LMFDB - Embedded newform 702.2.bc.a.665.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [702,2,Mod(305,702)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("702.305"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(702, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([2, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 702 = 2 \cdot 3^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	702.bc (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$5.60549822189$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 234)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			665.9
Character	$\chi$	$=$	702.665
Dual form			702.2.bc.a.683.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.965926 - 0.258819i) q^{2} +(0.866025 - 0.500000i) q^{4} +(-2.84756 + 0.763001i) q^{5} +(-1.37958 - 1.37958i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.55305 + 1.47400i) q^{10} +(-0.207457 - 0.774238i) q^{11} +(-3.58657 - 0.369493i) q^{13} +(-1.68964 - 0.975511i) q^{14} +(0.500000 - 0.866025i) q^{16} +(4.02058 - 6.96385i) q^{17} +(-1.18319 - 4.41574i) q^{19} +(-2.08456 + 2.08456i) q^{20} +(-0.400775 - 0.694163i) q^{22} -6.99376 q^{23} +(3.19629 - 1.84538i) q^{25} +(-3.55999 + 0.571370i) q^{26} +(-1.88454 - 0.504962i) q^{28} +(-6.82146 - 3.93837i) q^{29} +(0.619046 + 2.31031i) q^{31} +(0.258819 - 0.965926i) q^{32} +(2.08121 - 7.76717i) q^{34} +(4.98106 + 2.87582i) q^{35} +(-2.09658 + 7.82455i) q^{37} +(-2.28576 - 3.95904i) q^{38} +(-1.47400 + 2.55305i) q^{40} +(3.66359 + 3.66359i) q^{41} +2.33382i q^{43} +(-0.566782 - 0.566782i) q^{44} +(-6.75546 + 1.81012i) q^{46} +(5.14869 + 1.37959i) q^{47} -3.19351i q^{49} +(2.60976 - 2.60976i) q^{50} +(-3.29081 + 1.47329i) q^{52} -8.27924i q^{53} +(1.18149 + 2.04640i) q^{55} -1.95102 q^{56} +(-7.60835 - 2.03865i) q^{58} +(8.52709 + 2.28483i) q^{59} -4.93917 q^{61} +(1.19590 + 2.07137i) q^{62} -1.00000i q^{64} +(10.4949 - 1.68440i) q^{65} +(0.549015 - 0.549015i) q^{67} -8.04117i q^{68} +(5.55565 + 1.48863i) q^{70} +(2.57304 - 0.689443i) q^{71} +(5.68293 + 5.68293i) q^{73} +8.10057i q^{74} +(-3.23255 - 3.23255i) q^{76} +(-0.781921 + 1.35433i) q^{77} +(0.554497 + 0.960416i) q^{79} +(-0.763001 + 2.84756i) q^{80} +(4.48696 + 2.59055i) q^{82} +(-0.614312 + 2.29264i) q^{83} +(-6.13542 + 22.8977i) q^{85} +(0.604036 + 2.25429i) q^{86} +(-0.694163 - 0.400775i) q^{88} +(2.84070 + 0.761164i) q^{89} +(4.43822 + 5.45771i) q^{91} +(-6.05678 + 3.49688i) q^{92} +5.33031 q^{94} +(6.73843 + 11.6713i) q^{95} +(2.59780 - 2.59780i) q^{97} +(-0.826542 - 3.08469i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 8 q^{7} + 24 q^{11} + 28 q^{16} - 8 q^{19} - 4 q^{28} - 4 q^{31} + 24 q^{35} - 4 q^{37} - 36 q^{38} + 48 q^{41} + 36 q^{47} + 24 q^{50} + 8 q^{52} + 36 q^{65} + 28 q^{67} + 24 q^{71} + 28 q^{73}+ \cdots - 48 q^{98}+O(q^{100}) $ 56 * q - 8 * q^7 + 24 * q^11 + 28 * q^16 - 8 * q^19 - 4 * q^28 - 4 * q^31 + 24 * q^35 - 4 * q^37 - 36 * q^38 + 48 * q^41 + 36 * q^47 + 24 * q^50 + 8 * q^52 + 36 * q^65 + 28 * q^67 + 24 * q^71 + 28 * q^73 + 4 * q^76 - 24 * q^77 - 24 * q^79 + 96 * q^83 - 72 * q^85 + 4 * q^91 + 24 * q^92 - 52 * q^97 - 48 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/702\mathbb{Z}\right)^\times$.

$n$	$379$	$677$
$\chi(n)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$3$		0			0
$3$		0			0
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$	−2.84756	+	0.763001i	−1.27347	+	0.341224i	−0.831358	−	0.555737i	$-0.812436\pi$
$5$	−2.84756	+	0.763001i	−1.27347	+	0.341224i	−0.442109	+	0.896962i	$0.645769\pi$
$6$		0			0
$7$	−1.37958	−	1.37958i	−0.521433	−	0.521433i	0.396571	−	0.918004i	$-0.370200\pi$
$7$	−1.37958	−	1.37958i	−0.521433	−	0.521433i	−0.918004	+	0.396571i	$0.870200\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$		0			0
$10$	−2.55305	+	1.47400i	−0.807345	+	0.466121i
$11$	−0.207457	−	0.774238i	−0.0625505	−	0.233442i	0.927572	−	0.373643i	$-0.121892\pi$
$11$	−0.207457	−	0.774238i	−0.0625505	−	0.233442i	−0.990123	+	0.140202i	$0.955225\pi$
$12$		0			0
$13$	−3.58657	−	0.369493i	−0.994735	−	0.102479i
$13$	−3.58657	−	0.369493i	−0.994735	−	0.102479i
$14$	−1.68964	−	0.975511i	−0.451574	−	0.260716i
$15$		0			0
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	4.02058	−	6.96385i	0.975135	−	1.68898i	0.295645	−	0.955298i	$-0.404465\pi$
$17$	4.02058	−	6.96385i	0.975135	−	1.68898i	0.679490	−	0.733685i	$-0.262201\pi$
$18$		0			0
$19$	−1.18319	−	4.41574i	−0.271443	−	1.01304i	−0.958188	−	0.286141i	$-0.907627\pi$
$19$	−1.18319	−	4.41574i	−0.271443	−	1.01304i	0.686744	−	0.726899i	$-0.259039\pi$
$20$	−2.08456	+	2.08456i	−0.466121	+	0.466121i
$21$		0			0
$22$	−0.400775	−	0.694163i	−0.0854456	−	0.147996i
$23$	−6.99376			−1.45830			−0.729150	−	0.684354i	$-0.760084\pi$
$23$	−6.99376			−1.45830			−0.729150	+	0.684354i	$0.760084\pi$
$24$		0			0
$25$	3.19629	−	1.84538i	0.639258	−	0.369076i
$26$	−3.55999	+	0.571370i	−0.698172	+	0.112055i
$27$		0			0
$28$	−1.88454	−	0.504962i	−0.356145	−	0.0954288i
$29$	−6.82146	−	3.93837i	−1.26671	−	0.731337i	−0.292348	−	0.956312i	$-0.594437\pi$
$29$	−6.82146	−	3.93837i	−1.26671	−	0.731337i	−0.974365	+	0.224975i	$0.927770\pi$
$30$		0			0
$31$	0.619046	+	2.31031i	0.111184	+	0.414944i	0.998973	−	0.0453062i	$-0.0144263\pi$
$31$	0.619046	+	2.31031i	0.111184	+	0.414944i	−0.887789	+	0.460250i	$0.847760\pi$
$32$	0.258819	−	0.965926i	0.0457532	−	0.170753i
$33$		0			0
$34$	2.08121	−	7.76717i	0.356924	−	1.33206i
$35$	4.98106	+	2.87582i	0.841953	+	0.486102i
$36$		0			0
$37$	−2.09658	+	7.82455i	−0.344676	+	1.28635i	0.548314	+	0.836272i	$0.315270\pi$
$37$	−2.09658	+	7.82455i	−0.344676	+	1.28635i	−0.892990	+	0.450076i	$0.851397\pi$
$38$	−2.28576	−	3.95904i	−0.370798	−	0.642242i
$39$		0			0
$40$	−1.47400	+	2.55305i	−0.233061	+	0.403673i
$41$	3.66359	+	3.66359i	0.572156	+	0.572156i	0.932730	−	0.360574i	$-0.117419\pi$
$41$	3.66359	+	3.66359i	0.572156	+	0.572156i	−0.360574	+	0.932730i	$0.617419\pi$
$42$		0			0
$43$			2.33382i			0.355904i	0.984039	+	0.177952i	$0.0569471\pi$
$43$			2.33382i			0.355904i	−0.984039	+	0.177952i	$0.943053\pi$
$44$	−0.566782	−	0.566782i	−0.0854456	−	0.0854456i
$45$		0			0
$46$	−6.75546	+	1.81012i	−0.996038	+	0.266887i
$47$	5.14869	+	1.37959i	0.751013	+	0.201233i	0.613968	−	0.789331i	$-0.289573\pi$
$47$	5.14869	+	1.37959i	0.751013	+	0.201233i	0.137046	+	0.990565i	$0.456239\pi$
$48$		0			0
$49$		−	3.19351i		−	0.456216i
$50$	2.60976	−	2.60976i	0.369076	−	0.369076i
$51$		0			0
$52$	−3.29081	+	1.47329i	−0.456353	+	0.204309i
$53$		−	8.27924i		−	1.13724i	−0.822600	−	0.568620i	$-0.807477\pi$
$53$		−	8.27924i		−	1.13724i	0.822600	−	0.568620i	$-0.192523\pi$
$54$		0			0
$55$	1.18149	+	2.04640i	0.159312	+	0.275936i
$56$	−1.95102			−0.260716
$57$		0			0
$58$	−7.60835	−	2.03865i	−0.999025	−	0.267688i
$59$	8.52709	+	2.28483i	1.11013	+	0.297459i	0.766884	−	0.641786i	$-0.221806\pi$
$59$	8.52709	+	2.28483i	1.11013	+	0.297459i	0.343248	+	0.939245i	$0.388473\pi$
$60$		0			0
$61$	−4.93917			−0.632396			−0.316198	−	0.948693i	$-0.602406\pi$
$61$	−4.93917			−0.632396			−0.316198	+	0.948693i	$0.602406\pi$
$62$	1.19590	+	2.07137i	0.151880	+	0.263064i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	10.4949	−	1.68440i	1.30173	−	0.208924i
$66$		0			0
$67$	0.549015	−	0.549015i	0.0670729	−	0.0670729i	−0.672775	−	0.739847i	$-0.734898\pi$
$67$	0.549015	−	0.549015i	0.0670729	−	0.0670729i	0.739847	+	0.672775i	$0.234898\pi$
$68$		−	8.04117i		−	0.975135i
$69$		0			0
$70$	5.55565	+	1.48863i	0.664027	+	0.177926i
$71$	2.57304	−	0.689443i	0.305363	−	0.0818218i	−0.102884	−	0.994693i	$-0.532807\pi$
$71$	2.57304	−	0.689443i	0.305363	−	0.0818218i	0.408247	+	0.912872i	$0.366140\pi$
$72$		0			0
$73$	5.68293	+	5.68293i	0.665137	+	0.665137i	0.956586	−	0.291449i	$-0.0941375\pi$
$73$	5.68293	+	5.68293i	0.665137	+	0.665137i	−0.291449	+	0.956586i	$0.594137\pi$
$74$			8.10057i			0.941672i
$75$		0			0
$76$	−3.23255	−	3.23255i	−0.370798	−	0.370798i
$77$	−0.781921	+	1.35433i	−0.0891082	+	0.154340i
$78$		0			0
$79$	0.554497	+	0.960416i	0.0623857	+	0.108055i	0.895531	−	0.444998i	$-0.146796\pi$
$79$	0.554497	+	0.960416i	0.0623857	+	0.108055i	−0.833146	+	0.553054i	$0.813462\pi$
$80$	−0.763001	+	2.84756i	−0.0853061	+	0.318367i
$81$		0			0
$82$	4.48696	+	2.59055i	0.495502	+	0.286078i
$83$	−0.614312	+	2.29264i	−0.0674295	+	0.251650i	−0.991410	−	0.130789i	$-0.958249\pi$
$83$	−0.614312	+	2.29264i	−0.0674295	+	0.251650i	0.923981	+	0.382439i	$0.124916\pi$
$84$		0			0
$85$	−6.13542	+	22.8977i	−0.665479	+	2.48360i
$86$	0.604036	+	2.25429i	0.0651349	+	0.243087i
$87$		0			0
$88$	−0.694163	−	0.400775i	−0.0739980	−	0.0427228i
$89$	2.84070	+	0.761164i	0.301114	+	0.0806832i	0.406213	−	0.913779i	$-0.366849\pi$
$89$	2.84070	+	0.761164i	0.301114	+	0.0806832i	−0.105099	+	0.994462i	$0.533516\pi$
$90$		0			0
$91$	4.43822	+	5.45771i	0.465252	+	0.572123i
$92$	−6.05678	+	3.49688i	−0.631463	+	0.364575i
$93$		0			0
$94$	5.33031			0.549780
$95$	6.73843	+	11.6713i	0.691348	+	1.19745i
$96$		0			0
$97$	2.59780	−	2.59780i	0.263767	−	0.263767i	−0.562816	−	0.826582i	$-0.690282\pi$
$97$	2.59780	−	2.59780i	0.263767	−	0.263767i	0.826582	+	0.562816i	$0.190282\pi$
$98$	−0.826542	−	3.08469i	−0.0834933	−	0.311601i
$99$		0			0
$100$	1.84538	−	3.19629i	0.184538	−	0.319629i
$101$	6.82190	−	11.8159i	0.678804	−	1.17572i	−0.296537	−	0.955021i	$-0.595832\pi$
$101$	6.82190	−	11.8159i	0.678804	−	1.17572i	0.975341	−	0.220702i	$-0.0708349\pi$
$102$		0			0
$103$	−11.6669	−	6.73592i	−1.14958	−	0.663710i	−0.200794	−	0.979633i	$-0.564352\pi$
$103$	−11.6669	−	6.73592i	−1.14958	−	0.663710i	−0.948785	+	0.315924i	$0.897686\pi$
$104$	−2.79736	+	2.27482i	−0.274304	+	0.223064i
$105$		0			0
$106$	−2.14282	−	7.99713i	−0.208129	−	0.776750i
$107$	−16.0522	+	9.26775i	−1.55183	+	0.895947i	−0.553833	+	0.832628i	$0.686835\pi$
$107$	−16.0522	+	9.26775i	−1.55183	+	0.895947i	−0.997993	+	0.0633192i	$0.979831\pi$
$108$		0			0
$109$	4.23071	−	4.23071i	0.405229	−	0.405229i	−0.474842	−	0.880071i	$-0.657495\pi$
$109$	4.23071	−	4.23071i	0.405229	−	0.405229i	0.880071	+	0.474842i	$0.157495\pi$
$110$	1.67088	+	1.67088i	0.159312	+	0.159312i
$111$		0			0
$112$	−1.88454	+	0.504962i	−0.178073	+	0.0477144i
$113$	5.17811	−	2.98958i	0.487116	−	0.281236i	−0.236261	−	0.971690i	$-0.575922\pi$
$113$	5.17811	−	2.98958i	0.487116	−	0.281236i	0.723377	+	0.690453i	$0.242589\pi$
$114$		0			0
$115$	19.9151	−	5.33625i	1.85710	−	0.497608i
$116$	−7.87674			−0.731337
$117$		0			0
$118$	8.82789			0.812673
$119$	−15.1539	+	4.06048i	−1.38916	+	0.372224i
$120$		0			0
$121$	8.96987	−	5.17876i	0.815443	−	0.470796i
$122$	−4.77087	+	1.27835i	−0.431935	+	0.115737i
$123$		0			0
$124$	1.69127	+	1.69127i	0.151880	+	0.151880i
$125$	2.72919	−	2.72919i	0.244106	−	0.244106i
$126$		0			0
$127$	1.93815	−	1.11899i	0.171983	−	0.0992946i	−0.411537	−	0.911393i	$-0.635008\pi$
$127$	1.93815	−	1.11899i	0.171983	−	0.0992946i	0.583521	+	0.812098i	$0.301675\pi$
$128$	−0.258819	−	0.965926i	−0.0228766	−	0.0853766i
$129$		0			0
$130$	9.70133	−	4.34328i	0.850863	−	0.380931i
$131$	−7.37842	−	4.25993i	−0.644656	−	0.372192i	0.141750	−	0.989903i	$-0.454727\pi$
$131$	−7.37842	−	4.25993i	−0.644656	−	0.372192i	−0.786406	+	0.617710i	$0.788060\pi$
$132$		0			0
$133$	−4.45956	+	7.72418i	−0.386693	+	0.669772i
$134$	0.388212	−	0.672403i	0.0335364	−	0.0580868i
$135$		0			0
$136$	−2.08121	−	7.76717i	−0.178462	−	0.666029i
$137$	−8.21858	+	8.21858i	−0.702161	+	0.702161i	−0.964874	−	0.262713i	$-0.915383\pi$
$137$	−8.21858	+	8.21858i	−0.702161	+	0.702161i	0.262713	+	0.964874i	$0.415383\pi$
$138$		0			0
$139$	−11.4143	−	19.7701i	−0.968147	−	1.67688i	−0.700910	−	0.713250i	$-0.747222\pi$
$139$	−11.4143	−	19.7701i	−0.968147	−	1.67688i	−0.267238	−	0.963631i	$-0.586111\pi$
$140$	5.75163			0.486102
$141$		0			0
$142$	2.30692	−	1.33190i	0.193593	−	0.111771i
$143$	0.457981	+	2.85351i	0.0382983	+	0.238623i
$144$		0			0
$145$	22.4295	+	6.00996i	1.86267	+	0.499100i
$146$	6.96014	+	4.01844i	0.576026	+	0.332568i
$147$		0			0
$148$	2.09658	+	7.82455i	0.172338	+	0.643174i
$149$	−2.01425	+	7.51729i	−0.165014	+	0.615840i	0.833025	+	0.553236i	$0.186607\pi$
$149$	−2.01425	+	7.51729i	−0.165014	+	0.615840i	−0.998038	+	0.0626041i	$0.980059\pi$
$150$		0			0
$151$	2.05706	−	7.67704i	0.167401	−	0.624748i	−0.830321	−	0.557285i	$-0.811843\pi$
$151$	2.05706	−	7.67704i	0.167401	−	0.624748i	0.997722	−	0.0674629i	$-0.0214904\pi$
$152$	−3.95904	−	2.28576i	−0.321121	−	0.185399i
$153$		0			0
$154$	−0.404752	+	1.51056i	−0.0326159	+	0.121724i
$155$	−3.52554	−	6.10641i	−0.283178	−	0.490479i
$156$		0			0
$157$	1.97021	−	3.41251i	0.157240	−	0.272348i	−0.776632	−	0.629954i	$-0.783074\pi$
$157$	1.97021	−	3.41251i	0.157240	−	0.272348i	0.933872	+	0.357606i	$0.116407\pi$
$158$	0.784177	+	0.784177i	0.0623857	+	0.0623857i
$159$		0			0
$160$			2.94801i			0.233061i
$161$	9.64846	+	9.64846i	0.760405	+	0.760405i
$162$		0			0
$163$	−19.9290	+	5.33996i	−1.56096	+	0.418258i	−0.932967	−	0.359962i	$-0.882790\pi$
$163$	−19.9290	+	5.33996i	−1.56096	+	0.418258i	−0.627992	+	0.778220i	$0.716123\pi$
$164$	5.00455	+	1.34097i	0.390790	+	0.104712i
$165$		0			0
$166$			2.37352i			0.184221i
$167$	3.99041	−	3.99041i	0.308787	−	0.308787i	−0.535652	−	0.844439i	$-0.679934\pi$
$167$	3.99041	−	3.99041i	0.308787	−	0.308787i	0.844439	+	0.535652i	$0.179934\pi$
$168$		0			0
$169$	12.7269	+	2.65042i	0.978996	+	0.203879i
$170$			23.7054i			1.81812i
$171$		0			0
$172$	1.16691	+	2.02114i	0.0889759	+	0.154111i
$173$	16.4329			1.24937			0.624687	−	0.780876i	$-0.285227\pi$
$173$	16.4329			1.24937			0.624687	+	0.780876i	$0.285227\pi$
$174$		0			0
$175$	−6.95539	−	1.86369i	−0.525778	−	0.140882i
$176$	−0.774238	−	0.207457i	−0.0583604	−	0.0156376i
$177$		0			0
$178$	2.94091			0.220431
$179$	3.02863	+	5.24575i	0.226371	+	0.392085i	0.956730	−	0.290978i	$-0.0939806\pi$
$179$	3.02863	+	5.24575i	0.226371	+	0.392085i	−0.730359	+	0.683063i	$0.760647\pi$
$180$		0			0
$181$			12.2487i			0.910436i	0.890380	+	0.455218i	$0.150439\pi$
$181$			12.2487i			0.910436i	−0.890380	+	0.455218i	$0.849561\pi$
$182$	5.69955	+	4.12305i	0.422479	+	0.305621i
$183$		0			0
$184$	−4.94534	+	4.94534i	−0.364575	+	0.364575i
$185$		−	23.8806i		−	1.75573i
$186$		0			0
$187$	−6.22578	−	1.66819i	−0.455274	−	0.121990i
$188$	5.14869	−	1.37959i	0.375507	−	0.100617i
$189$		0			0
$190$	9.52957	+	9.52957i	0.691348	+	0.691348i
$191$		−	0.420709i		−	0.0304415i	−0.999884	−	0.0152207i	$-0.995155\pi$
$191$		−	0.420709i		−	0.0304415i	0.999884	−	0.0152207i	$-0.00484510\pi$
$192$		0			0
$193$	−9.60907	−	9.60907i	−0.691676	−	0.691676i	0.270924	−	0.962601i	$-0.412671\pi$
$193$	−9.60907	−	9.60907i	−0.691676	−	0.691676i	−0.962601	+	0.270924i	$0.912671\pi$
$194$	1.83692	−	3.18164i	0.131883	−	0.228429i
$195$		0			0
$196$	−1.59676	−	2.76566i	−0.114054	−	0.197547i
$197$	−0.239457	+	0.893667i	−0.0170606	+	0.0636712i	−0.973931	−	0.226843i	$-0.927160\pi$
$197$	−0.239457	+	0.893667i	−0.0170606	+	0.0636712i	0.956871	+	0.290514i	$0.0938263\pi$
$198$		0			0
$199$	11.1074	+	6.41286i	0.787382	+	0.454595i	0.839040	−	0.544070i	$-0.183117\pi$
$199$	11.1074	+	6.41286i	0.787382	+	0.454595i	−0.0516579	+	0.998665i	$0.516451\pi$
$200$	0.955238	−	3.56500i	0.0675455	−	0.252083i
$201$		0			0
$202$	3.53128	−	13.1789i	0.248460	−	0.927264i
$203$	3.97745	+	14.8441i	0.279162	+	1.04185i
$204$		0			0
$205$	−13.2276	−	7.63696i	−0.923855	−	0.533388i
$206$	−13.0128	−	3.48677i	−0.906644	−	0.242935i
$207$		0			0
$208$	−2.11327	+	2.92131i	−0.146529	+	0.202557i
$209$	−3.17337	+	1.83215i	−0.219507	+	0.126732i
$210$		0			0
$211$	6.84606			0.471302			0.235651	−	0.971838i	$-0.424278\pi$
$211$	6.84606			0.471302			0.235651	+	0.971838i	$0.424278\pi$
$212$	−4.13962	−	7.17003i	−0.284310	−	0.492440i
$213$		0			0
$214$	−13.1066	+	13.1066i	−0.895947	+	0.895947i
$215$	−1.78070	−	6.64568i	−0.121443	−	0.453231i
$216$		0			0
$217$	2.33324	−	4.04129i	0.158390	−	0.274340i
$218$	2.99156	−	5.18154i	0.202614	−	0.350938i
$219$		0			0
$220$	2.04640	+	1.18149i	0.137968	+	0.0796560i
$221$	−16.9932	+	23.4908i	−1.14309	+	1.58016i
$222$		0			0
$223$	4.57899	+	17.0890i	0.306632	+	1.14436i	0.931532	+	0.363660i	$0.118473\pi$
$223$	4.57899	+	17.0890i	0.306632	+	1.14436i	−0.624900	+	0.780705i	$0.714860\pi$
$224$	−1.68964	+	0.975511i	−0.112893	+	0.0651791i
$225$		0			0
$226$	4.22791	−	4.22791i	0.281236	−	0.281236i
$227$	−13.6942	−	13.6942i	−0.908916	−	0.908916i	0.0872689	−	0.996185i	$-0.472186\pi$
$227$	−13.6942	−	13.6942i	−0.908916	−	0.908916i	−0.996185	+	0.0872689i	$0.972186\pi$
$228$		0			0
$229$	25.0861	−	6.72179i	1.65773	−	0.444188i	0.695971	−	0.718070i	$-0.254974\pi$
$229$	25.0861	−	6.72179i	1.65773	−	0.444188i	0.961763	+	0.273882i	$0.0883077\pi$
$230$	17.8554	−	10.3088i	1.17735	−	0.679745i
$231$		0			0
$232$	−7.60835	+	2.03865i	−0.499512	+	0.133844i
$233$	11.9090			0.780184			0.390092	−	0.920776i	$-0.372443\pi$
$233$	11.9090			0.780184			0.390092	+	0.920776i	$0.372443\pi$
$234$		0			0
$235$	−15.7138			−1.02506
$236$	8.52709	−	2.28483i	0.555066	−	0.148730i
$237$		0			0
$238$	−13.5866	+	7.84425i	−0.880691	+	0.508467i
$239$	−8.96480	+	2.40211i	−0.579885	+	0.155380i	−0.536826	−	0.843693i	$-0.680377\pi$
$239$	−8.96480	+	2.40211i	−0.579885	+	0.155380i	−0.0430587	+	0.999073i	$0.513710\pi$
$240$		0			0
$241$	−6.92428	−	6.92428i	−0.446032	−	0.446032i	0.448001	−	0.894033i	$-0.352136\pi$
$241$	−6.92428	−	6.92428i	−0.446032	−	0.446032i	−0.894033	+	0.448001i	$0.852136\pi$
$242$	7.32387	−	7.32387i	0.470796	−	0.470796i
$243$		0			0
$244$	−4.27745	+	2.46959i	−0.273836	+	0.158099i
$245$	2.43665	+	9.09371i	0.155672	+	0.580976i
$246$		0			0
$247$	2.61202	+	16.2745i	0.166199	+	1.03552i
$248$	2.07137	+	1.19590i	0.131532	+	0.0759400i
$249$		0			0
$250$	1.92983	−	3.34257i	0.122053	−	0.211402i
$251$	−7.05445	+	12.2187i	−0.445273	+	0.771235i	−0.998071	−	0.0620799i	$-0.980227\pi$
$251$	−7.05445	+	12.2187i	−0.445273	+	0.771235i	0.552798	+	0.833315i	$0.313560\pi$
$252$		0			0
$253$	1.45090	+	5.41484i	0.0912174	+	0.340428i
$254$	1.58250	−	1.58250i	0.0992946	−	0.0992946i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	5.11976			0.319362			0.159681	−	0.987169i	$-0.448953\pi$
$257$	5.11976			0.319362			0.159681	+	0.987169i	$0.448953\pi$
$258$		0			0
$259$	13.6870	−	7.90220i	0.850469	−	0.491019i
$260$	8.24664	−	6.70618i	0.511435	−	0.415900i
$261$		0			0
$262$	−8.22956	−	2.20510i	−0.508424	−	0.136232i
$263$	−12.4904	−	7.21136i	−0.770194	−	0.444671i	0.0627501	−	0.998029i	$-0.480013\pi$
$263$	−12.4904	−	7.21136i	−0.770194	−	0.444671i	−0.832944	+	0.553358i	$0.813346\pi$
$264$		0			0
$265$	6.31706	+	23.5756i	0.388054	+	1.44824i
$266$	−2.30844	+	8.61521i	−0.141539	+	0.528232i
$267$		0			0
$268$	0.200953	−	0.749969i	0.0122752	−	0.0458116i
$269$	10.3656	+	5.98459i	0.632002	+	0.364887i	0.781527	−	0.623871i	$-0.214441\pi$
$269$	10.3656	+	5.98459i	0.632002	+	0.364887i	−0.149525	+	0.988758i	$0.547774\pi$
$270$		0			0
$271$	6.16812	−	23.0197i	0.374687	−	1.39835i	−0.479115	−	0.877752i	$-0.659042\pi$
$271$	6.16812	−	23.0197i	0.374687	−	1.39835i	0.853802	−	0.520598i	$-0.174291\pi$
$272$	−4.02058	−	6.96385i	−0.243784	−	0.422246i
$273$		0			0
$274$	−5.81141	+	10.0657i	−0.351080	+	0.608089i
$275$	−2.09185	−	2.09185i	−0.126143	−	0.126143i
$276$		0			0
$277$		−	9.44410i		−	0.567441i	−0.958907	−	0.283721i	$-0.908431\pi$
$277$		−	9.44410i		−	0.567441i	0.958907	−	0.283721i	$-0.0915688\pi$
$278$	−16.1422	−	16.1422i	−0.968147	−	0.968147i
$279$		0			0
$280$	5.55565	−	1.48863i	0.332014	−	0.0889628i
$281$	−18.8382	−	5.04768i	−1.12379	−	0.301119i	−0.351376	−	0.936235i	$-0.614286\pi$
$281$	−18.8382	−	5.04768i	−1.12379	−	0.301119i	−0.772417	+	0.635115i	$0.780953\pi$
$282$		0			0
$283$		−	20.7236i		−	1.23189i	−0.787789	−	0.615946i	$-0.788774\pi$
$283$		−	20.7236i		−	1.23189i	0.787789	−	0.615946i	$-0.211226\pi$
$284$	1.88359	−	1.88359i	0.111771	−	0.111771i
$285$		0			0
$286$	1.18092	+	2.63775i	0.0698292	+	0.155973i
$287$		−	10.1084i		−	0.596682i
$288$		0			0
$289$	−23.8302	−	41.2751i	−1.40178	−	2.42795i
$290$	23.2207			1.36357
$291$		0			0
$292$	7.76303	+	2.08010i	0.454297	+	0.121729i
$293$	−18.6486	−	4.99688i	−1.08946	−	0.291921i	−0.330996	−	0.943632i	$-0.607385\pi$
$293$	−18.6486	−	4.99688i	−1.08946	−	0.291921i	−0.758467	+	0.651711i	$0.774051\pi$
$294$		0			0
$295$	−26.0247			−1.51522
$296$	4.05028	+	7.01530i	0.235418	+	0.407756i
$297$		0			0
$298$			7.78247i			0.450826i
$299$	25.0836	+	2.58415i	1.45062	+	0.149445i
$300$		0			0
$301$	3.21969	−	3.21969i	0.185580	−	0.185580i
$302$		−	7.94785i		−	0.457348i
$303$		0			0
$304$	−4.41574	−	1.18319i	−0.253260	−	0.0678608i
$305$	14.0646	−	3.76859i	0.805335	−	0.215789i
$306$		0			0
$307$	−15.5762	−	15.5762i	−0.888978	−	0.888978i	0.105447	−	0.994425i	$-0.466373\pi$
$307$	−15.5762	−	15.5762i	−0.888978	−	0.888978i	−0.994425	+	0.105447i	$0.966373\pi$
$308$			1.56384i			0.0891082i
$309$		0			0
$310$	−4.98586	−	4.98586i	−0.283178	−	0.283178i
$311$	4.85889	−	8.41584i	0.275522	−	0.477218i	−0.694745	−	0.719257i	$-0.744483\pi$
$311$	4.85889	−	8.41584i	0.275522	−	0.477218i	0.970267	+	0.242038i	$0.0778159\pi$
$312$		0			0
$313$	2.74916	+	4.76168i	0.155392	+	0.269146i	0.933202	−	0.359353i	$-0.117003\pi$
$313$	2.74916	+	4.76168i	0.155392	+	0.269146i	−0.777810	+	0.628500i	$0.783669\pi$
$314$	1.01986	−	3.80616i	0.0575539	−	0.214794i
$315$		0			0
$316$	0.960416	+	0.554497i	0.0540276	+	0.0311929i
$317$	−0.270848	+	1.01082i	−0.0152123	+	0.0567731i	−0.973115	−	0.230321i	$-0.926022\pi$
$317$	−0.270848	+	1.01082i	−0.0152123	+	0.0567731i	0.957902	+	0.287094i	$0.0926892\pi$
$318$		0			0
$319$	−1.63408	+	6.09847i	−0.0914910	+	0.341449i
$320$	0.763001	+	2.84756i	0.0426530	+	0.159183i
$321$		0			0
$322$	11.8169	+	6.82249i	0.658530	+	0.380203i
$323$	−35.5077	−	9.51426i	−1.97570	−	0.529388i
$324$		0			0
$325$	−12.1456	+	5.43757i	−0.673715	+	0.301622i
$326$	−17.8678	+	10.3160i	−0.989609	+	0.571351i
$327$		0			0
$328$	5.18109			0.286078
$329$	−5.19978	−	9.00629i	−0.286673	−	0.496533i
$330$		0			0
$331$	−8.72945	+	8.72945i	−0.479814	+	0.479814i	−0.905072	−	0.425258i	$-0.860183\pi$
$331$	−8.72945	+	8.72945i	−0.479814	+	0.479814i	0.425258	+	0.905072i	$0.360183\pi$
$332$	0.614312	+	2.29264i	0.0337147	+	0.125825i
$333$		0			0
$334$	2.82165	−	4.88724i	0.154394	−	0.267418i
$335$	−1.14445	+	1.98225i	−0.0625282	+	0.108302i
$336$		0			0
$337$	18.3428	+	10.5902i	0.999195	+	0.576886i	0.908010	−	0.418948i	$-0.137601\pi$
$337$	18.3428	+	10.5902i	0.999195	+	0.576886i	0.0911852	+	0.995834i	$0.470934\pi$
$338$	12.9793	−	0.733864i	0.705979	−	0.0399170i
$339$		0			0
$340$	6.13542	+	22.8977i	0.332740	+	1.24180i
$341$	1.66031	−	0.958578i	0.0899106	−	0.0519099i
$342$		0			0
$343$	−14.0628	+	14.0628i	−0.759319	+	0.759319i
$344$	1.65026	+	1.65026i	0.0889759	+	0.0889759i
$345$		0			0
$346$	15.8730	−	4.25316i	0.853338	−	0.228651i
$347$	2.17991	−	1.25857i	0.117024	−	0.0675636i	−0.440346	−	0.897828i	$-0.645144\pi$
$347$	2.17991	−	1.25857i	0.117024	−	0.0675636i	0.557369	+	0.830265i	$0.311811\pi$
$348$		0			0
$349$	17.1855	−	4.60485i	0.919921	−	0.246492i	0.232369	−	0.972628i	$-0.425352\pi$
$349$	17.1855	−	4.60485i	0.919921	−	0.246492i	0.687552	+	0.726136i	$0.258686\pi$
$350$	−7.20075			−0.384896
$351$		0			0
$352$	−0.801550			−0.0427228
$353$	3.01498	−	0.807861i	0.160471	−	0.0429981i	−0.177689	−	0.984087i	$-0.556862\pi$
$353$	3.01498	−	0.807861i	0.160471	−	0.0429981i	0.338160	+	0.941089i	$0.390195\pi$
$354$		0			0
$355$	−6.80082	+	3.92646i	−0.360950	+	0.208395i
$356$	2.84070	−	0.761164i	0.150557	−	0.0403416i
$357$		0			0
$358$	4.28313	+	4.28313i	0.226371	+	0.226371i
$359$	−14.3618	+	14.3618i	−0.757986	+	0.757986i	−0.975956	−	0.217970i	$-0.930057\pi$
$359$	−14.3618	+	14.3618i	−0.757986	+	0.757986i	0.217970	+	0.975956i	$0.430057\pi$
$360$		0			0
$361$	−1.64433	+	0.949354i	−0.0865436	+	0.0499660i
$362$	3.17019	+	11.8313i	0.166621	+	0.621839i
$363$		0			0
$364$	6.57246	+	2.50741i	0.344491	+	0.131424i
$365$	−20.5186	−	11.8464i	−1.07399	−	0.620069i
$366$		0			0
$367$	−11.6102	+	20.1095i	−0.606049	+	1.04971i	0.385835	+	0.922568i	$0.373913\pi$
$367$	−11.6102	+	20.1095i	−0.606049	+	1.04971i	−0.991885	+	0.127141i	$0.959420\pi$
$368$	−3.49688	+	6.05678i	−0.182288	+	0.315731i
$369$		0			0
$370$	−6.18074	−	23.0668i	−0.321321	−	1.19919i
$371$	−11.4219	+	11.4219i	−0.592994	+	0.592994i
$372$		0			0
$373$	−12.6570	−	21.9226i	−0.655355	−	1.13511i	−0.981805	−	0.189893i	$-0.939186\pi$
$373$	−12.6570	−	21.9226i	−0.655355	−	1.13511i	0.326450	−	0.945214i	$-0.394148\pi$
$374$	−6.44540			−0.333284
$375$		0			0
$376$	4.61619	−	2.66516i	0.238062	−	0.137445i
$377$	23.0104	+	16.6457i	1.18510	+	0.857298i
$378$		0			0
$379$	−22.2862	−	5.97156i	−1.14476	−	0.306738i	−0.363898	−	0.931439i	$-0.618554\pi$
$379$	−22.2862	−	5.97156i	−1.14476	−	0.306738i	−0.780865	+	0.624700i	$0.785221\pi$
$380$	11.6713	+	6.73843i	0.598725	+	0.345674i
$381$		0			0
$382$	−0.108888	−	0.406374i	−0.00557117	−	0.0207919i
$383$	6.17345	−	23.0396i	0.315448	−	1.17727i	−0.608123	−	0.793843i	$-0.708077\pi$
$383$	6.17345	−	23.0396i	0.315448	−	1.17727i	0.923571	−	0.383426i	$-0.125256\pi$
$384$		0			0
$385$	1.19321	−	4.45313i	0.0608118	−	0.226953i
$386$	−11.7687	−	6.79464i	−0.599009	−	0.345838i
$387$		0			0
$388$	0.950861	−	3.54866i	0.0482726	−	0.180156i
$389$	12.4984	+	21.6479i	0.633694	+	1.09759i	0.986790	+	0.162004i	$0.0517957\pi$
$389$	12.4984	+	21.6479i	0.633694	+	1.09759i	−0.353096	+	0.935587i	$0.614871\pi$
$390$		0			0
$391$	−28.1190	+	48.7035i	−1.42204	+	2.46304i
$392$	−2.25815	−	2.25815i	−0.114054	−	0.114054i
$393$		0			0
$394$			0.925192i			0.0466105i
$395$	−2.31176	−	2.31176i	−0.116317	−	0.116317i
$396$		0			0
$397$	20.3908	−	5.46370i	1.02338	−	0.274215i	0.292173	−	0.956366i	$-0.405622\pi$
$397$	20.3908	−	5.46370i	1.02338	−	0.274215i	0.731212	+	0.682150i	$0.238955\pi$
$398$	12.3887	+	3.31954i	0.620989	+	0.166393i
$399$		0			0
$400$		−	3.69076i		−	0.184538i
$401$	12.5004	−	12.5004i	0.624242	−	0.624242i	−0.322371	−	0.946613i	$-0.604480\pi$
$401$	12.5004	−	12.5004i	0.624242	−	0.624242i	0.946613	+	0.322371i	$0.104480\pi$
$402$		0			0
$403$	−1.36661	−	8.51482i	−0.0680756	−	0.424154i
$404$		−	13.6438i		−	0.678804i
$405$		0			0
$406$	7.68385	+	13.3088i	0.381343	+	0.660506i
$407$	6.49301			0.321847
$408$		0			0
$409$	20.2046	+	5.41382i	0.999055	+	0.267696i	0.721050	−	0.692884i	$-0.243660\pi$
$409$	20.2046	+	5.41382i	0.999055	+	0.267696i	0.278005	+	0.960580i	$0.410327\pi$
$410$	−14.7535	−	3.95318i	−0.728622	−	0.195234i
$411$		0			0
$412$	−13.4718			−0.663710
$413$	−8.61171	−	14.9159i	−0.423754	−	0.733964i
$414$		0			0
$415$		−	6.99715i		−	0.343477i
$416$	−1.28518	+	3.36873i	−0.0630109	+	0.165165i
$417$		0			0
$418$	−2.59105	+	2.59105i	−0.126732	+	0.126732i
$419$			17.8998i			0.874462i	0.899349	+	0.437231i	$0.144041\pi$
$419$			17.8998i			0.874462i	−0.899349	+	0.437231i	$0.855959\pi$
$420$		0			0
$421$	0.922884	+	0.247286i	0.0449786	+	0.0120520i	0.281238	−	0.959638i	$-0.409255\pi$
$421$	0.922884	+	0.247286i	0.0449786	+	0.0120520i	−0.236260	+	0.971690i	$0.575922\pi$
$422$	6.61278	−	1.77189i	0.321905	−	0.0862542i
$423$		0			0
$424$	−5.85430	−	5.85430i	−0.284310	−	0.284310i
$425$		−	29.6780i		−	1.43959i
$426$		0			0
$427$	6.81399	+	6.81399i	0.329752	+	0.329752i
$428$	−9.26775	+	16.0522i	−0.447974	+	0.775913i
$429$		0			0
$430$	−3.44006	−	5.95835i	−0.165894	−	0.287337i
$431$	10.1624	−	37.9267i	0.489507	−	1.82687i	−0.0693375	−	0.997593i	$-0.522089\pi$
$431$	10.1624	−	37.9267i	0.489507	−	1.82687i	0.558845	−	0.829272i	$-0.311245\pi$
$432$		0			0
$433$	9.53436	+	5.50467i	0.458192	+	0.264537i	0.711284	−	0.702905i	$-0.248114\pi$
$433$	9.53436	+	5.50467i	0.458192	+	0.264537i	−0.253092	+	0.967442i	$0.581447\pi$
$434$	1.20777	−	4.50747i	0.0579749	−	0.216365i
$435$		0			0
$436$	1.54855	−	5.77926i	0.0741620	−	0.276776i
$437$	8.27498	+	30.8826i	0.395846	+	1.47732i
$438$		0			0
$439$	3.69190	+	2.13152i	0.176205	+	0.101732i	0.585508	−	0.810666i	$-0.300895\pi$
$439$	3.69190	+	2.13152i	0.176205	+	0.101732i	−0.409304	+	0.912398i	$0.634228\pi$
$440$	2.28246	+	0.611584i	0.108812	+	0.0291561i
$441$		0			0
$442$	−10.3343	+	27.0885i	−0.491553	+	1.28847i
$443$	−24.9846	+	14.4249i	−1.18705	+	0.685346i	−0.957636	−	0.287981i	$-0.907016\pi$
$443$	−24.9846	+	14.4249i	−1.18705	+	0.685346i	−0.229419	+	0.973328i	$0.573683\pi$
$444$		0			0
$445$	−8.66983			−0.410989
$446$	8.84592	+	15.3216i	0.418866	+	0.725498i
$447$		0			0
$448$	−1.37958	+	1.37958i	−0.0651791	+	0.0651791i
$449$	−6.56424	−	24.4981i	−0.309786	−	1.15614i	−0.928747	−	0.370714i	$-0.879113\pi$
$449$	−6.56424	−	24.4981i	−0.309786	−	1.15614i	0.618961	−	0.785421i	$-0.287554\pi$
$450$		0			0
$451$	2.07645	−	3.59652i	0.0977764	−	0.169354i
$452$	2.98958	−	5.17811i	0.140618	−	0.243558i
$453$		0			0
$454$	−16.7719	−	9.68326i	−0.787144	−	0.454458i
$455$	−16.8023	−	12.1548i	−0.787705	−	0.569825i
$456$		0			0
$457$	−7.44528	−	27.7862i	−0.348275	−	1.29978i	−0.888739	−	0.458414i	$-0.848418\pi$
$457$	−7.44528	−	27.7862i	−0.348275	−	1.29978i	0.540463	−	0.841368i	$-0.318249\pi$
$458$	22.4916	−	12.9855i	1.05096	−	0.606773i
$459$		0			0
$460$	14.5789	−	14.5789i	0.679745	−	0.679745i
$461$	−26.1642	−	26.1642i	−1.21859	−	1.21859i	−0.968126	−	0.250464i	$-0.919417\pi$
$461$	−26.1642	−	26.1642i	−1.21859	−	1.21859i	−0.250464	−	0.968126i	$-0.580583\pi$
$462$		0			0
$463$	−2.40613	+	0.644720i	−0.111822	+	0.0299627i	−0.314296	−	0.949325i	$-0.601769\pi$
$463$	−2.40613	+	0.644720i	−0.111822	+	0.0299627i	0.202474	+	0.979288i	$0.435102\pi$
$464$	−6.82146	+	3.93837i	−0.316678	+	0.182834i
$465$		0			0
$466$	11.5032	−	3.08227i	0.532875	−	0.142784i
$467$	31.2741			1.44719			0.723596	−	0.690223i	$-0.242488\pi$
$467$	31.2741			1.44719			0.723596	+	0.690223i	$0.242488\pi$
$468$		0			0
$469$	−1.51482			−0.0699480
$470$	−15.1784	+	4.06703i	−0.700126	+	0.187598i
$471$		0			0
$472$	7.64518	−	4.41394i	0.351898	−	0.203168i
$473$	1.80693	−	0.484165i	0.0830827	−	0.0222619i
$474$		0			0
$475$	−11.9305	−	11.9305i	−0.547411	−	0.547411i
$476$	−11.0934	+	11.0934i	−0.508467	+	0.508467i
$477$		0			0
$478$	−8.03762	+	4.64052i	−0.367632	+	0.212253i
$479$	−1.43340	−	5.34951i	−0.0654936	−	0.244426i	0.925416	−	0.378952i	$-0.123715\pi$
$479$	−1.43340	−	5.34951i	−0.0654936	−	0.244426i	−0.990910	+	0.134526i	$0.957049\pi$
$480$		0			0
$481$	10.4107	−	27.2886i	0.474685	−	1.24425i
$482$	−8.48048	−	4.89621i	−0.386275	−	0.223016i
$483$		0			0
$484$	5.17876	−	8.96987i	0.235398	−	0.407721i
$485$	−5.41526	+	9.37951i	−0.245894	+	0.425902i
$486$		0			0
$487$	−0.759319	−	2.83382i	−0.0344080	−	0.128412i	0.946586	−	0.322453i	$-0.104507\pi$
$487$	−0.759319	−	2.83382i	−0.0344080	−	0.128412i	−0.980994	+	0.194040i	$0.937841\pi$
$488$	−3.49252	+	3.49252i	−0.158099	+	0.158099i
$489$		0			0
$490$	4.70725	+	8.15320i	0.212652	+	0.368324i
$491$	35.6988			1.61106			0.805531	−	0.592553i	$-0.201880\pi$
$491$	35.6988			1.61106			0.805531	+	0.592553i	$0.201880\pi$
$492$		0			0
$493$	−54.8525	+	31.6691i	−2.47043	+	1.42630i
$494$	6.73518	+	15.0440i	0.303030	+	0.676860i
$495$		0			0
$496$	2.31031	+	0.619046i	0.103736	+	0.0277960i
$497$	−4.50085	−	2.59857i	−0.201891	−	0.116562i
$498$		0			0
$499$	4.71922	+	17.6124i	0.211261	+	0.788438i	0.987449	+	0.157936i	$0.0504841\pi$
$499$	4.71922	+	17.6124i	0.211261	+	0.788438i	−0.776188	+	0.630502i	$0.782849\pi$
$500$	0.998954	−	3.72815i	0.0446746	−	0.166728i
$501$		0			0
$502$	−3.65165	+	13.6281i	−0.162981	+	0.608254i
$503$	−20.2816	−	11.7096i	−0.904310	−	0.522104i	−0.0257142	−	0.999669i	$-0.508186\pi$
$503$	−20.2816	−	11.7096i	−0.904310	−	0.522104i	−0.878596	+	0.477565i	$0.841519\pi$
$504$		0			0
$505$	−10.4102	+	38.8515i	−0.463249	+	1.72887i
$506$	2.80293	+	4.85481i	0.124605	+	0.215823i
$507$		0			0
$508$	1.11899	−	1.93815i	0.0496473	−	0.0859917i
$509$	−2.33968	−	2.33968i	−0.103705	−	0.103705i	0.653351	−	0.757055i	$-0.273363\pi$
$509$	−2.33968	−	2.33968i	−0.103705	−	0.103705i	−0.757055	+	0.653351i	$0.773363\pi$
$510$		0			0
$511$		−	15.6801i		−	0.693648i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$		0			0
$514$	4.94531	−	1.32509i	0.218128	−	0.0584473i
$515$	38.3618	+	10.2790i	1.69042	+	0.452948i
$516$		0			0
$517$		−	4.27252i		−	0.187905i
$518$	11.1754	−	11.1754i	0.491019	−	0.491019i
$519$		0			0
$520$	6.22995	−	8.61206i	0.273201	−	0.377664i
$521$			7.00178i			0.306754i	0.988168	+	0.153377i	$0.0490148\pi$
$521$			7.00178i			0.306754i	−0.988168	+	0.153377i	$0.950985\pi$
$522$		0			0
$523$	−21.4957	−	37.2316i	−0.939940	−	1.62802i	−0.765580	−	0.643341i	$-0.777548\pi$
$523$	−21.4957	−	37.2316i	−0.939940	−	1.62802i	−0.174360	−	0.984682i	$-0.555786\pi$
$524$	−8.51987			−0.372192
$525$		0			0
$526$	−13.9313	−	3.73287i	−0.607433	−	0.162761i
$527$	18.5776	+	4.97785i	0.809253	+	0.216839i
$528$		0			0
$529$	25.9127			1.12664
$530$	12.2036	+	21.1373i	0.530092	+	0.918146i
$531$		0			0
$532$			8.91912i			0.386693i
$533$	−11.7860	−	14.4934i	−0.510510	−	0.627778i
$534$		0			0
$535$	38.6383	−	38.6383i	1.67048	−	1.67048i
$536$		−	0.776425i		−	0.0335364i
$537$		0			0
$538$	11.5613	+	3.09785i	0.498445	+	0.133558i
$539$	−2.47254	+	0.662515i	−0.106500	+	0.0285365i
$540$		0			0
$541$	8.12664	+	8.12664i	0.349391	+	0.349391i	0.859883	−	0.510491i	$-0.170536\pi$
$541$	8.12664	+	8.12664i	0.349391	+	0.349391i	−0.510491	+	0.859883i	$0.670536\pi$
$542$		−	23.8318i		−	1.02366i
$543$		0			0
$544$	−5.68596	−	5.68596i	−0.243784	−	0.243784i
$545$	−8.81916	+	15.2752i	−0.377771	+	0.654319i
$546$		0			0
$547$	2.01972	+	3.49826i	0.0863570	+	0.149575i	0.905969	−	0.423345i	$-0.139144\pi$
$547$	2.01972	+	3.49826i	0.0863570	+	0.149575i	−0.819612	+	0.572919i	$0.805811\pi$
$548$	−3.00821	+	11.2268i	−0.128504	+	0.479585i
$549$		0			0
$550$	−2.56199	−	1.47916i	−0.109243	−	0.0630717i
$551$	−9.31971	+	34.7816i	−0.397033	+	1.48175i
$552$		0			0
$553$	0.559999	−	2.08995i	0.0238136	−	0.0888735i
$554$	−2.44431	−	9.12230i	−0.103849	−	0.387570i
$555$		0			0
$556$	−19.7701	−	11.4143i	−0.838440	−	0.484074i
$557$	22.2275	+	5.95584i	0.941810	+	0.252357i	0.696883	−	0.717185i	$-0.254570\pi$
$557$	22.2275	+	5.95584i	0.941810	+	0.252357i	0.244926	+	0.969542i	$0.421236\pi$
$558$		0			0
$559$	0.862329	−	8.37039i	0.0364726	−	0.354030i
$560$	4.98106	−	2.87582i	0.210488	−	0.121525i
$561$		0			0
$562$	−19.5027			−0.822674
$563$	−2.44455	−	4.23408i	−0.103025	−	0.178445i	0.809904	−	0.586562i	$-0.199519\pi$
$563$	−2.44455	−	4.23408i	−0.103025	−	0.178445i	−0.912930	+	0.408117i	$0.866186\pi$
$564$		0			0
$565$	−12.4639	+	12.4639i	−0.524361	+	0.524361i
$566$	−5.36367	−	20.0175i	−0.225452	−	0.841397i
$567$		0			0
$568$	1.33190	−	2.30692i	0.0558853	−	0.0967963i
$569$	10.6832	−	18.5038i	0.447863	−	0.775721i	−0.550384	−	0.834912i	$-0.685519\pi$
$569$	10.6832	−	18.5038i	0.447863	−	0.775721i	0.998247	+	0.0591908i	$0.0188520\pi$
$570$		0			0
$571$	21.5820	+	12.4604i	0.903179	+	0.521451i	0.878230	−	0.478238i	$-0.158724\pi$
$571$	21.5820	+	12.4604i	0.903179	+	0.521451i	0.0249486	+	0.999689i	$0.492058\pi$
$572$	1.82338	+	2.24222i	0.0762393	+	0.0937521i
$573$		0			0
$574$	−2.61625	−	9.76399i	−0.109200	−	0.407541i
$575$	−22.3541	+	12.9061i	−0.932230	+	0.538223i
$576$		0			0
$577$	−4.11164	+	4.11164i	−0.171170	+	0.171170i	−0.787493	−	0.616323i	$-0.788621\pi$
$577$	−4.11164	+	4.11164i	−0.171170	+	0.171170i	0.616323	+	0.787493i	$0.288621\pi$
$578$	−33.7010	−	33.7010i	−1.40178	−	1.40178i
$579$		0			0
$580$	22.4295	−	6.00996i	0.931333	−	0.249550i
$581$	4.01038	−	2.31539i	0.166379	−	0.0960587i
$582$		0			0
$583$	−6.41010	+	1.71758i	−0.265479	+	0.0711350i
$584$	8.03688			0.332568
$585$		0			0
$586$	−19.3065			−0.797542
$587$	17.3963	−	4.66134i	0.718024	−	0.192394i	0.118734	−	0.992926i	$-0.462116\pi$
$587$	17.3963	−	4.66134i	0.718024	−	0.192394i	0.599290	+	0.800532i	$0.295450\pi$
$588$		0			0
$589$	9.46928	−	5.46709i	0.390175	−	0.225268i
$590$	−25.1379	+	6.73569i	−1.03491	+	0.277304i
$591$		0			0
$592$	5.72797	+	5.72797i	0.235418	+	0.235418i
$593$	−8.08152	+	8.08152i	−0.331868	+	0.331868i	−0.853296	−	0.521427i	$-0.825400\pi$
$593$	−8.08152	+	8.08152i	−0.331868	+	0.331868i	0.521427	+	0.853296i	$0.325400\pi$
$594$		0			0
$595$	40.0535	−	23.1249i	1.64203	−	0.948029i
$596$	2.01425	+	7.51729i	0.0825069	+	0.307920i
$597$		0			0
$598$	24.8977	−	3.99602i	1.01814	−	0.163410i
$599$	0.103217	+	0.0595921i	0.00421731	+	0.00243487i	0.502107	−	0.864805i	$-0.332558\pi$
$599$	0.103217	+	0.0595921i	0.00421731	+	0.00243487i	−0.497890	+	0.867240i	$0.665892\pi$
$600$		0			0
$601$	−13.5435	+	23.4581i	−0.552452	+	0.956875i	0.445645	+	0.895210i	$0.352974\pi$
$601$	−13.5435	+	23.4581i	−0.552452	+	0.956875i	−0.998097	+	0.0616651i	$0.980359\pi$
$602$	2.27666	−	3.94330i	0.0927899	−	0.160717i
$603$		0			0
$604$	−2.05706	−	7.67704i	−0.0837004	−	0.312374i
$605$	−21.5908	+	21.5908i	−0.877792	+	0.877792i
$606$		0			0
$607$	9.24915	+	16.0200i	0.375412	+	0.650232i	0.990389	−	0.138313i	$-0.0441680\pi$
$607$	9.24915	+	16.0200i	0.375412	+	0.650232i	−0.614977	+	0.788545i	$0.710835\pi$
$608$	−4.57151			−0.185399
$609$		0			0
$610$	12.6100	−	7.28036i	0.510562	−	0.294773i
$611$	−17.9564	−	6.85039i	−0.726437	−	0.277137i
$612$		0			0
$613$	−21.0392	−	5.63743i	−0.849764	−	0.227694i	−0.192447	−	0.981307i	$-0.561642\pi$
$613$	−21.0392	−	5.63743i	−0.849764	−	0.227694i	−0.657317	+	0.753614i	$0.728309\pi$
$614$	−19.0768	−	11.0140i	−0.769878	−	0.444489i
$615$		0			0
$616$	0.404752	+	1.51056i	0.0163079	+	0.0608620i
$617$	−0.679941	+	2.53758i	−0.0273734	+	0.102159i	−0.978261	−	0.207377i	$-0.933507\pi$
$617$	−0.679941	+	2.53758i	−0.0273734	+	0.102159i	0.950888	+	0.309536i	$0.100174\pi$
$618$		0			0
$619$	−3.69004	+	13.7714i	−0.148315	+	0.553520i	0.851270	+	0.524728i	$0.175833\pi$
$619$	−3.69004	+	13.7714i	−0.148315	+	0.553520i	−0.999585	+	0.0287923i	$0.990834\pi$
$620$	−6.10641	−	3.52554i	−0.245239	−	0.141589i
$621$		0			0
$622$	2.51514	−	9.38665i	0.100848	−	0.376370i
$623$	−2.86889	−	4.96907i	−0.114940	−	0.199081i
$624$		0			0
$625$	−14.9160	+	25.8354i	−0.596642	+	1.03341i
$626$	3.88790	+	3.88790i	0.155392	+	0.155392i
$627$		0			0
$628$		−	3.94043i		−	0.157240i
$629$	46.0595	+	46.0595i	1.83651	+	1.83651i
$630$		0			0
$631$	34.0030	−	9.11109i	1.35364	−	0.362707i	0.492163	−	0.870503i	$-0.336206\pi$
$631$	34.0030	−	9.11109i	1.35364	−	0.362707i	0.861477	+	0.507797i	$0.169540\pi$
$632$	1.07121	+	0.287029i	0.0426103	+	0.0114174i
$633$		0			0
$634$			1.04647i			0.0415608i
$635$	−4.66521	+	4.66521i	−0.185133	+	0.185133i
$636$		0			0
$637$	−1.17998	+	11.4537i	−0.0467525	+	0.453814i
$638$			6.31360i			0.249958i
$639$		0			0
$640$	1.47400	+	2.55305i	0.0582651	+	0.100918i
$641$	−5.81916			−0.229843			−0.114922	−	0.993375i	$-0.536662\pi$
$641$	−5.81916			−0.229843			−0.114922	+	0.993375i	$0.536662\pi$
$642$		0			0
$643$	5.74185	+	1.53852i	0.226436	+	0.0606735i	0.370253	−	0.928931i	$-0.379271\pi$
$643$	5.74185	+	1.53852i	0.226436	+	0.0606735i	−0.143817	+	0.989604i	$0.545938\pi$
$644$	13.1800	+	3.53158i	0.519367	+	0.139164i
$645$		0			0
$646$	−36.7603			−1.44631
$647$	2.47586	+	4.28832i	0.0973362	+	0.168591i	0.910581	−	0.413330i	$-0.135634\pi$
$647$	2.47586	+	4.28832i	0.0973362	+	0.168591i	−0.813245	+	0.581921i	$0.802301\pi$
$648$		0			0
$649$		−	7.07600i		−	0.277757i
$650$	−10.3244	+	8.39579i	−0.404955	+	0.329310i
$651$		0			0
$652$	−14.5890	+	14.5890i	−0.571351	+	0.571351i
$653$			20.4897i			0.801824i	0.916117	+	0.400912i	$0.131307\pi$
$653$			20.4897i			0.801824i	−0.916117	+	0.400912i	$0.868693\pi$
$654$		0			0
$655$	24.2608	+	6.50067i	0.947949	+	0.254002i
$656$	5.00455	−	1.34097i	0.195395	−	0.0523559i
$657$		0			0
$658$	−7.35360	−	7.35360i	−0.286673	−	0.286673i
$659$		−	4.80810i		−	0.187297i	−0.995605	−	0.0936484i	$-0.970147\pi$
$659$		−	4.80810i		−	0.187297i	0.995605	−	0.0936484i	$-0.0298530\pi$
$660$		0			0
$661$	−28.8974	−	28.8974i	−1.12398	−	1.12398i	−0.991138	−	0.132839i	$-0.957591\pi$
$661$	−28.8974	−	28.8974i	−1.12398	−	1.12398i	−0.132839	−	0.991138i	$-0.542409\pi$
$662$	−6.17265	+	10.6913i	−0.239907	+	0.415531i
$663$		0			0
$664$	1.18676	+	2.05553i	0.0460552	+	0.0797699i
$665$	6.80530	−	25.3977i	0.263898	−	0.984881i
$666$		0			0
$667$	47.7077	+	27.5440i	1.84725	+	1.06651i
$668$	1.46059	−	5.45101i	0.0565120	−	0.210906i
$669$		0			0
$670$	−0.592413	+	2.21091i	−0.0228869	+	0.0854151i
$671$	1.02466	+	3.82410i	0.0395567	+	0.147628i
$672$		0			0
$673$	22.6393	+	13.0708i	0.872680	+	0.503842i	0.868238	−	0.496148i	$-0.165253\pi$
$673$	22.6393	+	13.0708i	0.872680	+	0.503842i	0.00444195	+	0.999990i	$0.498586\pi$
$674$	20.4587	+	5.48190i	0.788040	+	0.211155i
$675$		0			0
$676$	12.3471	−	4.06814i	0.474887	−	0.156467i
$677$	34.5645	−	19.9558i	1.32842	−	0.766964i	0.343365	−	0.939202i	$-0.388433\pi$
$677$	34.5645	−	19.9558i	1.32842	−	0.766964i	0.985055	+	0.172238i	$0.0551000\pi$
$678$		0			0
$679$	−7.16775			−0.275073
$680$	11.8527	+	20.5295i	0.454531	+	0.787271i
$681$		0			0
$682$	1.35563	−	1.35563i	0.0519099	−	0.0519099i
$683$	9.69531	+	36.1834i	0.370981	+	1.38452i	0.859129	+	0.511759i	$0.171006\pi$
$683$	9.69531	+	36.1834i	0.370981	+	1.38452i	−0.488148	+	0.872761i	$0.662327\pi$
$684$		0			0
$685$	17.1321	−	29.6737i	0.654584	−	1.13377i
$686$	−9.94388	+	17.2233i	−0.379659	+	0.657589i
$687$		0			0
$688$	2.02114	+	1.16691i	0.0770554	+	0.0444880i
$689$	−3.05912	+	29.6941i	−0.116543	+	1.13125i
$690$		0			0
$691$	12.0361	+	44.9193i	0.457875	+	1.70881i	0.679496	+	0.733679i	$0.262199\pi$
$691$	12.0361	+	44.9193i	0.457875	+	1.70881i	−0.221621	+	0.975133i	$0.571135\pi$
$692$	14.2313	−	8.21647i	0.540994	−	0.312343i
$693$		0			0
$694$	1.77989	−	1.77989i	0.0675636	−	0.0675636i
$695$	47.5875	+	47.5875i	1.80510	+	1.80510i
$696$		0			0
$697$	40.2424	−	10.7829i	1.52429	−	0.408433i
$698$	15.4081	−	8.89589i	0.583206	−	0.336714i
$699$		0			0
$700$	−6.95539	+	1.86369i	−0.262889	+	0.0704409i
$701$	−27.1053			−1.02375			−0.511876	−	0.859059i	$-0.671049\pi$
$701$	−27.1053			−1.02375			−0.511876	+	0.859059i	$0.671049\pi$
$702$		0			0
$703$	37.0318			1.39668
$704$	−0.774238	+	0.207457i	−0.0291802	+	0.00781881i
$705$		0			0
$706$	2.70316	−	1.56067i	0.101735	−	0.0587365i
$707$	−25.7123	+	6.88960i	−0.967012	+	0.259110i
$708$		0			0
$709$	32.1360	+	32.1360i	1.20689	+	1.20689i	0.972028	+	0.234865i	$0.0754647\pi$
$709$	32.1360	+	32.1360i	1.20689	+	1.20689i	0.234865	+	0.972028i	$0.424535\pi$
$710$	−5.55285	+	5.55285i	−0.208395	+	0.208395i
$711$		0			0
$712$	2.54690	−	1.47046i	0.0954492	−	0.0551076i
$713$	−4.32946	−	16.1578i	−0.162140	−	0.605113i
$714$		0			0
$715$	−3.48136	−	7.77610i	−0.130196	−	0.290810i
$716$	5.24575	+	3.02863i	0.196043	+	0.113185i
$717$		0			0
$718$	−10.1553	+	17.5895i	−0.378993	+	0.656435i
$719$	10.2199	−	17.7014i	0.381138	−	0.660150i	−0.610087	−	0.792334i	$-0.708866\pi$
$719$	10.2199	−	17.7014i	0.381138	−	0.660150i	0.991225	+	0.132184i	$0.0421990\pi$
$720$		0			0
$721$	6.80276	+	25.3882i	0.253348	+	0.945508i
$722$	−1.34259	+	1.34259i	−0.0499660	+	0.0499660i
$723$		0			0
$724$	6.12433	+	10.6077i	0.227609	+	0.394230i
$725$	−29.0711			−1.07967
$726$		0			0
$727$	25.7087	−	14.8430i	0.953485	−	0.550495i	0.0593229	−	0.998239i	$-0.481106\pi$
$727$	25.7087	−	14.8430i	0.953485	−	0.550495i	0.894162	+	0.447744i	$0.147773\pi$
$728$	6.99748	+	0.720889i	0.259344	+	0.0267179i
$729$		0			0
$730$	−22.8855	−	6.13215i	−0.847030	−	0.226961i
$731$	16.2524	+	9.38330i	0.601115	+	0.347054i
$732$		0			0
$733$	−0.441496	−	1.64769i	−0.0163070	−	0.0608587i	0.957293	−	0.289120i	$-0.0933626\pi$
$733$	−0.441496	−	1.64769i	−0.0163070	−	0.0608587i	−0.973600	+	0.228261i	$0.926696\pi$
$734$	−6.00990	+	22.4293i	−0.221829	+	0.827879i
$735$		0			0
$736$	−1.81012	+	6.75546i	−0.0667219	+	0.249009i
$737$	−0.538965	−	0.311172i	−0.0198530	−	0.0114622i
$738$		0			0
$739$	−12.2243	+	45.6218i	−0.449679	+	1.67822i	0.253600	+	0.967309i	$0.418385\pi$
$739$	−12.2243	+	45.6218i	−0.449679	+	1.67822i	−0.703279	+	0.710914i	$0.748281\pi$
$740$	−11.9403	−	20.6812i	−0.438933	−	0.760255i
$741$		0			0
$742$	−8.07649	+	13.9889i	−0.296497	+	0.513548i
$743$	22.8373	+	22.8373i	0.837819	+	0.837819i	0.988571	−	0.150753i	$-0.0481698\pi$
$743$	22.8373	+	22.8373i	0.837819	+	0.837819i	−0.150753	+	0.988571i	$0.548170\pi$
$744$		0			0
$745$		−	22.9428i		−	0.840558i
$746$	−17.8997	−	17.8997i	−0.655355	−	0.655355i
$747$		0			0
$748$	−6.22578	+	1.66819i	−0.227637	+	0.0609952i
$749$	34.9309	+	9.35972i	1.27635	+	0.341997i
$750$		0			0
$751$		−	36.8858i		−	1.34598i	−0.739651	−	0.672991i	$-0.765009\pi$
$751$		−	36.8858i		−	1.34598i	0.739651	−	0.672991i	$-0.234991\pi$
$752$	3.76910	−	3.76910i	0.137445	−	0.137445i
$753$		0			0
$754$	26.5346	+	10.1230i	0.966333	+	0.368658i
$755$			23.4303i			0.852717i
$756$		0			0
$757$	−6.73813	−	11.6708i	−0.244902	−	0.424182i	0.717202	−	0.696865i	$-0.245422\pi$
$757$	−6.73813	−	11.6708i	−0.244902	−	0.424182i	−0.962104	+	0.272683i	$0.912089\pi$
$758$	−23.0723			−0.838025
$759$		0			0
$760$	13.0176	+	3.48807i	0.472199	+	0.126525i
$761$	39.5762	+	10.6044i	1.43463	+	0.384409i	0.890651	−	0.454687i	$-0.150249\pi$
$761$	39.5762	+	10.6044i	1.43463	+	0.384409i	0.543983	+	0.839096i	$0.316915\pi$
$762$		0			0
$763$	−11.6732			−0.422599
$764$	−0.210355	−	0.364345i	−0.00761037	−	0.0131815i
$765$		0			0
$766$		−	23.8524i		−	0.861821i
$767$	−29.7388	−	11.3454i	−1.07380	−	0.409658i
$768$		0			0
$769$	−15.4846	+	15.4846i	−0.558390	+	0.558390i	−0.928849	−	0.370459i	$-0.879200\pi$
$769$	−15.4846	+	15.4846i	−0.558390	+	0.558390i	0.370459	+	0.928849i	$0.379200\pi$
$770$		−	4.61022i		−	0.166141i
$771$		0			0
$772$	−13.1262	−	3.51716i	−0.472424	−	0.126586i
$773$	−34.2518	+	9.17773i	−1.23195	+	0.330100i	−0.815338	−	0.578985i	$-0.803449\pi$
$773$	−34.2518	+	9.17773i	−1.23195	+	0.330100i	−0.416611	+	0.909085i	$0.636782\pi$
$774$		0			0
$775$	6.24205	+	6.24205i	0.224221	+	0.224221i
$776$		−	3.67384i		−	0.131883i
$777$		0			0
$778$	17.6754	+	17.6754i	0.633694	+	0.633694i
$779$	11.8427	−	20.5122i	0.424309	−	0.734925i
$780$		0			0
$781$	−1.06759	−	1.84911i	−0.0382012	−	0.0661665i
$782$	−14.5555	+	54.3217i	−0.520502	+	1.94254i
$783$		0			0
$784$	−2.76566	−	1.59676i	−0.0987736	−	0.0570270i
$785$	−3.00655	+	11.2206i	−0.107308	+	0.400480i
$786$		0			0
$787$	−1.37584	+	5.13469i	−0.0490432	+	0.183032i	−0.986102	−	0.166139i	$-0.946870\pi$
$787$	−1.37584	+	5.13469i	−0.0490432	+	0.183032i	0.937059	+	0.349171i	$0.113537\pi$
$788$	0.239457	+	0.893667i	0.00853032	+	0.0318356i
$789$		0			0
$790$	−2.83132	−	1.63466i	−0.100734	−	0.0581586i
$791$	−11.2680	−	3.01925i	−0.400644	−	0.107352i
$792$		0			0
$793$	17.7147	+	1.82499i	0.629067	+	0.0648073i
$794$	18.2819	−	10.5551i	0.648800	−	0.374585i
$795$		0			0
$796$	12.8257			0.454595
$797$	2.55627	+	4.42759i	0.0905478	+	0.156833i	0.907742	−	0.419529i	$-0.137805\pi$
$797$	2.55627	+	4.42759i	0.0905478	+	0.156833i	−0.817194	+	0.576363i	$0.804472\pi$
$798$		0			0
$799$	30.3080	−	30.3080i	1.07222	−	1.07222i
$800$	−0.955238	−	3.56500i	−0.0337728	−	0.126042i
$801$		0			0
$802$	8.83914	−	15.3098i	0.312121	−	0.540609i
$803$	3.22098	−	5.57891i	0.113666	−	0.196875i
$804$		0			0
$805$	−34.8363	−	20.1128i	−1.22782	−	0.708882i
$806$	−3.52384	−	7.87098i	−0.124122	−	0.277244i
$807$		0			0
$808$	−3.53128	−	13.1789i	−0.124230	−	0.463632i
$809$	12.6443	−	7.30018i	0.444549	−	0.256661i	−0.260976	−	0.965345i	$-0.584044\pi$
$809$	12.6443	−	7.30018i	0.444549	−	0.256661i	0.705525	+	0.708685i	$0.250711\pi$
$810$		0			0
$811$	−20.1306	+	20.1306i	−0.706880	+	0.706880i	−0.965878	−	0.258998i	$-0.916608\pi$
$811$	−20.1306	+	20.1306i	−0.706880	+	0.706880i	0.258998	+	0.965878i	$0.416608\pi$
$812$	10.8666	+	10.8666i	0.381343	+	0.381343i
$813$		0			0
$814$	6.27177	−	1.68052i	0.219825	−	0.0589021i
$815$	52.6746	−	30.4117i	1.84511	−	1.06527i
$816$		0			0
$817$	10.3055	−	2.76136i	0.360545	−	0.0966077i
$818$	20.9174			0.731359
$819$		0			0
$820$	−15.2739			−0.533388
$821$	−4.87897	+	1.30731i	−0.170277	+	0.0456256i	−0.342950	−	0.939354i	$-0.611426\pi$
$821$	−4.87897	+	1.30731i	−0.170277	+	0.0456256i	0.172673	+	0.984979i	$0.444760\pi$
$822$		0			0
$823$	−38.3390	+	22.1350i	−1.33641	+	0.771579i	−0.986274	−	0.165118i	$-0.947199\pi$
$823$	−38.3390	+	22.1350i	−1.33641	+	0.771579i	−0.350140	+	0.936697i	$0.613866\pi$
$824$	−13.0128	+	3.48677i	−0.453322	+	0.121467i
$825$		0			0
$826$	−12.1788	−	12.1788i	−0.423754	−	0.423754i
$827$	14.3305	−	14.3305i	0.498320	−	0.498320i	−0.412595	−	0.910915i	$-0.635377\pi$
$827$	14.3305	−	14.3305i	0.498320	−	0.498320i	0.910915	+	0.412595i	$0.135377\pi$
$828$		0			0
$829$	18.5330	−	10.7000i	0.643677	−	0.371627i	−0.142352	−	0.989816i	$-0.545467\pi$
$829$	18.5330	−	10.7000i	0.643677	−	0.371627i	0.786030	+	0.618189i	$0.212133\pi$
$830$	−1.81100	−	6.75873i	−0.0628606	−	0.234599i
$831$		0			0
$832$	−0.369493	+	3.58657i	−0.0128099	+	0.124342i
$833$	−22.2391	−	12.8398i	−0.770541	−	0.444872i
$834$		0			0
$835$	−8.31824	+	14.4076i	−0.287865	+	0.498596i
$836$	−1.83215	+	3.17337i	−0.0633662	+	0.109753i
$837$		0			0
$838$	4.63281	+	17.2899i	0.160038	+	0.597269i
$839$	−34.4148	+	34.4148i	−1.18813	+	1.18813i	−0.210549	+	0.977583i	$0.567525\pi$
$839$	−34.4148	+	34.4148i	−1.18813	+	1.18813i	−0.977583	+	0.210549i	$0.932475\pi$
$840$		0			0
$841$	16.5215	+	28.6161i	0.569708	+	0.986763i
$842$	0.955439			0.0329266
$843$		0			0
$844$	5.92886	−	3.42303i	0.204080	−	0.117825i
$845$	−38.2630	+	2.16344i	−1.31629	+	0.0744246i
$846$		0			0
$847$	−19.5192	−	5.23015i	−0.670687	−	0.179710i
$848$	−7.17003	−	4.13962i	−0.246220	−	0.142155i
$849$		0			0
$850$	−7.68123	−	28.6667i	−0.263464	−	0.983261i
$851$	14.6630	−	54.7230i	0.502641	−	1.87588i
$852$		0			0
$853$	−0.430304	+	1.60592i	−0.0147333	+	0.0549855i	−0.972901	−	0.231221i	$-0.925728\pi$
$853$	−0.430304	+	1.60592i	−0.0147333	+	0.0549855i	0.958168	+	0.286207i	$0.0923945\pi$
$854$	8.34540	+	4.81822i	0.285574	+	0.164876i
$855$		0			0
$856$	−4.79734	+	17.9039i	−0.163970	+	0.611943i
$857$	−6.29501	−	10.9033i	−0.215033	−	0.372449i	0.738249	−	0.674528i	$-0.235653\pi$
$857$	−6.29501	−	10.9033i	−0.215033	−	0.372449i	−0.953283	+	0.302079i	$0.902319\pi$
$858$		0			0
$859$	11.6155	−	20.1186i	0.396315	−	0.686438i	−0.596953	−	0.802276i	$-0.703622\pi$
$859$	11.6155	−	20.1186i	0.396315	−	0.686438i	0.993268	+	0.115838i	$0.0369554\pi$
$860$	−4.86497	−	4.86497i	−0.165894	−	0.165894i
$861$		0			0
$862$		−	39.2646i		−	1.33736i
$863$	−21.8752	−	21.8752i	−0.744642	−	0.744642i	0.228826	−	0.973467i	$-0.426511\pi$
$863$	−21.8752	−	21.8752i	−0.744642	−	0.744642i	−0.973467	+	0.228826i	$0.926511\pi$
$864$		0			0
$865$	−46.7937	+	12.5383i	−1.59103	+	0.426316i
$866$	10.6342	+	2.84942i	0.361365	+	0.0968274i
$867$		0			0
$868$		−	4.66648i		−	0.158390i
$869$	0.628557	−	0.628557i	0.0213223	−	0.0213223i
$870$		0			0
$871$	−2.17194	+	1.76622i	−0.0735933	+	0.0598462i
$872$		−	5.98313i		−	0.202614i
$873$		0			0
$874$	15.9860	+	27.6886i	0.540735	+	0.936581i
$875$	−7.53029			−0.254570
$876$		0			0
$877$	−25.8463	−	6.92550i	−0.872769	−	0.233858i	−0.205484	−	0.978660i	$-0.565877\pi$
$877$	−25.8463	−	6.92550i	−0.872769	−	0.233858i	−0.667285	+	0.744803i	$0.732544\pi$
$878$	4.11778	+	1.10336i	0.138968	+	0.0372364i
$879$		0			0
$880$	2.36298			0.0796560
$881$	−11.3559	−	19.6690i	−0.382589	−	0.662664i	0.608842	−	0.793291i	$-0.291634\pi$
$881$	−11.3559	−	19.6690i	−0.382589	−	0.662664i	−0.991432	+	0.130627i	$0.958301\pi$
$882$		0			0
$883$			11.3387i			0.381577i	0.981631	+	0.190789i	$0.0611045\pi$
$883$			11.3387i			0.381577i	−0.981631	+	0.190789i	$0.938895\pi$
$884$	−2.97115	+	28.8402i	−0.0999307	+	0.970001i
$885$		0			0
$886$	−20.3999	+	20.3999i	−0.685346	+	0.685346i
$887$		−	17.8989i		−	0.600985i	−0.953784	−	0.300492i	$-0.902849\pi$
$887$		−	17.8989i		−	0.600985i	0.953784	−	0.300492i	$-0.0971510\pi$
$888$		0			0
$889$	−4.21758	−	1.13010i	−0.141453	−	0.0379023i
$890$	−8.37441	+	2.24392i	−0.280711	+	0.0752163i
$891$		0			0
$892$	12.5100	+	12.5100i	0.418866	+	0.418866i
$893$		−	24.3676i		−	0.815430i
$894$		0			0
$895$	−12.6267	−	12.6267i	−0.422065	−	0.422065i
$896$	−0.975511	+	1.68964i	−0.0325895	+	0.0564467i
$897$		0			0
$898$	−12.6811	−	21.9644i	−0.423175	−	0.732961i
$899$	4.87606	−	18.1977i	0.162626	−	0.606928i
$900$		0			0
$901$	−57.6554	−	33.2874i	−1.92078	−	1.10896i
$902$	1.07485	−	4.01140i	0.0357886	−	0.133565i
$903$		0			0
$904$	1.54752	−	5.77543i	0.0514698	−	0.192088i
$905$	−9.34574	−	34.8788i	−0.310663	−	1.15941i
$906$		0			0
$907$	−42.4694	−	24.5197i	−1.41017	−	0.814165i	−0.414770	−	0.909926i	$-0.636138\pi$
$907$	−42.4694	−	24.5197i	−1.41017	−	0.814165i	−0.995404	+	0.0957617i	$0.969471\pi$
$908$	−18.7066	−	5.01242i	−0.620801	−	0.166343i
$909$		0			0
$910$	−19.3757	−	7.39185i	−0.642298	−	0.245038i
$911$	49.7924	−	28.7477i	1.64970	−	0.952453i	0.672506	−	0.740092i	$-0.265218\pi$
$911$	49.7924	−	28.7477i	1.64970	−	0.952453i	0.977191	−	0.212362i	$-0.0681155\pi$
$912$		0			0
$913$	1.90249			0.0629634
$914$	−14.3832	−	24.9124i	−0.475753	−	0.824029i
$915$		0			0
$916$	18.3643	−	18.3643i	0.606773	−	0.606773i
$917$	4.30221	+	16.0561i	0.142071	+	0.530218i
$918$		0			0
$919$	−18.6828	+	32.3595i	−0.616288	+	1.06744i	0.373869	+	0.927482i	$0.378031\pi$
$919$	−18.6828	+	32.3595i	−0.616288	+	1.06744i	−0.990157	+	0.139961i	$0.955302\pi$
$920$	10.3088	−	17.8554i	0.339872	−	0.588676i
$921$		0			0
$922$	−32.0445	−	18.5009i	−1.05533	−	0.609295i
$923$	−9.48312	+	1.52202i	−0.312141	+	0.0500978i
$924$		0			0
$925$	7.73797	+	28.8785i	0.254423	+	0.949519i
$926$	−2.15728	+	1.24550i	−0.0708925	+	0.0409298i
$927$		0			0
$928$	−5.56970	+	5.56970i	−0.182834	+	0.182834i
$929$	13.3388	+	13.3388i	0.437632	+	0.437632i	0.891214	−	0.453582i	$-0.149854\pi$
$929$	13.3388	+	13.3388i	0.437632	+	0.437632i	−0.453582	+	0.891214i	$0.649854\pi$
$930$		0			0
$931$	−14.1017	+	3.77854i	−0.462165	+	0.123837i
$932$	10.3135	−	5.95449i	0.337830	−	0.195046i
$933$		0			0
$934$	30.2085	−	8.09433i	0.988451	−	0.264855i
$935$	19.0011			0.621402
$936$		0			0
$937$	38.9992			1.27405			0.637025	−	0.770843i	$-0.280165\pi$
$937$	38.9992			1.27405			0.637025	+	0.770843i	$0.280165\pi$
$938$	−1.46321	+	0.392065i	−0.0477754	+	0.0128014i
$939$		0			0
$940$	−13.6086	+	7.85691i	−0.443862	+	0.256264i
$941$	52.8136	−	14.1514i	1.72167	−	0.461321i	0.743437	−	0.668806i	$-0.233195\pi$
$941$	52.8136	−	14.1514i	1.72167	−	0.461321i	0.978238	+	0.207485i	$0.0665279\pi$
$942$		0			0
$943$	−25.6223	−	25.6223i	−0.834375	−	0.834375i
$944$	6.24226	−	6.24226i	0.203168	−	0.203168i
$945$		0			0
$946$	1.62005	−	0.935336i	0.0526723	−	0.0304104i
$947$	−0.410138	−	1.53066i	−0.0133277	−	0.0497397i	0.958942	−	0.283603i	$-0.0915298\pi$
$947$	−0.410138	−	1.53066i	−0.0133277	−	0.0497397i	−0.972269	+	0.233863i	$0.924863\pi$
$948$		0			0
$949$	−18.2824	−	22.4820i	−0.593473	−	0.729798i
$950$	−14.6119	−	8.43617i	−0.474072	−	0.273705i
$951$		0			0
$952$	−7.84425	+	13.5866i	−0.254234	+	0.440345i
$953$	−10.7911	+	18.6908i	−0.349559	+	0.605454i	−0.986171	−	0.165730i	$-0.947002\pi$
$953$	−10.7911	+	18.6908i	−0.349559	+	0.605454i	0.636612	+	0.771184i	$0.280335\pi$
$954$		0			0
$955$	0.321002	+	1.19799i	0.0103874	+	0.0387662i
$956$	−6.56269	+	6.56269i	−0.212253	+	0.212253i
$957$		0			0
$958$	−2.76911	−	4.79624i	−0.0894659	−	0.154960i
$959$	22.6764			0.732259
$960$		0			0
$961$	21.8925	−	12.6396i	0.706209	−	0.407730i
$962$	2.99310	−	29.0532i	0.0965015	−	0.936714i
$963$		0			0
$964$	−9.45875	−	2.53446i	−0.304646	−	0.0816296i
$965$	34.6941	+	20.0307i	1.11684	+	0.644810i
$966$		0			0
$967$	12.5386	+	46.7947i	0.403215	+	1.50482i	0.807325	+	0.590107i	$0.200915\pi$
$967$	12.5386	+	46.7947i	0.403215	+	1.50482i	−0.404110	+	0.914710i	$0.632419\pi$
$968$	2.68072	−	10.0046i	0.0861617	−	0.321560i
$969$		0			0
$970$	−2.80315	+	10.4615i	−0.0900036	+	0.335898i
$971$	−1.30561	−	0.753792i	−0.0418989	−	0.0241903i	0.478904	−	0.877867i	$-0.341034\pi$
$971$	−1.30561	−	0.753792i	−0.0418989	−	0.0241903i	−0.520803	+	0.853677i	$0.674367\pi$
$972$		0			0
$973$	−11.5276	+	43.0214i	−0.369557	+	1.37920i
$974$	−1.46689	−	2.54073i	−0.0470022	−	0.0814102i
$975$		0			0
$976$	−2.46959	+	4.27745i	−0.0790495	+	0.136918i
$977$	−22.2801	−	22.2801i	−0.712804	−	0.712804i	0.254317	−	0.967121i	$-0.418149\pi$
$977$	−22.2801	−	22.2801i	−0.712804	−	0.712804i	−0.967121	+	0.254317i	$0.918149\pi$
$978$		0			0
$979$		−	2.35729i		−	0.0753393i
$980$	6.65706	+	6.65706i	0.212652	+	0.212652i
$981$		0			0
$982$	34.4824	−	9.23952i	1.10038	−	0.294845i
$983$	13.9059	+	3.72607i	0.443529	+	0.118843i	0.473670	−	0.880702i	$-0.342929\pi$
$983$	13.9059	+	3.72607i	0.443529	+	0.118843i	−0.0301410	+	0.999546i	$0.509596\pi$
$984$		0			0
$985$		−	2.72748i		−	0.0869046i
$986$	−44.7869	+	44.7869i	−1.42630	+	1.42630i
$987$		0			0
$988$	10.3993	+	12.7882i	0.330847	+	0.406845i
$989$		−	16.3222i		−	0.519014i
$990$		0			0
$991$	9.55307	+	16.5464i	0.303463	+	0.525614i	0.976918	−	0.213615i	$-0.0685236\pi$
$991$	9.55307	+	16.5464i	0.303463	+	0.525614i	−0.673455	+	0.739229i	$0.735190\pi$
$992$	2.39181			0.0759400
$993$		0			0
$994$	−5.02005	−	1.34512i	−0.159226	−	0.0426646i
$995$	−36.5220	−	9.78603i	−1.15782	−	0.310238i
$996$		0			0
$997$	4.95003			0.156769			0.0783845	−	0.996923i	$-0.475024\pi$
$997$	4.95003			0.156769			0.0783845	+	0.996923i	$0.475024\pi$
$998$	9.11683	+	15.7908i	0.288588	+	0.499850i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	702.2.bc.a.665.9		56
3.2	odd	2		234.2.z.a.41.6	yes	56
9.2	odd	6		702.2.bb.a.197.9		56
9.7	even	3		234.2.y.a.119.1	yes	56
13.7	odd	12		702.2.bb.a.449.9		56
39.20	even	12		234.2.y.a.59.1	✓	56
117.7	odd	12		234.2.z.a.137.6	yes	56
117.20	even	12	inner	702.2.bc.a.683.9		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
234.2.y.a.59.1	✓	56	39.20	even	12
234.2.y.a.119.1	yes	56	9.7	even	3
234.2.z.a.41.6	yes	56	3.2	odd	2
234.2.z.a.137.6	yes	56	117.7	odd	12
702.2.bb.a.197.9		56	9.2	odd	6
702.2.bb.a.449.9		56	13.7	odd	12
702.2.bc.a.665.9		56	1.1	even	1	trivial
702.2.bc.a.683.9		56	117.20	even	12	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 702 = 2 \cdot 3^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	702.bc (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.965926 - 0.258819i) q^{2} +(0.866025 - 0.500000i) q^{4} +(-2.84756 + 0.763001i) q^{5} +(-1.37958 - 1.37958i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.55305 + 1.47400i) q^{10} +(-0.207457 - 0.774238i) q^{11} +(-3.58657 - 0.369493i) q^{13} +(-1.68964 - 0.975511i) q^{14} +(0.500000 - 0.866025i) q^{16} +(4.02058 - 6.96385i) q^{17} +(-1.18319 - 4.41574i) q^{19} +(-2.08456 + 2.08456i) q^{20} +(-0.400775 - 0.694163i) q^{22} -6.99376 q^{23} +(3.19629 - 1.84538i) q^{25} +(-3.55999 + 0.571370i) q^{26} +(-1.88454 - 0.504962i) q^{28} +(-6.82146 - 3.93837i) q^{29} +(0.619046 + 2.31031i) q^{31} +(0.258819 - 0.965926i) q^{32} +(2.08121 - 7.76717i) q^{34} +(4.98106 + 2.87582i) q^{35} +(-2.09658 + 7.82455i) q^{37} +(-2.28576 - 3.95904i) q^{38} +(-1.47400 + 2.55305i) q^{40} +(3.66359 + 3.66359i) q^{41} +2.33382i q^{43} +(-0.566782 - 0.566782i) q^{44} +(-6.75546 + 1.81012i) q^{46} +(5.14869 + 1.37959i) q^{47} -3.19351i q^{49} +(2.60976 - 2.60976i) q^{50} +(-3.29081 + 1.47329i) q^{52} -8.27924i q^{53} +(1.18149 + 2.04640i) q^{55} -1.95102 q^{56} +(-7.60835 - 2.03865i) q^{58} +(8.52709 + 2.28483i) q^{59} -4.93917 q^{61} +(1.19590 + 2.07137i) q^{62} -1.00000i q^{64} +(10.4949 - 1.68440i) q^{65} +(0.549015 - 0.549015i) q^{67} -8.04117i q^{68} +(5.55565 + 1.48863i) q^{70} +(2.57304 - 0.689443i) q^{71} +(5.68293 + 5.68293i) q^{73} +8.10057i q^{74} +(-3.23255 - 3.23255i) q^{76} +(-0.781921 + 1.35433i) q^{77} +(0.554497 + 0.960416i) q^{79} +(-0.763001 + 2.84756i) q^{80} +(4.48696 + 2.59055i) q^{82} +(-0.614312 + 2.29264i) q^{83} +(-6.13542 + 22.8977i) q^{85} +(0.604036 + 2.25429i) q^{86} +(-0.694163 - 0.400775i) q^{88} +(2.84070 + 0.761164i) q^{89} +(4.43822 + 5.45771i) q^{91} +(-6.05678 + 3.49688i) q^{92} +5.33031 q^{94} +(6.73843 + 11.6713i) q^{95} +(2.59780 - 2.59780i) q^{97} +(-0.826542 - 3.08469i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{7} + 24 q^{11} + 28 q^{16} - 8 q^{19} - 4 q^{28} - 4 q^{31} + 24 q^{35} - 4 q^{37} - 36 q^{38} + 48 q^{41} + 36 q^{47} + 24 q^{50} + 8 q^{52} + 36 q^{65} + 28 q^{67} + 24 q^{71} + 28 q^{73}+ \cdots - 48 q^{98}+O(q^{100}) \) 56 * q - 8 * q^7 + 24 * q^11 + 28 * q^16 - 8 * q^19 - 4 * q^28 - 4 * q^31 + 24 * q^35 - 4 * q^37 - 36 * q^38 + 48 * q^41 + 36 * q^47 + 24 * q^50 + 8 * q^52 + 36 * q^65 + 28 * q^67 + 24 * q^71 + 28 * q^73 + 4 * q^76 - 24 * q^77 - 24 * q^79 + 96 * q^83 - 72 * q^85 + 4 * q^91 + 24 * q^92 - 52 * q^97 - 48 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more