LMFDB - Embedded newform 700.2.be.e.443.16

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)

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")

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);

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			443.16
Character	$\chi$	$=$	700.443
Dual form			700.2.be.e.207.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.34754 + 0.429119i) q^{2} +(2.71477 + 0.727420i) q^{3} +(1.63171 + 1.15651i) q^{4} +(3.34610 + 2.14518i) q^{6} +(-2.59868 - 0.496852i) q^{7} +(1.70252 + 2.25864i) q^{8} +(4.24276 + 2.44956i) q^{9} +(2.75736 - 1.59196i) q^{11} +(3.58846 + 4.32659i) q^{12} +(-2.41925 - 2.41925i) q^{13} +(-3.28861 - 1.78467i) q^{14} +(1.32498 + 3.77418i) q^{16} +(-2.24094 - 0.600458i) q^{17} +(4.66612 + 5.12151i) q^{18} +(-1.39787 + 2.42118i) q^{19} +(-6.69340 - 3.23917i) q^{21} +(4.39878 - 0.961994i) q^{22} +(-1.39288 - 5.19830i) q^{23} +(2.97897 + 7.37012i) q^{24} +(-2.22189 - 4.29818i) q^{26} +(3.77420 + 3.77420i) q^{27} +(-3.66569 - 3.81611i) q^{28} +1.72334i q^{29} +(-3.01685 + 1.74178i) q^{31} +(0.165897 + 5.65442i) 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} +(-2.92265 + 2.66278i) q^{38} +(-4.80790 - 8.32752i) q^{39} +2.72503 q^{41} +(-7.62961 - 7.23716i) q^{42} +(-3.96477 + 3.96477i) q^{43} +(6.34034 + 0.591276i) q^{44} +(0.353728 - 7.60261i) q^{46} +(-6.10452 + 1.63570i) q^{47} +(0.851615 + 11.2098i) q^{48} +(6.50628 + 2.58232i) q^{49} +(-5.64685 - 3.26021i) q^{51} +(-1.14965 - 6.74541i) q^{52} +(3.37866 - 12.6093i) q^{53} +(3.46629 + 6.70545i) q^{54} +(-3.30209 - 6.71537i) q^{56} +(-5.55610 + 5.55610i) q^{57} +(-0.739519 + 2.32227i) q^{58} +(-0.951402 - 1.64788i) q^{59} +(5.83980 - 10.1148i) q^{61} +(-4.81275 + 1.05253i) q^{62} +(-9.80850 - 8.47363i) q^{63} +(-2.20286 + 7.69073i) q^{64} +(12.6415 + 0.588172i) q^{66} +(1.51938 - 5.67039i) q^{67} +(-2.96214 - 3.57144i) q^{68} -15.1254i q^{69} +0.562181i q^{71} +(1.69071 + 13.7532i) q^{72} +(-0.866554 + 3.23402i) q^{73} +(-0.158369 + 3.40378i) q^{74} +(-5.08103 + 2.33403i) q^{76} +(-7.95646 + 2.76700i) q^{77} +(-2.90533 - 13.2848i) q^{78} +(-4.13532 + 7.16259i) q^{79} +(0.151981 + 0.263239i) q^{81} +(3.67208 + 1.16936i) q^{82} +(-4.38250 + 4.38250i) q^{83} +(-7.17559 - 13.0264i) q^{84} +(-7.04404 + 3.64132i) q^{86} +(-1.25360 + 4.67848i) q^{87} +(8.29011 + 3.51752i) q^{88} +(-2.51180 - 1.45019i) q^{89} +(5.08485 + 7.48887i) q^{91} +(3.73908 - 10.0930i) q^{92} +(-9.45706 + 2.53401i) q^{93} +(-8.92798 - 0.415394i) q^{94} +(-3.66277 + 15.4711i) q^{96} +(10.9216 - 10.9216i) q^{97} +(7.65933 + 6.27174i) 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 $

$2$	1.34754	+	0.429119i	0.952853	+	0.303433i
$2$	1.34754	+	0.429119i	0.952853	+	0.303433i
$3$	2.71477	+	0.727420i	1.56737	+	0.419976i	0.934988	−	0.354678i	$-0.115410\pi$
$3$	2.71477	+	0.727420i	1.56737	+	0.419976i	0.632384	+	0.774655i	$0.282076\pi$
$4$	1.63171	+	1.15651i	0.815857	+	0.578253i
$5$		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
$8$	1.70252	+	2.25864i	0.601931	+	0.798548i
$9$	4.24276	+	2.44956i	1.41425	+	0.816519i
$10$		0			0
$11$	2.75736	−	1.59196i	0.831375	−	0.479994i	−0.0229484	−	0.999737i	$-0.507305\pi$
$11$	2.75736	−	1.59196i	0.831375	−	0.479994i	0.854323	+	0.519742i	$0.173972\pi$
$12$	3.58846	+	4.32659i	1.03590	+	1.24898i
$13$	−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	$0.907355\pi$
$14$	−3.28861	−	1.78467i	−0.878918	−	0.476973i
$15$		0			0
$16$	1.32498	+	3.77418i	0.331246	+	0.943544i
$17$	−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	$0.674112\pi$
$18$	4.66612	+	5.12151i	1.09982	+	1.20715i
$19$	−1.39787	+	2.42118i	−0.320693	+	0.555456i	−0.980631	−	0.195863i	$-0.937249\pi$
$19$	−1.39787	+	2.42118i	−0.320693	+	0.555456i	0.659938	+	0.751320i	$0.270582\pi$
$20$		0			0
$21$	−6.69340	−	3.23917i	−1.46062	−	0.706845i
$22$	4.39878	−	0.961994i	0.937824	−	0.205098i
$23$	−1.39288	−	5.19830i	−0.290435	−	1.08392i	−0.944775	−	0.327719i	$-0.893720\pi$
$23$	−1.39288	−	5.19830i	−0.290435	−	1.08392i	0.654340	−	0.756201i	$-0.272947\pi$
$24$	2.97897	+	7.37012i	0.608079	+	1.50442i
$25$		0			0
$26$	−2.22189	−	4.29818i	−0.435748	−	0.842942i
$27$	3.77420	+	3.77420i	0.726345	+	0.726345i
$28$	−3.66569	−	3.81611i	−0.692751	−	0.721177i
$29$			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	−0.745825	−	0.666141i	$-0.767945\pi$
$31$	−3.01685	+	1.74178i	−0.541843	+	0.312833i	0.203983	+	0.978974i	$0.434611\pi$
$32$	0.165897	+	5.65442i	0.0293267	+	0.999570i
$33$	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	$0.853204\pi$
$38$	−2.92265	+	2.66278i	−0.474117	+	0.431959i
$39$	−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	$0.431745\pi$
$42$	−7.62961	−	7.23716i	−1.17728	−	1.11672i
$43$	−3.96477	+	3.96477i	−0.604622	+	0.604622i	−0.941536	−	0.336914i	$-0.890617\pi$
$43$	−3.96477	+	3.96477i	−0.604622	+	0.604622i	0.336914	+	0.941536i	$0.390617\pi$
$44$	6.34034	+	0.591276i	0.955842	+	0.0891383i
$45$		0			0
$46$	0.353728	−	7.60261i	0.0521544	−	1.12094i
$47$	−6.10452	+	1.63570i	−0.890435	+	0.238591i	−0.674904	−	0.737905i	$-0.735815\pi$
$47$	−6.10452	+	1.63570i	−0.890435	+	0.238591i	−0.215531	+	0.976497i	$0.569148\pi$
$48$	0.851615	+	11.2098i	0.122920	+	1.61800i
$49$	6.50628	+	2.58232i	0.929468	+	0.368903i
$50$		0			0
$51$	−5.64685	−	3.26021i	−0.790717	−	0.456521i
$52$	−1.14965	−	6.74541i	−0.159427	−	0.935420i
$53$	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	$-0.270610\pi$
$54$	3.46629	+	6.70545i	0.471703	+	0.912496i
$55$		0			0
$56$	−3.30209	−	6.71537i	−0.441261	−	0.897379i
$57$	−5.55610	+	5.55610i	−0.735924	+	0.735924i
$58$	−0.739519	+	2.32227i	−0.0971036	+	0.304929i
$59$	−0.951402	−	1.64788i	−0.123862	−	0.214535i	0.797426	−	0.603417i	$-0.206195\pi$
$59$	−0.951402	−	1.64788i	−0.123862	−	0.214535i	−0.921288	+	0.388882i	$0.872861\pi$
$60$		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	$-0.102180\pi$
$62$	−4.81275	+	1.05253i	−0.611220	+	0.133671i
$63$	−9.80850	−	8.47363i	−1.23575	−	1.06758i
$64$	−2.20286	+	7.69073i	−0.275358	+	0.961342i
$65$		0			0
$66$	12.6415	+	0.588172i	1.55606	+	0.0723990i
$67$	1.51938	−	5.67039i	0.185621	−	0.692748i	−0.808875	−	0.587980i	$-0.799923\pi$
$67$	1.51938	−	5.67039i	0.185621	−	0.692748i	0.994497	−	0.104768i	$-0.0334100\pi$
$68$	−2.96214	−	3.57144i	−0.359212	−	0.433100i
$69$		−	15.1254i		−	1.82088i
$70$		0			0
$71$			0.562181i			0.0667186i	0.999443	+	0.0333593i	$0.0106206\pi$
$71$			0.562181i			0.0667186i	−0.999443	+	0.0333593i	$0.989379\pi$
$72$	1.69071	+	13.7532i	0.199253	+	1.62084i
$73$	−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	$0.146107\pi$
$74$	−0.158369	+	3.40378i	−0.0184100	+	0.395682i
$75$		0			0
$76$	−5.08103	+	2.33403i	−0.582834	+	0.267731i
$77$	−7.95646	+	2.76700i	−0.906723	+	0.315329i
$78$	−2.90533	−	13.2848i	−0.328963	−	1.50421i
$79$	−4.13532	+	7.16259i	−0.465260	+	0.805855i	−0.999213	−	0.0396596i	$-0.987373\pi$
$79$	−4.13532	+	7.16259i	−0.465260	+	0.805855i	0.533953	+	0.845514i	$0.320706\pi$
$80$		0			0
$81$	0.151981	+	0.263239i	0.0168868	+	0.0292487i
$82$	3.67208	+	1.16936i	0.405513	+	0.129134i
$83$	−4.38250	+	4.38250i	−0.481042	+	0.481042i	−0.905464	−	0.424423i	$-0.860477\pi$
$83$	−4.38250	+	4.38250i	−0.481042	+	0.481042i	0.424423	+	0.905464i	$0.360477\pi$
$84$	−7.17559	−	13.0264i	−0.782921	−	1.42129i
$85$		0			0
$86$	−7.04404	+	3.64132i	−0.759578	+	0.392654i
$87$	−1.25360	+	4.67848i	−0.134400	+	0.501586i
$88$	8.29011	+	3.51752i	0.883729	+	0.374969i
$89$	−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
$92$	3.73908	−	10.0930i	0.389826	−	1.05227i
$93$	−9.45706	+	2.53401i	−0.980652	+	0.262765i
$94$	−8.92798	−	0.415394i	−0.920850	−	0.0428446i
$95$		0			0
$96$	−3.66277	+	15.4711i	−0.373830	+	1.57902i
$97$	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	$-0.0368885\pi$
$98$	7.65933	+	6.27174i	0.773709	+	0.633541i
$99$	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	$0.640111\pi$
$102$	−6.21032	−	6.81642i	−0.614914	−	0.674926i
$103$	3.39107	+	12.6556i	0.334132	+	1.24700i	0.904807	+	0.425821i	$0.140015\pi$
$103$	3.39107	+	12.6556i	0.334132	+	1.24700i	−0.570676	+	0.821176i	$0.693319\pi$
$104$	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	−0.239577	−	0.970877i	$-0.577009\pi$
$107$	0.397018	−	0.106381i	0.0383812	−	0.0102842i	0.277959	+	0.960593i	$0.410342\pi$
$108$	1.79353	+	10.5233i	0.172582	+	1.01260i
$109$	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
$112$	−1.56800	−	10.4662i	−0.148162	−	0.988963i
$113$	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	$0.468432\pi$
$114$	−9.87128	+	5.10283i	−0.924530	+	0.477924i
$115$		0			0
$116$	−1.99306	+	2.81201i	−0.185051	+	0.261088i
$117$	−4.33820	−	16.1904i	−0.401067	−	1.49680i
$118$	−0.574915	−	2.62884i	−0.0529252	−	0.242004i
$119$	5.52515	+	2.67381i	0.506489	+	0.245108i
$120$		0			0
$121$	−0.431317	+	0.747063i	−0.0392106	+	0.0679148i
$122$	12.2098	−	11.1241i	1.10542	−	1.00713i
$123$	7.39783	+	1.98224i	0.667040	+	0.178733i
$124$	−6.93702	−	0.646921i	−0.622963	−	0.0580952i
$125$		0			0
$126$	−9.58112	−	15.6275i	−0.853554	−	1.39221i
$127$	−1.32146	−	1.32146i	−0.117261	−	0.117261i	0.646042	−	0.763302i	$-0.276423\pi$
$127$	−1.32146	−	1.32146i	−0.117261	−	0.117261i	−0.763302	+	0.646042i	$0.776423\pi$
$128$	−6.26868	+	9.41826i	−0.554078	+	0.832465i
$129$	−13.6475	+	7.87939i	−1.20159	+	0.693741i
$130$		0			0
$131$	−3.52422	−	2.03471i	−0.307912	−	0.177773i	0.338080	−	0.941118i	$-0.390223\pi$
$131$	−3.52422	−	2.03471i	−0.307912	−	0.177773i	−0.645992	+	0.763344i	$0.723556\pi$
$132$	16.7824	+	6.21727i	1.46072	+	0.541144i
$133$	4.83558	−	5.59733i	0.419298	−	0.485350i
$134$	4.48068	−	6.98907i	0.387072	−	0.603764i
$135$		0			0
$136$	−2.45903	−	6.08376i	−0.210860	−	0.521678i
$137$	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	$0.341615\pi$
$138$	6.49058	−	20.3820i	0.552515	−	1.73503i
$139$	−17.0814			−1.44882			−0.724411	−	0.689369i	$-0.757888\pi$
$139$	−17.0814			−1.44882			−0.724411	+	0.689369i	$0.757888\pi$
$140$		0			0
$141$	−17.7622			−1.49585
$142$	−0.241242	+	0.757560i	−0.0202446	+	0.0635730i
$143$	−10.5221	−	2.81939i	−0.879902	−	0.235769i
$144$	−3.62347	+	19.2585i	−0.301956	+	1.60488i
$145$		0			0
$146$	−2.55549	+	3.98611i	−0.211494	+	0.329893i
$147$	15.7846	+	11.7432i	1.30189	+	0.968562i
$148$	−1.67403	+	4.51877i	−0.137605	+	0.371441i
$149$	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	−0.243527	−	0.969894i	$-0.578305\pi$
$151$	5.83274	−	3.36754i	0.474662	−	0.274046i	0.718189	+	0.695848i	$0.244971\pi$
$152$	−7.84845	+	0.964826i	−0.636593	+	0.0782577i
$153$	−8.03690	−	8.03690i	−0.649745	−	0.649745i
$154$	−11.9090	+	0.314371i	−0.959655	+	0.0253327i
$155$		0			0
$156$	1.78572	−	19.1485i	0.142972	−	1.53311i
$157$	−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	$0.733437\pi$
$158$	−8.64611	+	7.87732i	−0.687847	+	0.626686i
$159$	18.3446	−	31.7737i	1.45482	−	2.51982i
$160$		0			0
$161$	1.03686	+	14.2008i	0.0817163	+	1.11918i
$162$	0.0918394	+	0.419942i	0.00721558	+	0.0329937i
$163$	0.000732309		0.00273302i	5.73589e−5		0.000214066i	0.965954	−	0.258712i	$-0.0832981\pi$
$163$	0.000732309		0.00273302i	5.73589e−5		0.000214066i	−0.965897	+	0.258926i	$0.916631\pi$
$164$	4.44647	+	3.15152i	0.347211	+	0.246092i
$165$		0			0
$166$	−7.78619	+	4.02497i	−0.604326	+	0.312398i
$167$	−2.32482	−	2.32482i	−0.179900	−	0.179900i	0.611412	−	0.791312i	$-0.290602\pi$
$167$	−2.32482	−	2.32482i	−0.179900	−	0.179900i	−0.791312	+	0.611412i	$0.790602\pi$
$168$	−4.07952	−	20.6327i	−0.314742	−	1.59185i
$169$		−	1.29445i		−	0.0995729i
$170$		0			0
$171$	−11.8616	+	6.84831i	−0.907081	+	0.523703i
$172$	−11.0547	+	1.88409i	−0.842910	+	0.143661i
$173$	−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
$178$	−2.76244	−	3.03204i	−0.207054	−	0.227261i
$179$	9.08714	+	15.7394i	0.679205	+	1.17642i	0.975221	+	0.221235i	$0.0710086\pi$
$179$	9.08714	+	15.7394i	0.679205	+	1.17642i	−0.296016	+	0.955183i	$0.595658\pi$
$180$		0			0
$181$	−4.28458			−0.318471			−0.159235	−	0.987241i	$-0.550903\pi$
$181$	−4.28458			−0.318471			−0.159235	+	0.987241i	$0.550903\pi$
$182$	3.63841	+	12.2735i	0.269697	+	0.909775i
$183$	23.2114	−	23.2114i	1.71584	−	1.71584i
$184$	9.36965	−	11.9962i	0.690740	−	0.884371i
$185$		0			0
$186$	−13.8311	−	0.643525i	−1.01415	−	0.0471855i
$187$	−7.13498	+	1.91181i	−0.521761	+	0.139806i
$188$	−11.8525	−	4.39092i	−0.864434	−	0.320241i
$189$	−7.93272	−	11.6832i	−0.577020	−	0.849824i
$190$		0			0
$191$	10.0103	+	5.77946i	0.724321	+	0.418187i	0.816341	−	0.577570i	$-0.195999\pi$
$191$	10.0103	+	5.77946i	0.724321	+	0.418187i	−0.0920200	+	0.995757i	$0.529332\pi$
$192$	−11.5747	+	19.2762i	−0.835329	+	1.39114i
$193$	−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	$0.136549\pi$
$194$	19.4040	−	10.0306i	1.39312	−	0.720156i
$195$		0			0
$196$	7.62992	+	11.7382i	0.544994	+	0.838440i
$197$	−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	$0.360845\pi$
$198$	21.0194	+	6.69356i	1.49379	+	0.475691i
$199$	0.869824	+	1.50658i	0.0616602	+	0.106799i	0.895208	−	0.445649i	$-0.147027\pi$
$199$	0.869824	+	1.50658i	0.0616602	+	0.106799i	−0.833547	+	0.552448i	$0.813694\pi$
$200$		0			0
$201$	8.24951	−	14.2886i	0.581876	−	1.00784i
$202$	3.46418	+	15.8402i	0.243739	+	1.11451i
$203$	0.856247	−	4.47842i	0.0600968	−	0.314324i
$204$	−5.44359	−	11.8504i	−0.381128	−	0.829691i
$205$		0			0
$206$	−0.861178	+	18.5091i	−0.0600011	+	1.28959i
$207$	6.82387	−	25.4670i	0.474292	−	1.77008i
$208$	5.92521	−	12.3362i	0.410840	−	0.855358i
$209$			8.90141i			0.615723i
$210$		0			0
$211$		−	23.7584i		−	1.63560i	−0.575506	−	0.817798i	$-0.695195\pi$
$211$		−	23.7584i		−	1.63560i	0.575506	−	0.817798i	$-0.304805\pi$
$212$	20.0958	−	16.6674i	1.38018	−	1.14472i
$213$	−0.408942	+	1.52619i	−0.0280202	+	0.104573i
$214$	0.580647	+	0.0270159i	0.0396922	+	0.00184677i
$215$		0			0
$216$	−2.09890	+	14.9502i	−0.142812	+	1.01723i
$217$	8.70524	−	3.02740i	0.590950	−	0.205513i
$218$	10.0902	−	2.20668i	0.683393	−	0.149455i
$219$	−4.70499	+	8.14928i	−0.317934	+	0.550677i
$220$		0			0
$221$	3.96874	+	6.87406i	0.266966	+	0.462399i
$222$	−2.90592	+	9.12529i	−0.195032	+	0.612449i
$223$	−13.2313	+	13.2313i	−0.886031	+	0.886031i	−0.994139	−	0.108108i	$-0.965521\pi$
$223$	−13.2313	+	13.2313i	−0.886031	+	0.886031i	0.108108	+	0.994139i	$0.465521\pi$
$224$	2.37830	−	14.7765i	0.158907	−	0.987294i
$225$		0			0
$226$	10.6816	+	20.6633i	0.710530	+	1.37450i
$227$	−5.38070	+	20.0810i	−0.357130	+	1.33283i	0.520654	+	0.853768i	$0.325688\pi$
$227$	−5.38070	+	20.0810i	−0.357130	+	1.33283i	−0.877783	+	0.479058i	$0.840978\pi$
$228$	−15.4916	+	2.64030i	−1.02596	+	0.174858i
$229$	−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
$232$	−3.89241	+	2.93403i	−0.255549	+	0.192628i
$233$	−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	$0.420346\pi$
$234$	1.10171	−	23.6787i	0.0720208	−	1.54793i
$235$		0			0
$236$	0.353364	−	3.78917i	0.0230020	−	0.246654i
$237$	−16.4367	+	16.4367i	−1.06768	+	1.06768i
$238$	6.29796	+	5.97401i	0.408236	+	0.387237i
$239$	−24.1080			−1.55941			−0.779707	−	0.626145i	$-0.784632\pi$
$239$	−24.1080			−1.55941			−0.779707	+	0.626145i	$0.784632\pi$
$240$		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	$0.878121\pi$
$242$	−0.901794	+	0.821609i	−0.0579695	+	0.0528150i
$243$	−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
$248$	−9.07029	−	3.84856i	−0.575964	−	0.244384i
$249$	−15.0854	+	8.70955i	−0.955998	+	0.551945i
$250$		0			0
$251$		−	13.3373i		−	0.841841i	−0.907098	−	0.420920i	$-0.861707\pi$
$251$		−	13.3373i		−	0.841841i	0.907098	−	0.420920i	$-0.138293\pi$
$252$	−6.20485	−	25.1701i	−0.390869	−	1.58557i
$253$	−12.1162	−	12.1162i	−0.761736	−	0.761736i
$254$	−1.21365	−	2.34778i	−0.0761514	−	0.147313i
$255$		0			0
$256$	−12.4888	+	10.0015i	−0.780552	+	0.625091i
$257$	−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	$-0.184905\pi$
$258$	−21.7717	+	4.76137i	−1.35545	+	0.296430i
$259$	−0.464217	−	6.35786i	−0.0288450	−	0.395058i
$260$		0			0
$261$	−4.22143	+	7.31173i	−0.261300	+	0.452585i
$262$	−3.87589	−	4.25415i	−0.239453	−	0.262822i
$263$	10.3861	+	2.78295i	0.640435	+	0.171604i	0.564401	−	0.825501i	$-0.309107\pi$
$263$	10.3861	+	2.78295i	0.640435	+	0.171604i	0.0760347	+	0.997105i	$0.475774\pi$
$264$	19.9470	+	15.5797i	1.22765	+	0.958862i
$265$		0			0
$266$	8.91804	−	5.46758i	0.546800	−	0.335239i
$267$	−5.76406	−	5.76406i	−0.352755	−	0.352755i
$268$	9.03703	−	7.49529i	0.552024	−	0.457848i
$269$	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	0.828940	−	0.559337i	$-0.188944\pi$
$271$	12.4949	+	7.21392i	0.759010	+	0.438214i	−0.0699304	+	0.997552i	$0.522278\pi$
$272$	−0.702976	−	9.25330i	−0.0426242	−	0.561064i
$273$	8.35664	+	24.0294i	0.505767	+	1.45432i
$274$	19.1879	+	12.3013i	1.15918	+	0.743152i
$275$		0			0
$276$	17.4926	−	24.6803i	1.05293	−	1.48558i
$277$	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	$0.117994\pi$
$278$	−23.0178	−	7.32993i	−1.38051	−	0.439620i
$279$	−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	$0.598074\pi$
$282$	−23.9352	−	7.62209i	−1.42532	−	0.453889i
$283$	26.7548	+	7.16893i	1.59041	+	0.426148i	0.942128	−	0.335254i	$-0.108822\pi$
$283$	26.7548	+	7.16893i	1.59041	+	0.426148i	0.648280	+	0.761402i	$0.275489\pi$
$284$	−0.650166	+	0.917319i	−0.0385803	+	0.0544329i
$285$		0			0
$286$	−12.9691	−	8.31446i	−0.766877	−	0.491644i
$287$	−7.08148	−	1.35394i	−0.418007	−	0.0799204i
$288$	−13.1470	+	24.3967i	−0.774692	+	1.43759i
$289$	−10.0612	−	5.80882i	−0.591834	−	0.341695i
$290$		0			0
$291$	37.5943	−	21.7051i	2.20381	−	1.27237i
$292$	−5.15414	+	4.27483i	−0.301623	+	0.250165i
$293$	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	$0.709395\pi$
$294$	16.2311	+	22.5979i	0.946619	+	1.31793i
$295$		0			0
$296$	−4.19491	+	5.37085i	−0.243824	+	0.312174i
$297$	16.4152	+	4.39844i	0.952506	+	0.255223i
$298$	8.53225	+	9.36496i	0.494260	+	0.542498i
$299$	−9.20626	+	15.9457i	−0.532412	+	0.922164i
$300$		0			0
$301$	12.2731	−	8.33327i	0.707408	−	0.480322i
$302$	9.30491	−	2.03494i	0.535437	−	0.117098i
$303$	8.34018	+	31.1260i	0.479131	+	1.78814i
$304$	−10.9901	−	2.06778i	−0.630326	−	0.118595i
$305$		0			0
$306$	−7.38124	−	14.2788i	−0.421958	−	0.816265i
$307$	−13.3345	−	13.3345i	−0.761042	−	0.761042i	0.215469	−	0.976511i	$-0.430872\pi$
$307$	−13.3345	−	13.3345i	−0.761042	−	0.761042i	−0.976511	+	0.215469i	$0.930872\pi$
$308$	−16.1827	−	4.68675i	−0.922096	−	0.267052i
$309$			36.8239i			2.09484i
$310$		0			0
$311$	1.35454	−	0.782046i	0.0768091	−	0.0443457i	−0.461104	−	0.887346i	$-0.652546\pi$
$311$	1.35454	−	0.782046i	0.0768091	−	0.0443457i	0.537913	+	0.843001i	$0.319213\pi$
$312$	10.6233	−	25.0370i	0.601426	−	1.41744i
$313$	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	$0.637330\pi$
$318$	38.3547	−	34.9443i	2.15082	−	1.95958i
$319$	2.74350	+	4.75188i	0.153606	+	0.266054i
$320$		0			0
$321$	1.15520			0.0644768
$322$	−4.69660	+	19.5810i	−0.261731	+	1.09121i
$323$	4.58635	−	4.58635i	0.255191	−	0.255191i
$324$	−0.0564478	+	0.605297i	−0.00313599	+	0.0336276i
$325$		0			0
$326$	−0.000185973		0.00399709i	−1.03001e−5		0.000221378i
$327$	19.8272	−	5.31269i	1.09645	−	0.293792i
$328$	4.63941	+	6.15485i	0.256169	+	0.339845i
$329$	16.6764	−	1.21762i	0.919399	−	0.0671296i
$330$		0			0
$331$	−3.38809	−	1.95612i	−0.186226	−	0.107518i	0.403988	−	0.914764i	$-0.367624\pi$
$331$	−3.38809	−	1.95612i	−0.186226	−	0.107518i	−0.590215	+	0.807246i	$0.700957\pi$
$332$	−12.2194	+	2.08260i	−0.670625	+	0.114297i
$333$	−3.05513	+	11.4019i	−0.167420	+	0.624821i
$334$	−2.13515	−	4.13040i	−0.116830	−	0.226005i
$335$		0			0
$336$	3.35656	−	29.5539i	0.183115	−	1.61230i
$337$	−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	$0.411929\pi$
$338$	0.555471	−	1.74432i	0.0302137	−	0.0948783i
$339$	23.1137	+	40.0341i	1.25537	+	2.17436i
$340$		0			0
$341$	−5.54569	+	9.60542i	−0.300316	+	0.520163i
$342$	−18.9227	+	4.13831i	−1.02322	+	0.223774i
$343$	−15.6247	−	9.94328i	−0.843655	−	0.536886i
$344$	−15.7051	−	2.20488i	−0.846761	−	0.118879i
$345$		0			0
$346$	−22.7031	−	1.05631i	−1.22052	−	0.0567876i
$347$	1.55280	−	5.79511i	0.0833585	−	0.311098i	−0.911640	−	0.410990i	$-0.865183\pi$
$347$	1.55280	−	5.79511i	0.0833585	−	0.311098i	0.994998	+	0.0998921i	$0.0318498\pi$
$348$	−7.45621	+	6.18416i	−0.399695	+	0.331506i
$349$			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
$352$	9.45906	+	15.3272i	0.504169	+	0.816941i
$353$	−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	$0.714927\pi$
$354$	0.351508	−	7.55490i	0.0186825	−	0.401538i
$355$		0			0
$356$	−2.42139	−	5.27121i	−0.128333	−	0.279373i
$357$	13.0545	+	11.2779i	0.690918	+	0.596889i
$358$	5.49120	+	25.1089i	0.290219	+	1.32705i
$359$	4.20241	−	7.27878i	0.221795	−	0.384159i	−0.733558	−	0.679626i	$-0.762142\pi$
$359$	4.20241	−	7.27878i	0.221795	−	0.384159i	0.955353	+	0.295467i	$0.0954752\pi$
$360$		0			0
$361$	5.59193	+	9.68551i	0.294312	+	0.509764i
$362$	−5.77364	−	1.83859i	−0.303456	−	0.0966344i
$363$	−1.71435	+	1.71435i	−0.0899803	+	0.0899803i
$364$	−0.363904	+	18.1004i	−0.0190737	+	0.948717i
$365$		0			0
$366$	41.2387	−	21.3178i	2.15558	−	1.11430i
$367$	7.95960	−	29.7056i	0.415488	−	1.55062i	−0.368369	−	0.929679i	$-0.620084\pi$
$367$	7.95960	−	29.7056i	0.415488	−	1.55062i	0.783857	−	0.620941i	$-0.213249\pi$
$368$	17.7737	−	12.1446i	0.926521	−	0.633083i
$369$	11.5616	+	6.67511i	0.601875	+	0.347493i
$370$		0			0
$371$	−15.0450	+	31.0889i	−0.781099	+	1.61406i
$372$	−18.3618	−	6.80237i	−0.952017	−	0.352687i
$373$	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	$0.289380\pi$
$374$	−10.4350	−	0.485514i	−0.539583	−	0.0251053i
$375$		0			0
$376$	−14.0875	−	11.0031i	−0.726507	−	0.567440i
$377$	4.16920	−	4.16920i	0.214725	−	0.214725i
$378$	−5.67617	−	19.1476i	−0.291951	−	0.984844i
$379$	−1.92262			−0.0987586			−0.0493793	−	0.998780i	$-0.515724\pi$
$379$	−1.92262			−0.0987586			−0.0493793	+	0.998780i	$0.515724\pi$
$380$		0			0
$381$	−2.62620	−	4.54871i	−0.134544	−	0.233038i
$382$	11.0092	+	12.0836i	0.563280	+	0.618253i
$383$	4.13733	+	15.4407i	0.211408	+	0.788984i	0.987400	+	0.158242i	$0.0505827\pi$
$383$	4.13733	+	15.4407i	0.211408	+	0.788984i	−0.775993	+	0.630742i	$0.782751\pi$
$384$	−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
$388$	30.4519	−	5.19004i	1.54596	−	0.263484i
$389$	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
$392$	5.24454	+	19.0917i	0.264889	+	0.964279i
$393$	−8.08735	−	8.08735i	−0.407953	−	0.407953i
$394$	−12.0338	+	6.22073i	−0.606255	+	0.313396i
$395$		0			0
$396$	25.4521	+	18.0396i	1.27902	+	0.906526i
$397$	−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	$-0.177873\pi$
$398$	0.525620	+	2.40343i	0.0263469	+	0.120473i
$399$	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	$-0.0761376\pi$
$402$	17.2480	−	15.7144i	0.860253	−	0.783761i
$403$	11.5123	+	3.08472i	0.573470	+	0.153661i
$404$	−2.12921	+	22.8318i	−0.105932	+	1.13592i
$405$		0			0
$406$	3.07560	−	5.66741i	0.152639	−	0.281269i
$407$	5.42456	+	5.42456i	0.268885	+	0.268885i
$408$	−2.25024	−	18.3047i	−0.111403	−	0.906220i
$409$	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
$412$	−9.10307	+	24.5722i	−0.448476	+	1.21058i
$413$	1.65364	+	4.75501i	0.0813702	+	0.233979i
$414$	20.1238	−	31.3895i	0.989031	−	1.54271i
$415$		0			0
$416$	13.2781	−	14.0808i	0.651013	−	0.690369i
$417$	−46.3719	−	12.4253i	−2.27084	−	0.608471i
$418$	−3.81976	+	11.9950i	−0.186830	+	0.586694i
$419$	20.6976			1.01114			0.505572	−	0.862784i	$-0.331281\pi$
$419$	20.6976			1.01114			0.505572	+	0.862784i	$0.331281\pi$
$420$		0			0
$421$	26.7517			1.30380			0.651898	−	0.758306i	$-0.273973\pi$
$421$	26.7517			1.30380			0.651898	+	0.758306i	$0.273973\pi$
$422$	10.1952	−	32.0153i	0.496293	−	1.55848i
$423$	−29.9067	−	8.01348i	−1.45411	−	0.389629i
$424$	34.2321	−	13.8364i	1.66246	−	0.671957i
$425$		0			0
$426$	−1.20598	+	1.88112i	−0.0584300	+	0.0911404i
$427$	−20.2013	+	23.3837i	−0.977611	+	1.13162i
$428$	0.770850	+	0.285571i	0.0372605	+	0.0138036i
$429$	−26.5142	−	15.3080i	−1.28012	−	0.739076i
$430$		0			0
$431$	−34.9346	+	20.1695i	−1.68274	+	0.971531i	−0.722914	+	0.690937i	$0.757198\pi$
$431$	−34.9346	+	20.1695i	−1.68274	+	0.971531i	−0.959827	+	0.280594i	$0.909469\pi$
$432$	−9.24374	+	19.2452i	−0.444740	+	0.925937i
$433$	−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	$0.940558\pi$
$434$	13.0298	−	0.343956i	0.625448	−	0.0165104i
$435$		0			0
$436$	14.5438	+	1.35630i	0.696523	+	0.0649552i
$437$	14.5331	+	3.89412i	0.695210	+	0.186281i
$438$	−9.83716	+	8.96246i	−0.470038	+	0.428243i
$439$	2.87067	−	4.97215i	0.137010	−	0.237308i	−0.789354	−	0.613939i	$-0.789584\pi$
$439$	2.87067	−	4.97215i	0.137010	−	0.237308i	0.926363	+	0.376631i	$0.122918\pi$
$440$		0			0
$441$	21.2790	+	26.8936i	1.01329	+	1.28065i
$442$	2.39824	+	10.9661i	0.114073	+	0.521604i
$443$	−0.221517	−	0.826713i	−0.0105246	−	0.0392783i	0.960464	−	0.278405i	$-0.0898056\pi$
$443$	−0.221517	−	0.826713i	−0.0105246	−	0.0392783i	−0.970988	+	0.239126i	$0.923139\pi$
$444$	−7.83166	+	11.0497i	−0.371674	+	0.524395i
$445$		0			0
$446$	−23.5074	+	12.1518i	−1.11311	+	0.575407i
$447$	17.8032	+	17.8032i	0.842064	+	0.842064i
$448$	9.54570	−	18.8913i	0.450992	−	0.892528i
$449$		−	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
$452$	5.52687	+	32.4282i	0.259962	+	1.52529i
$453$	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	$-0.350397\pi$
$458$	−17.0247	−	18.6863i	−0.795513	−	0.873151i
$459$	−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	$0.683835\pi$
$462$	−32.5589	−	7.80940i	−1.51478	−	0.363326i
$463$	−1.84160	+	1.84160i	−0.0855866	+	0.0855866i	−0.748604	−	0.663017i	$-0.769276\pi$
$463$	−1.84160	+	1.84160i	−0.0855866	+	0.0855866i	0.663017	+	0.748604i	$0.269276\pi$
$464$	−6.50421	+	2.28341i	−0.301950	+	0.106004i
$465$		0			0
$466$	−0.498458	−	0.0231919i	−0.0230906	−	0.00107434i
$467$	8.01462	−	2.14751i	0.370872	−	0.0993749i	−0.0685687	−	0.997646i	$-0.521843\pi$
$467$	8.01462	−	2.14751i	0.370872	−	0.0993749i	0.439441	+	0.898271i	$0.355177\pi$
$468$	11.6456	−	31.4352i	0.538317	−	1.45309i
$469$	−6.76572	+	13.9806i	−0.312412	+	0.645565i
$470$		0			0
$471$	−27.7093	−	15.9980i	−1.27678	−	0.737147i
$472$	2.10217	−	4.95441i	0.0967603	−	0.228045i
$473$	−4.62053	+	17.2441i	−0.212452	+	0.792883i
$474$	−29.2023	+	15.0957i	−1.34131	+	0.693371i
$475$		0			0
$476$	5.92318	+	10.7528i	0.271488	+	0.492852i
$477$	45.2221	−	45.2221i	2.07058	−	2.07058i
$478$	−32.4864	−	10.3452i	−1.48589	−	0.473177i
$479$	−6.99926	−	12.1231i	−0.319805	−	0.553918i	0.660643	−	0.750701i	$-0.270284\pi$
$479$	−6.99926	−	12.1231i	−0.319805	−	0.553918i	−0.980447	+	0.196783i	$0.936951\pi$
$480$		0			0
$481$	4.12176	−	7.13910i	0.187936	−	0.325515i
$482$	−1.31559	−	6.01563i	−0.0599236	−	0.274005i
$483$	−7.51507	+	39.3060i	−0.341948	+	1.78849i
$484$	−1.56777	+	0.720172i	−0.0712622	+	0.0327351i
$485$		0			0
$486$	0.996328	−	21.4139i	0.0451943	−	0.971353i
$487$	−6.87083	+	25.6423i	−0.311347	+	1.16196i	0.615995	+	0.787750i	$0.288754\pi$
$487$	−6.87083	+	25.6423i	−0.311347	+	1.16196i	−0.927342	+	0.374214i	$0.877913\pi$
$488$	32.7881	−	4.03070i	1.48425	−	0.182461i
$489$			0.00795220i			0.000359611i
$490$		0			0
$491$			35.5868i			1.60601i	0.595973	+	0.803004i	$0.296766\pi$
$491$			35.5868i			1.60601i	−0.595973	+	0.803004i	$0.703234\pi$
$492$	9.77867	+	11.7901i	0.440856	+	0.531538i
$493$	1.03480	−	3.86191i	0.0466049	−	0.173932i
$494$	13.5126	+	0.628702i	0.607959	+	0.0282866i
$495$		0			0
$496$	−10.5711	−	9.07830i	−0.474655	−	0.407628i
$497$	0.279321	−	1.46093i	0.0125293	−	0.0655316i
$498$	−24.0656	+	5.26303i	−1.07840	+	0.235842i
$499$	4.94115	−	8.55833i	0.221196	−	0.383123i	−0.733975	−	0.679176i	$-0.762337\pi$
$499$	4.94115	−	8.55833i	0.221196	−	0.383123i	0.955172	+	0.296053i	$0.0956705\pi$
$500$		0			0
$501$	−4.62022	−	8.00245i	−0.206416	−	0.357523i
$502$	5.72327	−	17.9725i	0.255442	−	0.802151i
$503$	16.5308	−	16.5308i	0.737071	−	0.737071i	−0.234939	−	0.972010i	$-0.575489\pi$
$503$	16.5308	−	16.5308i	0.737071	−	0.737071i	0.972010	+	0.234939i	$0.0754890\pi$
$504$	2.43970	−	36.5803i	0.108673	−	1.62942i
$505$		0			0
$506$	−11.1277	−	21.5262i	−0.494687	−	0.956958i
$507$	0.941607	−	3.51413i	0.0418182	−	0.156068i
$508$	−0.627968	−	3.68452i	−0.0278616	−	0.163474i
$509$	−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
$512$	−21.1210	+	8.11815i	−0.933424	+	0.358775i
$513$	−14.4138	+	3.86218i	−0.636386	+	0.170519i
$514$	0.661113	−	14.2092i	0.0291604	−	0.626739i
$515$		0			0
$516$	−31.3814	−	2.92651i	−1.38149	−	0.128833i
$517$	−14.2284	+	14.2284i	−0.625763	+	0.625763i
$518$	2.10273	−	8.76666i	0.0923885	−	0.385185i
$519$	−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	$0.787982\pi$
$522$	−8.82613	+	8.04134i	−0.386309	+	0.351960i
$523$	−1.22075	−	4.55591i	−0.0533798	−	0.199216i	0.934086	−	0.357047i	$-0.116217\pi$
$523$	−1.22075	−	4.55591i	−0.0533798	−	0.199216i	−0.987466	+	0.157831i	$0.949550\pi$
$524$	−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
$528$	20.1938	+	29.5538i	0.878824	+	1.28616i
$529$	−5.16358	+	2.98119i	−0.224503	+	0.129617i
$530$		0			0
$531$		−	9.32205i		−	0.404542i
$532$	14.3636	−	3.54087i	0.622743	−	0.153516i
$533$	−6.59253	−	6.59253i	−0.285554	−	0.285554i
$534$	−5.29382	−	10.2408i	−0.229086	−	0.443161i
$535$		0			0
$536$	15.3941	−	6.22222i	0.664924	−	0.268759i
$537$	13.2203	+	49.3390i	0.570500	+	2.12913i
$538$	13.0627	−	2.85675i	0.563172	−	0.123163i
$539$	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	$0.299627\pi$
$542$	13.7417	+	15.0828i	0.590256	+	0.647862i
$543$	−11.6317	−	3.11669i	−0.499162	−	0.133750i
$544$	3.02348	−	12.7708i	0.129631	−	0.547545i
$545$		0			0
$546$	0.949434	+	35.9665i	0.0406320	+	1.53922i
$547$	−9.42028	−	9.42028i	−0.402782	−	0.402782i	0.476430	−	0.879212i	$-0.341931\pi$
$547$	−9.42028	−	9.42028i	−0.402782	−	0.402782i	−0.879212	+	0.476430i	$0.841931\pi$
$548$	20.5777	+	24.8104i	0.879035	+	1.05985i
$549$	49.5537	−	28.6098i	2.11490	−	1.22104i
$550$		0			0
$551$	−4.17252	−	2.40901i	−0.177756	−	0.102627i
$552$	34.1627	−	25.7512i	1.45406	−	1.09605i
$553$	14.3051	−	16.5586i	0.608316	−	0.704145i
$554$	39.3949	+	25.2560i	1.67373	+	1.07303i
$555$		0			0
$556$	−27.8719	−	19.7547i	−1.18203	−	0.837786i
$557$	−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	$0.880635\pi$
$558$	−22.9976	−	7.32349i	−0.973564	−	0.310028i
$559$	19.1836			0.811378
$560$		0			0
$561$	−20.7605			−0.876510
$562$	−13.7005	−	4.36286i	−0.577919	−	0.184036i
$563$	−36.6293	−	9.81479i	−1.54374	−	0.413644i	−0.616269	−	0.787536i	$-0.711357\pi$
$563$	−36.6293	−	9.81479i	−1.54374	−	0.413644i	−0.927472	+	0.373892i	$0.878023\pi$
$564$	−28.9828	−	20.5421i	−1.22040	−	0.864978i
$565$		0			0
$566$	32.9768	+	21.1414i	1.38612	+	0.888638i
$567$	−0.264159	−	0.759585i	−0.0110936	−	0.0318996i
$568$	−1.26976	+	0.957124i	−0.0532780	+	0.0401600i
$569$	−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	−0.155491	−	0.987837i	$-0.549696\pi$
$571$	14.8692	−	8.58473i	0.622256	−	0.359260i	0.777747	+	0.628578i	$0.216363\pi$
$572$	−13.9084	−	16.7693i	−0.581540	−	0.701160i
$573$	22.9716	+	22.9716i	0.959652	+	0.959652i
$574$	−8.96156	−	4.86328i	−0.374048	−	0.202989i
$575$		0			0
$576$	−28.1851	+	27.2339i	−1.17438	+	1.13474i
$577$	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	$0.363350\pi$
$578$	−11.0651	−	12.1450i	−0.460249	−	0.505167i
$579$	−6.49731	+	11.2537i	−0.270019	+	0.467687i
$580$		0			0
$581$	13.5662	−	9.21126i	0.562819	−	0.382147i
$582$	59.9737	−	13.1160i	2.48599	−	0.543675i
$583$	−10.7574	−	40.1471i	−0.445525	−	1.66272i
$584$	−8.77981	+	3.54876i	−0.363311	+	0.146849i
$585$		0			0
$586$	2.82840	+	5.47146i	0.116840	+	0.226024i
$587$	31.4917	+	31.4917i	1.29980	+	1.29980i	0.928520	+	0.371283i	$0.121082\pi$
$587$	31.4917	+	31.4917i	1.29980	+	1.29980i	0.371283	+	0.928520i	$0.378918\pi$
$588$	12.1749	+	37.4165i	0.502084	+	1.54303i
$589$		−	9.73911i		−	0.401293i
$590$		0			0
$591$	−23.3150	+	13.4609i	−0.959050	+	0.553708i
$592$	−7.95753	+	5.43731i	−0.327053	+	0.223472i
$593$	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
$598$	−19.2484	+	17.5369i	−0.787125	+	0.717136i
$599$	−0.0710719	−	0.123100i	−0.00290392	−	0.00502974i	0.864570	−	0.502513i	$-0.167591\pi$
$599$	−0.0710719	−	0.123100i	−0.00290392	−	0.00502974i	−0.867474	+	0.497483i	$0.834258\pi$
$600$		0			0
$601$	−13.9872			−0.570550			−0.285275	−	0.958446i	$-0.592085\pi$
$601$	−13.9872			−0.570550			−0.285275	+	0.958446i	$0.592085\pi$
$602$	20.1144	−	5.96279i	0.819801	−	0.243025i
$603$	20.3363	−	20.3363i	0.828157	−	0.828157i
$604$	13.4119	+	1.25075i	0.545724	+	0.0508923i
$605$		0			0
$606$	−2.11803	+	45.5223i	−0.0860390	+	1.84922i
$607$	31.6805	−	8.48876i	1.28587	−	0.344548i	0.449781	−	0.893139i	$-0.351502\pi$
$607$	31.6805	−	8.48876i	1.28587	−	0.344548i	0.836091	+	0.548591i	$0.184835\pi$
$608$	−13.9223	−	7.50247i	−0.564622	−	0.304265i
$609$	5.58221	−	11.5350i	0.226203	−	0.467423i
$610$		0			0
$611$	18.7255	+	10.8112i	0.757554	+	0.437374i
$612$	−3.81920	−	22.4087i	−0.154382	−	0.905817i
$613$	−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	$0.116671\pi$
$614$	−12.2467	−	23.6909i	−0.494236	−	0.956086i
$615$		0			0
$616$	−19.7957	−	13.2599i	−0.797590	−	0.534256i
$617$	−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	$0.426244\pi$
$618$	−15.8018	+	49.6215i	−0.635642	+	1.99607i
$619$	4.38197	+	7.58980i	0.176126	+	0.305060i	0.940551	−	0.339654i	$-0.110310\pi$
$619$	4.38197	+	7.58980i	0.176126	+	0.305060i	−0.764424	+	0.644714i	$0.776977\pi$
$620$		0			0
$621$	14.3624	−	24.8764i	0.576343	−	0.998255i
$622$	2.16089	−	0.472576i	0.0866437	−	0.0189486i
$623$	5.80684	+	5.01657i	0.232646	+	0.200985i
$624$	25.0592	−	29.1797i	1.00317	−	1.16812i
$625$		0			0
$626$	17.2038	+	0.800447i	0.687604	+	0.0319923i
$627$	−6.47506	+	24.1653i	−0.258589	+	0.965068i
$628$	−14.5353	−	17.5252i	−0.580022	−	0.699330i
$629$		−	5.58989i		−	0.222883i
$630$		0			0
$631$		−	31.2397i		−	1.24363i	−0.783164	−	0.621816i	$-0.786395\pi$
$631$		−	31.2397i		−	1.24363i	0.783164	−	0.621816i	$-0.213605\pi$
$632$	−23.2181	+	2.85425i	−0.923568	+	0.113536i
$633$	17.2823	−	64.4986i	0.686911	−	2.56359i
$634$	−1.80029	+	38.6932i	−0.0714985	+	1.53670i
$635$		0			0
$636$	66.6796	−	30.6300i	2.64402	−	1.21456i
$637$	−9.49304	−	21.9876i	−0.376128	−	0.871180i
$638$	1.65785	+	7.58062i	0.0656348	+	0.300120i
$639$	−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	$-0.613798\pi$
$642$	1.55667	+	0.495716i	0.0614369	+	0.0195644i
$643$	16.3136	−	16.3136i	0.643345	−	0.643345i	−0.308031	−	0.951376i	$-0.599670\pi$
$643$	16.3136	−	16.3136i	0.643345	−	0.643345i	0.951376	+	0.308031i	$0.0996701\pi$
$644$	−14.7314	+	24.3707i	−0.580499	+	0.960341i
$645$		0			0
$646$	8.14837	−	4.21219i	0.320593	−	0.165727i
$647$	4.17257	−	15.5722i	0.164041	−	0.612208i	−0.834120	−	0.551583i	$-0.814024\pi$
$647$	4.17257	−	15.5722i	0.164041	−	0.612208i	0.998161	−	0.0606248i	$-0.0193093\pi$
$648$	−0.335810	+	0.791438i	−0.0131919	+	0.0310906i
$649$	−5.24671	−	3.02919i	−0.205951	−	0.118906i
$650$		0			0
$651$	25.8349	−	1.88633i	1.01255	−	0.0739310i
$652$	−0.00196583	+	0.00530642i	−7.69879e−5	+	0.000207816i
$653$	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	$0.270566\pi$
$654$	28.9977	+	1.34918i	1.13390	+	0.0527572i
$655$		0			0
$656$	3.61062	+	10.2847i	0.140971	+	0.401552i
$657$	−11.5985	+	11.5985i	−0.452501	+	0.452501i
$658$	22.9946	+	5.51536i	0.896421	+	0.215011i
$659$	−0.119381			−0.00465044			−0.00232522	−	0.999997i	$-0.500740\pi$
$659$	−0.119381			−0.00465044			−0.00232522	+	0.999997i	$0.500740\pi$
$660$		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	$0.701542\pi$
$662$	−3.72618	−	4.08983i	−0.144822	−	0.158956i
$663$	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
$668$	−1.10477	−	6.48210i	−0.0427449	−	0.250800i
$669$	−45.5445	+	26.2951i	−1.76085	+	1.01663i
$670$		0			0
$671$		−	37.1869i		−	1.43559i
$672$	17.2052	−	38.3847i	0.663706	−	1.48072i
$673$	−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	$-0.650495\pi$
$674$	−22.4653	+	11.6131i	−0.865330	+	0.447321i
$675$		0			0
$676$	1.49704	−	2.11217i	0.0575784	−	0.0812373i
$677$	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	$0.885275\pi$
$678$	13.9672	+	63.8660i	0.536408	+	2.45276i
$679$	−33.8082	+	22.9554i	−1.29744	+	0.880946i
$680$		0			0
$681$	−29.2147	+	50.6014i	−1.11951	+	1.93905i
$682$	−11.5949	+	10.5639i	−0.443992	+	0.404513i
$683$	40.4498	+	10.8385i	1.54777	+	0.414724i	0.928767	−	0.370665i	$-0.120870\pi$
$683$	40.4498	+	10.8385i	1.54777	+	0.414724i	0.619003	+	0.785389i	$0.287537\pi$
$684$	−27.2749	−	2.54356i	−1.04288	−	0.0972553i
$685$		0			0
$686$	−16.7880	−	20.1038i	−0.640970	−	0.767566i
$687$	−35.5235	−	35.5235i	−1.35530	−	1.35530i
$688$	−20.2170	−	9.71049i	−0.770766	−	0.370209i
$689$	−38.6789	+	22.3313i	−1.47355	+	0.850755i
$690$		0			0
$691$	−29.5825	−	17.0795i	−1.12537	−	0.649734i	−0.182606	−	0.983186i	$-0.558453\pi$
$691$	−29.5825	−	17.0795i	−1.12537	−	0.649734i	−0.942767	+	0.333452i	$0.891787\pi$
$692$	−30.1400	−	11.1657i	−1.14575	−	0.424457i
$693$	−40.5352	−	7.75009i	−1.53981	−	0.294402i
$694$	4.57924	−	7.14280i	0.173826	−	0.271137i
$695$		0			0
$696$	−12.7013	+	5.13379i	−0.481440	+	0.194596i
$697$	−6.10663	−	1.63627i	−0.231305	−	0.0619780i
$698$	−6.51659	+	20.4637i	−0.246657	+	0.774562i
$699$	−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	$0.678371\pi$
$702$	7.83633	−	24.6080i	0.295763	−	0.928770i
$703$	−6.50664	−	1.74345i	−0.245402	−	0.0657554i
$704$	6.16927	+	24.7130i	0.232513	+	0.931406i
$705$		0			0
$706$	−26.2647	+	40.9682i	−0.988483	+	1.54186i
$707$	−9.96406	−	28.6515i	−0.374737	−	1.07755i
$708$	3.71562	−	10.0297i	0.139641	−	0.376938i
$709$	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
$712$	−1.00094	−	8.14221i	−0.0375118	−	0.305142i
$713$	13.2564	+	13.2564i	0.496456	+	0.496456i
$714$	12.7519	+	20.7993i	0.477228	+	0.778395i
$715$		0			0
$716$	−3.37509	+	36.1915i	−0.126133	+	1.35254i
$717$	−65.4475	−	17.5366i	−2.44418	−	0.654917i
$718$	8.78636	−	8.00510i	0.327904	−	0.298748i
$719$	14.3205	−	24.8039i	0.534066	−	0.925029i	−0.465142	−	0.885236i	$-0.653997\pi$
$719$	14.3205	−	24.8039i	0.534066	−	0.925029i	0.999208	−	0.0397933i	$-0.0126699\pi$
$720$		0			0
$721$	−2.52432	−	34.5728i	−0.0940106	−	1.28756i
$722$	3.37911	+	15.4512i	0.125757	+	0.575034i
$723$	−3.16736	−	11.8207i	−0.117795	−	0.439618i
$724$	−6.99122	−	4.95515i	−0.259827	−	0.184157i
$725$		0			0
$726$	−3.04582	+	1.57450i	−0.113041	+	0.0584350i
$727$	−35.3576	−	35.3576i	−1.31134	−	1.31134i	−0.920429	−	0.390911i	$-0.872160\pi$
$727$	−35.3576	−	35.3576i	−1.31134	−	1.31134i	−0.390911	−	0.920429i	$-0.627840\pi$
$728$	−8.25757	+	24.2348i	−0.306046	+	0.898200i
$729$		−	43.5147i		−	1.61166i
$730$		0			0
$731$	11.2655	−	6.50414i	0.416669	−	0.240564i
$732$	64.7186	−	11.0303i	2.39207	−	0.407690i
$733$	−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
$738$	12.7153	+	13.9563i	0.468058	+	0.513738i
$739$	−24.2010	−	41.9174i	−0.890249	−	1.54196i	−0.839576	−	0.543242i	$-0.817197\pi$
$739$	−24.2010	−	41.9174i	−0.890249	−	1.54196i	−0.0506730	−	0.998715i	$-0.516137\pi$
$740$		0			0
$741$	26.8832			0.987579
$742$	−33.6146	+	35.4374i	−1.23403	+	1.30095i
$743$	−3.78255	+	3.78255i	−0.138768	+	0.138768i	−0.773078	−	0.634310i	$-0.781284\pi$
$743$	−3.78255	+	3.78255i	−0.138768	+	0.138768i	0.634310	+	0.773078i	$0.281284\pi$
$744$	−21.8242	−	17.0459i	−0.800115	−	0.624931i
$745$		0			0
$746$	21.2435	+	0.988403i	0.777781	+	0.0361880i
$747$	−29.3290	+	7.85869i	−1.07309	+	0.287535i
$748$	−13.8533	−	5.13212i	−0.506526	−	0.187649i
$749$	−1.08458	+	0.0791901i	−0.0396296	+	0.00289354i
$750$		0			0
$751$	−15.5554	−	8.98090i	−0.567623	−	0.327718i	0.188576	−	0.982059i	$-0.439613\pi$
$751$	−15.5554	−	8.98090i	−0.567623	−	0.327718i	−0.756200	+	0.654341i	$0.772946\pi$
$752$	−14.2618	−	20.8723i	−0.520075	−	0.761133i
$753$	9.70180	−	36.2076i	0.353553	−	1.31948i
$754$	7.40724	−	3.82908i	0.269756	−	0.139447i
$755$		0			0
$756$	0.567715	−	28.2378i	0.0206476	−	1.02700i
$757$	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	$-0.106106\pi$
$758$	−2.59081	−	0.825034i	−0.0941024	−	0.0299666i
$759$	−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	$0.939636\pi$
$762$	−1.58697	−	7.25651i	−0.0574897	−	0.262876i
$763$	−18.2510	+	6.34710i	−0.660730	+	0.229781i
$764$	9.64999	+	21.0074i	0.349125	+	0.760022i
$765$		0			0
$766$	−1.05069	+	22.5824i	−0.0379631	+	0.815934i
$767$	−1.68495	+	6.28831i	−0.0608399	+	0.227058i
$768$	−41.1796	+	18.0670i	−1.48594	+	0.651937i
$769$		−	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
$772$	−7.11756	+	5.90328i	−0.256167	+	0.212464i
$773$	−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	$0.946720\pi$
$774$	−38.8057	−	1.80552i	−1.39484	−	0.0648982i
$775$		0			0
$776$	43.2622	+	6.07370i	1.55302	+	0.218033i
$777$	3.36460	−	17.5978i	0.120704	−	0.631318i
$778$	15.6550	−	3.42368i	0.561259	−	0.122745i
$779$	−3.80923	+	6.59778i	−0.136480	+	0.236390i
$780$		0			0
$781$	0.894971	+	1.55014i	0.0320246	+	0.0554682i
$782$	−5.35773	+	16.8246i	−0.191592	+	0.601646i
$783$	−6.50425	+	6.50425i	−0.232443	+	0.232443i
$784$	−1.12541	+	27.9774i	−0.0401933	+	0.999192i
$785$		0			0
$786$	−7.42758	−	14.3684i	−0.264933	−	0.512505i
$787$	−9.53044	+	35.5681i	−0.339724	+	1.26787i	0.558933	+	0.829213i	$0.311211\pi$
$787$	−9.53044	+	35.5681i	−0.339724	+	1.26787i	−0.898657	+	0.438653i	$0.855456\pi$
$788$	−18.8855	+	3.21873i	−0.672767	+	0.114662i
$789$	26.1715	+	15.1101i	0.931731	+	0.537935i
$790$		0			0
$791$	−24.4452	−	36.0024i	−0.869170	−	1.28010i
$792$	26.5565	+	35.2311i	0.943646	+	1.25188i
$793$	−38.5982	+	10.3424i	−1.37066	+	0.367268i
$794$	0.766546	−	16.4752i	0.0272037	−	0.584684i
$795$		0			0
$796$	−0.323065	+	3.46427i	−0.0114507	+	0.122788i
$797$	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	$0.183314\pi$
$798$	28.1877	−	8.35605i	0.997832	−	0.295801i
$799$	14.6620			0.518705
$800$		0			0
$801$	−7.10464	−	12.3056i	−0.251030	−	0.434797i
$802$	28.9284	−	26.3562i	1.02150	−	0.930670i
$803$	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
$808$	−12.6667	+	29.8530i	−0.445614	+	1.05022i
$809$	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	$0.0548473\pi$
$811$			9.76550i			0.342913i	−0.985192	+	0.171456i	$0.945153\pi$
$812$	6.57648	−	6.31725i	0.230789	−	0.221692i
$813$	28.6732	+	28.6732i	1.00561	+	1.00561i
$814$	4.98202	+	9.63757i	0.174620	+	0.337797i
$815$		0			0
$816$	4.82262	−	25.6319i	0.168826	−	0.897297i
$817$	−4.05719	−	15.1416i	−0.141943	−	0.529739i
$818$	19.1084	−	4.17892i	0.668109	−	0.146112i
$819$	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	$0.123964\pi$
$822$	43.1425	+	47.3530i	1.50477	+	1.65163i
$823$	−52.8907	−	14.1720i	−1.84365	−	0.494006i	−0.844517	−	0.535530i	$-0.820112\pi$
$823$	−52.8907	−	14.1720i	−1.84365	−	0.494006i	−0.999138	+	0.0415239i	$0.986779\pi$
$824$	−22.8111	+	29.2056i	−0.794663	+	1.01743i
$825$		0			0
$826$	0.187877	+	7.11716i	0.00653708	+	0.247638i
$827$	35.5553	+	35.5553i	1.23638	+	1.23638i	0.961470	+	0.274910i	$0.0886479\pi$
$827$	35.5553	+	35.5553i	1.23638	+	1.23638i	0.274910	+	0.961470i	$0.411352\pi$
$828$	40.5874	−	33.6631i	1.41051	−	1.16987i
$829$	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
$832$	23.9351	−	13.2765i	0.829800	−	0.460281i
$833$	−13.0296	−	9.69357i	−0.451449	−	0.335862i
$834$	−57.1560	−	36.6426i	−1.97915	−	1.26883i
$835$		0			0
$836$	−10.2945	+	14.5246i	−0.356044	+	0.502342i
$837$	−17.9600	−	4.81237i	−0.620789	−	0.166340i
$838$	27.8908	+	8.88173i	0.963472	+	0.306814i
$839$	−3.82948			−0.132208			−0.0661042	−	0.997813i	$-0.521057\pi$
$839$	−3.82948			−0.132208			−0.0661042	+	0.997813i	$0.521057\pi$
$840$		0			0
$841$	26.0301			0.897589
$842$	36.0489	+	11.4796i	1.24233	+	0.395614i
$843$	−27.6011	−	7.39570i	−0.950634	−	0.254722i
$844$	27.4767	−	38.7669i	0.945788	−	1.33441i
$845$		0			0
$846$	−36.8617	−	23.6320i	−1.26733	−	0.812485i
$847$	1.49203	−	1.72708i	0.0512669	−	0.0593431i
$848$	52.0665	−	3.95551i	1.78797	−	0.135833i
$849$	67.4183	+	38.9240i	2.31379	+	1.33587i
$850$		0			0
$851$	11.2296	−	6.48342i	0.384946	−	0.222249i
$852$	−2.43233	+	2.01737i	−0.0833302	+	0.0691138i
$853$	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	$0.740750\pi$
$854$	−37.2564	+	22.8416i	−1.27489	+	0.781624i
$855$		0			0
$856$	0.916206	+	0.715604i	0.0313153	+	0.0244588i
$857$	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	$0.433921\pi$
$858$	−29.1599	−	32.0058i	−0.995503	−	1.09266i
$859$	19.8151	−	34.3208i	0.676083	−	1.17101i	−0.300068	−	0.953918i	$-0.597009\pi$
$859$	19.8151	−	34.3208i	0.676083	−	1.17101i	0.976151	−	0.217093i	$-0.0696574\pi$
$860$		0			0
$861$	−18.2397	−	8.82684i	−0.621608	−	0.300818i
$862$	−55.7308	+	12.1881i	−1.89820	+	0.415128i
$863$	−2.57861	−	9.62351i	−0.0877769	−	0.327588i	0.908049	−	0.418865i	$-0.137572\pi$
$863$	−2.57861	−	9.62351i	−0.0877769	−	0.327588i	−0.995826	+	0.0912768i	$0.970905\pi$
$864$	−20.7148	+	21.9670i	−0.704731	+	0.747334i
$865$		0			0
$866$	−15.2306	−	29.4632i	−0.517558	−	1.00120i
$867$	−23.0883	−	23.0883i	−0.784120	−	0.784120i
$868$	17.7057	+	5.12781i	0.600970	+	0.174049i
$869$			26.3331i			0.893290i
$870$		0			0
$871$	−17.3938	+	10.0423i	−0.589368	+	0.340272i
$872$	19.0163	+	8.06870i	0.643974	+	0.273241i
$873$	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	$0.930460\pi$
$878$	6.00198	−	5.46830i	0.202557	−	0.184546i
$879$	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	$0.387401\pi$
$882$	17.1337	+	45.3714i	0.576922	+	1.52773i
$883$	−26.6080	+	26.6080i	−0.895429	+	0.895429i	−0.995028	−	0.0995985i	$-0.968244\pi$
$883$	−26.6080	+	26.6080i	−0.895429	+	0.895429i	0.0995985	+	0.995028i	$0.468244\pi$
$884$	−1.47404	+	15.8064i	−0.0495775	+	0.531626i
$885$		0			0
$886$	0.0562553	−	1.20908i	0.00188993	−	0.0406199i
$887$	7.10873	−	1.90478i	0.238688	−	0.0639562i	−0.137492	−	0.990503i	$-0.543904\pi$
$887$	7.10873	−	1.90478i	0.238688	−	0.0639562i	0.376180	+	0.926547i	$0.377238\pi$
$888$	−15.2951	+	11.5292i	−0.513269	+	0.386893i
$889$	2.77748	+	4.09062i	0.0931537	+	0.137195i
$890$		0			0
$891$	0.838132	+	0.483895i	0.0280785	+	0.0162111i
$892$	−36.8917	+	6.28760i	−1.23523	+	0.210524i
$893$	4.57299	−	17.0666i	0.153029	−	0.571112i
$894$	16.3508	+	31.6302i	0.546854	+	1.05787i
$895$		0			0
$896$	20.9698	−	21.3604i	0.700551	−	0.713602i
$897$	−36.5921	+	36.5921i	−1.22177	+	1.22177i
$898$	2.00037	−	6.28165i	0.0667532	−	0.209621i
$899$	−3.00169	−	5.19908i	−0.100112	−	0.173399i
$900$		0			0
$901$	−15.1427	+	26.2280i	−0.504478	+	0.873781i
$902$	11.9868	−	2.62146i	0.399117	−	0.0872852i
$903$	39.3804	−	13.6952i	1.31050	−	0.455748i
$904$	−6.46788	+	46.0699i	−0.215119	+	1.53226i
$905$		0			0
$906$	26.7409	+	1.24418i	0.888408	+	0.0413352i
$907$	3.60588	−	13.4573i	0.119731	−	0.446843i	−0.879866	−	0.475222i	$-0.842368\pi$
$907$	3.60588	−	13.4573i	0.119731	−	0.446843i	0.999597	+	0.0283786i	$0.00903439\pi$
$908$	−32.0036	+	26.5437i	−1.06208	+	0.880884i
$909$			56.1704i			1.86305i
$910$		0			0
$911$		−	9.10653i		−	0.301713i	−0.988556	−	0.150856i	$-0.951797\pi$
$911$		−	9.10653i		−	0.301713i	0.988556	−	0.150856i	$-0.0482031\pi$
$912$	−28.3315	−	13.6080i	−0.938148	−	0.450605i
$913$	−5.10735	+	19.0609i	−0.169029	+	0.630823i
$914$	2.09074	−	44.9359i	0.0691557	−	1.48635i
$915$		0			0
$916$	−14.9228	−	32.4860i	−0.493064	−	1.07337i
$917$	8.14737	+	7.03857i	0.269050	+	0.232434i
$918$	−3.74142	−	17.1079i	−0.123485	−	0.564644i
$919$	17.5872	−	30.4620i	0.580149	−	1.00485i	−0.415312	−	0.909679i	$-0.636328\pi$
$919$	17.5872	−	30.4620i	0.580149	−	1.00485i	0.995461	−	0.0951683i	$-0.0303389\pi$
$920$		0			0
$921$	−26.5004	−	45.9000i	−0.873217	−	1.51246i
$922$	−31.5923	−	10.0605i	−1.04044	−	0.331324i
$923$	1.36006	−	1.36006i	0.0447668	−	0.0447668i
$924$	−40.5231	−	24.4951i	−1.33311	−	0.805829i
$925$		0			0
$926$	−3.27190	+	1.69136i	−0.107521	+	0.0555817i
$927$	−16.6132	+	62.0014i	−0.545650	+	2.03639i
$928$	−9.74452	+	0.285898i	−0.319879	+	0.00938505i
$929$	−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
$932$	−0.661739	−	0.245150i	−0.0216760	−	0.00803015i
$933$	4.24615	−	1.13775i	0.139013	−	0.0372483i
$934$	11.7215	+	0.545370i	0.383540	+	0.0178451i
$935$		0			0
$936$	29.1823	−	37.3628i	0.953853	−	1.22124i
$937$	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	$0.137862\pi$
$938$	−15.1164	+	15.9361i	−0.493568	+	0.520333i
$939$	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	$0.865096\pi$
$942$	−30.4743	−	33.4484i	−0.992905	−	1.08981i
$943$	−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	−0.861413	−	0.507905i	$-0.830420\pi$
$947$	−41.6507	+	11.1603i	−1.35347	+	0.362660i	−0.492053	+	0.870565i	$0.663753\pi$
$948$	−45.8291	+	7.81083i	−1.48846	+	0.253684i
$949$	9.92033	−	5.72751i	0.322028	−	0.185923i
$950$		0			0
$951$			76.9801i			2.49625i
$952$	3.36749	+	17.0315i	0.109141	+	0.551994i
$953$	−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	$0.960687\pi$
$954$	80.3441	−	41.5328i	2.60123	−	1.34467i
$955$		0			0
$956$	−39.3373	−	27.8810i	−1.27226	−	0.901736i
$957$	3.99135	+	14.8959i	0.129022	+	0.481517i
$958$	−4.22953	−	19.3398i	−0.136650	−	0.624841i
$959$	−38.3826	−	18.5747i	−1.23944	−	0.599809i
$960$		0			0
$961$	−9.43240	+	16.3374i	−0.304271	+	0.527013i
$962$	8.61774	−	7.85148i	0.277847	−	0.253142i
$963$	1.94504	+	0.521171i	0.0626779	+	0.0167945i
$964$	0.808611	−	8.67084i	0.0260436	−	0.279269i
$965$		0			0
$966$	−26.9938	+	49.7415i	−0.868511	+	1.60041i
$967$	−9.65871	−	9.65871i	−0.310603	−	0.310603i	0.534540	−	0.845143i	$-0.320485\pi$
$967$	−9.65871	−	9.65871i	−0.310603	−	0.310603i	−0.845143	+	0.534540i	$0.820485\pi$
$968$	−2.42167	+	0.297700i	−0.0778353	+	0.00956845i
$969$	15.7871	−	9.11468i	0.507155	−	0.292806i
$970$		0			0
$971$	−18.9435	−	10.9371i	−0.607927	−	0.350987i	0.164226	−	0.986423i	$-0.447487\pi$
$971$	−18.9435	−	10.9371i	−0.607927	−	0.350987i	−0.772154	+	0.635436i	$0.780821\pi$
$972$	10.5317	−	28.4284i	0.337804	−	0.911843i
$973$	44.3890	+	8.48690i	1.42305	+	0.272078i
$974$	−20.2623	+	31.6056i	−0.649246	+	1.01271i
$975$		0			0
$976$	45.9128	+	8.63844i	1.46963	+	0.276510i
$977$	−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	$0.720197\pi$
$978$	−0.00341244	+	0.0107159i	−0.000109118	+	0.000342657i
$979$	−9.23458			−0.295138
$980$		0			0
$981$	35.7805			1.14238
$982$	−15.2709	+	47.9545i	−0.487315	+	1.53029i
$983$	46.8710	+	12.5590i	1.49495	+	0.400571i	0.911406	−	0.411508i	$-0.134998\pi$
$983$	46.8710	+	12.5590i	1.49495	+	0.400571i	0.583547	+	0.812080i	$0.301664\pi$
$984$	8.11777	+	20.0838i	0.258785	+	0.640248i
$985$		0			0
$986$	3.05165	−	4.76002i	0.0971842	−	0.151590i
$987$	46.1583	+	8.82518i	1.46923	+	0.280909i
$988$	17.9389	+	6.64569i	0.570712	+	0.211427i
$989$	26.1325	+	15.0876i	0.830965	+	0.479758i
$990$		0			0
$991$	−3.40592	+	1.96641i	−0.108193	+	0.0624650i	−0.553120	−	0.833102i	$-0.686563\pi$
$991$	−3.40592	+	1.96641i	−0.108193	+	0.0624650i	0.444927	+	0.895567i	$0.353230\pi$
$992$	−10.3492	−	16.7696i	−0.328589	−	0.532435i
$993$	−7.77497	−	7.77497i	−0.246731	−	0.246731i
$994$	1.00331	−	1.84879i	0.0318230	−	0.0586402i
$995$		0			0
$996$	−34.6877	−	3.23485i	−1.09912	−	0.102500i
$997$	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	$0.281247\pi$
$998$	10.3309	−	9.41233i	0.327020	−	0.297942i
$999$	−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.443.16		72
4.3	odd	2	inner	700.2.be.e.443.6		72
5.2	odd	4	inner	700.2.be.e.107.8		72
5.3	odd	4		140.2.w.b.107.11	yes	72
5.4	even	2		140.2.w.b.23.3	✓	72
7.4	even	3	inner	700.2.be.e.543.4		72
20.3	even	4		140.2.w.b.107.15	yes	72
20.7	even	4	inner	700.2.be.e.107.4		72
20.19	odd	2		140.2.w.b.23.13	yes	72
28.11	odd	6	inner	700.2.be.e.543.8		72
35.3	even	12		980.2.x.m.67.13		72
35.4	even	6		140.2.w.b.123.15	yes	72
35.9	even	6		980.2.k.k.883.11		36
35.13	even	4		980.2.x.m.667.11		72
35.18	odd	12		140.2.w.b.67.13	yes	72
35.19	odd	6		980.2.k.j.883.11		36
35.23	odd	12		980.2.k.k.687.2		36
35.24	odd	6		980.2.x.m.263.15		72
35.32	odd	12	inner	700.2.be.e.207.6		72
35.33	even	12		980.2.k.j.687.2		36
35.34	odd	2		980.2.x.m.863.3		72
140.3	odd	12		980.2.x.m.67.3		72
140.19	even	6		980.2.k.j.883.2		36
140.23	even	12		980.2.k.k.687.11		36
140.39	odd	6		140.2.w.b.123.11	yes	72
140.59	even	6		980.2.x.m.263.11		72
140.67	even	12	inner	700.2.be.e.207.16		72
140.79	odd	6		980.2.k.k.883.2		36
140.83	odd	4		980.2.x.m.667.15		72
140.103	odd	12		980.2.k.j.687.11		36
140.123	even	12		140.2.w.b.67.3	yes	72
140.139	even	2		980.2.x.m.863.13		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.w.b.23.3	✓	72	5.4	even	2
140.2.w.b.23.13	yes	72	20.19	odd	2
140.2.w.b.67.3	yes	72	140.123	even	12
140.2.w.b.67.13	yes	72	35.18	odd	12
140.2.w.b.107.11	yes	72	5.3	odd	4
140.2.w.b.107.15	yes	72	20.3	even	4
140.2.w.b.123.11	yes	72	140.39	odd	6
140.2.w.b.123.15	yes	72	35.4	even	6
700.2.be.e.107.4		72	20.7	even	4	inner
700.2.be.e.107.8		72	5.2	odd	4	inner
700.2.be.e.207.6		72	35.32	odd	12	inner
700.2.be.e.207.16		72	140.67	even	12	inner
700.2.be.e.443.6		72	4.3	odd	2	inner
700.2.be.e.443.16		72	1.1	even	1	trivial
700.2.be.e.543.4		72	7.4	even	3	inner
700.2.be.e.543.8		72	28.11	odd	6	inner
980.2.k.j.687.2		36	35.33	even	12
980.2.k.j.687.11		36	140.103	odd	12
980.2.k.j.883.2		36	140.19	even	6
980.2.k.j.883.11		36	35.19	odd	6
980.2.k.k.687.2		36	35.23	odd	12
980.2.k.k.687.11		36	140.23	even	12
980.2.k.k.883.2		36	140.79	odd	6
980.2.k.k.883.11		36	35.9	even	6
980.2.x.m.67.3		72	140.3	odd	12
980.2.x.m.67.13		72	35.3	even	12
980.2.x.m.263.11		72	140.59	even	6
980.2.x.m.263.15		72	35.24	odd	6
980.2.x.m.667.11		72	35.13	even	4
980.2.x.m.667.15		72	140.83	odd	4
980.2.x.m.863.3		72	35.34	odd	2
980.2.x.m.863.13		72	140.139	even	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+(1.34754 + 0.429119i) q^{2} +(2.71477 + 0.727420i) q^{3} +(1.63171 + 1.15651i) q^{4} +(3.34610 + 2.14518i) q^{6} +(-2.59868 - 0.496852i) q^{7} +(1.70252 + 2.25864i) q^{8} +(4.24276 + 2.44956i) q^{9} +(2.75736 - 1.59196i) q^{11} +(3.58846 + 4.32659i) q^{12} +(-2.41925 - 2.41925i) q^{13} +(-3.28861 - 1.78467i) q^{14} +(1.32498 + 3.77418i) q^{16} +(-2.24094 - 0.600458i) q^{17} +(4.66612 + 5.12151i) q^{18} +(-1.39787 + 2.42118i) q^{19} +(-6.69340 - 3.23917i) q^{21} +(4.39878 - 0.961994i) q^{22} +(-1.39288 - 5.19830i) q^{23} +(2.97897 + 7.37012i) q^{24} +(-2.22189 - 4.29818i) q^{26} +(3.77420 + 3.77420i) q^{27} +(-3.66569 - 3.81611i) q^{28} +1.72334i q^{29} +(-3.01685 + 1.74178i) q^{31} +(0.165897 + 5.65442i) 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} +(-2.92265 + 2.66278i) q^{38} +(-4.80790 - 8.32752i) q^{39} +2.72503 q^{41} +(-7.62961 - 7.23716i) q^{42} +(-3.96477 + 3.96477i) q^{43} +(6.34034 + 0.591276i) q^{44} +(0.353728 - 7.60261i) q^{46} +(-6.10452 + 1.63570i) q^{47} +(0.851615 + 11.2098i) q^{48} +(6.50628 + 2.58232i) q^{49} +(-5.64685 - 3.26021i) q^{51} +(-1.14965 - 6.74541i) q^{52} +(3.37866 - 12.6093i) q^{53} +(3.46629 + 6.70545i) q^{54} +(-3.30209 - 6.71537i) q^{56} +(-5.55610 + 5.55610i) q^{57} +(-0.739519 + 2.32227i) q^{58} +(-0.951402 - 1.64788i) q^{59} +(5.83980 - 10.1148i) q^{61} +(-4.81275 + 1.05253i) q^{62} +(-9.80850 - 8.47363i) q^{63} +(-2.20286 + 7.69073i) q^{64} +(12.6415 + 0.588172i) q^{66} +(1.51938 - 5.67039i) q^{67} +(-2.96214 - 3.57144i) q^{68} -15.1254i q^{69} +0.562181i q^{71} +(1.69071 + 13.7532i) q^{72} +(-0.866554 + 3.23402i) q^{73} +(-0.158369 + 3.40378i) q^{74} +(-5.08103 + 2.33403i) q^{76} +(-7.95646 + 2.76700i) q^{77} +(-2.90533 - 13.2848i) q^{78} +(-4.13532 + 7.16259i) q^{79} +(0.151981 + 0.263239i) q^{81} +(3.67208 + 1.16936i) q^{82} +(-4.38250 + 4.38250i) q^{83} +(-7.17559 - 13.0264i) q^{84} +(-7.04404 + 3.64132i) q^{86} +(-1.25360 + 4.67848i) q^{87} +(8.29011 + 3.51752i) q^{88} +(-2.51180 - 1.45019i) q^{89} +(5.08485 + 7.48887i) q^{91} +(3.73908 - 10.0930i) q^{92} +(-9.45706 + 2.53401i) q^{93} +(-8.92798 - 0.415394i) q^{94} +(-3.66277 + 15.4711i) q^{96} +(10.9216 - 10.9216i) q^{97} +(7.65933 + 6.27174i) 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

Fields

Representations

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Database

Properties

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