LMFDB - Embedded newform 966.2.s.a.181.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(97,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 11, 1]))

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

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

chi := DirichletCharacter("966.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.s (of order $22$, degree $10$, 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:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$16$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			181.1
Character	$\chi$	$=$	966.181
Dual form			966.2.s.a.475.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.142315 - 0.989821i) q^{2} +(-0.909632 - 0.415415i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(-2.74900 + 3.17251i) q^{5} +(-0.281733 + 0.959493i) q^{6} +(1.98395 + 1.75041i) q^{7} +(0.415415 + 0.909632i) q^{8} +(0.654861 + 0.755750i) q^{9} +O(q^{10})$	\(q+(-0.142315 - 0.989821i) q^{2} +(-0.909632 - 0.415415i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(-2.74900 + 3.17251i) q^{5} +(-0.281733 + 0.959493i) q^{6} +(1.98395 + 1.75041i) q^{7} +(0.415415 + 0.909632i) q^{8} +(0.654861 + 0.755750i) q^{9} +(3.53144 + 2.26952i) q^{10} +(1.66621 + 0.239565i) q^{11} +(0.989821 + 0.142315i) q^{12} +(0.367232 - 0.571424i) q^{13} +(1.45025 - 2.21286i) q^{14} +(3.81849 - 1.74384i) q^{15} +(0.841254 - 0.540641i) q^{16} +(-7.72704 - 2.26886i) q^{17} +(0.654861 - 0.755750i) q^{18} +(2.39735 - 0.703925i) q^{19} +(1.74384 - 3.81849i) q^{20} +(-1.07751 - 2.41639i) q^{21} -1.68335i q^{22} +(-1.65525 + 4.50113i) q^{23} -1.00000i q^{24} +(-1.79627 - 12.4933i) q^{25} +(-0.617871 - 0.282172i) q^{26} +(-0.281733 - 0.959493i) q^{27} +(-2.39673 - 1.12057i) q^{28} +(-2.30377 - 0.676447i) q^{29} +(-2.26952 - 3.53144i) q^{30} +(-4.21654 + 1.92563i) q^{31} +(-0.654861 - 0.755750i) q^{32} +(-1.41612 - 0.910086i) q^{33} +(-1.14610 + 7.97129i) q^{34} +(-11.0071 + 1.48222i) q^{35} +(-0.841254 - 0.540641i) q^{36} +(-0.899700 + 0.779595i) q^{37} +(-1.03794 - 2.27277i) q^{38} +(-0.571424 + 0.367232i) q^{39} +(-4.02779 - 1.18267i) q^{40} +(5.71873 + 4.95531i) q^{41} +(-2.23845 + 1.41044i) q^{42} +(-2.74000 - 1.25132i) q^{43} +(-1.66621 + 0.239565i) q^{44} -4.19784 q^{45} +(4.69088 + 0.997826i) q^{46} -4.94803i q^{47} +(-0.989821 + 0.142315i) q^{48} +(0.872103 + 6.94546i) q^{49} +(-12.1105 + 3.55598i) q^{50} +(6.08625 + 5.27376i) q^{51} +(-0.191368 + 0.651739i) q^{52} +(-5.63964 - 8.77545i) q^{53} +(-0.909632 + 0.415415i) q^{54} +(-5.34044 + 4.62751i) q^{55} +(-0.768070 + 2.53181i) q^{56} +(-2.47313 - 0.355582i) q^{57} +(-0.341702 + 2.37659i) q^{58} +(-2.47445 + 3.85033i) q^{59} +(-3.17251 + 2.74900i) q^{60} +(-5.41332 - 11.8535i) q^{61} +(2.50611 + 3.89958i) q^{62} +(-0.0236646 + 2.64565i) q^{63} +(-0.654861 + 0.755750i) q^{64} +(0.803330 + 2.73589i) q^{65} +(-0.699287 + 1.53123i) q^{66} +(-11.3758 + 1.63559i) q^{67} +8.05326 q^{68} +(3.37551 - 3.40675i) q^{69} +(3.03360 + 10.6841i) q^{70} +(-1.01355 - 7.04940i) q^{71} +(-0.415415 + 0.909632i) q^{72} +(3.69944 + 12.5991i) q^{73} +(0.899700 + 0.779595i) q^{74} +(-3.55598 + 12.1105i) q^{75} +(-2.10192 + 1.35082i) q^{76} +(2.88634 + 3.39185i) q^{77} +(0.444816 + 0.513345i) q^{78} +(4.27094 - 6.64571i) q^{79} +(-0.597414 + 4.15511i) q^{80} +(-0.142315 + 0.989821i) q^{81} +(4.09101 - 6.36573i) q^{82} +(-4.75752 - 5.49047i) q^{83} +(1.71464 + 2.01494i) q^{84} +(28.4396 - 18.2770i) q^{85} +(-0.848637 + 2.89019i) q^{86} +(1.81457 + 1.57234i) q^{87} +(0.474253 + 1.61516i) q^{88} +(-3.25180 + 7.12044i) q^{89} +(0.597414 + 4.15511i) q^{90} +(1.72880 - 0.490868i) q^{91} +(0.320088 - 4.78514i) q^{92} +4.63544 q^{93} +(-4.89767 + 0.704178i) q^{94} +(-4.35709 + 9.54071i) q^{95} +(0.281733 + 0.959493i) q^{96} +(1.14392 - 1.32016i) q^{97} +(6.75065 - 1.85167i) q^{98} +(0.910086 + 1.41612i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q - 16 q^{2} - 16 q^{4} - 16 q^{8} + 16 q^{9}+O(q^{10}) $ 160 * q - 16 * q^2 - 16 * q^4 - 16 * q^8 + 16 * q^9	$ 160 q - 16 q^{2} - 16 q^{4} - 16 q^{8} + 16 q^{9} - 22 q^{14} - 16 q^{16} + 16 q^{18} - 36 q^{23} + 96 q^{25} + 22 q^{28} - 20 q^{29} - 16 q^{32} - 50 q^{35} + 16 q^{36} + 22 q^{37} + 4 q^{39} - 110 q^{43} + 8 q^{46} - 36 q^{50} + 22 q^{51} - 88 q^{53} + 22 q^{57} + 24 q^{58} - 16 q^{64} - 72 q^{70} + 48 q^{71} + 16 q^{72} - 22 q^{74} + 24 q^{77} + 4 q^{78} + 88 q^{79} - 16 q^{81} + 22 q^{84} + 76 q^{85} + 44 q^{86} - 44 q^{88} + 8 q^{92} - 14 q^{95} + 22 q^{98} - 22 q^{99}+O(q^{100}) $ 160 * q - 16 * q^2 - 16 * q^4 - 16 * q^8 + 16 * q^9 - 22 * q^14 - 16 * q^16 + 16 * q^18 - 36 * q^23 + 96 * q^25 + 22 * q^28 - 20 * q^29 - 16 * q^32 - 50 * q^35 + 16 * q^36 + 22 * q^37 + 4 * q^39 - 110 * q^43 + 8 * q^46 - 36 * q^50 + 22 * q^51 - 88 * q^53 + 22 * q^57 + 24 * q^58 - 16 * q^64 - 72 * q^70 + 48 * q^71 + 16 * q^72 - 22 * q^74 + 24 * q^77 + 4 * q^78 + 88 * q^79 - 16 * q^81 + 22 * q^84 + 76 * q^85 + 44 * q^86 - 44 * q^88 + 8 * q^92 - 14 * q^95 + 22 * q^98 - 22 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{22}\right)$

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 $

$2$	−0.142315	−	0.989821i	−0.100632	−	0.699909i
$2$	−0.142315	−	0.989821i	−0.100632	−	0.699909i
$3$	−0.909632	−	0.415415i	−0.525176	−	0.239840i
$3$	−0.909632	−	0.415415i	−0.525176	−	0.239840i
$4$	−0.959493	+	0.281733i	−0.479746	+	0.140866i
$5$	−2.74900	+	3.17251i	−1.22939	+	1.41879i	−0.354088	+	0.935212i	$0.615209\pi$
$5$	−2.74900	+	3.17251i	−1.22939	+	1.41879i	−0.875301	+	0.483578i	$0.839337\pi$
$6$	−0.281733	+	0.959493i	−0.115017	+	0.391711i
$7$	1.98395	+	1.75041i	0.749862	+	0.661594i
$7$	1.98395	+	1.75041i	0.749862	+	0.661594i
$8$	0.415415	+	0.909632i	0.146871	+	0.321603i
$9$	0.654861	+	0.755750i	0.218287	+	0.251917i
$10$	3.53144	+	2.26952i	1.11674	+	0.717686i
$11$	1.66621	+	0.239565i	0.502382	+	0.0722316i	0.388847	−	0.921302i	$-0.372874\pi$
$11$	1.66621	+	0.239565i	0.502382	+	0.0722316i	0.113535	+	0.993534i	$0.463783\pi$
$12$	0.989821	+	0.142315i	0.285737	+	0.0410828i
$13$	0.367232	−	0.571424i	0.101852	−	0.158485i	−0.786587	−	0.617479i	$-0.788154\pi$
$13$	0.367232	−	0.571424i	0.101852	−	0.158485i	0.888439	+	0.458995i	$0.151790\pi$
$14$	1.45025	−	2.21286i	0.387596	−	0.591413i
$15$	3.81849	−	1.74384i	0.985929	−	0.450259i
$16$	0.841254	−	0.540641i	0.210313	−	0.135160i
$17$	−7.72704	−	2.26886i	−1.87408	−	0.550280i	−0.997631	−	0.0687916i	$-0.978086\pi$
$17$	−7.72704	−	2.26886i	−1.87408	−	0.550280i	−0.876452	−	0.481489i	$-0.840096\pi$
$18$	0.654861	−	0.755750i	0.154352	−	0.178132i
$19$	2.39735	−	0.703925i	0.549990	−	0.161491i	0.00508115	−	0.999987i	$-0.498383\pi$
$19$	2.39735	−	0.703925i	0.549990	−	0.161491i	0.544908	+	0.838496i	$0.316564\pi$
$20$	1.74384	−	3.81849i	0.389935	−	0.853839i
$21$	−1.07751	−	2.41639i	−0.235133	−	0.527300i
$22$		−	1.68335i		−	0.358891i
$23$	−1.65525	+	4.50113i	−0.345144	+	0.938550i
$23$	−1.65525	+	4.50113i	−0.345144	+	0.938550i
$24$		−	1.00000i		−	0.204124i
$25$	−1.79627	−	12.4933i	−0.359254	−	2.49867i
$26$	−0.617871	−	0.282172i	−0.121174	−	0.0553385i
$27$	−0.281733	−	0.959493i	−0.0542195	−	0.184655i
$28$	−2.39673	−	1.12057i	−0.452940	−	0.211767i
$29$	−2.30377	−	0.676447i	−0.427799	−	0.125613i	0.0607432	−	0.998153i	$-0.480653\pi$
$29$	−2.30377	−	0.676447i	−0.427799	−	0.125613i	−0.488542	+	0.872540i	$0.662471\pi$
$30$	−2.26952	−	3.53144i	−0.414356	−	0.644750i
$31$	−4.21654	+	1.92563i	−0.757313	+	0.345853i	−0.756368	−	0.654146i	$-0.773028\pi$
$31$	−4.21654	+	1.92563i	−0.757313	+	0.345853i	−0.000945212		1.00000i	$0.500301\pi$
$32$	−0.654861	−	0.755750i	−0.115764	−	0.133599i
$33$	−1.41612	−	0.910086i	−0.246515	−	0.158426i
$34$	−1.14610	+	7.97129i	−0.196554	+	1.36706i
$35$	−11.0071	+	1.48222i	−1.86054	+	0.250540i
$36$	−0.841254	−	0.540641i	−0.140209	−	0.0901068i
$37$	−0.899700	+	0.779595i	−0.147910	+	0.128165i	−0.725673	−	0.688040i	$-0.758471\pi$
$37$	−0.899700	+	0.779595i	−0.147910	+	0.128165i	0.577763	+	0.816205i	$0.303926\pi$
$38$	−1.03794	−	2.27277i	−0.168376	−	0.368692i
$39$	−0.571424	+	0.367232i	−0.0915011	+	0.0588042i
$40$	−4.02779	−	1.18267i	−0.636850	−	0.186996i
$41$	5.71873	+	4.95531i	0.893115	+	0.773889i	0.974872	−	0.222764i	$-0.0715078\pi$
$41$	5.71873	+	4.95531i	0.893115	+	0.773889i	−0.0817574	+	0.996652i	$0.526053\pi$
$42$	−2.23845	+	1.41044i	−0.345401	+	0.217635i
$43$	−2.74000	−	1.25132i	−0.417846	−	0.190824i	0.195387	−	0.980726i	$-0.437404\pi$
$43$	−2.74000	−	1.25132i	−0.417846	−	0.190824i	−0.613232	+	0.789902i	$0.710131\pi$
$44$	−1.66621	+	0.239565i	−0.251191	+	0.0361158i
$45$	−4.19784			−0.625776
$46$	4.69088	+	0.997826i	0.691632	+	0.147121i
$47$		−	4.94803i		−	0.721744i	−0.932615	−	0.360872i	$-0.882479\pi$
$47$		−	4.94803i		−	0.721744i	0.932615	−	0.360872i	$-0.117521\pi$
$48$	−0.989821	+	0.142315i	−0.142868	+	0.0205414i
$49$	0.872103	+	6.94546i	0.124586	+	0.992209i
$50$	−12.1105	+	3.55598i	−1.71269	+	0.502891i
$51$	6.08625	+	5.27376i	0.852245	+	0.738474i
$52$	−0.191368	+	0.651739i	−0.0265379	+	0.0903799i
$53$	−5.63964	−	8.77545i	−0.774664	−	1.20540i	−0.974239	−	0.225518i	$-0.927593\pi$
$53$	−5.63964	−	8.77545i	−0.774664	−	1.20540i	0.199575	−	0.979882i	$-0.436044\pi$
$54$	−0.909632	+	0.415415i	−0.123785	+	0.0565308i
$55$	−5.34044	+	4.62751i	−0.720104	+	0.623974i
$56$	−0.768070	+	2.53181i	−0.102638	+	0.338327i
$57$	−2.47313	−	0.355582i	−0.327574	−	0.0470980i
$58$	−0.341702	+	2.37659i	−0.0448676	+	0.312061i
$59$	−2.47445	+	3.85033i	−0.322147	+	0.501270i	−0.964123	−	0.265454i	$-0.914478\pi$
$59$	−2.47445	+	3.85033i	−0.322147	+	0.501270i	0.641977	+	0.766724i	$0.278114\pi$
$60$	−3.17251	+	2.74900i	−0.409570	+	0.354894i
$61$	−5.41332	−	11.8535i	−0.693104	−	1.51769i	−0.848137	−	0.529778i	$-0.822275\pi$
$61$	−5.41332	−	11.8535i	−0.693104	−	1.51769i	0.155032	−	0.987909i	$-0.450452\pi$
$62$	2.50611	+	3.89958i	0.318276	+	0.495247i
$63$	−0.0236646	+	2.64565i	−0.00298146	+	0.333320i
$64$	−0.654861	+	0.755750i	−0.0818576	+	0.0944687i
$65$	0.803330	+	2.73589i	0.0996409	+	0.339346i
$66$	−0.699287	+	1.53123i	−0.0860763	+	0.188481i
$67$	−11.3758	+	1.63559i	−1.38977	+	0.199819i	−0.796235	−	0.604987i	$-0.793178\pi$
$67$	−11.3758	+	1.63559i	−1.38977	+	0.199819i	−0.593538	+	0.804806i	$0.702269\pi$
$68$	8.05326			0.976601
$69$	3.37551	−	3.40675i	0.406363	−	0.410125i
$70$	3.03360	+	10.6841i	0.362585	+	1.27699i
$71$	−1.01355	−	7.04940i	−0.120286	−	0.836610i	−0.957231	−	0.289323i	$-0.906570\pi$
$71$	−1.01355	−	7.04940i	−0.120286	−	0.836610i	0.836945	−	0.547287i	$-0.184339\pi$
$72$	−0.415415	+	0.909632i	−0.0489571	+	0.107201i
$73$	3.69944	+	12.5991i	0.432986	+	1.47462i	0.830499	+	0.557020i	$0.188055\pi$
$73$	3.69944	+	12.5991i	0.432986	+	1.47462i	−0.397513	+	0.917597i	$0.630127\pi$
$74$	0.899700	+	0.779595i	0.104588	+	0.0906260i
$75$	−3.55598	+	12.1105i	−0.410609	+	1.39841i
$76$	−2.10192	+	1.35082i	−0.241107	+	0.154950i
$77$	2.88634	+	3.39185i	0.328929	+	0.386537i
$78$	0.444816	+	0.513345i	0.0503655	+	0.0581249i
$79$	4.27094	−	6.64571i	0.480518	−	0.747701i	−0.513361	−	0.858173i	$-0.671600\pi$
$79$	4.27094	−	6.64571i	0.480518	−	0.747701i	0.993879	+	0.110472i	$0.0352362\pi$
$80$	−0.597414	+	4.15511i	−0.0667929	+	0.464555i
$81$	−0.142315	+	0.989821i	−0.0158128	+	0.109980i
$82$	4.09101	−	6.36573i	0.451776	−	0.702978i
$83$	−4.75752	−	5.49047i	−0.522205	−	0.602657i	0.431976	−	0.901885i	$-0.357816\pi$
$83$	−4.75752	−	5.49047i	−0.522205	−	0.602657i	−0.954182	+	0.299228i	$0.903271\pi$
$84$	1.71464	+	2.01494i	0.187083	+	0.219848i
$85$	28.4396	−	18.2770i	3.08471	−	1.98242i
$86$	−0.848637	+	2.89019i	−0.0915108	+	0.311657i
$87$	1.81457	+	1.57234i	0.194543	+	0.168572i
$88$	0.474253	+	1.61516i	0.0505556	+	0.172176i
$89$	−3.25180	+	7.12044i	−0.344690	+	0.754765i	−1.00000		0.000594772i	$-0.999811\pi$
$89$	−3.25180	+	7.12044i	−0.344690	+	0.754765i	0.655310	+	0.755360i	$0.272538\pi$
$90$	0.597414	+	4.15511i	0.0629730	+	0.437987i
$91$	1.72880	−	0.490868i	0.181227	−	0.0514570i
$92$	0.320088	−	4.78514i	0.0333715	−	0.498885i
$93$	4.63544			0.480673
$94$	−4.89767	+	0.704178i	−0.505156	+	0.0726304i
$95$	−4.35709	+	9.54071i	−0.447028	+	0.978856i
$96$	0.281733	+	0.959493i	0.0287542	+	0.0979278i
$97$	1.14392	−	1.32016i	0.116148	−	0.134042i	−0.694698	−	0.719301i	$-0.744462\pi$
$97$	1.14392	−	1.32016i	0.116148	−	0.134042i	0.810846	+	0.585260i	$0.199007\pi$
$98$	6.75065	−	1.85167i	0.681919	−	0.187047i
$99$	0.910086	+	1.41612i	0.0914670	+	0.142325i
$100$	5.24329	+	11.4812i	0.524329	+	1.14812i
$101$	−4.94631	+	4.28600i	−0.492176	+	0.426473i	−0.865259	−	0.501325i	$-0.832846\pi$
$101$	−4.94631	+	4.28600i	−0.492176	+	0.426473i	0.373083	+	0.927798i	$0.378301\pi$
$102$	4.35392	−	6.77483i	0.431102	−	0.670808i
$103$	1.29274	−	8.99118i	0.127377	−	0.885928i	−0.821483	−	0.570232i	$-0.806853\pi$
$103$	1.29274	−	8.99118i	0.127377	−	0.885928i	0.948861	−	0.315695i	$-0.102238\pi$
$104$	0.672340	+	0.0966678i	0.0659283	+	0.00947906i
$105$	10.6281	+	3.22423i	1.03720	+	0.314653i
$106$	−7.88352	+	6.83111i	−0.765715	+	0.663496i
$107$	−3.90688	+	1.78421i	−0.377692	+	0.172486i	−0.595210	−	0.803570i	$-0.702931\pi$
$107$	−3.90688	+	1.78421i	−0.377692	+	0.172486i	0.217518	+	0.976056i	$0.430204\pi$
$108$	0.540641	+	0.841254i	0.0520232	+	0.0809497i
$109$	4.32680	−	14.7357i	0.414432	−	1.41143i	−0.442857	−	0.896592i	$-0.646035\pi$
$109$	4.32680	−	14.7357i	0.414432	−	1.41143i	0.857289	−	0.514835i	$-0.172147\pi$
$110$	5.34044	+	4.62751i	0.509191	+	0.441216i
$111$	1.14225	−	0.335395i	0.108418	−	0.0318343i
$112$	2.61535	+	0.399938i	0.247127	+	0.0377906i
$113$	−4.54873	+	0.654008i	−0.427908	+	0.0615239i	−0.352904	−	0.935659i	$-0.614806\pi$
$113$	−4.54873	+	0.654008i	−0.427908	+	0.0615239i	−0.0750037	+	0.997183i	$0.523897\pi$
$114$			2.49856i			0.234011i
$115$	−9.72960	−	17.6249i	−0.907290	−	1.64353i
$116$	2.40103			0.222930
$117$	0.672340	−	0.0966678i	0.0621578	−	0.00893695i
$118$	4.16329	+	1.90131i	0.383262	+	0.175030i
$119$	−11.3586	−	18.0268i	−1.04124	−	1.65252i
$120$	3.17251	+	2.74900i	0.289609	+	0.250948i
$121$	−7.83555	−	2.30073i	−0.712323	−	0.209157i
$122$	−10.9625	+	7.04515i	−0.992495	+	0.637838i
$123$	−3.14343	−	6.88315i	−0.283433	−	0.620633i
$124$	3.50323	−	3.03557i	0.314599	−	0.272602i
$125$	26.9160	+	17.2979i	2.40744	+	1.54717i
$126$	2.62208	−	0.353091i	0.233594	−	0.0314558i
$127$	−0.547793	+	3.80999i	−0.0486088	+	0.338082i	0.950976	+	0.309265i	$0.100083\pi$
$127$	−0.547793	+	3.80999i	−0.0486088	+	0.338082i	−0.999585	+	0.0288166i	$0.990826\pi$
$128$	0.841254	+	0.540641i	0.0743570	+	0.0477863i
$129$	1.97258	+	2.27647i	0.173676	+	0.200432i
$130$	2.59372	−	1.18451i	0.227484	−	0.103889i
$131$	−0.969357	−	1.50835i	−0.0846931	−	0.131785i	0.796322	−	0.604872i	$-0.206776\pi$
$131$	−0.969357	−	1.50835i	−0.0846931	−	0.131785i	−0.881016	+	0.473087i	$0.843140\pi$
$132$	1.61516	+	0.474253i	0.140582	+	0.0412785i
$133$	5.98838	+	2.79980i	0.519258	+	0.242774i
$134$	3.23789	+	11.0272i	0.279711	+	0.952607i
$135$	3.81849	+	1.74384i	0.328643	+	0.150086i
$136$	−1.14610	−	7.97129i	−0.0982771	−	0.683532i
$137$			17.5032i			1.49540i	0.664037	+	0.747700i	$0.268842\pi$
$137$			17.5032i			1.49540i	−0.664037	+	0.747700i	$0.731158\pi$
$138$	−3.85246	−	2.85632i	−0.327943	−	0.243146i
$139$			10.2425i			0.868758i	0.900730	+	0.434379i	$0.143032\pi$
$139$			10.2425i			0.868758i	−0.900730	+	0.434379i	$0.856968\pi$
$140$	10.1436	−	4.52323i	0.857293	−	0.382283i
$141$	−2.05549	+	4.50089i	−0.173103	+	0.379043i
$142$	−6.83341	+	2.00647i	−0.573447	+	0.168379i
$143$	0.748780	−	0.864138i	0.0626161	−	0.0722629i
$144$	0.959493	+	0.281733i	0.0799577	+	0.0234777i
$145$	8.47909	−	5.44918i	0.704150	−	0.452530i
$146$	11.9444	−	5.45483i	0.988526	−	0.451445i
$147$	2.09196	−	6.68010i	0.172542	−	0.550965i
$148$	0.643619	−	1.00149i	0.0529051	−	0.0823220i
$149$	−15.4672	−	2.22384i	−1.26712	−	0.182184i	−0.524218	−	0.851584i	$-0.675642\pi$
$149$	−15.4672	−	2.22384i	−1.26712	−	0.182184i	−0.742902	+	0.669400i	$0.766551\pi$
$150$	12.4933	+	1.79627i	1.02008	+	0.146665i
$151$	−4.41793	−	2.83923i	−0.359526	−	0.231053i	0.348391	−	0.937349i	$-0.386728\pi$
$151$	−4.41793	−	2.83923i	−0.359526	−	0.231053i	−0.707916	+	0.706296i	$0.750365\pi$
$152$	1.63621	+	1.88828i	0.132714	+	0.153160i
$153$	−3.34544	−	7.32550i	−0.270463	−	0.592232i
$154$	2.94655	−	3.33967i	0.237440	−	0.269118i
$155$	5.48218	−	18.6706i	0.440339	−	1.49966i
$156$	0.444816	−	0.513345i	0.0356138	−	0.0411005i
$157$	−10.7823	+	3.16597i	−0.860522	+	0.252672i	−0.682079	−	0.731278i	$-0.738924\pi$
$157$	−10.7823	+	3.16597i	−0.860522	+	0.252672i	−0.178443	+	0.983950i	$0.557106\pi$
$158$	−7.18588	−	3.28168i	−0.571678	−	0.261077i
$159$	1.48454	+	10.3252i	0.117732	+	0.818843i
$160$	4.19784			0.331868
$161$	−11.1628	+	6.03263i	−0.879749	+	0.475438i
$162$	1.00000			0.0785674
$163$	1.49829	+	10.4209i	0.117355	+	0.816225i	0.960449	+	0.278458i	$0.0898232\pi$
$163$	1.49829	+	10.4209i	0.117355	+	0.816225i	−0.843093	+	0.537768i	$0.819268\pi$
$164$	−6.88315	−	3.14343i	−0.537484	−	0.245461i
$165$	6.78017	−	1.99084i	0.527835	−	0.154986i
$166$	−4.75752	+	5.49047i	−0.369255	+	0.426143i
$167$	5.40929	−	18.4224i	0.418584	−	1.42557i	−0.433022	−	0.901383i	$-0.642553\pi$
$167$	5.40929	−	18.4224i	0.418584	−	1.42557i	0.851606	−	0.524182i	$-0.175629\pi$
$168$	1.75041	−	1.98395i	0.135047	−	0.153065i
$169$	5.20873	+	11.4055i	0.400671	+	0.877348i
$170$	−22.1384	−	25.5491i	−1.69794	−	1.95952i
$171$	2.10192	+	1.35082i	0.160738	+	0.103300i
$172$	2.98155	+	0.428682i	0.227341	+	0.0326867i
$173$	−0.886884	−	0.127515i	−0.0674286	−	0.00969476i	0.108518	−	0.994094i	$-0.465389\pi$
$173$	−0.886884	−	0.127515i	−0.0674286	−	0.00969476i	−0.175947	+	0.984400i	$0.556299\pi$
$174$	1.29809	−	2.01987i	0.0984082	−	0.153126i
$175$	18.3048	−	27.9304i	1.38371	−	2.11134i
$176$	1.53123	−	0.699287i	0.115420	−	0.0527108i
$177$	3.85033	−	2.47445i	0.289408	−	0.185991i
$178$	7.51074	+	2.20535i	0.562954	+	0.165298i
$179$	−10.3986	+	12.0006i	−0.777224	+	0.896965i	−0.996906	−	0.0786068i	$-0.974953\pi$
$179$	−10.3986	+	12.0006i	−0.777224	+	0.896965i	0.219681	+	0.975572i	$0.429498\pi$
$180$	4.02779	−	1.18267i	0.300214	−	0.0881508i
$181$	2.61054	−	5.71629i	0.194040	−	0.424889i	−0.787456	−	0.616371i	$-0.788602\pi$
$181$	2.61054	−	5.71629i	0.194040	−	0.424889i	0.981496	+	0.191482i	$0.0613295\pi$
$182$	−0.731906	−	1.64134i	−0.0542525	−	0.121665i
$183$			13.0311i			0.963287i
$184$	−4.78199	+	0.364166i	−0.352533	+	0.0268467i
$185$		−	4.99741i		−	0.367417i
$186$	−0.659692	−	4.58826i	−0.0483709	−	0.336427i
$187$	−12.3314	−	5.63154i	−0.901758	−	0.411819i
$188$	1.39402	+	4.74760i	0.101669	+	0.346254i
$189$	1.12057	−	2.39673i	0.0815092	−	0.174337i
$190$	10.0637	+	2.95496i	0.730096	+	0.214375i
$191$	−3.98518	−	6.20106i	−0.288357	−	0.448693i	0.666609	−	0.745408i	$-0.267745\pi$
$191$	−3.98518	−	6.20106i	−0.288357	−	0.448693i	−0.954966	+	0.296715i	$0.904109\pi$
$192$	0.909632	−	0.415415i	0.0656470	−	0.0299800i
$193$	−0.222382	−	0.256643i	−0.0160074	−	0.0184735i	0.747689	−	0.664049i	$-0.231163\pi$
$193$	−0.222382	−	0.256643i	−0.0160074	−	0.0184735i	−0.763697	+	0.645575i	$0.776618\pi$
$194$	−1.46952	−	0.944402i	−0.105505	−	0.0678041i
$195$	0.405796	−	2.82237i	0.0290596	−	0.202114i
$196$	−2.79354	−	6.41842i	−0.199539	−	0.458459i
$197$	3.16356	+	2.03309i	0.225394	+	0.144852i	0.648465	−	0.761245i	$-0.275411\pi$
$197$	3.16356	+	2.03309i	0.225394	+	0.144852i	−0.423071	+	0.906097i	$0.639048\pi$
$198$	1.27219	−	1.10236i	0.0904105	−	0.0783411i
$199$	−0.593116	−	1.29874i	−0.0420448	−	0.0920654i	0.887444	−	0.460915i	$-0.152479\pi$
$199$	−0.593116	−	1.29874i	−0.0420448	−	0.0920654i	−0.929489	+	0.368850i	$0.879752\pi$
$200$	10.6181	−	6.82387i	0.750817	−	0.482521i
$201$	11.0272	+	3.23789i	0.777800	+	0.228383i
$202$	4.94631	+	4.28600i	0.348021	+	0.301562i
$203$	−3.38649	−	5.37458i	−0.237685	−	0.377222i
$204$	−7.32550	−	3.34544i	−0.512888	−	0.234228i
$205$	−31.4415	+	4.52061i	−2.19597	+	0.315733i
$206$	−9.08364			−0.632887
$207$	−4.48568	+	1.69666i	−0.311777	+	0.117926i
$208$		−	0.679253i		−	0.0470978i
$209$	4.16313	−	0.598567i	0.287970	−	0.0414038i
$210$	1.67888	−	10.9788i	0.115853	−	0.757609i
$211$	0.607230	−	0.178299i	0.0418035	−	0.0122746i	−0.260764	−	0.965403i	$-0.583974\pi$
$211$	0.607230	−	0.178299i	0.0418035	−	0.0122746i	0.302567	+	0.953128i	$0.402156\pi$
$212$	7.88352	+	6.83111i	0.541442	+	0.469163i
$213$	−2.00647	+	6.83341i	−0.137481	+	0.468217i
$214$	2.32206	+	3.61319i	0.158733	+	0.246993i
$215$	11.5021	−	5.25282i	0.784434	−	0.358239i
$216$	0.755750	−	0.654861i	0.0514222	−	0.0445576i
$217$	−11.7361	−	3.56034i	−0.796695	−	0.241692i
$218$	−15.2015	−	2.18565i	−1.02958	−	0.148031i
$219$	1.86874	−	12.9974i	0.126278	−	0.878281i
$220$	3.82039	−	5.94464i	0.257571	−	0.400788i
$221$	−4.13410	+	3.58222i	−0.278090	+	0.240966i
$222$	−0.494541	−	1.08289i	−0.0331914	−	0.0726790i
$223$	14.3580	+	22.3416i	0.961486	+	1.49610i	0.865617	+	0.500707i	$0.166927\pi$
$223$	14.3580	+	22.3416i	0.961486	+	1.49610i	0.0958694	+	0.995394i	$0.469437\pi$
$224$	0.0236646	−	2.64565i	0.00158116	−	0.176770i
$225$	8.26553	−	9.53893i	0.551036	−	0.635929i
$226$	1.29470	+	4.40935i	0.0861223	+	0.293306i
$227$	8.07509	−	17.6820i	0.535962	−	1.17359i	−0.427072	−	0.904217i	$-0.640455\pi$
$227$	8.07509	−	17.6820i	0.535962	−	1.17359i	0.963035	−	0.269377i	$-0.0868177\pi$
$228$	2.47313	−	0.355582i	0.163787	−	0.0235490i
$229$	25.9850			1.71714			0.858570	−	0.512696i	$-0.171353\pi$
$229$	25.9850			1.71714			0.858570	+	0.512696i	$0.171353\pi$
$230$	−16.0608	+	12.1388i	−1.05902	+	0.800412i
$231$	−1.21648	−	4.28436i	−0.0800388	−	0.281890i
$232$	−0.341702	−	2.37659i	−0.0224338	−	0.156031i
$233$	−2.57195	+	5.63179i	−0.168494	+	0.368951i	−0.974977	−	0.222307i	$-0.928641\pi$
$233$	−2.57195	+	5.63179i	−0.168494	+	0.368951i	0.806483	+	0.591258i	$0.201368\pi$
$234$	−0.191368	−	0.651739i	−0.0125101	−	0.0426055i
$235$	15.6977	+	13.6021i	1.02400	+	0.887305i
$236$	1.28946	−	4.39150i	0.0839367	−	0.285862i
$237$	−6.64571	+	4.27094i	−0.431685	+	0.277427i
$238$	−16.2268	+	13.8085i	−1.05183	+	0.895070i
$239$	19.9259	+	22.9957i	1.28890	+	1.48747i	0.778673	+	0.627429i	$0.215893\pi$
$239$	19.9259	+	22.9957i	1.28890	+	1.48747i	0.510226	+	0.860040i	$0.329562\pi$
$240$	2.26952	−	3.53144i	0.146497	−	0.227954i
$241$	2.56736	−	17.8564i	0.165378	−	1.15023i	−0.722910	−	0.690942i	$-0.757196\pi$
$241$	2.56736	−	17.8564i	0.165378	−	1.15023i	0.888288	−	0.459287i	$-0.151895\pi$
$242$	−1.16219	+	8.08322i	−0.0747085	+	0.519609i
$243$	0.540641	−	0.841254i	0.0346821	−	0.0539664i
$244$	8.53356	+	9.84826i	0.546305	+	0.630470i
$245$	−24.4320	−	16.3263i	−1.56090	−	1.04305i
$246$	−6.36573	+	4.09101i	−0.405864	+	0.260833i
$247$	0.478144	−	1.62841i	0.0304235	−	0.103613i
$248$	−3.50323	−	3.03557i	−0.222455	−	0.192759i
$249$	2.04677	+	6.97065i	0.129709	+	0.441747i
$250$	13.2913	−	29.1038i	0.840613	−	1.84069i
$251$	−0.918544	−	6.38862i	−0.0579780	−	0.403246i	−0.998058	−	0.0622918i	$-0.980159\pi$
$251$	−0.918544	−	6.38862i	−0.0579780	−	0.403246i	0.940080	−	0.340954i	$-0.110750\pi$
$252$	−0.722658	−	2.54515i	−0.0455232	−	0.160329i
$253$	−3.83631	+	7.10329i	−0.241187	+	0.446580i
$254$	3.84916			0.241518
$255$	−33.4621	+	4.81113i	−2.09548	+	0.301285i
$256$	0.415415	−	0.909632i	0.0259634	−	0.0568520i
$257$	−4.07825	−	13.8892i	−0.254394	−	0.866387i	−0.983334	−	0.181809i	$-0.941805\pi$
$257$	−4.07825	−	13.8892i	−0.254394	−	0.866387i	0.728940	−	0.684578i	$-0.240013\pi$
$258$	1.97258	−	2.27647i	0.122807	−	0.141727i
$259$	−3.14957	−	0.0281721i	−0.195705	−	0.00175053i
$260$	−1.54158	−	2.39875i	−0.0956047	−	0.148764i
$261$	−0.997422	−	2.18405i	−0.0617389	−	0.135189i
$262$	−1.35504	+	1.17415i	−0.0837148	+	0.0725393i
$263$	−5.42450	+	8.44069i	−0.334489	+	0.520475i	−0.967234	−	0.253885i	$-0.918292\pi$
$263$	−5.42450	+	8.44069i	−0.334489	+	0.520475i	0.632745	+	0.774360i	$0.281928\pi$
$264$	0.239565	−	1.66621i	0.0147442	−	0.102548i
$265$	43.3436	+	6.23186i	2.66257	+	0.382820i
$266$	1.91907	−	6.32588i	0.117666	−	0.387864i
$267$	5.91588	−	5.12614i	0.362046	−	0.313714i
$268$	10.4542	−	4.77427i	0.638591	−	0.291635i
$269$	8.46756	+	13.1758i	0.516276	+	0.803341i	0.997305	−	0.0733632i	$-0.0233732\pi$
$269$	8.46756	+	13.1758i	0.516276	+	0.803341i	−0.481029	+	0.876705i	$0.659737\pi$
$270$	1.18267	−	4.02779i	0.0719748	−	0.245124i
$271$	7.65631	+	6.63423i	0.465088	+	0.403001i	0.855633	−	0.517583i	$-0.173168\pi$
$271$	7.65631	+	6.63423i	0.465088	+	0.403001i	−0.390545	+	0.920584i	$0.627714\pi$
$272$	−7.72704	+	2.26886i	−0.468521	+	0.137570i
$273$	−1.77648	−	0.271659i	−0.107518	−	0.0164416i
$274$	17.3250	−	2.49097i	1.04664	−	0.150485i
$275$		−	21.2469i		−	1.28124i
$276$	−2.27898	+	4.21974i	−0.137179	+	0.253999i
$277$	1.72961			0.103922			0.0519611	−	0.998649i	$-0.483453\pi$
$277$	1.72961			0.103922			0.0519611	+	0.998649i	$0.483453\pi$
$278$	10.1383	−	1.45766i	0.608052	−	0.0874247i
$279$	−4.21654	−	1.92563i	−0.252438	−	0.115284i
$280$	−5.92078	−	9.39665i	−0.353834	−	0.561558i
$281$	20.8877	+	18.0993i	1.24606	+	1.07971i	0.993699	+	0.112080i	$0.0357513\pi$
$281$	20.8877	+	18.0993i	1.24606	+	1.07971i	0.252357	+	0.967634i	$0.418794\pi$
$282$	4.74760	+	1.39402i	0.282715	+	0.0830128i
$283$	−16.4021	+	10.5410i	−0.975002	+	0.626596i	−0.928111	−	0.372304i	$-0.878568\pi$
$283$	−16.4021	+	10.5410i	−0.975002	+	0.626596i	−0.0468914	+	0.998900i	$0.514931\pi$
$284$	2.95854	+	6.47830i	0.175557	+	0.384416i
$285$	7.92671	−	6.86853i	0.469537	−	0.406857i
$286$	−0.961905	−	0.618179i	−0.0568786	−	0.0365537i
$287$	2.67182	+	19.8412i	0.157713	+	1.17119i
$288$	0.142315	−	0.989821i	0.00838598	−	0.0583258i
$289$	40.2581	+	25.8723i	2.36813	+	1.52190i
$290$	−6.60041	−	7.61728i	−0.387590	−	0.447302i
$291$	−1.58896	+	0.725655i	−0.0931466	+	0.0425386i
$292$	−7.09917	−	11.0465i	−0.415447	−	0.646449i
$293$	−17.0327	−	5.00125i	−0.995061	−	0.292176i	−0.256633	−	0.966509i	$-0.582613\pi$
$293$	−17.0327	−	5.00125i	−0.995061	−	0.292176i	−0.738428	+	0.674333i	$0.764431\pi$
$294$	−6.90982	−	1.11999i	−0.402989	−	0.0653189i
$295$	−5.41294	−	18.4348i	−0.315153	−	1.07331i
$296$	−1.08289	−	0.494541i	−0.0629419	−	0.0287446i
$297$	−0.239565	−	1.66621i	−0.0139010	−	0.0966834i
$298$			15.6262i			0.905203i
$299$	1.96419	+	2.59881i	0.113592	+	0.150293i
$300$		−	12.6218i		−	0.728721i
$301$	−3.24570	−	7.27868i	−0.187079	−	0.419536i
$302$	−2.18159	+	4.77702i	−0.125537	+	0.274887i
$303$	6.27979	−	1.84391i	0.360765	−	0.105930i
$304$	1.63621	−	1.88828i	0.0938429	−	0.108301i
$305$	52.4866	+	15.4115i	3.00538	+	0.882458i
$306$	−6.77483	+	4.35392i	−0.387291	+	0.248897i
$307$	−13.0486	+	5.95910i	−0.744724	+	0.340104i	−0.751376	−	0.659874i	$-0.770610\pi$
$307$	−13.0486	+	5.95910i	−0.744724	+	0.340104i	0.00665260	+	0.999978i	$0.497882\pi$
$308$	−3.72502	−	2.44128i	−0.212253	−	0.139105i
$309$	−4.91099	+	7.64165i	−0.279376	+	0.434718i
$310$	−19.2607	−	2.76928i	−1.09394	−	0.157284i
$311$	−9.60292	−	1.38069i	−0.544532	−	0.0782918i	−0.135441	−	0.990785i	$-0.543245\pi$
$311$	−9.60292	−	1.38069i	−0.544532	−	0.0782918i	−0.409091	+	0.912494i	$0.634154\pi$
$312$	−0.571424	−	0.367232i	−0.0323505	−	0.0207904i
$313$	14.1843	+	16.3695i	0.801743	+	0.925261i	0.998476	−	0.0551962i	$-0.0175784\pi$
$313$	14.1843	+	16.3695i	0.801743	+	0.925261i	−0.196732	+	0.980457i	$0.563033\pi$
$314$	4.66823	+	10.2220i	0.263444	+	0.576861i
$315$	−8.32829	−	7.34795i	−0.469246	−	0.414010i
$316$	−2.22562	+	7.57978i	−0.125201	+	0.426396i
$317$	15.7078	−	18.1278i	0.882240	−	1.01816i	−0.117446	−	0.993079i	$-0.537471\pi$
$317$	15.7078	−	18.1278i	0.882240	−	1.01816i	0.999685	−	0.0250797i	$-0.00798395\pi$
$318$	10.0088	−	2.93886i	0.561268	−	0.164803i
$319$	−3.67651	−	1.67901i	−0.205845	−	0.0940063i
$320$	−0.597414	−	4.15511i	−0.0333965	−	0.232278i
$321$	4.29501			0.239724
$322$	7.55985	+	10.1906i	0.421294	+	0.567901i
$323$	−20.1215			−1.11959
$324$	−0.142315	−	0.989821i	−0.00790638	−	0.0549901i
$325$	−7.79865	−	3.56152i	−0.432591	−	0.197558i
$326$	10.1016	−	2.96609i	0.559474	−	0.164276i
$327$	−10.0572	+	11.6067i	−0.556167	+	0.641851i
$328$	−2.13186	+	7.26045i	−0.117712	+	0.400891i
$329$	8.66110	−	9.81664i	0.477502	−	0.541209i
$330$	−2.93549	−	6.42783i	−0.161594	−	0.353840i
$331$	−10.8889	−	12.5665i	−0.598508	−	0.690715i	0.372971	−	0.927843i	$-0.378339\pi$
$331$	−10.8889	−	12.5665i	−0.598508	−	0.690715i	−0.971478	+	0.237129i	$0.923794\pi$
$332$	6.11165	+	3.92772i	0.335420	+	0.215562i
$333$	−1.17836	−	0.169422i	−0.0645735	−	0.00928427i
$334$	−19.0047	−	2.73246i	−1.03989	−	0.149514i
$335$	26.0831	−	40.5860i	1.42507	−	2.21745i
$336$	−2.21286	−	1.45025i	−0.120722	−	0.0791177i
$337$	−22.0447	+	10.0675i	−1.20085	+	0.548410i	−0.912485	−	0.409111i	$-0.865839\pi$
$337$	−22.0447	+	10.0675i	−1.20085	+	0.548410i	−0.288365	+	0.957521i	$0.593112\pi$
$338$	10.5482	−	6.77889i	0.573744	−	0.368723i
$339$	4.40935	+	1.29470i	0.239483	+	0.0703186i
$340$	−22.1384	+	25.5491i	−1.20062	+	1.38559i
$341$	−7.48697	+	2.19837i	−0.405442	+	0.119049i
$342$	1.03794	−	2.27277i	0.0561253	−	0.122897i
$343$	−10.4272	+	15.3060i	−0.563017	+	0.826445i
$344$		−	3.01221i		−	0.162407i
$345$	1.52871	+	20.0740i	0.0823029	+	1.08075i
$346$			0.896004i			0.0481695i
$347$	0.802065	+	5.57849i	0.0430571	+	0.299469i	0.999959	+	0.00905738i	$0.00288309\pi$
$347$	0.802065	+	5.57849i	0.0430571	+	0.299469i	−0.956902	+	0.290411i	$0.906208\pi$
$348$	−2.18405	−	0.997422i	−0.117077	−	0.0534674i
$349$	7.74347	+	26.3718i	0.414498	+	1.41165i	0.857200	+	0.514983i	$0.172202\pi$
$349$	7.74347	+	26.3718i	0.414498	+	1.41165i	−0.442702	+	0.896669i	$0.645980\pi$
$350$	−30.2511	−	14.1436i	−1.61699	−	0.756007i
$351$	−0.651739	−	0.191368i	−0.0347872	−	0.0102145i
$352$	−0.910086	−	1.41612i	−0.0485077	−	0.0754795i
$353$	24.2893	−	11.0925i	1.29279	−	0.590396i	0.354114	−	0.935202i	$-0.384783\pi$
$353$	24.2893	−	11.0925i	1.29279	−	0.590396i	0.938674	+	0.344806i	$0.112055\pi$
$354$	−2.99723	−	3.45898i	−0.159301	−	0.183843i
$355$	25.1506	+	16.1633i	1.33485	+	0.857858i
$356$	1.11402	−	7.74815i	0.0590427	−	0.410651i
$357$	2.84353	+	21.1163i	0.150496	+	1.11759i
$358$	13.3583	+	8.58485i	0.706008	+	0.453724i
$359$	24.3639	−	21.1115i	1.28588	−	1.11422i	0.298744	−	0.954333i	$-0.403432\pi$
$359$	24.3639	−	21.1115i	1.28588	−	1.11422i	0.987135	−	0.159888i	$-0.0511133\pi$
$360$	−1.74384	−	3.81849i	−0.0919086	−	0.201252i
$361$	−10.7320	+	6.89707i	−0.564845	+	0.363004i
$362$	−6.02963	−	1.77046i	−0.316910	−	0.0930532i
$363$	6.17171	+	5.34782i	0.323931	+	0.280688i
$364$	−1.52048	+	0.958044i	−0.0796946	+	0.0502151i
$365$	−50.1406	−	22.8985i	−2.62448	−	1.19856i
$366$	12.8985	−	1.85452i	0.674214	−	0.0969373i
$367$	−29.3467			−1.53189			−0.765943	−	0.642909i	$-0.777727\pi$
$367$	−29.3467			−1.53189			−0.765943	+	0.642909i	$0.777727\pi$
$368$	1.04101	+	4.68149i	0.0542662	+	0.244039i
$369$			7.56696i			0.393920i
$370$	−4.94655	+	0.711206i	−0.257159	+	0.0369738i
$371$	4.17191	−	27.2817i	0.216595	−	1.41640i
$372$	−4.44767	+	1.30595i	−0.230601	+	0.0677106i
$373$	−6.47034	−	5.60658i	−0.335021	−	0.290298i	0.471061	−	0.882100i	$-0.343871\pi$
$373$	−6.47034	−	5.60658i	−0.335021	−	0.290298i	−0.806083	+	0.591803i	$0.798416\pi$
$374$	−3.81928	+	13.0073i	−0.197490	+	0.672591i
$375$	−17.2979	−	26.9160i	−0.893259	−	1.38994i
$376$	4.50089	−	2.05549i	0.232116	−	0.106004i
$377$	−1.23256	+	1.06802i	−0.0634799	+	0.0550056i
$378$	−2.53181	−	0.768070i	−0.130222	−	0.0395053i
$379$	−17.4805	−	2.51332i	−0.897913	−	0.129100i	−0.322123	−	0.946698i	$-0.604396\pi$
$379$	−17.4805	−	2.51332i	−0.897913	−	0.129100i	−0.575790	+	0.817598i	$0.695305\pi$
$380$	1.49267	−	10.3818i	0.0765726	−	0.532574i
$381$	2.08102	−	3.23812i	0.106614	−	0.165894i
$382$	−5.57079	+	4.82712i	−0.285027	+	0.246977i
$383$	6.18428	+	13.5417i	0.316002	+	0.691947i	0.999269	−	0.0382207i	$-0.0121690\pi$
$383$	6.18428	+	13.5417i	0.316002	+	0.691947i	−0.683267	+	0.730168i	$0.739442\pi$
$384$	−0.540641	−	0.841254i	−0.0275895	−	0.0429300i
$385$	−18.6952	−	0.167224i	−0.952796	−	0.00852251i
$386$	−0.222382	+	0.256643i	−0.0113189	+	0.0130628i
$387$	−0.848637	−	2.89019i	−0.0431386	−	0.146917i
$388$	−0.725655	+	1.58896i	−0.0368396	+	0.0806674i
$389$	29.2599	−	4.20693i	1.48353	−	0.213300i	0.647537	−	0.762034i	$-0.275799\pi$
$389$	29.2599	−	4.20693i	1.48353	−	0.213300i	0.835997	+	0.548734i	$0.184890\pi$
$390$	−2.85139			−0.144386
$391$	23.0026	−	31.0249i	1.16329	−	1.56899i
$392$	−5.95553	+	3.67854i	−0.300800	+	0.185794i
$393$	0.255167	+	1.77473i	0.0128715	+	0.0895232i
$394$	1.56218	−	3.42070i	0.0787014	−	0.172332i
$395$	9.34280	+	31.8186i	0.470087	+	1.60097i
$396$	−1.27219	−	1.10236i	−0.0639299	−	0.0553955i
$397$	−2.29306	+	7.80946i	−0.115086	+	0.391946i	−0.996809	−	0.0798207i	$-0.974565\pi$
$397$	−2.29306	+	7.80946i	−0.115086	+	0.391946i	0.881724	+	0.471766i	$0.156383\pi$
$398$	−1.20111	+	0.771909i	−0.0602064	+	0.0386923i
$399$	−4.28414	−	5.03445i	−0.214475	−	0.252038i
$400$	−8.26553	−	9.53893i	−0.413277	−	0.476947i
$401$	−9.61930	+	14.9679i	−0.480365	+	0.747462i	−0.993862	−	0.110629i	$-0.964713\pi$
$401$	−9.61930	+	14.9679i	−0.480365	+	0.747462i	0.513497	+	0.858091i	$0.328350\pi$
$402$	1.63559	−	11.3758i	0.0815758	−	0.567372i
$403$	−0.448098	+	3.11659i	−0.0223213	+	0.155248i
$404$	3.53844	−	5.50593i	0.176044	−	0.273930i
$405$	−2.74900	−	3.17251i	−0.136599	−	0.157643i
$406$	−4.83793	+	4.11691i	−0.240102	+	0.204319i
$407$	−1.68585	+	1.08343i	−0.0835647	+	0.0537038i
$408$	−2.26886	+	7.72704i	−0.112326	+	0.382546i
$409$	2.42748	+	2.10342i	0.120031	+	0.104008i	0.712808	−	0.701359i	$-0.247423\pi$
$409$	2.42748	+	2.10342i	0.120031	+	0.104008i	−0.592777	+	0.805367i	$0.701968\pi$
$410$	8.94919	+	30.4782i	0.441969	+	1.50521i
$411$	7.27109	−	15.9215i	0.358657	−	0.785349i
$412$	1.29274	+	8.99118i	0.0636886	+	0.442964i
$413$	−11.6489	+	3.30753i	−0.573203	+	0.162753i
$414$	2.31777	+	4.19857i	0.113912	+	0.206348i
$415$	30.4970			1.49704
$416$	−0.672340	+	0.0966678i	−0.0329642	+	0.00473953i
$417$	4.25489	−	9.31691i	0.208363	−	0.456251i
$418$	−1.18495	−	4.03557i	−0.0579578	−	0.197386i
$419$	−7.28187	+	8.40372i	−0.355743	+	0.410549i	−0.905209	−	0.424967i	$-0.860286\pi$
$419$	−7.28187	+	8.40372i	−0.355743	+	0.410549i	0.549466	+	0.835516i	$0.314831\pi$
$420$	−11.1060	−	0.0993400i	−0.541916	−	0.00484730i
$421$	−8.52043	−	13.2580i	−0.415260	−	0.646157i	0.569112	−	0.822260i	$-0.307287\pi$
$421$	−8.52043	−	13.2580i	−0.415260	−	0.646157i	−0.984372	+	0.176103i	$0.943651\pi$
$422$	−0.262902	−	0.575675i	−0.0127979	−	0.0280234i
$423$	3.73947	−	3.24027i	0.181819	−	0.157547i
$424$	5.63964	−	8.77545i	0.273885	−	0.426173i
$425$	−14.4658	+	100.612i	−0.701696	+	4.88041i
$426$	7.04940	+	1.01355i	0.341545	+	0.0491067i
$427$	10.0088	−	32.9923i	0.484360	−	1.59661i
$428$	3.24595	−	2.81263i	0.156899	−	0.135954i
$429$	−1.04009	+	0.474993i	−0.0502160	+	0.0229329i
$430$	−6.83626	−	10.6374i	−0.329674	−	0.512983i
$431$	10.0332	−	34.1698i	0.483280	−	1.64590i	−0.251695	−	0.967807i	$-0.580988\pi$
$431$	10.0332	−	34.1698i	0.483280	−	1.64590i	0.734975	−	0.678094i	$-0.237194\pi$
$432$	−0.755750	−	0.654861i	−0.0363610	−	0.0315070i
$433$	−2.41981	+	0.710521i	−0.116289	+	0.0341455i	−0.339359	−	0.940657i	$-0.610210\pi$
$433$	−2.41981	+	0.710521i	−0.116289	+	0.0341455i	0.223070	+	0.974802i	$0.428392\pi$
$434$	−1.85389	+	12.1233i	−0.0889895	+	0.581936i
$435$	−9.97652	+	1.43441i	−0.478338	+	0.0687746i
$436$			15.3578i			0.735507i
$437$	−0.799759	+	11.9559i	−0.0382577	+	0.571930i
$438$	−13.1310			−0.627425
$439$	−28.0684	+	4.03563i	−1.33963	+	0.192610i	−0.774596	−	0.632456i	$-0.782047\pi$
$439$	−28.0684	+	4.03563i	−1.33963	+	0.192610i	−0.565036	+	0.825066i	$0.691138\pi$
$440$	−6.42783	−	2.93549i	−0.306435	−	0.139944i
$441$	−4.67792	+	5.20740i	−0.222758	+	0.247971i
$442$	4.13410	+	3.58222i	0.196639	+	0.170389i
$443$	−28.5271	−	8.37631i	−1.35536	−	0.397971i	−0.478237	−	0.878231i	$-0.658724\pi$
$443$	−28.5271	−	8.37631i	−1.35536	−	0.397971i	−0.877126	+	0.480260i	$0.840542\pi$
$444$	−1.00149	+	0.643619i	−0.0475286	+	0.0305448i
$445$	−13.6505	−	29.8904i	−0.647096	−	1.41694i
$446$	20.0708	−	17.3914i	0.950379	−	0.823508i
$447$	13.1456	+	8.44817i	0.621766	+	0.399585i
$448$	−2.62208	+	0.353091i	−0.123882	+	0.0166820i
$449$	−4.62534	+	32.1700i	−0.218283	+	1.51819i	0.526089	+	0.850430i	$0.323658\pi$
$449$	−4.62534	+	32.1700i	−0.218283	+	1.51819i	−0.744372	+	0.667765i	$0.767251\pi$
$450$	−10.6181	−	6.82387i	−0.500544	−	0.321680i
$451$	8.34149	+	9.62660i	0.392786	+	0.453299i
$452$	4.18021	−	1.90904i	0.196621	−	0.0897937i
$453$	2.83923	+	4.41793i	0.133399	+	0.207572i
$454$	−18.6512	−	5.47649i	−0.875344	−	0.257024i
$455$	−3.19518	+	6.83403i	−0.149792	+	0.320384i
$456$	−0.703925	−	2.39735i	−0.0329643	−	0.112266i
$457$	9.34680	+	4.26854i	0.437225	+	0.199674i	0.621852	−	0.783135i	$-0.286380\pi$
$457$	9.34680	+	4.26854i	0.437225	+	0.199674i	−0.184627	+	0.982809i	$0.559108\pi$
$458$	−3.69806	−	25.7206i	−0.172799	−	1.20184i
$459$			8.05326i			0.375894i
$460$	14.3010	+	14.1698i	0.666787	+	0.660671i
$461$			9.69457i			0.451521i	0.974183	+	0.225761i	$0.0724867\pi$
$461$			9.69457i			0.451521i	−0.974183	+	0.225761i	$0.927513\pi$
$462$	−4.06763	+	1.81383i	−0.189243	+	0.0843870i
$463$	−15.7499	+	34.4874i	−0.731959	+	1.60277i	0.0643856	+	0.997925i	$0.479491\pi$
$463$	−15.7499	+	34.4874i	−0.731959	+	1.60277i	−0.796345	+	0.604843i	$0.793236\pi$
$464$	−2.30377	+	0.676447i	−0.106950	+	0.0314033i
$465$	−12.7428	+	14.7060i	−0.590934	+	0.681974i
$466$	5.94049	+	1.74429i	0.275188	+	0.0808025i
$467$	−28.9956	+	18.6344i	−1.34176	+	0.862296i	−0.997075	−	0.0764238i	$-0.975650\pi$
$467$	−28.9956	+	18.6344i	−1.34176	+	0.862296i	−0.344683	+	0.938719i	$0.612013\pi$
$468$	−0.617871	+	0.282172i	−0.0285611	+	0.0130434i
$469$	−25.4319	−	16.6674i	−1.17434	−	0.769629i
$470$	11.2297	−	17.4737i	0.517986	−	0.806001i
$471$	11.1231	+	1.59926i	0.512527	+	0.0736902i
$472$	−4.53031	−	0.651360i	−0.208524	−	0.0299813i
$473$	−4.26565	−	2.74137i	−0.196135	−	0.126048i
$474$	5.17325	+	5.97025i	0.237615	+	0.274223i
$475$	−13.1007	−	28.6865i	−0.601100	−	1.31623i
$476$	15.9772	+	14.0965i	0.732316	+	0.646113i
$477$	2.93886	−	10.0088i	0.134561	−	0.458274i
$478$	19.9259	−	22.9957i	0.911390	−	1.05180i
$479$	6.60479	−	1.93934i	0.301781	−	0.0886108i	−0.127337	−	0.991860i	$-0.540643\pi$
$479$	6.60479	−	1.93934i	0.301781	−	0.0886108i	0.429117	+	0.903249i	$0.358825\pi$
$480$	−3.81849	−	1.74384i	−0.174289	−	0.0795952i
$481$	0.115081	+	0.800403i	0.00524722	+	0.0364952i
$482$	−18.0400			−0.821699
$483$	12.6601	−	0.850290i	0.576052	−	0.0386895i
$484$	8.16635			0.371198
$485$	1.04357	+	7.25822i	0.0473863	+	0.329579i
$486$	−0.909632	−	0.415415i	−0.0412617	−	0.0188436i
$487$	−7.03638	+	2.06607i	−0.318849	+	0.0936225i	−0.437241	−	0.899344i	$-0.644044\pi$
$487$	−7.03638	+	2.06607i	−0.318849	+	0.0936225i	0.118392	+	0.992967i	$0.462226\pi$
$488$	8.53356	−	9.84826i	0.386296	−	0.445810i
$489$	2.96609	−	10.1016i	0.134131	−	0.456809i
$490$	−12.6831	+	26.5068i	−0.572964	+	1.19745i
$491$	−0.532039	−	1.16500i	−0.0240106	−	0.0525758i	0.897247	−	0.441529i	$-0.145564\pi$
$491$	−0.532039	−	1.16500i	−0.0240106	−	0.0525758i	−0.921257	+	0.388954i	$0.872837\pi$
$492$	4.95531	+	5.71873i	0.223402	+	0.257820i
$493$	16.2665	+	10.4539i	0.732608	+	0.470819i
$494$	−1.67988	−	0.241530i	−0.0755814	−	0.0108670i
$495$	−6.99448	−	1.00565i	−0.314379	−	0.0452008i
$496$	−2.50611	+	3.89958i	−0.112528	+	0.175096i
$497$	10.3285	−	15.7598i	0.463298	−	0.706923i
$498$	6.60841	−	3.01796i	0.296130	−	0.135238i
$499$	−34.0846	+	21.9048i	−1.52584	+	0.980595i	−0.535101	+	0.844788i	$0.679726\pi$
$499$	−34.0846	+	21.9048i	−1.52584	+	0.980595i	−0.990735	+	0.135807i	$0.956637\pi$
$500$	−30.6991	−	9.01407i	−1.37291	−	0.403122i
$501$	−12.5734	+	14.5105i	−0.561738	+	0.648280i
$502$	−6.19287	+	1.81839i	−0.276401	+	0.0811587i
$503$	−5.07150	+	11.1050i	−0.226127	+	0.495149i	−0.988356	−	0.152158i	$-0.951378\pi$
$503$	−5.07150	+	11.1050i	−0.226127	+	0.495149i	0.762229	+	0.647307i	$0.224105\pi$
$504$	−2.41639	+	1.07751i	−0.107635	+	0.0479963i
$505$		−	27.4744i		−	1.22260i
$506$	7.57695	+	2.78636i	0.336837	+	0.123869i
$507$		−	12.5386i		−	0.556859i
$508$	−0.547793	−	3.80999i	−0.0243044	−	0.169041i
$509$	−3.66654	−	1.67445i	−0.162517	−	0.0742188i	0.332496	−	0.943105i	$-0.392109\pi$
$509$	−3.66654	−	1.67445i	−0.162517	−	0.0742188i	−0.495012	+	0.868886i	$0.664837\pi$
$510$	9.52432	+	32.4369i	0.421744	+	1.43633i
$511$	−14.7142	+	31.4716i	−0.650918	+	1.39222i
$512$	−0.959493	−	0.281733i	−0.0424040	−	0.0124509i
$513$	−1.35082	−	2.10192i	−0.0596403	−	0.0928021i
$514$	−13.1675	+	6.01338i	−0.580792	+	0.265239i
$515$	24.9709	+	28.8180i	1.10035	+	1.26987i
$516$	−2.53403	−	1.62852i	−0.111554	−	0.0716917i
$517$	1.18538	−	8.24447i	0.0521328	−	0.362591i
$518$	0.420346	+	3.12152i	0.0184689	+	0.137152i
$519$	0.753767	+	0.484417i	0.0330867	+	0.0212635i
$520$	−2.15494	+	1.86727i	−0.0945004	+	0.0818850i
$521$	−3.01035	−	6.59176i	−0.131886	−	0.288790i	0.832155	−	0.554543i	$-0.187107\pi$
$521$	−3.01035	−	6.59176i	−0.131886	−	0.288790i	−0.964041	+	0.265753i	$0.914380\pi$
$522$	−2.01987	+	1.29809i	−0.0884074	+	0.0568160i
$523$	−32.2675	−	9.47459i	−1.41096	−	0.414295i	−0.514526	−	0.857474i	$-0.672032\pi$
$523$	−32.2675	−	9.47459i	−1.41096	−	0.414295i	−0.896433	+	0.443179i	$0.853850\pi$
$524$	1.35504	+	1.17415i	0.0591953	+	0.0512930i
$525$	−28.2533	+	17.8023i	−1.23308	+	0.776955i
$526$	9.12676	+	4.16805i	0.397946	+	0.181736i
$527$	36.9504	−	5.31267i	1.60958	−	0.231423i
$528$	−1.68335			−0.0732582
$529$	−17.5203	−	14.9010i	−0.761752	−	0.647869i
$530$		−	43.7893i		−	1.90208i
$531$	−4.53031	+	0.651360i	−0.196599	+	0.0282666i
$532$	−6.53460	−	0.999269i	−0.283311	−	0.0433238i
$533$	4.93168	−	1.44807i	0.213615	−	0.0627230i
$534$	−5.91588	−	5.12614i	−0.256005	−	0.221830i
$535$	5.07956	−	17.2994i	0.219609	−	0.747918i
$536$	−6.21346	−	9.66833i	−0.268380	−	0.417608i
$537$	14.4441	−	6.59639i	0.623308	−	0.284655i
$538$	11.8366	−	10.2565i	0.510313	−	0.442188i
$539$	−0.210782	+	11.7815i	−0.00907903	+	0.507467i
$540$	−4.15511	−	0.597414i	−0.178807	−	0.0257086i
$541$	−4.41898	+	30.7347i	−0.189987	+	1.32139i	0.642048	+	0.766664i	$0.278085\pi$
$541$	−4.41898	+	30.7347i	−0.189987	+	1.32139i	−0.832035	+	0.554723i	$0.812824\pi$
$542$	5.47710	−	8.52253i	0.235262	−	0.366074i
$543$	−4.74927	+	4.11526i	−0.203811	+	0.176603i
$544$	3.34544	+	7.32550i	0.143435	+	0.314078i
$545$	34.8549	+	54.2353i	1.49302	+	2.32319i
$546$	−0.0160742	+	1.79706i	−0.000687914	+	0.0769072i
$547$	30.4999	−	35.1988i	1.30408	−	1.50499i	0.581992	−	0.813194i	$-0.302273\pi$
$547$	30.4999	−	35.1988i	1.30408	−	1.50499i	0.722091	−	0.691798i	$-0.243181\pi$
$548$	−4.93122	−	16.7942i	−0.210651	−	0.717413i
$549$	5.41332	−	11.8535i	0.231035	−	0.505896i
$550$	−21.0306	+	3.02375i	−0.896749	+	0.128933i
$551$	−5.99910			−0.255570
$552$	4.50113	+	1.65525i	0.191581	+	0.0704522i
$553$	20.1061	−	5.70884i	0.854997	−	0.242764i
$554$	−0.246149	−	1.71201i	−0.0104579	−	0.0727361i
$555$	−2.07600	+	4.54581i	−0.0881213	+	0.192959i
$556$	−2.88565	−	9.82762i	−0.122379	−	0.416784i
$557$	−4.04560	−	3.50553i	−0.171418	−	0.148534i	0.564927	−	0.825141i	$-0.308904\pi$
$557$	−4.04560	−	3.50553i	−0.171418	−	0.148534i	−0.736345	+	0.676607i	$0.763450\pi$
$558$	−1.30595	+	4.44767i	−0.0552854	+	0.188285i
$559$	−1.72125	+	1.10618i	−0.0728010	+	0.0467864i
$560$	−8.45840	+	7.19780i	−0.357432	+	0.304162i
$561$	8.87757	+	10.2453i	0.374811	+	0.432555i
$562$	14.9425	−	23.2509i	0.630309	−	0.980780i
$563$	−4.34906	+	30.2484i	−0.183291	+	1.27482i	0.665624	+	0.746287i	$0.268165\pi$
$563$	−4.34906	+	30.2484i	−0.183291	+	1.27482i	−0.848915	+	0.528529i	$0.822744\pi$
$564$	0.704178	−	4.89767i	0.0296512	−	0.206229i
$565$	10.4296	−	16.2288i	0.438776	−	0.682749i
$566$	12.7679	+	14.7350i	0.536677	+	0.619358i
$567$	−2.01494	+	1.71464i	−0.0846196	+	0.0720083i
$568$	5.99132	−	3.85039i	0.251390	−	0.161559i
$569$	−2.86724	+	9.76493i	−0.120201	+	0.409367i	−0.997507	−	0.0705639i	$-0.977520\pi$
$569$	−2.86724	+	9.76493i	−0.120201	+	0.409367i	0.877306	+	0.479931i	$0.159338\pi$
$570$	−7.92671	−	6.86853i	−0.332013	−	0.287691i
$571$	−0.0389780	−	0.132747i	−0.00163118	−	0.00555528i	0.958673	−	0.284509i	$-0.0918306\pi$
$571$	−0.0389780	−	0.132747i	−0.00163118	−	0.00555528i	−0.960305	+	0.278954i	$0.910012\pi$
$572$	−0.474993	+	1.04009i	−0.0198605	+	0.0434884i
$573$	1.04903	+	7.29619i	0.0438240	+	0.304803i
$574$	19.2590	−	5.46833i	0.803856	−	0.228244i
$575$	59.2074	+	12.5944i	2.46912	+	0.525222i
$576$	−1.00000			−0.0416667
$577$	−35.0599	+	5.04085i	−1.45956	+	0.209853i	−0.825927	−	0.563778i	$-0.809348\pi$
$577$	−35.0599	+	5.04085i	−1.45956	+	0.209853i	−0.633636	+	0.773631i	$0.718438\pi$
$578$	19.8797	−	43.5304i	0.826885	−	1.81063i
$579$	0.0956726	+	0.325831i	0.00397602	+	0.0135411i
$580$	−6.60041	+	7.61728i	−0.274067	+	0.316290i
$581$	0.171922	−	19.2204i	0.00713251	−	0.797398i
$582$	0.944402	+	1.46952i	0.0391467	+	0.0609135i
$583$	−7.29454	−	15.9728i	−0.302109	−	0.661526i
$584$	−9.92377	+	8.59899i	−0.410648	+	0.355829i
$585$	−1.54158	+	2.39875i	−0.0637365	+	0.0991759i
$586$	−2.52634	+	17.5711i	−0.104362	+	0.725855i
$587$	−18.2999	−	2.63113i	−0.755318	−	0.108598i	−0.246110	−	0.969242i	$-0.579153\pi$
$587$	−18.2999	−	2.63113i	−0.755318	−	0.108598i	−0.509208	+	0.860643i	$0.670062\pi$
$588$	−0.125216	+	6.99888i	−0.00516383	+	0.288629i
$589$	−8.75302	+	7.58454i	−0.360662	+	0.312515i
$590$	−17.4768	+	7.98138i	−0.719508	+	0.328588i
$591$	−2.03309	−	3.16356i	−0.0836303	−	0.130131i
$592$	−0.335395	+	1.14225i	−0.0137847	+	0.0469462i
$593$	21.2615	+	18.4232i	0.873106	+	0.756551i	0.971109	−	0.238635i	$-0.0767001\pi$
$593$	21.2615	+	18.4232i	0.873106	+	0.756551i	−0.0980032	+	0.995186i	$0.531246\pi$
$594$	−1.61516	+	0.474253i	−0.0662708	+	0.0194589i
$595$	88.4151	+	13.5204i	3.62467	+	0.554283i
$596$	15.4672	−	2.22384i	0.633560	−	0.0910922i
$597$			1.42777i			0.0584346i
$598$	2.29282	−	2.31405i	0.0937605	−	0.0946285i
$599$	−11.0109			−0.449893			−0.224946	−	0.974371i	$-0.572221\pi$
$599$	−11.0109			−0.449893			−0.224946	+	0.974371i	$0.572221\pi$
$600$	−12.4933	+	1.79627i	−0.510039	+	0.0733325i
$601$	4.88971	+	2.23305i	0.199455	+	0.0910882i	0.512639	−	0.858605i	$-0.328668\pi$
$601$	4.88971	+	2.23305i	0.199455	+	0.0910882i	−0.313183	+	0.949693i	$0.601395\pi$
$602$	−6.74268	+	4.24852i	−0.274811	+	0.173157i
$603$	−8.68565	−	7.52616i	−0.353707	−	0.306489i
$604$	5.03887	+	1.47955i	0.205029	+	0.0602019i
$605$	28.8390	−	18.5337i	1.17247	−	0.753502i
$606$	−2.71885	−	5.95346i	−0.110446	−	0.241843i
$607$	−10.4381	+	9.04463i	−0.423668	+	0.367110i	−0.840443	−	0.541899i	$-0.817705\pi$
$607$	−10.4381	+	9.04463i	−0.423668	+	0.367110i	0.416776	+	0.909009i	$0.363160\pi$
$608$	−2.10192	−	1.35082i	−0.0852441	−	0.0547831i
$609$	0.847780	+	6.29569i	0.0343538	+	0.255114i
$610$	7.78497	−	54.1457i	0.315204	−	2.19229i
$611$	−2.82742	−	1.81708i	−0.114385	−	0.0735110i
$612$	5.27376	+	6.08625i	0.213179	+	0.246022i
$613$	34.7202	−	15.8562i	1.40233	−	0.640425i	0.436528	−	0.899691i	$-0.356208\pi$
$613$	34.7202	−	15.8562i	1.40233	−	0.640425i	0.965806	+	0.259266i	$0.0834807\pi$
$614$	7.75546	+	12.0677i	0.312985	+	0.487014i
$615$	30.4782	+	8.94919i	1.22900	+	0.360866i
$616$	−1.88630	+	4.03453i	−0.0760013	+	0.162556i
$617$	−9.51827	−	32.4163i	−0.383191	−	1.30503i	−0.895052	−	0.445961i	$-0.852862\pi$
$617$	−9.51827	−	32.4163i	−0.383191	−	1.30503i	0.511861	−	0.859068i	$-0.328956\pi$
$618$	8.26277	+	3.77348i	0.332377	+	0.151792i
$619$	3.47733	+	24.1853i	0.139766	+	0.972091i	0.932151	+	0.362070i	$0.117930\pi$
$619$	3.47733	+	24.1853i	0.139766	+	0.972091i	−0.792385	+	0.610021i	$0.791161\pi$
$620$			19.4588i			0.781484i
$621$	4.78514	+	0.320088i	0.192021	+	0.0128447i
$622$			9.70167i			0.389002i
$623$	−18.9151	+	8.43460i	−0.757818	+	0.337925i
$624$	−0.282172	+	0.617871i	−0.0112959	+	0.0247346i
$625$	−68.3171	+	20.0597i	−2.73268	+	0.802388i
$626$	14.1843	−	16.3695i	0.566918	−	0.654258i
$627$	−4.03557	−	1.18495i	−0.161165	−	0.0473223i
$628$	9.45360	−	6.07546i	0.377240	−	0.242437i
$629$	8.72082	−	3.98266i	0.347722	−	0.158799i
$630$	−6.08792	+	9.28924i	−0.242548	+	0.370092i
$631$	−18.8275	+	29.2962i	−0.749512	+	1.16626i	0.231598	+	0.972812i	$0.425605\pi$
$631$	−18.8275	+	29.2962i	−0.749512	+	1.16626i	−0.981110	+	0.193452i	$0.938032\pi$
$632$	7.81936	+	1.12425i	0.311038	+	0.0447205i
$633$	−0.626424	−	0.0900662i	−0.0248981	−	0.00357981i
$634$	−20.1787	−	12.9681i	−0.801400	−	0.515029i
$635$	−10.5813	−	12.2115i	−0.419908	−	0.484599i
$636$	−4.33336	−	9.48873i	−0.171829	−	0.376253i
$637$	4.28907	+	2.05226i	0.169939	+	0.0813133i
$638$	−1.13869	+	3.87804i	−0.0450814	+	0.153533i
$639$	4.66385	−	5.38237i	0.184499	−	0.212923i
$640$	−4.02779	+	1.18267i	−0.159213	+	0.0467490i
$641$	29.3608	+	13.4086i	1.15968	+	0.529610i	0.899917	−	0.436062i	$-0.143627\pi$
$641$	29.3608	+	13.4086i	1.15968	+	0.529610i	0.259766	+	0.965671i	$0.416354\pi$
$642$	−0.611243	−	4.25129i	−0.0241239	−	0.167785i
$643$	−1.63850			−0.0646163			−0.0323082	−	0.999478i	$-0.510286\pi$
$643$	−1.63850			−0.0646163			−0.0323082	+	0.999478i	$0.510286\pi$
$644$	9.01101	−	8.93318i	0.355084	−	0.352017i
$645$	−12.6447			−0.497886
$646$	2.86359	+	19.9167i	0.112667	+	0.783613i
$647$	−26.5503	−	12.1251i	−1.04380	−	0.476687i	−0.181662	−	0.983361i	$-0.558148\pi$
$647$	−26.5503	−	12.1251i	−1.04380	−	0.476687i	−0.862138	+	0.506674i	$0.830875\pi$
$648$	−0.959493	+	0.281733i	−0.0376924	+	0.0110675i
$649$	−5.04537	+	5.82267i	−0.198048	+	0.228560i
$650$	−2.41541	+	8.22613i	−0.0947402	+	0.322655i
$651$	9.19647	+	8.11393i	0.360438	+	0.318010i
$652$	−4.37350	−	9.57663i	−0.171280	−	0.375050i
$653$	7.63546	+	8.81179i	0.298799	+	0.344832i	0.885219	−	0.465175i	$-0.154009\pi$
$653$	7.63546	+	8.81179i	0.298799	+	0.344832i	−0.586420	+	0.810007i	$0.699463\pi$
$654$	12.9198	+	8.30307i	0.505205	+	0.324676i
$655$	7.45002	+	1.07115i	0.291096	+	0.0418533i
$656$	7.48994	+	1.07689i	0.292433	+	0.0420455i
$657$	−7.09917	+	11.0465i	−0.276965	+	0.430966i
$658$	−10.9493	−	7.17589i	−0.426849	−	0.279745i
$659$	−34.5414	+	15.7745i	−1.34554	+	0.614488i	−0.952361	−	0.304974i	$-0.901352\pi$
$659$	−34.5414	+	15.7745i	−1.34554	+	0.614488i	−0.393180	+	0.919462i	$0.628625\pi$
$660$	−5.94464	+	3.82039i	−0.231395	+	0.148708i
$661$	7.54410	+	2.21515i	0.293432	+	0.0861593i	0.425135	−	0.905130i	$-0.360227\pi$
$661$	7.54410	+	2.21515i	0.293432	+	0.0861593i	−0.131704	+	0.991289i	$0.542045\pi$
$662$	−10.8889	+	12.5665i	−0.423209	+	0.488409i
$663$	5.24862	−	1.54113i	0.203840	−	0.0598527i
$664$	3.01796	−	6.60841i	0.117120	−	0.256456i
$665$	−25.3444	+	11.3016i	−0.982815	+	0.438255i
$666$			1.19047i			0.0461299i
$667$	6.85809	−	9.24986i	0.265546	−	0.358156i
$668$			19.2001i			0.742874i
$669$	−3.77952	−	26.2871i	−0.146125	−	1.01632i
$670$	−43.8849	−	20.0416i	−1.69542	−	0.774274i
$671$	−6.18005	−	21.0473i	−0.238578	−	0.812522i
$672$	−1.12057	+	2.39673i	−0.0432268	+	0.0924560i
$673$	−31.2930	−	9.18847i	−1.20626	−	0.354189i	−0.384016	−	0.923327i	$-0.625459\pi$
$673$	−31.2930	−	9.18847i	−1.20626	−	0.354189i	−0.822243	+	0.569137i	$0.807277\pi$
$674$	13.1023	+	20.3875i	0.504681	+	0.785298i
$675$	−11.4812	+	5.24329i	−0.441912	+	0.201814i
$676$	−8.21105	−	9.47605i	−0.315809	−	0.364464i
$677$	−28.4544	−	18.2866i	−1.09359	−	0.702810i	−0.135935	−	0.990718i	$-0.543404\pi$
$677$	−28.4544	−	18.2866i	−1.09359	−	0.702810i	−0.957658	+	0.287908i	$0.907040\pi$
$678$	0.654008	−	4.54873i	0.0251170	−	0.174693i
$679$	4.58031	−	0.616786i	0.175776	−	0.0236701i
$680$	28.4396	+	18.2770i	1.09061	+	0.700892i
$681$	−14.6907	+	12.7296i	−0.562950	+	0.487799i
$682$	3.24150	+	7.09790i	0.124124	+	0.271793i
$683$	−27.3223	+	17.5590i	−1.04546	+	0.671875i	−0.946331	−	0.323200i	$-0.895241\pi$
$683$	−27.3223	+	17.5590i	−1.04546	+	0.671875i	−0.0991273	+	0.995075i	$0.531605\pi$
$684$	−2.39735	−	0.703925i	−0.0916649	−	0.0269152i
$685$	−55.5291	−	48.1163i	−2.12166	−	1.83843i
$686$	16.6341	+	8.14282i	0.635094	+	0.310894i
$687$	−23.6368	−	10.7946i	−0.901801	−	0.411839i
$688$	−2.98155	+	0.428682i	−0.113670	+	0.0163433i
$689$	−7.08556			−0.269938
$690$	19.6521	−	4.36997i	0.748143	−	0.166362i
$691$			16.2251i			0.617232i	0.951187	+	0.308616i	$0.0998659\pi$
$691$			16.2251i			0.617232i	−0.951187	+	0.308616i	$0.900134\pi$
$692$	0.886884	−	0.127515i	0.0337143	−	0.00484738i
$693$	−0.673235	+	4.40254i	−0.0255741	+	0.167239i
$694$	5.40756	−	1.58780i	0.205268	−	0.0602722i
$695$	−32.4945	−	28.1566i	−1.23259	−	1.06804i
$696$	−0.676447	+	2.30377i	−0.0256407	+	0.0873241i
$697$	−32.9459	−	51.2649i	−1.24792	−	1.94180i
$698$	25.0014	−	11.4178i	0.946317	−	0.432169i
$699$	4.67906	−	4.05443i	0.176978	−	0.153352i
$700$	−9.69445	+	31.9561i	−0.366416	+	1.20783i
$701$	23.0637	+	3.31606i	0.871105	+	0.125246i	0.563348	−	0.826219i	$-0.309513\pi$
$701$	23.0637	+	3.31606i	0.871105	+	0.125246i	0.307756	+	0.951465i	$0.400422\pi$
$702$	−0.0966678	+	0.672340i	−0.00364849	+	0.0253758i
$703$	−1.60812	+	2.50228i	−0.0606514	+	0.0943754i
$704$	−1.27219	+	1.10236i	−0.0479474	+	0.0415467i
$705$	−8.62859	−	18.8940i	−0.324972	−	0.711588i
$706$	−14.4364	−	22.4634i	−0.543320	−	0.845422i
$707$	−17.3155	−	0.154883i	−0.651217	−	0.00582496i
$708$	−2.99723	+	3.45898i	−0.112643	+	0.129997i
$709$	−3.35011	−	11.4094i	−0.125816	−	0.428490i	0.872360	−	0.488864i	$-0.162589\pi$
$709$	−3.35011	−	11.4094i	−0.125816	−	0.428490i	−0.998176	+	0.0603744i	$0.980771\pi$
$710$	12.4195	−	27.1948i	0.466094	−	1.02060i
$711$	7.81936	−	1.12425i	0.293249	−	0.0421628i
$712$	−7.82783			−0.293360
$713$	−1.68807	−	22.1666i	−0.0632187	−	0.830146i
$714$	20.4967	−	5.81975i	0.767070	−	0.217799i
$715$	0.683094	+	4.75103i	0.0255463	+	0.177678i
$716$	6.59639	−	14.4441i	0.246519	−	0.539800i
$717$	−8.57247	−	29.1952i	−0.320145	−	1.09031i
$718$	−24.3639	−	21.1115i	−0.909254	−	0.787873i
$719$	7.40788	−	25.2289i	0.276267	−	0.940881i	−0.698115	−	0.715985i	$-0.745978\pi$
$719$	7.40788	−	25.2289i	0.276267	−	0.940881i	0.974383	−	0.224895i	$-0.0722040\pi$
$720$	−3.53144	+	2.26952i	−0.131609	+	0.0845801i
$721$	18.3030	−	15.5752i	0.681640	−	0.580052i
$722$	8.35419	+	9.64125i	0.310911	+	0.358810i
$723$	−9.75315	+	15.1762i	−0.362724	+	0.564409i
$724$	−0.894332	+	6.22022i	−0.0332376	+	0.231173i
$725$	−4.31290	+	29.9969i	−0.160177	+	1.11406i
$726$	4.41506	−	6.86997i	0.163858	−	0.254968i
$727$	6.74603	+	7.78534i	0.250197	+	0.288742i	0.866930	−	0.498430i	$-0.166090\pi$
$727$	6.74603	+	7.78534i	0.250197	+	0.288742i	−0.616734	+	0.787172i	$0.711544\pi$
$728$	1.16468	+	1.36866i	0.0431659	+	0.0507258i
$729$	−0.841254	+	0.540641i	−0.0311575	+	0.0200237i
$730$	−15.5296	+	52.8891i	−0.574777	+	1.95751i
$731$	18.3330	+	15.8857i	0.678071	+	0.587552i
$732$	−3.67129	−	12.5033i	−0.135695	−	0.462134i
$733$	−12.1147	+	26.5276i	−0.447468	+	0.979819i	0.542699	+	0.839928i	$0.317403\pi$
$733$	−12.1147	+	26.5276i	−0.447468	+	0.979819i	−0.990167	+	0.139891i	$0.955325\pi$
$734$	4.17647	+	29.0480i	0.154156	+	1.07218i
$735$	15.4419	+	25.0003i	0.569583	+	0.922151i
$736$	4.48568	−	1.69666i	0.165345	−	0.0625396i
$737$	−19.3463			−0.712630
$738$	7.48994	−	1.07689i	0.275708	−	0.0396409i
$739$	4.59288	−	10.0570i	0.168952	−	0.369953i	−0.806150	−	0.591712i	$-0.798452\pi$
$739$	4.59288	−	10.0570i	0.168952	−	0.369953i	0.975102	+	0.221759i	$0.0711797\pi$
$740$	1.40793	+	4.79498i	0.0517567	+	0.176267i
$741$	−1.11140	+	1.28262i	−0.0408283	+	0.0471183i
$742$	−27.5978	−	0.246855i	−1.01315	−	0.00906232i
$743$	14.5292	+	22.6079i	0.533026	+	0.829404i	0.998448	−	0.0556844i	$-0.0177341\pi$
$743$	14.5292	+	22.6079i	0.533026	+	0.829404i	−0.465423	+	0.885088i	$0.654098\pi$
$744$	1.92563	+	4.21654i	0.0705970	+	0.154586i
$745$	49.5744	−	42.9564i	1.81626	−	1.57380i
$746$	−4.62869	+	7.20238i	−0.169468	+	0.263698i
$747$	1.03391	−	7.19098i	0.0378287	−	0.263104i
$748$	13.4184	+	1.92928i	0.490626	+	0.0705414i
$749$	−10.8741	−	3.29887i	−0.397333	−	0.120538i
$750$	−24.1803	+	20.9524i	−0.882940	+	0.765072i
$751$	23.4276	−	10.6990i	0.854887	−	0.390414i	0.0607503	−	0.998153i	$-0.480651\pi$
$751$	23.4276	−	10.6990i	0.854887	−	0.390414i	0.794137	+	0.607739i	$0.207923\pi$
$752$	−2.67511	−	4.16255i	−0.0975511	−	0.151793i
$753$	−1.81839	+	6.19287i	−0.0662658	+	0.225681i
$754$	1.23256	+	1.06802i	0.0448870	+	0.0388948i
$755$	21.1524	−	6.21089i	0.769813	−	0.226037i
$756$	−0.399938	+	2.61535i	−0.0145456	+	0.0951193i
$757$	8.19794	−	1.17869i	0.297959	−	0.0428401i	0.00828599	−	0.999966i	$-0.497362\pi$
$757$	8.19794	−	1.17869i	0.297959	−	0.0428401i	0.289673	+	0.957126i	$0.406453\pi$
$758$			17.6602i			0.641449i
$759$	6.44045	−	4.86772i	0.233773	−	0.176687i
$760$	−10.4885			−0.380459
$761$	21.8186	−	3.13705i	0.790925	−	0.113718i	0.264999	−	0.964249i	$-0.414628\pi$
$761$	21.8186	−	3.13705i	0.790925	−	0.113718i	0.525925	+	0.850531i	$0.323719\pi$
$762$	−3.50132	−	1.59900i	−0.126840	−	0.0579257i
$763$	34.3778	−	21.6612i	1.24456	−	0.784190i
$764$	5.57079	+	4.82712i	0.201544	+	0.174639i
$765$	32.4369	+	9.52432i	1.17276	+	0.344352i
$766$	12.5237	−	8.04851i	0.452501	−	0.290805i
$767$	1.29147	+	2.82793i	0.0466323	+	0.102111i
$768$	−0.755750	+	0.654861i	−0.0272708	+	0.0236303i
$769$	32.9667	+	21.1864i	1.18881	+	0.764003i	0.976986	−	0.213305i	$-0.0684227\pi$
$769$	32.9667	+	21.1864i	1.18881	+	0.764003i	0.211826	+	0.977307i	$0.432059\pi$
$770$	2.49508	+	18.5287i	0.0899166	+	0.667729i
$771$	−2.06009	+	14.3283i	−0.0741924	+	0.516020i
$772$	0.285679	+	0.183594i	0.0102818	+	0.00660771i
$773$	−32.4146	−	37.4084i	−1.16587	−	1.34549i	−0.927281	−	0.374367i	$-0.877860\pi$
$773$	−32.4146	−	37.4084i	−1.16587	−	1.34549i	−0.238590	−	0.971120i	$-0.576685\pi$
$774$	−2.74000	+	1.25132i	−0.0984872	+	0.0449776i
$775$	31.6316	+	49.2198i	1.13624	+	1.76803i
$776$	1.67606	+	0.492136i	0.0601671	+	0.0176666i
$777$	2.85325	+	1.33401i	0.102360	+	0.0478572i
$778$	−8.32822	−	28.3633i	−0.298581	−	1.01687i
$779$	17.1979	+	7.85404i	0.616180	+	0.281400i
$780$	0.405796	+	2.82237i	0.0145298	+	0.101057i
$781$		−	11.9886i		−	0.428986i
$782$	−33.9827	−	18.3532i	−1.21522	−	0.656310i
$783$			2.40103i			0.0858057i
$784$	4.48866	+	5.37140i	0.160309	+	0.191836i
$785$	19.5965	−	42.9103i	0.699428	−	1.53153i
$786$	1.72035	−	0.505140i	0.0613628	−	0.0180178i
$787$	2.41960	−	2.79236i	0.0862493	−	0.0995370i	−0.710984	−	0.703208i	$-0.751750\pi$
$787$	2.41960	−	2.79236i	0.0862493	−	0.0995370i	0.797234	+	0.603671i	$0.206296\pi$
$788$	−3.60820	−	1.05946i	−0.128537	−	0.0377418i
$789$	8.44069	−	5.42450i	0.300496	−	0.193117i
$790$	30.1652	−	13.7760i	1.07323	−	0.490127i
$791$	−10.1692	−	6.66463i	−0.361576	−	0.236967i
$792$	−0.910086	+	1.41612i	−0.0323385	+	0.0503197i
$793$	−8.76133	−	1.25969i	−0.311124	−	0.0447329i
$794$	8.05631	+	1.15832i	0.285908	+	0.0411073i
$795$	−36.8379	−	23.6743i	−1.30650	−	0.839640i
$796$	0.934988	+	1.07903i	0.0331398	+	0.0382453i
$797$	9.53502	+	20.8788i	0.337748	+	0.739565i	0.999952	−	0.00975857i	$-0.00310630\pi$
$797$	9.53502	+	20.8788i	0.337748	+	0.739565i	−0.662205	+	0.749323i	$0.730379\pi$
$798$	−4.37351	+	4.95701i	−0.154821	+	0.175476i
$799$	−11.2264	+	38.2336i	−0.397162	+	1.35261i
$800$	−8.26553	+	9.53893i	−0.292231	+	0.337252i
$801$	−7.51074	+	2.20535i	−0.265379	+	0.0779223i
$802$	16.1845	+	7.39123i	0.571496	+	0.260993i
$803$	3.14574	+	21.8791i	0.111011	+	0.772096i
$804$	−11.4928			−0.405318
$805$	11.5478	−	51.9977i	0.407008	−	1.83268i
$806$	3.14864			0.110906
$807$	−2.22895	−	15.5027i	−0.0784626	−	0.545720i
$808$	−5.95346	−	2.71885i	−0.209442	−	0.0956489i
$809$	41.6119	−	12.2183i	1.46300	−	0.429574i	0.549180	−	0.835704i	$-0.314940\pi$
$809$	41.6119	−	12.2183i	1.46300	−	0.429574i	0.913815	+	0.406130i	$0.133122\pi$
$810$	−2.74900	+	3.17251i	−0.0965899	+	0.111471i
$811$	11.1405	−	37.9409i	0.391194	−	1.33229i	−0.494969	−	0.868911i	$-0.664820\pi$
$811$	11.1405	−	37.9409i	0.391194	−	1.33229i	0.886163	−	0.463374i	$-0.153361\pi$
$812$	4.76351	+	4.20279i	0.167166	+	0.147489i
$813$	−4.20847	−	9.21526i	−0.147597	−	0.323193i
$814$	1.31233	+	1.51451i	0.0459971	+	0.0530834i
$815$	−37.1791	−	23.8936i	−1.30233	−	0.836956i
$816$	7.97129	+	1.14610i	0.279051	+	0.0401215i
$817$	−7.44957	−	1.07109i	−0.260627	−	0.0374726i
$818$	1.73655	−	2.70212i	0.0607169	−	0.0944774i
$819$	1.50310	+	0.985089i	0.0525224	+	0.0344218i
$820$	28.8943	−	13.1956i	1.00903	−	0.460810i
$821$	37.0621	−	23.8184i	1.29348	−	0.831267i	0.300992	−	0.953627i	$-0.402682\pi$
$821$	37.0621	−	23.8184i	1.29348	−	0.831267i	0.992486	+	0.122359i	$0.0390460\pi$
$822$	−16.7942	−	4.93122i	−0.585765	−	0.171996i
$823$	−22.5358	+	26.0077i	−0.785548	+	0.906570i	−0.997497	−	0.0707104i	$-0.977473\pi$
$823$	−22.5358	+	26.0077i	−0.785548	+	0.906570i	0.211949	+	0.977281i	$0.432019\pi$
$824$	8.71569	−	2.55916i	0.303625	−	0.0891525i
$825$	−8.82628	+	19.3268i	−0.307292	+	0.672875i
$826$	4.93167	+	11.0596i	0.171595	+	0.384812i
$827$		−	49.3064i		−	1.71455i	−0.514857	−	0.857276i	$-0.672155\pi$
$827$		−	49.3064i		−	1.71455i	0.514857	−	0.857276i	$-0.327845\pi$
$828$	3.82598	−	2.89169i	0.132962	−	0.100493i
$829$		−	11.4002i		−	0.395946i	−0.980207	−	0.197973i	$-0.936564\pi$
$829$		−	11.4002i		−	0.395946i	0.980207	−	0.197973i	$-0.0634358\pi$
$830$	−4.34017	−	30.1866i	−0.150650	−	1.04779i
$831$	−1.57331	−	0.718506i	−0.0545775	−	0.0249247i
$832$	0.191368	+	0.651739i	0.00663448	+	0.0225950i
$833$	9.01954	−	55.6466i	0.312508	−	1.92804i
$834$	−9.82762	−	2.88565i	−0.340302	−	0.0999218i
$835$	43.5750	+	67.8041i	1.50798	+	2.34646i
$836$	−3.82586	+	1.74721i	−0.132320	+	0.0604285i
$837$	3.03557	+	3.50323i	0.104925	+	0.121089i
$838$	9.35450	+	6.01177i	0.323146	+	0.207673i
$839$	−0.287115	+	1.99693i	−0.00991231	+	0.0689416i	−0.994177	−	0.107758i	$-0.965633\pi$
$839$	−0.287115	+	1.99693i	−0.00991231	+	0.0689416i	0.984265	+	0.176699i	$0.0565420\pi$
$840$	1.48222	+	11.0071i	0.0511414	+	0.379780i
$841$	−19.5466	−	12.5618i	−0.674020	−	0.433167i
$842$	−11.9105	+	10.3205i	−0.410463	+	0.355668i
$843$	−11.4814	−	25.1408i	−0.395441	−	0.865894i
$844$	−0.532401	+	0.342153i	−0.0183260	+	0.0117774i
$845$	−50.5029	−	14.8290i	−1.73735	−	0.510133i
$846$	−3.73947	−	3.24027i	−0.128566	−	0.111403i
$847$	−11.5181	−	18.2800i	−0.395767	−	0.628108i
$848$	−9.48873	−	4.33336i	−0.325844	−	0.148808i
$849$	19.2987	−	2.77474i	0.662331	−	0.0952288i
$850$	101.647			3.48645
$851$	−2.01982	−	5.34009i	−0.0692387	−	0.183056i
$852$		−	7.12189i		−	0.243992i
$853$	−3.96737	+	0.570422i	−0.135840	+	0.0195309i	−0.209900	−	0.977723i	$-0.567314\pi$
$853$	−3.96737	+	0.570422i	−0.135840	+	0.0195309i	0.0740593	+	0.997254i	$0.476405\pi$
$854$	−34.0809	−	5.21164i	−1.16622	−	0.178339i
$855$	−10.0637	+	2.95496i	−0.344170	+	0.101058i
$856$	−3.24595	−	2.81263i	−0.110944	−	0.0961338i
$857$	7.80177	−	26.5704i	0.266503	−	0.907627i	−0.712136	−	0.702042i	$-0.752272\pi$
$857$	7.80177	−	26.5704i	0.266503	−	0.907627i	0.978639	−	0.205586i	$-0.0659099\pi$
$858$	0.618179	+	0.961905i	0.0211043	+	0.0328389i
$859$	30.6565	−	14.0003i	1.04598	−	0.477685i	0.183104	−	0.983093i	$-0.441385\pi$
$859$	30.6565	−	14.0003i	1.04598	−	0.477685i	0.862880	+	0.505408i	$0.168658\pi$
$860$	−9.55626	+	8.28055i	−0.325866	+	0.282364i
$861$	5.81196	−	19.1581i	0.198071	−	0.652907i
$862$	−35.2499	−	5.06816i	−1.20061	−	0.172622i
$863$	4.92848	−	34.2783i	0.167767	−	1.16685i	−0.715719	−	0.698389i	$-0.753901\pi$
$863$	4.92848	−	34.2783i	0.167767	−	1.16685i	0.883486	−	0.468458i	$-0.155190\pi$
$864$	−0.540641	+	0.841254i	−0.0183930	+	0.0286200i
$865$	2.84258	−	2.46311i	0.0966508	−	0.0837484i
$866$	1.04766	+	2.29406i	0.0356011	+	0.0779555i
$867$	−25.8723	−	40.2581i	−0.878671	−	1.36724i
$868$	12.2637	+	0.109696i	0.416258	+	0.00372332i
$869$	8.70837	−	10.0500i	0.295411	−	0.340923i
$870$	2.83961	+	9.67084i	0.0962719	+	0.327872i
$871$	−3.24294	+	7.10104i	−0.109883	+	0.240610i
$872$	15.2015	−	2.18565i	0.514788	−	0.0740154i
$873$	1.74682			0.0591209
$874$	11.9481	−	0.909890i	0.404149	−	0.0307775i
$875$	23.1216	+	81.4323i	0.781651	+	2.75291i
$876$	1.86874	+	12.9974i	0.0631389	+	0.439141i
$877$	3.12030	−	6.83251i	0.105365	−	0.230717i	−0.849605	−	0.527420i	$-0.823160\pi$
$877$	3.12030	−	6.83251i	0.105365	−	0.230717i	0.954970	+	0.296702i	$0.0958869\pi$
$878$	7.98911	+	27.2084i	0.269619	+	0.918239i
$879$	13.4159	+	11.6249i	0.452507	+	0.392099i
$880$	−1.99084	+	6.78017i	−0.0671111	+	0.228559i
$881$	7.35525	−	4.72693i	0.247805	−	0.159254i	−0.410842	−	0.911706i	$-0.634765\pi$
$881$	7.35525	−	4.72693i	0.247805	−	0.159254i	0.658647	+	0.752452i	$0.271129\pi$
$882$	5.82014	+	3.88922i	0.195974	+	0.130957i
$883$	35.7220	+	41.2254i	1.20214	+	1.38735i	0.901030	+	0.433758i	$0.142813\pi$
$883$	35.7220	+	41.2254i	1.20214	+	1.38735i	0.301113	+	0.953589i	$0.402642\pi$
$884$	2.95741	−	4.60183i	0.0994686	−	0.154776i
$885$	−2.73430	+	19.0175i	−0.0919125	+	0.639266i
$886$	−4.23122	+	29.4288i	−0.142151	+	0.988680i
$887$	11.7701	−	18.3146i	0.395201	−	0.614944i	−0.585450	−	0.810708i	$-0.699082\pi$
$887$	11.7701	−	18.3146i	0.395201	−	0.614944i	0.980651	+	0.195764i	$0.0627187\pi$
$888$	0.779595	+	0.899700i	0.0261615	+	0.0301920i
$889$	−7.75585	+	6.59995i	−0.260123	+	0.221355i
$890$	−27.6435	+	17.7654i	−0.926613	+	0.595498i
$891$	−0.474253	+	1.61516i	−0.0158881	+	0.0541099i
$892$	−20.0708	−	17.3914i	−0.672020	−	0.582308i
$893$	−3.48304	−	11.8622i	−0.116556	−	0.396952i
$894$	6.49137	−	14.2141i	0.217104	−	0.475391i
$895$	−9.48636	−	65.9791i	−0.317094	−	2.20544i
$896$	0.722658	+	2.54515i	0.0241423	+	0.0850273i
$897$	−0.707107	−	3.17991i	−0.0236096	−	0.106174i
$898$	32.5008			1.08457
$899$	11.0165	−	1.58394i	0.367422	−	0.0528272i
$900$	−5.24329	+	11.4812i	−0.174776	+	0.382707i
$901$	23.6674	+	80.6038i	0.788476	+	2.68530i
$902$	8.34149	−	9.62660i	0.277741	−	0.320531i
$903$	−0.0712826	+	7.96923i	−0.00237214	+	0.265199i
$904$	−2.48452	−	3.86598i	−0.0826338	−	0.128581i
$905$	10.9586	+	23.9961i	0.364277	+	0.797656i
$906$	3.96889	−	3.43907i	0.131858	−	0.114255i
$907$	1.73525	−	2.70010i	0.0576181	−	0.0896555i	−0.811249	−	0.584700i	$-0.801212\pi$
$907$	1.73525	−	2.70010i	0.0576181	−	0.0896555i	0.868867	+	0.495045i	$0.164848\pi$
$908$	−2.76640	+	19.2407i	−0.0918063	+	0.638527i
$909$	−6.47829	−	0.931437i	−0.214871	−	0.0308938i
$910$	7.21919	+	2.19007i	0.239314	+	0.0726002i
$911$	−28.4744	+	24.6732i	−0.943398	+	0.817459i	−0.983346	−	0.181743i	$-0.941826\pi$
$911$	−28.4744	+	24.6732i	−0.943398	+	0.817459i	0.0399485	+	0.999202i	$0.487281\pi$
$912$	−2.27277	+	1.03794i	−0.0752589	+	0.0343696i
$913$	−6.61171	−	10.2880i	−0.218816	−	0.340484i
$914$	2.89491	−	9.85914i	0.0957550	−	0.326111i
$915$	−41.3414	−	35.8225i	−1.36670	−	1.18425i
$916$	−24.9325	+	7.32083i	−0.823792	+	0.241887i
$917$	0.717081	−	4.68926i	0.0236801	−	0.154853i
$918$	7.97129	−	1.14610i	0.263092	−	0.0378269i
$919$		−	16.4390i		−	0.542272i	−0.962541	−	0.271136i	$-0.912601\pi$
$919$		−	16.4390i		−	0.542272i	0.962541	−	0.271136i	$-0.0873994\pi$
$920$	11.9903	−	16.1720i	0.395310	−	0.533175i
$921$	14.3449			0.472682
$922$	9.59590	−	1.37968i	0.316024	−	0.0454374i
$923$	−4.40041	−	2.00960i	−0.144841	−	0.0661468i
$924$	2.37425	+	3.76809i	0.0781072	+	0.123961i
$925$	11.3559	+	9.83990i	0.373378	+	0.323534i
$926$	36.3779	+	10.6815i	1.19545	+	0.351016i
$927$	7.64165	−	4.91099i	0.250985	−	0.161298i
$928$	0.997422	+	2.18405i	0.0327420	+	0.0716950i
$929$	−21.3310	+	18.4834i	−0.699846	+	0.606420i	−0.930359	−	0.366649i	$-0.880505\pi$
$929$	−21.3310	+	18.4834i	−0.699846	+	0.606420i	0.230513	+	0.973069i	$0.425959\pi$
$930$	16.3698	+	10.5202i	0.536786	+	0.344972i
$931$	6.97982	+	16.0368i	0.228754	+	0.525585i
$932$	0.881111	−	6.12826i	0.0288618	−	0.200738i
$933$	8.16156	+	5.24512i	0.267198	+	0.171717i
$934$	22.5712	+	26.0486i	0.738552	+	0.852335i
$935$	51.7650	−	23.6403i	1.69290	−	0.773120i
$936$	0.367232	+	0.571424i	0.0120034	+	0.0186776i
$937$	1.84026	+	0.540348i	0.0601186	+	0.0176524i	0.311654	−	0.950196i	$-0.399117\pi$
$937$	1.84026	+	0.540348i	0.0601186	+	0.0176524i	−0.251535	+	0.967848i	$0.580935\pi$
$938$	−12.8784	+	27.5451i	−0.420495	+	0.899379i
$939$	−6.10233	−	20.7826i	−0.199142	−	0.678215i
$940$	−18.8940	−	8.62859i	−0.616254	−	0.281434i
$941$	6.16151	+	42.8543i	0.200860	+	1.39701i	0.801741	+	0.597671i	$0.203907\pi$
$941$	6.16151	+	42.8543i	0.200860	+	1.39701i	−0.600882	+	0.799338i	$0.705184\pi$
$942$		−	11.2375i		−	0.366138i
$943$	−31.7704	+	17.5384i	−1.03459	+	0.571130i
$944$			4.57689i			0.148965i
$945$	4.52323	+	10.1436i	0.147141	+	0.329972i
$946$	−2.10640	+	4.61237i	−0.0684849	+	0.149961i
$947$	4.77167	−	1.40109i	0.155059	−	0.0455293i	−0.203282	−	0.979120i	$-0.565161\pi$
$947$	4.77167	−	1.40109i	0.155059	−	0.0455293i	0.358341	+	0.933591i	$0.383343\pi$
$948$	5.17325	−	5.97025i	0.168019	−	0.193905i
$949$	8.55800	+	2.51286i	0.277804	+	0.0815708i
$950$	−26.5301	+	17.0498i	−0.860749	+	0.553170i
$951$	−21.8189	+	9.96436i	−0.707527	+	0.323117i
$952$	11.6793	−	17.8208i	0.378527	−	0.577574i
$953$	15.5991	−	24.2727i	0.505304	−	0.786269i	−0.491090	−	0.871109i	$-0.663401\pi$
$953$	15.5991	−	24.2727i	0.505304	−	0.786269i	0.996395	+	0.0848397i	$0.0270378\pi$
$954$	−10.3252	−	1.48454i	−0.334291	−	0.0480638i
$955$	30.6282	+	4.40367i	0.991105	+	0.142499i
$956$	−25.5974	−	16.4505i	−0.827879	−	0.532046i
$957$	2.64679	+	3.05456i	0.0855585	+	0.0987398i
$958$	−2.85956	−	6.26156i	−0.0923882	−	0.202302i
$959$	−30.6379	+	34.7255i	−0.989348	+	1.12134i
$960$	−1.18267	+	4.02779i	−0.0381704	+	0.129996i
$961$	−6.22950	+	7.18923i	−0.200952	+	0.231911i
$962$	0.775878	−	0.227818i	0.0250153	−	0.00734516i
$963$	−3.90688	−	1.78421i	−0.125897	−	0.0574954i
$964$	2.56736	+	17.8564i	0.0826890	+	0.575115i
$965$	1.42553			0.0458894
$966$	−2.64335	−	12.4102i	−0.0850484	−	0.399291i
$967$	1.08253			0.0348117			0.0174058	−	0.999849i	$-0.494459\pi$
$967$	1.08253			0.0348117			0.0174058	+	0.999849i	$0.494459\pi$
$968$	−1.16219	−	8.08322i	−0.0373543	−	0.259805i
$969$	18.3032	+	8.35878i	0.587983	+	0.268523i
$970$	7.03583	−	2.06591i	0.225907	−	0.0663322i
$971$	38.8285	−	44.8105i	1.24607	−	1.43804i	0.390291	−	0.920692i	$-0.372374\pi$
$971$	38.8285	−	44.8105i	1.24607	−	1.43804i	0.855776	−	0.517346i	$-0.173080\pi$
$972$	−0.281733	+	0.959493i	−0.00903658	+	0.0307758i
$973$	−17.9286	+	20.3206i	−0.574765	+	0.651449i
$974$	3.04642	+	6.67073i	0.0976136	+	0.213744i
$975$	5.61439	+	6.47935i	0.179804	+	0.207505i
$976$	−10.9625	−	7.04515i	−0.350900	−	0.225510i
$977$	46.4709	+	6.68150i	1.48673	+	0.213760i	0.837336	−	0.546688i	$-0.184112\pi$
$977$	46.4709	+	6.68150i	1.48673	+	0.213760i	0.649398	+	0.760449i	$0.275021\pi$
$978$	−10.4209	−	1.49829i	−0.333223	−	0.0479102i
$979$	−7.12399	+	11.0851i	−0.227684	+	0.354283i
$980$	28.0420	+	8.78169i	0.895767	+	0.280521i
$981$	13.9700	−	6.37988i	0.446027	−	0.203694i
$982$	−1.07743	+	0.692421i	−0.0343821	+	0.0220960i
$983$	52.4633	+	15.4046i	1.67332	+	0.491331i	0.974579	−	0.224045i	$-0.0719262\pi$
$983$	52.4633	+	15.4046i	1.67332	+	0.491331i	0.698740	+	0.715376i	$0.253744\pi$
$984$	4.95531	−	5.71873i	0.157969	−	0.182306i
$985$	−15.1466	+	4.44745i	−0.482612	+	0.141708i
$986$	8.03250	−	17.5887i	0.255807	−	0.560139i
$987$	−11.9564	+	5.33158i	−0.380576	+	0.169706i
$988$			1.69715i			0.0539937i
$989$	10.1677	−	10.2618i	0.323315	−	0.326308i
$990$			7.06641i			0.224585i
$991$	−1.11004	−	7.72053i	−0.0352617	−	0.245251i	0.964565	−	0.263844i	$-0.0849903\pi$
$991$	−1.11004	−	7.72053i	−0.0352617	−	0.245251i	−0.999827	+	0.0185932i	$0.994081\pi$
$992$	4.21654	+	1.92563i	0.133875	+	0.0611388i
$993$	4.68459	+	15.9543i	0.148661	+	0.506293i
$994$	−17.0693	−	7.98056i	−0.541405	−	0.253128i
$995$	5.75075	+	1.68857i	0.182311	+	0.0535313i
$996$	−3.92772	−	6.11165i	−0.124455	−	0.193655i
$997$	−11.4819	+	5.24362i	−0.363637	+	0.166067i	−0.588850	−	0.808242i	$-0.700419\pi$
$997$	−11.4819	+	5.24362i	−0.363637	+	0.166067i	0.225214	+	0.974309i	$0.427692\pi$
$998$	26.5326	+	30.6203i	0.839876	+	0.969268i
$999$	1.00149	+	0.643619i	0.0316858	+	0.0203632i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.s.a.181.1	✓	160
7.6	odd	2	inner	966.2.s.a.181.16	yes	160
23.15	odd	22	inner	966.2.s.a.475.16	yes	160
161.153	even	22	inner	966.2.s.a.475.1	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.s.a.181.1	✓	160	1.1	even	1	trivial
966.2.s.a.181.16	yes	160	7.6	odd	2	inner
966.2.s.a.475.1	yes	160	161.153	even	22	inner
966.2.s.a.475.16	yes	160	23.15	odd	22	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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.s (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.142315 - 0.989821i) q^{2} +(-0.909632 - 0.415415i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(-2.74900 + 3.17251i) q^{5} +(-0.281733 + 0.959493i) q^{6} +(1.98395 + 1.75041i) q^{7} +(0.415415 + 0.909632i) q^{8} +(0.654861 + 0.755750i) q^{9} +O(q^{10})\)	\(q+(-0.142315 - 0.989821i) q^{2} +(-0.909632 - 0.415415i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(-2.74900 + 3.17251i) q^{5} +(-0.281733 + 0.959493i) q^{6} +(1.98395 + 1.75041i) q^{7} +(0.415415 + 0.909632i) q^{8} +(0.654861 + 0.755750i) q^{9} +(3.53144 + 2.26952i) q^{10} +(1.66621 + 0.239565i) q^{11} +(0.989821 + 0.142315i) q^{12} +(0.367232 - 0.571424i) q^{13} +(1.45025 - 2.21286i) q^{14} +(3.81849 - 1.74384i) q^{15} +(0.841254 - 0.540641i) q^{16} +(-7.72704 - 2.26886i) q^{17} +(0.654861 - 0.755750i) q^{18} +(2.39735 - 0.703925i) q^{19} +(1.74384 - 3.81849i) q^{20} +(-1.07751 - 2.41639i) q^{21} -1.68335i q^{22} +(-1.65525 + 4.50113i) q^{23} -1.00000i q^{24} +(-1.79627 - 12.4933i) q^{25} +(-0.617871 - 0.282172i) q^{26} +(-0.281733 - 0.959493i) q^{27} +(-2.39673 - 1.12057i) q^{28} +(-2.30377 - 0.676447i) q^{29} +(-2.26952 - 3.53144i) q^{30} +(-4.21654 + 1.92563i) q^{31} +(-0.654861 - 0.755750i) q^{32} +(-1.41612 - 0.910086i) q^{33} +(-1.14610 + 7.97129i) q^{34} +(-11.0071 + 1.48222i) q^{35} +(-0.841254 - 0.540641i) q^{36} +(-0.899700 + 0.779595i) q^{37} +(-1.03794 - 2.27277i) q^{38} +(-0.571424 + 0.367232i) q^{39} +(-4.02779 - 1.18267i) q^{40} +(5.71873 + 4.95531i) q^{41} +(-2.23845 + 1.41044i) q^{42} +(-2.74000 - 1.25132i) q^{43} +(-1.66621 + 0.239565i) q^{44} -4.19784 q^{45} +(4.69088 + 0.997826i) q^{46} -4.94803i q^{47} +(-0.989821 + 0.142315i) q^{48} +(0.872103 + 6.94546i) q^{49} +(-12.1105 + 3.55598i) q^{50} +(6.08625 + 5.27376i) q^{51} +(-0.191368 + 0.651739i) q^{52} +(-5.63964 - 8.77545i) q^{53} +(-0.909632 + 0.415415i) q^{54} +(-5.34044 + 4.62751i) q^{55} +(-0.768070 + 2.53181i) q^{56} +(-2.47313 - 0.355582i) q^{57} +(-0.341702 + 2.37659i) q^{58} +(-2.47445 + 3.85033i) q^{59} +(-3.17251 + 2.74900i) q^{60} +(-5.41332 - 11.8535i) q^{61} +(2.50611 + 3.89958i) q^{62} +(-0.0236646 + 2.64565i) q^{63} +(-0.654861 + 0.755750i) q^{64} +(0.803330 + 2.73589i) q^{65} +(-0.699287 + 1.53123i) q^{66} +(-11.3758 + 1.63559i) q^{67} +8.05326 q^{68} +(3.37551 - 3.40675i) q^{69} +(3.03360 + 10.6841i) q^{70} +(-1.01355 - 7.04940i) q^{71} +(-0.415415 + 0.909632i) q^{72} +(3.69944 + 12.5991i) q^{73} +(0.899700 + 0.779595i) q^{74} +(-3.55598 + 12.1105i) q^{75} +(-2.10192 + 1.35082i) q^{76} +(2.88634 + 3.39185i) q^{77} +(0.444816 + 0.513345i) q^{78} +(4.27094 - 6.64571i) q^{79} +(-0.597414 + 4.15511i) q^{80} +(-0.142315 + 0.989821i) q^{81} +(4.09101 - 6.36573i) q^{82} +(-4.75752 - 5.49047i) q^{83} +(1.71464 + 2.01494i) q^{84} +(28.4396 - 18.2770i) q^{85} +(-0.848637 + 2.89019i) q^{86} +(1.81457 + 1.57234i) q^{87} +(0.474253 + 1.61516i) q^{88} +(-3.25180 + 7.12044i) q^{89} +(0.597414 + 4.15511i) q^{90} +(1.72880 - 0.490868i) q^{91} +(0.320088 - 4.78514i) q^{92} +4.63544 q^{93} +(-4.89767 + 0.704178i) q^{94} +(-4.35709 + 9.54071i) q^{95} +(0.281733 + 0.959493i) q^{96} +(1.14392 - 1.32016i) q^{97} +(6.75065 - 1.85167i) q^{98} +(0.910086 + 1.41612i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q - 16 q^{2} - 16 q^{4} - 16 q^{8} + 16 q^{9}+O(q^{10}) \) 160 * q - 16 * q^2 - 16 * q^4 - 16 * q^8 + 16 * q^9	\( 160 q - 16 q^{2} - 16 q^{4} - 16 q^{8} + 16 q^{9} - 22 q^{14} - 16 q^{16} + 16 q^{18} - 36 q^{23} + 96 q^{25} + 22 q^{28} - 20 q^{29} - 16 q^{32} - 50 q^{35} + 16 q^{36} + 22 q^{37} + 4 q^{39} - 110 q^{43} + 8 q^{46} - 36 q^{50} + 22 q^{51} - 88 q^{53} + 22 q^{57} + 24 q^{58} - 16 q^{64} - 72 q^{70} + 48 q^{71} + 16 q^{72} - 22 q^{74} + 24 q^{77} + 4 q^{78} + 88 q^{79} - 16 q^{81} + 22 q^{84} + 76 q^{85} + 44 q^{86} - 44 q^{88} + 8 q^{92} - 14 q^{95} + 22 q^{98} - 22 q^{99}+O(q^{100}) \) 160 * q - 16 * q^2 - 16 * q^4 - 16 * q^8 + 16 * q^9 - 22 * q^14 - 16 * q^16 + 16 * q^18 - 36 * q^23 + 96 * q^25 + 22 * q^28 - 20 * q^29 - 16 * q^32 - 50 * q^35 + 16 * q^36 + 22 * q^37 + 4 * q^39 - 110 * q^43 + 8 * q^46 - 36 * q^50 + 22 * q^51 - 88 * q^53 + 22 * q^57 + 24 * q^58 - 16 * q^64 - 72 * q^70 + 48 * q^71 + 16 * q^72 - 22 * q^74 + 24 * q^77 + 4 * q^78 + 88 * q^79 - 16 * q^81 + 22 * q^84 + 76 * q^85 + 44 * q^86 - 44 * q^88 + 8 * q^92 - 14 * q^95 + 22 * q^98 - 22 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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