LMFDB - Embedded newform 300.11.k.c.193.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [300,11,Mod(157,300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(300, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 0, 1]))

N = Newforms(chi, 11, names="a")

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

chi := DirichletCharacter("300.157");

S:= CuspForms(chi, 11);

N := Newforms(S);

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	300.k (of order $4$, 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:	$190.607175802$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
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} - 63831600 x^{13} + 120528248672 x^{12} - 17600989215600 x^{11} + \cdots + 38\!\cdots\!56 $ x^16 - 63831600x^13 + 120528248672x^12 - 17600989215600x^11 + 2037236579280000x^10 - 3343396831784087400x^9 + 4317664424723438821024x^8 - 1093166020823780215242000x^7 + 122767222860388422207360000x^6 + 17394213048729389505235839600x^5 + 3322978970397292826674840245897x^4 - 837815701799476622071156318691400x^3 + 126631812340115852451399515174580000x^2 + 31278039886234045787552155897225466400*x + 3862835732371990949484385042694585728656
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{44}\cdot 3^{12}\cdot 5^{16} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			193.7
Root			$298.877 - 298.877i$ of defining polynomial
Character	$\chi$	$=$	300.193
Dual form			300.11.k.c.157.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(99.2043 + 99.2043i) q^{3} +(7200.85 - 7200.85i) q^{7} +19683.0i q^{9} +O(q^{10})$	$q+(99.2043 + 99.2043i) q^{3} +(7200.85 - 7200.85i) q^{7} +19683.0i q^{9} +210638. q^{11} +(150113. + 150113. i) q^{13} +(1.85604e6 - 1.85604e6i) q^{17} -3.28473e6i q^{19} +1.42871e6 q^{21} +(-6.83626e6 - 6.83626e6i) q^{23} +(-1.95264e6 + 1.95264e6i) q^{27} -5.70410e6i q^{29} -5.12482e7 q^{31} +(2.08962e7 + 2.08962e7i) q^{33} +(6.63937e7 - 6.63937e7i) q^{37} +2.97837e7i q^{39} +1.97853e8 q^{41} +(-8.01179e7 - 8.01179e7i) q^{43} +(-1.70118e8 + 1.70118e8i) q^{47} +1.78771e8i q^{49} +3.68255e8 q^{51} +(-1.87724e8 - 1.87724e8i) q^{53} +(3.25860e8 - 3.25860e8i) q^{57} -3.54998e8i q^{59} -1.18790e9 q^{61} +(1.41734e8 + 1.41734e8i) q^{63} +(-1.62475e9 + 1.62475e9i) q^{67} -1.35637e9i q^{69} +3.16296e8 q^{71} +(5.47815e8 + 5.47815e8i) q^{73} +(1.51677e9 - 1.51677e9i) q^{77} -4.50145e9i q^{79} -3.87420e8 q^{81} +(-2.12766e9 - 2.12766e9i) q^{83} +(5.65871e8 - 5.65871e8i) q^{87} +5.13652e9i q^{89} +2.16188e9 q^{91} +(-5.08405e9 - 5.08405e9i) q^{93} +(-6.06332e9 + 6.06332e9i) q^{97} +4.14599e9i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q - 331104 q^{11} + 555984 q^{21} - 140804816 q^{31} + 29553600 q^{41} + 471062304 q^{51} + 3576862832 q^{61} + 1853192640 q^{71} - 6198727824 q^{81} + 7033272240 q^{91}+O(q^{100}) $ 16 * q - 331104 * q^11 + 555984 * q^21 - 140804816 * q^31 + 29553600 * q^41 + 471062304 * q^51 + 3576862832 * q^61 + 1853192640 * q^71 - 6198727824 * q^81 + 7033272240 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$277$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	99.2043	+	99.2043i	0.408248	+	0.408248i
$3$	99.2043	+	99.2043i	0.408248	+	0.408248i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	7200.85	−	7200.85i	0.428443	−	0.428443i	−0.459654	−	0.888098i	$-0.652027\pi$
$7$	7200.85	−	7200.85i	0.428443	−	0.428443i	0.888098	+	0.459654i	$0.152027\pi$
$8$		0			0
$9$			19683.0i			0.333333i
$10$		0			0
$11$	210638.			1.30790			0.653949	−	0.756539i	$-0.273111\pi$
$11$	210638.			1.30790			0.653949	+	0.756539i	$0.273111\pi$
$12$		0			0
$13$	150113.	+	150113.i	0.404297	+	0.404297i	0.879744	−	0.475447i	$-0.157714\pi$
$13$	150113.	+	150113.i	0.404297	+	0.404297i	−0.475447	+	0.879744i	$0.657714\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	1.85604e6	−	1.85604e6i	1.30720	−	1.30720i	0.383780	−	0.923424i	$-0.374622\pi$
$17$	1.85604e6	−	1.85604e6i	1.30720	−	1.30720i	0.923424	−	0.383780i	$-0.125378\pi$
$18$		0			0
$19$		−	3.28473e6i		−	1.32658i	−0.748364	−	0.663288i	$-0.769160\pi$
$19$		−	3.28473e6i		−	1.32658i	0.748364	−	0.663288i	$-0.230840\pi$
$20$		0			0
$21$	1.42871e6			0.349823
$22$		0			0
$23$	−6.83626e6	−	6.83626e6i	−1.06213	−	1.06213i	−0.997937	−	0.0641964i	$-0.979552\pi$
$23$	−6.83626e6	−	6.83626e6i	−1.06213	−	1.06213i	−0.0641964	−	0.997937i	$-0.520448\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−1.95264e6	+	1.95264e6i	−0.136083	+	0.136083i
$28$		0			0
$29$		−	5.70410e6i		−	0.278098i	−0.990286	−	0.139049i	$-0.955596\pi$
$29$		−	5.70410e6i		−	0.278098i	0.990286	−	0.139049i	$-0.0444045\pi$
$30$		0			0
$31$	−5.12482e7			−1.79007			−0.895036	−	0.445994i	$-0.852850\pi$
$31$	−5.12482e7			−1.79007			−0.895036	+	0.445994i	$0.852850\pi$
$32$		0			0
$33$	2.08962e7	+	2.08962e7i	0.533947	+	0.533947i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	6.63937e7	−	6.63937e7i	0.957454	−	0.957454i	−0.0416768	−	0.999131i	$-0.513270\pi$
$37$	6.63937e7	−	6.63937e7i	0.957454	−	0.957454i	0.999131	+	0.0416768i	$0.0132700\pi$
$38$		0			0
$39$			2.97837e7i			0.330107i
$40$		0			0
$41$	1.97853e8			1.70775			0.853873	−	0.520481i	$-0.174247\pi$
$41$	1.97853e8			1.70775			0.853873	+	0.520481i	$0.174247\pi$
$42$		0			0
$43$	−8.01179e7	−	8.01179e7i	−0.544988	−	0.544988i	0.379999	−	0.924987i	$-0.375924\pi$
$43$	−8.01179e7	−	8.01179e7i	−0.544988	−	0.544988i	−0.924987	+	0.379999i	$0.875924\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−1.70118e8	+	1.70118e8i	−0.741757	+	0.741757i	−0.972916	−	0.231159i	$-0.925748\pi$
$47$	−1.70118e8	+	1.70118e8i	−0.741757	+	0.741757i	0.231159	+	0.972916i	$0.425748\pi$
$48$		0			0
$49$			1.78771e8i			0.632873i
$50$		0			0
$51$	3.68255e8			1.06733
$52$		0			0
$53$	−1.87724e8	−	1.87724e8i	−0.448891	−	0.448891i	0.446095	−	0.894986i	$-0.352814\pi$
$53$	−1.87724e8	−	1.87724e8i	−0.448891	−	0.448891i	−0.894986	+	0.446095i	$0.852814\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	3.25860e8	−	3.25860e8i	0.541572	−	0.541572i
$58$		0			0
$59$		−	3.54998e8i		−	0.496554i	−0.968689	−	0.248277i	$-0.920136\pi$
$59$		−	3.54998e8i		−	0.496554i	0.968689	−	0.248277i	$-0.0798643\pi$
$60$		0			0
$61$	−1.18790e9			−1.40647			−0.703236	−	0.710957i	$-0.748262\pi$
$61$	−1.18790e9			−1.40647			−0.703236	+	0.710957i	$0.748262\pi$
$62$		0			0
$63$	1.41734e8	+	1.41734e8i	0.142814	+	0.142814i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−1.62475e9	+	1.62475e9i	−1.20341	+	1.20341i	−0.230287	+	0.973123i	$0.573966\pi$
$67$	−1.62475e9	+	1.62475e9i	−1.20341	+	1.20341i	−0.973123	+	0.230287i	$0.926034\pi$
$68$		0			0
$69$		−	1.35637e9i		−	0.867229i
$70$		0			0
$71$	3.16296e8			0.175308			0.0876541	−	0.996151i	$-0.472063\pi$
$71$	3.16296e8			0.175308			0.0876541	+	0.996151i	$0.472063\pi$
$72$		0			0
$73$	5.47815e8	+	5.47815e8i	0.264253	+	0.264253i	0.826779	−	0.562526i	$-0.190171\pi$
$73$	5.47815e8	+	5.47815e8i	0.264253	+	0.264253i	−0.562526	+	0.826779i	$0.690171\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	1.51677e9	−	1.51677e9i	0.560360	−	0.560360i
$78$		0			0
$79$		−	4.50145e9i		−	1.46291i	−0.681890	−	0.731455i	$-0.738842\pi$
$79$		−	4.50145e9i		−	1.46291i	0.681890	−	0.731455i	$-0.261158\pi$
$80$		0			0
$81$	−3.87420e8			−0.111111
$82$		0			0
$83$	−2.12766e9	−	2.12766e9i	−0.540146	−	0.540146i	0.383426	−	0.923572i	$-0.374744\pi$
$83$	−2.12766e9	−	2.12766e9i	−0.540146	−	0.540146i	−0.923572	+	0.383426i	$0.874744\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	5.65871e8	−	5.65871e8i	0.113533	−	0.113533i
$88$		0			0
$89$			5.13652e9i			0.919853i	0.887957	+	0.459927i	$0.152124\pi$
$89$			5.13652e9i			0.919853i	−0.887957	+	0.459927i	$0.847876\pi$
$90$		0			0
$91$	2.16188e9			0.346437
$92$		0			0
$93$	−5.08405e9	−	5.08405e9i	−0.730794	−	0.730794i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−6.06332e9	+	6.06332e9i	−0.706076	+	0.706076i	−0.965708	−	0.259631i	$-0.916399\pi$
$97$	−6.06332e9	+	6.06332e9i	−0.706076	+	0.706076i	0.259631	+	0.965708i	$0.416399\pi$
$98$		0			0
$99$			4.14599e9i			0.435966i
$100$		0			0
$101$	−7.14748e9			−0.680058			−0.340029	−	0.940415i	$-0.610437\pi$
$101$	−7.14748e9			−0.680058			−0.340029	+	0.940415i	$0.610437\pi$
$102$		0			0
$103$	4.51140e9	+	4.51140e9i	0.389157	+	0.389157i	0.874387	−	0.485230i	$-0.161264\pi$
$103$	4.51140e9	+	4.51140e9i	0.389157	+	0.389157i	−0.485230	+	0.874387i	$0.661264\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−4.58736e9	+	4.58736e9i	−0.327072	+	0.327072i	−0.851472	−	0.524400i	$-0.824290\pi$
$107$	−4.58736e9	+	4.58736e9i	−0.327072	+	0.327072i	0.524400	+	0.851472i	$0.324290\pi$
$108$		0			0
$109$		−	1.64762e10i		−	1.07084i	−0.844586	−	0.535420i	$-0.820153\pi$
$109$		−	1.64762e10i		−	1.07084i	0.844586	−	0.535420i	$-0.179847\pi$
$110$		0			0
$111$	1.31731e10			0.781758
$112$		0			0
$113$	−1.88680e10	−	1.88680e10i	−1.02408	−	1.02408i	−0.999703	−	0.0243770i	$-0.992240\pi$
$113$	−1.88680e10	−	1.88680e10i	−1.02408	−	1.02408i	−0.0243770	−	0.999703i	$-0.507760\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−2.95467e9	+	2.95467e9i	−0.134766	+	0.134766i
$118$		0			0
$119$		−	2.67302e10i		−	1.12013i
$120$		0			0
$121$	1.84310e10			0.710596
$122$		0			0
$123$	1.96279e10	+	1.96279e10i	0.697185	+	0.697185i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	3.68890e10	−	3.68890e10i	1.11655	−	1.11655i	0.124305	−	0.992244i	$-0.460330\pi$
$127$	3.68890e10	−	3.68890e10i	1.11655	−	1.11655i	0.992244	−	0.124305i	$-0.0396703\pi$
$128$		0			0
$129$		−	1.58961e10i		−	0.444981i
$130$		0			0
$131$	−1.65971e10			−0.430205			−0.215103	−	0.976591i	$-0.569009\pi$
$131$	−1.65971e10			−0.430205			−0.215103	+	0.976591i	$0.569009\pi$
$132$		0			0
$133$	−2.36529e10	−	2.36529e10i	−0.568363	−	0.568363i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	3.12372e10	−	3.12372e10i	0.647245	−	0.647245i	−0.305081	−	0.952326i	$-0.598684\pi$
$137$	3.12372e10	−	3.12372e10i	0.647245	−	0.647245i	0.952326	+	0.305081i	$0.0986836\pi$
$138$		0			0
$139$			5.91915e10i			1.14074i	0.821389	+	0.570369i	$0.193200\pi$
$139$			5.91915e10i			1.14074i	−0.821389	+	0.570369i	$0.806800\pi$
$140$		0			0
$141$	−3.37529e10			−0.605642
$142$		0			0
$143$	3.16195e10	+	3.16195e10i	0.528779	+	0.528779i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−1.77348e10	+	1.77348e10i	−0.258369	+	0.258369i
$148$		0			0
$149$		−	4.20374e10i		−	0.572406i	−0.958169	−	0.286203i	$-0.907607\pi$
$149$		−	4.20374e10i		−	0.572406i	0.958169	−	0.286203i	$-0.0923932\pi$
$150$		0			0
$151$	−4.86489e10			−0.619710			−0.309855	−	0.950784i	$-0.600280\pi$
$151$	−4.86489e10			−0.619710			−0.309855	+	0.950784i	$0.600280\pi$
$152$		0			0
$153$	3.65325e10	+	3.65325e10i	0.435735	+	0.435735i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−2.97969e10	+	2.97969e10i	−0.312372	+	0.312372i	−0.845828	−	0.533456i	$-0.820893\pi$
$157$	−2.97969e10	+	2.97969e10i	−0.312372	+	0.312372i	0.533456	+	0.845828i	$0.320893\pi$
$158$		0			0
$159$		−	3.72461e10i		−	0.366518i
$160$		0			0
$161$	−9.84537e10			−0.910128
$162$		0			0
$163$	−1.07607e9	−	1.07607e9i	−0.00935197	−	0.00935197i	0.702415	−	0.711767i	$-0.252105\pi$
$163$	−1.07607e9	−	1.07607e9i	−0.00935197	−	0.00935197i	−0.711767	+	0.702415i	$0.752105\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−5.21867e10	+	5.21867e10i	−0.401770	+	0.401770i	−0.878856	−	0.477086i	$-0.841693\pi$
$167$	−5.21867e10	+	5.21867e10i	−0.401770	+	0.401770i	0.477086	+	0.878856i	$0.341693\pi$
$168$		0			0
$169$		−	9.27908e10i		−	0.673088i
$170$		0			0
$171$	6.46534e10			0.442192
$172$		0			0
$173$	8.38840e10	+	8.38840e10i	0.541313	+	0.541313i	0.923914	−	0.382601i	$-0.124971\pi$
$173$	8.38840e10	+	8.38840e10i	0.541313	+	0.541313i	−0.382601	+	0.923914i	$0.624971\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	3.52174e10	−	3.52174e10i	0.202717	−	0.202717i
$178$		0			0
$179$			2.61205e11i			1.42140i	0.703495	+	0.710700i	$0.251622\pi$
$179$			2.61205e11i			1.42140i	−0.703495	+	0.710700i	$0.748378\pi$
$180$		0			0
$181$	8.63194e10			0.444340			0.222170	−	0.975008i	$-0.428686\pi$
$181$	8.63194e10			0.444340			0.222170	+	0.975008i	$0.428686\pi$
$182$		0			0
$183$	−1.17845e11	−	1.17845e11i	−0.574190	−	0.574190i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	3.90954e11	−	3.90954e11i	1.70969	−	1.70969i
$188$		0			0
$189$			2.81213e10i			0.116608i
$190$		0			0
$191$	−1.12175e11			−0.441295			−0.220648	−	0.975354i	$-0.570817\pi$
$191$	−1.12175e11			−0.441295			−0.220648	+	0.975354i	$0.570817\pi$
$192$		0			0
$193$	2.61237e11	+	2.61237e11i	0.975548	+	0.975548i	0.999708	−	0.0241602i	$-0.00769119\pi$
$193$	2.61237e11	+	2.61237e11i	0.975548	+	0.975548i	−0.0241602	+	0.999708i	$0.507691\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	3.61273e11	−	3.61273e11i	1.21760	−	1.21760i	0.249128	−	0.968470i	$-0.419856\pi$
$197$	3.61273e11	−	3.61273e11i	1.21760	−	1.21760i	0.968470	−	0.249128i	$-0.0801441\pi$
$198$		0			0
$199$		−	5.69079e11i		−	1.82351i	−0.410738	−	0.911753i	$-0.634729\pi$
$199$		−	5.69079e11i		−	1.82351i	0.410738	−	0.911753i	$-0.365271\pi$
$200$		0			0
$201$	−3.22365e11			−0.982580
$202$		0			0
$203$	−4.10744e10	−	4.10744e10i	−0.119149	−	0.119149i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	1.34558e11	−	1.34558e11i	0.354045	−	0.354045i
$208$		0			0
$209$		−	6.91890e11i		−	1.73503i
$210$		0			0
$211$	−5.75272e11			−1.37550			−0.687750	−	0.725947i	$-0.741402\pi$
$211$	−5.75272e11			−1.37550			−0.687750	+	0.725947i	$0.741402\pi$
$212$		0			0
$213$	3.13780e10	+	3.13780e10i	0.0715693	+	0.0715693i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−3.69031e11	+	3.69031e11i	−0.766945	+	0.766945i
$218$		0			0
$219$			1.08691e11i			0.215762i
$220$		0			0
$221$	5.57232e11			1.05700
$222$		0			0
$223$	2.51294e11	+	2.51294e11i	0.455677	+	0.455677i	0.897234	−	0.441556i	$-0.145573\pi$
$223$	2.51294e11	+	2.51294e11i	0.455677	+	0.455677i	−0.441556	+	0.897234i	$0.645573\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	3.72972e11	−	3.72972e11i	0.618795	−	0.618795i	−0.326427	−	0.945222i	$-0.605845\pi$
$227$	3.72972e11	−	3.72972e11i	0.618795	−	0.618795i	0.945222	+	0.326427i	$0.105845\pi$
$228$		0			0
$229$			3.22170e11i			0.511573i	0.966733	+	0.255787i	$0.0823345\pi$
$229$			3.22170e11i			0.511573i	−0.966733	+	0.255787i	$0.917666\pi$
$230$		0			0
$231$	3.00941e11			0.457532
$232$		0			0
$233$	7.62647e10	+	7.62647e10i	0.111057	+	0.111057i	0.760451	−	0.649395i	$-0.224978\pi$
$233$	7.62647e10	+	7.62647e10i	0.111057	+	0.111057i	−0.649395	+	0.760451i	$0.724978\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	4.46564e11	−	4.46564e11i	0.597230	−	0.597230i
$238$		0			0
$239$		−	1.36039e12i		−	1.74452i	−0.489046	−	0.872258i	$-0.662655\pi$
$239$		−	1.36039e12i		−	1.74452i	0.489046	−	0.872258i	$-0.337345\pi$
$240$		0			0
$241$	−1.06297e12			−1.30749			−0.653744	−	0.756716i	$-0.726803\pi$
$241$	−1.06297e12			−1.30749			−0.653744	+	0.756716i	$0.726803\pi$
$242$		0			0
$243$	−3.84338e10	−	3.84338e10i	−0.0453609	−	0.0453609i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	4.93080e11	−	4.93080e11i	0.536331	−	0.536331i
$248$		0			0
$249$		−	4.22145e11i		−	0.441027i
$250$		0			0
$251$	−1.03689e12			−1.04079			−0.520394	−	0.853926i	$-0.674215\pi$
$251$	−1.03689e12			−1.04079			−0.520394	+	0.853926i	$0.674215\pi$
$252$		0			0
$253$	−1.43998e12	−	1.43998e12i	−1.38916	−	1.38916i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−4.62266e10	+	4.62266e10i	−0.0412313	+	0.0412313i	−0.727422	−	0.686191i	$-0.759282\pi$
$257$	−4.62266e10	+	4.62266e10i	−0.0412313	+	0.0412313i	0.686191	+	0.727422i	$0.259282\pi$
$258$		0			0
$259$		−	9.56182e11i		−	0.820430i
$260$		0			0
$261$	1.12274e11			0.0926992
$262$		0			0
$263$	3.01166e11	+	3.01166e11i	0.239346	+	0.239346i	0.816579	−	0.577233i	$-0.195868\pi$
$263$	3.01166e11	+	3.01166e11i	0.239346	+	0.239346i	−0.577233	+	0.816579i	$0.695868\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−5.09565e11	+	5.09565e11i	−0.375529	+	0.375529i
$268$		0			0
$269$		−	1.71412e12i		−	1.21697i	−0.793566	−	0.608484i	$-0.791778\pi$
$269$		−	1.71412e12i		−	1.21697i	0.793566	−	0.608484i	$-0.208222\pi$
$270$		0			0
$271$	−1.97362e11			−0.135026			−0.0675130	−	0.997718i	$-0.521506\pi$
$271$	−1.97362e11			−0.135026			−0.0675130	+	0.997718i	$0.521506\pi$
$272$		0			0
$273$	2.14468e11	+	2.14468e11i	0.141432	+	0.141432i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	1.69708e12	−	1.69708e12i	1.04065	−	1.04065i	0.0415119	−	0.999138i	$-0.486783\pi$
$277$	1.69708e12	−	1.69708e12i	1.04065	−	1.04065i	0.999138	−	0.0415119i	$-0.0132174\pi$
$278$		0			0
$279$		−	1.00872e12i		−	0.596691i
$280$		0			0
$281$	−2.40584e12			−1.37320			−0.686602	−	0.727034i	$-0.740898\pi$
$281$	−2.40584e12			−1.37320			−0.686602	+	0.727034i	$0.740898\pi$
$282$		0			0
$283$	1.11917e12	+	1.11917e12i	0.616542	+	0.616542i	0.944643	−	0.328101i	$-0.106409\pi$
$283$	1.11917e12	+	1.11917e12i	0.616542	+	0.616542i	−0.328101	+	0.944643i	$0.606409\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	1.42471e12	−	1.42471e12i	0.731673	−	0.731673i
$288$		0			0
$289$		−	4.87380e12i		−	2.41757i
$290$		0			0
$291$	−1.20301e12			−0.576509
$292$		0			0
$293$	2.41635e12	+	2.41635e12i	1.11898	+	1.11898i	0.991892	+	0.127088i	$0.0405629\pi$
$293$	2.41635e12	+	2.41635e12i	1.11898	+	1.11898i	0.127088	+	0.991892i	$0.459437\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−4.11300e11	+	4.11300e11i	−0.177982	+	0.177982i
$298$		0			0
$299$		−	2.05242e12i		−	0.858835i
$300$		0			0
$301$	−1.15383e12			−0.466993
$302$		0			0
$303$	−7.09061e11	−	7.09061e11i	−0.277633	−	0.277633i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	3.02668e12	−	3.02668e12i	1.10988	−	1.10988i	0.116709	−	0.993166i	$-0.462766\pi$
$307$	3.02668e12	−	3.02668e12i	1.10988	−	1.10988i	0.993166	−	0.116709i	$-0.0372344\pi$
$308$		0			0
$309$			8.95101e11i			0.317746i
$310$		0			0
$311$	1.69628e12			0.583035			0.291518	−	0.956565i	$-0.405840\pi$
$311$	1.69628e12			0.583035			0.291518	+	0.956565i	$0.405840\pi$
$312$		0			0
$313$	−5.40666e11	−	5.40666e11i	−0.179973	−	0.179973i	0.611371	−	0.791344i	$-0.290618\pi$
$313$	−5.40666e11	−	5.40666e11i	−0.179973	−	0.179973i	−0.791344	+	0.611371i	$0.790618\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	2.24802e12	−	2.24802e12i	0.702270	−	0.702270i	−0.262627	−	0.964897i	$-0.584589\pi$
$317$	2.24802e12	−	2.24802e12i	0.702270	−	0.702270i	0.964897	+	0.262627i	$0.0845889\pi$
$318$		0			0
$319$		−	1.20150e12i		−	0.363723i
$320$		0			0
$321$	−9.10172e11			−0.267054
$322$		0			0
$323$	−6.09661e12	−	6.09661e12i	−1.73411	−	1.73411i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	1.63451e12	−	1.63451e12i	0.437169	−	0.437169i
$328$		0			0
$329$			2.44999e12i			0.635602i
$330$		0			0
$331$	6.79825e12			1.71103			0.855515	−	0.517779i	$-0.173241\pi$
$331$	6.79825e12			1.71103			0.855515	+	0.517779i	$0.173241\pi$
$332$		0			0
$333$	1.30683e12	+	1.30683e12i	0.319151	+	0.319151i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	1.52159e11	−	1.52159e11i	0.0350064	−	0.0350064i	−0.689387	−	0.724393i	$-0.742120\pi$
$337$	1.52159e11	−	1.52159e11i	0.0350064	−	0.0350064i	0.724393	+	0.689387i	$0.242120\pi$
$338$		0			0
$339$		−	3.74358e12i		−	0.836158i
$340$		0			0
$341$	−1.07948e13			−2.34123
$342$		0			0
$343$	3.32136e12	+	3.32136e12i	0.699593	+	0.699593i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−1.75499e12	+	1.75499e12i	−0.348841	+	0.348841i	−0.859678	−	0.510836i	$-0.829336\pi$
$347$	−1.75499e12	+	1.75499e12i	−0.348841	+	0.348841i	0.510836	+	0.859678i	$0.329336\pi$
$348$		0			0
$349$		−	9.66511e11i		−	0.186672i	−0.995635	−	0.0933361i	$-0.970247\pi$
$349$		−	9.66511e11i		−	0.186672i	0.995635	−	0.0933361i	$-0.0297531\pi$
$350$		0			0
$351$	−5.86232e11			−0.110036
$352$		0			0
$353$	4.92472e12	+	4.92472e12i	0.898479	+	0.898479i	0.995302	−	0.0968229i	$-0.0308680\pi$
$353$	4.92472e12	+	4.92472e12i	0.898479	+	0.898479i	−0.0968229	+	0.995302i	$0.530868\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	2.65175e12	−	2.65175e12i	0.457290	−	0.457290i
$358$		0			0
$359$		−	4.76241e12i		−	0.798647i	−0.916810	−	0.399323i	$-0.869245\pi$
$359$		−	4.76241e12i		−	0.798647i	0.916810	−	0.399323i	$-0.130755\pi$
$360$		0			0
$361$	−4.65841e12			−0.759805
$362$		0			0
$363$	1.82844e12	+	1.82844e12i	0.290099	+	0.290099i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	3.16749e12	−	3.16749e12i	0.475756	−	0.475756i	−0.428015	−	0.903771i	$-0.640787\pi$
$367$	3.16749e12	−	3.16749e12i	0.475756	−	0.475756i	0.903771	+	0.428015i	$0.140787\pi$
$368$		0			0
$369$			3.89434e12i			0.569249i
$370$		0			0
$371$	−2.70354e12			−0.384648
$372$		0			0
$373$	3.95182e12	+	3.95182e12i	0.547335	+	0.547335i	0.925669	−	0.378334i	$-0.123503\pi$
$373$	3.95182e12	+	3.95182e12i	0.547335	+	0.547335i	−0.378334	+	0.925669i	$0.623503\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	8.56258e11	−	8.56258e11i	0.112434	−	0.112434i
$378$		0			0
$379$			7.42741e12i			0.949820i	0.880034	+	0.474910i	$0.157519\pi$
$379$			7.42741e12i			0.949820i	−0.880034	+	0.474910i	$0.842481\pi$
$380$		0			0
$381$	7.31909e12			0.911659
$382$		0			0
$383$	3.60761e12	+	3.60761e12i	0.437749	+	0.437749i	0.891254	−	0.453505i	$-0.149826\pi$
$383$	3.60761e12	+	3.60761e12i	0.437749	+	0.437749i	−0.453505	+	0.891254i	$0.649826\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	1.57696e12	−	1.57696e12i	0.181663	−	0.181663i
$388$		0			0
$389$		−	8.93967e12i		−	1.00363i	−0.864975	−	0.501815i	$-0.832666\pi$
$389$		−	8.93967e12i		−	1.00363i	0.864975	−	0.501815i	$-0.167334\pi$
$390$		0			0
$391$	−2.53768e13			−2.77685
$392$		0			0
$393$	−1.64650e12	−	1.64650e12i	−0.175631	−	0.175631i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−1.31198e12	+	1.31198e12i	−0.133038	+	0.133038i	−0.770490	−	0.637452i	$-0.779988\pi$
$397$	−1.31198e12	+	1.31198e12i	−0.133038	+	0.133038i	0.637452	+	0.770490i	$0.279988\pi$
$398$		0			0
$399$		−	4.69293e12i		−	0.464066i
$400$		0			0
$401$	1.36580e13			1.31724			0.658621	−	0.752474i	$-0.271140\pi$
$401$	1.36580e13			1.31724			0.658621	+	0.752474i	$0.271140\pi$
$402$		0			0
$403$	−7.69301e12	−	7.69301e12i	−0.723721	−	0.723721i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	1.39850e13	−	1.39850e13i	1.25225	−	1.25225i
$408$		0			0
$409$		−	1.61871e13i		−	1.41433i	−0.707047	−	0.707167i	$-0.749973\pi$
$409$		−	1.61871e13i		−	1.41433i	0.707047	−	0.707167i	$-0.250027\pi$
$410$		0			0
$411$	6.19773e12			0.528474
$412$		0			0
$413$	−2.55629e12	−	2.55629e12i	−0.212745	−	0.212745i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−5.87206e12	+	5.87206e12i	−0.465704	+	0.465704i
$418$		0			0
$419$			2.32208e13i			1.79807i	0.437878	+	0.899034i	$0.355730\pi$
$419$			2.32208e13i			1.79807i	−0.437878	+	0.899034i	$0.644270\pi$
$420$		0			0
$421$	1.09179e13			0.825525			0.412763	−	0.910839i	$-0.364564\pi$
$421$	1.09179e13			0.825525			0.412763	+	0.910839i	$0.364564\pi$
$422$		0			0
$423$	−3.34844e12	−	3.34844e12i	−0.247252	−	0.247252i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−8.55389e12	+	8.55389e12i	−0.602593	+	0.602593i
$428$		0			0
$429$			6.27358e12i			0.431746i
$430$		0			0
$431$	6.17083e10			0.00414913			0.00207457	−	0.999998i	$-0.499340\pi$
$431$	6.17083e10			0.00414913			0.00207457	+	0.999998i	$0.499340\pi$
$432$		0			0
$433$	4.78623e12	+	4.78623e12i	0.314452	+	0.314452i	0.846631	−	0.532180i	$-0.178627\pi$
$433$	4.78623e12	+	4.78623e12i	0.314452	+	0.314452i	−0.532180	+	0.846631i	$0.678627\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−2.24553e13	+	2.24553e13i	−1.40900	+	1.40900i
$438$		0			0
$439$			1.40285e13i			0.860379i	0.902739	+	0.430189i	$0.141553\pi$
$439$			1.40285e13i			0.860379i	−0.902739	+	0.430189i	$0.858447\pi$
$440$		0			0
$441$	−3.51875e12			−0.210958
$442$		0			0
$443$	1.29559e13	+	1.29559e13i	0.759360	+	0.759360i	0.976206	−	0.216846i	$-0.0695770\pi$
$443$	1.29559e13	+	1.29559e13i	0.759360	+	0.759360i	−0.216846	+	0.976206i	$0.569577\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	4.17029e12	−	4.17029e12i	0.233684	−	0.233684i
$448$		0			0
$449$		−	5.75644e12i		−	0.315444i	−0.987484	−	0.157722i	$-0.949585\pi$
$449$		−	5.75644e12i		−	0.315444i	0.987484	−	0.157722i	$-0.0504149\pi$
$450$		0			0
$451$	4.16754e13			2.23356
$452$		0			0
$453$	−4.82618e12	−	4.82618e12i	−0.252995	−	0.252995i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−3.80895e11	+	3.80895e11i	−0.0191084	+	0.0191084i	−0.716596	−	0.697488i	$-0.754301\pi$
$457$	−3.80895e11	+	3.80895e11i	−0.0191084	+	0.0191084i	0.697488	+	0.716596i	$0.254301\pi$
$458$		0			0
$459$			7.24837e12i			0.355776i
$460$		0			0
$461$	−2.80786e13			−1.34856			−0.674280	−	0.738476i	$-0.735546\pi$
$461$	−2.80786e13			−1.34856			−0.674280	+	0.738476i	$0.735546\pi$
$462$		0			0
$463$	−1.72017e13	−	1.72017e13i	−0.808473	−	0.808473i	0.175930	−	0.984403i	$-0.443707\pi$
$463$	−1.72017e13	−	1.72017e13i	−0.808473	−	0.808473i	−0.984403	+	0.175930i	$0.943707\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−2.53677e13	+	2.53677e13i	−1.14208	+	1.14208i	−0.154011	+	0.988069i	$0.549219\pi$
$467$	−2.53677e13	+	2.53677e13i	−1.14208	+	1.14208i	−0.988069	+	0.154011i	$0.950781\pi$
$468$		0			0
$469$			2.33992e13i			1.03119i
$470$		0			0
$471$	−5.91196e12			−0.255051
$472$		0			0
$473$	−1.68759e13	−	1.68759e13i	−0.712789	−	0.712789i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	3.69497e12	−	3.69497e12i	0.149630	−	0.149630i
$478$		0			0
$479$		−	1.52110e13i		−	0.603227i	−0.953430	−	0.301614i	$-0.902475\pi$
$479$		−	1.52110e13i		−	0.603227i	0.953430	−	0.301614i	$-0.0975253\pi$
$480$		0			0
$481$	1.99331e13			0.774192
$482$		0			0
$483$	−9.76703e12	−	9.76703e12i	−0.371558	−	0.371558i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	1.45349e13	−	1.45349e13i	0.530600	−	0.530600i	−0.390151	−	0.920751i	$-0.627577\pi$
$487$	1.45349e13	−	1.45349e13i	0.530600	−	0.530600i	0.920751	+	0.390151i	$0.127577\pi$
$488$		0			0
$489$		−	2.13502e11i		−	0.00763585i
$490$		0			0
$491$	2.13225e13			0.747189			0.373595	−	0.927592i	$-0.378125\pi$
$491$	2.13225e13			0.747189			0.373595	+	0.927592i	$0.378125\pi$
$492$		0			0
$493$	−1.05871e13	−	1.05871e13i	−0.363530	−	0.363530i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	2.27760e12	−	2.27760e12i	0.0751097	−	0.0751097i
$498$		0			0
$499$			1.85069e12i			0.0598178i	0.999553	+	0.0299089i	$0.00952171\pi$
$499$			1.85069e12i			0.0598178i	−0.999553	+	0.0299089i	$0.990478\pi$
$500$		0			0
$501$	−1.03543e13			−0.328044
$502$		0			0
$503$	−3.46692e11	−	3.46692e11i	−0.0107672	−	0.0107672i	0.701703	−	0.712470i	$-0.252424\pi$
$503$	−3.46692e11	−	3.46692e11i	−0.0107672	−	0.0107672i	−0.712470	+	0.701703i	$0.752424\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	9.20525e12	−	9.20525e12i	0.274787	−	0.274787i
$508$		0			0
$509$			1.14179e13i			0.334193i	0.985941	+	0.167096i	$0.0534391\pi$
$509$			1.14179e13i			0.334193i	−0.985941	+	0.167096i	$0.946561\pi$
$510$		0			0
$511$	7.88947e12			0.226435
$512$		0			0
$513$	6.41390e12	+	6.41390e12i	0.180524	+	0.180524i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−3.58334e13	+	3.58334e13i	−0.970142	+	0.970142i
$518$		0			0
$519$			1.66433e13i			0.441980i
$520$		0			0
$521$	2.65456e13			0.691520			0.345760	−	0.938323i	$-0.387621\pi$
$521$	2.65456e13			0.691520			0.345760	+	0.938323i	$0.387621\pi$
$522$		0			0
$523$	6.46695e12	+	6.46695e12i	0.165269	+	0.165269i	0.784896	−	0.619627i	$-0.212716\pi$
$523$	6.46695e12	+	6.46695e12i	0.165269	+	0.165269i	−0.619627	+	0.784896i	$0.712716\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−9.51190e13	+	9.51190e13i	−2.33999	+	2.33999i
$528$		0			0
$529$			5.20423e13i			1.25626i
$530$		0			0
$531$	6.98743e12			0.165518
$532$		0			0
$533$	2.97003e13	+	2.97003e13i	0.690437	+	0.690437i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−2.59127e13	+	2.59127e13i	−0.580284	+	0.580284i
$538$		0			0
$539$			3.76560e13i			0.827732i
$540$		0			0
$541$	1.19367e13			0.257572			0.128786	−	0.991672i	$-0.458892\pi$
$541$	1.19367e13			0.257572			0.128786	+	0.991672i	$0.458892\pi$
$542$		0			0
$543$	8.56326e12	+	8.56326e12i	0.181401	+	0.181401i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	1.36800e13	−	1.36800e13i	0.279351	−	0.279351i	−0.553499	−	0.832850i	$-0.686708\pi$
$547$	1.36800e13	−	1.36800e13i	0.279351	−	0.279351i	0.832850	+	0.553499i	$0.186708\pi$
$548$		0			0
$549$		−	2.33815e13i		−	0.468824i
$550$		0			0
$551$	−1.87365e13			−0.368918
$552$		0			0
$553$	−3.24143e13	−	3.24143e13i	−0.626774	−	0.626774i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−3.09569e13	+	3.09569e13i	−0.577406	+	0.577406i	−0.934188	−	0.356781i	$-0.883874\pi$
$557$	−3.09569e13	+	3.09569e13i	−0.577406	+	0.577406i	0.356781	+	0.934188i	$0.383874\pi$
$558$		0			0
$559$		−	2.40534e13i		−	0.440675i
$560$		0			0
$561$	7.75686e13			1.39596
$562$		0			0
$563$	−9.42373e12	−	9.42373e12i	−0.166602	−	0.166602i	0.618882	−	0.785484i	$-0.287586\pi$
$563$	−9.42373e12	−	9.42373e12i	−0.166602	−	0.166602i	−0.785484	+	0.618882i	$0.787586\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−2.78976e12	+	2.78976e12i	−0.0476048	+	0.0476048i
$568$		0			0
$569$			8.59536e13i			1.44113i	0.693388	+	0.720564i	$0.256117\pi$
$569$			8.59536e13i			1.44113i	−0.693388	+	0.720564i	$0.743883\pi$
$570$		0			0
$571$	−1.65179e12			−0.0272129			−0.0136065	−	0.999907i	$-0.504331\pi$
$571$	−1.65179e12			−0.0272129			−0.0136065	+	0.999907i	$0.504331\pi$
$572$		0			0
$573$	−1.11282e13	−	1.11282e13i	−0.180158	−	0.180158i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−1.15632e13	+	1.15632e13i	−0.180800	+	0.180800i	−0.791704	−	0.610904i	$-0.790806\pi$
$577$	−1.15632e13	+	1.15632e13i	−0.180800	+	0.180800i	0.610904	+	0.791704i	$0.290806\pi$
$578$		0			0
$579$			5.18317e13i			0.796531i
$580$		0			0
$581$	−3.06419e13			−0.462844
$582$		0			0
$583$	−3.95418e13	−	3.95418e13i	−0.587103	−	0.587103i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	2.25763e13	−	2.25763e13i	0.323938	−	0.323938i	−0.526337	−	0.850276i	$-0.676435\pi$
$587$	2.25763e13	−	2.25763e13i	0.323938	−	0.323938i	0.850276	+	0.526337i	$0.176435\pi$
$588$		0			0
$589$			1.68337e14i			2.37467i
$590$		0			0
$591$	7.16797e13			0.994165
$592$		0			0
$593$	5.57368e13	+	5.57368e13i	0.760097	+	0.760097i	0.976340	−	0.216243i	$-0.0693803\pi$
$593$	5.57368e13	+	5.57368e13i	0.760097	+	0.760097i	−0.216243	+	0.976340i	$0.569380\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	5.64551e13	−	5.64551e13i	0.744444	−	0.744444i
$598$		0			0
$599$			1.03949e14i			1.34799i	0.738734	+	0.673997i	$0.235424\pi$
$599$			1.03949e14i			1.34799i	−0.738734	+	0.673997i	$0.764576\pi$
$600$		0			0
$601$	5.36047e13			0.683645			0.341822	−	0.939765i	$-0.388956\pi$
$601$	5.36047e13			0.683645			0.341822	+	0.939765i	$0.388956\pi$
$602$		0			0
$603$	−3.19800e13	−	3.19800e13i	−0.401137	−	0.401137i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−2.03880e13	+	2.03880e13i	−0.247418	+	0.247418i	−0.819910	−	0.572492i	$-0.805977\pi$
$607$	−2.03880e13	+	2.03880e13i	−0.247418	+	0.247418i	0.572492	+	0.819910i	$0.305977\pi$
$608$		0			0
$609$		−	8.14951e12i		−	0.0972848i
$610$		0			0
$611$	−5.10738e13			−0.599780
$612$		0			0
$613$	7.50159e13	+	7.50159e13i	0.866665	+	0.866665i	0.992102	−	0.125437i	$-0.0400333\pi$
$613$	7.50159e13	+	7.50159e13i	0.866665	+	0.866665i	−0.125437	+	0.992102i	$0.540033\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	1.61989e13	−	1.61989e13i	0.181158	−	0.181158i	−0.610702	−	0.791860i	$-0.709113\pi$
$617$	1.61989e13	−	1.61989e13i	0.181158	−	0.181158i	0.791860	+	0.610702i	$0.209113\pi$
$618$		0			0
$619$		−	3.79955e13i		−	0.418098i	−0.977905	−	0.209049i	$-0.932963\pi$
$619$		−	3.79955e13i		−	0.418098i	0.977905	−	0.209049i	$-0.0670369\pi$
$620$		0			0
$621$	2.66975e13			0.289076
$622$		0			0
$623$	3.69873e13	+	3.69873e13i	0.394105	+	0.394105i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	6.86385e13	−	6.86385e13i	0.708321	−	0.708321i
$628$		0			0
$629$		−	2.46459e14i		−	2.50318i
$630$		0			0
$631$	3.49133e13			0.349015			0.174508	−	0.984656i	$-0.444167\pi$
$631$	3.49133e13			0.349015			0.174508	+	0.984656i	$0.444167\pi$
$632$		0			0
$633$	−5.70695e13	−	5.70695e13i	−0.561546	−	0.561546i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−2.68358e13	+	2.68358e13i	−0.255869	+	0.255869i
$638$		0			0
$639$			6.22566e12i			0.0584361i
$640$		0			0
$641$	−1.07560e14			−0.993943			−0.496971	−	0.867767i	$-0.665555\pi$
$641$	−1.07560e14			−0.993943			−0.496971	+	0.867767i	$0.665555\pi$
$642$		0			0
$643$	2.84495e13	+	2.84495e13i	0.258833	+	0.258833i	0.824579	−	0.565746i	$-0.191412\pi$
$643$	2.84495e13	+	2.84495e13i	0.258833	+	0.258833i	−0.565746	+	0.824579i	$0.691412\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−8.83966e13	+	8.83966e13i	−0.779676	+	0.779676i	−0.979776	−	0.200100i	$-0.935873\pi$
$647$	−8.83966e13	+	8.83966e13i	−0.779676	+	0.779676i	0.200100	+	0.979776i	$0.435873\pi$
$648$		0			0
$649$		−	7.47762e13i		−	0.649442i
$650$		0			0
$651$	−7.32189e13			−0.626208
$652$		0			0
$653$	−8.72650e13	−	8.72650e13i	−0.734978	−	0.734978i	0.236624	−	0.971601i	$-0.423959\pi$
$653$	−8.72650e13	−	8.72650e13i	−0.734978	−	0.734978i	−0.971601	+	0.236624i	$0.923959\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−1.07826e13	+	1.07826e13i	−0.0880843	+	0.0880843i
$658$		0			0
$659$			1.83344e14i			1.47516i	0.675259	+	0.737581i	$0.264032\pi$
$659$			1.83344e14i			1.47516i	−0.675259	+	0.737581i	$0.735968\pi$
$660$		0			0
$661$	1.83329e14			1.45286			0.726431	−	0.687240i	$-0.241178\pi$
$661$	1.83329e14			1.45286			0.726431	+	0.687240i	$0.241178\pi$
$662$		0			0
$663$	5.52798e13	+	5.52798e13i	0.431518	+	0.431518i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−3.89947e13	+	3.89947e13i	−0.295377	+	0.295377i
$668$		0			0
$669$			4.98588e13i			0.372059i
$670$		0			0
$671$	−2.50217e14			−1.83952
$672$		0			0
$673$	9.40905e13	+	9.40905e13i	0.681507	+	0.681507i	0.960340	−	0.278833i	$-0.0899475\pi$
$673$	9.40905e13	+	9.40905e13i	0.681507	+	0.681507i	−0.278833	+	0.960340i	$0.589948\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−1.28688e14	+	1.28688e14i	−0.904890	+	0.904890i	−0.995854	−	0.0909645i	$-0.971005\pi$
$677$	−1.28688e14	+	1.28688e14i	−0.904890	+	0.904890i	0.0909645	+	0.995854i	$0.471005\pi$
$678$		0			0
$679$			8.73221e13i			0.605027i
$680$		0			0
$681$	7.40009e13			0.505244
$682$		0			0
$683$	−9.01742e13	−	9.01742e13i	−0.606707	−	0.606707i	0.335377	−	0.942084i	$-0.391136\pi$
$683$	−9.01742e13	−	9.01742e13i	−0.606707	−	0.606707i	−0.942084	+	0.335377i	$0.891136\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−3.19607e13	+	3.19607e13i	−0.208849	+	0.208849i
$688$		0			0
$689$		−	5.63595e13i		−	0.362970i
$690$		0			0
$691$	−2.88538e13			−0.183152			−0.0915761	−	0.995798i	$-0.529190\pi$
$691$	−2.88538e13			−0.183152			−0.0915761	+	0.995798i	$0.529190\pi$
$692$		0			0
$693$	2.98547e13	+	2.98547e13i	0.186787	+	0.186787i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	3.67224e14	−	3.67224e14i	2.23237	−	2.23237i
$698$		0			0
$699$			1.51316e13i			0.0906773i
$700$		0			0
$701$	1.08852e14			0.643050			0.321525	−	0.946901i	$-0.395805\pi$
$701$	1.08852e14			0.643050			0.321525	+	0.946901i	$0.395805\pi$
$702$		0			0
$703$	−2.18086e14	−	2.18086e14i	−1.27014	−	1.27014i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−5.14679e13	+	5.14679e13i	−0.291367	+	0.291367i
$708$		0			0
$709$		−	9.60857e13i		−	0.536324i	−0.963374	−	0.268162i	$-0.913584\pi$
$709$		−	9.60857e13i		−	0.536324i	0.963374	−	0.268162i	$-0.0864163\pi$
$710$		0			0
$711$	8.86021e13			0.487636
$712$		0			0
$713$	3.50346e14	+	3.50346e14i	1.90130	+	1.90130i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	1.34957e14	−	1.34957e14i	0.712196	−	0.712196i
$718$		0			0
$719$		−	3.79279e14i		−	1.97385i	−0.161183	−	0.986925i	$-0.551531\pi$
$719$		−	3.79279e14i		−	1.97385i	0.161183	−	0.986925i	$-0.448469\pi$
$720$		0			0
$721$	6.49718e13			0.333464
$722$		0			0
$723$	−1.05452e14	−	1.05452e14i	−0.533780	−	0.533780i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	8.62253e12	−	8.62253e12i	0.0424583	−	0.0424583i	−0.685559	−	0.728017i	$-0.740442\pi$
$727$	8.62253e12	−	8.62253e12i	0.0424583	−	0.0424583i	0.728017	+	0.685559i	$0.240442\pi$
$728$		0			0
$729$		−	7.62560e12i		−	0.0370370i
$730$		0			0
$731$	−2.97405e14			−1.42482
$732$		0			0
$733$	−1.88332e14	−	1.88332e14i	−0.890027	−	0.890027i	0.104498	−	0.994525i	$-0.466676\pi$
$733$	−1.88332e14	−	1.88332e14i	−0.890027	−	0.890027i	−0.994525	+	0.104498i	$0.966676\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−3.42235e14	+	3.42235e14i	−1.57394	+	1.57394i
$738$		0			0
$739$		−	1.98337e14i		−	0.899875i	−0.893060	−	0.449938i	$-0.851446\pi$
$739$		−	1.98337e14i		−	0.899875i	0.893060	−	0.449938i	$-0.148554\pi$
$740$		0			0
$741$	9.78314e13			0.437913
$742$		0			0
$743$	2.66974e14	+	2.66974e14i	1.17903	+	1.17903i	0.979991	+	0.199041i	$0.0637826\pi$
$743$	2.66974e14	+	2.66974e14i	1.17903	+	1.17903i	0.199041	+	0.979991i	$0.436217\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	4.18787e13	−	4.18787e13i	0.180049	−	0.180049i
$748$		0			0
$749$			6.60658e13i			0.280264i
$750$		0			0
$751$	−2.86741e14			−1.20030			−0.600151	−	0.799887i	$-0.704893\pi$
$751$	−2.86741e14			−1.20030			−0.600151	+	0.799887i	$0.704893\pi$
$752$		0			0
$753$	−1.02864e14	−	1.02864e14i	−0.424900	−	0.424900i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	2.58996e14	−	2.58996e14i	1.04187	−	1.04187i	0.0427859	−	0.999084i	$-0.486377\pi$
$757$	2.58996e14	−	2.58996e14i	1.04187	−	1.04187i	0.999084	−	0.0427859i	$-0.0136233\pi$
$758$		0			0
$759$		−	2.85704e14i		−	1.13425i
$760$		0			0
$761$	−3.22759e14			−1.26461			−0.632303	−	0.774721i	$-0.717890\pi$
$761$	−3.22759e14			−1.26461			−0.632303	+	0.774721i	$0.717890\pi$
$762$		0			0
$763$	−1.18643e14	−	1.18643e14i	−0.458794	−	0.458794i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	5.32898e13	−	5.32898e13i	0.200755	−	0.200755i
$768$		0			0
$769$		−	4.09908e14i		−	1.52425i	−0.647432	−	0.762123i	$-0.724157\pi$
$769$		−	4.09908e14i		−	1.52425i	0.647432	−	0.762123i	$-0.275843\pi$
$770$		0			0
$771$	−9.17177e12			−0.0336652
$772$		0			0
$773$	−6.15259e13	−	6.15259e13i	−0.222926	−	0.222926i	0.586804	−	0.809729i	$-0.300386\pi$
$773$	−6.15259e13	−	6.15259e13i	−0.222926	−	0.222926i	−0.809729	+	0.586804i	$0.800386\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	9.48574e13	−	9.48574e13i	0.334939	−	0.334939i
$778$		0			0
$779$		−	6.49895e14i		−	2.26546i
$780$		0			0
$781$	6.66241e13			0.229285
$782$		0			0
$783$	1.11380e13	+	1.11380e13i	0.0378443	+	0.0378443i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	4.11706e14	−	4.11706e14i	1.36368	−	1.36368i	0.494514	−	0.869170i	$-0.335346\pi$
$787$	4.11706e14	−	4.11706e14i	1.36368	−	1.36368i	0.869170	−	0.494514i	$-0.164654\pi$
$788$		0			0
$789$			5.97539e13i			0.195425i
$790$		0			0
$791$	−2.71731e14			−0.877521
$792$		0			0
$793$	−1.78319e14	−	1.78319e14i	−0.568633	−	0.568633i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	3.03789e14	−	3.03789e14i	0.944669	−	0.944669i	−0.0538784	−	0.998548i	$-0.517158\pi$
$797$	3.03789e14	−	3.03789e14i	0.944669	−	0.944669i	0.998548	+	0.0538784i	$0.0171583\pi$
$798$		0			0
$799$			6.31494e14i			1.93926i
$800$		0			0
$801$	−1.01102e14			−0.306618
$802$		0			0
$803$	1.15391e14	+	1.15391e14i	0.345616	+	0.345616i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	1.70048e14	−	1.70048e14i	0.496825	−	0.496825i
$808$		0			0
$809$		−	1.38909e14i		−	0.400855i	−0.979709	−	0.200427i	$-0.935767\pi$
$809$		−	1.38909e14i		−	0.400855i	0.979709	−	0.200427i	$-0.0642331\pi$
$810$		0			0
$811$	2.49867e14			0.712205			0.356102	−	0.934447i	$-0.384105\pi$
$811$	2.49867e14			0.712205			0.356102	+	0.934447i	$0.384105\pi$
$812$		0			0
$813$	−1.95792e13	−	1.95792e13i	−0.0551241	−	0.0551241i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−2.63166e14	+	2.63166e14i	−0.722969	+	0.722969i
$818$		0			0
$819$			4.25522e13i			0.115479i
$820$		0			0
$821$	6.70383e13			0.179725			0.0898623	−	0.995954i	$-0.471357\pi$
$821$	6.70383e13			0.179725			0.0898623	+	0.995954i	$0.471357\pi$
$822$		0			0
$823$	1.62975e14	+	1.62975e14i	0.431640	+	0.431640i	0.889186	−	0.457546i	$-0.151271\pi$
$823$	1.62975e14	+	1.62975e14i	0.431640	+	0.431640i	−0.457546	+	0.889186i	$0.651271\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−6.94880e13	+	6.94880e13i	−0.179631	+	0.179631i	−0.791195	−	0.611564i	$-0.790541\pi$
$827$	−6.94880e13	+	6.94880e13i	−0.179631	+	0.179631i	0.611564	+	0.791195i	$0.290541\pi$
$828$		0			0
$829$		−	4.99402e14i		−	1.27549i	−0.770247	−	0.637745i	$-0.779867\pi$
$829$		−	4.99402e14i		−	1.27549i	0.770247	−	0.637745i	$-0.220133\pi$
$830$		0			0
$831$	3.36716e14			0.849687
$832$		0			0
$833$	3.31806e14	+	3.31806e14i	0.827294	+	0.827294i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	1.00069e14	−	1.00069e14i	0.243598	−	0.243598i
$838$		0			0
$839$			1.56567e14i			0.376608i	0.982111	+	0.188304i	$0.0602991\pi$
$839$			1.56567e14i			0.376608i	−0.982111	+	0.188304i	$0.939701\pi$
$840$		0			0
$841$	3.88170e14			0.922662
$842$		0			0
$843$	−2.38670e14	−	2.38670e14i	−0.560608	−	0.560608i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	1.32719e14	−	1.32719e14i	0.304450	−	0.304450i
$848$		0			0
$849$			2.22052e14i			0.503404i
$850$		0			0
$851$	−9.07768e14			−2.03389
$852$		0			0
$853$	4.29292e14	+	4.29292e14i	0.950623	+	0.950623i	0.998837	−	0.0482144i	$-0.0153531\pi$
$853$	4.29292e14	+	4.29292e14i	0.950623	+	0.950623i	−0.0482144	+	0.998837i	$0.515353\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−3.47238e14	+	3.47238e14i	−0.751144	+	0.751144i	−0.974693	−	0.223549i	$-0.928236\pi$
$857$	−3.47238e14	+	3.47238e14i	−0.751144	+	0.751144i	0.223549	+	0.974693i	$0.428236\pi$
$858$		0			0
$859$		−	1.29397e14i		−	0.276668i	−0.990386	−	0.138334i	$-0.955825\pi$
$859$		−	1.29397e14i		−	0.276668i	0.990386	−	0.138334i	$-0.0441747\pi$
$860$		0			0
$861$	2.82675e14			0.597408
$862$		0			0
$863$	−1.94609e14	−	1.94609e14i	−0.406544	−	0.406544i	0.473987	−	0.880532i	$-0.342814\pi$
$863$	−1.94609e14	−	1.94609e14i	−0.406544	−	0.406544i	−0.880532	+	0.473987i	$0.842814\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	4.83502e14	−	4.83502e14i	0.986968	−	0.986968i
$868$		0			0
$869$		−	9.48178e14i		−	1.91334i
$870$		0			0
$871$	−4.87792e14			−0.973070
$872$		0			0
$873$	−1.19344e14	−	1.19344e14i	−0.235359	−	0.235359i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	5.55851e13	−	5.55851e13i	0.107142	−	0.107142i	−0.651503	−	0.758646i	$-0.725861\pi$
$877$	5.55851e13	−	5.55851e13i	0.107142	−	0.107142i	0.758646	+	0.651503i	$0.225861\pi$
$878$		0			0
$879$			4.79425e14i			0.913643i
$880$		0			0
$881$	−7.19628e14			−1.35590			−0.677951	−	0.735107i	$-0.737132\pi$
$881$	−7.19628e14			−1.35590			−0.677951	+	0.735107i	$0.737132\pi$
$882$		0			0
$883$	6.65284e14	+	6.65284e14i	1.23938	+	1.23938i	0.960256	+	0.279121i	$0.0900430\pi$
$883$	6.65284e14	+	6.65284e14i	1.23938	+	1.23938i	0.279121	+	0.960256i	$0.409957\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−3.30153e14	+	3.30153e14i	−0.601309	+	0.601309i	−0.940660	−	0.339351i	$-0.889793\pi$
$887$	−3.30153e14	+	3.30153e14i	−0.601309	+	0.601309i	0.339351	+	0.940660i	$0.389793\pi$
$888$		0			0
$889$		−	5.31264e14i		−	0.956756i
$890$		0			0
$891$	−8.16055e13			−0.145322
$892$		0			0
$893$	5.58793e14	+	5.58793e14i	0.983997	+	0.983997i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	2.03609e14	−	2.03609e14i	0.350618	−	0.350618i
$898$		0			0
$899$			2.92325e14i			0.497815i
$900$		0			0
$901$	−6.96848e14			−1.17358
$902$		0			0
$903$	−1.14465e14	−	1.14465e14i	−0.190649	−	0.190649i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	6.30833e14	−	6.30833e14i	1.02773	−	1.02773i	0.0281233	−	0.999604i	$-0.491047\pi$
$907$	6.30833e14	−	6.30833e14i	1.02773	−	1.02773i	0.999604	−	0.0281233i	$-0.00895311\pi$
$908$		0			0
$909$		−	1.40684e14i		−	0.226686i
$910$		0			0
$911$	−8.65279e14			−1.37900			−0.689500	−	0.724286i	$-0.742170\pi$
$911$	−8.65279e14			−1.37900			−0.689500	+	0.724286i	$0.742170\pi$
$912$		0			0
$913$	−4.48166e14	−	4.48166e14i	−0.706455	−	0.706455i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−1.19513e14	+	1.19513e14i	−0.184319	+	0.184319i
$918$		0			0
$919$			2.78551e14i			0.424940i	0.977168	+	0.212470i	$0.0681507\pi$
$919$			2.78551e14i			0.424940i	−0.977168	+	0.212470i	$0.931849\pi$
$920$		0			0
$921$	6.00519e14			0.906209
$922$		0			0
$923$	4.74801e13	+	4.74801e13i	0.0708767	+	0.0708767i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−8.87979e13	+	8.87979e13i	−0.129719	+	0.129719i
$928$		0			0
$929$			4.74213e14i			0.685323i	0.939459	+	0.342661i	$0.111328\pi$
$929$			4.74213e14i			0.685323i	−0.939459	+	0.342661i	$0.888672\pi$
$930$		0			0
$931$	5.87215e14			0.839554
$932$		0			0
$933$	1.68278e14	+	1.68278e14i	0.238023	+	0.238023i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	9.03103e14	−	9.03103e14i	1.25037	−	1.25037i	0.294819	−	0.955553i	$-0.404741\pi$
$937$	9.03103e14	−	9.03103e14i	1.25037	−	1.25037i	0.955553	−	0.294819i	$-0.0952595\pi$
$938$		0			0
$939$		−	1.07273e14i		−	0.146947i
$940$		0			0
$941$	6.28701e14			0.852111			0.426056	−	0.904697i	$-0.359903\pi$
$941$	6.28701e14			0.852111			0.426056	+	0.904697i	$0.359903\pi$
$942$		0			0
$943$	−1.35257e15	−	1.35257e15i	−1.81386	−	1.81386i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−3.19493e14	+	3.19493e14i	−0.419481	+	0.419481i	−0.885025	−	0.465544i	$-0.845859\pi$
$947$	−3.19493e14	+	3.19493e14i	−0.419481	+	0.419481i	0.465544	+	0.885025i	$0.345859\pi$
$948$		0			0
$949$			1.64468e14i			0.213673i
$950$		0			0
$951$	4.46027e14			0.573401
$952$		0			0
$953$	4.81840e14	+	4.81840e14i	0.612969	+	0.612969i	0.943719	−	0.330749i	$-0.107301\pi$
$953$	4.81840e14	+	4.81840e14i	0.612969	+	0.612969i	−0.330749	+	0.943719i	$0.607301\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	1.19194e14	−	1.19194e14i	0.148489	−	0.148489i
$958$		0			0
$959$		−	4.49868e14i		−	0.554616i
$960$		0			0
$961$	1.80675e15			2.20436
$962$		0			0
$963$	−9.02930e13	−	9.02930e13i	−0.109024	−	0.109024i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−2.62561e14	+	2.62561e14i	−0.310525	+	0.310525i	−0.845113	−	0.534588i	$-0.820467\pi$
$967$	−2.62561e14	+	2.62561e14i	−0.310525	+	0.310525i	0.534588	+	0.845113i	$0.320467\pi$
$968$		0			0
$969$		−	1.20962e15i		−	1.41589i
$970$		0			0
$971$	−1.55443e15			−1.80083			−0.900417	−	0.435028i	$-0.856739\pi$
$971$	−1.55443e15			−1.80083			−0.900417	+	0.435028i	$0.856739\pi$
$972$		0			0
$973$	4.26229e14	+	4.26229e14i	0.488741	+	0.488741i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−2.84883e14	+	2.84883e14i	−0.320033	+	0.320033i	−0.848780	−	0.528747i	$-0.822662\pi$
$977$	−2.84883e14	+	2.84883e14i	−0.320033	+	0.320033i	0.528747	+	0.848780i	$0.322662\pi$
$978$		0			0
$979$			1.08195e15i			1.20307i
$980$		0			0
$981$	3.24301e14			0.356947
$982$		0			0
$983$	−2.12965e14	−	2.12965e14i	−0.232028	−	0.232028i	0.581511	−	0.813539i	$-0.302462\pi$
$983$	−2.12965e14	−	2.12965e14i	−0.232028	−	0.232028i	−0.813539	+	0.581511i	$0.802462\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−2.43050e14	+	2.43050e14i	−0.259483	+	0.259483i
$988$		0			0
$989$			1.09541e15i			1.15770i
$990$		0			0
$991$	−4.52939e14			−0.473884			−0.236942	−	0.971524i	$-0.576145\pi$
$991$	−4.52939e14			−0.473884			−0.236942	+	0.971524i	$0.576145\pi$
$992$		0			0
$993$	6.74416e14	+	6.74416e14i	0.698525	+	0.698525i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−1.08484e15	+	1.08484e15i	−1.10126	+	1.10126i	−0.107000	+	0.994259i	$0.534125\pi$
$997$	−1.08484e15	+	1.08484e15i	−1.10126	+	1.10126i	−0.994259	+	0.107000i	$0.965875\pi$
$998$		0			0
$999$			2.59286e14i			0.260586i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.11.k.c.193.7	yes	16
5.2	odd	4	inner	300.11.k.c.157.7	yes	16
5.3	odd	4	inner	300.11.k.c.157.2	✓	16
5.4	even	2	inner	300.11.k.c.193.2	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.11.k.c.157.2	✓	16	5.3	odd	4	inner
300.11.k.c.157.7	yes	16	5.2	odd	4	inner
300.11.k.c.193.2	yes	16	5.4	even	2	inner
300.11.k.c.193.7	yes	16	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	300.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(99.2043 + 99.2043i) q^{3} +(7200.85 - 7200.85i) q^{7} +19683.0i q^{9} +O(q^{10})\)	\(q+(99.2043 + 99.2043i) q^{3} +(7200.85 - 7200.85i) q^{7} +19683.0i q^{9} +210638. q^{11} +(150113. + 150113. i) q^{13} +(1.85604e6 - 1.85604e6i) q^{17} -3.28473e6i q^{19} +1.42871e6 q^{21} +(-6.83626e6 - 6.83626e6i) q^{23} +(-1.95264e6 + 1.95264e6i) q^{27} -5.70410e6i q^{29} -5.12482e7 q^{31} +(2.08962e7 + 2.08962e7i) q^{33} +(6.63937e7 - 6.63937e7i) q^{37} +2.97837e7i q^{39} +1.97853e8 q^{41} +(-8.01179e7 - 8.01179e7i) q^{43} +(-1.70118e8 + 1.70118e8i) q^{47} +1.78771e8i q^{49} +3.68255e8 q^{51} +(-1.87724e8 - 1.87724e8i) q^{53} +(3.25860e8 - 3.25860e8i) q^{57} -3.54998e8i q^{59} -1.18790e9 q^{61} +(1.41734e8 + 1.41734e8i) q^{63} +(-1.62475e9 + 1.62475e9i) q^{67} -1.35637e9i q^{69} +3.16296e8 q^{71} +(5.47815e8 + 5.47815e8i) q^{73} +(1.51677e9 - 1.51677e9i) q^{77} -4.50145e9i q^{79} -3.87420e8 q^{81} +(-2.12766e9 - 2.12766e9i) q^{83} +(5.65871e8 - 5.65871e8i) q^{87} +5.13652e9i q^{89} +2.16188e9 q^{91} +(-5.08405e9 - 5.08405e9i) q^{93} +(-6.06332e9 + 6.06332e9i) q^{97} +4.14599e9i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q - 331104 q^{11} + 555984 q^{21} - 140804816 q^{31} + 29553600 q^{41} + 471062304 q^{51} + 3576862832 q^{61} + 1853192640 q^{71} - 6198727824 q^{81} + 7033272240 q^{91}+O(q^{100}) \) 16 * q - 331104 * q^11 + 555984 * q^21 - 140804816 * q^31 + 29553600 * q^41 + 471062304 * q^51 + 3576862832 * q^61 + 1853192640 * q^71 - 6198727824 * q^81 + 7033272240 * q^91

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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