LMFDB - Embedded newform 1300.2.y.e.101.7

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			101.7
Root			$-0.979681 + 1.42836i$ of defining polynomial
Character	$\chi$	$=$	1300.101
Dual form			1300.2.y.e.901.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.979681 + 1.69686i) q^{3} +(2.47400 + 1.42836i) q^{7} +(-0.419550 + 0.726682i) q^{9} +O(q^{10})$	$q+(0.979681 + 1.69686i) q^{3} +(2.47400 + 1.42836i) q^{7} +(-0.419550 + 0.726682i) q^{9} +(4.84746 - 2.79868i) q^{11} +(-2.94331 - 2.08253i) q^{13} +(-1.96363 + 3.40111i) q^{17} +(7.09546 + 4.09657i) q^{19} +5.59737i q^{21} +(-0.178504 - 0.309177i) q^{23} +4.23399 q^{27} +(-1.90890 - 3.30631i) q^{29} -8.47182i q^{31} +(9.49793 + 5.48363i) q^{33} +(6.54609 - 3.77939i) q^{37} +(0.650247 - 7.03459i) q^{39} +(-6.85811 + 3.95953i) q^{41} +(-1.67282 + 2.89741i) q^{43} +8.64753i q^{47} +(0.580450 + 1.00537i) q^{49} -7.69492 q^{51} -0.581615 q^{53} +16.0533i q^{57} +(0.510653 + 0.294826i) q^{59} +(-2.90890 + 5.03836i) q^{61} +(-2.07593 + 1.19854i) q^{63} +(-10.5655 + 6.09997i) q^{67} +(0.349753 - 0.605790i) q^{69} +(2.11676 + 1.22211i) q^{71} -4.16506i q^{73} +15.9902 q^{77} -9.85582 q^{79} +(5.40661 + 9.36452i) q^{81} +6.09174i q^{83} +(3.74022 - 6.47825i) q^{87} +(-0.510653 + 0.294826i) q^{89} +(-4.30714 - 9.35629i) q^{91} +(14.3755 - 8.29968i) q^{93} +(4.08489 + 2.35841i) q^{97} +4.69675i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	0.979681	+	1.69686i	0.565619	+	0.979681i	0.996992	+	0.0775072i	$0.0246961\pi$
$3$	0.979681	+	1.69686i	0.565619	+	0.979681i	−0.431373	+	0.902174i	$0.641971\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	2.47400	+	1.42836i	0.935084	+	0.539871i	0.888416	−	0.459039i	$-0.151806\pi$
$7$	2.47400	+	1.42836i	0.935084	+	0.539871i	0.0466681	+	0.998910i	$0.485140\pi$
$8$		0			0
$9$	−0.419550	+	0.726682i	−0.139850	+	0.242227i
$10$		0			0
$11$	4.84746	−	2.79868i	1.46156	−	0.843835i	0.462481	−	0.886629i	$-0.346959\pi$
$11$	4.84746	−	2.79868i	1.46156	−	0.843835i	0.999084	+	0.0427946i	$0.0136261\pi$
$12$		0			0
$13$	−2.94331	−	2.08253i	−0.816328	−	0.577589i
$13$	−2.94331	−	2.08253i	−0.816328	−	0.577589i
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.96363	+	3.40111i	−0.476250	+	0.824889i	−0.999630	−	0.0272102i	$-0.991338\pi$
$17$	−1.96363	+	3.40111i	−0.476250	+	0.824889i	0.523380	+	0.852100i	$0.324671\pi$
$18$		0			0
$19$	7.09546	+	4.09657i	1.62781	+	0.939816i	0.984745	+	0.174005i	$0.0556709\pi$
$19$	7.09546	+	4.09657i	1.62781	+	0.939816i	0.643065	+	0.765811i	$0.277662\pi$
$20$		0			0
$21$			5.59737i			1.22145i
$22$		0			0
$23$	−0.178504	−	0.309177i	−0.0372206	−	0.0644679i	0.846815	−	0.531887i	$-0.178517\pi$
$23$	−0.178504	−	0.309177i	−0.0372206	−	0.0644679i	−0.884036	+	0.467420i	$0.845184\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	4.23399			0.814831
$28$		0			0
$29$	−1.90890	−	3.30631i	−0.354473	−	0.613966i	0.632554	−	0.774516i	$-0.282006\pi$
$29$	−1.90890	−	3.30631i	−0.354473	−	0.613966i	−0.987028	+	0.160550i	$0.948673\pi$
$30$		0			0
$31$		−	8.47182i		−	1.52158i	−0.648996	−	0.760792i	$-0.724811\pi$
$31$		−	8.47182i		−	1.52158i	0.648996	−	0.760792i	$-0.275189\pi$
$32$		0			0
$33$	9.49793	+	5.48363i	1.65338	+	0.954578i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	6.54609	−	3.77939i	1.07617	−	0.621327i	0.146309	−	0.989239i	$-0.453260\pi$
$37$	6.54609	−	3.77939i	1.07617	−	0.621327i	0.929861	+	0.367912i	$0.119927\pi$
$38$		0			0
$39$	0.650247	−	7.03459i	0.104123	−	1.12644i
$40$		0			0
$41$	−6.85811	+	3.95953i	−1.07106	+	0.618375i	−0.928470	−	0.371407i	$-0.878876\pi$
$41$	−6.85811	+	3.95953i	−1.07106	+	0.618375i	−0.142587	+	0.989782i	$0.545542\pi$
$42$		0			0
$43$	−1.67282	+	2.89741i	−0.255103	+	0.441851i	−0.964923	−	0.262531i	$-0.915443\pi$
$43$	−1.67282	+	2.89741i	−0.255103	+	0.441851i	0.709820	+	0.704383i	$0.248776\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$			8.64753i			1.26137i	0.776038	+	0.630686i	$0.217226\pi$
$47$			8.64753i			1.26137i	−0.776038	+	0.630686i	$0.782774\pi$
$48$		0			0
$49$	0.580450	+	1.00537i	0.0829214	+	0.143624i
$50$		0			0
$51$	−7.69492			−1.07750
$52$		0			0
$53$	−0.581615			−0.0798909			−0.0399455	−	0.999202i	$-0.512718\pi$
$53$	−0.581615			−0.0798909			−0.0399455	+	0.999202i	$0.512718\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$			16.0533i			2.12631i
$58$		0			0
$59$	0.510653	+	0.294826i	0.0664813	+	0.0383830i	0.532872	−	0.846196i	$-0.321113\pi$
$59$	0.510653	+	0.294826i	0.0664813	+	0.0383830i	−0.466391	+	0.884579i	$0.654446\pi$
$60$		0			0
$61$	−2.90890	+	5.03836i	−0.372446	+	0.645096i	−0.989941	−	0.141479i	$-0.954814\pi$
$61$	−2.90890	+	5.03836i	−0.372446	+	0.645096i	0.617495	+	0.786575i	$0.288148\pi$
$62$		0			0
$63$	−2.07593	+	1.19854i	−0.261543	+	0.151002i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−10.5655	+	6.09997i	−1.29078	+	0.745230i	−0.978792	−	0.204857i	$-0.934327\pi$
$67$	−10.5655	+	6.09997i	−1.29078	+	0.745230i	−0.311985	+	0.950087i	$0.600994\pi$
$68$		0			0
$69$	0.349753	−	0.605790i	0.0421053	−	0.0729286i
$70$		0			0
$71$	2.11676	+	1.22211i	0.251214	+	0.145038i	0.620320	−	0.784349i	$-0.287003\pi$
$71$	2.11676	+	1.22211i	0.251214	+	0.145038i	−0.369106	+	0.929387i	$0.620336\pi$
$72$		0			0
$73$		−	4.16506i		−	0.487483i	−0.969840	−	0.243741i	$-0.921625\pi$
$73$		−	4.16506i		−	0.487483i	0.969840	−	0.243741i	$-0.0783748\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	15.9902			1.82225
$78$		0			0
$79$	−9.85582			−1.10887			−0.554433	−	0.832228i	$-0.687065\pi$
$79$	−9.85582			−1.10887			−0.554433	+	0.832228i	$0.687065\pi$
$80$		0			0
$81$	5.40661	+	9.36452i	0.600734	+	1.04050i
$82$		0			0
$83$			6.09174i			0.668655i	0.942457	+	0.334327i	$0.108509\pi$
$83$			6.09174i			0.668655i	−0.942457	+	0.334327i	$0.891491\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	3.74022	−	6.47825i	0.400994	−	0.694542i
$88$		0			0
$89$	−0.510653	+	0.294826i	−0.0541291	+	0.0312515i	−0.526820	−	0.849977i	$-0.676616\pi$
$89$	−0.510653	+	0.294826i	−0.0541291	+	0.0312515i	0.472691	+	0.881228i	$0.343283\pi$
$90$		0			0
$91$	−4.30714	−	9.35629i	−0.451511	−	0.980806i
$92$		0			0
$93$	14.3755	−	8.29968i	1.49067	−	0.860637i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	4.08489	+	2.35841i	0.414758	+	0.239460i	0.692832	−	0.721099i	$-0.256363\pi$
$97$	4.08489	+	2.35841i	0.414758	+	0.239460i	−0.278074	+	0.960560i	$0.589696\pi$
$98$		0			0
$99$			4.69675i			0.472041i
$100$		0			0
$101$	−1.26701	−	2.19453i	−0.126072	−	0.218364i	0.796079	−	0.605192i	$-0.206904\pi$
$101$	−1.26701	−	2.19453i	−0.126072	−	0.218364i	−0.922152	+	0.386829i	$0.873570\pi$
$102$		0			0
$103$	0.930087			0.0916442			0.0458221	−	0.998950i	$-0.485409\pi$
$103$	0.930087			0.0916442			0.0458221	+	0.998950i	$0.485409\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−0.295075	−	0.511085i	−0.0285260	−	0.0494084i	0.851410	−	0.524501i	$-0.175748\pi$
$107$	−0.295075	−	0.511085i	−0.0285260	−	0.0494084i	−0.879936	+	0.475092i	$0.842415\pi$
$108$		0			0
$109$			4.88056i			0.467473i	0.972300	+	0.233737i	$0.0750953\pi$
$109$			4.88056i			0.467473i	−0.972300	+	0.233737i	$0.924905\pi$
$110$		0			0
$111$	12.8262	+	7.40518i	1.21740	+	0.702869i
$112$		0			0
$113$	−3.92299	+	6.79482i	−0.369044	+	0.639203i	−0.989416	−	0.145104i	$-0.953648\pi$
$113$	−3.92299	+	6.79482i	−0.369044	+	0.639203i	0.620372	+	0.784307i	$0.286982\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	2.74820	−	1.26513i	0.254071	−	0.116961i
$118$		0			0
$119$	−9.71604	+	5.60956i	−0.890668	+	0.514227i
$120$		0			0
$121$	10.1653	−	17.6067i	0.924114	−	1.60061i
$122$		0			0
$123$	−13.4375	−	7.75816i	−1.21162	−	0.699530i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−3.74022	−	6.47825i	−0.331891	−	0.574852i	0.650992	−	0.759085i	$-0.274353\pi$
$127$	−3.74022	−	6.47825i	−0.331891	−	0.574852i	−0.982883	+	0.184233i	$0.941020\pi$
$128$		0			0
$129$	−6.55533			−0.577165
$130$		0			0
$131$	2.86041			0.249915			0.124957	−	0.992162i	$-0.460121\pi$
$131$	2.86041			0.249915			0.124957	+	0.992162i	$0.460121\pi$
$132$		0			0
$133$	11.7028	+	20.2698i	1.01476	+	1.75761i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−14.1725	−	8.18250i	−1.21084	−	0.699078i	−0.247897	−	0.968786i	$-0.579739\pi$
$137$	−14.1725	−	8.18250i	−1.21084	−	0.699078i	−0.962942	+	0.269708i	$0.913073\pi$
$138$		0			0
$139$	0.898244	−	1.55580i	0.0761881	−	0.131962i	−0.825414	−	0.564528i	$-0.809058\pi$
$139$	0.898244	−	1.55580i	0.0761881	−	0.131962i	0.901602	+	0.432566i	$0.142392\pi$
$140$		0			0
$141$	−14.6736	+	8.47182i	−1.23574	+	0.713456i
$142$		0			0
$143$	−20.0959	−	1.85758i	−1.68051	−	0.155339i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−1.13731	+	1.96988i	−0.0938039	+	0.162473i
$148$		0			0
$149$	−18.5317	−	10.6993i	−1.51818	−	0.876521i	−0.999771	−	0.0213870i	$-0.993192\pi$
$149$	−18.5317	−	10.6993i	−1.51818	−	0.876521i	−0.518407	−	0.855134i	$-0.673475\pi$
$150$		0			0
$151$		−	8.34466i		−	0.679079i	−0.940592	−	0.339540i	$-0.889729\pi$
$151$		−	8.34466i		−	0.679079i	0.940592	−	0.339540i	$-0.110271\pi$
$152$		0			0
$153$	−1.64768	−	2.85387i	−0.133207	−	0.230722i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	2.68191			0.214040			0.107020	−	0.994257i	$-0.465869\pi$
$157$	2.68191			0.214040			0.107020	+	0.994257i	$0.465869\pi$
$158$		0			0
$159$	−0.569797	−	0.986917i	−0.0451878	−	0.0782676i
$160$		0			0
$161$		−	1.01987i		−	0.0803772i
$162$		0			0
$163$	6.27615	+	3.62354i	0.491586	+	0.283817i	0.725232	−	0.688504i	$-0.241732\pi$
$163$	6.27615	+	3.62354i	0.491586	+	0.283817i	−0.233646	+	0.972322i	$0.575066\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	11.0305	−	6.36847i	0.853566	−	0.492807i	−0.00828625	−	0.999966i	$-0.502638\pi$
$167$	11.0305	−	6.36847i	0.853566	−	0.492807i	0.861853	+	0.507159i	$0.169304\pi$
$168$		0			0
$169$	4.32616	+	12.2591i	0.332781	+	0.943004i
$170$		0			0
$171$	−5.95380	+	3.43743i	−0.455298	+	0.262867i
$172$		0			0
$173$	5.83703	−	10.1100i	0.443781	−	0.768651i	−0.554185	−	0.832393i	$-0.686970\pi$
$173$	5.83703	−	10.1100i	0.443781	−	0.768651i	0.997966	+	0.0637421i	$0.0203035\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$			1.15534i			0.0868407i
$178$		0			0
$179$	0.510653	+	0.884477i	0.0381680	+	0.0661089i	0.884478	−	0.466581i	$-0.154514\pi$
$179$	0.510653	+	0.884477i	0.0381680	+	0.0661089i	−0.846310	+	0.532690i	$0.821181\pi$
$180$		0			0
$181$	13.8771			1.03148			0.515739	−	0.856745i	$-0.327517\pi$
$181$	13.8771			1.03148			0.515739	+	0.856745i	$0.327517\pi$
$182$		0			0
$183$	−11.3992			−0.842651
$184$		0			0
$185$		0			0
$186$		0			0
$187$			21.9823i			1.60751i
$188$		0			0
$189$	10.4749	+	6.04767i	0.761935	+	0.439904i
$190$		0			0
$191$	−3.24135	+	5.61418i	−0.234536	+	0.406228i	−0.959138	−	0.282940i	$-0.908690\pi$
$191$	−3.24135	+	5.61418i	−0.234536	+	0.406228i	0.724602	+	0.689168i	$0.242024\pi$
$192$		0			0
$193$	18.9831	−	10.9599i	1.36643	−	0.788909i	0.375961	−	0.926636i	$-0.377313\pi$
$193$	18.9831	−	10.9599i	1.36643	−	0.788909i	0.990470	+	0.137726i	$0.0439795\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−16.4963	+	9.52412i	−1.17531	+	0.678566i	−0.954925	−	0.296847i	$-0.904065\pi$
$197$	−16.4963	+	9.52412i	−1.17531	+	0.678566i	−0.220385	+	0.975413i	$0.570731\pi$
$198$		0			0
$199$	5.84746	−	10.1281i	0.414516	−	0.717962i	−0.580862	−	0.814002i	$-0.697284\pi$
$199$	5.84746	−	10.1281i	0.414516	−	0.717962i	0.995377	+	0.0960401i	$0.0306177\pi$
$200$		0			0
$201$	−20.7016	−	11.9521i	−1.46018	−	0.843033i
$202$		0			0
$203$		−	10.9064i		−	0.765479i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	0.299565			0.0208212
$208$		0			0
$209$	45.8600			3.17220
$210$		0			0
$211$	−6.59946	−	11.4306i	−0.454326	−	0.786915i	0.544323	−	0.838876i	$-0.316786\pi$
$211$	−6.59946	−	11.4306i	−0.454326	−	0.786915i	−0.998649	+	0.0519600i	$0.983453\pi$
$212$		0			0
$213$			4.78913i			0.328146i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	12.1008	−	20.9593i	0.821459	−	1.42281i
$218$		0			0
$219$	7.06751	−	4.08043i	0.477578	−	0.275730i
$220$		0			0
$221$	12.8625	−	5.92120i	0.865223	−	0.398303i
$222$		0			0
$223$	2.28384	−	1.31858i	0.152938	−	0.0882985i	−0.421578	−	0.906792i	$-0.638524\pi$
$223$	2.28384	−	1.31858i	0.152938	−	0.0882985i	0.574516	+	0.818493i	$0.305190\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−18.3855	−	10.6149i	−1.22029	−	0.704535i	−0.255311	−	0.966859i	$-0.582178\pi$
$227$	−18.3855	−	10.6149i	−1.22029	−	0.704535i	−0.964980	+	0.262324i	$0.915511\pi$
$228$		0			0
$229$		−	10.0154i		−	0.661838i	−0.943659	−	0.330919i	$-0.892641\pi$
$229$		−	10.0154i		−	0.661838i	0.943659	−	0.330919i	$-0.107359\pi$
$230$		0			0
$231$	15.6653	+	27.1330i	1.03070	+	1.78522i
$232$		0			0
$233$	−17.9666			−1.17703			−0.588515	−	0.808486i	$-0.700287\pi$
$233$	−17.9666			−1.17703			−0.588515	+	0.808486i	$0.700287\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−9.65556	−	16.7239i	−0.627196	−	1.08634i
$238$		0			0
$239$		−	12.6771i		−	0.820014i	−0.912082	−	0.410007i	$-0.865526\pi$
$239$		−	12.6771i		−	0.820014i	0.912082	−	0.410007i	$-0.134474\pi$
$240$		0			0
$241$	7.38988	+	4.26655i	0.476024	+	0.274833i	0.718758	−	0.695260i	$-0.244711\pi$
$241$	7.38988	+	4.26655i	0.476024	+	0.274833i	−0.242734	+	0.970093i	$0.578044\pi$
$242$		0			0
$243$	−4.24252	+	7.34826i	−0.272158	+	0.471391i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−12.3529	−	26.8340i	−0.785998	−	1.70740i
$248$		0			0
$249$	−10.3368	+	5.96796i	−0.655069	+	0.378204i
$250$		0			0
$251$	−9.86247	+	17.0823i	−0.622514	+	1.07823i	0.366502	+	0.930417i	$0.380555\pi$
$251$	−9.86247	+	17.0823i	−0.622514	+	1.07823i	−0.989016	+	0.147808i	$0.952778\pi$
$252$		0			0
$253$	−1.73058	−	0.999150i	−0.108800	−	0.0628160i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−11.9885	−	20.7648i	−0.747824	−	1.29527i	−0.948863	−	0.315687i	$-0.897765\pi$
$257$	−11.9885	−	20.7648i	−0.747824	−	1.29527i	0.201039	−	0.979583i	$-0.435568\pi$
$258$		0			0
$259$	21.5934			1.34175
$260$		0			0
$261$	3.20351			0.198292
$262$		0			0
$263$	−0.315948	−	0.547238i	−0.0194822	−	0.0337441i	0.856120	−	0.516777i	$-0.172868\pi$
$263$	−0.315948	−	0.547238i	−0.0194822	−	0.0337441i	−0.875602	+	0.483033i	$0.839535\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−1.00055	−	0.577670i	−0.0612329	−	0.0353528i
$268$		0			0
$269$	3.68656	−	6.38531i	0.224774	−	0.389319i	−0.731478	−	0.681865i	$-0.761169\pi$
$269$	3.68656	−	6.38531i	0.224774	−	0.389319i	0.956252	+	0.292546i	$0.0945024\pi$
$270$		0			0
$271$	−10.0955	+	5.82862i	−0.613255	+	0.354063i	−0.774238	−	0.632894i	$-0.781867\pi$
$271$	−10.0955	+	5.82862i	−0.613255	+	0.354063i	0.160983	+	0.986957i	$0.448534\pi$
$272$		0			0
$273$	11.6567	−	16.4748i	0.705494	−	0.997100i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	0.460776	−	0.798087i	0.0276853	−	0.0479524i	−0.851851	−	0.523785i	$-0.824520\pi$
$277$	0.460776	−	0.798087i	0.0276853	−	0.0479524i	0.879536	+	0.475832i	$0.157853\pi$
$278$		0			0
$279$	6.15632	+	3.55435i	0.368569	+	0.212793i
$280$		0			0
$281$		−	13.3326i		−	0.795358i	−0.917525	−	0.397679i	$-0.869816\pi$
$281$		−	13.3326i		−	0.795358i	0.917525	−	0.397679i	$-0.130184\pi$
$282$		0			0
$283$	−2.60291	−	4.50837i	−0.154727	−	0.267995i	0.778233	−	0.627976i	$-0.216116\pi$
$283$	−2.60291	−	4.50837i	−0.154727	−	0.267995i	−0.932960	+	0.359981i	$0.882783\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−22.6226			−1.33537
$288$		0			0
$289$	0.788317	+	1.36541i	0.0463716	+	0.0803180i
$290$		0			0
$291$			9.24197i			0.541774i
$292$		0			0
$293$	−13.0302	−	7.52296i	−0.761230	−	0.439496i	0.0685075	−	0.997651i	$-0.478176\pi$
$293$	−13.0302	−	7.52296i	−0.761230	−	0.439496i	−0.829737	+	0.558155i	$0.811510\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	20.5241	−	11.8496i	1.19093	−	0.687583i
$298$		0			0
$299$	−0.118479	+	1.28174i	−0.00685180	+	0.0741251i
$300$		0			0
$301$	−8.27712	+	4.77880i	−0.477085	+	0.275445i
$302$		0			0
$303$	2.48253	−	4.29988i	0.142618	−	0.247021i
$304$		0			0
$305$		0			0
$306$		0			0
$307$		−	4.41991i		−	0.252258i	−0.992014	−	0.126129i	$-0.959745\pi$
$307$		−	4.41991i		−	0.252258i	0.992014	−	0.126129i	$-0.0402553\pi$
$308$		0			0
$309$	0.911189	+	1.57822i	0.0518357	+	0.0897821i
$310$		0			0
$311$	32.2076			1.82633			0.913164	−	0.407593i	$-0.133632\pi$
$311$	32.2076			1.82633			0.913164	+	0.407593i	$0.133632\pi$
$312$		0			0
$313$	18.8549			1.06574			0.532872	−	0.846196i	$-0.321113\pi$
$313$	18.8549			1.06574			0.532872	+	0.846196i	$0.321113\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$			23.9904i			1.34743i	0.738990	+	0.673716i	$0.235303\pi$
$317$			23.9904i			1.34743i	−0.738990	+	0.673716i	$0.764697\pi$
$318$		0			0
$319$	−18.5066	−	10.6848i	−1.03617	−	0.598234i
$320$		0			0
$321$	0.578158	−	1.00140i	0.0322697	−	0.0558927i
$322$		0			0
$323$	−27.8657	+	16.0883i	−1.55049	+	0.895175i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−8.28162	+	4.78140i	−0.457975	+	0.264412i
$328$		0			0
$329$	−12.3518	+	21.3940i	−0.680978	+	1.17949i
$330$		0			0
$331$	−6.24135	−	3.60345i	−0.343056	−	0.198063i	0.318567	−	0.947900i	$-0.396798\pi$
$331$	−6.24135	−	3.60345i	−0.343056	−	0.198063i	−0.661622	+	0.749837i	$0.730132\pi$
$332$		0			0
$333$			6.34257i			0.347570i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	20.1923			1.09995			0.549973	−	0.835183i	$-0.314638\pi$
$337$	20.1923			1.09995			0.549973	+	0.835183i	$0.314638\pi$
$338$		0			0
$339$	−15.3731			−0.834953
$340$		0			0
$341$	−23.7099	−	41.0668i	−1.28396	−	2.22389i
$342$		0			0
$343$		−	16.6807i		−	0.900675i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−4.16701	+	7.21747i	−0.223697	+	0.387454i	−0.955928	−	0.293602i	$-0.905146\pi$
$347$	−4.16701	+	7.21747i	−0.223697	+	0.387454i	0.732231	+	0.681056i	$0.238479\pi$
$348$		0			0
$349$	−19.2518	+	11.1150i	−1.03052	+	0.594973i	−0.917135	−	0.398577i	$-0.869504\pi$
$349$	−19.2518	+	11.1150i	−1.03052	+	0.594973i	−0.113389	+	0.993551i	$0.536171\pi$
$350$		0			0
$351$	−12.4619	−	8.81739i	−0.665169	−	0.470638i
$352$		0			0
$353$	−20.4565	+	11.8106i	−1.08879	+	0.628613i	−0.933254	−	0.359217i	$-0.883044\pi$
$353$	−20.4565	+	11.8106i	−1.08879	+	0.628613i	−0.155536	+	0.987830i	$0.549710\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−19.0372	−	10.9912i	−1.00756	−	0.581714i
$358$		0			0
$359$		−	2.91598i		−	0.153899i	−0.997035	−	0.0769497i	$-0.975482\pi$
$359$		−	2.91598i		−	0.153899i	0.997035	−	0.0769497i	$-0.0245181\pi$
$360$		0			0
$361$	24.0637	+	41.6795i	1.26651	+	2.19366i
$362$		0			0
$363$	39.8348			2.09079
$364$		0			0
$365$		0			0
$366$		0			0
$367$	7.55944	+	13.0933i	0.394600	+	0.683467i	0.993050	−	0.117693i	$-0.0375499\pi$
$367$	7.55944	+	13.0933i	0.394600	+	0.683467i	−0.598450	+	0.801160i	$0.704217\pi$
$368$		0			0
$369$		−	6.64489i		−	0.345919i
$370$		0			0
$371$	−1.43891	−	0.830758i	−0.0747047	−	0.0431308i
$372$		0			0
$373$	5.28840	−	9.15978i	0.273823	−	0.474275i	−0.696014	−	0.718028i	$-0.745045\pi$
$373$	5.28840	−	9.15978i	0.273823	−	0.474275i	0.969838	+	0.243752i	$0.0783784\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−1.26700	+	13.7068i	−0.0652537	+	0.705937i
$378$		0			0
$379$	−5.38724	+	3.11032i	−0.276724	+	0.159767i	−0.631939	−	0.775018i	$-0.717741\pi$
$379$	−5.38724	+	3.11032i	−0.276724	+	0.159767i	0.355215	+	0.934784i	$0.384408\pi$
$380$		0			0
$381$	7.32845	−	12.6932i	0.375448	−	0.650295i
$382$		0			0
$383$	−11.2463	−	6.49304i	−0.574657	−	0.331779i	0.184350	−	0.982861i	$-0.440982\pi$
$383$	−11.2463	−	6.49304i	−0.574657	−	0.331779i	−0.759007	+	0.651082i	$0.774315\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−1.40367	−	2.43122i	−0.0713523	−	0.123586i
$388$		0			0
$389$	0.474689			0.0240677			0.0120338	−	0.999928i	$-0.496169\pi$
$389$	0.474689			0.0240677			0.0120338	+	0.999928i	$0.496169\pi$
$390$		0			0
$391$	1.40206			0.0709052
$392$		0			0
$393$	2.80229	+	4.85370i	0.141357	+	0.244837i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−21.6600	−	12.5054i	−1.08709	−	0.627629i	−0.154286	−	0.988026i	$-0.549308\pi$
$397$	−21.6600	−	12.5054i	−1.08709	−	0.627629i	−0.932799	+	0.360397i	$0.882641\pi$
$398$		0			0
$399$	−22.9300	+	39.7159i	−1.14793	+	1.98828i
$400$		0			0
$401$	11.2970	−	6.52234i	0.564147	−	0.325710i	−0.190661	−	0.981656i	$-0.561063\pi$
$401$	11.2970	−	6.52234i	0.564147	−	0.325710i	0.754808	+	0.655946i	$0.227730\pi$
$402$		0			0
$403$	−17.6428	+	24.9352i	−0.878850	+	1.24211i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	21.1546	−	36.6408i	1.04859	−	1.81622i
$408$		0			0
$409$	−10.0173	−	5.78349i	−0.495324	−	0.285975i	0.231457	−	0.972845i	$-0.425651\pi$
$409$	−10.0173	−	5.78349i	−0.495324	−	0.285975i	−0.726780	+	0.686870i	$0.758984\pi$
$410$		0			0
$411$		−	32.0650i		−	1.58165i
$412$		0			0
$413$	0.842237	+	1.45880i	0.0414438	+	0.0717827i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	3.51997			0.172374
$418$		0			0
$419$	−8.22688	−	14.2494i	−0.401909	−	0.696128i	0.592047	−	0.805904i	$-0.298320\pi$
$419$	−8.22688	−	14.2494i	−0.401909	−	0.696128i	−0.993956	+	0.109776i	$0.964987\pi$
$420$		0			0
$421$		−	22.2913i		−	1.08641i	−0.839599	−	0.543206i	$-0.817210\pi$
$421$		−	22.2913i		−	1.08641i	0.839599	−	0.543206i	$-0.182790\pi$
$422$		0			0
$423$	−6.28400	−	3.62807i	−0.305539	−	0.176403i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−14.3932	+	8.30993i	−0.696537	+	0.402146i
$428$		0			0
$429$	−16.5355	−	35.9197i	−0.798344	−	1.73422i
$430$		0			0
$431$	−23.4893	+	13.5616i	−1.13144	+	0.653238i	−0.944297	−	0.329094i	$-0.893257\pi$
$431$	−23.4893	+	13.5616i	−1.13144	+	0.653238i	−0.187145	+	0.982332i	$0.559923\pi$
$432$		0			0
$433$	11.0205	−	19.0881i	0.529612	−	0.917315i	−0.469792	−	0.882777i	$-0.655671\pi$
$433$	11.0205	−	19.0881i	0.529612	−	0.917315i	0.999403	−	0.0345372i	$-0.0109957\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		−	2.92501i		−	0.139922i
$438$		0			0
$439$	13.1843	+	22.8358i	0.629251	+	1.08989i	0.987702	+	0.156346i	$0.0499715\pi$
$439$	13.1843	+	22.8358i	0.629251	+	1.08989i	−0.358451	+	0.933548i	$0.616695\pi$
$440$		0			0
$441$	−0.974111			−0.0463862
$442$		0			0
$443$	−40.3081			−1.91510			−0.957548	−	0.288274i	$-0.906918\pi$
$443$	−40.3081			−1.91510			−0.957548	+	0.288274i	$0.906918\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		−	41.9276i		−	1.98311i
$448$		0			0
$449$	0.993353	+	0.573512i	0.0468792	+	0.0270657i	0.523256	−	0.852175i	$-0.324717\pi$
$449$	0.993353	+	0.573512i	0.0468792	+	0.0270657i	−0.476377	+	0.879241i	$0.658050\pi$
$450$		0			0
$451$	−22.1630	+	38.3874i	−1.04361	+	1.80759i
$452$		0			0
$453$	14.1597	−	8.17511i	0.665281	−	0.384100i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	9.08357	−	5.24440i	0.424912	−	0.245323i	−0.272265	−	0.962222i	$-0.587773\pi$
$457$	9.08357	−	5.24440i	0.424912	−	0.245323i	0.697177	+	0.716899i	$0.254439\pi$
$458$		0			0
$459$	−8.31398	+	14.4002i	−0.388063	+	0.672145i
$460$		0			0
$461$	−2.20580	−	1.27352i	−0.102734	−	0.0593138i	0.447752	−	0.894158i	$-0.352225\pi$
$461$	−2.20580	−	1.27352i	−0.102734	−	0.0593138i	−0.550487	+	0.834844i	$0.685558\pi$
$462$		0			0
$463$			3.25551i			0.151296i	0.997135	+	0.0756482i	$0.0241026\pi$
$463$			3.25551i			0.151296i	−0.997135	+	0.0756482i	$0.975897\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	0.164237			0.00759998			0.00379999	−	0.999993i	$-0.498790\pi$
$467$	0.164237			0.00759998			0.00379999	+	0.999993i	$0.498790\pi$
$468$		0			0
$469$	−34.8519			−1.60931
$470$		0			0
$471$	2.62742	+	4.55082i	0.121065	+	0.209691i
$472$		0			0
$473$			18.7268i			0.861059i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	0.244017	−	0.422649i	0.0111727	−	0.0193518i
$478$		0			0
$479$	6.34346	−	3.66240i	0.289840	−	0.167339i	−0.348030	−	0.937483i	$-0.613149\pi$
$479$	6.34346	−	3.66240i	0.289840	−	0.167339i	0.637870	+	0.770144i	$0.279816\pi$
$480$		0			0
$481$	−27.1378	−	2.50850i	−1.23738	−	0.114378i
$482$		0			0
$483$	1.73058	−	0.999150i	0.0787440	−	0.0454629i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	27.6228	+	15.9481i	1.25171	+	0.722675i	0.971449	−	0.237248i	$-0.0762455\pi$
$487$	27.6228	+	15.9481i	1.25171	+	0.722675i	0.280261	+	0.959924i	$0.409579\pi$
$488$		0			0
$489$			14.1996i			0.642130i
$490$		0			0
$491$	3.47434	+	6.01773i	0.156795	+	0.271576i	0.933711	−	0.358027i	$-0.116551\pi$
$491$	3.47434	+	6.01773i	0.156795	+	0.271576i	−0.776916	+	0.629604i	$0.783217\pi$
$492$		0			0
$493$	14.9935			0.675272
$494$		0			0
$495$		0			0
$496$		0			0
$497$	3.49125	+	6.04702i	0.156604	+	0.271246i
$498$		0			0
$499$		−	14.5396i		−	0.650881i	−0.945563	−	0.325440i	$-0.894487\pi$
$499$		−	14.5396i		−	0.650881i	0.945563	−	0.325440i	$-0.105513\pi$
$500$		0			0
$501$	21.6128	+	12.4781i	0.965587	+	0.557482i
$502$		0			0
$503$	14.9369	−	25.8715i	0.666003	−	1.15355i	−0.313009	−	0.949750i	$-0.601337\pi$
$503$	14.9369	−	25.8715i	0.666003	−	1.15355i	0.979012	−	0.203801i	$-0.0653296\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−16.5636	+	19.3508i	−0.735616	+	0.859401i
$508$		0			0
$509$	19.6483	−	11.3440i	0.870896	−	0.502812i	0.00325001	−	0.999995i	$-0.498965\pi$
$509$	19.6483	−	11.3440i	0.870896	−	0.502812i	0.867646	+	0.497183i	$0.165632\pi$
$510$		0			0
$511$	5.94922	−	10.3043i	0.263178	−	0.455837i
$512$		0			0
$513$	30.0421	+	17.3448i	1.32639	+	0.765791i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	24.2017	+	41.9185i	1.06439	+	1.84358i
$518$		0			0
$519$	22.8737			1.00404
$520$		0			0
$521$	27.0167			1.18362			0.591812	−	0.806076i	$-0.298413\pi$
$521$	27.0167			1.18362			0.591812	+	0.806076i	$0.298413\pi$
$522$		0			0
$523$	−11.3581	−	19.6728i	−0.496655	−	0.860232i	0.503337	−	0.864090i	$-0.332105\pi$
$523$	−11.3581	−	19.6728i	−0.496655	−	0.860232i	−0.999993	+	0.00385780i	$0.998772\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	28.8135	+	16.6355i	1.25514	+	0.724654i
$528$		0			0
$529$	11.4363	−	19.8082i	0.497229	−	0.861226i
$530$		0			0
$531$	−0.428489	+	0.247388i	−0.0185948	+	0.0107357i
$532$		0			0
$533$	28.4314	+	2.62807i	1.23150	+	0.113835i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−1.00055	+	1.73301i	−0.0431771	+	0.0747849i
$538$		0			0
$539$	5.62742	+	3.24899i	0.242390	+	0.139944i
$540$		0			0
$541$			25.2514i			1.08564i	0.839848	+	0.542821i	$0.182644\pi$
$541$			25.2514i			1.08564i	−0.839848	+	0.542821i	$0.817356\pi$
$542$		0			0
$543$	13.5952	+	23.5475i	0.583424	+	1.01052i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−36.9221			−1.57867			−0.789337	−	0.613960i	$-0.789576\pi$
$547$	−36.9221			−1.57867			−0.789337	+	0.613960i	$0.789576\pi$
$548$		0			0
$549$	−2.44086	−	4.22769i	−0.104173	−	0.180433i
$550$		0			0
$551$		−	31.2797i		−	1.33256i
$552$		0			0
$553$	−24.3833	−	14.0777i	−1.03688	−	0.598645i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−23.2010	+	13.3951i	−0.983060	+	0.567570i	−0.903192	−	0.429236i	$-0.858783\pi$
$557$	−23.2010	+	13.3951i	−0.983060	+	0.567570i	−0.0798671	+	0.996806i	$0.525450\pi$
$558$		0			0
$559$	10.9576	−	5.04429i	0.463456	−	0.213351i
$560$		0			0
$561$	−37.3008	+	21.5357i	−1.57484	+	0.909236i
$562$		0			0
$563$	−7.19895	+	12.4689i	−0.303399	+	0.525503i	−0.976904	−	0.213680i	$-0.931455\pi$
$563$	−7.19895	+	12.4689i	−0.303399	+	0.525503i	0.673504	+	0.739183i	$0.264788\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$			30.8904i			1.29728i
$568$		0			0
$569$	15.4173	+	26.7035i	0.646325	+	1.11947i	0.983994	+	0.178203i	$0.0570283\pi$
$569$	15.4173	+	26.7035i	0.646325	+	1.11947i	−0.337669	+	0.941265i	$0.609638\pi$
$570$		0			0
$571$	36.5884			1.53118			0.765588	−	0.643331i	$-0.222448\pi$
$571$	36.5884			1.53118			0.765588	+	0.643331i	$0.222448\pi$
$572$		0			0
$573$	−12.7020			−0.530632
$574$		0			0
$575$		0			0
$576$		0			0
$577$			17.3008i			0.720241i	0.932906	+	0.360120i	$0.117264\pi$
$577$			17.3008i			0.720241i	−0.932906	+	0.360120i	$0.882736\pi$
$578$		0			0
$579$	37.1947	+	21.4744i	1.54576	+	0.892444i
$580$		0			0
$581$	−8.70122	+	15.0710i	−0.360987	+	0.625249i
$582$		0			0
$583$	−2.81936	+	1.62776i	−0.116766	+	0.0674147i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	6.81951	−	3.93725i	0.281471	−	0.162508i	−0.352618	−	0.935767i	$-0.614708\pi$
$587$	6.81951	−	3.93725i	0.281471	−	0.162508i	0.634089	+	0.773260i	$0.281375\pi$
$588$		0			0
$589$	34.7053	−	60.1114i	1.43001	−	2.47685i
$590$		0			0
$591$	−32.3222	−	18.6612i	−1.32956	−	0.767619i
$592$		0			0
$593$			43.2400i			1.77565i	0.460179	+	0.887826i	$0.347785\pi$
$593$			43.2400i			1.77565i	−0.460179	+	0.887826i	$0.652215\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	22.9146			0.937832
$598$		0			0
$599$	−2.10157			−0.0858676			−0.0429338	−	0.999078i	$-0.513670\pi$
$599$	−2.10157			−0.0858676			−0.0429338	+	0.999078i	$0.513670\pi$
$600$		0			0
$601$	17.2987	+	29.9623i	0.705630	+	1.22219i	0.966464	+	0.256804i	$0.0826694\pi$
$601$	17.2987	+	29.9623i	0.705630	+	1.22219i	−0.260833	+	0.965384i	$0.583997\pi$
$602$		0			0
$603$		−	10.2370i		−	0.416882i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	5.00993	−	8.67746i	0.203347	−	0.352207i	−0.746258	−	0.665657i	$-0.768151\pi$
$607$	5.00993	−	8.67746i	0.203347	−	0.352207i	0.949605	+	0.313450i	$0.101485\pi$
$608$		0			0
$609$	18.5066	−	10.6848i	0.749926	−	0.432970i
$610$		0			0
$611$	18.0087	−	25.4524i	0.728555	−	1.02969i
$612$		0			0
$613$	−35.5818	+	20.5432i	−1.43714	+	0.829731i	−0.997650	−	0.0685186i	$-0.978173\pi$
$613$	−35.5818	+	20.5432i	−1.43714	+	0.829731i	−0.439486	+	0.898249i	$0.644839\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−2.03603	−	1.17550i	−0.0819673	−	0.0473238i	0.458456	−	0.888717i	$-0.348403\pi$
$617$	−2.03603	−	1.17550i	−0.0819673	−	0.0473238i	−0.540423	+	0.841393i	$0.681736\pi$
$618$		0			0
$619$		−	14.1595i		−	0.569117i	−0.958659	−	0.284559i	$-0.908153\pi$
$619$		−	14.1595i		−	0.569117i	0.958659	−	0.284559i	$-0.0918471\pi$
$620$		0			0
$621$	−0.755781	−	1.30905i	−0.0303285	−	0.0525304i
$622$		0			0
$623$	−1.68447			−0.0674870
$624$		0			0
$625$		0			0
$626$		0			0
$627$	44.9281	+	77.8178i	1.79426	+	3.10774i
$628$		0			0
$629$			29.6853i			1.18363i
$630$		0			0
$631$	−5.36835	−	3.09942i	−0.213711	−	0.123386i	0.389324	−	0.921101i	$-0.372709\pi$
$631$	−5.36835	−	3.09942i	−0.213711	−	0.123386i	−0.603035	+	0.797715i	$0.706042\pi$
$632$		0			0
$633$	12.9307	−	22.3967i	0.513951	−	0.890189i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	0.385264	−	4.16792i	0.0152647	−	0.165139i
$638$		0			0
$639$	−1.77618	+	1.02548i	−0.0702645	+	0.0405672i
$640$		0			0
$641$	−7.85182	+	13.5997i	−0.310128	+	0.537158i	−0.978390	−	0.206769i	$-0.933705\pi$
$641$	−7.85182	+	13.5997i	−0.310128	+	0.537158i	0.668262	+	0.743926i	$0.267039\pi$
$642$		0			0
$643$	36.7006	+	21.1891i	1.44733	+	0.835616i	0.998322	−	0.0579112i	$-0.0184440\pi$
$643$	36.7006	+	21.1891i	1.44733	+	0.835616i	0.449008	+	0.893528i	$0.351777\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−18.6714	−	32.3398i	−0.734048	−	1.27141i	−0.955140	−	0.296155i	$-0.904295\pi$
$647$	−18.6714	−	32.3398i	−0.734048	−	1.27141i	0.221092	−	0.975253i	$-0.429038\pi$
$648$		0			0
$649$	3.30049			0.129556
$650$		0			0
$651$	47.4199			1.85853
$652$		0			0
$653$	−17.8384	−	30.8970i	−0.698069	−	1.20909i	−0.969135	−	0.246531i	$-0.920709\pi$
$653$	−17.8384	−	30.8970i	−0.698069	−	1.20909i	0.271066	−	0.962561i	$-0.412624\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	3.02667	+	1.74745i	0.118082	+	0.0681745i
$658$		0			0
$659$	−6.51065	+	11.2768i	−0.253619	+	0.439281i	−0.964520	−	0.264012i	$-0.914954\pi$
$659$	−6.51065	+	11.2768i	−0.253619	+	0.439281i	0.710900	+	0.703293i	$0.248288\pi$
$660$		0			0
$661$	−3.12096	+	1.80189i	−0.121391	+	0.0700853i	−0.559466	−	0.828853i	$-0.688994\pi$
$661$	−3.12096	+	1.80189i	−0.121391	+	0.0700853i	0.438075	+	0.898938i	$0.355660\pi$
$662$		0			0
$663$	22.6485	+	16.0249i	0.879597	+	0.622355i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−0.681490	+	1.18037i	−0.0263874	+	0.0457043i
$668$		0			0
$669$	4.47488	+	2.58357i	0.173009	+	0.0998867i
$670$		0			0
$671$			32.5643i			1.25713i
$672$		0			0
$673$	−9.89678	−	17.1417i	−0.381493	−	0.660765i	0.609783	−	0.792568i	$-0.291257\pi$
$673$	−9.89678	−	17.1417i	−0.381493	−	0.660765i	−0.991276	+	0.131804i	$0.957923\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	42.2737			1.62471			0.812355	−	0.583163i	$-0.198185\pi$
$677$	42.2737			1.62471			0.812355	+	0.583163i	$0.198185\pi$
$678$		0			0
$679$	6.73734	+	11.6694i	0.258556	+	0.447831i
$680$		0			0
$681$		−	41.5968i		−	1.59399i
$682$		0			0
$683$	15.0755	+	8.70386i	0.576849	+	0.333044i	0.759880	−	0.650063i	$-0.225258\pi$
$683$	15.0755	+	8.70386i	0.576849	+	0.333044i	−0.183031	+	0.983107i	$0.558591\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	16.9948	−	9.81193i	0.648390	−	0.374348i
$688$		0			0
$689$	1.71187	+	1.21123i	0.0652172	+	0.0461441i
$690$		0			0
$691$	−39.3977	+	22.7463i	−1.49876	+	0.865308i	−0.999999	−	0.00143250i	$-0.999544\pi$
$691$	−39.3977	+	22.7463i	−1.49876	+	0.865308i	−0.498759	+	0.866741i	$0.666211\pi$
$692$		0			0
$693$	−6.70867	+	11.6198i	−0.254841	+	0.441398i
$694$		0			0
$695$		0			0
$696$		0			0
$697$		−	31.1002i		−	1.17801i
$698$		0			0
$699$	−17.6015	−	30.4867i	−0.665751	−	1.15311i
$700$		0			0
$701$	−18.7036			−0.706427			−0.353213	−	0.935543i	$-0.614911\pi$
$701$	−18.7036			−0.706427			−0.353213	+	0.935543i	$0.614911\pi$
$702$		0			0
$703$	61.9300			2.33573
$704$		0			0
$705$		0			0
$706$		0			0
$707$		−	7.23902i		−	0.272251i
$708$		0			0
$709$	6.95338	+	4.01454i	0.261140	+	0.150769i	0.624854	−	0.780741i	$-0.285158\pi$
$709$	6.95338	+	4.01454i	0.261140	+	0.150769i	−0.363715	+	0.931510i	$0.618492\pi$
$710$		0			0
$711$	4.13501	−	7.16205i	0.155075	−	0.268598i
$712$		0			0
$713$	−2.61929	+	1.51225i	−0.0980933	+	0.0566342i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	21.5112	−	12.4195i	0.803352	−	0.463815i
$718$		0			0
$719$	−2.01466	+	3.48949i	−0.0751341	+	0.130136i	−0.901145	−	0.433519i	$-0.857272\pi$
$719$	−2.01466	+	3.48949i	−0.0751341	+	0.130136i	0.826010	+	0.563655i	$0.190605\pi$
$720$		0			0
$721$	2.30103	+	1.32850i	0.0856950	+	0.0494760i
$722$		0			0
$723$			16.7194i			0.621803i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−20.5996			−0.763997			−0.381998	−	0.924163i	$-0.624764\pi$
$727$	−20.5996			−0.763997			−0.381998	+	0.924163i	$0.624764\pi$
$728$		0			0
$729$	15.8144			0.585717
$730$		0			0
$731$	−6.56961	−	11.3789i	−0.242986	−	0.420864i
$732$		0			0
$733$			5.93875i			0.219353i	0.993967	+	0.109676i	$0.0349814\pi$
$733$			5.93875i			0.219353i	−0.993967	+	0.109676i	$0.965019\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−34.1438	+	59.1388i	−1.25770	+	2.17840i
$738$		0			0
$739$	−20.8499	+	12.0377i	−0.766975	+	0.442813i	−0.831794	−	0.555084i	$-0.812686\pi$
$739$	−20.8499	+	12.0377i	−0.766975	+	0.442813i	0.0648194	+	0.997897i	$0.479353\pi$
$740$		0			0
$741$	33.4315	−	47.2499i	1.22814	−	1.73577i
$742$		0			0
$743$	−0.859620	+	0.496302i	−0.0315364	+	0.0182075i	−0.515685	−	0.856778i	$-0.672463\pi$
$743$	−0.859620	+	0.496302i	−0.0315364	+	0.0182075i	0.484149	+	0.874986i	$0.339129\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−4.42676	−	2.55579i	−0.161967	−	0.0935114i
$748$		0			0
$749$		−	1.68590i		−	0.0616014i
$750$		0			0
$751$	−13.8054	−	23.9116i	−0.503766	−	0.872548i	−0.999991	−	0.00435392i	$-0.998614\pi$
$751$	−13.8054	−	23.9116i	−0.503766	−	0.872548i	0.496225	−	0.868194i	$-0.334719\pi$
$752$		0			0
$753$	−38.6483			−1.40842
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−5.20513	−	9.01555i	−0.189184	−	0.327676i	0.755795	−	0.654809i	$-0.227251\pi$
$757$	−5.20513	−	9.01555i	−0.189184	−	0.327676i	−0.944978	+	0.327133i	$0.893918\pi$
$758$		0			0
$759$		−	3.91539i		−	0.142120i
$760$		0			0
$761$	26.7558	+	15.4475i	0.969896	+	0.559970i	0.899205	−	0.437528i	$-0.144146\pi$
$761$	26.7558	+	15.4475i	0.969896	+	0.559970i	0.0706917	+	0.997498i	$0.477479\pi$
$762$		0			0
$763$	−6.97122	+	12.0745i	−0.252375	+	0.437127i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−0.889028	−	1.93121i	−0.0321009	−	0.0697320i
$768$		0			0
$769$	−46.0983	+	26.6148i	−1.66235	+	0.959756i	−0.690755	+	0.723089i	$0.742722\pi$
$769$	−46.0983	+	26.6148i	−1.66235	+	0.959756i	−0.971591	+	0.236666i	$0.923945\pi$
$770$		0			0
$771$	23.4899	−	40.6857i	0.845968	−	1.46526i
$772$		0			0
$773$	−15.5953	−	9.00393i	−0.560923	−	0.323849i	0.192593	−	0.981279i	$-0.438310\pi$
$773$	−15.5953	−	9.00393i	−0.560923	−	0.323849i	−0.753516	+	0.657430i	$0.771644\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	21.1546	+	36.6408i	0.758917	+	1.31448i
$778$		0			0
$779$	−64.8820			−2.32464
$780$		0			0
$781$	13.6812			0.489554
$782$		0			0
$783$	−8.08224	−	13.9989i	−0.288836	−	0.500278i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	46.7798	+	27.0083i	1.66752	+	0.962742i	0.968970	+	0.247180i	$0.0795039\pi$
$787$	46.7798	+	27.0083i	1.66752	+	0.962742i	0.698549	+	0.715562i	$0.253829\pi$
$788$		0			0
$789$	0.619056	−	1.07224i	0.0220390	−	0.0381726i
$790$		0			0
$791$	−19.4110	+	11.2069i	−0.690174	+	0.398472i
$792$		0			0
$793$	19.0543	−	8.77159i	0.676638	−	0.311488i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−8.31034	+	14.3939i	−0.294367	+	0.509859i	−0.974838	−	0.222917i	$-0.928442\pi$
$797$	−8.31034	+	14.3939i	−0.294367	+	0.509859i	0.680470	+	0.732776i	$0.261776\pi$
$798$		0			0
$799$	−29.4112	−	16.9805i	−1.04049	−	0.600728i
$800$		0			0
$801$		−	0.494776i		−	0.0174821i
$802$		0			0
$803$	−11.6567	−	20.1899i	−0.411355	−	0.712488i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	14.4466			0.508545
$808$		0			0
$809$	−8.52131	−	14.7593i	−0.299593	−	0.518911i	0.676450	−	0.736489i	$-0.263518\pi$
$809$	−8.52131	−	14.7593i	−0.299593	−	0.518911i	−0.976043	+	0.217578i	$0.930184\pi$
$810$		0			0
$811$			2.60366i			0.0914268i	0.998955	+	0.0457134i	$0.0145561\pi$
$811$			2.60366i			0.0914268i	−0.998955	+	0.0457134i	$0.985444\pi$
$812$		0			0
$813$	−19.7807	−	11.4204i	−0.693738	−	0.400530i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−23.7389	+	13.7057i	−0.830518	+	0.479500i
$818$		0			0
$819$	8.60611	+	0.795511i	0.300722	+	0.0277974i
$820$		0			0
$821$	−40.7265	+	23.5134i	−1.42136	+	0.820625i	−0.996416	−	0.0845933i	$-0.973041\pi$
$821$	−40.7265	+	23.5134i	−1.42136	+	0.820625i	−0.424948	+	0.905218i	$0.639708\pi$
$822$		0			0
$823$	−5.35111	+	9.26840i	−0.186528	+	0.323076i	−0.944090	−	0.329687i	$-0.893057\pi$
$823$	−5.35111	+	9.26840i	−0.186528	+	0.323076i	0.757562	+	0.652763i	$0.226390\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			13.8240i			0.480707i	0.970685	+	0.240354i	$0.0772634\pi$
$827$			13.8240i			0.480707i	−0.970685	+	0.240354i	$0.922737\pi$
$828$		0			0
$829$	24.1310	+	41.7961i	0.838104	+	1.45164i	0.891478	+	0.453065i	$0.149669\pi$
$829$	24.1310	+	41.7961i	0.838104	+	1.45164i	−0.0533731	+	0.998575i	$0.516997\pi$
$830$		0			0
$831$	1.80565			0.0626375
$832$		0			0
$833$	−4.55915			−0.157965
$834$		0			0
$835$		0			0
$836$		0			0
$837$		−	35.8695i		−	1.23983i
$838$		0			0
$839$	44.3752	+	25.6200i	1.53200	+	0.884502i	0.999269	+	0.0382177i	$0.0121680\pi$
$839$	44.3752	+	25.6200i	1.53200	+	0.884502i	0.532732	+	0.846284i	$0.321165\pi$
$840$		0			0
$841$	7.21222	−	12.4919i	0.248697	−	0.430756i
$842$		0			0
$843$	22.6236	−	13.0617i	0.779197	−	0.449869i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	50.2977	−	29.0394i	1.72825	−	0.997805i
$848$		0			0
$849$	5.10004	−	8.83353i	0.175033	−	0.303166i
$850$		0			0
$851$	−2.33700	−	1.34927i	−0.0801113	−	0.0462523i
$852$		0			0
$853$		−	21.3777i		−	0.731960i	−0.930623	−	0.365980i	$-0.880734\pi$
$853$		−	21.3777i		−	0.731960i	0.930623	−	0.365980i	$-0.119266\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−36.9615			−1.26258			−0.631291	−	0.775546i	$-0.717475\pi$
$857$	−36.9615			−1.26258			−0.631291	+	0.775546i	$0.717475\pi$
$858$		0			0
$859$	36.3529			1.24034			0.620172	−	0.784465i	$-0.287063\pi$
$859$	36.3529			1.24034			0.620172	+	0.784465i	$0.287063\pi$
$860$		0			0
$861$	−22.1630	−	38.3874i	−0.755312	−	1.30824i
$862$		0			0
$863$			41.0328i			1.39677i	0.715720	+	0.698387i	$0.246099\pi$
$863$			41.0328i			1.39677i	−0.715720	+	0.698387i	$0.753901\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−1.54460	+	2.67532i	−0.0524573	+	0.0908588i
$868$		0			0
$869$	−47.7757	+	27.5833i	−1.62068	+	0.935700i
$870$		0			0
$871$	43.8008	+	4.04876i	1.48413	+	0.137187i
$872$		0			0
$873$	−3.42763	+	1.97894i	−0.116008	+	0.0669771i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	14.5001	+	8.37164i	0.489634	+	0.282690i	0.724423	−	0.689356i	$-0.242106\pi$
$877$	14.5001	+	8.37164i	0.489634	+	0.282690i	−0.234789	+	0.972046i	$0.575440\pi$
$878$		0			0
$879$		−	29.4804i		−	0.994350i
$880$		0			0
$881$	26.3345	+	45.6127i	0.887232	+	1.53673i	0.843133	+	0.537704i	$0.180708\pi$
$881$	26.3345	+	45.6127i	0.887232	+	1.53673i	0.0440990	+	0.999027i	$0.485958\pi$
$882$		0			0
$883$	45.5891			1.53419			0.767097	−	0.641531i	$-0.221700\pi$
$883$	45.5891			1.53419			0.767097	+	0.641531i	$0.221700\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−10.0366	−	17.3838i	−0.336995	−	0.583692i	0.646871	−	0.762599i	$-0.276077\pi$
$887$	−10.0366	−	17.3838i	−0.336995	−	0.583692i	−0.983866	+	0.178907i	$0.942744\pi$
$888$		0			0
$889$		−	21.3696i		−	0.716713i
$890$		0			0
$891$	52.4166	+	30.2628i	1.75602	+	1.01384i
$892$		0			0
$893$	−35.4251	+	61.3582i	−1.18546	+	2.05327i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−2.29101	+	1.05466i	−0.0764945	+	0.0352140i
$898$		0			0
$899$	−28.0104	+	16.1718i	−0.934200	+	0.539361i
$900$		0			0
$901$	1.14208	−	1.97813i	0.0380481	−	0.0659012i
$902$		0			0
$903$	−16.2179	−	9.36340i	−0.539697	−	0.311594i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	19.1070	+	33.0943i	0.634438	+	1.09888i	0.986634	+	0.162953i	$0.0521018\pi$
$907$	19.1070	+	33.0943i	0.634438	+	1.09888i	−0.352196	+	0.935926i	$0.614565\pi$
$908$		0			0
$909$	2.12630			0.0705249
$910$		0			0
$911$	−36.3853			−1.20550			−0.602749	−	0.797931i	$-0.705928\pi$
$911$	−36.3853			−1.20550			−0.602749	+	0.797931i	$0.705928\pi$
$912$		0			0
$913$	17.0488	+	29.5295i	0.564234	+	0.977282i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	7.07664	+	4.08570i	0.233691	+	0.134922i
$918$		0			0
$919$	11.6508	−	20.1798i	0.384324	−	0.665669i	−0.607351	−	0.794434i	$-0.707768\pi$
$919$	11.6508	−	20.1798i	0.384324	−	0.665669i	0.991675	+	0.128765i	$0.0411012\pi$
$920$		0			0
$921$	7.49996	−	4.33011i	0.247132	−	0.142682i
$922$		0			0
$923$	−3.68521	−	8.00528i	−0.121300	−	0.263497i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−0.390218	+	0.675877i	−0.0128164	+	0.0221987i
$928$		0			0
$929$	3.17003	+	1.83022i	0.104005	+	0.0600475i	0.551100	−	0.834439i	$-0.314208\pi$
$929$	3.17003	+	1.83022i	0.104005	+	0.0600475i	−0.447095	+	0.894486i	$0.647541\pi$
$930$		0			0
$931$			9.51140i			0.311724i
$932$		0			0
$933$	31.5532	+	54.6518i	1.03301	+	1.78922i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−41.7022			−1.36235			−0.681175	−	0.732120i	$-0.738531\pi$
$937$	−41.7022			−1.36235			−0.681175	+	0.732120i	$0.738531\pi$
$938$		0			0
$939$	18.4718	+	31.9941i	0.602805	+	1.04409i
$940$		0			0
$941$			52.3086i			1.70521i	0.522554	+	0.852606i	$0.324979\pi$
$941$			52.3086i			1.70521i	−0.522554	+	0.852606i	$0.675021\pi$
$942$		0			0
$943$	2.44840	+	1.41358i	0.0797307	+	0.0460325i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−32.0703	+	18.5158i	−1.04214	+	0.601682i	−0.920440	−	0.390884i	$-0.872169\pi$
$947$	−32.0703	+	18.5158i	−1.04214	+	0.601682i	−0.121704	+	0.992566i	$0.538836\pi$
$948$		0			0
$949$	−8.67384	+	12.2591i	−0.281565	+	0.397946i
$950$		0			0
$951$	−40.7082	+	23.5029i	−1.32005	+	0.762134i
$952$		0			0
$953$	7.25776	−	12.5708i	0.235102	−	0.407209i	−0.724200	−	0.689590i	$-0.757791\pi$
$953$	7.25776	−	12.5708i	0.235102	−	0.407209i	0.959302	+	0.282381i	$0.0911243\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		−	41.8708i		−	1.35349i
$958$		0			0
$959$	−23.3752	−	40.4870i	−0.754824	−	1.30739i
$960$		0			0
$961$	−40.7717			−1.31522
$962$		0			0
$963$	0.495195			0.0159574
$964$		0			0
$965$		0			0
$966$		0			0
$967$		−	24.2765i		−	0.780680i	−0.920671	−	0.390340i	$-0.872357\pi$
$967$		−	24.2765i		−	0.780680i	0.920671	−	0.390340i	$-0.127643\pi$
$968$		0			0
$969$	−54.5990	−	31.5228i	−1.75397	−	1.01266i
$970$		0			0
$971$	−10.3284	+	17.8894i	−0.331456	+	0.574098i	−0.982798	−	0.184686i	$-0.940873\pi$
$971$	−10.3284	+	17.8894i	−0.331456	+	0.574098i	0.651342	+	0.758784i	$0.274206\pi$
$972$		0			0
$973$	4.44451	−	2.56604i	0.142485	−	0.0822635i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	21.8260	−	12.6013i	0.698277	−	0.403150i	−0.108429	−	0.994104i	$-0.534582\pi$
$977$	21.8260	−	12.6013i	0.698277	−	0.403150i	0.806705	+	0.590954i	$0.201249\pi$
$978$		0			0
$979$	−1.65025	+	2.85831i	−0.0527421	+	0.0913520i
$980$		0			0
$981$	−3.54662	−	2.04764i	−0.113235	−	0.0653761i
$982$		0			0
$983$		−	43.9686i		−	1.40238i	−0.712973	−	0.701191i	$-0.752652\pi$
$983$		−	43.9686i		−	1.40238i	0.712973	−	0.701191i	$-0.247348\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−48.4034			−1.54070
$988$		0			0
$989$	1.19442			0.0379803
$990$		0			0
$991$	−15.8117	−	27.3866i	−0.502275	−	0.869966i	−0.999997	−	0.00262873i	$-0.999163\pi$
$991$	−15.8117	−	27.3866i	−0.502275	−	0.869966i	0.497722	−	0.867337i	$-0.334170\pi$
$992$		0			0
$993$		−	14.1209i		−	0.448113i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−9.53853	+	16.5212i	−0.302088	+	0.523232i	−0.976609	−	0.215024i	$-0.931017\pi$
$997$	−9.53853	+	16.5212i	−0.302088	+	0.523232i	0.674521	+	0.738256i	$0.264350\pi$
$998$		0			0
$999$	27.7160	−	16.0019i	0.876897	−	0.506277i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1300.2.y.e.101.7		16
5.2	odd	4		260.2.z.a.49.7	yes	16
5.3	odd	4		260.2.z.a.49.2	✓	16
5.4	even	2	inner	1300.2.y.e.101.2		16
13.4	even	6	inner	1300.2.y.e.901.7		16
15.2	even	4		2340.2.cr.a.829.1		16
15.8	even	4		2340.2.cr.a.829.8		16
20.3	even	4		1040.2.df.d.49.7		16
20.7	even	4		1040.2.df.d.49.2		16
65.2	even	12		3380.2.c.e.2029.13		16
65.3	odd	12		3380.2.d.d.1689.3		16
65.4	even	6	inner	1300.2.y.e.901.2		16
65.17	odd	12		260.2.z.a.69.2	yes	16
65.23	odd	12		3380.2.d.d.1689.4		16
65.28	even	12		3380.2.c.e.2029.3		16
65.37	even	12		3380.2.c.e.2029.14		16
65.42	odd	12		3380.2.d.d.1689.14		16
65.43	odd	12		260.2.z.a.69.7	yes	16
65.62	odd	12		3380.2.d.d.1689.13		16
65.63	even	12		3380.2.c.e.2029.4		16
195.17	even	12		2340.2.cr.a.1369.8		16
195.173	even	12		2340.2.cr.a.1369.1		16
260.43	even	12		1040.2.df.d.849.2		16
260.147	even	12		1040.2.df.d.849.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
260.2.z.a.49.2	✓	16	5.3	odd	4
260.2.z.a.49.7	yes	16	5.2	odd	4
260.2.z.a.69.2	yes	16	65.17	odd	12
260.2.z.a.69.7	yes	16	65.43	odd	12
1040.2.df.d.49.2		16	20.7	even	4
1040.2.df.d.49.7		16	20.3	even	4
1040.2.df.d.849.2		16	260.43	even	12
1040.2.df.d.849.7		16	260.147	even	12
1300.2.y.e.101.2		16	5.4	even	2	inner
1300.2.y.e.101.7		16	1.1	even	1	trivial
1300.2.y.e.901.2		16	65.4	even	6	inner
1300.2.y.e.901.7		16	13.4	even	6	inner
2340.2.cr.a.829.1		16	15.2	even	4
2340.2.cr.a.829.8		16	15.8	even	4
2340.2.cr.a.1369.1		16	195.173	even	12
2340.2.cr.a.1369.8		16	195.17	even	12
3380.2.c.e.2029.3		16	65.28	even	12
3380.2.c.e.2029.4		16	65.63	even	12
3380.2.c.e.2029.13		16	65.2	even	12
3380.2.c.e.2029.14		16	65.37	even	12
3380.2.d.d.1689.3		16	65.3	odd	12
3380.2.d.d.1689.4		16	65.23	odd	12
3380.2.d.d.1689.13		16	65.62	odd	12
3380.2.d.d.1689.14		16	65.42	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)

\(f(q)\)	\(=\)	\(q+(0.979681 + 1.69686i) q^{3} +(2.47400 + 1.42836i) q^{7} +(-0.419550 + 0.726682i) q^{9} +O(q^{10})\)	\(q+(0.979681 + 1.69686i) q^{3} +(2.47400 + 1.42836i) q^{7} +(-0.419550 + 0.726682i) q^{9} +(4.84746 - 2.79868i) q^{11} +(-2.94331 - 2.08253i) q^{13} +(-1.96363 + 3.40111i) q^{17} +(7.09546 + 4.09657i) q^{19} +5.59737i q^{21} +(-0.178504 - 0.309177i) q^{23} +4.23399 q^{27} +(-1.90890 - 3.30631i) q^{29} -8.47182i q^{31} +(9.49793 + 5.48363i) q^{33} +(6.54609 - 3.77939i) q^{37} +(0.650247 - 7.03459i) q^{39} +(-6.85811 + 3.95953i) q^{41} +(-1.67282 + 2.89741i) q^{43} +8.64753i q^{47} +(0.580450 + 1.00537i) q^{49} -7.69492 q^{51} -0.581615 q^{53} +16.0533i q^{57} +(0.510653 + 0.294826i) q^{59} +(-2.90890 + 5.03836i) q^{61} +(-2.07593 + 1.19854i) q^{63} +(-10.5655 + 6.09997i) q^{67} +(0.349753 - 0.605790i) q^{69} +(2.11676 + 1.22211i) q^{71} -4.16506i q^{73} +15.9902 q^{77} -9.85582 q^{79} +(5.40661 + 9.36452i) q^{81} +6.09174i q^{83} +(3.74022 - 6.47825i) q^{87} +(-0.510653 + 0.294826i) q^{89} +(-4.30714 - 9.35629i) q^{91} +(14.3755 - 8.29968i) q^{93} +(4.08489 + 2.35841i) q^{97} +4.69675i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 10 q^{9}+O(q^{10}) \) 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

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Database

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