LMFDB - Embedded newform 600.2.w.k.293.17

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			293.17
Character	$\chi$	$=$	600.293
Dual form			600.2.w.k.557.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

$2$	0.313810	−	1.37896i	0.221897	−	0.975070i
$2$	0.313810	−	1.37896i	0.221897	−	0.975070i
$3$	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
$6$	2.44948	+	0.00830235i	0.999994	+	0.00338942i
$7$	−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	$0.309857\pi$
$8$	−1.75925	+	2.21473i	−0.621988	+	0.783027i
$9$	−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	$0.720800\pi$
$12$	0.780119	−	3.37512i	0.225201	−	0.974312i
$13$	−2.08220	+	2.08220i	−0.577500	+	0.577500i	−0.934214	−	0.356714i	$-0.883897\pi$
$13$	−2.08220	+	2.08220i	−0.577500	+	0.577500i	0.356714	+	0.934214i	$0.383897\pi$
$14$	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	$0.752957\pi$
$18$	0.913365	+	4.14316i	0.215282	+	0.976552i
$19$	−4.52348			−1.03776			−0.518878	−	0.854848i	$-0.673650\pi$
$19$	−4.52348			−1.03776			−0.518878	+	0.854848i	$0.673650\pi$
$20$		0			0
$21$	−1.44703	−	0.917384i	−0.315768	−	0.200190i
$22$	−1.33088	+	5.84820i	−0.283744	+	1.24684i
$23$	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	$0.0781580\pi$
$24$	−4.40933	−	2.13490i	−0.900051	−	0.435784i
$25$		0			0
$26$	2.21785	+	3.52469i	0.434957	+	0.691248i
$27$	−3.19041	−	4.10138i	−0.613994	−	0.789311i
$28$	1.86652	−	0.655807i	0.352740	−	0.123936i
$29$			3.90970i			0.726014i	0.931786	+	0.363007i	$0.118250\pi$
$29$			3.90970i			0.726014i	−0.931786	+	0.363007i	$0.881750\pi$
$30$		0			0
$31$	−10.2945			−1.84894			−0.924472	−	0.381250i	$-0.875494\pi$
$31$	−10.2945			−1.84894			−0.924472	+	0.381250i	$0.875494\pi$
$32$	5.08877	−	2.47071i	0.899576	−	0.436764i
$33$	−1.60570	−	7.16803i	−0.279516	−	1.24779i
$34$	−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	0.974537	+	0.224225i	$0.0719849\pi$
$37$	7.29179	+	7.29179i	1.19876	+	1.19876i	0.224225	+	0.974537i	$0.428015\pi$
$38$	−1.41951	+	6.23768i	−0.230275	+	1.01189i
$39$	−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	$-0.239368\pi$
$42$	−1.71913	+	1.70751i	−0.265267	+	0.263475i
$43$	−4.60454	+	4.60454i	−0.702185	+	0.702185i	−0.964879	−	0.262694i	$-0.915389\pi$
$43$	−4.60454	+	4.60454i	−0.702185	+	0.702185i	0.262694	+	0.964879i	$0.415389\pi$
$44$	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	$0.437800\pi$
$48$	−4.32762	+	5.41033i	−0.624639	+	0.780914i
$49$			6.02150i			0.860214i
$50$		0			0
$51$	0.0710510	−	0.112072i	0.00994913	−	0.0156932i
$52$	5.55638	−	1.95224i	0.770531	−	0.270728i
$53$	0.260132	+	0.260132i	0.0357319	+	0.0357319i	0.724747	−	0.689015i	$-0.241957\pi$
$53$	0.260132	+	0.260132i	0.0357319	+	0.0357319i	−0.689015	+	0.724747i	$0.741957\pi$
$54$	−6.65681	+	3.11238i	−0.905877	+	0.423541i
$55$		0			0
$56$	−0.318596	−	2.77966i	−0.0425742	−	0.371447i
$57$	−1.71264	−	7.64542i	−0.226844	−	1.01266i
$58$	5.39131	+	1.22690i	0.707914	+	0.161100i
$59$			2.89407i			0.376775i	0.982095	+	0.188388i	$0.0603261\pi$
$59$			2.89407i			0.376775i	−0.982095	+	0.188388i	$0.939674\pi$
$60$		0			0
$61$			6.70235i			0.858148i	0.903269	+	0.429074i	$0.141160\pi$
$61$			6.70235i			0.858148i	−0.903269	+	0.429074i	$0.858840\pi$
$62$	−3.23051	+	14.1957i	−0.410276	+	1.80285i
$63$	1.00267	−	2.79305i	0.126324	−	0.351892i
$64$	−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	0.591963	−	0.805965i	$-0.298353\pi$
$67$	−1.75168	−	1.75168i	−0.214002	−	0.214002i	−0.805965	+	0.591963i	$0.798353\pi$
$68$	0.0507920	+	0.144561i	0.00615943	+	0.0175307i
$69$	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	$-0.214402\pi$
$72$	1.93890	−	8.26079i	0.228502	−	0.973543i
$73$	−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
$78$	−5.11760	+	5.08302i	−0.579454	+	0.575539i
$79$			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
$82$	−12.0630	−	2.74519i	−1.33214	−	0.303155i
$83$	−5.61327	−	5.61327i	−0.616136	−	0.616136i	0.328402	−	0.944538i	$-0.393490\pi$
$83$	−5.61327	−	5.61327i	−0.616136	−	0.616136i	−0.944538	+	0.328402i	$0.893490\pi$
$84$	1.81511	+	2.90644i	0.198044	+	0.317118i
$85$		0			0
$86$	4.90451	+	7.79441i	0.528867	+	0.840493i
$87$	−6.60804	+	1.48026i	−0.708456	+	0.158700i
$88$	7.46102	−	9.39275i	0.795347	−	1.00127i
$89$	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
$92$	−9.30298	+	3.26862i	−0.969903	+	0.340777i
$93$	−3.89760	−	17.3994i	−0.404163	−	1.80423i
$94$	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	0.172162	−	0.985069i	$-0.444925\pi$
$97$	11.3974	−	11.3974i	1.15723	−	1.15723i	0.985069	−	0.172162i	$-0.0550753\pi$
$98$	8.30339	+	1.88961i	0.838769	+	0.190879i
$99$	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	$0.238721\pi$
$102$	−0.132246	−	0.133146i	−0.0130943	−	0.0131834i
$103$	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	−0.819964	−	0.572416i	$-0.806006\pi$
$107$	−2.56066	+	2.56066i	−0.247548	+	0.247548i	0.572416	+	0.819964i	$0.306006\pi$
$108$	2.20287	+	10.1561i	0.211971	+	0.977276i
$109$	−9.32403			−0.893080			−0.446540	−	0.894764i	$-0.647344\pi$
$109$	−9.32403			−0.893080			−0.446540	+	0.894764i	$0.647344\pi$
$110$		0			0
$111$	−9.56356	+	15.0851i	−0.907733	+	1.43181i
$112$	−3.93301	−	0.432954i	−0.371634	−	0.0409103i
$113$	−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	$0.373116\pi$
$114$	−11.0801	−	0.0375555i	−1.03775	−	0.00351740i
$115$		0			0
$116$	3.38370	−	7.04938i	0.314168	−	0.654518i
$117$	2.98480	−	8.31453i	0.275945	−	0.768678i
$118$	3.99079	+	0.908187i	0.367382	+	0.0836054i
$119$	0.0757843			0.00694714
$120$		0			0
$121$	6.98631			0.635120
$122$	9.24226	+	2.10326i	0.836755	+	0.190421i
$123$	14.7854	−	3.31206i	1.33316	−	0.298638i
$124$	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	$-0.968949\pi$
$127$	−10.1183	+	10.1183i	−0.897851	+	0.897851i	0.0973946	+	0.995246i	$0.468949\pi$
$128$	−11.3136	+	0.0506660i	−0.999990	+	0.00447828i
$129$	−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	$0.643460\pi$
$132$	−3.30850	+	14.3140i	−0.287968	+	1.24587i
$133$	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	$0.777149\pi$
$138$	8.56833	−	8.51045i	0.729385	−	0.724457i
$139$	5.04740			0.428115			0.214058	−	0.976821i	$-0.431332\pi$
$139$	5.04740			0.428115			0.214058	+	0.976821i	$0.431332\pi$
$140$		0			0
$141$	−10.5663	+	16.6667i	−0.889841	+	1.40359i
$142$	−14.4957	−	3.29879i	−1.21645	−	0.276828i
$143$	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
$147$	−10.1773	+	2.27980i	−0.839411	+	0.188035i
$148$	−6.83667	−	19.4582i	−0.561971	−	1.59945i
$149$		−	21.5110i		−	1.76225i	−0.472883	−	0.881125i	$-0.656787\pi$
$149$		−	21.5110i		−	1.76225i	0.472883	−	0.881125i	$-0.343213\pi$
$150$		0			0
$151$	1.40598			0.114417			0.0572087	−	0.998362i	$-0.481780\pi$
$151$	1.40598			0.114417			0.0572087	+	0.998362i	$0.481780\pi$
$152$	7.95792	−	10.0183i	0.645472	−	0.812591i
$153$	0.216321	+	0.0776561i	0.0174885	+	0.00627813i
$154$	−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	0.512919	−	0.858437i	$-0.328564\pi$
$157$	−4.32933	−	4.32933i	−0.345518	−	0.345518i	−0.858437	+	0.512919i	$0.828564\pi$
$158$	2.01582	+	0.458741i	0.160370	+	0.0364955i
$159$	−0.341178	+	0.538155i	−0.0270571	+	0.0426785i
$160$		0			0
$161$			4.87696i			0.384358i
$162$	−7.78077	−	10.0727i	−0.611315	−	0.791387i
$163$	−8.66748	+	8.66748i	−0.678890	+	0.678890i	−0.959749	−	0.280859i	$-0.909381\pi$
$163$	−8.66748	+	8.66748i	−0.678890	+	0.678890i	0.280859	+	0.959749i	$0.409381\pi$
$164$	−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	$0.782422\pi$
$168$	4.57745	−	1.59089i	0.353158	−	0.122740i
$169$			4.32885i			0.332988i
$170$		0			0
$171$	12.2736	−	5.78927i	0.938585	−	0.442717i
$172$	12.2872	−	4.31715i	0.936893	−	0.329179i
$173$	5.00691	+	5.00691i	0.380668	+	0.380668i	0.871343	−	0.490675i	$-0.163250\pi$
$173$	5.00691	+	5.00691i	0.380668	+	0.380668i	−0.490675	+	0.871343i	$0.663250\pi$
$174$	−0.0324597	+	9.57672i	−0.00246077	+	0.726009i
$175$		0			0
$176$	−10.6109	−	13.2360i	−0.799823	−	0.997698i
$177$	−4.89145	+	1.09572i	−0.367664	+	0.0823597i
$178$	1.70293	−	7.48307i	0.127640	−	0.560880i
$179$			5.06744i			0.378758i	0.981904	+	0.189379i	$0.0606475\pi$
$179$			5.06744i			0.378758i	−0.981904	+	0.189379i	$0.939352\pi$
$180$		0			0
$181$		−	4.31343i		−	0.320614i	−0.987067	−	0.160307i	$-0.948752\pi$
$181$		−	4.31343i		−	0.320614i	0.987067	−	0.160307i	$-0.0512485\pi$
$182$	−4.01670	−	0.914082i	−0.297738	−	0.0677563i
$183$	−11.3281	+	2.53758i	−0.837395	+	0.187583i
$184$	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
$188$	−7.55348	−	21.4983i	−0.550894	−	1.56793i
$189$	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	$0.745657\pi$
$192$	12.4853	−	6.00969i	0.901052	−	0.433712i
$193$	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	−0.905903	−	0.423485i	$-0.860807\pi$
$197$	−6.77107	+	6.77107i	−0.482419	+	0.482419i	0.423485	+	0.905903i	$0.360807\pi$
$198$	−3.87361	−	17.5713i	−0.275285	−	1.24873i
$199$			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
$202$	4.61528	−	20.2807i	0.324730	−	1.42694i
$203$	−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
$207$	−4.99741	+	13.9209i	−0.347344	+	0.967571i
$208$	−11.7080	−	1.28884i	−0.811804	−	0.0893651i
$209$	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	$-0.300654\pi$
$212$	−0.243896	−	0.694165i	−0.0167509	−	0.0476755i
$213$	17.7671	−	3.97998i	1.21738	−	0.272703i
$214$	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
$218$	−2.92597	+	12.8574i	−0.198172	+	0.870816i
$219$	5.94639	−	9.37952i	0.401820	−	0.633809i
$220$		0			0
$221$	0.225599			0.0151754
$222$	17.8005	+	17.9216i	1.19469	+	1.20282i
$223$	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	−0.803179	−	0.595738i	$-0.796860\pi$
$227$	−3.12540	+	3.12540i	−0.207440	+	0.207440i	0.595738	+	0.803179i	$0.296860\pi$
$228$	−3.52885	+	15.2673i	−0.233704	+	1.01110i
$229$	−18.7378			−1.23823			−0.619114	−	0.785301i	$-0.712508\pi$
$229$	−18.7378			−1.23823			−0.619114	+	0.785301i	$0.712508\pi$
$230$		0			0
$231$	6.13691	+	3.89065i	0.403779	+	0.255986i
$232$	−8.65895	−	6.87814i	−0.568488	−	0.451572i
$233$	−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	$0.419525\pi$
$234$	−10.5287	−	6.72509i	−0.688284	−	0.439633i
$235$		0			0
$236$	2.50470	−	5.21813i	0.163042	−	0.339672i
$237$	−2.47076	+	0.553470i	−0.160493	+	0.0359517i
$238$	0.0237819	−	0.104503i	0.00154155	−	0.00677395i
$239$	−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	$0.442469\pi$
$242$	2.19238	−	9.63383i	0.140931	−	0.619286i
$243$	13.9056	+	7.04513i	0.892046	+	0.451945i
$244$	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
$248$	18.1106	−	22.7995i	1.15002	−	1.44777i
$249$	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	$0.636455\pi$
$252$	−4.22514	+	4.16824i	−0.266158	+	0.262574i
$253$	−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	$0.847909\pi$
$258$	−11.3169	+	11.2405i	−0.704561	+	0.699801i
$259$	−10.2007			−0.633839
$260$		0			0
$261$	−5.00375	−	10.6082i	−0.309724	−	0.656633i
$262$	−3.12904	+	13.7497i	−0.193313	+	0.849462i
$263$	−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	$0.479160\pi$
$264$	18.7001	+	9.05415i	1.15091	+	0.557244i
$265$		0			0
$266$	−3.37013	−	5.35593i	−0.206636	−	0.328393i
$267$	2.05457	+	9.17187i	0.125738	+	0.561309i
$268$	1.64235	+	4.67437i	0.100322	+	0.285533i
$269$			11.8132i			0.720262i	0.932902	+	0.360131i	$0.117268\pi$
$269$			11.8132i			0.720262i	−0.932902	+	0.360131i	$0.882732\pi$
$270$		0			0
$271$	10.3503			0.628739			0.314369	−	0.949301i	$-0.398207\pi$
$271$	10.3503			0.628739			0.314369	+	0.949301i	$0.398207\pi$
$272$	0.0335321	−	0.304610i	0.00203318	−	0.0184697i
$273$	4.92320	−	1.10284i	0.297966	−	0.0667468i
$274$	−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	0.869411	−	0.494089i	$-0.164498\pi$
$277$	6.24661	+	6.24661i	0.375323	+	0.375323i	−0.494089	+	0.869411i	$0.664498\pi$
$278$	1.58393	−	6.96015i	0.0949976	−	0.417442i
$279$	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	$0.542620\pi$
$282$	19.6668	+	19.8006i	1.17114	+	1.17911i
$283$	−7.08141	+	7.08141i	−0.420946	+	0.420946i	−0.885529	−	0.464583i	$-0.846204\pi$
$283$	−7.08141	+	7.08141i	−0.420946	+	0.420946i	0.464583	+	0.885529i	$0.346204\pi$
$284$	−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
$288$	−10.6453	+	13.2165i	−0.627282	+	0.778792i
$289$		−	16.9941i		−	0.999655i
$290$		0			0
$291$	23.5787	+	14.9483i	1.38221	+	0.876285i
$292$	4.25087	+	12.0986i	0.248764	+	0.708018i
$293$	20.0947	+	20.0947i	1.17394	+	1.17394i	0.981261	+	0.192683i	$0.0617190\pi$
$293$	20.0947	+	20.0947i	1.17394	+	1.17394i	0.192683	+	0.981261i	$0.438281\pi$
$294$	−0.0499926	+	14.7495i	−0.00291563	+	0.860209i
$295$		0			0
$296$	−28.9774	+	3.32131i	−1.68428	+	0.193047i
$297$	13.5306	+	17.3941i	0.785125	+	1.00931i
$298$	−29.6628	−	6.75037i	−1.71832	−	0.391038i
$299$			14.5180i			0.839598i
$300$		0			0
$301$		−	6.44141i		−	0.371277i
$302$	0.441212	−	1.93879i	0.0253889	−	0.111565i
$303$	5.56832	+	24.8576i	0.319891	+	1.42803i
$304$	−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	0.975189	−	0.221375i	$-0.0710546\pi$
$307$	13.2079	+	13.2079i	0.753813	+	0.753813i	−0.221375	+	0.975189i	$0.571055\pi$
$308$	−7.91598	+	2.78130i	−0.451055	+	0.158479i
$309$	−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	$-0.121043\pi$
$312$	13.6264	−	4.73585i	0.771444	−	0.268114i
$313$	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	−0.423339	−	0.905971i	$-0.639142\pi$
$317$	8.59301	−	8.59301i	0.482632	−	0.482632i	0.905971	+	0.423339i	$0.139142\pi$
$318$	0.635028	+	0.639348i	0.0356106	+	0.0358528i
$319$		−	16.5812i		−	0.928367i
$320$		0			0
$321$	−5.29742	−	3.35844i	−0.295673	−	0.187450i
$322$	6.72512	+	1.53044i	0.374776	+	0.0852880i
$323$	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
$327$	−3.53018	−	15.7591i	−0.195219	−	0.871483i
$328$	19.3743	+	15.3898i	1.06977	+	0.849758i
$329$	−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	$0.868114\pi$
$332$	5.26292	+	14.9790i	0.288840	+	0.822082i
$333$	−29.1171	−	10.4526i	−1.59561	−	0.572800i
$334$	−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	−0.00361703	+	0.999993i	$0.501151\pi$
$337$	−18.4238	+	18.4238i	−1.00361	+	1.00361i	−0.999993	+	0.00361703i	$0.998849\pi$
$338$	5.96929	+	1.35844i	0.324687	+	0.0738891i
$339$	−11.7314	−	7.43740i	−0.637160	−	0.403944i
$340$		0			0
$341$	43.6592			2.36428
$342$	−4.13159	−	18.7415i	−0.223411	−	1.01342i
$343$	−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	$-0.559054\pi$
$347$	14.8721	−	14.8721i	0.798378	−	0.798378i	0.982840	+	0.184462i	$0.0590542\pi$
$348$	13.1957	+	3.05003i	0.707364	+	0.163499i
$349$	18.9090			1.01218			0.506088	−	0.862482i	$-0.331091\pi$
$349$	18.9090			1.01218			0.506088	+	0.862482i	$0.331091\pi$
$350$		0			0
$351$	15.1830	+	1.89683i	0.810408	+	0.101245i
$352$	−21.5816	+	10.4783i	−1.15030	+	0.558497i
$353$	−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	$0.382508\pi$
$354$	−0.0240276	+	7.08894i	−0.00127705	+	0.376773i
$355$		0			0
$356$	−9.78444	−	4.69653i	−0.518574	−	0.248915i
$357$	0.0286928	+	0.128088i	0.00151858	+	0.00677913i
$358$	6.98779	+	1.59021i	0.369316	+	0.0840454i
$359$	−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
$362$	−5.94803	−	1.35360i	−0.312621	−	0.0711434i
$363$	2.64509	+	11.8080i	0.138831	+	0.619760i
$364$	−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	$-0.704152\pi$
$367$	3.88878	−	3.88878i	0.202993	−	0.202993i	0.801281	+	0.598288i	$0.204152\pi$
$368$	19.6026	+	2.15789i	1.02185	+	0.112488i
$369$	11.1958	+	23.7358i	0.582832	+	1.23564i
$370$		0			0
$371$	−0.363906			−0.0188931
$372$	−8.03092	+	34.7451i	−0.416384	+	1.80145i
$373$	1.11844	−	1.11844i	0.0579104	−	0.0579104i	−0.677558	−	0.735469i	$-0.736962\pi$
$373$	1.11844	−	1.11844i	0.0579104	−	0.0579104i	0.735469	+	0.677558i	$0.236962\pi$
$374$	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
$378$	2.47920	−	6.83319i	0.127516	−	0.351462i
$379$	−30.6447			−1.57411			−0.787055	−	0.616882i	$-0.788395\pi$
$379$	−30.6447			−1.57411			−0.787055	+	0.616882i	$0.788395\pi$
$380$		0			0
$381$	−20.9324	−	13.2706i	−1.07240	−	0.679876i
$382$	27.3166	+	6.21646i	1.39764	+	0.318062i
$383$	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	$0.0486782\pi$
$384$	−4.36908	−	19.1026i	−0.222959	−	0.974828i
$385$		0			0
$386$	5.10392	−	3.21156i	0.259782	−	0.163464i
$387$	6.60051	−	18.3865i	0.335523	−	0.934640i
$388$	−30.4141	+	10.6860i	−1.54404	+	0.542501i
$389$		−	28.3988i		−	1.43988i	−0.694037	−	0.719939i	$-0.744170\pi$
$389$		−	28.3988i		−	1.43988i	0.694037	−	0.719939i	$-0.255830\pi$
$390$		0			0
$391$	−0.377718			−0.0191020
$392$	−13.3360	−	10.5933i	−0.673571	−	0.535043i
$393$	−3.77517	−	16.8528i	−0.190432	−	0.850113i
$394$	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	0.950981	−	0.309249i	$-0.100078\pi$
$397$	12.7864	+	12.7864i	0.641733	+	0.641733i	−0.309249	+	0.950981i	$0.600078\pi$
$398$	10.6849	+	2.43156i	0.535584	+	0.121883i
$399$	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	$0.909356\pi$
$402$	−4.27615	−	4.30524i	−0.213275	−	0.214726i
$403$	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
$408$	0.123213	+	0.354522i	0.00609998	+	0.0175514i
$409$			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
$412$	−7.58347	−	21.5837i	−0.373611	−	1.06335i
$413$	−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
$417$	1.91100	+	8.53094i	0.0935821	+	0.417762i
$418$	6.02019	−	26.4542i	0.294457	−	1.29392i
$419$		−	0.0216630i		−	0.00105831i	−1.00000		0.000529154i	$-0.999832\pi$
$419$		−	0.0216630i		−	0.00105831i	1.00000		0.000529154i	$-0.000168435\pi$
$420$		0			0
$421$		−	14.4526i		−	0.704375i	−0.935930	−	0.352187i	$-0.885438\pi$
$421$		−	14.4526i		−	0.704375i	0.935930	−	0.352187i	$-0.114562\pi$
$422$	−32.4584	−	7.38657i	−1.58005	−	0.359573i
$423$	−32.1699	−	11.5486i	−1.56416	−	0.561510i
$424$	−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
$428$	6.83313	−	2.40083i	0.330292	−	0.116049i
$429$	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	$-0.134299\pi$
$432$	4.81788	−	20.2185i	0.231800	−	0.972763i
$433$	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
$438$	−11.0679	−	11.1432i	−0.528846	−	0.532443i
$439$			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
$442$	0.0707953	−	0.311092i	0.00336739	−	0.0147971i
$443$	−16.9126	−	16.9126i	−0.803541	−	0.803541i	0.180106	−	0.983647i	$-0.442356\pi$
$443$	−16.9126	−	16.9126i	−0.803541	−	0.803541i	−0.983647	+	0.180106i	$0.942356\pi$
$444$	30.2991	−	18.9222i	1.43793	−	0.898007i
$445$		0			0
$446$	10.6817	−	6.72131i	0.505794	−	0.318263i
$447$	36.3571	−	8.14430i	1.71963	−	0.385212i
$448$	6.71669	+	4.18450i	0.317334	+	0.197699i
$449$	−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
$452$	15.1323	−	5.31675i	0.711761	−	0.250079i
$453$	0.532320	+	2.37634i	0.0250106	+	0.111650i
$454$	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	−0.0147169	+	0.999892i	$0.504685\pi$
$457$	−21.6899	+	21.6899i	−1.01461	+	1.01461i	−0.999892	+	0.0147169i	$0.995315\pi$
$458$	−5.88011	+	25.8386i	−0.274759	+	1.20736i
$459$	−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	$0.801928\pi$
$462$	7.29086	−	7.24161i	0.339202	−	0.336910i
$463$	−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	−0.226747	−	0.973954i	$-0.572809\pi$
$467$	16.1473	−	16.1473i	0.747207	−	0.747207i	0.973954	+	0.226747i	$0.0728090\pi$
$468$	−12.5776	+	12.4083i	−0.581401	+	0.573572i
$469$	2.45047			0.113152
$470$		0			0
$471$	5.67814	−	8.95640i	0.261635	−	0.412689i
$472$	−6.40959	−	5.09138i	−0.295025	−	0.234350i
$473$	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
$477$	−1.03874	−	0.372895i	−0.0475608	−	0.0170737i
$478$	−3.29879	+	14.4957i	−0.150883	+	0.663017i
$479$	−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
$482$	1.75142	−	7.69618i	0.0797751	−	0.350551i
$483$	−8.24286	+	1.84647i	−0.375063	+	0.0840172i
$484$	−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	$-0.514957\pi$
$487$	21.0072	−	21.0072i	0.951925	−	0.951925i	0.998896	+	0.0469714i	$0.0149569\pi$
$488$	−14.8439	−	11.7911i	−0.671953	−	0.533758i
$489$	−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	$0.452577\pi$
$492$	−29.5253	−	6.82442i	−1.33110	−	0.307668i
$493$	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
$498$	−13.7030	−	13.7962i	−0.614044	−	0.618221i
$499$	19.7716			0.885097			0.442548	−	0.896745i	$-0.354075\pi$
$499$	19.7716			0.885097			0.442548	+	0.896745i	$0.354075\pi$
$500$		0			0
$501$	2.43721	−	3.84433i	0.108887	−	0.171752i
$502$	−4.13321	+	18.1623i	−0.184474	+	0.810624i
$503$	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	$0.217129\pi$
$504$	4.42193	+	7.13432i	0.196968	+	0.317788i
$505$		0			0
$506$	15.7483	+	25.0278i	0.700099	+	1.11262i
$507$	−7.31646	+	1.63895i	−0.324935	+	0.0727882i
$508$	27.0007	−	9.48674i	1.19796	−	0.420906i
$509$			12.8288i			0.568627i	0.958731	+	0.284313i	$0.0917656\pi$
$509$			12.8288i			0.568627i	−0.958731	+	0.284313i	$0.908234\pi$
$510$		0			0
$511$	6.34253			0.280577
$512$	20.4428	+	9.70012i	0.903452	+	0.428689i
$513$	14.4317	+	18.5525i	0.637177	+	0.819113i
$514$	−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
$518$	−3.20107	+	14.0663i	−0.140647	+	0.618038i
$519$	−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	$0.939700\pi$
$522$	−16.1985	+	3.57099i	−0.708990	+	0.156298i
$523$	16.7947	−	16.7947i	0.734383	−	0.734383i	−0.237102	−	0.971485i	$-0.576197\pi$
$523$	16.7947	−	16.7947i	0.734383	−	0.734383i	0.971485	+	0.237102i	$0.0761975\pi$
$524$	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
$528$	18.3536	−	22.9454i	0.798737	−	0.998569i
$529$		−	1.30735i		−	0.0568411i
$530$		0			0
$531$	−3.70391	−	7.85249i	−0.160736	−	0.340769i
$532$	−8.44318	+	2.96653i	−0.366058	+	0.128615i
$533$	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
$537$	−8.56481	+	1.91859i	−0.369599	+	0.0827932i
$538$	16.2899	+	3.70709i	0.702306	+	0.159824i
$539$		−	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	$0.808597\pi$
$542$	3.24804	−	14.2727i	0.139515	−	0.613064i
$543$	7.29040	−	1.63311i	0.312861	−	0.0700834i
$544$	−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	0.601999	−	0.798497i	$-0.294371\pi$
$547$	−4.59571	−	4.59571i	−0.196498	−	0.196498i	−0.798497	+	0.601999i	$0.794371\pi$
$548$	1.32208	+	3.76284i	0.0564765	+	0.160740i
$549$	−8.57786	−	18.1855i	−0.366094	−	0.776140i
$550$		0			0
$551$		−	17.6855i		−	0.753426i
$552$	−22.8146	+	7.92917i	−0.971053	+	0.337488i
$553$	−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	$-0.895645\pi$
$557$	−14.7444	+	14.7444i	−0.624741	+	0.624741i	0.321999	+	0.946740i	$0.395645\pi$
$558$	−9.40263	−	42.6517i	−0.398045	−	1.80559i
$559$		−	19.1752i		−	0.811023i
$560$		0			0
$561$	−0.301329	+	0.475301i	−0.0127221	+	0.0200672i
$562$	45.8173	+	10.4267i	1.93269	+	0.439822i
$563$	−19.1553	−	19.1553i	−0.807301	−	0.807301i	0.176924	−	0.984225i	$-0.443385\pi$
$563$	−19.1553	−	19.1553i	−0.807301	−	0.807301i	−0.984225	+	0.176924i	$0.943385\pi$
$564$	33.4759	−	20.9061i	1.40959	−	0.880306i
$565$		0			0
$566$	7.54274	+	11.9872i	0.317045	+	0.503859i
$567$	0.854084	+	8.86166i	0.0358682	+	0.372155i
$568$	23.2814	+	18.4933i	0.976866	+	0.775962i
$569$	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	$0.0325709\pi$
$571$			4.88168i			0.204292i	−0.994769	+	0.102146i	$0.967429\pi$
$572$	−23.5648	+	8.27952i	−0.985292	+	0.346184i
$573$	−33.4815	+	7.50014i	−1.39871	+	0.313323i
$574$	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	$-0.787516\pi$
$577$	−3.99454	+	3.99454i	−0.166295	+	0.166295i	0.619054	+	0.785349i	$0.287516\pi$
$578$	−23.4342	−	5.33293i	−0.974733	−	0.221821i
$579$	−3.95451	+	6.23763i	−0.164344	+	0.259227i
$580$		0			0
$581$	7.85255			0.325779
$582$	28.0123	−	27.8230i	1.16115	−	1.15330i
$583$	−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	$-0.920998\pi$
$587$	−17.5340	+	17.5340i	−0.723707	+	0.723707i	0.245651	+	0.969358i	$0.420998\pi$
$588$	20.3233	+	4.69748i	0.838118	+	0.193721i
$589$	46.5669			1.91875
$590$		0			0
$591$	−14.0078	−	8.88062i	−0.576205	−	0.365300i
$592$	−4.51347	+	41.0009i	−0.185502	+	1.68513i
$593$	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	$-0.103826\pi$
$594$	28.2317	−	13.1997i	1.15836	−	0.541590i
$595$		0			0
$596$	−18.6169	+	38.7853i	−0.762580	+	1.58871i
$597$	−13.0963	+	2.93367i	−0.535994	+	0.120067i
$598$	20.0197	+	4.55590i	0.818667	+	0.186305i
$599$	−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	$0.769389\pi$
$602$	−8.88243	−	2.02138i	−0.362021	−	0.0823853i
$603$	6.99470	+	2.51100i	0.284846	+	0.102256i
$604$	−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	$-0.848214\pi$
$607$	−10.5809	+	10.5809i	−0.429465	+	0.429465i	0.458981	+	0.888446i	$0.348214\pi$
$608$	−23.0189	+	11.1762i	−0.933541	+	0.453254i
$609$	3.58670	−	5.65747i	0.145340	−	0.229252i
$610$		0			0
$611$	−33.5498			−1.35728
$612$	−0.322828	−	0.327235i	−0.0130496	−	0.0132277i
$613$	27.2783	−	27.2783i	1.10176	−	1.10176i	0.107564	−	0.994198i	$-0.465695\pi$
$613$	27.2783	−	27.2783i	1.10176	−	1.10176i	0.994198	−	0.107564i	$-0.0343050\pi$
$614$	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	$0.469904\pi$
$618$	19.7449	+	19.8792i	0.794257	+	0.799660i
$619$	47.6006			1.91323			0.956616	−	0.291353i	$-0.0941055\pi$
$619$	47.6006			1.91323			0.956616	+	0.291353i	$0.0941055\pi$
$620$		0			0
$621$	−25.4207	−	3.17584i	−1.02010	−	0.127442i
$622$	−18.0523	−	4.10816i	−0.723830	−	0.164722i
$623$	−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
$627$	7.26334	+	32.4244i	0.290070	+	1.29491i
$628$	4.05911	+	11.5528i	0.161976	+	0.461009i
$629$		−	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	$0.384775\pi$
$632$	−3.23760	−	2.57175i	−0.128785	−	0.102299i
$633$	39.7837	−	8.91187i	1.58126	−	0.354215i
$634$	−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
$638$	−22.8647	−	5.20333i	−0.905222	−	0.206002i
$639$	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	$0.999047\pi$
$642$	−6.29353	+	6.25101i	−0.248386	+	0.246708i
$643$	−6.08170	+	6.08170i	−0.239839	+	0.239839i	−0.816783	−	0.576945i	$-0.804245\pi$
$643$	−6.08170	+	6.08170i	−0.239839	+	0.239839i	0.576945	+	0.816783i	$0.304245\pi$
$644$	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	$0.673874\pi$
$648$	5.31155	+	24.8955i	0.208657	+	0.977989i
$649$		−	12.2738i		−	0.481789i
$650$		0			0
$651$	14.8965	+	9.44400i	0.583838	+	0.370139i
$652$	23.1292	−	8.12650i	0.905811	−	0.318258i
$653$	−26.0276	−	26.0276i	−1.01854	−	1.01854i	−0.999825	−	0.0187129i	$-0.994043\pi$
$653$	−26.0276	−	26.0276i	−1.01854	−	1.01854i	−0.0187129	−	0.999825i	$-0.505957\pi$
$654$	−22.8390	−	0.0774114i	−0.893075	−	0.00302703i
$655$		0			0
$656$	27.3017	−	21.8869i	1.06595	−	0.854540i
$657$	18.1043	+	6.49919i	0.706316	+	0.253557i
$658$	−3.53670	+	15.5411i	−0.137875	+	0.605856i
$659$			33.7716i			1.31555i	0.753213	+	0.657777i	$0.228503\pi$
$659$			33.7716i			1.31555i	−0.753213	+	0.657777i	$0.771497\pi$
$660$		0			0
$661$		−	44.5819i		−	1.73404i	−0.498277	−	0.867018i	$-0.666034\pi$
$661$		−	44.5819i		−	1.73404i	0.498277	−	0.867018i	$-0.333966\pi$
$662$	20.1997	+	4.59685i	0.785083	+	0.178662i
$663$	0.0854143	+	0.381300i	0.00331722	+	0.0148085i
$664$	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
$668$	1.74228	+	4.95879i	0.0674109	+	0.191861i
$669$	−8.27618	+	13.0544i	−0.319976	+	0.504713i
$670$		0			0
$671$		−	28.4249i		−	1.09733i
$672$	−9.63021	−	1.09316i	−0.371493	−	0.0421697i
$673$	−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	−0.570832	−	0.821067i	$-0.693379\pi$
$677$	6.51094	−	6.51094i	0.250236	−	0.250236i	0.821067	+	0.570832i	$0.193379\pi$
$678$	−13.9373	+	13.8431i	−0.535258	+	0.531642i
$679$			15.9441i			0.611880i
$680$		0			0
$681$	−6.46575	−	4.09913i	−0.247768	−	0.157079i
$682$	13.7007	−	60.2042i	0.524627	−	2.30534i
$683$	−9.23055	−	9.23055i	−0.353197	−	0.353197i	0.508101	−	0.861298i	$-0.330348\pi$
$683$	−9.23055	−	9.23055i	−0.353197	−	0.353197i	−0.861298	+	0.508101i	$0.830348\pi$
$684$	−27.1402	−	0.183983i	−1.03773	−	0.00703475i
$685$		0			0
$686$	−15.4178	+	9.70143i	−0.588656	+	0.370402i
$687$	−7.09433	−	31.6699i	−0.270666	−	1.20828i
$688$	−25.8908	−	2.85011i	−0.987077	−	0.108660i
$689$	−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	$0.950506\pi$
$692$	−4.69440	−	13.3610i	−0.178454	−	0.507908i
$693$	−4.25234	+	11.8454i	−0.161533	+	0.449970i
$694$	−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
$698$	5.93384	−	26.0747i	0.224599	−	0.986942i
$699$	−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	$0.688573\pi$
$702$	7.38022	−	20.3415i	0.278548	−	0.767739i
$703$	−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
$708$	9.76781	+	2.25771i	0.367097	+	0.0848501i
$709$	−19.7857			−0.743066			−0.371533	−	0.928420i	$-0.621168\pi$
$709$	−19.7857			−0.743066			−0.371533	+	0.928420i	$0.621168\pi$
$710$		0			0
$711$	−1.87091	−	3.96643i	−0.0701646	−	0.148753i
$712$	−9.54676	+	12.0185i	−0.357780	+	0.450413i
$713$	−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
$717$	−3.97998	−	17.7671i	−0.148635	−	0.663524i
$718$	−0.0237819	+	0.104503i	−0.000887532	+	0.00390003i
$719$	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
$722$	0.458741	−	2.01582i	0.0170726	−	0.0750211i
$723$	2.11309	+	9.43307i	0.0785865	+	0.350820i
$724$	−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	$-0.679331\pi$
$727$	8.39630	−	8.39630i	0.311401	−	0.311401i	0.845452	+	0.534051i	$0.179331\pi$
$728$	6.45120	+	5.12443i	0.239097	+	0.189924i
$729$	−6.64261	+	26.1701i	−0.246023	+	0.969264i
$730$		0			0
$731$	0.498885			0.0184519
$732$	22.6212	+	5.22863i	0.836104	+	0.193256i
$733$	−13.4915	+	13.4915i	−0.498321	+	0.498321i	−0.910915	−	0.412594i	$-0.864623\pi$
$733$	−13.4915	+	13.4915i	−0.498321	+	0.498321i	0.412594	+	0.910915i	$0.364623\pi$
$734$	−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
$738$	36.2440	−	7.99005i	1.33416	−	0.294118i
$739$	20.0345			0.736983			0.368491	−	0.929631i	$-0.379874\pi$
$739$	20.0345			0.736983			0.368491	+	0.929631i	$0.379874\pi$
$740$		0			0
$741$	19.4854	+	12.3533i	0.715814	+	0.453809i
$742$	−0.114197	+	0.501811i	−0.00419232	+	0.0184221i
$743$	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	$0.0478512\pi$
$744$	45.3918	+	21.9777i	1.66414	+	0.805740i
$745$		0			0
$746$	−1.19130	−	1.89325i	−0.0436166	−	0.0693169i
$747$	22.4145	+	8.04650i	0.820105	+	0.294406i
$748$	−0.215410	−	0.613089i	−0.00787617	−	0.0224168i
$749$		−	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	$0.464147\pi$
$752$	−4.98669	+	45.2997i	−0.181846	+	1.65191i
$753$	−4.98670	−	22.2612i	−0.181725	−	0.811245i
$754$	−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	0.701758	−	0.712415i	$-0.252399\pi$
$757$	−0.293203	−	0.293203i	−0.0106566	−	0.0106566i	−0.712415	+	0.701758i	$0.752399\pi$
$758$	−9.61660	+	42.2577i	−0.349291	+	1.53487i
$759$	−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	$-0.275182\pi$
$762$	−24.8685	+	24.7004i	−0.900889	+	0.894803i
$763$	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
$768$	−27.7128	+	0.0301756i	−0.999999	+	0.00108887i
$769$		−	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
$772$	−2.82694	−	8.04590i	−0.101744	−	0.289578i
$773$	21.3386	+	21.3386i	0.767496	+	0.767496i	0.977665	−	0.210169i	$-0.0674016\pi$
$773$	21.3386	+	21.3386i	0.767496	+	0.767496i	−0.210169	+	0.977665i	$0.567402\pi$
$774$	−23.2829	−	14.8717i	−0.836888	−	0.534552i
$775$		0			0
$776$	5.19136	+	45.2931i	0.186359	+	1.62593i
$777$	−3.86209	−	17.2408i	−0.138552	−	0.618511i
$778$	−39.1608	−	8.91184i	−1.40398	−	0.319505i
$779$			39.5710i			1.41778i
$780$		0			0
$781$			44.5819i			1.59527i
$782$	−0.118532	+	0.520857i	−0.00423869	+	0.0186258i
$783$	16.0352	−	12.4735i	0.573050	−	0.445768i
$784$	−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	0.184411	−	0.982849i	$-0.440962\pi$
$787$	−22.3990	−	22.3990i	−0.798438	−	0.798438i	−0.982849	+	0.184411i	$0.940962\pi$
$788$	18.0687	−	6.34846i	0.643669	−	0.226154i
$789$	−31.2831	−	19.8327i	−1.11371	−	0.706063i
$790$		0			0
$791$		−	7.93287i		−	0.282060i
$792$	−8.22294	+	35.0342i	−0.292189	+	1.24489i
$793$	−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	$-0.584892\pi$
$797$	19.7929	−	19.7929i	0.701102	−	0.701102i	0.964647	+	0.263545i	$0.0848918\pi$
$798$	7.77643	−	7.72389i	0.275283	−	0.273423i
$799$		−	0.872872i		−	0.0308800i
$800$		0			0
$801$	−14.7241	+	6.94514i	−0.520250	+	0.245394i
$802$	15.5151	+	3.53078i	0.547857	+	0.124676i
$803$	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
$807$	−19.9662	+	4.47259i	−0.702843	+	0.157443i
$808$	−25.8737	+	32.5726i	−0.910233	+	1.14590i
$809$	−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	$-0.861402\pi$
$811$		−	24.0234i		−	0.843577i	0.906694	−	0.421789i	$-0.138598\pi$
$812$	2.56401	+	7.29756i	0.0899791	+	0.256094i
$813$	3.91875	+	17.4938i	0.137437	+	0.613534i
$814$	−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
$818$	20.2228	+	4.60211i	0.707074	+	0.160909i
$819$	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	$0.418679\pi$
$822$	−3.44227	−	3.46569i	−0.120063	−	0.120880i
$823$	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	$-0.498016\pi$
$827$	28.9363	−	28.9363i	1.00621	−	1.00621i	0.999981	−	0.00623359i	$-0.00198423\pi$
$828$	21.0586	−	20.7750i	0.731836	−	0.721981i
$829$	−18.8808			−0.655758			−0.327879	−	0.944720i	$-0.606334\pi$
$829$	−18.8808			−0.655758			−0.327879	+	0.944720i	$0.606334\pi$
$830$		0			0
$831$	−8.19277	+	12.9228i	−0.284204	+	0.448288i
$832$	19.9946	+	12.4567i	0.693189	+	0.431857i
$833$	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
$837$	32.8436	+	42.2216i	1.13524	+	1.45939i
$838$	−0.0298724	−	0.00679807i	−0.00103192	−	0.000234835i
$839$	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
$842$	−19.9295	−	4.53536i	−0.686815	−	0.156299i
$843$	−56.1574	+	12.5797i	−1.93416	+	0.433269i
$844$	−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
$848$	−0.161017	+	1.46270i	−0.00552934	+	0.0502292i
$849$	−14.6498	−	9.28764i	−0.502781	−	0.318751i
$850$		0			0
$851$	50.8414			1.74282
$852$	−35.4794	−	8.20065i	−1.21550	−	0.280950i
$853$	11.2078	−	11.2078i	0.383746	−	0.383746i	−0.488703	−	0.872450i	$-0.662530\pi$
$853$	11.2078	−	11.2078i	0.383746	−	0.383746i	0.872450	+	0.488703i	$0.162530\pi$
$854$	−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	$0.910641\pi$
$858$	21.7039	−	21.5572i	0.740958	−	0.735952i
$859$	−7.84855			−0.267789			−0.133894	−	0.990996i	$-0.542748\pi$
$859$	−7.84855			−0.267789			−0.133894	+	0.990996i	$0.542748\pi$
$860$		0			0
$861$	−8.02520	+	12.6585i	−0.273498	+	0.431401i
$862$	−23.4465	−	5.33574i	−0.798592	−	0.181736i
$863$	−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	$0.437825\pi$
$864$	−26.3686	−	12.9884i	−0.897077	−	0.441875i
$865$		0			0
$866$	1.41056	−	0.887572i	0.0479327	−	0.0301609i
$867$	28.7229	−	6.43416i	0.975480	−	0.218516i
$868$	−19.2149	+	6.75120i	−0.652197	+	0.229151i
$869$		−	6.19972i		−	0.210311i
$870$		0			0
$871$	7.29471			0.247172
$872$	16.4033	−	20.6503i	0.555485	−	0.699306i
$873$	−16.3379	+	45.5114i	−0.552956	+	1.54033i
$874$	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	0.206076	−	0.978536i	$-0.433930\pi$
$877$	−22.8758	−	22.8758i	−0.772459	−	0.772459i	−0.978536	+	0.206076i	$0.933930\pi$
$878$	27.9367	+	6.35757i	0.942818	+	0.214558i
$879$	−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	$-0.0608006\pi$
$882$	−24.9480	+	5.49983i	−0.840044	+	0.185189i
$883$	−2.32921	+	2.32921i	−0.0783843	+	0.0783843i	−0.745212	−	0.666828i	$-0.767652\pi$
$883$	−2.32921	+	2.32921i	−0.0783843	+	0.0783843i	0.666828	+	0.745212i	$0.267652\pi$
$884$	−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	$0.521064\pi$
$888$	−16.5847	−	47.7191i	−0.556546	−	1.60135i
$889$		−	14.1547i		−	0.474734i
$890$		0			0
$891$	−24.2760	+	29.4545i	−0.813276	+	0.986763i
$892$	−5.91636	−	16.8389i	−0.198094	−	0.563806i
$893$	−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
$897$	−24.5378	+	5.49667i	−0.819294	+	0.183529i
$898$	−10.4683	+	46.0003i	−0.349332	+	1.53505i
$899$		−	40.2484i		−	1.34236i
$900$		0			0
$901$		−	0.0281844i		−	0.000938958i
$902$	51.1596	+	11.6424i	1.70343	+	0.387650i
$903$	10.8870	−	2.43879i	0.362298	−	0.0811578i
$904$	−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	0.955234	−	0.295851i	$-0.0956031\pi$
$907$	19.8583	+	19.8583i	0.659383	+	0.659383i	−0.295851	+	0.955234i	$0.595603\pi$
$908$	8.34016	−	2.93033i	0.276778	−	0.0972465i
$909$	−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	$0.730036\pi$
$912$	19.5759	−	24.4735i	0.648223	−	0.810399i
$913$	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
$918$	0.529228	+	0.192013i	0.0174671	+	0.00633737i
$919$		−	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
$922$	−10.9498	+	48.1159i	−0.360611	+	1.58461i
$923$	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
$927$	−32.2977	−	11.5944i	−1.06079	−	0.380810i
$928$	9.65973	+	19.8956i	0.317096	+	0.653105i
$929$	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
$932$	29.2495	−	10.2769i	0.958098	−	0.336630i
$933$	22.1263	−	4.95648i	0.724384	−	0.162268i
$934$	−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	$-0.761086\pi$
$937$	−1.50743	+	1.50743i	−0.0492455	+	0.0492455i	0.682055	+	0.731301i	$0.261086\pi$
$938$	0.768983	−	3.37910i	0.0251082	−	0.110331i
$939$	−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	$0.545812\pi$
$942$	−10.5686	−	10.6405i	−0.344345	−	0.346687i
$943$	−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	$-0.767152\pi$
$947$	−2.34399	+	2.34399i	−0.0761694	+	0.0761694i	0.667996	+	0.744165i	$0.267152\pi$
$948$	4.93390	+	1.14041i	0.160246	+	0.0370389i
$949$	18.8808			0.612897
$950$		0			0
$951$	17.7770	+	11.2702i	0.576459	+	0.365461i
$952$	−0.133323	+	0.167842i	−0.00432104	+	0.00543979i
$953$	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	$0.0588984\pi$
$954$	−0.840174	+	1.31537i	−0.0272016	+	0.0425865i
$955$		0			0
$956$	18.9537	+	9.09777i	0.613007	+	0.294243i
$957$	28.0249	−	6.27780i	0.905915	−	0.202933i
$958$	−3.27501	+	14.3912i	−0.105811	+	0.464958i
$959$	1.97261			0.0636990
$960$		0			0
$961$	74.9765			2.41860
$962$	−9.52915	+	41.8734i	−0.307232	+	1.35005i
$963$	3.67065	−	10.2251i	0.118285	−	0.329498i
$964$	−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	$-0.964089\pi$
$967$	−27.3981	+	27.3981i	−0.881063	+	0.881063i	0.112580	+	0.993643i	$0.464089\pi$
$968$	−12.2907	+	15.4728i	−0.395037	+	0.497316i
$969$	−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	$0.506044\pi$
$972$	−18.9752	−	24.7375i	−0.608629	−	0.793455i
$973$	−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	$0.773458\pi$
$978$	−21.3027	+	21.1588i	−0.681187	+	0.676585i
$979$	−23.0144			−0.735544
$980$		0			0
$981$	25.2990	−	11.9332i	0.807734	−	0.380996i
$982$	2.06430	−	9.07101i	0.0658743	−	0.289468i
$983$	−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	$0.324881\pi$
$984$	−18.6759	+	38.5725i	−0.595366	+	1.22965i
$985$		0			0
$986$	−0.225599	−	0.358530i	−0.00718454	−	0.0114179i
$987$	−4.26702	−	19.0485i	−0.135821	−	0.606320i
$988$	−25.1342	+	8.83093i	−0.799624	+	0.280949i
$989$			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	$0.568514\pi$
$992$	−52.3863	+	25.4347i	−1.66327	+	0.807551i
$993$	−24.7584	+	5.54608i	−0.785684	+	0.176000i
$994$	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	0.981794	−	0.189949i	$-0.0608324\pi$
$997$	25.0027	+	25.0027i	0.791844	+	0.791844i	−0.189949	+	0.981794i	$0.560832\pi$
$998$	6.20451	−	27.2641i	0.196400	−	0.863031i
$999$	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.293.17	yes	64
3.2	odd	2	inner	600.2.w.k.293.15	yes	64
5.2	odd	4	inner	600.2.w.k.557.32	yes	64
5.3	odd	4	inner	600.2.w.k.557.1	yes	64
5.4	even	2	inner	600.2.w.k.293.16	yes	64
8.5	even	2	inner	600.2.w.k.293.2	yes	64
15.2	even	4	inner	600.2.w.k.557.2	yes	64
15.8	even	4	inner	600.2.w.k.557.31	yes	64
15.14	odd	2	inner	600.2.w.k.293.18	yes	64
24.5	odd	2	inner	600.2.w.k.293.32	yes	64
40.13	odd	4	inner	600.2.w.k.557.18	yes	64
40.29	even	2	inner	600.2.w.k.293.31	yes	64
40.37	odd	4	inner	600.2.w.k.557.15	yes	64
120.29	odd	2	inner	600.2.w.k.293.1	✓	64
120.53	even	4	inner	600.2.w.k.557.16	yes	64
120.77	even	4	inner	600.2.w.k.557.17	yes	64

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

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

Fields

Representations

Groups

Database

Properties

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