LMFDB - Embedded newform 1512.2.c.e.757.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1512,2,Mod(757,1512)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1512, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1512.757");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1512 = 2^{3} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1512.c (of order $2$, degree $1$, 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:	$12.0733807856$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + x^{18} + 4x^{16} + 8x^{12} + 4x^{10} + 32x^{8} + 256x^{4} + 256x^{2} + 1024 $ x^20 + x^18 + 4x^16 + 8x^12 + 4x^10 + 32x^8 + 256x^4 + 256x^2 + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			757.17
Root			$1.19566 - 0.755240i$ of defining polynomial
Character	$\chi$	$=$	1512.757
Dual form			1512.2.c.e.757.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.19566 - 0.755240i) q^{2} +(0.859226 - 1.80603i) q^{4} -3.16969i q^{5} -1.00000 q^{7} +(-0.336637 - 2.80832i) q^{8} +O(q^{10})$	\(q+(1.19566 - 0.755240i) q^{2} +(0.859226 - 1.80603i) q^{4} -3.16969i q^{5} -1.00000 q^{7} +(-0.336637 - 2.80832i) q^{8} +(-2.39387 - 3.78988i) q^{10} -5.44696i q^{11} +3.61205i q^{13} +(-1.19566 + 0.755240i) q^{14} +(-2.52346 - 3.10357i) q^{16} -3.27628 q^{17} +3.20627i q^{19} +(-5.72454 - 2.72348i) q^{20} +(-4.11376 - 6.51273i) q^{22} -0.673274 q^{23} -5.04692 q^{25} +(2.72797 + 4.31880i) q^{26} +(-0.859226 + 1.80603i) q^{28} +2.85127i q^{29} +3.71845 q^{31} +(-5.36115 - 1.80501i) q^{32} +(-3.91734 + 2.47438i) q^{34} +3.16969i q^{35} -11.9988i q^{37} +(2.42150 + 3.83363i) q^{38} +(-8.90151 + 1.06703i) q^{40} +7.44602 q^{41} +12.5741i q^{43} +(-9.83735 - 4.68017i) q^{44} +(-0.805009 + 0.508483i) q^{46} +4.06341 q^{47} +1.00000 q^{49} +(-6.03442 + 3.81164i) q^{50} +(6.52346 + 3.10357i) q^{52} +0.291601i q^{53} -17.2652 q^{55} +(0.336637 + 2.80832i) q^{56} +(2.15339 + 3.40916i) q^{58} +0.0209587i q^{59} -5.34034i q^{61} +(4.44602 - 2.80832i) q^{62} +(-7.77335 + 1.89077i) q^{64} +11.4491 q^{65} -6.20714i q^{67} +(-2.81507 + 5.91705i) q^{68} +(2.39387 + 3.78988i) q^{70} -15.5050 q^{71} +1.35371 q^{73} +(-9.06200 - 14.3466i) q^{74} +(5.79061 + 2.75491i) q^{76} +5.44696i q^{77} -11.0846 q^{79} +(-9.83735 + 7.99858i) q^{80} +(8.90294 - 5.62353i) q^{82} -13.6442i q^{83} +10.3848i q^{85} +(9.49646 + 15.0344i) q^{86} +(-15.2968 + 1.83365i) q^{88} +5.93965 q^{89} -3.61205i q^{91} +(-0.578494 + 1.21595i) q^{92} +(4.85848 - 3.06885i) q^{94} +10.1629 q^{95} +9.60073 q^{97} +(1.19566 - 0.755240i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{4} - 20 q^{7}+O(q^{10}) $ 20 * q - 2 * q^4 - 20 * q^7	$ 20 q - 2 q^{4} - 20 q^{7} - 12 q^{10} - 14 q^{16} + 8 q^{22} - 28 q^{25} + 2 q^{28} + 36 q^{31} - 6 q^{34} - 16 q^{40} - 18 q^{46} + 20 q^{49} + 94 q^{52} + 48 q^{55} + 66 q^{58} + 22 q^{64} + 12 q^{70} + 12 q^{76} + 64 q^{79} - 92 q^{88} - 24 q^{94} + 56 q^{97}+O(q^{100}) $ 20 * q - 2 * q^4 - 20 * q^7 - 12 * q^10 - 14 * q^16 + 8 * q^22 - 28 * q^25 + 2 * q^28 + 36 * q^31 - 6 * q^34 - 16 * q^40 - 18 * q^46 + 20 * q^49 + 94 * q^52 + 48 * q^55 + 66 * q^58 + 22 * q^64 + 12 * q^70 + 12 * q^76 + 64 * q^79 - 92 * q^88 - 24 * q^94 + 56 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1081$	$1135$
$\chi(n)$	$-1$	$1$	$1$	$1$

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 $

$2$	1.19566	−	0.755240i	0.845462	−	0.534035i
$2$	1.19566	−	0.755240i	0.845462	−	0.534035i
$3$		0			0
$3$		0			0
$4$	0.859226	−	1.80603i	0.429613	−	0.903013i
$5$		−	3.16969i		−	1.41753i	−0.705446	−	0.708764i	$-0.749253\pi$
$5$		−	3.16969i		−	1.41753i	0.705446	−	0.708764i	$-0.250747\pi$
$6$		0			0
$7$	−1.00000			−0.377964
$7$	−1.00000			−0.377964
$8$	−0.336637	−	2.80832i	−0.119019	−	0.992892i
$9$		0			0
$10$	−2.39387	−	3.78988i	−0.757009	−	1.19847i
$11$		−	5.44696i		−	1.64232i	−0.570699	−	0.821160i	$-0.693327\pi$
$11$		−	5.44696i		−	1.64232i	0.570699	−	0.821160i	$-0.306673\pi$
$12$		0			0
$13$			3.61205i			1.00180i	0.865504	+	0.500902i	$0.166998\pi$
$13$			3.61205i			1.00180i	−0.865504	+	0.500902i	$0.833002\pi$
$14$	−1.19566	+	0.755240i	−0.319555	+	0.201846i
$15$		0			0
$16$	−2.52346	−	3.10357i	−0.630865	−	0.775892i
$17$	−3.27628			−0.794616			−0.397308	−	0.917685i	$-0.630055\pi$
$17$	−3.27628			−0.794616			−0.397308	+	0.917685i	$0.630055\pi$
$18$		0			0
$19$			3.20627i			0.735569i	0.929911	+	0.367785i	$0.119884\pi$
$19$			3.20627i			0.735569i	−0.929911	+	0.367785i	$0.880116\pi$
$20$	−5.72454	−	2.72348i	−1.28005	−	0.608988i
$21$		0			0
$22$	−4.11376	−	6.51273i	−0.877056	−	1.38852i
$23$	−0.673274			−0.140387			−0.0701936	−	0.997533i	$-0.522362\pi$
$23$	−0.673274			−0.140387			−0.0701936	+	0.997533i	$0.522362\pi$
$24$		0			0
$25$	−5.04692			−1.00938
$26$	2.72797	+	4.31880i	0.534998	+	0.846987i
$27$		0			0
$28$	−0.859226	+	1.80603i	−0.162378	+	0.341307i
$29$			2.85127i			0.529468i	0.964322	+	0.264734i	$0.0852841\pi$
$29$			2.85127i			0.529468i	−0.964322	+	0.264734i	$0.914716\pi$
$30$		0			0
$31$	3.71845			0.667854			0.333927	−	0.942599i	$-0.391626\pi$
$31$	3.71845			0.667854			0.333927	+	0.942599i	$0.391626\pi$
$32$	−5.36115	−	1.80501i	−0.947727	−	0.319084i
$33$		0			0
$34$	−3.91734	+	2.47438i	−0.671817	+	0.424353i
$35$			3.16969i			0.535775i
$36$		0			0
$37$		−	11.9988i		−	1.97260i	−0.164971	−	0.986298i	$-0.552753\pi$
$37$		−	11.9988i		−	1.97260i	0.164971	−	0.986298i	$-0.447247\pi$
$38$	2.42150	+	3.83363i	0.392820	+	0.621896i
$39$		0			0
$40$	−8.90151	+	1.06703i	−1.40745	+	0.168713i
$41$	7.44602			1.16287			0.581436	−	0.813592i	$-0.302491\pi$
$41$	7.44602			1.16287			0.581436	+	0.813592i	$0.302491\pi$
$42$		0			0
$43$			12.5741i			1.91753i	0.284195	+	0.958766i	$0.408274\pi$
$43$			12.5741i			1.91753i	−0.284195	+	0.958766i	$0.591726\pi$
$44$	−9.83735	−	4.68017i	−1.48304	−	0.705562i
$45$		0			0
$46$	−0.805009	+	0.508483i	−0.118692	+	0.0749717i
$47$	4.06341			0.592710			0.296355	−	0.955078i	$-0.404229\pi$
$47$	4.06341			0.592710			0.296355	+	0.955078i	$0.404229\pi$
$48$		0			0
$49$	1.00000			0.142857
$50$	−6.03442	+	3.81164i	−0.853397	+	0.539047i
$51$		0			0
$52$	6.52346	+	3.10357i	0.904641	+	0.430388i
$53$			0.291601i			0.0400545i	0.999799	+	0.0200272i	$0.00637529\pi$
$53$			0.291601i			0.0400545i	−0.999799	+	0.0200272i	$0.993625\pi$
$54$		0			0
$55$	−17.2652			−2.32803
$56$	0.336637	+	2.80832i	0.0449850	+	0.375278i
$57$		0			0
$58$	2.15339	+	3.40916i	0.282754	+	0.447645i
$59$			0.0209587i			0.00272859i	0.999999	+	0.00136430i	$0.000434269\pi$
$59$			0.0209587i			0.00272859i	−0.999999	+	0.00136430i	$0.999566\pi$
$60$		0			0
$61$		−	5.34034i		−	0.683760i	−0.939744	−	0.341880i	$-0.888936\pi$
$61$		−	5.34034i		−	0.683760i	0.939744	−	0.341880i	$-0.111064\pi$
$62$	4.44602	−	2.80832i	0.564645	−	0.356657i
$63$		0			0
$64$	−7.77335	+	1.89077i	−0.971669	+	0.236346i
$65$	11.4491			1.42008
$66$		0			0
$67$		−	6.20714i		−	0.758323i	−0.925331	−	0.379161i	$-0.876213\pi$
$67$		−	6.20714i		−	0.758323i	0.925331	−	0.379161i	$-0.123787\pi$
$68$	−2.81507	+	5.91705i	−0.341377	+	0.717548i
$69$		0			0
$70$	2.39387	+	3.78988i	0.286123	+	0.452978i
$71$	−15.5050			−1.84010			−0.920050	−	0.391801i	$-0.871852\pi$
$71$	−15.5050			−1.84010			−0.920050	+	0.391801i	$0.871852\pi$
$72$		0			0
$73$	1.35371			0.158440			0.0792198	−	0.996857i	$-0.474757\pi$
$73$	1.35371			0.158440			0.0792198	+	0.996857i	$0.474757\pi$
$74$	−9.06200	−	14.3466i	−1.05344	−	1.66776i
$75$		0			0
$76$	5.79061	+	2.75491i	0.664229	+	0.316010i
$77$			5.44696i			0.620738i
$78$		0			0
$79$	−11.0846			−1.24711			−0.623555	−	0.781779i	$-0.714312\pi$
$79$	−11.0846			−1.24711			−0.623555	+	0.781779i	$0.714312\pi$
$80$	−9.83735	+	7.99858i	−1.09985	+	0.894269i
$81$		0			0
$82$	8.90294	−	5.62353i	0.983165	−	0.621015i
$83$		−	13.6442i		−	1.49765i	−0.662768	−	0.748824i	$-0.730619\pi$
$83$		−	13.6442i		−	1.49765i	0.662768	−	0.748824i	$-0.269381\pi$
$84$		0			0
$85$			10.3848i			1.12639i
$86$	9.49646	+	15.0344i	1.02403	+	1.62120i
$87$		0			0
$88$	−15.2968	+	1.83365i	−1.63065	+	0.195467i
$89$	5.93965			0.629601			0.314801	−	0.949158i	$-0.398062\pi$
$89$	5.93965			0.629601			0.314801	+	0.949158i	$0.398062\pi$
$90$		0			0
$91$		−	3.61205i		−	0.378646i
$92$	−0.578494	+	1.21595i	−0.0603122	+	0.126772i
$93$		0			0
$94$	4.85848	−	3.06885i	0.501114	−	0.316528i
$95$	10.1629			1.04269
$96$		0			0
$97$	9.60073			0.974807			0.487403	−	0.873177i	$-0.337944\pi$
$97$	9.60073			0.974807			0.487403	+	0.873177i	$0.337944\pi$
$98$	1.19566	−	0.755240i	0.120780	−	0.0762907i
$99$		0			0
$100$	−4.33645	+	9.11487i	−0.433645	+	0.911487i
$101$		−	14.2123i		−	1.41418i	−0.707124	−	0.707090i	$-0.750008\pi$
$101$		−	14.2123i		−	1.41418i	0.707124	−	0.707090i	$-0.249992\pi$
$102$		0			0
$103$	1.69321			0.166837			0.0834187	−	0.996515i	$-0.473416\pi$
$103$	1.69321			0.166837			0.0834187	+	0.996515i	$0.473416\pi$
$104$	10.1438	−	1.21595i	0.994682	−	0.119234i
$105$		0			0
$106$	0.220228	+	0.348657i	0.0213905	+	0.0338645i
$107$		−	11.6644i		−	1.12764i	−0.825897	−	0.563821i	$-0.809331\pi$
$107$		−	11.6644i		−	1.12764i	0.825897	−	0.563821i	$-0.190669\pi$
$108$		0			0
$109$		−	14.0521i		−	1.34595i	−0.739667	−	0.672973i	$-0.765017\pi$
$109$		−	14.0521i		−	1.34595i	0.739667	−	0.672973i	$-0.234983\pi$
$110$	−20.6433	+	13.0393i	−1.96826	+	1.24325i
$111$		0			0
$112$	2.52346	+	3.10357i	0.238445	+	0.293260i
$113$	14.9455			1.40596			0.702979	−	0.711211i	$-0.251853\pi$
$113$	14.9455			1.40596			0.702979	+	0.711211i	$0.251853\pi$
$114$		0			0
$115$			2.13407i			0.199003i
$116$	5.14947	+	2.44989i	0.478116	+	0.227466i
$117$		0			0
$118$	0.0158289	+	0.0250596i	0.00145716	+	0.00230692i
$119$	3.27628			0.300336
$120$		0			0
$121$	−18.6693			−1.69721
$122$	−4.03324	−	6.38525i	−0.365152	−	0.578094i
$123$		0			0
$124$	3.19499	−	6.71562i	0.286919	−	0.603081i
$125$			0.148729i			0.0133028i
$126$		0			0
$127$	4.07216			0.361346			0.180673	−	0.983543i	$-0.442172\pi$
$127$	4.07216			0.361346			0.180673	+	0.983543i	$0.442172\pi$
$128$	−7.86633	+	8.13147i	−0.695292	+	0.718727i
$129$		0			0
$130$	13.6893	−	8.64680i	1.20063	−	0.758374i
$131$			17.8643i			1.56081i	0.625275	+	0.780404i	$0.284987\pi$
$131$			17.8643i			1.56081i	−0.625275	+	0.780404i	$0.715013\pi$
$132$		0			0
$133$		−	3.20627i		−	0.278019i
$134$	−4.68788	−	7.42165i	−0.404971	−	0.641133i
$135$		0			0
$136$	1.10292	+	9.20086i	0.0945744	+	0.788967i
$137$	21.1351			1.80569			0.902847	−	0.429963i	$-0.141473\pi$
$137$	21.1351			1.80569			0.902847	+	0.429963i	$0.141473\pi$
$138$		0			0
$139$			7.39359i			0.627116i	0.949569	+	0.313558i	$0.101521\pi$
$139$			7.39359i			0.627116i	−0.949569	+	0.313558i	$0.898479\pi$
$140$	5.72454	+	2.72348i	0.483812	+	0.230176i
$141$		0			0
$142$	−18.5387	+	11.7100i	−1.55574	+	0.982678i
$143$	19.6747			1.64528
$144$		0			0
$145$	9.03764			0.750535
$146$	1.61858	−	1.02237i	0.133955	−	0.0846123i
$147$		0			0
$148$	−21.6702	−	10.3097i	−1.78128	−	0.847453i
$149$			13.0541i			1.06944i	0.845030	+	0.534719i	$0.179582\pi$
$149$			13.0541i			1.06944i	−0.845030	+	0.534719i	$0.820418\pi$
$150$		0			0
$151$	−17.6477			−1.43615			−0.718073	−	0.695968i	$-0.754976\pi$
$151$	−17.6477			−1.43615			−0.718073	+	0.695968i	$0.754976\pi$
$152$	9.00425	−	1.07935i	0.730341	−	0.0875468i
$153$		0			0
$154$	4.11376	+	6.51273i	0.331496	+	0.524811i
$155$		−	11.7863i		−	0.946701i
$156$		0			0
$157$			3.00087i			0.239495i	0.992804	+	0.119748i	$0.0382085\pi$
$157$			3.00087i			0.239495i	−0.992804	+	0.119748i	$0.961791\pi$
$158$	−13.2534	+	8.37150i	−1.05438	+	0.666001i
$159$		0			0
$160$	−5.72132	+	16.9932i	−0.452310	+	1.34343i
$161$	0.673274			0.0530614
$162$		0			0
$163$			0.871148i			0.0682335i	0.999418	+	0.0341168i	$0.0108618\pi$
$163$			0.871148i			0.0682335i	−0.999418	+	0.0341168i	$0.989138\pi$
$164$	6.39781	−	13.4477i	0.499585	−	1.05009i
$165$		0			0
$166$	−10.3047	−	16.3139i	−0.799797	−	1.26621i
$167$	−7.49952			−0.580330			−0.290165	−	0.956977i	$-0.593710\pi$
$167$	−7.49952			−0.580330			−0.290165	+	0.956977i	$0.593710\pi$
$168$		0			0
$169$	−0.0469224			−0.00360941
$170$	7.84301	+	12.4167i	0.601531	+	0.952320i
$171$		0			0
$172$	22.7092	+	10.8040i	1.73156	+	0.823797i
$173$		−	0.652919i		−	0.0496405i	−0.999692	−	0.0248203i	$-0.992099\pi$
$173$		−	0.652919i		−	0.0496405i	0.999692	−	0.0248203i	$-0.00790135\pi$
$174$		0			0
$175$	5.04692			0.381511
$176$	−16.9050	+	13.7452i	−1.27426	+	1.03608i
$177$		0			0
$178$	7.10182	−	4.48586i	0.532304	−	0.336229i
$179$		−	4.43263i		−	0.331310i	−0.986184	−	0.165655i	$-0.947026\pi$
$179$		−	4.43263i		−	0.331310i	0.986184	−	0.165655i	$-0.0529738\pi$
$180$		0			0
$181$		−	21.9779i		−	1.63360i	−0.576920	−	0.816801i	$-0.695746\pi$
$181$		−	21.9779i		−	1.63360i	0.576920	−	0.816801i	$-0.304254\pi$
$182$	−2.72797	−	4.31880i	−0.202210	−	0.320131i
$183$		0			0
$184$	0.226649	+	1.89077i	0.0167088	+	0.139389i
$185$	−38.0326			−2.79621
$186$		0			0
$187$			17.8458i			1.30501i
$188$	3.49139	−	7.33863i	0.254636	−	0.535224i
$189$		0			0
$190$	12.1514	−	7.67541i	0.881555	−	0.556833i
$191$	6.67327			0.482861			0.241430	−	0.970418i	$-0.422383\pi$
$191$	6.67327			0.482861			0.241430	+	0.970418i	$0.422383\pi$
$192$		0			0
$193$	25.0305			1.80174			0.900868	−	0.434092i	$-0.142931\pi$
$193$	25.0305			1.80174			0.900868	+	0.434092i	$0.142931\pi$
$194$	11.4793	−	7.25086i	0.824162	−	0.520581i
$195$		0			0
$196$	0.859226	−	1.80603i	0.0613733	−	0.129002i
$197$		−	3.77971i		−	0.269293i	−0.990894	−	0.134646i	$-0.957010\pi$
$197$		−	3.77971i		−	0.269293i	0.990894	−	0.134646i	$-0.0429899\pi$
$198$		0			0
$199$	−7.18059			−0.509019			−0.254509	−	0.967070i	$-0.581914\pi$
$199$	−7.18059			−0.509019			−0.254509	+	0.967070i	$0.581914\pi$
$200$	1.69898	+	14.1734i	0.120136	+	1.00221i
$201$		0			0
$202$	−10.7337	−	16.9932i	−0.755222	−	1.19564i
$203$		−	2.85127i		−	0.200120i
$204$		0			0
$205$		−	23.6016i		−	1.64840i
$206$	2.02452	−	1.27878i	0.141055	−	0.0890970i
$207$		0			0
$208$	11.2103	−	9.11487i	0.777291	−	0.632003i
$209$	17.4644			1.20804
$210$		0			0
$211$		−	5.30442i		−	0.365171i	−0.983190	−	0.182586i	$-0.941553\pi$
$211$		−	5.30442i		−	0.365171i	0.983190	−	0.182586i	$-0.0584467\pi$
$212$	0.526639	+	0.250551i	0.0361697	+	0.0172079i
$213$		0			0
$214$	−8.80943	−	13.9467i	−0.602200	−	0.953379i
$215$	39.8560			2.71816
$216$		0			0
$217$	−3.71845			−0.252425
$218$	−10.6127	−	16.8016i	−0.718782	−	1.13795i
$219$		0			0
$220$	−14.8347	+	31.1813i	−1.00015	+	2.10224i
$221$		−	11.8341i		−	0.796048i
$222$		0			0
$223$	4.62678			0.309832			0.154916	−	0.987928i	$-0.450489\pi$
$223$	4.62678			0.309832			0.154916	+	0.987928i	$0.450489\pi$
$224$	5.36115	+	1.80501i	0.358207	+	0.120602i
$225$		0			0
$226$	17.8698	−	11.2875i	1.18868	−	0.750831i
$227$			9.92356i			0.658650i	0.944217	+	0.329325i	$0.106821\pi$
$227$			9.92356i			0.658650i	−0.944217	+	0.329325i	$0.893179\pi$
$228$		0			0
$229$			2.32546i			0.153671i	0.997044	+	0.0768355i	$0.0244816\pi$
$229$			2.32546i			0.153671i	−0.997044	+	0.0768355i	$0.975518\pi$
$230$	1.61173	+	2.55163i	0.106274	+	0.168249i
$231$		0			0
$232$	8.00729	−	0.959843i	0.525704	−	0.0630167i
$233$	3.23031			0.211625			0.105812	−	0.994386i	$-0.466256\pi$
$233$	3.23031			0.211625			0.105812	+	0.994386i	$0.466256\pi$
$234$		0			0
$235$		−	12.8797i		−	0.840182i
$236$	0.0378520	+	0.0180083i	0.00246396	+	0.00117224i
$237$		0			0
$238$	3.91734	−	2.47438i	0.253923	−	0.160390i
$239$	3.48961			0.225724			0.112862	−	0.993611i	$-0.463998\pi$
$239$	3.48961			0.225724			0.112862	+	0.993611i	$0.463998\pi$
$240$		0			0
$241$	9.77778			0.629842			0.314921	−	0.949118i	$-0.398022\pi$
$241$	9.77778			0.629842			0.314921	+	0.949118i	$0.398022\pi$
$242$	−22.3223	+	14.0998i	−1.43493	+	0.906371i
$243$		0			0
$244$	−9.64479	−	4.58856i	−0.617445	−	0.293752i
$245$		−	3.16969i		−	0.202504i
$246$		0			0
$247$	−11.5812			−0.736896
$248$	−1.25177	−	10.4426i	−0.0794873	−	0.663107i
$249$		0			0
$250$	0.112326	+	0.177830i	0.00710414	+	0.0112470i
$251$			25.2169i			1.59168i	0.605509	+	0.795838i	$0.292969\pi$
$251$			25.2169i			1.59168i	−0.605509	+	0.795838i	$0.707031\pi$
$252$		0			0
$253$			3.66729i			0.230561i
$254$	4.86894	−	3.07546i	0.305504	−	0.192971i
$255$		0			0
$256$	−3.26429	+	15.6635i	−0.204018	+	0.978967i
$257$	−6.12920			−0.382329			−0.191165	−	0.981558i	$-0.561226\pi$
$257$	−6.12920			−0.382329			−0.191165	+	0.981558i	$0.561226\pi$
$258$		0			0
$259$			11.9988i			0.745572i
$260$	9.83735	−	20.6773i	0.610086	−	1.28235i
$261$		0			0
$262$	13.4918	+	21.3597i	0.833526	+	1.31960i
$263$	1.27084			0.0783635			0.0391818	−	0.999232i	$-0.487525\pi$
$263$	1.27084			0.0783635			0.0391818	+	0.999232i	$0.487525\pi$
$264$		0			0
$265$	0.924284			0.0567783
$266$	−2.42150	−	3.83363i	−0.148472	−	0.235055i
$267$		0			0
$268$	−11.2103	−	5.33334i	−0.684775	−	0.325785i
$269$		−	19.8081i		−	1.20772i	−0.797091	−	0.603859i	$-0.793629\pi$
$269$		−	19.8081i		−	1.20772i	0.797091	−	0.603859i	$-0.206371\pi$
$270$		0			0
$271$	24.1532			1.46720			0.733600	−	0.679581i	$-0.237838\pi$
$271$	24.1532			1.46720			0.733600	+	0.679581i	$0.237838\pi$
$272$	8.26757	+	10.1682i	0.501295	+	0.616536i
$273$		0			0
$274$	25.2705	−	15.9621i	1.52665	−	0.964304i
$275$			27.4904i			1.65773i
$276$		0			0
$277$			1.31816i			0.0792005i	0.999216	+	0.0396003i	$0.0126084\pi$
$277$			1.31816i			0.0792005i	−0.999216	+	0.0396003i	$0.987392\pi$
$278$	5.58393	+	8.84025i	0.334902	+	0.530203i
$279$		0			0
$280$	8.90151	−	1.06703i	0.531967	−	0.0637675i
$281$	−24.7284			−1.47517			−0.737587	−	0.675252i	$-0.764035\pi$
$281$	−24.7284			−1.47517			−0.737587	+	0.675252i	$0.764035\pi$
$282$		0			0
$283$			18.6573i			1.10906i	0.832163	+	0.554532i	$0.187103\pi$
$283$			18.6573i			1.10906i	−0.832163	+	0.554532i	$0.812897\pi$
$284$	−13.3223	+	28.0024i	−0.790531	+	1.66163i
$285$		0			0
$286$	23.5243	−	14.8591i	1.39102	−	0.878638i
$287$	−7.44602			−0.439525
$288$		0			0
$289$	−6.26596			−0.368586
$290$	10.8060	−	6.82558i	0.634549	−	0.400812i
$291$		0			0
$292$	1.16314	−	2.44483i	0.0680677	−	0.143073i
$293$			14.4030i			0.841431i	0.907193	+	0.420715i	$0.138221\pi$
$293$			14.4030i			0.841431i	−0.907193	+	0.420715i	$0.861779\pi$
$294$		0			0
$295$	0.0664326			0.00386786
$296$	−33.6966	+	4.03925i	−1.95858	+	0.234777i
$297$		0			0
$298$	9.85901	+	15.6084i	0.571117	+	0.904169i
$299$		−	2.43190i		−	0.140640i
$300$		0			0
$301$		−	12.5741i		−	0.724759i
$302$	−21.1007	+	13.3282i	−1.21421	+	0.766952i
$303$		0			0
$304$	9.95089	−	8.09090i	0.570723	−	0.464045i
$305$	−16.9272			−0.969249
$306$		0			0
$307$			27.3734i			1.56228i	0.624353	+	0.781142i	$0.285363\pi$
$307$			27.3734i			1.56228i	−0.624353	+	0.781142i	$0.714637\pi$
$308$	9.83735	+	4.68017i	0.560535	+	0.266677i
$309$		0			0
$310$	−8.90151	−	14.0925i	−0.505572	−	0.800400i
$311$	27.9767			1.58641			0.793206	−	0.608953i	$-0.208410\pi$
$311$	27.9767			1.58641			0.793206	+	0.608953i	$0.208410\pi$
$312$		0			0
$313$	27.5228			1.55568			0.777841	−	0.628461i	$-0.216315\pi$
$313$	27.5228			1.55568			0.777841	+	0.628461i	$0.216315\pi$
$314$	2.26637	+	3.58803i	0.127899	+	0.202484i
$315$		0			0
$316$	−9.52414	+	20.0190i	−0.535775	+	1.12616i
$317$		−	1.73928i		−	0.0976879i	−0.998806	−	0.0488440i	$-0.984446\pi$
$317$		−	1.73928i		−	0.0976879i	0.998806	−	0.0488440i	$-0.0155537\pi$
$318$		0			0
$319$	15.5307			0.869555
$320$	5.99315	+	24.6391i	0.335027	+	1.37737i
$321$		0			0
$322$	0.805009	−	0.508483i	0.0448614	−	0.0283366i
$323$		−	10.5047i		−	0.584495i
$324$		0			0
$325$		−	18.2297i		−	1.01120i
$326$	0.657925	+	1.04160i	0.0364391	+	0.0576889i
$327$		0			0
$328$	−2.50660	−	20.9108i	−0.138404	−	1.15461i
$329$	−4.06341			−0.224023
$330$		0			0
$331$			13.7965i			0.758323i	0.925331	+	0.379161i	$0.123788\pi$
$331$			13.7965i			0.758323i	−0.925331	+	0.379161i	$0.876212\pi$
$332$	−24.6418	−	11.7235i	−1.35240	−	0.643409i
$333$		0			0
$334$	−8.96691	+	5.66394i	−0.490648	+	0.309917i
$335$	−19.6747			−1.07494
$336$		0			0
$337$	−1.96903			−0.107260			−0.0536300	−	0.998561i	$-0.517079\pi$
$337$	−1.96903			−0.107260			−0.0536300	+	0.998561i	$0.517079\pi$
$338$	−0.0561034	+	0.0354376i	−0.00305162	+	0.00192755i
$339$		0			0
$340$	18.7552	+	8.92289i	1.01714	+	0.483912i
$341$		−	20.2542i		−	1.09683i
$342$		0			0
$343$	−1.00000			−0.0539949
$344$	35.3121	−	4.23291i	1.90390	−	0.228223i
$345$		0			0
$346$	−0.493110	−	0.780672i	−0.0265098	−	0.0419692i
$347$		−	21.4183i		−	1.14979i	−0.818226	−	0.574897i	$-0.805042\pi$
$347$		−	21.4183i		−	1.14979i	0.818226	−	0.574897i	$-0.194958\pi$
$348$		0			0
$349$			24.2315i			1.29708i	0.761180	+	0.648541i	$0.224620\pi$
$349$			24.2315i			1.29708i	−0.761180	+	0.648541i	$0.775380\pi$
$350$	6.03442	−	3.81164i	0.322554	−	0.203741i
$351$		0			0
$352$	−9.83181	+	29.2020i	−0.524037	+	1.55647i
$353$	−20.1659			−1.07332			−0.536662	−	0.843797i	$-0.680315\pi$
$353$	−20.1659			−1.07332			−0.536662	+	0.843797i	$0.680315\pi$
$354$		0			0
$355$			49.1459i			2.60839i
$356$	5.10350	−	10.7272i	0.270485	−	0.568538i
$357$		0			0
$358$	−3.34769	−	5.29993i	−0.176931	−	0.280110i
$359$	19.8643			1.04840			0.524198	−	0.851597i	$-0.324365\pi$
$359$	19.8643			1.04840			0.524198	+	0.851597i	$0.324365\pi$
$360$		0			0
$361$	8.71982			0.458938
$362$	−16.5985	−	26.2781i	−0.872400	−	1.38115i
$363$		0			0
$364$	−6.52346	−	3.10357i	−0.341922	−	0.162671i
$365$		−	4.29083i		−	0.224592i
$366$		0			0
$367$	37.1713			1.94033			0.970163	−	0.242454i	$-0.0779523\pi$
$367$	37.1713			1.94033			0.970163	+	0.242454i	$0.0779523\pi$
$368$	1.69898	+	2.08955i	0.0885654	+	0.108925i
$369$		0			0
$370$	−45.4742	+	28.7237i	−2.36409	+	1.49327i
$371$		−	0.291601i		−	0.0151392i
$372$		0			0
$373$			23.6106i			1.22251i	0.791433	+	0.611256i	$0.209335\pi$
$373$			23.6106i			1.22251i	−0.791433	+	0.611256i	$0.790665\pi$
$374$	13.4778	+	21.3376i	0.696922	+	1.10334i
$375$		0			0
$376$	−1.36789	−	11.4114i	−0.0705437	−	0.588497i
$377$	−10.2989			−0.530422
$378$		0			0
$379$		−	15.2051i		−	0.781034i	−0.920596	−	0.390517i	$-0.872296\pi$
$379$		−	15.2051i		−	0.781034i	0.920596	−	0.390517i	$-0.127704\pi$
$380$	8.73221	−	18.3544i	0.447953	−	0.941563i
$381$		0			0
$382$	7.97899	−	5.03992i	0.408241	−	0.257865i
$383$	1.26331			0.0645522			0.0322761	−	0.999479i	$-0.489724\pi$
$383$	1.26331			0.0645522			0.0322761	+	0.999479i	$0.489724\pi$
$384$		0			0
$385$	17.2652			0.879914
$386$	29.9281	−	18.9040i	1.52330	−	0.962191i
$387$		0			0
$388$	8.24920	−	17.3392i	0.418790	−	0.880263i
$389$		−	12.3813i		−	0.627754i	−0.949464	−	0.313877i	$-0.898372\pi$
$389$		−	12.3813i		−	0.627754i	0.949464	−	0.313877i	$-0.101628\pi$
$390$		0			0
$391$	2.20584			0.111554
$392$	−0.336637	−	2.80832i	−0.0170027	−	0.141842i
$393$		0			0
$394$	−2.85458	−	4.51926i	−0.143812	−	0.227677i
$395$			35.1346i			1.76781i
$396$		0			0
$397$			19.0272i			0.954948i	0.878646	+	0.477474i	$0.158447\pi$
$397$			19.0272i			0.954948i	−0.878646	+	0.477474i	$0.841553\pi$
$398$	−8.58558	+	5.42307i	−0.430356	+	0.271834i
$399$		0			0
$400$	12.7357	+	15.6635i	0.636786	+	0.783174i
$401$	−6.06885			−0.303064			−0.151532	−	0.988452i	$-0.548421\pi$
$401$	−6.06885			−0.303064			−0.151532	+	0.988452i	$0.548421\pi$
$402$		0			0
$403$			13.4312i			0.669058i
$404$	−25.6678	−	12.2116i	−1.27702	−	0.607550i
$405$		0			0
$406$	−2.15339	−	3.40916i	−0.106871	−	0.169194i
$407$	−65.3572			−3.23963
$408$		0			0
$409$	28.9491			1.43144			0.715720	−	0.698387i	$-0.246099\pi$
$409$	28.9491			1.43144			0.715720	+	0.698387i	$0.246099\pi$
$410$	−17.8248	−	28.2195i	−0.880306	−	1.39366i
$411$		0			0
$412$	1.45485	−	3.05799i	0.0716755	−	0.150656i
$413$		−	0.0209587i		−	0.00103131i
$414$		0			0
$415$	−43.2480			−2.12296
$416$	6.51979	−	19.3648i	0.319659	−	0.949435i
$417$		0			0
$418$	20.8816	−	13.1898i	1.02135	−	0.645136i
$419$		−	4.30387i		−	0.210258i	−0.994459	−	0.105129i	$-0.966474\pi$
$419$		−	4.30387i		−	0.210258i	0.994459	−	0.105129i	$-0.0335255\pi$
$420$		0			0
$421$		−	18.0243i		−	0.878453i	−0.898376	−	0.439226i	$-0.855253\pi$
$421$		−	18.0243i		−	0.878453i	0.898376	−	0.439226i	$-0.144747\pi$
$422$	−4.00611	−	6.34231i	−0.195014	−	0.308739i
$423$		0			0
$424$	0.818909	−	0.0981635i	0.0397697	−	0.00476724i
$425$	16.5351			0.802073
$426$		0			0
$427$			5.34034i			0.258437i
$428$	−21.0662	−	10.0224i	−1.01828	−	0.484450i
$429$		0			0
$430$	47.6544	−	30.1008i	2.29810	−	1.45159i
$431$	11.0189			0.530760			0.265380	−	0.964144i	$-0.414503\pi$
$431$	11.0189			0.530760			0.265380	+	0.964144i	$0.414503\pi$
$432$		0			0
$433$	11.0881			0.532861			0.266430	−	0.963854i	$-0.414156\pi$
$433$	11.0881			0.532861			0.266430	+	0.963854i	$0.414156\pi$
$434$	−4.44602	+	2.80832i	−0.213416	+	0.134804i
$435$		0			0
$436$	−25.3784	−	12.0739i	−1.21541	−	0.578236i
$437$		−	2.15870i		−	0.103265i
$438$		0			0
$439$	−32.6928			−1.56034			−0.780171	−	0.625567i	$-0.784868\pi$
$439$	−32.6928			−1.56034			−0.780171	+	0.625567i	$0.784868\pi$
$440$	5.81209	+	48.4861i	0.277080	+	2.31149i
$441$		0			0
$442$	−8.93759	−	14.1496i	−0.425118	−	0.673029i
$443$		−	23.6225i		−	1.12234i	−0.827700	−	0.561171i	$-0.810351\pi$
$443$		−	23.6225i		−	1.12234i	0.827700	−	0.561171i	$-0.189649\pi$
$444$		0			0
$445$		−	18.8268i		−	0.892477i
$446$	5.53208	−	3.49433i	0.261951	−	0.165461i
$447$		0			0
$448$	7.77335	−	1.89077i	0.367256	−	0.0893305i
$449$	−8.75599			−0.413220			−0.206610	−	0.978423i	$-0.566243\pi$
$449$	−8.75599			−0.413220			−0.206610	+	0.978423i	$0.566243\pi$
$450$		0			0
$451$		−	40.5581i		−	1.90981i
$452$	12.8416	−	26.9920i	0.604018	−	1.26960i
$453$		0			0
$454$	7.49467	+	11.8652i	0.351742	+	0.556864i
$455$	−11.4491			−0.536741
$456$		0			0
$457$	15.8326			0.740618			0.370309	−	0.928909i	$-0.379252\pi$
$457$	15.8326			0.740618			0.370309	+	0.928909i	$0.379252\pi$
$458$	1.75628	+	2.78048i	0.0820657	+	0.129923i
$459$		0			0
$460$	3.85418	+	1.83365i	0.179702	+	0.0854942i
$461$			36.1188i			1.68222i	0.540865	+	0.841109i	$0.318097\pi$
$461$			36.1188i			1.68222i	−0.540865	+	0.841109i	$0.681903\pi$
$462$		0			0
$463$	8.28903			0.385224			0.192612	−	0.981275i	$-0.438304\pi$
$463$	8.28903			0.385224			0.192612	+	0.981275i	$0.438304\pi$
$464$	8.84912	−	7.19507i	0.410810	−	0.334023i
$465$		0			0
$466$	3.86237	−	2.43966i	0.178921	−	0.113015i
$467$		−	22.7640i		−	1.05339i	−0.850053	−	0.526697i	$-0.823430\pi$
$467$		−	22.7640i		−	1.05339i	0.850053	−	0.526697i	$-0.176570\pi$
$468$		0			0
$469$			6.20714i			0.286619i
$470$	−9.72730	−	15.3999i	−0.448687	−	0.710342i
$471$		0			0
$472$	0.0588589	−	0.00705548i	0.00270920	−	0.000324755i
$473$	68.4906			3.14920
$474$		0			0
$475$		−	16.1818i		−	0.742472i
$476$	2.81507	−	5.91705i	0.129028	−	0.271208i
$477$		0			0
$478$	4.17241	−	2.63549i	0.190841	−	0.120545i
$479$	−38.1931			−1.74509			−0.872543	−	0.488537i	$-0.837531\pi$
$479$	−38.1931			−1.74509			−0.872543	+	0.488537i	$0.837531\pi$
$480$		0			0
$481$	43.3404			1.97615
$482$	11.6909	−	7.38456i	0.532508	−	0.336358i
$483$		0			0
$484$	−16.0412	+	33.7173i	−0.729145	+	1.53261i
$485$		−	30.4313i		−	1.38182i
$486$		0			0
$487$	8.84028			0.400591			0.200296	−	0.979735i	$-0.435810\pi$
$487$	8.84028			0.400591			0.200296	+	0.979735i	$0.435810\pi$
$488$	−14.9974	+	1.79775i	−0.678900	+	0.0813805i
$489$		0			0
$490$	−2.39387	−	3.78988i	−0.108144	−	0.171209i
$491$		−	28.9660i		−	1.30722i	−0.756833	−	0.653608i	$-0.773254\pi$
$491$		−	28.9660i		−	1.30722i	0.756833	−	0.653608i	$-0.226746\pi$
$492$		0			0
$493$		−	9.34157i		−	0.420723i
$494$	−13.8473	+	8.74660i	−0.623017	+	0.393528i
$495$		0			0
$496$	−9.38337	−	11.5405i	−0.421326	−	0.518183i
$497$	15.5050			0.695492
$498$		0			0
$499$		−	0.417929i		−	0.0187091i	−0.999956	−	0.00935453i	$-0.997022\pi$
$499$		−	0.417929i		−	0.0187091i	0.999956	−	0.00935453i	$-0.00297768\pi$
$500$	0.268609	+	0.127792i	0.0120126	+	0.00571504i
$501$		0			0
$502$	19.0448	+	30.1509i	0.850011	+	1.34570i
$503$	−10.3133			−0.459848			−0.229924	−	0.973209i	$-0.573848\pi$
$503$	−10.3133			−0.459848			−0.229924	+	0.973209i	$0.573848\pi$
$504$		0			0
$505$	−45.0487			−2.00464
$506$	2.76968	+	4.38485i	0.123127	+	0.194930i
$507$		0			0
$508$	3.49891	−	7.35443i	0.155239	−	0.326300i
$509$			22.2340i			0.985505i	0.870169	+	0.492753i	$0.164009\pi$
$509$			22.2340i			0.985505i	−0.870169	+	0.492753i	$0.835991\pi$
$510$		0			0
$511$	−1.35371			−0.0598845
$512$	7.92669	+	21.1936i	0.350313	+	0.936633i
$513$		0			0
$514$	−7.32847	+	4.62902i	−0.323245	+	0.204177i
$515$		−	5.36696i		−	0.236497i
$516$		0			0
$517$		−	22.1332i		−	0.973418i
$518$	9.06200	+	14.3466i	0.398161	+	0.630353i
$519$		0			0
$520$	−3.85418	−	32.1527i	−0.169017	−	1.40999i
$521$	−29.3079			−1.28400			−0.642001	−	0.766704i	$-0.721896\pi$
$521$	−29.3079			−1.28400			−0.642001	+	0.766704i	$0.721896\pi$
$522$		0			0
$523$			1.15302i			0.0504181i	0.999682	+	0.0252090i	$0.00802514\pi$
$523$			1.15302i			0.0504181i	−0.999682	+	0.0252090i	$0.991975\pi$
$524$	32.2633	+	15.3494i	1.40943	+	0.670544i
$525$		0			0
$526$	1.51950	−	0.959791i	0.0662534	−	0.0418489i
$527$	−12.1827			−0.530687
$528$		0			0
$529$	−22.5467			−0.980291
$530$	1.10513	−	0.698056i	0.0480039	−	0.0303216i
$531$		0			0
$532$	−5.79061	−	2.75491i	−0.251055	−	0.119441i
$533$			26.8954i			1.16497i
$534$		0			0
$535$	−36.9726			−1.59846
$536$	−17.4316	+	2.08955i	−0.752933	+	0.0902549i
$537$		0			0
$538$	−14.9598	−	23.6838i	−0.644964	−	1.02108i
$539$		−	5.44696i		−	0.234617i
$540$		0			0
$541$		−	34.3825i		−	1.47822i	−0.673586	−	0.739109i	$-0.735247\pi$
$541$		−	34.3825i		−	1.47822i	0.673586	−	0.739109i	$-0.264753\pi$
$542$	28.8791	−	18.2414i	1.24046	−	0.783537i
$543$		0			0
$544$	17.5647	+	5.91372i	0.753078	+	0.253549i
$545$	−44.5407			−1.90792
$546$		0			0
$547$		−	17.1388i		−	0.732802i	−0.930457	−	0.366401i	$-0.880590\pi$
$547$		−	17.1388i		−	0.732802i	0.930457	−	0.366401i	$-0.119410\pi$
$548$	18.1598	−	38.1705i	0.775749	−	1.63056i
$549$		0			0
$550$	20.7618	+	32.8693i	0.885287	+	1.40155i
$551$	−9.14195			−0.389460
$552$		0			0
$553$	11.0846			0.471363
$554$	0.995526	+	1.57608i	0.0422958	+	0.0669610i
$555$		0			0
$556$	13.3530	+	6.35277i	0.566294	+	0.269417i
$557$			29.0976i			1.23290i	0.787393	+	0.616452i	$0.211430\pi$
$557$			29.0976i			1.23290i	−0.787393	+	0.616452i	$0.788570\pi$
$558$		0			0
$559$	−45.4183			−1.92099
$560$	9.83735	−	7.99858i	0.415704	−	0.338002i
$561$		0			0
$562$	−29.5669	+	18.6759i	−1.24720	+	0.787795i
$563$			31.6652i			1.33453i	0.744821	+	0.667264i	$0.232535\pi$
$563$			31.6652i			1.33453i	−0.744821	+	0.667264i	$0.767465\pi$
$564$		0			0
$565$		−	47.3727i		−	1.99298i
$566$	14.0908	+	22.3079i	0.592279	+	0.937671i
$567$		0			0
$568$	5.21954	+	43.5429i	0.219007	+	1.82702i
$569$	6.16080			0.258274			0.129137	−	0.991627i	$-0.458779\pi$
$569$	6.16080			0.258274			0.129137	+	0.991627i	$0.458779\pi$
$570$		0			0
$571$			41.0313i			1.71711i	0.512724	+	0.858553i	$0.328636\pi$
$571$			41.0313i			1.71711i	−0.512724	+	0.858553i	$0.671364\pi$
$572$	16.9050	−	35.5330i	0.706834	−	1.48571i
$573$		0			0
$574$	−8.90294	+	5.62353i	−0.371601	+	0.234722i
$575$	3.39796			0.141705
$576$		0			0
$577$	−25.4290			−1.05862			−0.529311	−	0.848428i	$-0.677550\pi$
$577$	−25.4290			−1.05862			−0.529311	+	0.848428i	$0.677550\pi$
$578$	−7.49199	+	4.73231i	−0.311626	+	0.196838i
$579$		0			0
$580$	7.76537	−	16.3222i	0.322440	−	0.677743i
$581$			13.6442i			0.566058i
$582$		0			0
$583$	1.58834			0.0657822
$584$	−0.455708	−	3.80165i	−0.0188573	−	0.157313i
$585$		0			0
$586$	10.8777	+	17.2211i	0.449354	+	0.711398i
$587$		−	3.55639i		−	0.146788i	−0.997303	−	0.0733939i	$-0.976617\pi$
$587$		−	3.55639i		−	0.146788i	0.997303	−	0.0733939i	$-0.0233830\pi$
$588$		0			0
$589$			11.9224i			0.491253i
$590$	0.0794311	−	0.0501725i	0.00327013	−	0.00206557i
$591$		0			0
$592$	−37.2392	+	30.2786i	−1.53052	+	1.24444i
$593$	2.57142			0.105596			0.0527978	−	0.998605i	$-0.483186\pi$
$593$	2.57142			0.105596			0.0527978	+	0.998605i	$0.483186\pi$
$594$		0			0
$595$		−	10.3848i		−	0.425735i
$596$	23.5761	+	11.2165i	0.965716	+	0.459444i
$597$		0			0
$598$	−1.83667	−	2.90774i	−0.0751069	−	0.118906i
$599$	−21.8400			−0.892357			−0.446178	−	0.894944i	$-0.647215\pi$
$599$	−21.8400			−0.892357			−0.446178	+	0.894944i	$0.647215\pi$
$600$		0			0
$601$	−43.8140			−1.78721			−0.893606	−	0.448853i	$-0.851833\pi$
$601$	−43.8140			−1.78721			−0.893606	+	0.448853i	$0.851833\pi$
$602$	−9.49646	−	15.0344i	−0.387047	−	0.612757i
$603$		0			0
$604$	−15.1633	+	31.8721i	−0.616987	+	1.29686i
$605$			59.1760i			2.40585i
$606$		0			0
$607$	17.9012			0.726588			0.363294	−	0.931675i	$-0.381652\pi$
$607$	17.9012			0.726588			0.363294	+	0.931675i	$0.381652\pi$
$608$	5.78735	−	17.1893i	0.234708	−	0.697119i
$609$		0			0
$610$	−20.2393	+	12.7841i	−0.819464	+	0.517613i
$611$			14.6773i			0.593778i
$612$		0			0
$613$			15.8902i			0.641798i	0.947113	+	0.320899i	$0.103985\pi$
$613$			15.8902i			0.641798i	−0.947113	+	0.320899i	$0.896015\pi$
$614$	20.6735	+	32.7294i	0.834315	+	1.32085i
$615$		0			0
$616$	15.2968	−	1.83365i	0.616326	−	0.0738797i
$617$	20.8402			0.838994			0.419497	−	0.907757i	$-0.362206\pi$
$617$	20.8402			0.838994			0.419497	+	0.907757i	$0.362206\pi$
$618$		0			0
$619$		−	31.4914i		−	1.26575i	−0.774255	−	0.632873i	$-0.781875\pi$
$619$		−	31.4914i		−	1.26575i	0.774255	−	0.632873i	$-0.218125\pi$
$620$	−21.2864	−	10.1271i	−0.854883	−	0.406715i
$621$		0			0
$622$	33.4507	−	21.1291i	1.34125	−	0.847200i
$623$	−5.93965			−0.237967
$624$		0			0
$625$	−24.7632			−0.990527
$626$	32.9081	−	20.7863i	1.31527	−	0.830789i
$627$		0			0
$628$	5.41964	+	2.57842i	0.216267	+	0.102890i
$629$			39.3116i			1.56746i
$630$		0			0
$631$	−10.6786			−0.425109			−0.212555	−	0.977149i	$-0.568178\pi$
$631$	−10.6786			−0.425109			−0.212555	+	0.977149i	$0.568178\pi$
$632$	3.73147	+	31.1290i	0.148430	+	1.23825i
$633$		0			0
$634$	−1.31358	−	2.07960i	−0.0521688	−	0.0825915i
$635$		−	12.9075i		−	0.512218i
$636$		0			0
$637$			3.61205i			0.143115i
$638$	18.5696	−	11.7294i	0.735176	−	0.464373i
$639$		0			0
$640$	25.7742	+	24.9338i	1.01882	+	0.985596i
$641$	24.7669			0.978232			0.489116	−	0.872219i	$-0.337319\pi$
$641$	24.7669			0.978232			0.489116	+	0.872219i	$0.337319\pi$
$642$		0			0
$643$			11.5834i			0.456805i	0.973567	+	0.228402i	$0.0733502\pi$
$643$			11.5834i			0.456805i	−0.973567	+	0.228402i	$0.926650\pi$
$644$	0.578494	−	1.21595i	0.0227959	−	0.0479151i
$645$		0			0
$646$	−7.93353	−	12.5600i	−0.312141	−	0.494168i
$647$	−30.1155			−1.18396			−0.591981	−	0.805952i	$-0.701654\pi$
$647$	−30.1155			−1.18396			−0.591981	+	0.805952i	$0.701654\pi$
$648$		0			0
$649$	0.114161			0.00448122
$650$	−13.7678	−	21.7967i	−0.540019	−	0.854935i
$651$		0			0
$652$	1.57332	+	0.748513i	0.0616158	+	0.0293140i
$653$		−	45.7814i		−	1.79157i	−0.444491	−	0.895783i	$-0.646616\pi$
$653$		−	45.7814i		−	1.79157i	0.444491	−	0.895783i	$-0.353384\pi$
$654$		0			0
$655$	56.6242			2.21249
$656$	−18.7897	−	23.1092i	−0.733616	−	0.902264i
$657$		0			0
$658$	−4.85848	+	3.06885i	−0.189403	+	0.119636i
$659$			34.3446i			1.33788i	0.743318	+	0.668938i	$0.233251\pi$
$659$			34.3446i			1.33788i	−0.743318	+	0.668938i	$0.766749\pi$
$660$		0			0
$661$			26.5119i			1.03120i	0.856831	+	0.515598i	$0.172430\pi$
$661$			26.5119i			1.03120i	−0.856831	+	0.515598i	$0.827570\pi$
$662$	10.4196	+	16.4960i	0.404971	+	0.641133i
$663$		0			0
$664$	−38.3174	+	4.59315i	−1.48700	+	0.178249i
$665$	−10.1629			−0.394100
$666$		0			0
$667$		−	1.91969i		−	0.0743305i
$668$	−6.44378	+	13.5443i	−0.249318	+	0.524046i
$669$		0			0
$670$	−23.5243	+	14.8591i	−0.908824	+	0.574057i
$671$	−29.0886			−1.12295
$672$		0			0
$673$	−26.2427			−1.01158			−0.505790	−	0.862657i	$-0.668799\pi$
$673$	−26.2427			−1.01158			−0.505790	+	0.862657i	$0.668799\pi$
$674$	−2.35430	+	1.48709i	−0.0906843	+	0.0572806i
$675$		0			0
$676$	−0.0403169	+	0.0847431i	−0.00155065	+	0.00325935i
$677$		−	3.23458i		−	0.124315i	−0.998066	−	0.0621576i	$-0.980202\pi$
$677$		−	3.23458i		−	0.124315i	0.998066	−	0.0621576i	$-0.0197981\pi$
$678$		0			0
$679$	−9.60073			−0.368442
$680$	29.1639	−	3.49590i	1.11838	−	0.134062i
$681$		0			0
$682$	−15.2968	−	24.2173i	−0.585745	−	0.927328i
$683$			0.708911i			0.0271257i	0.999908	+	0.0135629i	$0.00431733\pi$
$683$			0.708911i			0.0271257i	−0.999908	+	0.0135629i	$0.995683\pi$
$684$		0			0
$685$		−	66.9917i		−	2.55962i
$686$	−1.19566	+	0.755240i	−0.0456507	+	0.0288352i
$687$		0			0
$688$	39.0246	−	31.7303i	1.48780	−	1.20970i
$689$	−1.05328			−0.0401267
$690$		0			0
$691$		−	39.0071i		−	1.48390i	−0.670454	−	0.741951i	$-0.733901\pi$
$691$		−	39.0071i		−	1.48390i	0.670454	−	0.741951i	$-0.266099\pi$
$692$	−1.17919	−	0.561005i	−0.0448260	−	0.0213262i
$693$		0			0
$694$	−16.1759	−	25.6091i	−0.614030	−	0.972108i
$695$	23.4354			0.888955
$696$		0			0
$697$	−24.3953			−0.924037
$698$	18.3006	+	28.9727i	0.692687	+	1.09663i
$699$		0			0
$700$	4.33645	−	9.11487i	0.163902	−	0.344510i
$701$		−	16.2448i		−	0.613559i	−0.951781	−	0.306779i	$-0.900749\pi$
$701$		−	16.2448i		−	0.613559i	0.951781	−	0.306779i	$-0.0992514\pi$
$702$		0			0
$703$	38.4715			1.45098
$704$	10.2989	+	42.3411i	0.388156	+	1.59579i
$705$		0			0
$706$	−24.1117	+	15.2301i	−0.907456	+	0.573193i
$707$			14.2123i			0.534510i
$708$		0			0
$709$			25.1720i			0.945354i	0.881236	+	0.472677i	$0.156712\pi$
$709$			25.1720i			0.945354i	−0.881236	+	0.472677i	$0.843288\pi$
$710$	37.1169	+	58.7620i	1.39297	+	2.20530i
$711$		0			0
$712$	−1.99950	−	16.6804i	−0.0749345	−	0.625126i
$713$	−2.50354			−0.0937581
$714$		0			0
$715$		−	62.3626i		−	2.33223i
$716$	−8.00544	−	3.80863i	−0.299177	−	0.142335i
$717$		0			0
$718$	23.7510	−	15.0023i	0.886379	−	0.559880i
$719$	−7.92289			−0.295474			−0.147737	−	0.989027i	$-0.547199\pi$
$719$	−7.92289			−0.295474			−0.147737	+	0.989027i	$0.547199\pi$
$720$		0			0
$721$	−1.69321			−0.0630586
$722$	10.4260	−	6.58555i	0.388015	−	0.245089i
$723$		0			0
$724$	−39.6926	−	18.8839i	−1.47516	−	0.701816i
$725$		−	14.3901i		−	0.534436i
$726$		0			0
$727$	−6.10313			−0.226353			−0.113176	−	0.993575i	$-0.536102\pi$
$727$	−6.10313			−0.226353			−0.113176	+	0.993575i	$0.536102\pi$
$728$	−10.1438	+	1.21595i	−0.375955	+	0.0450661i
$729$		0			0
$730$	−3.24061	−	5.13039i	−0.119940	−	0.189884i
$731$		−	41.1963i		−	1.52370i
$732$		0			0
$733$		−	26.6568i		−	0.984591i	−0.870428	−	0.492296i	$-0.836158\pi$
$733$		−	26.6568i		−	0.984591i	0.870428	−	0.492296i	$-0.163842\pi$
$734$	44.4444	−	28.0732i	1.64047	−	1.03620i
$735$		0			0
$736$	3.60952	+	1.21526i	0.133049	+	0.0447953i
$737$	−33.8100			−1.24541
$738$		0			0
$739$			9.27736i			0.341273i	0.985334	+	0.170637i	$0.0545824\pi$
$739$			9.27736i			0.341273i	−0.985334	+	0.170637i	$0.945418\pi$
$740$	−32.6786	+	68.6878i	−1.20129	+	2.52501i
$741$		0			0
$742$	−0.220228	−	0.348657i	−0.00808484	−	0.0127996i
$743$	12.6494			0.464062			0.232031	−	0.972708i	$-0.425463\pi$
$743$	12.6494			0.464062			0.232031	+	0.972708i	$0.425463\pi$
$744$		0			0
$745$	41.3776			1.51596
$746$	17.8317	+	28.2304i	0.652865	+	1.03359i
$747$		0			0
$748$	32.2299	+	15.3336i	1.17844	+	0.560650i
$749$			11.6644i			0.426209i
$750$		0			0
$751$	−7.10625			−0.259311			−0.129655	−	0.991559i	$-0.541387\pi$
$751$	−7.10625			−0.259311			−0.129655	+	0.991559i	$0.541387\pi$
$752$	−10.2539	−	12.6111i	−0.373920	−	0.459879i
$753$		0			0
$754$	−12.3141	+	7.77817i	−0.448452	+	0.283264i
$755$			55.9376i			2.03578i
$756$		0			0
$757$			34.6019i			1.25763i	0.777556	+	0.628814i	$0.216459\pi$
$757$			34.6019i			1.25763i	−0.777556	+	0.628814i	$0.783541\pi$
$758$	−11.4835	−	18.1802i	−0.417100	−	0.660335i
$759$		0			0
$760$	−3.42120	−	28.5407i	−0.124100	−	1.03528i
$761$	−21.7114			−0.787039			−0.393520	−	0.919316i	$-0.628743\pi$
$761$	−21.7114			−0.787039			−0.393520	+	0.919316i	$0.628743\pi$
$762$		0			0
$763$			14.0521i			0.508720i
$764$	5.73385	−	12.0521i	0.207443	−	0.436030i
$765$		0			0
$766$	1.51050	−	0.954103i	0.0545764	−	0.0344731i
$767$	−0.0757040			−0.00273351
$768$		0			0
$769$	−5.94161			−0.214260			−0.107130	−	0.994245i	$-0.534166\pi$
$769$	−5.94161			−0.214260			−0.107130	+	0.994245i	$0.534166\pi$
$770$	20.6433	−	13.0393i	0.743934	−	0.469905i
$771$		0			0
$772$	21.5069	−	45.2058i	0.774050	−	1.62699i
$773$			1.14102i			0.0410398i	0.999789	+	0.0205199i	$0.00653215\pi$
$773$			1.14102i			0.0410398i	−0.999789	+	0.0205199i	$0.993468\pi$
$774$		0			0
$775$	−18.7667			−0.674121
$776$	−3.23196	−	26.9620i	−0.116021	−	0.967878i
$777$		0			0
$778$	−9.35081	−	14.8038i	−0.335243	−	0.530743i
$779$			23.8740i			0.855374i
$780$		0			0
$781$			84.4548i			3.02203i
$782$	2.63744	−	1.66593i	0.0943146	−	0.0595737i
$783$		0			0
$784$	−2.52346	−	3.10357i	−0.0901236	−	0.110842i
$785$	9.51181			0.339491
$786$		0			0
$787$			42.2224i			1.50507i	0.658555	+	0.752533i	$0.271168\pi$
$787$			42.2224i			1.50507i	−0.658555	+	0.752533i	$0.728832\pi$
$788$	−6.82625	−	3.24762i	−0.243175	−	0.115692i
$789$		0			0
$790$	26.5350	+	42.0092i	0.944075	+	1.49462i
$791$	−14.9455			−0.531402
$792$		0			0
$793$	19.2896			0.684993
$794$	14.3701	+	22.7501i	0.509976	+	0.807372i
$795$		0			0
$796$	−6.16975	+	12.9683i	−0.218681	+	0.459651i
$797$		−	37.0441i		−	1.31217i	−0.754687	−	0.656085i	$-0.772211\pi$
$797$		−	37.0441i		−	1.31217i	0.754687	−	0.656085i	$-0.227789\pi$
$798$		0			0
$799$	−13.3129			−0.470976
$800$	27.0573	+	9.10974i	0.956621	+	0.322078i
$801$		0			0
$802$	−7.25631	+	4.58344i	−0.256229	+	0.161847i
$803$		−	7.37359i		−	0.260208i
$804$		0			0
$805$		−	2.13407i		−	0.0752160i
$806$	10.1438	+	16.0593i	0.357300	+	0.565663i
$807$		0			0
$808$	−39.9128	+	4.78439i	−1.40413	+	0.168314i
$809$	18.7803			0.660279			0.330140	−	0.943932i	$-0.392904\pi$
$809$	18.7803			0.660279			0.330140	+	0.943932i	$0.392904\pi$
$810$		0			0
$811$			54.4054i			1.91043i	0.295909	+	0.955216i	$0.404377\pi$
$811$			54.4054i			1.91043i	−0.295909	+	0.955216i	$0.595623\pi$
$812$	−5.14947	−	2.44989i	−0.180711	−	0.0859741i
$813$		0			0
$814$	−78.1452	+	49.3603i	−2.73899	+	1.73008i
$815$	2.76127			0.0967229
$816$		0			0
$817$	−40.3160			−1.41048
$818$	34.6134	−	21.8635i	1.21023	−	0.764439i
$819$		0			0
$820$	−42.6250	−	20.2791i	−1.48853	−	0.708176i
$821$			26.7178i			0.932458i	0.884664	+	0.466229i	$0.154388\pi$
$821$			26.7178i			0.932458i	−0.884664	+	0.466229i	$0.845612\pi$
$822$		0			0
$823$	−15.5033			−0.540412			−0.270206	−	0.962802i	$-0.587092\pi$
$823$	−15.5033			−0.540412			−0.270206	+	0.962802i	$0.587092\pi$
$824$	−0.569998	−	4.75509i	−0.0198568	−	0.165651i
$825$		0			0
$826$	−0.0158289	−	0.0250596i	−0.000550756	−	0.000871935i
$827$			16.0053i			0.556559i	0.960500	+	0.278279i	$0.0897641\pi$
$827$			16.0053i			0.556559i	−0.960500	+	0.278279i	$0.910236\pi$
$828$		0			0
$829$			46.1590i			1.60317i	0.597881	+	0.801585i	$0.296009\pi$
$829$			46.1590i			1.60317i	−0.597881	+	0.801585i	$0.703991\pi$
$830$	−51.7100	+	32.6626i	−1.79488	+	1.13373i
$831$		0			0
$832$	−6.82956	−	28.0778i	−0.236772	−	0.973421i
$833$	−3.27628			−0.113517
$834$		0			0
$835$			23.7711i			0.822634i
$836$	15.0059	−	31.5412i	0.518990	−	1.09088i
$837$		0			0
$838$	−3.25045	−	5.14599i	−0.112285	−	0.177765i
$839$	−4.38306			−0.151320			−0.0756601	−	0.997134i	$-0.524106\pi$
$839$	−4.38306			−0.151320			−0.0756601	+	0.997134i	$0.524106\pi$
$840$		0			0
$841$	20.8703			0.719664
$842$	−13.6127	−	21.5511i	−0.469125	−	0.742699i
$843$		0			0
$844$	−9.57992	−	4.55770i	−0.329754	−	0.156882i
$845$			0.148729i			0.00511644i
$846$		0			0
$847$	18.6693			0.641486
$848$	0.905003	−	0.735843i	0.0310779	−	0.0252690i
$849$		0			0
$850$	19.7705	−	12.4880i	0.678122	−	0.428335i
$851$			8.07850i			0.276927i
$852$		0			0
$853$		−	15.5653i		−	0.532946i	−0.963842	−	0.266473i	$-0.914142\pi$
$853$		−	15.5653i		−	0.532946i	0.963842	−	0.266473i	$-0.0858583\pi$
$854$	4.03324	+	6.38525i	0.138015	+	0.218499i
$855$		0			0
$856$	−32.7575	+	3.92667i	−1.11963	+	0.134211i
$857$	30.2023			1.03169			0.515846	−	0.856681i	$-0.327478\pi$
$857$	30.2023			1.03169			0.515846	+	0.856681i	$0.327478\pi$
$858$		0			0
$859$			6.32139i			0.215683i	0.994168	+	0.107841i	$0.0343939\pi$
$859$			6.32139i			0.215683i	−0.994168	+	0.107841i	$0.965606\pi$
$860$	34.2453	−	71.9810i	1.16776	−	2.45453i
$861$		0			0
$862$	13.1749	−	8.32189i	0.448738	−	0.283445i
$863$	35.8902			1.22172			0.610858	−	0.791740i	$-0.290825\pi$
$863$	35.8902			1.22172			0.610858	+	0.791740i	$0.290825\pi$
$864$		0			0
$865$	−2.06955			−0.0703668
$866$	13.2577	−	8.37418i	0.450514	−	0.284566i
$867$		0			0
$868$	−3.19499	+	6.71562i	−0.108445	+	0.227943i
$869$			60.3771i			2.04815i
$870$		0			0
$871$	22.4205			0.759690
$872$	−39.4628	+	4.73045i	−1.33638	+	0.160193i
$873$		0			0
$874$	−1.63033	−	2.58108i	−0.0551469	−	0.0873063i
$875$		−	0.148729i		−	0.00502797i
$876$		0			0
$877$			32.3677i			1.09298i	0.837466	+	0.546490i	$0.184036\pi$
$877$			32.3677i			1.09298i	−0.837466	+	0.546490i	$0.815964\pi$
$878$	−39.0896	+	24.6909i	−1.31921	+	0.833277i
$879$		0			0
$880$	43.5679	+	53.5836i	1.46868	+	1.80630i
$881$	−33.1052			−1.11534			−0.557670	−	0.830062i	$-0.688305\pi$
$881$	−33.1052			−1.11534			−0.557670	+	0.830062i	$0.688305\pi$
$882$		0			0
$883$		−	19.7891i		−	0.665957i	−0.942934	−	0.332979i	$-0.891946\pi$
$883$		−	19.7891i		−	0.665957i	0.942934	−	0.332979i	$-0.108054\pi$
$884$	−21.3727	−	10.1682i	−0.718842	−	0.341993i
$885$		0			0
$886$	−17.8407	−	28.2446i	−0.599370	−	0.948897i
$887$	0.843244			0.0283133			0.0141567	−	0.999900i	$-0.495494\pi$
$887$	0.843244			0.0283133			0.0141567	+	0.999900i	$0.495494\pi$
$888$		0			0
$889$	−4.07216			−0.136576
$890$	−14.2188	−	22.5106i	−0.476614	−	0.754556i
$891$		0			0
$892$	3.97545	−	8.35609i	0.133108	−	0.279783i
$893$			13.0284i			0.435979i
$894$		0			0
$895$	−14.0500			−0.469641
$896$	7.86633	−	8.13147i	0.262796	−	0.271653i
$897$		0			0
$898$	−10.4692	+	6.61287i	−0.349362	+	0.220674i
$899$			10.6023i			0.353607i
$900$		0			0
$901$		−	0.955367i		−	0.0318279i
$902$	−30.6311	−	48.4939i	−1.01990	−	1.61467i
$903$		0			0
$904$	−5.03122	−	41.9719i	−0.167336	−	1.39596i
$905$	−69.6629			−2.31567
$906$		0			0
$907$		−	9.01198i		−	0.299238i	−0.988744	−	0.149619i	$-0.952195\pi$
$907$		−	9.01198i		−	0.299238i	0.988744	−	0.149619i	$-0.0478047\pi$
$908$	17.9222	+	8.52658i	0.594769	+	0.282965i
$909$		0			0
$910$	−13.6893	+	8.64680i	−0.453794	+	0.286639i
$911$	1.53535			0.0508685			0.0254343	−	0.999676i	$-0.491903\pi$
$911$	1.53535			0.0508685			0.0254343	+	0.999676i	$0.491903\pi$
$912$		0			0
$913$	−74.3195			−2.45962
$914$	18.9305	−	11.9574i	0.626165	−	0.395516i
$915$		0			0
$916$	4.19985	+	1.99810i	0.138767	+	0.0660191i
$917$		−	17.8643i		−	0.589930i
$918$		0			0
$919$	−22.4581			−0.740826			−0.370413	−	0.928867i	$-0.620784\pi$
$919$	−22.4581			−0.740826			−0.370413	+	0.928867i	$0.620784\pi$
$920$	5.99315	−	0.718405i	0.197588	−	0.0236851i
$921$		0			0
$922$	27.2783	+	43.1859i	0.898364	+	1.42225i
$923$		−	56.0047i		−	1.84342i
$924$		0			0
$925$			60.5572i			1.99111i
$926$	9.91089	−	6.26020i	0.325692	−	0.205723i
$927$		0			0
$928$	5.14657	−	15.2861i	0.168944	−	0.501791i
$929$	50.2178			1.64759			0.823797	−	0.566885i	$-0.191852\pi$
$929$	50.2178			1.64759			0.823797	+	0.566885i	$0.191852\pi$
$930$		0			0
$931$			3.20627i			0.105081i
$932$	2.77557	−	5.83403i	0.0909168	−	0.191100i
$933$		0			0
$934$	−17.1923	−	27.2181i	−0.562549	−	0.890605i
$935$	56.5655			1.84989
$936$		0			0
$937$	11.9114			0.389130			0.194565	−	0.980890i	$-0.437670\pi$
$937$	11.9114			0.389130			0.194565	+	0.980890i	$0.437670\pi$
$938$	4.68788	+	7.42165i	0.153065	+	0.242326i
$939$		0			0
$940$	−23.2612	−	11.0666i	−0.758695	−	0.360953i
$941$		−	59.5916i		−	1.94263i	−0.237795	−	0.971315i	$-0.576425\pi$
$941$		−	59.5916i		−	1.94263i	0.237795	−	0.971315i	$-0.423575\pi$
$942$		0			0
$943$	−5.01321			−0.163252
$944$	0.0650469	−	0.0528885i	0.00211709	−	0.00172137i
$945$		0			0
$946$	81.8918	−	51.7268i	2.66253	−	1.68178i
$947$			4.69613i			0.152604i	0.997085	+	0.0763018i	$0.0243113\pi$
$947$			4.69613i			0.152604i	−0.997085	+	0.0763018i	$0.975689\pi$
$948$		0			0
$949$			4.88966i			0.158725i
$950$	−12.2211	−	19.3480i	−0.396506	−	0.627732i
$951$		0			0
$952$	−1.10292	−	9.20086i	−0.0357458	−	0.298202i
$953$	−38.9727			−1.26245			−0.631224	−	0.775600i	$-0.717447\pi$
$953$	−38.9727			−1.26245			−0.631224	+	0.775600i	$0.717447\pi$
$954$		0			0
$955$		−	21.1522i		−	0.684469i
$956$	2.99837	−	6.30233i	0.0969741	−	0.203832i
$957$		0			0
$958$	−45.6661	+	28.8449i	−1.47540	+	0.931937i
$959$	−21.1351			−0.682488
$960$		0			0
$961$	−17.1731			−0.553971
$962$	51.8206	−	32.7324i	1.67076	−	1.05534i
$963$		0			0
$964$	8.40132	−	17.6589i	0.270588	−	0.568755i
$965$		−	79.3390i		−	2.55401i
$966$		0			0
$967$	40.5025			1.30247			0.651236	−	0.758875i	$-0.274251\pi$
$967$	40.5025			1.30247			0.651236	+	0.758875i	$0.274251\pi$
$968$	6.28479	+	52.4295i	0.202001	+	1.68515i
$969$		0			0
$970$	−22.9830	−	36.3857i	−0.737938	−	1.16827i
$971$			5.76542i			0.185021i	0.995712	+	0.0925105i	$0.0294892\pi$
$971$			5.76542i			0.185021i	−0.995712	+	0.0925105i	$0.970511\pi$
$972$		0			0
$973$		−	7.39359i		−	0.237028i
$974$	10.5700	−	6.67653i	0.338685	−	0.213930i
$975$		0			0
$976$	−16.5741	+	13.4761i	−0.530524	+	0.431361i
$977$	10.3362			0.330684			0.165342	−	0.986236i	$-0.447127\pi$
$977$	10.3362			0.330684			0.165342	+	0.986236i	$0.447127\pi$
$978$		0			0
$979$		−	32.3530i		−	1.03401i
$980$	−5.72454	−	2.72348i	−0.182864	−	0.0869983i
$981$		0			0
$982$	−21.8763	−	34.6336i	−0.698100	−	1.10520i
$983$	−22.9663			−0.732512			−0.366256	−	0.930514i	$-0.619361\pi$
$983$	−22.9663			−0.732512			−0.366256	+	0.930514i	$0.619361\pi$
$984$		0			0
$985$	−11.9805			−0.381730
$986$	−7.05513	−	11.1694i	−0.224681	−	0.355706i
$987$		0			0
$988$	−9.95089	+	20.9160i	−0.316580	+	0.665426i
$989$		−	8.46581i		−	0.269197i
$990$		0			0
$991$	−5.74450			−0.182480			−0.0912400	−	0.995829i	$-0.529083\pi$
$991$	−5.74450			−0.182480			−0.0912400	+	0.995829i	$0.529083\pi$
$992$	−19.9352	−	6.71184i	−0.632943	−	0.213101i
$993$		0			0
$994$	18.5387	−	11.7100i	0.588013	−	0.371417i
$995$			22.7602i			0.721548i
$996$		0			0
$997$			59.7098i			1.89103i	0.325580	+	0.945515i	$0.394441\pi$
$997$			59.7098i			1.89103i	−0.325580	+	0.945515i	$0.605559\pi$
$998$	−0.315636	−	0.499703i	−0.00999130	−	0.0158178i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1512.2.c.e.757.17	yes	20
3.2	odd	2	inner	1512.2.c.e.757.4	yes	20
4.3	odd	2		6048.2.c.e.3025.4		20
8.3	odd	2		6048.2.c.e.3025.17		20
8.5	even	2	inner	1512.2.c.e.757.18	yes	20
12.11	even	2		6048.2.c.e.3025.18		20
24.5	odd	2	inner	1512.2.c.e.757.3	✓	20
24.11	even	2		6048.2.c.e.3025.3		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1512.2.c.e.757.3	✓	20	24.5	odd	2	inner
1512.2.c.e.757.4	yes	20	3.2	odd	2	inner
1512.2.c.e.757.17	yes	20	1.1	even	1	trivial
1512.2.c.e.757.18	yes	20	8.5	even	2	inner
6048.2.c.e.3025.3		20	24.11	even	2
6048.2.c.e.3025.4		20	4.3	odd	2
6048.2.c.e.3025.17		20	8.3	odd	2
6048.2.c.e.3025.18		20	12.11	even	2

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:	\( N \)	\(=\)	\( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1512.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.19566 - 0.755240i) q^{2} +(0.859226 - 1.80603i) q^{4} -3.16969i q^{5} -1.00000 q^{7} +(-0.336637 - 2.80832i) q^{8} +O(q^{10})\)	\(q+(1.19566 - 0.755240i) q^{2} +(0.859226 - 1.80603i) q^{4} -3.16969i q^{5} -1.00000 q^{7} +(-0.336637 - 2.80832i) q^{8} +(-2.39387 - 3.78988i) q^{10} -5.44696i q^{11} +3.61205i q^{13} +(-1.19566 + 0.755240i) q^{14} +(-2.52346 - 3.10357i) q^{16} -3.27628 q^{17} +3.20627i q^{19} +(-5.72454 - 2.72348i) q^{20} +(-4.11376 - 6.51273i) q^{22} -0.673274 q^{23} -5.04692 q^{25} +(2.72797 + 4.31880i) q^{26} +(-0.859226 + 1.80603i) q^{28} +2.85127i q^{29} +3.71845 q^{31} +(-5.36115 - 1.80501i) q^{32} +(-3.91734 + 2.47438i) q^{34} +3.16969i q^{35} -11.9988i q^{37} +(2.42150 + 3.83363i) q^{38} +(-8.90151 + 1.06703i) q^{40} +7.44602 q^{41} +12.5741i q^{43} +(-9.83735 - 4.68017i) q^{44} +(-0.805009 + 0.508483i) q^{46} +4.06341 q^{47} +1.00000 q^{49} +(-6.03442 + 3.81164i) q^{50} +(6.52346 + 3.10357i) q^{52} +0.291601i q^{53} -17.2652 q^{55} +(0.336637 + 2.80832i) q^{56} +(2.15339 + 3.40916i) q^{58} +0.0209587i q^{59} -5.34034i q^{61} +(4.44602 - 2.80832i) q^{62} +(-7.77335 + 1.89077i) q^{64} +11.4491 q^{65} -6.20714i q^{67} +(-2.81507 + 5.91705i) q^{68} +(2.39387 + 3.78988i) q^{70} -15.5050 q^{71} +1.35371 q^{73} +(-9.06200 - 14.3466i) q^{74} +(5.79061 + 2.75491i) q^{76} +5.44696i q^{77} -11.0846 q^{79} +(-9.83735 + 7.99858i) q^{80} +(8.90294 - 5.62353i) q^{82} -13.6442i q^{83} +10.3848i q^{85} +(9.49646 + 15.0344i) q^{86} +(-15.2968 + 1.83365i) q^{88} +5.93965 q^{89} -3.61205i q^{91} +(-0.578494 + 1.21595i) q^{92} +(4.85848 - 3.06885i) q^{94} +10.1629 q^{95} +9.60073 q^{97} +(1.19566 - 0.755240i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{4} - 20 q^{7}+O(q^{10}) \) 20 * q - 2 * q^4 - 20 * q^7	\( 20 q - 2 q^{4} - 20 q^{7} - 12 q^{10} - 14 q^{16} + 8 q^{22} - 28 q^{25} + 2 q^{28} + 36 q^{31} - 6 q^{34} - 16 q^{40} - 18 q^{46} + 20 q^{49} + 94 q^{52} + 48 q^{55} + 66 q^{58} + 22 q^{64} + 12 q^{70} + 12 q^{76} + 64 q^{79} - 92 q^{88} - 24 q^{94} + 56 q^{97}+O(q^{100}) \) 20 * q - 2 * q^4 - 20 * q^7 - 12 * q^10 - 14 * q^16 + 8 * q^22 - 28 * q^25 + 2 * q^28 + 36 * q^31 - 6 * q^34 - 16 * q^40 - 18 * q^46 + 20 * q^49 + 94 * q^52 + 48 * q^55 + 66 * q^58 + 22 * q^64 + 12 * q^70 + 12 * q^76 + 64 * q^79 - 92 * q^88 - 24 * q^94 + 56 * q^97

Introduction

L-functions

Modular forms

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Database

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