LMFDB - Embedded newform 600.2.w.k.293.2

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			293.2
Character	$\chi$	$=$	600.293
Dual form			600.2.w.k.557.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.37896 + 0.313810i) q^{2} +(-0.378611 - 1.69016i) q^{3} +(1.80305 - 0.865461i) q^{4} +(1.05248 + 2.21185i) q^{6} +(-0.699464 + 0.699464i) q^{7} +(-2.21473 + 1.75925i) q^{8} +(-2.71331 + 1.27983i) q^{9} +O(q^{10})$	\(q+(-1.37896 + 0.313810i) q^{2} +(-0.378611 - 1.69016i) q^{3} +(1.80305 - 0.865461i) q^{4} +(1.05248 + 2.21185i) q^{6} +(-0.699464 + 0.699464i) q^{7} +(-2.21473 + 1.75925i) q^{8} +(-2.71331 + 1.27983i) q^{9} +4.24103 q^{11} +(-2.14542 - 2.71977i) 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} +(3.33991 - 2.61629i) q^{18} +4.52348 q^{19} +(1.44703 + 0.917384i) q^{21} +(-5.84820 + 1.33088i) q^{22} +(3.48621 - 3.48621i) q^{23} +(3.81194 + 3.07719i) q^{24} +(-2.21785 + 3.52469i) q^{26} +(3.19041 + 4.10138i) q^{27} +(-0.655807 + 1.86652i) q^{28} -3.90970i q^{29} -10.2945 q^{31} +(-2.47071 + 5.08877i) q^{32} +(-1.60570 - 7.16803i) q^{33} +(0.0917026 + 0.0577024i) q^{34} +(-3.78458 + 4.65585i) q^{36} +(-7.29179 - 7.29179i) q^{37} +(-6.23768 + 1.41951i) q^{38} +(-4.30761 - 2.73092i) q^{39} -8.74792i q^{41} +(-2.28328 - 0.810940i) 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} +(-6.22216 - 3.04709i) q^{48} +6.02150i q^{49} +(-0.0710510 + 0.112072i) q^{51} +(1.95224 - 5.55638i) q^{52} +(-0.260132 - 0.260132i) q^{53} +(-5.68649 - 4.65444i) q^{54} +(0.318596 - 2.77966i) q^{56} +(-1.71264 - 7.64542i) q^{57} +(1.22690 + 5.39131i) q^{58} -2.89407i q^{59} -6.70235i q^{61} +(14.1957 - 3.23051i) q^{62} +(1.00267 - 2.79305i) q^{63} +(1.81009 - 7.79253i) q^{64} +(4.46359 + 9.38053i) q^{66} +(1.75168 + 1.75168i) q^{67} +(-0.144561 - 0.0507920i) q^{68} +(-7.21219 - 4.57235i) q^{69} -10.5121i q^{71} +(3.75772 - 7.60786i) 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} +(6.79700 + 2.41405i) q^{78} +1.46184i q^{79} +(5.72408 - 6.94514i) q^{81} +(2.74519 + 12.0630i) q^{82} +(5.61327 + 5.61327i) q^{83} +(3.40303 + 0.401735i) q^{84} +(-4.90451 + 7.79441i) q^{86} +(-6.60804 + 1.48026i) q^{87} +(-9.39275 + 7.46102i) q^{88} +5.42662 q^{89} +2.91285i q^{91} +(3.26862 - 9.30298i) q^{92} +(3.89760 + 17.3994i) q^{93} +(-13.6375 - 8.58116i) q^{94} +(9.53630 + 2.24924i) 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 $\left(\mathbb{Z}/600\mathbb{Z}\right)^\times$.

$n$	$151$	$301$	$401$	$577$
$\chi(n)$	$1$	$-1$	$-1$	$e\left(\frac{3}{4}\right)$

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
$3$	−0.378611	−	1.69016i	−0.218591	−	0.975817i
$3$	−0.378611	−	1.69016i	−0.218591	−	0.975817i
$4$	1.80305	−	0.865461i	0.901523	−	0.432731i
$5$		0			0
$5$		0			0
$6$	1.05248	+	2.21185i	0.429672	+	0.902985i
$7$	−0.699464	+	0.699464i	−0.264372	+	0.264372i	−0.826828	−	0.562455i	$-0.809857\pi$
$7$	−0.699464	+	0.699464i	−0.264372	+	0.264372i	0.562455	+	0.826828i	$0.309857\pi$
$8$	−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	$-0.279200\pi$
$11$	4.24103			1.27872			0.639359	+	0.768908i	$0.279200\pi$
$12$	−2.14542	−	2.71977i	−0.619331	−	0.785130i
$13$	2.08220	−	2.08220i	0.577500	−	0.577500i	−0.356714	−	0.934214i	$-0.616103\pi$
$13$	2.08220	−	2.08220i	0.577500	−	0.577500i	0.934214	+	0.356714i	$0.116103\pi$
$14$	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	0.700507	−	0.713646i	$-0.252957\pi$
$17$	−0.0541732	−	0.0541732i	−0.0131389	−	0.0131389i	−0.713646	+	0.700507i	$0.752957\pi$
$18$	3.33991	−	2.61629i	0.787225	−	0.616666i
$19$	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	−0.243081	−	0.970006i	$-0.578158\pi$
$23$	3.48621	−	3.48621i	0.726925	−	0.726925i	0.970006	+	0.243081i	$0.0781580\pi$
$24$	3.81194	+	3.07719i	0.778109	+	0.628129i
$25$		0			0
$26$	−2.21785	+	3.52469i	−0.434957	+	0.691248i
$27$	3.19041	+	4.10138i	0.613994	+	0.789311i
$28$	−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
$33$	−1.60570	−	7.16803i	−0.279516	−	1.24779i
$34$	0.0917026	+	0.0577024i	0.0157269	+	0.00989588i
$35$		0			0
$36$	−3.78458	+	4.65585i	−0.630763	+	0.775975i
$37$	−7.29179	−	7.29179i	−1.19876	−	1.19876i	−0.974537	−	0.224225i	$-0.928015\pi$
$37$	−7.29179	−	7.29179i	−1.19876	−	1.19876i	−0.224225	−	0.974537i	$-0.571985\pi$
$38$	−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	$-0.239368\pi$
$42$	−2.28328	−	0.810940i	−0.352318	−	0.125131i
$43$	4.60454	−	4.60454i	0.702185	−	0.702185i	−0.262694	−	0.964879i	$-0.584611\pi$
$43$	4.60454	−	4.60454i	0.702185	−	0.702185i	0.964879	+	0.262694i	$0.0846110\pi$
$44$	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	0.980969	+	0.194165i	$0.0621996\pi$
$47$	8.05631	+	8.05631i	1.17513	+	1.17513i	0.194165	+	0.980969i	$0.437800\pi$
$48$	−6.22216	−	3.04709i	−0.898091	−	0.439810i
$49$			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	0.689015	−	0.724747i	$-0.258043\pi$
$53$	−0.260132	−	0.260132i	−0.0357319	−	0.0357319i	−0.724747	+	0.689015i	$0.758043\pi$
$54$	−5.68649	−	4.65444i	−0.773833	−	0.633390i
$55$		0			0
$56$	0.318596	−	2.77966i	0.0425742	−	0.371447i
$57$	−1.71264	−	7.64542i	−0.226844	−	1.01266i
$58$	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	$-0.858840\pi$
$61$		−	6.70235i		−	0.858148i	0.903269	−	0.429074i	$-0.141160\pi$
$62$	14.1957	−	3.23051i	1.80285	−	0.410276i
$63$	1.00267	−	2.79305i	0.126324	−	0.351892i
$64$	1.81009	−	7.79253i	0.226262	−	0.974067i
$65$		0			0
$66$	4.46359	+	9.38053i	0.549430	+	1.15466i
$67$	1.75168	+	1.75168i	0.214002	+	0.214002i	0.805965	−	0.591963i	$-0.201647\pi$
$67$	1.75168	+	1.75168i	0.214002	+	0.214002i	−0.591963	+	0.805965i	$0.701647\pi$
$68$	−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	$-0.214402\pi$
$72$	3.75772	−	7.60786i	0.442852	−	0.896595i
$73$	−4.53385	−	4.53385i	−0.530647	−	0.530647i	0.390118	−	0.920765i	$-0.372434\pi$
$73$	−4.53385	−	4.53385i	−0.530647	−	0.530647i	−0.920765	+	0.390118i	$0.872434\pi$
$74$	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
$78$	6.79700	+	2.41405i	0.769609	+	0.273338i
$79$			1.46184i			0.164470i	0.996613	+	0.0822352i	$0.0262059\pi$
$79$			1.46184i			0.164470i	−0.996613	+	0.0822352i	$0.973794\pi$
$80$		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	0.944538	−	0.328402i	$-0.106510\pi$
$83$	5.61327	+	5.61327i	0.616136	+	0.616136i	−0.328402	+	0.944538i	$0.606510\pi$
$84$	3.40303	+	0.401735i	0.371301	+	0.0438329i
$85$		0			0
$86$	−4.90451	+	7.79441i	−0.528867	+	0.840493i
$87$	−6.60804	+	1.48026i	−0.708456	+	0.158700i
$88$	−9.39275	+	7.46102i	−1.00127	+	0.795347i
$89$	5.42662			0.575220			0.287610	−	0.957748i	$-0.407139\pi$
$89$	5.42662			0.575220			0.287610	+	0.957748i	$0.407139\pi$
$90$		0			0
$91$			2.91285i			0.305350i
$92$	3.26862	−	9.30298i	0.340777	−	0.969903i
$93$	3.89760	+	17.3994i	0.404163	+	1.80423i
$94$	−13.6375	−	8.58116i	−1.40660	−	0.885079i
$95$		0			0
$96$	9.53630	+	2.24924i	0.973294	+	0.229562i
$97$	11.3974	−	11.3974i	1.15723	−	1.15723i	0.172162	−	0.985069i	$-0.444925\pi$
$97$	11.3974	−	11.3974i	1.15723	−	1.15723i	0.985069	−	0.172162i	$-0.0550753\pi$
$98$	−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	$-0.761279\pi$
$101$	−14.7072			−1.46342			−0.731712	+	0.681614i	$0.761279\pi$
$102$	0.0628069	−	0.176839i	0.00621881	−	0.0175097i
$103$	8.08829	+	8.08829i	0.796963	+	0.796963i	0.982616	−	0.185652i	$-0.0594398\pi$
$103$	8.08829	+	8.08829i	0.796963	+	0.796963i	−0.185652	+	0.982616i	$0.559440\pi$
$104$	−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	−0.572416	−	0.819964i	$-0.693994\pi$
$107$	2.56066	−	2.56066i	0.247548	−	0.247548i	0.819964	+	0.572416i	$0.193994\pi$
$108$	9.30204	+	4.63380i	0.895089	+	0.445888i
$109$	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	−0.921598	−	0.388145i	$-0.873116\pi$
$113$	−5.67068	+	5.67068i	−0.533453	+	0.533453i	0.388145	+	0.921598i	$0.373116\pi$
$114$	4.76086	+	10.0053i	0.445896	+	0.937079i
$115$		0			0
$116$	−3.38370	−	7.04938i	−0.314168	−	0.654518i
$117$	−2.98480	+	8.31453i	−0.275945	+	0.768678i
$118$	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
$123$	−14.7854	+	3.31206i	−1.33316	+	0.298638i
$124$	−18.5614	+	8.90948i	−1.66687	+	0.800095i
$125$		0			0
$126$	−0.506147	+	4.16615i	−0.0450912	+	0.371150i
$127$	−10.1183	+	10.1183i	−0.897851	+	0.897851i	−0.995246	−	0.0973946i	$-0.968949\pi$
$127$	−10.1183	+	10.1183i	−0.897851	+	0.897851i	0.0973946	+	0.995246i	$0.468949\pi$
$128$	−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	$-0.356540\pi$
$131$	9.97112			0.871181			0.435590	+	0.900145i	$0.356540\pi$
$132$	−9.09880	−	11.5346i	−0.791949	−	1.00396i
$133$	−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	0.644300	−	0.764773i	$-0.277149\pi$
$137$	−1.41009	−	1.41009i	−0.120472	−	0.120472i	−0.764773	+	0.644300i	$0.777149\pi$
$138$	11.3801	+	4.04182i	0.968742	+	0.344063i
$139$	−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
$144$	−2.79431	+	11.6701i	−0.232859	+	0.972510i
$145$		0			0
$146$	7.67476	+	4.82922i	0.635168	+	0.399669i
$147$	10.1773	−	2.27980i	0.839411	−	0.188035i
$148$	−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
$153$	0.216321	+	0.0776561i	0.0174885	+	0.00627813i
$154$	3.15970	−	5.02150i	0.254616	−	0.404644i
$155$		0			0
$156$	−10.1303	−	1.19591i	−0.811076	−	0.0957494i
$157$	4.32933	+	4.32933i	0.345518	+	0.345518i	0.858437	−	0.512919i	$-0.171436\pi$
$157$	4.32933	+	4.32933i	0.345518	+	0.345518i	−0.512919	+	0.858437i	$0.671436\pi$
$158$	−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
$162$	−5.71381	+	11.3733i	−0.448919	+	0.893572i
$163$	8.66748	−	8.66748i	0.678890	−	0.678890i	−0.280859	−	0.959749i	$-0.590619\pi$
$163$	8.66748	−	8.66748i	0.678890	−	0.678890i	0.959749	+	0.280859i	$0.0906195\pi$
$164$	−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	0.631544	−	0.775340i	$-0.282422\pi$
$167$	−1.85826	−	1.85826i	−0.143797	−	0.143797i	−0.775340	+	0.631544i	$0.782422\pi$
$168$	−4.81870	+	0.513928i	−0.371771	+	0.0396504i
$169$			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	0.490675	−	0.871343i	$-0.336750\pi$
$173$	−5.00691	−	5.00691i	−0.380668	−	0.380668i	−0.871343	+	0.490675i	$0.836750\pi$
$174$	8.64768	−	4.11488i	0.655579	−	0.311948i
$175$		0			0
$176$	10.6109	−	13.2360i	0.799823	−	0.997698i
$177$	−4.89145	+	1.09572i	−0.367664	+	0.0823597i
$178$	−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	$0.0512485\pi$
$181$			4.31343i			0.320614i	−0.987067	+	0.160307i	$0.948752\pi$
$182$	−0.914082	−	4.01670i	−0.0677563	−	0.297738i
$183$	−11.3281	+	2.53758i	−0.837395	+	0.187583i
$184$	−1.58792	+	13.8541i	−0.117063	+	1.02134i
$185$		0			0
$186$	−10.8347	−	22.7699i	−0.794440	−	1.66957i
$187$	−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	$0.745657\pi$
$192$	−13.8560	−	0.109017i	−0.999969	−	0.00786764i
$193$	3.01513	+	3.01513i	0.217034	+	0.217034i	0.807247	−	0.590213i	$-0.200956\pi$
$193$	3.01513	+	3.01513i	0.217034	+	0.217034i	−0.590213	+	0.807247i	$0.700956\pi$
$194$	−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	−0.423485	−	0.905903i	$-0.639193\pi$
$197$	6.77107	−	6.77107i	0.482419	−	0.482419i	0.905903	+	0.423485i	$0.139193\pi$
$198$	14.1647	−	11.0958i	1.00664	−	0.788542i
$199$			7.74852i			0.549278i	0.961547	+	0.274639i	$0.0885583\pi$
$199$			7.74852i			0.549278i	−0.961547	+	0.274639i	$0.911442\pi$
$200$		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
$204$	−0.0311142	+	0.263563i	−0.00217843	+	0.0184531i
$205$		0			0
$206$	−13.6916	−	8.61522i	−0.953939	−	0.600251i
$207$	−4.99741	+	13.9209i	−0.347344	+	0.967571i
$208$	−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	$0.300654\pi$
$211$			23.5384i			1.62045i	−0.586121	+	0.810224i	$0.699346\pi$
$212$	−0.694165	−	0.243896i	−0.0476755	−	0.0167509i
$213$	−17.7671	+	3.97998i	−1.21738	+	0.272703i
$214$	−2.72748	+	4.33460i	−0.186446	+	0.296307i
$215$		0			0
$216$	−14.2812	−	3.47075i	−0.971716	−	0.236154i
$217$	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
$222$	8.45390	−	23.8028i	0.567389	−	1.59754i
$223$	6.31021	+	6.31021i	0.422563	+	0.422563i	0.886085	−	0.463522i	$-0.153415\pi$
$223$	6.31021	+	6.31021i	0.422563	+	0.422563i	−0.463522	+	0.886085i	$0.653415\pi$
$224$	−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	−0.595738	−	0.803179i	$-0.703140\pi$
$227$	3.12540	−	3.12540i	0.207440	−	0.207440i	0.803179	+	0.595738i	$0.203140\pi$
$228$	−9.70478	−	12.3028i	−0.642714	−	0.814774i
$229$	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	−0.968211	−	0.250134i	$-0.919525\pi$
$233$	−10.9610	+	10.9610i	−0.718078	+	0.718078i	0.250134	+	0.968211i	$0.419525\pi$
$234$	1.50673	−	12.4020i	0.0984979	−	0.810747i
$235$		0			0
$236$	−2.50470	−	5.21813i	−0.163042	−	0.339672i
$237$	2.47076	−	0.553470i	0.160493	−	0.0359517i
$238$	−0.104503	+	0.0237819i	−0.00677395	+	0.00154155i
$239$	−10.5121			−0.679968			−0.339984	−	0.940431i	$-0.610422\pi$
$239$	−10.5121			−0.679968			−0.339984	+	0.940431i	$0.610422\pi$
$240$		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
$243$	−13.9056	−	7.04513i	−0.892046	−	0.451945i
$244$	−5.80063	−	12.0847i	−0.371347	−	0.773641i
$245$		0			0
$246$	19.3491	−	9.20700i	1.23365	−	0.587017i
$247$	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	$-0.363545\pi$
$251$	13.1711			0.831349			0.415675	+	0.909513i	$0.363545\pi$
$252$	−0.609424	−	5.90378i	−0.0383901	−	0.371903i
$253$	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	0.459835	−	0.888004i	$-0.347909\pi$
$257$	−6.86408	−	6.86408i	−0.428169	−	0.428169i	−0.888004	+	0.459835i	$0.847909\pi$
$258$	15.0307	+	5.33838i	0.935772	+	0.332353i
$259$	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	−0.997858	−	0.0654229i	$-0.979160\pi$
$263$	−15.1216	+	15.1216i	−0.932435	+	0.932435i	0.0654229	+	0.997858i	$0.479160\pi$
$264$	16.1665	+	13.0505i	0.994982	+	0.803200i
$265$		0			0
$266$	3.37013	−	5.35593i	0.206636	−	0.328393i
$267$	−2.05457	−	9.17187i	−0.125738	−	0.561309i
$268$	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
$273$	4.92320	−	1.10284i	0.297966	−	0.0667468i
$274$	2.38695	+	1.50195i	0.144201	+	0.0907364i
$275$		0			0
$276$	−16.9611	−	2.00230i	−1.02094	−	0.120524i
$277$	−6.24661	−	6.24661i	−0.375323	−	0.375323i	0.494089	−	0.869411i	$-0.335502\pi$
$277$	−6.24661	−	6.24661i	−0.375323	−	0.375323i	−0.869411	+	0.494089i	$0.835502\pi$
$278$	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	$0.542620\pi$
$282$	−9.34027	+	26.2985i	−0.556205	+	1.56605i
$283$	7.08141	−	7.08141i	0.420946	−	0.420946i	−0.464583	−	0.885529i	$-0.653796\pi$
$283$	7.08141	−	7.08141i	0.420946	−	0.420946i	0.885529	+	0.464583i	$0.153796\pi$
$284$	−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
$288$	0.191036	−	16.9695i	0.0112569	−	0.999937i
$289$		−	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	−0.981261	−	0.192683i	$-0.938281\pi$
$293$	−20.0947	−	20.0947i	−1.17394	−	1.17394i	−0.192683	−	0.981261i	$-0.561719\pi$
$294$	−13.3187	+	6.33750i	−0.776761	+	0.369610i
$295$		0			0
$296$	28.9774	+	3.32131i	1.68428	+	0.193047i
$297$	13.5306	+	17.3941i	0.785125	+	1.00931i
$298$	−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
$303$	5.56832	+	24.8576i	0.319891	+	1.42803i
$304$	11.3175	−	14.1175i	0.649105	−	0.809693i
$305$		0			0
$306$	−0.322666	−	0.0392009i	−0.0184456	−	0.00224096i
$307$	−13.2079	−	13.2079i	−0.753813	−	0.753813i	0.221375	−	0.975189i	$-0.428945\pi$
$307$	−13.2079	−	13.2079i	−0.753813	−	0.753813i	−0.975189	+	0.221375i	$0.928945\pi$
$308$	−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	$-0.121043\pi$
$312$	14.3446	−	1.52989i	0.812102	−	0.0866131i
$313$	13.8188	+	13.8188i	0.781087	+	0.781087i	0.980014	−	0.198927i	$-0.0637458\pi$
$313$	13.8188	+	13.8188i	0.781087	+	0.781087i	−0.198927	+	0.980014i	$0.563746\pi$
$314$	−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	−0.905971	−	0.423339i	$-0.860858\pi$
$317$	−8.59301	+	8.59301i	−0.482632	+	0.482632i	0.423339	+	0.905971i	$0.360858\pi$
$318$	0.301591	−	0.849158i	0.0169124	−	0.0476184i
$319$		−	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
$324$	4.31004	−	17.4764i	0.239447	−	0.970910i
$325$		0			0
$326$	−9.23214	+	14.6720i	−0.511321	+	0.812608i
$327$	−3.53018	−	15.7591i	−0.195219	−	0.871483i
$328$	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	$-0.868114\pi$
$331$		−	14.6485i		−	0.805155i	0.915386	−	0.402578i	$-0.131886\pi$
$332$	14.9790	+	5.26292i	0.822082	+	0.288840i
$333$	29.1171	+	10.4526i	1.59561	+	0.572800i
$334$	3.14561	+	1.97933i	0.172120	+	0.108304i
$335$		0			0
$336$	6.48350	−	2.22084i	0.353704	−	0.121157i
$337$	−18.4238	+	18.4238i	−1.00361	+	1.00361i	−0.00361703	+	0.999993i	$0.501151\pi$
$337$	−18.4238	+	18.4238i	−1.00361	+	1.00361i	−0.999993	+	0.00361703i	$0.998849\pi$
$338$	−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
$342$	15.1080	−	11.8347i	0.816948	−	0.639949i
$343$	−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	−0.982840	−	0.184462i	$-0.940946\pi$
$347$	−14.8721	+	14.8721i	−0.798378	+	0.798378i	0.184462	+	0.982840i	$0.440946\pi$
$348$	−10.6335	+	8.38797i	−0.570015	+	0.449642i
$349$	−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	−0.932648	−	0.360787i	$-0.882508\pi$
$353$	−10.7443	+	10.7443i	−0.571861	+	0.571861i	0.360787	+	0.932648i	$0.382508\pi$
$354$	6.40124	−	3.04594i	0.340222	−	0.161890i
$355$		0			0
$356$	9.78444	−	4.69653i	0.518574	−	0.248915i
$357$	−0.0286928	−	0.128088i	−0.00151858	−	0.00677913i
$358$	1.59021	+	6.98779i	0.0840454	+	0.369316i
$359$	−0.0757843			−0.00399974			−0.00199987	−	0.999998i	$-0.500637\pi$
$359$	−0.0757843			−0.00399974			−0.00199987	+	0.999998i	$0.500637\pi$
$360$		0			0
$361$	1.46184			0.0769392
$362$	−1.35360	−	5.94803i	−0.0711434	−	0.312621i
$363$	−2.64509	−	11.8080i	−0.138831	−	0.619760i
$364$	2.52096	+	5.25201i	0.132134	+	0.275280i
$365$		0			0
$366$	14.8246	−	7.05408i	0.774895	−	0.368723i
$367$	3.88878	−	3.88878i	0.202993	−	0.202993i	−0.598288	−	0.801281i	$-0.704152\pi$
$367$	3.88878	−	3.88878i	0.202993	−	0.202993i	0.801281	+	0.598288i	$0.204152\pi$
$368$	−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
$372$	22.0860	+	27.9986i	1.14511	+	1.45166i
$373$	−1.11844	+	1.11844i	−0.0579104	+	0.0579104i	−0.735469	−	0.677558i	$-0.763038\pi$
$373$	−1.11844	+	1.11844i	−0.0579104	+	0.0579104i	0.677558	+	0.735469i	$0.263038\pi$
$374$	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
$378$	7.23311	−	0.721877i	0.372031	−	0.0371294i
$379$	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	−0.152332	−	0.988329i	$-0.548678\pi$
$383$	16.3608	−	16.3608i	0.835998	−	0.835998i	0.988329	+	0.152332i	$0.0486782\pi$
$384$	19.1410	−	4.19781i	0.976786	−	0.214219i
$385$		0			0
$386$	−5.10392	−	3.21156i	−0.259782	−	0.163464i
$387$	−6.60051	+	18.3865i	−0.335523	+	0.934640i
$388$	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
$393$	−3.77517	−	16.8528i	−0.190432	−	0.850113i
$394$	−7.21219	+	11.4618i	−0.363345	+	0.577439i
$395$		0			0
$396$	−16.0505	+	19.7456i	−0.806568	+	0.992254i
$397$	−12.7864	−	12.7864i	−0.641733	−	0.641733i	0.309249	−	0.950981i	$-0.399922\pi$
$397$	−12.7864	−	12.7864i	−0.641733	−	0.641733i	−0.950981	+	0.309249i	$0.899922\pi$
$398$	−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	$0.909356\pi$
$402$	−2.03085	+	5.71806i	−0.101290	+	0.285191i
$403$	−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
$408$	−0.0398035	−	0.373206i	−0.00197057	−	0.0184765i
$409$			14.6653i			0.725152i	0.931954	+	0.362576i	$0.118103\pi$
$409$			14.6653i			0.725152i	−0.931954	+	0.362576i	$0.881897\pi$
$410$		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
$414$	2.52270	−	20.7646i	0.123984	−	1.02052i
$415$		0			0
$416$	5.45135	+	15.7404i	0.267274	+	0.771736i
$417$	1.91100	+	8.53094i	0.0935821	+	0.417762i
$418$	−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	$0.114562\pi$
$421$			14.4526i			0.704375i	−0.935930	+	0.352187i	$0.885438\pi$
$422$	−7.38657	−	32.4584i	−0.359573	−	1.58005i
$423$	−32.1699	−	11.5486i	−1.56416	−	0.561510i
$424$	1.03376	+	0.118487i	0.0502039	+	0.00575422i
$425$		0			0
$426$	23.2511	−	11.0637i	1.12652	−	0.536038i
$427$	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	$-0.134299\pi$
$432$	20.7824	+	0.304413i	0.999893	+	0.0146461i
$433$	0.833286	+	0.833286i	0.0400451	+	0.0400451i	0.726846	−	0.686801i	$-0.240985\pi$
$433$	0.833286	+	0.833286i	0.0400451	+	0.0400451i	−0.686801	+	0.726846i	$0.740985\pi$
$434$	−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
$438$	5.25643	−	14.8000i	0.251162	−	0.707171i
$439$			20.2593i			0.966924i	0.875365	+	0.483462i	$0.160621\pi$
$439$			20.2593i			0.966924i	−0.875365	+	0.483462i	$0.839379\pi$
$440$		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	0.983647	−	0.180106i	$-0.0576440\pi$
$443$	16.9126	+	16.9126i	0.803541	+	0.803541i	−0.180106	+	0.983647i	$0.557644\pi$
$444$	−4.18802	+	35.4760i	−0.198755	+	1.68361i
$445$		0			0
$446$	−10.6817	−	6.72131i	−0.505794	−	0.318263i
$447$	36.3571	−	8.14430i	1.71963	−	0.385212i
$448$	4.18450	+	6.71669i	0.197699	+	0.317334i
$449$	−33.3587			−1.57430			−0.787148	−	0.616764i	$-0.788443\pi$
$449$	−33.3587			−1.57430			−0.787148	+	0.616764i	$0.788443\pi$
$450$		0			0
$451$		−	37.1002i		−	1.74698i
$452$	−5.31675	+	15.1323i	−0.250079	+	0.711761i
$453$	−0.532320	−	2.37634i	−0.0250106	−	0.111650i
$454$	−3.32901	+	5.29058i	−0.156238	+	0.248299i
$455$		0			0
$456$	17.2432	+	13.9196i	0.807488	+	0.651846i
$457$	−21.6899	+	21.6899i	−1.01461	+	1.01461i	−0.0147169	+	0.999892i	$0.504685\pi$
$457$	−21.6899	+	21.6899i	−1.01461	+	1.01461i	−0.999892	+	0.0147169i	$0.995315\pi$
$458$	−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	$-0.198072\pi$
$461$	34.8929			1.62513			0.812563	+	0.582873i	$0.198072\pi$
$462$	−9.68346	−	3.43922i	−0.450515	−	0.160007i
$463$	−9.79796	−	9.79796i	−0.455350	−	0.455350i	0.441776	−	0.897126i	$-0.354349\pi$
$463$	−9.79796	−	9.79796i	−0.455350	−	0.455350i	−0.897126	+	0.441776i	$0.854349\pi$
$464$	−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	−0.973954	−	0.226747i	$-0.927191\pi$
$467$	−16.1473	+	16.1473i	−0.747207	+	0.747207i	0.226747	+	0.973954i	$0.427191\pi$
$468$	1.81417	+	17.5747i	0.0838600	+	0.812391i
$469$	−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
$474$	−3.23338	+	1.53856i	−0.148514	+	0.0706684i
$475$		0			0
$476$	0.136643	−	0.0655884i	0.00626301	−	0.00300624i
$477$	1.03874	+	0.372895i	0.0475608	+	0.0170737i
$478$	14.4957	−	3.29879i	0.663017	−	0.150883i
$479$	−10.4363			−0.476845			−0.238423	−	0.971161i	$-0.576630\pi$
$479$	−10.4363			−0.476845			−0.238423	+	0.971161i	$0.576630\pi$
$480$		0			0
$481$	−30.3660			−1.38457
$482$	−7.69618	+	1.75142i	−0.350551	+	0.0797751i
$483$	8.24286	−	1.84647i	0.375063	−	0.0840172i
$484$	12.5967	−	6.04638i	0.572575	−	0.274836i
$485$		0			0
$486$	21.3861	+	5.35121i	0.970092	+	0.242736i
$487$	21.0072	−	21.0072i	0.951925	−	0.951925i	−0.0469714	−	0.998896i	$-0.514957\pi$
$487$	21.0072	−	21.0072i	0.951925	−	0.951925i	0.998896	+	0.0469714i	$0.0149569\pi$
$488$	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	$-0.547423\pi$
$491$	−6.57817			−0.296869			−0.148434	+	0.988922i	$0.547423\pi$
$492$	−23.7923	+	18.7680i	−1.07264	+	0.846127i
$493$	−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
$498$	−6.50787	+	18.3236i	−0.291625	+	0.821098i
$499$	−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	−0.630450	−	0.776230i	$-0.717129\pi$
$503$	3.26952	−	3.26952i	0.145781	−	0.145781i	0.776230	+	0.630450i	$0.217129\pi$
$504$	2.69303	+	7.94981i	0.119957	+	0.354113i
$505$		0			0
$506$	−15.7483	+	25.0278i	−0.700099	+	1.11262i
$507$	7.31646	−	1.63895i	0.324935	−	0.0727882i
$508$	−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
$513$	14.4317	+	18.5525i	0.637177	+	0.819113i
$514$	11.6193	+	7.31125i	0.512505	+	0.322486i
$515$		0			0
$516$	−22.4020	−	2.64460i	−0.986192	−	0.116422i
$517$	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	$0.939700\pi$
$522$	−10.2289	−	13.0581i	−0.447708	−	0.571536i
$523$	−16.7947	+	16.7947i	−0.734383	+	0.734383i	−0.971485	−	0.237102i	$-0.923803\pi$
$523$	−16.7947	+	16.7947i	−0.734383	+	0.734383i	0.237102	+	0.971485i	$0.423803\pi$
$524$	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
$528$	−26.3883	−	12.9228i	−1.14840	−	0.562393i
$529$		−	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
$534$	5.71140	+	12.0029i	0.247156	+	0.519415i
$535$		0			0
$536$	−6.96114	−	0.797865i	−0.300676	−	0.0344625i
$537$	−8.56481	+	1.91859i	−0.369599	+	0.0827932i
$538$	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	$-0.808597\pi$
$541$		−	26.3168i		−	1.13145i	0.824595	−	0.565724i	$-0.191403\pi$
$542$	−14.2727	+	3.24804i	−0.613064	+	0.139515i
$543$	7.29040	−	1.63311i	0.312861	−	0.0700834i
$544$	0.409521	−	0.141829i	0.0175581	−	0.00608086i
$545$		0			0
$546$	−6.44280	+	3.06571i	−0.275726	+	0.131200i
$547$	4.59571	+	4.59571i	0.196498	+	0.196498i	0.798497	−	0.601999i	$-0.205629\pi$
$547$	4.59571	+	4.59571i	0.196498	+	0.196498i	−0.601999	+	0.798497i	$0.705629\pi$
$548$	−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
$552$	24.0170	−	2.56148i	1.02223	−	0.109024i
$553$	−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	−0.321999	−	0.946740i	$-0.604355\pi$
$557$	14.7444	−	14.7444i	0.624741	−	0.624741i	0.946740	+	0.321999i	$0.104355\pi$
$558$	−34.3827	+	26.9334i	−1.45554	+	1.14018i
$559$		−	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	0.984225	−	0.176924i	$-0.0566145\pi$
$563$	19.1553	+	19.1553i	0.807301	+	0.807301i	−0.176924	+	0.984225i	$0.556615\pi$
$564$	4.62712	−	39.1955i	0.194837	−	1.65043i
$565$		0			0
$566$	−7.54274	+	11.9872i	−0.317045	+	0.503859i
$567$	0.854084	+	8.86166i	0.0358682	+	0.372155i
$568$	18.4933	+	23.2814i	0.775962	+	0.976866i
$569$	23.8118			0.998241			0.499121	−	0.866532i	$-0.333656\pi$
$569$	23.8118			0.998241			0.499121	+	0.866532i	$0.333656\pi$
$570$		0			0
$571$		−	4.88168i		−	0.204292i	−0.994769	−	0.102146i	$-0.967429\pi$
$571$		−	4.88168i		−	0.204292i	0.994769	−	0.102146i	$-0.0325709\pi$
$572$	8.27952	−	23.5648i	0.346184	−	0.985292i
$573$	33.4815	−	7.50014i	1.39871	−	0.313323i
$574$	−10.3578	−	6.51748i	−0.432326	−	0.272034i
$575$		0			0
$576$	5.06176	+	23.4601i	0.210907	+	0.977506i
$577$	−3.99454	+	3.99454i	−0.166295	+	0.166295i	−0.785349	−	0.619054i	$-0.787516\pi$
$577$	−3.99454	+	3.99454i	−0.166295	+	0.166295i	0.619054	+	0.785349i	$0.287516\pi$
$578$	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
$582$	37.2049	+	13.2138i	1.54219	+	0.547732i
$583$	−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	−0.245651	−	0.969358i	$-0.579002\pi$
$587$	17.5340	−	17.5340i	0.723707	−	0.723707i	0.969358	+	0.245651i	$0.0790018\pi$
$588$	16.3771	−	12.9187i	0.675380	−	0.532757i
$589$	−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	0.320425	−	0.947274i	$-0.396174\pi$
$593$	30.8705	−	30.8705i	1.26770	−	1.26770i	0.947274	−	0.320425i	$-0.103826\pi$
$594$	−24.1166	−	19.7396i	−0.989514	−	0.809927i
$595$		0			0
$596$	18.6169	+	38.7853i	0.762580	+	1.58871i
$597$	13.0963	−	2.93367i	0.535994	−	0.120067i
$598$	4.55590	+	20.0197i	0.186305	+	0.818667i
$599$	−19.0515			−0.778423			−0.389211	−	0.921148i	$-0.627252\pi$
$599$	−19.0515			−0.778423			−0.389211	+	0.921148i	$0.627252\pi$
$600$		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
$603$	−6.99470	−	2.51100i	−0.284846	−	0.102256i
$604$	2.53505	−	1.21682i	0.103150	−	0.0495119i
$605$		0			0
$606$	−15.4790	−	32.5302i	−0.628793	−	1.32145i
$607$	−10.5809	+	10.5809i	−0.429465	+	0.429465i	−0.888446	−	0.458981i	$-0.848214\pi$
$607$	−10.5809	+	10.5809i	−0.429465	+	0.429465i	0.458981	+	0.888446i	$0.348214\pi$
$608$	−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
$612$	0.457245	−	0.0471996i	0.0184830	−	0.00190793i
$613$	−27.2783	+	27.2783i	−1.10176	+	1.10176i	−0.107564	+	0.994198i	$0.534305\pi$
$613$	−27.2783	+	27.2783i	−1.10176	+	1.10176i	−0.994198	+	0.107564i	$0.965695\pi$
$614$	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	0.995534	+	0.0944087i	$0.0300960\pi$
$617$	27.0736	+	27.0736i	1.08994	+	1.08994i	0.0944087	+	0.995534i	$0.469904\pi$
$618$	−9.37736	+	26.4029i	−0.377213	+	1.06208i
$619$	−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
$624$	−19.3005	+	6.61113i	−0.772637	+	0.264657i
$625$		0			0
$626$	−23.3921	−	14.7191i	−0.934935	−	0.588293i
$627$	−7.26334	−	32.4244i	−0.290070	−	1.29491i
$628$	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
$633$	39.7837	−	8.91187i	1.58126	−	0.354215i
$634$	9.15282	−	14.5460i	0.363505	−	0.577694i
$635$		0			0
$636$	−0.149406	+	1.26560i	−0.00592435	+	0.0501841i
$637$	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	$0.999047\pi$
$642$	8.35883	+	2.96876i	0.329897	+	0.117168i
$643$	6.08170	−	6.08170i	0.239839	−	0.239839i	−0.576945	−	0.816783i	$-0.695755\pi$
$643$	6.08170	−	6.08170i	0.239839	−	0.239839i	0.816783	+	0.576945i	$0.195755\pi$
$644$	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	0.854482	−	0.519480i	$-0.173874\pi$
$647$	8.52118	+	8.52118i	0.335002	+	0.335002i	−0.519480	+	0.854482i	$0.673874\pi$
$648$	−0.459097	+	25.4517i	−0.0180350	+	0.999837i
$649$		−	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	0.999825	+	0.0187129i	$0.00595686\pi$
$653$	26.0276	+	26.0276i	1.01854	+	1.01854i	0.0187129	+	0.999825i	$0.494043\pi$
$654$	9.81334	+	20.6234i	0.383732	+	0.806438i
$655$		0			0
$656$	−27.3017	−	21.8869i	−1.06595	−	0.854540i
$657$	18.1043	+	6.49919i	0.706316	+	0.253557i
$658$	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	$0.333966\pi$
$661$			44.5819i			1.73404i	−0.498277	+	0.867018i	$0.666034\pi$
$662$	4.59685	+	20.1997i	0.178662	+	0.785083i
$663$	0.0854143	+	0.381300i	0.00331722	+	0.0148085i
$664$	−22.3070	−	2.55676i	−0.865680	−	0.0992217i
$665$		0			0
$666$	−43.4314	−	5.27649i	−1.68293	−	0.204460i
$667$	−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
$672$	−8.24355	+	5.09703i	−0.318002	+	0.196622i
$673$	−15.8002	−	15.8002i	−0.609052	−	0.609052i	0.333647	−	0.942698i	$-0.391721\pi$
$673$	−15.8002	−	15.8002i	−0.609052	−	0.609052i	−0.942698	+	0.333647i	$0.891721\pi$
$674$	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	−0.821067	−	0.570832i	$-0.806621\pi$
$677$	−6.51094	+	6.51094i	−0.250236	+	0.250236i	0.570832	+	0.821067i	$0.306621\pi$
$678$	−18.5110	−	6.57444i	−0.710910	−	0.252490i
$679$			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	0.861298	−	0.508101i	$-0.169652\pi$
$683$	9.23055	+	9.23055i	0.353197	+	0.353197i	−0.508101	+	0.861298i	$0.669652\pi$
$684$	−17.1195	+	21.0606i	−0.654579	+	0.805274i
$685$		0			0
$686$	15.4178	+	9.70143i	0.588656	+	0.370402i
$687$	−7.09433	−	31.6699i	−0.270666	−	1.20828i
$688$	−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	$-0.950506\pi$
$691$		−	8.14177i		−	0.309727i	0.987936	−	0.154864i	$-0.0494938\pi$
$692$	−13.3610	−	4.69440i	−0.507908	−	0.178454i
$693$	4.25234	−	11.8454i	0.161533	−	0.449970i
$694$	15.8410	−	25.1751i	0.601316	−	0.955632i
$695$		0			0
$696$	12.0309	−	14.9036i	0.456031	−	0.564918i
$697$	−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	$-0.311427\pi$
$701$	29.5673			1.11674			0.558371	+	0.829591i	$0.311427\pi$
$702$	−21.5319	+	2.14893i	−0.812671	+	0.0811060i
$703$	−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
$708$	−7.87120	+	6.20900i	−0.295818	+	0.233348i
$709$	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
$714$	0.0797613	+	0.167624i	0.00298499	+	0.00627316i
$715$		0			0
$716$	−4.38567	−	9.13683i	−0.163900	−	0.341460i
$717$	3.97998	+	17.7671i	0.148635	+	0.663524i
$718$	0.104503	−	0.0237819i	0.00390003	−	0.000887532i
$719$	9.82970			0.366586			0.183293	−	0.983058i	$-0.441324\pi$
$719$	9.82970			0.366586			0.183293	+	0.983058i	$0.441324\pi$
$720$		0			0
$721$	−11.3149			−0.421390
$722$	−2.01582	+	0.458741i	−0.0750211	+	0.0170726i
$723$	−2.11309	−	9.43307i	−0.0785865	−	0.350820i
$724$	3.73310	+	7.77731i	0.138740	+	0.289041i
$725$		0			0
$726$	7.35294	+	15.4527i	0.272893	+	0.573503i
$727$	8.39630	−	8.39630i	0.311401	−	0.311401i	−0.534051	−	0.845452i	$-0.679331\pi$
$727$	8.39630	−	8.39630i	0.311401	−	0.311401i	0.845452	+	0.534051i	$0.179331\pi$
$728$	−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
$732$	−18.2289	+	14.3794i	−0.673758	+	0.531477i
$733$	13.4915	−	13.4915i	0.498321	−	0.498321i	−0.412594	−	0.910915i	$-0.635377\pi$
$733$	13.4915	−	13.4915i	0.498321	−	0.498321i	0.910915	+	0.412594i	$0.135377\pi$
$734$	−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
$738$	−22.8871	−	29.2173i	−0.842486	−	1.07550i
$739$	−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	−0.149763	−	0.988722i	$-0.547851\pi$
$743$	22.8684	−	22.8684i	0.838958	−	0.838958i	0.988722	+	0.149763i	$0.0478512\pi$
$744$	−39.2420	−	31.6781i	−1.43868	−	1.16138i
$745$		0			0
$746$	1.19130	−	1.89325i	0.0436166	−	0.0693169i
$747$	−22.4145	−	8.04650i	−0.820105	−	0.294406i
$748$	−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
$753$	−4.98670	−	22.2612i	−0.181725	−	0.811245i
$754$	13.7805	+	8.67115i	0.501856	+	0.315785i
$755$		0			0
$756$	−9.74761	+	3.26526i	−0.354517	+	0.118756i
$757$	0.293203	+	0.293203i	0.0106566	+	0.0106566i	0.712415	−	0.701758i	$-0.247601\pi$
$757$	0.293203	+	0.293203i	0.0106566	+	0.0106566i	−0.701758	+	0.712415i	$0.747601\pi$
$758$	−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	$-0.275182\pi$
$762$	−33.0294	−	11.7309i	−1.19653	−	0.424964i
$763$	−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
$768$	−25.0773	+	11.7952i	−0.904900	+	0.425624i
$769$		−	11.0782i		−	0.399490i	−0.979848	−	0.199745i	$-0.935989\pi$
$769$		−	11.0782i		−	0.399490i	0.979848	−	0.199745i	$-0.0640113\pi$
$770$		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	0.210169	−	0.977665i	$-0.432598\pi$
$773$	−21.3386	−	21.3386i	−0.767496	−	0.767496i	−0.977665	+	0.210169i	$0.932598\pi$
$774$	3.33194	−	27.4256i	0.119764	−	0.985791i
$775$		0			0
$776$	−5.19136	+	45.2931i	−0.186359	+	1.62593i
$777$	−3.86209	−	17.2408i	−0.138552	−	0.618511i
$778$	−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
$783$	16.0352	−	12.4735i	0.573050	−	0.445768i
$784$	18.7927	+	15.0655i	0.671168	+	0.538054i
$785$		0			0
$786$	10.4944	+	22.0546i	0.374322	+	0.786663i
$787$	22.3990	+	22.3990i	0.798438	+	0.798438i	0.982849	−	0.184411i	$-0.0590378\pi$
$787$	22.3990	+	22.3990i	0.798438	+	0.798438i	−0.184411	+	0.982849i	$0.559038\pi$
$788$	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
$792$	15.9366	−	32.2651i	0.566282	−	1.14649i
$793$	−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	−0.964647	−	0.263545i	$-0.915108\pi$
$797$	−19.7929	+	19.7929i	−0.701102	+	0.701102i	0.263545	+	0.964647i	$0.415108\pi$
$798$	−10.3284	−	3.66827i	−0.365620	−	0.129855i
$799$		−	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
$804$	1.00607	−	8.52226i	0.0354815	−	0.300557i
$805$		0			0
$806$	22.8317	−	36.2849i	0.804212	−	1.27808i
$807$	−19.9662	+	4.47259i	−0.702843	+	0.157443i
$808$	32.5726	−	25.8737i	1.14590	−	0.910233i
$809$	−19.9408			−0.701082			−0.350541	−	0.936547i	$-0.614002\pi$
$809$	−19.9408			−0.701082			−0.350541	+	0.936547i	$0.614002\pi$
$810$		0			0
$811$			24.0234i			0.843577i	0.906694	+	0.421789i	$0.138598\pi$
$811$			24.0234i			0.843577i	−0.906694	+	0.421789i	$0.861402\pi$
$812$	7.29756	+	2.56401i	0.256094	+	0.0899791i
$813$	−3.91875	−	17.4938i	−0.137437	−	0.613534i
$814$	52.3483	+	32.9393i	1.83481	+	1.15452i
$815$		0			0
$816$	0.172003	+	0.502145i	0.00602131	+	0.0175786i
$817$	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	$-0.581321\pi$
$821$	−14.4816			−0.505413			−0.252706	+	0.967543i	$0.581321\pi$
$822$	1.63482	−	4.60300i	0.0570210	−	0.160548i
$823$	21.7093	+	21.7093i	0.756740	+	0.756740i	0.975728	−	0.218987i	$-0.0702754\pi$
$823$	21.7093	+	21.7093i	0.756740	+	0.756740i	−0.218987	+	0.975728i	$0.570275\pi$
$824$	−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	−0.00623359	+	0.999981i	$0.501984\pi$
$827$	−28.9363	+	28.9363i	−1.00621	+	1.00621i	−0.999981	+	0.00623359i	$0.998016\pi$
$828$	3.03744	+	29.4251i	0.105558	+	1.02259i
$829$	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
$834$	−5.31228	−	11.1641i	−0.183949	−	0.386582i
$835$		0			0
$836$	34.5900	−	16.6032i	1.19632	−	0.574233i
$837$	−32.8436	−	42.2216i	−1.13524	−	1.45939i
$838$	−0.00679807	−	0.0298724i	−0.000234835	−	0.00103192i
$839$	26.4522			0.913233			0.456616	−	0.889664i	$-0.349061\pi$
$839$	26.4522			0.913233			0.456616	+	0.889664i	$0.349061\pi$
$840$		0			0
$841$	13.7142			0.472904
$842$	−4.53536	−	19.9295i	−0.156299	−	0.686815i
$843$	56.1574	−	12.5797i	1.93416	−	0.433269i
$844$	20.3715	+	42.4407i	0.701217	+	1.46087i
$845$		0			0
$846$	47.9850	+	5.82972i	1.64976	+	0.200430i
$847$	−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
$852$	−28.5904	+	22.5528i	−0.979490	+	0.772647i
$853$	−11.2078	+	11.2078i	−0.383746	+	0.383746i	−0.872450	−	0.488703i	$-0.837470\pi$
$853$	−11.2078	+	11.2078i	−0.383746	+	0.383746i	0.488703	+	0.872450i	$0.337470\pi$
$854$	−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	0.277057	−	0.960854i	$-0.410641\pi$
$857$	−20.0179	−	20.0179i	−0.683797	−	0.683797i	−0.960854	+	0.277057i	$0.910641\pi$
$858$	28.8263	+	10.2381i	0.984113	+	0.349522i
$859$	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	−0.980984	−	0.194088i	$-0.937825\pi$
$863$	−23.1165	+	23.1165i	−0.786896	+	0.786896i	0.194088	+	0.980984i	$0.437825\pi$
$864$	−28.7535	+	6.10195i	−0.978215	+	0.207592i
$865$		0			0
$866$	−1.41056	−	0.887572i	−0.0479327	−	0.0301609i
$867$	−28.7229	+	6.43416i	−0.975480	+	0.218516i
$868$	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
$873$	−16.3379	+	45.5114i	−0.552956	+	1.54033i
$874$	−16.7972	+	26.6946i	−0.568172	+	0.902958i
$875$		0			0
$876$	−2.60401	+	22.0581i	−0.0879813	+	0.745274i
$877$	22.8758	+	22.8758i	0.772459	+	0.772459i	0.978536	−	0.206076i	$-0.0660696\pi$
$877$	22.8758	+	22.8758i	0.772459	+	0.772459i	−0.206076	+	0.978536i	$0.566070\pi$
$878$	−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	$-0.0608006\pi$
$882$	15.7540	+	20.1113i	0.530465	+	0.677182i
$883$	2.32921	−	2.32921i	0.0783843	−	0.0783843i	−0.666828	−	0.745212i	$-0.732348\pi$
$883$	2.32921	−	2.32921i	0.0783843	−	0.0783843i	0.745212	+	0.666828i	$0.232348\pi$
$884$	−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	0.997811	−	0.0661260i	$-0.0210639\pi$
$887$	27.7480	+	27.7480i	0.931685	+	0.931685i	−0.0661260	+	0.997811i	$0.521064\pi$
$888$	−5.35761	−	50.2341i	−0.179790	−	1.68575i
$889$		−	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
$894$	−47.5792	+	22.6399i	−1.59129	+	0.757190i
$895$		0			0
$896$	−7.87801	−	7.94889i	−0.263186	−	0.265554i
$897$	−24.5378	+	5.49667i	−0.819294	+	0.183529i
$898$	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
$903$	10.8870	−	2.43879i	0.362298	−	0.0811578i
$904$	2.58291	−	22.5352i	0.0859065	−	0.749509i
$905$		0			0
$906$	1.47977	+	3.10983i	0.0491620	+	0.103317i
$907$	−19.8583	−	19.8583i	−0.659383	−	0.659383i	0.295851	−	0.955234i	$-0.404397\pi$
$907$	−19.8583	−	19.8583i	−0.659383	−	0.659383i	−0.955234	+	0.295851i	$0.904397\pi$
$908$	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	$0.730036\pi$
$912$	−28.1458	−	13.7835i	−0.932000	−	0.456416i
$913$	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
$918$	0.0559091	+	0.560201i	0.00184527	+	0.0184894i
$919$		−	0.337489i		−	0.0111327i	−0.999985	−	0.00556636i	$-0.998228\pi$
$919$		−	0.337489i		−	0.0111327i	0.999985	−	0.00556636i	$-0.00177184\pi$
$920$		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
$924$	14.4323	+	1.70377i	0.474789	+	0.0560499i
$925$		0			0
$926$	16.5857	+	10.4363i	0.545039	+	0.342957i
$927$	−32.2977	−	11.5944i	−1.06079	−	0.380810i
$928$	19.8956	+	9.65973i	0.653105	+	0.317096i
$929$	39.1863			1.28566			0.642830	−	0.766009i	$-0.277760\pi$
$929$	39.1863			1.28566			0.642830	+	0.766009i	$0.277760\pi$
$930$		0			0
$931$			27.2381i			0.892693i
$932$	−10.2769	+	29.2495i	−0.336630	+	0.958098i
$933$	−22.1263	+	4.95648i	−0.724384	+	0.162268i
$934$	17.1992	−	27.3336i	0.562776	−	0.894382i
$935$		0			0
$936$	−8.01678	−	23.6655i	−0.262037	−	0.773530i
$937$	−1.50743	+	1.50743i	−0.0492455	+	0.0492455i	−0.731301	−	0.682055i	$-0.761086\pi$
$937$	−1.50743	+	1.50743i	−0.0492455	+	0.0492455i	0.682055	+	0.731301i	$0.261086\pi$
$938$	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	$-0.454188\pi$
$941$	8.79941			0.286852			0.143426	+	0.989661i	$0.454188\pi$
$942$	−5.01931	+	14.1324i	−0.163538	+	0.460457i
$943$	−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	−0.667996	−	0.744165i	$-0.732848\pi$
$947$	2.34399	−	2.34399i	0.0761694	−	0.0761694i	0.744165	+	0.667996i	$0.232848\pi$
$948$	3.97588	−	3.13628i	0.129131	−	0.101862i
$949$	−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	−0.183981	−	0.982930i	$-0.558898\pi$
$953$	24.6641	−	24.6641i	0.798949	−	0.798949i	0.982930	+	0.183981i	$0.0588984\pi$
$954$	−1.54940	−	0.188237i	−0.0501637	−	0.00609441i
$955$		0			0
$956$	−18.9537	+	9.09777i	−0.613007	+	0.294243i
$957$	−28.0249	+	6.27780i	−0.905915	+	0.202933i
$958$	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
$963$	−3.67065	+	10.2251i	−0.118285	+	0.329498i
$964$	10.0631	−	4.83027i	0.324110	−	0.155573i
$965$		0			0
$966$	−10.7871	+	5.13289i	−0.347070	+	0.165148i
$967$	−27.3981	+	27.3981i	−0.881063	+	0.881063i	−0.993643	−	0.112580i	$-0.964089\pi$
$967$	−27.3981	+	27.3981i	−0.881063	+	0.881063i	0.112580	+	0.993643i	$0.464089\pi$
$968$	−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	$-0.493956\pi$
$971$	1.18320			0.0379706			0.0189853	+	0.999820i	$0.493956\pi$
$972$	−31.1698	−	0.667928i	−0.999770	−	0.0214238i
$973$	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	0.653123	−	0.757251i	$-0.273458\pi$
$977$	−3.25473	−	3.25473i	−0.104128	−	0.104128i	−0.757251	+	0.653123i	$0.773458\pi$
$978$	28.2935	+	10.0489i	0.904727	+	0.321327i
$979$	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	−0.852445	−	0.522817i	$-0.824881\pi$
$983$	−10.3348	+	10.3348i	−0.329628	+	0.329628i	0.522817	+	0.852445i	$0.324881\pi$
$984$	26.9190	−	33.3465i	0.858148	−	1.06305i
$985$		0			0
$986$	0.225599	−	0.358530i	0.00718454	−	0.0114179i
$987$	4.26702	+	19.0485i	0.135821	+	0.606320i
$988$	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
$993$	−24.7584	+	5.54608i	−0.785684	+	0.176000i
$994$	−12.4466	−	7.83182i	−0.394782	−	0.248410i
$995$		0			0
$996$	3.22397	−	27.3096i	0.102155	−	0.865339i
$997$	−25.0027	−	25.0027i	−0.791844	−	0.791844i	0.189949	−	0.981794i	$-0.439168\pi$
$997$	−25.0027	−	25.0027i	−0.791844	−	0.791844i	−0.981794	+	0.189949i	$0.939168\pi$
$998$	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.293.2	yes	64
3.2	odd	2	inner	600.2.w.k.293.32	yes	64
5.2	odd	4	inner	600.2.w.k.557.15	yes	64
5.3	odd	4	inner	600.2.w.k.557.18	yes	64
5.4	even	2	inner	600.2.w.k.293.31	yes	64
8.5	even	2	inner	600.2.w.k.293.17	yes	64
15.2	even	4	inner	600.2.w.k.557.17	yes	64
15.8	even	4	inner	600.2.w.k.557.16	yes	64
15.14	odd	2	inner	600.2.w.k.293.1	✓	64
24.5	odd	2	inner	600.2.w.k.293.15	yes	64
40.13	odd	4	inner	600.2.w.k.557.1	yes	64
40.29	even	2	inner	600.2.w.k.293.16	yes	64
40.37	odd	4	inner	600.2.w.k.557.32	yes	64
120.29	odd	2	inner	600.2.w.k.293.18	yes	64
120.53	even	4	inner	600.2.w.k.557.31	yes	64
120.77	even	4	inner	600.2.w.k.557.2	yes	64

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.37896 + 0.313810i) q^{2} +(-0.378611 - 1.69016i) q^{3} +(1.80305 - 0.865461i) q^{4} +(1.05248 + 2.21185i) q^{6} +(-0.699464 + 0.699464i) q^{7} +(-2.21473 + 1.75925i) q^{8} +(-2.71331 + 1.27983i) q^{9} +O(q^{10})\)	\(q+(-1.37896 + 0.313810i) q^{2} +(-0.378611 - 1.69016i) q^{3} +(1.80305 - 0.865461i) q^{4} +(1.05248 + 2.21185i) q^{6} +(-0.699464 + 0.699464i) q^{7} +(-2.21473 + 1.75925i) q^{8} +(-2.71331 + 1.27983i) q^{9} +4.24103 q^{11} +(-2.14542 - 2.71977i) 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} +(3.33991 - 2.61629i) q^{18} +4.52348 q^{19} +(1.44703 + 0.917384i) q^{21} +(-5.84820 + 1.33088i) q^{22} +(3.48621 - 3.48621i) q^{23} +(3.81194 + 3.07719i) q^{24} +(-2.21785 + 3.52469i) q^{26} +(3.19041 + 4.10138i) q^{27} +(-0.655807 + 1.86652i) q^{28} -3.90970i q^{29} -10.2945 q^{31} +(-2.47071 + 5.08877i) q^{32} +(-1.60570 - 7.16803i) q^{33} +(0.0917026 + 0.0577024i) q^{34} +(-3.78458 + 4.65585i) q^{36} +(-7.29179 - 7.29179i) q^{37} +(-6.23768 + 1.41951i) q^{38} +(-4.30761 - 2.73092i) q^{39} -8.74792i q^{41} +(-2.28328 - 0.810940i) 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} +(-6.22216 - 3.04709i) q^{48} +6.02150i q^{49} +(-0.0710510 + 0.112072i) q^{51} +(1.95224 - 5.55638i) q^{52} +(-0.260132 - 0.260132i) q^{53} +(-5.68649 - 4.65444i) q^{54} +(0.318596 - 2.77966i) q^{56} +(-1.71264 - 7.64542i) q^{57} +(1.22690 + 5.39131i) q^{58} -2.89407i q^{59} -6.70235i q^{61} +(14.1957 - 3.23051i) q^{62} +(1.00267 - 2.79305i) q^{63} +(1.81009 - 7.79253i) q^{64} +(4.46359 + 9.38053i) q^{66} +(1.75168 + 1.75168i) q^{67} +(-0.144561 - 0.0507920i) q^{68} +(-7.21219 - 4.57235i) q^{69} -10.5121i q^{71} +(3.75772 - 7.60786i) 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} +(6.79700 + 2.41405i) q^{78} +1.46184i q^{79} +(5.72408 - 6.94514i) q^{81} +(2.74519 + 12.0630i) q^{82} +(5.61327 + 5.61327i) q^{83} +(3.40303 + 0.401735i) q^{84} +(-4.90451 + 7.79441i) q^{86} +(-6.60804 + 1.48026i) q^{87} +(-9.39275 + 7.46102i) q^{88} +5.42662 q^{89} +2.91285i q^{91} +(3.26862 - 9.30298i) q^{92} +(3.89760 + 17.3994i) q^{93} +(-13.6375 - 8.58116i) q^{94} +(9.53630 + 2.24924i) 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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