LMFDB - Embedded newform 1764.2.e.i.1079.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1764,2,Mod(1079,1764)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1764, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1764.1079");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1764.e (of order $2$, degree $1$, 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:	$14.0856109166$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + x^{12} - 10x^{10} + 4x^{8} - 40x^{6} + 16x^{4} + 256 $ x^16 + x^12 - 10x^10 + 4x^8 - 40x^6 + 16x^4 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{10} $
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1079.5
Root			$-0.658334 - 1.25164i$ of defining polynomial
Character	$\chi$	$=$	1764.1079
Dual form			1764.2.e.i.1079.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.658334 - 1.25164i) q^{2} +(-1.13319 + 1.64799i) q^{4} -2.08104i q^{5} +(2.80871 + 0.333415i) q^{8} +O(q^{10})$	\(q+(-0.658334 - 1.25164i) q^{2} +(-1.13319 + 1.64799i) q^{4} -2.08104i q^{5} +(2.80871 + 0.333415i) q^{8} +(-2.60471 + 1.37002i) q^{10} +4.26812 q^{11} -4.80655 q^{13} +(-1.43175 - 3.73498i) q^{16} +3.20515i q^{17} -2.81615i q^{19} +(3.42954 + 2.35822i) q^{20} +(-2.80985 - 5.34213i) q^{22} -4.66122 q^{23} +0.669258 q^{25} +(3.16432 + 6.01605i) q^{26} -3.87198i q^{29} -10.2861i q^{31} +(-3.73227 + 4.25090i) q^{32} +(4.01168 - 2.11006i) q^{34} +0.273782 q^{37} +(-3.52480 + 1.85397i) q^{38} +(0.693851 - 5.84504i) q^{40} -0.387186i q^{41} +0.907954i q^{43} +(-4.83659 + 7.03382i) q^{44} +(3.06864 + 5.83416i) q^{46} +7.85764 q^{47} +(-0.440596 - 0.837668i) q^{50} +(5.44674 - 7.92115i) q^{52} -11.7070i q^{53} -8.88214i q^{55} +(-4.84631 + 2.54906i) q^{58} -3.70504 q^{59} -8.02337 q^{61} +(-12.8745 + 6.77170i) q^{62} +(7.77767 + 1.87293i) q^{64} +10.0026i q^{65} +1.40397i q^{67} +(-5.28206 - 3.63205i) q^{68} +11.9134 q^{71} -12.2824 q^{73} +(-0.180240 - 0.342675i) q^{74} +(4.64099 + 3.19124i) q^{76} +0.826277i q^{79} +(-7.77266 + 2.97954i) q^{80} +(-0.484616 + 0.254898i) q^{82} -5.69055 q^{83} +6.67006 q^{85} +(1.13643 - 0.597737i) q^{86} +(11.9879 + 1.42305i) q^{88} -3.02258i q^{89} +(5.28206 - 7.68166i) q^{92} +(-5.17296 - 9.83492i) q^{94} -5.86053 q^{95} -15.2972 q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q + 8 q^{13} - 4 q^{16} - 16 q^{22} - 24 q^{25} - 8 q^{34} - 8 q^{37} + 52 q^{40} + 24 q^{46} + 52 q^{52} + 12 q^{58} + 16 q^{61} + 60 q^{64} + 8 q^{73} + 36 q^{76} - 68 q^{82} - 16 q^{85} - 44 q^{88} - 60 q^{94} - 88 q^{97}+O(q^{100}) $ 16 * q + 8 * q^13 - 4 * q^16 - 16 * q^22 - 24 * q^25 - 8 * q^34 - 8 * q^37 + 52 * q^40 + 24 * q^46 + 52 * q^52 + 12 * q^58 + 16 * q^61 + 60 * q^64 + 8 * q^73 + 36 * q^76 - 68 * q^82 - 16 * q^85 - 44 * q^88 - 60 * q^94 - 88 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times$.

$n$	$785$	$883$	$1081$
$\chi(n)$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−0.658334	−	1.25164i	−0.465513	−	0.885041i
$2$	−0.658334	−	1.25164i	−0.465513	−	0.885041i
$3$		0			0
$3$		0			0
$4$	−1.13319	+	1.64799i	−0.566596	+	0.823996i
$5$		−	2.08104i		−	0.930671i	−0.885134	−	0.465335i	$-0.845934\pi$
$5$		−	2.08104i		−	0.930671i	0.885134	−	0.465335i	$-0.154066\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	2.80871	+	0.333415i	0.993028	+	0.117880i
$9$		0			0
$10$	−2.60471	+	1.37002i	−0.823682	+	0.433239i
$11$	4.26812			1.28689			0.643443	−	0.765494i	$-0.277505\pi$
$11$	4.26812			1.28689			0.643443	+	0.765494i	$0.277505\pi$
$12$		0			0
$13$	−4.80655			−1.33310			−0.666548	−	0.745462i	$-0.732229\pi$
$13$	−4.80655			−1.33310			−0.666548	+	0.745462i	$0.732229\pi$
$14$		0			0
$15$		0			0
$16$	−1.43175	−	3.73498i	−0.357938	−	0.933745i
$17$			3.20515i			0.777363i	0.921372	+	0.388681i	$0.127069\pi$
$17$			3.20515i			0.777363i	−0.921372	+	0.388681i	$0.872931\pi$
$18$		0			0
$19$		−	2.81615i		−	0.646069i	−0.946387	−	0.323034i	$-0.895297\pi$
$19$		−	2.81615i		−	0.646069i	0.946387	−	0.323034i	$-0.104703\pi$
$20$	3.42954	+	2.35822i	0.766869	+	0.527314i
$21$		0			0
$22$	−2.80985	−	5.34213i	−0.599062	−	1.13895i
$23$	−4.66122			−0.971933			−0.485966	−	0.873978i	$-0.661532\pi$
$23$	−4.66122			−0.971933			−0.485966	+	0.873978i	$0.661532\pi$
$24$		0			0
$25$	0.669258			0.133852
$26$	3.16432	+	6.01605i	0.620573	+	1.17985i
$27$		0			0
$28$		0			0
$29$		−	3.87198i		−	0.719009i	−0.933143	−	0.359504i	$-0.882946\pi$
$29$		−	3.87198i		−	0.719009i	0.933143	−	0.359504i	$-0.117054\pi$
$30$		0			0
$31$		−	10.2861i		−	1.84744i	−0.383069	−	0.923720i	$-0.625133\pi$
$31$		−	10.2861i		−	1.84744i	0.383069	−	0.923720i	$-0.374867\pi$
$32$	−3.73227	+	4.25090i	−0.659778	+	0.751461i
$33$		0			0
$34$	4.01168	−	2.11006i	0.687998	−	0.361872i
$35$		0			0
$36$		0			0
$37$	0.273782			0.0450094			0.0225047	−	0.999747i	$-0.492836\pi$
$37$	0.273782			0.0450094			0.0225047	+	0.999747i	$0.492836\pi$
$38$	−3.52480	+	1.85397i	−0.571797	+	0.300753i
$39$		0			0
$40$	0.693851	−	5.84504i	0.109707	−	0.924182i
$41$		−	0.387186i		−	0.0604683i	−0.999543	−	0.0302341i	$-0.990375\pi$
$41$		−	0.387186i		−	0.0604683i	0.999543	−	0.0302341i	$-0.00962529\pi$
$42$		0			0
$43$			0.907954i			0.138462i	0.997601	+	0.0692308i	$0.0220545\pi$
$43$			0.907954i			0.138462i	−0.997601	+	0.0692308i	$0.977945\pi$
$44$	−4.83659	+	7.03382i	−0.729144	+	1.06039i
$45$		0			0
$46$	3.06864	+	5.83416i	0.452447	+	0.860200i
$47$	7.85764			1.14616			0.573078	−	0.819501i	$-0.305749\pi$
$47$	7.85764			1.14616			0.573078	+	0.819501i	$0.305749\pi$
$48$		0			0
$49$		0			0
$50$	−0.440596	−	0.837668i	−0.0623096	−	0.118464i
$51$		0			0
$52$	5.44674	−	7.92115i	0.755327	−	1.09847i
$53$		−	11.7070i		−	1.60807i	−0.594579	−	0.804037i	$-0.702681\pi$
$53$		−	11.7070i		−	1.60807i	0.594579	−	0.804037i	$-0.297319\pi$
$54$		0			0
$55$		−	8.88214i		−	1.19767i
$56$		0			0
$57$		0			0
$58$	−4.84631	+	2.54906i	−0.636352	+	0.334708i
$59$	−3.70504			−0.482355			−0.241177	−	0.970481i	$-0.577534\pi$
$59$	−3.70504			−0.482355			−0.241177	+	0.970481i	$0.577534\pi$
$60$		0			0
$61$	−8.02337			−1.02729			−0.513644	−	0.858004i	$-0.671705\pi$
$61$	−8.02337			−1.02729			−0.513644	+	0.858004i	$0.671705\pi$
$62$	−12.8745	+	6.77170i	−1.63506	+	0.860007i
$63$		0			0
$64$	7.77767	+	1.87293i	0.972209	+	0.234116i
$65$			10.0026i			1.24067i
$66$		0			0
$67$			1.40397i			0.171523i	0.996316	+	0.0857613i	$0.0273322\pi$
$67$			1.40397i			0.171523i	−0.996316	+	0.0857613i	$0.972668\pi$
$68$	−5.28206	−	3.63205i	−0.640544	−	0.440451i
$69$		0			0
$70$		0			0
$71$	11.9134			1.41386			0.706931	−	0.707282i	$-0.250079\pi$
$71$	11.9134			1.41386			0.706931	+	0.707282i	$0.250079\pi$
$72$		0			0
$73$	−12.2824			−1.43754			−0.718770	−	0.695248i	$-0.755295\pi$
$73$	−12.2824			−1.43754			−0.718770	+	0.695248i	$0.755295\pi$
$74$	−0.180240	−	0.342675i	−0.0209525	−	0.0398352i
$75$		0			0
$76$	4.64099	+	3.19124i	0.532358	+	0.366060i
$77$		0			0
$78$		0			0
$79$			0.826277i			0.0929634i	0.998919	+	0.0464817i	$0.0148009\pi$
$79$			0.826277i			0.0929634i	−0.998919	+	0.0464817i	$0.985199\pi$
$80$	−7.77266	+	2.97954i	−0.869009	+	0.333123i
$81$		0			0
$82$	−0.484616	+	0.254898i	−0.0535169	+	0.0281487i
$83$	−5.69055			−0.624619			−0.312310	−	0.949980i	$-0.601103\pi$
$83$	−5.69055			−0.624619			−0.312310	+	0.949980i	$0.601103\pi$
$84$		0			0
$85$	6.67006			0.723469
$86$	1.13643	−	0.597737i	0.122544	−	0.0644557i
$87$		0			0
$88$	11.9879	+	1.42305i	1.27791	+	0.151698i
$89$		−	3.02258i		−	0.320393i	−0.987085	−	0.160197i	$-0.948787\pi$
$89$		−	3.02258i		−	0.320393i	0.987085	−	0.160197i	$-0.0512128\pi$
$90$		0			0
$91$		0			0
$92$	5.28206	−	7.68166i	0.550693	−	0.800868i
$93$		0			0
$94$	−5.17296	−	9.83492i	−0.533550	−	1.01439i
$95$	−5.86053			−0.601277
$96$		0			0
$97$	−15.2972			−1.55319			−0.776595	−	0.630000i	$-0.783055\pi$
$97$	−15.2972			−1.55319			−0.776595	+	0.630000i	$0.783055\pi$
$98$		0			0
$99$		0			0
$100$	−0.758398	+	1.10293i	−0.0758398	+	0.110293i
$101$		−	0.387186i		−	0.0385264i	−0.999814	−	0.0192632i	$-0.993868\pi$
$101$		−	0.387186i		−	0.0385264i	0.999814	−	0.0192632i	$-0.00613205\pi$
$102$		0			0
$103$		−	13.5359i		−	1.33374i	−0.745176	−	0.666868i	$-0.767634\pi$
$103$		−	13.5359i		−	1.33374i	0.745176	−	0.666868i	$-0.232366\pi$
$104$	−13.5002	−	1.60257i	−1.32380	−	0.157145i
$105$		0			0
$106$	−14.6529	+	7.70709i	−1.42321	+	0.748579i
$107$	−10.8841			−1.05220			−0.526102	−	0.850421i	$-0.676347\pi$
$107$	−10.8841			−1.05220			−0.526102	+	0.850421i	$0.676347\pi$
$108$		0			0
$109$	−18.7160			−1.79267			−0.896334	−	0.443380i	$-0.853779\pi$
$109$	−18.7160			−1.79267			−0.896334	+	0.443380i	$0.853779\pi$
$110$	−11.1172	+	5.84742i	−1.05998	+	0.557529i
$111$		0			0
$112$		0			0
$113$			13.1377i			1.23589i	0.786221	+	0.617945i	$0.212035\pi$
$113$			13.1377i			1.23589i	−0.786221	+	0.617945i	$0.787965\pi$
$114$		0			0
$115$			9.70021i			0.904549i
$116$	6.38099	+	4.38769i	0.592460	+	0.407387i
$117$		0			0
$118$	2.43915	+	4.63736i	0.224542	+	0.426904i
$119$		0			0
$120$		0			0
$121$	7.21682			0.656075
$122$	5.28206	+	10.0423i	0.478215	+	0.909191i
$123$		0			0
$124$	16.9514	+	11.6561i	1.52228	+	1.04675i
$125$		−	11.7980i		−	1.05524i
$126$		0			0
$127$			4.80602i			0.426465i	0.977001	+	0.213233i	$0.0683992\pi$
$127$			4.80602i			0.426465i	−0.977001	+	0.213233i	$0.931601\pi$
$128$	−2.77608	−	10.9678i	−0.245373	−	0.969429i
$129$		0			0
$130$	12.5197	−	6.58508i	1.09805	−	0.577550i
$131$	−14.7167			−1.28581			−0.642903	−	0.765947i	$-0.722270\pi$
$131$	−14.7167			−1.28581			−0.642903	+	0.765947i	$0.722270\pi$
$132$		0			0
$133$		0			0
$134$	1.75726	−	0.924284i	0.151805	−	0.0798459i
$135$		0			0
$136$	−1.06864	+	9.00233i	−0.0916355	+	0.771943i
$137$			3.96793i			0.339003i	0.985530	+	0.169502i	$0.0542158\pi$
$137$			3.96793i			0.339003i	−0.985530	+	0.169502i	$0.945784\pi$
$138$		0			0
$139$		−	19.1682i		−	1.62583i	−0.582383	−	0.812915i	$-0.697879\pi$
$139$		−	19.1682i		−	1.62583i	0.582383	−	0.812915i	$-0.302121\pi$
$140$		0			0
$141$		0			0
$142$	−7.84301	−	14.9113i	−0.658171	−	1.25133i
$143$	−20.5149			−1.71554
$144$		0			0
$145$	−8.05776			−0.669160
$146$	8.08590	+	15.3731i	0.669194	+	1.27228i
$147$		0			0
$148$	−0.310247	+	0.451190i	−0.0255022	+	0.0370876i
$149$			5.65685i			0.463428i	0.972784	+	0.231714i	$0.0744333\pi$
$149$			5.65685i			0.463428i	−0.972784	+	0.231714i	$0.925567\pi$
$150$		0			0
$151$		−	9.67845i		−	0.787621i	−0.919192	−	0.393811i	$-0.871157\pi$
$151$		−	9.67845i		−	0.787621i	0.919192	−	0.393811i	$-0.128843\pi$
$152$	0.938946	−	7.90973i	0.0761586	−	0.641564i
$153$		0			0
$154$		0			0
$155$	−21.4058			−1.71936
$156$		0			0
$157$	5.88608			0.469760			0.234880	−	0.972024i	$-0.424530\pi$
$157$	5.88608			0.469760			0.234880	+	0.972024i	$0.424530\pi$
$158$	1.03420	−	0.543967i	0.0822765	−	0.0432757i
$159$		0			0
$160$	8.84631	+	7.76701i	0.699363	+	0.614036i
$161$		0			0
$162$		0			0
$163$		−	9.70021i		−	0.759779i	−0.925032	−	0.379890i	$-0.875962\pi$
$163$		−	9.70021i		−	0.759779i	0.925032	−	0.379890i	$-0.124038\pi$
$164$	0.638079	+	0.438756i	0.0498256	+	0.0342611i
$165$		0			0
$166$	3.74629	+	7.12251i	0.290768	+	0.552814i
$167$	18.4218			1.42552			0.712759	−	0.701409i	$-0.247445\pi$
$167$	18.4218			1.42552			0.712759	+	0.701409i	$0.247445\pi$
$168$		0			0
$169$	10.1029			0.777146
$170$	−4.39113	−	8.34849i	−0.336784	−	0.640300i
$171$		0			0
$172$	−1.49630	−	1.02889i	−0.114092	−	0.0784518i
$173$		−	7.08153i		−	0.538399i	−0.963084	−	0.269199i	$-0.913241\pi$
$173$		−	7.08153i		−	0.538399i	0.963084	−	0.269199i	$-0.0867591\pi$
$174$		0			0
$175$		0			0
$176$	−6.11089	−	15.9413i	−0.460626	−	1.20162i
$177$		0			0
$178$	−3.78318	+	1.98987i	−0.283561	+	0.149147i
$179$	21.1204			1.57861			0.789305	−	0.614002i	$-0.210441\pi$
$179$	21.1204			1.57861			0.789305	+	0.614002i	$0.210441\pi$
$180$		0			0
$181$	−6.13809			−0.456240			−0.228120	−	0.973633i	$-0.573258\pi$
$181$	−6.13809			−0.456240			−0.228120	+	0.973633i	$0.573258\pi$
$182$		0			0
$183$		0			0
$184$	−13.0920	−	1.55412i	−0.965156	−	0.114571i
$185$		−	0.569752i		−	0.0418890i
$186$		0			0
$187$			13.6800i			1.00038i
$188$	−8.90422	+	12.9493i	−0.649407	+	0.944427i
$189$		0			0
$190$	3.85819	+	7.33525i	0.279902	+	0.532155i
$191$	11.7979			0.853667			0.426833	−	0.904330i	$-0.359629\pi$
$191$	11.7979			0.853667			0.426833	+	0.904330i	$0.359629\pi$
$192$		0			0
$193$	−15.8073			−1.13784			−0.568919	−	0.822394i	$-0.692638\pi$
$193$	−15.8073			−1.13784			−0.568919	+	0.822394i	$0.692638\pi$
$194$	10.0706	+	19.1465i	0.723030	+	1.37464i
$195$		0			0
$196$		0			0
$197$		−	2.17812i		−	0.155185i	−0.996985	−	0.0775924i	$-0.975277\pi$
$197$		−	2.17812i		−	0.155185i	0.996985	−	0.0775924i	$-0.0247233\pi$
$198$		0			0
$199$		−	5.48009i		−	0.388473i	−0.980955	−	0.194237i	$-0.937777\pi$
$199$		−	5.48009i		−	0.388473i	0.980955	−	0.194237i	$-0.0622230\pi$
$200$	1.87975	+	0.223141i	0.132918	+	0.0157784i
$201$		0			0
$202$	−0.484616	+	0.254898i	−0.0340975	+	0.0179345i
$203$		0			0
$204$		0			0
$205$	−0.805750			−0.0562760
$206$	−16.9421	+	8.91118i	−1.18041	+	0.620871i
$207$		0			0
$208$	6.88179	+	17.9524i	0.477167	+	1.24477i
$209$		−	12.0196i		−	0.831416i
$210$		0			0
$211$			8.80046i			0.605849i	0.953015	+	0.302924i	$0.0979629\pi$
$211$			8.80046i			0.605849i	−0.953015	+	0.302924i	$0.902037\pi$
$212$	19.2930	+	13.2662i	1.32505	+	0.911128i
$213$		0			0
$214$	7.16537	+	13.6229i	0.489815	+	0.931244i
$215$	1.88949			0.128862
$216$		0			0
$217$		0			0
$218$	12.3214	+	23.4256i	0.834510	+	1.58658i
$219$		0			0
$220$	14.6377	+	10.0652i	0.986873	+	0.678593i
$221$		−	15.4057i		−	1.03630i
$222$		0			0
$223$			21.1499i			1.41630i	0.706060	+	0.708152i	$0.250471\pi$
$223$			21.1499i			1.41630i	−0.706060	+	0.708152i	$0.749529\pi$
$224$		0			0
$225$		0			0
$226$	16.4436	−	8.64900i	1.09381	−	0.575323i
$227$	28.0950			1.86473			0.932364	−	0.361522i	$-0.117743\pi$
$227$	28.0950			1.86473			0.932364	+	0.361522i	$0.117743\pi$
$228$		0			0
$229$	−13.6357			−0.901070			−0.450535	−	0.892759i	$-0.648767\pi$
$229$	−13.6357			−0.901070			−0.450535	+	0.892759i	$0.648767\pi$
$230$	12.1411	−	6.38598i	0.800563	−	0.421079i
$231$		0			0
$232$	1.29098	−	10.8753i	0.0847567	−	0.713996i
$233$		−	4.31273i		−	0.282536i	−0.989971	−	0.141268i	$-0.954882\pi$
$233$		−	4.31273i		−	0.282536i	0.989971	−	0.141268i	$-0.0451180\pi$
$234$		0			0
$235$		−	16.3521i		−	1.06669i
$236$	4.19851	−	6.10587i	0.273300	−	0.397458i
$237$		0			0
$238$		0			0
$239$	−7.22142			−0.467115			−0.233558	−	0.972343i	$-0.575037\pi$
$239$	−7.22142			−0.467115			−0.233558	+	0.972343i	$0.575037\pi$
$240$		0			0
$241$	4.73479			0.304995			0.152497	−	0.988304i	$-0.451268\pi$
$241$	4.73479			0.304995			0.152497	+	0.988304i	$0.451268\pi$
$242$	−4.75108	−	9.03284i	−0.305411	−	0.580653i
$243$		0			0
$244$	9.09201	−	13.2224i	0.582057	−	0.846480i
$245$		0			0
$246$		0			0
$247$			13.5359i			0.861272i
$248$	3.42954	−	28.8907i	0.217776	−	1.83456i
$249$		0			0
$250$	−14.7668	+	7.76701i	−0.933933	+	0.491229i
$251$	−2.26312			−0.142847			−0.0714233	−	0.997446i	$-0.522754\pi$
$251$	−2.26312			−0.142847			−0.0714233	+	0.997446i	$0.522754\pi$
$252$		0			0
$253$	−19.8947			−1.25077
$254$	6.01539	−	3.16397i	0.377439	−	0.198525i
$255$		0			0
$256$	−11.9002	+	10.6951i	−0.743760	+	0.668447i
$257$			18.0411i			1.12537i	0.826670	+	0.562687i	$0.190232\pi$
$257$			18.0411i			1.12537i	−0.826670	+	0.562687i	$0.809768\pi$
$258$		0			0
$259$		0			0
$260$	−16.4843	−	11.3349i	−1.02231	−	0.702961i
$261$		0			0
$262$	9.68853	+	18.4200i	0.598559	+	1.13799i
$263$	−0.670707			−0.0413576			−0.0206788	−	0.999786i	$-0.506583\pi$
$263$	−0.670707			−0.0413576			−0.0206788	+	0.999786i	$0.506583\pi$
$264$		0			0
$265$	−24.3627			−1.49659
$266$		0			0
$267$		0			0
$268$	−2.31374	−	1.59097i	−0.141334	−	0.0971840i
$269$		−	9.49691i		−	0.579037i	−0.957172	−	0.289518i	$-0.906505\pi$
$269$		−	9.49691i		−	0.579037i	0.957172	−	0.289518i	$-0.0934952\pi$
$270$		0			0
$271$			17.1702i			1.04301i	0.853247	+	0.521507i	$0.174630\pi$
$271$			17.1702i			1.04301i	−0.853247	+	0.521507i	$0.825370\pi$
$272$	11.9712	−	4.58899i	0.725859	−	0.278248i
$273$		0			0
$274$	4.96641	−	2.61223i	0.300032	−	0.157810i
$275$	2.85647			0.172252
$276$		0			0
$277$	9.84871			0.591752			0.295876	−	0.955226i	$-0.404389\pi$
$277$	9.84871			0.591752			0.295876	+	0.955226i	$0.404389\pi$
$278$	−23.9917	+	12.6191i	−1.43893	+	0.756844i
$279$		0			0
$280$		0			0
$281$		−	7.25476i		−	0.432783i	−0.976307	−	0.216391i	$-0.930571\pi$
$281$		−	7.25476i		−	0.432783i	0.976307	−	0.216391i	$-0.0694287\pi$
$282$		0			0
$283$			2.81615i			0.167403i	0.996491	+	0.0837013i	$0.0266742\pi$
$283$			2.81615i			0.167403i	−0.996491	+	0.0837013i	$0.973326\pi$
$284$	−13.5002	+	19.6332i	−0.801089	+	1.16502i
$285$		0			0
$286$	13.5057	+	25.6772i	0.798607	+	1.51833i
$287$		0			0
$288$		0			0
$289$	6.72702			0.395707
$290$	5.30470	+	10.0854i	0.311503	+	0.592234i
$291$		0			0
$292$	13.9183	−	20.2412i	0.814505	−	1.18453i
$293$		−	6.86151i		−	0.400854i	−0.979709	−	0.200427i	$-0.935767\pi$
$293$		−	6.86151i		−	0.400854i	0.979709	−	0.200427i	$-0.0642329\pi$
$294$		0			0
$295$			7.71034i			0.448913i
$296$	0.768972	+	0.0912829i	0.0446956	+	0.00530571i
$297$		0			0
$298$	7.08033	−	3.72410i	0.410152	−	0.215731i
$299$	22.4044			1.29568
$300$		0			0
$301$		0			0
$302$	−12.1139	+	6.37166i	−0.697077	+	0.366648i
$303$		0			0
$304$	−10.5183	+	4.03203i	−0.603263	+	0.231253i
$305$			16.6970i			0.956066i
$306$		0			0
$307$			8.29624i			0.473491i	0.971572	+	0.236746i	$0.0760808\pi$
$307$			8.29624i			0.473491i	−0.971572	+	0.236746i	$0.923919\pi$
$308$		0			0
$309$		0			0
$310$	14.0922	+	26.7923i	0.800383	+	1.52170i
$311$	17.3609			0.984444			0.492222	−	0.870470i	$-0.336185\pi$
$311$	17.3609			0.984444			0.492222	+	0.870470i	$0.336185\pi$
$312$		0			0
$313$	7.95161			0.449452			0.224726	−	0.974422i	$-0.427851\pi$
$313$	7.95161			0.449452			0.224726	+	0.974422i	$0.427851\pi$
$314$	−3.87501	−	7.36724i	−0.218679	−	0.415757i
$315$		0			0
$316$	−1.36170	−	0.936330i	−0.0766015	−	0.0526727i
$317$		−	2.18306i		−	0.122613i	−0.998119	−	0.0613063i	$-0.980473\pi$
$317$		−	2.18306i		−	0.122613i	0.998119	−	0.0613063i	$-0.0195266\pi$
$318$		0			0
$319$		−	16.5261i		−	0.925282i
$320$	3.89765	−	16.1857i	0.217885	−	0.904806i
$321$		0			0
$322$		0			0
$323$	9.02618			0.502230
$324$		0			0
$325$	−3.21682			−0.178437
$326$	−12.1411	+	6.38598i	−0.672436	+	0.353687i
$327$		0			0
$328$	0.129094	−	1.08749i	0.00712800	−	0.0600467i
$329$		0			0
$330$		0			0
$331$			13.4760i			0.740710i	0.928890	+	0.370355i	$0.120764\pi$
$331$			13.4760i			0.740710i	−0.928890	+	0.370355i	$0.879236\pi$
$332$	6.44849	−	9.37798i	0.353907	−	0.514684i
$333$		0			0
$334$	−12.1277	−	23.0574i	−0.663597	−	1.26164i
$335$	2.92173			0.159631
$336$		0			0
$337$	17.4188			0.948865			0.474432	−	0.880292i	$-0.342653\pi$
$337$	17.4188			0.948865			0.474432	+	0.880292i	$0.342653\pi$
$338$	−6.65109	−	12.6452i	−0.361771	−	0.687806i
$339$		0			0
$340$	−7.55845	+	10.9922i	−0.409915	+	0.596136i
$341$		−	43.9023i		−	2.37744i
$342$		0			0
$343$		0			0
$344$	−0.302725	+	2.55018i	−0.0163219	+	0.137496i
$345$		0			0
$346$	−8.86351	+	4.66202i	−0.476505	+	0.250632i
$347$	−2.20865			−0.118567			−0.0592833	−	0.998241i	$-0.518882\pi$
$347$	−2.20865			−0.118567			−0.0592833	+	0.998241i	$0.518882\pi$
$348$		0			0
$349$	31.3253			1.67681			0.838403	−	0.545051i	$-0.183490\pi$
$349$	31.3253			1.67681			0.838403	+	0.545051i	$0.183490\pi$
$350$		0			0
$351$		0			0
$352$	−15.9298	+	18.1434i	−0.849059	+	0.967044i
$353$		−	6.90062i		−	0.367283i	−0.982993	−	0.183642i	$-0.941211\pi$
$353$		−	6.90062i		−	0.367283i	0.982993	−	0.183642i	$-0.0587886\pi$
$354$		0			0
$355$		−	24.7923i		−	1.31584i
$356$	4.98119	+	3.42517i	0.264003	+	0.181533i
$357$		0			0
$358$	−13.9043	−	26.4350i	−0.734863	−	1.39713i
$359$	−13.1472			−0.693883			−0.346941	−	0.937887i	$-0.612780\pi$
$359$	−13.1472			−0.693883			−0.346941	+	0.937887i	$0.612780\pi$
$360$		0			0
$361$	11.0693			0.582595
$362$	4.04091	+	7.68266i	0.212386	+	0.403792i
$363$		0			0
$364$		0			0
$365$			25.5601i			1.33788i
$366$		0			0
$367$			11.3057i			0.590153i	0.955474	+	0.295076i	$0.0953451\pi$
$367$			11.3057i			0.590153i	−0.955474	+	0.295076i	$0.904655\pi$
$368$	6.67373	+	17.4096i	0.347892	+	0.907537i
$369$		0			0
$370$	−0.713122	+	0.375087i	−0.0370735	+	0.0194998i
$371$		0			0
$372$		0			0
$373$	14.1536			0.732848			0.366424	−	0.930448i	$-0.380582\pi$
$373$	14.1536			0.732848			0.366424	+	0.930448i	$0.380582\pi$
$374$	17.1223	−	9.00598i	0.885375	−	0.465688i
$375$		0			0
$376$	22.0698	+	2.61986i	1.13816	+	0.135109i
$377$			18.6109i			0.958508i
$378$		0			0
$379$		−	16.2405i		−	0.834216i	−0.908857	−	0.417108i	$-0.863044\pi$
$379$		−	16.2405i		−	0.834216i	0.908857	−	0.417108i	$-0.136956\pi$
$380$	6.64110	−	9.65810i	0.340681	−	0.495450i
$381$		0			0
$382$	−7.76697	−	14.7667i	−0.397393	−	0.755530i
$383$	−2.71808			−0.138887			−0.0694436	−	0.997586i	$-0.522122\pi$
$383$	−2.71808			−0.138887			−0.0694436	+	0.997586i	$0.522122\pi$
$384$		0			0
$385$		0			0
$386$	10.4065	+	19.7851i	0.529678	+	1.00703i
$387$		0			0
$388$	17.3346	−	25.2096i	0.880031	−	1.27982i
$389$		−	20.0952i		−	1.01886i	−0.860511	−	0.509432i	$-0.829855\pi$
$389$		−	20.0952i		−	1.01886i	0.860511	−	0.509432i	$-0.170145\pi$
$390$		0			0
$391$		−	14.9399i		−	0.755544i
$392$		0			0
$393$		0			0
$394$	−2.72622	+	1.43393i	−0.137345	+	0.0722405i
$395$	1.71952			0.0865184
$396$		0			0
$397$	15.8635			0.796167			0.398083	−	0.917349i	$-0.369675\pi$
$397$	15.8635			0.796167			0.398083	+	0.917349i	$0.369675\pi$
$398$	−6.85909	+	3.60773i	−0.343815	+	0.180839i
$399$		0			0
$400$	−0.958213	−	2.49967i	−0.0479107	−	0.124983i
$401$		−	32.0023i		−	1.59812i	−0.601251	−	0.799060i	$-0.705331\pi$
$401$		−	32.0023i		−	1.59812i	0.601251	−	0.799060i	$-0.294669\pi$
$402$		0			0
$403$			49.4407i			2.46282i
$404$	0.638079	+	0.438756i	0.0317456	+	0.0218289i
$405$		0			0
$406$		0			0
$407$	1.16853			0.0579220
$408$		0			0
$409$	4.84094			0.239369			0.119684	−	0.992812i	$-0.461812\pi$
$409$	4.84094			0.239369			0.119684	+	0.992812i	$0.461812\pi$
$410$	0.530453	+	1.00851i	0.0261972	+	0.0498066i
$411$		0			0
$412$	22.3071	+	15.3388i	1.09899	+	0.755690i
$413$		0			0
$414$		0			0
$415$			11.8423i			0.581315i
$416$	17.9393	−	20.4322i	0.879548	−	1.00177i
$417$		0			0
$418$	−15.0442	+	7.91295i	−0.735838	+	0.387035i
$419$	9.95079			0.486128			0.243064	−	0.970010i	$-0.421848\pi$
$419$	9.95079			0.486128			0.243064	+	0.970010i	$0.421848\pi$
$420$		0			0
$421$	−2.27378			−0.110817			−0.0554087	−	0.998464i	$-0.517646\pi$
$421$	−2.27378			−0.110817			−0.0554087	+	0.998464i	$0.517646\pi$
$422$	11.0150	−	5.79365i	0.536201	−	0.282030i
$423$		0			0
$424$	3.90327	−	32.8814i	0.189560	−	1.59686i
$425$			2.14507i			0.104051i
$426$		0			0
$427$		0			0
$428$	12.3338	−	17.9369i	0.596175	−	0.867012i
$429$		0			0
$430$	−1.24392	−	2.36496i	−0.0599870	−	0.114048i
$431$	−28.5304			−1.37426			−0.687131	−	0.726533i	$-0.741130\pi$
$431$	−28.5304			−1.37426			−0.687131	+	0.726533i	$0.741130\pi$
$432$		0			0
$433$	−7.86191			−0.377819			−0.188910	−	0.981994i	$-0.560495\pi$
$433$	−7.86191			−0.377819			−0.188910	+	0.981994i	$0.560495\pi$
$434$		0			0
$435$		0			0
$436$	21.2088	−	30.8438i	1.01572	−	1.47715i
$437$			13.1267i			0.627935i
$438$		0			0
$439$		−	10.6705i		−	0.509275i	−0.967037	−	0.254637i	$-0.918044\pi$
$439$		−	10.6705i		−	0.509275i	0.967037	−	0.254637i	$-0.0819561\pi$
$440$	2.96144	−	24.9473i	0.141181	−	1.18932i
$441$		0			0
$442$	−19.2824	+	10.1421i	−0.917168	+	0.482411i
$443$	37.9805			1.80451			0.902254	−	0.431206i	$-0.141912\pi$
$443$	37.9805			1.80451			0.902254	+	0.431206i	$0.141912\pi$
$444$		0			0
$445$	−6.29013			−0.298181
$446$	26.4720	−	13.9237i	1.25349	−	0.659307i
$447$		0			0
$448$		0			0
$449$		−	24.0046i		−	1.13285i	−0.824114	−	0.566423i	$-0.808327\pi$
$449$		−	24.0046i		−	1.13285i	0.824114	−	0.566423i	$-0.191673\pi$
$450$		0			0
$451$		−	1.65255i		−	0.0778157i
$452$	−21.6508	−	14.8875i	−1.01837	−	0.700250i
$453$		0			0
$454$	−18.4959	−	35.1647i	−0.868054	−	1.65036i
$455$		0			0
$456$		0			0
$457$	15.0451			0.703782			0.351891	−	0.936041i	$-0.385539\pi$
$457$	15.0451			0.703782			0.351891	+	0.936041i	$0.385539\pi$
$458$	8.97683	+	17.0669i	0.419460	+	0.797484i
$459$		0			0
$460$	−15.9859	−	10.9922i	−0.745345	−	0.512514i
$461$		−	30.3714i		−	1.41454i	−0.706946	−	0.707268i	$-0.749927\pi$
$461$		−	30.3714i		−	1.41454i	0.706946	−	0.707268i	$-0.250073\pi$
$462$		0			0
$463$		−	23.7810i		−	1.10519i	−0.833448	−	0.552597i	$-0.813637\pi$
$463$		−	23.7810i		−	1.10519i	0.833448	−	0.552597i	$-0.186363\pi$
$464$	−14.4618	+	5.54372i	−0.671371	+	0.257361i
$465$		0			0
$466$	−5.39798	+	2.83922i	−0.250056	+	0.131524i
$467$	4.70359			0.217656			0.108828	−	0.994061i	$-0.465290\pi$
$467$	4.70359			0.217656			0.108828	+	0.994061i	$0.465290\pi$
$468$		0			0
$469$		0			0
$470$	−20.4669	+	10.7651i	−0.944067	+	0.496559i
$471$		0			0
$472$	−10.4064	−	1.23531i	−0.478992	−	0.0568599i
$473$			3.87525i			0.178184i
$474$		0			0
$475$		−	1.88473i		−	0.0864774i
$476$		0			0
$477$		0			0
$478$	4.75411	+	9.03860i	0.217448	+	0.413416i
$479$	4.09026			0.186889			0.0934444	−	0.995625i	$-0.470212\pi$
$479$	4.09026			0.186889			0.0934444	+	0.995625i	$0.470212\pi$
$480$		0			0
$481$	−1.31594			−0.0600019
$482$	−3.11708	−	5.92624i	−0.141979	−	0.269933i
$483$		0			0
$484$	−8.17804	+	11.8933i	−0.371729	+	0.540603i
$485$			31.8340i			1.44551i
$486$		0			0
$487$			5.60234i			0.253866i	0.991911	+	0.126933i	$0.0405133\pi$
$487$			5.60234i			0.253866i	−0.991911	+	0.126933i	$0.959487\pi$
$488$	−22.5353	−	2.67511i	−1.02012	−	0.121097i
$489$		0			0
$490$		0			0
$491$	10.3094			0.465257			0.232629	−	0.972566i	$-0.425267\pi$
$491$	10.3094			0.465257			0.232629	+	0.972566i	$0.425267\pi$
$492$		0			0
$493$	12.4103			0.558931
$494$	16.9421	−	8.91118i	0.762261	−	0.400933i
$495$		0			0
$496$	−38.4184	+	14.7272i	−1.72504	+	0.661270i
$497$		0			0
$498$		0			0
$499$			7.09619i			0.317669i	0.987305	+	0.158835i	$0.0507736\pi$
$499$			7.09619i			0.317669i	−0.987305	+	0.158835i	$0.949226\pi$
$500$	19.4430	+	13.3694i	0.869516	+	0.597896i
$501$		0			0
$502$	1.48989	+	2.83260i	0.0664969	+	0.126425i
$503$	−6.79674			−0.303052			−0.151526	−	0.988453i	$-0.548419\pi$
$503$	−6.79674			−0.303052			−0.151526	+	0.988453i	$0.548419\pi$
$504$		0			0
$505$	−0.805750			−0.0358554
$506$	13.0973	+	24.9009i	0.582248	+	1.10698i
$507$		0			0
$508$	−7.92028	−	5.44614i	−0.351406	−	0.241633i
$509$			19.4730i			0.863124i	0.902083	+	0.431562i	$0.142037\pi$
$509$			19.4730i			0.863124i	−0.902083	+	0.431562i	$0.857963\pi$
$510$		0			0
$511$		0			0
$512$	21.2207	+	7.85370i	0.937833	+	0.347088i
$513$		0			0
$514$	22.5809	−	11.8771i	0.996002	−	0.523876i
$515$	−28.1689			−1.24127
$516$		0			0
$517$	33.5373			1.47497
$518$		0			0
$519$		0			0
$520$	−3.33503	+	28.0945i	−0.146251	+	1.23202i
$521$		−	34.4540i		−	1.50946i	−0.656036	−	0.754729i	$-0.727768\pi$
$521$		−	34.4540i		−	1.50946i	0.656036	−	0.754729i	$-0.272232\pi$
$522$		0			0
$523$		−	21.5836i		−	0.943785i	−0.881656	−	0.471893i	$-0.843571\pi$
$523$		−	21.5836i		−	0.943785i	0.881656	−	0.471893i	$-0.156429\pi$
$524$	16.6769	−	24.2530i	0.728533	−	1.05950i
$525$		0			0
$526$	0.441549	+	0.839482i	0.0192525	+	0.0366031i
$527$	32.9685			1.43613
$528$		0			0
$529$	−1.27298			−0.0553471
$530$	16.0388	+	30.4932i	0.696681	+	1.32454i
$531$		0			0
$532$		0			0
$533$			1.86103i			0.0806100i
$534$		0			0
$535$			22.6503i			0.979256i
$536$	−0.468106	+	3.94335i	−0.0202191	+	0.170327i
$537$		0			0
$538$	−11.8867	+	6.25214i	−0.512472	+	0.269549i
$539$		0			0
$540$		0			0
$541$	−42.3525			−1.82087			−0.910437	−	0.413647i	$-0.864255\pi$
$541$	−42.3525			−1.82087			−0.910437	+	0.413647i	$0.864255\pi$
$542$	21.4908	−	11.3037i	0.923110	−	0.485536i
$543$		0			0
$544$	−13.6248	−	11.9625i	−0.584158	−	0.512887i
$545$			38.9488i			1.66838i
$546$		0			0
$547$		−	36.9243i		−	1.57877i	−0.613899	−	0.789385i	$-0.710400\pi$
$547$		−	36.9243i		−	1.57877i	0.613899	−	0.789385i	$-0.289600\pi$
$548$	−6.53912	−	4.49642i	−0.279337	−	0.192078i
$549$		0			0
$550$	−1.88051	−	3.57527i	−0.0801854	−	0.152450i
$551$	−10.9041			−0.464529
$552$		0			0
$553$		0			0
$554$	−6.48375	−	12.3270i	−0.275468	−	0.523725i
$555$		0			0
$556$	31.5891	+	21.7213i	1.33968	+	0.921188i
$557$			15.2199i			0.644886i	0.946589	+	0.322443i	$0.104504\pi$
$557$			15.2199i			0.644886i	−0.946589	+	0.322443i	$0.895496\pi$
$558$		0			0
$559$		−	4.36412i		−	0.184583i
$560$		0			0
$561$		0			0
$562$	−9.08033	+	4.77606i	−0.383031	+	0.201466i
$563$	−17.4348			−0.734789			−0.367395	−	0.930065i	$-0.619750\pi$
$563$	−17.4348			−0.734789			−0.367395	+	0.930065i	$0.619750\pi$
$564$		0			0
$565$	27.3401			1.15021
$566$	3.52480	−	1.85397i	0.148158	−	0.0779281i
$567$		0			0
$568$	33.4613	+	3.97211i	1.40400	+	0.166666i
$569$		−	20.8271i		−	0.873119i	−0.899675	−	0.436560i	$-0.856197\pi$
$569$		−	20.8271i		−	0.873119i	0.899675	−	0.436560i	$-0.143803\pi$
$570$		0			0
$571$		−	20.5640i		−	0.860577i	−0.902691	−	0.430289i	$-0.858412\pi$
$571$		−	20.5640i		−	0.860577i	0.902691	−	0.430289i	$-0.141588\pi$
$572$	23.2473	−	33.8084i	0.972019	−	1.41360i
$573$		0			0
$574$		0			0
$575$	−3.11956			−0.130095
$576$		0			0
$577$	3.16066			0.131580			0.0657900	−	0.997833i	$-0.479043\pi$
$577$	3.16066			0.131580			0.0657900	+	0.997833i	$0.479043\pi$
$578$	−4.42863	−	8.41978i	−0.184207	−	0.350217i
$579$		0			0
$580$	9.13098	−	13.2791i	0.379143	−	0.551385i
$581$		0			0
$582$		0			0
$583$		−	49.9667i		−	2.06941i
$584$	−34.4975	−	4.09512i	−1.42752	−	0.169457i
$585$		0			0
$586$	−8.58813	+	4.51717i	−0.354772	+	0.186603i
$587$	22.1152			0.912792			0.456396	−	0.889777i	$-0.349140\pi$
$587$	22.1152			0.912792			0.456396	+	0.889777i	$0.349140\pi$
$588$		0			0
$589$	−28.9672			−1.19357
$590$	9.65055	−	5.07598i	0.397307	−	0.208975i
$591$		0			0
$592$	−0.391988	−	1.02257i	−0.0161106	−	0.0420273i
$593$			41.6167i			1.70899i	0.519459	+	0.854496i	$0.326134\pi$
$593$			41.6167i			1.70899i	−0.519459	+	0.854496i	$0.673866\pi$
$594$		0			0
$595$		0			0
$596$	−9.32245	−	6.41030i	−0.381862	−	0.262576i
$597$		0			0
$598$	−14.7496	−	28.0422i	−0.603155	−	1.14673i
$599$	38.3312			1.56617			0.783086	−	0.621914i	$-0.213645\pi$
$599$	38.3312			1.56617			0.783086	+	0.621914i	$0.213645\pi$
$600$		0			0
$601$	29.3369			1.19668			0.598338	−	0.801244i	$-0.295828\pi$
$601$	29.3369			1.19668			0.598338	+	0.801244i	$0.295828\pi$
$602$		0			0
$603$		0			0
$604$	15.9500	+	10.9675i	0.648997	+	0.446263i
$605$		−	15.0185i		−	0.610590i
$606$		0			0
$607$			36.3384i			1.47493i	0.675385	+	0.737465i	$0.263978\pi$
$607$			36.3384i			1.47493i	−0.675385	+	0.737465i	$0.736022\pi$
$608$	11.9712	+	10.5106i	0.485495	+	0.426262i
$609$		0			0
$610$	20.8986	−	10.9922i	0.846158	−	0.445061i
$611$	−37.7681			−1.52794
$612$		0			0
$613$	27.9242			1.12785			0.563925	−	0.825826i	$-0.309291\pi$
$613$	27.9242			1.12785			0.563925	+	0.825826i	$0.309291\pi$
$614$	10.3839	−	5.46170i	0.419059	−	0.220416i
$615$		0			0
$616$		0			0
$617$		−	1.74855i		−	0.0703940i	−0.999380	−	0.0351970i	$-0.988794\pi$
$617$		−	1.74855i		−	0.0703940i	0.999380	−	0.0351970i	$-0.0112059\pi$
$618$		0			0
$619$		−	20.5640i		−	0.826538i	−0.910609	−	0.413269i	$-0.864387\pi$
$619$		−	20.5640i		−	0.826538i	0.910609	−	0.413269i	$-0.135613\pi$
$620$	24.2569	−	35.2766i	0.974181	−	1.41674i
$621$		0			0
$622$	−11.4293	−	21.7295i	−0.458271	−	0.871273i
$623$		0			0
$624$		0			0
$625$	−21.2058			−0.848232
$626$	−5.23482	−	9.95253i	−0.209225	−	0.397783i
$627$		0			0
$628$	−6.67006	+	9.70021i	−0.266164	+	0.387081i
$629$			0.877511i			0.0349887i
$630$		0			0
$631$			14.5144i			0.577810i	0.957358	+	0.288905i	$0.0932912\pi$
$631$			14.5144i			0.577810i	−0.957358	+	0.288905i	$0.906709\pi$
$632$	−0.275493	+	2.32077i	−0.0109585	+	0.0923153i
$633$		0			0
$634$	−2.73239	+	1.43718i	−0.108517	+	0.0570777i
$635$	10.0015			0.396899
$636$		0			0
$637$		0			0
$638$	−20.6846	+	10.8797i	−0.818912	+	0.430730i
$639$		0			0
$640$	−22.8245	+	5.77714i	−0.902219	+	0.228362i
$641$			50.3882i			1.99022i	0.0987947	+	0.995108i	$0.468501\pi$
$641$			50.3882i			1.99022i	−0.0987947	+	0.995108i	$0.531499\pi$
$642$		0			0
$643$			40.2212i			1.58617i	0.609111	+	0.793085i	$0.291526\pi$
$643$			40.2212i			1.58617i	−0.609111	+	0.793085i	$0.708474\pi$
$644$		0			0
$645$		0			0
$646$	−5.94224	−	11.2975i	−0.233794	−	0.444494i
$647$	20.2997			0.798062			0.399031	−	0.916937i	$-0.369347\pi$
$647$	20.2997			0.798062			0.399031	+	0.916937i	$0.369347\pi$
$648$		0			0
$649$	−15.8135			−0.620735
$650$	2.11774	+	4.02629i	0.0830648	+	0.157924i
$651$		0			0
$652$	15.9859	+	10.9922i	0.626055	+	0.430488i
$653$		−	19.0146i		−	0.744097i	−0.928213	−	0.372049i	$-0.878655\pi$
$653$		−	19.0146i		−	0.744097i	0.928213	−	0.372049i	$-0.121345\pi$
$654$		0			0
$655$			30.6262i			1.19666i
$656$	−1.44613	+	0.554355i	−0.0564619	+	0.0216439i
$657$		0			0
$658$		0			0
$659$	20.4920			0.798256			0.399128	−	0.916895i	$-0.369313\pi$
$659$	20.4920			0.798256			0.399128	+	0.916895i	$0.369313\pi$
$660$		0			0
$661$	−19.3541			−0.752788			−0.376394	−	0.926460i	$-0.622836\pi$
$661$	−19.3541			−0.752788			−0.376394	+	0.926460i	$0.622836\pi$
$662$	16.8671	−	8.87173i	0.655559	−	0.344810i
$663$		0			0
$664$	−15.9831	−	1.89732i	−0.620264	−	0.0736301i
$665$		0			0
$666$		0			0
$667$			18.0482i			0.698828i
$668$	−20.8754	+	30.3589i	−0.807693	+	1.17462i
$669$		0			0
$670$	−1.92347	−	3.65694i	−0.0743103	−	0.141280i
$671$	−34.2447			−1.32200
$672$		0			0
$673$	−18.9180			−0.729236			−0.364618	−	0.931157i	$-0.618800\pi$
$673$	−18.9180			−0.729236			−0.364618	+	0.931157i	$0.618800\pi$
$674$	−11.4674	−	21.8021i	−0.441709	−	0.839785i
$675$		0			0
$676$	−11.4485	+	16.6495i	−0.440328	+	0.640365i
$677$		−	6.86151i		−	0.263709i	−0.991269	−	0.131855i	$-0.957907\pi$
$677$		−	6.86151i		−	0.263709i	0.991269	−	0.131855i	$-0.0420932\pi$
$678$		0			0
$679$		0			0
$680$	18.7342	+	2.22390i	0.718425	+	0.0852825i
$681$		0			0
$682$	−54.9498	+	28.9024i	−2.10414	+	1.10673i
$683$	−22.4589			−0.859365			−0.429682	−	0.902980i	$-0.641374\pi$
$683$	−22.4589			−0.859365			−0.429682	+	0.902980i	$0.641374\pi$
$684$		0			0
$685$	8.25744			0.315500
$686$		0			0
$687$		0			0
$688$	3.39119	−	1.29997i	0.129288	−	0.0495608i
$689$			56.2700i			2.14372i
$690$		0			0
$691$			43.7202i			1.66320i	0.555379	+	0.831598i	$0.312573\pi$
$691$			43.7202i			1.66320i	−0.555379	+	0.831598i	$0.687427\pi$
$692$	11.6703	+	8.02473i	0.443638	+	0.305054i
$693$		0			0
$694$	1.45403	+	2.76443i	0.0551943	+	0.104936i
$695$	−39.8900			−1.51311
$696$		0			0
$697$	1.24099			0.0470058
$698$	−20.6225	−	39.2079i	−0.780574	−	1.48404i
$699$		0			0
$700$		0			0
$701$			5.48856i			0.207300i	0.994614	+	0.103650i	$0.0330522\pi$
$701$			5.48856i			0.207300i	−0.994614	+	0.103650i	$0.966948\pi$
$702$		0			0
$703$		−	0.771010i		−	0.0290792i
$704$	33.1960	+	7.99388i	1.25112	+	0.301281i
$705$		0			0
$706$	−8.63708	+	4.54292i	−0.325061	+	0.170975i
$707$		0			0
$708$		0			0
$709$	−10.7458			−0.403567			−0.201784	−	0.979430i	$-0.564674\pi$
$709$	−10.7458			−0.403567			−0.201784	+	0.979430i	$0.564674\pi$
$710$	−31.0310	+	16.3217i	−1.16457	+	0.612541i
$711$		0			0
$712$	1.00777	−	8.48955i	0.0377680	−	0.318159i
$713$			47.9459i			1.79559i
$714$		0			0
$715$			42.6924i			1.59661i
$716$	−23.9334	+	34.8062i	−0.894434	+	1.30077i
$717$		0			0
$718$	8.65526	+	16.4555i	0.323011	+	0.614115i
$719$	−3.76738			−0.140500			−0.0702498	−	0.997529i	$-0.522380\pi$
$719$	−3.76738			−0.140500			−0.0702498	+	0.997529i	$0.522380\pi$
$720$		0			0
$721$		0			0
$722$	−7.28731	−	13.8548i	−0.271206	−	0.515621i
$723$		0			0
$724$	6.95563	−	10.1155i	0.258504	−	0.375940i
$725$		−	2.59135i		−	0.0962405i
$726$		0			0
$727$			50.2752i			1.86460i	0.361683	+	0.932301i	$0.382202\pi$
$727$			50.2752i			1.86460i	−0.361683	+	0.932301i	$0.617798\pi$
$728$		0			0
$729$		0			0
$730$	31.9920	−	16.8271i	1.18408	−	0.622799i
$731$	−2.91013			−0.107635
$732$		0			0
$733$	9.41405			0.347716			0.173858	−	0.984771i	$-0.444377\pi$
$733$	9.41405			0.347716			0.173858	+	0.984771i	$0.444377\pi$
$734$	14.1506	−	7.44293i	0.522309	−	0.274724i
$735$		0			0
$736$	17.3969	−	19.8144i	0.641260	−	0.730369i
$737$			5.99232i			0.220730i
$738$		0			0
$739$		−	26.5889i		−	0.978088i	−0.872259	−	0.489044i	$-0.837346\pi$
$739$		−	26.5889i		−	0.978088i	0.872259	−	0.489044i	$-0.162654\pi$
$740$	0.938946	+	0.645638i	0.0345163	+	0.0237341i
$741$		0			0
$742$		0			0
$743$	−52.2920			−1.91841			−0.959204	−	0.282715i	$-0.908765\pi$
$743$	−52.2920			−1.91841			−0.959204	+	0.282715i	$0.908765\pi$
$744$		0			0
$745$	11.7722			0.431299
$746$	−9.31783	−	17.7152i	−0.341150	−	0.648600i
$747$		0			0
$748$	−22.5445	−	15.5020i	−0.824307	−	0.566810i
$749$		0			0
$750$		0			0
$751$		−	3.71055i		−	0.135400i	−0.997706	−	0.0676999i	$-0.978434\pi$
$751$		−	3.71055i		−	0.135400i	0.997706	−	0.0676999i	$-0.0215660\pi$
$752$	−11.2502	−	29.3481i	−0.410253	−	1.07022i
$753$		0			0
$754$	23.2940	−	12.2522i	0.848319	−	0.446198i
$755$	−20.1413			−0.733016
$756$		0			0
$757$	3.20123			0.116351			0.0581753	−	0.998306i	$-0.481472\pi$
$757$	3.20123			0.116351			0.0581753	+	0.998306i	$0.481472\pi$
$758$	−20.3272	+	10.6917i	−0.738316	+	0.388338i
$759$		0			0
$760$	−16.4605	−	1.95399i	−0.597085	−	0.0708786i
$761$			34.7601i			1.26005i	0.776573	+	0.630027i	$0.216956\pi$
$761$			34.7601i			1.26005i	−0.776573	+	0.630027i	$0.783044\pi$
$762$		0			0
$763$		0			0
$764$	−13.3693	+	19.4429i	−0.483684	+	0.703418i
$765$		0			0
$766$	1.78940	+	3.40205i	0.0646538	+	0.122921i
$767$	17.8084			0.643025
$768$		0			0
$769$	−21.6622			−0.781160			−0.390580	−	0.920569i	$-0.627726\pi$
$769$	−21.6622			−0.781160			−0.390580	+	0.920569i	$0.627726\pi$
$770$		0			0
$771$		0			0
$772$	17.9127	−	26.0504i	0.644694	−	0.937574i
$773$			24.1453i			0.868446i	0.900805	+	0.434223i	$0.142977\pi$
$773$			24.1453i			0.868446i	−0.900805	+	0.434223i	$0.857023\pi$
$774$		0			0
$775$		−	6.88406i		−	0.247283i
$776$	−42.9652	−	5.10030i	−1.54236	−	0.183090i
$777$		0			0
$778$	−25.1518	+	13.2293i	−0.901737	+	0.474295i
$779$	−1.09037			−0.0390666
$780$		0			0
$781$	50.8479			1.81948
$782$	−18.6994	+	9.83547i	−0.668688	+	0.351716i
$783$		0			0
$784$		0			0
$785$		−	12.2492i		−	0.437192i
$786$		0			0
$787$		−	4.06792i		−	0.145006i	−0.997368	−	0.0725028i	$-0.976901\pi$
$787$		−	4.06792i		−	0.145006i	0.997368	−	0.0725028i	$-0.0230986\pi$
$788$	3.58953	+	2.46823i	0.127872	+	0.0879270i
$789$		0			0
$790$	−1.13202	−	2.15221i	−0.0402754	−	0.0765723i
$791$		0			0
$792$		0			0
$793$	38.5647			1.36947
$794$	−10.4435	−	19.8554i	−0.370626	−	0.704640i
$795$		0			0
$796$	9.03114	+	6.20999i	0.320100	+	0.220107i
$797$		−	19.6098i		−	0.694614i	−0.937752	−	0.347307i	$-0.887096\pi$
$797$		−	19.6098i		−	0.694614i	0.937752	−	0.347307i	$-0.112904\pi$
$798$		0			0
$799$			25.1849i			0.890979i
$800$	−2.49785	+	2.84495i	−0.0883124	+	0.100584i
$801$		0			0
$802$	−40.0553	+	21.0682i	−1.41440	+	0.743945i
$803$	−52.4225			−1.84995
$804$		0			0
$805$		0			0
$806$	61.8818	−	32.5485i	2.17969	−	1.14647i
$807$		0			0
$808$	0.129094	−	1.08749i	0.00454149	−	0.0382578i
$809$			41.7772i			1.46881i	0.678712	+	0.734405i	$0.262538\pi$
$809$			41.7772i			1.46881i	−0.678712	+	0.734405i	$0.737462\pi$
$810$		0			0
$811$			4.61271i			0.161974i	0.996715	+	0.0809870i	$0.0258072\pi$
$811$			4.61271i			0.161974i	−0.996715	+	0.0809870i	$0.974193\pi$
$812$		0			0
$813$		0			0
$814$	−0.769285	−	1.46258i	−0.0269634	−	0.0512633i
$815$	−20.1866			−0.707104
$816$		0			0
$817$	2.55693			0.0894558
$818$	−3.18695	−	6.05910i	−0.111429	−	0.211851i
$819$		0			0
$820$	0.913069	−	1.32787i	0.0318858	−	0.0463712i
$821$			16.1901i			0.565039i	0.959261	+	0.282520i	$0.0911703\pi$
$821$			16.1901i			0.565039i	−0.959261	+	0.282520i	$0.908830\pi$
$822$		0			0
$823$			15.7251i			0.548142i	0.961709	+	0.274071i	$0.0883704\pi$
$823$			15.7251i			0.548142i	−0.961709	+	0.274071i	$0.911630\pi$
$824$	4.51309	−	38.0185i	0.157221	−	1.32444i
$825$		0			0
$826$		0			0
$827$	13.1854			0.458500			0.229250	−	0.973368i	$-0.426373\pi$
$827$	13.1854			0.458500			0.229250	+	0.973368i	$0.426373\pi$
$828$		0			0
$829$	34.8533			1.21050			0.605252	−	0.796034i	$-0.293072\pi$
$829$	34.8533			1.21050			0.605252	+	0.796034i	$0.293072\pi$
$830$	14.8222	−	7.79619i	0.514488	−	0.270610i
$831$		0			0
$832$	−37.3837	−	9.00233i	−1.29605	−	0.312099i
$833$		0			0
$834$		0			0
$835$		−	38.3365i		−	1.32669i
$836$	19.8083	+	13.6206i	0.685084	+	0.471077i
$837$		0			0
$838$	−6.55095	−	12.4548i	−0.226299	−	0.430243i
$839$	−10.2242			−0.352978			−0.176489	−	0.984303i	$-0.556474\pi$
$839$	−10.2242			−0.352978			−0.176489	+	0.984303i	$0.556474\pi$
$840$		0			0
$841$	14.0078			0.483027
$842$	1.49691	+	2.84595i	0.0515869	+	0.0980779i
$843$		0			0
$844$	−14.5031	−	9.97261i	−0.499217	−	0.343271i
$845$		−	21.0246i		−	0.723267i
$846$		0			0
$847$		0			0
$848$	−43.7253	+	16.7615i	−1.50153	+	0.575592i
$849$		0			0
$850$	2.68485	−	1.41218i	0.0920897	−	0.0484372i
$851$	−1.27616			−0.0437461
$852$		0			0
$853$	47.4094			1.62327			0.811634	−	0.584167i	$-0.198578\pi$
$853$	47.4094			1.62327			0.811634	+	0.584167i	$0.198578\pi$
$854$		0			0
$855$		0			0
$856$	−30.5702	−	3.62892i	−1.04487	−	0.124034i
$857$			16.9033i			0.577404i	0.957419	+	0.288702i	$0.0932237\pi$
$857$			16.9033i			0.577404i	−0.957419	+	0.288702i	$0.906776\pi$
$858$		0			0
$859$			11.3528i			0.387351i	0.981066	+	0.193676i	$0.0620409\pi$
$859$			11.3528i			0.387351i	−0.981066	+	0.193676i	$0.937959\pi$
$860$	−2.14116	+	3.11387i	−0.0730128	+	0.106182i
$861$		0			0
$862$	18.7826	+	35.7097i	0.639737	+	1.21628i
$863$	30.2928			1.03118			0.515590	−	0.856836i	$-0.327573\pi$
$863$	30.2928			1.03118			0.515590	+	0.856836i	$0.327573\pi$
$864$		0			0
$865$	−14.7370			−0.501072
$866$	5.17577	+	9.84026i	0.175880	+	0.334386i
$867$		0			0
$868$		0			0
$869$			3.52665i			0.119633i
$870$		0			0
$871$		−	6.74826i		−	0.228656i
$872$	−52.5677	−	6.24019i	−1.78017	−	0.211320i
$873$		0			0
$874$	16.4299	−	8.64176i	0.555748	−	0.292312i
$875$		0			0
$876$		0			0
$877$	−15.6434			−0.528241			−0.264121	−	0.964490i	$-0.585082\pi$
$877$	−15.6434			−0.528241			−0.264121	+	0.964490i	$0.585082\pi$
$878$	−13.3556	+	7.02475i	−0.450729	+	0.237074i
$879$		0			0
$880$	−33.1746	+	12.7170i	−1.11832	+	0.428691i
$881$			23.0836i			0.777705i	0.921300	+	0.388853i	$0.127128\pi$
$881$			23.0836i			0.777705i	−0.921300	+	0.388853i	$0.872872\pi$
$882$		0			0
$883$			13.4161i			0.451488i	0.974187	+	0.225744i	$0.0724813\pi$
$883$			13.4161i			0.451488i	−0.974187	+	0.225744i	$0.927519\pi$
$884$	25.3885	+	17.4576i	0.853907	+	0.587163i
$885$		0			0
$886$	−25.0039	−	47.5378i	−0.840021	−	1.59706i
$887$	−47.9744			−1.61082			−0.805412	−	0.592715i	$-0.798056\pi$
$887$	−47.9744			−1.61082			−0.805412	+	0.592715i	$0.798056\pi$
$888$		0			0
$889$		0			0
$890$	4.14101	+	7.87296i	0.138807	+	0.263902i
$891$		0			0
$892$	−34.8549	−	23.9669i	−1.16703	−	0.802471i
$893$		−	22.1283i		−	0.740495i
$894$		0			0
$895$		−	43.9524i		−	1.46917i
$896$		0			0
$897$		0			0
$898$	−30.0450	+	15.8030i	−1.00262	+	0.527355i
$899$	−39.8276			−1.32832
$900$		0			0
$901$	37.5225			1.25006
$902$	−2.06840	+	1.08793i	−0.0688701	+	0.0362242i
$903$		0			0
$904$	−4.38030	+	36.8999i	−0.145687	+	1.22727i
$905$			12.7736i			0.424610i
$906$		0			0
$907$		−	9.28828i		−	0.308412i	−0.988039	−	0.154206i	$-0.950718\pi$
$907$		−	9.28828i		−	0.308412i	0.988039	−	0.154206i	$-0.0492820\pi$
$908$	−31.8370	+	46.3003i	−1.05655	+	1.53653i
$909$		0			0
$910$		0			0
$911$	32.4981			1.07671			0.538354	−	0.842719i	$-0.319046\pi$
$911$	32.4981			1.07671			0.538354	+	0.842719i	$0.319046\pi$
$912$		0			0
$913$	−24.2879			−0.803814
$914$	−9.90474	−	18.8311i	−0.327620	−	0.622876i
$915$		0			0
$916$	15.4518	−	22.4715i	0.510543	−	0.742478i
$917$		0			0
$918$		0			0
$919$		−	0.444302i		−	0.0146562i	−0.999973	−	0.00732808i	$-0.997667\pi$
$919$		−	0.444302i		−	0.0146562i	0.999973	−	0.00732808i	$-0.00233262\pi$
$920$	−3.23420	+	27.2450i	−0.106628	+	0.898243i
$921$		0			0
$922$	−38.0139	+	19.9945i	−1.25192	+	0.658485i
$923$	−57.2624			−1.88482
$924$		0			0
$925$	0.183231			0.00602459
$926$	−29.7651	+	15.6558i	−0.978143	+	0.514482i
$927$		0			0
$928$	16.4594	+	14.4513i	0.540307	+	0.474386i
$929$		−	16.2849i		−	0.534289i	−0.963656	−	0.267145i	$-0.913920\pi$
$929$		−	16.2849i		−	0.534289i	0.963656	−	0.267145i	$-0.0860802\pi$
$930$		0			0
$931$		0			0
$932$	7.10735	+	4.88715i	0.232809	+	0.160084i
$933$		0			0
$934$	−3.09654	−	5.88719i	−0.101322	−	0.192635i
$935$	28.4686			0.931022
$936$		0			0
$937$	30.9796			1.01206			0.506029	−	0.862516i	$-0.331113\pi$
$937$	30.9796			1.01206			0.506029	+	0.862516i	$0.331113\pi$
$938$		0			0
$939$		0			0
$940$	26.9481	+	18.5301i	0.878951	+	0.604384i
$941$		−	10.9205i		−	0.355997i	−0.984031	−	0.177998i	$-0.943038\pi$
$941$		−	10.9205i		−	0.355997i	0.984031	−	0.177998i	$-0.0569622\pi$
$942$		0			0
$943$			1.80476i			0.0587711i
$944$	5.30470	+	13.8382i	0.172653	+	0.450396i
$945$		0			0
$946$	4.85041	−	2.55121i	0.157700	−	0.0829471i
$947$	−16.7899			−0.545598			−0.272799	−	0.962071i	$-0.587949\pi$
$947$	−16.7899			−0.545598			−0.272799	+	0.962071i	$0.587949\pi$
$948$		0			0
$949$	59.0357			1.91638
$950$	−2.35900	+	1.24078i	−0.0765360	+	0.0402563i
$951$		0			0
$952$		0			0
$953$		−	39.3512i		−	1.27471i	−0.770570	−	0.637355i	$-0.780028\pi$
$953$		−	39.3512i		−	1.27471i	0.770570	−	0.637355i	$-0.219972\pi$
$954$		0			0
$955$		−	24.5520i		−	0.794483i
$956$	8.18326	−	11.9008i	0.264665	−	0.384901i
$957$		0			0
$958$	−2.69276	−	5.11952i	−0.0869991	−	0.165404i
$959$		0			0
$960$		0			0
$961$	−74.8040			−2.41303
$962$	0.866332	+	1.64709i	0.0279317	+	0.0531042i
$963$		0			0
$964$	−5.36542	+	7.80290i	−0.172809	+	0.251314i
$965$			32.8958i			1.05895i
$966$		0			0
$967$		−	9.26652i		−	0.297991i	−0.988838	−	0.148996i	$-0.952396\pi$
$967$		−	9.26652i		−	0.297991i	0.988838	−	0.148996i	$-0.0476040\pi$
$968$	20.2699	+	2.40620i	0.651500	+	0.0773381i
$969$		0			0
$970$	39.8447	−	20.9574i	1.27934	−	0.672903i
$971$	29.1675			0.936028			0.468014	−	0.883721i	$-0.344970\pi$
$971$	29.1675			0.936028			0.468014	+	0.883721i	$0.344970\pi$
$972$		0			0
$973$		0			0
$974$	7.01209	−	3.68821i	0.224682	−	0.118178i
$975$		0			0
$976$	11.4875	+	29.9671i	0.367706	+	0.959224i
$977$		−	50.3622i		−	1.61123i	−0.592440	−	0.805615i	$-0.701835\pi$
$977$		−	50.3622i		−	1.61123i	0.592440	−	0.805615i	$-0.298165\pi$
$978$		0			0
$979$		−	12.9007i		−	0.412309i
$980$		0			0
$981$		0			0
$982$	−6.78704	−	12.9036i	−0.216583	−	0.411772i
$983$	−44.9746			−1.43447			−0.717233	−	0.696834i	$-0.754592\pi$
$983$	−44.9746			−1.43447			−0.717233	+	0.696834i	$0.754592\pi$
$984$		0			0
$985$	−4.53277			−0.144426
$986$	−8.17011	−	15.5332i	−0.260189	−	0.494677i
$987$		0			0
$988$	−22.3071	−	15.3388i	−0.709684	−	0.487993i
$989$		−	4.23218i		−	0.134575i
$990$		0			0
$991$			33.2149i			1.05511i	0.849522	+	0.527553i	$0.176890\pi$
$991$			33.2149i			1.05511i	−0.849522	+	0.527553i	$0.823110\pi$
$992$	43.7253	+	38.3905i	1.38828	+	1.21890i
$993$		0			0
$994$		0			0
$995$	−11.4043			−0.361541
$996$		0			0
$997$	−9.61928			−0.304646			−0.152323	−	0.988331i	$-0.548675\pi$
$997$	−9.61928			−0.304646			−0.152323	+	0.988331i	$0.548675\pi$
$998$	8.88185	−	4.67167i	0.281150	−	0.147879i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1764.2.e.i.1079.5		16
3.2	odd	2	inner	1764.2.e.i.1079.12		16
4.3	odd	2	inner	1764.2.e.i.1079.11		16
7.2	even	3		252.2.be.a.179.6	yes	32
7.4	even	3		252.2.be.a.107.16	yes	32
7.6	odd	2		1764.2.e.h.1079.5		16
12.11	even	2	inner	1764.2.e.i.1079.6		16
21.2	odd	6		252.2.be.a.179.11	yes	32
21.11	odd	6		252.2.be.a.107.1	✓	32
21.20	even	2		1764.2.e.h.1079.12		16
28.11	odd	6		252.2.be.a.107.11	yes	32
28.23	odd	6		252.2.be.a.179.1	yes	32
28.27	even	2		1764.2.e.h.1079.11		16
84.11	even	6		252.2.be.a.107.6	yes	32
84.23	even	6		252.2.be.a.179.16	yes	32
84.83	odd	2		1764.2.e.h.1079.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.be.a.107.1	✓	32	21.11	odd	6
252.2.be.a.107.6	yes	32	84.11	even	6
252.2.be.a.107.11	yes	32	28.11	odd	6
252.2.be.a.107.16	yes	32	7.4	even	3
252.2.be.a.179.1	yes	32	28.23	odd	6
252.2.be.a.179.6	yes	32	7.2	even	3
252.2.be.a.179.11	yes	32	21.2	odd	6
252.2.be.a.179.16	yes	32	84.23	even	6
1764.2.e.h.1079.5		16	7.6	odd	2
1764.2.e.h.1079.6		16	84.83	odd	2
1764.2.e.h.1079.11		16	28.27	even	2
1764.2.e.h.1079.12		16	21.20	even	2
1764.2.e.i.1079.5		16	1.1	even	1	trivial
1764.2.e.i.1079.6		16	12.11	even	2	inner
1764.2.e.i.1079.11		16	4.3	odd	2	inner
1764.2.e.i.1079.12		16	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1764.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.658334 - 1.25164i) q^{2} +(-1.13319 + 1.64799i) q^{4} -2.08104i q^{5} +(2.80871 + 0.333415i) q^{8} +O(q^{10})\)	\(q+(-0.658334 - 1.25164i) q^{2} +(-1.13319 + 1.64799i) q^{4} -2.08104i q^{5} +(2.80871 + 0.333415i) q^{8} +(-2.60471 + 1.37002i) q^{10} +4.26812 q^{11} -4.80655 q^{13} +(-1.43175 - 3.73498i) q^{16} +3.20515i q^{17} -2.81615i q^{19} +(3.42954 + 2.35822i) q^{20} +(-2.80985 - 5.34213i) q^{22} -4.66122 q^{23} +0.669258 q^{25} +(3.16432 + 6.01605i) q^{26} -3.87198i q^{29} -10.2861i q^{31} +(-3.73227 + 4.25090i) q^{32} +(4.01168 - 2.11006i) q^{34} +0.273782 q^{37} +(-3.52480 + 1.85397i) q^{38} +(0.693851 - 5.84504i) q^{40} -0.387186i q^{41} +0.907954i q^{43} +(-4.83659 + 7.03382i) q^{44} +(3.06864 + 5.83416i) q^{46} +7.85764 q^{47} +(-0.440596 - 0.837668i) q^{50} +(5.44674 - 7.92115i) q^{52} -11.7070i q^{53} -8.88214i q^{55} +(-4.84631 + 2.54906i) q^{58} -3.70504 q^{59} -8.02337 q^{61} +(-12.8745 + 6.77170i) q^{62} +(7.77767 + 1.87293i) q^{64} +10.0026i q^{65} +1.40397i q^{67} +(-5.28206 - 3.63205i) q^{68} +11.9134 q^{71} -12.2824 q^{73} +(-0.180240 - 0.342675i) q^{74} +(4.64099 + 3.19124i) q^{76} +0.826277i q^{79} +(-7.77266 + 2.97954i) q^{80} +(-0.484616 + 0.254898i) q^{82} -5.69055 q^{83} +6.67006 q^{85} +(1.13643 - 0.597737i) q^{86} +(11.9879 + 1.42305i) q^{88} -3.02258i q^{89} +(5.28206 - 7.68166i) q^{92} +(-5.17296 - 9.83492i) q^{94} -5.86053 q^{95} -15.2972 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q + 8 q^{13} - 4 q^{16} - 16 q^{22} - 24 q^{25} - 8 q^{34} - 8 q^{37} + 52 q^{40} + 24 q^{46} + 52 q^{52} + 12 q^{58} + 16 q^{61} + 60 q^{64} + 8 q^{73} + 36 q^{76} - 68 q^{82} - 16 q^{85} - 44 q^{88} - 60 q^{94} - 88 q^{97}+O(q^{100}) \) 16 * q + 8 * q^13 - 4 * q^16 - 16 * q^22 - 24 * q^25 - 8 * q^34 - 8 * q^37 + 52 * q^40 + 24 * q^46 + 52 * q^52 + 12 * q^58 + 16 * q^61 + 60 * q^64 + 8 * q^73 + 36 * q^76 - 68 * q^82 - 16 * q^85 - 44 * q^88 - 60 * q^94 - 88 * q^97

Introduction

L-functions

Modular forms

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Database

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