LMFDB - Embedded newform 2100.2.q.d.1201.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2100,2,Mod(1201,2100)]

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, 0, 4]))

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

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

chi := DirichletCharacter("2100.1201");

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.q (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$16.7685844245$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 420)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1201.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	2100.1201
Dual form			2100.2.q.d.1801.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{3} +(2.50000 + 0.866025i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	$q+(-0.500000 + 0.866025i) q^{3} +(2.50000 + 0.866025i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(2.00000 - 3.46410i) q^{11} -7.00000 q^{13} +(-3.00000 + 5.19615i) q^{17} +(-1.50000 - 2.59808i) q^{19} +(-2.00000 + 1.73205i) q^{21} +(-1.00000 - 1.73205i) q^{23} +1.00000 q^{27} -2.00000 q^{29} +(-3.50000 + 6.06218i) q^{31} +(2.00000 + 3.46410i) q^{33} +(-3.50000 - 6.06218i) q^{37} +(3.50000 - 6.06218i) q^{39} -8.00000 q^{41} -5.00000 q^{43} +(5.00000 + 8.66025i) q^{47} +(5.50000 + 4.33013i) q^{49} +(-3.00000 - 5.19615i) q^{51} +(-4.00000 + 6.92820i) q^{53} +3.00000 q^{57} +(-5.00000 + 8.66025i) q^{59} +(3.00000 + 5.19615i) q^{61} +(-0.500000 - 2.59808i) q^{63} +(1.50000 - 2.59808i) q^{67} +2.00000 q^{69} +(7.50000 - 12.9904i) q^{73} +(8.00000 - 6.92820i) q^{77} +(-0.500000 - 0.866025i) q^{79} +(-0.500000 + 0.866025i) q^{81} -8.00000 q^{83} +(1.00000 - 1.73205i) q^{87} +(-1.00000 - 1.73205i) q^{89} +(-17.5000 - 6.06218i) q^{91} +(-3.50000 - 6.06218i) q^{93} +10.0000 q^{97} -4.00000 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{3} + 5 q^{7} - q^{9}+O(q^{10}) $ 2 * q - q^3 + 5 * q^7 - q^9	$ 2 q - q^{3} + 5 q^{7} - q^{9} + 4 q^{11} - 14 q^{13} - 6 q^{17} - 3 q^{19} - 4 q^{21} - 2 q^{23} + 2 q^{27} - 4 q^{29} - 7 q^{31} + 4 q^{33} - 7 q^{37} + 7 q^{39} - 16 q^{41} - 10 q^{43} + 10 q^{47} + 11 q^{49} - 6 q^{51} - 8 q^{53} + 6 q^{57} - 10 q^{59} + 6 q^{61} - q^{63} + 3 q^{67} + 4 q^{69} + 15 q^{73} + 16 q^{77} - q^{79} - q^{81} - 16 q^{83} + 2 q^{87} - 2 q^{89} - 35 q^{91} - 7 q^{93} + 20 q^{97} - 8 q^{99}+O(q^{100}) $ 2 * q - q^3 + 5 * q^7 - q^9 + 4 * q^11 - 14 * q^13 - 6 * q^17 - 3 * q^19 - 4 * q^21 - 2 * q^23 + 2 * q^27 - 4 * q^29 - 7 * q^31 + 4 * q^33 - 7 * q^37 + 7 * q^39 - 16 * q^41 - 10 * q^43 + 10 * q^47 + 11 * q^49 - 6 * q^51 - 8 * q^53 + 6 * q^57 - 10 * q^59 + 6 * q^61 - q^63 + 3 * q^67 + 4 * q^69 + 15 * q^73 + 16 * q^77 - q^79 - q^81 - 16 * q^83 + 2 * q^87 - 2 * q^89 - 35 * q^91 - 7 * q^93 + 20 * q^97 - 8 * 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
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	2.50000	+	0.866025i	0.944911	+	0.327327i
$7$	2.50000	+	0.866025i	0.944911	+	0.327327i
$8$		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
$13$	−7.00000			−1.94145			−0.970725	−	0.240192i	$-0.922790\pi$
$13$	−7.00000			−1.94145			−0.970725	+	0.240192i	$0.922790\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−3.00000	+	5.19615i	−0.727607	+	1.26025i	0.230285	+	0.973123i	$0.426034\pi$
$17$	−3.00000	+	5.19615i	−0.727607	+	1.26025i	−0.957892	+	0.287129i	$0.907299\pi$
$18$		0			0
$19$	−1.50000	−	2.59808i	−0.344124	−	0.596040i	0.641071	−	0.767482i	$-0.278491\pi$
$19$	−1.50000	−	2.59808i	−0.344124	−	0.596040i	−0.985194	+	0.171442i	$0.945157\pi$
$20$		0			0
$21$	−2.00000	+	1.73205i	−0.436436	+	0.377964i
$22$		0			0
$23$	−1.00000	−	1.73205i	−0.208514	−	0.361158i	0.742732	−	0.669588i	$-0.233529\pi$
$23$	−1.00000	−	1.73205i	−0.208514	−	0.361158i	−0.951247	+	0.308431i	$0.900196\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$	−2.00000			−0.371391			−0.185695	−	0.982607i	$-0.559454\pi$
$29$	−2.00000			−0.371391			−0.185695	+	0.982607i	$0.559454\pi$
$30$		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
$33$	2.00000	+	3.46410i	0.348155	+	0.603023i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−3.50000	−	6.06218i	−0.575396	−	0.996616i	−0.995998	−	0.0893706i	$-0.971514\pi$
$37$	−3.50000	−	6.06218i	−0.575396	−	0.996616i	0.420602	−	0.907245i	$-0.361819\pi$
$38$		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
$43$	−5.00000			−0.762493			−0.381246	−	0.924473i	$-0.624505\pi$
$43$	−5.00000			−0.762493			−0.381246	+	0.924473i	$0.624505\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	5.00000	+	8.66025i	0.729325	+	1.26323i	0.957169	+	0.289530i	$0.0934991\pi$
$47$	5.00000	+	8.66025i	0.729325	+	1.26323i	−0.227844	+	0.973698i	$0.573168\pi$
$48$		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
$53$	−4.00000	+	6.92820i	−0.549442	+	0.951662i	0.448871	+	0.893597i	$0.351826\pi$
$53$	−4.00000	+	6.92820i	−0.549442	+	0.951662i	−0.998313	+	0.0580651i	$0.981507\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	3.00000			0.397360
$58$		0			0
$59$	−5.00000	+	8.66025i	−0.650945	+	1.12747i	0.331949	+	0.943297i	$0.392294\pi$
$59$	−5.00000	+	8.66025i	−0.650945	+	1.12747i	−0.982894	+	0.184172i	$0.941040\pi$
$60$		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
$63$	−0.500000	−	2.59808i	−0.0629941	−	0.327327i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	1.50000	−	2.59808i	0.183254	−	0.317406i	−0.759733	−	0.650236i	$-0.774670\pi$
$67$	1.50000	−	2.59808i	0.183254	−	0.317406i	0.942987	+	0.332830i	$0.108004\pi$
$68$		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
$73$	7.50000	−	12.9904i	0.877809	−	1.52041i	0.0240681	−	0.999710i	$-0.492338\pi$
$73$	7.50000	−	12.9904i	0.877809	−	1.52041i	0.853740	−	0.520699i	$-0.174329\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	8.00000	−	6.92820i	0.911685	−	0.789542i
$78$		0			0
$79$	−0.500000	−	0.866025i	−0.0562544	−	0.0974355i	0.836527	−	0.547926i	$-0.184582\pi$
$79$	−0.500000	−	0.866025i	−0.0562544	−	0.0974355i	−0.892781	+	0.450490i	$0.851249\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	−8.00000			−0.878114			−0.439057	−	0.898459i	$-0.644687\pi$
$83$	−8.00000			−0.878114			−0.439057	+	0.898459i	$0.644687\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	1.00000	−	1.73205i	0.107211	−	0.185695i
$88$		0			0
$89$	−1.00000	−	1.73205i	−0.106000	−	0.183597i	0.808146	−	0.588982i	$-0.200471\pi$
$89$	−1.00000	−	1.73205i	−0.106000	−	0.183597i	−0.914146	+	0.405385i	$0.867138\pi$
$90$		0			0
$91$	−17.5000	−	6.06218i	−1.83450	−	0.635489i
$92$		0			0
$93$	−3.50000	−	6.06218i	−0.362933	−	0.628619i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	10.0000			1.01535			0.507673	−	0.861550i	$-0.330506\pi$
$97$	10.0000			1.01535			0.507673	+	0.861550i	$0.330506\pi$
$98$		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
$103$	−3.50000	−	6.06218i	−0.344865	−	0.597324i	0.640464	−	0.767988i	$-0.278742\pi$
$103$	−3.50000	−	6.06218i	−0.344865	−	0.597324i	−0.985329	+	0.170664i	$0.945409\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	1.00000	+	1.73205i	0.0966736	+	0.167444i	0.910306	−	0.413936i	$-0.135846\pi$
$107$	1.00000	+	1.73205i	0.0966736	+	0.167444i	−0.813632	+	0.581380i	$0.802513\pi$
$108$		0			0
$109$	1.50000	−	2.59808i	0.143674	−	0.248851i	−0.785203	−	0.619238i	$-0.787442\pi$
$109$	1.50000	−	2.59808i	0.143674	−	0.248851i	0.928877	+	0.370387i	$0.120775\pi$
$110$		0			0
$111$	7.00000			0.664411
$112$		0			0
$113$	−18.0000			−1.69330			−0.846649	−	0.532152i	$-0.821383\pi$
$113$	−18.0000			−1.69330			−0.846649	+	0.532152i	$0.821383\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	3.50000	+	6.06218i	0.323575	+	0.560449i
$118$		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
$123$	4.00000	−	6.92820i	0.360668	−	0.624695i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−13.0000			−1.15356			−0.576782	−	0.816898i	$-0.695692\pi$
$127$	−13.0000			−1.15356			−0.576782	+	0.816898i	$0.695692\pi$
$128$		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
$133$	−1.50000	−	7.79423i	−0.130066	−	0.675845i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	9.00000	−	15.5885i	0.768922	−	1.33181i	−0.169226	−	0.985577i	$-0.554127\pi$
$137$	9.00000	−	15.5885i	0.768922	−	1.33181i	0.938148	−	0.346235i	$-0.112540\pi$
$138$		0			0
$139$	−13.0000			−1.10265			−0.551323	−	0.834292i	$-0.685877\pi$
$139$	−13.0000			−1.10265			−0.551323	+	0.834292i	$0.685877\pi$
$140$		0			0
$141$	−10.0000			−0.842152
$142$		0			0
$143$	−14.0000	+	24.2487i	−1.17074	+	2.02778i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−6.50000	+	2.59808i	−0.536111	+	0.214286i
$148$		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
$153$	6.00000			0.485071
$154$		0			0
$155$		0			0
$156$		0			0
$157$	7.00000	−	12.1244i	0.558661	−	0.967629i	−0.438948	−	0.898513i	$-0.644649\pi$
$157$	7.00000	−	12.1244i	0.558661	−	0.967629i	0.997609	−	0.0691164i	$-0.0220180\pi$
$158$		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
$163$	2.00000	+	3.46410i	0.156652	+	0.271329i	0.933659	−	0.358162i	$-0.116597\pi$
$163$	2.00000	+	3.46410i	0.156652	+	0.271329i	−0.777007	+	0.629492i	$0.783263\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−24.0000			−1.85718			−0.928588	−	0.371113i	$-0.878976\pi$
$167$	−24.0000			−1.85718			−0.928588	+	0.371113i	$0.878976\pi$
$168$		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		0.866025	−	0.500000i	$-0.166667\pi$
$173$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−5.00000	−	8.66025i	−0.375823	−	0.650945i
$178$		0			0
$179$	−7.00000	+	12.1244i	−0.523205	+	0.906217i	0.476431	+	0.879212i	$0.341930\pi$
$179$	−7.00000	+	12.1244i	−0.523205	+	0.906217i	−0.999635	+	0.0270049i	$0.991403\pi$
$180$		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
$183$	−6.00000			−0.443533
$184$		0			0
$185$		0			0
$186$		0			0
$187$	12.0000	+	20.7846i	0.877527	+	1.51992i
$188$		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
$193$	−11.5000	+	19.9186i	−0.827788	+	1.43377i	0.0719816	+	0.997406i	$0.477068\pi$
$193$	−11.5000	+	19.9186i	−0.827788	+	1.43377i	−0.899770	+	0.436365i	$0.856266\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−2.00000			−0.142494			−0.0712470	−	0.997459i	$-0.522698\pi$
$197$	−2.00000			−0.142494			−0.0712470	+	0.997459i	$0.522698\pi$
$198$		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
$203$	−5.00000	−	1.73205i	−0.350931	−	0.121566i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−1.00000	+	1.73205i	−0.0695048	+	0.120386i
$208$		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
$217$	−14.0000	+	12.1244i	−0.950382	+	0.823055i
$218$		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
$223$	12.0000			0.803579			0.401790	−	0.915732i	$-0.368388\pi$
$223$	12.0000			0.803579			0.401790	+	0.915732i	$0.368388\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	4.00000	−	6.92820i	0.265489	−	0.459841i	−0.702202	−	0.711977i	$-0.747800\pi$
$227$	4.00000	−	6.92820i	0.265489	−	0.459841i	0.967692	+	0.252136i	$0.0811332\pi$
$228$		0			0
$229$	−8.50000	−	14.7224i	−0.561696	−	0.972886i	−0.997349	−	0.0727709i	$-0.976816\pi$
$229$	−8.50000	−	14.7224i	−0.561696	−	0.972886i	0.435653	−	0.900115i	$-0.356518\pi$
$230$		0			0
$231$	2.00000	+	10.3923i	0.131590	+	0.683763i
$232$		0			0
$233$	3.00000	+	5.19615i	0.196537	+	0.340411i	0.947403	−	0.320043i	$-0.103697\pi$
$233$	3.00000	+	5.19615i	0.196537	+	0.340411i	−0.750867	+	0.660454i	$0.770364\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	1.00000			0.0649570
$238$		0			0
$239$	6.00000			0.388108			0.194054	−	0.980991i	$-0.437836\pi$
$239$	6.00000			0.388108			0.194054	+	0.980991i	$0.437836\pi$
$240$		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
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	10.5000	+	18.1865i	0.668099	+	1.15718i
$248$		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
$253$	−8.00000			−0.502956
$254$		0			0
$255$		0			0
$256$		0			0
$257$	8.00000	+	13.8564i	0.499026	+	0.864339i	0.999999	−	0.00112398i	$-0.000357774\pi$
$257$	8.00000	+	13.8564i	0.499026	+	0.864339i	−0.500973	+	0.865463i	$0.667024\pi$
$258$		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
$263$	6.00000	−	10.3923i	0.369976	−	0.640817i	−0.619586	−	0.784929i	$-0.712699\pi$
$263$	6.00000	−	10.3923i	0.369976	−	0.640817i	0.989561	+	0.144112i	$0.0460326\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	2.00000			0.122398
$268$		0			0
$269$	5.00000	−	8.66025i	0.304855	−	0.528025i	−0.672374	−	0.740212i	$-0.734725\pi$
$269$	5.00000	−	8.66025i	0.304855	−	0.528025i	0.977229	+	0.212187i	$0.0680585\pi$
$270$		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
$273$	14.0000	−	12.1244i	0.847319	−	0.733799i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	11.5000	−	19.9186i	0.690968	−	1.19679i	−0.280553	−	0.959839i	$-0.590518\pi$
$277$	11.5000	−	19.9186i	0.690968	−	1.19679i	0.971521	−	0.236953i	$-0.0761488\pi$
$278$		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
$283$	12.5000	−	21.6506i	0.743048	−	1.28700i	−0.208053	−	0.978117i	$-0.566713\pi$
$283$	12.5000	−	21.6506i	0.743048	−	1.28700i	0.951101	−	0.308879i	$-0.0999539\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−20.0000	−	6.92820i	−1.18056	−	0.408959i
$288$		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
$293$	12.0000			0.701047			0.350524	−	0.936554i	$-0.386004\pi$
$293$	12.0000			0.701047			0.350524	+	0.936554i	$0.386004\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	2.00000	−	3.46410i	0.116052	−	0.201008i
$298$		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
$303$	−6.00000	−	10.3923i	−0.344691	−	0.597022i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−11.0000			−0.627803			−0.313902	−	0.949456i	$-0.601636\pi$
$307$	−11.0000			−0.627803			−0.313902	+	0.949456i	$0.601636\pi$
$308$		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
$313$	10.5000	+	18.1865i	0.593495	+	1.02796i	0.993757	+	0.111563i	$0.0355857\pi$
$313$	10.5000	+	18.1865i	0.593495	+	1.02796i	−0.400262	+	0.916401i	$0.631081\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	9.00000	+	15.5885i	0.505490	+	0.875535i	0.999980	+	0.00635137i	$0.00202172\pi$
$317$	9.00000	+	15.5885i	0.505490	+	0.875535i	−0.494489	+	0.869184i	$0.664645\pi$
$318$		0			0
$319$	−4.00000	+	6.92820i	−0.223957	+	0.387905i
$320$		0			0
$321$	−2.00000			−0.111629
$322$		0			0
$323$	18.0000			1.00155
$324$		0			0
$325$		0			0
$326$		0			0
$327$	1.50000	+	2.59808i	0.0829502	+	0.143674i
$328$		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
$333$	−3.50000	+	6.06218i	−0.191799	+	0.332205i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−15.0000			−0.817102			−0.408551	−	0.912735i	$-0.633966\pi$
$337$	−15.0000			−0.817102			−0.408551	+	0.912735i	$0.633966\pi$
$338$		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
$343$	10.0000	+	15.5885i	0.539949	+	0.841698i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	4.00000	−	6.92820i	0.214731	−	0.371925i	−0.738458	−	0.674299i	$-0.764446\pi$
$347$	4.00000	−	6.92820i	0.214731	−	0.371925i	0.953189	+	0.302374i	$0.0977791\pi$
$348$		0			0
$349$	−6.00000			−0.321173			−0.160586	−	0.987022i	$-0.551338\pi$
$349$	−6.00000			−0.321173			−0.160586	+	0.987022i	$0.551338\pi$
$350$		0			0
$351$	−7.00000			−0.373632
$352$		0			0
$353$	−6.00000	+	10.3923i	−0.319348	+	0.553127i	−0.980352	−	0.197256i	$-0.936797\pi$
$353$	−6.00000	+	10.3923i	−0.319348	+	0.553127i	0.661004	+	0.750382i	$0.270130\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−3.00000	−	15.5885i	−0.158777	−	0.825029i
$358$		0			0
$359$	7.00000	+	12.1244i	0.369446	+	0.639899i	0.989479	−	0.144677i	$-0.0462142\pi$
$359$	7.00000	+	12.1244i	0.369446	+	0.639899i	−0.620033	+	0.784576i	$0.712881\pi$
$360$		0			0
$361$	5.00000	−	8.66025i	0.263158	−	0.455803i
$362$		0			0
$363$	5.00000			0.262432
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−2.50000	+	4.33013i	−0.130499	+	0.226031i	−0.923869	−	0.382709i	$-0.874991\pi$
$367$	−2.50000	+	4.33013i	−0.130499	+	0.226031i	0.793370	+	0.608740i	$0.208325\pi$
$368$		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
$373$	4.50000	+	7.79423i	0.233001	+	0.403570i	0.958690	−	0.284453i	$-0.0918121\pi$
$373$	4.50000	+	7.79423i	0.233001	+	0.403570i	−0.725689	+	0.688023i	$0.758479\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	14.0000			0.721037
$378$		0			0
$379$	−7.00000			−0.359566			−0.179783	−	0.983706i	$-0.557540\pi$
$379$	−7.00000			−0.359566			−0.179783	+	0.983706i	$0.557540\pi$
$380$		0			0
$381$	6.50000	−	11.2583i	0.333005	−	0.576782i
$382$		0			0
$383$	4.00000	+	6.92820i	0.204390	+	0.354015i	0.949938	−	0.312437i	$-0.101145\pi$
$383$	4.00000	+	6.92820i	0.204390	+	0.354015i	−0.745548	+	0.666452i	$0.767812\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	2.50000	+	4.33013i	0.127082	+	0.220113i
$388$		0			0
$389$	−8.00000	+	13.8564i	−0.405616	+	0.702548i	−0.994393	−	0.105748i	$-0.966276\pi$
$389$	−8.00000	+	13.8564i	−0.405616	+	0.702548i	0.588777	+	0.808296i	$0.299610\pi$
$390$		0			0
$391$	12.0000			0.606866
$392$		0			0
$393$	22.0000			1.10975
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−9.50000	−	16.4545i	−0.476791	−	0.825827i	0.522855	−	0.852422i	$-0.324867\pi$
$397$	−9.50000	−	16.4545i	−0.476791	−	0.825827i	−0.999646	+	0.0265948i	$0.991534\pi$
$398$		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
$403$	24.5000	−	42.4352i	1.22043	−	2.11385i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−28.0000			−1.38791
$408$		0			0
$409$	9.50000	−	16.4545i	0.469745	−	0.813622i	−0.529657	−	0.848212i	$-0.677679\pi$
$409$	9.50000	−	16.4545i	0.469745	−	0.813622i	0.999402	+	0.0345902i	$0.0110126\pi$
$410$		0			0
$411$	9.00000	+	15.5885i	0.443937	+	0.768922i
$412$		0			0
$413$	−20.0000	+	17.3205i	−0.984136	+	0.852286i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	6.50000	−	11.2583i	0.318306	−	0.551323i
$418$		0			0
$419$	−26.0000			−1.27018			−0.635092	−	0.772437i	$-0.719038\pi$
$419$	−26.0000			−1.27018			−0.635092	+	0.772437i	$0.719038\pi$
$420$		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
$423$	5.00000	−	8.66025i	0.243108	−	0.421076i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	3.00000	+	15.5885i	0.145180	+	0.754378i
$428$		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
$433$	23.0000			1.10531			0.552655	−	0.833410i	$-0.313615\pi$
$433$	23.0000			1.10531			0.552655	+	0.833410i	$0.313615\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−3.00000	+	5.19615i	−0.143509	+	0.248566i
$438$		0			0
$439$	14.0000	+	24.2487i	0.668184	+	1.15733i	0.978412	+	0.206666i	$0.0662612\pi$
$439$	14.0000	+	24.2487i	0.668184	+	1.15733i	−0.310228	+	0.950662i	$0.600405\pi$
$440$		0			0
$441$	1.00000	−	6.92820i	0.0476190	−	0.329914i
$442$		0			0
$443$	2.00000	+	3.46410i	0.0950229	+	0.164584i	0.909618	−	0.415445i	$-0.136374\pi$
$443$	2.00000	+	3.46410i	0.0950229	+	0.164584i	−0.814595	+	0.580030i	$0.803041\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−34.0000			−1.60456			−0.802280	−	0.596948i	$-0.796380\pi$
$449$	−34.0000			−1.60456			−0.802280	+	0.596948i	$0.796380\pi$
$450$		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
$457$	−4.50000	−	7.79423i	−0.210501	−	0.364599i	0.741370	−	0.671096i	$-0.234176\pi$
$457$	−4.50000	−	7.79423i	−0.210501	−	0.364599i	−0.951871	+	0.306497i	$0.900843\pi$
$458$		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
$463$	1.00000			0.0464739			0.0232370	−	0.999730i	$-0.492603\pi$
$463$	1.00000			0.0464739			0.0232370	+	0.999730i	$0.492603\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	9.00000	+	15.5885i	0.416470	+	0.721348i	0.995582	−	0.0939008i	$-0.0299336\pi$
$467$	9.00000	+	15.5885i	0.416470	+	0.721348i	−0.579111	+	0.815249i	$0.696600\pi$
$468$		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
$473$	−10.0000	+	17.3205i	−0.459800	+	0.796398i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	8.00000			0.366295
$478$		0			0
$479$	−20.0000	+	34.6410i	−0.913823	+	1.58279i	−0.105208	+	0.994450i	$0.533551\pi$
$479$	−20.0000	+	34.6410i	−0.913823	+	1.58279i	−0.808615	+	0.588338i	$0.799782\pi$
$480$		0			0
$481$	24.5000	+	42.4352i	1.11710	+	1.93488i
$482$		0			0
$483$	5.00000	+	1.73205i	0.227508	+	0.0788110i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	11.5000	−	19.9186i	0.521115	−	0.902597i	−0.478584	−	0.878042i	$-0.658850\pi$
$487$	11.5000	−	19.9186i	0.521115	−	0.902597i	0.999698	−	0.0245553i	$-0.00781698\pi$
$488$		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
$493$	6.00000	−	10.3923i	0.270226	−	0.468046i
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−3.50000	−	6.06218i	−0.156682	−	0.271380i	0.776989	−	0.629515i	$-0.216746\pi$
$499$	−3.50000	−	6.06218i	−0.156682	−	0.271380i	−0.933670	+	0.358134i	$0.883413\pi$
$500$		0			0
$501$	12.0000	−	20.7846i	0.536120	−	0.928588i
$502$		0			0
$503$	−6.00000			−0.267527			−0.133763	−	0.991013i	$-0.542706\pi$
$503$	−6.00000			−0.267527			−0.133763	+	0.991013i	$0.542706\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−18.0000	+	31.1769i	−0.799408	+	1.38462i
$508$		0			0
$509$	−7.00000	−	12.1244i	−0.310270	−	0.537403i	0.668151	−	0.744026i	$-0.267086\pi$
$509$	−7.00000	−	12.1244i	−0.310270	−	0.537403i	−0.978421	+	0.206623i	$0.933753\pi$
$510$		0			0
$511$	30.0000	−	25.9808i	1.32712	−	1.14932i
$512$		0			0
$513$	−1.50000	−	2.59808i	−0.0662266	−	0.114708i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	40.0000			1.75920
$518$		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
$523$	−0.500000	−	0.866025i	−0.0218635	−	0.0378686i	0.854887	−	0.518815i	$-0.173627\pi$
$523$	−0.500000	−	0.866025i	−0.0218635	−	0.0378686i	−0.876750	+	0.480946i	$0.840293\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−21.0000	−	36.3731i	−0.914774	−	1.58444i
$528$		0			0
$529$	9.50000	−	16.4545i	0.413043	−	0.715412i
$530$		0			0
$531$	10.0000			0.433963
$532$		0			0
$533$	56.0000			2.42563
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−7.00000	−	12.1244i	−0.302072	−	0.523205i
$538$		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
$543$	1.50000	−	2.59808i	0.0643712	−	0.111494i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−16.0000			−0.684111			−0.342055	−	0.939680i	$-0.611123\pi$
$547$	−16.0000			−0.684111			−0.342055	+	0.939680i	$0.611123\pi$
$548$		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
$553$	−0.500000	−	2.59808i	−0.0212622	−	0.110481i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−15.0000	+	25.9808i	−0.635570	+	1.10084i	0.350824	+	0.936442i	$0.385902\pi$
$557$	−15.0000	+	25.9808i	−0.635570	+	1.10084i	−0.986394	+	0.164399i	$0.947432\pi$
$558$		0			0
$559$	35.0000			1.48034
$560$		0			0
$561$	−24.0000			−1.01328
$562$		0			0
$563$	−7.00000	+	12.1244i	−0.295015	+	0.510981i	−0.974988	−	0.222256i	$-0.928658\pi$
$563$	−7.00000	+	12.1244i	−0.295015	+	0.510981i	0.679974	+	0.733237i	$0.261991\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−2.00000	+	1.73205i	−0.0839921	+	0.0727393i
$568$		0			0
$569$	−6.00000	−	10.3923i	−0.251533	−	0.435668i	0.712415	−	0.701758i	$-0.247601\pi$
$569$	−6.00000	−	10.3923i	−0.251533	−	0.435668i	−0.963948	+	0.266090i	$0.914268\pi$
$570$		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
$573$	−18.0000			−0.751961
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−17.5000	+	30.3109i	−0.728535	+	1.26186i	0.228968	+	0.973434i	$0.426465\pi$
$577$	−17.5000	+	30.3109i	−0.728535	+	1.26186i	−0.957503	+	0.288425i	$0.906868\pi$
$578$		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
$583$	16.0000	+	27.7128i	0.662652	+	1.14775i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	18.0000			0.742940			0.371470	−	0.928445i	$-0.378854\pi$
$587$	18.0000			0.742940			0.371470	+	0.928445i	$0.378854\pi$
$588$		0			0
$589$	21.0000			0.865290
$590$		0			0
$591$	1.00000	−	1.73205i	0.0411345	−	0.0712470i
$592$		0			0
$593$	−16.0000	−	27.7128i	−0.657041	−	1.13803i	−0.981378	−	0.192087i	$-0.938474\pi$
$593$	−16.0000	−	27.7128i	−0.657041	−	1.13803i	0.324337	−	0.945942i	$-0.394859\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−10.0000	+	17.3205i	−0.408589	+	0.707697i	−0.994732	−	0.102511i	$-0.967312\pi$
$599$	−10.0000	+	17.3205i	−0.408589	+	0.707697i	0.586143	+	0.810208i	$0.300646\pi$
$600$		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
$603$	−3.00000			−0.122169
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−6.50000	−	11.2583i	−0.263827	−	0.456962i	0.703429	−	0.710766i	$-0.251651\pi$
$607$	−6.50000	−	11.2583i	−0.263827	−	0.456962i	−0.967256	+	0.253804i	$0.918318\pi$
$608$		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
$613$	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
$615$		0			0
$616$		0			0
$617$	2.00000			0.0805170			0.0402585	−	0.999189i	$-0.487182\pi$
$617$	2.00000			0.0805170			0.0402585	+	0.999189i	$0.487182\pi$
$618$		0			0
$619$	−14.5000	+	25.1147i	−0.582804	+	1.00945i	0.412341	+	0.911030i	$0.364711\pi$
$619$	−14.5000	+	25.1147i	−0.582804	+	1.00945i	−0.995145	+	0.0984169i	$0.968622\pi$
$620$		0			0
$621$	−1.00000	−	1.73205i	−0.0401286	−	0.0695048i
$622$		0			0
$623$	−1.00000	−	5.19615i	−0.0400642	−	0.208179i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	6.00000	−	10.3923i	0.239617	−	0.415029i
$628$		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
$633$	2.00000	−	3.46410i	0.0794929	−	0.137686i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−38.5000	−	30.3109i	−1.52543	−	1.20096i
$638$		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
$643$	−5.00000			−0.197181			−0.0985904	−	0.995128i	$-0.531433\pi$
$643$	−5.00000			−0.197181			−0.0985904	+	0.995128i	$0.531433\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−22.0000	+	38.1051i	−0.864909	+	1.49807i	0.00222801	+	0.999998i	$0.499291\pi$
$647$	−22.0000	+	38.1051i	−0.864909	+	1.49807i	−0.867137	+	0.498069i	$0.834043\pi$
$648$		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
$653$	14.0000	+	24.2487i	0.547862	+	0.948925i	0.998421	+	0.0561784i	$0.0178916\pi$
$653$	14.0000	+	24.2487i	0.547862	+	0.948925i	−0.450558	+	0.892747i	$0.648775\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−15.0000			−0.585206
$658$		0			0
$659$	12.0000			0.467454			0.233727	−	0.972302i	$-0.424908\pi$
$659$	12.0000			0.467454			0.233727	+	0.972302i	$0.424908\pi$
$660$		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
$663$	21.0000	+	36.3731i	0.815572	+	1.41261i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	2.00000	+	3.46410i	0.0774403	+	0.134131i
$668$		0			0
$669$	−6.00000	+	10.3923i	−0.231973	+	0.401790i
$670$		0			0
$671$	24.0000			0.926510
$672$		0			0
$673$	−37.0000			−1.42625			−0.713123	−	0.701039i	$-0.752720\pi$
$673$	−37.0000			−1.42625			−0.713123	+	0.701039i	$0.752720\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	1.00000	+	1.73205i	0.0384331	+	0.0665681i	0.884602	−	0.466347i	$-0.154430\pi$
$677$	1.00000	+	1.73205i	0.0384331	+	0.0665681i	−0.846169	+	0.532915i	$0.821097\pi$
$678$		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
$683$	5.00000	−	8.66025i	0.191320	−	0.331375i	−0.754368	−	0.656452i	$-0.772057\pi$
$683$	5.00000	−	8.66025i	0.191320	−	0.331375i	0.945688	+	0.325076i	$0.105390\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	17.0000			0.648590
$688$		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
$693$	−10.0000	−	3.46410i	−0.379869	−	0.131590i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	24.0000	−	41.5692i	0.909065	−	1.57455i
$698$		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
$703$	−10.5000	+	18.1865i	−0.396015	+	0.685918i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−24.0000	+	20.7846i	−0.902613	+	0.781686i
$708$		0			0
$709$	−7.00000	−	12.1244i	−0.262891	−	0.455340i	0.704118	−	0.710083i	$-0.251342\pi$
$709$	−7.00000	−	12.1244i	−0.262891	−	0.455340i	−0.967009	+	0.254743i	$0.918009\pi$
$710$		0			0
$711$	−0.500000	+	0.866025i	−0.0187515	+	0.0324785i
$712$		0			0
$713$	14.0000			0.524304
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−3.00000	+	5.19615i	−0.112037	+	0.194054i
$718$		0			0
$719$	−25.0000	−	43.3013i	−0.932343	−	1.61486i	−0.779305	−	0.626644i	$-0.784428\pi$
$719$	−25.0000	−	43.3013i	−0.932343	−	1.61486i	−0.153037	−	0.988220i	$-0.548906\pi$
$720$		0			0
$721$	−3.50000	−	18.1865i	−0.130347	−	0.677302i
$722$		0			0
$723$	7.00000	+	12.1244i	0.260333	+	0.450910i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−23.0000			−0.853023			−0.426511	−	0.904482i	$-0.640258\pi$
$727$	−23.0000			−0.853023			−0.426511	+	0.904482i	$0.640258\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	15.0000	−	25.9808i	0.554795	−	0.960933i
$732$		0			0
$733$	−6.50000	−	11.2583i	−0.240083	−	0.415836i	0.720655	−	0.693294i	$-0.243841\pi$
$733$	−6.50000	−	11.2583i	−0.240083	−	0.415836i	−0.960738	+	0.277458i	$0.910508\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−6.00000	−	10.3923i	−0.221013	−	0.382805i
$738$		0			0
$739$	0.500000	−	0.866025i	0.0183928	−	0.0318573i	−0.856683	−	0.515844i	$-0.827478\pi$
$739$	0.500000	−	0.866025i	0.0183928	−	0.0318573i	0.875075	+	0.483987i	$0.160812\pi$
$740$		0			0
$741$	−21.0000			−0.771454
$742$		0			0
$743$	44.0000			1.61420			0.807102	−	0.590412i	$-0.201035\pi$
$743$	44.0000			1.61420			0.807102	+	0.590412i	$0.201035\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	4.00000	+	6.92820i	0.146352	+	0.253490i
$748$		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
$753$	−11.0000	+	19.0526i	−0.400862	+	0.694314i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−2.00000			−0.0726912			−0.0363456	−	0.999339i	$-0.511572\pi$
$757$	−2.00000			−0.0726912			−0.0363456	+	0.999339i	$0.511572\pi$
$758$		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
$763$	6.00000	−	5.19615i	0.217215	−	0.188113i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	35.0000	−	60.6218i	1.26378	−	2.18893i
$768$		0			0
$769$	−29.0000			−1.04577			−0.522883	−	0.852404i	$-0.675144\pi$
$769$	−29.0000			−1.04577			−0.522883	+	0.852404i	$0.675144\pi$
$770$		0			0
$771$	−16.0000			−0.576226
$772$		0			0
$773$	−6.00000	+	10.3923i	−0.215805	+	0.373785i	−0.953521	−	0.301326i	$-0.902571\pi$
$773$	−6.00000	+	10.3923i	−0.215805	+	0.373785i	0.737716	+	0.675111i	$0.235904\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	17.5000	+	6.06218i	0.627809	+	0.217479i
$778$		0			0
$779$	12.0000	+	20.7846i	0.429945	+	0.744686i
$780$		0			0
$781$		0			0
$782$		0			0
$783$	−2.00000			−0.0714742
$784$		0			0
$785$		0			0
$786$		0			0
$787$	2.00000	−	3.46410i	0.0712923	−	0.123482i	−0.828176	−	0.560469i	$-0.810621\pi$
$787$	2.00000	−	3.46410i	0.0712923	−	0.123482i	0.899468	+	0.436987i	$0.143954\pi$
$788$		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
$793$	−21.0000	−	36.3731i	−0.745732	−	1.29165i
$794$		0			0
$795$		0			0
$796$		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
$799$	−60.0000			−2.12265
$800$		0			0
$801$	−1.00000	+	1.73205i	−0.0353333	+	0.0611990i
$802$		0			0
$803$	−30.0000	−	51.9615i	−1.05868	−	1.83368i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	5.00000	+	8.66025i	0.176008	+	0.304855i
$808$		0			0
$809$	3.00000	−	5.19615i	0.105474	−	0.182687i	−0.808458	−	0.588555i	$-0.799697\pi$
$809$	3.00000	−	5.19615i	0.105474	−	0.182687i	0.913932	+	0.405868i	$0.133031\pi$
$810$		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
$813$	−16.0000			−0.561144
$814$		0			0
$815$		0			0
$816$		0			0
$817$	7.50000	+	12.9904i	0.262392	+	0.454476i
$818$		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
$823$	−12.0000	+	20.7846i	−0.418294	+	0.724506i	−0.995768	−	0.0919029i	$-0.970705\pi$
$823$	−12.0000	+	20.7846i	−0.418294	+	0.724506i	0.577474	+	0.816409i	$0.304038\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	10.0000			0.347734			0.173867	−	0.984769i	$-0.444374\pi$
$827$	10.0000			0.347734			0.173867	+	0.984769i	$0.444374\pi$
$828$		0			0
$829$	−12.5000	+	21.6506i	−0.434143	+	0.751958i	−0.997225	−	0.0744432i	$-0.976282\pi$
$829$	−12.5000	+	21.6506i	−0.434143	+	0.751958i	0.563082	+	0.826401i	$0.309615\pi$
$830$		0			0
$831$	11.5000	+	19.9186i	0.398931	+	0.690968i
$832$		0			0
$833$	−39.0000	+	15.5885i	−1.35127	+	0.540108i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−3.50000	+	6.06218i	−0.120978	+	0.209540i
$838$		0			0
$839$	−22.0000			−0.759524			−0.379762	−	0.925084i	$-0.623994\pi$
$839$	−22.0000			−0.759524			−0.379762	+	0.925084i	$0.623994\pi$
$840$		0			0
$841$	−25.0000			−0.862069
$842$		0			0
$843$	8.00000	−	13.8564i	0.275535	−	0.477240i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−2.50000	−	12.9904i	−0.0859010	−	0.446355i
$848$		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
$853$	23.0000			0.787505			0.393753	−	0.919216i	$-0.371177\pi$
$853$	23.0000			0.787505			0.393753	+	0.919216i	$0.371177\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	11.0000	−	19.0526i	0.375753	−	0.650823i	−0.614687	−	0.788771i	$-0.710717\pi$
$857$	11.0000	−	19.0526i	0.375753	−	0.650823i	0.990439	+	0.137948i	$0.0440508\pi$
$858$		0			0
$859$	−18.0000	−	31.1769i	−0.614152	−	1.06374i	−0.990533	−	0.137277i	$-0.956165\pi$
$859$	−18.0000	−	31.1769i	−0.614152	−	1.06374i	0.376381	−	0.926465i	$-0.377169\pi$
$860$		0			0
$861$	16.0000	−	13.8564i	0.545279	−	0.472225i
$862$		0			0
$863$	−1.00000	−	1.73205i	−0.0340404	−	0.0589597i	0.848503	−	0.529190i	$-0.177504\pi$
$863$	−1.00000	−	1.73205i	−0.0340404	−	0.0589597i	−0.882544	+	0.470230i	$0.844171\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	19.0000			0.645274
$868$		0			0
$869$	−4.00000			−0.135691
$870$		0			0
$871$	−10.5000	+	18.1865i	−0.355779	+	0.616227i
$872$		0			0
$873$	−5.00000	−	8.66025i	−0.169224	−	0.293105i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	25.0000	+	43.3013i	0.844190	+	1.46218i	0.886323	+	0.463068i	$0.153251\pi$
$877$	25.0000	+	43.3013i	0.844190	+	1.46218i	−0.0421327	+	0.999112i	$0.513415\pi$
$878$		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
$883$	−27.0000			−0.908622			−0.454311	−	0.890843i	$-0.650115\pi$
$883$	−27.0000			−0.908622			−0.454311	+	0.890843i	$0.650115\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	16.0000	+	27.7128i	0.537227	+	0.930505i	0.999052	+	0.0435339i	$0.0138616\pi$
$887$	16.0000	+	27.7128i	0.537227	+	0.930505i	−0.461825	+	0.886971i	$0.652805\pi$
$888$		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
$893$	15.0000	−	25.9808i	0.501956	−	0.869413i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−14.0000			−0.467446
$898$		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
$903$	10.0000	−	8.66025i	0.332779	−	0.288195i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−18.5000	+	32.0429i	−0.614282	+	1.06397i	0.376228	+	0.926527i	$0.377221\pi$
$907$	−18.5000	+	32.0429i	−0.614282	+	1.06397i	−0.990510	+	0.137441i	$0.956112\pi$
$908$		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
$913$	−16.0000	+	27.7128i	−0.529523	+	0.917160i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−11.0000	−	57.1577i	−0.363252	−	1.88751i
$918$		0			0
$919$	13.5000	+	23.3827i	0.445324	+	0.771324i	0.998075	−	0.0620230i	$-0.0197552\pi$
$919$	13.5000	+	23.3827i	0.445324	+	0.771324i	−0.552751	+	0.833347i	$0.686422\pi$
$920$		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
$927$	−3.50000	+	6.06218i	−0.114955	+	0.199108i
$928$		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
$937$	−9.00000			−0.294017			−0.147009	−	0.989135i	$-0.546964\pi$
$937$	−9.00000			−0.294017			−0.147009	+	0.989135i	$0.546964\pi$
$938$		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
$943$	8.00000	+	13.8564i	0.260516	+	0.451227i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	2.00000	+	3.46410i	0.0649913	+	0.112568i	0.896690	−	0.442659i	$-0.145965\pi$
$947$	2.00000	+	3.46410i	0.0649913	+	0.112568i	−0.831699	+	0.555227i	$0.812631\pi$
$948$		0			0
$949$	−52.5000	+	90.9327i	−1.70422	+	2.95180i
$950$		0			0
$951$	−18.0000			−0.583690
$952$		0			0
$953$	−16.0000			−0.518291			−0.259145	−	0.965838i	$-0.583441\pi$
$953$	−16.0000			−0.518291			−0.259145	+	0.965838i	$0.583441\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−4.00000	−	6.92820i	−0.129302	−	0.223957i
$958$		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
$963$	1.00000	−	1.73205i	0.0322245	−	0.0558146i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	17.0000			0.546683			0.273342	−	0.961917i	$-0.411871\pi$
$967$	17.0000			0.546683			0.273342	+	0.961917i	$0.411871\pi$
$968$		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
$973$	−32.5000	−	11.2583i	−1.04190	−	0.360925i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−12.0000	+	20.7846i	−0.383914	+	0.664959i	−0.991618	−	0.129205i	$-0.958757\pi$
$977$	−12.0000	+	20.7846i	−0.383914	+	0.664959i	0.607704	+	0.794164i	$0.292091\pi$
$978$		0			0
$979$	−8.00000			−0.255681
$980$		0			0
$981$	−3.00000			−0.0957826
$982$		0			0
$983$	−7.00000	+	12.1244i	−0.223265	+	0.386707i	−0.955798	−	0.294025i	$-0.905005\pi$
$983$	−7.00000	+	12.1244i	−0.223265	+	0.386707i	0.732532	+	0.680732i	$0.238338\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−25.0000	−	8.66025i	−0.795759	−	0.275659i
$988$		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
$993$	−7.00000			−0.222138
$994$		0			0
$995$		0			0
$996$		0			0
$997$	8.50000	−	14.7224i	0.269198	−	0.466264i	−0.699457	−	0.714675i	$-0.746575\pi$
$997$	8.50000	−	14.7224i	0.269198	−	0.466264i	0.968655	+	0.248410i	$0.0799082\pi$
$998$		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.q.d.1201.1		2
5.2	odd	4		2100.2.bc.d.949.2		4
5.3	odd	4		2100.2.bc.d.949.1		4
5.4	even	2		420.2.q.b.361.1	yes	2
7.2	even	3	inner	2100.2.q.d.1801.1		2
15.14	odd	2		1260.2.s.a.361.1		2
20.19	odd	2		1680.2.bg.j.1201.1		2
35.2	odd	12		2100.2.bc.d.1549.1		4
35.4	even	6		2940.2.a.b.1.1		1
35.9	even	6		420.2.q.b.121.1	✓	2
35.19	odd	6		2940.2.q.c.961.1		2
35.23	odd	12		2100.2.bc.d.1549.2		4
35.24	odd	6		2940.2.a.k.1.1		1
35.34	odd	2		2940.2.q.c.361.1		2
105.44	odd	6		1260.2.s.a.541.1		2
105.59	even	6		8820.2.a.l.1.1		1
105.74	odd	6		8820.2.a.bb.1.1		1
140.79	odd	6		1680.2.bg.j.961.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.q.b.121.1	✓	2	35.9	even	6
420.2.q.b.361.1	yes	2	5.4	even	2
1260.2.s.a.361.1		2	15.14	odd	2
1260.2.s.a.541.1		2	105.44	odd	6
1680.2.bg.j.961.1		2	140.79	odd	6
1680.2.bg.j.1201.1		2	20.19	odd	2
2100.2.q.d.1201.1		2	1.1	even	1	trivial
2100.2.q.d.1801.1		2	7.2	even	3	inner
2100.2.bc.d.949.1		4	5.3	odd	4
2100.2.bc.d.949.2		4	5.2	odd	4
2100.2.bc.d.1549.1		4	35.2	odd	12
2100.2.bc.d.1549.2		4	35.23	odd	12
2940.2.a.b.1.1		1	35.4	even	6
2940.2.a.k.1.1		1	35.24	odd	6
2940.2.q.c.361.1		2	35.34	odd	2
2940.2.q.c.961.1		2	35.19	odd	6
8820.2.a.l.1.1		1	105.59	even	6
8820.2.a.bb.1.1		1	105.74	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2100.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{3} +(2.50000 + 0.866025i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{3} +(2.50000 + 0.866025i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(2.00000 - 3.46410i) q^{11} -7.00000 q^{13} +(-3.00000 + 5.19615i) q^{17} +(-1.50000 - 2.59808i) q^{19} +(-2.00000 + 1.73205i) q^{21} +(-1.00000 - 1.73205i) q^{23} +1.00000 q^{27} -2.00000 q^{29} +(-3.50000 + 6.06218i) q^{31} +(2.00000 + 3.46410i) q^{33} +(-3.50000 - 6.06218i) q^{37} +(3.50000 - 6.06218i) q^{39} -8.00000 q^{41} -5.00000 q^{43} +(5.00000 + 8.66025i) q^{47} +(5.50000 + 4.33013i) q^{49} +(-3.00000 - 5.19615i) q^{51} +(-4.00000 + 6.92820i) q^{53} +3.00000 q^{57} +(-5.00000 + 8.66025i) q^{59} +(3.00000 + 5.19615i) q^{61} +(-0.500000 - 2.59808i) q^{63} +(1.50000 - 2.59808i) q^{67} +2.00000 q^{69} +(7.50000 - 12.9904i) q^{73} +(8.00000 - 6.92820i) q^{77} +(-0.500000 - 0.866025i) q^{79} +(-0.500000 + 0.866025i) q^{81} -8.00000 q^{83} +(1.00000 - 1.73205i) q^{87} +(-1.00000 - 1.73205i) q^{89} +(-17.5000 - 6.06218i) q^{91} +(-3.50000 - 6.06218i) q^{93} +10.0000 q^{97} -4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{3} + 5 q^{7} - q^{9}+O(q^{10}) \) 2 * q - q^3 + 5 * q^7 - q^9	\( 2 q - q^{3} + 5 q^{7} - q^{9} + 4 q^{11} - 14 q^{13} - 6 q^{17} - 3 q^{19} - 4 q^{21} - 2 q^{23} + 2 q^{27} - 4 q^{29} - 7 q^{31} + 4 q^{33} - 7 q^{37} + 7 q^{39} - 16 q^{41} - 10 q^{43} + 10 q^{47} + 11 q^{49} - 6 q^{51} - 8 q^{53} + 6 q^{57} - 10 q^{59} + 6 q^{61} - q^{63} + 3 q^{67} + 4 q^{69} + 15 q^{73} + 16 q^{77} - q^{79} - q^{81} - 16 q^{83} + 2 q^{87} - 2 q^{89} - 35 q^{91} - 7 q^{93} + 20 q^{97} - 8 q^{99}+O(q^{100}) \) 2 * q - q^3 + 5 * q^7 - q^9 + 4 * q^11 - 14 * q^13 - 6 * q^17 - 3 * q^19 - 4 * q^21 - 2 * q^23 + 2 * q^27 - 4 * q^29 - 7 * q^31 + 4 * q^33 - 7 * q^37 + 7 * q^39 - 16 * q^41 - 10 * q^43 + 10 * q^47 + 11 * q^49 - 6 * q^51 - 8 * q^53 + 6 * q^57 - 10 * q^59 + 6 * q^61 - q^63 + 3 * q^67 + 4 * q^69 + 15 * q^73 + 16 * q^77 - q^79 - q^81 - 16 * q^83 + 2 * q^87 - 2 * q^89 - 35 * q^91 - 7 * q^93 + 20 * q^97 - 8 * q^99

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