LMFDB - Embedded newform 350.2.o.a.157.1

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			157.1
Root			$0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	350.157
Dual form			350.2.o.a.243.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 + 0.965926i) q^{2} +(0.707107 - 0.189469i) q^{3} +(-0.866025 - 0.500000i) q^{4} +0.732051i q^{6} +(1.48356 + 2.19067i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.13397 + 1.23205i) q^{9} +O(q^{10})$	\(q+(-0.258819 + 0.965926i) q^{2} +(0.707107 - 0.189469i) q^{3} +(-0.866025 - 0.500000i) q^{4} +0.732051i q^{6} +(1.48356 + 2.19067i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.13397 + 1.23205i) q^{9} +(0.633975 - 1.09808i) q^{11} +(-0.707107 - 0.189469i) q^{12} +(4.38134 + 4.38134i) q^{13} +(-2.50000 + 0.866025i) q^{14} +(0.500000 + 0.866025i) q^{16} +(0.120118 + 0.448288i) q^{17} +(-0.637756 - 2.38014i) q^{18} +(1.46410 + 1.26795i) q^{21} +(0.896575 + 0.896575i) q^{22} +(5.01910 + 1.34486i) q^{23} +(0.366025 - 0.633975i) q^{24} +(-5.36603 + 3.09808i) q^{26} +(-2.82843 + 2.82843i) q^{27} +(-0.189469 - 2.63896i) q^{28} +3.46410i q^{29} +(-1.50000 - 0.866025i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(0.240237 - 0.896575i) q^{33} -0.464102 q^{34} +2.46410 q^{36} +(1.79315 - 6.69213i) q^{37} +(3.92820 + 2.26795i) q^{39} -11.1962i q^{41} +(-1.60368 + 1.08604i) q^{42} +(-7.58871 + 7.58871i) q^{43} +(-1.09808 + 0.633975i) q^{44} +(-2.59808 + 4.50000i) q^{46} +(-3.79435 - 1.01669i) q^{47} +(0.517638 + 0.517638i) q^{48} +(-2.59808 + 6.50000i) q^{49} +(0.169873 + 0.294229i) q^{51} +(-1.60368 - 5.98502i) q^{52} +(-2.12132 - 7.91688i) q^{53} +(-2.00000 - 3.46410i) q^{54} +(2.59808 + 0.500000i) q^{56} +(-3.34607 - 0.896575i) q^{58} +(7.09808 - 12.2942i) q^{59} +(-6.29423 + 3.63397i) q^{61} +(1.22474 - 1.22474i) q^{62} +(-5.86491 - 2.84701i) q^{63} -1.00000i q^{64} +(0.803848 + 0.464102i) q^{66} +(3.67423 - 0.984508i) q^{67} +(0.120118 - 0.448288i) q^{68} +3.80385 q^{69} +13.3923 q^{71} +(-0.637756 + 2.38014i) q^{72} +(-7.72741 + 2.07055i) q^{73} +(6.00000 + 3.46410i) q^{74} +(3.34607 - 0.240237i) q^{77} +(-3.20736 + 3.20736i) q^{78} +(9.86603 - 5.69615i) q^{79} +(2.23205 - 3.86603i) q^{81} +(10.8147 + 2.89778i) q^{82} +(4.24264 + 4.24264i) q^{83} +(-0.633975 - 1.83013i) q^{84} +(-5.36603 - 9.29423i) q^{86} +(0.656339 + 2.44949i) q^{87} +(-0.328169 - 1.22474i) q^{88} +(-5.59808 - 9.69615i) q^{89} +(-3.09808 + 16.0981i) q^{91} +(-3.67423 - 3.67423i) q^{92} +(-1.22474 - 0.328169i) q^{93} +(1.96410 - 3.40192i) q^{94} +(-0.633975 + 0.366025i) q^{96} +(8.05558 - 8.05558i) q^{97} +(-5.60609 - 4.19187i) 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 $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$3$	0.707107	−	0.189469i	0.408248	−	0.109390i	−0.0488497	−	0.998806i	$-0.515556\pi$
$3$	0.707107	−	0.189469i	0.408248	−	0.109390i	0.457098	+	0.889416i	$0.348889\pi$
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$		0			0
$5$		0			0
$6$			0.732051i			0.298858i
$7$	1.48356	+	2.19067i	0.560734	+	0.827996i
$7$	1.48356	+	2.19067i	0.560734	+	0.827996i
$8$	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	$0.105445\pi$
$12$	−0.707107	−	0.189469i	−0.204124	−	0.0546949i
$13$	4.38134	+	4.38134i	1.21517	+	1.21517i	0.969305	+	0.245860i	$0.0790704\pi$
$13$	4.38134	+	4.38134i	1.21517	+	1.21517i	0.245860	+	0.969305i	$0.420930\pi$
$14$	−2.50000	+	0.866025i	−0.668153	+	0.231455i
$15$		0			0
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	0.120118	+	0.448288i	0.0291330	+	0.108726i	0.978961	−	0.204046i	$-0.0654092\pi$
$17$	0.120118	+	0.448288i	0.0291330	+	0.108726i	−0.949828	+	0.312772i	$0.898743\pi$
$18$	−0.637756	−	2.38014i	−0.150321	−	0.561004i
$19$		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
$23$	5.01910	+	1.34486i	1.04655	+	0.280423i	0.740827	−	0.671696i	$-0.234434\pi$
$23$	5.01910	+	1.34486i	1.04655	+	0.280423i	0.305727	+	0.952119i	$0.401100\pi$
$24$	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
$28$	−0.189469	−	2.63896i	−0.0358062	−	0.498716i
$29$			3.46410i			0.643268i	0.946864	+	0.321634i	$0.104232\pi$
$29$			3.46410i			0.643268i	−0.946864	+	0.321634i	$0.895768\pi$
$30$		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	$0.716379\pi$
$32$	−0.965926	+	0.258819i	−0.170753	+	0.0457532i
$33$	0.240237	−	0.896575i	0.0418198	−	0.156074i
$34$	−0.464102			−0.0795928
$35$		0			0
$36$	2.46410			0.410684
$37$	1.79315	−	6.69213i	0.294792	−	1.10018i	−0.646590	−	0.762838i	$-0.723806\pi$
$37$	1.79315	−	6.69213i	0.294792	−	1.10018i	0.941382	−	0.337342i	$-0.109528\pi$
$38$		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	$-0.338661\pi$
$42$	−1.60368	+	1.08604i	−0.247454	+	0.167580i
$43$	−7.58871	+	7.58871i	−1.15727	+	1.15727i	−0.172206	+	0.985061i	$0.555089\pi$
$43$	−7.58871	+	7.58871i	−1.15727	+	1.15727i	−0.985061	+	0.172206i	$0.944911\pi$
$44$	−1.09808	+	0.633975i	−0.165541	+	0.0955753i
$45$		0			0
$46$	−2.59808	+	4.50000i	−0.383065	+	0.663489i
$47$	−3.79435	−	1.01669i	−0.553463	−	0.148300i	−0.0287617	−	0.999586i	$-0.509156\pi$
$47$	−3.79435	−	1.01669i	−0.553463	−	0.148300i	−0.524702	+	0.851286i	$0.675823\pi$
$48$	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
$52$	−1.60368	−	5.98502i	−0.222391	−	0.829973i
$53$	−2.12132	−	7.91688i	−0.291386	−	1.08747i	−0.944045	−	0.329815i	$-0.893014\pi$
$53$	−2.12132	−	7.91688i	−0.291386	−	1.08747i	0.652660	−	0.757651i	$-0.273653\pi$
$54$	−2.00000	−	3.46410i	−0.272166	−	0.471405i
$55$		0			0
$56$	2.59808	+	0.500000i	0.347183	+	0.0668153i
$57$		0			0
$58$	−3.34607	−	0.896575i	−0.439360	−	0.117726i
$59$	7.09808	−	12.2942i	0.924091	−	1.60057i	0.131074	−	0.991373i	$-0.458157\pi$
$59$	7.09808	−	12.2942i	0.924091	−	1.60057i	0.793017	−	0.609200i	$-0.208509\pi$
$60$		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
$63$	−5.86491	−	2.84701i	−0.738909	−	0.358689i
$64$		−	1.00000i		−	0.125000i
$65$		0			0
$66$	0.803848	+	0.464102i	0.0989468	+	0.0571270i
$67$	3.67423	−	0.984508i	0.448879	−	0.120277i	−0.0272957	−	0.999627i	$-0.508690\pi$
$67$	3.67423	−	0.984508i	0.448879	−	0.120277i	0.476175	+	0.879351i	$0.342023\pi$
$68$	0.120118	−	0.448288i	0.0145665	−	0.0543629i
$69$	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	$0.207635\pi$
$72$	−0.637756	+	2.38014i	−0.0751603	+	0.280502i
$73$	−7.72741	+	2.07055i	−0.904425	+	0.242340i	−0.680915	−	0.732362i	$-0.738418\pi$
$73$	−7.72741	+	2.07055i	−0.904425	+	0.242340i	−0.223509	+	0.974702i	$0.571751\pi$
$74$	6.00000	+	3.46410i	0.697486	+	0.402694i
$75$		0			0
$76$		0			0
$77$	3.34607	−	0.240237i	0.381320	−	0.0273775i
$78$	−3.20736	+	3.20736i	−0.363163	+	0.363163i
$79$	9.86603	−	5.69615i	1.11001	−	0.640867i	0.171181	−	0.985240i	$-0.445242\pi$
$79$	9.86603	−	5.69615i	1.11001	−	0.640867i	0.938833	+	0.344372i	$0.111908\pi$
$80$		0			0
$81$	2.23205	−	3.86603i	0.248006	−	0.429558i
$82$	10.8147	+	2.89778i	1.19428	+	0.320006i
$83$	4.24264	+	4.24264i	0.465690	+	0.465690i	0.900515	−	0.434825i	$-0.143190\pi$
$83$	4.24264	+	4.24264i	0.465690	+	0.465690i	−0.434825	+	0.900515i	$0.643190\pi$
$84$	−0.633975	−	1.83013i	−0.0691723	−	0.199683i
$85$		0			0
$86$	−5.36603	−	9.29423i	−0.578633	−	1.00222i
$87$	0.656339	+	2.44949i	0.0703669	+	0.262613i
$88$	−0.328169	−	1.22474i	−0.0349830	−	0.130558i
$89$	−5.59808	−	9.69615i	−0.593395	−	1.02779i	−0.993771	−	0.111439i	$-0.964454\pi$
$89$	−5.59808	−	9.69615i	−0.593395	−	1.02779i	0.400376	−	0.916351i	$-0.368879\pi$
$90$		0			0
$91$	−3.09808	+	16.0981i	−0.324767	+	1.68754i
$92$	−3.67423	−	3.67423i	−0.383065	−	0.383065i
$93$	−1.22474	−	0.328169i	−0.127000	−	0.0340296i
$94$	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	−0.167887	−	0.985806i	$-0.553694\pi$
$97$	8.05558	−	8.05558i	0.817920	−	0.817920i	0.985806	+	0.167887i	$0.0536942\pi$
$98$	−5.60609	−	4.19187i	−0.566300	−	0.423443i
$99$			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	$0.970231\pi$
$102$	−0.328169	+	0.0879327i	−0.0324936	+	0.00870664i
$103$	3.36465	−	12.5570i	0.331529	−	1.23728i	−0.576055	−	0.817411i	$-0.695409\pi$
$103$	3.36465	−	12.5570i	0.331529	−	1.23728i	0.907584	−	0.419871i	$-0.137925\pi$
$104$	6.19615			0.607583
$105$		0			0
$106$	8.19615			0.796081
$107$	−0.568406	+	2.12132i	−0.0549499	+	0.205076i	−0.987943	−	0.154819i	$-0.950521\pi$
$107$	−0.568406	+	2.12132i	−0.0549499	+	0.205076i	0.932993	+	0.359895i	$0.117187\pi$
$108$	3.86370	−	1.03528i	0.371785	−	0.0996195i
$109$	−8.83013	−	5.09808i	−0.845773	−	0.488307i	0.0134495	−	0.999910i	$-0.495719\pi$
$109$	−8.83013	−	5.09808i	−0.845773	−	0.488307i	−0.859222	+	0.511602i	$0.829052\pi$
$110$		0			0
$111$		−	5.07180i		−	0.481394i
$112$	−1.15539	+	2.38014i	−0.109175	+	0.224902i
$113$	−4.81105	+	4.81105i	−0.452585	+	0.452585i	−0.896212	−	0.443627i	$-0.853692\pi$
$113$	−4.81105	+	4.81105i	−0.452585	+	0.452585i	0.443627	+	0.896212i	$0.353692\pi$
$114$		0			0
$115$		0			0
$116$	1.73205	−	3.00000i	0.160817	−	0.278543i
$117$	−14.7477	−	3.95164i	−1.36343	−	0.365329i
$118$	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
$122$	−1.88108	−	7.02030i	−0.170305	−	0.635588i
$123$	−2.12132	−	7.91688i	−0.191273	−	0.713841i
$124$	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	$-0.150545\pi$
$127$	4.89898	+	4.89898i	0.434714	+	0.434714i	−0.455514	+	0.890228i	$0.650545\pi$
$128$	0.965926	+	0.258819i	0.0853766	+	0.0228766i
$129$	−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
$137$	−0.776457	+	0.208051i	−0.0663372	+	0.0177750i	−0.291835	−	0.956469i	$-0.594266\pi$
$137$	−0.776457	+	0.208051i	−0.0663372	+	0.0177750i	0.225498	+	0.974244i	$0.427599\pi$
$138$	−0.984508	+	3.67423i	−0.0838069	+	0.312772i
$139$	3.46410			0.293821			0.146911	−	0.989150i	$-0.453067\pi$
$139$	3.46410			0.293821			0.146911	+	0.989150i	$0.453067\pi$
$140$		0			0
$141$	−2.87564			−0.242173
$142$	−3.46618	+	12.9360i	−0.290876	+	1.08556i
$143$	7.58871	−	2.03339i	0.634599	−	0.170040i
$144$	−2.13397	−	1.23205i	−0.177831	−	0.102671i
$145$		0			0
$146$		−	8.00000i		−	0.662085i
$147$	−0.605571	+	5.08845i	−0.0499466	+	0.419688i
$148$	−4.89898	+	4.89898i	−0.402694	+	0.402694i
$149$	−7.09808	+	4.09808i	−0.581497	+	0.335727i	−0.761728	−	0.647897i	$-0.775649\pi$
$149$	−7.09808	+	4.09808i	−0.581497	+	0.335727i	0.180231	+	0.983624i	$0.442315\pi$
$150$		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
$157$	−0.517638	−	1.93185i	−0.0413120	−	0.154179i	0.942189	−	0.335083i	$-0.108764\pi$
$157$	−0.517638	−	1.93185i	−0.0413120	−	0.154179i	−0.983501	+	0.180904i	$0.942098\pi$
$158$	2.94855	+	11.0041i	0.234574	+	0.875441i
$159$	−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
$163$	14.0406	+	3.76217i	1.09974	+	0.294676i	0.762661	−	0.646799i	$-0.223893\pi$
$163$	14.0406	+	3.76217i	1.09974	+	0.294676i	0.337084	+	0.941475i	$0.390559\pi$
$164$	−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	−0.0363667	+	0.999339i	$0.511578\pi$
$167$	−13.3843	+	13.3843i	−1.03571	+	1.03571i	−0.999339	+	0.0363667i	$0.988422\pi$
$168$	1.93185	−	0.138701i	0.149046	−	0.0107010i
$169$			25.3923i			1.95325i
$170$		0			0
$171$		0			0
$172$	10.3664	−	2.77766i	0.790428	−	0.211795i
$173$	4.57081	−	17.0585i	0.347512	−	1.29693i	−0.542137	−	0.840290i	$-0.682385\pi$
$173$	4.57081	−	17.0585i	0.347512	−	1.29693i	0.889650	−	0.456644i	$-0.150949\pi$
$174$	−2.53590			−0.192246
$175$		0			0
$176$	1.26795			0.0955753
$177$	2.68973	−	10.0382i	0.202172	−	0.754517i
$178$	10.8147	−	2.89778i	0.810592	−	0.217198i
$179$	−7.09808	−	4.09808i	−0.530535	−	0.306305i	0.210699	−	0.977551i	$-0.432426\pi$
$179$	−7.09808	−	4.09808i	−0.530535	−	0.306305i	−0.741234	+	0.671246i	$0.765759\pi$
$180$		0			0
$181$		−	7.26795i		−	0.540222i	−0.962829	−	0.270111i	$-0.912940\pi$
$181$		−	7.26795i		−	0.540222i	0.962829	−	0.270111i	$-0.0870605\pi$
$182$	−14.7477	−	7.15900i	−1.09317	−	0.530660i
$183$	−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
$187$	0.568406	+	0.152304i	0.0415660	+	0.0111376i
$188$	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	$0.769148\pi$
$192$	−0.189469	−	0.707107i	−0.0136737	−	0.0510310i
$193$	3.13801	+	11.7112i	0.225879	+	0.842993i	0.982050	+	0.188619i	$0.0604011\pi$
$193$	3.13801	+	11.7112i	0.225879	+	0.842993i	−0.756171	+	0.654374i	$0.772932\pi$
$194$	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	$-0.155687\pi$
$197$	5.79555	+	5.79555i	0.412916	+	0.412916i	−0.469837	+	0.882753i	$0.655687\pi$
$198$	−3.01790	−	0.808643i	−0.214473	−	0.0574677i
$199$	−9.86603	+	17.0885i	−0.699384	+	1.21137i	0.269296	+	0.963057i	$0.413209\pi$
$199$	−9.86603	+	17.0885i	−0.699384	+	1.21137i	−0.968680	+	0.248311i	$0.920124\pi$
$200$		0			0
$201$	2.41154	−	1.39230i	0.170097	−	0.0982056i
$202$	11.5911	−	11.5911i	0.815548	−	0.815548i
$203$	−7.58871	+	5.13922i	−0.532623	+	0.360702i
$204$		−	0.339746i		−	0.0237870i
$205$		0			0
$206$	11.2583	+	6.50000i	0.784405	+	0.452876i
$207$	−12.3676	+	3.31388i	−0.859605	+	0.230331i
$208$	−1.60368	+	5.98502i	−0.111195	+	0.414987i
$209$		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	$0.614147\pi$
$212$	−2.12132	+	7.91688i	−0.145693	+	0.543733i
$213$	9.46979	−	2.53742i	0.648859	−	0.173861i
$214$	−1.90192	−	1.09808i	−0.130013	−	0.0750629i
$215$		0			0
$216$			4.00000i			0.272166i
$217$	−0.328169	−	4.57081i	−0.0222776	−	0.310287i
$218$	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
$222$	4.89898	+	1.31268i	0.328798	+	0.0881012i
$223$	6.64136	+	6.64136i	0.444739	+	0.444739i	0.893601	−	0.448862i	$-0.148171\pi$
$223$	6.64136	+	6.64136i	0.444739	+	0.444739i	−0.448862	+	0.893601i	$0.648171\pi$
$224$	−2.00000	−	1.73205i	−0.133631	−	0.115728i
$225$		0			0
$226$	−3.40192	−	5.89230i	−0.226293	−	0.391950i
$227$	7.10823	+	26.5283i	0.471790	+	1.76074i	0.633334	+	0.773879i	$0.281686\pi$
$227$	7.10823	+	26.5283i	0.471790	+	1.76074i	−0.161544	+	0.986866i	$0.551647\pi$
$228$		0			0
$229$	−7.09808	−	12.2942i	−0.469054	−	0.812425i	0.530320	−	0.847797i	$-0.322072\pi$
$229$	−7.09808	−	12.2942i	−0.469054	−	0.812425i	−0.999374	+	0.0353720i	$0.988738\pi$
$230$		0			0
$231$	2.32051	−	0.803848i	0.152678	−	0.0528893i
$232$	2.44949	+	2.44949i	0.160817	+	0.160817i
$233$	−5.79555	−	1.55291i	−0.379679	−	0.101735i	0.0639315	−	0.997954i	$-0.479636\pi$
$233$	−5.79555	−	1.55291i	−0.379679	−	0.101735i	−0.443611	+	0.896219i	$0.646303\pi$
$234$	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
$238$	−0.688524	−	1.01669i	−0.0446304	−	0.0659025i
$239$		−	22.8564i		−	1.47846i	−0.673454	−	0.739229i	$-0.735190\pi$
$239$		−	22.8564i		−	1.47846i	0.673454	−	0.739229i	$-0.264810\pi$
$240$		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	$0.702255\pi$
$242$	−9.07227	+	2.43091i	−0.583188	+	0.156265i
$243$	3.95164	−	14.7477i	0.253498	−	0.946066i
$244$	7.26795			0.465283
$245$		0			0
$246$	8.19615			0.522568
$247$		0			0
$248$	−1.67303	+	0.448288i	−0.106238	+	0.0284663i
$249$	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	$-0.0442666\pi$
$252$	3.65565	+	5.39804i	0.230284	+	0.340044i
$253$	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
$257$	−4.24264	−	1.13681i	−0.264649	−	0.0709124i	0.124055	−	0.992275i	$-0.460410\pi$
$257$	−4.24264	−	1.13681i	−0.264649	−	0.0709124i	−0.388703	+	0.921363i	$0.627077\pi$
$258$	−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
$262$	0.568406	+	2.12132i	0.0351162	+	0.131056i
$263$	0.928761	+	3.46618i	0.0572699	+	0.213734i	0.988631	−	0.150363i	$-0.0480443\pi$
$263$	0.928761	+	3.46618i	0.0572699	+	0.213734i	−0.931361	+	0.364097i	$0.881378\pi$
$264$	−0.464102	−	0.803848i	−0.0285635	−	0.0494734i
$265$		0			0
$266$		0			0
$267$	−5.79555	−	5.79555i	−0.354682	−	0.354682i
$268$	−3.67423	−	0.984508i	−0.224440	−	0.0601384i
$269$	6.29423	−	10.9019i	0.383766	−	0.664702i	−0.607831	−	0.794066i	$-0.707960\pi$
$269$	6.29423	−	10.9019i	0.383766	−	0.664702i	0.991597	+	0.129364i	$0.0412936\pi$
$270$		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
$273$	0.859411	+	11.9700i	0.0520139	+	0.724460i
$274$		−	0.803848i		−	0.0485622i
$275$		0			0
$276$	−3.29423	−	1.90192i	−0.198289	−	0.114482i
$277$	−6.36396	+	1.70522i	−0.382373	+	0.102457i	−0.444885	−	0.895588i	$-0.646756\pi$
$277$	−6.36396	+	1.70522i	−0.382373	+	0.102457i	0.0625119	+	0.998044i	$0.480089\pi$
$278$	−0.896575	+	3.34607i	−0.0537730	+	0.200684i
$279$	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	$0.239658\pi$
$282$	0.744272	−	2.77766i	0.0443207	−	0.165407i
$283$	−2.31079	+	0.619174i	−0.137362	+	0.0368061i	−0.326845	−	0.945078i	$-0.605986\pi$
$283$	−2.31079	+	0.619174i	−0.137362	+	0.0368061i	0.189483	+	0.981884i	$0.439319\pi$
$284$	−11.5981	−	6.69615i	−0.688219	−	0.397344i
$285$		0			0
$286$			7.85641i			0.464559i
$287$	24.5271	−	16.6102i	1.44779	−	0.980470i
$288$	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
$292$	7.72741	+	2.07055i	0.452212	+	0.121170i
$293$	−22.5259	−	22.5259i	−1.31598	−	1.31598i	−0.916932	−	0.399044i	$-0.869342\pi$
$293$	−22.5259	−	22.5259i	−1.31598	−	1.31598i	−0.399044	−	0.916932i	$-0.630658\pi$
$294$	−4.75833	−	1.90192i	−0.277511	−	0.110922i
$295$		0			0
$296$	−3.46410	−	6.00000i	−0.201347	−	0.348743i
$297$	1.31268	+	4.89898i	0.0761693	+	0.284268i
$298$	−2.12132	−	7.91688i	−0.122885	−	0.458612i
$299$	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
$303$	−11.5911	−	3.10583i	−0.665892	−	0.178425i
$304$		0			0
$305$		0			0
$306$	0.990381	−	0.571797i	0.0566163	−	0.0326874i
$307$	8.76268	−	8.76268i	0.500113	−	0.500113i	−0.411360	−	0.911473i	$-0.634946\pi$
$307$	8.76268	−	8.76268i	0.500113	−	0.500113i	0.911473	+	0.411360i	$0.134946\pi$
$308$	−3.01790	−	1.46498i	−0.171961	−	0.0834751i
$309$		−	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	$0.673922\pi$
$312$	4.38134	−	1.17398i	0.248045	−	0.0664634i
$313$	−4.91756	+	18.3526i	−0.277957	+	1.03735i	0.675877	+	0.737015i	$0.263765\pi$
$313$	−4.91756	+	18.3526i	−0.277957	+	1.03735i	−0.953834	+	0.300335i	$0.902902\pi$
$314$	2.00000			0.112867
$315$		0			0
$316$	−11.3923			−0.640867
$317$	4.24264	−	15.8338i	0.238290	−	0.889312i	−0.738347	−	0.674420i	$-0.764394\pi$
$317$	4.24264	−	15.8338i	0.238290	−	0.889312i	0.976638	−	0.214892i	$-0.0689398\pi$
$318$	5.79555	−	1.55291i	0.324999	−	0.0870831i
$319$	3.80385	+	2.19615i	0.212975	+	0.122961i
$320$		0			0
$321$			1.60770i			0.0897328i
$322$	−13.7124	+	0.984508i	−0.764164	+	0.0548645i
$323$		0			0
$324$	−3.86603	+	2.23205i	−0.214779	+	0.124003i
$325$		0			0
$326$	−7.26795	+	12.5885i	−0.402534	+	0.697210i
$327$	−7.20977	−	1.93185i	−0.398701	−	0.106832i
$328$	−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	$0.707619\pi$
$332$	−1.55291	−	5.79555i	−0.0852272	−	0.318072i
$333$	4.41851	+	16.4901i	0.242133	+	0.903651i
$334$	−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	$-0.174204\pi$
$337$	6.12372	+	6.12372i	0.333581	+	0.333581i	−0.520364	+	0.853945i	$0.674204\pi$
$338$	−24.5271	−	6.57201i	−1.33410	−	0.357470i
$339$	−2.49038	+	4.31347i	−0.135259	+	0.234275i
$340$		0			0
$341$	−1.90192	+	1.09808i	−0.102995	+	0.0594642i
$342$		0			0
$343$	−18.0938	+	3.95164i	−0.976972	+	0.213368i
$344$			10.7321i			0.578633i
$345$		0			0
$346$	15.2942	+	8.83013i	0.822223	+	0.474711i
$347$	5.79555	−	1.55291i	0.311122	−	0.0833648i	−0.0998797	−	0.995000i	$-0.531846\pi$
$347$	5.79555	−	1.55291i	0.311122	−	0.0833648i	0.411001	+	0.911635i	$0.365179\pi$
$348$	0.656339	−	2.44949i	0.0351835	−	0.131306i
$349$	16.9808			0.908959			0.454480	−	0.890757i	$-0.349825\pi$
$349$	16.9808			0.908959			0.454480	+	0.890757i	$0.349825\pi$
$350$		0			0
$351$	−24.7846			−1.32290
$352$	−0.328169	+	1.22474i	−0.0174915	+	0.0652791i
$353$	−22.7339	+	6.09154i	−1.21001	+	0.324220i	−0.806764	−	0.590874i	$-0.798783\pi$
$353$	−22.7339	+	6.09154i	−1.21001	+	0.324220i	−0.403241	+	0.915094i	$0.632116\pi$
$354$	9.00000	+	5.19615i	0.478345	+	0.276172i
$355$		0			0
$356$			11.1962i			0.593395i
$357$	−0.392541	+	0.808643i	−0.0207755	+	0.0427979i
$358$	5.79555	−	5.79555i	0.306305	−	0.306305i
$359$	9.00000	−	5.19615i	0.475002	−	0.274242i	−0.243329	−	0.969944i	$-0.578240\pi$
$359$	9.00000	−	5.19615i	0.475002	−	0.274242i	0.718331	+	0.695701i	$0.244906\pi$
$360$		0			0
$361$	9.50000	−	16.4545i	0.500000	−	0.866025i
$362$	7.02030	+	1.88108i	0.368979	+	0.0988676i
$363$	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
$367$	−4.76028	−	17.7656i	−0.248485	−	0.927357i	−0.971600	−	0.236630i	$-0.923957\pi$
$367$	−4.76028	−	17.7656i	−0.248485	−	0.927357i	0.723115	−	0.690727i	$-0.242709\pi$
$368$	1.34486	+	5.01910i	0.0701058	+	0.261639i
$369$	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
$373$	16.4022	+	4.39494i	0.849271	+	0.227562i	0.657103	−	0.753800i	$-0.271781\pi$
$373$	16.4022	+	4.39494i	0.849271	+	0.227562i	0.192168	+	0.981362i	$0.438448\pi$
$374$	−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
$378$	4.62158	−	9.52056i	0.237708	−	0.489685i
$379$		−	8.58846i		−	0.441159i	−0.975369	−	0.220580i	$-0.929205\pi$
$379$		−	8.58846i		−	0.441159i	0.975369	−	0.220580i	$-0.0707949\pi$
$380$		0			0
$381$	4.39230	+	2.53590i	0.225025	+	0.129918i
$382$	−5.34727	+	1.43280i	−0.273590	+	0.0733082i
$383$	−6.15591	+	22.9742i	−0.314552	+	1.17393i	0.609853	+	0.792514i	$0.291228\pi$
$383$	−6.15591	+	22.9742i	−0.314552	+	1.17393i	−0.924406	+	0.381411i	$0.875438\pi$
$384$	0.732051			0.0373573
$385$		0			0
$386$	−12.1244			−0.617113
$387$	6.84443	−	25.5438i	0.347922	−	1.29846i
$388$	−11.0041	+	2.94855i	−0.558650	+	0.149690i
$389$	3.50962	+	2.02628i	0.177945	+	0.102736i	0.586327	−	0.810075i	$-0.300574\pi$
$389$	3.50962	+	2.02628i	0.177945	+	0.102736i	−0.408382	+	0.912811i	$0.633907\pi$
$390$		0			0
$391$			2.41154i			0.121957i
$392$	2.75908	+	6.43331i	0.139354	+	0.324931i
$393$	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
$397$	−1.93185	−	0.517638i	−0.0969569	−	0.0259795i	0.210014	−	0.977698i	$-0.432649\pi$
$397$	−1.93185	−	0.517638i	−0.0969569	−	0.0259795i	−0.306971	+	0.951719i	$0.599316\pi$
$398$	−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	$0.744175\pi$
$402$	0.720710	+	2.68973i	0.0359457	+	0.134151i
$403$	−2.77766	−	10.3664i	−0.138365	−	0.516385i
$404$	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
$408$	0.328169	+	0.0879327i	0.0162468	+	0.00435332i
$409$	−6.40192	+	11.0885i	−0.316555	+	0.548289i	−0.979767	−	0.200143i	$-0.935859\pi$
$409$	−6.40192	+	11.0885i	−0.316555	+	0.548289i	0.663212	+	0.748432i	$0.269193\pi$
$410$		0			0
$411$	−0.509619	+	0.294229i	−0.0251376	+	0.0145132i
$412$	−9.19239	+	9.19239i	−0.452876	+	0.452876i
$413$	37.4631	−	2.68973i	1.84344	−	0.132353i
$414$		−	12.8038i		−	0.629275i
$415$		0			0
$416$	−5.36603	−	3.09808i	−0.263091	−	0.151896i
$417$	2.44949	−	0.656339i	0.119952	−	0.0321410i
$418$		0			0
$419$	−28.9808			−1.41580			−0.707901	−	0.706311i	$-0.750358\pi$
$419$	−28.9808			−1.41580			−0.707901	+	0.706311i	$0.750358\pi$
$420$		0			0
$421$	−15.6077			−0.760673			−0.380336	−	0.924848i	$-0.624192\pi$
$421$	−15.6077			−0.760673			−0.380336	+	0.924848i	$0.624192\pi$
$422$	2.63896	−	9.84873i	0.128462	−	0.479429i
$423$	9.34967	−	2.50524i	0.454597	−	0.121809i
$424$	−7.09808	−	4.09808i	−0.344713	−	0.199020i
$425$		0			0
$426$			9.80385i			0.474998i
$427$	−17.2987	−	8.39735i	−0.837144	−	0.406376i
$428$	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	$0.0278765\pi$
$432$	−3.86370	−	1.03528i	−0.185893	−	0.0498097i
$433$	−22.7525	−	22.7525i	−1.09342	−	1.09342i	−0.995161	−	0.0982548i	$-0.968674\pi$
$433$	−22.7525	−	22.7525i	−1.09342	−	1.09342i	−0.0982548	−	0.995161i	$-0.531326\pi$
$434$	4.50000	+	0.866025i	0.216007	+	0.0415705i
$435$		0			0
$436$	5.09808	+	8.83013i	0.244154	+	0.422886i
$437$		0			0
$438$	−1.51575	−	5.65685i	−0.0724253	−	0.270295i
$439$	−2.93782	−	5.08846i	−0.140215	−	0.242859i	0.787363	−	0.616490i	$-0.211446\pi$
$439$	−2.93782	−	5.08846i	−0.140215	−	0.242859i	−0.927577	+	0.373631i	$0.878113\pi$
$440$		0			0
$441$	−2.46410	−	17.0718i	−0.117338	−	0.812943i
$442$	−2.03339	−	2.03339i	−0.0967184	−	0.0967184i
$443$	11.5911	+	3.10583i	0.550710	+	0.147562i	0.523435	−	0.852066i	$-0.324650\pi$
$443$	11.5911	+	3.10583i	0.550710	+	0.147562i	0.0272752	+	0.999628i	$0.491317\pi$
$444$	−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
$448$	2.19067	−	1.48356i	0.103499	−	0.0700918i
$449$			8.32051i			0.392669i	0.980537	+	0.196335i	$0.0629039\pi$
$449$			8.32051i			0.392669i	−0.980537	+	0.196335i	$0.937096\pi$
$450$		0			0
$451$	−12.2942	−	7.09808i	−0.578913	−	0.334235i
$452$	6.57201	−	1.76097i	0.309121	−	0.0828288i
$453$	−3.48477	+	13.0053i	−0.163729	+	0.611043i
$454$	−27.4641			−1.28895
$455$		0			0
$456$		0			0
$457$	−8.42091	+	31.4273i	−0.393914	+	1.47011i	0.429709	+	0.902967i	$0.358616\pi$
$457$	−8.42091	+	31.4273i	−0.393914	+	1.47011i	−0.823623	+	0.567138i	$0.808051\pi$
$458$	13.7124	−	3.67423i	0.640740	−	0.171686i
$459$	−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	$0.811225\pi$
$462$	0.175865	+	2.44949i	0.00818200	+	0.113961i
$463$	6.60420	−	6.60420i	0.306923	−	0.306923i	−0.536792	−	0.843715i	$-0.680364\pi$
$463$	6.60420	−	6.60420i	0.306923	−	0.306923i	0.843715	+	0.536792i	$0.180364\pi$
$464$	−3.00000	+	1.73205i	−0.139272	+	0.0804084i
$465$		0			0
$466$	3.00000	−	5.19615i	0.138972	−	0.240707i
$467$	22.2856	+	5.97142i	1.03126	+	0.276324i	0.734486	−	0.678624i	$-0.237424\pi$
$467$	22.2856	+	5.97142i	1.03126	+	0.276324i	0.296771	+	0.954949i	$0.404090\pi$
$468$	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
$472$	−3.67423	−	13.7124i	−0.169120	−	0.631166i
$473$	3.52193	+	13.1440i	0.161939	+	0.604363i
$474$	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
$478$	22.0776	+	5.91567i	1.00981	+	0.270577i
$479$	−6.40192	+	11.0885i	−0.292511	+	0.506645i	−0.974403	−	0.224809i	$-0.927824\pi$
$479$	−6.40192	+	11.0885i	−0.292511	+	0.506645i	0.681892	+	0.731453i	$0.261158\pi$
$480$		0			0
$481$	37.1769	−	21.4641i	1.69512	−	0.978679i
$482$	2.44949	−	2.44949i	0.111571	−	0.111571i
$483$	5.64325	+	8.33298i	0.256777	+	0.379164i
$484$		−	9.39230i		−	0.426923i
$485$		0			0
$486$	13.2224	+	7.63397i	0.599782	+	0.346284i
$487$	−9.02150	+	2.41730i	−0.408803	+	0.109539i	−0.457359	−	0.889282i	$-0.651205\pi$
$487$	−9.02150	+	2.41730i	−0.408803	+	0.109539i	0.0485561	+	0.998820i	$0.484538\pi$
$488$	−1.88108	+	7.02030i	−0.0851527	+	0.317794i
$489$	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	$0.617981\pi$
$492$	−2.12132	+	7.91688i	−0.0956365	+	0.356920i
$493$	−1.55291	+	0.416102i	−0.0699397	+	0.0187403i
$494$		0			0
$495$		0			0
$496$		−	1.73205i		−	0.0777714i
$497$	19.8683	+	29.3381i	0.891217	+	1.31599i
$498$	−3.10583	+	3.10583i	−0.139176	+	0.139176i
$499$	−15.2487	+	8.80385i	−0.682626	+	0.394114i	−0.800844	−	0.598873i	$-0.795615\pi$
$499$	−15.2487	+	8.80385i	−0.682626	+	0.394114i	0.118218	+	0.992988i	$0.462282\pi$
$500$		0			0
$501$	−6.92820	+	12.0000i	−0.309529	+	0.536120i
$502$	4.24264	+	1.13681i	0.189358	+	0.0507384i
$503$	7.82894	+	7.82894i	0.349075	+	0.349075i	0.859765	−	0.510690i	$-0.170610\pi$
$503$	7.82894	+	7.82894i	0.349075	+	0.349075i	−0.510690	+	0.859765i	$0.670610\pi$
$504$	−6.16025	+	2.13397i	−0.274400	+	0.0950548i
$505$		0			0
$506$	3.29423	+	5.70577i	0.146446	+	0.253652i
$507$	4.81105	+	17.9551i	0.213666	+	0.797413i
$508$	−1.79315	−	6.69213i	−0.0795582	−	0.296915i
$509$	−17.4904	−	30.2942i	−0.775248	−	1.34277i	−0.934655	−	0.355555i	$-0.884292\pi$
$509$	−17.4904	−	30.2942i	−0.775248	−	1.34277i	0.159408	−	0.987213i	$-0.449042\pi$
$510$		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
$518$	1.31268	+	18.2832i	0.0576757	+	0.803319i
$519$		−	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	$0.403488\pi$
$522$	8.24504	−	2.20925i	0.360876	−	0.0966964i
$523$	2.58819	−	9.65926i	0.113174	−	0.422370i	−0.885970	−	0.463742i	$-0.846506\pi$
$523$	2.58819	−	9.65926i	0.113174	−	0.422370i	0.999144	+	0.0413724i	$0.0131730\pi$
$524$	−2.19615			−0.0959394
$525$		0			0
$526$	−3.58846			−0.156464
$527$	0.208051	−	0.776457i	0.00906285	−	0.0338230i
$528$	0.896575	−	0.240237i	0.0390184	−	0.0104550i
$529$	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
$537$	−5.79555	−	1.55291i	−0.250097	−	0.0670132i
$538$	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	$0.705408\pi$
$542$	6.00361	+	22.4058i	0.257877	+	0.962410i
$543$	−1.37705	−	5.13922i	−0.0590948	−	0.220545i
$544$	−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	$-0.457621\pi$
$547$	−20.0764	−	20.0764i	−0.858405	−	0.858405i	−0.991150	+	0.132746i	$0.957621\pi$
$548$	0.776457	+	0.208051i	0.0331686	+	0.00888750i
$549$	8.95448	−	15.5096i	0.382168	−	0.661934i
$550$		0			0
$551$		0			0
$552$	2.68973	−	2.68973i	0.114482	−	0.114482i
$553$	27.1153	+	13.1626i	1.15306	+	0.559731i
$554$		−	6.58846i		−	0.279917i
$555$		0			0
$556$	−3.00000	−	1.73205i	−0.127228	−	0.0734553i
$557$	−2.12132	+	0.568406i	−0.0898832	+	0.0240841i	−0.303480	−	0.952838i	$-0.598149\pi$
$557$	−2.12132	+	0.568406i	−0.0898832	+	0.0240841i	0.213597	+	0.976922i	$0.431482\pi$
$558$	−1.10463	+	4.12252i	−0.0467626	+	0.174520i
$559$	−66.4974			−2.81254
$560$		0			0
$561$	0.430781			0.0181876
$562$	−6.33178	+	23.6305i	−0.267090	+	0.996793i
$563$	−29.5462	+	7.91688i	−1.24522	+	0.333657i	−0.820489	−	0.571662i	$-0.806299\pi$
$563$	−29.5462	+	7.91688i	−1.24522	+	0.333657i	−0.424734	+	0.905318i	$0.639632\pi$
$564$	2.49038	+	1.43782i	0.104864	+	0.0605432i
$565$		0			0
$566$		−	2.39230i		−	0.100556i
$567$	11.7806	−	0.845807i	0.494738	−	0.0355206i
$568$	9.46979	−	9.46979i	0.397344	−	0.397344i
$569$	−20.5981	+	11.8923i	−0.863516	+	0.498551i	−0.865188	−	0.501447i	$-0.832801\pi$
$569$	−20.5981	+	11.8923i	−0.863516	+	0.498551i	0.00167195	+	0.999999i	$0.499468\pi$
$570$		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	$0.0496427\pi$
$572$	−7.58871	−	2.03339i	−0.317300	−	0.0850202i
$573$	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
$577$	−2.17209	−	8.10634i	−0.0904252	−	0.337472i	0.905861	−	0.423575i	$-0.139225\pi$
$577$	−2.17209	−	8.10634i	−0.0904252	−	0.337472i	−0.996286	+	0.0861036i	$0.972558\pi$
$578$	4.34418	+	16.2127i	0.180694	+	0.674359i
$579$	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
$583$	−10.0382	−	2.68973i	−0.415740	−	0.111397i
$584$	−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	−0.760433	−	0.649416i	$-0.775013\pi$
$587$	−2.68973	+	2.68973i	−0.111017	+	0.111017i	0.649416	+	0.760433i	$0.275013\pi$
$588$	3.06866	−	4.10394i	0.126550	−	0.169244i
$589$		0			0
$590$		0			0
$591$	5.19615	+	3.00000i	0.213741	+	0.123404i
$592$	6.69213	−	1.79315i	0.275045	−	0.0736980i
$593$	−8.78127	+	32.7721i	−0.360603	+	1.34579i	0.512681	+	0.858579i	$0.328652\pi$
$593$	−8.78127	+	32.7721i	−0.360603	+	1.34579i	−0.873284	+	0.487211i	$0.838014\pi$
$594$	−5.07180			−0.208098
$595$		0			0
$596$	8.19615			0.335727
$597$	−3.73861	+	13.9527i	−0.153011	+	0.571045i
$598$	−31.0991	+	8.33298i	−1.27174	+	0.340761i
$599$	24.1865	+	13.9641i	0.988235	+	0.570558i	0.904746	−	0.425951i	$-0.140060\pi$
$599$	24.1865	+	13.9641i	0.988235	+	0.570558i	0.0834887	+	0.996509i	$0.473394\pi$
$600$		0			0
$601$			2.78461i			0.113587i	0.998386	+	0.0567933i	$0.0180876\pi$
$601$			2.78461i			0.113587i	−0.998386	+	0.0567933i	$0.981912\pi$
$602$	12.3998	−	25.5438i	0.505376	−	1.04109i
$603$	−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
$607$	25.2850	+	6.77508i	1.02628	+	0.274992i	0.732419	−	0.680854i	$-0.238391\pi$
$607$	25.2850	+	6.77508i	1.02628	+	0.274992i	0.293866	+	0.955847i	$0.405058\pi$
$608$		0			0
$609$	−4.39230	+	5.07180i	−0.177985	+	0.205520i
$610$		0			0
$611$	−12.1699	−	21.0788i	−0.492340	−	0.852759i
$612$	0.295984	+	1.10463i	0.0119644	+	0.0446519i
$613$	−4.65874	−	17.3867i	−0.188165	−	0.702241i	−0.993931	−	0.110007i	$-0.964913\pi$
$613$	−4.65874	−	17.3867i	−0.188165	−	0.702241i	0.805766	−	0.592234i	$-0.201754\pi$
$614$	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	$-0.304156\pi$
$617$	−5.94786	−	5.94786i	−0.239452	−	0.239452i	−0.816623	+	0.577171i	$0.804156\pi$
$618$	9.19239	+	2.46309i	0.369772	+	0.0990801i
$619$	−12.4641	+	21.5885i	−0.500975	+	0.867713i	0.499025	+	0.866588i	$0.333692\pi$
$619$	−12.4641	+	21.5885i	−0.500975	+	0.867713i	−0.999999	+	0.00112567i	$0.999642\pi$
$620$		0			0
$621$	−18.0000	+	10.3923i	−0.722315	+	0.417029i
$622$	0.568406	−	0.568406i	0.0227910	−	0.0227910i
$623$	12.9360	−	26.6484i	0.518269	−	1.06765i
$624$			4.53590i			0.181581i
$625$		0			0
$626$	−16.4545	−	9.50000i	−0.657653	−	0.379696i
$627$		0			0
$628$	−0.517638	+	1.93185i	−0.0206560	+	0.0770893i
$629$	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	$0.612524\pi$
$632$	2.94855	−	11.0041i	0.117287	−	0.437720i
$633$	−7.20977	+	1.93185i	−0.286563	+	0.0767842i
$634$	14.1962	+	8.19615i	0.563801	+	0.325511i
$635$		0			0
$636$			6.00000i			0.237915i
$637$	−39.8618	+	17.0957i	−1.57938	+	0.677355i
$638$	−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	$0.987649\pi$
$642$	−1.55291	−	0.416102i	−0.0612886	−	0.0164222i
$643$	−14.8356	−	14.8356i	−0.585060	−	0.585060i	0.351229	−	0.936290i	$-0.385764\pi$
$643$	−14.8356	−	14.8356i	−0.585060	−	0.585060i	−0.936290	+	0.351229i	$0.885764\pi$
$644$	2.59808	−	13.5000i	0.102379	−	0.531975i
$645$		0			0
$646$		0			0
$647$	−6.62776	−	24.7351i	−0.260564	−	0.972438i	−0.964910	−	0.262581i	$-0.915426\pi$
$647$	−6.62776	−	24.7351i	−0.260564	−	0.972438i	0.704346	−	0.709857i	$-0.251240\pi$
$648$	−1.15539	−	4.31199i	−0.0453882	−	0.169391i
$649$	−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
$653$	−19.5080	−	5.22715i	−0.763406	−	0.204554i	−0.143950	−	0.989585i	$-0.545980\pi$
$653$	−19.5080	−	5.22715i	−0.763406	−	0.204554i	−0.619457	+	0.785031i	$0.712647\pi$
$654$	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
$658$	10.3664	−	0.744272i	0.404123	−	0.0290147i
$659$		−	29.3205i		−	1.14216i	−0.820893	−	0.571082i	$-0.806524\pi$
$659$		−	29.3205i		−	1.14216i	0.820893	−	0.571082i	$-0.193476\pi$
$660$		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	$0.711809\pi$
$662$	−13.5230	+	3.62347i	−0.525585	+	0.140830i
$663$	−0.544845	+	2.03339i	−0.0211600	+	0.0789702i
$664$	6.00000			0.232845
$665$		0			0
$666$	−17.0718			−0.661519
$667$	−4.65874	+	17.3867i	−0.180387	+	0.673214i
$668$	18.2832	−	4.89898i	0.707400	−	0.189547i
$669$	5.95448	+	3.43782i	0.230214	+	0.132914i
$670$		0			0
$671$			9.21539i			0.355756i
$672$	−1.74238	−	0.845807i	−0.0672139	−	0.0326277i
$673$	6.12372	−	6.12372i	0.236052	−	0.236052i	−0.579161	−	0.815213i	$-0.696620\pi$
$673$	6.12372	−	6.12372i	0.236052	−	0.236052i	0.815213	+	0.579161i	$0.196620\pi$
$674$	−7.50000	+	4.33013i	−0.288889	+	0.166790i
$675$		0			0
$676$	12.6962	−	21.9904i	0.488314	−	0.845784i
$677$	−6.45189	−	1.72878i	−0.247966	−	0.0664424i	0.132695	−	0.991157i	$-0.457637\pi$
$677$	−6.45189	−	1.72878i	−0.247966	−	0.0664424i	−0.380661	+	0.924715i	$0.624304\pi$
$678$	−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
$682$	−0.568406	−	2.12132i	−0.0217654	−	0.0812296i
$683$	−3.82654	−	14.2808i	−0.146418	−	0.546441i	−0.999688	−	0.0249712i	$-0.992051\pi$
$683$	−3.82654	−	14.2808i	−0.146418	−	0.546441i	0.853270	−	0.521470i	$-0.174616\pi$
$684$		0			0
$685$		0			0
$686$	0.866025	−	18.5000i	0.0330650	−	0.706333i
$687$	−7.34847	−	7.34847i	−0.280362	−	0.280362i
$688$	−10.3664	−	2.77766i	−0.395214	−	0.105897i
$689$	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
$693$	−6.84443	+	4.63518i	−0.259999	+	0.176076i
$694$			6.00000i			0.227757i
$695$		0			0
$696$	2.19615	+	1.26795i	0.0832449	+	0.0480615i
$697$	5.01910	−	1.34486i	0.190112	−	0.0509403i
$698$	−4.39494	+	16.4022i	−0.166351	+	0.620831i
$699$	−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	$0.753532\pi$
$702$	6.41473	−	23.9401i	0.242108	−	0.903561i
$703$		0			0
$704$	−1.09808	−	0.633975i	−0.0413853	−	0.0238938i
$705$		0			0
$706$		−	23.5359i		−	0.885785i
$707$	−3.10583	−	43.2586i	−0.116807	−	1.62691i
$708$	−7.34847	+	7.34847i	−0.276172	+	0.276172i
$709$	45.5429	−	26.2942i	1.71040	−	0.987500i	0.776393	−	0.630250i	$-0.217047\pi$
$709$	45.5429	−	26.2942i	1.71040	−	0.987500i	0.934008	−	0.357251i	$-0.116286\pi$
$710$		0			0
$711$	−14.0359	+	24.3109i	−0.526387	+	0.911730i
$712$	−10.8147	−	2.89778i	−0.405296	−	0.108599i
$713$	−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
$717$	−4.33057	−	16.1619i	−0.161728	−	0.603578i
$718$	2.68973	+	10.0382i	0.100380	+	0.374622i
$719$	19.7942	+	34.2846i	0.738200	+	1.27860i	0.953305	+	0.302009i	$0.0976573\pi$
$719$	19.7942	+	34.2846i	0.738200	+	1.27860i	−0.215105	+	0.976591i	$0.569009\pi$
$720$		0			0
$721$	32.5000	−	11.2583i	1.21036	−	0.419282i
$722$	13.4350	+	13.4350i	0.500000	+	0.500000i
$723$	−2.44949	−	0.656339i	−0.0910975	−	0.0244095i
$724$	−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	−0.910902	−	0.412624i	$-0.864612\pi$
$727$	−13.4350	+	13.4350i	−0.498278	+	0.498278i	0.412624	+	0.910902i	$0.364612\pi$
$728$	9.19239	+	13.5737i	0.340693	+	0.503076i
$729$			2.21539i			0.0820515i
$730$		0			0
$731$	−4.31347	−	2.49038i	−0.159539	−	0.0921101i
$732$	5.13922	−	1.37705i	0.189951	−	0.0508972i
$733$	3.62347	−	13.5230i	0.133836	−	0.499482i	−0.866164	−	0.499760i	$-0.833422\pi$
$733$	3.62347	−	13.5230i	0.133836	−	0.499482i	1.00000		0.000277595i	$8.83611e-5\pi$
$734$	18.3923			0.678872
$735$		0			0
$736$	−5.19615			−0.191533
$737$	1.24831	−	4.65874i	0.0459820	−	0.171607i
$738$	−26.6484	+	7.14042i	−0.980941	+	0.262842i
$739$	−17.3205	−	10.0000i	−0.637145	−	0.367856i	0.146369	−	0.989230i	$-0.453241\pi$
$739$	−17.3205	−	10.0000i	−0.637145	−	0.367856i	−0.783514	+	0.621374i	$0.786575\pi$
$740$		0			0
$741$		0			0
$742$	12.1595	+	17.9551i	0.446390	+	0.659151i
$743$	−24.8874	+	24.8874i	−0.913032	+	0.913032i	−0.996510	−	0.0834781i	$-0.973397\pi$
$743$	−24.8874	+	24.8874i	−0.913032	+	0.913032i	0.0834781	+	0.996510i	$0.473397\pi$
$744$	−1.09808	+	0.633975i	−0.0402574	+	0.0232426i
$745$		0			0
$746$	−8.49038	+	14.7058i	−0.310855	+	0.538417i
$747$	−14.2808	−	3.82654i	−0.522508	−	0.140006i
$748$	−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	$0.915552\pi$
$752$	−1.01669	−	3.79435i	−0.0370750	−	0.138366i
$753$	−0.832204	−	3.10583i	−0.0303272	−	0.113183i
$754$	−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	$-0.231917\pi$
$757$	2.20925	+	2.20925i	0.0802967	+	0.0802967i	−0.665818	+	0.746114i	$0.731917\pi$
$758$	8.29581	+	2.22286i	0.301317	+	0.0807378i
$759$	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
$763$	−1.93185	−	26.9072i	−0.0699377	−	0.974107i
$764$		−	5.53590i		−	0.200282i
$765$		0			0
$766$	−20.5981	−	11.8923i	−0.744239	−	0.429686i
$767$	84.9643	−	22.7661i	3.06788	−	0.822037i
$768$	−0.189469	+	0.707107i	−0.00683686	+	0.0255155i
$769$	9.71281			0.350253			0.175126	−	0.984546i	$-0.443967\pi$
$769$	9.71281			0.350253			0.175126	+	0.984546i	$0.443967\pi$
$770$		0			0
$771$	−3.21539			−0.115799
$772$	3.13801	−	11.7112i	0.112940	−	0.421496i
$773$	−17.6269	+	4.72311i	−0.633996	+	0.169879i	−0.561482	−	0.827489i	$-0.689769\pi$
$773$	−17.6269	+	4.72311i	−0.633996	+	0.169879i	−0.0725134	+	0.997367i	$0.523102\pi$
$774$	22.9019	+	13.2224i	0.823193	+	0.475270i
$775$		0			0
$776$		−	11.3923i		−	0.408960i
$777$	11.1106	−	7.52433i	0.398592	−	0.269934i
$778$	−2.86559	+	2.86559i	−0.102736	+	0.102736i
$779$		0			0
$780$		0			0
$781$	8.49038	−	14.7058i	0.303810	−	0.526214i
$782$	−2.32937	−	0.624153i	−0.0832982	−	0.0223197i
$783$	−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
$787$	−6.41473	−	23.9401i	−0.228660	−	0.853372i	−0.980905	−	0.194488i	$-0.937695\pi$
$787$	−6.41473	−	23.9401i	−0.228660	−	0.853372i	0.752244	−	0.658884i	$-0.228971\pi$
$788$	−2.12132	−	7.91688i	−0.0755689	−	0.282027i
$789$	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
$793$	−43.4988	−	11.6555i	−1.54469	−	0.413898i
$794$	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	−0.870676	−	0.491856i	$-0.836318\pi$
$797$	−10.6945	+	10.6945i	−0.378820	+	0.378820i	0.491856	+	0.870676i	$0.336318\pi$
$798$		0			0
$799$		−	1.82309i		−	0.0644961i
$800$		0			0
$801$	23.8923	+	13.7942i	0.844193	+	0.487395i
$802$	−10.6945	+	2.86559i	−0.377637	+	0.101188i
$803$	−2.62536	+	9.79796i	−0.0926468	+	0.345762i
$804$	−2.78461			−0.0982056
$805$		0			0
$806$	10.7321			0.378020
$807$	2.38512	−	8.90138i	0.0839601	−	0.313344i
$808$	−15.8338	+	4.24264i	−0.557029	+	0.149256i
$809$	16.3923	+	9.46410i	0.576323	+	0.332740i	0.759671	−	0.650308i	$-0.225360\pi$
$809$	16.3923	+	9.46410i	0.576323	+	0.332740i	−0.183348	+	0.983048i	$0.558693\pi$
$810$		0			0
$811$			23.9090i			0.839557i	0.907627	+	0.419779i	$0.137892\pi$
$811$			23.9090i			0.839557i	−0.907627	+	0.419779i	$0.862108\pi$
$812$	9.14162	−	0.656339i	0.320808	−	0.0230330i
$813$	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	$-0.355957\pi$
$822$	−0.152304	−	0.568406i	−0.00531221	−	0.0198254i
$823$	0.896575	+	3.34607i	0.0312527	+	0.116637i	0.979790	−	0.200029i	$-0.0641035\pi$
$823$	0.896575	+	3.34607i	0.0312527	+	0.116637i	−0.948537	+	0.316665i	$0.897437\pi$
$824$	−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	$-0.307832\pi$
$827$	−7.34847	−	7.34847i	−0.255531	−	0.255531i	−0.823234	+	0.567702i	$0.807832\pi$
$828$	12.3676	+	3.31388i	0.429803	+	0.115165i
$829$	0.169873	−	0.294229i	0.00589993	−	0.0102190i	−0.863060	−	0.505101i	$-0.831455\pi$
$829$	0.169873	−	0.294229i	0.00589993	−	0.0102190i	0.868960	+	0.494882i	$0.164789\pi$
$830$		0			0
$831$	−4.17691	+	2.41154i	−0.144896	+	0.0836555i
$832$	4.38134	−	4.38134i	0.151896	−	0.151896i
$833$	−3.22595	−	0.383917i	−0.111772	−	0.0133019i
$834$			2.53590i			0.0878110i
$835$		0			0
$836$		0			0
$837$	6.69213	−	1.79315i	0.231314	−	0.0619804i
$838$	7.50077	−	27.9933i	0.259110	−	0.967011i
$839$	−4.01924			−0.138760			−0.0693798	−	0.997590i	$-0.522102\pi$
$839$	−4.01924			−0.138760			−0.0693798	+	0.997590i	$0.522102\pi$
$840$		0			0
$841$	17.0000			0.586207
$842$	4.03957	−	15.0759i	0.139213	−	0.519549i
$843$	17.2987	−	4.63518i	0.595800	−	0.159644i
$844$	8.83013	+	5.09808i	0.303946	+	0.175483i
$845$		0			0
$846$			9.67949i			0.332788i
$847$	−10.8518	+	22.3550i	−0.372873	+	0.768127i
$848$	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
$852$	−9.46979	−	2.53742i	−0.324430	−	0.0869307i
$853$	−1.83032	−	1.83032i	−0.0626688	−	0.0626688i	0.675078	−	0.737747i	$-0.264110\pi$
$853$	−1.83032	−	1.83032i	−0.0626688	−	0.0626688i	−0.737747	+	0.675078i	$0.764110\pi$
$854$	12.5885	−	14.5359i	0.430768	−	0.497408i
$855$		0			0
$856$	1.09808	+	1.90192i	0.0375315	+	0.0650064i
$857$	9.20599	+	34.3572i	0.314471	+	1.17362i	0.924481	+	0.381227i	$0.124498\pi$
$857$	9.20599	+	34.3572i	0.314471	+	1.17362i	−0.610011	+	0.792393i	$0.708835\pi$
$858$	1.48854	+	5.55532i	0.0508180	+	0.189655i
$859$	−0.509619	−	0.882686i	−0.0173880	−	0.0301169i	0.857200	−	0.514983i	$-0.172202\pi$
$859$	−0.509619	−	0.882686i	−0.0173880	−	0.0301169i	−0.874588	+	0.484866i	$0.838868\pi$
$860$		0			0
$861$	14.1962	−	16.3923i	0.483804	−	0.558648i
$862$	12.3998	+	12.3998i	0.422337	+	0.422337i
$863$	22.4058	+	6.00361i	0.762701	+	0.204365i	0.619145	−	0.785277i	$-0.287479\pi$
$863$	22.4058	+	6.00361i	0.762701	+	0.204365i	0.143556	+	0.989642i	$0.454146\pi$
$864$	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
$868$	−2.00120	+	4.12252i	−0.0679252	+	0.139928i
$869$		−	14.4449i		−	0.490008i
$870$		0			0
$871$	20.4115	+	11.7846i	0.691619	+	0.399306i
$872$	−9.84873	+	2.63896i	−0.333520	+	0.0893664i
$873$	−7.26552	+	27.1153i	−0.245900	+	0.917713i
$874$		0			0
$875$		0			0
$876$	5.85641			0.197870
$877$	−10.8468	+	40.4810i	−0.366272	+	1.36694i	0.499417	+	0.866362i	$0.333548\pi$
$877$	−10.8468	+	40.4810i	−0.366272	+	1.36694i	−0.865689	+	0.500583i	$0.833119\pi$
$878$	5.67544	−	1.52073i	0.191537	−	0.0513221i
$879$	−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	$0.980747\pi$
$882$	17.1278	+	2.03837i	0.576725	+	0.0686354i
$883$	−27.4249	+	27.4249i	−0.922920	+	0.922920i	−0.997235	−	0.0743148i	$-0.976323\pi$
$883$	−27.4249	+	27.4249i	−0.922920	+	0.922920i	0.0743148	+	0.997235i	$0.476323\pi$
$884$	2.49038	−	1.43782i	0.0837606	−	0.0483592i
$885$		0			0
$886$	−6.00000	+	10.3923i	−0.201574	+	0.349136i
$887$	−10.0382	−	2.68973i	−0.337050	−	0.0903122i	0.0863246	−	0.996267i	$-0.472488\pi$
$887$	−10.0382	−	2.68973i	−0.337050	−	0.0903122i	−0.423374	+	0.905955i	$0.639154\pi$
$888$	−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
$892$	−2.43091	−	9.07227i	−0.0813928	−	0.303762i
$893$		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
$898$	−8.03699	−	2.15351i	−0.268198	−	0.0718634i
$899$	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
$903$	−20.7327	+	1.48854i	−0.689942	+	0.0495356i
$904$			6.80385i			0.226293i
$905$		0			0
$906$	−11.6603	−	6.73205i	−0.387386	−	0.223657i
$907$	−47.8294	+	12.8159i	−1.58815	+	0.425543i	−0.941437	−	0.337190i	$-0.890524\pi$
$907$	−47.8294	+	12.8159i	−1.58815	+	0.425543i	−0.646713	+	0.762733i	$0.723857\pi$
$908$	7.10823	−	26.5283i	0.235895	−	0.880372i
$909$	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
$913$	7.34847	−	1.96902i	0.243199	−	0.0651649i
$914$	−28.1769	−	16.2679i	−0.932009	−	0.538096i
$915$		0			0
$916$			14.1962i			0.469054i
$917$	5.22715	+	2.53742i	0.172616	+	0.0837931i
$918$	1.31268	−	1.31268i	0.0433248	−	0.0433248i
$919$	6.06218	−	3.50000i	0.199973	−	0.115454i	−0.396670	−	0.917961i	$-0.629834\pi$
$919$	6.06218	−	3.50000i	0.199973	−	0.115454i	0.596643	+	0.802507i	$0.296501\pi$
$920$		0			0
$921$	4.53590	−	7.85641i	0.149463	−	0.258877i
$922$	−23.1822	−	6.21166i	−0.763466	−	0.204570i
$923$	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
$927$	8.29083	+	30.9418i	0.272307	+	1.01626i
$928$	−0.896575	−	3.34607i	−0.0294315	−	0.109840i
$929$	1.60770	+	2.78461i	0.0527468	+	0.0913601i	0.891193	−	0.453624i	$-0.149869\pi$
$929$	1.60770	+	2.78461i	0.0527468	+	0.0913601i	−0.838446	+	0.544984i	$0.816536\pi$
$930$		0			0
$931$		0			0
$932$	4.24264	+	4.24264i	0.138972	+	0.138972i
$933$	−0.568406	−	0.152304i	−0.0186088	−	0.00498621i
$934$	−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	0.317163	−	0.948371i	$-0.397270\pi$
$937$	38.7386	−	38.7386i	1.26553	−	1.26553i	0.948371	−	0.317163i	$-0.102730\pi$
$938$	−8.33298	+	5.64325i	−0.272081	+	0.184259i
$939$			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	$0.755933\pi$
$942$	1.41421	−	0.378937i	0.0460776	−	0.0123464i
$943$	15.0573	−	56.1946i	0.490333	−	1.82995i
$944$	14.1962			0.462045
$945$		0			0
$946$	−13.6077			−0.442424
$947$	−5.37945	+	20.0764i	−0.174809	+	0.652395i	0.821775	+	0.569812i	$0.192984\pi$
$947$	−5.37945	+	20.0764i	−0.174809	+	0.652395i	−0.996584	+	0.0825835i	$0.973683\pi$
$948$	−8.05558	+	2.15849i	−0.261633	+	0.0701043i
$949$	−42.9282	−	24.7846i	−1.39351	−	0.804542i
$950$		0			0
$951$		−	12.0000i		−	0.389127i
$952$	0.0879327	+	1.22474i	0.00284992	+	0.0396942i
$953$	6.21166	−	6.21166i	0.201215	−	0.201215i	−0.599305	−	0.800521i	$-0.704556\pi$
$953$	6.21166	−	6.21166i	0.201215	−	0.201215i	0.800521	+	0.599305i	$0.204556\pi$
$954$	−17.4904	+	10.0981i	−0.566272	+	0.326937i
$955$		0			0
$956$	−11.4282	+	19.7942i	−0.369615	+	0.640191i
$957$	3.10583	+	0.832204i	0.100397	+	0.0269013i
$958$	−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
$962$	11.1106	+	41.4655i	0.358221	+	1.33690i
$963$	−1.40061	−	5.22715i	−0.0451340	−	0.168443i
$964$	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	$-0.367921\pi$
$967$	−15.9217	−	15.9217i	−0.512007	−	0.512007i	−0.915141	+	0.403134i	$0.867921\pi$
$968$	9.07227	+	2.43091i	0.291594	+	0.0781323i
$969$		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
$973$	5.13922	+	7.58871i	0.164756	+	0.243283i
$974$		−	9.33975i		−	0.299265i
$975$		0			0
$976$	−6.29423	−	3.63397i	−0.201473	−	0.116321i
$977$	−38.2395	+	10.2462i	−1.22339	+	0.327806i	−0.812003	−	0.583654i	$-0.801622\pi$
$977$	−38.2395	+	10.2462i	−1.22339	+	0.327806i	−0.411388	+	0.911460i	$0.634956\pi$
$978$	−2.75410	+	10.2784i	−0.0880663	+	0.328668i
$979$	−14.1962			−0.453711
$980$		0			0
$981$	25.1244			0.802159
$982$	4.15471	−	15.5056i	0.132582	−	0.494803i
$983$	52.6405	−	14.1050i	1.67897	−	0.449879i	0.711463	−	0.702723i	$-0.248033\pi$
$983$	52.6405	−	14.1050i	1.67897	−	0.449879i	0.967507	+	0.252845i	$0.0813661\pi$
$984$	−7.09808	−	4.09808i	−0.226278	−	0.130642i
$985$		0			0
$986$		−	1.60770i		−	0.0511994i
$987$	−4.26620	−	6.29959i	−0.135795	−	0.200518i
$988$		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	$0.264247\pi$
$992$	1.67303	+	0.448288i	0.0531188	+	0.0142331i
$993$	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
$997$	−5.48099	−	20.4553i	−0.173585	−	0.647827i	−0.996788	−	0.0800807i	$-0.974482\pi$
$997$	−5.48099	−	20.4553i	−0.173585	−	0.647827i	0.823204	−	0.567746i	$-0.192184\pi$
$998$	−4.55721	−	17.0077i	−0.144256	−	0.538370i
$999$	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.a.157.1	✓	8
5.2	odd	4		350.2.o.b.143.1	yes	8
5.3	odd	4		350.2.o.b.143.2	yes	8
5.4	even	2	inner	350.2.o.a.157.2	yes	8
7.5	odd	6		350.2.o.b.257.2	yes	8
35.12	even	12	inner	350.2.o.a.243.2	yes	8
35.19	odd	6		350.2.o.b.257.1	yes	8
35.33	even	12	inner	350.2.o.a.243.1	yes	8

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

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)

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

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