LMFDB - Embedded newform 750.2.l.c.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.c.743.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.891007 - 0.453990i) q^{2} +(1.11131 - 1.32853i) q^{3} +(0.587785 + 0.809017i) q^{4} +(-1.59332 + 0.679206i) q^{6} +(2.03922 + 2.03922i) q^{7} +(-0.156434 - 0.987688i) q^{8} +(-0.529988 - 2.95281i) q^{9} +O(q^{10})$	\(q+(-0.891007 - 0.453990i) q^{2} +(1.11131 - 1.32853i) q^{3} +(0.587785 + 0.809017i) q^{4} +(-1.59332 + 0.679206i) q^{6} +(2.03922 + 2.03922i) q^{7} +(-0.156434 - 0.987688i) q^{8} +(-0.529988 - 2.95281i) q^{9} +(-2.60836 + 0.847507i) q^{11} +(1.72801 + 0.118176i) 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} +(-0.868327 + 2.87159i) q^{18} +(3.04743 - 4.19443i) q^{19} +(4.97538 - 0.442965i) q^{21} +(2.70883 + 0.429036i) q^{22} +(0.515607 - 1.01194i) q^{23} +(-1.48602 - 0.889798i) q^{24} -5.91469i q^{26} +(-4.51188 - 2.57738i) 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} +(-1.77275 + 4.40713i) q^{33} +(-5.69132 - 1.84922i) q^{34} +(2.07736 - 2.16439i) q^{36} +(7.18975 - 3.66336i) q^{37} +(-4.61952 + 2.35376i) q^{38} +(9.98549 + 2.28924i) q^{39} +(-5.02666 - 1.63326i) q^{41} +(-4.63420 - 1.86409i) 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} +(0.920095 + 1.46746i) q^{48} +1.31687i q^{49} +(5.32473 - 8.89266i) q^{51} +(-2.68521 + 5.27002i) q^{52} +(5.29057 + 0.837944i) q^{53} +(2.85001 + 4.34482i) q^{54} +(1.69511 - 2.33312i) q^{56} +(-2.18579 - 8.70992i) 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} +(4.94069 - 7.10221i) q^{63} +(-0.951057 + 0.309017i) q^{64} +(3.58033 - 3.12197i) q^{66} +(-0.0721944 - 0.455818i) q^{67} +(4.23147 + 4.23147i) q^{68} +(-0.771390 - 1.80957i) q^{69} +(3.36294 + 4.62869i) q^{71} +(-2.83355 + 0.985385i) q^{72} +(-8.09812 - 4.12620i) q^{73} -8.06924 q^{74} +5.18460 q^{76} +(-7.04728 - 3.59077i) q^{77} +(-7.85784 - 6.57304i) q^{78} +(-6.90557 - 9.50470i) q^{79} +(-8.43823 + 3.12991i) q^{81} +(3.73730 + 3.73730i) q^{82} +(-1.88912 - 11.9275i) q^{83} +(3.28282 + 3.76480i) q^{84} +(4.18011 - 1.35820i) q^{86} +(-0.342708 + 5.01118i) 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} +(9.48072 - 2.37923i) q^{93} +(2.72849 - 3.75545i) q^{94} +(-0.153600 - 1.72523i) 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
$3$	1.11131	−	1.32853i	0.641614	−	0.767028i
$3$	1.11131	−	1.32853i	0.641614	−	0.767028i
$4$	0.587785	+	0.809017i	0.293893	+	0.404508i
$5$		0			0
$5$		0			0
$6$	−1.59332	+	0.679206i	−0.650471	+	0.277285i
$7$	2.03922	+	2.03922i	0.770754	+	0.770754i	0.978238	−	0.207484i	$-0.0665276\pi$
$7$	2.03922	+	2.03922i	0.770754	+	0.770754i	−0.207484	+	0.978238i	$0.566528\pi$
$8$	−0.156434	−	0.987688i	−0.0553079	−	0.349201i
$9$	−0.529988	−	2.95281i	−0.176663	−	0.984271i
$10$		0			0
$11$	−2.60836	+	0.847507i	−0.786450	+	0.255533i	−0.674592	−	0.738191i	$-0.735680\pi$
$11$	−2.60836	+	0.847507i	−0.786450	+	0.255533i	−0.111858	+	0.993724i	$0.535680\pi$
$12$	1.72801	+	0.118176i	0.498835	+	0.0341146i
$13$	2.68521	+	5.27002i	0.744744	+	1.46164i	0.882071	+	0.471116i	$0.156149\pi$
$13$	2.68521	+	5.27002i	0.744744	+	1.46164i	−0.137328	+	0.990526i	$0.543851\pi$
$14$	−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	$0.191520\pi$
$18$	−0.868327	+	2.87159i	−0.204667	+	0.676839i
$19$	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
$21$	4.97538	−	0.442965i	1.08572	−	0.0966630i
$22$	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
$27$	−4.51188	−	2.57738i	−0.868313	−	0.496017i
$28$	−0.451141	+	2.84839i	−0.0852576	+	0.538296i
$29$	−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
$33$	−1.77275	+	4.40713i	−0.308596	+	0.767182i
$34$	−5.69132	−	1.84922i	−0.976053	−	0.317139i
$35$		0			0
$36$	2.07736	−	2.16439i	0.346226	−	0.360732i
$37$	7.18975	−	3.66336i	1.18199	−	0.602253i	0.251243	−	0.967924i	$-0.419161\pi$
$37$	7.18975	−	3.66336i	1.18199	−	0.602253i	0.930744	+	0.365671i	$0.119161\pi$
$38$	−4.61952	+	2.35376i	−0.749384	+	0.381830i
$39$	9.98549	+	2.28924i	1.59896	+	0.366571i
$40$		0			0
$41$	−5.02666	−	1.63326i	−0.785033	−	0.255073i	−0.111045	−	0.993815i	$-0.535420\pi$
$41$	−5.02666	−	1.63326i	−0.785033	−	0.255073i	−0.673988	+	0.738743i	$0.735420\pi$
$42$	−4.63420	−	1.86409i	−0.715072	−	0.287635i
$43$	−3.10789	+	3.10789i	−0.473950	+	0.473950i	−0.903190	−	0.429241i	$-0.858781\pi$
$43$	−3.10789	+	3.10789i	−0.473950	+	0.473950i	0.429241	+	0.903190i	$0.358781\pi$
$44$	−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	$0.940063\pi$
$48$	0.920095	+	1.46746i	0.132804	+	0.211809i
$49$			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	$0.430081\pi$
$54$	2.85001	+	4.34482i	0.387837	+	0.591255i
$55$		0			0
$56$	1.69511	−	2.33312i	0.226519	−	0.311777i
$57$	−2.18579	−	8.70992i	−0.289516	−	1.15366i
$58$	2.86426	−	0.453655i	0.376096	−	0.0595678i
$59$	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	$0.994939\pi$
$62$	−2.56206	−	5.02833i	−0.325382	−	0.638599i
$63$	4.94069	−	7.10221i	0.622468	−	0.894795i
$64$	−0.951057	+	0.309017i	−0.118882	+	0.0386271i
$65$		0			0
$66$	3.58033	−	3.12197i	0.440708	−	0.384287i
$67$	−0.0721944	−	0.455818i	−0.00881995	−	0.0556870i	0.982886	−	0.184216i	$-0.0589745\pi$
$67$	−0.0721944	−	0.455818i	−0.00881995	−	0.0556870i	−0.991706	+	0.128529i	$0.958975\pi$
$68$	4.23147	+	4.23147i	0.513141	+	0.513141i
$69$	−0.771390	−	1.80957i	−0.0928645	−	0.217847i
$70$		0			0
$71$	3.36294	+	4.62869i	0.399107	+	0.549324i	0.960520	−	0.278212i	$-0.0897418\pi$
$71$	3.36294	+	4.62869i	0.399107	+	0.549324i	−0.561412	+	0.827536i	$0.689742\pi$
$72$	−2.83355	+	0.985385i	−0.333937	+	0.116129i
$73$	−8.09812	−	4.12620i	−0.947814	−	0.482935i	−0.0894583	−	0.995991i	$-0.528514\pi$
$73$	−8.09812	−	4.12620i	−0.947814	−	0.482935i	−0.858356	+	0.513055i	$0.828514\pi$
$74$	−8.06924			−0.938031
$75$		0			0
$76$	5.18460			0.594715
$77$	−7.04728	−	3.59077i	−0.803113	−	0.409206i
$78$	−7.85784	−	6.57304i	−0.889725	−	0.744250i
$79$	−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
$81$	−8.43823	+	3.12991i	−0.937581	+	0.347768i
$82$	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	$-0.280617\pi$
$84$	3.28282	+	3.76480i	0.358185	+	0.410773i
$85$		0			0
$86$	4.18011	−	1.35820i	0.450753	−	0.146458i
$87$	−0.342708	+	5.01118i	−0.0367421	+	0.537255i
$88$	1.24511	+	2.44367i	0.132729	+	0.260496i
$89$	−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
$92$	1.12174	−	0.177666i	0.116950	−	0.0185230i
$93$	9.48072	−	2.37923i	0.983105	−	0.246715i
$94$	2.72849	−	3.75545i	0.281423	−	0.387345i
$95$		0			0
$96$	−0.153600	−	1.72523i	−0.0156767	−	0.176080i
$97$	6.52722	+	1.03381i	0.662738	+	0.104967i	0.478737	−	0.877959i	$-0.341095\pi$
$97$	6.52722	+	1.03381i	0.662738	+	0.104967i	0.184002	+	0.982926i	$0.441095\pi$
$98$	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	$0.0561896\pi$
$101$			3.52971i			0.351219i	−0.984460	+	0.175610i	$0.943810\pi$
$102$	−8.78155	+	5.50604i	−0.869503	+	0.545179i
$103$	−1.00941	+	6.37316i	−0.0994601	+	0.627966i	0.886722	+	0.462303i	$0.152977\pi$
$103$	−1.00941	+	6.37316i	−0.0994601	+	0.627966i	−0.986182	+	0.165664i	$0.947023\pi$
$104$	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	$0.0453874\pi$
$108$	−0.566874	−	5.16514i	−0.0545474	−	0.497016i
$109$	−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
$111$	3.12314	−	13.6229i	0.296435	−	1.29303i
$112$	−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	$0.280235\pi$
$114$	−2.00666	+	8.75292i	−0.187941	+	0.819786i
$115$		0			0
$116$	−2.75803	−	0.896139i	−0.256077	−	0.0832044i
$117$	14.1383	−	10.7220i	1.30708	−	0.991247i
$118$	−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
$123$	−7.75601	+	4.86302i	−0.699336	+	0.438484i
$124$			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	$0.337637\pi$
$127$	−5.68850	+	11.1643i	−0.504773	+	0.990672i	−0.993018	+	0.117966i	$0.962363\pi$
$128$	0.987688	+	0.156434i	0.0873001	+	0.0138270i
$129$	0.675105	+	7.58276i	0.0594397	+	0.667625i
$130$		0			0
$131$	−7.00579	+	9.64264i	−0.612099	+	0.842482i	−0.996748	−	0.0805811i	$-0.974322\pi$
$131$	−7.00579	+	9.64264i	−0.612099	+	0.842482i	0.384649	+	0.923063i	$0.374322\pi$
$132$	−4.60744	+	1.15626i	−0.401026	+	0.100639i
$133$	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	$0.527321\pi$
$138$	−0.134216	+	1.96255i	−0.0114252	+	0.167063i
$139$	−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
$141$	5.28411	+	6.05991i	0.445002	+	0.510336i
$142$	−0.895020	−	5.65093i	−0.0751084	−	0.474216i
$143$	−11.4704	−	11.4704i	−0.959201	−	0.959201i
$144$	2.97207	+	0.408421i	0.247672	+	0.0340351i
$145$		0			0
$146$	5.34223	+	7.35294i	0.442126	+	0.608534i
$147$	1.74950	+	1.46344i	0.144296	+	0.120703i
$148$	7.18975	+	3.66336i	0.590994	+	0.301126i
$149$	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	$0.649567\pi$
$152$	−4.61952	−	2.35376i	−0.374692	−	0.190915i
$153$	−5.89674	−	16.9566i	−0.476724	−	1.37086i
$154$	4.64900	+	6.39880i	0.374627	+	0.515630i
$155$		0			0
$156$	4.01729	+	9.42401i	0.321641	+	0.754524i
$157$	−11.6119	−	11.6119i	−0.926732	−	0.926732i	0.0707617	−	0.997493i	$-0.477457\pi$
$157$	−11.6119	−	11.6119i	−0.926732	−	0.926732i	−0.997493	+	0.0707617i	$0.977457\pi$
$158$	1.83786	+	11.6038i	0.146213	+	0.923150i
$159$	6.99269	−	6.09747i	0.554556	−	0.483561i
$160$		0			0
$161$	3.11500	−	1.01213i	0.245497	−	0.0797667i
$162$	8.93946	+	1.04210i	0.702351	+	0.0818753i
$163$	−2.97400	−	5.83680i	−0.232941	−	0.457173i	0.744715	−	0.667383i	$-0.232585\pi$
$163$	−2.97400	−	5.83680i	−0.232941	−	0.457173i	−0.977656	+	0.210209i	$0.932585\pi$
$164$	−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	$0.678454\pi$
$168$	−1.21583	−	4.84483i	−0.0938035	−	0.373787i
$169$	−12.9216	+	17.7850i	−0.993968	+	1.36808i
$170$		0			0
$171$	−14.0005	−	6.77551i	−1.07064	−	0.518136i
$172$	−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
$177$	−2.71590	−	4.33158i	−0.204140	−	0.325581i
$178$	−0.203597	+	1.28546i	−0.0152603	+	0.0963496i
$179$	−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
$183$	−7.37605	−	2.96699i	−0.545253	−	0.219326i
$184$	−1.08014	−	0.350958i	−0.0796287	−	0.0258729i
$185$		0			0
$186$	−9.52753	−	2.18425i	−0.698593	−	0.160157i
$187$	−14.6234	+	7.45099i	−1.06937	+	0.544871i
$188$	−4.13604	+	2.10742i	−0.301652	+	0.153699i
$189$	−3.94488	−	14.4566i	−0.286948	−	1.05156i
$190$		0			0
$191$	−12.2756	−	3.98859i	−0.888232	−	0.288604i	−0.170861	−	0.985295i	$-0.554655\pi$
$191$	−12.2756	−	3.98859i	−0.888232	−	0.288604i	−0.717371	+	0.696691i	$0.754655\pi$
$192$	−0.646378	+	1.60692i	−0.0466483	+	0.115970i
$193$	3.91447	−	3.91447i	0.281770	−	0.281770i	−0.552045	−	0.833815i	$-0.686152\pi$
$193$	3.91447	−	3.91447i	0.281770	−	0.281770i	0.833815	+	0.552045i	$0.186152\pi$
$194$	−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	$0.685135\pi$
$198$	−0.168782	−	8.22604i	−0.0119948	−	0.584599i
$199$			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
$204$	10.3241	−	0.919171i	0.722832	−	0.0643548i
$205$		0			0
$206$	3.79275	−	5.22027i	0.264253	−	0.363713i
$207$	−3.26133	−	0.986179i	−0.226678	−	0.0685442i
$208$	−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
$213$	9.88661	+	0.676131i	0.677420	+	0.0463278i
$214$	−11.7945	+	3.83226i	−0.806254	+	0.261968i
$215$		0			0
$216$	−1.83984	+	4.85953i	−0.125185	+	0.330649i
$217$	2.54598	+	16.0747i	0.172832	+	1.09122i
$218$	1.97456	+	1.97456i	0.133734	+	0.133734i
$219$	−14.4813	+	6.17313i	−0.978555	+	0.417141i
$220$		0			0
$221$	20.8045	+	28.6349i	1.39946	+	1.92619i
$222$	−8.96742	+	10.7202i	−0.601854	+	0.719495i
$223$	4.84642	+	2.46937i	0.324540	+	0.165362i	0.608668	−	0.793425i	$-0.291704\pi$
$223$	4.84642	+	2.46937i	0.324540	+	0.165362i	−0.284128	+	0.958786i	$0.591704\pi$
$224$	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	$0.875726\pi$
$228$	5.76169	−	6.88791i	0.381577	−	0.456163i
$229$	−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
$231$	−12.6022	+	5.37208i	−0.829161	+	0.353457i
$232$	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	$0.550414\pi$
$234$	−17.4650	+	3.13471i	−1.14172	+	0.204923i
$235$		0			0
$236$	2.80729	−	0.912145i	0.182739	−	0.0593756i
$237$	−20.3015	−	1.38839i	−1.31872	−	0.0901857i
$238$	−7.83489	−	15.3768i	−0.507861	−	0.996733i
$239$	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	$-0.0500137\pi$
$242$	3.43537	−	0.544110i	0.220834	−	0.0349767i
$243$	−5.21929	+	14.6887i	−0.334817	+	0.942283i
$244$	2.69804	−	3.71353i	0.172724	−	0.237734i
$245$		0			0
$246$	9.11842	−	0.811827i	0.581369	−	0.0517602i
$247$	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	$-0.815938\pi$
$251$		−	17.3182i		−	1.09311i	0.837422	−	0.546557i	$-0.184062\pi$
$252$	8.64987	−	0.177478i	0.544891	−	0.0111801i
$253$	−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	$0.310585\pi$
$258$	2.84098	−	7.06278i	0.176872	−	0.439710i
$259$	22.1319	+	7.19110i	1.37521	+	0.446833i
$260$		0			0
$261$	6.27666	+	6.02427i	0.388515	+	0.372893i
$262$	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	$0.613381\pi$
$264$	4.63019	+	1.06150i	0.284968	+	0.0653308i
$265$		0			0
$266$	−14.2201	−	4.62038i	−0.871889	−	0.283294i
$267$	−2.09139	−	0.841253i	−0.127991	−	0.0514839i
$268$	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	$0.149051\pi$
$272$	−0.936136	+	5.91053i	−0.0567616	+	0.358378i
$273$	15.6944	+	25.0309i	0.949867	+	1.51494i
$274$		−	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	−0.864943	−	0.501870i	$-0.832646\pi$
$277$	0.823495	−	1.61620i	0.0494790	−	0.0971080i	0.914422	+	0.404762i	$0.132646\pi$
$278$	9.42893	+	1.49340i	0.565509	+	0.0895679i
$279$	7.37512	−	15.2395i	0.441537	−	0.912364i
$280$		0			0
$281$	13.4707	−	18.5409i	0.803597	−	1.10606i	−0.188683	−	0.982038i	$-0.560422\pi$
$281$	13.4707	−	18.5409i	0.803597	−	1.10606i	0.992280	−	0.124018i	$-0.0395782\pi$
$282$	−1.95703	−	7.79835i	−0.116540	−	0.464385i
$283$	−2.81001	+	0.445062i	−0.167038	+	0.0264562i	−0.239393	−	0.970923i	$-0.576948\pi$
$283$	−2.81001	+	0.445062i	−0.167038	+	0.0264562i	0.0723553	+	0.997379i	$0.476948\pi$
$284$	−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
$288$	−2.46271	−	1.71320i	−0.145117	−	0.100951i
$289$	17.8900	−	5.81283i	1.05236	−	0.341931i
$290$		0			0
$291$	8.62720	−	7.52273i	0.505735	−	0.440990i
$292$	−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	$0.877578\pi$
$294$	−0.894424	−	2.09819i	−0.0521639	−	0.122369i
$295$		0			0
$296$	−4.74298	−	6.52816i	−0.275680	−	0.379441i
$297$	13.9530	+	2.89888i	0.809633	+	0.168210i
$298$	−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
$303$	4.68933	+	3.92259i	0.269395	+	0.225347i
$304$	3.04743	+	4.19443i	0.174782	+	0.240567i
$305$		0			0
$306$	−2.44408	+	17.7855i	−0.139719	+	1.01673i
$307$	−23.1889	−	23.1889i	−1.32346	−	1.32346i	−0.910955	−	0.412506i	$-0.864654\pi$
$307$	−23.1889	−	23.1889i	−1.32346	−	1.32346i	−0.412506	−	0.910955i	$-0.635346\pi$
$308$	−1.23730	−	7.81197i	−0.0705014	−	0.445129i
$309$	7.34518	+	8.42358i	0.417852	+	0.479201i
$310$		0			0
$311$	9.84506	−	3.19885i	0.558262	−	0.181390i	−0.0162770	−	0.999868i	$-0.505181\pi$
$311$	9.84506	−	3.19885i	0.558262	−	0.181390i	0.574539	+	0.818477i	$0.305181\pi$
$312$	0.698977	−	10.2207i	0.0395718	−	0.578631i
$313$	6.22820	+	12.2235i	0.352039	+	0.690915i	0.997330	−	0.0730212i	$-0.0232641\pi$
$313$	6.22820	+	12.2235i	0.352039	+	0.690915i	−0.645292	+	0.763936i	$0.723264\pi$
$314$	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	$0.272180\pi$
$318$	−8.99872	+	2.25827i	−0.504623	+	0.126638i
$319$	4.67490	−	6.43445i	0.261744	−	0.360260i
$320$		0			0
$321$	−1.90486	−	21.3953i	−0.106319	−	1.19417i
$322$	−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
$327$	−4.09779	+	2.56931i	−0.226608	+	0.142083i
$328$	−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
$333$	−14.6277	−	19.2885i	−0.801593	−	1.05700i
$334$	16.1658	+	5.25258i	0.884552	+	0.287408i
$335$		0			0
$336$	−1.11619	+	4.86875i	−0.0608932	+	0.265612i
$337$	14.3569	−	7.31518i	0.782068	−	0.398483i	−0.0169001	−	0.999857i	$-0.505380\pi$
$337$	14.3569	−	7.31518i	0.782068	−	0.398483i	0.798968	+	0.601374i	$0.205380\pi$
$338$	19.5874	−	9.98030i	1.06542	−	0.542857i
$339$	1.78909	−	7.80387i	0.0971698	−	0.423848i
$340$		0			0
$341$	−14.7201	−	4.78284i	−0.797137	−	0.259006i
$342$	9.39851	+	12.3931i	0.508213	+	0.670143i
$343$	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	$-0.171980\pi$
$348$	−4.25557	+	2.66824i	−0.228123	+	0.143033i
$349$			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	$0.401391\pi$
$354$	0.453389	+	5.09246i	0.0240974	+	0.270661i
$355$		0			0
$356$	0.764995	−	1.05293i	0.0405447	−	0.0558049i
$357$	28.9924	−	7.27579i	1.53444	−	0.385076i
$358$	9.26645	−	1.46766i	0.489747	−	0.0775683i
$359$	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
$362$	−6.90373	−	13.5493i	−0.362852	−	0.712137i
$363$	−0.411041	+	6.01037i	−0.0215740	+	0.315463i
$364$	−16.2225	+	5.27101i	−0.850290	+	0.276276i
$365$		0			0
$366$	5.22512	+	5.99226i	0.273122	+	0.313221i
$367$	2.80465	+	17.7079i	0.146401	+	0.924343i	0.946084	+	0.323920i	$0.105001\pi$
$367$	2.80465	+	17.7079i	0.146401	+	0.924343i	−0.799683	+	0.600422i	$0.794999\pi$
$368$	0.803077	+	0.803077i	0.0418633	+	0.0418633i
$369$	−2.15865	+	15.7084i	−0.112375	+	0.817747i
$370$		0			0
$371$	9.07990	+	12.4974i	0.471405	+	0.648833i
$372$	7.49747	+	6.27159i	0.388726	+	0.325167i
$373$	−22.8020	−	11.6182i	−1.18064	−	0.601568i	−0.250269	−	0.968176i	$-0.580519\pi$
$373$	−22.8020	−	11.6182i	−1.18064	−	0.601568i	−0.930376	+	0.366608i	$0.880519\pi$
$374$	16.4122			0.848656
$375$		0			0
$376$	4.64199			0.239392
$377$	−15.2829	−	7.78702i	−0.787109	−	0.401052i
$378$	−3.04824	+	14.6719i	−0.156785	+	0.754639i
$379$	−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
$381$	8.51045	+	19.9643i	0.436004	+	1.02280i
$382$	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	$0.735861\pi$
$384$	1.30545	−	1.13833i	0.0666187	−	0.0580900i
$385$		0			0
$386$	−5.26495	+	1.71069i	−0.267979	+	0.0870717i
$387$	10.8242	+	7.52989i	0.550224	+	0.382766i
$388$	3.00023	+	5.88829i	0.152314	+	0.298932i
$389$	−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
$392$	1.30065	−	0.206003i	0.0656929	−	0.0104047i
$393$	5.02496	+	20.0234i	0.253475	+	1.01004i
$394$	15.0352	−	20.6942i	0.757462	−	1.04256i
$395$		0			0
$396$	−3.58416	+	7.40608i	−0.180111	+	0.372170i
$397$	−19.0036	−	3.00987i	−0.953762	−	0.151061i	−0.339889	−	0.940466i	$-0.610389\pi$
$397$	−19.0036	−	3.00987i	−0.953762	−	0.151061i	−0.613873	+	0.789405i	$0.710389\pi$
$398$	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	$0.283577\pi$
$401$			31.1439i			1.55525i	−0.628726	+	0.777627i	$0.716423\pi$
$402$	0.424623	+	0.677230i	0.0211783	+	0.0337772i
$403$	−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
$408$	−9.61614	−	3.86806i	−0.476070	−	0.191498i
$409$	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
$411$	33.5457	+	7.69057i	1.65469	+	0.379348i
$412$	−5.74931	+	2.92942i	−0.283248	+	0.144322i
$413$	7.58476	−	3.86463i	0.373222	−	0.190166i
$414$	2.45815	+	2.35930i	0.120811	+	0.115953i
$415$		0			0
$416$	5.62520	+	1.82774i	0.275798	+	0.0896122i
$417$	−6.17063	+	15.3404i	−0.302177	+	0.751223i
$418$	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	$0.193308\pi$
$422$	1.00913	−	6.37141i	0.0491238	−	0.310156i
$423$	13.9230	−	0.285673i	0.676962	−	0.0138899i
$424$		−	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
$429$	−27.9859	+	2.49162i	−1.35117	+	0.120297i
$430$		0			0
$431$	16.4092	−	22.5853i	0.790401	−	1.08789i	−0.203657	−	0.979042i	$-0.565283\pi$
$431$	16.4092	−	22.5853i	0.790401	−	1.08789i	0.994058	−	0.108852i	$-0.0347173\pi$
$432$	3.84548	−	3.49460i	0.185016	−	0.168134i
$433$	−2.57946	+	0.408546i	−0.123961	+	0.0196335i	−0.218107	−	0.975925i	$-0.569988\pi$
$433$	−2.57946	+	0.408546i	−0.123961	+	0.0196335i	0.0941457	+	0.995558i	$0.469988\pi$
$434$	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
$438$	15.7055	+	1.07407i	0.750436	+	0.0513213i
$439$	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
$441$	3.88846	−	0.697923i	0.185165	−	0.0332344i
$442$	−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	$0.764140\pi$
$444$	12.8569	−	5.48068i	0.610162	−	0.260102i
$445$		0			0
$446$	−3.19712	−	4.40046i	−0.151388	−	0.208368i
$447$	13.3456	−	15.9542i	0.631224	−	0.754607i
$448$	−2.56957	−	1.30926i	−0.121401	−	0.0618568i
$449$	−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
$452$	4.11863	+	2.09855i	0.193724	+	0.0987075i
$453$	−12.3663	+	14.7835i	−0.581019	+	0.694588i
$454$	11.5336	+	15.8746i	0.541296	+	0.745031i
$455$		0			0
$456$	−8.26075	+	3.52142i	−0.386845	+	0.164905i
$457$	11.0498	+	11.0498i	0.516886	+	0.516886i	0.916628	−	0.399742i	$-0.130900\pi$
$457$	11.0498	+	11.0498i	0.516886	+	0.516886i	−0.399742	+	0.916628i	$0.630900\pi$
$458$	2.73683	+	17.2797i	0.127884	+	0.807427i
$459$	−29.0804	−	11.0100i	−1.35736	−	0.513901i
$460$		0			0
$461$	−13.2689	+	4.31131i	−0.617992	+	0.200798i	−0.601249	−	0.799062i	$-0.705330\pi$
$461$	−13.2689	+	4.31131i	−0.617992	+	0.200798i	−0.0167435	+	0.999860i	$0.505330\pi$
$462$	13.6675	+	0.934699i	0.635868	+	0.0434861i
$463$	−14.9657	−	29.3718i	−0.695515	−	1.36502i	−0.920531	−	0.390669i	$-0.872244\pi$
$463$	−14.9657	−	29.3718i	−0.695515	−	1.36502i	0.225017	−	0.974355i	$-0.427756\pi$
$464$	−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	$0.422731\pi$
$468$	16.9845	+	5.13588i	0.785110	+	0.237406i
$469$	0.782294	−	1.07673i	0.0361230	−	0.0497190i
$470$		0			0
$471$	−28.3312	+	2.52237i	−1.30543	+	0.116225i
$472$	−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
$477$	−0.329645	−	16.0662i	−0.0150934	−	0.735619i
$478$	0.884293	−	5.58321i	0.0404466	−	0.255370i
$479$	−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
$483$	2.11709	−	5.26316i	0.0963309	−	0.239482i
$484$	−3.30796	−	1.07482i	−0.150362	−	0.0488555i
$485$		0			0
$486$	11.3190	−	10.7183i	0.513439	−	0.486190i
$487$	3.73900	−	1.90512i	0.169430	−	0.0863291i	−0.367219	−	0.930135i	$-0.619690\pi$
$487$	3.73900	−	1.90512i	0.169430	−	0.0863291i	0.536649	+	0.843806i	$0.319690\pi$
$488$	−4.08988	+	2.08390i	−0.185140	+	0.0943336i
$489$	−11.0594	−	2.53544i	−0.500123	−	0.114656i
$490$		0			0
$491$	−30.0362	−	9.75934i	−1.35551	−	0.440433i	−0.460970	−	0.887416i	$-0.652499\pi$
$491$	−30.0362	−	9.75934i	−1.35551	−	0.440433i	−0.894543	+	0.446983i	$0.852499\pi$
$492$	−8.49313	−	3.41633i	−0.382900	−	0.154020i
$493$	−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
$498$	11.1112	+	17.7212i	0.497904	+	0.794106i
$499$		−	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	$0.545265\pi$
$504$	−7.78767	−	3.76883i	−0.346890	−	0.167877i
$505$		0			0
$506$	1.83085	−	2.51995i	0.0813911	−	0.112025i
$507$	9.26810	+	36.9314i	0.411611	+	1.64018i
$508$	−12.3757	+	1.96012i	−0.549084	+	0.0869664i
$509$	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
$512$	0.453990	+	0.891007i	0.0200637	+	0.0393773i
$513$	−24.5603	+	11.0704i	−1.08436	+	0.488770i
$514$	5.76888	−	1.87442i	0.254454	−	0.0826772i
$515$		0			0
$516$	−5.73777	+	5.00321i	−0.252591	+	0.220254i
$517$	−1.99158	−	12.5743i	−0.0875896	−	0.553019i
$518$	−16.4550	−	16.4550i	−0.722991	−	0.722991i
$519$	4.61151	+	10.8180i	0.202423	+	0.474856i
$520$		0			0
$521$	−24.0053	−	33.0404i	−1.05169	−	1.44753i	−0.887334	−	0.461127i	$-0.847445\pi$
$521$	−24.0053	−	33.0404i	−1.05169	−	1.44753i	−0.164357	−	0.986401i	$-0.552555\pi$
$522$	−2.85758	−	8.21721i	−0.125073	−	0.359657i
$523$	24.2703	+	12.3663i	1.06126	+	0.540741i	0.895334	−	0.445396i	$-0.146937\pi$
$523$	24.2703	+	12.3663i	1.06126	+	0.540741i	0.165931	+	0.986137i	$0.446937\pi$
$524$	−11.9190			−0.520682
$525$		0			0
$526$	23.8782			1.04114
$527$	30.0906	+	15.3319i	1.31077	+	0.667868i
$528$	−3.64362	−	3.04786i	−0.158568	−	0.132641i
$529$	12.7609	+	17.5639i	0.554822	+	0.763646i
$530$		0			0
$531$	−8.77284	−	1.20556i	−0.380709	−	0.0523170i
$532$	10.5726	+	10.5726i	0.458379	+	0.458379i
$533$	−4.89032	−	30.8763i	−0.211823	−	1.33740i
$534$	1.48152	+	1.69903i	0.0641116	+	0.0735243i
$535$		0			0
$536$	−0.438912	+	0.142611i	−0.0189581	+	0.00615987i
$537$	−1.10873	+	16.2122i	−0.0478451	+	0.699606i
$538$	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
$543$	25.5467	−	6.41107i	1.09631	−	0.275125i
$544$	3.51743	−	4.84132i	0.150808	−	0.207570i
$545$		0			0
$546$	−2.62000	−	29.4278i	−0.112126	−	1.25939i
$547$	−22.1803	−	3.51301i	−0.948360	−	0.150205i	−0.336953	−	0.941522i	$-0.609396\pi$
$547$	−22.1803	−	3.51301i	−0.948360	−	0.150205i	−0.611407	+	0.791316i	$0.709396\pi$
$548$	−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
$552$	−1.66662	+	1.04497i	−0.0709362	+	0.0444770i
$553$	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	$0.234116\pi$
$558$	−13.4899	+	10.2302i	−0.571071	+	0.433081i
$559$	−24.7240	−	8.03333i	−1.04572	−	0.339773i
$560$		0			0
$561$	−6.35223	+	27.7080i	−0.268191	+	1.16983i
$562$	−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	$0.879586\pi$
$564$	−1.79665	+	7.83686i	−0.0756525	+	0.329991i
$565$		0			0
$566$	2.70579	+	0.879165i	0.113733	+	0.0369541i
$567$	−23.5900	−	10.8248i	−0.990688	−	0.454600i
$568$	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	$0.260060\pi$
$572$	2.53761	−	16.0218i	0.106103	−	0.669907i
$573$	−18.9409	+	11.8760i	−0.791269	+	0.496126i
$574$			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	$-0.622268\pi$
$577$	14.3066	−	28.0783i	0.595591	−	1.16891i	0.970330	−	0.241783i	$-0.0777324\pi$
$578$	−18.5791	−	2.94264i	−0.772789	−	0.122398i
$579$	−0.850312	−	9.55068i	−0.0353377	−	0.396913i
$580$		0			0
$581$	20.4704	−	28.1751i	0.849256	−	1.16890i
$582$	−11.1021	+	2.78613i	−0.460198	+	0.115489i
$583$	−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	$0.775315\pi$
$588$	−0.155623	+	2.27556i	−0.00641777	+	0.0938427i
$589$	27.8269	−	9.04151i	1.14659	−	0.372549i
$590$		0			0
$591$	29.1177	+	33.3927i	1.19774	+	1.37359i
$592$	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	$0.581347\pi$
$594$	−11.1161	−	8.91744i	−0.456100	−	0.365887i
$595$		0			0
$596$	7.05865	+	9.71540i	0.289134	+	0.397958i
$597$	0.102075	+	0.0853849i	0.00417764	+	0.00349457i
$598$	−5.98529	−	3.04966i	−0.244757	−	0.124710i
$599$	−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	$0.769258\pi$
$602$	11.2939	+	5.75450i	0.460303	+	0.234536i
$603$	−1.30768	+	0.454755i	−0.0532530	+	0.0185190i
$604$	−6.54069	−	9.00249i	−0.266137	−	0.366306i
$605$		0			0
$606$	−2.39740	−	5.62397i	−0.0973877	−	0.228458i
$607$	−23.2173	−	23.2173i	−0.942362	−	0.942362i	0.0560654	−	0.998427i	$-0.482144\pi$
$607$	−23.2173	−	23.2173i	−0.942362	−	0.942362i	−0.998427	+	0.0560654i	$0.982144\pi$
$608$	−0.811051	−	5.12077i	−0.0328925	−	0.207675i
$609$	−10.9178	+	9.52007i	−0.442411	+	0.385773i
$610$		0			0
$611$	−26.1121	+	8.48435i	−1.05638	+	0.343240i
$612$	10.2521	−	14.7374i	0.414417	−	0.595723i
$613$	−9.97216	−	19.5715i	−0.402772	−	0.790484i	0.597161	−	0.802122i	$-0.296295\pi$
$613$	−9.97216	−	19.5715i	−0.402772	−	0.790484i	−0.999932	+	0.0116379i	$0.996295\pi$
$614$	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	$0.408876\pi$
$618$	−2.72038	−	10.8401i	−0.109430	−	0.436053i
$619$	−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
$621$	−4.93451	+	3.23682i	−0.198015	+	0.129889i
$622$	−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
$627$	13.0831	+	20.8661i	0.522487	+	0.833312i
$628$	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
$633$	10.3660	+	4.16968i	0.412011	+	0.165730i
$634$	−17.9501	−	5.83235i	−0.712891	−	0.231632i
$635$		0			0
$636$	9.04315	+	2.07320i	0.358584	+	0.0822077i
$637$	−6.93992	+	3.53606i	−0.274970	+	0.140104i
$638$	−7.08655	+	3.61078i	−0.280559	+	0.142952i
$639$	11.8853	−	12.3833i	0.470177	−	0.489875i
$640$		0			0
$641$	18.3395	+	5.95888i	0.724368	+	0.235362i	0.647916	−	0.761712i	$-0.275641\pi$
$641$	18.3395	+	5.95888i	0.724368	+	0.235362i	0.0764522	+	0.997073i	$0.475641\pi$
$642$	−8.01603	+	19.9281i	−0.316367	+	0.786501i
$643$	−2.50826	+	2.50826i	−0.0989163	+	0.0989163i	−0.754833	−	0.655917i	$-0.772282\pi$
$643$	−2.50826	+	2.50826i	−0.0989163	+	0.0989163i	0.655917	+	0.754833i	$0.272282\pi$
$644$	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	$-0.213257\pi$
$648$	4.41141	+	7.84471i	0.173296	+	0.308169i
$649$			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	$0.563868\pi$
$654$	4.81760	−	0.428918i	0.188383	−	0.0167720i
$655$		0			0
$656$	3.10665	−	4.27594i	0.121294	−	0.166947i
$657$	−7.89200	+	26.0991i	−0.307896	+	1.01822i
$658$	13.2222	−	2.09419i	0.515456	−	0.0816401i
$659$	−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	$0.904526\pi$
$662$	14.4080	+	28.2773i	0.559984	+	1.09903i
$663$	61.1625	+	4.18282i	2.37536	+	0.162447i
$664$	−11.4851	+	3.73173i	−0.445708	+	0.144819i
$665$		0			0
$666$	4.27660	+	23.8270i	0.165715	+	0.923277i
$667$	0.515226	+	3.25301i	0.0199496	+	0.125957i
$668$	−12.0192	−	12.0192i	−0.465037	−	0.465037i
$669$	8.66651	−	3.69438i	0.335067	−	0.142833i
$670$		0			0
$671$	7.39961	+	10.1847i	0.285659	+	0.393176i
$672$	3.20490	−	3.83135i	0.123632	−	0.147797i
$673$	13.4197	+	6.83769i	0.517292	+	0.263574i	0.693088	−	0.720853i	$-0.256250\pi$
$673$	13.4197	+	6.83769i	0.517292	+	0.263574i	−0.175796	+	0.984427i	$0.556250\pi$
$674$	−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	$0.503133\pi$
$678$	−5.13697	+	6.14107i	−0.197284	+	0.235846i
$679$	11.2023	+	15.4186i	0.429904	+	0.591712i
$680$		0			0
$681$	−31.2643	+	13.3274i	−1.19805	+	0.510708i
$682$	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	$0.976473\pi$
$684$	−2.74778	−	15.3092i	−0.105064	−	0.585361i
$685$		0			0
$686$	−15.5874	+	5.06466i	−0.595130	+	0.193370i
$687$	−30.2317	−	2.06751i	−1.15341	−	0.0788803i
$688$	−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
$693$	−6.86790	+	22.7124i	−0.260890	+	0.862772i
$694$	−14.0633	+	19.3564i	−0.533834	+	0.734759i
$695$		0			0
$696$	5.00310	−	0.445433i	0.189642	−	0.0168841i
$697$	−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	$0.120405\pi$
$701$			19.5558i			0.738612i	−0.929308	+	0.369306i	$0.879595\pi$
$702$	−15.2444	+	26.6864i	−0.575363	+	1.00721i
$703$	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
$708$	1.90795	−	4.74325i	0.0717053	−	0.178262i
$709$	−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
$711$	−24.4058	+	25.4282i	−0.915287	+	0.953634i
$712$	−1.15963	+	0.590863i	−0.0434591	+	0.0221435i
$713$	5.71079	−	2.90979i	0.213871	−	0.108973i
$714$	−29.1356	−	6.67952i	−1.09037	−	0.249975i
$715$		0			0
$716$	−8.92277	−	2.89918i	−0.333460	−	0.108348i
$717$	9.08361	+	3.65385i	0.339233	+	0.136455i
$718$	−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
$722$	−1.23272	+	7.78310i	−0.0458772	+	0.289657i
$723$	−12.9704	−	20.6865i	−0.482376	−	0.769339i
$724$			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	−0.994713	−	0.102698i	$-0.967253\pi$
$727$	−8.81556	+	17.3015i	−0.326951	+	0.641677i	0.667762	+	0.744375i	$0.267253\pi$
$728$	16.8473	+	2.66836i	0.624404	+	0.0988959i
$729$	13.7142	+	23.2577i	0.507934	+	0.861396i
$730$		0			0
$731$	−15.4599	+	21.2787i	−0.571805	+	0.787022i
$732$	−1.93519	−	7.71130i	−0.0715266	−	0.285018i
$733$	23.9728	−	3.79691i	0.885454	−	0.140242i	0.302889	−	0.953026i	$-0.402049\pi$
$733$	23.9728	−	3.79691i	0.885454	−	0.140242i	0.582566	+	0.812784i	$0.302049\pi$
$734$	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
$738$	9.05484	−	13.0163i	0.333313	−	0.479136i
$739$	−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
$741$	40.0322	−	34.9072i	1.47062	−	1.28235i
$742$	−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	$0.953916\pi$
$744$	−3.83305	−	8.99180i	−0.140526	−	0.329656i
$745$		0			0
$746$	15.0422	+	20.7038i	0.550734	+	0.758020i
$747$	−34.2184	+	11.8996i	−1.25198	+	0.435385i
$748$	−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
$753$	−23.0077	−	19.2458i	−0.838449	−	0.701357i
$754$	10.0819	+	13.8766i	0.367162	+	0.505355i
$755$		0			0
$756$	9.37689	−	11.6889i	0.341034	−	0.425120i
$757$	6.35882	+	6.35882i	0.231115	+	0.231115i	0.813158	−	0.582043i	$-0.197746\pi$
$757$	6.35882	+	6.35882i	0.231115	+	0.231115i	−0.582043	+	0.813158i	$0.697746\pi$
$758$	1.52162	+	9.60713i	0.0552678	+	0.348947i
$759$	3.54569	+	4.06626i	0.128700	+	0.147596i
$760$		0			0
$761$	8.94031	−	2.90488i	0.324086	−	0.105302i	−0.142456	−	0.989801i	$-0.545500\pi$
$761$	8.94031	−	2.90488i	0.324086	−	0.105302i	0.466541	+	0.884499i	$0.345500\pi$
$762$	1.48075	−	21.6520i	0.0536419	−	0.784370i
$763$	−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
$768$	−1.67996	+	0.421593i	−0.0606203	+	0.0152129i
$769$	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
$771$	0.931697	+	10.4648i	0.0335543	+	0.376881i
$772$	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
$777$	34.1490	−	21.4114i	1.22509	−	0.768130i
$778$	−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
$783$	14.9787	−	1.64391i	0.535296	−	0.0587487i
$784$	−1.25241	−	0.406934i	−0.0447291	−	0.0145334i
$785$		0			0
$786$	4.61315	−	20.1222i	0.164545	−	0.717736i
$787$	16.6973	−	8.50770i	0.595194	−	0.303267i	−0.130322	−	0.991472i	$-0.541601\pi$
$787$	16.6973	−	8.50770i	0.595194	−	0.303267i	0.725516	+	0.688205i	$0.241601\pi$
$788$	−22.7914	+	11.6128i	−0.811911	+	0.413689i
$789$	−9.24190	+	40.3125i	−0.329020	+	1.43516i
$790$		0			0
$791$	12.6782	+	4.11941i	0.450786	+	0.146469i
$792$	6.55580	−	4.97169i	0.232950	−	0.176661i
$793$	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	$-0.274506\pi$
$798$	−21.9412	+	13.7571i	−0.776710	+	0.486997i
$799$			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
$804$	−0.0708861	−	0.796191i	−0.00249996	−	0.0280795i
$805$		0			0
$806$	19.6197	−	27.0043i	0.691076	−	0.951184i
$807$	−23.3478	+	5.85925i	−0.821883	+	0.206255i
$808$	3.48625	−	0.552168i	0.122646	−	0.0194252i
$809$	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	$0.788544\pi$
$812$	−3.79682	−	7.45167i	−0.133242	−	0.261502i
$813$	1.77675	−	25.9801i	0.0623132	−	0.911163i
$814$	21.0475	−	6.83874i	0.737714	−	0.239698i
$815$		0			0
$816$	6.81198	+	7.81211i	0.238467	+	0.273478i
$817$	3.56475	+	22.5070i	0.124715	+	0.787419i
$818$	−11.0947	−	11.0947i	−0.387916	−	0.387916i
$819$	50.6956	+	6.96659i	1.77145	+	0.243432i
$820$		0			0
$821$	7.95552	+	10.9498i	0.277650	+	0.382152i	0.924954	−	0.380080i	$-0.124104\pi$
$821$	7.95552	+	10.9498i	0.277650	+	0.382152i	−0.647304	+	0.762232i	$0.724104\pi$
$822$	−26.3980	−	22.0818i	−0.920737	−	0.770191i
$823$	−9.34343	−	4.76071i	−0.325691	−	0.165948i	0.283498	−	0.958973i	$-0.408505\pi$
$823$	−9.34343	−	4.76071i	−0.325691	−	0.165948i	−0.609189	+	0.793025i	$0.708505\pi$
$824$	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	$0.541294\pi$
$828$	−1.11912	−	3.21813i	−0.0388923	−	0.111838i
$829$	−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
$831$	−1.23201	−	2.89013i	−0.0427381	−	0.100258i
$832$	−4.18231	−	4.18231i	−0.144996	−	0.144996i
$833$	1.23277	+	7.78338i	0.0427128	+	0.269678i
$834$	12.4625	−	10.8670i	0.431540	−	0.376293i
$835$		0			0
$836$	−13.5233	+	4.39399i	−0.467713	+	0.151969i
$837$	−12.0501	−	26.7338i	−0.416512	−	0.924057i
$838$	1.56415	+	3.06981i	0.0540325	+	0.106045i
$839$	−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
$842$	−13.3324	+	2.11165i	−0.459466	+	0.0727722i
$843$	−9.66199	−	38.5009i	−0.332777	−	1.32604i
$844$	−3.79170	+	5.21883i	−0.130516	+	0.179640i
$845$		0			0
$846$	−12.5352	−	6.06639i	−0.430970	−	0.208567i
$847$	−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
$852$	5.26420	+	8.39586i	0.180349	+	0.287637i
$853$	−2.92787	+	18.4859i	−0.100248	+	0.632944i	0.885490	+	0.464659i	$0.153823\pi$
$853$	−2.92787	+	18.4859i	−0.100248	+	0.632944i	−0.985738	+	0.168285i	$0.946177\pi$
$854$	−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	$0.408916\pi$
$858$	26.0668	+	10.4853i	0.889905	+	0.357961i
$859$	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
$861$	−25.7330	−	5.89946i	−0.876979	−	0.201053i
$862$	−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	$0.207402\pi$
$864$	−5.01287	+	1.36790i	−0.170541	+	0.0465369i
$865$		0			0
$866$	2.48379	+	0.807033i	0.0844027	+	0.0274241i
$867$	12.1588	−	30.2273i	0.412936	−	1.02657i
$868$	−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
$873$	−0.406698	−	19.8216i	−0.0137647	−	0.670858i
$874$			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	$0.344730\pi$
$877$	−15.4427	+	30.3080i	−0.521463	+	1.02343i	−0.990143	+	0.140061i	$0.955270\pi$
$878$	−10.8939	−	1.72542i	−0.367651	−	0.0582302i
$879$	−23.0433	+	2.05158i	−0.777232	+	0.0691981i
$880$		0			0
$881$	27.1879	−	37.4210i	0.915985	−	1.26074i	−0.0490965	−	0.998794i	$-0.515634\pi$
$881$	27.1879	−	37.4210i	0.915985	−	1.26074i	0.965081	−	0.261951i	$-0.0843658\pi$
$882$	−3.78150	−	1.14347i	−0.127330	−	0.0385027i
$883$	−28.9570	+	4.58634i	−0.974480	+	0.154343i	−0.623315	−	0.781971i	$-0.714215\pi$
$883$	−28.9570	+	4.58634i	−0.974480	+	0.154343i	−0.351165	+	0.936313i	$0.614215\pi$
$884$	−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	$0.711342\pi$
$888$	−13.9438	−	0.953595i	−0.467922	−	0.0320005i
$889$	−34.3666	+	11.1664i	−1.15262	+	0.374509i
$890$		0			0
$891$	19.3573	−	15.3154i	0.648494	−	0.513085i
$892$	0.850889	+	5.37230i	0.0284899	+	0.179878i
$893$	17.0179	+	17.0179i	0.569481	+	0.569481i
$894$	−19.1340	+	8.15651i	−0.639938	+	0.272795i
$895$		0			0
$896$	1.69511	+	2.33312i	0.0566297	+	0.0779441i
$897$	7.46515	−	8.92433i	0.249254	−	0.297975i
$898$	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
$903$	−14.0863	+	16.8396i	−0.468761	+	0.560388i
$904$	−2.71701	−	3.73964i	−0.0903664	−	0.124379i
$905$		0			0
$906$	17.7300	−	7.55799i	0.589040	−	0.251097i
$907$	38.3276	+	38.3276i	1.27265	+	1.27265i	0.944694	+	0.327952i	$0.106358\pi$
$907$	38.3276	+	38.3276i	1.27265	+	1.27265i	0.327952	+	0.944694i	$0.393642\pi$
$908$	−3.06957	−	19.3805i	−0.101867	−	0.643164i
$909$	10.4226	−	1.87070i	0.345695	−	0.0620473i
$910$		0			0
$911$	−28.3746	+	9.21947i	−0.940093	+	0.305455i	−0.738683	−	0.674053i	$-0.764552\pi$
$911$	−28.3746	+	9.21947i	−0.940093	+	0.305455i	−0.201409	+	0.979507i	$0.564552\pi$
$912$	8.95907	+	0.612698i	0.296665	+	0.0202885i
$913$	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
$918$	20.9124	+	23.0122i	0.690213	+	0.759515i
$919$	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
$921$	−56.5772	+	5.03715i	−1.86428	+	0.165980i
$922$	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
$927$	19.3537	−	0.397100i	0.635660	−	0.0130425i
$928$	−0.453655	+	2.86426i	−0.0148919	+	0.0940240i
$929$	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
$933$	6.69112	−	16.6344i	0.219057	−	0.544585i
$934$	−3.51708	−	1.14277i	−0.115082	−	0.0373925i
$935$		0			0
$936$	−12.8017	−	12.2869i	−0.418436	−	0.401611i
$937$	−3.72797	+	1.89949i	−0.121787	+	0.0620538i	−0.513823	−	0.857896i	$-0.671771\pi$
$937$	−3.72797	+	1.89949i	−0.121787	+	0.0620538i	0.392035	+	0.919950i	$0.371771\pi$
$938$	−1.18586	+	0.604224i	−0.0387196	+	0.0197286i
$939$	23.1608	+	5.30976i	0.755824	+	0.173277i
$940$		0			0
$941$	−12.1196	−	3.93788i	−0.395086	−	0.128371i	0.104734	−	0.994500i	$-0.466601\pi$
$941$	−12.1196	−	3.93788i	−0.395086	−	0.128371i	−0.499821	+	0.866129i	$0.666601\pi$
$942$	26.3884	+	10.6146i	0.859781	+	0.345844i
$943$	−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	$-0.174060\pi$
$948$	−10.8097	−	17.2403i	−0.351083	−	0.559940i
$949$		−	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	$0.413718\pi$
$954$	−7.00017	+	14.4647i	−0.226639	+	0.468312i
$955$		0			0
$956$	−3.32263	+	4.57321i	−0.107462	+	0.147908i
$957$	−3.35311	−	13.3614i	−0.108391	−	0.431913i
$958$	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
$963$	−30.5412	−	21.2461i	−0.984177	−	0.684647i
$964$	13.4069	−	4.35617i	0.431807	−	0.140303i
$965$		0			0
$966$	−4.27577	+	3.72837i	−0.137571	+	0.119958i
$967$	0.593924	+	3.74989i	0.0190993	+	0.120588i	0.995396	−	0.0958486i	$-0.0305565\pi$
$967$	0.593924	+	3.74989i	0.0190993	+	0.120588i	−0.976297	+	0.216437i	$0.930556\pi$
$968$	2.45946	+	2.45946i	0.0790499	+	0.0790499i
$969$	−21.0729	−	49.4340i	−0.676958	−	1.58805i
$970$		0			0
$971$	1.56008	+	2.14727i	0.0500655	+	0.0689092i	0.833316	−	0.552797i	$-0.186440\pi$
$971$	1.56008	+	2.14727i	0.0500655	+	0.0689092i	−0.783250	+	0.621707i	$0.786440\pi$
$972$	−14.9513	+	4.41133i	−0.479562	+	0.141494i
$973$	−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	$0.557287\pi$
$978$	8.70293	+	7.27995i	0.278289	+	0.232787i
$979$	2.09807	+	2.88774i	0.0670546	+	0.0922927i
$980$		0			0
$981$	−1.14049	+	8.29933i	−0.0364131	+	0.264977i
$982$	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	$0.729931\pi$
$984$	6.01646	+	6.89978i	0.191798	+	0.219957i
$985$		0			0
$986$	16.5046	−	5.36268i	0.525614	−	0.170782i
$987$	−1.58203	+	23.1330i	−0.0503566	+	0.736331i
$988$	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
$993$	−53.3158	+	13.3799i	−1.69193	+	0.424597i
$994$	9.69837	−	13.3487i	0.307614	−	0.423394i
$995$		0			0
$996$	−1.85489	−	20.8341i	−0.0587744	−	0.660153i
$997$	−11.2375	−	1.77985i	−0.355896	−	0.0563684i	−0.0240735	−	0.999710i	$-0.507664\pi$
$997$	−11.2375	−	1.77985i	−0.355896	−	0.0563684i	−0.331823	+	0.943342i	$0.607664\pi$
$998$	−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.c.107.4		80
3.2	odd	2	inner	750.2.l.c.107.7		80
5.2	odd	4		750.2.l.b.143.7		80
5.3	odd	4		150.2.l.a.83.4	yes	80
5.4	even	2		750.2.l.a.107.7		80
15.2	even	4		750.2.l.b.143.2		80
15.8	even	4		150.2.l.a.83.9	yes	80
15.14	odd	2		750.2.l.a.107.4		80
25.3	odd	20	inner	750.2.l.c.743.7		80
25.4	even	10		750.2.l.b.257.2		80
25.21	even	5		150.2.l.a.47.9	yes	80
25.22	odd	20		750.2.l.a.743.4		80
75.29	odd	10		750.2.l.b.257.7		80
75.47	even	20		750.2.l.a.743.7		80
75.53	even	20	inner	750.2.l.c.743.4		80
75.71	odd	10		150.2.l.a.47.4	✓	80

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.891007 - 0.453990i) q^{2} +(1.11131 - 1.32853i) q^{3} +(0.587785 + 0.809017i) q^{4} +(-1.59332 + 0.679206i) q^{6} +(2.03922 + 2.03922i) q^{7} +(-0.156434 - 0.987688i) q^{8} +(-0.529988 - 2.95281i) q^{9} +O(q^{10})\)	\(q+(-0.891007 - 0.453990i) q^{2} +(1.11131 - 1.32853i) q^{3} +(0.587785 + 0.809017i) q^{4} +(-1.59332 + 0.679206i) q^{6} +(2.03922 + 2.03922i) q^{7} +(-0.156434 - 0.987688i) q^{8} +(-0.529988 - 2.95281i) q^{9} +(-2.60836 + 0.847507i) q^{11} +(1.72801 + 0.118176i) 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} +(-0.868327 + 2.87159i) q^{18} +(3.04743 - 4.19443i) q^{19} +(4.97538 - 0.442965i) q^{21} +(2.70883 + 0.429036i) q^{22} +(0.515607 - 1.01194i) q^{23} +(-1.48602 - 0.889798i) q^{24} -5.91469i q^{26} +(-4.51188 - 2.57738i) 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} +(-1.77275 + 4.40713i) q^{33} +(-5.69132 - 1.84922i) q^{34} +(2.07736 - 2.16439i) q^{36} +(7.18975 - 3.66336i) q^{37} +(-4.61952 + 2.35376i) q^{38} +(9.98549 + 2.28924i) q^{39} +(-5.02666 - 1.63326i) q^{41} +(-4.63420 - 1.86409i) 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} +(0.920095 + 1.46746i) q^{48} +1.31687i q^{49} +(5.32473 - 8.89266i) q^{51} +(-2.68521 + 5.27002i) q^{52} +(5.29057 + 0.837944i) q^{53} +(2.85001 + 4.34482i) q^{54} +(1.69511 - 2.33312i) q^{56} +(-2.18579 - 8.70992i) 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} +(4.94069 - 7.10221i) q^{63} +(-0.951057 + 0.309017i) q^{64} +(3.58033 - 3.12197i) q^{66} +(-0.0721944 - 0.455818i) q^{67} +(4.23147 + 4.23147i) q^{68} +(-0.771390 - 1.80957i) q^{69} +(3.36294 + 4.62869i) q^{71} +(-2.83355 + 0.985385i) q^{72} +(-8.09812 - 4.12620i) q^{73} -8.06924 q^{74} +5.18460 q^{76} +(-7.04728 - 3.59077i) q^{77} +(-7.85784 - 6.57304i) q^{78} +(-6.90557 - 9.50470i) q^{79} +(-8.43823 + 3.12991i) q^{81} +(3.73730 + 3.73730i) q^{82} +(-1.88912 - 11.9275i) q^{83} +(3.28282 + 3.76480i) q^{84} +(4.18011 - 1.35820i) q^{86} +(-0.342708 + 5.01118i) 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} +(9.48072 - 2.37923i) q^{93} +(2.72849 - 3.75545i) q^{94} +(-0.153600 - 1.72523i) 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

Varieties

Fields

Representations

Groups

Database

Properties

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