LMFDB - Embedded newform 950.2.bb.c.243.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(143,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([27, 34]))

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

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

chi := DirichletCharacter("950.143");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.bb (of order $36$, degree $12$, 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:	$72$
Relative dimension:	$6$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			243.5
Character	$\chi$	$=$	950.243
Dual form			950.2.bb.c.907.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.422618 + 0.906308i) q^{2} +(0.0850875 + 0.0595789i) q^{3} +(-0.642788 + 0.766044i) q^{4} +(-0.0180373 + 0.102295i) q^{6} +(-0.497281 - 1.85588i) q^{7} +(-0.965926 - 0.258819i) q^{8} +(-1.02237 - 2.80894i) q^{9} +O(q^{10})$	\(q+(0.422618 + 0.906308i) q^{2} +(0.0850875 + 0.0595789i) q^{3} +(-0.642788 + 0.766044i) q^{4} +(-0.0180373 + 0.102295i) q^{6} +(-0.497281 - 1.85588i) q^{7} +(-0.965926 - 0.258819i) q^{8} +(-1.02237 - 2.80894i) q^{9} +(0.891095 + 1.54342i) q^{11} +(-0.100333 + 0.0268842i) q^{12} +(-1.80918 - 2.58377i) q^{13} +(1.47184 - 1.23502i) q^{14} +(-0.173648 - 0.984808i) q^{16} +(-0.472276 + 0.220226i) q^{17} +(2.11369 - 2.11369i) q^{18} +(-3.96663 - 1.80717i) q^{19} +(0.0682588 - 0.187540i) q^{21} +(-1.02222 + 1.45988i) q^{22} +(-0.743856 - 8.50231i) q^{23} +(-0.0667681 - 0.0795711i) q^{24} +(1.57710 - 2.73162i) q^{26} +(0.161015 - 0.600917i) q^{27} +(1.74133 + 0.811996i) q^{28} +(0.154692 - 0.0563031i) q^{29} +(4.27808 + 2.46995i) q^{31} +(0.819152 - 0.573576i) q^{32} +(-0.0161343 + 0.184416i) q^{33} +(-0.399185 - 0.334956i) q^{34} +(2.80894 + 1.02237i) q^{36} +(-3.59853 - 3.59853i) q^{37} +(-0.0385181 - 4.35873i) q^{38} -0.327636i q^{39} +(1.27716 - 0.225198i) q^{41} +(0.198816 - 0.0173941i) q^{42} +(-10.1800 - 0.890632i) q^{43} +(-1.75511 - 0.309474i) q^{44} +(7.39135 - 4.26740i) q^{46} +(3.14539 - 6.74531i) q^{47} +(0.0438985 - 0.0941406i) q^{48} +(2.86518 - 1.65421i) q^{49} +(-0.0533056 - 0.00939921i) q^{51} +(3.14220 + 0.274907i) q^{52} +(4.79738 - 0.419717i) q^{53} +(0.612664 - 0.108029i) q^{54} +1.92135i q^{56} +(-0.229841 - 0.390095i) q^{57} +(0.116403 + 0.116403i) q^{58} +(1.86725 + 0.679624i) q^{59} +(8.61010 + 7.22473i) q^{61} +(-0.430541 + 4.92110i) q^{62} +(-4.70464 + 3.29423i) q^{63} +(0.866025 + 0.500000i) q^{64} +(-0.173957 + 0.0633150i) q^{66} +(4.58353 + 2.13734i) q^{67} +(0.134870 - 0.503343i) q^{68} +(0.443266 - 0.767759i) q^{69} +(-0.274869 - 0.327576i) q^{71} +(0.260527 + 2.97784i) q^{72} +(-2.14088 + 3.05749i) q^{73} +(1.74057 - 4.78218i) q^{74} +(3.93407 - 1.87699i) q^{76} +(2.42128 - 2.42128i) q^{77} +(0.296939 - 0.138465i) q^{78} +(1.49372 + 8.47132i) q^{79} +(-6.82010 + 5.72274i) q^{81} +(0.743852 + 1.06233i) q^{82} +(-6.91439 + 1.85270i) q^{83} +(0.0997877 + 0.172837i) q^{84} +(-3.49505 - 9.60258i) q^{86} +(0.0165168 + 0.00442566i) q^{87} +(-0.461265 - 1.72146i) q^{88} +(2.65723 - 15.0699i) q^{89} +(-3.89550 + 4.64247i) q^{91} +(6.99129 + 4.89536i) q^{92} +(0.216854 + 0.465045i) q^{93} +7.44263 q^{94} +0.103873 q^{96} +(-4.68417 - 10.0452i) q^{97} +(2.71010 + 1.89764i) q^{98} +(3.42435 - 4.08098i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 24 q^{6}+O(q^{10}) $ 72 * q + 24 * q^6	$ 72 q + 24 q^{6} + 24 q^{21} + 12 q^{26} + 36 q^{31} - 24 q^{36} + 48 q^{41} - 36 q^{46} + 156 q^{51} + 168 q^{61} - 36 q^{66} - 84 q^{71} - 48 q^{76} - 60 q^{81} - 60 q^{86} - 264 q^{91} + 24 q^{96}+O(q^{100}) $ 72 * q + 24 * q^6 + 24 * q^21 + 12 * q^26 + 36 * q^31 - 24 * q^36 + 48 * q^41 - 36 * q^46 + 156 * q^51 + 168 * q^61 - 36 * q^66 - 84 * q^71 - 48 * q^76 - 60 * q^81 - 60 * q^86 - 264 * q^91 + 24 * q^96

Display 100 coefficients 10 coefficients

Character values

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

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{11}{18}\right)$

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 $

$2$	0.422618	+	0.906308i	0.298836	+	0.640856i
$2$	0.422618	+	0.906308i	0.298836	+	0.640856i
$3$	0.0850875	+	0.0595789i	0.0491253	+	0.0343979i	0.597881	−	0.801585i	$-0.296009\pi$
$3$	0.0850875	+	0.0595789i	0.0491253	+	0.0343979i	−0.548756	+	0.835983i	$0.684898\pi$
$4$	−0.642788	+	0.766044i	−0.321394	+	0.383022i
$5$		0			0
$5$		0			0
$6$	−0.0180373	+	0.102295i	−0.00736370	+	0.0417616i
$7$	−0.497281	−	1.85588i	−0.187955	−	0.701456i	−0.993979	−	0.109573i	$-0.965052\pi$
$7$	−0.497281	−	1.85588i	−0.187955	−	0.701456i	0.806024	−	0.591883i	$-0.201615\pi$
$8$	−0.965926	−	0.258819i	−0.341506	−	0.0915064i
$9$	−1.02237	−	2.80894i	−0.340790	−	0.936313i
$10$		0			0
$11$	0.891095	+	1.54342i	0.268675	+	0.465359i	0.968520	−	0.248936i	$-0.0800808\pi$
$11$	0.891095	+	1.54342i	0.268675	+	0.465359i	−0.699845	+	0.714295i	$0.746748\pi$
$12$	−0.100333	+	0.0268842i	−0.0289637	+	0.00776081i
$13$	−1.80918	−	2.58377i	−0.501775	−	0.716610i	0.485745	−	0.874101i	$-0.338548\pi$
$13$	−1.80918	−	2.58377i	−0.501775	−	0.716610i	−0.987520	+	0.157491i	$0.949659\pi$
$14$	1.47184	−	1.23502i	0.393365	−	0.330072i
$15$		0			0
$16$	−0.173648	−	0.984808i	−0.0434120	−	0.246202i
$17$	−0.472276	+	0.220226i	−0.114544	+	0.0534126i	−0.479045	−	0.877790i	$-0.659017\pi$
$17$	−0.472276	+	0.220226i	−0.114544	+	0.0534126i	0.364502	+	0.931203i	$0.381239\pi$
$18$	2.11369	−	2.11369i	0.498202	−	0.498202i
$19$	−3.96663	−	1.80717i	−0.910007	−	0.414593i
$19$	−3.96663	−	1.80717i	−0.910007	−	0.414593i
$20$		0			0
$21$	0.0682588	−	0.187540i	0.0148953	−	0.0409245i
$22$	−1.02222	+	1.45988i	−0.217938	+	0.311248i
$23$	−0.743856	−	8.50231i	−0.155105	−	1.77286i	−0.532140	−	0.846656i	$-0.678612\pi$
$23$	−0.743856	−	8.50231i	−0.155105	−	1.77286i	0.377036	−	0.926199i	$-0.376943\pi$
$24$	−0.0667681	−	0.0795711i	−0.0136290	−	0.0162424i
$25$		0			0
$26$	1.57710	−	2.73162i	0.309295	−	0.535715i
$27$	0.161015	−	0.600917i	0.0309874	−	0.115647i
$28$	1.74133	+	0.811996i	0.329081	+	0.153453i
$29$	0.154692	−	0.0563031i	0.0287255	−	0.0104552i	−0.327617	−	0.944810i	$-0.606246\pi$
$29$	0.154692	−	0.0563031i	0.0287255	−	0.0104552i	0.356343	+	0.934355i	$0.384023\pi$
$30$		0			0
$31$	4.27808	+	2.46995i	0.768366	+	0.443616i	0.832291	−	0.554339i	$-0.187029\pi$
$31$	4.27808	+	2.46995i	0.768366	+	0.443616i	−0.0639257	+	0.997955i	$0.520362\pi$
$32$	0.819152	−	0.573576i	0.144807	−	0.101395i
$33$	−0.0161343	+	0.184416i	−0.00280863	+	0.0321028i
$34$	−0.399185	−	0.334956i	−0.0684596	−	0.0574444i
$35$		0			0
$36$	2.80894	+	1.02237i	0.468157	+	0.170395i
$37$	−3.59853	−	3.59853i	−0.591595	−	0.591595i	0.346467	−	0.938062i	$-0.387381\pi$
$37$	−3.59853	−	3.59853i	−0.591595	−	0.591595i	−0.938062	+	0.346467i	$0.887381\pi$
$38$	−0.0385181	−	4.35873i	−0.00624846	−	0.707079i
$39$		−	0.327636i		−	0.0524637i
$40$		0			0
$41$	1.27716	−	0.225198i	0.199459	−	0.0351701i	−0.0730258	−	0.997330i	$-0.523266\pi$
$41$	1.27716	−	0.225198i	0.199459	−	0.0351701i	0.272485	+	0.962160i	$0.412154\pi$
$42$	0.198816	−	0.0173941i	0.0306780	−	0.00268397i
$43$	−10.1800	−	0.890632i	−1.55243	−	0.135820i	−0.721586	−	0.692325i	$-0.756586\pi$
$43$	−10.1800	−	0.890632i	−1.55243	−	0.135820i	−0.830844	+	0.556505i	$0.812142\pi$
$44$	−1.75511	−	0.309474i	−0.264593	−	0.0466550i
$45$		0			0
$46$	7.39135	−	4.26740i	1.08979	−	0.629193i
$47$	3.14539	−	6.74531i	0.458803	−	0.983905i	−0.531767	−	0.846891i	$-0.678472\pi$
$47$	3.14539	−	6.74531i	0.458803	−	0.983905i	0.990569	−	0.137014i	$-0.0437506\pi$
$48$	0.0438985	−	0.0941406i	0.00633620	−	0.0135880i
$49$	2.86518	−	1.65421i	0.409312	−	0.236316i
$50$		0			0
$51$	−0.0533056	−	0.00939921i	−0.00746428	−	0.00131615i
$52$	3.14220	+	0.274907i	0.435745	+	0.0381227i
$53$	4.79738	−	0.419717i	0.658971	−	0.0576525i	0.247235	−	0.968956i	$-0.420478\pi$
$53$	4.79738	−	0.419717i	0.658971	−	0.0576525i	0.411736	+	0.911303i	$0.364922\pi$
$54$	0.612664	−	0.108029i	0.0833730	−	0.0147009i
$55$		0			0
$56$			1.92135i			0.256751i
$57$	−0.229841	−	0.390095i	−0.0304432	−	0.0516693i
$58$	0.116403	+	0.116403i	0.0152845	+	0.0152845i
$59$	1.86725	+	0.679624i	0.243096	+	0.0884795i	0.460695	−	0.887559i	$-0.347600\pi$
$59$	1.86725	+	0.679624i	0.243096	+	0.0884795i	−0.217599	+	0.976038i	$0.569823\pi$
$60$		0			0
$61$	8.61010	+	7.22473i	1.10241	+	0.925032i	0.997585	−	0.0694584i	$-0.0221271\pi$
$61$	8.61010	+	7.22473i	1.10241	+	0.925032i	0.104826	+	0.994491i	$0.466572\pi$
$62$	−0.430541	+	4.92110i	−0.0546787	+	0.624981i
$63$	−4.70464	+	3.29423i	−0.592729	+	0.415034i
$64$	0.866025	+	0.500000i	0.108253	+	0.0625000i
$65$		0			0
$66$	−0.173957	+	0.0633150i	−0.0214126	+	0.00779354i
$67$	4.58353	+	2.13734i	0.559968	+	0.261117i	0.681930	−	0.731418i	$-0.261141\pi$
$67$	4.58353	+	2.13734i	0.559968	+	0.261117i	−0.121962	+	0.992535i	$0.538919\pi$
$68$	0.134870	−	0.503343i	0.0163554	−	0.0610393i
$69$	0.443266	−	0.767759i	0.0533629	−	0.0924273i
$70$		0			0
$71$	−0.274869	−	0.327576i	−0.0326209	−	0.0388761i	0.749487	−	0.662019i	$-0.230300\pi$
$71$	−0.274869	−	0.327576i	−0.0326209	−	0.0388761i	−0.782108	+	0.623143i	$0.785856\pi$
$72$	0.260527	+	2.97784i	0.0307034	+	0.350941i
$73$	−2.14088	+	3.05749i	−0.250571	+	0.357852i	−0.924657	−	0.380800i	$-0.875649\pi$
$73$	−2.14088	+	3.05749i	−0.250571	+	0.357852i	0.674087	+	0.738652i	$0.264537\pi$
$74$	1.74057	−	4.78218i	0.202337	−	0.555917i
$75$		0			0
$76$	3.93407	−	1.87699i	0.451269	−	0.215305i
$77$	2.42128	−	2.42128i	0.275930	−	0.275930i
$78$	0.296939	−	0.138465i	0.0336217	−	0.0156780i
$79$	1.49372	+	8.47132i	0.168057	+	0.953098i	0.945856	+	0.324585i	$0.105225\pi$
$79$	1.49372	+	8.47132i	0.168057	+	0.953098i	−0.777799	+	0.628512i	$0.783664\pi$
$80$		0			0
$81$	−6.82010	+	5.72274i	−0.757789	+	0.635861i
$82$	0.743852	+	1.06233i	0.0821447	+	0.117315i
$83$	−6.91439	+	1.85270i	−0.758952	+	0.203361i	−0.617485	−	0.786582i	$-0.711849\pi$
$83$	−6.91439	+	1.85270i	−0.758952	+	0.203361i	−0.141467	+	0.989943i	$0.545182\pi$
$84$	0.0997877	+	0.172837i	0.0108877	+	0.0188581i
$85$		0			0
$86$	−3.49505	−	9.60258i	−0.376881	−	1.03547i
$87$	0.0165168	+	0.00442566i	0.00177079	+	0.000474481i
$88$	−0.461265	−	1.72146i	−0.0491710	−	0.183509i
$89$	2.65723	−	15.0699i	0.281666	−	1.59741i	−0.435291	−	0.900290i	$-0.643354\pi$
$89$	2.65723	−	15.0699i	0.281666	−	1.59741i	0.716957	−	0.697118i	$-0.245534\pi$
$90$		0			0
$91$	−3.89550	+	4.64247i	−0.408359	+	0.486664i
$92$	6.99129	+	4.89536i	0.728893	+	0.510376i
$93$	0.216854	+	0.465045i	0.0224867	+	0.0482229i
$94$	7.44263			0.767649
$95$		0			0
$96$	0.103873			0.0106015
$97$	−4.68417	−	10.0452i	−0.475605	−	1.01994i	−0.987019	−	0.160604i	$-0.948656\pi$
$97$	−4.68417	−	10.0452i	−0.475605	−	1.01994i	0.511414	−	0.859334i	$-0.329122\pi$
$98$	2.71010	+	1.89764i	0.273762	+	0.191690i
$99$	3.42435	−	4.08098i	0.344160	−	0.410154i
$100$		0			0
$101$	−0.145744	+	0.826553i	−0.0145020	+	0.0822451i	−0.991200	−	0.132374i	$-0.957740\pi$
$101$	−0.145744	+	0.826553i	−0.0145020	+	0.0822451i	0.976698	+	0.214619i	$0.0688511\pi$
$102$	−0.0140093	−	0.0522835i	−0.00138713	−	0.00517684i
$103$	2.50672	+	0.671673i	0.246994	+	0.0661819i	0.380192	−	0.924908i	$-0.375858\pi$
$103$	2.50672	+	0.671673i	0.246994	+	0.0661819i	−0.133198	+	0.991089i	$0.542525\pi$
$104$	1.07880	+	2.96398i	0.105785	+	0.290642i
$105$		0			0
$106$	2.40785	+	4.17053i	0.233872	+	0.405077i
$107$	−9.83066	+	2.63412i	−0.950366	+	0.254650i	−0.700518	−	0.713635i	$-0.747047\pi$
$107$	−9.83066	+	2.63412i	−0.950366	+	0.254650i	−0.249848	+	0.968285i	$0.580381\pi$
$108$	0.356831	+	0.509607i	0.0343360	+	0.0490370i
$109$	−2.17354	+	1.82382i	−0.208187	+	0.174690i	−0.740919	−	0.671594i	$-0.765610\pi$
$109$	−2.17354	+	1.82382i	−0.208187	+	0.174690i	0.532732	+	0.846284i	$0.321165\pi$
$110$		0			0
$111$	−0.0917934	−	0.520586i	−0.00871265	−	0.0494119i
$112$	−1.74133	+	0.811996i	−0.164540	+	0.0767264i
$113$	−1.71805	+	1.71805i	−0.161621	+	0.161621i	−0.783284	−	0.621664i	$-0.786457\pi$
$113$	−1.71805	+	1.71805i	−0.161621	+	0.161621i	0.621664	+	0.783284i	$0.286457\pi$
$114$	0.256411	−	0.373168i	0.0240151	−	0.0349504i
$115$		0			0
$116$	−0.0563031	+	0.154692i	−0.00522762	+	0.0143628i
$117$	−5.40801	+	7.72344i	−0.499971	+	0.714032i
$118$	0.173186	+	1.97953i	0.0159431	+	0.182230i
$119$	0.643566	+	0.766972i	0.0589956	+	0.0703082i
$120$		0			0
$121$	3.91190	−	6.77561i	0.355627	−	0.615965i
$122$	−2.90905	+	10.8567i	−0.263373	+	0.982920i
$123$	0.122088	+	0.0569304i	0.0110083	+	0.00513325i
$124$	−4.64199	+	1.68955i	−0.416863	+	0.151726i
$125$		0			0
$126$	−4.97385	−	2.87165i	−0.443106	−	0.255827i
$127$	0.386237	−	0.270446i	0.0342729	−	0.0239982i	−0.556314	−	0.830972i	$-0.687785\pi$
$127$	0.386237	−	0.270446i	0.0342729	−	0.0239982i	0.590587	+	0.806974i	$0.298896\pi$
$128$	−0.0871557	+	0.996195i	−0.00770355	+	0.0880520i
$129$	−0.813125	−	0.682293i	−0.0715917	−	0.0600725i
$130$		0			0
$131$	−11.0624	−	4.02637i	−0.966524	−	0.351786i	−0.189937	−	0.981796i	$-0.560828\pi$
$131$	−11.0624	−	4.02637i	−0.966524	−	0.351786i	−0.776587	+	0.630010i	$0.783051\pi$
$132$	−0.130900	−	0.130900i	−0.0113934	−	0.0113934i
$133$	−1.38136	+	8.26025i	−0.119779	+	0.716255i
$134$			5.05737i			0.436890i
$135$		0			0
$136$	0.513182	−	0.0904878i	0.0440050	−	0.00775927i
$137$	17.7329	−	1.55142i	1.51502	−	0.132547i	0.700907	−	0.713253i	$-0.252779\pi$
$137$	17.7329	−	1.55142i	1.51502	−	0.132547i	0.814114	+	0.580706i	$0.197223\pi$
$138$	0.883158	+	0.0772663i	0.0751794	+	0.00657735i
$139$	−0.485742	−	0.0856494i	−0.0412001	−	0.00726469i	0.153010	−	0.988225i	$-0.451103\pi$
$139$	−0.485742	−	0.0856494i	−0.0412001	−	0.00726469i	−0.194210	+	0.980960i	$0.562214\pi$
$140$		0			0
$141$	0.669512	−	0.386543i	0.0563831	−	0.0325528i
$142$	0.180720	−	0.387555i	0.0151657	−	0.0325229i
$143$	2.37570	−	5.09471i	0.198666	−	0.426041i
$144$	−2.58873	+	1.49461i	−0.215728	+	0.124550i
$145$		0			0
$146$	−3.67580	−	0.648142i	−0.304211	−	0.0536407i
$147$	0.342347	+	0.0299515i	0.0282363	+	0.00247036i
$148$	5.06972	−	0.443543i	0.416729	−	0.0364590i
$149$	−18.6705	+	3.29211i	−1.52955	+	0.269700i	−0.874177	−	0.485608i	$-0.838598\pi$
$149$	−18.6705	+	3.29211i	−1.52955	+	0.269700i	−0.655370	+	0.755308i	$0.727487\pi$
$150$		0			0
$151$			10.6982i			0.870608i	0.900284	+	0.435304i	$0.143359\pi$
$151$			10.6982i			0.870608i	−0.900284	+	0.435304i	$0.856641\pi$
$152$	3.36374	+	2.77223i	0.272835	+	0.224858i
$153$	1.10144	+	1.10144i	0.0890463	+	0.0890463i
$154$	3.21770	+	1.17115i	0.259290	+	0.0943737i
$155$		0			0
$156$	0.250983	+	0.210600i	0.0200948	+	0.0168615i
$157$	1.61720	−	18.4847i	0.129067	−	1.47524i	−0.605033	−	0.796200i	$-0.706840\pi$
$157$	1.61720	−	18.4847i	0.129067	−	1.47524i	0.734100	−	0.679042i	$-0.237604\pi$
$158$	−7.04635	+	4.93391i	−0.560577	+	0.392521i
$159$	0.433204	+	0.250110i	0.0343553	+	0.0198350i
$160$		0			0
$161$	−15.4094	+	5.60855i	−1.21443	+	0.442015i
$162$	−8.06887	−	3.76257i	−0.633950	−	0.295616i
$163$	−2.70587	+	10.0984i	−0.211940	+	0.790972i	0.775281	+	0.631616i	$0.217608\pi$
$163$	−2.70587	+	10.0984i	−0.211940	+	0.790972i	−0.987221	+	0.159355i	$0.949058\pi$
$164$	−0.648433	+	1.12312i	−0.0506341	+	0.0877008i
$165$		0			0
$166$	−4.60127	−	5.48358i	−0.357128	−	0.425608i
$167$	1.64335	+	18.7836i	0.127166	+	1.45352i	0.744924	+	0.667150i	$0.232486\pi$
$167$	1.64335	+	18.7836i	0.127166	+	1.45352i	−0.617757	+	0.786369i	$0.711958\pi$
$168$	−0.114472	+	0.163483i	−0.00883169	+	0.0126130i
$169$	1.04350	−	2.86700i	0.0802694	−	0.220538i
$170$		0			0
$171$	−1.02087	+	12.9896i	−0.0780675	+	0.993341i
$172$	7.22582	−	7.22582i	0.550964	−	0.550964i
$173$	3.49718	−	1.63076i	0.265886	−	0.123984i	−0.285104	−	0.958497i	$-0.592028\pi$
$173$	3.49718	−	1.63076i	0.265886	−	0.123984i	0.550990	+	0.834512i	$0.314250\pi$
$174$	0.00296929	+	0.0168397i	0.000225101	+	0.00127661i
$175$		0			0
$176$	1.36524	−	1.14557i	0.102909	−	0.0863505i
$177$	0.118389	+	0.169076i	0.00889863	+	0.0127086i
$178$	14.7810	−	3.96055i	1.10788	−	0.296856i
$179$	10.7222	+	18.5713i	0.801412	+	1.38809i	0.918687	+	0.394987i	$0.129251\pi$
$179$	10.7222	+	18.5713i	0.801412	+	1.38809i	−0.117274	+	0.993100i	$0.537416\pi$
$180$		0			0
$181$	−6.14237	−	16.8760i	−0.456559	−	1.25438i	−0.928031	−	0.372503i	$-0.878499\pi$
$181$	−6.14237	−	16.8760i	−0.456559	−	1.25438i	0.471472	−	0.881881i	$-0.343723\pi$
$182$	−5.85382	−	1.56853i	−0.433914	−	0.116267i
$183$	0.302170	+	1.12771i	0.0223371	+	0.0833631i
$184$	−1.48205	+	8.40513i	−0.109258	+	0.619634i
$185$		0			0
$186$	−0.329828	+	0.393073i	−0.0241841	+	0.0288215i
$187$	−0.760744	−	0.532679i	−0.0556311	−	0.0389533i
$188$	3.14539	+	6.74531i	0.229401	+	0.491953i
$189$	−1.19530			−0.0869452
$190$		0			0
$191$	−7.92472			−0.573412			−0.286706	−	0.958019i	$-0.592560\pi$
$191$	−7.92472			−0.573412			−0.286706	+	0.958019i	$0.592560\pi$
$192$	0.0438985	+	0.0941406i	0.00316810	+	0.00679401i
$193$	16.1233	+	11.2896i	1.16058	+	0.812645i	0.985124	−	0.171843i	$-0.0549721\pi$
$193$	16.1233	+	11.2896i	1.16058	+	0.812645i	0.175453	+	0.984488i	$0.443861\pi$
$194$	7.12445	−	8.49059i	0.511506	−	0.609589i
$195$		0			0
$196$	−0.574502	+	3.25816i	−0.0410359	+	0.232726i
$197$	−0.395824	−	1.47724i	−0.0282013	−	0.105249i	0.950391	−	0.311059i	$-0.100684\pi$
$197$	−0.395824	−	1.47724i	−0.0282013	−	0.105249i	−0.978592	+	0.205810i	$0.934017\pi$
$198$	5.14582	+	1.37882i	0.365697	+	0.0979883i
$199$	7.83440	+	21.5248i	0.555366	+	1.52586i	0.826285	+	0.563253i	$0.190450\pi$
$199$	7.83440	+	21.5248i	0.555366	+	1.52586i	−0.270919	+	0.962602i	$0.587327\pi$
$200$		0			0
$201$	0.262661	+	0.454942i	0.0185267	+	0.0320892i
$202$	−0.810705	+	0.217228i	−0.0570410	+	0.0152841i
$203$	−0.181417	−	0.259090i	−0.0127330	−	0.0181846i
$204$	0.0414644	−	0.0347928i	0.00290309	−	0.00243598i
$205$		0			0
$206$	0.450642	+	2.55572i	0.0313977	+	0.178065i
$207$	−23.1220	+	10.7820i	−1.60709	+	0.749398i
$208$	−2.23036	+	2.23036i	−0.154648	+	0.154648i
$209$	−0.745418	−	7.73254i	−0.0515617	−	0.534871i
$210$		0			0
$211$	5.91671	−	16.2560i	0.407323	−	1.11911i	−0.551269	−	0.834328i	$-0.685856\pi$
$211$	5.91671	−	16.2560i	0.407323	−	1.11911i	0.958592	−	0.284784i	$-0.0919218\pi$
$212$	−2.76218	+	3.94480i	−0.189707	+	0.270930i
$213$	−0.00387128	−	0.0442490i	−0.000265256	−	0.00303189i
$214$	−6.54194	−	7.79638i	−0.447198	−	0.532949i
$215$		0			0
$216$	−0.311058	+	0.538768i	−0.0211648	+	0.0366585i
$217$	2.45652	−	9.16785i	0.166759	−	0.622354i
$218$	−2.57152	−	1.19912i	−0.174165	−	0.0812145i
$219$	−0.364324	+	0.132603i	−0.0246187	+	0.00896048i
$220$		0			0
$221$	1.42344	+	0.821826i	0.0957512	+	0.0552820i
$222$	0.433018	−	0.303202i	0.0290623	−	0.0203496i
$223$	−0.548619	+	6.27075i	−0.0367383	+	0.419920i	0.955448	+	0.295158i	$0.0953724\pi$
$223$	−0.548619	+	6.27075i	−0.0367383	+	0.419920i	−0.992187	+	0.124762i	$0.960183\pi$
$224$	−1.47184	−	1.23502i	−0.0983412	−	0.0825181i
$225$		0			0
$226$	−2.28316	−	0.831003i	−0.151874	−	0.0552775i
$227$	−13.1230	−	13.1230i	−0.871004	−	0.871004i	0.121577	−	0.992582i	$-0.461205\pi$
$227$	−13.1230	−	13.1230i	−0.871004	−	0.871004i	−0.992582	+	0.121577i	$0.961205\pi$
$228$	0.446569	+	0.0746795i	0.0295748	+	0.00494577i
$229$			16.2374i			1.07299i	0.843902	+	0.536497i	$0.180253\pi$
$229$			16.2374i			1.07299i	−0.843902	+	0.536497i	$0.819747\pi$
$230$		0			0
$231$	0.350278	−	0.0617634i	0.0230466	−	0.00406373i
$232$	−0.163993	+	0.0143475i	−0.0107667	+	0.000941961i
$233$	10.7968	+	0.944595i	0.707320	+	0.0618825i	0.435139	−	0.900364i	$-0.356699\pi$
$233$	10.7968	+	0.944595i	0.707320	+	0.0618825i	0.272181	+	0.962246i	$0.412255\pi$
$234$	−9.28534	−	1.63726i	−0.607002	−	0.107031i
$235$		0			0
$236$	−1.72087	+	0.993544i	−0.112019	+	0.0646742i
$237$	−0.377615	+	0.809798i	−0.0245287	+	0.0526020i
$238$	−0.423130	+	0.907406i	−0.0274275	+	0.0588184i
$239$	−2.64356	+	1.52626i	−0.170998	+	0.0987256i	−0.583056	−	0.812432i	$-0.698143\pi$
$239$	−2.64356	+	1.52626i	−0.170998	+	0.0987256i	0.412059	+	0.911157i	$0.364810\pi$
$240$		0			0
$241$	−16.5905	−	2.92535i	−1.06869	−	0.188438i	−0.388478	−	0.921458i	$-0.626999\pi$
$241$	−16.5905	−	2.92535i	−1.06869	−	0.188438i	−0.680207	+	0.733020i	$0.738110\pi$
$242$	7.79403	+	0.681889i	0.501019	+	0.0438335i
$243$	−2.78050	+	0.243263i	−0.178369	+	0.0156053i
$244$	−11.0689	+	1.95175i	−0.708616	+	0.124948i
$245$		0			0
$246$			0.134709i			0.00858873i
$247$	2.50702	+	13.5184i	0.159518	+	0.860152i
$248$	−3.49304	−	3.49304i	−0.221808	−	0.221808i
$249$	−0.698710	−	0.254310i	−0.0442789	−	0.0161162i
$250$		0			0
$251$	−16.4630	−	13.8141i	−1.03914	−	0.871941i	−0.0472283	−	0.998884i	$-0.515039\pi$
$251$	−16.4630	−	13.8141i	−1.03914	−	0.871941i	−0.991910	+	0.126944i	$0.959483\pi$
$252$	0.500562	−	5.72145i	0.0315325	−	0.360418i
$253$	12.4598	−	8.72445i	0.783341	−	0.548502i
$254$	0.408338	+	0.235754i	0.0256214	+	0.0147925i
$255$		0			0
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	4.57134	+	2.13165i	0.285153	+	0.132969i	0.559932	−	0.828538i	$-0.310827\pi$
$257$	4.57134	+	2.13165i	0.285153	+	0.132969i	−0.274780	+	0.961507i	$0.588605\pi$
$258$	0.274726	−	1.02529i	0.0171037	−	0.0638318i
$259$	−4.88895	+	8.46792i	−0.303785	+	0.526171i
$260$		0			0
$261$	−0.316304	−	0.376957i	−0.0195787	−	0.0233330i
$262$	−1.02603	−	11.7275i	−0.0633881	−	0.724529i
$263$	2.08190	−	2.97326i	0.128375	−	0.183339i	−0.749819	−	0.661643i	$-0.769859\pi$
$263$	2.08190	−	2.97326i	0.128375	−	0.183339i	0.878194	+	0.478304i	$0.158748\pi$
$264$	0.0633150	−	0.173957i	0.00389677	−	0.0107063i
$265$		0			0
$266$	−8.07012	+	2.23900i	−0.494811	+	0.137282i
$267$	1.12395	−	1.12395i	0.0687844	−	0.0687844i
$268$	−4.58353	+	2.13734i	−0.279984	+	0.130559i
$269$	−3.65134	−	20.7078i	−0.222626	−	1.26258i	−0.867171	−	0.498010i	$-0.834064\pi$
$269$	−3.65134	−	20.7078i	−0.222626	−	1.26258i	0.644545	−	0.764567i	$-0.277047\pi$
$270$		0			0
$271$	−4.50771	+	3.78242i	−0.273824	+	0.229765i	−0.769350	−	0.638828i	$-0.779420\pi$
$271$	−4.50771	+	3.78242i	−0.273824	+	0.229765i	0.495526	+	0.868593i	$0.334975\pi$
$272$	0.298890	+	0.426859i	0.0181229	+	0.0258821i
$273$	−0.608052	+	0.162927i	−0.0368010	+	0.00986079i
$274$	8.90030	+	15.4158i	0.537687	+	0.931301i
$275$		0			0
$276$	0.303212	+	0.833067i	0.0182512	+	0.0501447i
$277$	4.29924	+	1.15198i	0.258316	+	0.0692156i	0.385653	−	0.922644i	$-0.373976\pi$
$277$	4.29924	+	1.15198i	0.258316	+	0.0692156i	−0.127337	+	0.991860i	$0.540643\pi$
$278$	−0.127659	−	0.476429i	−0.00765646	−	0.0285743i
$279$	2.56416	−	14.5421i	0.153512	−	0.870611i
$280$		0			0
$281$	8.26608	−	9.85114i	0.493113	−	0.587670i	−0.460893	−	0.887456i	$-0.652471\pi$
$281$	8.26608	−	9.85114i	0.493113	−	0.587670i	0.954006	+	0.299786i	$0.0969153\pi$
$282$	0.633275	+	0.443424i	0.0377110	+	0.0264055i
$283$	−5.68702	−	12.1958i	−0.338058	−	0.724968i	0.661633	−	0.749828i	$-0.269864\pi$
$283$	−5.68702	−	12.1958i	−0.338058	−	0.724968i	−0.999691	+	0.0248602i	$0.992086\pi$
$284$	0.427620			0.0253746
$285$		0			0
$286$	5.62139			0.332400
$287$	−1.05305	−	2.25827i	−0.0621596	−	0.133302i
$288$	−2.44862	−	1.71454i	−0.144286	−	0.101030i
$289$	−10.7528	+	12.8147i	−0.632520	+	0.753808i
$290$		0			0
$291$	0.199920	−	1.13380i	0.0117195	−	0.0664646i
$292$	−0.966043	−	3.60532i	−0.0565334	−	0.210986i
$293$	29.5834	+	7.92684i	1.72828	+	0.463091i	0.979786	−	0.200050i	$-0.0641106\pi$
$293$	29.5834	+	7.92684i	1.72828	+	0.463091i	0.748494	+	0.663141i	$0.230777\pi$
$294$	0.117537	+	0.322930i	0.00685490	+	0.0188337i
$295$		0			0
$296$	2.54455	+	4.40728i	0.147899	+	0.256168i
$297$	1.07095	−	0.286960i	0.0621427	−	0.0166511i
$298$	−10.8742	−	15.5299i	−0.629923	−	0.899623i
$299$	−20.6223	+	17.3041i	−1.19262	+	1.00072i
$300$		0			0
$301$	3.40940	+	19.3357i	0.196515	+	1.11449i
$302$	−9.69587	+	4.52126i	−0.557935	+	0.260169i
$303$	−0.0616461	+	0.0616461i	−0.00354148	+	0.00354148i
$304$	−1.09092	+	4.22018i	−0.0625683	+	0.242044i
$305$		0			0
$306$	−0.532756	+	1.46373i	−0.0304556	+	0.0836761i
$307$	−0.230507	+	0.329198i	−0.0131557	+	0.0187883i	−0.825676	−	0.564145i	$-0.809206\pi$
$307$	−0.230507	+	0.329198i	−0.0131557	+	0.0187883i	0.812520	+	0.582933i	$0.198095\pi$
$308$	0.298439	+	3.41117i	0.0170051	+	0.194370i
$309$	0.173273	+	0.206498i	0.00985714	+	0.0117473i
$310$		0			0
$311$	4.53424	−	7.85353i	0.257113	−	0.445333i	−0.708354	−	0.705857i	$-0.750562\pi$
$311$	4.53424	−	7.85353i	0.257113	−	0.445333i	0.965467	+	0.260524i	$0.0838954\pi$
$312$	−0.0847983	+	0.316472i	−0.00480076	+	0.0179167i
$313$	11.2132	+	5.22882i	0.633810	+	0.295551i	0.712845	−	0.701321i	$-0.247406\pi$
$313$	11.2132	+	5.22882i	0.633810	+	0.295551i	−0.0790351	+	0.996872i	$0.525184\pi$
$314$	17.4363	−	6.34630i	0.983988	−	0.358142i
$315$		0			0
$316$	−7.44955	−	4.30100i	−0.419070	−	0.241950i
$317$	−14.4848	+	10.1424i	−0.813549	+	0.569653i	−0.904634	−	0.426190i	$-0.859856\pi$
$317$	−14.4848	+	10.1424i	−0.813549	+	0.569653i	0.0910845	+	0.995843i	$0.470967\pi$
$318$	−0.0435971	+	0.498317i	−0.00244480	+	0.0279442i
$319$	0.224744	+	0.188583i	0.0125833	+	0.0105586i
$320$		0			0
$321$	−0.993404	−	0.361570i	−0.0554464	−	0.0201808i
$322$	−11.5953	−	11.5953i	−0.646183	−	0.646183i
$323$	2.27133	−	0.0200717i	0.126380	−	0.00111682i
$324$		−	8.90301i		−	0.494612i
$325$		0			0
$326$	−10.2959	+	1.81544i	−0.570235	+	0.100548i
$327$	−0.293602	+	0.0256869i	−0.0162362	+	0.00142049i
$328$	−1.29193	−	0.113029i	−0.0713350	−	0.00624100i
$329$	−14.0826	−	2.48315i	−0.776400	−	0.136900i
$330$		0			0
$331$	21.3514	−	12.3272i	1.17358	−	0.677567i	0.219059	−	0.975712i	$-0.429701\pi$
$331$	21.3514	−	12.3272i	1.17358	−	0.677567i	0.954521	+	0.298145i	$0.0963679\pi$
$332$	3.02523	−	6.48762i	0.166031	−	0.356055i
$333$	−6.42902	+	13.7871i	−0.352308	+	0.755527i
$334$	−16.3292	+	9.42768i	−0.893495	+	0.515860i
$335$		0			0
$336$	−0.196543	−	0.0346559i	−0.0107223	−	0.00189063i
$337$	27.6919	+	2.42273i	1.50848	+	0.131975i	0.811175	−	0.584803i	$-0.198828\pi$
$337$	27.6919	+	2.42273i	1.50848	+	0.131975i	0.697301	+	0.716778i	$0.254384\pi$
$338$	3.03939	−	0.265912i	0.165321	−	0.0144637i
$339$	−0.248544	+	0.0438250i	−0.0134991	+	0.00238025i
$340$		0			0
$341$			8.80384i			0.476755i
$342$	−12.2040	+	4.56443i	−0.659918	+	0.246816i
$343$	−14.0050	−	14.0050i	−0.756199	−	0.756199i
$344$	9.60258	+	3.49505i	0.517736	+	0.188441i
$345$		0			0
$346$	2.95594	+	2.48033i	0.158912	+	0.133343i
$347$	−0.590962	+	6.75473i	−0.0317245	+	0.362613i	0.963695	+	0.267007i	$0.0860346\pi$
$347$	−0.590962	+	6.75473i	−0.0317245	+	0.362613i	−0.995419	+	0.0956063i	$0.969521\pi$
$348$	−0.0140071	+	0.00980784i	−0.000750857	+	0.000525756i
$349$	19.7256	+	11.3886i	1.05589	+	0.609616i	0.924291	−	0.381688i	$-0.124657\pi$
$349$	19.7256	+	11.3886i	1.05589	+	0.609616i	0.131595	+	0.991304i	$0.457990\pi$
$350$		0			0
$351$	−1.84394	+	0.671139i	−0.0984222	+	0.0358227i
$352$	1.61521	+	0.753186i	0.0860911	+	0.0401449i
$353$	4.79246	−	17.8857i	0.255077	−	0.951959i	−0.712971	−	0.701193i	$-0.752651\pi$
$353$	4.79246	−	17.8857i	0.255077	−	0.951959i	0.968048	−	0.250766i	$-0.0806824\pi$
$354$	−0.103202	+	0.178751i	−0.00548513	+	0.00950052i
$355$		0			0
$356$	9.83619	+	11.7223i	0.521317	+	0.621281i
$357$	0.00906407	+	0.103603i	0.000479721	+	0.00548324i
$358$	−12.3000	+	17.5662i	−0.650073	+	0.928401i
$359$	10.9853	−	30.1819i	0.579783	−	1.59294i	−0.208763	−	0.977966i	$-0.566944\pi$
$359$	10.9853	−	30.1819i	0.579783	−	1.59294i	0.788546	−	0.614975i	$-0.210834\pi$
$360$		0			0
$361$	12.4683	+	14.3367i	0.656225	+	0.754565i
$362$	12.6990	−	12.6990i	0.667444	−	0.667444i
$363$	0.736537	−	0.343453i	0.0386582	−	0.0180266i
$364$	−1.05236	−	5.96825i	−0.0551588	−	0.312821i
$365$		0			0
$366$	−0.894354	+	0.750452i	−0.0467486	+	0.0392268i
$367$	11.3270	+	16.1767i	0.591266	+	0.844415i	0.997595	−	0.0693115i	$-0.0220802\pi$
$367$	11.3270	+	16.1767i	0.591266	+	0.844415i	−0.406329	+	0.913727i	$0.633191\pi$
$368$	−8.24398	+	2.20897i	−0.429747	+	0.115150i
$369$	−1.93830	−	3.35724i	−0.100904	−	0.174771i
$370$		0			0
$371$	−3.16459	−	8.69464i	−0.164297	−	0.451403i
$372$	−0.495636	−	0.132805i	−0.0256975	−	0.00688564i
$373$	5.60928	+	20.9341i	0.290438	+	1.08393i	0.944774	+	0.327724i	$0.106282\pi$
$373$	5.60928	+	20.9341i	0.290438	+	1.08393i	−0.654336	+	0.756204i	$0.727052\pi$
$374$	0.161266	−	0.914588i	0.00833889	−	0.0472922i
$375$		0			0
$376$	−4.78403	+	5.70139i	−0.246718	+	0.294027i
$377$	−0.425339	−	0.297826i	−0.0219061	−	0.0153388i
$378$	−0.505155	−	1.08331i	−0.0259824	−	0.0557194i
$379$	11.0607			0.568148			0.284074	−	0.958802i	$-0.408314\pi$
$379$	11.0607			0.568148			0.284074	+	0.958802i	$0.408314\pi$
$380$		0			0
$381$	0.0489768			0.00250916
$382$	−3.34913	−	7.18223i	−0.171356	−	0.367475i
$383$	−18.8270	−	13.1828i	−0.962017	−	0.673612i	−0.0167332	−	0.999860i	$-0.505327\pi$
$383$	−18.8270	−	13.1828i	−0.962017	−	0.673612i	−0.945284	+	0.326248i	$0.894215\pi$
$384$	−0.0667681	+	0.0795711i	−0.00340724	+	0.00406059i
$385$		0			0
$386$	−3.41789	+	19.3838i	−0.173966	+	0.986611i
$387$	7.90596	+	29.5055i	0.401883	+	1.49985i
$388$	10.7060	+	2.86867i	0.543515	+	0.145635i
$389$	−9.52199	−	26.1614i	−0.482784	−	1.32644i	−0.907097	−	0.420922i	$-0.861707\pi$
$389$	−9.52199	−	26.1614i	−0.482784	−	1.32644i	0.424313	−	0.905516i	$-0.360516\pi$
$390$		0			0
$391$	2.22373	+	3.85162i	0.112459	+	0.194785i
$392$	−3.19570	+	0.856284i	−0.161407	+	0.0432489i
$393$	−0.701383	−	1.00168i	−0.0353801	−	0.0505280i
$394$	1.17155	−	0.983045i	0.0590217	−	0.0495251i
$395$		0			0
$396$	0.925083	+	5.24641i	0.0464872	+	0.263642i
$397$	−18.5369	+	8.64390i	−0.930341	+	0.433825i	−0.827876	−	0.560912i	$-0.810451\pi$
$397$	−18.5369	+	8.64390i	−0.930341	+	0.433825i	−0.102465	+	0.994737i	$0.532673\pi$
$398$	−16.1972	+	16.1972i	−0.811891	+	0.811891i
$399$	−0.609673	+	0.620544i	−0.0305218	+	0.0310661i
$400$		0			0
$401$	11.6220	−	31.9312i	0.580376	−	1.59457i	−0.207165	−	0.978306i	$-0.566424\pi$
$401$	11.6220	−	31.9312i	0.580376	−	1.59457i	0.787541	−	0.616263i	$-0.211354\pi$
$402$	−0.301312	+	0.430319i	−0.0150281	+	0.0214624i
$403$	−1.35801	−	15.5222i	−0.0676474	−	0.773214i
$404$	−0.539494	−	0.642944i	−0.0268408	−	0.0319877i
$405$		0			0
$406$	0.158145	−	0.273916i	0.00784863	−	0.0135942i
$407$	2.34742	−	8.76068i	0.116357	−	0.434251i
$408$	0.0490565	+	0.0228754i	0.00242866	+	0.00113250i
$409$	36.3914	−	13.2454i	1.79944	−	0.654942i	0.801026	−	0.598629i	$-0.204288\pi$
$409$	36.3914	−	13.2454i	1.79944	−	0.654942i	0.998413	−	0.0563128i	$-0.0179344\pi$
$410$		0			0
$411$	1.60128	+	0.924498i	0.0789852	+	0.0456021i
$412$	−2.12582	+	1.48851i	−0.104732	+	0.0733338i
$413$	0.332751	−	3.80336i	0.0163736	−	0.187151i
$414$	−19.5435	−	16.3990i	−0.960513	−	0.805966i
$415$		0			0
$416$	−2.96398	−	1.07880i	−0.145321	−	0.0528926i
$417$	−0.0362277	−	0.0362277i	−0.00177408	−	0.00177408i
$418$	6.69303	−	3.94349i	0.327367	−	0.192882i
$419$			4.54855i			0.222211i	0.993809	+	0.111106i	$0.0354392\pi$
$419$			4.54855i			0.222211i	−0.993809	+	0.111106i	$0.964561\pi$
$420$		0			0
$421$	38.7285	−	6.82889i	1.88751	−	0.332820i	0.894144	−	0.447781i	$-0.147785\pi$
$421$	38.7285	−	6.82889i	1.88751	−	0.332820i	0.993370	+	0.114961i	$0.0366743\pi$
$422$	17.2335	−	1.50773i	0.838913	−	0.0733954i
$423$	−22.1629	−	1.93901i	−1.07760	−	0.0942777i
$424$	−4.74255	−	0.836239i	−0.230318	−	0.0406114i
$425$		0			0
$426$	0.0384671	−	0.0222090i	0.00186374	−	0.00107603i
$427$	9.12658	−	19.5720i	0.441666	−	0.947157i
$428$	4.30118	−	9.22390i	0.207905	−	0.445854i
$429$	0.505680	−	0.291954i	0.0244145	−	0.0140957i
$430$		0			0
$431$	−3.22490	−	0.568637i	−0.155338	−	0.0273903i	0.0954383	−	0.995435i	$-0.469575\pi$
$431$	−3.22490	−	0.568637i	−0.155338	−	0.0273903i	−0.250776	+	0.968045i	$0.580686\pi$
$432$	−0.619748	−	0.0542209i	−0.0298176	−	0.00260871i
$433$	−23.9140	+	2.09220i	−1.14923	+	0.100545i	−0.645812	−	0.763496i	$-0.723481\pi$
$433$	−23.9140	+	2.09220i	−1.14923	+	0.100545i	−0.503421	+	0.864041i	$0.667926\pi$
$434$	9.34707	−	1.64814i	0.448674	−	0.0791133i
$435$		0			0
$436$		−	2.83736i		−	0.135885i
$437$	−12.4145	+	35.0698i	−0.593867	+	1.67762i
$438$	−0.274149	−	0.274149i	−0.0130993	−	0.0130993i
$439$	31.1229	+	11.3278i	1.48542	+	0.540647i	0.952238	−	0.305356i	$-0.0987753\pi$
$439$	31.1229	+	11.3278i	1.48542	+	0.540647i	0.533178	+	0.846003i	$0.320998\pi$
$440$		0			0
$441$	−7.57586	−	6.35690i	−0.360755	−	0.302710i
$442$	−0.143254	+	1.63740i	−0.00681388	+	0.0778830i
$443$	−5.96737	+	4.17840i	−0.283518	+	0.198522i	−0.706682	−	0.707532i	$-0.749809\pi$
$443$	−5.96737	+	4.17840i	−0.283518	+	0.198522i	0.423163	+	0.906054i	$0.360920\pi$
$444$	0.457796	+	0.264309i	0.0217260	+	0.0125435i
$445$		0			0
$446$	−5.91509	+	2.15291i	−0.280087	+	0.101943i
$447$	−1.78477	−	0.832250i	−0.0844165	−	0.0393641i
$448$	0.497281	−	1.85588i	0.0234943	−	0.0876820i
$449$	13.3802	−	23.1752i	0.631450	−	1.09370i	−0.355806	−	0.934560i	$-0.615793\pi$
$449$	13.3802	−	23.1752i	0.631450	−	1.09370i	0.987255	−	0.159143i	$-0.0508732\pi$
$450$		0			0
$451$	1.48565	+	1.77053i	0.0699565	+	0.0833709i
$452$	−0.211761	−	2.42044i	−0.00996042	−	0.113848i
$453$	−0.637388	+	0.910284i	−0.0299471	+	0.0427689i
$454$	6.34746	−	17.4395i	0.297901	−	0.818476i
$455$		0			0
$456$	0.121046	+	0.436290i	0.00566848	+	0.0204312i
$457$	22.5584	−	22.5584i	1.05524	−	1.05524i	0.0568548	−	0.998382i	$-0.481893\pi$
$457$	22.5584	−	22.5584i	1.05524	−	1.05524i	0.998382	−	0.0568548i	$-0.0181072\pi$
$458$	−14.7160	+	6.86220i	−0.687636	+	0.320650i
$459$	0.0562939	+	0.319258i	0.00262757	+	0.0149017i
$460$		0			0
$461$	21.0803	−	17.6885i	0.981807	−	0.823834i	−0.00255366	−	0.999997i	$-0.500813\pi$
$461$	21.0803	−	17.6885i	0.981807	−	0.823834i	0.984361	+	0.176162i	$0.0563684\pi$
$462$	0.204010	+	0.291357i	0.00949142	+	0.0135552i
$463$	8.72076	−	2.33672i	0.405288	−	0.108597i	−0.0504152	−	0.998728i	$-0.516054\pi$
$463$	8.72076	−	2.33672i	0.405288	−	0.108597i	0.455703	+	0.890132i	$0.349388\pi$
$464$	−0.0823097	−	0.142565i	−0.00382113	−	0.00661839i
$465$		0			0
$466$	3.70682	+	10.1844i	0.171715	+	0.471783i
$467$	15.2101	+	4.07554i	0.703840	+	0.188593i	0.592950	−	0.805239i	$-0.297963\pi$
$467$	15.2101	+	4.07554i	0.703840	+	0.188593i	0.110890	+	0.993833i	$0.464630\pi$
$468$	−2.44030	−	9.10731i	−0.112803	−	0.420986i
$469$	1.68733	−	9.56933i	0.0779137	−	0.441871i
$470$		0			0
$471$	1.23890	−	1.47647i	0.0570857	−	0.0680321i
$472$	−1.62773	−	1.13975i	−0.0749222	−	0.0524611i
$473$	−7.69669	−	16.5056i	−0.353894	−	0.758929i
$474$	−0.893513			−0.0410404
$475$		0			0
$476$	−1.00121			−0.0458904
$477$	−6.08366	−	13.0465i	−0.278552	−	0.597356i
$478$	−2.50048	−	1.75085i	−0.114369	−	0.0800822i
$479$	−14.7751	+	17.6083i	−0.675092	+	0.804543i	−0.989467	−	0.144756i	$-0.953760\pi$
$479$	−14.7751	+	17.6083i	−0.675092	+	0.804543i	0.314376	+	0.949299i	$0.398205\pi$
$480$		0			0
$481$	−2.78741	+	15.8082i	−0.127095	+	0.720790i
$482$	−4.36017	−	16.2724i	−0.198600	−	0.741186i
$483$	−1.64529	−	0.440855i	−0.0748635	−	0.0200596i
$484$	2.67590	+	7.35197i	0.121632	+	0.334180i
$485$		0			0
$486$	−1.39556	−	2.41719i	−0.0633040	−	0.109646i
$487$	20.3977	−	5.46554i	0.924307	−	0.247667i	0.234881	−	0.972024i	$-0.424530\pi$
$487$	20.3977	−	5.46554i	0.924307	−	0.247667i	0.689425	+	0.724357i	$0.257863\pi$
$488$	−6.44682	−	9.20701i	−0.291834	−	0.416782i
$489$	−0.831890	+	0.698039i	−0.0376194	+	0.0315664i
$490$		0			0
$491$	6.79817	+	38.5543i	0.306797	+	1.73993i	0.614923	+	0.788587i	$0.289187\pi$
$491$	6.79817	+	38.5543i	0.306797	+	1.73993i	−0.308126	+	0.951346i	$0.599702\pi$
$492$	−0.122088	+	0.0569304i	−0.00550414	+	0.00256662i
$493$	−0.0606577	+	0.0606577i	−0.00273189	+	0.00273189i
$494$	−11.1923	+	7.98523i	−0.503564	+	0.359273i
$495$		0			0
$496$	1.68955	−	4.64199i	0.0758628	−	0.208431i
$497$	−0.471254	+	0.673020i	−0.0211386	+	0.0301891i
$498$	−0.0648048	−	0.740722i	−0.00290397	−	0.0331926i
$499$	2.83979	+	3.38433i	0.127127	+	0.151504i	0.825853	−	0.563885i	$-0.190694\pi$
$499$	2.83979	+	3.38433i	0.127127	+	0.151504i	−0.698727	+	0.715389i	$0.746250\pi$
$500$		0			0
$501$	−0.979278	+	1.69616i	−0.0437509	+	0.0757788i
$502$	5.56227	−	20.7587i	0.248256	−	0.926506i
$503$	6.80144	+	3.17156i	0.303261	+	0.141413i	0.568292	−	0.822827i	$-0.307604\pi$
$503$	6.80144	+	3.17156i	0.303261	+	0.141413i	−0.265031	+	0.964240i	$0.585382\pi$
$504$	5.39695	−	1.96433i	0.240399	−	0.0874981i
$505$		0			0
$506$	13.1728	+	7.60531i	0.585602	+	0.338097i
$507$	0.259602	−	0.181775i	0.0115293	−	0.00807291i
$508$	−0.0410946	+	0.469713i	−0.00182328	+	0.0208402i
$509$	4.17940	+	3.50693i	0.185248	+	0.155442i	0.730696	−	0.682703i	$-0.239196\pi$
$509$	4.17940	+	3.50693i	0.185248	+	0.155442i	−0.545447	+	0.838145i	$0.683640\pi$
$510$		0			0
$511$	6.73894	+	2.45277i	0.298113	+	0.108504i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−1.72465	+	2.09263i	−0.0761450	+	0.0923920i
$514$			5.04392i			0.222478i
$515$		0			0
$516$	1.04533	−	0.184320i	0.0460182	−	0.00811426i
$517$	13.2137	−	1.15605i	0.581138	−	0.0508430i
$518$	−9.74070	−	0.852201i	−0.427982	−	0.0374435i
$519$	0.394725	+	0.0696007i	0.0173265	+	0.00305513i
$520$		0			0
$521$	21.1105	−	12.1881i	0.924867	−	0.533972i	0.0396825	−	0.999212i	$-0.487365\pi$
$521$	21.1105	−	12.1881i	0.924867	−	0.533972i	0.885185	+	0.465240i	$0.154032\pi$
$522$	0.207963	−	0.445978i	0.00910229	−	0.0195199i
$523$	4.48476	−	9.61760i	0.196105	−	0.420548i	−0.783525	−	0.621360i	$-0.786580\pi$
$523$	4.48476	−	9.61760i	0.196105	−	0.420548i	0.979630	+	0.200812i	$0.0643580\pi$
$524$	10.1951	−	5.88616i	0.445377	−	0.257138i
$525$		0			0
$526$	3.57453	+	0.630287i	0.155857	+	0.0274818i
$527$	−2.56438	−	0.224354i	−0.111706	−	0.00977302i
$528$	0.184416	−	0.0161343i	0.00802569	−	0.000702157i
$529$	−49.0854	+	8.65509i	−2.13415	+	0.376308i
$530$		0			0
$531$		−	5.93983i		−	0.257766i
$532$	−5.43980	−	6.36777i	−0.235845	−	0.276078i
$533$	−2.89248	−	2.89248i	−0.125287	−	0.125287i
$534$	1.49364	+	0.543641i	0.0646362	+	0.0235256i
$535$		0			0
$536$	−3.87417	−	3.25081i	−0.167339	−	0.140414i
$537$	−0.194138	+	2.21900i	−0.00837766	+	0.0957571i
$538$	17.2245	−	12.0607i	0.742602	−	0.519975i
$539$	5.10630	+	2.94812i	0.219944	+	0.126985i
$540$		0			0
$541$	32.5899	−	11.8618i	1.40115	−	0.509977i	0.472630	−	0.881261i	$-0.343305\pi$
$541$	32.5899	−	11.8618i	1.40115	−	0.509977i	0.928519	+	0.371284i	$0.121082\pi$
$542$	−5.33307	−	2.48685i	−0.229075	−	0.106819i
$543$	0.482816	−	1.80189i	0.0207196	−	0.0773267i
$544$	−0.260549	+	0.451285i	−0.0111710	+	0.0193487i
$545$		0			0
$546$	−0.404636	−	0.482226i	−0.0173168	−	0.0206374i
$547$	2.97183	+	33.9682i	0.127066	+	1.45237i	0.745483	+	0.666524i	$0.232219\pi$
$547$	2.97183	+	33.9682i	0.127066	+	1.45237i	−0.618417	+	0.785850i	$0.712226\pi$
$548$	−10.2100	+	14.5814i	−0.436150	+	0.622886i
$549$	11.4911	−	31.5716i	0.490429	−	1.34744i
$550$		0			0
$551$	−0.715353	−	0.0562203i	−0.0304751	−	0.00239506i
$552$	−0.626872	+	0.626872i	−0.0266815	+	0.0266815i
$553$	14.9789	−	6.98479i	0.636969	−	0.297024i
$554$	0.772890	+	4.38328i	0.0328370	+	0.186228i
$555$		0			0
$556$	0.377840	−	0.317046i	0.0160240	−	0.0134457i
$557$	2.92431	+	4.17635i	0.123907	+	0.176958i	0.876313	−	0.481742i	$-0.159996\pi$
$557$	2.92431	+	4.17635i	0.123907	+	0.176958i	−0.752406	+	0.658700i	$0.771107\pi$
$558$	14.2632	−	3.82183i	0.603811	−	0.161791i
$559$	16.1162	+	27.9140i	0.681641	+	1.18064i
$560$		0			0
$561$	−0.0329934	−	0.0906486i	−0.00139298	−	0.00382719i
$562$	12.4216	+	3.32835i	0.523972	+	0.140398i
$563$	−0.523526	−	1.95382i	−0.0220640	−	0.0823439i	0.954016	−	0.299756i	$-0.0969052\pi$
$563$	−0.523526	−	1.95382i	−0.0220640	−	0.0823439i	−0.976080	+	0.217412i	$0.930239\pi$
$564$	−0.134245	+	0.761341i	−0.00565273	+	0.0320582i
$565$		0			0
$566$	8.64975	−	10.3084i	0.363576	−	0.433293i
$567$	14.0122	+	9.81147i	0.588458	+	0.412043i
$568$	0.180720	+	0.387555i	0.00758284	+	0.0162615i
$569$	3.48375			0.146047			0.0730233	−	0.997330i	$-0.476735\pi$
$569$	3.48375			0.146047			0.0730233	+	0.997330i	$0.476735\pi$
$570$		0			0
$571$	30.6767			1.28378			0.641889	−	0.766797i	$-0.278151\pi$
$571$	30.6767			1.28378			0.641889	+	0.766797i	$0.278151\pi$
$572$	2.37570	+	5.09471i	0.0993331	+	0.213021i
$573$	−0.674294	−	0.472146i	−0.0281691	−	0.0197242i
$574$	1.60165	−	1.90878i	0.0668517	−	0.0796707i
$575$		0			0
$576$	0.519071	−	2.94380i	0.0216280	−	0.122658i
$577$	−5.96848	−	22.2747i	−0.248471	−	0.927306i	−0.971607	−	0.236601i	$-0.923967\pi$
$577$	−5.96848	−	22.2747i	−0.248471	−	0.927306i	0.723136	−	0.690706i	$-0.242700\pi$
$578$	−16.1584	−	4.32964i	−0.672103	−	0.180089i
$579$	0.699264	+	1.92121i	0.0290604	+	0.0798429i
$580$		0			0
$581$	6.87679	+	11.9109i	0.285297	+	0.494149i
$582$	1.11206	−	0.297976i	0.0460965	−	0.0123515i
$583$	4.92272	+	7.03038i	0.203878	+	0.291169i
$584$	2.85926	−	2.39921i	0.118317	−	0.0992799i
$585$		0			0
$586$	5.31832	+	30.1617i	0.219698	+	1.24597i
$587$	−42.3403	+	19.7436i	−1.74757	+	0.814907i	−0.761590	+	0.648059i	$0.775581\pi$
$587$	−42.3403	+	19.7436i	−1.74757	+	0.814907i	−0.985983	+	0.166848i	$0.946641\pi$
$588$	−0.243001	+	0.243001i	−0.0100212	+	0.0100212i
$589$	−12.5059	−	17.5286i	−0.515298	−	0.722253i
$590$		0			0
$591$	0.0543324	−	0.149277i	0.00223494	−	0.00614044i
$592$	−2.91898	+	4.16874i	−0.119969	+	0.171334i
$593$	−1.03815	−	11.8661i	−0.0426316	−	0.487282i	−0.987257	−	0.159132i	$-0.949130\pi$
$593$	−1.03815	−	11.8661i	−0.0426316	−	0.487282i	0.944626	−	0.328150i	$-0.106425\pi$
$594$	0.712676	+	0.849334i	0.0292415	+	0.0348486i
$595$		0			0
$596$	9.47926	−	16.4186i	0.388285	−	0.672530i
$597$	−0.615817	+	2.29826i	−0.0252037	+	0.0940615i
$598$	−24.3982	−	11.3771i	−0.997718	−	0.465244i
$599$	−18.5531	+	6.75277i	−0.758059	+	0.275911i	−0.691993	−	0.721905i	$-0.743267\pi$
$599$	−18.5531	+	6.75277i	−0.758059	+	0.275911i	−0.0660658	+	0.997815i	$0.521045\pi$
$600$		0			0
$601$	−36.8154	−	21.2554i	−1.50173	−	0.867026i	−0.999998	−	0.00200500i	$-0.999362\pi$
$601$	−36.8154	−	21.2554i	−1.50173	−	0.867026i	−0.501735	−	0.865021i	$-0.667305\pi$
$602$	−16.0832	+	11.2616i	−0.655502	+	0.458987i
$603$	1.31758	−	15.0600i	0.0536560	−	0.613291i
$604$	−8.19530	−	6.87668i	−0.333462	−	0.279808i
$605$		0			0
$606$	−0.0819231	−	0.0298176i	−0.00332790	−	0.00121126i
$607$	−29.3349	−	29.3349i	−1.19067	−	1.19067i	−0.976881	−	0.213785i	$-0.931421\pi$
$607$	−29.3349	−	29.3349i	−1.19067	−	1.19067i	−0.213785	−	0.976881i	$-0.568579\pi$
$608$	−4.28582	+	0.794818i	−0.173813	+	0.0322341i
$609$		−	0.0328540i		−	0.00133131i
$610$		0			0
$611$	−23.1189	+	4.07649i	−0.935292	+	0.164917i
$612$	−1.55175	+	0.135760i	−0.0627256	+	0.00548778i
$613$	19.8737	+	1.73872i	0.802691	+	0.0702263i	0.481115	−	0.876658i	$-0.340232\pi$
$613$	19.8737	+	1.73872i	0.802691	+	0.0702263i	0.321576	+	0.946884i	$0.395788\pi$
$614$	−0.395771	−	0.0697850i	−0.0159720	−	0.00281630i
$615$		0			0
$616$	−2.96545	+	1.71210i	−0.119481	+	0.0689826i
$617$	4.57175	−	9.80414i	0.184052	−	0.394700i	−0.792534	−	0.609827i	$-0.791239\pi$
$617$	4.57175	−	9.80414i	0.184052	−	0.394700i	0.976586	+	0.215127i	$0.0690166\pi$
$618$	−0.113923	+	0.244308i	−0.00458265	+	0.00982753i
$619$	16.1014	−	9.29617i	0.647171	−	0.373645i	−0.140200	−	0.990123i	$-0.544775\pi$
$619$	16.1014	−	9.29617i	0.647171	−	0.373645i	0.787372	+	0.616479i	$0.211441\pi$
$620$		0			0
$621$	−5.22896	−	0.922007i	−0.209831	−	0.0369988i
$622$	9.03397	+	0.790370i	0.362229	+	0.0316910i
$623$	−29.2893	+	2.56248i	−1.17345	+	0.102664i
$624$	−0.322658	+	0.0568933i	−0.0129167	+	0.00227756i
$625$		0			0
$626$			12.3725i			0.494503i
$627$	0.397270	−	0.702354i	0.0158655	−	0.0280493i
$628$	13.1206	+	13.1206i	0.523569	+	0.523569i
$629$	2.49199	+	0.907010i	0.0993621	+	0.0361648i
$630$		0			0
$631$	−16.6856	−	14.0009i	−0.664244	−	0.557367i	0.247112	−	0.968987i	$-0.420519\pi$
$631$	−16.6856	−	14.0009i	−0.664244	−	0.557367i	−0.911355	+	0.411620i	$0.864963\pi$
$632$	0.749714	−	8.56927i	0.0298220	−	0.340867i
$633$	1.47196	−	1.03067i	0.0585050	−	0.0409656i
$634$	−15.3137	−	8.84136i	−0.608184	−	0.351135i
$635$		0			0
$636$	−0.470054	+	0.171086i	−0.0186388	+	0.00678398i
$637$	−9.45773	−	4.41021i	−0.374729	−	0.174739i
$638$	−0.0759331	+	0.283386i	−0.00300622	+	0.0112194i
$639$	−0.639123	+	1.10699i	−0.0252833	+	0.0437920i
$640$		0			0
$641$	6.22809	+	7.42235i	0.245995	+	0.293165i	0.874887	−	0.484327i	$-0.160936\pi$
$641$	6.22809	+	7.42235i	0.245995	+	0.293165i	−0.628892	+	0.777493i	$0.716491\pi$
$642$	−0.0921375	−	1.05314i	−0.00363638	−	0.0415640i
$643$	−4.33747	+	6.19456i	−0.171053	+	0.244289i	−0.895521	−	0.445019i	$-0.853197\pi$
$643$	−4.33747	+	6.19456i	−0.171053	+	0.244289i	0.724468	+	0.689309i	$0.242086\pi$
$644$	5.60855	−	15.4094i	0.221008	−	0.607214i
$645$		0			0
$646$	0.978096	+	2.05004i	0.0384827	+	0.0806577i
$647$	18.6318	−	18.6318i	0.732490	−	0.732490i	−0.238623	−	0.971112i	$-0.576696\pi$
$647$	18.6318	−	18.6318i	0.732490	−	0.732490i	0.971112	+	0.238623i	$0.0766959\pi$
$648$	8.06887	−	3.76257i	0.316975	−	0.147808i
$649$	0.614952	+	3.48757i	0.0241390	+	0.136899i
$650$		0			0
$651$	0.755230	−	0.633713i	0.0295998	−	0.0248372i
$652$	−5.99656	−	8.56397i	−0.234843	−	0.335391i
$653$	22.7134	−	6.08605i	0.888845	−	0.238165i	0.214626	−	0.976696i	$-0.431147\pi$
$653$	22.7134	−	6.08605i	0.888845	−	0.238165i	0.674220	+	0.738531i	$0.264480\pi$
$654$	−0.147362	−	0.255238i	−0.00576230	−	0.00998060i
$655$		0			0
$656$	−0.443554	−	1.21866i	−0.0173179	−	0.0475805i
$657$	10.7771	+	2.88771i	0.420453	+	0.112660i
$658$	−3.70108	−	13.8126i	−0.144283	−	0.538472i
$659$	8.76570	−	49.7128i	0.341463	−	1.93653i	−0.00900473	−	0.999959i	$-0.502866\pi$
$659$	8.76570	−	49.7128i	0.341463	−	1.93653i	0.350468	−	0.936575i	$-0.386023\pi$
$660$		0			0
$661$	−19.7419	+	23.5275i	−0.767871	+	0.915114i	−0.998318	−	0.0579713i	$-0.981537\pi$
$661$	−19.7419	+	23.5275i	−0.767871	+	0.915114i	0.230447	+	0.973085i	$0.425981\pi$
$662$	20.1958	+	14.1412i	0.784931	+	0.549615i
$663$	0.0721538	+	0.154734i	0.00280222	+	0.00600939i
$664$	7.15830			0.277796
$665$		0			0
$666$	−15.2124			−0.589467
$667$	−0.593775	−	1.27336i	−0.0229911	−	0.0493045i
$668$	−15.4454	−	10.8150i	−0.597601	−	0.418444i
$669$	−0.420285	+	0.500876i	−0.0162492	+	0.0193650i
$670$		0			0
$671$	−3.47839	+	19.7269i	−0.134282	+	0.761550i
$672$	−0.0516539	−	0.192775i	−0.00199259	−	0.00743646i
$673$	−13.3017	−	3.56417i	−0.512741	−	0.137389i	−0.00683432	−	0.999977i	$-0.502175\pi$
$673$	−13.3017	−	3.56417i	−0.512741	−	0.137389i	−0.505907	+	0.862588i	$0.668842\pi$
$674$	9.50738	+	26.1213i	0.366211	+	1.00616i
$675$		0			0
$676$	1.52550	+	2.64224i	0.0586730	+	0.101625i
$677$	−7.44910	+	1.99598i	−0.286292	+	0.0767117i	−0.399107	−	0.916904i	$-0.630680\pi$
$677$	−7.44910	+	1.99598i	−0.286292	+	0.0767117i	0.112815	+	0.993616i	$0.464013\pi$
$678$	−0.144758	−	0.206736i	−0.00555941	−	0.00793966i
$679$	−16.3134	+	13.6885i	−0.626050	+	0.525318i
$680$		0			0
$681$	−0.334749	−	1.89846i	−0.0128276	−	0.0727491i
$682$	−7.97899	+	3.72066i	−0.305531	+	0.142472i
$683$	−4.60816	+	4.60816i	−0.176327	+	0.176327i	−0.789752	−	0.613426i	$-0.789791\pi$
$683$	−4.60816	+	4.60816i	−0.176327	+	0.176327i	0.613426	+	0.789752i	$0.289791\pi$
$684$	−9.29442	−	9.13159i	−0.355381	−	0.349155i
$685$		0			0
$686$	6.77407	−	18.6116i	0.258635	−	0.710595i
$687$	−0.967404	+	1.38160i	−0.0369088	+	0.0527112i
$688$	0.890632	+	10.1800i	0.0339550	+	0.388108i
$689$	−9.76377	−	11.6360i	−0.371970	−	0.443297i
$690$		0			0
$691$	11.0033	−	19.0583i	0.418585	−	0.725010i	−0.577213	−	0.816594i	$-0.695860\pi$
$691$	11.0033	−	19.0583i	0.418585	−	0.725010i	0.995797	+	0.0915838i	$0.0291929\pi$
$692$	−0.998707	+	3.72723i	−0.0379652	+	0.141688i
$693$	−9.27666	−	4.32578i	−0.352391	−	0.164323i
$694$	−6.37162	+	2.31908i	−0.241863	+	0.0880310i
$695$		0			0
$696$	−0.0148086	−	0.00854973i	−0.000561317	−	0.000324077i
$697$	−0.553579	+	0.387620i	−0.0209683	+	0.0146822i
$698$	−1.98516	+	22.6905i	−0.0751393	+	0.858847i
$699$	0.862392	+	0.723633i	0.0326187	+	0.0273703i
$700$		0			0
$701$	−18.7299	−	6.81713i	−0.707419	−	0.257480i	−0.0368440	−	0.999321i	$-0.511730\pi$
$701$	−18.7299	−	6.81713i	−0.707419	−	0.257480i	−0.670575	+	0.741841i	$0.733953\pi$
$702$	−1.38754	−	1.38754i	−0.0523693	−	0.0523693i
$703$	7.77088	+	20.7772i	0.293084	+	0.783626i
$704$			1.78219i			0.0671688i
$705$		0			0
$706$	18.2353	−	3.21538i	0.686295	−	0.121012i
$707$	1.60646	−	0.140547i	0.0604170	−	0.00528581i
$708$	−0.205619	−	0.0179893i	−0.00772763	−	0.000676080i
$709$	−14.9116	−	2.62931i	−0.560015	−	0.0987458i	−0.113526	−	0.993535i	$-0.536215\pi$
$709$	−14.9116	−	2.62931i	−0.560015	−	0.0987458i	−0.446489	+	0.894789i	$0.647326\pi$
$710$		0			0
$711$	22.2683	−	12.8566i	0.835126	−	0.482160i
$712$	−6.46707	+	13.8687i	−0.242364	+	0.519751i
$713$	17.8180	−	38.2109i	0.667290	−	1.43101i
$714$	−0.0900653	+	0.0519992i	−0.00337061	+	0.00194602i
$715$		0			0
$716$	−21.1185	−	3.72377i	−0.789237	−	0.139164i
$717$	−0.315867	−	0.0276348i	−0.0117963	−	0.00103204i
$718$	31.9967	−	2.79935i	1.19411	−	0.104471i
$719$	−48.3984	+	8.53394i	−1.80496	+	0.318262i	−0.971983	−	0.235052i	$-0.924474\pi$
$719$	−48.3984	+	8.53394i	−1.80496	+	0.318262i	−0.832973	+	0.553314i	$0.813363\pi$
$720$		0			0
$721$		−	4.98617i		−	0.185695i
$722$	−7.72417	+	17.3591i	−0.287464	+	0.646038i
$723$	−1.23735	−	1.23735i	−0.0460176	−	0.0460176i
$724$	16.8760	+	6.14237i	0.627192	+	0.228279i
$725$		0			0
$726$	0.622548	+	0.522380i	0.0231049	+	0.0193873i
$727$	−0.990839	+	11.3253i	−0.0367482	+	0.420034i	0.955431	+	0.295214i	$0.0953909\pi$
$727$	−0.990839	+	11.3253i	−0.0367482	+	0.420034i	−0.992179	+	0.124820i	$0.960165\pi$
$728$	4.96432	−	3.47606i	0.183990	−	0.128831i
$729$	22.8796	+	13.2096i	0.847393	+	0.489243i
$730$		0			0
$731$	5.00389	−	1.82127i	0.185076	−	0.0673620i
$732$	−1.05811	−	0.493405i	−0.0391089	−	0.0182368i
$733$	−13.7124	+	51.1753i	−0.506478	+	1.89020i	−0.0537475	+	0.998555i	$0.517117\pi$
$733$	−13.7124	+	51.1753i	−0.506478	+	1.89020i	−0.452731	+	0.891647i	$0.649550\pi$
$734$	−9.87403	+	17.1023i	−0.364457	+	0.631258i
$735$		0			0
$736$	−5.48606	−	6.53803i	−0.202219	−	0.240995i
$737$	0.785551	+	8.97889i	0.0289361	+	0.330742i
$738$	2.22353	−	3.17553i	0.0818492	−	0.116893i
$739$	−3.75242	+	10.3097i	−0.138035	+	0.379248i	−0.989379	−	0.145360i	$-0.953566\pi$
$739$	−3.75242	+	10.3097i	−0.138035	+	0.379248i	0.851344	+	0.524608i	$0.175788\pi$
$740$		0			0
$741$	−0.592093	+	1.29961i	−0.0217511	+	0.0477423i
$742$	6.54261	−	6.54261i	0.240187	−	0.240187i
$743$	38.0504	−	17.7432i	1.39593	−	0.650934i	0.428379	−	0.903599i	$-0.359085\pi$
$743$	38.0504	−	17.7432i	1.39593	−	0.650934i	0.967554	+	0.252665i	$0.0813072\pi$
$744$	−0.0891024	−	0.505325i	−0.00326665	−	0.0185261i
$745$		0			0
$746$	−16.6022	+	13.9309i	−0.607849	+	0.510046i
$747$	12.2732	+	17.5279i	0.449053	+	0.641314i
$748$	0.897052	−	0.240364i	0.0327995	−	0.00878859i
$749$	9.77720	+	16.9346i	0.357251	+	0.618777i
$750$		0			0
$751$	3.13558	+	8.61495i	0.114419	+	0.314364i	0.983663	−	0.180020i	$-0.0576161\pi$
$751$	3.13558	+	8.61495i	0.114419	+	0.314364i	−0.869244	+	0.494383i	$0.835394\pi$
$752$	−7.18903	−	1.92629i	−0.262157	−	0.0702447i
$753$	−0.577768	−	2.15626i	−0.0210550	−	0.0785785i
$754$	0.0901656	−	0.511355i	0.00328364	−	0.0186224i
$755$		0			0
$756$	0.768323	−	0.915652i	0.0279437	−	0.0333019i
$757$	−12.0138	−	8.41213i	−0.436648	−	0.305744i	0.334505	−	0.942394i	$-0.391431\pi$
$757$	−12.0138	−	8.41213i	−0.436648	−	0.305744i	−0.771153	+	0.636650i	$0.780320\pi$
$758$	4.67443	+	10.0244i	0.169783	+	0.364101i
$759$	1.57997			0.0573492
$760$		0			0
$761$	−33.8114			−1.22566			−0.612832	−	0.790213i	$-0.709970\pi$
$761$	−33.8114			−1.22566			−0.612832	+	0.790213i	$0.709970\pi$
$762$	0.0206985	+	0.0443880i	0.000749827	+	0.00160801i
$763$	4.46564	+	3.12688i	0.161667	+	0.113201i
$764$	5.09391	−	6.07069i	0.184291	−	0.219630i
$765$		0			0
$766$	3.99106	−	22.6344i	0.144203	−	0.817815i
$767$	−1.62220	−	6.05412i	−0.0585741	−	0.218601i
$768$	−0.100333	−	0.0268842i	−0.00362047	−	0.000970101i
$769$	8.99018	+	24.7003i	0.324194	+	0.890716i	0.989550	+	0.144190i	$0.0460575\pi$
$769$	8.99018	+	24.7003i	0.324194	+	0.890716i	−0.665356	+	0.746526i	$0.731720\pi$
$770$		0			0
$771$	0.261963	+	0.453733i	0.00943436	+	0.0163408i
$772$	−19.0122	+	5.09430i	−0.684263	+	0.183348i
$773$	19.1551	+	27.3564i	0.688962	+	0.983940i	0.999443	+	0.0333602i	$0.0106209\pi$
$773$	19.1551	+	27.3564i	0.688962	+	0.983940i	−0.310481	+	0.950579i	$0.600490\pi$
$774$	−23.3998	+	19.6348i	−0.841089	+	0.705758i
$775$		0			0
$776$	1.92466	+	10.9153i	0.0690913	+	0.391836i
$777$	−0.920498	+	0.429235i	−0.0330227	+	0.0153987i
$778$	19.6862	−	19.6862i	0.705783	−	0.705783i
$779$	−5.47300	−	1.41477i	−0.196091	−	0.0506895i
$780$		0			0
$781$	0.260653	−	0.716139i	0.00932691	−	0.0256255i
$782$	−2.55096	+	3.64315i	−0.0912223	+	0.130279i
$783$	−0.00892581	−	0.102023i	−0.000318983	−	0.00364599i
$784$	−2.12662	−	2.53440i	−0.0759506	−	0.0905144i
$785$		0			0
$786$	0.611412	−	1.05900i	0.0218083	−	0.0377731i
$787$	3.52489	−	13.1551i	0.125649	−	0.468927i	−0.874213	−	0.485542i	$-0.838622\pi$
$787$	3.52489	−	13.1551i	0.125649	−	0.468927i	0.999862	+	0.0166147i	$0.00528888\pi$
$788$	1.38606	+	0.646330i	0.0493763	+	0.0230245i
$789$	0.354287	−	0.128950i	0.0126129	−	0.00459074i
$790$		0			0
$791$	4.04285	+	2.33414i	0.143747	+	0.0829924i
$792$	−4.36390	+	3.05564i	−0.155064	+	0.108577i
$793$	3.08987	−	35.3174i	0.109724	−	1.25416i
$794$	−15.6681	−	13.1471i	−0.556039	−	0.466572i
$795$		0			0
$796$	−21.5248	−	7.83440i	−0.762928	−	0.277683i
$797$	−24.6145	−	24.6145i	−0.871892	−	0.871892i	0.120787	−	0.992679i	$-0.461458\pi$
$797$	−24.6145	−	24.6145i	−0.871892	−	0.871892i	−0.992679	+	0.120787i	$0.961458\pi$
$798$	−0.820063	−	0.290298i	−0.0290299	−	0.0102764i
$799$			3.87835i			0.137206i
$800$		0			0
$801$	−45.0471	+	7.94303i	−1.59166	+	0.280653i
$802$	33.8512	−	2.96159i	1.19533	−	0.104578i
$803$	−6.62672	−	0.579763i	−0.233852	−	0.0204594i
$804$	−0.517341	−	0.0912213i	−0.0182452	−	0.00321713i
$805$		0			0
$806$	13.4939	−	7.79073i	0.475304	−	0.274417i
$807$	0.923065	−	1.97952i	0.0324934	−	0.0696824i
$808$	0.354705	−	0.760668i	0.0124785	−	0.0267602i
$809$	−34.9127	+	20.1569i	−1.22747	+	0.708678i	−0.966499	−	0.256670i	$-0.917375\pi$
$809$	−34.9127	+	20.1569i	−1.22747	+	0.708678i	−0.260967	+	0.965348i	$0.584041\pi$
$810$		0			0
$811$	−20.2416	−	3.56915i	−0.710780	−	0.125330i	−0.193443	−	0.981111i	$-0.561966\pi$
$811$	−20.2416	−	3.56915i	−0.710780	−	0.125330i	−0.517337	+	0.855782i	$0.673077\pi$
$812$	0.315087	+	0.0275666i	0.0110574	+	0.000967397i
$813$	−0.608902	+	0.0532720i	−0.0213551	+	0.00186833i
$814$	8.93193	−	1.57494i	0.313064	−	0.0552017i
$815$		0			0
$816$			0.0541279i			0.00189486i
$817$	38.7706	+	21.9297i	1.35641	+	0.767224i
$818$	27.3841	+	27.3841i	0.957462	+	0.957462i
$819$	17.0231	+	6.19589i	0.594834	+	0.216502i
$820$		0			0
$821$	30.8956	+	25.9245i	1.07826	+	0.904771i	0.995776	−	0.0918205i	$-0.0292686\pi$
$821$	30.8956	+	25.9245i	1.07826	+	0.904771i	0.0824891	+	0.996592i	$0.473713\pi$
$822$	−0.161151	+	1.84196i	−0.00562077	+	0.0642457i
$823$	−37.5430	+	26.2879i	−1.30867	+	0.916338i	−0.999400	−	0.0346369i	$-0.988973\pi$
$823$	−37.5430	+	26.2879i	−1.30867	+	0.916338i	−0.309267	+	0.950975i	$0.600084\pi$
$824$	−2.24746	−	1.29757i	−0.0782940	−	0.0452031i
$825$		0			0
$826$	3.58764	−	1.30579i	0.124830	−	0.0454344i
$827$	−51.3898	−	23.9634i	−1.78700	−	0.833290i	−0.964301	−	0.264810i	$-0.914691\pi$
$827$	−51.3898	−	23.9634i	−1.78700	−	0.833290i	−0.822696	−	0.568481i	$-0.807531\pi$
$828$	6.60307	−	24.6430i	0.229472	−	0.856403i
$829$	6.55890	−	11.3603i	0.227800	−	0.394561i	−0.729356	−	0.684135i	$-0.760180\pi$
$829$	6.55890	−	11.3603i	0.227800	−	0.394561i	0.957156	+	0.289573i	$0.0935134\pi$
$830$		0			0
$831$	0.297178	+	0.354163i	0.0103090	+	0.0122858i
$832$	−0.274907	−	3.14220i	−0.00953069	−	0.108936i
$833$	−0.988856	+	1.41223i	−0.0342618	+	0.0489309i
$834$	0.0175229	−	0.0481439i	0.000606770	−	0.00166709i
$835$		0			0
$836$	6.40261	+	4.39936i	0.221439	+	0.152155i
$837$	2.17307	−	2.17307i	0.0751123	−	0.0751123i
$838$	−4.12238	+	1.92230i	−0.142405	+	0.0664047i
$839$	−1.14937	−	6.51838i	−0.0396805	−	0.225039i	0.958518	−	0.285031i	$-0.0920038\pi$
$839$	−1.14937	−	6.51838i	−0.0396805	−	0.225039i	−0.998199	+	0.0599913i	$0.980893\pi$
$840$		0			0
$841$	−22.1945	+	18.6234i	−0.765329	+	0.642187i
$842$	22.5565	+	32.2140i	0.777347	+	1.11017i
$843$	1.29026	−	0.345724i	0.0444389	−	0.0119074i
$844$	8.64966	+	14.9816i	0.297733	+	0.515689i
$845$		0			0
$846$	−7.60912	−	20.9059i	−0.261607	−	0.718759i
$847$	−14.5200	−	3.89063i	−0.498914	−	0.133684i
$848$	−1.24640	−	4.65162i	−0.0428015	−	0.159737i
$849$	0.242721	−	1.37654i	0.00833017	−	0.0472427i
$850$		0			0
$851$	−27.9190	+	33.2726i	−0.957053	+	1.14057i
$852$	0.0363851	+	0.0254771i	0.00124653	+	0.000872832i
$853$	0.531905	+	1.14067i	0.0182121	+	0.0390559i	0.915203	−	0.402992i	$-0.132030\pi$
$853$	0.531905	+	1.14067i	0.0182121	+	0.0390559i	−0.896991	+	0.442048i	$0.854252\pi$
$854$	21.5953			0.738977
$855$		0			0
$856$	10.1774			0.347858
$857$	−22.7388	−	48.7636i	−0.776744	−	1.66573i	−0.745761	−	0.666213i	$-0.767914\pi$
$857$	−22.7388	−	48.7636i	−0.776744	−	1.66573i	−0.0309831	−	0.999520i	$-0.509864\pi$
$858$	0.478310	+	0.334916i	0.0163292	+	0.0114339i
$859$	−21.7618	+	25.9347i	−0.742502	+	0.884880i	−0.996608	−	0.0822966i	$-0.973775\pi$
$859$	−21.7618	+	25.9347i	−0.742502	+	0.884880i	0.254105	+	0.967177i	$0.418219\pi$
$860$		0			0
$861$	0.0449441	−	0.254890i	0.00153169	−	0.00868664i
$862$	−0.847541	−	3.16307i	−0.0288674	−	0.107735i
$863$	18.2893	+	4.90060i	0.622575	+	0.166818i	0.556298	−	0.830983i	$-0.312221\pi$
$863$	18.2893	+	4.90060i	0.622575	+	0.166818i	0.0662768	+	0.997801i	$0.478888\pi$
$864$	−0.212776	−	0.584597i	−0.00723878	−	0.0198884i
$865$		0			0
$866$	−12.0027	−	20.7892i	−0.407867	−	0.706447i
$867$	−1.67842	+	0.449732i	−0.0570022	+	0.0152737i
$868$	5.44396	+	7.77478i	0.184780	+	0.263893i
$869$	−11.7438	+	9.85419i	−0.398380	+	0.334281i
$870$		0			0
$871$	−2.77003	−	15.7096i	−0.0938589	−	0.532300i
$872$	2.57152	−	1.19912i	0.0870826	−	0.0406073i
$873$	−23.4275	+	23.4275i	−0.792900	+	0.792900i
$874$	−37.0306	+	3.56976i	−1.25258	+	0.120749i
$875$		0			0
$876$	0.132603	−	0.364324i	0.00448024	−	0.0123094i
$877$	−11.1881	+	15.9782i	−0.377794	+	0.539546i	−0.962352	−	0.271806i	$-0.912379\pi$
$877$	−11.1881	+	15.9782i	−0.377794	+	0.539546i	0.584558	+	0.811352i	$0.301268\pi$
$878$	2.88663	+	32.9943i	0.0974189	+	1.11350i
$879$	2.04490	+	2.43702i	0.0689729	+	0.0821987i
$880$		0			0
$881$	−5.67227	+	9.82465i	−0.191103	+	0.331001i	−0.945616	−	0.325284i	$-0.894540\pi$
$881$	−5.67227	+	9.82465i	−0.191103	+	0.331001i	0.754513	+	0.656285i	$0.227873\pi$
$882$	2.55961	−	9.55261i	0.0861866	−	0.321653i
$883$	6.43499	+	3.00069i	0.216555	+	0.100981i	0.527869	−	0.849326i	$-0.322991\pi$
$883$	6.43499	+	3.00069i	0.216555	+	0.100981i	−0.311314	+	0.950307i	$0.600769\pi$
$884$	−1.54453	+	0.562162i	−0.0519481	+	0.0189076i
$885$		0			0
$886$	−6.30884	−	3.64241i	−0.211949	−	0.122369i
$887$	6.62683	−	4.64015i	0.222507	−	0.155801i	−0.457008	−	0.889462i	$-0.651079\pi$
$887$	6.62683	−	4.64015i	0.222507	−	0.155801i	0.679515	+	0.733661i	$0.262190\pi$
$888$	−0.0460720	+	0.526606i	−0.00154608	+	0.0176717i
$889$	−0.693982	−	0.582320i	−0.0232754	−	0.0195304i
$890$		0			0
$891$	−14.9100	−	5.42678i	−0.499503	−	0.181804i
$892$	−4.45103	−	4.45103i	−0.149031	−	0.149031i
$893$	−24.6665	+	21.0719i	−0.825434	+	0.705144i
$894$		−	1.96927i		−	0.0658623i
$895$		0			0
$896$	1.89216	−	0.333638i	0.0632125	−	0.0111461i
$897$	−2.78566	+	0.243714i	−0.0930105	+	0.00813736i
$898$	26.6585	+	2.33232i	0.889607	+	0.0778305i
$899$	0.800849	+	0.141211i	0.0267098	+	0.00470966i
$900$		0			0
$901$	−2.17326	+	1.25473i	−0.0724017	+	0.0418011i
$902$	−0.976781	+	2.09471i	−0.0325233	+	0.0697463i
$903$	−0.861901	+	1.84835i	−0.0286823	+	0.0615093i
$904$	2.10417	−	1.21484i	0.0699838	−	0.0404051i
$905$		0			0
$906$	−1.09437	−	0.192967i	−0.0363580	−	0.00641089i
$907$	16.7816	+	1.46820i	0.557225	+	0.0487508i	0.362290	−	0.932065i	$-0.381995\pi$
$907$	16.7816	+	1.46820i	0.557225	+	0.0487508i	0.194935	+	0.980816i	$0.437551\pi$
$908$	18.4881	−	1.61750i	0.613550	−	0.0536786i
$909$	2.47074	−	0.435658i	0.0819493	−	0.0144499i
$910$		0			0
$911$		−	39.7727i		−	1.31773i	−0.752261	−	0.658865i	$-0.771037\pi$
$911$		−	39.7727i		−	1.31773i	0.752261	−	0.658865i	$-0.228963\pi$
$912$	−0.344257	+	0.294089i	−0.0113995	+	0.00973825i
$913$	−9.02088	−	9.02088i	−0.298547	−	0.298547i
$914$	29.9784	+	10.9113i	0.991599	+	0.360912i
$915$		0			0
$916$	−12.4385	−	10.4372i	−0.410981	−	0.344854i
$917$	−1.97135	+	22.5327i	−0.0650998	+	0.744094i
$918$	−0.265556	+	0.185944i	−0.00876464	+	0.00613707i
$919$	30.8139	+	17.7904i	1.01646	+	0.586852i	0.913076	−	0.407790i	$-0.133700\pi$
$919$	30.8139	+	17.7904i	1.01646	+	0.586852i	0.103381	+	0.994642i	$0.467034\pi$
$920$		0			0
$921$	−0.0392265	+	0.0142773i	−0.00129256	+	0.000470452i
$922$	24.9401	+	11.6298i	0.821359	+	0.383006i
$923$	−0.349095	+	1.30284i	−0.0114906	+	0.0428835i
$924$	−0.177841	+	0.308029i	−0.00585053	+	0.0101334i
$925$		0			0
$926$	5.80334	+	6.91615i	0.190710	+	0.227279i
$927$	−0.676105	−	7.72791i	−0.0222062	−	0.253818i
$928$	0.0944218	−	0.134848i	0.00309955	−	0.00442661i
$929$	6.19520	−	17.0212i	0.203258	−	0.558447i	−0.795620	−	0.605795i	$-0.792855\pi$
$929$	6.19520	−	17.0212i	0.203258	−	0.558447i	0.998878	+	0.0473487i	$0.0150772\pi$
$930$		0			0
$931$	−14.3546	+	1.38378i	−0.470452	+	0.0453516i
$932$	−7.66363	+	7.66363i	−0.251031	+	0.251031i
$933$	0.853712	−	0.398093i	0.0279493	−	0.0130330i
$934$	2.73438	+	15.5074i	0.0894717	+	0.507419i
$935$		0			0
$936$	7.22271	−	6.06057i	0.236082	−	0.198096i
$937$	3.93685	+	5.62240i	0.128611	+	0.183676i	0.878293	−	0.478122i	$-0.158682\pi$
$937$	3.93685	+	5.62240i	0.128611	+	0.183676i	−0.749682	+	0.661798i	$0.769794\pi$
$938$	9.38586	−	2.51493i	0.306459	−	0.0821155i
$939$	0.642580	+	1.11298i	0.0209698	+	0.0363208i
$940$		0			0
$941$	−6.63496	−	18.2294i	−0.216294	−	0.594262i	0.783333	−	0.621603i	$-0.213518\pi$
$941$	−6.63496	−	18.2294i	−0.216294	−	0.594262i	−0.999626	+	0.0273411i	$0.991296\pi$
$942$	1.86172	+	0.498846i	0.0606581	+	0.0162533i
$943$	−2.86473	−	10.6913i	−0.0932886	−	0.348158i
$944$	0.345054	−	1.95690i	0.0112306	−	0.0636917i
$945$		0			0
$946$	11.7064	−	13.9511i	0.380608	−	0.453591i
$947$	30.8052	+	21.5700i	1.00103	+	0.700932i	0.954570	−	0.297988i	$-0.0963156\pi$
$947$	30.8052	+	21.5700i	1.00103	+	0.700932i	0.0464647	+	0.998920i	$0.485204\pi$
$948$	−0.377615	−	0.809798i	−0.0122644	−	0.0263010i
$949$	11.7731			0.382170
$950$		0			0
$951$	−1.83675			−0.0595607
$952$	−0.423130	−	0.907406i	−0.0137137	−	0.0294092i
$953$	43.7442	+	30.6300i	1.41701	+	0.992203i	0.996383	+	0.0849706i	$0.0270796\pi$
$953$	43.7442	+	30.6300i	1.41701	+	0.992203i	0.420629	+	0.907233i	$0.361809\pi$
$954$	9.25304	−	11.0273i	0.299578	−	0.357023i
$955$		0			0
$956$	0.530065	−	3.00615i	0.0171435	−	0.0972257i
$957$	0.00788737	+	0.0294361i	0.000254963	+	0.000951533i
$958$	−22.2028	−	5.94921i	−0.717338	−	0.192210i
$959$	−11.6975	−	32.1385i	−0.377731	−	1.03781i
$960$		0			0
$961$	−3.29870	−	5.71351i	−0.106410	−	0.184307i
$962$	−15.5051	+	4.15457i	−0.499904	+	0.133949i
$963$	17.4497	+	24.9207i	0.562307	+	0.803058i
$964$	12.9051	−	10.8287i	0.415645	−	0.348768i
$965$		0			0
$966$	−0.295781	−	1.67746i	−0.00951660	−	0.0539713i
$967$	−24.7726	+	11.5517i	−0.796634	+	0.371477i	−0.777932	−	0.628349i	$-0.783731\pi$
$967$	−24.7726	+	11.5517i	−0.796634	+	0.371477i	−0.0187021	+	0.999825i	$0.505953\pi$
$968$	−5.53226	+	5.53226i	−0.177814	+	0.177814i
$969$	0.194457	+	0.133615i	0.00624687	+	0.00429235i
$970$		0			0
$971$	−14.1795	+	38.9579i	−0.455043	+	1.25022i	0.474091	+	0.880476i	$0.342777\pi$
$971$	−14.1795	+	38.9579i	−0.455043	+	1.25022i	−0.929134	+	0.369744i	$0.879445\pi$
$972$	1.60092	−	2.28636i	0.0513497	−	0.0733349i
$973$	0.0825954	+	0.944070i	0.00264789	+	0.0302655i
$974$	13.5739	+	16.1767i	0.434936	+	0.518336i
$975$		0			0
$976$	5.61984	−	9.73386i	0.179887	−	0.311573i
$977$	9.69583	−	36.1853i	0.310197	−	1.15767i	−0.618181	−	0.786035i	$-0.712130\pi$
$977$	9.69583	−	36.1853i	0.310197	−	1.15767i	0.928379	−	0.371636i	$-0.121203\pi$
$978$	−0.984210	−	0.458945i	−0.0314716	−	0.0146754i
$979$	25.6271	−	9.32749i	0.819045	−	0.298108i
$980$		0			0
$981$	7.34515	+	4.24073i	0.234513	+	0.135396i
$982$	−32.0691	+	22.4550i	−1.02336	+	0.716568i
$983$	−3.41567	+	39.0413i	−0.108943	+	1.24522i	0.723191	+	0.690648i	$0.242675\pi$
$983$	−3.41567	+	39.0413i	−0.108943	+	1.24522i	−0.832134	+	0.554575i	$0.812881\pi$
$984$	−0.103193	−	0.0865892i	−0.00328967	−	0.00276036i
$985$		0			0
$986$	−0.0806096	−	0.0293395i	−0.00256713	−	0.000934360i
$987$	−1.05031	−	1.05031i	−0.0334318	−	0.0334318i
$988$	−11.9671	−	6.76894i	−0.380725	−	0.215349i
$989$			87.2158i			2.77330i
$990$		0			0
$991$	−17.9511	+	3.16526i	−0.570234	+	0.100548i	−0.451329	−	0.892358i	$-0.649050\pi$
$991$	−17.9511	+	3.16526i	−0.570234	+	0.100548i	−0.118906	+	0.992906i	$0.537939\pi$
$992$	4.92110	−	0.430541i	0.156245	−	0.0136697i
$993$	2.55118	+	0.223200i	0.0809593	+	0.00708302i
$994$	−0.809124	−	0.142670i	−0.0256639	−	0.00452523i
$995$		0			0
$996$	0.643935	−	0.371776i	0.0204038	−	0.0117802i
$997$	7.84572	−	16.8252i	0.248477	−	0.532860i	−0.742023	−	0.670374i	$-0.766134\pi$
$997$	7.84572	−	16.8252i	0.248477	−	0.532860i	0.990500	+	0.137515i	$0.0439114\pi$
$998$	−1.86710	+	4.00401i	−0.0591020	+	0.126745i
$999$	−2.74184	+	1.58300i	−0.0867479	+	0.0500839i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.bb.c.243.5	yes	72
5.2	odd	4	inner	950.2.bb.c.357.2	yes	72
5.3	odd	4	inner	950.2.bb.c.357.5	yes	72
5.4	even	2	inner	950.2.bb.c.243.2	✓	72
19.14	odd	18	inner	950.2.bb.c.793.2	yes	72
95.14	odd	18	inner	950.2.bb.c.793.5	yes	72
95.33	even	36	inner	950.2.bb.c.907.2	yes	72
95.52	even	36	inner	950.2.bb.c.907.5	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.bb.c.243.2	✓	72	5.4	even	2	inner
950.2.bb.c.243.5	yes	72	1.1	even	1	trivial
950.2.bb.c.357.2	yes	72	5.2	odd	4	inner
950.2.bb.c.357.5	yes	72	5.3	odd	4	inner
950.2.bb.c.793.2	yes	72	19.14	odd	18	inner
950.2.bb.c.793.5	yes	72	95.14	odd	18	inner
950.2.bb.c.907.2	yes	72	95.33	even	36	inner
950.2.bb.c.907.5	yes	72	95.52	even	36	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.bb (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.422618 + 0.906308i) q^{2} +(0.0850875 + 0.0595789i) q^{3} +(-0.642788 + 0.766044i) q^{4} +(-0.0180373 + 0.102295i) q^{6} +(-0.497281 - 1.85588i) q^{7} +(-0.965926 - 0.258819i) q^{8} +(-1.02237 - 2.80894i) q^{9} +O(q^{10})\)	\(q+(0.422618 + 0.906308i) q^{2} +(0.0850875 + 0.0595789i) q^{3} +(-0.642788 + 0.766044i) q^{4} +(-0.0180373 + 0.102295i) q^{6} +(-0.497281 - 1.85588i) q^{7} +(-0.965926 - 0.258819i) q^{8} +(-1.02237 - 2.80894i) q^{9} +(0.891095 + 1.54342i) q^{11} +(-0.100333 + 0.0268842i) q^{12} +(-1.80918 - 2.58377i) q^{13} +(1.47184 - 1.23502i) q^{14} +(-0.173648 - 0.984808i) q^{16} +(-0.472276 + 0.220226i) q^{17} +(2.11369 - 2.11369i) q^{18} +(-3.96663 - 1.80717i) q^{19} +(0.0682588 - 0.187540i) q^{21} +(-1.02222 + 1.45988i) q^{22} +(-0.743856 - 8.50231i) q^{23} +(-0.0667681 - 0.0795711i) q^{24} +(1.57710 - 2.73162i) q^{26} +(0.161015 - 0.600917i) q^{27} +(1.74133 + 0.811996i) q^{28} +(0.154692 - 0.0563031i) q^{29} +(4.27808 + 2.46995i) q^{31} +(0.819152 - 0.573576i) q^{32} +(-0.0161343 + 0.184416i) q^{33} +(-0.399185 - 0.334956i) q^{34} +(2.80894 + 1.02237i) q^{36} +(-3.59853 - 3.59853i) q^{37} +(-0.0385181 - 4.35873i) q^{38} -0.327636i q^{39} +(1.27716 - 0.225198i) q^{41} +(0.198816 - 0.0173941i) q^{42} +(-10.1800 - 0.890632i) q^{43} +(-1.75511 - 0.309474i) q^{44} +(7.39135 - 4.26740i) q^{46} +(3.14539 - 6.74531i) q^{47} +(0.0438985 - 0.0941406i) q^{48} +(2.86518 - 1.65421i) q^{49} +(-0.0533056 - 0.00939921i) q^{51} +(3.14220 + 0.274907i) q^{52} +(4.79738 - 0.419717i) q^{53} +(0.612664 - 0.108029i) q^{54} +1.92135i q^{56} +(-0.229841 - 0.390095i) q^{57} +(0.116403 + 0.116403i) q^{58} +(1.86725 + 0.679624i) q^{59} +(8.61010 + 7.22473i) q^{61} +(-0.430541 + 4.92110i) q^{62} +(-4.70464 + 3.29423i) q^{63} +(0.866025 + 0.500000i) q^{64} +(-0.173957 + 0.0633150i) q^{66} +(4.58353 + 2.13734i) q^{67} +(0.134870 - 0.503343i) q^{68} +(0.443266 - 0.767759i) q^{69} +(-0.274869 - 0.327576i) q^{71} +(0.260527 + 2.97784i) q^{72} +(-2.14088 + 3.05749i) q^{73} +(1.74057 - 4.78218i) q^{74} +(3.93407 - 1.87699i) q^{76} +(2.42128 - 2.42128i) q^{77} +(0.296939 - 0.138465i) q^{78} +(1.49372 + 8.47132i) q^{79} +(-6.82010 + 5.72274i) q^{81} +(0.743852 + 1.06233i) q^{82} +(-6.91439 + 1.85270i) q^{83} +(0.0997877 + 0.172837i) q^{84} +(-3.49505 - 9.60258i) q^{86} +(0.0165168 + 0.00442566i) q^{87} +(-0.461265 - 1.72146i) q^{88} +(2.65723 - 15.0699i) q^{89} +(-3.89550 + 4.64247i) q^{91} +(6.99129 + 4.89536i) q^{92} +(0.216854 + 0.465045i) q^{93} +7.44263 q^{94} +0.103873 q^{96} +(-4.68417 - 10.0452i) q^{97} +(2.71010 + 1.89764i) q^{98} +(3.42435 - 4.08098i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 24 q^{6}+O(q^{10}) \) 72 * q + 24 * q^6	\( 72 q + 24 q^{6} + 24 q^{21} + 12 q^{26} + 36 q^{31} - 24 q^{36} + 48 q^{41} - 36 q^{46} + 156 q^{51} + 168 q^{61} - 36 q^{66} - 84 q^{71} - 48 q^{76} - 60 q^{81} - 60 q^{86} - 264 q^{91} + 24 q^{96}+O(q^{100}) \) 72 * q + 24 * q^6 + 24 * q^21 + 12 * q^26 + 36 * q^31 - 24 * q^36 + 48 * q^41 - 36 * q^46 + 156 * q^51 + 168 * q^61 - 36 * q^66 - 84 * q^71 - 48 * q^76 - 60 * q^81 - 60 * q^86 - 264 * q^91 + 24 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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