LMFDB - Embedded newform 300.11.k.c.157.5

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			157.5
Root			$180.068 + 180.068i$ of defining polynomial
Character	$\chi$	$=$	300.157
Dual form			300.11.k.c.193.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(99.2043 - 99.2043i) q^{3} +(-17321.8 - 17321.8i) q^{7} -19683.0i q^{9} +O(q^{10})$	$q+(99.2043 - 99.2043i) q^{3} +(-17321.8 - 17321.8i) q^{7} -19683.0i q^{9} -25019.3 q^{11} +(200818. - 200818. i) q^{13} +(-1.64230e6 - 1.64230e6i) q^{17} +1.78076e6i q^{19} -3.43679e6 q^{21} +(-2.10849e6 + 2.10849e6i) q^{23} +(-1.95264e6 - 1.95264e6i) q^{27} -457423. i q^{29} -1.63013e7 q^{31} +(-2.48203e6 + 2.48203e6i) q^{33} +(-3.60544e7 - 3.60544e7i) q^{37} -3.98440e7i q^{39} -1.20098e8 q^{41} +(1.74588e8 - 1.74588e8i) q^{43} +(-2.51304e8 - 2.51304e8i) q^{47} +3.17612e8i q^{49} -3.25846e8 q^{51} +(-1.67752e8 + 1.67752e8i) q^{53} +(1.76659e8 + 1.76659e8i) q^{57} +973194. i q^{59} +7.13667e8 q^{61} +(-3.40944e8 + 3.40944e8i) q^{63} +(3.85420e8 + 3.85420e8i) q^{67} +4.18343e8i q^{69} +2.86695e9 q^{71} +(-2.05996e9 + 2.05996e9i) q^{73} +(4.33379e8 + 4.33379e8i) q^{77} -1.26224e8i q^{79} -3.87420e8 q^{81} +(1.02756e9 - 1.02756e9i) q^{83} +(-4.53784e7 - 4.53784e7i) q^{87} +4.06168e9i q^{89} -6.95705e9 q^{91} +(-1.61716e9 + 1.61716e9i) q^{93} +(1.33700e9 + 1.33700e9i) q^{97} +4.92455e8i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

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

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
$7$	−17321.8	−	17321.8i	−1.03063	−	1.03063i	−0.999516	−	0.0311123i	$-0.990095\pi$
$7$	−17321.8	−	17321.8i	−1.03063	−	1.03063i	−0.0311123	−	0.999516i	$-0.509905\pi$
$8$		0			0
$9$		−	19683.0i		−	0.333333i
$10$		0			0
$11$	−25019.3			−0.155350			−0.0776752	−	0.996979i	$-0.524750\pi$
$11$	−25019.3			−0.155350			−0.0776752	+	0.996979i	$0.524750\pi$
$12$		0			0
$13$	200818.	−	200818.i	0.540861	−	0.540861i	−0.382920	−	0.923781i	$-0.625082\pi$
$13$	200818.	−	200818.i	0.540861	−	0.540861i	0.923781	+	0.382920i	$0.125082\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.64230e6	−	1.64230e6i	−1.15666	−	1.15666i	−0.985189	−	0.171474i	$-0.945147\pi$
$17$	−1.64230e6	−	1.64230e6i	−1.15666	−	1.15666i	−0.171474	−	0.985189i	$-0.554853\pi$
$18$		0			0
$19$			1.78076e6i			0.719180i	0.933110	+	0.359590i	$0.117083\pi$
$19$			1.78076e6i			0.719180i	−0.933110	+	0.359590i	$0.882917\pi$
$20$		0			0
$21$	−3.43679e6			−0.841504
$22$		0			0
$23$	−2.10849e6	+	2.10849e6i	−0.327592	+	0.327592i	−0.851670	−	0.524078i	$-0.824410\pi$
$23$	−2.10849e6	+	2.10849e6i	−0.327592	+	0.327592i	0.524078	+	0.851670i	$0.324410\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−1.95264e6	−	1.95264e6i	−0.136083	−	0.136083i
$28$		0			0
$29$		−	457423.i		−	0.0223012i	−0.999938	−	0.0111506i	$-0.996451\pi$
$29$		−	457423.i		−	0.0223012i	0.999938	−	0.0111506i	$-0.00354942\pi$
$30$		0			0
$31$	−1.63013e7			−0.569395			−0.284697	−	0.958617i	$-0.591893\pi$
$31$	−1.63013e7			−0.569395			−0.284697	+	0.958617i	$0.591893\pi$
$32$		0			0
$33$	−2.48203e6	+	2.48203e6i	−0.0634215	+	0.0634215i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−3.60544e7	−	3.60544e7i	−0.519936	−	0.519936i	0.397616	−	0.917552i	$-0.369838\pi$
$37$	−3.60544e7	−	3.60544e7i	−0.519936	−	0.519936i	−0.917552	+	0.397616i	$0.869838\pi$
$38$		0			0
$39$		−	3.98440e7i		−	0.441611i
$40$		0			0
$41$	−1.20098e8			−1.03661			−0.518306	−	0.855195i	$-0.673437\pi$
$41$	−1.20098e8			−1.03661			−0.518306	+	0.855195i	$0.673437\pi$
$42$		0			0
$43$	1.74588e8	−	1.74588e8i	1.18761	−	1.18761i	0.209881	−	0.977727i	$-0.432692\pi$
$43$	1.74588e8	−	1.74588e8i	1.18761	−	1.18761i	0.977727	−	0.209881i	$-0.0673077\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−2.51304e8	−	2.51304e8i	−1.09575	−	1.09575i	−0.994902	−	0.100843i	$-0.967846\pi$
$47$	−2.51304e8	−	2.51304e8i	−1.09575	−	1.09575i	−0.100843	−	0.994902i	$-0.532154\pi$
$48$		0			0
$49$			3.17612e8i			1.12439i
$50$		0			0
$51$	−3.25846e8			−0.944411
$52$		0			0
$53$	−1.67752e8	+	1.67752e8i	−0.401134	+	0.401134i	−0.878632	−	0.477499i	$-0.841543\pi$
$53$	−1.67752e8	+	1.67752e8i	−0.401134	+	0.401134i	0.477499	+	0.878632i	$0.341543\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	1.76659e8	+	1.76659e8i	0.293604	+	0.293604i
$58$		0			0
$59$			973194.i			0.00136125i	1.00000		0.000680627i	$0.000216650\pi$
$59$			973194.i			0.00136125i	−1.00000		0.000680627i	$0.999783\pi$
$60$		0			0
$61$	7.13667e8			0.844981			0.422490	−	0.906367i	$-0.361156\pi$
$61$	7.13667e8			0.844981			0.422490	+	0.906367i	$0.361156\pi$
$62$		0			0
$63$	−3.40944e8	+	3.40944e8i	−0.343543	+	0.343543i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	3.85420e8	+	3.85420e8i	0.285470	+	0.285470i	0.835286	−	0.549816i	$-0.185302\pi$
$67$	3.85420e8	+	3.85420e8i	0.285470	+	0.285470i	−0.549816	+	0.835286i	$0.685302\pi$
$68$		0			0
$69$			4.18343e8i			0.267477i
$70$		0			0
$71$	2.86695e9			1.58902			0.794509	−	0.607253i	$-0.207728\pi$
$71$	2.86695e9			1.58902			0.794509	+	0.607253i	$0.207728\pi$
$72$		0			0
$73$	−2.05996e9	+	2.05996e9i	−0.993673	+	0.993673i	−0.999980	−	0.00630706i	$-0.997992\pi$
$73$	−2.05996e9	+	2.05996e9i	−0.993673	+	0.993673i	0.00630706	+	0.999980i	$0.497992\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	4.33379e8	+	4.33379e8i	0.160108	+	0.160108i
$78$		0			0
$79$		−	1.26224e8i		−	0.0410209i	−0.999790	−	0.0205104i	$-0.993471\pi$
$79$		−	1.26224e8i		−	0.0410209i	0.999790	−	0.0205104i	$-0.00652914\pi$
$80$		0			0
$81$	−3.87420e8			−0.111111
$82$		0			0
$83$	1.02756e9	−	1.02756e9i	0.260866	−	0.260866i	−0.564540	−	0.825406i	$-0.690946\pi$
$83$	1.02756e9	−	1.02756e9i	0.260866	−	0.260866i	0.825406	+	0.564540i	$0.190946\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−4.53784e7	−	4.53784e7i	−0.00910443	−	0.00910443i
$88$		0			0
$89$			4.06168e9i			0.727370i	0.931522	+	0.363685i	$0.118481\pi$
$89$			4.06168e9i			0.727370i	−0.931522	+	0.363685i	$0.881519\pi$
$90$		0			0
$91$	−6.95705e9			−1.11485
$92$		0			0
$93$	−1.61716e9	+	1.61716e9i	−0.232454	+	0.232454i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	1.33700e9	+	1.33700e9i	0.155694	+	0.155694i	0.780655	−	0.624962i	$-0.214885\pi$
$97$	1.33700e9	+	1.33700e9i	0.155694	+	0.155694i	−0.624962	+	0.780655i	$0.714885\pi$
$98$		0			0
$99$			4.92455e8i			0.0517834i
$100$		0			0
$101$	1.06671e10			1.01493			0.507467	−	0.861671i	$-0.330582\pi$
$101$	1.06671e10			1.01493			0.507467	+	0.861671i	$0.330582\pi$
$102$		0			0
$103$	−1.35915e10	+	1.35915e10i	−1.17242	+	1.17242i	−0.190783	+	0.981632i	$0.561103\pi$
$103$	−1.35915e10	+	1.35915e10i	−1.17242	+	1.17242i	−0.981632	+	0.190783i	$0.938897\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−1.18057e10	−	1.18057e10i	−0.841730	−	0.841730i	0.147354	−	0.989084i	$-0.452924\pi$
$107$	−1.18057e10	−	1.18057e10i	−0.841730	−	0.841730i	−0.989084	+	0.147354i	$0.952924\pi$
$108$		0			0
$109$			1.09718e9i			0.0713090i	0.999364	+	0.0356545i	$0.0113516\pi$
$109$			1.09718e9i			0.0713090i	−0.999364	+	0.0356545i	$0.988648\pi$
$110$		0			0
$111$	−7.15351e9			−0.424526
$112$		0			0
$113$	1.95910e10	−	1.95910e10i	1.06332	−	1.06332i	0.0654650	−	0.997855i	$-0.479147\pi$
$113$	1.95910e10	−	1.95910e10i	1.06332	−	1.06332i	0.997855	−	0.0654650i	$-0.0208531\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−3.95270e9	−	3.95270e9i	−0.180287	−	0.180287i
$118$		0			0
$119$			5.68949e10i			2.38418i
$120$		0			0
$121$	−2.53115e10			−0.975866
$122$		0			0
$123$	−1.19142e10	+	1.19142e10i	−0.423195	+	0.423195i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−2.04950e10	−	2.04950e10i	−0.620341	−	0.620341i	0.325278	−	0.945619i	$-0.394542\pi$
$127$	−2.04950e10	−	2.04950e10i	−0.620341	−	0.620341i	−0.945619	+	0.325278i	$0.894542\pi$
$128$		0			0
$129$		−	3.46399e10i		−	0.969678i
$130$		0			0
$131$	1.01463e10			0.262996			0.131498	−	0.991316i	$-0.458021\pi$
$131$	1.01463e10			0.262996			0.131498	+	0.991316i	$0.458021\pi$
$132$		0			0
$133$	3.08459e10	−	3.08459e10i	0.741207	−	0.741207i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	3.02368e10	+	3.02368e10i	0.626517	+	0.626517i	0.947190	−	0.320673i	$-0.103909\pi$
$137$	3.02368e10	+	3.02368e10i	0.626517	+	0.626517i	−0.320673	+	0.947190i	$0.603909\pi$
$138$		0			0
$139$		−	5.18043e9i		−	0.0998370i	−0.998753	−	0.0499185i	$-0.984104\pi$
$139$		−	5.18043e9i		−	0.0998370i	0.998753	−	0.0499185i	$-0.0158962\pi$
$140$		0			0
$141$	−4.98609e10			−0.894673
$142$		0			0
$143$	−5.02433e9	+	5.02433e9i	−0.0840230	+	0.0840230i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	3.15085e10	+	3.15085e10i	0.459030	+	0.459030i
$148$		0			0
$149$		−	2.80619e10i		−	0.382108i	−0.981580	−	0.191054i	$-0.938809\pi$
$149$		−	2.80619e10i		−	0.382108i	0.981580	−	0.191054i	$-0.0611906\pi$
$150$		0			0
$151$	7.50051e10			0.955446			0.477723	−	0.878511i	$-0.341462\pi$
$151$	7.50051e10			0.955446			0.477723	+	0.878511i	$0.341462\pi$
$152$		0			0
$153$	−3.23253e10	+	3.23253e10i	−0.385554	+	0.385554i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	1.17806e11	+	1.17806e11i	1.23500	+	1.23500i	0.962018	+	0.272986i	$0.0880111\pi$
$157$	1.17806e11	+	1.17806e11i	1.23500	+	1.23500i	0.272986	+	0.962018i	$0.411989\pi$
$158$		0			0
$159$			3.32835e10i			0.327524i
$160$		0			0
$161$	7.30456e10			0.675250
$162$		0			0
$163$	−6.69635e10	+	6.69635e10i	−0.581970	+	0.581970i	−0.935444	−	0.353475i	$-0.885000\pi$
$163$	−6.69635e10	+	6.69635e10i	−0.581970	+	0.581970i	0.353475	+	0.935444i	$0.385000\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	7.83803e10	+	7.83803e10i	0.603427	+	0.603427i	0.941220	−	0.337793i	$-0.109681\pi$
$167$	7.83803e10	+	7.83803e10i	0.603427	+	0.603427i	−0.337793	+	0.941220i	$0.609681\pi$
$168$		0			0
$169$			5.72027e10i			0.414938i
$170$		0			0
$171$	3.50507e10			0.239727
$172$		0			0
$173$	1.19104e11	−	1.19104e11i	0.768591	−	0.768591i	−0.209268	−	0.977858i	$-0.567108\pi$
$173$	1.19104e11	−	1.19104e11i	0.768591	−	0.768591i	0.977858	+	0.209268i	$0.0671080\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	9.65451e7	+	9.65451e7i	0.000555730	+	0.000555730i
$178$		0			0
$179$			4.39941e10i			0.239403i	0.992810	+	0.119701i	$0.0381937\pi$
$179$			4.39941e10i			0.239403i	−0.992810	+	0.119701i	$0.961806\pi$
$180$		0			0
$181$	−3.48136e11			−1.79207			−0.896037	−	0.443980i	$-0.853566\pi$
$181$	−3.48136e11			−1.79207			−0.896037	+	0.443980i	$0.853566\pi$
$182$		0			0
$183$	7.07989e10	−	7.07989e10i	0.344962	−	0.344962i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	4.10891e10	+	4.10891e10i	0.179688	+	0.179688i
$188$		0			0
$189$			6.76463e10i			0.280501i
$190$		0			0
$191$	−3.08104e11			−1.21208			−0.606038	−	0.795436i	$-0.707242\pi$
$191$	−3.08104e11			−1.21208			−0.606038	+	0.795436i	$0.707242\pi$
$192$		0			0
$193$	2.03935e11	−	2.03935e11i	0.761561	−	0.761561i	−0.215043	−	0.976605i	$-0.568989\pi$
$193$	2.03935e11	−	2.03935e11i	0.761561	−	0.761561i	0.976605	+	0.215043i	$0.0689892\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−3.46318e10	−	3.46318e10i	−0.116720	−	0.116720i	0.646334	−	0.763054i	$-0.276301\pi$
$197$	−3.46318e10	−	3.46318e10i	−0.116720	−	0.116720i	−0.763054	+	0.646334i	$0.776301\pi$
$198$		0			0
$199$			1.41825e11i			0.454451i	0.973842	+	0.227226i	$0.0729655\pi$
$199$			1.41825e11i			0.454451i	−0.973842	+	0.227226i	$0.927034\pi$
$200$		0			0
$201$	7.64707e10			0.233085
$202$		0			0
$203$	−7.92338e9	+	7.92338e9i	−0.0229843	+	0.0229843i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	4.15015e10	+	4.15015e10i	0.109197	+	0.109197i
$208$		0			0
$209$		−	4.45534e10i		−	0.111725i
$210$		0			0
$211$	−8.17659e10			−0.195506			−0.0977530	−	0.995211i	$-0.531166\pi$
$211$	−8.17659e10			−0.195506			−0.0977530	+	0.995211i	$0.531166\pi$
$212$		0			0
$213$	2.84414e11	−	2.84414e11i	0.648714	−	0.648714i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	2.82367e11	+	2.82367e11i	0.586834	+	0.586834i
$218$		0			0
$219$			4.08713e11i			0.811331i
$220$		0			0
$221$	−6.59605e11			−1.25119
$222$		0			0
$223$	1.88546e11	−	1.88546e11i	0.341896	−	0.341896i	−0.515184	−	0.857080i	$-0.672276\pi$
$223$	1.88546e11	−	1.88546e11i	0.341896	−	0.341896i	0.857080	+	0.515184i	$0.172276\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	5.24206e11	+	5.24206e11i	0.869706	+	0.869706i	0.992440	−	0.122733i	$-0.0391660\pi$
$227$	5.24206e11	+	5.24206e11i	0.869706	+	0.869706i	−0.122733	+	0.992440i	$0.539166\pi$
$228$		0			0
$229$			9.05881e11i			1.43845i	0.694779	+	0.719223i	$0.255502\pi$
$229$			9.05881e11i			1.43845i	−0.694779	+	0.719223i	$0.744498\pi$
$230$		0			0
$231$	8.59861e10			0.130728
$232$		0			0
$233$	−5.85576e11	+	5.85576e11i	−0.852715	+	0.852715i	−0.990467	−	0.137752i	$-0.956012\pi$
$233$	−5.85576e11	+	5.85576e11i	−0.852715	+	0.852715i	0.137752	+	0.990467i	$0.456012\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−1.25219e10	−	1.25219e10i	−0.0167467	−	0.0167467i
$238$		0			0
$239$			1.16471e12i			1.49358i	0.665062	+	0.746788i	$0.268405\pi$
$239$			1.16471e12i			1.49358i	−0.665062	+	0.746788i	$0.731595\pi$
$240$		0			0
$241$	3.65985e11			0.450172			0.225086	−	0.974339i	$-0.427734\pi$
$241$	3.65985e11			0.450172			0.225086	+	0.974339i	$0.427734\pi$
$242$		0			0
$243$	−3.84338e10	+	3.84338e10i	−0.0453609	+	0.0453609i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	3.57609e11	+	3.57609e11i	0.388977	+	0.388977i
$248$		0			0
$249$		−	2.03877e11i		−	0.212996i
$250$		0			0
$251$	−1.87615e12			−1.88321			−0.941604	−	0.336723i	$-0.890681\pi$
$251$	−1.87615e12			−1.88321			−0.941604	+	0.336723i	$0.890681\pi$
$252$		0			0
$253$	5.27531e10	−	5.27531e10i	0.0508915	−	0.0508915i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	1.00792e12	+	1.00792e12i	0.898997	+	0.898997i	0.995348	−	0.0963502i	$-0.0307169\pi$
$257$	1.00792e12	+	1.00792e12i	0.898997	+	0.898997i	−0.0963502	+	0.995348i	$0.530717\pi$
$258$		0			0
$259$			1.24905e12i			1.07172i
$260$		0			0
$261$	−9.00347e9			−0.00743374
$262$		0			0
$263$	−8.03277e11	+	8.03277e11i	−0.638390	+	0.638390i	−0.950158	−	0.311768i	$-0.899079\pi$
$263$	−8.03277e11	+	8.03277e11i	−0.638390	+	0.638390i	0.311768	+	0.950158i	$0.399079\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	4.02936e11	+	4.02936e11i	0.296947	+	0.296947i
$268$		0			0
$269$			1.38234e12i			0.981418i	0.871324	+	0.490709i	$0.163262\pi$
$269$			1.38234e12i			0.981418i	−0.871324	+	0.490709i	$0.836738\pi$
$270$		0			0
$271$	1.31641e12			0.900625			0.450312	−	0.892871i	$-0.351313\pi$
$271$	1.31641e12			0.900625			0.450312	+	0.892871i	$0.351313\pi$
$272$		0			0
$273$	−6.90169e11	+	6.90169e11i	−0.455137	+	0.455137i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	1.04448e12	+	1.04448e12i	0.640475	+	0.640475i	0.950672	−	0.310197i	$-0.100395\pi$
$277$	1.04448e12	+	1.04448e12i	0.640475	+	0.640475i	−0.310197	+	0.950672i	$0.600395\pi$
$278$		0			0
$279$			3.20858e11i			0.189798i
$280$		0			0
$281$	4.14644e11			0.236670			0.118335	−	0.992974i	$-0.462244\pi$
$281$	4.14644e11			0.236670			0.118335	+	0.992974i	$0.462244\pi$
$282$		0			0
$283$	3.77789e11	−	3.77789e11i	0.208122	−	0.208122i	−0.595347	−	0.803469i	$-0.702985\pi$
$283$	3.77789e11	−	3.77789e11i	0.208122	−	0.208122i	0.803469	+	0.595347i	$0.202985\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	2.08031e12	+	2.08031e12i	1.06836	+	1.06836i
$288$		0			0
$289$			3.37828e12i			1.67574i
$290$		0			0
$291$	2.65271e11			0.127123
$292$		0			0
$293$	1.92339e12	−	1.92339e12i	0.890697	−	0.890697i	−0.103892	−	0.994589i	$-0.533130\pi$
$293$	1.92339e12	−	1.92339e12i	0.890697	−	0.890697i	0.994589	+	0.103892i	$0.0331295\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	4.88537e10	+	4.88537e10i	0.0211405	+	0.0211405i
$298$		0			0
$299$			8.46847e11i			0.354363i
$300$		0			0
$301$	−6.04836e12			−2.44796
$302$		0			0
$303$	1.05822e12	−	1.05822e12i	0.414345	−	0.414345i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	1.53039e12	+	1.53039e12i	0.561191	+	0.561191i	0.929646	−	0.368455i	$-0.120113\pi$
$307$	1.53039e12	+	1.53039e12i	0.561191	+	0.561191i	−0.368455	+	0.929646i	$0.620113\pi$
$308$		0			0
$309$			2.69667e12i			0.957273i
$310$		0			0
$311$	−6.28144e11			−0.215902			−0.107951	−	0.994156i	$-0.534429\pi$
$311$	−6.28144e11			−0.215902			−0.107951	+	0.994156i	$0.534429\pi$
$312$		0			0
$313$	−1.67712e12	+	1.67712e12i	−0.558267	+	0.558267i	−0.928814	−	0.370547i	$-0.879170\pi$
$313$	−1.67712e12	+	1.67712e12i	−0.558267	+	0.558267i	0.370547	+	0.928814i	$0.379170\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−4.10539e12	−	4.10539e12i	−1.28250	−	1.28250i	−0.939239	−	0.343264i	$-0.888467\pi$
$317$	−4.10539e12	−	4.10539e12i	−1.28250	−	1.28250i	−0.343264	−	0.939239i	$-0.611533\pi$
$318$		0			0
$319$			1.14444e10i			0.00346450i
$320$		0			0
$321$	−2.34235e12			−0.687270
$322$		0			0
$323$	2.92454e12	−	2.92454e12i	0.831849	−	0.831849i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	1.08845e11	+	1.08845e11i	0.0291118	+	0.0291118i
$328$		0			0
$329$			8.70605e12i			2.25861i
$330$		0			0
$331$	−5.89712e12			−1.48423			−0.742113	−	0.670274i	$-0.766176\pi$
$331$	−5.89712e12			−1.48423			−0.742113	+	0.670274i	$0.766176\pi$
$332$		0			0
$333$	−7.09659e11	+	7.09659e11i	−0.173312	+	0.173312i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	4.43049e11	+	4.43049e11i	0.101930	+	0.101930i	0.756233	−	0.654303i	$-0.227038\pi$
$337$	4.43049e11	+	4.43049e11i	0.101930	+	0.101930i	−0.654303	+	0.756233i	$0.727038\pi$
$338$		0			0
$339$		−	3.88702e12i		−	0.868197i
$340$		0			0
$341$	4.07847e11			0.0884557
$342$		0			0
$343$	6.08631e11	−	6.08631e11i	0.128199	−	0.128199i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	5.64533e12	+	5.64533e12i	1.12213	+	1.12213i	0.991421	+	0.130707i	$0.0417246\pi$
$347$	5.64533e12	+	5.64533e12i	1.12213	+	1.12213i	0.130707	+	0.991421i	$0.458275\pi$
$348$		0			0
$349$		−	1.32648e12i		−	0.256197i	−0.991761	−	0.128098i	$-0.959113\pi$
$349$		−	1.32648e12i		−	0.256197i	0.991761	−	0.128098i	$-0.0408873\pi$
$350$		0			0
$351$	−7.84250e11			−0.147204
$352$		0			0
$353$	2.73200e12	−	2.73200e12i	0.498433	−	0.498433i	−0.412517	−	0.910950i	$-0.635350\pi$
$353$	2.73200e12	−	2.73200e12i	0.498433	−	0.498433i	0.910950	+	0.412517i	$0.135350\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	5.64422e12	+	5.64422e12i	0.973337	+	0.973337i
$358$		0			0
$359$			4.57615e11i			0.0767411i	0.999264	+	0.0383706i	$0.0122167\pi$
$359$			4.57615e11i			0.0767411i	−0.999264	+	0.0383706i	$0.987783\pi$
$360$		0			0
$361$	2.95996e12			0.482780
$362$		0			0
$363$	−2.51101e12	+	2.51101e12i	−0.398396	+	0.398396i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	9.31094e12	+	9.31094e12i	1.39850	+	1.39850i	0.804358	+	0.594145i	$0.202509\pi$
$367$	9.31094e12	+	9.31094e12i	1.39850	+	1.39850i	0.594145	+	0.804358i	$0.297491\pi$
$368$		0			0
$369$			2.36389e12i			0.345537i
$370$		0			0
$371$	5.81153e12			0.826839
$372$		0			0
$373$	2.39555e12	−	2.39555e12i	0.331788	−	0.331788i	−0.521477	−	0.853265i	$-0.674619\pi$
$373$	2.39555e12	−	2.39555e12i	0.331788	−	0.331788i	0.853265	+	0.521477i	$0.174619\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−9.18589e10	−	9.18589e10i	−0.0120619	−	0.0120619i
$378$		0			0
$379$			1.28766e12i			0.164667i	0.996605	+	0.0823335i	$0.0262373\pi$
$379$			1.28766e12i			0.164667i	−0.996605	+	0.0823335i	$0.973763\pi$
$380$		0			0
$381$	−4.06640e12			−0.506506
$382$		0			0
$383$	1.14348e12	−	1.14348e12i	0.138751	−	0.138751i	−0.634320	−	0.773071i	$-0.718720\pi$
$383$	1.14348e12	−	1.14348e12i	0.138751	−	0.138751i	0.773071	+	0.634320i	$0.218720\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−3.43642e12	−	3.43642e12i	−0.395869	−	0.395869i
$388$		0			0
$389$		−	1.06333e13i		−	1.19376i	−0.802329	−	0.596882i	$-0.796406\pi$
$389$		−	1.06333e13i		−	1.19376i	0.802329	−	0.596882i	$-0.203594\pi$
$390$		0			0
$391$	6.92554e12			0.757826
$392$		0			0
$393$	1.00655e12	−	1.00655e12i	0.107368	−	0.107368i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	2.64600e11	+	2.64600e11i	0.0268311	+	0.0268311i	0.720395	−	0.693564i	$-0.243961\pi$
$397$	2.64600e11	+	2.64600e11i	0.0268311	+	0.0268311i	−0.693564	+	0.720395i	$0.743961\pi$
$398$		0			0
$399$		−	6.12010e12i		−	0.605193i
$400$		0			0
$401$	−1.11198e13			−1.07245			−0.536224	−	0.844076i	$-0.680150\pi$
$401$	−1.11198e13			−1.07245			−0.536224	+	0.844076i	$0.680150\pi$
$402$		0			0
$403$	−3.27359e12	+	3.27359e12i	−0.307964	+	0.307964i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	9.02057e11	+	9.02057e11i	0.0807722	+	0.0807722i
$408$		0			0
$409$			1.36798e12i			0.119526i	0.998213	+	0.0597631i	$0.0190345\pi$
$409$			1.36798e12i			0.119526i	−0.998213	+	0.0597631i	$0.980965\pi$
$410$		0			0
$411$	5.99924e12			0.511549
$412$		0			0
$413$	1.68574e10	−	1.68574e10i	0.00140295	−	0.00140295i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−5.13921e11	−	5.13921e11i	−0.0407583	−	0.0407583i
$418$		0			0
$419$			2.09671e13i			1.62356i	0.583963	+	0.811781i	$0.301501\pi$
$419$			2.09671e13i			1.62356i	−0.583963	+	0.811781i	$0.698499\pi$
$420$		0			0
$421$	6.78953e12			0.513369			0.256684	−	0.966495i	$-0.417370\pi$
$421$	6.78953e12			0.513369			0.256684	+	0.966495i	$0.417370\pi$
$422$		0			0
$423$	−4.94641e12	+	4.94641e12i	−0.365249	+	0.365249i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−1.23620e13	−	1.23620e13i	−0.870861	−	0.870861i
$428$		0			0
$429$			9.96871e11i			0.0686045i
$430$		0			0
$431$	−1.34121e13			−0.901798			−0.450899	−	0.892575i	$-0.648897\pi$
$431$	−1.34121e13			−0.901798			−0.450899	+	0.892575i	$0.648897\pi$
$432$		0			0
$433$	1.05542e13	−	1.05542e13i	0.693402	−	0.693402i	−0.269577	−	0.962979i	$-0.586884\pi$
$433$	1.05542e13	−	1.05542e13i	0.693402	−	0.693402i	0.962979	+	0.269577i	$0.0868839\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−3.75472e12	−	3.75472e12i	−0.235597	−	0.235597i
$438$		0			0
$439$			9.65138e10i			0.00591925i	0.999996	+	0.00295963i	$0.000942079\pi$
$439$			9.65138e10i			0.00591925i	−0.999996	+	0.00295963i	$0.999058\pi$
$440$		0			0
$441$	6.25156e12			0.374796
$442$		0			0
$443$	−2.34305e12	+	2.34305e12i	−0.137329	+	0.137329i	−0.772430	−	0.635100i	$-0.780959\pi$
$443$	−2.34305e12	+	2.34305e12i	−0.137329	+	0.137329i	0.635100	+	0.772430i	$0.280959\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−2.78387e12	−	2.78387e12i	−0.155995	−	0.155995i
$448$		0			0
$449$		−	2.84295e13i		−	1.55789i	−0.627092	−	0.778945i	$-0.715755\pi$
$449$		−	2.84295e13i		−	1.55789i	0.627092	−	0.778945i	$-0.284245\pi$
$450$		0			0
$451$	3.00477e12			0.161038
$452$		0			0
$453$	7.44083e12	−	7.44083e12i	0.390059	−	0.390059i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−4.05768e12	−	4.05768e12i	−0.203562	−	0.203562i	0.597962	−	0.801524i	$-0.295977\pi$
$457$	−4.05768e12	−	4.05768e12i	−0.203562	−	0.203562i	−0.801524	+	0.597962i	$0.795977\pi$
$458$		0			0
$459$			6.41362e12i			0.314804i
$460$		0			0
$461$	−3.98359e12			−0.191324			−0.0956621	−	0.995414i	$-0.530497\pi$
$461$	−3.98359e12			−0.191324			−0.0956621	+	0.995414i	$0.530497\pi$
$462$		0			0
$463$	−2.24134e13	+	2.24134e13i	−1.05342	+	1.05342i	−0.0549326	+	0.998490i	$0.517494\pi$
$463$	−2.24134e13	+	2.24134e13i	−1.05342	+	1.05342i	−0.998490	+	0.0549326i	$0.982506\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−2.33263e13	−	2.33263e13i	−1.05018	−	1.05018i	−0.998673	−	0.0515032i	$-0.983599\pi$
$467$	−2.33263e13	−	2.33263e13i	−1.05018	−	1.05018i	−0.0515032	−	0.998673i	$-0.516401\pi$
$468$		0			0
$469$		−	1.33523e13i		−	0.588427i
$470$		0			0
$471$	2.33737e13			1.00838
$472$		0			0
$473$	−4.36808e12	+	4.36808e12i	−0.184495	+	0.184495i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	3.30187e12	+	3.30187e12i	0.133711	+	0.133711i
$478$		0			0
$479$		−	8.27794e12i		−	0.328280i	−0.986437	−	0.164140i	$-0.947515\pi$
$479$		−	8.27794e12i		−	0.328280i	0.986437	−	0.164140i	$-0.0524849\pi$
$480$		0			0
$481$	−1.44807e13			−0.562426
$482$		0			0
$483$	7.24644e12	−	7.24644e12i	0.275670	−	0.275670i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−1.38737e13	−	1.38737e13i	−0.506464	−	0.506464i	0.406975	−	0.913439i	$-0.366584\pi$
$487$	−1.38737e13	−	1.38737e13i	−0.506464	−	0.506464i	−0.913439	+	0.406975i	$0.866584\pi$
$488$		0			0
$489$			1.32861e13i			0.475176i
$490$		0			0
$491$	−2.76440e13			−0.968709			−0.484354	−	0.874872i	$-0.660945\pi$
$491$	−2.76440e13			−0.968709			−0.484354	+	0.874872i	$0.660945\pi$
$492$		0			0
$493$	−7.51224e11	+	7.51224e11i	−0.0257950	+	0.0257950i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−4.96607e13	−	4.96607e13i	−1.63769	−	1.63769i
$498$		0			0
$499$		−	3.83890e13i		−	1.24081i	−0.784283	−	0.620404i	$-0.786969\pi$
$499$		−	3.83890e13i		−	1.24081i	0.784283	−	0.620404i	$-0.213031\pi$
$500$		0			0
$501$	1.55513e13			0.492696
$502$		0			0
$503$	−2.76657e13	+	2.76657e13i	−0.859215	+	0.859215i	−0.991246	−	0.132030i	$-0.957850\pi$
$503$	−2.76657e13	+	2.76657e13i	−0.859215	+	0.859215i	0.132030	+	0.991246i	$0.457850\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	5.67476e12	+	5.67476e12i	0.169398	+	0.169398i
$508$		0			0
$509$		−	3.10959e13i		−	0.910152i	−0.890453	−	0.455076i	$-0.849612\pi$
$509$		−	3.10959e13i		−	0.910152i	0.890453	−	0.455076i	$-0.150388\pi$
$510$		0			0
$511$	7.13641e13			2.04821
$512$		0			0
$513$	3.47718e12	−	3.47718e12i	0.0978680	−	0.0978680i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	6.28745e12	+	6.28745e12i	0.170224	+	0.170224i
$518$		0			0
$519$		−	2.36312e13i		−	0.627552i
$520$		0			0
$521$	5.06950e13			1.32062			0.660308	−	0.750995i	$-0.270426\pi$
$521$	5.06950e13			1.32062			0.660308	+	0.750995i	$0.270426\pi$
$522$		0			0
$523$	−3.09443e12	+	3.09443e12i	−0.0790810	+	0.0790810i	−0.745541	−	0.666460i	$-0.767809\pi$
$523$	−3.09443e12	+	3.09443e12i	−0.0790810	+	0.0790810i	0.666460	+	0.745541i	$0.267809\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	2.67715e13	+	2.67715e13i	0.658598	+	0.658598i
$528$		0			0
$529$			3.25350e13i			0.785367i
$530$		0			0
$531$	1.91554e10			0.000453751
$532$		0			0
$533$	−2.41178e13	+	2.41178e13i	−0.560663	+	0.560663i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	4.36440e12	+	4.36440e12i	0.0977358	+	0.0977358i
$538$		0			0
$539$		−	7.94644e12i		−	0.174674i
$540$		0			0
$541$	8.36222e13			1.80441			0.902206	−	0.431306i	$-0.141947\pi$
$541$	8.36222e13			1.80441			0.902206	+	0.431306i	$0.141947\pi$
$542$		0			0
$543$	−3.45366e13	+	3.45366e13i	−0.731611	+	0.731611i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−7.81408e12	−	7.81408e12i	−0.159566	−	0.159566i	0.622808	−	0.782375i	$-0.285992\pi$
$547$	−7.81408e12	−	7.81408e12i	−0.159566	−	0.159566i	−0.782375	+	0.622808i	$0.785992\pi$
$548$		0			0
$549$		−	1.40471e13i		−	0.281660i
$550$		0			0
$551$	8.14562e11			0.0160386
$552$		0			0
$553$	−2.18642e12	+	2.18642e12i	−0.0422773	+	0.0422773i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−6.11592e13	−	6.11592e13i	−1.14074	−	1.14074i	−0.988316	−	0.152422i	$-0.951293\pi$
$557$	−6.11592e13	−	6.11592e13i	−1.14074	−	1.14074i	−0.152422	−	0.988316i	$-0.548707\pi$
$558$		0			0
$559$		−	7.01210e13i		−	1.28466i
$560$		0			0
$561$	8.15244e12			0.146715
$562$		0			0
$563$	6.58943e13	−	6.58943e13i	1.16495	−	1.16495i	0.181567	−	0.983379i	$-0.441883\pi$
$563$	6.58943e13	−	6.58943e13i	1.16495	−	1.16495i	0.983379	−	0.181567i	$-0.0581169\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	6.71081e12	+	6.71081e12i	0.114514	+	0.114514i
$568$		0			0
$569$		−	1.02033e14i		−	1.71072i	−0.518035	−	0.855360i	$-0.673336\pi$
$569$		−	1.02033e14i		−	1.71072i	0.518035	−	0.855360i	$-0.326664\pi$
$570$		0			0
$571$	−2.77702e13			−0.457508			−0.228754	−	0.973484i	$-0.573465\pi$
$571$	−2.77702e13			−0.457508			−0.228754	+	0.973484i	$0.573465\pi$
$572$		0			0
$573$	−3.05652e13	+	3.05652e13i	−0.494828	+	0.494828i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−1.41906e13	−	1.41906e13i	−0.221881	−	0.221881i	0.587409	−	0.809290i	$-0.300148\pi$
$577$	−1.41906e13	−	1.41906e13i	−0.221881	−	0.221881i	−0.809290	+	0.587409i	$0.800148\pi$
$578$		0			0
$579$		−	4.04624e13i		−	0.621812i
$580$		0			0
$581$	−3.55983e13			−0.537711
$582$		0			0
$583$	4.19705e12	−	4.19705e12i	0.0623162	−	0.0623162i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−7.63403e13	−	7.63403e13i	−1.09538	−	1.09538i	−0.994944	−	0.100433i	$-0.967977\pi$
$587$	−7.63403e13	−	7.63403e13i	−1.09538	−	1.09538i	−0.100433	−	0.994944i	$-0.532023\pi$
$588$		0			0
$589$		−	2.90287e13i		−	0.409497i
$590$		0			0
$591$	−6.87126e12			−0.0953013
$592$		0			0
$593$	9.58857e13	−	9.58857e13i	1.30762	−	1.30762i	0.384485	−	0.923131i	$-0.374379\pi$
$593$	9.58857e13	−	9.58857e13i	1.30762	−	1.30762i	0.923131	−	0.384485i	$-0.125621\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	1.40697e13	+	1.40697e13i	0.185529	+	0.185529i
$598$		0			0
$599$			4.74683e13i			0.615559i	0.951458	+	0.307780i	$0.0995859\pi$
$599$			4.74683e13i			0.615559i	−0.951458	+	0.307780i	$0.900414\pi$
$600$		0			0
$601$	−5.72557e13			−0.730207			−0.365104	−	0.930967i	$-0.618966\pi$
$601$	−5.72557e13			−0.730207			−0.365104	+	0.930967i	$0.618966\pi$
$602$		0			0
$603$	7.58623e12	−	7.58623e12i	0.0951567	−	0.0951567i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−2.13915e13	−	2.13915e13i	−0.259596	−	0.259596i	0.565294	−	0.824890i	$-0.308763\pi$
$607$	−2.13915e13	−	2.13915e13i	−0.259596	−	0.259596i	−0.824890	+	0.565294i	$0.808763\pi$
$608$		0			0
$609$			1.57207e12i			0.0187666i
$610$		0			0
$611$	−1.00933e14			−1.18529
$612$		0			0
$613$	−3.01688e13	+	3.01688e13i	−0.348542	+	0.348542i	−0.859566	−	0.511024i	$-0.829266\pi$
$613$	−3.01688e13	+	3.01688e13i	−0.348542	+	0.348542i	0.511024	+	0.859566i	$0.329266\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−7.24200e13	−	7.24200e13i	−0.809903	−	0.809903i	0.174716	−	0.984619i	$-0.444099\pi$
$617$	−7.24200e13	−	7.24200e13i	−0.809903	−	0.809903i	−0.984619	+	0.174716i	$0.944099\pi$
$618$		0			0
$619$		−	1.63678e14i		−	1.80110i	−0.434752	−	0.900550i	$-0.643164\pi$
$619$		−	1.63678e14i		−	1.80110i	0.434752	−	0.900550i	$-0.356836\pi$
$620$		0			0
$621$	8.23425e12			0.0891592
$622$		0			0
$623$	7.03554e13	−	7.03554e13i	0.749648	−	0.749648i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−4.41989e12	−	4.41989e12i	−0.0456115	−	0.0456115i
$628$		0			0
$629$			1.18424e14i			1.20278i
$630$		0			0
$631$	8.97331e13			0.897028			0.448514	−	0.893776i	$-0.351953\pi$
$631$	8.97331e13			0.897028			0.448514	+	0.893776i	$0.351953\pi$
$632$		0			0
$633$	−8.11153e12	+	8.11153e12i	−0.0798150	+	0.0798150i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	6.37822e13	+	6.37822e13i	0.608138	+	0.608138i
$638$		0			0
$639$		−	5.64302e13i		−	0.529672i
$640$		0			0
$641$	8.94041e13			0.826166			0.413083	−	0.910693i	$-0.364452\pi$
$641$	8.94041e13			0.826166			0.413083	+	0.910693i	$0.364452\pi$
$642$		0			0
$643$	−7.62258e13	+	7.62258e13i	−0.693501	+	0.693501i	−0.963001	−	0.269499i	$-0.913142\pi$
$643$	−7.62258e13	+	7.62258e13i	−0.693501	+	0.693501i	0.269499	+	0.963001i	$0.413142\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	1.96202e13	+	1.96202e13i	0.173054	+	0.173054i	0.788320	−	0.615266i	$-0.210951\pi$
$647$	1.96202e13	+	1.96202e13i	0.173054	+	0.173054i	−0.615266	+	0.788320i	$0.710951\pi$
$648$		0			0
$649$		−	2.43487e10i		−	0.000211471i
$650$		0			0
$651$	5.60241e13			0.479148
$652$		0			0
$653$	1.27158e13	−	1.27158e13i	0.107097	−	0.107097i	−0.651528	−	0.758625i	$-0.725872\pi$
$653$	1.27158e13	−	1.27158e13i	0.107097	−	0.107097i	0.758625	+	0.651528i	$0.225872\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	4.05461e13	+	4.05461e13i	0.331224	+	0.331224i
$658$		0			0
$659$			5.76863e13i			0.464137i	0.972699	+	0.232068i	$0.0745493\pi$
$659$			5.76863e13i			0.464137i	−0.972699	+	0.232068i	$0.925451\pi$
$660$		0			0
$661$	4.04124e13			0.320264			0.160132	−	0.987096i	$-0.448808\pi$
$661$	4.04124e13			0.320264			0.160132	+	0.987096i	$0.448808\pi$
$662$		0			0
$663$	−6.54357e13	+	6.54357e13i	−0.510795	+	0.510795i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	9.64474e11	+	9.64474e11i	0.00730569	+	0.00730569i
$668$		0			0
$669$		−	3.74092e13i		−	0.279157i
$670$		0			0
$671$	−1.78555e13			−0.131268
$672$		0			0
$673$	−8.26189e13	+	8.26189e13i	−0.598417	+	0.598417i	−0.939891	−	0.341474i	$-0.889074\pi$
$673$	−8.26189e13	+	8.26189e13i	−0.598417	+	0.598417i	0.341474	+	0.939891i	$0.389074\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−4.33113e13	−	4.33113e13i	−0.304550	−	0.304550i	0.538241	−	0.842791i	$-0.319089\pi$
$677$	−4.33113e13	−	4.33113e13i	−0.304550	−	0.304550i	−0.842791	+	0.538241i	$0.819089\pi$
$678$		0			0
$679$		−	4.63182e13i		−	0.320925i
$680$		0			0
$681$	1.04007e14			0.710112
$682$		0			0
$683$	6.39056e13	−	6.39056e13i	0.429967	−	0.429967i	−0.458650	−	0.888617i	$-0.651667\pi$
$683$	6.39056e13	−	6.39056e13i	0.429967	−	0.429967i	0.888617	+	0.458650i	$0.151667\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	8.98673e13	+	8.98673e13i	0.587243	+	0.587243i
$688$		0			0
$689$			6.73754e13i			0.433915i
$690$		0			0
$691$	−2.61839e14			−1.66205			−0.831024	−	0.556237i	$-0.812245\pi$
$691$	−2.61839e14			−1.66205			−0.831024	+	0.556237i	$0.812245\pi$
$692$		0			0
$693$	8.53020e12	−	8.53020e12i	0.0533695	−	0.0533695i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	1.97236e14	+	1.97236e14i	1.19901	+	1.19901i
$698$		0			0
$699$			1.16183e14i			0.696239i
$700$		0			0
$701$	−2.70633e13			−0.159879			−0.0799393	−	0.996800i	$-0.525473\pi$
$701$	−2.70633e13			−0.159879			−0.0799393	+	0.996800i	$0.525473\pi$
$702$		0			0
$703$	6.42043e13	−	6.42043e13i	0.373927	−	0.373927i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−1.84772e14	−	1.84772e14i	−1.04602	−	1.04602i
$708$		0			0
$709$			2.44744e14i			1.36610i	0.730374	+	0.683048i	$0.239346\pi$
$709$			2.44744e14i			1.36610i	−0.730374	+	0.683048i	$0.760654\pi$
$710$		0			0
$711$	−2.48446e12			−0.0136736
$712$		0			0
$713$	3.43712e13	−	3.43712e13i	0.186529	−	0.186529i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	1.15544e14	+	1.15544e14i	0.609750	+	0.609750i
$718$		0			0
$719$		−	1.55815e14i		−	0.810893i	−0.914119	−	0.405446i	$-0.867116\pi$
$719$		−	1.55815e14i		−	0.810893i	0.914119	−	0.405446i	$-0.132884\pi$
$720$		0			0
$721$	4.70858e14			2.41665
$722$		0			0
$723$	3.63073e13	−	3.63073e13i	0.183782	−	0.183782i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	2.31542e14	+	2.31542e14i	1.14014	+	1.14014i	0.988424	+	0.151716i	$0.0484800\pi$
$727$	2.31542e14	+	2.31542e14i	1.14014	+	1.14014i	0.151716	+	0.988424i	$0.451520\pi$
$728$		0			0
$729$			7.62560e12i			0.0370370i
$730$		0			0
$731$	−5.73452e14			−2.74732
$732$		0			0
$733$	1.18484e13	−	1.18484e13i	0.0559937	−	0.0559937i	−0.678555	−	0.734549i	$-0.737394\pi$
$733$	1.18484e13	−	1.18484e13i	0.0559937	−	0.0559937i	0.734549	+	0.678555i	$0.237394\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−9.64295e12	−	9.64295e12i	−0.0443479	−	0.0443479i
$738$		0			0
$739$			3.62876e14i			1.64640i	0.567749	+	0.823202i	$0.307815\pi$
$739$			3.62876e14i			1.64640i	−0.567749	+	0.823202i	$0.692185\pi$
$740$		0			0
$741$	7.09527e13			0.317598
$742$		0			0
$743$	−2.39468e14	+	2.39468e14i	−1.05756	+	1.05756i	−0.0593169	+	0.998239i	$0.518892\pi$
$743$	−2.39468e14	+	2.39468e14i	−1.05756	+	1.05756i	−0.998239	+	0.0593169i	$0.981108\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−2.02255e13	−	2.02255e13i	−0.0869552	−	0.0869552i
$748$		0			0
$749$			4.08991e14i			1.73502i
$750$		0			0
$751$	1.97887e14			0.828357			0.414179	−	0.910196i	$-0.364069\pi$
$751$	1.97887e14			0.828357			0.414179	+	0.910196i	$0.364069\pi$
$752$		0			0
$753$	−1.86122e14	+	1.86122e14i	−0.768816	+	0.768816i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−1.98573e14	−	1.98573e14i	−0.798805	−	0.798805i	0.184102	−	0.982907i	$-0.441062\pi$
$757$	−1.98573e14	−	1.98573e14i	−0.798805	−	0.798805i	−0.982907	+	0.184102i	$0.941062\pi$
$758$		0			0
$759$		−	1.04667e13i		−	0.0415527i
$760$		0			0
$761$	−5.03296e14			−1.97197			−0.985984	−	0.166841i	$-0.946643\pi$
$761$	−5.03296e14			−1.97197			−0.985984	+	0.166841i	$0.946643\pi$
$762$		0			0
$763$	1.90050e13	−	1.90050e13i	0.0734930	−	0.0734930i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	1.95435e11	+	1.95435e11i	0.000736250	+	0.000736250i
$768$		0			0
$769$		−	3.56257e13i		−	0.132474i	−0.997804	−	0.0662371i	$-0.978901\pi$
$769$		−	3.56257e13i		−	0.132474i	0.997804	−	0.0662371i	$-0.0210994\pi$
$770$		0			0
$771$	1.99979e14			0.734028
$772$		0			0
$773$	2.00259e14	−	2.00259e14i	0.725597	−	0.725597i	−0.244142	−	0.969739i	$-0.578506\pi$
$773$	2.00259e14	−	2.00259e14i	0.725597	−	0.725597i	0.969739	+	0.244142i	$0.0785064\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	1.23911e14	+	1.23911e14i	0.437528	+	0.437528i
$778$		0			0
$779$		−	2.13866e14i		−	0.745510i
$780$		0			0
$781$	−7.17292e13			−0.246854
$782$		0			0
$783$	−8.93183e11	+	8.93183e11i	−0.00303481	+	0.00303481i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	1.04651e14	+	1.04651e14i	0.346634	+	0.346634i	0.858854	−	0.512220i	$-0.171177\pi$
$787$	1.04651e14	+	1.04651e14i	0.346634	+	0.346634i	−0.512220	+	0.858854i	$0.671177\pi$
$788$		0			0
$789$			1.59377e14i			0.521244i
$790$		0			0
$791$	−6.78701e14			−2.19177
$792$		0			0
$793$	1.43317e14	−	1.43317e14i	0.457017	−	0.457017i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−1.24009e14	−	1.24009e14i	−0.385620	−	0.385620i	0.487502	−	0.873122i	$-0.337908\pi$
$797$	−1.24009e14	−	1.24009e14i	−0.385620	−	0.385620i	−0.873122	+	0.487502i	$0.837908\pi$
$798$		0			0
$799$			8.25430e14i			2.53482i
$800$		0			0
$801$	7.99460e13			0.242457
$802$		0			0
$803$	5.15387e13	−	5.15387e13i	0.154367	−	0.154367i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	1.37134e14	+	1.37134e14i	0.400662	+	0.400662i
$808$		0			0
$809$			3.76828e14i			1.08743i	0.839271	+	0.543714i	$0.182982\pi$
$809$			3.76828e14i			1.08743i	−0.839271	+	0.543714i	$0.817018\pi$
$810$		0			0
$811$	−5.09045e14			−1.45095			−0.725474	−	0.688250i	$-0.758379\pi$
$811$	−5.09045e14			−1.45095			−0.725474	+	0.688250i	$0.758379\pi$
$812$		0			0
$813$	1.30593e14	−	1.30593e14i	0.367679	−	0.367679i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	3.10900e14	+	3.10900e14i	0.854104	+	0.854104i
$818$		0			0
$819$			1.36936e14i			0.371618i
$820$		0			0
$821$	−4.38403e14			−1.17532			−0.587662	−	0.809107i	$-0.699951\pi$
$821$	−4.38403e14			−1.17532			−0.587662	+	0.809107i	$0.699951\pi$
$822$		0			0
$823$	−3.06984e14	+	3.06984e14i	−0.813048	+	0.813048i	−0.985090	−	0.172041i	$-0.944964\pi$
$823$	−3.06984e14	+	3.06984e14i	−0.813048	+	0.813048i	0.172041	+	0.985090i	$0.444964\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−2.70430e14	−	2.70430e14i	−0.699080	−	0.699080i	0.265132	−	0.964212i	$-0.414585\pi$
$827$	−2.70430e14	−	2.70430e14i	−0.699080	−	0.699080i	−0.964212	+	0.265132i	$0.914585\pi$
$828$		0			0
$829$		−	6.97749e14i		−	1.78208i	−0.453927	−	0.891039i	$-0.649977\pi$
$829$		−	6.97749e14i		−	1.78208i	0.453927	−	0.891039i	$-0.350023\pi$
$830$		0			0
$831$	2.07234e14			0.522946
$832$		0			0
$833$	5.21613e14	−	5.21613e14i	1.30054	−	1.30054i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	3.18305e13	+	3.18305e13i	0.0774848	+	0.0774848i
$838$		0			0
$839$			7.39428e14i			1.77863i	0.457292	+	0.889316i	$0.348819\pi$
$839$			7.39428e14i			1.77863i	−0.457292	+	0.889316i	$0.651181\pi$
$840$		0			0
$841$	4.20498e14			0.999503
$842$		0			0
$843$	4.11345e13	−	4.11345e13i	0.0966202	−	0.0966202i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	4.38439e14	+	4.38439e14i	1.00576	+	1.00576i
$848$		0			0
$849$		−	7.49567e13i		−	0.169931i
$850$		0			0
$851$	1.52041e14			0.340653
$852$		0			0
$853$	2.90182e14	−	2.90182e14i	0.642577	−	0.642577i	−0.308611	−	0.951188i	$-0.599864\pi$
$853$	2.90182e14	−	2.90182e14i	0.642577	−	0.642577i	0.951188	+	0.308611i	$0.0998642\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	5.15570e14	+	5.15570e14i	1.11528	+	1.11528i	0.992425	+	0.122853i	$0.0392045\pi$
$857$	5.15570e14	+	5.15570e14i	1.11528	+	1.11528i	0.122853	+	0.992425i	$0.460795\pi$
$858$		0			0
$859$		−	3.60359e14i		−	0.770494i	−0.922814	−	0.385247i	$-0.874116\pi$
$859$		−	3.60359e14i		−	0.770494i	0.922814	−	0.385247i	$-0.125884\pi$
$860$		0			0
$861$	4.12751e14			0.872313
$862$		0			0
$863$	−1.51408e14	+	1.51408e14i	−0.316298	+	0.316298i	−0.847343	−	0.531046i	$-0.821799\pi$
$863$	−1.51408e14	+	1.51408e14i	−0.316298	+	0.316298i	0.531046	+	0.847343i	$0.321799\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	3.35140e14	+	3.35140e14i	0.684117	+	0.684117i
$868$		0			0
$869$			3.15803e12i			0.00637261i
$870$		0			0
$871$	1.54799e14			0.308799
$872$		0			0
$873$	2.63161e13	−	2.63161e13i	0.0518979	−	0.0518979i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	5.10979e14	+	5.10979e14i	0.984929	+	0.984929i	0.999888	−	0.0149588i	$-0.00476170\pi$
$877$	5.10979e14	+	5.10979e14i	0.984929	+	0.984929i	−0.0149588	+	0.999888i	$0.504762\pi$
$878$		0			0
$879$		−	3.81618e14i		−	0.727251i
$880$		0			0
$881$	−3.46106e14			−0.652123			−0.326061	−	0.945349i	$-0.605722\pi$
$881$	−3.46106e14			−0.652123			−0.326061	+	0.945349i	$0.605722\pi$
$882$		0			0
$883$	−6.55698e14	+	6.55698e14i	−1.22152	+	1.22152i	−0.254428	+	0.967092i	$0.581887\pi$
$883$	−6.55698e14	+	6.55698e14i	−1.22152	+	1.22152i	−0.967092	+	0.254428i	$0.918113\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−4.59458e14	−	4.59458e14i	−0.836812	−	0.836812i	0.151626	−	0.988438i	$-0.451549\pi$
$887$	−4.59458e14	−	4.59458e14i	−0.836812	−	0.836812i	−0.988438	+	0.151626i	$0.951549\pi$
$888$		0			0
$889$			7.10021e14i			1.27868i
$890$		0			0
$891$	9.69300e12			0.0172611
$892$		0			0
$893$	4.47512e14	−	4.47512e14i	0.788038	−	0.788038i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	8.40109e13	+	8.40109e13i	0.144668	+	0.144668i
$898$		0			0
$899$			7.45659e12i			0.0126982i
$900$		0			0
$901$	5.50998e14			0.927953
$902$		0			0
$903$	−6.00024e14	+	6.00024e14i	−0.999377	+	0.999377i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	7.57995e14	+	7.57995e14i	1.23490	+	1.23490i	0.962061	+	0.272834i	$0.0879611\pi$
$907$	7.57995e14	+	7.57995e14i	1.23490	+	1.23490i	0.272834	+	0.962061i	$0.412039\pi$
$908$		0			0
$909$		−	2.09960e14i		−	0.338312i
$910$		0			0
$911$	−9.29432e14			−1.48124			−0.740621	−	0.671924i	$-0.765468\pi$
$911$	−9.29432e14			−1.48124			−0.740621	+	0.671924i	$0.765468\pi$
$912$		0			0
$913$	−2.57089e13	+	2.57089e13i	−0.0405256	+	0.0405256i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−1.75751e14	−	1.75751e14i	−0.271051	−	0.271051i
$918$		0			0
$919$		−	1.02281e15i		−	1.56033i	−0.625572	−	0.780167i	$-0.715134\pi$
$919$		−	1.02281e15i		−	1.56033i	0.625572	−	0.780167i	$-0.284866\pi$
$920$		0			0
$921$	3.03643e14			0.458211
$922$		0			0
$923$	5.75736e14	−	5.75736e14i	0.859438	−	0.859438i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	2.67522e14	+	2.67522e14i	0.390805	+	0.390805i
$928$		0			0
$929$			7.54575e14i			1.09050i	0.838275	+	0.545248i	$0.183564\pi$
$929$			7.54575e14i			1.09050i	−0.838275	+	0.545248i	$0.816436\pi$
$930$		0			0
$931$	−5.65591e14			−0.808638
$932$		0			0
$933$	−6.23147e13	+	6.23147e13i	−0.0881418	+	0.0881418i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−6.66564e14	−	6.66564e14i	−0.922877	−	0.922877i	0.0743552	−	0.997232i	$-0.476310\pi$
$937$	−6.66564e14	−	6.66564e14i	−0.922877	−	0.922877i	−0.997232	+	0.0743552i	$0.976310\pi$
$938$		0			0
$939$			3.32755e14i			0.455823i
$940$		0			0
$941$	4.47427e14			0.606421			0.303210	−	0.952924i	$-0.401942\pi$
$941$	4.47427e14			0.606421			0.303210	+	0.952924i	$0.401942\pi$
$942$		0			0
$943$	2.53225e14	−	2.53225e14i	0.339585	−	0.339585i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−7.65473e14	−	7.65473e14i	−1.00503	−	1.00503i	−0.999987	−	0.00504553i	$-0.998394\pi$
$947$	−7.65473e14	−	7.65473e14i	−1.00503	−	1.00503i	−0.00504553	−	0.999987i	$-0.501606\pi$
$948$		0			0
$949$			8.27352e14i			1.07488i
$950$		0			0
$951$	−8.14545e14			−1.04716
$952$		0			0
$953$	6.07353e14	−	6.07353e14i	0.772639	−	0.772639i	−0.205928	−	0.978567i	$-0.566021\pi$
$953$	6.07353e14	−	6.07353e14i	0.772639	−	0.772639i	0.978567	+	0.205928i	$0.0660213\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	1.13534e12	+	1.13534e12i	0.00141438	+	0.00141438i
$958$		0			0
$959$		−	1.04751e15i		−	1.29141i
$960$		0			0
$961$	−5.53896e14			−0.675789
$962$		0			0
$963$	−2.32372e14	+	2.32372e14i	−0.280577	+	0.280577i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−6.09128e14	−	6.09128e14i	−0.720404	−	0.720404i	0.248284	−	0.968687i	$-0.420134\pi$
$967$	−6.09128e14	−	6.09128e14i	−0.720404	−	0.720404i	−0.968687	+	0.248284i	$0.920134\pi$
$968$		0			0
$969$		−	5.80253e14i		−	0.679202i
$970$		0			0
$971$	−1.64376e14			−0.190434			−0.0952168	−	0.995457i	$-0.530354\pi$
$971$	−1.64376e14			−0.190434			−0.0952168	+	0.995457i	$0.530354\pi$
$972$		0			0
$973$	−8.97341e13	+	8.97341e13i	−0.102895	+	0.102895i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−1.24356e15	−	1.24356e15i	−1.39700	−	1.39700i	−0.808503	−	0.588493i	$-0.799722\pi$
$977$	−1.24356e15	−	1.24356e15i	−1.39700	−	1.39700i	−0.588493	−	0.808503i	$-0.700278\pi$
$978$		0			0
$979$		−	1.01620e14i		−	0.112997i
$980$		0			0
$981$	2.15957e13			0.0237697
$982$		0			0
$983$	4.35152e14	−	4.35152e14i	0.474103	−	0.474103i	−0.429136	−	0.903240i	$-0.641182\pi$
$983$	4.35152e14	−	4.35152e14i	0.474103	−	0.474103i	0.903240	+	0.429136i	$0.141182\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	8.63678e14	+	8.63678e14i	0.922075	+	0.922075i
$988$		0			0
$989$			7.36237e14i			0.778101i
$990$		0			0
$991$	8.92534e14			0.933805			0.466903	−	0.884309i	$-0.345370\pi$
$991$	8.92534e14			0.933805			0.466903	+	0.884309i	$0.345370\pi$
$992$		0			0
$993$	−5.85020e14	+	5.85020e14i	−0.605933	+	0.605933i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	6.94862e14	+	6.94862e14i	0.705380	+	0.705380i	0.965560	−	0.260180i	$-0.0837820\pi$
$997$	6.94862e14	+	6.94862e14i	0.705380	+	0.705380i	−0.260180	+	0.965560i	$0.583782\pi$
$998$		0			0
$999$			1.40802e14i			0.141509i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.11.k.c.157.5	yes	16
5.2	odd	4	inner	300.11.k.c.193.4	yes	16
5.3	odd	4	inner	300.11.k.c.193.5	yes	16
5.4	even	2	inner	300.11.k.c.157.4	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.11.k.c.157.4	✓	16	5.4	even	2	inner
300.11.k.c.157.5	yes	16	1.1	even	1	trivial
300.11.k.c.193.4	yes	16	5.2	odd	4	inner
300.11.k.c.193.5	yes	16	5.3	odd	4	inner

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)

\(f(q)\)	\(=\)	\(q+(99.2043 - 99.2043i) q^{3} +(-17321.8 - 17321.8i) q^{7} -19683.0i q^{9} +O(q^{10})\)	\(q+(99.2043 - 99.2043i) q^{3} +(-17321.8 - 17321.8i) q^{7} -19683.0i q^{9} -25019.3 q^{11} +(200818. - 200818. i) q^{13} +(-1.64230e6 - 1.64230e6i) q^{17} +1.78076e6i q^{19} -3.43679e6 q^{21} +(-2.10849e6 + 2.10849e6i) q^{23} +(-1.95264e6 - 1.95264e6i) q^{27} -457423. i q^{29} -1.63013e7 q^{31} +(-2.48203e6 + 2.48203e6i) q^{33} +(-3.60544e7 - 3.60544e7i) q^{37} -3.98440e7i q^{39} -1.20098e8 q^{41} +(1.74588e8 - 1.74588e8i) q^{43} +(-2.51304e8 - 2.51304e8i) q^{47} +3.17612e8i q^{49} -3.25846e8 q^{51} +(-1.67752e8 + 1.67752e8i) q^{53} +(1.76659e8 + 1.76659e8i) q^{57} +973194. i q^{59} +7.13667e8 q^{61} +(-3.40944e8 + 3.40944e8i) q^{63} +(3.85420e8 + 3.85420e8i) q^{67} +4.18343e8i q^{69} +2.86695e9 q^{71} +(-2.05996e9 + 2.05996e9i) q^{73} +(4.33379e8 + 4.33379e8i) q^{77} -1.26224e8i q^{79} -3.87420e8 q^{81} +(1.02756e9 - 1.02756e9i) q^{83} +(-4.53784e7 - 4.53784e7i) q^{87} +4.06168e9i q^{89} -6.95705e9 q^{91} +(-1.61716e9 + 1.61716e9i) q^{93} +(1.33700e9 + 1.33700e9i) q^{97} +4.92455e8i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 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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