LMFDB - Embedded newform 414.2.i.f.325.1

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			325.1
Root			$-0.415415 - 0.909632i$ of defining polynomial
Character	$\chi$	$=$	414.325
Dual form			414.2.i.f.307.1

$q$-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 $\left(\mathbb{Z}/414\mathbb{Z}\right)^\times$.

$n$	$47$	$235$
$\chi(n)$	$1$	$e\left(\frac{8}{11}\right)$

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	−0.248456	−	0.968643i	$-0.579923\pi$
$5$	1.66741	−	1.92429i	0.745687	−	0.860569i	0.994143	+	0.108075i	$0.0344686\pi$
$6$		0			0
$7$	1.75667	−	1.12894i	0.663958	−	0.426700i	−0.164785	−	0.986330i	$-0.552693\pi$
$7$	1.75667	−	1.12894i	0.663958	−	0.426700i	0.828743	+	0.559629i	$0.189057\pi$
$8$	−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	−0.727401	−	0.686212i	$-0.759272\pi$
$11$	0.543474	−	3.77994i	0.163864	−	1.13970i	0.891265	−	0.453483i	$-0.149819\pi$
$12$		0			0
$13$	−5.21228	−	3.34973i	−1.44563	−	0.929047i	−0.999418	−	0.0341173i	$-0.989138\pi$
$13$	−5.21228	−	3.34973i	−1.44563	−	0.929047i	−0.446207	−	0.894930i	$-0.647226\pi$
$14$	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	0.429758	−	0.902944i	$-0.358599\pi$
$17$	1.24982	+	0.366979i	0.303125	+	0.0890055i	−0.126633	+	0.991950i	$0.540417\pi$
$18$		0			0
$19$	2.38000	−	0.698830i	0.546009	−	0.160323i	0.00291665	−	0.999996i	$-0.499072\pi$
$19$	2.38000	−	0.698830i	0.546009	−	0.160323i	0.543092	+	0.839673i	$0.317253\pi$
$20$	−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	0.848799	−	0.528716i	$-0.177326\pi$
$29$	6.87690	+	2.01924i	1.27701	+	0.374964i	0.428210	+	0.903679i	$0.359144\pi$
$30$		0			0
$31$	−1.67062	−	3.65814i	−0.300052	−	0.657022i	0.698214	−	0.715889i	$-0.253978\pi$
$31$	−1.67062	−	3.65814i	−0.300052	−	0.657022i	−0.998266	+	0.0588671i	$0.981251\pi$
$32$	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	0.874279	+	0.485423i	$0.161334\pi$
$37$	7.48386	+	8.63683i	1.23034	+	1.41989i	0.356059	+	0.934463i	$0.384120\pi$
$38$	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	−0.931546	−	0.363623i	$-0.881540\pi$
$41$	−2.81130	+	3.24442i	−0.439052	+	0.506693i	0.492494	+	0.870316i	$0.336085\pi$
$42$		0			0
$43$	−1.15394	+	2.52678i	−0.175974	+	0.385330i	−0.976981	−	0.213325i	$-0.931571\pi$
$43$	−1.15394	+	2.52678i	−0.175974	+	0.385330i	0.801007	+	0.598655i	$0.204298\pi$
$44$	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	−0.396764	−	0.917921i	$-0.629867\pi$
$53$	1.99027	−	1.27907i	0.273385	−	0.175694i	0.670148	+	0.742227i	$0.266230\pi$
$54$		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	0.506727	−	0.862106i	$-0.330855\pi$
$59$	−0.514407	−	0.330589i	−0.0669701	−	0.0430390i	−0.573697	+	0.819067i	$0.694491\pi$
$60$		0			0
$61$	1.67815	+	3.67464i	0.214865	+	0.470489i	0.986119	−	0.166038i	$-0.0530976\pi$
$61$	1.67815	+	3.67464i	0.214865	+	0.470489i	−0.771254	+	0.636527i	$0.780370\pi$
$62$	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	−0.726611	−	0.687049i	$-0.758906\pi$
$67$	−1.82531	−	12.6953i	−0.222997	−	1.55098i	0.503614	−	0.863929i	$-0.332003\pi$
$68$	−1.30258			−0.157961
$69$		0			0
$70$	5.31686			0.635487
$71$	−0.940875	−	6.54393i	−0.111661	−	0.776621i	−0.966304	−	0.257404i	$-0.917133\pi$
$71$	−0.940875	−	6.54393i	−0.111661	−	0.776621i	0.854642	−	0.519217i	$-0.173776\pi$
$72$		0			0
$73$	2.80644	−	0.824045i	0.328469	−	0.0964472i	−0.113340	−	0.993556i	$-0.536155\pi$
$73$	2.80644	−	0.824045i	0.328469	−	0.0964472i	0.441809	+	0.897109i	$0.354337\pi$
$74$	−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	0.448298	−	0.893884i	$-0.352030\pi$
$79$	−1.58724	−	1.02006i	−0.178578	−	0.114765i	−0.626876	+	0.779119i	$0.715667\pi$
$80$	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	0.994612	−	0.103663i	$-0.0330564\pi$
$83$	6.83698	+	7.89030i	0.750456	+	0.866073i	−0.244156	+	0.969736i	$0.578511\pi$
$84$		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	−0.987303	−	0.158846i	$-0.949223\pi$
$89$	−2.08216	+	4.55930i	−0.220709	+	0.483285i	0.766594	+	0.642132i	$0.221950\pi$
$90$		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	−0.999724	−	0.0234947i	$-0.992521\pi$
$97$	−8.21585	+	9.48159i	−0.834193	+	0.962710i	0.165531	+	0.986205i	$0.447066\pi$
$98$	−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	0.858819	−	0.512280i	$-0.171199\pi$
$101$	2.30675	+	2.66214i	0.229531	+	0.264893i	−0.629288	+	0.777172i	$0.716653\pi$
$102$		0			0
$103$	−0.222897	+	1.55028i	−0.0219627	+	0.152754i	−0.997852	−	0.0655137i	$-0.979131\pi$
$103$	−0.222897	+	1.55028i	−0.0219627	+	0.152754i	0.975889	+	0.218267i	$0.0700405\pi$
$104$	−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	0.828905	−	0.559389i	$-0.188964\pi$
$107$	−1.41373	−	3.09564i	−0.136671	−	0.299267i	−0.965576	+	0.260122i	$0.916237\pi$
$108$		0			0
$109$	8.27394	+	2.42945i	0.792499	+	0.232699i	0.652835	−	0.757500i	$-0.273579\pi$
$109$	8.27394	+	2.42945i	0.792499	+	0.232699i	0.139664	+	0.990199i	$0.455398\pi$
$110$	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	−0.999669	−	0.0257353i	$-0.991807\pi$
$113$	−0.507526	−	3.52992i	−0.0477441	−	0.332067i	0.951925	−	0.306332i	$-0.0991018\pi$
$114$		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	−0.923042	−	0.384699i	$-0.874305\pi$
$127$	0.800045	−	5.56443i	0.0709925	−	0.493764i	0.994035	−	0.109065i	$-0.0347856\pi$
$128$	−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	−0.799797	−	0.600271i	$-0.795059\pi$
$131$	−6.70728	+	4.31051i	−0.586018	+	0.376611i	0.213778	+	0.976882i	$0.431423\pi$
$132$		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	−0.699254	−	0.714874i	$-0.746484\pi$
$149$	2.11269	−	14.6941i	0.173079	−	1.20379i	0.872332	−	0.488914i	$-0.162607\pi$
$150$		0			0
$151$	3.24142	+	2.08313i	0.263783	+	0.169523i	0.665846	−	0.746089i	$-0.268071\pi$
$151$	3.24142	+	2.08313i	0.263783	+	0.169523i	−0.402064	+	0.915612i	$0.631707\pi$
$152$	−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	−0.987787	−	0.155810i	$-0.950201\pi$
$157$	−21.7336	+	6.38156i	−1.73453	+	0.509304i	−0.746742	+	0.665114i	$0.768383\pi$
$158$	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	0.768537	+	0.639806i	$0.220985\pi$
$163$	2.69879	+	18.7705i	0.211385	+	1.47022i	−0.557152	+	0.830411i	$0.688106\pi$
$164$	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	0.245162	−	0.969482i	$-0.421159\pi$
$167$	−0.939952	−	0.275995i	−0.0727356	−	0.0213571i	−0.317898	+	0.948125i	$0.602977\pi$
$168$		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	0.882884	+	0.469592i	$0.155599\pi$
$173$	−1.26974	+	8.83122i	−0.0965364	+	0.671425i	−0.979420	+	0.201833i	$0.935310\pi$
$174$		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	−0.924501	−	0.381180i	$-0.875518\pi$
$179$	−5.56076	+	6.41746i	−0.415631	+	0.479663i	0.508870	+	0.860843i	$0.330063\pi$
$180$		0			0
$181$	−0.223254	+	0.488859i	−0.0165944	+	0.0363366i	−0.917748	−	0.397164i	$-0.869994\pi$
$181$	−0.223254	+	0.488859i	−0.0165944	+	0.0363366i	0.901153	+	0.433500i	$0.142722\pi$
$182$	−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	0.686834	−	0.726815i	$-0.259000\pi$
$191$	22.5725	−	14.5065i	1.63329	−	1.04965i	0.946455	−	0.322836i	$-0.104636\pi$
$192$		0			0
$193$	0.919649	+	1.06133i	0.0661978	+	0.0763964i	0.787883	−	0.615826i	$-0.211177\pi$
$193$	0.919649	+	1.06133i	0.0661978	+	0.0763964i	−0.721685	+	0.692222i	$0.756632\pi$
$194$	−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	0.763877	−	0.645361i	$-0.223293\pi$
$197$	6.93589	+	4.45743i	0.494162	+	0.317579i	−0.269715	+	0.962940i	$0.586930\pi$
$198$		0			0
$199$	−1.29407	−	2.83361i	−0.0917339	−	0.200869i	0.858203	−	0.513310i	$-0.171581\pi$
$199$	−1.29407	−	2.83361i	−0.0917339	−	0.200869i	−0.949937	+	0.312441i	$0.898854\pi$
$200$	−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	0.542940	−	0.839772i	$-0.317311\pi$
$211$	21.1163	−	6.20030i	1.45370	−	0.426846i	0.910765	+	0.412926i	$0.135493\pi$
$212$	−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	−0.145852	−	0.989306i	$-0.546592\pi$
$223$	10.3556	−	6.65515i	0.693463	−	0.445662i	0.839316	+	0.543645i	$0.182956\pi$
$224$	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	−0.968789	−	0.247885i	$-0.920264\pi$
$227$	−2.21520	+	4.85061i	−0.147028	+	0.321946i	0.821761	+	0.569832i	$0.192992\pi$
$228$		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	0.518058	+	0.855346i	$0.326655\pi$
$233$	−7.13799	+	15.6300i	−0.467625	+	1.02396i	−0.985683	+	0.168610i	$0.946072\pi$
$234$		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	0.623606	−	0.781739i	$-0.285667\pi$
$239$	−3.69369	−	4.26274i	−0.238925	−	0.275734i	−0.862530	+	0.506005i	$0.831122\pi$
$240$		0			0
$241$	0.716936	−	4.98640i	0.0461819	−	0.321202i	−0.953615	−	0.301030i	$-0.902669\pi$
$241$	0.716936	−	4.98640i	0.0461819	−	0.321202i	0.999797	−	0.0201721i	$-0.00642141\pi$
$242$	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	−0.900800	−	0.434234i	$-0.857019\pi$
$251$	−2.51629	−	17.5012i	−0.158827	−	1.10466i	0.741973	−	0.670429i	$-0.233890\pi$
$252$		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	0.455922	−	0.890020i	$-0.349310\pi$
$257$	21.1716	−	6.21655i	1.32065	−	0.387778i	0.864727	+	0.502242i	$0.167491\pi$
$258$		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	0.726176	−	0.687509i	$-0.241296\pi$
$263$	6.52680	+	4.19452i	0.402460	+	0.258645i	−0.323716	+	0.946154i	$0.604932\pi$
$264$		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	−0.898655	−	0.438655i	$-0.855455\pi$
$269$	−14.3175	+	9.20132i	−0.872955	+	0.561014i	0.0256999	+	0.999670i	$0.491819\pi$
$270$		0			0
$271$	−7.62747	+	8.80257i	−0.463336	+	0.534718i	−0.938546	−	0.345154i	$-0.887827\pi$
$271$	−7.62747	+	8.80257i	−0.463336	+	0.534718i	0.475210	+	0.879872i	$0.342372\pi$
$272$	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	−0.849619	−	0.527397i	$-0.823168\pi$
$281$	−3.46454	+	3.99829i	−0.206677	+	0.238518i	0.642942	+	0.765915i	$0.277714\pi$
$282$		0			0
$283$	−12.9297	+	8.30943i	−0.768592	+	0.493944i	−0.865230	−	0.501375i	$-0.832828\pi$
$283$	−12.9297	+	8.30943i	−0.768592	+	0.493944i	0.0966376	+	0.995320i	$0.469191\pi$
$284$	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	−0.0339673	−	0.999423i	$-0.510814\pi$
$293$	−10.3195	−	3.03008i	−0.602871	−	0.177019i	−0.568904	+	0.822404i	$0.692632\pi$
$294$		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	−0.921658	−	0.388003i	$-0.873165\pi$
$307$	−10.7114	−	23.4548i	−0.611333	−	1.33863i	0.310325	−	0.950631i	$-0.399562\pi$
$308$	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	−0.811694	−	0.584083i	$-0.801454\pi$
$311$	2.32213	−	16.1508i	0.131676	−	0.915827i	0.943370	−	0.331743i	$-0.107637\pi$
$312$		0			0
$313$	−8.18796	−	9.44940i	−0.462811	−	0.534112i	0.475587	−	0.879669i	$-0.342236\pi$
$313$	−8.18796	−	9.44940i	−0.462811	−	0.534112i	−0.938398	+	0.345557i	$0.887690\pi$
$314$	−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	−0.947976	−	0.318342i	$-0.896874\pi$
$317$	−8.86597	+	10.2319i	−0.497963	+	0.574680i	0.450013	+	0.893022i	$0.351419\pi$
$318$		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	−0.984104	−	0.177594i	$-0.943169\pi$
$331$	−18.5543	−	21.4128i	−1.01984	−	1.17696i	−0.0357339	−	0.999361i	$-0.511377\pi$
$332$	−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	0.671943	−	0.740603i	$-0.265460\pi$
$337$	−6.01754	−	13.1766i	−0.327797	−	0.717774i	−0.999739	+	0.0228287i	$0.992733\pi$
$338$	−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	0.589886	+	0.807487i	$0.299173\pi$
$347$	4.68287	+	32.5701i	0.251390	+	1.74845i	−0.338496	+	0.940968i	$0.609918\pi$
$348$		0			0
$349$	10.8999	−	3.20050i	0.583458	−	0.171319i	0.0233345	−	0.999728i	$-0.492572\pi$
$349$	10.8999	−	3.20050i	0.583458	−	0.171319i	0.560124	+	0.828409i	$0.310754\pi$
$350$	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	0.892272	−	0.451499i	$-0.149110\pi$
$353$	−0.624933	−	1.36841i	−0.0332618	−	0.0728332i	−0.925534	+	0.378665i	$0.876383\pi$
$354$		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	0.989220	−	0.146438i	$-0.0467809\pi$
$359$	13.3293	+	15.3828i	0.703492	+	0.811873i	−0.285728	+	0.958311i	$0.592235\pi$
$360$		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	−0.962475	−	0.271371i	$-0.912523\pi$
$373$	−10.7554	+	12.4124i	−0.556892	+	0.642688i	0.405583	+	0.914058i	$0.367069\pi$
$374$	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	−0.648123	−	0.761536i	$-0.724446\pi$
$379$	3.66573	−	25.4957i	0.188296	−	1.30963i	0.836419	−	0.548091i	$-0.184645\pi$
$380$	−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	0.999468	−	0.0326054i	$-0.0103805\pi$
$383$	6.26867	+	13.7265i	0.320314	+	0.701390i	−0.679154	+	0.733996i	$0.737653\pi$
$384$		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	0.887351	+	0.461094i	$0.152543\pi$
$389$	3.27106	+	22.7507i	0.165849	+	1.15351i	−0.721502	+	0.692412i	$0.756548\pi$
$390$		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	0.902416	−	0.430866i	$-0.141792\pi$
$397$	28.4653	+	8.35817i	1.42863	+	0.419484i	0.526217	+	0.850350i	$0.323610\pi$
$398$	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	−0.244492	−	0.969651i	$-0.578621\pi$
$401$	−24.5924	−	15.8045i	−1.22808	−	0.789241i	−0.983592	+	0.180410i	$0.942258\pi$
$402$		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	−0.127677	+	0.991816i	$0.540752\pi$
$409$	−22.0687	+	25.4686i	−1.09123	+	1.25934i	−0.963550	+	0.267528i	$0.913793\pi$
$410$	−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	−0.596794	−	0.802394i	$-0.703559\pi$
$419$	5.77988	−	6.67033i	0.282366	−	0.325867i	0.879160	+	0.476527i	$0.158105\pi$
$420$		0			0
$421$	23.0285	−	14.7995i	1.12234	−	0.721283i	0.158391	−	0.987376i	$-0.449369\pi$
$421$	23.0285	−	14.7995i	1.12234	−	0.721283i	0.963947	+	0.266093i	$0.0857329\pi$
$422$	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	−0.494525	−	0.869163i	$-0.664658\pi$
$431$	−28.6589	−	8.41502i	−1.38045	−	0.405337i	−0.885926	+	0.463826i	$0.846476\pi$
$432$		0			0
$433$	−26.2406	+	7.70492i	−1.26104	+	0.370275i	−0.842882	−	0.538099i	$-0.819143\pi$
$433$	−26.2406	+	7.70492i	−1.26104	+	0.370275i	−0.418159	+	0.908374i	$0.637325\pi$
$434$	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	0.984615	+	0.174735i	$0.0559069\pi$
$439$	1.86711	+	12.9861i	0.0891124	+	0.619791i	−0.895503	+	0.445055i	$0.853184\pi$
$440$	−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	0.0268659	−	0.999639i	$-0.491447\pi$
$443$	−10.3339	−	3.03431i	−0.490979	−	0.144164i	−0.517845	+	0.855475i	$0.673265\pi$
$444$		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	−0.967974	−	0.251049i	$-0.919225\pi$
$449$	0.667871	−	4.64515i	0.0315188	−	0.219218i	0.999493	+	0.0318306i	$0.0101337\pi$
$450$		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	−0.830196	−	0.557472i	$-0.811771\pi$
$457$	2.88119	−	6.30892i	0.134776	−	0.295119i	0.964972	+	0.262353i	$0.0844986\pi$
$458$	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	−0.961392	−	0.275182i	$-0.911262\pi$
$463$	−2.66484	+	5.83519i	−0.123846	+	0.271185i	0.837546	+	0.546366i	$0.183989\pi$
$464$	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	−0.791123	−	0.611657i	$-0.790503\pi$
$467$	−12.1748	+	7.82429i	−0.563384	+	0.362065i	0.227739	+	0.973722i	$0.426867\pi$
$468$		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	−0.397427	−	0.917634i	$-0.630097\pi$
$479$	−5.15751	+	1.51438i	−0.235653	+	0.0691938i	0.161774	+	0.986828i	$0.448278\pi$
$480$		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	−0.350968	−	0.936387i	$-0.614147\pi$
$487$	−3.08891	+	0.906986i	−0.139972	+	0.0410994i	0.210996	+	0.977487i	$0.432329\pi$
$488$	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	−0.950015	−	0.312204i	$-0.898933\pi$
$491$	−12.4938	−	27.3575i	−0.563836	−	1.23463i	0.386179	−	0.922424i	$-0.373795\pi$
$492$		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	−0.161946	−	0.986800i	$-0.551777\pi$
$499$	14.9310	−	9.59557i	0.668403	−	0.429557i	0.830350	+	0.557243i	$0.188141\pi$
$500$	−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	0.529076	+	0.848575i	$0.322539\pi$
$503$	−10.2877	+	22.5269i	−0.458705	+	1.00442i	−0.987781	+	0.155850i	$0.950188\pi$
$504$		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	−0.374384	−	0.927274i	$-0.622146\pi$
$509$	12.8953	−	28.2367i	0.571572	−	1.25157i	0.945956	−	0.324295i	$-0.105127\pi$
$510$		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	−0.925103	−	0.379715i	$-0.876022\pi$
$521$	−13.8381	−	30.3013i	−0.606259	−	1.32752i	0.318844	−	0.947807i	$-0.396705\pi$
$522$		0			0
$523$	−29.7832	−	8.74514i	−1.30233	−	0.382398i	−0.444244	−	0.895906i	$-0.646528\pi$
$523$	−29.7832	−	8.74514i	−1.30233	−	0.382398i	−0.858085	+	0.513507i	$0.828346\pi$
$524$	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	−0.968030	−	0.250833i	$-0.919295\pi$
$541$	0.731645	−	5.08870i	0.0314559	−	0.218780i	0.999486	+	0.0320528i	$0.0102045\pi$
$542$	−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	−0.956681	−	0.291139i	$-0.905966\pi$
$547$	−12.4508	+	14.3689i	−0.532356	+	0.614371i	0.424325	+	0.905510i	$0.360511\pi$
$548$	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	−0.563118	−	0.826377i	$-0.690398\pi$
$557$	7.90600	−	9.12401i	0.334988	−	0.386597i	0.898105	+	0.439780i	$0.144944\pi$
$558$		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	0.821499	+	0.570210i	$0.193138\pi$
$563$	−3.02219	+	21.0198i	−0.127370	+	0.885879i	−0.948869	+	0.315669i	$0.897771\pi$
$564$		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	0.508844	−	0.860859i	$-0.330073\pi$
$569$	11.2469	+	3.30239i	0.471496	+	0.138444i	−0.0373485	+	0.999302i	$0.511891\pi$
$570$		0			0
$571$	42.5321	−	12.4886i	1.77991	−	0.522630i	0.784660	−	0.619927i	$-0.212838\pi$
$571$	42.5321	−	12.4886i	1.77991	−	0.522630i	0.995255	+	0.0972968i	$0.0310196\pi$
$572$	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	−0.863039	−	0.505138i	$-0.831442\pi$
$577$	−4.25824	−	29.6167i	−0.177273	−	1.23296i	0.685766	−	0.727822i	$-0.259467\pi$
$578$	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	−0.934976	−	0.354710i	$-0.884580\pi$
$587$	1.50360	−	10.4578i	0.0620602	−	0.431638i	0.997037	−	0.0769284i	$-0.0245113\pi$
$588$		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	−0.627444	−	0.778661i	$-0.715899\pi$
$593$	5.66384	−	6.53642i	0.232586	−	0.268419i	0.860030	+	0.510243i	$0.170444\pi$
$594$		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	−0.698744	−	0.715372i	$-0.746257\pi$
$601$	7.34180	−	16.0763i	0.299478	−	0.655766i	0.998222	+	0.0596061i	$0.0189845\pi$
$602$	−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	0.953689	+	0.300795i	$0.0972521\pi$
$607$	27.4879	+	31.7227i	1.11570	+	1.28758i	0.162010	+	0.986789i	$0.448202\pi$
$608$	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	0.998330	−	0.0577675i	$-0.0183982\pi$
$613$	7.45006	+	16.3134i	0.300905	+	0.658890i	−0.697425	+	0.716658i	$0.745671\pi$
$614$	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	−0.224083	−	0.974570i	$-0.571939\pi$
$617$	2.83913	−	0.833643i	0.114299	−	0.0335612i	0.338382	+	0.941009i	$0.390120\pi$
$618$		0			0
$619$	−3.98738	−	27.7328i	−0.160266	−	1.11468i	−0.898131	−	0.439728i	$-0.855075\pi$
$619$	−3.98738	−	27.7328i	−0.160266	−	1.11468i	0.737865	−	0.674949i	$-0.235834\pi$
$620$	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	0.499189	−	0.866493i	$-0.333631\pi$
$631$	−2.05053	−	1.31779i	−0.0816302	−	0.0524605i	−0.580819	+	0.814033i	$0.697268\pi$
$632$	−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	−0.934088	−	0.357043i	$-0.883785\pi$
$641$	−1.33060	+	2.91362i	−0.0525557	+	0.115081i	0.881532	+	0.472124i	$0.156512\pi$
$642$		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	−0.972925	−	0.231120i	$-0.925761\pi$
$647$	−4.09842	+	8.97429i	−0.161126	+	0.352816i	0.811800	+	0.583936i	$0.198488\pi$
$648$		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	0.567880	−	0.823111i	$-0.307764\pi$
$653$	−8.37325	−	9.66324i	−0.327671	−	0.378152i	−0.895551	+	0.444959i	$0.853218\pi$
$654$		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	0.946448	−	0.322855i	$-0.104643\pi$
$659$	2.12193	+	4.64638i	0.0826587	+	0.180997i	−0.863790	+	0.503853i	$0.831915\pi$
$660$		0			0
$661$	25.8606	+	7.59336i	1.00586	+	0.295348i	0.742859	−	0.669448i	$-0.233469\pi$
$661$	25.8606	+	7.59336i	1.00586	+	0.295348i	0.263002	+	0.964795i	$0.415287\pi$
$662$	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	−0.261335	−	0.965248i	$-0.584163\pi$
$673$	−26.0210	−	7.64046i	−1.00304	−	0.294518i	−0.741702	+	0.670730i	$0.765981\pi$
$674$	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	−0.00177304	−	0.999998i	$-0.500564\pi$
$677$	−23.7332	−	15.2524i	−0.912140	−	0.586197i	−0.910367	+	0.413802i	$0.864201\pi$
$678$		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	−0.503645	−	0.863911i	$-0.668008\pi$
$683$	1.90711	−	1.22563i	0.0729736	−	0.0468973i	0.576619	+	0.817013i	$0.304372\pi$
$684$		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	0.889734	+	0.456480i	$0.150890\pi$
$701$	−2.45078	+	17.0456i	−0.0925647	+	0.643802i	−0.982299	+	0.187322i	$0.940019\pi$
$702$		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	−0.858008	−	0.513637i	$-0.828298\pi$
$709$	−34.6715	+	10.1805i	−1.30212	+	0.382336i	−0.444109	+	0.895973i	$0.646480\pi$
$710$	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	0.741455	−	0.671003i	$-0.234136\pi$
$719$	26.8795	+	7.89253i	1.00244	+	0.294342i	0.260980	+	0.965344i	$0.415954\pi$
$720$		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	−0.916505	−	0.400024i	$-0.869002\pi$
$727$	−31.8709	−	36.7809i	−1.18202	−	1.36413i	−0.265520	−	0.964105i	$-0.585544\pi$
$728$	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	−0.934116	−	0.356968i	$-0.883810\pi$
$733$	−1.42468	+	3.11960i	−0.0526216	+	0.115225i	0.881495	+	0.472194i	$0.156538\pi$
$734$	−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	−0.979456	−	0.201657i	$-0.935367\pi$
$739$	−5.04671	+	11.0508i	−0.185646	+	0.406509i	0.793810	+	0.608166i	$0.208095\pi$
$740$	−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	0.387797	−	0.921745i	$-0.373236\pi$
$743$	37.8162	−	24.3030i	1.38734	−	0.891590i	0.999545	+	0.0301545i	$0.00959992\pi$
$744$		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	0.950665	−	0.310220i	$-0.100403\pi$
$751$	2.56678	+	5.62046i	0.0936631	+	0.205094i	−0.857002	+	0.515314i	$0.827675\pi$
$752$	−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	−0.993992	−	0.109454i	$-0.965090\pi$
$757$	−1.95623	−	13.6059i	−0.0711003	−	0.494513i	0.922892	−	0.385060i	$-0.125819\pi$
$758$	25.7579			0.935569
$759$		0			0
$760$	−6.31578			−0.229098
$761$	−7.27388	−	50.5910i	−0.263678	−	1.83392i	−0.504572	−	0.863369i	$-0.668350\pi$
$761$	−7.27388	−	50.5910i	−0.263678	−	1.83392i	0.240894	−	0.970551i	$-0.422559\pi$
$762$		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	0.755543	−	0.655099i	$-0.227373\pi$
$769$	13.1308	+	8.43865i	0.473509	+	0.304306i	−0.282035	+	0.959404i	$0.591009\pi$
$770$	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	0.723814	−	0.689995i	$-0.242387\pi$
$773$	−1.72841	−	1.99469i	−0.0621666	−	0.0717441i	−0.785981	+	0.618251i	$0.787842\pi$
$774$		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	−0.999993	−	0.00376486i	$-0.998802\pi$
$787$	−23.9564	+	27.6471i	−0.853953	+	0.985514i	0.146040	+	0.989279i	$0.453347\pi$
$788$	−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	0.997399	−	0.0720814i	$-0.0229641\pi$
$797$	8.18044	+	17.9127i	0.289766	+	0.634499i	−0.707633	+	0.706580i	$0.750237\pi$
$798$		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	−0.502904	−	0.864343i	$-0.667735\pi$
$809$	−13.0460	+	3.83066i	−0.458674	+	0.134679i	0.0442295	+	0.999021i	$0.485917\pi$
$810$		0			0
$811$	21.7495	+	6.38622i	0.763728	+	0.224251i	0.640323	−	0.768106i	$-0.278801\pi$
$811$	21.7495	+	6.38622i	0.763728	+	0.224251i	0.123405	+	0.992356i	$0.460619\pi$
$812$	−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	−0.275554	−	0.961286i	$-0.588861\pi$
$821$	13.8794	−	8.91972i	0.484393	−	0.311300i	0.759947	+	0.649985i	$0.225225\pi$
$822$		0			0
$823$	20.0185	−	23.1025i	0.697800	−	0.805304i	−0.290654	−	0.956828i	$-0.593873\pi$
$823$	20.0185	−	23.1025i	0.697800	−	0.805304i	0.988454	+	0.151524i	$0.0484182\pi$
$824$	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	0.889798	+	0.456355i	$0.150845\pi$
$839$	−2.68009	+	18.6404i	−0.0925270	+	0.643540i	−0.982325	+	0.187185i	$0.940064\pi$
$840$		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	0.982935	−	0.183953i	$-0.0588894\pi$
$853$	−0.350759	−	2.43958i	−0.0120098	−	0.0835297i	−0.994945	+	0.100423i	$0.967980\pi$
$854$	−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	0.0217395	−	0.999764i	$-0.493080\pi$
$857$	−14.6515	−	4.30206i	−0.500485	−	0.146956i	−0.522225	+	0.852808i	$0.674898\pi$
$858$		0			0
$859$	−1.64666	−	3.60568i	−0.0561833	−	0.123024i	0.879458	−	0.475976i	$-0.157905\pi$
$859$	−1.64666	−	3.60568i	−0.0561833	−	0.123024i	−0.935641	+	0.352952i	$0.885178\pi$
$860$	−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	−0.964898	−	0.262626i	$-0.915411\pi$
$863$	1.02540	−	7.13184i	0.0349052	−	0.242771i	0.999803	+	0.0198553i	$0.00632054\pi$
$864$		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	0.234086	+	0.972216i	$0.424790\pi$
$877$	−19.3665	+	42.4067i	−0.653960	+	1.43197i	−0.888045	+	0.459756i	$0.847937\pi$
$878$	−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	−0.556445	−	0.830885i	$-0.687835\pi$
$881$	−0.943904	+	0.606610i	−0.0318009	+	0.0204372i	0.524644	+	0.851322i	$0.324199\pi$
$882$		0			0
$883$	1.38840	+	1.60230i	0.0467235	+	0.0539218i	0.778630	−	0.627483i	$-0.215915\pi$
$883$	1.38840	+	1.60230i	0.0467235	+	0.0539218i	−0.731907	+	0.681405i	$0.761369\pi$
$884$	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	0.301412	−	0.953494i	$-0.402542\pi$
$887$	−13.1254	−	8.43516i	−0.440706	−	0.283225i	−0.742118	+	0.670269i	$0.766179\pi$
$888$		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	0.0403738	−	0.999185i	$-0.487145\pi$
$907$	−25.6515	−	16.4852i	−0.851745	−	0.547383i	−0.892118	+	0.451802i	$0.850781\pi$
$908$	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	0.219642	−	0.975581i	$-0.429511\pi$
$911$	−23.4601	−	27.0744i	−0.777267	−	0.897014i	−0.996909	+	0.0785669i	$0.974966\pi$
$912$		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	0.146841	−	0.989160i	$-0.453090\pi$
$929$	−26.0036	−	30.0097i	−0.853149	−	0.984586i	−0.999990	+	0.00457391i	$0.998544\pi$
$930$		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	−0.0621963	−	0.998064i	$-0.519810\pi$
$937$	−20.0227	−	5.87920i	−0.654113	−	0.192065i	−0.591917	+	0.805999i	$0.701629\pi$
$938$	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	−0.892750	−	0.450551i	$-0.851227\pi$
$941$	−5.00314	−	34.7976i	−0.163098	−	1.13437i	0.729653	−	0.683818i	$-0.239682\pi$
$942$		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	0.197331	−	0.980337i	$-0.436773\pi$
$947$	27.4913	−	8.07217i	0.893347	−	0.262310i	0.696016	+	0.718027i	$0.254954\pi$
$948$		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	0.779681	−	0.626177i	$-0.215381\pi$
$953$	16.4844	+	10.5939i	0.533982	+	0.343169i	−0.245699	+	0.969346i	$0.579018\pi$
$954$		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	−0.191311	−	0.981529i	$-0.561274\pi$
$971$	25.1610	−	29.0373i	0.807454	−	0.931852i	0.998765	+	0.0496774i	$0.0158193\pi$
$972$		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	−0.992307	−	0.123800i	$-0.960492\pi$
$977$	−0.166188	+	1.15586i	−0.00531683	+	0.0369794i	0.986990	+	0.160780i	$0.0514009\pi$
$978$		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	−0.721299	−	0.692624i	$-0.756455\pi$
$983$	−53.3799	−	15.6738i	−1.70255	−	0.499915i	−0.981256	+	0.192709i	$0.938273\pi$
$984$		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	−0.942137	−	0.335228i	$-0.891187\pi$
$991$	−4.17451	−	29.0344i	−0.132608	−	0.922307i	0.809529	−	0.587079i	$-0.199722\pi$
$992$	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	0.998283	−	0.0585684i	$-0.0186536\pi$
$997$	9.48155	+	20.7617i	0.300284	+	0.657530i	−0.698000	+	0.716098i	$0.745926\pi$
$998$	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.325.1		10
3.2	odd	2		46.2.c.a.3.1	✓	10
12.11	even	2		368.2.m.b.49.1		10
23.8	even	11	inner	414.2.i.f.307.1		10
23.10	odd	22		9522.2.a.bu.1.4		5
23.13	even	11		9522.2.a.bp.1.2		5
69.8	odd	22		46.2.c.a.31.1	yes	10
69.56	even	22		1058.2.a.l.1.5		5
69.59	odd	22		1058.2.a.m.1.5		5
276.59	even	22		8464.2.a.bx.1.1		5
276.215	even	22		368.2.m.b.353.1		10
276.263	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	3.2	odd	2
46.2.c.a.31.1	yes	10	69.8	odd	22
368.2.m.b.49.1		10	12.11	even	2
368.2.m.b.353.1		10	276.215	even	22
414.2.i.f.307.1		10	23.8	even	11	inner
414.2.i.f.325.1		10	1.1	even	1	trivial
1058.2.a.l.1.5		5	69.56	even	22
1058.2.a.m.1.5		5	69.59	odd	22
8464.2.a.bw.1.1		5	276.263	odd	22
8464.2.a.bx.1.1		5	276.59	even	22
9522.2.a.bp.1.2		5	23.13	even	11
9522.2.a.bu.1.4		5	23.10	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

Varieties

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Representations

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Database

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