LMFDB - Embedded newform 1176.2.u.c.521.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1176,2,Mod(521,1176)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1176, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 3, 1]))

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

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

chi := DirichletCharacter("1176.521");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1176 = 2^{3} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1176.u (of order $6$, degree $2$, 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:	$9.39040727770$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			521.9
Character	$\chi$	$=$	1176.521
Dual form			1176.2.u.c.1097.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.02370 - 1.39715i) q^{3} +(-0.244530 - 0.423539i) q^{5} +(-0.904057 + 2.86054i) q^{9} +(1.31874 + 0.761372i) q^{11} -0.652068i q^{13} +(-0.341421 + 0.775225i) q^{15} +(3.77769 - 6.54315i) q^{17} +(0.364587 - 0.210494i) q^{19} +(-5.11819 + 2.95499i) q^{23} +(2.38041 - 4.12299i) q^{25} +(4.92209 - 1.66524i) q^{27} -7.16356i q^{29} +(-6.39140 - 3.69008i) q^{31} +(-0.286244 - 2.62189i) q^{33} +(4.04609 + 7.00804i) q^{37} +(-0.911037 + 0.667525i) q^{39} -2.53185 q^{41} -5.56181 q^{43} +(1.43262 - 0.316585i) q^{45} +(-4.65721 - 8.06652i) q^{47} +(-13.0090 + 1.42025i) q^{51} +(-1.26640 - 0.731158i) q^{53} -0.744715i q^{55} +(-0.667322 - 0.293899i) q^{57} +(3.67844 - 6.37124i) q^{59} +(-9.65588 + 5.57482i) q^{61} +(-0.276176 + 0.159450i) q^{65} +(-7.31199 + 12.6647i) q^{67} +(9.36807 + 4.12584i) q^{69} -12.8513i q^{71} +(8.00657 + 4.62259i) q^{73} +(-8.19727 + 0.894936i) q^{75} +(-0.607201 - 1.05170i) q^{79} +(-7.36536 - 5.17218i) q^{81} -9.03219 q^{83} -3.69504 q^{85} +(-10.0086 + 7.33337i) q^{87} +(-4.77997 - 8.27914i) q^{89} +(1.38732 + 12.7073i) q^{93} +(-0.178305 - 0.102945i) q^{95} +4.95430i q^{97} +(-3.37015 + 3.08397i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 32 q^{15} - 8 q^{25} - 16 q^{37} + 64 q^{39} + 32 q^{43} - 48 q^{51} + 96 q^{57} - 16 q^{67} - 80 q^{81} - 128 q^{85} + 32 q^{93} - 112 q^{99}+O(q^{100}) $ 48 * q - 32 * q^15 - 8 * q^25 - 16 * q^37 + 64 * q^39 + 32 * q^43 - 48 * q^51 + 96 * q^57 - 16 * q^67 - 80 * q^81 - 128 * q^85 + 32 * q^93 - 112 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1176\mathbb{Z}\right)^\times$.

$n$	$295$	$589$	$785$	$1081$
$\chi(n)$	$1$	$1$	$-1$	$e\left(\frac{1}{6}\right)$

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			0
$2$		0			0
$3$	−1.02370	−	1.39715i	−0.591036	−	0.806645i
$3$	−1.02370	−	1.39715i	−0.591036	−	0.806645i
$4$		0			0
$5$	−0.244530	−	0.423539i	−0.109357	−	0.189412i	0.806153	−	0.591707i	$-0.201546\pi$
$5$	−0.244530	−	0.423539i	−0.109357	−	0.189412i	−0.915510	+	0.402295i	$0.868213\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−0.904057	+	2.86054i	−0.301352	+	0.953513i
$10$		0			0
$11$	1.31874	+	0.761372i	0.397614	+	0.229562i	0.685454	−	0.728116i	$-0.259604\pi$
$11$	1.31874	+	0.761372i	0.397614	+	0.229562i	−0.287840	+	0.957678i	$0.592937\pi$
$12$		0			0
$13$		−	0.652068i		−	0.180851i	−0.995903	−	0.0904255i	$-0.971177\pi$
$13$		−	0.652068i		−	0.180851i	0.995903	−	0.0904255i	$-0.0288227\pi$
$14$		0			0
$15$	−0.341421	+	0.775225i	−0.0881545	+	0.200162i
$16$		0			0
$17$	3.77769	−	6.54315i	0.916224	−	1.58695i	0.111125	−	0.993806i	$-0.464555\pi$
$17$	3.77769	−	6.54315i	0.916224	−	1.58695i	0.805099	−	0.593140i	$-0.202112\pi$
$18$		0			0
$19$	0.364587	−	0.210494i	0.0836420	−	0.0482907i	−0.457596	−	0.889160i	$-0.651289\pi$
$19$	0.364587	−	0.210494i	0.0836420	−	0.0482907i	0.541238	+	0.840870i	$0.317956\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−5.11819	+	2.95499i	−1.06722	+	0.616157i	−0.927420	−	0.374023i	$-0.877978\pi$
$23$	−5.11819	+	2.95499i	−1.06722	+	0.616157i	−0.139797	+	0.990180i	$0.544645\pi$
$24$		0			0
$25$	2.38041	−	4.12299i	0.476082	−	0.824598i
$26$		0			0
$27$	4.92209	−	1.66524i	0.947257	−	0.320476i
$28$		0			0
$29$		−	7.16356i		−	1.33024i	−0.746737	−	0.665120i	$-0.768381\pi$
$29$		−	7.16356i		−	1.33024i	0.746737	−	0.665120i	$-0.231619\pi$
$30$		0			0
$31$	−6.39140	−	3.69008i	−1.14793	−	0.662757i	−0.199548	−	0.979888i	$-0.563947\pi$
$31$	−6.39140	−	3.69008i	−1.14793	−	0.662757i	−0.948382	+	0.317131i	$0.897281\pi$
$32$		0			0
$33$	−0.286244	−	2.62189i	−0.0498288	−	0.456413i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	4.04609	+	7.00804i	0.665174	+	1.15211i	0.979238	+	0.202713i	$0.0649758\pi$
$37$	4.04609	+	7.00804i	0.665174	+	1.15211i	−0.314065	+	0.949402i	$0.601691\pi$
$38$		0			0
$39$	−0.911037	+	0.667525i	−0.145883	+	0.106890i
$40$		0			0
$41$	−2.53185			−0.395409			−0.197704	−	0.980262i	$-0.563349\pi$
$41$	−2.53185			−0.395409			−0.197704	+	0.980262i	$0.563349\pi$
$42$		0			0
$43$	−5.56181			−0.848168			−0.424084	−	0.905623i	$-0.639404\pi$
$43$	−5.56181			−0.848168			−0.424084	+	0.905623i	$0.639404\pi$
$44$		0			0
$45$	1.43262	−	0.316585i	0.213562	−	0.0471937i
$46$		0			0
$47$	−4.65721	−	8.06652i	−0.679323	−	1.17662i	−0.975185	−	0.221392i	$-0.928940\pi$
$47$	−4.65721	−	8.06652i	−0.679323	−	1.17662i	0.295862	−	0.955231i	$-0.404393\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−13.0090	+	1.42025i	−1.82162	+	0.198875i
$52$		0			0
$53$	−1.26640	−	0.731158i	−0.173954	−	0.100432i	0.410495	−	0.911863i	$-0.365356\pi$
$53$	−1.26640	−	0.731158i	−0.173954	−	0.100432i	−0.584449	+	0.811431i	$0.698689\pi$
$54$		0			0
$55$		−	0.744715i		−	0.100417i
$56$		0			0
$57$	−0.667322	−	0.293899i	−0.0883889	−	0.0389278i
$58$		0			0
$59$	3.67844	−	6.37124i	0.478892	−	0.829465i	−0.520815	−	0.853669i	$-0.674372\pi$
$59$	3.67844	−	6.37124i	0.478892	−	0.829465i	0.999707	+	0.0242046i	$0.00770531\pi$
$60$		0			0
$61$	−9.65588	+	5.57482i	−1.23631	+	0.713783i	−0.968338	−	0.249644i	$-0.919686\pi$
$61$	−9.65588	+	5.57482i	−1.23631	+	0.713783i	−0.267971	+	0.963427i	$0.586353\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−0.276176	+	0.159450i	−0.0342554	+	0.0197774i
$66$		0			0
$67$	−7.31199	+	12.6647i	−0.893302	+	1.54724i	−0.0574095	+	0.998351i	$0.518284\pi$
$67$	−7.31199	+	12.6647i	−0.893302	+	1.54724i	−0.835892	+	0.548893i	$0.815049\pi$
$68$		0			0
$69$	9.36807	+	4.12584i	1.12778	+	0.496693i
$70$		0			0
$71$		−	12.8513i		−	1.52516i	−0.646891	−	0.762582i	$-0.723931\pi$
$71$		−	12.8513i		−	1.52516i	0.646891	−	0.762582i	$-0.276069\pi$
$72$		0			0
$73$	8.00657	+	4.62259i	0.937098	+	0.541034i	0.889049	−	0.457811i	$-0.151366\pi$
$73$	8.00657	+	4.62259i	0.937098	+	0.541034i	0.0480485	+	0.998845i	$0.484700\pi$
$74$		0			0
$75$	−8.19727	+	0.894936i	−0.946540	+	0.103338i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−0.607201	−	1.05170i	−0.0683154	−	0.118326i	0.829844	−	0.557995i	$-0.188429\pi$
$79$	−0.607201	−	1.05170i	−0.0683154	−	0.118326i	−0.898160	+	0.439669i	$0.855096\pi$
$80$		0			0
$81$	−7.36536	−	5.17218i	−0.818374	−	0.574687i
$82$		0			0
$83$	−9.03219			−0.991412			−0.495706	−	0.868491i	$-0.665091\pi$
$83$	−9.03219			−0.991412			−0.495706	+	0.868491i	$0.665091\pi$
$84$		0			0
$85$	−3.69504			−0.400783
$86$		0			0
$87$	−10.0086	+	7.33337i	−1.07303	+	0.786220i
$88$		0			0
$89$	−4.77997	−	8.27914i	−0.506675	−	0.877588i	−0.999970	−	0.00772531i	$-0.997541\pi$
$89$	−4.77997	−	8.27914i	−0.506675	−	0.877588i	0.493295	−	0.869862i	$-0.335792\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	1.38732	+	12.7073i	0.143858	+	1.31769i
$94$		0			0
$95$	−0.178305	−	0.102945i	−0.0182937	−	0.0105619i
$96$		0			0
$97$			4.95430i			0.503033i	0.967853	+	0.251517i	$0.0809293\pi$
$97$			4.95430i			0.503033i	−0.967853	+	0.251517i	$0.919071\pi$
$98$		0			0
$99$	−3.37015	+	3.08397i	−0.338712	+	0.309951i
$100$		0			0
$101$	2.75513	−	4.77203i	0.274146	−	0.474835i	−0.695773	−	0.718261i	$-0.744938\pi$
$101$	2.75513	−	4.77203i	0.274146	−	0.474835i	0.969919	+	0.243427i	$0.0782715\pi$
$102$		0			0
$103$	7.95002	−	4.58995i	0.783339	−	0.452261i	−0.0542734	−	0.998526i	$-0.517284\pi$
$103$	7.95002	−	4.58995i	0.783339	−	0.452261i	0.837612	+	0.546265i	$0.183951\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	4.14771	−	2.39468i	0.400974	−	0.231503i	−0.285930	−	0.958250i	$-0.592303\pi$
$107$	4.14771	−	2.39468i	0.400974	−	0.231503i	0.686904	+	0.726748i	$0.258969\pi$
$108$		0			0
$109$	6.68814	−	11.5842i	0.640608	−	1.10957i	−0.344689	−	0.938717i	$-0.612016\pi$
$109$	6.68814	−	11.5842i	0.640608	−	1.10957i	0.985297	−	0.170849i	$-0.0546510\pi$
$110$		0			0
$111$	5.64928	−	12.8272i	0.536206	−	1.21750i
$112$		0			0
$113$		−	12.5764i		−	1.18309i	−0.806271	−	0.591546i	$-0.798518\pi$
$113$		−	12.5764i		−	1.18309i	0.806271	−	0.591546i	$-0.201482\pi$
$114$		0			0
$115$	2.50311	+	1.44517i	0.233416	+	0.134763i
$116$		0			0
$117$	1.86527	+	0.589506i	0.172444	+	0.0544999i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−4.34062	−	7.51818i	−0.394602	−	0.683471i
$122$		0			0
$123$	2.59187	+	3.53738i	0.233701	+	0.318954i
$124$		0			0
$125$	−4.77363			−0.426967
$126$		0			0
$127$	0.264143			0.0234389			0.0117194	−	0.999931i	$-0.496269\pi$
$127$	0.264143			0.0234389			0.0117194	+	0.999931i	$0.496269\pi$
$128$		0			0
$129$	5.69365	+	7.77068i	0.501298	+	0.684171i
$130$		0			0
$131$	3.75958	+	6.51179i	0.328476	+	0.568938i	0.982210	−	0.187787i	$-0.0601316\pi$
$131$	3.75958	+	6.51179i	0.328476	+	0.568938i	−0.653733	+	0.756725i	$0.726798\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−1.90890	−	1.67749i	−0.164292	−	0.144376i
$136$		0			0
$137$	0.0171515	+	0.00990240i	0.00146535	+	0.000846019i	0.500732	−	0.865602i	$-0.333064\pi$
$137$	0.0171515	+	0.00990240i	0.00146535	+	0.000846019i	−0.499267	+	0.866448i	$0.666397\pi$
$138$		0			0
$139$		−	10.1198i		−	0.858349i	−0.903222	−	0.429174i	$-0.858805\pi$
$139$		−	10.1198i		−	0.858349i	0.903222	−	0.429174i	$-0.141195\pi$
$140$		0			0
$141$	−6.50253	+	14.7645i	−0.547612	+	1.24340i
$142$		0			0
$143$	0.496466	−	0.859905i	0.0415166	−	0.0719089i
$144$		0			0
$145$	−3.03405	+	1.75171i	−0.251964	+	0.145471i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	12.1991	−	7.04315i	0.999388	−	0.576997i	0.0913212	−	0.995821i	$-0.470891\pi$
$149$	12.1991	−	7.04315i	0.999388	−	0.576997i	0.908067	+	0.418824i	$0.137558\pi$
$150$		0			0
$151$	−6.29018	+	10.8949i	−0.511887	+	0.886615i	0.488018	+	0.872834i	$0.337720\pi$
$151$	−6.29018	+	10.8949i	−0.511887	+	0.886615i	−0.999905	+	0.0137810i	$0.995613\pi$
$152$		0			0
$153$	15.3017	+	16.7216i	1.23707	+	1.35186i
$154$		0			0
$155$			3.60934i			0.289910i
$156$		0			0
$157$	−7.50874	−	4.33517i	−0.599263	−	0.345984i	0.169489	−	0.985532i	$-0.445788\pi$
$157$	−7.50874	−	4.33517i	−0.599263	−	0.345984i	−0.768751	+	0.639548i	$0.779122\pi$
$158$		0			0
$159$	0.274885	+	2.51784i	0.0217998	+	0.199678i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	1.67582	+	2.90260i	0.131260	+	0.227349i	0.924163	−	0.381999i	$-0.124764\pi$
$163$	1.67582	+	2.90260i	0.131260	+	0.227349i	−0.792902	+	0.609349i	$0.791431\pi$
$164$		0			0
$165$	−1.04048	+	0.762368i	−0.0810011	+	0.0593503i
$166$		0			0
$167$	−23.4014			−1.81085			−0.905426	−	0.424505i	$-0.860448\pi$
$167$	−23.4014			−1.81085			−0.905426	+	0.424505i	$0.860448\pi$
$168$		0			0
$169$	12.5748			0.967293
$170$		0			0
$171$	0.272520	+	1.23321i	0.0208401	+	0.0943062i
$172$		0			0
$173$	7.12063	+	12.3333i	0.541371	+	0.937683i	0.998826	+	0.0484497i	$0.0154280\pi$
$173$	7.12063	+	12.3333i	0.541371	+	0.937683i	−0.457454	+	0.889233i	$0.651239\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−12.6672	+	1.38294i	−0.952126	+	0.103948i
$178$		0			0
$179$	17.6031	+	10.1632i	1.31572	+	0.759632i	0.983037	−	0.183407i	$-0.0587126\pi$
$179$	17.6031	+	10.1632i	1.31572	+	0.759632i	0.332684	+	0.943039i	$0.392046\pi$
$180$		0			0
$181$		−	0.798480i		−	0.0593506i	−0.999560	−	0.0296753i	$-0.990553\pi$
$181$		−	0.798480i		−	0.0593506i	0.999560	−	0.0296753i	$-0.00944732\pi$
$182$		0			0
$183$	17.6736	+	7.78374i	1.30647	+	0.575390i
$184$		0			0
$185$	1.97879	−	3.42736i	0.145483	−	0.251984i
$186$		0			0
$187$	9.96354	−	5.75245i	0.728606	−	0.420661i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	18.2420	−	10.5320i	1.31995	−	0.762071i	0.336227	−	0.941781i	$-0.390849\pi$
$191$	18.2420	−	10.5320i	1.31995	−	0.762071i	0.983720	+	0.179710i	$0.0575158\pi$
$192$		0			0
$193$	8.95075	−	15.5032i	0.644289	−	1.11594i	−0.340176	−	0.940362i	$-0.610487\pi$
$193$	8.95075	−	15.5032i	0.644289	−	1.11594i	0.984465	−	0.175580i	$-0.0561801\pi$
$194$		0			0
$195$	0.505499	+	0.222629i	0.0361995	+	0.0159428i
$196$		0			0
$197$			19.1354i			1.36334i	0.731658	+	0.681672i	$0.238747\pi$
$197$			19.1354i			1.36334i	−0.731658	+	0.681672i	$0.761253\pi$
$198$		0			0
$199$	−10.8740	−	6.27810i	−0.770837	−	0.445043i	0.0623361	−	0.998055i	$-0.480145\pi$
$199$	−10.8740	−	6.27810i	−0.770837	−	0.445043i	−0.833173	+	0.553012i	$0.813478\pi$
$200$		0			0
$201$	25.1799	−	2.74901i	1.77605	−	0.193900i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	0.619115	+	1.07234i	0.0432408	+	0.0748953i
$206$		0			0
$207$	−3.82572	−	17.3123i	−0.265906	−	1.20328i
$208$		0			0
$209$	0.641058			0.0443429
$210$		0			0
$211$	8.96713			0.617322			0.308661	−	0.951172i	$-0.400119\pi$
$211$	8.96713			0.617322			0.308661	+	0.951172i	$0.400119\pi$
$212$		0			0
$213$	−17.9551	+	13.1559i	−1.23027	+	0.901427i
$214$		0			0
$215$	1.36003	+	2.35564i	0.0927534	+	0.160654i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−1.73790	−	15.9186i	−0.117437	−	1.07568i
$220$		0			0
$221$	−4.26658	−	2.46331i	−0.287001	−	0.165700i
$222$		0			0
$223$			10.9815i			0.735376i	0.929949	+	0.367688i	$0.119851\pi$
$223$			10.9815i			0.735376i	−0.929949	+	0.367688i	$0.880149\pi$
$224$		0			0
$225$	9.64195	+	10.5367i	0.642797	+	0.702445i
$226$		0			0
$227$	2.72532	−	4.72038i	0.180886	−	0.313303i	−0.761297	−	0.648404i	$-0.775437\pi$
$227$	2.72532	−	4.72038i	0.180886	−	0.313303i	0.942182	+	0.335101i	$0.108770\pi$
$228$		0			0
$229$	−11.0855	+	6.40019i	−0.732548	+	0.422937i	−0.819354	−	0.573289i	$-0.805667\pi$
$229$	−11.0855	+	6.40019i	−0.732548	+	0.422937i	0.0868056	+	0.996225i	$0.472334\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	13.9900	−	8.07713i	0.916515	−	0.529150i	0.0339934	−	0.999422i	$-0.489177\pi$
$233$	13.9900	−	8.07713i	0.916515	−	0.529150i	0.882522	+	0.470272i	$0.155844\pi$
$234$		0			0
$235$	−2.27766	+	3.94502i	−0.148578	+	0.257345i
$236$		0			0
$237$	−0.847792	+	1.92498i	−0.0550700	+	0.125041i
$238$		0			0
$239$			1.09590i			0.0708882i	0.999372	+	0.0354441i	$0.0112846\pi$
$239$			1.09590i			0.0708882i	−0.999372	+	0.0354441i	$0.988715\pi$
$240$		0			0
$241$	7.41331	+	4.28007i	0.477533	+	0.275704i	0.719388	−	0.694609i	$-0.244422\pi$
$241$	7.41331	+	4.28007i	0.477533	+	0.275704i	−0.241855	+	0.970312i	$0.577756\pi$
$242$		0			0
$243$	0.313646	+	15.5853i	0.0201204	+	0.999798i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−0.137257	−	0.237735i	−0.00873343	−	0.0151267i
$248$		0			0
$249$	9.24630	+	12.6193i	0.585960	+	0.799717i
$250$		0			0
$251$	−3.88353			−0.245127			−0.122563	−	0.992461i	$-0.539111\pi$
$251$	−3.88353			−0.245127			−0.122563	+	0.992461i	$0.539111\pi$
$252$		0			0
$253$	−8.99938			−0.565786
$254$		0			0
$255$	3.78263	+	5.16252i	0.236877	+	0.323290i
$256$		0			0
$257$	8.90592	+	15.4255i	0.555536	+	0.962217i	0.997862	+	0.0653624i	$0.0208203\pi$
$257$	8.90592	+	15.4255i	0.555536	+	0.962217i	−0.442325	+	0.896855i	$0.645846\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	20.4916	+	6.47626i	1.26840	+	0.400871i
$262$		0			0
$263$	4.74223	+	2.73793i	0.292418	+	0.168828i	0.639032	−	0.769180i	$-0.279335\pi$
$263$	4.74223	+	2.73793i	0.292418	+	0.168828i	−0.346614	+	0.938008i	$0.612669\pi$
$264$		0			0
$265$			0.715161i			0.0439320i
$266$		0			0
$267$	−6.67393	+	15.1537i	−0.408438	+	0.927393i
$268$		0			0
$269$	−6.07721	+	10.5260i	−0.370534	+	0.641784i	−0.989648	−	0.143518i	$-0.954159\pi$
$269$	−6.07721	+	10.5260i	−0.370534	+	0.641784i	0.619114	+	0.785301i	$0.287492\pi$
$270$		0			0
$271$	20.9346	−	12.0866i	1.27169	−	0.734208i	0.296380	−	0.955070i	$-0.404220\pi$
$271$	20.9346	−	12.0866i	1.27169	−	0.734208i	0.975305	+	0.220862i	$0.0708871\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	6.27826	−	3.62476i	0.378593	−	0.218581i
$276$		0			0
$277$	−1.46720	+	2.54127i	−0.0881556	+	0.152690i	−0.906732	−	0.421708i	$-0.861431\pi$
$277$	−1.46720	+	2.54127i	−0.0881556	+	0.152690i	0.818576	+	0.574398i	$0.194764\pi$
$278$		0			0
$279$	16.3338	−	14.9468i	0.977879	−	0.894842i
$280$		0			0
$281$			1.97450i			0.117789i	0.998264	+	0.0588944i	$0.0187575\pi$
$281$			1.97450i			0.117789i	−0.998264	+	0.0588944i	$0.981242\pi$
$282$		0			0
$283$	20.9184	+	12.0773i	1.24347	+	0.717919i	0.969799	−	0.243905i	$-0.0784284\pi$
$283$	20.9184	+	12.0773i	1.24347	+	0.717919i	0.273672	+	0.961823i	$0.411762\pi$
$284$		0			0
$285$	0.0387029	+	0.354504i	0.00229256	+	0.0209990i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−20.0419	−	34.7135i	−1.17893	−	2.04197i
$290$		0			0
$291$	6.92190	−	5.07174i	0.405769	−	0.297311i
$292$		0			0
$293$	−22.8829			−1.33683			−0.668417	−	0.743787i	$-0.733028\pi$
$293$	−22.8829			−1.33683			−0.668417	+	0.743787i	$0.733028\pi$
$294$		0			0
$295$	−3.59796			−0.209481
$296$		0			0
$297$	7.75880	+	1.55153i	0.450211	+	0.0900287i
$298$		0			0
$299$	1.92685	+	3.33741i	0.111433	+	0.193007i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−9.48769	+	1.03582i	−0.545053	+	0.0595061i
$304$		0			0
$305$	4.72231	+	2.72643i	0.270399	+	0.156115i
$306$		0			0
$307$			9.74121i			0.555961i	0.960587	+	0.277980i	$0.0896650\pi$
$307$			9.74121i			0.555961i	−0.960587	+	0.277980i	$0.910335\pi$
$308$		0			0
$309$	−14.5513	−	6.40862i	−0.827796	−	0.364574i
$310$		0			0
$311$	−11.0339	+	19.1113i	−0.625676	+	1.08370i	0.362733	+	0.931893i	$0.381844\pi$
$311$	−11.0339	+	19.1113i	−0.625676	+	1.08370i	−0.988410	+	0.151810i	$0.951490\pi$
$312$		0			0
$313$	13.5067	−	7.79812i	0.763446	−	0.440776i	−0.0670859	−	0.997747i	$-0.521370\pi$
$313$	13.5067	−	7.79812i	0.763446	−	0.440776i	0.830532	+	0.556972i	$0.188037\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	15.3149	−	8.84205i	0.860169	−	0.496619i	−0.00389987	−	0.999992i	$-0.501241\pi$
$317$	15.3149	−	8.84205i	0.860169	−	0.496619i	0.864069	+	0.503374i	$0.167908\pi$
$318$		0			0
$319$	5.45413	−	9.44684i	0.305373	−	0.528921i
$320$		0			0
$321$	−7.59176	−	3.34353i	−0.423731	−	0.186617i
$322$		0			0
$323$		−	3.18073i		−	0.176980i
$324$		0			0
$325$	−2.68847	−	1.55219i	−0.149129	−	0.0860999i
$326$		0			0
$327$	−23.0316	+	2.51447i	−1.27365	+	0.139050i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	6.33251	+	10.9682i	0.348066	+	0.602869i	0.985906	−	0.167301i	$-0.0535051\pi$
$331$	6.33251	+	10.9682i	0.348066	+	0.602869i	−0.637840	+	0.770169i	$0.720172\pi$
$332$		0			0
$333$	−23.7047	+	5.23834i	−1.29901	+	0.287059i
$334$		0			0
$335$	7.15202			0.390756
$336$		0			0
$337$	25.7617			1.40333			0.701663	−	0.712509i	$-0.252441\pi$
$337$	25.7617			1.40333			0.701663	+	0.712509i	$0.252441\pi$
$338$		0			0
$339$	−17.5712	+	12.8746i	−0.954336	+	0.699251i
$340$		0			0
$341$	−5.61904	−	9.73247i	−0.304288	−	0.527043i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−0.543324	−	4.97664i	−0.0292516	−	0.267933i
$346$		0			0
$347$	−28.5826	−	16.5022i	−1.53439	−	0.885883i	−0.999152	−	0.0411840i	$-0.986887\pi$
$347$	−28.5826	−	16.5022i	−1.53439	−	0.885883i	−0.535242	−	0.844699i	$-0.679780\pi$
$348$		0			0
$349$		−	29.1507i		−	1.56040i	−0.625528	−	0.780202i	$-0.715116\pi$
$349$		−	29.1507i		−	1.56040i	0.625528	−	0.780202i	$-0.284884\pi$
$350$		0			0
$351$	−1.08585	−	3.20954i	−0.0579585	−	0.171312i
$352$		0			0
$353$	−2.29057	+	3.96738i	−0.121915	+	0.211162i	−0.920523	−	0.390689i	$-0.872237\pi$
$353$	−2.29057	+	3.96738i	−0.121915	+	0.211162i	0.798608	+	0.601851i	$0.205570\pi$
$354$		0			0
$355$	−5.44301	+	3.14252i	−0.288885	+	0.166788i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	16.0021	−	9.23882i	0.844559	−	0.487606i	−0.0142524	−	0.999898i	$-0.504537\pi$
$359$	16.0021	−	9.23882i	0.844559	−	0.487606i	0.858811	+	0.512292i	$0.171204\pi$
$360$		0			0
$361$	−9.41138	+	16.3010i	−0.495336	+	0.857947i
$362$		0			0
$363$	−6.06051	+	13.7609i	−0.318094	+	0.722260i
$364$		0			0
$365$		−	4.52146i		−	0.236664i
$366$		0			0
$367$	9.78362	+	5.64857i	0.510701	+	0.294853i	0.733122	−	0.680098i	$-0.238063\pi$
$367$	9.78362	+	5.64857i	0.510701	+	0.294853i	−0.222421	+	0.974951i	$0.571396\pi$
$368$		0			0
$369$	2.28894	−	7.24246i	0.119157	−	0.377027i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	9.31497	+	16.1340i	0.482311	+	0.835387i	0.999794	−	0.0203065i	$-0.00646421\pi$
$373$	9.31497	+	16.1340i	0.482311	+	0.835387i	−0.517483	+	0.855694i	$0.673131\pi$
$374$		0			0
$375$	4.88679	+	6.66948i	0.252353	+	0.344411i
$376$		0			0
$377$	−4.67113			−0.240575
$378$		0			0
$379$	−5.62097			−0.288730			−0.144365	−	0.989525i	$-0.546114\pi$
$379$	−5.62097			−0.288730			−0.144365	+	0.989525i	$0.546114\pi$
$380$		0			0
$381$	−0.270404	−	0.369047i	−0.0138532	−	0.0189069i
$382$		0			0
$383$	10.0536	+	17.4133i	0.513713	+	0.889777i	0.999873	+	0.0159076i	$0.00506374\pi$
$383$	10.0536	+	17.4133i	0.513713	+	0.889777i	−0.486160	+	0.873870i	$0.661603\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	5.02819	−	15.9098i	0.255597	−	0.808739i
$388$		0			0
$389$	20.2353	+	11.6829i	1.02597	+	0.592345i	0.915828	−	0.401571i	$-0.131536\pi$
$389$	20.2353	+	11.6829i	1.02597	+	0.592345i	0.110143	+	0.993916i	$0.464869\pi$
$390$		0			0
$391$			44.6521i			2.25815i
$392$		0			0
$393$	5.24924	−	11.9188i	0.264789	−	0.601226i
$394$		0			0
$395$	−0.296958	+	0.514347i	−0.0149416	+	0.0258796i
$396$		0			0
$397$	−28.4398	+	16.4197i	−1.42735	+	0.824082i	−0.996911	−	0.0785363i	$-0.974975\pi$
$397$	−28.4398	+	16.4197i	−1.42735	+	0.824082i	−0.430441	+	0.902619i	$0.641642\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−28.5625	+	16.4906i	−1.42635	+	0.823501i	−0.996830	−	0.0795585i	$-0.974649\pi$
$401$	−28.5625	+	16.4906i	−1.42635	+	0.823501i	−0.429515	+	0.903060i	$0.641316\pi$
$402$		0			0
$403$	−2.40618	+	4.16763i	−0.119860	+	0.207604i
$404$		0			0
$405$	−0.389565	+	4.38427i	−0.0193576	+	0.217856i
$406$		0			0
$407$			12.3223i			0.610795i
$408$		0			0
$409$	14.5044	+	8.37414i	0.717198	+	0.414075i	0.813721	−	0.581256i	$-0.197439\pi$
$409$	14.5044	+	8.37414i	0.717198	+	0.414075i	−0.0965223	+	0.995331i	$0.530772\pi$
$410$		0			0
$411$	−0.00372289	−	0.0341003i	−0.000183637	−	0.00168204i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	2.20864	+	3.82549i	0.108418	+	0.187786i
$416$		0			0
$417$	−14.1389	+	10.3597i	−0.692383	+	0.507315i
$418$		0			0
$419$	22.5610			1.10218			0.551089	−	0.834446i	$-0.314212\pi$
$419$	22.5610			1.10218			0.551089	+	0.834446i	$0.314212\pi$
$420$		0			0
$421$	−13.7973			−0.672441			−0.336220	−	0.941783i	$-0.609149\pi$
$421$	−13.7973			−0.672441			−0.336220	+	0.941783i	$0.609149\pi$
$422$		0			0
$423$	27.2850	−	6.02953i	1.32664	−	0.293166i
$424$		0			0
$425$	−17.9849	−	31.1507i	−0.872395	−	1.51103i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−1.70965	+	0.186651i	−0.0825427	+	0.00901159i
$430$		0			0
$431$	−6.81430	−	3.93424i	−0.328233	−	0.189506i	0.326823	−	0.945086i	$-0.394022\pi$
$431$	−6.81430	−	3.93424i	−0.328233	−	0.189506i	−0.655057	+	0.755580i	$0.727355\pi$
$432$		0			0
$433$		−	23.7844i		−	1.14300i	−0.820601	−	0.571502i	$-0.806361\pi$
$433$		−	23.7844i		−	1.14300i	0.820601	−	0.571502i	$-0.193639\pi$
$434$		0			0
$435$	5.55337	+	2.44579i	0.266264	+	0.117267i
$436$		0			0
$437$	−1.24402	+	2.15470i	−0.0595094	+	0.103073i
$438$		0			0
$439$	−19.8458	+	11.4580i	−0.947189	+	0.546860i	−0.892207	−	0.451627i	$-0.850844\pi$
$439$	−19.8458	+	11.4580i	−0.947189	+	0.546860i	−0.0549827	+	0.998487i	$0.517510\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−13.1187	+	7.57407i	−0.623287	+	0.359855i	−0.778147	−	0.628082i	$-0.783840\pi$
$443$	−13.1187	+	7.57407i	−0.623287	+	0.359855i	0.154861	+	0.987936i	$0.450507\pi$
$444$		0			0
$445$	−2.33769	+	4.04901i	−0.110817	+	0.191941i
$446$		0			0
$447$	−22.3286	−	9.83386i	−1.05611	−	0.465125i
$448$		0			0
$449$		−	15.2140i		−	0.717993i	−0.933339	−	0.358997i	$-0.883119\pi$
$449$		−	15.2140i		−	0.717993i	0.933339	−	0.358997i	$-0.116881\pi$
$450$		0			0
$451$	−3.33884	−	1.92768i	−0.157220	−	0.0907710i
$452$		0			0
$453$	21.6611	−	2.36485i	1.01773	−	0.111110i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−11.5699	−	20.0396i	−0.541216	−	0.937414i	−0.998835	−	0.0482653i	$-0.984631\pi$
$457$	−11.5699	−	20.0396i	−0.541216	−	0.937414i	0.457618	−	0.889149i	$-0.348703\pi$
$458$		0			0
$459$	7.69818	−	38.4967i	0.359320	−	1.79687i
$460$		0			0
$461$	2.52672			0.117681			0.0588405	−	0.998267i	$-0.481260\pi$
$461$	2.52672			0.117681			0.0588405	+	0.998267i	$0.481260\pi$
$462$		0			0
$463$	−37.3811			−1.73725			−0.868624	−	0.495472i	$-0.834995\pi$
$463$	−37.3811			−1.73725			−0.868624	+	0.495472i	$0.834995\pi$
$464$		0			0
$465$	5.04280	−	3.69490i	0.233854	−	0.171347i
$466$		0			0
$467$	−13.1389	−	22.7572i	−0.607994	−	1.05308i	−0.991571	−	0.129567i	$-0.958641\pi$
$467$	−13.1389	−	22.7572i	−0.607994	−	1.05308i	0.383577	−	0.923509i	$-0.374692\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	1.62985	+	14.9288i	0.0750993	+	0.687882i
$472$		0			0
$473$	−7.33456	−	4.23461i	−0.337243	−	0.194707i
$474$		0			0
$475$		−	2.00425i		−	0.0919614i
$476$		0			0
$477$	3.23640	−	2.96158i	0.148185	−	0.135602i
$478$		0			0
$479$	5.24766	−	9.08921i	0.239772	−	0.415297i	−0.720877	−	0.693063i	$-0.756261\pi$
$479$	5.24766	−	9.08921i	0.239772	−	0.415297i	0.960649	+	0.277766i	$0.0895941\pi$
$480$		0			0
$481$	4.56972	−	2.63833i	0.208361	−	0.120297i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	2.09834	−	1.21148i	0.0952808	−	0.0550104i
$486$		0			0
$487$	7.43071	−	12.8704i	0.336718	−	0.583212i	−0.647096	−	0.762409i	$-0.724017\pi$
$487$	7.43071	−	12.8704i	0.336718	−	0.583212i	0.983813	+	0.179197i	$0.0573499\pi$
$488$		0			0
$489$	2.33983	−	5.31277i	0.105811	−	0.240252i
$490$		0			0
$491$		−	13.2061i		−	0.595981i	−0.954569	−	0.297990i	$-0.903684\pi$
$491$		−	13.2061i		−	0.595981i	0.954569	−	0.297990i	$-0.0963164\pi$
$492$		0			0
$493$	−46.8722	−	27.0617i	−2.11102	−	1.21880i
$494$		0			0
$495$	2.13029	+	0.673264i	0.0957492	+	0.0302610i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	16.1373	+	27.9506i	0.722404	+	1.25124i	0.960034	+	0.279884i	$0.0902960\pi$
$499$	16.1373	+	27.9506i	0.722404	+	1.25124i	−0.237630	+	0.971356i	$0.576371\pi$
$500$		0			0
$501$	23.9561	+	32.6952i	1.07028	+	1.46071i
$502$		0			0
$503$	35.5206			1.58379			0.791894	−	0.610659i	$-0.209095\pi$
$503$	35.5206			1.58379			0.791894	+	0.610659i	$0.209095\pi$
$504$		0			0
$505$	−2.69486			−0.119919
$506$		0			0
$507$	−12.8729	−	17.5689i	−0.571705	−	0.780262i
$508$		0			0
$509$	15.8697	+	27.4871i	0.703411	+	1.21834i	0.967262	+	0.253780i	$0.0816738\pi$
$509$	15.8697	+	27.4871i	0.703411	+	1.21834i	−0.263851	+	0.964563i	$0.584993\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	1.44401	−	1.64320i	0.0637544	−	0.0725490i
$514$		0			0
$515$	−3.88804	−	2.24476i	−0.171328	−	0.0989161i
$516$		0			0
$517$		−	14.1835i		−	0.623788i
$518$		0			0
$519$	9.94204	−	22.5742i	0.436407	−	0.990899i
$520$		0			0
$521$	6.43143	−	11.1396i	0.281766	−	0.488033i	−0.690054	−	0.723758i	$-0.742413\pi$
$521$	6.43143	−	11.1396i	0.281766	−	0.488033i	0.971820	+	0.235725i	$0.0757465\pi$
$522$		0			0
$523$	25.6383	−	14.8023i	1.12109	−	0.647260i	0.179409	−	0.983775i	$-0.442582\pi$
$523$	25.6383	−	14.8023i	1.12109	−	0.647260i	0.941678	+	0.336515i	$0.109248\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−48.2894	+	27.8799i	−2.10352	+	1.21447i
$528$		0			0
$529$	5.96390	−	10.3298i	0.259300	−	0.449121i
$530$		0			0
$531$	14.8997	+	16.2823i	0.646590	+	0.706591i
$532$		0			0
$533$			1.65094i			0.0715101i
$534$		0			0
$535$	−2.02848	−	1.17114i	−0.0876989	−	0.0506330i
$536$		0			0
$537$	−3.82093	−	34.9983i	−0.164886	−	1.51029i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	4.99513	+	8.65182i	0.214757	+	0.371971i	0.953198	−	0.302348i	$-0.0977706\pi$
$541$	4.99513	+	8.65182i	0.214757	+	0.371971i	−0.738440	+	0.674319i	$0.764437\pi$
$542$		0			0
$543$	−1.11560	+	0.817408i	−0.0478748	+	0.0350783i
$544$		0			0
$545$	−6.54182			−0.280221
$546$		0			0
$547$	36.1746			1.54671			0.773357	−	0.633970i	$-0.218576\pi$
$547$	36.1746			1.54671			0.773357	+	0.633970i	$0.218576\pi$
$548$		0			0
$549$	−7.21754	−	32.6610i	−0.308037	−	1.39394i
$550$		0			0
$551$	−1.50789	−	2.61174i	−0.0642382	−	0.111264i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−6.81423	+	0.743942i	−0.289248	+	0.0315786i
$556$		0			0
$557$	6.40214	+	3.69628i	0.271267	+	0.156616i	0.629463	−	0.777030i	$-0.283275\pi$
$557$	6.40214	+	3.69628i	0.271267	+	0.156616i	−0.358196	+	0.933646i	$0.616608\pi$
$558$		0			0
$559$			3.62668i			0.153392i
$560$		0			0
$561$	−18.2368	−	8.03175i	−0.769957	−	0.339101i
$562$		0			0
$563$	6.74518	−	11.6830i	0.284275	−	0.492379i	−0.688158	−	0.725561i	$-0.741580\pi$
$563$	6.74518	−	11.6830i	0.284275	−	0.492379i	0.972433	+	0.233182i	$0.0749137\pi$
$564$		0			0
$565$	−5.32662	+	3.07532i	−0.224092	+	0.129380i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−29.8855	+	17.2544i	−1.25286	+	0.723342i	−0.971677	−	0.236311i	$-0.924062\pi$
$569$	−29.8855	+	17.2544i	−1.25286	+	0.723342i	−0.281187	+	0.959653i	$0.590728\pi$
$570$		0			0
$571$	11.0628	−	19.1612i	0.462962	−	0.801873i	−0.536145	−	0.844126i	$-0.680120\pi$
$571$	11.0628	−	19.1612i	0.462962	−	0.801873i	0.999107	+	0.0422525i	$0.0134534\pi$
$572$		0			0
$573$	−33.3893	−	14.7051i	−1.39486	−	0.614316i
$574$		0			0
$575$			28.1363i			1.17337i
$576$		0			0
$577$	−2.16681	−	1.25101i	−0.0902056	−	0.0520802i	0.454219	−	0.890890i	$-0.349918\pi$
$577$	−2.16681	−	1.25101i	−0.0902056	−	0.0520802i	−0.544424	+	0.838810i	$0.683252\pi$
$578$		0			0
$579$	−30.8232	+	3.36511i	−1.28097	+	0.139849i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−1.11337	−	1.92841i	−0.0461109	−	0.0798665i
$584$		0			0
$585$	−0.206435	−	0.934165i	−0.00853504	−	0.0386230i
$586$		0			0
$587$	4.36635			0.180219			0.0901093	−	0.995932i	$-0.471278\pi$
$587$	4.36635			0.180219			0.0901093	+	0.995932i	$0.471278\pi$
$588$		0			0
$589$	−3.10696			−0.128020
$590$		0			0
$591$	26.7351	−	19.5890i	1.09973	−	0.805785i
$592$		0			0
$593$	−3.27519	−	5.67280i	−0.134496	−	0.232954i	0.790909	−	0.611934i	$-0.209608\pi$
$593$	−3.27519	−	5.67280i	−0.134496	−	0.232954i	−0.925405	+	0.378980i	$0.876275\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	2.36031	+	21.6195i	0.0966010	+	0.884828i
$598$		0			0
$599$	7.30262	+	4.21617i	0.298377	+	0.172268i	0.641713	−	0.766944i	$-0.278224\pi$
$599$	7.30262	+	4.21617i	0.298377	+	0.172268i	−0.343337	+	0.939212i	$0.611557\pi$
$600$		0			0
$601$			3.05803i			0.124740i	0.998053	+	0.0623699i	$0.0198659\pi$
$601$			3.05803i			0.124740i	−0.998053	+	0.0623699i	$0.980134\pi$
$602$		0			0
$603$	−29.6175	−	32.3659i	−1.20612	−	1.31804i
$604$		0			0
$605$	−2.12283	+	3.67685i	−0.0863053	+	0.149485i
$606$		0			0
$607$	−1.79290	+	1.03513i	−0.0727714	+	0.0420146i	−0.535944	−	0.844253i	$-0.680044\pi$
$607$	−1.79290	+	1.03513i	−0.0727714	+	0.0420146i	0.463173	+	0.886268i	$0.346711\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−5.25992	+	3.03681i	−0.212793	+	0.122856i
$612$		0			0
$613$	−14.0987	+	24.4196i	−0.569440	+	0.986299i	0.427181	+	0.904166i	$0.359507\pi$
$613$	−14.0987	+	24.4196i	−0.569440	+	0.986299i	−0.996621	+	0.0821331i	$0.973827\pi$
$614$		0			0
$615$	0.864427	−	1.96275i	0.0348570	−	0.0791459i
$616$		0			0
$617$			22.8152i			0.918505i	0.888306	+	0.459253i	$0.151883\pi$
$617$			22.8152i			0.918505i	−0.888306	+	0.459253i	$0.848117\pi$
$618$		0			0
$619$	3.10983	+	1.79546i	0.124995	+	0.0721657i	0.561194	−	0.827685i	$-0.310342\pi$
$619$	3.10983	+	1.79546i	0.124995	+	0.0721657i	−0.436199	+	0.899850i	$0.643676\pi$
$620$		0			0
$621$	−20.2714	+	23.0677i	−0.813463	+	0.925677i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−10.7347	−	18.5931i	−0.429390	−	0.743725i
$626$		0			0
$627$	−0.656254	−	0.895655i	−0.0262083	−	0.0357690i
$628$		0			0
$629$	61.1395			2.43779
$630$		0			0
$631$	14.4106			0.573678			0.286839	−	0.957979i	$-0.407395\pi$
$631$	14.4106			0.573678			0.286839	+	0.957979i	$0.407395\pi$
$632$		0			0
$633$	−9.17969	−	12.5284i	−0.364860	−	0.497960i
$634$		0			0
$635$	−0.0645910	−	0.111875i	−0.00256322	−	0.00443962i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	36.7615	+	11.6183i	1.45426	+	0.459612i
$640$		0			0
$641$	−12.2032	−	7.04551i	−0.481997	−	0.278281i	0.239251	−	0.970958i	$-0.423098\pi$
$641$	−12.2032	−	7.04551i	−0.481997	−	0.278281i	−0.721248	+	0.692677i	$0.756431\pi$
$642$		0			0
$643$		−	8.06888i		−	0.318205i	−0.987262	−	0.159103i	$-0.949140\pi$
$643$		−	8.06888i		−	0.318205i	0.987262	−	0.159103i	$-0.0508601\pi$
$644$		0			0
$645$	1.89892	−	4.31165i	0.0747698	−	0.169771i
$646$		0			0
$647$	21.6216	−	37.4496i	0.850031	−	1.47230i	−0.0311479	−	0.999515i	$-0.509916\pi$
$647$	21.6216	−	37.4496i	0.850031	−	1.47230i	0.881179	−	0.472782i	$-0.156750\pi$
$648$		0			0
$649$	9.70177	−	5.60132i	0.380828	−	0.219871i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−38.0536	+	21.9702i	−1.48915	+	0.859762i	−0.999923	−	0.0123939i	$-0.996055\pi$
$653$	−38.0536	+	21.9702i	−1.48915	+	0.859762i	−0.489228	+	0.872156i	$0.662721\pi$
$654$		0			0
$655$	1.83866	−	3.18466i	0.0718426	−	0.124435i
$656$		0			0
$657$	−20.4615	+	18.7240i	−0.798279	+	0.730493i
$658$		0			0
$659$		−	24.6275i		−	0.959351i	−0.877446	−	0.479676i	$-0.840754\pi$
$659$		−	24.6275i		−	0.959351i	0.877446	−	0.479676i	$-0.159246\pi$
$660$		0			0
$661$	−19.3064	−	11.1466i	−0.750933	−	0.433551i	0.0750980	−	0.997176i	$-0.476073\pi$
$661$	−19.3064	−	11.1466i	−0.750933	−	0.433551i	−0.826031	+	0.563625i	$0.809406\pi$
$662$		0			0
$663$	0.926102	+	8.48275i	0.0359668	+	0.329443i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	21.1682	+	36.6644i	0.819637	+	1.41965i
$668$		0			0
$669$	15.3428	−	11.2418i	0.593187	−	0.434634i
$670$		0			0
$671$	−16.9781			−0.655431
$672$		0			0
$673$	14.5042			0.559096			0.279548	−	0.960132i	$-0.409815\pi$
$673$	14.5042			0.559096			0.279548	+	0.960132i	$0.409815\pi$
$674$		0			0
$675$	4.85080	−	24.2577i	0.186708	−	0.933679i
$676$		0			0
$677$	−20.7863	−	36.0030i	−0.798884	−	1.38371i	−0.920344	−	0.391111i	$-0.872091\pi$
$677$	−20.7863	−	36.0030i	−0.798884	−	1.38371i	0.121460	−	0.992596i	$-0.461242\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−9.38500	+	1.02461i	−0.359634	+	0.0392630i
$682$		0			0
$683$	6.59064	+	3.80511i	0.252184	+	0.145599i	0.620764	−	0.783998i	$-0.286823\pi$
$683$	6.59064	+	3.80511i	0.252184	+	0.145599i	−0.368580	+	0.929596i	$0.620156\pi$
$684$		0			0
$685$		−	0.00968575i		−	0.000370073i
$686$		0			0
$687$	20.2903	+	8.93614i	0.774122	+	0.340935i
$688$		0			0
$689$	−0.476764	+	0.825780i	−0.0181633	+	0.0314597i
$690$		0			0
$691$	−1.82457	+	1.05341i	−0.0694098	+	0.0400738i	−0.534303	−	0.845293i	$-0.679426\pi$
$691$	−1.82457	+	1.05341i	−0.0694098	+	0.0400738i	0.464893	+	0.885367i	$0.346093\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−4.28612	+	2.47459i	−0.162582	+	0.0938667i
$696$		0			0
$697$	−9.56455	+	16.5663i	−0.362283	+	0.627493i
$698$		0			0
$699$	−25.6066	−	11.2775i	−0.968530	−	0.426555i
$700$		0			0
$701$		−	0.0201617i		−	0.000761498i	−1.00000		0.000380749i	$-0.999879\pi$
$701$		−	0.0201617i		−	0.000761498i	1.00000		0.000380749i	$-0.000121196\pi$
$702$		0			0
$703$	2.95031	+	1.70336i	0.111273	+	0.0642434i
$704$		0			0
$705$	7.84343	−	0.856305i	0.295401	−	0.0322503i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	2.59166	+	4.48888i	0.0973317	+	0.168583i	0.910579	−	0.413334i	$-0.135636\pi$
$709$	2.59166	+	4.48888i	0.0973317	+	0.168583i	−0.813248	+	0.581918i	$0.802303\pi$
$710$		0			0
$711$	3.55738	−	0.786122i	0.133412	−	0.0294819i
$712$		0			0
$713$	43.6165			1.63345
$714$		0			0
$715$	−0.485605			−0.0181606
$716$		0			0
$717$	1.53114	−	1.12188i	0.0571816	−	0.0418975i
$718$		0			0
$719$	−13.0697	−	22.6375i	−0.487419	−	0.844235i	0.512476	−	0.858701i	$-0.328728\pi$
$719$	−13.0697	−	22.6375i	−0.487419	−	0.844235i	−0.999895	+	0.0144668i	$0.995395\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−1.60913	−	14.7390i	−0.0598442	−	0.548151i
$724$		0			0
$725$	−29.5353	−	17.0522i	−1.09691	−	0.633303i
$726$		0			0
$727$			20.9197i			0.775867i	0.921687	+	0.387934i	$0.126811\pi$
$727$			20.9197i			0.775867i	−0.921687	+	0.387934i	$0.873189\pi$
$728$		0			0
$729$	21.4539	−	16.3930i	0.794590	−	0.607147i
$730$		0			0
$731$	−21.0108	+	36.3917i	−0.777112	+	1.34600i
$732$		0			0
$733$	−1.42523	+	0.822856i	−0.0526420	+	0.0303929i	−0.526090	−	0.850429i	$-0.676343\pi$
$733$	−1.42523	+	0.822856i	−0.0526420	+	0.0303929i	0.473448	+	0.880822i	$0.343009\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−19.2852	+	11.1343i	−0.710378	+	0.410137i
$738$		0			0
$739$	1.82710	−	3.16463i	0.0672109	−	0.116413i	−0.830462	−	0.557076i	$-0.811923\pi$
$739$	1.82710	−	3.16463i	0.0672109	−	0.116413i	0.897673	+	0.440663i	$0.145257\pi$
$740$		0			0
$741$	−0.191642	+	0.435139i	−0.00704014	+	0.0159852i
$742$		0			0
$743$		−	23.6421i		−	0.867346i	−0.901070	−	0.433673i	$-0.857217\pi$
$743$		−	23.6421i		−	0.867346i	0.901070	−	0.433673i	$-0.142783\pi$
$744$		0			0
$745$	−5.96610	−	3.44453i	−0.218581	−	0.126198i
$746$		0			0
$747$	8.16561	−	25.8369i	0.298764	−	0.945324i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−9.24296	−	16.0093i	−0.337280	−	0.584187i	0.646640	−	0.762796i	$-0.276174\pi$
$751$	−9.24296	−	16.0093i	−0.337280	−	0.584187i	−0.983920	+	0.178609i	$0.942840\pi$
$752$		0			0
$753$	3.97559	+	5.42588i	0.144879	+	0.197730i
$754$		0			0
$755$	6.15256			0.223914
$756$		0			0
$757$	−39.2439			−1.42634			−0.713172	−	0.700989i	$-0.752742\pi$
$757$	−39.2439			−1.42634			−0.713172	+	0.700989i	$0.752742\pi$
$758$		0			0
$759$	9.21271	+	12.5735i	0.334400	+	0.456389i
$760$		0			0
$761$	12.1576	+	21.0575i	0.440711	+	0.763334i	0.997742	−	0.0671572i	$-0.0213929\pi$
$761$	12.1576	+	21.0575i	0.440711	+	0.763334i	−0.557031	+	0.830492i	$0.688060\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	3.34053	−	10.5698i	0.120777	−	0.382152i
$766$		0			0
$767$	−4.15448	−	2.39859i	−0.150010	−	0.0866081i
$768$		0			0
$769$		−	2.38223i		−	0.0859053i	−0.999077	−	0.0429526i	$-0.986324\pi$
$769$		−	2.38223i		−	0.0859053i	0.999077	−	0.0429526i	$-0.0136765\pi$
$770$		0			0
$771$	12.4347	−	28.2341i	0.447826	−	1.01683i
$772$		0			0
$773$	−17.9700	+	31.1250i	−0.646337	+	1.11949i	0.337654	+	0.941270i	$0.390367\pi$
$773$	−17.9700	+	31.1250i	−0.646337	+	1.11949i	−0.983991	+	0.178219i	$0.942967\pi$
$774$		0			0
$775$	−30.4283	+	17.5678i	−1.09302	+	0.631054i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−0.923080	+	0.532940i	−0.0330728	+	0.0190946i
$780$		0			0
$781$	9.78460	−	16.9474i	0.350120	−	0.606426i
$782$		0			0
$783$	−11.9291	−	35.2597i	−0.426310	−	1.26008i
$784$		0			0
$785$			4.24033i			0.151344i
$786$		0			0
$787$	7.32505	+	4.22912i	0.261110	+	0.150752i	0.624841	−	0.780752i	$-0.285164\pi$
$787$	7.32505	+	4.22912i	0.261110	+	0.150752i	−0.363731	+	0.931504i	$0.618497\pi$
$788$		0			0
$789$	−1.02935	−	9.42843i	−0.0366457	−	0.335661i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	3.63516	+	6.29629i	0.129088	+	0.223588i
$794$		0			0
$795$	0.999188	−	0.732114i	0.0354375	−	0.0259654i
$796$		0			0
$797$	−22.7299			−0.805134			−0.402567	−	0.915390i	$-0.631882\pi$
$797$	−22.7299			−0.805134			−0.402567	+	0.915390i	$0.631882\pi$
$798$		0			0
$799$	−70.3739			−2.48965
$800$		0			0
$801$	28.0042	−	6.18846i	0.989479	−	0.218658i
$802$		0			0
$803$	7.03903	+	12.1920i	0.248402	+	0.430245i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	20.9277	−	2.28478i	0.736691	−	0.0804280i
$808$		0			0
$809$	34.8944	+	20.1463i	1.22682	+	0.708307i	0.966364	−	0.257178i	$-0.0827926\pi$
$809$	34.8944	+	20.1463i	1.22682	+	0.708307i	0.260459	+	0.965485i	$0.416126\pi$
$810$		0			0
$811$		−	47.7723i		−	1.67751i	−0.544507	−	0.838756i	$-0.683283\pi$
$811$		−	47.7723i		−	1.67751i	0.544507	−	0.838756i	$-0.316717\pi$
$812$		0			0
$813$	−38.3176	−	16.8757i	−1.34386	−	0.591855i
$814$		0			0
$815$	0.819576	−	1.41955i	0.0287085	−	0.0497246i
$816$		0			0
$817$	−2.02776	+	1.17073i	−0.0709425	+	0.0409587i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	2.56155	−	1.47891i	0.0893988	−	0.0516144i	−0.454634	−	0.890678i	$-0.650230\pi$
$821$	2.56155	−	1.47891i	0.0893988	−	0.0516144i	0.544033	+	0.839064i	$0.316897\pi$
$822$		0			0
$823$	−24.3551	+	42.1842i	−0.848964	+	1.47045i	0.0331698	+	0.999450i	$0.489440\pi$
$823$	−24.3551	+	42.1842i	−0.848964	+	1.47045i	−0.882134	+	0.470999i	$0.843894\pi$
$824$		0			0
$825$	−11.4914	−	5.06099i	−0.400080	−	0.176201i
$826$		0			0
$827$			53.0570i			1.84497i	0.386028	+	0.922487i	$0.373847\pi$
$827$			53.0570i			1.84497i	−0.386028	+	0.922487i	$0.626153\pi$
$828$		0			0
$829$	35.6250	+	20.5681i	1.23731	+	0.714360i	0.968543	−	0.248846i	$-0.0800514\pi$
$829$	35.6250	+	20.5681i	1.23731	+	0.714360i	0.268764	+	0.963206i	$0.413385\pi$
$830$		0			0
$831$	5.05251	−	0.551607i	0.175270	−	0.0191350i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	5.72234	+	9.91139i	0.198030	+	0.342998i
$836$		0			0
$837$	−37.6039	−	7.51965i	−1.29978	−	0.259917i
$838$		0			0
$839$	42.0861			1.45297			0.726486	−	0.687181i	$-0.241152\pi$
$839$	42.0861			1.45297			0.726486	+	0.687181i	$0.241152\pi$
$840$		0			0
$841$	−22.3166			−0.769536
$842$		0			0
$843$	2.75867	−	2.02130i	0.0950137	−	0.0696174i
$844$		0			0
$845$	−3.07492	−	5.32592i	−0.105781	−	0.183217i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−4.54055	−	41.5897i	−0.155831	−	1.42736i
$850$		0			0
$851$	−41.4173	−	23.9123i	−1.41977	−	0.819703i
$852$		0			0
$853$			21.7333i			0.744134i	0.928206	+	0.372067i	$0.121351\pi$
$853$			21.7333i			0.744134i	−0.928206	+	0.372067i	$0.878649\pi$
$854$		0			0
$855$	0.455675	−	0.416981i	0.0155838	−	0.0142605i
$856$		0			0
$857$	−2.71077	+	4.69519i	−0.0925982	+	0.160385i	−0.908604	−	0.417659i	$-0.862851\pi$
$857$	−2.71077	+	4.69519i	−0.0925982	+	0.160385i	0.816005	+	0.578044i	$0.196184\pi$
$858$		0			0
$859$	−2.39371	+	1.38201i	−0.0816722	+	0.0471535i	−0.540280	−	0.841485i	$-0.681682\pi$
$859$	−2.39371	+	1.38201i	−0.0816722	+	0.0471535i	0.458608	+	0.888639i	$0.348348\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	4.40681	−	2.54427i	0.150009	−	0.0866080i	−0.423116	−	0.906075i	$-0.639064\pi$
$863$	4.40681	−	2.54427i	0.150009	−	0.0866080i	0.573126	+	0.819467i	$0.305731\pi$
$864$		0			0
$865$	3.48242	−	6.03173i	0.118406	−	0.205085i
$866$		0			0
$867$	−27.9830	+	63.5379i	−0.950354	+	2.15786i
$868$		0			0
$869$		−	1.84922i		−	0.0627306i
$870$		0			0
$871$	8.25827	+	4.76791i	0.279821	+	0.161555i
$872$		0			0
$873$	−14.1720	−	4.47897i	−0.479649	−	0.151590i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−4.13967	−	7.17011i	−0.139787	−	0.242118i	0.787629	−	0.616150i	$-0.211308\pi$
$877$	−4.13967	−	7.17011i	−0.139787	−	0.242118i	−0.927416	+	0.374032i	$0.877975\pi$
$878$		0			0
$879$	23.4254	+	31.9709i	0.790118	+	1.07835i
$880$		0			0
$881$	14.3278			0.482714			0.241357	−	0.970436i	$-0.422407\pi$
$881$	14.3278			0.482714			0.241357	+	0.970436i	$0.422407\pi$
$882$		0			0
$883$	55.7910			1.87752			0.938758	−	0.344576i	$-0.111977\pi$
$883$	55.7910			1.87752			0.938758	+	0.344576i	$0.111977\pi$
$884$		0			0
$885$	3.68325	+	5.02689i	0.123811	+	0.168977i
$886$		0			0
$887$	16.7623	+	29.0332i	0.562824	+	0.974840i	0.997248	+	0.0741320i	$0.0236186\pi$
$887$	16.7623	+	29.0332i	0.562824	+	0.974840i	−0.434424	+	0.900708i	$0.643048\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−5.77501	−	12.4285i	−0.193470	−	0.416371i
$892$		0			0
$893$	−3.39591	−	1.96063i	−0.113640	−	0.0656100i
$894$		0			0
$895$		−	9.94083i		−	0.332285i
$896$		0			0
$897$	2.69033	−	6.10862i	0.0898275	−	0.203961i
$898$		0			0
$899$	−26.4341	+	45.7852i	−0.881626	+	1.52702i
$900$		0			0
$901$	−9.56815	+	5.52417i	−0.318761	+	0.184037i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−0.338188	+	0.195253i	−0.0112417	+	0.00649042i
$906$		0			0
$907$	−3.39351	+	5.87774i	−0.112680	+	0.195167i	−0.916850	−	0.399232i	$-0.869277\pi$
$907$	−3.39351	+	5.87774i	−0.112680	+	0.195167i	0.804170	+	0.594399i	$0.202610\pi$
$908$		0			0
$909$	11.1598	+	12.1954i	0.370147	+	0.404494i
$910$		0			0
$911$			5.62793i			0.186462i	0.995645	+	0.0932308i	$0.0297194\pi$
$911$			5.62793i			0.186462i	−0.995645	+	0.0932308i	$0.970281\pi$
$912$		0			0
$913$	−11.9111	−	6.87686i	−0.394199	−	0.227591i
$914$		0			0
$915$	−1.02502	−	9.38884i	−0.0338863	−	0.310385i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−14.3617	−	24.8752i	−0.473748	−	0.820556i	0.525800	−	0.850608i	$-0.323766\pi$
$919$	−14.3617	−	24.8752i	−0.473748	−	0.820556i	−0.999548	+	0.0300524i	$0.990433\pi$
$920$		0			0
$921$	13.6099	−	9.97213i	0.448463	−	0.328593i
$922$		0			0
$923$	−8.37990			−0.275828
$924$		0			0
$925$	38.5254			1.26671
$926$		0			0
$927$	5.94245	+	26.8909i	0.195176	+	0.883214i
$928$		0			0
$929$	5.24240	+	9.08010i	0.171998	+	0.297909i	0.939118	−	0.343594i	$-0.111645\pi$
$929$	5.24240	+	9.08010i	0.171998	+	0.297909i	−0.767121	+	0.641503i	$0.778311\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	37.9969	−	4.14830i	1.24396	−	0.135809i
$934$		0			0
$935$	−4.87278	−	2.81330i	−0.159357	−	0.0920048i
$936$		0			0
$937$			45.3531i			1.48162i	0.671713	+	0.740811i	$0.265559\pi$
$937$			45.3531i			1.48162i	−0.671713	+	0.740811i	$0.734441\pi$
$938$		0			0
$939$	−24.7220	−	10.8880i	−0.806773	−	0.355315i
$940$		0			0
$941$	−14.7347	+	25.5213i	−0.480338	+	0.831969i	−0.999746	−	0.0225572i	$-0.992819\pi$
$941$	−14.7347	+	25.5213i	−0.480338	+	0.831969i	0.519408	+	0.854526i	$0.326153\pi$
$942$		0			0
$943$	12.9585	−	7.48159i	0.421987	−	0.243634i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	17.3729	−	10.0302i	0.564542	−	0.325939i	−0.190424	−	0.981702i	$-0.560986\pi$
$947$	17.3729	−	10.0302i	0.564542	−	0.325939i	0.754967	+	0.655763i	$0.227653\pi$
$948$		0			0
$949$	3.01425	−	5.22083i	0.0978465	−	0.169475i
$950$		0			0
$951$	−28.0316	−	12.3455i	−0.908986	−	0.400331i
$952$		0			0
$953$		−	4.51738i		−	0.146332i	−0.997320	−	0.0731661i	$-0.976690\pi$
$953$		−	4.51738i		−	0.146332i	0.997320	−	0.0731661i	$-0.0233103\pi$
$954$		0			0
$955$	−8.92146	−	5.15081i	−0.288692	−	0.166676i
$956$		0			0
$957$	−18.7821	+	2.05053i	−0.607138	+	0.0662842i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	11.7333	+	20.3227i	0.378495	+	0.655572i
$962$		0			0
$963$	3.10031	+	14.0296i	0.0999062	+	0.452098i
$964$		0			0
$965$	−8.75493			−0.281831
$966$		0			0
$967$	28.2943			0.909883			0.454942	−	0.890521i	$-0.349660\pi$
$967$	28.2943			0.909883			0.454942	+	0.890521i	$0.349660\pi$
$968$		0			0
$969$	−4.44396	+	3.25613i	−0.142760	+	0.104602i
$970$		0			0
$971$	−22.4658	−	38.9119i	−0.720962	−	1.24874i	−0.960615	−	0.277883i	$-0.910367\pi$
$971$	−22.4658	−	38.9119i	−0.720962	−	1.24874i	0.239653	−	0.970859i	$-0.422966\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	0.583559	+	5.34518i	0.0186888	+	0.171183i
$976$		0			0
$977$	−34.3384	−	19.8253i	−1.09858	−	0.634267i	−0.162734	−	0.986670i	$-0.552031\pi$
$977$	−34.3384	−	19.8253i	−1.09858	−	0.634267i	−0.935848	+	0.352403i	$0.885365\pi$
$978$		0			0
$979$		−	14.5573i		−	0.465254i
$980$		0			0
$981$	27.0906	+	29.6045i	0.864936	+	0.945198i
$982$		0			0
$983$	−0.546313	+	0.946242i	−0.0174247	+	0.0301804i	−0.874606	−	0.484834i	$-0.838880\pi$
$983$	−0.546313	+	0.946242i	−0.0174247	+	0.0301804i	0.857182	+	0.515014i	$0.172213\pi$
$984$		0			0
$985$	8.10460	−	4.67920i	0.258234	−	0.149092i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	28.4664	−	16.4351i	0.905179	−	0.522605i
$990$		0			0
$991$	24.3111	−	42.1081i	0.772269	−	1.33761i	−0.164048	−	0.986452i	$-0.552455\pi$
$991$	24.3111	−	42.1081i	0.772269	−	1.33761i	0.936317	−	0.351157i	$-0.114212\pi$
$992$		0			0
$993$	8.84164	−	20.0757i	0.280581	−	0.637083i
$994$		0			0
$995$			6.14075i			0.194675i
$996$		0			0
$997$	26.0510	+	15.0405i	0.825042	+	0.476338i	0.852152	−	0.523294i	$-0.175297\pi$
$997$	26.0510	+	15.0405i	0.825042	+	0.476338i	−0.0271100	+	0.999632i	$0.508630\pi$
$998$		0			0
$999$	31.5853	+	27.7565i	0.999315	+	0.878176i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1176.2.u.c.521.9		48
3.2	odd	2	inner	1176.2.u.c.521.1		48
7.2	even	3	inner	1176.2.u.c.1097.24		48
7.3	odd	6		1176.2.k.b.881.17	yes	24
7.4	even	3		1176.2.k.b.881.8	yes	24
7.5	odd	6	inner	1176.2.u.c.1097.1		48
7.6	odd	2	inner	1176.2.u.c.521.16		48
21.2	odd	6	inner	1176.2.u.c.1097.16		48
21.5	even	6	inner	1176.2.u.c.1097.9		48
21.11	odd	6		1176.2.k.b.881.18	yes	24
21.17	even	6		1176.2.k.b.881.7	✓	24
21.20	even	2	inner	1176.2.u.c.521.24		48
28.3	even	6		2352.2.k.j.881.8		24
28.11	odd	6		2352.2.k.j.881.17		24
84.11	even	6		2352.2.k.j.881.7		24
84.59	odd	6		2352.2.k.j.881.18		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1176.2.k.b.881.7	✓	24	21.17	even	6
1176.2.k.b.881.8	yes	24	7.4	even	3
1176.2.k.b.881.17	yes	24	7.3	odd	6
1176.2.k.b.881.18	yes	24	21.11	odd	6
1176.2.u.c.521.1		48	3.2	odd	2	inner
1176.2.u.c.521.9		48	1.1	even	1	trivial
1176.2.u.c.521.16		48	7.6	odd	2	inner
1176.2.u.c.521.24		48	21.20	even	2	inner
1176.2.u.c.1097.1		48	7.5	odd	6	inner
1176.2.u.c.1097.9		48	21.5	even	6	inner
1176.2.u.c.1097.16		48	21.2	odd	6	inner
1176.2.u.c.1097.24		48	7.2	even	3	inner
2352.2.k.j.881.7		24	84.11	even	6
2352.2.k.j.881.8		24	28.3	even	6
2352.2.k.j.881.17		24	28.11	odd	6
2352.2.k.j.881.18		24	84.59	odd	6

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:	\( N \)	\(=\)	\( 1176 = 2^{3} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1176.u (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.02370 - 1.39715i) q^{3} +(-0.244530 - 0.423539i) q^{5} +(-0.904057 + 2.86054i) q^{9} +(1.31874 + 0.761372i) q^{11} -0.652068i q^{13} +(-0.341421 + 0.775225i) q^{15} +(3.77769 - 6.54315i) q^{17} +(0.364587 - 0.210494i) q^{19} +(-5.11819 + 2.95499i) q^{23} +(2.38041 - 4.12299i) q^{25} +(4.92209 - 1.66524i) q^{27} -7.16356i q^{29} +(-6.39140 - 3.69008i) q^{31} +(-0.286244 - 2.62189i) q^{33} +(4.04609 + 7.00804i) q^{37} +(-0.911037 + 0.667525i) q^{39} -2.53185 q^{41} -5.56181 q^{43} +(1.43262 - 0.316585i) q^{45} +(-4.65721 - 8.06652i) q^{47} +(-13.0090 + 1.42025i) q^{51} +(-1.26640 - 0.731158i) q^{53} -0.744715i q^{55} +(-0.667322 - 0.293899i) q^{57} +(3.67844 - 6.37124i) q^{59} +(-9.65588 + 5.57482i) q^{61} +(-0.276176 + 0.159450i) q^{65} +(-7.31199 + 12.6647i) q^{67} +(9.36807 + 4.12584i) q^{69} -12.8513i q^{71} +(8.00657 + 4.62259i) q^{73} +(-8.19727 + 0.894936i) q^{75} +(-0.607201 - 1.05170i) q^{79} +(-7.36536 - 5.17218i) q^{81} -9.03219 q^{83} -3.69504 q^{85} +(-10.0086 + 7.33337i) q^{87} +(-4.77997 - 8.27914i) q^{89} +(1.38732 + 12.7073i) q^{93} +(-0.178305 - 0.102945i) q^{95} +4.95430i q^{97} +(-3.37015 + 3.08397i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 32 q^{15} - 8 q^{25} - 16 q^{37} + 64 q^{39} + 32 q^{43} - 48 q^{51} + 96 q^{57} - 16 q^{67} - 80 q^{81} - 128 q^{85} + 32 q^{93} - 112 q^{99}+O(q^{100}) \) 48 * q - 32 * q^15 - 8 * q^25 - 16 * q^37 + 64 * q^39 + 32 * q^43 - 48 * q^51 + 96 * q^57 - 16 * q^67 - 80 * q^81 - 128 * q^85 + 32 * q^93 - 112 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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