LMFDB - Embedded newform 2100.2.bc.d.949.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2100,2,Mod(949,2100)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2100, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 3, 4]))

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

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

chi := DirichletCharacter("2100.949");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2100.bc (of order $6$, 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:	$16.7685844245$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 420)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			949.1
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	2100.949
Dual form			2100.2.bc.d.1549.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{3} +(0.866025 - 2.50000i) q^{7} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	$q+(-0.866025 - 0.500000i) q^{3} +(0.866025 - 2.50000i) q^{7} +(0.500000 + 0.866025i) q^{9} +(2.00000 - 3.46410i) q^{11} -7.00000i q^{13} +(5.19615 + 3.00000i) q^{17} +(1.50000 + 2.59808i) q^{19} +(-2.00000 + 1.73205i) q^{21} +(1.73205 - 1.00000i) q^{23} -1.00000i q^{27} +2.00000 q^{29} +(-3.50000 + 6.06218i) q^{31} +(-3.46410 + 2.00000i) q^{33} +(-6.06218 + 3.50000i) q^{37} +(-3.50000 + 6.06218i) q^{39} -8.00000 q^{41} -5.00000i q^{43} +(8.66025 - 5.00000i) q^{47} +(-5.50000 - 4.33013i) q^{49} +(-3.00000 - 5.19615i) q^{51} +(-6.92820 - 4.00000i) q^{53} -3.00000i q^{57} +(5.00000 - 8.66025i) q^{59} +(3.00000 + 5.19615i) q^{61} +(2.59808 - 0.500000i) q^{63} +(-2.59808 - 1.50000i) q^{67} -2.00000 q^{69} +(12.9904 + 7.50000i) q^{73} +(-6.92820 - 8.00000i) q^{77} +(0.500000 + 0.866025i) q^{79} +(-0.500000 + 0.866025i) q^{81} -8.00000i q^{83} +(-1.73205 - 1.00000i) q^{87} +(1.00000 + 1.73205i) q^{89} +(-17.5000 - 6.06218i) q^{91} +(6.06218 - 3.50000i) q^{93} -10.0000i q^{97} +4.00000 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^9	$ 4 q + 2 q^{9} + 8 q^{11} + 6 q^{19} - 8 q^{21} + 8 q^{29} - 14 q^{31} - 14 q^{39} - 32 q^{41} - 22 q^{49} - 12 q^{51} + 20 q^{59} + 12 q^{61} - 8 q^{69} + 2 q^{79} - 2 q^{81} + 4 q^{89} - 70 q^{91} + 16 q^{99}+O(q^{100}) $ 4 * q + 2 * q^9 + 8 * q^11 + 6 * q^19 - 8 * q^21 + 8 * q^29 - 14 * q^31 - 14 * q^39 - 32 * q^41 - 22 * q^49 - 12 * q^51 + 20 * q^59 + 12 * q^61 - 8 * q^69 + 2 * q^79 - 2 * q^81 + 4 * q^89 - 70 * q^91 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times$.

$n$	$701$	$1051$	$1177$	$1501$
$\chi(n)$	$1$	$1$	$-1$	$e\left(\frac{2}{3}\right)$

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
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	0.866025	−	2.50000i	0.327327	−	0.944911i
$7$	0.866025	−	2.50000i	0.327327	−	0.944911i
$8$		0			0
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$		0			0
$11$	2.00000	−	3.46410i	0.603023	−	1.04447i	−0.389338	−	0.921095i	$-0.627296\pi$
$11$	2.00000	−	3.46410i	0.603023	−	1.04447i	0.992361	−	0.123371i	$-0.0393705\pi$
$12$		0			0
$13$		−	7.00000i		−	1.94145i	−0.240192	−	0.970725i	$-0.577210\pi$
$13$		−	7.00000i		−	1.94145i	0.240192	−	0.970725i	$-0.422790\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	5.19615	+	3.00000i	1.26025	+	0.727607i	0.973123	−	0.230285i	$-0.0739659\pi$
$17$	5.19615	+	3.00000i	1.26025	+	0.727607i	0.287129	+	0.957892i	$0.407299\pi$
$18$		0			0
$19$	1.50000	+	2.59808i	0.344124	+	0.596040i	0.985194	−	0.171442i	$-0.0548427\pi$
$19$	1.50000	+	2.59808i	0.344124	+	0.596040i	−0.641071	+	0.767482i	$0.721509\pi$
$20$		0			0
$21$	−2.00000	+	1.73205i	−0.436436	+	0.377964i
$22$		0			0
$23$	1.73205	−	1.00000i	0.361158	−	0.208514i	−0.308431	−	0.951247i	$-0.599804\pi$
$23$	1.73205	−	1.00000i	0.361158	−	0.208514i	0.669588	+	0.742732i	$0.266471\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$		−	1.00000i		−	0.192450i
$28$		0			0
$29$	2.00000			0.371391			0.185695	−	0.982607i	$-0.440546\pi$
$29$	2.00000			0.371391			0.185695	+	0.982607i	$0.440546\pi$
$30$		0			0
$31$	−3.50000	+	6.06218i	−0.628619	+	1.08880i	0.359211	+	0.933257i	$0.383046\pi$
$31$	−3.50000	+	6.06218i	−0.628619	+	1.08880i	−0.987829	+	0.155543i	$0.950287\pi$
$32$		0			0
$33$	−3.46410	+	2.00000i	−0.603023	+	0.348155i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−6.06218	+	3.50000i	−0.996616	+	0.575396i	−0.907245	−	0.420602i	$-0.861819\pi$
$37$	−6.06218	+	3.50000i	−0.996616	+	0.575396i	−0.0893706	+	0.995998i	$0.528486\pi$
$38$		0			0
$39$	−3.50000	+	6.06218i	−0.560449	+	0.970725i
$40$		0			0
$41$	−8.00000			−1.24939			−0.624695	−	0.780869i	$-0.714777\pi$
$41$	−8.00000			−1.24939			−0.624695	+	0.780869i	$0.714777\pi$
$42$		0			0
$43$		−	5.00000i		−	0.762493i	−0.924473	−	0.381246i	$-0.875495\pi$
$43$		−	5.00000i		−	0.762493i	0.924473	−	0.381246i	$-0.124505\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	8.66025	−	5.00000i	1.26323	−	0.729325i	0.289530	−	0.957169i	$-0.406501\pi$
$47$	8.66025	−	5.00000i	1.26323	−	0.729325i	0.973698	+	0.227844i	$0.0731676\pi$
$48$		0			0
$49$	−5.50000	−	4.33013i	−0.785714	−	0.618590i
$50$		0			0
$51$	−3.00000	−	5.19615i	−0.420084	−	0.727607i
$52$		0			0
$53$	−6.92820	−	4.00000i	−0.951662	−	0.549442i	−0.0580651	−	0.998313i	$-0.518493\pi$
$53$	−6.92820	−	4.00000i	−0.951662	−	0.549442i	−0.893597	+	0.448871i	$0.851826\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		−	3.00000i		−	0.397360i
$58$		0			0
$59$	5.00000	−	8.66025i	0.650945	−	1.12747i	−0.331949	−	0.943297i	$-0.607706\pi$
$59$	5.00000	−	8.66025i	0.650945	−	1.12747i	0.982894	−	0.184172i	$-0.0589603\pi$
$60$		0			0
$61$	3.00000	+	5.19615i	0.384111	+	0.665299i	0.991645	−	0.128994i	$-0.0411748\pi$
$61$	3.00000	+	5.19615i	0.384111	+	0.665299i	−0.607535	+	0.794293i	$0.707841\pi$
$62$		0			0
$63$	2.59808	−	0.500000i	0.327327	−	0.0629941i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−2.59808	−	1.50000i	−0.317406	−	0.183254i	0.332830	−	0.942987i	$-0.391996\pi$
$67$	−2.59808	−	1.50000i	−0.317406	−	0.183254i	−0.650236	+	0.759733i	$0.725330\pi$
$68$		0			0
$69$	−2.00000			−0.240772
$70$		0			0
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$		0			0
$73$	12.9904	+	7.50000i	1.52041	+	0.877809i	0.999710	+	0.0240681i	$0.00766187\pi$
$73$	12.9904	+	7.50000i	1.52041	+	0.877809i	0.520699	+	0.853740i	$0.325671\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−6.92820	−	8.00000i	−0.789542	−	0.911685i
$78$		0			0
$79$	0.500000	+	0.866025i	0.0562544	+	0.0974355i	0.892781	−	0.450490i	$-0.148751\pi$
$79$	0.500000	+	0.866025i	0.0562544	+	0.0974355i	−0.836527	+	0.547926i	$0.815418\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$		−	8.00000i		−	0.878114i	−0.898459	−	0.439057i	$-0.855313\pi$
$83$		−	8.00000i		−	0.878114i	0.898459	−	0.439057i	$-0.144687\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−1.73205	−	1.00000i	−0.185695	−	0.107211i
$88$		0			0
$89$	1.00000	+	1.73205i	0.106000	+	0.183597i	0.914146	−	0.405385i	$-0.132862\pi$
$89$	1.00000	+	1.73205i	0.106000	+	0.183597i	−0.808146	+	0.588982i	$0.799529\pi$
$90$		0			0
$91$	−17.5000	−	6.06218i	−1.83450	−	0.635489i
$92$		0			0
$93$	6.06218	−	3.50000i	0.628619	−	0.362933i
$94$		0			0
$95$		0			0
$96$		0			0
$97$		−	10.0000i		−	1.01535i	−0.861550	−	0.507673i	$-0.830506\pi$
$97$		−	10.0000i		−	1.01535i	0.861550	−	0.507673i	$-0.169494\pi$
$98$		0			0
$99$	4.00000			0.402015
$100$		0			0
$101$	−6.00000	+	10.3923i	−0.597022	+	1.03407i	0.396236	+	0.918149i	$0.370316\pi$
$101$	−6.00000	+	10.3923i	−0.597022	+	1.03407i	−0.993258	+	0.115924i	$0.963017\pi$
$102$		0			0
$103$	6.06218	−	3.50000i	0.597324	−	0.344865i	−0.170664	−	0.985329i	$-0.554591\pi$
$103$	6.06218	−	3.50000i	0.597324	−	0.344865i	0.767988	+	0.640464i	$0.221258\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	1.73205	−	1.00000i	0.167444	−	0.0966736i	−0.413936	−	0.910306i	$-0.635846\pi$
$107$	1.73205	−	1.00000i	0.167444	−	0.0966736i	0.581380	+	0.813632i	$0.302513\pi$
$108$		0			0
$109$	−1.50000	+	2.59808i	−0.143674	+	0.248851i	−0.928877	−	0.370387i	$-0.879225\pi$
$109$	−1.50000	+	2.59808i	−0.143674	+	0.248851i	0.785203	+	0.619238i	$0.212558\pi$
$110$		0			0
$111$	7.00000			0.664411
$112$		0			0
$113$		−	18.0000i		−	1.69330i	−0.532152	−	0.846649i	$-0.678617\pi$
$113$		−	18.0000i		−	1.69330i	0.532152	−	0.846649i	$-0.321383\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	6.06218	−	3.50000i	0.560449	−	0.323575i
$118$		0			0
$119$	12.0000	−	10.3923i	1.10004	−	0.952661i
$120$		0			0
$121$	−2.50000	−	4.33013i	−0.227273	−	0.393648i
$122$		0			0
$123$	6.92820	+	4.00000i	0.624695	+	0.360668i
$124$		0			0
$125$		0			0
$126$		0			0
$127$			13.0000i			1.15356i	0.816898	+	0.576782i	$0.195692\pi$
$127$			13.0000i			1.15356i	−0.816898	+	0.576782i	$0.804308\pi$
$128$		0			0
$129$	−2.50000	+	4.33013i	−0.220113	+	0.381246i
$130$		0			0
$131$	−11.0000	−	19.0526i	−0.961074	−	1.66463i	−0.719811	−	0.694170i	$-0.755772\pi$
$131$	−11.0000	−	19.0526i	−0.961074	−	1.66463i	−0.241264	−	0.970460i	$-0.577562\pi$
$132$		0			0
$133$	7.79423	−	1.50000i	0.675845	−	0.130066i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−15.5885	−	9.00000i	−1.33181	−	0.768922i	−0.346235	−	0.938148i	$-0.612540\pi$
$137$	−15.5885	−	9.00000i	−1.33181	−	0.768922i	−0.985577	+	0.169226i	$0.945873\pi$
$138$		0			0
$139$	13.0000			1.10265			0.551323	−	0.834292i	$-0.314123\pi$
$139$	13.0000			1.10265			0.551323	+	0.834292i	$0.314123\pi$
$140$		0			0
$141$	−10.0000			−0.842152
$142$		0			0
$143$	−24.2487	−	14.0000i	−2.02778	−	1.17074i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	2.59808	+	6.50000i	0.214286	+	0.536111i
$148$		0			0
$149$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$149$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$150$		0			0
$151$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$151$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$152$		0			0
$153$			6.00000i			0.485071i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−12.1244	−	7.00000i	−0.967629	−	0.558661i	−0.0691164	−	0.997609i	$-0.522018\pi$
$157$	−12.1244	−	7.00000i	−0.967629	−	0.558661i	−0.898513	+	0.438948i	$0.855351\pi$
$158$		0			0
$159$	4.00000	+	6.92820i	0.317221	+	0.549442i
$160$		0			0
$161$	−1.00000	−	5.19615i	−0.0788110	−	0.409514i
$162$		0			0
$163$	−3.46410	+	2.00000i	−0.271329	+	0.156652i	−0.629492	−	0.777007i	$-0.716737\pi$
$163$	−3.46410	+	2.00000i	−0.271329	+	0.156652i	0.358162	+	0.933659i	$0.383403\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$			24.0000i			1.85718i	0.371113	+	0.928588i	$0.378976\pi$
$167$			24.0000i			1.85718i	−0.371113	+	0.928588i	$0.621024\pi$
$168$		0			0
$169$	−36.0000			−2.76923
$170$		0			0
$171$	−1.50000	+	2.59808i	−0.114708	+	0.198680i
$172$		0			0
$173$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$173$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−8.66025	+	5.00000i	−0.650945	+	0.375823i
$178$		0			0
$179$	7.00000	−	12.1244i	0.523205	−	0.906217i	−0.476431	−	0.879212i	$-0.658070\pi$
$179$	7.00000	−	12.1244i	0.523205	−	0.906217i	0.999635	−	0.0270049i	$-0.00859697\pi$
$180$		0			0
$181$	−3.00000			−0.222988			−0.111494	−	0.993765i	$-0.535564\pi$
$181$	−3.00000			−0.222988			−0.111494	+	0.993765i	$0.535564\pi$
$182$		0			0
$183$		−	6.00000i		−	0.443533i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	20.7846	−	12.0000i	1.51992	−	0.877527i
$188$		0			0
$189$	−2.50000	−	0.866025i	−0.181848	−	0.0629941i
$190$		0			0
$191$	9.00000	+	15.5885i	0.651217	+	1.12794i	0.982828	+	0.184525i	$0.0590746\pi$
$191$	9.00000	+	15.5885i	0.651217	+	1.12794i	−0.331611	+	0.943416i	$0.607592\pi$
$192$		0			0
$193$	−19.9186	−	11.5000i	−1.43377	−	0.827788i	−0.436365	−	0.899770i	$-0.643734\pi$
$193$	−19.9186	−	11.5000i	−1.43377	−	0.827788i	−0.997406	+	0.0719816i	$0.977068\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			2.00000i			0.142494i	0.997459	+	0.0712470i	$0.0226979\pi$
$197$			2.00000i			0.142494i	−0.997459	+	0.0712470i	$0.977302\pi$
$198$		0			0
$199$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$199$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$200$		0			0
$201$	1.50000	+	2.59808i	0.105802	+	0.183254i
$202$		0			0
$203$	1.73205	−	5.00000i	0.121566	−	0.350931i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	1.73205	+	1.00000i	0.120386	+	0.0695048i
$208$		0			0
$209$	12.0000			0.830057
$210$		0			0
$211$	−4.00000			−0.275371			−0.137686	−	0.990476i	$-0.543966\pi$
$211$	−4.00000			−0.275371			−0.137686	+	0.990476i	$0.543966\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$		0			0
$216$		0			0
$217$	12.1244	+	14.0000i	0.823055	+	0.950382i
$218$		0			0
$219$	−7.50000	−	12.9904i	−0.506803	−	0.877809i
$220$		0			0
$221$	21.0000	−	36.3731i	1.41261	−	2.44672i
$222$		0			0
$223$			12.0000i			0.803579i	0.915732	+	0.401790i	$0.131612\pi$
$223$			12.0000i			0.803579i	−0.915732	+	0.401790i	$0.868388\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−6.92820	−	4.00000i	−0.459841	−	0.265489i	0.252136	−	0.967692i	$-0.418867\pi$
$227$	−6.92820	−	4.00000i	−0.459841	−	0.265489i	−0.711977	+	0.702202i	$0.752200\pi$
$228$		0			0
$229$	8.50000	+	14.7224i	0.561696	+	0.972886i	0.997349	+	0.0727709i	$0.0231842\pi$
$229$	8.50000	+	14.7224i	0.561696	+	0.972886i	−0.435653	+	0.900115i	$0.643482\pi$
$230$		0			0
$231$	2.00000	+	10.3923i	0.131590	+	0.683763i
$232$		0			0
$233$	−5.19615	+	3.00000i	−0.340411	+	0.196537i	−0.660454	−	0.750867i	$-0.729636\pi$
$233$	−5.19615	+	3.00000i	−0.340411	+	0.196537i	0.320043	+	0.947403i	$0.396303\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		−	1.00000i		−	0.0649570i
$238$		0			0
$239$	−6.00000			−0.388108			−0.194054	−	0.980991i	$-0.562164\pi$
$239$	−6.00000			−0.388108			−0.194054	+	0.980991i	$0.562164\pi$
$240$		0			0
$241$	7.00000	−	12.1244i	0.450910	−	0.780998i	−0.547533	−	0.836784i	$-0.684433\pi$
$241$	7.00000	−	12.1244i	0.450910	−	0.780998i	0.998443	+	0.0557856i	$0.0177663\pi$
$242$		0			0
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	18.1865	−	10.5000i	1.15718	−	0.668099i
$248$		0			0
$249$	−4.00000	+	6.92820i	−0.253490	+	0.439057i
$250$		0			0
$251$	22.0000			1.38863			0.694314	−	0.719672i	$-0.255708\pi$
$251$	22.0000			1.38863			0.694314	+	0.719672i	$0.255708\pi$
$252$		0			0
$253$		−	8.00000i		−	0.502956i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	13.8564	−	8.00000i	0.864339	−	0.499026i	−0.00112398	−	0.999999i	$-0.500358\pi$
$257$	13.8564	−	8.00000i	0.864339	−	0.499026i	0.865463	+	0.500973i	$0.167024\pi$
$258$		0			0
$259$	3.50000	+	18.1865i	0.217479	+	1.13006i
$260$		0			0
$261$	1.00000	+	1.73205i	0.0618984	+	0.107211i
$262$		0			0
$263$	10.3923	+	6.00000i	0.640817	+	0.369976i	0.784929	−	0.619586i	$-0.212699\pi$
$263$	10.3923	+	6.00000i	0.640817	+	0.369976i	−0.144112	+	0.989561i	$0.546033\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		−	2.00000i		−	0.122398i
$268$		0			0
$269$	−5.00000	+	8.66025i	−0.304855	+	0.528025i	−0.977229	−	0.212187i	$-0.931941\pi$
$269$	−5.00000	+	8.66025i	−0.304855	+	0.528025i	0.672374	+	0.740212i	$0.265275\pi$
$270$		0			0
$271$	8.00000	+	13.8564i	0.485965	+	0.841717i	0.999870	−	0.0161307i	$-0.00513477\pi$
$271$	8.00000	+	13.8564i	0.485965	+	0.841717i	−0.513905	+	0.857847i	$0.671801\pi$
$272$		0			0
$273$	12.1244	+	14.0000i	0.733799	+	0.847319i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−19.9186	−	11.5000i	−1.19679	−	0.690968i	−0.236953	−	0.971521i	$-0.576149\pi$
$277$	−19.9186	−	11.5000i	−1.19679	−	0.690968i	−0.959839	+	0.280553i	$0.909482\pi$
$278$		0			0
$279$	−7.00000			−0.419079
$280$		0			0
$281$	−16.0000			−0.954480			−0.477240	−	0.878773i	$-0.658363\pi$
$281$	−16.0000			−0.954480			−0.477240	+	0.878773i	$0.658363\pi$
$282$		0			0
$283$	21.6506	+	12.5000i	1.28700	+	0.743048i	0.978117	−	0.208053i	$-0.0667128\pi$
$283$	21.6506	+	12.5000i	1.28700	+	0.743048i	0.308879	+	0.951101i	$0.400046\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−6.92820	+	20.0000i	−0.408959	+	1.18056i
$288$		0			0
$289$	9.50000	+	16.4545i	0.558824	+	0.967911i
$290$		0			0
$291$	−5.00000	+	8.66025i	−0.293105	+	0.507673i
$292$		0			0
$293$			12.0000i			0.701047i	0.936554	+	0.350524i	$0.113996\pi$
$293$			12.0000i			0.701047i	−0.936554	+	0.350524i	$0.886004\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−3.46410	−	2.00000i	−0.201008	−	0.116052i
$298$		0			0
$299$	−7.00000	−	12.1244i	−0.404820	−	0.701170i
$300$		0			0
$301$	−12.5000	−	4.33013i	−0.720488	−	0.249584i
$302$		0			0
$303$	10.3923	−	6.00000i	0.597022	−	0.344691i
$304$		0			0
$305$		0			0
$306$		0			0
$307$			11.0000i			0.627803i	0.949456	+	0.313902i	$0.101636\pi$
$307$			11.0000i			0.627803i	−0.949456	+	0.313902i	$0.898364\pi$
$308$		0			0
$309$	−7.00000			−0.398216
$310$		0			0
$311$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$311$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$312$		0			0
$313$	−18.1865	+	10.5000i	−1.02796	+	0.593495i	−0.916401	−	0.400262i	$-0.868919\pi$
$313$	−18.1865	+	10.5000i	−1.02796	+	0.593495i	−0.111563	+	0.993757i	$0.535586\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	15.5885	−	9.00000i	0.875535	−	0.505490i	0.00635137	−	0.999980i	$-0.497978\pi$
$317$	15.5885	−	9.00000i	0.875535	−	0.505490i	0.869184	+	0.494489i	$0.164645\pi$
$318$		0			0
$319$	4.00000	−	6.92820i	0.223957	−	0.387905i
$320$		0			0
$321$	−2.00000			−0.111629
$322$		0			0
$323$			18.0000i			1.00155i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	2.59808	−	1.50000i	0.143674	−	0.0829502i
$328$		0			0
$329$	−5.00000	−	25.9808i	−0.275659	−	1.43237i
$330$		0			0
$331$	3.50000	+	6.06218i	0.192377	+	0.333207i	0.946038	−	0.324057i	$-0.105047\pi$
$331$	3.50000	+	6.06218i	0.192377	+	0.333207i	−0.753660	+	0.657264i	$0.771714\pi$
$332$		0			0
$333$	−6.06218	−	3.50000i	−0.332205	−	0.191799i
$334$		0			0
$335$		0			0
$336$		0			0
$337$			15.0000i			0.817102i	0.912735	+	0.408551i	$0.133966\pi$
$337$			15.0000i			0.817102i	−0.912735	+	0.408551i	$0.866034\pi$
$338$		0			0
$339$	−9.00000	+	15.5885i	−0.488813	+	0.846649i
$340$		0			0
$341$	14.0000	+	24.2487i	0.758143	+	1.31314i
$342$		0			0
$343$	−15.5885	+	10.0000i	−0.841698	+	0.539949i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−6.92820	−	4.00000i	−0.371925	−	0.214731i	0.302374	−	0.953189i	$-0.402221\pi$
$347$	−6.92820	−	4.00000i	−0.371925	−	0.214731i	−0.674299	+	0.738458i	$0.735554\pi$
$348$		0			0
$349$	6.00000			0.321173			0.160586	−	0.987022i	$-0.448662\pi$
$349$	6.00000			0.321173			0.160586	+	0.987022i	$0.448662\pi$
$350$		0			0
$351$	−7.00000			−0.373632
$352$		0			0
$353$	−10.3923	−	6.00000i	−0.553127	−	0.319348i	0.197256	−	0.980352i	$-0.436797\pi$
$353$	−10.3923	−	6.00000i	−0.553127	−	0.319348i	−0.750382	+	0.661004i	$0.770130\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−15.5885	+	3.00000i	−0.825029	+	0.158777i
$358$		0			0
$359$	−7.00000	−	12.1244i	−0.369446	−	0.639899i	0.620033	−	0.784576i	$-0.287119\pi$
$359$	−7.00000	−	12.1244i	−0.369446	−	0.639899i	−0.989479	+	0.144677i	$0.953786\pi$
$360$		0			0
$361$	5.00000	−	8.66025i	0.263158	−	0.455803i
$362$		0			0
$363$			5.00000i			0.262432i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	4.33013	+	2.50000i	0.226031	+	0.130499i	0.608740	−	0.793370i	$-0.291675\pi$
$367$	4.33013	+	2.50000i	0.226031	+	0.130499i	−0.382709	+	0.923869i	$0.625009\pi$
$368$		0			0
$369$	−4.00000	−	6.92820i	−0.208232	−	0.360668i
$370$		0			0
$371$	−16.0000	+	13.8564i	−0.830679	+	0.719389i
$372$		0			0
$373$	−7.79423	+	4.50000i	−0.403570	+	0.233001i	−0.688023	−	0.725689i	$-0.741521\pi$
$373$	−7.79423	+	4.50000i	−0.403570	+	0.233001i	0.284453	+	0.958690i	$0.408188\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	14.0000i		−	0.721037i
$378$		0			0
$379$	7.00000			0.359566			0.179783	−	0.983706i	$-0.442460\pi$
$379$	7.00000			0.359566			0.179783	+	0.983706i	$0.442460\pi$
$380$		0			0
$381$	6.50000	−	11.2583i	0.333005	−	0.576782i
$382$		0			0
$383$	−6.92820	+	4.00000i	−0.354015	+	0.204390i	−0.666452	−	0.745548i	$-0.732188\pi$
$383$	−6.92820	+	4.00000i	−0.354015	+	0.204390i	0.312437	+	0.949938i	$0.398855\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	4.33013	−	2.50000i	0.220113	−	0.127082i
$388$		0			0
$389$	8.00000	−	13.8564i	0.405616	−	0.702548i	−0.588777	−	0.808296i	$-0.700390\pi$
$389$	8.00000	−	13.8564i	0.405616	−	0.702548i	0.994393	+	0.105748i	$0.0337237\pi$
$390$		0			0
$391$	12.0000			0.606866
$392$		0			0
$393$			22.0000i			1.10975i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−16.4545	+	9.50000i	−0.825827	+	0.476791i	−0.852422	−	0.522855i	$-0.824867\pi$
$397$	−16.4545	+	9.50000i	−0.825827	+	0.476791i	0.0265948	+	0.999646i	$0.491534\pi$
$398$		0			0
$399$	−7.50000	−	2.59808i	−0.375470	−	0.130066i
$400$		0			0
$401$	16.0000	+	27.7128i	0.799002	+	1.38391i	0.920267	+	0.391292i	$0.127972\pi$
$401$	16.0000	+	27.7128i	0.799002	+	1.38391i	−0.121265	+	0.992620i	$0.538695\pi$
$402$		0			0
$403$	42.4352	+	24.5000i	2.11385	+	1.22043i
$404$		0			0
$405$		0			0
$406$		0			0
$407$			28.0000i			1.38791i
$408$		0			0
$409$	−9.50000	+	16.4545i	−0.469745	+	0.813622i	−0.999402	−	0.0345902i	$-0.988987\pi$
$409$	−9.50000	+	16.4545i	−0.469745	+	0.813622i	0.529657	+	0.848212i	$0.322321\pi$
$410$		0			0
$411$	9.00000	+	15.5885i	0.443937	+	0.768922i
$412$		0			0
$413$	−17.3205	−	20.0000i	−0.852286	−	0.984136i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−11.2583	−	6.50000i	−0.551323	−	0.318306i
$418$		0			0
$419$	26.0000			1.27018			0.635092	−	0.772437i	$-0.280962\pi$
$419$	26.0000			1.27018			0.635092	+	0.772437i	$0.280962\pi$
$420$		0			0
$421$	13.0000			0.633581			0.316791	−	0.948495i	$-0.397395\pi$
$421$	13.0000			0.633581			0.316791	+	0.948495i	$0.397395\pi$
$422$		0			0
$423$	8.66025	+	5.00000i	0.421076	+	0.243108i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	15.5885	−	3.00000i	0.754378	−	0.145180i
$428$		0			0
$429$	14.0000	+	24.2487i	0.675926	+	1.17074i
$430$		0			0
$431$	15.0000	−	25.9808i	0.722525	−	1.25145i	−0.237460	−	0.971397i	$-0.576315\pi$
$431$	15.0000	−	25.9808i	0.722525	−	1.25145i	0.959985	−	0.280052i	$-0.0903517\pi$
$432$		0			0
$433$			23.0000i			1.10531i	0.833410	+	0.552655i	$0.186385\pi$
$433$			23.0000i			1.10531i	−0.833410	+	0.552655i	$0.813615\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	5.19615	+	3.00000i	0.248566	+	0.143509i
$438$		0			0
$439$	−14.0000	−	24.2487i	−0.668184	−	1.15733i	−0.978412	−	0.206666i	$-0.933739\pi$
$439$	−14.0000	−	24.2487i	−0.668184	−	1.15733i	0.310228	−	0.950662i	$-0.399595\pi$
$440$		0			0
$441$	1.00000	−	6.92820i	0.0476190	−	0.329914i
$442$		0			0
$443$	−3.46410	+	2.00000i	−0.164584	+	0.0950229i	−0.580030	−	0.814595i	$-0.696959\pi$
$443$	−3.46410	+	2.00000i	−0.164584	+	0.0950229i	0.415445	+	0.909618i	$0.363626\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	34.0000			1.60456			0.802280	−	0.596948i	$-0.203620\pi$
$449$	34.0000			1.60456			0.802280	+	0.596948i	$0.203620\pi$
$450$		0			0
$451$	−16.0000	+	27.7128i	−0.753411	+	1.30495i
$452$		0			0
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−7.79423	+	4.50000i	−0.364599	+	0.210501i	−0.671096	−	0.741370i	$-0.734176\pi$
$457$	−7.79423	+	4.50000i	−0.364599	+	0.210501i	0.306497	+	0.951871i	$0.400843\pi$
$458$		0			0
$459$	3.00000	−	5.19615i	0.140028	−	0.242536i
$460$		0			0
$461$	30.0000			1.39724			0.698620	−	0.715493i	$-0.253798\pi$
$461$	30.0000			1.39724			0.698620	+	0.715493i	$0.253798\pi$
$462$		0			0
$463$			1.00000i			0.0464739i	0.999730	+	0.0232370i	$0.00739722\pi$
$463$			1.00000i			0.0464739i	−0.999730	+	0.0232370i	$0.992603\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	15.5885	−	9.00000i	0.721348	−	0.416470i	−0.0939008	−	0.995582i	$-0.529934\pi$
$467$	15.5885	−	9.00000i	0.721348	−	0.416470i	0.815249	+	0.579111i	$0.196600\pi$
$468$		0			0
$469$	−6.00000	+	5.19615i	−0.277054	+	0.239936i
$470$		0			0
$471$	7.00000	+	12.1244i	0.322543	+	0.558661i
$472$		0			0
$473$	−17.3205	−	10.0000i	−0.796398	−	0.459800i
$474$		0			0
$475$		0			0
$476$		0			0
$477$		−	8.00000i		−	0.366295i
$478$		0			0
$479$	20.0000	−	34.6410i	0.913823	−	1.58279i	0.105208	−	0.994450i	$-0.466449\pi$
$479$	20.0000	−	34.6410i	0.913823	−	1.58279i	0.808615	−	0.588338i	$-0.200218\pi$
$480$		0			0
$481$	24.5000	+	42.4352i	1.11710	+	1.93488i
$482$		0			0
$483$	−1.73205	+	5.00000i	−0.0788110	+	0.227508i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−19.9186	−	11.5000i	−0.902597	−	0.521115i	−0.0245553	−	0.999698i	$-0.507817\pi$
$487$	−19.9186	−	11.5000i	−0.902597	−	0.521115i	−0.878042	+	0.478584i	$0.841150\pi$
$488$		0			0
$489$	4.00000			0.180886
$490$		0			0
$491$	−4.00000			−0.180517			−0.0902587	−	0.995918i	$-0.528769\pi$
$491$	−4.00000			−0.180517			−0.0902587	+	0.995918i	$0.528769\pi$
$492$		0			0
$493$	10.3923	+	6.00000i	0.468046	+	0.270226i
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$	3.50000	+	6.06218i	0.156682	+	0.271380i	0.933670	−	0.358134i	$-0.116587\pi$
$499$	3.50000	+	6.06218i	0.156682	+	0.271380i	−0.776989	+	0.629515i	$0.783254\pi$
$500$		0			0
$501$	12.0000	−	20.7846i	0.536120	−	0.928588i
$502$		0			0
$503$		−	6.00000i		−	0.267527i	−0.991013	−	0.133763i	$-0.957294\pi$
$503$		−	6.00000i		−	0.267527i	0.991013	−	0.133763i	$-0.0427062\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	31.1769	+	18.0000i	1.38462	+	0.799408i
$508$		0			0
$509$	7.00000	+	12.1244i	0.310270	+	0.537403i	0.978421	−	0.206623i	$-0.0662474\pi$
$509$	7.00000	+	12.1244i	0.310270	+	0.537403i	−0.668151	+	0.744026i	$0.732914\pi$
$510$		0			0
$511$	30.0000	−	25.9808i	1.32712	−	1.14932i
$512$		0			0
$513$	2.59808	−	1.50000i	0.114708	−	0.0662266i
$514$		0			0
$515$		0			0
$516$		0			0
$517$		−	40.0000i		−	1.75920i
$518$		0			0
$519$		0			0
$520$		0			0
$521$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$521$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$522$		0			0
$523$	0.866025	−	0.500000i	0.0378686	−	0.0218635i	−0.480946	−	0.876750i	$-0.659707\pi$
$523$	0.866025	−	0.500000i	0.0378686	−	0.0218635i	0.518815	+	0.854887i	$0.326373\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−36.3731	+	21.0000i	−1.58444	+	0.914774i
$528$		0			0
$529$	−9.50000	+	16.4545i	−0.413043	+	0.715412i
$530$		0			0
$531$	10.0000			0.433963
$532$		0			0
$533$			56.0000i			2.42563i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−12.1244	+	7.00000i	−0.523205	+	0.302072i
$538$		0			0
$539$	−26.0000	+	10.3923i	−1.11990	+	0.447628i
$540$		0			0
$541$	−8.50000	−	14.7224i	−0.365444	−	0.632967i	0.623404	−	0.781900i	$-0.285749\pi$
$541$	−8.50000	−	14.7224i	−0.365444	−	0.632967i	−0.988847	+	0.148933i	$0.952416\pi$
$542$		0			0
$543$	2.59808	+	1.50000i	0.111494	+	0.0643712i
$544$		0			0
$545$		0			0
$546$		0			0
$547$			16.0000i			0.684111i	0.939680	+	0.342055i	$0.111123\pi$
$547$			16.0000i			0.684111i	−0.939680	+	0.342055i	$0.888877\pi$
$548$		0			0
$549$	−3.00000	+	5.19615i	−0.128037	+	0.221766i
$550$		0			0
$551$	3.00000	+	5.19615i	0.127804	+	0.221364i
$552$		0			0
$553$	2.59808	−	0.500000i	0.110481	−	0.0212622i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	25.9808	+	15.0000i	1.10084	+	0.635570i	0.936442	−	0.350824i	$-0.114098\pi$
$557$	25.9808	+	15.0000i	1.10084	+	0.635570i	0.164399	+	0.986394i	$0.447432\pi$
$558$		0			0
$559$	−35.0000			−1.48034
$560$		0			0
$561$	−24.0000			−1.01328
$562$		0			0
$563$	−12.1244	−	7.00000i	−0.510981	−	0.295015i	0.222256	−	0.974988i	$-0.428658\pi$
$563$	−12.1244	−	7.00000i	−0.510981	−	0.295015i	−0.733237	+	0.679974i	$0.761991\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	1.73205	+	2.00000i	0.0727393	+	0.0839921i
$568$		0			0
$569$	6.00000	+	10.3923i	0.251533	+	0.435668i	0.963948	−	0.266090i	$-0.0857319\pi$
$569$	6.00000	+	10.3923i	0.251533	+	0.435668i	−0.712415	+	0.701758i	$0.752399\pi$
$570$		0			0
$571$	20.5000	−	35.5070i	0.857898	−	1.48592i	−0.0160316	−	0.999871i	$-0.505103\pi$
$571$	20.5000	−	35.5070i	0.857898	−	1.48592i	0.873930	−	0.486052i	$-0.161563\pi$
$572$		0			0
$573$		−	18.0000i		−	0.751961i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	30.3109	+	17.5000i	1.26186	+	0.728535i	0.973434	−	0.228968i	$-0.0735351\pi$
$577$	30.3109	+	17.5000i	1.26186	+	0.728535i	0.288425	+	0.957503i	$0.406868\pi$
$578$		0			0
$579$	11.5000	+	19.9186i	0.477924	+	0.827788i
$580$		0			0
$581$	−20.0000	−	6.92820i	−0.829740	−	0.287430i
$582$		0			0
$583$	−27.7128	+	16.0000i	−1.14775	+	0.662652i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		−	18.0000i		−	0.742940i	−0.928445	−	0.371470i	$-0.878854\pi$
$587$		−	18.0000i		−	0.742940i	0.928445	−	0.371470i	$-0.121146\pi$
$588$		0			0
$589$	−21.0000			−0.865290
$590$		0			0
$591$	1.00000	−	1.73205i	0.0411345	−	0.0712470i
$592$		0			0
$593$	27.7128	−	16.0000i	1.13803	−	0.657041i	0.192087	−	0.981378i	$-0.438474\pi$
$593$	27.7128	−	16.0000i	1.13803	−	0.657041i	0.945942	+	0.324337i	$0.105141\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$	10.0000	−	17.3205i	0.408589	−	0.707697i	−0.586143	−	0.810208i	$-0.699354\pi$
$599$	10.0000	−	17.3205i	0.408589	−	0.707697i	0.994732	+	0.102511i	$0.0326876\pi$
$600$		0			0
$601$	−17.0000			−0.693444			−0.346722	−	0.937968i	$-0.612705\pi$
$601$	−17.0000			−0.693444			−0.346722	+	0.937968i	$0.612705\pi$
$602$		0			0
$603$		−	3.00000i		−	0.122169i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−11.2583	+	6.50000i	−0.456962	+	0.263827i	−0.710766	−	0.703429i	$-0.751651\pi$
$607$	−11.2583	+	6.50000i	−0.456962	+	0.263827i	0.253804	+	0.967256i	$0.418318\pi$
$608$		0			0
$609$	−4.00000	+	3.46410i	−0.162088	+	0.140372i
$610$		0			0
$611$	−35.0000	−	60.6218i	−1.41595	−	2.45249i
$612$		0			0
$613$	19.0526	+	11.0000i	0.769526	+	0.444286i	0.832705	−	0.553716i	$-0.186791\pi$
$613$	19.0526	+	11.0000i	0.769526	+	0.444286i	−0.0631797	+	0.998002i	$0.520124\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		−	2.00000i		−	0.0805170i	−0.999189	−	0.0402585i	$-0.987182\pi$
$617$		−	2.00000i		−	0.0805170i	0.999189	−	0.0402585i	$-0.0128181\pi$
$618$		0			0
$619$	14.5000	−	25.1147i	0.582804	−	1.00945i	−0.412341	−	0.911030i	$-0.635289\pi$
$619$	14.5000	−	25.1147i	0.582804	−	1.00945i	0.995145	−	0.0984169i	$-0.0313779\pi$
$620$		0			0
$621$	−1.00000	−	1.73205i	−0.0401286	−	0.0695048i
$622$		0			0
$623$	5.19615	−	1.00000i	0.208179	−	0.0400642i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−10.3923	−	6.00000i	−0.415029	−	0.239617i
$628$		0			0
$629$	−42.0000			−1.67465
$630$		0			0
$631$	−32.0000			−1.27390			−0.636950	−	0.770905i	$-0.719804\pi$
$631$	−32.0000			−1.27390			−0.636950	+	0.770905i	$0.719804\pi$
$632$		0			0
$633$	3.46410	+	2.00000i	0.137686	+	0.0794929i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−30.3109	+	38.5000i	−1.20096	+	1.52543i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−3.00000	+	5.19615i	−0.118493	+	0.205236i	−0.919171	−	0.393860i	$-0.871140\pi$
$641$	−3.00000	+	5.19615i	−0.118493	+	0.205236i	0.800678	+	0.599095i	$0.204473\pi$
$642$		0			0
$643$		−	5.00000i		−	0.197181i	−0.995128	−	0.0985904i	$-0.968567\pi$
$643$		−	5.00000i		−	0.197181i	0.995128	−	0.0985904i	$-0.0314334\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	38.1051	+	22.0000i	1.49807	+	0.864909i	0.999998	−	0.00222801i	$-0.000709199\pi$
$647$	38.1051	+	22.0000i	1.49807	+	0.864909i	0.498069	+	0.867137i	$0.334043\pi$
$648$		0			0
$649$	−20.0000	−	34.6410i	−0.785069	−	1.35978i
$650$		0			0
$651$	−3.50000	−	18.1865i	−0.137176	−	0.712786i
$652$		0			0
$653$	−24.2487	+	14.0000i	−0.948925	+	0.547862i	−0.892747	−	0.450558i	$-0.851225\pi$
$653$	−24.2487	+	14.0000i	−0.948925	+	0.547862i	−0.0561784	+	0.998421i	$0.517892\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$			15.0000i			0.585206i
$658$		0			0
$659$	−12.0000			−0.467454			−0.233727	−	0.972302i	$-0.575092\pi$
$659$	−12.0000			−0.467454			−0.233727	+	0.972302i	$0.575092\pi$
$660$		0			0
$661$	−7.50000	+	12.9904i	−0.291716	+	0.505267i	−0.974216	−	0.225619i	$-0.927560\pi$
$661$	−7.50000	+	12.9904i	−0.291716	+	0.505267i	0.682499	+	0.730886i	$0.260893\pi$
$662$		0			0
$663$	−36.3731	+	21.0000i	−1.41261	+	0.815572i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	3.46410	−	2.00000i	0.134131	−	0.0774403i
$668$		0			0
$669$	6.00000	−	10.3923i	0.231973	−	0.401790i
$670$		0			0
$671$	24.0000			0.926510
$672$		0			0
$673$		−	37.0000i		−	1.42625i	−0.701039	−	0.713123i	$-0.747280\pi$
$673$		−	37.0000i		−	1.42625i	0.701039	−	0.713123i	$-0.252720\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	1.73205	−	1.00000i	0.0665681	−	0.0384331i	−0.466347	−	0.884602i	$-0.654430\pi$
$677$	1.73205	−	1.00000i	0.0665681	−	0.0384331i	0.532915	+	0.846169i	$0.321097\pi$
$678$		0			0
$679$	−25.0000	−	8.66025i	−0.959412	−	0.332350i
$680$		0			0
$681$	4.00000	+	6.92820i	0.153280	+	0.265489i
$682$		0			0
$683$	8.66025	+	5.00000i	0.331375	+	0.191320i	0.656452	−	0.754368i	$-0.272057\pi$
$683$	8.66025	+	5.00000i	0.331375	+	0.191320i	−0.325076	+	0.945688i	$0.605390\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$		−	17.0000i		−	0.648590i
$688$		0			0
$689$	−28.0000	+	48.4974i	−1.06672	+	1.84760i
$690$		0			0
$691$	25.5000	+	44.1673i	0.970066	+	1.68020i	0.695341	+	0.718680i	$0.255253\pi$
$691$	25.5000	+	44.1673i	0.970066	+	1.68020i	0.274725	+	0.961523i	$0.411413\pi$
$692$		0			0
$693$	3.46410	−	10.0000i	0.131590	−	0.379869i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−41.5692	−	24.0000i	−1.57455	−	0.909065i
$698$		0			0
$699$	6.00000			0.226941
$700$		0			0
$701$	42.0000			1.58632			0.793159	−	0.609015i	$-0.208435\pi$
$701$	42.0000			1.58632			0.793159	+	0.609015i	$0.208435\pi$
$702$		0			0
$703$	−18.1865	−	10.5000i	−0.685918	−	0.396015i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	20.7846	+	24.0000i	0.781686	+	0.902613i
$708$		0			0
$709$	7.00000	+	12.1244i	0.262891	+	0.455340i	0.967009	−	0.254743i	$-0.0819909\pi$
$709$	7.00000	+	12.1244i	0.262891	+	0.455340i	−0.704118	+	0.710083i	$0.748658\pi$
$710$		0			0
$711$	−0.500000	+	0.866025i	−0.0187515	+	0.0324785i
$712$		0			0
$713$			14.0000i			0.524304i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	5.19615	+	3.00000i	0.194054	+	0.112037i
$718$		0			0
$719$	25.0000	+	43.3013i	0.932343	+	1.61486i	0.779305	+	0.626644i	$0.215572\pi$
$719$	25.0000	+	43.3013i	0.932343	+	1.61486i	0.153037	+	0.988220i	$0.451094\pi$
$720$		0			0
$721$	−3.50000	−	18.1865i	−0.130347	−	0.677302i
$722$		0			0
$723$	−12.1244	+	7.00000i	−0.450910	+	0.260333i
$724$		0			0
$725$		0			0
$726$		0			0
$727$			23.0000i			0.853023i	0.904482	+	0.426511i	$0.140258\pi$
$727$			23.0000i			0.853023i	−0.904482	+	0.426511i	$0.859742\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	15.0000	−	25.9808i	0.554795	−	0.960933i
$732$		0			0
$733$	11.2583	−	6.50000i	0.415836	−	0.240083i	−0.277458	−	0.960738i	$-0.589492\pi$
$733$	11.2583	−	6.50000i	0.415836	−	0.240083i	0.693294	+	0.720655i	$0.256159\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−10.3923	+	6.00000i	−0.382805	+	0.221013i
$738$		0			0
$739$	−0.500000	+	0.866025i	−0.0183928	+	0.0318573i	−0.875075	−	0.483987i	$-0.839188\pi$
$739$	−0.500000	+	0.866025i	−0.0183928	+	0.0318573i	0.856683	+	0.515844i	$0.172522\pi$
$740$		0			0
$741$	−21.0000			−0.771454
$742$		0			0
$743$			44.0000i			1.61420i	0.590412	+	0.807102i	$0.298965\pi$
$743$			44.0000i			1.61420i	−0.590412	+	0.807102i	$0.701035\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	6.92820	−	4.00000i	0.253490	−	0.146352i
$748$		0			0
$749$	−1.00000	−	5.19615i	−0.0365392	−	0.189863i
$750$		0			0
$751$	12.5000	+	21.6506i	0.456131	+	0.790043i	0.998752	−	0.0499348i	$-0.0159013\pi$
$751$	12.5000	+	21.6506i	0.456131	+	0.790043i	−0.542621	+	0.839978i	$0.682568\pi$
$752$		0			0
$753$	−19.0526	−	11.0000i	−0.694314	−	0.400862i
$754$		0			0
$755$		0			0
$756$		0			0
$757$			2.00000i			0.0726912i	0.999339	+	0.0363456i	$0.0115717\pi$
$757$			2.00000i			0.0726912i	−0.999339	+	0.0363456i	$0.988428\pi$
$758$		0			0
$759$	−4.00000	+	6.92820i	−0.145191	+	0.251478i
$760$		0			0
$761$	15.0000	+	25.9808i	0.543750	+	0.941802i	0.998684	+	0.0512772i	$0.0163292\pi$
$761$	15.0000	+	25.9808i	0.543750	+	0.941802i	−0.454935	+	0.890525i	$0.650337\pi$
$762$		0			0
$763$	5.19615	+	6.00000i	0.188113	+	0.217215i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−60.6218	−	35.0000i	−2.18893	−	1.26378i
$768$		0			0
$769$	29.0000			1.04577			0.522883	−	0.852404i	$-0.324856\pi$
$769$	29.0000			1.04577			0.522883	+	0.852404i	$0.324856\pi$
$770$		0			0
$771$	−16.0000			−0.576226
$772$		0			0
$773$	−10.3923	−	6.00000i	−0.373785	−	0.215805i	0.301326	−	0.953521i	$-0.402571\pi$
$773$	−10.3923	−	6.00000i	−0.373785	−	0.215805i	−0.675111	+	0.737716i	$0.735904\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	6.06218	−	17.5000i	0.217479	−	0.627809i
$778$		0			0
$779$	−12.0000	−	20.7846i	−0.429945	−	0.744686i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		−	2.00000i		−	0.0714742i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−3.46410	−	2.00000i	−0.123482	−	0.0712923i	0.436987	−	0.899468i	$-0.356046\pi$
$787$	−3.46410	−	2.00000i	−0.123482	−	0.0712923i	−0.560469	+	0.828176i	$0.689379\pi$
$788$		0			0
$789$	−6.00000	−	10.3923i	−0.213606	−	0.369976i
$790$		0			0
$791$	−45.0000	−	15.5885i	−1.60002	−	0.554262i
$792$		0			0
$793$	36.3731	−	21.0000i	1.29165	−	0.745732i
$794$		0			0
$795$		0			0
$796$		0			0
$797$		−	42.0000i		−	1.48772i	−0.668338	−	0.743858i	$-0.732994\pi$
$797$		−	42.0000i		−	1.48772i	0.668338	−	0.743858i	$-0.267006\pi$
$798$		0			0
$799$	60.0000			2.12265
$800$		0			0
$801$	−1.00000	+	1.73205i	−0.0353333	+	0.0611990i
$802$		0			0
$803$	51.9615	−	30.0000i	1.83368	−	1.05868i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	8.66025	−	5.00000i	0.304855	−	0.176008i
$808$		0			0
$809$	−3.00000	+	5.19615i	−0.105474	+	0.182687i	−0.913932	−	0.405868i	$-0.866969\pi$
$809$	−3.00000	+	5.19615i	−0.105474	+	0.182687i	0.808458	+	0.588555i	$0.200303\pi$
$810$		0			0
$811$	12.0000			0.421377			0.210688	−	0.977553i	$-0.432429\pi$
$811$	12.0000			0.421377			0.210688	+	0.977553i	$0.432429\pi$
$812$		0			0
$813$		−	16.0000i		−	0.561144i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	12.9904	−	7.50000i	0.454476	−	0.262392i
$818$		0			0
$819$	−3.50000	−	18.1865i	−0.122300	−	0.635489i
$820$		0			0
$821$	6.00000	+	10.3923i	0.209401	+	0.362694i	0.951526	−	0.307568i	$-0.0995151\pi$
$821$	6.00000	+	10.3923i	0.209401	+	0.362694i	−0.742125	+	0.670262i	$0.766182\pi$
$822$		0			0
$823$	−20.7846	−	12.0000i	−0.724506	−	0.418294i	0.0919029	−	0.995768i	$-0.470705\pi$
$823$	−20.7846	−	12.0000i	−0.724506	−	0.418294i	−0.816409	+	0.577474i	$0.804038\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	10.0000i		−	0.347734i	−0.984769	−	0.173867i	$-0.944374\pi$
$827$		−	10.0000i		−	0.347734i	0.984769	−	0.173867i	$-0.0556263\pi$
$828$		0			0
$829$	12.5000	−	21.6506i	0.434143	−	0.751958i	−0.563082	−	0.826401i	$-0.690385\pi$
$829$	12.5000	−	21.6506i	0.434143	−	0.751958i	0.997225	+	0.0744432i	$0.0237179\pi$
$830$		0			0
$831$	11.5000	+	19.9186i	0.398931	+	0.690968i
$832$		0			0
$833$	−15.5885	−	39.0000i	−0.540108	−	1.35127i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	6.06218	+	3.50000i	0.209540	+	0.120978i
$838$		0			0
$839$	22.0000			0.759524			0.379762	−	0.925084i	$-0.376006\pi$
$839$	22.0000			0.759524			0.379762	+	0.925084i	$0.376006\pi$
$840$		0			0
$841$	−25.0000			−0.862069
$842$		0			0
$843$	13.8564	+	8.00000i	0.477240	+	0.275535i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−12.9904	+	2.50000i	−0.446355	+	0.0859010i
$848$		0			0
$849$	−12.5000	−	21.6506i	−0.428999	−	0.743048i
$850$		0			0
$851$	−7.00000	+	12.1244i	−0.239957	+	0.415618i
$852$		0			0
$853$			23.0000i			0.787505i	0.919216	+	0.393753i	$0.128823\pi$
$853$			23.0000i			0.787505i	−0.919216	+	0.393753i	$0.871177\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−19.0526	−	11.0000i	−0.650823	−	0.375753i	0.137948	−	0.990439i	$-0.455949\pi$
$857$	−19.0526	−	11.0000i	−0.650823	−	0.375753i	−0.788771	+	0.614687i	$0.789283\pi$
$858$		0			0
$859$	18.0000	+	31.1769i	0.614152	+	1.06374i	0.990533	+	0.137277i	$0.0438352\pi$
$859$	18.0000	+	31.1769i	0.614152	+	1.06374i	−0.376381	+	0.926465i	$0.622831\pi$
$860$		0			0
$861$	16.0000	−	13.8564i	0.545279	−	0.472225i
$862$		0			0
$863$	1.73205	−	1.00000i	0.0589597	−	0.0340404i	−0.470230	−	0.882544i	$-0.655829\pi$
$863$	1.73205	−	1.00000i	0.0589597	−	0.0340404i	0.529190	+	0.848503i	$0.322496\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$		−	19.0000i		−	0.645274i
$868$		0			0
$869$	4.00000			0.135691
$870$		0			0
$871$	−10.5000	+	18.1865i	−0.355779	+	0.616227i
$872$		0			0
$873$	8.66025	−	5.00000i	0.293105	−	0.169224i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	43.3013	−	25.0000i	1.46218	−	0.844190i	0.463068	−	0.886323i	$-0.346749\pi$
$877$	43.3013	−	25.0000i	1.46218	−	0.844190i	0.999112	+	0.0421327i	$0.0134152\pi$
$878$		0			0
$879$	6.00000	−	10.3923i	0.202375	−	0.350524i
$880$		0			0
$881$	4.00000			0.134763			0.0673817	−	0.997727i	$-0.478535\pi$
$881$	4.00000			0.134763			0.0673817	+	0.997727i	$0.478535\pi$
$882$		0			0
$883$		−	27.0000i		−	0.908622i	−0.890843	−	0.454311i	$-0.849885\pi$
$883$		−	27.0000i		−	0.908622i	0.890843	−	0.454311i	$-0.150115\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	27.7128	−	16.0000i	0.930505	−	0.537227i	0.0435339	−	0.999052i	$-0.486138\pi$
$887$	27.7128	−	16.0000i	0.930505	−	0.537227i	0.886971	+	0.461825i	$0.152805\pi$
$888$		0			0
$889$	32.5000	+	11.2583i	1.09002	+	0.377592i
$890$		0			0
$891$	2.00000	+	3.46410i	0.0670025	+	0.116052i
$892$		0			0
$893$	25.9808	+	15.0000i	0.869413	+	0.501956i
$894$		0			0
$895$		0			0
$896$		0			0
$897$			14.0000i			0.467446i
$898$		0			0
$899$	−7.00000	+	12.1244i	−0.233463	+	0.404370i
$900$		0			0
$901$	−24.0000	−	41.5692i	−0.799556	−	1.38487i
$902$		0			0
$903$	8.66025	+	10.0000i	0.288195	+	0.332779i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	32.0429	+	18.5000i	1.06397	+	0.614282i	0.926527	−	0.376228i	$-0.122779\pi$
$907$	32.0429	+	18.5000i	1.06397	+	0.614282i	0.137441	+	0.990510i	$0.456112\pi$
$908$		0			0
$909$	−12.0000			−0.398015
$910$		0			0
$911$	−50.0000			−1.65657			−0.828287	−	0.560304i	$-0.810684\pi$
$911$	−50.0000			−1.65657			−0.828287	+	0.560304i	$0.810684\pi$
$912$		0			0
$913$	−27.7128	−	16.0000i	−0.917160	−	0.529523i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−57.1577	+	11.0000i	−1.88751	+	0.363252i
$918$		0			0
$919$	−13.5000	−	23.3827i	−0.445324	−	0.771324i	0.552751	−	0.833347i	$-0.313578\pi$
$919$	−13.5000	−	23.3827i	−0.445324	−	0.771324i	−0.998075	+	0.0620230i	$0.980245\pi$
$920$		0			0
$921$	5.50000	−	9.52628i	0.181231	−	0.313902i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$	6.06218	+	3.50000i	0.199108	+	0.114955i
$928$		0			0
$929$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$929$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$930$		0			0
$931$	3.00000	−	20.7846i	0.0983210	−	0.681188i
$932$		0			0
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$			9.00000i			0.294017i	0.989135	+	0.147009i	$0.0469645\pi$
$937$			9.00000i			0.294017i	−0.989135	+	0.147009i	$0.953036\pi$
$938$		0			0
$939$	21.0000			0.685309
$940$		0			0
$941$	−27.0000	+	46.7654i	−0.880175	+	1.52451i	−0.0290288	+	0.999579i	$0.509241\pi$
$941$	−27.0000	+	46.7654i	−0.880175	+	1.52451i	−0.851146	+	0.524929i	$0.824092\pi$
$942$		0			0
$943$	−13.8564	+	8.00000i	−0.451227	+	0.260516i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	3.46410	−	2.00000i	0.112568	−	0.0649913i	−0.442659	−	0.896690i	$-0.645965\pi$
$947$	3.46410	−	2.00000i	0.112568	−	0.0649913i	0.555227	+	0.831699i	$0.312631\pi$
$948$		0			0
$949$	52.5000	−	90.9327i	1.70422	−	2.95180i
$950$		0			0
$951$	−18.0000			−0.583690
$952$		0			0
$953$		−	16.0000i		−	0.518291i	−0.965838	−	0.259145i	$-0.916559\pi$
$953$		−	16.0000i		−	0.518291i	0.965838	−	0.259145i	$-0.0834409\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−6.92820	+	4.00000i	−0.223957	+	0.129302i
$958$		0			0
$959$	−36.0000	+	31.1769i	−1.16250	+	1.00676i
$960$		0			0
$961$	−9.00000	−	15.5885i	−0.290323	−	0.502853i
$962$		0			0
$963$	1.73205	+	1.00000i	0.0558146	+	0.0322245i
$964$		0			0
$965$		0			0
$966$		0			0
$967$		−	17.0000i		−	0.546683i	−0.961917	−	0.273342i	$-0.911871\pi$
$967$		−	17.0000i		−	0.546683i	0.961917	−	0.273342i	$-0.0881289\pi$
$968$		0			0
$969$	9.00000	−	15.5885i	0.289122	−	0.500773i
$970$		0			0
$971$	−24.0000	−	41.5692i	−0.770197	−	1.33402i	−0.937455	−	0.348107i	$-0.886825\pi$
$971$	−24.0000	−	41.5692i	−0.770197	−	1.33402i	0.167258	−	0.985913i	$-0.446509\pi$
$972$		0			0
$973$	11.2583	−	32.5000i	0.360925	−	1.04190i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	20.7846	+	12.0000i	0.664959	+	0.383914i	0.794164	−	0.607704i	$-0.207909\pi$
$977$	20.7846	+	12.0000i	0.664959	+	0.383914i	−0.129205	+	0.991618i	$0.541243\pi$
$978$		0			0
$979$	8.00000			0.255681
$980$		0			0
$981$	−3.00000			−0.0957826
$982$		0			0
$983$	−12.1244	−	7.00000i	−0.386707	−	0.223265i	0.294025	−	0.955798i	$-0.405005\pi$
$983$	−12.1244	−	7.00000i	−0.386707	−	0.223265i	−0.680732	+	0.732532i	$0.738338\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−8.66025	+	25.0000i	−0.275659	+	0.795759i
$988$		0			0
$989$	−5.00000	−	8.66025i	−0.158991	−	0.275380i
$990$		0			0
$991$	−15.5000	+	26.8468i	−0.492374	+	0.852816i	−0.999961	−	0.00878379i	$-0.997204\pi$
$991$	−15.5000	+	26.8468i	−0.492374	+	0.852816i	0.507588	+	0.861600i	$0.330537\pi$
$992$		0			0
$993$		−	7.00000i		−	0.222138i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−14.7224	−	8.50000i	−0.466264	−	0.269198i	0.248410	−	0.968655i	$-0.420092\pi$
$997$	−14.7224	−	8.50000i	−0.466264	−	0.269198i	−0.714675	+	0.699457i	$0.753425\pi$
$998$		0			0
$999$	3.50000	+	6.06218i	0.110735	+	0.191799i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2100.2.bc.d.949.1		4
5.2	odd	4		2100.2.q.d.1201.1		2
5.3	odd	4		420.2.q.b.361.1	yes	2
5.4	even	2	inner	2100.2.bc.d.949.2		4
7.2	even	3	inner	2100.2.bc.d.1549.2		4
15.8	even	4		1260.2.s.a.361.1		2
20.3	even	4		1680.2.bg.j.1201.1		2
35.2	odd	12		2100.2.q.d.1801.1		2
35.3	even	12		2940.2.a.k.1.1		1
35.9	even	6	inner	2100.2.bc.d.1549.1		4
35.13	even	4		2940.2.q.c.361.1		2
35.18	odd	12		2940.2.a.b.1.1		1
35.23	odd	12		420.2.q.b.121.1	✓	2
35.33	even	12		2940.2.q.c.961.1		2
105.23	even	12		1260.2.s.a.541.1		2
105.38	odd	12		8820.2.a.l.1.1		1
105.53	even	12		8820.2.a.bb.1.1		1
140.23	even	12		1680.2.bg.j.961.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.q.b.121.1	✓	2	35.23	odd	12
420.2.q.b.361.1	yes	2	5.3	odd	4
1260.2.s.a.361.1		2	15.8	even	4
1260.2.s.a.541.1		2	105.23	even	12
1680.2.bg.j.961.1		2	140.23	even	12
1680.2.bg.j.1201.1		2	20.3	even	4
2100.2.q.d.1201.1		2	5.2	odd	4
2100.2.q.d.1801.1		2	35.2	odd	12
2100.2.bc.d.949.1		4	1.1	even	1	trivial
2100.2.bc.d.949.2		4	5.4	even	2	inner
2100.2.bc.d.1549.1		4	35.9	even	6	inner
2100.2.bc.d.1549.2		4	7.2	even	3	inner
2940.2.a.b.1.1		1	35.18	odd	12
2940.2.a.k.1.1		1	35.3	even	12
2940.2.q.c.361.1		2	35.13	even	4
2940.2.q.c.961.1		2	35.33	even	12
8820.2.a.l.1.1		1	105.38	odd	12
8820.2.a.bb.1.1		1	105.53	even	12

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:	\( N \)	\(=\)	\( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2100.bc (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{3} +(0.866025 - 2.50000i) q^{7} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{3} +(0.866025 - 2.50000i) q^{7} +(0.500000 + 0.866025i) q^{9} +(2.00000 - 3.46410i) q^{11} -7.00000i q^{13} +(5.19615 + 3.00000i) q^{17} +(1.50000 + 2.59808i) q^{19} +(-2.00000 + 1.73205i) q^{21} +(1.73205 - 1.00000i) q^{23} -1.00000i q^{27} +2.00000 q^{29} +(-3.50000 + 6.06218i) q^{31} +(-3.46410 + 2.00000i) q^{33} +(-6.06218 + 3.50000i) q^{37} +(-3.50000 + 6.06218i) q^{39} -8.00000 q^{41} -5.00000i q^{43} +(8.66025 - 5.00000i) q^{47} +(-5.50000 - 4.33013i) q^{49} +(-3.00000 - 5.19615i) q^{51} +(-6.92820 - 4.00000i) q^{53} -3.00000i q^{57} +(5.00000 - 8.66025i) q^{59} +(3.00000 + 5.19615i) q^{61} +(2.59808 - 0.500000i) q^{63} +(-2.59808 - 1.50000i) q^{67} -2.00000 q^{69} +(12.9904 + 7.50000i) q^{73} +(-6.92820 - 8.00000i) q^{77} +(0.500000 + 0.866025i) q^{79} +(-0.500000 + 0.866025i) q^{81} -8.00000i q^{83} +(-1.73205 - 1.00000i) q^{87} +(1.00000 + 1.73205i) q^{89} +(-17.5000 - 6.06218i) q^{91} +(6.06218 - 3.50000i) q^{93} -10.0000i q^{97} +4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^9	\( 4 q + 2 q^{9} + 8 q^{11} + 6 q^{19} - 8 q^{21} + 8 q^{29} - 14 q^{31} - 14 q^{39} - 32 q^{41} - 22 q^{49} - 12 q^{51} + 20 q^{59} + 12 q^{61} - 8 q^{69} + 2 q^{79} - 2 q^{81} + 4 q^{89} - 70 q^{91} + 16 q^{99}+O(q^{100}) \) 4 * q + 2 * q^9 + 8 * q^11 + 6 * q^19 - 8 * q^21 + 8 * q^29 - 14 * q^31 - 14 * q^39 - 32 * q^41 - 22 * q^49 - 12 * q^51 + 20 * q^59 + 12 * q^61 - 8 * q^69 + 2 * q^79 - 2 * q^81 + 4 * q^89 - 70 * q^91 + 16 * q^99

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