LMFDB - Embedded newform 1568.2.q.c.1391.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1568,2,Mod(815,1568)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage: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")

magma://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:traces = [8,0,0,0,0,0,0,0,4,0,-8,0,0,0,0,0,0,0,0,0,0,0,-24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(23)] == traces)

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

Self dual:	no
Analytic conductor:	$12.5205430369$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.339738624.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{6} + 14x^{4} - 8x^{2} + 4 $ x^8 - 4x^6 + 14x^4 - 8*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 392)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1391.4
Root			$0.662827 - 0.382683i$ of defining polynomial
Character	$\chi$	$=$	1568.1391
Dual form			1568.2.q.c.815.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.26303 - 1.30656i) q^{3} +(-1.60021 + 2.77164i) q^{5} +(1.91421 - 3.31552i) q^{9} +(-1.00000 - 1.73205i) q^{11} +5.07517 q^{13} +8.36308i q^{15} +(0.274552 - 0.158513i) q^{17} +(4.13779 + 2.38896i) q^{19} +(1.24264 + 0.717439i) q^{23} +(-2.62132 - 4.54026i) q^{25} -2.16478i q^{27} +9.37769i q^{29} +(-1.32565 - 2.29610i) q^{31} +(-4.52607 - 2.61313i) q^{33} +(2.12132 + 1.22474i) q^{37} +(11.4853 - 6.63103i) q^{39} -4.46088i q^{41} +8.82843 q^{43} +(6.12627 + 10.6110i) q^{45} +(2.65131 - 4.59220i) q^{47} +(0.414214 - 0.717439i) q^{51} +(-3.00000 + 1.73205i) q^{53} +6.40083 q^{55} +12.4853 q^{57} +(2.26303 - 1.30656i) q^{59} +(1.98848 - 3.44415i) q^{61} +(-8.12132 + 14.0665i) q^{65} +(6.00000 + 10.3923i) q^{67} +3.74952 q^{69} +(-1.21193 + 0.699709i) q^{73} +(-11.8643 - 6.84984i) q^{75} +(-10.2426 - 5.91359i) q^{79} +(2.91421 + 5.04757i) q^{81} -8.47343i q^{83} +1.01461i q^{85} +(12.2525 + 21.2220i) q^{87} +(8.55014 + 4.93642i) q^{89} +(-6.00000 - 3.46410i) q^{93} +(-13.2426 + 7.64564i) q^{95} +3.82683i q^{97} -7.65685 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{9} - 8 q^{11} - 24 q^{23} - 4 q^{25} + 24 q^{39} + 48 q^{43} - 8 q^{51} - 24 q^{53} + 32 q^{57} - 48 q^{65} + 48 q^{67} - 48 q^{79} + 12 q^{81} - 48 q^{93} - 72 q^{95} - 16 q^{99}+O(q^{100}) $ 8 * q + 4 * q^9 - 8 * q^11 - 24 * q^23 - 4 * q^25 + 24 * q^39 + 48 * q^43 - 8 * q^51 - 24 * q^53 + 32 * q^57 - 48 * q^65 + 48 * q^67 - 48 * q^79 + 12 * q^81 - 48 * q^93 - 72 * q^95 - 16 * q^99

Character values

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

$n$	$197$	$1471$	$1473$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$

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
$3$	2.26303	−	1.30656i	1.30656	−	0.754344i	0.325042	−	0.945700i	$-0.394622\pi$
$3$	2.26303	−	1.30656i	1.30656	−	0.754344i	0.981521	+	0.191355i	$0.0612882\pi$
$4$		0			0
$5$	−1.60021	+	2.77164i	−0.715634	+	1.23951i	0.247080	+	0.968995i	$0.420529\pi$
$5$	−1.60021	+	2.77164i	−0.715634	+	1.23951i	−0.962714	+	0.270520i	$0.912805\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	1.91421	−	3.31552i	0.638071	−	1.10517i
$10$		0			0
$11$	−1.00000	−	1.73205i	−0.301511	−	0.522233i	0.674967	−	0.737848i	$-0.264158\pi$
$11$	−1.00000	−	1.73205i	−0.301511	−	0.522233i	−0.976478	+	0.215615i	$0.930824\pi$
$12$		0			0
$13$	5.07517			1.40760			0.703800	−	0.710399i	$-0.251485\pi$
$13$	5.07517			1.40760			0.703800	+	0.710399i	$0.251485\pi$
$14$		0			0
$15$			8.36308i			2.15934i
$16$		0			0
$17$	0.274552	−	0.158513i	0.0665886	−	0.0384450i	−0.466336	−	0.884608i	$-0.654426\pi$
$17$	0.274552	−	0.158513i	0.0665886	−	0.0384450i	0.532925	+	0.846163i	$0.321093\pi$
$18$		0			0
$19$	4.13779	+	2.38896i	0.949275	+	0.548064i	0.892855	−	0.450343i	$-0.148698\pi$
$19$	4.13779	+	2.38896i	0.949275	+	0.548064i	0.0564190	+	0.998407i	$0.482032\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	1.24264	+	0.717439i	0.259108	+	0.149596i	0.623928	−	0.781482i	$-0.285536\pi$
$23$	1.24264	+	0.717439i	0.259108	+	0.149596i	−0.364819	+	0.931078i	$0.618869\pi$
$24$		0			0
$25$	−2.62132	−	4.54026i	−0.524264	−	0.908052i
$26$		0			0
$27$		−	2.16478i		−	0.416613i
$28$		0			0
$29$			9.37769i			1.74139i	0.491820	+	0.870697i	$0.336332\pi$
$29$			9.37769i			1.74139i	−0.491820	+	0.870697i	$0.663668\pi$
$30$		0			0
$31$	−1.32565	−	2.29610i	−0.238095	−	0.412392i	0.722073	−	0.691817i	$-0.243189\pi$
$31$	−1.32565	−	2.29610i	−0.238095	−	0.412392i	−0.960168	+	0.279425i	$0.909856\pi$
$32$		0			0
$33$	−4.52607	−	2.61313i	−0.787887	−	0.454887i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	2.12132	+	1.22474i	0.348743	+	0.201347i	0.664131	−	0.747616i	$-0.268802\pi$
$37$	2.12132	+	1.22474i	0.348743	+	0.201347i	−0.315389	+	0.948963i	$0.602135\pi$
$38$		0			0
$39$	11.4853	−	6.63103i	1.83912	−	1.06181i
$40$		0			0
$41$		−	4.46088i		−	0.696673i	−0.937370	−	0.348337i	$-0.886747\pi$
$41$		−	4.46088i		−	0.696673i	0.937370	−	0.348337i	$-0.113253\pi$
$42$		0			0
$43$	8.82843			1.34632			0.673161	−	0.739496i	$-0.264936\pi$
$43$	8.82843			1.34632			0.673161	+	0.739496i	$0.264936\pi$
$44$		0			0
$45$	6.12627	+	10.6110i	0.913251	+	1.58180i
$46$		0			0
$47$	2.65131	−	4.59220i	0.386733	−	0.669841i	−0.605275	−	0.796017i	$-0.706937\pi$
$47$	2.65131	−	4.59220i	0.386733	−	0.669841i	0.992008	+	0.126175i	$0.0402701\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	0.414214	−	0.717439i	0.0580015	−	0.100462i
$52$		0			0
$53$	−3.00000	+	1.73205i	−0.412082	+	0.237915i	−0.691684	−	0.722200i	$-0.743131\pi$
$53$	−3.00000	+	1.73205i	−0.412082	+	0.237915i	0.279602	+	0.960116i	$0.409797\pi$
$54$		0			0
$55$	6.40083			0.863087
$56$		0			0
$57$	12.4853			1.65372
$58$		0			0
$59$	2.26303	−	1.30656i	0.294622	−	0.170100i	−0.345402	−	0.938455i	$-0.612258\pi$
$59$	2.26303	−	1.30656i	0.294622	−	0.170100i	0.640024	+	0.768355i	$0.278924\pi$
$60$		0			0
$61$	1.98848	−	3.44415i	0.254599	−	0.440978i	−0.710188	−	0.704013i	$-0.751390\pi$
$61$	1.98848	−	3.44415i	0.254599	−	0.440978i	0.964787	+	0.263034i	$0.0847232\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−8.12132	+	14.0665i	−1.00733	+	1.74474i
$66$		0			0
$67$	6.00000	+	10.3923i	0.733017	+	1.26962i	0.955588	+	0.294706i	$0.0952216\pi$
$67$	6.00000	+	10.3923i	0.733017	+	1.26962i	−0.222571	+	0.974916i	$0.571445\pi$
$68$		0			0
$69$	3.74952			0.451389
$70$		0			0
$71$		0			0		1.00000			$0$
$71$		0			0		−1.00000			$\pi$
$72$		0			0
$73$	−1.21193	+	0.699709i	−0.141846	+	0.0818947i	−0.569243	−	0.822169i	$-0.692764\pi$
$73$	−1.21193	+	0.699709i	−0.141846	+	0.0818947i	0.427398	+	0.904064i	$0.359430\pi$
$74$		0			0
$75$	−11.8643	−	6.84984i	−1.36997	−	0.790951i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−10.2426	−	5.91359i	−1.15239	−	0.665331i	−0.202919	−	0.979195i	$-0.565043\pi$
$79$	−10.2426	−	5.91359i	−1.15239	−	0.665331i	−0.949468	+	0.313864i	$0.898376\pi$
$80$		0			0
$81$	2.91421	+	5.04757i	0.323802	+	0.560841i
$82$		0			0
$83$		−	8.47343i		−	0.930080i	−0.885290	−	0.465040i	$-0.846040\pi$
$83$		−	8.47343i		−	0.930080i	0.885290	−	0.465040i	$-0.153960\pi$
$84$		0			0
$85$			1.01461i			0.110050i
$86$		0			0
$87$	12.2525	+	21.2220i	1.31361	+	2.27524i
$88$		0			0
$89$	8.55014	+	4.93642i	0.906313	+	0.523260i	0.879243	−	0.476374i	$-0.158049\pi$
$89$	8.55014	+	4.93642i	0.906313	+	0.523260i	0.0270697	+	0.999634i	$0.491382\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−6.00000	−	3.46410i	−0.622171	−	0.359211i
$94$		0			0
$95$	−13.2426	+	7.64564i	−1.35867	+	0.784426i
$96$		0			0
$97$			3.82683i			0.388556i	0.980946	+	0.194278i	$0.0622364\pi$
$97$			3.82683i			0.388556i	−0.980946	+	0.194278i	$0.937764\pi$
$98$		0			0
$99$	−7.65685			−0.769543
$100$		0			0
$101$	3.86324	+	6.69133i	0.384407	+	0.665812i	0.991687	−	0.128676i	$-0.0410727\pi$
$101$	3.86324	+	6.69133i	0.384407	+	0.665812i	−0.607280	+	0.794488i	$0.707739\pi$
$102$		0			0
$103$	7.72648	−	13.3827i	0.761313	−	1.31863i	−0.180862	−	0.983509i	$-0.557889\pi$
$103$	7.72648	−	13.3827i	0.761313	−	1.31863i	0.942174	−	0.335124i	$-0.108778\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−4.24264	+	7.34847i	−0.410152	+	0.710403i	−0.994906	−	0.100807i	$-0.967858\pi$
$107$	−4.24264	+	7.34847i	−0.410152	+	0.710403i	0.584754	+	0.811210i	$0.301191\pi$
$108$		0			0
$109$	0.363961	−	0.210133i	0.0348611	−	0.0201271i	−0.482468	−	0.875914i	$-0.660260\pi$
$109$	0.363961	−	0.210133i	0.0348611	−	0.0201271i	0.517329	+	0.855786i	$0.326926\pi$
$110$		0			0
$111$	6.40083			0.607539
$112$		0			0
$113$	−16.4853			−1.55080			−0.775402	−	0.631467i	$-0.782453\pi$
$113$	−16.4853			−1.55080			−0.775402	+	0.631467i	$0.782453\pi$
$114$		0			0
$115$	−3.97696	+	2.29610i	−0.370854	+	0.214112i
$116$		0			0
$117$	9.71496	−	16.8268i	0.898148	−	1.55564i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	3.50000	−	6.06218i	0.318182	−	0.551107i
$122$		0			0
$123$	−5.82843	−	10.0951i	−0.525532	−	0.910247i
$124$		0			0
$125$	0.776550			0.0694568
$126$		0			0
$127$			5.49333i			0.487454i	0.969844	+	0.243727i	$0.0783701\pi$
$127$			5.49333i			0.487454i	−0.969844	+	0.243727i	$0.921630\pi$
$128$		0			0
$129$	19.9790	−	11.5349i	1.75906	−	1.01559i
$130$		0			0
$131$	−3.03958	−	1.75490i	−0.265570	−	0.153327i	0.361303	−	0.932448i	$-0.382332\pi$
$131$	−3.03958	−	1.75490i	−0.265570	−	0.153327i	−0.626873	+	0.779122i	$0.715665\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	6.00000	+	3.46410i	0.516398	+	0.298142i
$136$		0			0
$137$	−0.121320	−	0.210133i	−0.0103651	−	0.0179529i	0.860796	−	0.508950i	$-0.169966\pi$
$137$	−0.121320	−	0.210133i	−0.0103651	−	0.0179529i	−0.871161	+	0.490997i	$0.836633\pi$
$138$		0			0
$139$		−	5.04054i		−	0.427533i	−0.976885	−	0.213767i	$-0.931427\pi$
$139$		−	5.04054i		−	0.427533i	0.976885	−	0.213767i	$-0.0685732\pi$
$140$		0			0
$141$		−	13.8564i		−	1.16692i
$142$		0			0
$143$	−5.07517	−	8.79045i	−0.424407	−	0.735095i
$144$		0			0
$145$	−25.9916	−	15.0062i	−2.15848	−	1.24620i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−17.4853	−	10.0951i	−1.43245	−	0.827025i	−0.435143	−	0.900361i	$-0.643302\pi$
$149$	−17.4853	−	10.0951i	−1.43245	−	0.827025i	−0.997307	+	0.0733360i	$0.976635\pi$
$150$		0			0
$151$	−13.2426	+	7.64564i	−1.07767	+	0.622194i	−0.930267	−	0.366883i	$-0.880425\pi$
$151$	−13.2426	+	7.64564i	−1.07767	+	0.622194i	−0.147404	+	0.989076i	$0.547092\pi$
$152$		0			0
$153$		−	1.21371i		−	0.0981225i
$154$		0			0
$155$	8.48528			0.681554
$156$		0			0
$157$	−11.9780	−	20.7465i	−0.955948	−	1.65575i	−0.732184	−	0.681107i	$-0.761499\pi$
$157$	−11.9780	−	20.7465i	−0.955948	−	1.65575i	−0.223764	−	0.974643i	$-0.571835\pi$
$158$		0			0
$159$	−4.52607	+	7.83938i	−0.358940	+	0.621703i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	4.07107	−	7.05130i	0.318871	−	0.552300i	−0.661382	−	0.750049i	$-0.730030\pi$
$163$	4.07107	−	7.05130i	0.318871	−	0.552300i	0.980253	+	0.197749i	$0.0633631\pi$
$164$		0			0
$165$	14.4853	−	8.36308i	1.12768	−	0.651065i
$166$		0			0
$167$	−14.3548			−1.11080			−0.555402	−	0.831582i	$-0.687436\pi$
$167$	−14.3548			−1.11080			−0.555402	+	0.831582i	$0.687436\pi$
$168$		0			0
$169$	12.7574			0.981335
$170$		0			0
$171$	15.8412	−	9.14594i	1.21141	−	0.699408i
$172$		0			0
$173$	3.47496	−	6.01882i	0.264197	−	0.457602i	−0.703156	−	0.711035i	$-0.748227\pi$
$173$	3.47496	−	6.01882i	0.264197	−	0.457602i	0.967353	+	0.253433i	$0.0815599\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	3.41421	−	5.91359i	0.256628	−	0.444493i
$178$		0			0
$179$	−10.2426	−	17.7408i	−0.765571	−	1.32601i	−0.939944	−	0.341328i	$-0.889123\pi$
$179$	−10.2426	−	17.7408i	−0.765571	−	1.32601i	0.174373	−	0.984680i	$-0.444210\pi$
$180$		0			0
$181$	2.10220			0.156256			0.0781278	−	0.996943i	$-0.475106\pi$
$181$	2.10220			0.156256			0.0781278	+	0.996943i	$0.475106\pi$
$182$		0			0
$183$		−	10.3923i		−	0.768221i
$184$		0			0
$185$	−6.78910	+	3.91969i	−0.499145	+	0.288181i
$186$		0			0
$187$	−0.549104	−	0.317025i	−0.0401545	−	0.0231832i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−10.2426	−	5.91359i	−0.741131	−	0.427892i	0.0813491	−	0.996686i	$-0.474077\pi$
$191$	−10.2426	−	5.91359i	−0.741131	−	0.427892i	−0.822481	+	0.568793i	$0.807410\pi$
$192$		0			0
$193$	7.07107	+	12.2474i	0.508987	+	0.881591i	0.999946	+	0.0104081i	$0.00331306\pi$
$193$	7.07107	+	12.2474i	0.508987	+	0.881591i	−0.490959	+	0.871183i	$0.663354\pi$
$194$		0			0
$195$			42.4441i			3.03948i
$196$		0			0
$197$			26.5241i			1.88977i	0.327409	+	0.944883i	$0.393824\pi$
$197$			26.5241i			1.88977i	−0.327409	+	0.944883i	$0.606176\pi$
$198$		0			0
$199$	−1.32565	−	2.29610i	−0.0939731	−	0.162766i	0.815206	−	0.579170i	$-0.196623\pi$
$199$	−1.32565	−	2.29610i	−0.0939731	−	0.162766i	−0.909180	+	0.416404i	$0.863290\pi$
$200$		0			0
$201$	27.1564	+	15.6788i	1.91546	+	1.10589i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	12.3640	+	7.13834i	0.863536	+	0.498563i
$206$		0			0
$207$	4.75736	−	2.74666i	0.330659	−	0.190906i
$208$		0			0
$209$		−	9.55582i		−	0.660990i
$210$		0			0
$211$	−20.4853			−1.41026			−0.705132	−	0.709076i	$-0.749112\pi$
$211$	−20.4853			−1.41026			−0.705132	+	0.709076i	$0.749112\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−14.1273	+	24.4692i	−0.963474	+	1.66879i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−1.82843	+	3.16693i	−0.123554	+	0.214001i
$220$		0			0
$221$	1.39340	−	0.804479i	0.0937301	−	0.0541151i
$222$		0			0
$223$	24.5051			1.64098			0.820491	−	0.571659i	$-0.193700\pi$
$223$	24.5051			1.64098			0.820491	+	0.571659i	$0.193700\pi$
$224$		0			0
$225$	−20.0711			−1.33807
$226$		0			0
$227$	−20.1399	+	11.6278i	−1.33673	+	0.771761i	−0.986321	−	0.164836i	$-0.947290\pi$
$227$	−20.1399	+	11.6278i	−1.33673	+	0.771761i	−0.350408	+	0.936597i	$0.613957\pi$
$228$		0			0
$229$	−8.77758	+	15.2032i	−0.580039	+	1.00466i	0.415435	+	0.909623i	$0.363629\pi$
$229$	−8.77758	+	15.2032i	−0.580039	+	1.00466i	−0.995474	+	0.0950341i	$0.969704\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	10.1213	−	17.5306i	0.663070	−	1.14847i	−0.316735	−	0.948514i	$-0.602587\pi$
$233$	10.1213	−	17.5306i	0.663070	−	1.14847i	0.979805	−	0.199956i	$-0.0640801\pi$
$234$		0			0
$235$	8.48528	+	14.6969i	0.553519	+	0.958723i
$236$		0			0
$237$	−30.9059			−2.00756
$238$		0			0
$239$		−	13.2621i		−	0.857851i	−0.903340	−	0.428926i	$-0.858892\pi$
$239$		−	13.2621i		−	0.857851i	0.903340	−	0.428926i	$-0.141108\pi$
$240$		0			0
$241$	−19.1554	+	11.0594i	−1.23391	+	0.712396i	−0.967842	−	0.251559i	$-0.919057\pi$
$241$	−19.1554	+	11.0594i	−1.23391	+	0.712396i	−0.266064	+	0.963955i	$0.585723\pi$
$242$		0			0
$243$	18.8142	+	10.8624i	1.20693	+	0.696822i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	21.0000	+	12.1244i	1.33620	+	0.771454i
$248$		0			0
$249$	−11.0711	−	19.1757i	−0.701600	−	1.21521i
$250$		0			0
$251$		−	19.1886i		−	1.21117i	−0.795780	−	0.605586i	$-0.792939\pi$
$251$		−	19.1886i		−	1.21117i	0.795780	−	0.605586i	$-0.207061\pi$
$252$		0			0
$253$		−	2.86976i		−	0.180420i
$254$		0			0
$255$	1.32565	+	2.29610i	0.0830157	+	0.143787i
$256$		0			0
$257$	7.06365	+	4.07820i	0.440619	+	0.254391i	0.703860	−	0.710339i	$-0.251458\pi$
$257$	7.06365	+	4.07820i	0.440619	+	0.254391i	−0.263241	+	0.964730i	$0.584792\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	31.0919	+	17.9509i	1.92454	+	1.11113i
$262$		0			0
$263$	7.75736	−	4.47871i	0.478339	−	0.276169i	−0.241385	−	0.970429i	$-0.577602\pi$
$263$	7.75736	−	4.47871i	0.478339	−	0.276169i	0.719724	+	0.694260i	$0.244268\pi$
$264$		0			0
$265$		−	11.0866i		−	0.681042i
$266$		0			0
$267$	25.7990			1.57887
$268$		0			0
$269$	−1.21193	−	2.09913i	−0.0738927	−	0.127986i	0.826711	−	0.562626i	$-0.190209\pi$
$269$	−1.21193	−	2.09913i	−0.0738927	−	0.127986i	−0.900604	+	0.434640i	$0.856876\pi$
$270$		0			0
$271$	−6.62827	+	11.4805i	−0.402639	+	0.697391i	−0.994044	−	0.108984i	$-0.965240\pi$
$271$	−6.62827	+	11.4805i	−0.402639	+	0.697391i	0.591405	+	0.806375i	$0.298574\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−5.24264	+	9.08052i	−0.316143	+	0.547576i
$276$		0			0
$277$	−14.4853	+	8.36308i	−0.870336	+	0.502489i	−0.867460	−	0.497507i	$-0.834249\pi$
$277$	−14.4853	+	8.36308i	−0.870336	+	0.502489i	−0.00287626	+	0.999996i	$0.500916\pi$
$278$		0			0
$279$	−10.1503			−0.607685
$280$		0			0
$281$	8.72792			0.520664			0.260332	−	0.965519i	$-0.416168\pi$
$281$	8.72792			0.520664			0.260332	+	0.965519i	$0.416168\pi$
$282$		0			0
$283$	0.160829	−	0.0928546i	0.00956028	−	0.00551963i	−0.495212	−	0.868772i	$-0.664910\pi$
$283$	0.160829	−	0.0928546i	0.00956028	−	0.00551963i	0.504773	+	0.863252i	$0.331576\pi$
$284$		0			0
$285$	−19.9790	+	34.6047i	−1.18346	+	2.04980i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−8.44975	+	14.6354i	−0.497044	+	0.860905i
$290$		0			0
$291$	5.00000	+	8.66025i	0.293105	+	0.507673i
$292$		0			0
$293$	−5.07517			−0.296495			−0.148247	−	0.988950i	$-0.547363\pi$
$293$	−5.07517			−0.296495			−0.148247	+	0.988950i	$0.547363\pi$
$294$		0			0
$295$			8.36308i			0.486917i
$296$		0			0
$297$	−3.74952	+	2.16478i	−0.217569	+	0.125614i
$298$		0			0
$299$	6.30661	+	3.64113i	0.364721	+	0.210572i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	17.4853	+	10.0951i	1.00450	+	0.579950i
$304$		0			0
$305$	6.36396	+	11.0227i	0.364399	+	0.631158i
$306$		0			0
$307$		−	6.04601i		−	0.345064i	−0.985004	−	0.172532i	$-0.944805\pi$
$307$		−	6.04601i		−	0.345064i	0.985004	−	0.172532i	$-0.0551948\pi$
$308$		0			0
$309$		−	40.3805i		−	2.29717i
$310$		0			0
$311$	−13.5782	−	23.5181i	−0.769949	−	1.33359i	−0.937590	−	0.347743i	$-0.886948\pi$
$311$	−13.5782	−	23.5181i	−0.769949	−	1.33359i	0.167641	−	0.985848i	$-0.446385\pi$
$312$		0			0
$313$	9.16586	+	5.29191i	0.518085	+	0.299116i	0.736151	−	0.676818i	$-0.236641\pi$
$313$	9.16586	+	5.29191i	0.518085	+	0.299116i	−0.218066	+	0.975934i	$0.569975\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	3.51472	+	2.02922i	0.197406	+	0.113973i	0.595445	−	0.803396i	$-0.296976\pi$
$317$	3.51472	+	2.02922i	0.197406	+	0.113973i	−0.398039	+	0.917369i	$0.630309\pi$
$318$		0			0
$319$	16.2426	−	9.37769i	0.909413	−	0.525050i
$320$		0			0
$321$			22.1731i			1.23758i
$322$		0			0
$323$	1.51472			0.0842812
$324$		0			0
$325$	−13.3036	−	23.0426i	−0.737954	−	1.27817i
$326$		0			0
$327$	0.549104	−	0.951076i	0.0303655	−	0.0525946i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	10.4142	−	18.0379i	0.572417	−	0.991455i	−0.423900	−	0.905709i	$-0.639339\pi$
$331$	10.4142	−	18.0379i	0.572417	−	0.991455i	0.996317	−	0.0857463i	$-0.0273274\pi$
$332$		0			0
$333$	8.12132	−	4.68885i	0.445046	−	0.256947i
$334$		0			0
$335$	−38.4050			−2.09829
$336$		0			0
$337$	4.24264			0.231111			0.115556	−	0.993301i	$-0.463135\pi$
$337$	4.24264			0.231111			0.115556	+	0.993301i	$0.463135\pi$
$338$		0			0
$339$	−37.3067	+	21.5391i	−2.02622	+	1.16984i
$340$		0			0
$341$	−2.65131	+	4.59220i	−0.143576	+	0.248682i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−6.00000	+	10.3923i	−0.323029	+	0.559503i
$346$		0			0
$347$	3.48528	+	6.03668i	0.187100	+	0.324066i	0.944282	−	0.329137i	$-0.106758\pi$
$347$	3.48528	+	6.03668i	0.187100	+	0.324066i	−0.757182	+	0.653204i	$0.773425\pi$
$348$		0			0
$349$	22.4029			1.19920			0.599600	−	0.800300i	$-0.295327\pi$
$349$	22.4029			1.19920			0.599600	+	0.800300i	$0.295327\pi$
$350$		0			0
$351$		−	10.9867i		−	0.586424i
$352$		0			0
$353$	−11.3623	+	6.56001i	−0.604753	+	0.349154i	−0.770909	−	0.636945i	$-0.780198\pi$
$353$	−11.3623	+	6.56001i	−0.604753	+	0.349154i	0.166156	+	0.986099i	$0.446864\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−15.0000	−	8.66025i	−0.791670	−	0.457071i	0.0488803	−	0.998805i	$-0.484435\pi$
$359$	−15.0000	−	8.66025i	−0.791670	−	0.457071i	−0.840550	+	0.541734i	$0.817768\pi$
$360$		0			0
$361$	1.91421	+	3.31552i	0.100748	+	0.174501i
$362$		0			0
$363$		−	18.2919i		−	0.960075i
$364$		0			0
$365$		−	4.47871i		−	0.234427i
$366$		0			0
$367$	−8.50303	−	14.7277i	−0.443855	−	0.768779i	0.554117	−	0.832439i	$-0.313056\pi$
$367$	−8.50303	−	14.7277i	−0.443855	−	0.768779i	−0.997972	+	0.0636601i	$0.979723\pi$
$368$		0			0
$369$	−14.7901	−	8.53909i	−0.769944	−	0.444527i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−7.97056	−	4.60181i	−0.412700	−	0.238273i	0.279249	−	0.960219i	$-0.409914\pi$
$373$	−7.97056	−	4.60181i	−0.412700	−	0.238273i	−0.691949	+	0.721946i	$0.743248\pi$
$374$		0			0
$375$	1.75736	−	1.01461i	0.0907496	−	0.0523943i
$376$		0			0
$377$			47.5934i			2.45118i
$378$		0			0
$379$	−17.3137			−0.889345			−0.444673	−	0.895693i	$-0.646680\pi$
$379$	−17.3137			−0.889345			−0.444673	+	0.895693i	$0.646680\pi$
$380$		0			0
$381$	7.17738	+	12.4316i	0.367708	+	0.636889i
$382$		0			0
$383$	2.65131	−	4.59220i	0.135476	−	0.234651i	−0.790303	−	0.612716i	$-0.790077\pi$
$383$	2.65131	−	4.59220i	0.135476	−	0.234651i	0.925779	+	0.378065i	$0.123410\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	16.8995	−	29.2708i	0.859050	−	1.48792i
$388$		0			0
$389$	3.15076	−	1.81909i	0.159750	−	0.0922316i	−0.417994	−	0.908450i	$-0.637267\pi$
$389$	3.15076	−	1.81909i	0.159750	−	0.0922316i	0.577744	+	0.816218i	$0.303933\pi$
$390$		0			0
$391$	0.454893			0.0230049
$392$		0			0
$393$	−9.17157			−0.462645
$394$		0			0
$395$	32.7807	−	18.9259i	1.64937	−	0.952267i
$396$		0			0
$397$	12.1388	−	21.0251i	0.609230	−	1.05522i	−0.382137	−	0.924105i	$-0.624812\pi$
$397$	12.1388	−	21.0251i	0.609230	−	1.05522i	0.991368	−	0.131112i	$-0.0418547\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−3.87868	+	6.71807i	−0.193692	+	0.335484i	−0.946471	−	0.322789i	$-0.895380\pi$
$401$	−3.87868	+	6.71807i	−0.193692	+	0.335484i	0.752779	+	0.658273i	$0.228713\pi$
$402$		0			0
$403$	−6.72792	−	11.6531i	−0.335142	−	0.580482i
$404$		0			0
$405$	−18.6534			−0.926893
$406$		0			0
$407$		−	4.89898i		−	0.242833i
$408$		0			0
$409$	−3.31414	+	1.91342i	−0.163873	+	0.0946124i	−0.579694	−	0.814834i	$-0.696828\pi$
$409$	−3.31414	+	1.91342i	−0.163873	+	0.0946124i	0.415820	+	0.909447i	$0.363495\pi$
$410$		0			0
$411$	−0.549104	−	0.317025i	−0.0270853	−	0.0156377i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	23.4853	+	13.5592i	1.15285	+	0.665597i
$416$		0			0
$417$	−6.58579	−	11.4069i	−0.322507	−	0.558599i
$418$		0			0
$419$			39.8309i			1.94587i	0.231082	+	0.972934i	$0.425774\pi$
$419$			39.8309i			1.94587i	−0.231082	+	0.972934i	$0.574226\pi$
$420$		0			0
$421$		−	26.5241i		−	1.29271i	−0.763038	−	0.646353i	$-0.776293\pi$
$421$		−	26.5241i		−	1.29271i	0.763038	−	0.646353i	$-0.223707\pi$
$422$		0			0
$423$	−10.1503	−	17.5809i	−0.493527	−	0.854813i
$424$		0			0
$425$	−1.43938	−	0.831025i	−0.0698201	−	0.0403106i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−22.9706	−	13.2621i	−1.10903	−	0.640298i
$430$		0			0
$431$	−6.51472	+	3.76127i	−0.313803	+	0.181174i	−0.648627	−	0.761106i	$-0.724656\pi$
$431$	−6.51472	+	3.76127i	−0.313803	+	0.181174i	0.334824	+	0.942281i	$0.391323\pi$
$432$		0			0
$433$		−	5.17186i		−	0.248544i	−0.992248	−	0.124272i	$-0.960341\pi$
$433$		−	5.17186i		−	0.248544i	0.992248	−	0.124272i	$-0.0396595\pi$
$434$		0			0
$435$	−78.4264			−3.76026
$436$		0			0
$437$	3.42786	+	5.93723i	0.163977	+	0.284016i
$438$		0			0
$439$	17.8768	−	30.9636i	0.853214	−	1.47781i	−0.0250778	−	0.999686i	$-0.507983\pi$
$439$	17.8768	−	30.9636i	0.853214	−	1.47781i	0.878292	−	0.478125i	$-0.158683\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−14.1421	+	24.4949i	−0.671913	+	1.16379i	0.305448	+	0.952209i	$0.401194\pi$
$443$	−14.1421	+	24.4949i	−0.671913	+	1.16379i	−0.977361	+	0.211579i	$0.932139\pi$
$444$		0			0
$445$	−27.3640	+	15.7986i	−1.29718	+	0.748925i
$446$		0			0
$447$	−52.7597			−2.49545
$448$		0			0
$449$	−5.65685			−0.266963			−0.133482	−	0.991051i	$-0.542616\pi$
$449$	−5.65685			−0.266963			−0.133482	+	0.991051i	$0.542616\pi$
$450$		0			0
$451$	−7.72648	+	4.46088i	−0.363826	+	0.210055i
$452$		0			0
$453$	−19.9790	+	34.6047i	−0.938697	+	1.62587i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	10.5858	−	18.3351i	0.495182	−	0.857681i	−0.504802	−	0.863235i	$-0.668435\pi$
$457$	10.5858	−	18.3351i	0.495182	−	0.857681i	0.999985	+	0.00555421i	$0.00176797\pi$
$458$		0			0
$459$	−0.343146	−	0.594346i	−0.0160167	−	0.0277417i
$460$		0			0
$461$	26.6073			1.23923			0.619613	−	0.784908i	$-0.287290\pi$
$461$	26.6073			1.23923			0.619613	+	0.784908i	$0.287290\pi$
$462$		0			0
$463$		−	18.7554i		−	0.871637i	−0.900035	−	0.435818i	$-0.856459\pi$
$463$		−	18.7554i		−	0.871637i	0.900035	−	0.435818i	$-0.143541\pi$
$464$		0			0
$465$	19.2025	−	11.0866i	0.890493	−	0.514127i
$466$		0			0
$467$	−0.0666175	−	0.0384616i	−0.00308269	−	0.00177979i	0.498458	−	0.866914i	$-0.333900\pi$
$467$	−0.0666175	−	0.0384616i	−0.00308269	−	0.00177979i	−0.501541	+	0.865134i	$0.667233\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−54.2132	−	31.3000i	−2.49801	−	1.44223i
$472$		0			0
$473$	−8.82843	−	15.2913i	−0.405932	−	0.703094i
$474$		0			0
$475$		−	25.0489i		−	1.14932i
$476$		0			0
$477$			13.2621i			0.607228i
$478$		0			0
$479$	5.85172	+	10.1355i	0.267372	+	0.463102i	0.968182	−	0.250246i	$-0.0805114\pi$
$479$	5.85172	+	10.1355i	0.267372	+	0.463102i	−0.700810	+	0.713348i	$0.747178\pi$
$480$		0			0
$481$	10.7661	+	6.21579i	0.490890	+	0.283416i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−10.6066	−	6.12372i	−0.481621	−	0.278064i
$486$		0			0
$487$	−29.4853	+	17.0233i	−1.33611	+	0.771401i	−0.986228	−	0.165394i	$-0.947110\pi$
$487$	−29.4853	+	17.0233i	−1.33611	+	0.771401i	−0.349878	+	0.936795i	$0.613777\pi$
$488$		0			0
$489$		−	21.2764i		−	0.962153i
$490$		0			0
$491$	31.7990			1.43507			0.717534	−	0.696523i	$-0.245271\pi$
$491$	31.7990			1.43507			0.717534	+	0.696523i	$0.245271\pi$
$492$		0			0
$493$	1.48648	+	2.57466i	0.0669478	+	0.115957i
$494$		0			0
$495$	12.2525	−	21.2220i	0.550711	−	0.953859i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−4.24264	+	7.34847i	−0.189927	+	0.328963i	−0.945226	−	0.326418i	$-0.894158\pi$
$499$	−4.24264	+	7.34847i	−0.189927	+	0.328963i	0.755299	+	0.655380i	$0.227492\pi$
$500$		0			0
$501$	−32.4853	+	18.7554i	−1.45134	+	0.837929i
$502$		0			0
$503$	24.5051			1.09263			0.546314	−	0.837580i	$-0.316031\pi$
$503$	24.5051			1.09263			0.546314	+	0.837580i	$0.316031\pi$
$504$		0			0
$505$	−24.7279			−1.10038
$506$		0			0
$507$	28.8703	−	16.6683i	1.28218	−	0.740265i
$508$		0			0
$509$	7.06365	−	12.2346i	0.313091	−	0.542289i	−0.665939	−	0.746006i	$-0.731969\pi$
$509$	7.06365	−	12.2346i	0.313091	−	0.542289i	0.979030	+	0.203717i	$0.0653022\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	5.17157	−	8.95743i	0.228331	−	0.395480i
$514$		0			0
$515$	24.7279	+	42.8300i	1.08964	+	1.88732i
$516$		0			0
$517$	−10.6052			−0.466418
$518$		0			0
$519$		−	18.1610i		−	0.797181i
$520$		0			0
$521$	16.1158	−	9.30445i	0.706045	−	0.407636i	−0.103550	−	0.994624i	$-0.533020\pi$
$521$	16.1158	−	9.30445i	0.706045	−	0.407636i	0.809595	+	0.586989i	$0.199687\pi$
$522$		0			0
$523$	−28.4154	−	16.4057i	−1.24252	−	0.717369i	−0.272914	−	0.962039i	$-0.587987\pi$
$523$	−28.4154	−	16.4057i	−1.24252	−	0.717369i	−0.969607	+	0.244669i	$0.921321\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−0.727922	−	0.420266i	−0.0317088	−	0.0183071i
$528$		0			0
$529$	−10.4706	−	18.1355i	−0.455242	−	0.788502i
$530$		0			0
$531$		−	10.0042i		−	0.434144i
$532$		0			0
$533$		−	22.6398i		−	0.980637i
$534$		0			0
$535$	−13.5782	−	23.5181i	−0.587037	−	1.01678i
$536$		0			0
$537$	−46.3589	−	26.7653i	−2.00053	−	1.15501i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	28.4558	+	16.4290i	1.22341	+	0.706337i	0.965644	−	0.259869i	$-0.0836795\pi$
$541$	28.4558	+	16.4290i	1.22341	+	0.706337i	0.257768	+	0.966207i	$0.417013\pi$
$542$		0			0
$543$	4.75736	−	2.74666i	0.204158	−	0.117871i
$544$		0			0
$545$			1.34502i			0.0576145i
$546$		0			0
$547$	15.1716			0.648690			0.324345	−	0.945939i	$-0.394856\pi$
$547$	15.1716			0.648690			0.324345	+	0.945939i	$0.394856\pi$
$548$		0			0
$549$	−7.61276	−	13.1857i	−0.324905	−	0.562751i
$550$		0			0
$551$	−22.4029	+	38.8029i	−0.954395	+	1.65306i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−10.2426	+	17.7408i	−0.434776	+	0.753054i
$556$		0			0
$557$	−14.4853	+	8.36308i	−0.613761	+	0.354355i	−0.774436	−	0.632652i	$-0.781966\pi$
$557$	−14.4853	+	8.36308i	−0.613761	+	0.354355i	0.160675	+	0.987007i	$0.448633\pi$
$558$		0			0
$559$	44.8058			1.89508
$560$		0			0
$561$	−1.65685			−0.0699524
$562$		0			0
$563$	14.5156	−	8.38057i	0.611759	−	0.353199i	−0.161895	−	0.986808i	$-0.551760\pi$
$563$	14.5156	−	8.38057i	0.611759	−	0.353199i	0.773653	+	0.633609i	$0.218427\pi$
$564$		0			0
$565$	26.3799	−	45.6912i	1.10981	−	1.92225i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−7.05025	+	12.2114i	−0.295562	+	0.511928i	−0.975115	−	0.221698i	$-0.928840\pi$
$569$	−7.05025	+	12.2114i	−0.295562	+	0.511928i	0.679554	+	0.733626i	$0.262174\pi$
$570$		0			0
$571$	−11.8284	−	20.4874i	−0.495004	−	0.857373i	0.504979	−	0.863132i	$-0.331500\pi$
$571$	−11.8284	−	20.4874i	−0.495004	−	0.857373i	−0.999983	+	0.00575900i	$0.998167\pi$
$572$		0			0
$573$	−30.9059			−1.29111
$574$		0			0
$575$		−	7.52255i		−	0.313712i
$576$		0			0
$577$	−1.82765	+	1.05520i	−0.0760862	+	0.0439284i	−0.537560	−	0.843225i	$-0.680654\pi$
$577$	−1.82765	+	1.05520i	−0.0760862	+	0.0439284i	0.461474	+	0.887154i	$0.347321\pi$
$578$		0			0
$579$	32.0041	+	18.4776i	1.33005	+	0.767902i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	6.00000	+	3.46410i	0.248495	+	0.143468i
$584$		0			0
$585$	31.0919	+	53.8527i	1.28549	+	2.22654i
$586$		0			0
$587$			43.2638i			1.78569i	0.450365	+	0.892845i	$0.351294\pi$
$587$			43.2638i			1.78569i	−0.450365	+	0.892845i	$0.648706\pi$
$588$		0			0
$589$		−	12.6677i		−	0.521964i
$590$		0			0
$591$	34.6554	+	60.0250i	1.42553	+	2.46910i
$592$		0			0
$593$	10.6523	+	6.15013i	0.437439	+	0.252556i	0.702511	−	0.711673i	$-0.252062\pi$
$593$	10.6523	+	6.15013i	0.437439	+	0.252556i	−0.265072	+	0.964229i	$0.585396\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−6.00000	−	3.46410i	−0.245564	−	0.141776i
$598$		0			0
$599$	30.7279	−	17.7408i	1.25551	−	0.724868i	0.283311	−	0.959028i	$-0.408567\pi$
$599$	30.7279	−	17.7408i	1.25551	−	0.724868i	0.972198	+	0.234160i	$0.0752339\pi$
$600$		0			0
$601$		−	35.1843i		−	1.43520i	−0.696456	−	0.717600i	$-0.745241\pi$
$601$		−	35.1843i		−	1.43520i	0.696456	−	0.717600i	$-0.254759\pi$
$602$		0			0
$603$	45.9411			1.87087
$604$		0			0
$605$	11.2014	+	19.4015i	0.455403	+	0.788782i
$606$		0			0
$607$	12.8017	−	22.1731i	0.519603	−	0.899979i	−0.480137	−	0.877193i	$-0.659413\pi$
$607$	12.8017	−	22.1731i	0.519603	−	0.899979i	0.999740	−	0.0227854i	$-0.00725346\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	13.4558	−	23.3062i	0.544365	−	0.942868i
$612$		0			0
$613$	23.3345	−	13.4722i	0.942473	−	0.544137i	0.0517380	−	0.998661i	$-0.483524\pi$
$613$	23.3345	−	13.4722i	0.942473	−	0.544137i	0.890735	+	0.454524i	$0.150191\pi$
$614$		0			0
$615$	37.3067			1.50435
$616$		0			0
$617$	−9.21320			−0.370910			−0.185455	−	0.982653i	$-0.559376\pi$
$617$	−9.21320			−0.370910			−0.185455	+	0.982653i	$0.559376\pi$
$618$		0			0
$619$	−25.2150	+	14.5579i	−1.01348	+	0.585131i	−0.912208	−	0.409728i	$-0.865624\pi$
$619$	−25.2150	+	14.5579i	−1.01348	+	0.585131i	−0.101270	+	0.994859i	$0.532290\pi$
$620$		0			0
$621$	1.55310	−	2.69005i	0.0623238	−	0.107948i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	11.8640	−	20.5490i	0.474558	−	0.821959i
$626$		0			0
$627$	−12.4853	−	21.6251i	−0.498614	−	0.863625i
$628$		0			0
$629$	0.776550			0.0309631
$630$		0			0
$631$			29.7420i			1.18401i	0.805934	+	0.592006i	$0.201664\pi$
$631$			29.7420i			1.18401i	−0.805934	+	0.592006i	$0.798336\pi$
$632$		0			0
$633$	−46.3589	+	26.7653i	−1.84260	+	1.06383i
$634$		0			0
$635$	−15.2255	−	8.79045i	−0.604206	−	0.348839i
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	8.46447	+	14.6609i	0.334326	+	0.579070i	0.983355	−	0.181694i	$-0.0581579\pi$
$641$	8.46447	+	14.6609i	0.334326	+	0.579070i	−0.649029	+	0.760764i	$0.724825\pi$
$642$		0			0
$643$			36.3981i			1.43540i	0.696353	+	0.717700i	$0.254805\pi$
$643$			36.3981i			1.43540i	−0.696353	+	0.717700i	$0.745195\pi$
$644$		0			0
$645$			73.8329i			2.90717i
$646$		0			0
$647$	5.85172	+	10.1355i	0.230055	+	0.398467i	0.957824	−	0.287355i	$-0.0927761\pi$
$647$	5.85172	+	10.1355i	0.230055	+	0.398467i	−0.727769	+	0.685822i	$0.759443\pi$
$648$		0			0
$649$	−4.52607	−	2.61313i	−0.177664	−	0.102574i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−30.3640	−	17.5306i	−1.18823	−	0.686027i	−0.230329	−	0.973113i	$-0.573980\pi$
$653$	−30.3640	−	17.5306i	−1.18823	−	0.686027i	−0.957905	+	0.287086i	$0.907313\pi$
$654$		0			0
$655$	9.72792	−	5.61642i	0.380101	−	0.219452i
$656$		0			0
$657$			5.35757i			0.209019i
$658$		0			0
$659$	−25.5147			−0.993912			−0.496956	−	0.867776i	$-0.665549\pi$
$659$	−25.5147			−0.993912			−0.496956	+	0.867776i	$0.665549\pi$
$660$		0			0
$661$	10.4249	+	18.0564i	0.405481	+	0.702314i	0.994377	−	0.105894i	$-0.0337706\pi$
$661$	10.4249	+	18.0564i	0.405481	+	0.702314i	−0.588896	+	0.808209i	$0.700437\pi$
$662$		0			0
$663$	2.10220	−	3.64113i	0.0816429	−	0.141410i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−6.72792	+	11.6531i	−0.260506	+	0.451210i
$668$		0			0
$669$	55.4558	−	32.0174i	2.14405	−	1.23787i
$670$		0			0
$671$	−7.95393			−0.307058
$672$		0			0
$673$	30.3848			1.17125			0.585624	−	0.810583i	$-0.300850\pi$
$673$	30.3848			1.17125			0.585624	+	0.810583i	$0.300850\pi$
$674$		0			0
$675$	−9.82868	+	5.67459i	−0.378306	+	0.218415i
$676$		0			0
$677$	0.501998	−	0.869487i	0.0192934	−	0.0334171i	−0.856218	−	0.516615i	$-0.827192\pi$
$677$	0.501998	−	0.869487i	0.0192934	−	0.0334171i	0.875511	+	0.483198i	$0.160525\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−30.3848	+	52.6280i	−1.16435	+	2.01671i
$682$		0			0
$683$	−7.07107	−	12.2474i	−0.270567	−	0.468636i	0.698440	−	0.715668i	$-0.253878\pi$
$683$	−7.07107	−	12.2474i	−0.270567	−	0.468636i	−0.969007	+	0.247033i	$0.920544\pi$
$684$		0			0
$685$	0.776550			0.0296705
$686$		0			0
$687$			45.8739i			1.75020i
$688$		0			0
$689$	−15.2255	+	8.79045i	−0.580046	+	0.334890i
$690$		0			0
$691$	17.2611	+	9.96570i	0.656643	+	0.379113i	0.790997	−	0.611820i	$-0.209562\pi$
$691$	17.2611	+	9.96570i	0.656643	+	0.379113i	−0.134354	+	0.990933i	$0.542896\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	13.9706	+	8.06591i	0.529934	+	0.305957i
$696$		0			0
$697$	−0.707107	−	1.22474i	−0.0267836	−	0.0463905i
$698$		0			0
$699$		−	52.8966i		−	2.00073i
$700$		0			0
$701$			6.15978i			0.232652i	0.993211	+	0.116326i	$0.0371117\pi$
$701$			6.15978i			0.232652i	−0.993211	+	0.116326i	$0.962888\pi$
$702$		0			0
$703$	5.85172	+	10.1355i	0.220702	+	0.382267i
$704$		0			0
$705$	38.4050	+	22.1731i	1.44641	+	0.835088i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	31.8198	+	18.3712i	1.19502	+	0.689944i	0.959440	−	0.281912i	$-0.0909685\pi$
$709$	31.8198	+	18.3712i	1.19502	+	0.689944i	0.235578	+	0.971856i	$0.424302\pi$
$710$		0			0
$711$	−39.2132	+	22.6398i	−1.47061	+	0.849057i
$712$		0			0
$713$		−	3.80430i		−	0.142472i
$714$		0			0
$715$	32.4853			1.21488
$716$		0			0
$717$	−17.3277	−	30.0125i	−0.647115	−	1.12084i
$718$		0			0
$719$	−14.6764	+	25.4203i	−0.547338	+	0.948017i	0.451118	+	0.892464i	$0.351025\pi$
$719$	−14.6764	+	25.4203i	−0.547338	+	0.948017i	−0.998456	+	0.0555524i	$0.982308\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−28.8995	+	50.0554i	−1.07478	+	1.86158i
$724$		0			0
$725$	42.5772	−	24.5819i	1.58128	−	0.912950i
$726$		0			0
$727$	−43.0643			−1.59716			−0.798582	−	0.601886i	$-0.794416\pi$
$727$	−43.0643			−1.59716			−0.798582	+	0.601886i	$0.794416\pi$
$728$		0			0
$729$	39.2843			1.45497
$730$		0			0
$731$	2.42386	−	1.39942i	0.0896498	−	0.0517593i
$732$		0			0
$733$	−3.70241	+	6.41276i	−0.136752	+	0.236861i	−0.926265	−	0.376872i	$-0.877000\pi$
$733$	−3.70241	+	6.41276i	−0.136752	+	0.236861i	0.789514	+	0.613733i	$0.210333\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	12.0000	−	20.7846i	0.442026	−	0.765611i
$738$		0			0
$739$	7.58579	+	13.1390i	0.279048	+	0.483325i	0.971148	−	0.238476i	$-0.0766479\pi$
$739$	7.58579	+	13.1390i	0.279048	+	0.483325i	−0.692101	+	0.721801i	$0.743315\pi$
$740$		0			0
$741$	63.3649			2.32777
$742$		0			0
$743$			13.2621i			0.486538i	0.969959	+	0.243269i	$0.0782197\pi$
$743$			13.2621i			0.486538i	−0.969959	+	0.243269i	$0.921780\pi$
$744$		0			0
$745$	55.9601	−	32.3086i	2.05022	−	1.18370i
$746$		0			0
$747$	−28.0938	−	16.2200i	−1.02790	−	0.593457i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	30.9411	+	17.8639i	1.12906	+	0.651862i	0.943698	−	0.330809i	$-0.107322\pi$
$751$	30.9411	+	17.8639i	1.12906	+	0.651862i	0.185360	+	0.982671i	$0.440655\pi$
$752$		0			0
$753$	−25.0711	−	43.4244i	−0.913641	−	1.58247i
$754$		0			0
$755$		−	48.9384i		−	1.78105i
$756$		0			0
$757$			35.9018i			1.30487i	0.757843	+	0.652437i	$0.226253\pi$
$757$			35.9018i			1.30487i	−0.757843	+	0.652437i	$0.773747\pi$
$758$		0			0
$759$	−3.74952	−	6.49435i	−0.136099	−	0.235730i
$760$		0			0
$761$	−18.9279	−	10.9280i	−0.686137	−	0.396141i	0.116026	−	0.993246i	$-0.462984\pi$
$761$	−18.9279	−	10.9280i	−0.686137	−	0.396141i	−0.802163	+	0.597105i	$0.796318\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	3.36396	+	1.94218i	0.121624	+	0.0702198i
$766$		0			0
$767$	11.4853	−	6.63103i	0.414709	−	0.239433i
$768$		0			0
$769$		−	46.1940i		−	1.66580i	−0.553425	−	0.832899i	$-0.686680\pi$
$769$		−	46.1940i		−	1.66580i	0.553425	−	0.832899i	$-0.313320\pi$
$770$		0			0
$771$	21.3137			0.767594
$772$		0			0
$773$	15.5001	+	26.8469i	0.557499	+	0.965616i	0.997704	+	0.0677190i	$0.0215721\pi$
$773$	15.5001	+	26.8469i	0.557499	+	0.965616i	−0.440206	+	0.897897i	$0.645095\pi$
$774$		0			0
$775$	−6.94993	+	12.0376i	−0.249649	+	0.432404i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	10.6569	−	18.4582i	0.381821	−	0.661334i
$780$		0			0
$781$		0			0
$782$		0			0
$783$	20.3007			0.725487
$784$		0			0
$785$	76.6690			2.73644
$786$		0			0
$787$	−33.6238	+	19.4127i	−1.19856	+	0.691989i	−0.960234	−	0.279196i	$-0.909932\pi$
$787$	−33.6238	+	19.4127i	−1.19856	+	0.691989i	−0.238326	+	0.971185i	$0.576599\pi$
$788$		0			0
$789$	11.7034	−	20.2710i	0.416654	−	0.721665i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	10.0919	−	17.4797i	0.358373	−	0.620721i
$794$		0			0
$795$	−14.4853	−	25.0892i	−0.513740	−	0.889824i
$796$		0			0
$797$	−13.4840			−0.477627			−0.238814	−	0.971065i	$-0.576759\pi$
$797$	−13.4840			−0.477627			−0.238814	+	0.971065i	$0.576759\pi$
$798$		0			0
$799$		−	1.68106i		−	0.0594718i
$800$		0			0
$801$	32.7336	−	18.8987i	1.15658	−	0.667754i
$802$		0			0
$803$	2.42386	+	1.39942i	0.0855362	+	0.0493844i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−5.48528	−	3.16693i	−0.193091	−	0.111481i
$808$		0			0
$809$	7.72792	+	13.3852i	0.271699	+	0.470597i	0.969297	−	0.245893i	$-0.0790811\pi$
$809$	7.72792	+	13.3852i	0.271699	+	0.470597i	−0.697598	+	0.716490i	$0.745748\pi$
$810$		0			0
$811$		−	28.4818i		−	1.00013i	−0.865988	−	0.500065i	$-0.833310\pi$
$811$		−	28.4818i		−	1.00013i	0.865988	−	0.500065i	$-0.166690\pi$
$812$		0			0
$813$			34.6410i			1.21491i
$814$		0			0
$815$	13.0291	+	22.5671i	0.456389	+	0.790490i
$816$		0			0
$817$	36.5302	+	21.0907i	1.27803	+	0.737871i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−15.5147	−	8.95743i	−0.541467	−	0.312616i	0.204206	−	0.978928i	$-0.434539\pi$
$821$	−15.5147	−	8.95743i	−0.541467	−	0.312616i	−0.745673	+	0.666312i	$0.767872\pi$
$822$		0			0
$823$	−18.0000	+	10.3923i	−0.627441	+	0.362253i	−0.779760	−	0.626078i	$-0.784659\pi$
$823$	−18.0000	+	10.3923i	−0.627441	+	0.362253i	0.152320	+	0.988331i	$0.451326\pi$
$824$		0			0
$825$			27.3994i			0.953923i
$826$		0			0
$827$	12.0000			0.417281			0.208640	−	0.977992i	$-0.433096\pi$
$827$	12.0000			0.417281			0.208640	+	0.977992i	$0.433096\pi$
$828$		0			0
$829$	−8.38931	−	14.5307i	−0.291373	−	0.504672i	0.682762	−	0.730641i	$-0.260779\pi$
$829$	−8.38931	−	14.5307i	−0.291373	−	0.504672i	−0.974135	+	0.225969i	$0.927445\pi$
$830$		0			0
$831$	−21.8538	+	37.8519i	−0.758099	+	1.31307i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	22.9706	−	39.7862i	0.794929	−	1.37686i
$836$		0			0
$837$	−4.97056	+	2.86976i	−0.171808	+	0.0991933i
$838$		0			0
$839$	30.4510			1.05129			0.525643	−	0.850705i	$-0.323825\pi$
$839$	30.4510			1.05129			0.525643	+	0.850705i	$0.323825\pi$
$840$		0			0
$841$	−58.9411			−2.03245
$842$		0			0
$843$	19.7516	−	11.4036i	0.680281	−	0.392760i
$844$		0			0
$845$	−20.4144	+	35.3588i	−0.702277	+	1.21638i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	0.242641	−	0.420266i	0.00832741	−	0.0144235i
$850$		0			0
$851$	1.75736	+	3.04384i	0.0602415	+	0.104341i
$852$		0			0
$853$	32.5532			1.11460			0.557301	−	0.830311i	$-0.311837\pi$
$853$	32.5532			1.11460			0.557301	+	0.830311i	$0.311837\pi$
$854$		0			0
$855$			58.5416i			2.00208i
$856$		0			0
$857$	29.8548	−	17.2367i	1.01982	−	0.588794i	0.105769	−	0.994391i	$-0.466270\pi$
$857$	29.8548	−	17.2367i	1.01982	−	0.588794i	0.914052	+	0.405597i	$0.132936\pi$
$858$		0			0
$859$	−38.5658	−	22.2660i	−1.31585	−	0.759705i	−0.332790	−	0.943001i	$-0.607990\pi$
$859$	−38.5658	−	22.2660i	−1.31585	−	0.759705i	−0.983058	+	0.183296i	$0.941323\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−3.51472	−	2.02922i	−0.119642	−	0.0690756i	0.438985	−	0.898495i	$-0.355338\pi$
$863$	−3.51472	−	2.02922i	−0.119642	−	0.0690756i	−0.558627	+	0.829419i	$0.688672\pi$
$864$		0			0
$865$	11.1213	+	19.2627i	0.378136	+	0.654951i
$866$		0			0
$867$			44.1605i			1.49977i
$868$		0			0
$869$			23.6544i			0.802419i
$870$		0			0
$871$	30.4510	+	52.7427i	1.03179	+	1.78712i
$872$		0			0
$873$	12.6879	+	7.32538i	0.429421	+	0.247926i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	27.8787	+	16.0958i	0.941396	+	0.543515i	0.890398	−	0.455183i	$-0.150426\pi$
$877$	27.8787	+	16.0958i	0.941396	+	0.543515i	0.0509984	+	0.998699i	$0.483760\pi$
$878$		0			0
$879$	−11.4853	+	6.63103i	−0.387389	+	0.223659i
$880$		0			0
$881$			34.8448i			1.17395i	0.809605	+	0.586975i	$0.199681\pi$
$881$			34.8448i			1.17395i	−0.809605	+	0.586975i	$0.800319\pi$
$882$		0			0
$883$	−38.4264			−1.29315			−0.646576	−	0.762850i	$-0.723800\pi$
$883$	−38.4264			−1.29315			−0.646576	+	0.762850i	$0.723800\pi$
$884$		0			0
$885$	10.9269	+	18.9259i	0.367303	+	0.636188i
$886$		0			0
$887$	19.9790	−	34.6047i	0.670830	−	1.16191i	−0.306839	−	0.951761i	$-0.599271\pi$
$887$	19.9790	−	34.6047i	0.670830	−	1.16191i	0.977669	−	0.210150i	$-0.0673953\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	5.82843	−	10.0951i	0.195260	−	0.338200i
$892$		0			0
$893$	21.9411	−	12.6677i	0.734232	−	0.423909i
$894$		0			0
$895$	65.5614			2.19147
$896$		0			0
$897$	19.0294			0.635374
$898$		0			0
$899$	21.5321	−	12.4316i	0.718137	−	0.414616i
$900$		0			0
$901$	−0.549104	+	0.951076i	−0.0182933	+	0.0316849i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−3.36396	+	5.82655i	−0.111822	+	0.193681i
$906$		0			0
$907$	−8.00000	−	13.8564i	−0.265636	−	0.460094i	0.702094	−	0.712084i	$-0.252248\pi$
$907$	−8.00000	−	13.8564i	−0.265636	−	0.460094i	−0.967730	+	0.251990i	$0.918915\pi$
$908$		0			0
$909$	29.5803			0.981115
$910$		0			0
$911$		−	5.49333i		−	0.182002i	−0.995851	−	0.0910010i	$-0.970993\pi$
$911$		−	5.49333i		−	0.182002i	0.995851	−	0.0910010i	$-0.0290066\pi$
$912$		0			0
$913$	−14.6764	+	8.47343i	−0.485718	+	0.280430i
$914$		0			0
$915$	28.8037	+	16.6298i	0.952221	+	0.549765i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	15.5147	+	8.95743i	0.511783	+	0.295478i	0.733566	−	0.679618i	$-0.237854\pi$
$919$	15.5147	+	8.95743i	0.511783	+	0.295478i	−0.221783	+	0.975096i	$0.571188\pi$
$920$		0			0
$921$	−7.89949	−	13.6823i	−0.260297	−	0.450848i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		−	12.8418i		−	0.422236i
$926$		0			0
$927$	−29.5803	−	51.2345i	−0.971543	−	1.68276i
$928$		0			0
$929$	1.37276	+	0.792563i	0.0450388	+	0.0260032i	0.522350	−	0.852731i	$-0.325055\pi$
$929$	1.37276	+	0.792563i	0.0450388	+	0.0260032i	−0.477312	+	0.878734i	$0.658389\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−61.4558	−	35.4815i	−2.01197	−	1.16161i
$934$		0			0
$935$	1.75736	−	1.01461i	0.0574718	−	0.0331814i
$936$		0			0
$937$			16.9694i			0.554366i	0.960817	+	0.277183i	$0.0894008\pi$
$937$			16.9694i			0.554366i	−0.960817	+	0.277183i	$0.910599\pi$
$938$		0			0
$939$	27.6569			0.902547
$940$		0			0
$941$	−1.21193	−	2.09913i	−0.0395078	−	0.0684296i	0.845595	−	0.533824i	$-0.179246\pi$
$941$	−1.21193	−	2.09913i	−0.0395078	−	0.0684296i	−0.885103	+	0.465395i	$0.845912\pi$
$942$		0			0
$943$	3.20041	−	5.54328i	0.104220	−	0.180514i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	25.7279	−	44.5621i	0.836045	−	1.44807i	−0.0571315	−	0.998367i	$-0.518195\pi$
$947$	25.7279	−	44.5621i	0.836045	−	1.44807i	0.893177	−	0.449706i	$-0.148471\pi$
$948$		0			0
$949$	−6.15076	+	3.55114i	−0.199662	+	0.115275i
$950$		0			0
$951$	10.6052			0.343898
$952$		0			0
$953$	−41.3137			−1.33828			−0.669141	−	0.743135i	$-0.733338\pi$
$953$	−41.3137			−1.33828			−0.669141	+	0.743135i	$0.733338\pi$
$954$		0			0
$955$	32.7807	−	18.9259i	1.06076	−	0.612429i
$956$		0			0
$957$	24.5051	−	42.4441i	0.792137	−	1.37202i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	11.9853	−	20.7591i	0.386622	−	0.669649i
$962$		0			0
$963$	16.2426	+	28.1331i	0.523412	+	0.906576i
$964$		0			0
$965$	−45.2607			−1.45699
$966$		0			0
$967$			21.0308i			0.676305i	0.941091	+	0.338152i	$0.109802\pi$
$967$			21.0308i			0.676305i	−0.941091	+	0.338152i	$0.890198\pi$
$968$		0			0
$969$	3.42786	−	1.97908i	0.110119	−	0.0635771i
$970$		0			0
$971$	21.4655	+	12.3931i	0.688861	+	0.397714i	0.803185	−	0.595729i	$-0.203137\pi$
$971$	21.4655	+	12.3931i	0.688861	+	0.397714i	−0.114324	+	0.993443i	$0.536470\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−60.2132	−	34.7641i	−1.92837	−	1.11334i
$976$		0			0
$977$	−18.6066	−	32.2276i	−0.595278	−	1.03105i	−0.993508	−	0.113766i	$-0.963709\pi$
$977$	−18.6066	−	32.2276i	−0.595278	−	1.03105i	0.398230	−	0.917286i	$-0.369625\pi$
$978$		0			0
$979$		−	19.7457i		−	0.631075i
$980$		0			0
$981$		−	1.60896i		−	0.0513701i
$982$		0			0
$983$	13.0291	+	22.5671i	0.415564	+	0.719777i	0.995487	−	0.0948934i	$-0.0302510\pi$
$983$	13.0291	+	22.5671i	0.415564	+	0.719777i	−0.579924	+	0.814671i	$0.696918\pi$
$984$		0			0
$985$	−73.5153	−	42.4441i	−2.34239	−	1.35238i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	10.9706	+	6.33386i	0.348844	+	0.201405i
$990$		0			0
$991$	27.9411	−	16.1318i	0.887579	−	0.512444i	0.0144292	−	0.999896i	$-0.495407\pi$
$991$	27.9411	−	16.1318i	0.887579	−	0.512444i	0.873150	+	0.487452i	$0.162074\pi$
$992$		0			0
$993$		−	54.4273i		−	1.72720i
$994$		0			0
$995$	8.48528			0.269002
$996$		0			0
$997$	−2.69841	−	4.67379i	−0.0854596	−	0.148020i	0.820127	−	0.572181i	$-0.193903\pi$
$997$	−2.69841	−	4.67379i	−0.0854596	−	0.148020i	−0.905587	+	0.424161i	$0.860569\pi$
$998$		0			0
$999$	2.65131	−	4.59220i	0.0838837	−	0.145291i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1568.2.q.c.1391.4		8
4.3	odd	2		392.2.m.c.19.3		8
7.2	even	3		1568.2.e.c.783.8		8
7.3	odd	6		1568.2.q.d.815.4		8
7.4	even	3		1568.2.q.d.815.1		8
7.5	odd	6		1568.2.e.c.783.1		8
7.6	odd	2	inner	1568.2.q.c.1391.1		8
8.3	odd	2		1568.2.q.d.1391.4		8
8.5	even	2		392.2.m.e.19.1		8
28.3	even	6		392.2.m.e.227.1		8
28.11	odd	6		392.2.m.e.227.2		8
28.19	even	6		392.2.e.c.195.6	yes	8
28.23	odd	6		392.2.e.c.195.5	✓	8
28.27	even	2		392.2.m.c.19.4		8
56.3	even	6	inner	1568.2.q.c.815.4		8
56.5	odd	6		392.2.e.c.195.8	yes	8
56.11	odd	6	inner	1568.2.q.c.815.1		8
56.13	odd	2		392.2.m.e.19.2		8
56.19	even	6		1568.2.e.c.783.2		8
56.27	even	2		1568.2.q.d.1391.1		8
56.37	even	6		392.2.e.c.195.7	yes	8
56.45	odd	6		392.2.m.c.227.3		8
56.51	odd	6		1568.2.e.c.783.7		8
56.53	even	6		392.2.m.c.227.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
392.2.e.c.195.5	✓	8	28.23	odd	6
392.2.e.c.195.6	yes	8	28.19	even	6
392.2.e.c.195.7	yes	8	56.37	even	6
392.2.e.c.195.8	yes	8	56.5	odd	6
392.2.m.c.19.3		8	4.3	odd	2
392.2.m.c.19.4		8	28.27	even	2
392.2.m.c.227.3		8	56.45	odd	6
392.2.m.c.227.4		8	56.53	even	6
392.2.m.e.19.1		8	8.5	even	2
392.2.m.e.19.2		8	56.13	odd	2
392.2.m.e.227.1		8	28.3	even	6
392.2.m.e.227.2		8	28.11	odd	6
1568.2.e.c.783.1		8	7.5	odd	6
1568.2.e.c.783.2		8	56.19	even	6
1568.2.e.c.783.7		8	56.51	odd	6
1568.2.e.c.783.8		8	7.2	even	3
1568.2.q.c.815.1		8	56.11	odd	6	inner
1568.2.q.c.815.4		8	56.3	even	6	inner
1568.2.q.c.1391.1		8	7.6	odd	2	inner
1568.2.q.c.1391.4		8	1.1	even	1	trivial
1568.2.q.d.815.1		8	7.4	even	3
1568.2.q.d.815.4		8	7.3	odd	6
1568.2.q.d.1391.1		8	56.27	even	2
1568.2.q.d.1391.4		8	8.3	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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(2.26303 - 1.30656i) q^{3} +(-1.60021 + 2.77164i) q^{5} +(1.91421 - 3.31552i) q^{9} +(-1.00000 - 1.73205i) q^{11} +5.07517 q^{13} +8.36308i q^{15} +(0.274552 - 0.158513i) q^{17} +(4.13779 + 2.38896i) q^{19} +(1.24264 + 0.717439i) q^{23} +(-2.62132 - 4.54026i) q^{25} -2.16478i q^{27} +9.37769i q^{29} +(-1.32565 - 2.29610i) q^{31} +(-4.52607 - 2.61313i) q^{33} +(2.12132 + 1.22474i) q^{37} +(11.4853 - 6.63103i) q^{39} -4.46088i q^{41} +8.82843 q^{43} +(6.12627 + 10.6110i) q^{45} +(2.65131 - 4.59220i) q^{47} +(0.414214 - 0.717439i) q^{51} +(-3.00000 + 1.73205i) q^{53} +6.40083 q^{55} +12.4853 q^{57} +(2.26303 - 1.30656i) q^{59} +(1.98848 - 3.44415i) q^{61} +(-8.12132 + 14.0665i) q^{65} +(6.00000 + 10.3923i) q^{67} +3.74952 q^{69} +(-1.21193 + 0.699709i) q^{73} +(-11.8643 - 6.84984i) q^{75} +(-10.2426 - 5.91359i) q^{79} +(2.91421 + 5.04757i) q^{81} -8.47343i q^{83} +1.01461i q^{85} +(12.2525 + 21.2220i) q^{87} +(8.55014 + 4.93642i) q^{89} +(-6.00000 - 3.46410i) q^{93} +(-13.2426 + 7.64564i) q^{95} +3.82683i q^{97} -7.65685 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{9} - 8 q^{11} - 24 q^{23} - 4 q^{25} + 24 q^{39} + 48 q^{43} - 8 q^{51} - 24 q^{53} + 32 q^{57} - 48 q^{65} + 48 q^{67} - 48 q^{79} + 12 q^{81} - 48 q^{93} - 72 q^{95} - 16 q^{99}+O(q^{100}) \) 8 * q + 4 * q^9 - 8 * q^11 - 24 * q^23 - 4 * q^25 + 24 * q^39 + 48 * q^43 - 8 * q^51 - 24 * q^53 + 32 * q^57 - 48 * q^65 + 48 * q^67 - 48 * q^79 + 12 * q^81 - 48 * q^93 - 72 * q^95 - 16 * q^99

Introduction

L-functions

Modular forms

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Representations

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Database

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