LMFDB - Embedded newform 600.2.w.k.557.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [600,2,Mod(293,600)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(600, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 2, 2, 3]))

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

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

chi := DirichletCharacter("600.293");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 600 = 2^{3} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	600.w (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.79102412128$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			557.1
Character	$\chi$	$=$	600.557
Dual form			600.2.w.k.293.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.37896 - 0.313810i) q^{2} +(-1.69016 + 0.378611i) q^{3} +(1.80305 + 0.865461i) q^{4} +(2.44948 + 0.00830235i) q^{6} +(0.699464 + 0.699464i) q^{7} +(-2.21473 - 1.75925i) q^{8} +(2.71331 - 1.27983i) q^{9} +O(q^{10})$	\(q+(-1.37896 - 0.313810i) q^{2} +(-1.69016 + 0.378611i) q^{3} +(1.80305 + 0.865461i) q^{4} +(2.44948 + 0.00830235i) q^{6} +(0.699464 + 0.699464i) q^{7} +(-2.21473 - 1.75925i) q^{8} +(2.71331 - 1.27983i) q^{9} -4.24103 q^{11} +(-3.37512 - 0.780119i) q^{12} +(-2.08220 - 2.08220i) q^{13} +(-0.745032 - 1.18403i) q^{14} +(2.50195 + 3.12093i) q^{16} +(-0.0541732 + 0.0541732i) q^{17} +(-4.14316 + 0.913365i) q^{18} +4.52348 q^{19} +(-1.44703 - 0.917384i) q^{21} +(5.84820 + 1.33088i) q^{22} +(3.48621 + 3.48621i) q^{23} +(4.40933 + 2.13490i) q^{24} +(2.21785 + 3.52469i) q^{26} +(-4.10138 + 3.19041i) q^{27} +(0.655807 + 1.86652i) q^{28} -3.90970i q^{29} -10.2945 q^{31} +(-2.47071 - 5.08877i) q^{32} +(7.16803 - 1.60570i) q^{33} +(0.0917026 - 0.0577024i) q^{34} +(5.99986 + 0.0406728i) q^{36} +(7.29179 - 7.29179i) q^{37} +(-6.23768 - 1.41951i) q^{38} +(4.30761 + 2.73092i) q^{39} -8.74792i q^{41} +(1.70751 + 1.71913i) q^{42} +(-4.60454 - 4.60454i) q^{43} +(-7.64677 - 3.67044i) q^{44} +(-3.71333 - 5.90135i) q^{46} +(8.05631 - 8.05631i) q^{47} +(-5.41033 - 4.32762i) q^{48} -6.02150i q^{49} +(0.0710510 - 0.112072i) q^{51} +(-1.95224 - 5.55638i) q^{52} +(-0.260132 + 0.260132i) q^{53} +(6.65681 - 3.11238i) q^{54} +(-0.318596 - 2.77966i) q^{56} +(-7.64542 + 1.71264i) q^{57} +(-1.22690 + 5.39131i) q^{58} -2.89407i q^{59} +6.70235i q^{61} +(14.1957 + 3.23051i) q^{62} +(2.79305 + 1.00267i) q^{63} +(1.81009 + 7.79253i) q^{64} +(-10.3883 - 0.0352105i) q^{66} +(-1.75168 + 1.75168i) q^{67} +(-0.144561 + 0.0507920i) q^{68} +(-7.21219 - 4.57235i) q^{69} -10.5121i q^{71} +(-8.26079 - 1.93890i) q^{72} +(4.53385 - 4.53385i) q^{73} +(-12.3433 + 7.76683i) q^{74} +(8.15604 + 3.91489i) q^{76} +(-2.96644 - 2.96644i) q^{77} +(-5.08302 - 5.11760i) q^{78} -1.46184i q^{79} +(5.72408 - 6.94514i) q^{81} +(-2.74519 + 12.0630i) q^{82} +(5.61327 - 5.61327i) q^{83} +(-1.81511 - 2.90644i) q^{84} +(4.90451 + 7.79441i) q^{86} +(1.48026 + 6.60804i) q^{87} +(9.39275 + 7.46102i) q^{88} -5.42662 q^{89} -2.91285i q^{91} +(3.26862 + 9.30298i) q^{92} +(17.3994 - 3.89760i) q^{93} +(-13.6375 + 8.58116i) q^{94} +(6.10256 + 7.66542i) q^{96} +(-11.3974 - 11.3974i) q^{97} +(-1.88961 + 8.30339i) q^{98} +(-11.5072 + 5.42779i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 12 q^{6}+O(q^{10}) $ 64 * q + 12 * q^6	$ 64 q + 12 q^{6} - 40 q^{16} + 32 q^{31} - 84 q^{36} - 128 q^{46} - 180 q^{66} + 168 q^{76} + 48 q^{81} + 228 q^{96}+O(q^{100}) $ 64 * q + 12 * q^6 - 40 * q^16 + 32 * q^31 - 84 * q^36 - 128 * q^46 - 180 * q^66 + 168 * q^76 + 48 * q^81 + 228 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/600\mathbb{Z}\right)^\times$.

$n$	$151$	$301$	$401$	$577$
$\chi(n)$	$1$	$-1$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−1.37896	−	0.313810i	−0.975070	−	0.221897i
$2$	−1.37896	−	0.313810i	−0.975070	−	0.221897i
$3$	−1.69016	+	0.378611i	−0.975817	+	0.218591i
$3$	−1.69016	+	0.378611i	−0.975817	+	0.218591i
$4$	1.80305	+	0.865461i	0.901523	+	0.432731i
$5$		0			0
$5$		0			0
$6$	2.44948	+	0.00830235i	0.999994	+	0.00338942i
$7$	0.699464	+	0.699464i	0.264372	+	0.264372i	0.826828	−	0.562455i	$-0.190143\pi$
$7$	0.699464	+	0.699464i	0.264372	+	0.264372i	−0.562455	+	0.826828i	$0.690143\pi$
$8$	−2.21473	−	1.75925i	−0.783027	−	0.621988i
$9$	2.71331	−	1.27983i	0.904436	−	0.426609i
$10$		0			0
$11$	−4.24103			−1.27872			−0.639359	−	0.768908i	$-0.720800\pi$
$11$	−4.24103			−1.27872			−0.639359	+	0.768908i	$0.720800\pi$
$12$	−3.37512	−	0.780119i	−0.974312	−	0.225201i
$13$	−2.08220	−	2.08220i	−0.577500	−	0.577500i	0.356714	−	0.934214i	$-0.383897\pi$
$13$	−2.08220	−	2.08220i	−0.577500	−	0.577500i	−0.934214	+	0.356714i	$0.883897\pi$
$14$	−0.745032	−	1.18403i	−0.199118	−	0.316445i
$15$		0			0
$16$	2.50195	+	3.12093i	0.625488	+	0.780233i
$17$	−0.0541732	+	0.0541732i	−0.0131389	+	0.0131389i	−0.713646	−	0.700507i	$-0.752957\pi$
$17$	−0.0541732	+	0.0541732i	−0.0131389	+	0.0131389i	0.700507	+	0.713646i	$0.252957\pi$
$18$	−4.14316	+	0.913365i	−0.976552	+	0.215282i
$19$	4.52348			1.03776			0.518878	−	0.854848i	$-0.326350\pi$
$19$	4.52348			1.03776			0.518878	+	0.854848i	$0.326350\pi$
$20$		0			0
$21$	−1.44703	−	0.917384i	−0.315768	−	0.200190i
$22$	5.84820	+	1.33088i	1.24684	+	0.283744i
$23$	3.48621	+	3.48621i	0.726925	+	0.726925i	0.970006	−	0.243081i	$-0.0781580\pi$
$23$	3.48621	+	3.48621i	0.726925	+	0.726925i	−0.243081	+	0.970006i	$0.578158\pi$
$24$	4.40933	+	2.13490i	0.900051	+	0.435784i
$25$		0			0
$26$	2.21785	+	3.52469i	0.434957	+	0.691248i
$27$	−4.10138	+	3.19041i	−0.789311	+	0.613994i
$28$	0.655807	+	1.86652i	0.123936	+	0.352740i
$29$		−	3.90970i		−	0.726014i	−0.931786	−	0.363007i	$-0.881750\pi$
$29$		−	3.90970i		−	0.726014i	0.931786	−	0.363007i	$-0.118250\pi$
$30$		0			0
$31$	−10.2945			−1.84894			−0.924472	−	0.381250i	$-0.875494\pi$
$31$	−10.2945			−1.84894			−0.924472	+	0.381250i	$0.875494\pi$
$32$	−2.47071	−	5.08877i	−0.436764	−	0.899576i
$33$	7.16803	−	1.60570i	1.24779	−	0.279516i
$34$	0.0917026	−	0.0577024i	0.0157269	−	0.00989588i
$35$		0			0
$36$	5.99986	+	0.0406728i	0.999977	+	0.00677880i
$37$	7.29179	−	7.29179i	1.19876	−	1.19876i	0.224225	−	0.974537i	$-0.428015\pi$
$37$	7.29179	−	7.29179i	1.19876	−	1.19876i	0.974537	−	0.224225i	$-0.0719849\pi$
$38$	−6.23768	−	1.41951i	−1.01189	−	0.230275i
$39$	4.30761	+	2.73092i	0.689770	+	0.437298i
$40$		0			0
$41$		−	8.74792i		−	1.36620i	−0.730327	−	0.683098i	$-0.760632\pi$
$41$		−	8.74792i		−	1.36620i	0.730327	−	0.683098i	$-0.239368\pi$
$42$	1.70751	+	1.71913i	0.263475	+	0.265267i
$43$	−4.60454	−	4.60454i	−0.702185	−	0.702185i	0.262694	−	0.964879i	$-0.415389\pi$
$43$	−4.60454	−	4.60454i	−0.702185	−	0.702185i	−0.964879	+	0.262694i	$0.915389\pi$
$44$	−7.64677	−	3.67044i	−1.15279	−	0.553340i
$45$		0			0
$46$	−3.71333	−	5.90135i	−0.547501	−	0.870106i
$47$	8.05631	−	8.05631i	1.17513	−	1.17513i	0.194165	−	0.980969i	$-0.437800\pi$
$47$	8.05631	−	8.05631i	1.17513	−	1.17513i	0.980969	−	0.194165i	$-0.0621996\pi$
$48$	−5.41033	−	4.32762i	−0.780914	−	0.624639i
$49$		−	6.02150i		−	0.860214i
$50$		0			0
$51$	0.0710510	−	0.112072i	0.00994913	−	0.0156932i
$52$	−1.95224	−	5.55638i	−0.270728	−	0.770531i
$53$	−0.260132	+	0.260132i	−0.0357319	+	0.0357319i	−0.724747	−	0.689015i	$-0.758043\pi$
$53$	−0.260132	+	0.260132i	−0.0357319	+	0.0357319i	0.689015	+	0.724747i	$0.258043\pi$
$54$	6.65681	−	3.11238i	0.905877	−	0.423541i
$55$		0			0
$56$	−0.318596	−	2.77966i	−0.0425742	−	0.371447i
$57$	−7.64542	+	1.71264i	−1.01266	+	0.226844i
$58$	−1.22690	+	5.39131i	−0.161100	+	0.707914i
$59$		−	2.89407i		−	0.376775i	−0.982095	−	0.188388i	$-0.939674\pi$
$59$		−	2.89407i		−	0.376775i	0.982095	−	0.188388i	$-0.0603261\pi$
$60$		0			0
$61$			6.70235i			0.858148i	0.903269	+	0.429074i	$0.141160\pi$
$61$			6.70235i			0.858148i	−0.903269	+	0.429074i	$0.858840\pi$
$62$	14.1957	+	3.23051i	1.80285	+	0.410276i
$63$	2.79305	+	1.00267i	0.351892	+	0.126324i
$64$	1.81009	+	7.79253i	0.226262	+	0.974067i
$65$		0			0
$66$	−10.3883	−	0.0352105i	−1.27871	−	0.00433411i
$67$	−1.75168	+	1.75168i	−0.214002	+	0.214002i	−0.805965	−	0.591963i	$-0.798353\pi$
$67$	−1.75168	+	1.75168i	−0.214002	+	0.214002i	0.591963	+	0.805965i	$0.298353\pi$
$68$	−0.144561	+	0.0507920i	−0.0175307	+	0.00615943i
$69$	−7.21219	−	4.57235i	−0.868245	−	0.550447i
$70$		0			0
$71$		−	10.5121i		−	1.24755i	−0.781603	−	0.623776i	$-0.785598\pi$
$71$		−	10.5121i		−	1.24755i	0.781603	−	0.623776i	$-0.214402\pi$
$72$	−8.26079	−	1.93890i	−0.973543	−	0.228502i
$73$	4.53385	−	4.53385i	0.530647	−	0.530647i	−0.390118	−	0.920765i	$-0.627566\pi$
$73$	4.53385	−	4.53385i	0.530647	−	0.530647i	0.920765	+	0.390118i	$0.127566\pi$
$74$	−12.3433	+	7.76683i	−1.43488	+	0.902875i
$75$		0			0
$76$	8.15604	+	3.91489i	0.935562	+	0.449069i
$77$	−2.96644	−	2.96644i	−0.338058	−	0.338058i
$78$	−5.08302	−	5.11760i	−0.575539	−	0.579454i
$79$		−	1.46184i		−	0.164470i	−0.996613	−	0.0822352i	$-0.973794\pi$
$79$		−	1.46184i		−	0.164470i	0.996613	−	0.0822352i	$-0.0262059\pi$
$80$		0			0
$81$	5.72408	−	6.94514i	0.636009	−	0.771682i
$82$	−2.74519	+	12.0630i	−0.303155	+	1.33214i
$83$	5.61327	−	5.61327i	0.616136	−	0.616136i	−0.328402	−	0.944538i	$-0.606510\pi$
$83$	5.61327	−	5.61327i	0.616136	−	0.616136i	0.944538	+	0.328402i	$0.106510\pi$
$84$	−1.81511	−	2.90644i	−0.198044	−	0.317118i
$85$		0			0
$86$	4.90451	+	7.79441i	0.528867	+	0.840493i
$87$	1.48026	+	6.60804i	0.158700	+	0.708456i
$88$	9.39275	+	7.46102i	1.00127	+	0.795347i
$89$	−5.42662			−0.575220			−0.287610	−	0.957748i	$-0.592861\pi$
$89$	−5.42662			−0.575220			−0.287610	+	0.957748i	$0.592861\pi$
$90$		0			0
$91$		−	2.91285i		−	0.305350i
$92$	3.26862	+	9.30298i	0.340777	+	0.969903i
$93$	17.3994	−	3.89760i	1.80423	−	0.404163i
$94$	−13.6375	+	8.58116i	−1.40660	+	0.885079i
$95$		0			0
$96$	6.10256	+	7.66542i	0.622840	+	0.782349i
$97$	−11.3974	−	11.3974i	−1.15723	−	1.15723i	−0.985069	−	0.172162i	$-0.944925\pi$
$97$	−11.3974	−	11.3974i	−1.15723	−	1.15723i	−0.172162	−	0.985069i	$-0.555075\pi$
$98$	−1.88961	+	8.30339i	−0.190879	+	0.838769i
$99$	−11.5072	+	5.42779i	−1.15652	+	0.545513i
$100$		0			0
$101$	14.7072			1.46342			0.731712	−	0.681614i	$-0.238721\pi$
$101$	14.7072			1.46342			0.731712	+	0.681614i	$0.238721\pi$
$102$	−0.133146	+	0.132246i	−0.0131834	+	0.0130943i
$103$	−8.08829	+	8.08829i	−0.796963	+	0.796963i	−0.982616	−	0.185652i	$-0.940560\pi$
$103$	−8.08829	+	8.08829i	−0.796963	+	0.796963i	0.185652	+	0.982616i	$0.440560\pi$
$104$	0.948415	+	8.27464i	0.0929997	+	0.811396i
$105$		0			0
$106$	0.440344	−	0.277079i	0.0427700	−	0.0269123i
$107$	2.56066	+	2.56066i	0.247548	+	0.247548i	0.819964	−	0.572416i	$-0.193994\pi$
$107$	2.56066	+	2.56066i	0.247548	+	0.247548i	−0.572416	+	0.819964i	$0.693994\pi$
$108$	−10.1561	+	2.20287i	−0.977276	+	0.211971i
$109$	9.32403			0.893080			0.446540	−	0.894764i	$-0.352656\pi$
$109$	9.32403			0.893080			0.446540	+	0.894764i	$0.352656\pi$
$110$		0			0
$111$	−9.56356	+	15.0851i	−0.907733	+	1.43181i
$112$	−0.432954	+	3.93301i	−0.0409103	+	0.371634i
$113$	−5.67068	−	5.67068i	−0.533453	−	0.533453i	0.388145	−	0.921598i	$-0.373116\pi$
$113$	−5.67068	−	5.67068i	−0.533453	−	0.533453i	−0.921598	+	0.388145i	$0.873116\pi$
$114$	11.0801	+	0.0375555i	1.03775	+	0.00351740i
$115$		0			0
$116$	3.38370	−	7.04938i	0.314168	−	0.654518i
$117$	−8.31453	−	2.98480i	−0.768678	−	0.275945i
$118$	−0.908187	+	3.99079i	−0.0836054	+	0.367382i
$119$	−0.0757843			−0.00694714
$120$		0			0
$121$	6.98631			0.635120
$122$	2.10326	−	9.24226i	0.190421	−	0.836755i
$123$	3.31206	+	14.7854i	0.298638	+	1.33316i
$124$	−18.5614	−	8.90948i	−1.66687	−	0.800095i
$125$		0			0
$126$	−3.53686	−	2.25912i	−0.315088	−	0.201259i
$127$	10.1183	+	10.1183i	0.897851	+	0.897851i	0.995246	−	0.0973946i	$-0.0310509\pi$
$127$	10.1183	+	10.1183i	0.897851	+	0.897851i	−0.0973946	+	0.995246i	$0.531051\pi$
$128$	−0.0506660	−	11.3136i	−0.00447828	−	0.999990i
$129$	9.52575	+	6.03909i	0.838695	+	0.531713i
$130$		0			0
$131$	−9.97112			−0.871181			−0.435590	−	0.900145i	$-0.643460\pi$
$131$	−9.97112			−0.871181			−0.435590	+	0.900145i	$0.643460\pi$
$132$	14.3140	+	3.30850i	1.24587	+	0.287968i
$133$	3.16401	+	3.16401i	0.274354	+	0.274354i
$134$	2.96519	−	1.86580i	0.256153	−	0.161180i
$135$		0			0
$136$	0.215283	−	0.0246751i	0.0184604	−	0.00211587i
$137$	−1.41009	+	1.41009i	−0.120472	+	0.120472i	−0.764773	−	0.644300i	$-0.777149\pi$
$137$	−1.41009	+	1.41009i	−0.120472	+	0.120472i	0.644300	+	0.764773i	$0.277149\pi$
$138$	8.51045	+	8.56833i	0.724457	+	0.729385i
$139$	−5.04740			−0.428115			−0.214058	−	0.976821i	$-0.568668\pi$
$139$	−5.04740			−0.428115			−0.214058	+	0.976821i	$0.568668\pi$
$140$		0			0
$141$	−10.5663	+	16.6667i	−0.889841	+	1.40359i
$142$	−3.29879	+	14.4957i	−0.276828	+	1.21645i
$143$	8.83069	+	8.83069i	0.738459	+	0.738459i
$144$	10.7828	+	5.26598i	0.898569	+	0.438832i
$145$		0			0
$146$	−7.67476	+	4.82922i	−0.635168	+	0.399669i
$147$	2.27980	+	10.1773i	0.188035	+	0.839411i
$148$	19.4582	−	6.83667i	1.59945	−	0.561971i
$149$			21.5110i			1.76225i	0.472883	+	0.881125i	$0.343213\pi$
$149$			21.5110i			1.76225i	−0.472883	+	0.881125i	$0.656787\pi$
$150$		0			0
$151$	1.40598			0.114417			0.0572087	−	0.998362i	$-0.481780\pi$
$151$	1.40598			0.114417			0.0572087	+	0.998362i	$0.481780\pi$
$152$	−10.0183	−	7.95792i	−0.812591	−	0.645472i
$153$	−0.0776561	+	0.216321i	−0.00627813	+	0.0174885i
$154$	3.15970	+	5.02150i	0.254616	+	0.404644i
$155$		0			0
$156$	5.40332	+	8.65205i	0.432612	+	0.692718i
$157$	−4.32933	+	4.32933i	−0.345518	+	0.345518i	−0.858437	−	0.512919i	$-0.828564\pi$
$157$	−4.32933	+	4.32933i	−0.345518	+	0.345518i	0.512919	+	0.858437i	$0.328564\pi$
$158$	−0.458741	+	2.01582i	−0.0364955	+	0.160370i
$159$	0.341178	−	0.538155i	0.0270571	−	0.0426785i
$160$		0			0
$161$			4.87696i			0.384358i
$162$	−10.0727	+	7.78077i	−0.791387	+	0.611315i
$163$	−8.66748	−	8.66748i	−0.678890	−	0.678890i	0.280859	−	0.959749i	$-0.409381\pi$
$163$	−8.66748	−	8.66748i	−0.678890	−	0.678890i	−0.959749	+	0.280859i	$0.909381\pi$
$164$	7.57099	−	15.7729i	0.591195	−	1.23166i
$165$		0			0
$166$	−9.50195	+	5.97896i	−0.737495	+	0.464057i
$167$	−1.85826	+	1.85826i	−0.143797	+	0.143797i	−0.775340	−	0.631544i	$-0.782422\pi$
$167$	−1.85826	+	1.85826i	−0.143797	+	0.143797i	0.631544	+	0.775340i	$0.282422\pi$
$168$	1.59089	+	4.57745i	0.122740	+	0.353158i
$169$		−	4.32885i		−	0.332988i
$170$		0			0
$171$	12.2736	−	5.78927i	0.938585	−	0.442717i
$172$	−4.31715	−	12.2872i	−0.329179	−	0.936893i
$173$	−5.00691	+	5.00691i	−0.380668	+	0.380668i	−0.871343	−	0.490675i	$-0.836750\pi$
$173$	−5.00691	+	5.00691i	−0.380668	+	0.380668i	0.490675	+	0.871343i	$0.336750\pi$
$174$	0.0324597	−	9.57672i	0.00246077	−	0.726009i
$175$		0			0
$176$	−10.6109	−	13.2360i	−0.799823	−	0.997698i
$177$	1.09572	+	4.89145i	0.0823597	+	0.367664i
$178$	7.48307	+	1.70293i	0.560880	+	0.127640i
$179$		−	5.06744i		−	0.378758i	−0.981904	−	0.189379i	$-0.939352\pi$
$179$		−	5.06744i		−	0.378758i	0.981904	−	0.189379i	$-0.0606475\pi$
$180$		0			0
$181$		−	4.31343i		−	0.320614i	−0.987067	−	0.160307i	$-0.948752\pi$
$181$		−	4.31343i		−	0.320614i	0.987067	−	0.160307i	$-0.0512485\pi$
$182$	−0.914082	+	4.01670i	−0.0677563	+	0.297738i
$183$	−2.53758	−	11.3281i	−0.187583	−	0.837395i
$184$	−1.58792	−	13.8541i	−0.117063	−	1.02134i
$185$		0			0
$186$	−25.2161	−	0.0854685i	−1.84893	−	0.00626685i
$187$	0.229750	−	0.229750i	0.0168010	−	0.0168010i
$188$	21.4983	−	7.55348i	1.56793	−	0.550894i
$189$	−5.10034	−	0.637192i	−0.370995	−	0.0463489i
$190$		0			0
$191$			19.8096i			1.43337i	0.697395	+	0.716687i	$0.254343\pi$
$191$			19.8096i			1.43337i	−0.697395	+	0.716687i	$0.745657\pi$
$192$	−6.00969	−	12.4853i	−0.433712	−	0.901052i
$193$	−3.01513	+	3.01513i	−0.217034	+	0.217034i	−0.807247	−	0.590213i	$-0.799044\pi$
$193$	−3.01513	+	3.01513i	−0.217034	+	0.217034i	0.590213	+	0.807247i	$0.299044\pi$
$194$	12.1399	+	19.2931i	0.871595	+	1.38517i
$195$		0			0
$196$	5.21138	−	10.8570i	0.372241	−	0.775503i
$197$	6.77107	+	6.77107i	0.482419	+	0.482419i	0.905903	−	0.423485i	$-0.139193\pi$
$197$	6.77107	+	6.77107i	0.482419	+	0.482419i	−0.423485	+	0.905903i	$0.639193\pi$
$198$	17.5713	−	3.87361i	1.24873	−	0.275285i
$199$		−	7.74852i		−	0.549278i	−0.961547	−	0.274639i	$-0.911442\pi$
$199$		−	7.74852i		−	0.549278i	0.961547	−	0.274639i	$-0.0885583\pi$
$200$		0			0
$201$	2.29742	−	3.62383i	0.162048	−	0.255605i
$202$	−20.2807	−	4.61528i	−1.42694	−	0.324730i
$203$	2.73470	−	2.73470i	0.191938	−	0.191938i
$204$	0.225102	−	0.140579i	0.0157603	−	0.00984252i
$205$		0			0
$206$	13.6916	−	8.61522i	0.953939	−	0.600251i
$207$	13.9209	+	4.99741i	0.967571	+	0.347344i
$208$	1.28884	−	11.7080i	0.0893651	−	0.811804i
$209$	−19.1842			−1.32700
$210$		0			0
$211$		−	23.5384i		−	1.62045i	−0.586121	−	0.810224i	$-0.699346\pi$
$211$		−	23.5384i		−	1.62045i	0.586121	−	0.810224i	$-0.300654\pi$
$212$	−0.694165	+	0.243896i	−0.0476755	+	0.0167509i
$213$	3.97998	+	17.7671i	0.272703	+	1.21738i
$214$	−2.72748	−	4.33460i	−0.186446	−	0.296307i
$215$		0			0
$216$	14.6962	+	0.149440i	0.999948	+	0.0101681i
$217$	−7.20062	−	7.20062i	−0.488810	−	0.488810i
$218$	−12.8574	−	2.92597i	−0.870816	−	0.198172i
$219$	−5.94639	+	9.37952i	−0.401820	+	0.633809i
$220$		0			0
$221$	0.225599			0.0151754
$222$	17.9216	−	17.8005i	1.20282	−	1.19469i
$223$	−6.31021	+	6.31021i	−0.422563	+	0.422563i	−0.886085	−	0.463522i	$-0.846585\pi$
$223$	−6.31021	+	6.31021i	−0.422563	+	0.422563i	0.463522	+	0.886085i	$0.346585\pi$
$224$	1.83124	−	5.28758i	0.122355	−	0.353291i
$225$		0			0
$226$	6.04011	+	9.59914i	0.401782	+	0.638525i
$227$	3.12540	+	3.12540i	0.207440	+	0.207440i	0.803179	−	0.595738i	$-0.203140\pi$
$227$	3.12540	+	3.12540i	0.207440	+	0.207440i	−0.595738	+	0.803179i	$0.703140\pi$
$228$	−15.2673	−	3.52885i	−1.01110	−	0.233704i
$229$	18.7378			1.23823			0.619114	−	0.785301i	$-0.287492\pi$
$229$	18.7378			1.23823			0.619114	+	0.785301i	$0.287492\pi$
$230$		0			0
$231$	6.13691	+	3.89065i	0.403779	+	0.255986i
$232$	−6.87814	+	8.65895i	−0.451572	+	0.568488i
$233$	−10.9610	−	10.9610i	−0.718078	−	0.718078i	0.250134	−	0.968211i	$-0.419525\pi$
$233$	−10.9610	−	10.9610i	−0.718078	−	0.718078i	−0.968211	+	0.250134i	$0.919525\pi$
$234$	10.5287	+	6.72509i	0.688284	+	0.439633i
$235$		0			0
$236$	2.50470	−	5.21813i	0.163042	−	0.339672i
$237$	0.553470	+	2.47076i	0.0359517	+	0.160493i
$238$	0.104503	+	0.0237819i	0.00677395	+	0.00154155i
$239$	10.5121			0.679968			0.339984	−	0.940431i	$-0.389578\pi$
$239$	10.5121			0.679968			0.339984	+	0.940431i	$0.389578\pi$
$240$		0			0
$241$	5.58116			0.359514			0.179757	−	0.983711i	$-0.442469\pi$
$241$	5.58116			0.359514			0.179757	+	0.983711i	$0.442469\pi$
$242$	−9.63383	−	2.19238i	−0.619286	−	0.140931i
$243$	−7.04513	+	13.9056i	−0.451945	+	0.892046i
$244$	−5.80063	+	12.0847i	−0.371347	+	0.773641i
$245$		0			0
$246$	0.0726283	−	21.4278i	0.00463061	−	1.36619i
$247$	−9.41881	−	9.41881i	−0.599304	−	0.599304i
$248$	22.7995	+	18.1106i	1.44777	+	1.15002i
$249$	−7.36210	+	11.6126i	−0.466554	+	0.735918i
$250$		0			0
$251$	−13.1711			−0.831349			−0.415675	−	0.909513i	$-0.636455\pi$
$251$	−13.1711			−0.831349			−0.415675	+	0.909513i	$0.636455\pi$
$252$	4.16824	+	4.22514i	0.262574	+	0.266158i
$253$	−14.7851	−	14.7851i	−0.929533	−	0.929533i
$254$	−10.7774	−	17.1279i	−0.676237	−	1.07470i
$255$		0			0
$256$	−3.48045	+	15.6169i	−0.217528	+	0.976054i
$257$	−6.86408	+	6.86408i	−0.428169	+	0.428169i	−0.888004	−	0.459835i	$-0.847909\pi$
$257$	−6.86408	+	6.86408i	−0.428169	+	0.428169i	0.459835	+	0.888004i	$0.347909\pi$
$258$	−11.2405	−	11.3169i	−0.699801	−	0.704561i
$259$	10.2007			0.633839
$260$		0			0
$261$	−5.00375	−	10.6082i	−0.309724	−	0.656633i
$262$	13.7497	+	3.12904i	0.849462	+	0.193313i
$263$	−15.1216	−	15.1216i	−0.932435	−	0.932435i	0.0654229	−	0.997858i	$-0.479160\pi$
$263$	−15.1216	−	15.1216i	−0.932435	−	0.932435i	−0.997858	+	0.0654229i	$0.979160\pi$
$264$	−18.7001	−	9.05415i	−1.15091	−	0.557244i
$265$		0			0
$266$	−3.37013	−	5.35593i	−0.206636	−	0.328393i
$267$	9.17187	−	2.05457i	0.561309	−	0.125738i
$268$	−4.67437	+	1.64235i	−0.285533	+	0.100322i
$269$		−	11.8132i		−	0.720262i	−0.932902	−	0.360131i	$-0.882732\pi$
$269$		−	11.8132i		−	0.720262i	0.932902	−	0.360131i	$-0.117268\pi$
$270$		0			0
$271$	10.3503			0.628739			0.314369	−	0.949301i	$-0.398207\pi$
$271$	10.3503			0.628739			0.314369	+	0.949301i	$0.398207\pi$
$272$	−0.304610	−	0.0335321i	−0.0184697	−	0.00203318i
$273$	1.10284	+	4.92320i	0.0667468	+	0.297966i
$274$	2.38695	−	1.50195i	0.144201	−	0.0907364i
$275$		0			0
$276$	−9.04671	−	14.4860i	−0.544548	−	0.871957i
$277$	6.24661	−	6.24661i	0.375323	−	0.375323i	−0.494089	−	0.869411i	$-0.664498\pi$
$277$	6.24661	−	6.24661i	0.375323	−	0.375323i	0.869411	+	0.494089i	$0.164498\pi$
$278$	6.96015	+	1.58393i	0.417442	+	0.0949976i
$279$	−27.9321	+	13.1752i	−1.67225	+	0.788777i
$280$		0			0
$281$			33.2260i			1.98210i	0.133495	+	0.991049i	$0.457380\pi$
$281$			33.2260i			1.98210i	−0.133495	+	0.991049i	$0.542620\pi$
$282$	19.8006	−	19.6668i	1.17911	−	1.17114i
$283$	−7.08141	−	7.08141i	−0.420946	−	0.420946i	0.464583	−	0.885529i	$-0.346204\pi$
$283$	−7.08141	−	7.08141i	−0.420946	−	0.420946i	−0.885529	+	0.464583i	$0.846204\pi$
$284$	9.09777	−	18.9537i	0.539854	−	1.12470i
$285$		0			0
$286$	−9.40598	−	14.9483i	−0.556187	−	0.883911i
$287$	6.11885	−	6.11885i	0.361184	−	0.361184i
$288$	−13.2165	−	10.6453i	−0.778792	−	0.627282i
$289$			16.9941i			0.999655i
$290$		0			0
$291$	23.5787	+	14.9483i	1.38221	+	0.876285i
$292$	12.0986	−	4.25087i	0.708018	−	0.248764i
$293$	−20.0947	+	20.0947i	−1.17394	+	1.17394i	−0.192683	+	0.981261i	$0.561719\pi$
$293$	−20.0947	+	20.0947i	−1.17394	+	1.17394i	−0.981261	+	0.192683i	$0.938281\pi$
$294$	0.0499926	−	14.7495i	0.00291563	−	0.860209i
$295$		0			0
$296$	−28.9774	+	3.32131i	−1.68428	+	0.193047i
$297$	17.3941	−	13.5306i	1.00931	−	0.785125i
$298$	6.75037	−	29.6628i	0.391038	−	1.71832i
$299$		−	14.5180i		−	0.839598i
$300$		0			0
$301$		−	6.44141i		−	0.371277i
$302$	−1.93879	−	0.441212i	−0.111565	−	0.0253889i
$303$	−24.8576	+	5.56832i	−1.42803	+	0.319891i
$304$	11.3175	+	14.1175i	0.649105	+	0.809693i
$305$		0			0
$306$	0.174968	−	0.273928i	0.0100023	−	0.0156594i
$307$	13.2079	−	13.2079i	0.753813	−	0.753813i	−0.221375	−	0.975189i	$-0.571055\pi$
$307$	13.2079	−	13.2079i	0.753813	−	0.753813i	0.975189	+	0.221375i	$0.0710546\pi$
$308$	−2.78130	−	7.91598i	−0.158479	−	0.451055i
$309$	10.6082	−	16.7329i	0.603481	−	0.951899i
$310$		0			0
$311$		−	13.0912i		−	0.742336i	−0.928566	−	0.371168i	$-0.878957\pi$
$311$		−	13.0912i		−	0.742336i	0.928566	−	0.371168i	$-0.121043\pi$
$312$	−4.73585	−	13.6264i	−0.268114	−	0.771444i
$313$	−13.8188	+	13.8188i	−0.781087	+	0.781087i	−0.980014	−	0.198927i	$-0.936254\pi$
$313$	−13.8188	+	13.8188i	−0.781087	+	0.781087i	0.198927	+	0.980014i	$0.436254\pi$
$314$	7.32854	−	4.61137i	0.413574	−	0.260235i
$315$		0			0
$316$	1.26517	−	2.63577i	0.0711714	−	0.148274i
$317$	−8.59301	−	8.59301i	−0.482632	−	0.482632i	0.423339	−	0.905971i	$-0.360858\pi$
$317$	−8.59301	−	8.59301i	−0.482632	−	0.482632i	−0.905971	+	0.423339i	$0.860858\pi$
$318$	−0.639348	+	0.635028i	−0.0358528	+	0.0356106i
$319$			16.5812i			0.928367i
$320$		0			0
$321$	−5.29742	−	3.35844i	−0.295673	−	0.187450i
$322$	1.53044	−	6.72512i	0.0852880	−	0.374776i
$323$	−0.245051	+	0.245051i	−0.0136350	+	0.0136350i
$324$	16.3315	−	7.56843i	0.907307	−	0.420469i
$325$		0			0
$326$	9.23214	+	14.6720i	0.511321	+	0.812608i
$327$	−15.7591	+	3.53018i	−0.871483	+	0.195219i
$328$	−15.3898	+	19.3743i	−0.849758	+	1.06977i
$329$	11.2702			0.621346
$330$		0			0
$331$			14.6485i			0.805155i	0.915386	+	0.402578i	$0.131886\pi$
$331$			14.6485i			0.805155i	−0.915386	+	0.402578i	$0.868114\pi$
$332$	14.9790	−	5.26292i	0.822082	−	0.288840i
$333$	10.4526	−	29.1171i	0.572800	−	1.59561i
$334$	3.14561	−	1.97933i	0.172120	−	0.108304i
$335$		0			0
$336$	−0.757315	−	6.81135i	−0.0413149	−	0.371589i
$337$	18.4238	+	18.4238i	1.00361	+	1.00361i	0.999993	+	0.00361703i	$0.00115134\pi$
$337$	18.4238	+	18.4238i	1.00361	+	1.00361i	0.00361703	+	0.999993i	$0.498849\pi$
$338$	−1.35844	+	5.96929i	−0.0738891	+	0.324687i
$339$	11.7314	+	7.43740i	0.637160	+	0.403944i
$340$		0			0
$341$	43.6592			2.36428
$342$	−18.7415	+	4.13159i	−1.01342	+	0.223411i
$343$	9.10807	−	9.10807i	0.491789	−	0.491789i
$344$	2.09730	+	18.2983i	0.113079	+	0.986581i
$345$		0			0
$346$	8.47553	−	5.33309i	0.455647	−	0.286709i
$347$	−14.8721	−	14.8721i	−0.798378	−	0.798378i	0.184462	−	0.982840i	$-0.440946\pi$
$347$	−14.8721	−	14.8721i	−0.798378	−	0.798378i	−0.982840	+	0.184462i	$0.940946\pi$
$348$	−3.05003	+	13.1957i	−0.163499	+	0.707364i
$349$	−18.9090			−1.01218			−0.506088	−	0.862482i	$-0.668909\pi$
$349$	−18.9090			−1.01218			−0.506088	+	0.862482i	$0.668909\pi$
$350$		0			0
$351$	15.1830	+	1.89683i	0.810408	+	0.101245i
$352$	10.4783	+	21.5816i	0.558497	+	1.15030i
$353$	−10.7443	−	10.7443i	−0.571861	−	0.571861i	0.360787	−	0.932648i	$-0.382508\pi$
$353$	−10.7443	−	10.7443i	−0.571861	−	0.571861i	−0.932648	+	0.360787i	$0.882508\pi$
$354$	0.0240276	−	7.08894i	0.00127705	−	0.376773i
$355$		0			0
$356$	−9.78444	−	4.69653i	−0.518574	−	0.248915i
$357$	0.128088	−	0.0286928i	0.00677913	−	0.00151858i
$358$	−1.59021	+	6.98779i	−0.0840454	+	0.369316i
$359$	0.0757843			0.00399974			0.00199987	−	0.999998i	$-0.499363\pi$
$359$	0.0757843			0.00399974			0.00199987	+	0.999998i	$0.499363\pi$
$360$		0			0
$361$	1.46184			0.0769392
$362$	−1.35360	+	5.94803i	−0.0711434	+	0.312621i
$363$	−11.8080	+	2.64509i	−0.619760	+	0.138831i
$364$	2.52096	−	5.25201i	0.132134	−	0.275280i
$365$		0			0
$366$	−0.0556453	+	16.4172i	−0.00290863	+	0.858143i
$367$	−3.88878	−	3.88878i	−0.202993	−	0.202993i	0.598288	−	0.801281i	$-0.295848\pi$
$367$	−3.88878	−	3.88878i	−0.202993	−	0.202993i	−0.801281	+	0.598288i	$0.795848\pi$
$368$	−2.15789	+	19.6026i	−0.112488	+	1.02185i
$369$	−11.1958	−	23.7358i	−0.582832	−	1.23564i
$370$		0			0
$371$	−0.363906			−0.0188931
$372$	34.7451	+	8.03092i	1.80145	+	0.416384i
$373$	1.11844	+	1.11844i	0.0579104	+	0.0579104i	0.735469	−	0.677558i	$-0.236962\pi$
$373$	1.11844	+	1.11844i	0.0579104	+	0.0579104i	−0.677558	+	0.735469i	$0.736962\pi$
$374$	−0.388913	+	0.244717i	−0.0201102	+	0.0126540i
$375$		0			0
$376$	−32.0156	+	3.66954i	−1.65108	+	0.189242i
$377$	−8.14080	+	8.14080i	−0.419273	+	0.419273i
$378$	6.83319	+	2.47920i	0.351462	+	0.127516i
$379$	30.6447			1.57411			0.787055	−	0.616882i	$-0.211605\pi$
$379$	30.6447			1.57411			0.787055	+	0.616882i	$0.211605\pi$
$380$		0			0
$381$	−20.9324	−	13.2706i	−1.07240	−	0.679876i
$382$	6.21646	−	27.3166i	0.318062	−	1.39764i
$383$	16.3608	+	16.3608i	0.835998	+	0.835998i	0.988329	−	0.152332i	$-0.0486782\pi$
$383$	16.3608	+	16.3608i	0.835998	+	0.835998i	−0.152332	+	0.988329i	$0.548678\pi$
$384$	4.36908	+	19.1026i	0.222959	+	0.974828i
$385$		0			0
$386$	5.10392	−	3.21156i	0.259782	−	0.163464i
$387$	−18.3865	−	6.60051i	−0.934640	−	0.335523i
$388$	−10.6860	−	30.4141i	−0.542501	−	1.54404i
$389$			28.3988i			1.43988i	0.694037	+	0.719939i	$0.255830\pi$
$389$			28.3988i			1.43988i	−0.694037	+	0.719939i	$0.744170\pi$
$390$		0			0
$391$	−0.377718			−0.0191020
$392$	−10.5933	+	13.3360i	−0.535043	+	0.673571i
$393$	16.8528	−	3.77517i	0.850113	−	0.190432i
$394$	−7.21219	−	11.4618i	−0.363345	−	0.577439i
$395$		0			0
$396$	−25.4456	−	0.172495i	−1.27869	−	0.00866818i
$397$	12.7864	−	12.7864i	0.641733	−	0.641733i	−0.309249	−	0.950981i	$-0.600078\pi$
$397$	12.7864	−	12.7864i	0.641733	−	0.641733i	0.950981	+	0.309249i	$0.100078\pi$
$398$	−2.43156	+	10.6849i	−0.121883	+	0.535584i
$399$	−6.54562	−	4.14976i	−0.327691	−	0.207748i
$400$		0			0
$401$			11.2513i			0.561864i	0.959728	+	0.280932i	$0.0906436\pi$
$401$			11.2513i			0.561864i	−0.959728	+	0.280932i	$0.909356\pi$
$402$	−4.30524	+	4.27615i	−0.214726	+	0.213275i
$403$	21.4352	+	21.4352i	1.06776	+	1.06776i
$404$	26.5178	+	12.7285i	1.31931	+	0.633269i
$405$		0			0
$406$	−4.62920	+	2.91285i	−0.229743	+	0.144562i
$407$	−30.9247	+	30.9247i	−1.53288	+	1.53288i
$408$	−0.354522	+	0.123213i	−0.0175514	+	0.00609998i
$409$		−	14.6653i		−	0.725152i	−0.931954	−	0.362576i	$-0.881897\pi$
$409$		−	14.6653i		−	0.725152i	0.931954	−	0.362576i	$-0.118103\pi$
$410$		0			0
$411$	1.84941	−	2.91716i	0.0912246	−	0.143893i
$412$	−21.5837	+	7.58347i	−1.06335	+	0.373611i
$413$	2.02429	−	2.02429i	0.0996090	−	0.0996090i
$414$	−17.6281	−	11.2597i	−0.866375	−	0.553386i
$415$		0			0
$416$	−5.45135	+	15.7404i	−0.267274	+	0.771736i
$417$	8.53094	−	1.91100i	0.417762	−	0.0935821i
$418$	26.4542	+	6.02019i	1.29392	+	0.294457i
$419$			0.0216630i			0.00105831i	1.00000		0.000529154i	$0.000168435\pi$
$419$			0.0216630i			0.00105831i	−1.00000		0.000529154i	$0.999832\pi$
$420$		0			0
$421$		−	14.4526i		−	0.704375i	−0.935930	−	0.352187i	$-0.885438\pi$
$421$		−	14.4526i		−	0.704375i	0.935930	−	0.352187i	$-0.114562\pi$
$422$	−7.38657	+	32.4584i	−0.359573	+	1.58005i
$423$	11.5486	−	32.1699i	0.561510	−	1.56416i
$424$	1.03376	−	0.118487i	0.0502039	−	0.00575422i
$425$		0			0
$426$	0.0872748	−	25.7490i	0.00422848	−	1.24754i
$427$	−4.68805	+	4.68805i	−0.226871	+	0.226871i
$428$	2.40083	+	6.83313i	0.116049	+	0.330292i
$429$	−18.2687	−	11.5819i	−0.882021	−	0.559180i
$430$		0			0
$431$		−	17.0031i		−	0.819010i	−0.912308	−	0.409505i	$-0.865701\pi$
$431$		−	17.0031i		−	0.819010i	0.912308	−	0.409505i	$-0.134299\pi$
$432$	−20.2185	−	4.81788i	−0.972763	−	0.231800i
$433$	−0.833286	+	0.833286i	−0.0400451	+	0.0400451i	−0.726846	−	0.686801i	$-0.759015\pi$
$433$	−0.833286	+	0.833286i	−0.0400451	+	0.0400451i	0.686801	+	0.726846i	$0.259015\pi$
$434$	7.66972	+	12.1890i	0.368158	+	0.585089i
$435$		0			0
$436$	16.8117	+	8.06959i	0.805133	+	0.386463i
$437$	15.7698	+	15.7698i	0.754372	+	0.754372i
$438$	11.1432	−	11.0679i	0.532443	−	0.528846i
$439$		−	20.2593i		−	0.966924i	−0.875365	−	0.483462i	$-0.839379\pi$
$439$		−	20.2593i		−	0.966924i	0.875365	−	0.483462i	$-0.160621\pi$
$440$		0			0
$441$	−7.70649	−	16.3382i	−0.366976	−	0.778009i
$442$	−0.311092	−	0.0707953i	−0.0147971	−	0.00336739i
$443$	16.9126	−	16.9126i	0.803541	−	0.803541i	−0.180106	−	0.983647i	$-0.557644\pi$
$443$	16.9126	−	16.9126i	0.803541	−	0.803541i	0.983647	+	0.180106i	$0.0576440\pi$
$444$	−30.2991	+	18.9222i	−1.43793	+	0.898007i
$445$		0			0
$446$	10.6817	−	6.72131i	0.505794	−	0.318263i
$447$	−8.14430	−	36.3571i	−0.385212	−	1.71963i
$448$	−4.18450	+	6.71669i	−0.197699	+	0.317334i
$449$	33.3587			1.57430			0.787148	−	0.616764i	$-0.211557\pi$
$449$	33.3587			1.57430			0.787148	+	0.616764i	$0.211557\pi$
$450$		0			0
$451$			37.1002i			1.74698i
$452$	−5.31675	−	15.1323i	−0.250079	−	0.711761i
$453$	−2.37634	+	0.532320i	−0.111650	+	0.0250106i
$454$	−3.32901	−	5.29058i	−0.156238	−	0.248299i
$455$		0			0
$456$	19.9455	+	9.65715i	0.934034	+	0.452238i
$457$	21.6899	+	21.6899i	1.01461	+	1.01461i	0.999892	+	0.0147169i	$0.00468469\pi$
$457$	21.6899	+	21.6899i	1.01461	+	1.01461i	0.0147169	+	0.999892i	$0.495315\pi$
$458$	−25.8386	−	5.88011i	−1.20736	−	0.274759i
$459$	0.0493502	−	0.395019i	0.00230347	−	0.0184379i
$460$		0			0
$461$	−34.8929			−1.62513			−0.812563	−	0.582873i	$-0.801928\pi$
$461$	−34.8929			−1.62513			−0.812563	+	0.582873i	$0.801928\pi$
$462$	−7.24161	−	7.29086i	−0.336910	−	0.339202i
$463$	9.79796	−	9.79796i	0.455350	−	0.455350i	−0.441776	−	0.897126i	$-0.645651\pi$
$463$	9.79796	−	9.79796i	0.455350	−	0.455350i	0.897126	+	0.441776i	$0.145651\pi$
$464$	12.2019	−	9.78190i	0.566460	−	0.454113i
$465$		0			0
$466$	11.6751	+	18.5544i	0.540837	+	0.859516i
$467$	−16.1473	−	16.1473i	−0.747207	−	0.747207i	0.226747	−	0.973954i	$-0.427191\pi$
$467$	−16.1473	−	16.1473i	−0.747207	−	0.747207i	−0.973954	+	0.226747i	$0.927191\pi$
$468$	−12.4083	−	12.5776i	−0.573572	−	0.581401i
$469$	−2.45047			−0.113152
$470$		0			0
$471$	5.67814	−	8.95640i	0.261635	−	0.412689i
$472$	−5.09138	+	6.40959i	−0.234350	+	0.295025i
$473$	19.5280	+	19.5280i	0.897897	+	0.897897i
$474$	0.0121368	−	3.58075i	0.000557459	−	0.164469i
$475$		0			0
$476$	−0.136643	−	0.0655884i	−0.00626301	−	0.00300624i
$477$	−0.372895	+	1.03874i	−0.0170737	+	0.0475608i
$478$	−14.4957	−	3.29879i	−0.663017	−	0.150883i
$479$	10.4363			0.476845			0.238423	−	0.971161i	$-0.423370\pi$
$479$	10.4363			0.476845			0.238423	+	0.971161i	$0.423370\pi$
$480$		0			0
$481$	−30.3660			−1.38457
$482$	−7.69618	−	1.75142i	−0.350551	−	0.0797751i
$483$	−1.84647	−	8.24286i	−0.0840172	−	0.375063i
$484$	12.5967	+	6.04638i	0.572575	+	0.274836i
$485$		0			0
$486$	14.0787	−	16.9644i	0.638621	−	0.769522i
$487$	−21.0072	−	21.0072i	−0.951925	−	0.951925i	0.0469714	−	0.998896i	$-0.485043\pi$
$487$	−21.0072	−	21.0072i	−0.951925	−	0.951925i	−0.998896	+	0.0469714i	$0.985043\pi$
$488$	11.7911	−	14.8439i	0.533758	−	0.671953i
$489$	17.9311	+	11.3679i	0.810871	+	0.514073i
$490$		0			0
$491$	6.57817			0.296869			0.148434	−	0.988922i	$-0.452577\pi$
$491$	6.57817			0.296869			0.148434	+	0.988922i	$0.452577\pi$
$492$	−6.82442	+	29.5253i	−0.307668	+	1.33110i
$493$	0.211801	+	0.211801i	0.00953904	+	0.00953904i
$494$	10.0324	+	15.9438i	0.451380	+	0.717348i
$495$		0			0
$496$	−25.7563	−	32.1284i	−1.15649	−	1.44261i
$497$	7.35280	−	7.35280i	0.329818	−	0.329818i
$498$	13.7962	−	13.7030i	0.618221	−	0.614044i
$499$	−19.7716			−0.885097			−0.442548	−	0.896745i	$-0.645925\pi$
$499$	−19.7716			−0.885097			−0.442548	+	0.896745i	$0.645925\pi$
$500$		0			0
$501$	2.43721	−	3.84433i	0.108887	−	0.171752i
$502$	18.1623	+	4.13321i	0.810624	+	0.184474i
$503$	3.26952	+	3.26952i	0.145781	+	0.145781i	0.776230	−	0.630450i	$-0.217129\pi$
$503$	3.26952	+	3.26952i	0.145781	+	0.145781i	−0.630450	+	0.776230i	$0.717129\pi$
$504$	−4.42193	−	7.13432i	−0.196968	−	0.317788i
$505$		0			0
$506$	15.7483	+	25.0278i	0.700099	+	1.11262i
$507$	1.63895	+	7.31646i	0.0727882	+	0.324935i
$508$	9.48674	+	27.0007i	0.420906	+	1.19796i
$509$		−	12.8288i		−	0.568627i	−0.958731	−	0.284313i	$-0.908234\pi$
$509$		−	12.8288i		−	0.568627i	0.958731	−	0.284313i	$-0.0917656\pi$
$510$		0			0
$511$	6.34253			0.280577
$512$	9.70012	−	20.4428i	0.428689	−	0.903452i
$513$	−18.5525	+	14.4317i	−0.819113	+	0.637177i
$514$	11.6193	−	7.31125i	0.512505	−	0.322486i
$515$		0			0
$516$	11.9488	+	19.1329i	0.526015	+	0.842280i
$517$	−34.1670	+	34.1670i	−1.50266	+	1.50266i
$518$	−14.0663	−	3.20107i	−0.618038	−	0.140647i
$519$	6.56683	−	10.3582i	0.288252	−	0.454673i
$520$		0			0
$521$			8.59635i			0.376613i	0.982110	+	0.188307i	$0.0602998\pi$
$521$			8.59635i			0.376613i	−0.982110	+	0.188307i	$0.939700\pi$
$522$	3.57099	+	16.1985i	0.156298	+	0.708990i
$523$	16.7947	+	16.7947i	0.734383	+	0.734383i	0.971485	−	0.237102i	$-0.0761975\pi$
$523$	16.7947	+	16.7947i	0.734383	+	0.734383i	−0.237102	+	0.971485i	$0.576197\pi$
$524$	−17.9784	−	8.62962i	−0.785390	−	0.376987i
$525$		0			0
$526$	16.1067	+	25.5973i	0.702285	+	1.11609i
$527$	0.557685	−	0.557685i	0.0242931	−	0.0242931i
$528$	22.9454	+	18.3536i	0.998569	+	0.798737i
$529$			1.30735i			0.0568411i
$530$		0			0
$531$	−3.70391	−	7.85249i	−0.160736	−	0.340769i
$532$	2.96653	+	8.44318i	0.128615	+	0.366058i
$533$	−18.2150	+	18.2150i	−0.788978	+	0.788978i
$534$	−13.2924	−	0.0450537i	−0.575217	−	0.00194966i
$535$		0			0
$536$	6.96114	−	0.797865i	0.300676	−	0.0344625i
$537$	1.91859	+	8.56481i	0.0827932	+	0.369599i
$538$	−3.70709	+	16.2899i	−0.159824	+	0.702306i
$539$			25.5374i			1.09997i
$540$		0			0
$541$			26.3168i			1.13145i	0.824595	+	0.565724i	$0.191403\pi$
$541$			26.3168i			1.13145i	−0.824595	+	0.565724i	$0.808597\pi$
$542$	−14.2727	−	3.24804i	−0.613064	−	0.139515i
$543$	1.63311	+	7.29040i	0.0700834	+	0.312861i
$544$	0.409521	+	0.141829i	0.0175581	+	0.00608086i
$545$		0			0
$546$	0.0241835	−	7.13496i	0.00103496	−	0.305348i
$547$	−4.59571	+	4.59571i	−0.196498	+	0.196498i	−0.798497	−	0.601999i	$-0.794371\pi$
$547$	−4.59571	+	4.59571i	−0.196498	+	0.196498i	0.601999	+	0.798497i	$0.294371\pi$
$548$	−3.76284	+	1.32208i	−0.160740	+	0.0564765i
$549$	8.57786	+	18.1855i	0.366094	+	0.776140i
$550$		0			0
$551$		−	17.6855i		−	0.753426i
$552$	7.92917	+	22.8146i	0.337488	+	0.971053i
$553$	1.02251	−	1.02251i	0.0434814	−	0.0434814i
$554$	−10.5741	+	6.65356i	−0.449249	+	0.282683i
$555$		0			0
$556$	−9.10070	−	4.36833i	−0.385956	−	0.185259i
$557$	14.7444	+	14.7444i	0.624741	+	0.624741i	0.946740	−	0.321999i	$-0.104355\pi$
$557$	14.7444	+	14.7444i	0.624741	+	0.624741i	−0.321999	+	0.946740i	$0.604355\pi$
$558$	42.6517	−	9.40263i	1.80559	−	0.398045i
$559$			19.1752i			0.811023i
$560$		0			0
$561$	−0.301329	+	0.475301i	−0.0127221	+	0.0200672i
$562$	10.4267	−	45.8173i	0.439822	−	1.93269i
$563$	19.1553	−	19.1553i	0.807301	−	0.807301i	−0.176924	−	0.984225i	$-0.556615\pi$
$563$	19.1553	−	19.1553i	0.807301	−	0.807301i	0.984225	+	0.176924i	$0.0566145\pi$
$564$	−33.4759	+	20.9061i	−1.40959	+	0.880306i
$565$		0			0
$566$	7.54274	+	11.9872i	0.317045	+	0.503859i
$567$	8.86166	−	0.854084i	0.372155	−	0.0358682i
$568$	−18.4933	+	23.2814i	−0.775962	+	0.976866i
$569$	−23.8118			−0.998241			−0.499121	−	0.866532i	$-0.666344\pi$
$569$	−23.8118			−0.998241			−0.499121	+	0.866532i	$0.666344\pi$
$570$		0			0
$571$			4.88168i			0.204292i	0.994769	+	0.102146i	$0.0325709\pi$
$571$			4.88168i			0.204292i	−0.994769	+	0.102146i	$0.967429\pi$
$572$	8.27952	+	23.5648i	0.346184	+	0.985292i
$573$	−7.50014	−	33.4815i	−0.313323	−	1.39871i
$574$	−10.3578	+	6.51748i	−0.432326	+	0.272034i
$575$		0			0
$576$	14.8844	+	18.8269i	0.620185	+	0.784456i
$577$	3.99454	+	3.99454i	0.166295	+	0.166295i	0.785349	−	0.619054i	$-0.212484\pi$
$577$	3.99454	+	3.99454i	0.166295	+	0.166295i	−0.619054	+	0.785349i	$0.712484\pi$
$578$	5.33293	−	23.4342i	0.221821	−	0.974733i
$579$	3.95451	−	6.23763i	0.164344	−	0.259227i
$580$		0			0
$581$	7.85255			0.325779
$582$	−27.8230	−	28.0123i	−1.15330	−	1.16115i
$583$	1.10323	−	1.10323i	0.0456911	−	0.0456911i
$584$	−18.0175	+	2.06511i	−0.745567	+	0.0854547i
$585$		0			0
$586$	34.0156	−	21.4038i	1.40517	−	0.884183i
$587$	17.5340	+	17.5340i	0.723707	+	0.723707i	0.969358	−	0.245651i	$-0.0790018\pi$
$587$	17.5340	+	17.5340i	0.723707	+	0.723707i	−0.245651	+	0.969358i	$0.579002\pi$
$588$	−4.69748	+	20.3233i	−0.193721	+	0.838118i
$589$	−46.5669			−1.91875
$590$		0			0
$591$	−14.0078	−	8.88062i	−0.576205	−	0.365300i
$592$	41.0009	+	4.51347i	1.68513	+	0.185502i
$593$	30.8705	+	30.8705i	1.26770	+	1.26770i	0.947274	+	0.320425i	$0.103826\pi$
$593$	30.8705	+	30.8705i	1.26770	+	1.26770i	0.320425	+	0.947274i	$0.396174\pi$
$594$	−28.2317	+	13.1997i	−1.15836	+	0.541590i
$595$		0			0
$596$	−18.6169	+	38.7853i	−0.762580	+	1.58871i
$597$	2.93367	+	13.0963i	0.120067	+	0.535994i
$598$	−4.55590	+	20.0197i	−0.186305	+	0.818667i
$599$	19.0515			0.778423			0.389211	−	0.921148i	$-0.372748\pi$
$599$	19.0515			0.778423			0.389211	+	0.921148i	$0.372748\pi$
$600$		0			0
$601$	−36.7161			−1.49768			−0.748841	−	0.662750i	$-0.769389\pi$
$601$	−36.7161			−1.49768			−0.748841	+	0.662750i	$0.769389\pi$
$602$	−2.02138	+	8.88243i	−0.0823853	+	0.362021i
$603$	−2.51100	+	6.99470i	−0.102256	+	0.284846i
$604$	2.53505	+	1.21682i	0.103150	+	0.0495119i
$605$		0			0
$606$	36.0250	+	0.122105i	1.46342	+	0.00496016i
$607$	10.5809	+	10.5809i	0.429465	+	0.429465i	0.888446	−	0.458981i	$-0.151786\pi$
$607$	10.5809	+	10.5809i	0.429465	+	0.429465i	−0.458981	+	0.888446i	$0.651786\pi$
$608$	−11.1762	−	23.0189i	−0.453254	−	0.933541i
$609$	−3.58670	+	5.65747i	−0.145340	+	0.229252i
$610$		0			0
$611$	−33.5498			−1.35728
$612$	−0.327235	+	0.322828i	−0.0132277	+	0.0130496i
$613$	27.2783	+	27.2783i	1.10176	+	1.10176i	0.994198	+	0.107564i	$0.0343050\pi$
$613$	27.2783	+	27.2783i	1.10176	+	1.10176i	0.107564	+	0.994198i	$0.465695\pi$
$614$	−22.3579	+	14.0683i	−0.902290	+	0.567752i
$615$		0			0
$616$	1.35117	+	11.7886i	0.0544403	+	0.474976i
$617$	27.0736	−	27.0736i	1.08994	−	1.08994i	0.0944087	−	0.995534i	$-0.469904\pi$
$617$	27.0736	−	27.0736i	1.08994	−	1.08994i	0.995534	−	0.0944087i	$-0.0300960\pi$
$618$	−19.8792	+	19.7449i	−0.799660	+	0.794257i
$619$	−47.6006			−1.91323			−0.956616	−	0.291353i	$-0.905894\pi$
$619$	−47.6006			−1.91323			−0.956616	+	0.291353i	$0.905894\pi$
$620$		0			0
$621$	−25.4207	−	3.17584i	−1.02010	−	0.127442i
$622$	−4.10816	+	18.0523i	−0.164722	+	0.723830i
$623$	−3.79572	−	3.79572i	−0.152072	−	0.152072i
$624$	2.25442	+	20.2764i	0.0902490	+	0.811706i
$625$		0			0
$626$	23.3921	−	14.7191i	0.934935	−	0.588293i
$627$	32.4244	−	7.26334i	1.29491	−	0.290070i
$628$	−11.5528	+	4.05911i	−0.461009	+	0.161976i
$629$			0.790038i			0.0315009i
$630$		0			0
$631$	17.7915			0.708269			0.354135	−	0.935194i	$-0.384775\pi$
$631$	17.7915			0.708269			0.354135	+	0.935194i	$0.384775\pi$
$632$	−2.57175	+	3.23760i	−0.102299	+	0.128785i
$633$	8.91187	+	39.7837i	0.354215	+	1.58126i
$634$	9.15282	+	14.5460i	0.363505	+	0.577694i
$635$		0			0
$636$	1.08091	−	0.675043i	0.0428609	−	0.0267672i
$637$	−12.5380	+	12.5380i	−0.496774	+	0.496774i
$638$	5.20333	−	22.8647i	0.206002	−	0.905222i
$639$	−13.4536	−	28.5224i	−0.532217	−	1.12833i
$640$		0			0
$641$			0.151569i			0.00598660i	0.999996	+	0.00299330i	$0.000952799\pi$
$641$			0.151569i			0.00598660i	−0.999996	+	0.00299330i	$0.999047\pi$
$642$	6.25101	+	6.29353i	0.246708	+	0.248386i
$643$	−6.08170	−	6.08170i	−0.239839	−	0.239839i	0.576945	−	0.816783i	$-0.304245\pi$
$643$	−6.08170	−	6.08170i	−0.239839	−	0.239839i	−0.816783	+	0.576945i	$0.804245\pi$
$644$	−4.22082	+	8.79338i	−0.166323	+	0.346508i
$645$		0			0
$646$	0.414814	−	0.261015i	0.0163207	−	0.0102695i
$647$	8.52118	−	8.52118i	0.335002	−	0.335002i	−0.519480	−	0.854482i	$-0.673874\pi$
$647$	8.52118	−	8.52118i	0.335002	−	0.335002i	0.854482	+	0.519480i	$0.173874\pi$
$648$	−24.8955	+	5.31155i	−0.977989	+	0.208657i
$649$			12.2738i			0.481789i
$650$		0			0
$651$	14.8965	+	9.44400i	0.583838	+	0.370139i
$652$	−8.12650	−	23.1292i	−0.318258	−	0.905811i
$653$	26.0276	−	26.0276i	1.01854	−	1.01854i	0.0187129	−	0.999825i	$-0.494043\pi$
$653$	26.0276	−	26.0276i	1.01854	−	1.01854i	0.999825	−	0.0187129i	$-0.00595686\pi$
$654$	22.8390	+	0.0774114i	0.893075	+	0.00302703i
$655$		0			0
$656$	27.3017	−	21.8869i	1.06595	−	0.854540i
$657$	6.49919	−	18.1043i	0.253557	−	0.706316i
$658$	−15.5411	−	3.53670i	−0.605856	−	0.137875i
$659$		−	33.7716i		−	1.31555i	−0.753213	−	0.657777i	$-0.771497\pi$
$659$		−	33.7716i		−	1.31555i	0.753213	−	0.657777i	$-0.228503\pi$
$660$		0			0
$661$		−	44.5819i		−	1.73404i	−0.498277	−	0.867018i	$-0.666034\pi$
$661$		−	44.5819i		−	1.73404i	0.498277	−	0.867018i	$-0.333966\pi$
$662$	4.59685	−	20.1997i	0.178662	−	0.785083i
$663$	−0.381300	+	0.0854143i	−0.0148085	+	0.00331722i
$664$	−22.3070	+	2.55676i	−0.865680	+	0.0992217i
$665$		0			0
$666$	−23.5510	+	36.8711i	−0.912581	+	1.42873i
$667$	13.6301	−	13.6301i	0.527758	−	0.527758i
$668$	−4.95879	+	1.74228i	−0.191861	+	0.0674109i
$669$	8.27618	−	13.0544i	0.319976	−	0.504713i
$670$		0			0
$671$		−	28.4249i		−	1.09733i
$672$	−1.09316	+	9.63021i	−0.0421697	+	0.371493i
$673$	15.8002	−	15.8002i	0.609052	−	0.609052i	−0.333647	−	0.942698i	$-0.608279\pi$
$673$	15.8002	−	15.8002i	0.609052	−	0.609052i	0.942698	+	0.333647i	$0.108279\pi$
$674$	−19.6241	−	31.1873i	−0.755892	−	1.20129i
$675$		0			0
$676$	3.74645	−	7.80511i	0.144094	−	0.300197i
$677$	−6.51094	−	6.51094i	−0.250236	−	0.250236i	0.570832	−	0.821067i	$-0.306621\pi$
$677$	−6.51094	−	6.51094i	−0.250236	−	0.250236i	−0.821067	+	0.570832i	$0.806621\pi$
$678$	−13.8431	−	13.9373i	−0.531642	−	0.535258i
$679$		−	15.9441i		−	0.611880i
$680$		0			0
$681$	−6.46575	−	4.09913i	−0.247768	−	0.157079i
$682$	−60.2042	−	13.7007i	−2.30534	−	0.524627i
$683$	9.23055	−	9.23055i	0.353197	−	0.353197i	−0.508101	−	0.861298i	$-0.669652\pi$
$683$	9.23055	−	9.23055i	0.353197	−	0.353197i	0.861298	+	0.508101i	$0.169652\pi$
$684$	27.1402	+	0.183983i	1.03773	+	0.00703475i
$685$		0			0
$686$	−15.4178	+	9.70143i	−0.588656	+	0.370402i
$687$	−31.6699	+	7.09433i	−1.20828	+	0.270666i
$688$	2.85011	−	25.8908i	0.108660	−	0.987077i
$689$	1.08330			0.0412704
$690$		0			0
$691$			8.14177i			0.309727i	0.987936	+	0.154864i	$0.0494938\pi$
$691$			8.14177i			0.309727i	−0.987936	+	0.154864i	$0.950506\pi$
$692$	−13.3610	+	4.69440i	−0.507908	+	0.178454i
$693$	−11.8454	−	4.25234i	−0.449970	−	0.161533i
$694$	15.8410	+	25.1751i	0.601316	+	0.955632i
$695$		0			0
$696$	8.34681	−	17.2392i	0.316385	−	0.653450i
$697$	0.473903	+	0.473903i	0.0179503	+	0.0179503i
$698$	26.0747	+	5.93384i	0.986942	+	0.224599i
$699$	22.6758	+	14.3759i	0.857678	+	0.543747i
$700$		0			0
$701$	−29.5673			−1.11674			−0.558371	−	0.829591i	$-0.688573\pi$
$701$	−29.5673			−1.11674			−0.558371	+	0.829591i	$0.688573\pi$
$702$	−20.3415	−	7.38022i	−0.767739	−	0.278548i
$703$	32.9842	−	32.9842i	1.24402	−	1.24402i
$704$	−7.67665	−	33.0483i	−0.289325	−	1.24556i
$705$		0			0
$706$	11.4443	+	18.1876i	0.430710	+	0.684499i
$707$	10.2872	+	10.2872i	0.386889	+	0.386889i
$708$	−2.25771	+	9.76781i	−0.0848501	+	0.367097i
$709$	19.7857			0.743066			0.371533	−	0.928420i	$-0.378832\pi$
$709$	19.7857			0.743066			0.371533	+	0.928420i	$0.378832\pi$
$710$		0			0
$711$	−1.87091	−	3.96643i	−0.0701646	−	0.148753i
$712$	12.0185	+	9.54676i	0.450413	+	0.357780i
$713$	−35.8888	−	35.8888i	−1.34404	−	1.34404i
$714$	−0.185632		0.000629188i	−0.00694710		2.35468e-5i
$715$		0			0
$716$	4.38567	−	9.13683i	0.163900	−	0.341460i
$717$	−17.7671	+	3.97998i	−0.663524	+	0.148635i
$718$	−0.104503	−	0.0237819i	−0.00390003	−	0.000887532i
$719$	−9.82970			−0.366586			−0.183293	−	0.983058i	$-0.558676\pi$
$719$	−9.82970			−0.366586			−0.183293	+	0.983058i	$0.558676\pi$
$720$		0			0
$721$	−11.3149			−0.421390
$722$	−2.01582	−	0.458741i	−0.0750211	−	0.0170726i
$723$	−9.43307	+	2.11309i	−0.350820	+	0.0785865i
$724$	3.73310	−	7.77731i	0.138740	−	0.289041i
$725$		0			0
$726$	17.1128	+	0.0580029i	0.635116	+	0.00215269i
$727$	−8.39630	−	8.39630i	−0.311401	−	0.311401i	0.534051	−	0.845452i	$-0.320669\pi$
$727$	−8.39630	−	8.39630i	−0.311401	−	0.311401i	−0.845452	+	0.534051i	$0.820669\pi$
$728$	−5.12443	+	6.45120i	−0.189924	+	0.239097i
$729$	6.64261	−	26.1701i	0.246023	−	0.969264i
$730$		0			0
$731$	0.498885			0.0184519
$732$	5.22863	−	22.6212i	0.193256	−	0.836104i
$733$	−13.4915	−	13.4915i	−0.498321	−	0.498321i	0.412594	−	0.910915i	$-0.364623\pi$
$733$	−13.4915	−	13.4915i	−0.498321	−	0.498321i	−0.910915	+	0.412594i	$0.864623\pi$
$734$	4.14212	+	6.58280i	0.152888	+	0.242975i
$735$		0			0
$736$	9.12713	−	26.3539i	0.336430	−	0.971419i
$737$	7.42892	−	7.42892i	0.273648	−	0.273648i
$738$	7.99005	+	36.2440i	0.294118	+	1.33416i
$739$	−20.0345			−0.736983			−0.368491	−	0.929631i	$-0.620126\pi$
$739$	−20.0345			−0.736983			−0.368491	+	0.929631i	$0.620126\pi$
$740$		0			0
$741$	19.4854	+	12.3533i	0.715814	+	0.453809i
$742$	0.501811	+	0.114197i	0.0184221	+	0.00419232i
$743$	22.8684	+	22.8684i	0.838958	+	0.838958i	0.988722	−	0.149763i	$-0.0478512\pi$
$743$	22.8684	+	22.8684i	0.838958	+	0.838958i	−0.149763	+	0.988722i	$0.547851\pi$
$744$	−45.3918	−	21.9777i	−1.66414	−	0.805740i
$745$		0			0
$746$	−1.19130	−	1.89325i	−0.0436166	−	0.0693169i
$747$	8.04650	−	22.4145i	0.294406	−	0.820105i
$748$	0.613089	−	0.215410i	0.0224168	−	0.00787617i
$749$			3.58217i			0.130890i
$750$		0			0
$751$	6.16044			0.224798			0.112399	−	0.993663i	$-0.464147\pi$
$751$	6.16044			0.224798			0.112399	+	0.993663i	$0.464147\pi$
$752$	45.2997	+	4.98669i	1.65191	+	0.181846i
$753$	22.2612	−	4.98670i	0.811245	−	0.181725i
$754$	13.7805	−	8.67115i	0.501856	−	0.315785i
$755$		0			0
$756$	−8.64468	−	5.56303i	−0.314404	−	0.202326i
$757$	−0.293203	+	0.293203i	−0.0106566	+	0.0106566i	−0.712415	−	0.701758i	$-0.752399\pi$
$757$	−0.293203	+	0.293203i	−0.0106566	+	0.0106566i	0.701758	+	0.712415i	$0.252399\pi$
$758$	−42.2577	−	9.61660i	−1.53487	−	0.349291i
$759$	30.5871	+	19.3915i	1.11024	+	0.703866i
$760$		0			0
$761$		−	41.9740i		−	1.52155i	−0.649013	−	0.760777i	$-0.724818\pi$
$761$		−	41.9740i		−	1.52155i	0.649013	−	0.760777i	$-0.275182\pi$
$762$	24.7004	+	24.8685i	0.894803	+	0.900889i
$763$	6.52182	+	6.52182i	0.236106	+	0.236106i
$764$	−17.1445	+	35.7177i	−0.620265	+	1.29222i
$765$		0			0
$766$	−17.4267	−	27.6950i	−0.629651	−	1.00066i
$767$	−6.02604	+	6.02604i	−0.217588	+	0.217588i
$768$	−0.0301756	−	27.7128i	−0.00108887	−	0.999999i
$769$			11.0782i			0.399490i	0.979848	+	0.199745i	$0.0640113\pi$
$769$			11.0782i			0.399490i	−0.979848	+	0.199745i	$0.935989\pi$
$770$		0			0
$771$	9.00260	−	14.2002i	0.324221	−	0.511409i
$772$	−8.04590	+	2.82694i	−0.289578	+	0.101744i
$773$	−21.3386	+	21.3386i	−0.767496	+	0.767496i	−0.977665	−	0.210169i	$-0.932598\pi$
$773$	−21.3386	+	21.3386i	−0.767496	+	0.767496i	0.210169	+	0.977665i	$0.432598\pi$
$774$	23.2829	+	14.8717i	0.836888	+	0.534552i
$775$		0			0
$776$	5.19136	+	45.2931i	0.186359	+	1.62593i
$777$	−17.2408	+	3.86209i	−0.618511	+	0.138552i
$778$	8.91184	−	39.1608i	0.319505	−	1.40398i
$779$		−	39.5710i		−	1.41778i
$780$		0			0
$781$			44.5819i			1.59527i
$782$	0.520857	+	0.118532i	0.0186258	+	0.00423869i
$783$	12.4735	+	16.0352i	0.445768	+	0.573050i
$784$	18.7927	−	15.0655i	0.671168	−	0.538054i
$785$		0			0
$786$	−24.4240	−	0.0827838i	−0.871176	−	0.00295280i
$787$	−22.3990	+	22.3990i	−0.798438	+	0.798438i	−0.982849	−	0.184411i	$-0.940962\pi$
$787$	−22.3990	+	22.3990i	−0.798438	+	0.798438i	0.184411	+	0.982849i	$0.440962\pi$
$788$	6.34846	+	18.0687i	0.226154	+	0.643669i
$789$	31.2831	+	19.8327i	1.11371	+	0.706063i
$790$		0			0
$791$		−	7.93287i		−	0.282060i
$792$	35.0342	+	8.22294i	1.24489	+	0.292189i
$793$	13.9557	−	13.9557i	0.495580	−	0.495580i
$794$	−21.6445	+	13.6194i	−0.768133	+	0.483336i
$795$		0			0
$796$	6.70604	−	13.9709i	0.237689	−	0.495187i
$797$	−19.7929	−	19.7929i	−0.701102	−	0.701102i	0.263545	−	0.964647i	$-0.415108\pi$
$797$	−19.7929	−	19.7929i	−0.701102	−	0.701102i	−0.964647	+	0.263545i	$0.915108\pi$
$798$	7.72389	+	7.77643i	0.273423	+	0.275283i
$799$			0.872872i			0.0308800i
$800$		0			0
$801$	−14.7241	+	6.94514i	−0.520250	+	0.245394i
$802$	3.53078	−	15.5151i	0.124676	−	0.547857i
$803$	−19.2282	+	19.2282i	−0.678548	+	0.678548i
$804$	7.27864	−	4.54561i	0.256698	−	0.160311i
$805$		0			0
$806$	−22.8317	−	36.2849i	−0.804212	−	1.27808i
$807$	4.47259	+	19.9662i	0.157443	+	0.702843i
$808$	−32.5726	−	25.8737i	−1.14590	−	0.910233i
$809$	19.9408			0.701082			0.350541	−	0.936547i	$-0.385998\pi$
$809$	19.9408			0.701082			0.350541	+	0.936547i	$0.385998\pi$
$810$		0			0
$811$		−	24.0234i		−	0.843577i	−0.906694	−	0.421789i	$-0.861402\pi$
$811$		−	24.0234i		−	0.843577i	0.906694	−	0.421789i	$-0.138598\pi$
$812$	7.29756	−	2.56401i	0.256094	−	0.0899791i
$813$	−17.4938	+	3.91875i	−0.613534	+	0.137437i
$814$	52.3483	−	32.9393i	1.83481	−	1.15452i
$815$		0			0
$816$	0.527536	−	0.0586537i	0.0184674	−	0.00205329i
$817$	−20.8285	−	20.8285i	−0.728697	−	0.728697i
$818$	−4.60211	+	20.2228i	−0.160909	+	0.707074i
$819$	−3.72795	−	7.90347i	−0.130265	−	0.276170i
$820$		0			0
$821$	14.4816			0.505413			0.252706	−	0.967543i	$-0.418679\pi$
$821$	14.4816			0.505413			0.252706	+	0.967543i	$0.418679\pi$
$822$	−3.46569	+	3.44227i	−0.120880	+	0.120063i
$823$	−21.7093	+	21.7093i	−0.756740	+	0.756740i	−0.975728	−	0.218987i	$-0.929725\pi$
$823$	−21.7093	+	21.7093i	−0.756740	+	0.756740i	0.218987	+	0.975728i	$0.429725\pi$
$824$	32.1427	−	3.68410i	1.11975	−	0.128342i
$825$		0			0
$826$	−3.42666	+	2.15617i	−0.119229	+	0.0750228i
$827$	−28.9363	−	28.9363i	−1.00621	−	1.00621i	−0.999981	−	0.00623359i	$-0.998016\pi$
$827$	−28.9363	−	28.9363i	−1.00621	−	1.00621i	−0.00623359	−	0.999981i	$-0.501984\pi$
$828$	20.7750	+	21.0586i	0.721981	+	0.731836i
$829$	18.8808			0.655758			0.327879	−	0.944720i	$-0.393666\pi$
$829$	18.8808			0.655758			0.327879	+	0.944720i	$0.393666\pi$
$830$		0			0
$831$	−8.19277	+	12.9228i	−0.284204	+	0.448288i
$832$	12.4567	−	19.9946i	0.431857	−	0.693189i
$833$	0.326204	+	0.326204i	0.0113023	+	0.0113023i
$834$	−12.3635	−	0.0419053i	−0.428113	−	0.00145106i
$835$		0			0
$836$	−34.5900	−	16.6032i	−1.19632	−	0.574233i
$837$	42.2216	−	32.8436i	1.45939	−	1.13524i
$838$	0.00679807	−	0.0298724i	0.000234835	−	0.00103192i
$839$	−26.4522			−0.913233			−0.456616	−	0.889664i	$-0.650939\pi$
$839$	−26.4522			−0.913233			−0.456616	+	0.889664i	$0.650939\pi$
$840$		0			0
$841$	13.7142			0.472904
$842$	−4.53536	+	19.9295i	−0.156299	+	0.686815i
$843$	−12.5797	−	56.1574i	−0.433269	−	1.93416i
$844$	20.3715	−	42.4407i	0.701217	−	1.46087i
$845$		0			0
$846$	−26.0202	+	40.7369i	−0.894594	+	1.40056i
$847$	4.88667	+	4.88667i	0.167908	+	0.167908i
$848$	−1.46270	−	0.161017i	−0.0502292	−	0.00552934i
$849$	14.6498	+	9.28764i	0.502781	+	0.318751i
$850$		0			0
$851$	50.8414			1.74282
$852$	−8.20065	+	35.4794i	−0.280950	+	1.21550i
$853$	11.2078	+	11.2078i	0.383746	+	0.383746i	0.872450	−	0.488703i	$-0.162530\pi$
$853$	11.2078	+	11.2078i	0.383746	+	0.383746i	−0.488703	+	0.872450i	$0.662530\pi$
$854$	7.93578	−	4.99347i	0.271557	−	0.170873i
$855$		0			0
$856$	−1.16634	−	10.1760i	−0.0398648	−	0.347809i
$857$	−20.0179	+	20.0179i	−0.683797	+	0.683797i	−0.960854	−	0.277057i	$-0.910641\pi$
$857$	−20.0179	+	20.0179i	−0.683797	+	0.683797i	0.277057	+	0.960854i	$0.410641\pi$
$858$	21.5572	+	21.7039i	0.735952	+	0.740958i
$859$	7.84855			0.267789			0.133894	−	0.990996i	$-0.457252\pi$
$859$	7.84855			0.267789			0.133894	+	0.990996i	$0.457252\pi$
$860$		0			0
$861$	−8.02520	+	12.6585i	−0.273498	+	0.431401i
$862$	−5.33574	+	23.4465i	−0.181736	+	0.798592i
$863$	−23.1165	−	23.1165i	−0.786896	−	0.786896i	0.194088	−	0.980984i	$-0.437825\pi$
$863$	−23.1165	−	23.1165i	−0.786896	−	0.786896i	−0.980984	+	0.194088i	$0.937825\pi$
$864$	26.3686	+	12.9884i	0.897077	+	0.441875i
$865$		0			0
$866$	1.41056	−	0.887572i	0.0479327	−	0.0301609i
$867$	−6.43416	−	28.7229i	−0.218516	−	0.975480i
$868$	−6.75120	−	19.2149i	−0.229151	−	0.652197i
$869$			6.19972i			0.210311i
$870$		0			0
$871$	7.29471			0.247172
$872$	−20.6503	−	16.4033i	−0.699306	−	0.555485i
$873$	−45.5114	−	16.3379i	−1.54033	−	0.552956i
$874$	−16.7972	−	26.6946i	−0.568172	−	0.902958i
$875$		0			0
$876$	−18.8392	+	11.7653i	−0.636519	+	0.397514i
$877$	−22.8758	+	22.8758i	−0.772459	+	0.772459i	−0.978536	−	0.206076i	$-0.933930\pi$
$877$	−22.8758	+	22.8758i	−0.772459	+	0.772459i	0.206076	+	0.978536i	$0.433930\pi$
$878$	−6.35757	+	27.9367i	−0.214558	+	0.942818i
$879$	26.3553	−	41.5714i	0.888941	−	1.40217i
$880$		0			0
$881$		−	11.2702i		−	0.379702i	−0.981813	−	0.189851i	$-0.939199\pi$
$881$		−	11.2702i		−	0.379702i	0.981813	−	0.189851i	$-0.0608006\pi$
$882$	5.49983	+	24.9480i	0.185189	+	0.840044i
$883$	−2.32921	−	2.32921i	−0.0783843	−	0.0783843i	0.666828	−	0.745212i	$-0.267652\pi$
$883$	−2.32921	−	2.32921i	−0.0783843	−	0.0783843i	−0.745212	+	0.666828i	$0.767652\pi$
$884$	0.406766	+	0.195247i	0.0136810	+	0.00656688i
$885$		0			0
$886$	−28.6291	+	18.0144i	−0.961813	+	0.605206i
$887$	27.7480	−	27.7480i	0.931685	−	0.931685i	−0.0661260	−	0.997811i	$-0.521064\pi$
$887$	27.7480	−	27.7480i	0.931685	−	0.931685i	0.997811	+	0.0661260i	$0.0210639\pi$
$888$	47.7191	−	16.5847i	1.60135	−	0.556546i
$889$			14.1547i			0.474734i
$890$		0			0
$891$	−24.2760	+	29.4545i	−0.813276	+	0.986763i
$892$	−16.8389	+	5.91636i	−0.563806	+	0.198094i
$893$	36.4425	−	36.4425i	1.21950	−	1.21950i
$894$	−0.178592	+	52.6907i	−0.00597301	+	1.76224i
$895$		0			0
$896$	7.87801	−	7.94889i	0.263186	−	0.265554i
$897$	5.49667	+	24.5378i	0.183529	+	0.819294i
$898$	−46.0003	−	10.4683i	−1.53505	−	0.349332i
$899$			40.2484i			1.34236i
$900$		0			0
$901$		−	0.0281844i		−	0.000938958i
$902$	11.6424	−	51.1596i	0.387650	−	1.70343i
$903$	2.43879	+	10.8870i	0.0811578	+	0.362298i
$904$	2.58291	+	22.5352i	0.0859065	+	0.749509i
$905$		0			0
$906$	3.44392	+	0.0116730i	0.114417	+	0.000387809i
$907$	19.8583	−	19.8583i	0.659383	−	0.659383i	−0.295851	−	0.955234i	$-0.595603\pi$
$907$	19.8583	−	19.8583i	0.659383	−	0.659383i	0.955234	+	0.295851i	$0.0956031\pi$
$908$	2.93033	+	8.34016i	0.0972465	+	0.276778i
$909$	39.9053	−	18.8227i	1.32357	−	0.624311i
$910$		0			0
$911$			45.2764i			1.50007i	0.661396	+	0.750037i	$0.269964\pi$
$911$			45.2764i			1.50007i	−0.661396	+	0.750037i	$0.730036\pi$
$912$	−24.4735	−	19.5759i	−0.810399	−	0.648223i
$913$	−23.8060	+	23.8060i	−0.787864	+	0.787864i
$914$	−23.1029	−	36.7159i	−0.764176	−	1.21445i
$915$		0			0
$916$	33.7851	+	16.2168i	1.11629	+	0.535819i
$917$	−6.97444	−	6.97444i	−0.230316	−	0.230316i
$918$	−0.192013	+	0.529228i	−0.00633737	+	0.0174671i
$919$			0.337489i			0.0111327i	0.999985	+	0.00556636i	$0.00177184\pi$
$919$			0.337489i			0.0111327i	−0.999985	+	0.00556636i	$0.998228\pi$
$920$		0			0
$921$	−17.3228	+	27.3241i	−0.570807	+	0.900360i
$922$	48.1159	+	10.9498i	1.58461	+	0.360611i
$923$	−21.8882	+	21.8882i	−0.720460	+	0.720460i
$924$	7.69792	+	12.3263i	0.253243	+	0.405505i
$925$		0			0
$926$	−16.5857	+	10.4363i	−0.545039	+	0.342957i
$927$	−11.5944	+	32.2977i	−0.380810	+	1.06079i
$928$	−19.8956	+	9.65973i	−0.653105	+	0.317096i
$929$	−39.1863			−1.28566			−0.642830	−	0.766009i	$-0.722240\pi$
$929$	−39.1863			−1.28566			−0.642830	+	0.766009i	$0.722240\pi$
$930$		0			0
$931$		−	27.2381i		−	0.892693i
$932$	−10.2769	−	29.2495i	−0.336630	−	0.958098i
$933$	4.95648	+	22.1263i	0.162268	+	0.724384i
$934$	17.1992	+	27.3336i	0.562776	+	0.894382i
$935$		0			0
$936$	13.1635	+	21.2378i	0.430261	+	0.694181i
$937$	1.50743	+	1.50743i	0.0492455	+	0.0492455i	0.731301	−	0.682055i	$-0.238914\pi$
$937$	1.50743	+	1.50743i	0.0492455	+	0.0492455i	−0.682055	+	0.731301i	$0.738914\pi$
$938$	3.37910	+	0.768983i	0.110331	+	0.0251082i
$939$	18.1241	−	28.5881i	0.591459	−	0.932936i
$940$		0			0
$941$	−8.79941			−0.286852			−0.143426	−	0.989661i	$-0.545812\pi$
$941$	−8.79941			−0.286852			−0.143426	+	0.989661i	$0.545812\pi$
$942$	−10.6405	+	10.5686i	−0.346687	+	0.344345i
$943$	30.4971	−	30.4971i	0.993122	−	0.993122i
$944$	9.03219	−	7.24082i	0.293973	−	0.235669i
$945$		0			0
$946$	−20.8002	−	33.0563i	−0.676272	−	1.07475i
$947$	2.34399	+	2.34399i	0.0761694	+	0.0761694i	0.744165	−	0.667996i	$-0.232848\pi$
$947$	2.34399	+	2.34399i	0.0761694	+	0.0761694i	−0.667996	+	0.744165i	$0.732848\pi$
$948$	−1.14041	+	4.93390i	−0.0370389	+	0.160246i
$949$	−18.8808			−0.612897
$950$		0			0
$951$	17.7770	+	11.2702i	0.576459	+	0.365461i
$952$	0.167842	+	0.133323i	0.00543979	+	0.00432104i
$953$	24.6641	+	24.6641i	0.798949	+	0.798949i	0.982930	−	0.183981i	$-0.0588984\pi$
$953$	24.6641	+	24.6641i	0.798949	+	0.798949i	−0.183981	+	0.982930i	$0.558898\pi$
$954$	0.840174	−	1.31537i	0.0272016	−	0.0425865i
$955$		0			0
$956$	18.9537	+	9.09777i	0.613007	+	0.294243i
$957$	−6.27780	−	28.0249i	−0.202933	−	0.905915i
$958$	−14.3912	−	3.27501i	−0.464958	−	0.105811i
$959$	−1.97261			−0.0636990
$960$		0			0
$961$	74.9765			2.41860
$962$	41.8734	+	9.52915i	1.35005	+	0.307232i
$963$	10.2251	+	3.67065i	0.329498	+	0.118285i
$964$	10.0631	+	4.83027i	0.324110	+	0.155573i
$965$		0			0
$966$	−0.0404902	+	11.9460i	−0.00130275	+	0.384356i
$967$	27.3981	+	27.3981i	0.881063	+	0.881063i	0.993643	−	0.112580i	$-0.0359114\pi$
$967$	27.3981	+	27.3981i	0.881063	+	0.881063i	−0.112580	+	0.993643i	$0.535911\pi$
$968$	−15.4728	−	12.2907i	−0.497316	−	0.395037i
$969$	0.321397	−	0.506955i	0.0103248	−	0.0162858i
$970$		0			0
$971$	−1.18320			−0.0379706			−0.0189853	−	0.999820i	$-0.506044\pi$
$971$	−1.18320			−0.0379706			−0.0189853	+	0.999820i	$0.506044\pi$
$972$	−24.7375	+	18.9752i	−0.793455	+	0.608629i
$973$	−3.53048	−	3.53048i	−0.113182	−	0.113182i
$974$	22.3757	+	35.5602i	0.716964	+	1.13942i
$975$		0			0
$976$	−20.9176	+	16.7690i	−0.669556	+	0.536762i
$977$	−3.25473	+	3.25473i	−0.104128	+	0.104128i	−0.757251	−	0.653123i	$-0.773458\pi$
$977$	−3.25473	+	3.25473i	−0.104128	+	0.104128i	0.653123	+	0.757251i	$0.273458\pi$
$978$	−21.1588	−	21.3027i	−0.676585	−	0.681187i
$979$	23.0144			0.735544
$980$		0			0
$981$	25.2990	−	11.9332i	0.807734	−	0.380996i
$982$	−9.07101	−	2.06430i	−0.289468	−	0.0658743i
$983$	−10.3348	−	10.3348i	−0.329628	−	0.329628i	0.522817	−	0.852445i	$-0.324881\pi$
$983$	−10.3348	−	10.3348i	−0.329628	−	0.329628i	−0.852445	+	0.522817i	$0.824881\pi$
$984$	18.6759	−	38.5725i	0.595366	−	1.22965i
$985$		0			0
$986$	−0.225599	−	0.358530i	−0.00718454	−	0.0114179i
$987$	−19.0485	+	4.26702i	−0.606320	+	0.135821i
$988$	−8.83093	−	25.1342i	−0.280949	−	0.799624i
$989$		−	32.1048i		−	1.02087i
$990$		0			0
$991$	−13.4473			−0.427169			−0.213584	−	0.976925i	$-0.568514\pi$
$991$	−13.4473			−0.427169			−0.213584	+	0.976925i	$0.568514\pi$
$992$	25.4347	+	52.3863i	0.807551	+	1.66327i
$993$	−5.54608	−	24.7584i	−0.176000	−	0.785684i
$994$	−12.4466	+	7.83182i	−0.394782	+	0.248410i
$995$		0			0
$996$	−23.3244	+	14.5664i	−0.739063	+	0.461555i
$997$	25.0027	−	25.0027i	0.791844	−	0.791844i	−0.189949	−	0.981794i	$-0.560832\pi$
$997$	25.0027	−	25.0027i	0.791844	−	0.791844i	0.981794	+	0.189949i	$0.0608324\pi$
$998$	27.2641	+	6.20451i	0.863031	+	0.196400i
$999$	−6.64261	+	53.1701i	−0.210163	+	1.68223i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	600.2.w.k.557.1	yes	64
3.2	odd	2	inner	600.2.w.k.557.31	yes	64
5.2	odd	4	inner	600.2.w.k.293.17	yes	64
5.3	odd	4	inner	600.2.w.k.293.16	yes	64
5.4	even	2	inner	600.2.w.k.557.32	yes	64
8.5	even	2	inner	600.2.w.k.557.18	yes	64
15.2	even	4	inner	600.2.w.k.293.15	yes	64
15.8	even	4	inner	600.2.w.k.293.18	yes	64
15.14	odd	2	inner	600.2.w.k.557.2	yes	64
24.5	odd	2	inner	600.2.w.k.557.16	yes	64
40.13	odd	4	inner	600.2.w.k.293.31	yes	64
40.29	even	2	inner	600.2.w.k.557.15	yes	64
40.37	odd	4	inner	600.2.w.k.293.2	yes	64
120.29	odd	2	inner	600.2.w.k.557.17	yes	64
120.53	even	4	inner	600.2.w.k.293.1	✓	64
120.77	even	4	inner	600.2.w.k.293.32	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
600.2.w.k.293.1	✓	64	120.53	even	4	inner
600.2.w.k.293.2	yes	64	40.37	odd	4	inner
600.2.w.k.293.15	yes	64	15.2	even	4	inner
600.2.w.k.293.16	yes	64	5.3	odd	4	inner
600.2.w.k.293.17	yes	64	5.2	odd	4	inner
600.2.w.k.293.18	yes	64	15.8	even	4	inner
600.2.w.k.293.31	yes	64	40.13	odd	4	inner
600.2.w.k.293.32	yes	64	120.77	even	4	inner
600.2.w.k.557.1	yes	64	1.1	even	1	trivial
600.2.w.k.557.2	yes	64	15.14	odd	2	inner
600.2.w.k.557.15	yes	64	40.29	even	2	inner
600.2.w.k.557.16	yes	64	24.5	odd	2	inner
600.2.w.k.557.17	yes	64	120.29	odd	2	inner
600.2.w.k.557.18	yes	64	8.5	even	2	inner
600.2.w.k.557.31	yes	64	3.2	odd	2	inner
600.2.w.k.557.32	yes	64	5.4	even	2	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:	\( N \)	\(=\)	\( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	600.w (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.37896 - 0.313810i) q^{2} +(-1.69016 + 0.378611i) q^{3} +(1.80305 + 0.865461i) q^{4} +(2.44948 + 0.00830235i) q^{6} +(0.699464 + 0.699464i) q^{7} +(-2.21473 - 1.75925i) q^{8} +(2.71331 - 1.27983i) q^{9} +O(q^{10})\)	\(q+(-1.37896 - 0.313810i) q^{2} +(-1.69016 + 0.378611i) q^{3} +(1.80305 + 0.865461i) q^{4} +(2.44948 + 0.00830235i) q^{6} +(0.699464 + 0.699464i) q^{7} +(-2.21473 - 1.75925i) q^{8} +(2.71331 - 1.27983i) q^{9} -4.24103 q^{11} +(-3.37512 - 0.780119i) q^{12} +(-2.08220 - 2.08220i) q^{13} +(-0.745032 - 1.18403i) q^{14} +(2.50195 + 3.12093i) q^{16} +(-0.0541732 + 0.0541732i) q^{17} +(-4.14316 + 0.913365i) q^{18} +4.52348 q^{19} +(-1.44703 - 0.917384i) q^{21} +(5.84820 + 1.33088i) q^{22} +(3.48621 + 3.48621i) q^{23} +(4.40933 + 2.13490i) q^{24} +(2.21785 + 3.52469i) q^{26} +(-4.10138 + 3.19041i) q^{27} +(0.655807 + 1.86652i) q^{28} -3.90970i q^{29} -10.2945 q^{31} +(-2.47071 - 5.08877i) q^{32} +(7.16803 - 1.60570i) q^{33} +(0.0917026 - 0.0577024i) q^{34} +(5.99986 + 0.0406728i) q^{36} +(7.29179 - 7.29179i) q^{37} +(-6.23768 - 1.41951i) q^{38} +(4.30761 + 2.73092i) q^{39} -8.74792i q^{41} +(1.70751 + 1.71913i) q^{42} +(-4.60454 - 4.60454i) q^{43} +(-7.64677 - 3.67044i) q^{44} +(-3.71333 - 5.90135i) q^{46} +(8.05631 - 8.05631i) q^{47} +(-5.41033 - 4.32762i) q^{48} -6.02150i q^{49} +(0.0710510 - 0.112072i) q^{51} +(-1.95224 - 5.55638i) q^{52} +(-0.260132 + 0.260132i) q^{53} +(6.65681 - 3.11238i) q^{54} +(-0.318596 - 2.77966i) q^{56} +(-7.64542 + 1.71264i) q^{57} +(-1.22690 + 5.39131i) q^{58} -2.89407i q^{59} +6.70235i q^{61} +(14.1957 + 3.23051i) q^{62} +(2.79305 + 1.00267i) q^{63} +(1.81009 + 7.79253i) q^{64} +(-10.3883 - 0.0352105i) q^{66} +(-1.75168 + 1.75168i) q^{67} +(-0.144561 + 0.0507920i) q^{68} +(-7.21219 - 4.57235i) q^{69} -10.5121i q^{71} +(-8.26079 - 1.93890i) q^{72} +(4.53385 - 4.53385i) q^{73} +(-12.3433 + 7.76683i) q^{74} +(8.15604 + 3.91489i) q^{76} +(-2.96644 - 2.96644i) q^{77} +(-5.08302 - 5.11760i) q^{78} -1.46184i q^{79} +(5.72408 - 6.94514i) q^{81} +(-2.74519 + 12.0630i) q^{82} +(5.61327 - 5.61327i) q^{83} +(-1.81511 - 2.90644i) q^{84} +(4.90451 + 7.79441i) q^{86} +(1.48026 + 6.60804i) q^{87} +(9.39275 + 7.46102i) q^{88} -5.42662 q^{89} -2.91285i q^{91} +(3.26862 + 9.30298i) q^{92} +(17.3994 - 3.89760i) q^{93} +(-13.6375 + 8.58116i) q^{94} +(6.10256 + 7.66542i) q^{96} +(-11.3974 - 11.3974i) q^{97} +(-1.88961 + 8.30339i) q^{98} +(-11.5072 + 5.42779i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 12 q^{6}+O(q^{10}) \) 64 * q + 12 * q^6	\( 64 q + 12 q^{6} - 40 q^{16} + 32 q^{31} - 84 q^{36} - 128 q^{46} - 180 q^{66} + 168 q^{76} + 48 q^{81} + 228 q^{96}+O(q^{100}) \) 64 * q + 12 * q^6 - 40 * q^16 + 32 * q^31 - 84 * q^36 - 128 * q^46 - 180 * q^66 + 168 * q^76 + 48 * q^81 + 228 * q^96

Introduction

L-functions

Modular forms

Varieties

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Database

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