LMFDB - Embedded newform 950.2.w.a.37.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(37,950)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([9, 10]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("950.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.w (of order $20$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$400$
Relative dimension:	$50$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			37.16
Character	$\chi$	$=$	950.37
Dual form			950.2.w.a.873.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.987688 + 0.156434i) q^{2} +(0.299107 - 0.587030i) q^{3} +(0.951057 - 0.309017i) q^{4} +(-2.03682 - 0.922698i) q^{5} +(-0.203592 + 0.626593i) q^{6} +(-0.375210 - 0.375210i) q^{7} +(-0.891007 + 0.453990i) q^{8} +(1.50822 + 2.07588i) q^{9} +O(q^{10})$	\(q+(-0.987688 + 0.156434i) q^{2} +(0.299107 - 0.587030i) q^{3} +(0.951057 - 0.309017i) q^{4} +(-2.03682 - 0.922698i) q^{5} +(-0.203592 + 0.626593i) q^{6} +(-0.375210 - 0.375210i) q^{7} +(-0.891007 + 0.453990i) q^{8} +(1.50822 + 2.07588i) q^{9} +(2.15608 + 0.592709i) q^{10} +(0.556470 + 0.404299i) q^{11} +(0.103065 - 0.650728i) q^{12} +(-0.882143 - 0.139718i) q^{13} +(0.429287 + 0.311895i) q^{14} +(-1.15088 + 0.919688i) q^{15} +(0.809017 - 0.587785i) q^{16} +(4.61490 - 2.35141i) q^{17} +(-1.81439 - 1.81439i) q^{18} +(-2.94930 + 3.20961i) q^{19} +(-2.22226 - 0.248126i) q^{20} +(-0.332487 + 0.108032i) q^{21} +(-0.612866 - 0.312271i) q^{22} +(7.85984 - 1.24488i) q^{23} +0.658839i q^{24} +(3.29726 + 3.75874i) q^{25} +0.893139 q^{26} +(3.62190 - 0.573653i) q^{27} +(-0.472792 - 0.240900i) q^{28} +(-2.36359 - 7.27438i) q^{29} +(0.992837 - 1.08840i) q^{30} +(-6.14318 - 1.99604i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(0.403780 - 0.205736i) q^{33} +(-4.19024 + 3.04439i) q^{34} +(0.418029 + 1.11044i) q^{35} +(2.07588 + 1.50822i) q^{36} +(1.12583 - 7.10824i) q^{37} +(2.41090 - 3.63147i) q^{38} +(-0.345873 + 0.476054i) q^{39} +(2.23371 - 0.102566i) q^{40} +(5.17021 + 7.11619i) q^{41} +(0.311494 - 0.158714i) q^{42} +(3.69146 - 3.69146i) q^{43} +(0.654170 + 0.212553i) q^{44} +(-1.15655 - 5.61982i) q^{45} +(-7.56833 + 2.45910i) q^{46} +(2.52392 - 4.95348i) q^{47} +(-0.103065 - 0.650728i) q^{48} -6.71843i q^{49} +(-3.84466 - 3.19665i) q^{50} -3.41240i q^{51} +(-0.882143 + 0.139718i) q^{52} +(-1.15842 + 2.27353i) q^{53} +(-3.48757 + 1.13318i) q^{54} +(-0.760383 - 1.33694i) q^{55} +(0.504657 + 0.163973i) q^{56} +(1.00198 + 2.69135i) q^{57} +(3.47245 + 6.81507i) q^{58} +(6.44166 - 4.68014i) q^{59} +(-0.810350 + 1.23032i) q^{60} +(-9.40967 - 6.83652i) q^{61} +(6.37980 + 1.01046i) q^{62} +(0.212994 - 1.34479i) q^{63} +(0.587785 - 0.809017i) q^{64} +(1.66785 + 1.09853i) q^{65} +(-0.366624 + 0.266368i) q^{66} +(-5.30207 - 10.4059i) q^{67} +(3.66240 - 3.66240i) q^{68} +(1.62015 - 4.98631i) q^{69} +(-0.586594 - 1.03138i) q^{70} +(1.54459 - 0.501867i) q^{71} +(-2.28626 - 1.16491i) q^{72} +(1.77787 - 0.281587i) q^{73} +7.19684i q^{74} +(3.19272 - 0.811325i) q^{75} +(-1.81313 + 3.96391i) q^{76} +(-0.0570961 - 0.360491i) q^{77} +(0.267144 - 0.524299i) q^{78} +(1.66408 + 5.12152i) q^{79} +(-2.19017 + 0.450733i) q^{80} +(-1.63217 + 5.02329i) q^{81} +(-6.21978 - 6.21978i) q^{82} +(7.32218 + 14.3706i) q^{83} +(-0.282831 + 0.205489i) q^{84} +(-11.5693 + 0.531234i) q^{85} +(-3.06854 + 4.22348i) q^{86} +(-4.97724 - 0.788318i) q^{87} +(-0.679367 - 0.107601i) q^{88} +(-1.96734 - 1.42935i) q^{89} +(2.02145 + 5.36971i) q^{90} +(0.278566 + 0.383413i) q^{91} +(7.09046 - 3.61277i) q^{92} +(-3.00920 + 3.00920i) q^{93} +(-1.71795 + 5.28732i) q^{94} +(8.96870 - 3.81608i) q^{95} +(0.203592 + 0.626593i) q^{96} +(0.931689 + 0.474719i) q^{97} +(1.05099 + 6.63572i) q^{98} +1.76494i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 400 q + 4 q^{5} - 4 q^{7}+O(q^{10}) $ 400 * q + 4 * q^5 - 4 * q^7	$ 400 q + 4 q^{5} - 4 q^{7} + 100 q^{16} + 40 q^{17} - 40 q^{19} - 76 q^{23} - 20 q^{25} - 4 q^{28} + 64 q^{30} + 8 q^{35} - 100 q^{36} + 4 q^{38} + 80 q^{39} + 32 q^{42} - 84 q^{43} - 144 q^{45} + 20 q^{47} - 16 q^{55} - 32 q^{57} - 16 q^{62} + 108 q^{63} - 100 q^{68} - 12 q^{73} + 256 q^{77} - 4 q^{80} + 100 q^{81} - 16 q^{82} + 116 q^{85} - 272 q^{87} - 4 q^{92} - 24 q^{93} - 56 q^{95}+O(q^{100}) $ 400 * q + 4 * q^5 - 4 * q^7 + 100 * q^16 + 40 * q^17 - 40 * q^19 - 76 * q^23 - 20 * q^25 - 4 * q^28 + 64 * q^30 + 8 * q^35 - 100 * q^36 + 4 * q^38 + 80 * q^39 + 32 * q^42 - 84 * q^43 - 144 * q^45 + 20 * q^47 - 16 * q^55 - 32 * q^57 - 16 * q^62 + 108 * q^63 - 100 * q^68 - 12 * q^73 + 256 * q^77 - 4 * q^80 + 100 * q^81 - 16 * q^82 + 116 * q^85 - 272 * q^87 - 4 * q^92 - 24 * q^93 - 56 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{9}{20}\right)$	$-1$

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 $

$2$	−0.987688	+	0.156434i	−0.698401	+	0.110616i
$2$	−0.987688	+	0.156434i	−0.698401	+	0.110616i
$3$	0.299107	−	0.587030i	0.172689	−	0.338922i	−0.788399	−	0.615165i	$-0.789089\pi$
$3$	0.299107	−	0.587030i	0.172689	−	0.338922i	0.961088	+	0.276243i	$0.0890895\pi$
$4$	0.951057	−	0.309017i	0.475528	−	0.154508i
$5$	−2.03682	−	0.922698i	−0.910893	−	0.412643i
$5$	−2.03682	−	0.922698i	−0.910893	−	0.412643i
$6$	−0.203592	+	0.626593i	−0.0831163	+	0.255806i
$7$	−0.375210	−	0.375210i	−0.141816	−	0.141816i	0.632634	−	0.774451i	$-0.281974\pi$
$7$	−0.375210	−	0.375210i	−0.141816	−	0.141816i	−0.774451	+	0.632634i	$0.781974\pi$
$8$	−0.891007	+	0.453990i	−0.315018	+	0.160510i
$9$	1.50822	+	2.07588i	0.502739	+	0.691961i
$10$	2.15608	+	0.592709i	0.681813	+	0.187431i
$11$	0.556470	+	0.404299i	0.167782	+	0.121901i	0.668508	−	0.743705i	$-0.266933\pi$
$11$	0.556470	+	0.404299i	0.167782	+	0.121901i	−0.500726	+	0.865606i	$0.666933\pi$
$12$	0.103065	−	0.650728i	0.0297523	−	0.187849i
$13$	−0.882143	−	0.139718i	−0.244663	−	0.0387507i	0.0328987	−	0.999459i	$-0.489526\pi$
$13$	−0.882143	−	0.139718i	−0.244663	−	0.0387507i	−0.277561	+	0.960708i	$0.589526\pi$
$14$	0.429287	+	0.311895i	0.114732	+	0.0833574i
$15$	−1.15088	+	0.919688i	−0.297155	+	0.237462i
$16$	0.809017	−	0.587785i	0.202254	−	0.146946i
$17$	4.61490	−	2.35141i	1.11928	−	0.570300i	0.206373	−	0.978473i	$-0.433834\pi$
$17$	4.61490	−	2.35141i	1.11928	−	0.570300i	0.912905	+	0.408173i	$0.133834\pi$
$18$	−1.81439	−	1.81439i	−0.427655	−	0.427655i
$19$	−2.94930	+	3.20961i	−0.676617	+	0.736336i
$19$	−2.94930	+	3.20961i	−0.676617	+	0.736336i
$20$	−2.22226	−	0.248126i	−0.496912	−	0.0554828i
$21$	−0.332487	+	0.108032i	−0.0725547	+	0.0235745i
$22$	−0.612866	−	0.312271i	−0.130663	−	0.0665763i
$23$	7.85984	−	1.24488i	1.63889	−	0.259575i	0.732112	−	0.681184i	$-0.238535\pi$
$23$	7.85984	−	1.24488i	1.63889	−	0.259575i	0.906777	+	0.421610i	$0.138535\pi$
$24$			0.658839i			0.134485i
$25$	3.29726	+	3.75874i	0.659451	+	0.751747i
$26$	0.893139			0.175159
$27$	3.62190	−	0.573653i	0.697036	−	0.110400i
$28$	−0.472792	−	0.240900i	−0.0893494	−	0.0455258i
$29$	−2.36359	−	7.27438i	−0.438907	−	1.35082i	−0.889029	−	0.457851i	$-0.848619\pi$
$29$	−2.36359	−	7.27438i	−0.438907	−	1.35082i	0.450122	−	0.892967i	$-0.351381\pi$
$30$	0.992837	−	1.08840i	0.181266	−	0.198714i
$31$	−6.14318	−	1.99604i	−1.10335	−	0.358500i	−0.299958	−	0.953952i	$-0.596973\pi$
$31$	−6.14318	−	1.99604i	−1.10335	−	0.358500i	−0.803390	+	0.595453i	$0.796973\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	0.403780	−	0.205736i	0.0702890	−	0.0358140i
$34$	−4.19024	+	3.04439i	−0.718620	+	0.522108i
$35$	0.418029	+	1.11044i	0.0706598	+	0.187699i
$36$	2.07588	+	1.50822i	0.345980	+	0.251369i
$37$	1.12583	−	7.10824i	0.185086	−	1.16859i	−0.703779	−	0.710419i	$-0.748506\pi$
$37$	1.12583	−	7.10824i	0.185086	−	1.16859i	0.888865	−	0.458169i	$-0.151494\pi$
$38$	2.41090	−	3.63147i	0.391099	−	0.589102i
$39$	−0.345873	+	0.476054i	−0.0553841	+	0.0762296i
$40$	2.23371	−	0.102566i	0.353181	−	0.0162172i
$41$	5.17021	+	7.11619i	0.807452	+	1.11136i	0.991712	+	0.128485i	$0.0410113\pi$
$41$	5.17021	+	7.11619i	0.807452	+	1.11136i	−0.184260	+	0.982878i	$0.558989\pi$
$42$	0.311494	−	0.158714i	0.0480646	−	0.0244901i
$43$	3.69146	−	3.69146i	0.562942	−	0.562942i	−0.367200	−	0.930142i	$-0.619684\pi$
$43$	3.69146	−	3.69146i	0.562942	−	0.562942i	0.930142	+	0.367200i	$0.119684\pi$
$44$	0.654170	+	0.212553i	0.0986198	+	0.0320435i
$45$	−1.15655	−	5.61982i	−0.172408	−	0.837754i
$46$	−7.56833	+	2.45910i	−1.11589	+	0.362574i
$47$	2.52392	−	4.95348i	0.368152	−	0.722539i	−0.630404	−	0.776268i	$-0.717111\pi$
$47$	2.52392	−	4.95348i	0.368152	−	0.722539i	0.998556	+	0.0537286i	$0.0171106\pi$
$48$	−0.103065	−	0.650728i	−0.0148762	−	0.0939244i
$49$		−	6.71843i		−	0.959776i
$50$	−3.84466	−	3.19665i	−0.543717	−	0.452075i
$51$		−	3.41240i		−	0.477832i
$52$	−0.882143	+	0.139718i	−0.122331	+	0.0193754i
$53$	−1.15842	+	2.27353i	−0.159121	+	0.312293i	−0.956778	−	0.290818i	$-0.906073\pi$
$53$	−1.15842	+	2.27353i	−0.159121	+	0.312293i	0.797657	+	0.603111i	$0.206073\pi$
$54$	−3.48757	+	1.13318i	−0.474599	+	0.154206i
$55$	−0.760383	−	1.33694i	−0.102530	−	0.180273i
$56$	0.504657	+	0.163973i	0.0674376	+	0.0219118i
$57$	1.00198	+	2.69135i	0.132716	+	0.356477i
$58$	3.47245	+	6.81507i	0.455955	+	0.894863i
$59$	6.44166	−	4.68014i	0.838632	−	0.609302i	−0.0833558	−	0.996520i	$-0.526564\pi$
$59$	6.44166	−	4.68014i	0.838632	−	0.609302i	0.921988	+	0.387218i	$0.126564\pi$
$60$	−0.810350	+	1.23032i	−0.104616	+	0.158833i
$61$	−9.40967	−	6.83652i	−1.20478	−	0.875327i	−0.210037	−	0.977693i	$-0.567359\pi$
$61$	−9.40967	−	6.83652i	−1.20478	−	0.875327i	−0.994747	+	0.102366i	$0.967359\pi$
$62$	6.37980	+	1.01046i	0.810235	+	0.128329i
$63$	0.212994	−	1.34479i	0.0268347	−	0.169428i
$64$	0.587785	−	0.809017i	0.0734732	−	0.101127i
$65$	1.66785	+	1.09853i	0.206871	+	0.136256i
$66$	−0.366624	+	0.266368i	−0.0451283	+	0.0327876i
$67$	−5.30207	−	10.4059i	−0.647751	−	1.27128i	−0.948257	−	0.317503i	$-0.897156\pi$
$67$	−5.30207	−	10.4059i	−0.647751	−	1.27128i	0.300506	−	0.953780i	$-0.402844\pi$
$68$	3.66240	−	3.66240i	0.444132	−	0.444132i
$69$	1.62015	−	4.98631i	0.195043	−	0.600281i
$70$	−0.586594	−	1.03138i	−0.0701114	−	0.123273i
$71$	1.54459	−	0.501867i	0.183309	−	0.0595606i	−0.215924	−	0.976410i	$-0.569276\pi$
$71$	1.54459	−	0.501867i	0.183309	−	0.0595606i	0.399233	+	0.916849i	$0.369276\pi$
$72$	−2.28626	−	1.16491i	−0.269438	−	0.137286i
$73$	1.77787	−	0.281587i	0.208084	−	0.0329573i	−0.0515221	−	0.998672i	$-0.516407\pi$
$73$	1.77787	−	0.281587i	0.208084	−	0.0329573i	0.259606	+	0.965715i	$0.416407\pi$
$74$			7.19684i			0.836616i
$75$	3.19272	−	0.811325i	0.368664	−	0.0936838i
$76$	−1.81313	+	3.96391i	−0.207980	+	0.454691i
$77$	−0.0570961	−	0.360491i	−0.00650670	−	0.0410817i
$78$	0.267144	−	0.524299i	0.0302481	−	0.0593652i
$79$	1.66408	+	5.12152i	0.187224	+	0.576216i	0.999980	−	0.00638854i	$-0.00203355\pi$
$79$	1.66408	+	5.12152i	0.187224	+	0.576216i	−0.812756	+	0.582605i	$0.802034\pi$
$80$	−2.19017	+	0.450733i	−0.244868	+	0.0503935i
$81$	−1.63217	+	5.02329i	−0.181352	+	0.558143i
$82$	−6.21978	−	6.21978i	−0.686860	−	0.686860i
$83$	7.32218	+	14.3706i	0.803714	+	1.57738i	0.816420	+	0.577458i	$0.195955\pi$
$83$	7.32218	+	14.3706i	0.803714	+	1.57738i	−0.0127064	+	0.999919i	$0.504045\pi$
$84$	−0.282831	+	0.205489i	−0.0308594	+	0.0224206i
$85$	−11.5693	+	0.531234i	−1.25487	+	0.0576204i
$86$	−3.06854	+	4.22348i	−0.330889	+	0.455430i
$87$	−4.97724	−	0.788318i	−0.533616	−	0.0845165i
$88$	−0.679367	−	0.107601i	−0.0724207	−	0.0114703i
$89$	−1.96734	−	1.42935i	−0.208537	−	0.151511i	0.478614	−	0.878025i	$-0.341139\pi$
$89$	−1.96734	−	1.42935i	−0.208537	−	0.151511i	−0.687152	+	0.726514i	$0.741139\pi$
$90$	2.02145	+	5.36971i	0.213079	+	0.566017i
$91$	0.278566	+	0.383413i	0.0292016	+	0.0401926i
$92$	7.09046	−	3.61277i	0.739232	−	0.376657i
$93$	−3.00920	+	3.00920i	−0.312040	+	0.312040i
$94$	−1.71795	+	5.28732i	−0.177193	+	0.545345i
$95$	8.96870	−	3.81608i	0.920169	−	0.391522i
$96$	0.203592	+	0.626593i	0.0207791	+	0.0639514i
$97$	0.931689	+	0.474719i	0.0945987	+	0.0482005i	0.500650	−	0.865650i	$-0.333094\pi$
$97$	0.931689	+	0.474719i	0.0945987	+	0.0482005i	−0.406051	+	0.913850i	$0.633094\pi$
$98$	1.05099	+	6.63572i	0.106166	+	0.670309i
$99$			1.76494i			0.177383i
$100$	4.29739	+	2.55586i	0.429739	+	0.255586i
$101$	12.8226			1.27590			0.637951	−	0.770077i	$-0.279782\pi$
$101$	12.8226			1.27590			0.637951	+	0.770077i	$0.279782\pi$
$102$	0.533818	+	3.37039i	0.0528558	+	0.333719i
$103$	−1.78327	+	3.49987i	−0.175711	+	0.344853i	−0.962019	−	0.272982i	$-0.911990\pi$
$103$	−1.78327	+	3.49987i	−0.175711	+	0.344853i	0.786308	+	0.617835i	$0.211990\pi$
$104$	0.849426	−	0.275995i	0.0832931	−	0.0270636i
$105$	0.776897	+	0.0867445i	0.0758174	+	0.00846539i
$106$	0.788500	−	2.42675i	0.0765859	−	0.235707i
$107$	4.22927	−	4.22927i	0.408859	−	0.408859i	−0.472482	−	0.881341i	$-0.656642\pi$
$107$	4.22927	−	4.22927i	0.408859	−	0.408859i	0.881341	+	0.472482i	$0.156642\pi$
$108$	3.26737	−	1.66481i	0.314403	−	0.160196i
$109$	14.4850	−	10.5240i	1.38741	−	1.00801i	0.391267	−	0.920277i	$-0.372037\pi$
$109$	14.4850	−	10.5240i	1.38741	−	1.00801i	0.996144	−	0.0877354i	$-0.0279630\pi$
$110$	0.960164	+	1.20153i	0.0915481	+	0.114561i
$111$	−3.83600	−	2.78702i	−0.364097	−	0.264532i
$112$	−0.524094	−	0.0830084i	−0.0495223	−	0.00784356i
$113$	7.79296	+	1.23428i	0.733100	+	0.116112i	0.511813	−	0.859097i	$-0.328974\pi$
$113$	7.79296	+	1.23428i	0.733100	+	0.116112i	0.221287	+	0.975209i	$0.428974\pi$
$114$	−1.41067	−	2.50147i	−0.132121	−	0.234284i
$115$	−17.1577	−	4.71667i	−1.59996	−	0.439832i
$116$	−4.49581	−	6.18795i	−0.417426	−	0.574537i
$117$	−1.04043	−	2.04195i	−0.0961874	−	0.188778i
$118$	−5.63022	+	5.63022i	−0.518303	+	0.518303i
$119$	−2.61383	−	0.849285i	−0.239609	−	0.0778538i
$120$	0.607909	−	1.34194i	0.0554943	−	0.122501i
$121$	−3.25299	−	10.0117i	−0.295726	−	0.910151i
$122$	10.3633	+	5.28036i	0.938248	+	0.478061i
$123$	5.72386	−	0.906571i	0.516103	−	0.0817427i
$124$	−6.45932			−0.580064
$125$	−3.24774	−	10.6982i	−0.290486	−	0.956879i
$126$			1.36155i			0.121297i
$127$	13.4738	−	2.13404i	1.19561	−	0.189365i	0.473276	−	0.880914i	$-0.343071\pi$
$127$	13.4738	−	2.13404i	1.19561	−	0.189365i	0.722330	+	0.691549i	$0.243071\pi$
$128$	−0.453990	+	0.891007i	−0.0401275	+	0.0787546i
$129$	−1.06286	−	3.27114i	−0.0935793	−	0.288007i
$130$	−1.81916	−	0.824098i	−0.159551	−	0.0722782i
$131$	3.70865	−	11.4140i	0.324026	−	0.997250i	−0.647852	−	0.761766i	$-0.724333\pi$
$131$	3.70865	−	11.4140i	0.324026	−	0.997250i	0.971878	−	0.235484i	$-0.0756674\pi$
$132$	0.320441	−	0.320441i	0.0278908	−	0.0278908i
$133$	2.31089	−	0.0976706i	0.200379	−	0.00846912i
$134$	6.86464	+	9.44836i	0.593014	+	0.816214i
$135$	−7.90647	−	2.17350i	−0.680481	−	0.187065i
$136$	−3.04439	+	4.19024i	−0.261054	+	0.359310i
$137$	−7.84117	−	1.24192i	−0.669916	−	0.106104i	−0.187794	−	0.982208i	$-0.560134\pi$
$137$	−7.84117	−	1.24192i	−0.669916	−	0.106104i	−0.482122	+	0.876104i	$0.660134\pi$
$138$	−0.820173	+	5.17837i	−0.0698177	+	0.440812i
$139$	−1.64299	+	2.26138i	−0.139356	+	0.191807i	−0.872991	−	0.487737i	$-0.837823\pi$
$139$	−1.64299	+	2.26138i	−0.139356	+	0.191807i	0.733634	+	0.679544i	$0.237823\pi$
$140$	0.740714	+	0.926914i	0.0626018	+	0.0783385i
$141$	−2.15292	−	2.96324i	−0.181308	−	0.249549i
$142$	−1.44706	+	0.737315i	−0.121435	+	0.0618741i
$143$	−0.434399	−	0.434399i	−0.0363262	−	0.0363262i
$144$	2.44035	+	0.792916i	0.203362	+	0.0660764i
$145$	−1.89785	+	16.9975i	−0.157608	+	1.41156i
$146$	−1.71193	+	0.556241i	−0.141681	+	0.0460348i
$147$	−3.94392	−	2.00953i	−0.325289	−	0.165743i
$148$	−1.12583	−	7.10824i	−0.0925430	−	0.584294i
$149$			22.9154i			1.87730i	0.344866	+	0.938652i	$0.387924\pi$
$149$			22.9154i			1.87730i	−0.344866	+	0.938652i	$0.612076\pi$
$150$	−3.02649	+	1.30079i	−0.247112	+	0.106209i
$151$			18.3076i			1.48985i	0.667148	+	0.744926i	$0.267515\pi$
$151$			18.3076i			1.48985i	−0.667148	+	0.744926i	$0.732485\pi$
$152$	1.17071	−	4.19874i	0.0949575	−	0.340563i
$153$	11.8415	+	6.03355i	0.957330	+	0.487784i
$154$	0.112786	+	0.347120i	0.00908858	+	0.0279718i
$155$	10.6708	+	9.73387i	0.857100	+	0.781844i
$156$	−0.181836	+	0.559635i	−0.0145586	+	0.0448067i
$157$	−1.55934	−	1.55934i	−0.124449	−	0.124449i	0.642139	−	0.766588i	$-0.278047\pi$
$157$	−1.55934	−	1.55934i	−0.124449	−	0.124449i	−0.766588	+	0.642139i	$0.778047\pi$
$158$	−2.44478	−	4.79815i	−0.194496	−	0.381720i
$159$	0.988137	+	1.36005i	0.0783644	+	0.107859i
$160$	2.09269	−	0.787802i	0.165442	−	0.0622812i
$161$	−3.41618	−	2.48200i	−0.269233	−	0.195609i
$162$	0.826255	−	5.21677i	0.0649167	−	0.409868i
$163$	0.286709	−	1.81021i	0.0224567	−	0.141786i	−0.973912	−	0.226924i	$-0.927133\pi$
$163$	0.286709	−	1.81021i	0.0224567	−	0.141786i	0.996369	+	0.0851378i	$0.0271331\pi$
$164$	7.11619	+	5.17021i	0.555681	+	0.403726i
$165$	−1.01226	+	0.0464802i	−0.0788042	+	0.00361848i
$166$	−9.48009	−	13.0482i	−0.735798	−	1.01274i
$167$	−7.97683	−	15.6554i	−0.617266	−	1.21145i	−0.962077	−	0.272780i	$-0.912057\pi$
$167$	−7.97683	−	15.6554i	−0.617266	−	1.21145i	0.344811	−	0.938672i	$-0.387943\pi$
$168$	0.247203	−	0.247203i	0.0190721	−	0.0190721i
$169$	−11.6051	−	3.77072i	−0.892698	−	0.290055i
$170$	11.3438	−	2.33454i	0.870030	−	0.179051i
$171$	−11.1110	−	1.28161i	−0.849677	−	0.0980075i
$172$	2.37006	−	4.65151i	0.180716	−	0.354674i
$173$	−2.82792	−	17.8548i	−0.215003	−	1.35747i	−0.825028	−	0.565092i	$-0.808841\pi$
$173$	−2.82792	−	17.8548i	−0.215003	−	1.35747i	0.610026	−	0.792382i	$-0.291159\pi$
$174$	5.03928			0.382027
$175$	0.173152	−	2.64748i	0.0130890	−	0.200131i
$176$	0.687835			0.0518475
$177$	−0.820638	−	5.18131i	−0.0616829	−	0.389451i
$178$	2.16671	+	1.10400i	0.162402	+	0.0827480i
$179$	4.46148	+	13.7310i	0.333467	+	1.02631i	0.967472	+	0.252977i	$0.0814098\pi$
$179$	4.46148	+	13.7310i	0.333467	+	1.02631i	−0.634005	+	0.773329i	$0.718590\pi$
$180$	−2.83657	−	4.98737i	−0.211425	−	0.371737i
$181$	16.1674	+	5.25312i	1.20172	+	0.390461i	0.840392	−	0.541979i	$-0.182325\pi$
$181$	16.1674	+	5.25312i	1.20172	+	0.390461i	0.361324	+	0.932440i	$0.382325\pi$
$182$	−0.335115	−	0.335115i	−0.0248404	−	0.0248404i
$183$	−6.82774	+	3.47890i	−0.504721	+	0.257168i
$184$	−6.43800	+	4.67748i	−0.474616	+	0.344829i
$185$	−8.85188	+	13.4394i	−0.650803	+	0.988083i
$186$	2.50141	−	3.44290i	0.183412	−	0.252445i
$187$	3.51873	+	0.557312i	0.257315	+	0.0407547i
$188$	0.869685	−	5.49097i	0.0634283	−	0.400470i
$189$	−1.57422	−	1.14373i	−0.114507	−	0.0831945i
$190$	−8.26131	+	5.17211i	−0.599338	+	0.375224i
$191$	−1.21150	+	0.880205i	−0.0876609	+	0.0636894i	−0.630752	−	0.775984i	$-0.717254\pi$
$191$	−1.21150	+	0.880205i	−0.0876609	+	0.0636894i	0.543092	+	0.839674i	$0.317254\pi$
$192$	−0.299107	−	0.587030i	−0.0215862	−	0.0423652i
$193$	17.5414	+	17.5414i	1.26266	+	1.26266i	0.949800	+	0.312859i	$0.101287\pi$
$193$	17.5414	+	17.5414i	1.26266	+	1.26266i	0.312859	+	0.949800i	$0.398713\pi$
$194$	−0.994481	−	0.323127i	−0.0713996	−	0.0231991i
$195$	1.14374	−	0.650499i	0.0819046	−	0.0465832i
$196$	−2.07611	−	6.38961i	−0.148294	−	0.456401i
$197$	2.18650	−	4.29124i	0.155781	−	0.305738i	−0.799904	−	0.600128i	$-0.795116\pi$
$197$	2.18650	−	4.29124i	0.155781	−	0.305738i	0.955686	+	0.294390i	$0.0951163\pi$
$198$	−0.276097	−	1.74321i	−0.0196214	−	0.123884i
$199$			22.4042i			1.58819i	0.607794	+	0.794095i	$0.292055\pi$
$199$			22.4042i			1.58819i	−0.607794	+	0.794095i	$0.707945\pi$
$200$	−4.64431	−	1.85213i	−0.328402	−	0.130966i
$201$	−7.69446			−0.542725
$202$	−12.6648	+	2.00590i	−0.891091	+	0.141135i
$203$	−1.84258	+	3.61626i	−0.129324	+	0.253812i
$204$	−1.05449	−	3.24539i	−0.0738291	−	0.227223i
$205$	−3.96469	−	19.2649i	−0.276906	−	1.34552i
$206$	1.21382	−	3.73575i	0.0845707	−	0.260282i
$207$	14.4386	+	14.4386i	1.00355	+	1.00355i
$208$	−0.795793	+	0.405477i	−0.0551783	+	0.0281148i
$209$	−2.93884	+	0.593653i	−0.203284	+	0.0410638i
$210$	−0.780902	+	0.0358570i	−0.0538874	+	0.00247437i
$211$	−16.0321	+	22.0662i	−1.10369	+	1.51910i	−0.273295	+	0.961930i	$0.588114\pi$
$211$	−16.0321	+	22.0662i	−1.10369	+	1.51910i	−0.830397	+	0.557172i	$0.811886\pi$
$212$	−0.399164	+	2.52022i	−0.0274147	+	0.173090i
$213$	0.167386	−	1.05683i	0.0114691	−	0.0724128i
$214$	−3.51560	+	4.83880i	−0.240321	+	0.330774i
$215$	−10.9249	+	4.11273i	−0.745074	+	0.280486i
$216$	−2.96671	+	2.15544i	−0.201859	+	0.146659i
$217$	1.55605	+	3.05392i	0.105632	+	0.207314i
$218$	−12.6603	+	12.6603i	−0.857467	+	0.857467i
$219$	0.366473	−	1.12789i	0.0247640	−	0.0762156i
$220$	−1.13630	−	1.03653i	−0.0766096	−	0.0698830i
$221$	−4.39954	+	1.42950i	−0.295945	+	0.0961583i
$222$	4.22476	+	2.15262i	0.283547	+	0.144475i
$223$	0.884091	+	5.58193i	0.0592031	+	0.373794i	0.999446	+	0.0332886i	$0.0105980\pi$
$223$	0.884091	+	5.58193i	0.0592031	+	0.373794i	−0.940243	+	0.340505i	$0.889402\pi$
$224$	0.530627			0.0354540
$225$	−2.82971	+	12.5137i	−0.188648	+	0.834247i
$226$	−7.89010			−0.524842
$227$	−19.3511	+	3.06491i	−1.28438	+	0.203425i	−0.761043	−	0.648702i	$-0.775312\pi$
$227$	−19.3511	+	3.06491i	−1.28438	+	0.203425i	−0.523335	+	0.852127i	$0.675312\pi$
$228$	1.78461	+	2.24999i	0.118189	+	0.149009i
$229$	−26.5727	+	8.63400i	−1.75598	+	0.570551i	−0.996771	−	0.0803007i	$-0.974412\pi$
$229$	−26.5727	+	8.63400i	−1.75598	+	0.570551i	−0.759205	+	0.650852i	$0.774412\pi$
$230$	17.6843	+	1.97454i	1.16607	+	0.130198i
$231$	−0.228696	−	0.0743080i	−0.0150471	−	0.00488911i
$232$	5.40847	+	5.40847i	0.355084	+	0.355084i
$233$	−3.91843	−	7.69034i	−0.256705	−	0.503811i	0.726303	−	0.687374i	$-0.241237\pi$
$233$	−3.91843	−	7.69034i	−0.256705	−	0.503811i	−0.983008	+	0.183563i	$0.941237\pi$
$234$	1.34705	+	1.85405i	0.0880593	+	0.121203i
$235$	−9.71134	+	7.76051i	−0.633498	+	0.506240i
$236$	4.68014	−	6.44166i	0.304651	−	0.419316i
$237$	3.50422	+	0.555015i	0.227624	+	0.0360521i
$238$	2.71451	+	0.429936i	0.175955	+	0.0278686i
$239$	3.01450	−	4.14910i	0.194992	−	0.268383i	−0.700314	−	0.713834i	$-0.746957\pi$
$239$	3.01450	−	4.14910i	0.194992	−	0.268383i	0.895306	+	0.445452i	$0.146957\pi$
$240$	−0.390500	+	1.42051i	−0.0252067	+	0.0916936i
$241$	−4.35743	−	5.99749i	−0.280687	−	0.386332i	0.645274	−	0.763951i	$-0.276743\pi$
$241$	−4.35743	−	5.99749i	−0.280687	−	0.386332i	−0.925961	+	0.377619i	$0.876743\pi$
$242$	4.77910	+	9.37952i	0.307212	+	0.602938i
$243$	10.2396	+	10.2396i	0.656872	+	0.656872i
$244$	−11.0617	−	3.59417i	−0.708154	−	0.230093i
$245$	−6.19909	+	13.6842i	−0.396045	+	0.874253i
$246$	−5.51157	+	1.79082i	−0.351405	+	0.114178i
$247$	3.05015	−	2.41927i	0.194076	−	0.153934i
$248$	6.37980	−	1.01046i	0.405118	−	0.0641643i
$249$	10.6261			0.673400
$250$	4.88132	+	10.0585i	0.308722	+	0.636153i
$251$	−13.0897			−0.826217			−0.413109	−	0.910682i	$-0.635557\pi$
$251$	−13.0897			−0.826217			−0.413109	+	0.910682i	$0.635557\pi$
$252$	−0.212994	−	1.34479i	−0.0134174	−	0.0847138i
$253$	4.87707	+	2.48499i	0.306619	+	0.156230i
$254$	−12.9741	+	4.21553i	−0.814066	+	0.264506i
$255$	−3.14862	+	6.95045i	−0.197174	+	0.435254i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−6.41655	+	6.41655i	−0.400254	+	0.400254i	−0.878322	−	0.478069i	$-0.841337\pi$
$257$	−6.41655	+	6.41655i	−0.400254	+	0.400254i	0.478069	+	0.878322i	$0.341337\pi$
$258$	1.56149	+	3.06460i	0.0972141	+	0.190793i
$259$	−3.08951	+	2.24466i	−0.191973	+	0.139476i
$260$	1.92568	+	0.529372i	0.119426	+	0.0328303i
$261$	11.5359	−	15.8779i	0.714057	−	0.982815i
$262$	−1.87744	+	11.8537i	−0.115989	+	0.732323i
$263$	−1.88869	+	11.9247i	−0.116461	+	0.735309i	0.858480	+	0.512847i	$0.171409\pi$
$263$	−1.88869	+	11.9247i	−0.116461	+	0.735309i	−0.974941	+	0.222462i	$0.928591\pi$
$264$	−0.266368	+	0.366624i	−0.0163938	+	0.0225642i
$265$	4.45727	−	3.56189i	0.273808	−	0.218805i
$266$	−2.26716	+	0.457971i	−0.139008	+	0.0280800i
$267$	−1.42752	+	0.727355i	−0.0873625	+	0.0445134i
$268$	−8.25817	−	8.25817i	−0.504448	−	0.504448i
$269$	−2.08272	+	6.40995i	−0.126986	+	0.390822i	−0.994258	−	0.107013i	$-0.965871\pi$
$269$	−2.08272	+	6.40995i	−0.126986	+	0.390822i	0.867272	+	0.497835i	$0.165871\pi$
$270$	8.14914	+	0.909893i	0.495941	+	0.0553743i
$271$	−2.43756	−	7.50204i	−0.148071	−	0.455717i	0.849322	−	0.527875i	$-0.177011\pi$
$271$	−2.43756	−	7.50204i	−0.148071	−	0.455717i	−0.997393	+	0.0721587i	$0.977011\pi$
$272$	2.35141	−	4.61490i	0.142575	−	0.279819i
$273$	0.308396	−	0.0488451i	0.0186649	−	0.00295624i
$274$	7.93891			0.479607
$275$	0.315171	+	3.42470i	0.0190055	+	0.206517i
$276$		−	5.24292i		−	0.315586i
$277$	−2.64879	−	16.7238i	−0.159151	−	1.00484i	−0.929930	−	0.367736i	$-0.880133\pi$
$277$	−2.64879	−	16.7238i	−0.159151	−	1.00484i	0.770780	−	0.637102i	$-0.219867\pi$
$278$	1.26900	−	2.49055i	0.0761096	−	0.149374i
$279$	−5.12170	−	15.7630i	−0.306628	−	0.943705i
$280$	−0.876596	−	0.799628i	−0.0523866	−	0.0477869i
$281$	0.0903109	+	0.0293438i	0.00538749	+	0.00175050i	0.311710	−	0.950177i	$-0.399098\pi$
$281$	0.0903109	+	0.0293438i	0.00538749	+	0.00175050i	−0.306322	+	0.951928i	$0.599098\pi$
$282$	2.58996	+	2.58996i	0.154230	+	0.154230i
$283$	11.1772	+	21.9366i	0.664418	+	1.30399i	0.939492	+	0.342570i	$0.111298\pi$
$283$	11.1772	+	21.9366i	0.664418	+	1.30399i	−0.275074	+	0.961423i	$0.588702\pi$
$284$	1.31390	−	0.954607i	0.0779659	−	0.0566455i
$285$	0.442443	−	6.40631i	0.0262081	−	0.379477i
$286$	0.497006	+	0.361096i	0.0293886	+	0.0213520i
$287$	0.730150	−	4.60998i	0.0430994	−	0.272119i
$288$	−2.53434	−	0.401400i	−0.149337	−	0.0236527i
$289$	5.77582	−	7.94974i	0.339754	−	0.467631i
$290$	−0.784502	−	17.0851i	−0.0460675	−	1.00327i
$291$	0.557349	−	0.404938i	0.0326724	−	0.0237379i
$292$	1.60384	−	0.817198i	0.0938577	−	0.0478229i
$293$	−1.24479	−	1.24479i	−0.0727214	−	0.0727214i	0.669811	−	0.742532i	$-0.266375\pi$
$293$	−1.24479	−	1.24479i	−0.0727214	−	0.0727214i	−0.742532	+	0.669811i	$0.766375\pi$
$294$	4.20972	+	1.36782i	0.245516	+	0.0797730i
$295$	−17.4388	+	3.58889i	−1.01533	+	0.208953i
$296$	2.22395	+	6.84461i	0.129264	+	0.397835i
$297$	2.24741	+	1.14511i	0.130408	+	0.0664462i
$298$	−3.58476	−	22.6333i	−0.207660	−	1.31111i
$299$	−7.10744			−0.411034
$300$	2.78575	−	1.75822i	0.160835	−	0.101511i
$301$	−2.77015			−0.159669
$302$	−2.86394	−	18.0822i	−0.164801	−	1.04051i
$303$	3.83534	−	7.52728i	0.220334	−	0.432431i
$304$	−0.499474	+	4.33019i	−0.0286468	+	0.248353i
$305$	12.8577	+	22.6070i	0.736232	+	1.29447i
$306$	−12.6396	−	4.10685i	−0.722557	−	0.234773i
$307$	−23.8977	+	23.8977i	−1.36391	+	1.36391i	−0.495044	+	0.868868i	$0.664848\pi$
$307$	−23.8977	+	23.8977i	−1.36391	+	1.36391i	−0.868868	+	0.495044i	$0.835152\pi$
$308$	−0.165699	−	0.325203i	−0.00944159	−	0.0185302i
$309$	1.52114	+	2.09367i	0.0865346	+	0.119105i
$310$	−12.0621	−	7.94475i	−0.685084	−	0.451232i
$311$	12.6037	+	9.15709i	0.714688	+	0.519251i	0.884683	−	0.466194i	$-0.154375\pi$
$311$	12.6037	+	9.15709i	0.714688	+	0.519251i	−0.169995	+	0.985445i	$0.554375\pi$
$312$	0.0920515	−	0.581190i	0.00521139	−	0.0329034i
$313$	2.37489	−	14.9945i	0.134237	−	0.847537i	−0.825041	−	0.565073i	$-0.808848\pi$
$313$	2.37489	−	14.9945i	0.134237	−	0.847537i	0.959278	−	0.282465i	$-0.0911520\pi$
$314$	1.78407	+	1.29621i	0.100681	+	0.0731491i
$315$	−1.67466	+	2.54256i	−0.0943567	+	0.143257i
$316$	3.16527	+	4.35663i	0.178061	+	0.245079i
$317$	−13.4994	−	26.4941i	−0.758203	−	1.48806i	−0.869320	−	0.494250i	$-0.835443\pi$
$317$	−13.4994	−	26.4941i	−0.758203	−	1.48806i	0.111117	−	0.993807i	$-0.464557\pi$
$318$	−1.18873	−	1.18873i	−0.0666607	−	0.0666607i
$319$	1.62576	−	5.00357i	0.0910250	−	0.280146i
$320$	−1.94369	+	1.10547i	−0.108656	+	0.0617978i
$321$	−1.21770	−	3.74771i	−0.0679657	−	0.209177i
$322$	3.76239	+	1.91703i	0.209670	+	0.106832i
$323$	−6.06363	+	21.7471i	−0.337389	+	1.21004i
$324$			5.28180i			0.293433i
$325$	−2.38349	−	3.77643i	−0.132212	−	0.209479i
$326$			1.83277i			0.101508i
$327$	−1.84532	−	11.6509i	−0.102047	−	0.644297i
$328$	−7.83738	−	3.99334i	−0.432747	−	0.220496i
$329$	−2.80560	+	0.911594i	−0.154678	+	0.0502578i
$330$	0.992524	−	0.204260i	0.0546367	−	0.0112441i
$331$	10.3616	+	3.36668i	0.569524	+	0.185049i	0.579602	−	0.814900i	$-0.303208\pi$
$331$	10.3616	+	3.36668i	0.569524	+	0.185049i	−0.0100782	+	0.999949i	$0.503208\pi$
$332$	11.4046	+	11.4046i	0.625907	+	0.625907i
$333$	16.4539	−	8.38366i	0.901666	−	0.459422i
$334$	10.3277	+	14.2148i	0.565105	+	0.777800i
$335$	1.19785	+	26.0871i	0.0654457	+	1.42529i
$336$	−0.205489	+	0.282831i	−0.0112103	+	0.0154297i
$337$	4.98813	−	31.4938i	0.271721	−	1.71558i	−0.353760	−	0.935336i	$-0.615097\pi$
$337$	4.98813	−	31.4938i	0.271721	−	1.71558i	0.625480	−	0.780240i	$-0.284903\pi$
$338$	12.0521	+	1.90886i	0.655546	+	0.103828i
$339$	3.05549	−	4.20552i	0.165951	−	0.228412i
$340$	−10.8389	+	4.08036i	−0.587824	+	0.221289i
$341$	−2.61150	−	3.59442i	−0.141421	−	0.194649i
$342$	11.1747	−	0.472302i	0.604256	−	0.0255391i
$343$	−5.14730	+	5.14730i	−0.277928	+	0.277928i
$344$	−1.61323	+	4.96500i	−0.0869793	+	0.267695i
$345$	−7.90081	+	8.66130i	−0.425365	+	0.466309i
$346$	5.58620	+	17.1926i	0.300316	+	0.924278i
$347$	6.53637	−	12.8283i	0.350891	−	0.688662i	−0.646339	−	0.763051i	$-0.723701\pi$
$347$	6.53637	−	12.8283i	0.350891	−	0.688662i	0.997229	+	0.0743891i	$0.0237007\pi$
$348$	−4.97724	+	0.788318i	−0.266808	+	0.0422583i
$349$		−	0.355644i		−	0.0190372i	−0.999955	−	0.00951860i	$-0.996970\pi$
$349$		−	0.355644i		−	0.0190372i	0.999955	−	0.00951860i	$-0.00302991\pi$
$350$	0.243137	+	2.64197i	0.0129962	+	0.141219i
$351$	−3.27519			−0.174817
$352$	−0.679367	+	0.107601i	−0.0362104	+	0.00573516i
$353$	6.30721	+	3.21368i	0.335699	+	0.171047i	0.613712	−	0.789530i	$-0.289676\pi$
$353$	6.30721	+	3.21368i	0.335699	+	0.171047i	−0.278013	+	0.960577i	$0.589676\pi$
$354$	1.62107	+	4.98914i	0.0861589	+	0.265170i
$355$	−3.60912	−	0.402976i	−0.191552	−	0.0213877i
$356$	−2.31274	−	0.751455i	−0.122575	−	0.0398270i
$357$	−1.28037	+	1.28037i	−0.0677643	+	0.0677643i
$358$	−6.55456	−	12.8641i	−0.346419	−	0.679887i
$359$	18.5456	+	25.5258i	0.978798	+	1.34720i	0.937474	+	0.348054i	$0.113157\pi$
$359$	18.5456	+	25.5258i	0.978798	+	1.34720i	0.0413237	+	0.999146i	$0.486843\pi$
$360$	3.58184	+	4.48224i	0.188780	+	0.236235i
$361$	−1.60322	−	18.9322i	−0.0843801	−	0.996434i
$362$	−16.7901	−	2.65930i	−0.882471	−	0.139770i
$363$	−6.85013	−	1.08495i	−0.359539	−	0.0569453i
$364$	0.383413	+	0.278566i	0.0200963	+	0.0146008i
$365$	−3.88102	−	1.06690i	−0.203142	−	0.0558439i
$366$	6.19945	−	4.50417i	0.324051	−	0.235437i
$367$	1.03704	−	0.528396i	0.0541329	−	0.0275821i	−0.426715	−	0.904386i	$-0.640329\pi$
$367$	1.03704	−	0.528396i	0.0541329	−	0.0275821i	0.480847	+	0.876804i	$0.340329\pi$
$368$	5.62702	−	5.62702i	0.293329	−	0.293329i
$369$	−6.97457	+	21.4655i	−0.363081	+	1.11745i
$370$	6.64051	−	14.6587i	0.345224	−	0.762068i
$371$	1.28770	−	0.418400i	0.0668541	−	0.0217222i
$372$	−1.93203	+	3.79182i	−0.100171	+	0.196597i
$373$	−2.25961	−	14.2666i	−0.116998	−	0.738698i	−0.974528	−	0.224264i	$-0.928002\pi$
$373$	−2.25961	−	14.2666i	−0.116998	−	0.738698i	0.857530	−	0.514434i	$-0.171998\pi$
$374$	−3.56259			−0.184217
$375$	−7.25160	−	1.29340i	−0.374471	−	0.0667906i
$376$			5.55942i			0.286705i
$377$	1.06866	+	6.74728i	0.0550390	+	0.347503i
$378$	1.73375	+	0.883392i	0.0891747	+	0.0454368i
$379$	−0.108828	−	0.334937i	−0.00559010	−	0.0172046i	0.948223	−	0.317607i	$-0.102879\pi$
$379$	−0.108828	−	0.334937i	−0.00559010	−	0.0172046i	−0.953813	+	0.300402i	$0.902879\pi$
$380$	7.35050	−	6.40079i	0.377073	−	0.328354i
$381$	2.77736	−	8.54782i	0.142288	−	0.437918i
$382$	1.05889	−	1.05889i	0.0541774	−	0.0541774i
$383$	−4.27414	+	2.17778i	−0.218398	+	0.111280i	−0.559767	−	0.828650i	$-0.689109\pi$
$383$	−4.27414	+	2.17778i	−0.218398	+	0.111280i	0.341369	+	0.939929i	$0.389109\pi$
$384$	0.387256	+	0.533012i	0.0197621	+	0.0272001i
$385$	−0.216329	+	0.786936i	−0.0110252	+	0.0401060i
$386$	−20.0695	−	14.5814i	−1.02151	−	0.742172i
$387$	13.2306	+	2.09551i	0.672547	+	0.106521i
$388$	1.03279	+	0.163577i	0.0524317	+	0.00830437i
$389$	9.36054	−	12.8837i	0.474598	−	0.653228i	−0.502857	−	0.864369i	$-0.667718\pi$
$389$	9.36054	−	12.8837i	0.474598	−	0.653228i	0.977456	+	0.211141i	$0.0677179\pi$
$390$	−1.02789	+	0.821410i	−0.0520494	+	0.0415937i
$391$	33.3451	−	24.2267i	1.68634	−	1.22520i
$392$	3.05011	+	5.98617i	0.154054	+	0.302347i
$393$	−5.59110	−	5.59110i	−0.282034	−	0.282034i
$394$	−1.48828	+	4.58045i	−0.0749785	+	0.230760i
$395$	1.33618	−	11.9671i	0.0672306	−	0.602128i
$396$	0.545396	+	1.67856i	0.0274072	+	0.0843506i
$397$	−13.7907	+	27.0658i	−0.692137	+	1.35840i	0.230631	+	0.973041i	$0.425921\pi$
$397$	−13.7907	+	27.0658i	−0.692137	+	1.35840i	−0.922768	+	0.385355i	$0.874079\pi$
$398$	−3.50478	−	22.1283i	−0.175679	−	1.10919i
$399$	0.633866	−	1.38577i	0.0317330	−	0.0693755i
$400$	4.87687	+	1.10280i	0.243843	+	0.0551401i
$401$		−	25.5429i		−	1.27555i	−0.770221	−	0.637777i	$-0.779854\pi$
$401$		−	25.5429i		−	1.27555i	0.770221	−	0.637777i	$-0.220146\pi$
$402$	7.59973	−	1.20368i	0.379040	−	0.0600340i
$403$	5.14029	+	2.61911i	0.256056	+	0.130467i
$404$	12.1951	−	3.96242i	0.606727	−	0.197138i
$405$	7.95940	−	8.72553i	0.395506	−	0.433575i
$406$	1.25418	−	3.85998i	0.0622441	−	0.191568i
$407$	3.50035	−	3.50035i	0.173506	−	0.173506i
$408$	1.54920	+	3.04048i	0.0766968	+	0.150526i
$409$	16.5921	−	12.0549i	0.820427	−	0.596075i	−0.0964079	−	0.995342i	$-0.530735\pi$
$409$	16.5921	−	12.0549i	0.820427	−	0.596075i	0.916835	+	0.399267i	$0.130735\pi$
$410$	6.92958	+	18.4075i	0.342228	+	0.909083i
$411$	−3.07439	+	4.23153i	−0.151648	+	0.208726i
$412$	−0.614474	+	3.87964i	−0.0302730	+	0.191136i
$413$	−4.17301	−	0.660940i	−0.205340	−	0.0325227i
$414$	−16.5195	−	12.0021i	−0.811888	−	0.589871i
$415$	−1.65424	−	36.0264i	−0.0812034	−	1.76847i
$416$	0.722565	−	0.524974i	0.0354267	−	0.0257390i
$417$	0.836067	+	1.64087i	0.0409424	+	0.0803540i
$418$	2.80979	−	1.04608i	0.137431	−	0.0511654i
$419$	−4.45107	−	1.44624i	−0.217449	−	0.0706534i	0.198267	−	0.980148i	$-0.436469\pi$
$419$	−4.45107	−	1.44624i	−0.217449	−	0.0706534i	−0.415715	+	0.909495i	$0.636469\pi$
$420$	0.765679	−	0.157575i	0.0373613	−	0.00768890i
$421$	1.76196	−	0.572495i	0.0858725	−	0.0279017i	−0.265766	−	0.964038i	$-0.585625\pi$
$421$	1.76196	−	0.572495i	0.0858725	−	0.0279017i	0.351638	+	0.936136i	$0.385625\pi$
$422$	12.3828	−	24.3025i	0.602783	−	1.18303i
$423$	14.0895	−	2.23155i	0.685053	−	0.108502i
$424$		−	2.55164i		−	0.123919i
$425$	24.0548	+	9.59299i	1.16683	+	0.465328i
$426$			1.07000i			0.0518419i
$427$	0.965470	+	6.09573i	0.0467223	+	0.294993i
$428$	2.71536	−	5.32919i	0.131252	−	0.257596i
$429$	−0.384937	+	0.125073i	−0.0185849	+	0.00603860i
$430$	10.1471	−	5.77113i	0.489334	−	0.278309i
$431$	11.8885	+	3.86280i	0.572648	+	0.186065i	0.581004	−	0.813900i	$-0.302660\pi$
$431$	11.8885	+	3.86280i	0.572648	+	0.186065i	−0.00835629	+	0.999965i	$0.502660\pi$
$432$	2.59300	−	2.59300i	0.124756	−	0.124756i
$433$	−24.4679	+	12.4670i	−1.17585	+	0.599127i	−0.929056	−	0.369940i	$-0.879378\pi$
$433$	−24.4679	+	12.4670i	−1.17585	+	0.599127i	−0.246798	+	0.969067i	$0.579378\pi$
$434$	−2.01463	−	2.77290i	−0.0967054	−	0.133104i
$435$	9.41036	+	6.19815i	0.451192	+	0.297179i
$436$	10.5240	−	14.4850i	0.504006	−	0.693705i
$437$	−19.1855	+	28.8985i	−0.917766	+	1.38241i
$438$	−0.185521	+	1.17133i	−0.00886452	+	0.0559684i
$439$	4.24917	+	3.08720i	0.202802	+	0.147344i	0.684551	−	0.728965i	$-0.259998\pi$
$439$	4.24917	+	3.08720i	0.202802	+	0.147344i	−0.481749	+	0.876309i	$0.659998\pi$
$440$	1.28446	+	0.846014i	0.0612344	+	0.0403321i
$441$	13.9467	−	10.1329i	0.664127	−	0.482517i
$442$	4.12175	−	2.10014i	0.196052	−	0.0998933i
$443$	24.4914	−	24.4914i	1.16362	−	1.16362i	0.179947	−	0.983676i	$-0.442407\pi$
$443$	24.4914	−	24.4914i	1.16362	−	1.16362i	0.983676	−	0.179947i	$-0.0575927\pi$
$444$	−4.50949	−	1.46522i	−0.214011	−	0.0695364i
$445$	2.68824	+	4.72659i	0.127435	+	0.224062i
$446$	−1.74641	−	5.37490i	−0.0826950	−	0.254509i
$447$	13.4520	+	6.85415i	0.636259	+	0.324190i
$448$	−0.524094	+	0.0830084i	−0.0247611	+	0.00392178i
$449$	28.2234			1.33194			0.665972	−	0.745977i	$-0.268017\pi$
$449$	28.2234			1.33194			0.665972	+	0.745977i	$0.268017\pi$
$450$	0.837301	−	12.8023i	0.0394708	−	0.603506i
$451$			6.05026i			0.284896i
$452$	7.79296	−	1.23428i	0.366550	−	0.0580558i
$453$	10.7471	+	5.47592i	0.504943	+	0.257281i
$454$	18.6334	−	6.05436i	0.874508	−	0.284145i
$455$	−0.213613	−	1.03797i	−0.0100144	−	0.0486610i
$456$	−2.11462	−	1.94312i	−0.0990260	−	0.0909947i
$457$	7.03946	+	7.03946i	0.329292	+	0.329292i	0.852317	−	0.523025i	$-0.175197\pi$
$457$	7.03946	+	7.03946i	0.329292	+	0.329292i	−0.523025	+	0.852317i	$0.675197\pi$
$458$	24.8949	−	12.6846i	1.16326	−	0.592712i
$459$	15.3658	−	11.1639i	0.717216	−	0.521088i
$460$	−17.7755	+	0.816203i	−0.828786	+	0.0380557i
$461$	−22.6633	−	16.4658i	−1.05553	−	0.766890i	−0.0822767	−	0.996610i	$-0.526219\pi$
$461$	−22.6633	−	16.4658i	−1.05553	−	0.766890i	−0.973257	+	0.229720i	$0.926219\pi$
$462$	0.237505	+	0.0376171i	0.0110497	+	0.00175011i
$463$	0.376152	−	2.37493i	0.0174813	−	0.110372i	−0.977405	−	0.211376i	$-0.932205\pi$
$463$	0.376152	−	2.37493i	0.0174813	−	0.110372i	0.994886	+	0.101004i	$0.0322054\pi$
$464$	−6.18795	−	4.49581i	−0.287269	−	0.208713i
$465$	8.90578	−	3.35261i	0.412996	−	0.155474i
$466$	5.07322	+	6.98269i	0.235012	+	0.323467i
$467$	10.4302	−	5.31444i	0.482651	−	0.245923i	−0.195696	−	0.980665i	$-0.562697\pi$
$467$	10.4302	−	5.31444i	0.482651	−	0.245923i	0.678347	+	0.734742i	$0.262697\pi$
$468$	−1.62050	−	1.62050i	−0.0749077	−	0.0749077i
$469$	−1.91501	+	5.89379i	−0.0884269	+	0.272150i
$470$	8.37776	−	9.18416i	0.386437	−	0.423634i
$471$	−1.38179	+	0.448970i	−0.0636694	+	0.0206874i
$472$	−3.61482	+	7.09449i	−0.166386	+	0.326550i
$473$	3.54664	−	0.561733i	0.163075	−	0.0258285i
$474$	−3.54791			−0.162961
$475$	−21.7887	−	0.502735i	−0.999734	−	0.0230670i
$476$	−2.74834			−0.125970
$477$	−6.46672	+	1.02423i	−0.296091	+	0.0468962i
$478$	−2.32832	+	4.56959i	−0.106495	+	0.209008i
$479$	−21.0988	+	6.85540i	−0.964027	+	0.313231i	−0.748402	−	0.663245i	$-0.769179\pi$
$479$	−21.0988	+	6.85540i	−0.964027	+	0.313231i	−0.215624	+	0.976476i	$0.569179\pi$
$480$	0.163475	−	1.46411i	0.00746159	−	0.0668272i
$481$	−1.98629	+	6.11319i	−0.0905672	+	0.278737i
$482$	5.24200	+	5.24200i	0.238766	+	0.238766i
$483$	−2.47881	+	1.26302i	−0.112790	+	0.0574693i
$484$	−6.18755	−	8.51643i	−0.281252	−	0.387110i
$485$	−1.45966	−	1.82658i	−0.0662797	−	0.0829410i
$486$	−11.7154	−	8.51172i	−0.531421	−	0.386100i
$487$	−1.73183	+	10.9344i	−0.0784769	+	0.495483i	0.916875	+	0.399175i	$0.130703\pi$
$487$	−1.73183	+	10.9344i	−0.0784769	+	0.495483i	−0.995352	+	0.0963083i	$0.969297\pi$
$488$	11.4878	+	1.81949i	0.520028	+	0.0823643i
$489$	−0.976889	−	0.709751i	−0.0441764	−	0.0320961i
$490$	3.98208	−	14.4855i	0.179892	−	0.654388i
$491$	−7.90364	+	5.74233i	−0.356686	+	0.259148i	−0.751669	−	0.659541i	$-0.770751\pi$
$491$	−7.90364	+	5.74233i	−0.356686	+	0.259148i	0.394982	+	0.918689i	$0.370751\pi$
$492$	5.16357	−	2.63097i	0.232792	−	0.118613i
$493$	−28.0128	−	28.0128i	−1.26163	−	1.26163i
$494$	−2.63414	+	2.86663i	−0.118516	+	0.128976i
$495$	1.62850	−	3.59486i	0.0731958	−	0.161577i
$496$	−6.14318	+	1.99604i	−0.275837	+	0.0896249i
$497$	−0.767850	−	0.391239i	−0.0344428	−	0.0175495i
$498$	−10.4953	+	1.66228i	−0.470304	+	0.0744888i
$499$			18.3214i			0.820177i	0.912046	+	0.410089i	$0.134502\pi$
$499$			18.3214i			0.820177i	−0.912046	+	0.410089i	$0.865498\pi$
$500$	−6.39472	−	9.17102i	−0.285980	−	0.410140i
$501$	−11.5761			−0.517183
$502$	12.9286	−	2.04769i	0.577031	−	0.0913927i
$503$	−21.6930	−	11.0532i	−0.967245	−	0.492836i	−0.102328	−	0.994751i	$-0.532629\pi$
$503$	−21.6930	−	11.0532i	−0.967245	−	0.492836i	−0.864917	+	0.501915i	$0.832629\pi$
$504$	0.420743	+	1.29491i	0.0187414	+	0.0576801i
$505$	−26.1174	−	11.8314i	−1.16221	−	0.526492i
$506$	−5.20576	−	1.69145i	−0.231424	−	0.0751943i
$507$	−5.68468	+	5.68468i	−0.252466	+	0.252466i
$508$	12.1549	−	6.19322i	0.539286	−	0.274780i
$509$	29.8973	−	21.7217i	1.32517	−	0.962796i	0.325322	−	0.945603i	$-0.394527\pi$
$509$	29.8973	−	21.7217i	1.32517	−	0.962796i	0.999852	−	0.0171923i	$-0.00547274\pi$
$510$	2.02256	−	7.35743i	0.0895607	−	0.325792i
$511$	−0.772730	−	0.561421i	−0.0341836	−	0.0248358i
$512$	−0.156434	+	0.987688i	−0.00691349	+	0.0436501i
$513$	−8.84089	+	13.3168i	−0.390335	+	0.587951i
$514$	5.33378	−	7.34133i	0.235263	−	0.323812i
$515$	6.86153	−	5.48318i	0.302355	−	0.241618i
$516$	−2.02167	−	2.78259i	−0.0889992	−	0.122497i
$517$	3.40718	−	1.73604i	0.149847	−	0.0763511i
$518$	2.70033	−	2.70033i	0.118646	−	0.118646i
$519$	−11.3271	−	3.68041i	−0.497206	−	0.161552i
$520$	−1.98479	−	0.221611i	−0.0870387	−	0.00971831i
$521$	7.46743	−	2.42631i	0.327154	−	0.106299i	−0.140835	−	0.990033i	$-0.544979\pi$
$521$	7.46743	−	2.42631i	0.327154	−	0.106299i	0.467989	+	0.883734i	$0.344979\pi$
$522$	−8.91007	+	17.4870i	−0.389983	+	0.765385i
$523$	3.43754	+	21.7038i	0.150313	+	0.949040i	0.941389	+	0.337322i	$0.109521\pi$
$523$	3.43754	+	21.7038i	0.150313	+	0.949040i	−0.791076	+	0.611718i	$0.790479\pi$
$524$		−	12.0014i		−	0.524285i
$525$	−1.50236	−	0.893524i	−0.0655683	−	0.0389966i
$526$		−	12.0733i		−	0.526423i
$527$	−33.0437	+	5.23360i	−1.43941	+	0.227979i
$528$	0.205736	−	0.403780i	0.00895351	−	0.0175723i
$529$	38.3530	−	12.4617i	1.66752	−	0.541811i
$530$	−3.84519	+	4.21531i	−0.167024	+	0.183101i
$531$	19.4308	+	6.31346i	0.843226	+	0.273981i
$532$	2.16760	−	0.806994i	0.0939775	−	0.0349876i
$533$	−3.56661	−	6.99987i	−0.154487	−	0.303198i
$534$	1.29616	−	0.941713i	0.0560902	−	0.0407519i
$535$	−12.5166	+	4.71192i	−0.541139	+	0.203714i
$536$	9.44836	+	6.86464i	0.408107	+	0.296507i
$537$	9.39499	+	1.48802i	0.405424	+	0.0642128i
$538$	1.05434	−	6.65684i	0.0454558	−	0.286997i
$539$	2.71626	−	3.73861i	0.116998	−	0.161033i
$540$	−8.19115	+	0.376116i	−0.352491	+	0.0161855i
$541$	−13.4633	+	9.78170i	−0.578835	+	0.420548i	−0.838304	−	0.545203i	$-0.816452\pi$
$541$	−13.4633	+	9.78170i	−0.578835	+	0.420548i	0.259469	+	0.965751i	$0.416452\pi$
$542$	3.58113	+	7.02836i	0.153823	+	0.301894i
$543$	7.91952	−	7.91952i	0.339859	−	0.339859i
$544$	−1.60053	+	4.92592i	−0.0686221	+	0.211197i
$545$	−39.2137	+	8.07013i	−1.67973	+	0.345686i
$546$	−0.296958	+	0.0964874i	−0.0127086	+	0.00412928i
$547$	−4.92488	−	2.50935i	−0.210573	−	0.107292i	0.345523	−	0.938410i	$-0.387701\pi$
$547$	−4.92488	−	2.50935i	−0.210573	−	0.107292i	−0.556096	+	0.831118i	$0.687701\pi$
$548$	−7.84117	+	1.24192i	−0.334958	+	0.0530522i
$549$		−	29.8443i		−	1.27372i
$550$	−0.847033	−	3.33324i	−0.0361176	−	0.142130i
$551$	30.3189	+	13.8681i	1.29163	+	0.590803i
$552$	0.820173	+	5.17837i	0.0349089	+	0.220406i
$553$	1.29727	−	2.54603i	0.0551654	−	0.108268i
$554$	5.23237	+	16.1036i	0.222302	+	0.684175i
$555$	5.24166	+	9.21612i	0.222496	+	0.391203i
$556$	−0.863769	+	2.65841i	−0.0366320	+	0.112742i
$557$	22.7146	+	22.7146i	0.962449	+	0.962449i	0.999320	−	0.0368706i	$-0.0117389\pi$
$557$	22.7146	+	22.7146i	0.962449	+	0.962449i	−0.0368706	+	0.999320i	$0.511739\pi$
$558$	7.52452	+	14.7677i	0.318538	+	0.625167i
$559$	−3.77216	+	2.74063i	−0.159545	+	0.115916i
$560$	0.990893	+	0.652654i	0.0418729	+	0.0275797i
$561$	1.37963	−	1.89890i	0.0582481	−	0.0801717i
$562$	−0.0937894	−	0.0148548i	−0.00395627	−	0.000626611i
$563$	35.0394	+	5.54969i	1.47673	+	0.233891i	0.842267	−	0.539060i	$-0.181220\pi$
$563$	35.0394	+	5.54969i	1.47673	+	0.233891i	0.634465	+	0.772951i	$0.281220\pi$
$564$	−2.96324	−	2.15292i	−0.124775	−	0.0906542i
$565$	−14.7340	−	9.70456i	−0.619863	−	0.408274i
$566$	−14.4713	−	19.9180i	−0.608273	−	0.837215i
$567$	2.49719	−	1.27238i	0.104872	−	0.0534351i
$568$	−1.14839	+	1.14839i	−0.0481856	+	0.0481856i
$569$	0.320906	−	0.987648i	0.0134531	−	0.0414043i	−0.944105	−	0.329646i	$-0.893071\pi$
$569$	0.320906	−	0.987648i	0.0134531	−	0.0414043i	0.957558	+	0.288242i	$0.0930706\pi$
$570$	0.565171	+	6.39665i	0.0236724	+	0.267926i
$571$	9.09299	+	27.9853i	0.380530	+	1.17115i	0.939672	+	0.342078i	$0.111131\pi$
$571$	9.09299	+	27.9853i	0.380530	+	1.17115i	−0.559142	+	0.829072i	$0.688869\pi$
$572$	−0.547374	−	0.278901i	−0.0228869	−	0.0116614i
$573$	0.154339	+	0.974461i	0.00644762	+	0.0407087i
$574$			4.66745i			0.194816i
$575$	30.5951	+	25.4384i	1.27590	+	1.06085i
$576$	2.56593			0.106914
$577$	−5.27302	−	33.2926i	−0.219519	−	1.38599i	−0.813526	−	0.581528i	$-0.802455\pi$
$577$	−5.27302	−	33.2926i	−0.219519	−	1.38599i	0.594007	−	0.804460i	$-0.297545\pi$
$578$	−4.46110	+	8.75540i	−0.185557	+	0.364177i
$579$	15.5441	−	5.05058i	0.645990	−	0.209895i
$580$	3.44754	+	16.7520i	0.143151	+	0.695590i
$581$	2.64463	−	8.13935i	0.109718	−	0.337677i
$582$	−0.487141	+	0.487141i	−0.0201926	+	0.0201926i
$583$	−1.56381	+	0.796802i	−0.0647665	+	0.0330002i
$584$	−1.45626	+	1.05803i	−0.0602603	+	0.0437817i
$585$	0.235055	+	5.11908i	0.00971831	+	0.211648i
$586$	1.42419	+	1.03474i	0.0588329	+	0.0427446i
$587$	−33.6141	−	5.32395i	−1.38740	−	0.219743i	−0.582345	−	0.812941i	$-0.697865\pi$
$587$	−33.6141	−	5.32395i	−1.38740	−	0.219743i	−0.805056	+	0.593199i	$0.797865\pi$
$588$	−4.37187	−	0.692436i	−0.180293	−	0.0285556i
$589$	24.5246	−	13.8303i	1.01052	−	0.569868i
$590$	16.6627	−	6.27274i	0.685993	−	0.258245i
$591$	−1.86509	−	2.56708i	−0.0767196	−	0.105595i
$592$	−3.26730	−	6.41243i	−0.134285	−	0.263549i
$593$	−4.41010	+	4.41010i	−0.181101	+	0.181101i	−0.791835	−	0.610734i	$-0.790874\pi$
$593$	−4.41010	+	4.41010i	−0.181101	+	0.181101i	0.610734	+	0.791835i	$0.290874\pi$
$594$	−2.39888	−	0.779442i	−0.0984271	−	0.0319809i
$595$	4.54026	+	4.14161i	0.186133	+	0.169790i
$596$	7.08125	+	21.7939i	0.290059	+	0.892711i
$597$	13.1519	+	6.70124i	0.538272	+	0.274263i
$598$	7.01993	−	1.11185i	0.287066	−	0.0454668i
$599$	−31.8352			−1.30075			−0.650376	−	0.759613i	$-0.725389\pi$
$599$	−31.8352			−1.30075			−0.650376	+	0.759613i	$0.725389\pi$
$600$	−2.47640	+	2.17236i	−0.101099	+	0.0886863i
$601$			36.1626i			1.47510i	0.675290	+	0.737552i	$0.264018\pi$
$601$			36.1626i			1.47510i	−0.675290	+	0.737552i	$0.735982\pi$
$602$	2.73604	−	0.433346i	0.111513	−	0.0176619i
$603$	13.6048	−	26.7008i	0.554028	−	1.08734i
$604$	5.65736	+	17.4116i	0.230195	+	0.708466i
$605$	−2.61200	+	23.3935i	−0.106193	+	0.951079i
$606$	−2.61059	+	8.03458i	−0.106048	+	0.326383i
$607$	15.9516	−	15.9516i	0.647457	−	0.647457i	−0.304921	−	0.952378i	$-0.598630\pi$
$607$	15.9516	−	15.9516i	0.647457	−	0.647457i	0.952378	+	0.304921i	$0.0986300\pi$
$608$	−0.184066	−	4.35501i	−0.00746488	−	0.176619i
$609$	1.57173	+	2.16330i	0.0636896	+	0.0876612i
$610$	−16.2360	−	20.3173i	−0.657374	−	0.822624i
$611$	−2.91855	+	4.01704i	−0.118072	+	0.162512i
$612$	13.1264	+	2.07902i	0.530604	+	0.0840394i
$613$	−2.33326	+	14.7317i	−0.0942397	+	0.595006i	0.894698	+	0.446672i	$0.147391\pi$
$613$	−2.33326	+	14.7317i	−0.0942397	+	0.595006i	−0.988937	+	0.148334i	$0.952609\pi$
$614$	19.8650	−	27.3419i	0.801687	−	1.10343i
$615$	−12.4950	−	3.43488i	−0.503845	−	0.138508i
$616$	0.214532	+	0.295278i	0.00864375	+	0.0118971i
$617$	14.1131	−	7.19099i	0.568173	−	0.289498i	−0.146210	−	0.989254i	$-0.546708\pi$
$617$	14.1131	−	7.19099i	0.568173	−	0.289498i	0.714383	+	0.699755i	$0.246708\pi$
$618$	−1.82993	−	1.82993i	−0.0736107	−	0.0736107i
$619$	−46.4810	−	15.1026i	−1.86823	−	0.607025i	−0.992182	−	0.124800i	$-0.960171\pi$
$619$	−46.4810	−	15.1026i	−1.86823	−	0.607025i	−0.876048	−	0.482225i	$-0.839829\pi$
$620$	13.1565	+	5.96001i	0.528377	+	0.239360i
$621$	27.7535	−	9.01764i	1.11371	−	0.361866i
$622$	−13.8810	−	7.07271i	−0.556576	−	0.283590i
$623$	0.201857	+	1.27447i	0.00808721	+	0.0510606i
$624$			0.588435i			0.0235563i
$625$	−3.25619	+	24.7870i	−0.130248	+	0.991481i
$626$			15.1814i			0.606770i
$627$	−0.530536	+	1.90275i	−0.0211876	+	0.0759887i
$628$	−1.96488	−	1.00116i	−0.0784073	−	0.0399505i
$629$	−11.5188	−	35.4511i	−0.459283	−	1.41353i
$630$	1.25630	−	2.77324i	0.0500523	−	0.110488i
$631$	1.22952	−	3.78407i	0.0489464	−	0.150641i	−0.923596	−	0.383367i	$-0.874764\pi$
$631$	1.22952	−	3.78407i	0.0489464	−	0.150641i	0.972542	+	0.232726i	$0.0747644\pi$
$632$	−3.80783	−	3.80783i	−0.151467	−	0.151467i
$633$	8.15824	+	16.0115i	0.324261	+	0.636398i
$634$	17.4778	+	24.0562i	0.694133	+	0.955392i
$635$	−29.4127	−	8.08559i	−1.16721	−	0.320867i
$636$	1.36005	+	0.988137i	0.0539297	+	0.0391822i
$637$	−0.938685	+	5.92662i	−0.0371920	+	0.234821i
$638$	−0.823012	+	5.19629i	−0.0325834	+	0.205723i
$639$	3.37139	+	2.44946i	0.133370	+	0.0968990i
$640$	1.74683	−	1.39592i	0.0690494	−	0.0551787i
$641$	−9.49893	−	13.0742i	−0.375185	−	0.516398i	0.579116	−	0.815245i	$-0.303398\pi$
$641$	−9.49893	−	13.0742i	−0.375185	−	0.516398i	−0.954301	+	0.298847i	$0.903398\pi$
$642$	1.78898	+	3.51108i	0.0706056	+	0.138571i
$643$	−11.0782	+	11.0782i	−0.436882	+	0.436882i	−0.890961	−	0.454079i	$-0.849968\pi$
$643$	−11.0782	+	11.0782i	−0.436882	+	0.436882i	0.454079	+	0.890961i	$0.349968\pi$
$644$	−4.01596	−	1.30487i	−0.158251	−	0.0514189i
$645$	−0.853425	+	7.64340i	−0.0336036	+	0.300959i
$646$	2.58698	−	22.4279i	0.101784	−	0.882413i
$647$	−5.64195	+	11.0729i	−0.221808	+	0.435323i	−0.974916	−	0.222575i	$-0.928554\pi$
$647$	−5.64195	+	11.0729i	−0.221808	+	0.435323i	0.753108	+	0.657897i	$0.228554\pi$
$648$	−0.826255	−	5.21677i	−0.0324584	−	0.204934i
$649$	5.47677			0.214982
$650$	2.94491	+	3.35708i	0.115509	+	0.131675i
$651$	2.25817			0.0885045
$652$	−0.286709	−	1.81021i	−0.0112284	−	0.0708931i
$653$	−37.4140	−	19.0634i	−1.46412	−	0.746007i	−0.473264	−	0.880920i	$-0.656924\pi$
$653$	−37.4140	−	19.0634i	−1.46412	−	0.746007i	−0.990857	+	0.134913i	$0.956924\pi$
$654$	3.64521	+	11.2188i	0.142539	+	0.438690i
$655$	−18.0856	+	19.8264i	−0.706661	+	0.774681i
$656$	8.36558	+	2.71814i	0.326621	+	0.106126i
$657$	3.26596	+	3.26596i	0.127417	+	0.127417i
$658$	2.62845	−	1.33926i	0.102468	−	0.0522099i
$659$	−28.5760	+	20.7617i	−1.11316	+	0.808760i	−0.983159	−	0.182753i	$-0.941499\pi$
$659$	−28.5760	+	20.7617i	−1.11316	+	0.808760i	−0.130004	+	0.991513i	$0.541499\pi$
$660$	−0.948351	+	0.357010i	−0.0369145	+	0.0138966i
$661$	20.9275	−	28.8042i	0.813985	−	1.12035i	−0.176711	−	0.984263i	$-0.556546\pi$
$661$	20.9275	−	28.8042i	0.813985	−	1.12035i	0.990696	−	0.136091i	$-0.0434541\pi$
$662$	−10.7607	−	1.70432i	−0.418225	−	0.0662404i
$663$	−0.476774	+	3.01023i	−0.0185164	+	0.116908i
$664$	−13.0482	−	9.48009i	−0.506369	−	0.367899i
$665$	−4.79698	−	1.93331i	−0.186019	−	0.0749707i
$666$	−14.9398	+	10.8544i	−0.578905	+	0.420599i
$667$	−27.6331	−	54.2330i	−1.06996	−	2.09991i
$668$	−12.4242	−	12.4242i	−0.480707	−	0.480707i
$669$	3.54120	+	1.15060i	0.136911	+	0.0444849i
$670$	−5.26403	−	25.5786i	−0.203367	−	0.988187i
$671$	−2.47220	−	7.60864i	−0.0954381	−	0.293728i
$672$	0.158714	−	0.311494i	0.00612253	−	0.0120161i
$673$	4.43528	+	28.0033i	0.170968	+	1.07945i	0.912664	+	0.408711i	$0.134022\pi$
$673$	4.43528	+	28.0033i	0.170968	+	1.07945i	−0.741696	+	0.670736i	$0.765978\pi$
$674$			31.8864i			1.22822i
$675$	14.0986	+	11.7223i	0.542654	+	0.451192i
$676$	−12.2023			−0.469319
$677$	−13.3595	+	2.11594i	−0.513449	+	0.0813223i	−0.407782	−	0.913079i	$-0.633698\pi$
$677$	−13.3595	+	2.11594i	−0.513449	+	0.0813223i	−0.105667	+	0.994402i	$0.533698\pi$
$678$	−2.35998	+	4.63172i	−0.0906345	+	0.177880i
$679$	−0.171460	−	0.527699i	−0.00658002	−	0.0202512i
$680$	10.0672	−	5.72571i	0.386059	−	0.219571i
$681$	−3.98885	+	12.2764i	−0.152853	+	0.470433i
$682$	3.14164	+	3.14164i	0.120300	+	0.120300i
$683$	−22.5726	+	11.5013i	−0.863718	+	0.440086i	−0.828959	−	0.559309i	$-0.811066\pi$
$683$	−22.5726	+	11.5013i	−0.863718	+	0.440086i	−0.0347593	+	0.999396i	$0.511066\pi$
$684$	−10.9632	+	2.21459i	−0.419188	+	0.0846769i
$685$	14.8251	+	9.76459i	0.566439	+	0.373086i
$686$	4.27871	−	5.88914i	0.163362	−	0.224848i
$687$	−2.87966	+	18.1815i	−0.109866	+	0.693666i
$688$	0.816668	−	5.15624i	0.0311352	−	0.196580i
$689$	1.33954	−	1.84373i	0.0510326	−	0.0702403i
$690$	6.44861	−	9.79062i	0.245494	−	0.372723i
$691$	−18.4618	+	13.4133i	−0.702320	+	0.510265i	−0.880687	−	0.473699i	$-0.842918\pi$
$691$	−18.4618	+	13.4133i	−0.702320	+	0.510265i	0.178367	+	0.983964i	$0.442918\pi$
$692$	−8.20694	−	16.1070i	−0.311981	−	0.612297i
$693$	0.662222	−	0.662222i	0.0251558	−	0.0251558i
$694$	−4.44910	+	13.6929i	−0.168885	+	0.519776i
$695$	5.43303	−	3.09003i	0.206087	−	0.117212i
$696$	4.79264	−	1.55722i	0.181665	−	0.0590264i
$697$	40.5931	+	20.6832i	1.53757	+	0.783432i
$698$	0.0556350	+	0.351266i	0.00210582	+	0.0132956i
$699$	−5.68649			−0.215083
$700$	−0.653440	−	2.57141i	−0.0246977	−	0.0971902i
$701$	33.0499			1.24828			0.624139	−	0.781313i	$-0.285450\pi$
$701$	33.0499			1.24828			0.624139	+	0.781313i	$0.285450\pi$
$702$	3.23487	−	0.512352i	0.122092	−	0.0193375i
$703$	19.4943	+	24.5778i	0.735240	+	0.926971i
$704$	0.654170	−	0.212553i	0.0246550	−	0.00801088i
$705$	1.65093	+	8.02206i	0.0621776	+	0.302128i
$706$	−6.73228	−	2.18745i	−0.253373	−	0.0823258i
$707$	−4.81119	−	4.81119i	−0.180943	−	0.180943i
$708$	−2.38158	−	4.67412i	−0.0895054	−	0.175664i
$709$	−1.08986	−	1.50007i	−0.0409307	−	0.0563362i	0.788061	−	0.615597i	$-0.211085\pi$
$709$	−1.08986	−	1.50007i	−0.0409307	−	0.0563362i	−0.828992	+	0.559261i	$0.811085\pi$
$710$	3.62772	−	0.166575i	0.136146	−	0.00625146i
$711$	−8.12188	+	11.1788i	−0.304594	+	0.419238i
$712$	2.40182	+	0.380411i	0.0900120	+	0.0142565i
$713$	−50.7692	−	8.04106i	−1.90132	−	0.301140i
$714$	1.06431	−	1.46490i	0.0398309	−	0.0548225i
$715$	0.483972	+	1.28561i	0.0180995	+	0.0480791i
$716$	8.48625	+	11.6803i	0.317146	+	0.436514i
$717$	−1.53399	−	3.01062i	−0.0572878	−	0.112434i
$718$	−22.3104	−	22.3104i	−0.832615	−	0.832615i
$719$	5.83606	+	1.89625i	0.217648	+	0.0707183i	0.415812	−	0.909451i	$-0.363498\pi$
$719$	5.83606	+	1.89625i	0.217648	+	0.0707183i	−0.198163	+	0.980169i	$0.563498\pi$
$720$	−4.23892	−	3.86673i	−0.157975	−	0.144104i
$721$	1.98229	−	0.644085i	0.0738243	−	0.0239870i
$722$	4.54514	+	18.4484i	0.169153	+	0.686577i
$723$	−4.82404	+	0.764053i	−0.179408	+	0.0284154i
$724$	16.9994			0.631779
$725$	19.5491	−	32.8696i	0.726035	−	1.22075i
$726$	6.93552			0.257401
$727$	0.923390	+	5.83005i	0.0342466	+	0.216225i	0.998877	−	0.0473821i	$-0.0150878\pi$
$727$	0.923390	+	5.83005i	0.0342466	+	0.216225i	−0.964630	+	0.263607i	$0.915088\pi$
$728$	−0.422270	−	0.215157i	−0.0156504	−	0.00797425i
$729$	−5.99616	+	1.94827i	−0.222080	+	0.0721582i
$730$	4.00014	+	0.446636i	0.148052	+	0.0165307i
$731$	8.35558	−	25.7158i	0.309042	−	0.951135i
$732$	−5.41852	+	5.41852i	−0.200274	+	0.200274i
$733$	−4.07705	−	8.00167i	−0.150589	−	0.295548i	0.803372	−	0.595477i	$-0.203037\pi$
$733$	−4.07705	−	8.00167i	−0.150589	−	0.295548i	−0.953962	+	0.299929i	$0.903037\pi$
$734$	−0.941609	+	0.684119i	−0.0347554	+	0.0252513i
$735$	6.17886	+	7.73209i	0.227911	+	0.285203i
$736$	−4.67748	+	6.43800i	−0.172414	+	0.237308i
$737$	1.25665	−	7.93420i	0.0462894	−	0.292260i
$738$	3.53075	−	22.2923i	0.129969	−	0.820591i
$739$	30.9678	−	42.6235i	1.13917	−	1.56793i	0.369816	−	0.929105i	$-0.379421\pi$
$739$	30.9678	−	42.6235i	1.13917	−	1.56793i	0.769352	−	0.638826i	$-0.220579\pi$
$740$	−4.26564	+	15.5170i	−0.156808	+	0.570416i
$741$	−0.507863	−	2.51415i	−0.0186568	−	0.0923595i
$742$	−1.20640	+	0.614689i	−0.0442882	+	0.0225660i
$743$	1.20504	+	1.20504i	0.0442086	+	0.0442086i	0.728865	−	0.684657i	$-0.240048\pi$
$743$	1.20504	+	1.20504i	0.0442086	+	0.0442086i	−0.684657	+	0.728865i	$0.740048\pi$
$744$	1.31507	−	4.04737i	0.0482128	−	0.148384i
$745$	21.1440	−	46.6745i	0.774656	−	1.71002i
$746$	4.46358	+	13.7375i	0.163423	+	0.502965i
$747$	−18.7882	+	36.8740i	−0.687425	+	1.34915i
$748$	3.51873	−	0.557312i	0.128657	−	0.0203773i
$749$	−3.17373			−0.115966
$750$	7.36465	+	0.143071i	0.268919	+	0.00522421i
$751$			29.2011i			1.06556i	0.846253	+	0.532782i	$0.178853\pi$
$751$			29.2011i			1.06556i	−0.846253	+	0.532782i	$0.821147\pi$
$752$	−0.869685	−	5.49097i	−0.0317141	−	0.200235i
$753$	−3.91523	+	7.68407i	−0.142679	+	0.280023i
$754$	−2.11101	−	6.49703i	−0.0768786	−	0.236608i
$755$	16.8924	−	37.2892i	0.614777	−	1.35709i
$756$	−1.85060	−	0.601297i	−0.0673057	−	0.0218690i
$757$	9.60237	+	9.60237i	0.349004	+	0.349004i	0.859739	−	0.510734i	$-0.170626\pi$
$757$	9.60237	+	9.60237i	0.349004	+	0.349004i	−0.510734	+	0.859739i	$0.670626\pi$
$758$	0.159884	+	0.313789i	0.00580723	+	0.0113973i
$759$	2.91753	−	2.11971i	0.105900	−	0.0769405i
$760$	−6.25870	+	7.47186i	−0.227027	+	0.271033i
$761$	19.9303	+	14.4802i	0.722472	+	0.524906i	0.887173	−	0.461437i	$-0.152666\pi$
$761$	19.9303	+	14.4802i	0.722472	+	0.524906i	−0.164701	+	0.986343i	$0.552666\pi$
$762$	−1.40599	+	8.87706i	−0.0509336	+	0.321582i
$763$	−9.38361	−	1.48622i	−0.339710	−	0.0538047i
$764$	−0.880205	+	1.21150i	−0.0318447	+	0.0438305i
$765$	−18.5519	−	23.2154i	−0.670744	−	0.839354i
$766$	3.88084	−	2.81959i	0.140220	−	0.101876i
$767$	−6.33636	+	3.22854i	−0.228793	+	0.116576i
$768$	−0.465869	−	0.465869i	−0.0168106	−	0.0168106i
$769$	−29.5148	−	9.58993i	−1.06433	−	0.345822i	−0.276053	−	0.961142i	$-0.589026\pi$
$769$	−29.5148	−	9.58993i	−1.06433	−	0.345822i	−0.788277	+	0.615321i	$0.789026\pi$
$770$	0.0905622	−	0.811089i	0.00326363	−	0.0292296i
$771$	1.84747	+	5.68594i	0.0665352	+	0.204774i
$772$	22.1035	+	11.2623i	0.795521	+	0.405338i
$773$	−0.956894	−	6.04159i	−0.0344171	−	0.217301i	0.964486	−	0.264136i	$-0.0850866\pi$
$773$	−0.956894	−	6.04159i	−0.0344171	−	0.217301i	−0.998903	+	0.0468346i	$0.985087\pi$
$774$	−13.3955			−0.481490
$775$	−12.7531	−	29.6721i	−0.458104	−	1.06585i
$776$	−1.04566			−0.0375370
$777$	0.393589	+	2.48503i	0.0141199	+	0.0891498i
$778$	−7.22984	+	14.1894i	−0.259202	+	0.508713i
$779$	−38.0887	−	4.39342i	−1.36467	−	0.157411i
$780$	0.886742	−	0.972095i	0.0317504	−	0.0348066i
$781$	1.06242	+	0.345202i	0.0380164	+	0.0123523i
$782$	−29.1447	+	29.1447i	−1.04221	+	1.04221i
$783$	−12.7337	−	24.9912i	−0.455064	−	0.893113i
$784$	−3.94900	−	5.43533i	−0.141036	−	0.194119i
$785$	1.73729	+	4.61489i	0.0620066	+	0.164712i
$786$	6.39691	+	4.64763i	0.228170	+	0.165775i
$787$	2.66538	−	16.8285i	0.0950105	−	0.599873i	−0.893540	−	0.448983i	$-0.851786\pi$
$787$	2.66538	−	16.8285i	0.0950105	−	0.599873i	0.988551	−	0.150890i	$-0.0482138\pi$
$788$	0.753416	−	4.75688i	0.0268393	−	0.169457i
$789$	6.43524	+	4.67547i	0.229101	+	0.166451i
$790$	0.552328	+	12.0287i	0.0196510	+	0.427964i
$791$	−2.46088	−	3.38711i	−0.0874989	−	0.120432i
$792$	−0.801265	−	1.57257i	−0.0284717	−	0.0558789i
$793$	7.34549	+	7.34549i	0.260846	+	0.260846i
$794$	9.38692	−	28.8900i	0.333129	−	1.02527i
$795$	−0.757737	−	3.68194i	−0.0268742	−	0.130585i
$796$	6.92327	+	21.3076i	0.245389	+	0.755229i
$797$	10.4494	+	5.32426i	0.370138	+	0.188595i	0.629159	−	0.777277i	$-0.283400\pi$
$797$	10.4494	+	5.32426i	0.370138	+	0.188595i	−0.259020	+	0.965872i	$0.583400\pi$
$798$	−0.409280	+	1.46787i	−0.0144883	+	0.0519621i
$799$		−	28.7946i		−	1.01868i
$800$	−4.98934	−	0.326315i	−0.176400	−	0.0115370i
$801$		−	6.23973i		−	0.220470i
$802$	3.99580	+	25.2285i	0.141097	+	0.890848i
$803$	1.10318	+	0.562097i	0.0389303	+	0.0198360i
$804$	−7.31787	+	2.37772i	−0.258081	+	0.0838557i
$805$	4.66800	+	8.20749i	0.164525	+	0.289276i
$806$	−5.48672	−	1.78274i	−0.193261	−	0.0627944i
$807$	3.13988	+	3.13988i	0.110529	+	0.110529i
$808$	−11.4251	+	5.82136i	−0.401932	+	0.204795i
$809$	4.55279	+	6.26638i	0.160068	+	0.220314i	0.881516	−	0.472154i	$-0.156523\pi$
$809$	4.55279	+	6.26638i	0.160068	+	0.220314i	−0.721449	+	0.692468i	$0.756523\pi$
$810$	−6.49643	+	9.86323i	−0.228261	+	0.346558i
$811$	−1.64622	+	2.26582i	−0.0578065	+	0.0795638i	−0.836942	−	0.547292i	$-0.815659\pi$
$811$	−1.64622	+	2.26582i	−0.0578065	+	0.0795638i	0.779135	+	0.626856i	$0.215659\pi$
$812$	−0.634909	+	4.00866i	−0.0222809	+	0.140676i
$813$	−5.13301	−	0.812990i	−0.180023	−	0.0285128i
$814$	−2.90968	+	4.00483i	−0.101984	+	0.140369i
$815$	−2.25425	+	3.42252i	−0.0789628	+	0.119885i
$816$	−2.00576	−	2.76069i	−0.0702157	−	0.0966436i
$817$	0.960920	+	22.7354i	0.0336183	+	0.795410i
$818$	−14.5020	+	14.5020i	−0.507052	+	0.507052i
$819$	−0.375782	+	1.15654i	−0.0131309	+	0.0404127i
$820$	−9.72384	−	17.0969i	−0.339571	−	0.597049i
$821$	2.55914	+	7.87624i	0.0893147	+	0.274883i	0.985730	−	0.168332i	$-0.0538380\pi$
$821$	2.55914	+	7.87624i	0.0893147	+	0.274883i	−0.896416	+	0.443214i	$0.853838\pi$
$822$	2.37458	−	4.66038i	0.0828230	−	0.162549i
$823$	−21.1172	+	3.34463i	−0.736098	+	0.116587i	−0.513217	−	0.858259i	$-0.671546\pi$
$823$	−21.1172	+	3.34463i	−0.736098	+	0.116587i	−0.222882	+	0.974846i	$0.571546\pi$
$824$		−	3.92800i		−	0.136838i
$825$	2.10467	+	0.839337i	0.0732753	+	0.0292219i
$826$	4.22503			0.147008
$827$	46.0400	−	7.29202i	1.60097	−	0.253569i	0.708846	−	0.705363i	$-0.249216\pi$
$827$	46.0400	−	7.29202i	1.60097	−	0.253569i	0.892122	+	0.451794i	$0.149216\pi$
$828$	18.1936	+	9.27012i	0.632273	+	0.322159i
$829$	14.5175	+	44.6803i	0.504214	+	1.55181i	0.802087	+	0.597207i	$0.203723\pi$
$829$	14.5175	+	44.6803i	0.504214	+	1.55181i	−0.297873	+	0.954606i	$0.596277\pi$
$830$	7.26965	+	35.3241i	0.252333	+	1.22612i
$831$	−10.6097	−	3.44729i	−0.368045	−	0.119585i
$832$	−0.631545	+	0.631545i	−0.0218949	+	0.0218949i
$833$	−15.7978	−	31.0049i	−0.547361	−	1.07426i
$834$	−1.08246	−	1.48988i	−0.0374826	−	0.0515904i
$835$	1.80214	+	39.2474i	0.0623656	+	1.35821i
$836$	−2.61156	+	1.47275i	−0.0903226	+	0.0509361i
$837$	−23.3951	−	3.70541i	−0.808652	−	0.128078i
$838$	4.62251	+	0.732133i	0.159682	+	0.0252911i
$839$	19.7633	+	14.3589i	0.682304	+	0.495723i	0.874121	−	0.485708i	$-0.161438\pi$
$839$	19.7633	+	14.3589i	0.682304	+	0.495723i	−0.191817	+	0.981431i	$0.561438\pi$
$840$	−0.731602	+	0.275414i	−0.0252427	+	0.00950268i
$841$	−23.8685	+	17.3415i	−0.823052	+	0.597983i
$842$	−1.65071	+	0.841077i	−0.0568871	+	0.0289854i
$843$	0.0442382	−	0.0442382i	0.00152365	−	0.00152365i
$844$	−8.42855	+	25.9404i	−0.290123	+	0.892906i
$845$	20.1582	+	18.3883i	0.693463	+	0.632575i
$846$	−13.5669	+	4.40815i	−0.466440	+	0.151555i
$847$	−2.53592	+	4.97703i	−0.0871354	+	0.171013i
$848$	0.399164	+	2.52022i	0.0137074	+	0.0865449i
$849$	16.2206			0.556690
$850$	−25.2594	−	5.71188i	−0.866389	−	0.195916i
$851$		−	57.2711i		−	1.96323i
$852$	−0.167386	−	1.05683i	−0.00573453	−	0.0362064i
$853$	−30.9361	−	15.7627i	−1.05923	−	0.539706i	−0.164532	−	0.986372i	$-0.552611\pi$
$853$	−30.9361	−	15.7627i	−1.05923	−	0.539706i	−0.894701	+	0.446666i	$0.852611\pi$
$854$	−1.90717	−	5.86965i	−0.0652619	−	0.200855i
$855$	21.4485	+	12.8625i	0.733522	+	0.439888i
$856$	−1.84826	+	5.68836i	−0.0631722	+	0.194424i
$857$	−27.0505	+	27.0505i	−0.924029	+	0.924029i	−0.997311	−	0.0732822i	$-0.976653\pi$
$857$	−27.0505	+	27.0505i	−0.924029	+	0.924029i	0.0732822	+	0.997311i	$0.476653\pi$
$858$	0.360632	−	0.183751i	0.0123118	−	0.00627315i
$859$	−11.6056	−	15.9737i	−0.395977	−	0.545016i	0.563752	−	0.825944i	$-0.309358\pi$
$859$	−11.6056	−	15.9737i	−0.395977	−	0.545016i	−0.959729	+	0.280929i	$0.909358\pi$
$860$	−9.11932	+	7.28743i	−0.310966	+	0.248499i
$861$	−2.48781	−	1.80750i	−0.0847842	−	0.0615993i
$862$	−12.3464	−	1.95548i	−0.420520	−	0.0666038i
$863$	5.99751	+	0.949913i	0.204158	+	0.0323354i	0.257676	−	0.966231i	$-0.417043\pi$
$863$	5.99751	+	0.949913i	0.204158	+	0.0323354i	−0.0535179	+	0.998567i	$0.517043\pi$
$864$	−2.15544	+	2.96671i	−0.0733295	+	0.100929i
$865$	−10.7146	+	38.9762i	−0.364308	+	1.32523i
$866$	22.2164	−	16.1412i	0.754944	−	0.548499i
$867$	−2.93915	−	5.76840i	−0.0998186	−	0.195905i
$868$	2.42360	+	2.42360i	0.0822625	+	0.0822625i
$869$	−1.14461	+	3.52276i	−0.0388284	+	0.119502i
$870$	−10.2641	−	4.64974i	−0.347986	−	0.157641i
$871$	3.22330	+	9.92029i	0.109217	+	0.336136i
$872$	−8.12844	+	15.9530i	−0.275264	+	0.540236i
$873$	0.419728	+	2.65006i	0.0142056	+	0.0896908i
$874$	14.4285	−	31.5440i	0.488053	−	1.06699i
$875$	−2.79550	+	5.23267i	−0.0945052	+	0.176897i
$876$		−	1.18593i		−	0.0400689i
$877$	14.8461	−	2.35139i	0.501316	−	0.0794007i	0.0993450	−	0.995053i	$-0.468325\pi$
$877$	14.8461	−	2.35139i	0.501316	−	0.0794007i	0.401971	+	0.915652i	$0.368325\pi$
$878$	−4.67980	−	2.38448i	−0.157936	−	0.0804722i
$879$	−1.10305	+	0.358404i	−0.0372051	+	0.0120887i
$880$	−1.40099	−	0.634664i	−0.0472275	−	0.0213945i
$881$	−5.29573	+	16.2986i	−0.178418	+	0.549113i	−0.999773	−	0.0213036i	$-0.993218\pi$
$881$	−5.29573	+	16.2986i	−0.178418	+	0.549113i	0.821355	+	0.570417i	$0.193218\pi$
$882$	−12.1898	+	12.1898i	−0.410453	+	0.410453i
$883$	−18.3136	−	35.9425i	−0.616302	−	1.20956i	−0.962470	−	0.271388i	$-0.912517\pi$
$883$	−18.3136	−	35.9425i	−0.616302	−	1.20956i	0.346168	−	0.938173i	$-0.387483\pi$
$884$	−3.74247	+	2.71906i	−0.125873	+	0.0914520i
$885$	−3.10929	+	11.3106i	−0.104518	+	0.380201i
$886$	−20.3586	+	28.0212i	−0.683961	+	0.941391i
$887$	3.59335	−	22.6875i	0.120653	−	0.761772i	−0.850966	−	0.525221i	$-0.823983\pi$
$887$	3.59335	−	22.6875i	0.120653	−	0.761772i	0.971619	−	0.236551i	$-0.0760172\pi$
$888$	4.68318	+	0.741744i	0.157157	+	0.0248913i
$889$	−5.85622	−	4.25479i	−0.196411	−	0.142701i
$890$	−3.39455	−	4.24786i	−0.113785	−	0.142389i
$891$	−2.93916	+	2.13543i	−0.0984657	+	0.0715395i
$892$	2.56573	+	5.03553i	0.0859070	+	0.168602i
$893$	8.45493	+	22.7101i	0.282933	+	0.759965i
$894$	−14.3586	−	4.66540i	−0.480225	−	0.156034i
$895$	3.58237	−	32.0842i	0.119745	−	1.07246i
$896$	0.504657	−	0.163973i	0.0168594	−	0.00547795i
$897$	−2.12588	+	4.17228i	−0.0709811	+	0.139308i
$898$	−27.8759	+	4.41511i	−0.930232	+	0.147334i
$899$			49.4056i			1.64777i
$900$	1.17573	+	12.7757i	0.0391910	+	0.425856i
$901$			13.2160i			0.440289i
$902$	−0.946470	−	5.97577i	−0.0315140	−	0.198971i
$903$	−0.828569	+	1.62616i	−0.0275730	+	0.0541152i
$904$	−7.50393	+	2.43817i	−0.249577	+	0.0810925i
$905$	−28.0831	−	25.6173i	−0.933513	−	0.851548i
$906$	−11.4714	−	3.72729i	−0.381112	−	0.123831i
$907$	32.5238	−	32.5238i	1.07994	−	1.07994i	0.0834210	−	0.996514i	$-0.473415\pi$
$907$	32.5238	−	32.5238i	1.07994	−	1.07994i	0.996514	−	0.0834210i	$-0.0265846\pi$
$908$	−17.4569	+	8.89472i	−0.579327	+	0.295182i
$909$	19.3393	+	26.6183i	0.641445	+	0.882874i
$910$	0.373358	+	0.991778i	0.0123767	+	0.0328771i
$911$	23.4612	−	32.2916i	0.777305	−	1.06987i	−0.218269	−	0.975889i	$-0.570041\pi$
$911$	23.4612	−	32.2916i	0.777305	−	1.06987i	0.995574	−	0.0939801i	$-0.0299590\pi$
$912$	2.39255	+	1.58839i	0.0792254	+	0.0525970i
$913$	−1.73544	+	10.9572i	−0.0574348	+	0.362629i
$914$	−8.05401	−	5.85158i	−0.266403	−	0.193553i
$915$	17.1168	−	0.785960i	0.565865	−	0.0259830i
$916$	−22.6041	+	16.4229i	−0.746861	+	0.542626i
$917$	−5.67419	+	2.89114i	−0.187378	+	0.0954740i
$918$	−13.4302	+	13.4302i	−0.443264	+	0.443264i
$919$	8.07716	+	2.62443i	0.266441	+	0.0865719i	0.439191	−	0.898394i	$-0.355265\pi$
$919$	8.07716	+	2.62443i	0.266441	+	0.0865719i	−0.172750	+	0.984966i	$0.555265\pi$
$920$	17.4290	−	3.58685i	0.574615	−	0.118255i
$921$	6.88069	+	21.1766i	0.226726	+	0.697792i
$922$	24.9601	+	12.7178i	0.822016	+	0.418838i
$923$	−1.43267	+	0.226912i	−0.0471568	+	0.00746891i
$924$	−0.240466			−0.00791074
$925$	30.4302	−	19.2060i	1.00054	−	0.631489i
$926$			2.40454i			0.0790179i
$927$	−9.95488	+	1.57670i	−0.326961	+	0.0517856i
$928$	6.81507	+	3.47245i	0.223716	+	0.113989i
$929$	−41.0652	+	13.3429i	−1.34730	+	0.437766i	−0.891785	−	0.452460i	$-0.850546\pi$
$929$	−41.0652	+	13.3429i	−1.34730	+	0.437766i	−0.455519	+	0.890226i	$0.650546\pi$
$930$	−8.27167	+	4.70451i	−0.271239	+	0.154267i
$931$	21.5636	+	19.8147i	0.706717	+	0.649401i
$932$	−6.10309	−	6.10309i	−0.199913	−	0.199913i
$933$	9.14532	−	4.65977i	0.299404	−	0.152554i
$934$	−9.47041	+	6.88065i	−0.309881	+	0.225142i
$935$	−6.65278	−	4.38186i	−0.217569	−	0.143302i
$936$	1.85405	+	1.34705i	0.0606016	+	0.0440296i
$937$	−23.4074	−	3.70736i	−0.764686	−	0.121114i	−0.238105	−	0.971239i	$-0.576526\pi$
$937$	−23.4074	−	3.70736i	−0.764686	−	0.121114i	−0.526581	+	0.850125i	$0.676526\pi$
$938$	0.969440	−	6.12080i	0.0316533	−	0.199851i
$939$	−8.09185	−	5.87908i	−0.264068	−	0.191856i
$940$	−6.83790	+	10.3817i	−0.223028	+	0.338612i
$941$	21.9770	+	30.2488i	0.716431	+	0.986082i	0.999635	+	0.0270225i	$0.00860258\pi$
$941$	21.9770	+	30.2488i	0.716431	+	0.986082i	−0.283204	+	0.959060i	$0.591397\pi$
$942$	1.29454	−	0.659601i	0.0421784	−	0.0214910i
$943$	49.4958	+	49.4958i	1.61181	+	1.61181i
$944$	2.46049	−	7.57262i	0.0800823	−	0.246468i
$945$	2.15107	+	3.78211i	0.0699743	+	0.123032i
$946$	−3.41510	+	1.10963i	−0.111035	+	0.0360773i
$947$	−9.57917	+	18.8002i	−0.311281	+	0.610924i	−0.992651	−	0.121016i	$-0.961385\pi$
$947$	−9.57917	+	18.8002i	−0.311281	+	0.610924i	0.681369	+	0.731940i	$0.261385\pi$
$948$	3.50422	−	0.555015i	0.113812	−	0.0180260i
$949$	−1.60768			−0.0521875
$950$	21.5991	−	2.91196i	0.700767	−	0.0944764i
$951$	−19.5906			−0.635269
$952$	2.71451	−	0.429936i	0.0879777	−	0.0139343i
$953$	−21.0840	+	41.3798i	−0.682979	+	1.34042i	0.245631	+	0.969363i	$0.421005\pi$
$953$	−21.0840	+	41.3798i	−0.682979	+	1.34042i	−0.928610	+	0.371058i	$0.878995\pi$
$954$	6.22688	−	2.02324i	0.201603	−	0.0655047i
$955$	3.27976	−	0.674971i	0.106131	−	0.0218415i
$956$	1.58481	−	4.87756i	0.0512566	−	0.157751i
$957$	−2.45097	−	2.45097i	−0.0792286	−	0.0792286i
$958$	19.7666	−	10.0716i	0.638629	−	0.325398i
$959$	2.47611	+	3.40807i	0.0799576	+	0.110052i
$960$	0.0675747	+	1.47166i	0.00218096	+	0.0474976i
$961$	8.67499	+	6.30275i	0.279838	+	0.203314i
$962$	1.00553	−	6.34865i	0.0324195	−	0.204689i
$963$	15.1581	+	2.40081i	0.488464	+	0.0773650i
$964$	−5.99749	−	4.35743i	−0.193166	−	0.140343i
$965$	−19.5432	−	51.9141i	−0.629119	−	1.67117i
$966$	2.25071	−	1.63524i	0.0724155	−	0.0526129i
$967$	−31.4232	+	16.0109i	−1.01050	+	0.514877i	−0.879194	−	0.476465i	$-0.841918\pi$
$967$	−31.4232	+	16.0109i	−1.01050	+	0.514877i	−0.131309	+	0.991341i	$0.541918\pi$
$968$	7.44363	+	7.44363i	0.239247	+	0.239247i
$969$	10.9525	+	10.0642i	0.351845	+	0.323309i
$970$	1.72743	+	1.57576i	0.0554644	+	0.0505945i
$971$	0.275061	−	0.0893726i	0.00882712	−	0.00286810i	−0.304600	−	0.952480i	$-0.598523\pi$
$971$	0.275061	−	0.0893726i	0.00882712	−	0.00286810i	0.313427	+	0.949612i	$0.398523\pi$
$972$	12.9027	+	6.57424i	0.413853	+	0.210869i
$973$	1.46496	−	0.232026i	0.0469643	−	0.00743842i
$974$		−	11.0707i		−	0.354727i
$975$	−2.92979	+	0.269625i	−0.0938285	+	0.00863492i
$976$	−11.6310			−0.372299
$977$	−41.9054	+	6.63716i	−1.34067	+	0.212342i	−0.785225	−	0.619210i	$-0.787453\pi$
$977$	−41.9054	+	6.63716i	−1.34067	+	0.212342i	−0.555447	+	0.831552i	$0.687453\pi$
$978$	1.07589	+	0.548194i	0.0344032	+	0.0175293i
$979$	−0.516877	−	1.59078i	−0.0165195	−	0.0508417i
$980$	−1.66702	+	14.9301i	−0.0532510	+	0.476925i
$981$	43.6930	+	14.1967i	1.39501	+	0.453266i
$982$	6.90803	−	6.90803i	0.220444	−	0.220444i
$983$	23.8623	−	12.1584i	0.761089	−	0.387794i	−0.0299570	−	0.999551i	$-0.509537\pi$
$983$	23.8623	−	12.1584i	0.761089	−	0.387794i	0.791046	+	0.611757i	$0.209537\pi$
$984$	−4.68842	+	3.40634i	−0.149461	+	0.108590i
$985$	−8.41302	+	6.72301i	−0.268061	+	0.214213i
$986$	32.0500	+	23.2857i	1.02068	+	0.741568i
$987$	−0.304040	+	1.91963i	−0.00967770	+	0.0611026i
$988$	2.15327	−	3.24341i	0.0685046	−	0.103187i
$989$	24.4189	−	33.6097i	0.776474	−	1.06873i
$990$	−1.04610	+	3.80535i	−0.0332471	+	0.120942i
$991$	1.00098	+	1.37773i	0.0317972	+	0.0437650i	0.824620	−	0.565688i	$-0.191389\pi$
$991$	1.00098	+	1.37773i	0.0317972	+	0.0437650i	−0.792822	+	0.609453i	$0.791389\pi$
$992$	5.75530	−	2.93247i	0.182731	−	0.0931061i
$993$	5.07556	−	5.07556i	0.161068	−	0.161068i
$994$	0.819600	+	0.266304i	0.0259961	+	0.00844666i
$995$	20.6723	−	45.6332i	0.655355	−	1.44667i
$996$	10.1060	−	3.28364i	0.320221	−	0.104046i
$997$	14.5004	−	28.4586i	0.459232	−	0.901294i	−0.539026	−	0.842289i	$-0.681207\pi$
$997$	14.5004	−	28.4586i	0.459232	−	0.901294i	0.998258	−	0.0590044i	$-0.0187926\pi$
$998$	−2.86609	−	18.0958i	−0.0907246	−	0.572813i
$999$		−	26.3912i		−	0.834981i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.w.a.37.16	✓	400
19.18	odd	2	inner	950.2.w.a.37.35	yes	400
25.23	odd	20	inner	950.2.w.a.873.35	yes	400
475.398	even	20	inner	950.2.w.a.873.16	yes	400

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.w.a.37.16	✓	400	1.1	even	1	trivial
950.2.w.a.37.35	yes	400	19.18	odd	2	inner
950.2.w.a.873.16	yes	400	475.398	even	20	inner
950.2.w.a.873.35	yes	400	25.23	odd	20	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.w (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.987688 + 0.156434i) q^{2} +(0.299107 - 0.587030i) q^{3} +(0.951057 - 0.309017i) q^{4} +(-2.03682 - 0.922698i) q^{5} +(-0.203592 + 0.626593i) q^{6} +(-0.375210 - 0.375210i) q^{7} +(-0.891007 + 0.453990i) q^{8} +(1.50822 + 2.07588i) q^{9} +O(q^{10})\)	\(q+(-0.987688 + 0.156434i) q^{2} +(0.299107 - 0.587030i) q^{3} +(0.951057 - 0.309017i) q^{4} +(-2.03682 - 0.922698i) q^{5} +(-0.203592 + 0.626593i) q^{6} +(-0.375210 - 0.375210i) q^{7} +(-0.891007 + 0.453990i) q^{8} +(1.50822 + 2.07588i) q^{9} +(2.15608 + 0.592709i) q^{10} +(0.556470 + 0.404299i) q^{11} +(0.103065 - 0.650728i) q^{12} +(-0.882143 - 0.139718i) q^{13} +(0.429287 + 0.311895i) q^{14} +(-1.15088 + 0.919688i) q^{15} +(0.809017 - 0.587785i) q^{16} +(4.61490 - 2.35141i) q^{17} +(-1.81439 - 1.81439i) q^{18} +(-2.94930 + 3.20961i) q^{19} +(-2.22226 - 0.248126i) q^{20} +(-0.332487 + 0.108032i) q^{21} +(-0.612866 - 0.312271i) q^{22} +(7.85984 - 1.24488i) q^{23} +0.658839i q^{24} +(3.29726 + 3.75874i) q^{25} +0.893139 q^{26} +(3.62190 - 0.573653i) q^{27} +(-0.472792 - 0.240900i) q^{28} +(-2.36359 - 7.27438i) q^{29} +(0.992837 - 1.08840i) q^{30} +(-6.14318 - 1.99604i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(0.403780 - 0.205736i) q^{33} +(-4.19024 + 3.04439i) q^{34} +(0.418029 + 1.11044i) q^{35} +(2.07588 + 1.50822i) q^{36} +(1.12583 - 7.10824i) q^{37} +(2.41090 - 3.63147i) q^{38} +(-0.345873 + 0.476054i) q^{39} +(2.23371 - 0.102566i) q^{40} +(5.17021 + 7.11619i) q^{41} +(0.311494 - 0.158714i) q^{42} +(3.69146 - 3.69146i) q^{43} +(0.654170 + 0.212553i) q^{44} +(-1.15655 - 5.61982i) q^{45} +(-7.56833 + 2.45910i) q^{46} +(2.52392 - 4.95348i) q^{47} +(-0.103065 - 0.650728i) q^{48} -6.71843i q^{49} +(-3.84466 - 3.19665i) q^{50} -3.41240i q^{51} +(-0.882143 + 0.139718i) q^{52} +(-1.15842 + 2.27353i) q^{53} +(-3.48757 + 1.13318i) q^{54} +(-0.760383 - 1.33694i) q^{55} +(0.504657 + 0.163973i) q^{56} +(1.00198 + 2.69135i) q^{57} +(3.47245 + 6.81507i) q^{58} +(6.44166 - 4.68014i) q^{59} +(-0.810350 + 1.23032i) q^{60} +(-9.40967 - 6.83652i) q^{61} +(6.37980 + 1.01046i) q^{62} +(0.212994 - 1.34479i) q^{63} +(0.587785 - 0.809017i) q^{64} +(1.66785 + 1.09853i) q^{65} +(-0.366624 + 0.266368i) q^{66} +(-5.30207 - 10.4059i) q^{67} +(3.66240 - 3.66240i) q^{68} +(1.62015 - 4.98631i) q^{69} +(-0.586594 - 1.03138i) q^{70} +(1.54459 - 0.501867i) q^{71} +(-2.28626 - 1.16491i) q^{72} +(1.77787 - 0.281587i) q^{73} +7.19684i q^{74} +(3.19272 - 0.811325i) q^{75} +(-1.81313 + 3.96391i) q^{76} +(-0.0570961 - 0.360491i) q^{77} +(0.267144 - 0.524299i) q^{78} +(1.66408 + 5.12152i) q^{79} +(-2.19017 + 0.450733i) q^{80} +(-1.63217 + 5.02329i) q^{81} +(-6.21978 - 6.21978i) q^{82} +(7.32218 + 14.3706i) q^{83} +(-0.282831 + 0.205489i) q^{84} +(-11.5693 + 0.531234i) q^{85} +(-3.06854 + 4.22348i) q^{86} +(-4.97724 - 0.788318i) q^{87} +(-0.679367 - 0.107601i) q^{88} +(-1.96734 - 1.42935i) q^{89} +(2.02145 + 5.36971i) q^{90} +(0.278566 + 0.383413i) q^{91} +(7.09046 - 3.61277i) q^{92} +(-3.00920 + 3.00920i) q^{93} +(-1.71795 + 5.28732i) q^{94} +(8.96870 - 3.81608i) q^{95} +(0.203592 + 0.626593i) q^{96} +(0.931689 + 0.474719i) q^{97} +(1.05099 + 6.63572i) q^{98} +1.76494i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 400 q + 4 q^{5} - 4 q^{7}+O(q^{10}) \) 400 * q + 4 * q^5 - 4 * q^7	\( 400 q + 4 q^{5} - 4 q^{7} + 100 q^{16} + 40 q^{17} - 40 q^{19} - 76 q^{23} - 20 q^{25} - 4 q^{28} + 64 q^{30} + 8 q^{35} - 100 q^{36} + 4 q^{38} + 80 q^{39} + 32 q^{42} - 84 q^{43} - 144 q^{45} + 20 q^{47} - 16 q^{55} - 32 q^{57} - 16 q^{62} + 108 q^{63} - 100 q^{68} - 12 q^{73} + 256 q^{77} - 4 q^{80} + 100 q^{81} - 16 q^{82} + 116 q^{85} - 272 q^{87} - 4 q^{92} - 24 q^{93} - 56 q^{95}+O(q^{100}) \) 400 * q + 4 * q^5 - 4 * q^7 + 100 * q^16 + 40 * q^17 - 40 * q^19 - 76 * q^23 - 20 * q^25 - 4 * q^28 + 64 * q^30 + 8 * q^35 - 100 * q^36 + 4 * q^38 + 80 * q^39 + 32 * q^42 - 84 * q^43 - 144 * q^45 + 20 * q^47 - 16 * q^55 - 32 * q^57 - 16 * q^62 + 108 * q^63 - 100 * q^68 - 12 * q^73 + 256 * q^77 - 4 * q^80 + 100 * q^81 - 16 * q^82 + 116 * q^85 - 272 * q^87 - 4 * q^92 - 24 * q^93 - 56 * q^95

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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