LMFDB - Embedded newform 700.2.be.e.443.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [700,2,Mod(107,700)] 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("700.107"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(700, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 3, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 700 = 2^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	700.be (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [72,-2,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$5.58952814149$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			443.6
Character	$\chi$	$=$	700.443
Dual form			700.2.be.e.207.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.952442 + 1.04540i) q^{2} +(-2.71477 - 0.727420i) q^{3} +(-0.185707 - 1.99136i) q^{4} +(3.34610 - 2.14518i) q^{6} +(2.59868 + 0.496852i) q^{7} +(2.25864 + 1.70252i) q^{8} +(4.24276 + 2.44956i) q^{9} +(-2.75736 + 1.59196i) q^{11} +(-0.944404 + 5.54117i) q^{12} +(-2.41925 - 2.41925i) q^{13} +(-2.99450 + 2.24343i) q^{14} +(-3.93103 + 0.739618i) q^{16} +(-2.24094 - 0.600458i) q^{17} +(-6.60174 + 2.10230i) q^{18} +(1.39787 - 2.42118i) q^{19} +(-6.69340 - 3.23917i) q^{21} +(0.961994 - 4.39878i) q^{22} +(1.39288 + 5.19830i) q^{23} +(-4.89323 - 6.26492i) q^{24} +(4.83327 - 0.224879i) q^{26} +(-3.77420 - 3.77420i) q^{27} +(0.506818 - 5.26718i) q^{28} +1.72334i q^{29} +(3.01685 - 1.74178i) q^{31} +(2.97088 - 4.81392i) q^{32} +(8.64362 - 2.31605i) q^{33} +(2.76208 - 1.77077i) q^{34} +(4.09004 - 8.90375i) q^{36} +(0.623610 + 2.32734i) q^{37} +(1.19970 + 3.76736i) q^{38} +(4.80790 + 8.32752i) q^{39} +2.72503 q^{41} +(9.76129 - 3.91213i) q^{42} +(3.96477 - 3.96477i) q^{43} +(3.68223 + 5.19525i) q^{44} +(-6.76092 - 3.49497i) q^{46} +(6.10452 - 1.63570i) q^{47} +(11.2098 + 0.851615i) q^{48} +(6.50628 + 2.58232i) q^{49} +(5.64685 + 3.26021i) q^{51} +(-4.36833 + 5.26687i) q^{52} +(3.37866 - 12.6093i) q^{53} +(7.54024 - 0.350826i) q^{54} +(5.02357 + 5.54651i) q^{56} +(-5.55610 + 5.55610i) q^{57} +(-1.80158 - 1.64139i) q^{58} +(0.951402 + 1.64788i) q^{59} +(5.83980 - 10.1148i) q^{61} +(-1.05253 + 4.81275i) q^{62} +(9.80850 + 8.47363i) q^{63} +(2.20286 + 7.69073i) q^{64} +(-5.81136 + 11.2419i) q^{66} +(-1.51938 + 5.67039i) q^{67} +(-0.779570 + 4.57403i) q^{68} -15.1254i q^{69} -0.562181i q^{71} +(5.41242 + 12.7560i) q^{72} +(-0.866554 + 3.23402i) q^{73} +(-3.02695 - 1.56474i) q^{74} +(-5.08103 - 2.33403i) q^{76} +(-7.95646 + 2.76700i) q^{77} +(-13.2848 - 2.90533i) q^{78} +(4.13532 - 7.16259i) q^{79} +(0.151981 + 0.263239i) q^{81} +(-2.59543 + 2.84874i) q^{82} +(4.38250 - 4.38250i) q^{83} +(-5.20734 + 13.9305i) q^{84} +(0.368541 + 7.92097i) q^{86} +(1.25360 - 4.67848i) q^{87} +(-8.93821 - 1.09879i) q^{88} +(-2.51180 - 1.45019i) q^{89} +(-5.08485 - 7.48887i) q^{91} +(10.0930 - 3.73908i) q^{92} +(-9.45706 + 2.53401i) q^{93} +(-4.10425 + 7.93955i) q^{94} +(-11.5670 + 10.9076i) q^{96} +(10.9216 - 10.9216i) q^{97} +(-8.89640 + 4.34213i) q^{98} -15.5984 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 2 q^{2} - 16 q^{6} + 4 q^{8} - 10 q^{12} - 28 q^{16} - 4 q^{17} + 20 q^{18} + 4 q^{21} + 16 q^{22} - 4 q^{26} - 42 q^{28} + 38 q^{32} + 64 q^{33} + 16 q^{36} + 4 q^{37} - 12 q^{38} - 40 q^{41} - 78 q^{42}+ \cdots + 90 q^{98}+O(q^{100}) $ 72 * q - 2 * q^2 - 16 * q^6 + 4 * q^8 - 10 * q^12 - 28 * q^16 - 4 * q^17 + 20 * q^18 + 4 * q^21 + 16 * q^22 - 4 * q^26 - 42 * q^28 + 38 * q^32 + 64 * q^33 + 16 * q^36 + 4 * q^37 - 12 * q^38 - 40 * q^41 - 78 * q^42 - 28 * q^46 - 12 * q^48 - 48 * q^52 + 24 * q^53 + 36 * q^56 + 16 * q^57 - 30 * q^58 - 20 * q^61 - 56 * q^62 + 44 * q^66 + 12 * q^68 - 44 * q^72 + 12 * q^73 + 112 * q^76 - 16 * q^77 - 64 * q^78 - 52 * q^81 + 34 * q^82 + 64 * q^86 - 16 * q^88 - 44 * q^92 - 12 * q^93 - 48 * q^96 + 24 * q^97 + 90 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/700\mathbb{Z}\right)^\times$.

$n$	$101$	$351$	$477$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.952442	+	1.04540i	−0.673478	+	0.739207i
$2$	−0.952442	+	1.04540i	−0.673478	+	0.739207i
$3$	−2.71477	−	0.727420i	−1.56737	−	0.419976i	−0.632384	−	0.774655i	$-0.717924\pi$
$3$	−2.71477	−	0.727420i	−1.56737	−	0.419976i	−0.934988	+	0.354678i	$0.884590\pi$
$4$	−0.185707	−	1.99136i	−0.0928534	−	0.995680i
$5$		0			0
$5$		0			0
$6$	3.34610	−	2.14518i	1.36604	−	0.875768i
$7$	2.59868	+	0.496852i	0.982209	+	0.187792i
$7$	2.59868	+	0.496852i	0.982209	+	0.187792i
$8$	2.25864	+	1.70252i	0.798548	+	0.601931i
$9$	4.24276	+	2.44956i	1.41425	+	0.816519i
$10$		0			0
$11$	−2.75736	+	1.59196i	−0.831375	+	0.479994i	−0.854323	−	0.519742i	$-0.826028\pi$
$11$	−2.75736	+	1.59196i	−0.831375	+	0.479994i	0.0229484	+	0.999737i	$0.492695\pi$
$12$	−0.944404	+	5.54117i	−0.272626	+	1.59960i
$13$	−2.41925	−	2.41925i	−0.670980	−	0.670980i	0.286962	−	0.957942i	$-0.407355\pi$
$13$	−2.41925	−	2.41925i	−0.670980	−	0.670980i	−0.957942	+	0.286962i	$0.907355\pi$
$14$	−2.99450	+	2.24343i	−0.800314	+	0.599581i
$15$		0			0
$16$	−3.93103	+	0.739618i	−0.982756	+	0.184905i
$17$	−2.24094	−	0.600458i	−0.543508	−	0.145632i	−0.0233890	−	0.999726i	$-0.507446\pi$
$17$	−2.24094	−	0.600458i	−0.543508	−	0.145632i	−0.520119	+	0.854094i	$0.674112\pi$
$18$	−6.60174	+	2.10230i	−1.55604	+	0.495517i
$19$	1.39787	−	2.42118i	0.320693	−	0.555456i	−0.659938	−	0.751320i	$-0.729418\pi$
$19$	1.39787	−	2.42118i	0.320693	−	0.555456i	0.980631	+	0.195863i	$0.0627510\pi$
$20$		0			0
$21$	−6.69340	−	3.23917i	−1.46062	−	0.706845i
$22$	0.961994	−	4.39878i	0.205098	−	0.937824i
$23$	1.39288	+	5.19830i	0.290435	+	1.08392i	0.944775	+	0.327719i	$0.106280\pi$
$23$	1.39288	+	5.19830i	0.290435	+	1.08392i	−0.654340	+	0.756201i	$0.727053\pi$
$24$	−4.89323	−	6.26492i	−0.998826	−	1.27882i
$25$		0			0
$26$	4.83327	−	0.224879i	0.947883	−	0.0441024i
$27$	−3.77420	−	3.77420i	−0.726345	−	0.726345i
$28$	0.506818	−	5.26718i	0.0957796	−	0.995403i
$29$			1.72334i			0.320017i	0.987116	+	0.160009i	$0.0511522\pi$
$29$			1.72334i			0.320017i	−0.987116	+	0.160009i	$0.948848\pi$
$30$		0			0
$31$	3.01685	−	1.74178i	0.541843	−	0.312833i	−0.203983	−	0.978974i	$-0.565389\pi$
$31$	3.01685	−	1.74178i	0.541843	−	0.312833i	0.745825	+	0.666141i	$0.232055\pi$
$32$	2.97088	−	4.81392i	0.525183	−	0.850990i
$33$	8.64362	−	2.31605i	1.50466	−	0.403173i
$34$	2.76208	−	1.77077i	0.473693	−	0.303684i
$35$		0			0
$36$	4.09004	−	8.90375i	0.681673	−	1.48396i
$37$	0.623610	+	2.32734i	0.102521	+	0.382613i	0.998052	−	0.0623856i	$-0.0198709\pi$
$37$	0.623610	+	2.32734i	0.102521	+	0.382613i	−0.895531	+	0.444999i	$0.853204\pi$
$38$	1.19970	+	3.76736i	0.194617	+	0.611146i
$39$	4.80790	+	8.32752i	0.769880	+	1.33347i
$40$		0			0
$41$	2.72503			0.425578			0.212789	−	0.977098i	$-0.431745\pi$
$41$	2.72503			0.425578			0.212789	+	0.977098i	$0.431745\pi$
$42$	9.76129	−	3.91213i	1.50620	−	0.603654i
$43$	3.96477	−	3.96477i	0.604622	−	0.604622i	−0.336914	−	0.941536i	$-0.609383\pi$
$43$	3.96477	−	3.96477i	0.604622	−	0.604622i	0.941536	+	0.336914i	$0.109383\pi$
$44$	3.68223	+	5.19525i	0.555117	+	0.783214i
$45$		0			0
$46$	−6.76092	−	3.49497i	−0.996843	−	0.515305i
$47$	6.10452	−	1.63570i	0.890435	−	0.238591i	0.215531	−	0.976497i	$-0.430852\pi$
$47$	6.10452	−	1.63570i	0.890435	−	0.238591i	0.674904	+	0.737905i	$0.264185\pi$
$48$	11.2098	+	0.851615i	1.61800	+	0.122920i
$49$	6.50628	+	2.58232i	0.929468	+	0.368903i
$50$		0			0
$51$	5.64685	+	3.26021i	0.790717	+	0.456521i
$52$	−4.36833	+	5.26687i	−0.605778	+	0.730384i
$53$	3.37866	−	12.6093i	0.464094	−	1.73202i	−0.195780	−	0.980648i	$-0.562724\pi$
$53$	3.37866	−	12.6093i	0.464094	−	1.73202i	0.659874	−	0.751376i	$-0.270610\pi$
$54$	7.54024	−	0.350826i	1.02610	−	0.0477414i
$55$		0			0
$56$	5.02357	+	5.54651i	0.671303	+	0.741183i
$57$	−5.55610	+	5.55610i	−0.735924	+	0.735924i
$58$	−1.80158	−	1.64139i	−0.236559	−	0.215525i
$59$	0.951402	+	1.64788i	0.123862	+	0.214535i	0.921288	−	0.388882i	$-0.127139\pi$
$59$	0.951402	+	1.64788i	0.123862	+	0.214535i	−0.797426	+	0.603417i	$0.793805\pi$
$60$		0			0
$61$	5.83980	−	10.1148i	0.747709	−	1.29507i	−0.201209	−	0.979548i	$-0.564487\pi$
$61$	5.83980	−	10.1148i	0.747709	−	1.29507i	0.948918	−	0.315522i	$-0.102180\pi$
$62$	−1.05253	+	4.81275i	−0.133671	+	0.611220i
$63$	9.80850	+	8.47363i	1.23575	+	1.06758i
$64$	2.20286	+	7.69073i	0.275358	+	0.961342i
$65$		0			0
$66$	−5.81136	+	11.2419i	−0.715329	+	1.38378i
$67$	−1.51938	+	5.67039i	−0.185621	+	0.692748i	0.808875	+	0.587980i	$0.200077\pi$
$67$	−1.51938	+	5.67039i	−0.185621	+	0.692748i	−0.994497	+	0.104768i	$0.966590\pi$
$68$	−0.779570	+	4.57403i	−0.0945367	+	0.554682i
$69$		−	15.1254i		−	1.82088i
$70$		0			0
$71$		−	0.562181i		−	0.0667186i	−0.999443	−	0.0333593i	$-0.989379\pi$
$71$		−	0.562181i		−	0.0667186i	0.999443	−	0.0333593i	$-0.0106206\pi$
$72$	5.41242	+	12.7560i	0.637860	+	1.50331i
$73$	−0.866554	+	3.23402i	−0.101423	+	0.378514i	−0.997915	−	0.0645454i	$-0.979440\pi$
$73$	−0.866554	+	3.23402i	−0.101423	+	0.378514i	0.896492	+	0.443059i	$0.146107\pi$
$74$	−3.02695	−	1.56474i	−0.351876	−	0.181897i
$75$		0			0
$76$	−5.08103	−	2.33403i	−0.582834	−	0.267731i
$77$	−7.95646	+	2.76700i	−0.906723	+	0.315329i
$78$	−13.2848	−	2.90533i	−1.50421	−	0.328963i
$79$	4.13532	−	7.16259i	0.465260	−	0.805855i	−0.533953	−	0.845514i	$-0.679294\pi$
$79$	4.13532	−	7.16259i	0.465260	−	0.805855i	0.999213	+	0.0396596i	$0.0126274\pi$
$80$		0			0
$81$	0.151981	+	0.263239i	0.0168868	+	0.0292487i
$82$	−2.59543	+	2.84874i	−0.286618	+	0.314590i
$83$	4.38250	−	4.38250i	0.481042	−	0.481042i	−0.424423	−	0.905464i	$-0.639523\pi$
$83$	4.38250	−	4.38250i	0.481042	−	0.481042i	0.905464	+	0.424423i	$0.139523\pi$
$84$	−5.20734	+	13.9305i	−0.568168	+	1.51994i
$85$		0			0
$86$	0.368541	+	7.92097i	0.0397408	+	0.854141i
$87$	1.25360	−	4.67848i	0.134400	−	0.501586i
$88$	−8.93821	−	1.09879i	−0.952816	−	0.117132i
$89$	−2.51180	−	1.45019i	−0.266250	−	0.153720i	0.360932	−	0.932592i	$-0.382459\pi$
$89$	−2.51180	−	1.45019i	−0.266250	−	0.153720i	−0.627182	+	0.778872i	$0.715792\pi$
$90$		0			0
$91$	−5.08485	−	7.48887i	−0.533037	−	0.785047i
$92$	10.0930	−	3.73908i	1.05227	−	0.389826i
$93$	−9.45706	+	2.53401i	−0.980652	+	0.262765i
$94$	−4.10425	+	7.93955i	−0.423321	+	0.818902i
$95$		0			0
$96$	−11.5670	+	10.9076i	−1.18055	+	1.11325i
$97$	10.9216	−	10.9216i	1.10892	−	1.10892i	0.115629	−	0.993292i	$-0.463111\pi$
$97$	10.9216	−	10.9216i	1.10892	−	1.10892i	0.993292	−	0.115629i	$-0.0368885\pi$
$98$	−8.89640	+	4.34213i	−0.898672	+	0.438621i
$99$	−15.5984			−1.56770
$100$		0			0
$101$	5.73271	+	9.92934i	0.570426	+	0.988007i	0.996522	+	0.0833288i	$0.0265552\pi$
$101$	5.73271	+	9.92934i	0.570426	+	0.988007i	−0.426096	+	0.904678i	$0.640111\pi$
$102$	−8.78651	+	2.79803i	−0.869994	+	0.277047i
$103$	−3.39107	−	12.6556i	−0.334132	−	1.24700i	−0.904807	−	0.425821i	$-0.859985\pi$
$103$	−3.39107	−	12.6556i	−0.334132	−	1.24700i	0.570676	−	0.821176i	$-0.306681\pi$
$104$	−1.34539	−	9.58302i	−0.131926	−	0.939693i
$105$		0			0
$106$	9.96376	+	15.5417i	0.967766	+	1.50954i
$107$	−0.397018	+	0.106381i	−0.0383812	+	0.0102842i	−0.277959	−	0.960593i	$-0.589658\pi$
$107$	−0.397018	+	0.106381i	−0.0383812	+	0.0102842i	0.239577	+	0.970877i	$0.422991\pi$
$108$	−6.81489	+	8.21668i	−0.655763	+	0.790650i
$109$	6.32499	−	3.65173i	0.605824	−	0.349773i	−0.165505	−	0.986209i	$-0.552926\pi$
$109$	6.32499	−	3.65173i	0.605824	−	0.349773i	0.771329	+	0.636436i	$0.219592\pi$
$110$		0			0
$111$		−	6.77183i		−	0.642753i
$112$	−10.5830	−	0.0311065i	−0.999996	−	0.00293929i
$113$	11.6304	+	11.6304i	1.09410	+	1.09410i	0.995086	+	0.0990127i	$0.0315684\pi$
$113$	11.6304	+	11.6304i	1.09410	+	1.09410i	0.0990127	+	0.995086i	$0.468432\pi$
$114$	−0.516461	−	11.1002i	−0.0483710	−	1.03963i
$115$		0			0
$116$	3.43180	−	0.320037i	0.318635	−	0.0297147i
$117$	−4.33820	−	16.1904i	−0.401067	−	1.49680i
$118$	−2.62884	−	0.574915i	−0.242004	−	0.0529252i
$119$	−5.52515	−	2.67381i	−0.506489	−	0.245108i
$120$		0			0
$121$	−0.431317	+	0.747063i	−0.0392106	+	0.0679148i
$122$	5.01193	+	15.7387i	0.453759	+	1.42491i
$123$	−7.39783	−	1.98224i	−0.667040	−	0.178733i
$124$	−4.02876	−	5.68418i	−0.361793	−	0.510454i
$125$		0			0
$126$	−18.2003	+	2.18312i	−1.62141	+	0.194488i
$127$	1.32146	+	1.32146i	0.117261	+	0.117261i	0.763302	−	0.646042i	$-0.223577\pi$
$127$	1.32146	+	1.32146i	0.117261	+	0.117261i	−0.646042	+	0.763302i	$0.723577\pi$
$128$	−10.1380	−	5.02211i	−0.896078	−	0.443896i
$129$	−13.6475	+	7.87939i	−1.20159	+	0.693741i
$130$		0			0
$131$	3.52422	+	2.03471i	0.307912	+	0.177773i	0.645992	−	0.763344i	$-0.276444\pi$
$131$	3.52422	+	2.03471i	0.307912	+	0.177773i	−0.338080	+	0.941118i	$0.609777\pi$
$132$	−6.21727	−	16.7824i	−0.541144	−	1.46072i
$133$	4.83558	−	5.59733i	0.419298	−	0.485350i
$134$	−4.48068	−	6.98907i	−0.387072	−	0.603764i
$135$		0			0
$136$	−4.03917	−	5.17146i	−0.346356	−	0.443449i
$137$	15.5676	+	4.17132i	1.33003	+	0.356380i	0.852726	−	0.522359i	$-0.174948\pi$
$137$	15.5676	+	4.17132i	1.33003	+	0.356380i	0.477303	+	0.878739i	$0.341615\pi$
$138$	15.8120	+	14.4061i	1.34601	+	1.22632i
$139$	17.0814			1.44882			0.724411	−	0.689369i	$-0.242112\pi$
$139$	17.0814			1.44882			0.724411	+	0.689369i	$0.242112\pi$
$140$		0			0
$141$	−17.7622			−1.49585
$142$	0.587702	+	0.535445i	0.0493189	+	0.0449336i
$143$	10.5221	+	2.81939i	0.879902	+	0.235769i
$144$	−18.4901	−	6.49125i	−1.54084	−	0.540937i
$145$		0			0
$146$	−2.55549	−	3.98611i	−0.211494	−	0.329893i
$147$	−15.7846	−	11.7432i	−1.30189	−	0.968562i
$148$	4.51877	−	1.67403i	0.371441	−	0.137605i
$149$	7.75810	+	4.47914i	0.635569	+	0.366946i	0.782905	−	0.622141i	$-0.213737\pi$
$149$	7.75810	+	4.47914i	0.635569	+	0.366946i	−0.147337	+	0.989086i	$0.547070\pi$
$150$		0			0
$151$	−5.83274	+	3.36754i	−0.474662	+	0.274046i	−0.718189	−	0.695848i	$-0.755029\pi$
$151$	−5.83274	+	3.36754i	−0.474662	+	0.274046i	0.243527	+	0.969894i	$0.421695\pi$
$152$	7.27937	−	3.08866i	0.590435	−	0.250524i
$153$	−8.03690	−	8.03690i	−0.649745	−	0.649745i
$154$	4.68546	−	10.9531i	0.377565	−	0.882623i
$155$		0			0
$156$	15.6902	−	11.1207i	1.25622	−	0.890371i
$157$	−10.9964	−	2.94647i	−0.877606	−	0.235154i	−0.208232	−	0.978080i	$-0.566771\pi$
$157$	−10.9964	−	2.94647i	−0.877606	−	0.235154i	−0.669374	+	0.742926i	$0.733437\pi$
$158$	3.54909	+	11.1450i	0.282350	+	0.886649i
$159$	−18.3446	+	31.7737i	−1.45482	+	2.51982i
$160$		0			0
$161$	1.03686	+	14.2008i	0.0817163	+	1.11918i
$162$	−0.419942	−	0.0918394i	−0.0329937	−	0.00721558i
$163$	−0.000732309	−	0.00273302i	−5.73589e−5	−	0.000214066i	0.965897	−	0.258926i	$-0.0833686\pi$
$163$	−0.000732309	−	0.00273302i	−5.73589e−5	−	0.000214066i	−0.965954	+	0.258712i	$0.916702\pi$
$164$	−0.506057	−	5.42652i	−0.0395164	−	0.423740i
$165$		0			0
$166$	0.407370	+	8.75552i	0.0316181	+	0.679560i
$167$	2.32482	+	2.32482i	0.179900	+	0.179900i	0.791312	−	0.611412i	$-0.209398\pi$
$167$	2.32482	+	2.32482i	0.179900	+	0.179900i	−0.611412	+	0.791312i	$0.709398\pi$
$168$	−9.60319	−	18.7117i	−0.740902	−	1.44364i
$169$		−	1.29445i		−	0.0995729i
$170$		0			0
$171$	11.8616	−	6.84831i	0.907081	−	0.523703i
$172$	−8.63157	−	7.15900i	−0.658151	−	0.545869i
$173$	−15.5233	+	4.15945i	−1.18021	+	0.316237i	−0.795010	−	0.606596i	$-0.792535\pi$
$173$	−15.5233	+	4.15945i	−1.18021	+	0.316237i	−0.385201	+	0.922833i	$0.625868\pi$
$174$	3.69689	+	5.76649i	0.280261	+	0.437157i
$175$		0			0
$176$	9.66180	−	8.29743i	0.728286	−	0.625443i
$177$	−1.38414	−	5.16567i	−0.104038	−	0.388276i
$178$	3.90837	−	1.24461i	0.292945	−	0.0932871i
$179$	−9.08714	−	15.7394i	−0.679205	−	1.17642i	−0.975221	−	0.221235i	$-0.928991\pi$
$179$	−9.08714	−	15.7394i	−0.679205	−	1.17642i	0.296016	−	0.955183i	$-0.404342\pi$
$180$		0			0
$181$	−4.28458			−0.318471			−0.159235	−	0.987241i	$-0.550903\pi$
$181$	−4.28458			−0.318471			−0.159235	+	0.987241i	$0.550903\pi$
$182$	12.6719	+	1.81703i	0.939301	+	0.134687i
$183$	−23.2114	+	23.2114i	−1.71584	+	1.71584i
$184$	−5.70419	+	14.1125i	−0.420518	+	1.04038i
$185$		0			0
$186$	6.35826	−	12.2999i	0.466210	−	0.901871i
$187$	7.13498	−	1.91181i	0.521761	−	0.139806i
$188$	−4.39092	−	11.8525i	−0.320241	−	0.864434i
$189$	−7.93272	−	11.6832i	−0.577020	−	0.849824i
$190$		0			0
$191$	−10.0103	−	5.77946i	−0.724321	−	0.418187i	0.0920200	−	0.995757i	$-0.470668\pi$
$191$	−10.0103	−	5.77946i	−0.724321	−	0.418187i	−0.816341	+	0.577570i	$0.804001\pi$
$192$	−0.385874	−	22.4810i	−0.0278481	−	1.62242i
$193$	−1.19666	+	4.46599i	−0.0861374	+	0.321469i	−0.995527	−	0.0944758i	$-0.969882\pi$
$193$	−1.19666	+	4.46599i	−0.0861374	+	0.321469i	0.909390	+	0.415945i	$0.136549\pi$
$194$	1.01521	+	21.8196i	0.0728876	+	1.56656i
$195$		0			0
$196$	3.93406	−	13.4359i	0.281005	−	0.959706i
$197$	−6.77330	+	6.77330i	−0.482578	+	0.482578i	−0.905954	−	0.423376i	$-0.860845\pi$
$197$	−6.77330	+	6.77330i	−0.482578	+	0.482578i	0.423376	+	0.905954i	$0.360845\pi$
$198$	14.8566	−	16.3065i	1.05581	−	1.15885i
$199$	−0.869824	−	1.50658i	−0.0616602	−	0.106799i	0.833547	−	0.552448i	$-0.186306\pi$
$199$	−0.869824	−	1.50658i	−0.0616602	−	0.106799i	−0.895208	+	0.445649i	$0.852973\pi$
$200$		0			0
$201$	8.24951	−	14.2886i	0.581876	−	1.00784i
$202$	−15.8402	−	3.46418i	−1.11451	−	0.243739i
$203$	−0.856247	+	4.47842i	−0.0600968	+	0.314324i
$204$	5.44359	−	11.8504i	0.381128	−	0.829691i
$205$		0			0
$206$	16.4599	+	8.50875i	1.14682	+	0.592833i
$207$	−6.82387	+	25.4670i	−0.474292	+	1.77008i
$208$	11.2995	+	7.72082i	0.783477	+	0.535342i
$209$			8.90141i			0.615723i
$210$		0			0
$211$			23.7584i			1.63560i	0.575506	+	0.817798i	$0.304805\pi$
$211$			23.7584i			1.63560i	−0.575506	+	0.817798i	$0.695195\pi$
$212$	−25.7371	−	4.38649i	−1.76763	−	0.301265i
$213$	−0.408942	+	1.52619i	−0.0280202	+	0.104573i
$214$	0.266927	−	0.516363i	0.0182467	−	0.0352978i
$215$		0			0
$216$	−2.09890	−	14.9502i	−0.142812	−	1.01723i
$217$	8.70524	−	3.02740i	0.590950	−	0.205513i
$218$	−2.20668	+	10.0902i	−0.149455	+	0.683393i
$219$	4.70499	−	8.14928i	0.317934	−	0.550677i
$220$		0			0
$221$	3.96874	+	6.87406i	0.266966	+	0.462399i
$222$	7.07924	+	6.44977i	0.475128	+	0.432881i
$223$	13.2313	−	13.2313i	0.886031	−	0.886031i	−0.108108	−	0.994139i	$-0.534479\pi$
$223$	13.2313	−	13.2313i	0.886031	−	0.886031i	0.994139	+	0.108108i	$0.0344793\pi$
$224$	10.1122	−	11.0338i	0.675648	−	0.737224i
$225$		0			0
$226$	−23.2357	+	1.08109i	−1.54562	+	0.0719133i
$227$	5.38070	−	20.0810i	0.357130	−	1.33283i	−0.520654	−	0.853768i	$-0.674312\pi$
$227$	5.38070	−	20.0810i	0.357130	−	1.33283i	0.877783	−	0.479058i	$-0.159022\pi$
$228$	12.0960	+	10.0324i	0.801077	+	0.664411i
$229$	−15.4800	−	8.93740i	−1.02295	−	0.590600i	−0.107992	−	0.994152i	$-0.534442\pi$
$229$	−15.4800	−	8.93740i	−1.02295	−	0.590600i	−0.914957	+	0.403552i	$0.867776\pi$
$230$		0			0
$231$	23.6127	−	1.72408i	1.55360	−	0.113436i
$232$	−2.93403	+	3.89241i	−0.192628	+	0.255549i
$233$	−0.340822	+	0.0913229i	−0.0223280	+	0.00598276i	−0.269966	−	0.962870i	$-0.587012\pi$
$233$	−0.340822	+	0.0913229i	−0.0223280	+	0.00598276i	0.247638	+	0.968853i	$0.420346\pi$
$234$	21.0573	+	10.8853i	1.37656	+	0.711592i
$235$		0			0
$236$	3.10483	−	2.20061i	0.202107	−	0.143247i
$237$	−16.4367	+	16.4367i	−1.06768	+	1.06768i
$238$	8.05758	−	3.22931i	0.522295	−	0.209325i
$239$	24.1080			1.55941			0.779707	−	0.626145i	$-0.215368\pi$
$239$	24.1080			1.55941			0.779707	+	0.626145i	$0.215368\pi$
$240$		0			0
$241$	−2.17712	−	3.77087i	−0.140240	−	0.242903i	0.787347	−	0.616510i	$-0.211454\pi$
$241$	−2.17712	−	3.77087i	−0.140240	−	0.242903i	−0.927587	+	0.373607i	$0.878121\pi$
$242$	−0.370172	−	1.16243i	−0.0237956	−	0.0747239i
$243$	3.92325	+	14.6418i	0.251677	+	0.939270i
$244$	−21.2267	−	9.75074i	−1.35890	−	0.624227i
$245$		0			0
$246$	9.11823	−	5.84569i	0.581357	−	0.372708i
$247$	−9.23923	+	2.47564i	−0.587878	+	0.157521i
$248$	9.77938	+	1.20220i	0.620991	+	0.0763397i
$249$	−15.0854	+	8.70955i	−0.955998	+	0.551945i
$250$		0			0
$251$			13.3373i			0.841841i	0.907098	+	0.420920i	$0.138293\pi$
$251$			13.3373i			0.841841i	−0.907098	+	0.420920i	$0.861707\pi$
$252$	15.0525	−	21.1059i	0.948221	−	1.32954i
$253$	−12.1162	−	12.1162i	−0.761736	−	0.761736i
$254$	−2.64006	+	0.122835i	−0.165652	+	0.00770734i
$255$		0			0
$256$	14.9059	−	5.81492i	0.931621	−	0.363432i
$257$	−2.60327	−	9.71554i	−0.162388	−	0.606039i	−0.998359	−	0.0572656i	$-0.981762\pi$
$257$	−2.60327	−	9.71554i	−0.162388	−	0.606039i	0.835971	−	0.548773i	$-0.184905\pi$
$258$	4.76137	−	21.7717i	0.296430	−	1.35545i
$259$	0.464217	+	6.35786i	0.0288450	+	0.395058i
$260$		0			0
$261$	−4.22143	+	7.31173i	−0.261300	+	0.452585i
$262$	−5.48369	+	1.74626i	−0.338784	+	0.107884i
$263$	−10.3861	−	2.78295i	−0.640435	−	0.171604i	−0.0760347	−	0.997105i	$-0.524226\pi$
$263$	−10.3861	−	2.78295i	−0.640435	−	0.171604i	−0.564401	+	0.825501i	$0.690893\pi$
$264$	23.4659	+	9.48480i	1.44423	+	0.583749i
$265$		0			0
$266$	1.24582	+	10.3862i	0.0763862	+	0.636821i
$267$	5.76406	+	5.76406i	0.352755	+	0.352755i
$268$	11.5739	+	1.97259i	0.706991	+	0.120495i
$269$	8.18828	−	4.72750i	0.499248	−	0.288241i	−0.229155	−	0.973390i	$-0.573596\pi$
$269$	8.18828	−	4.72750i	0.499248	−	0.288241i	0.728403	+	0.685149i	$0.240263\pi$
$270$		0			0
$271$	−12.4949	−	7.21392i	−0.759010	−	0.438214i	0.0699304	−	0.997552i	$-0.477722\pi$
$271$	−12.4949	−	7.21392i	−0.759010	−	0.438214i	−0.828940	+	0.559337i	$0.811056\pi$
$272$	9.25330	+	0.702976i	0.561064	+	0.0426242i
$273$	8.35664	+	24.0294i	0.505767	+	1.45432i
$274$	−19.1879	+	12.3013i	−1.15918	+	0.743152i
$275$		0			0
$276$	−30.1201	+	2.80889i	−1.81302	+	0.169075i
$277$	31.9620	+	8.56419i	1.92041	+	0.514572i	0.988332	+	0.152314i	$0.0486724\pi$
$277$	31.9620	+	8.56419i	1.92041	+	0.514572i	0.932078	+	0.362259i	$0.117994\pi$
$278$	−16.2690	+	17.8568i	−0.975750	+	1.07098i
$279$	17.0664			1.02174
$280$		0			0
$281$	−10.1670			−0.606514			−0.303257	−	0.952909i	$-0.598074\pi$
$281$	−10.1670			−0.606514			−0.303257	+	0.952909i	$0.598074\pi$
$282$	16.9175	−	18.5685i	1.00742	−	1.10574i
$283$	−26.7548	−	7.16893i	−1.59041	−	0.426148i	−0.648280	−	0.761402i	$-0.724511\pi$
$283$	−26.7548	−	7.16893i	−1.59041	−	0.426148i	−0.942128	+	0.335254i	$0.891178\pi$
$284$	−1.11950	+	0.104401i	−0.0664304	+	0.00619505i
$285$		0			0
$286$	−12.9691	+	8.31446i	−0.766877	+	0.491644i
$287$	7.08148	+	1.35394i	0.418007	+	0.0799204i
$288$	24.3967	−	13.1470i	1.43759	−	0.774692i
$289$	−10.0612	−	5.80882i	−0.591834	−	0.341695i
$290$		0			0
$291$	−37.5943	+	21.7051i	−2.20381	+	1.27237i
$292$	6.60103	+	1.12504i	0.386296	+	0.0658380i
$293$	3.07964	+	3.07964i	0.179914	+	0.179914i	0.791318	−	0.611404i	$-0.209395\pi$
$293$	3.07964	+	3.07964i	0.179914	+	0.179914i	−0.611404	+	0.791318i	$0.709395\pi$
$294$	27.3102	−	5.31645i	1.59276	−	0.310062i
$295$		0			0
$296$	−2.55384	+	6.31833i	−0.148439	+	0.367245i
$297$	16.4152	+	4.39844i	0.952506	+	0.255223i
$298$	−12.0716	+	3.84417i	−0.699291	+	0.222687i
$299$	9.20626	−	15.9457i	0.532412	−	0.922164i
$300$		0			0
$301$	12.2731	−	8.33327i	0.707408	−	0.480322i
$302$	2.03494	−	9.30491i	0.117098	−	0.535437i
$303$	−8.34018	−	31.1260i	−0.479131	−	1.78814i
$304$	−3.70431	+	10.5516i	−0.212457	+	0.605176i
$305$		0			0
$306$	16.0564	−	0.747062i	0.917885	−	0.0427067i
$307$	13.3345	+	13.3345i	0.761042	+	0.761042i	0.976511	−	0.215469i	$-0.0691280\pi$
$307$	13.3345	+	13.3345i	0.761042	+	0.761042i	−0.215469	+	0.976511i	$0.569128\pi$
$308$	6.98766	+	15.3303i	0.398159	+	0.873526i
$309$			36.8239i			2.09484i
$310$		0			0
$311$	−1.35454	+	0.782046i	−0.0768091	+	0.0443457i	−0.537913	−	0.843001i	$-0.680787\pi$
$311$	−1.35454	+	0.782046i	−0.0768091	+	0.0443457i	0.461104	+	0.887346i	$0.347454\pi$
$312$	−3.31847	+	26.9944i	−0.187871	+	1.52825i
$313$	11.7632	−	3.15193i	0.664893	−	0.178157i	0.0894395	−	0.995992i	$-0.471492\pi$
$313$	11.7632	−	3.15193i	0.664893	−	0.178157i	0.575453	+	0.817835i	$0.304826\pi$
$314$	13.5536	−	8.68922i	0.764876	−	0.490361i
$315$		0			0
$316$	−15.0313	−	6.90478i	−0.845574	−	0.388424i
$317$	7.08901	+	26.4565i	0.398158	+	1.48595i	0.816334	+	0.577581i	$0.196003\pi$
$317$	7.08901	+	26.4565i	0.398158	+	1.48595i	−0.418175	+	0.908366i	$0.637330\pi$
$318$	−15.7440	−	49.4400i	−0.882878	−	2.77245i
$319$	−2.74350	−	4.75188i	−0.153606	−	0.266054i
$320$		0			0
$321$	1.15520			0.0644768
$322$	−15.8330	−	12.4415i	−0.882337	−	0.693336i
$323$	−4.58635	+	4.58635i	−0.255191	+	0.255191i
$324$	0.495979	−	0.351534i	0.0275544	−	0.0195297i
$325$		0			0
$326$	0.00355457	+	0.00183749i	0.000196869	+	0.000101769i
$327$	−19.8272	+	5.31269i	−1.09645	+	0.293792i
$328$	6.15485	+	4.63941i	0.339845	+	0.256169i
$329$	16.6764	−	1.21762i	0.919399	−	0.0671296i
$330$		0			0
$331$	3.38809	+	1.95612i	0.186226	+	0.107518i	0.590215	−	0.807246i	$-0.299043\pi$
$331$	3.38809	+	1.95612i	0.186226	+	0.107518i	−0.403988	+	0.914764i	$0.632376\pi$
$332$	−9.54099	−	7.91327i	−0.523630	−	0.434297i
$333$	−3.05513	+	11.4019i	−0.167420	+	0.624821i
$334$	−4.64461	+	0.216101i	−0.254142	+	0.0118245i
$335$		0			0
$336$	28.7077	+	7.78271i	1.56613	+	0.424581i
$337$	−12.6447	+	12.6447i	−0.688801	+	0.688801i	−0.961967	−	0.273166i	$-0.911929\pi$
$337$	−12.6447	+	12.6447i	−0.688801	+	0.688801i	0.273166	+	0.961967i	$0.411929\pi$
$338$	1.35321	+	1.23289i	0.0736050	+	0.0670602i
$339$	−23.1137	−	40.0341i	−1.25537	−	2.17436i
$340$		0			0
$341$	−5.54569	+	9.60542i	−0.300316	+	0.520163i
$342$	−4.13831	+	18.9227i	−0.223774	+	1.02322i
$343$	15.6247	+	9.94328i	0.843655	+	0.536886i
$344$	15.7051	−	2.20488i	0.846761	−	0.118879i
$345$		0			0
$346$	10.4367	−	20.1896i	0.561083	−	1.08540i
$347$	−1.55280	+	5.79511i	−0.0833585	+	0.311098i	−0.994998	−	0.0998921i	$-0.968150\pi$
$347$	−1.55280	+	5.79511i	−0.0833585	+	0.311098i	0.911640	+	0.410990i	$0.134817\pi$
$348$	−9.54934	−	1.62753i	−0.511899	−	0.0872450i
$349$			15.1860i			0.812888i	0.913676	+	0.406444i	$0.133231\pi$
$349$			15.1860i			0.812888i	−0.913676	+	0.406444i	$0.866769\pi$
$350$		0			0
$351$			18.2615i			0.974725i
$352$	−0.528203	+	18.0032i	−0.0281533	+	0.959576i
$353$	−8.90620	+	33.2384i	−0.474029	+	1.76910i	0.151035	+	0.988528i	$0.451739\pi$
$353$	−8.90620	+	33.2384i	−0.474029	+	1.76910i	−0.625065	+	0.780573i	$0.714927\pi$
$354$	6.71849	+	3.47303i	0.357084	+	0.184590i
$355$		0			0
$356$	−2.42139	+	5.27121i	−0.128333	+	0.279373i
$357$	13.0545	+	11.2779i	0.690918	+	0.596889i
$358$	25.1089	+	5.49120i	1.32705	+	0.290219i
$359$	−4.20241	+	7.27878i	−0.221795	+	0.384159i	−0.955353	−	0.295467i	$-0.904525\pi$
$359$	−4.20241	+	7.27878i	−0.221795	+	0.384159i	0.733558	+	0.679626i	$0.237858\pi$
$360$		0			0
$361$	5.59193	+	9.68551i	0.294312	+	0.509764i
$362$	4.08082	−	4.47909i	0.214483	−	0.235416i
$363$	1.71435	−	1.71435i	0.0899803	−	0.0899803i
$364$	−13.9687	+	11.5165i	−0.732161	+	0.603629i
$365$		0			0
$366$	−2.15759	−	46.3727i	−0.112779	−	2.42394i
$367$	−7.95960	+	29.7056i	−0.415488	+	1.55062i	0.368369	+	0.929679i	$0.379916\pi$
$367$	−7.95960	+	29.7056i	−0.415488	+	1.55062i	−0.783857	+	0.620941i	$0.786751\pi$
$368$	−9.32020	−	19.4044i	−0.485849	−	1.01153i
$369$	11.5616	+	6.67511i	0.601875	+	0.347493i
$370$		0			0
$371$	15.0450	−	31.0889i	0.781099	−	1.61406i
$372$	6.80237	+	18.3618i	0.352687	+	0.952017i
$373$	14.5253	−	3.89204i	0.752091	−	0.201522i	0.137646	−	0.990482i	$-0.456046\pi$
$373$	14.5253	−	3.89204i	0.752091	−	0.201522i	0.614446	+	0.788959i	$0.289380\pi$
$374$	−4.79706	+	9.27977i	−0.248050	+	0.479846i
$375$		0			0
$376$	16.5727	+	6.69860i	0.854671	+	0.345454i
$377$	4.16920	−	4.16920i	0.214725	−	0.214725i
$378$	19.7690	+	2.83470i	1.01681	+	0.145801i
$379$	1.92262			0.0987586			0.0493793	−	0.998780i	$-0.484276\pi$
$379$	1.92262			0.0987586			0.0493793	+	0.998780i	$0.484276\pi$
$380$		0			0
$381$	−2.62620	−	4.54871i	−0.134544	−	0.233038i
$382$	15.5761	−	4.96015i	0.796941	−	0.253783i
$383$	−4.13733	−	15.4407i	−0.211408	−	0.788984i	−0.987400	−	0.158242i	$-0.949417\pi$
$383$	−4.13733	−	15.4407i	−0.211408	−	0.788984i	0.775993	−	0.630742i	$-0.217249\pi$
$384$	23.8691	+	21.0084i	1.21806	+	1.07208i
$385$		0			0
$386$	−3.52898	−	5.50459i	−0.179621	−	0.280176i
$387$	26.5335	−	7.10963i	1.34877	−	0.361403i
$388$	−23.7771	−	19.7206i	−1.20710	−	1.00116i
$389$	9.81327	−	5.66569i	0.497552	−	0.287262i	−0.230150	−	0.973155i	$-0.573922\pi$
$389$	9.81327	−	5.66569i	0.497552	−	0.287262i	0.727702	+	0.685893i	$0.240588\pi$
$390$		0			0
$391$		−	12.4854i		−	0.631415i
$392$	10.2989	+	16.9096i	0.520171	+	0.854062i
$393$	−8.08735	−	8.08735i	−0.407953	−	0.407953i
$394$	−0.629605	−	13.5320i	−0.0317190	−	0.681730i
$395$		0			0
$396$	2.89673	+	31.0620i	0.145566	+	1.56092i
$397$	−3.01844	−	11.2650i	−0.151491	−	0.565372i	−0.999380	−	0.0351987i	$-0.988794\pi$
$397$	−3.01844	−	11.2650i	−0.151491	−	0.565372i	0.847889	−	0.530173i	$-0.177873\pi$
$398$	2.40343	+	0.525620i	0.120473	+	0.0263469i
$399$	−17.1991	+	11.6780i	−0.861031	+	0.584630i
$400$		0			0
$401$	13.8361	−	23.9649i	0.690943	−	1.19675i	−0.280587	−	0.959829i	$-0.590529\pi$
$401$	13.8361	−	23.9649i	0.690943	−	1.19675i	0.971529	−	0.236919i	$-0.0761376\pi$
$402$	7.08004	+	22.2330i	0.353120	+	1.10888i
$403$	−11.5123	−	3.08472i	−0.573470	−	0.153661i
$404$	18.7083	−	13.2598i	0.930772	−	0.659701i
$405$		0			0
$406$	−3.86620	−	5.16056i	−0.191876	−	0.256114i
$407$	−5.42456	−	5.42456i	−0.268885	−	0.268885i
$408$	7.20361	+	16.9775i	0.356632	+	0.840511i
$409$	11.9780	−	6.91550i	0.592274	−	0.341950i	−0.173722	−	0.984795i	$-0.555579\pi$
$409$	11.9780	−	6.91550i	0.592274	−	0.341950i	0.765996	+	0.642845i	$0.222246\pi$
$410$		0			0
$411$	−39.2281	−	22.6483i	−1.93498	−	1.11716i
$412$	−24.5722	+	9.10307i	−1.21058	+	0.448476i
$413$	1.65364	+	4.75501i	0.0813702	+	0.233979i
$414$	−20.1238	−	31.3895i	−0.989031	−	1.54271i
$415$		0			0
$416$	−18.8334	+	4.45878i	−0.923383	+	0.218610i
$417$	−46.3719	−	12.4253i	−2.27084	−	0.608471i
$418$	−9.30550	−	8.47808i	−0.455147	−	0.414676i
$419$	−20.6976			−1.01114			−0.505572	−	0.862784i	$-0.668719\pi$
$419$	−20.6976			−1.01114			−0.505572	+	0.862784i	$0.668719\pi$
$420$		0			0
$421$	26.7517			1.30380			0.651898	−	0.758306i	$-0.273973\pi$
$421$	26.7517			1.30380			0.651898	+	0.758306i	$0.273973\pi$
$422$	−24.8369	−	22.6285i	−1.20904	−	1.10154i
$423$	29.9067	+	8.01348i	1.45411	+	0.389629i
$424$	29.0988	−	22.7276i	1.41316	−	1.10375i
$425$		0			0
$426$	−1.20598	−	1.88112i	−0.0584300	−	0.0911404i
$427$	20.2013	−	23.3837i	0.977611	−	1.13162i
$428$	0.285571	+	0.770850i	0.0138036	+	0.0372605i
$429$	−26.5142	−	15.3080i	−1.28012	−	0.739076i
$430$		0			0
$431$	34.9346	−	20.1695i	1.68274	−	0.971531i	0.722914	−	0.690937i	$-0.242802\pi$
$431$	34.9346	−	20.1695i	1.68274	−	0.971531i	0.959827	−	0.280594i	$-0.0905313\pi$
$432$	17.6279	+	12.0450i	0.848125	+	0.579516i
$433$	−16.5835	−	16.5835i	−0.796954	−	0.796954i	0.185660	−	0.982614i	$-0.440558\pi$
$433$	−16.5835	−	16.5835i	−0.796954	−	0.796954i	−0.982614	+	0.185660i	$0.940558\pi$
$434$	−5.12641	+	11.9839i	−0.246075	+	0.575243i
$435$		0			0
$436$	−8.44651	−	11.9172i	−0.404514	−	0.570729i
$437$	14.5331	+	3.89412i	0.695210	+	0.186281i
$438$	4.03800	+	12.6803i	0.192943	+	0.605888i
$439$	−2.87067	+	4.97215i	−0.137010	+	0.237308i	−0.926363	−	0.376631i	$-0.877082\pi$
$439$	−2.87067	+	4.97215i	−0.137010	+	0.237308i	0.789354	+	0.613939i	$0.210416\pi$
$440$		0			0
$441$	21.2790	+	26.8936i	1.01329	+	1.28065i
$442$	−10.9661	−	2.39824i	−0.521604	−	0.114073i
$443$	0.221517	+	0.826713i	0.0105246	+	0.0392783i	0.970988	−	0.239126i	$-0.0768610\pi$
$443$	0.221517	+	0.826713i	0.0105246	+	0.0392783i	−0.960464	+	0.278405i	$0.910194\pi$
$444$	−13.4851	+	1.25757i	−0.639976	+	0.0596819i
$445$		0			0
$446$	1.22990	+	26.4339i	0.0582373	+	1.25168i
$447$	−17.8032	−	17.8032i	−0.842064	−	0.842064i
$448$	1.90338	+	21.0803i	0.0899265	+	0.995948i
$449$		−	4.66158i		−	0.219993i	−0.993932	−	0.109997i	$-0.964916\pi$
$449$		−	4.66158i		−	0.219993i	0.993932	−	0.109997i	$-0.0350840\pi$
$450$		0			0
$451$	−7.51388	+	4.33814i	−0.353815	+	0.204275i
$452$	21.0005	−	25.3202i	0.987781	−	1.19096i
$453$	18.2842	−	4.89923i	0.859065	−	0.230186i
$454$	15.8678	+	24.7510i	0.744715	+	1.16162i
$455$		0			0
$456$	−22.0086	+	3.08984i	−1.03065	+	0.144695i
$457$	−8.23274	−	30.7250i	−0.385111	−	1.43726i	−0.837991	−	0.545684i	$-0.816270\pi$
$457$	−8.23274	−	30.7250i	−0.385111	−	1.43726i	0.452880	−	0.891572i	$-0.350397\pi$
$458$	24.0870	−	7.67041i	1.12551	−	0.358415i
$459$	6.19150	+	10.7240i	0.288995	+	0.500553i
$460$		0			0
$461$	−23.4445			−1.09192			−0.545959	−	0.837812i	$-0.683835\pi$
$461$	−23.4445			−1.09192			−0.545959	+	0.837812i	$0.683835\pi$
$462$	−20.6874	+	26.3267i	−0.962466	+	1.22483i
$463$	1.84160	−	1.84160i	0.0855866	−	0.0855866i	−0.663017	−	0.748604i	$-0.730724\pi$
$463$	1.84160	−	1.84160i	0.0855866	−	0.0855866i	0.748604	+	0.663017i	$0.230724\pi$
$464$	−1.27462	−	6.77451i	−0.0591726	−	0.314499i
$465$		0			0
$466$	0.229144	−	0.443274i	0.0106149	−	0.0205343i
$467$	−8.01462	+	2.14751i	−0.370872	+	0.0993749i	−0.439441	−	0.898271i	$-0.644823\pi$
$467$	−8.01462	+	2.14751i	−0.370872	+	0.0993749i	0.0685687	+	0.997646i	$0.478157\pi$
$468$	−31.4352	+	11.6456i	−1.45309	+	0.538317i
$469$	−6.76572	+	13.9806i	−0.312412	+	0.645565i
$470$		0			0
$471$	27.7093	+	15.9980i	1.27678	+	0.737147i
$472$	−0.656670	+	5.34173i	−0.0302257	+	0.245873i
$473$	−4.62053	+	17.2441i	−0.212452	+	0.792883i
$474$	−1.52785	−	32.8378i	−0.0701766	−	1.50829i
$475$		0			0
$476$	−4.29847	+	11.4991i	−0.197020	+	0.527060i
$477$	45.2221	−	45.2221i	2.07058	−	2.07058i
$478$	−22.9614	+	25.2024i	−1.05023	+	1.15273i
$479$	6.99926	+	12.1231i	0.319805	+	0.553918i	0.980447	−	0.196783i	$-0.0630494\pi$
$479$	6.99926	+	12.1231i	0.319805	+	0.553918i	−0.660643	+	0.750701i	$0.729716\pi$
$480$		0			0
$481$	4.12176	−	7.13910i	0.187936	−	0.325515i
$482$	6.01563	+	1.31559i	0.274005	+	0.0599236i
$483$	7.51507	−	39.3060i	0.341948	−	1.78849i
$484$	1.56777	+	0.720172i	0.0712622	+	0.0327351i
$485$		0			0
$486$	−19.0431	−	9.84409i	−0.863813	−	0.446537i
$487$	6.87083	−	25.6423i	0.311347	−	1.16196i	−0.615995	−	0.787750i	$-0.711246\pi$
$487$	6.87083	−	25.6423i	0.311347	−	1.16196i	0.927342	−	0.374214i	$-0.122087\pi$
$488$	30.4106	−	12.9033i	1.37662	−	0.584107i
$489$			0.00795220i			0.000359611i
$490$		0			0
$491$		−	35.5868i		−	1.60601i	−0.595973	−	0.803004i	$-0.703234\pi$
$491$		−	35.5868i		−	1.60601i	0.595973	−	0.803004i	$-0.296766\pi$
$492$	−2.57353	+	15.0999i	−0.116024	+	0.680754i
$493$	1.03480	−	3.86191i	0.0466049	−	0.173932i
$494$	6.21181	−	12.0166i	0.279482	−	0.540651i
$495$		0			0
$496$	−10.5711	+	9.07830i	−0.474655	+	0.407628i
$497$	0.279321	−	1.46093i	0.0125293	−	0.0655316i
$498$	5.26303	−	24.0656i	0.235842	−	1.07840i
$499$	−4.94115	+	8.55833i	−0.221196	+	0.383123i	−0.955172	−	0.296053i	$-0.904330\pi$
$499$	−4.94115	+	8.55833i	−0.221196	+	0.383123i	0.733975	+	0.679176i	$0.237663\pi$
$500$		0			0
$501$	−4.62022	−	8.00245i	−0.206416	−	0.357523i
$502$	−13.9427	−	12.7030i	−0.622295	−	0.566962i
$503$	−16.5308	+	16.5308i	−0.737071	+	0.737071i	−0.972010	−	0.234939i	$-0.924511\pi$
$503$	−16.5308	+	16.5308i	−0.737071	+	0.737071i	0.234939	+	0.972010i	$0.424511\pi$
$504$	7.72730	+	35.8380i	0.344201	+	1.59635i
$505$		0			0
$506$	24.2061	−	1.12624i	1.07609	−	0.0500676i
$507$	−0.941607	+	3.51413i	−0.0418182	+	0.156068i
$508$	2.38610	−	2.87690i	0.105866	−	0.127642i
$509$	−0.789343	−	0.455727i	−0.0349870	−	0.0201998i	0.482404	−	0.875949i	$-0.339764\pi$
$509$	−0.789343	−	0.455727i	−0.0349870	−	0.0201998i	−0.517391	+	0.855749i	$0.673097\pi$
$510$		0			0
$511$	−3.85873	+	7.97365i	−0.170700	+	0.352733i
$512$	−8.11815	+	21.1210i	−0.358775	+	0.933424i
$513$	−14.4138	+	3.86218i	−0.636386	+	0.170519i
$514$	12.6361	+	6.53204i	0.557352	+	0.288116i
$515$		0			0
$516$	18.2251	+	25.7138i	0.802316	+	1.13199i
$517$	−14.2284	+	14.2284i	−0.625763	+	0.625763i
$518$	−7.08863	−	5.57021i	−0.311456	−	0.244741i
$519$	45.1677			1.98264
$520$		0			0
$521$	3.24107	+	5.61370i	0.141994	+	0.245941i	0.928247	−	0.371963i	$-0.121315\pi$
$521$	3.24107	+	5.61370i	0.141994	+	0.245941i	−0.786254	+	0.617904i	$0.787982\pi$
$522$	−3.62299	−	11.3771i	−0.158574	−	0.497961i
$523$	1.22075	+	4.55591i	0.0533798	+	0.199216i	0.987466	−	0.157831i	$-0.0504502\pi$
$523$	1.22075	+	4.55591i	0.0533798	+	0.199216i	−0.934086	+	0.357047i	$0.883783\pi$
$524$	3.39736	−	7.39585i	0.148415	−	0.323089i
$525$		0			0
$526$	12.8015	−	8.20701i	0.558170	−	0.357842i
$527$	−7.80645	+	2.09173i	−0.340054	+	0.0911173i
$528$	−32.2653	+	15.4974i	−1.40417	+	0.674439i
$529$	−5.16358	+	2.98119i	−0.224503	+	0.129617i
$530$		0			0
$531$			9.32205i			0.404542i
$532$	−12.0443	−	8.58991i	−0.522187	−	0.372420i
$533$	−6.59253	−	6.59253i	−0.285554	−	0.285554i
$534$	−11.5157	+	0.535792i	−0.498332	+	0.0231860i
$535$		0			0
$536$	−13.0857	+	10.2206i	−0.565214	+	0.441462i
$537$	13.2203	+	49.3390i	0.570500	+	2.12913i
$538$	−2.85675	+	13.0627i	−0.123163	+	0.563172i
$539$	−22.0511	+	3.23736i	−0.949808	+	0.139443i
$540$		0			0
$541$	−9.43554	+	16.3428i	−0.405666	+	0.702633i	−0.994399	−	0.105694i	$-0.966294\pi$
$541$	−9.43554	+	16.3428i	−0.405666	+	0.702633i	0.588733	+	0.808328i	$0.299627\pi$
$542$	19.4421	−	6.19125i	0.835108	−	0.265937i
$543$	11.6317	+	3.11669i	0.499162	+	0.133750i
$544$	−9.54813	+	9.00382i	−0.409373	+	0.386036i
$545$		0			0
$546$	−33.0794	−	14.1506i	−1.41567	−	0.605590i
$547$	9.42028	+	9.42028i	0.402782	+	0.402782i	0.879212	−	0.476430i	$-0.158069\pi$
$547$	9.42028	+	9.42028i	0.402782	+	0.402782i	−0.476430	+	0.879212i	$0.658069\pi$
$548$	5.41559	−	31.7753i	0.231343	−	1.35737i
$549$	49.5537	−	28.6098i	2.11490	−	1.22104i
$550$		0			0
$551$	4.17252	+	2.40901i	0.177756	+	0.102627i
$552$	25.7512	−	34.1627i	1.09605	−	1.45406i
$553$	14.3051	−	16.5586i	0.608316	−	0.704145i
$554$	−39.3949	+	25.2560i	−1.67373	+	1.07303i
$555$		0			0
$556$	−3.17213	−	34.0151i	−0.134528	−	1.44256i
$557$	−36.6573	−	9.82230i	−1.55322	−	0.416184i	−0.622711	−	0.782452i	$-0.713969\pi$
$557$	−36.6573	−	9.82230i	−1.55322	−	0.416184i	−0.930509	+	0.366268i	$0.880635\pi$
$558$	−16.2547	+	17.8411i	−0.688117	+	0.755274i
$559$	−19.1836			−0.811378
$560$		0			0
$561$	−20.7605			−0.876510
$562$	9.68351	−	10.6286i	0.408474	−	0.448339i
$563$	36.6293	+	9.81479i	1.54374	+	0.413644i	0.927472	−	0.373892i	$-0.121977\pi$
$563$	36.6293	+	9.81479i	1.54374	+	0.413644i	0.616269	+	0.787536i	$0.288643\pi$
$564$	3.29856	+	35.3709i	0.138895	+	1.48938i
$565$		0			0
$566$	32.9768	−	21.1414i	1.38612	−	0.888638i
$567$	0.264159	+	0.759585i	0.0110936	+	0.0318996i
$568$	0.957124	−	1.26976i	0.0401600	−	0.0532780i
$569$	−7.96777	−	4.60019i	−0.334026	−	0.192850i	0.323601	−	0.946194i	$-0.395106\pi$
$569$	−7.96777	−	4.60019i	−0.334026	−	0.192850i	−0.657627	+	0.753344i	$0.728440\pi$
$570$		0			0
$571$	−14.8692	+	8.58473i	−0.622256	+	0.359260i	−0.777747	−	0.628578i	$-0.783637\pi$
$571$	−14.8692	+	8.58473i	−0.622256	+	0.359260i	0.155491	+	0.987837i	$0.450304\pi$
$572$	3.66039	−	21.4769i	0.153049	−	0.897993i
$573$	22.9716	+	22.9716i	0.959652	+	0.959652i
$574$	−8.16010	+	6.11341i	−0.340596	+	0.255169i
$575$		0			0
$576$	−9.49267	+	38.0259i	−0.395528	+	1.58441i
$577$	29.5776	+	7.92529i	1.23133	+	0.329934i	0.815097	−	0.579324i	$-0.196683\pi$
$577$	29.5776	+	7.92529i	1.23133	+	0.329934i	0.416233	+	0.909258i	$0.363350\pi$
$578$	15.6552	−	4.98534i	0.651171	−	0.207363i
$579$	6.49731	−	11.2537i	0.270019	−	0.467687i
$580$		0			0
$581$	13.5662	−	9.21126i	0.562819	−	0.382147i
$582$	13.1160	−	59.9737i	0.543675	−	2.48599i
$583$	10.7574	+	40.1471i	0.445525	+	1.66272i
$584$	−7.46322	+	5.82916i	−0.308830	+	0.241212i
$585$		0			0
$586$	−6.15262	+	0.286264i	−0.254162	+	0.0118255i
$587$	−31.4917	−	31.4917i	−1.29980	−	1.29980i	−0.928520	−	0.371283i	$-0.878918\pi$
$587$	−31.4917	−	31.4917i	−1.29980	−	1.29980i	−0.371283	−	0.928520i	$-0.621082\pi$
$588$	−20.4536	+	33.6136i	−0.843493	+	1.38620i
$589$		−	9.73911i		−	0.401293i
$590$		0			0
$591$	23.3150	−	13.4609i	0.959050	−	0.553708i
$592$	−4.17277	−	8.68761i	−0.171500	−	0.357059i
$593$	7.35708	−	1.97132i	0.302119	−	0.0809525i	−0.104575	−	0.994517i	$-0.533348\pi$
$593$	7.35708	−	1.97132i	0.302119	−	0.0809525i	0.406694	+	0.913564i	$0.366682\pi$
$594$	−20.2326	+	12.9711i	−0.830155	+	0.532212i
$595$		0			0
$596$	7.47885	−	16.2810i	0.306346	−	0.666895i
$597$	1.26546	+	4.72275i	0.0517917	+	0.193289i
$598$	7.90115	+	24.8116i	0.323102	+	1.01462i
$599$	0.0710719	+	0.123100i	0.00290392	+	0.00502974i	0.867474	−	0.497483i	$-0.165742\pi$
$599$	0.0710719	+	0.123100i	0.00290392	+	0.00502974i	−0.864570	+	0.502513i	$0.832409\pi$
$600$		0			0
$601$	−13.9872			−0.570550			−0.285275	−	0.958446i	$-0.592085\pi$
$601$	−13.9872			−0.570550			−0.285275	+	0.958446i	$0.592085\pi$
$602$	−2.97783	+	20.7672i	−0.121367	+	0.846407i
$603$	−20.3363	+	20.3363i	−0.828157	+	0.828157i
$604$	7.78915	+	10.9897i	0.316936	+	0.447165i
$605$		0			0
$606$	40.4825	+	20.9269i	1.64449	+	0.850097i
$607$	−31.6805	+	8.48876i	−1.28587	+	0.344548i	−0.836091	−	0.548591i	$-0.815165\pi$
$607$	−31.6805	+	8.48876i	−1.28587	+	0.344548i	−0.449781	+	0.893139i	$0.648498\pi$
$608$	−7.50247	−	13.9223i	−0.304265	−	0.564622i
$609$	5.58221	−	11.5350i	0.226203	−	0.467423i
$610$		0			0
$611$	−18.7255	−	10.8112i	−0.757554	−	0.437374i
$612$	−14.5119	+	17.4969i	−0.586607	+	0.707269i
$613$	−1.33983	+	5.00032i	−0.0541153	+	0.201961i	−0.987691	−	0.156420i	$-0.950005\pi$
$613$	−1.33983	+	5.00032i	−0.0541153	+	0.201961i	0.933575	+	0.358381i	$0.116671\pi$
$614$	−26.6402	+	1.23950i	−1.07511	+	0.0500220i
$615$		0			0
$616$	−22.6816	−	7.29638i	−0.913868	−	0.293979i
$617$	−18.4714	+	18.4714i	−0.743630	+	0.743630i	−0.973275	−	0.229644i	$-0.926244\pi$
$617$	−18.4714	+	18.4714i	−0.743630	+	0.743630i	0.229644	+	0.973275i	$0.426244\pi$
$618$	−38.4955	−	35.0726i	−1.54852	−	1.41083i
$619$	−4.38197	−	7.58980i	−0.176126	−	0.305060i	0.764424	−	0.644714i	$-0.223023\pi$
$619$	−4.38197	−	7.58980i	−0.176126	−	0.305060i	−0.940551	+	0.339654i	$0.889690\pi$
$620$		0			0
$621$	14.3624	−	24.8764i	0.576343	−	0.998255i
$622$	0.472576	−	2.16089i	0.0189486	−	0.0866437i
$623$	−5.80684	−	5.01657i	−0.232646	−	0.200985i
$624$	−25.0592	−	29.1797i	−1.00317	−	1.16812i
$625$		0			0
$626$	−7.90871	+	15.2992i	−0.316096	+	0.611478i
$627$	6.47506	−	24.1653i	0.258589	−	0.965068i
$628$	−3.82538	+	22.4449i	−0.152649	+	0.895649i
$629$		−	5.58989i		−	0.222883i
$630$		0			0
$631$			31.2397i			1.24363i	0.783164	+	0.621816i	$0.213605\pi$
$631$			31.2397i			1.24363i	−0.783164	+	0.621816i	$0.786395\pi$
$632$	21.5346	−	9.13722i	0.856602	−	0.363459i
$633$	17.2823	−	64.4986i	0.686911	−	2.56359i
$634$	−34.4094	−	17.7875i	−1.36657	−	0.706432i
$635$		0			0
$636$	66.6796	+	30.6300i	2.64402	+	1.21456i
$637$	−9.49304	−	21.9876i	−0.376128	−	0.871180i
$638$	7.58062	+	1.65785i	0.300120	+	0.0656348i
$639$	1.37709	−	2.38520i	0.0544770	−	0.0943569i
$640$		0			0
$641$	−24.9696	−	43.2485i	−0.986238	−	1.70821i	−0.636299	−	0.771443i	$-0.719535\pi$
$641$	−24.9696	−	43.2485i	−0.986238	−	1.70821i	−0.349939	−	0.936772i	$-0.613798\pi$
$642$	−1.10026	+	1.20764i	−0.0434237	+	0.0476617i
$643$	−16.3136	+	16.3136i	−0.643345	+	0.643345i	−0.951376	−	0.308031i	$-0.900330\pi$
$643$	−16.3136	+	16.3136i	−0.643345	+	0.643345i	0.308031	+	0.951376i	$0.400330\pi$
$644$	28.0863	−	4.70195i	1.10675	−	0.185283i
$645$		0			0
$646$	−0.426319	−	9.16279i	−0.0167733	−	0.360505i
$647$	−4.17257	+	15.5722i	−0.164041	+	0.612208i	0.834120	+	0.551583i	$0.185976\pi$
$647$	−4.17257	+	15.5722i	−0.164041	+	0.612208i	−0.998161	+	0.0606248i	$0.980691\pi$
$648$	−0.104899	+	0.853310i	−0.00412083	+	0.0335212i
$649$	−5.24671	−	3.02919i	−0.205951	−	0.118906i
$650$		0			0
$651$	−25.8349	+	1.88633i	−1.01255	+	0.0739310i
$652$	−0.00530642	+	0.00196583i	−0.000207816	+	7.69879e-5i
$653$	21.8713	−	5.86041i	0.855891	−	0.229335i	0.195914	−	0.980621i	$-0.437233\pi$
$653$	21.8713	−	5.86041i	0.855891	−	0.229335i	0.659977	+	0.751286i	$0.270566\pi$
$654$	13.3304	−	25.7873i	0.521261	−	1.00836i
$655$		0			0
$656$	−10.7122	+	2.01548i	−0.418240	+	0.0786914i
$657$	−11.5985	+	11.5985i	−0.452501	+	0.452501i
$658$	−14.6104	+	18.5931i	−0.569573	+	0.724836i
$659$	0.119381			0.00465044			0.00232522	−	0.999997i	$-0.499260\pi$
$659$	0.119381			0.00465044			0.00232522	+	0.999997i	$0.499260\pi$
$660$		0			0
$661$	10.3433	+	17.9151i	0.402307	+	0.696816i	0.994004	−	0.109344i	$-0.0348751\pi$
$661$	10.3433	+	17.9151i	0.402307	+	0.696816i	−0.591697	+	0.806161i	$0.701542\pi$
$662$	−5.27188	+	1.67881i	−0.204897	+	0.0652489i
$663$	−5.77388	−	21.5484i	−0.224239	−	0.836871i
$664$	17.3597	−	2.43718i	0.673689	−	0.0945810i
$665$		0			0
$666$	−9.00968	−	14.0535i	−0.349118	−	0.544562i
$667$	−8.95846	+	2.40041i	−0.346873	+	0.0929443i
$668$	4.19781	−	5.06128i	0.162418	−	0.195827i
$669$	−45.5445	+	26.2951i	−1.76085	+	1.01663i
$670$		0			0
$671$			37.1869i			1.43559i
$672$	−35.4784	+	22.5983i	−1.36861	+	0.871749i
$673$	−34.9098	−	34.9098i	−1.34568	−	1.34568i	−0.890299	−	0.455376i	$-0.849505\pi$
$673$	−34.9098	−	34.9098i	−1.34568	−	1.34568i	−0.455376	−	0.890299i	$-0.650495\pi$
$674$	−1.17537	−	25.2621i	−0.0452737	−	0.973058i
$675$		0			0
$676$	−2.57771	+	0.240388i	−0.0991427	+	0.00924569i
$677$	1.32612	+	4.94915i	0.0509669	+	0.190211i	0.986716	−	0.162456i	$-0.0519415\pi$
$677$	1.32612	+	4.94915i	0.0509669	+	0.190211i	−0.935749	+	0.352667i	$0.885275\pi$
$678$	63.8660	+	13.9672i	2.45276	+	0.536408i
$679$	33.8082	−	22.9554i	1.29744	−	0.880946i
$680$		0			0
$681$	−29.2147	+	50.6014i	−1.11951	+	1.93905i
$682$	−4.75952	−	14.9461i	−0.182251	−	0.572314i
$683$	−40.4498	−	10.8385i	−1.54777	−	0.414724i	−0.619003	−	0.785389i	$-0.712463\pi$
$683$	−40.4498	−	10.8385i	−1.54777	−	0.414724i	−0.928767	+	0.370665i	$0.879130\pi$
$684$	−15.8402	−	22.3490i	−0.605666	−	0.854534i
$685$		0			0
$686$	−25.2763	+	6.86361i	−0.965053	+	0.262054i
$687$	35.5235	+	35.5235i	1.35530	+	1.35530i
$688$	−12.6532	+	18.5180i	−0.482399	+	0.705994i
$689$	−38.6789	+	22.3313i	−1.47355	+	0.850755i
$690$		0			0
$691$	29.5825	+	17.0795i	1.12537	+	0.649734i	0.942767	−	0.333452i	$-0.108213\pi$
$691$	29.5825	+	17.0795i	1.12537	+	0.649734i	0.182606	+	0.983186i	$0.441547\pi$
$692$	11.1657	+	30.1400i	0.424457	+	1.14575i
$693$	−40.5352	−	7.75009i	−1.53981	−	0.294402i
$694$	−4.57924	−	7.14280i	−0.173826	−	0.271137i
$695$		0			0
$696$	10.7966	−	8.43272i	0.409245	−	0.319641i
$697$	−6.10663	−	1.63627i	−0.231305	−	0.0619780i
$698$	−15.8754	−	14.4638i	−0.600892	−	0.547462i
$699$	0.991682			0.0375089
$700$		0			0
$701$	−28.1444			−1.06300			−0.531499	−	0.847059i	$-0.678371\pi$
$701$	−28.1444			−1.06300			−0.531499	+	0.847059i	$0.678371\pi$
$702$	−19.0905	−	17.3930i	−0.720523	−	0.656456i
$703$	6.50664	+	1.74345i	0.245402	+	0.0657554i
$704$	−18.3174	−	17.6992i	−0.690364	−	0.667065i
$705$		0			0
$706$	−26.2647	−	40.9682i	−0.988483	−	1.54186i
$707$	9.96406	+	28.6515i	0.374737	+	1.07755i
$708$	−10.0297	+	3.71562i	−0.376938	+	0.139641i
$709$	3.23053	+	1.86515i	0.121325	+	0.0700471i	0.559434	−	0.828875i	$-0.311018\pi$
$709$	3.23053	+	1.86515i	0.121325	+	0.0700471i	−0.438109	+	0.898922i	$0.644352\pi$
$710$		0			0
$711$	35.0903	−	20.2594i	1.31599	−	0.759788i
$712$	−3.20427	−	7.55183i	−0.120085	−	0.283017i
$713$	13.2564	+	13.2564i	0.496456	+	0.496456i
$714$	−24.2235	+	2.90560i	−0.906543	+	0.108739i
$715$		0			0
$716$	−29.6553	+	21.0187i	−1.10827	+	0.785505i
$717$	−65.4475	−	17.5366i	−2.44418	−	0.654917i
$718$	−3.60666	−	11.3258i	−0.134599	−	0.422675i
$719$	−14.3205	+	24.8039i	−0.534066	+	0.925029i	0.465142	+	0.885236i	$0.346003\pi$
$719$	−14.3205	+	24.8039i	−0.534066	+	0.925029i	−0.999208	+	0.0397933i	$0.987330\pi$
$720$		0			0
$721$	−2.52432	−	34.5728i	−0.0940106	−	1.28756i
$722$	−15.4512	−	3.37911i	−0.575034	−	0.125757i
$723$	3.16736	+	11.8207i	0.117795	+	0.439618i
$724$	0.795677	+	8.53215i	0.0295711	+	0.317095i
$725$		0			0
$726$	0.159356	+	3.42500i	0.00591425	+	0.127114i
$727$	35.3576	+	35.3576i	1.31134	+	1.31134i	0.920429	+	0.390911i	$0.127840\pi$
$727$	35.3576	+	35.3576i	1.31134	+	1.31134i	0.390911	+	0.920429i	$0.372160\pi$
$728$	1.26511	−	25.5717i	0.0468883	−	0.947749i
$729$		−	43.5147i		−	1.61166i
$730$		0			0
$731$	−11.2655	+	6.50414i	−0.416669	+	0.240564i
$732$	50.5328	+	41.9118i	1.86775	+	1.54910i
$733$	−19.8341	+	5.31453i	−0.732589	+	0.196297i	−0.605782	−	0.795631i	$-0.707140\pi$
$733$	−19.8341	+	5.31453i	−0.732589	+	0.196297i	−0.126807	+	0.991927i	$0.540473\pi$
$734$	−23.4731	−	36.6138i	−0.866407	−	1.35144i
$735$		0			0
$736$	29.1623	+	8.73831i	1.07494	+	0.322098i
$737$	−4.83758	−	18.0541i	−0.178194	−	0.665031i
$738$	−17.9899	+	5.72883i	−0.662219	+	0.210881i
$739$	24.2010	+	41.9174i	0.890249	+	1.54196i	0.839576	+	0.543242i	$0.182803\pi$
$739$	24.2010	+	41.9174i	0.890249	+	1.54196i	0.0506730	+	0.998715i	$0.483863\pi$
$740$		0			0
$741$	26.8832			0.987579
$742$	18.1707	+	45.3384i	0.667068	+	1.66443i
$743$	3.78255	−	3.78255i	0.138768	−	0.138768i	−0.634310	−	0.773078i	$-0.718716\pi$
$743$	3.78255	−	3.78255i	0.138768	−	0.138768i	0.773078	+	0.634310i	$0.218716\pi$
$744$	−25.6743	−	10.3774i	−0.941264	−	0.380454i
$745$		0			0
$746$	−9.76578	+	18.8916i	−0.357551	+	0.691672i
$747$	29.3290	−	7.85869i	1.07309	−	0.287535i
$748$	−5.13212	−	13.8533i	−0.187649	−	0.506526i
$749$	−1.08458	+	0.0791901i	−0.0396296	+	0.00289354i
$750$		0			0
$751$	15.5554	+	8.98090i	0.567623	+	0.327718i	0.756200	−	0.654341i	$-0.227054\pi$
$751$	15.5554	+	8.98090i	0.567623	+	0.327718i	−0.188576	+	0.982059i	$0.560387\pi$
$752$	−22.7872	+	10.9450i	−0.830964	+	0.399123i
$753$	9.70180	−	36.2076i	0.353553	−	1.31948i
$754$	0.387544	+	8.32940i	0.0141135	+	0.303339i
$755$		0			0
$756$	−21.7922	+	17.9665i	−0.792574	+	0.653436i
$757$	35.0017	−	35.0017i	1.27216	−	1.27216i	0.327204	−	0.944954i	$-0.393894\pi$
$757$	35.0017	−	35.0017i	1.27216	−	1.27216i	0.944954	−	0.327204i	$-0.106106\pi$
$758$	−1.83119	+	2.00990i	−0.0665118	+	0.0730030i
$759$	24.0790	+	41.7061i	0.874013	+	1.51384i
$760$		0			0
$761$	−18.0493	+	31.2622i	−0.654285	+	1.13325i	0.327788	+	0.944751i	$0.393697\pi$
$761$	−18.0493	+	31.2622i	−0.654285	+	1.13325i	−0.982073	+	0.188503i	$0.939636\pi$
$762$	7.25651	+	1.58697i	0.262876	+	0.0574897i
$763$	18.2510	−	6.34710i	0.660730	−	0.229781i
$764$	−9.64999	+	21.0074i	−0.349125	+	0.760022i
$765$		0			0
$766$	20.0822	+	10.3813i	0.725601	+	0.375090i
$767$	1.68495	−	6.28831i	0.0608399	−	0.227058i
$768$	−44.6960	+	4.94329i	−1.61283	+	0.178375i
$769$		−	22.5137i		−	0.811865i	−0.913903	−	0.405933i	$-0.866947\pi$
$769$		−	22.5137i		−	0.811865i	0.913903	−	0.405933i	$-0.133053\pi$
$770$		0			0
$771$			28.2691i			1.01809i
$772$	9.11563	+	1.55361i	0.328079	+	0.0559158i
$773$	−5.98883	+	22.3506i	−0.215403	+	0.803896i	0.770621	+	0.637294i	$0.219946\pi$
$773$	−5.98883	+	22.3506i	−0.215403	+	0.803896i	−0.986024	+	0.166602i	$0.946720\pi$
$774$	−17.8392	+	34.5095i	−0.641218	+	1.24042i
$775$		0			0
$776$	43.2622	−	6.07370i	1.55302	−	0.218033i
$777$	3.36460	−	17.5978i	0.120704	−	0.631318i
$778$	−3.42368	+	15.6550i	−0.122745	+	0.561259i
$779$	3.80923	−	6.59778i	0.136480	−	0.236390i
$780$		0			0
$781$	0.894971	+	1.55014i	0.0320246	+	0.0554682i
$782$	13.0522	+	11.8917i	0.466747	+	0.425245i
$783$	6.50425	−	6.50425i	0.232443	−	0.232443i
$784$	−27.4863	−	5.33900i	−0.981653	−	0.190679i
$785$		0			0
$786$	16.1572	−	0.751751i	0.576309	−	0.0268141i
$787$	9.53044	−	35.5681i	0.339724	−	1.26787i	−0.558933	−	0.829213i	$-0.688789\pi$
$787$	9.53044	−	35.5681i	0.339724	−	1.26787i	0.898657	−	0.438653i	$-0.144544\pi$
$788$	14.7459	+	12.2302i	0.525302	+	0.435684i
$789$	26.1715	+	15.1101i	0.931731	+	0.537935i
$790$		0			0
$791$	24.4452	+	36.0024i	0.869170	+	1.28010i
$792$	−35.2311	−	26.5565i	−1.25188	−	0.943646i
$793$	−38.5982	+	10.3424i	−1.37066	+	0.367268i
$794$	14.6512	+	7.57376i	0.519953	+	0.268783i
$795$		0			0
$796$	−2.83861	+	2.01192i	−0.100612	+	0.0713105i
$797$	8.30328	−	8.30328i	0.294117	−	0.294117i	−0.544587	−	0.838704i	$-0.683314\pi$
$797$	8.30328	−	8.30328i	0.294117	−	0.294117i	0.838704	+	0.544587i	$0.183314\pi$
$798$	4.17304	−	29.1025i	0.147724	−	1.03022i
$799$	−14.6620			−0.518705
$800$		0			0
$801$	−7.10464	−	12.3056i	−0.251030	−	0.434797i
$802$	11.8747	+	37.2894i	0.419309	+	1.31673i
$803$	−2.75904	−	10.2969i	−0.0973645	−	0.363369i
$804$	−29.9857	−	13.7743i	−1.05751	−	0.485781i
$805$		0			0
$806$	14.1896	−	9.09693i	0.499807	−	0.320426i
$807$	−25.6682	+	6.87776i	−0.903562	+	0.242109i
$808$	−3.95679	+	32.1868i	−0.139199	+	1.13233i
$809$	27.1489	−	15.6744i	0.954504	−	0.551083i	0.0600265	−	0.998197i	$-0.480881\pi$
$809$	27.1489	−	15.6744i	0.954504	−	0.551083i	0.894477	+	0.447114i	$0.147548\pi$
$810$		0			0
$811$		−	9.76550i		−	0.342913i	−0.985192	−	0.171456i	$-0.945153\pi$
$811$		−	9.76550i		−	0.342913i	0.985192	−	0.171456i	$-0.0548473\pi$
$812$	9.07716	+	0.873423i	0.318546	+	0.0306511i
$813$	28.6732	+	28.6732i	1.00561	+	1.00561i
$814$	10.8374	−	0.504234i	0.379850	−	0.0176734i
$815$		0			0
$816$	−24.6092	−	8.63946i	−0.861495	−	0.302441i
$817$	−4.05719	−	15.1416i	−0.141943	−	0.529739i
$818$	−4.17892	+	19.1084i	−0.146112	+	0.668109i
$819$	−3.22937	−	44.2291i	−0.112843	−	1.54549i
$820$		0			0
$821$	3.83240	−	6.63791i	0.133752	−	0.231665i	−0.791368	−	0.611340i	$-0.790631\pi$
$821$	3.83240	−	6.63791i	0.133752	−	0.231665i	0.925120	+	0.379675i	$0.123964\pi$
$822$	61.0390	−	19.4377i	2.12898	−	0.677966i
$823$	52.8907	+	14.1720i	1.84365	+	0.494006i	0.999138	−	0.0415239i	$-0.0132213\pi$
$823$	52.8907	+	14.1720i	1.84365	+	0.494006i	0.844517	+	0.535530i	$0.179888\pi$
$824$	13.8873	−	34.3578i	0.483786	−	1.19691i
$825$		0			0
$826$	−6.54586	−	2.80016i	−0.227760	−	0.0974302i
$827$	−35.5553	−	35.5553i	−1.23638	−	1.23638i	−0.961470	−	0.274910i	$-0.911352\pi$
$827$	−35.5553	−	35.5553i	−1.23638	−	1.23638i	−0.274910	−	0.961470i	$-0.588648\pi$
$828$	51.9813	+	8.85938i	1.80647	+	0.307885i
$829$	23.4882	−	13.5609i	0.815780	−	0.470991i	−0.0331794	−	0.999449i	$-0.510563\pi$
$829$	23.4882	−	13.5609i	0.815780	−	0.470991i	0.848959	+	0.528459i	$0.177230\pi$
$830$		0			0
$831$	−80.5397	−	46.4996i	−2.79389	−	1.61305i
$832$	13.2765	−	23.9351i	0.460281	−	0.829800i
$833$	−13.0296	−	9.69357i	−0.451449	−	0.335862i
$834$	57.1560	−	36.6426i	1.97915	−	1.26883i
$835$		0			0
$836$	17.7259	−	1.65305i	0.613063	−	0.0571720i
$837$	−17.9600	−	4.81237i	−0.620789	−	0.166340i
$838$	19.7133	−	21.6372i	0.680984	−	0.747445i
$839$	3.82948			0.132208			0.0661042	−	0.997813i	$-0.478943\pi$
$839$	3.82948			0.132208			0.0661042	+	0.997813i	$0.478943\pi$
$840$		0			0
$841$	26.0301			0.897589
$842$	−25.4794	+	27.9661i	−0.878079	+	0.963775i
$843$	27.6011	+	7.39570i	0.950634	+	0.254722i
$844$	47.3115	−	4.41210i	1.62853	−	0.151871i
$845$		0			0
$846$	−36.8617	+	23.6320i	−1.26733	+	0.812485i
$847$	−1.49203	+	1.72708i	−0.0512669	+	0.0593431i
$848$	−3.95551	+	52.0665i	−0.135833	+	1.78797i
$849$	67.4183	+	38.9240i	2.31379	+	1.33587i
$850$		0			0
$851$	−11.2296	+	6.48342i	−0.384946	+	0.222249i
$852$	3.11514	+	0.530926i	0.106723	+	0.0181892i
$853$	1.20013	+	1.20013i	0.0410916	+	0.0410916i	0.727354	−	0.686262i	$-0.240750\pi$
$853$	1.20013	+	1.20013i	0.0410916	+	0.0410916i	−0.686262	+	0.727354i	$0.740750\pi$
$854$	5.20460	+	43.3900i	0.178098	+	1.48478i
$855$		0			0
$856$	−1.07783	−	0.435655i	−0.0368396	−	0.0148904i
$857$	25.5819	+	6.85466i	0.873862	+	0.234151i	0.667757	−	0.744379i	$-0.267254\pi$
$857$	25.5819	+	6.85466i	0.873862	+	0.234151i	0.206105	+	0.978530i	$0.433921\pi$
$858$	41.2561	−	13.1379i	1.40846	−	0.448519i
$859$	−19.8151	+	34.3208i	−0.676083	+	1.17101i	0.300068	+	0.953918i	$0.402991\pi$
$859$	−19.8151	+	34.3208i	−0.676083	+	1.17101i	−0.976151	+	0.217093i	$0.930343\pi$
$860$		0			0
$861$	−18.2397	−	8.82684i	−0.621608	−	0.300818i
$862$	−12.1881	+	55.7308i	−0.415128	+	1.89820i
$863$	2.57861	+	9.62351i	0.0877769	+	0.327588i	0.995826	−	0.0912768i	$-0.0290948\pi$
$863$	2.57861	+	9.62351i	0.0877769	+	0.327588i	−0.908049	+	0.418865i	$0.862428\pi$
$864$	−29.3814	+	6.95601i	−0.999575	+	0.236648i
$865$		0			0
$866$	33.1312	−	1.54150i	1.12585	−	0.0523825i
$867$	23.0883	+	23.0883i	0.784120	+	0.784120i
$868$	−7.64527	−	16.7731i	−0.259497	−	0.569315i
$869$			26.3331i			0.893290i
$870$		0			0
$871$	17.3938	−	10.0423i	0.589368	−	0.340272i
$872$	20.5030	+	2.52047i	0.694318	+	0.0853540i
$873$	73.0908	−	19.5846i	2.47375	−	0.662839i
$874$	−17.9128	+	11.4839i	−0.605909	+	0.388448i
$875$		0			0
$876$	−17.1019	−	7.85595i	−0.577820	−	0.265428i
$877$	−0.664074	−	2.47836i	−0.0224242	−	0.0836882i	0.953807	−	0.300420i	$-0.0971269\pi$
$877$	−0.664074	−	2.47836i	−0.0224242	−	0.0836882i	−0.976231	+	0.216732i	$0.930460\pi$
$878$	−2.46372	−	7.73668i	−0.0831464	−	0.261100i
$879$	−6.12031	−	10.6007i	−0.206433	−	0.357553i
$880$		0			0
$881$	20.5639			0.692816			0.346408	−	0.938084i	$-0.387401\pi$
$881$	20.5639			0.692816			0.346408	+	0.938084i	$0.387401\pi$
$882$	−48.3815	−	3.36965i	−1.62909	−	0.113462i
$883$	26.6080	−	26.6080i	0.895429	−	0.895429i	−0.0995985	−	0.995028i	$-0.531756\pi$
$883$	26.6080	−	26.6080i	0.895429	−	0.895429i	0.995028	+	0.0995985i	$0.0317558\pi$
$884$	12.9517	−	9.17974i	0.435613	−	0.308748i
$885$		0			0
$886$	−1.07522	−	0.555823i	−0.0361229	−	0.0186732i
$887$	−7.10873	+	1.90478i	−0.238688	+	0.0639562i	−0.376180	−	0.926547i	$-0.622762\pi$
$887$	−7.10873	+	1.90478i	−0.238688	+	0.0639562i	0.137492	+	0.990503i	$0.456096\pi$
$888$	11.5292	−	15.2951i	0.386893	−	0.513269i
$889$	2.77748	+	4.09062i	0.0931537	+	0.137195i
$890$		0			0
$891$	−0.838132	−	0.483895i	−0.0280785	−	0.0162111i
$892$	−28.8053	−	23.8911i	−0.964474	−	0.799932i
$893$	4.57299	−	17.0666i	0.153029	−	0.571112i
$894$	35.5680	−	1.65488i	1.18957	−	0.0553475i
$895$		0			0
$896$	−23.8501	−	18.0879i	−0.796775	−	0.604276i
$897$	−36.5921	+	36.5921i	−1.22177	+	1.22177i
$898$	4.87319	+	4.43988i	0.162621	+	0.148161i
$899$	3.00169	+	5.19908i	0.100112	+	0.173399i
$900$		0			0
$901$	−15.1427	+	26.2280i	−0.504478	+	0.873781i
$902$	2.62146	−	11.9868i	0.0872852	−	0.399117i
$903$	−39.3804	+	13.6952i	−1.31050	+	0.455748i
$904$	6.46788	+	46.0699i	0.215119	+	1.53226i
$905$		0			0
$906$	−12.2930	+	23.7804i	−0.408407	+	0.790052i
$907$	−3.60588	+	13.4573i	−0.119731	+	0.446843i	−0.999597	−	0.0283786i	$-0.990966\pi$
$907$	−3.60588	+	13.4573i	−0.119731	+	0.446843i	0.879866	+	0.475222i	$0.157632\pi$
$908$	−40.9878	−	6.98572i	−1.36023	−	0.231829i
$909$			56.1704i			1.86305i
$910$		0			0
$911$			9.10653i			0.301713i	0.988556	+	0.150856i	$0.0482031\pi$
$911$			9.10653i			0.301713i	−0.988556	+	0.150856i	$0.951797\pi$
$912$	17.7318	−	25.9506i	0.587158	−	0.859309i
$913$	−5.10735	+	19.0609i	−0.169029	+	0.630823i
$914$	39.9610	+	20.6573i	1.32179	+	0.683283i
$915$		0			0
$916$	−14.9228	+	32.4860i	−0.493064	+	1.07337i
$917$	8.14737	+	7.03857i	0.269050	+	0.232434i
$918$	−17.1079	−	3.74142i	−0.564644	−	0.123485i
$919$	−17.5872	+	30.4620i	−0.580149	+	1.00485i	0.415312	+	0.909679i	$0.363672\pi$
$919$	−17.5872	+	30.4620i	−0.580149	+	1.00485i	−0.995461	+	0.0951683i	$0.969661\pi$
$920$		0			0
$921$	−26.5004	−	45.9000i	−0.873217	−	1.51246i
$922$	22.3295	−	24.5088i	0.735384	−	0.807154i
$923$	−1.36006	+	1.36006i	−0.0447668	+	0.0447668i
$924$	−7.81830	−	46.7013i	−0.257203	−	1.53636i
$925$		0			0
$926$	0.171184	+	3.67923i	0.00562546	+	0.120907i
$927$	16.6132	−	62.0014i	0.545650	−	2.03639i
$928$	8.29605	+	5.11985i	0.272331	+	0.168067i
$929$	−32.5064	−	18.7676i	−1.06650	−	0.615745i	−0.139278	−	0.990253i	$-0.544478\pi$
$929$	−32.5064	−	18.7676i	−1.06650	−	0.615745i	−0.927223	+	0.374509i	$0.877811\pi$
$930$		0			0
$931$	15.3472	−	12.1431i	0.502983	−	0.397974i
$932$	0.245150	+	0.661739i	0.00803015	+	0.0216760i
$933$	4.24615	−	1.13775i	0.139013	−	0.0372483i
$934$	5.38846	−	10.4238i	0.176316	−	0.341078i
$935$		0			0
$936$	17.7660	−	43.9540i	0.580700	−	1.43668i
$937$	14.9371	−	14.9371i	0.487973	−	0.487973i	−0.419693	−	0.907666i	$-0.637862\pi$
$937$	14.9371	−	14.9371i	0.487973	−	0.487973i	0.907666	+	0.419693i	$0.137862\pi$
$938$	−8.17133	−	20.3886i	−0.266804	−	0.665711i
$939$	−34.2270			−1.11696
$940$		0			0
$941$	−3.05589	−	5.29296i	−0.0996192	−	0.172546i	0.811908	−	0.583786i	$-0.198429\pi$
$941$	−3.05589	−	5.29296i	−0.0996192	−	0.172546i	−0.911527	+	0.411240i	$0.865096\pi$
$942$	−43.1157	+	13.7300i	−1.40479	+	0.447349i
$943$	3.79564	+	14.1655i	0.123603	+	0.461293i
$944$	−4.95878	−	5.77417i	−0.161395	−	0.187933i
$945$		0			0
$946$	−13.6261	−	21.2543i	−0.443022	−	0.691036i
$947$	41.6507	−	11.1603i	1.35347	−	0.362660i	0.492053	−	0.870565i	$-0.336247\pi$
$947$	41.6507	−	11.1603i	1.35347	−	0.362660i	0.861413	+	0.507905i	$0.169580\pi$
$948$	35.7837	+	29.6789i	1.16220	+	0.963926i
$949$	9.92033	−	5.72751i	0.322028	−	0.185923i
$950$		0			0
$951$		−	76.9801i		−	2.49625i
$952$	−7.92707	−	15.4458i	−0.256918	−	0.500602i
$953$	−26.8326	−	26.8326i	−0.869193	−	0.869193i	0.123190	−	0.992383i	$-0.460687\pi$
$953$	−26.8326	−	26.8326i	−0.869193	−	0.869193i	−0.992383	+	0.123190i	$0.960687\pi$
$954$	4.20357	+	90.3464i	0.136096	+	2.92507i
$955$		0			0
$956$	−4.47701	−	48.0076i	−0.144797	−	1.55268i
$957$	3.99135	+	14.8959i	0.129022	+	0.481517i
$958$	−19.3398	−	4.22953i	−0.624841	−	0.136650i
$959$	38.3826	+	18.5747i	1.23944	+	0.599809i
$960$		0			0
$961$	−9.43240	+	16.3374i	−0.304271	+	0.527013i
$962$	3.53745	+	11.1085i	0.114052	+	0.358151i
$963$	−1.94504	−	0.521171i	−0.0626779	−	0.0167945i
$964$	−7.10486	+	5.03570i	−0.228832	+	0.162189i
$965$		0			0
$966$	33.9327	+	45.2930i	1.09177	+	1.45728i
$967$	9.65871	+	9.65871i	0.310603	+	0.310603i	0.845143	−	0.534540i	$-0.179515\pi$
$967$	9.65871	+	9.65871i	0.310603	+	0.310603i	−0.534540	+	0.845143i	$0.679515\pi$
$968$	−2.24608	+	0.953017i	−0.0721916	+	0.0306311i
$969$	15.7871	−	9.11468i	0.507155	−	0.292806i
$970$		0			0
$971$	18.9435	+	10.9371i	0.607927	+	0.350987i	0.772154	−	0.635436i	$-0.219179\pi$
$971$	18.9435	+	10.9371i	0.607927	+	0.350987i	−0.164226	+	0.986423i	$0.552513\pi$
$972$	28.4284	−	10.5317i	0.911843	−	0.337804i
$973$	44.3890	+	8.48690i	1.42305	+	0.272078i
$974$	20.2623	+	31.6056i	0.649246	+	1.01271i
$975$		0			0
$976$	−15.4753	+	44.0809i	−0.495352	+	1.41099i
$977$	−25.1707	−	6.74446i	−0.805281	−	0.215774i	−0.167380	−	0.985893i	$-0.553531\pi$
$977$	−25.1707	−	6.74446i	−0.805281	−	0.215774i	−0.637901	+	0.770118i	$0.720197\pi$
$978$	−0.00831321	−	0.00757402i	−0.000265827	−	0.000242190i
$979$	9.23458			0.295138
$980$		0			0
$981$	35.7805			1.14238
$982$	37.2023	+	33.8944i	1.18717	+	1.08161i
$983$	−46.8710	−	12.5590i	−1.49495	−	0.400571i	−0.583547	−	0.812080i	$-0.698336\pi$
$983$	−46.8710	−	12.5590i	−1.49495	−	0.400571i	−0.911406	+	0.411508i	$0.865002\pi$
$984$	−13.3342	−	17.0721i	−0.425078	−	0.544239i
$985$		0			0
$986$	3.05165	+	4.76002i	0.0971842	+	0.151590i
$987$	−46.1583	−	8.82518i	−1.46923	−	0.280909i
$988$	6.64569	+	17.9389i	0.211427	+	0.570712i
$989$	26.1325	+	15.0876i	0.830965	+	0.479758i
$990$		0			0
$991$	3.40592	−	1.96641i	0.108193	−	0.0624650i	−0.444927	−	0.895567i	$-0.646770\pi$
$991$	3.40592	−	1.96641i	0.108193	−	0.0624650i	0.553120	+	0.833102i	$0.313437\pi$
$992$	0.577912	−	19.6975i	0.0183487	−	0.625397i
$993$	−7.77497	−	7.77497i	−0.246731	−	0.246731i
$994$	1.26121	+	1.68345i	0.0400032	+	0.0533958i
$995$		0			0
$996$	20.1453	+	28.4230i	0.638329	+	0.900617i
$997$	49.5831	+	13.2857i	1.57031	+	0.420764i	0.935910	−	0.352240i	$-0.114580\pi$
$997$	49.5831	+	13.2857i	1.57031	+	0.420764i	0.634402	+	0.773004i	$0.281247\pi$
$998$	−4.24068	−	13.3168i	−0.134236	−	0.421535i
$999$	6.43023	−	11.1375i	0.203443	−	0.352374i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	700.2.be.e.443.6		72
4.3	odd	2	inner	700.2.be.e.443.16		72
5.2	odd	4	inner	700.2.be.e.107.4		72
5.3	odd	4		140.2.w.b.107.15	yes	72
5.4	even	2		140.2.w.b.23.13	yes	72
7.4	even	3	inner	700.2.be.e.543.8		72
20.3	even	4		140.2.w.b.107.11	yes	72
20.7	even	4	inner	700.2.be.e.107.8		72
20.19	odd	2		140.2.w.b.23.3	✓	72
28.11	odd	6	inner	700.2.be.e.543.4		72
35.3	even	12		980.2.x.m.67.3		72
35.4	even	6		140.2.w.b.123.11	yes	72
35.9	even	6		980.2.k.k.883.2		36
35.13	even	4		980.2.x.m.667.15		72
35.18	odd	12		140.2.w.b.67.3	yes	72
35.19	odd	6		980.2.k.j.883.2		36
35.23	odd	12		980.2.k.k.687.11		36
35.24	odd	6		980.2.x.m.263.11		72
35.32	odd	12	inner	700.2.be.e.207.16		72
35.33	even	12		980.2.k.j.687.11		36
35.34	odd	2		980.2.x.m.863.13		72
140.3	odd	12		980.2.x.m.67.13		72
140.19	even	6		980.2.k.j.883.11		36
140.23	even	12		980.2.k.k.687.2		36
140.39	odd	6		140.2.w.b.123.15	yes	72
140.59	even	6		980.2.x.m.263.15		72
140.67	even	12	inner	700.2.be.e.207.6		72
140.79	odd	6		980.2.k.k.883.11		36
140.83	odd	4		980.2.x.m.667.11		72
140.103	odd	12		980.2.k.j.687.2		36
140.123	even	12		140.2.w.b.67.13	yes	72
140.139	even	2		980.2.x.m.863.3		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.w.b.23.3	✓	72	20.19	odd	2
140.2.w.b.23.13	yes	72	5.4	even	2
140.2.w.b.67.3	yes	72	35.18	odd	12
140.2.w.b.67.13	yes	72	140.123	even	12
140.2.w.b.107.11	yes	72	20.3	even	4
140.2.w.b.107.15	yes	72	5.3	odd	4
140.2.w.b.123.11	yes	72	35.4	even	6
140.2.w.b.123.15	yes	72	140.39	odd	6
700.2.be.e.107.4		72	5.2	odd	4	inner
700.2.be.e.107.8		72	20.7	even	4	inner
700.2.be.e.207.6		72	140.67	even	12	inner
700.2.be.e.207.16		72	35.32	odd	12	inner
700.2.be.e.443.6		72	1.1	even	1	trivial
700.2.be.e.443.16		72	4.3	odd	2	inner
700.2.be.e.543.4		72	28.11	odd	6	inner
700.2.be.e.543.8		72	7.4	even	3	inner
980.2.k.j.687.2		36	140.103	odd	12
980.2.k.j.687.11		36	35.33	even	12
980.2.k.j.883.2		36	35.19	odd	6
980.2.k.j.883.11		36	140.19	even	6
980.2.k.k.687.2		36	140.23	even	12
980.2.k.k.687.11		36	35.23	odd	12
980.2.k.k.883.2		36	35.9	even	6
980.2.k.k.883.11		36	140.79	odd	6
980.2.x.m.67.3		72	35.3	even	12
980.2.x.m.67.13		72	140.3	odd	12
980.2.x.m.263.11		72	35.24	odd	6
980.2.x.m.263.15		72	140.59	even	6
980.2.x.m.667.11		72	140.83	odd	4
980.2.x.m.667.15		72	35.13	even	4
980.2.x.m.863.3		72	140.139	even	2
980.2.x.m.863.13		72	35.34	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	700.be (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.952442 + 1.04540i) q^{2} +(-2.71477 - 0.727420i) q^{3} +(-0.185707 - 1.99136i) q^{4} +(3.34610 - 2.14518i) q^{6} +(2.59868 + 0.496852i) q^{7} +(2.25864 + 1.70252i) q^{8} +(4.24276 + 2.44956i) q^{9} +(-2.75736 + 1.59196i) q^{11} +(-0.944404 + 5.54117i) q^{12} +(-2.41925 - 2.41925i) q^{13} +(-2.99450 + 2.24343i) q^{14} +(-3.93103 + 0.739618i) q^{16} +(-2.24094 - 0.600458i) q^{17} +(-6.60174 + 2.10230i) q^{18} +(1.39787 - 2.42118i) q^{19} +(-6.69340 - 3.23917i) q^{21} +(0.961994 - 4.39878i) q^{22} +(1.39288 + 5.19830i) q^{23} +(-4.89323 - 6.26492i) q^{24} +(4.83327 - 0.224879i) q^{26} +(-3.77420 - 3.77420i) q^{27} +(0.506818 - 5.26718i) q^{28} +1.72334i q^{29} +(3.01685 - 1.74178i) q^{31} +(2.97088 - 4.81392i) q^{32} +(8.64362 - 2.31605i) q^{33} +(2.76208 - 1.77077i) q^{34} +(4.09004 - 8.90375i) q^{36} +(0.623610 + 2.32734i) q^{37} +(1.19970 + 3.76736i) q^{38} +(4.80790 + 8.32752i) q^{39} +2.72503 q^{41} +(9.76129 - 3.91213i) q^{42} +(3.96477 - 3.96477i) q^{43} +(3.68223 + 5.19525i) q^{44} +(-6.76092 - 3.49497i) q^{46} +(6.10452 - 1.63570i) q^{47} +(11.2098 + 0.851615i) q^{48} +(6.50628 + 2.58232i) q^{49} +(5.64685 + 3.26021i) q^{51} +(-4.36833 + 5.26687i) q^{52} +(3.37866 - 12.6093i) q^{53} +(7.54024 - 0.350826i) q^{54} +(5.02357 + 5.54651i) q^{56} +(-5.55610 + 5.55610i) q^{57} +(-1.80158 - 1.64139i) q^{58} +(0.951402 + 1.64788i) q^{59} +(5.83980 - 10.1148i) q^{61} +(-1.05253 + 4.81275i) q^{62} +(9.80850 + 8.47363i) q^{63} +(2.20286 + 7.69073i) q^{64} +(-5.81136 + 11.2419i) q^{66} +(-1.51938 + 5.67039i) q^{67} +(-0.779570 + 4.57403i) q^{68} -15.1254i q^{69} -0.562181i q^{71} +(5.41242 + 12.7560i) q^{72} +(-0.866554 + 3.23402i) q^{73} +(-3.02695 - 1.56474i) q^{74} +(-5.08103 - 2.33403i) q^{76} +(-7.95646 + 2.76700i) q^{77} +(-13.2848 - 2.90533i) q^{78} +(4.13532 - 7.16259i) q^{79} +(0.151981 + 0.263239i) q^{81} +(-2.59543 + 2.84874i) q^{82} +(4.38250 - 4.38250i) q^{83} +(-5.20734 + 13.9305i) q^{84} +(0.368541 + 7.92097i) q^{86} +(1.25360 - 4.67848i) q^{87} +(-8.93821 - 1.09879i) q^{88} +(-2.51180 - 1.45019i) q^{89} +(-5.08485 - 7.48887i) q^{91} +(10.0930 - 3.73908i) q^{92} +(-9.45706 + 2.53401i) q^{93} +(-4.10425 + 7.93955i) q^{94} +(-11.5670 + 10.9076i) q^{96} +(10.9216 - 10.9216i) q^{97} +(-8.89640 + 4.34213i) q^{98} -15.5984 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 2 q^{2} - 16 q^{6} + 4 q^{8} - 10 q^{12} - 28 q^{16} - 4 q^{17} + 20 q^{18} + 4 q^{21} + 16 q^{22} - 4 q^{26} - 42 q^{28} + 38 q^{32} + 64 q^{33} + 16 q^{36} + 4 q^{37} - 12 q^{38} - 40 q^{41} - 78 q^{42}+ \cdots + 90 q^{98}+O(q^{100}) \) 72 * q - 2 * q^2 - 16 * q^6 + 4 * q^8 - 10 * q^12 - 28 * q^16 - 4 * q^17 + 20 * q^18 + 4 * q^21 + 16 * q^22 - 4 * q^26 - 42 * q^28 + 38 * q^32 + 64 * q^33 + 16 * q^36 + 4 * q^37 - 12 * q^38 - 40 * q^41 - 78 * q^42 - 28 * q^46 - 12 * q^48 - 48 * q^52 + 24 * q^53 + 36 * q^56 + 16 * q^57 - 30 * q^58 - 20 * q^61 - 56 * q^62 + 44 * q^66 + 12 * q^68 - 44 * q^72 + 12 * q^73 + 112 * q^76 - 16 * q^77 - 64 * q^78 - 52 * q^81 + 34 * q^82 + 64 * q^86 - 16 * q^88 - 44 * q^92 - 12 * q^93 - 48 * q^96 + 24 * q^97 + 90 * q^98

Introduction

L-functions

Modular forms

Varieties

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