LMFDB - Embedded newform 152.2.i.b.49.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [152,2,Mod(49,152)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("152.49"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(152, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 152 = 2^{3} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	152.i (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [2,0,-1,0,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.21372611072$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			49.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	152.49
Dual form			152.2.i.b.121.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 + 0.866025i) q^{3} +(2.00000 - 3.46410i) q^{5} +(1.00000 + 1.73205i) q^{9} +3.00000 q^{11} +(-1.00000 - 1.73205i) q^{13} +(2.00000 + 3.46410i) q^{15} +(-1.00000 + 1.73205i) q^{17} +(0.500000 + 4.33013i) q^{19} +(-3.00000 - 5.19615i) q^{23} +(-5.50000 - 9.52628i) q^{25} -5.00000 q^{27} +(2.00000 + 3.46410i) q^{29} -10.0000 q^{31} +(-1.50000 + 2.59808i) q^{33} +2.00000 q^{37} +2.00000 q^{39} +(-4.50000 + 7.79423i) q^{41} +(2.00000 - 3.46410i) q^{43} +8.00000 q^{45} +(6.00000 + 10.3923i) q^{47} -7.00000 q^{49} +(-1.00000 - 1.73205i) q^{51} +(1.00000 + 1.73205i) q^{53} +(6.00000 - 10.3923i) q^{55} +(-4.00000 - 1.73205i) q^{57} +(0.500000 - 0.866025i) q^{59} +(4.00000 + 6.92820i) q^{61} -8.00000 q^{65} +(-4.50000 - 7.79423i) q^{67} +6.00000 q^{69} +(3.00000 - 5.19615i) q^{71} +(4.50000 - 7.79423i) q^{73} +11.0000 q^{75} +(2.00000 - 3.46410i) q^{79} +(-0.500000 + 0.866025i) q^{81} -5.00000 q^{83} +(4.00000 + 6.92820i) q^{85} -4.00000 q^{87} +(9.00000 + 15.5885i) q^{89} +(5.00000 - 8.66025i) q^{93} +(16.0000 + 6.92820i) q^{95} +(-0.500000 + 0.866025i) q^{97} +(3.00000 + 5.19615i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{3} + 4 q^{5} + 2 q^{9} + 6 q^{11} - 2 q^{13} + 4 q^{15} - 2 q^{17} + q^{19} - 6 q^{23} - 11 q^{25} - 10 q^{27} + 4 q^{29} - 20 q^{31} - 3 q^{33} + 4 q^{37} + 4 q^{39} - 9 q^{41} + 4 q^{43} + 16 q^{45}+ \cdots + 6 q^{99}+O(q^{100}) $ 2 * q - q^3 + 4 * q^5 + 2 * q^9 + 6 * q^11 - 2 * q^13 + 4 * q^15 - 2 * q^17 + q^19 - 6 * q^23 - 11 * q^25 - 10 * q^27 + 4 * q^29 - 20 * q^31 - 3 * q^33 + 4 * q^37 + 4 * q^39 - 9 * q^41 + 4 * q^43 + 16 * q^45 + 12 * q^47 - 14 * q^49 - 2 * q^51 + 2 * q^53 + 12 * q^55 - 8 * q^57 + q^59 + 8 * q^61 - 16 * q^65 - 9 * q^67 + 12 * q^69 + 6 * q^71 + 9 * q^73 + 22 * q^75 + 4 * q^79 - q^81 - 10 * q^83 + 8 * q^85 - 8 * q^87 + 18 * q^89 + 10 * q^93 + 32 * q^95 - q^97 + 6 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/152\mathbb{Z}\right)^\times$.

$n$	$39$	$77$	$97$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i	−0.973494	−	0.228714i	$-0.926548\pi$
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i	0.684819	+	0.728714i	$0.259881\pi$
$4$		0			0
$5$	2.00000	−	3.46410i	0.894427	−	1.54919i	0.0599153	−	0.998203i	$-0.480917\pi$
$5$	2.00000	−	3.46410i	0.894427	−	1.54919i	0.834512	−	0.550990i	$-0.185750\pi$
$6$		0			0
$7$		0			0			−	1.00000i	$-0.5\pi$
$7$		0			0				1.00000i	$0.5\pi$
$8$		0			0
$9$	1.00000	+	1.73205i	0.333333	+	0.577350i
$10$		0			0
$11$	3.00000			0.904534			0.452267	−	0.891883i	$-0.350615\pi$
$11$	3.00000			0.904534			0.452267	+	0.891883i	$0.350615\pi$
$12$		0			0
$13$	−1.00000	−	1.73205i	−0.277350	−	0.480384i	0.693375	−	0.720577i	$-0.256123\pi$
$13$	−1.00000	−	1.73205i	−0.277350	−	0.480384i	−0.970725	+	0.240192i	$0.922790\pi$
$14$		0			0
$15$	2.00000	+	3.46410i	0.516398	+	0.894427i
$16$		0			0
$17$	−1.00000	+	1.73205i	−0.242536	+	0.420084i	−0.961436	−	0.275029i	$-0.911312\pi$
$17$	−1.00000	+	1.73205i	−0.242536	+	0.420084i	0.718900	+	0.695113i	$0.244646\pi$
$18$		0			0
$19$	0.500000	+	4.33013i	0.114708	+	0.993399i
$19$	0.500000	+	4.33013i	0.114708	+	0.993399i
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−3.00000	−	5.19615i	−0.625543	−	1.08347i	−0.988436	−	0.151642i	$-0.951544\pi$
$23$	−3.00000	−	5.19615i	−0.625543	−	1.08347i	0.362892	−	0.931831i	$-0.381789\pi$
$24$		0			0
$25$	−5.50000	−	9.52628i	−1.10000	−	1.90526i
$26$		0			0
$27$	−5.00000			−0.962250
$28$		0			0
$29$	2.00000	+	3.46410i	0.371391	+	0.643268i	0.989780	−	0.142605i	$-0.0455477\pi$
$29$	2.00000	+	3.46410i	0.371391	+	0.643268i	−0.618389	+	0.785872i	$0.712214\pi$
$30$		0			0
$31$	−10.0000			−1.79605			−0.898027	−	0.439941i	$-0.854999\pi$
$31$	−10.0000			−1.79605			−0.898027	+	0.439941i	$0.854999\pi$
$32$		0			0
$33$	−1.50000	+	2.59808i	−0.261116	+	0.452267i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	2.00000			0.328798			0.164399	−	0.986394i	$-0.447432\pi$
$37$	2.00000			0.328798			0.164399	+	0.986394i	$0.447432\pi$
$38$		0			0
$39$	2.00000			0.320256
$40$		0			0
$41$	−4.50000	+	7.79423i	−0.702782	+	1.21725i	0.264704	+	0.964330i	$0.414726\pi$
$41$	−4.50000	+	7.79423i	−0.702782	+	1.21725i	−0.967486	+	0.252924i	$0.918608\pi$
$42$		0			0
$43$	2.00000	−	3.46410i	0.304997	−	0.528271i	−0.672264	−	0.740312i	$-0.734678\pi$
$43$	2.00000	−	3.46410i	0.304997	−	0.528271i	0.977261	+	0.212041i	$0.0680112\pi$
$44$		0			0
$45$	8.00000			1.19257
$46$		0			0
$47$	6.00000	+	10.3923i	0.875190	+	1.51587i	0.856560	+	0.516047i	$0.172597\pi$
$47$	6.00000	+	10.3923i	0.875190	+	1.51587i	0.0186297	+	0.999826i	$0.494070\pi$
$48$		0			0
$49$	−7.00000			−1.00000
$50$		0			0
$51$	−1.00000	−	1.73205i	−0.140028	−	0.242536i
$52$		0			0
$53$	1.00000	+	1.73205i	0.137361	+	0.237915i	0.926497	−	0.376303i	$-0.122805\pi$
$53$	1.00000	+	1.73205i	0.137361	+	0.237915i	−0.789136	+	0.614218i	$0.789471\pi$
$54$		0			0
$55$	6.00000	−	10.3923i	0.809040	−	1.40130i
$56$		0			0
$57$	−4.00000	−	1.73205i	−0.529813	−	0.229416i
$58$		0			0
$59$	0.500000	−	0.866025i	0.0650945	−	0.112747i	−0.831641	−	0.555313i	$-0.812598\pi$
$59$	0.500000	−	0.866025i	0.0650945	−	0.112747i	0.896736	+	0.442566i	$0.145932\pi$
$60$		0			0
$61$	4.00000	+	6.92820i	0.512148	+	0.887066i	0.999901	+	0.0140840i	$0.00448323\pi$
$61$	4.00000	+	6.92820i	0.512148	+	0.887066i	−0.487753	+	0.872982i	$0.662183\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−8.00000			−0.992278
$66$		0			0
$67$	−4.50000	−	7.79423i	−0.549762	−	0.952217i	−0.998290	−	0.0584478i	$-0.981385\pi$
$67$	−4.50000	−	7.79423i	−0.549762	−	0.952217i	0.448528	−	0.893769i	$-0.351948\pi$
$68$		0			0
$69$	6.00000			0.722315
$70$		0			0
$71$	3.00000	−	5.19615i	0.356034	−	0.616670i	−0.631260	−	0.775571i	$-0.717462\pi$
$71$	3.00000	−	5.19615i	0.356034	−	0.616670i	0.987294	+	0.158901i	$0.0507952\pi$
$72$		0			0
$73$	4.50000	−	7.79423i	0.526685	−	0.912245i	−0.472831	−	0.881153i	$-0.656768\pi$
$73$	4.50000	−	7.79423i	0.526685	−	0.912245i	0.999517	−	0.0310925i	$-0.00989865\pi$
$74$		0			0
$75$	11.0000			1.27017
$76$		0			0
$77$		0			0
$78$		0			0
$79$	2.00000	−	3.46410i	0.225018	−	0.389742i	−0.731307	−	0.682048i	$-0.761089\pi$
$79$	2.00000	−	3.46410i	0.225018	−	0.389742i	0.956325	+	0.292306i	$0.0944227\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	−5.00000			−0.548821			−0.274411	−	0.961613i	$-0.588483\pi$
$83$	−5.00000			−0.548821			−0.274411	+	0.961613i	$0.588483\pi$
$84$		0			0
$85$	4.00000	+	6.92820i	0.433861	+	0.751469i
$86$		0			0
$87$	−4.00000			−0.428845
$88$		0			0
$89$	9.00000	+	15.5885i	0.953998	+	1.65237i	0.736644	+	0.676280i	$0.236409\pi$
$89$	9.00000	+	15.5885i	0.953998	+	1.65237i	0.217354	+	0.976093i	$0.430258\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	5.00000	−	8.66025i	0.518476	−	0.898027i
$94$		0			0
$95$	16.0000	+	6.92820i	1.64157	+	0.710819i
$96$		0			0
$97$	−0.500000	+	0.866025i	−0.0507673	+	0.0879316i	−0.890292	−	0.455389i	$-0.849500\pi$
$97$	−0.500000	+	0.866025i	−0.0507673	+	0.0879316i	0.839525	+	0.543321i	$0.182833\pi$
$98$		0			0
$99$	3.00000	+	5.19615i	0.301511	+	0.522233i
$100$		0			0
$101$	−6.00000	−	10.3923i	−0.597022	−	1.03407i	−0.993258	−	0.115924i	$-0.963017\pi$
$101$	−6.00000	−	10.3923i	−0.597022	−	1.03407i	0.396236	−	0.918149i	$-0.370316\pi$
$102$		0			0
$103$	−14.0000			−1.37946			−0.689730	−	0.724066i	$-0.742271\pi$
$103$	−14.0000			−1.37946			−0.689730	+	0.724066i	$0.742271\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	16.0000			1.54678			0.773389	−	0.633932i	$-0.218560\pi$
$107$	16.0000			1.54678			0.773389	+	0.633932i	$0.218560\pi$
$108$		0			0
$109$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$109$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$110$		0			0
$111$	−1.00000	+	1.73205i	−0.0949158	+	0.164399i
$112$		0			0
$113$	−1.00000			−0.0940721			−0.0470360	−	0.998893i	$-0.514978\pi$
$113$	−1.00000			−0.0940721			−0.0470360	+	0.998893i	$0.514978\pi$
$114$		0			0
$115$	−24.0000			−2.23801
$116$		0			0
$117$	2.00000	−	3.46410i	0.184900	−	0.320256i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−2.00000			−0.181818
$122$		0			0
$123$	−4.50000	−	7.79423i	−0.405751	−	0.702782i
$124$		0			0
$125$	−24.0000			−2.14663
$126$		0			0
$127$	3.00000	+	5.19615i	0.266207	+	0.461084i	0.967879	−	0.251416i	$-0.0808962\pi$
$127$	3.00000	+	5.19615i	0.266207	+	0.461084i	−0.701672	+	0.712500i	$0.747563\pi$
$128$		0			0
$129$	2.00000	+	3.46410i	0.176090	+	0.304997i
$130$		0			0
$131$	7.50000	−	12.9904i	0.655278	−	1.13497i	−0.326546	−	0.945181i	$-0.605885\pi$
$131$	7.50000	−	12.9904i	0.655278	−	1.13497i	0.981824	−	0.189794i	$-0.0607819\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−10.0000	+	17.3205i	−0.860663	+	1.49071i
$136$		0			0
$137$	−4.50000	−	7.79423i	−0.384461	−	0.665906i	0.607233	−	0.794524i	$-0.292279\pi$
$137$	−4.50000	−	7.79423i	−0.384461	−	0.665906i	−0.991694	+	0.128618i	$0.958946\pi$
$138$		0			0
$139$	6.50000	+	11.2583i	0.551323	+	0.954919i	0.998179	+	0.0603135i	$0.0192101\pi$
$139$	6.50000	+	11.2583i	0.551323	+	0.954919i	−0.446857	+	0.894606i	$0.647457\pi$
$140$		0			0
$141$	−12.0000			−1.01058
$142$		0			0
$143$	−3.00000	−	5.19615i	−0.250873	−	0.434524i
$144$		0			0
$145$	16.0000			1.32873
$146$		0			0
$147$	3.50000	−	6.06218i	0.288675	−	0.500000i
$148$		0			0
$149$	5.00000	−	8.66025i	0.409616	−	0.709476i	−0.585231	−	0.810867i	$-0.698996\pi$
$149$	5.00000	−	8.66025i	0.409616	−	0.709476i	0.994847	+	0.101391i	$0.0323294\pi$
$150$		0			0
$151$	2.00000			0.162758			0.0813788	−	0.996683i	$-0.474068\pi$
$151$	2.00000			0.162758			0.0813788	+	0.996683i	$0.474068\pi$
$152$		0			0
$153$	−4.00000			−0.323381
$154$		0			0
$155$	−20.0000	+	34.6410i	−1.60644	+	2.78243i
$156$		0			0
$157$	−4.00000	+	6.92820i	−0.319235	+	0.552931i	−0.980329	−	0.197372i	$-0.936759\pi$
$157$	−4.00000	+	6.92820i	−0.319235	+	0.552931i	0.661094	+	0.750303i	$0.270093\pi$
$158$		0			0
$159$	−2.00000			−0.158610
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−11.0000			−0.861586			−0.430793	−	0.902451i	$-0.641766\pi$
$163$	−11.0000			−0.861586			−0.430793	+	0.902451i	$0.641766\pi$
$164$		0			0
$165$	6.00000	+	10.3923i	0.467099	+	0.809040i
$166$		0			0
$167$	−8.00000	−	13.8564i	−0.619059	−	1.07224i	−0.989658	−	0.143448i	$-0.954181\pi$
$167$	−8.00000	−	13.8564i	−0.619059	−	1.07224i	0.370599	−	0.928793i	$-0.379152\pi$
$168$		0			0
$169$	4.50000	−	7.79423i	0.346154	−	0.599556i
$170$		0			0
$171$	−7.00000	+	5.19615i	−0.535303	+	0.397360i
$172$		0			0
$173$	13.0000	−	22.5167i	0.988372	−	1.71191i	0.362500	−	0.931984i	$-0.381923\pi$
$173$	13.0000	−	22.5167i	0.988372	−	1.71191i	0.625871	−	0.779926i	$-0.284744\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	0.500000	+	0.866025i	0.0375823	+	0.0650945i
$178$		0			0
$179$	9.00000			0.672692			0.336346	−	0.941739i	$-0.390809\pi$
$179$	9.00000			0.672692			0.336346	+	0.941739i	$0.390809\pi$
$180$		0			0
$181$	−7.00000	−	12.1244i	−0.520306	−	0.901196i	−0.999721	−	0.0236082i	$-0.992485\pi$
$181$	−7.00000	−	12.1244i	−0.520306	−	0.901196i	0.479415	−	0.877588i	$-0.340849\pi$
$182$		0			0
$183$	−8.00000			−0.591377
$184$		0			0
$185$	4.00000	−	6.92820i	0.294086	−	0.509372i
$186$		0			0
$187$	−3.00000	+	5.19615i	−0.219382	+	0.379980i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	12.0000			0.868290			0.434145	−	0.900843i	$-0.357051\pi$
$191$	12.0000			0.868290			0.434145	+	0.900843i	$0.357051\pi$
$192$		0			0
$193$	3.00000	−	5.19615i	0.215945	−	0.374027i	−0.737620	−	0.675216i	$-0.764050\pi$
$193$	3.00000	−	5.19615i	0.215945	−	0.374027i	0.953564	+	0.301189i	$0.0973836\pi$
$194$		0			0
$195$	4.00000	−	6.92820i	0.286446	−	0.496139i
$196$		0			0
$197$	−18.0000			−1.28245			−0.641223	−	0.767354i	$-0.721573\pi$
$197$	−18.0000			−1.28245			−0.641223	+	0.767354i	$0.721573\pi$
$198$		0			0
$199$	9.00000	+	15.5885i	0.637993	+	1.10504i	0.985873	+	0.167497i	$0.0535685\pi$
$199$	9.00000	+	15.5885i	0.637993	+	1.10504i	−0.347879	+	0.937539i	$0.613098\pi$
$200$		0			0
$201$	9.00000			0.634811
$202$		0			0
$203$		0			0
$204$		0			0
$205$	18.0000	+	31.1769i	1.25717	+	2.17749i
$206$		0			0
$207$	6.00000	−	10.3923i	0.417029	−	0.722315i
$208$		0			0
$209$	1.50000	+	12.9904i	0.103757	+	0.898563i
$210$		0			0
$211$	6.00000	−	10.3923i	0.413057	−	0.715436i	−0.582165	−	0.813070i	$-0.697794\pi$
$211$	6.00000	−	10.3923i	0.413057	−	0.715436i	0.995222	+	0.0976347i	$0.0311277\pi$
$212$		0			0
$213$	3.00000	+	5.19615i	0.205557	+	0.356034i
$214$		0			0
$215$	−8.00000	−	13.8564i	−0.545595	−	0.944999i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	4.50000	+	7.79423i	0.304082	+	0.526685i
$220$		0			0
$221$	4.00000			0.269069
$222$		0			0
$223$	−5.00000	+	8.66025i	−0.334825	+	0.579934i	−0.983451	−	0.181173i	$-0.942010\pi$
$223$	−5.00000	+	8.66025i	−0.334825	+	0.579934i	0.648626	+	0.761107i	$0.275344\pi$
$224$		0			0
$225$	11.0000	−	19.0526i	0.733333	−	1.27017i
$226$		0			0
$227$	19.0000			1.26107			0.630537	−	0.776159i	$-0.282835\pi$
$227$	19.0000			1.26107			0.630537	+	0.776159i	$0.282835\pi$
$228$		0			0
$229$	−8.00000			−0.528655			−0.264327	−	0.964433i	$-0.585150\pi$
$229$	−8.00000			−0.528655			−0.264327	+	0.964433i	$0.585150\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−5.50000	+	9.52628i	−0.360317	+	0.624087i	−0.988013	−	0.154371i	$-0.950665\pi$
$233$	−5.50000	+	9.52628i	−0.360317	+	0.624087i	0.627696	+	0.778459i	$0.283998\pi$
$234$		0			0
$235$	48.0000			3.13117
$236$		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
$241$	−10.5000	−	18.1865i	−0.676364	−	1.17150i	−0.976068	−	0.217465i	$-0.930221\pi$
$241$	−10.5000	−	18.1865i	−0.676364	−	1.17150i	0.299704	−	0.954032i	$-0.403112\pi$
$242$		0			0
$243$	−8.00000	−	13.8564i	−0.513200	−	0.888889i
$244$		0			0
$245$	−14.0000	+	24.2487i	−0.894427	+	1.54919i
$246$		0			0
$247$	7.00000	−	5.19615i	0.445399	−	0.330623i
$248$		0			0
$249$	2.50000	−	4.33013i	0.158431	−	0.274411i
$250$		0			0
$251$	−2.50000	−	4.33013i	−0.157799	−	0.273315i	0.776276	−	0.630393i	$-0.217106\pi$
$251$	−2.50000	−	4.33013i	−0.157799	−	0.273315i	−0.934075	+	0.357078i	$0.883773\pi$
$252$		0			0
$253$	−9.00000	−	15.5885i	−0.565825	−	0.980038i
$254$		0			0
$255$	−8.00000			−0.500979
$256$		0			0
$257$	−1.50000	−	2.59808i	−0.0935674	−	0.162064i	0.815442	−	0.578838i	$-0.196494\pi$
$257$	−1.50000	−	2.59808i	−0.0935674	−	0.162064i	−0.909010	+	0.416775i	$0.863160\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−4.00000	+	6.92820i	−0.247594	+	0.428845i
$262$		0			0
$263$	−8.00000	+	13.8564i	−0.493301	+	0.854423i	−0.999970	−	0.00771799i	$-0.997543\pi$
$263$	−8.00000	+	13.8564i	−0.493301	+	0.854423i	0.506669	+	0.862141i	$0.330877\pi$
$264$		0			0
$265$	8.00000			0.491436
$266$		0			0
$267$	−18.0000			−1.10158
$268$		0			0
$269$	−2.00000	+	3.46410i	−0.121942	+	0.211210i	−0.920534	−	0.390664i	$-0.872246\pi$
$269$	−2.00000	+	3.46410i	−0.121942	+	0.211210i	0.798591	+	0.601874i	$0.205579\pi$
$270$		0			0
$271$	10.0000	−	17.3205i	0.607457	−	1.05215i	−0.384201	−	0.923249i	$-0.625523\pi$
$271$	10.0000	−	17.3205i	0.607457	−	1.05215i	0.991658	−	0.128897i	$-0.0411435\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−16.5000	−	28.5788i	−0.994987	−	1.72337i
$276$		0			0
$277$	12.0000			0.721010			0.360505	−	0.932757i	$-0.382604\pi$
$277$	12.0000			0.721010			0.360505	+	0.932757i	$0.382604\pi$
$278$		0			0
$279$	−10.0000	−	17.3205i	−0.598684	−	1.03695i
$280$		0			0
$281$	6.50000	+	11.2583i	0.387757	+	0.671616i	0.992148	−	0.125073i	$-0.0399165\pi$
$281$	6.50000	+	11.2583i	0.387757	+	0.671616i	−0.604390	+	0.796689i	$0.706583\pi$
$282$		0			0
$283$	−6.50000	+	11.2583i	−0.386385	+	0.669238i	−0.991960	−	0.126550i	$-0.959610\pi$
$283$	−6.50000	+	11.2583i	−0.386385	+	0.669238i	0.605575	+	0.795788i	$0.292943\pi$
$284$		0			0
$285$	−14.0000	+	10.3923i	−0.829288	+	0.615587i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	6.50000	+	11.2583i	0.382353	+	0.662255i
$290$		0			0
$291$	−0.500000	−	0.866025i	−0.0293105	−	0.0507673i
$292$		0			0
$293$	−4.00000			−0.233682			−0.116841	−	0.993151i	$-0.537277\pi$
$293$	−4.00000			−0.233682			−0.116841	+	0.993151i	$0.537277\pi$
$294$		0			0
$295$	−2.00000	−	3.46410i	−0.116445	−	0.201688i
$296$		0			0
$297$	−15.0000			−0.870388
$298$		0			0
$299$	−6.00000	+	10.3923i	−0.346989	+	0.601003i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	12.0000			0.689382
$304$		0			0
$305$	32.0000			1.83231
$306$		0			0
$307$	−12.5000	+	21.6506i	−0.713413	+	1.23567i	0.250156	+	0.968206i	$0.419518\pi$
$307$	−12.5000	+	21.6506i	−0.713413	+	1.23567i	−0.963569	+	0.267461i	$0.913815\pi$
$308$		0			0
$309$	7.00000	−	12.1244i	0.398216	−	0.689730i
$310$		0			0
$311$	−2.00000			−0.113410			−0.0567048	−	0.998391i	$-0.518059\pi$
$311$	−2.00000			−0.113410			−0.0567048	+	0.998391i	$0.518059\pi$
$312$		0			0
$313$	9.50000	+	16.4545i	0.536972	+	0.930062i	0.999065	+	0.0432311i	$0.0137652\pi$
$313$	9.50000	+	16.4545i	0.536972	+	0.930062i	−0.462093	+	0.886831i	$0.652902\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−3.00000	−	5.19615i	−0.168497	−	0.291845i	0.769395	−	0.638774i	$-0.220558\pi$
$317$	−3.00000	−	5.19615i	−0.168497	−	0.291845i	−0.937892	+	0.346929i	$0.887225\pi$
$318$		0			0
$319$	6.00000	+	10.3923i	0.335936	+	0.581857i
$320$		0			0
$321$	−8.00000	+	13.8564i	−0.446516	+	0.773389i
$322$		0			0
$323$	−8.00000	−	3.46410i	−0.445132	−	0.192748i
$324$		0			0
$325$	−11.0000	+	19.0526i	−0.610170	+	1.05685i
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	13.0000			0.714545			0.357272	−	0.934000i	$-0.383707\pi$
$331$	13.0000			0.714545			0.357272	+	0.934000i	$0.383707\pi$
$332$		0			0
$333$	2.00000	+	3.46410i	0.109599	+	0.189832i
$334$		0			0
$335$	−36.0000			−1.96689
$336$		0			0
$337$	−1.50000	+	2.59808i	−0.0817102	+	0.141526i	−0.903985	−	0.427565i	$-0.859372\pi$
$337$	−1.50000	+	2.59808i	−0.0817102	+	0.141526i	0.822274	+	0.569091i	$0.192705\pi$
$338$		0			0
$339$	0.500000	−	0.866025i	0.0271563	−	0.0470360i
$340$		0			0
$341$	−30.0000			−1.62459
$342$		0			0
$343$		0			0
$344$		0			0
$345$	12.0000	−	20.7846i	0.646058	−	1.11901i
$346$		0			0
$347$	4.50000	−	7.79423i	0.241573	−	0.418416i	−0.719590	−	0.694399i	$-0.755670\pi$
$347$	4.50000	−	7.79423i	0.241573	−	0.418416i	0.961162	+	0.275983i	$0.0890035\pi$
$348$		0			0
$349$	−28.0000			−1.49881			−0.749403	−	0.662114i	$-0.769659\pi$
$349$	−28.0000			−1.49881			−0.749403	+	0.662114i	$0.769659\pi$
$350$		0			0
$351$	5.00000	+	8.66025i	0.266880	+	0.462250i
$352$		0			0
$353$	11.0000			0.585471			0.292735	−	0.956193i	$-0.405434\pi$
$353$	11.0000			0.585471			0.292735	+	0.956193i	$0.405434\pi$
$354$		0			0
$355$	−12.0000	−	20.7846i	−0.636894	−	1.10313i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	1.00000	−	1.73205i	0.0527780	−	0.0914141i	−0.838429	−	0.545010i	$-0.816526\pi$
$359$	1.00000	−	1.73205i	0.0527780	−	0.0914141i	0.891207	+	0.453596i	$0.149859\pi$
$360$		0			0
$361$	−18.5000	+	4.33013i	−0.973684	+	0.227901i
$362$		0			0
$363$	1.00000	−	1.73205i	0.0524864	−	0.0909091i
$364$		0			0
$365$	−18.0000	−	31.1769i	−0.942163	−	1.63187i
$366$		0			0
$367$	13.0000	+	22.5167i	0.678594	+	1.17536i	0.975404	+	0.220423i	$0.0707439\pi$
$367$	13.0000	+	22.5167i	0.678594	+	1.17536i	−0.296810	+	0.954937i	$0.595923\pi$
$368$		0			0
$369$	−18.0000			−0.937043
$370$		0			0
$371$		0			0
$372$		0			0
$373$	4.00000			0.207112			0.103556	−	0.994624i	$-0.466978\pi$
$373$	4.00000			0.207112			0.103556	+	0.994624i	$0.466978\pi$
$374$		0			0
$375$	12.0000	−	20.7846i	0.619677	−	1.07331i
$376$		0			0
$377$	4.00000	−	6.92820i	0.206010	−	0.356821i
$378$		0			0
$379$	−12.0000			−0.616399			−0.308199	−	0.951322i	$-0.599726\pi$
$379$	−12.0000			−0.616399			−0.308199	+	0.951322i	$0.599726\pi$
$380$		0			0
$381$	−6.00000			−0.307389
$382$		0			0
$383$	4.00000	−	6.92820i	0.204390	−	0.354015i	−0.745548	−	0.666452i	$-0.767812\pi$
$383$	4.00000	−	6.92820i	0.204390	−	0.354015i	0.949938	+	0.312437i	$0.101145\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	8.00000			0.406663
$388$		0			0
$389$	−2.00000	−	3.46410i	−0.101404	−	0.175637i	0.810859	−	0.585241i	$-0.199000\pi$
$389$	−2.00000	−	3.46410i	−0.101404	−	0.175637i	−0.912263	+	0.409604i	$0.865667\pi$
$390$		0			0
$391$	12.0000			0.606866
$392$		0			0
$393$	7.50000	+	12.9904i	0.378325	+	0.655278i
$394$		0			0
$395$	−8.00000	−	13.8564i	−0.402524	−	0.697191i
$396$		0			0
$397$	7.00000	−	12.1244i	0.351320	−	0.608504i	−0.635161	−	0.772380i	$-0.719066\pi$
$397$	7.00000	−	12.1244i	0.351320	−	0.608504i	0.986481	+	0.163876i	$0.0523996\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	1.50000	−	2.59808i	0.0749064	−	0.129742i	−0.826139	−	0.563466i	$-0.809468\pi$
$401$	1.50000	−	2.59808i	0.0749064	−	0.129742i	0.901046	+	0.433724i	$0.142801\pi$
$402$		0			0
$403$	10.0000	+	17.3205i	0.498135	+	0.862796i
$404$		0			0
$405$	2.00000	+	3.46410i	0.0993808	+	0.172133i
$406$		0			0
$407$	6.00000			0.297409
$408$		0			0
$409$	17.5000	+	30.3109i	0.865319	+	1.49878i	0.866730	+	0.498778i	$0.166218\pi$
$409$	17.5000	+	30.3109i	0.865319	+	1.49878i	−0.00141047	+	0.999999i	$0.500449\pi$
$410$		0			0
$411$	9.00000			0.443937
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−10.0000	+	17.3205i	−0.490881	+	0.850230i
$416$		0			0
$417$	−13.0000			−0.636613
$418$		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
$421$	11.0000	−	19.0526i	0.536107	−	0.928565i	−0.463002	−	0.886357i	$-0.653228\pi$
$421$	11.0000	−	19.0526i	0.536107	−	0.928565i	0.999109	−	0.0422075i	$-0.0134391\pi$
$422$		0			0
$423$	−12.0000	+	20.7846i	−0.583460	+	1.01058i
$424$		0			0
$425$	22.0000			1.06716
$426$		0			0
$427$		0			0
$428$		0			0
$429$	6.00000			0.289683
$430$		0			0
$431$	15.0000	+	25.9808i	0.722525	+	1.25145i	0.959985	+	0.280052i	$0.0903517\pi$
$431$	15.0000	+	25.9808i	0.722525	+	1.25145i	−0.237460	+	0.971397i	$0.576315\pi$
$432$		0			0
$433$	−5.00000	−	8.66025i	−0.240285	−	0.416185i	0.720511	−	0.693444i	$-0.243907\pi$
$433$	−5.00000	−	8.66025i	−0.240285	−	0.416185i	−0.960795	+	0.277259i	$0.910574\pi$
$434$		0			0
$435$	−8.00000	+	13.8564i	−0.383571	+	0.664364i
$436$		0			0
$437$	21.0000	−	15.5885i	1.00457	−	0.745697i
$438$		0			0
$439$	7.00000	−	12.1244i	0.334092	−	0.578664i	−0.649218	−	0.760602i	$-0.724904\pi$
$439$	7.00000	−	12.1244i	0.334092	−	0.578664i	0.983310	+	0.181938i	$0.0582371\pi$
$440$		0			0
$441$	−7.00000	−	12.1244i	−0.333333	−	0.577350i
$442$		0			0
$443$	−0.500000	−	0.866025i	−0.0237557	−	0.0411461i	0.853903	−	0.520432i	$-0.174229\pi$
$443$	−0.500000	−	0.866025i	−0.0237557	−	0.0411461i	−0.877659	+	0.479286i	$0.840896\pi$
$444$		0			0
$445$	72.0000			3.41313
$446$		0			0
$447$	5.00000	+	8.66025i	0.236492	+	0.409616i
$448$		0			0
$449$	33.0000			1.55737			0.778683	−	0.627417i	$-0.215888\pi$
$449$	33.0000			1.55737			0.778683	+	0.627417i	$0.215888\pi$
$450$		0			0
$451$	−13.5000	+	23.3827i	−0.635690	+	1.10105i
$452$		0			0
$453$	−1.00000	+	1.73205i	−0.0469841	+	0.0813788i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−11.0000			−0.514558			−0.257279	−	0.966337i	$-0.582826\pi$
$457$	−11.0000			−0.514558			−0.257279	+	0.966337i	$0.582826\pi$
$458$		0			0
$459$	5.00000	−	8.66025i	0.233380	−	0.404226i
$460$		0			0
$461$	−3.00000	+	5.19615i	−0.139724	+	0.242009i	−0.927392	−	0.374091i	$-0.877955\pi$
$461$	−3.00000	+	5.19615i	−0.139724	+	0.242009i	0.787668	+	0.616100i	$0.211288\pi$
$462$		0			0
$463$	−34.0000			−1.58011			−0.790057	−	0.613033i	$-0.789949\pi$
$463$	−34.0000			−1.58011			−0.790057	+	0.613033i	$0.789949\pi$
$464$		0			0
$465$	−20.0000	−	34.6410i	−0.927478	−	1.60644i
$466$		0			0
$467$	5.00000			0.231372			0.115686	−	0.993286i	$-0.463093\pi$
$467$	5.00000			0.231372			0.115686	+	0.993286i	$0.463093\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−4.00000	−	6.92820i	−0.184310	−	0.319235i
$472$		0			0
$473$	6.00000	−	10.3923i	0.275880	−	0.477839i
$474$		0			0
$475$	38.5000	−	28.5788i	1.76650	−	1.31129i
$476$		0			0
$477$	−2.00000	+	3.46410i	−0.0915737	+	0.158610i
$478$		0			0
$479$	−10.0000	−	17.3205i	−0.456912	−	0.791394i	0.541884	−	0.840453i	$-0.317711\pi$
$479$	−10.0000	−	17.3205i	−0.456912	−	0.791394i	−0.998796	+	0.0490589i	$0.984378\pi$
$480$		0			0
$481$	−2.00000	−	3.46410i	−0.0911922	−	0.157949i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	2.00000	+	3.46410i	0.0908153	+	0.157297i
$486$		0			0
$487$	−26.0000			−1.17817			−0.589086	−	0.808070i	$-0.700512\pi$
$487$	−26.0000			−1.17817			−0.589086	+	0.808070i	$0.700512\pi$
$488$		0			0
$489$	5.50000	−	9.52628i	0.248719	−	0.430793i
$490$		0			0
$491$	−8.00000	+	13.8564i	−0.361035	+	0.625331i	−0.988131	−	0.153611i	$-0.950910\pi$
$491$	−8.00000	+	13.8564i	−0.361035	+	0.625331i	0.627096	+	0.778942i	$0.284243\pi$
$492$		0			0
$493$	−8.00000			−0.360302
$494$		0			0
$495$	24.0000			1.07872
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−3.50000	+	6.06218i	−0.156682	+	0.271380i	−0.933670	−	0.358134i	$-0.883413\pi$
$499$	−3.50000	+	6.06218i	−0.156682	+	0.271380i	0.776989	+	0.629515i	$0.216746\pi$
$500$		0			0
$501$	16.0000			0.714827
$502$		0			0
$503$	3.00000	+	5.19615i	0.133763	+	0.231685i	0.925124	−	0.379664i	$-0.123960\pi$
$503$	3.00000	+	5.19615i	0.133763	+	0.231685i	−0.791361	+	0.611349i	$0.790627\pi$
$504$		0			0
$505$	−48.0000			−2.13597
$506$		0			0
$507$	4.50000	+	7.79423i	0.199852	+	0.346154i
$508$		0			0
$509$	−8.00000	−	13.8564i	−0.354594	−	0.614174i	0.632455	−	0.774597i	$-0.282047\pi$
$509$	−8.00000	−	13.8564i	−0.354594	−	0.614174i	−0.987048	+	0.160423i	$0.948714\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−2.50000	−	21.6506i	−0.110378	−	0.955899i
$514$		0			0
$515$	−28.0000	+	48.4974i	−1.23383	+	2.13705i
$516$		0			0
$517$	18.0000	+	31.1769i	0.791639	+	1.37116i
$518$		0			0
$519$	13.0000	+	22.5167i	0.570637	+	0.988372i
$520$		0			0
$521$	1.00000			0.0438108			0.0219054	−	0.999760i	$-0.493027\pi$
$521$	1.00000			0.0438108			0.0219054	+	0.999760i	$0.493027\pi$
$522$		0			0
$523$	−10.0000	−	17.3205i	−0.437269	−	0.757373i	0.560208	−	0.828352i	$-0.310721\pi$
$523$	−10.0000	−	17.3205i	−0.437269	−	0.757373i	−0.997478	+	0.0709788i	$0.977388\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	10.0000	−	17.3205i	0.435607	−	0.754493i
$528$		0			0
$529$	−6.50000	+	11.2583i	−0.282609	+	0.489493i
$530$		0			0
$531$	2.00000			0.0867926
$532$		0			0
$533$	18.0000			0.779667
$534$		0			0
$535$	32.0000	−	55.4256i	1.38348	−	2.39626i
$536$		0			0
$537$	−4.50000	+	7.79423i	−0.194189	+	0.336346i
$538$		0			0
$539$	−21.0000			−0.904534
$540$		0			0
$541$	−2.00000	−	3.46410i	−0.0859867	−	0.148933i	0.819825	−	0.572615i	$-0.194071\pi$
$541$	−2.00000	−	3.46410i	−0.0859867	−	0.148933i	−0.905811	+	0.423681i	$0.860738\pi$
$542$		0			0
$543$	14.0000			0.600798
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−14.0000	−	24.2487i	−0.598597	−	1.03680i	−0.993028	−	0.117875i	$-0.962392\pi$
$547$	−14.0000	−	24.2487i	−0.598597	−	1.03680i	0.394432	−	0.918925i	$-0.370941\pi$
$548$		0			0
$549$	−8.00000	+	13.8564i	−0.341432	+	0.591377i
$550$		0			0
$551$	−14.0000	+	10.3923i	−0.596420	+	0.442727i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	4.00000	+	6.92820i	0.169791	+	0.294086i
$556$		0			0
$557$	20.0000	+	34.6410i	0.847427	+	1.46779i	0.883497	+	0.468438i	$0.155183\pi$
$557$	20.0000	+	34.6410i	0.847427	+	1.46779i	−0.0360693	+	0.999349i	$0.511484\pi$
$558$		0			0
$559$	−8.00000			−0.338364
$560$		0			0
$561$	−3.00000	−	5.19615i	−0.126660	−	0.219382i
$562$		0			0
$563$	11.0000			0.463595			0.231797	−	0.972764i	$-0.425539\pi$
$563$	11.0000			0.463595			0.231797	+	0.972764i	$0.425539\pi$
$564$		0			0
$565$	−2.00000	+	3.46410i	−0.0841406	+	0.145736i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−46.0000			−1.92842			−0.964210	−	0.265139i	$-0.914582\pi$
$569$	−46.0000			−1.92842			−0.964210	+	0.265139i	$0.914582\pi$
$570$		0			0
$571$	17.0000			0.711428			0.355714	−	0.934595i	$-0.384238\pi$
$571$	17.0000			0.711428			0.355714	+	0.934595i	$0.384238\pi$
$572$		0			0
$573$	−6.00000	+	10.3923i	−0.250654	+	0.434145i
$574$		0			0
$575$	−33.0000	+	57.1577i	−1.37620	+	2.38364i
$576$		0			0
$577$	−37.0000			−1.54033			−0.770165	−	0.637845i	$-0.779826\pi$
$577$	−37.0000			−1.54033			−0.770165	+	0.637845i	$0.779826\pi$
$578$		0			0
$579$	3.00000	+	5.19615i	0.124676	+	0.215945i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	3.00000	+	5.19615i	0.124247	+	0.215203i
$584$		0			0
$585$	−8.00000	−	13.8564i	−0.330759	−	0.572892i
$586$		0			0
$587$	−2.00000	+	3.46410i	−0.0825488	+	0.142979i	−0.904344	−	0.426804i	$-0.859639\pi$
$587$	−2.00000	+	3.46410i	−0.0825488	+	0.142979i	0.821795	+	0.569783i	$0.192973\pi$
$588$		0			0
$589$	−5.00000	−	43.3013i	−0.206021	−	1.78420i
$590$		0			0
$591$	9.00000	−	15.5885i	0.370211	−	0.641223i
$592$		0			0
$593$	10.5000	+	18.1865i	0.431183	+	0.746831i	0.996976	−	0.0777165i	$-0.0247629\pi$
$593$	10.5000	+	18.1865i	0.431183	+	0.746831i	−0.565792	+	0.824548i	$0.691430\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−18.0000			−0.736691
$598$		0			0
$599$	−19.0000	−	32.9090i	−0.776319	−	1.34462i	−0.934050	−	0.357142i	$-0.883751\pi$
$599$	−19.0000	−	32.9090i	−0.776319	−	1.34462i	0.157731	−	0.987482i	$-0.449582\pi$
$600$		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
$603$	9.00000	−	15.5885i	0.366508	−	0.634811i
$604$		0			0
$605$	−4.00000	+	6.92820i	−0.162623	+	0.281672i
$606$		0			0
$607$		0			0			−	1.00000i	$-0.5\pi$
$607$		0			0				1.00000i	$0.5\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	12.0000	−	20.7846i	0.485468	−	0.840855i
$612$		0			0
$613$	11.0000	−	19.0526i	0.444286	−	0.769526i	−0.553716	−	0.832705i	$-0.686791\pi$
$613$	11.0000	−	19.0526i	0.444286	−	0.769526i	0.998002	+	0.0631797i	$0.0201241\pi$
$614$		0			0
$615$	−36.0000			−1.45166
$616$		0			0
$617$	−1.50000	−	2.59808i	−0.0603877	−	0.104595i	0.834251	−	0.551385i	$-0.185900\pi$
$617$	−1.50000	−	2.59808i	−0.0603877	−	0.104595i	−0.894639	+	0.446790i	$0.852567\pi$
$618$		0			0
$619$	−20.0000			−0.803868			−0.401934	−	0.915669i	$-0.631662\pi$
$619$	−20.0000			−0.803868			−0.401934	+	0.915669i	$0.631662\pi$
$620$		0			0
$621$	15.0000	+	25.9808i	0.601929	+	1.04257i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−20.5000	+	35.5070i	−0.820000	+	1.42028i
$626$		0			0
$627$	−12.0000	−	5.19615i	−0.479234	−	0.207514i
$628$		0			0
$629$	−2.00000	+	3.46410i	−0.0797452	+	0.138123i
$630$		0			0
$631$	4.00000	+	6.92820i	0.159237	+	0.275807i	0.934594	−	0.355716i	$-0.115763\pi$
$631$	4.00000	+	6.92820i	0.159237	+	0.275807i	−0.775356	+	0.631524i	$0.782430\pi$
$632$		0			0
$633$	6.00000	+	10.3923i	0.238479	+	0.413057i
$634$		0			0
$635$	24.0000			0.952411
$636$		0			0
$637$	7.00000	+	12.1244i	0.277350	+	0.480384i
$638$		0			0
$639$	12.0000			0.474713
$640$		0			0
$641$	−16.5000	+	28.5788i	−0.651711	+	1.12880i	0.330997	+	0.943632i	$0.392615\pi$
$641$	−16.5000	+	28.5788i	−0.651711	+	1.12880i	−0.982708	+	0.185164i	$0.940718\pi$
$642$		0			0
$643$	−2.50000	+	4.33013i	−0.0985904	+	0.170764i	−0.911101	−	0.412182i	$-0.864767\pi$
$643$	−2.50000	+	4.33013i	−0.0985904	+	0.170764i	0.812511	+	0.582946i	$0.198100\pi$
$644$		0			0
$645$	16.0000			0.629999
$646$		0			0
$647$	−14.0000			−0.550397			−0.275198	−	0.961387i	$-0.588744\pi$
$647$	−14.0000			−0.550397			−0.275198	+	0.961387i	$0.588744\pi$
$648$		0			0
$649$	1.50000	−	2.59808i	0.0588802	−	0.101983i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	36.0000			1.40879			0.704394	−	0.709809i	$-0.251219\pi$
$653$	36.0000			1.40879			0.704394	+	0.709809i	$0.251219\pi$
$654$		0			0
$655$	−30.0000	−	51.9615i	−1.17220	−	2.03030i
$656$		0			0
$657$	18.0000			0.702247
$658$		0			0
$659$	−6.00000	−	10.3923i	−0.233727	−	0.404827i	0.725175	−	0.688565i	$-0.241759\pi$
$659$	−6.00000	−	10.3923i	−0.233727	−	0.404827i	−0.958902	+	0.283738i	$0.908425\pi$
$660$		0			0
$661$	−10.0000	−	17.3205i	−0.388955	−	0.673690i	0.603354	−	0.797473i	$-0.293830\pi$
$661$	−10.0000	−	17.3205i	−0.388955	−	0.673690i	−0.992309	+	0.123784i	$0.960497\pi$
$662$		0			0
$663$	−2.00000	+	3.46410i	−0.0776736	+	0.134535i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	12.0000	−	20.7846i	0.464642	−	0.804783i
$668$		0			0
$669$	−5.00000	−	8.66025i	−0.193311	−	0.334825i
$670$		0			0
$671$	12.0000	+	20.7846i	0.463255	+	0.802381i
$672$		0			0
$673$	30.0000			1.15642			0.578208	−	0.815890i	$-0.303752\pi$
$673$	30.0000			1.15642			0.578208	+	0.815890i	$0.303752\pi$
$674$		0			0
$675$	27.5000	+	47.6314i	1.05848	+	1.83333i
$676$		0			0
$677$	−2.00000			−0.0768662			−0.0384331	−	0.999261i	$-0.512237\pi$
$677$	−2.00000			−0.0768662			−0.0384331	+	0.999261i	$0.512237\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−9.50000	+	16.4545i	−0.364041	+	0.630537i
$682$		0			0
$683$	−28.0000			−1.07139			−0.535695	−	0.844411i	$-0.679950\pi$
$683$	−28.0000			−1.07139			−0.535695	+	0.844411i	$0.679950\pi$
$684$		0			0
$685$	−36.0000			−1.37549
$686$		0			0
$687$	4.00000	−	6.92820i	0.152610	−	0.264327i
$688$		0			0
$689$	2.00000	−	3.46410i	0.0761939	−	0.131972i
$690$		0			0
$691$	36.0000			1.36950			0.684752	−	0.728776i	$-0.259910\pi$
$691$	36.0000			1.36950			0.684752	+	0.728776i	$0.259910\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	52.0000			1.97247
$696$		0			0
$697$	−9.00000	−	15.5885i	−0.340899	−	0.590455i
$698$		0			0
$699$	−5.50000	−	9.52628i	−0.208029	−	0.360317i
$700$		0			0
$701$	6.00000	−	10.3923i	0.226617	−	0.392512i	−0.730186	−	0.683248i	$-0.760567\pi$
$701$	6.00000	−	10.3923i	0.226617	−	0.392512i	0.956803	+	0.290736i	$0.0939001\pi$
$702$		0			0
$703$	1.00000	+	8.66025i	0.0377157	+	0.326628i
$704$		0			0
$705$	−24.0000	+	41.5692i	−0.903892	+	1.56559i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−9.00000	−	15.5885i	−0.338002	−	0.585437i	0.646055	−	0.763291i	$-0.276418\pi$
$709$	−9.00000	−	15.5885i	−0.338002	−	0.585437i	−0.984057	+	0.177854i	$0.943084\pi$
$710$		0			0
$711$	8.00000			0.300023
$712$		0			0
$713$	30.0000	+	51.9615i	1.12351	+	1.94597i
$714$		0			0
$715$	−24.0000			−0.897549
$716$		0			0
$717$	−6.00000	+	10.3923i	−0.224074	+	0.388108i
$718$		0			0
$719$	17.0000	−	29.4449i	0.633993	−	1.09811i	−0.352735	−	0.935723i	$-0.614748\pi$
$719$	17.0000	−	29.4449i	0.633993	−	1.09811i	0.986728	−	0.162385i	$-0.0519185\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	21.0000			0.780998
$724$		0			0
$725$	22.0000	−	38.1051i	0.817059	−	1.41519i
$726$		0			0
$727$	4.00000	−	6.92820i	0.148352	−	0.256953i	−0.782267	−	0.622944i	$-0.785937\pi$
$727$	4.00000	−	6.92820i	0.148352	−	0.256953i	0.930618	+	0.365991i	$0.119270\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$		0			0
$731$	4.00000	+	6.92820i	0.147945	+	0.256249i
$732$		0			0
$733$	22.0000			0.812589			0.406294	−	0.913742i	$-0.366821\pi$
$733$	22.0000			0.812589			0.406294	+	0.913742i	$0.366821\pi$
$734$		0			0
$735$	−14.0000	−	24.2487i	−0.516398	−	0.894427i
$736$		0			0
$737$	−13.5000	−	23.3827i	−0.497279	−	0.861312i
$738$		0			0
$739$	2.50000	−	4.33013i	0.0919640	−	0.159286i	−0.816373	−	0.577524i	$-0.804019\pi$
$739$	2.50000	−	4.33013i	0.0919640	−	0.159286i	0.908337	+	0.418238i	$0.137352\pi$
$740$		0			0
$741$	1.00000	+	8.66025i	0.0367359	+	0.318142i
$742$		0			0
$743$	3.00000	−	5.19615i	0.110059	−	0.190628i	−0.805735	−	0.592277i	$-0.798229\pi$
$743$	3.00000	−	5.19615i	0.110059	−	0.190628i	0.915794	+	0.401648i	$0.131563\pi$
$744$		0			0
$745$	−20.0000	−	34.6410i	−0.732743	−	1.26915i
$746$		0			0
$747$	−5.00000	−	8.66025i	−0.182940	−	0.316862i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−19.0000	−	32.9090i	−0.693320	−	1.20087i	−0.970744	−	0.240118i	$-0.922814\pi$
$751$	−19.0000	−	32.9090i	−0.693320	−	1.20087i	0.277424	−	0.960748i	$-0.410519\pi$
$752$		0			0
$753$	5.00000			0.182210
$754$		0			0
$755$	4.00000	−	6.92820i	0.145575	−	0.252143i
$756$		0			0
$757$	−7.00000	+	12.1244i	−0.254419	+	0.440667i	−0.964738	−	0.263213i	$-0.915218\pi$
$757$	−7.00000	+	12.1244i	−0.254419	+	0.440667i	0.710318	+	0.703881i	$0.248551\pi$
$758$		0			0
$759$	18.0000			0.653359
$760$		0			0
$761$	17.0000			0.616250			0.308125	−	0.951346i	$-0.400299\pi$
$761$	17.0000			0.616250			0.308125	+	0.951346i	$0.400299\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−8.00000	+	13.8564i	−0.289241	+	0.500979i
$766$		0			0
$767$	−2.00000			−0.0722158
$768$		0			0
$769$	−1.00000	−	1.73205i	−0.0360609	−	0.0624593i	0.847432	−	0.530904i	$-0.178148\pi$
$769$	−1.00000	−	1.73205i	−0.0360609	−	0.0624593i	−0.883493	+	0.468445i	$0.844814\pi$
$770$		0			0
$771$	3.00000			0.108042
$772$		0			0
$773$	−26.0000	−	45.0333i	−0.935155	−	1.61974i	−0.774357	−	0.632749i	$-0.781927\pi$
$773$	−26.0000	−	45.0333i	−0.935155	−	1.61974i	−0.160798	−	0.986987i	$-0.551407\pi$
$774$		0			0
$775$	55.0000	+	95.2628i	1.97566	+	3.42194i
$776$		0			0
$777$		0			0
$778$		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
$783$	−10.0000	−	17.3205i	−0.357371	−	0.618984i
$784$		0			0
$785$	16.0000	+	27.7128i	0.571064	+	0.989113i
$786$		0			0
$787$	41.0000			1.46149			0.730746	−	0.682649i	$-0.239172\pi$
$787$	41.0000			1.46149			0.730746	+	0.682649i	$0.239172\pi$
$788$		0			0
$789$	−8.00000	−	13.8564i	−0.284808	−	0.493301i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	8.00000	−	13.8564i	0.284088	−	0.492055i
$794$		0			0
$795$	−4.00000	+	6.92820i	−0.141865	+	0.245718i
$796$		0			0
$797$	42.0000			1.48772			0.743858	−	0.668338i	$-0.232994\pi$
$797$	42.0000			1.48772			0.743858	+	0.668338i	$0.232994\pi$
$798$		0			0
$799$	−24.0000			−0.849059
$800$		0			0
$801$	−18.0000	+	31.1769i	−0.635999	+	1.10158i
$802$		0			0
$803$	13.5000	−	23.3827i	0.476405	−	0.825157i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−2.00000	−	3.46410i	−0.0704033	−	0.121942i
$808$		0			0
$809$	21.0000			0.738321			0.369160	−	0.929366i	$-0.379645\pi$
$809$	21.0000			0.738321			0.369160	+	0.929366i	$0.379645\pi$
$810$		0			0
$811$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$811$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$812$		0			0
$813$	10.0000	+	17.3205i	0.350715	+	0.607457i
$814$		0			0
$815$	−22.0000	+	38.1051i	−0.770626	+	1.33476i
$816$		0			0
$817$	16.0000	+	6.92820i	0.559769	+	0.242387i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	19.0000	+	32.9090i	0.663105	+	1.14853i	0.979795	+	0.200002i	$0.0640949\pi$
$821$	19.0000	+	32.9090i	0.663105	+	1.14853i	−0.316691	+	0.948529i	$0.602572\pi$
$822$		0			0
$823$	13.0000	+	22.5167i	0.453152	+	0.784881i	0.998580	−	0.0532760i	$-0.0169663\pi$
$823$	13.0000	+	22.5167i	0.453152	+	0.784881i	−0.545428	+	0.838157i	$0.683633\pi$
$824$		0			0
$825$	33.0000			1.14891
$826$		0			0
$827$	27.5000	+	47.6314i	0.956269	+	1.65631i	0.731438	+	0.681908i	$0.238850\pi$
$827$	27.5000	+	47.6314i	0.956269	+	1.65631i	0.224831	+	0.974398i	$0.427817\pi$
$828$		0			0
$829$	−12.0000			−0.416777			−0.208389	−	0.978046i	$-0.566822\pi$
$829$	−12.0000			−0.416777			−0.208389	+	0.978046i	$0.566822\pi$
$830$		0			0
$831$	−6.00000	+	10.3923i	−0.208138	+	0.360505i
$832$		0			0
$833$	7.00000	−	12.1244i	0.242536	−	0.420084i
$834$		0			0
$835$	−64.0000			−2.21481
$836$		0			0
$837$	50.0000			1.72825
$838$		0			0
$839$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$839$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$840$		0			0
$841$	6.50000	−	11.2583i	0.224138	−	0.388218i
$842$		0			0
$843$	−13.0000			−0.447744
$844$		0			0
$845$	−18.0000	−	31.1769i	−0.619219	−	1.07252i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−6.50000	−	11.2583i	−0.223079	−	0.386385i
$850$		0			0
$851$	−6.00000	−	10.3923i	−0.205677	−	0.356244i
$852$		0			0
$853$	−21.0000	+	36.3731i	−0.719026	+	1.24539i	0.242360	+	0.970186i	$0.422079\pi$
$853$	−21.0000	+	36.3731i	−0.719026	+	1.24539i	−0.961386	+	0.275204i	$0.911255\pi$
$854$		0			0
$855$	4.00000	+	34.6410i	0.136797	+	1.18470i
$856$		0			0
$857$	17.5000	−	30.3109i	0.597789	−	1.03540i	−0.395358	−	0.918527i	$-0.629380\pi$
$857$	17.5000	−	30.3109i	0.597789	−	1.03540i	0.993147	−	0.116873i	$-0.0372871\pi$
$858$		0			0
$859$	−14.5000	−	25.1147i	−0.494734	−	0.856904i	0.505248	−	0.862974i	$-0.331401\pi$
$859$	−14.5000	−	25.1147i	−0.494734	−	0.856904i	−0.999982	+	0.00607046i	$0.998068\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	6.00000			0.204242			0.102121	−	0.994772i	$-0.467437\pi$
$863$	6.00000			0.204242			0.102121	+	0.994772i	$0.467437\pi$
$864$		0			0
$865$	−52.0000	−	90.0666i	−1.76805	−	3.06236i
$866$		0			0
$867$	−13.0000			−0.441503
$868$		0			0
$869$	6.00000	−	10.3923i	0.203536	−	0.352535i
$870$		0			0
$871$	−9.00000	+	15.5885i	−0.304953	+	0.528195i
$872$		0			0
$873$	−2.00000			−0.0676897
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−20.0000	+	34.6410i	−0.675352	+	1.16974i	0.301014	+	0.953620i	$0.402675\pi$
$877$	−20.0000	+	34.6410i	−0.675352	+	1.16974i	−0.976366	+	0.216124i	$0.930658\pi$
$878$		0			0
$879$	2.00000	−	3.46410i	0.0674583	−	0.116841i
$880$		0			0
$881$	7.00000			0.235836			0.117918	−	0.993023i	$-0.462378\pi$
$881$	7.00000			0.235836			0.117918	+	0.993023i	$0.462378\pi$
$882$		0			0
$883$	21.5000	+	37.2391i	0.723533	+	1.25320i	0.959575	+	0.281453i	$0.0908162\pi$
$883$	21.5000	+	37.2391i	0.723533	+	1.25320i	−0.236043	+	0.971743i	$0.575850\pi$
$884$		0			0
$885$	4.00000			0.134459
$886$		0			0
$887$	−16.0000	−	27.7128i	−0.537227	−	0.930505i	−0.999052	−	0.0435339i	$-0.986138\pi$
$887$	−16.0000	−	27.7128i	−0.537227	−	0.930505i	0.461825	−	0.886971i	$-0.347195\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−1.50000	+	2.59808i	−0.0502519	+	0.0870388i
$892$		0			0
$893$	−42.0000	+	31.1769i	−1.40548	+	1.04330i
$894$		0			0
$895$	18.0000	−	31.1769i	0.601674	−	1.04213i
$896$		0			0
$897$	−6.00000	−	10.3923i	−0.200334	−	0.346989i
$898$		0			0
$899$	−20.0000	−	34.6410i	−0.667037	−	1.15534i
$900$		0			0
$901$	−4.00000			−0.133259
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−56.0000			−1.86150
$906$		0			0
$907$	−24.5000	+	42.4352i	−0.813509	+	1.40904i	0.0968843	+	0.995296i	$0.469112\pi$
$907$	−24.5000	+	42.4352i	−0.813509	+	1.40904i	−0.910393	+	0.413744i	$0.864221\pi$
$908$		0			0
$909$	12.0000	−	20.7846i	0.398015	−	0.689382i
$910$		0			0
$911$	−14.0000			−0.463841			−0.231920	−	0.972735i	$-0.574501\pi$
$911$	−14.0000			−0.463841			−0.231920	+	0.972735i	$0.574501\pi$
$912$		0			0
$913$	−15.0000			−0.496428
$914$		0			0
$915$	−16.0000	+	27.7128i	−0.528944	+	0.916157i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−26.0000			−0.857661			−0.428830	−	0.903385i	$-0.641074\pi$
$919$	−26.0000			−0.857661			−0.428830	+	0.903385i	$0.641074\pi$
$920$		0			0
$921$	−12.5000	−	21.6506i	−0.411889	−	0.713413i
$922$		0			0
$923$	−12.0000			−0.394985
$924$		0			0
$925$	−11.0000	−	19.0526i	−0.361678	−	0.626444i
$926$		0			0
$927$	−14.0000	−	24.2487i	−0.459820	−	0.796432i
$928$		0			0
$929$	−10.5000	+	18.1865i	−0.344494	+	0.596681i	−0.985262	−	0.171054i	$-0.945283\pi$
$929$	−10.5000	+	18.1865i	−0.344494	+	0.596681i	0.640768	+	0.767735i	$0.278616\pi$
$930$		0			0
$931$	−3.50000	−	30.3109i	−0.114708	−	0.993399i
$932$		0			0
$933$	1.00000	−	1.73205i	0.0327385	−	0.0567048i
$934$		0			0
$935$	12.0000	+	20.7846i	0.392442	+	0.679729i
$936$		0			0
$937$	−5.50000	−	9.52628i	−0.179677	−	0.311210i	0.762093	−	0.647468i	$-0.224172\pi$
$937$	−5.50000	−	9.52628i	−0.179677	−	0.311210i	−0.941770	+	0.336258i	$0.890839\pi$
$938$		0			0
$939$	−19.0000			−0.620042
$940$		0			0
$941$	5.00000	+	8.66025i	0.162995	+	0.282316i	0.935942	−	0.352155i	$-0.114551\pi$
$941$	5.00000	+	8.66025i	0.162995	+	0.282316i	−0.772946	+	0.634472i	$0.781218\pi$
$942$		0			0
$943$	54.0000			1.75848
$944$		0			0
$945$		0			0
$946$		0			0
$947$	14.0000	−	24.2487i	0.454939	−	0.787977i	−0.543746	−	0.839250i	$-0.682994\pi$
$947$	14.0000	−	24.2487i	0.454939	−	0.787977i	0.998685	+	0.0512727i	$0.0163278\pi$
$948$		0			0
$949$	−18.0000			−0.584305
$950$		0			0
$951$	6.00000			0.194563
$952$		0			0
$953$	−0.500000	+	0.866025i	−0.0161966	+	0.0280533i	−0.874010	−	0.485908i	$-0.838489\pi$
$953$	−0.500000	+	0.866025i	−0.0161966	+	0.0280533i	0.857814	+	0.513961i	$0.171822\pi$
$954$		0			0
$955$	24.0000	−	41.5692i	0.776622	−	1.34515i
$956$		0			0
$957$	−12.0000			−0.387905
$958$		0			0
$959$		0			0
$960$		0			0
$961$	69.0000			2.22581
$962$		0			0
$963$	16.0000	+	27.7128i	0.515593	+	0.893033i
$964$		0			0
$965$	−12.0000	−	20.7846i	−0.386294	−	0.669080i
$966$		0			0
$967$	−27.0000	+	46.7654i	−0.868261	+	1.50387i	−0.00448958	+	0.999990i	$0.501429\pi$
$967$	−27.0000	+	46.7654i	−0.868261	+	1.50387i	−0.863772	+	0.503883i	$0.831904\pi$
$968$		0			0
$969$	7.00000	−	5.19615i	0.224872	−	0.166924i
$970$		0			0
$971$	−26.5000	+	45.8993i	−0.850425	+	1.47298i	0.0303994	+	0.999538i	$0.490322\pi$
$971$	−26.5000	+	45.8993i	−0.850425	+	1.47298i	−0.880825	+	0.473442i	$0.843011\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−11.0000	−	19.0526i	−0.352282	−	0.610170i
$976$		0			0
$977$	−47.0000			−1.50366			−0.751832	−	0.659355i	$-0.770829\pi$
$977$	−47.0000			−1.50366			−0.751832	+	0.659355i	$0.770829\pi$
$978$		0			0
$979$	27.0000	+	46.7654i	0.862924	+	1.49463i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−16.0000	+	27.7128i	−0.510321	+	0.883901i	0.489608	+	0.871943i	$0.337140\pi$
$983$	−16.0000	+	27.7128i	−0.510321	+	0.883901i	−0.999928	+	0.0119587i	$0.996193\pi$
$984$		0			0
$985$	−36.0000	+	62.3538i	−1.14706	+	1.98676i
$986$		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	$-0.873889\pi$
$991$	−4.00000	+	6.92820i	−0.127064	+	0.220082i	0.795474	+	0.605988i	$0.207222\pi$
$992$		0			0
$993$	−6.50000	+	11.2583i	−0.206271	+	0.357272i
$994$		0			0
$995$	72.0000			2.28255
$996$		0			0
$997$	16.0000	+	27.7128i	0.506725	+	0.877674i	0.999970	+	0.00778294i	$0.00247741\pi$
$997$	16.0000	+	27.7128i	0.506725	+	0.877674i	−0.493245	+	0.869891i	$0.664189\pi$
$998$		0			0
$999$	−10.0000			−0.316386

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	152.2.i.b.49.1	✓	2
3.2	odd	2		1368.2.s.a.505.1		2
4.3	odd	2		304.2.i.d.49.1		2
8.3	odd	2		1216.2.i.b.961.1		2
8.5	even	2		1216.2.i.f.961.1		2
12.11	even	2		2736.2.s.a.1873.1		2
19.7	even	3	inner	152.2.i.b.121.1	yes	2
19.8	odd	6		2888.2.a.a.1.1		1
19.11	even	3		2888.2.a.d.1.1		1
57.26	odd	6		1368.2.s.a.577.1		2
76.7	odd	6		304.2.i.d.273.1		2
76.11	odd	6		5776.2.a.e.1.1		1
76.27	even	6		5776.2.a.j.1.1		1
152.45	even	6		1216.2.i.f.577.1		2
152.83	odd	6		1216.2.i.b.577.1		2
228.83	even	6		2736.2.s.a.577.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.2.i.b.49.1	✓	2	1.1	even	1	trivial
152.2.i.b.121.1	yes	2	19.7	even	3	inner
304.2.i.d.49.1		2	4.3	odd	2
304.2.i.d.273.1		2	76.7	odd	6
1216.2.i.b.577.1		2	152.83	odd	6
1216.2.i.b.961.1		2	8.3	odd	2
1216.2.i.f.577.1		2	152.45	even	6
1216.2.i.f.961.1		2	8.5	even	2
1368.2.s.a.505.1		2	3.2	odd	2
1368.2.s.a.577.1		2	57.26	odd	6
2736.2.s.a.577.1		2	228.83	even	6
2736.2.s.a.1873.1		2	12.11	even	2
2888.2.a.a.1.1		1	19.8	odd	6
2888.2.a.d.1.1		1	19.11	even	3
5776.2.a.e.1.1		1	76.11	odd	6
5776.2.a.j.1.1		1	76.27	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 152 = 2^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	152.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{3} +(2.00000 - 3.46410i) q^{5} +(1.00000 + 1.73205i) q^{9} +3.00000 q^{11} +(-1.00000 - 1.73205i) q^{13} +(2.00000 + 3.46410i) q^{15} +(-1.00000 + 1.73205i) q^{17} +(0.500000 + 4.33013i) q^{19} +(-3.00000 - 5.19615i) q^{23} +(-5.50000 - 9.52628i) q^{25} -5.00000 q^{27} +(2.00000 + 3.46410i) q^{29} -10.0000 q^{31} +(-1.50000 + 2.59808i) q^{33} +2.00000 q^{37} +2.00000 q^{39} +(-4.50000 + 7.79423i) q^{41} +(2.00000 - 3.46410i) q^{43} +8.00000 q^{45} +(6.00000 + 10.3923i) q^{47} -7.00000 q^{49} +(-1.00000 - 1.73205i) q^{51} +(1.00000 + 1.73205i) q^{53} +(6.00000 - 10.3923i) q^{55} +(-4.00000 - 1.73205i) q^{57} +(0.500000 - 0.866025i) q^{59} +(4.00000 + 6.92820i) q^{61} -8.00000 q^{65} +(-4.50000 - 7.79423i) q^{67} +6.00000 q^{69} +(3.00000 - 5.19615i) q^{71} +(4.50000 - 7.79423i) q^{73} +11.0000 q^{75} +(2.00000 - 3.46410i) q^{79} +(-0.500000 + 0.866025i) q^{81} -5.00000 q^{83} +(4.00000 + 6.92820i) q^{85} -4.00000 q^{87} +(9.00000 + 15.5885i) q^{89} +(5.00000 - 8.66025i) q^{93} +(16.0000 + 6.92820i) q^{95} +(-0.500000 + 0.866025i) q^{97} +(3.00000 + 5.19615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{3} + 4 q^{5} + 2 q^{9} + 6 q^{11} - 2 q^{13} + 4 q^{15} - 2 q^{17} + q^{19} - 6 q^{23} - 11 q^{25} - 10 q^{27} + 4 q^{29} - 20 q^{31} - 3 q^{33} + 4 q^{37} + 4 q^{39} - 9 q^{41} + 4 q^{43} + 16 q^{45}+ \cdots + 6 q^{99}+O(q^{100}) \) 2 * q - q^3 + 4 * q^5 + 2 * q^9 + 6 * q^11 - 2 * q^13 + 4 * q^15 - 2 * q^17 + q^19 - 6 * q^23 - 11 * q^25 - 10 * q^27 + 4 * q^29 - 20 * q^31 - 3 * q^33 + 4 * q^37 + 4 * q^39 - 9 * q^41 + 4 * q^43 + 16 * q^45 + 12 * q^47 - 14 * q^49 - 2 * q^51 + 2 * q^53 + 12 * q^55 - 8 * q^57 + q^59 + 8 * q^61 - 16 * q^65 - 9 * q^67 + 12 * q^69 + 6 * q^71 + 9 * q^73 + 22 * q^75 + 4 * q^79 - q^81 - 10 * q^83 + 8 * q^85 - 8 * q^87 + 18 * q^89 + 10 * q^93 + 32 * q^95 - q^97 + 6 * q^99

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