LMFDB - Embedded newform 414.2.i.f.307.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [414,2,Mod(55,414)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(414, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 10]))

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

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

chi := DirichletCharacter("414.55");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 414 = 2 \cdot 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	414.i (of order $11$, degree $10$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.30580664368$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 46)
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			307.1
Root			$-0.415415 + 0.909632i$ of defining polynomial
Character	$\chi$	$=$	414.307
Dual form			414.2.i.f.325.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.142315 - 0.989821i) q^{2} +(-0.959493 - 0.281733i) q^{4} +(1.66741 + 1.92429i) q^{5} +(1.75667 + 1.12894i) q^{7} +(-0.415415 + 0.909632i) q^{8} +O(q^{10})$	\(q+(0.142315 - 0.989821i) q^{2} +(-0.959493 - 0.281733i) q^{4} +(1.66741 + 1.92429i) q^{5} +(1.75667 + 1.12894i) q^{7} +(-0.415415 + 0.909632i) q^{8} +(2.14200 - 1.37658i) q^{10} +(0.543474 + 3.77994i) q^{11} +(-5.21228 + 3.34973i) q^{13} +(1.36745 - 1.57812i) q^{14} +(0.841254 + 0.540641i) q^{16} +(1.24982 - 0.366979i) q^{17} +(2.38000 + 0.698830i) q^{19} +(-1.05773 - 2.31611i) q^{20} +3.81881 q^{22} +(1.33380 - 4.60662i) q^{23} +(-0.211072 + 1.46804i) q^{25} +(2.57385 + 5.63594i) q^{26} +(-1.36745 - 1.57812i) q^{28} +(6.87690 - 2.01924i) q^{29} +(-1.67062 + 3.65814i) q^{31} +(0.654861 - 0.755750i) q^{32} +(-0.185376 - 1.28932i) q^{34} +(0.756669 + 5.26275i) q^{35} +(7.48386 - 8.63683i) q^{37} +(1.03043 - 2.25632i) q^{38} +(-2.44306 + 0.717348i) q^{40} +(-2.81130 - 3.24442i) q^{41} +(-1.15394 - 2.52678i) q^{43} +(0.543474 - 3.77994i) q^{44} +(-4.36992 - 1.97581i) q^{46} -9.34150 q^{47} +(-1.09653 - 2.40107i) q^{49} +(1.42306 + 0.417848i) q^{50} +(5.94487 - 1.74557i) q^{52} +(1.99027 + 1.27907i) q^{53} +(-6.36752 + 7.34850i) q^{55} +(-1.75667 + 1.12894i) q^{56} +(-1.02000 - 7.09427i) q^{58} +(-0.514407 + 0.330589i) q^{59} +(1.67815 - 3.67464i) q^{61} +(3.38316 + 2.17422i) q^{62} +(-0.654861 - 0.755750i) q^{64} +(-15.1368 - 4.44457i) q^{65} +(-1.82531 + 12.6953i) q^{67} -1.30258 q^{68} +5.31686 q^{70} +(-0.940875 + 6.54393i) q^{71} +(2.80644 + 0.824045i) q^{73} +(-7.48386 - 8.63683i) q^{74} +(-2.08671 - 1.34105i) q^{76} +(-3.31264 + 7.25366i) q^{77} +(-1.58724 + 1.02006i) q^{79} +(0.362362 + 2.52028i) q^{80} +(-3.61148 + 2.32096i) q^{82} +(6.83698 - 7.89030i) q^{83} +(2.79013 + 1.79310i) q^{85} +(-2.66528 + 0.782598i) q^{86} +(-3.66412 - 1.07588i) q^{88} +(-2.08216 - 4.55930i) q^{89} -12.9379 q^{91} +(-2.57760 + 4.04425i) q^{92} +(-1.32943 + 9.24642i) q^{94} +(2.62367 + 5.74504i) q^{95} +(-8.21585 - 9.48159i) q^{97} +(-2.53268 + 0.743663i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + q^{2} - q^{4} + 6 q^{5} + 3 q^{7} + q^{8}+O(q^{10}) $ 10 * q + q^2 - q^4 + 6 * q^5 + 3 * q^7 + q^8	$ 10 q + q^{2} - q^{4} + 6 q^{5} + 3 q^{7} + q^{8} - 6 q^{10} + 12 q^{11} - 14 q^{13} - 3 q^{14} - q^{16} - 15 q^{17} + 2 q^{19} - 5 q^{20} + 10 q^{22} + q^{23} + 13 q^{25} + 3 q^{26} + 3 q^{28} + 8 q^{29} - 21 q^{31} + q^{32} - 7 q^{34} - 7 q^{35} + 28 q^{37} + 9 q^{38} - 6 q^{40} + 31 q^{41} + 11 q^{43} + 12 q^{44} - 12 q^{46} - 18 q^{47} - 24 q^{49} - 2 q^{50} + 8 q^{52} + 21 q^{53} + 5 q^{55} - 3 q^{56} - 8 q^{58} + 5 q^{59} + 37 q^{61} - q^{62} - q^{64} - 37 q^{65} - 13 q^{67} - 26 q^{68} + 18 q^{70} - 49 q^{71} - 8 q^{73} - 28 q^{74} - 20 q^{76} + 8 q^{77} + 8 q^{79} - 5 q^{80} + 2 q^{82} + 7 q^{83} - 42 q^{85} - 22 q^{86} - q^{88} + 13 q^{89} - 24 q^{91} + 23 q^{92} - 37 q^{94} + 10 q^{95} - 32 q^{97} + 24 q^{98}+O(q^{100}) $ 10 * q + q^2 - q^4 + 6 * q^5 + 3 * q^7 + q^8 - 6 * q^10 + 12 * q^11 - 14 * q^13 - 3 * q^14 - q^16 - 15 * q^17 + 2 * q^19 - 5 * q^20 + 10 * q^22 + q^23 + 13 * q^25 + 3 * q^26 + 3 * q^28 + 8 * q^29 - 21 * q^31 + q^32 - 7 * q^34 - 7 * q^35 + 28 * q^37 + 9 * q^38 - 6 * q^40 + 31 * q^41 + 11 * q^43 + 12 * q^44 - 12 * q^46 - 18 * q^47 - 24 * q^49 - 2 * q^50 + 8 * q^52 + 21 * q^53 + 5 * q^55 - 3 * q^56 - 8 * q^58 + 5 * q^59 + 37 * q^61 - q^62 - q^64 - 37 * q^65 - 13 * q^67 - 26 * q^68 + 18 * q^70 - 49 * q^71 - 8 * q^73 - 28 * q^74 - 20 * q^76 + 8 * q^77 + 8 * q^79 - 5 * q^80 + 2 * q^82 + 7 * q^83 - 42 * q^85 - 22 * q^86 - q^88 + 13 * q^89 - 24 * q^91 + 23 * q^92 - 37 * q^94 + 10 * q^95 - 32 * q^97 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/414\mathbb{Z}\right)^\times$.

$n$	$47$	$235$
$\chi(n)$	$1$	$e\left(\frac{3}{11}\right)$

Coefficient data

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

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

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

$2$	0.142315	−	0.989821i	0.100632	−	0.699909i
$2$	0.142315	−	0.989821i	0.100632	−	0.699909i
$3$		0			0
$3$		0			0
$4$	−0.959493	−	0.281733i	−0.479746	−	0.140866i
$5$	1.66741	+	1.92429i	0.745687	+	0.860569i	0.994143	−	0.108075i	$-0.0344686\pi$
$5$	1.66741	+	1.92429i	0.745687	+	0.860569i	−0.248456	+	0.968643i	$0.579923\pi$
$6$		0			0
$7$	1.75667	+	1.12894i	0.663958	+	0.426700i	0.828743	−	0.559629i	$-0.189057\pi$
$7$	1.75667	+	1.12894i	0.663958	+	0.426700i	−0.164785	+	0.986330i	$0.552693\pi$
$8$	−0.415415	+	0.909632i	−0.146871	+	0.321603i
$9$		0			0
$10$	2.14200	−	1.37658i	0.677360	−	0.435313i
$11$	0.543474	+	3.77994i	0.163864	+	1.13970i	0.891265	+	0.453483i	$0.149819\pi$
$11$	0.543474	+	3.77994i	0.163864	+	1.13970i	−0.727401	+	0.686212i	$0.759272\pi$
$12$		0			0
$13$	−5.21228	+	3.34973i	−1.44563	+	0.929047i	−0.446207	+	0.894930i	$0.647226\pi$
$13$	−5.21228	+	3.34973i	−1.44563	+	0.929047i	−0.999418	+	0.0341173i	$0.989138\pi$
$14$	1.36745	−	1.57812i	0.365467	−	0.421771i
$15$		0			0
$16$	0.841254	+	0.540641i	0.210313	+	0.135160i
$17$	1.24982	−	0.366979i	0.303125	−	0.0890055i	−0.126633	−	0.991950i	$-0.540417\pi$
$17$	1.24982	−	0.366979i	0.303125	−	0.0890055i	0.429758	+	0.902944i	$0.358599\pi$
$18$		0			0
$19$	2.38000	+	0.698830i	0.546009	+	0.160323i	0.543092	−	0.839673i	$-0.317253\pi$
$19$	2.38000	+	0.698830i	0.546009	+	0.160323i	0.00291665	+	0.999996i	$0.499072\pi$
$20$	−1.05773	−	2.31611i	−0.236516	−	0.517897i
$21$		0			0
$22$	3.81881			0.814174
$23$	1.33380	−	4.60662i	0.278116	−	0.960548i
$23$	1.33380	−	4.60662i	0.278116	−	0.960548i
$24$		0			0
$25$	−0.211072	+	1.46804i	−0.0422145	+	0.293608i
$26$	2.57385	+	5.63594i	0.504773	+	1.10530i
$27$		0			0
$28$	−1.36745	−	1.57812i	−0.258424	−	0.298237i
$29$	6.87690	−	2.01924i	1.27701	−	0.374964i	0.428210	−	0.903679i	$-0.359144\pi$
$29$	6.87690	−	2.01924i	1.27701	−	0.374964i	0.848799	+	0.528716i	$0.177326\pi$
$30$		0			0
$31$	−1.67062	+	3.65814i	−0.300052	+	0.657022i	−0.998266	−	0.0588671i	$-0.981251\pi$
$31$	−1.67062	+	3.65814i	−0.300052	+	0.657022i	0.698214	+	0.715889i	$0.253978\pi$
$32$	0.654861	−	0.755750i	0.115764	−	0.133599i
$33$		0			0
$34$	−0.185376	−	1.28932i	−0.0317918	−	0.221117i
$35$	0.756669	+	5.26275i	0.127900	+	0.889566i
$36$		0			0
$37$	7.48386	−	8.63683i	1.23034	−	1.41989i	0.356059	−	0.934463i	$-0.384120\pi$
$37$	7.48386	−	8.63683i	1.23034	−	1.41989i	0.874279	−	0.485423i	$-0.161334\pi$
$38$	1.03043	−	2.25632i	0.167157	−	0.366023i
$39$		0			0
$40$	−2.44306	+	0.717348i	−0.386282	+	0.113423i
$41$	−2.81130	−	3.24442i	−0.439052	−	0.506693i	0.492494	−	0.870316i	$-0.336085\pi$
$41$	−2.81130	−	3.24442i	−0.439052	−	0.506693i	−0.931546	+	0.363623i	$0.881540\pi$
$42$		0			0
$43$	−1.15394	−	2.52678i	−0.175974	−	0.385330i	0.801007	−	0.598655i	$-0.204298\pi$
$43$	−1.15394	−	2.52678i	−0.175974	−	0.385330i	−0.976981	+	0.213325i	$0.931571\pi$
$44$	0.543474	−	3.77994i	0.0819318	−	0.569848i
$45$		0			0
$46$	−4.36992	−	1.97581i	−0.644309	−	0.291318i
$47$	−9.34150			−1.36260			−0.681299	−	0.732005i	$-0.738585\pi$
$47$	−9.34150			−1.36260			−0.681299	+	0.732005i	$0.738585\pi$
$48$		0			0
$49$	−1.09653	−	2.40107i	−0.156647	−	0.343010i
$50$	1.42306	+	0.417848i	0.201251	+	0.0590926i
$51$		0			0
$52$	5.94487	−	1.74557i	0.824405	−	0.242067i
$53$	1.99027	+	1.27907i	0.273385	+	0.175694i	0.670148	−	0.742227i	$-0.266230\pi$
$53$	1.99027	+	1.27907i	0.273385	+	0.175694i	−0.396764	+	0.917921i	$0.629867\pi$
$54$		0			0
$55$	−6.36752	+	7.34850i	−0.858596	+	0.990872i
$56$	−1.75667	+	1.12894i	−0.234745	+	0.150861i
$57$		0			0
$58$	−1.02000	−	7.09427i	−0.133933	−	0.931524i
$59$	−0.514407	+	0.330589i	−0.0669701	+	0.0430390i	−0.573697	−	0.819067i	$-0.694491\pi$
$59$	−0.514407	+	0.330589i	−0.0669701	+	0.0430390i	0.506727	+	0.862106i	$0.330855\pi$
$60$		0			0
$61$	1.67815	−	3.67464i	0.214865	−	0.470489i	−0.771254	−	0.636527i	$-0.780370\pi$
$61$	1.67815	−	3.67464i	0.214865	−	0.470489i	0.986119	+	0.166038i	$0.0530976\pi$
$62$	3.38316	+	2.17422i	0.429661	+	0.276127i
$63$		0			0
$64$	−0.654861	−	0.755750i	−0.0818576	−	0.0944687i
$65$	−15.1368	−	4.44457i	−1.87749	−	0.551281i
$66$		0			0
$67$	−1.82531	+	12.6953i	−0.222997	+	1.55098i	0.503614	+	0.863929i	$0.332003\pi$
$67$	−1.82531	+	12.6953i	−0.222997	+	1.55098i	−0.726611	+	0.687049i	$0.758906\pi$
$68$	−1.30258			−0.157961
$69$		0			0
$70$	5.31686			0.635487
$71$	−0.940875	+	6.54393i	−0.111661	+	0.776621i	0.854642	+	0.519217i	$0.173776\pi$
$71$	−0.940875	+	6.54393i	−0.111661	+	0.776621i	−0.966304	+	0.257404i	$0.917133\pi$
$72$		0			0
$73$	2.80644	+	0.824045i	0.328469	+	0.0964472i	0.441809	−	0.897109i	$-0.354337\pi$
$73$	2.80644	+	0.824045i	0.328469	+	0.0964472i	−0.113340	+	0.993556i	$0.536155\pi$
$74$	−7.48386	−	8.63683i	−0.869981	−	1.00401i
$75$		0			0
$76$	−2.08671	−	1.34105i	−0.239362	−	0.153828i
$77$	−3.31264	+	7.25366i	−0.377510	+	0.826631i
$78$		0			0
$79$	−1.58724	+	1.02006i	−0.178578	+	0.114765i	−0.626876	−	0.779119i	$-0.715667\pi$
$79$	−1.58724	+	1.02006i	−0.178578	+	0.114765i	0.448298	+	0.893884i	$0.352030\pi$
$80$	0.362362	+	2.52028i	0.0405133	+	0.281776i
$81$		0			0
$82$	−3.61148	+	2.32096i	−0.398822	+	0.256307i
$83$	6.83698	−	7.89030i	0.750456	−	0.866073i	−0.244156	−	0.969736i	$-0.578511\pi$
$83$	6.83698	−	7.89030i	0.750456	−	0.866073i	0.994612	+	0.103663i	$0.0330564\pi$
$84$		0			0
$85$	2.79013	+	1.79310i	0.302632	+	0.194490i
$86$	−2.66528	+	0.782598i	−0.287405	+	0.0843897i
$87$		0			0
$88$	−3.66412	−	1.07588i	−0.390597	−	0.114690i
$89$	−2.08216	−	4.55930i	−0.220709	−	0.483285i	0.766594	−	0.642132i	$-0.221950\pi$
$89$	−2.08216	−	4.55930i	−0.220709	−	0.483285i	−0.987303	+	0.158846i	$0.949223\pi$
$90$		0			0
$91$	−12.9379			−1.35626
$92$	−2.57760	+	4.04425i	−0.268734	+	0.421642i
$93$		0			0
$94$	−1.32943	+	9.24642i	−0.137121	+	0.953696i
$95$	2.62367	+	5.74504i	0.269183	+	0.589429i
$96$		0			0
$97$	−8.21585	−	9.48159i	−0.834193	−	0.962710i	0.165531	−	0.986205i	$-0.447066\pi$
$97$	−8.21585	−	9.48159i	−0.834193	−	0.962710i	−0.999724	+	0.0234947i	$0.992521\pi$
$98$	−2.53268	+	0.743663i	−0.255840	+	0.0751213i
$99$		0			0
$100$	0.616117	−	1.34911i	0.0616117	−	0.134911i
$101$	2.30675	−	2.66214i	0.229531	−	0.264893i	−0.629288	−	0.777172i	$-0.716653\pi$
$101$	2.30675	−	2.66214i	0.229531	−	0.264893i	0.858819	+	0.512280i	$0.171199\pi$
$102$		0			0
$103$	−0.222897	−	1.55028i	−0.0219627	−	0.152754i	0.975889	−	0.218267i	$-0.0700405\pi$
$103$	−0.222897	−	1.55028i	−0.0219627	−	0.152754i	−0.997852	+	0.0655137i	$0.979131\pi$
$104$	−0.881761	−	6.13278i	−0.0864637	−	0.601368i
$105$		0			0
$106$	1.54929	−	1.78798i	0.150481	−	0.173664i
$107$	−1.41373	+	3.09564i	−0.136671	+	0.299267i	−0.965576	−	0.260122i	$-0.916237\pi$
$107$	−1.41373	+	3.09564i	−0.136671	+	0.299267i	0.828905	+	0.559389i	$0.188964\pi$
$108$		0			0
$109$	8.27394	−	2.42945i	0.792499	−	0.232699i	0.139664	−	0.990199i	$-0.455398\pi$
$109$	8.27394	−	2.42945i	0.792499	−	0.232699i	0.652835	+	0.757500i	$0.273579\pi$
$110$	6.36752	+	7.34850i	0.607119	+	0.700652i
$111$		0			0
$112$	0.867451	+	1.89945i	0.0819664	+	0.179481i
$113$	−0.507526	+	3.52992i	−0.0477441	+	0.332067i	0.951925	+	0.306332i	$0.0991018\pi$
$113$	−0.507526	+	3.52992i	−0.0477441	+	0.332067i	−0.999669	+	0.0257353i	$0.991807\pi$
$114$		0			0
$115$	11.0885	−	5.11450i	1.03400	−	0.476930i
$116$	−7.16723			−0.665460
$117$		0			0
$118$	0.254017	+	0.556219i	0.0233841	+	0.0512041i
$119$	2.60981	+	0.766310i	0.239241	+	0.0702475i
$120$		0			0
$121$	−3.43819	+	1.00954i	−0.312563	+	0.0917767i
$122$	−3.39841	−	2.18402i	−0.307677	−	0.197732i
$123$		0			0
$124$	2.63357	−	3.03930i	0.236501	−	0.272937i
$125$	7.53312	−	4.84124i	0.673783	−	0.433014i
$126$		0			0
$127$	0.800045	+	5.56443i	0.0709925	+	0.493764i	0.994035	+	0.109065i	$0.0347856\pi$
$127$	0.800045	+	5.56443i	0.0709925	+	0.493764i	−0.923042	+	0.384699i	$0.874305\pi$
$128$	−0.841254	+	0.540641i	−0.0743570	+	0.0477863i
$129$		0			0
$130$	−6.55353	+	14.3502i	−0.574783	+	1.25860i
$131$	−6.70728	−	4.31051i	−0.586018	−	0.376611i	0.213778	−	0.976882i	$-0.431423\pi$
$131$	−6.70728	−	4.31051i	−0.586018	−	0.376611i	−0.799797	+	0.600271i	$0.795059\pi$
$132$		0			0
$133$	3.39193	+	3.91449i	0.294117	+	0.339430i
$134$	12.3063	+	3.61346i	1.06310	+	0.312155i
$135$		0			0
$136$	−0.185376	+	1.28932i	−0.0158959	+	0.110558i
$137$	−2.06934			−0.176796			−0.0883979	−	0.996085i	$-0.528175\pi$
$137$	−2.06934			−0.176796			−0.0883979	+	0.996085i	$0.528175\pi$
$138$		0			0
$139$	−13.0620			−1.10790			−0.553950	−	0.832550i	$-0.686880\pi$
$139$	−13.0620			−1.10790			−0.553950	+	0.832550i	$0.686880\pi$
$140$	0.756669	−	5.26275i	0.0639502	−	0.444783i
$141$		0			0
$142$	6.34342	+	1.86260i	0.532328	+	0.156306i
$143$	−15.4945	−	17.8816i	−1.29572	−	1.49534i
$144$		0			0
$145$	15.3522	+	9.86626i	1.27493	+	0.819348i
$146$	1.21506	−	2.66060i	0.100559	−	0.220193i
$147$		0			0
$148$	−9.61399	+	6.17853i	−0.790265	+	0.507872i
$149$	2.11269	+	14.6941i	0.173079	+	1.20379i	0.872332	+	0.488914i	$0.162607\pi$
$149$	2.11269	+	14.6941i	0.173079	+	1.20379i	−0.699254	+	0.714874i	$0.746484\pi$
$150$		0			0
$151$	3.24142	−	2.08313i	0.263783	−	0.169523i	−0.402064	−	0.915612i	$-0.631707\pi$
$151$	3.24142	−	2.08313i	0.263783	−	0.169523i	0.665846	+	0.746089i	$0.268071\pi$
$152$	−1.62436	+	1.87462i	−0.131753	+	0.152052i
$153$		0			0
$154$	6.70839	+	4.31122i	0.540577	+	0.347408i
$155$	−9.82493	+	2.88486i	−0.789157	+	0.231718i
$156$		0			0
$157$	−21.7336	−	6.38156i	−1.73453	−	0.509304i	−0.746742	−	0.665114i	$-0.768383\pi$
$157$	−21.7336	−	6.38156i	−1.73453	−	0.509304i	−0.987787	+	0.155810i	$0.950201\pi$
$158$	0.783785	+	1.71625i	0.0623546	+	0.136538i
$159$		0			0
$160$	2.54620			0.201295
$161$	7.54365	−	6.58653i	0.594523	−	0.519091i
$162$		0			0
$163$	2.69879	−	18.7705i	0.211385	−	1.47022i	−0.557152	−	0.830411i	$-0.688106\pi$
$163$	2.69879	−	18.7705i	0.211385	−	1.47022i	0.768537	−	0.639806i	$-0.220985\pi$
$164$	1.78337	+	3.90503i	0.139258	+	0.304932i
$165$		0			0
$166$	−6.83698	−	7.89030i	−0.530653	−	0.612406i
$167$	−0.939952	+	0.275995i	−0.0727356	+	0.0213571i	−0.317898	−	0.948125i	$-0.602977\pi$
$167$	−0.939952	+	0.275995i	−0.0727356	+	0.0213571i	0.245162	+	0.969482i	$0.421159\pi$
$168$		0			0
$169$	10.5468	−	23.0942i	0.811289	−	1.77648i
$170$	2.17193	−	2.50654i	0.166579	−	0.192243i
$171$		0			0
$172$	0.395323	+	2.74953i	0.0301431	+	0.209650i
$173$	−1.26974	−	8.83122i	−0.0965364	−	0.671425i	−0.979420	−	0.201833i	$-0.935310\pi$
$173$	−1.26974	−	8.83122i	−0.0965364	−	0.671425i	0.882884	−	0.469592i	$-0.155599\pi$
$174$		0			0
$175$	−2.02812	+	2.34057i	−0.153311	+	0.176931i
$176$	−1.58639	+	3.47372i	−0.119579	+	0.261841i
$177$		0			0
$178$	−4.80922	+	1.41211i	−0.360466	+	0.105842i
$179$	−5.56076	−	6.41746i	−0.415631	−	0.479663i	0.508870	−	0.860843i	$-0.330063\pi$
$179$	−5.56076	−	6.41746i	−0.415631	−	0.479663i	−0.924501	+	0.381180i	$0.875518\pi$
$180$		0			0
$181$	−0.223254	−	0.488859i	−0.0165944	−	0.0363366i	0.901153	−	0.433500i	$-0.142722\pi$
$181$	−0.223254	−	0.488859i	−0.0165944	−	0.0363366i	−0.917748	+	0.397164i	$0.869994\pi$
$182$	−1.84125	+	12.8062i	−0.136483	+	0.949259i
$183$		0			0
$184$	3.63625	+	3.12693i	0.268068	+	0.230520i
$185$	29.0984			2.13936
$186$		0			0
$187$	2.06640	+	4.52479i	0.151110	+	0.330885i
$188$	8.96311	+	2.63181i	0.653702	+	0.191944i
$189$		0			0
$190$	6.05995	−	1.77936i	0.439635	−	0.129088i
$191$	22.5725	+	14.5065i	1.63329	+	1.04965i	0.946455	+	0.322836i	$0.104636\pi$
$191$	22.5725	+	14.5065i	1.63329	+	1.04965i	0.686834	+	0.726815i	$0.259000\pi$
$192$		0			0
$193$	0.919649	−	1.06133i	0.0661978	−	0.0763964i	−0.721685	−	0.692222i	$-0.756632\pi$
$193$	0.919649	−	1.06133i	0.0661978	−	0.0763964i	0.787883	+	0.615826i	$0.211177\pi$
$194$	−10.5543	+	6.78285i	−0.757756	+	0.486980i
$195$		0			0
$196$	0.375655	+	2.61274i	0.0268325	+	0.186624i
$197$	6.93589	−	4.45743i	0.494162	−	0.317579i	−0.269715	−	0.962940i	$-0.586930\pi$
$197$	6.93589	−	4.45743i	0.494162	−	0.317579i	0.763877	+	0.645361i	$0.223293\pi$
$198$		0			0
$199$	−1.29407	+	2.83361i	−0.0917339	+	0.200869i	−0.949937	−	0.312441i	$-0.898854\pi$
$199$	−1.29407	+	2.83361i	−0.0917339	+	0.200869i	0.858203	+	0.513310i	$0.171581\pi$
$200$	−1.24769	−	0.801844i	−0.0882253	−	0.0566989i
$201$		0			0
$202$	−2.30675	−	2.66214i	−0.162303	−	0.187307i
$203$	14.3600	+	4.21649i	1.00788	+	0.295940i
$204$		0			0
$205$	1.55561	−	10.8195i	0.108649	−	0.755669i
$206$	−1.56622			−0.109124
$207$		0			0
$208$	−6.19584			−0.429604
$209$	−1.34807	+	9.37605i	−0.0932481	+	0.648555i
$210$		0			0
$211$	21.1163	+	6.20030i	1.45370	+	0.426846i	0.910765	−	0.412926i	$-0.135493\pi$
$211$	21.1163	+	6.20030i	1.45370	+	0.426846i	0.542940	+	0.839772i	$0.317311\pi$
$212$	−1.54929	−	1.78798i	−0.106406	−	0.122799i
$213$		0			0
$214$	2.86294	+	1.83990i	0.195706	+	0.125773i
$215$	2.93817	−	6.43369i	0.200381	−	0.438774i
$216$		0			0
$217$	−7.06456	+	4.54012i	−0.479573	+	0.308203i
$218$	−1.22721	−	8.53547i	−0.0831175	−	0.578095i
$219$		0			0
$220$	8.17990	−	5.25690i	0.551489	−	0.354420i
$221$	−5.28511	+	6.09934i	−0.355515	+	0.410286i
$222$		0			0
$223$	10.3556	+	6.65515i	0.693463	+	0.445662i	0.839316	−	0.543645i	$-0.182956\pi$
$223$	10.3556	+	6.65515i	0.693463	+	0.445662i	−0.145852	+	0.989306i	$0.546592\pi$
$224$	2.00357	−	0.588302i	0.133869	−	0.0393075i
$225$		0			0
$226$	3.42177	+	1.00472i	0.227612	+	0.0668331i
$227$	−2.21520	−	4.85061i	−0.147028	−	0.321946i	0.821761	−	0.569832i	$-0.192992\pi$
$227$	−2.21520	−	4.85061i	−0.147028	−	0.321946i	−0.968789	+	0.247885i	$0.920264\pi$
$228$		0			0
$229$	14.1070			0.932216			0.466108	−	0.884728i	$-0.345656\pi$
$229$	14.1070			0.932216			0.466108	+	0.884728i	$0.345656\pi$
$230$	−3.48439	−	11.7035i	−0.229754	−	0.771704i
$231$		0			0
$232$	−1.02000	+	7.09427i	−0.0669664	+	0.465762i
$233$	−7.13799	−	15.6300i	−0.467625	−	1.02396i	−0.985683	−	0.168610i	$-0.946072\pi$
$233$	−7.13799	−	15.6300i	−0.467625	−	1.02396i	0.518058	−	0.855346i	$-0.326655\pi$
$234$		0			0
$235$	−15.5761	−	17.9758i	−1.01607	−	1.17261i
$236$	0.586707	−	0.172273i	0.0381914	−	0.0112140i
$237$		0			0
$238$	1.12992	−	2.47419i	0.0732421	−	0.160378i
$239$	−3.69369	+	4.26274i	−0.238925	+	0.275734i	−0.862530	−	0.506005i	$-0.831122\pi$
$239$	−3.69369	+	4.26274i	−0.238925	+	0.275734i	0.623606	+	0.781739i	$0.285667\pi$
$240$		0			0
$241$	0.716936	+	4.98640i	0.0461819	+	0.321202i	0.999797	+	0.0201721i	$0.00642141\pi$
$241$	0.716936	+	4.98640i	0.0461819	+	0.321202i	−0.953615	+	0.301030i	$0.902669\pi$
$242$	0.509962	+	3.54687i	0.0327816	+	0.228001i
$243$		0			0
$244$	−2.64544	+	3.05300i	−0.169357	+	0.195448i
$245$	2.79199	−	6.11360i	0.178374	−	0.390584i
$246$		0			0
$247$	−14.7461	+	4.32984i	−0.938271	+	0.275501i
$248$	−2.63357	−	3.03930i	−0.167232	−	0.192995i
$249$		0			0
$250$	−3.71989	−	8.14543i	−0.235267	−	0.515162i
$251$	−2.51629	+	17.5012i	−0.158827	+	1.10466i	0.741973	+	0.670429i	$0.233890\pi$
$251$	−2.51629	+	17.5012i	−0.158827	+	1.10466i	−0.900800	+	0.434234i	$0.857019\pi$
$252$		0			0
$253$	18.1377	+	2.53810i	1.14031	+	0.159569i
$254$	5.62165			0.352734
$255$		0			0
$256$	0.415415	+	0.909632i	0.0259634	+	0.0568520i
$257$	21.1716	+	6.21655i	1.32065	+	0.387778i	0.864727	−	0.502242i	$-0.167491\pi$
$257$	21.1716	+	6.21655i	1.32065	+	0.387778i	0.455922	+	0.890020i	$0.349310\pi$
$258$		0			0
$259$	22.8971	−	6.72321i	1.42276	−	0.417760i
$260$	13.2715	+	8.52907i	0.823063	+	0.528951i
$261$		0			0
$262$	−5.22118	+	6.02556i	−0.322566	+	0.372261i
$263$	6.52680	−	4.19452i	0.402460	−	0.258645i	−0.323716	−	0.946154i	$-0.604932\pi$
$263$	6.52680	−	4.19452i	0.402460	−	0.258645i	0.726176	+	0.687509i	$0.241296\pi$
$264$		0			0
$265$	0.857290	+	5.96258i	0.0526629	+	0.366279i
$266$	4.35737	−	2.80031i	0.267168	−	0.171698i
$267$		0			0
$268$	5.32805	−	11.6668i	0.325462	−	0.712663i
$269$	−14.3175	−	9.20132i	−0.872955	−	0.561014i	0.0256999	−	0.999670i	$-0.491819\pi$
$269$	−14.3175	−	9.20132i	−0.872955	−	0.561014i	−0.898655	+	0.438655i	$0.855455\pi$
$270$		0			0
$271$	−7.62747	−	8.80257i	−0.463336	−	0.534718i	0.475210	−	0.879872i	$-0.342372\pi$
$271$	−7.62747	−	8.80257i	−0.463336	−	0.534718i	−0.938546	+	0.345154i	$0.887827\pi$
$272$	1.24982	+	0.366979i	0.0757812	+	0.0222514i
$273$		0			0
$274$	−0.294498	+	2.04828i	−0.0177913	+	0.123741i
$275$	−5.66382			−0.341541
$276$		0			0
$277$	16.8299			1.01121			0.505604	−	0.862766i	$-0.331270\pi$
$277$	16.8299			1.01121			0.505604	+	0.862766i	$0.331270\pi$
$278$	−1.85891	+	12.9290i	−0.111490	+	0.775430i
$279$		0			0
$280$	−5.10149	−	1.49793i	−0.304873	−	0.0895186i
$281$	−3.46454	−	3.99829i	−0.206677	−	0.238518i	0.642942	−	0.765915i	$-0.277714\pi$
$281$	−3.46454	−	3.99829i	−0.206677	−	0.238518i	−0.849619	+	0.527397i	$0.823168\pi$
$282$		0			0
$283$	−12.9297	−	8.30943i	−0.768592	−	0.493944i	0.0966376	−	0.995320i	$-0.469191\pi$
$283$	−12.9297	−	8.30943i	−0.768592	−	0.493944i	−0.865230	+	0.501375i	$0.832828\pi$
$284$	2.74640	−	6.01378i	0.162969	−	0.356852i
$285$		0			0
$286$	−19.9047	+	12.7920i	−1.17699	+	0.756406i
$287$	−1.27577	−	8.87317i	−0.0753062	−	0.523766i
$288$		0			0
$289$	−12.8739	+	8.27358i	−0.757291	+	0.486681i
$290$	11.9507	−	13.7918i	0.701768	−	0.809884i
$291$		0			0
$292$	−2.46060	−	1.58133i	−0.143996	−	0.0925404i
$293$	−10.3195	+	3.03008i	−0.602871	+	0.177019i	−0.568904	−	0.822404i	$-0.692632\pi$
$293$	−10.3195	+	3.03008i	−0.602871	+	0.177019i	−0.0339673	+	0.999423i	$0.510814\pi$
$294$		0			0
$295$	−1.49387	−	0.438641i	−0.0869767	−	0.0255387i
$296$	4.74743	+	10.3954i	0.275939	+	0.604222i
$297$		0			0
$298$	14.8452			0.859959
$299$	8.47881	+	28.4788i	0.490342	+	1.64697i
$300$		0			0
$301$	0.825496	−	5.74145i	0.0475808	−	0.330932i
$302$	−1.60063	−	3.50489i	−0.0921058	−	0.201683i
$303$		0			0
$304$	1.62436	+	1.87462i	0.0931637	+	0.107517i
$305$	9.86922	−	2.89786i	0.565110	−	0.165931i
$306$		0			0
$307$	−10.7114	+	23.4548i	−0.611333	+	1.33863i	0.310325	+	0.950631i	$0.399562\pi$
$307$	−10.7114	+	23.4548i	−0.611333	+	1.33863i	−0.921658	+	0.388003i	$0.873165\pi$
$308$	5.22204	−	6.02656i	0.297553	−	0.343395i
$309$		0			0
$310$	1.45726	+	10.1355i	0.0827670	+	0.575657i
$311$	2.32213	+	16.1508i	0.131676	+	0.915827i	0.943370	+	0.331743i	$0.107637\pi$
$311$	2.32213	+	16.1508i	0.131676	+	0.915827i	−0.811694	+	0.584083i	$0.801454\pi$
$312$		0			0
$313$	−8.18796	+	9.44940i	−0.462811	+	0.534112i	−0.938398	−	0.345557i	$-0.887690\pi$
$313$	−8.18796	+	9.44940i	−0.462811	+	0.534112i	0.475587	+	0.879669i	$0.342236\pi$
$314$	−9.40962	+	20.6042i	−0.531015	+	1.16276i
$315$		0			0
$316$	1.81033	−	0.531560i	0.101839	−	0.0299026i
$317$	−8.86597	−	10.2319i	−0.497963	−	0.574680i	0.450013	−	0.893022i	$-0.351419\pi$
$317$	−8.86597	−	10.2319i	−0.497963	−	0.574680i	−0.947976	+	0.318342i	$0.896874\pi$
$318$		0			0
$319$	11.3700	+	24.8969i	0.636600	+	1.39396i
$320$	0.362362	−	2.52028i	0.0202567	−	0.140888i
$321$		0			0
$322$	−5.44592	−	8.40423i	−0.303489	−	0.468349i
$323$	3.23101			0.179778
$324$		0			0
$325$	−3.81737	−	8.35886i	−0.211749	−	0.463666i
$326$	−18.1953	−	5.34263i	−1.00775	−	0.295901i
$327$		0			0
$328$	4.11908	−	1.20947i	0.227438	−	0.0667819i
$329$	−16.4099	−	10.5460i	−0.904709	−	0.581421i
$330$		0			0
$331$	−18.5543	+	21.4128i	−1.01984	+	1.17696i	−0.0357339	+	0.999361i	$0.511377\pi$
$331$	−18.5543	+	21.4128i	−1.01984	+	1.17696i	−0.984104	+	0.177594i	$0.943169\pi$
$332$	−8.78299	+	5.64449i	−0.482029	+	0.309781i
$333$		0			0
$334$	0.139416	+	0.969662i	0.00762853	+	0.0530576i
$335$	−27.4730	+	17.6558i	−1.50101	+	0.964640i
$336$		0			0
$337$	−6.01754	+	13.1766i	−0.327797	+	0.717774i	−0.999739	−	0.0228287i	$-0.992733\pi$
$337$	−6.01754	+	13.1766i	−0.327797	+	0.717774i	0.671943	+	0.740603i	$0.265460\pi$
$338$	−21.3582	−	13.7261i	−1.16173	−	0.746599i
$339$		0			0
$340$	−2.17193	−	2.50654i	−0.117789	−	0.135936i
$341$	−14.7355	−	4.32674i	−0.797973	−	0.234306i
$342$		0			0
$343$	2.86466	−	19.9241i	0.154677	−	1.07580i
$344$	2.77780			0.149769
$345$		0			0
$346$	−8.92203			−0.479651
$347$	4.68287	−	32.5701i	0.251390	−	1.74845i	−0.338496	−	0.940968i	$-0.609918\pi$
$347$	4.68287	−	32.5701i	0.251390	−	1.74845i	0.589886	−	0.807487i	$-0.299173\pi$
$348$		0			0
$349$	10.8999	+	3.20050i	0.583458	+	0.171319i	0.560124	−	0.828409i	$-0.310754\pi$
$349$	10.8999	+	3.20050i	0.583458	+	0.171319i	0.0233345	+	0.999728i	$0.492572\pi$
$350$	2.02812	+	2.34057i	0.108407	+	0.125109i
$351$		0			0
$352$	3.21259	+	2.06461i	0.171232	+	0.110044i
$353$	−0.624933	+	1.36841i	−0.0332618	+	0.0728332i	−0.925534	−	0.378665i	$-0.876383\pi$
$353$	−0.624933	+	1.36841i	−0.0332618	+	0.0728332i	0.892272	+	0.451499i	$0.149110\pi$
$354$		0			0
$355$	−14.1612	+	9.10087i	−0.751600	+	0.483024i
$356$	0.713318	+	4.96123i	0.0378058	+	0.262945i
$357$		0			0
$358$	−7.14352	+	4.59086i	−0.377547	+	0.242635i
$359$	13.3293	−	15.3828i	0.703492	−	0.811873i	−0.285728	−	0.958311i	$-0.592235\pi$
$359$	13.3293	−	15.3828i	0.703492	−	0.811873i	0.989220	+	0.146438i	$0.0467809\pi$
$360$		0			0
$361$	−10.8078	−	6.94575i	−0.568831	−	0.365566i
$362$	−0.515656	+	0.151410i	−0.0271023	+	0.00795794i
$363$		0			0
$364$	12.4138	+	3.64502i	0.650661	+	0.191051i
$365$	3.09377	+	6.77442i	0.161936	+	0.354589i
$366$		0			0
$367$	−12.2425			−0.639051			−0.319525	−	0.947578i	$-0.603523\pi$
$367$	−12.2425			−0.639051			−0.319525	+	0.947578i	$0.603523\pi$
$368$	3.61259	−	3.15423i	0.188319	−	0.164426i
$369$		0			0
$370$	4.14113	−	28.8022i	0.215287	−	1.49736i
$371$	2.05225	+	4.49380i	0.106548	+	0.233306i
$372$		0			0
$373$	−10.7554	−	12.4124i	−0.556892	−	0.642688i	0.405583	−	0.914058i	$-0.367069\pi$
$373$	−10.7554	−	12.4124i	−0.556892	−	0.642688i	−0.962475	+	0.271371i	$0.912523\pi$
$374$	4.77281	−	1.40142i	0.246796	−	0.0724659i
$375$		0			0
$376$	3.88060	−	8.49733i	0.200127	−	0.438216i
$377$	−29.0804	+	33.5606i	−1.49772	+	1.72846i
$378$		0			0
$379$	3.66573	+	25.4957i	0.188296	+	1.30963i	0.836419	+	0.548091i	$0.184645\pi$
$379$	3.66573	+	25.4957i	0.188296	+	1.30963i	−0.648123	+	0.761536i	$0.724446\pi$
$380$	−0.898830	−	6.25150i	−0.0461090	−	0.320695i
$381$		0			0
$382$	17.5712	−	20.2783i	0.899021	−	1.03753i
$383$	6.26867	−	13.7265i	0.320314	−	0.701390i	−0.679154	−	0.733996i	$-0.737653\pi$
$383$	6.26867	−	13.7265i	0.320314	−	0.701390i	0.999468	+	0.0326054i	$0.0103805\pi$
$384$		0			0
$385$	−19.4817	+	5.72033i	−0.992877	+	0.291535i
$386$	−0.919649	−	1.06133i	−0.0468089	−	0.0540204i
$387$		0			0
$388$	5.21177	+	11.4122i	0.264588	+	0.579366i
$389$	3.27106	−	22.7507i	0.165849	−	1.15351i	−0.721502	−	0.692412i	$-0.756548\pi$
$389$	3.27106	−	22.7507i	0.165849	−	1.15351i	0.887351	−	0.461094i	$-0.152543\pi$
$390$		0			0
$391$	−0.0235341	−	6.24691i	−0.00119017	−	0.315920i
$392$	2.63960			0.133320
$393$		0			0
$394$	−3.42498	−	7.49965i	−0.172548	−	0.377827i
$395$	−4.60945	−	1.35346i	−0.231927	−	0.0680998i
$396$		0			0
$397$	28.4653	−	8.35817i	1.42863	−	0.419484i	0.526217	−	0.850350i	$-0.323610\pi$
$397$	28.4653	−	8.35817i	1.42863	−	0.419484i	0.902416	+	0.430866i	$0.141792\pi$
$398$	2.62060	+	1.68416i	0.131359	+	0.0844193i
$399$		0			0
$400$	−0.971248	+	1.12088i	−0.0485624	+	0.0560440i
$401$	−24.5924	+	15.8045i	−1.22808	+	0.789241i	−0.983592	−	0.180410i	$-0.942258\pi$
$401$	−24.5924	+	15.8045i	−1.22808	+	0.789241i	−0.244492	+	0.969651i	$0.578621\pi$
$402$		0			0
$403$	−3.54606	−	24.6634i	−0.176642	−	1.22857i
$404$	−2.96333	+	1.90441i	−0.147431	+	0.0947481i
$405$		0			0
$406$	6.21722	−	13.6138i	0.308555	−	0.675642i
$407$	36.7140	+	23.5947i	1.81985	+	1.16954i
$408$		0			0
$409$	−22.0687	−	25.4686i	−1.09123	−	1.25934i	−0.963550	−	0.267528i	$-0.913793\pi$
$409$	−22.0687	−	25.4686i	−1.09123	−	1.25934i	−0.127677	−	0.991816i	$-0.540752\pi$
$410$	−10.4880	−	3.07956i	−0.517966	−	0.152089i
$411$		0			0
$412$	−0.222897	+	1.55028i	−0.0109813	+	0.0763769i
$413$	−1.27686			−0.0628301
$414$		0			0
$415$	26.5833			1.30492
$416$	−0.881761	+	6.13278i	−0.0432319	+	0.300684i
$417$		0			0
$418$	9.08877	+	2.66870i	0.444546	+	0.130531i
$419$	5.77988	+	6.67033i	0.282366	+	0.325867i	0.879160	−	0.476527i	$-0.158105\pi$
$419$	5.77988	+	6.67033i	0.282366	+	0.325867i	−0.596794	+	0.802394i	$0.703559\pi$
$420$		0			0
$421$	23.0285	+	14.7995i	1.12234	+	0.721283i	0.963947	−	0.266093i	$-0.0857329\pi$
$421$	23.0285	+	14.7995i	1.12234	+	0.721283i	0.158391	+	0.987376i	$0.449369\pi$
$422$	9.14235	−	20.0189i	0.445043	−	0.974507i
$423$		0			0
$424$	−1.99027	+	1.27907i	−0.0966561	+	0.0621171i
$425$	0.274938	+	1.91224i	0.0133365	+	0.0927572i
$426$		0			0
$427$	7.09640	−	4.56058i	0.343419	−	0.220702i
$428$	2.22861	−	2.57195i	0.107724	−	0.124320i
$429$		0			0
$430$	−5.95006	−	3.82387i	−0.286937	−	0.184403i
$431$	−28.6589	+	8.41502i	−1.38045	+	0.405337i	−0.885926	−	0.463826i	$-0.846476\pi$
$431$	−28.6589	+	8.41502i	−1.38045	+	0.405337i	−0.494525	+	0.869163i	$0.664658\pi$
$432$		0			0
$433$	−26.2406	−	7.70492i	−1.26104	−	0.370275i	−0.418159	−	0.908374i	$-0.637325\pi$
$433$	−26.2406	−	7.70492i	−1.26104	−	0.370275i	−0.842882	+	0.538099i	$0.819143\pi$
$434$	3.48851	+	7.63878i	0.167454	+	0.366673i
$435$		0			0
$436$	−8.62324			−0.412978
$437$	6.39368	−	10.0317i	0.305851	−	0.479879i
$438$		0			0
$439$	1.86711	−	12.9861i	0.0891124	−	0.619791i	−0.895503	−	0.445055i	$-0.853184\pi$
$439$	1.86711	−	12.9861i	0.0891124	−	0.619791i	0.984615	−	0.174735i	$-0.0559069\pi$
$440$	−4.03927	−	8.84477i	−0.192565	−	0.421658i
$441$		0			0
$442$	5.28511	+	6.09934i	0.251387	+	0.290116i
$443$	−10.3339	+	3.03431i	−0.490979	+	0.144164i	−0.517845	−	0.855475i	$-0.673265\pi$
$443$	−10.3339	+	3.03431i	−0.490979	+	0.144164i	0.0268659	+	0.999639i	$0.491447\pi$
$444$		0			0
$445$	5.30161	−	11.6089i	0.251320	−	0.550315i
$446$	8.06117	−	9.30308i	0.381707	−	0.440514i
$447$		0			0
$448$	−0.297176	−	2.06690i	−0.0140402	−	0.0976519i
$449$	0.667871	+	4.64515i	0.0315188	+	0.219218i	0.999493	−	0.0318306i	$-0.0101337\pi$
$449$	0.667871	+	4.64515i	0.0315188	+	0.219218i	−0.967974	+	0.251049i	$0.919225\pi$
$450$		0			0
$451$	10.7358	−	12.3898i	0.505531	−	0.583414i
$452$	1.48146	−	3.24395i	0.0696821	−	0.152583i
$453$		0			0
$454$	−5.11649	+	1.50234i	−0.240129	+	0.0705082i
$455$	−21.5727	−	24.8962i	−1.01134	−	1.16715i
$456$		0			0
$457$	2.88119	+	6.30892i	0.134776	+	0.295119i	0.964972	−	0.262353i	$-0.0844986\pi$
$457$	2.88119	+	6.30892i	0.134776	+	0.295119i	−0.830196	+	0.557472i	$0.811771\pi$
$458$	2.00763	−	13.9634i	0.0938105	−	0.652467i
$459$		0			0
$460$	−12.0802	+	1.78335i	−0.563243	+	0.0831491i
$461$	21.3273			0.993312			0.496656	−	0.867947i	$-0.334561\pi$
$461$	21.3273			0.993312			0.496656	+	0.867947i	$0.334561\pi$
$462$		0			0
$463$	−2.66484	−	5.83519i	−0.123846	−	0.271185i	0.837546	−	0.546366i	$-0.183989\pi$
$463$	−2.66484	−	5.83519i	−0.123846	−	0.271185i	−0.961392	+	0.275182i	$0.911262\pi$
$464$	6.87690	+	2.01924i	0.319252	+	0.0937409i
$465$		0			0
$466$	−16.4868	+	4.84095i	−0.763734	+	0.224253i
$467$	−12.1748	−	7.82429i	−0.563384	−	0.362065i	0.227739	−	0.973722i	$-0.426867\pi$
$467$	−12.1748	−	7.82429i	−0.563384	−	0.362065i	−0.791123	+	0.611657i	$0.790503\pi$
$468$		0			0
$469$	−17.5387	+	20.2408i	−0.809863	+	0.934632i
$470$	−20.0095	+	12.8593i	−0.922970	+	0.593157i
$471$		0			0
$472$	−0.0870222	−	0.605253i	−0.00400552	−	0.0278590i
$473$	8.92395	−	5.73507i	0.410324	−	0.263699i
$474$		0			0
$475$	−1.52826	+	3.34643i	−0.0701215	+	0.153545i
$476$	−2.28820	−	1.47054i	−0.104880	−	0.0674020i
$477$		0			0
$478$	3.69369	+	4.26274i	0.168945	+	0.194973i
$479$	−5.15751	−	1.51438i	−0.235653	−	0.0691938i	0.161774	−	0.986828i	$-0.448278\pi$
$479$	−5.15751	−	1.51438i	−0.235653	−	0.0691938i	−0.397427	+	0.917634i	$0.630097\pi$
$480$		0			0
$481$	−10.0769	+	70.0864i	−0.459467	+	3.19567i
$482$	5.03768			0.229460
$483$		0			0
$484$	3.58334			0.162879
$485$	4.54617	−	31.6193i	0.206431	−	1.43576i
$486$		0			0
$487$	−3.08891	−	0.906986i	−0.139972	−	0.0410994i	0.210996	−	0.977487i	$-0.432329\pi$
$487$	−3.08891	−	0.906986i	−0.139972	−	0.0410994i	−0.350968	+	0.936387i	$0.614147\pi$
$488$	2.64544	+	3.05300i	0.119753	+	0.138203i
$489$		0			0
$490$	−5.65403	−	3.63363i	−0.255423	−	0.164151i
$491$	−12.4938	+	27.3575i	−0.563836	+	1.23463i	0.386179	+	0.922424i	$0.373795\pi$
$491$	−12.4938	+	27.3575i	−0.563836	+	1.23463i	−0.950015	+	0.312204i	$0.898933\pi$
$492$		0			0
$493$	7.85384	−	5.04736i	0.353719	−	0.227322i
$494$	2.18718	+	15.2122i	0.0984061	+	0.684429i
$495$		0			0
$496$	−3.38316	+	2.17422i	−0.151908	+	0.0976255i
$497$	−9.04052	+	10.4333i	−0.405523	+	0.467998i
$498$		0			0
$499$	14.9310	+	9.59557i	0.668403	+	0.429557i	0.830350	−	0.557243i	$-0.188141\pi$
$499$	14.9310	+	9.59557i	0.668403	+	0.429557i	−0.161946	+	0.986800i	$0.551777\pi$
$500$	−8.59191	+	2.52281i	−0.384242	+	0.112824i
$501$		0			0
$502$	16.9649	+	4.98135i	0.757182	+	0.222329i
$503$	−10.2877	−	22.5269i	−0.458705	−	1.00442i	−0.987781	−	0.155850i	$-0.950188\pi$
$503$	−10.2877	−	22.5269i	−0.458705	−	1.00442i	0.529076	−	0.848575i	$-0.322539\pi$
$504$		0			0
$505$	8.96902			0.399116
$506$	5.09352	−	17.5918i	0.226435	−	0.782053i
$507$		0			0
$508$	0.800045	−	5.56443i	0.0354963	−	0.246882i
$509$	12.8953	+	28.2367i	0.571572	+	1.25157i	0.945956	+	0.324295i	$0.105127\pi$
$509$	12.8953	+	28.2367i	0.571572	+	1.25157i	−0.374384	+	0.927274i	$0.622146\pi$
$510$		0			0
$511$	3.99969	+	4.61588i	0.176936	+	0.204195i
$512$	0.959493	−	0.281733i	0.0424040	−	0.0124509i
$513$		0			0
$514$	9.16631	−	20.0714i	0.404308	−	0.885312i
$515$	2.61153	−	3.01387i	0.115078	−	0.132807i
$516$		0			0
$517$	−5.07686	−	35.3104i	−0.223280	−	1.55295i
$518$	−3.39617	−	23.6209i	−0.149219	−	1.03784i
$519$		0			0
$520$	10.3310	−	11.9226i	0.453044	−	0.522841i
$521$	−13.8381	+	30.3013i	−0.606259	+	1.32752i	0.318844	+	0.947807i	$0.396705\pi$
$521$	−13.8381	+	30.3013i	−0.606259	+	1.32752i	−0.925103	+	0.379715i	$0.876022\pi$
$522$		0			0
$523$	−29.7832	+	8.74514i	−1.30233	+	0.382398i	−0.858085	−	0.513507i	$-0.828346\pi$
$523$	−29.7832	+	8.74514i	−1.30233	+	0.382398i	−0.444244	+	0.895906i	$0.646528\pi$
$524$	5.22118	+	6.02556i	0.228088	+	0.263228i
$525$		0			0
$526$	−3.22296	−	7.05731i	−0.140528	−	0.307713i
$527$	−0.745503	+	5.18509i	−0.0324746	+	0.225866i
$528$		0			0
$529$	−19.4420	−	12.2886i	−0.845303	−	0.534287i
$530$	6.02390			0.261661
$531$		0			0
$532$	−2.15169	−	4.71154i	−0.0932876	−	0.204271i
$533$	25.5212	+	7.49370i	1.10545	+	0.324588i
$534$		0			0
$535$	−8.31418	+	2.44126i	−0.359453	+	0.105545i
$536$	−10.7898	−	6.93418i	−0.466048	−	0.299511i
$537$		0			0
$538$	−11.1453	+	12.8623i	−0.480506	+	0.554534i
$539$	8.47997	−	5.44975i	0.365258	−	0.234737i
$540$		0			0
$541$	0.731645	+	5.08870i	0.0314559	+	0.218780i	0.999486	−	0.0320528i	$-0.0102045\pi$
$541$	0.731645	+	5.08870i	0.0314559	+	0.218780i	−0.968030	+	0.250833i	$0.919295\pi$
$542$	−9.79847	+	6.29709i	−0.420880	+	0.270483i
$543$		0			0
$544$	0.541111	−	1.18487i	0.0231999	−	0.0508008i
$545$	18.4710	+	11.8706i	0.791210	+	0.508480i
$546$		0			0
$547$	−12.4508	−	14.3689i	−0.532356	−	0.614371i	0.424325	−	0.905510i	$-0.360511\pi$
$547$	−12.4508	−	14.3689i	−0.532356	−	0.614371i	−0.956681	+	0.291139i	$0.905966\pi$
$548$	1.98552	+	0.583001i	0.0848172	+	0.0249046i
$549$		0			0
$550$	−0.806046	+	5.60617i	−0.0343699	+	0.239048i
$551$	17.7781			0.757373
$552$		0			0
$553$	−3.93983			−0.167539
$554$	2.39514	−	16.6586i	0.101760	−	0.707754i
$555$		0			0
$556$	12.5329	+	3.67998i	0.531511	+	0.156066i
$557$	7.90600	+	9.12401i	0.334988	+	0.386597i	0.898105	−	0.439780i	$-0.144944\pi$
$557$	7.90600	+	9.12401i	0.334988	+	0.386597i	−0.563118	+	0.826377i	$0.690398\pi$
$558$		0			0
$559$	14.4787	+	9.30489i	0.612383	+	0.393555i
$560$	−2.20870	+	4.83639i	−0.0933348	+	0.204375i
$561$		0			0
$562$	−4.45065	+	2.86026i	−0.187739	+	0.120653i
$563$	−3.02219	−	21.0198i	−0.127370	−	0.885879i	−0.948869	−	0.315669i	$-0.897771\pi$
$563$	−3.02219	−	21.0198i	−0.127370	−	0.885879i	0.821499	−	0.570210i	$-0.193138\pi$
$564$		0			0
$565$	−7.63885	+	4.90919i	−0.321369	+	0.206531i
$566$	−10.0649	+	11.6156i	−0.423061	+	0.488238i
$567$		0			0
$568$	−5.56171	−	3.57430i	−0.233364	−	0.149974i
$569$	11.2469	−	3.30239i	0.471496	−	0.138444i	−0.0373485	−	0.999302i	$-0.511891\pi$
$569$	11.2469	−	3.30239i	0.471496	−	0.138444i	0.508844	+	0.860859i	$0.330073\pi$
$570$		0			0
$571$	42.5321	+	12.4886i	1.77991	+	0.522630i	0.995255	−	0.0972968i	$-0.0310196\pi$
$571$	42.5321	+	12.4886i	1.77991	+	0.522630i	0.784660	+	0.619927i	$0.212838\pi$
$572$	9.82904	+	21.5226i	0.410973	+	0.899905i
$573$		0			0
$574$	−8.96441			−0.374167
$575$	6.48118	+	2.93040i	0.270284	+	0.122206i
$576$		0			0
$577$	−4.25824	+	29.6167i	−0.177273	+	1.23296i	0.685766	+	0.727822i	$0.259467\pi$
$577$	−4.25824	+	29.6167i	−0.177273	+	1.23296i	−0.863039	+	0.505138i	$0.831442\pi$
$578$	6.35721	+	13.9204i	0.264425	+	0.579011i
$579$		0			0
$580$	−11.9507	−	13.7918i	−0.496225	−	0.572674i
$581$	20.9180	−	6.14208i	0.867825	−	0.254816i
$582$		0			0
$583$	−3.75315	+	8.21825i	−0.155440	+	0.340365i
$584$	−1.91542	+	2.21051i	−0.0792604	+	0.0914714i
$585$		0			0
$586$	1.53062	+	10.6457i	0.0632292	+	0.439769i
$587$	1.50360	+	10.4578i	0.0620602	+	0.431638i	0.997037	+	0.0769284i	$0.0245113\pi$
$587$	1.50360	+	10.4578i	0.0620602	+	0.431638i	−0.934976	+	0.354710i	$0.884580\pi$
$588$		0			0
$589$	−6.53249	+	7.53889i	−0.269167	+	0.310635i
$590$	−0.646777	+	1.41624i	−0.0266274	+	0.0583058i
$591$		0			0
$592$	10.9652	−	3.21969i	0.450669	−	0.132328i
$593$	5.66384	+	6.53642i	0.232586	+	0.268419i	0.860030	−	0.510243i	$-0.170444\pi$
$593$	5.66384	+	6.53642i	0.232586	+	0.268419i	−0.627444	+	0.778661i	$0.715899\pi$
$594$		0			0
$595$	2.87701	+	6.29978i	0.117946	+	0.258266i
$596$	2.11269	−	14.6941i	0.0865393	−	0.601894i
$597$		0			0
$598$	29.3956	−	4.33955i	1.20208	−	0.177457i
$599$	−20.5800			−0.840877			−0.420439	−	0.907321i	$-0.638124\pi$
$599$	−20.5800			−0.840877			−0.420439	+	0.907321i	$0.638124\pi$
$600$		0			0
$601$	7.34180	+	16.0763i	0.299478	+	0.655766i	0.998222	−	0.0596061i	$-0.0189845\pi$
$601$	7.34180	+	16.0763i	0.299478	+	0.655766i	−0.698744	+	0.715372i	$0.746257\pi$
$602$	−5.56553	−	1.63419i	−0.226834	−	0.0666045i
$603$		0			0
$604$	−3.69700	+	1.08554i	−0.150429	+	0.0441699i
$605$	−7.67551	−	4.93275i	−0.312054	−	0.200545i
$606$		0			0
$607$	27.4879	−	31.7227i	1.11570	−	1.28758i	0.162010	−	0.986789i	$-0.448202\pi$
$607$	27.4879	−	31.7227i	1.11570	−	1.28758i	0.953689	−	0.300795i	$-0.0972521\pi$
$608$	2.08671	−	1.34105i	0.0846272	−	0.0543866i
$609$		0			0
$610$	−1.46383	−	10.1812i	−0.0592688	−	0.412224i
$611$	48.6905	−	31.2915i	1.96981	−	1.26592i
$612$		0			0
$613$	7.45006	−	16.3134i	0.300905	−	0.658890i	−0.697425	−	0.716658i	$-0.745671\pi$
$613$	7.45006	−	16.3134i	0.300905	−	0.658890i	0.998330	+	0.0577675i	$0.0183982\pi$
$614$	21.6916	+	13.9404i	0.875403	+	0.562587i
$615$		0			0
$616$	−5.22204	−	6.02656i	−0.210402	−	0.242817i
$617$	2.83913	+	0.833643i	0.114299	+	0.0335612i	0.338382	−	0.941009i	$-0.390120\pi$
$617$	2.83913	+	0.833643i	0.114299	+	0.0335612i	−0.224083	+	0.974570i	$0.571939\pi$
$618$		0			0
$619$	−3.98738	+	27.7328i	−0.160266	+	1.11468i	0.737865	+	0.674949i	$0.235834\pi$
$619$	−3.98738	+	27.7328i	−0.160266	+	1.11468i	−0.898131	+	0.439728i	$0.855075\pi$
$620$	10.2397			0.411237
$621$		0			0
$622$	16.3169			0.654247
$623$	1.48952	−	10.3598i	0.0596763	−	0.415058i
$624$		0			0
$625$	28.9920	+	8.51283i	1.15968	+	0.340513i
$626$	8.18796	+	9.44940i	0.327257	+	0.377674i
$627$		0			0
$628$	19.0553	+	12.2461i	0.760391	+	0.488673i
$629$	6.18391	−	13.5409i	0.246569	−	0.539910i
$630$		0			0
$631$	−2.05053	+	1.31779i	−0.0816302	+	0.0524605i	−0.580819	−	0.814033i	$-0.697268\pi$
$631$	−2.05053	+	1.31779i	−0.0816302	+	0.0524605i	0.499189	+	0.866493i	$0.333631\pi$
$632$	−0.268513	−	1.86755i	−0.0106809	−	0.0742871i
$633$		0			0
$634$	−11.3895	+	7.31958i	−0.452335	+	0.290698i
$635$	−9.37358	+	10.8177i	−0.371979	+	0.429287i
$636$		0			0
$637$	13.7583	+	8.84195i	0.545126	+	0.350331i
$638$	26.2616	−	7.71110i	1.03971	−	0.305286i
$639$		0			0
$640$	−2.44306	−	0.717348i	−0.0965705	−	0.0283557i
$641$	−1.33060	−	2.91362i	−0.0525557	−	0.115081i	0.881532	−	0.472124i	$-0.156512\pi$
$641$	−1.33060	−	2.91362i	−0.0525557	−	0.115081i	−0.934088	+	0.357043i	$0.883785\pi$
$642$		0			0
$643$	35.8609			1.41422			0.707108	−	0.707105i	$-0.249999\pi$
$643$	35.8609			1.41422			0.707108	+	0.707105i	$0.249999\pi$
$644$	−9.09372	+	4.19444i	−0.358343	+	0.165284i
$645$		0			0
$646$	0.459821	−	3.19813i	0.0180914	−	0.125829i
$647$	−4.09842	−	8.97429i	−0.161126	−	0.352816i	0.811800	−	0.583936i	$-0.198488\pi$
$647$	−4.09842	−	8.97429i	−0.161126	−	0.352816i	−0.972925	+	0.231120i	$0.925761\pi$
$648$		0			0
$649$	−1.52917	−	1.76476i	−0.0600254	−	0.0692730i
$650$	−8.81705	+	2.58892i	−0.345833	+	0.101546i
$651$		0			0
$652$	−7.87772	+	17.2498i	−0.308515	+	0.675554i
$653$	−8.37325	+	9.66324i	−0.327671	+	0.378152i	−0.895551	−	0.444959i	$-0.853218\pi$
$653$	−8.37325	+	9.66324i	−0.327671	+	0.378152i	0.567880	+	0.823111i	$0.307764\pi$
$654$		0			0
$655$	−2.88910	−	20.0941i	−0.112886	−	0.785143i
$656$	−0.610955	−	4.24928i	−0.0238538	−	0.165907i
$657$		0			0
$658$	−12.7741	+	14.7420i	−0.497984	+	0.574705i
$659$	2.12193	−	4.64638i	0.0826587	−	0.180997i	−0.863790	−	0.503853i	$-0.831915\pi$
$659$	2.12193	−	4.64638i	0.0826587	−	0.180997i	0.946448	+	0.322855i	$0.104643\pi$
$660$		0			0
$661$	25.8606	−	7.59336i	1.00586	−	0.295348i	0.263002	−	0.964795i	$-0.415287\pi$
$661$	25.8606	−	7.59336i	1.00586	−	0.295348i	0.742859	+	0.669448i	$0.233469\pi$
$662$	18.5543	+	21.4128i	0.721134	+	0.832233i
$663$		0			0
$664$	4.33708	+	9.49689i	0.168311	+	0.368551i
$665$	−1.87690	+	13.0541i	−0.0727829	+	0.506216i
$666$		0			0
$667$	−0.129492	−	34.3726i	−0.00501396	−	1.33091i
$668$	0.979634			0.0379032
$669$		0			0
$670$	13.5663	+	29.7060i	0.524111	+	1.14764i
$671$	14.8019	+	4.34624i	0.571423	+	0.167785i
$672$		0			0
$673$	−26.0210	+	7.64046i	−1.00304	+	0.294518i	−0.741702	−	0.670730i	$-0.765981\pi$
$673$	−26.0210	+	7.64046i	−1.00304	+	0.294518i	−0.261335	+	0.965248i	$0.584163\pi$
$674$	12.1861	+	7.83152i	0.469390	+	0.301659i
$675$		0			0
$676$	−16.6259	+	19.1873i	−0.639459	+	0.737974i
$677$	−23.7332	+	15.2524i	−0.912140	+	0.586197i	−0.910367	−	0.413802i	$-0.864201\pi$
$677$	−23.7332	+	15.2524i	−0.912140	+	0.586197i	−0.00177304	+	0.999998i	$0.500564\pi$
$678$		0			0
$679$	−3.72835	−	25.9312i	−0.143081	−	0.995149i
$680$	−2.79013	+	1.79310i	−0.106996	+	0.0687624i
$681$		0			0
$682$	−6.37978	+	13.9698i	−0.244294	+	0.534930i
$683$	1.90711	+	1.22563i	0.0729736	+	0.0468973i	0.576619	−	0.817013i	$-0.304372\pi$
$683$	1.90711	+	1.22563i	0.0729736	+	0.0468973i	−0.503645	+	0.863911i	$0.668008\pi$
$684$		0			0
$685$	−3.45043	−	3.98201i	−0.131834	−	0.152145i
$686$	−19.3136	−	5.67099i	−0.737398	−	0.216520i
$687$		0			0
$688$	0.395323	−	2.74953i	0.0150715	−	0.104825i
$689$	−14.6584			−0.558439
$690$		0			0
$691$	2.62969			0.100038			0.0500191	−	0.998748i	$-0.484072\pi$
$691$	2.62969			0.100038			0.0500191	+	0.998748i	$0.484072\pi$
$692$	−1.26974	+	8.83122i	−0.0482682	+	0.335713i
$693$		0			0
$694$	−31.5721	−	9.27042i	−1.19846	−	0.351900i
$695$	−21.7796	−	25.1350i	−0.826147	−	0.953424i
$696$		0			0
$697$	−4.70425	−	3.02324i	−0.178186	−	0.114513i
$698$	4.71914	−	10.3335i	0.178622	−	0.391128i
$699$		0			0
$700$	2.60538	−	1.67438i	0.0984741	−	0.0632854i
$701$	−2.45078	−	17.0456i	−0.0925647	−	0.643802i	−0.982299	−	0.187322i	$-0.940019\pi$
$701$	−2.45078	−	17.0456i	−0.0925647	−	0.643802i	0.889734	−	0.456480i	$-0.150890\pi$
$702$		0			0
$703$	23.8472	−	15.3257i	0.899416	−	0.578019i
$704$	2.50079	−	2.88607i	0.0942521	−	0.108773i
$705$		0			0
$706$	1.26555	+	0.813317i	0.0476295	+	0.0306096i
$707$	7.05760	−	2.07230i	0.265428	−	0.0779368i
$708$		0			0
$709$	−34.6715	−	10.1805i	−1.30212	−	0.382336i	−0.444109	−	0.895973i	$-0.646480\pi$
$709$	−34.6715	−	10.1805i	−1.30212	−	0.382336i	−0.858008	+	0.513637i	$0.828298\pi$
$710$	6.99289	+	15.3123i	0.262438	+	0.574660i
$711$		0			0
$712$	5.01225			0.187842
$713$	14.6234	+	12.5751i	0.547652	+	0.470942i
$714$		0			0
$715$	8.57377	−	59.6319i	0.320641	−	2.23011i
$716$	3.52750	+	7.72416i	0.131829	+	0.288665i
$717$		0			0
$718$	−13.3293	−	15.3828i	−0.497444	−	0.574081i
$719$	26.8795	−	7.89253i	1.00244	−	0.294342i	0.260980	−	0.965344i	$-0.415954\pi$
$719$	26.8795	−	7.89253i	1.00244	−	0.294342i	0.741455	+	0.671003i	$0.234136\pi$
$720$		0			0
$721$	1.35862	−	2.97497i	0.0505977	−	0.110794i
$722$	−8.41316	+	9.70930i	−0.313105	+	0.361343i
$723$		0			0
$724$	0.0764836	+	0.531955i	0.00284249	+	0.0197699i
$725$	1.51280	+	10.5218i	0.0561841	+	0.390769i
$726$		0			0
$727$	−31.8709	+	36.7809i	−1.18202	+	1.36413i	−0.265520	+	0.964105i	$0.585544\pi$
$727$	−31.8709	+	36.7809i	−1.18202	+	1.36413i	−0.916505	+	0.400024i	$0.869002\pi$
$728$	5.37459	−	11.7687i	0.199196	−	0.436178i
$729$		0			0
$730$	7.14576	−	2.09818i	0.264476	−	0.0776573i
$731$	−2.36949	−	2.73454i	−0.0876388	−	0.101141i
$732$		0			0
$733$	−1.42468	−	3.11960i	−0.0526216	−	0.115225i	0.881495	−	0.472194i	$-0.156538\pi$
$733$	−1.42468	−	3.11960i	−0.0526216	−	0.115225i	−0.934116	+	0.356968i	$0.883810\pi$
$734$	−1.74228	+	12.1178i	−0.0643088	+	0.447278i
$735$		0			0
$736$	−2.60800	−	4.02471i	−0.0961323	−	0.148353i
$737$	−48.9795			−1.80418
$738$		0			0
$739$	−5.04671	−	11.0508i	−0.185646	−	0.406509i	0.793810	−	0.608166i	$-0.208095\pi$
$739$	−5.04671	−	11.0508i	−0.185646	−	0.406509i	−0.979456	+	0.201657i	$0.935367\pi$
$740$	−27.9197	−	8.19797i	−1.02635	−	0.301363i
$741$		0			0
$742$	4.74013	−	1.39183i	0.174015	−	0.0510956i
$743$	37.8162	+	24.3030i	1.38734	+	0.891590i	0.999545	−	0.0301545i	$-0.00959992\pi$
$743$	37.8162	+	24.3030i	1.38734	+	0.891590i	0.387797	+	0.921745i	$0.373236\pi$
$744$		0			0
$745$	−24.7530	+	28.5665i	−0.906879	+	1.04659i
$746$	−13.8167	+	8.87943i	−0.505864	+	0.325099i
$747$		0			0
$748$	−0.707918	−	4.92368i	−0.0258840	−	0.180027i
$749$	−5.97826	+	3.84200i	−0.218441	+	0.140383i
$750$		0			0
$751$	2.56678	−	5.62046i	0.0936631	−	0.205094i	−0.857002	−	0.515314i	$-0.827675\pi$
$751$	2.56678	−	5.62046i	0.0936631	−	0.205094i	0.950665	+	0.310220i	$0.100403\pi$
$752$	−7.85857	−	5.05040i	−0.286573	−	0.184169i
$753$		0			0
$754$	29.0804	+	33.5606i	1.05905	+	1.22220i
$755$	9.41331	+	2.76400i	0.342585	+	0.100592i
$756$		0			0
$757$	−1.95623	+	13.6059i	−0.0711003	+	0.494513i	0.922892	+	0.385060i	$0.125819\pi$
$757$	−1.95623	+	13.6059i	−0.0711003	+	0.494513i	−0.993992	+	0.109454i	$0.965090\pi$
$758$	25.7579			0.935569
$759$		0			0
$760$	−6.31578			−0.229098
$761$	−7.27388	+	50.5910i	−0.263678	+	1.83392i	0.240894	+	0.970551i	$0.422559\pi$
$761$	−7.27388	+	50.5910i	−0.263678	+	1.83392i	−0.504572	+	0.863369i	$0.668350\pi$
$762$		0			0
$763$	17.2773	+	5.07306i	0.625479	+	0.183657i
$764$	−17.5712	−	20.2783i	−0.635704	−	0.733642i
$765$		0			0
$766$	−12.6946	−	8.15835i	−0.458676	−	0.294773i
$767$	1.57385	−	3.44624i	0.0568283	−	0.124437i
$768$		0			0
$769$	13.1308	−	8.43865i	0.473509	−	0.304306i	−0.282035	−	0.959404i	$-0.591009\pi$
$769$	13.1308	−	8.43865i	0.473509	−	0.304306i	0.755543	+	0.655099i	$0.227373\pi$
$770$	2.88958	+	20.0974i	0.104133	+	0.724262i
$771$		0			0
$772$	−1.18141	+	0.759245i	−0.0425198	+	0.0273258i
$773$	−1.72841	+	1.99469i	−0.0621666	+	0.0717441i	−0.785981	−	0.618251i	$-0.787842\pi$
$773$	−1.72841	+	1.99469i	−0.0621666	+	0.0717441i	0.723814	+	0.689995i	$0.242387\pi$
$774$		0			0
$775$	−5.01768	−	3.22467i	−0.180240	−	0.115833i
$776$	12.0377	−	3.53460i	0.432130	−	0.126885i
$777$		0			0
$778$	−22.0536	−	6.47552i	−0.790660	−	0.232159i
$779$	−4.42360	−	9.68633i	−0.158492	−	0.347049i
$780$		0			0
$781$	−25.2470			−0.903409
$782$	−6.18667	−	0.865733i	−0.221235	−	0.0309586i
$783$		0			0
$784$	0.375655	−	2.61274i	0.0134162	−	0.0933121i
$785$	−23.9588	−	52.4624i	−0.855125	−	1.87246i
$786$		0			0
$787$	−23.9564	−	27.6471i	−0.853953	−	0.985514i	0.146040	−	0.989279i	$-0.453347\pi$
$787$	−23.9564	−	27.6471i	−0.853953	−	0.985514i	−0.999993	+	0.00376486i	$0.998802\pi$
$788$	−7.91074	+	2.32280i	−0.281809	+	0.0827465i
$789$		0			0
$790$	−1.99567	+	4.36992i	−0.0710029	+	0.155475i
$791$	−4.87664	+	5.62794i	−0.173393	+	0.200106i
$792$		0			0
$793$	3.56204	+	24.7746i	0.126492	+	0.879770i
$794$	−4.22206	−	29.3651i	−0.149835	−	1.04213i
$795$		0			0
$796$	2.03997	−	2.35425i	0.0723047	−	0.0834441i
$797$	8.18044	−	17.9127i	0.289766	−	0.634499i	−0.707633	−	0.706580i	$-0.750237\pi$
$797$	8.18044	−	17.9127i	0.289766	−	0.634499i	0.997399	+	0.0720814i	$0.0229641\pi$
$798$		0			0
$799$	−11.6752	+	3.42814i	−0.413038	+	0.121279i
$800$	0.971248	+	1.12088i	0.0343388	+	0.0396291i
$801$		0			0
$802$	12.1438	+	26.5913i	0.428813	+	0.938970i
$803$	−1.58962	+	11.0560i	−0.0560964	+	0.390159i
$804$		0			0
$805$	25.2527	+	3.53375i	0.890042	+	0.124548i
$806$	−24.9170			−0.877664
$807$		0			0
$808$	1.46330	+	3.20419i	0.0514789	+	0.112723i
$809$	−13.0460	−	3.83066i	−0.458674	−	0.134679i	0.0442295	−	0.999021i	$-0.485917\pi$
$809$	−13.0460	−	3.83066i	−0.458674	−	0.134679i	−0.502904	+	0.864343i	$0.667735\pi$
$810$		0			0
$811$	21.7495	−	6.38622i	0.763728	−	0.224251i	0.123405	−	0.992356i	$-0.460619\pi$
$811$	21.7495	−	6.38622i	0.763728	−	0.224251i	0.640323	+	0.768106i	$0.278801\pi$
$812$	−12.5904	−	8.09138i	−0.441838	−	0.283952i
$813$		0			0
$814$	28.5795	−	32.9825i	1.00171	−	1.15603i
$815$	40.6198	−	26.1048i	1.42285	−	0.914410i
$816$		0			0
$817$	−0.980588	−	6.82014i	−0.0343064	−	0.238606i
$818$	−28.3501	+	18.2195i	−0.991239	+	0.637030i
$819$		0			0
$820$	−4.54081	+	9.94299i	−0.158572	+	0.347224i
$821$	13.8794	+	8.91972i	0.484393	+	0.311300i	0.759947	−	0.649985i	$-0.225225\pi$
$821$	13.8794	+	8.91972i	0.484393	+	0.311300i	−0.275554	+	0.961286i	$0.588861\pi$
$822$		0			0
$823$	20.0185	+	23.1025i	0.697800	+	0.805304i	0.988454	−	0.151524i	$-0.0484182\pi$
$823$	20.0185	+	23.1025i	0.697800	+	0.805304i	−0.290654	+	0.956828i	$0.593873\pi$
$824$	1.50278	+	0.441256i	0.0523518	+	0.0153719i
$825$		0			0
$826$	−0.181716	+	1.26386i	−0.00632270	+	0.0439754i
$827$	−24.1171			−0.838633			−0.419316	−	0.907840i	$-0.637730\pi$
$827$	−24.1171			−0.838633			−0.419316	+	0.907840i	$0.637730\pi$
$828$		0			0
$829$	−11.3407			−0.393879			−0.196939	−	0.980416i	$-0.563100\pi$
$829$	−11.3407			−0.393879			−0.196939	+	0.980416i	$0.563100\pi$
$830$	3.78319	−	26.3127i	0.131316	−	0.913326i
$831$		0			0
$832$	5.94487	+	1.74557i	0.206101	+	0.0605168i
$833$	−2.25160	−	2.59849i	−0.0780135	−	0.0900324i
$834$		0			0
$835$	−2.09838	−	1.34854i	−0.0726173	−	0.0466683i
$836$	3.93501	−	8.61646i	0.136095	−	0.298006i
$837$		0			0
$838$	7.42500	−	4.77176i	0.256492	−	0.164838i
$839$	−2.68009	−	18.6404i	−0.0925270	−	0.643540i	−0.982325	−	0.187185i	$-0.940064\pi$
$839$	−2.68009	−	18.6404i	−0.0925270	−	0.643540i	0.889798	−	0.456355i	$-0.150845\pi$
$840$		0			0
$841$	18.8181	−	12.0937i	0.648900	−	0.417023i
$842$	17.9262	−	20.6879i	0.617776	−	0.712951i
$843$		0			0
$844$	−18.5141	−	11.8983i	−0.637281	−	0.409556i
$845$	62.0256	−	18.2124i	2.13375	−	0.626524i
$846$		0			0
$847$	−7.17947	−	2.10808i	−0.246690	−	0.0724346i
$848$	0.982805	+	2.15204i	0.0337497	+	0.0739014i
$849$		0			0
$850$	1.93190			0.0662637
$851$	−29.8047	−	45.9951i	−1.02169	−	1.57669i
$852$		0			0
$853$	−0.350759	+	2.43958i	−0.0120098	+	0.0835297i	−0.994945	−	0.100423i	$-0.967980\pi$
$853$	−0.350759	+	2.43958i	−0.0120098	+	0.0835297i	0.982935	+	0.183953i	$0.0588894\pi$
$854$	−3.50424	−	7.67321i	−0.119913	−	0.262572i
$855$		0			0
$856$	−2.22861	−	2.57195i	−0.0761723	−	0.0879075i
$857$	−14.6515	+	4.30206i	−0.500485	+	0.146956i	−0.522225	−	0.852808i	$-0.674898\pi$
$857$	−14.6515	+	4.30206i	−0.500485	+	0.146956i	0.0217395	+	0.999764i	$0.493080\pi$
$858$		0			0
$859$	−1.64666	+	3.60568i	−0.0561833	+	0.123024i	−0.935641	−	0.352952i	$-0.885178\pi$
$859$	−1.64666	+	3.60568i	−0.0561833	+	0.123024i	0.879458	+	0.475976i	$0.157905\pi$
$860$	−4.63173	+	5.34530i	−0.157941	+	0.182273i
$861$		0			0
$862$	4.25077	+	29.5648i	0.144782	+	1.00698i
$863$	1.02540	+	7.13184i	0.0349052	+	0.242771i	0.999803	−	0.0198553i	$-0.00632054\pi$
$863$	1.02540	+	7.13184i	0.0349052	+	0.242771i	−0.964898	+	0.262626i	$0.915411\pi$
$864$		0			0
$865$	14.8767	−	17.1686i	0.505821	−	0.583749i
$866$	−11.3609	+	24.8769i	−0.386060	+	0.845353i
$867$		0			0
$868$	8.05749	−	2.36589i	0.273489	−	0.0803036i
$869$	−4.71837	−	5.44529i	−0.160060	−	0.184719i
$870$		0			0
$871$	−33.0118	−	72.2857i	−1.11856	−	2.44931i
$872$	−1.22721	+	8.53547i	−0.0415587	+	0.289047i
$873$		0			0
$874$	−9.01963	−	7.75626i	−0.305094	−	0.262359i
$875$	18.6987			0.632131
$876$		0			0
$877$	−19.3665	−	42.4067i	−0.653960	−	1.43197i	−0.888045	−	0.459756i	$-0.847937\pi$
$877$	−19.3665	−	42.4067i	−0.653960	−	1.43197i	0.234086	−	0.972216i	$-0.424790\pi$
$878$	−12.5882	−	3.69622i	−0.424830	−	0.124741i
$879$		0			0
$880$	−9.32960	+	2.73942i	−0.314501	+	0.0923457i
$881$	−0.943904	−	0.606610i	−0.0318009	−	0.0204372i	0.524644	−	0.851322i	$-0.324199\pi$
$881$	−0.943904	−	0.606610i	−0.0318009	−	0.0204372i	−0.556445	+	0.830885i	$0.687835\pi$
$882$		0			0
$883$	1.38840	−	1.60230i	0.0467235	−	0.0539218i	−0.731907	−	0.681405i	$-0.761369\pi$
$883$	1.38840	−	1.60230i	0.0467235	−	0.0539218i	0.778630	+	0.627483i	$0.215915\pi$
$884$	6.78940	−	4.36329i	0.228352	−	0.146753i
$885$		0			0
$886$	1.53276	+	10.6605i	0.0514939	+	0.358148i
$887$	−13.1254	+	8.43516i	−0.440706	+	0.283225i	−0.742118	−	0.670269i	$-0.766179\pi$
$887$	−13.1254	+	8.43516i	−0.440706	+	0.283225i	0.301412	+	0.953494i	$0.402542\pi$
$888$		0			0
$889$	−4.87651	+	10.6781i	−0.163553	+	0.358131i
$890$	−10.7362	−	6.89976i	−0.359880	−	0.231281i
$891$		0			0
$892$	−8.06117	−	9.30308i	−0.269908	−	0.311490i
$893$	−22.2328	−	6.52813i	−0.743991	−	0.218455i
$894$		0			0
$895$	3.07700	−	21.4010i	0.102853	−	0.715358i
$896$	−2.08816			−0.0697604
$897$		0			0
$898$	4.69291			0.156605
$899$	−4.10201	+	28.5301i	−0.136810	+	0.951532i
$900$		0			0
$901$	2.95686	+	0.868213i	0.0985074	+	0.0289244i
$902$	−10.7358	−	12.3898i	−0.357465	−	0.412536i
$903$		0			0
$904$	−3.00010	−	1.92805i	−0.0997818	−	0.0641258i
$905$	0.568451	−	1.24473i	0.0188959	−	0.0413763i
$906$		0			0
$907$	−25.6515	+	16.4852i	−0.851745	+	0.547383i	−0.892118	−	0.451802i	$-0.850781\pi$
$907$	−25.6515	+	16.4852i	−0.851745	+	0.547383i	0.0403738	+	0.999185i	$0.487145\pi$
$908$	0.758893	+	5.27822i	0.0251848	+	0.175164i
$909$		0			0
$910$	−27.7130	+	17.8100i	−0.918676	+	0.590397i
$911$	−23.4601	+	27.0744i	−0.777267	+	0.897014i	−0.996909	−	0.0785669i	$-0.974966\pi$
$911$	−23.4601	+	27.0744i	−0.777267	+	0.897014i	0.219642	+	0.975581i	$0.429511\pi$
$912$		0			0
$913$	33.5406	+	21.5552i	1.11003	+	0.713374i
$914$	6.65474	−	1.95401i	0.220119	−	0.0646328i
$915$		0			0
$916$	−13.5356	−	3.97440i	−0.447227	−	0.131318i
$917$	−6.91616	−	15.1443i	−0.228392	−	0.500108i
$918$		0			0
$919$	29.8477			0.984585			0.492292	−	0.870430i	$-0.336159\pi$
$919$	29.8477			0.984585			0.492292	+	0.870430i	$0.336159\pi$
$920$	0.0460029	+	12.2111i	0.00151667	+	0.402587i
$921$		0			0
$922$	3.03519	−	21.1102i	0.0999588	−	0.695228i
$923$	−17.0163	−	37.2604i	−0.560097	−	1.22644i
$924$		0			0
$925$	11.0996	+	12.8096i	0.364952	+	0.421177i
$926$	−6.15505	+	1.80729i	−0.202267	+	0.0593911i
$927$		0			0
$928$	2.97737	−	6.51954i	0.0977371	−	0.214014i
$929$	−26.0036	+	30.0097i	−0.853149	+	0.984586i	−0.999990	−	0.00457391i	$-0.998544\pi$
$929$	−26.0036	+	30.0097i	−0.853149	+	0.984586i	0.146841	+	0.989160i	$0.453090\pi$
$930$		0			0
$931$	−0.931802	−	6.48083i	−0.0305386	−	0.212401i
$932$	2.44536	+	17.0079i	0.0801006	+	0.557112i
$933$		0			0
$934$	−9.47731	+	10.9374i	−0.310107	+	0.357883i
$935$	−5.26148	+	11.5210i	−0.172069	+	0.376778i
$936$		0			0
$937$	−20.0227	+	5.87920i	−0.654113	+	0.192065i	−0.591917	−	0.805999i	$-0.701629\pi$
$937$	−20.0227	+	5.87920i	−0.654113	+	0.192065i	−0.0621963	+	0.998064i	$0.519810\pi$
$938$	17.5387	+	20.2408i	0.572660	+	0.660884i
$939$		0			0
$940$	9.88079	+	21.6359i	0.322276	+	0.705686i
$941$	−5.00314	+	34.7976i	−0.163098	+	1.13437i	0.729653	+	0.683818i	$0.239682\pi$
$941$	−5.00314	+	34.7976i	−0.163098	+	1.13437i	−0.892750	+	0.450551i	$0.851227\pi$
$942$		0			0
$943$	−18.6955	+	8.62323i	−0.608810	+	0.280811i
$944$	−0.611476			−0.0199019
$945$		0			0
$946$	−4.40669	−	9.64930i	−0.143274	−	0.313726i
$947$	27.4913	+	8.07217i	0.893347	+	0.262310i	0.696016	−	0.718027i	$-0.254954\pi$
$947$	27.4913	+	8.07217i	0.893347	+	0.262310i	0.197331	+	0.980337i	$0.436773\pi$
$948$		0			0
$949$	−17.3883	+	5.10565i	−0.564447	+	0.165737i
$950$	3.09487	+	1.98895i	0.100411	+	0.0645302i
$951$		0			0
$952$	−1.78121	+	2.05563i	−0.0577295	+	0.0666234i
$953$	16.4844	−	10.5939i	0.533982	−	0.343169i	−0.245699	−	0.969346i	$-0.579018\pi$
$953$	16.4844	−	10.5939i	0.533982	−	0.343169i	0.779681	+	0.626177i	$0.215381\pi$
$954$		0			0
$955$	9.72289	+	67.6242i	0.314625	+	2.18827i
$956$	4.74502	−	3.04944i	0.153465	−	0.0986259i
$957$		0			0
$958$	−2.23296	+	4.88949i	−0.0721436	+	0.157972i
$959$	−3.63515	−	2.33617i	−0.117385	−	0.0754388i
$960$		0			0
$961$	9.70963	+	11.2055i	0.313214	+	0.361468i
$962$	67.9390	+	19.9487i	2.19044	+	0.643171i
$963$		0			0
$964$	0.716936	−	4.98640i	0.0230910	−	0.160601i
$965$	3.57574			0.115107
$966$		0			0
$967$	−45.4032			−1.46007			−0.730035	−	0.683410i	$-0.760496\pi$
$967$	−45.4032			−1.46007			−0.730035	+	0.683410i	$0.760496\pi$
$968$	0.509962	−	3.54687i	0.0163908	−	0.114001i
$969$		0			0
$970$	−30.6505	−	8.99980i	−0.984129	−	0.288966i
$971$	25.1610	+	29.0373i	0.807454	+	0.931852i	0.998765	−	0.0496774i	$-0.0158193\pi$
$971$	25.1610	+	29.0373i	0.807454	+	0.931852i	−0.191311	+	0.981529i	$0.561274\pi$
$972$		0			0
$973$	−22.9455	−	14.7462i	−0.735600	−	0.472741i
$974$	−1.33735	+	2.92839i	−0.0428515	+	0.0938317i
$975$		0			0
$976$	3.39841	−	2.18402i	0.108780	−	0.0699089i
$977$	−0.166188	−	1.15586i	−0.00531683	−	0.0369794i	0.986990	−	0.160780i	$-0.0514009\pi$
$977$	−0.166188	−	1.15586i	−0.00531683	−	0.0369794i	−0.992307	+	0.123800i	$0.960492\pi$
$978$		0			0
$979$	16.1023	−	10.3483i	0.514632	−	0.330734i
$980$	−4.40129	+	5.07936i	−0.140594	+	0.162254i
$981$		0			0
$982$	25.3010	+	16.2600i	0.807388	+	0.518877i
$983$	−53.3799	+	15.6738i	−1.70255	+	0.499915i	−0.981256	−	0.192709i	$-0.938273\pi$
$983$	−53.3799	+	15.6738i	−1.70255	+	0.499915i	−0.721299	+	0.692624i	$0.756455\pi$
$984$		0			0
$985$	20.1423	+	5.91432i	0.641788	+	0.188446i
$986$	−3.87827	−	8.49222i	−0.123509	−	0.270447i
$987$		0			0
$988$	15.3686			0.488941
$989$	−13.1791	+	1.94556i	−0.419069	+	0.0618654i
$990$		0			0
$991$	−4.17451	+	29.0344i	−0.132608	+	0.922307i	0.809529	+	0.587079i	$0.199722\pi$
$991$	−4.17451	+	29.0344i	−0.132608	+	0.922307i	−0.942137	+	0.335228i	$0.891187\pi$
$992$	1.67062	+	3.65814i	0.0530422	+	0.116146i
$993$		0			0
$994$	9.04052	+	10.4333i	0.286748	+	0.330925i
$995$	−7.61042	+	2.23462i	−0.241267	+	0.0708422i
$996$		0			0
$997$	9.48155	−	20.7617i	0.300284	−	0.657530i	−0.698000	−	0.716098i	$-0.745926\pi$
$997$	9.48155	−	20.7617i	0.300284	−	0.657530i	0.998283	+	0.0585684i	$0.0186536\pi$
$998$	11.6228	−	13.4134i	0.367913	−	0.424595i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	414.2.i.f.307.1		10
3.2	odd	2		46.2.c.a.31.1	yes	10
12.11	even	2		368.2.m.b.353.1		10
23.3	even	11	inner	414.2.i.f.325.1		10
23.7	odd	22		9522.2.a.bu.1.4		5
23.16	even	11		9522.2.a.bp.1.2		5
69.26	odd	22		46.2.c.a.3.1	✓	10
69.53	even	22		1058.2.a.l.1.5		5
69.62	odd	22		1058.2.a.m.1.5		5
276.95	even	22		368.2.m.b.49.1		10
276.131	even	22		8464.2.a.bx.1.1		5
276.191	odd	22		8464.2.a.bw.1.1		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
46.2.c.a.3.1	✓	10	69.26	odd	22
46.2.c.a.31.1	yes	10	3.2	odd	2
368.2.m.b.49.1		10	276.95	even	22
368.2.m.b.353.1		10	12.11	even	2
414.2.i.f.307.1		10	1.1	even	1	trivial
414.2.i.f.325.1		10	23.3	even	11	inner
1058.2.a.l.1.5		5	69.53	even	22
1058.2.a.m.1.5		5	69.62	odd	22
8464.2.a.bw.1.1		5	276.191	odd	22
8464.2.a.bx.1.1		5	276.131	even	22
9522.2.a.bp.1.2		5	23.16	even	11
9522.2.a.bu.1.4		5	23.7	odd	22

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:	\( N \)	\(=\)	\( 414 = 2 \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	414.i (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.142315 - 0.989821i) q^{2} +(-0.959493 - 0.281733i) q^{4} +(1.66741 + 1.92429i) q^{5} +(1.75667 + 1.12894i) q^{7} +(-0.415415 + 0.909632i) q^{8} +O(q^{10})\)	\(q+(0.142315 - 0.989821i) q^{2} +(-0.959493 - 0.281733i) q^{4} +(1.66741 + 1.92429i) q^{5} +(1.75667 + 1.12894i) q^{7} +(-0.415415 + 0.909632i) q^{8} +(2.14200 - 1.37658i) q^{10} +(0.543474 + 3.77994i) q^{11} +(-5.21228 + 3.34973i) q^{13} +(1.36745 - 1.57812i) q^{14} +(0.841254 + 0.540641i) q^{16} +(1.24982 - 0.366979i) q^{17} +(2.38000 + 0.698830i) q^{19} +(-1.05773 - 2.31611i) q^{20} +3.81881 q^{22} +(1.33380 - 4.60662i) q^{23} +(-0.211072 + 1.46804i) q^{25} +(2.57385 + 5.63594i) q^{26} +(-1.36745 - 1.57812i) q^{28} +(6.87690 - 2.01924i) q^{29} +(-1.67062 + 3.65814i) q^{31} +(0.654861 - 0.755750i) q^{32} +(-0.185376 - 1.28932i) q^{34} +(0.756669 + 5.26275i) q^{35} +(7.48386 - 8.63683i) q^{37} +(1.03043 - 2.25632i) q^{38} +(-2.44306 + 0.717348i) q^{40} +(-2.81130 - 3.24442i) q^{41} +(-1.15394 - 2.52678i) q^{43} +(0.543474 - 3.77994i) q^{44} +(-4.36992 - 1.97581i) q^{46} -9.34150 q^{47} +(-1.09653 - 2.40107i) q^{49} +(1.42306 + 0.417848i) q^{50} +(5.94487 - 1.74557i) q^{52} +(1.99027 + 1.27907i) q^{53} +(-6.36752 + 7.34850i) q^{55} +(-1.75667 + 1.12894i) q^{56} +(-1.02000 - 7.09427i) q^{58} +(-0.514407 + 0.330589i) q^{59} +(1.67815 - 3.67464i) q^{61} +(3.38316 + 2.17422i) q^{62} +(-0.654861 - 0.755750i) q^{64} +(-15.1368 - 4.44457i) q^{65} +(-1.82531 + 12.6953i) q^{67} -1.30258 q^{68} +5.31686 q^{70} +(-0.940875 + 6.54393i) q^{71} +(2.80644 + 0.824045i) q^{73} +(-7.48386 - 8.63683i) q^{74} +(-2.08671 - 1.34105i) q^{76} +(-3.31264 + 7.25366i) q^{77} +(-1.58724 + 1.02006i) q^{79} +(0.362362 + 2.52028i) q^{80} +(-3.61148 + 2.32096i) q^{82} +(6.83698 - 7.89030i) q^{83} +(2.79013 + 1.79310i) q^{85} +(-2.66528 + 0.782598i) q^{86} +(-3.66412 - 1.07588i) q^{88} +(-2.08216 - 4.55930i) q^{89} -12.9379 q^{91} +(-2.57760 + 4.04425i) q^{92} +(-1.32943 + 9.24642i) q^{94} +(2.62367 + 5.74504i) q^{95} +(-8.21585 - 9.48159i) q^{97} +(-2.53268 + 0.743663i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + q^{2} - q^{4} + 6 q^{5} + 3 q^{7} + q^{8}+O(q^{10}) \) 10 * q + q^2 - q^4 + 6 * q^5 + 3 * q^7 + q^8	\( 10 q + q^{2} - q^{4} + 6 q^{5} + 3 q^{7} + q^{8} - 6 q^{10} + 12 q^{11} - 14 q^{13} - 3 q^{14} - q^{16} - 15 q^{17} + 2 q^{19} - 5 q^{20} + 10 q^{22} + q^{23} + 13 q^{25} + 3 q^{26} + 3 q^{28} + 8 q^{29} - 21 q^{31} + q^{32} - 7 q^{34} - 7 q^{35} + 28 q^{37} + 9 q^{38} - 6 q^{40} + 31 q^{41} + 11 q^{43} + 12 q^{44} - 12 q^{46} - 18 q^{47} - 24 q^{49} - 2 q^{50} + 8 q^{52} + 21 q^{53} + 5 q^{55} - 3 q^{56} - 8 q^{58} + 5 q^{59} + 37 q^{61} - q^{62} - q^{64} - 37 q^{65} - 13 q^{67} - 26 q^{68} + 18 q^{70} - 49 q^{71} - 8 q^{73} - 28 q^{74} - 20 q^{76} + 8 q^{77} + 8 q^{79} - 5 q^{80} + 2 q^{82} + 7 q^{83} - 42 q^{85} - 22 q^{86} - q^{88} + 13 q^{89} - 24 q^{91} + 23 q^{92} - 37 q^{94} + 10 q^{95} - 32 q^{97} + 24 q^{98}+O(q^{100}) \) 10 * q + q^2 - q^4 + 6 * q^5 + 3 * q^7 + q^8 - 6 * q^10 + 12 * q^11 - 14 * q^13 - 3 * q^14 - q^16 - 15 * q^17 + 2 * q^19 - 5 * q^20 + 10 * q^22 + q^23 + 13 * q^25 + 3 * q^26 + 3 * q^28 + 8 * q^29 - 21 * q^31 + q^32 - 7 * q^34 - 7 * q^35 + 28 * q^37 + 9 * q^38 - 6 * q^40 + 31 * q^41 + 11 * q^43 + 12 * q^44 - 12 * q^46 - 18 * q^47 - 24 * q^49 - 2 * q^50 + 8 * q^52 + 21 * q^53 + 5 * q^55 - 3 * q^56 - 8 * q^58 + 5 * q^59 + 37 * q^61 - q^62 - q^64 - 37 * q^65 - 13 * q^67 - 26 * q^68 + 18 * q^70 - 49 * q^71 - 8 * q^73 - 28 * q^74 - 20 * q^76 + 8 * q^77 + 8 * q^79 - 5 * q^80 + 2 * q^82 + 7 * q^83 - 42 * q^85 - 22 * q^86 - q^88 + 13 * q^89 - 24 * q^91 + 23 * q^92 - 37 * q^94 + 10 * q^95 - 32 * q^97 + 24 * q^98

Introduction

L-functions

Modular forms

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Database

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