LMFDB - Embedded newform 300.2.w.a.127.13

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			127.13
Character	$\chi$	$=$	300.127
Dual form			300.2.w.a.163.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.482036 + 1.32953i) q^{2} +(0.891007 - 0.453990i) q^{3} +(-1.53528 - 1.28176i) q^{4} +(2.23568 - 0.0415918i) q^{5} +(0.174095 + 1.40346i) q^{6} +(-1.15642 + 1.15642i) q^{7} +(2.44420 - 1.42334i) q^{8} +(0.587785 - 0.809017i) q^{9} +(-1.02238 + 2.99245i) q^{10} +(0.574557 + 0.790810i) q^{11} +(-1.94985 - 0.445054i) q^{12} +(3.66677 - 0.580759i) q^{13} +(-0.980056 - 2.09493i) q^{14} +(1.97312 - 1.05204i) q^{15} +(0.714179 + 3.93573i) q^{16} +(1.54304 - 3.02838i) q^{17} +(0.792276 + 1.17145i) q^{18} +(1.54393 + 4.75171i) q^{19} +(-3.48571 - 2.80175i) q^{20} +(-0.505375 + 1.55538i) q^{21} +(-1.32836 + 0.382689i) 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} +(3.25769 - 0.293177i) q^{28} +(-6.16400 - 2.00281i) q^{29} +(0.447593 + 3.13044i) q^{30} +(-3.69657 + 1.20109i) q^{31} +(-5.57691 - 0.947644i) q^{32} +(0.870954 + 0.443773i) q^{33} +(3.28251 + 3.51129i) q^{34} +(-2.53729 + 2.63349i) q^{35} +(-1.93938 + 0.488669i) q^{36} +(1.23176 + 7.77702i) q^{37} +(-7.06176 - 0.237810i) q^{38} +(3.00346 - 2.18214i) q^{39} +(5.40524 - 3.28380i) q^{40} +(-2.58309 - 1.87673i) q^{41} +(-1.82431 - 1.42166i) q^{42} +(-6.18535 - 6.18535i) q^{43} +(0.131522 - 1.95056i) q^{44} +(1.28045 - 1.83315i) q^{45} +(-1.14733 + 2.07592i) q^{46} +(-4.67720 - 9.17952i) q^{47} +(2.42312 + 3.18253i) q^{48} +4.32538i q^{49} +(-2.16126 + 6.73268i) q^{50} -3.39883i q^{51} +(-6.37392 - 3.80829i) q^{52} +(-0.989011 - 1.94104i) q^{53} +(1.23775 + 0.684086i) q^{54} +(1.31742 + 1.74410i) q^{55} +(-1.18054 + 4.47250i) q^{56} +(3.53288 + 3.53288i) q^{57} +(5.63406 - 7.22978i) q^{58} +(2.96719 + 2.15579i) q^{59} +(-4.37776 - 0.913900i) q^{60} +(-3.48146 + 2.52943i) q^{61} +(0.185003 - 5.49366i) q^{62} +(0.255837 + 1.61529i) q^{63} +(3.94819 - 6.95786i) q^{64} +(8.17357 - 1.45090i) q^{65} +(-1.00984 + 0.944041i) q^{66} +(-6.00029 - 3.05730i) q^{67} +(-6.25065 + 2.67161i) q^{68} +(1.59508 - 0.518274i) q^{69} +(-2.27822 - 4.64283i) q^{70} +(2.89032 + 0.939123i) q^{71} +(0.285155 - 2.81402i) 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} +(1.45344 + 5.04504i) q^{78} +(-0.430746 + 1.32570i) q^{79} +(1.76037 + 8.76933i) q^{80} +(-0.309017 - 0.951057i) q^{81} +(3.74030 - 2.52964i) q^{82} +(7.43080 - 14.5838i) q^{83} +(2.76952 - 1.74018i) q^{84} +(3.32378 - 6.83466i) q^{85} +(11.2052 - 5.24202i) q^{86} +(-6.40142 + 1.01389i) q^{87} +(2.52992 + 1.11510i) q^{88} +(1.66905 + 2.29725i) q^{89} +(1.82000 + 2.58604i) q^{90} +(-3.56873 + 4.91193i) q^{91} +(-2.20693 - 2.52607i) q^{92} +(-2.74839 + 2.74839i) q^{93} +(14.4590 - 1.79360i) q^{94} +(3.64936 + 10.5591i) q^{95} +(-5.39929 + 1.68751i) q^{96} +(-12.3696 + 6.30263i) q^{97} +(-5.75071 - 2.08499i) 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 $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.482036	+	1.32953i	−0.340851	+	0.940117i
$2$	−0.482036	+	1.32953i	−0.340851	+	0.940117i
$3$	0.891007	−	0.453990i	0.514423	−	0.262112i
$3$	0.891007	−	0.453990i	0.514423	−	0.262112i
$4$	−1.53528	−	1.28176i	−0.767641	−	0.640880i
$5$	2.23568	−	0.0415918i	0.999827	−	0.0186004i
$5$	2.23568	−	0.0415918i	0.999827	−	0.0186004i
$6$	0.174095	+	1.40346i	0.0710739	+	0.572959i
$7$	−1.15642	+	1.15642i	−0.437086	+	0.437086i	−0.891030	−	0.453944i	$-0.850017\pi$
$7$	−1.15642	+	1.15642i	−0.437086	+	0.437086i	0.453944	+	0.891030i	$0.350017\pi$
$8$	2.44420	−	1.42334i	0.864154	−	0.503227i
$9$	0.587785	−	0.809017i	0.195928	−	0.269672i
$10$	−1.02238	+	2.99245i	−0.323306	+	0.946295i
$11$	0.574557	+	0.790810i	0.173235	+	0.238438i	0.886802	−	0.462149i	$-0.152922\pi$
$11$	0.574557	+	0.790810i	0.173235	+	0.238438i	−0.713567	+	0.700587i	$0.752922\pi$
$12$	−1.94985	−	0.445054i	−0.562874	−	0.128476i
$13$	3.66677	−	0.580759i	1.01698	−	0.161074i	0.374379	−	0.927276i	$-0.377856\pi$
$13$	3.66677	−	0.580759i	1.01698	−	0.161074i	0.642600	+	0.766202i	$0.277856\pi$
$14$	−0.980056	−	2.09493i	−0.261931	−	0.559894i
$15$	1.97312	−	1.05204i	0.509458	−	0.271635i
$16$	0.714179	+	3.93573i	0.178545	+	0.983932i
$17$	1.54304	−	3.02838i	0.374241	−	0.734489i	−0.624682	−	0.780879i	$-0.714772\pi$
$17$	1.54304	−	3.02838i	0.374241	−	0.734489i	0.998923	+	0.0463896i	$0.0147716\pi$
$18$	0.792276	+	1.17145i	0.186741	+	0.276114i
$19$	1.54393	+	4.75171i	0.354201	+	1.09012i	0.956471	+	0.291826i	$0.0942628\pi$
$19$	1.54393	+	4.75171i	0.354201	+	1.09012i	−0.602271	+	0.798292i	$0.705737\pi$
$20$	−3.48571	−	2.80175i	−0.779429	−	0.626491i
$21$	−0.505375	+	1.55538i	−0.110282	+	0.339412i
$22$	−1.32836	+	0.382689i	−0.283207	+	0.0815897i
$23$	1.65652	+	0.262367i	0.345409	+	0.0547073i	0.326729	−	0.945118i	$-0.394054\pi$
$23$	1.65652	+	0.262367i	0.345409	+	0.0547073i	0.0186799	+	0.999826i	$0.494054\pi$
$24$	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
$28$	3.25769	−	0.293177i	0.615645	−	0.0554053i
$29$	−6.16400	−	2.00281i	−1.14463	−	0.371912i	−0.325510	−	0.945539i	$-0.605536\pi$
$29$	−6.16400	−	2.00281i	−1.14463	−	0.371912i	−0.819117	+	0.573627i	$0.805536\pi$
$30$	0.447593	+	3.13044i	0.0817189	+	0.571538i
$31$	−3.69657	+	1.20109i	−0.663924	+	0.215722i	−0.621544	−	0.783380i	$-0.713494\pi$
$31$	−3.69657	+	1.20109i	−0.663924	+	0.215722i	−0.0423804	+	0.999102i	$0.513494\pi$
$32$	−5.57691	−	0.947644i	−0.985868	−	0.167521i
$33$	0.870954	+	0.443773i	0.151614	+	0.0772510i
$34$	3.28251	+	3.51129i	0.562946	+	0.602182i
$35$	−2.53729	+	2.63349i	−0.428881	+	0.445141i
$36$	−1.93938	+	0.488669i	−0.323230	+	0.0814448i
$37$	1.23176	+	7.77702i	0.202500	+	1.27853i	0.854155	+	0.520019i	$0.174075\pi$
$37$	1.23176	+	7.77702i	0.202500	+	1.27853i	−0.651655	+	0.758516i	$0.725925\pi$
$38$	−7.06176	−	0.237810i	−1.14557	−	0.0385778i
$39$	3.00346	−	2.18214i	0.480938	−	0.349422i
$40$	5.40524	−	3.28380i	0.854644	−	0.519214i
$41$	−2.58309	−	1.87673i	−0.403411	−	0.293095i	0.367518	−	0.930016i	$-0.380208\pi$
$41$	−2.58309	−	1.87673i	−0.403411	−	0.293095i	−0.770929	+	0.636921i	$0.780208\pi$
$42$	−1.82431	−	1.42166i	−0.281498	−	0.219367i
$43$	−6.18535	−	6.18535i	−0.943257	−	0.943257i	0.0552173	−	0.998474i	$-0.482415\pi$
$43$	−6.18535	−	6.18535i	−0.943257	−	0.943257i	−0.998474	+	0.0552173i	$0.982415\pi$
$44$	0.131522	−	1.95056i	0.0198277	−	0.294058i
$45$	1.28045	−	1.83315i	0.190878	−	0.273270i
$46$	−1.14733	+	2.07592i	−0.169164	+	0.306077i
$47$	−4.67720	−	9.17952i	−0.682240	−	1.33897i	−0.929067	−	0.369911i	$-0.879388\pi$
$47$	−4.67720	−	9.17952i	−0.682240	−	1.33897i	0.246827	−	0.969059i	$-0.420612\pi$
$48$	2.42312	+	3.18253i	0.349747	+	0.459358i
$49$			4.32538i			0.617911i
$50$	−2.16126	+	6.73268i	−0.305648	+	0.952144i
$51$		−	3.39883i		−	0.475931i
$52$	−6.37392	−	3.80829i	−0.883903	−	0.528115i
$53$	−0.989011	−	1.94104i	−0.135851	−	0.266623i	0.813052	−	0.582192i	$-0.197805\pi$
$53$	−0.989011	−	1.94104i	−0.135851	−	0.266623i	−0.948903	+	0.315569i	$0.897805\pi$
$54$	1.23775	+	0.684086i	0.168437	+	0.0930923i
$55$	1.31742	+	1.74410i	0.177640	+	0.235175i
$56$	−1.18054	+	4.47250i	−0.157756	+	0.597664i
$57$	3.53288	+	3.53288i	0.467942	+	0.467942i
$58$	5.63406	−	7.22978i	0.739788	−	0.949316i
$59$	2.96719	+	2.15579i	0.386295	+	0.280659i	0.763935	−	0.645293i	$-0.223265\pi$
$59$	2.96719	+	2.15579i	0.386295	+	0.280659i	−0.377641	+	0.925952i	$0.623265\pi$
$60$	−4.37776	−	0.913900i	−0.565166	−	0.117984i
$61$	−3.48146	+	2.52943i	−0.445755	+	0.323860i	−0.787918	−	0.615781i	$-0.788841\pi$
$61$	−3.48146	+	2.52943i	−0.445755	+	0.323860i	0.342162	+	0.939641i	$0.388841\pi$
$62$	0.185003	−	5.49366i	0.0234954	−	0.697695i
$63$	0.255837	+	1.61529i	0.0322324	+	0.203508i
$64$	3.94819	−	6.95786i	0.493524	−	0.869732i
$65$	8.17357	−	1.45090i	1.01381	−	0.179962i
$66$	−1.00984	+	0.944041i	−0.124303	+	0.116203i
$67$	−6.00029	−	3.05730i	−0.733052	−	0.373509i	0.0472734	−	0.998882i	$-0.484947\pi$
$67$	−6.00029	−	3.05730i	−0.733052	−	0.373509i	−0.780326	+	0.625373i	$0.784947\pi$
$68$	−6.25065	+	2.67161i	−0.758002	+	0.323980i
$69$	1.59508	−	0.518274i	0.192025	−	0.0623929i
$70$	−2.27822	−	4.64283i	−0.272300	−	0.554925i
$71$	2.89032	+	0.939123i	0.343018	+	0.111453i	0.475460	−	0.879737i	$-0.342282\pi$
$71$	2.89032	+	0.939123i	0.343018	+	0.111453i	−0.132442	+	0.991191i	$0.542282\pi$
$72$	0.285155	−	2.81402i	0.0336058	−	0.331635i
$73$	2.20940	−	13.9496i	0.258590	−	1.63268i	−0.426691	−	0.904397i	$-0.640321\pi$
$73$	2.20940	−	13.9496i	0.258590	−	1.63268i	0.685282	−	0.728278i	$-0.259679\pi$
$74$	−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
$78$	1.45344	+	5.04504i	0.164569	+	0.571239i
$79$	−0.430746	+	1.32570i	−0.0484628	+	0.149153i	−0.972359	−	0.233489i	$-0.924986\pi$
$79$	−0.430746	+	1.32570i	−0.0484628	+	0.149153i	0.923897	+	0.382642i	$0.124986\pi$
$80$	1.76037	+	8.76933i	0.196816	+	0.980441i
$81$	−0.309017	−	0.951057i	−0.0343352	−	0.105673i
$82$	3.74030	−	2.52964i	0.413047	−	0.279352i
$83$	7.43080	−	14.5838i	0.815636	−	1.60078i	0.0163181	−	0.999867i	$-0.494806\pi$
$83$	7.43080	−	14.5838i	0.815636	−	1.60078i	0.799318	−	0.600909i	$-0.205194\pi$
$84$	2.76952	−	1.74018i	0.302180	−	0.189869i
$85$	3.32378	−	6.83466i	0.360514	−	0.741323i
$86$	11.2052	−	5.24202i	1.20828	−	0.565262i
$87$	−6.40142	+	1.01389i	−0.686304	+	0.108700i
$88$	2.52992	+	1.11510i	0.269691	+	0.118870i
$89$	1.66905	+	2.29725i	0.176919	+	0.243508i	0.888262	−	0.459337i	$-0.151913\pi$
$89$	1.66905	+	2.29725i	0.176919	+	0.243508i	−0.711343	+	0.702845i	$0.751913\pi$
$90$	1.82000	+	2.58604i	0.191845	+	0.272593i
$91$	−3.56873	+	4.91193i	−0.374104	+	0.514910i
$92$	−2.20693	−	2.52607i	−0.230089	−	0.263361i
$93$	−2.74839	+	2.74839i	−0.284994	+	0.284994i
$94$	14.4590	−	1.79360i	1.49133	−	0.184995i
$95$	3.64936	+	10.5591i	0.374416	+	1.08334i
$96$	−5.39929	+	1.68751i	−0.551063	+	0.172231i
$97$	−12.3696	+	6.30263i	−1.25594	+	0.639935i	−0.950040	−	0.312128i	$-0.898958\pi$
$97$	−12.3696	+	6.30263i	−1.25594	+	0.639935i	−0.305903	+	0.952063i	$0.598958\pi$
$98$	−5.75071	−	2.08499i	−0.580909	−	0.210616i
$99$	0.977494			0.0982419
$100$	−7.90947	−	6.11885i	−0.790947	−	0.611885i
$101$	−12.8704			−1.28065			−0.640325	−	0.768104i	$-0.721200\pi$
$101$	−12.8704			−1.28065			−0.640325	+	0.768104i	$0.721200\pi$
$102$	4.51883	+	1.63836i	0.447431	+	0.162222i
$103$	−10.3758	+	5.28675i	−1.02236	+	0.520919i	−0.883025	−	0.469327i	$-0.844497\pi$
$103$	−10.3758	+	5.28675i	−1.02236	+	0.520919i	−0.139336	+	0.990245i	$0.544497\pi$
$104$	8.13569	−	6.63856i	0.797770	−	0.650964i
$105$	−1.06517	+	3.49836i	−0.103950	+	0.341405i
$106$	3.05741	−	0.379263i	0.296962	−	0.0368372i
$107$	10.7876	−	10.7876i	1.04287	−	1.04287i	0.0438342	−	0.999039i	$-0.486043\pi$
$107$	10.7876	−	10.7876i	1.04287	−	1.04287i	0.999039	−	0.0438342i	$-0.0139573\pi$
$108$	−1.50615	+	1.31587i	−0.144929	+	0.126619i
$109$	−10.1748	+	14.0045i	−0.974573	+	1.34138i	−0.0348708	+	0.999392i	$0.511102\pi$
$109$	−10.1748	+	14.0045i	−0.974573	+	1.34138i	−0.939702	+	0.341993i	$0.888898\pi$
$110$	−2.95387	+	0.910820i	−0.281641	+	0.0868433i
$111$	4.62820	+	6.37017i	0.439289	+	0.604630i
$112$	−5.37725	−	3.72547i	−0.508103	−	0.352024i
$113$	−13.6135	+	2.15616i	−1.28065	+	0.202835i	−0.759430	−	0.650589i	$-0.774522\pi$
$113$	−13.6135	+	2.15616i	−1.28065	+	0.202835i	−0.521218	+	0.853424i	$0.674522\pi$
$114$	−6.40004	+	2.99408i	−0.599418	+	0.280421i
$115$	3.71437	+	0.517672i	0.346366	+	0.0482731i
$116$	6.89636	+	10.9756i	0.640311	+	1.01906i
$117$	1.68543	−	3.30784i	0.155818	−	0.305810i
$118$	−4.29647	+	2.90578i	−0.395522	+	0.267499i
$119$	1.71768	+	5.28648i	0.157460	+	0.484611i
$120$	3.32530	−	5.37982i	0.303557	−	0.491108i
$121$	3.10392	−	9.55289i	0.282175	−	0.868445i
$122$	−1.68475	−	5.84797i	−0.152530	−	0.529450i
$123$	−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	0.658807	+	0.752312i	$0.271061\pi$
$127$	−2.25651	+	14.2470i	−0.200233	+	1.26422i	−0.859040	+	0.511908i	$0.828939\pi$
$128$	7.34748	+	8.60317i	0.649432	+	0.760420i
$129$	−8.31928	−	2.70310i	−0.732472	−	0.237994i
$130$	−2.01095	+	11.5664i	−0.176372	+	1.01444i
$131$	−15.8689	+	5.15611i	−1.38647	+	0.450491i	−0.904791	−	0.425857i	$-0.859973\pi$
$131$	−15.8689	+	5.15611i	−1.38647	+	0.450491i	−0.481679	+	0.876348i	$0.659973\pi$
$132$	−0.768348	−	1.79767i	−0.0668762	−	0.156467i
$133$	−7.28041	−	3.70956i	−0.631292	−	0.321659i
$134$	6.95712	−	6.50382i	0.601004	−	0.561844i
$135$	0.308658	−	2.21466i	0.0265650	−	0.190608i
$136$	−0.538936	−	9.59822i	−0.0462134	−	0.823040i
$137$	2.25985	+	14.2681i	0.193072	+	1.21901i	0.873731	+	0.486409i	$0.161694\pi$
$137$	2.25985	+	14.2681i	0.193072	+	1.21901i	−0.680659	+	0.732601i	$0.738306\pi$
$138$	−0.0798294	+	2.37053i	−0.00679553	+	0.201793i
$139$	18.6136	−	13.5236i	1.57879	−	1.14706i	0.660721	−	0.750632i	$-0.270251\pi$
$139$	18.6136	−	13.5236i	1.57879	−	1.14706i	0.918067	−	0.396425i	$-0.129749\pi$
$140$	7.27096	−	0.790944i	0.614508	−	0.0668469i
$141$	−8.33483	−	6.05561i	−0.701919	−	0.509974i
$142$	−2.64183	+	3.39007i	−0.221697	+	0.284488i
$143$	2.56604	+	2.56604i	0.214583	+	0.214583i
$144$	3.60385	+	1.73558i	0.300321	+	0.144632i
$145$	−13.8640	−	4.22126i	−1.15135	−	0.350557i
$146$	17.4813	+	9.66166i	1.44677	+	0.799605i
$147$	1.96368	+	3.85394i	0.161962	+	0.317868i
$148$	8.07718	−	13.5187i	0.663940	−	1.11123i
$149$			4.23779i			0.347173i	0.984819	+	0.173586i	$0.0555356\pi$
$149$			4.23779i			0.347173i	−0.984819	+	0.173586i	$0.944464\pi$
$150$	1.13088	+	6.98005i	0.0923356	+	0.569919i
$151$		−	1.91070i		−	0.155490i	−0.996973	−	0.0777451i	$-0.975228\pi$
$151$		−	1.91070i		−	0.155490i	0.996973	−	0.0777451i	$-0.0247720\pi$
$152$	10.5370	+	9.41659i	0.854661	+	0.763786i
$153$	−1.54304	−	3.02838i	−0.124747	−	0.244830i
$154$	1.09359	−	1.97869i	0.0881243	−	0.159448i
$155$	−8.21440	+	2.83900i	−0.659797	+	0.228034i
$156$	−7.40813	−	0.499514i	−0.593125	−	0.0399932i
$157$	15.1998	+	15.1998i	1.21308	+	1.21308i	0.970009	+	0.243071i	$0.0781547\pi$
$157$	15.1998	+	15.1998i	1.21308	+	1.21308i	0.243071	+	0.970009i	$0.421845\pi$
$158$	−1.55492	−	1.21173i	−0.123703	−	0.0963997i
$159$	−1.76243	−	1.28048i	−0.139770	−	0.101549i
$160$	−12.5076	−	1.88668i	−0.988814	−	0.149155i
$161$	−2.21904	+	1.61223i	−0.174885	+	0.127061i
$162$	1.41341	+	0.0475977i	0.111048	+	0.00373963i
$163$	2.32827	+	14.7001i	0.182364	+	1.15140i	0.893738	+	0.448589i	$0.148073\pi$
$163$	2.32827	+	14.7001i	0.182364	+	1.15140i	−0.711374	+	0.702814i	$0.751927\pi$
$164$	1.56026	+	6.19221i	0.121836	+	0.483530i
$165$	1.96563	+	0.955911i	0.153024	+	0.0744175i
$166$	15.8076	+	16.9093i	1.22691	+	1.31242i
$167$	13.6609	+	6.96060i	1.05712	+	0.538627i	0.894040	−	0.447986i	$-0.147859\pi$
$167$	13.6609	+	6.96060i	1.05712	+	0.538627i	0.163075	+	0.986614i	$0.447859\pi$
$168$	0.978608	+	4.52098i	0.0755012	+	0.348801i
$169$	0.744179	−	0.241798i	0.0572445	−	0.0185999i
$170$	7.48468	+	7.71361i	0.574049	+	0.591607i
$171$	4.75171	+	1.54393i	0.363373	+	0.118067i
$172$	1.56812	+	17.4244i	0.119568	+	1.32860i
$173$	3.15268	−	19.9053i	0.239694	−	1.51337i	−0.514942	−	0.857225i	$-0.672186\pi$
$173$	3.15268	−	19.9053i	0.239694	−	1.51337i	0.754636	−	0.656144i	$-0.227814\pi$
$174$	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
$178$	−3.85880	+	1.11169i	−0.289229	+	0.0833246i
$179$	−2.12634	+	6.54421i	−0.158930	+	0.489137i	−0.998538	−	0.0540563i	$-0.982785\pi$
$179$	−2.12634	+	6.54421i	−0.158930	+	0.489137i	0.839608	+	0.543193i	$0.182785\pi$
$180$	−4.31552	+	1.17317i	−0.321660	+	0.0874430i
$181$	1.02571	+	3.15681i	0.0762404	+	0.234644i	0.981913	−	0.189335i	$-0.0606331\pi$
$181$	1.02571	+	3.15681i	0.0762404	+	0.234644i	−0.905672	+	0.423979i	$0.860633\pi$
$182$	−4.81029	−	7.11245i	−0.356562	−	0.527210i
$183$	−1.95367	+	3.83429i	−0.144419	+	0.283439i
$184$	4.42230	−	1.71652i	0.326016	−	0.126544i
$185$	3.07728	+	17.3357i	0.226246	+	1.27455i
$186$	−2.32923	−	4.97888i	−0.170787	−	0.365069i
$187$	3.28143	−	0.519728i	0.239962	−	0.0380062i
$188$	−4.58513	+	20.0882i	−0.334405	+	1.46508i
$189$	0.961280	+	1.32309i	0.0699228	+	0.0962405i
$190$	−15.7977	−	0.237955i	−1.14609	−	0.0172631i
$191$	−4.95656	+	6.82212i	−0.358644	+	0.493631i	−0.949770	−	0.312948i	$-0.898683\pi$
$191$	−4.95656	+	6.82212i	−0.358644	+	0.493631i	0.591126	+	0.806579i	$0.298683\pi$
$192$	0.359066	−	7.99194i	0.0259133	−	0.576768i
$193$	9.61516	−	9.61516i	0.692114	−	0.692114i	−0.270583	−	0.962697i	$-0.587216\pi$
$193$	9.61516	−	9.61516i	0.692114	−	0.692114i	0.962697	+	0.270583i	$0.0872163\pi$
$194$	−2.41691	−	19.4838i	−0.173524	−	1.39886i
$195$	6.62401	−	5.00349i	0.474355	−	0.358307i
$196$	5.54410	−	6.64067i	0.396007	−	0.474334i
$197$	6.82019	−	3.47506i	0.485918	−	0.247588i	−0.193827	−	0.981036i	$-0.562090\pi$
$197$	6.82019	−	3.47506i	0.485918	−	0.247588i	0.679746	+	0.733448i	$0.262090\pi$
$198$	−0.471188	+	1.29960i	−0.0334859	+	0.0923589i
$199$	−13.8690			−0.983146			−0.491573	−	0.870836i	$-0.663578\pi$
$199$	−13.8690			−0.983146			−0.491573	+	0.870836i	$0.663578\pi$
$200$	11.9478	−	7.56634i	0.844839	−	0.535021i
$201$	−6.73429			−0.475000
$202$	6.20399	−	17.1115i	0.436511	−	1.20396i
$203$	9.44427	−	4.81210i	0.662858	−	0.337743i
$204$	−4.35648	+	5.21816i	−0.305015	+	0.365344i
$205$	−5.85303	−	4.08833i	−0.408793	−	0.285541i
$206$	−2.02734	−	16.3433i	−0.141252	−	1.13869i
$207$	1.18594	−	1.18594i	0.0824284	−	0.0824284i
$208$	4.90444	+	14.0166i	0.340062	+	0.971879i
$209$	−2.87063	+	3.95108i	−0.198566	+	0.273302i
$210$	−4.13771	−	3.10250i	−0.285529	−	0.214093i
$211$	−5.56295	−	7.65675i	−0.382970	−	0.527112i	0.573399	−	0.819277i	$-0.305625\pi$
$211$	−5.56295	−	7.65675i	−0.382970	−	0.527112i	−0.956368	+	0.292164i	$0.905625\pi$
$212$	−0.969542	+	4.24772i	−0.0665884	+	0.291735i
$213$	3.00165	−	0.475414i	0.205670	−	0.0325749i
$214$	9.14235	+	19.5423i	0.624958	+	1.33589i
$215$	−14.0857	−	13.5712i	−0.960639	−	0.925549i
$216$	−1.02346	−	2.63676i	−0.0696378	−	0.179409i
$217$	2.88583	−	5.66376i	0.195903	−	0.384481i
$218$	−13.7147	−	20.2784i	−0.928875	−	1.37343i
$219$	−4.36439	−	13.4322i	−0.294918	−	0.907665i
$220$	0.212914	−	4.36630i	0.0143547	−	0.294376i
$221$	3.89920	−	12.0005i	0.262288	−	0.807240i
$222$	−10.7003	+	3.08266i	−0.718155	+	0.206895i
$223$	−2.66635	−	0.422309i	−0.178552	−	0.0282799i	0.0665180	−	0.997785i	$-0.478811\pi$
$223$	−2.66635	−	0.422309i	−0.178552	−	0.0282799i	−0.245070	+	0.969505i	$0.578811\pi$
$224$	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	−0.847861	−	0.530218i	$-0.822110\pi$
$227$	1.84338	−	11.6386i	0.122349	−	0.772482i	0.970210	−	0.242264i	$-0.0778900\pi$
$228$	−0.895659	−	9.95228i	−0.0593165	−	0.659106i
$229$	3.90033	+	1.26729i	0.257741	+	0.0837451i	0.435037	−	0.900412i	$-0.356735\pi$
$229$	3.90033	+	1.26729i	0.257741	+	0.0837451i	−0.177297	+	0.984157i	$0.556735\pi$
$230$	−2.47872	+	4.68881i	−0.163442	+	0.309171i
$231$	−1.52038	+	0.494001i	−0.100034	+	0.0325029i
$232$	−17.9167	+	3.87823i	−1.17629	+	0.254618i
$233$	7.40542	+	3.77325i	0.485145	+	0.247194i	0.679415	−	0.733754i	$-0.262234\pi$
$233$	7.40542	+	3.77325i	0.485145	+	0.247194i	−0.194270	+	0.980948i	$0.562234\pi$
$234$	3.58542	+	3.83532i	0.234386	+	0.250723i
$235$	−10.8385	−	20.3279i	−0.707027	−	1.32605i
$236$	−1.79226	−	7.11296i	−0.116666	−	0.463014i
$237$	0.218058	+	1.37676i	0.0141644	+	0.0894304i
$238$	−7.85650	−	0.264573i	−0.509261	−	0.0171497i
$239$	−8.99618	+	6.53610i	−0.581914	+	0.422785i	−0.839414	−	0.543493i	$-0.817101\pi$
$239$	−8.99618	+	6.53610i	−0.581914	+	0.422785i	0.257499	+	0.966278i	$0.417101\pi$
$240$	5.54969	+	7.01434i	0.358231	+	0.452773i
$241$	0.884285	+	0.642471i	0.0569618	+	0.0413852i	0.615902	−	0.787823i	$-0.288792\pi$
$241$	0.884285	+	0.642471i	0.0569618	+	0.0413852i	−0.558940	+	0.829208i	$0.688792\pi$
$242$	11.2046	+	8.73159i	0.720260	+	0.561288i
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$	8.58714	+	0.579013i	0.549735	+	0.0370675i
$245$	0.179900	+	9.67017i	0.0114934	+	0.617804i
$246$	2.18420	−	3.95199i	0.139260	−	0.251969i
$247$	8.42082	+	16.5268i	0.535804	+	1.05157i
$248$	−7.32559	+	8.19719i	−0.465175	+	0.520522i
$249$		−	16.3677i		−	1.03726i
$250$	−4.55186	+	15.1420i	−0.287885	+	0.957665i
$251$		−	27.5973i		−	1.74193i	−0.491348	−	0.870964i	$-0.663496\pi$
$251$		−	27.5973i		−	1.74193i	0.491348	−	0.870964i	$-0.336504\pi$
$252$	1.67764	−	2.80785i	0.105681	−	0.176878i
$253$	0.744283	+	1.46074i	0.0467927	+	0.0918358i
$254$	−17.8541	−	9.86768i	−1.12027	−	0.619153i
$255$	−0.141363	−	7.59869i	−0.00885252	−	0.475849i
$256$	−14.9799	+	5.62163i	−0.936243	+	0.351352i
$257$	8.15087	+	8.15087i	0.508437	+	0.508437i	0.914047	−	0.405609i	$-0.132941\pi$
$257$	8.15087	+	8.15087i	0.508437	+	0.508437i	−0.405609	+	0.914047i	$0.632941\pi$
$258$	7.60403	−	9.75771i	0.473407	−	0.607488i
$259$	−10.4179	−	7.56908i	−0.647340	−	0.470320i
$260$	−14.4084	−	8.24902i	−0.893574	−	0.511583i
$261$	−5.24341	+	3.80956i	−0.324559	+	0.235806i
$262$	0.794191	−	23.5835i	0.0490653	−	1.45699i
$263$	2.64700	+	16.7125i	0.163221	+	1.03054i	0.924241	+	0.381810i	$0.124699\pi$
$263$	2.64700	+	16.7125i	0.163221	+	1.03054i	−0.761020	+	0.648729i	$0.775301\pi$
$264$	2.76042	−	0.154997i	0.169892	−	0.00953938i
$265$	−2.29184	−	4.29842i	−0.140787	−	0.264050i
$266$	8.44138	−	7.89136i	0.517574	−	0.483850i
$267$	2.53007	+	1.28913i	0.154837	+	0.0788936i
$268$	5.29341	+	12.3848i	0.323347	+	0.756520i
$269$	−4.74451	+	1.54159i	−0.289278	+	0.0939922i	−0.450061	−	0.892998i	$-0.648598\pi$
$269$	−4.74451	+	1.54159i	−0.289278	+	0.0939922i	0.160783	+	0.986990i	$0.448598\pi$
$270$	2.79567	+	1.47792i	0.170139	+	0.0899432i
$271$	26.7320	+	8.68575i	1.62385	+	0.527622i	0.972846	−	0.231451i	$-0.0743474\pi$
$271$	26.7320	+	8.68575i	1.62385	+	0.527622i	0.651006	+	0.759073i	$0.274347\pi$
$272$	13.0209	+	3.91016i	0.789506	+	0.237088i
$273$	−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	−0.699301	−	0.714827i	$-0.746505\pi$
$277$	−26.3841	−	4.17884i	−1.58527	−	0.251082i	−0.885969	+	0.463745i	$0.846505\pi$
$278$	9.00753	+	31.2662i	0.540236	+	1.87522i
$279$	−1.20109	+	3.69657i	−0.0719073	+	0.221308i
$280$	−2.45329	+	10.0482i	−0.146612	+	0.600495i
$281$	0.691214	+	2.12734i	0.0412344	+	0.126906i	0.969555	−	0.244875i	$-0.0787470\pi$
$281$	0.691214	+	2.12734i	0.0412344	+	0.126906i	−0.928320	+	0.371782i	$0.878747\pi$
$282$	12.0688	−	8.16235i	0.718686	−	0.486061i
$283$	7.65378	−	15.0214i	0.454970	−	0.892929i	−0.543593	−	0.839349i	$-0.682937\pi$
$283$	7.65378	−	15.0214i	0.454970	−	0.892929i	0.998564	−	0.0535804i	$-0.0170633\pi$
$284$	−3.23373	−	5.14652i	−0.191886	−	0.305390i
$285$	8.04533	+	7.75146i	0.476564	+	0.459157i
$286$	−4.64854	+	2.17469i	−0.274874	+	0.128592i
$287$	5.15743	−	0.816856i	0.304433	−	0.0482175i
$288$	−4.04469	+	3.95481i	−0.238336	+	0.233039i
$289$	3.20224	+	4.40750i	0.188367	+	0.259265i
$290$	12.2953	−	16.3978i	0.722002	−	0.962912i
$291$	−8.16006	+	11.2314i	−0.478351	+	0.658394i
$292$	−21.2721	+	18.5846i	−1.24485	+	1.08758i
$293$	7.35935	−	7.35935i	0.429938	−	0.429938i	−0.458669	−	0.888607i	$-0.651674\pi$
$293$	7.35935	−	7.35935i	0.429938	−	0.429938i	0.888607	+	0.458669i	$0.151674\pi$
$294$	−6.07048	+	0.753026i	−0.354038	+	0.0439174i
$295$	6.72334	+	4.69624i	0.391448	+	0.273426i
$296$	14.0800	+	17.2554i	0.818385	+	1.00295i
$297$	0.870954	−	0.443773i	0.0505379	−	0.0257503i
$298$	−5.63425	−	2.04277i	−0.326383	−	0.118334i
$299$	6.22645			0.360085
$300$	−9.82529	−	1.86111i	−0.567263	−	0.107451i
$301$	14.3057			0.824569
$302$	2.54032	+	0.921025i	0.146179	+	0.0529990i
$303$	−11.4676	+	5.84302i	−0.658795	+	0.335673i
$304$	−17.5988	+	9.47005i	−1.00936	+	0.543144i
$305$	−7.67823	+	5.79979i	−0.439654	+	0.332095i
$306$	4.77011	−	0.591718i	0.272689	−	0.0338263i
$307$	1.88086	−	1.88086i	0.107346	−	0.107346i	−0.651394	−	0.758740i	$-0.725815\pi$
$307$	1.88086	−	1.88086i	0.107346	−	0.107346i	0.758740	+	0.651394i	$0.225815\pi$
$308$	2.10357	+	2.40776i	0.119862	+	0.137195i
$309$	−6.84479	+	9.42105i	−0.389387	+	0.535945i
$310$	0.185116	−	12.2898i	0.0105139	−	0.698012i
$311$	−7.58700	−	10.4426i	−0.430219	−	0.592146i	0.537784	−	0.843082i	$-0.319261\pi$
$311$	−7.58700	−	10.4426i	−0.430219	−	0.592146i	−0.968004	+	0.250937i	$0.919261\pi$
$312$	4.23511	−	9.60852i	0.239766	−	0.543975i
$313$	8.32486	−	1.31853i	0.470549	−	0.0745276i	0.0833429	−	0.996521i	$-0.473440\pi$
$313$	8.32486	−	1.31853i	0.470549	−	0.0745276i	0.387206	+	0.921993i	$0.373440\pi$
$314$	−27.5355	+	12.8817i	−1.55392	+	0.726957i
$315$	0.639153	+	3.60064i	0.0360122	+	0.202873i
$316$	2.36055	−	1.48321i	0.132791	−	0.0834371i
$317$	8.53106	−	16.7431i	0.479152	−	0.940389i	−0.517266	−	0.855825i	$-0.673050\pi$
$317$	8.53106	−	16.7431i	0.479152	−	0.940389i	0.996418	−	0.0845641i	$-0.0269498\pi$
$318$	2.55199	−	1.72596i	0.143108	−	0.0967870i
$319$	−1.95773	−	6.02528i	−0.109612	−	0.337351i
$320$	8.53751	−	15.7198i	0.477261	−	0.878761i
$321$	4.71434	−	14.5092i	0.263129	−	0.809827i
$322$	−1.07384	−	3.72743i	−0.0598429	−	0.207722i
$323$	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
$328$	−8.98481	−	0.910464i	−0.496103	−	0.0502719i
$329$	16.0242	+	5.20658i	0.883443	+	0.287048i
$330$	−2.21842	+	2.15258i	−0.122120	+	0.118495i
$331$	28.4519	−	9.24458i	1.56386	−	0.508128i	0.606022	−	0.795448i	$-0.292764\pi$
$331$	28.4519	−	9.24458i	1.56386	−	0.508128i	0.957835	+	0.287320i	$0.0927642\pi$
$332$	−30.1013	+	12.8657i	−1.65202	+	0.706096i
$333$	7.01575	+	3.57470i	0.384461	+	0.195893i
$334$	−15.8394	+	14.8073i	−0.866692	+	0.810221i
$335$	−13.5419	−	6.58559i	−0.739873	−	0.359809i
$336$	−6.48249	−	0.878194i	−0.353649	−	0.0479094i
$337$	−1.67435	−	10.5714i	−0.0912078	−	0.575863i	−0.990392	−	0.138292i	$-0.955839\pi$
$337$	−1.67435	−	10.5714i	−0.0912078	−	0.575863i	0.899184	−	0.437571i	$-0.144161\pi$
$338$	−0.0372440	+	1.10596i	−0.00202581	+	0.0601564i
$339$	−11.1508	+	8.10154i	−0.605629	+	0.440015i
$340$	−13.8633	+	6.23284i	−0.751845	+	0.338023i
$341$	−3.07372	−	2.23319i	−0.166451	−	0.120934i
$342$	−4.34319	+	5.57330i	−0.234853	+	0.301370i
$343$	−13.0969	−	13.0969i	−0.707167	−	0.707167i
$344$	−23.9221	−	6.31434i	−1.28979	−	0.340446i
$345$	3.54454	−	1.22504i	0.190832	−	0.0659538i
$346$	24.9449	+	13.7866i	1.34104	+	0.741174i
$347$	−6.08901	−	11.9504i	−0.326875	−	0.641529i	0.667828	−	0.744316i	$-0.267224\pi$
$347$	−6.08901	−	11.9504i	−0.326875	−	0.641529i	−0.994703	+	0.102786i	$0.967224\pi$
$348$	11.1275	+	6.64849i	0.596499	+	0.356396i
$349$			11.8463i			0.634116i	0.948406	+	0.317058i	$0.102695\pi$
$349$			11.8463i			0.634116i	−0.948406	+	0.317058i	$0.897305\pi$
$350$	−5.28649	−	10.2851i	−0.282575	−	0.549764i
$351$		−	3.71248i		−	0.198157i
$352$	−2.45485	−	4.95475i	−0.130844	−	0.264089i
$353$	14.3565	+	28.1762i	0.764120	+	1.49967i	0.863350	+	0.504606i	$0.168362\pi$
$353$	14.3565	+	28.1762i	0.764120	+	1.49967i	−0.0992300	+	0.995065i	$0.531638\pi$
$354$	−2.50898	+	4.53963i	−0.133351	+	0.241278i
$355$	6.50090	+	1.97936i	0.345032	+	0.105054i
$356$	0.382063	−	5.66625i	0.0202493	−	0.300311i
$357$	3.93048	+	3.93048i	0.208023	+	0.208023i
$358$	−7.67572	−	5.98158i	−0.405675	−	0.316136i
$359$	0.764560	+	0.555486i	0.0403520	+	0.0293174i	0.607778	−	0.794107i	$-0.292061\pi$
$359$	0.764560	+	0.555486i	0.0403520	+	0.0293174i	−0.567426	+	0.823424i	$0.692061\pi$
$360$	0.520475	−	6.30310i	0.0274314	−	0.332203i
$361$	−4.82376	+	3.50467i	−0.253882	+	0.184456i
$362$	−4.69149	−	0.157989i	−0.246579	−	0.00830374i
$363$	−1.57131	−	9.92084i	−0.0824722	−	0.520709i
$364$	11.7749	−	2.96694i	0.617174	−	0.155510i
$365$	4.35932	−	31.2787i	0.228177	−	1.63720i
$366$	−4.15605	−	4.44572i	−0.217240	−	0.232381i
$367$	3.97266	+	2.02417i	0.207371	+	0.105661i	0.554592	−	0.832123i	$-0.312875\pi$
$367$	3.97266	+	2.02417i	0.207371	+	0.105661i	−0.347221	+	0.937783i	$0.612875\pi$
$368$	0.150448	+	6.70699i	0.00784262	+	0.349626i
$369$	−3.03661	+	0.986653i	−0.158079	+	0.0513631i
$370$	−24.5316	−	4.26512i	−1.27534	−	0.221733i
$371$	3.38838	+	1.10095i	0.175916	+	0.0571585i
$372$	7.74232	−	0.696774i	0.401421	−	0.0361260i
$373$	−1.49600	+	9.44535i	−0.0774598	+	0.489062i	0.918209	+	0.396095i	$0.129635\pi$
$373$	−1.49600	+	9.44535i	−0.0774598	+	0.489062i	−0.995669	+	0.0929666i	$0.970365\pi$
$374$	−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
$378$	−2.22245	+	0.640270i	−0.114311	+	0.0329319i
$379$	0.907685	−	2.79357i	0.0466246	−	0.143496i	−0.925034	−	0.379884i	$-0.875964\pi$
$379$	0.907685	−	2.79357i	0.0466246	−	0.143496i	0.971659	+	0.236388i	$0.0759638\pi$
$380$	7.93145	−	20.8888i	0.406875	−	1.07157i
$381$	4.45745	+	13.7186i	0.228362	+	0.702827i
$382$	−6.68094	−	9.87838i	−0.341827	−	0.505422i
$383$	−11.7564	+	23.0732i	−0.600723	+	1.17898i	0.367764	+	0.929919i	$0.380124\pi$
$383$	−11.7564	+	23.0732i	−0.600723	+	1.17898i	−0.968487	+	0.249066i	$0.919876\pi$
$384$	10.4524	+	4.32979i	0.533397	+	0.220954i
$385$	−3.54041	−	0.493427i	−0.180436	−	0.0251474i
$386$	8.14875	+	17.4185i	0.414760	+	0.886576i
$387$	−8.63971	+	1.36840i	−0.439181	+	0.0695595i
$388$	27.0693	+	6.17856i	1.37423	+	0.313669i
$389$	−5.82961	−	8.02377i	−0.295573	−	0.406821i	0.635241	−	0.772314i	$-0.280901\pi$
$389$	−5.82961	−	8.02377i	−0.295573	−	0.406821i	−0.930814	+	0.365492i	$0.880901\pi$
$390$	3.45925	+	11.2187i	0.175166	+	0.568079i
$391$	3.35062	−	4.61173i	0.169448	−	0.233225i
$392$	6.15649	+	10.5721i	0.310950	+	0.533970i
$393$	−11.7984	+	11.7984i	−0.595152	+	0.595152i
$394$	1.33260	+	10.7427i	0.0671356	+	0.541211i
$395$	−0.907873	+	2.98176i	−0.0456801	+	0.150029i
$396$	−1.50073	−	1.25291i	−0.0754145	−	0.0629613i
$397$	21.3376	−	10.8721i	1.07090	−	0.545653i	0.172585	−	0.984995i	$-0.444788\pi$
$397$	21.3376	−	10.8721i	1.07090	−	0.545653i	0.898320	+	0.439341i	$0.144788\pi$
$398$	6.68535	−	18.4392i	0.335106	−	0.924272i
$399$	−8.17100			−0.409062
$400$	4.30036	+	19.5322i	0.215018	+	0.976610i
$401$	6.16472			0.307851			0.153926	−	0.988082i	$-0.450808\pi$
$401$	6.16472			0.307851			0.153926	+	0.988082i	$0.450808\pi$
$402$	3.24617	−	8.95341i	0.161904	−	0.446556i
$403$	−12.8569	+	6.55093i	−0.640449	+	0.326325i
$404$	19.7596	+	16.4967i	0.983079	+	0.820743i
$405$	−0.730420	−	2.11341i	−0.0362948	−	0.105016i
$406$	1.84533	+	14.8760i	0.0915820	+	0.738284i
$407$	−5.44243	+	5.44243i	−0.269771	+	0.269771i
$408$	−4.83769	−	8.30740i	−0.239502	−	0.411278i
$409$	−0.203968	+	0.280737i	−0.0100855	+	0.0138816i	−0.814030	−	0.580823i	$-0.802731\pi$
$409$	−0.203968	+	0.280737i	−0.0100855	+	0.0138816i	0.803944	+	0.594704i	$0.202731\pi$
$410$	8.25691	−	5.81103i	0.407780	−	0.286986i
$411$	8.49115	+	11.6871i	0.418837	+	0.576480i
$412$	22.7062	+	5.18268i	1.11865	+	0.255332i
$413$	−5.92431	+	0.938319i	−0.291516	+	0.0461717i
$414$	1.00507	+	2.14840i	0.0493965	+	0.105588i
$415$	16.0063	−	32.9137i	0.785720	−	1.61567i
$416$	−20.9996	−	0.235947i	−1.02959	−	0.0115682i
$417$	10.4453	−	20.5000i	0.511508	−	1.00389i
$418$	−3.86932	−	5.72114i	−0.189255	−	0.279830i
$419$	8.61814	+	26.5239i	0.421024	+	1.29578i	0.906751	+	0.421668i	$0.138555\pi$
$419$	8.61814	+	26.5239i	0.421024	+	1.29578i	−0.485727	+	0.874111i	$0.661445\pi$
$420$	6.11939	−	4.00568i	0.298596	−	0.195457i
$421$	4.87173	−	14.9936i	0.237433	−	0.730745i	−0.759356	−	0.650676i	$-0.774486\pi$
$421$	4.87173	−	14.9936i	0.237433	−	0.730745i	0.996789	−	0.0800694i	$-0.0255142\pi$
$422$	12.8614	−	3.70526i	0.626083	−	0.180369i
$423$	−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
$428$	−30.3890	+	2.73487i	−1.46891	+	0.132195i
$429$	3.45131	+	1.12140i	0.166631	+	0.0541417i
$430$	24.8331	−	12.1855i	1.19756	−	0.587639i
$431$	−11.2786	+	3.66463i	−0.543269	+	0.176519i	−0.567779	−	0.823181i	$-0.692197\pi$
$431$	−11.2786	+	3.66463i	−0.543269	+	0.176519i	0.0245103	+	0.999700i	$0.492197\pi$
$432$	3.99899	−	0.0897033i	0.192402	−	0.00431585i
$433$	3.48035	+	1.77333i	0.167255	+	0.0852207i	0.535614	−	0.844463i	$-0.320080\pi$
$433$	3.48035	+	1.77333i	0.167255	+	0.0852207i	−0.368359	+	0.929684i	$0.620080\pi$
$434$	6.13904	+	6.56693i	0.294684	+	0.315223i
$435$	−14.2694	+	2.53297i	−0.684164	+	0.121447i
$436$	33.5716	−	8.45909i	1.60779	−	0.405117i
$437$	1.31085	+	8.27639i	0.0627065	+	0.395913i
$438$	19.9623	+	0.672244i	0.953835	+	0.0321211i
$439$	5.00770	−	3.63831i	0.239005	−	0.173647i	−0.461835	−	0.886966i	$-0.652809\pi$
$439$	5.00770	−	3.63831i	0.239005	−	0.173647i	0.700840	+	0.713319i	$0.252809\pi$
$440$	5.70248	+	2.38779i	0.271855	+	0.113833i
$441$	3.49931	+	2.54239i	0.166634	+	0.121066i
$442$	14.0754	+	10.9688i	0.669499	+	0.521731i
$443$	4.96290	+	4.96290i	0.235794	+	0.235794i	0.815106	−	0.579312i	$-0.196679\pi$
$443$	4.96290	+	4.96290i	0.235794	+	0.235794i	−0.579312	+	0.815106i	$0.696679\pi$
$444$	1.05944	−	15.7122i	0.0502790	−	0.745670i
$445$	3.82701	+	5.06650i	0.181418	+	0.240175i
$446$	1.84675	−	3.34142i	0.0874461	−	0.158221i
$447$	1.92391	+	3.77589i	0.0909980	+	0.178594i
$448$	3.48044	+	12.6120i	0.164435	+	0.595861i
$449$		−	22.5446i		−	1.06395i	−0.846761	−	0.531973i	$-0.821451\pi$
$449$		−	22.5446i		−	1.06395i	0.846761	−	0.531973i	$-0.178549\pi$
$450$	4.17649	+	5.70586i	0.196882	+	0.268977i
$451$		−	3.12102i		−	0.146963i
$452$	23.6642	+	14.1389i	1.11307	+	0.665038i
$453$	−0.867438	−	1.70244i	−0.0407558	−	0.0799877i
$454$	14.5853	+	8.06106i	0.684521	+	0.378324i
$455$	−7.77424	+	11.1299i	−0.364462	+	0.521780i
$456$	13.6636	+	3.60656i	0.639855	+	0.168892i
$457$	−3.08538	−	3.08538i	−0.144328	−	0.144328i	0.631251	−	0.775579i	$-0.282542\pi$
$457$	−3.08538	−	3.08538i	−0.144328	−	0.144328i	−0.775579	+	0.631251i	$0.782542\pi$
$458$	−3.56500	+	4.57470i	−0.166581	+	0.213762i
$459$	−2.74971	−	1.99778i	−0.128345	−	0.0932484i
$460$	−5.03907	−	5.55570i	−0.234948	−	0.259036i
$461$	−28.0983	+	20.4146i	−1.30867	+	0.950804i	−1.00000		0.000364875i	$-0.999884\pi$
$461$	−28.0983	+	20.4146i	−1.30867	+	0.950804i	−0.308670	+	0.951169i	$0.599884\pi$
$462$	0.0760906	−	2.25951i	0.00354005	−	0.105122i
$463$	−0.272846	−	1.72268i	−0.0126802	−	0.0800597i	0.980537	−	0.196336i	$-0.0629043\pi$
$463$	−0.272846	−	1.72268i	−0.0126802	−	0.0800597i	−0.993217	+	0.116276i	$0.962904\pi$
$464$	3.48029	−	25.6902i	0.161569	−	1.19264i
$465$	−6.03021	+	6.25883i	−0.279644	+	0.290246i
$466$	−8.58632	+	8.02686i	−0.397753	+	0.371837i
$467$	−31.3897	−	15.9938i	−1.45254	−	0.740107i	−0.463272	−	0.886216i	$-0.653325\pi$
$467$	−31.3897	−	15.9938i	−1.45254	−	0.740107i	−0.989268	+	0.146109i	$0.953325\pi$
$468$	−6.82747	+	2.91815i	−0.315600	+	0.134892i
$469$	10.4744	−	3.40334i	0.483663	−	0.157152i
$470$	32.2511	−	4.61129i	1.48763	−	0.212703i
$471$	20.4437	+	6.64257i	0.941998	+	0.306074i
$472$	10.3208	+	1.04585i	0.475054	+	0.0481389i
$473$	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
$478$	−4.35344	−	15.1113i	−0.199122	−	0.691175i
$479$	−8.73304	+	26.8775i	−0.399023	+	1.22807i	0.526761	+	0.850013i	$0.323406\pi$
$479$	−8.73304	+	26.8775i	−0.399023	+	1.22807i	−0.925784	+	0.378053i	$0.876594\pi$
$480$	−12.0009	+	3.99730i	−0.547764	+	0.182451i
$481$	9.03315	+	27.8012i	0.411876	+	1.26762i
$482$	−1.28044	+	0.865987i	−0.0583224	+	0.0394446i
$483$	−1.24525	+	2.44393i	−0.0566606	+	0.111203i
$484$	−17.0099	+	10.6879i	−0.773178	+	0.485813i
$485$	−27.3923	+	14.6051i	−1.24382	+	0.663185i
$486$	1.28097	−	0.599266i	0.0581059	−	0.0271833i
$487$	20.4192	−	3.23409i	0.925283	−	0.146550i	0.324430	−	0.945910i	$-0.394828\pi$
$487$	20.4192	−	3.23409i	0.925283	−	0.146550i	0.600853	+	0.799359i	$0.294828\pi$
$488$	−4.90913	+	11.1377i	−0.222226	+	0.504181i
$489$	8.74823	+	12.0409i	0.395609	+	0.544508i
$490$	−12.9435	−	4.42219i	−0.584726	−	0.199774i
$491$	−8.93859	+	12.3029i	−0.403393	+	0.555223i	−0.961591	−	0.274485i	$-0.911493\pi$
$491$	−8.93859	+	12.3029i	−0.403393	+	0.555223i	0.558199	+	0.829707i	$0.311493\pi$
$492$	4.20141	+	4.80895i	0.189414	+	0.216804i
$493$	−15.5765	+	15.5765i	−0.701531	+	0.701531i
$494$	−26.0319	+	3.22919i	−1.17123	+	0.145288i
$495$	2.18537	−	0.0406558i	0.0982249	−	0.00182734i
$496$	−7.36717	−	13.6909i	−0.330796	−	0.614740i
$497$	−4.42845	+	2.25641i	−0.198643	+	0.101214i
$498$	21.7613	+	7.88985i	0.975149	+	0.353552i
$499$	12.1532			0.544051			0.272025	−	0.962290i	$-0.412307\pi$
$499$	12.1532			0.544051			0.272025	+	0.962290i	$0.412307\pi$
$500$	−17.9375	−	13.3508i	−0.802191	−	0.597067i
$501$	15.3320			0.684985
$502$	36.6914	+	13.3029i	1.63762	+	0.593738i
$503$	20.2930	−	10.3398i	0.904820	−	0.461029i	0.0612957	−	0.998120i	$-0.480477\pi$
$503$	20.2930	−	10.3398i	0.904820	−	0.461029i	0.843524	+	0.537091i	$0.180477\pi$
$504$	2.92443	+	3.58395i	0.130264	+	0.159642i
$505$	−28.7740	+	0.535302i	−1.28043	+	0.0238206i
$506$	−2.30086	+	0.285415i	−0.102286	+	0.0126883i
$507$	0.553294	−	0.553294i	0.0245727	−	0.0245727i
$508$	21.7257	−	18.9809i	0.963921	−	0.842142i
$509$	23.4284	−	32.2465i	1.03845	−	1.42930i	0.140036	−	0.990146i	$-0.455278\pi$
$509$	23.4284	−	32.2465i	1.03845	−	1.42930i	0.898412	−	0.439154i	$-0.144722\pi$
$510$	10.1708	+	3.47490i	0.450371	+	0.153871i
$511$	13.5766	+	18.6866i	0.600594	+	0.826646i
$512$	−0.253250	−	22.6260i	−0.0111922	−	0.999937i
$513$	4.93474	−	0.781585i	0.217874	−	0.0345078i
$514$	−14.7658	+	6.90778i	−0.651292	+	0.304689i
$515$	−22.9771	+	12.2510i	−1.01249	+	0.539845i
$516$	9.30771	+	14.8133i	0.409749	+	0.652121i
$517$	4.57194	−	8.97293i	0.201074	−	0.394629i
$518$	15.0851	−	10.2024i	0.662802	−	0.448266i
$519$	−6.22774	−	19.1670i	−0.273367	−	0.841338i
$520$	17.9127	−	15.1801i	0.785523	−	0.665690i
$521$	−2.01724	+	6.20841i	−0.0883767	+	0.271996i	−0.985471	−	0.169844i	$-0.945674\pi$
$521$	−2.01724	+	6.20841i	−0.0883767	+	0.271996i	0.897094	+	0.441839i	$0.145674\pi$
$522$	−2.53740	−	8.80760i	−0.111059	−	0.385498i
$523$	20.1531	+	3.19194i	0.881234	+	0.139574i	0.580622	−	0.814173i	$-0.302809\pi$
$523$	20.1531	+	3.19194i	0.881234	+	0.139574i	0.300612	+	0.953747i	$0.402809\pi$
$524$	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
$528$	−1.12455	+	3.74477i	−0.0489399	+	0.162970i
$529$	−19.1991	−	6.23816i	−0.834742	−	0.271224i
$530$	6.81961	−	0.975073i	0.296225	−	0.0423545i
$531$	3.48814	−	1.13336i	0.151372	−	0.0491838i
$532$	6.42272	+	15.0270i	0.278460	+	0.651501i
$533$	−10.5615	−	5.38137i	−0.457470	−	0.233093i
$534$	−2.93352	+	2.74238i	−0.126946	+	0.118674i
$535$	23.6689	−	24.5662i	1.02329	−	1.06209i
$536$	−19.0175	+	1.06782i	−0.821430	+	0.0461230i
$537$	1.07642	+	6.79627i	0.0464511	+	0.293281i
$538$	0.237449	−	7.05106i	0.0102372	−	0.303993i
$539$	−3.42055	+	2.48518i	−0.147334	+	0.107044i
$540$	−3.31254	+	3.00451i	−0.142549	+	0.129293i
$541$	−21.6765	−	15.7489i	−0.931945	−	0.677097i	0.0145235	−	0.999895i	$-0.495377\pi$
$541$	−21.6765	−	15.7489i	−0.931945	−	0.677097i	−0.946468	+	0.322797i	$0.895377\pi$
$542$	−24.4337	+	31.3540i	−1.04952	+	1.34677i
$543$	2.34708	+	2.34708i	0.100723	+	0.100723i
$544$	−11.4752	+	15.4268i	−0.491995	+	0.661417i
$545$	−22.1652	+	31.7327i	−0.949454	+	1.35928i
$546$	−7.51498	−	4.15341i	−0.321612	−	0.177750i
$547$	1.09113	+	2.14147i	0.0466534	+	0.0915625i	0.913156	−	0.407610i	$-0.133638\pi$
$547$	1.09113	+	2.14147i	0.0466534	+	0.0915625i	−0.866503	+	0.499172i	$0.833638\pi$
$548$	14.8188	−	24.8022i	0.633029	−	1.05950i
$549$			4.30332i			0.183661i
$550$	−6.56603	+	2.15916i	−0.279977	+	0.0920669i
$551$		−	32.3818i		−	1.37951i
$552$	3.16102	−	3.53711i	0.134542	−	0.150550i
$553$	−1.03494	−	2.03119i	−0.0440103	−	0.0863751i
$554$	18.2740	−	33.0641i	0.776388	−	1.40476i
$555$	10.6121	+	14.0492i	0.450460	+	0.596354i
$556$	−45.9112	−	3.09569i	−1.94707	−	0.131287i
$557$	−17.1440	−	17.1440i	−0.726416	−	0.726416i	0.243488	−	0.969904i	$-0.421708\pi$
$557$	−17.1440	−	17.1440i	−0.726416	−	0.726416i	−0.969904	+	0.243488i	$0.921708\pi$
$558$	−4.33572	−	3.37876i	−0.183546	−	0.143034i
$559$	−26.2724	−	19.0881i	−1.11121	−	0.807339i
$560$	−12.1768	−	8.10531i	−0.514562	−	0.342512i
$561$	2.68782	−	1.95282i	0.113480	−	0.0824481i
$562$	−3.16154	−	0.106467i	−0.133362	−	0.00449105i
$563$	3.26270	+	20.5999i	0.137506	+	0.868181i	0.955936	+	0.293574i	$0.0948449\pi$
$563$	3.26270	+	20.5999i	0.137506	+	0.868181i	−0.818430	+	0.574606i	$0.805155\pi$
$564$	5.03447	+	19.9803i	0.211989	+	0.841323i
$565$	−30.3457	+	5.38670i	−1.27665	+	0.226620i
$566$	16.2819	+	17.4168i	0.684381	+	0.732081i
$567$	1.45718	+	0.742468i	0.0611956	+	0.0311807i
$568$	8.40121	−	1.81852i	0.352507	−	0.0763033i
$569$	−14.5574	+	4.72997i	−0.610276	+	0.198291i	−0.597818	−	0.801632i	$-0.703966\pi$
$569$	−14.5574	+	4.72997i	−0.610276	+	0.198291i	−0.0124579	+	0.999922i	$0.503966\pi$
$570$	−14.1839	+	6.96000i	−0.594099	+	0.291522i
$571$	−36.1142	−	11.7342i	−1.51133	−	0.491062i	−0.568034	−	0.823005i	$-0.692296\pi$
$571$	−36.1142	−	11.7342i	−1.51133	−	0.491062i	−0.943299	+	0.331943i	$0.892296\pi$
$572$	−0.650544	−	7.22863i	−0.0272006	−	0.302244i
$573$	−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	−0.483878	−	0.875135i	$-0.660772\pi$
$577$	−29.1734	−	4.62061i	−1.21451	−	0.192359i	−0.730627	+	0.682777i	$0.760772\pi$
$578$	−7.40349	+	2.13288i	−0.307945	+	0.0887163i
$579$	4.20198	−	12.9324i	0.174628	−	0.537450i
$580$	15.8746	+	24.2512i	0.659155	+	1.00698i
$581$	8.27184	+	25.4581i	0.343174	+	1.05618i
$582$	−10.9989	−	16.2629i	−0.455921	−	0.674121i
$583$	0.966752	−	1.89736i	0.0400388	−	0.0785806i
$584$	−14.4548	−	37.2403i	−0.598145	−	1.54101i
$585$	3.63050	−	7.46538i	0.150103	−	0.308655i
$586$	6.23698	+	13.3319i	0.257647	+	0.550737i
$587$	8.67609	−	1.37416i	0.358100	−	0.0567175i	0.0252077	−	0.999682i	$-0.491975\pi$
$587$	8.67609	−	1.37416i	0.358100	−	0.0567175i	0.332893	+	0.942965i	$0.391975\pi$
$588$	1.92503	−	8.43385i	0.0793867	−	0.347806i
$589$	−11.4145	−	15.7107i	−0.470325	−	0.647347i
$590$	−9.48467	+	6.67510i	−0.390478	+	0.274810i
$591$	4.49919	−	6.19260i	0.185072	−	0.254729i
$592$	−29.7285	+	10.4021i	−1.22184	+	0.427522i
$593$	−16.2759	+	16.2759i	−0.668372	+	0.668372i	−0.957339	−	0.288967i	$-0.906688\pi$
$593$	−16.2759	+	16.2759i	−0.668372	+	0.668372i	0.288967	+	0.957339i	$0.406688\pi$
$594$	0.170177	+	1.37187i	0.00698243	+	0.0562886i
$595$	4.06006	+	11.7474i	0.166446	+	0.481598i
$596$	5.43183	−	6.50619i	0.222496	−	0.266504i
$597$	−12.3573	+	6.29638i	−0.505753	+	0.257694i
$598$	−3.00138	+	8.27823i	−0.122735	+	0.338522i
$599$	22.8730			0.934566			0.467283	−	0.884108i	$-0.345233\pi$
$599$	22.8730			0.934566			0.467283	+	0.884108i	$0.345233\pi$
$600$	7.21054	−	12.1659i	0.294369	−	0.496669i
$601$	28.0770			1.14529			0.572643	−	0.819805i	$-0.305918\pi$
$601$	28.0770			1.14529			0.572643	+	0.819805i	$0.305918\pi$
$602$	−6.89589	+	19.0199i	−0.281056	+	0.775192i
$603$	−6.00029	+	3.05730i	−0.244351	+	0.124503i
$604$	−2.44906	+	2.93346i	−0.0996506	+	0.119361i
$605$	6.54206	−	21.4863i	0.265973	−	0.873543i
$606$	−2.24066	−	18.0630i	−0.0910207	−	0.733759i
$607$	−16.1309	+	16.1309i	−0.654732	+	0.654732i	−0.954129	−	0.299397i	$-0.903214\pi$
$607$	−16.1309	+	16.1309i	−0.654732	+	0.654732i	0.299397	+	0.954129i	$0.403214\pi$
$608$	−4.10741	−	27.9630i	−0.166577	−	1.13405i
$609$	6.23026	−	8.57522i	0.252463	−	0.347485i
$610$	−4.00979	−	13.0041i	−0.162352	−	0.526521i
$611$	−22.4813	−	30.9429i	−0.909496	−	1.25181i
$612$	−1.51266	+	6.62721i	−0.0611457	+	0.267889i
$613$	8.76640	−	1.38846i	0.354071	−	0.0560794i	0.0231347	−	0.999732i	$-0.492635\pi$
$613$	8.76640	−	1.38846i	0.354071	−	0.0560794i	0.330937	+	0.943653i	$0.392635\pi$
$614$	1.59401	+	3.40729i	0.0643290	+	0.137507i
$615$	−7.07115	−	0.985506i	−0.285136	−	0.0397395i
$616$	−4.21519	+	1.63613i	−0.169835	+	0.0659214i
$617$	9.82315	−	19.2790i	0.395465	−	0.776144i	−0.604323	−	0.796740i	$-0.706556\pi$
$617$	9.82315	−	19.2790i	0.395465	−	0.776144i	0.999788	+	0.0205955i	$0.00655621\pi$
$618$	−9.22610	−	13.6416i	−0.371128	−	0.548747i
$619$	7.47376	+	23.0019i	0.300396	+	0.924524i	0.981355	+	0.192202i	$0.0615630\pi$
$619$	7.47376	+	23.0019i	0.300396	+	0.924524i	−0.680959	+	0.732321i	$0.738437\pi$
$620$	16.2503	+	6.17023i	0.652629	+	0.247802i
$621$	0.518274	−	1.59508i	0.0207976	−	0.0640085i
$622$	17.5409	−	5.05340i	0.703327	−	0.202623i
$623$	−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
$628$	−3.85348	−	42.8186i	−0.153771	−	1.70865i
$629$	25.4524	+	8.26999i	1.01485	+	0.329746i
$630$	−5.09524	−	0.885867i	−0.202999	−	0.0352938i
$631$	26.5940	−	8.64091i	1.05869	−	0.343989i	0.272616	−	0.962123i	$-0.412111\pi$
$631$	26.5940	−	8.64091i	1.05869	−	0.343989i	0.786073	+	0.618134i	$0.212111\pi$
$632$	0.834098	+	3.85337i	0.0331786	+	0.153279i
$633$	−8.43272	−	4.29669i	−0.335171	−	0.170778i
$634$	18.1482	+	19.4131i	0.720756	+	0.770992i
$635$	−4.45227	+	31.9457i	−0.176683	+	1.26773i
$636$	1.06456	+	4.22491i	0.0422124	+	0.167529i
$637$	2.51200	+	15.8602i	0.0995292	+	0.628403i
$638$	8.95446	+	0.301548i	0.354511	+	0.0119384i
$639$	2.45865	−	1.78632i	0.0972629	−	0.0706656i
$640$	16.7844	+	18.9283i	0.663464	+	0.748209i
$641$	3.18368	+	2.31308i	0.125748	+	0.0913611i	0.648881	−	0.760890i	$-0.275237\pi$
$641$	3.18368	+	2.31308i	0.125748	+	0.0913611i	−0.523134	+	0.852251i	$0.675237\pi$
$642$	17.0179	+	13.2618i	0.671644	+	0.523402i
$643$	−1.48607	−	1.48607i	−0.0586048	−	0.0586048i	0.677197	−	0.735802i	$-0.263194\pi$
$643$	−1.48607	−	1.48607i	−0.0586048	−	0.0586048i	−0.735802	+	0.677197i	$0.763194\pi$
$644$	5.47335	+	0.369056i	0.215680	+	0.0145429i
$645$	−18.7117	−	5.69725i	−0.736772	−	0.224329i
$646$	−11.6167	+	21.0187i	−0.457054	+	0.826971i
$647$	−10.7848	−	21.1664i	−0.423994	−	0.832135i	−0.999893	−	0.0146144i	$-0.995348\pi$
$647$	−10.7848	−	21.1664i	−0.423994	−	0.832135i	0.575899	−	0.817521i	$-0.304652\pi$
$648$	−2.10898	−	1.88473i	−0.0828484	−	0.0740393i
$649$			3.58510i			0.140727i
$650$	−4.01478	+	25.9423i	−0.157472	+	1.01754i
$651$		−	6.35659i		−	0.249134i
$652$	15.2675	−	25.5531i	0.597921	−	1.00074i
$653$	1.32509	+	2.60064i	0.0518549	+	0.101771i	0.915480	−	0.402364i	$-0.131811\pi$
$653$	1.32509	+	2.60064i	0.0518549	+	0.101771i	−0.863625	+	0.504135i	$0.831811\pi$
$654$	−21.4261	−	11.8418i	−0.837825	−	0.463053i
$655$	−35.2633	+	12.1874i	−1.37785	+	0.476202i
$656$	5.54149	−	11.5067i	0.216359	−	0.449260i
$657$	−9.98680	−	9.98680i	−0.389622	−	0.389622i
$658$	−14.6465	+	18.7948i	−0.570982	+	0.732700i
$659$	26.9961	+	19.6138i	1.05162	+	0.764046i	0.972520	−	0.232821i	$-0.0747957\pi$
$659$	26.9961	+	19.6138i	1.05162	+	0.764046i	0.0790990	+	0.996867i	$0.474796\pi$
$660$	−1.79255	−	3.98706i	−0.0697749	−	0.155196i
$661$	−3.15278	+	2.29063i	−0.122629	+	0.0890950i	−0.647409	−	0.762143i	$-0.724147\pi$
$661$	−3.15278	+	2.29063i	−0.122629	+	0.0890950i	0.524780	+	0.851238i	$0.324147\pi$
$662$	−1.42394	+	42.2838i	−0.0553428	+	1.64340i
$663$	−1.97390	−	12.4627i	−0.0766599	−	0.484012i
$664$	−2.59535	−	46.2221i	−0.100719	−	1.79377i
$665$	−16.4310	−	7.99058i	−0.637166	−	0.309861i
$666$	−8.13451	+	7.60449i	−0.315206	+	0.294668i
$667$	−9.68533	−	4.93492i	−0.375017	−	0.191081i
$668$	−12.0516	−	28.1965i	−0.466290	−	1.09096i
$669$	−2.56746	+	0.834219i	−0.0992638	+	0.0322528i
$670$	15.2834	−	14.8298i	0.590449	−	0.572926i
$671$	−4.00059	−	1.29987i	−0.154441	−	0.0501810i
$672$	4.29238	−	8.19532i	0.165582	−	0.316142i
$673$	−6.76456	+	42.7098i	−0.260755	+	1.64634i	0.415442	+	0.909619i	$0.363627\pi$
$673$	−6.76456	+	42.7098i	−0.260755	+	1.64634i	−0.676197	+	0.736721i	$0.736373\pi$
$674$	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	−0.196776	−	0.980449i	$-0.563047\pi$
$677$	−17.8725	−	2.83072i	−0.686896	−	0.108794i	−0.490120	+	0.871655i	$0.663047\pi$
$678$	−5.39612	−	18.7305i	−0.207237	−	0.719342i
$679$	7.01598	−	21.5930i	0.269249	−	0.828662i
$680$	−1.60410	−	21.4361i	−0.0615143	−	0.822038i
$681$	−3.64136	−	11.2070i	−0.139537	−	0.429452i
$682$	4.45073	−	3.01012i	0.170427	−	0.115263i
$683$	17.9286	−	35.1869i	0.686020	−	1.34639i	−0.240685	−	0.970603i	$-0.577372\pi$
$683$	17.9286	−	35.1869i	0.686020	−	1.34639i	0.926706	−	0.375788i	$-0.122628\pi$
$684$	−5.31628	−	8.46092i	−0.203273	−	0.323511i
$685$	5.64575	+	31.8050i	0.215713	+	1.21521i
$686$	23.7259	−	11.0995i	0.905858	−	0.423781i
$687$	4.05055	−	0.641545i	0.154538	−	0.0244765i
$688$	19.9264	−	28.7613i	0.759687	−	1.09651i
$689$	−4.75375	−	6.54298i	−0.181104	−	0.249268i
$690$	−0.0798782	+	5.30308i	−0.00304091	+	0.201885i
$691$	−20.7179	+	28.5157i	−0.788146	+	1.08479i	0.206190	+	0.978512i	$0.433893\pi$
$691$	−20.7179	+	28.5157i	−0.788146	+	1.08479i	−0.994336	+	0.106278i	$0.966107\pi$
$692$	−30.3540	+	26.5192i	−1.15389	+	1.00811i
$693$	−1.13040	+	1.13040i	−0.0429402	+	0.0429402i
$694$	18.8235	−	2.33499i	0.714529	−	0.0886352i
$695$	41.0517	−	31.0086i	1.55718	−	1.17622i
$696$	−14.2032	+	11.5895i	−0.538372	+	0.439301i
$697$	−9.66924	+	4.92672i	−0.366248	+	0.186613i
$698$	−15.7499	−	5.71033i	−0.596144	−	0.216139i
$699$	8.31130			0.314362
$700$	16.2226	−	2.07071i	0.613158	−	0.0782655i
$701$	41.8330			1.58001			0.790005	−	0.613100i	$-0.210078\pi$
$701$	41.8330			1.58001			0.790005	+	0.613100i	$0.210078\pi$
$702$	4.93584	+	1.78955i	0.186291	+	0.0675422i
$703$	−35.0524	+	17.8601i	−1.32203	+	0.673607i
$704$	7.77080	−	0.875414i	0.292873	−	0.0329934i
$705$	−18.8859	−	13.1918i	−0.711284	−	0.496830i
$706$	−44.3814	+	5.50539i	−1.67032	+	0.207198i
$707$	14.8836	−	14.8836i	0.559754	−	0.559754i
$708$	−4.82613	−	5.52402i	−0.181377	−	0.207606i
$709$	22.6320	−	31.1503i	0.849962	−	1.16987i	−0.133909	−	0.990994i	$-0.542753\pi$
$709$	22.6320	−	31.1503i	0.849962	−	1.16987i	0.983871	−	0.178879i	$-0.0572470\pi$
$710$	−5.76529	+	7.68899i	−0.216367	+	0.288563i
$711$	0.819328	+	1.12771i	0.0307272	+	0.0422924i
$712$	7.34926	+	3.23930i	0.275425	+	0.121398i
$713$	−6.43858	+	1.01977i	−0.241127	+	0.0381907i
$714$	−7.12031	+	3.33104i	−0.266471	+	0.124661i
$715$	5.84357	+	5.63011i	0.218537	+	0.210554i
$716$	11.6526	−	7.32174i	0.435480	−	0.273626i
$717$	−5.04832	+	9.90789i	−0.188533	+	0.370017i
$718$	−1.10708	+	0.748739i	−0.0413158	+	0.0279427i
$719$	−11.1156	−	34.2102i	−0.414540	−	1.27582i	−0.912661	−	0.408717i	$-0.865976\pi$
$719$	−11.1156	−	34.2102i	−0.414540	−	1.27582i	0.498121	−	0.867108i	$-0.334024\pi$
$720$	8.12925	+	3.73031i	0.302959	+	0.139020i
$721$	5.88512	−	18.1125i	0.219173	−	0.674546i
$722$	−2.33432	−	8.10270i	−0.0868744	−	0.301551i
$723$	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	−0.834530	−	0.550963i	$-0.814261\pi$
$727$	3.48933	−	22.0307i	0.129412	−	0.817075i	0.963942	−	0.266113i	$-0.0857393\pi$
$728$	−1.73131	+	17.0853i	−0.0641667	+	0.633222i
$729$	−0.951057	−	0.309017i	−0.0352243	−	0.0114451i
$730$	39.4845	+	20.8733i	1.46139	+	0.772556i
$731$	−28.2758	+	9.18736i	−1.04582	+	0.339807i
$732$	7.91406	−	3.38258i	0.292512	−	0.125024i
$733$	−22.9079	−	11.6722i	−0.846124	−	0.431122i	−0.0235109	−	0.999724i	$-0.507484\pi$
$733$	−22.9079	−	11.6722i	−0.846124	−	0.431122i	−0.822613	+	0.568602i	$0.807484\pi$
$734$	−4.60615	+	4.30603i	−0.170016	+	0.158938i
$735$	4.55046	+	8.53451i	0.167846	+	0.314800i
$736$	−8.98965	−	3.03299i	−0.331363	−	0.111798i
$737$	−1.02977	−	6.50168i	−0.0379319	−	0.239493i
$738$	0.151973	−	4.51285i	0.00559422	−	0.166120i
$739$	−6.76750	+	4.91688i	−0.248947	+	0.180870i	−0.705260	−	0.708949i	$-0.749170\pi$
$739$	−6.76750	+	4.91688i	−0.248947	+	0.180870i	0.456313	+	0.889819i	$0.349170\pi$
$740$	17.4957	−	30.5595i	0.643156	−	1.12339i
$741$	15.0060	+	10.9025i	0.551260	+	0.400514i
$742$	−3.09706	+	3.97424i	−0.113697	+	0.145899i
$743$	−0.563949	−	0.563949i	−0.0206893	−	0.0206893i	0.696686	−	0.717376i	$-0.254657\pi$
$743$	−0.563949	−	0.563949i	−0.0206893	−	0.0206893i	−0.717376	+	0.696686i	$0.754657\pi$
$744$	−2.80570	+	10.6295i	−0.102862	+	0.389696i
$745$	0.176257	+	9.47434i	0.00645757	+	0.347113i
$746$	−11.8367	−	6.54197i	−0.433373	−	0.239519i
$747$	−7.43080	−	14.5838i	−0.271879	−	0.533592i
$748$	−5.70409	−	3.40808i	−0.208562	−	0.124612i
$749$			24.9499i			0.911651i
$750$	2.81859	+	15.5581i	0.102920	+	0.568103i
$751$			41.2218i			1.50420i	0.659046	+	0.752102i	$0.270960\pi$
$751$			41.2218i			1.50420i	−0.659046	+	0.752102i	$0.729040\pi$
$752$	32.7877	−	24.9640i	1.19565	−	0.910344i
$753$	−12.5289	−	24.5894i	−0.456579	−	0.896087i
$754$	16.4600	−	29.7820i	0.599439	−	1.08459i
$755$	−0.0794693	−	4.27171i	−0.00289219	−	0.155463i
$756$	0.220047	−	3.26344i	0.00800303	−	0.118690i
$757$	20.8498	+	20.8498i	0.757797	+	0.757797i	0.975921	−	0.218124i	$-0.0699937\pi$
$757$	20.8498	+	20.8498i	0.757797	+	0.757797i	−0.218124	+	0.975921i	$0.569994\pi$
$758$	3.27658	+	2.55339i	0.119011	+	0.0927434i
$759$	1.32632	+	0.963629i	0.0481424	+	0.0349775i
$760$	23.9490	+	20.6142i	0.868720	+	0.747757i
$761$	13.7177	−	9.96648i	0.497266	−	0.361285i	−0.310706	−	0.950506i	$-0.600565\pi$
$761$	13.7177	−	9.96648i	0.497266	−	0.361285i	0.807972	+	0.589221i	$0.200565\pi$
$762$	−20.3879	−	0.686578i	−0.738577	−	0.0248721i
$763$	−4.42866	−	27.9615i	−0.160328	−	1.01227i
$764$	16.3540	−	4.12075i	0.591668	−	0.149083i
$765$	−3.57569	−	6.70631i	−0.129279	−	0.242467i
$766$	−25.0094	−	26.7525i	−0.903627	−	0.966608i
$767$	12.1320	+	6.18155i	0.438060	+	0.223203i
$768$	−10.7950	+	11.8096i	−0.389532	+	0.426144i
$769$	38.5078	−	12.5119i	1.38863	−	0.451192i	0.483130	−	0.875549i	$-0.339500\pi$
$769$	38.5078	−	12.5119i	1.38863	−	0.451192i	0.905495	+	0.424357i	$0.139500\pi$
$770$	2.36263	−	4.46921i	0.0851432	−	0.161059i
$771$	10.9629	+	3.56206i	0.394819	+	0.128284i
$772$	−27.0863	+	2.43764i	−0.974857	+	0.0877327i
$773$	−4.17413	+	26.3544i	−0.150133	+	0.947902i	0.791478	+	0.611198i	$0.209312\pi$
$773$	−4.17413	+	26.3544i	−0.150133	+	0.947902i	−0.941611	+	0.336704i	$0.890688\pi$
$774$	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
$778$	13.4779	−	3.88287i	0.483206	−	0.139208i
$779$	4.92956	−	15.1716i	0.176620	−	0.543580i
$780$	−16.5830	−	0.808637i	−0.593766	−	0.0289539i
$781$	0.917987	+	2.82527i	0.0328482	+	0.101096i
$782$	4.51630	+	6.67776i	0.161502	+	0.238796i
$783$	−2.94241	+	5.77480i	−0.105153	+	0.206375i
$784$	−17.0235	+	3.08910i	−0.607983	+	0.110325i
$785$	34.6142	+	33.3498i	1.23543	+	1.19031i
$786$	−9.99906	−	21.3736i	−0.356655	−	0.762372i
$787$	−44.4189	+	7.03527i	−1.58336	+	0.250780i	−0.885219	−	0.465175i	$-0.845991\pi$
$787$	−44.4189	+	7.03527i	−1.58336	+	0.250780i	−0.698146	+	0.715956i	$0.745991\pi$
$788$	−14.9251	−	3.40665i	−0.531685	−	0.121357i
$789$	9.94582	+	13.6893i	0.354081	+	0.487350i
$790$	−3.52670	−	2.64436i	−0.125474	−	0.0940821i
$791$	13.2495	−	18.2363i	0.471097	−	0.648410i
$792$	2.38919	−	1.39131i	0.0848961	−	0.0494380i
$793$	−11.2967	+	11.2967i	−0.401158	+	0.401158i
$794$	4.16918	+	33.6097i	0.147959	+	1.19276i
$795$	−3.99349	−	2.78944i	−0.141634	−	0.0989314i
$796$	21.2928	+	17.7767i	0.754703	+	0.630079i
$797$	−25.8044	+	13.1480i	−0.914037	+	0.465725i	−0.846739	−	0.532008i	$-0.821438\pi$
$797$	−25.8044	+	13.1480i	−0.914037	+	0.465725i	−0.0672976	+	0.997733i	$0.521438\pi$
$798$	3.93872	−	10.8636i	0.139429	−	0.384566i
$799$	−35.0161			−1.23878
$800$	−28.0415	−	3.69779i	−0.991417	−	0.130737i
$801$	2.83956			0.100331
$802$	−2.97162	+	8.19615i	−0.104931	+	0.289416i
$803$	12.3009	−	6.26762i	0.434089	−	0.221179i
$804$	10.3390	+	8.63174i	0.364629	+	0.304418i
$805$	−4.89402	+	3.69673i	−0.172491	+	0.130292i
$806$	−2.51213	−	20.2514i	−0.0884860	−	0.713326i
$807$	−3.52753	+	3.52753i	−0.124175	+	0.124175i
$808$	−31.4577	+	18.3189i	−1.10668	+	0.644458i
$809$	19.7275	−	27.1526i	0.693584	−	0.954636i	−0.306413	−	0.951899i	$-0.599129\pi$
$809$	19.7275	−	27.1526i	0.693584	−	0.954636i	0.999996	−	0.00273720i	$-0.000871280\pi$
$810$	3.16192	+	0.0476268i	0.111099	+	0.00167343i
$811$	−8.32953	−	11.4646i	−0.292489	−	0.402577i	0.637331	−	0.770590i	$-0.280038\pi$
$811$	−8.32953	−	11.4646i	−0.292489	−	0.402577i	−0.929821	+	0.368013i	$0.880038\pi$
$812$	−20.6676	−	4.71737i	−0.725289	−	0.165547i
$813$	27.7616	−	4.39701i	0.973642	−	0.154210i
$814$	−4.61240	−	9.85930i	−0.161665	−	0.345568i
$815$	5.81668	+	32.7680i	0.203749	+	1.14781i
$816$	13.3769	−	2.42737i	0.468284	−	0.0849750i
$817$	19.8413	−	38.9407i	0.694159	−	1.36236i
$818$	−0.274928	−	0.406506i	−0.00961263	−	0.0142131i
$819$	1.87619	+	5.77432i	0.0655594	+	0.201771i
$820$	3.74579	+	13.7789i	0.130809	+	0.481180i
$821$	13.6386	−	41.9754i	0.475992	−	1.46495i	−0.368624	−	0.929579i	$-0.620171\pi$
$821$	13.6386	−	41.9754i	0.475992	−	1.46495i	0.844616	−	0.535373i	$-0.179829\pi$
$822$	−19.6313	+	5.65561i	−0.684720	+	0.197262i
$823$	26.4425	+	4.18808i	0.921728	+	0.145987i	0.599225	−	0.800581i	$-0.295476\pi$
$823$	26.4425	+	4.18808i	0.921728	+	0.145987i	0.322503	+	0.946568i	$0.395476\pi$
$824$	−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	−0.939397	−	0.342830i	$-0.888614\pi$
$827$	1.72439	−	10.8874i	0.0599630	−	0.378591i	0.999360	−	0.0357611i	$-0.0113855\pi$
$828$	−3.34084	+	0.300660i	−0.116102	+	0.0104487i
$829$	10.5473	+	3.42701i	0.366321	+	0.119025i	0.486393	−	0.873740i	$-0.338312\pi$
$829$	10.5473	+	3.42701i	0.366321	+	0.119025i	−0.120071	+	0.992765i	$0.538312\pi$
$830$	36.0440	+	37.1464i	1.25111	+	1.28937i
$831$	−25.4056	+	8.25478i	−0.881310	+	0.286355i
$832$	10.4363	−	27.8058i	0.361813	−	0.963993i
$833$	13.0989	+	6.67421i	0.453849	+	0.231248i
$834$	22.2203	+	23.7690i	0.769427	+	0.823055i
$835$	30.8310	+	14.9935i	1.06695	+	0.518871i
$836$	9.47156	−	2.38656i	0.327581	−	0.0825410i
$837$	0.608030	+	3.83895i	0.0210166	+	0.132694i
$838$	−39.4185	−	1.32745i	−1.36169	−	0.0458559i
$839$	−5.75338	+	4.18007i	−0.198629	+	0.144312i	−0.682654	−	0.730742i	$-0.739174\pi$
$839$	−5.75338	+	4.18007i	−0.198629	+	0.144312i	0.484025	+	0.875054i	$0.339174\pi$
$840$	2.37589	+	10.0668i	0.0819760	+	0.347337i
$841$	10.5222	+	7.64481i	0.362834	+	0.263614i
$842$	17.5861	+	13.7046i	0.606056	+	0.472291i
$843$	1.58167	+	1.58167i	0.0544755	+	0.0544755i
$844$	−1.27342	+	18.8856i	−0.0438329	+	0.650071i
$845$	1.65369	−	0.571536i	0.0568887	−	0.0196614i
$846$	7.04774	−	12.7518i	0.242306	−	0.438417i
$847$	7.45773	+	14.6366i	0.256251	+	0.502920i
$848$	6.93308	−	5.27873i	0.238083	−	0.181272i
$849$		−	16.8589i		−	0.578596i
$850$	17.0542	+	16.9339i	0.584954	+	0.580827i
$851$			13.2060i			0.452695i
$852$	−5.21774	−	3.11750i	−0.178757	−	0.106804i
$853$	−3.82112	−	7.49937i	−0.130833	−	0.256774i	0.816292	−	0.577640i	$-0.196026\pi$
$853$	−3.82112	−	7.49937i	−0.130833	−	0.256774i	−0.947125	+	0.320866i	$0.896026\pi$
$854$	8.71100	+	4.81443i	0.298084	+	0.164747i
$855$	10.6875	+	3.25409i	0.365506	+	0.111288i
$856$	11.0125	−	41.7213i	0.376401	−	1.42601i
$857$	27.4409	+	27.4409i	0.937362	+	0.937362i	0.998151	−	0.0607885i	$-0.0193615\pi$
$857$	27.4409	+	27.4409i	0.937362	+	0.937362i	−0.0607885	+	0.998151i	$0.519362\pi$
$858$	−3.15459	+	4.04806i	−0.107696	+	0.138198i
$859$	34.5693	+	25.1160i	1.17949	+	0.856948i	0.992114	−	0.125340i	$-0.0400022\pi$
$859$	34.5693	+	25.1160i	1.17949	+	0.856948i	0.187374	+	0.982289i	$0.440002\pi$
$860$	4.23052	+	38.8902i	0.144260	+	1.32614i
$861$	4.22446	−	3.06925i	0.143969	−	0.104600i
$862$	0.564460	−	16.7616i	0.0192256	−	0.570903i
$863$	−4.41919	−	27.9017i	−0.150431	−	0.949785i	−0.941244	−	0.337727i	$-0.890342\pi$
$863$	−4.41919	−	27.9017i	−0.150431	−	0.949785i	0.790813	−	0.612058i	$-0.209658\pi$
$864$	−1.80840	+	5.36001i	−0.0615230	+	0.182351i
$865$	6.22050	−	44.6329i	0.211503	−	1.51757i
$866$	−4.03534	+	3.77241i	−0.137127	+	0.128192i
$867$	4.85418	+	2.47333i	0.164857	+	0.0839986i
$868$	−11.6901	+	4.99652i	−0.396789	+	0.169593i
$869$	−1.29587	+	0.421052i	−0.0439592	+	0.0142832i
$870$	3.51070	−	20.1925i	0.119024	−	0.684589i
$871$	−23.7772	−	7.72570i	−0.805661	−	0.261775i
$872$	−4.93616	+	48.7120i	−0.167160	+	1.64960i
$873$	−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	−0.0278947	−	0.999611i	$-0.508880\pi$
$877$	−10.7595	−	1.70413i	−0.363321	−	0.0575444i	−0.335426	+	0.942067i	$0.608880\pi$
$878$	2.42333	+	8.41167i	0.0817835	+	0.283880i
$879$	3.21616	−	9.89831i	0.108478	−	0.333862i
$880$	−5.92343	+	6.43059i	−0.199679	+	0.216775i
$881$	17.5572	+	54.0356i	0.591518	+	1.82051i	0.571345	+	0.820710i	$0.306422\pi$
$881$	17.5572	+	54.0356i	0.591518	+	1.82051i	0.0201739	+	0.999796i	$0.493578\pi$
$882$	−5.06697	+	3.42689i	−0.170614	+	0.115389i
$883$	2.37742	−	4.66595i	0.0800066	−	0.157022i	−0.847537	−	0.530736i	$-0.821916\pi$
$883$	2.37742	−	4.66595i	0.0800066	−	0.157022i	0.927544	+	0.373714i	$0.121916\pi$
$884$	−21.3681	+	13.4263i	−0.718688	+	0.451575i
$885$	8.12259	+	1.13205i	0.273038	+	0.0380533i
$886$	−8.99060	+	4.20601i	−0.302045	+	0.141304i
$887$	−3.92752	+	0.622058i	−0.131873	+	0.0208867i	−0.222022	−	0.975042i	$-0.571266\pi$
$887$	−3.92752	+	0.622058i	−0.131873	+	0.0208867i	0.0901489	+	0.995928i	$0.471266\pi$
$888$	20.3792	+	8.98244i	0.683880	+	0.301431i
$889$	−13.8661	−	19.0851i	−0.465054	−	0.640092i
$890$	−8.58081	+	2.64587i	−0.287629	+	0.0886899i
$891$	0.574557	−	0.790810i	0.0192484	−	0.0264931i
$892$	3.55230	+	4.06599i	0.118940	+	0.136139i
$893$	36.3972	−	36.3972i	1.21799	−	1.21799i
$894$	−5.94755	+	0.737776i	−0.198916	+	0.0246749i
$895$	−4.48164	+	14.7192i	−0.149805	+	0.492009i
$896$	−18.4457	−	1.45210i	−0.616227	−	0.0485114i
$897$	5.54781	−	2.82675i	0.185236	−	0.0943824i
$898$	29.9737	+	10.8673i	1.00023	+	0.362648i
$899$	25.1912			0.840174
$900$	−9.59932	+	2.80232i	−0.319977	+	0.0934108i
$901$	−7.40429			−0.246673
$902$	4.14948	+	1.50445i	0.138162	+	0.0500925i
$903$	12.7465	−	6.49467i	0.424177	−	0.216129i
$904$	−30.2050	+	24.6467i	−1.00460	+	0.819738i
$905$	2.42446	+	7.01496i	0.0805917	+	0.233185i
$906$	2.68158	−	0.332642i	0.0890895	−	0.0110513i
$907$	−6.99767	+	6.99767i	−0.232354	+	0.232354i	−0.813675	−	0.581321i	$-0.802536\pi$
$907$	−6.99767	+	6.99767i	−0.232354	+	0.232354i	0.581321	+	0.813675i	$0.302536\pi$
$908$	−17.7480	+	15.5058i	−0.588989	+	0.514578i
$909$	−7.56501	+	10.4123i	−0.250916	+	0.345356i
$910$	−11.0501	−	15.7011i	−0.366307	−	0.520486i
$911$	32.8488	+	45.2125i	1.08833	+	1.49796i	0.850007	+	0.526771i	$0.176597\pi$
$911$	32.8488	+	45.2125i	1.08833	+	1.49796i	0.238322	+	0.971186i	$0.423403\pi$
$912$	−11.3813	+	16.4276i	−0.376874	+	0.543971i
$913$	15.8024	−	2.50285i	0.522983	−	0.0828323i
$914$	5.58935	−	2.61483i	0.184879	−	0.0864907i
$915$	−4.20830	+	8.65350i	−0.139122	+	0.286076i
$916$	−4.36373	−	6.94493i	−0.144182	−	0.229467i
$917$	12.3885	−	24.3137i	0.409103	−	0.802910i
$918$	3.98156	−	2.69281i	0.131411	−	0.0888759i
$919$	−1.90011	−	5.84793i	−0.0626788	−	0.192905i	0.914814	−	0.403876i	$-0.132337\pi$
$919$	−1.90011	−	5.84793i	−0.0626788	−	0.192905i	−0.977492	+	0.210971i	$0.932337\pi$
$920$	9.81546	−	4.02152i	0.323606	−	0.132586i
$921$	0.821966	−	2.52975i	0.0270847	−	0.0833581i
$922$	−13.5974	−	47.1981i	−0.447806	−	1.55439i
$923$	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
$928$	32.4782	+	17.0107i	1.06615	+	0.558405i
$929$	20.9750	+	6.81520i	0.688168	+	0.223599i	0.632168	−	0.774831i	$-0.282165\pi$
$929$	20.9750	+	6.81520i	0.688168	+	0.223599i	0.0560003	+	0.998431i	$0.482165\pi$
$930$	−5.41450	−	11.0343i	−0.177548	−	0.361829i
$931$	−20.5530	+	6.67806i	−0.673596	+	0.218865i
$932$	−6.53300	−	15.2850i	−0.213996	−	0.500676i
$933$	−11.5009	−	5.86000i	−0.376523	−	0.191848i
$934$	36.3952	−	34.0238i	1.19089	−	1.11329i
$935$	7.31462	−	1.29843i	0.239214	−	0.0424631i
$936$	−0.588670	−	10.4840i	−0.0192413	−	0.342679i
$937$	−1.61961	−	10.2258i	−0.0529102	−	0.334062i	−0.999917	−	0.0128498i	$-0.995910\pi$
$937$	−1.61961	−	10.2258i	−0.0529102	−	0.334062i	0.947007	−	0.321212i	$-0.104090\pi$
$938$	−0.524214	+	15.5665i	−0.0171162	+	0.508265i
$939$	6.81890	−	4.95422i	0.222526	−	0.161675i
$940$	−9.41538	+	45.1015i	−0.307096	+	1.47105i
$941$	−1.46640	−	1.06540i	−0.0478034	−	0.0347312i	0.563627	−	0.826029i	$-0.309406\pi$
$941$	−1.46640	−	1.06540i	−0.0478034	−	0.0347312i	−0.611430	+	0.791298i	$0.709406\pi$
$942$	−18.6861	+	23.9785i	−0.608826	+	0.781263i
$943$	−3.78655	−	3.78655i	−0.123307	−	0.123307i
$944$	−6.36548	+	13.2176i	−0.207179	+	0.430198i
$945$	2.20414	+	2.91802i	0.0717008	+	0.0949233i
$946$	10.5834	+	5.84930i	0.344097	+	0.190177i
$947$	11.7110	+	22.9842i	0.380557	+	0.746885i	0.999249	−	0.0387487i	$-0.0123372\pi$
$947$	11.7110	+	22.9842i	0.380557	+	0.746885i	−0.618692	+	0.785633i	$0.712337\pi$
$948$	1.42990	−	2.39322i	0.0464410	−	0.0777281i
$949$		−	52.4330i		−	1.70205i
$950$	−35.3286	+	0.125064i	−1.14621	+	0.00405763i
$951$		−	18.7913i		−	0.609349i
$952$	11.7228	+	10.4763i	0.379939	+	0.339540i
$953$	10.9366	+	21.4643i	0.354271	+	0.695296i	0.997522	−	0.0703598i	$-0.0224147\pi$
$953$	10.9366	+	21.4643i	0.354271	+	0.695296i	−0.643251	+	0.765656i	$0.722415\pi$
$954$	1.49027	−	2.69642i	0.0482492	−	0.0872998i
$955$	−10.7975	+	15.4582i	−0.349400	+	0.500217i
$956$	22.1894	+	1.49618i	0.717656	+	0.0483900i
$957$	−4.47977	−	4.47977i	−0.144810	−	0.144810i
$958$	−31.5248	−	24.5668i	−1.01852	−	0.793716i
$959$	−19.1133	−	13.8866i	−0.617202	−	0.448423i
$960$	0.470357	−	17.8824i	0.0151807	−	0.577151i
$961$	−12.8575	+	9.34152i	−0.414758	+	0.301339i
$962$	−41.3167	−	1.39137i	−1.33210	−	0.0448596i
$963$	−2.38655	−	15.0681i	−0.0769055	−	0.485562i
$964$	−0.534133	−	2.11982i	−0.0172033	−	0.0682747i
$965$	21.0965	−	21.8963i	0.679121	−	0.704868i
$966$	−2.64902	−	2.83365i	−0.0852308	−	0.0911712i
$967$	−23.2179	−	11.8301i	−0.746638	−	0.380431i	0.0389013	−	0.999243i	$-0.487614\pi$
$967$	−23.2179	−	11.8301i	−0.746638	−	0.380431i	−0.785539	+	0.618812i	$0.787614\pi$
$968$	−6.01044	−	27.7671i	−0.193183	−	0.892468i
$969$	16.1503	−	5.24754i	0.518821	−	0.168575i
$970$	−6.21381	−	43.4591i	−0.199513	−	1.39539i
$971$	5.43069	+	1.76454i	0.174279	+	0.0566268i	0.394857	−	0.918743i	$-0.370794\pi$
$971$	5.43069	+	1.76454i	0.174279	+	0.0566268i	−0.220578	+	0.975369i	$0.570794\pi$
$972$	0.179266	+	1.99195i	0.00574997	+	0.0638918i
$973$	−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	−0.0587177	−	0.998275i	$-0.518701\pi$
$977$	−13.2231	−	2.09434i	−0.423045	−	0.0670038i	−0.364328	+	0.931271i	$0.618701\pi$
$978$	−20.2257	+	5.82685i	−0.646745	+	0.186322i
$979$	−0.857724	+	2.63980i	−0.0274130	+	0.0843684i
$980$	12.1186	−	15.0770i	0.387116	−	0.481618i
$981$	5.34923	+	16.4632i	0.170788	+	0.525631i
$982$	−12.0483	−	17.8145i	−0.384477	−	0.568485i
$983$	−7.50817	+	14.7356i	−0.239473	+	0.469993i	−0.979195	−	0.202920i	$-0.934957\pi$
$983$	−7.50817	+	14.7356i	−0.239473	+	0.469993i	0.739722	+	0.672913i	$0.234957\pi$
$984$	−8.41886	+	3.26779i	−0.268384	+	0.104173i
$985$	15.1032	−	8.05279i	0.481229	−	0.256583i
$986$	−13.2009	−	28.2178i	−0.420404	−	0.898639i
$987$	16.6414	−	2.63574i	0.529702	−	0.0838966i
$988$	8.25506	−	36.1668i	0.262628	−	1.15062i
$989$	−8.62333	−	11.8690i	−0.274206	−	0.377412i
$990$	−0.999373	+	2.92510i	−0.0317622	+	0.0929658i
$991$	17.3344	−	23.8587i	0.550644	−	0.757896i	−0.439455	−	0.898264i	$-0.644829\pi$
$991$	17.3344	−	23.8587i	0.550644	−	0.757896i	0.990099	+	0.140368i	$0.0448286\pi$
$992$	21.7537	−	3.19534i	0.690680	−	0.101452i
$993$	21.1539	−	21.1539i	0.671298	−	0.671298i
$994$	−0.865280	−	6.97542i	−0.0274450	−	0.221247i
$995$	−31.0066	+	0.576836i	−0.982976	+	0.0182869i
$996$	−20.9795	+	25.1291i	−0.664761	+	0.796245i
$997$	30.7633	−	15.6747i	0.974284	−	0.496423i	0.107013	−	0.994258i	$-0.465872\pi$
$997$	30.7633	−	15.6747i	0.974284	−	0.496423i	0.867272	+	0.497835i	$0.165872\pi$
$998$	−5.85827	+	16.1580i	−0.185440	+	0.511472i
$999$	7.87396			0.249121

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.w.a.127.13	✓	240	1.1	even	1	trivial
300.2.w.a.127.15	yes	240	4.3	odd	2	inner
300.2.w.a.163.13	yes	240	100.63	even	20	inner
300.2.w.a.163.15	yes	240	25.13	odd	20	inner
900.2.bj.f.127.16		240	12.11	even	2
900.2.bj.f.127.18		240	3.2	odd	2
900.2.bj.f.163.16		240	75.38	even	20
900.2.bj.f.163.18		240	300.263	odd	20

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+(-0.482036 + 1.32953i) q^{2} +(0.891007 - 0.453990i) q^{3} +(-1.53528 - 1.28176i) q^{4} +(2.23568 - 0.0415918i) q^{5} +(0.174095 + 1.40346i) q^{6} +(-1.15642 + 1.15642i) q^{7} +(2.44420 - 1.42334i) q^{8} +(0.587785 - 0.809017i) q^{9} +(-1.02238 + 2.99245i) q^{10} +(0.574557 + 0.790810i) q^{11} +(-1.94985 - 0.445054i) q^{12} +(3.66677 - 0.580759i) q^{13} +(-0.980056 - 2.09493i) q^{14} +(1.97312 - 1.05204i) q^{15} +(0.714179 + 3.93573i) q^{16} +(1.54304 - 3.02838i) q^{17} +(0.792276 + 1.17145i) q^{18} +(1.54393 + 4.75171i) q^{19} +(-3.48571 - 2.80175i) q^{20} +(-0.505375 + 1.55538i) q^{21} +(-1.32836 + 0.382689i) 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} +(3.25769 - 0.293177i) q^{28} +(-6.16400 - 2.00281i) q^{29} +(0.447593 + 3.13044i) q^{30} +(-3.69657 + 1.20109i) q^{31} +(-5.57691 - 0.947644i) q^{32} +(0.870954 + 0.443773i) q^{33} +(3.28251 + 3.51129i) q^{34} +(-2.53729 + 2.63349i) q^{35} +(-1.93938 + 0.488669i) q^{36} +(1.23176 + 7.77702i) q^{37} +(-7.06176 - 0.237810i) q^{38} +(3.00346 - 2.18214i) q^{39} +(5.40524 - 3.28380i) q^{40} +(-2.58309 - 1.87673i) q^{41} +(-1.82431 - 1.42166i) q^{42} +(-6.18535 - 6.18535i) q^{43} +(0.131522 - 1.95056i) q^{44} +(1.28045 - 1.83315i) q^{45} +(-1.14733 + 2.07592i) q^{46} +(-4.67720 - 9.17952i) q^{47} +(2.42312 + 3.18253i) q^{48} +4.32538i q^{49} +(-2.16126 + 6.73268i) q^{50} -3.39883i q^{51} +(-6.37392 - 3.80829i) q^{52} +(-0.989011 - 1.94104i) q^{53} +(1.23775 + 0.684086i) q^{54} +(1.31742 + 1.74410i) q^{55} +(-1.18054 + 4.47250i) q^{56} +(3.53288 + 3.53288i) q^{57} +(5.63406 - 7.22978i) q^{58} +(2.96719 + 2.15579i) q^{59} +(-4.37776 - 0.913900i) q^{60} +(-3.48146 + 2.52943i) q^{61} +(0.185003 - 5.49366i) q^{62} +(0.255837 + 1.61529i) q^{63} +(3.94819 - 6.95786i) q^{64} +(8.17357 - 1.45090i) q^{65} +(-1.00984 + 0.944041i) q^{66} +(-6.00029 - 3.05730i) q^{67} +(-6.25065 + 2.67161i) q^{68} +(1.59508 - 0.518274i) q^{69} +(-2.27822 - 4.64283i) q^{70} +(2.89032 + 0.939123i) q^{71} +(0.285155 - 2.81402i) 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} +(1.45344 + 5.04504i) q^{78} +(-0.430746 + 1.32570i) q^{79} +(1.76037 + 8.76933i) q^{80} +(-0.309017 - 0.951057i) q^{81} +(3.74030 - 2.52964i) q^{82} +(7.43080 - 14.5838i) q^{83} +(2.76952 - 1.74018i) q^{84} +(3.32378 - 6.83466i) q^{85} +(11.2052 - 5.24202i) q^{86} +(-6.40142 + 1.01389i) q^{87} +(2.52992 + 1.11510i) q^{88} +(1.66905 + 2.29725i) q^{89} +(1.82000 + 2.58604i) q^{90} +(-3.56873 + 4.91193i) q^{91} +(-2.20693 - 2.52607i) q^{92} +(-2.74839 + 2.74839i) q^{93} +(14.4590 - 1.79360i) q^{94} +(3.64936 + 10.5591i) q^{95} +(-5.39929 + 1.68751i) q^{96} +(-12.3696 + 6.30263i) q^{97} +(-5.75071 - 2.08499i) 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

Related objects

Downloads

Learn more