LMFDB - Embedded newform 1300.2.y.c.101.3

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:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 19x^{8} + 120x^{6} + 301x^{4} + 271x^{2} + 75 $ x^10 + 19x^8 + 120x^6 + 301x^4 + 271x^2 + 75
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.3
Root			$-3.01615i$ of defining polynomial
Character	$\chi$	$=$	1300.101
Dual form			1300.2.y.c.901.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.330430 - 0.572322i) q^{3} +(1.16835 + 0.674550i) q^{7} +(1.28163 - 2.21985i) q^{9} +O(q^{10})$	$q+(-0.330430 - 0.572322i) q^{3} +(1.16835 + 0.674550i) q^{7} +(1.28163 - 2.21985i) q^{9} +(1.30955 - 0.756069i) q^{11} +(2.69540 - 2.39474i) q^{13} +(-2.50662 + 4.34160i) q^{17} +(1.33827 + 0.772651i) q^{19} -0.891566i q^{21} +(1.14165 + 1.97740i) q^{23} -3.67654 q^{27} +(-1.55542 - 2.69407i) q^{29} -4.96378i q^{31} +(-0.865429 - 0.499656i) q^{33} +(-1.30955 + 0.756069i) q^{37} +(-2.26121 - 0.751342i) q^{39} +(9.14574 - 5.28029i) q^{41} +(2.97790 - 5.15788i) q^{43} +6.87657i q^{47} +(-2.58997 - 4.48595i) q^{49} +3.31306 q^{51} +3.77414 q^{53} -1.02123i q^{57} +(10.1595 + 5.86559i) q^{59} +(4.81617 - 8.34186i) q^{61} +(2.99480 - 1.72905i) q^{63} +(-2.79422 + 1.61324i) q^{67} +(0.754473 - 1.30679i) q^{69} +(0.316312 + 0.182623i) q^{71} +0.367494i q^{73} +2.04002 q^{77} +8.56083 q^{79} +(-2.63005 - 4.55539i) q^{81} -14.1658i q^{83} +(-1.02792 + 1.78041i) q^{87} +(0.148342 - 0.0856456i) q^{89} +(4.76456 - 0.979727i) q^{91} +(-2.84088 + 1.64018i) q^{93} +(-12.8494 - 7.41862i) q^{97} -3.87601i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - q^{3} - 8 q^{9}+O(q^{10}) $ 10 * q - q^3 - 8 * q^9	$ 10 q - q^{3} - 8 q^{9} + 3 q^{11} - 4 q^{13} + 12 q^{17} - 12 q^{19} + 3 q^{23} + 14 q^{27} + 3 q^{29} + 30 q^{33} - 3 q^{37} + 16 q^{39} + 12 q^{41} + 8 q^{43} + 19 q^{49} - 24 q^{51} + 24 q^{53} - 6 q^{59} + q^{61} - 24 q^{63} - 48 q^{67} + 45 q^{71} - 24 q^{77} + 16 q^{79} + 7 q^{81} - 21 q^{87} + 12 q^{89} - 3 q^{91} - 93 q^{93} + 15 q^{97}+O(q^{100}) $ 10 * q - q^3 - 8 * q^9 + 3 * q^11 - 4 * q^13 + 12 * q^17 - 12 * q^19 + 3 * q^23 + 14 * q^27 + 3 * q^29 + 30 * q^33 - 3 * q^37 + 16 * q^39 + 12 * q^41 + 8 * q^43 + 19 * q^49 - 24 * q^51 + 24 * q^53 - 6 * q^59 + q^61 - 24 * q^63 - 48 * q^67 + 45 * q^71 - 24 * q^77 + 16 * q^79 + 7 * q^81 - 21 * q^87 + 12 * q^89 - 3 * q^91 - 93 * q^93 + 15 * q^97

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
$3$	−0.330430	−	0.572322i	−0.190774	−	0.330430i	0.754733	−	0.656032i	$-0.227766\pi$
$3$	−0.330430	−	0.572322i	−0.190774	−	0.330430i	−0.945507	+	0.325602i	$0.894433\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	1.16835	+	0.674550i	0.441596	+	0.254956i	0.704275	−	0.709928i	$-0.251272\pi$
$7$	1.16835	+	0.674550i	0.441596	+	0.254956i	−0.262678	+	0.964884i	$0.584606\pi$
$8$		0			0
$9$	1.28163	−	2.21985i	0.427211	−	0.739950i
$10$		0			0
$11$	1.30955	−	0.756069i	0.394844	−	0.227963i	−0.289413	−	0.957204i	$-0.593460\pi$
$11$	1.30955	−	0.756069i	0.394844	−	0.227963i	0.684257	+	0.729241i	$0.260127\pi$
$12$		0			0
$13$	2.69540	−	2.39474i	0.747570	−	0.664183i
$13$	2.69540	−	2.39474i	0.747570	−	0.664183i
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−2.50662	+	4.34160i	−0.607946	+	1.05299i	0.383633	+	0.923486i	$0.374673\pi$
$17$	−2.50662	+	4.34160i	−0.607946	+	1.05299i	−0.991578	+	0.129507i	$0.958660\pi$
$18$		0			0
$19$	1.33827	+	0.772651i	0.307020	+	0.177258i	0.645592	−	0.763682i	$-0.276611\pi$
$19$	1.33827	+	0.772651i	0.307020	+	0.177258i	−0.338572	+	0.940940i	$0.609944\pi$
$20$		0			0
$21$		−	0.891566i		−	0.194556i
$22$		0			0
$23$	1.14165	+	1.97740i	0.238051	+	0.412316i	0.960155	−	0.279468i	$-0.0901582\pi$
$23$	1.14165	+	1.97740i	0.238051	+	0.412316i	−0.722104	+	0.691784i	$0.756825\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−3.67654			−0.707551
$28$		0			0
$29$	−1.55542	−	2.69407i	−0.288835	−	0.500277i	0.684697	−	0.728828i	$-0.259935\pi$
$29$	−1.55542	−	2.69407i	−0.288835	−	0.500277i	−0.973532	+	0.228551i	$0.926601\pi$
$30$		0			0
$31$		−	4.96378i		−	0.891520i	−0.895152	−	0.445760i	$-0.852933\pi$
$31$		−	4.96378i		−	0.891520i	0.895152	−	0.445760i	$-0.147067\pi$
$32$		0			0
$33$	−0.865429	−	0.499656i	−0.150652	−	0.0869789i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−1.30955	+	0.756069i	−0.215289	+	0.124297i	−0.603767	−	0.797161i	$-0.706334\pi$
$37$	−1.30955	+	0.756069i	−0.215289	+	0.124297i	0.388478	+	0.921458i	$0.373001\pi$
$38$		0			0
$39$	−2.26121	−	0.751342i	−0.362083	−	0.120311i
$40$		0			0
$41$	9.14574	−	5.28029i	1.42832	−	0.824643i	0.431335	−	0.902192i	$-0.358043\pi$
$41$	9.14574	−	5.28029i	1.42832	−	0.824643i	0.996989	+	0.0775485i	$0.0247093\pi$
$42$		0			0
$43$	2.97790	−	5.15788i	0.454126	−	0.786569i	−0.544511	−	0.838753i	$-0.683285\pi$
$43$	2.97790	−	5.15788i	0.454126	−	0.786569i	0.998637	+	0.0521840i	$0.0166182\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$			6.87657i			1.00305i	0.865143	+	0.501525i	$0.167228\pi$
$47$			6.87657i			1.00305i	−0.865143	+	0.501525i	$0.832772\pi$
$48$		0			0
$49$	−2.58997	−	4.48595i	−0.369995	−	0.640850i
$50$		0			0
$51$	3.31306			0.463921
$52$		0			0
$53$	3.77414			0.518418			0.259209	−	0.965821i	$-0.416538\pi$
$53$	3.77414			0.518418			0.259209	+	0.965821i	$0.416538\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		−	1.02123i		−	0.135265i
$58$		0			0
$59$	10.1595	+	5.86559i	1.32266	+	0.763635i	0.984151	−	0.177330i	$-0.0567459\pi$
$59$	10.1595	+	5.86559i	1.32266	+	0.763635i	0.338504	+	0.940965i	$0.390079\pi$
$60$		0			0
$61$	4.81617	−	8.34186i	0.616648	−	1.06807i	−0.373445	−	0.927652i	$-0.621824\pi$
$61$	4.81617	−	8.34186i	0.616648	−	1.06807i	0.990093	−	0.140413i	$-0.0448431\pi$
$62$		0			0
$63$	2.99480	−	1.72905i	0.377309	−	0.217840i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−2.79422	+	1.61324i	−0.341368	+	0.197089i	−0.660877	−	0.750494i	$-0.729815\pi$
$67$	−2.79422	+	1.61324i	−0.341368	+	0.197089i	0.319509	+	0.947583i	$0.396482\pi$
$68$		0			0
$69$	0.754473	−	1.30679i	0.0908278	−	0.157318i
$70$		0			0
$71$	0.316312	+	0.182623i	0.0375393	+	0.0216733i	0.518652	−	0.854985i	$-0.326434\pi$
$71$	0.316312	+	0.182623i	0.0375393	+	0.0216733i	−0.481113	+	0.876659i	$0.659767\pi$
$72$		0			0
$73$			0.367494i			0.0430119i	0.999769	+	0.0215059i	$0.00684608\pi$
$73$			0.367494i			0.0430119i	−0.999769	+	0.0215059i	$0.993154\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	2.04002			0.232482
$78$		0			0
$79$	8.56083			0.963169			0.481584	−	0.876400i	$-0.340061\pi$
$79$	8.56083			0.963169			0.481584	+	0.876400i	$0.340061\pi$
$80$		0			0
$81$	−2.63005	−	4.55539i	−0.292228	−	0.506154i
$82$		0			0
$83$		−	14.1658i		−	1.55490i	−0.628945	−	0.777450i	$-0.716513\pi$
$83$		−	14.1658i		−	1.55490i	0.628945	−	0.777450i	$-0.283487\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−1.02792	+	1.78041i	−0.110204	+	0.190880i
$88$		0			0
$89$	0.148342	−	0.0856456i	0.0157243	−	0.00907841i	−0.492117	−	0.870529i	$-0.663777\pi$
$89$	0.148342	−	0.0856456i	0.0157243	−	0.00907841i	0.507842	+	0.861451i	$0.330444\pi$
$90$		0			0
$91$	4.76456	−	0.979727i	0.499462	−	0.102703i
$92$		0			0
$93$	−2.84088	+	1.64018i	−0.294585	+	0.170079i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−12.8494	−	7.41862i	−1.30466	−	0.753247i	−0.323462	−	0.946241i	$-0.604847\pi$
$97$	−12.8494	−	7.41862i	−1.30466	−	0.753247i	−0.981200	+	0.192994i	$0.938180\pi$
$98$		0			0
$99$		−	3.87601i		−	0.389553i
$100$		0			0
$101$	−2.28129	−	3.95130i	−0.226996	−	0.393169i	0.729920	−	0.683532i	$-0.239557\pi$
$101$	−2.28129	−	3.95130i	−0.226996	−	0.393169i	−0.956917	+	0.290363i	$0.906224\pi$
$102$		0			0
$103$	3.18745			0.314068			0.157034	−	0.987593i	$-0.449807\pi$
$103$	3.18745			0.314068			0.157034	+	0.987593i	$0.449807\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	2.74333	+	4.75159i	0.265208	+	0.459354i	0.967618	−	0.252419i	$-0.0812261\pi$
$107$	2.74333	+	4.75159i	0.265208	+	0.459354i	−0.702410	+	0.711772i	$0.747893\pi$
$108$		0			0
$109$		−	7.22411i		−	0.691944i	−0.938245	−	0.345972i	$-0.887549\pi$
$109$		−	7.22411i		−	0.691944i	0.938245	−	0.345972i	$-0.112451\pi$
$110$		0			0
$111$	0.865429	+	0.499656i	0.0821429	+	0.0474252i
$112$		0			0
$113$	−1.12632	+	1.95084i	−0.105955	+	0.183520i	−0.914128	−	0.405426i	$-0.867123\pi$
$113$	−1.12632	+	1.95084i	−0.105955	+	0.183520i	0.808173	+	0.588945i	$0.200457\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−1.86146	−	9.05257i	−0.172092	−	0.836911i
$118$		0			0
$119$	−5.85725	+	3.38169i	−0.536933	+	0.309999i
$120$		0			0
$121$	−4.35672	+	7.54606i	−0.396065	+	0.686006i
$122$		0			0
$123$	−6.04405	−	3.48954i	−0.544974	−	0.314641i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	2.56448	+	4.44181i	0.227561	+	0.394147i	0.957085	−	0.289809i	$-0.0935916\pi$
$127$	2.56448	+	4.44181i	0.227561	+	0.394147i	−0.729524	+	0.683955i	$0.760258\pi$
$128$		0			0
$129$	−3.93596			−0.346542
$130$		0			0
$131$	−0.189876			−0.0165896			−0.00829478	−	0.999966i	$-0.502640\pi$
$131$	−0.189876			−0.0165896			−0.00829478	+	0.999966i	$0.502640\pi$
$132$		0			0
$133$	1.04238	+	1.80546i	0.0903860	+	0.156553i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	2.63963	+	1.52399i	0.225519	+	0.130204i	0.608503	−	0.793551i	$-0.291770\pi$
$137$	2.63963	+	1.52399i	0.225519	+	0.130204i	−0.382984	+	0.923755i	$0.625104\pi$
$138$		0			0
$139$	−7.42120	+	12.8539i	−0.629458	+	1.09025i	0.358203	+	0.933644i	$0.383390\pi$
$139$	−7.42120	+	12.8539i	−0.629458	+	1.09025i	−0.987661	+	0.156609i	$0.949944\pi$
$140$		0			0
$141$	3.93561	−	2.27223i	0.331438	−	0.191356i
$142$		0			0
$143$	1.71917	−	5.17395i	0.143764	−	0.432667i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−1.71161	+	2.96459i	−0.141171	+	0.244515i
$148$		0			0
$149$	−2.02924	−	1.17158i	−0.166242	−	0.0959799i	0.414571	−	0.910017i	$-0.363932\pi$
$149$	−2.02924	−	1.17158i	−0.166242	−	0.0959799i	−0.580813	+	0.814037i	$0.697265\pi$
$150$		0			0
$151$		−	4.71649i		−	0.383823i	−0.981412	−	0.191911i	$-0.938531\pi$
$151$		−	4.71649i		−	0.383823i	0.981412	−	0.191911i	$-0.0614686\pi$
$152$		0			0
$153$	6.42514	+	11.1287i	0.519442	+	0.899699i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	3.63986			0.290493			0.145246	−	0.989396i	$-0.453603\pi$
$157$	3.63986			0.290493			0.145246	+	0.989396i	$0.453603\pi$
$158$		0			0
$159$	−1.24709	−	2.16002i	−0.0989006	−	0.171301i
$160$		0			0
$161$			3.08040i			0.242770i
$162$		0			0
$163$	12.5554	+	7.24884i	0.983411	+	0.567773i	0.903298	−	0.429013i	$-0.141139\pi$
$163$	12.5554	+	7.24884i	0.983411	+	0.567773i	0.0801131	+	0.996786i	$0.474472\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	8.39887	−	4.84909i	0.649924	−	0.375234i	−0.138503	−	0.990362i	$-0.544229\pi$
$167$	8.39887	−	4.84909i	0.649924	−	0.375234i	0.788427	+	0.615128i	$0.210896\pi$
$168$		0			0
$169$	1.53039	−	12.9096i	0.117723	−	0.993047i
$170$		0			0
$171$	3.43034	−	1.98051i	0.262325	−	0.151453i
$172$		0			0
$173$	−0.639111	+	1.10697i	−0.0485907	+	0.0841615i	−0.889298	−	0.457329i	$-0.848806\pi$
$173$	−0.639111	+	1.10697i	−0.0485907	+	0.0841615i	0.840707	+	0.541490i	$0.182140\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		−	7.75268i		−	0.582727i
$178$		0			0
$179$	11.8049	+	20.4467i	0.882341	+	1.52826i	0.848731	+	0.528825i	$0.177367\pi$
$179$	11.8049	+	20.4467i	0.882341	+	1.52826i	0.0336106	+	0.999435i	$0.489299\pi$
$180$		0			0
$181$	−18.0325			−1.34035			−0.670173	−	0.742205i	$-0.733780\pi$
$181$	−18.0325			−1.34035			−0.670173	+	0.742205i	$0.733780\pi$
$182$		0			0
$183$	−6.36564			−0.470562
$184$		0			0
$185$		0			0
$186$		0			0
$187$			7.58072i			0.554357i
$188$		0			0
$189$	−4.29550	−	2.48001i	−0.312452	−	0.180394i
$190$		0			0
$191$	−8.33208	+	14.4316i	−0.602888	+	1.04423i	0.389493	+	0.921029i	$0.372650\pi$
$191$	−8.33208	+	14.4316i	−0.602888	+	1.04423i	−0.992381	+	0.123204i	$0.960683\pi$
$192$		0			0
$193$	−17.3576	+	10.0214i	−1.24943	+	0.721358i	−0.970996	−	0.239097i	$-0.923148\pi$
$193$	−17.3576	+	10.0214i	−1.24943	+	0.721358i	−0.278433	+	0.960456i	$0.589815\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−3.65250	+	2.10877i	−0.260230	+	0.150244i	−0.624439	−	0.781073i	$-0.714672\pi$
$197$	−3.65250	+	2.10877i	−0.260230	+	0.150244i	0.364210	+	0.931317i	$0.381339\pi$
$198$		0			0
$199$	0.227881	−	0.394701i	0.0161540	−	0.0279796i	−0.857835	−	0.513925i	$-0.828191\pi$
$199$	0.227881	−	0.394701i	0.0161540	−	0.0279796i	0.873989	+	0.485945i	$0.161524\pi$
$200$		0			0
$201$	1.84659	+	1.06613i	0.130248	+	0.0751988i
$202$		0			0
$203$		−	4.19684i		−	0.294560i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	5.85271			0.406791
$208$		0			0
$209$	2.33671			0.161634
$210$		0			0
$211$	8.77365	+	15.1964i	0.604003	+	1.04616i	0.992208	+	0.124591i	$0.0397619\pi$
$211$	8.77365	+	15.1964i	0.604003	+	1.04616i	−0.388205	+	0.921573i	$0.626905\pi$
$212$		0			0
$213$		−	0.241376i		−	0.0165388i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	3.34831	−	5.79945i	0.227298	−	0.393692i
$218$		0			0
$219$	0.210325	−	0.121431i	0.0142124	−	0.00820554i
$220$		0			0
$221$	3.64066	+	17.7051i	0.244898	+	1.19097i
$222$		0			0
$223$	−24.1611	+	13.9494i	−1.61794	+	0.934121i	−0.630494	+	0.776194i	$0.717148\pi$
$223$	−24.1611	+	13.9494i	−1.61794	+	0.934121i	−0.987451	+	0.157927i	$0.949519\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	4.31150	+	2.48924i	0.286164	+	0.165217i	0.636211	−	0.771515i	$-0.280501\pi$
$227$	4.31150	+	2.48924i	0.286164	+	0.165217i	−0.350047	+	0.936732i	$0.613834\pi$
$228$		0			0
$229$		−	14.5966i		−	0.964573i	−0.876014	−	0.482286i	$-0.839806\pi$
$229$		−	14.5966i		−	0.964573i	0.876014	−	0.482286i	$-0.160194\pi$
$230$		0			0
$231$	−0.674085	−	1.16755i	−0.0443516	−	0.0768192i
$232$		0			0
$233$	6.27395			0.411020			0.205510	−	0.978655i	$-0.434115\pi$
$233$	6.27395			0.411020			0.205510	+	0.978655i	$0.434115\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−2.82876	−	4.89955i	−0.183748	−	0.318260i
$238$		0			0
$239$			13.9244i			0.900697i	0.892853	+	0.450348i	$0.148700\pi$
$239$			13.9244i			0.900697i	−0.892853	+	0.450348i	$0.851300\pi$
$240$		0			0
$241$	−16.2431	−	9.37794i	−1.04631	−	0.604087i	−0.124695	−	0.992195i	$-0.539795\pi$
$241$	−16.2431	−	9.37794i	−1.04631	−	0.604087i	−0.921614	+	0.388109i	$0.873129\pi$
$242$		0			0
$243$	−7.25291	+	12.5624i	−0.465274	+	0.805879i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	5.45748	−	1.12221i	0.347251	−	0.0714046i
$248$		0			0
$249$	−8.10740	+	4.68081i	−0.513786	+	0.296634i
$250$		0			0
$251$	−6.76497	+	11.7173i	−0.427001	+	0.739588i	−0.996605	−	0.0823316i	$-0.973763\pi$
$251$	−6.76497	+	11.7173i	−0.427001	+	0.739588i	0.569604	+	0.821919i	$0.307097\pi$
$252$		0			0
$253$	2.99010	+	1.72633i	0.187986	+	0.108534i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	4.23457	+	7.33449i	0.264145	+	0.457513i	0.967339	−	0.253485i	$-0.0815768\pi$
$257$	4.23457	+	7.33449i	0.264145	+	0.457513i	−0.703194	+	0.710998i	$0.748243\pi$
$258$		0			0
$259$	−2.04002			−0.126761
$260$		0			0
$261$	−7.97392			−0.493573
$262$		0			0
$263$	−15.6231	−	27.0600i	−0.963363	−	1.66859i	−0.713951	−	0.700195i	$-0.753096\pi$
$263$	−15.6231	−	27.0600i	−0.963363	−	1.66859i	−0.249411	−	0.968398i	$-0.580237\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−0.0980337	−	0.0565998i	−0.00599956	−	0.00346385i
$268$		0			0
$269$	−6.18323	+	10.7097i	−0.376998	+	0.652980i	−0.990624	−	0.136617i	$-0.956377\pi$
$269$	−6.18323	+	10.7097i	−0.376998	+	0.652980i	0.613626	+	0.789597i	$0.289710\pi$
$270$		0			0
$271$	−18.7939	+	10.8507i	−1.14165	+	0.659132i	−0.946839	−	0.321709i	$-0.895743\pi$
$271$	−18.7939	+	10.8507i	−1.14165	+	0.659132i	−0.194811	+	0.980841i	$0.562409\pi$
$272$		0			0
$273$	−2.13507	−	2.40313i	−0.129221	−	0.145444i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	15.9398	−	27.6086i	0.957731	−	1.65884i	0.229738	−	0.973252i	$-0.426213\pi$
$277$	15.9398	−	27.6086i	0.957731	−	1.65884i	0.727992	−	0.685586i	$-0.240454\pi$
$278$		0			0
$279$	−11.0188	−	6.36173i	−0.659681	−	0.380867i
$280$		0			0
$281$			19.1680i			1.14347i	0.820439	+	0.571734i	$0.193729\pi$
$281$			19.1680i			1.14347i	−0.820439	+	0.571734i	$0.806271\pi$
$282$		0			0
$283$	13.4282	+	23.2584i	0.798226	+	1.38257i	0.920771	+	0.390105i	$0.127561\pi$
$283$	13.4282	+	23.2584i	0.798226	+	1.38257i	−0.122545	+	0.992463i	$0.539106\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	14.2473			0.840990
$288$		0			0
$289$	−4.06633	−	7.04310i	−0.239196	−	0.414300i
$290$		0			0
$291$			9.80535i			0.574800i
$292$		0			0
$293$	7.83879	+	4.52573i	0.457947	+	0.264396i	0.711181	−	0.703009i	$-0.248161\pi$
$293$	7.83879	+	4.52573i	0.457947	+	0.264396i	−0.253234	+	0.967405i	$0.581494\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−4.81461	+	2.77972i	−0.279372	+	0.161296i
$298$		0			0
$299$	7.81258	+	2.59592i	0.451813	+	0.150126i
$300$		0			0
$301$	6.95849	−	4.01749i	0.401081	−	0.231564i
$302$		0			0
$303$	−1.50761	+	2.61126i	−0.0866100	+	0.150013i
$304$		0			0
$305$		0			0
$306$		0			0
$307$		−	14.8983i		−	0.850293i	−0.905125	−	0.425146i	$-0.860223\pi$
$307$		−	14.8983i		−	0.850293i	0.905125	−	0.425146i	$-0.139777\pi$
$308$		0			0
$309$	−1.05323	−	1.82424i	−0.0599161	−	0.103778i
$310$		0			0
$311$	−25.4282			−1.44190			−0.720950	−	0.692987i	$-0.756294\pi$
$311$	−25.4282			−1.44190			−0.720950	+	0.692987i	$0.756294\pi$
$312$		0			0
$313$	26.3284			1.48817			0.744084	−	0.668086i	$-0.232886\pi$
$313$	26.3284			1.48817			0.744084	+	0.668086i	$0.232886\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		−	9.26716i		−	0.520496i	−0.965542	−	0.260248i	$-0.916196\pi$
$317$		−	9.26716i		−	0.520496i	0.965542	−	0.260248i	$-0.0838043\pi$
$318$		0			0
$319$	−4.07381	−	2.35201i	−0.228089	−	0.131687i
$320$		0			0
$321$	1.81296	−	3.14014i	0.101190	−	0.175265i
$322$		0			0
$323$	−6.70908	+	3.87349i	−0.373303	+	0.215527i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−4.13452	+	2.38706i	−0.228639	+	0.132005i
$328$		0			0
$329$	−4.63859	+	8.03427i	−0.255734	+	0.442944i
$330$		0			0
$331$	22.5768	+	13.0347i	1.24094	+	0.716454i	0.969285	−	0.245942i	$-0.0790971\pi$
$331$	22.5768	+	13.0347i	1.24094	+	0.716454i	0.271651	+	0.962396i	$0.412430\pi$
$332$		0			0
$333$			3.87601i			0.212404i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	6.64587			0.362024			0.181012	−	0.983481i	$-0.442063\pi$
$337$	6.64587			0.362024			0.181012	+	0.983481i	$0.442063\pi$
$338$		0			0
$339$	1.48868			0.0808539
$340$		0			0
$341$	−3.75296	−	6.50031i	−0.203234	−	0.352011i
$342$		0			0
$343$		−	16.4319i		−	0.887241i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−9.17608	+	15.8934i	−0.492598	+	0.853205i	−0.999964	−	0.00852610i	$-0.997286\pi$
$347$	−9.17608	+	15.8934i	−0.492598	+	0.853205i	0.507366	+	0.861731i	$0.330619\pi$
$348$		0			0
$349$	−10.9342	+	6.31287i	−0.585295	+	0.337920i	−0.763235	−	0.646121i	$-0.776390\pi$
$349$	−10.9342	+	6.31287i	−0.585295	+	0.337920i	0.177940	+	0.984041i	$0.443057\pi$
$350$		0			0
$351$	−9.90976	+	8.80438i	−0.528944	+	0.469943i
$352$		0			0
$353$	−27.3597	+	15.7961i	−1.45621	+	0.840743i	−0.998822	−	0.0485237i	$-0.984548\pi$
$353$	−27.3597	+	15.7961i	−1.45621	+	0.840743i	−0.457388	+	0.889267i	$0.651215\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	3.87083	+	2.23482i	0.204866	+	0.118279i
$358$		0			0
$359$			30.2464i			1.59635i	0.602428	+	0.798173i	$0.294200\pi$
$359$			30.2464i			1.59635i	−0.602428	+	0.798173i	$0.705800\pi$
$360$		0			0
$361$	−8.30602	−	14.3865i	−0.437159	−	0.757182i
$362$		0			0
$363$	5.75837			0.302236
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−7.00649	−	12.1356i	−0.365736	−	0.633473i	0.623158	−	0.782096i	$-0.285849\pi$
$367$	−7.00649	−	12.1356i	−0.365736	−	0.633473i	−0.988894	+	0.148623i	$0.952516\pi$
$368$		0			0
$369$		−	27.0696i		−	1.40919i
$370$		0			0
$371$	4.40953	+	2.54584i	0.228931	+	0.132174i
$372$		0			0
$373$	−12.0724	+	20.9101i	−0.625087	+	1.08268i	0.363437	+	0.931619i	$0.381603\pi$
$373$	−12.0724	+	20.9101i	−0.625087	+	1.08268i	−0.988524	+	0.151064i	$0.951730\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−10.6441	−	3.53677i	−0.548199	−	0.182153i
$378$		0			0
$379$	−9.54458	+	5.51056i	−0.490272	+	0.283059i	−0.724687	−	0.689078i	$-0.758016\pi$
$379$	−9.54458	+	5.51056i	−0.490272	+	0.283059i	0.234415	+	0.972137i	$0.424682\pi$
$380$		0			0
$381$	1.69476	−	2.93542i	0.0868253	−	0.150386i
$382$		0			0
$383$	−27.9028	−	16.1097i	−1.42576	−	0.823166i	−0.428982	−	0.903313i	$-0.641128\pi$
$383$	−27.9028	−	16.1097i	−1.42576	−	0.823166i	−0.996783	+	0.0801474i	$0.974461\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−7.63315	−	13.2210i	−0.388015	−	0.672062i
$388$		0			0
$389$	32.0717			1.62610			0.813050	−	0.582194i	$-0.197806\pi$
$389$	32.0717			1.62610			0.813050	+	0.582194i	$0.197806\pi$
$390$		0			0
$391$	−11.4468			−0.578888
$392$		0			0
$393$	0.0627408	+	0.108670i	0.00316486	+	0.00548169i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	2.04002	+	1.17781i	0.102386	+	0.0591125i	0.550319	−	0.834955i	$-0.314506\pi$
$397$	2.04002	+	1.17781i	0.102386	+	0.0591125i	−0.447933	+	0.894067i	$0.647840\pi$
$398$		0			0
$399$	0.688869	−	1.19316i	0.0344866	−	0.0597326i
$400$		0			0
$401$	−4.39273	+	2.53614i	−0.219362	+	0.126649i	−0.605655	−	0.795727i	$-0.707089\pi$
$401$	−4.39273	+	2.53614i	−0.219362	+	0.126649i	0.386293	+	0.922376i	$0.373755\pi$
$402$		0			0
$403$	−11.8870	−	13.3794i	−0.592132	−	0.666474i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−1.14328	+	1.98022i	−0.0566703	+	0.0981558i
$408$		0			0
$409$	−12.8902	−	7.44214i	−0.637378	−	0.367990i	0.146226	−	0.989251i	$-0.453287\pi$
$409$	−12.8902	−	7.44214i	−0.637378	−	0.367990i	−0.783604	+	0.621261i	$0.786621\pi$
$410$		0			0
$411$		−	2.01429i		−	0.0993578i
$412$		0			0
$413$	7.91327	+	13.7062i	0.389387	+	0.674437i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	9.80875			0.480337
$418$		0			0
$419$	4.68381	+	8.11259i	0.228819	+	0.396326i	0.957458	−	0.288572i	$-0.0931803\pi$
$419$	4.68381	+	8.11259i	0.228819	+	0.396326i	−0.728639	+	0.684897i	$0.759847\pi$
$420$		0			0
$421$			5.93693i			0.289348i	0.989479	+	0.144674i	$0.0462134\pi$
$421$			5.93693i			0.289348i	−0.989479	+	0.144674i	$0.953787\pi$
$422$		0			0
$423$	15.2650	+	8.81323i	0.742208	+	0.428514i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	11.2540	−	6.49750i	0.544619	−	0.314436i
$428$		0			0
$429$	−3.52923	+	0.725709i	−0.170393	+	0.0350376i
$430$		0			0
$431$	17.1118	−	9.87948i	0.824244	−	0.475878i	−0.0276335	−	0.999618i	$-0.508797\pi$
$431$	17.1118	−	9.87948i	0.824244	−	0.475878i	0.851878	+	0.523740i	$0.175464\pi$
$432$		0			0
$433$	1.28044	−	2.21779i	0.0615342	−	0.106580i	−0.833617	−	0.552343i	$-0.813734\pi$
$433$	1.28044	−	2.21779i	0.0615342	−	0.106580i	0.895151	+	0.445762i	$0.147067\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$			3.52839i			0.168786i
$438$		0			0
$439$	15.7800	+	27.3318i	0.753138	+	1.30447i	0.946294	+	0.323306i	$0.104794\pi$
$439$	15.7800	+	27.3318i	0.753138	+	1.30447i	−0.193156	+	0.981168i	$0.561872\pi$
$440$		0			0
$441$	−13.2775			−0.632263
$442$		0			0
$443$	18.0881			0.859392			0.429696	−	0.902974i	$-0.358621\pi$
$443$	18.0881			0.859392			0.429696	+	0.902974i	$0.358621\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$			1.54851i			0.0732419i
$448$		0			0
$449$	22.9979	+	13.2778i	1.08534	+	0.626620i	0.932331	−	0.361605i	$-0.117771\pi$
$449$	22.9979	+	13.2778i	1.08534	+	0.626620i	0.153007	+	0.988225i	$0.451104\pi$
$450$		0			0
$451$	7.98453	−	13.8296i	0.375977	−	0.651211i
$452$		0			0
$453$	−2.69935	+	1.55847i	−0.126827	+	0.0732234i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−16.9398	+	9.78021i	−0.792411	+	0.457499i	−0.840811	−	0.541329i	$-0.817921\pi$
$457$	−16.9398	+	9.78021i	−0.792411	+	0.457499i	0.0483996	+	0.998828i	$0.484588\pi$
$458$		0			0
$459$	9.21571	−	15.9621i	0.430152	−	0.745046i
$460$		0			0
$461$	16.1165	+	9.30486i	0.750620	+	0.433371i	0.825918	−	0.563791i	$-0.190657\pi$
$461$	16.1165	+	9.30486i	0.750620	+	0.433371i	−0.0752980	+	0.997161i	$0.523991\pi$
$462$		0			0
$463$		−	23.6823i		−	1.10061i	−0.834964	−	0.550305i	$-0.814512\pi$
$463$		−	23.6823i		−	1.10061i	0.834964	−	0.550305i	$-0.185488\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	16.2482			0.751877			0.375938	−	0.926645i	$-0.377320\pi$
$467$	16.2482			0.751877			0.375938	+	0.926645i	$0.377320\pi$
$468$		0			0
$469$	−4.35284			−0.200996
$470$		0			0
$471$	−1.20272	−	2.08317i	−0.0554184	−	0.0959875i
$472$		0			0
$473$		−	9.00600i		−	0.414096i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	4.83705	−	8.37802i	0.221474	−	0.383603i
$478$		0			0
$479$	−14.3253	+	8.27070i	−0.654538	+	0.377898i	−0.790193	−	0.612858i	$-0.790020\pi$
$479$	−14.3253	+	8.27070i	−0.654538	+	0.377898i	0.135655	+	0.990756i	$0.456686\pi$
$480$		0			0
$481$	−1.71917	+	5.17395i	−0.0783875	+	0.235912i
$482$		0			0
$483$	1.76298	−	1.01786i	0.0802185	−	0.0463142i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	4.61376	+	2.66376i	0.209069	+	0.120706i	0.600879	−	0.799340i	$-0.294817\pi$
$487$	4.61376	+	2.66376i	0.209069	+	0.120706i	−0.391809	+	0.920046i	$0.628151\pi$
$488$		0			0
$489$		−	9.58094i		−	0.433265i
$490$		0			0
$491$	−10.0979	−	17.4901i	−0.455713	−	0.789317i	0.543016	−	0.839722i	$-0.317282\pi$
$491$	−10.0979	−	17.4901i	−0.455713	−	0.789317i	−0.998729	+	0.0504048i	$0.983949\pi$
$492$		0			0
$493$	15.5954			0.702384
$494$		0			0
$495$		0			0
$496$		0			0
$497$	0.246376	+	0.426736i	0.0110515	+	0.0191417i
$498$		0			0
$499$		−	32.7484i		−	1.46602i	−0.680217	−	0.733011i	$-0.738114\pi$
$499$		−	32.7484i		−	1.46602i	0.680217	−	0.733011i	$-0.261886\pi$
$500$		0			0
$501$	−5.55048	−	3.20457i	−0.247977	−	0.143170i
$502$		0			0
$503$	−16.6379	+	28.8176i	−0.741846	+	1.28491i	0.209808	+	0.977743i	$0.432716\pi$
$503$	−16.6379	+	28.8176i	−0.741846	+	1.28491i	−0.951654	+	0.307172i	$0.900617\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−7.89414	+	3.38985i	−0.350591	+	0.150548i
$508$		0			0
$509$	−26.9659	+	15.5688i	−1.19524	+	0.690073i	−0.959491	−	0.281740i	$-0.909088\pi$
$509$	−26.9659	+	15.5688i	−1.19524	+	0.690073i	−0.235751	+	0.971813i	$0.575755\pi$
$510$		0			0
$511$	−0.247893	+	0.429363i	−0.0109661	+	0.0189939i
$512$		0			0
$513$	−4.92021	−	2.84068i	−0.217232	−	0.125419i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	5.19916	+	9.00521i	0.228659	+	0.396049i
$518$		0			0
$519$	0.844726			0.0370794
$520$		0			0
$521$	8.67250			0.379949			0.189975	−	0.981789i	$-0.439159\pi$
$521$	8.67250			0.379949			0.189975	+	0.981789i	$0.439159\pi$
$522$		0			0
$523$	−0.459179	−	0.795322i	−0.0200785	−	0.0347770i	0.855812	−	0.517288i	$-0.173058\pi$
$523$	−0.459179	−	0.795322i	−0.0200785	−	0.0347770i	−0.875890	+	0.482511i	$0.839725\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	21.5507	+	12.4423i	0.938765	+	0.541996i
$528$		0			0
$529$	8.89326	−	15.4036i	0.386664	−	0.669721i
$530$		0			0
$531$	26.0415	−	15.0351i	1.13010	−	0.652466i
$532$		0			0
$533$	12.0065	−	36.1342i	0.520059	−	1.56515i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	7.80141	−	13.5124i	0.336656	−	0.583105i
$538$		0			0
$539$	−6.78338	−	3.91638i	−0.292181	−	0.168691i
$540$		0			0
$541$		−	3.22797i		−	0.138781i	−0.997590	−	0.0693906i	$-0.977895\pi$
$541$		−	3.22797i		−	0.138781i	0.997590	−	0.0693906i	$-0.0221055\pi$
$542$		0			0
$543$	5.95849	+	10.3204i	0.255703	+	0.442891i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−37.1178			−1.58704			−0.793522	−	0.608542i	$-0.791755\pi$
$547$	−37.1178			−1.58704			−0.793522	+	0.608542i	$0.791755\pi$
$548$		0			0
$549$	−12.3451	−	21.3824i	−0.526877	−	0.912578i
$550$		0			0
$551$		−	4.80720i		−	0.204793i
$552$		0			0
$553$	10.0021	+	5.77471i	0.425332	+	0.245565i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−33.5700	+	19.3817i	−1.42241	+	0.821228i	−0.996504	−	0.0835410i	$-0.973377\pi$
$557$	−33.5700	+	19.3817i	−1.42241	+	0.821228i	−0.425904	+	0.904769i	$0.640044\pi$
$558$		0			0
$559$	−4.32516	−	21.0339i	−0.182935	−	0.889639i
$560$		0			0
$561$	4.33861	−	2.50490i	0.183176	−	0.105757i
$562$		0			0
$563$	22.1343	−	38.3378i	0.932852	−	1.61575i	0.154430	−	0.988004i	$-0.450646\pi$
$563$	22.1343	−	38.3378i	0.932852	−	1.61575i	0.778421	−	0.627743i	$-0.216021\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$		−	7.09641i		−	0.298021i
$568$		0			0
$569$	12.2931	+	21.2923i	0.515353	+	0.892618i	0.999841	+	0.0178204i	$0.00567270\pi$
$569$	12.2931	+	21.2923i	0.515353	+	0.892618i	−0.484488	+	0.874798i	$0.660994\pi$
$570$		0			0
$571$	29.6719			1.24173			0.620865	−	0.783918i	$-0.286782\pi$
$571$	29.6719			1.24173			0.620865	+	0.783918i	$0.286782\pi$
$572$		0			0
$573$	11.0127			0.460062
$574$		0			0
$575$		0			0
$576$		0			0
$577$		−	8.07230i		−	0.336054i	−0.985782	−	0.168027i	$-0.946260\pi$
$577$		−	8.07230i		−	0.336054i	0.985782	−	0.168027i	$-0.0537396\pi$
$578$		0			0
$579$	11.4710	+	6.62277i	0.476717	+	0.275233i
$580$		0			0
$581$	9.55554	−	16.5507i	0.396431	−	0.686638i
$582$		0			0
$583$	4.94242	−	2.85351i	0.204694	−	0.118180i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−39.5057	+	22.8086i	−1.63057	+	0.941413i	−0.646658	+	0.762780i	$0.723834\pi$
$587$	−39.5057	+	22.8086i	−1.63057	+	0.941413i	−0.983916	+	0.178633i	$0.942833\pi$
$588$		0			0
$589$	3.83527	−	6.64287i	0.158029	−	0.273715i
$590$		0			0
$591$	2.41379	+	1.39360i	0.0992901	+	0.0573252i
$592$		0			0
$593$		−	25.5307i		−	1.04842i	−0.851589	−	0.524210i	$-0.824361\pi$
$593$		−	25.5307i		−	1.04842i	0.851589	−	0.524210i	$-0.175639\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−0.301195			−0.0123271
$598$		0			0
$599$	9.37490			0.383048			0.191524	−	0.981488i	$-0.438657\pi$
$599$	9.37490			0.383048			0.191524	+	0.981488i	$0.438657\pi$
$600$		0			0
$601$	1.25869	+	2.18011i	0.0513429	+	0.0889285i	0.890555	−	0.454876i	$-0.150317\pi$
$601$	1.25869	+	2.18011i	0.0513429	+	0.0889285i	−0.839212	+	0.543805i	$0.816983\pi$
$602$		0			0
$603$			8.27032i			0.336794i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−11.4974	+	19.9141i	−0.466665	+	0.808287i	−0.999275	−	0.0380736i	$-0.987878\pi$
$607$	−11.4974	+	19.9141i	−0.466665	+	0.808287i	0.532610	+	0.846361i	$0.321211\pi$
$608$		0			0
$609$	−2.40194	+	1.38676i	−0.0973317	+	0.0561945i
$610$		0			0
$611$	16.4676	+	18.5351i	0.666209	+	0.749851i
$612$		0			0
$613$	−24.8879	+	14.3690i	−1.00521	+	0.580360i	−0.909787	−	0.415076i	$-0.863755\pi$
$613$	−24.8879	+	14.3690i	−1.00521	+	0.580360i	−0.0954267	+	0.995436i	$0.530422\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	5.63234	+	3.25183i	0.226749	+	0.130914i	0.609072	−	0.793115i	$-0.291542\pi$
$617$	5.63234	+	3.25183i	0.226749	+	0.130914i	−0.382322	+	0.924029i	$0.624876\pi$
$618$		0			0
$619$		−	17.8159i		−	0.716081i	−0.933706	−	0.358041i	$-0.883445\pi$
$619$		−	17.8159i		−	0.716081i	0.933706	−	0.358041i	$-0.116555\pi$
$620$		0			0
$621$	−4.19733	−	7.26999i	−0.168433	−	0.291735i
$622$		0			0
$623$	0.231089			0.00925838
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−0.772119	−	1.33735i	−0.0308355	−	0.0534086i
$628$		0			0
$629$		−	7.58072i		−	0.302263i
$630$		0			0
$631$	−31.3227	−	18.0842i	−1.24694	−	0.719919i	−0.276439	−	0.961031i	$-0.589155\pi$
$631$	−31.3227	−	18.0842i	−1.24694	−	0.719919i	−0.970497	+	0.241112i	$0.922488\pi$
$632$		0			0
$633$	5.79816	−	10.0427i	0.230456	−	0.399162i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−17.7237	−	5.88914i	−0.702239	−	0.233336i
$638$		0			0
$639$	0.810791	−	0.468110i	0.0320744	−	0.0185181i
$640$		0			0
$641$	6.52714	−	11.3053i	0.257806	−	0.446534i	−0.707848	−	0.706365i	$-0.750334\pi$
$641$	6.52714	−	11.3053i	0.257806	−	0.446534i	0.965654	+	0.259831i	$0.0836670\pi$
$642$		0			0
$643$	6.16125	+	3.55720i	0.242976	+	0.140282i	0.616544	−	0.787321i	$-0.288532\pi$
$643$	6.16125	+	3.55720i	0.242976	+	0.140282i	−0.373568	+	0.927603i	$0.621866\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	23.1158	+	40.0378i	0.908777	+	1.57405i	0.815766	+	0.578382i	$0.196316\pi$
$647$	23.1158	+	40.0378i	0.908777	+	1.57405i	0.0930111	+	0.995665i	$0.470351\pi$
$648$		0			0
$649$	17.7392			0.696323
$650$		0			0
$651$	−4.42554			−0.173450
$652$		0			0
$653$	−14.6595	−	25.3910i	−0.573671	−	0.993627i	−0.996185	−	0.0872706i	$-0.972186\pi$
$653$	−14.6595	−	25.3910i	−0.573671	−	0.993627i	0.422514	−	0.906356i	$-0.361148\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	0.815781	+	0.470991i	0.0318266	+	0.0183751i
$658$		0			0
$659$	−8.22325	+	14.2431i	−0.320333	+	0.554832i	−0.980557	−	0.196236i	$-0.937128\pi$
$659$	−8.22325	+	14.2431i	−0.320333	+	0.554832i	0.660224	+	0.751069i	$0.270461\pi$
$660$		0			0
$661$	16.3480	−	9.43853i	0.635864	−	0.367116i	−0.147156	−	0.989113i	$-0.547012\pi$
$661$	16.3480	−	9.43853i	0.635864	−	0.367116i	0.783020	+	0.621997i	$0.213678\pi$
$662$		0			0
$663$	8.93003	−	7.93393i	0.346814	−	0.308128i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	3.55150	−	6.15139i	0.137515	−	0.238183i
$668$		0			0
$669$	15.9671	+	9.21861i	0.617324	+	0.356412i
$670$		0			0
$671$		−	14.5654i		−	0.562292i
$672$		0			0
$673$	19.5949	+	33.9394i	0.755329	+	1.30827i	0.945211	+	0.326461i	$0.105856\pi$
$673$	19.5949	+	33.9394i	0.755329	+	1.30827i	−0.189882	+	0.981807i	$0.560811\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	24.8275			0.954200			0.477100	−	0.878849i	$-0.341688\pi$
$677$	24.8275			0.954200			0.477100	+	0.878849i	$0.341688\pi$
$678$		0			0
$679$	−10.0085	−	17.3352i	−0.384089	−	0.665263i
$680$		0			0
$681$		−	3.29009i		−	0.126076i
$682$		0			0
$683$	28.5441	+	16.4799i	1.09221	+	0.630587i	0.934163	−	0.356845i	$-0.116148\pi$
$683$	28.5441	+	16.4799i	1.09221	+	0.630587i	0.158044	+	0.987432i	$0.449481\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−8.35398	+	4.82317i	−0.318724	+	0.184015i
$688$		0			0
$689$	10.1728	−	9.03810i	0.387554	−	0.344324i
$690$		0			0
$691$	38.3746	−	22.1556i	1.45984	−	0.842838i	0.460836	−	0.887485i	$-0.347550\pi$
$691$	38.3746	−	22.1556i	1.45984	−	0.842838i	0.999003	+	0.0446469i	$0.0142163\pi$
$692$		0			0
$693$	2.61456	−	4.52855i	0.0993189	−	0.172025i
$694$		0			0
$695$		0			0
$696$		0			0
$697$			52.9428i			2.00535i
$698$		0			0
$699$	−2.07310	−	3.59072i	−0.0784119	−	0.135813i
$700$		0			0
$701$	10.0543			0.379745			0.189872	−	0.981809i	$-0.439193\pi$
$701$	10.0543			0.379745			0.189872	+	0.981809i	$0.439193\pi$
$702$		0			0
$703$	−2.33671			−0.0881306
$704$		0			0
$705$		0			0
$706$		0			0
$707$		−	6.15536i		−	0.231496i
$708$		0			0
$709$	17.7307	+	10.2368i	0.665889	+	0.384451i	0.794517	−	0.607242i	$-0.207724\pi$
$709$	17.7307	+	10.2368i	0.665889	+	0.384451i	−0.128628	+	0.991693i	$0.541057\pi$
$710$		0			0
$711$	10.9718	−	19.0038i	0.411476	−	0.712697i
$712$		0			0
$713$	9.81537	−	5.66690i	0.367588	−	0.212227i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	7.96926	−	4.60105i	0.297617	−	0.171829i
$718$		0			0
$719$	13.9490	−	24.1603i	0.520209	−	0.901029i	−0.479515	−	0.877534i	$-0.659187\pi$
$719$	13.9490	−	24.1603i	0.520209	−	0.901029i	0.999724	−	0.0234949i	$-0.00747934\pi$
$720$		0			0
$721$	3.72406	+	2.15009i	0.138691	+	0.0800735i
$722$		0			0
$723$			12.3950i			0.460976i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	8.41991			0.312277			0.156139	−	0.987735i	$-0.450095\pi$
$727$	8.41991			0.312277			0.156139	+	0.987735i	$0.450095\pi$
$728$		0			0
$729$	−6.19401			−0.229408
$730$		0			0
$731$	14.9290	+	25.8577i	0.552168	+	0.956383i
$732$		0			0
$733$		−	31.8877i		−	1.17780i	−0.808206	−	0.588900i	$-0.799561\pi$
$733$		−	31.8877i		−	1.17780i	0.808206	−	0.588900i	$-0.200439\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−2.43944	+	4.22524i	−0.0898580	+	0.155639i
$738$		0			0
$739$	11.4800	−	6.62799i	0.422299	−	0.243815i	−0.273761	−	0.961798i	$-0.588268\pi$
$739$	11.4800	−	6.62799i	0.422299	−	0.243815i	0.696061	+	0.717983i	$0.254934\pi$
$740$		0			0
$741$	−2.44558	−	2.75262i	−0.0898407	−	0.101120i
$742$		0			0
$743$	−28.4067	+	16.4006i	−1.04214	+	0.601680i	−0.920439	−	0.390887i	$-0.872168\pi$
$743$	−28.4067	+	16.4006i	−1.04214	+	0.601680i	−0.121701	+	0.992567i	$0.538835\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−31.4460	−	18.1553i	−1.15055	−	0.664269i
$748$		0			0
$749$			7.40206i			0.270465i
$750$		0			0
$751$	−17.6662	−	30.5987i	−0.644647	−	1.11656i	−0.984383	−	0.176041i	$-0.943671\pi$
$751$	−17.6662	−	30.5987i	−0.644647	−	1.11656i	0.339736	−	0.940521i	$-0.389662\pi$
$752$		0			0
$753$	8.94141			0.325843
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−2.28885	−	3.96441i	−0.0831897	−	0.144089i	0.821429	−	0.570311i	$-0.193177\pi$
$757$	−2.28885	−	3.96441i	−0.0831897	−	0.144089i	−0.904618	+	0.426222i	$0.859844\pi$
$758$		0			0
$759$		−	2.28173i		−	0.0828217i
$760$		0			0
$761$	14.5681	+	8.41091i	0.528094	+	0.304895i	0.740240	−	0.672343i	$-0.234712\pi$
$761$	14.5681	+	8.41091i	0.528094	+	0.304895i	−0.212146	+	0.977238i	$0.568045\pi$
$762$		0			0
$763$	4.87302	−	8.44032i	0.176415	−	0.305560i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	41.4306	−	8.51929i	1.49597	−	0.307614i
$768$		0			0
$769$	−34.9017	+	20.1505i	−1.25859	+	0.726645i	−0.972800	−	0.231648i	$-0.925588\pi$
$769$	−34.9017	+	20.1505i	−1.25859	+	0.726645i	−0.285787	+	0.958293i	$0.592255\pi$
$770$		0			0
$771$	2.79846	−	4.84708i	0.100784	−	0.174563i
$772$		0			0
$773$	−32.9579	−	19.0283i	−1.18541	−	0.684400i	−0.228154	−	0.973625i	$-0.573269\pi$
$773$	−32.9579	−	19.0283i	−1.18541	−	0.684400i	−0.957261	+	0.289226i	$0.906602\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	0.674085	+	1.16755i	0.0241827	+	0.0418856i
$778$		0			0
$779$	16.3193			0.584699
$780$		0			0
$781$	0.552301			0.0197629
$782$		0			0
$783$	5.71858	+	9.90487i	0.204365	+	0.353971i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−12.9882	−	7.49874i	−0.462980	−	0.267301i	0.250317	−	0.968164i	$-0.419465\pi$
$787$	−12.9882	−	7.49874i	−0.462980	−	0.267301i	−0.713296	+	0.700863i	$0.752799\pi$
$788$		0			0
$789$	−10.3247	+	17.8829i	−0.367569	+	0.636648i
$790$		0			0
$791$	−2.63188	+	1.51951i	−0.0935788	+	0.0540277i
$792$		0			0
$793$	−6.99509	−	34.0182i	−0.248403	−	1.20802i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−24.2698	+	42.0365i	−0.859681	+	1.48901i	0.0125527	+	0.999921i	$0.496004\pi$
$797$	−24.2698	+	42.0365i	−0.859681	+	1.48901i	−0.872234	+	0.489090i	$0.837329\pi$
$798$		0			0
$799$	−29.8553	−	17.2370i	−1.05621	−	0.609801i
$800$		0			0
$801$		−	0.439064i		−	0.0155136i
$802$		0			0
$803$	0.277850	+	0.481251i	0.00980513	+	0.0169830i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	8.17251			0.287686
$808$		0			0
$809$	14.1853	+	24.5697i	0.498728	+	0.863823i	0.999999	−	0.00146765i	$-0.000467167\pi$
$809$	14.1853	+	24.5697i	0.498728	+	0.863823i	−0.501270	+	0.865291i	$0.667134\pi$
$810$		0			0
$811$			7.98776i			0.280488i	0.990117	+	0.140244i	$0.0447888\pi$
$811$			7.98776i			0.280488i	−0.990117	+	0.140244i	$0.955211\pi$
$812$		0			0
$813$	12.4202	+	7.17078i	0.435594	+	0.251490i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	7.97048	−	4.60176i	0.278852	−	0.160995i
$818$		0			0
$819$	3.93156	−	11.8323i	0.137380	−	0.413453i
$820$		0			0
$821$	40.1724	−	23.1936i	1.40203	−	0.809461i	0.407426	−	0.913238i	$-0.366426\pi$
$821$	40.1724	−	23.1936i	1.40203	−	0.809461i	0.994601	+	0.103777i	$0.0330929\pi$
$822$		0			0
$823$	−8.59283	+	14.8832i	−0.299527	+	0.518797i	−0.976028	−	0.217646i	$-0.930162\pi$
$823$	−8.59283	+	14.8832i	−0.299527	+	0.518797i	0.676501	+	0.736442i	$0.263496\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	34.7802i		−	1.20943i	−0.796444	−	0.604713i	$-0.793288\pi$
$827$		−	34.7802i		−	1.20943i	0.796444	−	0.604713i	$-0.206712\pi$
$828$		0			0
$829$	2.05473	+	3.55890i	0.0713637	+	0.123606i	0.899499	−	0.436922i	$-0.143932\pi$
$829$	2.05473	+	3.55890i	0.0713637	+	0.123606i	−0.828135	+	0.560528i	$0.810598\pi$
$830$		0			0
$831$	−21.0680			−0.730840
$832$		0			0
$833$	25.9683			0.899748
$834$		0			0
$835$		0			0
$836$		0			0
$837$			18.2495i			0.630796i
$838$		0			0
$839$	−26.6256	−	15.3723i	−0.919216	−	0.530710i	−0.0358314	−	0.999358i	$-0.511408\pi$
$839$	−26.6256	−	15.3723i	−0.919216	−	0.530710i	−0.883385	+	0.468648i	$0.844741\pi$
$840$		0			0
$841$	9.66132	−	16.7339i	0.333149	−	0.577031i
$842$		0			0
$843$	10.9703	−	6.33369i	0.377836	−	0.218144i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−10.1804	+	5.87765i	−0.349802	+	0.201958i
$848$		0			0
$849$	8.87419	−	15.3705i	0.304561	−	0.527516i
$850$		0			0
$851$	−2.99010	−	1.72633i	−0.102499	−	0.0591780i
$852$		0			0
$853$			18.3577i			0.628555i	0.949331	+	0.314278i	$0.101762\pi$
$853$			18.3577i			0.628555i	−0.949331	+	0.314278i	$0.898238\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−48.2757			−1.64907			−0.824534	−	0.565813i	$-0.808563\pi$
$857$	−48.2757			−1.64907			−0.824534	+	0.565813i	$0.808563\pi$
$858$		0			0
$859$	35.9454			1.22644			0.613221	−	0.789912i	$-0.289874\pi$
$859$	35.9454			1.22644			0.613221	+	0.789912i	$0.289874\pi$
$860$		0			0
$861$	−4.70773	−	8.15403i	−0.160439	−	0.277889i
$862$		0			0
$863$		−	47.3814i		−	1.61288i	−0.591314	−	0.806441i	$-0.701391\pi$
$863$		−	47.3814i		−	1.61288i	0.591314	−	0.806441i	$-0.298609\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−2.68728	+	4.65451i	−0.0912648	+	0.158075i
$868$		0			0
$869$	11.2108	−	6.47258i	0.380301	−	0.219567i
$870$		0			0
$871$	−3.66824	+	11.0398i	−0.124293	+	0.374068i
$872$		0			0
$873$	−32.9365	+	19.0159i	−1.11473	+	0.643590i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−25.6141	−	14.7883i	−0.864926	−	0.499365i	0.000732813	−	1.00000i	$-0.499767\pi$
$877$	−25.6141	−	14.7883i	−0.864926	−	0.499365i	−0.865659	+	0.500635i	$0.833100\pi$
$878$		0			0
$879$		−	5.98175i		−	0.201759i
$880$		0			0
$881$	1.58518	+	2.74562i	0.0534062	+	0.0925022i	0.891493	−	0.453035i	$-0.149659\pi$
$881$	1.58518	+	2.74562i	0.0534062	+	0.0925022i	−0.838086	+	0.545538i	$0.816326\pi$
$882$		0			0
$883$	48.9555			1.64748			0.823742	−	0.566965i	$-0.191883\pi$
$883$	48.9555			1.64748			0.823742	+	0.566965i	$0.191883\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	4.33307	+	7.50510i	0.145490	+	0.251997i	0.929556	−	0.368682i	$-0.120191\pi$
$887$	4.33307	+	7.50510i	0.145490	+	0.251997i	−0.784065	+	0.620678i	$0.786857\pi$
$888$		0			0
$889$			6.91947i			0.232072i
$890$		0			0
$891$	−6.88837	−	3.97700i	−0.230769	−	0.133235i
$892$		0			0
$893$	−5.31319	+	9.20271i	−0.177799	+	0.307957i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−1.09581	−	5.32908i	−0.0365880	−	0.177933i
$898$		0			0
$899$	−13.3728	+	7.72077i	−0.446007	+	0.257502i
$900$		0			0
$901$	−9.46035	+	16.3858i	−0.315170	+	0.545890i
$902$		0			0
$903$	−4.59859	−	2.65500i	−0.153032	−	0.0883528i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−6.79783	−	11.7742i	−0.225718	−	0.390956i	0.730816	−	0.682574i	$-0.239140\pi$
$907$	−6.79783	−	11.7742i	−0.225718	−	0.390956i	−0.956535	+	0.291618i	$0.905806\pi$
$908$		0			0
$909$	−11.6951			−0.387901
$910$		0			0
$911$	−43.5030			−1.44132			−0.720659	−	0.693289i	$-0.756161\pi$
$911$	−43.5030			−1.44132			−0.720659	+	0.693289i	$0.756161\pi$
$912$		0			0
$913$	−10.7103	−	18.5508i	−0.354460	−	0.613943i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−0.221843	−	0.128081i	−0.00732589	−	0.00422961i
$918$		0			0
$919$	−4.36167	+	7.55464i	−0.143878	+	0.249205i	−0.928954	−	0.370195i	$-0.879291\pi$
$919$	−4.36167	+	7.55464i	−0.143878	+	0.249205i	0.785076	+	0.619400i	$0.212624\pi$
$920$		0			0
$921$	−8.52664	+	4.92286i	−0.280962	+	0.162214i
$922$		0			0
$923$	1.28992	−	0.265244i	0.0424583	−	0.00873062i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	4.08513	−	7.07565i	0.134173	−	0.232395i
$928$		0			0
$929$	11.8293	+	6.82967i	0.388108	+	0.224074i	0.681340	−	0.731967i	$-0.261398\pi$
$929$	11.8293	+	6.82967i	0.388108	+	0.224074i	−0.293232	+	0.956041i	$0.594731\pi$
$930$		0			0
$931$		−	8.00456i		−	0.262339i
$932$		0			0
$933$	8.40224	+	14.5531i	0.275077	+	0.476447i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	11.2886			0.368783			0.184392	−	0.982853i	$-0.440969\pi$
$937$	11.2886			0.368783			0.184392	+	0.982853i	$0.440969\pi$
$938$		0			0
$939$	−8.69969	−	15.0683i	−0.283904	−	0.491736i
$940$		0			0
$941$			38.3764i			1.25103i	0.780211	+	0.625517i	$0.215112\pi$
$941$			38.3764i			1.25103i	−0.780211	+	0.625517i	$0.784888\pi$
$942$		0			0
$943$	20.8825	+	12.0565i	0.680028	+	0.392614i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	6.53190	−	3.77119i	0.212258	−	0.122547i	−0.390102	−	0.920772i	$-0.627560\pi$
$947$	6.53190	−	3.77119i	0.212258	−	0.122547i	0.602360	+	0.798224i	$0.294227\pi$
$948$		0			0
$949$	0.880053	+	0.990543i	0.0285677	+	0.0321544i
$950$		0			0
$951$	−5.30380	+	3.06215i	−0.171987	+	0.0992970i
$952$		0			0
$953$	12.5364	−	21.7136i	0.406093	−	0.703374i	−0.588355	−	0.808603i	$-0.700224\pi$
$953$	12.5364	−	21.7136i	0.406093	−	0.703374i	0.994448	+	0.105229i	$0.0335575\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$			3.10871i			0.100490i
$958$		0			0
$959$	2.05602	+	3.56113i	0.0663923	+	0.114995i
$960$		0			0
$961$	6.36093			0.205191
$962$		0			0
$963$	14.0638			0.453199
$964$		0			0
$965$		0			0
$966$		0			0
$967$		−	56.5027i		−	1.81700i	−0.417881	−	0.908502i	$-0.637227\pi$
$967$		−	56.5027i		−	1.81700i	0.417881	−	0.908502i	$-0.362773\pi$
$968$		0			0
$969$	4.43377	+	2.55984i	0.142433	+	0.0822338i
$970$		0			0
$971$	2.69811	−	4.67327i	0.0865866	−	0.149972i	−0.819480	−	0.573108i	$-0.805737\pi$
$971$	2.69811	−	4.67327i	0.0865866	−	0.149972i	0.906066	+	0.423136i	$0.139071\pi$
$972$		0			0
$973$	−17.3412	+	10.0119i	−0.555933	+	0.320968i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	38.4748	−	22.2134i	1.23092	−	0.710671i	0.263697	−	0.964606i	$-0.415058\pi$
$977$	38.4748	−	22.2134i	1.23092	−	0.710671i	0.967221	+	0.253935i	$0.0817249\pi$
$978$		0			0
$979$	0.129508	−	0.224314i	0.00413909	−	0.00716911i
$980$		0			0
$981$	−16.0364	−	9.25865i	−0.512004	−	0.295606i
$982$		0			0
$983$			7.16040i			0.228381i	0.993459	+	0.114191i	$0.0364274\pi$
$983$			7.16040i			0.228381i	−0.993459	+	0.114191i	$0.963573\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	6.13092			0.195149
$988$		0			0
$989$	13.5989			0.432420
$990$		0			0
$991$	7.60271	+	13.1683i	0.241508	+	0.418304i	0.961144	−	0.276047i	$-0.0890246\pi$
$991$	7.60271	+	13.1683i	0.241508	+	0.418304i	−0.719636	+	0.694352i	$0.755691\pi$
$992$		0			0
$993$		−	17.2283i		−	0.546723i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−3.78422	+	6.55446i	−0.119847	+	0.207582i	−0.919707	−	0.392605i	$-0.871574\pi$
$997$	−3.78422	+	6.55446i	−0.119847	+	0.207582i	0.799860	+	0.600187i	$0.204907\pi$
$998$		0			0
$999$	4.81461	−	2.77972i	0.152328	−	0.0879464i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1300.2.y.c.101.3	✓	10
5.2	odd	4		1300.2.ba.d.49.5		20
5.3	odd	4		1300.2.ba.d.49.6		20
5.4	even	2		1300.2.y.d.101.3	yes	10
13.4	even	6	inner	1300.2.y.c.901.3	yes	10
65.4	even	6		1300.2.y.d.901.3	yes	10
65.17	odd	12		1300.2.ba.d.849.6		20
65.43	odd	12		1300.2.ba.d.849.5		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1300.2.y.c.101.3	✓	10	1.1	even	1	trivial
1300.2.y.c.901.3	yes	10	13.4	even	6	inner
1300.2.y.d.101.3	yes	10	5.4	even	2
1300.2.y.d.901.3	yes	10	65.4	even	6
1300.2.ba.d.49.5		20	5.2	odd	4
1300.2.ba.d.49.6		20	5.3	odd	4
1300.2.ba.d.849.5		20	65.43	odd	12
1300.2.ba.d.849.6		20	65.17	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)

\(f(q)\)	\(=\)	\(q+(-0.330430 - 0.572322i) q^{3} +(1.16835 + 0.674550i) q^{7} +(1.28163 - 2.21985i) q^{9} +O(q^{10})\)	\(q+(-0.330430 - 0.572322i) q^{3} +(1.16835 + 0.674550i) q^{7} +(1.28163 - 2.21985i) q^{9} +(1.30955 - 0.756069i) q^{11} +(2.69540 - 2.39474i) q^{13} +(-2.50662 + 4.34160i) q^{17} +(1.33827 + 0.772651i) q^{19} -0.891566i q^{21} +(1.14165 + 1.97740i) q^{23} -3.67654 q^{27} +(-1.55542 - 2.69407i) q^{29} -4.96378i q^{31} +(-0.865429 - 0.499656i) q^{33} +(-1.30955 + 0.756069i) q^{37} +(-2.26121 - 0.751342i) q^{39} +(9.14574 - 5.28029i) q^{41} +(2.97790 - 5.15788i) q^{43} +6.87657i q^{47} +(-2.58997 - 4.48595i) q^{49} +3.31306 q^{51} +3.77414 q^{53} -1.02123i q^{57} +(10.1595 + 5.86559i) q^{59} +(4.81617 - 8.34186i) q^{61} +(2.99480 - 1.72905i) q^{63} +(-2.79422 + 1.61324i) q^{67} +(0.754473 - 1.30679i) q^{69} +(0.316312 + 0.182623i) q^{71} +0.367494i q^{73} +2.04002 q^{77} +8.56083 q^{79} +(-2.63005 - 4.55539i) q^{81} -14.1658i q^{83} +(-1.02792 + 1.78041i) q^{87} +(0.148342 - 0.0856456i) q^{89} +(4.76456 - 0.979727i) q^{91} +(-2.84088 + 1.64018i) q^{93} +(-12.8494 - 7.41862i) q^{97} -3.87601i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - q^{3} - 8 q^{9}+O(q^{10}) \) 10 * q - q^3 - 8 * q^9	\( 10 q - q^{3} - 8 q^{9} + 3 q^{11} - 4 q^{13} + 12 q^{17} - 12 q^{19} + 3 q^{23} + 14 q^{27} + 3 q^{29} + 30 q^{33} - 3 q^{37} + 16 q^{39} + 12 q^{41} + 8 q^{43} + 19 q^{49} - 24 q^{51} + 24 q^{53} - 6 q^{59} + q^{61} - 24 q^{63} - 48 q^{67} + 45 q^{71} - 24 q^{77} + 16 q^{79} + 7 q^{81} - 21 q^{87} + 12 q^{89} - 3 q^{91} - 93 q^{93} + 15 q^{97}+O(q^{100}) \) 10 * q - q^3 - 8 * q^9 + 3 * q^11 - 4 * q^13 + 12 * q^17 - 12 * q^19 + 3 * q^23 + 14 * q^27 + 3 * q^29 + 30 * q^33 - 3 * q^37 + 16 * q^39 + 12 * q^41 + 8 * q^43 + 19 * q^49 - 24 * q^51 + 24 * q^53 - 6 * q^59 + q^61 - 24 * q^63 - 48 * q^67 + 45 * q^71 - 24 * q^77 + 16 * q^79 + 7 * q^81 - 21 * q^87 + 12 * q^89 - 3 * q^91 - 93 * q^93 + 15 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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