LMFDB - Embedded newform 750.2.l.b.143.2

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			143.2
Character	$\chi$	$=$	750.143
Dual form			750.2.l.b.257.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{3}{20}\right)$	$-1$

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 $

$2$	−0.453990	+	0.891007i	−0.321020	+	0.630037i
$2$	−0.453990	+	0.891007i	−0.321020	+	0.630037i
$3$	−1.60692	+	0.646378i	−0.927756	+	0.373187i
$3$	−1.60692	+	0.646378i	−0.927756	+	0.373187i
$4$	−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	−0.978238	−	0.207484i	$-0.933472\pi$
$7$	−2.03922	+	2.03922i	−0.770754	+	0.770754i	0.207484	+	0.978238i	$0.433472\pi$
$8$	0.987688	−	0.156434i	0.349201	−	0.0553079i
$9$	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	$0.264320\pi$
$12$	1.46746	+	0.920095i	0.423618	+	0.265608i
$13$	5.27002	−	2.68521i	1.46164	−	0.744744i	0.471116	−	0.882071i	$-0.343851\pi$
$13$	5.27002	−	2.68521i	1.46164	−	0.744744i	0.990526	+	0.137328i	$0.0438513\pi$
$14$	−0.891173	−	2.74275i	−0.238176	−	0.733031i
$15$		0			0
$16$	−0.309017	+	0.951057i	−0.0772542	+	0.237764i
$17$	−0.936136	−	5.91053i	−0.227046	−	1.43351i	−0.793073	−	0.609127i	$-0.791520\pi$
$17$	−0.936136	−	5.91053i	−0.227046	−	1.43351i	0.566026	−	0.824387i	$-0.308480\pi$
$18$	0.868327	+	2.87159i	0.204667	+	0.676839i
$19$	−3.04743	+	4.19443i	−0.699129	+	0.962269i	0.300834	+	0.953677i	$0.402735\pi$
$19$	−3.04743	+	4.19443i	−0.699129	+	0.962269i	−0.999963	+	0.00859233i	$0.997265\pi$
$20$		0			0
$21$	1.95876	−	4.59498i	0.427437	−	1.00271i
$22$	−0.429036	+	2.70883i	−0.0914707	+	0.577523i
$23$	1.01194	+	0.515607i	0.211003	+	0.107512i	0.556298	−	0.830983i	$-0.312221\pi$
$23$	1.01194	+	0.515607i	0.211003	+	0.107512i	−0.345295	+	0.938494i	$0.612221\pi$
$24$	−1.48602	+	0.889798i	−0.303333	+	0.181629i
$25$		0			0
$26$			5.91469i			1.15997i
$27$	−2.13524	+	4.73716i	−0.410928	+	0.911668i
$28$	2.84839	+	0.451141i	0.538296	+	0.0852576i
$29$	−2.34612	+	1.70456i	−0.435664	+	0.316528i	−0.783910	−	0.620875i	$-0.786777\pi$
$29$	−2.34612	+	1.70456i	−0.435664	+	0.316528i	0.348246	+	0.937403i	$0.386777\pi$
$30$		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
$33$	−3.64362	+	3.04786i	−0.634272	+	0.530565i
$34$	5.69132	+	1.84922i	0.976053	+	0.317139i
$35$		0			0
$36$	−2.95281	−	0.529988i	−0.492136	−	0.0883313i
$37$	3.66336	+	7.18975i	0.602253	+	1.18199i	0.967924	+	0.251243i	$0.0808395\pi$
$37$	3.66336	+	7.18975i	0.602253	+	1.18199i	−0.365671	+	0.930744i	$0.619161\pi$
$38$	−2.35376	−	4.61952i	−0.381830	−	0.749384i
$39$	−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	$0.464580\pi$
$42$	3.20490	+	3.83135i	0.494527	+	0.591190i
$43$	3.10789	+	3.10789i	0.473950	+	0.473950i	0.903190	−	0.429241i	$-0.141219\pi$
$43$	3.10789	+	3.10789i	0.473950	+	0.473950i	−0.429241	+	0.903190i	$0.641219\pi$
$44$	−2.21880	−	1.61205i	−0.334497	−	0.243026i
$45$		0			0
$46$	−0.918819	+	0.667561i	−0.135473	+	0.0984265i
$47$	4.58484	+	0.726167i	0.668768	+	0.105922i	0.481581	−	0.876402i	$-0.340063\pi$
$47$	4.58484	+	0.726167i	0.668768	+	0.105922i	0.187187	+	0.982324i	$0.440063\pi$
$48$	−0.118176	−	1.72801i	−0.0170573	−	0.249417i
$49$		−	1.31687i		−	0.188124i
$50$		0			0
$51$	5.32473	+	8.89266i	0.745612	+	1.24522i
$52$	−5.27002	−	2.68521i	−0.730821	−	0.372372i
$53$	−0.837944	+	5.29057i	−0.115100	+	0.726715i	0.860872	+	0.508821i	$0.169919\pi$
$53$	−0.837944	+	5.29057i	−0.115100	+	0.726715i	−0.975972	+	0.217894i	$0.930081\pi$
$54$	−3.25146	−	4.05314i	−0.442468	−	0.551563i
$55$		0			0
$56$	−1.69511	+	2.33312i	−0.226519	+	0.311777i
$57$	2.18579	−	8.70992i	0.289516	−	1.15366i
$58$	−0.453655	−	2.86426i	−0.0595678	−	0.376096i
$59$	0.912145	−	2.80729i	0.118751	−	0.365478i	−0.873960	−	0.485998i	$-0.838456\pi$
$59$	0.912145	−	2.80729i	0.118751	−	0.365478i	0.992711	+	0.120520i	$0.0384562\pi$
$60$		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	$0.994939\pi$
$62$	−5.02833	+	2.56206i	−0.638599	+	0.325382i
$63$	−0.177478	+	8.64987i	−0.0223601	+	1.08978i
$64$	0.951057	−	0.309017i	0.118882	−	0.0386271i
$65$		0			0
$66$	−1.06150	−	4.63019i	−0.130662	−	0.569937i
$67$	0.455818	−	0.0721944i	0.0556870	−	0.00881995i	−0.128529	−	0.991706i	$-0.541025\pi$
$67$	0.455818	−	0.0721944i	0.0556870	−	0.00881995i	0.184216	+	0.982886i	$0.441025\pi$
$68$	−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	$0.910258\pi$
$72$	1.81277	−	2.39037i	0.213637	−	0.281707i
$73$	−4.12620	+	8.09812i	−0.482935	+	0.947814i	0.513055	+	0.858356i	$0.328514\pi$
$73$	−4.12620	+	8.09812i	−0.482935	+	0.947814i	−0.995991	+	0.0894583i	$0.971486\pi$
$74$	−8.06924			−0.938031
$75$		0			0
$76$	5.18460			0.594715
$77$	−3.59077	+	7.04728i	−0.409206	+	0.803113i
$78$	−3.82312	−	9.50443i	−0.432884	−	1.07617i
$79$	6.90557	+	9.50470i	0.776937	+	1.06936i	0.995613	+	0.0935650i	$0.0298263\pi$
$79$	6.90557	+	9.50470i	0.776937	+	1.06936i	−0.218676	+	0.975798i	$0.570174\pi$
$80$		0			0
$81$	0.369168	−	8.99243i	0.0410187	−	0.999158i
$82$	−3.73730	+	3.73730i	−0.412716	+	0.412716i
$83$	11.9275	−	1.88912i	1.30921	−	0.207358i	0.537462	−	0.843288i	$-0.319383\pi$
$83$	11.9275	−	1.88912i	1.30921	−	0.207358i	0.771747	+	0.635930i	$0.219383\pi$
$84$	−4.86875	+	1.11619i	−0.531224	+	0.121786i
$85$		0			0
$86$	−4.18011	+	1.35820i	−0.450753	+	0.146458i
$87$	2.66824	−	4.25557i	0.286066	−	0.456245i
$88$	2.44367	−	1.24511i	0.260496	−	0.132729i
$89$	−0.402182	−	1.23779i	−0.0426312	−	0.131205i	0.927476	−	0.373884i	$-0.121974\pi$
$89$	−0.402182	−	1.23779i	−0.0426312	−	0.131205i	−0.970107	+	0.242678i	$0.921974\pi$
$90$		0			0
$91$	−5.27101	+	16.2225i	−0.552552	+	1.70058i
$92$	−0.177666	−	1.12174i	−0.0185230	−	0.116950i
$93$	−9.48072	−	2.37923i	−0.983105	−	0.246715i
$94$	−2.72849	+	3.75545i	−0.281423	+	0.387345i
$95$		0			0
$96$	1.59332	+	0.679206i	0.162618	+	0.0693212i
$97$	−1.03381	+	6.52722i	−0.104967	+	0.662738i	0.877959	+	0.478737i	$0.158905\pi$
$97$	−1.03381	+	6.52722i	−0.104967	+	0.662738i	−0.982926	+	0.184002i	$0.941095\pi$
$98$	1.17334	+	0.597845i	0.118525	+	0.0603915i
$99$	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	$-0.0561896\pi$
$102$	−10.3408	+	0.707192i	−1.02389	+	0.0700225i
$103$	6.37316	+	1.00941i	0.627966	+	0.0994601i	0.462303	−	0.886722i	$-0.347023\pi$
$103$	6.37316	+	1.00941i	0.627966	+	0.0994601i	0.165664	+	0.986182i	$0.447023\pi$
$104$	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	$-0.454613\pi$
$107$	−8.76915	−	8.76915i	−0.847745	−	0.847745i	−0.989851	+	0.142106i	$0.954613\pi$
$108$	5.08751	−	1.05699i	0.489546	−	0.101709i
$109$	2.65577	+	0.862912i	0.254377	+	0.0826520i	0.433430	−	0.901187i	$-0.357303\pi$
$109$	2.65577	+	0.862912i	0.254377	+	0.0826520i	−0.179053	+	0.983839i	$0.557303\pi$
$110$		0			0
$111$	−10.5340	−	9.18544i	−0.999846	−	0.871844i
$112$	−1.30926	−	2.56957i	−0.123714	−	0.242802i
$113$	2.09855	+	4.11863i	0.197415	+	0.387449i	0.968399	−	0.249406i	$-0.0802353\pi$
$113$	2.09855	+	4.11863i	0.197415	+	0.387449i	−0.770984	+	0.636854i	$0.780235\pi$
$114$	6.76826	+	5.90178i	0.633906	+	0.552752i
$115$		0			0
$116$	2.75803	+	0.896139i	0.256077	+	0.0832044i
$117$	5.82824	−	16.7596i	0.538821	−	1.54942i
$118$	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
$122$	4.53366	+	0.718062i	0.410459	+	0.0650103i
$123$	−9.13316	+	0.624604i	−0.823509	+	0.0563186i
$124$		−	5.64343i		−	0.506795i
$125$		0			0
$126$	−7.62652	−	4.08509i	−0.679424	−	0.363929i
$127$	−11.1643	−	5.68850i	−0.990672	−	0.504773i	−0.117966	−	0.993018i	$-0.537637\pi$
$127$	−11.1643	−	5.68850i	−0.990672	−	0.504773i	−0.872707	+	0.488245i	$0.837637\pi$
$128$	−0.156434	+	0.987688i	−0.0138270	+	0.0873001i
$129$	−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	$0.0256776\pi$
$132$	4.60744	+	1.15626i	0.401026	+	0.100639i
$133$	−2.33899	−	14.7678i	−0.202816	−	1.28053i
$134$	−0.142611	+	0.438912i	−0.0123197	+	0.0379162i
$135$		0			0
$136$	−1.84922	−	5.69132i	−0.158569	−	0.488026i
$137$	17.7044	−	9.02083i	1.51259	−	0.770702i	0.516268	−	0.856427i	$-0.327321\pi$
$137$	17.7044	−	9.02083i	1.51259	−	0.770702i	0.996319	+	0.0857255i	$0.0273208\pi$
$138$	1.04497	−	1.66662i	0.0889540	−	0.141872i
$139$	9.07922	−	2.95002i	0.770090	−	0.250217i	0.102486	−	0.994734i	$-0.467320\pi$
$139$	9.07922	−	2.95002i	0.770090	−	0.250217i	0.667603	+	0.744517i	$0.267320\pi$
$140$		0			0
$141$	−7.83686	+	1.79665i	−0.659982	+	0.151305i
$142$	5.65093	−	0.895020i	0.474216	−	0.0751084i
$143$	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
$147$	0.851194	+	2.11610i	0.0702053	+	0.174533i
$148$	3.66336	−	7.18975i	0.301126	−	0.590994i
$149$	12.0089			0.983807			0.491903	−	0.870650i	$-0.336301\pi$
$149$	12.0089			0.983807			0.491903	+	0.870650i	$0.336301\pi$
$150$		0			0
$151$	−11.1277			−0.905558			−0.452779	−	0.891623i	$-0.649567\pi$
$151$	−11.1277			−0.905558			−0.452779	+	0.891623i	$0.649567\pi$
$152$	−2.35376	+	4.61952i	−0.190915	+	0.374692i
$153$	−14.3044	−	10.8480i	−1.15645	−	0.877009i
$154$	−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	−0.0707617	−	0.997493i	$-0.522543\pi$
$157$	11.6119	−	11.6119i	0.926732	−	0.926732i	0.997493	+	0.0707617i	$0.0225430\pi$
$158$	−11.6038	+	1.83786i	−0.923150	+	0.146213i
$159$	−2.07320	−	9.04315i	−0.164415	−	0.717169i
$160$		0			0
$161$	−3.11500	+	1.01213i	−0.245497	+	0.0797667i
$162$	7.84471	+	4.41141i	0.616339	+	0.346593i
$163$	−5.83680	+	2.97400i	−0.457173	+	0.232941i	−0.667383	−	0.744715i	$-0.732585\pi$
$163$	−5.83680	+	2.97400i	−0.457173	+	0.232941i	0.210209	+	0.977656i	$0.432585\pi$
$164$	−1.63326	−	5.02666i	−0.127536	−	0.392516i
$165$		0			0
$166$	−3.73173	+	11.4851i	−0.289639	+	0.891416i
$167$	2.65903	+	16.7884i	0.205762	+	1.29913i	0.846920	+	0.531720i	$0.178454\pi$
$167$	2.65903	+	16.7884i	0.205762	+	1.29913i	−0.641159	+	0.767408i	$0.721546\pi$
$168$	1.21583	−	4.84483i	0.0938035	−	0.373787i
$169$	12.9216	−	17.7850i	0.993968	−	1.36808i
$170$		0			0
$171$	2.11750	+	15.4090i	0.161929	+	1.17836i
$172$	0.687565	−	4.34111i	0.0524263	−	0.331007i
$173$	−6.04954	−	3.08240i	−0.459938	−	0.234350i	0.208639	−	0.977993i	$-0.433097\pi$
$173$	−6.04954	−	3.08240i	−0.459938	−	0.234350i	−0.668578	+	0.743642i	$0.733097\pi$
$174$	2.58038	+	4.30941i	0.195618	+	0.326696i
$175$		0			0
$176$			2.74259i			0.206731i
$177$	0.348829	+	5.10069i	0.0262196	+	0.383391i
$178$	1.28546	+	0.203597i	0.0963496	+	0.0152603i
$179$	−7.59016	+	5.51457i	−0.567315	+	0.412179i	−0.834129	−	0.551569i	$-0.814029\pi$
$179$	−7.59016	+	5.51457i	−0.567315	+	0.412179i	0.266814	+	0.963748i	$0.414029\pi$
$180$		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
$183$	5.10110	+	6.09819i	0.377084	+	0.450791i
$184$	1.08014	+	0.350958i	0.0796287	+	0.0258729i
$185$		0			0
$186$	6.42407	−	7.36724i	0.471036	−	0.540192i
$187$	−7.45099	−	14.6234i	−0.544871	−	1.06937i
$188$	−2.10742	−	4.13604i	−0.153699	−	0.301652i
$189$	−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	$0.445345\pi$
$192$	−1.32853	+	1.11131i	−0.0958784	+	0.0802018i
$193$	−3.91447	−	3.91447i	−0.281770	−	0.281770i	0.552045	−	0.833815i	$-0.313848\pi$
$193$	−3.91447	−	3.91447i	−0.281770	−	0.281770i	−0.833815	+	0.552045i	$0.813848\pi$
$194$	−5.34645	−	3.88442i	−0.383853	−	0.278885i
$195$		0			0
$196$	−1.06537	+	0.774035i	−0.0760977	+	0.0552882i
$197$	25.2645	+	4.00150i	1.80002	+	0.285095i	0.964445	−	0.264282i	$-0.0851351\pi$
$197$	25.2645	+	4.00150i	1.80002	+	0.285095i	0.835574	+	0.549378i	$0.185135\pi$
$198$	4.69860	+	6.75421i	0.333915	+	0.480001i
$199$		−	0.0768328i		−	0.00544653i	−0.999996	−	0.00272327i	$-0.999133\pi$
$199$		−	0.0768328i		−	0.00544653i	0.999996	−	0.00272327i	$-0.000866844\pi$
$200$		0			0
$201$	−0.685798	+	0.410641i	−0.0483725	+	0.0289644i
$202$	3.14499	+	1.60245i	0.221281	+	0.112748i
$203$	1.30829	−	8.26024i	0.0918242	−	0.579755i
$204$	4.06451	−	9.53477i	0.284573	−	0.667568i
$205$		0			0
$206$	−3.79275	+	5.22027i	−0.264253	+	0.363713i
$207$	3.26133	−	0.986179i	0.226678	−	0.0685442i
$208$	0.925261	+	5.84187i	0.0641553	+	0.405061i
$209$	−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	$0.828726\pi$
$212$	4.77269	−	2.43181i	0.327790	−	0.167017i
$213$	8.39586	+	5.26420i	0.575275	+	0.360697i
$214$	11.7945	−	3.83226i	0.806254	−	0.261968i
$215$		0			0
$216$	−1.36790	+	5.01287i	−0.0930738	+	0.341082i
$217$	−16.0747	+	2.54598i	−1.09122	+	0.172832i
$218$	−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
$222$	12.9666	−	5.21578i	0.870264	−	0.350061i
$223$	2.46937	−	4.84642i	0.165362	−	0.324540i	−0.793425	−	0.608668i	$-0.791704\pi$
$223$	2.46937	−	4.84642i	0.165362	−	0.324540i	0.958786	+	0.284128i	$0.0917040\pi$
$224$	2.88390			0.192689
$225$		0			0
$226$	−4.62245			−0.307481
$227$	−8.90823	+	17.4834i	−0.591260	+	1.16041i	0.380575	+	0.924750i	$0.375726\pi$
$227$	−8.90823	+	17.4834i	−0.591260	+	1.16041i	−0.971835	+	0.235662i	$0.924274\pi$
$228$	−8.33125	+	3.35122i	−0.551750	+	0.221940i
$229$	10.2833	+	14.1538i	0.679543	+	0.935310i	0.999928	−	0.0119768i	$-0.00381244\pi$
$229$	10.2833	+	14.1538i	0.679543	+	0.935310i	−0.320385	+	0.947287i	$0.603812\pi$
$230$		0			0
$231$	1.21487	−	13.6454i	0.0799327	−	0.897803i
$232$	−2.05059	+	2.05059i	−0.134628	+	0.134628i
$233$	−28.6649	+	4.54007i	−1.87790	+	0.297430i	−0.987484	−	0.157718i	$-0.949586\pi$
$233$	−28.6649	+	4.54007i	−1.87790	+	0.297430i	−0.890416	+	0.455148i	$0.849586\pi$
$234$	12.2869	+	12.8017i	0.803221	+	0.836872i
$235$		0			0
$236$	−2.80729	+	0.912145i	−0.182739	+	0.0593756i
$237$	−17.2403	−	10.8097i	−1.11988	−	0.702165i
$238$	−15.3768	+	7.83489i	−0.996733	+	0.507861i
$239$	1.74681	+	5.37613i	0.112992	+	0.347753i	0.991523	−	0.129932i	$-0.0414759\pi$
$239$	1.74681	+	5.37613i	0.112992	+	0.347753i	−0.878531	+	0.477685i	$0.841476\pi$
$240$		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	$-0.0500137\pi$
$242$	−0.544110	−	3.43537i	−0.0349767	−	0.220834i
$243$	5.21929	+	14.6887i	0.334817	+	0.942283i
$244$	−2.69804	+	3.71353i	−0.172724	+	0.237734i
$245$		0			0
$246$	3.58984	−	8.42127i	0.228880	−	0.536920i
$247$	−4.79711	+	30.2878i	−0.305233	+	1.92716i
$248$	5.02833	+	2.56206i	0.319299	+	0.162691i
$249$	−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	$0.815938\pi$
$252$	7.10221	−	4.94069i	0.447397	−	0.311234i
$253$	3.07648	+	0.487266i	0.193416	+	0.0306341i
$254$	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	$-0.189415\pi$
$257$	4.28914	+	4.28914i	0.267549	+	0.267549i	−0.560563	+	0.828112i	$0.689415\pi$
$258$	5.83919	−	4.88445i	0.363532	−	0.304093i
$259$	−22.1319	−	7.19110i	−1.37521	−	0.446833i
$260$		0			0
$261$	−1.53695	+	8.56306i	−0.0951347	+	0.530040i
$262$	5.41110	+	10.6199i	0.334299	+	0.656098i
$263$	−10.8405	−	21.2757i	−0.668454	−	1.31191i	−0.937230	−	0.348711i	$-0.886619\pi$
$263$	−10.8405	−	21.2757i	−0.668454	−	1.31191i	0.268777	−	0.963203i	$-0.413381\pi$
$264$	−3.12197	+	3.58033i	−0.192144	+	0.220354i
$265$		0			0
$266$	14.2201	+	4.62038i	0.871889	+	0.283294i
$267$	1.44635	+	1.72907i	0.0885154	+	0.105817i
$268$	−0.326329	−	0.326329i	−0.0199337	−	0.0199337i
$269$	−11.2436	−	8.16896i	−0.685535	−	0.498070i	0.189654	−	0.981851i	$-0.439263\pi$
$269$	−11.2436	−	8.16896i	−0.685535	−	0.498070i	−0.875189	+	0.483781i	$0.839263\pi$
$270$		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	$0.149051\pi$
$272$	5.91053	+	0.936136i	0.358378	+	0.0567616i
$273$	−2.01578	−	29.4753i	−0.122000	−	1.78393i
$274$			19.8701i			1.20040i
$275$		0			0
$276$	1.01056	+	1.68771i	0.0608288	+	0.101588i
$277$	1.61620	+	0.823495i	0.0971080	+	0.0494790i	0.501870	−	0.864943i	$-0.332646\pi$
$277$	1.61620	+	0.823495i	0.0971080	+	0.0494790i	−0.404762	+	0.914422i	$0.632646\pi$
$278$	−1.49340	+	9.42893i	−0.0895679	+	0.565509i
$279$	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	$0.960422\pi$
$282$	1.95703	−	7.79835i	0.116540	−	0.464385i
$283$	0.445062	+	2.81001i	0.0264562	+	0.167038i	0.997379	−	0.0723553i	$-0.0230516\pi$
$283$	0.445062	+	2.81001i	0.0264562	+	0.167038i	−0.970923	+	0.239393i	$0.923052\pi$
$284$	−1.76800	+	5.44135i	−0.104912	+	0.322885i
$285$		0			0
$286$	5.01274	+	15.4276i	0.296409	+	0.912255i
$287$	−13.5811	+	6.91991i	−0.801666	+	0.408469i
$288$	−2.99937	−	0.0615410i	−0.176739	−	0.00362634i
$289$	−17.8900	+	5.81283i	−1.05236	+	0.341931i
$290$		0			0
$291$	−2.55780	−	11.1570i	−0.149941	−	0.654032i
$292$	8.97684	−	1.42179i	0.525330	−	0.0832041i
$293$	9.44461	−	9.44461i	0.551760	−	0.551760i	−0.375189	−	0.926948i	$-0.622422\pi$
$293$	9.44461	−	9.44461i	0.551760	−	0.551760i	0.926948	+	0.375189i	$0.122422\pi$
$294$	−2.27189	−	0.202270i	−0.132500	−	0.0117966i
$295$		0			0
$296$	4.74298	+	6.52816i	0.275680	+	0.379441i
$297$	−1.55470	+	14.1659i	−0.0902130	+	0.821987i
$298$	−5.45192	+	10.7000i	−0.315821	+	0.619834i
$299$	6.71745			0.388480
$300$		0			0
$301$	−12.6754			−0.730597
$302$	5.05186	−	9.91484i	0.290702	−	0.570535i
$303$	2.28153	+	5.67196i	0.131070	+	0.325846i
$304$	−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	0.412506	−	0.910955i	$-0.364654\pi$
$307$	23.1889	−	23.1889i	1.32346	−	1.32346i	0.910955	−	0.412506i	$-0.135346\pi$
$308$	7.81197	−	1.23730i	0.445129	−	0.0705014i
$309$	−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	$0.494819\pi$
$312$	−5.44207	+	8.67954i	−0.308097	+	0.491382i
$313$	12.2235	−	6.22820i	0.690915	−	0.352039i	−0.0730212	−	0.997330i	$-0.523264\pi$
$313$	12.2235	−	6.22820i	0.690915	−	0.352039i	0.763936	+	0.645292i	$0.223264\pi$
$314$	5.07459	+	15.6180i	0.286376	+	0.881374i
$315$		0			0
$316$	3.63047	−	11.1734i	0.204230	−	0.628556i
$317$	−2.95253	−	18.6415i	−0.165830	−	1.04701i	−0.920453	−	0.390853i	$-0.872180\pi$
$317$	−2.95253	−	18.6415i	−0.165830	−	1.04701i	0.754623	−	0.656159i	$-0.227820\pi$
$318$	8.99872	+	2.25827i	0.504623	+	0.126638i
$319$	−4.67490	+	6.43445i	−0.261744	+	0.360260i
$320$		0			0
$321$	19.7595	+	8.42314i	1.10287	+	0.470134i
$322$	0.512371	−	3.23498i	0.0285533	−	0.180279i
$323$	27.6441	+	14.0854i	1.53816	+	0.783732i
$324$	−7.49202	+	4.98695i	−0.416223	+	0.277053i
$325$		0			0
$326$		−	6.55079i		−	0.362815i
$327$	−4.82538	+	0.330001i	−0.266844	+	0.0182491i
$328$	5.22028	+	0.826810i	0.288241	+	0.0456530i
$329$	−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
$333$	22.8646	+	7.95131i	1.25297	+	0.435729i
$334$	−16.1658	−	5.25258i	−0.884552	−	0.287408i
$335$		0			0
$336$	3.76480	+	3.28282i	0.205386	+	0.179093i
$337$	7.31518	+	14.3569i	0.398483	+	0.782068i	0.999857	−	0.0169001i	$-0.00537972\pi$
$337$	7.31518	+	14.3569i	0.398483	+	0.782068i	−0.601374	+	0.798968i	$0.705380\pi$
$338$	9.98030	+	19.5874i	0.542857	+	1.06542i
$339$	−6.03440	−	5.26186i	−0.327744	−	0.285785i
$340$		0			0
$341$	14.7201	+	4.78284i	0.797137	+	0.259006i
$342$	−14.6908	−	5.10883i	−0.794390	−	0.276254i
$343$	−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
$347$	−23.6313	−	3.74283i	−1.26859	−	0.200925i	−0.514384	−	0.857560i	$-0.671980\pi$
$347$	−23.6313	−	3.74283i	−1.26859	−	0.200925i	−0.754209	+	0.656634i	$0.771980\pi$
$348$	−5.01118	+	0.342708i	−0.268628	+	0.0183711i
$349$		−	24.8956i		−	1.33263i	−0.745670	−	0.666315i	$-0.767871\pi$
$349$		−	24.8956i		−	1.33263i	0.745670	−	0.666315i	$-0.232129\pi$
$350$		0			0
$351$	1.46750	+	30.6986i	0.0783293	+	1.63857i
$352$	−2.44367	−	1.24511i	−0.130248	−	0.0663646i
$353$	−2.64576	+	16.7047i	−0.140820	+	0.889101i	0.811578	+	0.584244i	$0.198609\pi$
$353$	−2.64576	+	16.7047i	−0.140820	+	0.889101i	−0.952398	+	0.304857i	$0.901391\pi$
$354$	−4.70311	−	2.00485i	−0.249968	−	0.106557i
$355$		0			0
$356$	−0.764995	+	1.05293i	−0.0405447	+	0.0558049i
$357$	−28.9924	−	7.27579i	−1.53444	−	0.385076i
$358$	−1.46766	−	9.26645i	−0.0775683	−	0.489747i
$359$	1.67961	−	5.16932i	0.0886466	−	0.272826i	−0.896899	−	0.442235i	$-0.854186\pi$
$359$	1.67961	−	5.16932i	0.0886466	−	0.272826i	0.985546	+	0.169409i	$0.0541858\pi$
$360$		0			0
$361$	−2.43509	−	7.49444i	−0.128163	−	0.394444i
$362$	−13.5493	+	6.90373i	−0.712137	+	0.362852i
$363$	3.20027	−	5.10410i	0.167971	−	0.267896i
$364$	16.2225	−	5.27101i	0.850290	−	0.276276i
$365$		0			0
$366$	−7.74938	+	1.77659i	−0.405066	+	0.0928640i
$367$	−17.7079	+	2.80465i	−0.924343	+	0.146401i	−0.600422	−	0.799683i	$-0.705001\pi$
$367$	−17.7079	+	2.80465i	−0.924343	+	0.146401i	−0.323920	+	0.946084i	$0.605001\pi$
$368$	−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
$372$	3.64779	+	9.06854i	0.189129	+	0.470182i
$373$	−11.6182	+	22.8020i	−0.601568	+	1.18064i	0.366608	+	0.930376i	$0.380519\pi$
$373$	−11.6182	+	22.8020i	−0.601568	+	1.18064i	−0.968176	+	0.250269i	$0.919481\pi$
$374$	16.4122			0.848656
$375$		0			0
$376$	4.64199			0.239392
$377$	−7.78702	+	15.2829i	−0.401052	+	0.787109i
$378$	14.8957	+	1.63481i	0.766154	+	0.0840853i
$379$	5.71732	+	7.86922i	0.293679	+	0.404215i	0.930205	−	0.367041i	$-0.119629\pi$
$379$	5.71732	+	7.86922i	0.293679	+	0.404215i	−0.636526	+	0.771255i	$0.719629\pi$
$380$		0			0
$381$	21.6171	+	1.92460i	1.10748	+	0.0986003i
$382$	−9.12687	+	9.12687i	−0.466971	+	0.466971i
$383$	−24.0895	+	3.81540i	−1.23092	+	0.194958i	−0.737808	−	0.675010i	$-0.764139\pi$
$383$	−24.0895	+	3.81540i	−1.23092	+	0.194958i	−0.493108	+	0.869968i	$0.664139\pi$
$384$	−0.387043	−	1.68825i	−0.0197512	−	0.0861533i
$385$		0			0
$386$	5.26495	−	1.71069i	0.267979	−	0.0870717i
$387$	13.1829	+	0.270487i	0.670125	+	0.0137496i
$388$	5.88829	−	3.00023i	0.298932	−	0.152314i
$389$	−5.49358	−	16.9075i	−0.278536	−	0.857245i	−0.988262	−	0.152767i	$-0.951181\pi$
$389$	−5.49358	−	16.9075i	−0.278536	−	0.857245i	0.709726	−	0.704477i	$-0.248819\pi$
$390$		0			0
$391$	2.10020	−	6.46376i	0.106212	−	0.326886i
$392$	−0.206003	−	1.30065i	−0.0104047	−	0.0656929i
$393$	−5.02496	+	20.0234i	−0.253475	+	1.01004i
$394$	−15.0352	+	20.6942i	−0.757462	+	1.04256i
$395$		0			0
$396$	−8.15117	+	1.12013i	−0.409612	+	0.0562888i
$397$	3.00987	−	19.0036i	0.151061	−	0.953762i	−0.789405	−	0.613873i	$-0.789611\pi$
$397$	3.00987	−	19.0036i	0.151061	−	0.953762i	0.940466	−	0.339889i	$-0.110389\pi$
$398$	0.0684585	+	0.0348814i	0.00343152	+	0.00174845i
$399$	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	$-0.283577\pi$
$402$	−0.0545384	−	0.797478i	−0.00272013	−	0.0397746i
$403$	32.9681	+	5.22164i	1.64226	+	0.260108i
$404$	−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
$408$	6.65030	+	7.95020i	0.329239	+	0.393594i
$409$	−14.9223	−	4.84855i	−0.737860	−	0.239745i	−0.0841106	−	0.996456i	$-0.526805\pi$
$409$	−14.9223	−	4.84855i	−0.737860	−	0.239745i	−0.653749	+	0.756711i	$0.726805\pi$
$410$		0			0
$411$	−22.6187	+	25.9395i	−1.11570	+	1.27950i
$412$	−2.92942	−	5.74931i	−0.144322	−	0.283248i
$413$	3.86463	+	7.58476i	0.190166	+	0.373222i
$414$	−0.601920	+	3.35358i	−0.0295827	+	0.164819i
$415$		0			0
$416$	−5.62520	−	1.82774i	−0.275798	−	0.0896122i
$417$	−12.6828	+	10.6091i	−0.621078	+	0.519528i
$418$	−10.0545	−	10.0545i	−0.491783	−	0.491783i
$419$	−2.78733	−	2.02511i	−0.136170	−	0.0989333i	0.517615	−	0.855614i	$-0.326820\pi$
$419$	−2.78733	−	2.02511i	−0.136170	−	0.0989333i	−0.653785	+	0.756680i	$0.726820\pi$
$420$		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	$0.193308\pi$
$422$	−6.37141	−	1.00913i	−0.310156	−	0.0491238i
$423$	11.4319	−	7.95265i	0.555838	−	0.386671i
$424$			5.35652i			0.260135i
$425$		0			0
$426$	−8.50208	+	5.09087i	−0.411927	+	0.246653i
$427$	11.7948	+	6.00974i	0.570790	+	0.290832i
$428$	−1.94001	+	12.2488i	−0.0937741	+	0.592066i
$429$	−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	$0.965283\pi$
$432$	−3.84548	−	3.49460i	−0.185016	−	0.168134i
$433$	0.408546	+	2.57946i	0.0196335	+	0.123961i	0.995558	−	0.0941457i	$-0.0300119\pi$
$433$	0.408546	+	2.57946i	0.0196335	+	0.123961i	−0.975925	+	0.218107i	$0.930012\pi$
$434$	5.02927	−	15.4785i	0.241413	−	0.742992i
$435$		0			0
$436$	−0.862912	−	2.65577i	−0.0413260	−	0.127188i
$437$	−5.24649	+	2.67322i	−0.250974	+	0.127877i
$438$	13.3373	+	8.36250i	0.637282	+	0.399576i
$439$	−10.4899	+	3.40836i	−0.500653	+	0.162672i	−0.548447	−	0.836185i	$-0.684781\pi$
$439$	−10.4899	+	3.40836i	−0.500653	+	0.162672i	0.0477940	+	0.998857i	$0.484781\pi$
$440$		0			0
$441$	−2.73560	−	2.85021i	−0.130267	−	0.135724i
$442$	34.9589	−	5.53695i	1.66283	−	0.263366i
$443$	1.32181	−	1.32181i	0.0628009	−	0.0628009i	−0.675009	−	0.737810i	$-0.735860\pi$
$443$	1.32181	−	1.32181i	0.0628009	−	0.0628009i	0.737810	+	0.675009i	$0.235860\pi$
$444$	−1.23943	+	13.9213i	−0.0588208	+	0.660675i
$445$		0			0
$446$	3.19712	+	4.40046i	0.151388	+	0.208368i
$447$	−19.2973	+	7.76229i	−0.912733	+	0.367144i
$448$	−1.30926	+	2.56957i	−0.0618568	+	0.121401i
$449$	−20.5238			−0.968579			−0.484289	−	0.874908i	$-0.660922\pi$
$449$	−20.5238			−0.968579			−0.484289	+	0.874908i	$0.660922\pi$
$450$		0			0
$451$	14.4955			0.682569
$452$	2.09855	−	4.11863i	0.0987075	−	0.193724i
$453$	17.8813	−	7.19269i	0.840137	−	0.337942i
$454$	−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	−0.916628	−	0.399742i	$-0.869100\pi$
$457$	−11.0498	+	11.0498i	−0.516886	+	0.516886i	0.399742	+	0.916628i	$0.369100\pi$
$458$	−17.2797	+	2.73683i	−0.807427	+	0.127884i
$459$	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	$0.294670\pi$
$462$	11.6066	+	7.27735i	0.539989	+	0.338573i
$463$	−29.3718	+	14.9657i	−1.36502	+	0.695515i	−0.974355	−	0.225017i	$-0.927756\pi$
$463$	−29.3718	+	14.9657i	−1.36502	+	0.695515i	−0.390669	+	0.920531i	$0.627756\pi$
$464$	−0.896139	−	2.75803i	−0.0416022	−	0.128038i
$465$		0			0
$466$	8.96836	−	27.6018i	0.415451	−	1.27863i
$467$	−0.578507	−	3.65255i	−0.0267701	−	0.169020i	0.970681	−	0.240371i	$-0.0772690\pi$
$467$	−0.578507	−	3.65255i	−0.0267701	−	0.169020i	−0.997451	+	0.0713509i	$0.977269\pi$
$468$	−16.9845	+	5.13588i	−0.785110	+	0.237406i
$469$	−0.782294	+	1.07673i	−0.0361230	+	0.0497190i
$470$		0			0
$471$	−11.1537	+	26.1651i	−0.513937	+	1.20562i
$472$	0.461757	−	2.91542i	0.0212541	−	0.134193i
$473$	10.7405	+	5.47254i	0.493847	+	0.251628i
$474$	17.4585	−	10.4538i	0.801894	−	0.480157i
$475$		0			0
$476$		−	17.2578i		−	0.791012i
$477$	9.17677	+	13.1916i	0.420175	+	0.604000i
$478$	−5.58321	−	0.884293i	−0.255370	−	0.0404466i
$479$	−4.35190	+	3.16184i	−0.198844	+	0.144468i	−0.682752	−	0.730651i	$-0.739217\pi$
$479$	−4.35190	+	3.16184i	−0.198844	+	0.144468i	0.483908	+	0.875119i	$0.339217\pi$
$480$		0			0
$481$	38.6120	+	28.0533i	1.76056	+	1.27912i
$482$	9.96798	+	9.96798i	0.454029	+	0.454029i
$483$	4.35135	−	3.63988i	0.197993	−	0.165620i
$484$	3.30796	+	1.07482i	0.150362	+	0.0488555i
$485$		0			0
$486$	−15.4573	−	2.01813i	−0.701156	−	0.0915443i
$487$	1.90512	+	3.73900i	0.0863291	+	0.169430i	0.930135	−	0.367219i	$-0.119690\pi$
$487$	1.90512	+	3.73900i	0.0863291	+	0.169430i	−0.843806	+	0.536649i	$0.819690\pi$
$488$	−2.08390	−	4.08988i	−0.0943336	−	0.185140i
$489$	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	$0.347501\pi$
$492$	5.87365	+	7.02175i	0.264805	+	0.316565i
$493$	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
$497$	16.2967	+	2.58115i	0.731007	+	0.115780i
$498$	−1.42712	−	20.8677i	−0.0639506	−	0.935106i
$499$			10.2536i			0.459015i	0.973307	+	0.229508i	$0.0737116\pi$
$499$			10.2536i			0.459015i	−0.973307	+	0.229508i	$0.926288\pi$
$500$		0			0
$501$	−15.1245	−	25.2590i	−0.675714	−	1.12849i
$502$	−15.4306	−	7.86229i	−0.688702	−	0.350911i
$503$	−0.104371	+	0.658974i	−0.00465369	+	0.0293822i	−0.989906	−	0.141726i	$-0.954735\pi$
$503$	−0.104371	+	0.658974i	−0.00465369	+	0.0293822i	0.985252	+	0.171108i	$0.0547348\pi$
$504$	1.17785	+	8.57114i	0.0524654	+	0.381789i
$505$		0			0
$506$	−1.83085	+	2.51995i	−0.0813911	+	0.112025i
$507$	−9.26810	+	36.9314i	−0.411611	+	1.64018i
$508$	1.96012	+	12.3757i	0.0869664	+	0.549084i
$509$	8.01814	−	24.6773i	0.355398	−	1.09380i	−0.600381	−	0.799714i	$-0.704984\pi$
$509$	8.01814	−	24.6773i	0.355398	−	1.09380i	0.955779	−	0.294087i	$-0.0950156\pi$
$510$		0			0
$511$	−8.09964	−	24.9281i	−0.358307	−	1.10276i
$512$	0.891007	−	0.453990i	0.0393773	−	0.0200637i
$513$	−13.3627	−	23.3923i	−0.589978	−	1.03280i
$514$	−5.76888	+	1.87442i	−0.254454	+	0.0826772i
$515$		0			0
$516$	1.70114	+	7.42026i	0.0748885	+	0.326659i
$517$	12.5743	−	1.99158i	0.553019	−	0.0875896i
$518$	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	$0.447445\pi$
$522$	−6.93199	−	5.25698i	−0.303405	−	0.230092i
$523$	12.3663	−	24.2703i	0.540741	−	1.06126i	−0.445396	−	0.895334i	$-0.646937\pi$
$523$	12.3663	−	24.2703i	0.540741	−	1.06126i	0.986137	−	0.165931i	$-0.0530628\pi$
$524$	−11.9190			−0.520682
$525$		0			0
$526$	23.8782			1.04114
$527$	15.3319	−	30.0906i	0.667868	−	1.31077i
$528$	−1.77275	−	4.40713i	−0.0771491	−	0.191796i
$529$	−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
$533$	30.8763	−	4.89032i	1.33740	−	0.211823i
$534$	−2.19724	+	0.503731i	−0.0950839	+	0.0217986i
$535$		0			0
$536$	0.438912	−	0.142611i	0.0189581	−	0.00615987i
$537$	8.63229	−	13.7676i	0.372511	−	0.594116i
$538$	12.3831	−	6.30950i	0.533873	−	0.272022i
$539$	−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	$-0.00737544\pi$
$542$	2.35194	+	14.8496i	0.101025	+	0.637844i
$543$	−25.5467	−	6.41107i	−1.09631	−	0.275125i
$544$	−3.51743	+	4.84132i	−0.150808	+	0.207570i
$545$		0			0
$546$	27.1779	+	11.5855i	1.16311	+	0.495812i
$547$	3.51301	−	22.1803i	0.150205	−	0.948360i	−0.791316	−	0.611407i	$-0.790604\pi$
$547$	3.51301	−	22.1803i	0.150205	−	0.948360i	0.941522	−	0.336953i	$-0.109396\pi$
$548$	−17.7044	−	9.02083i	−0.756293	−	0.385351i
$549$	−12.1388	−	6.50207i	−0.518072	−	0.277502i
$550$		0			0
$551$		−	15.0352i		−	0.640520i
$552$	−1.96255	+	0.134216i	−0.0835315	+	0.00571260i
$553$	−33.4642	−	5.30021i	−1.42304	−	0.225388i
$554$	−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	$-0.265884\pi$
$557$	−1.66485	−	1.66485i	−0.0705420	−	0.0705420i	−0.741498	+	0.670956i	$0.765884\pi$
$558$	−5.56095	+	15.9909i	−0.235414	+	0.676951i
$559$	24.7240	+	8.03333i	1.04572	+	0.339773i
$560$		0			0
$561$	21.4254	+	18.6825i	0.904581	+	0.788775i
$562$	−10.4045	−	20.4199i	−0.438886	−	0.861362i
$563$	−21.4512	−	42.1004i	−0.904062	−	1.77432i	−0.534729	−	0.845023i	$-0.679586\pi$
$563$	−21.4512	−	42.1004i	−0.904062	−	1.77432i	−0.369332	−	0.929297i	$-0.620414\pi$
$564$	6.05991	+	5.28411i	0.255168	+	0.222501i
$565$		0			0
$566$	−2.70579	−	0.879165i	−0.113733	−	0.0369541i
$567$	17.5848	+	19.0904i	0.738490	+	0.801721i
$568$	−4.04562	−	4.04562i	−0.169750	−	0.169750i
$569$	19.9798	+	14.5162i	0.837599	+	0.608551i	0.921699	−	0.387906i	$-0.126802\pi$
$569$	19.9798	+	14.5162i	0.837599	+	0.608551i	−0.0841003	+	0.996457i	$0.526802\pi$
$570$		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	$0.260060\pi$
$572$	−16.0218	−	2.53761i	−0.669907	−	0.106103i
$573$	−22.3041	+	1.52534i	−0.931766	+	0.0637221i
$574$		−	15.2424i		−	0.636206i
$575$		0			0
$576$	1.41652	−	2.64452i	0.0590216	−	0.110188i
$577$	28.0783	+	14.3066i	1.16891	+	0.595591i	0.927130	−	0.374739i	$-0.122268\pi$
$577$	28.0783	+	14.3066i	1.16891	+	0.595591i	0.241783	+	0.970330i	$0.422268\pi$
$578$	2.94264	−	18.5791i	0.122398	−	0.772789i
$579$	8.82048	+	3.76002i	0.366567	+	0.156261i
$580$		0			0
$581$	−20.4704	+	28.1751i	−0.849256	+	1.16890i
$582$	11.1021	+	2.78613i	0.460198	+	0.115489i
$583$	2.29814	+	14.5099i	0.0951791	+	0.600937i
$584$	−2.80857	+	8.64390i	−0.116220	+	0.357687i
$585$		0			0
$586$	4.12744	+	12.7030i	0.170503	+	0.524755i
$587$	10.0374	−	5.11433i	0.414289	−	0.211091i	−0.234407	−	0.972139i	$-0.575315\pi$
$587$	10.0374	−	5.11433i	0.414289	−	0.211091i	0.648696	+	0.761048i	$0.275315\pi$
$588$	1.21164	−	1.93244i	0.0499673	−	0.0796926i
$589$	−27.8269	+	9.04151i	−1.14659	+	0.372549i
$590$		0			0
$591$	−43.1845	+	9.90032i	−1.77637	+	0.407245i
$592$	−7.96990	+	1.26231i	−0.327561	+	0.0518805i
$593$	−17.4049	+	17.4049i	−0.714734	+	0.714734i	−0.967522	−	0.252788i	$-0.918653\pi$
$593$	−17.4049	+	17.4049i	−0.714734	+	0.714734i	0.252788	+	0.967522i	$0.418653\pi$
$594$	−11.9161	−	7.81642i	−0.488922	−	0.320711i
$595$		0			0
$596$	−7.05865	−	9.71540i	−0.289134	−	0.397958i
$597$	0.0496631	+	0.123464i	0.00203257	+	0.00505306i
$598$	−3.04966	+	5.98529i	−0.124710	+	0.244757i
$599$	−25.8531			−1.05633			−0.528165	−	0.849142i	$-0.677120\pi$
$599$	−25.8531			−1.05633			−0.528165	+	0.849142i	$0.677120\pi$
$600$		0			0
$601$	−36.7027			−1.49714			−0.748568	−	0.663058i	$-0.769258\pi$
$601$	−36.7027			−1.49714			−0.748568	+	0.663058i	$0.769258\pi$
$602$	5.75450	−	11.2939i	0.234536	−	0.460303i
$603$	0.836594	−	1.10315i	0.0340687	−	0.0449239i
$604$	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	−0.0560654	−	0.998427i	$-0.517856\pi$
$607$	23.2173	−	23.2173i	0.942362	−	0.942362i	0.998427	+	0.0560654i	$0.0178555\pi$
$608$	5.12077	−	0.811051i	0.207675	−	0.0328925i
$609$	3.23692	+	14.1192i	0.131166	+	0.572139i
$610$		0			0
$611$	26.1121	−	8.48435i	1.05638	−	0.343240i
$612$	−0.368274	+	17.9488i	−0.0148866	+	0.725539i
$613$	−19.5715	+	9.97216i	−0.790484	+	0.402772i	−0.802122	−	0.597161i	$-0.796295\pi$
$613$	−19.5715	+	9.97216i	−0.790484	+	0.402772i	0.0116379	+	0.999932i	$0.496295\pi$
$614$	10.1339	+	31.1890i	0.408972	+	1.25869i
$615$		0			0
$616$	−2.44412	+	7.52224i	−0.0984766	+	0.303080i
$617$	−1.00125	−	6.32162i	−0.0403086	−	0.254499i	0.959303	−	0.282380i	$-0.0911239\pi$
$617$	−1.00125	−	6.32162i	−0.0403086	−	0.254499i	−0.999611	+	0.0278814i	$0.991124\pi$
$618$	2.72038	−	10.8401i	0.109430	−	0.436053i
$619$	14.0949	−	19.4000i	0.566524	−	0.779753i	−0.425614	−	0.904905i	$-0.639942\pi$
$619$	14.0949	−	19.4000i	0.566524	−	0.779753i	0.992138	+	0.125152i	$0.0399418\pi$
$620$		0			0
$621$	−4.60325	+	3.69276i	−0.184722	+	0.148185i
$622$	1.61936	−	10.2243i	0.0649306	−	0.409956i
$623$	3.34426	+	1.70399i	0.133985	+	0.0682688i
$624$	−5.26288	−	8.78935i	−0.210684	−	0.351856i
$625$		0			0
$626$			13.7188i			0.548313i
$627$	−1.68038	−	24.5711i	−0.0671079	−	0.981274i
$628$	−16.2195	−	2.56892i	−0.647230	−	0.102511i
$629$	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
$633$	−7.16886	−	8.57013i	−0.284937	−	0.340632i
$634$	17.9501	+	5.83235i	0.712891	+	0.231632i
$635$		0			0
$636$	−6.09747	+	6.99269i	−0.241780	+	0.277278i
$637$	−3.53606	−	6.93992i	−0.140104	−	0.274970i
$638$	−3.61078	−	7.08655i	−0.142952	−	0.280559i
$639$	−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	$0.724359\pi$
$642$	−16.4757	+	13.7818i	−0.650244	+	0.543925i
$643$	2.50826	+	2.50826i	0.0989163	+	0.0989163i	0.754833	−	0.655917i	$-0.227718\pi$
$643$	2.50826	+	2.50826i	0.0989163	+	0.0989163i	−0.655917	+	0.754833i	$0.727718\pi$
$644$	2.64978	+	1.92518i	0.104416	+	0.0758627i
$645$		0			0
$646$	−25.1003	+	18.2365i	−0.987560	+	0.717504i
$647$	−36.9778	−	5.85671i	−1.45375	−	0.230251i	−0.620960	−	0.783842i	$-0.713257\pi$
$647$	−36.9778	−	5.85671i	−1.45375	−	0.230251i	−0.832789	+	0.553591i	$0.813257\pi$
$648$	−1.04210	−	8.93946i	−0.0409376	−	0.351175i
$649$		−	8.09547i		−	0.317775i
$650$		0			0
$651$	24.1851	−	14.4815i	0.947889	−	0.567576i
$652$	5.83680	+	2.97400i	0.228587	+	0.116471i
$653$	0.348209	−	2.19851i	0.0136265	−	0.0860342i	−0.979938	−	0.199303i	$-0.936132\pi$
$653$	0.348209	−	2.19851i	0.0136265	−	0.0860342i	0.993564	+	0.113269i	$0.0361322\pi$
$654$	1.89664	−	4.44926i	0.0741647	−	0.173980i
$655$		0			0
$656$	−3.10665	+	4.27594i	−0.121294	+	0.166947i
$657$	7.89200	+	26.0991i	0.307896	+	1.01822i
$658$	−2.09419	−	13.2222i	−0.0816401	−	0.515456i
$659$	−4.81311	+	14.8132i	−0.187492	+	0.577041i	−0.999982	−	0.00593344i	$-0.998111\pi$
$659$	−4.81311	+	14.8132i	−0.187492	+	0.577041i	0.812490	+	0.582975i	$0.198111\pi$
$660$		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	$0.904526\pi$
$662$	28.2773	−	14.4080i	1.09903	−	0.559984i
$663$	51.9401	+	32.5665i	2.01719	+	1.26478i
$664$	11.4851	−	3.73173i	0.445708	−	0.144819i
$665$		0			0
$666$	−17.4650	+	16.7627i	−0.676755	+	0.649542i
$667$	−3.25301	+	0.515226i	−0.125957	+	0.0199496i
$668$	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
$672$	−4.63420	+	1.86409i	−0.178768	+	0.0719088i
$673$	6.83769	−	13.4197i	0.263574	−	0.517292i	−0.720853	−	0.693088i	$-0.756250\pi$
$673$	6.83769	−	13.4197i	0.263574	−	0.517292i	0.984427	+	0.175796i	$0.0562498\pi$
$674$	−16.1131			−0.620652
$675$		0			0
$676$	−21.9835			−0.845520
$677$	10.5178	−	20.6424i	0.404233	−	0.793351i	−0.595719	−	0.803193i	$-0.703133\pi$
$677$	10.5178	−	20.6424i	0.404233	−	0.793351i	0.999952	+	0.00984177i	$0.00313278\pi$
$678$	7.42791	−	2.98785i	0.285267	−	0.114748i
$679$	−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
$683$	4.28854	−	0.679239i	0.164097	−	0.0259903i	−0.0738455	−	0.997270i	$-0.523527\pi$
$683$	4.28854	−	0.679239i	0.164097	−	0.0259903i	0.237942	+	0.971279i	$0.423527\pi$
$684$	11.2215	−	10.7703i	0.429065	−	0.411812i
$685$		0			0
$686$	15.5874	−	5.06466i	0.595130	−	0.193370i
$687$	−25.6732	−	16.0971i	−0.979495	−	0.614144i
$688$	−3.91618	+	1.99539i	−0.149303	+	0.0760736i
$689$	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	$0.909741\pi$
$692$	1.06212	+	6.70597i	0.0403758	+	0.254923i
$693$	6.86790	+	22.7124i	0.260890	+	0.862772i
$694$	14.0633	−	19.3564i	0.533834	−	0.734759i
$695$		0			0
$696$	1.96968	−	4.62058i	0.0746603	−	0.175143i
$697$	4.94780	−	31.2392i	0.187411	−	1.18327i
$698$	22.1821	+	11.3024i	0.839606	+	0.427801i
$699$	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	$-0.120405\pi$
$702$	−28.0188	−	12.6293i	−1.05750	−	0.476662i
$703$	−41.3208	−	6.54457i	−1.55844	−	0.246833i
$704$	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
$708$	3.92151	−	3.28032i	0.147379	−	0.123282i
$709$	21.2009	+	6.88858i	0.796216	+	0.258706i	0.678749	−	0.734371i	$-0.262523\pi$
$709$	21.2009	+	6.88858i	0.796216	+	0.258706i	0.117467	+	0.993077i	$0.462523\pi$
$710$		0			0
$711$	34.6910	+	6.22654i	1.30101	+	0.233514i
$712$	−0.590863	−	1.15963i	−0.0221435	−	0.0434591i
$713$	2.90979	+	5.71079i	0.108973	+	0.213871i
$714$	19.6451	−	22.5293i	0.735198	−	0.843138i
$715$		0			0
$716$	8.92277	+	2.89918i	0.333460	+	0.108348i
$717$	−6.28201	−	7.50992i	−0.234606	−	0.280463i
$718$	3.84337	+	3.84337i	0.143433	+	0.143433i
$719$	2.20624	+	1.60292i	0.0822787	+	0.0597790i	0.628164	−	0.778081i	$-0.283807\pi$
$719$	2.20624	+	1.60292i	0.0822787	+	0.0597790i	−0.545885	+	0.837860i	$0.683807\pi$
$720$		0			0
$721$	−15.0547	+	10.9379i	−0.560667	+	0.407348i
$722$	7.78310	+	1.23272i	0.289657	+	0.0458772i
$723$	1.66592	+	24.3596i	0.0619561	+	0.905942i
$724$		−	15.2068i		−	0.565155i
$725$		0			0
$726$	3.09489	+	5.16867i	0.114862	+	0.191827i
$727$	−17.3015	−	8.81556i	−0.641677	−	0.326951i	0.102698	−	0.994713i	$-0.467253\pi$
$727$	−17.3015	−	8.81556i	−0.641677	−	0.326951i	−0.744375	+	0.667762i	$0.767253\pi$
$728$	−2.66836	+	16.8473i	−0.0988959	+	0.624404i
$729$	−17.8815	−	20.2300i	−0.662276	−	0.749260i
$730$		0			0
$731$	15.4599	−	21.2787i	0.571805	−	0.787022i
$732$	1.93519	−	7.71130i	0.0715266	−	0.285018i
$733$	−3.79691	−	23.9728i	−0.140242	−	0.885454i	−0.953026	−	0.302889i	$-0.902049\pi$
$733$	−3.79691	−	23.9728i	−0.140242	−	0.885454i	0.812784	−	0.582566i	$-0.197951\pi$
$734$	5.54024	−	17.0511i	0.204494	−	0.629368i
$735$		0			0
$736$	−0.350958	−	1.08014i	−0.0129365	−	0.0398144i
$737$	1.12775	−	0.574618i	0.0415412	−	0.0211663i
$738$	−0.325265	+	15.8527i	−0.0119732	+	0.583546i
$739$	6.13821	−	1.99443i	0.225798	−	0.0733662i	−0.193933	−	0.981015i	$-0.562124\pi$
$739$	6.13821	−	1.99443i	0.225798	−	0.0733662i	0.419731	+	0.907649i	$0.362124\pi$
$740$		0			0
$741$	−11.8688	−	51.7708i	−0.436010	−	1.90185i
$742$	15.2575	−	2.41654i	0.560119	−	0.0887141i
$743$	23.0403	−	23.0403i	0.845265	−	0.845265i	−0.144273	−	0.989538i	$-0.546084\pi$
$743$	23.0403	−	23.0403i	0.845265	−	0.845265i	0.989538	+	0.144273i	$0.0460842\pi$
$744$	−9.73619	−	0.866828i	−0.356946	−	0.0317794i
$745$		0			0
$746$	−15.0422	−	20.7038i	−0.550734	−	0.758020i
$747$	21.8913	−	28.8664i	0.800961	−	1.05617i
$748$	−7.45099	+	14.6234i	−0.272435	+	0.534684i
$749$	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	$0.305769\pi$
$752$	−2.10742	+	4.13604i	−0.0768497	+	0.150826i
$753$	−11.1941	−	27.8290i	−0.407936	−	1.01414i
$754$	−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	−0.813158	−	0.582043i	$-0.802254\pi$
$757$	−6.35882	+	6.35882i	−0.231115	+	0.231115i	0.582043	+	0.813158i	$0.302254\pi$
$758$	−9.60713	+	1.52162i	−0.348947	+	0.0552678i
$759$	−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	$0.454500\pi$
$762$	−11.5288	+	18.3872i	−0.417644	+	0.666098i
$763$	−7.17538	+	3.65604i	−0.259766	+	0.132358i
$764$	−3.98859	−	12.2756i	−0.144302	−	0.444116i
$765$		0			0
$766$	7.53686	−	23.1961i	0.272318	−	0.838108i
$767$	−2.73115	−	17.2438i	−0.0986161	−	0.622637i
$768$	1.67996	+	0.421593i	0.0606203	+	0.0152129i
$769$	−15.8011	+	21.7484i	−0.569803	+	0.784266i	−0.992531	−	0.121990i	$-0.961072\pi$
$769$	−15.8011	+	21.7484i	−0.569803	+	0.784266i	0.422728	+	0.906256i	$0.361072\pi$
$770$		0			0
$771$	−9.66471	−	4.11990i	−0.348066	−	0.148375i
$772$	−0.866006	+	5.46774i	−0.0311682	+	0.196788i
$773$	19.3692	+	9.86911i	0.696662	+	0.354967i	0.766191	−	0.642613i	$-0.222150\pi$
$773$	19.3692	+	9.86911i	0.696662	+	0.354967i	−0.0695289	+	0.997580i	$0.522150\pi$
$774$	−6.22592	+	11.6233i	−0.223786	+	0.417789i
$775$		0			0
$776$			6.60858i			0.237234i
$777$	40.2124	−	2.75007i	1.44261	−	0.0986582i
$778$	17.5587	+	2.78103i	0.629511	+	0.0997048i
$779$	−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
$783$	−3.06523	−	14.7536i	−0.109542	−	0.527251i
$784$	1.25241	+	0.406934i	0.0447291	+	0.0145334i
$785$		0			0
$786$	−15.5597	−	13.5677i	−0.554995	−	0.483943i
$787$	8.50770	+	16.6973i	0.303267	+	0.595194i	0.991472	−	0.130322i	$-0.0416010\pi$
$787$	8.50770	+	16.6973i	0.303267	+	0.595194i	−0.688205	+	0.725516i	$0.741601\pi$
$788$	−11.6128	−	22.7914i	−0.413689	−	0.811911i
$789$	31.1720	+	27.1813i	1.10975	+	0.967678i
$790$		0			0
$791$	−12.6782	−	4.11941i	−0.450786	−	0.146469i
$792$	2.70251	−	7.77127i	0.0960294	−	0.276140i
$793$	−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
$797$	−47.5041	−	7.52391i	−1.68268	−	0.266511i	−0.759398	−	0.650627i	$-0.774506\pi$
$797$	−47.5041	−	7.52391i	−1.68268	−	0.266511i	−0.923285	+	0.384116i	$0.874506\pi$
$798$	−25.8370	+	1.76696i	−0.914622	+	0.0625497i
$799$		−	27.7786i		−	0.982737i
$800$		0			0
$801$	−3.44181	−	1.84358i	−0.121610	−	0.0651397i
$802$	27.7494	+	14.1390i	0.979867	+	0.499267i
$803$	−3.89939	+	24.6198i	−0.137607	+	0.868814i
$804$	0.735318	+	0.313453i	0.0259327	+	0.0110546i
$805$		0			0
$806$	−19.6197	+	27.0043i	−0.691076	+	0.951184i
$807$	23.3478	+	5.85925i	0.821883	+	0.206255i
$808$	−0.552168	−	3.48625i	−0.0194252	−	0.122646i
$809$	5.14657	−	15.8395i	0.180944	−	0.556887i	−0.818911	−	0.573920i	$-0.805422\pi$
$809$	5.14657	−	15.8395i	0.180944	−	0.556887i	0.999855	+	0.0170329i	$0.00542201\pi$
$810$		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	$0.788544\pi$
$812$	−7.45167	+	3.79682i	−0.261502	+	0.133242i
$813$	−13.8333	+	22.0627i	−0.485156	+	0.773773i
$814$	−21.0475	+	6.83874i	−0.737714	+	0.239698i
$815$		0			0
$816$	−10.1029	+	2.31614i	−0.353671	+	0.0810812i
$817$	−22.5070	+	3.56475i	−0.787419	+	0.124715i
$818$	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	$0.875896\pi$
$822$	−12.8436	−	31.9297i	−0.447972	−	1.11367i
$823$	−4.76071	+	9.34343i	−0.165948	+	0.325691i	−0.958973	−	0.283498i	$-0.908505\pi$
$823$	−4.76071	+	9.34343i	−0.165948	+	0.325691i	0.793025	+	0.609189i	$0.208505\pi$
$824$	6.45260			0.224787
$825$		0			0
$826$	−8.51258			−0.296191
$827$	8.74498	−	17.1630i	0.304093	−	0.596815i	−0.687504	−	0.726180i	$-0.741294\pi$
$827$	8.74498	−	17.1630i	0.304093	−	0.596815i	0.991597	+	0.129365i	$0.0412938\pi$
$828$	−2.71480	−	2.05881i	−0.0943457	−	0.0715485i
$829$	18.5685	+	25.5573i	0.644909	+	0.887641i	0.998865	−	0.0476205i	$-0.0151638\pi$
$829$	18.5685	+	25.5573i	0.644909	+	0.887641i	−0.353956	+	0.935262i	$0.615164\pi$
$830$		0			0
$831$	−3.12939	−	0.278615i	−0.108557	−	0.00966503i
$832$	4.18231	−	4.18231i	0.144996	−	0.144996i
$833$	−7.78338	+	1.23277i	−0.269678	+	0.0427128i
$834$	−3.69489	−	16.1168i	−0.127943	−	0.558080i
$835$		0			0
$836$	13.5233	−	4.39399i	0.467713	−	0.151969i
$837$	−25.4625	+	14.5453i	−0.880112	+	0.502758i
$838$	3.06981	−	1.56415i	0.106045	−	0.0540325i
$839$	−12.7405	−	39.2113i	−0.439852	−	1.35373i	−0.888032	−	0.459782i	$-0.847927\pi$
$839$	−12.7405	−	39.2113i	−0.439852	−	1.35373i	0.448179	−	0.893944i	$-0.352073\pi$
$840$		0			0
$841$	−6.36272	+	19.5824i	−0.219404	+	0.675256i
$842$	2.11165	+	13.3324i	0.0727722	+	0.459466i
$843$	9.66199	−	38.5009i	0.332777	−	1.32604i
$844$	3.79170	−	5.21883i	0.130516	−	0.179640i
$845$		0			0
$846$	1.89589	+	13.7963i	0.0651820	+	0.474327i
$847$	1.56916	−	9.90726i	0.0539169	−	0.340418i
$848$	−4.77269	−	2.43181i	−0.163895	−	0.0835086i
$849$	−2.53151	−	4.22779i	−0.0868812	−	0.145097i
$850$		0			0
$851$			9.16443i			0.314153i
$852$	−0.676131	−	9.88661i	−0.0231639	−	0.338710i
$853$	18.4859	+	2.92787i	0.632944	+	0.100248i	0.464659	−	0.885490i	$-0.346177\pi$
$853$	18.4859	+	2.92787i	0.632944	+	0.100248i	0.168285	+	0.985738i	$0.446177\pi$
$854$	−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	$-0.0910842\pi$
$857$	19.8211	+	19.8211i	0.677078	+	0.677078i	−0.282260	+	0.959338i	$0.591084\pi$
$858$	−18.0272	−	21.5508i	−0.615437	−	0.735734i
$859$	−35.8942	−	11.6627i	−1.22469	−	0.397927i	−0.375904	−	0.926659i	$-0.622668\pi$
$859$	−35.8942	−	11.6627i	−1.22469	−	0.397927i	−0.848789	+	0.528732i	$0.822668\pi$
$860$		0			0
$861$	17.3508	−	19.8983i	0.591315	−	0.678131i
$862$	−12.6740	−	24.8742i	−0.431679	−	0.847217i
$863$	11.5537	+	22.6754i	0.393292	+	0.771879i	0.999730	−	0.0232522i	$-0.00740208\pi$
$863$	11.5537	+	22.6754i	0.393292	+	0.771879i	−0.606438	+	0.795131i	$0.707402\pi$
$864$	4.85953	−	1.83984i	0.165324	−	0.0625925i
$865$		0			0
$866$	−2.48379	−	0.807033i	−0.0844027	−	0.0274241i
$867$	24.9906	−	20.9045i	0.848725	−	0.709954i
$868$	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
$872$	2.75806	+	0.436834i	0.0933998	+	0.0147931i
$873$	11.3218	+	16.2750i	0.383185	+	0.550826i
$874$		−	5.88827i		−	0.199174i
$875$		0			0
$876$	−13.5061	+	8.08714i	−0.456327	+	0.273239i
$877$	−30.3080	−	15.4427i	−1.02343	−	0.521463i	−0.140061	−	0.990143i	$-0.544730\pi$
$877$	−30.3080	−	15.4427i	−1.02343	−	0.521463i	−0.883368	+	0.468679i	$0.844730\pi$
$878$	1.72542	−	10.8939i	0.0582302	−	0.367651i
$879$	−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	$0.915634\pi$
$882$	3.78150	−	1.14347i	0.127330	−	0.0385027i
$883$	4.58634	+	28.9570i	0.154343	+	0.974480i	0.936313	+	0.351165i	$0.114215\pi$
$883$	4.58634	+	28.9570i	0.154343	+	0.974480i	−0.781971	+	0.623315i	$0.785785\pi$
$884$	−10.9376	+	33.6624i	−0.367870	+	1.13219i
$885$		0			0
$886$	0.577651	+	1.77783i	0.0194065	+	0.0597272i
$887$	22.3947	−	11.4107i	0.751940	−	0.383133i	−0.0356241	−	0.999365i	$-0.511342\pi$
$887$	22.3947	−	11.4107i	0.751940	−	0.383133i	0.787564	+	0.616233i	$0.211342\pi$
$888$	−11.8413	−	7.42447i	−0.397367	−	0.249149i
$889$	34.3666	−	11.1664i	1.15262	−	0.374509i
$890$		0			0
$891$	−6.65822	−	23.7683i	−0.223059	−	0.796270i
$892$	−5.37230	+	0.850889i	−0.179878	+	0.0284899i
$893$	−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
$897$	−10.7944	+	4.34201i	−0.360415	+	0.144976i
$898$	9.31762	−	18.2869i	0.310933	−	0.610240i
$899$	−16.3657			−0.545828
$900$		0			0
$901$	32.0545			1.06789
$902$	−6.58084	+	12.9156i	−0.219118	+	0.430043i
$903$	20.3683	−	8.19310i	0.677816	−	0.272649i
$904$	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	−0.327952	+	0.944694i	$0.606358\pi$
$907$	−38.3276	+	38.3276i	−1.27265	+	1.27265i	−0.944694	+	0.327952i	$0.893642\pi$
$908$	19.3805	−	3.06957i	0.643164	−	0.101867i
$909$	−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	$0.235448\pi$
$912$	7.60818	+	4.77033i	0.251932	+	0.157961i
$913$	29.5101	−	15.0361i	0.976640	−	0.497623i
$914$	−4.82892	−	14.8619i	−0.159727	−	0.491588i
$915$		0			0
$916$	5.40628	−	16.6388i	0.178628	−	0.549762i
$917$	5.37713	+	33.9499i	0.177569	+	1.12112i
$918$	−20.9124	+	23.0122i	−0.690213	+	0.759515i
$919$	−8.11678	+	11.1718i	−0.267748	+	0.368523i	−0.921628	−	0.388075i	$-0.873140\pi$
$919$	−8.11678	+	11.1718i	−0.267748	+	0.368523i	0.653880	+	0.756598i	$0.273140\pi$
$920$		0			0
$921$	−22.2739	+	52.2515i	−0.733951	+	1.72175i
$922$	−2.18253	+	13.7799i	−0.0718777	+	0.453818i
$923$	−30.1518	−	15.3631i	−0.992457	−	0.505682i
$924$	−11.7535	+	7.03773i	−0.386661	+	0.231524i
$925$		0			0
$926$		−	32.9648i		−	1.08329i
$927$	15.8909	−	11.0546i	0.521926	−	0.363080i
$928$	2.86426	+	0.453655i	0.0940240	+	0.0148919i
$929$	0.637117	−	0.462892i	0.0209031	−	0.0151870i	−0.577285	−	0.816543i	$-0.695888\pi$
$929$	0.637117	−	0.462892i	0.0209031	−	0.0151870i	0.598188	+	0.801356i	$0.295888\pi$
$930$		0			0
$931$	5.52351	+	4.01306i	0.181026	+	0.131523i
$932$	20.5218	+	20.5218i	0.672214	+	0.672214i
$933$	13.7526	−	11.5039i	0.450239	−	0.376622i
$934$	3.51708	+	1.14277i	0.115082	+	0.0373925i
$935$		0			0
$936$	3.13471	−	17.4650i	0.102461	−	0.570860i
$937$	−1.89949	−	3.72797i	−0.0620538	−	0.121787i	0.857896	−	0.513823i	$-0.171771\pi$
$937$	−1.89949	−	3.72797i	−0.0620538	−	0.121787i	−0.919950	+	0.392035i	$0.871771\pi$
$938$	−0.604224	−	1.18586i	−0.0197286	−	0.0387196i
$939$	−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	$0.533399\pi$
$942$	−18.2496	−	21.8168i	−0.594604	−	0.710829i
$943$	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
$947$	−39.3427	−	6.23127i	−1.27847	−	0.202489i	−0.519980	−	0.854179i	$-0.674060\pi$
$947$	−39.3427	−	6.23127i	−1.27847	−	0.202489i	−0.758486	+	0.651690i	$0.774060\pi$
$948$	1.38839	+	20.3015i	0.0450929	+	0.659362i
$949$			53.7570i			1.74503i
$950$		0			0
$951$	16.7940	+	28.0470i	0.544581	+	0.909486i
$952$	15.3768	+	7.83489i	0.498366	+	0.253930i
$953$	−4.01002	+	25.3183i	−0.129897	+	0.820139i	0.833590	+	0.552384i	$0.186282\pi$
$953$	−4.01002	+	25.3183i	−0.129897	+	0.820139i	−0.963487	+	0.267755i	$0.913718\pi$
$954$	−15.9199	+	2.18771i	−0.515427	+	0.0708299i
$955$		0			0
$956$	3.32263	−	4.57321i	0.107462	−	0.147908i
$957$	3.35311	−	13.3614i	0.108391	−	0.431913i
$958$	−0.841500	−	5.31302i	−0.0271876	−	0.171656i
$959$	−17.7077	+	54.4987i	−0.571811	+	1.75985i
$960$		0			0
$961$	0.262130	+	0.806752i	0.00845579	+	0.0260243i
$962$	−42.5251	+	21.6676i	−1.37106	+	0.698592i
$963$	−37.1965	−	0.763197i	−1.19864	−	0.0245937i
$964$	−13.4069	+	4.35617i	−0.431807	+	0.140303i
$965$		0			0
$966$	1.26768	+	5.52955i	0.0407871	+	0.177910i
$967$	−3.74989	+	0.593924i	−0.120588	+	0.0190993i	−0.216437	−	0.976297i	$-0.569444\pi$
$967$	−3.74989	+	0.593924i	−0.120588	+	0.0190993i	0.0958486	+	0.995396i	$0.469444\pi$
$968$	−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	$0.813560\pi$
$972$	8.81562	−	12.8563i	0.282761	−	0.412366i
$973$	−12.4988	+	24.5303i	−0.400694	+	0.786406i
$974$	−4.19638			−0.134461
$975$		0			0
$976$	4.59018			0.146928
$977$	8.15001	−	15.9953i	0.260742	−	0.511735i	−0.723107	−	0.690736i	$-0.757287\pi$
$977$	8.15001	−	15.9953i	0.260742	−	0.511735i	0.983849	+	0.179001i	$0.0572867\pi$
$978$	4.23429	+	10.5266i	0.135398	+	0.336604i
$979$	−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
$983$	−39.4883	+	6.25433i	−1.25948	+	0.199482i	−0.750254	−	0.661150i	$-0.770069\pi$
$983$	−39.4883	+	6.25433i	−1.25948	+	0.199482i	−0.509227	+	0.860632i	$0.670069\pi$
$984$	−8.92300	+	2.04565i	−0.284455	+	0.0652131i
$985$		0			0
$986$	−16.5046	+	5.36268i	−0.525614	+	0.170782i
$987$	12.3173	−	19.6449i	0.392065	−	0.625303i
$988$	27.3230	−	13.9218i	0.869260	−	0.442910i
$989$	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	$0.876620\pi$
$992$	−0.882826	−	5.57395i	−0.0280298	−	0.176973i
$993$	53.3158	+	13.3799i	1.69193	+	0.424597i
$994$	−9.69837	+	13.3487i	−0.307614	+	0.423394i
$995$		0			0
$996$	19.2412	+	8.20219i	0.609681	+	0.259896i
$997$	1.77985	−	11.2375i	0.0563684	−	0.355896i	−0.943342	−	0.331823i	$-0.892336\pi$
$997$	1.77985	−	11.2375i	0.0563684	−	0.355896i	0.999710	−	0.0240735i	$-0.00766359\pi$
$998$	−9.13605	−	4.65505i	−0.289197	−	0.147353i
$999$	−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.b.143.2		80
3.2	odd	2	inner	750.2.l.b.143.7		80
5.2	odd	4		750.2.l.a.107.4		80
5.3	odd	4		750.2.l.c.107.7		80
5.4	even	2		150.2.l.a.83.9	yes	80
15.2	even	4		750.2.l.a.107.7		80
15.8	even	4		750.2.l.c.107.4		80
15.14	odd	2		150.2.l.a.83.4	yes	80
25.3	odd	20		150.2.l.a.47.4	✓	80
25.4	even	10		750.2.l.c.743.4		80
25.21	even	5		750.2.l.a.743.7		80
25.22	odd	20	inner	750.2.l.b.257.7		80
75.29	odd	10		750.2.l.c.743.7		80
75.47	even	20	inner	750.2.l.b.257.2		80
75.53	even	20		150.2.l.a.47.9	yes	80
75.71	odd	10		750.2.l.a.743.4		80

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

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)

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

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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