LMFDB - Embedded newform 750.2.l.a.107.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [750,2,Mod(107,750)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(750, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 13]))

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

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

chi := DirichletCharacter("750.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 750 = 2 \cdot 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	750.l (of order $20$, degree $8$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.98878015160$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 150)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			107.4
Character	$\chi$	$=$	750.107
Dual form			750.2.l.a.743.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.891007 - 0.453990i) q^{2} +(0.646378 + 1.60692i) q^{3} +(0.587785 + 0.809017i) q^{4} +(0.153600 - 1.72523i) q^{6} +(-2.03922 - 2.03922i) q^{7} +(-0.156434 - 0.987688i) q^{8} +(-2.16439 + 2.07736i) q^{9} +O(q^{10})$	\(q+(-0.891007 - 0.453990i) q^{2} +(0.646378 + 1.60692i) q^{3} +(0.587785 + 0.809017i) q^{4} +(0.153600 - 1.72523i) q^{6} +(-2.03922 - 2.03922i) q^{7} +(-0.156434 - 0.987688i) q^{8} +(-2.16439 + 2.07736i) q^{9} +(2.60836 - 0.847507i) q^{11} +(-0.920095 + 1.46746i) q^{12} +(-2.68521 - 5.27002i) q^{13} +(0.891173 + 2.74275i) q^{14} +(-0.309017 + 0.951057i) q^{16} +(5.91053 - 0.936136i) q^{17} +(2.87159 - 0.868327i) q^{18} +(3.04743 - 4.19443i) q^{19} +(1.95876 - 4.59498i) q^{21} +(-2.70883 - 0.429036i) q^{22} +(0.515607 - 1.01194i) q^{23} +(1.48602 - 0.889798i) q^{24} +5.91469i q^{26} +(-4.73716 - 2.13524i) q^{27} +(0.451141 - 2.84839i) q^{28} +(2.34612 - 1.70456i) q^{29} +(4.56563 + 3.31712i) q^{31} +(0.707107 - 0.707107i) q^{32} +(3.04786 + 3.64362i) q^{33} +(-5.69132 - 1.84922i) q^{34} +(-2.95281 - 0.529988i) q^{36} +(-7.18975 + 3.66336i) q^{37} +(-4.61952 + 2.35376i) q^{38} +(6.73285 - 7.72135i) q^{39} +(5.02666 + 1.63326i) q^{41} +(-3.83135 + 3.20490i) q^{42} +(3.10789 - 3.10789i) q^{43} +(2.21880 + 1.61205i) q^{44} +(-0.918819 + 0.667561i) q^{46} +(-0.726167 + 4.58484i) q^{47} +(-1.72801 + 0.118176i) q^{48} +1.31687i q^{49} +(5.32473 + 8.89266i) q^{51} +(2.68521 - 5.27002i) q^{52} +(5.29057 + 0.837944i) q^{53} +(3.25146 + 4.05314i) q^{54} +(-1.69511 + 2.33312i) q^{56} +(8.70992 + 2.18579i) q^{57} +(-2.86426 + 0.453655i) q^{58} +(-0.912145 + 2.80729i) q^{59} +(-1.41844 - 4.36552i) q^{61} +(-2.56206 - 5.02833i) q^{62} +(8.64987 + 0.177478i) q^{63} +(-0.951057 + 0.309017i) q^{64} +(-1.06150 - 4.63019i) q^{66} +(0.0721944 + 0.455818i) q^{67} +(4.23147 + 4.23147i) q^{68} +(1.95938 + 0.174447i) q^{69} +(-3.36294 - 4.62869i) q^{71} +(2.39037 + 1.81277i) q^{72} +(8.09812 + 4.12620i) q^{73} +8.06924 q^{74} +5.18460 q^{76} +(-7.04728 - 3.59077i) q^{77} +(-9.50443 + 3.82312i) q^{78} +(-6.90557 - 9.50470i) q^{79} +(0.369168 - 8.99243i) q^{81} +(-3.73730 - 3.73730i) q^{82} +(-1.88912 - 11.9275i) q^{83} +(4.86875 - 1.11619i) q^{84} +(-4.18011 + 1.35820i) q^{86} +(4.25557 + 2.66824i) q^{87} +(-1.24511 - 2.44367i) q^{88} +(0.402182 + 1.23779i) q^{89} +(-5.27101 + 16.2225i) q^{91} +(1.12174 - 0.177666i) q^{92} +(-2.37923 + 9.48072i) q^{93} +(2.72849 - 3.75545i) q^{94} +(1.59332 + 0.679206i) q^{96} +(-6.52722 - 1.03381i) q^{97} +(0.597845 - 1.17334i) q^{98} +(-3.88493 + 7.25283i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 4 q^{3} - 4 q^{7}+O(q^{10}) $ 80 * q - 4 * q^3 - 4 * q^7	$ 80 q - 4 q^{3} - 4 q^{7} - 16 q^{12} + 20 q^{16} + 8 q^{18} + 40 q^{19} - 4 q^{22} + 56 q^{27} - 4 q^{28} + 96 q^{33} + 40 q^{34} + 64 q^{37} + 40 q^{39} + 4 q^{42} + 24 q^{43} - 16 q^{48} + 64 q^{57} - 20 q^{58} - 4 q^{63} + 104 q^{67} - 140 q^{69} - 8 q^{72} + 60 q^{73} + 60 q^{78} - 80 q^{79} - 40 q^{81} - 96 q^{82} - 60 q^{84} - 80 q^{87} - 24 q^{88} - 12 q^{93} + 12 q^{97}+O(q^{100}) $ 80 * q - 4 * q^3 - 4 * q^7 - 16 * q^12 + 20 * q^16 + 8 * q^18 + 40 * q^19 - 4 * q^22 + 56 * q^27 - 4 * q^28 + 96 * q^33 + 40 * q^34 + 64 * q^37 + 40 * q^39 + 4 * q^42 + 24 * q^43 - 16 * q^48 + 64 * q^57 - 20 * q^58 - 4 * q^63 + 104 * q^67 - 140 * q^69 - 8 * q^72 + 60 * q^73 + 60 * q^78 - 80 * q^79 - 40 * q^81 - 96 * q^82 - 60 * q^84 - 80 * q^87 - 24 * q^88 - 12 * q^93 + 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/750\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{13}{20}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.891007	−	0.453990i	−0.630037	−	0.321020i
$2$	−0.891007	−	0.453990i	−0.630037	−	0.321020i
$3$	0.646378	+	1.60692i	0.373187	+	0.927756i
$3$	0.646378	+	1.60692i	0.373187	+	0.927756i
$4$	0.587785	+	0.809017i	0.293893	+	0.404508i
$5$		0			0
$5$		0			0
$6$	0.153600	−	1.72523i	0.0627067	−	0.704321i
$7$	−2.03922	−	2.03922i	−0.770754	−	0.770754i	0.207484	−	0.978238i	$-0.433472\pi$
$7$	−2.03922	−	2.03922i	−0.770754	−	0.770754i	−0.978238	+	0.207484i	$0.933472\pi$
$8$	−0.156434	−	0.987688i	−0.0553079	−	0.349201i
$9$	−2.16439	+	2.07736i	−0.721463	+	0.692453i
$10$		0			0
$11$	2.60836	−	0.847507i	0.786450	−	0.255533i	0.111858	−	0.993724i	$-0.464320\pi$
$11$	2.60836	−	0.847507i	0.786450	−	0.255533i	0.674592	+	0.738191i	$0.264320\pi$
$12$	−0.920095	+	1.46746i	−0.265608	+	0.423618i
$13$	−2.68521	−	5.27002i	−0.744744	−	1.46164i	−0.882071	−	0.471116i	$-0.843851\pi$
$13$	−2.68521	−	5.27002i	−0.744744	−	1.46164i	0.137328	−	0.990526i	$-0.456149\pi$
$14$	0.891173	+	2.74275i	0.238176	+	0.733031i
$15$		0			0
$16$	−0.309017	+	0.951057i	−0.0772542	+	0.237764i
$17$	5.91053	−	0.936136i	1.43351	−	0.227046i	0.609127	−	0.793073i	$-0.291520\pi$
$17$	5.91053	−	0.936136i	1.43351	−	0.227046i	0.824387	+	0.566026i	$0.191520\pi$
$18$	2.87159	−	0.868327i	0.676839	−	0.204667i
$19$	3.04743	−	4.19443i	0.699129	−	0.962269i	−0.300834	−	0.953677i	$-0.597265\pi$
$19$	3.04743	−	4.19443i	0.699129	−	0.962269i	0.999963	−	0.00859233i	$-0.00273506\pi$
$20$		0			0
$21$	1.95876	−	4.59498i	0.427437	−	1.00271i
$22$	−2.70883	−	0.429036i	−0.577523	−	0.0914707i
$23$	0.515607	−	1.01194i	0.107512	−	0.211003i	−0.830983	−	0.556298i	$-0.812221\pi$
$23$	0.515607	−	1.01194i	0.107512	−	0.211003i	0.938494	+	0.345295i	$0.112221\pi$
$24$	1.48602	−	0.889798i	0.303333	−	0.181629i
$25$		0			0
$26$			5.91469i			1.15997i
$27$	−4.73716	−	2.13524i	−0.911668	−	0.410928i
$28$	0.451141	−	2.84839i	0.0852576	−	0.538296i
$29$	2.34612	−	1.70456i	0.435664	−	0.316528i	−0.348246	−	0.937403i	$-0.613223\pi$
$29$	2.34612	−	1.70456i	0.435664	−	0.316528i	0.783910	+	0.620875i	$0.213223\pi$
$30$		0			0
$31$	4.56563	+	3.31712i	0.820011	+	0.595773i	0.916716	−	0.399540i	$-0.130830\pi$
$31$	4.56563	+	3.31712i	0.820011	+	0.595773i	−0.0967046	+	0.995313i	$0.530830\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	3.04786	+	3.64362i	0.530565	+	0.634272i
$34$	−5.69132	−	1.84922i	−0.976053	−	0.317139i
$35$		0			0
$36$	−2.95281	−	0.529988i	−0.492136	−	0.0883313i
$37$	−7.18975	+	3.66336i	−1.18199	+	0.602253i	−0.930744	−	0.365671i	$-0.880839\pi$
$37$	−7.18975	+	3.66336i	−1.18199	+	0.602253i	−0.251243	+	0.967924i	$0.580839\pi$
$38$	−4.61952	+	2.35376i	−0.749384	+	0.381830i
$39$	6.73285	−	7.72135i	1.07812	−	1.23641i
$40$		0			0
$41$	5.02666	+	1.63326i	0.785033	+	0.255073i	0.673988	−	0.738743i	$-0.264580\pi$
$41$	5.02666	+	1.63326i	0.785033	+	0.255073i	0.111045	+	0.993815i	$0.464580\pi$
$42$	−3.83135	+	3.20490i	−0.591190	+	0.494527i
$43$	3.10789	−	3.10789i	0.473950	−	0.473950i	−0.429241	−	0.903190i	$-0.641219\pi$
$43$	3.10789	−	3.10789i	0.473950	−	0.473950i	0.903190	+	0.429241i	$0.141219\pi$
$44$	2.21880	+	1.61205i	0.334497	+	0.243026i
$45$		0			0
$46$	−0.918819	+	0.667561i	−0.135473	+	0.0984265i
$47$	−0.726167	+	4.58484i	−0.105922	+	0.668768i	0.876402	+	0.481581i	$0.159937\pi$
$47$	−0.726167	+	4.58484i	−0.105922	+	0.668768i	−0.982324	+	0.187187i	$0.940063\pi$
$48$	−1.72801	+	0.118176i	−0.249417	+	0.0170573i
$49$			1.31687i			0.188124i
$50$		0			0
$51$	5.32473	+	8.89266i	0.745612	+	1.24522i
$52$	2.68521	−	5.27002i	0.372372	−	0.730821i
$53$	5.29057	+	0.837944i	0.726715	+	0.115100i	0.508821	−	0.860872i	$-0.330081\pi$
$53$	5.29057	+	0.837944i	0.726715	+	0.115100i	0.217894	+	0.975972i	$0.430081\pi$
$54$	3.25146	+	4.05314i	0.442468	+	0.551563i
$55$		0			0
$56$	−1.69511	+	2.33312i	−0.226519	+	0.311777i
$57$	8.70992	+	2.18579i	1.15366	+	0.289516i
$58$	−2.86426	+	0.453655i	−0.376096	+	0.0595678i
$59$	−0.912145	+	2.80729i	−0.118751	+	0.365478i	−0.992711	−	0.120520i	$-0.961544\pi$
$59$	−0.912145	+	2.80729i	−0.118751	+	0.365478i	0.873960	+	0.485998i	$0.161544\pi$
$60$		0			0
$61$	−1.41844	−	4.36552i	−0.181613	−	0.558947i	0.818261	−	0.574847i	$-0.194939\pi$
$61$	−1.41844	−	4.36552i	−0.181613	−	0.558947i	−0.999874	+	0.0159002i	$0.994939\pi$
$62$	−2.56206	−	5.02833i	−0.325382	−	0.638599i
$63$	8.64987	+	0.177478i	1.08978	+	0.0223601i
$64$	−0.951057	+	0.309017i	−0.118882	+	0.0386271i
$65$		0			0
$66$	−1.06150	−	4.63019i	−0.130662	−	0.569937i
$67$	0.0721944	+	0.455818i	0.00881995	+	0.0556870i	0.991706	−	0.128529i	$-0.0410255\pi$
$67$	0.0721944	+	0.455818i	0.00881995	+	0.0556870i	−0.982886	+	0.184216i	$0.941025\pi$
$68$	4.23147	+	4.23147i	0.513141	+	0.513141i
$69$	1.95938	+	0.174447i	0.235882	+	0.0210009i
$70$		0			0
$71$	−3.36294	−	4.62869i	−0.399107	−	0.549324i	0.561412	−	0.827536i	$-0.310258\pi$
$71$	−3.36294	−	4.62869i	−0.399107	−	0.549324i	−0.960520	+	0.278212i	$0.910258\pi$
$72$	2.39037	+	1.81277i	0.281707	+	0.213637i
$73$	8.09812	+	4.12620i	0.947814	+	0.482935i	0.858356	−	0.513055i	$-0.171486\pi$
$73$	8.09812	+	4.12620i	0.947814	+	0.482935i	0.0894583	+	0.995991i	$0.471486\pi$
$74$	8.06924			0.938031
$75$		0			0
$76$	5.18460			0.594715
$77$	−7.04728	−	3.59077i	−0.803113	−	0.409206i
$78$	−9.50443	+	3.82312i	−1.07617	+	0.432884i
$79$	−6.90557	−	9.50470i	−0.776937	−	1.06936i	−0.995613	−	0.0935650i	$-0.970174\pi$
$79$	−6.90557	−	9.50470i	−0.776937	−	1.06936i	0.218676	−	0.975798i	$-0.429826\pi$
$80$		0			0
$81$	0.369168	−	8.99243i	0.0410187	−	0.999158i
$82$	−3.73730	−	3.73730i	−0.412716	−	0.412716i
$83$	−1.88912	−	11.9275i	−0.207358	−	1.30921i	−0.843288	−	0.537462i	$-0.819383\pi$
$83$	−1.88912	−	11.9275i	−0.207358	−	1.30921i	0.635930	−	0.771747i	$-0.280617\pi$
$84$	4.86875	−	1.11619i	0.531224	−	0.121786i
$85$		0			0
$86$	−4.18011	+	1.35820i	−0.450753	+	0.146458i
$87$	4.25557	+	2.66824i	0.456245	+	0.286066i
$88$	−1.24511	−	2.44367i	−0.132729	−	0.260496i
$89$	0.402182	+	1.23779i	0.0426312	+	0.131205i	0.970107	−	0.242678i	$-0.0780260\pi$
$89$	0.402182	+	1.23779i	0.0426312	+	0.131205i	−0.927476	+	0.373884i	$0.878026\pi$
$90$		0			0
$91$	−5.27101	+	16.2225i	−0.552552	+	1.70058i
$92$	1.12174	−	0.177666i	0.116950	−	0.0185230i
$93$	−2.37923	+	9.48072i	−0.246715	+	0.983105i
$94$	2.72849	−	3.75545i	0.281423	−	0.387345i
$95$		0			0
$96$	1.59332	+	0.679206i	0.162618	+	0.0693212i
$97$	−6.52722	−	1.03381i	−0.662738	−	0.104967i	−0.184002	−	0.982926i	$-0.558905\pi$
$97$	−6.52722	−	1.03381i	−0.662738	−	0.104967i	−0.478737	+	0.877959i	$0.658905\pi$
$98$	0.597845	−	1.17334i	0.0603915	−	0.118525i
$99$	−3.88493	+	7.25283i	−0.390450	+	0.728937i
$100$		0			0
$101$		−	3.52971i		−	0.351219i	−0.984460	−	0.175610i	$-0.943810\pi$
$101$		−	3.52971i		−	0.351219i	0.984460	−	0.175610i	$-0.0561896\pi$
$102$	−0.707192	−	10.3408i	−0.0700225	−	1.02389i
$103$	1.00941	−	6.37316i	0.0994601	−	0.627966i	−0.886722	−	0.462303i	$-0.847023\pi$
$103$	1.00941	−	6.37316i	0.0994601	−	0.627966i	0.986182	−	0.165664i	$-0.0529766\pi$
$104$	−4.78508	+	3.47657i	−0.469216	+	0.340905i
$105$		0			0
$106$	−4.33351	−	3.14848i	−0.420908	−	0.305807i
$107$	8.76915	−	8.76915i	0.847745	−	0.847745i	−0.142106	−	0.989851i	$-0.545387\pi$
$107$	8.76915	−	8.76915i	0.847745	−	0.847745i	0.989851	+	0.142106i	$0.0453874\pi$
$108$	−1.05699	−	5.08751i	−0.101709	−	0.489546i
$109$	−2.65577	−	0.862912i	−0.254377	−	0.0826520i	0.179053	−	0.983839i	$-0.442697\pi$
$109$	−2.65577	−	0.862912i	−0.254377	−	0.0826520i	−0.433430	+	0.901187i	$0.642697\pi$
$110$		0			0
$111$	−10.5340	−	9.18544i	−0.999846	−	0.871844i
$112$	2.56957	−	1.30926i	0.242802	−	0.123714i
$113$	4.11863	−	2.09855i	0.387449	−	0.197415i	−0.249406	−	0.968399i	$-0.580235\pi$
$113$	4.11863	−	2.09855i	0.387449	−	0.197415i	0.636854	+	0.770984i	$0.280235\pi$
$114$	−6.76826	−	5.90178i	−0.633906	−	0.552752i
$115$		0			0
$116$	2.75803	+	0.896139i	0.256077	+	0.0832044i
$117$	16.7596	+	5.82824i	1.54942	+	0.538821i
$118$	2.08721	−	2.08721i	0.192143	−	0.192143i
$119$	−13.9619	−	10.1439i	−1.27988	−	0.929890i
$120$		0			0
$121$	−2.81392	+	2.04443i	−0.255811	+	0.185857i
$122$	−0.718062	+	4.53366i	−0.0650103	+	0.410459i
$123$	0.624604	+	9.13316i	0.0563186	+	0.823509i
$124$			5.64343i			0.506795i
$125$		0			0
$126$	−7.62652	−	4.08509i	−0.679424	−	0.363929i
$127$	5.68850	−	11.1643i	0.504773	−	0.990672i	−0.488245	−	0.872707i	$-0.662363\pi$
$127$	5.68850	−	11.1643i	0.504773	−	0.990672i	0.993018	−	0.117966i	$-0.0376373\pi$
$128$	0.987688	+	0.156434i	0.0873001	+	0.0138270i
$129$	7.00302	+	2.98527i	0.616581	+	0.262838i
$130$		0			0
$131$	7.00579	−	9.64264i	0.612099	−	0.842482i	−0.384649	−	0.923063i	$-0.625678\pi$
$131$	7.00579	−	9.64264i	0.612099	−	0.842482i	0.996748	+	0.0805811i	$0.0256776\pi$
$132$	−1.15626	+	4.60744i	−0.100639	+	0.401026i
$133$	−14.7678	+	2.33899i	−1.28053	+	0.202816i
$134$	0.142611	−	0.438912i	0.0123197	−	0.0379162i
$135$		0			0
$136$	−1.84922	−	5.69132i	−0.158569	−	0.488026i
$137$	9.02083	+	17.7044i	0.770702	+	1.51259i	0.856427	+	0.516268i	$0.172679\pi$
$137$	9.02083	+	17.7044i	0.770702	+	1.51259i	−0.0857255	+	0.996319i	$0.527321\pi$
$138$	−1.66662	−	1.04497i	−0.141872	−	0.0889540i
$139$	−9.07922	+	2.95002i	−0.770090	+	0.250217i	−0.667603	−	0.744517i	$-0.732680\pi$
$139$	−9.07922	+	2.95002i	−0.770090	+	0.250217i	−0.102486	+	0.994734i	$0.532680\pi$
$140$		0			0
$141$	−7.83686	+	1.79665i	−0.659982	+	0.151305i
$142$	0.895020	+	5.65093i	0.0751084	+	0.474216i
$143$	−11.4704	−	11.4704i	−0.959201	−	0.959201i
$144$	−1.30685	−	2.70040i	−0.108904	−	0.225033i
$145$		0			0
$146$	−5.34223	−	7.35294i	−0.442126	−	0.608534i
$147$	−2.11610	+	0.851194i	−0.174533	+	0.0702053i
$148$	−7.18975	−	3.66336i	−0.590994	−	0.301126i
$149$	−12.0089			−0.983807			−0.491903	−	0.870650i	$-0.663699\pi$
$149$	−12.0089			−0.983807			−0.491903	+	0.870650i	$0.663699\pi$
$150$		0			0
$151$	−11.1277			−0.905558			−0.452779	−	0.891623i	$-0.649567\pi$
$151$	−11.1277			−0.905558			−0.452779	+	0.891623i	$0.649567\pi$
$152$	−4.61952	−	2.35376i	−0.374692	−	0.190915i
$153$	−10.8480	+	14.3044i	−0.877009	+	1.15645i
$154$	4.64900	+	6.39880i	0.374627	+	0.515630i
$155$		0			0
$156$	10.2042	+	0.908493i	0.816988	+	0.0727376i
$157$	11.6119	+	11.6119i	0.926732	+	0.926732i	0.997493	−	0.0707617i	$-0.0225430\pi$
$157$	11.6119	+	11.6119i	0.926732	+	0.926732i	−0.0707617	+	0.997493i	$0.522543\pi$
$158$	1.83786	+	11.6038i	0.146213	+	0.923150i
$159$	2.07320	+	9.04315i	0.164415	+	0.717169i
$160$		0			0
$161$	−3.11500	+	1.01213i	−0.245497	+	0.0797667i
$162$	−4.41141	+	7.84471i	−0.346593	+	0.616339i
$163$	2.97400	+	5.83680i	0.232941	+	0.457173i	0.977656	−	0.210209i	$-0.0674145\pi$
$163$	2.97400	+	5.83680i	0.232941	+	0.457173i	−0.744715	+	0.667383i	$0.767415\pi$
$164$	1.63326	+	5.02666i	0.127536	+	0.392516i
$165$		0			0
$166$	−3.73173	+	11.4851i	−0.289639	+	0.891416i
$167$	−16.7884	+	2.65903i	−1.29913	+	0.205762i	−0.767408	−	0.641159i	$-0.778454\pi$
$167$	−16.7884	+	2.65903i	−1.29913	+	0.205762i	−0.531720	+	0.846920i	$0.678454\pi$
$168$	−4.84483	−	1.21583i	−0.373787	−	0.0938035i
$169$	−12.9216	+	17.7850i	−0.993968	+	1.36808i
$170$		0			0
$171$	2.11750	+	15.4090i	0.161929	+	1.17836i
$172$	4.34111	+	0.687565i	0.331007	+	0.0524263i
$173$	−3.08240	+	6.04954i	−0.234350	+	0.459938i	−0.977993	−	0.208639i	$-0.933097\pi$
$173$	−3.08240	+	6.04954i	−0.234350	+	0.459938i	0.743642	+	0.668578i	$0.233097\pi$
$174$	−2.58038	−	4.30941i	−0.195618	−	0.326696i
$175$		0			0
$176$			2.74259i			0.206731i
$177$	−5.10069	+	0.348829i	−0.383391	+	0.0262196i
$178$	0.203597	−	1.28546i	0.0152603	−	0.0963496i
$179$	7.59016	−	5.51457i	0.567315	−	0.412179i	−0.266814	−	0.963748i	$-0.585971\pi$
$179$	7.59016	−	5.51457i	0.567315	−	0.412179i	0.834129	+	0.551569i	$0.185971\pi$
$180$		0			0
$181$	12.3025	+	8.93831i	0.914440	+	0.664379i	0.942134	−	0.335237i	$-0.108816\pi$
$181$	12.3025	+	8.93831i	0.914440	+	0.664379i	−0.0276940	+	0.999616i	$0.508816\pi$
$182$	12.0614	−	12.0614i	0.894048	−	0.894048i
$183$	6.09819	−	5.10110i	0.450791	−	0.377084i
$184$	−1.08014	−	0.350958i	−0.0796287	−	0.0258729i
$185$		0			0
$186$	6.42407	−	7.36724i	0.471036	−	0.540192i
$187$	14.6234	−	7.45099i	1.06937	−	0.544871i
$188$	−4.13604	+	2.10742i	−0.301652	+	0.153699i
$189$	5.30590	+	14.0144i	0.385947	+	1.01940i
$190$		0			0
$191$	12.2756	+	3.98859i	0.888232	+	0.288604i	0.717371	−	0.696691i	$-0.245345\pi$
$191$	12.2756	+	3.98859i	0.888232	+	0.288604i	0.170861	+	0.985295i	$0.445345\pi$
$192$	−1.11131	−	1.32853i	−0.0802018	−	0.0958784i
$193$	−3.91447	+	3.91447i	−0.281770	+	0.281770i	−0.833815	−	0.552045i	$-0.813848\pi$
$193$	−3.91447	+	3.91447i	−0.281770	+	0.281770i	0.552045	+	0.833815i	$0.313848\pi$
$194$	5.34645	+	3.88442i	0.383853	+	0.278885i
$195$		0			0
$196$	−1.06537	+	0.774035i	−0.0760977	+	0.0552882i
$197$	−4.00150	+	25.2645i	−0.285095	+	1.80002i	0.264282	+	0.964445i	$0.414865\pi$
$197$	−4.00150	+	25.2645i	−0.285095	+	1.80002i	−0.549378	+	0.835574i	$0.685135\pi$
$198$	6.75421	−	4.69860i	0.480001	−	0.333915i
$199$			0.0768328i			0.00544653i	0.999996	+	0.00272327i	$0.000866844\pi$
$199$			0.0768328i			0.00544653i	−0.999996	+	0.00272327i	$0.999133\pi$
$200$		0			0
$201$	−0.685798	+	0.410641i	−0.0483725	+	0.0289644i
$202$	−1.60245	+	3.14499i	−0.112748	+	0.221281i
$203$	−8.26024	−	1.30829i	−0.579755	−	0.0918242i
$204$	−4.06451	+	9.53477i	−0.284573	+	0.667568i
$205$		0			0
$206$	−3.79275	+	5.22027i	−0.264253	+	0.363713i
$207$	0.986179	+	3.26133i	0.0685442	+	0.226678i
$208$	5.84187	−	0.925261i	0.405061	−	0.0641553i
$209$	4.39399	−	13.5233i	0.303939	−	0.935427i
$210$		0			0
$211$	1.99342	+	6.13511i	0.137232	+	0.422358i	0.995931	−	0.0901236i	$-0.0287262\pi$
$211$	1.99342	+	6.13511i	0.137232	+	0.422358i	−0.858698	+	0.512482i	$0.828726\pi$
$212$	2.43181	+	4.77269i	0.167017	+	0.327790i
$213$	5.26420	−	8.39586i	0.360697	−	0.575275i
$214$	−11.7945	+	3.83226i	−0.806254	+	0.261968i
$215$		0			0
$216$	−1.36790	+	5.01287i	−0.0930738	+	0.341082i
$217$	−2.54598	−	16.0747i	−0.172832	−	1.09122i
$218$	1.97456	+	1.97456i	0.133734	+	0.133734i
$219$	−1.39603	+	15.6801i	−0.0943347	+	1.05957i
$220$		0			0
$221$	−20.8045	−	28.6349i	−1.39946	−	1.92619i
$222$	5.21578	+	12.9666i	0.350061	+	0.870264i
$223$	−4.84642	−	2.46937i	−0.324540	−	0.165362i	0.284128	−	0.958786i	$-0.408296\pi$
$223$	−4.84642	−	2.46937i	−0.324540	−	0.165362i	−0.608668	+	0.793425i	$0.708296\pi$
$224$	−2.88390			−0.192689
$225$		0			0
$226$	−4.62245			−0.307481
$227$	−17.4834	−	8.90823i	−1.16041	−	0.591260i	−0.235662	−	0.971835i	$-0.575726\pi$
$227$	−17.4834	−	8.90823i	−1.16041	−	0.591260i	−0.924750	+	0.380575i	$0.875726\pi$
$228$	3.35122	+	8.33125i	0.221940	+	0.551750i
$229$	−10.2833	−	14.1538i	−0.679543	−	0.935310i	0.320385	−	0.947287i	$-0.396188\pi$
$229$	−10.2833	−	14.1538i	−0.679543	−	0.935310i	−0.999928	+	0.0119768i	$0.996188\pi$
$230$		0			0
$231$	1.21487	−	13.6454i	0.0799327	−	0.897803i
$232$	−2.05059	−	2.05059i	−0.134628	−	0.134628i
$233$	4.54007	+	28.6649i	0.297430	+	1.87790i	0.455148	+	0.890416i	$0.349586\pi$
$233$	4.54007	+	28.6649i	0.297430	+	1.87790i	−0.157718	+	0.987484i	$0.550414\pi$
$234$	−12.2869	−	12.8017i	−0.803221	−	0.836872i
$235$		0			0
$236$	−2.80729	+	0.912145i	−0.182739	+	0.0593756i
$237$	10.8097	−	17.2403i	0.702165	−	1.11988i
$238$	7.83489	+	15.3768i	0.507861	+	0.996733i
$239$	−1.74681	−	5.37613i	−0.112992	−	0.347753i	0.878531	−	0.477685i	$-0.158524\pi$
$239$	−1.74681	−	5.37613i	−0.112992	−	0.347753i	−0.991523	+	0.129932i	$0.958524\pi$
$240$		0			0
$241$	4.35617	−	13.4069i	0.280605	−	0.863614i	−0.707076	−	0.707137i	$-0.749986\pi$
$241$	4.35617	−	13.4069i	0.280605	−	0.863614i	0.987682	−	0.156477i	$-0.0500137\pi$
$242$	3.43537	−	0.544110i	0.220834	−	0.0349767i
$243$	14.6887	−	5.21929i	0.942283	−	0.334817i
$244$	2.69804	−	3.71353i	0.172724	−	0.237734i
$245$		0			0
$246$	3.58984	−	8.42127i	0.228880	−	0.536920i
$247$	−30.2878	−	4.79711i	−1.92716	−	0.305233i
$248$	2.56206	−	5.02833i	0.162691	−	0.319299i
$249$	17.9454	−	10.7453i	1.13724	−	0.680957i
$250$		0			0
$251$			17.3182i			1.09311i	0.837422	+	0.546557i	$0.184062\pi$
$251$			17.3182i			1.09311i	−0.837422	+	0.546557i	$0.815938\pi$
$252$	4.94069	+	7.10221i	0.311234	+	0.447397i
$253$	0.487266	−	3.07648i	0.0306341	−	0.193416i
$254$	−10.1370	+	7.36495i	−0.636051	+	0.462118i
$255$		0			0
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	−4.28914	+	4.28914i	−0.267549	+	0.267549i	−0.828112	−	0.560563i	$-0.810585\pi$
$257$	−4.28914	+	4.28914i	−0.267549	+	0.267549i	0.560563	+	0.828112i	$0.310585\pi$
$258$	−4.88445	−	5.83919i	−0.304093	−	0.363532i
$259$	22.1319	+	7.19110i	1.37521	+	0.446833i
$260$		0			0
$261$	−1.53695	+	8.56306i	−0.0951347	+	0.530040i
$262$	−10.6199	+	5.41110i	−0.656098	+	0.334299i
$263$	−21.2757	+	10.8405i	−1.31191	+	0.668454i	−0.963203	−	0.268777i	$-0.913381\pi$
$263$	−21.2757	+	10.8405i	−1.31191	+	0.668454i	−0.348711	+	0.937230i	$0.613381\pi$
$264$	3.12197	−	3.58033i	0.192144	−	0.220354i
$265$		0			0
$266$	14.2201	+	4.62038i	0.871889	+	0.283294i
$267$	−1.72907	+	1.44635i	−0.105817	+	0.0885154i
$268$	−0.326329	+	0.326329i	−0.0199337	+	0.0199337i
$269$	11.2436	+	8.16896i	0.685535	+	0.498070i	0.875189	−	0.483781i	$-0.160737\pi$
$269$	11.2436	+	8.16896i	0.685535	+	0.498070i	−0.189654	+	0.981851i	$0.560737\pi$
$270$		0			0
$271$	12.1633	−	8.83716i	0.738868	−	0.536819i	−0.153488	−	0.988151i	$-0.549051\pi$
$271$	12.1633	−	8.83716i	0.738868	−	0.536819i	0.892357	+	0.451331i	$0.149051\pi$
$272$	−0.936136	+	5.91053i	−0.0567616	+	0.358378i
$273$	−29.4753	+	2.01578i	−1.78393	+	0.122000i
$274$		−	19.8701i		−	1.20040i
$275$		0			0
$276$	1.01056	+	1.68771i	0.0608288	+	0.101588i
$277$	−0.823495	+	1.61620i	−0.0494790	+	0.0971080i	−0.914422	−	0.404762i	$-0.867354\pi$
$277$	−0.823495	+	1.61620i	−0.0494790	+	0.0971080i	0.864943	+	0.501870i	$0.167354\pi$
$278$	9.42893	+	1.49340i	0.565509	+	0.0895679i
$279$	−16.7727	+	2.30490i	−1.00415	+	0.137991i
$280$		0			0
$281$	−13.4707	+	18.5409i	−0.803597	+	1.10606i	0.188683	+	0.982038i	$0.439578\pi$
$281$	−13.4707	+	18.5409i	−0.803597	+	1.10606i	−0.992280	+	0.124018i	$0.960422\pi$
$282$	7.79835	+	1.95703i	0.464385	+	0.116540i
$283$	2.81001	−	0.445062i	0.167038	−	0.0264562i	−0.0723553	−	0.997379i	$-0.523052\pi$
$283$	2.81001	−	0.445062i	0.167038	−	0.0264562i	0.239393	+	0.970923i	$0.423052\pi$
$284$	1.76800	−	5.44135i	0.104912	−	0.322885i
$285$		0			0
$286$	5.01274	+	15.4276i	0.296409	+	0.912255i
$287$	−6.91991	−	13.5811i	−0.408469	−	0.801666i
$288$	−0.0615410	+	2.99937i	−0.00362634	+	0.176739i
$289$	17.8900	−	5.81283i	1.05236	−	0.341931i
$290$		0			0
$291$	−2.55780	−	11.1570i	−0.149941	−	0.654032i
$292$	1.42179	+	8.97684i	0.0832041	+	0.525330i
$293$	−9.44461	−	9.44461i	−0.551760	−	0.551760i	0.375189	−	0.926948i	$-0.377578\pi$
$293$	−9.44461	−	9.44461i	−0.551760	−	0.551760i	−0.926948	+	0.375189i	$0.877578\pi$
$294$	2.27189	+	0.202270i	0.132500	+	0.0117966i
$295$		0			0
$296$	4.74298	+	6.52816i	0.275680	+	0.379441i
$297$	−14.1659	−	1.55470i	−0.821987	−	0.0902130i
$298$	10.7000	+	5.45192i	0.619834	+	0.315821i
$299$	−6.71745			−0.388480
$300$		0			0
$301$	−12.6754			−0.730597
$302$	9.91484	+	5.05186i	0.570535	+	0.290702i
$303$	5.67196	−	2.28153i	0.325846	−	0.131070i
$304$	3.04743	+	4.19443i	0.174782	+	0.240567i
$305$		0			0
$306$	16.1597	−	7.82047i	0.923790	−	0.447066i
$307$	23.1889	+	23.1889i	1.32346	+	1.32346i	0.910955	+	0.412506i	$0.135346\pi$
$307$	23.1889	+	23.1889i	1.32346	+	1.32346i	0.412506	+	0.910955i	$0.364654\pi$
$308$	−1.23730	−	7.81197i	−0.0705014	−	0.445129i
$309$	10.8936	−	2.49743i	0.619717	−	0.142074i
$310$		0			0
$311$	−9.84506	+	3.19885i	−0.558262	+	0.181390i	−0.574539	−	0.818477i	$-0.694819\pi$
$311$	−9.84506	+	3.19885i	−0.558262	+	0.181390i	0.0162770	+	0.999868i	$0.494819\pi$
$312$	−8.67954	−	5.44207i	−0.491382	−	0.308097i
$313$	−6.22820	−	12.2235i	−0.352039	−	0.690915i	0.645292	−	0.763936i	$-0.276736\pi$
$313$	−6.22820	−	12.2235i	−0.352039	−	0.690915i	−0.997330	+	0.0730212i	$0.976736\pi$
$314$	−5.07459	−	15.6180i	−0.286376	−	0.881374i
$315$		0			0
$316$	3.63047	−	11.1734i	0.204230	−	0.628556i
$317$	18.6415	−	2.95253i	1.04701	−	0.165830i	0.390853	−	0.920453i	$-0.372180\pi$
$317$	18.6415	−	2.95253i	1.04701	−	0.165830i	0.656159	+	0.754623i	$0.272180\pi$
$318$	2.25827	−	8.99872i	0.126638	−	0.504623i
$319$	4.67490	−	6.43445i	0.261744	−	0.360260i
$320$		0			0
$321$	19.7595	+	8.42314i	1.10287	+	0.470134i
$322$	3.23498	+	0.512371i	0.180279	+	0.0285533i
$323$	14.0854	−	27.6441i	0.783732	−	1.53816i
$324$	7.49202	−	4.98695i	0.416223	−	0.277053i
$325$		0			0
$326$		−	6.55079i		−	0.362815i
$327$	−0.330001	−	4.82538i	−0.0182491	−	0.266844i
$328$	0.826810	−	5.22028i	0.0456530	−	0.288241i
$329$	10.8303	−	7.86870i	0.597096	−	0.433815i
$330$		0			0
$331$	−25.6753	−	18.6542i	−1.41124	−	1.02533i	−0.993141	−	0.116926i	$-0.962696\pi$
$331$	−25.6753	−	18.6542i	−1.41124	−	1.02533i	−0.418100	−	0.908401i	$-0.637304\pi$
$332$	8.53912	−	8.53912i	0.468645	−	0.468645i
$333$	7.95131	−	22.8646i	0.435729	−	1.25297i
$334$	16.1658	+	5.25258i	0.884552	+	0.287408i
$335$		0			0
$336$	3.76480	+	3.28282i	0.205386	+	0.179093i
$337$	−14.3569	+	7.31518i	−0.782068	+	0.398483i	−0.798968	−	0.601374i	$-0.794620\pi$
$337$	−14.3569	+	7.31518i	−0.782068	+	0.398483i	0.0169001	+	0.999857i	$0.494620\pi$
$338$	19.5874	−	9.98030i	1.06542	−	0.542857i
$339$	6.03440	+	5.26186i	0.327744	+	0.285785i
$340$		0			0
$341$	14.7201	+	4.78284i	0.797137	+	0.259006i
$342$	5.10883	−	14.6908i	0.276254	−	0.794390i
$343$	−11.5892	+	11.5892i	−0.625757	+	0.625757i
$344$	−3.55581	−	2.58345i	−0.191717	−	0.139290i
$345$		0			0
$346$	5.49287	−	3.99080i	0.295299	−	0.214547i
$347$	3.74283	−	23.6313i	0.200925	−	1.26859i	−0.656634	−	0.754209i	$-0.728020\pi$
$347$	3.74283	−	23.6313i	0.200925	−	1.26859i	0.857560	−	0.514384i	$-0.171980\pi$
$348$	0.342708	+	5.01118i	0.0183711	+	0.268628i
$349$			24.8956i			1.33263i	0.745670	+	0.666315i	$0.232129\pi$
$349$			24.8956i			1.33263i	−0.745670	+	0.666315i	$0.767871\pi$
$350$		0			0
$351$	1.46750	+	30.6986i	0.0783293	+	1.63857i
$352$	1.24511	−	2.44367i	0.0663646	−	0.130248i
$353$	16.7047	+	2.64576i	0.889101	+	0.140820i	0.584244	−	0.811578i	$-0.301391\pi$
$353$	16.7047	+	2.64576i	0.889101	+	0.140820i	0.304857	+	0.952398i	$0.401391\pi$
$354$	4.70311	+	2.00485i	0.249968	+	0.106557i
$355$		0			0
$356$	−0.764995	+	1.05293i	−0.0405447	+	0.0558049i
$357$	7.27579	−	28.9924i	0.385076	−	1.53444i
$358$	−9.26645	+	1.46766i	−0.489747	+	0.0775683i
$359$	−1.67961	+	5.16932i	−0.0886466	+	0.272826i	−0.985546	−	0.169409i	$-0.945814\pi$
$359$	−1.67961	+	5.16932i	−0.0886466	+	0.272826i	0.896899	+	0.442235i	$0.145814\pi$
$360$		0			0
$361$	−2.43509	−	7.49444i	−0.128163	−	0.394444i
$362$	−6.90373	−	13.5493i	−0.362852	−	0.712137i
$363$	−5.10410	−	3.20027i	−0.267896	−	0.167971i
$364$	−16.2225	+	5.27101i	−0.850290	+	0.276276i
$365$		0			0
$366$	−7.74938	+	1.77659i	−0.405066	+	0.0928640i
$367$	−2.80465	−	17.7079i	−0.146401	−	0.924343i	−0.946084	−	0.323920i	$-0.894999\pi$
$367$	−2.80465	−	17.7079i	−0.146401	−	0.924343i	0.799683	−	0.600422i	$-0.205001\pi$
$368$	0.803077	+	0.803077i	0.0418633	+	0.0418633i
$369$	−14.2725	+	6.90716i	−0.742998	+	0.359573i
$370$		0			0
$371$	−9.07990	−	12.4974i	−0.471405	−	0.648833i
$372$	−9.06854	+	3.64779i	−0.470182	+	0.189129i
$373$	22.8020	+	11.6182i	1.18064	+	0.601568i	0.930376	−	0.366608i	$-0.119481\pi$
$373$	22.8020	+	11.6182i	1.18064	+	0.601568i	0.250269	+	0.968176i	$0.419481\pi$
$374$	−16.4122			−0.848656
$375$		0			0
$376$	4.64199			0.239392
$377$	−15.2829	−	7.78702i	−0.787109	−	0.401052i
$378$	1.63481	−	14.8957i	0.0840853	−	0.766154i
$379$	−5.71732	−	7.86922i	−0.293679	−	0.404215i	0.636526	−	0.771255i	$-0.280371\pi$
$379$	−5.71732	−	7.86922i	−0.293679	−	0.404215i	−0.930205	+	0.367041i	$0.880371\pi$
$380$		0			0
$381$	21.6171	+	1.92460i	1.10748	+	0.0986003i
$382$	−9.12687	−	9.12687i	−0.466971	−	0.466971i
$383$	3.81540	+	24.0895i	0.194958	+	1.23092i	0.869968	+	0.493108i	$0.164139\pi$
$383$	3.81540	+	24.0895i	0.194958	+	1.23092i	−0.675010	+	0.737808i	$0.735861\pi$
$384$	0.387043	+	1.68825i	0.0197512	+	0.0861533i
$385$		0			0
$386$	5.26495	−	1.71069i	0.267979	−	0.0870717i
$387$	−0.270487	+	13.1829i	−0.0137496	+	0.670125i
$388$	−3.00023	−	5.88829i	−0.152314	−	0.298932i
$389$	5.49358	+	16.9075i	0.278536	+	0.857245i	0.988262	+	0.152767i	$0.0488186\pi$
$389$	5.49358	+	16.9075i	0.278536	+	0.857245i	−0.709726	+	0.704477i	$0.751181\pi$
$390$		0			0
$391$	2.10020	−	6.46376i	0.106212	−	0.326886i
$392$	1.30065	−	0.206003i	0.0656929	−	0.0104047i
$393$	20.0234	+	5.02496i	1.01004	+	0.253475i
$394$	15.0352	−	20.6942i	0.757462	−	1.04256i
$395$		0			0
$396$	−8.15117	+	1.12013i	−0.409612	+	0.0562888i
$397$	19.0036	+	3.00987i	0.953762	+	0.151061i	0.613873	−	0.789405i	$-0.289611\pi$
$397$	19.0036	+	3.00987i	0.953762	+	0.151061i	0.339889	+	0.940466i	$0.389611\pi$
$398$	0.0348814	−	0.0684585i	0.00174845	−	0.00343152i
$399$	−13.3041	−	22.2188i	−0.666040	−	1.11233i
$400$		0			0
$401$		−	31.1439i		−	1.55525i	−0.628726	−	0.777627i	$-0.716423\pi$
$401$		−	31.1439i		−	1.55525i	0.628726	−	0.777627i	$-0.283577\pi$
$402$	0.797478	−	0.0545384i	0.0397746	−	0.00272013i
$403$	5.22164	−	32.9681i	0.260108	−	1.64226i
$404$	2.85559	−	2.07471i	0.142071	−	0.103221i
$405$		0			0
$406$	6.76598	+	4.91577i	0.335790	+	0.243966i
$407$	−15.6487	+	15.6487i	−0.775678	+	0.775678i
$408$	7.95020	−	6.65030i	0.393594	−	0.329239i
$409$	14.9223	+	4.84855i	0.737860	+	0.239745i	0.653749	−	0.756711i	$-0.273195\pi$
$409$	14.9223	+	4.84855i	0.737860	+	0.239745i	0.0841106	+	0.996456i	$0.473195\pi$
$410$		0			0
$411$	−22.6187	+	25.9395i	−1.11570	+	1.27950i
$412$	5.74931	−	2.92942i	0.283248	−	0.144322i
$413$	7.58476	−	3.86463i	0.373222	−	0.190166i
$414$	0.601920	−	3.35358i	0.0295827	−	0.164819i
$415$		0			0
$416$	−5.62520	−	1.82774i	−0.275798	−	0.0896122i
$417$	−10.6091	−	12.6828i	−0.519528	−	0.621078i
$418$	−10.0545	+	10.0545i	−0.491783	+	0.491783i
$419$	2.78733	+	2.02511i	0.136170	+	0.0989333i	0.653785	−	0.756680i	$-0.273180\pi$
$419$	2.78733	+	2.02511i	0.136170	+	0.0989333i	−0.517615	+	0.855614i	$0.673180\pi$
$420$		0			0
$421$	10.9206	−	7.93429i	0.532238	−	0.386694i	−0.288956	−	0.957342i	$-0.593308\pi$
$421$	10.9206	−	7.93429i	0.532238	−	0.386694i	0.821194	+	0.570649i	$0.193308\pi$
$422$	1.00913	−	6.37141i	0.0491238	−	0.310156i
$423$	−7.95265	−	11.4319i	−0.386671	−	0.555838i
$424$		−	5.35652i		−	0.260135i
$425$		0			0
$426$	−8.50208	+	5.09087i	−0.411927	+	0.246653i
$427$	−6.00974	+	11.7948i	−0.290832	+	0.570790i
$428$	12.2488	+	1.94001i	0.592066	+	0.0937741i
$429$	11.0178	−	25.8462i	0.531944	−	1.24787i
$430$		0			0
$431$	−16.4092	+	22.5853i	−0.790401	+	1.08789i	0.203657	+	0.979042i	$0.434717\pi$
$431$	−16.4092	+	22.5853i	−0.790401	+	1.08789i	−0.994058	+	0.108852i	$0.965283\pi$
$432$	3.49460	−	3.84548i	0.168134	−	0.185016i
$433$	2.57946	−	0.408546i	0.123961	−	0.0196335i	−0.0941457	−	0.995558i	$-0.530012\pi$
$433$	2.57946	−	0.408546i	0.123961	−	0.0196335i	0.218107	+	0.975925i	$0.430012\pi$
$434$	−5.02927	+	15.4785i	−0.241413	+	0.742992i
$435$		0			0
$436$	−0.862912	−	2.65577i	−0.0413260	−	0.127188i
$437$	−2.67322	−	5.24649i	−0.127877	−	0.250974i
$438$	8.36250	−	13.3373i	0.399576	−	0.637282i
$439$	10.4899	−	3.40836i	0.500653	−	0.162672i	−0.0477940	−	0.998857i	$-0.515219\pi$
$439$	10.4899	−	3.40836i	0.500653	−	0.162672i	0.548447	+	0.836185i	$0.315219\pi$
$440$		0			0
$441$	−2.73560	−	2.85021i	−0.130267	−	0.135724i
$442$	5.53695	+	34.9589i	0.263366	+	1.66283i
$443$	−1.32181	−	1.32181i	−0.0628009	−	0.0628009i	0.675009	−	0.737810i	$-0.264140\pi$
$443$	−1.32181	−	1.32181i	−0.0628009	−	0.0628009i	−0.737810	+	0.675009i	$0.764140\pi$
$444$	1.23943	−	13.9213i	0.0588208	−	0.660675i
$445$		0			0
$446$	3.19712	+	4.40046i	0.151388	+	0.208368i
$447$	−7.76229	−	19.2973i	−0.367144	−	0.912733i
$448$	2.56957	+	1.30926i	0.121401	+	0.0618568i
$449$	20.5238			0.968579			0.484289	−	0.874908i	$-0.339078\pi$
$449$	20.5238			0.968579			0.484289	+	0.874908i	$0.339078\pi$
$450$		0			0
$451$	14.4955			0.682569
$452$	4.11863	+	2.09855i	0.193724	+	0.0987075i
$453$	−7.19269	−	17.8813i	−0.337942	−	0.840137i
$454$	11.5336	+	15.8746i	0.541296	+	0.745031i
$455$		0			0
$456$	0.796353	−	8.94462i	0.0372926	−	0.418870i
$457$	−11.0498	−	11.0498i	−0.516886	−	0.516886i	0.399742	−	0.916628i	$-0.369100\pi$
$457$	−11.0498	−	11.0498i	−0.516886	−	0.516886i	−0.916628	+	0.399742i	$0.869100\pi$
$458$	2.73683	+	17.2797i	0.127884	+	0.807427i
$459$	−29.9980	−	8.18580i	−1.40019	−	0.382080i
$460$		0			0
$461$	13.2689	−	4.31131i	0.617992	−	0.200798i	0.0167435	−	0.999860i	$-0.494670\pi$
$461$	13.2689	−	4.31131i	0.617992	−	0.200798i	0.601249	+	0.799062i	$0.294670\pi$
$462$	−7.27735	+	11.6066i	−0.338573	+	0.539989i
$463$	14.9657	+	29.3718i	0.695515	+	1.36502i	0.920531	+	0.390669i	$0.127756\pi$
$463$	14.9657	+	29.3718i	0.695515	+	1.36502i	−0.225017	+	0.974355i	$0.572244\pi$
$464$	0.896139	+	2.75803i	0.0416022	+	0.128038i
$465$		0			0
$466$	8.96836	−	27.6018i	0.415451	−	1.27863i
$467$	3.65255	−	0.578507i	0.169020	−	0.0267701i	−0.0713509	−	0.997451i	$-0.522731\pi$
$467$	3.65255	−	0.578507i	0.169020	−	0.0267701i	0.240371	+	0.970681i	$0.422731\pi$
$468$	5.13588	+	16.9845i	0.237406	+	0.785110i
$469$	0.782294	−	1.07673i	0.0361230	−	0.0497190i
$470$		0			0
$471$	−11.1537	+	26.1651i	−0.513937	+	1.20562i
$472$	2.91542	+	0.461757i	0.134193	+	0.0212541i
$473$	5.47254	−	10.7405i	0.251628	−	0.493847i
$474$	−17.4585	+	10.4538i	−0.801894	+	0.480157i
$475$		0			0
$476$		−	17.2578i		−	0.791012i
$477$	−13.1916	+	9.17677i	−0.604000	+	0.420175i
$478$	−0.884293	+	5.58321i	−0.0404466	+	0.255370i
$479$	4.35190	−	3.16184i	0.198844	−	0.144468i	−0.483908	−	0.875119i	$-0.660783\pi$
$479$	4.35190	−	3.16184i	0.198844	−	0.144468i	0.682752	+	0.730651i	$0.260783\pi$
$480$		0			0
$481$	38.6120	+	28.0533i	1.76056	+	1.27912i
$482$	−9.96798	+	9.96798i	−0.454029	+	0.454029i
$483$	−3.63988	−	4.35135i	−0.165620	−	0.197993i
$484$	−3.30796	−	1.07482i	−0.150362	−	0.0488555i
$485$		0			0
$486$	−15.4573	−	2.01813i	−0.701156	−	0.0915443i
$487$	−3.73900	+	1.90512i	−0.169430	+	0.0863291i	−0.536649	−	0.843806i	$-0.680310\pi$
$487$	−3.73900	+	1.90512i	−0.169430	+	0.0863291i	0.367219	+	0.930135i	$0.380310\pi$
$488$	−4.08988	+	2.08390i	−0.185140	+	0.0943336i
$489$	−7.45695	+	8.55176i	−0.337215	+	0.386724i
$490$		0			0
$491$	30.0362	+	9.75934i	1.35551	+	0.440433i	0.894543	−	0.446983i	$-0.147501\pi$
$491$	30.0362	+	9.75934i	1.35551	+	0.440433i	0.460970	+	0.887416i	$0.347501\pi$
$492$	−7.02175	+	5.87365i	−0.316565	+	0.264805i
$493$	12.2711	−	12.2711i	0.552664	−	0.552664i
$494$	24.8088	+	18.0246i	1.11620	+	0.810966i
$495$		0			0
$496$	−4.56563	+	3.31712i	−0.205003	+	0.148943i
$497$	−2.58115	+	16.2967i	−0.115780	+	0.731007i
$498$	−20.8677	+	1.42712i	−0.935106	+	0.0639506i
$499$		−	10.2536i		−	0.459015i	−0.973307	−	0.229508i	$-0.926288\pi$
$499$		−	10.2536i		−	0.459015i	0.973307	−	0.229508i	$-0.0737116\pi$
$500$		0			0
$501$	−15.1245	−	25.2590i	−0.675714	−	1.12849i
$502$	7.86229	−	15.4306i	0.350911	−	0.688702i
$503$	0.658974	+	0.104371i	0.0293822	+	0.00465369i	0.171108	−	0.985252i	$-0.445265\pi$
$503$	0.658974	+	0.104371i	0.0293822	+	0.00465369i	−0.141726	+	0.989906i	$0.545265\pi$
$504$	−1.17785	−	8.57114i	−0.0524654	−	0.381789i
$505$		0			0
$506$	−1.83085	+	2.51995i	−0.0813911	+	0.112025i
$507$	−36.9314	−	9.26810i	−1.64018	−	0.411611i
$508$	12.3757	−	1.96012i	0.549084	−	0.0869664i
$509$	−8.01814	+	24.6773i	−0.355398	+	1.09380i	0.600381	+	0.799714i	$0.295016\pi$
$509$	−8.01814	+	24.6773i	−0.355398	+	1.09380i	−0.955779	+	0.294087i	$0.904984\pi$
$510$		0			0
$511$	−8.09964	−	24.9281i	−0.358307	−	1.10276i
$512$	0.453990	+	0.891007i	0.0200637	+	0.0393773i
$513$	−23.3923	+	13.3627i	−1.03280	+	0.589978i
$514$	5.76888	−	1.87442i	0.254454	−	0.0826772i
$515$		0			0
$516$	1.70114	+	7.42026i	0.0748885	+	0.326659i
$517$	1.99158	+	12.5743i	0.0875896	+	0.553019i
$518$	−16.4550	−	16.4550i	−0.722991	−	0.722991i
$519$	−11.7135	−	1.04287i	−0.514167	−	0.0457771i
$520$		0			0
$521$	24.0053	+	33.0404i	1.05169	+	1.44753i	0.887334	+	0.461127i	$0.152555\pi$
$521$	24.0053	+	33.0404i	1.05169	+	1.44753i	0.164357	+	0.986401i	$0.447445\pi$
$522$	5.25698	−	6.93199i	0.230092	−	0.303405i
$523$	−24.2703	−	12.3663i	−1.06126	−	0.540741i	−0.165931	−	0.986137i	$-0.553063\pi$
$523$	−24.2703	−	12.3663i	−1.06126	−	0.540741i	−0.895334	+	0.445396i	$0.853063\pi$
$524$	11.9190			0.520682
$525$		0			0
$526$	23.8782			1.04114
$527$	30.0906	+	15.3319i	1.31077	+	0.667868i
$528$	−4.40713	+	1.77275i	−0.191796	+	0.0771491i
$529$	12.7609	+	17.5639i	0.554822	+	0.763646i
$530$		0			0
$531$	−3.85751	−	7.97093i	−0.167402	−	0.345909i
$532$	−10.5726	−	10.5726i	−0.458379	−	0.458379i
$533$	−4.89032	−	30.8763i	−0.211823	−	1.33740i
$534$	2.19724	−	0.503731i	0.0950839	−	0.0217986i
$535$		0			0
$536$	0.438912	−	0.142611i	0.0189581	−	0.00615987i
$537$	13.7676	+	8.63229i	0.594116	+	0.372511i
$538$	−6.30950	−	12.3831i	−0.272022	−	0.533873i
$539$	1.11605	+	3.43486i	0.0480718	+	0.147950i
$540$		0			0
$541$	4.75771	−	14.6427i	0.204550	−	0.629540i	−0.795182	−	0.606371i	$-0.792625\pi$
$541$	4.75771	−	14.6427i	0.204550	−	0.629540i	0.999732	−	0.0231685i	$-0.00737544\pi$
$542$	−14.8496	+	2.35194i	−0.637844	+	0.101025i
$543$	−6.41107	+	25.5467i	−0.275125	+	1.09631i
$544$	3.51743	−	4.84132i	0.150808	−	0.207570i
$545$		0			0
$546$	27.1779	+	11.5855i	1.16311	+	0.495812i
$547$	22.1803	+	3.51301i	0.948360	+	0.150205i	0.611407	−	0.791316i	$-0.290604\pi$
$547$	22.1803	+	3.51301i	0.948360	+	0.150205i	0.336953	+	0.941522i	$0.390604\pi$
$548$	−9.02083	+	17.7044i	−0.385351	+	0.756293i
$549$	12.1388	+	6.50207i	0.518072	+	0.277502i
$550$		0			0
$551$		−	15.0352i		−	0.640520i
$552$	−0.134216	−	1.96255i	−0.00571260	−	0.0835315i
$553$	−5.30021	+	33.4642i	−0.225388	+	1.42304i
$554$	1.46748	−	1.06619i	0.0623472	−	0.0452979i
$555$		0			0
$556$	−7.72325	−	5.61127i	−0.327539	−	0.237971i
$557$	1.66485	−	1.66485i	0.0705420	−	0.0705420i	−0.670956	−	0.741498i	$-0.734116\pi$
$557$	1.66485	−	1.66485i	0.0705420	−	0.0705420i	0.741498	+	0.670956i	$0.234116\pi$
$558$	15.9909	+	5.56095i	0.676951	+	0.235414i
$559$	−24.7240	−	8.03333i	−1.04572	−	0.339773i
$560$		0			0
$561$	21.4254	+	18.6825i	0.904581	+	0.788775i
$562$	20.4199	−	10.4045i	0.861362	−	0.438886i
$563$	−42.1004	+	21.4512i	−1.77432	+	0.904062i	−0.845023	+	0.534729i	$0.820414\pi$
$563$	−42.1004	+	21.4512i	−1.77432	+	0.904062i	−0.929297	+	0.369332i	$0.879586\pi$
$564$	−6.05991	−	5.28411i	−0.255168	−	0.222501i
$565$		0			0
$566$	−2.70579	−	0.879165i	−0.113733	−	0.0369541i
$567$	−19.0904	+	17.5848i	−0.801721	+	0.738490i
$568$	−4.04562	+	4.04562i	−0.169750	+	0.169750i
$569$	−19.9798	−	14.5162i	−0.837599	−	0.608551i	0.0841003	−	0.996457i	$-0.473198\pi$
$569$	−19.9798	−	14.5162i	−0.837599	−	0.608551i	−0.921699	+	0.387906i	$0.873198\pi$
$570$		0			0
$571$	4.83866	−	3.51549i	0.202491	−	0.147119i	−0.481919	−	0.876216i	$-0.660060\pi$
$571$	4.83866	−	3.51549i	0.202491	−	0.147119i	0.684410	+	0.729097i	$0.260060\pi$
$572$	2.53761	−	16.0218i	0.106103	−	0.669907i
$573$	1.52534	+	22.3041i	0.0637221	+	0.931766i
$574$			15.2424i			0.636206i
$575$		0			0
$576$	1.41652	−	2.64452i	0.0590216	−	0.110188i
$577$	−14.3066	+	28.0783i	−0.595591	+	1.16891i	0.374739	+	0.927130i	$0.377732\pi$
$577$	−14.3066	+	28.0783i	−0.595591	+	1.16891i	−0.970330	+	0.241783i	$0.922268\pi$
$578$	−18.5791	−	2.94264i	−0.772789	−	0.122398i
$579$	−8.82048	−	3.76002i	−0.366567	−	0.156261i
$580$		0			0
$581$	−20.4704	+	28.1751i	−0.849256	+	1.16890i
$582$	−2.78613	+	11.1021i	−0.115489	+	0.460198i
$583$	14.5099	−	2.29814i	0.600937	−	0.0951791i
$584$	2.80857	−	8.64390i	0.116220	−	0.357687i
$585$		0			0
$586$	4.12744	+	12.7030i	0.170503	+	0.524755i
$587$	5.11433	+	10.0374i	0.211091	+	0.414289i	0.972139	−	0.234407i	$-0.0753147\pi$
$587$	5.11433	+	10.0374i	0.211091	+	0.414289i	−0.761048	+	0.648696i	$0.775315\pi$
$588$	−1.93244	−	1.21164i	−0.0796926	−	0.0499673i
$589$	27.8269	−	9.04151i	1.14659	−	0.372549i
$590$		0			0
$591$	−43.1845	+	9.90032i	−1.77637	+	0.407245i
$592$	−1.26231	−	7.96990i	−0.0518805	−	0.327561i
$593$	17.4049	+	17.4049i	0.714734	+	0.714734i	0.967522	−	0.252788i	$-0.0813475\pi$
$593$	17.4049	+	17.4049i	0.714734	+	0.714734i	−0.252788	+	0.967522i	$0.581347\pi$
$594$	11.9161	+	7.81642i	0.488922	+	0.320711i
$595$		0			0
$596$	−7.05865	−	9.71540i	−0.289134	−	0.397958i
$597$	−0.123464	+	0.0496631i	−0.00505306	+	0.00203257i
$598$	5.98529	+	3.04966i	0.244757	+	0.124710i
$599$	25.8531			1.05633			0.528165	−	0.849142i	$-0.322880\pi$
$599$	25.8531			1.05633			0.528165	+	0.849142i	$0.322880\pi$
$600$		0			0
$601$	−36.7027			−1.49714			−0.748568	−	0.663058i	$-0.769258\pi$
$601$	−36.7027			−1.49714			−0.748568	+	0.663058i	$0.769258\pi$
$602$	11.2939	+	5.75450i	0.460303	+	0.234536i
$603$	−1.10315	−	0.836594i	−0.0449239	−	0.0340687i
$604$	−6.54069	−	9.00249i	−0.266137	−	0.366306i
$605$		0			0
$606$	−6.08955	−	0.542162i	−0.247371	−	0.0220238i
$607$	23.2173	+	23.2173i	0.942362	+	0.942362i	0.998427	−	0.0560654i	$-0.0178555\pi$
$607$	23.2173	+	23.2173i	0.942362	+	0.942362i	−0.0560654	+	0.998427i	$0.517856\pi$
$608$	−0.811051	−	5.12077i	−0.0328925	−	0.207675i
$609$	−3.23692	−	14.1192i	−0.131166	−	0.572139i
$610$		0			0
$611$	26.1121	−	8.48435i	1.05638	−	0.343240i
$612$	−17.9488	−	0.368274i	−0.725539	−	0.0148866i
$613$	9.97216	+	19.5715i	0.402772	+	0.790484i	0.999932	−	0.0116379i	$-0.00370454\pi$
$613$	9.97216	+	19.5715i	0.402772	+	0.790484i	−0.597161	+	0.802122i	$0.703705\pi$
$614$	−10.1339	−	31.1890i	−0.408972	−	1.25869i
$615$		0			0
$616$	−2.44412	+	7.52224i	−0.0984766	+	0.303080i
$617$	6.32162	−	1.00125i	0.254499	−	0.0403086i	−0.0278814	−	0.999611i	$-0.508876\pi$
$617$	6.32162	−	1.00125i	0.254499	−	0.0403086i	0.282380	+	0.959303i	$0.408876\pi$
$618$	−10.8401	−	2.72038i	−0.436053	−	0.109430i
$619$	−14.0949	+	19.4000i	−0.566524	+	0.779753i	−0.992138	−	0.125152i	$-0.960058\pi$
$619$	−14.0949	+	19.4000i	−0.566524	+	0.779753i	0.425614	+	0.904905i	$0.360058\pi$
$620$		0			0
$621$	−4.60325	+	3.69276i	−0.184722	+	0.148185i
$622$	10.2243	+	1.61936i	0.409956	+	0.0649306i
$623$	1.70399	−	3.34426i	0.0682688	−	0.133985i
$624$	5.26288	+	8.78935i	0.210684	+	0.351856i
$625$		0			0
$626$			13.7188i			0.548313i
$627$	24.5711	−	1.68038i	0.981274	−	0.0671079i
$628$	−2.56892	+	16.2195i	−0.102511	+	0.647230i
$629$	−39.0658	+	28.3830i	−1.55766	+	1.13170i
$630$		0			0
$631$	−23.7895	−	17.2841i	−0.947046	−	0.688069i	0.00306072	−	0.999995i	$-0.499026\pi$
$631$	−23.7895	−	17.2841i	−0.947046	−	0.688069i	−0.950106	+	0.311926i	$0.899026\pi$
$632$	−8.30741	+	8.30741i	−0.330451	+	0.330451i
$633$	−8.57013	+	7.16886i	−0.340632	+	0.284937i
$634$	−17.9501	−	5.83235i	−0.712891	−	0.231632i
$635$		0			0
$636$	−6.09747	+	6.99269i	−0.241780	+	0.277278i
$637$	6.93992	−	3.53606i	0.274970	−	0.140104i
$638$	−7.08655	+	3.61078i	−0.280559	+	0.142952i
$639$	16.8941	+	3.03226i	0.668322	+	0.119954i
$640$		0			0
$641$	−18.3395	−	5.95888i	−0.724368	−	0.235362i	−0.0764522	−	0.997073i	$-0.524359\pi$
$641$	−18.3395	−	5.95888i	−0.724368	−	0.235362i	−0.647916	+	0.761712i	$0.724359\pi$
$642$	−13.7818	−	16.4757i	−0.543925	−	0.650244i
$643$	2.50826	−	2.50826i	0.0989163	−	0.0989163i	−0.655917	−	0.754833i	$-0.727718\pi$
$643$	2.50826	−	2.50826i	0.0989163	−	0.0989163i	0.754833	+	0.655917i	$0.227718\pi$
$644$	−2.64978	−	1.92518i	−0.104416	−	0.0758627i
$645$		0			0
$646$	−25.1003	+	18.2365i	−0.987560	+	0.717504i
$647$	5.85671	−	36.9778i	0.230251	−	1.45375i	−0.553591	−	0.832789i	$-0.686743\pi$
$647$	5.85671	−	36.9778i	0.230251	−	1.45375i	0.783842	−	0.620960i	$-0.213257\pi$
$648$	−8.93946	+	1.04210i	−0.351175	+	0.0409376i
$649$			8.09547i			0.317775i
$650$		0			0
$651$	24.1851	−	14.4815i	0.947889	−	0.567576i
$652$	−2.97400	+	5.83680i	−0.116471	+	0.228587i
$653$	−2.19851	−	0.348209i	−0.0860342	−	0.0136265i	0.113269	−	0.993564i	$-0.463868\pi$
$653$	−2.19851	−	0.348209i	−0.0860342	−	0.0136265i	−0.199303	+	0.979938i	$0.563868\pi$
$654$	−1.89664	+	4.44926i	−0.0741647	+	0.173980i
$655$		0			0
$656$	−3.10665	+	4.27594i	−0.121294	+	0.166947i
$657$	−26.0991	+	7.89200i	−1.01822	+	0.307896i
$658$	−13.2222	+	2.09419i	−0.515456	+	0.0816401i
$659$	4.81311	−	14.8132i	0.187492	−	0.577041i	−0.812490	−	0.582975i	$-0.801889\pi$
$659$	4.81311	−	14.8132i	0.187492	−	0.577041i	0.999982	+	0.00593344i	$0.00188868\pi$
$660$		0			0
$661$	−0.225919	−	0.695307i	−0.00878723	−	0.0270443i	0.946567	−	0.322508i	$-0.104526\pi$
$661$	−0.225919	−	0.695307i	−0.00878723	−	0.0270443i	−0.955354	+	0.295464i	$0.904526\pi$
$662$	14.4080	+	28.2773i	0.559984	+	1.09903i
$663$	32.5665	−	51.9401i	1.26478	−	2.01719i
$664$	−11.4851	+	3.73173i	−0.445708	+	0.144819i
$665$		0			0
$666$	−17.4650	+	16.7627i	−0.676755	+	0.649542i
$667$	−0.515226	−	3.25301i	−0.0199496	−	0.125957i
$668$	−12.0192	−	12.0192i	−0.465037	−	0.465037i
$669$	0.835468	−	9.38397i	0.0323011	−	0.362805i
$670$		0			0
$671$	−7.39961	−	10.1847i	−0.285659	−	0.393176i
$672$	−1.86409	−	4.63420i	−0.0719088	−	0.178768i
$673$	−13.4197	−	6.83769i	−0.517292	−	0.263574i	0.175796	−	0.984427i	$-0.443750\pi$
$673$	−13.4197	−	6.83769i	−0.517292	−	0.263574i	−0.693088	+	0.720853i	$0.743750\pi$
$674$	16.1131			0.620652
$675$		0			0
$676$	−21.9835			−0.845520
$677$	20.6424	+	10.5178i	0.793351	+	0.404233i	0.803193	−	0.595719i	$-0.203133\pi$
$677$	20.6424	+	10.5178i	0.793351	+	0.404233i	−0.00984177	+	0.999952i	$0.503133\pi$
$678$	−2.98785	−	7.42791i	−0.114748	−	0.285267i
$679$	11.2023	+	15.4186i	0.429904	+	0.591712i
$680$		0			0
$681$	3.01394	−	33.8525i	0.115494	−	1.29723i
$682$	−10.9443	−	10.9443i	−0.419080	−	0.419080i
$683$	−0.679239	−	4.28854i	−0.0259903	−	0.164097i	0.971279	−	0.237942i	$-0.0764728\pi$
$683$	−0.679239	−	4.28854i	−0.0259903	−	0.164097i	−0.997270	+	0.0738455i	$0.976473\pi$
$684$	−11.2215	+	10.7703i	−0.429065	+	0.411812i
$685$		0			0
$686$	15.5874	−	5.06466i	0.595130	−	0.193370i
$687$	16.0971	−	25.6732i	0.614144	−	0.979495i
$688$	1.99539	+	3.91618i	0.0760736	+	0.149303i
$689$	−9.79031	−	30.1315i	−0.372981	−	1.14792i
$690$		0			0
$691$	−9.14266	+	28.1382i	−0.347803	+	1.07043i	0.612263	+	0.790654i	$0.290259\pi$
$691$	−9.14266	+	28.1382i	−0.347803	+	1.07043i	−0.960066	+	0.279774i	$0.909741\pi$
$692$	−6.70597	+	1.06212i	−0.254923	+	0.0403758i
$693$	22.7124	−	6.86790i	0.862772	−	0.260890i
$694$	−14.0633	+	19.3564i	−0.533834	+	0.734759i
$695$		0			0
$696$	1.96968	−	4.62058i	0.0746603	−	0.175143i
$697$	31.2392	+	4.94780i	1.18327	+	0.187411i
$698$	11.3024	−	22.1821i	0.427801	−	0.839606i
$699$	−43.1276	+	25.8239i	−1.63124	+	0.976750i
$700$		0			0
$701$		−	19.5558i		−	0.738612i	−0.929308	−	0.369306i	$-0.879595\pi$
$701$		−	19.5558i		−	0.738612i	0.929308	−	0.369306i	$-0.120405\pi$
$702$	12.6293	−	28.0188i	0.476662	−	1.05750i
$703$	−6.54457	+	41.3208i	−0.246833	+	1.55844i
$704$	−2.21880	+	1.61205i	−0.0836243	+	0.0607566i
$705$		0			0
$706$	−13.6828	−	9.94116i	−0.514960	−	0.374140i
$707$	−7.19787	+	7.19787i	−0.270704	+	0.270704i
$708$	−3.28032	−	3.92151i	−0.123282	−	0.147379i
$709$	−21.2009	−	6.88858i	−0.796216	−	0.258706i	−0.117467	−	0.993077i	$-0.537477\pi$
$709$	−21.2009	−	6.88858i	−0.796216	−	0.258706i	−0.678749	+	0.734371i	$0.737477\pi$
$710$		0			0
$711$	34.6910	+	6.22654i	1.30101	+	0.233514i
$712$	1.15963	−	0.590863i	0.0434591	−	0.0221435i
$713$	5.71079	−	2.90979i	0.213871	−	0.108973i
$714$	−19.6451	+	22.5293i	−0.735198	+	0.843138i
$715$		0			0
$716$	8.92277	+	2.89918i	0.333460	+	0.108348i
$717$	7.50992	−	6.28201i	0.280463	−	0.234606i
$718$	3.84337	−	3.84337i	0.143433	−	0.143433i
$719$	−2.20624	−	1.60292i	−0.0822787	−	0.0597790i	0.545885	−	0.837860i	$-0.316193\pi$
$719$	−2.20624	−	1.60292i	−0.0822787	−	0.0597790i	−0.628164	+	0.778081i	$0.716193\pi$
$720$		0			0
$721$	−15.0547	+	10.9379i	−0.560667	+	0.407348i
$722$	−1.23272	+	7.78310i	−0.0458772	+	0.289657i
$723$	24.3596	−	1.66592i	0.905942	−	0.0619561i
$724$			15.2068i			0.565155i
$725$		0			0
$726$	3.09489	+	5.16867i	0.114862	+	0.191827i
$727$	8.81556	−	17.3015i	0.326951	−	0.641677i	−0.667762	−	0.744375i	$-0.732747\pi$
$727$	8.81556	−	17.3015i	0.326951	−	0.641677i	0.994713	+	0.102698i	$0.0327475\pi$
$728$	16.8473	+	2.66836i	0.624404	+	0.0988959i
$729$	17.8815	+	20.2300i	0.662276	+	0.749260i
$730$		0			0
$731$	15.4599	−	21.2787i	0.571805	−	0.787022i
$732$	7.71130	+	1.93519i	0.285018	+	0.0715266i
$733$	−23.9728	+	3.79691i	−0.885454	+	0.140242i	−0.582566	−	0.812784i	$-0.697951\pi$
$733$	−23.9728	+	3.79691i	−0.885454	+	0.140242i	−0.302889	+	0.953026i	$0.597951\pi$
$734$	−5.54024	+	17.0511i	−0.204494	+	0.629368i
$735$		0			0
$736$	−0.350958	−	1.08014i	−0.0129365	−	0.0398144i
$737$	0.574618	+	1.12775i	0.0211663	+	0.0415412i
$738$	15.8527	+	0.325265i	0.583546	+	0.0119732i
$739$	−6.13821	+	1.99443i	−0.225798	+	0.0733662i	−0.419731	−	0.907649i	$-0.637876\pi$
$739$	−6.13821	+	1.99443i	−0.225798	+	0.0733662i	0.193933	+	0.981015i	$0.437876\pi$
$740$		0			0
$741$	−11.8688	−	51.7708i	−0.436010	−	1.90185i
$742$	2.41654	+	15.2575i	0.0887141	+	0.560119i
$743$	−23.0403	−	23.0403i	−0.845265	−	0.845265i	0.144273	−	0.989538i	$-0.453916\pi$
$743$	−23.0403	−	23.0403i	−0.845265	−	0.845265i	−0.989538	+	0.144273i	$0.953916\pi$
$744$	9.73619	+	0.866828i	0.356946	+	0.0317794i
$745$		0			0
$746$	−15.0422	−	20.7038i	−0.550734	−	0.758020i
$747$	28.8664	+	21.8913i	1.05617	+	0.800961i
$748$	14.6234	+	7.45099i	0.534684	+	0.272435i
$749$	−35.7645			−1.30681
$750$		0			0
$751$	31.4069			1.14606			0.573028	−	0.819536i	$-0.305769\pi$
$751$	31.4069			1.14606			0.573028	+	0.819536i	$0.305769\pi$
$752$	−4.13604	−	2.10742i	−0.150826	−	0.0768497i
$753$	−27.8290	+	11.1941i	−1.01414	+	0.407936i
$754$	10.0819	+	13.8766i	0.367162	+	0.505355i
$755$		0			0
$756$	−8.21914	+	12.5300i	−0.298927	+	0.455712i
$757$	−6.35882	−	6.35882i	−0.231115	−	0.231115i	0.582043	−	0.813158i	$-0.302254\pi$
$757$	−6.35882	−	6.35882i	−0.231115	−	0.231115i	−0.813158	+	0.582043i	$0.802254\pi$
$758$	1.52162	+	9.60713i	0.0552678	+	0.348947i
$759$	5.25861	−	1.20557i	0.190875	−	0.0437594i
$760$		0			0
$761$	−8.94031	+	2.90488i	−0.324086	+	0.105302i	−0.466541	−	0.884499i	$-0.654500\pi$
$761$	−8.94031	+	2.90488i	−0.324086	+	0.105302i	0.142456	+	0.989801i	$0.454500\pi$
$762$	−18.3872	−	11.5288i	−0.666098	−	0.417644i
$763$	3.65604	+	7.17538i	0.132358	+	0.259766i
$764$	3.98859	+	12.2756i	0.144302	+	0.444116i
$765$		0			0
$766$	7.53686	−	23.1961i	0.272318	−	0.838108i
$767$	17.2438	−	2.73115i	0.622637	−	0.0986161i
$768$	0.421593	−	1.67996i	0.0152129	−	0.0606203i
$769$	15.8011	−	21.7484i	0.569803	−	0.784266i	−0.422728	−	0.906256i	$-0.638928\pi$
$769$	15.8011	−	21.7484i	0.569803	−	0.784266i	0.992531	+	0.121990i	$0.0389276\pi$
$770$		0			0
$771$	−9.66471	−	4.11990i	−0.348066	−	0.148375i
$772$	−5.46774	−	0.866006i	−0.196788	−	0.0311682i
$773$	9.86911	−	19.3692i	0.354967	−	0.696662i	−0.642613	−	0.766191i	$-0.722150\pi$
$773$	9.86911	−	19.3692i	0.354967	−	0.696662i	0.997580	+	0.0695289i	$0.0221496\pi$
$774$	6.22592	−	11.6233i	0.223786	−	0.417789i
$775$		0			0
$776$			6.60858i			0.237234i
$777$	2.75007	+	40.2124i	0.0986582	+	1.44261i
$778$	2.78103	−	17.5587i	0.0997048	−	0.629511i
$779$	22.1690	−	16.1067i	0.794288	−	0.577084i
$780$		0			0
$781$	−12.6946	−	9.22316i	−0.454248	−	0.330031i
$782$	−4.80578	+	4.80578i	−0.171854	+	0.171854i
$783$	−14.7536	+	3.06523i	−0.527251	+	0.109542i
$784$	−1.25241	−	0.406934i	−0.0447291	−	0.0145334i
$785$		0			0
$786$	−15.5597	−	13.5677i	−0.554995	−	0.483943i
$787$	−16.6973	+	8.50770i	−0.595194	+	0.303267i	−0.725516	−	0.688205i	$-0.758399\pi$
$787$	−16.6973	+	8.50770i	−0.595194	+	0.303267i	0.130322	+	0.991472i	$0.458399\pi$
$788$	−22.7914	+	11.6128i	−0.811911	+	0.413689i
$789$	−31.1720	−	27.1813i	−1.10975	−	0.967678i
$790$		0			0
$791$	−12.6782	−	4.11941i	−0.450786	−	0.146469i
$792$	7.77127	+	2.70251i	0.276140	+	0.0960294i
$793$	−19.1976	+	19.1976i	−0.681725	+	0.681725i
$794$	−15.5659	−	11.3093i	−0.552412	−	0.401351i
$795$		0			0
$796$	−0.0621591	+	0.0451612i	−0.00220317	+	0.00160070i
$797$	7.52391	−	47.5041i	0.266511	−	1.68268i	−0.384116	−	0.923285i	$-0.625494\pi$
$797$	7.52391	−	47.5041i	0.266511	−	1.68268i	0.650627	−	0.759398i	$-0.274506\pi$
$798$	1.76696	+	25.8370i	0.0625497	+	0.914622i
$799$			27.7786i			0.982737i
$800$		0			0
$801$	−3.44181	−	1.84358i	−0.121610	−	0.0651397i
$802$	−14.1390	+	27.7494i	−0.499267	+	0.979867i
$803$	24.6198	+	3.89939i	0.868814	+	0.137607i
$804$	−0.735318	−	0.313453i	−0.0259327	−	0.0110546i
$805$		0			0
$806$	−19.6197	+	27.0043i	−0.691076	+	0.951184i
$807$	−5.85925	+	23.3478i	−0.206255	+	0.821883i
$808$	−3.48625	+	0.552168i	−0.122646	+	0.0194252i
$809$	−5.14657	+	15.8395i	−0.180944	+	0.556887i	−0.999855	−	0.0170329i	$-0.994578\pi$
$809$	−5.14657	+	15.8395i	−0.180944	+	0.556887i	0.818911	+	0.573920i	$0.194578\pi$
$810$		0			0
$811$	6.03759	+	18.5818i	0.212008	+	0.652495i	0.999352	+	0.0359809i	$0.0114556\pi$
$811$	6.03759	+	18.5818i	0.212008	+	0.652495i	−0.787344	+	0.616514i	$0.788544\pi$
$812$	−3.79682	−	7.45167i	−0.133242	−	0.261502i
$813$	22.0627	+	13.8333i	0.773773	+	0.485156i
$814$	21.0475	−	6.83874i	0.737714	−	0.239698i
$815$		0			0
$816$	−10.1029	+	2.31614i	−0.353671	+	0.0810812i
$817$	−3.56475	−	22.5070i	−0.124715	−	0.787419i
$818$	−11.0947	−	11.0947i	−0.387916	−	0.387916i
$819$	−22.2914	−	46.0616i	−0.778925	−	1.60952i
$820$		0			0
$821$	−7.95552	−	10.9498i	−0.277650	−	0.382152i	0.647304	−	0.762232i	$-0.275896\pi$
$821$	−7.95552	−	10.9498i	−0.277650	−	0.382152i	−0.924954	+	0.380080i	$0.875896\pi$
$822$	31.9297	−	12.8436i	1.11367	−	0.447972i
$823$	9.34343	+	4.76071i	0.325691	+	0.165948i	0.609189	−	0.793025i	$-0.291495\pi$
$823$	9.34343	+	4.76071i	0.325691	+	0.165948i	−0.283498	+	0.958973i	$0.591495\pi$
$824$	−6.45260			−0.224787
$825$		0			0
$826$	−8.51258			−0.296191
$827$	17.1630	+	8.74498i	0.596815	+	0.304093i	0.726180	−	0.687504i	$-0.241294\pi$
$827$	17.1630	+	8.74498i	0.596815	+	0.304093i	−0.129365	+	0.991597i	$0.541294\pi$
$828$	−2.05881	+	2.71480i	−0.0715485	+	0.0943457i
$829$	−18.5685	−	25.5573i	−0.644909	−	0.887641i	0.353956	−	0.935262i	$-0.384836\pi$
$829$	−18.5685	−	25.5573i	−0.644909	−	0.887641i	−0.998865	+	0.0476205i	$0.984836\pi$
$830$		0			0
$831$	−3.12939	−	0.278615i	−0.108557	−	0.00966503i
$832$	4.18231	+	4.18231i	0.144996	+	0.144996i
$833$	1.23277	+	7.78338i	0.0427128	+	0.269678i
$834$	3.69489	+	16.1168i	0.127943	+	0.558080i
$835$		0			0
$836$	13.5233	−	4.39399i	0.467713	−	0.151969i
$837$	−14.5453	−	25.4625i	−0.502758	−	0.880112i
$838$	−1.56415	−	3.06981i	−0.0540325	−	0.106045i
$839$	12.7405	+	39.2113i	0.439852	+	1.35373i	0.888032	+	0.459782i	$0.152073\pi$
$839$	12.7405	+	39.2113i	0.439852	+	1.35373i	−0.448179	+	0.893944i	$0.647927\pi$
$840$		0			0
$841$	−6.36272	+	19.5824i	−0.219404	+	0.675256i
$842$	−13.3324	+	2.11165i	−0.459466	+	0.0727722i
$843$	−38.5009	−	9.66199i	−1.32604	−	0.332777i
$844$	−3.79170	+	5.21883i	−0.130516	+	0.179640i
$845$		0			0
$846$	1.89589	+	13.7963i	0.0651820	+	0.474327i
$847$	9.90726	+	1.56916i	0.340418	+	0.0539169i
$848$	−2.43181	+	4.77269i	−0.0835086	+	0.163895i
$849$	2.53151	+	4.22779i	0.0868812	+	0.145097i
$850$		0			0
$851$			9.16443i			0.314153i
$852$	9.88661	−	0.676131i	0.338710	−	0.0231639i
$853$	2.92787	−	18.4859i	0.100248	−	0.632944i	−0.885490	−	0.464659i	$-0.846177\pi$
$853$	2.92787	−	18.4859i	0.100248	−	0.632944i	0.985738	−	0.168285i	$-0.0538229\pi$
$854$	10.7094	−	7.78087i	0.366470	−	0.266256i
$855$		0			0
$856$	−10.0330	−	7.28939i	−0.342920	−	0.249146i
$857$	−19.8211	+	19.8211i	−0.677078	+	0.677078i	−0.959338	−	0.282260i	$-0.908916\pi$
$857$	−19.8211	+	19.8211i	−0.677078	+	0.677078i	0.282260	+	0.959338i	$0.408916\pi$
$858$	−21.5508	+	18.0272i	−0.735734	+	0.615437i
$859$	35.8942	+	11.6627i	1.22469	+	0.397927i	0.848789	−	0.528732i	$-0.177332\pi$
$859$	35.8942	+	11.6627i	1.22469	+	0.397927i	0.375904	+	0.926659i	$0.377332\pi$
$860$		0			0
$861$	17.3508	−	19.8983i	0.591315	−	0.678131i
$862$	24.8742	−	12.6740i	0.847217	−	0.431679i
$863$	22.6754	−	11.5537i	0.771879	−	0.393292i	−0.0232522	−	0.999730i	$-0.507402\pi$
$863$	22.6754	−	11.5537i	0.771879	−	0.393292i	0.795131	+	0.606438i	$0.207402\pi$
$864$	−4.85953	+	1.83984i	−0.165324	+	0.0625925i
$865$		0			0
$866$	−2.48379	−	0.807033i	−0.0844027	−	0.0274241i
$867$	20.9045	+	24.9906i	0.709954	+	0.848725i
$868$	11.5082	−	11.5082i	0.390614	−	0.390614i
$869$	−26.0675	−	18.9392i	−0.884280	−	0.642467i
$870$		0			0
$871$	2.20831	−	1.60443i	0.0748258	−	0.0543641i
$872$	−0.436834	+	2.75806i	−0.0147931	+	0.0933998i
$873$	16.2750	−	11.3218i	0.550826	−	0.383185i
$874$			5.88827i			0.199174i
$875$		0			0
$876$	−13.5061	+	8.08714i	−0.456327	+	0.273239i
$877$	15.4427	−	30.3080i	0.521463	−	1.02343i	−0.468679	−	0.883368i	$-0.655270\pi$
$877$	15.4427	−	30.3080i	0.521463	−	1.02343i	0.990143	−	0.140061i	$-0.0447300\pi$
$878$	−10.8939	−	1.72542i	−0.367651	−	0.0582302i
$879$	9.07195	−	21.2815i	0.305989	−	0.717808i
$880$		0			0
$881$	−27.1879	+	37.4210i	−0.915985	+	1.26074i	0.0490965	+	0.998794i	$0.484366\pi$
$881$	−27.1879	+	37.4210i	−0.915985	+	1.26074i	−0.965081	+	0.261951i	$0.915634\pi$
$882$	1.14347	+	3.78150i	0.0385027	+	0.127330i
$883$	28.9570	−	4.58634i	0.974480	−	0.154343i	0.351165	−	0.936313i	$-0.385785\pi$
$883$	28.9570	−	4.58634i	0.974480	−	0.154343i	0.623315	+	0.781971i	$0.285785\pi$
$884$	10.9376	−	33.6624i	0.367870	−	1.13219i
$885$		0			0
$886$	0.577651	+	1.77783i	0.0194065	+	0.0597272i
$887$	11.4107	+	22.3947i	0.383133	+	0.751940i	0.999365	−	0.0356241i	$-0.0113419\pi$
$887$	11.4107	+	22.3947i	0.383133	+	0.751940i	−0.616233	+	0.787564i	$0.711342\pi$
$888$	−7.42447	+	11.8413i	−0.249149	+	0.397367i
$889$	−34.3666	+	11.1664i	−1.15262	+	0.374509i
$890$		0			0
$891$	−6.65822	−	23.7683i	−0.223059	−	0.796270i
$892$	−0.850889	−	5.37230i	−0.0284899	−	0.179878i
$893$	17.0179	+	17.0179i	0.569481	+	0.569481i
$894$	−1.84456	+	20.7181i	−0.0616913	+	0.692916i
$895$		0			0
$896$	−1.69511	−	2.33312i	−0.0566297	−	0.0779441i
$897$	−4.34201	−	10.7944i	−0.144976	−	0.360415i
$898$	−18.2869	−	9.31762i	−0.610240	−	0.310933i
$899$	16.3657			0.545828
$900$		0			0
$901$	32.0545			1.06789
$902$	−12.9156	−	6.58084i	−0.430043	−	0.219118i
$903$	−8.19310	−	20.3683i	−0.272649	−	0.677816i
$904$	−2.71701	−	3.73964i	−0.0903664	−	0.124379i
$905$		0			0
$906$	−1.70921	+	19.1978i	−0.0567846	+	0.637803i
$907$	−38.3276	−	38.3276i	−1.27265	−	1.27265i	−0.944694	−	0.327952i	$-0.893642\pi$
$907$	−38.3276	−	38.3276i	−1.27265	−	1.27265i	−0.327952	−	0.944694i	$-0.606358\pi$
$908$	−3.06957	−	19.3805i	−0.101867	−	0.643164i
$909$	7.33247	+	7.63967i	0.243203	+	0.253392i
$910$		0			0
$911$	28.3746	−	9.21947i	0.940093	−	0.305455i	0.201409	−	0.979507i	$-0.435448\pi$
$911$	28.3746	−	9.21947i	0.940093	−	0.305455i	0.738683	+	0.674053i	$0.235448\pi$
$912$	−4.77033	+	7.60818i	−0.157961	+	0.251932i
$913$	−15.0361	−	29.5101i	−0.497623	−	0.976640i
$914$	4.82892	+	14.8619i	0.159727	+	0.491588i
$915$		0			0
$916$	5.40628	−	16.6388i	0.178628	−	0.549762i
$917$	−33.9499	+	5.37713i	−1.12112	+	0.177569i
$918$	23.0122	+	20.9124i	0.759515	+	0.690213i
$919$	8.11678	−	11.1718i	0.267748	−	0.368523i	−0.653880	−	0.756598i	$-0.726860\pi$
$919$	8.11678	−	11.1718i	0.267748	−	0.368523i	0.921628	+	0.388075i	$0.126860\pi$
$920$		0			0
$921$	−22.2739	+	52.2515i	−0.733951	+	1.72175i
$922$	−13.7799	−	2.18253i	−0.453818	−	0.0718777i
$923$	−15.3631	+	30.1518i	−0.505682	+	0.992457i
$924$	11.7535	−	7.03773i	0.386661	−	0.231524i
$925$		0			0
$926$		−	32.9648i		−	1.08329i
$927$	11.0546	+	15.8909i	0.363080	+	0.521926i
$928$	0.453655	−	2.86426i	0.0148919	−	0.0940240i
$929$	−0.637117	+	0.462892i	−0.0209031	+	0.0151870i	−0.598188	−	0.801356i	$-0.704112\pi$
$929$	−0.637117	+	0.462892i	−0.0209031	+	0.0151870i	0.577285	+	0.816543i	$0.304112\pi$
$930$		0			0
$931$	5.52351	+	4.01306i	0.181026	+	0.131523i
$932$	−20.5218	+	20.5218i	−0.672214	+	0.672214i
$933$	−11.5039	−	13.7526i	−0.376622	−	0.450239i
$934$	−3.51708	−	1.14277i	−0.115082	−	0.0373925i
$935$		0			0
$936$	3.13471	−	17.4650i	0.102461	−	0.570860i
$937$	3.72797	−	1.89949i	0.121787	−	0.0620538i	−0.392035	−	0.919950i	$-0.628229\pi$
$937$	3.72797	−	1.89949i	0.121787	−	0.0620538i	0.513823	+	0.857896i	$0.328229\pi$
$938$	−1.18586	+	0.604224i	−0.0387196	+	0.0197286i
$939$	15.6165	−	17.9093i	0.509625	−	0.584447i
$940$		0			0
$941$	12.1196	+	3.93788i	0.395086	+	0.128371i	0.499821	−	0.866129i	$-0.333399\pi$
$941$	12.1196	+	3.93788i	0.395086	+	0.128371i	−0.104734	+	0.994500i	$0.533399\pi$
$942$	21.8168	−	18.2496i	0.710829	−	0.594604i
$943$	4.24454	−	4.24454i	0.138221	−	0.138221i
$944$	−2.38803	−	1.73500i	−0.0777236	−	0.0564695i
$945$		0			0
$946$	−9.75214	+	7.08535i	−0.317069	+	0.230364i
$947$	6.23127	−	39.3427i	0.202489	−	1.27847i	−0.651690	−	0.758486i	$-0.725940\pi$
$947$	6.23127	−	39.3427i	0.202489	−	1.27847i	0.854179	−	0.519980i	$-0.174060\pi$
$948$	20.3015	−	1.38839i	0.659362	−	0.0450929i
$949$		−	53.7570i		−	1.74503i
$950$		0			0
$951$	16.7940	+	28.0470i	0.544581	+	0.909486i
$952$	−7.83489	+	15.3768i	−0.253930	+	0.498366i
$953$	25.3183	+	4.01002i	0.820139	+	0.129897i	0.552384	−	0.833590i	$-0.313718\pi$
$953$	25.3183	+	4.01002i	0.820139	+	0.129897i	0.267755	+	0.963487i	$0.413718\pi$
$954$	15.9199	−	2.18771i	0.515427	−	0.0708299i
$955$		0			0
$956$	3.32263	−	4.57321i	0.107462	−	0.147908i
$957$	13.3614	+	3.35311i	0.431913	+	0.108391i
$958$	−5.31302	+	0.841500i	−0.171656	+	0.0271876i
$959$	17.7077	−	54.4987i	0.571811	−	1.75985i
$960$		0			0
$961$	0.262130	+	0.806752i	0.00845579	+	0.0260243i
$962$	−21.6676	−	42.5251i	−0.698592	−	1.37106i
$963$	−0.763197	+	37.1965i	−0.0245937	+	1.19864i
$964$	13.4069	−	4.35617i	0.431807	−	0.140303i
$965$		0			0
$966$	1.26768	+	5.52955i	0.0407871	+	0.177910i
$967$	−0.593924	−	3.74989i	−0.0190993	−	0.120588i	0.976297	−	0.216437i	$-0.0694435\pi$
$967$	−0.593924	−	3.74989i	−0.0190993	−	0.120588i	−0.995396	+	0.0958486i	$0.969444\pi$
$968$	2.45946	+	2.45946i	0.0790499	+	0.0790499i
$969$	53.5264	+	4.76554i	1.71952	+	0.153091i
$970$		0			0
$971$	−1.56008	−	2.14727i	−0.0500655	−	0.0689092i	0.783250	−	0.621707i	$-0.213560\pi$
$971$	−1.56008	−	2.14727i	−0.0500655	−	0.0689092i	−0.833316	+	0.552797i	$0.813560\pi$
$972$	12.8563	+	8.81562i	0.412366	+	0.282761i
$973$	24.5303	+	12.4988i	0.786406	+	0.400694i
$974$	4.19638			0.134461
$975$		0			0
$976$	4.59018			0.146928
$977$	15.9953	+	8.15001i	0.511735	+	0.260742i	0.690736	−	0.723107i	$-0.257287\pi$
$977$	15.9953	+	8.15001i	0.511735	+	0.260742i	−0.179001	+	0.983849i	$0.557287\pi$
$978$	10.5266	−	4.23429i	0.336604	−	0.135398i
$979$	2.09807	+	2.88774i	0.0670546	+	0.0922927i
$980$		0			0
$981$	7.54070	−	3.64931i	0.240756	−	0.116513i
$982$	−22.3318	−	22.3318i	−0.712635	−	0.712635i
$983$	6.25433	+	39.4883i	0.199482	+	1.25948i	0.860632	+	0.509227i	$0.170069\pi$
$983$	6.25433	+	39.4883i	0.199482	+	1.25948i	−0.661150	+	0.750254i	$0.729931\pi$
$984$	8.92300	−	2.04565i	0.284455	−	0.0652131i
$985$		0			0
$986$	−16.5046	+	5.36268i	−0.525614	+	0.170782i
$987$	19.6449	+	12.3173i	0.625303	+	0.392065i
$988$	−13.9218	−	27.3230i	−0.442910	−	0.869260i
$989$	−1.54254	−	4.74745i	−0.0490499	−	0.150960i
$990$		0			0
$991$	−12.5601	+	38.6560i	−0.398984	+	1.22795i	0.526831	+	0.849970i	$0.323380\pi$
$991$	−12.5601	+	38.6560i	−0.398984	+	1.22795i	−0.925815	+	0.377977i	$0.876620\pi$
$992$	5.57395	−	0.882826i	0.176973	−	0.0280298i
$993$	13.3799	−	53.3158i	0.424597	−	1.69193i
$994$	9.69837	−	13.3487i	0.307614	−	0.423394i
$995$		0			0
$996$	19.2412	+	8.20219i	0.609681	+	0.259896i
$997$	11.2375	+	1.77985i	0.355896	+	0.0563684i	0.331823	−	0.943342i	$-0.392336\pi$
$997$	11.2375	+	1.77985i	0.355896	+	0.0563684i	0.0240735	+	0.999710i	$0.492336\pi$
$998$	−4.65505	+	9.13605i	−0.147353	+	0.289197i
$999$	41.8812	−	2.00207i	1.32506	−	0.0633427i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	750.2.l.a.107.4		80
3.2	odd	2	inner	750.2.l.a.107.7		80
5.2	odd	4		150.2.l.a.83.9	yes	80
5.3	odd	4		750.2.l.b.143.2		80
5.4	even	2		750.2.l.c.107.7		80
15.2	even	4		150.2.l.a.83.4	yes	80
15.8	even	4		750.2.l.b.143.7		80
15.14	odd	2		750.2.l.c.107.4		80
25.3	odd	20	inner	750.2.l.a.743.7		80
25.4	even	10		150.2.l.a.47.4	✓	80
25.21	even	5		750.2.l.b.257.7		80
25.22	odd	20		750.2.l.c.743.4		80
75.29	odd	10		150.2.l.a.47.9	yes	80
75.47	even	20		750.2.l.c.743.7		80
75.53	even	20	inner	750.2.l.a.743.4		80
75.71	odd	10		750.2.l.b.257.2		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.l.a.47.4	✓	80	25.4	even	10
150.2.l.a.47.9	yes	80	75.29	odd	10
150.2.l.a.83.4	yes	80	15.2	even	4
150.2.l.a.83.9	yes	80	5.2	odd	4
750.2.l.a.107.4		80	1.1	even	1	trivial
750.2.l.a.107.7		80	3.2	odd	2	inner
750.2.l.a.743.4		80	75.53	even	20	inner
750.2.l.a.743.7		80	25.3	odd	20	inner
750.2.l.b.143.2		80	5.3	odd	4
750.2.l.b.143.7		80	15.8	even	4
750.2.l.b.257.2		80	75.71	odd	10
750.2.l.b.257.7		80	25.21	even	5
750.2.l.c.107.4		80	15.14	odd	2
750.2.l.c.107.7		80	5.4	even	2
750.2.l.c.743.4		80	25.22	odd	20
750.2.l.c.743.7		80	75.47	even	20

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 750 = 2 \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	750.l (of order \(20\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.891007 - 0.453990i) q^{2} +(0.646378 + 1.60692i) q^{3} +(0.587785 + 0.809017i) q^{4} +(0.153600 - 1.72523i) q^{6} +(-2.03922 - 2.03922i) q^{7} +(-0.156434 - 0.987688i) q^{8} +(-2.16439 + 2.07736i) q^{9} +O(q^{10})\)	\(q+(-0.891007 - 0.453990i) q^{2} +(0.646378 + 1.60692i) q^{3} +(0.587785 + 0.809017i) q^{4} +(0.153600 - 1.72523i) q^{6} +(-2.03922 - 2.03922i) q^{7} +(-0.156434 - 0.987688i) q^{8} +(-2.16439 + 2.07736i) q^{9} +(2.60836 - 0.847507i) q^{11} +(-0.920095 + 1.46746i) q^{12} +(-2.68521 - 5.27002i) q^{13} +(0.891173 + 2.74275i) q^{14} +(-0.309017 + 0.951057i) q^{16} +(5.91053 - 0.936136i) q^{17} +(2.87159 - 0.868327i) q^{18} +(3.04743 - 4.19443i) q^{19} +(1.95876 - 4.59498i) q^{21} +(-2.70883 - 0.429036i) q^{22} +(0.515607 - 1.01194i) q^{23} +(1.48602 - 0.889798i) q^{24} +5.91469i q^{26} +(-4.73716 - 2.13524i) q^{27} +(0.451141 - 2.84839i) q^{28} +(2.34612 - 1.70456i) q^{29} +(4.56563 + 3.31712i) q^{31} +(0.707107 - 0.707107i) q^{32} +(3.04786 + 3.64362i) q^{33} +(-5.69132 - 1.84922i) q^{34} +(-2.95281 - 0.529988i) q^{36} +(-7.18975 + 3.66336i) q^{37} +(-4.61952 + 2.35376i) q^{38} +(6.73285 - 7.72135i) q^{39} +(5.02666 + 1.63326i) q^{41} +(-3.83135 + 3.20490i) q^{42} +(3.10789 - 3.10789i) q^{43} +(2.21880 + 1.61205i) q^{44} +(-0.918819 + 0.667561i) q^{46} +(-0.726167 + 4.58484i) q^{47} +(-1.72801 + 0.118176i) q^{48} +1.31687i q^{49} +(5.32473 + 8.89266i) q^{51} +(2.68521 - 5.27002i) q^{52} +(5.29057 + 0.837944i) q^{53} +(3.25146 + 4.05314i) q^{54} +(-1.69511 + 2.33312i) q^{56} +(8.70992 + 2.18579i) q^{57} +(-2.86426 + 0.453655i) q^{58} +(-0.912145 + 2.80729i) q^{59} +(-1.41844 - 4.36552i) q^{61} +(-2.56206 - 5.02833i) q^{62} +(8.64987 + 0.177478i) q^{63} +(-0.951057 + 0.309017i) q^{64} +(-1.06150 - 4.63019i) q^{66} +(0.0721944 + 0.455818i) q^{67} +(4.23147 + 4.23147i) q^{68} +(1.95938 + 0.174447i) q^{69} +(-3.36294 - 4.62869i) q^{71} +(2.39037 + 1.81277i) q^{72} +(8.09812 + 4.12620i) q^{73} +8.06924 q^{74} +5.18460 q^{76} +(-7.04728 - 3.59077i) q^{77} +(-9.50443 + 3.82312i) q^{78} +(-6.90557 - 9.50470i) q^{79} +(0.369168 - 8.99243i) q^{81} +(-3.73730 - 3.73730i) q^{82} +(-1.88912 - 11.9275i) q^{83} +(4.86875 - 1.11619i) q^{84} +(-4.18011 + 1.35820i) q^{86} +(4.25557 + 2.66824i) q^{87} +(-1.24511 - 2.44367i) q^{88} +(0.402182 + 1.23779i) q^{89} +(-5.27101 + 16.2225i) q^{91} +(1.12174 - 0.177666i) q^{92} +(-2.37923 + 9.48072i) q^{93} +(2.72849 - 3.75545i) q^{94} +(1.59332 + 0.679206i) q^{96} +(-6.52722 - 1.03381i) q^{97} +(0.597845 - 1.17334i) q^{98} +(-3.88493 + 7.25283i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 4 q^{3} - 4 q^{7}+O(q^{10}) \) 80 * q - 4 * q^3 - 4 * q^7	\( 80 q - 4 q^{3} - 4 q^{7} - 16 q^{12} + 20 q^{16} + 8 q^{18} + 40 q^{19} - 4 q^{22} + 56 q^{27} - 4 q^{28} + 96 q^{33} + 40 q^{34} + 64 q^{37} + 40 q^{39} + 4 q^{42} + 24 q^{43} - 16 q^{48} + 64 q^{57} - 20 q^{58} - 4 q^{63} + 104 q^{67} - 140 q^{69} - 8 q^{72} + 60 q^{73} + 60 q^{78} - 80 q^{79} - 40 q^{81} - 96 q^{82} - 60 q^{84} - 80 q^{87} - 24 q^{88} - 12 q^{93} + 12 q^{97}+O(q^{100}) \) 80 * q - 4 * q^3 - 4 * q^7 - 16 * q^12 + 20 * q^16 + 8 * q^18 + 40 * q^19 - 4 * q^22 + 56 * q^27 - 4 * q^28 + 96 * q^33 + 40 * q^34 + 64 * q^37 + 40 * q^39 + 4 * q^42 + 24 * q^43 - 16 * q^48 + 64 * q^57 - 20 * q^58 - 4 * q^63 + 104 * q^67 - 140 * q^69 - 8 * q^72 + 60 * q^73 + 60 * q^78 - 80 * q^79 - 40 * q^81 - 96 * q^82 - 60 * q^84 - 80 * q^87 - 24 * q^88 - 12 * q^93 + 12 * q^97

Introduction

L-functions

Modular forms

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Database

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