LMFDB - Embedded newform 403.2.i.a.216.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(216,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1, 2]))

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

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

chi := DirichletCharacter("403.216");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.i (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$34$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			216.3
Character	$\chi$	$=$	403.216
Dual form			403.2.i.a.278.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.78306 - 1.78306i) q^{2} -0.329930i q^{3} +4.35859i q^{4} +(-1.02687 - 1.02687i) q^{5} +(-0.588285 + 0.588285i) q^{6} +(-0.568114 + 0.568114i) q^{7} +(4.20550 - 4.20550i) q^{8} +2.89115 q^{9} +O(q^{10})$	\(q+(-1.78306 - 1.78306i) q^{2} -0.329930i q^{3} +4.35859i q^{4} +(-1.02687 - 1.02687i) q^{5} +(-0.588285 + 0.588285i) q^{6} +(-0.568114 + 0.568114i) q^{7} +(4.20550 - 4.20550i) q^{8} +2.89115 q^{9} +3.66195i q^{10} +(3.35577 + 3.35577i) q^{11} +1.43803 q^{12} +(-3.54120 + 0.678174i) q^{13} +2.02596 q^{14} +(-0.338796 + 0.338796i) q^{15} -6.28011 q^{16} +3.41386 q^{17} +(-5.15508 - 5.15508i) q^{18} +(-0.418609 - 0.418609i) q^{19} +(4.47571 - 4.47571i) q^{20} +(0.187438 + 0.187438i) q^{21} -11.9671i q^{22} +8.46997 q^{23} +(-1.38752 - 1.38752i) q^{24} -2.89106i q^{25} +(7.52338 + 5.10493i) q^{26} -1.94367i q^{27} +(-2.47617 - 2.47617i) q^{28} +3.26311i q^{29} +1.20819 q^{30} +(-1.25057 - 5.42550i) q^{31} +(2.78680 + 2.78680i) q^{32} +(1.10717 - 1.10717i) q^{33} +(-6.08710 - 6.08710i) q^{34} +1.16676 q^{35} +12.6013i q^{36} +(0.776727 + 0.776727i) q^{37} +1.49281i q^{38} +(0.223750 + 1.16835i) q^{39} -8.63702 q^{40} +(-2.20106 - 2.20106i) q^{41} -0.668425i q^{42} +4.38144 q^{43} +(-14.6264 + 14.6264i) q^{44} +(-2.96884 - 2.96884i) q^{45} +(-15.1024 - 15.1024i) q^{46} +(0.166587 - 0.166587i) q^{47} +2.07200i q^{48} +6.35449i q^{49} +(-5.15493 + 5.15493i) q^{50} -1.12634i q^{51} +(-2.95588 - 15.4346i) q^{52} -10.9998i q^{53} +(-3.46567 + 3.46567i) q^{54} -6.89189i q^{55} +4.77840i q^{56} +(-0.138112 + 0.138112i) q^{57} +(5.81831 - 5.81831i) q^{58} +(8.34811 - 8.34811i) q^{59} +(-1.47667 - 1.47667i) q^{60} +6.12008i q^{61} +(-7.44415 + 11.9038i) q^{62} +(-1.64250 + 1.64250i) q^{63} +2.62217i q^{64} +(4.33276 + 2.93996i) q^{65} -3.94830 q^{66} +(-7.92334 - 7.92334i) q^{67} +14.8796i q^{68} -2.79450i q^{69} +(-2.08040 - 2.08040i) q^{70} +(4.69072 + 4.69072i) q^{71} +(12.1587 - 12.1587i) q^{72} +(8.08162 + 8.08162i) q^{73} -2.76990i q^{74} -0.953850 q^{75} +(1.82454 - 1.82454i) q^{76} -3.81292 q^{77} +(1.68427 - 2.48219i) q^{78} +15.8278i q^{79} +(6.44887 + 6.44887i) q^{80} +8.03216 q^{81} +7.84924i q^{82} +(2.95351 - 2.95351i) q^{83} +(-0.816965 + 0.816965i) q^{84} +(-3.50560 - 3.50560i) q^{85} +(-7.81236 - 7.81236i) q^{86} +1.07660 q^{87} +28.2253 q^{88} +(4.68071 + 4.68071i) q^{89} +10.5872i q^{90} +(1.62652 - 2.39708i) q^{91} +36.9171i q^{92} +(-1.79004 + 0.412600i) q^{93} -0.594067 q^{94} +0.859715i q^{95} +(0.919449 - 0.919449i) q^{96} +(-0.339413 - 0.339413i) q^{97} +(11.3304 - 11.3304i) q^{98} +(9.70202 + 9.70202i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - 4 q^{2} - 4 q^{5} + 8 q^{7} + 16 q^{8} - 60 q^{9}+O(q^{10}) $ 68 * q - 4 * q^2 - 4 * q^5 + 8 * q^7 + 16 * q^8 - 60 * q^9	$ 68 q - 4 q^{2} - 4 q^{5} + 8 q^{7} + 16 q^{8} - 60 q^{9} - 48 q^{14} - 40 q^{16} + 4 q^{18} - 24 q^{19} - 16 q^{20} + 44 q^{28} + 24 q^{31} + 28 q^{32} - 40 q^{35} - 24 q^{39} + 24 q^{40} + 20 q^{41} - 24 q^{45} - 36 q^{47} + 80 q^{50} + 28 q^{59} - 76 q^{63} + 152 q^{66} - 32 q^{67} - 48 q^{70} + 20 q^{71} - 32 q^{72} + 72 q^{76} + 84 q^{78} - 20 q^{80} + 52 q^{81} - 112 q^{87} - 8 q^{93} - 16 q^{94} - 4 q^{97} - 92 q^{98}+O(q^{100}) $ 68 * q - 4 * q^2 - 4 * q^5 + 8 * q^7 + 16 * q^8 - 60 * q^9 - 48 * q^14 - 40 * q^16 + 4 * q^18 - 24 * q^19 - 16 * q^20 + 44 * q^28 + 24 * q^31 + 28 * q^32 - 40 * q^35 - 24 * q^39 + 24 * q^40 + 20 * q^41 - 24 * q^45 - 36 * q^47 + 80 * q^50 + 28 * q^59 - 76 * q^63 + 152 * q^66 - 32 * q^67 - 48 * q^70 + 20 * q^71 - 32 * q^72 + 72 * q^76 + 84 * q^78 - 20 * q^80 + 52 * q^81 - 112 * q^87 - 8 * q^93 - 16 * q^94 - 4 * q^97 - 92 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.78306	−	1.78306i	−1.26081	−	1.26081i	−0.950700	−	0.310112i	$-0.899633\pi$
$2$	−1.78306	−	1.78306i	−1.26081	−	1.26081i	−0.310112	−	0.950700i	$-0.600367\pi$
$3$		−	0.329930i		−	0.190485i	−0.995454	−	0.0952427i	$-0.969637\pi$
$3$		−	0.329930i		−	0.190485i	0.995454	−	0.0952427i	$-0.0303627\pi$
$4$			4.35859i			2.17929i
$5$	−1.02687	−	1.02687i	−0.459231	−	0.459231i	0.439172	−	0.898403i	$-0.355272\pi$
$5$	−1.02687	−	1.02687i	−0.459231	−	0.459231i	−0.898403	+	0.439172i	$0.855272\pi$
$6$	−0.588285	+	0.588285i	−0.240166	+	0.240166i
$7$	−0.568114	+	0.568114i	−0.214727	+	0.214727i	−0.806272	−	0.591545i	$-0.798518\pi$
$7$	−0.568114	+	0.568114i	−0.214727	+	0.214727i	0.591545	+	0.806272i	$0.298518\pi$
$8$	4.20550	−	4.20550i	1.48687	−	1.48687i
$9$	2.89115			0.963715
$10$			3.66195i			1.15801i
$11$	3.35577	+	3.35577i	1.01180	+	1.01180i	0.999930	+	0.0118728i	$0.00377933\pi$
$11$	3.35577	+	3.35577i	1.01180	+	1.01180i	0.0118728	+	0.999930i	$0.496221\pi$
$12$	1.43803			0.415124
$13$	−3.54120	+	0.678174i	−0.982151	+	0.188092i
$13$	−3.54120	+	0.678174i	−0.982151	+	0.188092i
$14$	2.02596			0.541460
$15$	−0.338796	+	0.338796i	−0.0874769	+	0.0874769i
$16$	−6.28011			−1.57003
$17$	3.41386			0.827982			0.413991	−	0.910281i	$-0.364134\pi$
$17$	3.41386			0.827982			0.413991	+	0.910281i	$0.364134\pi$
$18$	−5.15508	−	5.15508i	−1.21506	−	1.21506i
$19$	−0.418609	−	0.418609i	−0.0960354	−	0.0960354i	0.657457	−	0.753492i	$-0.271632\pi$
$19$	−0.418609	−	0.418609i	−0.0960354	−	0.0960354i	−0.753492	+	0.657457i	$0.771632\pi$
$20$	4.47571	−	4.47571i	1.00080	−	1.00080i
$21$	0.187438	+	0.187438i	0.0409023	+	0.0409023i
$22$		−	11.9671i		−	2.55138i
$23$	8.46997			1.76611			0.883055	−	0.469269i	$-0.155482\pi$
$23$	8.46997			1.76611			0.883055	+	0.469269i	$0.155482\pi$
$24$	−1.38752	−	1.38752i	−0.283226	−	0.283226i
$25$		−	2.89106i		−	0.578213i
$26$	7.52338	+	5.10493i	1.47546	+	1.00116i
$27$		−	1.94367i		−	0.374059i
$28$	−2.47617	−	2.47617i	−0.467953	−	0.467953i
$29$			3.26311i			0.605944i	0.952999	+	0.302972i	$0.0979789\pi$
$29$			3.26311i			0.605944i	−0.952999	+	0.302972i	$0.902021\pi$
$30$	1.20819			0.220584
$31$	−1.25057	−	5.42550i	−0.224609	−	0.974449i
$31$	−1.25057	−	5.42550i	−0.224609	−	0.974449i
$32$	2.78680	+	2.78680i	0.492641	+	0.492641i
$33$	1.10717	−	1.10717i	0.192734	−	0.192734i
$34$	−6.08710	−	6.08710i	−1.04393	−	1.04393i
$35$	1.16676			0.197219
$36$			12.6013i			2.10022i
$37$	0.776727	+	0.776727i	0.127693	+	0.127693i	0.768065	−	0.640372i	$-0.221220\pi$
$37$	0.776727	+	0.776727i	0.127693	+	0.127693i	−0.640372	+	0.768065i	$0.721220\pi$
$38$			1.49281i			0.242165i
$39$	0.223750	+	1.16835i	0.0358287	+	0.187086i
$40$	−8.63702			−1.36563
$41$	−2.20106	−	2.20106i	−0.343748	−	0.343748i	0.514026	−	0.857774i	$-0.328153\pi$
$41$	−2.20106	−	2.20106i	−0.343748	−	0.343748i	−0.857774	+	0.514026i	$0.828153\pi$
$42$		−	0.668425i		−	0.103140i
$43$	4.38144			0.668163			0.334082	−	0.942544i	$-0.391574\pi$
$43$	4.38144			0.668163			0.334082	+	0.942544i	$0.391574\pi$
$44$	−14.6264	+	14.6264i	−2.20501	+	2.20501i
$45$	−2.96884	−	2.96884i	−0.442568	−	0.442568i
$46$	−15.1024	−	15.1024i	−2.22673	−	2.22673i
$47$	0.166587	−	0.166587i	0.0242992	−	0.0242992i	−0.694853	−	0.719152i	$-0.744530\pi$
$47$	0.166587	−	0.166587i	0.0242992	−	0.0242992i	0.719152	+	0.694853i	$0.244530\pi$
$48$			2.07200i			0.299067i
$49$			6.35449i			0.907785i
$50$	−5.15493	+	5.15493i	−0.729018	+	0.729018i
$51$		−	1.12634i		−	0.157718i
$52$	−2.95588	−	15.4346i	−0.409907	−	2.14040i
$53$		−	10.9998i		−	1.51094i	−0.655185	−	0.755468i	$-0.727409\pi$
$53$		−	10.9998i		−	1.51094i	0.655185	−	0.755468i	$-0.272591\pi$
$54$	−3.46567	+	3.46567i	−0.471618	+	0.471618i
$55$		−	6.89189i		−	0.929303i
$56$			4.77840i			0.638540i
$57$	−0.138112	+	0.138112i	−0.0182933	+	0.0182933i
$58$	5.81831	−	5.81831i	0.763982	−	0.763982i
$59$	8.34811	−	8.34811i	1.08683	−	1.08683i	0.0909784	−	0.995853i	$-0.471001\pi$
$59$	8.34811	−	8.34811i	1.08683	−	1.08683i	0.995853	−	0.0909784i	$-0.0289994\pi$
$60$	−1.47667	−	1.47667i	−0.190638	−	0.190638i
$61$			6.12008i			0.783596i	0.920051	+	0.391798i	$0.128147\pi$
$61$			6.12008i			0.783596i	−0.920051	+	0.391798i	$0.871853\pi$
$62$	−7.44415	+	11.9038i	−0.945408	+	1.51179i
$63$	−1.64250	+	1.64250i	−0.206935	+	0.206935i
$64$			2.62217i			0.327772i
$65$	4.33276	+	2.93996i	0.537412	+	0.364657i
$66$	−3.94830			−0.486002
$67$	−7.92334	−	7.92334i	−0.967990	−	0.967990i	0.0315137	−	0.999503i	$-0.489967\pi$
$67$	−7.92334	−	7.92334i	−0.967990	−	0.967990i	−0.999503	+	0.0315137i	$0.989967\pi$
$68$			14.8796i			1.80442i
$69$		−	2.79450i		−	0.336418i
$70$	−2.08040	−	2.08040i	−0.248656	−	0.248656i
$71$	4.69072	+	4.69072i	0.556686	+	0.556686i	0.928362	−	0.371677i	$-0.121217\pi$
$71$	4.69072	+	4.69072i	0.556686	+	0.556686i	−0.371677	+	0.928362i	$0.621217\pi$
$72$	12.1587	−	12.1587i	1.43292	−	1.43292i
$73$	8.08162	+	8.08162i	0.945882	+	0.945882i	0.998609	−	0.0527266i	$-0.0167912\pi$
$73$	8.08162	+	8.08162i	0.945882	+	0.945882i	−0.0527266	+	0.998609i	$0.516791\pi$
$74$		−	2.76990i		−	0.321994i
$75$	−0.953850			−0.110141
$76$	1.82454	−	1.82454i	0.209289	−	0.209289i
$77$	−3.81292			−0.434522
$78$	1.68427	−	2.48219i	0.190706	−	0.281053i
$79$			15.8278i			1.78077i	0.455209	+	0.890385i	$0.349564\pi$
$79$			15.8278i			1.78077i	−0.455209	+	0.890385i	$0.650436\pi$
$80$	6.44887	+	6.44887i	0.721005	+	0.721005i
$81$	8.03216			0.892463
$82$			7.84924i			0.866804i
$83$	2.95351	−	2.95351i	0.324190	−	0.324190i	−0.526182	−	0.850372i	$-0.676377\pi$
$83$	2.95351	−	2.95351i	0.324190	−	0.324190i	0.850372	+	0.526182i	$0.176377\pi$
$84$	−0.816965	+	0.816965i	−0.0891381	+	0.0891381i
$85$	−3.50560	−	3.50560i	−0.380235	−	0.380235i
$86$	−7.81236	−	7.81236i	−0.842428	−	0.842428i
$87$	1.07660			0.115424
$88$	28.2253			3.00883
$89$	4.68071	+	4.68071i	0.496155	+	0.496155i	0.910239	−	0.414084i	$-0.135898\pi$
$89$	4.68071	+	4.68071i	0.496155	+	0.496155i	−0.414084	+	0.910239i	$0.635898\pi$
$90$			10.5872i			1.11599i
$91$	1.62652	−	2.39708i	0.170506	−	0.251283i
$92$			36.9171i			3.84887i
$93$	−1.79004	+	0.412600i	−0.185618	+	0.0427846i
$94$	−0.594067			−0.0612733
$95$			0.859715i			0.0882049i
$96$	0.919449	−	0.919449i	0.0938409	−	0.0938409i
$97$	−0.339413	−	0.339413i	−0.0344622	−	0.0344622i	0.689666	−	0.724128i	$-0.257757\pi$
$97$	−0.339413	−	0.339413i	−0.0344622	−	0.0344622i	−0.724128	+	0.689666i	$0.757757\pi$
$98$	11.3304	−	11.3304i	1.14455	−	1.14455i
$99$	9.70202	+	9.70202i	0.975089	+	0.975089i
$100$	12.6010			1.26010
$101$		−	3.94617i		−	0.392659i	−0.980538	−	0.196329i	$-0.937098\pi$
$101$		−	3.94617i		−	0.392659i	0.980538	−	0.196329i	$-0.0629022\pi$
$102$	−2.00832	+	2.00832i	−0.198853	+	0.198853i
$103$		−	12.6243i		−	1.24391i	−0.783054	−	0.621953i	$-0.786339\pi$
$103$		−	12.6243i		−	1.24391i	0.783054	−	0.621953i	$-0.213661\pi$
$104$	−12.0404	+	17.7445i	−1.18066	+	1.74000i
$105$		−	0.384950i		−	0.0375673i
$106$	−19.6132	+	19.6132i	−1.90501	+	1.90501i
$107$	3.48413			0.336824			0.168412	−	0.985717i	$-0.446136\pi$
$107$	3.48413			0.336824			0.168412	+	0.985717i	$0.446136\pi$
$108$	8.47165			0.815184
$109$	10.0435	+	10.0435i	0.961991	+	0.961991i	0.999304	−	0.0373131i	$-0.0118799\pi$
$109$	10.0435	+	10.0435i	0.961991	+	0.961991i	−0.0373131	+	0.999304i	$0.511880\pi$
$110$	−12.2886	+	12.2886i	−1.17168	+	1.17168i
$111$	0.256266	−	0.256266i	0.0243237	−	0.0243237i
$112$	3.56781	−	3.56781i	0.337127	−	0.337127i
$113$	9.80884			0.922738			0.461369	−	0.887208i	$-0.347358\pi$
$113$	9.80884			0.922738			0.461369	+	0.887208i	$0.347358\pi$
$114$	0.492522			0.0461289
$115$	−8.69758	−	8.69758i	−0.811054	−	0.811054i
$116$	−14.2225			−1.32053
$117$	−10.2381	+	1.96070i	−0.946514	+	0.181267i
$118$	−29.7703			−2.74058
$119$	−1.93946	+	1.93946i	−0.177790	+	0.177790i
$120$			2.84961i			0.260133i
$121$			11.5224i			1.04749i
$122$	10.9124	−	10.9124i	0.987967	−	0.987967i
$123$	−0.726197	+	0.726197i	−0.0654790	+	0.0654790i
$124$	23.6475	−	5.45071i	2.12361	−	0.489488i
$125$	−8.10312	+	8.10312i	−0.724765	+	0.724765i
$126$	5.85734			0.521813
$127$	3.46790			0.307726			0.153863	−	0.988092i	$-0.450829\pi$
$127$	3.46790			0.307726			0.153863	+	0.988092i	$0.450829\pi$
$128$	10.2491	−	10.2491i	0.905899	−	0.905899i
$129$		−	1.44557i		−	0.127275i
$130$	−2.48344	−	12.9677i	−0.217812	−	1.13734i
$131$	0.824427			0.0720305			0.0360152	−	0.999351i	$-0.488534\pi$
$131$	0.824427			0.0720305			0.0360152	+	0.999351i	$0.488534\pi$
$132$	4.82570	+	4.82570i	0.420023	+	0.420023i
$133$	0.475634			0.0412427
$134$			28.2555i			2.44091i
$135$	−1.99590	+	1.99590i	−0.171780	+	0.171780i
$136$	14.3570	−	14.3570i	1.23110	−	1.23110i
$137$	−1.00122	−	1.00122i	−0.0855398	−	0.0855398i	0.663042	−	0.748582i	$-0.269265\pi$
$137$	−1.00122	−	1.00122i	−0.0855398	−	0.0855398i	−0.748582	+	0.663042i	$0.769265\pi$
$138$	−4.98275	+	4.98275i	−0.424160	+	0.424160i
$139$		−	4.72191i		−	0.400507i	−0.979744	−	0.200253i	$-0.935823\pi$
$139$		−	4.72191i		−	0.400507i	0.979744	−	0.200253i	$-0.0641765\pi$
$140$			5.08543i			0.429797i
$141$	−0.0549620	−	0.0549620i	−0.00462864	−	0.00462864i
$142$		−	16.7276i		−	1.40375i
$143$	−14.1592	−	9.60764i	−1.18405	−	0.803432i
$144$	−18.1567			−1.51306
$145$	3.35080	−	3.35080i	0.278269	−	0.278269i
$146$		−	28.8200i		−	2.38516i
$147$	2.09654			0.172920
$148$	−3.38543	+	3.38543i	−0.278281	+	0.278281i
$149$	4.04960	+	4.04960i	0.331756	+	0.331756i	0.853253	−	0.521497i	$-0.174626\pi$
$149$	4.04960	+	4.04960i	0.331756	+	0.331756i	−0.521497	+	0.853253i	$0.674626\pi$
$150$	1.70077	+	1.70077i	0.138867	+	0.138867i
$151$	−2.53125	−	2.53125i	−0.205990	−	0.205990i	0.596570	−	0.802561i	$-0.296530\pi$
$151$	−2.53125	−	2.53125i	−0.205990	−	0.205990i	−0.802561	+	0.596570i	$0.796530\pi$
$152$	−3.52091			−0.285584
$153$	9.86996			0.797939
$154$	6.79865	+	6.79865i	0.547851	+	0.547851i
$155$	−4.28713	+	6.85547i	−0.344350	+	0.550645i
$156$	−5.09235	+	0.975235i	−0.407714	+	0.0780813i
$157$	−16.0893			−1.28406			−0.642031	−	0.766679i	$-0.721908\pi$
$157$	−16.0893			−1.28406			−0.642031	+	0.766679i	$0.721908\pi$
$158$	28.2219	−	28.2219i	2.24521	−	2.24521i
$159$	−3.62916			−0.287811
$160$		−	5.72337i		−	0.452472i
$161$	−4.81191	+	4.81191i	−0.379231	+	0.379231i
$162$	−14.3218	−	14.3218i	−1.12523	−	1.12523i
$163$	−11.8799	+	11.8799i	−0.930503	+	0.930503i	−0.997737	−	0.0672340i	$-0.978583\pi$
$163$	−11.8799	+	11.8799i	−0.930503	+	0.930503i	0.0672340	+	0.997737i	$0.478583\pi$
$164$	9.59352	−	9.59352i	0.749128	−	0.749128i
$165$	−2.27385			−0.177019
$166$	−10.5326			−0.817485
$167$	−14.2121	−	14.2121i	−1.09977	−	1.09977i	−0.994437	−	0.105329i	$-0.966410\pi$
$167$	−14.2121	−	14.2121i	−1.09977	−	1.09977i	−0.105329	−	0.994437i	$-0.533590\pi$
$168$	1.57654			0.121633
$169$	12.0802	−	4.80310i	0.929243	−	0.369469i
$170$			12.5014i			0.958811i
$171$	−1.21026	−	1.21026i	−0.0925508	−	0.0925508i
$172$			19.0969i			1.45612i
$173$			10.9894i			0.835509i	0.908560	+	0.417755i	$0.137183\pi$
$173$			10.9894i			0.835509i	−0.908560	+	0.417755i	$0.862817\pi$
$174$	−1.91964	−	1.91964i	−0.145527	−	0.145527i
$175$	1.64245	+	1.64245i	0.124158	+	0.124158i
$176$	−21.0746	−	21.0746i	−1.58856	−	1.58856i
$177$	−2.75429	−	2.75429i	−0.207025	−	0.207025i
$178$		−	16.6920i		−	1.25112i
$179$	−20.9105			−1.56292			−0.781462	−	0.623953i	$-0.785526\pi$
$179$	−20.9105			−1.56292			−0.781462	+	0.623953i	$0.785526\pi$
$180$	12.9399	−	12.9399i	0.964486	−	0.964486i
$181$	−19.3768			−1.44027			−0.720134	−	0.693835i	$-0.755920\pi$
$181$	−19.3768			−1.44027			−0.720134	+	0.693835i	$0.755920\pi$
$182$	−7.17432	+	1.37395i	−0.531796	+	0.101844i
$183$	2.01920			0.149263
$184$	35.6204	−	35.6204i	2.62597	−	2.62597i
$185$		−	1.59520i		−	0.117281i
$186$	3.92743	+	2.45605i	0.287973	+	0.180086i
$187$	11.4561	+	11.4561i	0.837754	+	0.837754i
$188$	0.726082	+	0.726082i	0.0529550	+	0.0529550i
$189$	1.10422	+	1.10422i	0.0803205	+	0.0803205i
$190$	1.53292	−	1.53292i	0.111210	−	0.111210i
$191$	−14.9377			−1.08085			−0.540425	−	0.841392i	$-0.681737\pi$
$191$	−14.9377			−1.08085			−0.540425	+	0.841392i	$0.681737\pi$
$192$	0.865135			0.0624357
$193$	−1.64983	+	1.64983i	−0.118758	+	0.118758i	−0.763988	−	0.645230i	$-0.776761\pi$
$193$	−1.64983	+	1.64983i	−0.118758	+	0.118758i	0.645230	+	0.763988i	$0.276761\pi$
$194$			1.21039i			0.0869007i
$195$	0.969982	−	1.42951i	0.0694619	−	0.102369i
$196$	−27.6966			−1.97833
$197$	−16.8611	+	16.8611i	−1.20131	+	1.20131i	−0.227537	+	0.973770i	$0.573067\pi$
$197$	−16.8611	+	16.8611i	−1.20131	+	1.20131i	−0.973770	+	0.227537i	$0.926933\pi$
$198$		−	34.5985i		−	2.45881i
$199$	−7.41002			−0.525282			−0.262641	−	0.964894i	$-0.584594\pi$
$199$	−7.41002			−0.525282			−0.262641	+	0.964894i	$0.584594\pi$
$200$	−12.1584	−	12.1584i	−0.859726	−	0.859726i
$201$	−2.61415	+	2.61415i	−0.184388	+	0.184388i
$202$	−7.03625	+	7.03625i	−0.495069	+	0.495069i
$203$	−1.85382	−	1.85382i	−0.130112	−	0.130112i
$204$	4.90923			0.343715
$205$			4.52042i			0.315720i
$206$	−22.5098	+	22.5098i	−1.56833	+	1.56833i
$207$	24.4879			1.70203
$208$	22.2391	−	4.25901i	1.54200	−	0.295309i
$209$		−	2.80951i		−	0.194338i
$210$	−0.686388	+	0.686388i	−0.0473652	+	0.0473652i
$211$	18.1458			1.24921			0.624605	−	0.780941i	$-0.285260\pi$
$211$	18.1458			1.24921			0.624605	+	0.780941i	$0.285260\pi$
$212$	47.9435			3.29277
$213$	1.54761	−	1.54761i	0.106041	−	0.106041i
$214$	−6.21240	−	6.21240i	−0.424671	−	0.424671i
$215$	−4.49918	−	4.49918i	−0.306842	−	0.306842i
$216$	−8.17409	−	8.17409i	−0.556176	−	0.556176i
$217$	3.79277	+	2.37184i	0.257470	+	0.161011i
$218$		−	35.8162i		−	2.42578i
$219$	2.66637	−	2.66637i	0.180177	−	0.180177i
$220$	30.0389			2.02522
$221$	−12.0891	+	2.31519i	−0.813204	+	0.155737i
$222$	−0.913873			−0.0613352
$223$	−3.62099	+	3.62099i	−0.242480	+	0.242480i	−0.817875	−	0.575396i	$-0.804848\pi$
$223$	−3.62099	+	3.62099i	−0.242480	+	0.242480i	0.575396	+	0.817875i	$0.304848\pi$
$224$	−3.16643			−0.211566
$225$		−	8.35849i		−	0.557233i
$226$	−17.4897	−	17.4897i	−1.16340	−	1.16340i
$227$	3.14369	+	3.14369i	0.208654	+	0.208654i	0.803695	−	0.595041i	$-0.202864\pi$
$227$	3.14369	+	3.14369i	0.208654	+	0.208654i	−0.595041	+	0.803695i	$0.702864\pi$
$228$	−0.601972	−	0.601972i	−0.0398665	−	0.0398665i
$229$	−11.6346	−	11.6346i	−0.768833	−	0.768833i	0.209068	−	0.977901i	$-0.432957\pi$
$229$	−11.6346	−	11.6346i	−0.768833	−	0.768833i	−0.977901	+	0.209068i	$0.932957\pi$
$230$			31.0166i			2.04517i
$231$			1.25800i			0.0827701i
$232$	13.7230	+	13.7230i	0.900959	+	0.900959i
$233$		−	23.2111i		−	1.52061i	−0.649565	−	0.760306i	$-0.725049\pi$
$233$		−	23.2111i		−	1.52061i	0.649565	−	0.760306i	$-0.274951\pi$
$234$	21.7512	+	14.7591i	1.42192	+	0.964833i
$235$	−0.342127			−0.0223179
$236$	36.3860	+	36.3860i	2.36852	+	2.36852i
$237$	5.22208			0.339210
$238$	6.91633			0.448319
$239$	11.0274	−	11.0274i	0.713306	−	0.713306i	−0.253919	−	0.967225i	$-0.581720\pi$
$239$	11.0274	−	11.0274i	0.713306	−	0.713306i	0.967225	+	0.253919i	$0.0817198\pi$
$240$	2.12768	−	2.12768i	0.137341	−	0.137341i
$241$	14.6378	+	14.6378i	0.942902	+	0.942902i	0.998456	−	0.0555536i	$-0.0176924\pi$
$241$	14.6378	+	14.6378i	0.942902	+	0.942902i	−0.0555536	+	0.998456i	$0.517692\pi$
$242$	20.5450	−	20.5450i	1.32069	−	1.32069i
$243$		−	8.48106i		−	0.544060i
$244$	−26.6749			−1.70768
$245$	6.52526	−	6.52526i	0.416883	−	0.416883i
$246$	2.58970			0.165113
$247$	1.76627	+	1.19849i	0.112385	+	0.0762578i
$248$	−28.0762	−	17.5577i	−1.78284	−	1.11491i
$249$	−0.974453	−	0.974453i	−0.0617535	−	0.0617535i
$250$	28.8967			1.82758
$251$	15.2822			0.964605			0.482302	−	0.876005i	$-0.339801\pi$
$251$	15.2822			0.964605			0.482302	+	0.876005i	$0.339801\pi$
$252$	−7.15898	−	7.15898i	−0.450973	−	0.450973i
$253$	28.4233	+	28.4233i	1.78696	+	1.78696i
$254$	−6.18346	−	6.18346i	−0.387985	−	0.387985i
$255$	−1.15660	+	1.15660i	−0.0724293	+	0.0724293i
$256$	−31.3050			−1.95657
$257$			2.33040i			0.145366i	0.997355	+	0.0726831i	$0.0231562\pi$
$257$			2.33040i			0.145366i	−0.997355	+	0.0726831i	$0.976844\pi$
$258$	−2.57753	+	2.57753i	−0.160470	+	0.160470i
$259$	−0.882538			−0.0548383
$260$	−12.8141	+	18.8847i	−0.794695	+	1.17118i
$261$			9.43413i			0.583958i
$262$	−1.47000	−	1.47000i	−0.0908169	−	0.0908169i
$263$			13.3461i			0.822957i	0.911420	+	0.411478i	$0.134987\pi$
$263$			13.3461i			0.822957i	−0.911420	+	0.411478i	$0.865013\pi$
$264$		−	9.31240i		−	0.573138i
$265$	−11.2954	+	11.2954i	−0.693869	+	0.693869i
$266$	−0.848084	−	0.848084i	−0.0519993	−	0.0519993i
$267$	1.54431	−	1.54431i	0.0945102	−	0.0945102i
$268$	34.5346	−	34.5346i	2.10953	−	2.10953i
$269$			1.92391i			0.117303i	0.998279	+	0.0586513i	$0.0186800\pi$
$269$			1.92391i			0.117303i	−0.998279	+	0.0586513i	$0.981320\pi$
$270$	7.11761			0.433164
$271$	−14.3132	−	14.3132i	−0.869466	−	0.869466i	0.122948	−	0.992413i	$-0.460765\pi$
$271$	−14.3132	−	14.3132i	−0.869466	−	0.869466i	−0.992413	+	0.122948i	$0.960765\pi$
$272$	−21.4394			−1.29995
$273$	−0.790870	−	0.536639i	−0.0478657	−	0.0324789i
$274$			3.57046i			0.215699i
$275$	9.70175	−	9.70175i	0.585037	−	0.585037i
$276$	12.1801			0.733154
$277$	−8.05317			−0.483868			−0.241934	−	0.970293i	$-0.577782\pi$
$277$	−8.05317			−0.483868			−0.241934	+	0.970293i	$0.577782\pi$
$278$	−8.41943	+	8.41943i	−0.504964	+	0.504964i
$279$	−3.61557	−	15.6859i	−0.216459	−	0.939092i
$280$	4.90681	−	4.90681i	0.293238	−	0.293238i
$281$	−4.32633	+	4.32633i	−0.258087	+	0.258087i	−0.824276	−	0.566188i	$-0.808417\pi$
$281$	−4.32633	+	4.32633i	−0.258087	+	0.258087i	0.566188	+	0.824276i	$0.308417\pi$
$282$			0.196001i			0.0116717i
$283$		−	5.88114i		−	0.349597i	−0.984604	−	0.174799i	$-0.944073\pi$
$283$		−	5.88114i		−	0.349597i	0.984604	−	0.174799i	$-0.0559275\pi$
$284$	−20.4449	+	20.4449i	−1.21318	+	1.21318i
$285$	0.283646			0.0168018
$286$	8.11575	+	42.3777i	0.479894	+	2.50585i
$287$	2.50091			0.147624
$288$	8.05704	+	8.05704i	0.474765	+	0.474765i
$289$	−5.34557			−0.314446
$290$	−11.9493			−0.701689
$291$	−0.111983	+	0.111983i	−0.00656455	+	0.00656455i
$292$	−35.2245	+	35.2245i	−2.06136	+	2.06136i
$293$	−15.4682	+	15.4682i	−0.903661	+	0.903661i	−0.995751	−	0.0920893i	$-0.970645\pi$
$293$	−15.4682	+	15.4682i	−0.903661	+	0.903661i	0.0920893	+	0.995751i	$0.470645\pi$
$294$	−3.73825	−	3.73825i	−0.218019	−	0.218019i
$295$	−17.1449			−0.998214
$296$	6.53304			0.379725
$297$	6.52250	−	6.52250i	0.378474	−	0.378474i
$298$		−	14.4413i		−	0.836563i
$299$	−29.9938	+	5.74412i	−1.73459	+	0.332191i
$300$		−	4.15744i		−	0.240030i
$301$	−2.48916	+	2.48916i	−0.143473	+	0.143473i
$302$			9.02674i			0.519430i
$303$	−1.30196			−0.0747958
$304$	2.62891	+	2.62891i	0.150778	+	0.150778i
$305$	6.28454	−	6.28454i	0.359852	−	0.359852i
$306$	−17.5987	−	17.5987i	−1.00605	−	1.00605i
$307$	−5.74909	+	5.74909i	−0.328118	+	0.328118i	−0.851870	−	0.523753i	$-0.824532\pi$
$307$	−5.74909	+	5.74909i	−0.328118	+	0.328118i	0.523753	+	0.851870i	$0.324532\pi$
$308$		−	16.6189i		−	0.946951i
$309$	−4.16513			−0.236946
$310$	19.8679	−	4.57951i	1.12842	−	0.260099i
$311$		−	3.87750i		−	0.219873i	−0.993939	−	0.109936i	$-0.964935\pi$
$311$		−	3.87750i		−	0.219873i	0.993939	−	0.109936i	$-0.0350647\pi$
$312$	5.85447	+	3.97250i	0.331444	+	0.224899i
$313$			23.6688i			1.33784i	0.743335	+	0.668919i	$0.233243\pi$
$313$			23.6688i			1.33784i	−0.743335	+	0.668919i	$0.766757\pi$
$314$	28.6881	+	28.6881i	1.61896	+	1.61896i
$315$	3.37328			0.190063
$316$	−68.9869			−3.88082
$317$	2.10083	+	2.10083i	0.117995	+	0.117995i	0.763639	−	0.645644i	$-0.223411\pi$
$317$	2.10083	+	2.10083i	0.117995	+	0.117995i	−0.645644	+	0.763639i	$0.723411\pi$
$318$	6.47100	+	6.47100i	0.362876	+	0.362876i
$319$	−10.9502	+	10.9502i	−0.613096	+	0.613096i
$320$	2.69264	−	2.69264i	0.150523	−	0.150523i
$321$		−	1.14952i		−	0.0641600i
$322$	17.1598			0.956279
$323$	−1.42907	−	1.42907i	−0.0795156	−	0.0795156i
$324$			35.0089i			1.94494i
$325$	1.96065	+	10.2378i	0.108757	+	0.567893i
$326$	42.3650			2.34638
$327$	3.31365	−	3.31365i	0.183245	−	0.183245i
$328$	−18.5131			−1.02222
$329$			0.189280i			0.0104354i
$330$	4.05440	+	4.05440i	0.223187	+	0.223187i
$331$	15.1441	−	15.1441i	0.832394	−	0.832394i	−0.155450	−	0.987844i	$-0.549683\pi$
$331$	15.1441	−	15.1441i	0.832394	−	0.832394i	0.987844	+	0.155450i	$0.0496826\pi$
$332$	12.8731	+	12.8731i	0.706505	+	0.706505i
$333$	2.24563	+	2.24563i	0.123060	+	0.123060i
$334$			50.6820i			2.77320i
$335$			16.2725i			0.889063i
$336$	−1.17713	−	1.17713i	−0.0642177	−	0.0642177i
$337$	−17.2163			−0.937830			−0.468915	−	0.883243i	$-0.655355\pi$
$337$	−17.2163			−0.937830			−0.468915	+	0.883243i	$0.655355\pi$
$338$	−30.1038	−	12.9754i	−1.63743	−	0.705770i
$339$		−	3.23623i		−	0.175768i
$340$	15.2795	−	15.2795i	0.828645	−	0.828645i
$341$	14.0101	−	22.4033i	0.758690	−	1.21321i
$342$			4.31592i			0.233378i
$343$	−7.58687	−	7.58687i	−0.409653	−	0.409653i
$344$	18.4261	−	18.4261i	0.993470	−	0.993470i
$345$	−2.86960	+	2.86960i	−0.154494	+	0.154494i
$346$	19.5947	−	19.5947i	1.05342	−	1.05342i
$347$		−	0.795098i		−	0.0426831i	−0.999772	−	0.0213415i	$-0.993206\pi$
$347$		−	0.795098i		−	0.0426831i	0.999772	−	0.0213415i	$-0.00679374\pi$
$348$			4.69245i			0.251542i
$349$	21.2049	−	21.2049i	1.13507	−	1.13507i	0.145753	−	0.989321i	$-0.453440\pi$
$349$	21.2049	−	21.2049i	1.13507	−	1.13507i	0.989321	−	0.145753i	$-0.0465604\pi$
$350$		−	5.85718i		−	0.313079i
$351$	1.31815	+	6.88291i	0.0703574	+	0.367383i
$352$			18.7037i			0.996910i
$353$	−8.26574	+	8.26574i	−0.439941	+	0.439941i	−0.891992	−	0.452051i	$-0.850692\pi$
$353$	−8.26574	+	8.26574i	−0.439941	+	0.439941i	0.452051	+	0.891992i	$0.350692\pi$
$354$			9.82213i			0.522040i
$355$		−	9.63354i		−	0.511295i
$356$	−20.4013	+	20.4013i	−1.08127	+	1.08127i
$357$	0.639887	+	0.639887i	0.0338664	+	0.0338664i
$358$	37.2846	+	37.2846i	1.97055	+	1.97055i
$359$	6.24733	−	6.24733i	0.329721	−	0.329721i	−0.522759	−	0.852480i	$-0.675097\pi$
$359$	6.24733	−	6.24733i	0.329721	−	0.329721i	0.852480	+	0.522759i	$0.175097\pi$
$360$	−24.9709			−1.31608
$361$		−	18.6495i		−	0.981554i
$362$	34.5500	+	34.5500i	1.81591	+	1.81591i
$363$	3.80158			0.199531
$364$	10.4479	+	7.08934i	0.547618	+	0.371582i
$365$		−	16.5976i		−	0.868758i
$366$	−3.60035	−	3.60035i	−0.188193	−	0.188193i
$367$		−	29.0417i		−	1.51597i	−0.652275	−	0.757983i	$-0.726185\pi$
$367$		−	29.0417i		−	1.51597i	0.652275	−	0.757983i	$-0.273815\pi$
$368$	−53.1923			−2.77284
$369$	−6.36359	−	6.36359i	−0.331275	−	0.331275i
$370$	−2.84433	+	2.84433i	−0.147870	+	0.147870i
$371$	6.24913	+	6.24913i	0.324439	+	0.324439i
$372$	−1.79835	−	7.80204i	−0.0932403	−	0.404517i
$373$	18.0553			0.934866			0.467433	−	0.884029i	$-0.345179\pi$
$373$	18.0553			0.934866			0.467433	+	0.884029i	$0.345179\pi$
$374$		−	40.8538i		−	2.11250i
$375$	2.67347	+	2.67347i	0.138057	+	0.138057i
$376$		−	1.40116i		−	0.0722592i
$377$	−2.21296	−	11.5553i	−0.113973	−	0.595129i
$378$		−	3.93779i		−	0.202538i
$379$	−19.5453	−	19.5453i	−1.00397	−	1.00397i	−0.999992	−	0.00398018i	$-0.998733\pi$
$379$	−19.5453	−	19.5453i	−1.00397	−	1.00397i	−0.00398018	−	0.999992i	$-0.501267\pi$
$380$	−3.74714			−0.192224
$381$		−	1.14416i		−	0.0586173i
$382$	26.6347	+	26.6347i	1.36275	+	1.36275i
$383$	9.20504	−	9.20504i	0.470355	−	0.470355i	−0.431674	−	0.902030i	$-0.642077\pi$
$383$	9.20504	−	9.20504i	0.470355	−	0.470355i	0.902030	+	0.431674i	$0.142077\pi$
$384$	−3.38148	−	3.38148i	−0.172561	−	0.172561i
$385$	3.91538	+	3.91538i	0.199546	+	0.199546i
$386$	5.88350			0.299462
$387$	12.6674			0.643919
$388$	1.47936	−	1.47936i	0.0751033	−	0.0751033i
$389$	−17.9135			−0.908251			−0.454126	−	0.890938i	$-0.650048\pi$
$389$	−17.9135			−0.908251			−0.454126	+	0.890938i	$0.650048\pi$
$390$	−4.27843	+	0.819362i	−0.216647	+	0.0414900i
$391$	28.9153			1.46231
$392$	26.7238	+	26.7238i	1.34976	+	1.34976i
$393$		−	0.272003i		−	0.0137208i
$394$	60.1287			3.02924
$395$	16.2532	−	16.2532i	0.817785	−	0.817785i
$396$	−42.2871	+	42.2871i	−2.12501	+	2.12501i
$397$	−21.0886	+	21.0886i	−1.05841	+	1.05841i	−0.0602202	+	0.998185i	$0.519180\pi$
$397$	−21.0886	+	21.0886i	−1.05841	+	1.05841i	−0.998185	+	0.0602202i	$0.980820\pi$
$398$	13.2125	+	13.2125i	0.662282	+	0.662282i
$399$		−	0.156926i		−	0.00785614i
$400$			18.1562i			0.907810i
$401$	7.62597	+	7.62597i	0.380823	+	0.380823i	0.871398	−	0.490576i	$-0.163214\pi$
$401$	7.62597	+	7.62597i	0.380823	+	0.380823i	−0.490576	+	0.871398i	$0.663214\pi$
$402$	9.32236			0.464957
$403$	8.10794	+	18.3647i	0.403885	+	0.914810i
$404$	17.1997			0.855719
$405$	−8.24801	−	8.24801i	−0.409847	−	0.409847i
$406$			6.61092i			0.328095i
$407$			5.21303i			0.258400i
$408$	−4.73680	−	4.73680i	−0.234506	−	0.234506i
$409$	5.34884	−	5.34884i	0.264483	−	0.264483i	−0.562389	−	0.826873i	$-0.690118\pi$
$409$	5.34884	−	5.34884i	0.264483	−	0.264483i	0.826873	+	0.562389i	$0.190118\pi$
$410$	8.06017	−	8.06017i	0.398064	−	0.398064i
$411$	−0.330332	+	0.330332i	−0.0162941	+	0.0162941i
$412$	55.0240			2.71084
$413$			9.48535i			0.466744i
$414$	−43.6634	−	43.6634i	−2.14594	−	2.14594i
$415$	−6.06576			−0.297757
$416$	−11.7585	−	7.97866i	−0.576509	−	0.391186i
$417$	−1.55790			−0.0762907
$418$	−5.00951	+	5.00951i	−0.245023	+	0.245023i
$419$	−26.0801			−1.27410			−0.637049	−	0.770824i	$-0.719845\pi$
$419$	−26.0801			−1.27410			−0.637049	+	0.770824i	$0.719845\pi$
$420$	1.67784			0.0818701
$421$	−6.95007	−	6.95007i	−0.338726	−	0.338726i	0.517162	−	0.855888i	$-0.326988\pi$
$421$	−6.95007	−	6.95007i	−0.338726	−	0.338726i	−0.855888	+	0.517162i	$0.826988\pi$
$422$	−32.3551	−	32.3551i	−1.57502	−	1.57502i
$423$	0.481626	−	0.481626i	0.0234175	−	0.0234175i
$424$	−46.2595	−	46.2595i	−2.24656	−	2.24656i
$425$		−	9.86968i		−	0.478750i
$426$	−5.51896			−0.267394
$427$	−3.47690	−	3.47690i	−0.168259	−	0.168259i
$428$			15.1859i			0.734037i
$429$	−3.16985	+	4.67156i	−0.153042	+	0.225545i
$430$			16.0446i			0.773739i
$431$	1.83827	+	1.83827i	0.0885465	+	0.0885465i	0.749993	−	0.661446i	$-0.230057\pi$
$431$	1.83827	+	1.83827i	0.0885465	+	0.0885465i	−0.661446	+	0.749993i	$0.730057\pi$
$432$			12.2064i			0.587283i
$433$	−7.27338			−0.349536			−0.174768	−	0.984610i	$-0.555918\pi$
$433$	−7.27338			−0.349536			−0.174768	+	0.984610i	$0.555918\pi$
$434$	−2.53360	−	10.9918i	−0.121617	−	0.527625i
$435$	−1.10553	−	1.10553i	−0.0530061	−	0.0530061i
$436$	−43.7754	+	43.7754i	−2.09646	+	2.09646i
$437$	−3.54560	−	3.54560i	−0.169609	−	0.169609i
$438$	−9.50859			−0.454338
$439$		−	8.72905i		−	0.416615i	−0.978063	−	0.208307i	$-0.933205\pi$
$439$		−	8.72905i		−	0.416615i	0.978063	−	0.208307i	$-0.0667954\pi$
$440$	−28.9838	−	28.9838i	−1.38175	−	1.38175i
$441$			18.3718i			0.874846i
$442$	25.6838	+	17.4275i	1.22165	+	0.828943i
$443$	−3.18056			−0.151113			−0.0755565	−	0.997142i	$-0.524073\pi$
$443$	−3.18056			−0.151113			−0.0755565	+	0.997142i	$0.524073\pi$
$444$	1.11696	+	1.11696i	0.0530084	+	0.0530084i
$445$		−	9.61300i		−	0.455700i
$446$	12.9129			0.611442
$447$	1.33608	−	1.33608i	0.0631946	−	0.0631946i
$448$	−1.48969	−	1.48969i	−0.0703814	−	0.0703814i
$449$	17.6552	+	17.6552i	0.833199	+	0.833199i	0.987953	−	0.154754i	$-0.0494584\pi$
$449$	17.6552	+	17.6552i	0.833199	+	0.833199i	−0.154754	+	0.987953i	$0.549458\pi$
$450$	−14.9037	+	14.9037i	−0.702566	+	0.702566i
$451$		−	14.7725i		−	0.695611i
$452$			42.7527i			2.01092i
$453$	−0.835137	+	0.835137i	−0.0392382	+	0.0392382i
$454$		−	11.2108i		−	0.526147i
$455$	−4.13173	+	0.791267i	−0.193699	+	0.0370952i
$456$			1.16166i			0.0543995i
$457$	−15.9121	+	15.9121i	−0.744338	+	0.744338i	−0.973410	−	0.229072i	$-0.926431\pi$
$457$	−15.9121	+	15.9121i	−0.744338	+	0.744338i	0.229072	+	0.973410i	$0.426431\pi$
$458$			41.4902i			1.93871i
$459$		−	6.63541i		−	0.309714i
$460$	37.9092	−	37.9092i	1.76752	−	1.76752i
$461$	−13.0195	+	13.0195i	−0.606378	+	0.606378i	−0.941998	−	0.335620i	$-0.891054\pi$
$461$	−13.0195	+	13.0195i	−0.606378	+	0.606378i	0.335620	+	0.941998i	$0.391054\pi$
$462$	2.24308	−	2.24308i	0.104358	−	0.104358i
$463$	15.7235	+	15.7235i	0.730731	+	0.730731i	0.970765	−	0.240033i	$-0.0771584\pi$
$463$	15.7235	+	15.7235i	0.730731	+	0.730731i	−0.240033	+	0.970765i	$0.577158\pi$
$464$		−	20.4927i		−	0.951348i
$465$	2.26183	+	1.41445i	0.104890	+	0.0655937i
$466$	−41.3868	+	41.3868i	−1.91721	+	1.91721i
$467$			3.98385i			0.184351i	0.995743	+	0.0921753i	$0.0293820\pi$
$467$			3.98385i			0.184351i	−0.995743	+	0.0921753i	$0.970618\pi$
$468$	−8.54589	−	44.6237i	−0.395034	−	2.06273i
$469$	9.00271			0.415707
$470$	0.610031	+	0.610031i	0.0281386	+	0.0281386i
$471$			5.30833i			0.244595i
$472$		−	70.2159i		−	3.23195i
$473$	14.7031	+	14.7031i	0.676049	+	0.676049i
$474$	−9.31127	−	9.31127i	−0.427681	−	0.427681i
$475$	−1.21022	+	1.21022i	−0.0555289	+	0.0555289i
$476$	−8.45330	−	8.45330i	−0.387456	−	0.387456i
$477$		−	31.8020i		−	1.45611i
$478$	−39.3251			−1.79869
$479$	26.2220	−	26.2220i	1.19811	−	1.19811i	0.223383	−	0.974731i	$-0.428290\pi$
$479$	26.2220	−	26.2220i	1.19811	−	1.19811i	0.974731	−	0.223383i	$-0.0717101\pi$
$480$	−1.88831			−0.0861893
$481$	−3.27730	−	2.22379i	−0.149432	−	0.101396i
$482$		−	52.2000i		−	2.37764i
$483$	1.58759	+	1.58759i	0.0722380	+	0.0722380i
$484$	−50.2212			−2.28278
$485$			0.697069i			0.0316523i
$486$	−15.1222	+	15.1222i	−0.685958	+	0.685958i
$487$	6.25097	−	6.25097i	0.283259	−	0.283259i	−0.551149	−	0.834407i	$-0.685810\pi$
$487$	6.25097	−	6.25097i	0.283259	−	0.283259i	0.834407	+	0.551149i	$0.185810\pi$
$488$	25.7380	+	25.7380i	1.16510	+	1.16510i
$489$	3.91953	+	3.91953i	0.177247	+	0.177247i
$490$	−23.2698			−1.05122
$491$	−20.3362			−0.917759			−0.458879	−	0.888499i	$-0.651749\pi$
$491$	−20.3362			−0.917759			−0.458879	+	0.888499i	$0.651749\pi$
$492$	−3.16519	−	3.16519i	−0.142698	−	0.142698i
$493$			11.1398i			0.501711i
$494$	−1.01238	−	5.28632i	−0.0455493	−	0.237843i
$495$		−	19.9255i		−	0.895583i
$496$	7.85370	+	34.0727i	0.352641	+	1.52991i
$497$	−5.32972			−0.239071
$498$			3.47501i			0.155719i
$499$	11.8747	−	11.8747i	0.531584	−	0.531584i	−0.389459	−	0.921044i	$-0.627338\pi$
$499$	11.8747	−	11.8747i	0.531584	−	0.531584i	0.921044	+	0.389459i	$0.127338\pi$
$500$	−35.3181	−	35.3181i	−1.57948	−	1.57948i
$501$	−4.68901	+	4.68901i	−0.209490	+	0.209490i
$502$	−27.2491	−	27.2491i	−1.21619	−	1.21619i
$503$	32.7292			1.45932			0.729662	−	0.683809i	$-0.239678\pi$
$503$	32.7292			1.45932			0.729662	+	0.683809i	$0.239678\pi$
$504$			13.8150i			0.615371i
$505$	−4.05222	+	4.05222i	−0.180321	+	0.180321i
$506$		−	101.361i		−	4.50603i
$507$	−1.58469	−	3.98561i	−0.0703785	−	0.177007i
$508$			15.1151i			0.670625i
$509$	20.9009	−	20.9009i	0.926418	−	0.926418i	−0.0710542	−	0.997472i	$-0.522636\pi$
$509$	20.9009	−	20.9009i	0.926418	−	0.926418i	0.997472	+	0.0710542i	$0.0226363\pi$
$510$	4.12458			0.182639
$511$	−9.18256			−0.406213
$512$	35.3205	+	35.3205i	1.56096	+	1.56096i
$513$	−0.813636	+	0.813636i	−0.0359229	+	0.0359229i
$514$	4.15523	−	4.15523i	0.183280	−	0.183280i
$515$	−12.9635	+	12.9635i	−0.571241	+	0.571241i
$516$	6.30064			0.277370
$517$	1.11805			0.0491719
$518$	1.57362	+	1.57362i	0.0691407	+	0.0691407i
$519$	3.62574			0.159152
$520$	30.5854	−	5.85740i	1.34126	−	0.256864i
$521$	−32.8969			−1.44124			−0.720620	−	0.693330i	$-0.756143\pi$
$521$	−32.8969			−1.44124			−0.720620	+	0.693330i	$0.756143\pi$
$522$	16.8216	−	16.8216i	0.736261	−	0.736261i
$523$			41.6590i			1.82162i	0.412825	+	0.910811i	$0.364542\pi$
$523$			41.6590i			1.82162i	−0.412825	+	0.910811i	$0.635458\pi$
$524$			3.59334i			0.156976i
$525$	0.541895	−	0.541895i	0.0236503	−	0.0236503i
$526$	23.7969	−	23.7969i	1.03759	−	1.03759i
$527$	−4.26926	−	18.5219i	−0.185972	−	0.806826i
$528$	−6.95314	+	6.95314i	−0.302597	+	0.302597i
$529$	48.7404			2.11915
$530$	40.2806			1.74968
$531$	24.1356	−	24.1356i	1.04740	−	1.04740i
$532$			2.07309i			0.0898800i
$533$	9.28710	+	6.30169i	0.402269	+	0.272957i
$534$	−5.50719			−0.238319
$535$	−3.57776	−	3.57776i	−0.154680	−	0.154680i
$536$	−66.6431			−2.87854
$537$			6.89901i			0.297714i
$538$	3.43043	−	3.43043i	0.147897	−	0.147897i
$539$	−21.3242	+	21.3242i	−0.918499	+	0.918499i
$540$	−8.69930	−	8.69930i	−0.374358	−	0.374358i
$541$	−23.8032	+	23.8032i	−1.02338	+	1.02338i	−0.0236594	+	0.999720i	$0.507532\pi$
$541$	−23.8032	+	23.8032i	−1.02338	+	1.02338i	−0.999720	+	0.0236594i	$0.992468\pi$
$542$			51.0425i			2.19247i
$543$			6.39301i			0.274350i
$544$	9.51373	+	9.51373i	0.407898	+	0.407898i
$545$		−	20.6267i		−	0.883553i
$546$	0.453309	+	2.36703i	0.0193998	+	0.101299i
$547$	−30.4226			−1.30078			−0.650388	−	0.759603i	$-0.725393\pi$
$547$	−30.4226			−1.30078			−0.650388	+	0.759603i	$0.725393\pi$
$548$	4.36389	−	4.36389i	0.186416	−	0.186416i
$549$			17.6940i			0.755163i
$550$	−34.5975			−1.47524
$551$	1.36597	−	1.36597i	0.0581921	−	0.0581921i
$552$	−11.7523	−	11.7523i	−0.500209	−	0.500209i
$553$	−8.99200	−	8.99200i	−0.382379	−	0.382379i
$554$	14.3593	+	14.3593i	0.610067	+	0.610067i
$555$	−0.526305			−0.0223404
$556$	20.5808			0.872822
$557$	14.4961	+	14.4961i	0.614218	+	0.614218i	0.944042	−	0.329824i	$-0.106989\pi$
$557$	14.4961	+	14.4961i	0.614218	+	0.614218i	−0.329824	+	0.944042i	$0.606989\pi$
$558$	−21.5221	+	34.4157i	−0.911104	+	1.45693i
$559$	−15.5155	+	2.97138i	−0.656238	+	0.125676i
$560$	−7.32738			−0.309638
$561$	3.77972	−	3.77972i	0.159580	−	0.159580i
$562$	15.4282			0.650799
$563$		−	7.27534i		−	0.306619i	−0.988178	−	0.153309i	$-0.951007\pi$
$563$		−	7.27534i		−	0.306619i	0.988178	−	0.153309i	$-0.0489931\pi$
$564$	0.239557	−	0.239557i	0.0100872	−	0.0100872i
$565$	−10.0724	−	10.0724i	−0.423750	−	0.423750i
$566$	−10.4864	+	10.4864i	−0.440777	+	0.440777i
$567$	−4.56318	+	4.56318i	−0.191636	+	0.191636i
$568$	39.4536			1.65544
$569$	−7.83658			−0.328527			−0.164263	−	0.986417i	$-0.552525\pi$
$569$	−7.83658			−0.328527			−0.164263	+	0.986417i	$0.552525\pi$
$570$	−0.505757	−	0.505757i	−0.0211838	−	0.0211838i
$571$	−31.2920			−1.30953			−0.654765	−	0.755833i	$-0.727232\pi$
$571$	−31.2920			−1.30953			−0.654765	+	0.755833i	$0.727232\pi$
$572$	41.8757	−	61.7143i	1.75091	−	2.58040i
$573$			4.92839i			0.205886i
$574$	−4.45926	−	4.45926i	−0.186126	−	0.186126i
$575$		−	24.4872i		−	1.02119i
$576$			7.58109i			0.315879i
$577$	19.8689	+	19.8689i	0.827153	+	0.827153i	0.987122	−	0.159969i	$-0.0511393\pi$
$577$	19.8689	+	19.8689i	0.827153	+	0.827153i	−0.159969	+	0.987122i	$0.551139\pi$
$578$	9.53147	+	9.53147i	0.396457	+	0.396457i
$579$	0.544331	+	0.544331i	0.0226216	+	0.0226216i
$580$	14.6047	+	14.6047i	0.606429	+	0.606429i
$581$			3.35586i			0.139225i
$582$	0.399344			0.0165533
$583$	36.9127	−	36.9127i	1.52877	−	1.52877i
$584$	67.9745			2.81280
$585$	12.5266	+	8.49985i	0.517913	+	0.351426i
$586$	55.1613			2.27869
$587$	−6.43905	+	6.43905i	−0.265768	+	0.265768i	−0.827392	−	0.561624i	$-0.810177\pi$
$587$	−6.43905	+	6.43905i	−0.265768	+	0.265768i	0.561624	+	0.827392i	$0.310177\pi$
$588$			9.13795i			0.376843i
$589$	−1.74766	+	2.79466i	−0.0720112	+	0.115152i
$590$	30.5703	+	30.5703i	1.25856	+	1.25856i
$591$	5.56300	+	5.56300i	0.228831	+	0.228831i
$592$	−4.87793	−	4.87793i	−0.200482	−	0.200482i
$593$	−15.2656	+	15.2656i	−0.626883	+	0.626883i	−0.947283	−	0.320399i	$-0.896183\pi$
$593$	−15.2656	+	15.2656i	−0.626883	+	0.626883i	0.320399	+	0.947283i	$0.396183\pi$
$594$	−23.2600			−0.954369
$595$	3.98316			0.163293
$596$	−17.6505	+	17.6505i	−0.722993	+	0.722993i
$597$			2.44479i			0.100059i
$598$	63.7228	+	43.2386i	2.60582	+	1.76816i
$599$	24.9284			1.01855			0.509273	−	0.860605i	$-0.329915\pi$
$599$	24.9284			1.01855			0.509273	+	0.860605i	$0.329915\pi$
$600$	−4.01141	+	4.01141i	−0.163765	+	0.163765i
$601$			26.9778i			1.10045i	0.835017	+	0.550224i	$0.185458\pi$
$601$			26.9778i			1.10045i	−0.835017	+	0.550224i	$0.814542\pi$
$602$	8.87661			0.361784
$603$	−22.9075	−	22.9075i	−0.932866	−	0.932866i
$604$	11.0327	−	11.0327i	0.448914	−	0.448914i
$605$	11.8320	−	11.8320i	0.481039	−	0.481039i
$606$	2.32147	+	2.32147i	0.0943034	+	0.0943034i
$607$	−9.98339			−0.405213			−0.202607	−	0.979260i	$-0.564941\pi$
$607$	−9.98339			−0.405213			−0.202607	+	0.979260i	$0.564941\pi$
$608$		−	2.33315i		−	0.0946219i
$609$	−0.611631	+	0.611631i	−0.0247845	+	0.0247845i
$610$	−22.4114			−0.907411
$611$	−0.476941	+	0.702891i	−0.0192950	+	0.0284359i
$612$			43.0191i			1.73894i
$613$	−25.3238	+	25.3238i	−1.02282	+	1.02282i	−0.0230862	+	0.999733i	$0.507349\pi$
$613$	−25.3238	+	25.3238i	−1.02282	+	1.02282i	−0.999733	+	0.0230862i	$0.992651\pi$
$614$	20.5019			0.827390
$615$	1.49142			0.0601400
$616$	−16.0352	+	16.0352i	−0.646077	+	0.646077i
$617$	−31.0304	−	31.0304i	−1.24924	−	1.24924i	−0.956058	−	0.293179i	$-0.905287\pi$
$617$	−31.0304	−	31.0304i	−1.24924	−	1.24924i	−0.293179	−	0.956058i	$-0.594713\pi$
$618$	7.42667	+	7.42667i	0.298744	+	0.298744i
$619$	32.2710	+	32.2710i	1.29708	+	1.29708i	0.930311	+	0.366771i	$0.119537\pi$
$619$	32.2710	+	32.2710i	1.29708	+	1.29708i	0.366771	+	0.930311i	$0.380463\pi$
$620$	−29.8802	−	18.6858i	−1.20002	−	0.750440i
$621$		−	16.4628i		−	0.660630i
$622$	−6.91380	+	6.91380i	−0.277218	+	0.277218i
$623$	−5.31836			−0.213075
$624$	−1.40518	−	7.33735i	−0.0562520	−	0.293729i
$625$	2.18642			0.0874568
$626$	42.2028	−	42.2028i	1.68676	−	1.68676i
$627$	−0.926942			−0.0370185
$628$		−	70.1264i		−	2.79835i
$629$	2.65164	+	2.65164i	0.105728	+	0.105728i
$630$	−6.01474	−	6.01474i	−0.239633	−	0.239633i
$631$	−18.1930	−	18.1930i	−0.724250	−	0.724250i	0.245218	−	0.969468i	$-0.421141\pi$
$631$	−18.1930	−	18.1930i	−0.724250	−	0.724250i	−0.969468	+	0.245218i	$0.921141\pi$
$632$	66.5638	+	66.5638i	2.64777	+	2.64777i
$633$		−	5.98686i		−	0.237956i
$634$		−	7.49181i		−	0.297538i
$635$	−3.56109	−	3.56109i	−0.141317	−	0.141317i
$636$		−	15.8180i		−	0.627225i
$637$	−4.30945	−	22.5025i	−0.170747	−	0.891582i
$638$	39.0498			1.54600
$639$	13.5615	+	13.5615i	0.536487	+	0.536487i
$640$	−21.0490			−0.832035
$641$	11.9322			0.471296			0.235648	−	0.971839i	$-0.424279\pi$
$641$	11.9322			0.471296			0.235648	+	0.971839i	$0.424279\pi$
$642$	−2.04966	+	2.04966i	−0.0808936	+	0.0808936i
$643$	−22.9296	+	22.9296i	−0.904256	+	0.904256i	−0.995801	−	0.0915447i	$-0.970820\pi$
$643$	−22.9296	+	22.9296i	−0.904256	+	0.904256i	0.0915447	+	0.995801i	$0.470820\pi$
$644$	−20.9731	−	20.9731i	−0.826456	−	0.826456i
$645$	−1.48442	+	1.48442i	−0.0584488	+	0.0584488i
$646$			5.09623i			0.200508i
$647$	41.7851			1.64274			0.821371	−	0.570394i	$-0.193210\pi$
$647$	41.7851			1.64274			0.821371	+	0.570394i	$0.193210\pi$
$648$	33.7792	−	33.7792i	1.32697	−	1.32697i
$649$	56.0287			2.19932
$650$	14.7587	−	21.7506i	0.578884	−	0.853128i
$651$	0.782541	−	1.25135i	0.0306702	−	0.0490442i
$652$	−51.7794	−	51.7794i	−2.02784	−	2.02784i
$653$	−1.90443			−0.0745260			−0.0372630	−	0.999305i	$-0.511864\pi$
$653$	−1.90443			−0.0745260			−0.0372630	+	0.999305i	$0.511864\pi$
$654$	−11.8168			−0.462075
$655$	−0.846581	−	0.846581i	−0.0330787	−	0.0330787i
$656$	13.8229	+	13.8229i	0.539694	+	0.539694i
$657$	23.3652	+	23.3652i	0.911561	+	0.911561i
$658$	0.337498	−	0.337498i	0.0131570	−	0.0131570i
$659$	−6.14743			−0.239470			−0.119735	−	0.992806i	$-0.538204\pi$
$659$	−6.14743			−0.239470			−0.119735	+	0.992806i	$0.538204\pi$
$660$		−	9.91075i		−	0.385776i
$661$	−19.6521	+	19.6521i	−0.764377	+	0.764377i	−0.977110	−	0.212733i	$-0.931763\pi$
$661$	−19.6521	+	19.6521i	−0.764377	+	0.764377i	0.212733	+	0.977110i	$0.431763\pi$
$662$	−54.0055			−2.09898
$663$	0.763852	+	3.98858i	0.0296655	+	0.154903i
$664$		−	24.8420i		−	0.964055i
$665$	−0.488416	−	0.488416i	−0.0189400	−	0.0189400i
$666$		−	8.00818i		−	0.310311i
$667$			27.6384i			1.07016i
$668$	61.9448	−	61.9448i	2.39671	−	2.39671i
$669$	1.19468	+	1.19468i	0.0461888	+	0.0461888i
$670$	29.0148	−	29.0148i	1.12094	−	1.12094i
$671$	−20.5376	+	20.5376i	−0.792844	+	0.792844i
$672$			1.04470i			0.0403003i
$673$	−30.7849			−1.18667			−0.593336	−	0.804955i	$-0.702189\pi$
$673$	−30.7849			−1.18667			−0.593336	+	0.804955i	$0.702189\pi$
$674$	30.6976	+	30.6976i	1.18243	+	1.18243i
$675$	−5.61927			−0.216286
$676$	20.9347	+	52.6524i	0.805182	+	2.02509i
$677$		−	46.6456i		−	1.79274i	−0.443309	−	0.896369i	$-0.646196\pi$
$677$		−	46.6456i		−	1.79274i	0.443309	−	0.896369i	$-0.353804\pi$
$678$	−5.77039	+	5.77039i	−0.221611	+	0.221611i
$679$	0.385651			0.0147999
$680$	−29.4855			−1.13072
$681$	1.03720	−	1.03720i	0.0397456	−	0.0397456i
$682$	−64.9273	+	14.9656i	−2.48619	+	0.573063i
$683$	32.3690	−	32.3690i	1.23857	−	1.23857i	0.277978	−	0.960588i	$-0.410336\pi$
$683$	32.3690	−	32.3690i	1.23857	−	1.23857i	0.960588	−	0.277978i	$-0.0896641\pi$
$684$	5.27502	−	5.27502i	0.201695	−	0.201695i
$685$			2.05625i			0.0785651i
$686$			27.0557i			1.03299i
$687$	−3.83859	+	3.83859i	−0.146451	+	0.146451i
$688$	−27.5159			−1.04903
$689$	7.45977	+	38.9524i	0.284195	+	1.48397i
$690$	10.2333			0.389575
$691$	−9.04222	−	9.04222i	−0.343982	−	0.343982i	0.513880	−	0.857862i	$-0.328208\pi$
$691$	−9.04222	−	9.04222i	−0.343982	−	0.343982i	−0.857862	+	0.513880i	$0.828208\pi$
$692$	−47.8983			−1.82082
$693$	−11.0237			−0.418756
$694$	−1.41770	+	1.41770i	−0.0538153	+	0.0538153i
$695$	−4.84880	+	4.84880i	−0.183925	+	0.183925i
$696$	4.52763	−	4.52763i	0.171619	−	0.171619i
$697$	−7.51412	−	7.51412i	−0.284617	−	0.284617i
$698$	−75.6192			−2.86223
$699$	−7.65806			−0.289655
$700$	−7.15878	+	7.15878i	−0.270576	+	0.270576i
$701$		−	30.2210i		−	1.14143i	−0.821147	−	0.570716i	$-0.806666\pi$
$701$		−	30.2210i		−	1.14143i	0.821147	−	0.570716i	$-0.193334\pi$
$702$	9.92230	−	14.6230i	0.374493	−	0.551908i
$703$		−	0.650289i		−	0.0245261i
$704$	−8.79941	+	8.79941i	−0.331640	+	0.331640i
$705$			0.112878i			0.00425123i
$706$	29.4766			1.10936
$707$	2.24188	+	2.24188i	0.0843144	+	0.0843144i
$708$	12.0048	−	12.0048i	0.451169	−	0.451169i
$709$	21.9874	+	21.9874i	0.825753	+	0.825753i	0.986926	−	0.161173i	$-0.0515278\pi$
$709$	21.9874	+	21.9874i	0.825753	+	0.825753i	−0.161173	+	0.986926i	$0.551528\pi$
$710$	−17.1772	+	17.1772i	−0.644647	+	0.644647i
$711$			45.7605i			1.71615i
$712$	39.3695			1.47543
$713$	−10.5923	−	45.9538i	−0.396684	−	1.72099i
$714$		−	2.28191i		−	0.0853983i
$715$	4.67391	+	24.4056i	0.174794	+	0.912716i
$716$		−	91.1402i		−	3.40607i
$717$	−3.63829	−	3.63829i	−0.135874	−	0.135874i
$718$	−22.2787			−0.831433
$719$	31.4687			1.17359			0.586793	−	0.809737i	$-0.300390\pi$
$719$	31.4687			1.17359			0.586793	+	0.809737i	$0.300390\pi$
$720$	18.6446	+	18.6446i	0.694844	+	0.694844i
$721$	7.17202	+	7.17202i	0.267100	+	0.267100i
$722$	−33.2532	+	33.2532i	−1.23756	+	1.23756i
$723$	4.82945	−	4.82945i	0.179609	−	0.179609i
$724$		−	84.4556i		−	3.13877i
$725$	9.43386			0.350365
$726$	−6.77843	−	6.77843i	−0.251571	−	0.251571i
$727$			38.8857i			1.44219i	0.692837	+	0.721095i	$0.256361\pi$
$727$			38.8857i			1.44219i	−0.692837	+	0.721095i	$0.743639\pi$
$728$	−3.24059	−	16.9213i	−0.120104	−	0.627143i
$729$	21.2983			0.788827
$730$	−29.5945	+	29.5945i	−1.09534	+	1.09534i
$731$	14.9576			0.553227
$732$			8.80085i			0.325289i
$733$	22.9337	+	22.9337i	0.847075	+	0.847075i	0.989767	−	0.142692i	$-0.0455758\pi$
$733$	22.9337	+	22.9337i	0.847075	+	0.847075i	−0.142692	+	0.989767i	$0.545576\pi$
$734$	−51.7831	+	51.7831i	−1.91135	+	1.91135i
$735$	−2.15288	−	2.15288i	−0.0794102	−	0.0794102i
$736$	23.6041	+	23.6041i	0.870058	+	0.870058i
$737$		−	53.1778i		−	1.95883i
$738$			22.6933i			0.835352i
$739$	−27.2900	−	27.2900i	−1.00388	−	1.00388i	−0.999992	−	0.00388811i	$-0.998762\pi$
$739$	−27.2900	−	27.2900i	−1.00388	−	1.00388i	−0.00388811	−	0.999992i	$-0.501238\pi$
$740$	6.95281			0.255591
$741$	0.395417	−	0.582744i	0.0145260	−	0.0214077i
$742$		−	22.2851i		−	0.818112i
$743$	−26.1503	+	26.1503i	−0.959361	+	0.959361i	−0.999206	−	0.0398445i	$-0.987314\pi$
$743$	−26.1503	+	26.1503i	−0.959361	+	0.959361i	0.0398445	+	0.999206i	$0.487314\pi$
$744$	−5.79281	+	9.26319i	−0.212375	+	0.339605i
$745$		−	8.31684i		−	0.304705i
$746$	−32.1936	−	32.1936i	−1.17869	−	1.17869i
$747$	8.53903	−	8.53903i	0.312427	−	0.312427i
$748$	−49.9325	+	49.9325i	−1.82571	+	1.82571i
$749$	−1.97938	+	1.97938i	−0.0723250	+	0.0723250i
$750$		−	9.53388i		−	0.348128i
$751$		−	22.7996i		−	0.831970i	−0.909372	−	0.415985i	$-0.863437\pi$
$751$		−	22.7996i		−	0.831970i	0.909372	−	0.415985i	$-0.136563\pi$
$752$	−1.04618	+	1.04618i	−0.0381503	+	0.0381503i
$753$		−	5.04207i		−	0.183743i
$754$	−16.6580	+	24.5496i	−0.606647	+	0.894044i
$755$			5.19855i			0.189195i
$756$	−4.81286	+	4.81286i	−0.175042	+	0.175042i
$757$		−	41.6790i		−	1.51485i	−0.652923	−	0.757424i	$-0.726458\pi$
$757$		−	41.6790i		−	1.51485i	0.652923	−	0.757424i	$-0.273542\pi$
$758$			69.7006i			2.53164i
$759$	9.37770	−	9.37770i	0.340389	−	0.340389i
$760$	3.61553	+	3.61553i	0.131149	+	0.131149i
$761$	−38.1284	−	38.1284i	−1.38215	−	1.38215i	−0.840784	−	0.541371i	$-0.817905\pi$
$761$	−38.1284	−	38.1284i	−1.38215	−	1.38215i	−0.541371	−	0.840784i	$-0.682095\pi$
$762$	−2.04011	+	2.04011i	−0.0739054	+	0.0739054i
$763$	−11.4117			−0.413130
$764$		−	65.1071i		−	2.35549i
$765$	−10.1352	−	10.1352i	−0.366439	−	0.366439i
$766$	−32.8262			−1.18606
$767$	−23.9008	+	35.2238i	−0.863009	+	1.27186i
$768$			10.3285i			0.372697i
$769$	−22.8814	−	22.8814i	−0.825126	−	0.825126i	0.161712	−	0.986838i	$-0.448298\pi$
$769$	−22.8814	−	22.8814i	−0.825126	−	0.825126i	−0.986838	+	0.161712i	$0.948298\pi$
$770$		−	13.9627i		−	0.503181i
$771$	0.768869			0.0276901
$772$	−7.19095	−	7.19095i	−0.258808	−	0.258808i
$773$	10.6809	−	10.6809i	0.384164	−	0.384164i	−0.488436	−	0.872600i	$-0.662432\pi$
$773$	10.6809	−	10.6809i	0.384164	−	0.384164i	0.872600	+	0.488436i	$0.162432\pi$
$774$	−22.5867	−	22.5867i	−0.811861	−	0.811861i
$775$	−15.6855	+	3.61547i	−0.563439	+	0.129872i
$776$	−2.85480			−0.102481
$777$			0.291176i			0.0104459i
$778$	31.9408	+	31.9408i	1.14513	+	1.14513i
$779$			1.84277i			0.0660240i
$780$	6.23064	+	4.22775i	0.223093	+	0.151378i
$781$			31.4819i			1.12651i
$782$	−51.5576	−	51.5576i	−1.84370	−	1.84370i
$783$	6.34240			0.226659
$784$		−	39.9069i		−	1.42525i
$785$	16.5216	+	16.5216i	0.589682	+	0.589682i
$786$	−0.484998	+	0.484998i	−0.0172993	+	0.0172993i
$787$	8.06090	+	8.06090i	0.287340	+	0.287340i	0.836028	−	0.548688i	$-0.184872\pi$
$787$	8.06090	+	8.06090i	0.287340	+	0.287340i	−0.548688	+	0.836028i	$0.684872\pi$
$788$	−73.4907	−	73.4907i	−2.61800	−	2.61800i
$789$	4.40329			0.156761
$790$	−57.9606			−2.06215
$791$	−5.57254	+	5.57254i	−0.198137	+	0.198137i
$792$	81.6036			2.89966
$793$	−4.15048	−	21.6724i	−0.147388	−	0.769609i
$794$	75.2043			2.66890
$795$	3.72669	+	3.72669i	0.132172	+	0.132172i
$796$		−	32.2972i		−	1.14474i
$797$	−48.6354			−1.72275			−0.861377	−	0.507966i	$-0.830397\pi$
$797$	−48.6354			−1.72275			−0.861377	+	0.507966i	$0.830397\pi$
$798$	−0.279809	+	0.279809i	−0.00990511	+	0.00990511i
$799$	0.568703	−	0.568703i	0.0201193	−	0.0201193i
$800$	8.05681	−	8.05681i	0.284851	−	0.284851i
$801$	13.5326	+	13.5326i	0.478152	+	0.478152i
$802$		−	27.1951i		−	0.960291i
$803$			54.2401i			1.91409i
$804$	−11.3940	−	11.3940i	−0.401835	−	0.401835i
$805$	9.88243			0.348310
$806$	18.2883	−	47.2022i	0.644179	−	1.66263i
$807$	0.634755			0.0223444
$808$	−16.5956	−	16.5956i	−0.583832	−	0.583832i
$809$			24.0012i			0.843838i	0.906633	+	0.421919i	$0.138643\pi$
$809$			24.0012i			0.843838i	−0.906633	+	0.421919i	$0.861357\pi$
$810$			29.4133i			1.03348i
$811$	13.6152	+	13.6152i	0.478094	+	0.478094i	0.904522	−	0.426428i	$-0.140228\pi$
$811$	13.6152	+	13.6152i	0.478094	+	0.478094i	−0.426428	+	0.904522i	$0.640228\pi$
$812$	8.08002	−	8.08002i	0.283553	−	0.283553i
$813$	−4.72236	+	4.72236i	−0.165620	+	0.165620i
$814$	9.29513	−	9.29513i	0.325794	−	0.325794i
$815$	24.3982			0.854633
$816$			7.07350i			0.247622i
$817$	−1.83411	−	1.83411i	−0.0641673	−	0.0641673i
$818$	−19.0746			−0.666927
$819$	4.70251	−	6.93032i	0.164319	−	0.242165i
$820$	−19.7027			−0.688047
$821$	−0.825508	+	0.825508i	−0.0288104	+	0.0288104i	−0.721365	−	0.692555i	$-0.756485\pi$
$821$	−0.825508	+	0.825508i	−0.0288104	+	0.0288104i	0.692555	+	0.721365i	$0.256485\pi$
$822$	1.17800			0.0410875
$823$	−2.62824			−0.0916147			−0.0458074	−	0.998950i	$-0.514586\pi$
$823$	−2.62824			−0.0916147			−0.0458074	+	0.998950i	$0.514586\pi$
$824$	−53.0913	−	53.0913i	−1.84952	−	1.84952i
$825$	−3.20090	−	3.20090i	−0.111441	−	0.111441i
$826$	16.9129	−	16.9129i	0.588476	−	0.588476i
$827$	6.52124	+	6.52124i	0.226766	+	0.226766i	0.811340	−	0.584574i	$-0.198738\pi$
$827$	6.52124	+	6.52124i	0.226766	+	0.226766i	−0.584574	+	0.811340i	$0.698738\pi$
$828$			106.733i			3.70922i
$829$	−14.2126			−0.493622			−0.246811	−	0.969064i	$-0.579383\pi$
$829$	−14.2126			−0.493622			−0.246811	+	0.969064i	$0.579383\pi$
$830$	10.8156	+	10.8156i	0.375415	+	0.375415i
$831$			2.65699i			0.0921698i
$832$	−1.77829	−	9.28563i	−0.0616511	−	0.321921i
$833$			21.6933i			0.751630i
$834$	2.77782	+	2.77782i	0.0961882	+	0.0961882i
$835$			29.1881i			1.01009i
$836$	12.2455			0.423519
$837$	−10.5454	+	2.43069i	−0.364502	+	0.0840169i
$838$	46.5024	+	46.5024i	1.60640	+	1.60640i
$839$	−34.9707	+	34.9707i	−1.20732	+	1.20732i	−0.235432	+	0.971891i	$0.575651\pi$
$839$	−34.9707	+	34.9707i	−1.20732	+	1.20732i	−0.971891	+	0.235432i	$0.924349\pi$
$840$	−1.61890	−	1.61890i	−0.0558575	−	0.0558575i
$841$	18.3521			0.632832
$842$			24.7847i			0.854138i
$843$	1.42739	+	1.42739i	0.0491619	+	0.0491619i
$844$			79.0902i			2.72240i
$845$	−17.3370	−	7.47261i	−0.596409	−	0.257066i
$846$	−1.71753			−0.0590501
$847$	−6.54602	−	6.54602i	−0.224924	−	0.224924i
$848$			69.0798i			2.37221i
$849$	−1.94037			−0.0665932
$850$	−17.5982	+	17.5982i	−0.603614	+	0.603614i
$851$	6.57885	+	6.57885i	0.225520	+	0.225520i
$852$	6.74539	+	6.74539i	0.231093	+	0.231093i
$853$	23.9515	−	23.9515i	0.820084	−	0.820084i	−0.166035	−	0.986120i	$-0.553097\pi$
$853$	23.9515	−	23.9515i	0.820084	−	0.820084i	0.986120	+	0.166035i	$0.0530966\pi$
$854$			12.3990i			0.424286i
$855$			2.48556i			0.0850044i
$856$	14.6525	−	14.6525i	0.500812	−	0.500812i
$857$		−	47.3466i		−	1.61733i	−0.588270	−	0.808665i	$-0.700191\pi$
$857$		−	47.3466i		−	1.61733i	0.588270	−	0.808665i	$-0.299809\pi$
$858$	13.9817	−	2.67763i	0.477327	−	0.0914129i
$859$		−	34.1482i		−	1.16512i	−0.812787	−	0.582561i	$-0.802051\pi$
$859$		−	34.1482i		−	1.16512i	0.812787	−	0.582561i	$-0.197949\pi$
$860$	19.6101	−	19.6101i	0.668698	−	0.668698i
$861$		−	0.825125i		−	0.0281202i
$862$		−	6.55549i		−	0.223281i
$863$	−33.8578	+	33.8578i	−1.15253	+	1.15253i	−0.166490	+	0.986043i	$0.553243\pi$
$863$	−33.8578	+	33.8578i	−1.15253	+	1.15253i	−0.986043	+	0.166490i	$0.946757\pi$
$864$	5.41661	−	5.41661i	0.184277	−	0.184277i
$865$	11.2847	−	11.2847i	0.383692	−	0.383692i
$866$	12.9689	+	12.9689i	0.440700	+	0.440700i
$867$			1.76367i			0.0598973i
$868$	−10.3379	+	16.5311i	−0.350890	+	0.561102i
$869$	−53.1145	+	53.1145i	−1.80179	+	1.80179i
$870$			3.94245i			0.133661i
$871$	33.4315	+	22.6847i	1.13278	+	0.768642i
$872$	84.4756			2.86070
$873$	−0.981294	−	0.981294i	−0.0332118	−	0.0332118i
$874$			12.6440i			0.427690i
$875$		−	9.20699i		−	0.311253i
$876$	11.6216	+	11.6216i	0.392658	+	0.392658i
$877$	−26.2796	−	26.2796i	−0.887398	−	0.887398i	0.106874	−	0.994273i	$-0.465916\pi$
$877$	−26.2796	−	26.2796i	−0.887398	−	0.887398i	−0.994273	+	0.106874i	$0.965916\pi$
$878$	−15.5644	+	15.5644i	−0.525273	+	0.525273i
$879$	5.10343	+	5.10343i	0.172134	+	0.172134i
$880$			43.2818i			1.45903i
$881$	46.0993			1.55312			0.776562	−	0.630041i	$-0.216962\pi$
$881$	46.0993			1.55312			0.776562	+	0.630041i	$0.216962\pi$
$882$	32.7579	−	32.7579i	1.10302	−	1.10302i
$883$	29.1650			0.981480			0.490740	−	0.871306i	$-0.336727\pi$
$883$	29.1650			0.981480			0.490740	+	0.871306i	$0.336727\pi$
$884$	−10.0910	−	52.6916i	−0.339396	−	1.77221i
$885$			5.65662i			0.190145i
$886$	5.67113	+	5.67113i	0.190525	+	0.190525i
$887$	−45.1637			−1.51645			−0.758225	−	0.651993i	$-0.773933\pi$
$887$	−45.1637			−1.51645			−0.758225	+	0.651993i	$0.773933\pi$
$888$		−	2.15545i		−	0.0723321i
$889$	−1.97016	+	1.97016i	−0.0660770	+	0.0660770i
$890$	−17.1405	+	17.1405i	−0.574552	+	0.574552i
$891$	26.9541	+	26.9541i	0.902996	+	0.902996i
$892$	−15.7824	−	15.7824i	−0.528434	−	0.528434i
$893$	−0.139469			−0.00466716
$894$	−4.76463			−0.159353
$895$	21.4724	+	21.4724i	0.717744	+	0.717744i
$896$			11.6453i			0.389042i
$897$	1.89516	+	9.89588i	0.0632775	+	0.330414i
$898$		−	62.9604i		−	2.10102i
$899$	17.7040	−	4.08074i	0.590462	−	0.136100i
$900$	36.4312			1.21437
$901$		−	37.5517i		−	1.25103i
$902$	−26.3402	+	26.3402i	−0.877034	+	0.877034i
$903$	0.821248	+	0.821248i	0.0273294	+	0.0273294i
$904$	41.2510	−	41.2510i	1.37199	−	1.37199i
$905$	19.8975	+	19.8975i	0.661417	+	0.661417i
$906$	2.97819			0.0989439
$907$			17.8245i			0.591851i	0.955211	+	0.295926i	$0.0956281\pi$
$907$			17.8245i			0.591851i	−0.955211	+	0.295926i	$0.904372\pi$
$908$	−13.7021	+	13.7021i	−0.454719	+	0.454719i
$909$		−	11.4090i		−	0.378411i
$910$	8.77799	+	5.95624i	0.290987	+	0.197447i
$911$			36.3252i			1.20351i	0.798682	+	0.601753i	$0.205531\pi$
$911$			36.3252i			1.20351i	−0.798682	+	0.601753i	$0.794469\pi$
$912$	0.867356	−	0.867356i	0.0287210	−	0.0287210i
$913$	19.8226			0.656033
$914$	56.7445			1.87694
$915$	−2.07346	−	2.07346i	−0.0685465	−	0.0685465i
$916$	50.7102	−	50.7102i	1.67551	−	1.67551i
$917$	−0.468368	+	0.468368i	−0.0154669	+	0.0154669i
$918$	−11.8313	+	11.8313i	−0.390491	+	0.390491i
$919$	53.4232			1.76227			0.881135	−	0.472865i	$-0.156780\pi$
$919$	53.4232			1.76227			0.881135	+	0.472865i	$0.156780\pi$
$920$	−73.1553			−2.41186
$921$	1.89680	+	1.89680i	0.0625017	+	0.0625017i
$922$	46.4290			1.52906
$923$	−19.7919	−	13.4296i	−0.651458	−	0.442042i
$924$	−5.48309			−0.180380
$925$	2.24557	−	2.24557i	0.0738338	−	0.0738338i
$926$		−	56.0717i		−	1.84263i
$927$		−	36.4986i		−	1.19877i
$928$	−9.09362	+	9.09362i	−0.298513	+	0.298513i
$929$	14.6883	−	14.6883i	0.481908	−	0.481908i	−0.423833	−	0.905741i	$-0.639316\pi$
$929$	14.6883	−	14.6883i	0.481908	−	0.481908i	0.905741	+	0.423833i	$0.139316\pi$
$930$	−1.51092	−	6.55502i	−0.0495450	−	0.214948i
$931$	2.66005	−	2.66005i	0.0871795	−	0.0871795i
$932$	101.168			3.31386
$933$	−1.27931			−0.0418826
$934$	7.10343	−	7.10343i	0.232431	−	0.232431i
$935$		−	23.5279i		−	0.769446i
$936$	−34.8106	+	51.3021i	−1.13782	+	1.67686i
$937$	−21.9582			−0.717342			−0.358671	−	0.933464i	$-0.616770\pi$
$937$	−21.9582			−0.717342			−0.358671	+	0.933464i	$0.616770\pi$
$938$	−16.0524	−	16.0524i	−0.524128	−	0.524128i
$939$	7.80905			0.254839
$940$		−	1.49119i		−	0.0486372i
$941$	−8.20872	+	8.20872i	−0.267597	+	0.267597i	−0.828131	−	0.560534i	$-0.810596\pi$
$941$	−8.20872	+	8.20872i	−0.267597	+	0.267597i	0.560534	+	0.828131i	$0.310596\pi$
$942$	9.46506	−	9.46506i	0.308388	−	0.308388i
$943$	−18.6429	−	18.6429i	−0.607098	−	0.607098i
$944$	−52.4270	+	52.4270i	−1.70635	+	1.70635i
$945$		−	2.26780i		−	0.0737714i
$946$		−	52.4329i		−	1.70474i
$947$	−7.64439	−	7.64439i	−0.248409	−	0.248409i	0.571908	−	0.820318i	$-0.306203\pi$
$947$	−7.64439	−	7.64439i	−0.248409	−	0.248409i	−0.820318	+	0.571908i	$0.806203\pi$
$948$			22.7609i			0.739239i
$949$	−34.0994	−	23.1379i	−1.10691	−	0.751087i
$950$	4.31580			0.140023
$951$	0.693129	−	0.693129i	0.0224762	−	0.0224762i
$952$			16.3128i			0.528700i
$953$	10.5391			0.341396			0.170698	−	0.985323i	$-0.445398\pi$
$953$	10.5391			0.341396			0.170698	+	0.985323i	$0.445398\pi$
$954$	−56.7048	+	56.7048i	−1.83588	+	1.83588i
$955$	15.3391	+	15.3391i	0.496361	+	0.496361i
$956$	48.0641	+	48.0641i	1.55450	+	1.55450i
$957$	3.61282	+	3.61282i	0.116786	+	0.116786i
$958$	−93.5107			−3.02119
$959$	1.13761			0.0367354
$960$	−0.888383	−	0.888383i	−0.0286724	−	0.0286724i
$961$	−27.8722	+	13.5699i	−0.899102	+	0.437739i
$962$	1.87847	+	9.80875i	0.0605644	+	0.316247i
$963$	10.0731			0.324602
$964$	−63.8000	+	63.8000i	−2.05486	+	2.05486i
$965$	3.38834			0.109075
$966$		−	5.66154i		−	0.182157i
$967$	5.61152	−	5.61152i	0.180454	−	0.180454i	−0.611099	−	0.791554i	$-0.709272\pi$
$967$	5.61152	−	5.61152i	0.180454	−	0.180454i	0.791554	+	0.611099i	$0.209272\pi$
$968$	48.4573	+	48.4573i	1.55748	+	1.55748i
$969$	−0.471494	+	0.471494i	−0.0151466	+	0.0151466i
$970$	1.24291	−	1.24291i	0.0399076	−	0.0399076i
$971$	−5.69433			−0.182740			−0.0913699	−	0.995817i	$-0.529125\pi$
$971$	−5.69433			−0.182740			−0.0913699	+	0.995817i	$0.529125\pi$
$972$	36.9654			1.18567
$973$	2.68258	+	2.68258i	0.0859995	+	0.0859995i
$974$	−22.2917			−0.714271
$975$	3.37777	−	0.646877i	0.108175	−	0.0207166i
$976$		−	38.4347i		−	1.23027i
$977$	23.7222	+	23.7222i	0.758942	+	0.758942i	0.976130	−	0.217188i	$-0.0696885\pi$
$977$	23.7222	+	23.7222i	0.758942	+	0.758942i	−0.217188	+	0.976130i	$0.569689\pi$
$978$		−	13.9775i		−	0.446951i
$979$			31.4148i			1.00402i
$980$	28.4409	+	28.4409i	0.908511	+	0.908511i
$981$	29.0372	+	29.0372i	0.927085	+	0.927085i
$982$	36.2606	+	36.2606i	1.15712	+	1.15712i
$983$	−34.2054	−	34.2054i	−1.09098	−	1.09098i	−0.995424	−	0.0955582i	$-0.969536\pi$
$983$	−34.2054	−	34.2054i	−1.09098	−	1.09098i	−0.0955582	−	0.995424i	$-0.530464\pi$
$984$			6.10804i			0.194717i
$985$	34.6285			1.10336
$986$	19.8629	−	19.8629i	0.632563	−	0.632563i
$987$	0.0624493			0.00198778
$988$	−5.22370	+	7.69842i	−0.166188	+	0.244919i
$989$	37.1107			1.18005
$990$	−35.5283	+	35.5283i	−1.12916	+	1.12916i
$991$		−	33.6432i		−	1.06871i	−0.845260	−	0.534355i	$-0.820554\pi$
$991$		−	33.6432i		−	1.06871i	0.845260	−	0.534355i	$-0.179446\pi$
$992$	11.6347	−	18.6049i	0.369402	−	0.590705i
$993$	−4.99649	−	4.99649i	−0.158559	−	0.158559i
$994$	9.50320	+	9.50320i	0.301423	+	0.301423i
$995$	7.60915	+	7.60915i	0.241226	+	0.241226i
$996$	4.24724	−	4.24724i	0.134579	−	0.134579i
$997$	0.755891			0.0239393			0.0119696	−	0.999928i	$-0.496190\pi$
$997$	0.755891			0.0239393			0.0119696	+	0.999928i	$0.496190\pi$
$998$	−42.3465			−1.34046
$999$	1.50970	−	1.50970i	0.0477648	−	0.0477648i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.i.a.216.3	✓	68
13.5	odd	4	inner	403.2.i.a.278.3	yes	68
31.30	odd	2	inner	403.2.i.a.216.4	yes	68
403.278	even	4	inner	403.2.i.a.278.4	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.i.a.216.3	✓	68	1.1	even	1	trivial
403.2.i.a.216.4	yes	68	31.30	odd	2	inner
403.2.i.a.278.3	yes	68	13.5	odd	4	inner
403.2.i.a.278.4	yes	68	403.278	even	4	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:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.78306 - 1.78306i) q^{2} -0.329930i q^{3} +4.35859i q^{4} +(-1.02687 - 1.02687i) q^{5} +(-0.588285 + 0.588285i) q^{6} +(-0.568114 + 0.568114i) q^{7} +(4.20550 - 4.20550i) q^{8} +2.89115 q^{9} +O(q^{10})\)	\(q+(-1.78306 - 1.78306i) q^{2} -0.329930i q^{3} +4.35859i q^{4} +(-1.02687 - 1.02687i) q^{5} +(-0.588285 + 0.588285i) q^{6} +(-0.568114 + 0.568114i) q^{7} +(4.20550 - 4.20550i) q^{8} +2.89115 q^{9} +3.66195i q^{10} +(3.35577 + 3.35577i) q^{11} +1.43803 q^{12} +(-3.54120 + 0.678174i) q^{13} +2.02596 q^{14} +(-0.338796 + 0.338796i) q^{15} -6.28011 q^{16} +3.41386 q^{17} +(-5.15508 - 5.15508i) q^{18} +(-0.418609 - 0.418609i) q^{19} +(4.47571 - 4.47571i) q^{20} +(0.187438 + 0.187438i) q^{21} -11.9671i q^{22} +8.46997 q^{23} +(-1.38752 - 1.38752i) q^{24} -2.89106i q^{25} +(7.52338 + 5.10493i) q^{26} -1.94367i q^{27} +(-2.47617 - 2.47617i) q^{28} +3.26311i q^{29} +1.20819 q^{30} +(-1.25057 - 5.42550i) q^{31} +(2.78680 + 2.78680i) q^{32} +(1.10717 - 1.10717i) q^{33} +(-6.08710 - 6.08710i) q^{34} +1.16676 q^{35} +12.6013i q^{36} +(0.776727 + 0.776727i) q^{37} +1.49281i q^{38} +(0.223750 + 1.16835i) q^{39} -8.63702 q^{40} +(-2.20106 - 2.20106i) q^{41} -0.668425i q^{42} +4.38144 q^{43} +(-14.6264 + 14.6264i) q^{44} +(-2.96884 - 2.96884i) q^{45} +(-15.1024 - 15.1024i) q^{46} +(0.166587 - 0.166587i) q^{47} +2.07200i q^{48} +6.35449i q^{49} +(-5.15493 + 5.15493i) q^{50} -1.12634i q^{51} +(-2.95588 - 15.4346i) q^{52} -10.9998i q^{53} +(-3.46567 + 3.46567i) q^{54} -6.89189i q^{55} +4.77840i q^{56} +(-0.138112 + 0.138112i) q^{57} +(5.81831 - 5.81831i) q^{58} +(8.34811 - 8.34811i) q^{59} +(-1.47667 - 1.47667i) q^{60} +6.12008i q^{61} +(-7.44415 + 11.9038i) q^{62} +(-1.64250 + 1.64250i) q^{63} +2.62217i q^{64} +(4.33276 + 2.93996i) q^{65} -3.94830 q^{66} +(-7.92334 - 7.92334i) q^{67} +14.8796i q^{68} -2.79450i q^{69} +(-2.08040 - 2.08040i) q^{70} +(4.69072 + 4.69072i) q^{71} +(12.1587 - 12.1587i) q^{72} +(8.08162 + 8.08162i) q^{73} -2.76990i q^{74} -0.953850 q^{75} +(1.82454 - 1.82454i) q^{76} -3.81292 q^{77} +(1.68427 - 2.48219i) q^{78} +15.8278i q^{79} +(6.44887 + 6.44887i) q^{80} +8.03216 q^{81} +7.84924i q^{82} +(2.95351 - 2.95351i) q^{83} +(-0.816965 + 0.816965i) q^{84} +(-3.50560 - 3.50560i) q^{85} +(-7.81236 - 7.81236i) q^{86} +1.07660 q^{87} +28.2253 q^{88} +(4.68071 + 4.68071i) q^{89} +10.5872i q^{90} +(1.62652 - 2.39708i) q^{91} +36.9171i q^{92} +(-1.79004 + 0.412600i) q^{93} -0.594067 q^{94} +0.859715i q^{95} +(0.919449 - 0.919449i) q^{96} +(-0.339413 - 0.339413i) q^{97} +(11.3304 - 11.3304i) q^{98} +(9.70202 + 9.70202i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 4 q^{2} - 4 q^{5} + 8 q^{7} + 16 q^{8} - 60 q^{9}+O(q^{10}) \) 68 * q - 4 * q^2 - 4 * q^5 + 8 * q^7 + 16 * q^8 - 60 * q^9	\( 68 q - 4 q^{2} - 4 q^{5} + 8 q^{7} + 16 q^{8} - 60 q^{9} - 48 q^{14} - 40 q^{16} + 4 q^{18} - 24 q^{19} - 16 q^{20} + 44 q^{28} + 24 q^{31} + 28 q^{32} - 40 q^{35} - 24 q^{39} + 24 q^{40} + 20 q^{41} - 24 q^{45} - 36 q^{47} + 80 q^{50} + 28 q^{59} - 76 q^{63} + 152 q^{66} - 32 q^{67} - 48 q^{70} + 20 q^{71} - 32 q^{72} + 72 q^{76} + 84 q^{78} - 20 q^{80} + 52 q^{81} - 112 q^{87} - 8 q^{93} - 16 q^{94} - 4 q^{97} - 92 q^{98}+O(q^{100}) \) 68 * q - 4 * q^2 - 4 * q^5 + 8 * q^7 + 16 * q^8 - 60 * q^9 - 48 * q^14 - 40 * q^16 + 4 * q^18 - 24 * q^19 - 16 * q^20 + 44 * q^28 + 24 * q^31 + 28 * q^32 - 40 * q^35 - 24 * q^39 + 24 * q^40 + 20 * q^41 - 24 * q^45 - 36 * q^47 + 80 * q^50 + 28 * q^59 - 76 * q^63 + 152 * q^66 - 32 * q^67 - 48 * q^70 + 20 * q^71 - 32 * q^72 + 72 * q^76 + 84 * q^78 - 20 * q^80 + 52 * q^81 - 112 * q^87 - 8 * q^93 - 16 * q^94 - 4 * q^97 - 92 * q^98

Introduction

L-functions

Modular forms

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Database

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