LMFDB - Embedded newform 350.2.o.b.143.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [350,2,Mod(143,350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(350, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([9, 2]))

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

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

chi := DirichletCharacter("350.143");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	350.o (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.79476407074$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			143.1
Root			$0.258819 - 0.965926i$ of defining polynomial
Character	$\chi$	$=$	350.143
Dual form			350.2.o.b.257.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 - 0.258819i) q^{2} +(-0.189469 - 0.707107i) q^{3} +(0.866025 + 0.500000i) q^{4} +0.732051i q^{6} +(-2.19067 + 1.48356i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.13397 - 1.23205i) q^{9} +O(q^{10})$	\(q+(-0.965926 - 0.258819i) q^{2} +(-0.189469 - 0.707107i) q^{3} +(0.866025 + 0.500000i) q^{4} +0.732051i q^{6} +(-2.19067 + 1.48356i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.13397 - 1.23205i) q^{9} +(0.633975 - 1.09808i) q^{11} +(0.189469 - 0.707107i) q^{12} +(4.38134 - 4.38134i) q^{13} +(2.50000 - 0.866025i) q^{14} +(0.500000 + 0.866025i) q^{16} +(-0.448288 + 0.120118i) q^{17} +(-2.38014 + 0.637756i) q^{18} +(1.46410 + 1.26795i) q^{21} +(-0.896575 + 0.896575i) q^{22} +(1.34486 - 5.01910i) q^{23} +(-0.366025 + 0.633975i) q^{24} +(-5.36603 + 3.09808i) q^{26} +(-2.82843 - 2.82843i) q^{27} +(-2.63896 + 0.189469i) q^{28} -3.46410i q^{29} +(-1.50000 - 0.866025i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(-0.896575 - 0.240237i) q^{33} +0.464102 q^{34} +2.46410 q^{36} +(6.69213 + 1.79315i) q^{37} +(-3.92820 - 2.26795i) q^{39} -11.1962i q^{41} +(-1.08604 - 1.60368i) q^{42} +(7.58871 + 7.58871i) q^{43} +(1.09808 - 0.633975i) q^{44} +(-2.59808 + 4.50000i) q^{46} +(1.01669 - 3.79435i) q^{47} +(0.517638 - 0.517638i) q^{48} +(2.59808 - 6.50000i) q^{49} +(0.169873 + 0.294229i) q^{51} +(5.98502 - 1.60368i) q^{52} +(-7.91688 + 2.12132i) q^{53} +(2.00000 + 3.46410i) q^{54} +(2.59808 + 0.500000i) q^{56} +(-0.896575 + 3.34607i) q^{58} +(-7.09808 + 12.2942i) q^{59} +(-6.29423 + 3.63397i) q^{61} +(1.22474 + 1.22474i) q^{62} +(-2.84701 + 5.86491i) q^{63} +1.00000i q^{64} +(0.803848 + 0.464102i) q^{66} +(0.984508 + 3.67423i) q^{67} +(-0.448288 - 0.120118i) q^{68} -3.80385 q^{69} +13.3923 q^{71} +(-2.38014 - 0.637756i) q^{72} +(2.07055 + 7.72741i) q^{73} +(-6.00000 - 3.46410i) q^{74} +(0.240237 + 3.34607i) q^{77} +(3.20736 + 3.20736i) q^{78} +(-9.86603 + 5.69615i) q^{79} +(2.23205 - 3.86603i) q^{81} +(-2.89778 + 10.8147i) q^{82} +(4.24264 - 4.24264i) q^{83} +(0.633975 + 1.83013i) q^{84} +(-5.36603 - 9.29423i) q^{86} +(-2.44949 + 0.656339i) q^{87} +(-1.22474 + 0.328169i) q^{88} +(5.59808 + 9.69615i) q^{89} +(-3.09808 + 16.0981i) q^{91} +(3.67423 - 3.67423i) q^{92} +(-0.328169 + 1.22474i) q^{93} +(-1.96410 + 3.40192i) q^{94} +(-0.633975 + 0.366025i) q^{96} +(8.05558 + 8.05558i) q^{97} +(-4.19187 + 5.60609i) q^{98} -3.12436i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 24 q^{9}+O(q^{10}) $ 8 * q + 24 * q^9	$ 8 q + 24 q^{9} + 12 q^{11} + 20 q^{14} + 4 q^{16} - 16 q^{21} + 4 q^{24} - 36 q^{26} - 12 q^{31} - 24 q^{34} - 8 q^{36} + 24 q^{39} - 12 q^{44} + 36 q^{51} + 16 q^{54} - 36 q^{59} + 12 q^{61} + 48 q^{66} - 72 q^{69} + 24 q^{71} - 48 q^{74} - 72 q^{79} + 4 q^{81} + 12 q^{84} - 36 q^{86} + 24 q^{89} - 4 q^{91} + 12 q^{94} - 12 q^{96}+O(q^{100}) $ 8 * q + 24 * q^9 + 12 * q^11 + 20 * q^14 + 4 * q^16 - 16 * q^21 + 4 * q^24 - 36 * q^26 - 12 * q^31 - 24 * q^34 - 8 * q^36 + 24 * q^39 - 12 * q^44 + 36 * q^51 + 16 * q^54 - 36 * q^59 + 12 * q^61 + 48 * q^66 - 72 * q^69 + 24 * q^71 - 48 * q^74 - 72 * q^79 + 4 * q^81 + 12 * q^84 - 36 * q^86 + 24 * q^89 - 4 * q^91 + 12 * q^94 - 12 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$3$	−0.189469	−	0.707107i	−0.109390	−	0.408248i	0.889416	−	0.457098i	$-0.151111\pi$
$3$	−0.189469	−	0.707107i	−0.109390	−	0.408248i	−0.998806	+	0.0488497i	$0.984444\pi$
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$		0			0
$5$		0			0
$6$			0.732051i			0.298858i
$7$	−2.19067	+	1.48356i	−0.827996	+	0.560734i
$7$	−2.19067	+	1.48356i	−0.827996	+	0.560734i
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	2.13397	−	1.23205i	0.711325	−	0.410684i
$10$		0			0
$11$	0.633975	−	1.09808i	0.191151	−	0.331082i	−0.754481	−	0.656322i	$-0.772111\pi$
$11$	0.633975	−	1.09808i	0.191151	−	0.331082i	0.945632	+	0.325239i	$0.105445\pi$
$12$	0.189469	−	0.707107i	0.0546949	−	0.204124i
$13$	4.38134	−	4.38134i	1.21517	−	1.21517i	0.245860	−	0.969305i	$-0.420930\pi$
$13$	4.38134	−	4.38134i	1.21517	−	1.21517i	0.969305	−	0.245860i	$-0.0790704\pi$
$14$	2.50000	−	0.866025i	0.668153	−	0.231455i
$15$		0			0
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−0.448288	+	0.120118i	−0.108726	+	0.0291330i	−0.312772	−	0.949828i	$-0.601257\pi$
$17$	−0.448288	+	0.120118i	−0.108726	+	0.0291330i	0.204046	+	0.978961i	$0.434591\pi$
$18$	−2.38014	+	0.637756i	−0.561004	+	0.150321i
$19$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$19$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$20$		0			0
$21$	1.46410	+	1.26795i	0.319493	+	0.276689i
$22$	−0.896575	+	0.896575i	−0.191151	+	0.191151i
$23$	1.34486	−	5.01910i	0.280423	−	1.04655i	−0.671696	−	0.740827i	$-0.734434\pi$
$23$	1.34486	−	5.01910i	0.280423	−	1.04655i	0.952119	−	0.305727i	$-0.0988995\pi$
$24$	−0.366025	+	0.633975i	−0.0747146	+	0.129410i
$25$		0			0
$26$	−5.36603	+	3.09808i	−1.05236	+	0.607583i
$27$	−2.82843	−	2.82843i	−0.544331	−	0.544331i
$28$	−2.63896	+	0.189469i	−0.498716	+	0.0358062i
$29$		−	3.46410i		−	0.643268i	−0.946864	−	0.321634i	$-0.895768\pi$
$29$		−	3.46410i		−	0.643268i	0.946864	−	0.321634i	$-0.104232\pi$
$30$		0			0
$31$	−1.50000	−	0.866025i	−0.269408	−	0.155543i	0.359211	−	0.933257i	$-0.383046\pi$
$31$	−1.50000	−	0.866025i	−0.269408	−	0.155543i	−0.628619	+	0.777714i	$0.716379\pi$
$32$	−0.258819	−	0.965926i	−0.0457532	−	0.170753i
$33$	−0.896575	−	0.240237i	−0.156074	−	0.0418198i
$34$	0.464102			0.0795928
$35$		0			0
$36$	2.46410			0.410684
$37$	6.69213	+	1.79315i	1.10018	+	0.294792i	0.762838	−	0.646590i	$-0.223806\pi$
$37$	6.69213	+	1.79315i	1.10018	+	0.294792i	0.337342	+	0.941382i	$0.390472\pi$
$38$		0			0
$39$	−3.92820	−	2.26795i	−0.629016	−	0.363163i
$40$		0			0
$41$		−	11.1962i		−	1.74855i	−0.485435	−	0.874273i	$-0.661339\pi$
$41$		−	11.1962i		−	1.74855i	0.485435	−	0.874273i	$-0.338661\pi$
$42$	−1.08604	−	1.60368i	−0.167580	−	0.247454i
$43$	7.58871	+	7.58871i	1.15727	+	1.15727i	0.985061	+	0.172206i	$0.0550894\pi$
$43$	7.58871	+	7.58871i	1.15727	+	1.15727i	0.172206	+	0.985061i	$0.444911\pi$
$44$	1.09808	−	0.633975i	0.165541	−	0.0955753i
$45$		0			0
$46$	−2.59808	+	4.50000i	−0.383065	+	0.663489i
$47$	1.01669	−	3.79435i	0.148300	−	0.553463i	−0.851286	−	0.524702i	$-0.824177\pi$
$47$	1.01669	−	3.79435i	0.148300	−	0.553463i	0.999586	−	0.0287617i	$-0.00915640\pi$
$48$	0.517638	−	0.517638i	0.0747146	−	0.0747146i
$49$	2.59808	−	6.50000i	0.371154	−	0.928571i
$50$		0			0
$51$	0.169873	+	0.294229i	0.0237870	+	0.0412002i
$52$	5.98502	−	1.60368i	0.829973	−	0.222391i
$53$	−7.91688	+	2.12132i	−1.08747	+	0.291386i	−0.757651	−	0.652660i	$-0.773653\pi$
$53$	−7.91688	+	2.12132i	−1.08747	+	0.291386i	−0.329815	+	0.944045i	$0.606986\pi$
$54$	2.00000	+	3.46410i	0.272166	+	0.471405i
$55$		0			0
$56$	2.59808	+	0.500000i	0.347183	+	0.0668153i
$57$		0			0
$58$	−0.896575	+	3.34607i	−0.117726	+	0.439360i
$59$	−7.09808	+	12.2942i	−0.924091	+	1.60057i	−0.131074	+	0.991373i	$0.541843\pi$
$59$	−7.09808	+	12.2942i	−0.924091	+	1.60057i	−0.793017	+	0.609200i	$0.791491\pi$
$60$		0			0
$61$	−6.29423	+	3.63397i	−0.805893	+	0.465283i	−0.845528	−	0.533931i	$-0.820714\pi$
$61$	−6.29423	+	3.63397i	−0.805893	+	0.465283i	0.0396344	+	0.999214i	$0.487381\pi$
$62$	1.22474	+	1.22474i	0.155543	+	0.155543i
$63$	−2.84701	+	5.86491i	−0.358689	+	0.738909i
$64$			1.00000i			0.125000i
$65$		0			0
$66$	0.803848	+	0.464102i	0.0989468	+	0.0571270i
$67$	0.984508	+	3.67423i	0.120277	+	0.448879i	0.999627	−	0.0272957i	$-0.00868958\pi$
$67$	0.984508	+	3.67423i	0.120277	+	0.448879i	−0.879351	+	0.476175i	$0.842023\pi$
$68$	−0.448288	−	0.120118i	−0.0543629	−	0.0145665i
$69$	−3.80385			−0.457929
$70$		0			0
$71$	13.3923			1.58937			0.794687	−	0.607019i	$-0.207635\pi$
$71$	13.3923			1.58937			0.794687	+	0.607019i	$0.207635\pi$
$72$	−2.38014	−	0.637756i	−0.280502	−	0.0751603i
$73$	2.07055	+	7.72741i	0.242340	+	0.904425i	0.974702	+	0.223509i	$0.0717512\pi$
$73$	2.07055	+	7.72741i	0.242340	+	0.904425i	−0.732362	+	0.680915i	$0.761582\pi$
$74$	−6.00000	−	3.46410i	−0.697486	−	0.402694i
$75$		0			0
$76$		0			0
$77$	0.240237	+	3.34607i	0.0273775	+	0.381320i
$78$	3.20736	+	3.20736i	0.363163	+	0.363163i
$79$	−9.86603	+	5.69615i	−1.11001	+	0.640867i	−0.938833	−	0.344372i	$-0.888092\pi$
$79$	−9.86603	+	5.69615i	−1.11001	+	0.640867i	−0.171181	+	0.985240i	$0.554758\pi$
$80$		0			0
$81$	2.23205	−	3.86603i	0.248006	−	0.429558i
$82$	−2.89778	+	10.8147i	−0.320006	+	1.19428i
$83$	4.24264	−	4.24264i	0.465690	−	0.465690i	−0.434825	−	0.900515i	$-0.643190\pi$
$83$	4.24264	−	4.24264i	0.465690	−	0.465690i	0.900515	+	0.434825i	$0.143190\pi$
$84$	0.633975	+	1.83013i	0.0691723	+	0.199683i
$85$		0			0
$86$	−5.36603	−	9.29423i	−0.578633	−	1.00222i
$87$	−2.44949	+	0.656339i	−0.262613	+	0.0703669i
$88$	−1.22474	+	0.328169i	−0.130558	+	0.0349830i
$89$	5.59808	+	9.69615i	0.593395	+	1.02779i	0.993771	+	0.111439i	$0.0355461\pi$
$89$	5.59808	+	9.69615i	0.593395	+	1.02779i	−0.400376	+	0.916351i	$0.631121\pi$
$90$		0			0
$91$	−3.09808	+	16.0981i	−0.324767	+	1.68754i
$92$	3.67423	−	3.67423i	0.383065	−	0.383065i
$93$	−0.328169	+	1.22474i	−0.0340296	+	0.127000i
$94$	−1.96410	+	3.40192i	−0.202582	+	0.350882i
$95$		0			0
$96$	−0.633975	+	0.366025i	−0.0647048	+	0.0373573i
$97$	8.05558	+	8.05558i	0.817920	+	0.817920i	0.985806	−	0.167887i	$-0.0536942\pi$
$97$	8.05558	+	8.05558i	0.817920	+	0.817920i	−0.167887	+	0.985806i	$0.553694\pi$
$98$	−4.19187	+	5.60609i	−0.423443	+	0.566300i
$99$		−	3.12436i		−	0.314010i
$100$		0			0
$101$	−14.1962	−	8.19615i	−1.41257	−	0.815548i	−0.416940	−	0.908934i	$-0.636897\pi$
$101$	−14.1962	−	8.19615i	−1.41257	−	0.815548i	−0.995630	+	0.0933864i	$0.970231\pi$
$102$	−0.0879327	−	0.328169i	−0.00870664	−	0.0324936i
$103$	−12.5570	−	3.36465i	−1.23728	−	0.331529i	−0.419871	−	0.907584i	$-0.637925\pi$
$103$	−12.5570	−	3.36465i	−1.23728	−	0.331529i	−0.817411	+	0.576055i	$0.804591\pi$
$104$	−6.19615			−0.607583
$105$		0			0
$106$	8.19615			0.796081
$107$	−2.12132	−	0.568406i	−0.205076	−	0.0549499i	0.154819	−	0.987943i	$-0.450521\pi$
$107$	−2.12132	−	0.568406i	−0.205076	−	0.0549499i	−0.359895	+	0.932993i	$0.617187\pi$
$108$	−1.03528	−	3.86370i	−0.0996195	−	0.371785i
$109$	8.83013	+	5.09808i	0.845773	+	0.488307i	0.859222	−	0.511602i	$-0.170948\pi$
$109$	8.83013	+	5.09808i	0.845773	+	0.488307i	−0.0134495	+	0.999910i	$0.504281\pi$
$110$		0			0
$111$		−	5.07180i		−	0.481394i
$112$	−2.38014	−	1.15539i	−0.224902	−	0.109175i
$113$	4.81105	+	4.81105i	0.452585	+	0.452585i	0.896212	−	0.443627i	$-0.146308\pi$
$113$	4.81105	+	4.81105i	0.452585	+	0.452585i	−0.443627	+	0.896212i	$0.646308\pi$
$114$		0			0
$115$		0			0
$116$	1.73205	−	3.00000i	0.160817	−	0.278543i
$117$	3.95164	−	14.7477i	0.365329	−	1.36343i
$118$	10.0382	−	10.0382i	0.924091	−	0.924091i
$119$	0.803848	−	0.928203i	0.0736886	−	0.0850883i
$120$		0			0
$121$	4.69615	+	8.13397i	0.426923	+	0.739452i
$122$	7.02030	−	1.88108i	0.635588	−	0.170305i
$123$	−7.91688	+	2.12132i	−0.713841	+	0.191273i
$124$	−0.866025	−	1.50000i	−0.0777714	−	0.134704i
$125$		0			0
$126$	4.26795	−	4.92820i	0.380219	−	0.439039i
$127$	−4.89898	+	4.89898i	−0.434714	+	0.434714i	−0.890228	−	0.455514i	$-0.849455\pi$
$127$	−4.89898	+	4.89898i	−0.434714	+	0.434714i	0.455514	+	0.890228i	$0.349455\pi$
$128$	0.258819	−	0.965926i	0.0228766	−	0.0853766i
$129$	3.92820	−	6.80385i	0.345859	−	0.599045i
$130$		0			0
$131$	1.90192	−	1.09808i	0.166172	−	0.0959394i	−0.414608	−	0.910000i	$-0.636081\pi$
$131$	1.90192	−	1.09808i	0.166172	−	0.0959394i	0.580780	+	0.814061i	$0.302748\pi$
$132$	−0.656339	−	0.656339i	−0.0571270	−	0.0571270i
$133$		0			0
$134$		−	3.80385i		−	0.328602i
$135$		0			0
$136$	0.401924	+	0.232051i	0.0344647	+	0.0198982i
$137$	−0.208051	−	0.776457i	−0.0177750	−	0.0663372i	0.956469	−	0.291835i	$-0.0942658\pi$
$137$	−0.208051	−	0.776457i	−0.0177750	−	0.0663372i	−0.974244	+	0.225498i	$0.927599\pi$
$138$	3.67423	+	0.984508i	0.312772	+	0.0838069i
$139$	−3.46410			−0.293821			−0.146911	−	0.989150i	$-0.546933\pi$
$139$	−3.46410			−0.293821			−0.146911	+	0.989150i	$0.546933\pi$
$140$		0			0
$141$	−2.87564			−0.242173
$142$	−12.9360	−	3.46618i	−1.08556	−	0.290876i
$143$	−2.03339	−	7.58871i	−0.170040	−	0.634599i
$144$	2.13397	+	1.23205i	0.177831	+	0.102671i
$145$		0			0
$146$		−	8.00000i		−	0.662085i
$147$	−5.08845	−	0.605571i	−0.419688	−	0.0499466i
$148$	4.89898	+	4.89898i	0.402694	+	0.402694i
$149$	7.09808	−	4.09808i	0.581497	−	0.335727i	−0.180231	−	0.983624i	$-0.557685\pi$
$149$	7.09808	−	4.09808i	0.581497	−	0.335727i	0.761728	+	0.647897i	$0.224351\pi$
$150$		0			0
$151$	−9.19615	+	15.9282i	−0.748372	+	1.29622i	0.200230	+	0.979749i	$0.435831\pi$
$151$	−9.19615	+	15.9282i	−0.748372	+	1.29622i	−0.948603	+	0.316470i	$0.897502\pi$
$152$		0			0
$153$	−0.808643	+	0.808643i	−0.0653749	+	0.0653749i
$154$	0.633975	−	3.29423i	0.0510871	−	0.265457i
$155$		0			0
$156$	−2.26795	−	3.92820i	−0.181581	−	0.314508i
$157$	1.93185	−	0.517638i	0.154179	−	0.0413120i	−0.180904	−	0.983501i	$-0.557902\pi$
$157$	1.93185	−	0.517638i	0.154179	−	0.0413120i	0.335083	+	0.942189i	$0.391236\pi$
$158$	11.0041	−	2.94855i	0.875441	−	0.234574i
$159$	3.00000	+	5.19615i	0.237915	+	0.412082i
$160$		0			0
$161$	4.50000	+	12.9904i	0.354650	+	1.02379i
$162$	−3.15660	+	3.15660i	−0.248006	+	0.248006i
$163$	3.76217	−	14.0406i	0.294676	−	1.09974i	−0.646799	−	0.762661i	$-0.723893\pi$
$163$	3.76217	−	14.0406i	0.294676	−	1.09974i	0.941475	−	0.337084i	$-0.109441\pi$
$164$	5.59808	−	9.69615i	0.437136	−	0.757142i
$165$		0			0
$166$	−5.19615	+	3.00000i	−0.403300	+	0.232845i
$167$	−13.3843	−	13.3843i	−1.03571	−	1.03571i	−0.999339	−	0.0363667i	$-0.988422\pi$
$167$	−13.3843	−	13.3843i	−1.03571	−	1.03571i	−0.0363667	−	0.999339i	$-0.511578\pi$
$168$	−0.138701	−	1.93185i	−0.0107010	−	0.149046i
$169$		−	25.3923i		−	1.95325i
$170$		0			0
$171$		0			0
$172$	2.77766	+	10.3664i	0.211795	+	0.790428i
$173$	−17.0585	−	4.57081i	−1.29693	−	0.347512i	−0.456644	−	0.889650i	$-0.650949\pi$
$173$	−17.0585	−	4.57081i	−1.29693	−	0.347512i	−0.840290	+	0.542137i	$0.817615\pi$
$174$	2.53590			0.192246
$175$		0			0
$176$	1.26795			0.0955753
$177$	10.0382	+	2.68973i	0.754517	+	0.202172i
$178$	−2.89778	−	10.8147i	−0.217198	−	0.810592i
$179$	7.09808	+	4.09808i	0.530535	+	0.306305i	0.741234	−	0.671246i	$-0.234241\pi$
$179$	7.09808	+	4.09808i	0.530535	+	0.306305i	−0.210699	+	0.977551i	$0.567574\pi$
$180$		0			0
$181$		−	7.26795i		−	0.540222i	−0.962829	−	0.270111i	$-0.912940\pi$
$181$		−	7.26795i		−	0.540222i	0.962829	−	0.270111i	$-0.0870605\pi$
$182$	7.15900	−	14.7477i	0.530660	−	1.09317i
$183$	3.76217	+	3.76217i	0.278107	+	0.278107i
$184$	−4.50000	+	2.59808i	−0.331744	+	0.191533i
$185$		0			0
$186$	0.633975	−	1.09808i	0.0464853	−	0.0805149i
$187$	−0.152304	+	0.568406i	−0.0111376	+	0.0415660i
$188$	2.77766	−	2.77766i	0.202582	−	0.202582i
$189$	10.3923	+	2.00000i	0.755929	+	0.145479i
$190$		0			0
$191$	2.76795	+	4.79423i	0.200282	+	0.346898i	0.948619	−	0.316420i	$-0.102481\pi$
$191$	2.76795	+	4.79423i	0.200282	+	0.346898i	−0.748337	+	0.663318i	$0.769148\pi$
$192$	0.707107	−	0.189469i	0.0510310	−	0.0136737i
$193$	11.7112	−	3.13801i	0.842993	−	0.225879i	0.188619	−	0.982050i	$-0.439599\pi$
$193$	11.7112	−	3.13801i	0.842993	−	0.225879i	0.654374	+	0.756171i	$0.272932\pi$
$194$	−5.69615	−	9.86603i	−0.408960	−	0.708339i
$195$		0			0
$196$	5.50000	−	4.33013i	0.392857	−	0.309295i
$197$	−5.79555	+	5.79555i	−0.412916	+	0.412916i	−0.882753	−	0.469837i	$-0.844313\pi$
$197$	−5.79555	+	5.79555i	−0.412916	+	0.412916i	0.469837	+	0.882753i	$0.344313\pi$
$198$	−0.808643	+	3.01790i	−0.0574677	+	0.214473i
$199$	9.86603	−	17.0885i	0.699384	−	1.21137i	−0.269296	−	0.963057i	$-0.586791\pi$
$199$	9.86603	−	17.0885i	0.699384	−	1.21137i	0.968680	−	0.248311i	$-0.0798756\pi$
$200$		0			0
$201$	2.41154	−	1.39230i	0.170097	−	0.0982056i
$202$	11.5911	+	11.5911i	0.815548	+	0.815548i
$203$	5.13922	+	7.58871i	0.360702	+	0.532623i
$204$			0.339746i			0.0237870i
$205$		0			0
$206$	11.2583	+	6.50000i	0.784405	+	0.452876i
$207$	−3.31388	−	12.3676i	−0.230331	−	0.859605i
$208$	5.98502	+	1.60368i	0.414987	+	0.111195i
$209$		0			0
$210$		0			0
$211$	−10.1962			−0.701932			−0.350966	−	0.936388i	$-0.614147\pi$
$211$	−10.1962			−0.701932			−0.350966	+	0.936388i	$0.614147\pi$
$212$	−7.91688	−	2.12132i	−0.543733	−	0.145693i
$213$	−2.53742	−	9.46979i	−0.173861	−	0.648859i
$214$	1.90192	+	1.09808i	0.130013	+	0.0750629i
$215$		0			0
$216$			4.00000i			0.272166i
$217$	4.57081	−	0.328169i	0.310287	−	0.0222776i
$218$	−7.20977	−	7.20977i	−0.488307	−	0.488307i
$219$	5.07180	−	2.92820i	0.342720	−	0.197870i
$220$		0			0
$221$	−1.43782	+	2.49038i	−0.0967184	+	0.167521i
$222$	−1.31268	+	4.89898i	−0.0881012	+	0.328798i
$223$	6.64136	−	6.64136i	0.444739	−	0.444739i	−0.448862	−	0.893601i	$-0.648171\pi$
$223$	6.64136	−	6.64136i	0.444739	−	0.444739i	0.893601	+	0.448862i	$0.148171\pi$
$224$	2.00000	+	1.73205i	0.133631	+	0.115728i
$225$		0			0
$226$	−3.40192	−	5.89230i	−0.226293	−	0.391950i
$227$	−26.5283	+	7.10823i	−1.76074	+	0.471790i	−0.986866	−	0.161544i	$-0.948353\pi$
$227$	−26.5283	+	7.10823i	−1.76074	+	0.471790i	−0.773879	+	0.633334i	$0.781686\pi$
$228$		0			0
$229$	7.09808	+	12.2942i	0.469054	+	0.812425i	0.999374	−	0.0353720i	$-0.0112616\pi$
$229$	7.09808	+	12.2942i	0.469054	+	0.812425i	−0.530320	+	0.847797i	$0.677928\pi$
$230$		0			0
$231$	2.32051	−	0.803848i	0.152678	−	0.0528893i
$232$	−2.44949	+	2.44949i	−0.160817	+	0.160817i
$233$	−1.55291	+	5.79555i	−0.101735	+	0.379679i	−0.997954	−	0.0639315i	$-0.979636\pi$
$233$	−1.55291	+	5.79555i	−0.101735	+	0.379679i	0.896219	+	0.443611i	$0.146303\pi$
$234$	−7.63397	+	13.2224i	−0.499049	+	0.864377i
$235$		0			0
$236$	−12.2942	+	7.09808i	−0.800286	+	0.462045i
$237$	5.89709	+	5.89709i	0.383057	+	0.383057i
$238$	−1.01669	+	0.688524i	−0.0659025	+	0.0446304i
$239$			22.8564i			1.47846i	0.673454	+	0.739229i	$0.264810\pi$
$239$			22.8564i			1.47846i	−0.673454	+	0.739229i	$0.735190\pi$
$240$		0			0
$241$	−3.00000	−	1.73205i	−0.193247	−	0.111571i	0.400255	−	0.916404i	$-0.368922\pi$
$241$	−3.00000	−	1.73205i	−0.193247	−	0.111571i	−0.593502	+	0.804833i	$0.702255\pi$
$242$	−2.43091	−	9.07227i	−0.156265	−	0.583188i
$243$	−14.7477	−	3.95164i	−0.946066	−	0.253498i
$244$	−7.26795			−0.465283
$245$		0			0
$246$	8.19615			0.522568
$247$		0			0
$248$	0.448288	+	1.67303i	0.0284663	+	0.106238i
$249$	−3.80385	−	2.19615i	−0.241059	−	0.139176i
$250$		0			0
$251$		−	4.39230i		−	0.277240i	−0.990346	−	0.138620i	$-0.955733\pi$
$251$		−	4.39230i		−	0.277240i	0.990346	−	0.138620i	$-0.0442666\pi$
$252$	−5.39804	+	3.65565i	−0.340044	+	0.230284i
$253$	−4.65874	−	4.65874i	−0.292893	−	0.292893i
$254$	6.00000	−	3.46410i	0.376473	−	0.217357i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	1.13681	−	4.24264i	0.0709124	−	0.264649i	−0.921363	−	0.388703i	$-0.872923\pi$
$257$	1.13681	−	4.24264i	0.0709124	−	0.264649i	0.992275	+	0.124055i	$0.0395898\pi$
$258$	−5.55532	+	5.55532i	−0.345859	+	0.345859i
$259$	−17.3205	+	6.00000i	−1.07624	+	0.372822i
$260$		0			0
$261$	−4.26795	−	7.39230i	−0.264179	−	0.457572i
$262$	−2.12132	+	0.568406i	−0.131056	+	0.0351162i
$263$	3.46618	−	0.928761i	0.213734	−	0.0572699i	−0.150363	−	0.988631i	$-0.548044\pi$
$263$	3.46618	−	0.928761i	0.213734	−	0.0572699i	0.364097	+	0.931361i	$0.381378\pi$
$264$	0.464102	+	0.803848i	0.0285635	+	0.0494734i
$265$		0			0
$266$		0			0
$267$	5.79555	−	5.79555i	0.354682	−	0.354682i
$268$	−0.984508	+	3.67423i	−0.0601384	+	0.224440i
$269$	−6.29423	+	10.9019i	−0.383766	+	0.664702i	−0.991597	−	0.129364i	$-0.958706\pi$
$269$	−6.29423	+	10.9019i	−0.383766	+	0.664702i	0.607831	+	0.794066i	$0.292040\pi$
$270$		0			0
$271$	20.0885	−	11.5981i	1.22029	−	0.704533i	0.255308	−	0.966860i	$-0.417823\pi$
$271$	20.0885	−	11.5981i	1.22029	−	0.704533i	0.964979	+	0.262327i	$0.0844899\pi$
$272$	−0.328169	−	0.328169i	−0.0198982	−	0.0198982i
$273$	11.9700	−	0.859411i	0.724460	−	0.0520139i
$274$			0.803848i			0.0485622i
$275$		0			0
$276$	−3.29423	−	1.90192i	−0.198289	−	0.114482i
$277$	−1.70522	−	6.36396i	−0.102457	−	0.382373i	0.895588	−	0.444885i	$-0.146756\pi$
$277$	−1.70522	−	6.36396i	−0.102457	−	0.382373i	−0.998044	+	0.0625119i	$0.980089\pi$
$278$	3.34607	+	0.896575i	0.200684	+	0.0537730i
$279$	−4.26795			−0.255515
$280$		0			0
$281$	24.4641			1.45941			0.729703	−	0.683764i	$-0.239658\pi$
$281$	24.4641			1.45941			0.729703	+	0.683764i	$0.239658\pi$
$282$	2.77766	+	0.744272i	0.165407	+	0.0443207i
$283$	0.619174	+	2.31079i	0.0368061	+	0.137362i	0.981884	−	0.189483i	$-0.0606812\pi$
$283$	0.619174	+	2.31079i	0.0368061	+	0.137362i	−0.945078	+	0.326845i	$0.894014\pi$
$284$	11.5981	+	6.69615i	0.688219	+	0.397344i
$285$		0			0
$286$			7.85641i			0.464559i
$287$	16.6102	+	24.5271i	0.980470	+	1.44779i
$288$	−1.74238	−	1.74238i	−0.102671	−	0.102671i
$289$	−14.5359	+	8.39230i	−0.855053	+	0.493665i
$290$		0			0
$291$	4.16987	−	7.22243i	0.244442	−	0.423386i
$292$	−2.07055	+	7.72741i	−0.121170	+	0.452212i
$293$	−22.5259	+	22.5259i	−1.31598	+	1.31598i	−0.399044	+	0.916932i	$0.630658\pi$
$293$	−22.5259	+	22.5259i	−1.31598	+	1.31598i	−0.916932	+	0.399044i	$0.869342\pi$
$294$	4.75833	+	1.90192i	0.277511	+	0.110922i
$295$		0			0
$296$	−3.46410	−	6.00000i	−0.201347	−	0.348743i
$297$	−4.89898	+	1.31268i	−0.284268	+	0.0761693i
$298$	−7.91688	+	2.12132i	−0.458612	+	0.122885i
$299$	−16.0981	−	27.8827i	−0.930976	−	1.61250i
$300$		0			0
$301$	−27.8827	−	5.36603i	−1.60713	−	0.309293i
$302$	13.0053	−	13.0053i	0.748372	−	0.748372i
$303$	−3.10583	+	11.5911i	−0.178425	+	0.665892i
$304$		0			0
$305$		0			0
$306$	0.990381	−	0.571797i	0.0566163	−	0.0326874i
$307$	8.76268	+	8.76268i	0.500113	+	0.500113i	0.911473	−	0.411360i	$-0.134946\pi$
$307$	8.76268	+	8.76268i	0.500113	+	0.500113i	−0.411360	+	0.911473i	$0.634946\pi$
$308$	−1.46498	+	3.01790i	−0.0834751	+	0.171961i
$309$			9.51666i			0.541384i
$310$		0			0
$311$	−0.696152	−	0.401924i	−0.0394752	−	0.0227910i	0.480133	−	0.877196i	$-0.340589\pi$
$311$	−0.696152	−	0.401924i	−0.0394752	−	0.0227910i	−0.519608	+	0.854405i	$0.673922\pi$
$312$	1.17398	+	4.38134i	0.0664634	+	0.248045i
$313$	18.3526	+	4.91756i	1.03735	+	0.277957i	0.737015	−	0.675877i	$-0.236235\pi$
$313$	18.3526	+	4.91756i	1.03735	+	0.277957i	0.300335	+	0.953834i	$0.402902\pi$
$314$	−2.00000			−0.112867
$315$		0			0
$316$	−11.3923			−0.640867
$317$	15.8338	+	4.24264i	0.889312	+	0.238290i	0.674420	−	0.738347i	$-0.264394\pi$
$317$	15.8338	+	4.24264i	0.889312	+	0.238290i	0.214892	+	0.976638i	$0.431060\pi$
$318$	−1.55291	−	5.79555i	−0.0870831	−	0.324999i
$319$	−3.80385	−	2.19615i	−0.212975	−	0.122961i
$320$		0			0
$321$			1.60770i			0.0897328i
$322$	−0.984508	−	13.7124i	−0.0548645	−	0.764164i
$323$		0			0
$324$	3.86603	−	2.23205i	0.214779	−	0.124003i
$325$		0			0
$326$	−7.26795	+	12.5885i	−0.402534	+	0.697210i
$327$	1.93185	−	7.20977i	0.106832	−	0.398701i
$328$	−7.91688	+	7.91688i	−0.437136	+	0.437136i
$329$	3.40192	+	9.82051i	0.187554	+	0.541422i
$330$		0			0
$331$	7.00000	+	12.1244i	0.384755	+	0.666415i	0.991735	−	0.128302i	$-0.0409527\pi$
$331$	7.00000	+	12.1244i	0.384755	+	0.666415i	−0.606980	+	0.794717i	$0.707619\pi$
$332$	5.79555	−	1.55291i	0.318072	−	0.0852272i
$333$	16.4901	−	4.41851i	0.903651	−	0.242133i
$334$	9.46410	+	16.3923i	0.517853	+	0.896947i
$335$		0			0
$336$	−0.366025	+	1.90192i	−0.0199683	+	0.103758i
$337$	−6.12372	+	6.12372i	−0.333581	+	0.333581i	−0.853945	−	0.520364i	$-0.825796\pi$
$337$	−6.12372	+	6.12372i	−0.333581	+	0.333581i	0.520364	+	0.853945i	$0.325796\pi$
$338$	−6.57201	+	24.5271i	−0.357470	+	1.33410i
$339$	2.49038	−	4.31347i	0.135259	−	0.234275i
$340$		0			0
$341$	−1.90192	+	1.09808i	−0.102995	+	0.0594642i
$342$		0			0
$343$	3.95164	+	18.0938i	0.213368	+	0.976972i
$344$		−	10.7321i		−	0.578633i
$345$		0			0
$346$	15.2942	+	8.83013i	0.822223	+	0.474711i
$347$	1.55291	+	5.79555i	0.0833648	+	0.311122i	0.995000	−	0.0998797i	$-0.0318458\pi$
$347$	1.55291	+	5.79555i	0.0833648	+	0.311122i	−0.911635	+	0.411001i	$0.865179\pi$
$348$	−2.44949	−	0.656339i	−0.131306	−	0.0351835i
$349$	−16.9808			−0.908959			−0.454480	−	0.890757i	$-0.650175\pi$
$349$	−16.9808			−0.908959			−0.454480	+	0.890757i	$0.650175\pi$
$350$		0			0
$351$	−24.7846			−1.32290
$352$	−1.22474	−	0.328169i	−0.0652791	−	0.0174915i
$353$	6.09154	+	22.7339i	0.324220	+	1.21001i	0.915094	+	0.403241i	$0.132116\pi$
$353$	6.09154	+	22.7339i	0.324220	+	1.21001i	−0.590874	+	0.806764i	$0.701217\pi$
$354$	−9.00000	−	5.19615i	−0.478345	−	0.276172i
$355$		0			0
$356$			11.1962i			0.593395i
$357$	−0.808643	−	0.392541i	−0.0427979	−	0.0207755i
$358$	−5.79555	−	5.79555i	−0.306305	−	0.306305i
$359$	−9.00000	+	5.19615i	−0.475002	+	0.274242i	−0.718331	−	0.695701i	$-0.755094\pi$
$359$	−9.00000	+	5.19615i	−0.475002	+	0.274242i	0.243329	+	0.969944i	$0.421760\pi$
$360$		0			0
$361$	9.50000	−	16.4545i	0.500000	−	0.866025i
$362$	−1.88108	+	7.02030i	−0.0988676	+	0.368979i
$363$	4.86181	−	4.86181i	0.255179	−	0.255179i
$364$	−10.7321	+	12.3923i	−0.562512	+	0.649533i
$365$		0			0
$366$	−2.66025	−	4.60770i	−0.139054	−	0.240848i
$367$	17.7656	−	4.76028i	0.927357	−	0.248485i	0.236630	−	0.971600i	$-0.423957\pi$
$367$	17.7656	−	4.76028i	0.927357	−	0.248485i	0.690727	+	0.723115i	$0.257291\pi$
$368$	5.01910	−	1.34486i	0.261639	−	0.0701058i
$369$	−13.7942	−	23.8923i	−0.718099	−	1.24378i
$370$		0			0
$371$	14.1962	−	16.3923i	0.737028	−	0.851046i
$372$	−0.896575	+	0.896575i	−0.0464853	+	0.0464853i
$373$	4.39494	−	16.4022i	0.227562	−	0.849271i	−0.753800	−	0.657103i	$-0.771781\pi$
$373$	4.39494	−	16.4022i	0.227562	−	0.849271i	0.981362	−	0.192168i	$-0.0615519\pi$
$374$	0.294229	−	0.509619i	0.0152142	−	0.0263518i
$375$		0			0
$376$	−3.40192	+	1.96410i	−0.175441	+	0.101291i
$377$	−15.1774	−	15.1774i	−0.781676	−	0.781676i
$378$	−9.52056	−	4.62158i	−0.489685	−	0.237708i
$379$			8.58846i			0.441159i	0.975369	+	0.220580i	$0.0707949\pi$
$379$			8.58846i			0.441159i	−0.975369	+	0.220580i	$0.929205\pi$
$380$		0			0
$381$	4.39230	+	2.53590i	0.225025	+	0.129918i
$382$	−1.43280	−	5.34727i	−0.0733082	−	0.273590i
$383$	22.9742	+	6.15591i	1.17393	+	0.314552i	0.792514	−	0.609853i	$-0.208772\pi$
$383$	22.9742	+	6.15591i	1.17393	+	0.314552i	0.381411	+	0.924406i	$0.375438\pi$
$384$	−0.732051			−0.0373573
$385$		0			0
$386$	−12.1244			−0.617113
$387$	25.5438	+	6.84443i	1.29846	+	0.347922i
$388$	2.94855	+	11.0041i	0.149690	+	0.558650i
$389$	−3.50962	−	2.02628i	−0.177945	−	0.102736i	0.408382	−	0.912811i	$-0.366093\pi$
$389$	−3.50962	−	2.02628i	−0.177945	−	0.102736i	−0.586327	+	0.810075i	$0.699426\pi$
$390$		0			0
$391$			2.41154i			0.121957i
$392$	−6.43331	+	2.75908i	−0.324931	+	0.139354i
$393$	−1.13681	−	1.13681i	−0.0573446	−	0.0573446i
$394$	7.09808	−	4.09808i	0.357596	−	0.206458i
$395$		0			0
$396$	1.56218	−	2.70577i	0.0785024	−	0.135970i
$397$	0.517638	−	1.93185i	0.0259795	−	0.0969569i	−0.951719	−	0.306971i	$-0.900684\pi$
$397$	0.517638	−	1.93185i	0.0259795	−	0.0969569i	0.977698	+	0.210014i	$0.0673511\pi$
$398$	−13.9527	+	13.9527i	−0.699384	+	0.699384i
$399$		0			0
$400$		0			0
$401$	5.53590	+	9.58846i	0.276450	+	0.478825i	0.970500	−	0.241102i	$-0.0775088\pi$
$401$	5.53590	+	9.58846i	0.276450	+	0.478825i	−0.694050	+	0.719927i	$0.744175\pi$
$402$	−2.68973	+	0.720710i	−0.134151	+	0.0359457i
$403$	−10.3664	+	2.77766i	−0.516385	+	0.138365i
$404$	−8.19615	−	14.1962i	−0.407774	−	0.706285i
$405$		0			0
$406$	−3.00000	−	8.66025i	−0.148888	−	0.429801i
$407$	6.21166	−	6.21166i	0.307900	−	0.307900i
$408$	0.0879327	−	0.328169i	0.00435332	−	0.0162468i
$409$	6.40192	−	11.0885i	0.316555	−	0.548289i	−0.663212	−	0.748432i	$-0.730807\pi$
$409$	6.40192	−	11.0885i	0.316555	−	0.548289i	0.979767	+	0.200143i	$0.0641406\pi$
$410$		0			0
$411$	−0.509619	+	0.294229i	−0.0251376	+	0.0145132i
$412$	−9.19239	−	9.19239i	−0.452876	−	0.452876i
$413$	−2.68973	−	37.4631i	−0.132353	−	1.84344i
$414$			12.8038i			0.629275i
$415$		0			0
$416$	−5.36603	−	3.09808i	−0.263091	−	0.151896i
$417$	0.656339	+	2.44949i	0.0321410	+	0.119952i
$418$		0			0
$419$	28.9808			1.41580			0.707901	−	0.706311i	$-0.249642\pi$
$419$	28.9808			1.41580			0.707901	+	0.706311i	$0.249642\pi$
$420$		0			0
$421$	−15.6077			−0.760673			−0.380336	−	0.924848i	$-0.624192\pi$
$421$	−15.6077			−0.760673			−0.380336	+	0.924848i	$0.624192\pi$
$422$	9.84873	+	2.63896i	0.479429	+	0.128462i
$423$	−2.50524	−	9.34967i	−0.121809	−	0.454597i
$424$	7.09808	+	4.09808i	0.344713	+	0.199020i
$425$		0			0
$426$			9.80385i			0.474998i
$427$	8.39735	−	17.2987i	0.406376	−	0.837144i
$428$	−1.55291	−	1.55291i	−0.0750629	−	0.0750629i
$429$	−4.98076	+	2.87564i	−0.240473	+	0.138837i
$430$		0			0
$431$	8.76795	−	15.1865i	0.422337	−	0.731510i	−0.573830	−	0.818974i	$-0.694543\pi$
$431$	8.76795	−	15.1865i	0.422337	−	0.731510i	0.996168	+	0.0874646i	$0.0278765\pi$
$432$	1.03528	−	3.86370i	0.0498097	−	0.185893i
$433$	−22.7525	+	22.7525i	−1.09342	+	1.09342i	−0.0982548	+	0.995161i	$0.531326\pi$
$433$	−22.7525	+	22.7525i	−1.09342	+	1.09342i	−0.995161	+	0.0982548i	$0.968674\pi$
$434$	−4.50000	−	0.866025i	−0.216007	−	0.0415705i
$435$		0			0
$436$	5.09808	+	8.83013i	0.244154	+	0.422886i
$437$		0			0
$438$	−5.65685	+	1.51575i	−0.270295	+	0.0724253i
$439$	2.93782	+	5.08846i	0.140215	+	0.242859i	0.927577	−	0.373631i	$-0.121887\pi$
$439$	2.93782	+	5.08846i	0.140215	+	0.242859i	−0.787363	+	0.616490i	$0.788554\pi$
$440$		0			0
$441$	−2.46410	−	17.0718i	−0.117338	−	0.812943i
$442$	2.03339	−	2.03339i	0.0967184	−	0.0967184i
$443$	3.10583	−	11.5911i	0.147562	−	0.550710i	−0.852066	−	0.523435i	$-0.824650\pi$
$443$	3.10583	−	11.5911i	0.147562	−	0.550710i	0.999628	−	0.0272752i	$-0.00868305\pi$
$444$	2.53590	−	4.39230i	0.120348	−	0.208450i
$445$		0			0
$446$	−8.13397	+	4.69615i	−0.385155	+	0.222369i
$447$	−4.24264	−	4.24264i	−0.200670	−	0.200670i
$448$	−1.48356	−	2.19067i	−0.0700918	−	0.103499i
$449$		−	8.32051i		−	0.392669i	−0.980537	−	0.196335i	$-0.937096\pi$
$449$		−	8.32051i		−	0.392669i	0.980537	−	0.196335i	$-0.0629039\pi$
$450$		0			0
$451$	−12.2942	−	7.09808i	−0.578913	−	0.334235i
$452$	1.76097	+	6.57201i	0.0828288	+	0.309121i
$453$	13.0053	+	3.48477i	0.611043	+	0.163729i
$454$	27.4641			1.28895
$455$		0			0
$456$		0			0
$457$	−31.4273	−	8.42091i	−1.47011	−	0.393914i	−0.567138	−	0.823623i	$-0.691949\pi$
$457$	−31.4273	−	8.42091i	−1.47011	−	0.393914i	−0.902967	+	0.429709i	$0.858616\pi$
$458$	−3.67423	−	13.7124i	−0.171686	−	0.640740i
$459$	1.60770	+	0.928203i	0.0750408	+	0.0433248i
$460$		0			0
$461$			24.0000i			1.11779i	0.829238	+	0.558896i	$0.188775\pi$
$461$			24.0000i			1.11779i	−0.829238	+	0.558896i	$0.811225\pi$
$462$	−2.44949	+	0.175865i	−0.113961	+	0.00818200i
$463$	−6.60420	−	6.60420i	−0.306923	−	0.306923i	0.536792	−	0.843715i	$-0.319636\pi$
$463$	−6.60420	−	6.60420i	−0.306923	−	0.306923i	−0.843715	+	0.536792i	$0.819636\pi$
$464$	3.00000	−	1.73205i	0.139272	−	0.0804084i
$465$		0			0
$466$	3.00000	−	5.19615i	0.138972	−	0.240707i
$467$	−5.97142	+	22.2856i	−0.276324	+	1.03126i	0.678624	+	0.734486i	$0.262576\pi$
$467$	−5.97142	+	22.2856i	−0.276324	+	1.03126i	−0.954949	+	0.296771i	$0.904090\pi$
$468$	10.7961	−	10.7961i	0.499049	−	0.499049i
$469$	−7.60770	−	6.58846i	−0.351291	−	0.304227i
$470$		0			0
$471$	−0.732051	−	1.26795i	−0.0337311	−	0.0584240i
$472$	13.7124	−	3.67423i	0.631166	−	0.169120i
$473$	13.1440	−	3.52193i	0.604363	−	0.161939i
$474$	−4.16987	−	7.22243i	−0.191529	−	0.331737i
$475$		0			0
$476$	1.16025	−	0.401924i	0.0531802	−	0.0184221i
$477$	−14.2808	+	14.2808i	−0.653875	+	0.653875i
$478$	5.91567	−	22.0776i	0.270577	−	1.00981i
$479$	6.40192	−	11.0885i	0.292511	−	0.506645i	−0.681892	−	0.731453i	$-0.738842\pi$
$479$	6.40192	−	11.0885i	0.292511	−	0.506645i	0.974403	+	0.224809i	$0.0721757\pi$
$480$		0			0
$481$	37.1769	−	21.4641i	1.69512	−	0.978679i
$482$	2.44949	+	2.44949i	0.111571	+	0.111571i
$483$	8.33298	−	5.64325i	0.379164	−	0.256777i
$484$			9.39230i			0.426923i
$485$		0			0
$486$	13.2224	+	7.63397i	0.599782	+	0.346284i
$487$	−2.41730	−	9.02150i	−0.109539	−	0.408803i	0.889282	−	0.457359i	$-0.151205\pi$
$487$	−2.41730	−	9.02150i	−0.109539	−	0.408803i	−0.998820	+	0.0485561i	$0.984538\pi$
$488$	7.02030	+	1.88108i	0.317794	+	0.0851527i
$489$	−10.6410			−0.481203
$490$		0			0
$491$	−16.0526			−0.724442			−0.362221	−	0.932092i	$-0.617981\pi$
$491$	−16.0526			−0.724442			−0.362221	+	0.932092i	$0.617981\pi$
$492$	−7.91688	−	2.12132i	−0.356920	−	0.0956365i
$493$	0.416102	+	1.55291i	0.0187403	+	0.0699397i
$494$		0			0
$495$		0			0
$496$		−	1.73205i		−	0.0777714i
$497$	−29.3381	+	19.8683i	−1.31599	+	0.891217i
$498$	3.10583	+	3.10583i	0.139176	+	0.139176i
$499$	15.2487	−	8.80385i	0.682626	−	0.394114i	−0.118218	−	0.992988i	$-0.537718\pi$
$499$	15.2487	−	8.80385i	0.682626	−	0.394114i	0.800844	+	0.598873i	$0.204385\pi$
$500$		0			0
$501$	−6.92820	+	12.0000i	−0.309529	+	0.536120i
$502$	−1.13681	+	4.24264i	−0.0507384	+	0.189358i
$503$	7.82894	−	7.82894i	0.349075	−	0.349075i	−0.510690	−	0.859765i	$-0.670610\pi$
$503$	7.82894	−	7.82894i	0.349075	−	0.349075i	0.859765	+	0.510690i	$0.170610\pi$
$504$	6.16025	−	2.13397i	0.274400	−	0.0950548i
$505$		0			0
$506$	3.29423	+	5.70577i	0.146446	+	0.253652i
$507$	−17.9551	+	4.81105i	−0.797413	+	0.213666i
$508$	−6.69213	+	1.79315i	−0.296915	+	0.0795582i
$509$	17.4904	+	30.2942i	0.775248	+	1.34277i	0.934655	+	0.355555i	$0.115708\pi$
$509$	17.4904	+	30.2942i	0.775248	+	1.34277i	−0.159408	+	0.987213i	$0.550958\pi$
$510$		0			0
$511$	−16.0000	−	13.8564i	−0.707798	−	0.612971i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$		0			0
$514$	−2.19615	+	3.80385i	−0.0968681	+	0.167781i
$515$		0			0
$516$	6.80385	−	3.92820i	0.299523	−	0.172930i
$517$	−3.52193	−	3.52193i	−0.154894	−	0.154894i
$518$	18.2832	−	1.31268i	0.803319	−	0.0576757i
$519$			12.9282i			0.567485i
$520$		0			0
$521$	29.0885	+	16.7942i	1.27439	+	0.735769i	0.975811	−	0.218617i	$-0.0701545\pi$
$521$	29.0885	+	16.7942i	1.27439	+	0.735769i	0.298578	+	0.954385i	$0.403488\pi$
$522$	2.20925	+	8.24504i	0.0966964	+	0.360876i
$523$	−9.65926	−	2.58819i	−0.422370	−	0.113174i	0.0413724	−	0.999144i	$-0.486827\pi$
$523$	−9.65926	−	2.58819i	−0.422370	−	0.113174i	−0.463742	+	0.885970i	$0.653494\pi$
$524$	2.19615			0.0959394
$525$		0			0
$526$	−3.58846			−0.156464
$527$	0.776457	+	0.208051i	0.0338230	+	0.00906285i
$528$	−0.240237	−	0.896575i	−0.0104550	−	0.0390184i
$529$	−3.46410	−	2.00000i	−0.150613	−	0.0869565i
$530$		0			0
$531$			34.9808i			1.51804i
$532$		0			0
$533$	−49.0542	−	49.0542i	−2.12477	−	2.12477i
$534$	−7.09808	+	4.09808i	−0.307164	+	0.177341i
$535$		0			0
$536$	1.90192	−	3.29423i	0.0821506	−	0.142289i
$537$	1.55291	−	5.79555i	0.0670132	−	0.250097i
$538$	8.90138	−	8.90138i	0.383766	−	0.383766i
$539$	−5.49038	−	6.97372i	−0.236487	−	0.300379i
$540$		0			0
$541$	9.09808	+	15.7583i	0.391157	+	0.677504i	0.992602	−	0.121410i	$-0.0387417\pi$
$541$	9.09808	+	15.7583i	0.391157	+	0.677504i	−0.601446	+	0.798914i	$0.705408\pi$
$542$	−22.4058	+	6.00361i	−0.962410	+	0.257877i
$543$	−5.13922	+	1.37705i	−0.220545	+	0.0590948i
$544$	0.232051	+	0.401924i	0.00994910	+	0.0172323i
$545$		0			0
$546$	−11.7846	−	2.26795i	−0.504335	−	0.0970593i
$547$	20.0764	−	20.0764i	0.858405	−	0.858405i	−0.132746	−	0.991150i	$-0.542379\pi$
$547$	20.0764	−	20.0764i	0.858405	−	0.858405i	0.991150	+	0.132746i	$0.0423793\pi$
$548$	0.208051	−	0.776457i	0.00888750	−	0.0331686i
$549$	−8.95448	+	15.5096i	−0.382168	+	0.661934i
$550$		0			0
$551$		0			0
$552$	2.68973	+	2.68973i	0.114482	+	0.114482i
$553$	13.1626	−	27.1153i	0.559731	−	1.15306i
$554$			6.58846i			0.279917i
$555$		0			0
$556$	−3.00000	−	1.73205i	−0.127228	−	0.0734553i
$557$	−0.568406	−	2.12132i	−0.0240841	−	0.0898832i	0.952838	−	0.303480i	$-0.0981487\pi$
$557$	−0.568406	−	2.12132i	−0.0240841	−	0.0898832i	−0.976922	+	0.213597i	$0.931482\pi$
$558$	4.12252	+	1.10463i	0.174520	+	0.0467626i
$559$	66.4974			2.81254
$560$		0			0
$561$	0.430781			0.0181876
$562$	−23.6305	−	6.33178i	−0.996793	−	0.267090i
$563$	7.91688	+	29.5462i	0.333657	+	1.24522i	0.905318	+	0.424734i	$0.139632\pi$
$563$	7.91688	+	29.5462i	0.333657	+	1.24522i	−0.571662	+	0.820489i	$0.693701\pi$
$564$	−2.49038	−	1.43782i	−0.104864	−	0.0605432i
$565$		0			0
$566$		−	2.39230i		−	0.100556i
$567$	0.845807	+	11.7806i	0.0355206	+	0.494738i
$568$	−9.46979	−	9.46979i	−0.397344	−	0.397344i
$569$	20.5981	−	11.8923i	0.863516	−	0.498551i	−0.00167195	−	0.999999i	$-0.500532\pi$
$569$	20.5981	−	11.8923i	0.863516	−	0.498551i	0.865188	+	0.501447i	$0.167199\pi$
$570$		0			0
$571$	8.58846	−	14.8756i	0.359416	−	0.622526i	−0.628448	−	0.777852i	$-0.716309\pi$
$571$	8.58846	−	14.8756i	0.359416	−	0.622526i	0.987863	+	0.155326i	$0.0496427\pi$
$572$	2.03339	−	7.58871i	0.0850202	−	0.317300i
$573$	2.86559	−	2.86559i	0.119712	−	0.119712i
$574$	−9.69615	−	27.9904i	−0.404710	−	1.16830i
$575$		0			0
$576$	1.23205	+	2.13397i	0.0513355	+	0.0889156i
$577$	8.10634	−	2.17209i	0.337472	−	0.0904252i	−0.0861036	−	0.996286i	$-0.527442\pi$
$577$	8.10634	−	2.17209i	0.337472	−	0.0904252i	0.423575	+	0.905861i	$0.360775\pi$
$578$	16.2127	−	4.34418i	0.674359	−	0.180694i
$579$	−4.43782	−	7.68653i	−0.184430	−	0.319441i
$580$		0			0
$581$	−3.00000	+	15.5885i	−0.124461	+	0.646718i
$582$	−5.89709	+	5.89709i	−0.244442	+	0.244442i
$583$	−2.68973	+	10.0382i	−0.111397	+	0.415740i
$584$	4.00000	−	6.92820i	0.165521	−	0.286691i
$585$		0			0
$586$	27.5885	−	15.9282i	1.13967	−	0.657988i
$587$	−2.68973	−	2.68973i	−0.111017	−	0.111017i	0.649416	−	0.760433i	$-0.275013\pi$
$587$	−2.68973	−	2.68973i	−0.111017	−	0.111017i	−0.760433	+	0.649416i	$0.775013\pi$
$588$	−4.10394	−	3.06866i	−0.169244	−	0.126550i
$589$		0			0
$590$		0			0
$591$	5.19615	+	3.00000i	0.213741	+	0.123404i
$592$	1.79315	+	6.69213i	0.0736980	+	0.275045i
$593$	32.7721	+	8.78127i	1.34579	+	0.360603i	0.858579	−	0.512681i	$-0.171348\pi$
$593$	32.7721	+	8.78127i	1.34579	+	0.360603i	0.487211	+	0.873284i	$0.338014\pi$
$594$	5.07180			0.208098
$595$		0			0
$596$	8.19615			0.335727
$597$	−13.9527	−	3.73861i	−0.571045	−	0.153011i
$598$	8.33298	+	31.0991i	0.340761	+	1.27174i
$599$	−24.1865	−	13.9641i	−0.988235	−	0.570558i	−0.0834887	−	0.996509i	$-0.526606\pi$
$599$	−24.1865	−	13.9641i	−0.988235	−	0.570558i	−0.904746	+	0.425951i	$0.859940\pi$
$600$		0			0
$601$			2.78461i			0.113587i	0.998386	+	0.0567933i	$0.0180876\pi$
$601$			2.78461i			0.113587i	−0.998386	+	0.0567933i	$0.981912\pi$
$602$	25.5438	+	12.3998i	1.04109	+	0.505376i
$603$	6.62776	+	6.62776i	0.269903	+	0.269903i
$604$	−15.9282	+	9.19615i	−0.648109	+	0.374186i
$605$		0			0
$606$	6.00000	−	10.3923i	0.243733	−	0.422159i
$607$	−6.77508	+	25.2850i	−0.274992	+	1.02628i	0.680854	+	0.732419i	$0.261609\pi$
$607$	−6.77508	+	25.2850i	−0.274992	+	1.02628i	−0.955847	+	0.293866i	$0.905058\pi$
$608$		0			0
$609$	4.39230	−	5.07180i	0.177985	−	0.205520i
$610$		0			0
$611$	−12.1699	−	21.0788i	−0.492340	−	0.852759i
$612$	−1.10463	+	0.295984i	−0.0446519	+	0.0119644i
$613$	−17.3867	+	4.65874i	−0.702241	+	0.188165i	−0.592234	−	0.805766i	$-0.701754\pi$
$613$	−17.3867	+	4.65874i	−0.702241	+	0.188165i	−0.110007	+	0.993931i	$0.535087\pi$
$614$	−6.19615	−	10.7321i	−0.250056	−	0.433110i
$615$		0			0
$616$	2.19615	−	2.53590i	0.0884855	−	0.102174i
$617$	5.94786	−	5.94786i	0.239452	−	0.239452i	−0.577171	−	0.816623i	$-0.695844\pi$
$617$	5.94786	−	5.94786i	0.239452	−	0.239452i	0.816623	+	0.577171i	$0.195844\pi$
$618$	2.46309	−	9.19239i	0.0990801	−	0.369772i
$619$	12.4641	−	21.5885i	0.500975	−	0.867713i	−0.499025	−	0.866588i	$-0.666308\pi$
$619$	12.4641	−	21.5885i	0.500975	−	0.867713i	0.999999	−	0.00112567i	$-0.000358312\pi$
$620$		0			0
$621$	−18.0000	+	10.3923i	−0.722315	+	0.417029i
$622$	0.568406	+	0.568406i	0.0227910	+	0.0227910i
$623$	−26.6484	−	12.9360i	−1.06765	−	0.518269i
$624$		−	4.53590i		−	0.181581i
$625$		0			0
$626$	−16.4545	−	9.50000i	−0.657653	−	0.379696i
$627$		0			0
$628$	1.93185	+	0.517638i	0.0770893	+	0.0206560i
$629$	−3.21539			−0.128206
$630$		0			0
$631$	−17.3923			−0.692377			−0.346188	−	0.938165i	$-0.612524\pi$
$631$	−17.3923			−0.692377			−0.346188	+	0.938165i	$0.612524\pi$
$632$	11.0041	+	2.94855i	0.437720	+	0.117287i
$633$	1.93185	+	7.20977i	0.0767842	+	0.286563i
$634$	−14.1962	−	8.19615i	−0.563801	−	0.325511i
$635$		0			0
$636$			6.00000i			0.237915i
$637$	−17.0957	−	39.8618i	−0.677355	−	1.57938i
$638$	3.10583	+	3.10583i	0.122961	+	0.122961i
$639$	28.5788	−	16.5000i	1.13056	−	0.652730i
$640$		0			0
$641$	−13.5000	+	23.3827i	−0.533218	+	0.923561i	0.466029	+	0.884769i	$0.345684\pi$
$641$	−13.5000	+	23.3827i	−0.533218	+	0.923561i	−0.999247	+	0.0387913i	$0.987649\pi$
$642$	0.416102	−	1.55291i	0.0164222	−	0.0612886i
$643$	−14.8356	+	14.8356i	−0.585060	+	0.585060i	−0.936290	−	0.351229i	$-0.885764\pi$
$643$	−14.8356	+	14.8356i	−0.585060	+	0.585060i	0.351229	+	0.936290i	$0.385764\pi$
$644$	−2.59808	+	13.5000i	−0.102379	+	0.531975i
$645$		0			0
$646$		0			0
$647$	24.7351	−	6.62776i	0.972438	−	0.260564i	0.262581	−	0.964910i	$-0.415426\pi$
$647$	24.7351	−	6.62776i	0.972438	−	0.260564i	0.709857	+	0.704346i	$0.248760\pi$
$648$	−4.31199	+	1.15539i	−0.169391	+	0.0453882i
$649$	9.00000	+	15.5885i	0.353281	+	0.611900i
$650$		0			0
$651$	−1.09808	−	3.16987i	−0.0430370	−	0.124237i
$652$	10.2784	−	10.2784i	0.402534	−	0.402534i
$653$	−5.22715	+	19.5080i	−0.204554	+	0.763406i	0.785031	+	0.619457i	$0.212647\pi$
$653$	−5.22715	+	19.5080i	−0.204554	+	0.763406i	−0.989585	+	0.143950i	$0.954020\pi$
$654$	−3.73205	+	6.46410i	−0.145935	+	0.252766i
$655$		0			0
$656$	9.69615	−	5.59808i	0.378571	−	0.218568i
$657$	13.9391	+	13.9391i	0.543815	+	0.543815i
$658$	−0.744272	−	10.3664i	−0.0290147	−	0.404123i
$659$			29.3205i			1.14216i	0.820893	+	0.571082i	$0.193476\pi$
$659$			29.3205i			1.14216i	−0.820893	+	0.571082i	$0.806524\pi$
$660$		0			0
$661$	−6.29423	−	3.63397i	−0.244817	−	0.141345i	0.372572	−	0.928003i	$-0.378476\pi$
$661$	−6.29423	−	3.63397i	−0.244817	−	0.141345i	−0.617389	+	0.786658i	$0.711809\pi$
$662$	−3.62347	−	13.5230i	−0.140830	−	0.525585i
$663$	2.03339	+	0.544845i	0.0789702	+	0.0211600i
$664$	−6.00000			−0.232845
$665$		0			0
$666$	−17.0718			−0.661519
$667$	−17.3867	−	4.65874i	−0.673214	−	0.180387i
$668$	−4.89898	−	18.2832i	−0.189547	−	0.707400i
$669$	−5.95448	−	3.43782i	−0.230214	−	0.132914i
$670$		0			0
$671$			9.21539i			0.355756i
$672$	0.845807	−	1.74238i	0.0326277	−	0.0672139i
$673$	−6.12372	−	6.12372i	−0.236052	−	0.236052i	0.579161	−	0.815213i	$-0.303380\pi$
$673$	−6.12372	−	6.12372i	−0.236052	−	0.236052i	−0.815213	+	0.579161i	$0.803380\pi$
$674$	7.50000	−	4.33013i	0.288889	−	0.166790i
$675$		0			0
$676$	12.6962	−	21.9904i	0.488314	−	0.845784i
$677$	1.72878	−	6.45189i	0.0664424	−	0.247966i	−0.924715	−	0.380661i	$-0.875696\pi$
$677$	1.72878	−	6.45189i	0.0664424	−	0.247966i	0.991157	+	0.132695i	$0.0423630\pi$
$678$	−3.52193	+	3.52193i	−0.135259	+	0.135259i
$679$	−29.5981	−	5.69615i	−1.13587	−	0.218598i
$680$		0			0
$681$	10.0526	+	17.4115i	0.385215	+	0.667212i
$682$	2.12132	−	0.568406i	0.0812296	−	0.0217654i
$683$	−14.2808	+	3.82654i	−0.546441	+	0.146418i	−0.521470	−	0.853270i	$-0.674616\pi$
$683$	−14.2808	+	3.82654i	−0.546441	+	0.146418i	−0.0249712	+	0.999688i	$0.507949\pi$
$684$		0			0
$685$		0			0
$686$	0.866025	−	18.5000i	0.0330650	−	0.706333i
$687$	7.34847	−	7.34847i	0.280362	−	0.280362i
$688$	−2.77766	+	10.3664i	−0.105897	+	0.395214i
$689$	−25.3923	+	43.9808i	−0.967370	+	1.67553i
$690$		0			0
$691$	21.5885	−	12.4641i	0.821264	−	0.474157i	−0.0295884	−	0.999562i	$-0.509420\pi$
$691$	21.5885	−	12.4641i	0.821264	−	0.474157i	0.850852	+	0.525405i	$0.176086\pi$
$692$	−12.4877	−	12.4877i	−0.474711	−	0.474711i
$693$	4.63518	+	6.84443i	0.176076	+	0.259999i
$694$		−	6.00000i		−	0.227757i
$695$		0			0
$696$	2.19615	+	1.26795i	0.0832449	+	0.0480615i
$697$	1.34486	+	5.01910i	0.0509403	+	0.190112i
$698$	16.4022	+	4.39494i	0.620831	+	0.166351i
$699$	4.39230			0.166132
$700$		0			0
$701$	−37.8564			−1.42982			−0.714908	−	0.699218i	$-0.753532\pi$
$701$	−37.8564			−1.42982			−0.714908	+	0.699218i	$0.753532\pi$
$702$	23.9401	+	6.41473i	0.903561	+	0.242108i
$703$		0			0
$704$	1.09808	+	0.633975i	0.0413853	+	0.0238938i
$705$		0			0
$706$		−	23.5359i		−	0.885785i
$707$	43.2586	−	3.10583i	1.62691	−	0.116807i
$708$	7.34847	+	7.34847i	0.276172	+	0.276172i
$709$	−45.5429	+	26.2942i	−1.71040	+	0.987500i	−0.776393	+	0.630250i	$0.782953\pi$
$709$	−45.5429	+	26.2942i	−1.71040	+	0.987500i	−0.934008	+	0.357251i	$0.883714\pi$
$710$		0			0
$711$	−14.0359	+	24.3109i	−0.526387	+	0.911730i
$712$	2.89778	−	10.8147i	0.108599	−	0.405296i
$713$	−6.36396	+	6.36396i	−0.238332	+	0.238332i
$714$	0.679492	+	0.588457i	0.0254293	+	0.0220225i
$715$		0			0
$716$	4.09808	+	7.09808i	0.153152	+	0.265268i
$717$	16.1619	−	4.33057i	0.603578	−	0.161728i
$718$	10.0382	−	2.68973i	0.374622	−	0.100380i
$719$	−19.7942	−	34.2846i	−0.738200	−	1.27860i	−0.953305	−	0.302009i	$-0.902343\pi$
$719$	−19.7942	−	34.2846i	−0.738200	−	1.27860i	0.215105	−	0.976591i	$-0.430991\pi$
$720$		0			0
$721$	32.5000	−	11.2583i	1.21036	−	0.419282i
$722$	−13.4350	+	13.4350i	−0.500000	+	0.500000i
$723$	−0.656339	+	2.44949i	−0.0244095	+	0.0910975i
$724$	3.63397	−	6.29423i	0.135056	−	0.233923i
$725$		0			0
$726$	−5.95448	+	3.43782i	−0.220992	+	0.127590i
$727$	−13.4350	−	13.4350i	−0.498278	−	0.498278i	0.412624	−	0.910902i	$-0.364612\pi$
$727$	−13.4350	−	13.4350i	−0.498278	−	0.498278i	−0.910902	+	0.412624i	$0.864612\pi$
$728$	13.5737	−	9.19239i	0.503076	−	0.340693i
$729$		−	2.21539i		−	0.0820515i
$730$		0			0
$731$	−4.31347	−	2.49038i	−0.159539	−	0.0921101i
$732$	1.37705	+	5.13922i	0.0508972	+	0.189951i
$733$	−13.5230	−	3.62347i	−0.499482	−	0.133836i	0.000277595	−	1.00000i	$-0.499912\pi$
$733$	−13.5230	−	3.62347i	−0.499482	−	0.133836i	−0.499760	+	0.866164i	$0.666578\pi$
$734$	−18.3923			−0.678872
$735$		0			0
$736$	−5.19615			−0.191533
$737$	4.65874	+	1.24831i	0.171607	+	0.0459820i
$738$	7.14042	+	26.6484i	0.262842	+	0.980941i
$739$	17.3205	+	10.0000i	0.637145	+	0.367856i	0.783514	−	0.621374i	$-0.213425\pi$
$739$	17.3205	+	10.0000i	0.637145	+	0.367856i	−0.146369	+	0.989230i	$0.546759\pi$
$740$		0			0
$741$		0			0
$742$	−17.9551	+	12.1595i	−0.659151	+	0.446390i
$743$	24.8874	+	24.8874i	0.913032	+	0.913032i	0.996510	−	0.0834781i	$-0.0266029\pi$
$743$	24.8874	+	24.8874i	0.913032	+	0.913032i	−0.0834781	+	0.996510i	$0.526603\pi$
$744$	1.09808	−	0.633975i	0.0402574	−	0.0232426i
$745$		0			0
$746$	−8.49038	+	14.7058i	−0.310855	+	0.538417i
$747$	3.82654	−	14.2808i	0.140006	−	0.522508i
$748$	−0.416102	+	0.416102i	−0.0152142	+	0.0152142i
$749$	5.49038	−	1.90192i	0.200614	−	0.0694948i
$750$		0			0
$751$	−7.00000	−	12.1244i	−0.255434	−	0.442424i	0.709580	−	0.704625i	$-0.248885\pi$
$751$	−7.00000	−	12.1244i	−0.255434	−	0.442424i	−0.965013	+	0.262201i	$0.915552\pi$
$752$	3.79435	−	1.01669i	0.138366	−	0.0370750i
$753$	−3.10583	+	0.832204i	−0.113183	+	0.0303272i
$754$	10.7321	+	18.5885i	0.390838	+	0.676952i
$755$		0			0
$756$	8.00000	+	6.92820i	0.290957	+	0.251976i
$757$	−2.20925	+	2.20925i	−0.0802967	+	0.0802967i	−0.746114	−	0.665818i	$-0.768083\pi$
$757$	−2.20925	+	2.20925i	−0.0802967	+	0.0802967i	0.665818	+	0.746114i	$0.268083\pi$
$758$	2.22286	−	8.29581i	0.0807378	−	0.301317i
$759$	−2.41154	+	4.17691i	−0.0875335	+	0.151612i
$760$		0			0
$761$	−34.2846	+	19.7942i	−1.24282	+	0.717540i	−0.969667	−	0.244431i	$-0.921399\pi$
$761$	−34.2846	+	19.7942i	−1.24282	+	0.717540i	−0.273150	+	0.961972i	$0.588065\pi$
$762$	−3.58630	−	3.58630i	−0.129918	−	0.129918i
$763$	−26.9072	+	1.93185i	−0.974107	+	0.0699377i
$764$			5.53590i			0.200282i
$765$		0			0
$766$	−20.5981	−	11.8923i	−0.744239	−	0.429686i
$767$	22.7661	+	84.9643i	0.822037	+	3.06788i
$768$	0.707107	+	0.189469i	0.0255155	+	0.00683686i
$769$	−9.71281			−0.350253			−0.175126	−	0.984546i	$-0.556033\pi$
$769$	−9.71281			−0.350253			−0.175126	+	0.984546i	$0.556033\pi$
$770$		0			0
$771$	−3.21539			−0.115799
$772$	11.7112	+	3.13801i	0.421496	+	0.112940i
$773$	4.72311	+	17.6269i	0.169879	+	0.633996i	0.997367	+	0.0725134i	$0.0231020\pi$
$773$	4.72311	+	17.6269i	0.169879	+	0.633996i	−0.827489	+	0.561482i	$0.810231\pi$
$774$	−22.9019	−	13.2224i	−0.823193	−	0.475270i
$775$		0			0
$776$		−	11.3923i		−	0.408960i
$777$	7.52433	+	11.1106i	0.269934	+	0.398592i
$778$	2.86559	+	2.86559i	0.102736	+	0.102736i
$779$		0			0
$780$		0			0
$781$	8.49038	−	14.7058i	0.303810	−	0.526214i
$782$	0.624153	−	2.32937i	0.0223197	−	0.0832982i
$783$	−9.79796	+	9.79796i	−0.350150	+	0.350150i
$784$	6.92820	−	1.00000i	0.247436	−	0.0357143i
$785$		0			0
$786$	0.803848	+	1.39230i	0.0286723	+	0.0496619i
$787$	23.9401	−	6.41473i	0.853372	−	0.228660i	0.194488	−	0.980905i	$-0.437695\pi$
$787$	23.9401	−	6.41473i	0.853372	−	0.228660i	0.658884	+	0.752244i	$0.271029\pi$
$788$	−7.91688	+	2.12132i	−0.282027	+	0.0755689i
$789$	−1.31347	−	2.27499i	−0.0467606	−	0.0809918i
$790$		0			0
$791$	−17.6769	−	3.40192i	−0.628519	−	0.120958i
$792$	−2.20925	+	2.20925i	−0.0785024	+	0.0785024i
$793$	−11.6555	+	43.4988i	−0.413898	+	1.54469i
$794$	−1.00000	+	1.73205i	−0.0354887	+	0.0614682i
$795$		0			0
$796$	17.0885	−	9.86603i	0.605684	−	0.349692i
$797$	−10.6945	−	10.6945i	−0.378820	−	0.378820i	0.491856	−	0.870676i	$-0.336318\pi$
$797$	−10.6945	−	10.6945i	−0.378820	−	0.378820i	−0.870676	+	0.491856i	$0.836318\pi$
$798$		0			0
$799$			1.82309i			0.0644961i
$800$		0			0
$801$	23.8923	+	13.7942i	0.844193	+	0.487395i
$802$	−2.86559	−	10.6945i	−0.101188	−	0.377637i
$803$	9.79796	+	2.62536i	0.345762	+	0.0926468i
$804$	2.78461			0.0982056
$805$		0			0
$806$	10.7321			0.378020
$807$	8.90138	+	2.38512i	0.313344	+	0.0839601i
$808$	4.24264	+	15.8338i	0.149256	+	0.557029i
$809$	−16.3923	−	9.46410i	−0.576323	−	0.332740i	0.183348	−	0.983048i	$-0.441307\pi$
$809$	−16.3923	−	9.46410i	−0.576323	−	0.332740i	−0.759671	+	0.650308i	$0.774640\pi$
$810$		0			0
$811$			23.9090i			0.839557i	0.907627	+	0.419779i	$0.137892\pi$
$811$			23.9090i			0.839557i	−0.907627	+	0.419779i	$0.862108\pi$
$812$	0.656339	+	9.14162i	0.0230330	+	0.320808i
$813$	−12.0072	−	12.0072i	−0.421111	−	0.421111i
$814$	−7.60770	+	4.39230i	−0.266650	+	0.153950i
$815$		0			0
$816$	−0.169873	+	0.294229i	−0.00594674	+	0.0103001i
$817$		0			0
$818$	−9.05369	+	9.05369i	−0.316555	+	0.316555i
$819$	13.2224	+	38.1699i	0.462029	+	1.33376i
$820$		0			0
$821$	−16.0526	−	27.8038i	−0.560238	−	0.970361i	−0.997475	−	0.0710147i	$-0.977376\pi$
$821$	−16.0526	−	27.8038i	−0.560238	−	0.970361i	0.437237	−	0.899346i	$-0.355957\pi$
$822$	0.568406	−	0.152304i	0.0198254	−	0.00531221i
$823$	3.34607	−	0.896575i	0.116637	−	0.0312527i	−0.200029	−	0.979790i	$-0.564104\pi$
$823$	3.34607	−	0.896575i	0.116637	−	0.0312527i	0.316665	+	0.948537i	$0.397437\pi$
$824$	6.50000	+	11.2583i	0.226438	+	0.392203i
$825$		0			0
$826$	−7.09808	+	36.8827i	−0.246974	+	1.28331i
$827$	7.34847	−	7.34847i	0.255531	−	0.255531i	−0.567702	−	0.823234i	$-0.692168\pi$
$827$	7.34847	−	7.34847i	0.255531	−	0.255531i	0.823234	+	0.567702i	$0.192168\pi$
$828$	3.31388	−	12.3676i	0.115165	−	0.429803i
$829$	−0.169873	+	0.294229i	−0.00589993	+	0.0102190i	−0.868960	−	0.494882i	$-0.835211\pi$
$829$	−0.169873	+	0.294229i	−0.00589993	+	0.0102190i	0.863060	+	0.505101i	$0.168545\pi$
$830$		0			0
$831$	−4.17691	+	2.41154i	−0.144896	+	0.0836555i
$832$	4.38134	+	4.38134i	0.151896	+	0.151896i
$833$	−0.383917	+	3.22595i	−0.0133019	+	0.111772i
$834$		−	2.53590i		−	0.0878110i
$835$		0			0
$836$		0			0
$837$	1.79315	+	6.69213i	0.0619804	+	0.231314i
$838$	−27.9933	−	7.50077i	−0.967011	−	0.259110i
$839$	4.01924			0.138760			0.0693798	−	0.997590i	$-0.477898\pi$
$839$	4.01924			0.138760			0.0693798	+	0.997590i	$0.477898\pi$
$840$		0			0
$841$	17.0000			0.586207
$842$	15.0759	+	4.03957i	0.519549	+	0.139213i
$843$	−4.63518	−	17.2987i	−0.159644	−	0.595800i
$844$	−8.83013	−	5.09808i	−0.303946	−	0.175483i
$845$		0			0
$846$			9.67949i			0.332788i
$847$	−22.3550	−	10.8518i	−0.768127	−	0.372873i
$848$	−5.79555	−	5.79555i	−0.199020	−	0.199020i
$849$	1.51666	−	0.875644i	0.0520517	−	0.0300520i
$850$		0			0
$851$	18.0000	−	31.1769i	0.617032	−	1.06873i
$852$	2.53742	−	9.46979i	0.0869307	−	0.324430i
$853$	−1.83032	+	1.83032i	−0.0626688	+	0.0626688i	−0.737747	−	0.675078i	$-0.764110\pi$
$853$	−1.83032	+	1.83032i	−0.0626688	+	0.0626688i	0.675078	+	0.737747i	$0.264110\pi$
$854$	−12.5885	+	14.5359i	−0.430768	+	0.497408i
$855$		0			0
$856$	1.09808	+	1.90192i	0.0375315	+	0.0650064i
$857$	−34.3572	+	9.20599i	−1.17362	+	0.314471i	−0.792393	−	0.610011i	$-0.791165\pi$
$857$	−34.3572	+	9.20599i	−1.17362	+	0.314471i	−0.381227	+	0.924481i	$0.624498\pi$
$858$	5.55532	−	1.48854i	0.189655	−	0.0508180i
$859$	0.509619	+	0.882686i	0.0173880	+	0.0301169i	0.874588	−	0.484866i	$-0.161132\pi$
$859$	0.509619	+	0.882686i	0.0173880	+	0.0301169i	−0.857200	+	0.514983i	$0.827798\pi$
$860$		0			0
$861$	14.1962	−	16.3923i	0.483804	−	0.558648i
$862$	−12.3998	+	12.3998i	−0.422337	+	0.422337i
$863$	6.00361	−	22.4058i	0.204365	−	0.762701i	−0.785277	−	0.619145i	$-0.787479\pi$
$863$	6.00361	−	22.4058i	0.204365	−	0.762701i	0.989642	−	0.143556i	$-0.0458539\pi$
$864$	−2.00000	+	3.46410i	−0.0680414	+	0.117851i
$865$		0			0
$866$	27.8660	−	16.0885i	0.946926	−	0.546708i
$867$	8.68835	+	8.68835i	0.295072	+	0.295072i
$868$	4.12252	+	2.00120i	0.139928	+	0.0679252i
$869$			14.4449i			0.490008i
$870$		0			0
$871$	20.4115	+	11.7846i	0.691619	+	0.399306i
$872$	−2.63896	−	9.84873i	−0.0893664	−	0.333520i
$873$	27.1153	+	7.26552i	0.917713	+	0.245900i
$874$		0			0
$875$		0			0
$876$	5.85641			0.197870
$877$	−40.4810	−	10.8468i	−1.36694	−	0.366272i	−0.500583	−	0.865689i	$-0.666881\pi$
$877$	−40.4810	−	10.8468i	−1.36694	−	0.366272i	−0.866362	+	0.499417i	$0.833548\pi$
$878$	−1.52073	−	5.67544i	−0.0513221	−	0.191537i
$879$	20.1962	+	11.6603i	0.681199	+	0.393291i
$880$		0			0
$881$			3.58846i			0.120898i	0.998171	+	0.0604491i	$0.0192533\pi$
$881$			3.58846i			0.120898i	−0.998171	+	0.0604491i	$0.980747\pi$
$882$	−2.03837	+	17.1278i	−0.0686354	+	0.576725i
$883$	27.4249	+	27.4249i	0.922920	+	0.922920i	0.997235	−	0.0743148i	$-0.0236770\pi$
$883$	27.4249	+	27.4249i	0.922920	+	0.922920i	−0.0743148	+	0.997235i	$0.523677\pi$
$884$	−2.49038	+	1.43782i	−0.0837606	+	0.0483592i
$885$		0			0
$886$	−6.00000	+	10.3923i	−0.201574	+	0.349136i
$887$	2.68973	−	10.0382i	0.0903122	−	0.337050i	−0.905955	−	0.423374i	$-0.860846\pi$
$887$	2.68973	−	10.0382i	0.0903122	−	0.337050i	0.996267	+	0.0863246i	$0.0275122\pi$
$888$	−3.58630	+	3.58630i	−0.120348	+	0.120348i
$889$	3.46410	−	18.0000i	0.116182	−	0.603701i
$890$		0			0
$891$	−2.83013	−	4.90192i	−0.0948128	−	0.164221i
$892$	9.07227	−	2.43091i	0.303762	−	0.0813928i
$893$		0			0
$894$	3.00000	+	5.19615i	0.100335	+	0.173785i
$895$		0			0
$896$	0.866025	+	2.50000i	0.0289319	+	0.0835191i
$897$	−16.6660	+	16.6660i	−0.556460	+	0.556460i
$898$	−2.15351	+	8.03699i	−0.0718634	+	0.268198i
$899$	−3.00000	+	5.19615i	−0.100056	+	0.173301i
$900$		0			0
$901$	3.29423	−	1.90192i	0.109747	−	0.0633623i
$902$	10.0382	+	10.0382i	0.334235	+	0.334235i
$903$	1.48854	+	20.7327i	0.0495356	+	0.689942i
$904$		−	6.80385i		−	0.226293i
$905$		0			0
$906$	−11.6603	−	6.73205i	−0.387386	−	0.223657i
$907$	−12.8159	−	47.8294i	−0.425543	−	1.58815i	−0.762733	−	0.646713i	$-0.776143\pi$
$907$	−12.8159	−	47.8294i	−0.425543	−	1.58815i	0.337190	−	0.941437i	$-0.390524\pi$
$908$	−26.5283	−	7.10823i	−0.880372	−	0.235895i
$909$	−40.3923			−1.33973
$910$		0			0
$911$	52.1769			1.72870			0.864349	−	0.502892i	$-0.167731\pi$
$911$	52.1769			1.72870			0.864349	+	0.502892i	$0.167731\pi$
$912$		0			0
$913$	−1.96902	−	7.34847i	−0.0651649	−	0.243199i
$914$	28.1769	+	16.2679i	0.932009	+	0.538096i
$915$		0			0
$916$			14.1962i			0.469054i
$917$	−2.53742	+	5.22715i	−0.0837931	+	0.172616i
$918$	−1.31268	−	1.31268i	−0.0433248	−	0.0433248i
$919$	−6.06218	+	3.50000i	−0.199973	+	0.115454i	−0.596643	−	0.802507i	$-0.703499\pi$
$919$	−6.06218	+	3.50000i	−0.199973	+	0.115454i	0.396670	+	0.917961i	$0.370166\pi$
$920$		0			0
$921$	4.53590	−	7.85641i	0.149463	−	0.258877i
$922$	6.21166	−	23.1822i	0.204570	−	0.763466i
$923$	58.6763	−	58.6763i	1.93135	−	1.93135i
$924$	2.41154	+	0.464102i	0.0793339	+	0.0152678i
$925$		0			0
$926$	4.66987	+	8.08846i	0.153462	+	0.265803i
$927$	−30.9418	+	8.29083i	−1.01626	+	0.272307i
$928$	−3.34607	+	0.896575i	−0.109840	+	0.0294315i
$929$	−1.60770	−	2.78461i	−0.0527468	−	0.0913601i	0.838446	−	0.544984i	$-0.183464\pi$
$929$	−1.60770	−	2.78461i	−0.0527468	−	0.0913601i	−0.891193	+	0.453624i	$0.850131\pi$
$930$		0			0
$931$		0			0
$932$	−4.24264	+	4.24264i	−0.138972	+	0.138972i
$933$	−0.152304	+	0.568406i	−0.00498621	+	0.0186088i
$934$	11.5359	−	19.9808i	0.377466	−	0.653791i
$935$		0			0
$936$	−13.2224	+	7.63397i	−0.432189	+	0.249524i
$937$	38.7386	+	38.7386i	1.26553	+	1.26553i	0.948371	+	0.317163i	$0.102730\pi$
$937$	38.7386	+	38.7386i	1.26553	+	1.26553i	0.317163	+	0.948371i	$0.397270\pi$
$938$	5.64325	+	8.33298i	0.184259	+	0.272081i
$939$		−	13.9090i		−	0.453902i
$940$		0			0
$941$	−14.7058	−	8.49038i	−0.479394	−	0.276779i	0.240770	−	0.970582i	$-0.422600\pi$
$941$	−14.7058	−	8.49038i	−0.479394	−	0.276779i	−0.720164	+	0.693804i	$0.755933\pi$
$942$	0.378937	+	1.41421i	0.0123464	+	0.0460776i
$943$	−56.1946	−	15.0573i	−1.82995	−	0.490333i
$944$	−14.1962			−0.462045
$945$		0			0
$946$	−13.6077			−0.442424
$947$	−20.0764	−	5.37945i	−0.652395	−	0.174809i	−0.0825835	−	0.996584i	$-0.526317\pi$
$947$	−20.0764	−	5.37945i	−0.652395	−	0.174809i	−0.569812	+	0.821775i	$0.692984\pi$
$948$	2.15849	+	8.05558i	0.0701043	+	0.261633i
$949$	42.9282	+	24.7846i	1.39351	+	0.804542i
$950$		0			0
$951$		−	12.0000i		−	0.389127i
$952$	−1.22474	+	0.0879327i	−0.0396942	+	0.00284992i
$953$	−6.21166	−	6.21166i	−0.201215	−	0.201215i	0.599305	−	0.800521i	$-0.295444\pi$
$953$	−6.21166	−	6.21166i	−0.201215	−	0.201215i	−0.800521	+	0.599305i	$0.795444\pi$
$954$	17.4904	−	10.0981i	0.566272	−	0.326937i
$955$		0			0
$956$	−11.4282	+	19.7942i	−0.369615	+	0.640191i
$957$	−0.832204	+	3.10583i	−0.0269013	+	0.100397i
$958$	−9.05369	+	9.05369i	−0.292511	+	0.292511i
$959$	1.60770	+	1.39230i	0.0519152	+	0.0449599i
$960$		0			0
$961$	−14.0000	−	24.2487i	−0.451613	−	0.782216i
$962$	−41.4655	+	11.1106i	−1.33690	+	0.358221i
$963$	−5.22715	+	1.40061i	−0.168443	+	0.0451340i
$964$	−1.73205	−	3.00000i	−0.0557856	−	0.0966235i
$965$		0			0
$966$	−9.50962	+	3.29423i	−0.305967	+	0.105990i
$967$	15.9217	−	15.9217i	0.512007	−	0.512007i	−0.403134	−	0.915141i	$-0.632079\pi$
$967$	15.9217	−	15.9217i	0.512007	−	0.512007i	0.915141	+	0.403134i	$0.132079\pi$
$968$	2.43091	−	9.07227i	0.0781323	−	0.291594i
$969$		0			0
$970$		0			0
$971$	−37.3923	+	21.5885i	−1.19998	+	0.692807i	−0.960550	−	0.278108i	$-0.910293\pi$
$971$	−37.3923	+	21.5885i	−1.19998	+	0.692807i	−0.239426	+	0.970915i	$0.576959\pi$
$972$	−10.7961	−	10.7961i	−0.346284	−	0.346284i
$973$	7.58871	−	5.13922i	0.243283	−	0.164756i
$974$			9.33975i			0.299265i
$975$		0			0
$976$	−6.29423	−	3.63397i	−0.201473	−	0.116321i
$977$	−10.2462	−	38.2395i	−0.327806	−	1.22339i	−0.911460	−	0.411388i	$-0.865044\pi$
$977$	−10.2462	−	38.2395i	−0.327806	−	1.22339i	0.583654	−	0.812003i	$-0.301622\pi$
$978$	10.2784	+	2.75410i	0.328668	+	0.0880663i
$979$	14.1962			0.453711
$980$		0			0
$981$	25.1244			0.802159
$982$	15.5056	+	4.15471i	0.494803	+	0.132582i
$983$	−14.1050	−	52.6405i	−0.449879	−	1.67897i	−0.702723	−	0.711463i	$-0.748033\pi$
$983$	−14.1050	−	52.6405i	−0.449879	−	1.67897i	0.252845	−	0.967507i	$-0.418634\pi$
$984$	7.09808	+	4.09808i	0.226278	+	0.130642i
$985$		0			0
$986$		−	1.60770i		−	0.0511994i
$987$	6.29959	−	4.26620i	0.200518	−	0.135795i
$988$		0			0
$989$	48.2942	−	27.8827i	1.53567	−	0.886618i
$990$		0			0
$991$	−9.50000	+	16.4545i	−0.301777	+	0.522694i	−0.976539	−	0.215342i	$-0.930913\pi$
$991$	−9.50000	+	16.4545i	−0.301777	+	0.522694i	0.674761	+	0.738036i	$0.264247\pi$
$992$	−0.448288	+	1.67303i	−0.0142331	+	0.0531188i
$993$	7.24693	−	7.24693i	0.229974	−	0.229974i
$994$	33.4808	−	11.5981i	1.06195	−	0.367869i
$995$		0			0
$996$	−2.19615	−	3.80385i	−0.0695878	−	0.120530i
$997$	20.4553	−	5.48099i	0.647827	−	0.173585i	0.0800807	−	0.996788i	$-0.474482\pi$
$997$	20.4553	−	5.48099i	0.647827	−	0.173585i	0.567746	+	0.823204i	$0.307816\pi$
$998$	−17.0077	+	4.55721i	−0.538370	+	0.144256i
$999$	−13.8564	−	24.0000i	−0.438397	−	0.759326i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.2.o.b.143.1	yes	8
5.2	odd	4		350.2.o.a.157.2	yes	8
5.3	odd	4		350.2.o.a.157.1	✓	8
5.4	even	2	inner	350.2.o.b.143.2	yes	8
7.5	odd	6		350.2.o.a.243.2	yes	8
35.12	even	12	inner	350.2.o.b.257.1	yes	8
35.19	odd	6		350.2.o.a.243.1	yes	8
35.33	even	12	inner	350.2.o.b.257.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
350.2.o.a.157.1	✓	8	5.3	odd	4
350.2.o.a.157.2	yes	8	5.2	odd	4
350.2.o.a.243.1	yes	8	35.19	odd	6
350.2.o.a.243.2	yes	8	7.5	odd	6
350.2.o.b.143.1	yes	8	1.1	even	1	trivial
350.2.o.b.143.2	yes	8	5.4	even	2	inner
350.2.o.b.257.1	yes	8	35.12	even	12	inner
350.2.o.b.257.2	yes	8	35.33	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	350.o (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.965926 - 0.258819i) q^{2} +(-0.189469 - 0.707107i) q^{3} +(0.866025 + 0.500000i) q^{4} +0.732051i q^{6} +(-2.19067 + 1.48356i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.13397 - 1.23205i) q^{9} +O(q^{10})\)	\(q+(-0.965926 - 0.258819i) q^{2} +(-0.189469 - 0.707107i) q^{3} +(0.866025 + 0.500000i) q^{4} +0.732051i q^{6} +(-2.19067 + 1.48356i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.13397 - 1.23205i) q^{9} +(0.633975 - 1.09808i) q^{11} +(0.189469 - 0.707107i) q^{12} +(4.38134 - 4.38134i) q^{13} +(2.50000 - 0.866025i) q^{14} +(0.500000 + 0.866025i) q^{16} +(-0.448288 + 0.120118i) q^{17} +(-2.38014 + 0.637756i) q^{18} +(1.46410 + 1.26795i) q^{21} +(-0.896575 + 0.896575i) q^{22} +(1.34486 - 5.01910i) q^{23} +(-0.366025 + 0.633975i) q^{24} +(-5.36603 + 3.09808i) q^{26} +(-2.82843 - 2.82843i) q^{27} +(-2.63896 + 0.189469i) q^{28} -3.46410i q^{29} +(-1.50000 - 0.866025i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(-0.896575 - 0.240237i) q^{33} +0.464102 q^{34} +2.46410 q^{36} +(6.69213 + 1.79315i) q^{37} +(-3.92820 - 2.26795i) q^{39} -11.1962i q^{41} +(-1.08604 - 1.60368i) q^{42} +(7.58871 + 7.58871i) q^{43} +(1.09808 - 0.633975i) q^{44} +(-2.59808 + 4.50000i) q^{46} +(1.01669 - 3.79435i) q^{47} +(0.517638 - 0.517638i) q^{48} +(2.59808 - 6.50000i) q^{49} +(0.169873 + 0.294229i) q^{51} +(5.98502 - 1.60368i) q^{52} +(-7.91688 + 2.12132i) q^{53} +(2.00000 + 3.46410i) q^{54} +(2.59808 + 0.500000i) q^{56} +(-0.896575 + 3.34607i) q^{58} +(-7.09808 + 12.2942i) q^{59} +(-6.29423 + 3.63397i) q^{61} +(1.22474 + 1.22474i) q^{62} +(-2.84701 + 5.86491i) q^{63} +1.00000i q^{64} +(0.803848 + 0.464102i) q^{66} +(0.984508 + 3.67423i) q^{67} +(-0.448288 - 0.120118i) q^{68} -3.80385 q^{69} +13.3923 q^{71} +(-2.38014 - 0.637756i) q^{72} +(2.07055 + 7.72741i) q^{73} +(-6.00000 - 3.46410i) q^{74} +(0.240237 + 3.34607i) q^{77} +(3.20736 + 3.20736i) q^{78} +(-9.86603 + 5.69615i) q^{79} +(2.23205 - 3.86603i) q^{81} +(-2.89778 + 10.8147i) q^{82} +(4.24264 - 4.24264i) q^{83} +(0.633975 + 1.83013i) q^{84} +(-5.36603 - 9.29423i) q^{86} +(-2.44949 + 0.656339i) q^{87} +(-1.22474 + 0.328169i) q^{88} +(5.59808 + 9.69615i) q^{89} +(-3.09808 + 16.0981i) q^{91} +(3.67423 - 3.67423i) q^{92} +(-0.328169 + 1.22474i) q^{93} +(-1.96410 + 3.40192i) q^{94} +(-0.633975 + 0.366025i) q^{96} +(8.05558 + 8.05558i) q^{97} +(-4.19187 + 5.60609i) q^{98} -3.12436i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 24 q^{9}+O(q^{10}) \) 8 * q + 24 * q^9	\( 8 q + 24 q^{9} + 12 q^{11} + 20 q^{14} + 4 q^{16} - 16 q^{21} + 4 q^{24} - 36 q^{26} - 12 q^{31} - 24 q^{34} - 8 q^{36} + 24 q^{39} - 12 q^{44} + 36 q^{51} + 16 q^{54} - 36 q^{59} + 12 q^{61} + 48 q^{66} - 72 q^{69} + 24 q^{71} - 48 q^{74} - 72 q^{79} + 4 q^{81} + 12 q^{84} - 36 q^{86} + 24 q^{89} - 4 q^{91} + 12 q^{94} - 12 q^{96}+O(q^{100}) \) 8 * q + 24 * q^9 + 12 * q^11 + 20 * q^14 + 4 * q^16 - 16 * q^21 + 4 * q^24 - 36 * q^26 - 12 * q^31 - 24 * q^34 - 8 * q^36 + 24 * q^39 - 12 * q^44 + 36 * q^51 + 16 * q^54 - 36 * q^59 + 12 * q^61 + 48 * q^66 - 72 * q^69 + 24 * q^71 - 48 * q^74 - 72 * q^79 + 4 * q^81 + 12 * q^84 - 36 * q^86 + 24 * q^89 - 4 * q^91 + 12 * q^94 - 12 * q^96

Introduction

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