LMFDB - Embedded newform 300.11.k.c.157.4

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			157.4
Root			$178.843 + 178.843i$ of defining polynomial
Character	$\chi$	$=$	300.157
Dual form			300.11.k.c.193.4

$q$-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	$0.00990494\pi$
$7$	17321.8	+	17321.8i	1.03063	+	1.03063i	0.0311123	+	0.999516i	$0.490095\pi$
$8$		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	−0.923781	−	0.382920i	$-0.874918\pi$
$13$	−200818.	+	200818.i	−0.540861	+	0.540861i	0.382920	+	0.923781i	$0.374918\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	1.64230e6	+	1.64230e6i	1.15666	+	1.15666i	0.985189	+	0.171474i	$0.0548530\pi$
$17$	1.64230e6	+	1.64230e6i	1.15666	+	1.15666i	0.171474	+	0.985189i	$0.445147\pi$
$18$		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	−0.524078	−	0.851670i	$-0.675590\pi$
$23$	2.10849e6	−	2.10849e6i	0.327592	−	0.327592i	0.851670	+	0.524078i	$0.175590\pi$
$24$		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	0.917552	−	0.397616i	$-0.130162\pi$
$37$	3.60544e7	+	3.60544e7i	0.519936	+	0.519936i	−0.397616	+	0.917552i	$0.630162\pi$
$38$		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	$0.567308\pi$
$43$	−1.74588e8	+	1.74588e8i	−1.18761	+	1.18761i	−0.977727	+	0.209881i	$0.932692\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	2.51304e8	+	2.51304e8i	1.09575	+	1.09575i	0.994902	+	0.100843i	$0.0321541\pi$
$47$	2.51304e8	+	2.51304e8i	1.09575	+	1.09575i	0.100843	+	0.994902i	$0.467846\pi$
$48$		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	−0.477499	−	0.878632i	$-0.658457\pi$
$53$	1.67752e8	−	1.67752e8i	0.401134	−	0.401134i	0.878632	+	0.477499i	$0.158457\pi$
$54$		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	0.549816	−	0.835286i	$-0.314698\pi$
$67$	−3.85420e8	−	3.85420e8i	−0.285470	−	0.285470i	−0.835286	+	0.549816i	$0.814698\pi$
$68$		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	−0.00630706	−	0.999980i	$-0.502008\pi$
$73$	2.05996e9	−	2.05996e9i	0.993673	−	0.993673i	0.999980	+	0.00630706i	$0.00200761\pi$
$74$		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	−0.825406	−	0.564540i	$-0.809054\pi$
$83$	−1.02756e9	+	1.02756e9i	−0.260866	+	0.260866i	0.564540	+	0.825406i	$0.309054\pi$
$84$		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	0.624962	−	0.780655i	$-0.285115\pi$
$97$	−1.33700e9	−	1.33700e9i	−0.155694	−	0.155694i	−0.780655	+	0.624962i	$0.785115\pi$
$98$		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	$-0.438897\pi$
$103$	1.35915e10	−	1.35915e10i	1.17242	−	1.17242i	0.981632	−	0.190783i	$-0.0611028\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	1.18057e10	+	1.18057e10i	0.841730	+	0.841730i	0.989084	−	0.147354i	$-0.0470756\pi$
$107$	1.18057e10	+	1.18057e10i	0.841730	+	0.841730i	−0.147354	+	0.989084i	$0.547076\pi$
$108$		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	$0.520853\pi$
$113$	−1.95910e10	+	1.95910e10i	−1.06332	+	1.06332i	−0.997855	+	0.0654650i	$0.979147\pi$
$114$		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	0.945619	−	0.325278i	$-0.105458\pi$
$127$	2.04950e10	+	2.04950e10i	0.620341	+	0.620341i	−0.325278	+	0.945619i	$0.605458\pi$
$128$		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	0.320673	−	0.947190i	$-0.396091\pi$
$137$	−3.02368e10	−	3.02368e10i	−0.626517	−	0.626517i	−0.947190	+	0.320673i	$0.896091\pi$
$138$		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	$-0.911989\pi$
$157$	−1.17806e11	−	1.17806e11i	−1.23500	−	1.23500i	−0.272986	−	0.962018i	$-0.588011\pi$
$158$		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	−0.353475	−	0.935444i	$-0.615000\pi$
$163$	6.69635e10	−	6.69635e10i	0.581970	−	0.581970i	0.935444	+	0.353475i	$0.115000\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−7.83803e10	−	7.83803e10i	−0.603427	−	0.603427i	0.337793	−	0.941220i	$-0.390319\pi$
$167$	−7.83803e10	−	7.83803e10i	−0.603427	−	0.603427i	−0.941220	+	0.337793i	$0.890319\pi$
$168$		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	−0.977858	−	0.209268i	$-0.932892\pi$
$173$	−1.19104e11	+	1.19104e11i	−0.768591	+	0.768591i	0.209268	+	0.977858i	$0.432892\pi$
$174$		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	−0.976605	−	0.215043i	$-0.931011\pi$
$193$	−2.03935e11	+	2.03935e11i	−0.761561	+	0.761561i	0.215043	+	0.976605i	$0.431011\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	3.46318e10	+	3.46318e10i	0.116720	+	0.116720i	0.763054	−	0.646334i	$-0.223699\pi$
$197$	3.46318e10	+	3.46318e10i	0.116720	+	0.116720i	−0.646334	+	0.763054i	$0.723699\pi$
$198$		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	−0.857080	−	0.515184i	$-0.827724\pi$
$223$	−1.88546e11	+	1.88546e11i	−0.341896	+	0.341896i	0.515184	+	0.857080i	$0.327724\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−5.24206e11	−	5.24206e11i	−0.869706	−	0.869706i	0.122733	−	0.992440i	$-0.460834\pi$
$227$	−5.24206e11	−	5.24206e11i	−0.869706	−	0.869706i	−0.992440	+	0.122733i	$0.960834\pi$
$228$		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	−0.137752	−	0.990467i	$-0.543988\pi$
$233$	5.85576e11	−	5.85576e11i	0.852715	−	0.852715i	0.990467	+	0.137752i	$0.0439876\pi$
$234$		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	0.0963502	−	0.995348i	$-0.469283\pi$
$257$	−1.00792e12	−	1.00792e12i	−0.898997	−	0.898997i	−0.995348	+	0.0963502i	$0.969283\pi$
$258$		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	−0.311768	−	0.950158i	$-0.600921\pi$
$263$	8.03277e11	−	8.03277e11i	0.638390	−	0.638390i	0.950158	+	0.311768i	$0.100921\pi$
$264$		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	0.310197	−	0.950672i	$-0.399605\pi$
$277$	−1.04448e12	−	1.04448e12i	−0.640475	−	0.640475i	−0.950672	+	0.310197i	$0.899605\pi$
$278$		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	−0.803469	−	0.595347i	$-0.797015\pi$
$283$	−3.77789e11	+	3.77789e11i	−0.208122	+	0.208122i	0.595347	+	0.803469i	$0.297015\pi$
$284$		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	−0.994589	−	0.103892i	$-0.966870\pi$
$293$	−1.92339e12	+	1.92339e12i	−0.890697	+	0.890697i	0.103892	+	0.994589i	$0.466870\pi$
$294$		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	0.368455	−	0.929646i	$-0.379887\pi$
$307$	−1.53039e12	−	1.53039e12i	−0.561191	−	0.561191i	−0.929646	+	0.368455i	$0.879887\pi$
$308$		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	−0.370547	−	0.928814i	$-0.620830\pi$
$313$	1.67712e12	−	1.67712e12i	0.558267	−	0.558267i	0.928814	+	0.370547i	$0.120830\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	4.10539e12	+	4.10539e12i	1.28250	+	1.28250i	0.939239	+	0.343264i	$0.111533\pi$
$317$	4.10539e12	+	4.10539e12i	1.28250	+	1.28250i	0.343264	+	0.939239i	$0.388467\pi$
$318$		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	0.654303	−	0.756233i	$-0.272962\pi$
$337$	−4.43049e11	−	4.43049e11i	−0.101930	−	0.101930i	−0.756233	+	0.654303i	$0.772962\pi$
$338$		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	$-0.958275\pi$
$347$	−5.64533e12	−	5.64533e12i	−1.12213	−	1.12213i	−0.130707	−	0.991421i	$-0.541725\pi$
$348$		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	−0.910950	−	0.412517i	$-0.864650\pi$
$353$	−2.73200e12	+	2.73200e12i	−0.498433	+	0.498433i	0.412517	+	0.910950i	$0.364650\pi$
$354$		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	$-0.797491\pi$
$367$	−9.31094e12	−	9.31094e12i	−1.39850	−	1.39850i	−0.594145	−	0.804358i	$-0.702509\pi$
$368$		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	−0.853265	−	0.521477i	$-0.825381\pi$
$373$	−2.39555e12	+	2.39555e12i	−0.331788	+	0.331788i	0.521477	+	0.853265i	$0.325381\pi$
$374$		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	−0.773071	−	0.634320i	$-0.781280\pi$
$383$	−1.14348e12	+	1.14348e12i	−0.138751	+	0.138751i	0.634320	+	0.773071i	$0.281280\pi$
$384$		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	0.693564	−	0.720395i	$-0.256039\pi$
$397$	−2.64600e11	−	2.64600e11i	−0.0268311	−	0.0268311i	−0.720395	+	0.693564i	$0.756039\pi$
$398$		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	−0.962979	−	0.269577i	$-0.913116\pi$
$433$	−1.05542e13	+	1.05542e13i	−0.693402	+	0.693402i	0.269577	+	0.962979i	$0.413116\pi$
$434$		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	−0.635100	−	0.772430i	$-0.719041\pi$
$443$	2.34305e12	−	2.34305e12i	0.137329	−	0.137329i	0.772430	+	0.635100i	$0.219041\pi$
$444$		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	0.801524	−	0.597962i	$-0.204023\pi$
$457$	4.05768e12	+	4.05768e12i	0.203562	+	0.203562i	−0.597962	+	0.801524i	$0.704023\pi$
$458$		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	$-0.482506\pi$
$463$	2.24134e13	−	2.24134e13i	1.05342	−	1.05342i	0.998490	−	0.0549326i	$-0.0174944\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	2.33263e13	+	2.33263e13i	1.05018	+	1.05018i	0.998673	+	0.0515032i	$0.0164012\pi$
$467$	2.33263e13	+	2.33263e13i	1.05018	+	1.05018i	0.0515032	+	0.998673i	$0.483599\pi$
$468$		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	0.913439	−	0.406975i	$-0.133416\pi$
$487$	1.38737e13	+	1.38737e13i	0.506464	+	0.506464i	−0.406975	+	0.913439i	$0.633416\pi$
$488$		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	−0.132030	−	0.991246i	$-0.542150\pi$
$503$	2.76657e13	−	2.76657e13i	0.859215	−	0.859215i	0.991246	+	0.132030i	$0.0421497\pi$
$504$		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	−0.666460	−	0.745541i	$-0.732191\pi$
$523$	3.09443e12	−	3.09443e12i	0.0790810	−	0.0790810i	0.745541	+	0.666460i	$0.232191\pi$
$524$		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	0.782375	−	0.622808i	$-0.214008\pi$
$547$	7.81408e12	+	7.81408e12i	0.159566	+	0.159566i	−0.622808	+	0.782375i	$0.714008\pi$
$548$		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	$0.0487072\pi$
$557$	6.11592e13	+	6.11592e13i	1.14074	+	1.14074i	0.152422	+	0.988316i	$0.451293\pi$
$558$		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	$0.558117\pi$
$563$	−6.58943e13	+	6.58943e13i	−1.16495	+	1.16495i	−0.983379	+	0.181567i	$0.941883\pi$
$564$		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	0.809290	−	0.587409i	$-0.199852\pi$
$577$	1.41906e13	+	1.41906e13i	0.221881	+	0.221881i	−0.587409	+	0.809290i	$0.699852\pi$
$578$		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	$0.0320229\pi$
$587$	7.63403e13	+	7.63403e13i	1.09538	+	1.09538i	0.100433	+	0.994944i	$0.467977\pi$
$588$		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	$0.625621\pi$
$593$	−9.58857e13	+	9.58857e13i	−1.30762	+	1.30762i	−0.923131	+	0.384485i	$0.874379\pi$
$594$		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	0.824890	−	0.565294i	$-0.191237\pi$
$607$	2.13915e13	+	2.13915e13i	0.259596	+	0.259596i	−0.565294	+	0.824890i	$0.691237\pi$
$608$		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	−0.511024	−	0.859566i	$-0.670734\pi$
$613$	3.01688e13	−	3.01688e13i	0.348542	−	0.348542i	0.859566	+	0.511024i	$0.170734\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	7.24200e13	+	7.24200e13i	0.809903	+	0.809903i	0.984619	−	0.174716i	$-0.0559008\pi$
$617$	7.24200e13	+	7.24200e13i	0.809903	+	0.809903i	−0.174716	+	0.984619i	$0.555901\pi$
$618$		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	−0.269499	−	0.963001i	$-0.586858\pi$
$643$	7.62258e13	−	7.62258e13i	0.693501	−	0.693501i	0.963001	+	0.269499i	$0.0868582\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−1.96202e13	−	1.96202e13i	−0.173054	−	0.173054i	0.615266	−	0.788320i	$-0.289049\pi$
$647$	−1.96202e13	−	1.96202e13i	−0.173054	−	0.173054i	−0.788320	+	0.615266i	$0.789049\pi$
$648$		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	−0.758625	−	0.651528i	$-0.774128\pi$
$653$	−1.27158e13	+	1.27158e13i	−0.107097	+	0.107097i	0.651528	+	0.758625i	$0.274128\pi$
$654$		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	−0.341474	−	0.939891i	$-0.610926\pi$
$673$	8.26189e13	−	8.26189e13i	0.598417	−	0.598417i	0.939891	+	0.341474i	$0.110926\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	4.33113e13	+	4.33113e13i	0.304550	+	0.304550i	0.842791	−	0.538241i	$-0.180911\pi$
$677$	4.33113e13	+	4.33113e13i	0.304550	+	0.304550i	−0.538241	+	0.842791i	$0.680911\pi$
$678$		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	−0.888617	−	0.458650i	$-0.848333\pi$
$683$	−6.39056e13	+	6.39056e13i	−0.429967	+	0.429967i	0.458650	+	0.888617i	$0.348333\pi$
$684$		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	$-0.951520\pi$
$727$	−2.31542e14	−	2.31542e14i	−1.14014	−	1.14014i	−0.151716	−	0.988424i	$-0.548480\pi$
$728$		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	−0.734549	−	0.678555i	$-0.762606\pi$
$733$	−1.18484e13	+	1.18484e13i	−0.0559937	+	0.0559937i	0.678555	+	0.734549i	$0.262606\pi$
$734$		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	$-0.481108\pi$
$743$	2.39468e14	−	2.39468e14i	1.05756	−	1.05756i	0.998239	−	0.0593169i	$-0.0188922\pi$
$744$		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	0.982907	−	0.184102i	$-0.0589377\pi$
$757$	1.98573e14	+	1.98573e14i	0.798805	+	0.798805i	−0.184102	+	0.982907i	$0.558938\pi$
$758$		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	−0.969739	−	0.244142i	$-0.921494\pi$
$773$	−2.00259e14	+	2.00259e14i	−0.725597	+	0.725597i	0.244142	+	0.969739i	$0.421494\pi$
$774$		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	0.512220	−	0.858854i	$-0.328823\pi$
$787$	−1.04651e14	−	1.04651e14i	−0.346634	−	0.346634i	−0.858854	+	0.512220i	$0.828823\pi$
$788$		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	0.873122	−	0.487502i	$-0.162092\pi$
$797$	1.24009e14	+	1.24009e14i	0.385620	+	0.385620i	−0.487502	+	0.873122i	$0.662092\pi$
$798$		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	−0.172041	−	0.985090i	$-0.555036\pi$
$823$	3.06984e14	−	3.06984e14i	0.813048	−	0.813048i	0.985090	+	0.172041i	$0.0550363\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	2.70430e14	+	2.70430e14i	0.699080	+	0.699080i	0.964212	−	0.265132i	$-0.0854155\pi$
$827$	2.70430e14	+	2.70430e14i	0.699080	+	0.699080i	−0.265132	+	0.964212i	$0.585415\pi$
$828$		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	−0.951188	−	0.308611i	$-0.900136\pi$
$853$	−2.90182e14	+	2.90182e14i	−0.642577	+	0.642577i	0.308611	+	0.951188i	$0.400136\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−5.15570e14	−	5.15570e14i	−1.11528	−	1.11528i	−0.992425	−	0.122853i	$-0.960795\pi$
$857$	−5.15570e14	−	5.15570e14i	−1.11528	−	1.11528i	−0.122853	−	0.992425i	$-0.539205\pi$
$858$		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	−0.531046	−	0.847343i	$-0.678201\pi$
$863$	1.51408e14	−	1.51408e14i	0.316298	−	0.316298i	0.847343	+	0.531046i	$0.178201\pi$
$864$		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	0.0149588	−	0.999888i	$-0.495238\pi$
$877$	−5.10979e14	−	5.10979e14i	−0.984929	−	0.984929i	−0.999888	+	0.0149588i	$0.995238\pi$
$878$		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	$-0.418113\pi$
$883$	6.55698e14	−	6.55698e14i	1.22152	−	1.22152i	0.967092	−	0.254428i	$-0.0818870\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	4.59458e14	+	4.59458e14i	0.836812	+	0.836812i	0.988438	−	0.151626i	$-0.0484509\pi$
$887$	4.59458e14	+	4.59458e14i	0.836812	+	0.836812i	−0.151626	+	0.988438i	$0.548451\pi$
$888$		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	$-0.912039\pi$
$907$	−7.57995e14	−	7.57995e14i	−1.23490	−	1.23490i	−0.272834	−	0.962061i	$-0.587961\pi$
$908$		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	0.997232	−	0.0743552i	$-0.0236899\pi$
$937$	6.66564e14	+	6.66564e14i	0.922877	+	0.922877i	−0.0743552	+	0.997232i	$0.523690\pi$
$938$		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	$0.00160605\pi$
$947$	7.65473e14	+	7.65473e14i	1.00503	+	1.00503i	0.00504553	+	0.999987i	$0.498394\pi$
$948$		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	−0.978567	−	0.205928i	$-0.933979\pi$
$953$	−6.07353e14	+	6.07353e14i	−0.772639	+	0.772639i	0.205928	+	0.978567i	$0.433979\pi$
$954$		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	0.968687	−	0.248284i	$-0.0798665\pi$
$967$	6.09128e14	+	6.09128e14i	0.720404	+	0.720404i	−0.248284	+	0.968687i	$0.579866\pi$
$968$		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	$0.200278\pi$
$977$	1.24356e15	+	1.24356e15i	1.39700	+	1.39700i	0.588493	+	0.808503i	$0.299722\pi$
$978$		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	−0.903240	−	0.429136i	$-0.858818\pi$
$983$	−4.35152e14	+	4.35152e14i	−0.474103	+	0.474103i	0.429136	+	0.903240i	$0.358818\pi$
$984$		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	0.260180	−	0.965560i	$-0.416218\pi$
$997$	−6.94862e14	−	6.94862e14i	−0.705380	−	0.705380i	−0.965560	+	0.260180i	$0.916218\pi$
$998$		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.157.4	✓	16
5.2	odd	4	inner	300.11.k.c.193.5	yes	16
5.3	odd	4	inner	300.11.k.c.193.4	yes	16
5.4	even	2	inner	300.11.k.c.157.5	yes	16

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