LMFDB - Embedded newform 639.2.z.a.269.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [639,2,Mod(35,639)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(639, base_ring=CyclotomicField(70))

chi = DirichletCharacter(H, H._module([35, 29]))

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

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

chi := DirichletCharacter("639.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 639 = 3^{2} \cdot 71 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	639.z (of order $70$, degree $24$, 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:	$5.10244068916$
Analytic rank:	$0$
Dimension:	$576$
Relative dimension:	$24$ over $\Q(\zeta_{70})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{70}]$

Embedding invariants

Embedding label			269.9
Character	$\chi$	$=$	639.269
Dual form			639.2.z.a.620.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.934550 - 0.399446i) q^{2} +(-0.668298 - 0.698985i) q^{4} +(-0.633263 - 0.205760i) q^{5} +(-1.48125 - 1.69543i) q^{7} +(1.05958 + 2.82325i) q^{8} +O(q^{10})$	\(q+(-0.934550 - 0.399446i) q^{2} +(-0.668298 - 0.698985i) q^{4} +(-0.633263 - 0.205760i) q^{5} +(-1.48125 - 1.69543i) q^{7} +(1.05958 + 2.82325i) q^{8} +(0.509626 + 0.445247i) q^{10} +(5.30327 - 1.46361i) q^{11} +(0.879653 - 3.18735i) q^{13} +(0.707072 + 2.17614i) q^{14} +(0.0507277 - 1.12954i) q^{16} +(-2.83889 + 2.06257i) q^{17} +(-1.64192 - 3.05120i) q^{19} +(0.279386 + 0.580151i) q^{20} +(-5.54081 - 0.750553i) q^{22} +(-0.150196 + 0.658050i) q^{23} +(-3.68640 - 2.67833i) q^{25} +(-2.09525 + 2.62736i) q^{26} +(-0.195162 + 2.16843i) q^{28} +(-7.74592 + 1.04926i) q^{29} +(-9.76233 + 0.438427i) q^{31} +(2.11818 - 4.39845i) q^{32} +(3.47697 - 0.793595i) q^{34} +(0.589172 + 1.37844i) q^{35} +(1.11456 + 4.88321i) q^{37} +(0.315668 + 3.50736i) q^{38} +(-0.0900841 - 2.00588i) q^{40} +(0.638627 + 0.800813i) q^{41} +(2.89012 + 0.260116i) q^{43} +(-4.56721 - 2.72878i) q^{44} +(0.403220 - 0.554985i) q^{46} +(-4.05275 + 0.735465i) q^{47} +(0.259259 - 1.91393i) q^{49} +(2.37528 + 3.97555i) q^{50} +(-2.81578 + 1.51524i) q^{52} +(-5.03324 + 5.26436i) q^{53} +(-3.65952 - 0.164349i) q^{55} +(3.21711 - 5.97839i) q^{56} +(7.65807 + 2.11349i) q^{58} +(-2.11856 - 3.20949i) q^{59} +(4.42150 - 5.06081i) q^{61} +(9.29851 + 3.48979i) q^{62} +(-5.43946 + 4.75231i) q^{64} +(-1.21288 + 1.83743i) q^{65} +(7.61203 - 7.27784i) q^{67} +(3.33893 + 0.605927i) q^{68} -1.52356i q^{70} +(-8.11309 + 2.27548i) q^{71} +(-0.108990 + 0.254996i) q^{73} +(0.908965 - 5.00881i) q^{74} +(-1.03545 + 3.18679i) q^{76} +(-10.3369 - 6.82335i) q^{77} +(-14.7083 + 5.52012i) q^{79} +(-0.264538 + 0.704859i) q^{80} +(-0.276948 - 1.00350i) q^{82} +(12.0142 - 7.93050i) q^{83} +(2.22216 - 0.722023i) q^{85} +(-2.59706 - 1.39754i) q^{86} +(9.75138 + 13.4216i) q^{88} +(-8.88649 - 8.49635i) q^{89} +(-6.70691 + 3.22988i) q^{91} +(0.560342 - 0.334789i) q^{92} +(4.08128 + 0.931525i) q^{94} +(0.411954 + 2.27006i) q^{95} +(-9.84890 - 7.85424i) q^{97} +(-1.00680 + 1.68510i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 576 q - 24 q^{4}+O(q^{10}) $ 576 * q - 24 * q^4	$ 576 q - 24 q^{4} - 16 q^{10} + 76 q^{16} - 8 q^{19} + 20 q^{22} + 168 q^{25} - 20 q^{28} - 28 q^{31} + 40 q^{37} + 32 q^{40} + 52 q^{43} - 20 q^{46} - 208 q^{52} - 92 q^{55} + 56 q^{58} + 56 q^{61} - 144 q^{64} - 16 q^{67} - 44 q^{73} - 336 q^{76} + 88 q^{79} - 124 q^{82} + 60 q^{85} - 260 q^{88} + 80 q^{91} + 56 q^{94} - 56 q^{97}+O(q^{100}) $ 576 * q - 24 * q^4 - 16 * q^10 + 76 * q^16 - 8 * q^19 + 20 * q^22 + 168 * q^25 - 20 * q^28 - 28 * q^31 + 40 * q^37 + 32 * q^40 + 52 * q^43 - 20 * q^46 - 208 * q^52 - 92 * q^55 + 56 * q^58 + 56 * q^61 - 144 * q^64 - 16 * q^67 - 44 * q^73 - 336 * q^76 + 88 * q^79 - 124 * q^82 + 60 * q^85 - 260 * q^88 + 80 * q^91 + 56 * q^94 - 56 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/639\mathbb{Z}\right)^\times$.

$n$	$433$	$569$
$\chi(n)$	$e\left(\frac{19}{70}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.934550	−	0.399446i	−0.660827	−	0.282451i	0.0363618	−	0.999339i	$-0.488423\pi$
$2$	−0.934550	−	0.399446i	−0.660827	−	0.282451i	−0.697189	+	0.716888i	$0.745566\pi$
$3$		0			0
$3$		0			0
$4$	−0.668298	−	0.698985i	−0.334149	−	0.349493i
$5$	−0.633263	−	0.205760i	−0.283204	−	0.0920186i	0.163971	−	0.986465i	$-0.447570\pi$
$5$	−0.633263	−	0.205760i	−0.283204	−	0.0920186i	−0.447175	+	0.894447i	$0.647570\pi$
$6$		0			0
$7$	−1.48125	−	1.69543i	−0.559861	−	0.640812i	0.401580	−	0.915824i	$-0.368461\pi$
$7$	−1.48125	−	1.69543i	−0.559861	−	0.640812i	−0.961441	+	0.275012i	$0.911318\pi$
$8$	1.05958	+	2.82325i	0.374619	+	0.998168i
$9$		0			0
$10$	0.509626	+	0.445247i	0.161158	+	0.140800i
$11$	5.30327	−	1.46361i	1.59900	−	0.441295i	0.650870	−	0.759189i	$-0.274404\pi$
$11$	5.30327	−	1.46361i	1.59900	−	0.441295i	0.948126	+	0.317894i	$0.102976\pi$
$12$		0			0
$13$	0.879653	−	3.18735i	0.243972	−	0.884012i	−0.734668	−	0.678427i	$-0.762662\pi$
$13$	0.879653	−	3.18735i	0.243972	−	0.884012i	0.978639	−	0.205584i	$-0.0659095\pi$
$14$	0.707072	+	2.17614i	0.188973	+	0.581599i
$15$		0			0
$16$	0.0507277	−	1.12954i	0.0126819	−	0.282385i
$17$	−2.83889	+	2.06257i	−0.688531	+	0.500247i	−0.876177	−	0.481990i	$-0.839914\pi$
$17$	−2.83889	+	2.06257i	−0.688531	+	0.500247i	0.187646	+	0.982237i	$0.439914\pi$
$18$		0			0
$19$	−1.64192	−	3.05120i	−0.376683	−	0.699994i	0.619712	−	0.784829i	$-0.287249\pi$
$19$	−1.64192	−	3.05120i	−0.376683	−	0.699994i	−0.996395	+	0.0848354i	$0.972964\pi$
$20$	0.279386	+	0.580151i	0.0624726	+	0.129726i
$21$		0			0
$22$	−5.54081	−	0.750553i	−1.18130	−	0.160019i
$23$	−0.150196	+	0.658050i	−0.0313179	+	0.137213i	−0.988170	−	0.153363i	$-0.950990\pi$
$23$	−0.150196	+	0.658050i	−0.0313179	+	0.137213i	0.956852	+	0.290576i	$0.0938468\pi$
$24$		0			0
$25$	−3.68640	−	2.67833i	−0.737280	−	0.535665i
$26$	−2.09525	+	2.62736i	−0.410913	+	0.515269i
$27$		0			0
$28$	−0.195162	+	2.16843i	−0.0368821	+	0.409794i
$29$	−7.74592	+	1.04926i	−1.43838	+	0.194842i	−0.811536	−	0.584302i	$-0.801368\pi$
$29$	−7.74592	+	1.04926i	−1.43838	+	0.194842i	−0.626845	+	0.779144i	$0.715654\pi$
$30$		0			0
$31$	−9.76233	+	0.438427i	−1.75337	+	0.0787437i	−0.898193	−	0.439600i	$-0.855120\pi$
$31$	−9.76233	+	0.438427i	−1.75337	+	0.0787437i	−0.855172	+	0.518344i	$0.826549\pi$
$32$	2.11818	−	4.39845i	0.374445	−	0.777544i
$33$		0			0
$34$	3.47697	−	0.793595i	0.596295	−	0.136100i
$35$	0.589172	+	1.37844i	0.0995882	+	0.232998i
$36$		0			0
$37$	1.11456	+	4.88321i	0.183233	+	0.802795i	0.980078	+	0.198612i	$0.0636433\pi$
$37$	1.11456	+	4.88321i	0.183233	+	0.802795i	−0.796846	+	0.604183i	$0.793500\pi$
$38$	0.315668	+	3.50736i	0.0512081	+	0.568969i
$39$		0			0
$40$	−0.0900841	−	2.00588i	−0.0142435	−	0.317157i
$41$	0.638627	+	0.800813i	0.0997368	+	0.125066i	0.829195	−	0.558959i	$-0.188799\pi$
$41$	0.638627	+	0.800813i	0.0997368	+	0.125066i	−0.729458	+	0.684025i	$0.760228\pi$
$42$		0			0
$43$	2.89012	+	0.260116i	0.440740	+	0.0396673i	0.307787	−	0.951455i	$-0.400411\pi$
$43$	2.89012	+	0.260116i	0.440740	+	0.0396673i	0.132952	+	0.991122i	$0.457554\pi$
$44$	−4.56721	−	2.72878i	−0.688533	−	0.411379i
$45$		0			0
$46$	0.403220	−	0.554985i	0.0594516	−	0.0818281i
$47$	−4.05275	+	0.735465i	−0.591154	+	0.107279i	−0.465887	−	0.884844i	$-0.654265\pi$
$47$	−4.05275	+	0.735465i	−0.591154	+	0.107279i	−0.125267	+	0.992123i	$0.539979\pi$
$48$		0			0
$49$	0.259259	−	1.91393i	0.0370371	−	0.273419i
$50$	2.37528	+	3.97555i	0.335915	+	0.562227i
$51$		0			0
$52$	−2.81578	+	1.51524i	−0.390479	+	0.210125i
$53$	−5.03324	+	5.26436i	−0.691369	+	0.723115i	−0.971551	−	0.236832i	$-0.923891\pi$
$53$	−5.03324	+	5.26436i	−0.691369	+	0.723115i	0.280182	+	0.959947i	$0.409605\pi$
$54$		0			0
$55$	−3.65952	−	0.164349i	−0.493450	−	0.0221608i
$56$	3.21711	−	5.97839i	0.429904	−	0.798896i
$57$		0			0
$58$	7.65807	+	2.11349i	1.00555	+	0.277515i
$59$	−2.11856	−	3.20949i	−0.275813	−	0.417839i	0.670094	−	0.742276i	$-0.266254\pi$
$59$	−2.11856	−	3.20949i	−0.275813	−	0.417839i	−0.945907	+	0.324437i	$0.894825\pi$
$60$		0			0
$61$	4.42150	−	5.06081i	0.566115	−	0.647970i	−0.396759	−	0.917923i	$-0.629865\pi$
$61$	4.42150	−	5.06081i	0.566115	−	0.647970i	0.962874	+	0.269952i	$0.0870080\pi$
$62$	9.29851	+	3.48979i	1.18091	+	0.443204i
$63$		0			0
$64$	−5.43946	+	4.75231i	−0.679932	+	0.594039i
$65$	−1.21288	+	1.83743i	−0.150439	+	0.227906i
$66$		0			0
$67$	7.61203	−	7.27784i	0.929957	−	0.889130i	−0.0641053	−	0.997943i	$-0.520419\pi$
$67$	7.61203	−	7.27784i	0.929957	−	0.889130i	0.994062	+	0.108813i	$0.0347051\pi$
$68$	3.33893	+	0.605927i	0.404905	+	0.0734794i
$69$		0			0
$70$		−	1.52356i		−	0.182100i
$71$	−8.11309	+	2.27548i	−0.962846	+	0.270049i
$71$	−8.11309	+	2.27548i	−0.962846	+	0.270049i
$72$		0			0
$73$	−0.108990	+	0.254996i	−0.0127564	+	0.0298450i	−0.925785	−	0.378051i	$-0.876594\pi$
$73$	−0.108990	+	0.254996i	−0.0127564	+	0.0298450i	0.913029	+	0.407896i	$0.133737\pi$
$74$	0.908965	−	5.00881i	0.105665	−	0.582262i
$75$		0			0
$76$	−1.03545	+	3.18679i	−0.118774	+	0.365550i
$77$	−10.3369	−	6.82335i	−1.17800	−	0.777593i
$78$		0			0
$79$	−14.7083	+	5.52012i	−1.65481	+	0.621062i	−0.991829	−	0.127571i	$-0.959282\pi$
$79$	−14.7083	+	5.52012i	−1.65481	+	0.621062i	−0.662984	+	0.748633i	$0.730710\pi$
$80$	−0.264538	+	0.704859i	−0.0295762	+	0.0788056i
$81$		0			0
$82$	−0.276948	−	1.00350i	−0.0305837	−	0.110818i
$83$	12.0142	−	7.93050i	1.31873	−	0.870485i	0.321649	−	0.946859i	$-0.395763\pi$
$83$	12.0142	−	7.93050i	1.31873	−	0.870485i	0.997079	+	0.0763736i	$0.0243342\pi$
$84$		0			0
$85$	2.22216	−	0.722023i	0.241027	−	0.0783144i
$86$	−2.59706	−	1.39754i	−0.280049	−	0.150701i
$87$		0			0
$88$	9.75138	+	13.4216i	1.03950	+	1.43075i
$89$	−8.88649	−	8.49635i	−0.941966	−	0.900611i	0.0532236	−	0.998583i	$-0.483050\pi$
$89$	−8.88649	−	8.49635i	−0.941966	−	0.900611i	−0.995189	+	0.0979713i	$0.968765\pi$
$90$		0			0
$91$	−6.70691	+	3.22988i	−0.703076	+	0.338583i
$92$	0.560342	−	0.334789i	0.0584197	−	0.0349042i
$93$		0			0
$94$	4.08128	+	0.931525i	0.420951	+	0.0960794i
$95$	0.411954	+	2.27006i	0.0422656	+	0.232903i
$96$		0			0
$97$	−9.84890	−	7.85424i	−1.00000	−	0.797477i	−0.0206827	−	0.999786i	$-0.506584\pi$
$97$	−9.84890	−	7.85424i	−1.00000	−	0.797477i	−0.979322	+	0.202309i	$0.935155\pi$
$98$	−1.00680	+	1.68510i	−0.101702	+	0.170221i
$99$		0			0
$100$	0.591504	+	4.36666i	0.0591504	+	0.436666i
$101$	9.42526	−	7.51639i	0.937848	−	0.747909i	−0.0299723	−	0.999551i	$-0.509542\pi$
$101$	9.42526	−	7.51639i	0.937848	−	0.747909i	0.967820	+	0.251642i	$0.0809705\pi$
$102$		0			0
$103$	16.9745	+	8.17450i	1.67255	+	0.805457i	0.997720	+	0.0674836i	$0.0214970\pi$
$103$	16.9745	+	8.17450i	1.67255	+	0.805457i	0.674829	+	0.737974i	$0.264217\pi$
$104$	9.93074	−	0.893782i	0.973789	−	0.0876426i
$105$		0			0
$106$	6.80664	−	2.90930i	0.661119	−	0.282576i
$107$	−11.5290	+	4.92772i	−1.11455	+	0.476381i	−0.869899	−	0.493230i	$-0.835816\pi$
$107$	−11.5290	+	4.92772i	−1.11455	+	0.476381i	−0.244650	+	0.969611i	$0.578673\pi$
$108$		0			0
$109$	−6.31333	+	0.568210i	−0.604708	+	0.0544247i	−0.387763	−	0.921759i	$-0.626752\pi$
$109$	−6.31333	+	0.568210i	−0.604708	+	0.0544247i	−0.216945	+	0.976184i	$0.569609\pi$
$110$	3.35436	+	1.61537i	0.319825	+	0.154020i
$111$		0			0
$112$	−1.99020	+	1.58713i	−0.188056	+	0.149970i
$113$	0.156814	+	1.15765i	0.0147518	+	0.108902i	0.996829	−	0.0795794i	$-0.0253577\pi$
$113$	0.156814	+	1.15765i	0.0147518	+	0.108902i	−0.982077	+	0.188482i	$0.939643\pi$
$114$		0			0
$115$	0.230513	−	0.385814i	0.0214955	−	0.0359774i
$116$	5.91000	+	4.71307i	0.548730	+	0.437597i
$117$		0			0
$118$	0.697887	+	3.84568i	0.0642457	+	0.354023i
$119$	7.70205	+	1.75794i	0.706046	+	0.161150i
$120$		0			0
$121$	16.5396	−	9.88195i	1.50360	−	0.898360i
$122$	−6.15363	+	2.96343i	−0.557124	+	0.268297i
$123$		0			0
$124$	6.83060	+	6.53072i	0.613406	+	0.586476i
$125$	3.74026	+	5.14803i	0.334539	+	0.460454i
$126$		0			0
$127$	13.4306	+	7.22730i	1.19177	+	0.641319i	0.944782	−	0.327699i	$-0.106273\pi$
$127$	13.4306	+	7.22730i	1.19177	+	0.641319i	0.246989	+	0.969018i	$0.420559\pi$
$128$	−2.30422	+	0.748685i	−0.203666	+	0.0661750i
$129$		0			0
$130$	1.86745	−	1.23269i	0.163786	−	0.108114i
$131$	0.0898906	+	0.325711i	0.00785378	+	0.0284575i	0.967785	−	0.251779i	$-0.0810156\pi$
$131$	0.0898906	+	0.325711i	0.00785378	+	0.0284575i	−0.959931	+	0.280237i	$0.909587\pi$
$132$		0			0
$133$	−2.74100	+	7.30336i	−0.237675	+	0.633282i
$134$	−10.0209	+	3.76092i	−0.865676	+	0.324894i
$135$		0			0
$136$	−8.83118	−	5.82941i	−0.757268	−	0.499868i
$137$	2.38643	−	7.34467i	0.203886	−	0.627497i	−0.795871	−	0.605466i	$-0.792987\pi$
$137$	2.38643	−	7.34467i	0.203886	−	0.627497i	0.999757	−	0.0220311i	$-0.00701327\pi$
$138$		0			0
$139$	−0.138981	+	0.765851i	−0.0117883	+	0.0649586i	−0.989288	−	0.145980i	$-0.953366\pi$
$139$	−0.138981	+	0.765851i	−0.0117883	+	0.0649586i	0.977499	+	0.210939i	$0.0676521\pi$
$140$	0.569764	−	1.33303i	0.0481538	−	0.112661i
$141$		0			0
$142$	8.49102	+	1.11419i	0.712550	+	0.0935009i
$143$		−	18.1909i		−	1.52120i
$144$		0			0
$145$	5.12110	+	0.929343i	0.425284	+	0.0771777i
$146$	0.203714	−	0.194770i	0.0168595	−	0.0161193i
$147$		0			0
$148$	2.66843	−	4.04250i	0.219344	−	0.332292i
$149$	10.9965	−	9.60734i	0.900867	−	0.787064i	−0.0768386	−	0.997044i	$-0.524483\pi$
$149$	10.9965	−	9.60734i	0.900867	−	0.787064i	0.977706	+	0.209980i	$0.0673398\pi$
$150$		0			0
$151$	−6.49054	−	2.43594i	−0.528193	−	0.198234i	0.0730090	−	0.997331i	$-0.476740\pi$
$151$	−6.49054	−	2.43594i	−0.528193	−	0.198234i	−0.601202	+	0.799097i	$0.705311\pi$
$152$	6.87454	−	7.86855i	0.557599	−	0.638223i
$153$		0			0
$154$	6.93482	+	10.5058i	0.558824	+	0.846582i
$155$	6.27233	+	1.73105i	0.503806	+	0.139042i
$156$		0			0
$157$	7.19026	−	13.3617i	0.573845	−	1.06638i	−0.413902	−	0.910321i	$-0.635834\pi$
$157$	7.19026	−	13.3617i	0.573845	−	1.06638i	0.987747	−	0.156061i	$-0.0498798\pi$
$158$	15.9506	+	0.716344i	1.26896	+	0.0569893i
$159$		0			0
$160$	−2.24639	+	2.34954i	−0.177593	+	0.185748i
$161$	1.33815	−	0.720091i	0.105461	−	0.0567512i
$162$		0			0
$163$	−5.54106	−	9.27417i	−0.434009	−	0.726409i	0.560823	−	0.827935i	$-0.310485\pi$
$163$	−5.54106	−	9.27417i	−0.434009	−	0.726409i	−0.994833	+	0.101526i	$0.967627\pi$
$164$	0.132963	−	0.981573i	0.0103827	−	0.0766480i
$165$		0			0
$166$	−14.3957	+	2.61243i	−1.11732	+	0.202764i
$167$	−4.04118	+	5.56220i	−0.312716	+	0.430416i	−0.936226	−	0.351399i	$-0.885706\pi$
$167$	−4.04118	+	5.56220i	−0.312716	+	0.430416i	0.623510	+	0.781815i	$0.285706\pi$
$168$		0			0
$169$	1.77443	+	1.06017i	0.136494	+	0.0815516i
$170$	−2.36513	−	0.212865i	−0.181397	−	0.0163260i
$171$		0			0
$172$	−1.74965	−	2.19399i	−0.133409	−	0.167290i
$173$	0.370766	+	8.25575i	0.0281888	+	0.627673i	0.962511	+	0.271243i	$0.0874347\pi$
$173$	0.370766	+	8.25575i	0.0281888	+	0.627673i	−0.934322	+	0.356430i	$0.883994\pi$
$174$		0			0
$175$	0.919574	+	10.2173i	0.0695133	+	0.772356i
$176$	−1.38418	−	6.06451i	−0.104337	−	0.457129i
$177$		0			0
$178$	4.91103	+	11.4899i	0.368098	+	0.861207i
$179$	1.54189	−	0.351927i	0.115246	−	0.0263043i	−0.164509	−	0.986376i	$-0.552604\pi$
$179$	1.54189	−	0.351927i	0.115246	−	0.0263043i	0.279755	+	0.960071i	$0.409747\pi$
$180$		0			0
$181$	8.93196	−	18.5474i	0.663907	−	1.37862i	−0.248218	−	0.968704i	$-0.579845\pi$
$181$	8.93196	−	18.5474i	0.663907	−	1.37862i	0.912125	−	0.409913i	$-0.134441\pi$
$182$	7.55811	−	0.339435i	0.560244	−	0.0251606i
$183$		0			0
$184$	−2.01698	+	0.273219i	−0.148694	+	0.0201419i
$185$	0.298957	−	3.32169i	0.0219798	−	0.244215i
$186$		0			0
$187$	−12.0366	+	15.0934i	−0.880203	+	1.10374i
$188$	3.22252	+	2.34130i	0.235027	+	0.170757i
$189$		0			0
$190$	0.521772	−	2.28603i	0.0378533	−	0.165846i
$191$	6.68958	+	0.906165i	0.484041	+	0.0655678i	0.372189	−	0.928157i	$-0.378607\pi$
$191$	6.68958	+	0.906165i	0.484041	+	0.0655678i	0.111852	+	0.993725i	$0.464322\pi$
$192$		0			0
$193$	−5.97766	−	12.4127i	−0.430282	−	0.893489i	−0.997550	−	0.0699560i	$-0.977714\pi$
$193$	−5.97766	−	12.4127i	−0.430282	−	0.893489i	0.567268	−	0.823533i	$-0.308000\pi$
$194$	6.06695	+	11.2743i	0.435582	+	0.809446i
$195$		0			0
$196$	−1.51107	+	1.09786i	−0.107934	+	0.0784184i
$197$	−0.658246	+	14.6570i	−0.0468981	+	1.04427i	0.828234	+	0.560382i	$0.189346\pi$
$197$	−0.658246	+	14.6570i	−0.0468981	+	1.04427i	−0.875132	+	0.483884i	$0.839226\pi$
$198$		0			0
$199$	−4.91745	−	15.1344i	−0.348589	−	1.07285i	−0.959634	−	0.281251i	$-0.909251\pi$
$199$	−4.91745	−	15.1344i	−0.348589	−	1.07285i	0.611045	−	0.791596i	$-0.290749\pi$
$200$	3.65553	−	13.2455i	0.258485	−	0.936600i
$201$		0			0
$202$	−11.8108	+	3.25956i	−0.831003	+	0.229342i
$203$	13.2526	+	11.5785i	0.930150	+	0.812648i
$204$		0			0
$205$	−0.239644	−	0.638529i	−0.0167375	−	0.0445968i
$206$	−12.5983	−	14.4199i	−0.877763	−	1.00468i
$207$		0			0
$208$	−3.55562	−	1.15529i	−0.246538	−	0.0801050i
$209$	−13.1733	−	13.7782i	−0.911218	−	0.953059i
$210$		0			0
$211$	11.0641	+	4.72903i	0.761684	+	0.325560i	0.738573	−	0.674173i	$-0.235500\pi$
$211$	11.0641	+	4.72903i	0.761684	+	0.325560i	0.0231113	+	0.999733i	$0.492643\pi$
$212$	7.04341			0.483744
$213$		0			0
$214$	12.7428			0.871078
$215$	−1.77669	−	0.759393i	−0.121169	−	0.0517902i
$216$		0			0
$217$	15.2038	+	15.9019i	1.03210	+	1.07949i
$218$	6.12710	+	1.99081i	0.414979	+	0.134835i
$219$		0			0
$220$	2.33077	+	2.66778i	0.157141	+	0.179862i
$221$	4.07690	+	10.8629i	0.274242	+	0.730716i
$222$		0			0
$223$	17.6342	+	15.4066i	1.18087	+	1.03170i	0.998828	+	0.0484094i	$0.0154152\pi$
$223$	17.6342	+	15.4066i	1.18087	+	1.03170i	0.182047	+	0.983290i	$0.441728\pi$
$224$	−10.5948	+	2.92399i	−0.707897	+	0.195367i
$225$		0			0
$226$	0.315866	−	1.14452i	0.0210111	−	0.0761321i
$227$	1.42469	+	4.38475i	0.0945600	+	0.291026i	0.987139	−	0.159866i	$-0.0511061\pi$
$227$	1.42469	+	4.38475i	0.0945600	+	0.291026i	−0.892579	+	0.450892i	$0.851106\pi$
$228$		0			0
$229$	−0.110126	+	2.45214i	−0.00727730	+	0.162042i	0.992063	+	0.125738i	$0.0401298\pi$
$229$	−0.110126	+	2.45214i	−0.00727730	+	0.162042i	−0.999341	+	0.0363038i	$0.988442\pi$
$230$	−0.369538	+	0.268485i	−0.0243666	+	0.0177034i
$231$		0			0
$232$	−11.1697	−	20.7569i	−0.733330	−	1.36276i
$233$	4.03042	+	8.36925i	0.264041	+	0.548288i	0.990269	−	0.139167i	$-0.0444424\pi$
$233$	4.03042	+	8.36925i	0.264041	+	0.548288i	−0.726228	+	0.687454i	$0.758728\pi$
$234$		0			0
$235$	2.71779	+	0.368149i	0.177289	+	0.0240154i
$236$	−0.827551	+	3.62574i	−0.0538690	+	0.236015i
$237$		0			0
$238$	−6.49575	−	4.71944i	−0.421057	−	0.305916i
$239$	−11.9153	+	14.9413i	−0.770737	+	0.966473i	−0.999976	−	0.00689672i	$-0.997805\pi$
$239$	−11.9153	+	14.9413i	−0.770737	+	0.966473i	0.229239	+	0.973370i	$0.426376\pi$
$240$		0			0
$241$	1.04931	−	11.6587i	0.0675917	−	0.751005i	−0.888680	−	0.458527i	$-0.848377\pi$
$241$	1.04931	−	11.6587i	0.0675917	−	0.751005i	0.956272	−	0.292478i	$-0.0944799\pi$
$242$	−19.4044	+	2.62850i	−1.24736	+	0.168967i
$243$		0			0
$244$	−6.49231	+	0.291570i	−0.415628	+	0.0186659i
$245$	−0.557989	+	1.15868i	−0.0356486	+	0.0740251i
$246$		0			0
$247$	−11.1696	+	2.54938i	−0.710702	+	0.162213i
$248$	−11.5818	−	27.0969i	−0.735443	−	1.72065i
$249$		0			0
$250$	−1.43910	−	6.30512i	−0.0910169	−	0.398771i
$251$	2.23153	+	24.7944i	0.140853	+	1.56501i	0.686587	+	0.727048i	$0.259108\pi$
$251$	2.23153	+	24.7944i	0.140853	+	1.56501i	−0.545734	+	0.837959i	$0.683749\pi$
$252$		0			0
$253$	0.166600	+	3.70964i	0.0104741	+	0.233223i
$254$	−9.66463	−	12.1191i	−0.606413	−	0.760418i
$255$		0			0
$256$	16.8404	+	1.51566i	1.05252	+	0.0947288i
$257$	−10.1310	−	6.05297i	−0.631952	−	0.377574i	0.160915	−	0.986968i	$-0.448555\pi$
$257$	−10.1310	−	6.05297i	−0.631952	−	0.377574i	−0.792867	+	0.609395i	$0.791413\pi$
$258$		0			0
$259$	6.62819	−	9.12293i	0.411856	−	0.566871i
$260$	2.09491	−	0.380169i	0.129921	−	0.0235771i
$261$		0			0
$262$	0.0460968	−	0.340300i	0.00284787	−	0.0210238i
$263$	−4.03157	−	6.74771i	−0.248597	−	0.416082i	0.708560	−	0.705651i	$-0.249345\pi$
$263$	−4.03157	−	6.74771i	−0.248597	−	0.416082i	−0.957157	+	0.289569i	$0.906488\pi$
$264$		0			0
$265$	4.27056	−	2.29809i	0.262338	−	0.141170i
$266$	5.47890	−	5.73048i	0.335933	−	0.351358i
$267$		0			0
$268$	−10.1742	−	0.456924i	−0.621489	−	0.0279111i
$269$	1.95285	−	3.62901i	0.119068	−	0.221265i	−0.814085	−	0.580746i	$-0.802761\pi$
$269$	1.95285	−	3.62901i	0.119068	−	0.221265i	0.933152	+	0.359482i	$0.117047\pi$
$270$		0			0
$271$	3.44067	+	0.949565i	0.209006	+	0.0576820i	0.368972	−	0.929441i	$-0.379710\pi$
$271$	3.44067	+	0.949565i	0.209006	+	0.0576820i	−0.159966	+	0.987123i	$0.551138\pi$
$272$	2.18575	+	3.31127i	0.132530	+	0.200775i
$273$		0			0
$274$	−5.16403	+	5.91071i	−0.311971	+	0.357079i
$275$	−23.4700	−	8.80844i	−1.41529	−	0.531169i
$276$		0			0
$277$	−13.3878	+	11.6966i	−0.804396	+	0.702780i	−0.958443	−	0.285284i	$-0.907912\pi$
$277$	−13.3878	+	11.6966i	−0.804396	+	0.702780i	0.154047	+	0.988064i	$0.450769\pi$
$278$	0.435801	−	0.660211i	0.0261376	−	0.0395968i
$279$		0			0
$280$	−3.26739	+	3.12394i	−0.195264	+	0.186691i
$281$	−9.62283	−	1.74629i	−0.574050	−	0.104175i	−0.116234	−	0.993222i	$-0.537082\pi$
$281$	−9.62283	−	1.74629i	−0.574050	−	0.104175i	−0.457816	+	0.889047i	$0.651368\pi$
$282$		0			0
$283$		−	21.9296i		−	1.30358i	−0.758399	−	0.651791i	$-0.774018\pi$
$283$		−	21.9296i		−	1.30358i	0.758399	−	0.651791i	$-0.225982\pi$
$284$	7.01249	+	4.15023i	0.416115	+	0.246271i
$285$		0			0
$286$	−7.26626	+	17.0003i	−0.429663	+	1.00525i
$287$	0.411754	−	2.26895i	0.0243051	−	0.133932i
$288$		0			0
$289$	−1.44821	+	4.45714i	−0.0851890	+	0.262185i
$290$	−4.41470	−	2.91412i	−0.259240	−	0.171123i
$291$		0			0
$292$	0.251076	−	0.0942305i	0.0146931	−	0.00551442i
$293$	10.4563	−	27.8606i	0.610861	−	1.62763i	−0.157428	−	0.987530i	$-0.550320\pi$
$293$	10.4563	−	27.8606i	0.610861	−	1.62763i	0.768289	−	0.640103i	$-0.221108\pi$
$294$		0			0
$295$	0.681225	+	2.46836i	0.0396625	+	0.143714i
$296$	−12.6055	+	8.32084i	−0.732682	+	0.483639i
$297$		0			0
$298$	−14.1144	+	4.58604i	−0.817624	+	0.265662i
$299$	1.96531	+	1.05758i	0.113657	+	0.0611615i
$300$		0			0
$301$	−3.83999	−	5.28530i	−0.221334	−	0.304640i
$302$	5.09271	+	4.86913i	0.293053	+	0.280187i
$303$		0			0
$304$	−3.52975	+	1.69984i	−0.202445	+	0.0974923i
$305$	−3.84128	+	2.29506i	−0.219951	+	0.131415i
$306$		0			0
$307$	−7.42194	−	1.69401i	−0.423593	−	0.0966823i	0.00541026	−	0.999985i	$-0.498278\pi$
$307$	−7.42194	−	1.69401i	−0.423593	−	0.0966823i	−0.429003	+	0.903303i	$0.641135\pi$
$308$	2.13873	+	11.7854i	0.121866	+	0.671535i
$309$		0			0
$310$	−5.17035	−	4.12322i	−0.293656	−	0.234183i
$311$	−8.63177	+	14.4472i	−0.489463	+	0.819223i	−0.999154	−	0.0411347i	$-0.986903\pi$
$311$	−8.63177	+	14.4472i	−0.489463	+	0.819223i	0.509691	+	0.860358i	$0.329760\pi$
$312$		0			0
$313$	−3.40542	−	25.1398i	−0.192486	−	1.42099i	−0.787026	−	0.616920i	$-0.788380\pi$
$313$	−3.40542	−	25.1398i	−0.192486	−	1.42099i	0.594541	−	0.804066i	$-0.297334\pi$
$314$	−12.0569	+	9.61510i	−0.680413	+	0.542611i
$315$		0			0
$316$	13.6880	+	6.59180i	0.770011	+	0.370818i
$317$	21.3251	−	1.91929i	1.19774	−	0.107798i	0.527244	−	0.849714i	$-0.323225\pi$
$317$	21.3251	−	1.91929i	1.19774	−	0.107798i	0.670493	+	0.741916i	$0.266083\pi$
$318$		0			0
$319$	−39.5430	+	16.9015i	−2.21398	+	0.946302i
$320$	4.42244	−	1.89024i	0.247222	−	0.105668i
$321$		0			0
$322$	−1.53821	+	0.138441i	−0.0857211	+	0.00771504i
$323$	10.9546	+	5.27543i	0.609528	+	0.293533i
$324$		0			0
$325$	−11.7795	+	9.39385i	−0.653410	+	0.521077i
$326$	1.47387	+	10.8805i	0.0816300	+	0.602617i
$327$		0			0
$328$	−1.58421	+	2.65153i	−0.0874736	+	0.146406i
$329$	7.25007	+	5.78174i	0.399709	+	0.318758i
$330$		0			0
$331$	−3.93084	−	21.6607i	−0.216059	−	1.19058i	−0.891449	−	0.453121i	$-0.850311\pi$
$331$	−3.93084	−	21.6607i	−0.216059	−	1.19058i	0.675391	−	0.737460i	$-0.263975\pi$
$332$	−13.5724	−	3.09780i	−0.744880	−	0.170014i
$333$		0			0
$334$	5.99848	−	3.58393i	0.328222	−	0.196104i
$335$	−6.31790	+	3.04254i	−0.345184	+	0.166232i
$336$		0			0
$337$	−12.7430	−	12.1835i	−0.694154	−	0.663679i	0.259100	−	0.965851i	$-0.416574\pi$
$337$	−12.7430	−	12.1835i	−0.694154	−	0.663679i	−0.953254	+	0.302172i	$0.902288\pi$
$338$	−1.23481	−	1.69957i	−0.0671648	−	0.0924444i
$339$		0			0
$340$	−1.98975	−	1.07073i	−0.107909	−	0.0580684i
$341$	−51.1306	+	16.6133i	−2.76888	+	0.899663i
$342$		0			0
$343$	−16.7814	+	11.0773i	−0.906110	+	0.598118i
$344$	2.32795	+	8.43514i	0.125515	+	0.454793i
$345$		0			0
$346$	2.95123	−	7.86351i	0.158659	−	0.422745i
$347$	−0.481933	+	0.180872i	−0.0258715	+	0.00970974i	−0.364277	−	0.931291i	$-0.618684\pi$
$347$	−0.481933	+	0.180872i	−0.0258715	+	0.00970974i	0.338406	+	0.941000i	$0.390112\pi$
$348$		0			0
$349$	10.2091	+	6.73899i	0.546482	+	0.360730i	0.793775	−	0.608211i	$-0.208113\pi$
$349$	10.2091	+	6.73899i	0.546482	+	0.360730i	−0.247293	+	0.968941i	$0.579541\pi$
$350$	3.22187	−	9.91591i	0.172216	−	0.530028i
$351$		0			0
$352$	4.79568	−	26.4264i	0.255611	−	1.40853i
$353$	6.02898	−	14.1055i	0.320890	−	0.750760i	−0.678972	−	0.734164i	$-0.737574\pi$
$353$	6.02898	−	14.1055i	0.320890	−	0.750760i	0.999862	−	0.0165962i	$-0.00528297\pi$
$354$		0			0
$355$	5.60592	+	0.228371i	0.297532	+	0.0121207i
$356$			11.8896i			0.630149i
$357$		0			0
$358$	−1.58155	−	0.287009i	−0.0835876	−	0.0151689i
$359$	−1.18283	+	1.13090i	−0.0624271	+	0.0596865i	−0.721632	−	0.692277i	$-0.756607\pi$
$359$	−1.18283	+	1.13090i	−0.0624271	+	0.0596865i	0.659204	+	0.751964i	$0.270893\pi$
$360$		0			0
$361$	3.85312	−	5.83723i	0.202796	−	0.307222i
$362$	−15.7560	+	13.7656i	−0.828119	+	0.723506i
$363$		0			0
$364$	6.73986	+	2.52951i	0.353265	+	0.132582i
$365$	0.121487	−	0.139054i	0.00635894	−	0.00727839i
$366$		0			0
$367$	−2.63045	−	3.98496i	−0.137308	−	0.208013i	0.759413	−	0.650609i	$-0.225486\pi$
$367$	−2.63045	−	3.98496i	−0.137308	−	0.208013i	−0.896721	+	0.442596i	$0.854058\pi$
$368$	0.735674	+	0.203033i	0.0383497	+	0.0105838i
$369$		0			0
$370$	−1.60623	+	2.98487i	−0.0835037	+	0.155176i
$371$	16.3808	+	0.735665i	0.850451	+	0.0381938i
$372$		0			0
$373$	−6.27450	+	6.56262i	−0.324881	+	0.339799i	−0.864984	−	0.501800i	$-0.832671\pi$
$373$	−6.27450	+	6.56262i	−0.324881	+	0.339799i	0.540102	+	0.841599i	$0.318386\pi$
$374$	17.2778	−	9.29758i	0.893413	−	0.480766i
$375$		0			0
$376$	−6.37062	−	10.6626i	−0.328540	−	0.549883i
$377$	−3.46937	+	25.6119i	−0.178682	+	1.31908i
$378$		0			0
$379$	−1.74887	+	0.317373i	−0.0898333	+	0.0163023i	−0.223287	−	0.974753i	$-0.571679\pi$
$379$	−1.74887	+	0.317373i	−0.0898333	+	0.0163023i	0.133454	+	0.991055i	$0.457393\pi$
$380$	1.31143	−	1.80502i	0.0672748	−	0.0925958i
$381$		0			0
$382$	−5.88978	−	3.51898i	−0.301348	−	0.180047i
$383$	13.8557	+	1.24704i	0.707995	+	0.0637207i	0.437784	−	0.899080i	$-0.355764\pi$
$383$	13.8557	+	1.24704i	0.707995	+	0.0637207i	0.270211	+	0.962801i	$0.412906\pi$
$384$		0			0
$385$	5.14203	+	6.44790i	0.262062	+	0.328616i
$386$	0.628206	+	13.9881i	0.0319748	+	0.711975i
$387$		0			0
$388$	1.09201	+	12.1332i	0.0554383	+	0.615970i
$389$	1.51513	+	6.63821i	0.0768200	+	0.336570i	0.998704	−	0.0508956i	$-0.0162076\pi$
$389$	1.51513	+	6.63821i	0.0768200	+	0.336570i	−0.921884	+	0.387466i	$0.873350\pi$
$390$		0			0
$391$	−0.930886	−	2.17792i	−0.0470770	−	0.110142i
$392$	5.67820	−	1.29601i	0.286793	−	0.0654585i
$393$		0			0
$394$	6.46983	−	13.4348i	0.325946	−	0.676833i
$395$	10.4501	−	0.469312i	0.525799	−	0.0236137i
$396$		0			0
$397$	22.5782	−	3.05843i	1.13317	−	0.153498i	0.456456	−	0.889746i	$-0.349119\pi$
$397$	22.5782	−	3.05843i	1.13317	−	0.153498i	0.676712	+	0.736248i	$0.263404\pi$
$398$	−1.44975	+	16.1081i	−0.0726696	+	0.807425i
$399$		0			0
$400$	−3.21228	+	4.02807i	−0.160614	+	0.201404i
$401$	−26.5985	−	19.3249i	−1.32826	−	0.965041i	−0.999789	−	0.0205281i	$-0.993465\pi$
$401$	−26.5985	−	19.3249i	−1.32826	−	0.965041i	−0.328475	−	0.944513i	$-0.606535\pi$
$402$		0			0
$403$	−7.19004	+	31.5016i	−0.358161	+	1.56921i
$404$	−11.5527	−	1.56492i	−0.574770	−	0.0778579i
$405$		0			0
$406$	−7.76026	−	16.1143i	−0.385135	−	0.799741i
$407$	13.0579	+	24.2657i	0.647258	+	1.20281i
$408$		0			0
$409$	17.1876	−	12.4875i	0.849873	−	0.617469i	−0.0752382	−	0.997166i	$-0.523972\pi$
$409$	17.1876	−	12.4875i	0.849873	−	0.617469i	0.925111	+	0.379697i	$0.123972\pi$
$410$	−0.0310985	+	0.692463i	−0.00153585	+	0.0341983i
$411$		0			0
$412$	−5.63019	−	17.3279i	−0.277380	−	0.853687i
$413$	−2.30333	+	8.34593i	−0.113340	+	0.410676i
$414$		0			0
$415$	−9.23992	+	2.55006i	−0.453570	+	0.125177i
$416$	−12.1561	−	10.6205i	−0.596004	−	0.520713i
$417$		0			0
$418$	6.80748	+	18.1385i	0.332965	+	0.887181i
$419$	−16.1077	−	18.4368i	−0.786915	−	0.900696i	0.210118	−	0.977676i	$-0.432615\pi$
$419$	−16.1077	−	18.4368i	−0.786915	−	0.900696i	−0.997033	+	0.0769798i	$0.975472\pi$
$420$		0			0
$421$	−24.9348	−	8.10181i	−1.21525	−	0.394858i	−0.369898	−	0.929072i	$-0.620608\pi$
$421$	−24.9348	−	8.10181i	−1.21525	−	0.394858i	−0.845349	+	0.534214i	$0.820608\pi$
$422$	−8.45097	−	8.83902i	−0.411387	−	0.430277i
$423$		0			0
$424$	−20.1957	−	8.63206i	−0.980790	−	0.419210i
$425$	15.9895			0.775605
$426$		0			0
$427$	−15.1296			−0.732173
$428$	11.1492	+	4.76540i	0.538917	+	0.230344i
$429$		0			0
$430$	1.35707	+	1.41938i	0.0654436	+	0.0684487i
$431$	17.8196	+	5.78995i	0.858341	+	0.278892i	0.704936	−	0.709271i	$-0.250976\pi$
$431$	17.8196	+	5.78995i	0.858341	+	0.278892i	0.153406	+	0.988163i	$0.450976\pi$
$432$		0			0
$433$	20.9683	+	24.0001i	1.00767	+	1.15337i	0.988139	+	0.153563i	$0.0490748\pi$
$433$	20.9683	+	24.0001i	1.00767	+	1.15337i	0.0195321	+	0.999809i	$0.493782\pi$
$434$	−7.85675	−	20.9342i	−0.377136	−	1.00488i
$435$		0			0
$436$	4.61636	+	4.03319i	0.221084	+	0.193155i
$437$	2.25445	−	0.622189i	0.107845	−	0.0297633i
$438$		0			0
$439$	4.15065	−	15.0395i	0.198100	−	0.717798i	−0.795610	−	0.605809i	$-0.792849\pi$
$439$	4.15065	−	15.0395i	0.198100	−	0.717798i	0.993709	−	0.111989i	$-0.0357220\pi$
$440$	−3.41356	−	10.5059i	−0.162735	−	0.500848i
$441$		0			0
$442$	0.529058	−	11.7804i	0.0251647	−	0.560336i
$443$	−3.71832	+	2.70152i	−0.176663	+	0.128353i	−0.672603	−	0.740004i	$-0.734824\pi$
$443$	−3.71832	+	2.70152i	−0.176663	+	0.128353i	0.495940	+	0.868357i	$0.334824\pi$
$444$		0			0
$445$	3.87928	+	7.20891i	0.183895	+	0.341735i
$446$	−10.3260	−	21.4421i	−0.488949	−	1.01531i
$447$		0			0
$448$	16.1144	+	2.18285i	0.761334	+	0.103130i
$449$	9.06789	−	39.7290i	0.427940	−	1.87493i	−0.0536959	−	0.998557i	$-0.517100\pi$
$449$	9.06789	−	39.7290i	0.427940	−	1.87493i	0.481636	−	0.876371i	$-0.340043\pi$
$450$		0			0
$451$	4.55889	+	3.31223i	0.214670	+	0.155967i
$452$	0.704379	−	0.883263i	0.0331312	−	0.0415452i
$453$		0			0
$454$	0.420024	−	4.66685i	0.0197127	−	0.219026i
$455$	4.91182	−	0.665352i	0.230270	−	0.0311922i
$456$		0			0
$457$	29.4820	−	1.32404i	1.37911	−	0.0619359i	0.657092	−	0.753811i	$-0.271786\pi$
$457$	29.4820	−	1.32404i	1.37911	−	0.0619359i	0.722017	+	0.691875i	$0.243215\pi$
$458$	1.08241	−	2.24766i	0.0505779	−	0.105026i
$459$		0			0
$460$	−0.423730	+	0.0967137i	−0.0197565	+	0.00450930i
$461$	0.180271	+	0.421765i	0.00839606	+	0.0196436i	0.923673	−	0.383181i	$-0.125171\pi$
$461$	0.180271	+	0.421765i	0.00839606	+	0.0196436i	−0.915277	+	0.402824i	$0.868029\pi$
$462$		0			0
$463$	7.06296	+	30.9449i	0.328244	+	1.43813i	0.822476	+	0.568800i	$0.192592\pi$
$463$	7.06296	+	30.9449i	0.328244	+	1.43813i	−0.494232	+	0.869330i	$0.664551\pi$
$464$	0.792244	+	8.80256i	0.0367790	+	0.408648i
$465$		0			0
$466$	−0.423565	−	9.43142i	−0.0196213	−	0.436902i
$467$	6.63449	+	8.31939i	0.307008	+	0.384975i	0.911270	−	0.411810i	$-0.135103\pi$
$467$	6.63449	+	8.31939i	0.307008	+	0.384975i	−0.604262	+	0.796786i	$0.706532\pi$
$468$		0			0
$469$	−23.6144	−	2.12533i	−1.09041	−	0.0981388i
$470$	−2.39285	−	1.42966i	−0.110374	−	0.0659454i
$471$		0			0
$472$	6.81638	−	9.38194i	0.313749	−	0.431839i
$473$	15.7078	−	2.85055i	0.722246	−	0.131068i
$474$		0			0
$475$	−2.11933	+	15.6455i	−0.0972417	+	0.717867i
$476$	−3.91849	−	6.55845i	−0.179604	−	0.300606i
$477$		0			0
$478$	17.1037	−	9.20389i	0.782305	−	0.420976i
$479$	12.0294	−	12.5818i	0.549639	−	0.574877i	−0.388364	−	0.921506i	$-0.626960\pi$
$479$	12.0294	−	12.5818i	0.549639	−	0.574877i	0.938002	+	0.346629i	$0.112674\pi$
$480$		0			0
$481$	16.5449	+	0.743033i	0.754384	+	0.0338794i
$482$	−5.63766	+	10.4765i	−0.256789	+	0.477193i
$483$		0			0
$484$	−17.9607	−	4.95685i	−0.816397	−	0.225311i
$485$	4.62086	+	7.00031i	0.209823	+	0.317868i
$486$		0			0
$487$	7.13513	−	8.16681i	0.323323	−	0.370073i	−0.568323	−	0.822805i	$-0.692408\pi$
$487$	7.13513	−	8.16681i	0.323323	−	0.370073i	0.891647	+	0.452732i	$0.149551\pi$
$488$	18.9729	+	7.12063i	0.858861	+	0.322336i
$489$		0			0
$490$	0.984297	−	0.859955i	0.0444660	−	0.0388488i
$491$	−1.67609	+	2.53916i	−0.0756407	+	0.114591i	−0.870425	−	0.492302i	$-0.836156\pi$
$491$	−1.67609	+	2.53916i	−0.0756407	+	0.114591i	0.794784	+	0.606893i	$0.207584\pi$
$492$		0			0
$493$	19.8256	−	18.9552i	0.892901	−	0.853701i
$494$	11.4569	+	2.07911i	0.515468	+	0.0935437i
$495$		0			0
$496$			11.0492i			0.496123i
$497$	15.8754	+	10.3846i	0.712111	+	0.465814i
$498$		0			0
$499$	8.88480	−	20.7870i	0.397738	−	0.930555i	−0.594256	−	0.804276i	$-0.702554\pi$
$499$	8.88480	−	20.7870i	0.397738	−	0.930555i	0.991995	−	0.126279i	$-0.0403036\pi$
$500$	1.09879	−	6.05481i	0.0491392	−	0.270779i
$501$		0			0
$502$	7.81853	−	24.0629i	0.348958	−	1.07398i
$503$	26.9325	+	17.7780i	1.20086	+	0.792680i	0.983055	−	0.183312i	$-0.0586818\pi$
$503$	26.9325	+	17.7780i	1.20086	+	0.792680i	0.217805	+	0.975992i	$0.430110\pi$
$504$		0			0
$505$	−7.51524	+	2.82052i	−0.334424	+	0.125511i
$506$	1.32611	−	3.53340i	0.0589526	−	0.157079i
$507$		0			0
$508$	−3.92386	−	14.2178i	−0.174093	−	0.630812i
$509$	−17.4614	+	11.5262i	−0.773962	+	0.510888i	−0.875075	−	0.483987i	$-0.839188\pi$
$509$	−17.4614	+	11.5262i	−0.773962	+	0.510888i	0.101113	+	0.994875i	$0.467760\pi$
$510$		0			0
$511$	0.593769	−	0.192927i	0.0262668	−	0.00853460i
$512$	−10.8657	−	5.84710i	−0.480202	−	0.258408i
$513$		0			0
$514$	7.05006	+	9.70357i	0.310965	+	0.428006i
$515$	−9.06736	−	8.66929i	−0.399556	−	0.382014i
$516$		0			0
$517$	−20.4164	+	9.83202i	−0.897912	+	0.432412i
$518$	−9.83849	+	5.87823i	−0.432279	+	0.258274i
$519$		0			0
$520$	−6.47268	−	1.47735i	−0.283846	−	0.0647859i
$521$	−0.416678	−	2.29609i	−0.0182550	−	0.100593i	0.973516	−	0.228620i	$-0.0734214\pi$
$521$	−0.416678	−	2.29609i	−0.0182550	−	0.100593i	−0.991771	+	0.128027i	$0.959136\pi$
$522$		0			0
$523$	6.66125	+	5.31217i	0.291276	+	0.232285i	0.758215	−	0.652005i	$-0.226072\pi$
$523$	6.66125	+	5.31217i	0.291276	+	0.232285i	−0.466939	+	0.884290i	$0.654643\pi$
$524$	0.167594	−	0.280505i	0.00732137	−	0.0122539i
$525$		0			0
$526$	1.07236	+	7.91647i	0.0467571	+	0.345175i
$527$	26.8099	−	21.3801i	1.16786	−	0.931334i
$528$		0			0
$529$	20.3118	+	9.78165i	0.883122	+	0.425289i
$530$	−4.90901	+	0.441819i	−0.213234	+	0.0191914i
$531$		0			0
$532$	6.93675	−	2.96491i	0.300746	−	0.128545i
$533$	3.11424	−	1.33109i	0.134893	−	0.0576559i
$534$		0			0
$535$	8.31481	−	0.748346i	0.359481	−	0.0323538i
$536$	28.6127	+	13.7792i	1.23588	+	0.595169i
$537$		0			0
$538$	−3.27463	+	2.61143i	−0.141179	+	0.112587i
$539$	−1.42632	−	10.5295i	−0.0614361	−	0.453540i
$540$		0			0
$541$	8.44891	−	14.1411i	0.363247	−	0.607973i	−0.621201	−	0.783652i	$-0.713355\pi$
$541$	8.44891	−	14.1411i	0.363247	−	0.607973i	0.984448	+	0.175679i	$0.0562119\pi$
$542$	−2.83618	−	2.26178i	−0.121824	−	0.0971517i
$543$		0			0
$544$	3.05884	+	16.8556i	0.131147	+	0.722678i
$545$	4.11492	+	0.939203i	0.176264	+	0.0402310i
$546$		0			0
$547$	−24.0623	+	14.3766i	−1.02883	+	0.614698i	−0.925028	−	0.379900i	$-0.875959\pi$
$547$	−24.0623	+	14.3766i	−1.02883	+	0.614698i	−0.103804	+	0.994598i	$0.533101\pi$
$548$	−6.72866	+	3.24035i	−0.287434	+	0.138421i
$549$		0			0
$550$	18.4154	+	17.6069i	0.785235	+	0.750762i
$551$	15.9197	+	21.9116i	0.678201	+	0.933464i
$552$		0			0
$553$	31.1457	+	16.7602i	1.32445	+	0.712717i
$554$	17.1837	−	5.58334i	0.730067	−	0.237213i
$555$		0			0
$556$	0.628200	−	0.414671i	0.0266416	−	0.0175860i
$557$	−7.99035	−	28.9524i	−0.338562	−	1.22675i	−0.912917	−	0.408146i	$-0.866176\pi$
$557$	−7.99035	−	28.9524i	−0.338562	−	1.22675i	0.574355	−	0.818607i	$-0.305253\pi$
$558$		0			0
$559$	3.37138	−	8.98302i	0.142594	−	0.379941i
$560$	1.58689	−	0.595568i	0.0670582	−	0.0251674i
$561$		0			0
$562$	8.29547	+	5.47579i	0.349923	+	0.230982i
$563$	−0.502829	+	1.54755i	−0.0211917	+	0.0652213i	−0.961093	−	0.276225i	$-0.910917\pi$
$563$	−0.502829	+	1.54755i	−0.0211917	+	0.0652213i	0.939901	+	0.341446i	$0.110917\pi$
$564$		0			0
$565$	0.138892	−	0.765360i	0.00584325	−	0.0321989i
$566$	−8.75970	+	20.4943i	−0.368198	+	0.861442i
$567$		0			0
$568$	−15.0207	−	20.4942i	−0.630255	−	0.859917i
$569$		−	21.4501i		−	0.899234i	−0.893222	−	0.449617i	$-0.851561\pi$
$569$		−	21.4501i		−	0.899234i	0.893222	−	0.449617i	$-0.148439\pi$
$570$		0			0
$571$	−37.0960	−	6.73194i	−1.55242	−	0.281723i	−0.666480	−	0.745523i	$-0.732200\pi$
$571$	−37.0960	−	6.73194i	−1.55242	−	0.281723i	−0.885940	+	0.463800i	$0.846486\pi$
$572$	−12.7151	+	12.1569i	−0.531647	+	0.508306i
$573$		0			0
$574$	−1.29113	+	1.95598i	−0.0538907	+	0.0816409i
$575$	2.31615	−	2.02356i	0.0965902	−	0.0843883i
$576$		0			0
$577$	17.6821	+	6.63621i	0.736116	+	0.276269i	0.691142	−	0.722719i	$-0.257108\pi$
$577$	17.6821	+	6.63621i	0.736116	+	0.276269i	0.0449742	+	0.998988i	$0.485679\pi$
$578$	3.13382	−	3.58694i	0.130350	−	0.149197i
$579$		0			0
$580$	−2.77283	−	4.20065i	−0.115135	−	0.174423i
$581$	−31.2416	−	8.62215i	−1.29612	−	0.357707i
$582$		0			0
$583$	−18.9877	+	35.2850i	−0.786389	+	1.46136i
$584$	−0.835399	−	0.0375178i	−0.0345691	−	0.00155250i
$585$		0			0
$586$	−20.9007	+	21.8604i	−0.863400	+	0.903046i
$587$	14.8982	−	8.01707i	0.614915	−	0.330900i	−0.136589	−	0.990628i	$-0.543614\pi$
$587$	14.8982	−	8.01707i	0.614915	−	0.330900i	0.751505	+	0.659728i	$0.229328\pi$
$588$		0			0
$589$	17.3667	+	29.0670i	0.715582	+	1.19768i
$590$	0.349339	−	2.57892i	0.0143821	−	0.106173i
$591$		0			0
$592$	5.57232	−	1.01123i	0.229021	−	0.0415612i
$593$	2.85943	−	3.93567i	0.117423	−	0.161618i	−0.746260	−	0.665655i	$-0.768152\pi$
$593$	2.85943	−	3.93567i	0.117423	−	0.161618i	0.863682	+	0.504036i	$0.168152\pi$
$594$		0			0
$595$	−4.51571	−	2.69801i	−0.185126	−	0.110608i
$596$	−14.0643	−	1.26581i	−0.576097	−	0.0518497i
$597$		0			0
$598$	−1.41424	−	1.77340i	−0.0578325	−	0.0725197i
$599$	−1.83102	−	40.7708i	−0.0748134	−	1.66585i	−0.588971	−	0.808154i	$-0.700467\pi$
$599$	−1.83102	−	40.7708i	−0.0748134	−	1.66585i	0.514158	−	0.857696i	$-0.328105\pi$
$600$		0			0
$601$	1.52980	+	16.9975i	0.0624018	+	0.693341i	0.964895	+	0.262636i	$0.0845920\pi$
$601$	1.52980	+	16.9975i	0.0624018	+	0.693341i	−0.902493	+	0.430704i	$0.858265\pi$
$602$	1.47748	+	6.47325i	0.0602174	+	0.263830i
$603$		0			0
$604$	2.63493	+	6.16473i	0.107214	+	0.250839i
$605$	−12.5072	+	2.85469i	−0.508491	+	0.116060i
$606$		0			0
$607$	−1.68912	+	3.50750i	−0.0685594	+	0.142365i	−0.932432	−	0.361345i	$-0.882318\pi$
$607$	−1.68912	+	3.50750i	−0.0685594	+	0.142365i	0.863873	+	0.503710i	$0.168032\pi$
$608$	−16.8985	+	0.758910i	−0.685323	+	0.0307779i
$609$		0			0
$610$	4.50662	−	0.610464i	0.182468	−	0.0247170i
$611$	−1.22083	+	13.5645i	−0.0493893	+	0.548760i
$612$		0			0
$613$	3.48008	−	4.36389i	0.140559	−	0.176256i	−0.706569	−	0.707644i	$-0.749758\pi$
$613$	3.48008	−	4.36389i	0.140559	−	0.176256i	0.847128	+	0.531388i	$0.178329\pi$
$614$	6.25951	+	4.54780i	0.252613	+	0.183534i
$615$		0			0
$616$	8.31117	−	36.4136i	0.334866	−	1.46715i
$617$	41.5461	+	5.62781i	1.67258	+	0.226567i	0.908302	−	0.418315i	$-0.137379\pi$
$617$	41.5461	+	5.62781i	1.67258	+	0.226567i	0.764283	+	0.644882i	$0.223093\pi$
$618$		0			0
$619$	20.1401	+	41.8214i	0.809501	+	1.68095i	0.729328	+	0.684164i	$0.239833\pi$
$619$	20.1401	+	41.8214i	0.809501	+	1.68095i	0.0801727	+	0.996781i	$0.474453\pi$
$620$	−2.98181	−	5.54113i	−0.119752	−	0.222537i
$621$		0			0
$622$	13.8377	−	10.0537i	0.554840	−	0.403115i
$623$	−1.24184	+	27.6517i	−0.0497532	+	1.10784i
$624$		0			0
$625$	5.73108	+	17.6385i	0.229243	+	0.705538i
$626$	−6.85946	+	24.8547i	−0.274159	+	0.993393i
$627$		0			0
$628$	−14.1449	+	3.90374i	−0.564443	+	0.155776i
$629$	−13.2361	−	11.5640i	−0.527757	−	0.461088i
$630$		0			0
$631$	−0.231369	−	0.616480i	−0.00921065	−	0.0245417i	0.931549	−	0.363615i	$-0.118458\pi$
$631$	−0.231369	−	0.616480i	−0.00921065	−	0.0245417i	−0.940760	+	0.339074i	$0.889886\pi$
$632$	−31.1693	−	35.6762i	−1.23985	−	1.41912i
$633$		0			0
$634$	−20.6960	−	6.72455i	−0.821944	−	0.267066i
$635$	−7.01801	−	7.34026i	−0.278501	−	0.291289i
$636$		0			0
$637$	−5.87230	−	2.50994i	−0.232669	−	0.0994476i
$638$	43.7062			1.73034
$639$		0			0
$640$	1.61322			0.0637683
$641$	−38.4530	−	16.4356i	−1.51880	−	0.649167i	−0.537784	−	0.843083i	$-0.680738\pi$
$641$	−38.4530	−	16.4356i	−1.51880	−	0.649167i	−0.981018	+	0.193915i	$0.937881\pi$
$642$		0			0
$643$	29.8878	+	31.2602i	1.17866	+	1.23278i	0.966815	+	0.255477i	$0.0822324\pi$
$643$	29.8878	+	31.2602i	1.17866	+	1.23278i	0.211843	+	0.977304i	$0.432053\pi$
$644$	−1.39762	−	0.454114i	−0.0550739	−	0.0178946i
$645$		0			0
$646$	−8.13033	−	9.30591i	−0.319883	−	0.366136i
$647$	3.07985	+	8.20624i	0.121081	+	0.322620i	0.982774	−	0.184810i	$-0.0591669\pi$
$647$	3.07985	+	8.20624i	0.121081	+	0.322620i	−0.861693	+	0.507430i	$0.830595\pi$
$648$		0			0
$649$	−15.9328	−	13.9200i	−0.625415	−	0.546409i
$650$	14.7609	−	4.07374i	0.578969	−	0.159785i
$651$		0			0
$652$	−2.77943	+	10.0710i	−0.108851	+	0.394412i
$653$	8.44646	+	25.9955i	0.330535	+	1.01728i	0.968880	+	0.247532i	$0.0796197\pi$
$653$	8.44646	+	25.9955i	0.330535	+	1.01728i	−0.638344	+	0.769751i	$0.720380\pi$
$654$		0			0
$655$	0.0100938	−	0.224757i	0.000394399	−	0.00878198i
$656$	0.936947	−	0.680732i	0.0365816	−	0.0265781i
$657$		0			0
$658$	−4.46606	−	8.29934i	−0.174105	−	0.323542i
$659$	−18.0461	−	37.4730i	−0.702974	−	1.45974i	−0.879724	−	0.475486i	$-0.842272\pi$
$659$	−18.0461	−	37.4730i	−0.702974	−	1.45974i	0.176749	−	0.984256i	$-0.443442\pi$
$660$		0			0
$661$	−12.2586	−	1.66054i	−0.476806	−	0.0645877i	−0.108112	−	0.994139i	$-0.534481\pi$
$661$	−12.2586	−	1.66054i	−0.476806	−	0.0645877i	−0.368694	+	0.929551i	$0.620195\pi$
$662$	−4.97872	+	21.8132i	−0.193503	+	0.847794i
$663$		0			0
$664$	35.1198	+	25.5160i	1.36291	+	0.990213i
$665$	3.23851	−	4.06096i	0.125584	−	0.157477i
$666$		0			0
$667$	0.472940	−	5.25479i	0.0183123	−	0.203466i
$668$	6.58861	−	0.892488i	0.254921	−	0.0345314i
$669$		0			0
$670$	7.11973	−	0.319747i	0.275059	−	0.0123529i
$671$	16.0414	−	33.3102i	0.619269	−	1.28593i
$672$		0			0
$673$	−3.34482	+	0.763434i	−0.128933	+	0.0294282i	−0.286501	−	0.958080i	$-0.592492\pi$
$673$	−3.34482	+	0.763434i	−0.128933	+	0.0294282i	0.157567	+	0.987508i	$0.449635\pi$
$674$	7.04228	+	16.4762i	0.271259	+	0.634641i
$675$		0			0
$676$	−0.444803	−	1.94881i	−0.0171078	−	0.0749542i
$677$	−3.18217	−	35.3568i	−0.122301	−	1.35887i	−0.789388	−	0.613894i	$-0.789602\pi$
$677$	−3.18217	−	35.3568i	−0.122301	−	1.35887i	0.667087	−	0.744980i	$-0.267541\pi$
$678$		0			0
$679$	1.27240	+	28.3322i	0.0488303	+	1.08729i
$680$	4.39301	+	5.50865i	0.168464	+	0.211247i
$681$		0			0
$682$	54.4202	+	4.89791i	2.08386	+	0.187551i
$683$	13.2876	+	7.93898i	0.508437	+	0.303777i	0.744112	−	0.668055i	$-0.232873\pi$
$683$	13.2876	+	7.93898i	0.508437	+	0.303777i	−0.235675	+	0.971832i	$0.575730\pi$
$684$		0			0
$685$	−3.02247	+	4.16008i	−0.115483	+	0.158948i
$686$	20.1078	−	3.64903i	0.767721	−	0.139321i
$687$		0			0
$688$	0.440421	−	3.25132i	0.0167909	−	0.123955i
$689$	12.3518	+	20.6735i	0.470568	+	0.787598i
$690$		0			0
$691$	25.4943	−	13.7191i	0.969850	−	0.521898i	0.0893783	−	0.995998i	$-0.471512\pi$
$691$	25.4943	−	13.7191i	0.969850	−	0.521898i	0.880471	+	0.474099i	$0.157226\pi$
$692$	5.52286	−	5.77646i	0.209948	−	0.219588i
$693$		0			0
$694$	0.522639	+	0.0234718i	0.0198391	+	0.000890976i
$695$	0.245593	−	0.456389i	0.00931588	−	0.0173118i
$696$		0			0
$697$	−3.46472	−	0.956203i	−0.131236	−	0.0362188i
$698$	−6.84908	−	10.3759i	−0.259242	−	0.392734i
$699$		0			0
$700$	6.52720	−	7.47098i	0.246705	−	0.282376i
$701$	−2.30899	−	0.866577i	−0.0872092	−	0.0327302i	0.307389	−	0.951584i	$-0.400545\pi$
$701$	−2.30899	−	0.866577i	−0.0872092	−	0.0327302i	−0.394598	+	0.918854i	$0.629116\pi$
$702$		0			0
$703$	13.0696	−	11.4186i	0.492931	−	0.430661i
$704$	−21.8914	+	33.1640i	−0.825063	+	1.24992i
$705$		0			0
$706$	−11.2688	+	10.7741i	−0.424106	+	0.405487i
$707$	−26.7047	−	4.84619i	−1.00433	−	0.182260i
$708$		0			0
$709$		−	36.1477i		−	1.35756i	−0.734343	−	0.678778i	$-0.762510\pi$
$709$		−	36.1477i		−	1.35756i	0.734343	−	0.678778i	$-0.237490\pi$
$710$	−5.14779	−	2.45269i	−0.193193	−	0.0920477i
$711$		0			0
$712$	14.5713	−	34.0913i	0.546084	−	1.27763i
$713$	1.17775	−	6.48994i	0.0441071	−	0.243050i
$714$		0			0
$715$	−3.74294	+	11.5196i	−0.139978	+	0.430809i
$716$	−1.27644	−	0.842568i	−0.0477027	−	0.0314883i
$717$		0			0
$718$	1.55714	−	0.584405i	0.0581120	−	0.0218098i
$719$	−0.222128	+	0.591859i	−0.00828399	+	0.0220726i	−0.940312	−	0.340314i	$-0.889467\pi$
$719$	−0.222128	+	0.591859i	−0.00828399	+	0.0220726i	0.932028	+	0.362387i	$0.118038\pi$
$720$		0			0
$721$	−11.2843	−	40.8876i	−0.420248	−	1.52273i
$722$	−5.93259	+	3.91607i	−0.220788	+	0.145741i
$723$		0			0
$724$	−18.9336	+	6.15189i	−0.703661	+	0.228633i
$725$	31.3648	+	16.8781i	1.16486	+	0.626838i
$726$		0			0
$727$	−2.03448	−	2.80023i	−0.0754548	−	0.103855i	0.769621	−	0.638501i	$-0.220445\pi$
$727$	−2.03448	−	2.80023i	−0.0754548	−	0.103855i	−0.845076	+	0.534646i	$0.820445\pi$
$728$	−16.2253	−	15.5129i	−0.601349	−	0.574948i
$729$		0			0
$730$	−0.169080	+	0.0814248i	−0.00625795	+	0.00301367i
$731$	−8.74124	+	5.22265i	−0.323306	+	0.193167i
$732$		0			0
$733$	−23.7907	−	5.43007i	−0.878728	−	0.200564i	−0.240721	−	0.970594i	$-0.577384\pi$
$733$	−23.7907	−	5.43007i	−0.878728	−	0.200564i	−0.638007	+	0.770030i	$0.720241\pi$
$734$	0.866510	+	4.77487i	0.0319835	+	0.176243i
$735$		0			0
$736$	2.57626	+	2.05450i	0.0949621	+	0.0757298i
$737$	29.7167	−	49.7374i	1.09463	−	1.83210i
$738$		0			0
$739$	3.90686	+	28.8416i	0.143716	+	1.06096i	0.908861	+	0.417098i	$0.136953\pi$
$739$	3.90686	+	28.8416i	0.143716	+	1.06096i	−0.765145	+	0.643858i	$0.777333\pi$
$740$	−2.52160	+	2.01091i	−0.0926960	+	0.0739226i
$741$		0			0
$742$	−15.0149	−	7.23078i	−0.551213	−	0.265450i
$743$	−41.0804	+	3.69730i	−1.50709	+	0.135641i	−0.812160	−	0.583434i	$-0.801709\pi$
$743$	−41.0804	+	3.69730i	−1.50709	+	0.135641i	−0.694933	+	0.719075i	$0.744566\pi$
$744$		0			0
$745$	−8.94048	+	3.82134i	−0.327554	+	0.140003i
$746$	8.48525	−	3.62677i	0.310667	−	0.132785i
$747$		0			0
$748$	18.5941	−	1.67350i	0.679868	−	0.0611892i
$749$	25.4319	+	12.2474i	0.929263	+	0.447509i
$750$		0			0
$751$	−13.5796	+	10.8294i	−0.495527	+	0.395170i	−0.839118	−	0.543950i	$-0.816928\pi$
$751$	−13.5796	+	10.8294i	−0.495527	+	0.395170i	0.343591	+	0.939120i	$0.388357\pi$
$752$	0.625151	+	4.61505i	0.0227969	+	0.168294i
$753$		0			0
$754$	13.4729	−	22.5498i	0.490654	−	0.821216i
$755$	3.60900	+	2.87808i	0.131345	+	0.104744i
$756$		0			0
$757$	3.67232	+	20.2361i	0.133473	+	0.735495i	0.979358	+	0.202131i	$0.0647867\pi$
$757$	3.67232	+	20.2361i	0.133473	+	0.735495i	−0.845886	+	0.533364i	$0.820928\pi$
$758$	1.76118	+	0.401977i	0.0639688	+	0.0146005i
$759$		0			0
$760$	−5.97243	+	3.56836i	−0.216643	+	0.129438i
$761$	−7.84701	+	3.77892i	−0.284454	+	0.136986i	−0.570670	−	0.821179i	$-0.693317\pi$
$761$	−7.84701	+	3.77892i	−0.284454	+	0.136986i	0.286217	+	0.958165i	$0.407602\pi$
$762$		0			0
$763$	10.3150	+	9.86215i	0.373428	+	0.357034i
$764$	−3.83724	−	5.28151i	−0.138826	−	0.191078i
$765$		0			0
$766$	−12.4508	−	6.70004i	−0.449864	−	0.242082i
$767$	−12.0934	+	3.92937i	−0.436666	+	0.141881i
$768$		0			0
$769$	−40.9835	+	27.0529i	−1.47790	+	0.975554i	−0.482902	+	0.875674i	$0.660417\pi$
$769$	−40.9835	+	27.0529i	−1.47790	+	0.975554i	−0.995000	+	0.0998798i	$0.968154\pi$
$770$	−2.22990	−	8.07985i	−0.0803599	−	0.291178i
$771$		0			0
$772$	−4.68146	+	12.4737i	−0.168490	+	0.448939i
$773$	−17.8235	+	6.68929i	−0.641068	+	0.240597i	−0.650674	−	0.759357i	$-0.725514\pi$
$773$	−17.8235	+	6.68929i	−0.641068	+	0.240597i	0.00960611	+	0.999954i	$0.496942\pi$
$774$		0			0
$775$	37.1621	+	24.5305i	1.33490	+	0.881161i
$776$	11.7387	−	36.1281i	0.421396	−	1.29692i
$777$		0			0
$778$	1.23564	−	6.80895i	0.0442999	−	0.244113i
$779$	1.39487	−	3.26345i	0.0499763	−	0.116925i
$780$		0			0
$781$	−39.6955	+	23.9419i	−1.42042	+	0.856708i
$782$			2.40721i			0.0860817i
$783$		0			0
$784$	−2.14871	−	0.389933i	−0.0767396	−	0.0139262i
$785$	−7.30263	+	6.98203i	−0.260642	+	0.249199i
$786$		0			0
$787$	−9.87121	+	14.9543i	−0.351871	+	0.533061i	−0.966804	−	0.255517i	$-0.917754\pi$
$787$	−9.87121	+	14.9543i	−0.351871	+	0.533061i	0.614934	+	0.788579i	$0.289183\pi$
$788$	10.6849	−	9.33513i	0.380634	−	0.332550i
$789$		0			0
$790$	−9.95356	−	3.73563i	−0.354132	−	0.132908i
$791$	1.73043	−	1.98063i	0.0615268	−	0.0704231i
$792$		0			0
$793$	−12.2412	−	18.5446i	−0.434697	−	0.658539i
$794$	−22.3221	−	6.16052i	−0.792183	−	0.218629i
$795$		0			0
$796$	−7.29237	+	13.5515i	−0.258471	+	0.480320i
$797$	−33.6583	−	1.51160i	−1.19224	−	0.0535435i	−0.560118	−	0.828413i	$-0.689244\pi$
$797$	−33.6583	−	1.51160i	−1.19224	−	0.0535435i	−0.632121	+	0.774869i	$0.717816\pi$
$798$		0			0
$799$	9.98834	−	10.4470i	0.353362	−	0.369588i
$800$	−19.5890	+	10.5413i	−0.692574	+	0.372690i
$801$		0			0
$802$	17.1383	+	28.6848i	0.605176	+	1.01289i
$803$	−0.204791	+	1.51183i	−0.00722693	+	0.0533513i
$804$		0			0
$805$	−0.995570	+	0.180669i	−0.0350892	+	0.00636776i
$806$	19.3026	−	26.5678i	0.679906	−	0.935811i
$807$		0			0
$808$	31.2075	+	18.6456i	1.09787	+	0.655949i
$809$	−9.54547	−	0.859108i	−0.335601	−	0.0302046i	−0.0794426	−	0.996839i	$-0.525314\pi$
$809$	−9.54547	−	0.859108i	−0.335601	−	0.0302046i	−0.256158	+	0.966635i	$0.582457\pi$
$810$		0			0
$811$	11.0991	+	13.9179i	0.389743	+	0.488722i	0.937534	−	0.347893i	$-0.113103\pi$
$811$	11.0991	+	13.9179i	0.389743	+	0.488722i	−0.547791	+	0.836615i	$0.684531\pi$
$812$	−0.763526	−	17.0012i	−0.0267945	−	0.596626i
$813$		0			0
$814$	−2.51046	−	27.8935i	−0.0879915	−	0.977665i
$815$	1.60070	+	7.01312i	0.0560701	+	0.245659i
$816$		0			0
$817$	−3.95169	−	9.24544i	−0.138252	−	0.323457i
$818$	−21.0508	+	4.80470i	−0.736023	+	0.167993i
$819$		0			0
$820$	−0.286169	+	0.594236i	−0.00999345	+	0.0207516i
$821$	−2.79519	+	0.125532i	−0.0975529	+	0.00438111i	−0.0935878	−	0.995611i	$-0.529834\pi$
$821$	−2.79519	+	0.125532i	−0.0975529	+	0.00438111i	−0.00396513	+	0.999992i	$0.501262\pi$
$822$		0			0
$823$	−34.3157	+	4.64838i	−1.19617	+	0.162032i	−0.705114	−	0.709094i	$-0.749104\pi$
$823$	−34.3157	+	4.64838i	−1.19617	+	0.162032i	−0.491058	+	0.871127i	$0.663390\pi$
$824$	−5.09273	+	56.5848i	−0.177414	+	1.97123i
$825$		0			0
$826$	5.48633	−	6.87964i	0.190894	−	0.239373i
$827$	1.02487	+	0.744609i	0.0356381	+	0.0258926i	0.605462	−	0.795874i	$-0.292988\pi$
$827$	1.02487	+	0.744609i	0.0356381	+	0.0258926i	−0.569824	+	0.821767i	$0.692988\pi$
$828$		0			0
$829$	10.5416	−	46.1856i	0.366124	−	1.60409i	−0.371199	−	0.928553i	$-0.621053\pi$
$829$	10.5416	−	46.1856i	0.366124	−	1.60409i	0.737323	−	0.675540i	$-0.236090\pi$
$830$	9.65378	+	1.30769i	0.335088	+	0.0453907i
$831$		0			0
$832$	10.3624	+	21.5178i	0.359253	+	0.745996i
$833$	3.21161	+	5.96817i	0.111276	+	0.206785i
$834$		0			0
$835$	3.70361	−	2.69083i	0.128169	−	0.0931199i
$836$	−0.827060	+	18.4159i	−0.0286045	+	0.636928i
$837$		0			0
$838$	7.68899	+	23.6643i	0.265612	+	0.817469i
$839$	−15.1204	+	54.7875i	−0.522014	+	1.89147i	−0.0744439	+	0.997225i	$0.523718\pi$
$839$	−15.1204	+	54.7875i	−0.522014	+	1.89147i	−0.447570	+	0.894249i	$0.647710\pi$
$840$		0			0
$841$	30.9434	−	8.53984i	1.06701	−	0.294477i
$842$	20.0666	+	17.5316i	0.691540	+	0.604180i
$843$		0			0
$844$	−4.08860	−	10.8940i	−0.140736	−	0.374989i
$845$	−0.905539	−	1.03647i	−0.0311515	−	0.0356558i
$846$		0			0
$847$	−41.2535	−	13.4041i	−1.41749	−	0.460569i
$848$	5.69098	+	5.95230i	0.195429	+	0.204403i
$849$		0			0
$850$	−14.9430	−	6.38694i	−0.512541	−	0.219070i
$851$	−3.38080			−0.115892
$852$		0			0
$853$	−6.25980			−0.214332			−0.107166	−	0.994241i	$-0.534178\pi$
$853$	−6.25980			−0.214332			−0.107166	+	0.994241i	$0.534178\pi$
$854$	14.1394	+	6.04346i	0.483839	+	0.206803i
$855$		0			0
$856$	−26.1281	−	27.3278i	−0.893039	−	0.934046i
$857$	−5.18438	−	1.68451i	−0.177095	−	0.0575417i	0.219127	−	0.975696i	$-0.429679\pi$
$857$	−5.18438	−	1.68451i	−0.177095	−	0.0575417i	−0.396222	+	0.918155i	$0.629679\pi$
$858$		0			0
$859$	15.6846	+	17.9525i	0.535152	+	0.612531i	0.955557	−	0.294806i	$-0.0952550\pi$
$859$	15.6846	+	17.9525i	0.535152	+	0.612531i	−0.420405	+	0.907336i	$0.638112\pi$
$860$	0.656553	+	1.74938i	0.0223883	+	0.0596534i
$861$		0			0
$862$	−14.3406	−	12.5290i	−0.488442	−	0.426739i
$863$	32.5488	−	8.98291i	1.10798	−	0.305782i	0.336272	−	0.941765i	$-0.390834\pi$
$863$	32.5488	−	8.98291i	1.10798	−	0.305782i	0.771703	+	0.635983i	$0.219405\pi$
$864$		0			0
$865$	1.46391	−	5.30435i	0.0497744	−	0.180353i
$866$	−10.0092	−	30.8050i	−0.340125	−	1.04680i
$867$		0			0
$868$	0.954538	−	21.2545i	0.0323991	−	0.721423i
$869$	−69.9229	+	50.8019i	−2.37197	+	1.72334i
$870$		0			0
$871$	−16.5011	−	30.6642i	−0.559118	−	1.03902i
$872$	−8.29369	−	17.2220i	−0.280860	−	0.583212i
$873$		0			0
$874$	−2.35543	−	0.319064i	−0.0796735	−	0.0107925i
$875$	3.18785	−	13.9669i	0.107769	−	0.472167i
$876$		0			0
$877$	−6.42945	−	4.67127i	−0.217107	−	0.157738i	0.473916	−	0.880570i	$-0.342840\pi$
$877$	−6.42945	−	4.67127i	−0.217107	−	0.157738i	−0.691024	+	0.722832i	$0.742840\pi$
$878$	−9.88647	+	12.3972i	−0.333652	+	0.418387i
$879$		0			0
$880$	−0.371278	+	4.12524i	−0.0125158	+	0.139062i
$881$	−19.3917	+	2.62679i	−0.653323	+	0.0884987i	−0.453392	−	0.891311i	$-0.649786\pi$
$881$	−19.3917	+	2.62679i	−0.653323	+	0.0884987i	−0.199931	+	0.979810i	$0.564072\pi$
$882$		0			0
$883$	1.97961	−	0.0889044i	0.0666192	−	0.00299187i	−0.0115303	−	0.999934i	$-0.503670\pi$
$883$	1.97961	−	0.0889044i	0.0666192	−	0.00299187i	0.0781495	+	0.996942i	$0.475099\pi$
$884$	4.86840	−	10.1093i	0.163742	−	0.340014i
$885$		0			0
$886$	4.55407	−	1.03944i	0.152997	−	0.0349205i
$887$	7.68617	+	17.9827i	0.258076	+	0.603800i	0.997593	−	0.0693383i	$-0.0220888\pi$
$887$	7.68617	+	17.9827i	0.258076	+	0.603800i	−0.739517	+	0.673138i	$0.764946\pi$
$888$		0			0
$889$	−7.64069	−	33.4761i	−0.256261	−	1.12275i
$890$	−0.745812	−	8.28665i	−0.0249997	−	0.277769i
$891$		0			0
$892$	−1.01597	−	22.6222i	−0.0340170	−	0.757448i
$893$	8.89835	+	11.1582i	0.297772	+	0.373394i
$894$		0			0
$895$	−1.04884	−	0.0943970i	−0.0350587	−	0.00315534i
$896$	4.68247	+	2.79764i	0.156430	+	0.0934627i
$897$		0			0
$898$	−24.3440	+	33.5066i	−0.812370	+	1.11813i
$899$	75.1582	−	13.6392i	2.50667	−	0.454893i
$900$		0			0
$901$	3.43068	−	25.3263i	0.114293	−	0.843742i
$902$	−2.93746	−	4.91647i	−0.0978066	−	0.163701i
$903$		0			0
$904$	−3.10216	+	1.66934i	−0.103176	+	0.0555215i
$905$	−9.47259	+	9.90755i	−0.314879	+	0.329338i
$906$		0			0
$907$	−34.5510	−	1.55169i	−1.14725	−	0.0515230i	−0.536892	−	0.843651i	$-0.680402\pi$
$907$	−34.5510	−	1.55169i	−1.14725	−	0.0515230i	−0.610355	+	0.792128i	$0.708973\pi$
$908$	2.11275	−	3.92616i	0.0701142	−	0.130294i
$909$		0			0
$910$	−4.85612	−	1.34020i	−0.160979	−	0.0444273i
$911$	24.3633	+	36.9088i	0.807191	+	1.22284i	0.971642	+	0.236457i	$0.0759863\pi$
$911$	24.3633	+	36.9088i	0.807191	+	1.22284i	−0.164451	+	0.986385i	$0.552585\pi$
$912$		0			0
$913$	52.1074	−	59.6417i	1.72450	−	1.97385i
$914$	−28.0813	−	10.5391i	−0.928846	−	0.348602i
$915$		0			0
$916$	1.78760	−	1.56178i	0.0590641	−	0.0516028i
$917$	0.419070	−	0.634864i	0.0138389	−	0.0209651i
$918$		0			0
$919$	7.89617	−	7.54951i	0.260471	−	0.249035i	−0.549517	−	0.835483i	$-0.685188\pi$
$919$	7.89617	−	7.54951i	0.260471	−	0.249035i	0.809987	+	0.586447i	$0.199474\pi$
$920$	1.33350	+	0.241994i	0.0439641	+	0.00797831i
$921$		0			0
$922$		−	0.466169i		−	0.0153525i
$923$	0.116042	+	27.8609i	0.00381957	+	0.917052i
$924$		0			0
$925$	8.97011	−	20.9866i	0.294935	−	0.690036i
$926$	5.76011	−	31.7408i	0.189289	−	1.04307i
$927$		0			0
$928$	−11.7922	+	36.2926i	−0.387097	+	1.19136i
$929$	26.3356	+	17.3840i	0.864045	+	0.570351i	0.903363	−	0.428876i	$-0.141090\pi$
$929$	26.3356	+	17.3840i	0.864045	+	0.570351i	−0.0393189	+	0.999227i	$0.512519\pi$
$930$		0			0
$931$	−6.26547	+	2.35147i	−0.205342	+	0.0770663i
$932$	3.15646	−	8.41036i	0.103393	−	0.275490i
$933$		0			0
$934$	−2.87712	−	10.4250i	−0.0941422	−	0.341116i
$935$	10.7279	−	7.08145i	0.350841	−	0.231588i
$936$		0			0
$937$	14.8231	−	4.81631i	0.484249	−	0.157342i	−0.0567104	−	0.998391i	$-0.518061\pi$
$937$	14.8231	−	4.81631i	0.484249	−	0.157342i	0.540960	+	0.841049i	$0.318061\pi$
$938$	21.2199	+	11.4189i	0.692854	+	0.372841i
$939$		0			0
$940$	−1.55896	−	2.14573i	−0.0508477	−	0.0699859i
$941$	−7.47618	−	7.14796i	−0.243717	−	0.233017i	0.559312	−	0.828957i	$-0.311065\pi$
$941$	−7.47618	−	7.14796i	−0.243717	−	0.233017i	−0.803029	+	0.595940i	$0.796780\pi$
$942$		0			0
$943$	−0.622894	+	0.299970i	−0.0202842	+	0.00976836i
$944$	−3.73271	+	2.23019i	−0.121489	+	0.0725866i
$945$		0			0
$946$	−15.8184	−	3.61044i	−0.514300	−	0.117386i
$947$	2.45462	+	13.5261i	0.0797643	+	0.439538i	0.998954	+	0.0457230i	$0.0145592\pi$
$947$	2.45462	+	13.5261i	0.0797643	+	0.439538i	−0.919190	+	0.393815i	$0.871155\pi$
$948$		0			0
$949$	0.716886	+	0.571698i	0.0232711	+	0.0185581i
$950$	8.23017	−	13.7750i	0.267022	−	0.446920i
$951$		0			0
$952$	3.19785	+	23.6075i	0.103643	+	0.765123i
$953$	35.1855	−	28.0595i	1.13977	−	0.908935i	0.143037	−	0.989717i	$-0.454313\pi$
$953$	35.1855	−	28.0595i	1.13977	−	0.908935i	0.996732	+	0.0807818i	$0.0257417\pi$
$954$		0			0
$955$	−4.04981	−	1.95029i	−0.131049	−	0.0631098i
$956$	18.4067	−	1.65664i	0.595316	−	0.0535794i
$957$		0			0
$958$	−16.2678	+	6.95321i	−0.525590	+	0.224648i
$959$	−15.9873	+	6.83328i	−0.516256	+	0.220658i
$960$		0			0
$961$	64.2356	−	5.78131i	2.07212	−	0.186494i
$962$	−15.1653	−	7.30320i	−0.488948	−	0.235465i
$963$		0			0
$964$	−8.85054	+	7.05807i	−0.285057	+	0.227325i
$965$	1.23139	+	9.09050i	0.0396399	+	0.292634i
$966$		0			0
$967$	15.1888	−	25.4217i	0.488438	−	0.817507i	−0.510668	−	0.859778i	$-0.670602\pi$
$967$	15.1888	−	25.4217i	0.488438	−	0.817507i	0.999106	+	0.0422704i	$0.0134591\pi$
$968$	45.4243	+	36.2246i	1.45999	+	1.16430i
$969$		0			0
$970$	−1.52218	−	8.38792i	−0.0488744	−	0.269320i
$971$	15.9273	+	3.63530i	0.511131	+	0.116662i	0.470305	−	0.882504i	$-0.344144\pi$
$971$	15.9273	+	3.63530i	0.511131	+	0.116662i	0.0408261	+	0.999166i	$0.487001\pi$
$972$		0			0
$973$	1.50431	−	0.898785i	0.0482261	−	0.0288137i
$974$	−9.93033	+	4.78220i	−0.318188	+	0.153231i
$975$		0			0
$976$	−5.49210	−	5.25098i	−0.175798	−	0.168080i
$977$	−23.7060	−	32.6286i	−0.758423	−	1.04388i	−0.997344	−	0.0728408i	$-0.976794\pi$
$977$	−23.7060	−	32.6286i	−0.758423	−	1.04388i	0.238920	−	0.971039i	$-0.423206\pi$
$978$		0			0
$979$	−59.5628	−	32.0521i	−1.90364	−	1.02439i
$980$	1.18280	−	0.384315i	0.0377832	−	0.0122765i
$981$		0			0
$982$	2.58064	−	1.70347i	0.0823517	−	0.0543599i
$983$	−12.8498	−	46.5601i	−0.409844	−	1.48504i	−0.819650	−	0.572865i	$-0.805832\pi$
$983$	−12.8498	−	46.5601i	−0.409844	−	1.48504i	0.409806	−	0.912173i	$-0.365597\pi$
$984$		0			0
$985$	3.43266	−	9.14629i	0.109374	−	0.291425i
$986$	−26.0996	+	9.79536i	−0.831182	+	0.311948i
$987$		0			0
$988$	9.24658	+	6.10361i	0.294173	+	0.194182i
$989$	−0.605253	+	1.86278i	−0.0192459	+	0.0592328i
$990$		0			0
$991$	5.34757	−	29.4676i	0.169871	−	0.936068i	−0.780548	−	0.625096i	$-0.785060\pi$
$991$	5.34757	−	29.4676i	0.169871	−	0.936068i	0.950419	−	0.310972i	$-0.100654\pi$
$992$	−18.7500	+	43.8678i	−0.595313	+	1.39280i
$993$		0			0
$994$	−10.6883	−	16.0463i	−0.339012	−	0.508959i
$995$			10.5959i			0.335911i
$996$		0			0
$997$	−48.0146	−	8.71337i	−1.52064	−	0.275955i	−0.646984	−	0.762504i	$-0.723970\pi$
$997$	−48.0146	−	8.71337i	−1.52064	−	0.275955i	−0.873654	+	0.486548i	$0.838256\pi$
$998$	−16.6066	+	15.8775i	−0.525672	+	0.502594i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	639.2.z.a.269.9	✓	576
3.2	odd	2	inner	639.2.z.a.269.16	yes	576
71.52	odd	70	inner	639.2.z.a.620.16	yes	576
213.194	even	70	inner	639.2.z.a.620.9	yes	576

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
639.2.z.a.269.9	✓	576	1.1	even	1	trivial
639.2.z.a.269.16	yes	576	3.2	odd	2	inner
639.2.z.a.620.9	yes	576	213.194	even	70	inner
639.2.z.a.620.16	yes	576	71.52	odd	70	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 639 = 3^{2} \cdot 71 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	639.z (of order \(70\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.934550 - 0.399446i) q^{2} +(-0.668298 - 0.698985i) q^{4} +(-0.633263 - 0.205760i) q^{5} +(-1.48125 - 1.69543i) q^{7} +(1.05958 + 2.82325i) q^{8} +O(q^{10})\)	\(q+(-0.934550 - 0.399446i) q^{2} +(-0.668298 - 0.698985i) q^{4} +(-0.633263 - 0.205760i) q^{5} +(-1.48125 - 1.69543i) q^{7} +(1.05958 + 2.82325i) q^{8} +(0.509626 + 0.445247i) q^{10} +(5.30327 - 1.46361i) q^{11} +(0.879653 - 3.18735i) q^{13} +(0.707072 + 2.17614i) q^{14} +(0.0507277 - 1.12954i) q^{16} +(-2.83889 + 2.06257i) q^{17} +(-1.64192 - 3.05120i) q^{19} +(0.279386 + 0.580151i) q^{20} +(-5.54081 - 0.750553i) q^{22} +(-0.150196 + 0.658050i) q^{23} +(-3.68640 - 2.67833i) q^{25} +(-2.09525 + 2.62736i) q^{26} +(-0.195162 + 2.16843i) q^{28} +(-7.74592 + 1.04926i) q^{29} +(-9.76233 + 0.438427i) q^{31} +(2.11818 - 4.39845i) q^{32} +(3.47697 - 0.793595i) q^{34} +(0.589172 + 1.37844i) q^{35} +(1.11456 + 4.88321i) q^{37} +(0.315668 + 3.50736i) q^{38} +(-0.0900841 - 2.00588i) q^{40} +(0.638627 + 0.800813i) q^{41} +(2.89012 + 0.260116i) q^{43} +(-4.56721 - 2.72878i) q^{44} +(0.403220 - 0.554985i) q^{46} +(-4.05275 + 0.735465i) q^{47} +(0.259259 - 1.91393i) q^{49} +(2.37528 + 3.97555i) q^{50} +(-2.81578 + 1.51524i) q^{52} +(-5.03324 + 5.26436i) q^{53} +(-3.65952 - 0.164349i) q^{55} +(3.21711 - 5.97839i) q^{56} +(7.65807 + 2.11349i) q^{58} +(-2.11856 - 3.20949i) q^{59} +(4.42150 - 5.06081i) q^{61} +(9.29851 + 3.48979i) q^{62} +(-5.43946 + 4.75231i) q^{64} +(-1.21288 + 1.83743i) q^{65} +(7.61203 - 7.27784i) q^{67} +(3.33893 + 0.605927i) q^{68} -1.52356i q^{70} +(-8.11309 + 2.27548i) q^{71} +(-0.108990 + 0.254996i) q^{73} +(0.908965 - 5.00881i) q^{74} +(-1.03545 + 3.18679i) q^{76} +(-10.3369 - 6.82335i) q^{77} +(-14.7083 + 5.52012i) q^{79} +(-0.264538 + 0.704859i) q^{80} +(-0.276948 - 1.00350i) q^{82} +(12.0142 - 7.93050i) q^{83} +(2.22216 - 0.722023i) q^{85} +(-2.59706 - 1.39754i) q^{86} +(9.75138 + 13.4216i) q^{88} +(-8.88649 - 8.49635i) q^{89} +(-6.70691 + 3.22988i) q^{91} +(0.560342 - 0.334789i) q^{92} +(4.08128 + 0.931525i) q^{94} +(0.411954 + 2.27006i) q^{95} +(-9.84890 - 7.85424i) q^{97} +(-1.00680 + 1.68510i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 576 q - 24 q^{4}+O(q^{10}) \) 576 * q - 24 * q^4	\( 576 q - 24 q^{4} - 16 q^{10} + 76 q^{16} - 8 q^{19} + 20 q^{22} + 168 q^{25} - 20 q^{28} - 28 q^{31} + 40 q^{37} + 32 q^{40} + 52 q^{43} - 20 q^{46} - 208 q^{52} - 92 q^{55} + 56 q^{58} + 56 q^{61} - 144 q^{64} - 16 q^{67} - 44 q^{73} - 336 q^{76} + 88 q^{79} - 124 q^{82} + 60 q^{85} - 260 q^{88} + 80 q^{91} + 56 q^{94} - 56 q^{97}+O(q^{100}) \) 576 * q - 24 * q^4 - 16 * q^10 + 76 * q^16 - 8 * q^19 + 20 * q^22 + 168 * q^25 - 20 * q^28 - 28 * q^31 + 40 * q^37 + 32 * q^40 + 52 * q^43 - 20 * q^46 - 208 * q^52 - 92 * q^55 + 56 * q^58 + 56 * q^61 - 144 * q^64 - 16 * q^67 - 44 * q^73 - 336 * q^76 + 88 * q^79 - 124 * q^82 + 60 * q^85 - 260 * q^88 + 80 * q^91 + 56 * q^94 - 56 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more