LMFDB - Embedded newform 600.2.w.j.293.15

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:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 120)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			293.15
Character	$\chi$	$=$	600.293
Dual form			600.2.w.j.557.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.39193 + 0.250043i) q^{2} +(-1.40091 + 1.01856i) q^{3} +(1.87496 + 0.696087i) q^{4} +(-2.20465 + 1.06748i) q^{6} +(2.29041 - 2.29041i) q^{7} +(2.43576 + 1.43773i) q^{8} +(0.925085 - 2.85381i) q^{9} +O(q^{10})$	\(q+(1.39193 + 0.250043i) q^{2} +(-1.40091 + 1.01856i) q^{3} +(1.87496 + 0.696087i) q^{4} +(-2.20465 + 1.06748i) q^{6} +(2.29041 - 2.29041i) q^{7} +(2.43576 + 1.43773i) q^{8} +(0.925085 - 2.85381i) q^{9} +2.28378 q^{11} +(-3.33565 + 0.934597i) q^{12} +(-1.05635 + 1.05635i) q^{13} +(3.76080 - 2.61540i) q^{14} +(3.03093 + 2.61026i) q^{16} +(3.04391 + 3.04391i) q^{17} +(2.00123 - 3.74100i) q^{18} -3.36831 q^{19} +(-0.875741 + 5.54157i) q^{21} +(3.17887 + 0.571043i) q^{22} +(3.68785 - 3.68785i) q^{23} +(-4.87669 + 0.466842i) q^{24} +(-1.73449 + 1.20623i) q^{26} +(1.61081 + 4.94017i) q^{27} +(5.88875 - 2.70010i) q^{28} +2.71461i q^{29} -6.49196 q^{31} +(3.56617 + 4.39118i) q^{32} +(-3.19937 + 2.32616i) q^{33} +(3.47581 + 4.99803i) q^{34} +(3.72099 - 4.70683i) q^{36} +(-2.31197 - 2.31197i) q^{37} +(-4.68847 - 0.842223i) q^{38} +(0.403895 - 2.55579i) q^{39} +10.8056i q^{41} +(-2.60460 + 7.49452i) q^{42} +(1.16384 - 1.16384i) q^{43} +(4.28199 + 1.58971i) q^{44} +(6.05536 - 4.21112i) q^{46} +(-1.83768 - 1.83768i) q^{47} +(-6.90475 - 0.569569i) q^{48} -3.49196i q^{49} +(-7.36463 - 1.16384i) q^{51} +(-2.71591 + 1.24529i) q^{52} +(5.82856 + 5.82856i) q^{53} +(1.00688 + 7.27916i) q^{54} +(8.87188 - 2.28592i) q^{56} +(4.71870 - 3.43082i) q^{57} +(-0.678770 + 3.77856i) q^{58} -7.41311i q^{59} -8.97044i q^{61} +(-9.03638 - 1.62327i) q^{62} +(-4.41757 - 8.65522i) q^{63} +(3.86589 + 7.00392i) q^{64} +(-5.03494 + 2.43788i) q^{66} +(-8.66367 - 8.66367i) q^{67} +(3.58837 + 7.82602i) q^{68} +(-1.41005 + 8.92262i) q^{69} -7.37570i q^{71} +(6.35628 - 5.62118i) q^{72} +(-1.83441 - 1.83441i) q^{73} +(-2.64001 - 3.79620i) q^{74} +(-6.31544 - 2.34464i) q^{76} +(5.23080 - 5.23080i) q^{77} +(1.20125 - 3.45650i) q^{78} -8.28844i q^{79} +(-7.28844 - 5.28003i) q^{81} +(-2.70185 + 15.0406i) q^{82} +(-5.27928 - 5.27928i) q^{83} +(-5.49939 + 9.78061i) q^{84} +(1.91100 - 1.32898i) q^{86} +(-2.76499 - 3.80292i) q^{87} +(5.56275 + 3.28345i) q^{88} -11.5311 q^{89} +4.83893i q^{91} +(9.48162 - 4.34749i) q^{92} +(9.09464 - 6.61243i) q^{93} +(-2.09843 - 3.01742i) q^{94} +(-9.46854 - 2.51929i) q^{96} +(2.79647 - 2.79647i) q^{97} +(0.873141 - 4.86058i) q^{98} +(2.11269 - 6.51747i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 4 q^{6}+O(q^{10}) $ 32 * q - 4 * q^6	$ 32 q - 4 q^{6} + 8 q^{12} + 28 q^{16} + 20 q^{18} + 52 q^{22} - 12 q^{28} - 32 q^{31} - 8 q^{33} - 20 q^{36} - 16 q^{42} + 24 q^{46} - 44 q^{48} - 8 q^{52} + 16 q^{57} - 28 q^{58} - 48 q^{63} + 16 q^{66} - 32 q^{72} + 64 q^{73} - 88 q^{76} - 64 q^{78} + 48 q^{81} - 64 q^{82} + 8 q^{87} + 52 q^{88} - 52 q^{96} - 16 q^{97}+O(q^{100}) $ 32 * q - 4 * q^6 + 8 * q^12 + 28 * q^16 + 20 * q^18 + 52 * q^22 - 12 * q^28 - 32 * q^31 - 8 * q^33 - 20 * q^36 - 16 * q^42 + 24 * q^46 - 44 * q^48 - 8 * q^52 + 16 * q^57 - 28 * q^58 - 48 * q^63 + 16 * q^66 - 32 * q^72 + 64 * q^73 - 88 * q^76 - 64 * q^78 + 48 * q^81 - 64 * q^82 + 8 * q^87 + 52 * q^88 - 52 * q^96 - 16 * q^97

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 $

$2$	1.39193	+	0.250043i	0.984246	+	0.176807i
$2$	1.39193	+	0.250043i	0.984246	+	0.176807i
$3$	−1.40091	+	1.01856i	−0.808814	+	0.588064i
$3$	−1.40091	+	1.01856i	−0.808814	+	0.588064i
$4$	1.87496	+	0.696087i	0.937478	+	0.348043i
$5$		0			0
$5$		0			0
$6$	−2.20465	+	1.06748i	−0.900046	+	0.435795i
$7$	2.29041	−	2.29041i	0.865694	−	0.865694i	−0.126298	−	0.991992i	$-0.540310\pi$
$7$	2.29041	−	2.29041i	0.865694	−	0.865694i	0.991992	+	0.126298i	$0.0403097\pi$
$8$	2.43576	+	1.43773i	0.861172	+	0.508313i
$9$	0.925085	−	2.85381i	0.308362	−	0.951269i
$10$		0			0
$11$	2.28378			0.688586			0.344293	−	0.938862i	$-0.388119\pi$
$11$	2.28378			0.688586			0.344293	+	0.938862i	$0.388119\pi$
$12$	−3.33565	+	0.934597i	−0.962918	+	0.269795i
$13$	−1.05635	+	1.05635i	−0.292977	+	0.292977i	−0.838255	−	0.545278i	$-0.816424\pi$
$13$	−1.05635	+	1.05635i	−0.292977	+	0.292977i	0.545278	+	0.838255i	$0.316424\pi$
$14$	3.76080	−	2.61540i	1.00512	−	0.698994i
$15$		0			0
$16$	3.03093	+	2.61026i	0.757732	+	0.652566i
$17$	3.04391	+	3.04391i	0.738256	+	0.738256i	0.972240	−	0.233984i	$-0.0751764\pi$
$17$	3.04391	+	3.04391i	0.738256	+	0.738256i	−0.233984	+	0.972240i	$0.575176\pi$
$18$	2.00123	−	3.74100i	0.471695	−	0.881762i
$19$	−3.36831			−0.772744			−0.386372	−	0.922343i	$-0.626272\pi$
$19$	−3.36831			−0.772744			−0.386372	+	0.922343i	$0.626272\pi$
$20$		0			0
$21$	−0.875741	+	5.54157i	−0.191102	+	1.20927i
$22$	3.17887	+	0.571043i	0.677737	+	0.121747i
$23$	3.68785	−	3.68785i	0.768969	−	0.768969i	−0.208956	−	0.977925i	$-0.567006\pi$
$23$	3.68785	−	3.68785i	0.768969	−	0.768969i	0.977925	+	0.208956i	$0.0670065\pi$
$24$	−4.87669	+	0.466842i	−0.995449	+	0.0952936i
$25$		0			0
$26$	−1.73449	+	1.20623i	−0.340162	+	0.236561i
$27$	1.61081	+	4.94017i	0.310000	+	0.950737i
$28$	5.88875	−	2.70010i	1.11287	−	0.510270i
$29$			2.71461i			0.504091i	0.967715	+	0.252045i	$0.0811032\pi$
$29$			2.71461i			0.504091i	−0.967715	+	0.252045i	$0.918897\pi$
$30$		0			0
$31$	−6.49196			−1.16599			−0.582995	−	0.812475i	$-0.698119\pi$
$31$	−6.49196			−1.16599			−0.582995	+	0.812475i	$0.698119\pi$
$32$	3.56617	+	4.39118i	0.630416	+	0.776258i
$33$	−3.19937	+	2.32616i	−0.556938	+	0.404932i
$34$	3.47581	+	4.99803i	0.596096	+	0.857154i
$35$		0			0
$36$	3.72099	−	4.70683i	0.620165	−	0.784471i
$37$	−2.31197	−	2.31197i	−0.380085	−	0.380085i	0.491048	−	0.871133i	$-0.336614\pi$
$37$	−2.31197	−	2.31197i	−0.380085	−	0.380085i	−0.871133	+	0.491048i	$0.836614\pi$
$38$	−4.68847	−	0.842223i	−0.760570	−	0.136627i
$39$	0.403895	−	2.55579i	0.0646749	−	0.409254i
$40$		0			0
$41$			10.8056i			1.68754i	0.536702	+	0.843772i	$0.319670\pi$
$41$			10.8056i			1.68754i	−0.536702	+	0.843772i	$0.680330\pi$
$42$	−2.60460	+	7.49452i	−0.401899	+	1.15643i
$43$	1.16384	−	1.16384i	0.177484	−	0.177484i	−0.612774	−	0.790258i	$-0.709946\pi$
$43$	1.16384	−	1.16384i	0.177484	−	0.177484i	0.790258	+	0.612774i	$0.209946\pi$
$44$	4.28199	+	1.58971i	0.645534	+	0.239658i
$45$		0			0
$46$	6.05536	−	4.21112i	0.892814	−	0.620895i
$47$	−1.83768	−	1.83768i	−0.268053	−	0.268053i	0.560262	−	0.828315i	$-0.310700\pi$
$47$	−1.83768	−	1.83768i	−0.268053	−	0.268053i	−0.828315	+	0.560262i	$0.810700\pi$
$48$	−6.90475	−	0.569569i	−0.996615	−	0.0822102i
$49$		−	3.49196i		−	0.498852i
$50$		0			0
$51$	−7.36463	−	1.16384i	−1.03125	−	0.162970i
$52$	−2.71591	+	1.24529i	−0.376629	+	0.172691i
$53$	5.82856	+	5.82856i	0.800615	+	0.800615i	0.983192	−	0.182577i	$-0.0584439\pi$
$53$	5.82856	+	5.82856i	0.800615	+	0.800615i	−0.182577	+	0.983192i	$0.558444\pi$
$54$	1.00688	+	7.27916i	0.137019	+	0.990568i
$55$		0			0
$56$	8.87188	−	2.28592i	1.18556	−	0.305468i
$57$	4.71870	−	3.43082i	0.625007	−	0.454423i
$58$	−0.678770	+	3.77856i	−0.0891268	+	0.496149i
$59$		−	7.41311i		−	0.965104i	−0.875867	−	0.482552i	$-0.839710\pi$
$59$		−	7.41311i		−	0.965104i	0.875867	−	0.482552i	$-0.160290\pi$
$60$		0			0
$61$		−	8.97044i		−	1.14855i	−0.818663	−	0.574274i	$-0.805284\pi$
$61$		−	8.97044i		−	1.14855i	0.818663	−	0.574274i	$-0.194716\pi$
$62$	−9.03638	−	1.62327i	−1.14762	−	0.206155i
$63$	−4.41757	−	8.65522i	−0.556561	−	1.09045i
$64$	3.86589	+	7.00392i	0.483236	+	0.875490i
$65$		0			0
$66$	−5.03494	+	2.43788i	−0.619759	+	0.300082i
$67$	−8.66367	−	8.66367i	−1.05844	−	1.05844i	−0.998183	−	0.0602525i	$-0.980809\pi$
$67$	−8.66367	−	8.66367i	−1.05844	−	1.05844i	−0.0602525	−	0.998183i	$-0.519191\pi$
$68$	3.58837	+	7.82602i	0.435154	+	0.949044i
$69$	−1.41005	+	8.92262i	−0.169750	+	1.07416i
$70$		0			0
$71$		−	7.37570i		−	0.875334i	−0.899137	−	0.437667i	$-0.855805\pi$
$71$		−	7.37570i		−	0.875334i	0.899137	−	0.437667i	$-0.144195\pi$
$72$	6.35628	−	5.62118i	0.749095	−	0.662463i
$73$	−1.83441	−	1.83441i	−0.214701	−	0.214701i	0.591560	−	0.806261i	$-0.298512\pi$
$73$	−1.83441	−	1.83441i	−0.214701	−	0.214701i	−0.806261	+	0.591560i	$0.798512\pi$
$74$	−2.64001	−	3.79620i	−0.306895	−	0.441299i
$75$		0			0
$76$	−6.31544	−	2.34464i	−0.724431	−	0.268948i
$77$	5.23080	−	5.23080i	0.596104	−	0.596104i
$78$	1.20125	−	3.45650i	0.136015	−	0.391371i
$79$		−	8.28844i		−	0.932522i	−0.884647	−	0.466261i	$-0.845601\pi$
$79$		−	8.28844i		−	0.932522i	0.884647	−	0.466261i	$-0.154399\pi$
$80$		0			0
$81$	−7.28844	−	5.28003i	−0.809826	−	0.586670i
$82$	−2.70185	+	15.0406i	−0.298370	+	1.66096i
$83$	−5.27928	−	5.27928i	−0.579476	−	0.579476i	0.355283	−	0.934759i	$-0.384384\pi$
$83$	−5.27928	−	5.27928i	−0.579476	−	0.579476i	−0.934759	+	0.355283i	$0.884384\pi$
$84$	−5.49939	+	9.78061i	−0.600032	+	1.06715i
$85$		0			0
$86$	1.91100	−	1.32898i	0.206068	−	0.143308i
$87$	−2.76499	−	3.80292i	−0.296438	−	0.407716i
$88$	5.56275	+	3.28345i	0.592991	+	0.350017i
$89$	−11.5311			−1.22230			−0.611149	−	0.791515i	$-0.709292\pi$
$89$	−11.5311			−1.22230			−0.611149	+	0.791515i	$0.709292\pi$
$90$		0			0
$91$			4.83893i			0.507258i
$92$	9.48162	−	4.34749i	0.988527	−	0.453258i
$93$	9.09464	−	6.61243i	0.943070	−	0.685677i
$94$	−2.09843	−	3.01742i	−0.216436	−	0.311224i
$95$		0			0
$96$	−9.46854	−	2.51929i	−0.966379	−	0.257124i
$97$	2.79647	−	2.79647i	0.283939	−	0.283939i	−0.550739	−	0.834678i	$-0.685654\pi$
$97$	2.79647	−	2.79647i	0.283939	−	0.283939i	0.834678	+	0.550739i	$0.185654\pi$
$98$	0.873141	−	4.86058i	0.0882005	−	0.490993i
$99$	2.11269	−	6.51747i	0.212333	−	0.655030i
$100$		0			0
$101$	8.94251			0.889813			0.444907	−	0.895577i	$-0.353237\pi$
$101$	8.94251			0.889813			0.444907	+	0.895577i	$0.353237\pi$
$102$	−9.96006	−	3.46146i	−0.986193	−	0.342736i
$103$	2.54400	+	2.54400i	0.250668	+	0.250668i	0.821244	−	0.570577i	$-0.193280\pi$
$103$	2.54400	+	2.54400i	0.250668	+	0.250668i	−0.570577	+	0.821244i	$0.693280\pi$
$104$	−4.09174	+	1.05427i	−0.401228	+	0.103380i
$105$		0			0
$106$	6.65558	+	9.57036i	0.646447	+	0.929556i
$107$	−5.14834	+	5.14834i	−0.497709	+	0.497709i	−0.910724	−	0.413015i	$-0.864476\pi$
$107$	−5.14834	+	5.14834i	−0.497709	+	0.497709i	0.413015	+	0.910724i	$0.364476\pi$
$108$	−0.418595	+	10.3839i	−0.0402793	+	0.999188i
$109$	−1.40528			−0.134601			−0.0673005	−	0.997733i	$-0.521439\pi$
$109$	−1.40528			−0.134601			−0.0673005	+	0.997733i	$0.521439\pi$
$110$		0			0
$111$	5.59372	+	0.883983i	0.530933	+	0.0839040i
$112$	12.9206	−	0.963489i	1.22089	−	0.0910412i
$113$	−13.2872	+	13.2872i	−1.24995	+	1.24995i	−0.294212	+	0.955740i	$0.595057\pi$
$113$	−13.2872	+	13.2872i	−1.24995	+	1.24995i	−0.955740	+	0.294212i	$0.904943\pi$
$114$	7.42596	−	3.59559i	0.695505	−	0.336758i
$115$		0			0
$116$	−1.88960	+	5.08978i	−0.175445	+	0.472574i
$117$	2.03740	+	3.99181i	0.188357	+	0.369043i
$118$	1.85360	−	10.3186i	0.170637	−	0.949900i
$119$	13.9436			1.27821
$120$		0			0
$121$	−5.78435			−0.525850
$122$	2.24300	−	12.4863i	0.203071	−	1.13045i
$123$	−11.0061	−	15.1376i	−0.992384	−	1.36491i
$124$	−12.1721	−	4.51897i	−1.09309	−	0.405815i
$125$		0			0
$126$	−3.98478	−	13.1521i	−0.354993	−	1.17168i
$127$	−7.16362	+	7.16362i	−0.635668	+	0.635668i	−0.949484	−	0.313816i	$-0.898393\pi$
$127$	−7.16362	+	7.16362i	−0.635668	+	0.635668i	0.313816	+	0.949484i	$0.398393\pi$
$128$	3.62978	+	10.7156i	0.320830	+	0.947137i
$129$	−0.444996	+	2.81587i	−0.0391797	+	0.247924i
$130$		0			0
$131$	2.74859			0.240145			0.120073	−	0.992765i	$-0.461687\pi$
$131$	2.74859			0.240145			0.120073	+	0.992765i	$0.461687\pi$
$132$	−7.61788	+	2.13441i	−0.663051	+	0.185777i
$133$	−7.71482	+	7.71482i	−0.668960	+	0.668960i
$134$	−9.89296	−	14.2255i	−0.854622	−	1.22890i
$135$		0			0
$136$	3.03793	+	11.7905i	0.260501	+	1.01103i
$137$	−10.1741	−	10.1741i	−0.869232	−	0.869232i	0.123155	−	0.992387i	$-0.460699\pi$
$137$	−10.1741	−	10.1741i	−0.869232	−	0.869232i	−0.992387	+	0.123155i	$0.960699\pi$
$138$	−4.19374	+	12.0671i	−0.356995	+	1.02722i
$139$	0.857068			0.0726955			0.0363478	−	0.999339i	$-0.488428\pi$
$139$	0.857068			0.0726955			0.0363478	+	0.999339i	$0.488428\pi$
$140$		0			0
$141$	4.44620	+	0.702638i	0.374437	+	0.0591728i
$142$	1.84424	−	10.2665i	0.154765	−	0.861544i
$143$	−2.41246	+	2.41246i	−0.201740	+	0.201740i
$144$	10.2531	−	6.23497i	0.854421	−	0.519581i
$145$		0			0
$146$	−2.09469	−	3.01206i	−0.173358	−	0.249280i
$147$	3.55676	+	4.89192i	0.293357	+	0.403478i
$148$	−2.72551	−	5.94417i	−0.224036	−	0.488608i
$149$		−	7.83812i		−	0.642124i	−0.947058	−	0.321062i	$-0.895960\pi$
$149$		−	7.83812i		−	0.642124i	0.947058	−	0.321062i	$-0.104040\pi$
$150$		0			0
$151$	5.96120			0.485116			0.242558	−	0.970137i	$-0.422014\pi$
$151$	5.96120			0.485116			0.242558	+	0.970137i	$0.422014\pi$
$152$	−8.20441	−	4.84271i	−0.665466	−	0.392796i
$153$	11.5026	−	5.87086i	0.929930	−	0.474631i
$154$	8.58884	−	5.97299i	0.692109	−	0.481318i
$155$		0			0
$156$	2.53634	−	4.51085i	0.203069	−	0.361157i
$157$	−1.60455	−	1.60455i	−0.128057	−	0.128057i	0.640173	−	0.768231i	$-0.278863\pi$
$157$	−1.60455	−	1.60455i	−0.128057	−	0.128057i	−0.768231	+	0.640173i	$0.778863\pi$
$158$	2.07247	−	11.5370i	0.164877	−	0.917831i
$159$	−14.1020	−	2.22856i	−1.11836	−	0.176736i
$160$		0			0
$161$		−	16.8934i		−	1.33138i
$162$	−8.82478	−	9.17187i	−0.693340	−	0.720610i
$163$	−9.91929	+	9.91929i	−0.776939	+	0.776939i	−0.979309	−	0.202370i	$-0.935136\pi$
$163$	−9.91929	+	9.91929i	−0.776939	+	0.776939i	0.202370	+	0.979309i	$0.435136\pi$
$164$	−7.52160	+	20.2599i	−0.587338	+	1.58204i
$165$		0			0
$166$	−6.02835	−	8.66845i	−0.467891	−	0.672802i
$167$	1.02989	+	1.02989i	0.0796952	+	0.0796952i	0.745831	−	0.666136i	$-0.232053\pi$
$167$	1.02989	+	1.02989i	0.0796952	+	0.0796952i	−0.666136	+	0.745831i	$0.732053\pi$
$168$	−10.1004	+	12.2389i	−0.779259	+	0.944249i
$169$			10.7683i			0.828328i
$170$		0			0
$171$	−3.11598	+	9.61252i	−0.238285	+	0.735088i
$172$	2.99229	−	1.37202i	0.228160	−	0.104615i
$173$	6.58294	+	6.58294i	0.500492	+	0.500492i	0.911591	−	0.411099i	$-0.134855\pi$
$173$	6.58294	+	6.58294i	0.500492	+	0.500492i	−0.411099	+	0.911591i	$0.634855\pi$
$174$	−2.89778	−	5.98478i	−0.219680	−	0.453705i
$175$		0			0
$176$	6.92197	+	5.96127i	0.521763	+	0.449348i
$177$	7.55067	+	10.3851i	0.567543	+	0.780590i
$178$	−16.0506	−	2.88328i	−1.20304	−	0.216111i
$179$			9.12480i			0.682019i	0.940060	+	0.341010i	$0.110769\pi$
$179$			9.12480i			0.682019i	−0.940060	+	0.341010i	$0.889231\pi$
$180$		0			0
$181$			2.94123i			0.218620i	0.994008	+	0.109310i	$0.0348641\pi$
$181$			2.94123i			0.218620i	−0.994008	+	0.109310i	$0.965136\pi$
$182$	−1.20994	+	6.73547i	−0.0896868	+	0.499266i
$183$	9.13690	+	12.5668i	0.675419	+	0.928962i
$184$	14.2848	−	3.68061i	1.05309	−	0.271338i
$185$		0			0
$186$	14.3125	−	6.93001i	1.04945	−	0.508133i
$187$	6.95162	+	6.95162i	0.508353	+	0.508353i
$188$	−2.16638	−	4.72475i	−0.158000	−	0.344588i
$189$	15.0044	+	7.62561i	1.09141	+	0.554682i
$190$		0			0
$191$			1.93237i			0.139822i	0.997553	+	0.0699108i	$0.0222715\pi$
$191$			1.93237i			0.139822i	−0.997553	+	0.0699108i	$0.977729\pi$
$192$	−12.5496	−	5.87422i	−0.905692	−	0.423935i
$193$	6.07278	+	6.07278i	0.437128	+	0.437128i	0.891044	−	0.453916i	$-0.149973\pi$
$193$	6.07278	+	6.07278i	0.437128	+	0.437128i	−0.453916	+	0.891044i	$0.649973\pi$
$194$	4.59175	−	3.19327i	0.329668	−	0.229263i
$195$		0			0
$196$	2.43071	−	6.54728i	0.173622	−	0.467663i
$197$	13.4343	−	13.4343i	0.957153	−	0.957153i	−0.0419662	−	0.999119i	$-0.513362\pi$
$197$	13.4343	−	13.4343i	0.957153	−	0.957153i	0.999119	+	0.0419662i	$0.0133622\pi$
$198$	4.57037	−	8.54362i	0.324802	−	0.607169i
$199$			18.4880i			1.31058i	0.755377	+	0.655290i	$0.227454\pi$
$199$			18.4880i			1.31058i	−0.755377	+	0.655290i	$0.772546\pi$
$200$		0			0
$201$	20.9614	+	3.31256i	1.47851	+	0.233650i
$202$	12.4474	+	2.23601i	0.875795	+	0.157325i
$203$	6.21757	+	6.21757i	0.436388	+	0.436388i
$204$	−12.9982	−	7.30857i	−0.910058	−	0.511702i
$205$		0			0
$206$	2.90497	+	4.17719i	0.202399	+	0.291038i
$207$	−7.11284	−	13.9360i	−0.494376	−	0.968617i
$208$	−5.95905	+	0.444365i	−0.413185	+	0.0308111i
$209$	−7.69249			−0.532101
$210$		0			0
$211$		−	16.4703i		−	1.13386i	−0.823766	−	0.566930i	$-0.808131\pi$
$211$		−	16.4703i		−	1.13386i	0.823766	−	0.566930i	$-0.191869\pi$
$212$	6.87112	+	14.9855i	0.471910	+	1.02921i
$213$	7.51256	+	10.3327i	0.514752	+	0.707983i
$214$	−8.45345	+	5.87884i	−0.577866	+	0.401869i
$215$		0			0
$216$	−3.17907	+	14.3490i	−0.216308	+	0.976325i
$217$	−14.8693	+	14.8693i	−1.00939	+	1.00939i
$218$	−1.95605	−	0.351380i	−0.132480	−	0.0237984i
$219$	4.43829	+	0.701388i	0.299912	+	0.0473954i
$220$		0			0
$221$	−6.43084			−0.432585
$222$	7.56506	+	2.62912i	0.507733	+	0.176455i
$223$	−4.42933	−	4.42933i	−0.296610	−	0.296610i	0.543074	−	0.839685i	$-0.317260\pi$
$223$	−4.42933	−	4.42933i	−0.296610	−	0.296610i	−0.839685	+	0.543074i	$0.817260\pi$
$224$	18.2256	+	1.88960i	1.21775	+	0.126255i
$225$		0			0
$226$	−21.8172	+	15.1725i	−1.45126	+	1.00926i
$227$	−10.1132	+	10.1132i	−0.671238	+	0.671238i	−0.958001	−	0.286764i	$-0.907421\pi$
$227$	−10.1132	+	10.1132i	−0.671238	+	0.671238i	0.286764	+	0.958001i	$0.407421\pi$
$228$	11.2355	−	3.14801i	0.744089	−	0.208482i
$229$	−14.7318			−0.973503			−0.486752	−	0.873540i	$-0.661818\pi$
$229$	−14.7318			−0.973503			−0.486752	+	0.873540i	$0.661818\pi$
$230$		0			0
$231$	−2.00000	+	12.6557i	−0.131590	+	0.832685i
$232$	−3.90287	+	6.61215i	−0.256236	+	0.434109i
$233$	5.91148	−	5.91148i	0.387274	−	0.387274i	−0.486440	−	0.873714i	$-0.661705\pi$
$233$	5.91148	−	5.91148i	0.387274	−	0.387274i	0.873714	+	0.486440i	$0.161705\pi$
$234$	1.83780	+	6.06578i	0.120140	+	0.396532i
$235$		0			0
$236$	5.16016	−	13.8993i	0.335898	−	0.904765i
$237$	8.44224	+	11.6113i	0.548383	+	0.754237i
$238$	19.4086	+	3.48650i	1.25807	+	0.225996i
$239$	24.4787			1.58339			0.791697	−	0.610914i	$-0.209198\pi$
$239$	24.4787			1.58339			0.791697	+	0.610914i	$0.209198\pi$
$240$		0			0
$241$	7.20044			0.463821			0.231911	−	0.972737i	$-0.425502\pi$
$241$	7.20044			0.463821			0.231911	+	0.972737i	$0.425502\pi$
$242$	−8.05142	−	1.44634i	−0.517565	−	0.0929740i
$243$	15.5884	−	0.0268543i	0.999999	−	0.00172270i
$244$	6.24420	−	16.8192i	0.399744	−	1.07674i
$245$		0			0
$246$	−11.5347	−	23.8225i	−0.735423	−	1.51887i
$247$	3.55810	−	3.55810i	0.226397	−	0.226397i
$248$	−15.8129	−	9.33366i	−1.00412	−	0.592688i
$249$	12.7730	+	2.01854i	0.809457	+	0.127920i
$250$		0			0
$251$	−17.5748			−1.10931			−0.554656	−	0.832080i	$-0.687150\pi$
$251$	−17.5748			−1.10931			−0.554656	+	0.832080i	$0.687150\pi$
$252$	−2.25797	−	19.3032i	−0.142239	−	1.21599i
$253$	8.42223	−	8.42223i	0.529501	−	0.529501i
$254$	−11.7625	+	8.18006i	−0.738044	+	0.513263i
$255$		0			0
$256$	2.37304	+	15.8230i	0.148315	+	0.988940i
$257$	1.75603	+	1.75603i	0.109538	+	0.109538i	0.759752	−	0.650213i	$-0.225321\pi$
$257$	1.75603	+	1.75603i	0.109538	+	0.109538i	−0.650213	+	0.759752i	$0.725321\pi$
$258$	−1.32349	+	3.80824i	−0.0823972	+	0.237091i
$259$	−10.5907			−0.658075
$260$		0			0
$261$	7.74698	+	2.51125i	0.479526	+	0.155442i
$262$	3.82585	+	0.687265i	0.236362	+	0.0424594i
$263$	12.6682	−	12.6682i	0.781156	−	0.781156i	−0.198870	−	0.980026i	$-0.563727\pi$
$263$	12.6682	−	12.6682i	0.781156	−	0.781156i	0.980026	+	0.198870i	$0.0637272\pi$
$264$	−11.1373	+	1.06616i	−0.685452	+	0.0656178i
$265$		0			0
$266$	−12.6676	+	8.80948i	−0.776698	+	0.540144i
$267$	16.1541	−	11.7451i	0.988613	−	0.718790i
$268$	−10.2133	−	22.2747i	−0.623879	−	1.36064i
$269$		−	8.45856i		−	0.515728i	−0.966181	−	0.257864i	$-0.916981\pi$
$269$		−	8.45856i		−	0.515728i	0.966181	−	0.257864i	$-0.0830186\pi$
$270$		0			0
$271$	−2.72369			−0.165453			−0.0827263	−	0.996572i	$-0.526363\pi$
$271$	−2.72369			−0.165453			−0.0827263	+	0.996572i	$0.526363\pi$
$272$	1.28046	+	17.1713i	0.0776392	+	1.04116i
$273$	−4.92872	−	6.77889i	−0.298300	−	0.410277i
$274$	−11.6177	−	16.7056i	−0.701852	−	1.00922i
$275$		0			0
$276$	−8.85470	+	15.7480i	−0.532990	+	0.947918i
$277$	−18.4490	−	18.4490i	−1.10849	−	1.10849i	−0.993349	−	0.115146i	$-0.963266\pi$
$277$	−18.4490	−	18.4490i	−1.10849	−	1.10849i	−0.115146	−	0.993349i	$-0.536734\pi$
$278$	1.19298	+	0.214304i	0.0715503	+	0.0128531i
$279$	−6.00561	+	18.5268i	−0.359547	+	1.10917i
$280$		0			0
$281$			21.0738i			1.25716i	0.777746	+	0.628579i	$0.216363\pi$
$281$			21.0738i			1.25716i	−0.777746	+	0.628579i	$0.783637\pi$
$282$	6.01312	+	2.08977i	0.358076	+	0.124444i
$283$	−2.63446	+	2.63446i	−0.156602	+	0.156602i	−0.781059	−	0.624457i	$-0.785320\pi$
$283$	−2.63446	+	2.63446i	−0.156602	+	0.156602i	0.624457	+	0.781059i	$0.285320\pi$
$284$	5.13412	−	13.8291i	0.304654	−	0.820607i
$285$		0			0
$286$	−3.96120	+	2.75477i	−0.234231	+	0.162893i
$287$	24.7492	+	24.7492i	1.46090	+	1.46090i
$288$	15.8306	−	6.11495i	0.932826	−	0.360327i
$289$			1.53076i			0.0900446i
$290$		0			0
$291$	−1.06924	+	6.76597i	−0.0626797	+	0.396628i
$292$	−2.16253	−	4.71635i	−0.126553	−	0.276003i
$293$	−17.1460	−	17.1460i	−1.00168	−	1.00168i	−0.999999	−	0.00168124i	$-0.999465\pi$
$293$	−17.1460	−	17.1460i	−1.00168	−	1.00168i	−0.00168124	−	0.999999i	$-0.500535\pi$
$294$	3.72758	+	7.69856i	0.217397	+	0.448989i
$295$		0			0
$296$	−2.30743	−	8.95538i	−0.134117	−	0.520521i
$297$	3.67873	+	11.2823i	0.213461	+	0.654664i
$298$	1.95987	−	10.9101i	0.113532	−	0.632008i
$299$			7.79128i			0.450581i
$300$		0			0
$301$		−	5.33135i		−	0.307294i
$302$	8.29760	+	1.49056i	0.477473	+	0.0857720i
$303$	−12.5276	+	9.10846i	−0.719694	+	0.523267i
$304$	−10.2091	−	8.79219i	−0.585533	−	0.504267i
$305$		0			0
$306$	17.4788	−	5.29569i	0.999198	−	0.302735i
$307$	3.18267	+	3.18267i	0.181644	+	0.181644i	0.792072	−	0.610428i	$-0.209002\pi$
$307$	3.18267	+	3.18267i	0.181644	+	0.181644i	−0.610428	+	0.792072i	$0.709002\pi$
$308$	13.4486	−	6.16643i	0.766305	−	0.351365i
$309$	−6.15511	−	0.972701i	−0.350152	−	0.0553350i
$310$		0			0
$311$		−	6.88470i		−	0.390395i	−0.980764	−	0.195198i	$-0.937465\pi$
$311$		−	6.88470i		−	0.390395i	0.980764	−	0.195198i	$-0.0625349\pi$
$312$	4.65832	−	5.64461i	0.263725	−	0.319563i
$313$	−2.20044	−	2.20044i	−0.124376	−	0.124376i	0.642179	−	0.766555i	$-0.278031\pi$
$313$	−2.20044	−	2.20044i	−0.124376	−	0.124376i	−0.766555	+	0.642179i	$0.778031\pi$
$314$	−1.83222	−	2.63464i	−0.103398	−	0.148681i
$315$		0			0
$316$	5.76947	−	15.5405i	0.324558	−	0.874219i
$317$	−12.2682	+	12.2682i	−0.689052	+	0.689052i	−0.962022	−	0.272971i	$-0.911994\pi$
$317$	−12.2682	+	12.2682i	−0.689052	+	0.689052i	0.272971	+	0.962022i	$0.411994\pi$
$318$	−19.0718	−	6.62811i	−1.06949	−	0.371686i
$319$			6.19958i			0.347110i
$320$		0			0
$321$	1.96847	−	12.4562i	0.109869	−	0.695239i
$322$	4.22407	−	23.5144i	0.235398	−	1.31041i
$323$	−10.2528	−	10.2528i	−0.570483	−	0.570483i
$324$	−9.99015	−	14.9732i	−0.555008	−	0.831845i
$325$		0			0
$326$	−16.2872	+	11.3267i	−0.902067	+	0.627330i
$327$	1.96866	−	1.43135i	0.108867	−	0.0791540i
$328$	−15.5354	+	26.3198i	−0.857800	+	1.45327i
$329$	−8.41808			−0.464104
$330$		0			0
$331$		−	22.1105i		−	1.21530i	−0.794204	−	0.607651i	$-0.792112\pi$
$331$		−	22.1105i		−	1.21530i	0.794204	−	0.607651i	$-0.207888\pi$
$332$	−6.22358	−	13.5732i	−0.341563	−	0.744929i
$333$	−8.73668	+	4.45915i	−0.478767	+	0.244360i
$334$	1.17602	+	1.69105i	0.0643489	+	0.0925303i
$335$		0			0
$336$	−17.1193	+	14.5102i	−0.933932	+	0.791595i
$337$	−2.03793	+	2.03793i	−0.111013	+	0.111013i	−0.760432	−	0.649418i	$-0.775013\pi$
$337$	−2.03793	+	2.03793i	−0.111013	+	0.111013i	0.649418	+	0.760432i	$0.275013\pi$
$338$	−2.69253	+	14.9887i	−0.146454	+	0.815279i
$339$	5.08036	−	32.1478i	0.275927	−	1.74603i
$340$		0			0
$341$	−14.8262			−0.802885
$342$	−6.74077	+	12.6009i	−0.364499	+	0.681376i
$343$	8.03485	+	8.03485i	0.433841	+	0.433841i
$344$	4.50813	−	1.16156i	0.243062	−	0.0626270i
$345$		0			0
$346$	7.51699	+	10.8090i	0.404116	+	0.581097i
$347$	2.80739	−	2.80739i	0.150709	−	0.150709i	−0.627726	−	0.778435i	$-0.716014\pi$
$347$	2.80739	−	2.80739i	0.150709	−	0.150709i	0.778435	+	0.627726i	$0.216014\pi$
$348$	−2.53707	−	9.05498i	−0.136001	−	0.485398i
$349$	36.8980			1.97511			0.987554	−	0.157283i	$-0.0502735\pi$
$349$	36.8980			1.97511			0.987554	+	0.157283i	$0.0502735\pi$
$350$		0			0
$351$	−6.92010	−	3.51696i	−0.369367	−	0.187721i
$352$	8.14435	+	10.0285i	0.434095	+	0.534520i
$353$	2.00153	−	2.00153i	0.106531	−	0.106531i	−0.651832	−	0.758363i	$-0.725999\pi$
$353$	2.00153	−	2.00153i	0.106531	−	0.106531i	0.758363	+	0.651832i	$0.225999\pi$
$354$	7.91331	+	16.3433i	0.420588	+	0.868638i
$355$		0			0
$356$	−21.6204	−	8.02667i	−1.14588	−	0.425413i
$357$	−19.5337	+	14.2023i	−1.03383	+	0.751668i
$358$	−2.28159	+	12.7011i	−0.120586	+	0.671274i
$359$	−12.9584			−0.683920			−0.341960	−	0.939714i	$-0.611091\pi$
$359$	−12.9584			−0.683920			−0.341960	+	0.939714i	$0.611091\pi$
$360$		0			0
$361$	−7.65447			−0.402867
$362$	−0.735434	+	4.09400i	−0.0386536	+	0.215176i
$363$	8.10334	−	5.89168i	0.425315	−	0.309233i
$364$	−3.36831	+	9.07278i	−0.176548	+	0.475543i
$365$		0			0
$366$	9.57573	+	19.7767i	0.500531	+	1.03375i
$367$	−20.3623	+	20.3623i	−1.06291	+	1.06291i	−0.0650212	+	0.997884i	$0.520711\pi$
$367$	−20.3623	+	20.3623i	−1.06291	+	1.06291i	−0.997884	+	0.0650212i	$0.979289\pi$
$368$	20.8039	−	1.55134i	1.08448	−	0.0808691i
$369$	30.8370	+	9.99605i	1.60531	+	0.520374i
$370$		0			0
$371$	26.6996			1.38617
$372$	21.6549	−	6.06737i	1.12275	−	0.314578i
$373$	10.1764	−	10.1764i	0.526916	−	0.526916i	−0.392735	−	0.919652i	$-0.628471\pi$
$373$	10.1764	−	10.1764i	0.526916	−	0.526916i	0.919652	+	0.392735i	$0.128471\pi$
$374$	7.93799	+	11.4144i	0.410464	+	0.590224i
$375$		0			0
$376$	−1.83407	−	7.11823i	−0.0945850	−	0.367095i
$377$	−2.86757	−	2.86757i	−0.147687	−	0.147687i
$378$	18.9784	+	14.3661i	0.976145	+	0.738913i
$379$	13.0462			0.670137			0.335068	−	0.942194i	$-0.391241\pi$
$379$	13.0462			0.670137			0.335068	+	0.942194i	$0.391241\pi$
$380$		0			0
$381$	2.73902	−	17.3321i	0.140324	−	0.887951i
$382$	−0.483176	+	2.68973i	−0.0247214	+	0.137619i
$383$	11.1099	−	11.1099i	0.567687	−	0.567687i	−0.363793	−	0.931480i	$-0.618518\pi$
$383$	11.1099	−	11.1099i	0.567687	−	0.567687i	0.931480	+	0.363793i	$0.118518\pi$
$384$	−15.9995	−	11.3145i	−0.816469	−	0.577389i
$385$		0			0
$386$	6.93445	+	9.97137i	0.352954	+	0.507529i
$387$	−2.24473	−	4.39803i	−0.114106	−	0.223565i
$388$	7.18986	−	3.29668i	0.365010	−	0.167364i
$389$			14.2176i			0.720861i	0.932786	+	0.360431i	$0.117370\pi$
$389$			14.2176i			0.720861i	−0.932786	+	0.360431i	$0.882630\pi$
$390$		0			0
$391$	22.4509			1.13539
$392$	5.02048	−	8.50559i	0.253573	−	0.429597i
$393$	−3.85052	+	2.79959i	−0.194233	+	0.141221i
$394$	22.0588	−	15.3405i	1.11130	−	0.772842i
$395$		0			0
$396$	8.49793	−	10.7494i	0.427037	−	0.540176i
$397$	24.3286	+	24.3286i	1.22102	+	1.22102i	0.967271	+	0.253746i	$0.0816626\pi$
$397$	24.3286	+	24.3286i	1.22102	+	1.22102i	0.253746	+	0.967271i	$0.418337\pi$
$398$	−4.62280	+	25.7341i	−0.231720	+	1.28993i
$399$	2.94977	−	18.6657i	0.147673	−	0.934455i
$400$		0			0
$401$			21.3193i			1.06463i	0.846545	+	0.532317i	$0.178679\pi$
$401$			21.3193i			1.06463i	−0.846545	+	0.532317i	$0.821321\pi$
$402$	28.3486	+	9.85213i	1.41390	+	0.491380i
$403$	6.85775	−	6.85775i	0.341609	−	0.341609i
$404$	16.7668	+	6.22476i	0.834181	+	0.309694i
$405$		0			0
$406$	7.09979	+	10.2091i	0.352357	+	0.506670i
$407$	−5.28003	−	5.28003i	−0.261721	−	0.261721i
$408$	−16.2652	−	13.4232i	−0.805248	−	0.664545i
$409$		−	0.899012i		−	0.0444533i	−0.999753	−	0.0222266i	$-0.992924\pi$
$409$		−	0.899012i		−	0.0444533i	0.999753	−	0.0222266i	$-0.00707554\pi$
$410$		0			0
$411$	24.6159	+	3.89008i	1.21421	+	0.191883i
$412$	2.99904	+	6.54073i	0.147752	+	0.322239i
$413$	−16.9791	−	16.9791i	−0.835485	−	0.835485i
$414$	−6.41600	−	21.1765i	−0.315329	−	1.04077i
$415$		0			0
$416$	−8.40571	−	0.871492i	−0.412124	−	0.0427284i
$417$	−1.20067	+	0.872972i	−0.0587972	+	0.0427496i
$418$	−10.7074	−	1.92345i	−0.523718	−	0.0940792i
$419$			31.7713i			1.55213i	0.630653	+	0.776065i	$0.282787\pi$
$419$			31.7713i			1.55213i	−0.630653	+	0.776065i	$0.717213\pi$
$420$		0			0
$421$			21.3473i			1.04040i	0.854044	+	0.520201i	$0.174143\pi$
$421$			21.3473i			1.04040i	−0.854044	+	0.520201i	$0.825857\pi$
$422$	4.11828	−	22.9255i	0.200475	−	1.11600i
$423$	−6.94439	+	3.54437i	−0.337648	+	0.172333i
$424$	5.81712	+	22.5769i	0.282504	+	1.09643i
$425$		0			0
$426$	7.87338	+	16.2608i	0.381466	+	0.787841i
$427$	−20.5460	−	20.5460i	−0.994291	−	0.994291i
$428$	−13.2366	+	6.06923i	−0.639815	+	0.293367i
$429$	0.922407	−	5.83686i	0.0445342	−	0.281806i
$430$		0			0
$431$		−	5.92452i		−	0.285374i	−0.989768	−	0.142687i	$-0.954426\pi$
$431$		−	5.92452i		−	0.285374i	0.989768	−	0.142687i	$-0.0455743\pi$
$432$	−8.01292	+	19.1779i	−0.385522	+	0.922699i
$433$	19.7804	+	19.7804i	0.950585	+	0.950585i	0.998835	−	0.0482500i	$-0.0153644\pi$
$433$	19.7804	+	19.7804i	0.950585	+	0.950585i	−0.0482500	+	0.998835i	$0.515364\pi$
$434$	−24.4150	+	16.9791i	−1.17196	+	0.815021i
$435$		0			0
$436$	−2.63483	−	0.978194i	−0.126186	−	0.0468470i
$437$	−12.4218	+	12.4218i	−0.594217	+	0.594217i
$438$	6.00242	+	2.08605i	0.286807	+	0.0996753i
$439$		−	16.2344i		−	0.774827i	−0.921906	−	0.387413i	$-0.873369\pi$
$439$		−	16.2344i		−	0.774827i	0.921906	−	0.387413i	$-0.126631\pi$
$440$		0			0
$441$	−9.96539	−	3.23036i	−0.474542	−	0.153827i
$442$	−8.95130	−	1.60799i	−0.425770	−	0.0764841i
$443$	28.5774	+	28.5774i	1.35775	+	1.35775i	0.876682	+	0.481070i	$0.159752\pi$
$443$	28.5774	+	28.5774i	1.35775	+	1.35775i	0.481070	+	0.876682i	$0.340248\pi$
$444$	9.87266	+	5.55115i	0.468536	+	0.263446i
$445$		0			0
$446$	−5.05781	−	7.27286i	−0.239494	−	0.344380i
$447$	7.98357	+	10.9805i	0.377610	+	0.519359i
$448$	24.8963	+	7.18739i	1.17624	+	0.339572i
$449$	−2.81035			−0.132628			−0.0663142	−	0.997799i	$-0.521124\pi$
$449$	−2.81035			−0.132628			−0.0663142	+	0.997799i	$0.521124\pi$
$450$		0			0
$451$			24.6775i			1.16202i
$452$	−34.1619	+	15.6639i	−1.60684	+	0.736766i
$453$	−8.35110	+	6.07182i	−0.392369	+	0.285279i
$454$	−16.6057	+	11.5482i	−0.779342	+	0.541983i
$455$		0			0
$456$	16.4262	−	1.57247i	0.769227	−	0.0736376i
$457$	29.1068	−	29.1068i	1.36156	−	1.36156i	0.489623	−	0.871934i	$-0.337134\pi$
$457$	29.1068	−	29.1068i	1.36156	−	1.36156i	0.871934	−	0.489623i	$-0.162866\pi$
$458$	−20.5057	−	3.68358i	−0.958166	−	0.172122i
$459$	−10.1343	+	19.9406i	−0.473028	+	0.930747i
$460$		0			0
$461$	−27.6096			−1.28591			−0.642954	−	0.765905i	$-0.722291\pi$
$461$	−27.6096			−1.28591			−0.642954	+	0.765905i	$0.722291\pi$
$462$	−5.94834	+	17.1158i	−0.276742	+	0.796301i
$463$	−15.0078	−	15.0078i	−0.697470	−	0.697470i	0.266395	−	0.963864i	$-0.414168\pi$
$463$	−15.0078	−	15.0078i	−0.697470	−	0.697470i	−0.963864	+	0.266395i	$0.914168\pi$
$464$	−7.08585	+	8.22779i	−0.328953	+	0.381966i
$465$		0			0
$466$	9.70650	−	6.75026i	0.449645	−	0.312700i
$467$	13.7467	−	13.7467i	0.636119	−	0.636119i	−0.313477	−	0.949596i	$-0.601494\pi$
$467$	13.7467	−	13.7467i	0.636119	−	0.636119i	0.949596	+	0.313477i	$0.101494\pi$
$468$	1.04138	+	8.90269i	0.0481380	+	0.411527i
$469$	−39.6867			−1.83256
$470$		0			0
$471$	3.88216	+	0.613503i	0.178881	+	0.0282687i
$472$	10.6580	−	18.0566i	0.490575	−	0.831121i
$473$	2.65796	−	2.65796i	0.122213	−	0.122213i
$474$	8.84770	+	18.2731i	0.406389	+	0.839313i
$475$		0			0
$476$	26.1437	+	9.70595i	1.19829	+	0.444872i
$477$	22.0255	−	11.2417i	1.00848	−	0.514721i
$478$	34.0727	+	6.12072i	1.55845	+	0.279955i
$479$	−37.7789			−1.72616			−0.863081	−	0.505066i	$-0.831468\pi$
$479$	−37.7789			−1.72616			−0.863081	+	0.505066i	$0.831468\pi$
$480$		0			0
$481$	4.88447			0.222713
$482$	10.0225	+	1.80042i	0.456514	+	0.0820069i
$483$	17.2069	+	23.6661i	0.782939	+	1.07684i
$484$	−10.8454	−	4.02641i	−0.492973	−	0.183018i
$485$		0			0
$486$	21.7048	+	3.86040i	0.984549	+	0.175111i
$487$	16.6047	−	16.6047i	0.752429	−	0.752429i	−0.222503	−	0.974932i	$-0.571423\pi$
$487$	16.6047	−	16.6047i	0.752429	−	0.752429i	0.974932	+	0.222503i	$0.0714228\pi$
$488$	12.8970	−	21.8499i	0.583822	−	0.989097i
$489$	3.79265	−	23.9994i	0.171510	−	1.08529i
$490$		0			0
$491$	6.31858			0.285154			0.142577	−	0.989784i	$-0.454461\pi$
$491$	6.31858			0.285154			0.142577	+	0.989784i	$0.454461\pi$
$492$	−10.0988	−	36.0435i	−0.455291	−	1.62497i
$493$	−8.26303	+	8.26303i	−0.372148	+	0.372148i
$494$	5.84232	−	4.06296i	0.262858	−	0.182801i
$495$		0			0
$496$	−19.6767	−	16.9457i	−0.883508	−	0.760886i
$497$	−16.8934	−	16.8934i	−0.757771	−	0.757771i
$498$	17.2745	+	6.00347i	0.774087	+	0.269022i
$499$	29.5722			1.32383			0.661917	−	0.749577i	$-0.269743\pi$
$499$	29.5722			1.32383			0.661917	+	0.749577i	$0.269743\pi$
$500$		0			0
$501$	−2.49178	−	0.393779i	−0.111324	−	0.0175927i
$502$	−24.4630	−	4.39446i	−1.09184	−	0.196134i
$503$	−24.2566	+	24.2566i	−1.08155	+	1.08155i	−0.0851818	+	0.996365i	$0.527147\pi$
$503$	−24.2566	+	24.2566i	−1.08155	+	1.08155i	−0.996365	+	0.0851818i	$0.972853\pi$
$504$	1.68368	−	27.4333i	0.0749970	−	1.22198i
$505$		0			0
$506$	13.8291	−	9.61727i	0.614779	−	0.427540i
$507$	−10.9681	−	15.0854i	−0.487110	−	0.669964i
$508$	−18.4180	+	8.44498i	−0.817165	+	0.374685i
$509$		−	36.5584i		−	1.62042i	−0.586138	−	0.810211i	$-0.699352\pi$
$509$		−	36.5584i		−	1.62042i	0.586138	−	0.810211i	$-0.300648\pi$
$510$		0			0
$511$	−8.40310			−0.371731
$512$	−0.653333	+	22.6180i	−0.0288735	+	0.999583i
$513$	−5.42570	−	16.6400i	−0.239551	−	0.734676i
$514$	2.00519	+	2.88336i	0.0884453	+	0.127180i
$515$		0			0
$516$	−2.79444	+	4.96989i	−0.123018	+	0.218787i
$517$	−4.19685	−	4.19685i	−0.184577	−	0.184577i
$518$	−14.7416	−	2.64813i	−0.647707	−	0.116352i
$519$	−15.9272	−	2.51699i	−0.699126	−	0.110484i
$520$		0			0
$521$		−	29.0118i		−	1.27103i	−0.772089	−	0.635515i	$-0.780788\pi$
$521$		−	29.0118i		−	1.27103i	0.772089	−	0.635515i	$-0.219212\pi$
$522$	10.1554	+	5.43256i	0.444488	+	0.237777i
$523$	−1.09850	+	1.09850i	−0.0480342	+	0.0480342i	−0.730716	−	0.682682i	$-0.760814\pi$
$523$	−1.09850	+	1.09850i	−0.0480342	+	0.0480342i	0.682682	+	0.730716i	$0.260814\pi$
$524$	5.15348	+	1.91325i	0.225131	+	0.0835809i
$525$		0			0
$526$	20.8009	−	14.4657i	0.906963	−	0.630735i
$527$	−19.7609	−	19.7609i	−0.860800	−	0.860800i
$528$	−15.7689	−	1.30077i	−0.686255	−	0.0566088i
$529$		−	4.20044i		−	0.182628i
$530$		0			0
$531$	−21.1556	−	6.85775i	−0.918074	−	0.297601i
$532$	−19.8351	+	9.09477i	−0.859962	+	0.394308i
$533$	−11.4144	−	11.4144i	−0.494412	−	0.494412i
$534$	25.4222	−	12.3092i	1.10012	−	0.532672i
$535$		0			0
$536$	−8.64667	−	33.5586i	−0.373479	−	1.44951i
$537$	−9.29412	−	12.7830i	−0.401071	−	0.551627i
$538$	2.11501	−	11.7738i	0.0911844	−	0.507603i
$539$		−	7.97487i		−	0.343502i
$540$		0			0
$541$		−	1.84481i		−	0.0793147i	−0.999213	−	0.0396574i	$-0.987373\pi$
$541$		−	1.84481i		−	0.0793147i	0.999213	−	0.0396574i	$-0.0126266\pi$
$542$	−3.79120	−	0.681040i	−0.162846	−	0.0292532i
$543$	−2.99581	−	4.12039i	−0.128563	−	0.176823i
$544$	−2.51125	+	24.2214i	−0.107669	+	1.03849i
$545$		0			0
$546$	−5.16544	−	10.6682i	−0.221060	−	0.456555i
$547$	21.0963	+	21.0963i	0.902012	+	0.902012i	0.995610	−	0.0935978i	$-0.0298368\pi$
$547$	21.0963	+	21.0963i	0.902012	+	0.902012i	−0.0935978	+	0.995610i	$0.529837\pi$
$548$	−11.9940	−	26.1581i	−0.512356	−	1.11742i
$549$	−25.5999	−	8.29842i	−1.09258	−	0.354168i
$550$		0			0
$551$		−	9.14366i		−	0.389533i
$552$	−16.2628	+	19.7061i	−0.692192	+	0.838748i
$553$	−18.9839	−	18.9839i	−0.807279	−	0.807279i
$554$	−21.0668	−	30.2929i	−0.895041	−	1.28702i
$555$		0			0
$556$	1.60697	+	0.596593i	0.0681505	+	0.0253012i
$557$	9.36550	−	9.36550i	0.396829	−	0.396829i	−0.480284	−	0.877113i	$-0.659466\pi$
$557$	9.36550	−	9.36550i	0.396829	−	0.396829i	0.877113	+	0.480284i	$0.159466\pi$
$558$	−12.9919	+	24.2864i	−0.549992	+	1.02813i
$559$			2.45884i			0.103998i
$560$		0			0
$561$	−16.8192	−	2.65796i	−0.710107	−	0.112219i
$562$	−5.26936	+	29.3333i	−0.222274	+	1.23735i
$563$	3.03352	+	3.03352i	0.127848	+	0.127848i	0.768135	−	0.640288i	$-0.221185\pi$
$563$	3.03352	+	3.03352i	0.127848	+	0.127848i	−0.640288	+	0.768135i	$0.721185\pi$
$564$	7.84733	+	4.41235i	0.330432	+	0.185794i
$565$		0			0
$566$	−4.32572	+	3.00826i	−0.181823	+	0.126447i
$567$	−28.7869	+	4.60008i	−1.20894	+	0.193185i
$568$	10.6042	−	17.9654i	0.444944	−	0.753813i
$569$	23.6605			0.991898			0.495949	−	0.868352i	$-0.334820\pi$
$569$	23.6605			0.991898			0.495949	+	0.868352i	$0.334820\pi$
$570$		0			0
$571$			13.8475i			0.579498i	0.957103	+	0.289749i	$0.0935718\pi$
$571$			13.8475i			0.579498i	−0.957103	+	0.289749i	$0.906428\pi$
$572$	−6.20254	+	2.84398i	−0.259341	+	0.118913i
$573$	−1.96823	−	2.70707i	−0.0822240	−	0.113090i
$574$	28.2608	+	40.6375i	1.17958	+	1.69618i
$575$		0			0
$576$	23.5641	−	4.55328i	0.981838	−	0.189720i
$577$	7.31424	−	7.31424i	0.304496	−	0.304496i	−0.538274	−	0.842770i	$-0.680923\pi$
$577$	7.31424	−	7.31424i	0.304496	−	0.304496i	0.842770	+	0.538274i	$0.180923\pi$
$578$	−0.382755	+	2.13071i	−0.0159205	+	0.0886260i
$579$	−14.6929	−	2.32193i	−0.610615	−	0.0964963i
$580$		0			0
$581$	−24.1834			−1.00330
$582$	−3.18009	+	9.15043i	−0.131819	+	0.379297i
$583$	13.3112	+	13.3112i	0.551292	+	0.551292i
$584$	−1.83081	−	7.10557i	−0.0757594	−	0.294030i
$585$		0			0
$586$	−19.5788	−	28.1533i	−0.808795	−	1.16300i
$587$	−7.53359	+	7.53359i	−0.310944	+	0.310944i	−0.845275	−	0.534331i	$-0.820564\pi$
$587$	−7.53359	+	7.53359i	−0.310944	+	0.310944i	0.534331	+	0.845275i	$0.320564\pi$
$588$	3.26358	+	11.6479i	0.134588	+	0.480353i
$589$	21.8670			0.901012
$590$		0			0
$591$	−5.13661	+	32.5038i	−0.211292	+	1.33703i
$592$	−0.972558	−	13.0423i	−0.0399719	−	0.536033i
$593$	18.0049	−	18.0049i	0.739373	−	0.739373i	−0.233084	−	0.972457i	$-0.574882\pi$
$593$	18.0049	−	18.0049i	0.739373	−	0.739373i	0.972457	+	0.233084i	$0.0748816\pi$
$594$	2.29949	+	16.6240i	0.0943493	+	0.682091i
$595$		0			0
$596$	5.45601	−	14.6961i	0.223487	−	0.601977i
$597$	−18.8311	−	25.9000i	−0.770705	−	1.06002i
$598$	−1.94816	+	10.8449i	−0.0796660	+	0.443483i
$599$	19.8681			0.811789			0.405895	−	0.913920i	$-0.366960\pi$
$599$	19.8681			0.811789			0.405895	+	0.913920i	$0.366960\pi$
$600$		0			0
$601$	−16.4386			−0.670546			−0.335273	−	0.942121i	$-0.608828\pi$
$601$	−16.4386			−0.670546			−0.335273	+	0.942121i	$0.608828\pi$
$602$	1.33307	−	7.42088i	0.0543318	−	0.302453i
$603$	−32.7391	+	16.7098i	−1.33324	+	0.680476i
$604$	11.1770	+	4.14951i	0.454786	+	0.168841i
$605$		0			0
$606$	−19.7151	+	9.54591i	−0.800873	+	0.387776i
$607$	17.5088	−	17.5088i	0.710659	−	0.710659i	−0.256014	−	0.966673i	$-0.582409\pi$
$607$	17.5088	−	17.5088i	0.710659	−	0.710659i	0.966673	+	0.256014i	$0.0824094\pi$
$608$	−12.0120	−	14.7909i	−0.487150	−	0.599849i
$609$	−15.0432	−	2.37730i	−0.609581	−	0.0963329i
$610$		0			0
$611$	3.88245			0.157067
$612$	25.6535	−	3.00080i	1.03698	−	0.121300i
$613$	−24.2075	+	24.2075i	−0.977730	+	0.977730i	−0.999757	−	0.0220274i	$-0.992988\pi$
$613$	−24.2075	+	24.2075i	−0.977730	+	0.977730i	0.0220274	+	0.999757i	$0.492988\pi$
$614$	3.63425	+	5.22586i	0.146667	+	0.210899i
$615$		0			0
$616$	20.2614	−	5.22053i	0.816356	−	0.210341i
$617$	3.33572	+	3.33572i	0.134291	+	0.134291i	0.771057	−	0.636766i	$-0.219728\pi$
$617$	3.33572	+	3.33572i	0.134291	+	0.134291i	−0.636766	+	0.771057i	$0.719728\pi$
$618$	−8.32429	−	2.89298i	−0.334852	−	0.116373i
$619$	−46.6044			−1.87319			−0.936595	−	0.350413i	$-0.886041\pi$
$619$	−46.6044			−1.87319			−0.936595	+	0.350413i	$0.886041\pi$
$620$		0			0
$621$	24.1590	+	12.2782i	0.969468	+	0.492707i
$622$	1.72147	−	9.58304i	0.0690247	−	0.384245i
$623$	−26.4110	+	26.4110i	−1.05814	+	1.05814i
$624$	7.89546	−	6.69214i	0.316071	−	0.267900i
$625$		0			0
$626$	−2.51266	−	3.61307i	−0.100426	−	0.144407i
$627$	10.7765	−	7.83524i	0.430371	−	0.312909i
$628$	−1.89156	−	4.12538i	−0.0754815	−	0.164620i
$629$		−	14.0748i		−	0.561201i
$630$		0			0
$631$	−20.4082			−0.812437			−0.406219	−	0.913776i	$-0.633153\pi$
$631$	−20.4082			−0.812437			−0.406219	+	0.913776i	$0.633153\pi$
$632$	11.9165	−	20.1887i	0.474013	−	0.803062i
$633$	16.7759	+	23.0733i	0.666782	+	0.917082i
$634$	−20.1441	+	14.0090i	−0.800025	+	0.556367i
$635$		0			0
$636$	−24.8894	−	13.9947i	−0.986928	−	0.554924i
$637$	3.68872	+	3.68872i	0.146152	+	0.146152i
$638$	−1.55016	+	8.62940i	−0.0613715	+	0.341641i
$639$	−21.0488	−	6.82314i	−0.832678	−	0.269919i
$640$		0			0
$641$			13.1821i			0.520663i	0.965519	+	0.260331i	$0.0838318\pi$
$641$			13.1821i			0.520663i	−0.965519	+	0.260331i	$0.916168\pi$
$642$	5.85458	−	16.8460i	0.231062	−	0.664860i
$643$	22.6851	−	22.6851i	0.894614	−	0.894614i	−0.100339	−	0.994953i	$-0.531993\pi$
$643$	22.6851	−	22.6851i	0.894614	−	0.894614i	0.994953	+	0.100339i	$0.0319928\pi$
$644$	11.7592	−	31.6743i	0.463379	−	1.24814i
$645$		0			0
$646$	−11.7076	−	16.8349i	−0.460630	−	0.662361i
$647$	19.2111	+	19.2111i	0.755268	+	0.755268i	0.975457	−	0.220189i	$-0.0706675\pi$
$647$	19.2111	+	19.2111i	0.755268	+	0.755268i	−0.220189	+	0.975457i	$0.570668\pi$
$648$	−10.1617	−	23.3397i	−0.399188	−	0.916869i
$649$		−	16.9299i		−	0.664557i
$650$		0			0
$651$	5.68528	−	35.9756i	0.222824	−	1.41000i
$652$	−25.5029	+	11.6936i	−0.998772	+	0.457955i
$653$	−6.30369	−	6.30369i	−0.246683	−	0.246683i	0.572925	−	0.819608i	$-0.305809\pi$
$653$	−6.30369	−	6.30369i	−0.246683	−	0.246683i	−0.819608	+	0.572925i	$0.805809\pi$
$654$	3.09815	−	1.50010i	0.121147	−	0.0586585i
$655$		0			0
$656$	−28.2054	+	32.7508i	−1.10123	+	1.27871i
$657$	−6.93204	+	3.53807i	−0.270444	+	0.138033i
$658$	−11.7174	−	2.10488i	−0.456792	−	0.0820568i
$659$			33.0388i			1.28701i	0.765442	+	0.643505i	$0.222520\pi$
$659$			33.0388i			1.28701i	−0.765442	+	0.643505i	$0.777480\pi$
$660$		0			0
$661$			1.50452i			0.0585192i	0.999572	+	0.0292596i	$0.00931495\pi$
$661$			1.50452i			0.0585192i	−0.999572	+	0.0292596i	$0.990685\pi$
$662$	5.52857	−	30.7763i	0.214874	−	1.19616i
$663$	9.00901	−	6.55017i	0.349881	−	0.254388i
$664$	−5.26891	−	20.4492i	−0.204474	−	0.793584i
$665$		0			0
$666$	−13.2759	+	4.02229i	−0.514429	+	0.155860i
$667$	10.0111	+	10.0111i	0.387630	+	0.387630i
$668$	1.21411	+	2.64789i	0.0469751	+	0.102450i
$669$	10.7166	+	1.69356i	0.414328	+	0.0654768i
$670$		0			0
$671$		−	20.4865i		−	0.790873i
$672$	−27.4570	+	15.9166i	−1.05918	+	0.613998i
$673$	−29.5487	−	29.5487i	−1.13902	−	1.13902i	−0.988627	−	0.150391i	$-0.951947\pi$
$673$	−29.5487	−	29.5487i	−1.13902	−	1.13902i	−0.150391	−	0.988627i	$-0.548053\pi$
$674$	−3.34624	+	2.32710i	−0.128892	+	0.0896365i
$675$		0			0
$676$	−7.49565	+	20.1900i	−0.288294	+	0.776540i
$677$	−16.5034	+	16.5034i	−0.634278	+	0.634278i	−0.949138	−	0.314860i	$-0.898042\pi$
$677$	−16.5034	+	16.5034i	−0.634278	+	0.634278i	0.314860	+	0.949138i	$0.398042\pi$
$678$	15.1099	−	43.4773i	0.580291	−	1.66974i
$679$		−	12.8102i		−	0.491609i
$680$		0			0
$681$	3.86680	−	24.4686i	0.148176	−	0.937637i
$682$	−20.6371	−	3.70719i	−0.790236	−	0.141956i
$683$	1.06473	+	1.06473i	0.0407406	+	0.0407406i	0.727184	−	0.686443i	$-0.240829\pi$
$683$	1.06473	+	1.06473i	0.0407406	+	0.0407406i	−0.686443	+	0.727184i	$0.740829\pi$
$684$	−12.5335	+	15.8541i	−0.479229	+	0.606195i
$685$		0			0
$686$	9.17492	+	13.1930i	0.350300	+	0.503712i
$687$	20.6379	−	15.0052i	0.787384	−	0.572482i
$688$	6.56545	−	0.489584i	0.250306	−	0.0186652i
$689$	−12.3139			−0.469124
$690$		0			0
$691$			16.7696i			0.637945i	0.947764	+	0.318972i	$0.103338\pi$
$691$			16.7696i			0.637945i	−0.947764	+	0.318972i	$0.896662\pi$
$692$	7.76043	+	16.9250i	0.295007	+	0.643393i
$693$	−10.0888	−	19.7666i	−0.383240	−	0.750872i
$694$	4.60967	−	3.20573i	0.174981	−	0.121688i
$695$		0			0
$696$	−1.26729	−	13.2383i	−0.0480366	−	0.501797i
$697$	−32.8911	+	32.8911i	−1.24584	+	1.24584i
$698$	51.3596	+	9.22610i	1.94399	+	0.349213i
$699$	−2.26026	+	14.3026i	−0.0854908	+	0.540974i
$700$		0			0
$701$	40.5328			1.53090			0.765451	−	0.643495i	$-0.222516\pi$
$701$	40.5328			1.53090			0.765451	+	0.643495i	$0.222516\pi$
$702$	−8.75292	−	6.62570i	−0.330358	−	0.250071i
$703$	7.78743	+	7.78743i	0.293709	+	0.293709i
$704$	8.82884	+	15.9954i	0.332749	+	0.602850i
$705$		0			0
$706$	3.28646	−	2.28553i	0.123688	−	0.0860169i
$707$	20.4820	−	20.4820i	0.770306	−	0.770306i
$708$	6.92827	+	24.7275i	0.260380	+	0.929316i
$709$	−22.2655			−0.836199			−0.418099	−	0.908401i	$-0.637304\pi$
$709$	−22.2655			−0.836199			−0.418099	+	0.908401i	$0.637304\pi$
$710$		0			0
$711$	−23.6536	−	7.66751i	−0.887079	−	0.287554i
$712$	−28.0871	−	16.5786i	−1.05261	−	0.621310i
$713$	−23.9414	+	23.9414i	−0.896611	+	0.896611i
$714$	−30.7408	+	14.8845i	−1.15045	+	0.557037i
$715$		0			0
$716$	−6.35165	+	17.1086i	−0.237372	+	0.639378i
$717$	−34.2924	+	24.9329i	−1.28067	+	0.931137i
$718$	−18.0373	−	3.24017i	−0.673146	−	0.120922i
$719$	36.9961			1.37972			0.689861	−	0.723942i	$-0.257672\pi$
$719$	36.9961			1.37972			0.689861	+	0.723942i	$0.257672\pi$
$720$		0			0
$721$	11.6536			0.434003
$722$	−10.6545	−	1.91395i	−0.396520	−	0.0712297i
$723$	−10.0872	+	7.33405i	−0.375145	+	0.272756i
$724$	−2.04735	+	5.51468i	−0.0760892	+	0.204952i
$725$		0			0
$726$	12.7525	−	6.17465i	0.473289	−	0.229163i
$727$	25.8439	−	25.8439i	0.958497	−	0.958497i	−0.0406756	−	0.999172i	$-0.512951\pi$
$727$	25.8439	−	25.8439i	0.958497	−	0.958497i	0.999172	+	0.0406756i	$0.0129510\pi$
$728$	−6.95705	+	11.7865i	−0.257846	+	0.436836i
$729$	−21.8106	+	15.9153i	−0.807800	+	0.589456i
$730$		0			0
$731$	7.08525			0.262058
$732$	8.38375	+	29.9222i	0.309872	+	1.10596i
$733$	37.3652	−	37.3652i	1.38012	−	1.38012i	0.535719	−	0.844397i	$-0.320041\pi$
$733$	37.3652	−	37.3652i	1.38012	−	1.38012i	0.844397	−	0.535719i	$-0.179959\pi$
$734$	−33.4345	+	23.2515i	−1.23409	+	0.858230i
$735$		0			0
$736$	29.3455	+	3.04250i	1.08169	+	0.112148i
$737$	−19.7859	−	19.7859i	−0.728824	−	0.728824i
$738$	40.4236	+	21.6244i	1.48801	+	0.796005i
$739$	1.28705			0.0473450			0.0236725	−	0.999720i	$-0.492464\pi$
$739$	1.28705			0.0473450			0.0236725	+	0.999720i	$0.492464\pi$
$740$		0			0
$741$	−1.36044	+	8.60870i	−0.0499772	+	0.316248i
$742$	37.1641	+	6.67605i	1.36434	+	0.245085i
$743$	7.11771	−	7.11771i	0.261123	−	0.261123i	−0.564387	−	0.825510i	$-0.690887\pi$
$743$	7.11771	−	7.11771i	0.261123	−	0.261123i	0.825510	+	0.564387i	$0.190887\pi$
$744$	31.6593	−	3.03072i	1.16068	−	0.111111i
$745$		0			0
$746$	16.7095	−	11.6204i	0.611777	−	0.425452i
$747$	−19.9498	+	10.1823i	−0.729925	+	0.372549i
$748$	8.19506	+	17.8729i	0.299641	+	0.653499i
$749$			23.5836i			0.861727i
$750$		0			0
$751$	−24.0090			−0.876102			−0.438051	−	0.898950i	$-0.644331\pi$
$751$	−24.0090			−0.876102			−0.438051	+	0.898950i	$0.644331\pi$
$752$	−0.773042	−	10.3667i	−0.0281899	−	0.378034i
$753$	24.6207	−	17.9009i	0.897227	−	0.652346i
$754$	−3.27445	−	4.70848i	−0.119248	−	0.171473i
$755$		0			0
$756$	22.8246	+	24.7421i	0.830122	+	0.899861i
$757$	5.24365	+	5.24365i	0.190584	+	0.190584i	0.795948	−	0.605365i	$-0.206973\pi$
$757$	5.24365	+	5.24365i	0.190584	+	0.190584i	−0.605365	+	0.795948i	$0.706973\pi$
$758$	18.1594	+	3.26210i	0.659579	+	0.118485i
$759$	−3.22025	+	20.3773i	−0.116888	+	0.739649i
$760$		0			0
$761$		−	41.1375i		−	1.49123i	−0.666376	−	0.745616i	$-0.732155\pi$
$761$		−	41.1375i		−	1.49123i	0.666376	−	0.745616i	$-0.267845\pi$
$762$	8.14630	−	23.4403i	0.295109	−	0.849152i
$763$	−3.21866	+	3.21866i	−0.116523	+	0.116523i
$764$	−1.34510	+	3.62311i	−0.0486639	+	0.131080i
$765$		0			0
$766$	18.2421	−	12.6862i	0.659115	−	0.458372i
$767$	7.83080	+	7.83080i	0.282754	+	0.282754i
$768$	−19.4411	−	19.7496i	−0.701519	−	0.712651i
$769$		−	43.5085i		−	1.56896i	−0.620156	−	0.784478i	$-0.712931\pi$
$769$		−	43.5085i		−	1.56896i	0.620156	−	0.784478i	$-0.287069\pi$
$770$		0			0
$771$	−4.24865	−	0.671420i	−0.153012	−	0.0241806i
$772$	7.15902	+	15.6134i	0.257659	+	0.561938i
$773$	34.3280	+	34.3280i	1.23469	+	1.23469i	0.962141	+	0.272551i	$0.0878672\pi$
$773$	34.3280	+	34.3280i	1.23469	+	1.23469i	0.272551	+	0.962141i	$0.412133\pi$
$774$	−2.02481	−	6.68305i	−0.0727804	−	0.240217i
$775$		0			0
$776$	10.8321	−	2.79099i	0.388850	−	0.100191i
$777$	14.8366	−	10.7872i	0.532260	−	0.386990i
$778$	−3.55501	+	19.7900i	−0.127453	+	0.709505i
$779$		−	36.3965i		−	1.30404i
$780$		0			0
$781$		−	16.8445i		−	0.602742i
$782$	31.2502	+	5.61370i	1.11751	+	0.200746i
$783$	−13.4106	+	4.37271i	−0.479257	+	0.156268i
$784$	9.11494	−	10.5839i	0.325534	−	0.377996i
$785$		0			0
$786$	−6.05968	+	2.93405i	−0.216142	+	0.104654i
$787$	−7.25839	−	7.25839i	−0.258734	−	0.258734i	0.565805	−	0.824539i	$-0.308565\pi$
$787$	−7.25839	−	7.25839i	−0.258734	−	0.258734i	−0.824539	+	0.565805i	$0.808565\pi$
$788$	34.5401	−	15.8373i	1.23044	−	0.564180i
$789$	−4.84370	+	30.6503i	−0.172440	+	1.09118i
$790$		0			0
$791$			60.8662i			2.16415i
$792$	14.5164	−	12.8375i	0.515816	−	0.456162i
$793$	9.47588	+	9.47588i	0.336499	+	0.336499i
$794$	27.7806	+	39.9470i	0.985896	+	1.41766i
$795$		0			0
$796$	−12.8693	+	34.6642i	−0.456139	+	1.22864i
$797$	8.85790	−	8.85790i	0.313763	−	0.313763i	−0.532602	−	0.846366i	$-0.678786\pi$
$797$	8.85790	−	8.85790i	0.313763	−	0.313763i	0.846366	+	0.532602i	$0.178786\pi$
$798$	8.77312	−	25.2439i	0.310565	−	0.893624i
$799$		−	11.1874i		−	0.395783i
$800$		0			0
$801$	−10.6673	+	32.9077i	−0.376910	+	1.16273i
$802$	−5.33074	+	29.6750i	−0.188235	+	1.04786i
$803$	−4.18939	−	4.18939i	−0.147840	−	0.147840i
$804$	36.9960	+	20.8019i	1.30475	+	0.733626i
$805$		0			0
$806$	11.2603	−	7.83080i	0.396626	−	0.275828i
$807$	8.61553	+	11.8497i	0.303281	+	0.417128i
$808$	21.7818	+	12.8569i	0.766283	+	0.452304i
$809$	−2.43744			−0.0856959			−0.0428480	−	0.999082i	$-0.513643\pi$
$809$	−2.43744			−0.0856959			−0.0428480	+	0.999082i	$0.513643\pi$
$810$		0			0
$811$		−	1.17131i		−	0.0411302i	−0.999789	−	0.0205651i	$-0.993453\pi$
$811$		−	1.17131i		−	0.0411302i	0.999789	−	0.0205651i	$-0.00654654\pi$
$812$	7.32971	+	15.9857i	0.257223	+	0.560987i
$813$	3.81564	−	2.77423i	0.133820	−	0.0972967i
$814$	−6.02921	−	8.66968i	−0.211324	−	0.303872i
$815$		0			0
$816$	−19.2837	−	22.7511i	−0.675065	−	0.796449i
$817$	−3.92018	+	3.92018i	−0.137150	+	0.137150i
$818$	0.224792	−	1.25136i	0.00785965	−	0.0437529i
$819$	13.8094	+	4.47642i	0.482539	+	0.156419i
$820$		0			0
$821$	43.2743			1.51028			0.755142	−	0.655562i	$-0.227568\pi$
$821$	43.2743			1.51028			0.755142	+	0.655562i	$0.227568\pi$
$822$	33.2910	+	11.5698i	1.16116	+	0.403542i
$823$	−33.8787	−	33.8787i	−1.18094	−	1.18094i	−0.979501	−	0.201437i	$-0.935439\pi$
$823$	−33.8787	−	33.8787i	−1.18094	−	1.18094i	−0.201437	−	0.979501i	$-0.564561\pi$
$824$	2.53901	+	9.85415i	0.0884505	+	0.343286i
$825$		0			0
$826$	−19.3882	−	27.8792i	−0.674603	−	0.970042i
$827$	−10.2673	+	10.2673i	−0.357030	+	0.357030i	−0.862717	−	0.505687i	$-0.831239\pi$
$827$	−10.2673	+	10.2673i	−0.357030	+	0.357030i	0.505687	+	0.862717i	$0.331239\pi$
$828$	−3.63561	−	31.0805i	−0.126346	−	1.08012i
$829$	31.4237			1.09139			0.545695	−	0.837984i	$-0.316266\pi$
$829$	31.4237			1.09139			0.545695	+	0.837984i	$0.316266\pi$
$830$		0			0
$831$	44.6368	+	7.05400i	1.54843	+	0.244701i
$832$	−11.4823	−	3.31485i	−0.398076	−	0.114922i
$833$	10.6292	−	10.6292i	0.368280	−	0.368280i
$834$	−1.88954	+	0.914899i	−0.0654293	+	0.0316804i
$835$		0			0
$836$	−14.4231	−	5.35464i	−0.498833	−	0.185194i
$837$	−10.4573	−	32.0714i	−0.361457	−	1.10855i
$838$	−7.94419	+	44.2235i	−0.274428	+	1.52768i
$839$	2.39839			0.0828015			0.0414007	−	0.999143i	$-0.486818\pi$
$839$	2.39839			0.0828015			0.0414007	+	0.999143i	$0.486818\pi$
$840$		0			0
$841$	21.6309			0.745893
$842$	−5.33774	+	29.7140i	−0.183951	+	1.02401i
$843$	−21.4649	−	29.5224i	−0.739289	−	1.01681i
$844$	11.4647	−	30.8810i	0.394632	−	1.06297i
$845$		0			0
$846$	−10.5524	+	3.19713i	−0.362798	+	0.109920i
$847$	−13.2485	+	13.2485i	−0.455225	+	0.455225i
$848$	2.45186	+	32.8800i	0.0841971	+	1.12911i
$849$	1.00729	−	6.37397i	0.0345700	−	0.218754i
$850$		0			0
$851$	−17.0524			−0.584548
$852$	6.89330	+	24.6027i	0.236161	+	0.842875i
$853$	−21.9385	+	21.9385i	−0.751159	+	0.751159i	−0.974695	−	0.223537i	$-0.928240\pi$
$853$	−21.9385	+	21.9385i	−0.751159	+	0.751159i	0.223537	+	0.974695i	$0.428240\pi$
$854$	−23.4613	−	33.7360i	−0.802828	−	1.15442i
$855$		0			0
$856$	−19.9420	+	5.13824i	−0.681605	+	0.175621i
$857$	30.2305	+	30.2305i	1.03265	+	1.03265i	0.999449	+	0.0332059i	$0.0105717\pi$
$857$	30.2305	+	30.2305i	1.03265	+	1.03265i	0.0332059	+	0.999449i	$0.489428\pi$
$858$	2.74340	−	7.89388i	0.0936580	−	0.269493i
$859$	45.9867			1.56905			0.784523	−	0.620099i	$-0.212908\pi$
$859$	45.9867			1.56905			0.784523	+	0.620099i	$0.212908\pi$
$860$		0			0
$861$	−59.8797	−	9.46286i	−2.04069	−	0.322494i
$862$	1.48139	−	8.24654i	0.0504562	−	0.280878i
$863$	12.2703	−	12.2703i	0.417687	−	0.417687i	−0.466719	−	0.884406i	$-0.654564\pi$
$863$	12.2703	−	12.2703i	0.417687	−	0.417687i	0.884406	+	0.466719i	$0.154564\pi$
$864$	−15.9488	+	24.6908i	−0.542588	+	0.839999i
$865$		0			0
$866$	22.5870	+	32.4789i	0.767539	+	1.10368i
$867$	−1.55916	−	2.14445i	−0.0529520	−	0.0728294i
$868$	−38.2295	+	17.5289i	−1.29759	+	0.594971i
$869$		−	18.9290i		−	0.642121i
$870$		0			0
$871$	18.3037			0.620196
$872$	−3.42292	−	2.02040i	−0.115915	−	0.0684195i
$873$	−5.39363	−	10.5676i	−0.182547	−	0.357658i
$874$	−20.3963	+	14.1844i	−0.689917	+	0.479793i
$875$		0			0
$876$	7.83337	+	4.40451i	0.264665	+	0.148814i
$877$	23.5029	+	23.5029i	0.793638	+	0.793638i	0.982084	−	0.188446i	$-0.0603449\pi$
$877$	23.5029	+	23.5029i	0.793638	+	0.793638i	−0.188446	+	0.982084i	$0.560345\pi$
$878$	4.05931	−	22.5972i	0.136995	−	0.762620i
$879$	41.4841	+	6.55579i	1.39922	+	0.221121i
$880$		0			0
$881$			22.0210i			0.741907i	0.928652	+	0.370953i	$0.120969\pi$
$881$			22.0210i			0.741907i	−0.928652	+	0.370953i	$0.879031\pi$
$882$	−13.0634	−	6.98822i	−0.439868	−	0.235306i
$883$	3.98395	−	3.98395i	0.134070	−	0.134070i	−0.636887	−	0.770957i	$-0.719778\pi$
$883$	3.98395	−	3.98395i	0.134070	−	0.134070i	0.770957	+	0.636887i	$0.219778\pi$
$884$	−12.0575	−	4.47642i	−0.405539	−	0.150558i
$885$		0			0
$886$	32.6322	+	46.9234i	1.09630	+	1.57642i
$887$	10.9002	+	10.9002i	0.365994	+	0.365994i	0.866014	−	0.500020i	$-0.166674\pi$
$887$	10.9002	+	10.9002i	0.365994	+	0.365994i	−0.500020	+	0.866014i	$0.666674\pi$
$888$	12.3541	+	10.1954i	0.414575	+	0.342136i
$889$			32.8152i			1.10059i
$890$		0			0
$891$	−16.6452	−	12.0584i	−0.557635	−	0.403972i
$892$	−5.22161	−	11.3880i	−0.174832	−	0.381299i
$893$	6.18988	+	6.18988i	0.207136	+	0.207136i
$894$	8.36700	+	17.2803i	0.279834	+	0.577941i
$895$		0			0
$896$	32.8569	+	16.2295i	1.09767	+	0.542190i
$897$	−7.93586	−	10.9149i	−0.264971	−	0.364437i
$898$	−3.91182	−	0.702708i	−0.130539	−	0.0234497i
$899$		−	17.6232i		−	0.587765i
$900$		0			0
$901$			35.4832i			1.18212i
$902$	−6.17044	+	34.3495i	−0.205453	+	1.14371i
$903$	5.43028	+	7.46873i	0.180708	+	0.248544i
$904$	−51.4677	+	13.2611i	−1.71179	+	0.441057i
$905$		0			0
$906$	−13.1424	+	6.36344i	−0.436627	+	0.211411i
$907$	−0.400640	−	0.400640i	−0.0133030	−	0.0133030i	0.700424	−	0.713727i	$-0.252994\pi$
$907$	−0.400640	−	0.400640i	−0.0133030	−	0.0133030i	−0.713727	+	0.700424i	$0.752994\pi$
$908$	−26.0015	+	11.9222i	−0.862891	+	0.395651i
$909$	8.27258	−	25.5202i	0.274384	−	0.846452i
$910$		0			0
$911$			17.8858i			0.592583i	0.955098	+	0.296291i	$0.0957499\pi$
$911$			17.8858i			0.592583i	−0.955098	+	0.296291i	$0.904250\pi$
$912$	23.2574	+	1.91849i	0.770128	+	0.0635274i
$913$	−12.0567	−	12.0567i	−0.399019	−	0.399019i
$914$	47.7926	−	33.2367i	1.58084	−	1.09937i
$915$		0			0
$916$	−27.6215	−	10.2546i	−0.912638	−	0.338821i
$917$	6.29539	−	6.29539i	0.207892	−	0.207892i
$918$	−19.0923	+	25.2220i	−0.630138	+	0.832448i
$919$		−	26.4904i		−	0.873838i	−0.899501	−	0.436919i	$-0.856070\pi$
$919$		−	26.4904i		−	0.873838i	0.899501	−	0.436919i	$-0.143930\pi$
$920$		0			0
$921$	−7.70035	−	1.21690i	−0.253735	−	0.0400981i
$922$	−38.4307	−	6.90359i	−1.26565	−	0.227358i
$923$	7.79128	+	7.79128i	0.256453	+	0.256453i
$924$	−12.5594	+	22.3368i	−0.413174	+	0.734826i
$925$		0			0
$926$	−17.1372	−	24.6424i	−0.563164	−	0.809799i
$927$	9.61350	−	4.90667i	0.315749	−	0.161156i
$928$	−11.9203	+	9.68077i	−0.391304	+	0.317787i
$929$	1.35917			0.0445930			0.0222965	−	0.999751i	$-0.492902\pi$
$929$	1.35917			0.0445930			0.0222965	+	0.999751i	$0.492902\pi$
$930$		0			0
$931$			11.7620i			0.385485i
$932$	15.1987	−	6.96886i	0.497849	−	0.228273i
$933$	7.01246	+	9.64483i	0.229578	+	0.315757i
$934$	22.5717	−	15.6972i	0.738568	−	0.513627i
$935$		0			0
$936$	−0.776518	+	12.6523i	−0.0253813	+	0.413555i
$937$	23.4121	−	23.4121i	0.764841	−	0.764841i	−0.212352	−	0.977193i	$-0.568112\pi$
$937$	23.4121	−	23.4121i	0.764841	−	0.764841i	0.977193	+	0.212352i	$0.0681123\pi$
$938$	−55.2413	−	9.92339i	−1.80369	−	0.324010i
$939$	5.32388	+	0.841340i	0.173738	+	0.0274561i
$940$		0			0
$941$	−24.1656			−0.787776			−0.393888	−	0.919159i	$-0.628870\pi$
$941$	−24.1656			−0.787776			−0.393888	+	0.919159i	$0.628870\pi$
$942$	5.25031	+	1.82466i	0.171064	+	0.0594507i
$943$	39.8492	+	39.8492i	1.29767	+	1.29767i
$944$	19.3502	−	22.4686i	0.629795	−	0.731290i
$945$		0			0
$946$	4.36431	−	3.03510i	0.141896	−	0.0986795i
$947$	−19.2733	+	19.2733i	−0.626298	+	0.626298i	−0.947135	−	0.320837i	$-0.896036\pi$
$947$	−19.2733	+	19.2733i	−0.626298	+	0.626298i	0.320837	+	0.947135i	$0.396036\pi$
$948$	7.74635	+	27.6473i	0.251590	+	0.897942i
$949$	3.87554			0.125805
$950$		0			0
$951$	4.69076	−	29.6825i	0.152108	−	0.962521i
$952$	33.9633	+	20.0471i	1.10076	+	0.649730i
$953$	0.681413	−	0.681413i	0.0220731	−	0.0220731i	−0.695984	−	0.718057i	$-0.745032\pi$
$953$	0.681413	−	0.681413i	0.0220731	−	0.0220731i	0.718057	+	0.695984i	$0.245032\pi$
$954$	33.4689	−	10.1403i	1.08360	−	0.328306i
$955$		0			0
$956$	45.8965	+	17.0393i	1.48440	+	0.551090i
$957$	−6.31462	−	8.68504i	−0.204123	−	0.280747i
$958$	−52.5857	−	9.44635i	−1.69897	−	0.305198i
$959$	−46.6058			−1.50498
$960$		0			0
$961$	11.1456			0.359534
$962$	6.79886	+	1.22133i	0.219204	+	0.0393772i
$963$	9.92972	+	19.4550i	0.319981	+	0.626929i
$964$	13.5005	+	5.01213i	0.434822	+	0.161430i
$965$		0			0
$966$	18.0333	+	37.2440i	0.580211	+	1.19831i
$967$	−25.1663	+	25.1663i	−0.809294	+	0.809294i	−0.984527	−	0.175233i	$-0.943932\pi$
$967$	−25.1663	+	25.1663i	−0.809294	+	0.809294i	0.175233	+	0.984527i	$0.443932\pi$
$968$	−14.0893	−	8.31631i	−0.452847	−	0.267296i
$969$	24.8064	+	3.92018i	0.796896	+	0.125934i
$970$		0			0
$971$	−33.6303			−1.07925			−0.539623	−	0.841907i	$-0.681433\pi$
$971$	−33.6303			−1.07925			−0.539623	+	0.841907i	$0.681433\pi$
$972$	29.2463	+	10.8005i	0.938077	+	0.346428i
$973$	1.96304	−	1.96304i	0.0629321	−	0.0629321i
$974$	27.2644	−	18.9607i	0.873609	−	0.607540i
$975$		0			0
$976$	23.4152	−	27.1888i	0.749503	−	0.870291i
$977$	7.94992	+	7.94992i	0.254341	+	0.254341i	0.822748	−	0.568407i	$-0.192440\pi$
$977$	7.94992	+	7.94992i	0.254341	+	0.254341i	−0.568407	+	0.822748i	$0.692440\pi$
$978$	11.2800	−	32.4572i	0.360694	−	1.03787i
$979$	−26.3346			−0.841657
$980$		0			0
$981$	−1.30000	+	4.01039i	−0.0415058	+	0.128042i
$982$	8.79505	+	1.57992i	0.280661	+	0.0504172i
$983$	13.3438	−	13.3438i	0.425602	−	0.425602i	−0.461525	−	0.887127i	$-0.652698\pi$
$983$	13.3438	−	13.3438i	0.425602	−	0.425602i	0.887127	+	0.461525i	$0.152698\pi$
$984$	−5.04448	−	52.6953i	−0.160812	−	1.67986i
$985$		0			0
$986$	−13.5677	+	9.43547i	−0.432084	+	0.300487i
$987$	11.7929	−	8.57429i	0.375374	−	0.272923i
$988$	9.14803	−	4.19454i	0.291038	−	0.133446i
$989$		−	8.58414i		−	0.272960i
$990$		0			0
$991$	15.8549			0.503648			0.251824	−	0.967773i	$-0.418970\pi$
$991$	15.8549			0.503648			0.251824	+	0.967773i	$0.418970\pi$
$992$	−23.1514	−	28.5074i	−0.735059	−	0.905109i
$993$	22.5208	+	30.9747i	0.714675	+	0.982954i
$994$	−19.2904	−	27.7385i	−0.611854	−	0.879812i
$995$		0			0
$996$	22.5438	+	12.6758i	0.714327	+	0.401648i
$997$	1.32422	+	1.32422i	0.0419385	+	0.0419385i	0.727765	−	0.685827i	$-0.240559\pi$
$997$	1.32422	+	1.32422i	0.0419385	+	0.0419385i	−0.685827	+	0.727765i	$0.740559\pi$
$998$	41.1626	+	7.39433i	1.30298	+	0.234063i
$999$	7.69739	−	15.1457i	0.243535	−	0.479187i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	600.2.w.j.293.15		32
3.2	odd	2	inner	600.2.w.j.293.2		32
5.2	odd	4	inner	600.2.w.j.557.7		32
5.3	odd	4		120.2.w.c.77.10	yes	32
5.4	even	2		120.2.w.c.53.2	✓	32
8.5	even	2	inner	600.2.w.j.293.10		32
15.2	even	4	inner	600.2.w.j.557.10		32
15.8	even	4		120.2.w.c.77.7	yes	32
15.14	odd	2		120.2.w.c.53.15	yes	32
20.3	even	4		480.2.bi.c.17.12		32
20.19	odd	2		480.2.bi.c.113.4		32
24.5	odd	2	inner	600.2.w.j.293.7		32
40.3	even	4		480.2.bi.c.17.5		32
40.13	odd	4		120.2.w.c.77.15	yes	32
40.19	odd	2		480.2.bi.c.113.13		32
40.29	even	2		120.2.w.c.53.7	yes	32
40.37	odd	4	inner	600.2.w.j.557.2		32
60.23	odd	4		480.2.bi.c.17.13		32
60.59	even	2		480.2.bi.c.113.5		32
120.29	odd	2		120.2.w.c.53.10	yes	32
120.53	even	4		120.2.w.c.77.2	yes	32
120.59	even	2		480.2.bi.c.113.12		32
120.77	even	4	inner	600.2.w.j.557.15		32
120.83	odd	4		480.2.bi.c.17.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.2.w.c.53.2	✓	32	5.4	even	2
120.2.w.c.53.7	yes	32	40.29	even	2
120.2.w.c.53.10	yes	32	120.29	odd	2
120.2.w.c.53.15	yes	32	15.14	odd	2
120.2.w.c.77.2	yes	32	120.53	even	4
120.2.w.c.77.7	yes	32	15.8	even	4
120.2.w.c.77.10	yes	32	5.3	odd	4
120.2.w.c.77.15	yes	32	40.13	odd	4
480.2.bi.c.17.4		32	120.83	odd	4
480.2.bi.c.17.5		32	40.3	even	4
480.2.bi.c.17.12		32	20.3	even	4
480.2.bi.c.17.13		32	60.23	odd	4
480.2.bi.c.113.4		32	20.19	odd	2
480.2.bi.c.113.5		32	60.59	even	2
480.2.bi.c.113.12		32	120.59	even	2
480.2.bi.c.113.13		32	40.19	odd	2
600.2.w.j.293.2		32	3.2	odd	2	inner
600.2.w.j.293.7		32	24.5	odd	2	inner
600.2.w.j.293.10		32	8.5	even	2	inner
600.2.w.j.293.15		32	1.1	even	1	trivial
600.2.w.j.557.2		32	40.37	odd	4	inner
600.2.w.j.557.7		32	5.2	odd	4	inner
600.2.w.j.557.10		32	15.2	even	4	inner
600.2.w.j.557.15		32	120.77	even	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)

\(f(q)\)	\(=\)	\(q+(1.39193 + 0.250043i) q^{2} +(-1.40091 + 1.01856i) q^{3} +(1.87496 + 0.696087i) q^{4} +(-2.20465 + 1.06748i) q^{6} +(2.29041 - 2.29041i) q^{7} +(2.43576 + 1.43773i) q^{8} +(0.925085 - 2.85381i) q^{9} +O(q^{10})\)	\(q+(1.39193 + 0.250043i) q^{2} +(-1.40091 + 1.01856i) q^{3} +(1.87496 + 0.696087i) q^{4} +(-2.20465 + 1.06748i) q^{6} +(2.29041 - 2.29041i) q^{7} +(2.43576 + 1.43773i) q^{8} +(0.925085 - 2.85381i) q^{9} +2.28378 q^{11} +(-3.33565 + 0.934597i) q^{12} +(-1.05635 + 1.05635i) q^{13} +(3.76080 - 2.61540i) q^{14} +(3.03093 + 2.61026i) q^{16} +(3.04391 + 3.04391i) q^{17} +(2.00123 - 3.74100i) q^{18} -3.36831 q^{19} +(-0.875741 + 5.54157i) q^{21} +(3.17887 + 0.571043i) q^{22} +(3.68785 - 3.68785i) q^{23} +(-4.87669 + 0.466842i) q^{24} +(-1.73449 + 1.20623i) q^{26} +(1.61081 + 4.94017i) q^{27} +(5.88875 - 2.70010i) q^{28} +2.71461i q^{29} -6.49196 q^{31} +(3.56617 + 4.39118i) q^{32} +(-3.19937 + 2.32616i) q^{33} +(3.47581 + 4.99803i) q^{34} +(3.72099 - 4.70683i) q^{36} +(-2.31197 - 2.31197i) q^{37} +(-4.68847 - 0.842223i) q^{38} +(0.403895 - 2.55579i) q^{39} +10.8056i q^{41} +(-2.60460 + 7.49452i) q^{42} +(1.16384 - 1.16384i) q^{43} +(4.28199 + 1.58971i) q^{44} +(6.05536 - 4.21112i) q^{46} +(-1.83768 - 1.83768i) q^{47} +(-6.90475 - 0.569569i) q^{48} -3.49196i q^{49} +(-7.36463 - 1.16384i) q^{51} +(-2.71591 + 1.24529i) q^{52} +(5.82856 + 5.82856i) q^{53} +(1.00688 + 7.27916i) q^{54} +(8.87188 - 2.28592i) q^{56} +(4.71870 - 3.43082i) q^{57} +(-0.678770 + 3.77856i) q^{58} -7.41311i q^{59} -8.97044i q^{61} +(-9.03638 - 1.62327i) q^{62} +(-4.41757 - 8.65522i) q^{63} +(3.86589 + 7.00392i) q^{64} +(-5.03494 + 2.43788i) q^{66} +(-8.66367 - 8.66367i) q^{67} +(3.58837 + 7.82602i) q^{68} +(-1.41005 + 8.92262i) q^{69} -7.37570i q^{71} +(6.35628 - 5.62118i) q^{72} +(-1.83441 - 1.83441i) q^{73} +(-2.64001 - 3.79620i) q^{74} +(-6.31544 - 2.34464i) q^{76} +(5.23080 - 5.23080i) q^{77} +(1.20125 - 3.45650i) q^{78} -8.28844i q^{79} +(-7.28844 - 5.28003i) q^{81} +(-2.70185 + 15.0406i) q^{82} +(-5.27928 - 5.27928i) q^{83} +(-5.49939 + 9.78061i) q^{84} +(1.91100 - 1.32898i) q^{86} +(-2.76499 - 3.80292i) q^{87} +(5.56275 + 3.28345i) q^{88} -11.5311 q^{89} +4.83893i q^{91} +(9.48162 - 4.34749i) q^{92} +(9.09464 - 6.61243i) q^{93} +(-2.09843 - 3.01742i) q^{94} +(-9.46854 - 2.51929i) q^{96} +(2.79647 - 2.79647i) q^{97} +(0.873141 - 4.86058i) q^{98} +(2.11269 - 6.51747i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 4 q^{6}+O(q^{10}) \) 32 * q - 4 * q^6	\( 32 q - 4 q^{6} + 8 q^{12} + 28 q^{16} + 20 q^{18} + 52 q^{22} - 12 q^{28} - 32 q^{31} - 8 q^{33} - 20 q^{36} - 16 q^{42} + 24 q^{46} - 44 q^{48} - 8 q^{52} + 16 q^{57} - 28 q^{58} - 48 q^{63} + 16 q^{66} - 32 q^{72} + 64 q^{73} - 88 q^{76} - 64 q^{78} + 48 q^{81} - 64 q^{82} + 8 q^{87} + 52 q^{88} - 52 q^{96} - 16 q^{97}+O(q^{100}) \) 32 * q - 4 * q^6 + 8 * q^12 + 28 * q^16 + 20 * q^18 + 52 * q^22 - 12 * q^28 - 32 * q^31 - 8 * q^33 - 20 * q^36 - 16 * q^42 + 24 * q^46 - 44 * q^48 - 8 * q^52 + 16 * q^57 - 28 * q^58 - 48 * q^63 + 16 * q^66 - 32 * q^72 + 64 * q^73 - 88 * q^76 - 64 * q^78 + 48 * q^81 - 64 * q^82 + 8 * q^87 + 52 * q^88 - 52 * q^96 - 16 * q^97

Introduction

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