LMFDB - Embedded newform 304.2.i.c.273.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [304,2,Mod(49,304)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(304, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("304.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 304 = 2^{4} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	304.i (of order $3$, degree $2$, not 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:	$2.42745222145$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 38)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			273.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	304.273
Dual form			304.2.i.c.49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{3} +4.00000 q^{7} +(1.00000 - 1.73205i) q^{9} +O(q^{10})$	$q+(0.500000 + 0.866025i) q^{3} +4.00000 q^{7} +(1.00000 - 1.73205i) q^{9} -3.00000 q^{11} +(-1.00000 + 1.73205i) q^{13} +(3.00000 + 5.19615i) q^{17} +(3.50000 - 2.59808i) q^{19} +(2.00000 + 3.46410i) q^{21} +(-3.00000 + 5.19615i) q^{23} +(2.50000 - 4.33013i) q^{25} +5.00000 q^{27} -2.00000 q^{31} +(-1.50000 - 2.59808i) q^{33} -10.0000 q^{37} -2.00000 q^{39} +(-4.50000 - 7.79423i) q^{41} +(-2.00000 - 3.46410i) q^{43} +9.00000 q^{49} +(-3.00000 + 5.19615i) q^{51} +(-3.00000 + 5.19615i) q^{53} +(4.00000 + 1.73205i) q^{57} +(-4.50000 - 7.79423i) q^{59} +(2.00000 - 3.46410i) q^{61} +(4.00000 - 6.92820i) q^{63} +(-3.50000 + 6.06218i) q^{67} -6.00000 q^{69} +(-3.00000 - 5.19615i) q^{71} +(0.500000 + 0.866025i) q^{73} +5.00000 q^{75} -12.0000 q^{77} +(-2.00000 - 3.46410i) q^{79} +(-0.500000 - 0.866025i) q^{81} -3.00000 q^{83} +(-3.00000 + 5.19615i) q^{89} +(-4.00000 + 6.92820i) q^{91} +(-1.00000 - 1.73205i) q^{93} +(-8.50000 - 14.7224i) q^{97} +(-3.00000 + 5.19615i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{3} + 8 q^{7} + 2 q^{9}+O(q^{10}) $ 2 * q + q^3 + 8 * q^7 + 2 * q^9	$ 2 q + q^{3} + 8 q^{7} + 2 q^{9} - 6 q^{11} - 2 q^{13} + 6 q^{17} + 7 q^{19} + 4 q^{21} - 6 q^{23} + 5 q^{25} + 10 q^{27} - 4 q^{31} - 3 q^{33} - 20 q^{37} - 4 q^{39} - 9 q^{41} - 4 q^{43} + 18 q^{49} - 6 q^{51} - 6 q^{53} + 8 q^{57} - 9 q^{59} + 4 q^{61} + 8 q^{63} - 7 q^{67} - 12 q^{69} - 6 q^{71} + q^{73} + 10 q^{75} - 24 q^{77} - 4 q^{79} - q^{81} - 6 q^{83} - 6 q^{89} - 8 q^{91} - 2 q^{93} - 17 q^{97} - 6 q^{99}+O(q^{100}) $ 2 * q + q^3 + 8 * q^7 + 2 * q^9 - 6 * q^11 - 2 * q^13 + 6 * q^17 + 7 * q^19 + 4 * q^21 - 6 * q^23 + 5 * q^25 + 10 * q^27 - 4 * q^31 - 3 * q^33 - 20 * q^37 - 4 * q^39 - 9 * q^41 - 4 * q^43 + 18 * q^49 - 6 * q^51 - 6 * q^53 + 8 * q^57 - 9 * q^59 + 4 * q^61 + 8 * q^63 - 7 * q^67 - 12 * q^69 - 6 * q^71 + q^73 + 10 * q^75 - 24 * q^77 - 4 * q^79 - q^81 - 6 * q^83 - 6 * q^89 - 8 * q^91 - 2 * q^93 - 17 * q^97 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/304\mathbb{Z}\right)^\times$.

$n$	$97$	$191$	$229$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i	0.973494	−	0.228714i	$-0.0734519\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i	−0.684819	+	0.728714i	$0.740119\pi$
$4$		0			0
$5$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$5$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$6$		0			0
$7$	4.00000			1.51186			0.755929	−	0.654654i	$-0.227186\pi$
$7$	4.00000			1.51186			0.755929	+	0.654654i	$0.227186\pi$
$8$		0			0
$9$	1.00000	−	1.73205i	0.333333	−	0.577350i
$10$		0			0
$11$	−3.00000			−0.904534			−0.452267	−	0.891883i	$-0.649385\pi$
$11$	−3.00000			−0.904534			−0.452267	+	0.891883i	$0.649385\pi$
$12$		0			0
$13$	−1.00000	+	1.73205i	−0.277350	+	0.480384i	−0.970725	−	0.240192i	$-0.922790\pi$
$13$	−1.00000	+	1.73205i	−0.277350	+	0.480384i	0.693375	+	0.720577i	$0.256123\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	3.00000	+	5.19615i	0.727607	+	1.26025i	0.957892	+	0.287129i	$0.0927008\pi$
$17$	3.00000	+	5.19615i	0.727607	+	1.26025i	−0.230285	+	0.973123i	$0.573966\pi$
$18$		0			0
$19$	3.50000	−	2.59808i	0.802955	−	0.596040i
$19$	3.50000	−	2.59808i	0.802955	−	0.596040i
$20$		0			0
$21$	2.00000	+	3.46410i	0.436436	+	0.755929i
$22$		0			0
$23$	−3.00000	+	5.19615i	−0.625543	+	1.08347i	0.362892	+	0.931831i	$0.381789\pi$
$23$	−3.00000	+	5.19615i	−0.625543	+	1.08347i	−0.988436	+	0.151642i	$0.951544\pi$
$24$		0			0
$25$	2.50000	−	4.33013i	0.500000	−	0.866025i
$26$		0			0
$27$	5.00000			0.962250
$28$		0			0
$29$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$29$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$30$		0			0
$31$	−2.00000			−0.359211			−0.179605	−	0.983739i	$-0.557482\pi$
$31$	−2.00000			−0.359211			−0.179605	+	0.983739i	$0.557482\pi$
$32$		0			0
$33$	−1.50000	−	2.59808i	−0.261116	−	0.452267i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−10.0000			−1.64399			−0.821995	−	0.569495i	$-0.807139\pi$
$37$	−10.0000			−1.64399			−0.821995	+	0.569495i	$0.807139\pi$
$38$		0			0
$39$	−2.00000			−0.320256
$40$		0			0
$41$	−4.50000	−	7.79423i	−0.702782	−	1.21725i	−0.967486	−	0.252924i	$-0.918608\pi$
$41$	−4.50000	−	7.79423i	−0.702782	−	1.21725i	0.264704	−	0.964330i	$-0.414726\pi$
$42$		0			0
$43$	−2.00000	−	3.46410i	−0.304997	−	0.528271i	0.672264	−	0.740312i	$-0.265322\pi$
$43$	−2.00000	−	3.46410i	−0.304997	−	0.528271i	−0.977261	+	0.212041i	$0.931989\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$47$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$48$		0			0
$49$	9.00000			1.28571
$50$		0			0
$51$	−3.00000	+	5.19615i	−0.420084	+	0.727607i
$52$		0			0
$53$	−3.00000	+	5.19615i	−0.412082	+	0.713746i	−0.995117	−	0.0987002i	$-0.968532\pi$
$53$	−3.00000	+	5.19615i	−0.412082	+	0.713746i	0.583036	+	0.812447i	$0.301865\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	4.00000	+	1.73205i	0.529813	+	0.229416i
$58$		0			0
$59$	−4.50000	−	7.79423i	−0.585850	−	1.01472i	−0.994769	−	0.102151i	$-0.967427\pi$
$59$	−4.50000	−	7.79423i	−0.585850	−	1.01472i	0.408919	−	0.912571i	$-0.365906\pi$
$60$		0			0
$61$	2.00000	−	3.46410i	0.256074	−	0.443533i	−0.709113	−	0.705095i	$-0.750904\pi$
$61$	2.00000	−	3.46410i	0.256074	−	0.443533i	0.965187	+	0.261562i	$0.0842377\pi$
$62$		0			0
$63$	4.00000	−	6.92820i	0.503953	−	0.872872i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−3.50000	+	6.06218i	−0.427593	+	0.740613i	−0.996659	−	0.0816792i	$-0.973972\pi$
$67$	−3.50000	+	6.06218i	−0.427593	+	0.740613i	0.569066	+	0.822292i	$0.307305\pi$
$68$		0			0
$69$	−6.00000			−0.722315
$70$		0			0
$71$	−3.00000	−	5.19615i	−0.356034	−	0.616670i	0.631260	−	0.775571i	$-0.282538\pi$
$71$	−3.00000	−	5.19615i	−0.356034	−	0.616670i	−0.987294	+	0.158901i	$0.949205\pi$
$72$		0			0
$73$	0.500000	+	0.866025i	0.0585206	+	0.101361i	0.893801	−	0.448463i	$-0.148028\pi$
$73$	0.500000	+	0.866025i	0.0585206	+	0.101361i	−0.835281	+	0.549823i	$0.814695\pi$
$74$		0			0
$75$	5.00000			0.577350
$76$		0			0
$77$	−12.0000			−1.36753
$78$		0			0
$79$	−2.00000	−	3.46410i	−0.225018	−	0.389742i	0.731307	−	0.682048i	$-0.238911\pi$
$79$	−2.00000	−	3.46410i	−0.225018	−	0.389742i	−0.956325	+	0.292306i	$0.905577\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	−3.00000			−0.329293			−0.164646	−	0.986353i	$-0.552648\pi$
$83$	−3.00000			−0.329293			−0.164646	+	0.986353i	$0.552648\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−3.00000	+	5.19615i	−0.317999	+	0.550791i	−0.980071	−	0.198650i	$-0.936344\pi$
$89$	−3.00000	+	5.19615i	−0.317999	+	0.550791i	0.662071	+	0.749441i	$0.269678\pi$
$90$		0			0
$91$	−4.00000	+	6.92820i	−0.419314	+	0.726273i
$92$		0			0
$93$	−1.00000	−	1.73205i	−0.103695	−	0.179605i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−8.50000	−	14.7224i	−0.863044	−	1.49484i	−0.868976	−	0.494854i	$-0.835222\pi$
$97$	−8.50000	−	14.7224i	−0.863044	−	1.49484i	0.00593185	−	0.999982i	$-0.498112\pi$
$98$		0			0
$99$	−3.00000	+	5.19615i	−0.301511	+	0.522233i
$100$		0			0
$101$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$101$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$102$		0			0
$103$	−2.00000			−0.197066			−0.0985329	−	0.995134i	$-0.531415\pi$
$103$	−2.00000			−0.197066			−0.0985329	+	0.995134i	$0.531415\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		0			0			−	1.00000i	$-0.5\pi$
$107$		0			0				1.00000i	$0.5\pi$
$108$		0			0
$109$	8.00000	+	13.8564i	0.766261	+	1.32720i	0.939577	+	0.342337i	$0.111218\pi$
$109$	8.00000	+	13.8564i	0.766261	+	1.32720i	−0.173316	+	0.984866i	$0.555448\pi$
$110$		0			0
$111$	−5.00000	−	8.66025i	−0.474579	−	0.821995i
$112$		0			0
$113$	15.0000			1.41108			0.705541	−	0.708669i	$-0.250704\pi$
$113$	15.0000			1.41108			0.705541	+	0.708669i	$0.250704\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	2.00000	+	3.46410i	0.184900	+	0.320256i
$118$		0			0
$119$	12.0000	+	20.7846i	1.10004	+	1.90532i
$120$		0			0
$121$	−2.00000			−0.181818
$122$		0			0
$123$	4.50000	−	7.79423i	0.405751	−	0.702782i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	1.00000	−	1.73205i	0.0887357	−	0.153695i	−0.818241	−	0.574875i	$-0.805051\pi$
$127$	1.00000	−	1.73205i	0.0887357	−	0.153695i	0.906977	+	0.421180i	$0.138384\pi$
$128$		0			0
$129$	2.00000	−	3.46410i	0.176090	−	0.304997i
$130$		0			0
$131$	4.50000	+	7.79423i	0.393167	+	0.680985i	0.992865	−	0.119241i	$-0.0380462\pi$
$131$	4.50000	+	7.79423i	0.393167	+	0.680985i	−0.599699	+	0.800226i	$0.704713\pi$
$132$		0			0
$133$	14.0000	−	10.3923i	1.21395	−	0.901127i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−4.50000	+	7.79423i	−0.384461	+	0.665906i	−0.991694	−	0.128618i	$-0.958946\pi$
$137$	−4.50000	+	7.79423i	−0.384461	+	0.665906i	0.607233	+	0.794524i	$0.292279\pi$
$138$		0			0
$139$	5.50000	−	9.52628i	0.466504	−	0.808008i	−0.532764	−	0.846264i	$-0.678847\pi$
$139$	5.50000	−	9.52628i	0.466504	−	0.808008i	0.999268	+	0.0382553i	$0.0121800\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	3.00000	−	5.19615i	0.250873	−	0.434524i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	4.50000	+	7.79423i	0.371154	+	0.642857i
$148$		0			0
$149$	−9.00000	−	15.5885i	−0.737309	−	1.27706i	−0.953703	−	0.300750i	$-0.902763\pi$
$149$	−9.00000	−	15.5885i	−0.737309	−	1.27706i	0.216394	−	0.976306i	$-0.430570\pi$
$150$		0			0
$151$	10.0000			0.813788			0.406894	−	0.913475i	$-0.366612\pi$
$151$	10.0000			0.813788			0.406894	+	0.913475i	$0.366612\pi$
$152$		0			0
$153$	12.0000			0.970143
$154$		0			0
$155$		0			0
$156$		0			0
$157$	8.00000	+	13.8564i	0.638470	+	1.10586i	0.985769	+	0.168107i	$0.0537655\pi$
$157$	8.00000	+	13.8564i	0.638470	+	1.10586i	−0.347299	+	0.937754i	$0.612901\pi$
$158$		0			0
$159$	−6.00000			−0.475831
$160$		0			0
$161$	−12.0000	+	20.7846i	−0.945732	+	1.63806i
$162$		0			0
$163$	19.0000			1.48819			0.744097	−	0.668071i	$-0.232880\pi$
$163$	19.0000			1.48819			0.744097	+	0.668071i	$0.232880\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−12.0000	+	20.7846i	−0.928588	+	1.60836i	−0.142901	+	0.989737i	$0.545643\pi$
$167$	−12.0000	+	20.7846i	−0.928588	+	1.60836i	−0.785687	+	0.618624i	$0.787690\pi$
$168$		0			0
$169$	4.50000	+	7.79423i	0.346154	+	0.599556i
$170$		0			0
$171$	−1.00000	−	8.66025i	−0.0764719	−	0.662266i
$172$		0			0
$173$	−3.00000	−	5.19615i	−0.228086	−	0.395056i	0.729155	−	0.684349i	$-0.239913\pi$
$173$	−3.00000	−	5.19615i	−0.228086	−	0.395056i	−0.957241	+	0.289292i	$0.906580\pi$
$174$		0			0
$175$	10.0000	−	17.3205i	0.755929	−	1.30931i
$176$		0			0
$177$	4.50000	−	7.79423i	0.338241	−	0.585850i
$178$		0			0
$179$	−9.00000			−0.672692			−0.336346	−	0.941739i	$-0.609191\pi$
$179$	−9.00000			−0.672692			−0.336346	+	0.941739i	$0.609191\pi$
$180$		0			0
$181$	−1.00000	+	1.73205i	−0.0743294	+	0.128742i	−0.900794	−	0.434246i	$-0.857015\pi$
$181$	−1.00000	+	1.73205i	−0.0743294	+	0.128742i	0.826465	+	0.562988i	$0.190348\pi$
$182$		0			0
$183$	4.00000			0.295689
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−9.00000	−	15.5885i	−0.658145	−	1.13994i
$188$		0			0
$189$	20.0000			1.45479
$190$		0			0
$191$	−12.0000			−0.868290			−0.434145	−	0.900843i	$-0.642949\pi$
$191$	−12.0000			−0.868290			−0.434145	+	0.900843i	$0.642949\pi$
$192$		0			0
$193$	−1.00000	−	1.73205i	−0.0719816	−	0.124676i	0.827788	−	0.561041i	$-0.189599\pi$
$193$	−1.00000	−	1.73205i	−0.0719816	−	0.124676i	−0.899770	+	0.436365i	$0.856266\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	18.0000			1.28245			0.641223	−	0.767354i	$-0.278427\pi$
$197$	18.0000			1.28245			0.641223	+	0.767354i	$0.278427\pi$
$198$		0			0
$199$	−5.00000	+	8.66025i	−0.354441	+	0.613909i	−0.987022	−	0.160585i	$-0.948662\pi$
$199$	−5.00000	+	8.66025i	−0.354441	+	0.613909i	0.632581	+	0.774494i	$0.281995\pi$
$200$		0			0
$201$	−7.00000			−0.493742
$202$		0			0
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$	6.00000	+	10.3923i	0.417029	+	0.722315i
$208$		0			0
$209$	−10.5000	+	7.79423i	−0.726300	+	0.539138i
$210$		0			0
$211$	10.0000	+	17.3205i	0.688428	+	1.19239i	0.972346	+	0.233544i	$0.0750324\pi$
$211$	10.0000	+	17.3205i	0.688428	+	1.19239i	−0.283918	+	0.958849i	$0.591634\pi$
$212$		0			0
$213$	3.00000	−	5.19615i	0.205557	−	0.356034i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−8.00000			−0.543075
$218$		0			0
$219$	−0.500000	+	0.866025i	−0.0337869	+	0.0585206i
$220$		0			0
$221$	−12.0000			−0.807207
$222$		0			0
$223$	7.00000	+	12.1244i	0.468755	+	0.811907i	0.999362	−	0.0357107i	$-0.0113695\pi$
$223$	7.00000	+	12.1244i	0.468755	+	0.811907i	−0.530607	+	0.847618i	$0.678036\pi$
$224$		0			0
$225$	−5.00000	−	8.66025i	−0.333333	−	0.577350i
$226$		0			0
$227$	−3.00000			−0.199117			−0.0995585	−	0.995032i	$-0.531743\pi$
$227$	−3.00000			−0.199117			−0.0995585	+	0.995032i	$0.531743\pi$
$228$		0			0
$229$	−16.0000			−1.05731			−0.528655	−	0.848837i	$-0.677303\pi$
$229$	−16.0000			−1.05731			−0.528655	+	0.848837i	$0.677303\pi$
$230$		0			0
$231$	−6.00000	−	10.3923i	−0.394771	−	0.683763i
$232$		0			0
$233$	−1.50000	−	2.59808i	−0.0982683	−	0.170206i	0.812700	−	0.582683i	$-0.197997\pi$
$233$	−1.50000	−	2.59808i	−0.0982683	−	0.170206i	−0.910968	+	0.412477i	$0.864664\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	2.00000	−	3.46410i	0.129914	−	0.225018i
$238$		0			0
$239$	12.0000			0.776215			0.388108	−	0.921614i	$-0.373129\pi$
$239$	12.0000			0.776215			0.388108	+	0.921614i	$0.373129\pi$
$240$		0			0
$241$	−2.50000	+	4.33013i	−0.161039	+	0.278928i	−0.935242	−	0.354010i	$-0.884818\pi$
$241$	−2.50000	+	4.33013i	−0.161039	+	0.278928i	0.774202	+	0.632938i	$0.218151\pi$
$242$		0			0
$243$	8.00000	−	13.8564i	0.513200	−	0.888889i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	1.00000	+	8.66025i	0.0636285	+	0.551039i
$248$		0			0
$249$	−1.50000	−	2.59808i	−0.0950586	−	0.164646i
$250$		0			0
$251$	−1.50000	+	2.59808i	−0.0946792	+	0.163989i	−0.909475	−	0.415759i	$-0.863516\pi$
$251$	−1.50000	+	2.59808i	−0.0946792	+	0.163989i	0.814795	+	0.579748i	$0.196849\pi$
$252$		0			0
$253$	9.00000	−	15.5885i	0.565825	−	0.980038i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−1.50000	+	2.59808i	−0.0935674	+	0.162064i	−0.909010	−	0.416775i	$-0.863160\pi$
$257$	−1.50000	+	2.59808i	−0.0935674	+	0.162064i	0.815442	+	0.578838i	$0.196494\pi$
$258$		0			0
$259$	−40.0000			−2.48548
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−6.00000	−	10.3923i	−0.369976	−	0.640817i	0.619586	−	0.784929i	$-0.287301\pi$
$263$	−6.00000	−	10.3923i	−0.369976	−	0.640817i	−0.989561	+	0.144112i	$0.953967\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−6.00000			−0.367194
$268$		0			0
$269$	−6.00000	−	10.3923i	−0.365826	−	0.633630i	0.623082	−	0.782157i	$-0.285880\pi$
$269$	−6.00000	−	10.3923i	−0.365826	−	0.633630i	−0.988908	+	0.148527i	$0.952547\pi$
$270$		0			0
$271$	−8.00000	−	13.8564i	−0.485965	−	0.841717i	0.513905	−	0.857847i	$-0.328199\pi$
$271$	−8.00000	−	13.8564i	−0.485965	−	0.841717i	−0.999870	+	0.0161307i	$0.994865\pi$
$272$		0			0
$273$	−8.00000			−0.484182
$274$		0			0
$275$	−7.50000	+	12.9904i	−0.452267	+	0.783349i
$276$		0			0
$277$	8.00000			0.480673			0.240337	−	0.970690i	$-0.422742\pi$
$277$	8.00000			0.480673			0.240337	+	0.970690i	$0.422742\pi$
$278$		0			0
$279$	−2.00000	+	3.46410i	−0.119737	+	0.207390i
$280$		0			0
$281$	−13.5000	+	23.3827i	−0.805342	+	1.39489i	0.110717	+	0.993852i	$0.464685\pi$
$281$	−13.5000	+	23.3827i	−0.805342	+	1.39489i	−0.916060	+	0.401042i	$0.868648\pi$
$282$		0			0
$283$	2.50000	+	4.33013i	0.148610	+	0.257399i	0.930714	−	0.365748i	$-0.119187\pi$
$283$	2.50000	+	4.33013i	0.148610	+	0.257399i	−0.782104	+	0.623148i	$0.785854\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−18.0000	−	31.1769i	−1.06251	−	1.84032i
$288$		0			0
$289$	−9.50000	+	16.4545i	−0.558824	+	0.967911i
$290$		0			0
$291$	8.50000	−	14.7224i	0.498279	−	0.863044i
$292$		0			0
$293$	24.0000			1.40209			0.701047	−	0.713115i	$-0.252716\pi$
$293$	24.0000			1.40209			0.701047	+	0.713115i	$0.252716\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−15.0000			−0.870388
$298$		0			0
$299$	−6.00000	−	10.3923i	−0.346989	−	0.601003i
$300$		0			0
$301$	−8.00000	−	13.8564i	−0.461112	−	0.798670i
$302$		0			0
$303$		0			0
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−3.50000	−	6.06218i	−0.199756	−	0.345987i	0.748694	−	0.662916i	$-0.230681\pi$
$307$	−3.50000	−	6.06218i	−0.199756	−	0.345987i	−0.948449	+	0.316929i	$0.897348\pi$
$308$		0			0
$309$	−1.00000	−	1.73205i	−0.0568880	−	0.0985329i
$310$		0			0
$311$	30.0000			1.70114			0.850572	−	0.525859i	$-0.176256\pi$
$311$	30.0000			1.70114			0.850572	+	0.525859i	$0.176256\pi$
$312$		0			0
$313$	9.50000	−	16.4545i	0.536972	−	0.930062i	−0.462093	−	0.886831i	$-0.652902\pi$
$313$	9.50000	−	16.4545i	0.536972	−	0.930062i	0.999065	−	0.0432311i	$-0.0137652\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	9.00000	−	15.5885i	0.505490	−	0.875535i	−0.494489	−	0.869184i	$-0.664645\pi$
$317$	9.00000	−	15.5885i	0.505490	−	0.875535i	0.999980	−	0.00635137i	$-0.00202172\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$		0			0
$322$		0			0
$323$	24.0000	+	10.3923i	1.33540	+	0.578243i
$324$		0			0
$325$	5.00000	+	8.66025i	0.277350	+	0.480384i
$326$		0			0
$327$	−8.00000	+	13.8564i	−0.442401	+	0.766261i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−5.00000			−0.274825			−0.137412	−	0.990514i	$-0.543879\pi$
$331$	−5.00000			−0.274825			−0.137412	+	0.990514i	$0.543879\pi$
$332$		0			0
$333$	−10.0000	+	17.3205i	−0.547997	+	0.949158i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−5.50000	−	9.52628i	−0.299604	−	0.518930i	0.676441	−	0.736497i	$-0.263521\pi$
$337$	−5.50000	−	9.52628i	−0.299604	−	0.518930i	−0.976045	+	0.217567i	$0.930188\pi$
$338$		0			0
$339$	7.50000	+	12.9904i	0.407344	+	0.705541i
$340$		0			0
$341$	6.00000			0.324918
$342$		0			0
$343$	8.00000			0.431959
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−4.50000	−	7.79423i	−0.241573	−	0.418416i	0.719590	−	0.694399i	$-0.244330\pi$
$347$	−4.50000	−	7.79423i	−0.241573	−	0.418416i	−0.961162	+	0.275983i	$0.910997\pi$
$348$		0			0
$349$	−4.00000			−0.214115			−0.107058	−	0.994253i	$-0.534143\pi$
$349$	−4.00000			−0.214115			−0.107058	+	0.994253i	$0.534143\pi$
$350$		0			0
$351$	−5.00000	+	8.66025i	−0.266880	+	0.462250i
$352$		0			0
$353$	3.00000			0.159674			0.0798369	−	0.996808i	$-0.474560\pi$
$353$	3.00000			0.159674			0.0798369	+	0.996808i	$0.474560\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−12.0000	+	20.7846i	−0.635107	+	1.10004i
$358$		0			0
$359$	−3.00000	−	5.19615i	−0.158334	−	0.274242i	0.775934	−	0.630814i	$-0.217279\pi$
$359$	−3.00000	−	5.19615i	−0.158334	−	0.274242i	−0.934268	+	0.356572i	$0.883946\pi$
$360$		0			0
$361$	5.50000	−	18.1865i	0.289474	−	0.957186i
$362$		0			0
$363$	−1.00000	−	1.73205i	−0.0524864	−	0.0909091i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−11.0000	+	19.0526i	−0.574195	+	0.994535i	0.421933	+	0.906627i	$0.361352\pi$
$367$	−11.0000	+	19.0526i	−0.574195	+	0.994535i	−0.996129	+	0.0879086i	$0.971982\pi$
$368$		0			0
$369$	−18.0000			−0.937043
$370$		0			0
$371$	−12.0000	+	20.7846i	−0.623009	+	1.07908i
$372$		0			0
$373$	−4.00000			−0.207112			−0.103556	−	0.994624i	$-0.533022\pi$
$373$	−4.00000			−0.207112			−0.103556	+	0.994624i	$0.533022\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	28.0000			1.43826			0.719132	−	0.694874i	$-0.244540\pi$
$379$	28.0000			1.43826			0.719132	+	0.694874i	$0.244540\pi$
$380$		0			0
$381$	2.00000			0.102463
$382$		0			0
$383$	−18.0000	−	31.1769i	−0.919757	−	1.59307i	−0.799783	−	0.600289i	$-0.795052\pi$
$383$	−18.0000	−	31.1769i	−0.919757	−	1.59307i	−0.119974	−	0.992777i	$-0.538281\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−8.00000			−0.406663
$388$		0			0
$389$	18.0000	−	31.1769i	0.912636	−	1.58073i	0.102311	−	0.994753i	$-0.467376\pi$
$389$	18.0000	−	31.1769i	0.912636	−	1.58073i	0.810326	−	0.585980i	$-0.199290\pi$
$390$		0			0
$391$	−36.0000			−1.82060
$392$		0			0
$393$	−4.50000	+	7.79423i	−0.226995	+	0.393167i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	5.00000	+	8.66025i	0.250943	+	0.434646i	0.963786	−	0.266678i	$-0.0859261\pi$
$397$	5.00000	+	8.66025i	0.250943	+	0.434646i	−0.712843	+	0.701324i	$0.752593\pi$
$398$		0			0
$399$	16.0000	+	6.92820i	0.801002	+	0.346844i
$400$		0			0
$401$	13.5000	+	23.3827i	0.674158	+	1.16768i	0.976714	+	0.214544i	$0.0688266\pi$
$401$	13.5000	+	23.3827i	0.674158	+	1.16768i	−0.302556	+	0.953131i	$0.597840\pi$
$402$		0			0
$403$	2.00000	−	3.46410i	0.0996271	−	0.172559i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	30.0000			1.48704
$408$		0			0
$409$	−2.50000	+	4.33013i	−0.123617	+	0.214111i	−0.921192	−	0.389109i	$-0.872783\pi$
$409$	−2.50000	+	4.33013i	−0.123617	+	0.214111i	0.797574	+	0.603220i	$0.206116\pi$
$410$		0			0
$411$	−9.00000			−0.443937
$412$		0			0
$413$	−18.0000	−	31.1769i	−0.885722	−	1.53412i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	11.0000			0.538672
$418$		0			0
$419$	12.0000			0.586238			0.293119	−	0.956076i	$-0.405307\pi$
$419$	12.0000			0.586238			0.293119	+	0.956076i	$0.405307\pi$
$420$		0			0
$421$	5.00000	+	8.66025i	0.243685	+	0.422075i	0.961761	−	0.273890i	$-0.0883103\pi$
$421$	5.00000	+	8.66025i	0.243685	+	0.422075i	−0.718076	+	0.695965i	$0.754977\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	30.0000			1.45521
$426$		0			0
$427$	8.00000	−	13.8564i	0.387147	−	0.670559i
$428$		0			0
$429$	6.00000			0.289683
$430$		0			0
$431$	−15.0000	+	25.9808i	−0.722525	+	1.25145i	0.237460	+	0.971397i	$0.423685\pi$
$431$	−15.0000	+	25.9808i	−0.722525	+	1.25145i	−0.959985	+	0.280052i	$0.909648\pi$
$432$		0			0
$433$	−13.0000	+	22.5167i	−0.624740	+	1.08208i	0.363851	+	0.931457i	$0.381462\pi$
$433$	−13.0000	+	22.5167i	−0.624740	+	1.08208i	−0.988591	+	0.150624i	$0.951872\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	3.00000	+	25.9808i	0.143509	+	1.24283i
$438$		0			0
$439$	7.00000	+	12.1244i	0.334092	+	0.578664i	0.983310	−	0.181938i	$-0.0582371\pi$
$439$	7.00000	+	12.1244i	0.334092	+	0.578664i	−0.649218	+	0.760602i	$0.724904\pi$
$440$		0			0
$441$	9.00000	−	15.5885i	0.428571	−	0.742307i
$442$		0			0
$443$	4.50000	−	7.79423i	0.213801	−	0.370315i	−0.739100	−	0.673596i	$-0.764749\pi$
$443$	4.50000	−	7.79423i	0.213801	−	0.370315i	0.952901	+	0.303281i	$0.0980821\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	9.00000	−	15.5885i	0.425685	−	0.737309i
$448$		0			0
$449$	9.00000			0.424736			0.212368	−	0.977190i	$-0.431882\pi$
$449$	9.00000			0.424736			0.212368	+	0.977190i	$0.431882\pi$
$450$		0			0
$451$	13.5000	+	23.3827i	0.635690	+	1.10105i
$452$		0			0
$453$	5.00000	+	8.66025i	0.234920	+	0.406894i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	5.00000			0.233890			0.116945	−	0.993138i	$-0.462690\pi$
$457$	5.00000			0.233890			0.116945	+	0.993138i	$0.462690\pi$
$458$		0			0
$459$	15.0000	+	25.9808i	0.700140	+	1.21268i
$460$		0			0
$461$	−3.00000	−	5.19615i	−0.139724	−	0.242009i	0.787668	−	0.616100i	$-0.211288\pi$
$461$	−3.00000	−	5.19615i	−0.139724	−	0.242009i	−0.927392	+	0.374091i	$0.877955\pi$
$462$		0			0
$463$	34.0000			1.58011			0.790057	−	0.613033i	$-0.210051\pi$
$463$	34.0000			1.58011			0.790057	+	0.613033i	$0.210051\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	27.0000			1.24941			0.624705	−	0.780860i	$-0.285219\pi$
$467$	27.0000			1.24941			0.624705	+	0.780860i	$0.285219\pi$
$468$		0			0
$469$	−14.0000	+	24.2487i	−0.646460	+	1.11970i
$470$		0			0
$471$	−8.00000	+	13.8564i	−0.368621	+	0.638470i
$472$		0			0
$473$	6.00000	+	10.3923i	0.275880	+	0.477839i
$474$		0			0
$475$	−2.50000	−	21.6506i	−0.114708	−	0.993399i
$476$		0			0
$477$	6.00000	+	10.3923i	0.274721	+	0.475831i
$478$		0			0
$479$	18.0000	−	31.1769i	0.822441	−	1.42451i	−0.0814184	−	0.996680i	$-0.525945\pi$
$479$	18.0000	−	31.1769i	0.822441	−	1.42451i	0.903859	−	0.427830i	$-0.140722\pi$
$480$		0			0
$481$	10.0000	−	17.3205i	0.455961	−	0.789747i
$482$		0			0
$483$	−24.0000			−1.09204
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−2.00000			−0.0906287			−0.0453143	−	0.998973i	$-0.514429\pi$
$487$	−2.00000			−0.0906287			−0.0453143	+	0.998973i	$0.514429\pi$
$488$		0			0
$489$	9.50000	+	16.4545i	0.429605	+	0.744097i
$490$		0			0
$491$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$491$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−12.0000	−	20.7846i	−0.538274	−	0.932317i
$498$		0			0
$499$	−12.5000	−	21.6506i	−0.559577	−	0.969216i	−0.997532	−	0.0702185i	$-0.977630\pi$
$499$	−12.5000	−	21.6506i	−0.559577	−	0.969216i	0.437955	−	0.898997i	$-0.355703\pi$
$500$		0			0
$501$	−24.0000			−1.07224
$502$		0			0
$503$	3.00000	−	5.19615i	0.133763	−	0.231685i	−0.791361	−	0.611349i	$-0.790627\pi$
$503$	3.00000	−	5.19615i	0.133763	−	0.231685i	0.925124	+	0.379664i	$0.123960\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−4.50000	+	7.79423i	−0.199852	+	0.346154i
$508$		0			0
$509$	12.0000	−	20.7846i	0.531891	−	0.921262i	−0.467416	−	0.884037i	$-0.654815\pi$
$509$	12.0000	−	20.7846i	0.531891	−	0.921262i	0.999307	−	0.0372243i	$-0.0118516\pi$
$510$		0			0
$511$	2.00000	+	3.46410i	0.0884748	+	0.153243i
$512$		0			0
$513$	17.5000	−	12.9904i	0.772644	−	0.573539i
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$	3.00000	−	5.19615i	0.131685	−	0.228086i
$520$		0			0
$521$	9.00000			0.394297			0.197149	−	0.980374i	$-0.436832\pi$
$521$	9.00000			0.394297			0.197149	+	0.980374i	$0.436832\pi$
$522$		0			0
$523$	−14.0000	+	24.2487i	−0.612177	+	1.06032i	0.378695	+	0.925521i	$0.376373\pi$
$523$	−14.0000	+	24.2487i	−0.612177	+	1.06032i	−0.990873	+	0.134801i	$0.956961\pi$
$524$		0			0
$525$	20.0000			0.872872
$526$		0			0
$527$	−6.00000	−	10.3923i	−0.261364	−	0.452696i
$528$		0			0
$529$	−6.50000	−	11.2583i	−0.282609	−	0.489493i
$530$		0			0
$531$	−18.0000			−0.781133
$532$		0			0
$533$	18.0000			0.779667
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−4.50000	−	7.79423i	−0.194189	−	0.336346i
$538$		0			0
$539$	−27.0000			−1.16297
$540$		0			0
$541$	−22.0000	+	38.1051i	−0.945854	+	1.63827i	−0.191821	+	0.981430i	$0.561439\pi$
$541$	−22.0000	+	38.1051i	−0.945854	+	1.63827i	−0.754032	+	0.656837i	$0.771894\pi$
$542$		0			0
$543$	−2.00000			−0.0858282
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−2.00000	+	3.46410i	−0.0855138	+	0.148114i	−0.905610	−	0.424111i	$-0.860587\pi$
$547$	−2.00000	+	3.46410i	−0.0855138	+	0.148114i	0.820096	+	0.572226i	$0.193920\pi$
$548$		0			0
$549$	−4.00000	−	6.92820i	−0.170716	−	0.295689i
$550$		0			0
$551$		0			0
$552$		0			0
$553$	−8.00000	−	13.8564i	−0.340195	−	0.589234i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−12.0000	+	20.7846i	−0.508456	+	0.880672i	0.491496	+	0.870880i	$0.336450\pi$
$557$	−12.0000	+	20.7846i	−0.508456	+	0.880672i	−0.999952	+	0.00979220i	$0.996883\pi$
$558$		0			0
$559$	8.00000			0.338364
$560$		0			0
$561$	9.00000	−	15.5885i	0.379980	−	0.658145i
$562$		0			0
$563$	21.0000			0.885044			0.442522	−	0.896758i	$-0.354084\pi$
$563$	21.0000			0.885044			0.442522	+	0.896758i	$0.354084\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−2.00000	−	3.46410i	−0.0839921	−	0.145479i
$568$		0			0
$569$	−6.00000			−0.251533			−0.125767	−	0.992060i	$-0.540139\pi$
$569$	−6.00000			−0.251533			−0.125767	+	0.992060i	$0.540139\pi$
$570$		0			0
$571$	7.00000			0.292941			0.146470	−	0.989215i	$-0.453209\pi$
$571$	7.00000			0.292941			0.146470	+	0.989215i	$0.453209\pi$
$572$		0			0
$573$	−6.00000	−	10.3923i	−0.250654	−	0.434145i
$574$		0			0
$575$	15.0000	+	25.9808i	0.625543	+	1.08347i
$576$		0			0
$577$	11.0000			0.457936			0.228968	−	0.973434i	$-0.426465\pi$
$577$	11.0000			0.457936			0.228968	+	0.973434i	$0.426465\pi$
$578$		0			0
$579$	1.00000	−	1.73205i	0.0415586	−	0.0719816i
$580$		0			0
$581$	−12.0000			−0.497844
$582$		0			0
$583$	9.00000	−	15.5885i	0.372742	−	0.645608i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−6.00000	−	10.3923i	−0.247647	−	0.428936i	0.715226	−	0.698893i	$-0.246324\pi$
$587$	−6.00000	−	10.3923i	−0.247647	−	0.428936i	−0.962872	+	0.269957i	$0.912990\pi$
$588$		0			0
$589$	−7.00000	+	5.19615i	−0.288430	+	0.214104i
$590$		0			0
$591$	9.00000	+	15.5885i	0.370211	+	0.641223i
$592$		0			0
$593$	10.5000	−	18.1865i	0.431183	−	0.746831i	−0.565792	−	0.824548i	$-0.691430\pi$
$593$	10.5000	−	18.1865i	0.431183	−	0.746831i	0.996976	+	0.0777165i	$0.0247629\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−10.0000			−0.409273
$598$		0			0
$599$	−3.00000	+	5.19615i	−0.122577	+	0.212309i	−0.920783	−	0.390075i	$-0.872449\pi$
$599$	−3.00000	+	5.19615i	−0.122577	+	0.212309i	0.798206	+	0.602384i	$0.205782\pi$
$600$		0			0
$601$	−13.0000			−0.530281			−0.265141	−	0.964210i	$-0.585418\pi$
$601$	−13.0000			−0.530281			−0.265141	+	0.964210i	$0.585418\pi$
$602$		0			0
$603$	7.00000	+	12.1244i	0.285062	+	0.493742i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−20.0000			−0.811775			−0.405887	−	0.913923i	$-0.633038\pi$
$607$	−20.0000			−0.811775			−0.405887	+	0.913923i	$0.633038\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−1.00000	−	1.73205i	−0.0403896	−	0.0699569i	0.845124	−	0.534570i	$-0.179527\pi$
$613$	−1.00000	−	1.73205i	−0.0403896	−	0.0699569i	−0.885514	+	0.464614i	$0.846193\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−1.50000	+	2.59808i	−0.0603877	+	0.104595i	−0.894639	−	0.446790i	$-0.852567\pi$
$617$	−1.50000	+	2.59808i	−0.0603877	+	0.104595i	0.834251	+	0.551385i	$0.185900\pi$
$618$		0			0
$619$	4.00000			0.160774			0.0803868	−	0.996764i	$-0.474384\pi$
$619$	4.00000			0.160774			0.0803868	+	0.996764i	$0.474384\pi$
$620$		0			0
$621$	−15.0000	+	25.9808i	−0.601929	+	1.04257i
$622$		0			0
$623$	−12.0000	+	20.7846i	−0.480770	+	0.832718i
$624$		0			0
$625$	−12.5000	−	21.6506i	−0.500000	−	0.866025i
$626$		0			0
$627$	−12.0000	−	5.19615i	−0.479234	−	0.207514i
$628$		0			0
$629$	−30.0000	−	51.9615i	−1.19618	−	2.07184i
$630$		0			0
$631$	−14.0000	+	24.2487i	−0.557331	+	0.965326i	0.440387	+	0.897808i	$0.354841\pi$
$631$	−14.0000	+	24.2487i	−0.557331	+	0.965326i	−0.997718	+	0.0675178i	$0.978492\pi$
$632$		0			0
$633$	−10.0000	+	17.3205i	−0.397464	+	0.688428i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−9.00000	+	15.5885i	−0.356593	+	0.617637i
$638$		0			0
$639$	−12.0000			−0.474713
$640$		0			0
$641$	19.5000	+	33.7750i	0.770204	+	1.33403i	0.937451	+	0.348117i	$0.113179\pi$
$641$	19.5000	+	33.7750i	0.770204	+	1.33403i	−0.167247	+	0.985915i	$0.553488\pi$
$642$		0			0
$643$	−21.5000	−	37.2391i	−0.847877	−	1.46857i	−0.883099	−	0.469187i	$-0.844547\pi$
$643$	−21.5000	−	37.2391i	−0.847877	−	1.46857i	0.0352216	−	0.999380i	$-0.488786\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−18.0000			−0.707653			−0.353827	−	0.935311i	$-0.615120\pi$
$647$	−18.0000			−0.707653			−0.353827	+	0.935311i	$0.615120\pi$
$648$		0			0
$649$	13.5000	+	23.3827i	0.529921	+	0.917851i
$650$		0			0
$651$	−4.00000	−	6.92820i	−0.156772	−	0.271538i
$652$		0			0
$653$	−12.0000			−0.469596			−0.234798	−	0.972044i	$-0.575443\pi$
$653$	−12.0000			−0.469596			−0.234798	+	0.972044i	$0.575443\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	2.00000			0.0780274
$658$		0			0
$659$	18.0000	−	31.1769i	0.701180	−	1.21448i	−0.266872	−	0.963732i	$-0.585990\pi$
$659$	18.0000	−	31.1769i	0.701180	−	1.21448i	0.968052	−	0.250748i	$-0.0806766\pi$
$660$		0			0
$661$	20.0000	−	34.6410i	0.777910	−	1.34738i	−0.155235	−	0.987878i	$-0.549613\pi$
$661$	20.0000	−	34.6410i	0.777910	−	1.34738i	0.933144	−	0.359502i	$-0.117053\pi$
$662$		0			0
$663$	−6.00000	−	10.3923i	−0.233021	−	0.403604i
$664$		0			0
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$	−7.00000	+	12.1244i	−0.270636	+	0.468755i
$670$		0			0
$671$	−6.00000	+	10.3923i	−0.231627	+	0.401190i
$672$		0			0
$673$	14.0000			0.539660			0.269830	−	0.962908i	$-0.413032\pi$
$673$	14.0000			0.539660			0.269830	+	0.962908i	$0.413032\pi$
$674$		0			0
$675$	12.5000	−	21.6506i	0.481125	−	0.833333i
$676$		0			0
$677$	−42.0000			−1.61419			−0.807096	−	0.590421i	$-0.798962\pi$
$677$	−42.0000			−1.61419			−0.807096	+	0.590421i	$0.798962\pi$
$678$		0			0
$679$	−34.0000	−	58.8897i	−1.30480	−	2.25998i
$680$		0			0
$681$	−1.50000	−	2.59808i	−0.0574801	−	0.0995585i
$682$		0			0
$683$	36.0000			1.37750			0.688751	−	0.724998i	$-0.258159\pi$
$683$	36.0000			1.37750			0.688751	+	0.724998i	$0.258159\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−8.00000	−	13.8564i	−0.305219	−	0.528655i
$688$		0			0
$689$	−6.00000	−	10.3923i	−0.228582	−	0.395915i
$690$		0			0
$691$	−44.0000			−1.67384			−0.836919	−	0.547326i	$-0.815646\pi$
$691$	−44.0000			−1.67384			−0.836919	+	0.547326i	$0.815646\pi$
$692$		0			0
$693$	−12.0000	+	20.7846i	−0.455842	+	0.789542i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	27.0000	−	46.7654i	1.02270	−	1.77136i
$698$		0			0
$699$	1.50000	−	2.59808i	0.0567352	−	0.0982683i
$700$		0			0
$701$	12.0000	+	20.7846i	0.453234	+	0.785024i	0.998585	−	0.0531839i	$-0.0169370\pi$
$701$	12.0000	+	20.7846i	0.453234	+	0.785024i	−0.545351	+	0.838208i	$0.683604\pi$
$702$		0			0
$703$	−35.0000	+	25.9808i	−1.32005	+	0.979883i
$704$		0			0
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−7.00000	+	12.1244i	−0.262891	+	0.455340i	−0.967009	−	0.254743i	$-0.918009\pi$
$709$	−7.00000	+	12.1244i	−0.262891	+	0.455340i	0.704118	+	0.710083i	$0.251342\pi$
$710$		0			0
$711$	−8.00000			−0.300023
$712$		0			0
$713$	6.00000	−	10.3923i	0.224702	−	0.389195i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	6.00000	+	10.3923i	0.224074	+	0.388108i
$718$		0			0
$719$	15.0000	+	25.9808i	0.559406	+	0.968919i	0.997546	+	0.0700124i	$0.0223039\pi$
$719$	15.0000	+	25.9808i	0.559406	+	0.968919i	−0.438141	+	0.898906i	$0.644363\pi$
$720$		0			0
$721$	−8.00000			−0.297936
$722$		0			0
$723$	−5.00000			−0.185952
$724$		0			0
$725$		0			0
$726$		0			0
$727$	16.0000	+	27.7128i	0.593407	+	1.02781i	0.993770	+	0.111454i	$0.0355509\pi$
$727$	16.0000	+	27.7128i	0.593407	+	1.02781i	−0.400362	+	0.916357i	$0.631116\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$		0			0
$731$	12.0000	−	20.7846i	0.443836	−	0.768747i
$732$		0			0
$733$	−22.0000			−0.812589			−0.406294	−	0.913742i	$-0.633179\pi$
$733$	−22.0000			−0.812589			−0.406294	+	0.913742i	$0.633179\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	10.5000	−	18.1865i	0.386772	−	0.669910i
$738$		0			0
$739$	17.5000	+	30.3109i	0.643748	+	1.11500i	0.984589	+	0.174883i	$0.0559548\pi$
$739$	17.5000	+	30.3109i	0.643748	+	1.11500i	−0.340841	+	0.940121i	$0.610712\pi$
$740$		0			0
$741$	−7.00000	+	5.19615i	−0.257151	+	0.190885i
$742$		0			0
$743$	−9.00000	−	15.5885i	−0.330178	−	0.571885i	0.652369	−	0.757902i	$-0.273775\pi$
$743$	−9.00000	−	15.5885i	−0.330178	−	0.571885i	−0.982547	+	0.186017i	$0.940442\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−3.00000	+	5.19615i	−0.109764	+	0.190117i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	19.0000	−	32.9090i	0.693320	−	1.20087i	−0.277424	−	0.960748i	$-0.589481\pi$
$751$	19.0000	−	32.9090i	0.693320	−	1.20087i	0.970744	−	0.240118i	$-0.0771860\pi$
$752$		0			0
$753$	−3.00000			−0.109326
$754$		0			0
$755$		0			0
$756$		0			0
$757$	5.00000	+	8.66025i	0.181728	+	0.314762i	0.942469	−	0.334293i	$-0.108498\pi$
$757$	5.00000	+	8.66025i	0.181728	+	0.314762i	−0.760741	+	0.649056i	$0.775164\pi$
$758$		0			0
$759$	18.0000			0.653359
$760$		0			0
$761$	−39.0000			−1.41375			−0.706874	−	0.707339i	$-0.749895\pi$
$761$	−39.0000			−1.41375			−0.706874	+	0.707339i	$0.749895\pi$
$762$		0			0
$763$	32.0000	+	55.4256i	1.15848	+	2.00654i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	18.0000			0.649942
$768$		0			0
$769$	−1.00000	+	1.73205i	−0.0360609	+	0.0624593i	−0.883493	−	0.468445i	$-0.844814\pi$
$769$	−1.00000	+	1.73205i	−0.0360609	+	0.0624593i	0.847432	+	0.530904i	$0.178148\pi$
$770$		0			0
$771$	−3.00000			−0.108042
$772$		0			0
$773$	24.0000	−	41.5692i	0.863220	−	1.49514i	−0.00558380	−	0.999984i	$-0.501777\pi$
$773$	24.0000	−	41.5692i	0.863220	−	1.49514i	0.868804	−	0.495156i	$-0.164889\pi$
$774$		0			0
$775$	−5.00000	+	8.66025i	−0.179605	+	0.311086i
$776$		0			0
$777$	−20.0000	−	34.6410i	−0.717496	−	1.24274i
$778$		0			0
$779$	−36.0000	−	15.5885i	−1.28983	−	0.558514i
$780$		0			0
$781$	9.00000	+	15.5885i	0.322045	+	0.557799i
$782$		0			0
$783$		0			0
$784$		0			0
$785$		0			0
$786$		0			0
$787$	7.00000			0.249523			0.124762	−	0.992187i	$-0.460183\pi$
$787$	7.00000			0.249523			0.124762	+	0.992187i	$0.460183\pi$
$788$		0			0
$789$	6.00000	−	10.3923i	0.213606	−	0.369976i
$790$		0			0
$791$	60.0000			2.13335
$792$		0			0
$793$	4.00000	+	6.92820i	0.142044	+	0.246028i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	6.00000			0.212531			0.106265	−	0.994338i	$-0.466111\pi$
$797$	6.00000			0.212531			0.106265	+	0.994338i	$0.466111\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$	6.00000	+	10.3923i	0.212000	+	0.367194i
$802$		0			0
$803$	−1.50000	−	2.59808i	−0.0529339	−	0.0916841i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	6.00000	−	10.3923i	0.211210	−	0.365826i
$808$		0			0
$809$	45.0000			1.58212			0.791058	−	0.611741i	$-0.209531\pi$
$809$	45.0000			1.58212			0.791058	+	0.611741i	$0.209531\pi$
$810$		0			0
$811$	−8.00000	+	13.8564i	−0.280918	+	0.486564i	−0.971611	−	0.236584i	$-0.923972\pi$
$811$	−8.00000	+	13.8564i	−0.280918	+	0.486564i	0.690693	+	0.723148i	$0.257306\pi$
$812$		0			0
$813$	8.00000	−	13.8564i	0.280572	−	0.485965i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−16.0000	−	6.92820i	−0.559769	−	0.242387i
$818$		0			0
$819$	8.00000	+	13.8564i	0.279543	+	0.484182i
$820$		0			0
$821$	−9.00000	+	15.5885i	−0.314102	+	0.544041i	−0.979246	−	0.202674i	$-0.935037\pi$
$821$	−9.00000	+	15.5885i	−0.314102	+	0.544041i	0.665144	+	0.746715i	$0.268370\pi$
$822$		0			0
$823$	7.00000	−	12.1244i	0.244005	−	0.422628i	−0.717847	−	0.696201i	$-0.754872\pi$
$823$	7.00000	−	12.1244i	0.244005	−	0.422628i	0.961851	+	0.273573i	$0.0882054\pi$
$824$		0			0
$825$	−15.0000			−0.522233
$826$		0			0
$827$	−19.5000	+	33.7750i	−0.678081	+	1.17447i	0.297477	+	0.954729i	$0.403855\pi$
$827$	−19.5000	+	33.7750i	−0.678081	+	1.17447i	−0.975558	+	0.219742i	$0.929478\pi$
$828$		0			0
$829$	44.0000			1.52818			0.764092	−	0.645108i	$-0.223188\pi$
$829$	44.0000			1.52818			0.764092	+	0.645108i	$0.223188\pi$
$830$		0			0
$831$	4.00000	+	6.92820i	0.138758	+	0.240337i
$832$		0			0
$833$	27.0000	+	46.7654i	0.935495	+	1.62032i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−10.0000			−0.345651
$838$		0			0
$839$	−6.00000	−	10.3923i	−0.207143	−	0.358782i	0.743670	−	0.668546i	$-0.233083\pi$
$839$	−6.00000	−	10.3923i	−0.207143	−	0.358782i	−0.950813	+	0.309764i	$0.899750\pi$
$840$		0			0
$841$	14.5000	+	25.1147i	0.500000	+	0.866025i
$842$		0			0
$843$	−27.0000			−0.929929
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−8.00000			−0.274883
$848$		0			0
$849$	−2.50000	+	4.33013i	−0.0857998	+	0.148610i
$850$		0			0
$851$	30.0000	−	51.9615i	1.02839	−	1.78122i
$852$		0			0
$853$	11.0000	+	19.0526i	0.376633	+	0.652347i	0.990570	−	0.137008i	$-0.0437485\pi$
$853$	11.0000	+	19.0526i	0.376633	+	0.652347i	−0.613937	+	0.789355i	$0.710415\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	1.50000	+	2.59808i	0.0512390	+	0.0887486i	0.890507	−	0.454969i	$-0.150350\pi$
$857$	1.50000	+	2.59808i	0.0512390	+	0.0887486i	−0.839268	+	0.543718i	$0.817016\pi$
$858$		0			0
$859$	−21.5000	+	37.2391i	−0.733571	+	1.27058i	0.221777	+	0.975097i	$0.428814\pi$
$859$	−21.5000	+	37.2391i	−0.733571	+	1.27058i	−0.955348	+	0.295484i	$0.904519\pi$
$860$		0			0
$861$	18.0000	−	31.1769i	0.613438	−	1.06251i
$862$		0			0
$863$	−18.0000			−0.612727			−0.306364	−	0.951915i	$-0.599112\pi$
$863$	−18.0000			−0.612727			−0.306364	+	0.951915i	$0.599112\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−19.0000			−0.645274
$868$		0			0
$869$	6.00000	+	10.3923i	0.203536	+	0.352535i
$870$		0			0
$871$	−7.00000	−	12.1244i	−0.237186	−	0.410818i
$872$		0			0
$873$	−34.0000			−1.15073
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−10.0000	−	17.3205i	−0.337676	−	0.584872i	0.646319	−	0.763067i	$-0.276307\pi$
$877$	−10.0000	−	17.3205i	−0.337676	−	0.584872i	−0.983995	+	0.178195i	$0.942974\pi$
$878$		0			0
$879$	12.0000	+	20.7846i	0.404750	+	0.701047i
$880$		0			0
$881$	−9.00000			−0.303218			−0.151609	−	0.988441i	$-0.548445\pi$
$881$	−9.00000			−0.303218			−0.151609	+	0.988441i	$0.548445\pi$
$882$		0			0
$883$	−9.50000	+	16.4545i	−0.319700	+	0.553737i	−0.980425	−	0.196891i	$-0.936916\pi$
$883$	−9.50000	+	16.4545i	−0.319700	+	0.553737i	0.660725	+	0.750628i	$0.270249\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	24.0000	−	41.5692i	0.805841	−	1.39576i	−0.109881	−	0.993945i	$-0.535047\pi$
$887$	24.0000	−	41.5692i	0.805841	−	1.39576i	0.915722	−	0.401813i	$-0.131620\pi$
$888$		0			0
$889$	4.00000	−	6.92820i	0.134156	−	0.232364i
$890$		0			0
$891$	1.50000	+	2.59808i	0.0502519	+	0.0870388i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$	6.00000	−	10.3923i	0.200334	−	0.346989i
$898$		0			0
$899$		0			0
$900$		0			0
$901$	−36.0000			−1.19933
$902$		0			0
$903$	8.00000	−	13.8564i	0.266223	−	0.461112i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	8.50000	+	14.7224i	0.282238	+	0.488850i	0.971936	−	0.235247i	$-0.0755899\pi$
$907$	8.50000	+	14.7224i	0.282238	+	0.488850i	−0.689698	+	0.724097i	$0.742257\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−30.0000			−0.993944			−0.496972	−	0.867766i	$-0.665555\pi$
$911$	−30.0000			−0.993944			−0.496972	+	0.867766i	$0.665555\pi$
$912$		0			0
$913$	9.00000			0.297857
$914$		0			0
$915$		0			0
$916$		0			0
$917$	18.0000	+	31.1769i	0.594412	+	1.02955i
$918$		0			0
$919$	10.0000			0.329870			0.164935	−	0.986304i	$-0.447259\pi$
$919$	10.0000			0.329870			0.164935	+	0.986304i	$0.447259\pi$
$920$		0			0
$921$	3.50000	−	6.06218i	0.115329	−	0.199756i
$922$		0			0
$923$	12.0000			0.394985
$924$		0			0
$925$	−25.0000	+	43.3013i	−0.821995	+	1.42374i
$926$		0			0
$927$	−2.00000	+	3.46410i	−0.0656886	+	0.113776i
$928$		0			0
$929$	1.50000	+	2.59808i	0.0492134	+	0.0852401i	0.889583	−	0.456774i	$-0.150995\pi$
$929$	1.50000	+	2.59808i	0.0492134	+	0.0852401i	−0.840369	+	0.542014i	$0.817662\pi$
$930$		0			0
$931$	31.5000	−	23.3827i	1.03237	−	0.766337i
$932$		0			0
$933$	15.0000	+	25.9808i	0.491078	+	0.850572i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−17.5000	+	30.3109i	−0.571700	+	0.990214i	0.424691	+	0.905338i	$0.360383\pi$
$937$	−17.5000	+	30.3109i	−0.571700	+	0.990214i	−0.996392	+	0.0848755i	$0.972951\pi$
$938$		0			0
$939$	19.0000			0.620042
$940$		0			0
$941$	21.0000	−	36.3731i	0.684580	−	1.18573i	−0.288988	−	0.957333i	$-0.593319\pi$
$941$	21.0000	−	36.3731i	0.684580	−	1.18573i	0.973568	−	0.228395i	$-0.0733479\pi$
$942$		0			0
$943$	54.0000			1.75848
$944$		0			0
$945$		0			0
$946$		0			0
$947$	30.0000	+	51.9615i	0.974869	+	1.68852i	0.680367	+	0.732872i	$0.261821\pi$
$947$	30.0000	+	51.9615i	0.974869	+	1.68852i	0.294502	+	0.955651i	$0.404846\pi$
$948$		0			0
$949$	−2.00000			−0.0649227
$950$		0			0
$951$	18.0000			0.583690
$952$		0			0
$953$	7.50000	+	12.9904i	0.242949	+	0.420800i	0.961553	−	0.274620i	$-0.0885520\pi$
$953$	7.50000	+	12.9904i	0.242949	+	0.420800i	−0.718604	+	0.695419i	$0.755219\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−18.0000	+	31.1769i	−0.581250	+	1.00676i
$960$		0			0
$961$	−27.0000			−0.870968
$962$		0			0
$963$		0			0
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−17.0000	−	29.4449i	−0.546683	−	0.946883i	−0.998499	−	0.0547717i	$-0.982557\pi$
$967$	−17.0000	−	29.4449i	−0.546683	−	0.946883i	0.451816	−	0.892111i	$-0.350776\pi$
$968$		0			0
$969$	3.00000	+	25.9808i	0.0963739	+	0.834622i
$970$		0			0
$971$	10.5000	+	18.1865i	0.336961	+	0.583634i	0.983860	−	0.178942i	$-0.0572676\pi$
$971$	10.5000	+	18.1865i	0.336961	+	0.583634i	−0.646899	+	0.762576i	$0.723934\pi$
$972$		0			0
$973$	22.0000	−	38.1051i	0.705288	−	1.22159i
$974$		0			0
$975$	−5.00000	+	8.66025i	−0.160128	+	0.277350i
$976$		0			0
$977$	33.0000			1.05576			0.527882	−	0.849318i	$-0.322986\pi$
$977$	33.0000			1.05576			0.527882	+	0.849318i	$0.322986\pi$
$978$		0			0
$979$	9.00000	−	15.5885i	0.287641	−	0.498209i
$980$		0			0
$981$	32.0000			1.02168
$982$		0			0
$983$	12.0000	+	20.7846i	0.382741	+	0.662926i	0.991453	−	0.130465i	$-0.0416470\pi$
$983$	12.0000	+	20.7846i	0.382741	+	0.662926i	−0.608712	+	0.793391i	$0.708314\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$	24.0000			0.763156
$990$		0			0
$991$	4.00000	+	6.92820i	0.127064	+	0.220082i	0.922538	−	0.385906i	$-0.126111\pi$
$991$	4.00000	+	6.92820i	0.127064	+	0.220082i	−0.795474	+	0.605988i	$0.792778\pi$
$992$		0			0
$993$	−2.50000	−	4.33013i	−0.0793351	−	0.137412i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	2.00000	−	3.46410i	0.0633406	−	0.109709i	−0.832616	−	0.553851i	$-0.813158\pi$
$997$	2.00000	−	3.46410i	0.0633406	−	0.109709i	0.895957	+	0.444141i	$0.146491\pi$
$998$		0			0
$999$	−50.0000			−1.58193

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	304.2.i.c.273.1		2
3.2	odd	2		2736.2.s.m.577.1		2
4.3	odd	2		38.2.c.a.7.1	✓	2
8.3	odd	2		1216.2.i.h.577.1		2
8.5	even	2		1216.2.i.d.577.1		2
12.11	even	2		342.2.g.b.235.1		2
19.7	even	3		5776.2.a.g.1.1		1
19.11	even	3	inner	304.2.i.c.49.1		2
19.12	odd	6		5776.2.a.n.1.1		1
20.3	even	4		950.2.j.e.349.2		4
20.7	even	4		950.2.j.e.349.1		4
20.19	odd	2		950.2.e.d.501.1		2
57.11	odd	6		2736.2.s.m.1873.1		2
76.3	even	18		722.2.e.i.595.1		6
76.7	odd	6		722.2.a.c.1.1		1
76.11	odd	6		38.2.c.a.11.1	yes	2
76.15	even	18		722.2.e.i.245.1		6
76.23	odd	18		722.2.e.j.245.1		6
76.27	even	6		722.2.c.b.429.1		2
76.31	even	6		722.2.a.d.1.1		1
76.35	odd	18		722.2.e.j.595.1		6
76.43	odd	18		722.2.e.j.99.1		6
76.47	odd	18		722.2.e.j.415.1		6
76.51	even	18		722.2.e.i.423.1		6
76.55	odd	18		722.2.e.j.389.1		6
76.59	even	18		722.2.e.i.389.1		6
76.63	odd	18		722.2.e.j.423.1		6
76.67	even	18		722.2.e.i.415.1		6
76.71	even	18		722.2.e.i.99.1		6
76.75	even	2		722.2.c.b.653.1		2
152.11	odd	6		1216.2.i.h.961.1		2
152.125	even	6		1216.2.i.d.961.1		2
228.11	even	6		342.2.g.b.163.1		2
228.83	even	6		6498.2.a.s.1.1		1
228.107	odd	6		6498.2.a.e.1.1		1
380.87	even	12		950.2.j.e.49.2		4
380.163	even	12		950.2.j.e.49.1		4
380.239	odd	6		950.2.e.d.201.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.2.c.a.7.1	✓	2	4.3	odd	2
38.2.c.a.11.1	yes	2	76.11	odd	6
304.2.i.c.49.1		2	19.11	even	3	inner
304.2.i.c.273.1		2	1.1	even	1	trivial
342.2.g.b.163.1		2	228.11	even	6
342.2.g.b.235.1		2	12.11	even	2
722.2.a.c.1.1		1	76.7	odd	6
722.2.a.d.1.1		1	76.31	even	6
722.2.c.b.429.1		2	76.27	even	6
722.2.c.b.653.1		2	76.75	even	2
722.2.e.i.99.1		6	76.71	even	18
722.2.e.i.245.1		6	76.15	even	18
722.2.e.i.389.1		6	76.59	even	18
722.2.e.i.415.1		6	76.67	even	18
722.2.e.i.423.1		6	76.51	even	18
722.2.e.i.595.1		6	76.3	even	18
722.2.e.j.99.1		6	76.43	odd	18
722.2.e.j.245.1		6	76.23	odd	18
722.2.e.j.389.1		6	76.55	odd	18
722.2.e.j.415.1		6	76.47	odd	18
722.2.e.j.423.1		6	76.63	odd	18
722.2.e.j.595.1		6	76.35	odd	18
950.2.e.d.201.1		2	380.239	odd	6
950.2.e.d.501.1		2	20.19	odd	2
950.2.j.e.49.1		4	380.163	even	12
950.2.j.e.49.2		4	380.87	even	12
950.2.j.e.349.1		4	20.7	even	4
950.2.j.e.349.2		4	20.3	even	4
1216.2.i.d.577.1		2	8.5	even	2
1216.2.i.d.961.1		2	152.125	even	6
1216.2.i.h.577.1		2	8.3	odd	2
1216.2.i.h.961.1		2	152.11	odd	6
2736.2.s.m.577.1		2	3.2	odd	2
2736.2.s.m.1873.1		2	57.11	odd	6
5776.2.a.g.1.1		1	19.7	even	3
5776.2.a.n.1.1		1	19.12	odd	6
6498.2.a.e.1.1		1	228.107	odd	6
6498.2.a.s.1.1		1	228.83	even	6

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:	\( N \)	\(=\)	\( 304 = 2^{4} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	304.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{3} +4.00000 q^{7} +(1.00000 - 1.73205i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{3} +4.00000 q^{7} +(1.00000 - 1.73205i) q^{9} -3.00000 q^{11} +(-1.00000 + 1.73205i) q^{13} +(3.00000 + 5.19615i) q^{17} +(3.50000 - 2.59808i) q^{19} +(2.00000 + 3.46410i) q^{21} +(-3.00000 + 5.19615i) q^{23} +(2.50000 - 4.33013i) q^{25} +5.00000 q^{27} -2.00000 q^{31} +(-1.50000 - 2.59808i) q^{33} -10.0000 q^{37} -2.00000 q^{39} +(-4.50000 - 7.79423i) q^{41} +(-2.00000 - 3.46410i) q^{43} +9.00000 q^{49} +(-3.00000 + 5.19615i) q^{51} +(-3.00000 + 5.19615i) q^{53} +(4.00000 + 1.73205i) q^{57} +(-4.50000 - 7.79423i) q^{59} +(2.00000 - 3.46410i) q^{61} +(4.00000 - 6.92820i) q^{63} +(-3.50000 + 6.06218i) q^{67} -6.00000 q^{69} +(-3.00000 - 5.19615i) q^{71} +(0.500000 + 0.866025i) q^{73} +5.00000 q^{75} -12.0000 q^{77} +(-2.00000 - 3.46410i) q^{79} +(-0.500000 - 0.866025i) q^{81} -3.00000 q^{83} +(-3.00000 + 5.19615i) q^{89} +(-4.00000 + 6.92820i) q^{91} +(-1.00000 - 1.73205i) q^{93} +(-8.50000 - 14.7224i) q^{97} +(-3.00000 + 5.19615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{3} + 8 q^{7} + 2 q^{9}+O(q^{10}) \) 2 * q + q^3 + 8 * q^7 + 2 * q^9	\( 2 q + q^{3} + 8 q^{7} + 2 q^{9} - 6 q^{11} - 2 q^{13} + 6 q^{17} + 7 q^{19} + 4 q^{21} - 6 q^{23} + 5 q^{25} + 10 q^{27} - 4 q^{31} - 3 q^{33} - 20 q^{37} - 4 q^{39} - 9 q^{41} - 4 q^{43} + 18 q^{49} - 6 q^{51} - 6 q^{53} + 8 q^{57} - 9 q^{59} + 4 q^{61} + 8 q^{63} - 7 q^{67} - 12 q^{69} - 6 q^{71} + q^{73} + 10 q^{75} - 24 q^{77} - 4 q^{79} - q^{81} - 6 q^{83} - 6 q^{89} - 8 q^{91} - 2 q^{93} - 17 q^{97} - 6 q^{99}+O(q^{100}) \) 2 * q + q^3 + 8 * q^7 + 2 * q^9 - 6 * q^11 - 2 * q^13 + 6 * q^17 + 7 * q^19 + 4 * q^21 - 6 * q^23 + 5 * q^25 + 10 * q^27 - 4 * q^31 - 3 * q^33 - 20 * q^37 - 4 * q^39 - 9 * q^41 - 4 * q^43 + 18 * q^49 - 6 * q^51 - 6 * q^53 + 8 * q^57 - 9 * q^59 + 4 * q^61 + 8 * q^63 - 7 * q^67 - 12 * q^69 - 6 * q^71 + q^73 + 10 * q^75 - 24 * q^77 - 4 * q^79 - q^81 - 6 * q^83 - 6 * q^89 - 8 * q^91 - 2 * q^93 - 17 * q^97 - 6 * q^99

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