LMFDB - Embedded newform 300.2.w.a.163.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [300,2,Mod(67,300)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(300, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([10, 0, 13])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("300.67"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	300.w (of order $20$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$2.39551206064$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			163.15
Character	$\chi$	$=$	300.163
Dual form			300.2.w.a.127.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0475977 + 1.41341i) q^{2} +(-0.891007 - 0.453990i) q^{3} +(-1.99547 - 0.134550i) q^{4} +(2.23568 + 0.0415918i) q^{5} +(0.684086 - 1.23775i) q^{6} +(1.15642 + 1.15642i) q^{7} +(0.285155 - 2.81402i) q^{8} +(0.587785 + 0.809017i) q^{9} +(-0.165200 + 3.15796i) q^{10} +(-0.574557 + 0.790810i) q^{11} +(1.71689 + 1.02581i) q^{12} +(3.66677 + 0.580759i) q^{13} +(-1.68954 + 1.57946i) q^{14} +(-1.97312 - 1.05204i) q^{15} +(3.96379 + 0.536982i) q^{16} +(1.54304 + 3.02838i) q^{17} +(-1.17145 + 0.792276i) q^{18} +(-1.54393 + 4.75171i) q^{19} +(-4.45564 - 0.383807i) q^{20} +(-0.505375 - 1.55538i) q^{21} +(-1.09039 - 0.849726i) q^{22} +(-1.65652 + 0.262367i) q^{23} +(-1.53161 + 2.37785i) q^{24} +(4.99654 + 0.185972i) q^{25} +(-0.995382 + 5.15501i) q^{26} +(-0.156434 - 0.987688i) q^{27} +(-2.15201 - 2.46320i) q^{28} +(-6.16400 + 2.00281i) q^{29} +(1.58088 - 2.73876i) q^{30} +(3.69657 + 1.20109i) q^{31} +(-0.947644 + 5.57691i) q^{32} +(0.870954 - 0.443773i) q^{33} +(-4.35379 + 2.03680i) q^{34} +(2.53729 + 2.63349i) q^{35} +(-1.06405 - 1.69345i) q^{36} +(1.23176 - 7.77702i) q^{37} +(-6.64264 - 2.40837i) q^{38} +(-3.00346 - 2.18214i) q^{39} +(0.754555 - 6.27938i) q^{40} +(-2.58309 + 1.87673i) q^{41} +(2.22245 - 0.640270i) q^{42} +(6.18535 - 6.18535i) q^{43} +(1.25291 - 1.50073i) q^{44} +(1.28045 + 1.83315i) q^{45} +(-0.291986 - 2.35384i) q^{46} +(4.67720 - 9.17952i) q^{47} +(-3.28798 - 2.27798i) q^{48} -4.32538i q^{49} +(-0.500679 + 7.05332i) q^{50} -3.39883i q^{51} +(-7.23878 - 1.65225i) q^{52} +(-0.989011 + 1.94104i) q^{53} +(1.40346 - 0.174095i) q^{54} +(-1.31742 + 1.74410i) q^{55} +(3.58395 - 2.92443i) q^{56} +(3.53288 - 3.53288i) q^{57} +(-2.53740 - 8.80760i) q^{58} +(-2.96719 + 2.15579i) q^{59} +(3.79576 + 2.36479i) q^{60} +(-3.48146 - 2.52943i) q^{61} +(-1.87358 + 5.16761i) q^{62} +(-0.255837 + 1.61529i) q^{63} +(-7.83737 - 1.60486i) q^{64} +(8.17357 + 1.45090i) q^{65} +(0.585779 + 1.25214i) q^{66} +(6.00029 - 3.05730i) q^{67} +(-2.67161 - 6.25065i) q^{68} +(1.59508 + 0.518274i) q^{69} +(-3.84297 + 3.46089i) q^{70} +(-2.89032 + 0.939123i) q^{71} +(2.44420 - 1.42334i) q^{72} +(2.20940 + 13.9496i) q^{73} +(10.9335 + 2.11115i) q^{74} +(-4.36752 - 2.43408i) q^{75} +(3.72020 - 9.27416i) q^{76} +(-1.57894 + 0.250079i) q^{77} +(3.22722 - 4.14126i) q^{78} +(0.430746 + 1.32570i) q^{79} +(8.83944 + 1.36538i) q^{80} +(-0.309017 + 0.951057i) q^{81} +(-2.52964 - 3.74030i) q^{82} +(-7.43080 - 14.5838i) q^{83} +(0.799182 + 3.17172i) q^{84} +(3.32378 + 6.83466i) q^{85} +(8.44804 + 9.03686i) q^{86} +(6.40142 + 1.01389i) q^{87} +(2.06151 + 1.84231i) q^{88} +(1.66905 - 2.29725i) q^{89} +(-2.65194 + 1.72255i) q^{90} +(3.56873 + 4.91193i) q^{91} +(3.34084 - 0.300660i) q^{92} +(-2.74839 - 2.74839i) q^{93} +(12.7518 + 7.04774i) q^{94} +(-3.64936 + 10.5591i) q^{95} +(3.37622 - 4.53885i) q^{96} +(-12.3696 - 6.30263i) q^{97} +(6.11354 + 0.205878i) q^{98} -0.977494 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 12 q^{8} + 8 q^{10} + 8 q^{12} + 4 q^{13} + 20 q^{17} - 20 q^{20} - 12 q^{22} + 20 q^{25} + 4 q^{28} - 8 q^{30} - 20 q^{32} - 8 q^{33} - 4 q^{37} - 76 q^{38} - 92 q^{40} - 20 q^{42} - 140 q^{44}+ \cdots + 256 q^{98}+O(q^{100}) $ 240 * q + 12 * q^8 + 8 * q^10 + 8 * q^12 + 4 * q^13 + 20 * q^17 - 20 * q^20 - 12 * q^22 + 20 * q^25 + 4 * q^28 - 8 * q^30 - 20 * q^32 - 8 * q^33 - 4 * q^37 - 76 * q^38 - 92 * q^40 - 20 * q^42 - 140 * q^44 - 4 * q^45 - 16 * q^48 - 164 * q^50 - 172 * q^52 - 4 * q^53 - 120 * q^58 + 20 * q^60 - 44 * q^62 - 60 * q^64 - 20 * q^65 + 16 * q^68 - 44 * q^70 + 12 * q^72 - 44 * q^73 - 48 * q^77 + 24 * q^78 - 4 * q^80 + 60 * q^81 + 24 * q^82 + 80 * q^84 - 64 * q^85 + 60 * q^88 - 260 * q^89 + 48 * q^90 + 144 * q^92 - 64 * q^93 + 40 * q^94 - 20 * q^96 - 180 * q^97 + 256 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$277$
$\chi(n)$	$1$	$-1$	$e\left(\frac{19}{20}\right)$

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 $

$2$	−0.0475977	+	1.41341i	−0.0336566	+	0.999433i
$2$	−0.0475977	+	1.41341i	−0.0336566	+	0.999433i
$3$	−0.891007	−	0.453990i	−0.514423	−	0.262112i
$3$	−0.891007	−	0.453990i	−0.514423	−	0.262112i
$4$	−1.99547	−	0.134550i	−0.997734	−	0.0672751i
$5$	2.23568	+	0.0415918i	0.999827	+	0.0186004i
$5$	2.23568	+	0.0415918i	0.999827	+	0.0186004i
$6$	0.684086	−	1.23775i	0.279277	−	0.505310i
$7$	1.15642	+	1.15642i	0.437086	+	0.437086i	0.891030	−	0.453944i	$-0.149983\pi$
$7$	1.15642	+	1.15642i	0.437086	+	0.437086i	−0.453944	+	0.891030i	$0.649983\pi$
$8$	0.285155	−	2.81402i	0.100817	−	0.994905i
$9$	0.587785	+	0.809017i	0.195928	+	0.269672i
$10$	−0.165200	+	3.15796i	−0.0522407	+	0.998635i
$11$	−0.574557	+	0.790810i	−0.173235	+	0.238438i	−0.886802	−	0.462149i	$-0.847078\pi$
$11$	−0.574557	+	0.790810i	−0.173235	+	0.238438i	0.713567	+	0.700587i	$0.247078\pi$
$12$	1.71689	+	1.02581i	0.495624	+	0.296126i
$13$	3.66677	+	0.580759i	1.01698	+	0.161074i	0.642600	−	0.766202i	$-0.277856\pi$
$13$	3.66677	+	0.580759i	1.01698	+	0.161074i	0.374379	+	0.927276i	$0.377856\pi$
$14$	−1.68954	+	1.57946i	−0.451549	+	0.422128i
$15$	−1.97312	−	1.05204i	−0.509458	−	0.271635i
$16$	3.96379	+	0.536982i	0.990948	+	0.134245i
$17$	1.54304	+	3.02838i	0.374241	+	0.734489i	0.998923	−	0.0463896i	$-0.0147716\pi$
$17$	1.54304	+	3.02838i	0.374241	+	0.734489i	−0.624682	+	0.780879i	$0.714772\pi$
$18$	−1.17145	+	0.792276i	−0.276114	+	0.186741i
$19$	−1.54393	+	4.75171i	−0.354201	+	1.09012i	0.602271	+	0.798292i	$0.294263\pi$
$19$	−1.54393	+	4.75171i	−0.354201	+	1.09012i	−0.956471	+	0.291826i	$0.905737\pi$
$20$	−4.45564	−	0.383807i	−0.996311	−	0.0858218i
$21$	−0.505375	−	1.55538i	−0.110282	−	0.339412i
$22$	−1.09039	−	0.849726i	−0.232472	−	0.181162i
$23$	−1.65652	+	0.262367i	−0.345409	+	0.0547073i	−0.326729	−	0.945118i	$-0.605946\pi$
$23$	−1.65652	+	0.262367i	−0.345409	+	0.0547073i	−0.0186799	+	0.999826i	$0.505946\pi$
$24$	−1.53161	+	2.37785i	−0.312639	+	0.485376i
$25$	4.99654	+	0.185972i	0.999308	+	0.0371944i
$26$	−0.995382	+	5.15501i	−0.195210	+	1.01098i
$27$	−0.156434	−	0.987688i	−0.0301058	−	0.190081i
$28$	−2.15201	−	2.46320i	−0.406691	−	0.465501i
$29$	−6.16400	+	2.00281i	−1.14463	+	0.371912i	−0.819117	−	0.573627i	$-0.805536\pi$
$29$	−6.16400	+	2.00281i	−1.14463	+	0.371912i	−0.325510	+	0.945539i	$0.605536\pi$
$30$	1.58088	−	2.73876i	0.288627	−	0.500028i
$31$	3.69657	+	1.20109i	0.663924	+	0.215722i	0.621544	−	0.783380i	$-0.286506\pi$
$31$	3.69657	+	1.20109i	0.663924	+	0.215722i	0.0423804	+	0.999102i	$0.486506\pi$
$32$	−0.947644	+	5.57691i	−0.167521	+	0.985868i
$33$	0.870954	−	0.443773i	0.151614	−	0.0772510i
$34$	−4.35379	+	2.03680i	−0.746669	+	0.349309i
$35$	2.53729	+	2.63349i	0.428881	+	0.445141i
$36$	−1.06405	−	1.69345i	−0.177342	−	0.282242i
$37$	1.23176	−	7.77702i	0.202500	−	1.27853i	−0.651655	−	0.758516i	$-0.725925\pi$
$37$	1.23176	−	7.77702i	0.202500	−	1.27853i	0.854155	−	0.520019i	$-0.174075\pi$
$38$	−6.64264	−	2.40837i	−1.07758	−	0.390690i
$39$	−3.00346	−	2.18214i	−0.480938	−	0.349422i
$40$	0.754555	−	6.27938i	0.119306	−	0.992858i
$41$	−2.58309	+	1.87673i	−0.403411	+	0.293095i	−0.770929	−	0.636921i	$-0.780208\pi$
$41$	−2.58309	+	1.87673i	−0.403411	+	0.293095i	0.367518	+	0.930016i	$0.380208\pi$
$42$	2.22245	−	0.640270i	0.342932	−	0.0987958i
$43$	6.18535	−	6.18535i	0.943257	−	0.943257i	−0.0552173	−	0.998474i	$-0.517585\pi$
$43$	6.18535	−	6.18535i	0.943257	−	0.943257i	0.998474	+	0.0552173i	$0.0175852\pi$
$44$	1.25291	−	1.50073i	0.188884	−	0.226243i
$45$	1.28045	+	1.83315i	0.190878	+	0.273270i
$46$	−0.291986	−	2.35384i	−0.0430511	−	0.347054i
$47$	4.67720	−	9.17952i	0.682240	−	1.33897i	−0.246827	−	0.969059i	$-0.579388\pi$
$47$	4.67720	−	9.17952i	0.682240	−	1.33897i	0.929067	−	0.369911i	$-0.120612\pi$
$48$	−3.28798	−	2.27798i	−0.474579	−	0.328798i
$49$		−	4.32538i		−	0.617911i
$50$	−0.500679	+	7.05332i	−0.0708067	+	0.997490i
$51$		−	3.39883i		−	0.475931i
$52$	−7.23878	−	1.65225i	−1.00384	−	0.229126i
$53$	−0.989011	+	1.94104i	−0.135851	+	0.266623i	−0.948903	−	0.315569i	$-0.897805\pi$
$53$	−0.989011	+	1.94104i	−0.135851	+	0.266623i	0.813052	+	0.582192i	$0.197805\pi$
$54$	1.40346	−	0.174095i	0.190986	−	0.0236913i
$55$	−1.31742	+	1.74410i	−0.177640	+	0.235175i
$56$	3.58395	−	2.92443i	0.478925	−	0.390793i
$57$	3.53288	−	3.53288i	0.467942	−	0.467942i
$58$	−2.53740	−	8.80760i	−0.333177	−	1.15649i
$59$	−2.96719	+	2.15579i	−0.386295	+	0.280659i	−0.763935	−	0.645293i	$-0.776735\pi$
$59$	−2.96719	+	2.15579i	−0.386295	+	0.280659i	0.377641	+	0.925952i	$0.376735\pi$
$60$	3.79576	+	2.36479i	0.490030	+	0.305293i
$61$	−3.48146	−	2.52943i	−0.445755	−	0.323860i	0.342162	−	0.939641i	$-0.388841\pi$
$61$	−3.48146	−	2.52943i	−0.445755	−	0.323860i	−0.787918	+	0.615781i	$0.788841\pi$
$62$	−1.87358	+	5.16761i	−0.237945	+	0.656287i
$63$	−0.255837	+	1.61529i	−0.0322324	+	0.203508i
$64$	−7.83737	−	1.60486i	−0.979672	−	0.200607i
$65$	8.17357	+	1.45090i	1.01381	+	0.179962i
$66$	0.585779	+	1.25214i	0.0721044	+	0.154128i
$67$	6.00029	−	3.05730i	0.733052	−	0.373509i	−0.0472734	−	0.998882i	$-0.515053\pi$
$67$	6.00029	−	3.05730i	0.733052	−	0.373509i	0.780326	+	0.625373i	$0.215053\pi$
$68$	−2.67161	−	6.25065i	−0.323980	−	0.758002i
$69$	1.59508	+	0.518274i	0.192025	+	0.0623929i
$70$	−3.84297	+	3.46089i	−0.459323	+	0.413656i
$71$	−2.89032	+	0.939123i	−0.343018	+	0.111453i	−0.475460	−	0.879737i	$-0.657718\pi$
$71$	−2.89032	+	0.939123i	−0.343018	+	0.111453i	0.132442	+	0.991191i	$0.457718\pi$
$72$	2.44420	−	1.42334i	0.288051	−	0.167742i
$73$	2.20940	+	13.9496i	0.258590	+	1.63268i	0.685282	+	0.728278i	$0.259679\pi$
$73$	2.20940	+	13.9496i	0.258590	+	1.63268i	−0.426691	+	0.904397i	$0.640321\pi$
$74$	10.9335	+	2.11115i	1.27099	+	0.245416i
$75$	−4.36752	−	2.43408i	−0.504318	−	0.281064i
$76$	3.72020	−	9.27416i	0.426736	−	1.06382i
$77$	−1.57894	+	0.250079i	−0.179937	+	0.0284992i
$78$	3.22722	−	4.14126i	0.365411	−	0.468905i
$79$	0.430746	+	1.32570i	0.0484628	+	0.149153i	0.972359	−	0.233489i	$-0.0750143\pi$
$79$	0.430746	+	1.32570i	0.0484628	+	0.149153i	−0.923897	+	0.382642i	$0.875014\pi$
$80$	8.83944	+	1.36538i	0.988280	+	0.152654i
$81$	−0.309017	+	0.951057i	−0.0343352	+	0.105673i
$82$	−2.52964	−	3.74030i	−0.279352	−	0.413047i
$83$	−7.43080	−	14.5838i	−0.815636	−	1.60078i	−0.799318	−	0.600909i	$-0.794806\pi$
$83$	−7.43080	−	14.5838i	−0.815636	−	1.60078i	−0.0163181	−	0.999867i	$-0.505194\pi$
$84$	0.799182	+	3.17172i	0.0871979	+	0.346063i
$85$	3.32378	+	6.83466i	0.360514	+	0.741323i
$86$	8.44804	+	9.03686i	0.910976	+	0.974470i
$87$	6.40142	+	1.01389i	0.686304	+	0.108700i
$88$	2.06151	+	1.84231i	0.219758	+	0.196391i
$89$	1.66905	−	2.29725i	0.176919	−	0.243508i	−0.711343	−	0.702845i	$-0.751913\pi$
$89$	1.66905	−	2.29725i	0.176919	−	0.243508i	0.888262	+	0.459337i	$0.151913\pi$
$90$	−2.65194	+	1.72255i	−0.279540	+	0.181573i
$91$	3.56873	+	4.91193i	0.374104	+	0.514910i
$92$	3.34084	−	0.300660i	0.348306	−	0.0313460i
$93$	−2.74839	−	2.74839i	−0.284994	−	0.284994i
$94$	12.7518	+	7.04774i	1.31525	+	0.726918i
$95$	−3.64936	+	10.5591i	−0.374416	+	1.08334i
$96$	3.37622	−	4.53885i	0.344584	−	0.463244i
$97$	−12.3696	−	6.30263i	−1.25594	−	0.639935i	−0.305903	−	0.952063i	$-0.598958\pi$
$97$	−12.3696	−	6.30263i	−1.25594	−	0.639935i	−0.950040	+	0.312128i	$0.898958\pi$
$98$	6.11354	+	0.205878i	0.617561	+	0.0207968i
$99$	−0.977494			−0.0982419
$100$	−9.94542	−	1.04339i	−0.994542	−	0.104339i
$101$	−12.8704			−1.28065			−0.640325	−	0.768104i	$-0.721200\pi$
$101$	−12.8704			−1.28065			−0.640325	+	0.768104i	$0.721200\pi$
$102$	4.80394	+	0.161776i	0.475661	+	0.0160182i
$103$	10.3758	+	5.28675i	1.02236	+	0.520919i	0.883025	−	0.469327i	$-0.155503\pi$
$103$	10.3758	+	5.28675i	1.02236	+	0.520919i	0.139336	+	0.990245i	$0.455503\pi$
$104$	2.67986	−	10.1527i	0.262782	−	0.995558i
$105$	−1.06517	−	3.49836i	−0.103950	−	0.341405i
$106$	−2.69642	−	1.49027i	−0.261899	−	0.144748i
$107$	−10.7876	−	10.7876i	−1.04287	−	1.04287i	−0.999039	−	0.0438342i	$-0.986043\pi$
$107$	−10.7876	−	10.7876i	−1.04287	−	1.04287i	−0.0438342	−	0.999039i	$-0.513957\pi$
$108$	0.179266	+	1.99195i	0.0172499	+	0.191675i
$109$	−10.1748	−	14.0045i	−0.974573	−	1.34138i	−0.939702	−	0.341993i	$-0.888898\pi$
$109$	−10.1748	−	14.0045i	−0.974573	−	1.34138i	−0.0348708	−	0.999392i	$-0.511102\pi$
$110$	−2.40243	−	1.94507i	−0.229063	−	0.185455i
$111$	−4.62820	+	6.37017i	−0.439289	+	0.604630i
$112$	3.96284	+	5.20479i	0.374453	+	0.491807i
$113$	−13.6135	−	2.15616i	−1.28065	−	0.202835i	−0.521218	−	0.853424i	$-0.674522\pi$
$113$	−13.6135	−	2.15616i	−1.28065	−	0.202835i	−0.759430	+	0.650589i	$0.774522\pi$
$114$	4.82526	+	5.16157i	0.451927	+	0.483426i
$115$	−3.71437	+	0.517672i	−0.346366	+	0.0482731i
$116$	12.5695	−	3.16717i	1.16705	−	0.294064i
$117$	1.68543	+	3.30784i	0.155818	+	0.305810i
$118$	−2.90578	−	4.29647i	−0.267499	−	0.395522i
$119$	−1.71768	+	5.28648i	−0.157460	+	0.484611i
$120$	−3.52309	+	5.25241i	−0.321613	+	0.479477i
$121$	3.10392	+	9.55289i	0.282175	+	0.868445i
$122$	3.74083	−	4.80034i	0.338679	−	0.434603i
$123$	3.15357	−	0.499476i	0.284348	−	0.0450362i
$124$	−7.21479	−	2.89411i	−0.647907	−	0.259899i
$125$	11.1629	+	0.623590i	0.998443	+	0.0557756i
$126$	−2.27090	−	0.438487i	−0.202308	−	0.0390636i
$127$	2.25651	+	14.2470i	0.200233	+	1.26422i	0.859040	+	0.511908i	$0.171061\pi$
$127$	2.25651	+	14.2470i	0.200233	+	1.26422i	−0.658807	+	0.752312i	$0.728939\pi$
$128$	2.64137	−	11.0011i	0.233466	−	0.972365i
$129$	−8.31928	+	2.70310i	−0.732472	+	0.237994i
$130$	−2.43976	+	11.4836i	−0.213981	+	1.00718i
$131$	15.8689	+	5.15611i	1.38647	+	0.450491i	0.904791	−	0.425857i	$-0.140027\pi$
$131$	15.8689	+	5.15611i	1.38647	+	0.450491i	0.481679	+	0.876348i	$0.340027\pi$
$132$	−1.79767	+	0.768348i	−0.156467	+	0.0668762i
$133$	−7.28041	+	3.70956i	−0.631292	+	0.321659i
$134$	4.03563	+	8.62641i	0.348625	+	0.745208i
$135$	−0.308658	−	2.21466i	−0.0265650	−	0.190608i
$136$	8.96191	−	3.47857i	0.768477	−	0.298285i
$137$	2.25985	−	14.2681i	0.193072	−	1.21901i	−0.680659	−	0.732601i	$-0.738306\pi$
$137$	2.25985	−	14.2681i	0.193072	−	1.21901i	0.873731	−	0.486409i	$-0.161694\pi$
$138$	−0.808457	+	2.22984i	−0.0688204	+	0.189817i
$139$	−18.6136	−	13.5236i	−1.57879	−	1.14706i	−0.918067	−	0.396425i	$-0.870251\pi$
$139$	−18.6136	−	13.5236i	−1.57879	−	1.14706i	−0.660721	−	0.750632i	$-0.729749\pi$
$140$	−4.70875	−	5.59644i	−0.397962	−	0.472985i
$141$	−8.33483	+	6.05561i	−0.701919	+	0.509974i
$142$	−1.18979	−	4.12992i	−0.0998454	−	0.346575i
$143$	−2.56604	+	2.56604i	−0.214583	+	0.214583i
$144$	1.89543	+	3.52241i	0.157953	+	0.293534i
$145$	−13.8640	+	4.22126i	−1.15135	+	0.350557i
$146$	−19.8217	+	2.45882i	−1.64045	+	0.203494i
$147$	−1.96368	+	3.85394i	−0.161962	+	0.317868i
$148$	−3.50434	+	15.3531i	−0.288055	+	1.26201i
$149$		−	4.23779i		−	0.347173i	−0.984819	−	0.173586i	$-0.944464\pi$
$149$		−	4.23779i		−	0.347173i	0.984819	−	0.173586i	$-0.0555356\pi$
$150$	3.64825	−	6.05725i	0.297878	−	0.494572i
$151$		−	1.91070i		−	0.155490i	−0.996973	−	0.0777451i	$-0.975228\pi$
$151$		−	1.91070i		−	0.155490i	0.996973	−	0.0777451i	$-0.0247720\pi$
$152$	12.9311	+	5.69960i	1.04885	+	0.462299i
$153$	−1.54304	+	3.02838i	−0.124747	+	0.244830i
$154$	−0.278311	−	2.24359i	−0.0224270	−	0.180794i
$155$	8.21440	+	2.83900i	0.659797	+	0.228034i
$156$	5.69970	+	4.75851i	0.456341	+	0.380985i
$157$	15.1998	−	15.1998i	1.21308	−	1.21308i	0.243071	−	0.970009i	$-0.421845\pi$
$157$	15.1998	−	15.1998i	1.21308	−	1.21308i	0.970009	−	0.243071i	$-0.0781547\pi$
$158$	−1.89426	+	0.545722i	−0.150700	+	0.0434153i
$159$	1.76243	−	1.28048i	0.139770	−	0.101549i
$160$	−2.35058	+	12.4288i	−0.185830	+	0.982582i
$161$	−2.21904	−	1.61223i	−0.174885	−	0.127061i
$162$	−1.32953	−	0.482036i	−0.104457	−	0.0378724i
$163$	−2.32827	+	14.7001i	−0.182364	+	1.15140i	0.711374	+	0.702814i	$0.248073\pi$
$163$	−2.32827	+	14.7001i	−0.182364	+	1.15140i	−0.893738	+	0.448589i	$0.851927\pi$
$164$	5.40699	−	3.39739i	0.422215	−	0.265292i
$165$	1.96563	−	0.955911i	0.153024	−	0.0744175i
$166$	20.9666	−	9.80863i	1.62732	−	0.761297i
$167$	−13.6609	+	6.96060i	−1.05712	+	0.538627i	−0.894040	−	0.447986i	$-0.852141\pi$
$167$	−13.6609	+	6.96060i	−1.05712	+	0.538627i	−0.163075	+	0.986614i	$0.552141\pi$
$168$	−4.52098	+	0.978608i	−0.348801	+	0.0755012i
$169$	0.744179	+	0.241798i	0.0572445	+	0.0185999i
$170$	−9.81840	+	4.37256i	−0.753037	+	0.335360i
$171$	−4.75171	+	1.54393i	−0.363373	+	0.118067i
$172$	−13.1749	+	11.5104i	−1.00458	+	0.877662i
$173$	3.15268	+	19.9053i	0.239694	+	1.51337i	0.754636	+	0.656144i	$0.227814\pi$
$173$	3.15268	+	19.9053i	0.239694	+	1.51337i	−0.514942	+	0.857225i	$0.672186\pi$
$174$	−1.73773	+	8.99959i	−0.131737	+	0.682257i
$175$	5.56304	+	5.99317i	0.420527	+	0.453041i
$176$	−2.70207	+	2.82608i	−0.203676	+	0.213024i
$177$	3.62249	−	0.573746i	0.272283	−	0.0431254i
$178$	3.16752	+	2.46840i	0.237416	+	0.185014i
$179$	2.12634	+	6.54421i	0.158930	+	0.489137i	0.998538	−	0.0540563i	$-0.0172150\pi$
$179$	2.12634	+	6.54421i	0.158930	+	0.489137i	−0.839608	+	0.543193i	$0.817215\pi$
$180$	−2.30845	−	3.83028i	−0.172062	−	0.285492i
$181$	1.02571	−	3.15681i	0.0762404	−	0.234644i	−0.905672	−	0.423979i	$-0.860633\pi$
$181$	1.02571	−	3.15681i	0.0762404	−	0.234644i	0.981913	+	0.189335i	$0.0606331\pi$
$182$	−7.11245	+	4.81029i	−0.527210	+	0.356562i
$183$	1.95367	+	3.83429i	0.144419	+	0.283439i
$184$	0.265941	+	4.73629i	0.0196054	+	0.349164i
$185$	3.07728	−	17.3357i	0.226246	−	1.27455i
$186$	4.01542	−	3.75379i	0.294425	−	0.275241i
$187$	−3.28143	−	0.519728i	−0.239962	−	0.0380062i
$188$	−10.5683	+	17.6881i	−0.770773	+	1.29004i
$189$	0.961280	−	1.32309i	0.0699228	−	0.0962405i
$190$	−14.7507	−	5.66064i	−1.07013	−	0.410666i
$191$	4.95656	+	6.82212i	0.358644	+	0.493631i	0.949770	−	0.312948i	$-0.101317\pi$
$191$	4.95656	+	6.82212i	0.358644	+	0.493631i	−0.591126	+	0.806579i	$0.701317\pi$
$192$	6.25456	+	4.98803i	0.451384	+	0.359980i
$193$	9.61516	+	9.61516i	0.692114	+	0.692114i	0.962697	−	0.270583i	$-0.0872163\pi$
$193$	9.61516	+	9.61516i	0.692114	+	0.692114i	−0.270583	+	0.962697i	$0.587216\pi$
$194$	9.49697	−	17.1834i	0.681843	−	1.23369i
$195$	−6.62401	−	5.00349i	−0.474355	−	0.358307i
$196$	−0.581981	+	8.63116i	−0.0415701	+	0.616511i
$197$	6.82019	+	3.47506i	0.485918	+	0.247588i	0.679746	−	0.733448i	$-0.262090\pi$
$197$	6.82019	+	3.47506i	0.485918	+	0.247588i	−0.193827	+	0.981036i	$0.562090\pi$
$198$	0.0465264	−	1.38160i	0.00330649	−	0.0981862i
$199$	13.8690			0.983146			0.491573	−	0.870836i	$-0.336422\pi$
$199$	13.8690			0.983146			0.491573	+	0.870836i	$0.336422\pi$
$200$	1.94812	−	14.0073i	0.137753	−	0.990467i
$201$	−6.73429			−0.475000
$202$	0.612599	−	18.1911i	0.0431023	−	1.27992i
$203$	−9.44427	−	4.81210i	−0.662858	−	0.337743i
$204$	−0.457313	+	6.78225i	−0.0320183	+	0.474853i
$205$	−5.85303	+	4.08833i	−0.408793	+	0.285541i
$206$	−7.96622	+	14.4137i	−0.555033	+	1.00425i
$207$	−1.18594	−	1.18594i	−0.0824284	−	0.0824284i
$208$	14.2225	+	4.27100i	0.986150	+	0.296140i
$209$	−2.87063	−	3.95108i	−0.198566	−	0.273302i
$210$	4.99533	−	1.33900i	0.344710	−	0.0924001i
$211$	5.56295	−	7.65675i	0.382970	−	0.527112i	−0.573399	−	0.819277i	$-0.694375\pi$
$211$	5.56295	−	7.65675i	0.382970	−	0.527112i	0.956368	+	0.292164i	$0.0943754\pi$
$212$	2.23471	−	3.74022i	0.153480	−	0.256879i
$213$	3.00165	+	0.475414i	0.205670	+	0.0325749i
$214$	15.7607	−	14.7338i	1.07738	−	1.00718i
$215$	14.0857	−	13.5712i	0.960639	−	0.925549i
$216$	−2.82398	+	0.158565i	−0.192147	+	0.0107890i
$217$	2.88583	+	5.66376i	0.195903	+	0.384481i
$218$	20.2784	−	13.7147i	1.37343	−	0.928875i
$219$	4.36439	−	13.4322i	0.294918	−	0.907665i
$220$	2.86353	−	3.30304i	0.193059	−	0.222691i
$221$	3.89920	+	12.0005i	0.262288	+	0.807240i
$222$	−8.78338	−	6.84476i	−0.589502	−	0.459390i
$223$	2.66635	−	0.422309i	0.178552	−	0.0282799i	−0.0665180	−	0.997785i	$-0.521189\pi$
$223$	2.66635	−	0.422309i	0.178552	−	0.0282799i	0.245070	+	0.969505i	$0.421189\pi$
$224$	−7.54514	+	5.35339i	−0.504131	+	0.357688i
$225$	2.78644	+	4.15160i	0.185763	+	0.276773i
$226$	3.69552	−	19.1388i	0.245822	−	1.27310i
$227$	−1.84338	−	11.6386i	−0.122349	−	0.772482i	−0.970210	−	0.242264i	$-0.922110\pi$
$227$	−1.84338	−	11.6386i	−0.122349	−	0.772482i	0.847861	−	0.530218i	$-0.177890\pi$
$228$	−7.52510	+	6.57440i	−0.498362	+	0.435401i
$229$	3.90033	−	1.26729i	0.257741	−	0.0837451i	−0.177297	−	0.984157i	$-0.556735\pi$
$229$	3.90033	−	1.26729i	0.257741	−	0.0837451i	0.435037	+	0.900412i	$0.356735\pi$
$230$	−0.554888	−	5.27457i	−0.0365883	−	0.347795i
$231$	1.52038	+	0.494001i	0.100034	+	0.0325029i
$232$	3.87823	+	17.9167i	0.254618	+	1.17629i
$233$	7.40542	−	3.77325i	0.485145	−	0.247194i	−0.194270	−	0.980948i	$-0.562234\pi$
$233$	7.40542	−	3.77325i	0.485145	−	0.247194i	0.679415	+	0.733754i	$0.262234\pi$
$234$	−4.75556	+	2.22476i	−0.310881	+	0.145437i
$235$	10.8385	−	20.3279i	0.707027	−	1.32605i
$236$	6.21099	−	3.90257i	0.404301	−	0.254036i
$237$	0.218058	−	1.37676i	0.0141644	−	0.0894304i
$238$	−7.39022	−	2.67942i	−0.479037	−	0.173681i
$239$	8.99618	+	6.53610i	0.581914	+	0.422785i	0.839414	−	0.543493i	$-0.182899\pi$
$239$	8.99618	+	6.53610i	0.581914	+	0.422785i	−0.257499	+	0.966278i	$0.582899\pi$
$240$	−7.25613	−	5.22959i	−0.468381	−	0.337568i
$241$	0.884285	−	0.642471i	0.0569618	−	0.0413852i	−0.558940	−	0.829208i	$-0.688792\pi$
$241$	0.884285	−	0.642471i	0.0569618	−	0.0413852i	0.615902	+	0.787823i	$0.288792\pi$
$242$	−13.6499	+	3.93243i	−0.877450	+	0.252786i
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$	6.60681	+	5.51583i	0.422957	+	0.353115i
$245$	0.179900	−	9.67017i	0.0114934	−	0.617804i
$246$	0.555863	+	4.48106i	0.0354405	+	0.285702i
$247$	−8.42082	+	16.5268i	−0.535804	+	1.05157i
$248$	4.43398	−	10.0597i	0.281558	−	0.638793i
$249$			16.3677i			1.03726i
$250$	−1.41272	+	15.7481i	−0.0893482	+	0.996000i
$251$		−	27.5973i		−	1.74193i	−0.491348	−	0.870964i	$-0.663496\pi$
$251$		−	27.5973i		−	1.74193i	0.491348	−	0.870964i	$-0.336504\pi$
$252$	0.727853	−	3.18884i	0.0458504	−	0.200878i
$253$	0.744283	−	1.46074i	0.0467927	−	0.0918358i
$254$	−20.2443	+	2.51125i	−1.27024	+	0.157570i
$255$	0.141363	−	7.59869i	0.00885252	−	0.475849i
$256$	15.4233	+	4.25697i	0.963956	+	0.266060i
$257$	8.15087	−	8.15087i	0.508437	−	0.508437i	−0.405609	−	0.914047i	$-0.632941\pi$
$257$	8.15087	−	8.15087i	0.508437	−	0.508437i	0.914047	+	0.405609i	$0.132941\pi$
$258$	−3.42461	−	11.8872i	−0.213207	−	0.740067i
$259$	10.4179	−	7.56908i	0.647340	−	0.470320i
$260$	−16.1149	−	3.99498i	−0.999403	−	0.247758i
$261$	−5.24341	−	3.80956i	−0.324559	−	0.235806i
$262$	−8.04303	+	22.1838i	−0.496900	+	1.37052i
$263$	−2.64700	+	16.7125i	−0.163221	+	1.03054i	0.761020	+	0.648729i	$0.224699\pi$
$263$	−2.64700	+	16.7125i	−0.163221	+	1.03054i	−0.924241	+	0.381810i	$0.875301\pi$
$264$	−1.00043	−	2.57742i	−0.0615721	−	0.158629i
$265$	−2.29184	+	4.29842i	−0.140787	+	0.264050i
$266$	−4.89660	−	10.4668i	−0.300230	−	0.641760i
$267$	−2.53007	+	1.28913i	−0.154837	+	0.0788936i
$268$	−12.3848	+	5.29341i	−0.756520	+	0.323347i
$269$	−4.74451	−	1.54159i	−0.289278	−	0.0939922i	0.160783	−	0.986990i	$-0.448598\pi$
$269$	−4.74451	−	1.54159i	−0.289278	−	0.0939922i	−0.450061	+	0.892998i	$0.648598\pi$
$270$	3.14492	−	0.330848i	0.191394	−	0.0201348i
$271$	−26.7320	+	8.68575i	−1.62385	+	0.527622i	−0.972846	−	0.231451i	$-0.925653\pi$
$271$	−26.7320	+	8.68575i	−1.62385	+	0.527622i	−0.651006	+	0.759073i	$0.725653\pi$
$272$	4.49009	+	12.8324i	0.272252	+	0.778081i
$273$	−0.949789	−	5.99673i	−0.0574839	−	0.362939i
$274$	20.0592	+	3.87323i	1.21182	+	0.233991i
$275$	−3.01786	+	3.84446i	−0.181984	+	0.231830i
$276$	−3.11321	−	1.24882i	−0.187393	−	0.0751700i
$277$	−26.3841	+	4.17884i	−1.58527	+	0.251082i	−0.885969	−	0.463745i	$-0.846505\pi$
$277$	−26.3841	+	4.17884i	−1.58527	+	0.251082i	−0.699301	+	0.714827i	$0.746505\pi$
$278$	20.0004	−	25.6651i	1.19954	−	1.53929i
$279$	1.20109	+	3.69657i	0.0719073	+	0.221308i
$280$	8.13420	−	6.38903i	0.486111	−	0.381818i
$281$	0.691214	−	2.12734i	0.0412344	−	0.126906i	−0.928320	−	0.371782i	$-0.878747\pi$
$281$	0.691214	−	2.12734i	0.0412344	−	0.126906i	0.969555	+	0.244875i	$0.0787470\pi$
$282$	−8.16235	−	12.0688i	−0.486061	−	0.718686i
$283$	−7.65378	−	15.0214i	−0.454970	−	0.892929i	−0.998564	−	0.0535804i	$-0.982937\pi$
$283$	−7.65378	−	15.0214i	−0.454970	−	0.892929i	0.543593	−	0.839349i	$-0.317063\pi$
$284$	5.89391	−	1.48510i	0.349739	−	0.0881243i
$285$	8.04533	−	7.75146i	0.476564	−	0.459157i
$286$	−3.50473	−	3.74901i	−0.207239	−	0.221683i
$287$	−5.15743	−	0.816856i	−0.304433	−	0.0482175i
$288$	−5.06883	+	2.51137i	−0.298684	+	0.147984i
$289$	3.20224	−	4.40750i	0.188367	−	0.259265i
$290$	−5.30649	−	19.7965i	−0.311608	−	1.16249i
$291$	8.16006	+	11.2314i	0.478351	+	0.658394i
$292$	−2.53186	−	28.1332i	−0.148166	−	1.64637i
$293$	7.35935	+	7.35935i	0.429938	+	0.429938i	0.888607	−	0.458669i	$-0.151674\pi$
$293$	7.35935	+	7.35935i	0.429938	+	0.429938i	−0.458669	+	0.888607i	$0.651674\pi$
$294$	−5.35374	−	2.95893i	−0.312237	−	0.172568i
$295$	−6.72334	+	4.69624i	−0.391448	+	0.273426i
$296$	−21.5334	−	5.68384i	−1.25160	−	0.330367i
$297$	0.870954	+	0.443773i	0.0505379	+	0.0257503i
$298$	5.98974	+	0.201709i	0.346976	+	0.0116847i
$299$	−6.22645			−0.360085
$300$	8.38774	+	5.44479i	0.484267	+	0.314355i
$301$	14.3057			0.824569
$302$	2.70060	+	0.0909447i	0.155402	+	0.00523328i
$303$	11.4676	+	5.84302i	0.658795	+	0.335673i
$304$	−8.67138	+	18.0058i	−0.497338	+	1.03270i
$305$	−7.67823	−	5.79979i	−0.439654	−	0.332095i
$306$	−4.20690	−	2.32509i	−0.240493	−	0.132916i
$307$	−1.88086	−	1.88086i	−0.107346	−	0.107346i	0.651394	−	0.758740i	$-0.274185\pi$
$307$	−1.88086	−	1.88086i	−0.107346	−	0.107346i	−0.758740	+	0.651394i	$0.774185\pi$
$308$	3.18437	−	0.286579i	0.181446	−	0.0163294i
$309$	−6.84479	−	9.42105i	−0.389387	−	0.535945i
$310$	−4.40366	+	11.4752i	−0.250111	+	0.651748i
$311$	7.58700	−	10.4426i	0.430219	−	0.592146i	−0.537784	−	0.843082i	$-0.680739\pi$
$311$	7.58700	−	10.4426i	0.430219	−	0.592146i	0.968004	+	0.250937i	$0.0807386\pi$
$312$	−6.99702	+	7.82953i	−0.396128	+	0.443260i
$313$	8.32486	+	1.31853i	0.470549	+	0.0745276i	0.387206	−	0.921993i	$-0.373440\pi$
$313$	8.32486	+	1.31853i	0.470549	+	0.0745276i	0.0833429	+	0.996521i	$0.473440\pi$
$314$	20.7602	+	22.2071i	1.17156	+	1.25322i
$315$	−0.639153	+	3.60064i	−0.0360122	+	0.202873i
$316$	−0.681168	−	2.70335i	−0.0383187	−	0.152075i
$317$	8.53106	+	16.7431i	0.479152	+	0.940389i	0.996418	+	0.0845641i	$0.0269498\pi$
$317$	8.53106	+	16.7431i	0.479152	+	0.940389i	−0.517266	+	0.855825i	$0.673050\pi$
$318$	1.72596	+	2.55199i	0.0967870	+	0.143108i
$319$	1.95773	−	6.02528i	0.109612	−	0.337351i
$320$	−17.4551	−	3.91392i	−0.975771	−	0.218795i
$321$	4.71434	+	14.5092i	0.263129	+	0.809827i
$322$	2.38437	−	3.05969i	0.132876	−	0.170510i
$323$	−16.7723	+	2.65647i	−0.933237	+	0.147810i
$324$	0.744599	−	1.85623i	0.0413666	−	0.103124i
$325$	18.2132	+	3.58370i	1.01028	+	0.198788i
$326$	−20.6665	−	3.99050i	−1.14461	−	0.221013i
$327$	2.70796	+	17.0974i	0.149750	+	0.945486i
$328$	4.54456	+	7.80402i	0.250931	+	0.430905i
$329$	16.0242	−	5.20658i	0.883443	−	0.287048i
$330$	1.25754	+	2.82375i	0.0692251	+	0.155442i
$331$	−28.4519	−	9.24458i	−1.56386	−	0.508128i	−0.606022	−	0.795448i	$-0.707236\pi$
$331$	−28.4519	−	9.24458i	−1.56386	−	0.508128i	−0.957835	+	0.287320i	$0.907236\pi$
$332$	12.8657	+	30.1013i	0.706096	+	1.65202i
$333$	7.01575	−	3.57470i	0.384461	−	0.195893i
$334$	−9.18797	−	19.6399i	−0.502743	−	1.07465i
$335$	13.5419	−	6.58559i	0.739873	−	0.359809i
$336$	−1.16799	−	6.43659i	−0.0637190	−	0.351145i
$337$	−1.67435	+	10.5714i	−0.0912078	+	0.575863i	0.899184	+	0.437571i	$0.144161\pi$
$337$	−1.67435	+	10.5714i	−0.0912078	+	0.575863i	−0.990392	+	0.138292i	$0.955839\pi$
$338$	−0.377182	+	1.04032i	−0.0205160	+	0.0565861i
$339$	11.1508	+	8.10154i	0.605629	+	0.440015i
$340$	−5.71289	−	14.0856i	−0.309825	−	0.763897i
$341$	−3.07372	+	2.23319i	−0.166451	+	0.120934i
$342$	−1.95603	−	6.78962i	−0.105770	−	0.367141i
$343$	13.0969	−	13.0969i	0.707167	−	0.707167i
$344$	−15.6419	−	19.1695i	−0.843354	−	1.03355i
$345$	3.54454	+	1.22504i	0.190832	+	0.0659538i
$346$	−28.2844	+	3.50860i	−1.52058	+	0.188623i
$347$	6.08901	−	11.9504i	0.326875	−	0.641529i	−0.667828	−	0.744316i	$-0.732776\pi$
$347$	6.08901	−	11.9504i	0.326875	−	0.641529i	0.994703	+	0.102786i	$0.0327758\pi$
$348$	−12.6374	−	2.88449i	−0.677436	−	0.154625i
$349$		−	11.8463i		−	0.634116i	−0.948406	−	0.317058i	$-0.897305\pi$
$349$		−	11.8463i		−	0.634116i	0.948406	−	0.317058i	$-0.102695\pi$
$350$	−8.73561	+	7.57761i	−0.466938	+	0.405041i
$351$		−	3.71248i		−	0.198157i
$352$	−3.86580	−	3.95366i	−0.206048	−	0.210731i
$353$	14.3565	−	28.1762i	0.764120	−	1.49967i	−0.0992300	−	0.995065i	$-0.531638\pi$
$353$	14.3565	−	28.1762i	0.764120	−	1.49967i	0.863350	−	0.504606i	$-0.168362\pi$
$354$	0.638517	+	5.14738i	0.0339368	+	0.273580i
$355$	−6.50090	+	1.97936i	−0.345032	+	0.105054i
$356$	−3.63963	+	4.35952i	−0.192900	+	0.231054i
$357$	3.93048	−	3.93048i	0.208023	−	0.208023i
$358$	−9.35087	+	2.69391i	−0.494209	+	0.142378i
$359$	−0.764560	+	0.555486i	−0.0403520	+	0.0293174i	−0.607778	−	0.794107i	$-0.707939\pi$
$359$	−0.764560	+	0.555486i	−0.0403520	+	0.0293174i	0.567426	+	0.823424i	$0.307939\pi$
$360$	5.52364	−	3.08048i	0.291122	−	0.162356i
$361$	−4.82376	−	3.50467i	−0.253882	−	0.184456i
$362$	4.41305	+	1.60001i	0.231945	+	0.0840945i
$363$	1.57131	−	9.92084i	0.0824722	−	0.520709i
$364$	−6.46038	−	10.2818i	−0.338616	−	0.538912i
$365$	4.35932	+	31.2787i	0.228177	+	1.63720i
$366$	−5.51242	+	2.57883i	−0.288139	+	0.134798i
$367$	−3.97266	+	2.02417i	−0.207371	+	0.105661i	−0.554592	−	0.832123i	$-0.687125\pi$
$367$	−3.97266	+	2.02417i	−0.207371	+	0.105661i	0.347221	+	0.937783i	$0.387125\pi$
$368$	−6.70699	+	0.150448i	−0.349626	+	0.00784262i
$369$	−3.03661	−	0.986653i	−0.158079	−	0.0513631i
$370$	24.3560	+	5.17461i	1.26621	+	0.269015i
$371$	−3.38838	+	1.10095i	−0.175916	+	0.0571585i
$372$	5.11452	+	5.85412i	0.265176	+	0.303522i
$373$	−1.49600	−	9.44535i	−0.0774598	−	0.489062i	−0.995669	−	0.0929666i	$-0.970365\pi$
$373$	−1.49600	−	9.44535i	−0.0774598	−	0.489062i	0.918209	−	0.396095i	$-0.129635\pi$
$374$	0.890778	−	4.61328i	0.0460610	−	0.238547i
$375$	−9.66314	−	5.62349i	−0.499003	−	0.290396i
$376$	−24.4976	−	15.7793i	−1.26337	−	0.813755i
$377$	−23.7651	+	3.76402i	−1.22397	+	0.193857i
$378$	1.82431	+	1.42166i	0.0938326	+	0.0731223i
$379$	−0.907685	−	2.79357i	−0.0466246	−	0.143496i	0.925034	−	0.379884i	$-0.124036\pi$
$379$	−0.907685	−	2.79357i	−0.0466246	−	0.143496i	−0.971659	+	0.236388i	$0.924036\pi$
$380$	8.70291	−	20.5793i	0.446450	−	1.05570i
$381$	4.45745	−	13.7186i	0.228362	−	0.702827i
$382$	−9.87838	+	6.68094i	−0.505422	+	0.341827i
$383$	11.7564	+	23.0732i	0.600723	+	1.17898i	0.968487	+	0.249066i	$0.0801235\pi$
$383$	11.7564	+	23.0732i	0.600723	+	1.17898i	−0.367764	+	0.929919i	$0.619876\pi$
$384$	−7.34785	+	8.60285i	−0.374968	+	0.439013i
$385$	−3.54041	+	0.493427i	−0.180436	+	0.0251474i
$386$	−14.0478	+	13.1325i	−0.715016	+	0.668428i
$387$	8.63971	+	1.36840i	0.439181	+	0.0695595i
$388$	23.8351	+	14.2410i	1.21005	+	0.722979i
$389$	−5.82961	+	8.02377i	−0.295573	+	0.406821i	−0.930814	−	0.365492i	$-0.880901\pi$
$389$	−5.82961	+	8.02377i	−0.295573	+	0.406821i	0.635241	+	0.772314i	$0.280901\pi$
$390$	7.38727	−	9.12430i	0.374069	−	0.462027i
$391$	−3.35062	−	4.61173i	−0.169448	−	0.233225i
$392$	−12.1717	−	1.23340i	−0.614763	−	0.0622962i
$393$	−11.7984	−	11.7984i	−0.595152	−	0.595152i
$394$	−5.23631	+	9.47433i	−0.263802	+	0.477310i
$395$	0.907873	+	2.98176i	0.0456801	+	0.150029i
$396$	1.95056	+	0.131522i	0.0980193	+	0.00660923i
$397$	21.3376	+	10.8721i	1.07090	+	0.545653i	0.898320	−	0.439341i	$-0.144788\pi$
$397$	21.3376	+	10.8721i	1.07090	+	0.545653i	0.172585	+	0.984995i	$0.444788\pi$
$398$	−0.660131	+	19.6026i	−0.0330894	+	0.982589i
$399$	8.17100			0.409062
$400$	19.7054	+	3.42021i	0.985269	+	0.171010i
$401$	6.16472			0.307851			0.153926	−	0.988082i	$-0.450808\pi$
$401$	6.16472			0.307851			0.153926	+	0.988082i	$0.450808\pi$
$402$	0.320536	−	9.51832i	0.0159869	−	0.474731i
$403$	12.8569	+	6.55093i	0.640449	+	0.326325i
$404$	25.6824	+	1.73171i	1.27775	+	0.0861558i
$405$	−0.730420	+	2.11341i	−0.0362948	+	0.105016i
$406$	7.25100	−	13.1196i	0.359861	−	0.651115i
$407$	5.44243	+	5.44243i	0.269771	+	0.269771i
$408$	−9.56435	−	0.969191i	−0.473506	−	0.0479821i
$409$	−0.203968	−	0.280737i	−0.0100855	−	0.0138816i	0.803944	−	0.594704i	$-0.202731\pi$
$409$	−0.203968	−	0.280737i	−0.0100855	−	0.0138816i	−0.814030	+	0.580823i	$0.802731\pi$
$410$	−5.49990	−	8.46733i	−0.271621	−	0.418172i
$411$	−8.49115	+	11.6871i	−0.418837	+	0.576480i
$412$	−19.9933	−	11.9456i	−0.984999	−	0.588518i
$413$	−5.92431	−	0.938319i	−0.291516	−	0.0461717i
$414$	1.73267	−	1.61977i	0.0851560	−	0.0796074i
$415$	−16.0063	−	32.9137i	−0.785720	−	1.61567i
$416$	−6.71363	+	19.8989i	−0.329163	+	0.975624i
$417$	10.4453	+	20.5000i	0.511508	+	1.00389i
$418$	5.72114	−	3.86932i	0.279830	−	0.189255i
$419$	−8.61814	+	26.5239i	−0.421024	+	1.29578i	0.485727	+	0.874111i	$0.338555\pi$
$419$	−8.61814	+	26.5239i	−0.421024	+	1.29578i	−0.906751	+	0.421668i	$0.861445\pi$
$420$	1.65480	+	7.12419i	0.0807459	+	0.347625i
$421$	4.87173	+	14.9936i	0.237433	+	0.730745i	0.996789	+	0.0800694i	$0.0255142\pi$
$421$	4.87173	+	14.9936i	0.237433	+	0.730745i	−0.759356	+	0.650676i	$0.774486\pi$
$422$	10.5574	+	8.22719i	0.513924	+	0.400493i
$423$	10.1756	−	1.61165i	0.494754	−	0.0783613i
$424$	5.18011	+	3.33659i	0.251568	+	0.162039i
$425$	7.14664	+	15.4184i	0.346663	+	0.747901i
$426$	−0.814828	+	4.21994i	−0.0394785	+	0.204457i
$427$	−1.10095	−	6.95112i	−0.0532787	−	0.336388i
$428$	20.0748	+	22.9777i	0.970351	+	1.11067i
$429$	3.45131	−	1.12140i	0.166631	−	0.0541417i
$430$	18.5113	+	20.5549i	0.892693	+	0.991245i
$431$	11.2786	+	3.66463i	0.543269	+	0.176519i	0.567779	−	0.823181i	$-0.307803\pi$
$431$	11.2786	+	3.66463i	0.543269	+	0.176519i	−0.0245103	+	0.999700i	$0.507803\pi$
$432$	−0.0897033	−	3.99899i	−0.00431585	−	0.192402i
$433$	3.48035	−	1.77333i	0.167255	−	0.0852207i	−0.368359	−	0.929684i	$-0.620080\pi$
$433$	3.48035	−	1.77333i	0.167255	−	0.0852207i	0.535614	+	0.844463i	$0.320080\pi$
$434$	−8.14259	+	3.80929i	−0.390857	+	0.182852i
$435$	14.2694	+	2.53297i	0.684164	+	0.121447i
$436$	18.4193	+	29.3145i	0.882123	+	1.40391i
$437$	1.31085	−	8.27639i	0.0627065	−	0.395913i
$438$	18.7775	+	6.80803i	0.897225	+	0.325300i
$439$	−5.00770	−	3.63831i	−0.239005	−	0.173647i	0.461835	−	0.886966i	$-0.347191\pi$
$439$	−5.00770	−	3.63831i	−0.239005	−	0.173647i	−0.700840	+	0.713319i	$0.747191\pi$
$440$	4.53226	+	4.20457i	0.216067	+	0.200445i
$441$	3.49931	−	2.54239i	0.166634	−	0.121066i
$442$	−17.1472	+	4.93998i	−0.815611	+	0.234971i
$443$	−4.96290	+	4.96290i	−0.235794	+	0.235794i	−0.815106	−	0.579312i	$-0.803321\pi$
$443$	−4.96290	+	4.96290i	−0.235794	+	0.235794i	0.579312	+	0.815106i	$0.303321\pi$
$444$	10.0925	−	12.0888i	0.478971	−	0.573707i
$445$	3.82701	−	5.06650i	0.181418	−	0.240175i
$446$	0.469984	+	3.78876i	0.0222544	+	0.179403i
$447$	−1.92391	+	3.77589i	−0.0909980	+	0.178594i
$448$	−7.20741	−	10.9192i	−0.340518	−	0.515884i
$449$			22.5446i			1.06395i	0.846761	+	0.531973i	$0.178549\pi$
$449$			22.5446i			1.06395i	−0.846761	+	0.531973i	$0.821451\pi$
$450$	−6.00055	+	3.74078i	−0.282869	+	0.176342i
$451$		−	3.12102i		−	0.146963i
$452$	26.8752	+	6.13425i	1.26410	+	0.288531i
$453$	−0.867438	+	1.70244i	−0.0407558	+	0.0799877i
$454$	16.5379	−	2.05148i	0.776163	−	0.0962807i
$455$	7.77424	+	11.1299i	0.364462	+	0.521780i
$456$	−8.93417	−	10.9490i	−0.418381	−	0.512734i
$457$	−3.08538	+	3.08538i	−0.144328	+	0.144328i	−0.775579	−	0.631251i	$-0.782542\pi$
$457$	−3.08538	+	3.08538i	−0.144328	+	0.144328i	0.631251	+	0.775579i	$0.282542\pi$
$458$	1.60556	+	5.57309i	0.0750229	+	0.260413i
$459$	2.74971	−	1.99778i	0.128345	−	0.0932484i
$460$	7.48155	−	0.533229i	0.348829	−	0.0248619i
$461$	−28.0983	−	20.4146i	−1.30867	−	0.950804i	−0.308670	−	0.951169i	$-0.599884\pi$
$461$	−28.0983	−	20.4146i	−1.30867	−	0.950804i	−1.00000		0.000364875i	$0.999884\pi$
$462$	−0.770593	+	2.12541i	−0.0358513	+	0.0988829i
$463$	0.272846	−	1.72268i	0.0126802	−	0.0800597i	−0.980537	−	0.196336i	$-0.937096\pi$
$463$	0.272846	−	1.72268i	0.0126802	−	0.0800597i	0.993217	+	0.116276i	$0.0370957\pi$
$464$	−25.5083	+	4.62875i	−1.18419	+	0.214884i
$465$	−6.03021	−	6.25883i	−0.279644	−	0.290246i
$466$	4.98068	+	10.6465i	0.230725	+	0.493190i
$467$	31.3897	−	15.9938i	1.45254	−	0.740107i	0.463272	−	0.886216i	$-0.346675\pi$
$467$	31.3897	−	15.9938i	1.45254	−	0.740107i	0.989268	+	0.146109i	$0.0466751\pi$
$468$	−2.91815	−	6.82747i	−0.134892	−	0.315600i
$469$	10.4744	+	3.40334i	0.483663	+	0.157152i
$470$	28.2159	+	16.2869i	1.30150	+	0.751257i
$471$	−20.4437	+	6.64257i	−0.941998	+	0.306074i
$472$	5.22031	+	8.96444i	0.240284	+	0.412622i
$473$	1.33760	+	8.44527i	0.0615029	+	0.388314i
$474$	1.93555	+	0.373736i	0.0889030	+	0.0171663i
$475$	−8.59797	+	23.4550i	−0.394502	+	1.07619i
$476$	4.13888	−	10.3179i	0.189705	−	0.472920i
$477$	−2.15166	+	0.340790i	−0.0985179	+	0.0156037i
$478$	−9.66641	+	12.4042i	−0.442131	+	0.567355i
$479$	8.73304	+	26.8775i	0.399023	+	1.22807i	0.925784	+	0.378053i	$0.123406\pi$
$479$	8.73304	+	26.8775i	0.399023	+	1.22807i	−0.526761	+	0.850013i	$0.676594\pi$
$480$	7.73694	−	10.0070i	0.353141	−	0.456754i
$481$	9.03315	−	27.8012i	0.411876	−	1.26762i
$482$	0.865987	+	1.28044i	0.0394446	+	0.0583224i
$483$	1.24525	+	2.44393i	0.0566606	+	0.111203i
$484$	−4.90844	−	19.4801i	−0.223111	−	0.885461i
$485$	−27.3923	−	14.6051i	−1.24382	−	0.663185i
$486$	0.965777	+	1.03309i	0.0438085	+	0.0468619i
$487$	−20.4192	−	3.23409i	−0.925283	−	0.146550i	−0.324430	−	0.945910i	$-0.605172\pi$
$487$	−20.4192	−	3.23409i	−0.925283	−	0.146550i	−0.600853	+	0.799359i	$0.705172\pi$
$488$	−8.11060	+	9.07560i	−0.367150	+	0.410833i
$489$	8.74823	−	12.0409i	0.395609	−	0.544508i
$490$	13.6594	+	0.714551i	0.617068	+	0.0322801i
$491$	8.93859	+	12.3029i	0.403393	+	0.555223i	0.961591	−	0.274485i	$-0.0885073\pi$
$491$	8.93859	+	12.3029i	0.403393	+	0.555223i	−0.558199	+	0.829707i	$0.688507\pi$
$492$	−6.36005	+	0.572376i	−0.286733	+	0.0258047i
$493$	−15.5765	−	15.5765i	−0.701531	−	0.701531i
$494$	−22.9584	−	12.6887i	−1.03295	−	0.570893i
$495$	−2.18537	−	0.0406558i	−0.0982249	−	0.00182734i
$496$	14.0075	+	6.74586i	0.628955	+	0.302898i
$497$	−4.42845	−	2.25641i	−0.198643	−	0.101214i
$498$	−23.1344	−	0.779066i	−1.03668	−	0.0349108i
$499$	−12.1532			−0.544051			−0.272025	−	0.962290i	$-0.587693\pi$
$499$	−12.1532			−0.544051			−0.272025	+	0.962290i	$0.587693\pi$
$500$	−22.1914	−	2.74633i	−0.992429	−	0.122820i
$501$	15.3320			0.684985
$502$	39.0064	+	1.31357i	1.74094	+	0.0586274i
$503$	−20.2930	−	10.3398i	−0.904820	−	0.461029i	−0.0612957	−	0.998120i	$-0.519523\pi$
$503$	−20.2930	−	10.3398i	−0.904820	−	0.461029i	−0.843524	+	0.537091i	$0.819523\pi$
$504$	4.47250	+	1.18054i	0.199221	+	0.0525853i
$505$	−28.7740	−	0.535302i	−1.28043	−	0.0238206i
$506$	2.02920	+	1.12151i	0.0902089	+	0.0498570i
$507$	−0.553294	−	0.553294i	−0.0245727	−	0.0245727i
$508$	−2.58585	−	28.7331i	−0.114729	−	1.27483i
$509$	23.4284	+	32.2465i	1.03845	+	1.42930i	0.898412	+	0.439154i	$0.144722\pi$
$509$	23.4284	+	32.2465i	1.03845	+	1.42930i	0.140036	+	0.990146i	$0.455278\pi$
$510$	10.7334	+	0.561485i	0.475281	+	0.0248630i
$511$	−13.5766	+	18.6866i	−0.600594	+	0.826646i
$512$	−6.75096	+	21.5969i	−0.298353	+	0.954456i
$513$	4.93474	+	0.781585i	0.217874	+	0.0345078i
$514$	11.1326	+	11.9085i	0.491037	+	0.525261i
$515$	22.9771	+	12.2510i	1.01249	+	0.539845i
$516$	16.9646	−	4.27459i	0.746823	−	0.188178i
$517$	4.57194	+	8.97293i	0.201074	+	0.394629i
$518$	10.2024	+	15.0851i	0.448266	+	0.662802i
$519$	6.22774	−	19.1670i	0.273367	−	0.841338i
$520$	6.41359	−	22.5868i	0.281254	−	0.990498i
$521$	−2.01724	−	6.20841i	−0.0883767	−	0.271996i	0.897094	−	0.441839i	$-0.145674\pi$
$521$	−2.01724	−	6.20841i	−0.0883767	−	0.271996i	−0.985471	+	0.169844i	$0.945674\pi$
$522$	5.63406	−	7.22978i	0.246596	−	0.316439i
$523$	−20.1531	+	3.19194i	−0.881234	+	0.139574i	−0.580622	−	0.814173i	$-0.697191\pi$
$523$	−20.1531	+	3.19194i	−0.881234	+	0.139574i	−0.300612	+	0.953747i	$0.597191\pi$
$524$	−30.9721	−	12.4240i	−1.35302	−	0.542745i
$525$	−2.23587	−	7.86552i	−0.0975812	−	0.343279i
$526$	−23.4957	−	4.53678i	−1.02446	−	0.197813i
$527$	2.06659	+	13.0479i	0.0900221	+	0.568377i
$528$	3.69058	−	1.29134i	0.160612	−	0.0561983i
$529$	−19.1991	+	6.23816i	−0.834742	+	0.271224i
$530$	−5.96635	−	3.44392i	−0.259162	−	0.149594i
$531$	−3.48814	−	1.13336i	−0.151372	−	0.0491838i
$532$	15.0270	−	6.42272i	0.651501	−	0.278460i
$533$	−10.5615	+	5.38137i	−0.457470	+	0.233093i
$534$	−1.70165	−	3.63738i	−0.0736376	−	0.157405i
$535$	−23.6689	−	24.5662i	−1.02329	−	1.06209i
$536$	−6.89229	−	17.7567i	−0.297701	−	0.766974i
$537$	1.07642	−	6.79627i	0.0464511	−	0.293281i
$538$	2.40472	−	6.63258i	0.103675	−	0.285951i
$539$	3.42055	+	2.48518i	0.147334	+	0.107044i
$540$	0.317934	+	4.46082i	0.0136817	+	0.191963i
$541$	−21.6765	+	15.7489i	−0.931945	+	0.677097i	−0.946468	−	0.322797i	$-0.895377\pi$
$541$	−21.6765	+	15.7489i	−0.931945	+	0.677097i	0.0145235	+	0.999895i	$0.495377\pi$
$542$	−11.0042	−	38.1967i	−0.472669	−	1.64069i
$543$	−2.34708	+	2.34708i	−0.100723	+	0.100723i
$544$	−18.3512	+	5.73555i	−0.786803	+	0.245910i
$545$	−22.1652	−	31.7327i	−0.949454	−	1.35928i
$546$	8.52106	−	1.05701i	0.364668	−	0.0452360i
$547$	−1.09113	+	2.14147i	−0.0466534	+	0.0915625i	−0.913156	−	0.407610i	$-0.866362\pi$
$547$	−1.09113	+	2.14147i	−0.0466534	+	0.0915625i	0.866503	+	0.499172i	$0.166362\pi$
$548$	−6.42925	+	28.1676i	−0.274644	+	1.20326i
$549$		−	4.30332i		−	0.183661i
$550$	−5.29016	−	4.44847i	−0.225573	−	0.189684i
$551$		−	32.3818i		−	1.37951i
$552$	1.91328	−	4.34080i	0.0814345	−	0.184757i
$553$	−1.03494	+	2.03119i	−0.0440103	+	0.0863751i
$554$	−4.65060	−	37.4906i	−0.197585	−	1.59282i
$555$	−10.6121	+	14.0492i	−0.450460	+	0.596354i
$556$	35.3233	+	29.4904i	1.49804	+	1.25067i
$557$	−17.1440	+	17.1440i	−0.726416	+	0.726416i	−0.969904	−	0.243488i	$-0.921708\pi$
$557$	−17.1440	+	17.1440i	−0.726416	+	0.726416i	0.243488	+	0.969904i	$0.421708\pi$
$558$	−5.28195	+	1.52169i	−0.223603	+	0.0644181i
$559$	26.2724	−	19.0881i	1.11121	−	0.807339i
$560$	8.64316	+	11.8011i	0.365240	+	0.498686i
$561$	2.68782	+	1.95282i	0.113480	+	0.0824481i
$562$	2.97391	+	1.07823i	0.125447	+	0.0454822i
$563$	−3.26270	+	20.5999i	−0.137506	+	0.868181i	0.818430	+	0.574606i	$0.194845\pi$
$563$	−3.26270	+	20.5999i	−0.137506	+	0.868181i	−0.955936	+	0.293574i	$0.905155\pi$
$564$	17.4467	−	10.9623i	0.734638	−	0.461597i
$565$	−30.3457	−	5.38670i	−1.27665	−	0.226620i
$566$	21.5957	−	10.1030i	0.907736	−	0.424659i
$567$	−1.45718	+	0.742468i	−0.0611956	+	0.0311807i
$568$	1.81852	+	8.40121i	0.0763033	+	0.352507i
$569$	−14.5574	−	4.72997i	−0.610276	−	0.198291i	−0.0124579	−	0.999922i	$-0.503966\pi$
$569$	−14.5574	−	4.72997i	−0.610276	−	0.198291i	−0.597818	+	0.801632i	$0.703966\pi$
$570$	10.5731	+	11.7403i	0.442857	+	0.491748i
$571$	36.1142	−	11.7342i	1.51133	−	0.491062i	0.568034	−	0.823005i	$-0.307704\pi$
$571$	36.1142	−	11.7342i	1.51133	−	0.491062i	0.943299	+	0.331943i	$0.107704\pi$
$572$	5.46571	−	4.77519i	0.228533	−	0.199661i
$573$	−1.31915	−	8.32878i	−0.0551082	−	0.347940i
$574$	1.40004	−	7.25069i	0.0584364	−	0.302638i
$575$	−8.32567	+	1.00286i	−0.347204	+	0.0418222i
$576$	−3.30833	−	7.28388i	−0.137847	−	0.303495i
$577$	−29.1734	+	4.62061i	−1.21451	+	0.192359i	−0.730627	−	0.682777i	$-0.760772\pi$
$577$	−29.1734	+	4.62061i	−1.21451	+	0.192359i	−0.483878	+	0.875135i	$0.660772\pi$
$578$	6.07720	+	4.73587i	0.252778	+	0.196986i
$579$	−4.20198	−	12.9324i	−0.174628	−	0.537450i
$580$	28.2332	−	6.55799i	1.17232	−	0.272306i
$581$	8.27184	−	25.4581i	0.343174	−	1.05618i
$582$	−16.2629	+	10.9989i	−0.674121	+	0.455921i
$583$	−0.966752	−	1.89736i	−0.0400388	−	0.0785806i
$584$	39.8844	−	2.23949i	1.65043	−	0.0926708i
$585$	3.63050	+	7.46538i	0.150103	+	0.308655i
$586$	−10.7521	+	10.0515i	−0.444165	+	0.415224i
$587$	−8.67609	−	1.37416i	−0.358100	−	0.0567175i	−0.0252077	−	0.999682i	$-0.508025\pi$
$587$	−8.67609	−	1.37416i	−0.358100	−	0.0567175i	−0.332893	+	0.942965i	$0.608025\pi$
$588$	4.43701	−	7.42621i	0.182979	−	0.306252i
$589$	−11.4145	+	15.7107i	−0.470325	+	0.647347i
$590$	−6.31771	−	9.72639i	−0.260096	−	0.400429i
$591$	−4.49919	−	6.19260i	−0.185072	−	0.254729i
$592$	9.05856	−	30.1651i	0.372304	−	1.23978i
$593$	−16.2759	−	16.2759i	−0.668372	−	0.668372i	0.288967	−	0.957339i	$-0.406688\pi$
$593$	−16.2759	−	16.2759i	−0.668372	−	0.668372i	−0.957339	+	0.288967i	$0.906688\pi$
$594$	−0.668690	+	1.20989i	−0.0274367	+	0.0496426i
$595$	−4.06006	+	11.7474i	−0.166446	+	0.481598i
$596$	−0.570195	+	8.45637i	−0.0233561	+	0.346386i
$597$	−12.3573	−	6.29638i	−0.505753	−	0.257694i
$598$	0.296365	−	8.80055i	0.0121192	−	0.359881i
$599$	−22.8730			−0.934566			−0.467283	−	0.884108i	$-0.654767\pi$
$599$	−22.8730			−0.934566			−0.467283	+	0.884108i	$0.654767\pi$
$600$	−8.09497	+	11.5962i	−0.330476	+	0.473412i
$601$	28.0770			1.14529			0.572643	−	0.819805i	$-0.305918\pi$
$601$	28.0770			1.14529			0.572643	+	0.819805i	$0.305918\pi$
$602$	−0.680920	+	20.2199i	−0.0277522	+	0.824102i
$603$	6.00029	+	3.05730i	0.244351	+	0.124503i
$604$	−0.257085	+	3.81273i	−0.0104606	+	0.155138i
$605$	6.54206	+	21.4863i	0.265973	+	0.873543i
$606$	−8.80443	+	15.9303i	−0.357656	+	0.647124i
$607$	16.1309	+	16.1309i	0.654732	+	0.654732i	0.954129	−	0.299397i	$-0.0967855\pi$
$607$	16.1309	+	16.1309i	0.654732	+	0.654732i	−0.299397	+	0.954129i	$0.596786\pi$
$608$	−25.0368	−	13.1133i	−1.01538	−	0.531813i
$609$	6.23026	+	8.57522i	0.252463	+	0.347485i
$610$	8.56297	−	10.5764i	0.346704	−	0.428228i
$611$	22.4813	−	30.9429i	0.909496	−	1.25181i
$612$	3.48655	−	5.83542i	0.140935	−	0.235883i
$613$	8.76640	+	1.38846i	0.354071	+	0.0560794i	0.330937	−	0.943653i	$-0.392635\pi$
$613$	8.76640	+	1.38846i	0.354071	+	0.0560794i	0.0231347	+	0.999732i	$0.492635\pi$
$614$	2.74795	−	2.56891i	0.110898	−	0.103673i
$615$	7.07115	−	0.985506i	0.285136	−	0.0397395i
$616$	0.253486	+	4.51447i	0.0102132	+	0.181893i
$617$	9.82315	+	19.2790i	0.395465	+	0.776144i	0.999788	−	0.0205955i	$-0.00655621\pi$
$617$	9.82315	+	19.2790i	0.395465	+	0.776144i	−0.604323	+	0.796740i	$0.706556\pi$
$618$	13.6416	−	9.22610i	0.548747	−	0.371128i
$619$	−7.47376	+	23.0019i	−0.300396	+	0.924524i	0.680959	+	0.732321i	$0.261563\pi$
$619$	−7.47376	+	23.0019i	−0.300396	+	0.924524i	−0.981355	+	0.192202i	$0.938437\pi$
$620$	−16.0096	−	6.77038i	−0.642961	−	0.271905i
$621$	0.518274	+	1.59508i	0.0207976	+	0.0640085i
$622$	14.3986	+	11.2206i	0.577331	+	0.449905i
$623$	4.58672	−	0.726464i	0.183763	−	0.0291052i
$624$	−10.7333	−	10.2623i	−0.429676	−	0.410823i
$625$	24.9308	+	1.85843i	0.997233	+	0.0743374i
$626$	−2.25987	+	11.7037i	−0.0903224	+	0.467774i
$627$	0.763995	+	4.82368i	0.0305110	+	0.192639i
$628$	−32.3760	+	28.2857i	−1.29194	+	1.12872i
$629$	25.4524	−	8.26999i	1.01485	−	0.329746i
$630$	−5.05876	−	1.07477i	−0.201546	−	0.0428198i
$631$	−26.5940	−	8.64091i	−1.05869	−	0.343989i	−0.272616	−	0.962123i	$-0.587889\pi$
$631$	−26.5940	−	8.64091i	−1.05869	−	0.343989i	−0.786073	+	0.618134i	$0.787889\pi$
$632$	3.85337	−	0.834098i	0.153279	−	0.0331786i
$633$	−8.43272	+	4.29669i	−0.335171	+	0.170778i
$634$	−24.0710	+	11.2610i	−0.955983	+	0.447230i
$635$	4.45227	+	31.9457i	0.176683	+	1.26773i
$636$	−3.68916	+	2.31802i	−0.146285	+	0.0919156i
$637$	2.51200	−	15.8602i	0.0995292	−	0.628403i
$638$	8.42302	+	3.05387i	0.333470	+	0.120904i
$639$	−2.45865	−	1.78632i	−0.0972629	−	0.0706656i
$640$	6.36281	−	24.4850i	0.251512	−	0.967854i
$641$	3.18368	−	2.31308i	0.125748	−	0.0913611i	−0.523134	−	0.852251i	$-0.675237\pi$
$641$	3.18368	−	2.31308i	0.125748	−	0.0913611i	0.648881	+	0.760890i	$0.275237\pi$
$642$	−20.7319	+	5.97270i	−0.818224	+	0.235724i
$643$	1.48607	−	1.48607i	0.0586048	−	0.0586048i	−0.677197	−	0.735802i	$-0.736806\pi$
$643$	1.48607	−	1.48607i	0.0586048	−	0.0586048i	0.735802	+	0.677197i	$0.236806\pi$
$644$	4.21111	+	3.51573i	0.165941	+	0.138539i
$645$	−18.7117	+	5.69725i	−0.736772	+	0.224329i
$646$	−2.95637	−	23.8326i	−0.116317	−	0.937683i
$647$	10.7848	−	21.1664i	0.423994	−	0.832135i	−0.575899	−	0.817521i	$-0.695348\pi$
$647$	10.7848	−	21.1664i	0.423994	−	0.832135i	0.999893	−	0.0146144i	$-0.00465208\pi$
$648$	2.58817	+	1.14078i	0.101673	+	0.0448140i
$649$		−	3.58510i		−	0.140727i
$650$	−5.93215	+	25.5721i	−0.232678	+	1.00302i
$651$		−	6.35659i		−	0.249134i
$652$	6.62390	−	29.0204i	0.259412	−	1.13653i
$653$	1.32509	−	2.60064i	0.0518549	−	0.101771i	−0.863625	−	0.504135i	$-0.831811\pi$
$653$	1.32509	−	2.60064i	0.0518549	−	0.101771i	0.915480	+	0.402364i	$0.131811\pi$
$654$	−24.2945	+	3.01366i	−0.949990	+	0.117844i
$655$	35.2633	+	12.1874i	1.37785	+	0.476202i
$656$	−11.2466	+	6.05188i	−0.439106	+	0.236286i
$657$	−9.98680	+	9.98680i	−0.389622	+	0.389622i
$658$	6.59633	+	22.8966i	0.257152	+	0.892604i
$659$	−26.9961	+	19.6138i	−1.05162	+	0.764046i	−0.972520	−	0.232821i	$-0.925204\pi$
$659$	−26.9961	+	19.6138i	−1.05162	+	0.764046i	−0.0790990	+	0.996867i	$0.525204\pi$
$660$	−4.05098	+	1.64301i	−0.157684	+	0.0639542i
$661$	−3.15278	−	2.29063i	−0.122629	−	0.0890950i	0.524780	−	0.851238i	$-0.324147\pi$
$661$	−3.15278	−	2.29063i	−0.122629	−	0.0890950i	−0.647409	+	0.762143i	$0.724147\pi$
$662$	14.4206	−	39.7742i	0.560474	−	1.54587i
$663$	1.97390	−	12.4627i	0.0766599	−	0.484012i
$664$	−43.1579	+	16.7518i	−1.67485	+	0.650094i
$665$	−16.4310	+	7.99058i	−0.637166	+	0.309861i
$666$	4.71860	+	10.0863i	0.182842	+	0.390836i
$667$	9.68533	−	4.93492i	0.375017	−	0.191081i
$668$	28.1965	−	12.0516i	1.09096	−	0.466290i
$669$	−2.56746	−	0.834219i	−0.0992638	−	0.0322528i
$670$	8.66359	+	19.4537i	0.334704	+	0.751564i
$671$	4.00059	−	1.29987i	0.154441	−	0.0501810i
$672$	9.15315	−	1.34448i	0.353091	−	0.0518645i
$673$	−6.76456	−	42.7098i	−0.260755	−	1.64634i	−0.676197	−	0.736721i	$-0.736373\pi$
$673$	−6.76456	−	42.7098i	−0.260755	−	1.64634i	0.415442	−	0.909619i	$-0.363627\pi$
$674$	−14.8621	−	2.86973i	−0.572467	−	0.110538i
$675$	−0.597949	−	4.96412i	−0.0230151	−	0.191069i
$676$	−1.45245	−	0.582631i	−0.0558635	−	0.0224089i
$677$	−17.8725	+	2.83072i	−0.686896	+	0.108794i	−0.490120	−	0.871655i	$-0.663047\pi$
$677$	−17.8725	+	2.83072i	−0.686896	+	0.108794i	−0.196776	+	0.980449i	$0.563047\pi$
$678$	−11.9816	+	15.3751i	−0.460150	+	0.590477i
$679$	−7.01598	−	21.5930i	−0.269249	−	0.828662i
$680$	20.1806	−	7.40423i	0.773892	−	0.283939i
$681$	−3.64136	+	11.2070i	−0.139537	+	0.429452i
$682$	−3.01012	−	4.45073i	−0.115263	−	0.170427i
$683$	−17.9286	−	35.1869i	−0.686020	−	1.34639i	−0.926706	−	0.375788i	$-0.877372\pi$
$683$	−17.9286	−	35.1869i	−0.686020	−	1.34639i	0.240685	−	0.970603i	$-0.422628\pi$
$684$	9.68963	−	2.44151i	0.370492	−	0.0933535i
$685$	5.64575	−	31.8050i	0.215713	−	1.21521i
$686$	17.8880	+	19.1347i	0.682965	+	0.730567i
$687$	−4.05055	−	0.641545i	−0.154538	−	0.0244765i
$688$	27.8389	−	21.1960i	1.06135	−	0.808091i
$689$	−4.75375	+	6.54298i	−0.181104	+	0.249268i
$690$	−1.90020	+	4.95159i	−0.0723392	+	0.188504i
$691$	20.7179	+	28.5157i	0.788146	+	1.08479i	0.994336	+	0.106278i	$0.0338933\pi$
$691$	20.7179	+	28.5157i	0.788146	+	1.08479i	−0.206190	+	0.978512i	$0.566107\pi$
$692$	−3.61282	−	40.1445i	−0.137339	−	1.52607i
$693$	−1.13040	−	1.13040i	−0.0429402	−	0.0429402i
$694$	16.6010	+	9.17510i	0.630164	+	0.348282i
$695$	−41.0517	−	31.0086i	−1.55718	−	1.17622i
$696$	4.67848	−	17.7246i	0.177337	−	0.671849i
$697$	−9.66924	−	4.92672i	−0.366248	−	0.186613i
$698$	16.7437	+	0.563855i	0.633757	+	0.0213422i
$699$	−8.31130			−0.314362
$700$	−10.2945	−	12.7077i	−0.389096	−	0.480306i
$701$	41.8330			1.58001			0.790005	−	0.613100i	$-0.210078\pi$
$701$	41.8330			1.58001			0.790005	+	0.613100i	$0.210078\pi$
$702$	5.24726	+	0.176705i	0.198045	+	0.00666931i
$703$	35.0524	+	17.8601i	1.32203	+	0.673607i
$704$	5.77215	−	5.27579i	0.217546	−	0.198839i
$705$	−18.8859	+	13.1918i	−0.711284	+	0.496830i
$706$	39.1413	+	21.6328i	1.47310	+	0.814161i
$707$	−14.8836	−	14.8836i	−0.559754	−	0.559754i
$708$	−7.30576	+	0.657485i	−0.274567	+	0.0247098i
$709$	22.6320	+	31.1503i	0.849962	+	1.16987i	0.983871	+	0.178879i	$0.0572470\pi$
$709$	22.6320	+	31.1503i	0.849962	+	1.16987i	−0.133909	+	0.990994i	$0.542753\pi$
$710$	−2.48823	−	9.28266i	−0.0933817	−	0.348372i
$711$	−0.819328	+	1.12771i	−0.0307272	+	0.0422924i
$712$	−5.98856	−	5.35181i	−0.224431	−	0.200567i
$713$	−6.43858	−	1.01977i	−0.241127	−	0.0381907i
$714$	5.36830	+	5.74247i	0.200904	+	0.214906i
$715$	−5.84357	+	5.63011i	−0.218537	+	0.210554i
$716$	−3.36253	−	13.3449i	−0.125663	−	0.498721i
$717$	−5.04832	−	9.90789i	−0.188533	−	0.370017i
$718$	−0.748739	−	1.10708i	−0.0279427	−	0.0413158i
$719$	11.1156	−	34.2102i	0.414540	−	1.27582i	−0.498121	−	0.867108i	$-0.665976\pi$
$719$	11.1156	−	34.2102i	0.414540	−	1.27582i	0.912661	−	0.408717i	$-0.134024\pi$
$720$	4.09108	+	7.95381i	0.152465	+	0.296421i
$721$	5.88512	+	18.1125i	0.219173	+	0.674546i
$722$	5.18314	−	6.65115i	0.192896	−	0.247530i
$723$	−1.07958	+	0.170989i	−0.0401500	+	0.00635914i
$724$	−2.47152	+	6.16131i	−0.0918534	+	0.228983i
$725$	−31.1711	+	8.86076i	−1.15767	+	0.329081i
$726$	13.9474	+	2.69311i	0.517638	+	0.0999508i
$727$	−3.48933	−	22.0307i	−0.129412	−	0.817075i	−0.963942	−	0.266113i	$-0.914261\pi$
$727$	−3.48933	−	22.0307i	−0.129412	−	0.817075i	0.834530	−	0.550963i	$-0.185739\pi$
$728$	14.8399	−	8.64180i	0.550003	−	0.320286i
$729$	−0.951057	+	0.309017i	−0.0352243	+	0.0114451i
$730$	−44.4172	+	4.67272i	−1.64396	+	0.172945i
$731$	28.2758	+	9.18736i	1.04582	+	0.339807i
$732$	−3.38258	−	7.91406i	−0.125024	−	0.292512i
$733$	−22.9079	+	11.6722i	−0.846124	+	0.431122i	−0.822613	−	0.568602i	$-0.807484\pi$
$733$	−22.9079	+	11.6722i	−0.846124	+	0.431122i	−0.0235109	+	0.999724i	$0.507484\pi$
$734$	−2.67190	−	5.71135i	−0.0986215	−	0.210810i
$735$	−4.55046	+	8.53451i	−0.167846	+	0.314800i
$736$	0.106593	−	9.48691i	0.00392906	−	0.349692i
$737$	−1.02977	+	6.50168i	−0.0379319	+	0.239493i
$738$	1.53908	−	4.24501i	0.0566544	−	0.156261i
$739$	6.76750	+	4.91688i	0.248947	+	0.180870i	0.705260	−	0.708949i	$-0.250830\pi$
$739$	6.76750	+	4.91688i	0.248947	+	0.180870i	−0.456313	+	0.889819i	$0.650830\pi$
$740$	−8.47314	+	34.1788i	−0.311479	+	1.25644i
$741$	15.0060	−	10.9025i	0.551260	−	0.400514i
$742$	−1.39482	−	4.84158i	−0.0512054	−	0.177740i
$743$	0.563949	−	0.563949i	0.0206893	−	0.0206893i	−0.696686	−	0.717376i	$-0.745343\pi$
$743$	0.563949	−	0.563949i	0.0206893	−	0.0206893i	0.717376	+	0.696686i	$0.245343\pi$
$744$	−8.51772	+	6.95029i	−0.312275	+	0.254810i
$745$	0.176257	−	9.47434i	0.00645757	−	0.347113i
$746$	13.4214	−	1.66488i	0.491392	−	0.0609557i
$747$	7.43080	−	14.5838i	0.271879	−	0.533592i
$748$	6.47806	+	1.47862i	0.236861	+	0.0540636i
$749$		−	24.9499i		−	0.911651i
$750$	8.40825	−	13.3903i	0.307026	−	0.488946i
$751$			41.2218i			1.50420i	0.659046	+	0.752102i	$0.270960\pi$
$751$			41.2218i			1.50420i	−0.659046	+	0.752102i	$0.729040\pi$
$752$	23.4687	−	33.8741i	0.855815	−	1.23526i
$753$	−12.5289	+	24.5894i	−0.456579	+	0.896087i
$754$	−4.18895	−	33.7691i	−0.152553	−	1.22980i
$755$	0.0794693	−	4.27171i	0.00289219	−	0.155463i
$756$	−2.09623	+	2.51084i	−0.0762390	+	0.0913184i
$757$	20.8498	−	20.8498i	0.757797	−	0.757797i	−0.218124	−	0.975921i	$-0.569994\pi$
$757$	20.8498	−	20.8498i	0.757797	−	0.757797i	0.975921	+	0.218124i	$0.0699937\pi$
$758$	3.99166	−	1.14997i	0.144984	−	0.0417686i
$759$	−1.32632	+	0.963629i	−0.0481424	+	0.0349775i
$760$	28.6729	+	13.2803i	1.04007	+	0.481728i
$761$	13.7177	+	9.96648i	0.497266	+	0.361285i	0.807972	−	0.589221i	$-0.200565\pi$
$761$	13.7177	+	9.96648i	0.497266	+	0.361285i	−0.310706	+	0.950506i	$0.600565\pi$
$762$	19.1779	+	6.95320i	0.694743	+	0.251888i
$763$	4.42866	−	27.9615i	0.160328	−	1.01227i
$764$	−8.97274	−	14.2802i	−0.324622	−	0.516640i
$765$	−3.57569	+	6.70631i	−0.129279	+	0.242467i
$766$	−33.1715	+	15.5184i	−1.19854	+	0.560702i
$767$	−12.1320	+	6.18155i	−0.438060	+	0.223203i
$768$	−11.8096	−	10.7950i	−0.426144	−	0.389532i
$769$	38.5078	+	12.5119i	1.38863	+	0.451192i	0.905495	−	0.424357i	$-0.139500\pi$
$769$	38.5078	+	12.5119i	1.38863	+	0.451192i	0.483130	+	0.875549i	$0.339500\pi$
$770$	−0.528900	−	5.02754i	−0.0190602	−	0.181180i
$771$	−10.9629	+	3.56206i	−0.394819	+	0.128284i
$772$	−17.8930	−	20.4805i	−0.643984	−	0.737108i
$773$	−4.17413	−	26.3544i	−0.150133	−	0.947902i	−0.941611	−	0.336704i	$-0.890688\pi$
$773$	−4.17413	−	26.3544i	−0.150133	−	0.947902i	0.791478	−	0.611198i	$-0.209312\pi$
$774$	−2.34534	+	12.1463i	−0.0843014	+	0.436591i
$775$	18.2467	+	6.68875i	0.655441	+	0.240267i
$776$	−21.2629	+	33.0110i	−0.763295	+	1.18503i
$777$	−12.7187	+	2.01445i	−0.456283	+	0.0722681i
$778$	−11.0634	−	8.62155i	−0.396643	−	0.309098i
$779$	−4.92956	−	15.1716i	−0.176620	−	0.543580i
$780$	12.5448	+	10.8756i	0.449175	+	0.389408i
$781$	0.917987	−	2.82527i	0.0328482	−	0.101096i
$782$	6.67776	−	4.51630i	0.238796	−	0.161502i
$783$	2.94241	+	5.77480i	0.105153	+	0.206375i
$784$	2.32265	−	17.1449i	0.0829518	−	0.612318i
$785$	34.6142	−	33.3498i	1.23543	−	1.19031i
$786$	17.2376	−	16.1145i	0.614846	−	0.574784i
$787$	44.4189	+	7.03527i	1.58336	+	0.250780i	0.885219	−	0.465175i	$-0.154009\pi$
$787$	44.4189	+	7.03527i	1.58336	+	0.250780i	0.698146	+	0.715956i	$0.254009\pi$
$788$	−13.1419	−	7.85203i	−0.468161	−	0.279717i
$789$	9.94582	−	13.6893i	0.354081	−	0.487350i
$790$	−4.25767	+	1.14127i	−0.151481	+	0.0406047i
$791$	−13.2495	−	18.2363i	−0.471097	−	0.648410i
$792$	−0.278737	+	2.75068i	−0.00990449	+	0.0977413i
$793$	−11.2967	−	11.2967i	−0.401158	−	0.401158i
$794$	−16.3823	+	29.6414i	−0.581387	+	1.05193i
$795$	3.99349	−	2.78944i	0.141634	−	0.0989314i
$796$	−27.6751	−	1.86607i	−0.980918	−	0.0661412i
$797$	−25.8044	−	13.1480i	−0.914037	−	0.465725i	−0.0672976	−	0.997733i	$-0.521438\pi$
$797$	−25.8044	−	13.1480i	−0.914037	−	0.465725i	−0.846739	+	0.532008i	$0.821438\pi$
$798$	−0.388920	+	11.5490i	−0.0137676	+	0.408830i
$799$	35.0161			1.23878
$800$	−5.77209	+	27.6890i	−0.204074	+	0.978955i
$801$	2.83956			0.100331
$802$	−0.293426	+	8.71329i	−0.0103612	+	0.307677i
$803$	−12.3009	−	6.26762i	−0.434089	−	0.221179i
$804$	13.4381	+	0.906100i	0.473924	+	0.0319557i
$805$	−4.89402	−	3.69673i	−0.172491	−	0.130292i
$806$	−9.87113	+	17.8603i	−0.347696	+	0.629104i
$807$	3.52753	+	3.52753i	0.124175	+	0.124175i
$808$	−3.67004	+	36.2174i	−0.129112	+	1.27412i
$809$	19.7275	+	27.1526i	0.693584	+	0.954636i	0.999996	+	0.00273720i	$0.000871280\pi$
$809$	19.7275	+	27.1526i	0.693584	+	0.954636i	−0.306413	+	0.951899i	$0.599129\pi$
$810$	−2.95235	−	1.13298i	−0.103735	−	0.0398088i
$811$	8.32953	−	11.4646i	0.292489	−	0.402577i	−0.637331	−	0.770590i	$-0.719962\pi$
$811$	8.32953	−	11.4646i	0.292489	−	0.402577i	0.929821	+	0.368013i	$0.119962\pi$
$812$	18.1983	+	10.8731i	0.638634	+	0.381572i
$813$	27.7616	+	4.39701i	0.973642	+	0.154210i
$814$	−7.95144	+	7.43335i	−0.278698	+	0.260539i
$815$	−5.81668	+	32.7680i	−0.203749	+	1.14781i
$816$	1.82511	−	13.4722i	0.0638916	−	0.471623i
$817$	19.8413	+	38.9407i	0.694159	+	1.36236i
$818$	0.406506	−	0.274928i	0.0142131	−	0.00961263i
$819$	−1.87619	+	5.77432i	−0.0655594	+	0.201771i
$820$	12.2296	−	7.37060i	0.427077	−	0.257393i
$821$	13.6386	+	41.9754i	0.475992	+	1.46495i	0.844616	+	0.535373i	$0.179829\pi$
$821$	13.6386	+	41.9754i	0.475992	+	1.46495i	−0.368624	+	0.929579i	$0.620171\pi$
$822$	−16.1145	−	12.5578i	−0.562057	−	0.438002i
$823$	−26.4425	+	4.18808i	−0.921728	+	0.145987i	−0.599225	−	0.800581i	$-0.704524\pi$
$823$	−26.4425	+	4.18808i	−0.921728	+	0.145987i	−0.322503	+	0.946568i	$0.604524\pi$
$824$	17.8357	−	27.6902i	0.621336	−	0.964634i
$825$	4.43429	−	2.05536i	0.154382	−	0.0715584i
$826$	1.60822	−	8.32884i	0.0559570	−	0.289797i
$827$	−1.72439	−	10.8874i	−0.0599630	−	0.378591i	−0.999360	−	0.0357611i	$-0.988614\pi$
$827$	−1.72439	−	10.8874i	−0.0599630	−	0.378591i	0.939397	−	0.342830i	$-0.111386\pi$
$828$	2.20693	+	2.52607i	0.0766963	+	0.0877870i
$829$	10.5473	−	3.42701i	0.366321	−	0.119025i	−0.120071	−	0.992765i	$-0.538312\pi$
$829$	10.5473	−	3.42701i	0.366321	−	0.119025i	0.486393	+	0.873740i	$0.338312\pi$
$830$	47.2825	−	21.0569i	1.64120	−	0.730896i
$831$	25.4056	+	8.25478i	0.881310	+	0.286355i
$832$	−27.8058	−	10.4363i	−0.963993	−	0.361813i
$833$	13.0989	−	6.67421i	0.453849	−	0.231248i
$834$	−29.4722	+	13.7877i	−1.02054	+	0.477431i
$835$	−30.8310	+	14.9935i	−1.06695	+	0.518871i
$836$	5.19663	+	8.27050i	0.179729	+	0.286041i
$837$	0.608030	−	3.83895i	0.0210166	−	0.132694i
$838$	−37.0790	−	13.4435i	−1.28087	−	0.464397i
$839$	5.75338	+	4.18007i	0.198629	+	0.144312i	0.682654	−	0.730742i	$-0.260826\pi$
$839$	5.75338	+	4.18007i	0.198629	+	0.144312i	−0.484025	+	0.875054i	$0.660826\pi$
$840$	−10.1482	+	1.99982i	−0.350145	+	0.0690003i
$841$	10.5222	−	7.64481i	0.362834	−	0.263614i
$842$	−21.4241	+	6.17210i	−0.738322	+	0.212704i
$843$	−1.58167	+	1.58167i	−0.0544755	+	0.0544755i
$844$	−12.1309	+	14.5303i	−0.417563	+	0.500154i
$845$	1.65369	+	0.571536i	0.0568887	+	0.0196614i
$846$	1.79360	+	14.4590i	0.0616651	+	0.497111i
$847$	−7.45773	+	14.6366i	−0.256251	+	0.502920i
$848$	−4.96254	+	7.16281i	−0.170414	+	0.245972i
$849$			16.8589i			0.578596i
$850$	−22.1327	+	9.36728i	−0.759145	+	0.321295i
$851$			13.2060i			0.452695i
$852$	−5.92573	−	1.35255i	−0.203012	−	0.0463375i
$853$	−3.82112	+	7.49937i	−0.130833	+	0.256774i	−0.947125	−	0.320866i	$-0.896026\pi$
$853$	−3.82112	+	7.49937i	−0.130833	+	0.256774i	0.816292	+	0.577640i	$0.196026\pi$
$854$	9.87720	−	1.22524i	0.337991	−	0.0419268i
$855$	−10.6875	+	3.25409i	−0.365506	+	0.111288i
$856$	−33.4325	+	27.2803i	−1.14270	+	0.932420i
$857$	27.4409	−	27.4409i	0.937362	−	0.937362i	−0.0607885	−	0.998151i	$-0.519362\pi$
$857$	27.4409	−	27.4409i	0.937362	−	0.937362i	0.998151	+	0.0607885i	$0.0193615\pi$
$858$	1.42073	+	4.93150i	0.0485028	+	0.168359i
$859$	−34.5693	+	25.1160i	−1.17949	+	0.856948i	−0.992114	−	0.125340i	$-0.959998\pi$
$859$	−34.5693	+	25.1160i	−1.17949	+	0.856948i	−0.187374	+	0.982289i	$0.559998\pi$
$860$	−29.9336	+	25.1857i	−1.02073	+	0.858825i
$861$	4.22446	+	3.06925i	0.143969	+	0.104600i
$862$	−5.71646	+	15.7668i	−0.194703	+	0.537020i
$863$	4.41919	−	27.9017i	0.150431	−	0.949785i	−0.790813	−	0.612058i	$-0.790342\pi$
$863$	4.41919	−	27.9017i	0.150431	−	0.949785i	0.941244	−	0.337727i	$-0.109658\pi$
$864$	5.65650	+	0.0635551i	0.192438	+	0.00216219i
$865$	6.22050	+	44.6329i	0.211503	+	1.51757i
$866$	2.34079	+	5.00358i	0.0795432	+	0.170028i
$867$	−4.85418	+	2.47333i	−0.164857	+	0.0839986i
$868$	−4.99652	−	11.6901i	−0.169593	−	0.396789i
$869$	−1.29587	−	0.421052i	−0.0439592	−	0.0142832i
$870$	−4.25932	+	20.0479i	−0.144404	+	0.679688i
$871$	23.7772	−	7.72570i	0.805661	−	0.261775i
$872$	−42.3102	+	24.6387i	−1.43280	+	0.834373i
$873$	−2.17174	−	13.7118i	−0.0735022	−	0.464074i
$874$	11.6356	+	2.24671i	0.393579	+	0.0759961i
$875$	12.1879	+	13.6302i	0.412027	+	0.460785i
$876$	−10.5163	+	26.2163i	−0.355313	+	0.885768i
$877$	−10.7595	+	1.70413i	−0.363321	+	0.0575444i	−0.335426	−	0.942067i	$-0.608880\pi$
$877$	−10.7595	+	1.70413i	−0.363321	+	0.0575444i	−0.0278947	+	0.999611i	$0.508880\pi$
$878$	5.38079	−	6.90477i	0.181593	−	0.233025i
$879$	−3.21616	−	9.89831i	−0.108478	−	0.333862i
$880$	−6.15852	+	6.20583i	−0.207604	+	0.209198i
$881$	17.5572	−	54.0356i	0.591518	−	1.82051i	0.0201739	−	0.999796i	$-0.493578\pi$
$881$	17.5572	−	54.0356i	0.591518	−	1.82051i	0.571345	−	0.820710i	$-0.306422\pi$
$882$	3.42689	+	5.06697i	0.115389	+	0.170614i
$883$	−2.37742	−	4.66595i	−0.0800066	−	0.157022i	0.847537	−	0.530736i	$-0.178084\pi$
$883$	−2.37742	−	4.66595i	−0.0800066	−	0.157022i	−0.927544	+	0.373714i	$0.878084\pi$
$884$	−6.16606	−	24.4712i	−0.207387	−	0.823057i
$885$	8.12259	−	1.13205i	0.273038	−	0.0380533i
$886$	−6.77840	−	7.25084i	−0.227725	−	0.243597i
$887$	3.92752	+	0.622058i	0.131873	+	0.0208867i	0.222022	−	0.975042i	$-0.428734\pi$
$887$	3.92752	+	0.622058i	0.131873	+	0.0208867i	−0.0901489	+	0.995928i	$0.528734\pi$
$888$	16.6060	+	14.8403i	0.557261	+	0.498008i
$889$	−13.8661	+	19.0851i	−0.465054	+	0.640092i
$890$	6.97890	+	5.65030i	0.233933	+	0.189398i
$891$	−0.574557	−	0.790810i	−0.0192484	−	0.0264931i
$892$	−5.37744	+	0.483946i	−0.180050	+	0.0162037i
$893$	36.3972	+	36.3972i	1.21799	+	1.21799i
$894$	−5.24532	−	2.89901i	−0.175430	−	0.0969573i
$895$	4.48164	+	14.7192i	0.149805	+	0.492009i
$896$	15.7764	−	9.66732i	0.527052	−	0.322962i
$897$	5.54781	+	2.82675i	0.185236	+	0.0943824i
$898$	−31.8649	−	1.07307i	−1.06334	−	0.0358089i
$899$	−25.1912			−0.840174
$900$	−5.00165	−	8.65930i	−0.166722	−	0.288643i
$901$	−7.40429			−0.246673
$902$	4.41129	+	0.148553i	0.146880	+	0.00494628i
$903$	−12.7465	−	6.49467i	−0.424177	−	0.216129i
$904$	−9.94942	+	37.6937i	−0.330913	+	1.25367i
$905$	2.42446	−	7.01496i	0.0805917	−	0.233185i
$906$	−2.36497	−	1.30708i	−0.0785707	−	0.0434248i
$907$	6.99767	+	6.99767i	0.232354	+	0.232354i	0.813675	−	0.581321i	$-0.197464\pi$
$907$	6.99767	+	6.99767i	0.232354	+	0.232354i	−0.581321	+	0.813675i	$0.697464\pi$
$908$	2.11242	+	23.4725i	0.0701032	+	0.778963i
$909$	−7.56501	−	10.4123i	−0.250916	−	0.345356i
$910$	−16.1012	+	10.4584i	−0.533751	+	0.346694i
$911$	−32.8488	+	45.2125i	−1.08833	+	1.49796i	−0.238322	+	0.971186i	$0.576597\pi$
$911$	−32.8488	+	45.2125i	−1.08833	+	1.49796i	−0.850007	+	0.526771i	$0.823403\pi$
$912$	15.9007	−	12.1065i	0.526525	−	0.400887i
$913$	15.8024	+	2.50285i	0.522983	+	0.0828323i
$914$	−4.21405	−	4.50776i	−0.139388	−	0.149104i
$915$	4.20830	+	8.65350i	0.139122	+	0.286076i
$916$	−7.95349	+	2.00405i	−0.262791	+	0.0662158i
$917$	12.3885	+	24.3137i	0.409103	+	0.802910i
$918$	2.69281	+	3.98156i	0.0888759	+	0.131411i
$919$	1.90011	−	5.84793i	0.0626788	−	0.192905i	−0.914814	−	0.403876i	$-0.867663\pi$
$919$	1.90011	−	5.84793i	0.0626788	−	0.192905i	0.977492	+	0.210971i	$0.0676626\pi$
$920$	0.397568	+	10.5999i	0.0131074	+	0.349468i
$921$	0.821966	+	2.52975i	0.0270847	+	0.0833581i
$922$	30.1917	−	38.7428i	0.994311	−	1.27593i
$923$	−11.1435	+	1.76496i	−0.366794	+	0.0580945i
$924$	−2.96740	−	1.19033i	−0.0976203	−	0.0391590i
$925$	7.60084	−	38.6291i	0.249914	−	1.27012i
$926$	2.42187	+	0.467639i	0.0795876	+	0.0153676i
$927$	1.82169	+	11.5017i	0.0598321	+	0.377765i
$928$	−5.32820	−	36.2740i	−0.174907	−	1.19075i
$929$	20.9750	−	6.81520i	0.688168	−	0.223599i	0.0560003	−	0.998431i	$-0.482165\pi$
$929$	20.9750	−	6.81520i	0.688168	−	0.223599i	0.632168	+	0.774831i	$0.282165\pi$
$930$	9.13333	−	8.22526i	0.299494	−	0.269717i
$931$	20.5530	+	6.67806i	0.673596	+	0.218865i
$932$	−15.2850	+	6.53300i	−0.500676	+	0.213996i
$933$	−11.5009	+	5.86000i	−0.376523	+	0.191848i
$934$	21.1118	+	45.1278i	0.690800	+	1.47663i
$935$	−7.31462	−	1.29843i	−0.239214	−	0.0424631i
$936$	9.78892	−	3.79958i	0.319961	−	0.124193i
$937$	−1.61961	+	10.2258i	−0.0529102	+	0.334062i	0.947007	+	0.321212i	$0.104090\pi$
$937$	−1.61961	+	10.2258i	−0.0529102	+	0.334062i	−0.999917	+	0.0128498i	$0.995910\pi$
$938$	−5.30888	+	14.6427i	−0.173341	+	0.478100i
$939$	−6.81890	−	4.95422i	−0.222526	−	0.161675i
$940$	−24.3631	+	39.1055i	−0.794635	+	1.27548i
$941$	−1.46640	+	1.06540i	−0.0478034	+	0.0347312i	−0.611430	−	0.791298i	$-0.709406\pi$
$941$	−1.46640	+	1.06540i	−0.0478034	+	0.0347312i	0.563627	+	0.826029i	$0.309406\pi$
$942$	−8.41562	−	29.2116i	−0.274196	−	0.951766i
$943$	3.78655	−	3.78655i	0.123307	−	0.123307i
$944$	−12.9189	+	6.95177i	−0.420475	+	0.226261i
$945$	2.20414	−	2.91802i	0.0717008	−	0.0949233i
$946$	−12.0003	+	1.48860i	−0.390164	+	0.0483987i
$947$	−11.7110	+	22.9842i	−0.380557	+	0.746885i	−0.999249	−	0.0387487i	$-0.987663\pi$
$947$	−11.7110	+	22.9842i	−0.380557	+	0.746885i	0.618692	+	0.785633i	$0.287663\pi$
$948$	−0.620371	+	2.71795i	−0.0201487	+	0.0882749i
$949$			52.4330i			1.70205i
$950$	−32.7424	−	13.2689i	−1.06230	−	0.430499i
$951$		−	18.7913i		−	0.609349i
$952$	14.3864	+	6.34105i	0.466267	+	0.205515i
$953$	10.9366	−	21.4643i	0.354271	−	0.695296i	−0.643251	−	0.765656i	$-0.722415\pi$
$953$	10.9366	−	21.4643i	0.354271	−	0.695296i	0.997522	+	0.0703598i	$0.0224147\pi$
$954$	−0.379263	−	3.05741i	−0.0122791	−	0.0989872i
$955$	10.7975	+	15.4582i	0.349400	+	0.500217i
$956$	−17.0722	−	14.2530i	−0.552153	−	0.460976i
$957$	−4.47977	+	4.47977i	−0.144810	+	0.144810i
$958$	−38.4047	+	11.0641i	−1.24080	+	0.357464i
$959$	19.1133	−	13.8866i	0.617202	−	0.448423i
$960$	13.7757	+	11.4118i	0.444610	+	0.368314i
$961$	−12.8575	−	9.34152i	−0.414758	−	0.301339i
$962$	38.8646	+	14.0908i	1.25304	+	0.454307i
$963$	2.38655	−	15.0681i	0.0769055	−	0.485562i
$964$	−1.85101	+	1.16305i	−0.0596170	+	0.0374593i
$965$	21.0965	+	21.8963i	0.679121	+	0.704868i
$966$	−3.51355	+	1.64372i	−0.113047	+	0.0528858i
$967$	23.2179	−	11.8301i	0.746638	−	0.380431i	−0.0389013	−	0.999243i	$-0.512386\pi$
$967$	23.2179	−	11.8301i	0.746638	−	0.380431i	0.785539	+	0.618812i	$0.212386\pi$
$968$	27.7671	−	6.01044i	0.892468	−	0.193183i
$969$	16.1503	+	5.24754i	0.518821	+	0.168575i
$970$	21.9469	−	38.0215i	0.704672	−	1.22080i
$971$	−5.43069	+	1.76454i	−0.174279	+	0.0566268i	−0.394857	−	0.918743i	$-0.629206\pi$
$971$	−5.43069	+	1.76454i	−0.174279	+	0.0566268i	0.220578	+	0.975369i	$0.429206\pi$
$972$	−1.50615	+	1.31587i	−0.0483098	+	0.0422065i
$973$	−5.88623	−	37.1642i	−0.188704	−	1.19143i
$974$	5.54300	−	28.7068i	0.177609	−	0.919826i
$975$	−14.6011	−	11.4617i	−0.467609	−	0.367068i
$976$	−12.4415	−	11.8956i	−0.398243	−	0.380769i
$977$	−13.2231	+	2.09434i	−0.423045	+	0.0670038i	−0.364328	−	0.931271i	$-0.618701\pi$
$977$	−13.2231	+	2.09434i	−0.423045	+	0.0670038i	−0.0587177	+	0.998275i	$0.518701\pi$
$978$	16.6024	+	12.9380i	0.530885	+	0.413711i
$979$	0.857724	+	2.63980i	0.0274130	+	0.0843684i
$980$	−1.66011	+	19.2723i	−0.0530302	+	0.615631i
$981$	5.34923	−	16.4632i	0.170788	−	0.525631i
$982$	−17.8145	+	12.0483i	−0.568485	+	0.384477i
$983$	7.50817	+	14.7356i	0.239473	+	0.469993i	0.979195	−	0.202920i	$-0.0650430\pi$
$983$	7.50817	+	14.7356i	0.239473	+	0.469993i	−0.739722	+	0.672913i	$0.765043\pi$
$984$	−0.506279	−	9.01662i	−0.0161396	−	0.287439i
$985$	15.1032	+	8.05279i	0.481229	+	0.256583i
$986$	22.7574	−	21.2746i	0.724745	−	0.677523i
$987$	−16.6414	−	2.63574i	−0.529702	−	0.0838966i
$988$	19.0272	−	31.8457i	0.605335	−	1.01315i
$989$	−8.62333	+	11.8690i	−0.274206	+	0.377412i
$990$	0.161482	−	3.08689i	0.00513222	−	0.0981077i
$991$	−17.3344	−	23.8587i	−0.550644	−	0.757896i	0.439455	−	0.898264i	$-0.355171\pi$
$991$	−17.3344	−	23.8587i	−0.550644	−	0.757896i	−0.990099	+	0.140368i	$0.955171\pi$
$992$	−10.2014	+	19.4773i	−0.323895	+	0.618404i
$993$	21.1539	+	21.1539i	0.671298	+	0.671298i
$994$	3.40002	−	6.15183i	0.107842	−	0.195124i
$995$	31.0066	+	0.576836i	0.982976	+	0.0182869i
$996$	2.20228	−	32.6613i	0.0697820	−	1.03491i
$997$	30.7633	+	15.6747i	0.974284	+	0.496423i	0.867272	−	0.497835i	$-0.165872\pi$
$997$	30.7633	+	15.6747i	0.974284	+	0.496423i	0.107013	+	0.994258i	$0.465872\pi$
$998$	0.578463	−	17.1774i	0.0183109	−	0.543743i
$999$	−7.87396			−0.249121

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.2.w.a.163.15	yes	240
3.2	odd	2		900.2.bj.f.163.16		240
4.3	odd	2	inner	300.2.w.a.163.13	yes	240
12.11	even	2		900.2.bj.f.163.18		240
25.2	odd	20	inner	300.2.w.a.127.13	✓	240
75.2	even	20		900.2.bj.f.127.18		240
100.27	even	20	inner	300.2.w.a.127.15	yes	240
300.227	odd	20		900.2.bj.f.127.16		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.w.a.127.13	✓	240	25.2	odd	20	inner
300.2.w.a.127.15	yes	240	100.27	even	20	inner
300.2.w.a.163.13	yes	240	4.3	odd	2	inner
300.2.w.a.163.15	yes	240	1.1	even	1	trivial
900.2.bj.f.127.16		240	300.227	odd	20
900.2.bj.f.127.18		240	75.2	even	20
900.2.bj.f.163.16		240	3.2	odd	2
900.2.bj.f.163.18		240	12.11	even	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	300.w (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0475977 + 1.41341i) q^{2} +(-0.891007 - 0.453990i) q^{3} +(-1.99547 - 0.134550i) q^{4} +(2.23568 + 0.0415918i) q^{5} +(0.684086 - 1.23775i) q^{6} +(1.15642 + 1.15642i) q^{7} +(0.285155 - 2.81402i) q^{8} +(0.587785 + 0.809017i) q^{9} +(-0.165200 + 3.15796i) q^{10} +(-0.574557 + 0.790810i) q^{11} +(1.71689 + 1.02581i) q^{12} +(3.66677 + 0.580759i) q^{13} +(-1.68954 + 1.57946i) q^{14} +(-1.97312 - 1.05204i) q^{15} +(3.96379 + 0.536982i) q^{16} +(1.54304 + 3.02838i) q^{17} +(-1.17145 + 0.792276i) q^{18} +(-1.54393 + 4.75171i) q^{19} +(-4.45564 - 0.383807i) q^{20} +(-0.505375 - 1.55538i) q^{21} +(-1.09039 - 0.849726i) q^{22} +(-1.65652 + 0.262367i) q^{23} +(-1.53161 + 2.37785i) q^{24} +(4.99654 + 0.185972i) q^{25} +(-0.995382 + 5.15501i) q^{26} +(-0.156434 - 0.987688i) q^{27} +(-2.15201 - 2.46320i) q^{28} +(-6.16400 + 2.00281i) q^{29} +(1.58088 - 2.73876i) q^{30} +(3.69657 + 1.20109i) q^{31} +(-0.947644 + 5.57691i) q^{32} +(0.870954 - 0.443773i) q^{33} +(-4.35379 + 2.03680i) q^{34} +(2.53729 + 2.63349i) q^{35} +(-1.06405 - 1.69345i) q^{36} +(1.23176 - 7.77702i) q^{37} +(-6.64264 - 2.40837i) q^{38} +(-3.00346 - 2.18214i) q^{39} +(0.754555 - 6.27938i) q^{40} +(-2.58309 + 1.87673i) q^{41} +(2.22245 - 0.640270i) q^{42} +(6.18535 - 6.18535i) q^{43} +(1.25291 - 1.50073i) q^{44} +(1.28045 + 1.83315i) q^{45} +(-0.291986 - 2.35384i) q^{46} +(4.67720 - 9.17952i) q^{47} +(-3.28798 - 2.27798i) q^{48} -4.32538i q^{49} +(-0.500679 + 7.05332i) q^{50} -3.39883i q^{51} +(-7.23878 - 1.65225i) q^{52} +(-0.989011 + 1.94104i) q^{53} +(1.40346 - 0.174095i) q^{54} +(-1.31742 + 1.74410i) q^{55} +(3.58395 - 2.92443i) q^{56} +(3.53288 - 3.53288i) q^{57} +(-2.53740 - 8.80760i) q^{58} +(-2.96719 + 2.15579i) q^{59} +(3.79576 + 2.36479i) q^{60} +(-3.48146 - 2.52943i) q^{61} +(-1.87358 + 5.16761i) q^{62} +(-0.255837 + 1.61529i) q^{63} +(-7.83737 - 1.60486i) q^{64} +(8.17357 + 1.45090i) q^{65} +(0.585779 + 1.25214i) q^{66} +(6.00029 - 3.05730i) q^{67} +(-2.67161 - 6.25065i) q^{68} +(1.59508 + 0.518274i) q^{69} +(-3.84297 + 3.46089i) q^{70} +(-2.89032 + 0.939123i) q^{71} +(2.44420 - 1.42334i) q^{72} +(2.20940 + 13.9496i) q^{73} +(10.9335 + 2.11115i) q^{74} +(-4.36752 - 2.43408i) q^{75} +(3.72020 - 9.27416i) q^{76} +(-1.57894 + 0.250079i) q^{77} +(3.22722 - 4.14126i) q^{78} +(0.430746 + 1.32570i) q^{79} +(8.83944 + 1.36538i) q^{80} +(-0.309017 + 0.951057i) q^{81} +(-2.52964 - 3.74030i) q^{82} +(-7.43080 - 14.5838i) q^{83} +(0.799182 + 3.17172i) q^{84} +(3.32378 + 6.83466i) q^{85} +(8.44804 + 9.03686i) q^{86} +(6.40142 + 1.01389i) q^{87} +(2.06151 + 1.84231i) q^{88} +(1.66905 - 2.29725i) q^{89} +(-2.65194 + 1.72255i) q^{90} +(3.56873 + 4.91193i) q^{91} +(3.34084 - 0.300660i) q^{92} +(-2.74839 - 2.74839i) q^{93} +(12.7518 + 7.04774i) q^{94} +(-3.64936 + 10.5591i) q^{95} +(3.37622 - 4.53885i) q^{96} +(-12.3696 - 6.30263i) q^{97} +(6.11354 + 0.205878i) q^{98} -0.977494 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 12 q^{8} + 8 q^{10} + 8 q^{12} + 4 q^{13} + 20 q^{17} - 20 q^{20} - 12 q^{22} + 20 q^{25} + 4 q^{28} - 8 q^{30} - 20 q^{32} - 8 q^{33} - 4 q^{37} - 76 q^{38} - 92 q^{40} - 20 q^{42} - 140 q^{44}+ \cdots + 256 q^{98}+O(q^{100}) \) 240 * q + 12 * q^8 + 8 * q^10 + 8 * q^12 + 4 * q^13 + 20 * q^17 - 20 * q^20 - 12 * q^22 + 20 * q^25 + 4 * q^28 - 8 * q^30 - 20 * q^32 - 8 * q^33 - 4 * q^37 - 76 * q^38 - 92 * q^40 - 20 * q^42 - 140 * q^44 - 4 * q^45 - 16 * q^48 - 164 * q^50 - 172 * q^52 - 4 * q^53 - 120 * q^58 + 20 * q^60 - 44 * q^62 - 60 * q^64 - 20 * q^65 + 16 * q^68 - 44 * q^70 + 12 * q^72 - 44 * q^73 - 48 * q^77 + 24 * q^78 - 4 * q^80 + 60 * q^81 + 24 * q^82 + 80 * q^84 - 64 * q^85 + 60 * q^88 - 260 * q^89 + 48 * q^90 + 144 * q^92 - 64 * q^93 + 40 * q^94 - 20 * q^96 - 180 * q^97 + 256 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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