LMFDB - Embedded newform 605.2.j.k.124.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [605,2,Mod(9,605)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(605, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 6]))

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

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

chi := DirichletCharacter("605.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.j (of order $10$, degree $4$, 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:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			124.6
Character	$\chi$	$=$	605.124
Dual form			605.2.j.k.444.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.193000 - 0.265641i) q^{2} +(0.914917 - 0.297274i) q^{3} +(0.584718 - 1.79958i) q^{4} +(-0.789281 + 2.09214i) q^{5} +(-0.255547 - 0.185666i) q^{6} +(-3.11241 - 1.01128i) q^{7} +(-1.21545 + 0.394924i) q^{8} +(-1.67835 + 1.21939i) q^{9} +O(q^{10})$	\(q+(-0.193000 - 0.265641i) q^{2} +(0.914917 - 0.297274i) q^{3} +(0.584718 - 1.79958i) q^{4} +(-0.789281 + 2.09214i) q^{5} +(-0.255547 - 0.185666i) q^{6} +(-3.11241 - 1.01128i) q^{7} +(-1.21545 + 0.394924i) q^{8} +(-1.67835 + 1.21939i) q^{9} +(0.708089 - 0.194116i) q^{10} -1.82028i q^{12} +(-3.06077 - 4.21278i) q^{13} +(0.332056 + 1.02196i) q^{14} +(-0.100188 + 2.14876i) q^{15} +(-2.72213 - 1.97774i) q^{16} +(-2.11658 + 2.91322i) q^{17} +(0.647842 + 0.210497i) q^{18} +(-1.54799 - 4.76423i) q^{19} +(3.30345 + 2.64368i) q^{20} -3.14823 q^{21} -5.84372i q^{23} +(-0.994636 + 0.722645i) q^{24} +(-3.75407 - 3.30257i) q^{25} +(-0.528362 + 1.62613i) q^{26} +(-2.86941 + 3.94940i) q^{27} +(-3.63977 + 5.00971i) q^{28} +(0.632843 - 1.94769i) q^{29} +(0.590136 - 0.388097i) q^{30} +(2.63491 - 1.91437i) q^{31} +3.66082i q^{32} +1.18237 q^{34} +(4.57232 - 5.71341i) q^{35} +(1.21303 + 3.73332i) q^{36} +(5.93174 + 1.92734i) q^{37} +(-0.966815 + 1.33071i) q^{38} +(-4.05270 - 2.94446i) q^{39} +(0.133098 - 2.85460i) q^{40} +(3.15369 + 9.70607i) q^{41} +(0.607607 + 0.836299i) q^{42} +0.596820i q^{43} +(-1.22645 - 4.47378i) q^{45} +(-1.55233 + 1.12784i) q^{46} +(0.914917 - 0.297274i) q^{47} +(-3.07846 - 1.00025i) q^{48} +(3.00130 + 2.18058i) q^{49} +(-0.152764 + 1.63463i) q^{50} +(-1.07047 + 3.29456i) q^{51} +(-9.37091 + 3.04479i) q^{52} +(0.231164 + 0.318170i) q^{53} +1.60292 q^{54} +4.18237 q^{56} +(-2.83257 - 3.89870i) q^{57} +(-0.639526 + 0.207795i) q^{58} +(0.162990 - 0.501632i) q^{59} +(3.80828 + 1.43672i) q^{60} +(4.30825 + 3.13012i) q^{61} +(-1.01707 - 0.330467i) q^{62} +(6.45688 - 2.09797i) q^{63} +(-4.47180 + 3.24895i) q^{64} +(11.2295 - 3.07847i) q^{65} +8.45057i q^{67} +(4.00496 + 5.51235i) q^{68} +(-1.73719 - 5.34652i) q^{69} +(-2.40017 - 0.111910i) q^{70} +(-10.1349 - 7.36345i) q^{71} +(1.55839 - 2.14493i) q^{72} +(-8.09851 - 2.63136i) q^{73} +(-0.632843 - 1.94769i) q^{74} +(-4.41643 - 1.90559i) q^{75} -9.47874 q^{76} +1.64484i q^{78} +(2.29142 - 1.66482i) q^{79} +(6.28624 - 4.13407i) q^{80} +(0.472007 - 1.45269i) q^{81} +(1.96967 - 2.71102i) q^{82} +(7.13612 - 9.82203i) q^{83} +(-1.84082 + 5.66548i) q^{84} +(-4.42428 - 6.72752i) q^{85} +(0.158540 - 0.115186i) q^{86} -1.97010i q^{87} -9.00000 q^{89} +(-0.951718 + 1.18923i) q^{90} +(5.26605 + 16.2072i) q^{91} +(-10.5162 - 3.41693i) q^{92} +(1.84163 - 2.53478i) q^{93} +(-0.255547 - 0.185666i) q^{94} +(11.1892 + 0.521708i) q^{95} +(1.08827 + 3.34934i) q^{96} +(-6.63855 - 9.13717i) q^{97} -1.21812i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 20 q^{4} + 6 q^{5} + 20 q^{9}+O(q^{10}) $ 48 * q + 20 * q^4 + 6 * q^5 + 20 * q^9	$ 48 q + 20 q^{4} + 6 q^{5} + 20 q^{9} + 32 q^{14} - 20 q^{15} - 36 q^{16} - 26 q^{20} + 10 q^{25} - 20 q^{26} - 8 q^{31} + 48 q^{34} - 92 q^{36} - 72 q^{45} + 4 q^{49} + 192 q^{56} + 32 q^{59} + 92 q^{60} - 28 q^{64} + 16 q^{69} + 12 q^{70} - 112 q^{71} - 36 q^{75} + 106 q^{80} + 20 q^{81} + 56 q^{86} - 432 q^{89} - 72 q^{91}+O(q^{100}) $ 48 * q + 20 * q^4 + 6 * q^5 + 20 * q^9 + 32 * q^14 - 20 * q^15 - 36 * q^16 - 26 * q^20 + 10 * q^25 - 20 * q^26 - 8 * q^31 + 48 * q^34 - 92 * q^36 - 72 * q^45 + 4 * q^49 + 192 * q^56 + 32 * q^59 + 92 * q^60 - 28 * q^64 + 16 * q^69 + 12 * q^70 - 112 * q^71 - 36 * q^75 + 106 * q^80 + 20 * q^81 + 56 * q^86 - 432 * q^89 - 72 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$-1$	$e\left(\frac{4}{5}\right)$

Coefficient data

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

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

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

$2$	−0.193000	−	0.265641i	−0.136471	−	0.187837i	0.735311	−	0.677729i	$-0.237036\pi$
$2$	−0.193000	−	0.265641i	−0.136471	−	0.187837i	−0.871783	+	0.489893i	$0.837036\pi$
$3$	0.914917	−	0.297274i	0.528227	−	0.171631i	−0.0327485	−	0.999464i	$-0.510426\pi$
$3$	0.914917	−	0.297274i	0.528227	−	0.171631i	0.560976	+	0.827832i	$0.310426\pi$
$4$	0.584718	−	1.79958i	0.292359	−	0.899788i
$5$	−0.789281	+	2.09214i	−0.352977	+	0.935632i
$5$	−0.789281	+	2.09214i	−0.352977	+	0.935632i
$6$	−0.255547	−	0.185666i	−0.104327	−	0.0757977i
$7$	−3.11241	−	1.01128i	−1.17638	−	0.382230i	−0.345360	−	0.938470i	$-0.612243\pi$
$7$	−3.11241	−	1.01128i	−1.17638	−	0.382230i	−0.831021	+	0.556240i	$0.812243\pi$
$8$	−1.21545	+	0.394924i	−0.429727	+	0.139627i
$9$	−1.67835	+	1.21939i	−0.559450	+	0.406464i
$10$	0.708089	−	0.194116i	0.223917	−	0.0613848i
$11$		0			0
$11$		0			0
$12$		−	1.82028i		−	0.525471i
$13$	−3.06077	−	4.21278i	−0.848904	−	1.16842i	−0.984103	−	0.177598i	$-0.943167\pi$
$13$	−3.06077	−	4.21278i	−0.848904	−	1.16842i	0.135199	−	0.990818i	$-0.456833\pi$
$14$	0.332056	+	1.02196i	0.0887457	+	0.273131i
$15$	−0.100188	+	2.14876i	−0.0258685	+	0.554808i
$16$	−2.72213	−	1.97774i	−0.680533	−	0.494436i
$17$	−2.11658	+	2.91322i	−0.513345	+	0.706559i	−0.984479	−	0.175503i	$-0.943845\pi$
$17$	−2.11658	+	2.91322i	−0.513345	+	0.706559i	0.471134	+	0.882062i	$0.343845\pi$
$18$	0.647842	+	0.210497i	0.152698	+	0.0496145i
$19$	−1.54799	−	4.76423i	−0.355134	−	1.09299i	−0.955932	−	0.293589i	$-0.905150\pi$
$19$	−1.54799	−	4.76423i	−0.355134	−	1.09299i	0.600798	−	0.799401i	$-0.294850\pi$
$20$	3.30345	+	2.64368i	0.738674	+	0.591145i
$21$	−3.14823			−0.687000
$22$		0			0
$23$		−	5.84372i		−	1.21850i	−0.792978	−	0.609250i	$-0.791470\pi$
$23$		−	5.84372i		−	1.21850i	0.792978	−	0.609250i	$-0.208530\pi$
$24$	−0.994636	+	0.722645i	−0.203029	+	0.147509i
$25$	−3.75407	−	3.30257i	−0.750814	−	0.660514i
$26$	−0.528362	+	1.62613i	−0.103620	+	0.318911i
$27$	−2.86941	+	3.94940i	−0.552217	+	0.760062i
$28$	−3.63977	+	5.00971i	−0.687851	+	0.946746i
$29$	0.632843	−	1.94769i	0.117516	−	0.361677i	−0.874947	−	0.484218i	$-0.839104\pi$
$29$	0.632843	−	1.94769i	0.117516	−	0.361677i	0.992463	+	0.122541i	$0.0391042\pi$
$30$	0.590136	−	0.388097i	0.107744	−	0.0708564i
$31$	2.63491	−	1.91437i	0.473243	−	0.343831i	−0.325461	−	0.945556i	$-0.605519\pi$
$31$	2.63491	−	1.91437i	0.473243	−	0.343831i	0.798704	+	0.601724i	$0.205519\pi$
$32$			3.66082i			0.647147i
$33$		0			0
$34$	1.18237			0.202775
$35$	4.57232	−	5.71341i	0.772862	−	0.965742i
$36$	1.21303	+	3.73332i	0.202172	+	0.622220i
$37$	5.93174	+	1.92734i	0.975173	+	0.316853i	0.752902	−	0.658132i	$-0.228653\pi$
$37$	5.93174	+	1.92734i	0.975173	+	0.316853i	0.222270	+	0.974985i	$0.428653\pi$
$38$	−0.966815	+	1.33071i	−0.156838	+	0.215869i
$39$	−4.05270	−	2.94446i	−0.648951	−	0.471491i
$40$	0.133098	−	2.85460i	0.0210447	−	0.451351i
$41$	3.15369	+	9.70607i	0.492524	+	1.51583i	0.820780	+	0.571245i	$0.193539\pi$
$41$	3.15369	+	9.70607i	0.492524	+	1.51583i	−0.328256	+	0.944589i	$0.606461\pi$
$42$	0.607607	+	0.836299i	0.0937558	+	0.129044i
$43$			0.596820i			0.0910142i	0.998964	+	0.0455071i	$0.0144904\pi$
$43$			0.596820i			0.0910142i	−0.998964	+	0.0455071i	$0.985510\pi$
$44$		0			0
$45$	−1.22645	−	4.47378i	−0.182828	−	0.666912i
$46$	−1.55233	+	1.12784i	−0.228879	+	0.166290i
$47$	0.914917	−	0.297274i	0.133454	−	0.0433619i	−0.241528	−	0.970394i	$-0.577649\pi$
$47$	0.914917	−	0.297274i	0.133454	−	0.0433619i	0.374983	+	0.927032i	$0.377649\pi$
$48$	−3.07846	−	1.00025i	−0.444337	−	0.144374i
$49$	3.00130	+	2.18058i	0.428758	+	0.311511i
$50$	−0.152764	+	1.63463i	−0.0216041	+	0.231172i
$51$	−1.07047	+	3.29456i	−0.149895	+	0.461330i
$52$	−9.37091	+	3.04479i	−1.29951	+	0.422237i
$53$	0.231164	+	0.318170i	0.0317529	+	0.0437041i	0.824598	−	0.565719i	$-0.191401\pi$
$53$	0.231164	+	0.318170i	0.0317529	+	0.0437041i	−0.792845	+	0.609423i	$0.791401\pi$
$54$	1.60292			0.218129
$55$		0			0
$56$	4.18237			0.558893
$57$	−2.83257	−	3.89870i	−0.375183	−	0.516395i
$58$	−0.639526	+	0.207795i	−0.0839738	+	0.0272848i
$59$	0.162990	−	0.501632i	0.0212195	−	0.0653069i	−0.939886	−	0.341488i	$-0.889069\pi$
$59$	0.162990	−	0.501632i	0.0212195	−	0.0653069i	0.961106	+	0.276181i	$0.0890690\pi$
$60$	3.80828	+	1.43672i	0.491647	+	0.185479i
$61$	4.30825	+	3.13012i	0.551615	+	0.400771i	0.828380	−	0.560166i	$-0.189263\pi$
$61$	4.30825	+	3.13012i	0.551615	+	0.400771i	−0.276766	+	0.960937i	$0.589263\pi$
$62$	−1.01707	−	0.330467i	−0.129168	−	0.0419693i
$63$	6.45688	−	2.09797i	0.813490	−	0.264319i
$64$	−4.47180	+	3.24895i	−0.558975	+	0.406119i
$65$	11.2295	−	3.07847i	1.39285	−	0.381837i
$66$		0			0
$67$			8.45057i			1.03240i	0.856468	+	0.516201i	$0.172654\pi$
$67$			8.45057i			1.03240i	−0.856468	+	0.516201i	$0.827346\pi$
$68$	4.00496	+	5.51235i	0.485672	+	0.668471i
$69$	−1.73719	−	5.34652i	−0.209133	−	0.643645i
$70$	−2.40017	−	0.111910i	−0.286875	−	0.0133758i
$71$	−10.1349	−	7.36345i	−1.20279	−	0.873881i	−0.208237	−	0.978078i	$-0.566772\pi$
$71$	−10.1349	−	7.36345i	−1.20279	−	0.873881i	−0.994557	+	0.104198i	$0.966772\pi$
$72$	1.55839	−	2.14493i	0.183658	−	0.252783i
$73$	−8.09851	−	2.63136i	−0.947859	−	0.307978i	−0.206013	−	0.978549i	$-0.566049\pi$
$73$	−8.09851	−	2.63136i	−0.947859	−	0.307978i	−0.741845	+	0.670571i	$0.766049\pi$
$74$	−0.632843	−	1.94769i	−0.0735665	−	0.226415i
$75$	−4.41643	−	1.90559i	−0.509965	−	0.220038i
$76$	−9.47874			−1.08729
$77$		0			0
$78$			1.64484i			0.186242i
$79$	2.29142	−	1.66482i	0.257805	−	0.187306i	−0.451374	−	0.892335i	$-0.649066\pi$
$79$	2.29142	−	1.66482i	0.257805	−	0.187306i	0.709179	+	0.705029i	$0.249066\pi$
$80$	6.28624	−	4.13407i	0.702823	−	0.462203i
$81$	0.472007	−	1.45269i	0.0524452	−	0.161410i
$82$	1.96967	−	2.71102i	0.217514	−	0.299382i
$83$	7.13612	−	9.82203i	0.783291	−	1.07811i	−0.211620	−	0.977352i	$-0.567874\pi$
$83$	7.13612	−	9.82203i	0.783291	−	1.07811i	0.994911	−	0.100755i	$-0.0321260\pi$
$84$	−1.84082	+	5.66548i	−0.200850	+	0.618154i
$85$	−4.42428	−	6.72752i	−0.479880	−	0.729702i
$86$	0.158540	−	0.115186i	0.0170958	−	0.0124208i
$87$		−	1.97010i		−	0.211217i
$88$		0			0
$89$	−9.00000			−0.953998			−0.476999	−	0.878904i	$-0.658275\pi$
$89$	−9.00000			−0.953998			−0.476999	+	0.878904i	$0.658275\pi$
$90$	−0.951718	+	1.18923i	−0.100320	+	0.125356i
$91$	5.26605	+	16.2072i	0.552032	+	1.69898i
$92$	−10.5162	−	3.41693i	−1.09639	−	0.356239i
$93$	1.84163	−	2.53478i	0.190968	−	0.262845i
$94$	−0.255547	−	0.185666i	−0.0263577	−	0.0191500i
$95$	11.1892	+	0.521708i	1.14799	+	0.0535261i
$96$	1.08827	+	3.34934i	0.111071	+	0.341841i
$97$	−6.63855	−	9.13717i	−0.674042	−	0.927739i	0.325801	−	0.945438i	$-0.394366\pi$
$97$	−6.63855	−	9.13717i	−0.674042	−	0.927739i	−0.999843	+	0.0176989i	$0.994366\pi$
$98$		−	1.21812i		−	0.123049i
$99$		0			0
$100$	−8.13829	+	4.82466i	−0.813829	+	0.482466i
$101$	−10.6524	+	7.73940i	−1.05995	+	0.770099i	−0.974079	−	0.226207i	$-0.927367\pi$
$101$	−10.6524	+	7.73940i	−1.05995	+	0.770099i	−0.0858713	+	0.996306i	$0.527367\pi$
$102$	1.08177	−	0.351488i	0.107111	−	0.0348025i
$103$	2.64611	+	0.859773i	0.260729	+	0.0847159i	0.436465	−	0.899721i	$-0.356230\pi$
$103$	2.64611	+	0.859773i	0.260729	+	0.0847159i	−0.175736	+	0.984437i	$0.556230\pi$
$104$	5.38395	+	3.91167i	0.527939	+	0.383570i
$105$	2.48484	−	6.58652i	0.242495	−	0.642779i
$106$	0.0399046	−	0.122814i	0.00387587	−	0.0119287i
$107$	15.1696	−	4.92889i	1.46650	−	0.476494i	0.536449	−	0.843933i	$-0.319765\pi$
$107$	15.1696	−	4.92889i	1.46650	−	0.476494i	0.930048	+	0.367439i	$0.119765\pi$
$108$	5.42945	+	7.47299i	0.522449	+	0.719089i
$109$	3.90911			0.374425			0.187212	−	0.982319i	$-0.440055\pi$
$109$	3.90911			0.374425			0.187212	+	0.982319i	$0.440055\pi$
$110$		0			0
$111$	6.00000			0.569495
$112$	6.47234	+	8.90841i	0.611578	+	0.841765i
$113$	−9.39413	+	3.05234i	−0.883725	+	0.287140i	−0.715503	−	0.698609i	$-0.753803\pi$
$113$	−9.39413	+	3.05234i	−0.883725	+	0.287140i	−0.168222	+	0.985749i	$0.553803\pi$
$114$	−0.488970	+	1.50489i	−0.0457962	+	0.140946i
$115$	12.2259	+	4.61234i	1.14007	+	0.430103i
$116$	−3.13498	−	2.27770i	−0.291076	−	0.211479i
$117$	10.2741	+	3.33825i	0.949839	+	0.308621i
$118$	−0.164711	+	0.0535179i	−0.0151629	+	0.00492672i
$119$	9.53376	−	6.92668i	0.873958	−	0.634968i
$120$	−0.726825	−	2.65129i	−0.0663497	−	0.242028i
$121$		0			0
$122$		−	1.74856i		−	0.158307i
$123$	5.77073	+	7.94273i	0.520329	+	0.716172i
$124$	−1.90438	−	5.86108i	−0.171018	−	0.526341i
$125$	9.87244	−	5.24737i	0.883018	−	0.469339i
$126$	−1.80348	−	1.31031i	−0.160667	−	0.116731i
$127$	3.18337	−	4.38154i	0.282479	−	0.388798i	−0.644074	−	0.764963i	$-0.722757\pi$
$127$	3.18337	−	4.38154i	0.282479	−	0.388798i	0.926553	+	0.376164i	$0.122757\pi$
$128$	8.68940	+	2.82336i	0.768042	+	0.249552i
$129$	0.177419	+	0.546041i	0.0156209	+	0.0480762i
$130$	−2.98506	−	2.38888i	−0.261807	−	0.209519i
$131$	−19.1241			−1.67088			−0.835440	−	0.549582i	$-0.814787\pi$
$131$	−19.1241			−1.67088			−0.835440	+	0.549582i	$0.814787\pi$
$132$		0			0
$133$			16.3937i			1.42152i
$134$	2.24482	−	1.63096i	0.193923	−	0.140893i
$135$	−5.99791	−	9.12037i	−0.516218	−	0.784957i
$136$	1.42210	−	4.37676i	0.121944	−	0.375304i
$137$	9.42975	−	12.9789i	0.805638	−	1.10887i	−0.186344	−	0.982485i	$-0.559664\pi$
$137$	9.42975	−	12.9789i	0.805638	−	1.10887i	0.991982	−	0.126381i	$-0.0403362\pi$
$138$	−1.08498	+	1.49335i	−0.0923596	+	0.127122i
$139$	3.88415	−	11.9542i	0.329449	−	1.01394i	−0.639943	−	0.768422i	$-0.721042\pi$
$139$	3.88415	−	11.9542i	0.329449	−	1.01394i	0.969392	−	0.245518i	$-0.0789579\pi$
$140$	−7.60819	−	11.5690i	−0.643010	−	0.977755i
$141$	0.748700	−	0.543963i	0.0630519	−	0.0458099i
$142$			4.11339i			0.345188i
$143$		0			0
$144$	6.98034			0.581695
$145$	3.57535	+	2.86127i	0.296916	+	0.237616i
$146$	0.864010	+	2.65915i	0.0715060	+	0.220073i
$147$	3.39417	+	1.10283i	0.279947	+	0.0909602i
$148$	6.93679	−	9.54767i	0.570201	−	0.784814i
$149$	11.2679	+	8.18663i	0.923105	+	0.670675i	0.944295	−	0.329100i	$-0.106745\pi$
$149$	11.2679	+	8.18663i	0.923105	+	0.670675i	−0.0211897	+	0.999775i	$0.506745\pi$
$150$	0.346167	+	1.54096i	0.0282644	+	0.125819i
$151$	4.95461	+	15.2487i	0.403201	+	1.24092i	0.922388	+	0.386264i	$0.126235\pi$
$151$	4.95461	+	15.2487i	0.403201	+	1.24092i	−0.519188	+	0.854660i	$0.673765\pi$
$152$	3.76302	+	5.17936i	0.305221	+	0.420101i
$153$		−	7.47034i		−	0.603941i
$154$		0			0
$155$	1.92544	+	7.02357i	0.154655	+	0.564146i
$156$	−7.66846	+	5.57146i	−0.613968	+	0.446074i
$157$	−2.16354	+	0.702976i	−0.172669	+	0.0561036i	−0.394076	−	0.919078i	$-0.628935\pi$
$157$	−2.16354	+	0.702976i	−0.172669	+	0.0561036i	0.221407	+	0.975182i	$0.428935\pi$
$158$	−0.884488	−	0.287387i	−0.0703661	−	0.0228633i
$159$	0.306080	+	0.222380i	0.0242737	+	0.0176359i
$160$	−7.65893	−	2.88942i	−0.605492	−	0.228428i
$161$	−5.90967	+	18.1881i	−0.465747	+	1.43342i
$162$	−0.476991	+	0.154984i	−0.0374760	+	0.0121767i
$163$	−13.2660	−	18.2590i	−1.03907	−	1.43016i	−0.897914	−	0.440172i	$-0.854918\pi$
$163$	−13.2660	−	18.2590i	−1.03907	−	1.43016i	−0.141158	−	0.989987i	$-0.545082\pi$
$164$	19.3108			1.50792
$165$		0			0
$166$	−3.98640			−0.309405
$167$	2.23918	+	3.08197i	0.173273	+	0.238490i	0.886817	−	0.462120i	$-0.152911\pi$
$167$	2.23918	+	3.08197i	0.173273	+	0.238490i	−0.713544	+	0.700610i	$0.752911\pi$
$168$	3.82652	−	1.24331i	0.295222	−	0.0959236i
$169$	−4.36204	+	13.4250i	−0.335541	+	1.03269i
$170$	−0.933222	+	2.47368i	−0.0715749	+	0.189722i
$171$	8.40755	+	6.10844i	0.642942	+	0.467124i
$172$	1.07402	+	0.348971i	0.0818935	+	0.0266088i
$173$	0.903172	−	0.293458i	0.0686669	−	0.0223112i	−0.274482	−	0.961592i	$-0.588506\pi$
$173$	0.903172	−	0.293458i	0.0686669	−	0.0223112i	0.343149	+	0.939281i	$0.388506\pi$
$174$	−0.523341	+	0.380229i	−0.0396744	+	0.0288251i
$175$	8.34438	+	14.0754i	0.630776	+	1.06400i
$176$		0			0
$177$		−	0.507404i		−	0.0381388i
$178$	1.73700	+	2.39077i	0.130193	+	0.179196i
$179$	−1.12336	−	3.45734i	−0.0839637	−	0.258414i	0.900257	−	0.435359i	$-0.143378\pi$
$179$	−1.12336	−	3.45734i	−0.0839637	−	0.258414i	−0.984221	+	0.176945i	$0.943378\pi$
$180$	−8.76804	−	0.408818i	−0.653531	−	0.0304715i
$181$	−10.1683	−	7.38772i	−0.755806	−	0.549125i	0.141815	−	0.989893i	$-0.454706\pi$
$181$	−10.1683	−	7.38772i	−0.755806	−	0.549125i	−0.897621	+	0.440768i	$0.854706\pi$
$182$	3.28896	−	4.52687i	0.243794	−	0.335554i
$183$	4.87219	+	1.58307i	0.360163	+	0.117024i
$184$	2.30783	+	7.10276i	0.170135	+	0.523623i
$185$	−8.71407	+	10.8888i	−0.640671	+	0.800561i
$186$	−1.02878			−0.0754335
$187$		0			0
$188$		−	1.82028i		−	0.132758i
$189$	12.9247	−	9.39037i	0.940137	−	0.683049i
$190$	−2.02093	−	3.07301i	−0.146614	−	0.222940i
$191$	−0.827102	+	2.54556i	−0.0598470	+	0.184190i	−0.976511	−	0.215470i	$-0.930872\pi$
$191$	−0.827102	+	2.54556i	−0.0598470	+	0.184190i	0.916664	+	0.399660i	$0.130872\pi$
$192$	−3.12549	+	4.30187i	−0.225563	+	0.310461i
$193$	0.228197	−	0.314086i	0.0164260	−	0.0226084i	−0.800725	−	0.599032i	$-0.795552\pi$
$193$	0.228197	−	0.314086i	0.0164260	−	0.0226084i	0.817151	+	0.576424i	$0.195552\pi$
$194$	−1.14597	+	3.52694i	−0.0822761	+	0.253220i
$195$	9.35893	−	6.15479i	0.670207	−	0.440754i
$196$	5.67903	−	4.12605i	0.405645	−	0.294718i
$197$		−	18.5416i		−	1.32104i	−0.750810	−	0.660518i	$-0.770337\pi$
$197$		−	18.5416i		−	1.32104i	0.750810	−	0.660518i	$-0.229663\pi$
$198$		0			0
$199$	−10.1491			−0.719451			−0.359726	−	0.933058i	$-0.617130\pi$
$199$	−10.1491			−0.719451			−0.359726	+	0.933058i	$0.617130\pi$
$200$	5.86715	+	2.53154i	0.414870	+	0.179007i
$201$	2.51214	+	7.73157i	0.177193	+	0.545343i
$202$	4.11181	+	1.33601i	0.289306	+	0.0940011i
$203$	−3.93934	+	5.42204i	−0.276488	+	0.380552i
$204$	5.30288	+	3.85277i	0.371276	+	0.269748i
$205$	−22.7956	−	1.06286i	−1.59211	−	0.0742337i
$206$	−0.282307	−	0.868851i	−0.0196693	−	0.0605358i
$207$	7.12580	+	9.80782i	0.495277	+	0.681690i
$208$			17.5212i			1.21487i
$209$		0			0
$210$	−2.22922	+	0.611121i	−0.153831	+	0.0421714i
$211$	−6.85522	+	4.98061i	−0.471933	+	0.342879i	−0.798194	−	0.602400i	$-0.794211\pi$
$211$	−6.85522	+	4.98061i	−0.471933	+	0.342879i	0.326261	+	0.945280i	$0.394211\pi$
$212$	0.707738	−	0.229958i	0.0486076	−	0.0157936i
$213$	−11.4616	−	3.72409i	−0.785334	−	0.255170i
$214$	−4.23703	−	3.07839i	−0.289638	−	0.210434i
$215$	−1.24863	−	0.471059i	−0.0851558	−	0.0321260i
$216$	1.92791	−	5.93350i	0.131178	−	0.403724i
$217$	−10.1369	+	3.29368i	−0.688138	+	0.223589i
$218$	−0.754457	−	1.03842i	−0.0510982	−	0.0703307i
$219$	−8.19170			−0.553544
$220$		0			0
$221$	18.7511			1.26134
$222$	−1.15800	−	1.59385i	−0.0777197	−	0.106972i
$223$	22.5466	−	7.32582i	1.50983	−	0.490573i	0.566963	−	0.823743i	$-0.308118\pi$
$223$	22.5466	−	7.32582i	1.50983	−	0.490573i	0.942867	+	0.333170i	$0.108118\pi$
$224$	3.70213	−	11.3940i	0.247359	−	0.761292i
$225$	10.3278	+	0.965182i	0.688518	+	0.0643455i
$226$	2.62389	+	1.90637i	0.174539	+	0.126810i
$227$	0.681510	+	0.221436i	0.0452334	+	0.0146972i	0.331546	−	0.943439i	$-0.392430\pi$
$227$	0.681510	+	0.221436i	0.0452334	+	0.0146972i	−0.286313	+	0.958136i	$0.592430\pi$
$228$	−8.67226	+	2.81779i	−0.574334	+	0.186613i
$229$	10.6379	−	7.72885i	0.702969	−	0.510737i	−0.177929	−	0.984043i	$-0.556940\pi$
$229$	10.6379	−	7.72885i	0.702969	−	0.510737i	0.880898	+	0.473306i	$0.156940\pi$
$230$	−1.13436	−	4.13788i	−0.0747975	−	0.272843i
$231$		0			0
$232$			2.61725i			0.171831i
$233$	−15.8306	−	21.7890i	−1.03710	−	1.42744i	−0.899482	−	0.436958i	$-0.856056\pi$
$233$	−15.8306	−	21.7890i	−1.03710	−	1.42744i	−0.137617	−	0.990486i	$-0.543944\pi$
$234$	−1.09612	−	3.37350i	−0.0716554	−	0.220533i
$235$	−0.100188	+	2.14876i	−0.00653555	+	0.140170i
$236$	−0.807421	−	0.586626i	−0.0525586	−	0.0381861i
$237$	1.60155	−	2.20435i	0.104032	−	0.143188i
$238$	−3.68002	−	1.19571i	−0.238540	−	0.0775065i
$239$	−1.54799	−	4.76423i	−0.100131	−	0.308173i	0.888426	−	0.459021i	$-0.151800\pi$
$239$	−1.54799	−	4.76423i	−0.100131	−	0.308173i	−0.988557	+	0.150848i	$0.951800\pi$
$240$	4.52243	−	5.65107i	0.291922	−	0.364775i
$241$	−4.69354			−0.302337			−0.151169	−	0.988508i	$-0.548304\pi$
$241$	−4.69354			−0.302337			−0.151169	+	0.988508i	$0.548304\pi$
$242$		0			0
$243$		−	16.1146i		−	1.03375i
$244$	8.15200	−	5.92278i	0.521879	−	0.379167i
$245$	−6.93094	+	4.55805i	−0.442801	+	0.291203i
$246$	0.996168	−	3.06589i	0.0635133	−	0.195474i
$247$	−15.3326	+	21.1036i	−0.975593	+	1.34279i
$248$	−2.44657	+	3.36742i	−0.155357	+	0.213831i
$249$	3.60912	−	11.1077i	0.228719	−	0.703923i
$250$	−3.29930	−	1.60979i	−0.208666	−	0.101812i
$251$	−3.54215	+	2.57352i	−0.223578	+	0.162439i	−0.693936	−	0.720037i	$-0.744125\pi$
$251$	−3.54215	+	2.57352i	−0.223578	+	0.162439i	0.470358	+	0.882476i	$0.344125\pi$
$252$		−	12.8464i		−	0.809244i
$253$		0			0
$254$	−1.77831			−0.111581
$255$	−6.04776	−	4.83989i	−0.378726	−	0.303086i
$256$	2.48910	+	7.66066i	0.155569	+	0.478791i
$257$	−6.19724	−	2.01360i	−0.386573	−	0.125605i	0.109281	−	0.994011i	$-0.465145\pi$
$257$	−6.19724	−	2.01360i	−0.386573	−	0.125605i	−0.495854	+	0.868406i	$0.665145\pi$
$258$	0.110809	−	0.152516i	0.00689867	−	0.00949520i
$259$	−16.5130	−	11.9974i	−1.02606	−	0.745480i
$260$	1.02616	−	22.0084i	0.0636399	−	1.36490i
$261$	1.31287	+	4.04059i	0.0812645	+	0.250107i
$262$	3.69094	+	5.08015i	0.228027	+	0.313852i
$263$		−	4.28212i		−	0.264047i	−0.991247	−	0.132023i	$-0.957853\pi$
$263$		−	4.28212i		−	0.264047i	0.991247	−	0.132023i	$-0.0421474\pi$
$264$		0			0
$265$	−0.848110	+	0.232501i	−0.0520990	+	0.0142824i
$266$	4.35485	−	3.16398i	0.267013	−	0.193996i
$267$	−8.23425	+	2.67547i	−0.503928	+	0.163736i
$268$	15.2074	+	4.94120i	0.928942	+	0.301832i
$269$	8.59311	+	6.24326i	0.523931	+	0.380658i	0.818083	−	0.575101i	$-0.195037\pi$
$269$	8.59311	+	6.24326i	0.523931	+	0.380658i	−0.294152	+	0.955759i	$0.595037\pi$
$270$	−1.26515	+	3.35352i	−0.0769947	+	0.204089i
$271$	3.29121	−	10.1293i	0.199927	−	0.615311i	−0.799957	−	0.600057i	$-0.795144\pi$
$271$	3.29121	−	10.1293i	0.199927	−	0.615311i	0.999884	−	0.0152536i	$-0.00485557\pi$
$272$	11.5232	−	3.74412i	0.698697	−	0.227020i
$273$	9.63599	+	13.2628i	0.583197	+	0.802702i
$274$	−5.26768			−0.318232
$275$		0			0
$276$	−10.6372			−0.640286
$277$	−4.32056	−	5.94674i	−0.259597	−	0.357305i	0.659246	−	0.751927i	$-0.270876\pi$
$277$	−4.32056	−	5.94674i	−0.259597	−	0.357305i	−0.918844	+	0.394622i	$0.870876\pi$
$278$	−3.92516	+	1.27536i	−0.235415	+	0.0764911i
$279$	−2.08793	+	6.42598i	−0.125001	+	0.384713i
$280$	−3.30107	+	8.75009i	−0.197276	+	0.522918i
$281$	−22.8380	−	16.5928i	−1.36240	−	0.989843i	−0.998288	−	0.0584888i	$-0.981372\pi$
$281$	−22.8380	−	16.5928i	−1.36240	−	0.989843i	−0.364114	−	0.931354i	$-0.618628\pi$
$282$	−0.288998	−	0.0939011i	−0.0172096	−	0.00559173i
$283$	−9.56929	+	3.10925i	−0.568835	+	0.184826i	−0.579293	−	0.815120i	$-0.696671\pi$
$283$	−9.56929	+	3.10925i	−0.568835	+	0.184826i	0.0104576	+	0.999945i	$0.496671\pi$
$284$	−19.1771	+	13.9330i	−1.13795	+	0.826772i
$285$	10.3923	−	2.84895i	0.615587	−	0.168757i
$286$		0			0
$287$		−	33.3986i		−	1.97146i
$288$	−4.46398	−	6.14414i	−0.263042	−	0.362047i
$289$	1.24635	+	3.83586i	0.0733144	+	0.225639i
$290$	0.0700314	−	1.50198i	0.00411238	−	0.0881995i
$291$	−8.78996	−	6.38628i	−0.515277	−	0.374371i
$292$	−9.47068	+	13.0353i	−0.554230	+	0.762832i
$293$	−0.0232822	−	0.00756484i	−0.00136016	−	0.000441943i	0.308337	−	0.951277i	$-0.400228\pi$
$293$	−0.0232822	−	0.00756484i	−0.00136016	−	0.000441943i	−0.309697	+	0.950835i	$0.600228\pi$
$294$	−0.362116	−	1.11448i	−0.0211190	−	0.0649977i
$295$	0.920837	+	0.736926i	0.0536132	+	0.0429055i
$296$	−7.97090			−0.463299
$297$		0			0
$298$		−	4.57325i		−	0.264921i
$299$	−24.6184	+	17.8863i	−1.42372	+	1.03439i
$300$	−6.01161	+	6.83347i	−0.347081	+	0.394531i
$301$	0.603555	−	1.85755i	0.0347883	−	0.107067i
$302$	3.09445	−	4.25915i	0.178066	−	0.245086i
$303$	−7.44531	+	10.2476i	−0.427722	+	0.588708i
$304$	−5.20860	+	16.0304i	−0.298733	+	0.919407i
$305$	−9.94907	+	6.54289i	−0.569682	+	0.374645i
$306$	−1.98443	+	1.44177i	−0.113442	+	0.0824207i
$307$			32.9698i			1.88169i	0.338839	+	0.940844i	$0.389966\pi$
$307$			32.9698i			1.88169i	−0.338839	+	0.940844i	$0.610034\pi$
$308$		0			0
$309$	2.67656			0.152264
$310$	1.49414	−	1.86702i	0.0848614	−	0.106040i
$311$	−1.49121	−	4.58948i	−0.0845590	−	0.260246i	0.899833	−	0.436234i	$-0.143688\pi$
$311$	−1.49121	−	4.58948i	−0.0845590	−	0.260246i	−0.984392	+	0.175988i	$0.943688\pi$
$312$	6.08870	+	1.97834i	0.344705	+	0.112001i
$313$	−10.0312	+	13.8068i	−0.566999	+	0.780408i	−0.992195	−	0.124694i	$-0.960205\pi$
$313$	−10.0312	+	13.8068i	−0.566999	+	0.780408i	0.425196	+	0.905101i	$0.360205\pi$
$314$	0.604302	+	0.439051i	0.0341027	+	0.0247771i
$315$	−0.707061	+	15.1645i	−0.0398384	+	0.854426i
$316$	−1.65613	−	5.09704i	−0.0931645	−	0.286731i
$317$	1.00897	+	1.38873i	0.0566695	+	0.0779989i	0.836411	−	0.548102i	$-0.184650\pi$
$317$	1.00897	+	1.38873i	0.0566695	+	0.0779989i	−0.779742	+	0.626101i	$0.784650\pi$
$318$		−	0.124227i		−	0.00696629i
$319$		0			0
$320$	−3.26774	−	11.9199i	−0.182672	−	0.666345i
$321$	12.4136	−	9.01904i	0.692862	−	0.503394i
$322$	5.97207	−	1.94044i	0.332810	−	0.108137i
$323$	17.1557	+	5.57423i	0.954569	+	0.310158i
$324$	−2.33823	−	1.69882i	−0.129902	−	0.0943791i
$325$	−2.42268	+	25.9235i	−0.134386	+	1.43798i
$326$	−2.29003	+	7.04798i	−0.126833	+	0.390351i
$327$	3.57651	−	1.16208i	0.197781	−	0.0642631i
$328$	−7.66632	−	10.5518i	−0.423302	−	0.582625i
$329$	−3.14823			−0.173567
$330$		0			0
$331$	0.892186			0.0490390			0.0245195	−	0.999699i	$-0.492194\pi$
$331$	0.892186			0.0490390			0.0245195	+	0.999699i	$0.492194\pi$
$332$	−13.5029	−	18.5851i	−0.741066	−	1.01999i
$333$	−12.3057	+	3.99837i	−0.674350	+	0.219110i
$334$	0.386537	−	1.18964i	0.0211504	−	0.0650941i
$335$	−17.6797	−	6.66988i	−0.965947	−	0.364414i
$336$	8.56989	+	6.22639i	0.467526	+	0.339677i
$337$	−17.8662	−	5.80507i	−0.973233	−	0.316222i	−0.221112	−	0.975248i	$-0.570969\pi$
$337$	−17.8662	−	5.80507i	−0.973233	−	0.316222i	−0.752120	+	0.659026i	$0.770969\pi$
$338$	4.40810	−	1.43228i	0.239769	−	0.0779056i
$339$	−7.68746	+	5.58527i	−0.417526	+	0.303350i
$340$	−14.6936	+	4.02812i	−0.796874	+	0.218456i
$341$		0			0
$342$		−	3.41232i		−	0.184517i
$343$	6.32892	+	8.71102i	0.341730	+	0.470351i
$344$	−0.235699	−	0.725406i	−0.0127080	−	0.0391113i
$345$	12.5568	+	0.585472i	0.676034	+	0.0315207i
$346$	−0.252266	−	0.183282i	−0.0135619	−	0.00985332i
$347$	−12.3199	+	16.9569i	−0.661366	+	0.910292i	−0.999526	−	0.0307966i	$-0.990196\pi$
$347$	−12.3199	+	16.9569i	−0.661366	+	0.910292i	0.338160	+	0.941089i	$0.390196\pi$
$348$	−3.54535	−	1.15195i	−0.190051	−	0.0617512i
$349$	−8.40114	−	25.8560i	−0.449703	−	1.38404i	−0.877243	−	0.480046i	$-0.840620\pi$
$349$	−8.40114	−	25.8560i	−0.449703	−	1.38404i	0.427541	−	0.903996i	$-0.359380\pi$
$350$	2.12854	−	4.93316i	0.113775	−	0.263688i
$351$	25.4205			1.35685
$352$		0			0
$353$			8.66841i			0.461373i	0.973028	+	0.230686i	$0.0740972\pi$
$353$			8.66841i			0.461373i	−0.973028	+	0.230686i	$0.925903\pi$
$354$	−0.134787	+	0.0979288i	−0.00716387	+	0.00520486i
$355$	23.4046	−	15.3918i	1.24219	−	0.816912i
$356$	−5.26246	+	16.1962i	−0.278910	+	0.858396i
$357$	6.66347	−	9.17148i	0.352668	−	0.485406i
$358$	−0.701604	+	0.965675i	−0.0370809	+	0.0510375i
$359$	−2.13366	+	6.56672i	−0.112610	+	0.346578i	−0.991441	−	0.130555i	$-0.958324\pi$
$359$	−2.13366	+	6.56672i	−0.112610	+	0.346578i	0.878831	+	0.477133i	$0.158324\pi$
$360$	3.25749	+	4.95331i	0.171685	+	0.261063i
$361$	−4.93033	+	3.58209i	−0.259491	+	0.188531i
$362$			4.12695i			0.216908i
$363$		0			0
$364$	32.2453			1.69011
$365$	11.8972	−	14.8663i	0.622727	−	0.778137i
$366$	−0.519802	−	1.59979i	−0.0271705	−	0.0836222i
$367$	−15.4927	−	5.03389i	−0.808714	−	0.262767i	−0.124661	−	0.992199i	$-0.539784\pi$
$367$	−15.4927	−	5.03389i	−0.808714	−	0.262767i	−0.684053	+	0.729432i	$0.739784\pi$
$368$	−11.5574	+	15.9074i	−0.602471	+	0.829230i
$369$	−17.1285	−	12.4446i	−0.891675	−	0.647840i
$370$	4.57433	+	0.213282i	0.237808	+	0.0110880i
$371$	−0.397718	−	1.22405i	−0.0206485	−	0.0635496i
$372$	−3.48470	−	4.79628i	−0.180673	−	0.248675i
$373$			3.69622i			0.191383i	0.995411	+	0.0956915i	$0.0305062\pi$
$373$			3.69622i			0.191383i	−0.995411	+	0.0956915i	$0.969494\pi$
$374$		0			0
$375$	7.47255	−	7.73573i	0.385881	−	0.399471i
$376$	−0.994636	+	0.722645i	−0.0512944	+	0.0372676i
$377$	−10.1422	+	3.29540i	−0.522349	+	0.169722i
$378$	−4.98894	−	1.62101i	−0.256603	−	0.0833755i
$379$	−2.99480	−	2.17585i	−0.153833	−	0.111766i	0.508206	−	0.861235i	$-0.330309\pi$
$379$	−2.99480	−	2.17585i	−0.153833	−	0.111766i	−0.662039	+	0.749469i	$0.730309\pi$
$380$	7.48139	−	19.8308i	0.383787	−	1.01730i
$381$	1.61000	−	4.95508i	0.0824829	−	0.253856i
$382$	0.835835	−	0.271579i	0.0427651	−	0.0138952i
$383$	18.4393	+	25.3796i	0.942206	+	1.29684i	0.954904	+	0.296916i	$0.0959581\pi$
$383$	18.4393	+	25.3796i	0.942206	+	1.29684i	−0.0126977	+	0.999919i	$0.504042\pi$
$384$	8.78939			0.448532
$385$		0			0
$386$	−0.127476			−0.00648836
$387$	−0.727758	−	1.00167i	−0.0369940	−	0.0509179i
$388$	−20.3247	+	6.60390i	−1.03183	+	0.335262i
$389$	4.27237	−	13.1490i	0.216618	−	0.666680i	−0.782417	−	0.622755i	$-0.786013\pi$
$389$	4.27237	−	13.1490i	0.216618	−	0.666680i	0.999035	−	0.0439258i	$-0.0139865\pi$
$390$	−3.44124	−	1.29824i	−0.174254	−	0.0657392i
$391$	17.0240	+	12.3687i	0.860943	+	0.625512i
$392$	−4.50910	−	1.46510i	−0.227744	−	0.0739985i
$393$	−17.4969	+	5.68510i	−0.882604	+	0.286775i
$394$	−4.92542	+	3.57853i	−0.248139	+	0.180284i
$395$	1.67445	+	6.10798i	0.0842505	+	0.307326i
$396$		0			0
$397$			9.73413i			0.488542i	0.969707	+	0.244271i	$0.0785486\pi$
$397$			9.73413i			0.488542i	−0.969707	+	0.244271i	$0.921451\pi$
$398$	1.95877	+	2.69602i	0.0981845	+	0.135139i
$399$	4.87344	+	14.9989i	0.243977	+	0.750884i
$400$	3.68743	+	16.4146i	0.184372	+	0.820731i
$401$	21.1775	+	15.3863i	1.05755	+	0.768357i	0.973634	−	0.228115i	$-0.0732563\pi$
$401$	21.1775	+	15.3863i	1.05755	+	0.768357i	0.0839190	+	0.996473i	$0.473256\pi$
$402$	1.56898	−	2.15952i	0.0782536	−	0.107707i
$403$	−16.1297	−	5.24085i	−0.803477	−	0.261065i
$404$	7.69901	+	23.6951i	0.383040	+	1.17888i
$405$	2.66668	+	2.13408i	0.132508	+	0.106043i
$406$	2.20061			0.109214
$407$		0			0
$408$		−	4.42713i		−	0.219175i
$409$	−2.14035	+	1.55505i	−0.105833	+	0.0768925i	−0.639443	−	0.768838i	$-0.720835\pi$
$409$	−2.14035	+	1.55505i	−0.105833	+	0.0768925i	0.533610	+	0.845731i	$0.320835\pi$
$410$	4.11720	+	6.26058i	0.203334	+	0.309188i
$411$	4.76913	−	14.6779i	0.235244	−	0.724006i
$412$	3.09445	−	4.25915i	0.152453	−	0.209833i
$413$	−1.01458	+	1.39646i	−0.0499244	+	0.0687151i
$414$	1.23008	−	3.78581i	0.0604554	−	0.186062i
$415$	14.9166	+	22.6821i	0.732228	+	1.11342i
$416$	15.4222	−	11.2049i	0.756137	−	0.549366i
$417$		−	12.0917i		−	0.592135i
$418$		0			0
$419$	−24.3118			−1.18771			−0.593855	−	0.804572i	$-0.702395\pi$
$419$	−24.3118			−1.18771			−0.593855	+	0.804572i	$0.702395\pi$
$420$	−10.4000	−	8.32291i	−0.507469	−	0.406116i
$421$	−8.61916	−	26.5270i	−0.420072	−	1.29285i	−0.907635	−	0.419761i	$-0.862114\pi$
$421$	−8.61916	−	26.5270i	−0.420072	−	1.29285i	0.487563	−	0.873088i	$-0.337886\pi$
$422$	2.64611	+	0.859773i	0.128811	+	0.0418531i
$423$	−1.17306	+	1.61457i	−0.0570360	+	0.0785033i
$424$	−0.406622	−	0.295428i	−0.0197473	−	0.0143473i
$425$	17.5669	−	3.94628i	0.852119	−	0.191423i
$426$	1.22281	+	3.76341i	0.0592452	+	0.182338i
$427$	−10.2436	−	14.0991i	−0.495723	−	0.682304i
$428$		−	30.1808i		−	1.45884i
$429$		0			0
$430$	0.115852	+	0.422602i	0.00558689	+	0.0203797i
$431$	16.2108	−	11.7778i	0.780847	−	0.567318i	−0.124386	−	0.992234i	$-0.539696\pi$
$431$	16.2108	−	11.7778i	0.780847	−	0.567318i	0.905233	+	0.424915i	$0.139696\pi$
$432$	15.6218	−	5.07583i	0.751604	−	0.244211i
$433$	−4.17012	−	1.35495i	−0.200403	−	0.0651150i	0.207095	−	0.978321i	$-0.433599\pi$
$433$	−4.17012	−	1.35495i	−0.200403	−	0.0651150i	−0.407499	+	0.913206i	$0.633599\pi$
$434$	2.83135	+	2.05710i	0.135909	+	0.0987439i
$435$	4.12173	+	1.55497i	0.197622	+	0.0745549i
$436$	2.28572	−	7.03474i	0.109466	−	0.336903i
$437$	−27.8409	+	9.04605i	−1.33181	+	0.432731i
$438$	1.58099	+	2.17605i	0.0755428	+	0.103976i
$439$	−34.2675			−1.63550			−0.817750	−	0.575573i	$-0.804779\pi$
$439$	−34.2675			−1.63550			−0.817750	+	0.575573i	$0.804779\pi$
$440$		0			0
$441$	−7.69622			−0.366487
$442$	−3.61896	−	4.98107i	−0.172136	−	0.236925i
$443$	17.5881	−	5.71470i	0.835634	−	0.271514i	0.140217	−	0.990121i	$-0.455220\pi$
$443$	17.5881	−	5.71470i	0.835634	−	0.271514i	0.695416	+	0.718607i	$0.255220\pi$
$444$	3.50831	−	10.7975i	0.166497	−	0.512425i
$445$	7.10353	−	18.8292i	0.336740	−	0.892591i
$446$	−6.29752	−	4.57542i	−0.298196	−	0.216652i
$447$	12.7429	+	4.14042i	0.602718	+	0.195835i
$448$	17.2037	−	5.58982i	0.812799	−	0.264094i
$449$	15.1859	−	11.0332i	0.716666	−	0.520688i	−0.168651	−	0.985676i	$-0.553941\pi$
$449$	15.1859	−	11.0332i	0.716666	−	0.520688i	0.885317	+	0.464988i	$0.153941\pi$
$450$	−1.73686	−	2.92976i	−0.0818766	−	0.138110i
$451$		0			0
$452$			18.6902i			0.879113i
$453$	9.06612	+	12.4784i	0.425963	+	0.586288i
$454$	−0.0727087	−	0.223774i	−0.00341239	−	0.0105022i
$455$	−38.0641	−	1.77478i	−1.78447	−	0.0832028i
$456$	4.98254	+	3.62003i	0.233329	+	0.169523i
$457$	8.52231	−	11.7300i	0.398657	−	0.548704i	−0.561749	−	0.827308i	$-0.689871\pi$
$457$	8.52231	−	11.7300i	0.398657	−	0.548704i	0.960406	+	0.278603i	$0.0898714\pi$
$458$	−4.10620	−	1.33419i	−0.191870	−	0.0623424i
$459$	−5.43214	−	16.7184i	−0.253551	−	0.780349i
$460$	15.4489	−	19.3045i	0.720311	−	0.900075i
$461$	15.2150			0.708632			0.354316	−	0.935126i	$-0.384714\pi$
$461$	15.2150			0.708632			0.354316	+	0.935126i	$0.384714\pi$
$462$		0			0
$463$			9.08060i			0.422011i	0.977485	+	0.211006i	$0.0676739\pi$
$463$			9.08060i			0.422011i	−0.977485	+	0.211006i	$0.932326\pi$
$464$	−5.57472	+	4.05027i	−0.258800	+	0.188029i
$465$	3.84955	+	5.85359i	0.178518	+	0.271454i
$466$	−2.73275	+	8.41053i	−0.126592	+	0.389610i
$467$	−10.1593	+	13.9831i	−0.470116	+	0.647059i	−0.976568	−	0.215209i	$-0.930957\pi$
$467$	−10.1593	+	13.9831i	−0.470116	+	0.647059i	0.506452	+	0.862268i	$0.330957\pi$
$468$	12.0149	−	16.5371i	0.555388	−	0.764426i
$469$	8.54593	−	26.3017i	0.394614	−	1.21450i
$470$	0.590136	−	0.388097i	0.0272210	−	0.0179016i
$471$	−1.77048	+	1.28633i	−0.0815795	+	0.0592709i
$472$			0.674078i			0.0310269i
$473$		0			0
$474$	−0.894665			−0.0410933
$475$	−9.92294	+	22.9976i	−0.455296	+	1.05520i
$476$	−6.89053	−	21.2069i	−0.315827	−	0.972015i
$477$	−0.775950	−	0.252121i	−0.0355283	−	0.0115438i
$478$	−0.966815	+	1.33071i	−0.0442211	+	0.0608651i
$479$	26.3987	+	19.1798i	1.20619	+	0.876346i	0.994879	−	0.101074i	$-0.0322278\pi$
$479$	26.3987	+	19.1798i	1.20619	+	0.876346i	0.211308	+	0.977420i	$0.432228\pi$
$480$	−7.86623	−	0.366770i	−0.359043	−	0.0167407i
$481$	−10.0362	−	30.8883i	−0.457612	−	1.40839i
$482$	0.905851	+	1.24680i	0.0412604	+	0.0567901i
$483$			18.3974i			0.837110i
$484$		0			0
$485$	24.3559	−	6.67694i	1.10594	−	0.303184i
$486$	−4.28070	+	3.11011i	−0.194176	+	0.141077i
$487$	14.5096	−	4.71445i	0.657493	−	0.213632i	0.0387776	−	0.999248i	$-0.487654\pi$
$487$	14.5096	−	4.71445i	0.657493	−	0.213632i	0.618715	+	0.785616i	$0.287654\pi$
$488$	−6.47263	−	2.10308i	−0.293002	−	0.0952022i
$489$	−17.5652	−	12.7619i	−0.794326	−	0.577112i
$490$	2.54847	+	0.961440i	0.115128	+	0.0434334i
$491$	2.06112	−	6.34349i	0.0930172	−	0.286278i	−0.893715	−	0.448636i	$-0.851910\pi$
$491$	2.06112	−	6.34349i	0.0930172	−	0.286278i	0.986732	+	0.162358i	$0.0519100\pi$
$492$	17.6678	−	5.74062i	0.796526	−	0.258807i
$493$	4.33459	+	5.96605i	0.195220	+	0.268697i
$494$	8.56518			0.385365
$495$		0			0
$496$	−10.9587			−0.492060
$497$	24.0975	+	33.1674i	1.08092	+	1.48776i
$498$	−3.64723	+	1.18506i	−0.163436	+	0.0531036i
$499$	1.90018	−	5.84815i	0.0850637	−	0.261799i	−0.899473	−	0.436976i	$-0.856050\pi$
$499$	1.90018	−	5.84815i	0.0850637	−	0.261799i	0.984537	+	0.175176i	$0.0560496\pi$
$500$	−3.67045	−	20.8344i	−0.164147	−	0.931744i
$501$	2.96486	+	2.15409i	0.132460	+	0.0962378i
$502$	1.36727	+	0.444252i	0.0610241	+	0.0198279i
$503$	24.4498	−	7.94424i	1.09016	−	0.354216i	0.291855	−	0.956463i	$-0.405728\pi$
$503$	24.4498	−	7.94424i	1.09016	−	0.354216i	0.798310	+	0.602247i	$0.205728\pi$
$504$	−7.01948	+	5.09995i	−0.312673	+	0.227170i
$505$	−7.78416	−	28.3948i	−0.346391	−	1.26355i
$506$		0			0
$507$			13.5795i			0.603085i
$508$	−6.02353	−	8.29068i	−0.267251	−	0.367839i
$509$	5.20549	+	16.0209i	0.230729	+	0.710112i	0.997659	+	0.0683812i	$0.0217834\pi$
$509$	5.20549	+	16.0209i	0.230729	+	0.710112i	−0.766930	+	0.641731i	$0.778217\pi$
$510$	−0.118459	+	2.54063i	−0.00524547	+	0.112501i
$511$	22.5448	+	16.3798i	0.997325	+	0.724599i
$512$	12.2953	−	16.9230i	0.543380	−	0.747898i
$513$	23.2577	+	7.55688i	1.02685	+	0.333644i
$514$	0.661168	+	2.03487i	0.0291629	+	0.0897541i
$515$	−3.88729	+	4.85742i	−0.171294	+	0.214043i
$516$	1.08638			0.0478253
$517$		0			0
$518$			6.70201i			0.294469i
$519$	0.739089	−	0.536980i	0.0324424	−	0.0235708i
$520$	−12.4332	+	8.17654i	−0.545231	+	0.358565i
$521$	−7.77819	+	23.9388i	−0.340769	+	1.04878i	0.623042	+	0.782189i	$0.285897\pi$
$521$	−7.77819	+	23.9388i	−0.340769	+	1.04878i	−0.963810	+	0.266589i	$0.914103\pi$
$522$	0.819965	−	1.12859i	0.0358889	−	0.0493968i
$523$	10.5269	−	14.4890i	0.460308	−	0.633560i	−0.514264	−	0.857632i	$-0.671935\pi$
$523$	10.5269	−	14.4890i	0.460308	−	0.633560i	0.974573	+	0.224072i	$0.0719350\pi$
$524$	−11.1822	+	34.4152i	−0.488496	+	1.50344i
$525$	11.8187	+	10.3972i	0.515809	+	0.453773i
$526$	−1.13751	+	0.826447i	−0.0495977	+	0.0360348i
$527$			11.7280i			0.510879i
$528$		0			0
$529$	−11.1491			−0.484744
$530$	0.225447	+	0.180420i	0.00979278	+	0.00783695i
$531$	0.338132	+	1.04066i	0.0146737	+	0.0451609i
$532$	29.5018	+	9.58570i	1.27906	+	0.415593i
$533$	31.2369	−	42.9939i	1.35302	−	1.86227i
$534$	2.29992	+	1.67099i	0.0995274	+	0.0723109i
$535$	−1.66114	+	35.6271i	−0.0718175	+	1.54029i
$536$	−3.33733	−	10.2713i	−0.144151	−	0.443651i
$537$	−2.05556	−	2.82923i	−0.0887038	−	0.122090i
$538$		−	3.48763i		−	0.150362i
$539$		0			0
$540$	−19.9199	+	5.46085i	−0.857215	+	0.234998i
$541$	7.64091	−	5.55145i	0.328508	−	0.238675i	−0.411289	−	0.911505i	$-0.634921\pi$
$541$	7.64091	−	5.55145i	0.328508	−	0.238675i	0.739797	+	0.672830i	$0.234921\pi$
$542$	−3.32596	+	1.08067i	−0.142862	+	0.0464188i
$543$	−11.4994	−	3.73637i	−0.493484	−	0.160343i
$544$	−10.6648	−	7.74840i	−0.457248	−	0.332210i
$545$	−3.08539	+	8.17839i	−0.132163	+	0.350324i
$546$	1.66341	−	5.11943i	0.0711872	−	0.219092i
$547$	−14.5554	+	4.72933i	−0.622343	+	0.202212i	−0.603180	−	0.797605i	$-0.706100\pi$
$547$	−14.5554	+	4.72933i	−0.622343	+	0.202212i	−0.0191628	+	0.999816i	$0.506100\pi$
$548$	−17.8428	−	24.5586i	−0.762209	−	1.04909i
$549$	−11.0476			−0.471500
$550$		0			0
$551$	−10.2589			−0.437044
$552$	4.22294	+	5.81238i	0.179740	+	0.247391i
$553$	−8.81546	+	2.86432i	−0.374872	+	0.121803i
$554$	−0.745833	+	2.29544i	−0.0316874	+	0.0975239i
$555$	−4.73569	+	12.5528i	−0.201019	+	0.532837i
$556$	−19.2413	−	13.9796i	−0.816013	−	0.592868i
$557$	9.46153	+	3.07424i	0.400898	+	0.130260i	0.502524	−	0.864563i	$-0.332405\pi$
$557$	9.46153	+	3.07424i	0.400898	+	0.130260i	−0.101627	+	0.994823i	$0.532405\pi$
$558$	2.10997	−	0.685572i	0.0893223	−	0.0290226i
$559$	2.51427	−	1.82673i	0.106342	−	0.0772623i
$560$	−23.7461	+	6.50977i	−1.00346	+	0.275088i
$561$		0			0
$562$			9.26912i			0.390994i
$563$	16.4826	+	22.6864i	0.694661	+	0.956118i	0.999993	+	0.00387226i	$0.00123258\pi$
$563$	16.4826	+	22.6864i	0.694661	+	0.956118i	−0.305332	+	0.952246i	$0.598767\pi$
$564$	−0.541124	−	1.66541i	−0.0227854	−	0.0701263i
$565$	1.02871	−	22.0630i	0.0432780	−	0.928195i
$566$	2.67281	+	1.94191i	0.112347	+	0.0816247i
$567$	−2.93816	+	4.04403i	−0.123391	+	0.169833i
$568$	15.2265	+	4.94739i	0.638890	+	0.207588i
$569$	6.29686	+	19.3797i	0.263978	+	0.812441i	0.991927	+	0.126810i	$0.0404738\pi$
$569$	6.29686	+	19.3797i	0.263978	+	0.812441i	−0.727949	+	0.685631i	$0.759526\pi$
$570$	−2.76251	−	2.21078i	−0.115709	−	0.0925993i
$571$	43.6546			1.82689			0.913444	−	0.406964i	$-0.133412\pi$
$571$	43.6546			1.82689			0.913444	+	0.406964i	$0.133412\pi$
$572$		0			0
$573$			2.57485i			0.107566i
$574$	−8.87204	+	6.44592i	−0.370312	+	0.269047i
$575$	−19.2993	+	21.9377i	−0.804837	+	0.914867i
$576$	3.54350	−	10.9058i	0.147646	−	0.454407i
$577$	22.0210	−	30.3094i	0.916748	−	1.26180i	−0.0480615	−	0.998844i	$-0.515304\pi$
$577$	22.0210	−	30.3094i	0.916748	−	1.26180i	0.964809	−	0.262951i	$-0.0846957\pi$
$578$	0.778417	−	1.07140i	0.0323779	−	0.0445644i
$579$	0.115411	−	0.355200i	0.00479633	−	0.0147616i
$580$	7.23964	−	4.76107i	0.300610	−	0.197693i
$581$	−32.1434	+	23.3536i	−1.33353	+	0.968869i
$582$			3.56753i			0.147879i
$583$		0			0
$584$	10.8825			0.450322
$585$	−15.0932	+	18.8600i	−0.624028	+	0.779763i
$586$	0.00248392	+	0.00764472i	0.000102610	+	0.000315800i
$587$	5.72456	+	1.86002i	0.236278	+	0.0767714i	0.424763	−	0.905305i	$-0.360358\pi$
$587$	5.72456	+	1.86002i	0.236278	+	0.0767714i	−0.188485	+	0.982076i	$0.560358\pi$
$588$	3.96926	−	5.46322i	0.163690	−	0.225300i
$589$	−13.1993	−	9.58988i	−0.543869	−	0.395144i
$590$	0.0180367	−	0.386839i	0.000742560	−	0.0159259i
$591$	−5.51195	−	16.9640i	−0.226731	−	0.697807i
$592$	−12.3352	−	16.9779i	−0.506974	−	0.697789i
$593$			14.3574i			0.589589i	0.955561	+	0.294794i	$0.0952511\pi$
$593$			14.3574i			0.589589i	−0.955561	+	0.294794i	$0.904749\pi$
$594$		0			0
$595$	6.96674	+	25.4130i	0.285609	+	1.04183i
$596$	21.3210	−	15.4906i	0.873343	−	0.634521i
$597$	−9.28559	+	3.01707i	−0.380034	+	0.123481i
$598$	9.50267	+	3.08760i	0.388593	+	0.126261i
$599$	22.6097	+	16.4269i	0.923806	+	0.671184i	0.944468	−	0.328602i	$-0.106578\pi$
$599$	22.6097	+	16.4269i	0.923806	+	0.671184i	−0.0206626	+	0.999787i	$0.506578\pi$
$600$	6.12052	+	0.571993i	0.249869	+	0.0233515i
$601$	−6.35457	+	19.5573i	−0.259208	+	0.797761i	0.733763	+	0.679405i	$0.237762\pi$
$601$	−6.35457	+	19.5573i	−0.259208	+	0.797761i	−0.992971	+	0.118355i	$0.962238\pi$
$602$	−0.609928	+	0.198178i	−0.0248588	+	0.00807712i
$603$	−10.3046	−	14.1830i	−0.419634	−	0.577577i
$604$	30.3383			1.23445
$605$		0			0
$606$	4.15912			0.168953
$607$	11.2701	+	15.5120i	0.457439	+	0.629611i	0.973975	−	0.226654i	$-0.0727788\pi$
$607$	11.2701	+	15.5120i	0.457439	+	0.629611i	−0.516536	+	0.856265i	$0.672779\pi$
$608$	17.4410	−	5.66692i	0.707326	−	0.229824i
$609$	−1.99234	+	6.13178i	−0.0807335	+	0.248472i
$610$	3.65823	+	1.38011i	0.148117	+	0.0558789i
$611$	−4.05270	−	2.94446i	−0.163955	−	0.119120i
$612$	−13.4434	−	4.36804i	−0.543419	−	0.176568i
$613$	−17.1700	+	5.57888i	−0.693491	+	0.225329i	−0.634492	−	0.772929i	$-0.718791\pi$
$613$	−17.1700	+	5.57888i	−0.693491	+	0.225329i	−0.0589988	+	0.998258i	$0.518791\pi$
$614$	8.75815	−	6.36317i	0.353450	−	0.256797i
$615$	−21.1720	+	5.80411i	−0.853738	+	0.234044i
$616$		0			0
$617$			32.0433i			1.29001i	0.764176	+	0.645007i	$0.223146\pi$
$617$			32.0433i			1.29001i	−0.764176	+	0.645007i	$0.776854\pi$
$618$	−0.516575	−	0.711004i	−0.0207797	−	0.0286008i
$619$	1.64083	+	5.04996i	0.0659506	+	0.202975i	0.978601	−	0.205765i	$-0.0659682\pi$
$619$	1.64083	+	5.04996i	0.0659506	+	0.202975i	−0.912651	+	0.408740i	$0.865968\pi$
$620$	13.7653	+	0.641819i	0.552827	+	0.0257761i
$621$	23.0792	+	16.7680i	0.926136	+	0.672877i
$622$	−0.931352	+	1.28190i	−0.0373438	+	0.0513994i
$623$	28.0117	+	9.10156i	1.12227	+	0.364646i
$624$	5.20860	+	16.0304i	0.208511	+	0.641730i
$625$	3.18608	+	24.7961i	0.127443	+	0.991846i
$626$	5.60369			0.223968
$627$		0			0
$628$			4.30450i			0.171768i
$629$	−18.1698	+	13.2011i	−0.724476	+	0.526362i
$630$	4.16479	−	2.73893i	0.165929	−	0.109122i
$631$	12.1729	−	37.4644i	0.484597	−	1.49144i	−0.347967	−	0.937507i	$-0.613128\pi$
$631$	12.1729	−	37.4644i	0.484597	−	1.49144i	0.832564	−	0.553929i	$-0.186872\pi$
$632$	−2.12764	+	2.92844i	−0.0846329	+	0.116487i
$633$	−4.79135	+	6.59472i	−0.190439	+	0.262117i
$634$	0.174173	−	0.536049i	0.00691729	−	0.0212892i
$635$	6.65419	+	10.1183i	0.264064	+	0.401533i
$636$	0.579160	−	0.420785i	0.0229652	−	0.0166852i
$637$		−	19.3181i		−	0.765410i
$638$		0			0
$639$	25.9889			1.02810
$640$	−12.7652	+	15.9510i	−0.504590	+	0.630518i
$641$	−14.6057	−	44.9517i	−0.576890	−	1.77548i	−0.629653	−	0.776876i	$-0.716803\pi$
$641$	−14.6057	−	44.9517i	−0.576890	−	1.77548i	0.0527635	−	0.998607i	$-0.483197\pi$
$642$	−4.79166	−	1.55690i	−0.189112	−	0.0614461i
$643$	1.39810	−	1.92433i	0.0551358	−	0.0758880i	−0.780559	−	0.625082i	$-0.785065\pi$
$643$	1.39810	−	1.92433i	0.0551358	−	0.0758880i	0.835695	+	0.549194i	$0.185065\pi$
$644$	29.2754	+	21.2698i	1.15361	+	0.838147i
$645$	−1.28243	−	0.0597943i	−0.0504954	−	0.00235440i
$646$	−1.83030	−	5.63309i	−0.0720122	−	0.221631i
$647$	−0.523292	−	0.720250i	−0.0205727	−	0.0283159i	0.798607	−	0.601853i	$-0.205571\pi$
$647$	−0.523292	−	0.720250i	−0.0205727	−	0.0283159i	−0.819179	+	0.573537i	$0.805571\pi$
$648$			1.95208i			0.0766849i
$649$		0			0
$650$	7.35392	−	4.35966i	0.288445	−	0.171000i
$651$	−8.29529	+	6.02688i	−0.325118	+	0.236212i
$652$	−40.6154	+	13.1967i	−1.59062	+	0.516824i
$653$	−12.4143	−	4.03364i	−0.485808	−	0.157849i	0.0558643	−	0.998438i	$-0.482209\pi$
$653$	−12.4143	−	4.03364i	−0.485808	−	0.157849i	−0.541672	+	0.840590i	$0.682209\pi$
$654$	−0.998961	−	0.725787i	−0.0390625	−	0.0283805i
$655$	15.0943	−	40.0102i	0.589783	−	1.56333i
$656$	10.6114	−	32.6584i	0.414304	−	1.27510i
$657$	16.8008	−	5.45891i	0.655462	−	0.212972i
$658$	0.607607	+	0.836299i	0.0236870	+	0.0326023i
$659$	−24.8805			−0.969205			−0.484603	−	0.874734i	$-0.661036\pi$
$659$	−24.8805			−0.969205			−0.484603	+	0.874734i	$0.661036\pi$
$660$		0			0
$661$	−33.1788			−1.29051			−0.645253	−	0.763969i	$-0.723248\pi$
$661$	−33.1788			−1.29051			−0.645253	+	0.763969i	$0.723248\pi$
$662$	−0.172192	−	0.237001i	−0.00669241	−	0.00921132i
$663$	17.1557	−	5.57423i	0.666272	−	0.216485i
$664$	−4.79465	+	14.7564i	−0.186069	+	0.572660i
$665$	−34.2979	−	12.9393i	−1.33002	−	0.501763i
$666$	3.43713	+	2.49722i	0.133186	+	0.0967655i
$667$	−11.3818	−	3.69816i	−0.440704	−	0.143193i
$668$	6.85553	−	2.22750i	0.265248	−	0.0861844i
$669$	18.4504	−	13.4050i	0.713335	−	0.518269i
$670$	1.64039	+	5.98375i	0.0633738	+	0.231173i
$671$		0			0
$672$		−	11.5251i		−	0.444590i
$673$	−14.0009	−	19.2706i	−0.539694	−	0.742825i	0.448875	−	0.893595i	$-0.351825\pi$
$673$	−14.0009	−	19.2706i	−0.539694	−	0.742825i	−0.988569	+	0.150769i	$0.951825\pi$
$674$	1.90610	+	5.86637i	0.0734202	+	0.225964i
$675$	23.8151	−	5.34990i	0.916644	−	0.205918i
$676$	21.6087	+	15.6996i	0.831104	+	0.603832i
$677$	1.09937	−	1.51315i	0.0422522	−	0.0581551i	−0.787368	−	0.616483i	$-0.788557\pi$
$677$	1.09937	−	1.51315i	0.0422522	−	0.0581551i	0.829620	+	0.558328i	$0.188557\pi$
$678$	2.96736	+	0.964152i	0.113961	+	0.0370280i
$679$	11.4216	+	35.1521i	0.438321	+	1.34901i
$680$	8.03435	+	6.42972i	0.308103	+	0.246568i
$681$	0.689352			0.0264160
$682$		0			0
$683$		−	9.51629i		−	0.364131i	−0.983286	−	0.182065i	$-0.941722\pi$
$683$		−	9.51629i		−	0.364131i	0.983286	−	0.182065i	$-0.0582782\pi$
$684$	15.9086	−	11.5583i	0.608282	−	0.441943i
$685$	19.7110	+	29.9724i	0.753118	+	1.14519i
$686$	1.09252	−	3.36245i	0.0417128	−	0.128379i
$687$	7.43516	−	10.2336i	0.283669	−	0.390437i
$688$	1.18036	−	1.62462i	0.0450007	−	0.0619382i
$689$	0.632843	−	1.94769i	0.0241094	−	0.0742011i
$690$	−2.26793	−	3.44859i	−0.0863386	−	0.131286i
$691$	3.69460	−	2.68428i	0.140549	−	0.102115i	−0.515289	−	0.857016i	$-0.672315\pi$
$691$	3.69460	−	2.68428i	0.140549	−	0.102115i	0.655838	+	0.754902i	$0.272315\pi$
$692$		−	1.79692i		−	0.0683085i
$693$		0			0
$694$	6.88217			0.261244
$695$	21.9441	+	17.5614i	0.832386	+	0.666141i
$696$	0.778042	+	2.39457i	0.0294916	+	0.0907658i
$697$	−34.9509	−	11.3562i	−1.32386	−	0.430149i
$698$	−5.24701	+	7.22189i	−0.198602	+	0.273353i
$699$	−20.9610	−	15.2291i	−0.792818	−	0.576016i
$700$	30.2088	−	6.78621i	1.14179	−	0.256495i
$701$	−8.88594	−	27.3481i	−0.335617	−	1.03292i	−0.966417	−	0.256978i	$-0.917273\pi$
$701$	−8.88594	−	27.3481i	−0.335617	−	1.03292i	0.630800	−	0.775946i	$-0.282727\pi$
$702$	−4.90616	−	6.75274i	−0.185171	−	0.254866i
$703$		−	31.2437i		−	1.17838i
$704$		0			0
$705$	0.547109	+	1.99572i	0.0206053	+	0.0751633i
$706$	2.30269	−	1.67300i	0.0866628	−	0.0629642i
$707$	40.9813	−	13.3156i	1.54126	−	0.500786i
$708$	−0.913112	−	0.296688i	−0.0343168	−	0.0111502i
$709$	−29.4596	−	21.4037i	−1.10638	−	0.803831i	−0.124289	−	0.992246i	$-0.539665\pi$
$709$	−29.4596	−	21.4037i	−1.10638	−	0.803831i	−0.982090	+	0.188415i	$0.939665\pi$
$710$	−8.60578	−	3.24663i	−0.322969	−	0.121844i
$711$	−1.81575	+	5.58829i	−0.0680958	+	0.209577i
$712$	10.9391	−	3.55432i	0.409959	−	0.133204i
$713$	−11.1871	−	15.3977i	−0.418959	−	0.576647i
$714$	−3.72237			−0.139306
$715$		0			0
$716$	−6.87859			−0.257065
$717$	−2.83257	−	3.89870i	−0.105784	−	0.145600i
$718$	2.15618	−	0.700587i	0.0804681	−	0.0261457i
$719$	−12.0899	+	37.2090i	−0.450879	+	1.38766i	0.425027	+	0.905181i	$0.360265\pi$
$719$	−12.0899	+	37.2090i	−0.450879	+	1.38766i	−0.875906	+	0.482482i	$0.839735\pi$
$720$	−5.50945	+	14.6038i	−0.205325	+	0.544252i
$721$	−7.36631	−	5.35194i	−0.274336	−	0.199317i
$722$	1.90310	+	0.618355i	0.0708261	+	0.0230128i
$723$	−4.29420	+	1.39527i	−0.159703	+	0.0518906i
$724$	−19.2404	+	13.9789i	−0.715063	+	0.519523i
$725$	−8.80812	+	5.22176i	−0.327126	+	0.193931i
$726$		0			0
$727$		−	32.8912i		−	1.21987i	−0.792453	−	0.609933i	$-0.791196\pi$
$727$		−	32.8912i		−	1.21987i	0.792453	−	0.609933i	$-0.208804\pi$
$728$	−12.8013	−	17.6194i	−0.474446	−	0.653019i
$729$	−3.37443	−	10.3854i	−0.124979	−	0.384646i
$730$	−6.24525	−	0.291191i	−0.231147	−	0.0107774i
$731$	−1.73867	−	1.26322i	−0.0643069	−	0.0467217i
$732$	5.69771	−	7.84223i	0.210594	−	0.289857i
$733$	−11.3420	−	3.68523i	−0.418925	−	0.136117i	0.0919667	−	0.995762i	$-0.470685\pi$
$733$	−11.3420	−	3.68523i	−0.418925	−	0.136117i	−0.510892	+	0.859645i	$0.670685\pi$
$734$	1.65288	+	5.08705i	0.0610090	+	0.187766i
$735$	−4.98624	+	6.23063i	−0.183920	+	0.229820i
$736$	21.3928			0.788549
$737$		0			0
$738$			6.95184i			0.255901i
$739$	30.1302	−	21.8909i	1.10836	−	0.805268i	0.125952	−	0.992036i	$-0.459801\pi$
$739$	30.1302	−	21.8909i	1.10836	−	0.805268i	0.982404	+	0.186768i	$0.0598013\pi$
$740$	14.5000	+	22.0485i	0.533029	+	0.810519i
$741$	−7.75454	+	23.8660i	−0.284870	+	0.876740i
$742$	−0.248399	+	0.341892i	−0.00911901	+	0.0125512i
$743$	−7.84414	+	10.7965i	−0.287774	+	0.396086i	−0.928289	−	0.371859i	$-0.878721\pi$
$743$	−7.84414	+	10.7965i	−0.287774	+	0.396086i	0.640516	+	0.767945i	$0.278721\pi$
$744$	−1.23736	+	3.80821i	−0.0453639	+	0.139616i
$745$	−26.0211	+	17.1125i	−0.953340	+	0.626953i
$746$	0.981868	−	0.713369i	0.0359487	−	0.0261183i
$747$			25.1865i			0.921527i
$748$		0			0
$749$	−52.1984			−1.90729
$750$	−3.49713	−	0.492025i	−0.127697	−	0.0179662i
$751$	0.245976	+	0.757037i	0.00897580	+	0.0276247i	0.955444	−	0.295172i	$-0.0953770\pi$
$751$	0.245976	+	0.757037i	0.00897580	+	0.0276247i	−0.946468	+	0.322797i	$0.895377\pi$
$752$	−3.07846	−	1.00025i	−0.112260	−	0.0364754i
$753$	−2.47573	+	3.40755i	−0.0902205	+	0.124178i
$754$	2.83283	+	2.05817i	0.103166	+	0.0749543i
$755$	−35.8130	−	1.66981i	−1.30337	−	0.0607708i
$756$	−9.34137	−	28.7498i	−0.339742	−	1.04562i
$757$	23.9048	+	32.9022i	0.868836	+	1.19585i	0.979390	+	0.201979i	$0.0647374\pi$
$757$	23.9048	+	32.9022i	0.868836	+	1.19585i	−0.110554	+	0.993870i	$0.535263\pi$
$758$			1.21548i			0.0441483i
$759$		0			0
$760$	−13.8060	+	3.78479i	−0.500796	+	0.137289i
$761$	−4.66827	+	3.39169i	−0.169224	+	0.122949i	−0.669174	−	0.743106i	$-0.733352\pi$
$761$	−4.66827	+	3.39169i	−0.169224	+	0.122949i	0.499949	+	0.866055i	$0.333352\pi$
$762$	−1.62700	+	0.528645i	−0.0589401	+	0.0191508i
$763$	−12.1668	−	3.95322i	−0.440466	−	0.143116i
$764$	4.09730	+	2.97686i	0.148235	+	0.107699i
$765$	15.6290	+	5.89620i	0.565067	+	0.213178i
$766$	3.18307	−	9.79649i	0.115009	−	0.353962i
$767$	−2.61214	+	0.848736i	−0.0943189	+	0.0306461i
$768$	4.55464	+	6.26892i	0.164351	+	0.226210i
$769$	−16.4209			−0.592152			−0.296076	−	0.955164i	$-0.595678\pi$
$769$	−16.4209			−0.592152			−0.296076	+	0.955164i	$0.595678\pi$
$770$		0			0
$771$	−6.26855			−0.225756
$772$	−0.431791	−	0.594309i	−0.0155405	−	0.0213897i
$773$	−23.3808	+	7.59689i	−0.840950	+	0.273241i	−0.697651	−	0.716438i	$-0.745771\pi$
$773$	−23.3808	+	7.59689i	−0.840950	+	0.273241i	−0.143299	+	0.989679i	$0.545771\pi$
$774$	−0.125629	+	0.386645i	−0.00451563	+	0.0138977i
$775$	−16.2140	−	1.51528i	−0.582423	−	0.0544304i
$776$	11.6773	+	8.48407i	0.419191	+	0.304560i
$777$	−18.6745	−	6.06771i	−0.669943	−	0.217678i
$778$	−4.31748	+	1.40283i	−0.154789	+	0.0502940i
$779$	41.3601	−	30.0499i	1.48188	−	1.07665i
$780$	−5.60369	−	20.4409i	−0.200644	−	0.731902i
$781$		0			0
$782$		−	6.90944i		−	0.247081i
$783$	5.87632	+	8.08807i	0.210003	+	0.289044i
$784$	−3.85732	−	11.8716i	−0.137762	−	0.423987i
$785$	0.236919	−	5.08127i	0.00845599	−	0.181358i
$786$	4.88710	+	3.55069i	0.174317	+	0.126649i
$787$	−1.07856	+	1.48451i	−0.0384465	+	0.0529171i	−0.827807	−	0.561012i	$-0.810412\pi$
$787$	−1.07856	+	1.48451i	−0.0384465	+	0.0529171i	0.789361	+	0.613929i	$0.210412\pi$
$788$	−33.3670	−	10.8416i	−1.18865	−	0.386216i
$789$	−1.27296	−	3.91778i	−0.0453187	−	0.139477i
$790$	1.29936	−	1.62364i	0.0462293	−	0.0577665i
$791$	32.3252			1.14935
$792$		0			0
$793$		−	27.7303i		−	0.984732i
$794$	2.58579	−	1.87868i	0.0917661	−	0.0666720i
$795$	−0.706833	+	0.464841i	−0.0250688	+	0.0164862i
$796$	−5.93436	+	18.2641i	−0.210338	+	0.647354i
$797$	−24.6903	+	33.9833i	−0.874576	+	1.20375i	0.103318	+	0.994648i	$0.467054\pi$
$797$	−24.6903	+	33.9833i	−0.874576	+	1.20375i	−0.977894	+	0.209102i	$0.932946\pi$
$798$	3.04375	−	4.18937i	0.107748	−	0.148302i
$799$	−1.07047	+	3.29456i	−0.0378704	+	0.116553i
$800$	12.0901	−	13.7430i	0.427450	−	0.485887i
$801$	15.1052	−	10.9745i	0.533714	−	0.387766i
$802$		−	8.59517i		−	0.303506i
$803$		0			0
$804$	15.3824			0.542496
$805$	−33.3876	−	26.7194i	−1.17676	−	0.941733i
$806$	1.72084	+	5.29619i	0.0606139	+	0.186550i
$807$	9.71794	+	3.15755i	0.342088	+	0.111151i
$808$	9.89097	−	13.6137i	0.347963	−	0.478930i
$809$	21.9090	+	15.9179i	0.770281	+	0.559642i	0.902046	−	0.431639i	$-0.142065\pi$
$809$	21.9090	+	15.9179i	0.770281	+	0.559642i	−0.131765	+	0.991281i	$0.542065\pi$
$810$	0.0522330	−	1.12026i	0.00183528	−	0.0393618i
$811$	−0.317909	−	0.978424i	−0.0111633	−	0.0343571i	0.945320	−	0.326145i	$-0.105750\pi$
$811$	−0.317909	−	0.978424i	−0.0111633	−	0.0343571i	−0.956483	+	0.291788i	$0.905750\pi$
$812$	7.45397	+	10.2595i	0.261583	+	0.360038i
$813$		−	10.2459i		−	0.359338i
$814$		0			0
$815$	48.6710	−	13.3427i	1.70487	−	0.467374i
$816$	9.42974	−	6.85111i	0.330107	−	0.239837i
$817$	2.84339	−	0.923874i	0.0994777	−	0.0323222i
$818$	0.826173	+	0.268440i	0.0288865	+	0.00938578i
$819$	−28.6013	−	20.7800i	−0.999409	−	0.726113i
$820$	−15.2417	+	40.4009i	−0.532262	+	1.41086i
$821$	3.55571	−	10.9434i	0.124095	−	0.381926i	−0.869640	−	0.493687i	$-0.835649\pi$
$821$	3.55571	−	10.9434i	0.124095	−	0.381926i	0.993735	+	0.111761i	$0.0356490\pi$
$822$	−4.81949	+	1.56595i	−0.168099	+	0.0546187i
$823$	16.9071	+	23.2706i	0.589343	+	0.811162i	0.994681	−	0.103006i	$-0.0328460\pi$
$823$	16.9071	+	23.2706i	0.589343	+	0.811162i	−0.405337	+	0.914167i	$0.632846\pi$
$824$	−3.55576			−0.123871
$825$		0			0
$826$	0.566771			0.0197205
$827$	−31.7695	−	43.7269i	−1.10473	−	1.52053i	−0.828957	−	0.559312i	$-0.811065\pi$
$827$	−31.7695	−	43.7269i	−1.10473	−	1.52053i	−0.275775	−	0.961222i	$-0.588935\pi$
$828$	21.8165	−	7.08861i	0.758175	−	0.246346i
$829$	−1.43658	+	4.42133i	−0.0498943	+	0.153559i	−0.972899	−	0.231229i	$-0.925725\pi$
$829$	−1.43658	+	4.42133i	−0.0498943	+	0.153559i	0.923005	+	0.384788i	$0.125725\pi$
$830$	3.14639	−	8.34010i	0.109213	−	0.289489i
$831$	−5.72077	−	4.15638i	−0.198451	−	0.144183i
$832$	27.3743	+	8.89444i	0.949032	+	0.308359i
$833$	−12.7050	+	4.12810i	−0.440202	+	0.143030i
$834$	−3.21206	+	2.33370i	−0.111225	+	0.0808094i
$835$	−8.21525	+	2.25213i	−0.284300	+	0.0779383i
$836$		0			0
$837$			15.8994i			0.549564i
$838$	4.69217	+	6.45822i	0.162088	+	0.223096i
$839$	−1.52812	−	4.70308i	−0.0527566	−	0.162368i	0.921207	−	0.389073i	$-0.127205\pi$
$839$	−1.52812	−	4.70308i	−0.0527566	−	0.162368i	−0.973963	+	0.226705i	$0.927205\pi$
$840$	−0.419024	+	8.98692i	−0.0144577	+	0.310078i
$841$	20.0685	+	14.5806i	0.692017	+	0.502779i
$842$	−5.38318	+	7.40931i	−0.185517	+	0.255342i
$843$	−25.8275	−	8.39186i	−0.889546	−	0.289031i
$844$	4.95461	+	15.2487i	0.170545	+	0.524883i
$845$	−24.6440	−	19.7221i	−0.847779	−	0.678460i
$846$	0.655297			0.0225296
$847$		0			0
$848$		−	1.32329i		−	0.0454418i
$849$	−7.83080	+	5.68941i	−0.268752	+	0.195260i
$850$	−4.43870	−	3.90486i	−0.152246	−	0.133935i
$851$	11.2628	−	34.6635i	0.386085	−	1.18825i
$852$	−13.4036	+	18.4484i	−0.459198	+	0.632032i
$853$	−17.2312	+	23.7167i	−0.589985	+	0.812045i	−0.994746	−	0.102378i	$-0.967355\pi$
$853$	−17.2312	+	23.7167i	−0.589985	+	0.812045i	0.404760	+	0.914423i	$0.367355\pi$
$854$	−1.76829	+	5.44225i	−0.0605097	+	0.186230i
$855$	−19.4156	+	12.7685i	−0.664000	+	0.436672i
$856$	−16.4913	+	11.9817i	−0.563662	+	0.409524i
$857$		−	0.656701i		−	0.0224325i	−0.999937	−	0.0112162i	$-0.996430\pi$
$857$		−	0.656701i		−	0.0224325i	0.999937	−	0.0112162i	$-0.00357032\pi$
$858$		0			0
$859$	40.0569			1.36672			0.683361	−	0.730080i	$-0.260517\pi$
$859$	40.0569			1.36672			0.683361	+	0.730080i	$0.260517\pi$
$860$	−1.57780	+	1.97157i	−0.0538026	+	0.0672298i
$861$	−9.92855	−	30.5569i	−0.338364	−	1.04138i
$862$	−6.25736	−	2.03314i	−0.213126	−	0.0692490i
$863$	−11.7149	+	16.1242i	−0.398780	+	0.548873i	−0.960437	−	0.278496i	$-0.910164\pi$
$863$	−11.7149	+	16.1242i	−0.398780	+	0.548873i	0.561657	+	0.827370i	$0.310164\pi$
$864$	−14.4580	−	10.5044i	−0.491872	−	0.357366i
$865$	−0.0989020	+	2.12118i	−0.00336277	+	0.0721223i
$866$	0.444900	+	1.36926i	0.0151183	+	0.0465294i
$867$	2.28060	+	3.13898i	0.0774534	+	0.106605i
$868$			20.1680i			0.684546i
$869$		0			0
$870$	−0.382428	−	1.39501i	−0.0129655	−	0.0472952i
$871$	35.6004	−	25.8652i	1.20627	−	0.876410i
$872$	−4.75133	+	1.54380i	−0.160900	+	0.0522797i
$873$	22.2836	+	7.24038i	0.754186	+	0.245050i
$874$	7.77628	+	5.64980i	0.263037	+	0.191107i
$875$	−36.0337	+	6.34813i	−1.21816	+	0.214606i
$876$	−4.78983	+	14.7416i	−0.161833	+	0.498072i
$877$	4.55567	−	1.48023i	0.153834	−	0.0499837i	−0.231088	−	0.972933i	$-0.574228\pi$
$877$	4.55567	−	1.48023i	0.153834	−	0.0499837i	0.384922	+	0.922949i	$0.374228\pi$
$878$	6.61362	+	9.10287i	0.223199	+	0.307207i
$879$	−0.0235501			−0.000794325
$880$		0			0
$881$	33.9748			1.14464			0.572320	−	0.820031i	$-0.306044\pi$
$881$	33.9748			1.14464			0.572320	+	0.820031i	$0.306044\pi$
$882$	1.48537	+	2.04443i	0.0500149	+	0.0688396i
$883$	−37.3521	+	12.1364i	−1.25700	+	0.408423i	−0.860424	−	0.509579i	$-0.829801\pi$
$883$	−37.3521	+	12.1364i	−1.25700	+	0.408423i	−0.396574	+	0.918003i	$0.629801\pi$
$884$	10.9641	−	33.7440i	0.368763	−	1.13494i
$885$	1.06156	+	0.400484i	0.0356839	+	0.0134621i
$886$	−4.91255	−	3.56918i	−0.165040	−	0.119909i
$887$	31.6244	+	10.2754i	1.06184	+	0.345014i	0.787306	−	0.616562i	$-0.211475\pi$
$887$	31.6244	+	10.2754i	1.06184	+	0.345014i	0.274538	+	0.961576i	$0.411475\pi$
$888$	−7.29271	+	2.36955i	−0.244727	+	0.0795167i
$889$	−14.3390	+	10.4179i	−0.480913	+	0.349404i
$890$	−6.37280	+	1.74704i	−0.213617	+	0.0585610i
$891$		0			0
$892$		−	44.8578i		−	1.50195i
$893$	−2.83257	−	3.89870i	−0.0947884	−	0.130465i
$894$	−1.35951	−	4.18414i	−0.0454688	−	0.139939i
$895$	8.11987	+	0.378596i	0.271417	+	0.0126551i
$896$	−24.1898	−	17.5749i	−0.808124	−	0.587137i
$897$	−17.2066	+	23.6829i	−0.574512	+	0.790748i
$898$	−5.86174	−	1.90459i	−0.195609	−	0.0635571i
$899$	−2.06112	−	6.34349i	−0.0687423	−	0.211567i
$900$	7.77575	−	18.0213i	0.259192	−	0.600708i
$901$	−1.41618			−0.0471797
$902$		0			0
$903$		−	1.87893i		−	0.0625267i
$904$	10.2127	−	7.41994i	0.339668	−	0.246783i
$905$	23.4818	−	15.4425i	0.780561	−	0.513327i
$906$	1.56503	−	4.81667i	0.0519947	−	0.160023i
$907$	−10.7857	+	14.8452i	−0.358133	+	0.492928i	−0.949627	−	0.313381i	$-0.898538\pi$
$907$	−10.7857	+	14.8452i	−0.358133	+	0.492928i	0.591494	+	0.806309i	$0.298538\pi$
$908$	0.796982	−	1.09695i	0.0264488	−	0.0364036i
$909$	8.44104	−	25.9789i	0.279972	−	0.861664i
$910$	6.87491	+	10.4539i	0.227901	+	0.346545i
$911$	−31.3996	+	22.8132i	−1.04032	+	0.755834i	−0.970347	−	0.241715i	$-0.922290\pi$
$911$	−31.3996	+	22.8132i	−1.04032	+	0.755834i	−0.0699688	+	0.997549i	$0.522290\pi$
$912$			16.2149i			0.536928i
$913$		0			0
$914$	−4.76076			−0.157472
$915$	−7.15753	+	8.94380i	−0.236621	+	0.295673i
$916$	−7.68852	−	23.6628i	−0.254036	−	0.781842i
$917$	59.5221	+	19.3399i	1.96559	+	0.638660i
$918$	−3.39270	+	4.66965i	−0.111976	+	0.154121i
$919$	0.794192	+	0.577015i	0.0261980	+	0.0190340i	0.600807	−	0.799394i	$-0.294846\pi$
$919$	0.794192	+	0.577015i	0.0261980	+	0.0190340i	−0.574609	+	0.818428i	$0.694846\pi$
$920$	−16.6815	−	0.777789i	−0.549972	−	0.0256430i
$921$	9.80109	+	30.1647i	0.322957	+	0.993959i
$922$	−2.93649	−	4.04173i	−0.0967080	−	0.133107i
$923$			65.2340i			2.14720i
$924$		0			0
$925$	−15.9030	−	26.8254i	−0.522888	−	0.882012i
$926$	2.41218	−	1.75255i	0.0792692	−	0.0575925i
$927$	−5.48950	+	1.78365i	−0.180299	+	0.0585826i
$928$	7.13014	+	2.31672i	0.234058	+	0.0760502i
$929$	28.3237	+	20.5784i	0.929270	+	0.675154i	0.945814	−	0.324709i	$-0.105266\pi$
$929$	28.3237	+	20.5784i	0.929270	+	0.675154i	−0.0165438	+	0.999863i	$0.505266\pi$
$930$	0.811994	−	2.15234i	0.0266263	−	0.0705780i
$931$	5.74277	−	17.6744i	0.188212	−	0.579256i
$932$	−48.4674	+	15.7480i	−1.58760	+	0.515843i
$933$	−2.72867	−	3.75570i	−0.0893327	−	0.122956i
$934$	5.67522			0.185699
$935$		0			0
$936$	−13.8060			−0.451263
$937$	−18.1364	−	24.9626i	−0.592491	−	0.815493i	0.402504	−	0.915418i	$-0.368140\pi$
$937$	−18.1364	−	24.9626i	−0.592491	−	0.815493i	−0.994995	+	0.0999247i	$0.968140\pi$
$938$	−8.63617	+	2.80606i	−0.281981	+	0.0916211i
$939$	−5.07334	+	15.6141i	−0.165562	+	0.509548i
$940$	3.80828	+	1.43672i	0.124212	+	0.0468605i
$941$	−24.3325	−	17.6786i	−0.793216	−	0.576306i	0.115700	−	0.993284i	$-0.463089\pi$
$941$	−24.3325	−	17.6786i	−0.793216	−	0.576306i	−0.908916	+	0.416979i	$0.863089\pi$
$942$	0.683404	+	0.222052i	0.0222665	+	0.00723483i
$943$	56.7196	−	18.4293i	1.84704	−	0.600141i
$944$	−1.43578	+	1.04315i	−0.0467306	+	0.0339518i
$945$	9.44468	+	34.4520i	0.307236	+	1.12072i
$946$		0			0
$947$			10.1860i			0.331002i	0.986210	+	0.165501i	$0.0529241\pi$
$947$			10.1860i			0.331002i	−0.986210	+	0.165501i	$0.947076\pi$
$948$	−3.03044	−	4.17104i	−0.0984240	−	0.135469i
$949$	13.7023	+	42.1713i	0.444795	+	1.36894i
$950$	8.02424	−	1.80259i	0.260341	−	0.0584838i
$951$	1.33596	+	0.970632i	0.0433215	+	0.0314749i
$952$	−8.85231	+	12.1842i	−0.286905	+	0.394891i
$953$	−38.1823	−	12.4062i	−1.23685	−	0.401876i	−0.383656	−	0.923476i	$-0.625335\pi$
$953$	−38.1823	−	12.4062i	−1.23685	−	0.401876i	−0.853190	+	0.521601i	$0.825335\pi$
$954$	0.0827842	+	0.254784i	0.00268024	+	0.00824892i
$955$	−4.67284	−	3.73957i	−0.151209	−	0.121010i
$956$	−9.47874			−0.306564
$957$		0			0
$958$		−	10.7143i		−	0.346162i
$959$	−42.4747	+	30.8597i	−1.37158	+	0.996511i
$960$	−6.53321	−	9.93434i	−0.210858	−	0.320630i
$961$	−6.30161	+	19.3944i	−0.203278	+	0.625625i
$962$	−6.26822	+	8.62746i	−0.202096	+	0.278161i
$963$	−19.4496	+	26.7701i	−0.626754	+	0.862653i
$964$	−2.74440	+	8.44638i	−0.0883910	+	0.272040i
$965$	0.476999	+	0.725321i	0.0153552	+	0.0233489i
$966$	4.88710	−	3.55069i	0.157240	−	0.114241i
$967$		−	58.0856i		−	1.86791i	−0.357395	−	0.933953i	$-0.616335\pi$
$967$		−	58.0856i		−	1.86791i	0.357395	−	0.933953i	$-0.383665\pi$
$968$		0			0
$969$	17.3531			0.557462
$970$	−6.47435	−	5.18128i	−0.207879	−	0.166361i
$971$	10.1395	+	31.2061i	0.325392	+	1.00145i	0.971264	+	0.238007i	$0.0764940\pi$
$971$	10.1395	+	31.2061i	0.325392	+	1.00145i	−0.645872	+	0.763446i	$0.723506\pi$
$972$	−28.9994	−	9.42248i	−0.930156	−	0.302226i
$973$	−24.1781	+	33.2784i	−0.775116	+	1.06686i
$974$	−4.05270	−	2.94446i	−0.129857	−	0.0943466i
$975$	5.48984	+	24.4380i	0.175816	+	0.782643i
$976$	−5.53703	−	17.0412i	−0.177236	−	0.545476i
$977$	10.5357	+	14.5012i	0.337068	+	0.463934i	0.943582	−	0.331138i	$-0.107433\pi$
$977$	10.5357	+	14.5012i	0.337068	+	0.463934i	−0.606514	+	0.795073i	$0.707433\pi$
$978$			7.12908i			0.227963i
$979$		0			0
$980$	4.14992	+	15.1379i	0.132564	+	0.483563i
$981$	−6.56086	+	4.76674i	−0.209472	+	0.152190i
$982$	−2.08289	+	0.676771i	−0.0664676	+	0.0215966i
$983$	16.2408	+	5.27695i	0.518001	+	0.168309i	0.556338	−	0.830956i	$-0.312206\pi$
$983$	16.2408	+	5.27695i	0.518001	+	0.168309i	−0.0383371	+	0.999265i	$0.512206\pi$
$984$	−10.1508	−	7.37501i	−0.323596	−	0.235107i
$985$	38.7916	+	14.6346i	1.23600	+	0.466296i
$986$	0.748255	−	2.30289i	0.0238293	−	0.0733390i
$987$	−2.88037	+	0.935888i	−0.0916831	+	0.0297896i
$988$	29.0122	+	39.9319i	0.923002	+	1.27040i
$989$	3.48765			0.110901
$990$		0			0
$991$	17.5551			0.557658			0.278829	−	0.960341i	$-0.410054\pi$
$991$	17.5551			0.557658			0.278829	+	0.960341i	$0.410054\pi$
$992$	7.00817	+	9.64592i	0.222510	+	0.306258i
$993$	0.816276	−	0.265224i	0.0259037	−	0.00841663i
$994$	4.15981	−	12.8026i	0.131941	−	0.406073i
$995$	8.01051	−	21.2333i	0.253950	−	0.673142i
$996$	−17.8789	−	12.9898i	−0.566514	−	0.411596i
$997$	14.4605	+	4.69851i	0.457969	+	0.148803i	0.528911	−	0.848677i	$-0.322600\pi$
$997$	14.4605	+	4.69851i	0.457969	+	0.148803i	−0.0709419	+	0.997480i	$0.522600\pi$
$998$	−1.92024	+	0.623925i	−0.0607843	+	0.0197500i
$999$	−24.6324	+	17.8965i	−0.779335	+	0.566220i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.j.k.124.6		48
5.4	even	2	inner	605.2.j.k.124.7		48
11.2	odd	10		605.2.b.h.364.5	✓	12
11.3	even	5	inner	605.2.j.k.269.5		48
11.4	even	5	inner	605.2.j.k.444.7		48
11.5	even	5	inner	605.2.j.k.9.8		48
11.6	odd	10	inner	605.2.j.k.9.6		48
11.7	odd	10	inner	605.2.j.k.444.5		48
11.8	odd	10	inner	605.2.j.k.269.7		48
11.9	even	5		605.2.b.h.364.7	yes	12
11.10	odd	2	inner	605.2.j.k.124.8		48
55.2	even	20		3025.2.a.bo.1.7		12
55.4	even	10	inner	605.2.j.k.444.6		48
55.9	even	10		605.2.b.h.364.6	yes	12
55.13	even	20		3025.2.a.bo.1.6		12
55.14	even	10	inner	605.2.j.k.269.8		48
55.19	odd	10	inner	605.2.j.k.269.6		48
55.24	odd	10		605.2.b.h.364.8	yes	12
55.29	odd	10	inner	605.2.j.k.444.8		48
55.39	odd	10	inner	605.2.j.k.9.7		48
55.42	odd	20		3025.2.a.bo.1.5		12
55.49	even	10	inner	605.2.j.k.9.5		48
55.53	odd	20		3025.2.a.bo.1.8		12
55.54	odd	2	inner	605.2.j.k.124.5		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
605.2.b.h.364.5	✓	12	11.2	odd	10
605.2.b.h.364.6	yes	12	55.9	even	10
605.2.b.h.364.7	yes	12	11.9	even	5
605.2.b.h.364.8	yes	12	55.24	odd	10
605.2.j.k.9.5		48	55.49	even	10	inner
605.2.j.k.9.6		48	11.6	odd	10	inner
605.2.j.k.9.7		48	55.39	odd	10	inner
605.2.j.k.9.8		48	11.5	even	5	inner
605.2.j.k.124.5		48	55.54	odd	2	inner
605.2.j.k.124.6		48	1.1	even	1	trivial
605.2.j.k.124.7		48	5.4	even	2	inner
605.2.j.k.124.8		48	11.10	odd	2	inner
605.2.j.k.269.5		48	11.3	even	5	inner
605.2.j.k.269.6		48	55.19	odd	10	inner
605.2.j.k.269.7		48	11.8	odd	10	inner
605.2.j.k.269.8		48	55.14	even	10	inner
605.2.j.k.444.5		48	11.7	odd	10	inner
605.2.j.k.444.6		48	55.4	even	10	inner
605.2.j.k.444.7		48	11.4	even	5	inner
605.2.j.k.444.8		48	55.29	odd	10	inner
3025.2.a.bo.1.5		12	55.42	odd	20
3025.2.a.bo.1.6		12	55.13	even	20
3025.2.a.bo.1.7		12	55.2	even	20
3025.2.a.bo.1.8		12	55.53	odd	20

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.j (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.193000 - 0.265641i) q^{2} +(0.914917 - 0.297274i) q^{3} +(0.584718 - 1.79958i) q^{4} +(-0.789281 + 2.09214i) q^{5} +(-0.255547 - 0.185666i) q^{6} +(-3.11241 - 1.01128i) q^{7} +(-1.21545 + 0.394924i) q^{8} +(-1.67835 + 1.21939i) q^{9} +O(q^{10})\)	\(q+(-0.193000 - 0.265641i) q^{2} +(0.914917 - 0.297274i) q^{3} +(0.584718 - 1.79958i) q^{4} +(-0.789281 + 2.09214i) q^{5} +(-0.255547 - 0.185666i) q^{6} +(-3.11241 - 1.01128i) q^{7} +(-1.21545 + 0.394924i) q^{8} +(-1.67835 + 1.21939i) q^{9} +(0.708089 - 0.194116i) q^{10} -1.82028i q^{12} +(-3.06077 - 4.21278i) q^{13} +(0.332056 + 1.02196i) q^{14} +(-0.100188 + 2.14876i) q^{15} +(-2.72213 - 1.97774i) q^{16} +(-2.11658 + 2.91322i) q^{17} +(0.647842 + 0.210497i) q^{18} +(-1.54799 - 4.76423i) q^{19} +(3.30345 + 2.64368i) q^{20} -3.14823 q^{21} -5.84372i q^{23} +(-0.994636 + 0.722645i) q^{24} +(-3.75407 - 3.30257i) q^{25} +(-0.528362 + 1.62613i) q^{26} +(-2.86941 + 3.94940i) q^{27} +(-3.63977 + 5.00971i) q^{28} +(0.632843 - 1.94769i) q^{29} +(0.590136 - 0.388097i) q^{30} +(2.63491 - 1.91437i) q^{31} +3.66082i q^{32} +1.18237 q^{34} +(4.57232 - 5.71341i) q^{35} +(1.21303 + 3.73332i) q^{36} +(5.93174 + 1.92734i) q^{37} +(-0.966815 + 1.33071i) q^{38} +(-4.05270 - 2.94446i) q^{39} +(0.133098 - 2.85460i) q^{40} +(3.15369 + 9.70607i) q^{41} +(0.607607 + 0.836299i) q^{42} +0.596820i q^{43} +(-1.22645 - 4.47378i) q^{45} +(-1.55233 + 1.12784i) q^{46} +(0.914917 - 0.297274i) q^{47} +(-3.07846 - 1.00025i) q^{48} +(3.00130 + 2.18058i) q^{49} +(-0.152764 + 1.63463i) q^{50} +(-1.07047 + 3.29456i) q^{51} +(-9.37091 + 3.04479i) q^{52} +(0.231164 + 0.318170i) q^{53} +1.60292 q^{54} +4.18237 q^{56} +(-2.83257 - 3.89870i) q^{57} +(-0.639526 + 0.207795i) q^{58} +(0.162990 - 0.501632i) q^{59} +(3.80828 + 1.43672i) q^{60} +(4.30825 + 3.13012i) q^{61} +(-1.01707 - 0.330467i) q^{62} +(6.45688 - 2.09797i) q^{63} +(-4.47180 + 3.24895i) q^{64} +(11.2295 - 3.07847i) q^{65} +8.45057i q^{67} +(4.00496 + 5.51235i) q^{68} +(-1.73719 - 5.34652i) q^{69} +(-2.40017 - 0.111910i) q^{70} +(-10.1349 - 7.36345i) q^{71} +(1.55839 - 2.14493i) q^{72} +(-8.09851 - 2.63136i) q^{73} +(-0.632843 - 1.94769i) q^{74} +(-4.41643 - 1.90559i) q^{75} -9.47874 q^{76} +1.64484i q^{78} +(2.29142 - 1.66482i) q^{79} +(6.28624 - 4.13407i) q^{80} +(0.472007 - 1.45269i) q^{81} +(1.96967 - 2.71102i) q^{82} +(7.13612 - 9.82203i) q^{83} +(-1.84082 + 5.66548i) q^{84} +(-4.42428 - 6.72752i) q^{85} +(0.158540 - 0.115186i) q^{86} -1.97010i q^{87} -9.00000 q^{89} +(-0.951718 + 1.18923i) q^{90} +(5.26605 + 16.2072i) q^{91} +(-10.5162 - 3.41693i) q^{92} +(1.84163 - 2.53478i) q^{93} +(-0.255547 - 0.185666i) q^{94} +(11.1892 + 0.521708i) q^{95} +(1.08827 + 3.34934i) q^{96} +(-6.63855 - 9.13717i) q^{97} -1.21812i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 20 q^{4} + 6 q^{5} + 20 q^{9}+O(q^{10}) \) 48 * q + 20 * q^4 + 6 * q^5 + 20 * q^9	\( 48 q + 20 q^{4} + 6 q^{5} + 20 q^{9} + 32 q^{14} - 20 q^{15} - 36 q^{16} - 26 q^{20} + 10 q^{25} - 20 q^{26} - 8 q^{31} + 48 q^{34} - 92 q^{36} - 72 q^{45} + 4 q^{49} + 192 q^{56} + 32 q^{59} + 92 q^{60} - 28 q^{64} + 16 q^{69} + 12 q^{70} - 112 q^{71} - 36 q^{75} + 106 q^{80} + 20 q^{81} + 56 q^{86} - 432 q^{89} - 72 q^{91}+O(q^{100}) \) 48 * q + 20 * q^4 + 6 * q^5 + 20 * q^9 + 32 * q^14 - 20 * q^15 - 36 * q^16 - 26 * q^20 + 10 * q^25 - 20 * q^26 - 8 * q^31 + 48 * q^34 - 92 * q^36 - 72 * q^45 + 4 * q^49 + 192 * q^56 + 32 * q^59 + 92 * q^60 - 28 * q^64 + 16 * q^69 + 12 * q^70 - 112 * q^71 - 36 * q^75 + 106 * q^80 + 20 * q^81 + 56 * q^86 - 432 * q^89 - 72 * q^91

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