LMFDB - Embedded newform 750.2.l.b.143.7

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			143.7
Character	$\chi$	$=$	750.143
Dual form			750.2.l.b.257.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.453990 - 0.891007i) q^{2} +(-1.32853 - 1.11131i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(-1.59332 + 0.679206i) q^{6} +(-2.03922 + 2.03922i) q^{7} +(-0.987688 + 0.156434i) q^{8} +(0.529988 + 2.95281i) q^{9} +O(q^{10})$	\(q+(0.453990 - 0.891007i) q^{2} +(-1.32853 - 1.11131i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(-1.59332 + 0.679206i) q^{6} +(-2.03922 + 2.03922i) q^{7} +(-0.987688 + 0.156434i) q^{8} +(0.529988 + 2.95281i) q^{9} +(-2.60836 + 0.847507i) q^{11} +(-0.118176 + 1.72801i) 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} +(2.87159 + 0.868327i) q^{18} +(-3.04743 + 4.19443i) q^{19} +(4.97538 - 0.442965i) q^{21} +(-0.429036 + 2.70883i) q^{22} +(-1.01194 - 0.515607i) q^{23} +(1.48602 + 0.889798i) q^{24} -5.91469i q^{26} +(2.57738 - 4.51188i) 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} +(4.40713 + 1.77275i) q^{33} +(5.69132 + 1.84922i) q^{34} +(2.07736 - 2.16439i) q^{36} +(3.66336 + 7.18975i) q^{37} +(2.35376 + 4.61952i) q^{38} +(-9.98549 - 2.28924i) q^{39} +(-5.02666 - 1.63326i) q^{41} +(1.86409 - 4.63420i) 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} +(1.46746 - 0.920095i) q^{48} -1.31687i q^{49} +(5.32473 - 8.89266i) q^{51} +(-5.27002 - 2.68521i) q^{52} +(0.837944 - 5.29057i) q^{53} +(-2.85001 - 4.34482i) q^{54} +(1.69511 - 2.33312i) q^{56} +(8.70992 - 2.18579i) 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} +(-7.10221 - 4.94069i) q^{63} +(0.951057 - 0.309017i) q^{64} +(3.58033 - 3.12197i) q^{66} +(0.455818 - 0.0721944i) q^{67} +(4.23147 - 4.23147i) q^{68} +(0.771390 + 1.80957i) q^{69} +(3.36294 + 4.62869i) q^{71} +(-0.985385 - 2.83355i) q^{72} +(-4.12620 + 8.09812i) q^{73} +8.06924 q^{74} +5.18460 q^{76} +(3.59077 - 7.04728i) q^{77} +(-6.57304 + 7.85784i) q^{78} +(6.90557 + 9.50470i) q^{79} +(-8.43823 + 3.12991i) q^{81} +(-3.73730 + 3.73730i) q^{82} +(-11.9275 + 1.88912i) q^{83} +(-3.28282 - 3.76480i) q^{84} +(4.18011 - 1.35820i) q^{86} +(-5.01118 - 0.342708i) 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} +(-2.37923 - 9.48072i) q^{93} +(-2.72849 + 3.75545i) q^{94} +(-0.153600 - 1.72523i) 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
$3$	−1.32853	−	1.11131i	−0.767028	−	0.641614i
$3$	−1.32853	−	1.11131i	−0.767028	−	0.641614i
$4$	−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	$-0.933472\pi$
$7$	−2.03922	+	2.03922i	−0.770754	+	0.770754i	0.207484	+	0.978238i	$0.433472\pi$
$8$	−0.987688	+	0.156434i	−0.349201	+	0.0553079i
$9$	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	$0.535680\pi$
$12$	−0.118176	+	1.72801i	−0.0341146	+	0.498835i
$13$	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	$0.208480\pi$
$17$	0.936136	+	5.91053i	0.227046	+	1.43351i	−0.566026	+	0.824387i	$0.691520\pi$
$18$	2.87159	+	0.868327i	0.676839	+	0.204667i
$19$	−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
$21$	4.97538	−	0.442965i	1.08572	−	0.0966630i
$22$	−0.429036	+	2.70883i	−0.0914707	+	0.577523i
$23$	−1.01194	−	0.515607i	−0.211003	−	0.107512i	0.345295	−	0.938494i	$-0.387779\pi$
$23$	−1.01194	−	0.515607i	−0.211003	−	0.107512i	−0.556298	+	0.830983i	$0.687779\pi$
$24$	1.48602	+	0.889798i	0.303333	+	0.181629i
$25$		0			0
$26$		−	5.91469i		−	1.15997i
$27$	2.57738	−	4.51188i	0.496017	−	0.868313i
$28$	2.84839	+	0.451141i	0.538296	+	0.0852576i
$29$	2.34612	−	1.70456i	0.435664	−	0.316528i	−0.348246	−	0.937403i	$-0.613223\pi$
$29$	2.34612	−	1.70456i	0.435664	−	0.316528i	0.783910	+	0.620875i	$0.213223\pi$
$30$		0			0
$31$	4.56563	+	3.31712i	0.820011	+	0.595773i	0.916716	−	0.399540i	$-0.130830\pi$
$31$	4.56563	+	3.31712i	0.820011	+	0.595773i	−0.0967046	+	0.995313i	$0.530830\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	4.40713	+	1.77275i	0.767182	+	0.308596i
$34$	5.69132	+	1.84922i	0.976053	+	0.317139i
$35$		0			0
$36$	2.07736	−	2.16439i	0.346226	−	0.360732i
$37$	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
$39$	−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	$0.735420\pi$
$42$	1.86409	−	4.63420i	0.287635	−	0.715072i
$43$	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	−0.187187	−	0.982324i	$-0.559937\pi$
$47$	−4.58484	−	0.726167i	−0.668768	−	0.105922i	−0.481581	+	0.876402i	$0.659937\pi$
$48$	1.46746	−	0.920095i	0.211809	−	0.132804i
$49$		−	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	$-0.830081\pi$
$53$	0.837944	−	5.29057i	0.115100	−	0.726715i	0.975972	−	0.217894i	$-0.0699187\pi$
$54$	−2.85001	−	4.34482i	−0.387837	−	0.591255i
$55$		0			0
$56$	1.69511	−	2.33312i	0.226519	−	0.311777i
$57$	8.70992	−	2.18579i	1.15366	−	0.289516i
$58$	−0.453655	−	2.86426i	−0.0595678	−	0.376096i
$59$	−0.912145	+	2.80729i	−0.118751	+	0.365478i	−0.992711	−	0.120520i	$-0.961544\pi$
$59$	−0.912145	+	2.80729i	−0.118751	+	0.365478i	0.873960	+	0.485998i	$0.161544\pi$
$60$		0			0
$61$	−1.41844	−	4.36552i	−0.181613	−	0.558947i	0.818261	−	0.574847i	$-0.194939\pi$
$61$	−1.41844	−	4.36552i	−0.181613	−	0.558947i	−0.999874	+	0.0159002i	$0.994939\pi$
$62$	5.02833	−	2.56206i	0.638599	−	0.325382i
$63$	−7.10221	−	4.94069i	−0.894795	−	0.622468i
$64$	0.951057	−	0.309017i	0.118882	−	0.0386271i
$65$		0			0
$66$	3.58033	−	3.12197i	0.440708	−	0.384287i
$67$	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
$69$	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	$0.689742\pi$
$72$	−0.985385	−	2.83355i	−0.116129	−	0.333937i
$73$	−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
$78$	−6.57304	+	7.85784i	−0.744250	+	0.889725i
$79$	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
$81$	−8.43823	+	3.12991i	−0.937581	+	0.347768i
$82$	−3.73730	+	3.73730i	−0.412716	+	0.412716i
$83$	−11.9275	+	1.88912i	−1.30921	+	0.207358i	−0.771747	−	0.635930i	$-0.780617\pi$
$83$	−11.9275	+	1.88912i	−1.30921	+	0.207358i	−0.537462	+	0.843288i	$0.680617\pi$
$84$	−3.28282	−	3.76480i	−0.358185	−	0.410773i
$85$		0			0
$86$	4.18011	−	1.35820i	0.450753	−	0.146458i
$87$	−5.01118	−	0.342708i	−0.537255	−	0.0367421i
$88$	2.44367	−	1.24511i	0.260496	−	0.132729i
$89$	0.402182	+	1.23779i	0.0426312	+	0.131205i	0.970107	−	0.242678i	$-0.0780260\pi$
$89$	0.402182	+	1.23779i	0.0426312	+	0.131205i	−0.927476	+	0.373884i	$0.878026\pi$
$90$		0			0
$91$	−5.27101	+	16.2225i	−0.552552	+	1.70058i
$92$	0.177666	+	1.12174i	0.0185230	+	0.116950i
$93$	−2.37923	−	9.48072i	−0.246715	−	0.983105i
$94$	−2.72849	+	3.75545i	−0.281423	+	0.387345i
$95$		0			0
$96$	−0.153600	−	1.72523i	−0.0156767	−	0.176080i
$97$	−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	$0.0561896\pi$
$101$			3.52971i			0.351219i	−0.984460	+	0.175610i	$0.943810\pi$
$102$	−5.50604	−	8.78155i	−0.545179	−	0.869503i
$103$	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	0.989851	−	0.142106i	$-0.0453874\pi$
$107$	8.76915	+	8.76915i	0.847745	+	0.847745i	−0.142106	+	0.989851i	$0.545387\pi$
$108$	−5.16514	+	0.566874i	−0.497016	+	0.0545474i
$109$	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
$111$	3.12314	−	13.6229i	0.296435	−	1.29303i
$112$	−1.30926	−	2.56957i	−0.123714	−	0.242802i
$113$	−2.09855	−	4.11863i	−0.197415	−	0.387449i	0.770984	−	0.636854i	$-0.219765\pi$
$113$	−2.09855	−	4.11863i	−0.197415	−	0.387449i	−0.968399	+	0.249406i	$0.919765\pi$
$114$	2.00666	−	8.75292i	0.187941	−	0.819786i
$115$		0			0
$116$	−2.75803	−	0.896139i	−0.256077	−	0.0832044i
$117$	10.7220	+	14.1383i	0.991247	+	1.30708i
$118$	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
$123$	4.86302	+	7.75601i	0.438484	+	0.699336i
$124$		−	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
$129$	−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	$0.374322\pi$
$132$	−1.15626	−	4.60744i	−0.100639	−	0.401026i
$133$	−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	−0.996319	−	0.0857255i	$-0.972679\pi$
$137$	−17.7044	+	9.02083i	−1.51259	+	0.770702i	−0.516268	+	0.856427i	$0.672679\pi$
$138$	1.96255	+	0.134216i	0.167063	+	0.0114252i
$139$	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
$141$	5.28411	+	6.05991i	0.445002	+	0.510336i
$142$	5.65093	−	0.895020i	0.474216	−	0.0751084i
$143$	−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
$147$	−1.46344	+	1.74950i	−0.120703	+	0.144296i
$148$	3.66336	−	7.18975i	0.301126	−	0.590994i
$149$	−12.0089			−0.983807			−0.491903	−	0.870650i	$-0.663699\pi$
$149$	−12.0089			−0.983807			−0.491903	+	0.870650i	$0.663699\pi$
$150$		0			0
$151$	−11.1277			−0.905558			−0.452779	−	0.891623i	$-0.649567\pi$
$151$	−11.1277			−0.905558			−0.452779	+	0.891623i	$0.649567\pi$
$152$	2.35376	−	4.61952i	0.190915	−	0.374692i
$153$	−16.9566	+	5.89674i	−1.37086	+	0.476724i
$154$	−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	$-0.522543\pi$
$157$	11.6119	−	11.6119i	0.926732	−	0.926732i	0.997493	+	0.0707617i	$0.0225430\pi$
$158$	11.6038	−	1.83786i	0.923150	−	0.146213i
$159$	−6.99269	+	6.09747i	−0.554556	+	0.483561i
$160$		0			0
$161$	3.11500	−	1.01213i	0.245497	−	0.0797667i
$162$	−1.04210	+	8.93946i	−0.0818753	+	0.702351i
$163$	−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	$-0.821546\pi$
$167$	−2.65903	−	16.7884i	−0.205762	−	1.29913i	0.641159	−	0.767408i	$-0.278454\pi$
$168$	−4.84483	+	1.21583i	−0.373787	+	0.0938035i
$169$	12.9216	−	17.7850i	0.993968	−	1.36808i
$170$		0			0
$171$	−14.0005	−	6.77551i	−1.07064	−	0.518136i
$172$	0.687565	−	4.34111i	0.0524263	−	0.331007i
$173$	6.04954	+	3.08240i	0.459938	+	0.234350i	0.668578	−	0.743642i	$-0.266903\pi$
$173$	6.04954	+	3.08240i	0.459938	+	0.234350i	−0.208639	+	0.977993i	$0.566903\pi$
$174$	−2.58038	+	4.30941i	−0.195618	+	0.326696i
$175$		0			0
$176$		−	2.74259i		−	0.206731i
$177$	4.33158	−	2.71590i	0.325581	−	0.204140i
$178$	1.28546	+	0.203597i	0.0963496	+	0.0152603i
$179$	7.59016	−	5.51457i	0.567315	−	0.412179i	−0.266814	−	0.963748i	$-0.585971\pi$
$179$	7.59016	−	5.51457i	0.567315	−	0.412179i	0.834129	+	0.551569i	$0.185971\pi$
$180$		0			0
$181$	12.3025	+	8.93831i	0.914440	+	0.664379i	0.942134	−	0.335237i	$-0.108816\pi$
$181$	12.3025	+	8.93831i	0.914440	+	0.664379i	−0.0276940	+	0.999616i	$0.508816\pi$
$182$	12.0614	+	12.0614i	0.894048	+	0.894048i
$183$	−2.96699	+	7.37605i	−0.219326	+	0.545253i
$184$	1.08014	+	0.350958i	0.0796287	+	0.0258729i
$185$		0			0
$186$	−9.52753	−	2.18425i	−0.698593	−	0.160157i
$187$	−7.45099	−	14.6234i	−0.544871	−	1.06937i
$188$	2.10742	+	4.13604i	0.153699	+	0.301652i
$189$	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	$0.754655\pi$
$192$	−1.60692	−	0.646378i	−0.115970	−	0.0466483i
$193$	−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	−0.835574	−	0.549378i	$-0.814865\pi$
$197$	−25.2645	−	4.00150i	−1.80002	−	0.285095i	−0.964445	+	0.264282i	$0.914865\pi$
$198$	−8.22604	+	0.168782i	−0.584599	+	0.0119948i
$199$		−	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
$204$	−10.3241	+	0.919171i	−0.722832	+	0.0643548i
$205$		0			0
$206$	3.79275	−	5.22027i	0.264253	−	0.363713i
$207$	0.986179	−	3.26133i	0.0685442	−	0.226678i
$208$	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
$213$	0.676131	−	9.88661i	0.0463278	−	0.677420i
$214$	11.7945	−	3.83226i	0.806254	−	0.261968i
$215$		0			0
$216$	−1.83984	+	4.85953i	−0.125185	+	0.330649i
$217$	−16.0747	+	2.54598i	−1.09122	+	0.172832i
$218$	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
$222$	−10.7202	−	8.96742i	−0.719495	−	0.601854i
$223$	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	$-0.624274\pi$
$227$	8.90823	−	17.4834i	0.591260	−	1.16041i	0.971835	−	0.235662i	$-0.0757260\pi$
$228$	−6.88791	−	5.76169i	−0.456163	−	0.381577i
$229$	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
$231$	−12.6022	+	5.37208i	−0.829161	+	0.353457i
$232$	−2.05059	+	2.05059i	−0.134628	+	0.134628i
$233$	28.6649	−	4.54007i	1.87790	−	0.297430i	0.890416	−	0.455148i	$-0.150414\pi$
$233$	28.6649	−	4.54007i	1.87790	−	0.297430i	0.987484	+	0.157718i	$0.0504138\pi$
$234$	17.4650	−	3.13471i	1.14172	−	0.204923i
$235$		0			0
$236$	2.80729	−	0.912145i	0.182739	−	0.0593756i
$237$	1.38839	−	20.3015i	0.0901857	−	1.31872i
$238$	−15.3768	+	7.83489i	−0.996733	+	0.507861i
$239$	−1.74681	−	5.37613i	−0.112992	−	0.347753i	0.878531	−	0.477685i	$-0.158524\pi$
$239$	−1.74681	−	5.37613i	−0.112992	−	0.347753i	−0.991523	+	0.129932i	$0.958524\pi$
$240$		0			0
$241$	4.35617	−	13.4069i	0.280605	−	0.863614i	−0.707076	−	0.707137i	$-0.749986\pi$
$241$	4.35617	−	13.4069i	0.280605	−	0.863614i	0.987682	−	0.156477i	$-0.0500137\pi$
$242$	0.544110	+	3.43537i	0.0349767	+	0.220834i
$243$	14.6887	+	5.21929i	0.942283	+	0.334817i
$244$	−2.69804	+	3.71353i	−0.172724	+	0.237734i
$245$		0			0
$246$	9.11842	−	0.811827i	0.581369	−	0.0517602i
$247$	−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	$-0.815938\pi$
$251$		−	17.3182i		−	1.09311i	0.837422	−	0.546557i	$-0.184062\pi$
$252$	0.177478	+	8.64987i	0.0111801	+	0.544891i
$253$	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	0.560563	−	0.828112i	$-0.310585\pi$
$257$	−4.28914	−	4.28914i	−0.267549	−	0.267549i	−0.828112	+	0.560563i	$0.810585\pi$
$258$	−7.06278	−	2.84098i	−0.439710	−	0.176872i
$259$	−22.1319	−	7.19110i	−1.37521	−	0.446833i
$260$		0			0
$261$	6.27666	+	6.02427i	0.388515	+	0.372893i
$262$	5.41110	+	10.6199i	0.334299	+	0.656098i
$263$	10.8405	+	21.2757i	0.668454	+	1.31191i	0.937230	+	0.348711i	$0.113381\pi$
$263$	10.8405	+	21.2757i	0.668454	+	1.31191i	−0.268777	+	0.963203i	$0.586619\pi$
$264$	−4.63019	−	1.06150i	−0.284968	−	0.0653308i
$265$		0			0
$266$	−14.2201	−	4.62038i	−0.871889	−	0.283294i
$267$	0.841253	−	2.09139i	0.0514839	−	0.127991i
$268$	−0.326329	−	0.326329i	−0.0199337	−	0.0199337i
$269$	11.2436	+	8.16896i	0.685535	+	0.498070i	0.875189	−	0.483781i	$-0.160737\pi$
$269$	11.2436	+	8.16896i	0.685535	+	0.498070i	−0.189654	+	0.981851i	$0.560737\pi$
$270$		0			0
$271$	12.1633	−	8.83716i	0.738868	−	0.536819i	−0.153488	−	0.988151i	$-0.549051\pi$
$271$	12.1633	−	8.83716i	0.738868	−	0.536819i	0.892357	+	0.451331i	$0.149051\pi$
$272$	−5.91053	−	0.936136i	−0.358378	−	0.0567616i
$273$	25.0309	−	15.6944i	1.51494	−	0.949867i
$274$			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
$279$	−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	$-0.0395782\pi$
$282$	7.79835	−	1.95703i	0.464385	−	0.116540i
$283$	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
$288$	−1.71320	+	2.46271i	−0.100951	+	0.145117i
$289$	−17.8900	+	5.81283i	−1.05236	+	0.341931i
$290$		0			0
$291$	8.62720	−	7.52273i	0.505735	−	0.440990i
$292$	8.97684	−	1.42179i	0.525330	−	0.0832041i
$293$	−9.44461	+	9.44461i	−0.551760	+	0.551760i	−0.926948	−	0.375189i	$-0.877578\pi$
$293$	−9.44461	+	9.44461i	−0.551760	+	0.551760i	0.375189	+	0.926948i	$0.377578\pi$
$294$	0.894424	+	2.09819i	0.0521639	+	0.122369i
$295$		0			0
$296$	−4.74298	−	6.52816i	−0.275680	−	0.379441i
$297$	−2.89888	+	13.9530i	−0.168210	+	0.809633i
$298$	−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
$303$	3.92259	−	4.68933i	0.225347	−	0.269395i
$304$	−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	0.412506	−	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
$309$	−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	$0.305181\pi$
$312$	10.2207	+	0.698977i	0.578631	+	0.0395718i
$313$	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	$0.127820\pi$
$317$	2.95253	+	18.6415i	0.165830	+	1.04701i	−0.754623	+	0.656159i	$0.772180\pi$
$318$	2.25827	+	8.99872i	0.126638	+	0.504623i
$319$	−4.67490	+	6.43445i	−0.261744	+	0.360260i
$320$		0			0
$321$	−1.90486	−	21.3953i	−0.106319	−	1.19417i
$322$	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
$327$	−2.56931	−	4.09779i	−0.142083	−	0.226608i
$328$	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
$333$	−19.2885	+	14.6277i	−1.05700	+	0.801593i
$334$	−16.1658	−	5.25258i	−0.884552	−	0.287408i
$335$		0			0
$336$	−1.11619	+	4.86875i	−0.0608932	+	0.265612i
$337$	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
$339$	−1.78909	+	7.80387i	−0.0971698	+	0.423848i
$340$		0			0
$341$	−14.7201	−	4.78284i	−0.797137	−	0.259006i
$342$	−12.3931	+	9.39851i	−0.670143	+	0.508213i
$343$	−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	0.754209	−	0.656634i	$-0.228020\pi$
$347$	23.6313	+	3.74283i	1.26859	+	0.200925i	0.514384	+	0.857560i	$0.328020\pi$
$348$	2.66824	+	4.25557i	0.143033	+	0.228123i
$349$		−	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	$-0.801391\pi$
$353$	2.64576	−	16.7047i	0.140820	−	0.889101i	0.952398	−	0.304857i	$-0.0986087\pi$
$354$	−0.453389	−	5.09246i	−0.0240974	−	0.270661i
$355$		0			0
$356$	0.764995	−	1.05293i	0.0405447	−	0.0558049i
$357$	7.27579	+	28.9924i	0.385076	+	1.53444i
$358$	−1.46766	−	9.26645i	−0.0775683	−	0.489747i
$359$	−1.67961	+	5.16932i	−0.0886466	+	0.272826i	−0.985546	−	0.169409i	$-0.945814\pi$
$359$	−1.67961	+	5.16932i	−0.0886466	+	0.272826i	0.896899	+	0.442235i	$0.145814\pi$
$360$		0			0
$361$	−2.43509	−	7.49444i	−0.128163	−	0.394444i
$362$	13.5493	−	6.90373i	0.712137	−	0.362852i
$363$	6.01037	+	0.411041i	0.315463	+	0.0215740i
$364$	16.2225	−	5.27101i	0.850290	−	0.276276i
$365$		0			0
$366$	5.22512	+	5.99226i	0.273122	+	0.313221i
$367$	−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
$369$	2.15865	−	15.7084i	0.112375	−	0.817747i
$370$		0			0
$371$	9.07990	+	12.4974i	0.471405	+	0.648833i
$372$	−6.27159	+	7.49747i	−0.325167	+	0.388726i
$373$	−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
$378$	14.6719	+	3.04824i	0.754639	+	0.156785i
$379$	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
$381$	8.51045	+	19.9643i	0.436004	+	1.02280i
$382$	−9.12687	+	9.12687i	−0.466971	+	0.466971i
$383$	24.0895	−	3.81540i	1.23092	−	0.194958i	0.493108	−	0.869968i	$-0.335861\pi$
$383$	24.0895	−	3.81540i	1.23092	−	0.194958i	0.737808	+	0.675010i	$0.235861\pi$
$384$	−1.30545	+	1.13833i	−0.0666187	+	0.0580900i
$385$		0			0
$386$	−5.26495	+	1.71069i	−0.267979	+	0.0870717i
$387$	−7.52989	+	10.8242i	−0.382766	+	0.550224i
$388$	5.88829	−	3.00023i	0.298932	−	0.152314i
$389$	5.49358	+	16.9075i	0.278536	+	0.857245i	0.988262	+	0.152767i	$0.0488186\pi$
$389$	5.49358	+	16.9075i	0.278536	+	0.857245i	−0.709726	+	0.704477i	$0.751181\pi$
$390$		0			0
$391$	2.10020	−	6.46376i	0.106212	−	0.326886i
$392$	0.206003	+	1.30065i	0.0104047	+	0.0656929i
$393$	20.0234	−	5.02496i	1.01004	−	0.253475i
$394$	−15.0352	+	20.6942i	−0.757462	+	1.04256i
$395$		0			0
$396$	−3.58416	+	7.40608i	−0.180111	+	0.372170i
$397$	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	$0.283577\pi$
$401$			31.1439i			1.55525i	−0.628726	+	0.777627i	$0.716423\pi$
$402$	−0.677230	+	0.424623i	−0.0337772	+	0.0211783i
$403$	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
$408$	−3.86806	+	9.61614i	−0.191498	+	0.476070i
$409$	−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
$411$	33.5457	+	7.69057i	1.65469	+	0.379348i
$412$	−2.92942	−	5.74931i	−0.144322	−	0.283248i
$413$	−3.86463	−	7.58476i	−0.190166	−	0.373222i
$414$	−2.45815	−	2.35930i	−0.120811	−	0.115953i
$415$		0			0
$416$	5.62520	+	1.82774i	0.275798	+	0.0896122i
$417$	−15.3404	−	6.17063i	−0.751223	−	0.302177i
$418$	−10.0545	−	10.0545i	−0.491783	−	0.491783i
$419$	2.78733	+	2.02511i	0.136170	+	0.0989333i	0.653785	−	0.756680i	$-0.273180\pi$
$419$	2.78733	+	2.02511i	0.136170	+	0.0989333i	−0.517615	+	0.855614i	$0.673180\pi$
$420$		0			0
$421$	10.9206	−	7.93429i	0.532238	−	0.386694i	−0.288956	−	0.957342i	$-0.593308\pi$
$421$	10.9206	−	7.93429i	0.532238	−	0.386694i	0.821194	+	0.570649i	$0.193308\pi$
$422$	6.37141	+	1.00913i	0.310156	+	0.0491238i
$423$	−0.285673	−	13.9230i	−0.0138899	−	0.676962i
$424$			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
$429$	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	$-0.0347173\pi$
$432$	3.49460	+	3.84548i	0.168134	+	0.185016i
$433$	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
$438$	1.07407	−	15.7055i	0.0513213	−	0.750436i
$439$	−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
$441$	3.88846	−	0.697923i	0.185165	−	0.0332344i
$442$	34.9589	−	5.53695i	1.66283	−	0.263366i
$443$	−1.32181	+	1.32181i	−0.0628009	+	0.0628009i	−0.737810	−	0.675009i	$-0.764140\pi$
$443$	−1.32181	+	1.32181i	−0.0628009	+	0.0628009i	0.675009	+	0.737810i	$0.264140\pi$
$444$	−12.8569	+	5.48068i	−0.610162	+	0.260102i
$445$		0			0
$446$	−3.19712	−	4.40046i	−0.151388	−	0.208368i
$447$	15.9542	+	13.3456i	0.754607	+	0.631224i
$448$	−1.30926	+	2.56957i	−0.0618568	+	0.121401i
$449$	20.5238			0.968579			0.484289	−	0.874908i	$-0.339078\pi$
$449$	20.5238			0.968579			0.484289	+	0.874908i	$0.339078\pi$
$450$		0			0
$451$	14.4955			0.682569
$452$	−2.09855	+	4.11863i	−0.0987075	+	0.193724i
$453$	14.7835	+	12.3663i	0.694588	+	0.581019i
$454$	−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	$-0.869100\pi$
$457$	−11.0498	+	11.0498i	−0.516886	+	0.516886i	0.399742	+	0.916628i	$0.369100\pi$
$458$	17.2797	−	2.73683i	0.807427	−	0.127884i
$459$	29.0804	+	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	$0.505330\pi$
$462$	−0.934699	+	13.6675i	−0.0434861	+	0.635868i
$463$	−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	0.997451	−	0.0713509i	$-0.0227310\pi$
$467$	0.578507	+	3.65255i	0.0267701	+	0.169020i	−0.970681	+	0.240371i	$0.922731\pi$
$468$	5.13588	−	16.9845i	0.237406	−	0.785110i
$469$	−0.782294	+	1.07673i	−0.0361230	+	0.0497190i
$470$		0			0
$471$	−28.3312	+	2.52237i	−1.30543	+	0.116225i
$472$	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
$477$	16.0662	−	0.329645i	0.735619	−	0.0150934i
$478$	−5.58321	−	0.884293i	−0.255370	−	0.0404466i
$479$	4.35190	−	3.16184i	0.198844	−	0.144468i	−0.483908	−	0.875119i	$-0.660783\pi$
$479$	4.35190	−	3.16184i	0.198844	−	0.144468i	0.682752	+	0.730651i	$0.260783\pi$
$480$		0			0
$481$	38.6120	+	28.0533i	1.76056	+	1.27912i
$482$	−9.96798	−	9.96798i	−0.454029	−	0.454029i
$483$	−5.26316	−	2.11709i	−0.239482	−	0.0963309i
$484$	3.30796	+	1.07482i	0.150362	+	0.0488555i
$485$		0			0
$486$	11.3190	−	10.7183i	0.513439	−	0.486190i
$487$	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
$489$	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	$0.852499\pi$
$492$	3.41633	−	8.49313i	0.154020	−	0.382900i
$493$	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
$498$	17.7212	−	11.1112i	0.794106	−	0.497904i
$499$			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	−0.985252	−	0.171108i	$-0.945265\pi$
$503$	0.104371	−	0.658974i	0.00465369	−	0.0293822i	0.989906	+	0.141726i	$0.0452652\pi$
$504$	7.78767	+	3.76883i	0.346890	+	0.167877i
$505$		0			0
$506$	1.83085	−	2.51995i	0.0813911	−	0.112025i
$507$	−36.9314	+	9.26810i	−1.64018	+	0.411611i
$508$	1.96012	+	12.3757i	0.0869664	+	0.549084i
$509$	−8.01814	+	24.6773i	−0.355398	+	1.09380i	0.600381	+	0.799714i	$0.295016\pi$
$509$	−8.01814	+	24.6773i	−0.355398	+	1.09380i	−0.955779	+	0.294087i	$0.904984\pi$
$510$		0			0
$511$	−8.09964	−	24.9281i	−0.358307	−	1.10276i
$512$	−0.891007	+	0.453990i	−0.0393773	+	0.0200637i
$513$	11.0704	+	24.5603i	0.488770	+	1.08436i
$514$	−5.76888	+	1.87442i	−0.254454	+	0.0826772i
$515$		0			0
$516$	−5.73777	+	5.00321i	−0.252591	+	0.220254i
$517$	12.5743	−	1.99158i	0.553019	−	0.0875896i
$518$	−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	$-0.552555\pi$
$522$	8.21721	−	2.85758i	0.359657	−	0.125073i
$523$	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
$528$	−3.04786	+	3.64362i	−0.132641	+	0.158568i
$529$	−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
$533$	−30.8763	+	4.89032i	−1.33740	+	0.211823i
$534$	−1.48152	−	1.69903i	−0.0641116	−	0.0735243i
$535$		0			0
$536$	−0.438912	+	0.142611i	−0.0189581	+	0.00615987i
$537$	−16.2122	−	1.10873i	−0.699606	−	0.0478451i
$538$	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
$543$	−6.41107	−	25.5467i	−0.275125	−	1.09631i
$544$	−3.51743	+	4.84132i	−0.150808	+	0.207570i
$545$		0			0
$546$	−2.62000	−	29.4278i	−0.112126	−	1.25939i
$547$	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
$552$	−1.04497	−	1.66662i	−0.0444770	−	0.0709362i
$553$	−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	0.741498	−	0.670956i	$-0.234116\pi$
$557$	1.66485	+	1.66485i	0.0705420	+	0.0705420i	−0.670956	+	0.741498i	$0.734116\pi$
$558$	10.2302	+	13.4899i	0.433081	+	0.571071i
$559$	24.7240	+	8.03333i	1.04572	+	0.339773i
$560$		0			0
$561$	−6.35223	+	27.7080i	−0.268191	+	1.16983i
$562$	−10.4045	−	20.4199i	−0.438886	−	0.861362i
$563$	21.4512	+	42.1004i	0.904062	+	1.77432i	0.534729	+	0.845023i	$0.320414\pi$
$563$	21.4512	+	42.1004i	0.904062	+	1.77432i	0.369332	+	0.929297i	$0.379586\pi$
$564$	1.79665	−	7.83686i	0.0756525	−	0.329991i
$565$		0			0
$566$	2.70579	+	0.879165i	0.113733	+	0.0369541i
$567$	10.8248	−	23.5900i	0.454600	−	0.990688i
$568$	−4.04562	−	4.04562i	−0.169750	−	0.169750i
$569$	−19.9798	−	14.5162i	−0.837599	−	0.608551i	0.0841003	−	0.996457i	$-0.473198\pi$
$569$	−19.9798	−	14.5162i	−0.837599	−	0.608551i	−0.921699	+	0.387906i	$0.873198\pi$
$570$		0			0
$571$	4.83866	−	3.51549i	0.202491	−	0.147119i	−0.481919	−	0.876216i	$-0.660060\pi$
$571$	4.83866	−	3.51549i	0.202491	−	0.147119i	0.684410	+	0.729097i	$0.260060\pi$
$572$	16.0218	+	2.53761i	0.669907	+	0.106103i
$573$	11.8760	+	18.9409i	0.496126	+	0.791269i
$574$		−	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
$579$	0.850312	+	9.55068i	0.0353377	+	0.396913i
$580$		0			0
$581$	20.4704	−	28.1751i	0.849256	−	1.16890i
$582$	−2.78613	−	11.1021i	−0.115489	−	0.460198i
$583$	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	−0.648696	−	0.761048i	$-0.724685\pi$
$587$	−10.0374	+	5.11433i	−0.414289	+	0.211091i	0.234407	+	0.972139i	$0.424685\pi$
$588$	2.27556	+	0.155623i	0.0938427	+	0.00641777i
$589$	−27.8269	+	9.04151i	−1.14659	+	0.372549i
$590$		0			0
$591$	29.1177	+	33.3927i	1.19774	+	1.37359i
$592$	−7.96990	+	1.26231i	−0.327561	+	0.0518805i
$593$	17.4049	−	17.4049i	0.714734	−	0.714734i	−0.252788	−	0.967522i	$-0.581347\pi$
$593$	17.4049	−	17.4049i	0.714734	−	0.714734i	0.967522	+	0.252788i	$0.0813475\pi$
$594$	11.1161	+	8.91744i	0.456100	+	0.365887i
$595$		0			0
$596$	7.05865	+	9.71540i	0.289134	+	0.397958i
$597$	−0.0853849	+	0.102075i	−0.00349457	+	0.00417764i
$598$	−3.04966	+	5.98529i	−0.124710	+	0.244757i
$599$	25.8531			1.05633			0.528165	−	0.849142i	$-0.322880\pi$
$599$	25.8531			1.05633			0.528165	+	0.849142i	$0.322880\pi$
$600$		0			0
$601$	−36.7027			−1.49714			−0.748568	−	0.663058i	$-0.769258\pi$
$601$	−36.7027			−1.49714			−0.748568	+	0.663058i	$0.769258\pi$
$602$	−5.75450	+	11.2939i	−0.234536	+	0.460303i
$603$	0.454755	+	1.30768i	0.0185190	+	0.0532530i
$604$	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	$-0.517856\pi$
$607$	23.2173	−	23.2173i	0.942362	−	0.942362i	0.998427	+	0.0560654i	$0.0178555\pi$
$608$	−5.12077	+	0.811051i	−0.207675	+	0.0328925i
$609$	10.9178	−	9.52007i	0.442411	−	0.385773i
$610$		0			0
$611$	−26.1121	+	8.48435i	−1.05638	+	0.343240i
$612$	14.7374	+	10.2521i	0.595723	+	0.414417i
$613$	−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	0.999611	−	0.0278814i	$-0.00887607\pi$
$617$	1.00125	+	6.32162i	0.0403086	+	0.254499i	−0.959303	+	0.282380i	$0.908876\pi$
$618$	−10.8401	+	2.72038i	−0.436053	+	0.109430i
$619$	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
$621$	−4.93451	+	3.23682i	−0.198015	+	0.129889i
$622$	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
$627$	−20.8661	+	13.0831i	−0.833312	+	0.522487i
$628$	−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
$633$	4.16968	−	10.3660i	0.165730	−	0.412011i
$634$	17.9501	+	5.83235i	0.712891	+	0.231632i
$635$		0			0
$636$	9.04315	+	2.07320i	0.358584	+	0.0822077i
$637$	−3.53606	−	6.93992i	−0.140104	−	0.274970i
$638$	3.61078	+	7.08655i	0.142952	+	0.280559i
$639$	−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	$0.475641\pi$
$642$	−19.9281	−	8.01603i	−0.786501	−	0.316367i
$643$	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	0.832789	−	0.553591i	$-0.186743\pi$
$647$	36.9778	+	5.85671i	1.45375	+	0.230251i	0.620960	+	0.783842i	$0.286743\pi$
$648$	7.84471	−	4.41141i	0.308169	−	0.173296i
$649$		−	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	−0.993564	−	0.113269i	$-0.963868\pi$
$653$	−0.348209	+	2.19851i	−0.0136265	+	0.0860342i	0.979938	+	0.199303i	$0.0638678\pi$
$654$	−4.81760	+	0.428918i	−0.188383	+	0.0167720i
$655$		0			0
$656$	3.10665	−	4.27594i	0.121294	−	0.166947i
$657$	−26.0991	−	7.89200i	−1.01822	−	0.307896i
$658$	−2.09419	−	13.2222i	−0.0816401	−	0.515456i
$659$	4.81311	−	14.8132i	0.187492	−	0.577041i	−0.812490	−	0.582975i	$-0.801889\pi$
$659$	4.81311	−	14.8132i	0.187492	−	0.577041i	0.999982	+	0.00593344i	$0.00188868\pi$
$660$		0			0
$661$	−0.225919	−	0.695307i	−0.00878723	−	0.0270443i	0.946567	−	0.322508i	$-0.104526\pi$
$661$	−0.225919	−	0.695307i	−0.00878723	−	0.0270443i	−0.955354	+	0.295464i	$0.904526\pi$
$662$	−28.2773	+	14.4080i	−1.09903	+	0.559984i
$663$	4.18282	−	61.1625i	0.162447	−	2.37536i
$664$	11.4851	−	3.73173i	0.445708	−	0.144819i
$665$		0			0
$666$	4.27660	+	23.8270i	0.165715	+	0.923277i
$667$	−3.25301	+	0.515226i	−0.125957	+	0.0199496i
$668$	−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
$672$	3.83135	+	3.20490i	0.147797	+	0.123632i
$673$	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	−0.999952	−	0.00984177i	$-0.996867\pi$
$677$	−10.5178	+	20.6424i	−0.404233	+	0.793351i	0.595719	+	0.803193i	$0.296867\pi$
$678$	6.14107	+	5.13697i	0.235846	+	0.197284i
$679$	−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
$683$	−4.28854	+	0.679239i	−0.164097	+	0.0259903i	−0.237942	−	0.971279i	$-0.576473\pi$
$683$	−4.28854	+	0.679239i	−0.164097	+	0.0259903i	0.0738455	+	0.997270i	$0.476473\pi$
$684$	2.74778	+	15.3092i	0.105064	+	0.585361i
$685$		0			0
$686$	−15.5874	+	5.06466i	−0.595130	+	0.193370i
$687$	2.06751	−	30.2317i	0.0788803	−	1.15341i
$688$	−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
$693$	22.7124	+	6.86790i	0.862772	+	0.260890i
$694$	14.0633	−	19.3564i	0.533834	−	0.734759i
$695$		0			0
$696$	5.00310	−	0.445433i	0.189642	−	0.0168841i
$697$	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	$0.120405\pi$
$701$			19.5558i			0.738612i	−0.929308	+	0.369306i	$0.879595\pi$
$702$	−26.6864	−	15.2444i	−1.00721	−	0.575363i
$703$	−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
$708$	−4.74325	−	1.90795i	−0.178262	−	0.0717053i
$709$	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
$711$	−24.4058	+	25.4282i	−0.915287	+	0.953634i
$712$	−0.590863	−	1.15963i	−0.0221435	−	0.0434591i
$713$	−2.90979	−	5.71079i	−0.108973	−	0.213871i
$714$	29.1356	+	6.67952i	1.09037	+	0.249975i
$715$		0			0
$716$	−8.92277	−	2.89918i	−0.333460	−	0.108348i
$717$	−3.65385	+	9.08361i	−0.136455	+	0.339233i
$718$	3.84337	+	3.84337i	0.143433	+	0.143433i
$719$	−2.20624	−	1.60292i	−0.0822787	−	0.0597790i	0.545885	−	0.837860i	$-0.316193\pi$
$719$	−2.20624	−	1.60292i	−0.0822787	−	0.0597790i	−0.628164	+	0.778081i	$0.716193\pi$
$720$		0			0
$721$	−15.0547	+	10.9379i	−0.560667	+	0.407348i
$722$	−7.78310	−	1.23272i	−0.289657	−	0.0458772i
$723$	−20.6865	+	12.9704i	−0.769339	+	0.482376i
$724$		−	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
$729$	−13.7142	−	23.2577i	−0.507934	−	0.861396i
$730$		0			0
$731$	−15.4599	+	21.2787i	−0.571805	+	0.787022i
$732$	7.71130	−	1.93519i	0.285018	−	0.0715266i
$733$	−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
$738$	−13.0163	−	9.05484i	−0.479136	−	0.333313i
$739$	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
$741$	40.0322	−	34.9072i	1.47062	−	1.28235i
$742$	15.2575	−	2.41654i	0.560119	−	0.0887141i
$743$	−23.0403	+	23.0403i	−0.845265	+	0.845265i	−0.989538	−	0.144273i	$-0.953916\pi$
$743$	−23.0403	+	23.0403i	−0.845265	+	0.845265i	0.144273	+	0.989538i	$0.453916\pi$
$744$	3.83305	+	8.99180i	0.140526	+	0.329656i
$745$		0			0
$746$	15.0422	+	20.7038i	0.550734	+	0.758020i
$747$	−11.8996	−	34.2184i	−0.435385	−	1.25198i
$748$	−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
$753$	−19.2458	+	23.0077i	−0.701357	+	0.838449i
$754$	−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	$-0.802254\pi$
$757$	−6.35882	+	6.35882i	−0.231115	+	0.231115i	0.582043	+	0.813158i	$0.302254\pi$
$758$	9.60713	−	1.52162i	0.348947	−	0.0552678i
$759$	−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	$0.345500\pi$
$762$	21.6520	+	1.48075i	0.784370	+	0.0536419i
$763$	−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
$768$	0.421593	+	1.67996i	0.0152129	+	0.0606203i
$769$	−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
$771$	0.931697	+	10.4648i	0.0335543	+	0.376881i
$772$	−0.866006	+	5.46774i	−0.0311682	+	0.196788i
$773$	−19.3692	−	9.86911i	−0.696662	−	0.354967i	0.0695289	−	0.997580i	$-0.477850\pi$
$773$	−19.3692	−	9.86911i	−0.696662	−	0.354967i	−0.766191	+	0.642613i	$0.777850\pi$
$774$	6.22592	+	11.6233i	0.223786	+	0.417789i
$775$		0			0
$776$		−	6.60858i		−	0.237234i
$777$	21.4114	+	34.1490i	0.768130	+	1.22509i
$778$	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
$783$	−1.64391	−	14.9787i	−0.0587487	−	0.535296i
$784$	1.25241	+	0.406934i	0.0447291	+	0.0145334i
$785$		0			0
$786$	4.61315	−	20.1222i	0.164545	−	0.717736i
$787$	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
$789$	9.24190	−	40.3125i	0.329020	−	1.43516i
$790$		0			0
$791$	12.6782	+	4.11941i	0.450786	+	0.146469i
$792$	4.97169	+	6.55580i	0.176661	+	0.232950i
$793$	−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	0.923285	−	0.384116i	$-0.125494\pi$
$797$	47.5041	+	7.52391i	1.68268	+	0.266511i	0.759398	+	0.650627i	$0.225494\pi$
$798$	13.7571	+	21.9412i	0.486997	+	0.776710i
$799$		−	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
$804$	0.0708861	+	0.796191i	0.00249996	+	0.0280795i
$805$		0			0
$806$	19.6197	−	27.0043i	0.691076	−	0.951184i
$807$	−5.85925	−	23.3478i	−0.206255	−	0.821883i
$808$	−0.552168	−	3.48625i	−0.0194252	−	0.122646i
$809$	−5.14657	+	15.8395i	−0.180944	+	0.556887i	−0.999855	−	0.0170329i	$-0.994578\pi$
$809$	−5.14657	+	15.8395i	−0.180944	+	0.556887i	0.818911	+	0.573920i	$0.194578\pi$
$810$		0			0
$811$	6.03759	+	18.5818i	0.212008	+	0.652495i	0.999352	+	0.0359809i	$0.0114556\pi$
$811$	6.03759	+	18.5818i	0.212008	+	0.652495i	−0.787344	+	0.616514i	$0.788544\pi$
$812$	7.45167	−	3.79682i	0.261502	−	0.133242i
$813$	−25.9801	−	1.77675i	−0.911163	−	0.0623132i
$814$	−21.0475	+	6.83874i	−0.737714	+	0.239698i
$815$		0			0
$816$	6.81198	+	7.81211i	0.238467	+	0.273478i
$817$	−22.5070	+	3.56475i	−0.787419	+	0.124715i
$818$	−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	$0.724104\pi$
$822$	22.0818	−	26.3980i	0.770191	−	0.920737i
$823$	−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	−0.991597	−	0.129365i	$-0.958706\pi$
$827$	−8.74498	+	17.1630i	−0.304093	+	0.596815i	0.687504	+	0.726180i	$0.258706\pi$
$828$	−3.21813	+	1.11912i	−0.111838	+	0.0388923i
$829$	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
$831$	−1.23201	−	2.89013i	−0.0427381	−	0.100258i
$832$	4.18231	−	4.18231i	0.144996	−	0.144996i
$833$	7.78338	−	1.23277i	0.269678	−	0.0427128i
$834$	−12.4625	+	10.8670i	−0.431540	+	0.376293i
$835$		0			0
$836$	−13.5233	+	4.39399i	−0.467713	+	0.151969i
$837$	26.7338	−	12.0501i	0.924057	−	0.416512i
$838$	3.06981	−	1.56415i	0.106045	−	0.0540325i
$839$	12.7405	+	39.2113i	0.439852	+	1.35373i	0.888032	+	0.459782i	$0.152073\pi$
$839$	12.7405	+	39.2113i	0.439852	+	1.35373i	−0.448179	+	0.893944i	$0.647927\pi$
$840$		0			0
$841$	−6.36272	+	19.5824i	−0.219404	+	0.675256i
$842$	−2.11165	−	13.3324i	−0.0727722	−	0.459466i
$843$	−38.5009	+	9.66199i	−1.32604	+	0.332777i
$844$	3.79170	−	5.21883i	0.130516	−	0.179640i
$845$		0			0
$846$	−12.5352	−	6.06639i	−0.430970	−	0.208567i
$847$	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
$852$	−8.39586	+	5.26420i	−0.287637	+	0.180349i
$853$	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	0.282260	−	0.959338i	$-0.408916\pi$
$857$	−19.8211	−	19.8211i	−0.677078	−	0.677078i	−0.959338	+	0.282260i	$0.908916\pi$
$858$	10.4853	−	26.0668i	0.357961	−	0.889905i
$859$	−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
$861$	−25.7330	−	5.89946i	−0.876979	−	0.201053i
$862$	−12.6740	−	24.8742i	−0.431679	−	0.847217i
$863$	−11.5537	−	22.6754i	−0.393292	−	0.771879i	0.606438	−	0.795131i	$-0.292598\pi$
$863$	−11.5537	−	22.6754i	−0.393292	−	0.771879i	−0.999730	+	0.0232522i	$0.992598\pi$
$864$	5.01287	−	1.36790i	0.170541	−	0.0465369i
$865$		0			0
$866$	2.48379	+	0.807033i	0.0844027	+	0.0274241i
$867$	30.2273	+	12.1588i	1.02657	+	0.412936i
$868$	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
$873$	−19.8216	+	0.406698i	−0.670858	+	0.0137647i
$874$		−	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
$879$	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	$-0.0843658\pi$
$882$	1.14347	−	3.78150i	0.0385027	−	0.127330i
$883$	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	−0.787564	−	0.616233i	$-0.788658\pi$
$887$	−22.3947	+	11.4107i	−0.751940	+	0.383133i	0.0356241	+	0.999365i	$0.488658\pi$
$888$	−0.953595	+	13.9438i	−0.0320005	+	0.467922i
$889$	34.3666	−	11.1664i	1.15262	−	0.374509i
$890$		0			0
$891$	19.3573	−	15.3154i	0.648494	−	0.513085i
$892$	−5.37230	+	0.850889i	−0.179878	+	0.0284899i
$893$	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
$897$	8.92433	+	7.46515i	0.297975	+	0.249254i
$898$	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
$903$	16.8396	+	14.0863i	0.560388	+	0.468761i
$904$	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	−0.327952	+	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
$909$	−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	$0.564552\pi$
$912$	−0.612698	+	8.95907i	−0.0202885	+	0.296665i
$913$	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
$918$	23.0122	−	20.9124i	0.759515	−	0.690213i
$919$	−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
$921$	−56.5772	+	5.03715i	−1.86428	+	0.165980i
$922$	−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
$927$	0.397100	+	19.3537i	0.0130425	+	0.635660i
$928$	2.86426	+	0.453655i	0.0940240	+	0.0148919i
$929$	−0.637117	+	0.462892i	−0.0209031	+	0.0151870i	−0.598188	−	0.801356i	$-0.704112\pi$
$929$	−0.637117	+	0.462892i	−0.0209031	+	0.0151870i	0.577285	+	0.816543i	$0.304112\pi$
$930$		0			0
$931$	5.52351	+	4.01306i	0.181026	+	0.131523i
$932$	−20.5218	−	20.5218i	−0.672214	−	0.672214i
$933$	−16.6344	−	6.69112i	−0.544585	−	0.219057i
$934$	3.51708	+	1.14277i	0.115082	+	0.0373925i
$935$		0			0
$936$	−12.8017	−	12.2869i	−0.418436	−	0.401611i
$937$	−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
$939$	−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	$0.666601\pi$
$942$	−10.6146	+	26.3884i	−0.345844	+	0.859781i
$943$	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	0.758486	−	0.651690i	$-0.225940\pi$
$947$	39.3427	+	6.23127i	1.27847	+	0.202489i	0.519980	+	0.854179i	$0.325940\pi$
$948$	−17.2403	+	10.8097i	−0.559940	+	0.351083i
$949$			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	$-0.813718\pi$
$953$	4.01002	−	25.3183i	0.129897	−	0.820139i	0.963487	−	0.267755i	$-0.0862819\pi$
$954$	7.00017	−	14.4647i	0.226639	−	0.468312i
$955$		0			0
$956$	−3.32263	+	4.57321i	−0.107462	+	0.147908i
$957$	13.3614	−	3.35311i	0.431913	−	0.108391i
$958$	−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
$963$	−21.2461	+	30.5412i	−0.684647	+	0.984177i
$964$	−13.4069	+	4.35617i	−0.431807	+	0.140303i
$965$		0			0
$966$	−4.27577	+	3.72837i	−0.137571	+	0.119958i
$967$	−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
$969$	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	$0.786440\pi$
$972$	−4.41133	−	14.9513i	−0.141494	−	0.479562i
$973$	−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	−0.983849	−	0.179001i	$-0.942713\pi$
$977$	−8.15001	+	15.9953i	−0.260742	+	0.511735i	0.723107	+	0.690736i	$0.242713\pi$
$978$	7.27995	−	8.70293i	0.232787	−	0.278289i
$979$	−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
$983$	39.4883	−	6.25433i	1.25948	−	0.199482i	0.509227	−	0.860632i	$-0.329931\pi$
$983$	39.4883	−	6.25433i	1.25948	−	0.199482i	0.750254	+	0.661150i	$0.229931\pi$
$984$	−6.01646	−	6.89978i	−0.191798	−	0.219957i
$985$		0			0
$986$	16.5046	−	5.36268i	0.525614	−	0.170782i
$987$	−23.1330	−	1.58203i	−0.736331	−	0.0503566i
$988$	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
$993$	13.3799	+	53.3158i	0.424597	+	1.69193i
$994$	−9.69837	+	13.3487i	−0.307614	+	0.423394i
$995$		0			0
$996$	−1.85489	−	20.8341i	−0.0587744	−	0.660153i
$997$	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.143.7		80
3.2	odd	2	inner	750.2.l.b.143.2		80
5.2	odd	4		750.2.l.a.107.7		80
5.3	odd	4		750.2.l.c.107.4		80
5.4	even	2		150.2.l.a.83.4	yes	80
15.2	even	4		750.2.l.a.107.4		80
15.8	even	4		750.2.l.c.107.7		80
15.14	odd	2		150.2.l.a.83.9	yes	80
25.3	odd	20		150.2.l.a.47.9	yes	80
25.4	even	10		750.2.l.c.743.7		80
25.21	even	5		750.2.l.a.743.4		80
25.22	odd	20	inner	750.2.l.b.257.2		80
75.29	odd	10		750.2.l.c.743.4		80
75.47	even	20	inner	750.2.l.b.257.7		80
75.53	even	20		150.2.l.a.47.4	✓	80
75.71	odd	10		750.2.l.a.743.7		80

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

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