LMFDB - Embedded newform 1300.2.y.e.101.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1300,2,Mod(101,1300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1300, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5]))

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

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

chi := DirichletCharacter("1300.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1300 = 2^{2} \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1300.y (of order $6$, degree $2$, 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:	$10.3805522628$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 7x^{14} + 21x^{12} + 22x^{10} - 26x^{8} + 198x^{6} + 1701x^{4} + 5103x^{2} + 6561 $ x^16 + 7x^14 + 21x^12 + 22x^10 - 26x^8 + 198x^6 + 1701x^4 + 5103*x^2 + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{12} $
Twist minimal:	no (minimal twist has level 260)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.8
Root			$-1.65307 - 0.517063i$ of defining polynomial
Character	$\chi$	$=$	1300.101
Dual form			1300.2.y.e.901.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.65307 + 2.86320i) q^{3} +(-0.895580 - 0.517063i) q^{7} +(-3.96529 + 6.86809i) q^{9} +O(q^{10})$	$q+(1.65307 + 2.86320i) q^{3} +(-0.895580 - 0.517063i) q^{7} +(-3.96529 + 6.86809i) q^{9} +(-2.96091 + 1.70948i) q^{11} +(-0.455025 + 3.57672i) q^{13} +(1.19805 - 2.07508i) q^{17} +(5.37246 + 3.10179i) q^{19} -3.41897i q^{21} +(-3.62751 - 6.28304i) q^{23} -16.3012 q^{27} +(-0.902796 - 1.56369i) q^{29} +5.80053i q^{31} +(-9.78921 - 5.65180i) q^{33} +(-1.23585 + 0.713520i) q^{37} +(-10.9931 + 4.60975i) q^{39} +(-3.60158 + 2.07937i) q^{41} +(-1.07886 + 1.86864i) q^{43} -3.50894i q^{47} +(-2.96529 - 5.13604i) q^{49} +7.92183 q^{51} +4.55382 q^{53} +20.5099i q^{57} +(5.06250 + 2.92283i) q^{59} +(-1.90280 + 3.29574i) q^{61} +(7.10247 - 4.10061i) q^{63} +(-6.59603 + 3.80822i) q^{67} +(11.9931 - 20.7726i) q^{69} +(9.49745 + 5.48336i) q^{71} +7.15345i q^{73} +3.53565 q^{77} +12.8524 q^{79} +(-15.0512 - 26.0694i) q^{81} -0.706694i q^{83} +(2.98477 - 5.16978i) q^{87} +(-5.06250 + 2.92283i) q^{89} +(2.25690 - 2.96796i) q^{91} +(-16.6081 + 9.58870i) q^{93} +(-13.8528 - 7.99794i) q^{97} -27.1144i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 10 q^{9}+O(q^{10}) $ 16 * q - 10 * q^9	$ 16 q - 10 q^{9} - 6 q^{11} + 18 q^{19} - 12 q^{29} - 18 q^{39} - 48 q^{41} + 6 q^{49} + 44 q^{51} + 30 q^{59} - 28 q^{61} + 34 q^{69} - 18 q^{71} + 16 q^{79} - 44 q^{81} - 30 q^{89} - 10 q^{91}+O(q^{100}) $ 16 * q - 10 * q^9 - 6 * q^11 + 18 * q^19 - 12 * q^29 - 18 * q^39 - 48 * q^41 + 6 * q^49 + 44 * q^51 + 30 * q^59 - 28 * q^61 + 34 * q^69 - 18 * q^71 + 16 * q^79 - 44 * q^81 - 30 * q^89 - 10 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1300\mathbb{Z}\right)^\times$.

$n$	$301$	$651$	$677$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.65307	+	2.86320i	0.954401	+	1.65307i	0.735732	+	0.677273i	$0.236838\pi$
$3$	1.65307	+	2.86320i	0.954401	+	1.65307i	0.218669	+	0.975799i	$0.429828\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−0.895580	−	0.517063i	−0.338497	−	0.195432i	0.321110	−	0.947042i	$-0.395944\pi$
$7$	−0.895580	−	0.517063i	−0.338497	−	0.195432i	−0.659607	+	0.751610i	$0.729277\pi$
$8$		0			0
$9$	−3.96529	+	6.86809i	−1.32176	+	2.28936i
$10$		0			0
$11$	−2.96091	+	1.70948i	−0.892749	+	0.515429i	−0.874841	−	0.484411i	$-0.839034\pi$
$11$	−2.96091	+	1.70948i	−0.892749	+	0.515429i	−0.0179086	+	0.999840i	$0.505701\pi$
$12$		0			0
$13$	−0.455025	+	3.57672i	−0.126201	+	0.992005i
$13$	−0.455025	+	3.57672i	−0.126201	+	0.992005i
$14$		0			0
$15$		0			0
$16$		0			0
$17$	1.19805	−	2.07508i	0.290569	−	0.503280i	−0.683375	−	0.730067i	$-0.739489\pi$
$17$	1.19805	−	2.07508i	0.290569	−	0.503280i	0.973944	+	0.226787i	$0.0728221\pi$
$18$		0			0
$19$	5.37246	+	3.10179i	1.23253	+	0.711600i	0.967556	−	0.252656i	$-0.0813041\pi$
$19$	5.37246	+	3.10179i	1.23253	+	0.711600i	0.264972	+	0.964256i	$0.414637\pi$
$20$		0			0
$21$		−	3.41897i		−	0.746080i
$22$		0			0
$23$	−3.62751	−	6.28304i	−0.756389	−	1.31010i	−0.944681	−	0.327991i	$-0.893629\pi$
$23$	−3.62751	−	6.28304i	−0.756389	−	1.31010i	0.188292	−	0.982113i	$-0.439705\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−16.3012			−3.13717
$28$		0			0
$29$	−0.902796	−	1.56369i	−0.167645	−	0.290370i	0.769946	−	0.638109i	$-0.220283\pi$
$29$	−0.902796	−	1.56369i	−0.167645	−	0.290370i	−0.937591	+	0.347739i	$0.886950\pi$
$30$		0			0
$31$			5.80053i			1.04181i	0.853616	+	0.520903i	$0.174405\pi$
$31$			5.80053i			1.04181i	−0.853616	+	0.520903i	$0.825595\pi$
$32$		0			0
$33$	−9.78921	−	5.65180i	−1.70408	−	0.983852i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−1.23585	+	0.713520i	−0.203173	+	0.117302i	−0.598135	−	0.801396i	$-0.704091\pi$
$37$	−1.23585	+	0.713520i	−0.203173	+	0.117302i	0.394962	+	0.918698i	$0.370758\pi$
$38$		0			0
$39$	−10.9931	+	4.60975i	−1.76030	+	0.738151i
$40$		0			0
$41$	−3.60158	+	2.07937i	−0.562472	+	0.324744i	−0.754137	−	0.656717i	$-0.771945\pi$
$41$	−3.60158	+	2.07937i	−0.562472	+	0.324744i	0.191665	+	0.981460i	$0.438611\pi$
$42$		0			0
$43$	−1.07886	+	1.86864i	−0.164525	+	0.284965i	−0.936486	−	0.350704i	$-0.885942\pi$
$43$	−1.07886	+	1.86864i	−0.164525	+	0.284965i	0.771962	+	0.635669i	$0.219276\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$		−	3.50894i		−	0.511832i	−0.966699	−	0.255916i	$-0.917623\pi$
$47$		−	3.50894i		−	0.511832i	0.966699	−	0.255916i	$-0.0823770\pi$
$48$		0			0
$49$	−2.96529	−	5.13604i	−0.423613	−	0.733719i
$50$		0			0
$51$	7.92183			1.10928
$52$		0			0
$53$	4.55382			0.625515			0.312757	−	0.949833i	$-0.398747\pi$
$53$	4.55382			0.625515			0.312757	+	0.949833i	$0.398747\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$			20.5099i			2.71661i
$58$		0			0
$59$	5.06250	+	2.92283i	0.659081	+	0.380520i	0.791927	−	0.610616i	$-0.209078\pi$
$59$	5.06250	+	2.92283i	0.659081	+	0.380520i	−0.132846	+	0.991137i	$0.542412\pi$
$60$		0			0
$61$	−1.90280	+	3.29574i	−0.243628	+	0.421976i	−0.961745	−	0.273946i	$-0.911671\pi$
$61$	−1.90280	+	3.29574i	−0.243628	+	0.421976i	0.718117	+	0.695922i	$0.245004\pi$
$62$		0			0
$63$	7.10247	−	4.10061i	0.894827	−	0.516629i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−6.59603	+	3.80822i	−0.805833	+	0.465248i	−0.845507	−	0.533965i	$-0.820702\pi$
$67$	−6.59603	+	3.80822i	−0.805833	+	0.465248i	0.0396734	+	0.999213i	$0.487368\pi$
$68$		0			0
$69$	11.9931	−	20.7726i	1.44380	−	2.50073i
$70$		0			0
$71$	9.49745	+	5.48336i	1.12714	+	0.650755i	0.943214	−	0.332185i	$-0.107786\pi$
$71$	9.49745	+	5.48336i	1.12714	+	0.650755i	0.183926	+	0.982940i	$0.441119\pi$
$72$		0			0
$73$			7.15345i			0.837248i	0.908160	+	0.418624i	$0.137487\pi$
$73$			7.15345i			0.837248i	−0.908160	+	0.418624i	$0.862513\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	3.53565			0.402924
$78$		0			0
$79$	12.8524			1.44601			0.723005	−	0.690843i	$-0.242760\pi$
$79$	12.8524			1.44601			0.723005	+	0.690843i	$0.242760\pi$
$80$		0			0
$81$	−15.0512	−	26.0694i	−1.67236	−	2.89660i
$82$		0			0
$83$		−	0.706694i		−	0.0775698i	−0.999248	−	0.0387849i	$-0.987651\pi$
$83$		−	0.706694i		−	0.0775698i	0.999248	−	0.0387849i	$-0.0123487\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	2.98477	−	5.16978i	0.320001	−	0.554258i
$88$		0			0
$89$	−5.06250	+	2.92283i	−0.536623	+	0.309820i	−0.743709	−	0.668503i	$-0.766935\pi$
$89$	−5.06250	+	2.92283i	−0.536623	+	0.309820i	0.207086	+	0.978323i	$0.433602\pi$
$90$		0			0
$91$	2.25690	−	2.96796i	0.236588	−	0.311127i
$92$		0			0
$93$	−16.6081	+	9.58870i	−1.72218	+	0.994302i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−13.8528	−	7.99794i	−1.40654	−	0.812068i	−0.411490	−	0.911414i	$-0.634992\pi$
$97$	−13.8528	−	7.99794i	−1.40654	−	0.812068i	−0.995053	+	0.0993461i	$0.968325\pi$
$98$		0			0
$99$		−	27.1144i		−	2.72510i
$100$		0			0
$101$	2.99562	+	5.18857i	0.298076	+	0.516282i	0.975696	−	0.219130i	$-0.0703219\pi$
$101$	2.99562	+	5.18857i	0.298076	+	0.516282i	−0.677620	+	0.735412i	$0.736989\pi$
$102$		0			0
$103$	11.7096			1.15378			0.576890	−	0.816822i	$-0.304266\pi$
$103$	11.7096			1.15378			0.576890	+	0.816822i	$0.304266\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	6.78110	+	11.7452i	0.655554	+	1.13545i	0.981755	+	0.190152i	$0.0608980\pi$
$107$	6.78110	+	11.7452i	0.655554	+	1.13545i	−0.326201	+	0.945300i	$0.605769\pi$
$108$		0			0
$109$			1.39533i			0.133648i	0.997765	+	0.0668240i	$0.0212866\pi$
$109$			1.39533i			0.133648i	−0.997765	+	0.0668240i	$0.978713\pi$
$110$		0			0
$111$	−4.08591	−	2.35900i	−0.387817	−	0.223906i
$112$		0			0
$113$	−2.10810	+	3.65133i	−0.198313	+	0.343488i	−0.947982	−	0.318325i	$-0.896880\pi$
$113$	−2.10810	+	3.65133i	−0.198313	+	0.343488i	0.749669	+	0.661813i	$0.230213\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−22.7609	−	17.3079i	−2.10425	−	1.60012i
$118$		0			0
$119$	−2.14589	+	1.23893i	−0.196714	+	0.113573i
$120$		0			0
$121$	0.344677	−	0.596999i	0.0313343	−	0.0542726i
$122$		0			0
$123$	−11.9073	−	6.87471i	−1.07365	−	0.619871i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−2.98477	−	5.16978i	−0.264856	−	0.458744i	0.702670	−	0.711516i	$-0.251991\pi$
$127$	−2.98477	−	5.16978i	−0.264856	−	0.458744i	−0.967526	+	0.252772i	$0.918658\pi$
$128$		0			0
$129$	−7.13374			−0.628091
$130$		0			0
$131$	19.0556			1.66489			0.832447	−	0.554105i	$-0.186940\pi$
$131$	19.0556			1.66489			0.832447	+	0.554105i	$0.186940\pi$
$132$		0			0
$133$	−3.20765	−	5.55581i	−0.278138	−	0.481750i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−0.400964	−	0.231497i	−0.0342567	−	0.0197781i	0.482774	−	0.875745i	$-0.339629\pi$
$137$	−0.400964	−	0.231497i	−0.0342567	−	0.0197781i	−0.517031	+	0.855967i	$0.672963\pi$
$138$		0			0
$139$	−4.65970	+	8.07084i	−0.395231	+	0.684559i	−0.993131	−	0.117011i	$-0.962669\pi$
$139$	−4.65970	+	8.07084i	−0.395231	+	0.684559i	0.597900	+	0.801571i	$0.296002\pi$
$140$		0			0
$141$	10.0468	−	5.80053i	0.846095	−	0.488493i
$142$		0			0
$143$	−4.76707	−	11.3682i	−0.398642	−	0.950659i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	9.80368	−	16.9805i	0.808594	−	1.40053i
$148$		0			0
$149$	9.44524	+	5.45321i	0.773784	+	0.446744i	0.834223	−	0.551427i	$-0.185917\pi$
$149$	9.44524	+	5.45321i	0.773784	+	0.446744i	−0.0604387	+	0.998172i	$0.519250\pi$
$150$		0			0
$151$		−	4.85943i		−	0.395455i	−0.980257	−	0.197727i	$-0.936644\pi$
$151$		−	4.85943i		−	0.395455i	0.980257	−	0.197727i	$-0.0633561\pi$
$152$		0			0
$153$	9.50121	+	16.4566i	0.768127	+	1.33044i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	8.80782			0.702940			0.351470	−	0.936199i	$-0.385682\pi$
$157$	8.80782			0.702940			0.351470	+	0.936199i	$0.385682\pi$
$158$		0			0
$159$	7.52779	+	13.0385i	0.596992	+	1.03402i
$160$		0			0
$161$			7.50261i			0.591289i
$162$		0			0
$163$	16.1253	+	9.30996i	1.26303	+	0.729212i	0.973660	−	0.228004i	$-0.0732201\pi$
$163$	16.1253	+	9.30996i	1.26303	+	0.729212i	0.289372	+	0.957217i	$0.406553\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	12.4508	−	7.18849i	0.963474	−	0.556262i	0.0662334	−	0.997804i	$-0.478902\pi$
$167$	12.4508	−	7.18849i	0.963474	−	0.556262i	0.897240	+	0.441542i	$0.145568\pi$
$168$		0			0
$169$	−12.5859	−	3.25499i	−0.968147	−	0.250384i
$170$		0			0
$171$	−42.6068	+	24.5990i	−3.25822	+	1.88113i
$172$		0			0
$173$	10.9666	−	18.9947i	0.833773	−	1.44414i	−0.0612532	−	0.998122i	$-0.519510\pi$
$173$	10.9666	−	18.9947i	0.833773	−	1.44414i	0.895026	−	0.446014i	$-0.147157\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$			19.3266i			1.45268i
$178$		0			0
$179$	5.06250	+	8.76850i	0.378389	+	0.655388i	0.990828	−	0.135129i	$-0.0431450\pi$
$179$	5.06250	+	8.76850i	0.378389	+	0.655388i	−0.612439	+	0.790518i	$0.709812\pi$
$180$		0			0
$181$	0.272578			0.0202606			0.0101303	−	0.999949i	$-0.496775\pi$
$181$	0.272578			0.0202606			0.0101303	+	0.999949i	$0.496775\pi$
$182$		0			0
$183$	−12.5818			−0.930076
$184$		0			0
$185$		0			0
$186$		0			0
$187$			8.19217i			0.599071i
$188$		0			0
$189$	14.5990	+	8.42876i	1.06192	+	0.613102i
$190$		0			0
$191$	7.39587	−	12.8100i	0.535147	−	0.926901i	−0.464010	−	0.885830i	$-0.653590\pi$
$191$	7.39587	−	12.8100i	0.535147	−	0.926901i	0.999156	−	0.0410710i	$-0.0130770\pi$
$192$		0			0
$193$	−6.06585	+	3.50212i	−0.436629	+	0.252088i	−0.702167	−	0.712013i	$-0.747784\pi$
$193$	−6.06585	+	3.50212i	−0.436629	+	0.252088i	0.265538	+	0.964101i	$0.414451\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−8.34230	+	4.81643i	−0.594365	+	0.343157i	−0.766821	−	0.641861i	$-0.778163\pi$
$197$	−8.34230	+	4.81643i	−0.594365	+	0.343157i	0.172457	+	0.985017i	$0.444829\pi$
$198$		0			0
$199$	−1.96091	+	3.39640i	−0.139006	+	0.240765i	−0.927120	−	0.374763i	$-0.877724\pi$
$199$	−1.96091	+	3.39640i	−0.139006	+	0.240765i	0.788115	+	0.615528i	$0.211057\pi$
$200$		0			0
$201$	−21.8074	−	12.5905i	−1.53818	−	0.888067i
$202$		0			0
$203$			1.86721i			0.131052i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	57.5366			3.99907
$208$		0			0
$209$	−21.2099			−1.46712
$210$		0			0
$211$	7.29429	+	12.6341i	0.502160	+	0.869766i	0.999997	+	0.00249580i	$0.000794440\pi$
$211$	7.29429	+	12.6341i	0.502160	+	0.869766i	−0.497837	+	0.867271i	$0.665872\pi$
$212$		0			0
$213$			36.2575i			2.48433i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	2.99924	−	5.19484i	0.203602	−	0.352649i
$218$		0			0
$219$	−20.4818	+	11.8252i	−1.38403	+	0.799070i
$220$		0			0
$221$	6.87684	+	5.22929i	0.462586	+	0.351760i
$222$		0			0
$223$	2.60093	−	1.50165i	0.174171	−	0.100558i	−0.410380	−	0.911915i	$-0.634604\pi$
$223$	2.60093	−	1.50165i	0.174171	−	0.100558i	0.584551	+	0.811357i	$0.301271\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−10.1162	−	5.84058i	−0.671435	−	0.387653i	0.125185	−	0.992133i	$-0.460047\pi$
$227$	−10.1162	−	5.84058i	−0.671435	−	0.387653i	−0.796620	+	0.604480i	$0.793381\pi$
$228$		0			0
$229$			18.5293i			1.22445i	0.790684	+	0.612224i	$0.209725\pi$
$229$			18.5293i			1.22445i	−0.790684	+	0.612224i	$0.790275\pi$
$230$		0			0
$231$	5.84468	+	10.1233i	0.384552	+	0.666063i
$232$		0			0
$233$	11.1750			0.732097			0.366048	−	0.930596i	$-0.380710\pi$
$233$	11.1750			0.732097			0.366048	+	0.930596i	$0.380710\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	21.2460	+	36.7991i	1.38007	+	2.39036i
$238$		0			0
$239$		−	2.16507i		−	0.140047i	−0.997545	−	0.0700235i	$-0.977693\pi$
$239$		−	2.16507i		−	0.140047i	0.997545	−	0.0700235i	$-0.0223074\pi$
$240$		0			0
$241$	16.7318	+	9.66011i	1.07779	+	0.622262i	0.930299	−	0.366801i	$-0.119547\pi$
$241$	16.7318	+	9.66011i	1.07779	+	0.622262i	0.147491	+	0.989063i	$0.452880\pi$
$242$		0			0
$243$	25.3096	−	43.8375i	1.62361	−	2.81218i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−13.5389	+	17.8044i	−0.861457	+	1.13287i
$248$		0			0
$249$	2.02341	−	1.16822i	0.128228	−	0.0740327i
$250$		0			0
$251$	−3.87684	+	6.71488i	−0.244704	+	0.423840i	−0.962048	−	0.272879i	$-0.912024\pi$
$251$	−3.87684	+	6.71488i	−0.244704	+	0.423840i	0.717344	+	0.696719i	$0.245357\pi$
$252$		0			0
$253$	21.4815	+	12.4024i	1.35053	+	0.779730i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−8.90366	−	15.4216i	−0.555395	−	0.961973i	−0.997873	−	0.0651933i	$-0.979234\pi$
$257$	−8.90366	−	15.4216i	−0.555395	−	0.961973i	0.442477	−	0.896780i	$-0.354100\pi$
$258$		0			0
$259$	1.47574			0.0916980
$260$		0			0
$261$	14.3194			0.886348
$262$		0			0
$263$	−8.30316	−	14.3815i	−0.511995	−	0.886801i	−0.999903	−	0.0139065i	$-0.995573\pi$
$263$	−8.30316	−	14.3815i	−0.511995	−	0.886801i	0.487908	−	0.872895i	$-0.337760\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−16.7373	−	9.66330i	−1.02431	−	0.591385i
$268$		0			0
$269$	2.96967	−	5.14362i	0.181064	−	0.313612i	−0.761179	−	0.648542i	$-0.775379\pi$
$269$	2.96967	−	5.14362i	0.181064	−	0.313612i	0.942243	+	0.334930i	$0.108713\pi$
$270$		0			0
$271$	−8.37246	+	4.83384i	−0.508591	+	0.293635i	−0.732254	−	0.681031i	$-0.761532\pi$
$271$	−8.37246	+	4.83384i	−0.508591	+	0.293635i	0.223663	+	0.974666i	$0.428198\pi$
$272$		0			0
$273$	12.2287	+	1.55572i	0.740115	+	0.0941562i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	10.3590	−	17.9423i	0.622411	−	1.07805i	−0.366624	−	0.930369i	$-0.619487\pi$
$277$	10.3590	−	17.9423i	0.622411	−	1.07805i	0.989035	−	0.147679i	$-0.0471801\pi$
$278$		0			0
$279$	−39.8386	−	23.0008i	−2.38507	−	1.37702i
$280$		0			0
$281$			27.7700i			1.65662i	0.560272	+	0.828309i	$0.310697\pi$
$281$			27.7700i			1.65662i	−0.560272	+	0.828309i	$0.689303\pi$
$282$		0			0
$283$	−12.7885	−	22.1502i	−0.760194	−	1.31670i	−0.942750	−	0.333500i	$-0.891770\pi$
$283$	−12.7885	−	22.1502i	−0.760194	−	1.31670i	0.182556	−	0.983196i	$-0.441563\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	4.30067			0.253861
$288$		0			0
$289$	5.62937	+	9.75035i	0.331139	+	0.573550i
$290$		0			0
$291$		−	52.8847i		−	3.10016i
$292$		0			0
$293$	−24.5929	−	14.1987i	−1.43673	−	0.829497i	−0.439109	−	0.898434i	$-0.644706\pi$
$293$	−24.5929	−	14.1987i	−1.43673	−	0.829497i	−0.997621	+	0.0689370i	$0.978039\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	48.2665	−	27.8667i	2.80071	−	1.61699i
$298$		0			0
$299$	24.1233	−	10.1157i	1.39509	−	0.585005i
$300$		0			0
$301$	1.93241	−	1.11568i	0.111382	−	0.0643067i
$302$		0			0
$303$	−9.90396	+	17.1542i	−0.568968	+	0.985481i
$304$		0			0
$305$		0			0
$306$		0			0
$307$			11.5519i			0.659302i	0.944103	+	0.329651i	$0.106931\pi$
$307$			11.5519i			0.659302i	−0.944103	+	0.329651i	$0.893069\pi$
$308$		0			0
$309$	19.3568	+	33.5269i	1.10117	+	1.90728i
$310$		0			0
$311$	−1.03807			−0.0588634			−0.0294317	−	0.999567i	$-0.509370\pi$
$311$	−1.03807			−0.0588634			−0.0294317	+	0.999567i	$0.509370\pi$
$312$		0			0
$313$	−29.6339			−1.67501			−0.837504	−	0.546432i	$-0.815986\pi$
$313$	−29.6339			−1.67501			−0.837504	+	0.546432i	$0.815986\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$			20.4445i			1.14828i	0.818759	+	0.574138i	$0.194663\pi$
$317$			20.4445i			1.14828i	−0.818759	+	0.574138i	$0.805337\pi$
$318$		0			0
$319$	5.34620	+	3.08663i	0.299330	+	0.172818i
$320$		0			0
$321$	−22.4193	+	38.8313i	−1.25132	+	2.16735i
$322$		0			0
$323$	12.8729	−	7.43219i	0.716269	−	0.413538i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−3.99510	+	2.30657i	−0.220930	+	0.127554i
$328$		0			0
$329$	−1.81435	+	3.14254i	−0.100028	+	0.173254i
$330$		0			0
$331$	4.39587	+	2.53796i	0.241619	+	0.139499i	0.615921	−	0.787808i	$-0.288784\pi$
$331$	4.39587	+	2.53796i	0.241619	+	0.139499i	−0.374302	+	0.927307i	$0.622118\pi$
$332$		0			0
$333$		−	11.3173i		−	0.620182i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	10.4909			0.571473			0.285737	−	0.958308i	$-0.407762\pi$
$337$	10.4909			0.571473			0.285737	+	0.958308i	$0.407762\pi$
$338$		0			0
$339$	−13.9393			−0.757081
$340$		0			0
$341$	−9.91593	−	17.1749i	−0.536977	−	0.930072i
$342$		0			0
$343$			13.3719i			0.722012i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	15.9491	−	27.6247i	0.856193	−	1.48297i	−0.0193399	−	0.999813i	$-0.506156\pi$
$347$	15.9491	−	27.6247i	0.856193	−	1.48297i	0.875533	−	0.483158i	$-0.160510\pi$
$348$		0			0
$349$	28.4661	−	16.4349i	1.52376	−	0.879741i	0.524151	−	0.851625i	$-0.324383\pi$
$349$	28.4661	−	16.4349i	1.52376	−	0.879741i	0.999605	−	0.0281153i	$-0.00895056\pi$
$350$		0			0
$351$	7.41745	−	58.3049i	0.395914	−	3.11209i
$352$		0			0
$353$	23.6988	−	13.6825i	1.26136	−	0.728245i	0.288021	−	0.957624i	$-0.407003\pi$
$353$	23.6988	−	13.6825i	1.26136	−	0.728245i	0.973337	+	0.229379i	$0.0736695\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−7.09463	−	4.09609i	−0.375488	−	0.216788i
$358$		0			0
$359$			0.625579i			0.0330168i	0.999864	+	0.0165084i	$0.00525502\pi$
$359$			0.625579i			0.0330168i	−0.999864	+	0.0165084i	$0.994745\pi$
$360$		0			0
$361$	9.74225	+	16.8741i	0.512750	+	0.888109i
$362$		0			0
$363$	2.27911			0.119622
$364$		0			0
$365$		0			0
$366$		0			0
$367$	1.98891	+	3.44490i	0.103820	+	0.179822i	0.913256	−	0.407387i	$-0.133560\pi$
$367$	1.98891	+	3.44490i	0.103820	+	0.179822i	−0.809435	+	0.587209i	$0.800227\pi$
$368$		0			0
$369$		−	32.9813i		−	1.71694i
$370$		0			0
$371$	−4.07831	−	2.35461i	−0.211735	−	0.122245i
$372$		0			0
$373$	−14.1246	+	24.4645i	−0.731343	+	1.26672i	0.224966	+	0.974367i	$0.427773\pi$
$373$	−14.1246	+	24.4645i	−0.731343	+	1.26672i	−0.956309	+	0.292357i	$0.905560\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	6.00368	−	2.51754i	0.309205	−	0.129660i
$378$		0			0
$379$	14.1642	−	8.17771i	0.727567	−	0.420061i	−0.0899646	−	0.995945i	$-0.528675\pi$
$379$	14.1642	−	8.17771i	0.727567	−	0.420061i	0.817531	+	0.575884i	$0.195342\pi$
$380$		0			0
$381$	9.86809	−	17.0920i	0.505557	−	0.875651i
$382$		0			0
$383$	18.0708	+	10.4332i	0.923376	+	0.533111i	0.884710	−	0.466141i	$-0.154356\pi$
$383$	18.0708	+	10.4332i	0.923376	+	0.533111i	0.0386654	+	0.999252i	$0.487689\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−8.55600	−	14.8194i	−0.434926	−	0.753314i
$388$		0			0
$389$	3.54177			0.179575			0.0897874	−	0.995961i	$-0.471381\pi$
$389$	3.54177			0.179575			0.0897874	+	0.995961i	$0.471381\pi$
$390$		0			0
$391$	−17.3837			−0.879133
$392$		0			0
$393$	31.5002	+	54.5600i	1.58898	+	2.75219i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	23.9705	+	13.8394i	1.20305	+	0.694578i	0.961231	−	0.275744i	$-0.0889243\pi$
$397$	23.9705	+	13.8394i	1.20305	+	0.694578i	0.241814	+	0.970323i	$0.422258\pi$
$398$		0			0
$399$	10.6049	−	18.3683i	0.530911	−	0.919565i
$400$		0			0
$401$	10.6799	−	6.16604i	0.533328	−	0.307917i	−0.209043	−	0.977907i	$-0.567035\pi$
$401$	10.6799	−	6.16604i	0.533328	−	0.307917i	0.742371	+	0.669989i	$0.233701\pi$
$402$		0			0
$403$	−20.7469	−	2.63939i	−1.03348	−	0.131477i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	2.43950	−	4.22534i	0.120922	−	0.209442i
$408$		0			0
$409$	−31.2917	−	18.0663i	−1.54728	−	0.893321i	−0.998348	−	0.0574521i	$-0.981702\pi$
$409$	−31.2917	−	18.0663i	−1.54728	−	0.893321i	−0.548929	−	0.835869i	$-0.684964\pi$
$410$		0			0
$411$		−	1.53072i		−	0.0755049i
$412$		0			0
$413$	−3.02258	−	5.23526i	−0.148731	−	0.257610i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−30.8113			−1.50883
$418$		0			0
$419$	−6.26566	−	10.8524i	−0.306097	−	0.530176i	0.671408	−	0.741088i	$-0.265690\pi$
$419$	−6.26566	−	10.8524i	−0.306097	−	0.530176i	−0.977505	+	0.210912i	$0.932357\pi$
$420$		0			0
$421$			7.74907i			0.377667i	0.982009	+	0.188833i	$0.0604706\pi$
$421$			7.74907i			0.377667i	−0.982009	+	0.188833i	$0.939529\pi$
$422$		0			0
$423$	24.0997	+	13.9140i	1.17177	+	0.676521i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	3.40821	−	1.96773i	0.164935	−	0.0952252i
$428$		0			0
$429$	24.6693	−	32.4416i	1.19104	−	1.56629i
$430$		0			0
$431$	−18.9375	+	10.9336i	−0.912188	+	0.526652i	−0.881134	−	0.472866i	$-0.843219\pi$
$431$	−18.9375	+	10.9336i	−0.912188	+	0.526652i	−0.0310532	+	0.999518i	$0.509886\pi$
$432$		0			0
$433$	0.126574	−	0.219232i	0.00608275	−	0.0105356i	−0.862968	−	0.505259i	$-0.831397\pi$
$433$	0.126574	−	0.219232i	0.00608275	−	0.0105356i	0.869051	+	0.494723i	$0.164730\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		−	45.0072i		−	2.15299i
$438$		0			0
$439$	−6.98432	−	12.0972i	−0.333344	−	0.577368i	0.649822	−	0.760087i	$-0.274844\pi$
$439$	−6.98432	−	12.0972i	−0.333344	−	0.577368i	−0.983165	+	0.182719i	$0.941510\pi$
$440$		0			0
$441$	47.0330			2.23967
$442$		0			0
$443$	28.5957			1.35862			0.679310	−	0.733851i	$-0.262279\pi$
$443$	28.5957			1.35862			0.679310	+	0.733851i	$0.262279\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$			36.0582i			1.70549i
$448$		0			0
$449$	−15.7293	−	9.08129i	−0.742309	−	0.428572i	0.0805990	−	0.996747i	$-0.474317\pi$
$449$	−15.7293	−	9.08129i	−0.742309	−	0.428572i	−0.822908	+	0.568174i	$0.807650\pi$
$450$		0			0
$451$	7.10932	−	12.3137i	0.334765	−	0.579829i
$452$		0			0
$453$	13.9135	−	8.03298i	0.653715	−	0.377422i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−7.86337	+	4.53992i	−0.367833	+	0.212368i	−0.672511	−	0.740087i	$-0.734784\pi$
$457$	−7.86337	+	4.53992i	−0.367833	+	0.212368i	0.304678	+	0.952455i	$0.401451\pi$
$458$		0			0
$459$	−19.5296	+	33.8263i	−0.911564	+	1.57888i
$460$		0			0
$461$	−32.7734	−	18.9217i	−1.52641	−	0.881273i	−0.999509	−	0.0313456i	$-0.990021\pi$
$461$	−32.7734	−	18.9217i	−1.52641	−	0.881273i	−0.526900	−	0.849927i	$-0.676646\pi$
$462$		0			0
$463$			15.5694i			0.723570i	0.932262	+	0.361785i	$0.117833\pi$
$463$			15.5694i			0.723570i	−0.932262	+	0.361785i	$0.882167\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−4.19255			−0.194008			−0.0970040	−	0.995284i	$-0.530926\pi$
$467$	−4.19255			−0.194008			−0.0970040	+	0.995284i	$0.530926\pi$
$468$		0			0
$469$	7.87636			0.363697
$470$		0			0
$471$	14.5599	+	25.2186i	0.670887	+	1.16201i
$472$		0			0
$473$		−	7.37719i		−	0.339204i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−18.0572	+	31.2760i	−0.826783	+	1.43203i
$478$		0			0
$479$	10.7058	−	6.18102i	0.489162	−	0.282418i	−0.235064	−	0.971980i	$-0.575530\pi$
$479$	10.7058	−	6.18102i	0.489162	−	0.282418i	0.724227	+	0.689562i	$0.242197\pi$
$480$		0			0
$481$	−1.98972	−	4.74497i	−0.0907234	−	0.216352i
$482$		0			0
$483$	−21.4815	+	12.4024i	−0.977443	+	0.564327i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−1.20427	−	0.695283i	−0.0545705	−	0.0315063i	0.472467	−	0.881349i	$-0.343364\pi$
$487$	−1.20427	−	0.695283i	−0.0545705	−	0.0315063i	−0.527037	+	0.849842i	$0.676697\pi$
$488$		0			0
$489$			61.5601i			2.78384i
$490$		0			0
$491$	−2.90025	−	5.02338i	−0.130886	−	0.226702i	0.793132	−	0.609050i	$-0.208449\pi$
$491$	−2.90025	−	5.02338i	−0.130886	−	0.226702i	−0.924019	+	0.382348i	$0.875116\pi$
$492$		0			0
$493$	−4.32637			−0.194850
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−5.67049	−	9.82157i	−0.254356	−	0.440558i
$498$		0			0
$499$		−	27.8242i		−	1.24558i	−0.782388	−	0.622792i	$-0.785998\pi$
$499$		−	27.8242i		−	1.24558i	0.782388	−	0.622792i	$-0.214002\pi$
$500$		0			0
$501$	41.1642	+	23.7662i	1.83908	+	1.06179i
$502$		0			0
$503$	−5.02953	+	8.71140i	−0.224256	+	0.388422i	−0.956096	−	0.293054i	$-0.905328\pi$
$503$	−5.02953	+	8.71140i	−0.224256	+	0.388422i	0.731840	+	0.681476i	$0.238662\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−11.4857	−	41.4168i	−0.510097	−	1.83938i
$508$		0			0
$509$	−2.00505	+	1.15762i	−0.0888724	+	0.0513105i	−0.543778	−	0.839229i	$-0.683006\pi$
$509$	−2.00505	+	1.15762i	−0.0888724	+	0.0513105i	0.454905	+	0.890540i	$0.349673\pi$
$510$		0			0
$511$	3.69878	−	6.40648i	0.163625	−	0.283406i
$512$		0			0
$513$	−87.5777	−	50.5630i	−3.86665	−	2.23241i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	5.99849	+	10.3897i	0.263813	+	0.456938i
$518$		0			0
$519$	72.5141			3.18301
$520$		0			0
$521$	−2.78299			−0.121925			−0.0609626	−	0.998140i	$-0.519417\pi$
$521$	−2.78299			−0.121925			−0.0609626	+	0.998140i	$0.519417\pi$
$522$		0			0
$523$	−13.6300	−	23.6078i	−0.595997	−	1.03230i	−0.993405	−	0.114655i	$-0.963424\pi$
$523$	−13.6300	−	23.6078i	−0.595997	−	1.03230i	0.397408	−	0.917642i	$-0.369910\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	12.0366	+	6.94931i	0.524321	+	0.302717i
$528$		0			0
$529$	−14.8177	+	25.6650i	−0.644248	+	1.11587i
$530$		0			0
$531$	−40.1485	+	23.1798i	−1.74230	+	1.00592i
$532$		0			0
$533$	−5.79854	−	13.8280i	−0.251162	−	0.598958i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−16.7373	+	28.9899i	−0.722269	+	1.25101i
$538$		0			0
$539$	17.5599	+	10.1382i	0.756361	+	0.436685i
$540$		0			0
$541$		−	22.5466i		−	0.969353i	−0.874693	−	0.484677i	$-0.838937\pi$
$541$		−	22.5466i		−	0.969353i	0.874693	−	0.484677i	$-0.161063\pi$
$542$		0			0
$543$	0.450591	+	0.780447i	0.0193367	+	0.0334922i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−1.51141			−0.0646233			−0.0323117	−	0.999478i	$-0.510287\pi$
$547$	−1.51141			−0.0646233			−0.0323117	+	0.999478i	$0.510287\pi$
$548$		0			0
$549$	−15.0903	−	26.1371i	−0.644038	−	1.11551i
$550$		0			0
$551$		−	11.2011i		−	0.477185i
$552$		0			0
$553$	−11.5104	−	6.64551i	−0.489470	−	0.282596i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−30.3618	+	17.5294i	−1.28647	+	0.742745i	−0.978023	−	0.208496i	$-0.933143\pi$
$557$	−30.3618	+	17.5294i	−1.28647	+	0.742745i	−0.308449	+	0.951241i	$0.599810\pi$
$558$		0			0
$559$	−6.19271	−	4.70907i	−0.261924	−	0.199172i
$560$		0			0
$561$	−23.4559	+	13.5422i	−0.990307	+	0.571754i
$562$		0			0
$563$	10.6460	−	18.4393i	0.448674	−	0.777125i	−0.549626	−	0.835411i	$-0.685230\pi$
$563$	10.6460	−	18.4393i	0.448674	−	0.777125i	0.998300	+	0.0582852i	$0.0185633\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$			31.1297i			1.30732i
$568$		0			0
$569$	−0.488701	−	0.846455i	−0.0204874	−	0.0354853i	0.855600	−	0.517638i	$-0.173188\pi$
$569$	−0.488701	−	0.846455i	−0.0204874	−	0.0354853i	−0.876087	+	0.482152i	$0.839855\pi$
$570$		0			0
$571$	−24.5468			−1.02725			−0.513625	−	0.858015i	$-0.671698\pi$
$571$	−24.5468			−1.02725			−0.513625	+	0.858015i	$0.671698\pi$
$572$		0			0
$573$	48.9036			2.04298
$574$		0			0
$575$		0			0
$576$		0			0
$577$			23.8270i			0.991932i	0.868342	+	0.495966i	$0.165186\pi$
$577$			23.8270i			0.991932i	−0.868342	+	0.495966i	$0.834814\pi$
$578$		0			0
$579$	−20.0546	−	11.5785i	−0.833439	−	0.481186i
$580$		0			0
$581$	−0.365406	+	0.632901i	−0.0151596	+	0.0262572i
$582$		0			0
$583$	−13.4835	+	7.78468i	−0.558428	+	0.322409i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−13.2172	+	7.63094i	−0.545532	+	0.314963i	−0.747318	−	0.664467i	$-0.768659\pi$
$587$	−13.2172	+	7.63094i	−0.545532	+	0.314963i	0.201786	+	0.979430i	$0.435325\pi$
$588$		0			0
$589$	−17.9921	+	31.1632i	−0.741350	+	1.28406i
$590$		0			0
$591$	−27.5809	−	15.9238i	−1.13452	−	0.655018i
$592$		0			0
$593$		−	35.9654i		−	1.47692i	−0.674296	−	0.738461i	$-0.735553\pi$
$593$		−	35.9654i		−	1.47692i	0.674296	−	0.738461i	$-0.264447\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−12.9661			−0.530668
$598$		0			0
$599$	−6.60243			−0.269768			−0.134884	−	0.990861i	$-0.543066\pi$
$599$	−6.60243			−0.269768			−0.134884	+	0.990861i	$0.543066\pi$
$600$		0			0
$601$	−14.9409	−	25.8783i	−0.609451	−	1.05560i	−0.991331	−	0.131388i	$-0.958057\pi$
$601$	−14.9409	−	25.8783i	−0.609451	−	1.05560i	0.381881	−	0.924212i	$-0.375277\pi$
$602$		0			0
$603$		−	60.4028i		−	2.45979i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	12.2450	−	21.2089i	0.497008	−	0.860843i	−0.502986	−	0.864294i	$-0.667765\pi$
$607$	12.2450	−	21.2089i	0.497008	−	0.860843i	0.999994	+	0.00345162i	$0.00109869\pi$
$608$		0			0
$609$	−5.34620	+	3.08663i	−0.216639	+	0.125077i
$610$		0			0
$611$	12.5505	+	1.59666i	0.507740	+	0.0645938i
$612$		0			0
$613$	−28.3242	+	16.3530i	−1.14400	+	0.660490i	−0.947419	−	0.319997i	$-0.896318\pi$
$613$	−28.3242	+	16.3530i	−1.14400	+	0.660490i	−0.196584	+	0.980487i	$0.562985\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	12.4429	+	7.18390i	0.500932	+	0.289213i	0.729098	−	0.684409i	$-0.239940\pi$
$617$	12.4429	+	7.18390i	0.500932	+	0.289213i	−0.228167	+	0.973622i	$0.573273\pi$
$618$		0			0
$619$		−	11.1681i		−	0.448883i	−0.974488	−	0.224442i	$-0.927944\pi$
$619$		−	11.1681i		−	0.448883i	0.974488	−	0.224442i	$-0.0720558\pi$
$620$		0			0
$621$	59.1329	+	102.421i	2.37292	+	4.11002i
$622$		0			0
$623$	6.04516			0.242194
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−35.0614	−	60.7282i	−1.40022	−	2.42525i
$628$		0			0
$629$			3.41932i			0.136337i
$630$		0			0
$631$	36.0259	+	20.7996i	1.43417	+	0.828018i	0.997435	−	0.0715729i	$-0.0228019\pi$
$631$	36.0259	+	20.7996i	1.43417	+	0.828018i	0.436734	+	0.899591i	$0.356135\pi$
$632$		0			0
$633$	−24.1160	+	41.7701i	−0.958524	+	1.66021i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	19.7195	−	8.26901i	0.781313	−	0.327630i
$638$		0			0
$639$	−75.3203	+	43.4862i	−2.97963	+	1.72029i
$640$		0			0
$641$	2.68565	−	4.65169i	0.106077	−	0.183731i	−0.808101	−	0.589044i	$-0.799504\pi$
$641$	2.68565	−	4.65169i	0.106077	−	0.183731i	0.914178	+	0.405314i	$0.132838\pi$
$642$		0			0
$643$	15.2046	+	8.77839i	0.599612	+	0.346186i	0.768889	−	0.639383i	$-0.220810\pi$
$643$	15.2046	+	8.77839i	0.599612	+	0.346186i	−0.169277	+	0.985568i	$0.554143\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	18.8732	+	32.6893i	0.741982	+	1.28515i	0.951592	+	0.307365i	$0.0994474\pi$
$647$	18.8732	+	32.6893i	0.741982	+	1.28515i	−0.209610	+	0.977785i	$0.567219\pi$
$648$		0			0
$649$	−19.9862			−0.784525
$650$		0			0
$651$	19.8319			0.777272
$652$		0			0
$653$	−6.35766	−	11.0118i	−0.248794	−	0.430925i	0.714397	−	0.699741i	$-0.246701\pi$
$653$	−6.35766	−	11.0118i	−0.248794	−	0.430925i	−0.963192	+	0.268816i	$0.913368\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−49.1305	−	28.3655i	−1.91676	−	1.10664i
$658$		0			0
$659$	−11.0625	+	19.1608i	−0.430934	+	0.746399i	−0.996954	−	0.0779923i	$-0.975149\pi$
$659$	−11.0625	+	19.1608i	−0.430934	+	0.746399i	0.566020	+	0.824391i	$0.308482\pi$
$660$		0			0
$661$	0.612035	−	0.353359i	0.0238054	−	0.0137441i	−0.488050	−	0.872816i	$-0.662292\pi$
$661$	0.612035	−	0.353359i	0.0238054	−	0.0137441i	0.511855	+	0.859072i	$0.328958\pi$
$662$		0			0
$663$	−3.60463	+	28.3342i	−0.139992	+	1.10041i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−6.54981	+	11.3446i	−0.253610	+	0.439265i
$668$		0			0
$669$	8.59903	+	4.96466i	0.332458	+	0.191945i
$670$		0			0
$671$		−	13.0112i		−	0.502292i
$672$		0			0
$673$	13.4663	+	23.3244i	0.519090	+	0.899090i	0.999754	+	0.0221849i	$0.00706224\pi$
$673$	13.4663	+	23.3244i	0.519090	+	0.899090i	−0.480664	+	0.876905i	$0.659604\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−21.5208			−0.827111			−0.413556	−	0.910479i	$-0.635713\pi$
$677$	−21.5208			−0.827111			−0.413556	+	0.910479i	$0.635713\pi$
$678$		0			0
$679$	8.27088	+	14.3256i	0.317407	+	0.549766i
$680$		0			0
$681$		−	38.6196i		−	1.47991i
$682$		0			0
$683$	17.8031	+	10.2786i	0.681215	+	0.393300i	0.800313	−	0.599583i	$-0.204667\pi$
$683$	17.8031	+	10.2786i	0.681215	+	0.393300i	−0.119098	+	0.992883i	$0.538000\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−53.0531	+	30.6302i	−2.02410	+	1.16862i
$688$		0			0
$689$	−2.07210	+	16.2877i	−0.0789407	+	0.620514i
$690$		0			0
$691$	17.2344	−	9.95031i	0.655629	−	0.378528i	−0.134980	−	0.990848i	$-0.543097\pi$
$691$	17.2344	−	9.95031i	0.655629	−	0.378528i	0.790610	+	0.612321i	$0.209764\pi$
$692$		0			0
$693$	−14.0199	+	24.2831i	−0.532571	+	0.922440i
$694$		0			0
$695$		0			0
$696$		0			0
$697$			9.96475i			0.377442i
$698$		0			0
$699$	18.4730	+	31.9962i	0.698714	+	1.21021i
$700$		0			0
$701$	2.37131			0.0895631			0.0447816	−	0.998997i	$-0.485741\pi$
$701$	2.37131			0.0895631			0.0447816	+	0.998997i	$0.485741\pi$
$702$		0			0
$703$	−8.85276			−0.333888
$704$		0			0
$705$		0			0
$706$		0			0
$707$		−	6.19571i		−	0.233014i
$708$		0			0
$709$	0.916777	+	0.529301i	0.0344303	+	0.0198783i	0.517116	−	0.855915i	$-0.327005\pi$
$709$	0.916777	+	0.529301i	0.0344303	+	0.0198783i	−0.482686	+	0.875793i	$0.660339\pi$
$710$		0			0
$711$	−50.9636	+	88.2715i	−1.91128	+	3.31044i
$712$		0			0
$713$	36.4450	−	21.0415i	1.36487	−	0.788011i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	6.19905	−	3.57902i	0.231508	−	0.133661i
$718$		0			0
$719$	5.60426	−	9.70687i	0.209004	−	0.362005i	−0.742397	−	0.669960i	$-0.766311\pi$
$719$	5.60426	−	9.70687i	0.209004	−	0.362005i	0.951401	+	0.307955i	$0.0996446\pi$
$720$		0			0
$721$	−10.4869	−	6.05460i	−0.390551	−	0.225485i
$722$		0			0
$723$			63.8754i			2.37555i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−38.9060			−1.44294			−0.721472	−	0.692443i	$-0.756534\pi$
$727$	−38.9060			−1.44294			−0.721472	+	0.692443i	$0.756534\pi$
$728$		0			0
$729$	77.0471			2.85360
$730$		0			0
$731$	2.58505	+	4.47745i	0.0956117	+	0.165604i
$732$		0			0
$733$			24.7392i			0.913765i	0.889527	+	0.456882i	$0.151034\pi$
$733$			24.7392i			0.913765i	−0.889527	+	0.456882i	$0.848966\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	13.0202	−	22.5516i	0.479605	−	0.830700i
$738$		0			0
$739$	−0.302370	+	0.174574i	−0.0111229	+	0.00642179i	−0.505551	−	0.862797i	$-0.668711\pi$
$739$	−0.302370	+	0.174574i	−0.0111229	+	0.00642179i	0.494428	+	0.869218i	$0.335377\pi$
$740$		0			0
$741$	−73.3584	−	9.33253i	−2.69489	−	0.342839i
$742$		0			0
$743$	−6.68184	+	3.85776i	−0.245133	+	0.141528i	−0.617534	−	0.786544i	$-0.711868\pi$
$743$	−6.68184	+	3.85776i	−0.245133	+	0.141528i	0.372401	+	0.928072i	$0.378535\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	4.85364	+	2.80225i	0.177585	+	0.102529i
$748$		0			0
$749$		−	14.0250i		−	0.512463i
$750$		0			0
$751$	1.71161	+	2.96460i	0.0624575	+	0.108180i	0.895563	−	0.444934i	$-0.146773\pi$
$751$	1.71161	+	2.96460i	0.0624575	+	0.108180i	−0.833106	+	0.553114i	$0.813440\pi$
$752$		0			0
$753$	−25.6348			−0.934183
$754$		0			0
$755$		0			0
$756$		0			0
$757$	5.63976	+	9.76835i	0.204981	+	0.355037i	0.950127	−	0.311865i	$-0.100954\pi$
$757$	5.63976	+	9.76835i	0.204981	+	0.355037i	−0.745146	+	0.666901i	$0.767620\pi$
$758$		0			0
$759$			82.0079i			2.97670i
$760$		0			0
$761$	−33.1329	−	19.1293i	−1.20107	−	0.693435i	−0.240273	−	0.970705i	$-0.577237\pi$
$761$	−33.1329	−	19.1293i	−1.20107	−	0.693435i	−0.960792	+	0.277270i	$0.910570\pi$
$762$		0			0
$763$	0.721472	−	1.24963i	0.0261190	−	0.0452395i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−12.7577	+	16.7772i	−0.460655	+	0.605789i
$768$		0			0
$769$	−33.7503	+	19.4857i	−1.21707	+	0.702674i	−0.964289	−	0.264851i	$-0.914677\pi$
$769$	−33.7503	+	19.4857i	−1.21707	+	0.702674i	−0.252777	+	0.967525i	$0.581344\pi$
$770$		0			0
$771$	29.4368	−	50.9860i	1.06014	−	1.83622i
$772$		0			0
$773$	25.0126	+	14.4410i	0.899640	+	0.519407i	0.877083	−	0.480338i	$-0.159486\pi$
$773$	25.0126	+	14.4410i	0.899640	+	0.519407i	0.0225567	+	0.999746i	$0.492819\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	2.43950	+	4.22534i	0.0875167	+	0.151583i
$778$		0			0
$779$	−25.7991			−0.924350
$780$		0			0
$781$	−37.4949			−1.34167
$782$		0			0
$783$	14.7167	+	25.4900i	0.525931	+	0.910939i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−2.63389	−	1.52068i	−0.0938879	−	0.0542062i	0.452321	−	0.891855i	$-0.350596\pi$
$787$	−2.63389	−	1.52068i	−0.0938879	−	0.0542062i	−0.546209	+	0.837649i	$0.683930\pi$
$788$		0			0
$789$	27.4514	−	47.5473i	0.977297	−	1.69273i
$790$		0			0
$791$	3.77594	−	2.18004i	0.134257	−	0.0775132i
$792$		0			0
$793$	−10.9221	−	8.30542i	−0.387856	−	0.294934i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	21.1457	−	36.6254i	0.749018	−	1.29734i	−0.199275	−	0.979944i	$-0.563859\pi$
$797$	21.1457	−	36.6254i	0.749018	−	1.29734i	0.948294	−	0.317394i	$-0.102808\pi$
$798$		0			0
$799$	−7.28133	−	4.20388i	−0.257595	−	0.148723i
$800$		0			0
$801$		−	46.3595i		−	1.63803i
$802$		0			0
$803$	−12.2287	−	21.1807i	−0.431542	−	0.747452i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	19.6363			0.691230
$808$		0			0
$809$	−17.6250	−	30.5274i	−0.619662	−	1.07329i	−0.989547	−	0.144208i	$-0.953936\pi$
$809$	−17.6250	−	30.5274i	−0.619662	−	1.07329i	0.369886	−	0.929077i	$-0.379397\pi$
$810$		0			0
$811$			30.1607i			1.05908i	0.848284	+	0.529542i	$0.177636\pi$
$811$			30.1607i			1.05908i	−0.848284	+	0.529542i	$0.822364\pi$
$812$		0			0
$813$	−27.6806	−	15.9814i	−0.970800	−	0.560492i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−11.5923	+	6.69281i	−0.405563	+	0.234152i
$818$		0			0
$819$	11.4350	+	27.2694i	0.399570	+	0.952872i
$820$		0			0
$821$	3.92434	−	2.26572i	0.136960	−	0.0790741i	−0.429954	−	0.902851i	$-0.641470\pi$
$821$	3.92434	−	2.26572i	0.136960	−	0.0790741i	0.566915	+	0.823777i	$0.308137\pi$
$822$		0			0
$823$	9.97249	−	17.2729i	0.347619	−	0.602094i	−0.638207	−	0.769865i	$-0.720324\pi$
$823$	9.97249	−	17.2729i	0.347619	−	0.602094i	0.985826	+	0.167771i	$0.0536569\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	12.3377i		−	0.429025i	−0.976721	−	0.214512i	$-0.931184\pi$
$827$		−	12.3377i		−	0.429025i	0.976721	−	0.214512i	$-0.0688163\pi$
$828$		0			0
$829$	−18.7968	−	32.5570i	−0.652840	−	1.13075i	−0.982431	−	0.186628i	$-0.940244\pi$
$829$	−18.7968	−	32.5570i	−0.652840	−	1.13075i	0.329591	−	0.944124i	$-0.393089\pi$
$830$		0			0
$831$	68.4966			2.37612
$832$		0			0
$833$	−14.2102			−0.492355
$834$		0			0
$835$		0			0
$836$		0			0
$837$		−	94.5557i		−	3.26832i
$838$		0			0
$839$	20.7606	+	11.9861i	0.716736	+	0.413808i	0.813550	−	0.581495i	$-0.197532\pi$
$839$	20.7606	+	11.9861i	0.716736	+	0.413808i	−0.0968144	+	0.995302i	$0.530865\pi$
$840$		0			0
$841$	12.8699	−	22.2914i	0.443790	−	0.768667i
$842$		0			0
$843$	−79.5111	+	45.9058i	−2.73851	+	1.58108i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−0.617372	+	0.356440i	−0.0212132	+	0.0122474i
$848$		0			0
$849$	42.2804	−	73.2319i	1.45106	−	2.51331i
$850$		0			0
$851$	8.96614	+	5.17660i	0.307355	+	0.177452i
$852$		0			0
$853$		−	38.8952i		−	1.33175i	−0.746065	−	0.665873i	$-0.768059\pi$
$853$		−	38.8952i		−	1.33175i	0.746065	−	0.665873i	$-0.231941\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−44.4570			−1.51862			−0.759312	−	0.650727i	$-0.774464\pi$
$857$	−44.4570			−1.51862			−0.759312	+	0.650727i	$0.774464\pi$
$858$		0			0
$859$	46.8129			1.59724			0.798618	−	0.601838i	$-0.205565\pi$
$859$	46.8129			1.59724			0.798618	+	0.601838i	$0.205565\pi$
$860$		0			0
$861$	7.10932	+	12.3137i	0.242285	+	0.419650i
$862$		0			0
$863$		−	28.9384i		−	0.985073i	−0.870292	−	0.492537i	$-0.836070\pi$
$863$		−	28.9384i		−	0.985073i	0.870292	−	0.492537i	$-0.163930\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−18.6115	+	32.2361i	−0.632079	+	1.09479i
$868$		0			0
$869$	−38.0549	+	21.9710i	−1.29092	+	0.745315i
$870$		0			0
$871$	−10.6196	−	25.3250i	−0.359831	−	0.858105i
$872$		0			0
$873$	109.861	−	63.4283i	3.71824	−	2.14672i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	1.58011	+	0.912276i	0.0533565	+	0.0308054i	0.526441	−	0.850212i	$-0.323526\pi$
$877$	1.58011	+	0.912276i	0.0533565	+	0.0308054i	−0.473084	+	0.881017i	$0.656859\pi$
$878$		0			0
$879$		−	93.8858i		−	3.16669i
$880$		0			0
$881$	−5.47740	−	9.48714i	−0.184538	−	0.319630i	0.758882	−	0.651228i	$-0.225746\pi$
$881$	−5.47740	−	9.48714i	−0.184538	−	0.319630i	−0.943421	+	0.331598i	$0.892412\pi$
$882$		0			0
$883$	−15.8747			−0.534227			−0.267113	−	0.963665i	$-0.586070\pi$
$883$	−15.8747			−0.534227			−0.267113	+	0.963665i	$0.586070\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−2.97769	−	5.15751i	−0.0999811	−	0.173172i	0.811695	−	0.584081i	$-0.198545\pi$
$887$	−2.97769	−	5.15751i	−0.0999811	−	0.173172i	−0.911677	+	0.410908i	$0.865212\pi$
$888$		0			0
$889$			6.17327i			0.207045i
$890$		0			0
$891$	89.1306	+	51.4596i	2.98599	+	1.72396i
$892$		0			0
$893$	10.8840	−	18.8517i	0.364220	−	0.630847i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	68.8408	+	52.3480i	2.29853	+	1.74785i
$898$		0			0
$899$	9.07023	−	5.23670i	0.302509	−	0.174654i
$900$		0			0
$901$	5.45569	−	9.44953i	0.181755	−	0.314809i
$902$		0			0
$903$	6.38884	+	3.68860i	0.212607	+	0.122749i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−19.0943	−	33.0723i	−0.634015	−	1.09815i	−0.986723	−	0.162413i	$-0.948072\pi$
$907$	−19.0943	−	33.0723i	−0.634015	−	1.09815i	0.352707	−	0.935734i	$-0.385261\pi$
$908$		0			0
$909$	−47.5141			−1.57594
$910$		0			0
$911$	33.7516			1.11824			0.559121	−	0.829086i	$-0.311139\pi$
$911$	33.7516			1.11824			0.559121	+	0.829086i	$0.311139\pi$
$912$		0			0
$913$	1.20808	+	2.09246i	0.0399817	+	0.0692504i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−17.0658	−	9.85294i	−0.563562	−	0.325373i
$918$		0			0
$919$	10.5062	−	18.1973i	0.346568	−	0.600273i	−0.639070	−	0.769149i	$-0.720680\pi$
$919$	10.5062	−	18.1973i	0.346568	−	0.600273i	0.985637	+	0.168876i	$0.0540137\pi$
$920$		0			0
$921$	−33.0755	+	19.0961i	−1.08987	+	0.629239i
$922$		0			0
$923$	−23.9340	+	31.4747i	−0.787798	+	1.03600i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−46.4319	+	80.4225i	−1.52502	+	2.64142i
$928$		0			0
$929$	33.3099	+	19.2315i	1.09286	+	0.630965i	0.934337	−	0.356390i	$-0.115992\pi$
$929$	33.3099	+	19.2315i	1.09286	+	0.630965i	0.158526	+	0.987355i	$0.449326\pi$
$930$		0			0
$931$		−	36.7909i		−	1.20577i
$932$		0			0
$933$	−1.71600	−	2.97220i	−0.0561793	−	0.0973054i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	45.7434			1.49437			0.747186	−	0.664615i	$-0.231404\pi$
$937$	45.7434			1.49437			0.747186	+	0.664615i	$0.231404\pi$
$938$		0			0
$939$	−48.9870	−	84.8479i	−1.59863	−	2.76891i
$940$		0			0
$941$		−	58.6037i		−	1.91043i	−0.295917	−	0.955214i	$-0.595625\pi$
$941$		−	58.6037i		−	1.91043i	0.295917	−	0.955214i	$-0.404375\pi$
$942$		0			0
$943$	26.1296	+	15.0859i	0.850896	+	0.491265i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	35.2500	−	20.3516i	1.14547	−	0.661338i	0.197692	−	0.980264i	$-0.436655\pi$
$947$	35.2500	−	20.3516i	1.14547	−	0.661338i	0.947780	+	0.318926i	$0.103322\pi$
$948$		0			0
$949$	−25.5859	−	3.25499i	−0.830554	−	0.105662i
$950$		0			0
$951$	−58.5367	+	33.7962i	−1.89818	+	1.09592i
$952$		0			0
$953$	1.50581	−	2.60814i	0.0487779	−	0.0844859i	−0.840606	−	0.541648i	$-0.817801\pi$
$953$	1.50581	−	2.60814i	0.0487779	−	0.0844859i	0.889384	+	0.457162i	$0.151134\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$			20.4097i			0.659752i
$958$		0			0
$959$	0.239397	+	0.414647i	0.00773052	+	0.0133897i
$960$		0			0
$961$	−2.64620			−0.0853612
$962$		0			0
$963$	−107.556			−3.46595
$964$		0			0
$965$		0			0
$966$		0			0
$967$		−	37.8156i		−	1.21607i	−0.793912	−	0.608033i	$-0.791959\pi$
$967$		−	37.8156i		−	1.21607i	0.793912	−	0.608033i	$-0.208041\pi$
$968$		0			0
$969$	42.5597	+	24.5719i	1.36722	+	0.789362i
$970$		0			0
$971$	−12.8681	+	22.2882i	−0.412957	+	0.715262i	−0.995212	−	0.0977445i	$-0.968837\pi$
$971$	−12.8681	+	22.2882i	−0.412957	+	0.715262i	0.582255	+	0.813006i	$0.302171\pi$
$972$		0			0
$973$	8.34626	−	4.81872i	0.267569	−	0.154481i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	20.8908	−	12.0613i	0.668355	−	0.385875i	−0.127098	−	0.991890i	$-0.540566\pi$
$977$	20.8908	−	12.0613i	0.668355	−	0.385875i	0.795453	+	0.606015i	$0.207233\pi$
$978$		0			0
$979$	9.99308	−	17.3085i	0.319380	−	0.553183i
$980$		0			0
$981$	−9.58322	−	5.53288i	−0.305969	−	0.176651i
$982$		0			0
$983$		−	22.5964i		−	0.720715i	−0.932814	−	0.360357i	$-0.882655\pi$
$983$		−	22.5964i		−	0.720715i	0.932814	−	0.360357i	$-0.117345\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−11.9970			−0.381868
$988$		0			0
$989$	15.6543			0.497779
$990$		0			0
$991$	−7.57562	−	13.1214i	−0.240648	−	0.416814i	0.720251	−	0.693713i	$-0.244026\pi$
$991$	−7.57562	−	13.1214i	−0.240648	−	0.416814i	−0.960899	+	0.276899i	$0.910693\pi$
$992$		0			0
$993$			16.7817i			0.532552i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−26.7679	+	46.3633i	−0.847747	+	1.46834i	0.0354673	+	0.999371i	$0.488708\pi$
$997$	−26.7679	+	46.3633i	−0.847747	+	1.46834i	−0.883214	+	0.468970i	$0.844625\pi$
$998$		0			0
$999$	20.1459	−	11.6312i	0.637388	−	0.367996i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1300.2.y.e.101.8		16
5.2	odd	4		260.2.z.a.49.8	yes	16
5.3	odd	4		260.2.z.a.49.1	✓	16
5.4	even	2	inner	1300.2.y.e.101.1		16
13.4	even	6	inner	1300.2.y.e.901.8		16
15.2	even	4		2340.2.cr.a.829.6		16
15.8	even	4		2340.2.cr.a.829.3		16
20.3	even	4		1040.2.df.d.49.8		16
20.7	even	4		1040.2.df.d.49.1		16
65.2	even	12		3380.2.c.e.2029.16		16
65.3	odd	12		3380.2.d.d.1689.2		16
65.4	even	6	inner	1300.2.y.e.901.1		16
65.17	odd	12		260.2.z.a.69.1	yes	16
65.23	odd	12		3380.2.d.d.1689.1		16
65.28	even	12		3380.2.c.e.2029.2		16
65.37	even	12		3380.2.c.e.2029.15		16
65.42	odd	12		3380.2.d.d.1689.15		16
65.43	odd	12		260.2.z.a.69.8	yes	16
65.62	odd	12		3380.2.d.d.1689.16		16
65.63	even	12		3380.2.c.e.2029.1		16
195.17	even	12		2340.2.cr.a.1369.3		16
195.173	even	12		2340.2.cr.a.1369.6		16
260.43	even	12		1040.2.df.d.849.1		16
260.147	even	12		1040.2.df.d.849.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
260.2.z.a.49.1	✓	16	5.3	odd	4
260.2.z.a.49.8	yes	16	5.2	odd	4
260.2.z.a.69.1	yes	16	65.17	odd	12
260.2.z.a.69.8	yes	16	65.43	odd	12
1040.2.df.d.49.1		16	20.7	even	4
1040.2.df.d.49.8		16	20.3	even	4
1040.2.df.d.849.1		16	260.43	even	12
1040.2.df.d.849.8		16	260.147	even	12
1300.2.y.e.101.1		16	5.4	even	2	inner
1300.2.y.e.101.8		16	1.1	even	1	trivial
1300.2.y.e.901.1		16	65.4	even	6	inner
1300.2.y.e.901.8		16	13.4	even	6	inner
2340.2.cr.a.829.3		16	15.8	even	4
2340.2.cr.a.829.6		16	15.2	even	4
2340.2.cr.a.1369.3		16	195.17	even	12
2340.2.cr.a.1369.6		16	195.173	even	12
3380.2.c.e.2029.1		16	65.63	even	12
3380.2.c.e.2029.2		16	65.28	even	12
3380.2.c.e.2029.15		16	65.37	even	12
3380.2.c.e.2029.16		16	65.2	even	12
3380.2.d.d.1689.1		16	65.23	odd	12
3380.2.d.d.1689.2		16	65.3	odd	12
3380.2.d.d.1689.15		16	65.42	odd	12
3380.2.d.d.1689.16		16	65.62	odd	12

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:	\( N \)	\(=\)	\( 1300 = 2^{2} \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1300.y (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.65307 + 2.86320i) q^{3} +(-0.895580 - 0.517063i) q^{7} +(-3.96529 + 6.86809i) q^{9} +O(q^{10})\)	\(q+(1.65307 + 2.86320i) q^{3} +(-0.895580 - 0.517063i) q^{7} +(-3.96529 + 6.86809i) q^{9} +(-2.96091 + 1.70948i) q^{11} +(-0.455025 + 3.57672i) q^{13} +(1.19805 - 2.07508i) q^{17} +(5.37246 + 3.10179i) q^{19} -3.41897i q^{21} +(-3.62751 - 6.28304i) q^{23} -16.3012 q^{27} +(-0.902796 - 1.56369i) q^{29} +5.80053i q^{31} +(-9.78921 - 5.65180i) q^{33} +(-1.23585 + 0.713520i) q^{37} +(-10.9931 + 4.60975i) q^{39} +(-3.60158 + 2.07937i) q^{41} +(-1.07886 + 1.86864i) q^{43} -3.50894i q^{47} +(-2.96529 - 5.13604i) q^{49} +7.92183 q^{51} +4.55382 q^{53} +20.5099i q^{57} +(5.06250 + 2.92283i) q^{59} +(-1.90280 + 3.29574i) q^{61} +(7.10247 - 4.10061i) q^{63} +(-6.59603 + 3.80822i) q^{67} +(11.9931 - 20.7726i) q^{69} +(9.49745 + 5.48336i) q^{71} +7.15345i q^{73} +3.53565 q^{77} +12.8524 q^{79} +(-15.0512 - 26.0694i) q^{81} -0.706694i q^{83} +(2.98477 - 5.16978i) q^{87} +(-5.06250 + 2.92283i) q^{89} +(2.25690 - 2.96796i) q^{91} +(-16.6081 + 9.58870i) q^{93} +(-13.8528 - 7.99794i) q^{97} -27.1144i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 10 q^{9}+O(q^{10}) \) 16 * q - 10 * q^9	\( 16 q - 10 q^{9} - 6 q^{11} + 18 q^{19} - 12 q^{29} - 18 q^{39} - 48 q^{41} + 6 q^{49} + 44 q^{51} + 30 q^{59} - 28 q^{61} + 34 q^{69} - 18 q^{71} + 16 q^{79} - 44 q^{81} - 30 q^{89} - 10 q^{91}+O(q^{100}) \) 16 * q - 10 * q^9 - 6 * q^11 + 18 * q^19 - 12 * q^29 - 18 * q^39 - 48 * q^41 + 6 * q^49 + 44 * q^51 + 30 * q^59 - 28 * q^61 + 34 * q^69 - 18 * q^71 + 16 * q^79 - 44 * q^81 - 30 * q^89 - 10 * q^91

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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