LMFDB - Embedded newform 1156.2.e.c.829.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1156,2,Mod(829,1156)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1156, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("1156.829");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1156 = 2^{2} \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1156.e (of order $4$, 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:	$9.23070647366$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(i, \sqrt{13})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 7x^{2} + 9 $ x^4 + 7*x^2 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 68)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			829.2
Root			$2.30278i$ of defining polynomial
Character	$\chi$	$=$	1156.829
Dual form			1156.2.e.c.905.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.30278 + 2.30278i) q^{3} +(1.00000 + 1.00000i) q^{5} +(-2.30278 + 2.30278i) q^{7} +7.60555i q^{9} +O(q^{10})$	\(q+(2.30278 + 2.30278i) q^{3} +(1.00000 + 1.00000i) q^{5} +(-2.30278 + 2.30278i) q^{7} +7.60555i q^{9} +(0.302776 - 0.302776i) q^{11} +2.60555 q^{13} +4.60555i q^{15} -0.605551i q^{19} -10.6056 q^{21} +(4.30278 - 4.30278i) q^{23} -3.00000i q^{25} +(-10.6056 + 10.6056i) q^{27} +(1.60555 + 1.60555i) q^{29} +(-4.30278 - 4.30278i) q^{31} +1.39445 q^{33} -4.60555 q^{35} +(-3.00000 - 3.00000i) q^{37} +(6.00000 + 6.00000i) q^{39} +(-1.00000 + 1.00000i) q^{41} +3.39445i q^{43} +(-7.60555 + 7.60555i) q^{45} -4.00000 q^{47} -3.60555i q^{49} +5.21110i q^{53} +0.605551 q^{55} +(1.39445 - 1.39445i) q^{57} +8.60555i q^{59} +(6.21110 - 6.21110i) q^{61} +(-17.5139 - 17.5139i) q^{63} +(2.60555 + 2.60555i) q^{65} +9.21110 q^{67} +19.8167 q^{69} +(-2.90833 - 2.90833i) q^{71} +(7.00000 + 7.00000i) q^{73} +(6.90833 - 6.90833i) q^{75} +1.39445i q^{77} +(0.302776 - 0.302776i) q^{79} -26.0278 q^{81} -17.8167i q^{83} +7.39445i q^{87} +7.81665 q^{89} +(-6.00000 + 6.00000i) q^{91} -19.8167i q^{93} +(0.605551 - 0.605551i) q^{95} +(7.60555 + 7.60555i) q^{97} +(2.30278 + 2.30278i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3} + 4 q^{5} - 2 q^{7}+O(q^{10}) $ 4 * q + 2 * q^3 + 4 * q^5 - 2 * q^7	$ 4 q + 2 q^{3} + 4 q^{5} - 2 q^{7} - 6 q^{11} - 4 q^{13} - 28 q^{21} + 10 q^{23} - 28 q^{27} - 8 q^{29} - 10 q^{31} + 20 q^{33} - 4 q^{35} - 12 q^{37} + 24 q^{39} - 4 q^{41} - 16 q^{45} - 16 q^{47} - 12 q^{55} + 20 q^{57} - 4 q^{61} - 34 q^{63} - 4 q^{65} + 8 q^{67} + 36 q^{69} + 10 q^{71} + 28 q^{73} + 6 q^{75} - 6 q^{79} - 32 q^{81} - 12 q^{89} - 24 q^{91} - 12 q^{95} + 16 q^{97} + 2 q^{99}+O(q^{100}) $ 4 * q + 2 * q^3 + 4 * q^5 - 2 * q^7 - 6 * q^11 - 4 * q^13 - 28 * q^21 + 10 * q^23 - 28 * q^27 - 8 * q^29 - 10 * q^31 + 20 * q^33 - 4 * q^35 - 12 * q^37 + 24 * q^39 - 4 * q^41 - 16 * q^45 - 16 * q^47 - 12 * q^55 + 20 * q^57 - 4 * q^61 - 34 * q^63 - 4 * q^65 + 8 * q^67 + 36 * q^69 + 10 * q^71 + 28 * q^73 + 6 * q^75 - 6 * q^79 - 32 * q^81 - 12 * q^89 - 24 * q^91 - 12 * q^95 + 16 * q^97 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1156\mathbb{Z}\right)^\times$.

$n$	$579$	$581$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$

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
$3$	2.30278	+	2.30278i	1.32951	+	1.32951i	0.905798	+	0.423710i	$0.139273\pi$
$3$	2.30278	+	2.30278i	1.32951	+	1.32951i	0.423710	+	0.905798i	$0.360727\pi$
$4$		0			0
$5$	1.00000	+	1.00000i	0.447214	+	0.447214i	0.894427	−	0.447214i	$-0.147584\pi$
$5$	1.00000	+	1.00000i	0.447214	+	0.447214i	−0.447214	+	0.894427i	$0.647584\pi$
$6$		0			0
$7$	−2.30278	+	2.30278i	−0.870367	+	0.870367i	−0.992512	−	0.122145i	$-0.961023\pi$
$7$	−2.30278	+	2.30278i	−0.870367	+	0.870367i	0.122145	+	0.992512i	$0.461023\pi$
$8$		0			0
$9$			7.60555i			2.53518i
$10$		0			0
$11$	0.302776	−	0.302776i	0.0912903	−	0.0912903i	−0.659987	−	0.751277i	$-0.729438\pi$
$11$	0.302776	−	0.302776i	0.0912903	−	0.0912903i	0.751277	+	0.659987i	$0.229438\pi$
$12$		0			0
$13$	2.60555			0.722650			0.361325	−	0.932440i	$-0.382325\pi$
$13$	2.60555			0.722650			0.361325	+	0.932440i	$0.382325\pi$
$14$		0			0
$15$			4.60555i			1.18915i
$16$		0			0
$17$		0			0
$17$		0			0
$18$		0			0
$19$		−	0.605551i		−	0.138923i	−0.997585	−	0.0694615i	$-0.977872\pi$
$19$		−	0.605551i		−	0.138923i	0.997585	−	0.0694615i	$-0.0221281\pi$
$20$		0			0
$21$	−10.6056			−2.31432
$22$		0			0
$23$	4.30278	−	4.30278i	0.897191	−	0.897191i	−0.0979961	−	0.995187i	$-0.531243\pi$
$23$	4.30278	−	4.30278i	0.897191	−	0.897191i	0.995187	+	0.0979961i	$0.0312433\pi$
$24$		0			0
$25$		−	3.00000i		−	0.600000i
$26$		0			0
$27$	−10.6056	+	10.6056i	−2.04104	+	2.04104i
$28$		0			0
$29$	1.60555	+	1.60555i	0.298143	+	0.298143i	0.840286	−	0.542143i	$-0.182387\pi$
$29$	1.60555	+	1.60555i	0.298143	+	0.298143i	−0.542143	+	0.840286i	$0.682387\pi$
$30$		0			0
$31$	−4.30278	−	4.30278i	−0.772801	−	0.772801i	0.205794	−	0.978595i	$-0.434022\pi$
$31$	−4.30278	−	4.30278i	−0.772801	−	0.772801i	−0.978595	+	0.205794i	$0.934022\pi$
$32$		0			0
$33$	1.39445			0.242742
$34$		0			0
$35$	−4.60555			−0.778480
$36$		0			0
$37$	−3.00000	−	3.00000i	−0.493197	−	0.493197i	0.416115	−	0.909312i	$-0.363391\pi$
$37$	−3.00000	−	3.00000i	−0.493197	−	0.493197i	−0.909312	+	0.416115i	$0.863391\pi$
$38$		0			0
$39$	6.00000	+	6.00000i	0.960769	+	0.960769i
$40$		0			0
$41$	−1.00000	+	1.00000i	−0.156174	+	0.156174i	−0.780869	−	0.624695i	$-0.785223\pi$
$41$	−1.00000	+	1.00000i	−0.156174	+	0.156174i	0.624695	+	0.780869i	$0.285223\pi$
$42$		0			0
$43$			3.39445i			0.517649i	0.965924	+	0.258824i	$0.0833351\pi$
$43$			3.39445i			0.517649i	−0.965924	+	0.258824i	$0.916665\pi$
$44$		0			0
$45$	−7.60555	+	7.60555i	−1.13377	+	1.13377i
$46$		0			0
$47$	−4.00000			−0.583460			−0.291730	−	0.956501i	$-0.594231\pi$
$47$	−4.00000			−0.583460			−0.291730	+	0.956501i	$0.594231\pi$
$48$		0			0
$49$		−	3.60555i		−	0.515079i
$50$		0			0
$51$		0			0
$52$		0			0
$53$			5.21110i			0.715800i	0.933760	+	0.357900i	$0.116507\pi$
$53$			5.21110i			0.715800i	−0.933760	+	0.357900i	$0.883493\pi$
$54$		0			0
$55$	0.605551			0.0816525
$56$		0			0
$57$	1.39445	−	1.39445i	0.184699	−	0.184699i
$58$		0			0
$59$			8.60555i			1.12035i	0.828375	+	0.560174i	$0.189266\pi$
$59$			8.60555i			1.12035i	−0.828375	+	0.560174i	$0.810734\pi$
$60$		0			0
$61$	6.21110	−	6.21110i	0.795250	−	0.795250i	−0.187092	−	0.982342i	$-0.559906\pi$
$61$	6.21110	−	6.21110i	0.795250	−	0.795250i	0.982342	+	0.187092i	$0.0599063\pi$
$62$		0			0
$63$	−17.5139	−	17.5139i	−2.20654	−	2.20654i
$64$		0			0
$65$	2.60555	+	2.60555i	0.323179	+	0.323179i
$66$		0			0
$67$	9.21110			1.12532			0.562658	−	0.826690i	$-0.309779\pi$
$67$	9.21110			1.12532			0.562658	+	0.826690i	$0.309779\pi$
$68$		0			0
$69$	19.8167			2.38564
$70$		0			0
$71$	−2.90833	−	2.90833i	−0.345155	−	0.345155i	0.513146	−	0.858301i	$-0.328480\pi$
$71$	−2.90833	−	2.90833i	−0.345155	−	0.345155i	−0.858301	+	0.513146i	$0.828480\pi$
$72$		0			0
$73$	7.00000	+	7.00000i	0.819288	+	0.819288i	0.986005	−	0.166717i	$-0.0533166\pi$
$73$	7.00000	+	7.00000i	0.819288	+	0.819288i	−0.166717	+	0.986005i	$0.553317\pi$
$74$		0			0
$75$	6.90833	−	6.90833i	0.797705	−	0.797705i
$76$		0			0
$77$			1.39445i			0.158912i
$78$		0			0
$79$	0.302776	−	0.302776i	0.0340649	−	0.0340649i	−0.689869	−	0.723934i	$-0.742332\pi$
$79$	0.302776	−	0.302776i	0.0340649	−	0.0340649i	0.723934	+	0.689869i	$0.242332\pi$
$80$		0			0
$81$	−26.0278			−2.89197
$82$		0			0
$83$		−	17.8167i		−	1.95563i	−0.209466	−	0.977816i	$-0.567173\pi$
$83$		−	17.8167i		−	1.95563i	0.209466	−	0.977816i	$-0.432827\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$			7.39445i			0.792768i
$88$		0			0
$89$	7.81665			0.828564			0.414282	−	0.910149i	$-0.364033\pi$
$89$	7.81665			0.828564			0.414282	+	0.910149i	$0.364033\pi$
$90$		0			0
$91$	−6.00000	+	6.00000i	−0.628971	+	0.628971i
$92$		0			0
$93$		−	19.8167i		−	2.05489i
$94$		0			0
$95$	0.605551	−	0.605551i	0.0621282	−	0.0621282i
$96$		0			0
$97$	7.60555	+	7.60555i	0.772227	+	0.772227i	0.978495	−	0.206269i	$-0.0661321\pi$
$97$	7.60555	+	7.60555i	0.772227	+	0.772227i	−0.206269	+	0.978495i	$0.566132\pi$
$98$		0			0
$99$	2.30278	+	2.30278i	0.231438	+	0.231438i
$100$		0			0
$101$	10.6056			1.05529			0.527646	−	0.849464i	$-0.323075\pi$
$101$	10.6056			1.05529			0.527646	+	0.849464i	$0.323075\pi$
$102$		0			0
$103$	−13.2111			−1.30173			−0.650864	−	0.759194i	$-0.725593\pi$
$103$	−13.2111			−1.30173			−0.650864	+	0.759194i	$0.725593\pi$
$104$		0			0
$105$	−10.6056	−	10.6056i	−1.03500	−	1.03500i
$106$		0			0
$107$	−5.69722	−	5.69722i	−0.550771	−	0.550771i	0.375892	−	0.926663i	$-0.377336\pi$
$107$	−5.69722	−	5.69722i	−0.550771	−	0.550771i	−0.926663	+	0.375892i	$0.877336\pi$
$108$		0			0
$109$	6.21110	−	6.21110i	0.594916	−	0.594916i	−0.344039	−	0.938955i	$-0.611795\pi$
$109$	6.21110	−	6.21110i	0.594916	−	0.594916i	0.938955	+	0.344039i	$0.111795\pi$
$110$		0			0
$111$		−	13.8167i		−	1.31142i
$112$		0			0
$113$	−9.60555	+	9.60555i	−0.903614	+	0.903614i	−0.995747	−	0.0921325i	$-0.970632\pi$
$113$	−9.60555	+	9.60555i	−0.903614	+	0.903614i	0.0921325	+	0.995747i	$0.470632\pi$
$114$		0			0
$115$	8.60555			0.802472
$116$		0			0
$117$			19.8167i			1.83205i
$118$		0			0
$119$		0			0
$120$		0			0
$121$			10.8167i			0.983332i
$122$		0			0
$123$	−4.60555			−0.415269
$124$		0			0
$125$	8.00000	−	8.00000i	0.715542	−	0.715542i
$126$		0			0
$127$			0.605551i			0.0537340i	0.999639	+	0.0268670i	$0.00855306\pi$
$127$			0.605551i			0.0537340i	−0.999639	+	0.0268670i	$0.991447\pi$
$128$		0			0
$129$	−7.81665	+	7.81665i	−0.688218	+	0.688218i
$130$		0			0
$131$	6.30278	+	6.30278i	0.550676	+	0.550676i	0.926636	−	0.375960i	$-0.122687\pi$
$131$	6.30278	+	6.30278i	0.550676	+	0.550676i	−0.375960	+	0.926636i	$0.622687\pi$
$132$		0			0
$133$	1.39445	+	1.39445i	0.120914	+	0.120914i
$134$		0			0
$135$	−21.2111			−1.82556
$136$		0			0
$137$	−2.60555			−0.222607			−0.111304	−	0.993786i	$-0.535503\pi$
$137$	−2.60555			−0.222607			−0.111304	+	0.993786i	$0.535503\pi$
$138$		0			0
$139$	−0.302776	−	0.302776i	−0.0256811	−	0.0256811i	0.694150	−	0.719831i	$-0.255781\pi$
$139$	−0.302776	−	0.302776i	−0.0256811	−	0.0256811i	−0.719831	+	0.694150i	$0.755781\pi$
$140$		0			0
$141$	−9.21110	−	9.21110i	−0.775715	−	0.775715i
$142$		0			0
$143$	0.788897	−	0.788897i	0.0659709	−	0.0659709i
$144$		0			0
$145$			3.21110i			0.266668i
$146$		0			0
$147$	8.30278	−	8.30278i	0.684801	−	0.684801i
$148$		0			0
$149$	8.42221			0.689974			0.344987	−	0.938607i	$-0.387883\pi$
$149$	8.42221			0.689974			0.344987	+	0.938607i	$0.387883\pi$
$150$		0			0
$151$		−	4.60555i		−	0.374794i	−0.982284	−	0.187397i	$-0.939995\pi$
$151$		−	4.60555i		−	0.374794i	0.982284	−	0.187397i	$-0.0600052\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		−	8.60555i		−	0.691215i
$156$		0			0
$157$	−8.42221			−0.672165			−0.336083	−	0.941833i	$-0.609102\pi$
$157$	−8.42221			−0.672165			−0.336083	+	0.941833i	$0.609102\pi$
$158$		0			0
$159$	−12.0000	+	12.0000i	−0.951662	+	0.951662i
$160$		0			0
$161$			19.8167i			1.56177i
$162$		0			0
$163$	4.30278	−	4.30278i	0.337019	−	0.337019i	−0.518225	−	0.855244i	$-0.673407\pi$
$163$	4.30278	−	4.30278i	0.337019	−	0.337019i	0.855244	+	0.518225i	$0.173407\pi$
$164$		0			0
$165$	1.39445	+	1.39445i	0.108558	+	0.108558i
$166$		0			0
$167$	−14.9083	−	14.9083i	−1.15364	−	1.15364i	−0.985817	−	0.167824i	$-0.946326\pi$
$167$	−14.9083	−	14.9083i	−1.15364	−	1.15364i	−0.167824	−	0.985817i	$-0.553674\pi$
$168$		0			0
$169$	−6.21110			−0.477777
$170$		0			0
$171$	4.60555			0.352195
$172$		0			0
$173$	14.8167	+	14.8167i	1.12649	+	1.12649i	0.990744	+	0.135746i	$0.0433430\pi$
$173$	14.8167	+	14.8167i	1.12649	+	1.12649i	0.135746	+	0.990744i	$0.456657\pi$
$174$		0			0
$175$	6.90833	+	6.90833i	0.522220	+	0.522220i
$176$		0			0
$177$	−19.8167	+	19.8167i	−1.48951	+	1.48951i
$178$		0			0
$179$			15.0278i			1.12323i	0.827400	+	0.561614i	$0.189819\pi$
$179$			15.0278i			1.12323i	−0.827400	+	0.561614i	$0.810181\pi$
$180$		0			0
$181$	13.0000	−	13.0000i	0.966282	−	0.966282i	−0.0331674	−	0.999450i	$-0.510559\pi$
$181$	13.0000	−	13.0000i	0.966282	−	0.966282i	0.999450	+	0.0331674i	$0.0105595\pi$
$182$		0			0
$183$	28.6056			2.11458
$184$		0			0
$185$		−	6.00000i		−	0.441129i
$186$		0			0
$187$		0			0
$188$		0			0
$189$		−	48.8444i		−	3.55291i
$190$		0			0
$191$	6.78890			0.491227			0.245614	−	0.969368i	$-0.421011\pi$
$191$	6.78890			0.491227			0.245614	+	0.969368i	$0.421011\pi$
$192$		0			0
$193$	8.21110	−	8.21110i	0.591048	−	0.591048i	−0.346866	−	0.937915i	$-0.612754\pi$
$193$	8.21110	−	8.21110i	0.591048	−	0.591048i	0.937915	+	0.346866i	$0.112754\pi$
$194$		0			0
$195$			12.0000i			0.859338i
$196$		0			0
$197$	17.6056	−	17.6056i	1.25434	−	1.25434i	0.300590	−	0.953753i	$-0.402816\pi$
$197$	17.6056	−	17.6056i	1.25434	−	1.25434i	0.953753	−	0.300590i	$-0.0971836\pi$
$198$		0			0
$199$	10.1194	+	10.1194i	0.717347	+	0.717347i	0.968061	−	0.250714i	$-0.0806653\pi$
$199$	10.1194	+	10.1194i	0.717347	+	0.717347i	−0.250714	+	0.968061i	$0.580665\pi$
$200$		0			0
$201$	21.2111	+	21.2111i	1.49612	+	1.49612i
$202$		0			0
$203$	−7.39445			−0.518989
$204$		0			0
$205$	−2.00000			−0.139686
$206$		0			0
$207$	32.7250	+	32.7250i	2.27454	+	2.27454i
$208$		0			0
$209$	−0.183346	−	0.183346i	−0.0126823	−	0.0126823i
$210$		0			0
$211$	−15.5139	+	15.5139i	−1.06802	+	1.06802i	−0.0705082	+	0.997511i	$0.522462\pi$
$211$	−15.5139	+	15.5139i	−1.06802	+	1.06802i	−0.997511	+	0.0705082i	$0.977538\pi$
$212$		0			0
$213$		−	13.3944i		−	0.917773i
$214$		0			0
$215$	−3.39445	+	3.39445i	−0.231499	+	0.231499i
$216$		0			0
$217$	19.8167			1.34524
$218$		0			0
$219$			32.2389i			2.17850i
$220$		0			0
$221$		0			0
$222$		0			0
$223$			17.8167i			1.19309i	0.802579	+	0.596546i	$0.203461\pi$
$223$			17.8167i			1.19309i	−0.802579	+	0.596546i	$0.796539\pi$
$224$		0			0
$225$	22.8167			1.52111
$226$		0			0
$227$	0.302776	−	0.302776i	0.0200959	−	0.0200959i	−0.696987	−	0.717083i	$-0.745477\pi$
$227$	0.302776	−	0.302776i	0.0200959	−	0.0200959i	0.717083	+	0.696987i	$0.245477\pi$
$228$		0			0
$229$		−	4.60555i		−	0.304343i	−0.988354	−	0.152172i	$-0.951373\pi$
$229$		−	4.60555i		−	0.304343i	0.988354	−	0.152172i	$-0.0486267\pi$
$230$		0			0
$231$	−3.21110	+	3.21110i	−0.211275	+	0.211275i
$232$		0			0
$233$	−5.60555	−	5.60555i	−0.367232	−	0.367232i	0.499235	−	0.866467i	$-0.333614\pi$
$233$	−5.60555	−	5.60555i	−0.367232	−	0.367232i	−0.866467	+	0.499235i	$0.833614\pi$
$234$		0			0
$235$	−4.00000	−	4.00000i	−0.260931	−	0.260931i
$236$		0			0
$237$	1.39445			0.0905792
$238$		0			0
$239$	−14.7889			−0.956614			−0.478307	−	0.878193i	$-0.658749\pi$
$239$	−14.7889			−0.956614			−0.478307	+	0.878193i	$0.658749\pi$
$240$		0			0
$241$	−9.00000	−	9.00000i	−0.579741	−	0.579741i	0.355091	−	0.934832i	$-0.384450\pi$
$241$	−9.00000	−	9.00000i	−0.579741	−	0.579741i	−0.934832	+	0.355091i	$0.884450\pi$
$242$		0			0
$243$	−28.1194	−	28.1194i	−1.80386	−	1.80386i
$244$		0			0
$245$	3.60555	−	3.60555i	0.230350	−	0.230350i
$246$		0			0
$247$		−	1.57779i		−	0.100393i
$248$		0			0
$249$	41.0278	−	41.0278i	2.60003	−	2.60003i
$250$		0			0
$251$	−12.0000			−0.757433			−0.378717	−	0.925513i	$-0.623635\pi$
$251$	−12.0000			−0.757433			−0.378717	+	0.925513i	$0.623635\pi$
$252$		0			0
$253$		−	2.60555i		−	0.163810i
$254$		0			0
$255$		0			0
$256$		0			0
$257$		−	19.3944i		−	1.20979i	−0.796304	−	0.604896i	$-0.793215\pi$
$257$		−	19.3944i		−	1.20979i	0.796304	−	0.604896i	$-0.206785\pi$
$258$		0			0
$259$	13.8167			0.858525
$260$		0			0
$261$	−12.2111	+	12.2111i	−0.755848	+	0.755848i
$262$		0			0
$263$		−	23.0278i		−	1.41995i	−0.704226	−	0.709976i	$-0.748706\pi$
$263$		−	23.0278i		−	1.41995i	0.704226	−	0.709976i	$-0.251294\pi$
$264$		0			0
$265$	−5.21110	+	5.21110i	−0.320115	+	0.320115i
$266$		0			0
$267$	18.0000	+	18.0000i	1.10158	+	1.10158i
$268$		0			0
$269$	−17.4222	−	17.4222i	−1.06225	−	1.06225i	−0.997929	−	0.0643214i	$-0.979512\pi$
$269$	−17.4222	−	17.4222i	−1.06225	−	1.06225i	−0.0643214	−	0.997929i	$-0.520488\pi$
$270$		0			0
$271$	1.21110			0.0735692			0.0367846	−	0.999323i	$-0.488288\pi$
$271$	1.21110			0.0735692			0.0367846	+	0.999323i	$0.488288\pi$
$272$		0			0
$273$	−27.6333			−1.67244
$274$		0			0
$275$	−0.908327	−	0.908327i	−0.0547742	−	0.0547742i
$276$		0			0
$277$	−3.60555	−	3.60555i	−0.216637	−	0.216637i	0.590443	−	0.807079i	$-0.298953\pi$
$277$	−3.60555	−	3.60555i	−0.216637	−	0.216637i	−0.807079	+	0.590443i	$0.798953\pi$
$278$		0			0
$279$	32.7250	−	32.7250i	1.95919	−	1.95919i
$280$		0			0
$281$		−	18.4222i		−	1.09898i	−0.835501	−	0.549488i	$-0.814823\pi$
$281$		−	18.4222i		−	1.09898i	0.835501	−	0.549488i	$-0.185177\pi$
$282$		0			0
$283$	−2.11943	+	2.11943i	−0.125987	+	0.125987i	−0.767289	−	0.641302i	$-0.778395\pi$
$283$	−2.11943	+	2.11943i	−0.125987	+	0.125987i	0.641302	+	0.767289i	$0.278395\pi$
$284$		0			0
$285$	2.78890			0.165200
$286$		0			0
$287$		−	4.60555i		−	0.271857i
$288$		0			0
$289$		0			0
$290$		0			0
$291$			35.0278i			2.05336i
$292$		0			0
$293$	−21.6333			−1.26383			−0.631916	−	0.775037i	$-0.717731\pi$
$293$	−21.6333			−1.26383			−0.631916	+	0.775037i	$0.717731\pi$
$294$		0			0
$295$	−8.60555	+	8.60555i	−0.501035	+	0.501035i
$296$		0			0
$297$			6.42221i			0.372654i
$298$		0			0
$299$	11.2111	−	11.2111i	0.648355	−	0.648355i
$300$		0			0
$301$	−7.81665	−	7.81665i	−0.450544	−	0.450544i
$302$		0			0
$303$	24.4222	+	24.4222i	1.40302	+	1.40302i
$304$		0			0
$305$	12.4222			0.711293
$306$		0			0
$307$	21.2111			1.21058			0.605291	−	0.796004i	$-0.293057\pi$
$307$	21.2111			1.21058			0.605291	+	0.796004i	$0.293057\pi$
$308$		0			0
$309$	−30.4222	−	30.4222i	−1.73066	−	1.73066i
$310$		0			0
$311$	−18.9083	−	18.9083i	−1.07219	−	1.07219i	−0.997183	−	0.0750101i	$-0.976101\pi$
$311$	−18.9083	−	18.9083i	−1.07219	−	1.07219i	−0.0750101	−	0.997183i	$-0.523899\pi$
$312$		0			0
$313$	−6.21110	+	6.21110i	−0.351072	+	0.351072i	−0.860508	−	0.509436i	$-0.829854\pi$
$313$	−6.21110	+	6.21110i	−0.351072	+	0.351072i	0.509436	+	0.860508i	$0.329854\pi$
$314$		0			0
$315$		−	35.0278i		−	1.97359i
$316$		0			0
$317$	−19.6056	+	19.6056i	−1.10116	+	1.10116i	−0.106886	+	0.994271i	$0.534088\pi$
$317$	−19.6056	+	19.6056i	−1.10116	+	1.10116i	−0.994271	+	0.106886i	$0.965912\pi$
$318$		0			0
$319$	0.972244			0.0544352
$320$		0			0
$321$		−	26.2389i		−	1.46451i
$322$		0			0
$323$		0			0
$324$		0			0
$325$		−	7.81665i		−	0.433590i
$326$		0			0
$327$	28.6056			1.58189
$328$		0			0
$329$	9.21110	−	9.21110i	0.507825	−	0.507825i
$330$		0			0
$331$			3.39445i			0.186576i	0.995639	+	0.0932879i	$0.0297377\pi$
$331$			3.39445i			0.186576i	−0.995639	+	0.0932879i	$0.970262\pi$
$332$		0			0
$333$	22.8167	−	22.8167i	1.25034	−	1.25034i
$334$		0			0
$335$	9.21110	+	9.21110i	0.503256	+	0.503256i
$336$		0			0
$337$	16.2111	+	16.2111i	0.883075	+	0.883075i	0.993846	−	0.110771i	$-0.0353320\pi$
$337$	16.2111	+	16.2111i	0.883075	+	0.883075i	−0.110771	+	0.993846i	$0.535332\pi$
$338$		0			0
$339$	−44.2389			−2.40273
$340$		0			0
$341$	−2.60555			−0.141099
$342$		0			0
$343$	−7.81665	−	7.81665i	−0.422060	−	0.422060i
$344$		0			0
$345$	19.8167	+	19.8167i	1.06689	+	1.06689i
$346$		0			0
$347$	5.51388	−	5.51388i	0.296000	−	0.296000i	−0.543445	−	0.839445i	$-0.682880\pi$
$347$	5.51388	−	5.51388i	0.296000	−	0.296000i	0.839445	+	0.543445i	$0.182880\pi$
$348$		0			0
$349$		−	23.6333i		−	1.26506i	−0.774535	−	0.632531i	$-0.782016\pi$
$349$		−	23.6333i		−	1.26506i	0.774535	−	0.632531i	$-0.217984\pi$
$350$		0			0
$351$	−27.6333	+	27.6333i	−1.47496	+	1.47496i
$352$		0			0
$353$	−31.2111			−1.66120			−0.830600	−	0.556870i	$-0.812002\pi$
$353$	−31.2111			−1.66120			−0.830600	+	0.556870i	$0.812002\pi$
$354$		0			0
$355$		−	5.81665i		−	0.308716i
$356$		0			0
$357$		0			0
$358$		0			0
$359$		−	16.6056i		−	0.876407i	−0.898876	−	0.438204i	$-0.855615\pi$
$359$		−	16.6056i		−	0.876407i	0.898876	−	0.438204i	$-0.144385\pi$
$360$		0			0
$361$	18.6333			0.980700
$362$		0			0
$363$	−24.9083	+	24.9083i	−1.30735	+	1.30735i
$364$		0			0
$365$			14.0000i			0.732793i
$366$		0			0
$367$	6.90833	−	6.90833i	0.360612	−	0.360612i	−0.503426	−	0.864038i	$-0.667927\pi$
$367$	6.90833	−	6.90833i	0.360612	−	0.360612i	0.864038	+	0.503426i	$0.167927\pi$
$368$		0			0
$369$	−7.60555	−	7.60555i	−0.395929	−	0.395929i
$370$		0			0
$371$	−12.0000	−	12.0000i	−0.623009	−	0.623009i
$372$		0			0
$373$	21.0278			1.08878			0.544388	−	0.838834i	$-0.316762\pi$
$373$	21.0278			1.08878			0.544388	+	0.838834i	$0.316762\pi$
$374$		0			0
$375$	36.8444			1.90264
$376$		0			0
$377$	4.18335	+	4.18335i	0.215453	+	0.215453i
$378$		0			0
$379$	20.7250	+	20.7250i	1.06457	+	1.06457i	0.997766	+	0.0668047i	$0.0212804\pi$
$379$	20.7250	+	20.7250i	1.06457	+	1.06457i	0.0668047	+	0.997766i	$0.478720\pi$
$380$		0			0
$381$	−1.39445	+	1.39445i	−0.0714398	+	0.0714398i
$382$		0			0
$383$			19.3944i			0.991010i	0.868605	+	0.495505i	$0.165017\pi$
$383$			19.3944i			0.991010i	−0.868605	+	0.495505i	$0.834983\pi$
$384$		0			0
$385$	−1.39445	+	1.39445i	−0.0710677	+	0.0710677i
$386$		0			0
$387$	−25.8167			−1.31233
$388$		0			0
$389$		−	10.1833i		−	0.516316i	−0.966103	−	0.258158i	$-0.916884\pi$
$389$		−	10.1833i		−	0.516316i	0.966103	−	0.258158i	$-0.0831155\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$			29.0278i			1.46426i
$394$		0			0
$395$	0.605551			0.0304686
$396$		0			0
$397$	9.00000	−	9.00000i	0.451697	−	0.451697i	−0.444220	−	0.895918i	$-0.646519\pi$
$397$	9.00000	−	9.00000i	0.451697	−	0.451697i	0.895918	+	0.444220i	$0.146519\pi$
$398$		0			0
$399$			6.42221i			0.321512i
$400$		0			0
$401$	7.00000	−	7.00000i	0.349563	−	0.349563i	−0.510384	−	0.859947i	$-0.670497\pi$
$401$	7.00000	−	7.00000i	0.349563	−	0.349563i	0.859947	+	0.510384i	$0.170497\pi$
$402$		0			0
$403$	−11.2111	−	11.2111i	−0.558465	−	0.558465i
$404$		0			0
$405$	−26.0278	−	26.0278i	−1.29333	−	1.29333i
$406$		0			0
$407$	−1.81665			−0.0900482
$408$		0			0
$409$	23.2111			1.14772			0.573858	−	0.818955i	$-0.305446\pi$
$409$	23.2111			1.14772			0.573858	+	0.818955i	$0.305446\pi$
$410$		0			0
$411$	−6.00000	−	6.00000i	−0.295958	−	0.295958i
$412$		0			0
$413$	−19.8167	−	19.8167i	−0.975114	−	0.975114i
$414$		0			0
$415$	17.8167	−	17.8167i	0.874585	−	0.874585i
$416$		0			0
$417$		−	1.39445i		−	0.0682864i
$418$		0			0
$419$	−2.30278	+	2.30278i	−0.112498	+	0.112498i	−0.761115	−	0.648617i	$-0.775348\pi$
$419$	−2.30278	+	2.30278i	−0.112498	+	0.112498i	0.648617	+	0.761115i	$0.275348\pi$
$420$		0			0
$421$	18.6056			0.906779			0.453390	−	0.891312i	$-0.350215\pi$
$421$	18.6056			0.906779			0.453390	+	0.891312i	$0.350215\pi$
$422$		0			0
$423$		−	30.4222i		−	1.47918i
$424$		0			0
$425$		0			0
$426$		0			0
$427$			28.6056i			1.38432i
$428$		0			0
$429$	3.63331			0.175418
$430$		0			0
$431$	1.88057	−	1.88057i	0.0905839	−	0.0905839i	−0.660363	−	0.750947i	$-0.729597\pi$
$431$	1.88057	−	1.88057i	0.0905839	−	0.0905839i	0.750947	+	0.660363i	$0.229597\pi$
$432$		0			0
$433$			15.0278i			0.722188i	0.932529	+	0.361094i	$0.117597\pi$
$433$			15.0278i			0.722188i	−0.932529	+	0.361094i	$0.882403\pi$
$434$		0			0
$435$	−7.39445	+	7.39445i	−0.354537	+	0.354537i
$436$		0			0
$437$	−2.60555	−	2.60555i	−0.124640	−	0.124640i
$438$		0			0
$439$	26.3028	+	26.3028i	1.25536	+	1.25536i	0.953282	+	0.302081i	$0.0976812\pi$
$439$	26.3028	+	26.3028i	1.25536	+	1.25536i	0.302081	+	0.953282i	$0.402319\pi$
$440$		0			0
$441$	27.4222			1.30582
$442$		0			0
$443$	−17.2111			−0.817724			−0.408862	−	0.912596i	$-0.634074\pi$
$443$	−17.2111			−0.817724			−0.408862	+	0.912596i	$0.634074\pi$
$444$		0			0
$445$	7.81665	+	7.81665i	0.370545	+	0.370545i
$446$		0			0
$447$	19.3944	+	19.3944i	0.917326	+	0.917326i
$448$		0			0
$449$	16.8167	−	16.8167i	0.793627	−	0.793627i	−0.188455	−	0.982082i	$-0.560348\pi$
$449$	16.8167	−	16.8167i	0.793627	−	0.793627i	0.982082	+	0.188455i	$0.0603479\pi$
$450$		0			0
$451$			0.605551i			0.0285143i
$452$		0			0
$453$	10.6056	−	10.6056i	0.498292	−	0.498292i
$454$		0			0
$455$	−12.0000			−0.562569
$456$		0			0
$457$			36.6056i			1.71234i	0.516698	+	0.856168i	$0.327161\pi$
$457$			36.6056i			1.71234i	−0.516698	+	0.856168i	$0.672839\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$		−	29.2111i		−	1.36050i	−0.732982	−	0.680248i	$-0.761872\pi$
$461$		−	29.2111i		−	1.36050i	0.732982	−	0.680248i	$-0.238128\pi$
$462$		0			0
$463$	−39.6333			−1.84192			−0.920958	−	0.389662i	$-0.872592\pi$
$463$	−39.6333			−1.84192			−0.920958	+	0.389662i	$0.872592\pi$
$464$		0			0
$465$	19.8167	−	19.8167i	0.918975	−	0.918975i
$466$		0			0
$467$		−	16.2389i		−	0.751445i	−0.926732	−	0.375722i	$-0.877395\pi$
$467$		−	16.2389i		−	0.751445i	0.926732	−	0.375722i	$-0.122605\pi$
$468$		0			0
$469$	−21.2111	+	21.2111i	−0.979438	+	0.979438i
$470$		0			0
$471$	−19.3944	−	19.3944i	−0.893649	−	0.893649i
$472$		0			0
$473$	1.02776	+	1.02776i	0.0472563	+	0.0472563i
$474$		0			0
$475$	−1.81665			−0.0833538
$476$		0			0
$477$	−39.6333			−1.81468
$478$		0			0
$479$	−12.3028	−	12.3028i	−0.562128	−	0.562128i	0.367783	−	0.929912i	$-0.380117\pi$
$479$	−12.3028	−	12.3028i	−0.562128	−	0.562128i	−0.929912	+	0.367783i	$0.880117\pi$
$480$		0			0
$481$	−7.81665	−	7.81665i	−0.356409	−	0.356409i
$482$		0			0
$483$	−45.6333	+	45.6333i	−2.07639	+	2.07639i
$484$		0			0
$485$			15.2111i			0.690701i
$486$		0			0
$487$	17.3305	−	17.3305i	0.785321	−	0.785321i	−0.195402	−	0.980723i	$-0.562601\pi$
$487$	17.3305	−	17.3305i	0.785321	−	0.785321i	0.980723	+	0.195402i	$0.0626011\pi$
$488$		0			0
$489$	19.8167			0.896140
$490$		0			0
$491$			9.81665i			0.443019i	0.975158	+	0.221510i	$0.0710984\pi$
$491$			9.81665i			0.443019i	−0.975158	+	0.221510i	$0.928902\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$			4.60555i			0.207004i
$496$		0			0
$497$	13.3944			0.600823
$498$		0			0
$499$	−10.3028	+	10.3028i	−0.461216	+	0.461216i	−0.899054	−	0.437838i	$-0.855744\pi$
$499$	−10.3028	+	10.3028i	−0.461216	+	0.461216i	0.437838	+	0.899054i	$0.355744\pi$
$500$		0			0
$501$		−	68.6611i		−	3.06755i
$502$		0			0
$503$	−27.5139	+	27.5139i	−1.22678	+	1.22678i	−0.261609	+	0.965174i	$0.584253\pi$
$503$	−27.5139	+	27.5139i	−1.22678	+	1.22678i	−0.965174	+	0.261609i	$0.915747\pi$
$504$		0			0
$505$	10.6056	+	10.6056i	0.471941	+	0.471941i
$506$		0			0
$507$	−14.3028	−	14.3028i	−0.635209	−	0.635209i
$508$		0			0
$509$	−3.21110			−0.142330			−0.0711648	−	0.997465i	$-0.522672\pi$
$509$	−3.21110			−0.142330			−0.0711648	+	0.997465i	$0.522672\pi$
$510$		0			0
$511$	−32.2389			−1.42616
$512$		0			0
$513$	6.42221	+	6.42221i	0.283547	+	0.283547i
$514$		0			0
$515$	−13.2111	−	13.2111i	−0.582151	−	0.582151i
$516$		0			0
$517$	−1.21110	+	1.21110i	−0.0532642	+	0.0532642i
$518$		0			0
$519$			68.2389i			2.99535i
$520$		0			0
$521$	−13.0000	+	13.0000i	−0.569540	+	0.569540i	−0.932000	−	0.362459i	$-0.881937\pi$
$521$	−13.0000	+	13.0000i	−0.569540	+	0.569540i	0.362459	+	0.932000i	$0.381937\pi$
$522$		0			0
$523$	−12.0000			−0.524723			−0.262362	−	0.964970i	$-0.584501\pi$
$523$	−12.0000			−0.524723			−0.262362	+	0.964970i	$0.584501\pi$
$524$		0			0
$525$			31.8167i			1.38859i
$526$		0			0
$527$		0			0
$528$		0			0
$529$		−	14.0278i		−	0.609902i
$530$		0			0
$531$	−65.4500			−2.84029
$532$		0			0
$533$	−2.60555	+	2.60555i	−0.112859	+	0.112859i
$534$		0			0
$535$		−	11.3944i		−	0.492625i
$536$		0			0
$537$	−34.6056	+	34.6056i	−1.49334	+	1.49334i
$538$		0			0
$539$	−1.09167	−	1.09167i	−0.0470217	−	0.0470217i
$540$		0			0
$541$	−3.00000	−	3.00000i	−0.128980	−	0.128980i	0.639670	−	0.768650i	$-0.279071\pi$
$541$	−3.00000	−	3.00000i	−0.128980	−	0.128980i	−0.768650	+	0.639670i	$0.779071\pi$
$542$		0			0
$543$	59.8722			2.56936
$544$		0			0
$545$	12.4222			0.532109
$546$		0			0
$547$	11.5139	+	11.5139i	0.492298	+	0.492298i	0.909030	−	0.416732i	$-0.136825\pi$
$547$	11.5139	+	11.5139i	0.492298	+	0.492298i	−0.416732	+	0.909030i	$0.636825\pi$
$548$		0			0
$549$	47.2389	+	47.2389i	2.01611	+	2.01611i
$550$		0			0
$551$	0.972244	−	0.972244i	0.0414190	−	0.0414190i
$552$		0			0
$553$			1.39445i			0.0592980i
$554$		0			0
$555$	13.8167	−	13.8167i	0.586484	−	0.586484i
$556$		0			0
$557$	−21.3944			−0.906512			−0.453256	−	0.891380i	$-0.649738\pi$
$557$	−21.3944			−0.906512			−0.453256	+	0.891380i	$0.649738\pi$
$558$		0			0
$559$			8.84441i			0.374079i
$560$		0			0
$561$		0			0
$562$		0			0
$563$		−	20.6056i		−	0.868420i	−0.900812	−	0.434210i	$-0.857028\pi$
$563$		−	20.6056i		−	0.868420i	0.900812	−	0.434210i	$-0.142972\pi$
$564$		0			0
$565$	−19.2111			−0.808217
$566$		0			0
$567$	59.9361	−	59.9361i	2.51708	−	2.51708i
$568$		0			0
$569$			30.4222i			1.27537i	0.770299	+	0.637683i	$0.220107\pi$
$569$			30.4222i			1.27537i	−0.770299	+	0.637683i	$0.779893\pi$
$570$		0			0
$571$	−2.30278	+	2.30278i	−0.0963682	+	0.0963682i	−0.753647	−	0.657279i	$-0.771707\pi$
$571$	−2.30278	+	2.30278i	−0.0963682	+	0.0963682i	0.657279	+	0.753647i	$0.271707\pi$
$572$		0			0
$573$	15.6333	+	15.6333i	0.653091	+	0.653091i
$574$		0			0
$575$	−12.9083	−	12.9083i	−0.538314	−	0.538314i
$576$		0			0
$577$	−31.4500			−1.30928			−0.654640	−	0.755941i	$-0.727180\pi$
$577$	−31.4500			−1.30928			−0.654640	+	0.755941i	$0.727180\pi$
$578$		0			0
$579$	37.8167			1.57161
$580$		0			0
$581$	41.0278	+	41.0278i	1.70212	+	1.70212i
$582$		0			0
$583$	1.57779	+	1.57779i	0.0653456	+	0.0653456i
$584$		0			0
$585$	−19.8167	+	19.8167i	−0.819318	+	0.819318i
$586$		0			0
$587$			4.60555i			0.190091i	0.995473	+	0.0950457i	$0.0302997\pi$
$587$			4.60555i			0.190091i	−0.995473	+	0.0950457i	$0.969700\pi$
$588$		0			0
$589$	−2.60555	+	2.60555i	−0.107360	+	0.107360i
$590$		0			0
$591$	81.0833			3.33532
$592$		0			0
$593$		−	1.57779i		−	0.0647923i	−0.999475	−	0.0323961i	$-0.989686\pi$
$593$		−	1.57779i		−	0.0647923i	0.999475	−	0.0323961i	$-0.0103138\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$			46.6056i			1.90744i
$598$		0			0
$599$	26.0555			1.06460			0.532300	−	0.846556i	$-0.321328\pi$
$599$	26.0555			1.06460			0.532300	+	0.846556i	$0.321328\pi$
$600$		0			0
$601$	4.21110	−	4.21110i	0.171774	−	0.171774i	−0.615984	−	0.787759i	$-0.711241\pi$
$601$	4.21110	−	4.21110i	0.171774	−	0.171774i	0.787759	+	0.615984i	$0.211241\pi$
$602$		0			0
$603$			70.0555i			2.85288i
$604$		0			0
$605$	−10.8167	+	10.8167i	−0.439760	+	0.439760i
$606$		0			0
$607$	−9.51388	−	9.51388i	−0.386156	−	0.386156i	0.487158	−	0.873314i	$-0.338034\pi$
$607$	−9.51388	−	9.51388i	−0.386156	−	0.386156i	−0.873314	+	0.487158i	$0.838034\pi$
$608$		0			0
$609$	−17.0278	−	17.0278i	−0.690000	−	0.690000i
$610$		0			0
$611$	−10.4222			−0.421637
$612$		0			0
$613$	40.4222			1.63264			0.816319	−	0.577602i	$-0.196011\pi$
$613$	40.4222			1.63264			0.816319	+	0.577602i	$0.196011\pi$
$614$		0			0
$615$	−4.60555	−	4.60555i	−0.185714	−	0.185714i
$616$		0			0
$617$	−1.60555	−	1.60555i	−0.0646371	−	0.0646371i	0.674049	−	0.738686i	$-0.264554\pi$
$617$	−1.60555	−	1.60555i	−0.0646371	−	0.0646371i	−0.738686	+	0.674049i	$0.764554\pi$
$618$		0			0
$619$	−14.4861	+	14.4861i	−0.582246	+	0.582246i	−0.935520	−	0.353274i	$-0.885068\pi$
$619$	−14.4861	+	14.4861i	−0.582246	+	0.582246i	0.353274	+	0.935520i	$0.385068\pi$
$620$		0			0
$621$			91.2666i			3.66240i
$622$		0			0
$623$	−18.0000	+	18.0000i	−0.721155	+	0.721155i
$624$		0			0
$625$	1.00000			0.0400000
$626$		0			0
$627$		−	0.844410i		−	0.0337225i
$628$		0			0
$629$		0			0
$630$		0			0
$631$		−	24.2389i		−	0.964934i	−0.875914	−	0.482467i	$-0.839741\pi$
$631$		−	24.2389i		−	0.964934i	0.875914	−	0.482467i	$-0.160259\pi$
$632$		0			0
$633$	−71.4500			−2.83988
$634$		0			0
$635$	−0.605551	+	0.605551i	−0.0240306	+	0.0240306i
$636$		0			0
$637$		−	9.39445i		−	0.372222i
$638$		0			0
$639$	22.1194	−	22.1194i	0.875031	−	0.875031i
$640$		0			0
$641$	−30.8167	−	30.8167i	−1.21718	−	1.21718i	−0.968614	−	0.248571i	$-0.920039\pi$
$641$	−30.8167	−	30.8167i	−1.21718	−	1.21718i	−0.248571	−	0.968614i	$-0.579961\pi$
$642$		0			0
$643$	−4.11943	−	4.11943i	−0.162454	−	0.162454i	0.621199	−	0.783653i	$-0.286646\pi$
$643$	−4.11943	−	4.11943i	−0.162454	−	0.162454i	−0.783653	+	0.621199i	$0.786646\pi$
$644$		0			0
$645$	−15.6333			−0.615561
$646$		0			0
$647$	−17.2111			−0.676638			−0.338319	−	0.941031i	$-0.609858\pi$
$647$	−17.2111			−0.676638			−0.338319	+	0.941031i	$0.609858\pi$
$648$		0			0
$649$	2.60555	+	2.60555i	0.102277	+	0.102277i
$650$		0			0
$651$	45.6333	+	45.6333i	1.78851	+	1.78851i
$652$		0			0
$653$	−24.8167	+	24.8167i	−0.971151	+	0.971151i	−0.999595	−	0.0284447i	$-0.990945\pi$
$653$	−24.8167	+	24.8167i	−0.971151	+	0.971151i	0.0284447	+	0.999595i	$0.490945\pi$
$654$		0			0
$655$			12.6056i			0.492540i
$656$		0			0
$657$	−53.2389	+	53.2389i	−2.07705	+	2.07705i
$658$		0			0
$659$	−32.0000			−1.24654			−0.623272	−	0.782006i	$-0.714197\pi$
$659$	−32.0000			−1.24654			−0.623272	+	0.782006i	$0.714197\pi$
$660$		0			0
$661$			1.21110i			0.0471064i	0.999723	+	0.0235532i	$0.00749791\pi$
$661$			1.21110i			0.0471064i	−0.999723	+	0.0235532i	$0.992502\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$			2.78890i			0.108149i
$666$		0			0
$667$	13.8167			0.534983
$668$		0			0
$669$	−41.0278	+	41.0278i	−1.58622	+	1.58622i
$670$		0			0
$671$		−	3.76114i		−	0.145197i
$672$		0			0
$673$	−5.60555	+	5.60555i	−0.216078	+	0.216078i	−0.806843	−	0.590765i	$-0.798826\pi$
$673$	−5.60555	+	5.60555i	−0.216078	+	0.216078i	0.590765	+	0.806843i	$0.298826\pi$
$674$		0			0
$675$	31.8167	+	31.8167i	1.22462	+	1.22462i
$676$		0			0
$677$	16.0278	+	16.0278i	0.615997	+	0.615997i	0.944502	−	0.328505i	$-0.106545\pi$
$677$	16.0278	+	16.0278i	0.615997	+	0.615997i	−0.328505	+	0.944502i	$0.606545\pi$
$678$		0			0
$679$	−35.0278			−1.34424
$680$		0			0
$681$	1.39445			0.0534354
$682$		0			0
$683$	0.724981	+	0.724981i	0.0277406	+	0.0277406i	0.720841	−	0.693100i	$-0.243756\pi$
$683$	0.724981	+	0.724981i	0.0277406	+	0.0277406i	−0.693100	+	0.720841i	$0.743756\pi$
$684$		0			0
$685$	−2.60555	−	2.60555i	−0.0995530	−	0.0995530i
$686$		0			0
$687$	10.6056	−	10.6056i	0.404627	−	0.404627i
$688$		0			0
$689$			13.5778i			0.517273i
$690$		0			0
$691$	5.51388	−	5.51388i	0.209758	−	0.209758i	−0.594407	−	0.804165i	$-0.702613\pi$
$691$	5.51388	−	5.51388i	0.209758	−	0.209758i	0.804165	+	0.594407i	$0.202613\pi$
$692$		0			0
$693$	−10.6056			−0.402872
$694$		0			0
$695$		−	0.605551i		−	0.0229699i
$696$		0			0
$697$		0			0
$698$		0			0
$699$		−	25.8167i		−	0.976476i
$700$		0			0
$701$	−7.81665			−0.295231			−0.147615	−	0.989045i	$-0.547160\pi$
$701$	−7.81665			−0.295231			−0.147615	+	0.989045i	$0.547160\pi$
$702$		0			0
$703$	−1.81665	+	1.81665i	−0.0685164	+	0.0685164i
$704$		0			0
$705$		−	18.4222i		−	0.693820i
$706$		0			0
$707$	−24.4222	+	24.4222i	−0.918492	+	0.918492i
$708$		0			0
$709$	−14.3944	−	14.3944i	−0.540595	−	0.540595i	0.383108	−	0.923703i	$-0.374854\pi$
$709$	−14.3944	−	14.3944i	−0.540595	−	0.540595i	−0.923703	+	0.383108i	$0.874854\pi$
$710$		0			0
$711$	2.30278	+	2.30278i	0.0863608	+	0.0863608i
$712$		0			0
$713$	−37.0278			−1.38670
$714$		0			0
$715$	1.57779			0.0590062
$716$		0			0
$717$	−34.0555	−	34.0555i	−1.27183	−	1.27183i
$718$		0			0
$719$	4.72498	+	4.72498i	0.176212	+	0.176212i	0.789702	−	0.613490i	$-0.210235\pi$
$719$	4.72498	+	4.72498i	0.176212	+	0.176212i	−0.613490	+	0.789702i	$0.710235\pi$
$720$		0			0
$721$	30.4222	−	30.4222i	1.13298	−	1.13298i
$722$		0			0
$723$		−	41.4500i		−	1.54154i
$724$		0			0
$725$	4.81665	−	4.81665i	0.178886	−	0.178886i
$726$		0			0
$727$	−6.42221			−0.238186			−0.119093	−	0.992883i	$-0.537999\pi$
$727$	−6.42221			−0.238186			−0.119093	+	0.992883i	$0.537999\pi$
$728$		0			0
$729$		−	51.4222i		−	1.90453i
$730$		0			0
$731$		0			0
$732$		0			0
$733$			46.0555i			1.70110i	0.525895	+	0.850550i	$0.323731\pi$
$733$			46.0555i			1.70110i	−0.525895	+	0.850550i	$0.676269\pi$
$734$		0			0
$735$	16.6056			0.612505
$736$		0			0
$737$	2.78890	−	2.78890i	0.102730	−	0.102730i
$738$		0			0
$739$		−	34.6611i		−	1.27503i	−0.770439	−	0.637514i	$-0.779963\pi$
$739$		−	34.6611i		−	1.27503i	0.770439	−	0.637514i	$-0.220037\pi$
$740$		0			0
$741$	3.63331	−	3.63331i	0.133473	−	0.133473i
$742$		0			0
$743$	−14.7250	−	14.7250i	−0.540207	−	0.540207i	0.383383	−	0.923590i	$-0.374759\pi$
$743$	−14.7250	−	14.7250i	−0.540207	−	0.540207i	−0.923590	+	0.383383i	$0.874759\pi$
$744$		0			0
$745$	8.42221	+	8.42221i	0.308566	+	0.308566i
$746$		0			0
$747$	135.505			4.95789
$748$		0			0
$749$	26.2389			0.958747
$750$		0			0
$751$	−1.69722	−	1.69722i	−0.0619326	−	0.0619326i	0.675462	−	0.737395i	$-0.263944\pi$
$751$	−1.69722	−	1.69722i	−0.0619326	−	0.0619326i	−0.737395	+	0.675462i	$0.763944\pi$
$752$		0			0
$753$	−27.6333	−	27.6333i	−1.00701	−	1.00701i
$754$		0			0
$755$	4.60555	−	4.60555i	0.167613	−	0.167613i
$756$		0			0
$757$		−	39.0278i		−	1.41849i	−0.704963	−	0.709244i	$-0.749036\pi$
$757$		−	39.0278i		−	1.41849i	0.704963	−	0.709244i	$-0.250964\pi$
$758$		0			0
$759$	6.00000	−	6.00000i	0.217786	−	0.217786i
$760$		0			0
$761$	−31.4500			−1.14006			−0.570030	−	0.821624i	$-0.693068\pi$
$761$	−31.4500			−1.14006			−0.570030	+	0.821624i	$0.693068\pi$
$762$		0			0
$763$			28.6056i			1.03559i
$764$		0			0
$765$		0			0
$766$		0			0
$767$			22.4222i			0.809619i
$768$		0			0
$769$	−18.6056			−0.670933			−0.335467	−	0.942052i	$-0.608894\pi$
$769$	−18.6056			−0.670933			−0.335467	+	0.942052i	$0.608894\pi$
$770$		0			0
$771$	44.6611	−	44.6611i	1.60843	−	1.60843i
$772$		0			0
$773$			28.6056i			1.02887i	0.857529	+	0.514435i	$0.171998\pi$
$773$			28.6056i			1.02887i	−0.857529	+	0.514435i	$0.828002\pi$
$774$		0			0
$775$	−12.9083	+	12.9083i	−0.463681	+	0.463681i
$776$		0			0
$777$	31.8167	+	31.8167i	1.14142	+	1.14142i
$778$		0			0
$779$	0.605551	+	0.605551i	0.0216961	+	0.0216961i
$780$		0			0
$781$	−1.76114			−0.0630186
$782$		0			0
$783$	−34.0555			−1.21704
$784$		0			0
$785$	−8.42221	−	8.42221i	−0.300601	−	0.300601i
$786$		0			0
$787$	−14.7250	−	14.7250i	−0.524889	−	0.524889i	0.394155	−	0.919044i	$-0.371037\pi$
$787$	−14.7250	−	14.7250i	−0.524889	−	0.524889i	−0.919044	+	0.394155i	$0.871037\pi$
$788$		0			0
$789$	53.0278	−	53.0278i	1.88784	−	1.88784i
$790$		0			0
$791$		−	44.2389i		−	1.57295i
$792$		0			0
$793$	16.1833	−	16.1833i	0.574687	−	0.574687i
$794$		0			0
$795$	−24.0000			−0.851192
$796$		0			0
$797$		−	3.63331i		−	0.128698i	−0.997927	−	0.0643492i	$-0.979503\pi$
$797$		−	3.63331i		−	0.128698i	0.997927	−	0.0643492i	$-0.0204971\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$			59.4500i			2.10056i
$802$		0			0
$803$	4.23886			0.149586
$804$		0			0
$805$	−19.8167	+	19.8167i	−0.698445	+	0.698445i
$806$		0			0
$807$		−	80.2389i		−	2.82454i
$808$		0			0
$809$	20.8167	−	20.8167i	0.731875	−	0.731875i	−0.239116	−	0.970991i	$-0.576858\pi$
$809$	20.8167	−	20.8167i	0.731875	−	0.731875i	0.970991	+	0.239116i	$0.0768577\pi$
$810$		0			0
$811$	−10.7250	−	10.7250i	−0.376605	−	0.376605i	0.493271	−	0.869876i	$-0.335801\pi$
$811$	−10.7250	−	10.7250i	−0.376605	−	0.376605i	−0.869876	+	0.493271i	$0.835801\pi$
$812$		0			0
$813$	2.78890	+	2.78890i	0.0978109	+	0.0978109i
$814$		0			0
$815$	8.60555			0.301439
$816$		0			0
$817$	2.05551			0.0719133
$818$		0			0
$819$	−45.6333	−	45.6333i	−1.59456	−	1.59456i
$820$		0			0
$821$	−12.8167	−	12.8167i	−0.447304	−	0.447304i	0.447153	−	0.894457i	$-0.352438\pi$
$821$	−12.8167	−	12.8167i	−0.447304	−	0.447304i	−0.894457	+	0.447153i	$0.852438\pi$
$822$		0			0
$823$	−12.9083	+	12.9083i	−0.449956	+	0.449956i	−0.895340	−	0.445384i	$-0.853067\pi$
$823$	−12.9083	+	12.9083i	−0.449956	+	0.449956i	0.445384	+	0.895340i	$0.353067\pi$
$824$		0			0
$825$		−	4.18335i		−	0.145645i
$826$		0			0
$827$	−6.30278	+	6.30278i	−0.219169	+	0.219169i	−0.808148	−	0.588979i	$-0.799530\pi$
$827$	−6.30278	+	6.30278i	−0.219169	+	0.219169i	0.588979	+	0.808148i	$0.299530\pi$
$828$		0			0
$829$	−18.8444			−0.654493			−0.327247	−	0.944939i	$-0.606121\pi$
$829$	−18.8444			−0.654493			−0.327247	+	0.944939i	$0.606121\pi$
$830$		0			0
$831$		−	16.6056i		−	0.576040i
$832$		0			0
$833$		0			0
$834$		0			0
$835$		−	29.8167i		−	1.03185i
$836$		0			0
$837$	91.2666			3.15464
$838$		0			0
$839$	14.9083	−	14.9083i	0.514693	−	0.514693i	−0.401268	−	0.915961i	$-0.631430\pi$
$839$	14.9083	−	14.9083i	0.514693	−	0.514693i	0.915961	+	0.401268i	$0.131430\pi$
$840$		0			0
$841$		−	23.8444i		−	0.822221i
$842$		0			0
$843$	42.4222	−	42.4222i	1.46110	−	1.46110i
$844$		0			0
$845$	−6.21110	−	6.21110i	−0.213668	−	0.213668i
$846$		0			0
$847$	−24.9083	−	24.9083i	−0.855860	−	0.855860i
$848$		0			0
$849$	−9.76114			−0.335001
$850$		0			0
$851$	−25.8167			−0.884983
$852$		0			0
$853$	−29.4222	−	29.4222i	−1.00740	−	1.00740i	−0.999972	−	0.00742468i	$-0.997637\pi$
$853$	−29.4222	−	29.4222i	−1.00740	−	1.00740i	−0.00742468	−	0.999972i	$-0.502363\pi$
$854$		0			0
$855$	4.60555	+	4.60555i	0.157507	+	0.157507i
$856$		0			0
$857$	18.6333	−	18.6333i	0.636502	−	0.636502i	−0.313189	−	0.949691i	$-0.601397\pi$
$857$	18.6333	−	18.6333i	0.636502	−	0.636502i	0.949691	+	0.313189i	$0.101397\pi$
$858$		0			0
$859$		−	1.81665i		−	0.0619834i	−0.999520	−	0.0309917i	$-0.990133\pi$
$859$		−	1.81665i		−	0.0619834i	0.999520	−	0.0309917i	$-0.00986655\pi$
$860$		0			0
$861$	10.6056	−	10.6056i	0.361436	−	0.361436i
$862$		0			0
$863$	−52.4777			−1.78636			−0.893181	−	0.449697i	$-0.851532\pi$
$863$	−52.4777			−1.78636			−0.893181	+	0.449697i	$0.851532\pi$
$864$		0			0
$865$			29.6333i			1.00756i
$866$		0			0
$867$		0			0
$868$		0			0
$869$		−	0.183346i		−	0.00621959i
$870$		0			0
$871$	24.0000			0.813209
$872$		0			0
$873$	−57.8444	+	57.8444i	−1.95774	+	1.95774i
$874$		0			0
$875$			36.8444i			1.24557i
$876$		0			0
$877$	−1.78890	+	1.78890i	−0.0604068	+	0.0604068i	−0.736665	−	0.676258i	$-0.763600\pi$
$877$	−1.78890	+	1.78890i	−0.0604068	+	0.0604068i	0.676258	+	0.736665i	$0.263600\pi$
$878$		0			0
$879$	−49.8167	−	49.8167i	−1.68027	−	1.68027i
$880$		0			0
$881$	24.2111	+	24.2111i	0.815693	+	0.815693i	0.985481	−	0.169788i	$-0.0543083\pi$
$881$	24.2111	+	24.2111i	0.815693	+	0.815693i	−0.169788	+	0.985481i	$0.554308\pi$
$882$		0			0
$883$	25.5778			0.860761			0.430381	−	0.902647i	$-0.358379\pi$
$883$	25.5778			0.860761			0.430381	+	0.902647i	$0.358379\pi$
$884$		0			0
$885$	−39.6333			−1.33226
$886$		0			0
$887$	11.6972	+	11.6972i	0.392754	+	0.392754i	0.875668	−	0.482914i	$-0.160421\pi$
$887$	11.6972	+	11.6972i	0.392754	+	0.392754i	−0.482914	+	0.875668i	$0.660421\pi$
$888$		0			0
$889$	−1.39445	−	1.39445i	−0.0467683	−	0.0467683i
$890$		0			0
$891$	−7.88057	+	7.88057i	−0.264009	+	0.264009i
$892$		0			0
$893$			2.42221i			0.0810560i
$894$		0			0
$895$	−15.0278	+	15.0278i	−0.502322	+	0.502322i
$896$		0			0
$897$	51.6333			1.72399
$898$		0			0
$899$		−	13.8167i		−	0.460811i
$900$		0			0
$901$		0			0
$902$		0			0
$903$		−	36.0000i		−	1.19800i
$904$		0			0
$905$	26.0000			0.864269
$906$		0			0
$907$	−24.5416	+	24.5416i	−0.814892	+	0.814892i	−0.985363	−	0.170471i	$-0.945471\pi$
$907$	−24.5416	+	24.5416i	−0.814892	+	0.814892i	0.170471	+	0.985363i	$0.445471\pi$
$908$		0			0
$909$			80.6611i			2.67536i
$910$		0			0
$911$	−4.72498	+	4.72498i	−0.156546	+	0.156546i	−0.781034	−	0.624488i	$-0.785307\pi$
$911$	−4.72498	+	4.72498i	−0.156546	+	0.156546i	0.624488	+	0.781034i	$0.285307\pi$
$912$		0			0
$913$	−5.39445	−	5.39445i	−0.178530	−	0.178530i
$914$		0			0
$915$	28.6056	+	28.6056i	0.945670	+	0.945670i
$916$		0			0
$917$	−29.0278			−0.958581
$918$		0			0
$919$	40.8444			1.34733			0.673666	−	0.739036i	$-0.264718\pi$
$919$	40.8444			1.34733			0.673666	+	0.739036i	$0.264718\pi$
$920$		0			0
$921$	48.8444	+	48.8444i	1.60948	+	1.60948i
$922$		0			0
$923$	−7.57779	−	7.57779i	−0.249426	−	0.249426i
$924$		0			0
$925$	−9.00000	+	9.00000i	−0.295918	+	0.295918i
$926$		0			0
$927$		−	100.478i		−	3.30012i
$928$		0			0
$929$	−1.00000	+	1.00000i	−0.0328089	+	0.0328089i	−0.723321	−	0.690512i	$-0.757385\pi$
$929$	−1.00000	+	1.00000i	−0.0328089	+	0.0328089i	0.690512	+	0.723321i	$0.257385\pi$
$930$		0			0
$931$	−2.18335			−0.0715563
$932$		0			0
$933$		−	87.0833i		−	2.85098i
$934$		0			0
$935$		0			0
$936$		0			0
$937$		−	6.42221i		−	0.209804i	−0.994483	−	0.104902i	$-0.966547\pi$
$937$		−	6.42221i		−	0.209804i	0.994483	−	0.104902i	$-0.0334529\pi$
$938$		0			0
$939$	−28.6056			−0.933507
$940$		0			0
$941$	16.0278	−	16.0278i	0.522490	−	0.522490i	−0.395833	−	0.918323i	$-0.629544\pi$
$941$	16.0278	−	16.0278i	0.522490	−	0.522490i	0.918323	+	0.395833i	$0.129544\pi$
$942$		0			0
$943$			8.60555i			0.280235i
$944$		0			0
$945$	48.8444	−	48.8444i	1.58891	−	1.58891i
$946$		0			0
$947$	9.27502	+	9.27502i	0.301398	+	0.301398i	0.841560	−	0.540163i	$-0.181637\pi$
$947$	9.27502	+	9.27502i	0.301398	+	0.301398i	−0.540163	+	0.841560i	$0.681637\pi$
$948$		0			0
$949$	18.2389	+	18.2389i	0.592058	+	0.592058i
$950$		0			0
$951$	−90.2944			−2.92800
$952$		0			0
$953$	50.2389			1.62740			0.813698	−	0.581288i	$-0.197451\pi$
$953$	50.2389			1.62740			0.813698	+	0.581288i	$0.197451\pi$
$954$		0			0
$955$	6.78890	+	6.78890i	0.219684	+	0.219684i
$956$		0			0
$957$	2.23886	+	2.23886i	0.0723720	+	0.0723720i
$958$		0			0
$959$	6.00000	−	6.00000i	0.193750	−	0.193750i
$960$		0			0
$961$			6.02776i			0.194444i
$962$		0			0
$963$	43.3305	−	43.3305i	1.39631	−	1.39631i
$964$		0			0
$965$	16.4222			0.528649
$966$		0			0
$967$		−	21.8167i		−	0.701576i	−0.936455	−	0.350788i	$-0.885914\pi$
$967$		−	21.8167i		−	0.701576i	0.936455	−	0.350788i	$-0.114086\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$		−	55.0278i		−	1.76592i	−0.469444	−	0.882962i	$-0.655546\pi$
$971$		−	55.0278i		−	1.76592i	0.469444	−	0.882962i	$-0.344454\pi$
$972$		0			0
$973$	1.39445			0.0447040
$974$		0			0
$975$	18.0000	−	18.0000i	0.576461	−	0.576461i
$976$		0			0
$977$		−	16.8444i		−	0.538900i	−0.963014	−	0.269450i	$-0.913158\pi$
$977$		−	16.8444i		−	0.538900i	0.963014	−	0.269450i	$-0.0868420\pi$
$978$		0			0
$979$	2.36669	−	2.36669i	0.0756398	−	0.0756398i
$980$		0			0
$981$	47.2389	+	47.2389i	1.50822	+	1.50822i
$982$		0			0
$983$	−8.11943	−	8.11943i	−0.258970	−	0.258970i	0.565665	−	0.824635i	$-0.308619\pi$
$983$	−8.11943	−	8.11943i	−0.258970	−	0.258970i	−0.824635	+	0.565665i	$0.808619\pi$
$984$		0			0
$985$	35.2111			1.12192
$986$		0			0
$987$	42.4222			1.35031
$988$		0			0
$989$	14.6056	+	14.6056i	0.464430	+	0.464430i
$990$		0			0
$991$	23.5139	+	23.5139i	0.746943	+	0.746943i	0.973904	−	0.226961i	$-0.0728790\pi$
$991$	23.5139	+	23.5139i	0.746943	+	0.746943i	−0.226961	+	0.973904i	$0.572879\pi$
$992$		0			0
$993$	−7.81665	+	7.81665i	−0.248054	+	0.248054i
$994$		0			0
$995$			20.2389i			0.641615i
$996$		0			0
$997$	−39.2389	+	39.2389i	−1.24271	+	1.24271i	−0.283834	+	0.958874i	$0.591606\pi$
$997$	−39.2389	+	39.2389i	−1.24271	+	1.24271i	−0.958874	+	0.283834i	$0.908394\pi$
$998$		0			0
$999$	63.6333			2.01327

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1156.2.e.c.829.2		4
17.2	even	8		1156.2.a.h.1.4		4
17.3	odd	16		1156.2.h.e.1001.4		16
17.4	even	4	inner	1156.2.e.c.905.2		4
17.5	odd	16		1156.2.h.e.733.1		16
17.6	odd	16		1156.2.h.e.757.4		16
17.7	odd	16		1156.2.h.e.977.4		16
17.8	even	8		1156.2.b.a.577.1		4
17.9	even	8		1156.2.b.a.577.4		4
17.10	odd	16		1156.2.h.e.977.1		16
17.11	odd	16		1156.2.h.e.757.1		16
17.12	odd	16		1156.2.h.e.733.4		16
17.13	even	4		68.2.e.a.21.1	yes	4
17.14	odd	16		1156.2.h.e.1001.1		16
17.15	even	8		1156.2.a.h.1.1		4
17.16	even	2		68.2.e.a.13.1	✓	4
51.47	odd	4		612.2.k.e.361.2		4
51.50	odd	2		612.2.k.e.217.2		4
68.15	odd	8		4624.2.a.bq.1.4		4
68.19	odd	8		4624.2.a.bq.1.1		4
68.47	odd	4		272.2.o.g.225.2		4
68.67	odd	2		272.2.o.g.81.2		4
85.13	odd	4		1700.2.m.a.1449.1		4
85.33	odd	4		1700.2.m.b.149.2		4
85.47	odd	4		1700.2.m.b.1449.2		4
85.64	even	4		1700.2.o.c.701.2		4
85.67	odd	4		1700.2.m.a.149.1		4
85.84	even	2		1700.2.o.c.1101.2		4
136.13	even	4		1088.2.o.t.769.2		4
136.67	odd	2		1088.2.o.s.897.1		4
136.101	even	2		1088.2.o.t.897.2		4
136.115	odd	4		1088.2.o.s.769.1		4
204.47	even	4		2448.2.be.u.1585.1		4
204.203	even	2		2448.2.be.u.1441.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
68.2.e.a.13.1	✓	4	17.16	even	2
68.2.e.a.21.1	yes	4	17.13	even	4
272.2.o.g.81.2		4	68.67	odd	2
272.2.o.g.225.2		4	68.47	odd	4
612.2.k.e.217.2		4	51.50	odd	2
612.2.k.e.361.2		4	51.47	odd	4
1088.2.o.s.769.1		4	136.115	odd	4
1088.2.o.s.897.1		4	136.67	odd	2
1088.2.o.t.769.2		4	136.13	even	4
1088.2.o.t.897.2		4	136.101	even	2
1156.2.a.h.1.1		4	17.15	even	8
1156.2.a.h.1.4		4	17.2	even	8
1156.2.b.a.577.1		4	17.8	even	8
1156.2.b.a.577.4		4	17.9	even	8
1156.2.e.c.829.2		4	1.1	even	1	trivial
1156.2.e.c.905.2		4	17.4	even	4	inner
1156.2.h.e.733.1		16	17.5	odd	16
1156.2.h.e.733.4		16	17.12	odd	16
1156.2.h.e.757.1		16	17.11	odd	16
1156.2.h.e.757.4		16	17.6	odd	16
1156.2.h.e.977.1		16	17.10	odd	16
1156.2.h.e.977.4		16	17.7	odd	16
1156.2.h.e.1001.1		16	17.14	odd	16
1156.2.h.e.1001.4		16	17.3	odd	16
1700.2.m.a.149.1		4	85.67	odd	4
1700.2.m.a.1449.1		4	85.13	odd	4
1700.2.m.b.149.2		4	85.33	odd	4
1700.2.m.b.1449.2		4	85.47	odd	4
1700.2.o.c.701.2		4	85.64	even	4
1700.2.o.c.1101.2		4	85.84	even	2
2448.2.be.u.1441.1		4	204.203	even	2
2448.2.be.u.1585.1		4	204.47	even	4
4624.2.a.bq.1.1		4	68.19	odd	8
4624.2.a.bq.1.4		4	68.15	odd	8

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:	\( N \)	\(=\)	\( 1156 = 2^{2} \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1156.e (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.30278 + 2.30278i) q^{3} +(1.00000 + 1.00000i) q^{5} +(-2.30278 + 2.30278i) q^{7} +7.60555i q^{9} +O(q^{10})\)	\(q+(2.30278 + 2.30278i) q^{3} +(1.00000 + 1.00000i) q^{5} +(-2.30278 + 2.30278i) q^{7} +7.60555i q^{9} +(0.302776 - 0.302776i) q^{11} +2.60555 q^{13} +4.60555i q^{15} -0.605551i q^{19} -10.6056 q^{21} +(4.30278 - 4.30278i) q^{23} -3.00000i q^{25} +(-10.6056 + 10.6056i) q^{27} +(1.60555 + 1.60555i) q^{29} +(-4.30278 - 4.30278i) q^{31} +1.39445 q^{33} -4.60555 q^{35} +(-3.00000 - 3.00000i) q^{37} +(6.00000 + 6.00000i) q^{39} +(-1.00000 + 1.00000i) q^{41} +3.39445i q^{43} +(-7.60555 + 7.60555i) q^{45} -4.00000 q^{47} -3.60555i q^{49} +5.21110i q^{53} +0.605551 q^{55} +(1.39445 - 1.39445i) q^{57} +8.60555i q^{59} +(6.21110 - 6.21110i) q^{61} +(-17.5139 - 17.5139i) q^{63} +(2.60555 + 2.60555i) q^{65} +9.21110 q^{67} +19.8167 q^{69} +(-2.90833 - 2.90833i) q^{71} +(7.00000 + 7.00000i) q^{73} +(6.90833 - 6.90833i) q^{75} +1.39445i q^{77} +(0.302776 - 0.302776i) q^{79} -26.0278 q^{81} -17.8167i q^{83} +7.39445i q^{87} +7.81665 q^{89} +(-6.00000 + 6.00000i) q^{91} -19.8167i q^{93} +(0.605551 - 0.605551i) q^{95} +(7.60555 + 7.60555i) q^{97} +(2.30278 + 2.30278i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} + 4 q^{5} - 2 q^{7}+O(q^{10}) \) 4 * q + 2 * q^3 + 4 * q^5 - 2 * q^7	\( 4 q + 2 q^{3} + 4 q^{5} - 2 q^{7} - 6 q^{11} - 4 q^{13} - 28 q^{21} + 10 q^{23} - 28 q^{27} - 8 q^{29} - 10 q^{31} + 20 q^{33} - 4 q^{35} - 12 q^{37} + 24 q^{39} - 4 q^{41} - 16 q^{45} - 16 q^{47} - 12 q^{55} + 20 q^{57} - 4 q^{61} - 34 q^{63} - 4 q^{65} + 8 q^{67} + 36 q^{69} + 10 q^{71} + 28 q^{73} + 6 q^{75} - 6 q^{79} - 32 q^{81} - 12 q^{89} - 24 q^{91} - 12 q^{95} + 16 q^{97} + 2 q^{99}+O(q^{100}) \) 4 * q + 2 * q^3 + 4 * q^5 - 2 * q^7 - 6 * q^11 - 4 * q^13 - 28 * q^21 + 10 * q^23 - 28 * q^27 - 8 * q^29 - 10 * q^31 + 20 * q^33 - 4 * q^35 - 12 * q^37 + 24 * q^39 - 4 * q^41 - 16 * q^45 - 16 * q^47 - 12 * q^55 + 20 * q^57 - 4 * q^61 - 34 * q^63 - 4 * q^65 + 8 * q^67 + 36 * q^69 + 10 * q^71 + 28 * q^73 + 6 * q^75 - 6 * q^79 - 32 * q^81 - 12 * q^89 - 24 * q^91 - 12 * q^95 + 16 * q^97 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more