LMFDB - Embedded newform 1568.2.q.g.815.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1568,2,Mod(815,1568)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1568, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1568.815");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1568 = 2^{5} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1568.q (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$12.5205430369$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.144054149089536.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3x^{11} + x^{9} + 48x^{8} - 189x^{7} + 431x^{6} - 654x^{5} + 624x^{4} - 340x^{3} + 96x^{2} - 12x + 4 $ x^12 - 3x^11 + x^9 + 48x^8 - 189x^7 + 431x^6 - 654x^5 + 624x^4 - 340x^3 + 96x^2 - 12*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{23}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 56)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			815.1
Root			$1.09935 - 0.468876i$ of defining polynomial
Character	$\chi$	$=$	1568.815
Dual form			1568.2.q.g.1391.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.27230 - 1.31191i) q^{3} +(-1.03926 - 1.80005i) q^{5} +(1.94224 + 3.36406i) q^{9} +(0.669938 - 1.16037i) q^{11} +2.50406 q^{13} +5.45368i q^{15} +(2.78212 + 1.60626i) q^{17} +(3.55442 - 2.05215i) q^{19} +(5.54952 - 3.20402i) q^{23} +(0.339877 - 0.588684i) q^{25} -2.32073i q^{27} +4.66151i q^{29} +(2.21897 - 3.84337i) q^{31} +(-3.04461 + 1.75780i) q^{33} +(5.50178 - 3.17646i) q^{37} +(-5.68997 - 3.28511i) q^{39} +5.55076i q^{41} +(4.03699 - 6.99227i) q^{45} +(-0.565988 - 0.980320i) q^{47} +(-4.21455 - 7.29981i) q^{51} +(-7.43567 - 4.29299i) q^{53} -2.78496 q^{55} -10.7690 q^{57} +(6.29193 + 3.63265i) q^{59} +(-2.57219 - 4.45517i) q^{61} +(-2.60236 - 4.50743i) q^{65} +(-3.93243 + 6.81116i) q^{67} -16.8136 q^{69} -5.29150i q^{71} +(-0.480369 - 0.277341i) q^{73} +(-1.54461 + 0.891779i) q^{75} +(-5.26862 + 3.04184i) q^{79} +(2.78212 - 4.81877i) q^{81} +0.503175i q^{83} -6.67728i q^{85} +(6.11551 - 10.5924i) q^{87} +(-1.50000 + 0.866025i) q^{89} +(-10.0844 + 5.82221i) q^{93} +(-7.38794 - 4.26543i) q^{95} -17.2234i q^{97} +5.20473 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{3} + 6 q^{11} + 6 q^{17} - 6 q^{19} + 6 q^{33} - 6 q^{51} - 36 q^{57} + 42 q^{59} - 12 q^{65} - 30 q^{67} - 18 q^{73} + 24 q^{75} + 6 q^{81} - 18 q^{89} + 24 q^{99}+O(q^{100}) $ 12 * q - 6 * q^3 + 6 * q^11 + 6 * q^17 - 6 * q^19 + 6 * q^33 - 6 * q^51 - 36 * q^57 + 42 * q^59 - 12 * q^65 - 30 * q^67 - 18 * q^73 + 24 * q^75 + 6 * q^81 - 18 * q^89 + 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1568\mathbb{Z}\right)^\times$.

$n$	$197$	$1471$	$1473$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−2.27230	−	1.31191i	−1.31191	−	0.757434i	−0.329502	−	0.944155i	$-0.606881\pi$
$3$	−2.27230	−	1.31191i	−1.31191	−	0.757434i	−0.982413	+	0.186720i	$0.940214\pi$
$4$		0			0
$5$	−1.03926	−	1.80005i	−0.464771	−	0.805007i	0.534420	−	0.845219i	$-0.320530\pi$
$5$	−1.03926	−	1.80005i	−0.464771	−	0.805007i	−0.999191	+	0.0402117i	$0.987197\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	1.94224	+	3.36406i	0.647414	+	1.12135i
$10$		0			0
$11$	0.669938	−	1.16037i	0.201994	−	0.349864i	−0.747177	−	0.664625i	$-0.768591\pi$
$11$	0.669938	−	1.16037i	0.201994	−	0.349864i	0.949171	+	0.314761i	$0.101925\pi$
$12$		0			0
$13$	2.50406			0.694500			0.347250	−	0.937773i	$-0.387116\pi$
$13$	2.50406			0.694500			0.347250	+	0.937773i	$0.387116\pi$
$14$		0			0
$15$			5.45368i			1.40814i
$16$		0			0
$17$	2.78212	+	1.60626i	0.674763	+	0.389575i	0.797879	−	0.602818i	$-0.205955\pi$
$17$	2.78212	+	1.60626i	0.674763	+	0.389575i	−0.123116	+	0.992392i	$0.539289\pi$
$18$		0			0
$19$	3.55442	−	2.05215i	0.815440	−	0.470795i	−0.0334012	−	0.999442i	$-0.510634\pi$
$19$	3.55442	−	2.05215i	0.815440	−	0.470795i	0.848842	+	0.528647i	$0.177301\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	5.54952	−	3.20402i	1.15716	−	0.668084i	0.206535	−	0.978439i	$-0.433781\pi$
$23$	5.54952	−	3.20402i	1.15716	−	0.668084i	0.950621	+	0.310355i	$0.100448\pi$
$24$		0			0
$25$	0.339877	−	0.588684i	0.0679754	−	0.117737i
$26$		0			0
$27$		−	2.32073i		−	0.446626i
$28$		0			0
$29$			4.66151i			0.865621i	0.901485	+	0.432811i	$0.142478\pi$
$29$			4.66151i			0.865621i	−0.901485	+	0.432811i	$0.857522\pi$
$30$		0			0
$31$	2.21897	−	3.84337i	0.398539	−	0.690290i	−0.595007	−	0.803721i	$-0.702851\pi$
$31$	2.21897	−	3.84337i	0.398539	−	0.690290i	0.993546	+	0.113430i	$0.0361839\pi$
$32$		0			0
$33$	−3.04461	+	1.75780i	−0.529998	+	0.305994i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	5.50178	−	3.17646i	0.904488	−	0.522206i	0.0258343	−	0.999666i	$-0.491776\pi$
$37$	5.50178	−	3.17646i	0.904488	−	0.522206i	0.878653	+	0.477460i	$0.158442\pi$
$38$		0			0
$39$	−5.68997	−	3.28511i	−0.911125	−	0.526038i
$40$		0			0
$41$			5.55076i			0.866882i	0.901182	+	0.433441i	$0.142701\pi$
$41$			5.55076i			0.866882i	−0.901182	+	0.433441i	$0.857299\pi$
$42$		0			0
$43$		0			0			−	1.00000i	$-0.5\pi$
$43$		0			0				1.00000i	$0.5\pi$
$44$		0			0
$45$	4.03699	−	6.99227i	0.601799	−	1.04235i
$46$		0			0
$47$	−0.565988	−	0.980320i	−0.0825579	−	0.142994i	0.821790	−	0.569790i	$-0.192976\pi$
$47$	−0.565988	−	0.980320i	−0.0825579	−	0.142994i	−0.904348	+	0.426796i	$0.859642\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−4.21455	−	7.29981i	−0.590154	−	1.02218i
$52$		0			0
$53$	−7.43567	−	4.29299i	−1.02137	−	0.589687i	−0.106868	−	0.994273i	$-0.534082\pi$
$53$	−7.43567	−	4.29299i	−1.02137	−	0.589687i	−0.914500	+	0.404586i	$0.867416\pi$
$54$		0			0
$55$	−2.78496			−0.375524
$56$		0			0
$57$	−10.7690			−1.42638
$58$		0			0
$59$	6.29193	+	3.63265i	0.819140	+	0.472931i	0.850120	−	0.526589i	$-0.176529\pi$
$59$	6.29193	+	3.63265i	0.819140	+	0.472931i	−0.0309798	+	0.999520i	$0.509863\pi$
$60$		0			0
$61$	−2.57219	−	4.45517i	−0.329336	−	0.570426i	0.653045	−	0.757319i	$-0.273491\pi$
$61$	−2.57219	−	4.45517i	−0.329336	−	0.570426i	−0.982380	+	0.186893i	$0.940158\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−2.60236	−	4.50743i	−0.322784	−	0.559078i
$66$		0			0
$67$	−3.93243	+	6.81116i	−0.480422	+	0.832116i	−0.999748	−	0.0224607i	$-0.992850\pi$
$67$	−3.93243	+	6.81116i	−0.480422	+	0.832116i	0.519325	+	0.854577i	$0.326183\pi$
$68$		0			0
$69$	−16.8136			−2.02412
$70$		0			0
$71$		−	5.29150i		−	0.627986i	−0.949425	−	0.313993i	$-0.898333\pi$
$71$		−	5.29150i		−	0.627986i	0.949425	−	0.313993i	$-0.101667\pi$
$72$		0			0
$73$	−0.480369	−	0.277341i	−0.0562230	−	0.0324604i	0.471625	−	0.881799i	$-0.343668\pi$
$73$	−0.480369	−	0.277341i	−0.0562230	−	0.0324604i	−0.527848	+	0.849339i	$0.677001\pi$
$74$		0			0
$75$	−1.54461	+	0.891779i	−0.178356	+	0.102974i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−5.26862	+	3.04184i	−0.592766	+	0.342233i	−0.766190	−	0.642614i	$-0.777850\pi$
$79$	−5.26862	+	3.04184i	−0.592766	+	0.342233i	0.173425	+	0.984847i	$0.444517\pi$
$80$		0			0
$81$	2.78212	−	4.81877i	0.309124	−	0.535419i
$82$		0			0
$83$			0.503175i			0.0552307i	0.999619	+	0.0276153i	$0.00879135\pi$
$83$			0.503175i			0.0552307i	−0.999619	+	0.0276153i	$0.991209\pi$
$84$		0			0
$85$		−	6.67728i		−	0.724252i
$86$		0			0
$87$	6.11551	−	10.5924i	0.655651	−	1.13562i
$88$		0			0
$89$	−1.50000	+	0.866025i	−0.159000	+	0.0917985i	−0.577389	−	0.816469i	$-0.695928\pi$
$89$	−1.50000	+	0.866025i	−0.159000	+	0.0917985i	0.418389	+	0.908268i	$0.362595\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−10.0844	+	5.82221i	−1.04570	+	0.603735i
$94$		0			0
$95$	−7.38794	−	4.26543i	−0.757986	−	0.437624i
$96$		0			0
$97$		−	17.2234i		−	1.74878i	−0.485228	−	0.874388i	$-0.661263\pi$
$97$		−	17.2234i		−	1.74878i	0.485228	−	0.874388i	$-0.338737\pi$
$98$		0			0
$99$	5.20473			0.523095
$100$		0			0
$101$	0.613725	−	1.06300i	0.0610679	−	0.105773i	−0.833875	−	0.551953i	$-0.813883\pi$
$101$	0.613725	−	1.06300i	0.0610679	−	0.105773i	0.894943	+	0.446180i	$0.147216\pi$
$102$		0			0
$103$	−7.62804	−	13.2122i	−0.751613	−	1.30183i	−0.947041	−	0.321114i	$-0.895943\pi$
$103$	−7.62804	−	13.2122i	−0.751613	−	1.30183i	0.195427	−	0.980718i	$-0.437391\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	5.55442	+	9.62054i	0.536966	+	0.930053i	0.999065	+	0.0432246i	$0.0137631\pi$
$107$	5.55442	+	9.62054i	0.536966	+	0.930053i	−0.462099	+	0.886828i	$0.652904\pi$
$108$		0			0
$109$	−10.9109	−	6.29938i	−1.04507	−	0.603372i	−0.123805	−	0.992307i	$-0.539510\pi$
$109$	−10.9109	−	6.29938i	−1.04507	−	0.603372i	−0.921265	+	0.388935i	$0.872843\pi$
$110$		0			0
$111$	−16.6690			−1.58215
$112$		0			0
$113$	20.0629			1.88736			0.943680	−	0.330860i	$-0.107339\pi$
$113$	20.0629			1.88736			0.943680	+	0.330860i	$0.107339\pi$
$114$		0			0
$115$	−11.5348	−	6.65961i	−1.07562	−	0.621012i
$116$		0			0
$117$	4.86348	+	8.42380i	0.449629	+	0.778780i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	4.60236	+	7.97153i	0.418397	+	0.724685i
$122$		0			0
$123$	7.28212	−	12.6130i	0.656607	−	1.13728i
$124$		0			0
$125$	−11.8055			−1.05591
$126$		0			0
$127$		−	14.6145i		−	1.29683i	−0.761287	−	0.648415i	$-0.775432\pi$
$127$		−	14.6145i		−	1.29683i	0.761287	−	0.648415i	$-0.224568\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−5.27230	+	3.04397i	−0.460643	+	0.265953i	−0.712315	−	0.701860i	$-0.752353\pi$
$131$	−5.27230	+	3.04397i	−0.460643	+	0.265953i	0.251671	+	0.967813i	$0.419020\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−4.17744	+	2.41185i	−0.359537	+	0.207579i
$136$		0			0
$137$	−6.98685	+	12.1016i	−0.596927	+	1.03391i	0.396345	+	0.918102i	$0.370278\pi$
$137$	−6.98685	+	12.1016i	−0.596927	+	1.03391i	−0.993272	+	0.115806i	$0.963055\pi$
$138$		0			0
$139$		−	0.503175i		−	0.0426788i	−0.999772	−	0.0213394i	$-0.993207\pi$
$139$		−	0.503175i		−	0.0426788i	0.999772	−	0.0213394i	$-0.00679305\pi$
$140$		0			0
$141$			2.97011i			0.250129i
$142$		0			0
$143$	1.67756	−	2.90562i	0.140285	−	0.242981i
$144$		0			0
$145$	8.39096	−	4.84452i	0.696832	−	0.402316i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	4.77077	−	2.75440i	0.390836	−	0.225649i	−0.291686	−	0.956514i	$-0.594216\pi$
$149$	4.77077	−	2.75440i	0.390836	−	0.225649i	0.682522	+	0.730865i	$0.260883\pi$
$150$		0			0
$151$	−6.09511	−	3.51901i	−0.496013	−	0.286373i	0.231053	−	0.972941i	$-0.425783\pi$
$151$	−6.09511	−	3.51901i	−0.496013	−	0.286373i	−0.727066	+	0.686568i	$0.759116\pi$
$152$		0			0
$153$			12.4790i			1.00886i
$154$		0			0
$155$	−9.22436			−0.740918
$156$		0			0
$157$	7.15477	−	12.3924i	0.571013	−	0.989023i	−0.425450	−	0.904982i	$-0.639884\pi$
$157$	7.15477	−	12.3924i	0.571013	−	0.989023i	0.996462	−	0.0840409i	$-0.0267827\pi$
$158$		0			0
$159$	11.2641	+	19.5099i	0.893299	+	1.54724i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	4.15679	+	7.19977i	0.325585	+	0.563929i	0.981631	−	0.190792i	$-0.0611055\pi$
$163$	4.15679	+	7.19977i	0.325585	+	0.563929i	−0.656046	+	0.754721i	$0.727772\pi$
$164$		0			0
$165$	6.32828	+	3.65363i	0.492656	+	0.284435i
$166$		0			0
$167$	−2.50406			−0.193770			−0.0968848	−	0.995296i	$-0.530888\pi$
$167$	−2.50406			−0.193770			−0.0968848	+	0.995296i	$0.530888\pi$
$168$		0			0
$169$	−6.72971			−0.517670
$170$		0			0
$171$	13.8071	+	7.97153i	1.05585	+	0.609598i
$172$		0			0
$173$	−2.71682	−	4.70568i	−0.206556	−	0.357766i	0.744071	−	0.668100i	$-0.232892\pi$
$173$	−2.71682	−	4.70568i	−0.206556	−	0.357766i	−0.950627	+	0.310334i	$0.899559\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−9.53146	−	16.5090i	−0.716428	−	1.24089i
$178$		0			0
$179$	1.75915	−	3.04694i	0.131485	−	0.227739i	−0.792764	−	0.609529i	$-0.791359\pi$
$179$	1.75915	−	3.04694i	0.131485	−	0.227739i	0.924249	+	0.381790i	$0.124692\pi$
$180$		0			0
$181$	22.1981			1.64997			0.824985	−	0.565154i	$-0.191183\pi$
$181$	22.1981			1.64997			0.824985	+	0.565154i	$0.191183\pi$
$182$		0			0
$183$			13.4980i			0.997801i
$184$		0			0
$185$	−11.4356	−	6.60233i	−0.840760	−	0.485413i
$186$		0			0
$187$	3.72770	−	2.15219i	0.272596	−	0.157383i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	1.13615	−	0.655958i	0.0822091	−	0.0474635i	−0.458332	−	0.888781i	$-0.651553\pi$
$191$	1.13615	−	0.655958i	0.0822091	−	0.0474635i	0.540541	+	0.841318i	$0.318220\pi$
$192$		0			0
$193$	5.64697	−	9.78084i	0.406478	−	0.704040i	−0.588014	−	0.808851i	$-0.700090\pi$
$193$	5.64697	−	9.78084i	0.406478	−	0.704040i	0.994492	+	0.104810i	$0.0334235\pi$
$194$		0			0
$195$			13.6563i			0.977950i
$196$		0			0
$197$		−	5.92149i		−	0.421889i	−0.977498	−	0.210944i	$-0.932346\pi$
$197$		−	5.92149i		−	0.421889i	0.977498	−	0.210944i	$-0.0676539\pi$
$198$		0			0
$199$	−9.30560	+	16.1178i	−0.659657	+	1.14256i	0.321048	+	0.947063i	$0.395965\pi$
$199$	−9.30560	+	16.1178i	−0.659657	+	1.14256i	−0.980704	+	0.195496i	$0.937368\pi$
$200$		0			0
$201$	17.8713	−	10.3180i	1.26055	−	0.727777i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	9.99164	−	5.76868i	0.697847	−	0.402902i
$206$		0			0
$207$	21.5570	+	12.4460i	1.49832	+	0.865054i
$208$		0			0
$209$		−	5.49925i		−	0.380391i
$210$		0			0
$211$	−5.72971			−0.394449			−0.197225	−	0.980358i	$-0.563193\pi$
$211$	−5.72971			−0.394449			−0.197225	+	0.980358i	$0.563193\pi$
$212$		0			0
$213$	−6.94200	+	12.0239i	−0.475658	+	0.823864i
$214$		0			0
$215$		0			0
$216$		0			0
$217$		0			0
$218$		0			0
$219$	0.727697	+	1.26041i	0.0491732	+	0.0851704i
$220$		0			0
$221$	6.96658	+	4.02216i	0.468623	+	0.270560i
$222$		0			0
$223$	20.8668			1.39734			0.698672	−	0.715442i	$-0.253775\pi$
$223$	20.8668			1.39734			0.698672	+	0.715442i	$0.253775\pi$
$224$		0			0
$225$	2.64049			0.176033
$226$		0			0
$227$	14.2775	+	8.24309i	0.947628	+	0.547113i	0.892343	−	0.451357i	$-0.149060\pi$
$227$	14.2775	+	8.24309i	0.947628	+	0.547113i	0.0552847	+	0.998471i	$0.482393\pi$
$228$		0			0
$229$	−4.24976	−	7.36079i	−0.280832	−	0.486415i	0.690758	−	0.723086i	$-0.257277\pi$
$229$	−4.24976	−	7.36079i	−0.280832	−	0.486415i	−0.971590	+	0.236671i	$0.923944\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−2.23751	−	3.87548i	−0.146584	−	0.253891i	0.783379	−	0.621545i	$-0.213495\pi$
$233$	−2.23751	−	3.87548i	−0.146584	−	0.253891i	−0.929963	+	0.367653i	$0.880161\pi$
$234$		0			0
$235$	−1.17642	+	2.03762i	−0.0767410	+	0.132919i
$236$		0			0
$237$	15.9625			1.03688
$238$		0			0
$239$			24.5675i			1.58914i	0.607171	+	0.794571i	$0.292304\pi$
$239$			24.5675i			1.58914i	−0.607171	+	0.794571i	$0.707696\pi$
$240$		0			0
$241$	5.02498	+	2.90117i	0.323687	+	0.186881i	0.653035	−	0.757328i	$-0.273495\pi$
$241$	5.02498	+	2.90117i	0.323687	+	0.186881i	−0.329348	+	0.944209i	$0.606829\pi$
$242$		0			0
$243$	−18.6731	+	10.7809i	−1.19788	+	0.691596i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	8.90047	−	5.13869i	0.566323	−	0.326967i
$248$		0			0
$249$	0.660123	−	1.14337i	0.0418336	−	0.0724579i
$250$		0			0
$251$		−	18.8010i		−	1.18671i	−0.804942	−	0.593353i	$-0.797804\pi$
$251$		−	18.8010i		−	1.18671i	0.804942	−	0.593353i	$-0.202196\pi$
$252$		0			0
$253$		−	8.58598i		−	0.539796i
$254$		0			0
$255$	−8.76002	+	15.1728i	−0.548574	+	0.950157i
$256$		0			0
$257$	−10.9106	+	6.29923i	−0.680584	+	0.392935i	−0.800075	−	0.599900i	$-0.795207\pi$
$257$	−10.9106	+	6.29923i	−0.680584	+	0.392935i	0.119491	+	0.992835i	$0.461874\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−15.6816	+	9.05379i	−0.970668	+	0.560415i
$262$		0			0
$263$	4.27292	+	2.46697i	0.263479	+	0.152120i	0.625921	−	0.779887i	$-0.284723\pi$
$263$	4.27292	+	2.46697i	0.263479	+	0.152120i	−0.362441	+	0.932007i	$0.618057\pi$
$264$		0			0
$265$			17.8461i			1.09628i
$266$		0			0
$267$	4.54461			0.278125
$268$		0			0
$269$	−13.1502	+	22.7769i	−0.801783	+	1.38873i	0.116658	+	0.993172i	$0.462782\pi$
$269$	−13.1502	+	22.7769i	−0.801783	+	1.38873i	−0.918441	+	0.395558i	$0.870551\pi$
$270$		0			0
$271$	−14.0490	−	24.3336i	−0.853418	−	1.47816i	−0.878105	−	0.478468i	$-0.841192\pi$
$271$	−14.0490	−	24.3336i	−0.853418	−	1.47816i	0.0246868	−	0.999695i	$-0.492141\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−0.455393	−	0.788764i	−0.0274612	−	0.0475643i
$276$		0			0
$277$	23.3982	+	13.5090i	1.40586	+	0.811675i	0.994986	−	0.100017i	$-0.0318897\pi$
$277$	23.3982	+	13.5090i	1.40586	+	0.811675i	0.410876	+	0.911691i	$0.365223\pi$
$278$		0			0
$279$	17.2391			1.03208
$280$		0			0
$281$	−20.0629			−1.19685			−0.598426	−	0.801178i	$-0.704207\pi$
$281$	−20.0629			−1.19685			−0.598426	+	0.801178i	$0.704207\pi$
$282$		0			0
$283$	−4.75248	−	2.74385i	−0.282506	−	0.163105i	0.352052	−	0.935981i	$-0.385484\pi$
$283$	−4.75248	−	2.74385i	−0.282506	−	0.163105i	−0.634557	+	0.772876i	$0.718817\pi$
$284$		0			0
$285$	11.1918	+	19.3847i	0.662943	+	1.14825i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−3.33988	−	5.78484i	−0.196463	−	0.340284i
$290$		0			0
$291$	−22.5957	+	39.1369i	−1.32458	+	2.29425i
$292$		0			0
$293$	13.6931			0.799957			0.399978	−	0.916525i	$-0.369018\pi$
$293$	13.6931			0.799957			0.399978	+	0.916525i	$0.369018\pi$
$294$		0			0
$295$		−	15.1011i		−	0.879218i
$296$		0			0
$297$	−2.69291	−	1.55475i	−0.156258	−	0.0902157i
$298$		0			0
$299$	13.8963	−	8.02304i	0.803644	−	0.463984i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−2.78914	+	1.61031i	−0.160232	+	0.0925099i
$304$		0			0
$305$	−5.34636	+	9.26016i	−0.306131	+	0.530235i
$306$		0			0
$307$			24.4197i			1.39371i	0.717213	+	0.696854i	$0.245417\pi$
$307$			24.4197i			1.39371i	−0.717213	+	0.696854i	$0.754583\pi$
$308$		0			0
$309$			40.0294i			2.27719i
$310$		0			0
$311$	−8.61539	+	14.9223i	−0.488534	+	0.846165i	−0.999913	−	0.0131898i	$-0.995801\pi$
$311$	−8.61539	+	14.9223i	−0.488534	+	0.846165i	0.511379	+	0.859355i	$0.329135\pi$
$312$		0			0
$313$	−15.0446	+	8.68601i	−0.850371	+	0.490962i	−0.860776	−	0.508984i	$-0.830021\pi$
$313$	−15.0446	+	8.68601i	−0.850371	+	0.490962i	0.0104047	+	0.999946i	$0.496688\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	16.7863	−	9.69155i	0.942810	−	0.544332i	0.0519701	−	0.998649i	$-0.483450\pi$
$317$	16.7863	−	9.69155i	0.942810	−	0.544332i	0.890840	+	0.454317i	$0.150117\pi$
$318$		0			0
$319$	5.40907	+	3.12293i	0.302850	+	0.174850i
$320$		0			0
$321$		−	29.1477i		−	1.62687i
$322$		0			0
$323$	13.1851			0.733639
$324$		0			0
$325$	0.851071	−	1.47410i	0.0472089	−	0.0817682i
$326$		0			0
$327$	16.5285	+	28.6282i	0.914029	+	1.58314i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−10.4008	−	18.0147i	−0.571678	−	0.990176i	−0.996394	−	0.0848492i	$-0.972959\pi$
$331$	−10.4008	−	18.0147i	−0.571678	−	0.990176i	0.424715	−	0.905327i	$-0.360374\pi$
$332$		0			0
$333$	21.3716	+	12.3389i	1.17116	+	0.676167i
$334$		0			0
$335$	16.3473			0.893146
$336$		0			0
$337$	10.3332			0.562886			0.281443	−	0.959578i	$-0.409187\pi$
$337$	10.3332			0.562886			0.281443	+	0.959578i	$0.409187\pi$
$338$		0			0
$339$	−45.5890	−	26.3208i	−2.47606	−	1.42955i
$340$		0			0
$341$	−2.97315	−	5.14965i	−0.161005	−	0.278869i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	17.4737	+	30.2653i	0.940752	+	1.62943i
$346$		0			0
$347$	16.8169	−	29.1277i	0.902779	−	1.56366i	0.0789080	−	0.996882i	$-0.474857\pi$
$347$	16.8169	−	29.1277i	0.902779	−	1.56366i	0.823871	−	0.566777i	$-0.191810\pi$
$348$		0			0
$349$	13.3546			0.714858			0.357429	−	0.933940i	$-0.383653\pi$
$349$	13.3546			0.714858			0.357429	+	0.933940i	$0.383653\pi$
$350$		0			0
$351$		−	5.81125i		−	0.310182i
$352$		0			0
$353$	−6.80175	−	3.92699i	−0.362021	−	0.209013i	0.307946	−	0.951404i	$-0.400358\pi$
$353$	−6.80175	−	3.92699i	−0.362021	−	0.209013i	−0.669967	+	0.742391i	$0.733692\pi$
$354$		0			0
$355$	−9.52498	+	5.49925i	−0.505533	+	0.291870i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	0.140453	−	0.0810905i	0.00741282	−	0.00427979i	−0.496289	−	0.868157i	$-0.665304\pi$
$359$	0.140453	−	0.0810905i	0.00741282	−	0.00427979i	0.503702	+	0.863878i	$0.331971\pi$
$360$		0			0
$361$	−1.07739	+	1.86609i	−0.0567047	+	0.0982154i
$362$		0			0
$363$		−	24.1516i		−	1.26763i
$364$		0			0
$365$			1.15292i			0.0603466i
$366$		0			0
$367$	10.1321	−	17.5493i	0.528891	−	0.916066i	−0.470541	−	0.882378i	$-0.655941\pi$
$367$	10.1321	−	17.5493i	0.528891	−	0.916066i	0.999432	−	0.0336883i	$-0.0107254\pi$
$368$		0			0
$369$	−18.6731	+	10.7809i	−0.972082	+	0.561232i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−5.78269	+	3.33864i	−0.299416	+	0.172868i	−0.642181	−	0.766553i	$-0.721970\pi$
$373$	−5.78269	+	3.33864i	−0.299416	+	0.172868i	0.342764	+	0.939421i	$0.388637\pi$
$374$		0			0
$375$	26.8256	+	15.4878i	1.38527	+	0.799786i
$376$		0			0
$377$			11.6727i			0.601174i
$378$		0			0
$379$	4.60350			0.236466			0.118233	−	0.992986i	$-0.462277\pi$
$379$	4.60350			0.236466			0.118233	+	0.992986i	$0.462277\pi$
$380$		0			0
$381$	−19.1730	+	33.2086i	−0.982264	+	1.70133i
$382$		0			0
$383$	5.71038	+	9.89066i	0.291787	+	0.505389i	0.974232	−	0.225547i	$-0.0724170\pi$
$383$	5.71038	+	9.89066i	0.291787	+	0.505389i	−0.682446	+	0.730936i	$0.739084\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−26.0307	−	15.0288i	−1.31981	−	0.761991i	−0.336109	−	0.941823i	$-0.609111\pi$
$389$	−26.0307	−	15.0288i	−1.31981	−	0.761991i	−0.983697	+	0.179832i	$0.942445\pi$
$390$		0			0
$391$	20.5859			1.04107
$392$		0			0
$393$	15.9737			0.805766
$394$		0			0
$395$	10.9509	+	6.32252i	0.551001	+	0.318120i
$396$		0			0
$397$	2.17124	+	3.76069i	0.108971	+	0.188744i	0.915354	−	0.402651i	$-0.131911\pi$
$397$	2.17124	+	3.76069i	0.108971	+	0.188744i	−0.806383	+	0.591394i	$0.798578\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	9.98685	+	17.2977i	0.498719	+	0.863807i	0.999999	−	0.00147805i	$-0.000470479\pi$
$401$	9.98685	+	17.2977i	0.498719	+	0.863807i	−0.501279	+	0.865285i	$0.667137\pi$
$402$		0			0
$403$	5.55643	−	9.62402i	0.276786	−	0.479407i
$404$		0			0
$405$	−11.5654			−0.574688
$406$		0			0
$407$		−	8.51212i		−	0.421930i
$408$		0			0
$409$	26.4356	+	15.2626i	1.30715	+	0.754686i	0.981620	−	0.190844i	$-0.0611225\pi$
$409$	26.4356	+	15.2626i	1.30715	+	0.754686i	0.325534	+	0.945530i	$0.394456\pi$
$410$		0			0
$411$	31.7525	−	18.3323i	1.56623	−	0.904266i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	0.905741	−	0.522930i	0.0444611	−	0.0256696i
$416$		0			0
$417$	−0.660123	+	1.14337i	−0.0323264	+	0.0559909i
$418$		0			0
$419$			2.08070i			0.101649i	0.998708	+	0.0508245i	$0.0161849\pi$
$419$			2.08070i			0.101649i	−0.998708	+	0.0508245i	$0.983815\pi$
$420$		0			0
$421$		−	30.4039i		−	1.48180i	−0.671618	−	0.740898i	$-0.734400\pi$
$421$		−	30.4039i		−	1.48180i	0.671618	−	0.740898i	$-0.265600\pi$
$422$		0			0
$423$	2.19857	−	3.80804i	0.106898	−	0.185153i
$424$		0			0
$425$	1.89116	−	1.09186i	0.0917345	−	0.0529630i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−7.62386	+	4.40164i	−0.368084	+	0.212513i
$430$		0			0
$431$	−2.32280	−	1.34107i	−0.111885	−	0.0645970i	0.443013	−	0.896515i	$-0.353910\pi$
$431$	−2.32280	−	1.34107i	−0.111885	−	0.0645970i	−0.554898	+	0.831918i	$0.687243\pi$
$432$		0			0
$433$			29.4673i			1.41611i	0.706158	+	0.708054i	$0.250427\pi$
$433$			29.4673i			1.41611i	−0.706158	+	0.708054i	$0.749573\pi$
$434$		0			0
$435$	−25.4224			−1.21891
$436$		0			0
$437$	13.1502	−	22.7769i	0.629061	−	1.08957i
$438$		0			0
$439$	−3.77648	−	6.54106i	−0.180242	−	0.312188i	0.761721	−	0.647905i	$-0.224355\pi$
$439$	−3.77648	−	6.54106i	−0.180242	−	0.312188i	−0.941963	+	0.335717i	$0.891021\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−3.75915	−	6.51104i	−0.178603	−	0.309349i	0.762799	−	0.646635i	$-0.223824\pi$
$443$	−3.75915	−	6.51104i	−0.178603	−	0.309349i	−0.941402	+	0.337286i	$0.890491\pi$
$444$		0			0
$445$	3.11778	+	1.80005i	0.147797	+	0.0853306i
$446$		0			0
$447$	−14.4542			−0.683659
$448$		0			0
$449$	−14.3332			−0.676426			−0.338213	−	0.941070i	$-0.609822\pi$
$449$	−14.3332			−0.676426			−0.338213	+	0.941070i	$0.609822\pi$
$450$		0			0
$451$	6.44092	+	3.71866i	0.303291	+	0.175105i
$452$		0			0
$453$	9.23329	+	15.9925i	0.433818	+	0.751394i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−6.48037	−	11.2243i	−0.303139	−	0.525052i	0.673706	−	0.738999i	$-0.264701\pi$
$457$	−6.48037	−	11.2243i	−0.303139	−	0.525052i	−0.976845	+	0.213947i	$0.931368\pi$
$458$		0			0
$459$	3.72770	−	6.45656i	0.173994	−	0.301366i
$460$		0			0
$461$	−33.3871			−1.55499			−0.777496	−	0.628888i	$-0.783510\pi$
$461$	−33.3871			−1.55499			−0.777496	+	0.628888i	$0.783510\pi$
$462$		0			0
$463$		−	29.7739i		−	1.38371i	−0.722036	−	0.691855i	$-0.756794\pi$
$463$		−	29.7739i		−	1.38371i	0.722036	−	0.691855i	$-0.243206\pi$
$464$		0			0
$465$	20.9605	+	12.1016i	0.972022	+	0.561197i
$466$		0			0
$467$	23.5399	−	13.5908i	1.08930	−	0.628907i	0.155909	−	0.987771i	$-0.450169\pi$
$467$	23.5399	−	13.5908i	1.08930	−	0.628907i	0.933390	+	0.358865i	$0.116836\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−32.5156	+	18.7729i	−1.49824	+	0.865009i
$472$		0			0
$473$		0			0
$474$		0			0
$475$		−	2.78991i		−	0.128010i
$476$		0			0
$477$		−	33.3521i		−	1.52709i
$478$		0			0
$479$	−17.2187	+	29.8237i	−0.786744	+	1.36268i	0.141208	+	0.989980i	$0.454901\pi$
$479$	−17.2187	+	29.8237i	−0.786744	+	1.36268i	−0.927952	+	0.372700i	$0.878432\pi$
$480$		0			0
$481$	13.7768	−	7.95402i	0.628167	−	0.362672i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−31.0031	+	17.8996i	−1.40778	+	0.812781i
$486$		0			0
$487$	6.82613	+	3.94107i	0.309321	+	0.178587i	0.646623	−	0.762810i	$-0.276181\pi$
$487$	6.82613	+	3.94107i	0.309321	+	0.178587i	−0.337301	+	0.941397i	$0.609514\pi$
$488$		0			0
$489$		−	21.8134i		−	0.986436i
$490$		0			0
$491$	8.06291			0.363874			0.181937	−	0.983310i	$-0.441763\pi$
$491$	8.06291			0.363874			0.181937	+	0.983310i	$0.441763\pi$
$492$		0			0
$493$	−7.48759	+	12.9689i	−0.337224	+	0.584089i
$494$		0			0
$495$	−5.40907	−	9.36878i	−0.243120	−	0.421095i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−12.0216	−	20.8221i	−0.538163	−	0.932125i	−0.999003	−	0.0446419i	$-0.985785\pi$
$499$	−12.0216	−	20.8221i	−0.538163	−	0.932125i	0.460841	−	0.887483i	$-0.347548\pi$
$500$		0			0
$501$	5.68997	+	3.28511i	0.254209	+	0.146768i
$502$		0			0
$503$	−40.8993			−1.82361			−0.911804	−	0.410626i	$-0.865310\pi$
$503$	−40.8993			−1.82361			−0.911804	+	0.410626i	$0.865310\pi$
$504$		0			0
$505$	−2.55128			−0.113530
$506$		0			0
$507$	15.2919	+	8.82880i	0.679139	+	0.392101i
$508$		0			0
$509$	2.02661	+	3.51019i	0.0898278	+	0.155586i	0.907438	−	0.420186i	$-0.138035\pi$
$509$	2.02661	+	3.51019i	0.0898278	+	0.155586i	−0.817610	+	0.575772i	$0.804702\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−4.76249	−	8.24887i	−0.210269	−	0.364197i
$514$		0			0
$515$	−15.8550	+	27.4617i	−0.698656	+	1.21011i
$516$		0			0
$517$	−1.51671			−0.0667048
$518$		0			0
$519$			14.2570i			0.625811i
$520$		0			0
$521$	−27.1927	−	15.6997i	−1.19133	−	0.687817i	−0.232725	−	0.972543i	$-0.574764\pi$
$521$	−27.1927	−	15.6997i	−1.19133	−	0.687817i	−0.958609	+	0.284725i	$0.908098\pi$
$522$		0			0
$523$	−11.7132	+	6.76263i	−0.512183	+	0.295709i	−0.733731	−	0.679440i	$-0.762223\pi$
$523$	−11.7132	+	6.76263i	−0.512183	+	0.295709i	0.221547	+	0.975150i	$0.428889\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	12.3469	−	7.12848i	0.537839	−	0.310522i
$528$		0			0
$529$	9.03146	−	15.6429i	0.392672	−	0.680128i
$530$		0			0
$531$			28.2219i			1.22473i
$532$		0			0
$533$			13.8994i			0.602050i
$534$		0			0
$535$	11.5450	−	19.9965i	0.499133	−	0.864524i
$536$		0			0
$537$	−7.99465	+	4.61572i	−0.344995	+	0.199183i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−27.1543	+	15.6775i	−1.16745	+	0.674030i	−0.953079	−	0.302722i	$-0.902105\pi$
$541$	−27.1543	+	15.6775i	−1.16745	+	0.674030i	−0.214375	+	0.976751i	$0.568771\pi$
$542$		0			0
$543$	−50.4408	−	29.1220i	−2.16462	−	1.24974i
$544$		0			0
$545$			26.1868i			1.12172i
$546$		0			0
$547$	44.7293			1.91249			0.956244	−	0.292571i	$-0.0945108\pi$
$547$	44.7293			1.91249			0.956244	+	0.292571i	$0.0945108\pi$
$548$		0			0
$549$	9.99164	−	17.3060i	0.426433	−	0.738604i
$550$		0			0
$551$	9.56611	+	16.5690i	0.407530	+	0.705863i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	17.3234	+	30.0050i	0.735337	+	1.27364i
$556$		0			0
$557$	10.5345	+	6.08208i	0.446360	+	0.257706i	0.706292	−	0.707921i	$-0.250367\pi$
$557$	10.5345	+	6.08208i	0.446360	+	0.257706i	−0.259932	+	0.965627i	$0.583700\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	−11.2939			−0.476831
$562$		0			0
$563$	−31.4311	−	18.1468i	−1.32466	−	0.764794i	−0.340194	−	0.940355i	$-0.610493\pi$
$563$	−31.4311	−	18.1468i	−1.32466	−	0.764794i	−0.984469	+	0.175561i	$0.943826\pi$
$564$		0			0
$565$	−20.8506	−	36.1143i	−0.877191	−	1.51934i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−6.01830	−	10.4240i	−0.252300	−	0.436997i	0.711858	−	0.702323i	$-0.247854\pi$
$569$	−6.01830	−	10.4240i	−0.252300	−	0.436997i	−0.964159	+	0.265326i	$0.914520\pi$
$570$		0			0
$571$	4.10570	−	7.11128i	0.171818	−	0.297598i	−0.767237	−	0.641363i	$-0.778369\pi$
$571$	4.10570	−	7.11128i	0.171818	−	0.297598i	0.939056	+	0.343765i	$0.111702\pi$
$572$		0			0
$573$	−3.44225			−0.143802
$574$		0			0
$575$		−	4.35589i		−	0.181653i
$576$		0			0
$577$	−14.5500	−	8.40042i	−0.605722	−	0.349714i	0.165567	−	0.986199i	$-0.447055\pi$
$577$	−14.5500	−	8.40042i	−0.605722	−	0.349714i	−0.771289	+	0.636485i	$0.780388\pi$
$578$		0			0
$579$	−25.6633	+	14.8167i	−1.06653	+	0.615761i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−9.96289	+	5.75208i	−0.412621	+	0.238227i
$584$		0			0
$585$	10.1088	−	17.5090i	0.417949	−	0.723909i
$586$		0			0
$587$		−	25.4261i		−	1.04945i	−0.851273	−	0.524723i	$-0.824169\pi$
$587$		−	25.4261i		−	1.04945i	0.851273	−	0.524723i	$-0.175831\pi$
$588$		0			0
$589$		−	18.2146i		−	0.750521i
$590$		0			0
$591$	−7.76849	+	13.4554i	−0.319553	+	0.553482i
$592$		0			0
$593$	19.0694	−	11.0097i	0.783086	−	0.452115i	−0.0544368	−	0.998517i	$-0.517336\pi$
$593$	19.0694	−	11.0097i	0.783086	−	0.452115i	0.837523	+	0.546402i	$0.184003\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	42.2903	−	24.4163i	1.73083	−	0.999294i
$598$		0			0
$599$	0.500607	+	0.289026i	0.0204543	+	0.0118093i	0.510192	−	0.860060i	$-0.329574\pi$
$599$	0.500607	+	0.289026i	0.0204543	+	0.0118093i	−0.489738	+	0.871870i	$0.662908\pi$
$600$		0			0
$601$		−	27.3186i		−	1.11435i	−0.830395	−	0.557175i	$-0.811885\pi$
$601$		−	27.3186i		−	1.11435i	0.830395	−	0.557175i	$-0.188115\pi$
$602$		0			0
$603$	−30.5509			−1.24413
$604$		0			0
$605$	9.56611	−	16.5690i	0.388918	−	0.673625i
$606$		0			0
$607$	5.99963	+	10.3917i	0.243518	+	0.421785i	0.961714	−	0.274056i	$-0.0883653\pi$
$607$	5.99963	+	10.3917i	0.243518	+	0.421785i	−0.718196	+	0.695841i	$0.755032\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−1.41727	−	2.45478i	−0.0573364	−	0.0993096i
$612$		0			0
$613$	−3.96050	−	2.28659i	−0.159963	−	0.0923547i	0.417882	−	0.908501i	$-0.362773\pi$
$613$	−3.96050	−	2.28659i	−0.159963	−	0.0923547i	−0.577845	+	0.816147i	$0.696106\pi$
$614$		0			0
$615$	−30.2721			−1.22069
$616$		0			0
$617$	5.12621			0.206373			0.103187	−	0.994662i	$-0.467096\pi$
$617$	5.12621			0.206373			0.103187	+	0.994662i	$0.467096\pi$
$618$		0			0
$619$	39.5293	+	22.8222i	1.58881	+	0.917303i	0.993503	+	0.113808i	$0.0363049\pi$
$619$	39.5293	+	22.8222i	1.58881	+	0.917303i	0.595312	+	0.803495i	$0.297028\pi$
$620$		0			0
$621$	−7.43567	−	12.8790i	−0.298383	−	0.516815i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	10.5696	+	18.3071i	0.422783	+	0.732282i
$626$		0			0
$627$	−7.21455	+	12.4960i	−0.288121	+	0.499041i
$628$		0			0
$629$	20.4088			0.813753
$630$		0			0
$631$			17.1345i			0.682113i	0.940043	+	0.341057i	$0.110785\pi$
$631$			17.1345i			0.682113i	−0.940043	+	0.341057i	$0.889215\pi$
$632$		0			0
$633$	13.0196	+	7.51689i	0.517484	+	0.298769i
$634$		0			0
$635$	−26.3069	+	15.1883i	−1.04396	+	0.602729i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	17.8009	−	10.2774i	0.704194	−	0.406567i
$640$		0			0
$641$	−4.02498	+	6.97146i	−0.158977	+	0.275356i	−0.934500	−	0.355963i	$-0.884153\pi$
$641$	−4.02498	+	6.97146i	−0.158977	+	0.275356i	0.775523	+	0.631319i	$0.217486\pi$
$642$		0			0
$643$		−	22.2710i		−	0.878283i	−0.898418	−	0.439142i	$-0.855283\pi$
$643$		−	22.2710i		−	0.878283i	0.898418	−	0.439142i	$-0.144717\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	18.9125	−	32.7574i	0.743528	−	1.28783i	−0.207352	−	0.978266i	$-0.566484\pi$
$647$	18.9125	−	32.7574i	0.743528	−	1.28783i	0.950879	−	0.309561i	$-0.100182\pi$
$648$		0			0
$649$	8.43042	−	4.86730i	0.330923	−	0.191058i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	25.6130	−	14.7877i	1.00231	−	0.578686i	0.0933818	−	0.995630i	$-0.470232\pi$
$653$	25.6130	−	14.7877i	1.00231	−	0.578686i	0.908932	+	0.416944i	$0.136899\pi$
$654$		0			0
$655$	10.9586	+	6.32694i	0.428188	+	0.247214i
$656$		0			0
$657$		−	2.15466i		−	0.0840611i
$658$		0			0
$659$	−18.3961			−0.716611			−0.358305	−	0.933604i	$-0.616645\pi$
$659$	−18.3961			−0.716611			−0.358305	+	0.933604i	$0.616645\pi$
$660$		0			0
$661$	−5.92732	+	10.2664i	−0.230546	+	0.399317i	−0.957969	−	0.286872i	$-0.907385\pi$
$661$	−5.92732	+	10.2664i	−0.230546	+	0.399317i	0.727423	+	0.686189i	$0.240718\pi$
$662$		0			0
$663$	−10.5535	−	18.2791i	−0.409862	−	0.709902i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	14.9356	+	25.8692i	0.578308	+	1.00166i
$668$		0			0
$669$	−47.4157	−	27.3755i	−1.83320	−	1.05840i
$670$		0			0
$671$	−6.89285			−0.266095
$672$		0			0
$673$	10.8738			0.419154			0.209577	−	0.977792i	$-0.432791\pi$
$673$	10.8738			0.419154			0.209577	+	0.977792i	$0.432791\pi$
$674$		0			0
$675$	−1.36618	−	0.788764i	−0.0525843	−	0.0303595i
$676$		0			0
$677$	22.7163	+	39.3458i	0.873060	+	1.51218i	0.858815	+	0.512285i	$0.171201\pi$
$677$	22.7163	+	39.3458i	0.873060	+	1.51218i	0.0142443	+	0.999899i	$0.495466\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−21.6285	−	37.4616i	−0.828805	−	1.43553i
$682$		0			0
$683$	12.3693	−	21.4243i	0.473299	−	0.819778i	−0.526234	−	0.850340i	$-0.676396\pi$
$683$	12.3693	−	21.4243i	0.473299	−	0.819778i	0.999533	+	0.0305620i	$0.00972970\pi$
$684$		0			0
$685$	29.0446			1.10974
$686$		0			0
$687$			22.3013i			0.850847i
$688$		0			0
$689$	−18.6193	−	10.7499i	−0.709340	−	0.409538i
$690$		0			0
$691$	−4.10457	+	2.36977i	−0.156145	+	0.0901504i	−0.576037	−	0.817424i	$-0.695401\pi$
$691$	−4.10457	+	2.36977i	−0.156145	+	0.0901504i	0.419892	+	0.907574i	$0.362068\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−0.905741	+	0.522930i	−0.0343567	+	0.0198359i
$696$		0			0
$697$	−8.91594	+	15.4429i	−0.337715	+	0.584940i
$698$		0			0
$699$			11.7417i			0.444112i
$700$		0			0
$701$			39.8121i			1.50368i	0.659345	+	0.751840i	$0.270834\pi$
$701$			39.8121i			1.50368i	−0.659345	+	0.751840i	$0.729166\pi$
$702$		0			0
$703$	13.0371	−	22.5809i	0.491704	−	0.851656i
$704$		0			0
$705$	5.34636	−	3.08672i	0.201355	−	0.116253i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	4.97242	−	2.87083i	0.186743	−	0.107816i	−0.403714	−	0.914885i	$-0.632281\pi$
$709$	4.97242	−	2.87083i	0.186743	−	0.107816i	0.590457	+	0.807069i	$0.298948\pi$
$710$		0			0
$711$	−20.4659	−	11.8160i	−0.767529	−	0.443133i
$712$		0			0
$713$		−	28.4385i		−	1.06503i
$714$		0			0
$715$	−6.97370			−0.260801
$716$		0			0
$717$	32.2305	−	55.8249i	1.20367	−	2.08482i
$718$		0			0
$719$	−7.62804	−	13.2122i	−0.284478	−	0.492730i	0.688005	−	0.725706i	$-0.258487\pi$
$719$	−7.62804	−	13.2122i	−0.284478	−	0.492730i	−0.972482	+	0.232976i	$0.925154\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−7.61218	−	13.1847i	−0.283100	−	0.490344i
$724$		0			0
$725$	2.74416	+	1.58434i	0.101915	+	0.0588409i
$726$		0			0
$727$	40.8993			1.51687			0.758435	−	0.651749i	$-0.225964\pi$
$727$	40.8993			1.51687			0.758435	+	0.651749i	$0.225964\pi$
$728$		0			0
$729$	39.8818			1.47710
$730$		0			0
$731$		0			0
$732$		0			0
$733$	−12.2037	−	21.1374i	−0.450753	−	0.780728i	0.547680	−	0.836688i	$-0.315511\pi$
$733$	−12.2037	−	21.1374i	−0.450753	−	0.780728i	−0.998433	+	0.0559605i	$0.982178\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	5.26897	+	9.12612i	0.194085	+	0.336165i
$738$		0			0
$739$	−15.3996	+	26.6730i	−0.566485	+	0.981181i	0.430425	+	0.902626i	$0.358364\pi$
$739$	−15.3996	+	26.6730i	−0.566485	+	0.981181i	−0.996910	+	0.0785545i	$0.974970\pi$
$740$		0			0
$741$	−26.9661			−0.990624
$742$		0			0
$743$			23.9376i			0.878184i	0.898442	+	0.439092i	$0.144700\pi$
$743$			23.9376i			0.878184i	−0.898442	+	0.439092i	$0.855300\pi$
$744$		0			0
$745$	−9.91613	−	5.72508i	−0.363299	−	0.209751i
$746$		0			0
$747$	−1.69271	+	0.977288i	−0.0619331	+	0.0357571i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	11.9543	−	6.90181i	0.436218	−	0.251851i	−0.265774	−	0.964035i	$-0.585627\pi$
$751$	11.9543	−	6.90181i	0.436218	−	0.251851i	0.701992	+	0.712185i	$0.252294\pi$
$752$		0			0
$753$	−24.6653	+	42.7215i	−0.898853	+	1.55686i
$754$		0			0
$755$			14.6287i			0.532392i
$756$		0			0
$757$		−	2.14156i		−	0.0778362i	−0.999242	−	0.0389181i	$-0.987609\pi$
$757$		−	2.14156i		−	0.0778362i	0.999242	−	0.0389181i	$-0.0123911\pi$
$758$		0			0
$759$	−11.2641	+	19.5099i	−0.408860	+	0.708166i
$760$		0			0
$761$	−36.8321	+	21.2650i	−1.33516	+	0.770856i	−0.986086	−	0.166239i	$-0.946838\pi$
$761$	−36.8321	+	21.2650i	−1.33516	+	0.770856i	−0.349076	+	0.937094i	$0.613504\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	22.4628	−	12.9689i	0.812143	−	0.468891i
$766$		0			0
$767$	15.7554	+	9.09636i	0.568893	+	0.328450i
$768$		0			0
$769$			15.6459i			0.564206i	0.959384	+	0.282103i	$0.0910320\pi$
$769$			15.6459i			0.564206i	−0.959384	+	0.282103i	$0.908968\pi$
$770$		0			0
$771$	33.0562			1.19049
$772$		0			0
$773$	−15.2125	+	26.3489i	−0.547156	+	0.947703i	0.451311	+	0.892367i	$0.350956\pi$
$773$	−15.2125	+	26.3489i	−0.547156	+	0.947703i	−0.998468	+	0.0553362i	$0.982377\pi$
$774$		0			0
$775$	−1.50836	−	2.61255i	−0.0541817	−	0.0938455i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	11.3910	+	19.7297i	0.408124	+	0.706891i
$780$		0			0
$781$	−6.14009	−	3.54498i	−0.219710	−	0.126849i
$782$		0			0
$783$	10.8181			0.386609
$784$		0			0
$785$	−29.7427			−1.06156
$786$		0			0
$787$	−28.3722	−	16.3807i	−1.01136	−	0.583909i	−0.0997704	−	0.995010i	$-0.531811\pi$
$787$	−28.3722	−	16.3807i	−1.01136	−	0.583909i	−0.911590	+	0.411102i	$0.865144\pi$
$788$		0			0
$789$	−6.47291	−	11.2114i	−0.230442	−	0.399137i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−6.44092	−	11.1560i	−0.228724	−	0.396161i
$794$		0			0
$795$	23.4126	−	40.5518i	0.830359	−	1.43822i
$796$		0			0
$797$	−28.3790			−1.00523			−0.502617	−	0.864509i	$-0.667630\pi$
$797$	−28.3790			−1.00523			−0.502617	+	0.864509i	$0.667630\pi$
$798$		0			0
$799$		−	3.63649i		−	0.128650i
$800$		0			0
$801$	−5.82673	−	3.36406i	−0.205877	−	0.118863i
$802$		0			0
$803$	−0.643636	+	0.371603i	−0.0227134	+	0.0131136i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	59.7626	−	34.5040i	2.10374	−	1.21460i
$808$		0			0
$809$	4.08387	−	7.07347i	0.143581	−	0.248690i	−0.785262	−	0.619164i	$-0.787472\pi$
$809$	4.08387	−	7.07347i	0.143581	−	0.248690i	0.928843	+	0.370474i	$0.120805\pi$
$810$		0			0
$811$			22.2710i			0.782041i	0.920382	+	0.391021i	$0.127878\pi$
$811$			22.2710i			0.782041i	−0.920382	+	0.391021i	$0.872122\pi$
$812$		0			0
$813$			73.7246i			2.58563i
$814$		0			0
$815$	8.63997	−	14.9649i	0.302645	−	0.524196i
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−4.52231	+	2.61096i	−0.157830	+	0.0911230i	−0.576835	−	0.816861i	$-0.695712\pi$
$821$	−4.52231	+	2.61096i	−0.157830	+	0.0911230i	0.419005	+	0.907984i	$0.362379\pi$
$822$		0			0
$823$	−8.29368	−	4.78836i	−0.289099	−	0.166912i	0.348436	−	0.937333i	$-0.386713\pi$
$823$	−8.29368	−	4.78836i	−0.289099	−	0.166912i	−0.637536	+	0.770421i	$0.720046\pi$
$824$		0			0
$825$			2.38975i			0.0832004i
$826$		0			0
$827$	−40.6664			−1.41411			−0.707055	−	0.707159i	$-0.749977\pi$
$827$	−40.6664			−1.41411			−0.707055	+	0.707159i	$0.749977\pi$
$828$		0			0
$829$	16.6171	−	28.7816i	0.577134	−	0.999625i	−0.418672	−	0.908137i	$-0.637504\pi$
$829$	16.6171	−	28.7816i	0.577134	−	0.999625i	0.995806	−	0.0914880i	$-0.0291623\pi$
$830$		0			0
$831$	−35.4452	−	61.3929i	−1.22958	−	2.12970i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	2.60236	+	4.50743i	0.0900586	+	0.155986i
$836$		0			0
$837$	−8.91945	−	5.14965i	−0.308301	−	0.177998i
$838$		0			0
$839$	15.0243			0.518698			0.259349	−	0.965784i	$-0.416492\pi$
$839$	15.0243			0.518698			0.259349	+	0.965784i	$0.416492\pi$
$840$		0			0
$841$	7.27029			0.250700
$842$		0			0
$843$	45.5890	+	26.3208i	1.57017	+	0.906538i
$844$		0			0
$845$	6.99392	+	12.1138i	0.240598	+	0.416728i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	7.19938	+	12.4697i	0.247082	+	0.427959i
$850$		0			0
$851$	20.3548	−	35.2556i	0.697755	−	1.20855i
$852$		0			0
$853$	−12.5203			−0.428686			−0.214343	−	0.976758i	$-0.568761\pi$
$853$	−12.5203			−0.428686			−0.214343	+	0.976758i	$0.568761\pi$
$854$		0			0
$855$		−	33.1380i		−	1.13329i
$856$		0			0
$857$	46.8265	+	27.0353i	1.59956	+	0.923509i	0.991571	+	0.129566i	$0.0413585\pi$
$857$	46.8265	+	27.0353i	1.59956	+	0.923509i	0.607993	+	0.793942i	$0.291975\pi$
$858$		0			0
$859$	17.0990	−	9.87213i	0.583411	−	0.336833i	−0.179077	−	0.983835i	$-0.557311\pi$
$859$	17.0990	−	9.87213i	0.583411	−	0.336833i	0.762488	+	0.647002i	$0.223978\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−26.3755	+	15.2279i	−0.897833	+	0.518364i	−0.876497	−	0.481408i	$-0.840126\pi$
$863$	−26.3755	+	15.2279i	−0.897833	+	0.518364i	−0.0213367	+	0.999772i	$0.506792\pi$
$864$		0			0
$865$	−5.64697	+	9.78084i	−0.192003	+	0.332559i
$866$		0			0
$867$			17.5265i			0.595232i
$868$		0			0
$869$			8.15137i			0.276516i
$870$		0			0
$871$	−9.84701	+	17.0555i	−0.333653	+	0.577905i
$872$		0			0
$873$	57.9407	−	33.4521i	1.96100	−	1.13218i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−18.3275	+	10.5814i	−0.618877	+	0.357309i	−0.776432	−	0.630201i	$-0.782972\pi$
$877$	−18.3275	+	10.5814i	−0.618877	+	0.357309i	0.157555	+	0.987510i	$0.449639\pi$
$878$		0			0
$879$	−31.1148	−	17.9641i	−1.04948	−	0.605915i
$880$		0			0
$881$			11.5367i			0.388681i	0.980934	+	0.194340i	$0.0622566\pi$
$881$			11.5367i			0.388681i	−0.980934	+	0.194340i	$0.937743\pi$
$882$		0			0
$883$	−49.8555			−1.67777			−0.838886	−	0.544307i	$-0.816793\pi$
$883$	−49.8555			−1.67777			−0.838886	+	0.544307i	$0.816793\pi$
$884$		0			0
$885$	−19.8113	+	34.3142i	−0.665950	+	1.15346i
$886$		0			0
$887$	5.56575	+	9.64015i	0.186879	+	0.323685i	0.944208	−	0.329349i	$-0.106829\pi$
$887$	5.56575	+	9.64015i	0.186879	+	0.323685i	−0.757329	+	0.653034i	$0.773496\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−3.72770	−	6.45656i	−0.124883	−	0.216303i
$892$		0			0
$893$	−4.02352	−	2.32298i	−0.134642	−	0.0777356i
$894$		0			0
$895$	−7.31287			−0.244442
$896$		0			0
$897$	−42.1022			−1.40575
$898$		0			0
$899$	17.9159	+	10.3438i	0.597530	+	0.344984i
$900$		0			0
$901$	−13.7913	−	23.8872i	−0.459454	−	0.795798i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−23.0696	−	39.9577i	−0.766859	−	1.32824i
$906$		0			0
$907$	−7.20674	+	12.4824i	−0.239296	+	0.414473i	−0.960512	−	0.278237i	$-0.910250\pi$
$907$	−7.20674	+	12.4824i	−0.239296	+	0.414473i	0.721217	+	0.692710i	$0.243583\pi$
$908$		0			0
$909$	4.76801			0.158145
$910$		0			0
$911$			19.1909i			0.635823i	0.948120	+	0.317911i	$0.102981\pi$
$911$			19.1909i			0.635823i	−0.948120	+	0.317911i	$0.897019\pi$
$912$		0			0
$913$	0.583868	+	0.337096i	0.0193232	+	0.0111563i
$914$		0			0
$915$	24.2971	−	14.0279i	0.803237	−	0.463749i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−22.4285	+	12.9491i	−0.739848	+	0.427151i	−0.822014	−	0.569467i	$-0.807150\pi$
$919$	−22.4285	+	12.9491i	−0.739848	+	0.427151i	0.0821662	+	0.996619i	$0.473816\pi$
$920$		0			0
$921$	32.0366	−	55.4890i	1.05564	−	1.82843i
$922$		0			0
$923$		−	13.2502i		−	0.436136i
$924$		0			0
$925$		−	4.31842i		−	0.141989i
$926$		0			0
$927$	29.6310	−	51.3224i	0.973210	−	1.68565i
$928$		0			0
$929$	36.7480	−	21.2165i	1.20566	−	0.696090i	0.243854	−	0.969812i	$-0.421588\pi$
$929$	36.7480	−	21.2165i	1.20566	−	0.696090i	0.961809	+	0.273722i	$0.0882548\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	39.1536	−	22.6053i	1.28183	−	0.740065i
$934$		0			0
$935$	−7.74809	−	4.47336i	−0.253390	−	0.146295i
$936$		0			0
$937$		−	46.5547i		−	1.52088i	−0.649410	−	0.760439i	$-0.724984\pi$
$937$		−	46.5547i		−	1.52088i	0.649410	−	0.760439i	$-0.275016\pi$
$938$		0			0
$939$	45.5812			1.48749
$940$		0			0
$941$	1.48937	−	2.57967i	0.0485522	−	0.0840949i	−0.840728	−	0.541458i	$-0.817873\pi$
$941$	1.48937	−	2.57967i	0.0485522	−	0.0840949i	0.889280	+	0.457363i	$0.151206\pi$
$942$		0			0
$943$	17.7847	+	30.8040i	0.579150	+	1.00312i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−13.5270	−	23.4294i	−0.439568	−	0.761354i	0.558088	−	0.829782i	$-0.311535\pi$
$947$	−13.5270	−	23.4294i	−0.439568	−	0.761354i	−0.997656	+	0.0684276i	$0.978202\pi$
$948$		0			0
$949$	−1.20287	−	0.694478i	−0.0390469	−	0.0225437i
$950$		0			0
$951$	−50.8580			−1.64918
$952$		0			0
$953$	28.7293			0.930634			0.465317	−	0.885144i	$-0.345940\pi$
$953$	28.7293			0.930634			0.465317	+	0.885144i	$0.345940\pi$
$954$		0			0
$955$	−2.36152	−	1.36342i	−0.0764169	−	0.0441193i
$956$		0			0
$957$	−8.19403	−	14.1925i	−0.264875	−	0.458778i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	5.65232	+	9.79010i	0.182333	+	0.315810i
$962$		0			0
$963$	−21.5761	+	37.3708i	−0.695279	+	1.20426i
$964$		0			0
$965$	−23.4747			−0.755677
$966$		0			0
$967$		−	13.3546i		−	0.429453i	−0.976674	−	0.214727i	$-0.931114\pi$
$967$		−	13.3546i		−	0.429453i	0.976674	−	0.214727i	$-0.0688861\pi$
$968$		0			0
$969$	−29.9605	−	17.2977i	−0.962471	−	0.555683i
$970$		0			0
$971$	−1.71876	+	0.992325i	−0.0551575	+	0.0318452i	−0.527325	−	0.849664i	$-0.676805\pi$
$971$	−1.71876	+	0.992325i	−0.0551575	+	0.0318452i	0.472168	+	0.881509i	$0.343472\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−3.86778	+	2.23306i	−0.123868	+	0.0715153i
$976$		0			0
$977$	31.2242	−	54.0818i	0.998950	−	1.73023i	0.459792	−	0.888027i	$-0.347924\pi$
$977$	31.2242	−	54.0818i	0.998950	−	1.73023i	0.539158	−	0.842205i	$-0.318743\pi$
$978$		0			0
$979$			2.32073i			0.0741710i
$980$		0			0
$981$		−	48.9397i		−	1.56252i
$982$		0			0
$983$	−3.64021	+	6.30503i	−0.116105	+	0.201099i	−0.918221	−	0.396069i	$-0.870374\pi$
$983$	−3.64021	+	6.30503i	−0.116105	+	0.201099i	0.802116	+	0.597168i	$0.203707\pi$
$984$		0			0
$985$	−10.6590	+	6.15397i	−0.339624	+	0.196082i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	31.3345	+	18.0910i	0.995373	+	0.574679i	0.906876	−	0.421398i	$-0.138460\pi$
$991$	31.3345	+	18.0910i	0.995373	+	0.574679i	0.0884967	+	0.996076i	$0.471794\pi$
$992$		0			0
$993$			54.5797i			1.73204i
$994$		0			0
$995$	38.6838			1.22636
$996$		0			0
$997$	17.1218	−	29.6559i	0.542254	−	0.939211i	−0.456520	−	0.889713i	$-0.650904\pi$
$997$	17.1218	−	29.6559i	0.542254	−	0.939211i	0.998774	−	0.0494984i	$-0.0157623\pi$
$998$		0			0
$999$	−7.37171	−	12.7682i	−0.233231	−	0.403967i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1568.2.q.g.815.1		12
4.3	odd	2		392.2.m.g.227.5		12
7.2	even	3		224.2.q.a.47.5		12
7.3	odd	6		1568.2.e.e.783.1		12
7.4	even	3		1568.2.e.e.783.12		12
7.5	odd	6	inner	1568.2.q.g.1391.2		12
7.6	odd	2		224.2.q.a.143.6		12
8.3	odd	2	inner	1568.2.q.g.815.2		12
8.5	even	2		392.2.m.g.227.2		12
21.2	odd	6		2016.2.bs.a.271.5		12
21.20	even	2		2016.2.bs.a.1711.2		12
28.3	even	6		392.2.e.e.195.8		12
28.11	odd	6		392.2.e.e.195.7		12
28.19	even	6		392.2.m.g.19.1		12
28.23	odd	6		56.2.m.a.19.1	yes	12
28.27	even	2		56.2.m.a.3.5	yes	12
56.3	even	6		1568.2.e.e.783.2		12
56.5	odd	6		392.2.m.g.19.6		12
56.11	odd	6		1568.2.e.e.783.11		12
56.13	odd	2		56.2.m.a.3.2	✓	12
56.19	even	6	inner	1568.2.q.g.1391.1		12
56.27	even	2		224.2.q.a.143.5		12
56.37	even	6		56.2.m.a.19.6	yes	12
56.45	odd	6		392.2.e.e.195.6		12
56.51	odd	6		224.2.q.a.47.6		12
56.53	even	6		392.2.e.e.195.5		12
84.23	even	6		504.2.bk.a.19.6		12
84.83	odd	2		504.2.bk.a.451.2		12
168.83	odd	2		2016.2.bs.a.1711.5		12
168.107	even	6		2016.2.bs.a.271.2		12
168.125	even	2		504.2.bk.a.451.5		12
168.149	odd	6		504.2.bk.a.19.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.2.m.a.3.2	✓	12	56.13	odd	2
56.2.m.a.3.5	yes	12	28.27	even	2
56.2.m.a.19.1	yes	12	28.23	odd	6
56.2.m.a.19.6	yes	12	56.37	even	6
224.2.q.a.47.5		12	7.2	even	3
224.2.q.a.47.6		12	56.51	odd	6
224.2.q.a.143.5		12	56.27	even	2
224.2.q.a.143.6		12	7.6	odd	2
392.2.e.e.195.5		12	56.53	even	6
392.2.e.e.195.6		12	56.45	odd	6
392.2.e.e.195.7		12	28.11	odd	6
392.2.e.e.195.8		12	28.3	even	6
392.2.m.g.19.1		12	28.19	even	6
392.2.m.g.19.6		12	56.5	odd	6
392.2.m.g.227.2		12	8.5	even	2
392.2.m.g.227.5		12	4.3	odd	2
504.2.bk.a.19.1		12	168.149	odd	6
504.2.bk.a.19.6		12	84.23	even	6
504.2.bk.a.451.2		12	84.83	odd	2
504.2.bk.a.451.5		12	168.125	even	2
1568.2.e.e.783.1		12	7.3	odd	6
1568.2.e.e.783.2		12	56.3	even	6
1568.2.e.e.783.11		12	56.11	odd	6
1568.2.e.e.783.12		12	7.4	even	3
1568.2.q.g.815.1		12	1.1	even	1	trivial
1568.2.q.g.815.2		12	8.3	odd	2	inner
1568.2.q.g.1391.1		12	56.19	even	6	inner
1568.2.q.g.1391.2		12	7.5	odd	6	inner
2016.2.bs.a.271.2		12	168.107	even	6
2016.2.bs.a.271.5		12	21.2	odd	6
2016.2.bs.a.1711.2		12	21.20	even	2
2016.2.bs.a.1711.5		12	168.83	odd	2

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:	\( N \)	\(=\)	\( 1568 = 2^{5} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1568.q (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.27230 - 1.31191i) q^{3} +(-1.03926 - 1.80005i) q^{5} +(1.94224 + 3.36406i) q^{9} +(0.669938 - 1.16037i) q^{11} +2.50406 q^{13} +5.45368i q^{15} +(2.78212 + 1.60626i) q^{17} +(3.55442 - 2.05215i) q^{19} +(5.54952 - 3.20402i) q^{23} +(0.339877 - 0.588684i) q^{25} -2.32073i q^{27} +4.66151i q^{29} +(2.21897 - 3.84337i) q^{31} +(-3.04461 + 1.75780i) q^{33} +(5.50178 - 3.17646i) q^{37} +(-5.68997 - 3.28511i) q^{39} +5.55076i q^{41} +(4.03699 - 6.99227i) q^{45} +(-0.565988 - 0.980320i) q^{47} +(-4.21455 - 7.29981i) q^{51} +(-7.43567 - 4.29299i) q^{53} -2.78496 q^{55} -10.7690 q^{57} +(6.29193 + 3.63265i) q^{59} +(-2.57219 - 4.45517i) q^{61} +(-2.60236 - 4.50743i) q^{65} +(-3.93243 + 6.81116i) q^{67} -16.8136 q^{69} -5.29150i q^{71} +(-0.480369 - 0.277341i) q^{73} +(-1.54461 + 0.891779i) q^{75} +(-5.26862 + 3.04184i) q^{79} +(2.78212 - 4.81877i) q^{81} +0.503175i q^{83} -6.67728i q^{85} +(6.11551 - 10.5924i) q^{87} +(-1.50000 + 0.866025i) q^{89} +(-10.0844 + 5.82221i) q^{93} +(-7.38794 - 4.26543i) q^{95} -17.2234i q^{97} +5.20473 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{3} + 6 q^{11} + 6 q^{17} - 6 q^{19} + 6 q^{33} - 6 q^{51} - 36 q^{57} + 42 q^{59} - 12 q^{65} - 30 q^{67} - 18 q^{73} + 24 q^{75} + 6 q^{81} - 18 q^{89} + 24 q^{99}+O(q^{100}) \) 12 * q - 6 * q^3 + 6 * q^11 + 6 * q^17 - 6 * q^19 + 6 * q^33 - 6 * q^51 - 36 * q^57 + 42 * q^59 - 12 * q^65 - 30 * q^67 - 18 * q^73 + 24 * q^75 + 6 * q^81 - 18 * q^89 + 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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