999372	+	0.0354441i	$0.988715\pi$
$200$	0.866025	−	0.500000i	0.0612372	−	0.0353553i
$201$	−6.92820	−	12.0000i	−0.488678	−	0.846415i
$202$	11.8301	−	6.83013i	0.832365	−	0.480566i
$203$	−11.6603	−	6.73205i	−0.818389	−	0.472497i
$204$	1.09808	+	0.633975i	0.0768807	+	0.0443871i
$205$	−3.86603	+	2.23205i	−0.270015	+	0.155893i
$206$	0.0980762	+	0.169873i	0.00683329	+	0.0118356i
$207$		0			0
$208$		−	3.19615i		−	0.221613i
$209$	2.19615	+	1.26795i	0.151911	+	0.0877059i
$210$	−2.36603	−	4.09808i	−0.163271	−	0.282794i
$211$	−2.39230			−0.164693			−0.0823465	−	0.996604i	$-0.526241\pi$
$211$	−2.39230			−0.164693			−0.0823465	+	0.996604i	$0.526241\pi$
$212$	−13.3923			−0.919787
$213$	−10.7321	−	18.5885i	−0.735348	−	1.27366i
$214$			16.1244i			1.10224i
$215$	−0.767949	+	1.33013i	−0.0523737	+	0.0907139i
$216$			5.19615i			0.353553i
$217$	18.7583	+	10.8301i	1.27340	+	0.735197i
$218$	5.00000	−	8.66025i	0.338643	−	0.586546i
$219$	4.90192	−	8.49038i	0.331241	−	0.573727i
$220$	−4.09808	+	2.36603i	−0.276292	+	0.159517i
$221$	2.33975			0.157388
$222$	10.5000	−	0.866025i	0.704714	−	0.0581238i
$223$	10.5885			0.709056			0.354528	−	0.935045i	$-0.384642\pi$
$223$	10.5885			0.709056			0.354528	+	0.935045i	$0.384642\pi$
$224$	−2.36603	+	1.36603i	−0.158087	+	0.0912714i
$225$		0			0
$226$	−4.19615	+	7.26795i	−0.279124	+	0.483457i
$227$	11.1340	+	6.42820i	0.738988	+	0.426655i	0.821701	−	0.569919i	$-0.193025\pi$
$227$	11.1340	+	6.42820i	0.738988	+	0.426655i	−0.0827133	+	0.996573i	$0.526359\pi$
$228$			0.928203i			0.0614718i
$229$	−10.3660	+	17.9545i	−0.685006	+	1.18647i	0.288429	+	0.957501i	$0.406867\pi$
$229$	−10.3660	+	17.9545i	−0.685006	+	1.18647i	−0.973435	+	0.228964i	$0.926466\pi$
$230$		−	1.26795i		−	0.0836061i
$231$	11.1962	+	19.3923i	0.736653	+	1.27592i
$232$	−4.92820			−0.323552
$233$	16.7321			1.09615			0.548077	−	0.836428i	$-0.315360\pi$
$233$	16.7321			1.09615			0.548077	+	0.836428i	$0.315360\pi$
$234$		0			0
$235$	5.83013	+	3.36603i	0.380316	+	0.219575i
$236$			5.66025i			0.368451i
$237$	−18.0000	+	10.3923i	−1.16923	+	0.675053i
$238$	−1.00000	−	1.73205i	−0.0648204	−	0.112272i
$239$	18.9282	−	10.9282i	1.22436	−	0.706887i	0.258518	−	0.966006i	$-0.416766\pi$
$239$	18.9282	−	10.9282i	1.22436	−	0.706887i	0.965845	+	0.259120i	$0.0834324\pi$
$240$	−1.50000	−	0.866025i	−0.0968246	−	0.0559017i
$241$	3.46410	+	2.00000i	0.223142	+	0.128831i	0.607404	−	0.794393i	$-0.292211\pi$
$241$	3.46410	+	2.00000i	0.223142	+	0.128831i	−0.384262	+	0.923224i	$0.625544\pi$
$242$	9.86603	−	5.69615i	0.634212	−	0.366163i
$243$		0			0
$244$	0.464102	−	0.267949i	0.0297111	−	0.0171537i
$245$			0.464102i			0.0296504i
$246$	6.69615	+	3.86603i	0.426931	+	0.246489i
$247$	0.856406	+	1.48334i	0.0544918	+	0.0943826i
$248$	7.92820			0.503441
$249$	14.7846			0.936937
$250$	−0.500000	−	0.866025i	−0.0316228	−	0.0547723i
$251$			3.46410i			0.218652i	0.994006	+	0.109326i	$0.0348693\pi$
$251$			3.46410i			0.218652i	−0.994006	+	0.109326i	$0.965131\pi$
$252$		0			0
$253$			6.00000i			0.377217i
$254$	2.19615	+	1.26795i	0.137799	+	0.0795582i
$255$	0.633975	−	1.09808i	0.0397010	−	0.0687642i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	0.169873	−	0.0980762i	0.0105964	−	0.00611783i	−0.494692	−	0.869068i	$-0.664719\pi$
$257$	0.169873	−	0.0980762i	0.0105964	−	0.00611783i	0.505289	+	0.862950i	$0.331386\pi$
$258$	2.66025			0.165620
$259$	−15.0263	−	7.09808i	−0.933688	−	0.441053i
$260$	−3.19615			−0.198217
$261$		0			0
$262$	−5.00000	+	8.66025i	−0.308901	+	0.535032i
$263$	−3.36603	+	5.83013i	−0.207558	+	0.359501i	−0.950945	−	0.309361i	$-0.899885\pi$
$263$	−3.36603	+	5.83013i	−0.207558	+	0.359501i	0.743387	+	0.668862i	$0.233218\pi$
$264$	7.09808	+	4.09808i	0.436856	+	0.252219i
$265$			13.3923i			0.822683i
$266$	0.732051	−	1.26795i	0.0448849	−	0.0777430i
$267$		−	15.4641i		−	0.946388i
$268$	4.00000	+	6.92820i	0.244339	+	0.423207i
$269$	−7.12436			−0.434380			−0.217190	−	0.976129i	$-0.569689\pi$
$269$	−7.12436			−0.434380			−0.217190	+	0.976129i	$0.569689\pi$
$270$	5.19615			0.316228
$271$	12.7942	+	22.1603i	0.777194	+	1.34614i	0.933553	+	0.358439i	$0.116691\pi$
$271$	12.7942	+	22.1603i	0.777194	+	1.34614i	−0.156359	+	0.987700i	$0.549976\pi$
$272$	−0.633975	−	0.366025i	−0.0384404	−	0.0221936i
$273$			15.1244i			0.915368i
$274$	4.90192	−	2.83013i	0.296136	−	0.170974i
$275$	2.36603	+	4.09808i	0.142677	+	0.247123i
$276$	−1.90192	+	1.09808i	−0.114482	+	0.0660964i
$277$	20.5526	+	11.8660i	1.23488	+	0.712960i	0.968044	−	0.250781i	$-0.0806873\pi$
$277$	20.5526	+	11.8660i	1.23488	+	0.712960i	0.266840	+	0.963741i	$0.414021\pi$
$278$	−10.0981	−	5.83013i	−0.605642	−	0.349668i
$279$		0			0
$280$	1.36603	+	2.36603i	0.0816356	+	0.141397i
$281$	5.08846	−	2.93782i	0.303552	−	0.175256i	−0.340486	−	0.940250i	$-0.610591\pi$
$281$	5.08846	−	2.93782i	0.303552	−	0.175256i	0.644037	+	0.764994i	$0.277258\pi$
$282$		−	11.6603i		−	0.694358i
$283$	11.7224	+	6.76795i	0.696826	+	0.402313i	0.806164	−	0.591692i	$-0.201540\pi$
$283$	11.7224	+	6.76795i	0.696826	+	0.402313i	−0.109338	+	0.994005i	$0.534873\pi$
$284$	6.19615	+	10.7321i	0.367674	+	0.636830i
$285$	0.928203			0.0549820
$286$	15.1244			0.894322
$287$	−6.09808	−	10.5622i	−0.359958	−	0.623466i
$288$		0			0
$289$	−8.23205	+	14.2583i	−0.484238	+	0.838725i
$290$			4.92820i			0.289394i
$291$	−21.5885	−	12.4641i	−1.26554	−	0.730659i
$292$	−2.83013	+	4.90192i	−0.165621	+	0.286863i
$293$	14.2321	−	24.6506i	0.831445	−	1.44011i	−0.0654468	−	0.997856i	$-0.520847\pi$
$293$	14.2321	−	24.6506i	0.831445	−	1.44011i	0.896892	−	0.442249i	$-0.145819\pi$
$294$	0.696152	−	0.401924i	0.0406004	−	0.0234407i
$295$	5.66025			0.329553
$296$	−6.06218	+	0.500000i	−0.352357	+	0.0290619i
$297$	−24.5885			−1.42677
$298$	−10.3923	+	6.00000i	−0.602010	+	0.347571i
$299$	−2.02628	+	3.50962i	−0.117183	+	0.202967i
$300$	−0.866025	+	1.50000i	−0.0500000	+	0.0866025i
$301$	−3.63397	−	2.09808i	−0.209459	−	0.120931i
$302$		−	22.6603i		−	1.30395i
$303$	−11.8301	+	20.4904i	−0.679623	+	1.17714i
$304$		−	0.535898i		−	0.0307359i
$305$	−0.267949	−	0.464102i	−0.0153427	−	0.0265744i
$306$		0			0
$307$	−13.1962			−0.753144			−0.376572	−	0.926387i	$-0.622897\pi$
$307$	−13.1962			−0.753144			−0.376572	+	0.926387i	$0.622897\pi$
$308$	−6.46410	−	11.1962i	−0.368326	−	0.637960i
$309$	−0.294229	−	0.169873i	−0.0167381	−	0.00966374i
$310$		−	7.92820i		−	0.450292i
$311$	−27.1865	+	15.6962i	−1.54161	+	0.890047i	−0.542869	+	0.839817i	$0.682662\pi$
$311$	−27.1865	+	15.6962i	−1.54161	+	0.890047i	−0.998738	+	0.0502299i	$0.984005\pi$
$312$	2.76795	+	4.79423i	0.156704	+	0.271420i
$313$	18.1244	−	10.4641i	1.02445	−	0.591466i	0.109060	−	0.994035i	$-0.465216\pi$
$313$	18.1244	−	10.4641i	1.02445	−	0.591466i	0.915390	+	0.402569i	$0.131883\pi$
$314$	3.86603	+	2.23205i	0.218172	+	0.125962i
$315$		0			0
$316$	10.3923	−	6.00000i	0.584613	−	0.337526i
$317$	−16.1603	−	27.9904i	−0.907650	−	1.57210i	−0.817320	−	0.576185i	$-0.804541\pi$
$317$	−16.1603	−	27.9904i	−0.907650	−	1.57210i	−0.0903307	−	0.995912i	$-0.528792\pi$
$318$	20.0885	−	11.5981i	1.12650	−	0.650388i
$319$		−	23.3205i		−	1.30570i
$320$	0.866025	+	0.500000i	0.0484123	+	0.0279508i
$321$	−13.9641	−	24.1865i	−0.779400	−	1.34996i
$322$	3.46410			0.193047
$323$	0.392305			0.0218284
$324$	−4.50000	−	7.79423i	−0.250000	−	0.433013i
$325$			3.19615i			0.177291i
$326$	−2.50000	+	4.33013i	−0.138462	+	0.239824i
$327$			17.3205i			0.957826i
$328$	−3.86603	−	2.23205i	−0.213466	−	0.123244i
$329$	−9.19615	+	15.9282i	−0.507000	+	0.878150i
$330$	4.09808	−	7.09808i	0.225592	−	0.390736i
$331$	−5.02628	+	2.90192i	−0.276269	+	0.159504i	−0.631733	−	0.775186i	$-0.717656\pi$
$331$	−5.02628	+	2.90192i	−0.276269	+	0.159504i	0.355464	+	0.934690i	$0.384323\pi$
$332$	−8.53590			−0.468468
$333$		0			0
$334$	−11.8564			−0.648754
$335$	6.92820	−	4.00000i	0.378528	−	0.218543i
$336$	2.36603	−	4.09808i	0.129077	−	0.223568i
$337$	−16.1244	+	27.9282i	−0.878350	+	1.52135i	−0.0251984	+	0.999682i	$0.508022\pi$
$337$	−16.1244	+	27.9282i	−0.878350	+	1.52135i	−0.853151	+	0.521664i	$0.825312\pi$
$338$	−2.41154	−	1.39230i	−0.131171	−	0.0757314i
$339$		−	14.5359i		−	0.789482i
$340$	−0.366025	+	0.633975i	−0.0198505	+	0.0343821i
$341$			37.5167i			2.03164i
$342$		0			0
$343$	17.8564			0.964155
$344$	−1.53590			−0.0828101
$345$	1.09808	+	1.90192i	0.0591184	+	0.102396i
$346$	−5.19615	−	3.00000i	−0.279347	−	0.161281i
$347$		−	15.0718i		−	0.809096i	−0.914517	−	0.404548i	$-0.867429\pi$
$347$		−	15.0718i		−	0.809096i	0.914517	−	0.404548i	$-0.132571\pi$
$348$	7.39230	−	4.26795i	0.396269	−	0.228786i
$349$	−6.46410	−	11.1962i	−0.346015	−	0.599316i	0.639522	−	0.768773i	$-0.279132\pi$
$349$	−6.46410	−	11.1962i	−0.346015	−	0.599316i	−0.985538	+	0.169456i	$0.945799\pi$
$350$	2.36603	−	1.36603i	0.126469	−	0.0730171i
$351$	−14.3827	−	8.30385i	−0.767691	−	0.443227i
$352$	−4.09808	−	2.36603i	−0.218428	−	0.126110i
$353$	−23.8301	+	13.7583i	−1.26835	+	0.732282i	−0.974676	−	0.223624i	$-0.928211\pi$
$353$	−23.8301	+	13.7583i	−1.26835	+	0.732282i	−0.293674	+	0.955906i	$0.594878\pi$
$354$	−4.90192	−	8.49038i	−0.260534	−	0.451259i
$355$	10.7321	−	6.19615i	0.569598	−	0.328858i
$356$			8.92820i			0.473194i
$357$	3.00000	+	1.73205i	0.158777	+	0.0916698i
$358$	6.00000	+	10.3923i	0.317110	+	0.549250i
$359$	−28.2679			−1.49193			−0.745963	−	0.665988i	$-0.768010\pi$
$359$	−28.2679			−1.49193			−0.745963	+	0.665988i	$0.768010\pi$
$360$		0			0
$361$	−9.35641	−	16.2058i	−0.492442	−	0.852935i
$362$			3.66025i			0.192379i
$363$	−9.86603	+	17.0885i	−0.517832	+	0.896911i
$364$		−	8.73205i		−	0.457684i
$365$	4.90192	+	2.83013i	0.256578	+	0.148136i
$366$	−0.464102	+	0.803848i	−0.0242590	+	0.0420178i
$367$	−16.1244	+	27.9282i	−0.841685	+	1.45784i	0.0467851	+	0.998905i	$0.485102\pi$
$367$	−16.1244	+	27.9282i	−0.841685	+	1.45784i	−0.888470	+	0.458935i	$0.848231\pi$
$368$	1.09808	−	0.633975i	0.0572412	−	0.0330482i
$369$		0			0
$370$	0.500000	+	6.06218i	0.0259938	+	0.315158i
$371$	−36.5885			−1.89958
$372$	−11.8923	+	6.86603i	−0.616587	+	0.355987i
$373$	6.76795	−	11.7224i	0.350431	−	0.606965i	−0.635894	−	0.771777i	$-0.719368\pi$
$373$	6.76795	−	11.7224i	0.350431	−	0.606965i	0.986325	+	0.164812i	$0.0527017\pi$
$374$	1.73205	−	3.00000i	0.0895622	−	0.155126i
$375$	1.50000	+	0.866025i	0.0774597	+	0.0447214i
$376$			6.73205i			0.347179i
$377$	7.87564	−	13.6410i	0.405616	−	0.702548i
$378$			14.1962i			0.730171i
$379$	−6.56218	−	11.3660i	−0.337076	−	0.583834i	0.646805	−	0.762655i	$-0.276105\pi$
$379$	−6.56218	−	11.3660i	−0.337076	−	0.583834i	−0.983881	+	0.178822i	$0.942771\pi$
$380$	−0.535898			−0.0274910
$381$	−4.39230			−0.225025
$382$	−10.6962	−	18.5263i	−0.547263	−	0.947887i
$383$	32.4904	+	18.7583i	1.66018	+	0.958506i	0.972627	+	0.232373i	$0.0746489\pi$
$383$	32.4904	+	18.7583i	1.66018	+	0.958506i	0.687554	+	0.726133i	$0.258684\pi$
$384$		−	1.73205i		−	0.0883883i
$385$	−11.1962	+	6.46410i	−0.570609	+	0.329441i
$386$	−7.29423	−	12.6340i	−0.371266	−	0.643052i
$387$		0			0
$388$	12.4641	+	7.19615i	0.632769	+	0.365329i
$389$	12.9282	+	7.46410i	0.655486	+	0.378445i	0.790555	−	0.612391i	$-0.209792\pi$
$389$	12.9282	+	7.46410i	0.655486	+	0.378445i	−0.135069	+	0.990836i	$0.543126\pi$
$390$	4.79423	−	2.76795i	0.242765	−	0.140161i
$391$	0.464102	+	0.803848i	0.0234706	+	0.0406523i
$392$	−0.401924	+	0.232051i	−0.0203002	+	0.0117203i
$393$		−	17.3205i		−	0.873704i
$394$	−22.7942	−	13.1603i	−1.14836	−	0.663004i
$395$	−6.00000	−	10.3923i	−0.301893	−	0.522894i
$396$		0			0
$397$	3.53590			0.177462			0.0887308	−	0.996056i	$-0.471719\pi$
$397$	3.53590			0.177462			0.0887308	+	0.996056i	$0.471719\pi$
$398$	0.500000	+	0.866025i	0.0250627	+	0.0434099i
$399$			2.53590i			0.126954i
$400$	0.500000	−	0.866025i	0.0250000	−	0.0433013i
$401$			4.92820i			0.246103i	0.992400	+	0.123051i	$0.0392680\pi$
$401$			4.92820i			0.246103i	−0.992400	+	0.123051i	$0.960732\pi$
$402$	−12.0000	−	6.92820i	−0.598506	−	0.345547i
$403$	−12.6699	+	21.9449i	−0.631131	+	1.09315i
$404$	6.83013	−	11.8301i	0.339812	−	0.588571i
$405$	−7.79423	+	4.50000i	−0.387298	+	0.223607i
$406$	−13.4641			−0.668212
$407$	−2.36603	−	28.6865i	−0.117280	−	1.42194i
$408$	1.26795			0.0627728
$409$	21.8205	−	12.5981i	1.07895	−	0.622935i	0.148340	−	0.988936i	$-0.452607\pi$
$409$	21.8205	−	12.5981i	1.07895	−	0.622935i	0.930614	+	0.366002i	$0.119274\pi$
$410$	−2.23205	+	3.86603i	−0.110233	+	0.190929i
$411$	−4.90192	+	8.49038i	−0.241794	+	0.418800i
$412$	0.169873	+	0.0980762i	0.00836904	+	0.00483187i
$413$			15.4641i			0.760939i
$414$		0			0
$415$			8.53590i			0.419011i
$416$	−1.59808	−	2.76795i	−0.0783521	−	0.135710i
$417$	20.1962			0.989010
$418$	2.53590			0.124035
$419$	−14.0263	−	24.2942i	−0.685229	−	1.18685i	−0.973365	−	0.229261i	$-0.926369\pi$
$419$	−14.0263	−	24.2942i	−0.685229	−	1.18685i	0.288136	−	0.957589i	$-0.406964\pi$
$420$	−4.09808	−	2.36603i	−0.199966	−	0.115450i
$421$			20.5885i			1.00342i	0.865036	+	0.501710i	$0.167296\pi$
$421$			20.5885i			1.00342i	−0.865036	+	0.501710i	$0.832704\pi$
$422$	−2.07180	+	1.19615i	−0.100853	+	0.0582278i
$423$		0			0
$424$	−11.5981	+	6.69615i	−0.563252	+	0.325194i
$425$	0.633975	+	0.366025i	0.0307523	+	0.0177548i
$426$	−18.5885	−	10.7321i	−0.900614	−	0.519970i
$427$	1.26795	−	0.732051i	0.0613604	−	0.0354264i
$428$	8.06218	+	13.9641i	0.389700	+	0.674980i
$429$	−22.6865	+	13.0981i	−1.09532	+	0.632381i
$430$			1.53590i			0.0740676i
$431$	15.4019	+	8.89230i	0.741885	+	0.428327i	0.822754	−	0.568397i	$-0.192436\pi$
$431$	15.4019	+	8.89230i	0.741885	+	0.428327i	−0.0808696	+	0.996725i	$0.525770\pi$
$432$	2.59808	+	4.50000i	0.125000	+	0.216506i
$433$	−12.7846			−0.614389			−0.307195	−	0.951647i	$-0.599390\pi$
$433$	−12.7846			−0.614389			−0.307195	+	0.951647i	$0.599390\pi$
$434$	21.6603			1.03973
$435$	−4.26795	−	7.39230i	−0.204633	−	0.354434i
$436$		−	10.0000i		−	0.478913i
$437$	−0.339746	+	0.588457i	−0.0162523	+	0.0281497i
$438$		−	9.80385i		−	0.468446i
$439$	−27.5263	−	15.8923i	−1.31376	−	0.758498i	−0.331041	−	0.943616i	$-0.607400\pi$
$439$	−27.5263	−	15.8923i	−1.31376	−	0.758498i	−0.982716	+	0.185118i	$0.940733\pi$
$440$	−2.36603	+	4.09808i	−0.112796	+	0.195368i
$441$		0			0
$442$	2.02628	−	1.16987i	0.0963803	−	0.0556452i
$443$	30.2679			1.43807			0.719037	−	0.694972i	$-0.244583\pi$
$443$	30.2679			1.43807			0.719037	+	0.694972i	$0.244583\pi$
$444$	8.66025	−	6.00000i	0.410997	−	0.284747i
$445$	8.92820			0.423237
$446$	9.16987	−	5.29423i	0.434206	−	0.250689i
$447$	10.3923	−	18.0000i	0.491539	−	0.851371i
$448$	−1.36603	+	2.36603i	−0.0645386	+	0.111784i
$449$	−14.3038	−	8.25833i	−0.675040	−	0.389735i	0.122943	−	0.992414i	$-0.460767\pi$
$449$	−14.3038	−	8.25833i	−0.675040	−	0.389735i	−0.797984	+	0.602679i	$0.794100\pi$
$450$		0			0
$451$	10.5622	−	18.2942i	0.497354	−	0.861442i
$452$			8.39230i			0.394741i
$453$	19.6244	+	33.9904i	0.922033	+	1.59701i
$454$	12.8564			0.603381
$455$	−8.73205			−0.409365
$456$	0.464102	+	0.803848i	0.0217335	+	0.0376436i
$457$	−1.60770	−	0.928203i	−0.0752048	−	0.0434195i	0.461926	−	0.886918i	$-0.347159\pi$
$457$	−1.60770	−	0.928203i	−0.0752048	−	0.0434195i	−0.537131	+	0.843499i	$0.680492\pi$
$458$			20.7321i			0.968745i
$459$	−3.29423	+	1.90192i	−0.153761	+	0.0887742i
$460$	−0.633975	−	1.09808i	−0.0295592	−	0.0511981i
$461$	27.0000	−	15.5885i	1.25752	−	0.726027i	0.284925	−	0.958550i	$-0.408031\pi$
$461$	27.0000	−	15.5885i	1.25752	−	0.726027i	0.972591	+	0.232523i	$0.0746981\pi$
$462$	19.3923	+	11.1962i	0.902212	+	0.520892i
$463$	−1.60770	−	0.928203i	−0.0747159	−	0.0431373i	0.462177	−	0.886788i	$-0.347069\pi$
$463$	−1.60770	−	0.928203i	−0.0747159	−	0.0431373i	−0.536893	+	0.843651i	$0.680402\pi$
$464$	−4.26795	+	2.46410i	−0.198135	+	0.114393i
$465$	6.86603	+	11.8923i	0.318404	+	0.551492i
$466$	14.4904	−	8.36603i	0.671254	−	0.387549i
$467$		−	1.00000i		−	0.0462745i	−0.999732	−	0.0231372i	$-0.992635\pi$
$467$		−	1.00000i		−	0.0462745i	0.999732	−	0.0231372i	$-0.00736547\pi$
$468$		0			0
$469$	10.9282	+	18.9282i	0.504618	+	0.874023i
$470$	6.73205			0.310526
$471$	−7.73205			−0.356274
$472$	2.83013	+	4.90192i	0.130267	+	0.225629i
$473$		−	7.26795i		−	0.334181i
$474$	−10.3923	+	18.0000i	−0.477334	+	0.826767i
$475$			0.535898i			0.0245887i
$476$	−1.73205	−	1.00000i	−0.0793884	−	0.0458349i
$477$		0			0
$478$	10.9282	−	18.9282i	0.499844	−	0.865756i
$479$	9.74167	−	5.62436i	0.445108	−	0.256983i	−0.260654	−	0.965432i	$-0.583938\pi$
$479$	9.74167	−	5.62436i	0.445108	−	0.256983i	0.705762	+	0.708449i	$0.250605\pi$
$480$	−1.73205			−0.0790569
$481$	8.30385	−	17.5788i	0.378623	−	0.801526i
$482$	4.00000			0.182195
$483$	−5.19615	+	3.00000i	−0.236433	+	0.136505i
$484$	5.69615	−	9.86603i	0.258916	−	0.448456i
$485$	7.19615	−	12.4641i	0.326760	−	0.565966i
$486$		0			0
$487$			34.7846i			1.57624i	0.615521	+	0.788121i	$0.288946\pi$
$487$			34.7846i			1.57624i	−0.615521	+	0.788121i	$0.711054\pi$
$488$	0.267949	−	0.464102i	0.0121295	−	0.0210089i
$489$		−	8.66025i		−	0.391630i
$490$	0.232051	+	0.401924i	0.0104830	+	0.0181571i
$491$	−16.7321			−0.755107			−0.377553	−	0.925988i	$-0.623235\pi$
$491$	−16.7321			−0.755107			−0.377553	+	0.925988i	$0.623235\pi$
$492$	7.73205			0.348588
$493$	−1.80385	−	3.12436i	−0.0812412	−	0.140714i
$494$	1.48334	+	0.856406i	0.0667386	+	0.0385315i
$495$		0			0
$496$	6.86603	−	3.96410i	0.308294	−	0.177993i
$497$	16.9282	+	29.3205i	0.759334	+	1.31520i
$498$	12.8038	−	7.39230i	0.573754	−	0.331257i
$499$	12.9282	+	7.46410i	0.578746	+	0.334139i	0.760635	−	0.649180i	$-0.224888\pi$
$499$	12.9282	+	7.46410i	0.578746	+	0.334139i	−0.181889	+	0.983319i	$0.558221\pi$
$500$	−0.866025	−	0.500000i	−0.0387298	−	0.0223607i
$501$	17.7846	−	10.2679i	0.794558	−	0.458738i
$502$	1.73205	+	3.00000i	0.0773052	+	0.133897i
$503$	−1.90192	+	1.09808i	−0.0848026	+	0.0489608i	−0.541802	−	0.840506i	$-0.682258\pi$
$503$	−1.90192	+	1.09808i	−0.0848026	+	0.0489608i	0.456999	+	0.889467i	$0.348924\pi$
$504$		0			0
$505$	−11.8301	−	6.83013i	−0.526434	−	0.303937i
$506$	3.00000	+	5.19615i	0.133366	+	0.230997i
$507$	4.82309			0.214201
$508$	2.53590			0.112512
$509$	7.83013	+	13.5622i	0.347064	+	0.601133i	0.985727	−	0.168354i	$-0.0538452\pi$
$509$	7.83013	+	13.5622i	0.347064	+	0.601133i	−0.638662	+	0.769487i	$0.720512\pi$
$510$		−	1.26795i		−	0.0561457i
$511$	−7.73205	+	13.3923i	−0.342046	+	0.592441i
$512$			1.00000i			0.0441942i
$513$	−2.41154	−	1.39230i	−0.106472	−	0.0614718i
$514$	0.0980762	−	0.169873i	0.00432596	−	0.00749278i
$515$	0.0980762	−	0.169873i	0.00432175	−	0.00748550i
$516$	2.30385	−	1.33013i	0.101421	−	0.0585556i
$517$	−31.8564			−1.40104
$518$	−16.5622	+	1.36603i	−0.727700	+	0.0600197i
$519$	10.3923			0.456172
$520$	−2.76795	+	1.59808i	−0.121383	+	0.0700803i
$521$	−1.69615	+	2.93782i	−0.0743098	+	0.128708i	−0.900786	−	0.434263i	$-0.857009\pi$
$521$	−1.69615	+	2.93782i	−0.0743098	+	0.128708i	0.826476	+	0.562972i	$0.190342\pi$
$522$		0			0
$523$	−8.72243	−	5.03590i	−0.381405	−	0.220204i	0.297024	−	0.954870i	$-0.404006\pi$
$523$	−8.72243	−	5.03590i	−0.381405	−	0.220204i	−0.678430	+	0.734665i	$0.737339\pi$
$524$			10.0000i			0.436852i
$525$	−2.36603	+	4.09808i	−0.103262	+	0.178855i
$526$			6.73205i			0.293531i
$527$	2.90192	+	5.02628i	0.126410	+	0.218948i
$528$	8.19615			0.356692
$529$	21.3923			0.930100
$530$	6.69615	+	11.5981i	0.290862	+	0.503788i
$531$		0			0
$532$		−	1.46410i		−	0.0634769i
$533$	12.3564	−	7.13397i	0.535215	−	0.309007i
$534$	−7.73205	−	13.3923i	−0.334599	−	0.579542i
$535$	13.9641	−	8.06218i	0.603721	−	0.348558i
$536$	6.92820	+	4.00000i	0.299253	+	0.172774i
$537$	−18.0000	−	10.3923i	−0.776757	−	0.448461i
$538$	−6.16987	+	3.56218i	−0.266002	+	0.153576i
$539$	−1.09808	−	1.90192i	−0.0472975	−	0.0819217i
$540$	4.50000	−	2.59808i	0.193649	−	0.111803i
$541$		−	8.24871i		−	0.354640i	−0.984153	−	0.177320i	$-0.943257\pi$
$541$		−	8.24871i		−	0.354640i	0.984153	−	0.177320i	$-0.0567427\pi$
$542$	22.1603	+	12.7942i	0.951864	+	0.549559i
$543$	−3.16987	−	5.49038i	−0.136032	−	0.235615i
$544$	−0.732051			−0.0313864
$545$	−10.0000			−0.428353
$546$	7.56218	+	13.0981i	0.323631	+	0.560546i
$547$			29.7846i			1.27350i	0.771071	+	0.636749i	$0.219721\pi$
$547$			29.7846i			1.27350i	−0.771071	+	0.636749i	$0.780279\pi$
$548$	2.83013	−	4.90192i	0.120897	−	0.209400i
$549$		0			0
$550$	4.09808	+	2.36603i	0.174743	+	0.100888i
$551$	1.32051	−	2.28719i	0.0562555	−	0.0974374i
$552$	−1.09808	+	1.90192i	−0.0467372	+	0.0809513i
$553$	28.3923	−	16.3923i	1.20736	−	0.697072i
$554$	23.7321			1.00828
$555$	−6.00000	−	8.66025i	−0.254686	−	0.367607i
$556$	−11.6603			−0.494505
$557$	16.5000	−	9.52628i	0.699127	−	0.403641i	−0.107895	−	0.994162i	$-0.534411\pi$
$557$	16.5000	−	9.52628i	0.699127	−	0.403641i	0.807022	+	0.590521i	$0.201078\pi$
$558$		0			0
$559$	2.45448	−	4.25129i	0.103814	−	0.179810i
$560$	2.36603	+	1.36603i	0.0999828	+	0.0577251i
$561$			6.00000i			0.253320i
$562$	2.93782	−	5.08846i	0.123925	−	0.214644i
$563$			12.2487i			0.516222i	0.966115	+	0.258111i	$0.0831000\pi$
$563$			12.2487i			0.516222i	−0.966115	+	0.258111i	$0.916900\pi$
$564$	−5.83013	−	10.0981i	−0.245493	−	0.425206i
$565$	8.39230			0.353067
$566$	13.5359			0.568956
$567$	−12.2942	−	21.2942i	−0.516309	−	0.894274i
$568$	10.7321	+	6.19615i	0.450307	+	0.259985i
$569$			27.9808i			1.17301i	0.809944	+	0.586507i	$0.199497\pi$
$569$			27.9808i			1.17301i	−0.809944	+	0.586507i	$0.800503\pi$
$570$	0.803848	−	0.464102i	0.0336695	−	0.0194391i
$571$	−5.26795	−	9.12436i	−0.220457	−	0.381842i	0.734490	−	0.678620i	$-0.237421\pi$
$571$	−5.26795	−	9.12436i	−0.220457	−	0.381842i	−0.954947	+	0.296777i	$0.904088\pi$
$572$	13.0981	−	7.56218i	0.547658	−	0.316191i
$573$	32.0885	+	18.5263i	1.34051	+	0.773946i
$574$	−10.5622	−	6.09808i	−0.440857	−	0.254529i
$575$	−1.09808	+	0.633975i	−0.0457929	+	0.0264386i
$576$		0			0
$577$	−4.22243	+	2.43782i	−0.175782	+	0.101488i	−0.585309	−	0.810810i	$-0.699027\pi$
$577$	−4.22243	+	2.43782i	−0.175782	+	0.101488i	0.409527	+	0.912298i	$0.365694\pi$
$578$			16.4641i			0.684816i
$579$	21.8827	+	12.6340i	0.909413	+	0.525050i
$580$	2.46410	+	4.26795i	0.102316	+	0.177217i
$581$	−23.3205			−0.967498
$582$	−24.9282			−1.03331
$583$	−31.6865	−	54.8827i	−1.31232	−	2.27301i
$584$			5.66025i			0.234223i
$585$		0			0
$586$		−	28.4641i		−	1.17584i
$587$	15.4019	+	8.89230i	0.635705	+	0.367025i	0.782958	−	0.622074i	$-0.213710\pi$
$587$	15.4019	+	8.89230i	0.635705	+	0.367025i	−0.147253	+	0.989099i	$0.547043\pi$
$588$	0.401924	−	0.696152i	0.0165751	−	0.0287088i
$589$	−2.12436	+	3.67949i	−0.0875325	+	0.151611i
$590$	4.90192	−	2.83013i	0.201809	−	0.116514i
$591$	45.5885			1.87526
$592$	−5.00000	+	3.46410i	−0.205499	+	0.142374i
$593$	27.8038			1.14177			0.570884	−	0.821031i	$-0.306601\pi$
$593$	27.8038			1.14177			0.570884	+	0.821031i	$0.306601\pi$
$594$	−21.2942	+	12.2942i	−0.873713	+	0.504438i
$595$	−1.00000	+	1.73205i	−0.0409960	+	0.0710072i
$596$	−6.00000	+	10.3923i	−0.245770	+	0.425685i
$597$	−1.50000	−	0.866025i	−0.0613909	−	0.0354441i
$598$			4.05256i			0.165721i
$599$	−4.25833	+	7.37564i	−0.173991	+	0.301361i	−0.939812	−	0.341693i	$-0.889000\pi$
$599$	−4.25833	+	7.37564i	−0.173991	+	0.301361i	0.765821	+	0.643054i	$0.222333\pi$
$600$			1.73205i			0.0707107i
$601$	−14.6962	−	25.4545i	−0.599469	−	1.03831i	−0.992900	−	0.118956i	$-0.962045\pi$
$601$	−14.6962	−	25.4545i	−0.599469	−	1.03831i	0.393431	−	0.919354i	$-0.371288\pi$
$602$	−4.19615			−0.171022
$603$		0			0
$604$	−11.3301	−	19.6244i	−0.461016	−	0.798504i
$605$	−9.86603	−	5.69615i	−0.401111	−	0.231582i
$606$			23.6603i			0.961132i
$607$	34.6865	−	20.0263i	1.40788	−	0.812842i	0.412699	−	0.910867i	$-0.364586\pi$
$607$	34.6865	−	20.0263i	1.40788	−	0.812842i	0.995184	+	0.0980258i	$0.0312528\pi$
$608$	−0.267949	−	0.464102i	−0.0108668	−	0.0188218i
$609$	20.1962	−	11.6603i	0.818389	−	0.472497i
$610$	−0.464102	−	0.267949i	−0.0187909	−	0.0108489i
$611$	−18.6340	−	10.7583i	−0.753850	−	0.435235i
$612$		0			0
$613$	12.0000	+	20.7846i	0.484675	+	0.839482i	0.999845	−	0.0176058i	$-0.00560439\pi$
$613$	12.0000	+	20.7846i	0.484675	+	0.839482i	−0.515170	+	0.857088i	$0.672271\pi$
$614$	−11.4282	+	6.59808i	−0.461205	+	0.266277i
$615$		−	7.73205i		−	0.311786i
$616$	−11.1962	−	6.46410i	−0.451106	−	0.260446i
$617$	−19.0526	−	33.0000i	−0.767027	−	1.32853i	−0.939168	−	0.343458i	$-0.888402\pi$
$617$	−19.0526	−	33.0000i	−0.767027	−	1.32853i	0.172141	−	0.985072i	$-0.444932\pi$
$618$	−0.339746			−0.0136666
$619$	0.143594			0.00577151			0.00288576	−	0.999996i	$-0.499081\pi$
$619$	0.143594			0.00577151			0.00288576	+	0.999996i	$0.499081\pi$
$620$	−3.96410	−	6.86603i	−0.159202	−	0.275746i
$621$		−	6.58846i		−	0.264386i
$622$	−15.6962	+	27.1865i	−0.629358	+	1.09008i
$623$			24.3923i			0.977257i
$624$	4.79423	+	2.76795i	0.191923	+	0.110807i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	10.4641	−	18.1244i	0.418230	−	0.724395i
$627$	−3.80385	+	2.19615i	−0.151911	+	0.0877059i
$628$	4.46410			0.178137
$629$	−2.53590	−	3.66025i	−0.101113	−	0.145944i
$630$		0			0
$631$	36.3109	−	20.9641i	1.44551	−	0.834568i	0.447304	−	0.894382i	$-0.352384\pi$
$631$	36.3109	−	20.9641i	1.44551	−	0.834568i	0.998210	+	0.0598142i	$0.0190508\pi$
$632$	6.00000	−	10.3923i	0.238667	−	0.413384i
$633$	2.07180	−	3.58846i	0.0823465	−	0.142628i
$634$	−27.9904	−	16.1603i	−1.11164	−	0.641806i
$635$		−	2.53590i		−	0.100634i
$636$	11.5981	−	20.0885i	0.459894	−	0.796559i
$637$		−	1.48334i		−	0.0587721i
$638$	−11.6603	−	20.1962i	−0.461634	−	0.799573i
$639$		0			0
$640$	1.00000			0.0395285
$641$	10.8923	+	18.8660i	0.430220	+	0.745163i	0.996892	−	0.0787804i	$-0.0251026\pi$
$641$	10.8923	+	18.8660i	0.430220	+	0.745163i	−0.566672	+	0.823944i	$0.691769\pi$
$642$	−24.1865	−	13.9641i	−0.954566	−	0.551119i
$643$		−	35.7846i		−	1.41121i	−0.708607	−	0.705604i	$-0.750676\pi$
$643$		−	35.7846i		−	1.41121i	0.708607	−	0.705604i	$-0.249324\pi$
$644$	3.00000	−	1.73205i	0.118217	−	0.0682524i
$645$	−1.33013	−	2.30385i	−0.0523737	−	0.0907139i
$646$	0.339746	−	0.196152i	0.0133671	−	0.00771751i
$647$	22.3923	+	12.9282i	0.880332	+	0.508260i	0.870768	−	0.491694i	$-0.163622\pi$
$647$	22.3923	+	12.9282i	0.880332	+	0.508260i	0.00956437	+	0.999954i	$0.496956\pi$
$648$	−7.79423	−	4.50000i	−0.306186	−	0.176777i
$649$	−23.1962	+	13.3923i	−0.910529	+	0.525694i
$650$	1.59808	+	2.76795i	0.0626817	+	0.108568i
$651$	−32.4904	+	18.7583i	−1.27340	+	0.735197i
$652$			5.00000i			0.195815i
$653$	11.5526	+	6.66987i	0.452087	+	0.261012i	0.708711	−	0.705499i	$-0.249277\pi$
$653$	11.5526	+	6.66987i	0.452087	+	0.261012i	−0.256624	+	0.966511i	$0.582610\pi$
$654$	8.66025	+	15.0000i	0.338643	+	0.586546i
$655$	10.0000			0.390732
$656$	−4.46410			−0.174294
$657$		0			0
$658$			18.3923i			0.717007i
$659$	21.1244	−	36.5885i	0.822888	−	1.42528i	−0.0806346	−	0.996744i	$-0.525695\pi$
$659$	21.1244	−	36.5885i	0.822888	−	1.42528i	0.903523	−	0.428540i	$-0.140972\pi$
$660$		−	8.19615i		−	0.319035i
$661$	−38.6147	−	22.2942i	−1.50194	−	0.867145i	−0.999997	−	0.00224354i	$-0.999286\pi$
$661$	−38.6147	−	22.2942i	−1.50194	−	0.867145i	−0.501942	−	0.864901i	$-0.667381\pi$
$662$	−2.90192	+	5.02628i	−0.112786	+	0.195352i
$663$	−2.02628	+	3.50962i	−0.0786942	+	0.136302i
$664$	−7.39230	+	4.26795i	−0.286877	+	0.165629i
$665$	−1.46410			−0.0567754
$666$		0			0
$667$	6.24871			0.241951
$668$	−10.2679	+	5.92820i	−0.397279	+	0.229369i
$669$	−9.16987	+	15.8827i	−0.354528	+	0.614060i
$670$	4.00000	−	6.92820i	0.154533	−	0.267660i
$671$	2.19615	+	1.26795i	0.0847815	+	0.0489486i
$672$		−	4.73205i		−	0.182543i
$673$	−8.70577	+	15.0788i	−0.335583	+	0.581247i	−0.983597	−	0.180382i	$-0.942267\pi$
$673$	−8.70577	+	15.0788i	−0.335583	+	0.581247i	0.648014	+	0.761629i	$0.275600\pi$
$674$			32.2487i			1.24217i
$675$	−2.59808	−	4.50000i	−0.100000	−	0.173205i
$676$	−2.78461			−0.107100
$677$	28.7846			1.10628			0.553141	−	0.833088i	$-0.313429\pi$
$677$	28.7846			1.10628			0.553141	+	0.833088i	$0.313429\pi$
$678$	−7.26795	−	12.5885i	−0.279124	−	0.483457i
$679$	34.0526	+	19.6603i	1.30682	+	0.754491i
$680$			0.732051i			0.0280729i
$681$	−19.2846	+	11.1340i	−0.738988	+	0.426655i
$682$	18.7583	+	32.4904i	0.718294	+	1.24412i
$683$	−5.25833	+	3.03590i	−0.201204	+	0.116165i	−0.597217	−	0.802080i	$-0.703727\pi$
$683$	−5.25833	+	3.03590i	−0.201204	+	0.116165i	0.396013	+	0.918245i	$0.370394\pi$
$684$		0			0
$685$	−4.90192	−	2.83013i	−0.187293	−	0.108134i
$686$	15.4641	−	8.92820i	0.590422	−	0.340880i
$687$	−17.9545	−	31.0981i	−0.685006	−	1.18647i
$688$	−1.33013	+	0.767949i	−0.0507106	+	0.0292778i
$689$		−	42.8038i		−	1.63070i
$690$	1.90192	+	1.09808i	0.0724050	+	0.0418030i
$691$	−9.75833	−	16.9019i	−0.371224	−	0.642979i	0.618530	−	0.785761i	$-0.287729\pi$
$691$	−9.75833	−	16.9019i	−0.371224	−	0.642979i	−0.989754	+	0.142782i	$0.954395\pi$
$692$	−6.00000			−0.228086
$693$		0			0
$694$	−7.53590	−	13.0526i	−0.286059	−	0.495468i
$695$			11.6603i			0.442299i
$696$	4.26795	−	7.39230i	0.161776	−	0.280205i
$697$		−	3.26795i		−	0.123782i
$698$	−11.1962	−	6.46410i	−0.423781	−	0.244670i
$699$	−14.4904	+	25.0981i	−0.548077	+	0.949296i
$700$	1.36603	−	2.36603i	0.0516309	−	0.0894274i
$701$	−22.8564	+	13.1962i	−0.863275	+	0.498412i	−0.865107	−	0.501587i	$-0.832750\pi$
$701$	−22.8564	+	13.1962i	−0.863275	+	0.498412i	0.00183293	+	0.999998i	$0.499417\pi$
$702$	−16.6077			−0.626817
$703$	1.39230	−	2.94744i	0.0525118	−	0.111165i
$704$	−4.73205			−0.178346
$705$	−10.0981	+	5.83013i	−0.380316	+	0.219575i
$706$	−13.7583	+	23.8301i	−0.517802	+	0.896859i
$707$	18.6603	−	32.3205i	0.701791	−	1.21554i
$708$	−8.49038	−	4.90192i	−0.319088	−	0.184226i
$709$			32.3923i			1.21652i	0.793738	+	0.608259i	$0.208132\pi$
$709$			32.3923i			1.21652i	−0.793738	+	0.608259i	$0.791868\pi$
$710$	6.19615	−	10.7321i	0.232537	−	0.402767i
$711$		0			0
$712$	4.46410	+	7.73205i	0.167299	+	0.289771i
$713$	−10.0526			−0.376471
$714$	3.46410			0.129641
$715$	−7.56218	−	13.0981i	−0.282809	−	0.489840i
$716$	10.3923	+	6.00000i	0.388379	+	0.224231i
$717$			37.8564i			1.41377i
$718$	−24.4808	+	14.1340i	−0.913614	+	0.527475i
$719$	−0.937822	−	1.62436i	−0.0349749	−	0.0605782i	0.848008	−	0.529983i	$-0.177802\pi$
$719$	−0.937822	−	1.62436i	−0.0349749	−	0.0605782i	−0.882983	+	0.469405i	$0.844468\pi$
$720$		0			0
$721$	0.464102	+	0.267949i	0.0172840	+	0.00997895i
$722$	−16.2058	−	9.35641i	−0.603116	−	0.348209i
$723$	−6.00000	+	3.46410i	−0.223142	+	0.128831i
$724$	1.83013	+	3.16987i	0.0680161	+	0.117807i
$725$	4.26795	−	2.46410i	0.158508	−	0.0915144i
$726$			19.7321i			0.732325i
$727$	6.92820	+	4.00000i	0.256953	+	0.148352i	0.622944	−	0.782267i	$-0.285937\pi$
$727$	6.92820	+	4.00000i	0.256953	+	0.148352i	−0.365991	+	0.930618i	$0.619270\pi$
$728$	−4.36603	−	7.56218i	−0.161816	−	0.280273i
$729$	27.0000			1.00000
$730$	5.66025			0.209495
$731$	−0.562178	−	0.973721i	−0.0207929	−	0.0360144i
$732$			0.928203i			0.0343074i
$733$	5.66025	−	9.80385i	0.209066	−	0.362113i	−0.742354	−	0.670007i	$-0.766291\pi$
$733$	5.66025	−	9.80385i	0.209066	−	0.362113i	0.951421	+	0.307894i	$0.0996242\pi$
$734$			32.2487i			1.19032i
$735$	−0.696152	−	0.401924i	−0.0256780	−	0.0148252i
$736$	0.633975	−	1.09808i	0.0233686	−	0.0404756i
$737$	−18.9282	+	32.7846i	−0.697229	+	1.20764i
$738$		0			0
$739$	31.2679			1.15021			0.575105	−	0.818080i	$-0.304961\pi$
$739$	31.2679			1.15021			0.575105	+	0.818080i	$0.304961\pi$
$740$	3.46410	+	5.00000i	0.127343	+	0.183804i
$741$	−2.96668			−0.108984
$742$	−31.6865	+	18.2942i	−1.16325	+	0.671602i
$743$	−4.16987	+	7.22243i	−0.152978	+	0.264965i	−0.932321	−	0.361632i	$-0.882220\pi$
$743$	−4.16987	+	7.22243i	−0.152978	+	0.264965i	0.779343	+	0.626597i	$0.215553\pi$
$744$	−6.86603	+	11.8923i	−0.251721	+	0.435993i
$745$	10.3923	+	6.00000i	0.380745	+	0.219823i
$746$		−	13.5359i		−	0.495584i
$747$		0			0
$748$		−	3.46410i		−	0.126660i
$749$	22.0263	+	38.1506i	0.804823	+	1.39399i
$750$	1.73205			0.0632456
$751$	3.33975			0.121869			0.0609345	−	0.998142i	$-0.480592\pi$
$751$	3.33975			0.121869			0.0609345	+	0.998142i	$0.480592\pi$
$752$	3.36603	+	5.83013i	0.122746	+	0.212603i
$753$	−5.19615	−	3.00000i	−0.189358	−	0.109326i
$754$		−	15.7513i		−	0.573628i
$755$	−19.6244	+	11.3301i	−0.714203	+	0.412346i
$756$	7.09808	+	12.2942i	0.258155	+	0.447137i
$757$	40.9641	−	23.6506i	1.48887	−	0.859597i	0.488946	−	0.872314i	$-0.337381\pi$
$757$	40.9641	−	23.6506i	1.48887	−	0.859597i	0.999919	+	0.0127168i	$0.00404801\pi$
$758$	−11.3660	−	6.56218i	−0.412833	−	0.238349i
$759$	−9.00000	−	5.19615i	−0.326679	−	0.188608i
$760$	−0.464102	+	0.267949i	−0.0168347	+	0.00971954i
$761$	26.7846	+	46.3923i	0.970941	+	1.68172i	0.692726	+	0.721201i	$0.256410\pi$
$761$	26.7846	+	46.3923i	0.970941	+	1.68172i	0.278216	+	0.960519i	$0.410257\pi$
$762$	−3.80385	+	2.19615i	−0.137799	+	0.0795582i
$763$		−	27.3205i		−	0.989069i
$764$	−18.5263	−	10.6962i	−0.670257	−	0.386973i
$765$		0			0
$766$	37.5167			1.35553
$767$	−18.0910			−0.653229
$768$	−0.866025	−	1.50000i	−0.0312500	−	0.0541266i
$769$		−	21.3205i		−	0.768837i	−0.923159	−	0.384419i	$-0.874402\pi$
$769$		−	21.3205i		−	0.768837i	0.923159	−	0.384419i	$-0.125598\pi$
$770$	−6.46410	+	11.1962i	−0.232950	+	0.403481i
$771$			0.339746i			0.0122357i
$772$	−12.6340	−	7.29423i	−0.454707	−	0.262525i
$773$	9.16025	−	15.8660i	0.329471	−	0.570661i	−0.652936	−	0.757413i	$-0.726463\pi$
$773$	9.16025	−	15.8660i	0.329471	−	0.570661i	0.982407	+	0.186752i	$0.0597961\pi$
$774$		0			0
$775$	−6.86603	+	3.96410i	−0.246635	+	0.142395i
$776$	14.3923			0.516654
$777$	23.6603	−	16.3923i	0.848807	−	0.588071i
$778$	14.9282			0.535202
$779$	2.07180	−	1.19615i	0.0742298	−	0.0428566i
$780$	2.76795	−	4.79423i	0.0991085	−	0.171661i
$781$	−29.3205	+	50.7846i	−1.04917	+	1.81722i
$782$	0.803848	+	0.464102i	0.0287455	+	0.0165962i
$783$			25.6077i			0.915144i
$784$	−0.232051	+	0.401924i	−0.00828753	+	0.0143544i
$785$		−	4.46410i		−	0.159331i
$786$	−8.66025	−	15.0000i	−0.308901	−	0.535032i
$787$	−41.0526			−1.46337			−0.731683	−	0.681645i	$-0.761265\pi$
$787$	−41.0526			−1.46337			−0.731683	+	0.681645i	$0.761265\pi$
$788$	−26.3205			−0.937629
$789$	−5.83013	−	10.0981i	−0.207558	−	0.359501i
$790$	−10.3923	−	6.00000i	−0.369742	−	0.213470i
$791$			22.9282i			0.815233i
$792$		0			0
$793$	0.856406	+	1.48334i	0.0304119	+	0.0526749i
$794$	3.06218	−	1.76795i	0.108673	−	0.0627422i
$795$	−20.0885	−	11.5981i	−0.712464	−	0.411341i
$796$	0.866025	+	0.500000i	0.0306955	+	0.0177220i
$797$	2.64359	−	1.52628i	0.0936409	−	0.0540636i	−0.452448	−	0.891791i	$-0.649449\pi$
$797$	2.64359	−	1.52628i	0.0936409	−	0.0540636i	0.546089	+	0.837727i	$0.316116\pi$
$798$	1.26795	+	2.19615i	0.0448849	+	0.0777430i
$799$	−4.26795	+	2.46410i	−0.150989	+	0.0871736i
$800$		−	1.00000i		−	0.0353553i
$801$		0			0
$802$	2.46410	+	4.26795i	0.0870105	+	0.150707i
$803$	−26.7846			−0.945208
$804$	−13.8564			−0.488678
$805$	−1.73205	−	3.00000i	−0.0610468	−	0.105736i
$806$			25.3397i			0.892554i
$807$	6.16987	−	10.6865i	0.217190	−	0.376184i
$808$		−	13.6603i		−	0.480566i
$809$	−30.5718	−	17.6506i	−1.07485	−	0.620563i	−0.145345	−	0.989381i	$-0.546429\pi$
$809$	−30.5718	−	17.6506i	−1.07485	−	0.620563i	−0.929502	+	0.368818i	$0.879763\pi$
$810$	−4.50000	+	7.79423i	−0.158114	+	0.273861i
$811$	21.3205	−	36.9282i	0.748664	−	1.29672i	−0.199799	−	0.979837i	$-0.564029\pi$
$811$	21.3205	−	36.9282i	0.748664	−	1.29672i	0.948463	−	0.316888i	$-0.102638\pi$
$812$	−11.6603	+	6.73205i	−0.409195	+	0.236249i
$813$	−44.3205			−1.55439
$814$	−16.3923	−	23.6603i	−0.574550	−	0.829291i
$815$	5.00000			0.175142
$816$	1.09808	−	0.633975i	0.0384404	−	0.0221936i
$817$	0.411543	−	0.712813i	0.0143981	−	0.0249382i
$818$	12.5981	−	21.8205i	0.440481	−	0.762936i
$819$		0			0
$820$			4.46410i			0.155893i
$821$	21.2487	−	36.8038i	0.741585	−	1.28446i	−0.210188	−	0.977661i	$-0.567408\pi$
$821$	21.2487	−	36.8038i	0.741585	−	1.28446i	0.951773	−	0.306802i	$-0.0992590\pi$
$822$			9.80385i			0.341948i
$823$	−16.8301	−	29.1506i	−0.586661	−	1.01613i	−0.994666	−	0.103147i	$-0.967109\pi$
$823$	−16.8301	−	29.1506i	−0.586661	−	1.01613i	0.408005	−	0.912980i	$-0.366225\pi$
$824$	0.196152			0.00683329
$825$	−8.19615			−0.285353
$826$	7.73205	+	13.3923i	0.269032	+	0.465978i
$827$	12.8038	+	7.39230i	0.445233	+	0.257056i	0.705815	−	0.708396i	$-0.250581\pi$
$827$	12.8038	+	7.39230i	0.445233	+	0.257056i	−0.260582	+	0.965452i	$0.583914\pi$
$828$		0			0
$829$	−25.0981	+	14.4904i	−0.871692	+	0.503272i	−0.867910	−	0.496721i	$-0.834537\pi$
$829$	−25.0981	+	14.4904i	−0.871692	+	0.503272i	−0.00378200	+	0.999993i	$0.501204\pi$
$830$	4.26795	+	7.39230i	0.148143	+	0.256591i
$831$	−35.5981	+	20.5526i	−1.23488	+	0.712960i
$832$	−2.76795	−	1.59808i	−0.0959614	−	0.0554033i
$833$	−0.294229	−	0.169873i	−0.0101944	−	0.00588575i
$834$	17.4904	−	10.0981i	0.605642	−	0.349668i
$835$	5.92820	+	10.2679i	0.205154	+	0.355337i
$836$	2.19615	−	1.26795i	0.0759555	−	0.0438529i
$837$		−	41.1962i		−	1.42395i
$838$	−24.2942	−	14.0263i	−0.839230	−	0.484530i
$839$	−24.5263	−	42.4808i	−0.846741	−	1.46660i	−0.884100	−	0.467297i	$-0.845228\pi$
$839$	−24.5263	−	42.4808i	−0.846741	−	1.46660i	0.0373593	−	0.999302i	$-0.488105\pi$
$840$	−4.73205			−0.163271
$841$	4.71281			0.162511
$842$	10.2942	+	17.8301i	0.354763	+	0.614467i
$843$			10.1769i			0.350512i
$844$	−1.19615	+	2.07180i	−0.0411733	+	0.0713142i
$845$			2.78461i			0.0957935i
$846$		0			0
$847$	15.5622	−	26.9545i	0.534723	−	0.926167i
$848$	−6.69615	+	11.5981i	−0.229947	+	0.398280i
$849$	−20.3038	+	11.7224i	−0.696826	+	0.402313i
$850$	0.732051			0.0251091
$851$	7.68653	−	0.633975i	0.263491	−	0.0217324i
$852$	−21.4641			−0.735348
$853$	−38.2128	+	22.0622i	−1.30838	+	0.755395i	−0.981826	−	0.189783i	$-0.939221\pi$
$853$	−38.2128	+	22.0622i	−1.30838	+	0.755395i	−0.326556	+	0.945178i	$0.605888\pi$
$854$	0.732051	−	1.26795i	0.0250503	−	0.0433883i
$855$		0			0
$856$	13.9641	+	8.06218i	0.477283	+	0.275560i
$857$			44.4449i			1.51821i	0.650970	+	0.759104i	$0.274363\pi$
$857$			44.4449i			1.51821i	−0.650970	+	0.759104i	$0.725637\pi$
$858$	−13.0981	+	22.6865i	−0.447161	+	0.774505i
$859$		−	42.9282i		−	1.46469i	−0.680933	−	0.732346i	$-0.738426\pi$
$859$		−	42.9282i		−	1.46469i	0.680933	−	0.732346i	$-0.261574\pi$
$860$	0.767949	+	1.33013i	0.0261869	+	0.0453570i
$861$	21.1244			0.719916
$862$	17.7846			0.605746
$863$	16.1962	+	28.0526i	0.551323	+	0.954920i	0.998179	+	0.0603143i	$0.0192103\pi$
$863$	16.1962	+	28.0526i	0.551323	+	0.954920i	−0.446856	+	0.894606i	$0.647456\pi$
$864$	4.50000	+	2.59808i	0.153093	+	0.0883883i
$865$			6.00000i			0.204006i
$866$	−11.0718	+	6.39230i	−0.376235	+	0.217219i
$867$	−14.2583	−	24.6962i	−0.484238	−	0.838725i
$868$	18.7583	−	10.8301i	0.636699	−	0.367598i
$869$	49.1769	+	28.3923i	1.66821	+	0.963143i
$870$	−7.39230	−	4.26795i	−0.250623	−	0.144697i
$871$	−22.1436	+	12.7846i	−0.750307	+	0.433190i
$872$	−5.00000	−	8.66025i	−0.169321	−	0.293273i
$873$		0			0
$874$			0.679492i			0.0229842i
$875$	−2.36603	−	1.36603i	−0.0799863	−	0.0461801i
$876$	−4.90192	−	8.49038i	−0.165621	−	0.286863i
$877$	1.53590			0.0518636			0.0259318	−	0.999664i	$-0.491745\pi$
$877$	1.53590			0.0518636			0.0259318	+	0.999664i	$0.491745\pi$
$878$	−31.7846			−1.07268
$879$	24.6506	+	42.6962i	0.831445	+	1.44011i
$880$			4.73205i			0.159517i
$881$	−6.53590	+	11.3205i	−0.220200	+	0.381398i	−0.954869	−	0.297029i	$-0.904004\pi$
$881$	−6.53590	+	11.3205i	−0.220200	+	0.381398i	0.734669	+	0.678426i	$0.237338\pi$
$882$		0			0
$883$	−40.9186	−	23.6244i	−1.37702	−	0.795023i	−0.385220	−	0.922825i	$-0.625875\pi$
$883$	−40.9186	−	23.6244i	−1.37702	−	0.795023i	−0.991800	+	0.127802i	$0.959208\pi$
$884$	1.16987	−	2.02628i	0.0393471	−	0.0681512i
$885$	−4.90192	+	8.49038i	−0.164776	+	0.285401i
$886$	26.2128	−	15.1340i	0.880637	−	0.508436i
$887$	6.00000			0.201460			0.100730	−	0.994914i	$-0.467882\pi$
$887$	6.00000			0.201460			0.100730	+	0.994914i	$0.467882\pi$
$888$	4.50000	−	9.52628i	0.151010	−	0.319681i
$889$	6.92820			0.232364
$890$	7.73205	−	4.46410i	0.259179	−	0.149637i
$891$	21.2942	−	36.8827i	0.713384	−	1.23562i
$892$	5.29423	−	9.16987i	0.177264	−	0.307030i
$893$	−3.12436	−	1.80385i	−0.104553	−	0.0603635i
$894$		−	20.7846i		−	0.695141i
$895$	6.00000	−	10.3923i	0.200558	−	0.347376i
$896$			2.73205i			0.0912714i
$897$	−3.50962	−	6.07884i	−0.117183	−	0.202967i
$898$	−16.5167			−0.551168
$899$	39.0718			1.30312
$900$		0			0
$901$	−8.49038	−	4.90192i	−0.282856	−	0.163307i
$902$		−	21.1244i		−	0.703364i
$903$	6.29423	−	3.63397i	0.209459	−	0.120931i
$904$	4.19615	+	7.26795i	0.139562	+	0.241728i
$905$	3.16987	−	1.83013i	0.105370	−	0.0608355i
$906$	33.9904	+	19.6244i	1.12925	+	0.651976i
$907$	−0.803848	−	0.464102i	−0.0266913	−	0.0154102i	0.486595	−	0.873628i	$-0.338239\pi$
$907$	−0.803848	−	0.464102i	−0.0266913	−	0.0154102i	−0.513286	+	0.858217i	$0.671572\pi$
$908$	11.1340	−	6.42820i	0.369494	−	0.213327i
$909$		0			0
$910$	−7.56218	+	4.36603i	−0.250684	+	0.144732i
$911$			17.9282i			0.593988i	0.954879	+	0.296994i	$0.0959841\pi$
$911$			17.9282i			0.593988i	−0.954879	+	0.296994i	$0.904016\pi$
$912$	0.803848	+	0.464102i	0.0266181	+	0.0153679i
$913$	−20.1962	−	34.9808i	−0.668395	−	1.15769i
$914$	−1.85641			−0.0614045
$915$	0.928203			0.0306855
$916$	10.3660	+	17.9545i	0.342503	+	0.593233i
$917$			27.3205i			0.902203i
$918$	−1.90192	+	3.29423i	−0.0627728	+	0.108726i
$919$		−	55.4641i		−	1.82959i	−0.403916	−	0.914796i	$-0.632351\pi$
$919$		−	55.4641i		−	1.82959i	0.403916	−	0.914796i	$-0.367649\pi$
$920$	−1.09808	−	0.633975i	−0.0362025	−	0.0209015i
$921$	11.4282	−	19.7942i	0.376572	−	0.652242i
$922$	15.5885	−	27.0000i	0.513378	−	0.889198i
$923$	−34.3013	+	19.8038i	−1.12904	+	0.651852i
$924$	22.3923			0.736653
$925$	5.00000	−	3.46410i	0.164399	−	0.113899i
$926$	−1.85641			−0.0610053
$927$		0			0
$928$	−2.46410	+	4.26795i	−0.0808881	+	0.140102i
$929$	−17.9641	+	31.1147i	−0.589383	+	1.02084i	0.404930	+	0.914348i	$0.367296\pi$
$929$	−17.9641	+	31.1147i	−0.589383	+	1.02084i	−0.994313	+	0.106494i	$0.966038\pi$
$930$	11.8923	+	6.86603i	0.389964	+	0.225146i
$931$		−	0.248711i		−	0.00815118i
$932$	8.36603	−	14.4904i	0.274038	−	0.474648i
$933$		−	54.3731i		−	1.78009i
$934$	−0.500000	−	0.866025i	−0.0163605	−	0.0283372i
$935$	−3.46410			−0.113288
$936$		0			0
$937$	7.58846	+	13.1436i	0.247904	+	0.429382i	0.962944	−	0.269701i	$-0.0869249\pi$
$937$	7.58846	+	13.1436i	0.247904	+	0.429382i	−0.715040	+	0.699084i	$0.753592\pi$
$938$	18.9282	+	10.9282i	0.618028	+	0.356818i
$939$			36.2487i			1.18293i
$940$	5.83013	−	3.36603i	0.190158	−	0.109788i
$941$	15.0263	+	26.0263i	0.489843	+	0.848432i	0.999932	−	0.0116892i	$-0.00372087\pi$
$941$	15.0263	+	26.0263i	0.489843	+	0.848432i	−0.510089	+	0.860122i	$0.670388\pi$
$942$	−6.69615	+	3.86603i	−0.218172	+	0.125962i
$943$	4.90192	+	2.83013i	0.159629	+	0.0921616i
$944$	4.90192	+	2.83013i	0.159544	+	0.0921128i
$945$	12.2942	−	7.09808i	0.399931	−	0.230900i
$946$	−3.63397	−	6.29423i	−0.118151	−	0.204643i
$947$	20.1340	−	11.6244i	0.654266	−	0.377741i	−0.135823	−	0.990733i	$-0.543368\pi$
$947$	20.1340	−	11.6244i	0.654266	−	0.377741i	0.790089	+	0.612992i	$0.210034\pi$
$948$			20.7846i			0.675053i
$949$	−15.6673	−	9.04552i	−0.508582	−	0.293630i
$950$	0.267949	+	0.464102i	0.00869342	+	0.0150574i
$951$	55.9808			1.81530
$952$	−2.00000			−0.0648204
$953$	20.6865	+	35.8301i	0.670103	+	1.16065i	0.977875	+	0.209192i	$0.0670832\pi$
$953$	20.6865	+	35.8301i	0.670103	+	1.16065i	−0.307772	+	0.951460i	$0.599583\pi$
$954$		0			0
$955$	−10.6962	+	18.5263i	−0.346119	+	0.599496i
$956$		−	21.8564i		−	0.706887i
$957$	34.9808	+	20.1962i	1.13077	+	0.652849i
$958$	5.62436	−	9.74167i	0.181715	−	0.314739i
$959$	7.73205	−	13.3923i	0.249681	−	0.432460i
$960$	−1.50000	+	0.866025i	−0.0484123	+	0.0279508i
$961$	−31.8564			−1.02763
$962$	−1.59808	−	19.3756i	−0.0515240	−	0.624696i
$963$		0			0
$964$	3.46410	−	2.00000i	0.111571	−	0.0644157i
$965$	−7.29423	+	12.6340i	−0.234810	+	0.406702i
$966$	−3.00000	+	5.19615i	−0.0965234	+	0.167183i
$967$	9.80385	+	5.66025i	0.315270	+	0.182021i	0.649283	−	0.760547i	$-0.275069\pi$
$967$	9.80385	+	5.66025i	0.315270	+	0.182021i	−0.334012	+	0.942569i	$0.608403\pi$
$968$		−	11.3923i		−	0.366163i
$969$	−0.339746	+	0.588457i	−0.0109142	+	0.0189040i
$970$		−	14.3923i		−	0.462109i
$971$	22.5622	+	39.0788i	0.724055	+	1.25410i	0.959362	+	0.282179i	$0.0910571\pi$
$971$	22.5622	+	39.0788i	0.724055	+	1.25410i	−0.235307	+	0.971921i	$0.575610\pi$
$972$		0			0
$973$	−31.8564			−1.02127
$974$	17.3923	+	30.1244i	0.557285	+	0.965247i
$975$	−4.79423	−	2.76795i	−0.153538	−	0.0886453i
$976$		−	0.535898i		−	0.0171537i
$977$	−12.8038	+	7.39230i	−0.409631	+	0.236501i	−0.690631	−	0.723207i	$-0.742667\pi$
$977$	−12.8038	+	7.39230i	−0.409631	+	0.236501i	0.281000	+	0.959708i	$0.409334\pi$
$978$	−4.33013	−	7.50000i	−0.138462	−	0.239824i
$979$	−36.5885	+	21.1244i	−1.16937	+	0.675137i
$980$	0.401924	+	0.232051i	0.0128390	+	0.00741259i
$981$		0			0
$982$	−14.4904	+	8.36603i	−0.462407	+	0.266971i
$983$	−3.58846	−	6.21539i	−0.114454	−	0.198240i	0.803107	−	0.595834i	$-0.203179\pi$
$983$	−3.58846	−	6.21539i	−0.114454	−	0.198240i	−0.917561	+	0.397594i	$0.869845\pi$
$984$	6.69615	−	3.86603i	0.213466	−	0.123244i
$985$			26.3205i			0.838641i
$986$	−3.12436	−	1.80385i	−0.0994998	−	0.0574462i
$987$	−15.9282	−	27.5885i	−0.507000	−	0.878150i
$988$	1.71281			0.0544918
$989$	1.94744			0.0619250
$990$		0			0
$991$			55.1051i			1.75047i	0.483696	+	0.875236i	$0.339294\pi$
$991$			55.1051i			1.75047i	−0.483696	+	0.875236i	$0.660706\pi$
$992$	3.96410	−	6.86603i	0.125860	−	0.217997i
$993$		−	10.0526i		−	0.319008i
$994$	29.3205	+	16.9282i	0.929990	+	0.536930i
$995$	0.500000	−	0.866025i	0.0158511	−	0.0274549i
$996$	7.39230	−	12.8038i	0.234234	−	0.405705i
$997$	−11.7679	+	6.79423i	−0.372695	+	0.215175i	−0.674635	−	0.738151i	$-0.735699\pi$
$997$	−11.7679	+	6.79423i	−0.372695	+	0.215175i	0.301940	+	0.953327i	$0.402366\pi$
$998$	14.9282			0.472544
$999$	2.59808	+	31.5000i	0.0821995	+	0.996616i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.l.a.11.2	✓	4
37.27	even	6	inner	370.2.l.a.101.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.l.a.11.2	✓	4	1.1	even	1	trivial
370.2.l.a.101.2	yes	4	37.27	even	6	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.l (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{5} +1.73205i q^{6} +(1.36603 - 2.36603i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{5} +1.73205i q^{6} +(1.36603 - 2.36603i) q^{7} -1.00000i q^{8} -1.00000 q^{10} +4.73205 q^{11} +(0.866025 + 1.50000i) q^{12} +(2.76795 + 1.59808i) q^{13} -2.73205i q^{14} +(1.50000 - 0.866025i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.633975 - 0.366025i) q^{17} +(0.464102 + 0.267949i) q^{19} +(-0.866025 + 0.500000i) q^{20} +(2.36603 + 4.09808i) q^{21} +(4.09808 - 2.36603i) q^{22} +1.26795i q^{23} +(1.50000 + 0.866025i) q^{24} +(0.500000 + 0.866025i) q^{25} +3.19615 q^{26} -5.19615 q^{27} +(-1.36603 - 2.36603i) q^{28} -4.92820i q^{29} +(0.866025 - 1.50000i) q^{30} +7.92820i q^{31} +(-0.866025 - 0.500000i) q^{32} +(-4.09808 + 7.09808i) q^{33} +(0.366025 - 0.633975i) q^{34} +(-2.36603 + 1.36603i) q^{35} +(-0.500000 - 6.06218i) q^{37} +0.535898 q^{38} +(-4.79423 + 2.76795i) q^{39} +(-0.500000 + 0.866025i) q^{40} +(2.23205 - 3.86603i) q^{41} +(4.09808 + 2.36603i) q^{42} -1.53590i q^{43} +(2.36603 - 4.09808i) q^{44} +(0.633975 + 1.09808i) q^{46} -6.73205 q^{47} +1.73205 q^{48} +(-0.232051 - 0.401924i) q^{49} +(0.866025 + 0.500000i) q^{50} +1.26795i q^{51} +(2.76795 - 1.59808i) q^{52} +(-6.69615 - 11.5981i) q^{53} +(-4.50000 + 2.59808i) q^{54} +(-4.09808 - 2.36603i) q^{55} +(-2.36603 - 1.36603i) q^{56} +(-0.803848 + 0.464102i) q^{57} +(-2.46410 - 4.26795i) q^{58} +(-4.90192 + 2.83013i) q^{59} -1.73205i q^{60} +(0.464102 + 0.267949i) q^{61} +(3.96410 + 6.86603i) q^{62} -1.00000 q^{64} +(-1.59808 - 2.76795i) q^{65} +8.19615i q^{66} +(-4.00000 + 6.92820i) q^{67} -0.732051i q^{68} +(-1.90192 - 1.09808i) q^{69} +(-1.36603 + 2.36603i) q^{70} +(-6.19615 + 10.7321i) q^{71} -5.66025 q^{73} +(-3.46410 - 5.00000i) q^{74} -1.73205 q^{75} +(0.464102 - 0.267949i) q^{76} +(6.46410 - 11.1962i) q^{77} +(-2.76795 + 4.79423i) q^{78} +(10.3923 + 6.00000i) q^{79} +1.00000i q^{80} +(4.50000 - 7.79423i) q^{81} -4.46410i q^{82} +(-4.26795 - 7.39230i) q^{83} +4.73205 q^{84} -0.732051 q^{85} +(-0.767949 - 1.33013i) q^{86} +(7.39230 + 4.26795i) q^{87} -4.73205i q^{88} +(-7.73205 + 4.46410i) q^{89} +(7.56218 - 4.36603i) q^{91} +(1.09808 + 0.633975i) q^{92} +(-11.8923 - 6.86603i) q^{93} +(-5.83013 + 3.36603i) q^{94} +(-0.267949 - 0.464102i) q^{95} +(1.50000 - 0.866025i) q^{96} +14.3923i q^{97} +(-0.401924 - 0.232051i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4} + 2 q^{7}+O(q^{10}) \) 4 * q + 2 * q^4 + 2 * q^7	\( 4 q + 2 q^{4} + 2 q^{7} - 4 q^{10} + 12 q^{11} + 18 q^{13} + 6 q^{15} - 2 q^{16} + 6 q^{17} - 12 q^{19} + 6 q^{21} + 6 q^{22} + 6 q^{24} + 2 q^{25} - 8 q^{26} - 2 q^{28} - 6 q^{33} - 2 q^{34} - 6 q^{35} - 2 q^{37} + 16 q^{38} + 12 q^{39} - 2 q^{40} + 2 q^{41} + 6 q^{42} + 6 q^{44} + 6 q^{46} - 20 q^{47} + 6 q^{49} + 18 q^{52} - 6 q^{53} - 18 q^{54} - 6 q^{55} - 6 q^{56} - 24 q^{57} + 4 q^{58} - 30 q^{59} - 12 q^{61} + 2 q^{62} - 4 q^{64} + 4 q^{65} - 16 q^{67} - 18 q^{69} - 2 q^{70} - 4 q^{71} + 12 q^{73} - 12 q^{76} + 12 q^{77} - 18 q^{78} + 18 q^{81} - 24 q^{83} + 12 q^{84} + 4 q^{85} - 10 q^{86} - 12 q^{87} - 24 q^{89} + 6 q^{91} - 6 q^{92} - 6 q^{93} - 6 q^{94} - 8 q^{95} + 6 q^{96} - 12 q^{98}+O(q^{100}) \) 4 * q + 2 * q^4 + 2 * q^7 - 4 * q^10 + 12 * q^11 + 18 * q^13 + 6 * q^15 - 2 * q^16 + 6 * q^17 - 12 * q^19 + 6 * q^21 + 6 * q^22 + 6 * q^24 + 2 * q^25 - 8 * q^26 - 2 * q^28 - 6 * q^33 - 2 * q^34 - 6 * q^35 - 2 * q^37 + 16 * q^38 + 12 * q^39 - 2 * q^40 + 2 * q^41 + 6 * q^42 + 6 * q^44 + 6 * q^46 - 20 * q^47 + 6 * q^49 + 18 * q^52 - 6 * q^53 - 18 * q^54 - 6 * q^55 - 6 * q^56 - 24 * q^57 + 4 * q^58 - 30 * q^59 - 12 * q^61 + 2 * q^62 - 4 * q^64 + 4 * q^65 - 16 * q^67 - 18 * q^69 - 2 * q^70 - 4 * q^71 + 12 * q^73 - 12 * q^76 + 12 * q^77 - 18 * q^78 + 18 * q^81 - 24 * q^83 + 12 * q^84 + 4 * q^85 - 10 * q^86 - 12 * q^87 - 24 * q^89 + 6 * q^91 - 6 * q^92 - 6 * q^93 - 6 * q^94 - 8 * q^95 + 6 * q^96 - 12 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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