LMFDB - Embedded newform 2100.2.q.c.1801.1

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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1801.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	2100.1801
Dual form			2100.2.q.c.1201.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{3} +(2.00000 + 1.73205i) q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{3} +(2.00000 + 1.73205i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(-1.00000 - 1.73205i) q^{11} -2.00000 q^{13} +(-1.00000 - 1.73205i) q^{17} +(-2.00000 + 3.46410i) q^{19} +(0.500000 - 2.59808i) q^{21} +(4.00000 - 6.92820i) q^{23} +1.00000 q^{27} +4.00000 q^{29} +(-1.50000 - 2.59808i) q^{31} +(-1.00000 + 1.73205i) q^{33} +(4.50000 - 7.79423i) q^{37} +(1.00000 + 1.73205i) q^{39} +6.00000 q^{41} -1.00000 q^{43} +(3.00000 - 5.19615i) q^{47} +(1.00000 + 6.92820i) q^{49} +(-1.00000 + 1.73205i) q^{51} +(-1.00000 - 1.73205i) q^{53} +4.00000 q^{57} +(3.00000 + 5.19615i) q^{59} +(0.500000 - 0.866025i) q^{61} +(-2.50000 + 0.866025i) q^{63} +(-6.00000 - 10.3923i) q^{67} -8.00000 q^{69} +10.0000 q^{71} +(-0.500000 - 0.866025i) q^{73} +(1.00000 - 5.19615i) q^{77} +(-3.50000 + 6.06218i) q^{79} +(-0.500000 - 0.866025i) q^{81} +18.0000 q^{83} +(-2.00000 - 3.46410i) q^{87} +(-5.00000 + 8.66025i) q^{89} +(-4.00000 - 3.46410i) q^{91} +(-1.50000 + 2.59808i) q^{93} +5.00000 q^{97} +2.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{3} + 4 q^{7} - q^{9}+O(q^{10}) $ 2 * q - q^3 + 4 * q^7 - q^9	$ 2 q - q^{3} + 4 q^{7} - q^{9} - 2 q^{11} - 4 q^{13} - 2 q^{17} - 4 q^{19} + q^{21} + 8 q^{23} + 2 q^{27} + 8 q^{29} - 3 q^{31} - 2 q^{33} + 9 q^{37} + 2 q^{39} + 12 q^{41} - 2 q^{43} + 6 q^{47} + 2 q^{49} - 2 q^{51} - 2 q^{53} + 8 q^{57} + 6 q^{59} + q^{61} - 5 q^{63} - 12 q^{67} - 16 q^{69} + 20 q^{71} - q^{73} + 2 q^{77} - 7 q^{79} - q^{81} + 36 q^{83} - 4 q^{87} - 10 q^{89} - 8 q^{91} - 3 q^{93} + 10 q^{97} + 4 q^{99}+O(q^{100}) $ 2 * q - q^3 + 4 * q^7 - q^9 - 2 * q^11 - 4 * q^13 - 2 * q^17 - 4 * q^19 + q^21 + 8 * q^23 + 2 * q^27 + 8 * q^29 - 3 * q^31 - 2 * q^33 + 9 * q^37 + 2 * q^39 + 12 * q^41 - 2 * q^43 + 6 * q^47 + 2 * q^49 - 2 * q^51 - 2 * q^53 + 8 * q^57 + 6 * q^59 + q^61 - 5 * q^63 - 12 * q^67 - 16 * q^69 + 20 * q^71 - q^73 + 2 * q^77 - 7 * q^79 - q^81 + 36 * q^83 - 4 * q^87 - 10 * q^89 - 8 * q^91 - 3 * q^93 + 10 * q^97 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$7$	2.00000	+	1.73205i	0.755929	+	0.654654i
$7$	2.00000	+	1.73205i	0.755929	+	0.654654i
$8$		0			0
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	−1.00000	−	1.73205i	−0.301511	−	0.522233i	0.674967	−	0.737848i	$-0.264158\pi$
$11$	−1.00000	−	1.73205i	−0.301511	−	0.522233i	−0.976478	+	0.215615i	$0.930824\pi$
$12$		0			0
$13$	−2.00000			−0.554700			−0.277350	−	0.960769i	$-0.589456\pi$
$13$	−2.00000			−0.554700			−0.277350	+	0.960769i	$0.589456\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.00000	−	1.73205i	−0.242536	−	0.420084i	0.718900	−	0.695113i	$-0.244646\pi$
$17$	−1.00000	−	1.73205i	−0.242536	−	0.420084i	−0.961436	+	0.275029i	$0.911312\pi$
$18$		0			0
$19$	−2.00000	+	3.46410i	−0.458831	+	0.794719i	−0.998899	−	0.0469020i	$-0.985065\pi$
$19$	−2.00000	+	3.46410i	−0.458831	+	0.794719i	0.540068	+	0.841621i	$0.318398\pi$
$20$		0			0
$21$	0.500000	−	2.59808i	0.109109	−	0.566947i
$22$		0			0
$23$	4.00000	−	6.92820i	0.834058	−	1.44463i	−0.0607377	−	0.998154i	$-0.519345\pi$
$23$	4.00000	−	6.92820i	0.834058	−	1.44463i	0.894795	−	0.446476i	$-0.147321\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$	4.00000			0.742781			0.371391	−	0.928477i	$-0.378881\pi$
$29$	4.00000			0.742781			0.371391	+	0.928477i	$0.378881\pi$
$30$		0			0
$31$	−1.50000	−	2.59808i	−0.269408	−	0.466628i	0.699301	−	0.714827i	$-0.253495\pi$
$31$	−1.50000	−	2.59808i	−0.269408	−	0.466628i	−0.968709	+	0.248199i	$0.920161\pi$
$32$		0			0
$33$	−1.00000	+	1.73205i	−0.174078	+	0.301511i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	4.50000	−	7.79423i	0.739795	−	1.28136i	−0.212792	−	0.977098i	$-0.568256\pi$
$37$	4.50000	−	7.79423i	0.739795	−	1.28136i	0.952587	−	0.304266i	$-0.0984111\pi$
$38$		0			0
$39$	1.00000	+	1.73205i	0.160128	+	0.277350i
$40$		0			0
$41$	6.00000			0.937043			0.468521	−	0.883452i	$-0.344787\pi$
$41$	6.00000			0.937043			0.468521	+	0.883452i	$0.344787\pi$
$42$		0			0
$43$	−1.00000			−0.152499			−0.0762493	−	0.997089i	$-0.524294\pi$
$43$	−1.00000			−0.152499			−0.0762493	+	0.997089i	$0.524294\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	3.00000	−	5.19615i	0.437595	−	0.757937i	−0.559908	−	0.828554i	$-0.689164\pi$
$47$	3.00000	−	5.19615i	0.437595	−	0.757937i	0.997503	+	0.0706177i	$0.0224970\pi$
$48$		0			0
$49$	1.00000	+	6.92820i	0.142857	+	0.989743i
$50$		0			0
$51$	−1.00000	+	1.73205i	−0.140028	+	0.242536i
$52$		0			0
$53$	−1.00000	−	1.73205i	−0.137361	−	0.237915i	0.789136	−	0.614218i	$-0.210529\pi$
$53$	−1.00000	−	1.73205i	−0.137361	−	0.237915i	−0.926497	+	0.376303i	$0.877195\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	4.00000			0.529813
$58$		0			0
$59$	3.00000	+	5.19615i	0.390567	+	0.676481i	0.992524	−	0.122047i	$-0.0389457\pi$
$59$	3.00000	+	5.19615i	0.390567	+	0.676481i	−0.601958	+	0.798528i	$0.705612\pi$
$60$		0			0
$61$	0.500000	−	0.866025i	0.0640184	−	0.110883i	−0.832240	−	0.554416i	$-0.812942\pi$
$61$	0.500000	−	0.866025i	0.0640184	−	0.110883i	0.896258	+	0.443533i	$0.146275\pi$
$62$		0			0
$63$	−2.50000	+	0.866025i	−0.314970	+	0.109109i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−6.00000	−	10.3923i	−0.733017	−	1.26962i	−0.955588	−	0.294706i	$-0.904778\pi$
$67$	−6.00000	−	10.3923i	−0.733017	−	1.26962i	0.222571	−	0.974916i	$-0.428555\pi$
$68$		0			0
$69$	−8.00000			−0.963087
$70$		0			0
$71$	10.0000			1.18678			0.593391	−	0.804914i	$-0.297789\pi$
$71$	10.0000			1.18678			0.593391	+	0.804914i	$0.297789\pi$
$72$		0			0
$73$	−0.500000	−	0.866025i	−0.0585206	−	0.101361i	0.835281	−	0.549823i	$-0.185305\pi$
$73$	−0.500000	−	0.866025i	−0.0585206	−	0.101361i	−0.893801	+	0.448463i	$0.851972\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	1.00000	−	5.19615i	0.113961	−	0.592157i
$78$		0			0
$79$	−3.50000	+	6.06218i	−0.393781	+	0.682048i	−0.992945	−	0.118578i	$-0.962166\pi$
$79$	−3.50000	+	6.06218i	−0.393781	+	0.682048i	0.599164	+	0.800626i	$0.295500\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	18.0000			1.97576			0.987878	−	0.155230i	$-0.0496119\pi$
$83$	18.0000			1.97576			0.987878	+	0.155230i	$0.0496119\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−2.00000	−	3.46410i	−0.214423	−	0.371391i
$88$		0			0
$89$	−5.00000	+	8.66025i	−0.529999	+	0.917985i	0.469389	+	0.882992i	$0.344474\pi$
$89$	−5.00000	+	8.66025i	−0.529999	+	0.917985i	−0.999388	+	0.0349934i	$0.988859\pi$
$90$		0			0
$91$	−4.00000	−	3.46410i	−0.419314	−	0.363137i
$92$		0			0
$93$	−1.50000	+	2.59808i	−0.155543	+	0.269408i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	5.00000			0.507673			0.253837	−	0.967247i	$-0.418307\pi$
$97$	5.00000			0.507673			0.253837	+	0.967247i	$0.418307\pi$
$98$		0			0
$99$	2.00000			0.201008
$100$		0			0
$101$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$101$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$102$		0			0
$103$	5.50000	−	9.52628i	0.541931	−	0.938652i	−0.456862	−	0.889538i	$-0.651027\pi$
$103$	5.50000	−	9.52628i	0.541931	−	0.938652i	0.998793	−	0.0491146i	$-0.0156400\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$107$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$108$		0			0
$109$	−7.00000	−	12.1244i	−0.670478	−	1.16130i	−0.977769	−	0.209687i	$-0.932756\pi$
$109$	−7.00000	−	12.1244i	−0.670478	−	1.16130i	0.307290	−	0.951616i	$-0.400578\pi$
$110$		0			0
$111$	−9.00000			−0.854242
$112$		0			0
$113$	−6.00000			−0.564433			−0.282216	−	0.959351i	$-0.591070\pi$
$113$	−6.00000			−0.564433			−0.282216	+	0.959351i	$0.591070\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	1.00000	−	1.73205i	0.0924500	−	0.160128i
$118$		0			0
$119$	1.00000	−	5.19615i	0.0916698	−	0.476331i
$120$		0			0
$121$	3.50000	−	6.06218i	0.318182	−	0.551107i
$122$		0			0
$123$	−3.00000	−	5.19615i	−0.270501	−	0.468521i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	17.0000			1.50851			0.754253	−	0.656584i	$-0.227999\pi$
$127$	17.0000			1.50851			0.754253	+	0.656584i	$0.227999\pi$
$128$		0			0
$129$	0.500000	+	0.866025i	0.0440225	+	0.0762493i
$130$		0			0
$131$	11.0000	−	19.0526i	0.961074	−	1.66463i	0.241264	−	0.970460i	$-0.422438\pi$
$131$	11.0000	−	19.0526i	0.961074	−	1.66463i	0.719811	−	0.694170i	$-0.244228\pi$
$132$		0			0
$133$	−10.0000	+	3.46410i	−0.867110	+	0.300376i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−8.00000	−	13.8564i	−0.683486	−	1.18383i	−0.973910	−	0.226935i	$-0.927130\pi$
$137$	−8.00000	−	13.8564i	−0.683486	−	1.18383i	0.290424	−	0.956898i	$-0.406204\pi$
$138$		0			0
$139$	5.00000			0.424094			0.212047	−	0.977259i	$-0.431987\pi$
$139$	5.00000			0.424094			0.212047	+	0.977259i	$0.431987\pi$
$140$		0			0
$141$	−6.00000			−0.505291
$142$		0			0
$143$	2.00000	+	3.46410i	0.167248	+	0.289683i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	5.50000	−	4.33013i	0.453632	−	0.357143i
$148$		0			0
$149$	−4.00000	+	6.92820i	−0.327693	+	0.567581i	−0.982054	−	0.188602i	$-0.939604\pi$
$149$	−4.00000	+	6.92820i	−0.327693	+	0.567581i	0.654361	+	0.756182i	$0.272938\pi$
$150$		0			0
$151$	−3.50000	−	6.06218i	−0.284826	−	0.493333i	0.687741	−	0.725956i	$-0.258602\pi$
$151$	−3.50000	−	6.06218i	−0.284826	−	0.493333i	−0.972567	+	0.232623i	$0.925269\pi$
$152$		0			0
$153$	2.00000			0.161690
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−1.50000	−	2.59808i	−0.119713	−	0.207349i	0.799941	−	0.600079i	$-0.204864\pi$
$157$	−1.50000	−	2.59808i	−0.119713	−	0.207349i	−0.919654	+	0.392730i	$0.871531\pi$
$158$		0			0
$159$	−1.00000	+	1.73205i	−0.0793052	+	0.137361i
$160$		0			0
$161$	20.0000	−	6.92820i	1.57622	−	0.546019i
$162$		0			0
$163$	0.500000	−	0.866025i	0.0391630	−	0.0678323i	−0.845780	−	0.533533i	$-0.820864\pi$
$163$	0.500000	−	0.866025i	0.0391630	−	0.0678323i	0.884943	+	0.465700i	$0.154198\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−8.00000			−0.619059			−0.309529	−	0.950890i	$-0.600171\pi$
$167$	−8.00000			−0.619059			−0.309529	+	0.950890i	$0.600171\pi$
$168$		0			0
$169$	−9.00000			−0.692308
$170$		0			0
$171$	−2.00000	−	3.46410i	−0.152944	−	0.264906i
$172$		0			0
$173$	3.00000	−	5.19615i	0.228086	−	0.395056i	−0.729155	−	0.684349i	$-0.760087\pi$
$173$	3.00000	−	5.19615i	0.228086	−	0.395056i	0.957241	+	0.289292i	$0.0934200\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	3.00000	−	5.19615i	0.225494	−	0.390567i
$178$		0			0
$179$	−8.00000	−	13.8564i	−0.597948	−	1.03568i	−0.993124	−	0.117071i	$-0.962650\pi$
$179$	−8.00000	−	13.8564i	−0.597948	−	1.03568i	0.395175	−	0.918606i	$-0.370684\pi$
$180$		0			0
$181$	−15.0000			−1.11494			−0.557471	−	0.830197i	$-0.688228\pi$
$181$	−15.0000			−1.11494			−0.557471	+	0.830197i	$0.688228\pi$
$182$		0			0
$183$	−1.00000			−0.0739221
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−2.00000	+	3.46410i	−0.146254	+	0.253320i
$188$		0			0
$189$	2.00000	+	1.73205i	0.145479	+	0.125988i
$190$		0			0
$191$	2.00000	−	3.46410i	0.144715	−	0.250654i	−0.784552	−	0.620063i	$-0.787107\pi$
$191$	2.00000	−	3.46410i	0.144715	−	0.250654i	0.929267	+	0.369410i	$0.120440\pi$
$192$		0			0
$193$	0.500000	+	0.866025i	0.0359908	+	0.0623379i	0.883460	−	0.468507i	$-0.155208\pi$
$193$	0.500000	+	0.866025i	0.0359908	+	0.0623379i	−0.847469	+	0.530845i	$0.821875\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−18.0000			−1.28245			−0.641223	−	0.767354i	$-0.721573\pi$
$197$	−18.0000			−1.28245			−0.641223	+	0.767354i	$0.721573\pi$
$198$		0			0
$199$	−1.50000	−	2.59808i	−0.106332	−	0.184173i	0.807950	−	0.589252i	$-0.200577\pi$
$199$	−1.50000	−	2.59808i	−0.106332	−	0.184173i	−0.914282	+	0.405079i	$0.867244\pi$
$200$		0			0
$201$	−6.00000	+	10.3923i	−0.423207	+	0.733017i
$202$		0			0
$203$	8.00000	+	6.92820i	0.561490	+	0.486265i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	4.00000	+	6.92820i	0.278019	+	0.481543i
$208$		0			0
$209$	8.00000			0.553372
$210$		0			0
$211$	−9.00000			−0.619586			−0.309793	−	0.950804i	$-0.600260\pi$
$211$	−9.00000			−0.619586			−0.309793	+	0.950804i	$0.600260\pi$
$212$		0			0
$213$	−5.00000	−	8.66025i	−0.342594	−	0.593391i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	1.50000	−	7.79423i	0.101827	−	0.529107i
$218$		0			0
$219$	−0.500000	+	0.866025i	−0.0337869	+	0.0585206i
$220$		0			0
$221$	2.00000	+	3.46410i	0.134535	+	0.233021i
$222$		0			0
$223$	17.0000			1.13840			0.569202	−	0.822198i	$-0.307252\pi$
$223$	17.0000			1.13840			0.569202	+	0.822198i	$0.307252\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	1.00000	+	1.73205i	0.0663723	+	0.114960i	0.897302	−	0.441417i	$-0.145524\pi$
$227$	1.00000	+	1.73205i	0.0663723	+	0.114960i	−0.830930	+	0.556378i	$0.812191\pi$
$228$		0			0
$229$	−13.0000	+	22.5167i	−0.859064	+	1.48794i	0.0137585	+	0.999905i	$0.495620\pi$
$229$	−13.0000	+	22.5167i	−0.859064	+	1.48794i	−0.872823	+	0.488037i	$0.837713\pi$
$230$		0			0
$231$	−5.00000	+	1.73205i	−0.328976	+	0.113961i
$232$		0			0
$233$	2.00000	−	3.46410i	0.131024	−	0.226941i	−0.793047	−	0.609160i	$-0.791507\pi$
$233$	2.00000	−	3.46410i	0.131024	−	0.226941i	0.924072	+	0.382219i	$0.124840\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	7.00000			0.454699
$238$		0			0
$239$	18.0000			1.16432			0.582162	−	0.813073i	$-0.302207\pi$
$239$	18.0000			1.16432			0.582162	+	0.813073i	$0.302207\pi$
$240$		0			0
$241$	5.50000	+	9.52628i	0.354286	+	0.613642i	0.986996	−	0.160748i	$-0.0513906\pi$
$241$	5.50000	+	9.52628i	0.354286	+	0.613642i	−0.632709	+	0.774389i	$0.718057\pi$
$242$		0			0
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	4.00000	−	6.92820i	0.254514	−	0.440831i
$248$		0			0
$249$	−9.00000	−	15.5885i	−0.570352	−	0.987878i
$250$		0			0
$251$		0			0			−	1.00000i	$-0.5\pi$
$251$		0			0				1.00000i	$0.5\pi$
$252$		0			0
$253$	−16.0000			−1.00591
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−11.0000	+	19.0526i	−0.686161	+	1.18847i	0.286909	+	0.957958i	$0.407372\pi$
$257$	−11.0000	+	19.0526i	−0.686161	+	1.18847i	−0.973070	+	0.230508i	$0.925961\pi$
$258$		0			0
$259$	22.5000	−	7.79423i	1.39808	−	0.484310i
$260$		0			0
$261$	−2.00000	+	3.46410i	−0.123797	+	0.214423i
$262$		0			0
$263$	11.0000	+	19.0526i	0.678289	+	1.17483i	0.975496	+	0.220018i	$0.0706116\pi$
$263$	11.0000	+	19.0526i	0.678289	+	1.17483i	−0.297207	+	0.954813i	$0.596055\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	10.0000			0.611990
$268$		0			0
$269$	6.00000	+	10.3923i	0.365826	+	0.633630i	0.988908	−	0.148527i	$-0.0474530\pi$
$269$	6.00000	+	10.3923i	0.365826	+	0.633630i	−0.623082	+	0.782157i	$0.714120\pi$
$270$		0			0
$271$	−8.00000	+	13.8564i	−0.485965	+	0.841717i	−0.999870	−	0.0161307i	$-0.994865\pi$
$271$	−8.00000	+	13.8564i	−0.485965	+	0.841717i	0.513905	+	0.857847i	$0.328199\pi$
$272$		0			0
$273$	−1.00000	+	5.19615i	−0.0605228	+	0.314485i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	1.00000	+	1.73205i	0.0600842	+	0.104069i	0.894503	−	0.447062i	$-0.147530\pi$
$277$	1.00000	+	1.73205i	0.0600842	+	0.104069i	−0.834419	+	0.551131i	$0.814196\pi$
$278$		0			0
$279$	3.00000			0.179605
$280$		0			0
$281$	30.0000			1.78965			0.894825	−	0.446417i	$-0.147300\pi$
$281$	30.0000			1.78965			0.894825	+	0.446417i	$0.147300\pi$
$282$		0			0
$283$	−8.00000	−	13.8564i	−0.475551	−	0.823678i	0.524057	−	0.851683i	$-0.324418\pi$
$283$	−8.00000	−	13.8564i	−0.475551	−	0.823678i	−0.999608	+	0.0280052i	$0.991084\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	12.0000	+	10.3923i	0.708338	+	0.613438i
$288$		0			0
$289$	6.50000	−	11.2583i	0.382353	−	0.662255i
$290$		0			0
$291$	−2.50000	−	4.33013i	−0.146553	−	0.253837i
$292$		0			0
$293$	−6.00000			−0.350524			−0.175262	−	0.984522i	$-0.556077\pi$
$293$	−6.00000			−0.350524			−0.175262	+	0.984522i	$0.556077\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−1.00000	−	1.73205i	−0.0580259	−	0.100504i
$298$		0			0
$299$	−8.00000	+	13.8564i	−0.462652	+	0.801337i
$300$		0			0
$301$	−2.00000	−	1.73205i	−0.115278	−	0.0998337i
$302$		0			0
$303$		0			0
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−7.00000			−0.399511			−0.199756	−	0.979846i	$-0.564015\pi$
$307$	−7.00000			−0.399511			−0.199756	+	0.979846i	$0.564015\pi$
$308$		0			0
$309$	−11.0000			−0.625768
$310$		0			0
$311$	16.0000	+	27.7128i	0.907277	+	1.57145i	0.817832	+	0.575458i	$0.195176\pi$
$311$	16.0000	+	27.7128i	0.907277	+	1.57145i	0.0894452	+	0.995992i	$0.471491\pi$
$312$		0			0
$313$	−13.5000	+	23.3827i	−0.763065	+	1.32167i	0.178198	+	0.983995i	$0.442973\pi$
$313$	−13.5000	+	23.3827i	−0.763065	+	1.32167i	−0.941263	+	0.337673i	$0.890360\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−17.0000	+	29.4449i	−0.954815	+	1.65379i	−0.220024	+	0.975494i	$0.570614\pi$
$317$	−17.0000	+	29.4449i	−0.954815	+	1.65379i	−0.734791	+	0.678294i	$0.762720\pi$
$318$		0			0
$319$	−4.00000	−	6.92820i	−0.223957	−	0.387905i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	8.00000			0.445132
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−7.00000	+	12.1244i	−0.387101	+	0.670478i
$328$		0			0
$329$	15.0000	−	5.19615i	0.826977	−	0.286473i
$330$		0			0
$331$	−13.5000	+	23.3827i	−0.742027	+	1.28523i	0.209544	+	0.977799i	$0.432802\pi$
$331$	−13.5000	+	23.3827i	−0.742027	+	1.28523i	−0.951571	+	0.307429i	$0.900531\pi$
$332$		0			0
$333$	4.50000	+	7.79423i	0.246598	+	0.427121i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	9.00000			0.490261			0.245131	−	0.969490i	$-0.421169\pi$
$337$	9.00000			0.490261			0.245131	+	0.969490i	$0.421169\pi$
$338$		0			0
$339$	3.00000	+	5.19615i	0.162938	+	0.282216i
$340$		0			0
$341$	−3.00000	+	5.19615i	−0.162459	+	0.281387i
$342$		0			0
$343$	−10.0000	+	15.5885i	−0.539949	+	0.841698i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−13.0000	−	22.5167i	−0.697877	−	1.20876i	−0.969201	−	0.246270i	$-0.920795\pi$
$347$	−13.0000	−	22.5167i	−0.697877	−	1.20876i	0.271325	−	0.962488i	$-0.412538\pi$
$348$		0			0
$349$	−34.0000			−1.81998			−0.909989	−	0.414632i	$-0.863910\pi$
$349$	−34.0000			−1.81998			−0.909989	+	0.414632i	$0.863910\pi$
$350$		0			0
$351$	−2.00000			−0.106752
$352$		0			0
$353$	−8.00000	−	13.8564i	−0.425797	−	0.737502i	0.570697	−	0.821160i	$-0.306673\pi$
$353$	−8.00000	−	13.8564i	−0.425797	−	0.737502i	−0.996495	+	0.0836583i	$0.973340\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−5.00000	+	1.73205i	−0.264628	+	0.0916698i
$358$		0			0
$359$	15.0000	−	25.9808i	0.791670	−	1.37121i	−0.133263	−	0.991081i	$-0.542545\pi$
$359$	15.0000	−	25.9808i	0.791670	−	1.37121i	0.924932	−	0.380131i	$-0.124121\pi$
$360$		0			0
$361$	1.50000	+	2.59808i	0.0789474	+	0.136741i
$362$		0			0
$363$	−7.00000			−0.367405
$364$		0			0
$365$		0			0
$366$		0			0
$367$	17.5000	+	30.3109i	0.913493	+	1.58222i	0.809093	+	0.587680i	$0.199959\pi$
$367$	17.5000	+	30.3109i	0.913493	+	1.58222i	0.104399	+	0.994535i	$0.466708\pi$
$368$		0			0
$369$	−3.00000	+	5.19615i	−0.156174	+	0.270501i
$370$		0			0
$371$	1.00000	−	5.19615i	0.0519174	−	0.269771i
$372$		0			0
$373$	5.00000	−	8.66025i	0.258890	−	0.448411i	−0.707055	−	0.707159i	$-0.749977\pi$
$373$	5.00000	−	8.66025i	0.258890	−	0.448411i	0.965945	+	0.258748i	$0.0833099\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−8.00000			−0.412021
$378$		0			0
$379$	28.0000			1.43826			0.719132	−	0.694874i	$-0.244540\pi$
$379$	28.0000			1.43826			0.719132	+	0.694874i	$0.244540\pi$
$380$		0			0
$381$	−8.50000	−	14.7224i	−0.435468	−	0.754253i
$382$		0			0
$383$	16.0000	−	27.7128i	0.817562	−	1.41606i	−0.0899119	−	0.995950i	$-0.528659\pi$
$383$	16.0000	−	27.7128i	0.817562	−	1.41606i	0.907474	−	0.420109i	$-0.138008\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	0.500000	−	0.866025i	0.0254164	−	0.0440225i
$388$		0			0
$389$	−5.00000	−	8.66025i	−0.253510	−	0.439092i	0.710980	−	0.703213i	$-0.248252\pi$
$389$	−5.00000	−	8.66025i	−0.253510	−	0.439092i	−0.964490	+	0.264120i	$0.914918\pi$
$390$		0			0
$391$	−16.0000			−0.809155
$392$		0			0
$393$	−22.0000			−1.10975
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−13.5000	+	23.3827i	−0.677546	+	1.17354i	0.298172	+	0.954512i	$0.403623\pi$
$397$	−13.5000	+	23.3827i	−0.677546	+	1.17354i	−0.975718	+	0.219031i	$0.929710\pi$
$398$		0			0
$399$	8.00000	+	6.92820i	0.400501	+	0.346844i
$400$		0			0
$401$	1.00000	−	1.73205i	0.0499376	−	0.0864945i	−0.839976	−	0.542623i	$-0.817431\pi$
$401$	1.00000	−	1.73205i	0.0499376	−	0.0864945i	0.889914	+	0.456129i	$0.150764\pi$
$402$		0			0
$403$	3.00000	+	5.19615i	0.149441	+	0.258839i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−18.0000			−0.892227
$408$		0			0
$409$	7.00000	+	12.1244i	0.346128	+	0.599511i	0.985558	−	0.169338i	$-0.0541630\pi$
$409$	7.00000	+	12.1244i	0.346128	+	0.599511i	−0.639430	+	0.768849i	$0.720830\pi$
$410$		0			0
$411$	−8.00000	+	13.8564i	−0.394611	+	0.683486i
$412$		0			0
$413$	−3.00000	+	15.5885i	−0.147620	+	0.767058i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−2.50000	−	4.33013i	−0.122426	−	0.212047i
$418$		0			0
$419$	8.00000			0.390826			0.195413	−	0.980721i	$-0.437395\pi$
$419$	8.00000			0.390826			0.195413	+	0.980721i	$0.437395\pi$
$420$		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
$423$	3.00000	+	5.19615i	0.145865	+	0.252646i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	2.50000	−	0.866025i	0.120983	−	0.0419099i
$428$		0			0
$429$	2.00000	−	3.46410i	0.0965609	−	0.167248i
$430$		0			0
$431$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$431$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$432$		0			0
$433$	−5.00000			−0.240285			−0.120142	−	0.992757i	$-0.538335\pi$
$433$	−5.00000			−0.240285			−0.120142	+	0.992757i	$0.538335\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	16.0000	+	27.7128i	0.765384	+	1.32568i
$438$		0			0
$439$	5.50000	−	9.52628i	0.262501	−	0.454665i	−0.704405	−	0.709798i	$-0.748786\pi$
$439$	5.50000	−	9.52628i	0.262501	−	0.454665i	0.966906	+	0.255134i	$0.0821195\pi$
$440$		0			0
$441$	−6.50000	−	2.59808i	−0.309524	−	0.123718i
$442$		0			0
$443$	3.00000	−	5.19615i	0.142534	−	0.246877i	−0.785916	−	0.618333i	$-0.787808\pi$
$443$	3.00000	−	5.19615i	0.142534	−	0.246877i	0.928450	+	0.371457i	$0.121142\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	8.00000			0.378387
$448$		0			0
$449$	32.0000			1.51017			0.755087	−	0.655625i	$-0.227595\pi$
$449$	32.0000			1.51017			0.755087	+	0.655625i	$0.227595\pi$
$450$		0			0
$451$	−6.00000	−	10.3923i	−0.282529	−	0.489355i
$452$		0			0
$453$	−3.50000	+	6.06218i	−0.164444	+	0.284826i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−18.5000	+	32.0429i	−0.865393	+	1.49891i	0.00126243	+	0.999999i	$0.499598\pi$
$457$	−18.5000	+	32.0429i	−0.865393	+	1.49891i	−0.866656	+	0.498906i	$0.833735\pi$
$458$		0			0
$459$	−1.00000	−	1.73205i	−0.0466760	−	0.0808452i
$460$		0			0
$461$	14.0000			0.652045			0.326023	−	0.945362i	$-0.394291\pi$
$461$	14.0000			0.652045			0.326023	+	0.945362i	$0.394291\pi$
$462$		0			0
$463$	−9.00000			−0.418265			−0.209133	−	0.977887i	$-0.567064\pi$
$463$	−9.00000			−0.418265			−0.209133	+	0.977887i	$0.567064\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−3.00000	+	5.19615i	−0.138823	+	0.240449i	−0.927052	−	0.374934i	$-0.877665\pi$
$467$	−3.00000	+	5.19615i	−0.138823	+	0.240449i	0.788228	+	0.615383i	$0.210999\pi$
$468$		0			0
$469$	6.00000	−	31.1769i	0.277054	−	1.43962i
$470$		0			0
$471$	−1.50000	+	2.59808i	−0.0691164	+	0.119713i
$472$		0			0
$473$	1.00000	+	1.73205i	0.0459800	+	0.0796398i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	2.00000			0.0915737
$478$		0			0
$479$	−16.0000	−	27.7128i	−0.731059	−	1.26623i	−0.956431	−	0.291958i	$-0.905693\pi$
$479$	−16.0000	−	27.7128i	−0.731059	−	1.26623i	0.225372	−	0.974273i	$-0.427640\pi$
$480$		0			0
$481$	−9.00000	+	15.5885i	−0.410365	+	0.710772i
$482$		0			0
$483$	−16.0000	−	13.8564i	−0.728025	−	0.630488i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	5.50000	+	9.52628i	0.249229	+	0.431677i	0.963312	−	0.268384i	$-0.0864896\pi$
$487$	5.50000	+	9.52628i	0.249229	+	0.431677i	−0.714083	+	0.700061i	$0.753156\pi$
$488$		0			0
$489$	−1.00000			−0.0452216
$490$		0			0
$491$	−36.0000			−1.62466			−0.812329	−	0.583200i	$-0.801800\pi$
$491$	−36.0000			−1.62466			−0.812329	+	0.583200i	$0.801800\pi$
$492$		0			0
$493$	−4.00000	−	6.92820i	−0.180151	−	0.312031i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	20.0000	+	17.3205i	0.897123	+	0.776931i
$498$		0			0
$499$	−18.0000	+	31.1769i	−0.805791	+	1.39567i	0.109965	+	0.993935i	$0.464926\pi$
$499$	−18.0000	+	31.1769i	−0.805791	+	1.39567i	−0.915756	+	0.401735i	$0.868407\pi$
$500$		0			0
$501$	4.00000	+	6.92820i	0.178707	+	0.309529i
$502$		0			0
$503$	40.0000			1.78351			0.891756	−	0.452517i	$-0.149474\pi$
$503$	40.0000			1.78351			0.891756	+	0.452517i	$0.149474\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	4.50000	+	7.79423i	0.199852	+	0.346154i
$508$		0			0
$509$	−9.00000	+	15.5885i	−0.398918	+	0.690946i	−0.993593	−	0.113020i	$-0.963948\pi$
$509$	−9.00000	+	15.5885i	−0.398918	+	0.690946i	0.594675	+	0.803966i	$0.297281\pi$
$510$		0			0
$511$	0.500000	−	2.59808i	0.0221187	−	0.114932i
$512$		0			0
$513$	−2.00000	+	3.46410i	−0.0883022	+	0.152944i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−12.0000			−0.527759
$518$		0			0
$519$	−6.00000			−0.263371
$520$		0			0
$521$	3.00000	+	5.19615i	0.131432	+	0.227648i	0.924229	−	0.381839i	$-0.124709\pi$
$521$	3.00000	+	5.19615i	0.131432	+	0.227648i	−0.792797	+	0.609486i	$0.791376\pi$
$522$		0			0
$523$	−0.500000	+	0.866025i	−0.0218635	+	0.0378686i	−0.876750	−	0.480946i	$-0.840293\pi$
$523$	−0.500000	+	0.866025i	−0.0218635	+	0.0378686i	0.854887	+	0.518815i	$0.173627\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−3.00000	+	5.19615i	−0.130682	+	0.226348i
$528$		0			0
$529$	−20.5000	−	35.5070i	−0.891304	−	1.54378i
$530$		0			0
$531$	−6.00000			−0.260378
$532$		0			0
$533$	−12.0000			−0.519778
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−8.00000	+	13.8564i	−0.345225	+	0.597948i
$538$		0			0
$539$	11.0000	−	8.66025i	0.473804	−	0.373024i
$540$		0			0
$541$	5.00000	−	8.66025i	0.214967	−	0.372333i	−0.738296	−	0.674477i	$-0.764369\pi$
$541$	5.00000	−	8.66025i	0.214967	−	0.372333i	0.953262	+	0.302144i	$0.0977023\pi$
$542$		0			0
$543$	7.50000	+	12.9904i	0.321856	+	0.557471i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	12.0000			0.513083			0.256541	−	0.966533i	$-0.417417\pi$
$547$	12.0000			0.513083			0.256541	+	0.966533i	$0.417417\pi$
$548$		0			0
$549$	0.500000	+	0.866025i	0.0213395	+	0.0369611i
$550$		0			0
$551$	−8.00000	+	13.8564i	−0.340811	+	0.590303i
$552$		0			0
$553$	−17.5000	+	6.06218i	−0.744176	+	0.257790i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−9.00000	−	15.5885i	−0.381342	−	0.660504i	0.609912	−	0.792469i	$-0.291205\pi$
$557$	−9.00000	−	15.5885i	−0.381342	−	0.660504i	−0.991254	+	0.131965i	$0.957871\pi$
$558$		0			0
$559$	2.00000			0.0845910
$560$		0			0
$561$	4.00000			0.168880
$562$		0			0
$563$	17.0000	+	29.4449i	0.716465	+	1.24095i	0.962392	+	0.271665i	$0.0875742\pi$
$563$	17.0000	+	29.4449i	0.716465	+	1.24095i	−0.245927	+	0.969288i	$0.579092\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	0.500000	−	2.59808i	0.0209980	−	0.109109i
$568$		0			0
$569$	2.00000	−	3.46410i	0.0838444	−	0.145223i	−0.821054	−	0.570851i	$-0.806613\pi$
$569$	2.00000	−	3.46410i	0.0838444	−	0.145223i	0.904898	+	0.425628i	$0.139947\pi$
$570$		0			0
$571$	−2.00000	−	3.46410i	−0.0836974	−	0.144968i	0.821138	−	0.570730i	$-0.193340\pi$
$571$	−2.00000	−	3.46410i	−0.0836974	−	0.144968i	−0.904835	+	0.425762i	$0.860006\pi$
$572$		0			0
$573$	−4.00000			−0.167102
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−15.5000	−	26.8468i	−0.645273	−	1.11765i	−0.984238	−	0.176847i	$-0.943410\pi$
$577$	−15.5000	−	26.8468i	−0.645273	−	1.11765i	0.338965	−	0.940799i	$-0.389923\pi$
$578$		0			0
$579$	0.500000	−	0.866025i	0.0207793	−	0.0359908i
$580$		0			0
$581$	36.0000	+	31.1769i	1.49353	+	1.29344i
$582$		0			0
$583$	−2.00000	+	3.46410i	−0.0828315	+	0.143468i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−42.0000			−1.73353			−0.866763	−	0.498721i	$-0.833803\pi$
$587$	−42.0000			−1.73353			−0.866763	+	0.498721i	$0.833803\pi$
$588$		0			0
$589$	12.0000			0.494451
$590$		0			0
$591$	9.00000	+	15.5885i	0.370211	+	0.641223i
$592$		0			0
$593$	12.0000	−	20.7846i	0.492781	−	0.853522i	−0.507184	−	0.861838i	$-0.669314\pi$
$593$	12.0000	−	20.7846i	0.492781	−	0.853522i	0.999965	+	0.00831589i	$0.00264706\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−1.50000	+	2.59808i	−0.0613909	+	0.106332i
$598$		0			0
$599$	−24.0000	−	41.5692i	−0.980613	−	1.69847i	−0.660006	−	0.751260i	$-0.729446\pi$
$599$	−24.0000	−	41.5692i	−0.980613	−	1.69847i	−0.320607	−	0.947212i	$-0.603887\pi$
$600$		0			0
$601$	−26.0000			−1.06056			−0.530281	−	0.847822i	$-0.677914\pi$
$601$	−26.0000			−1.06056			−0.530281	+	0.847822i	$0.677914\pi$
$602$		0			0
$603$	12.0000			0.488678
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−21.5000	+	37.2391i	−0.872658	+	1.51149i	−0.0134214	+	0.999910i	$0.504272\pi$
$607$	−21.5000	+	37.2391i	−0.872658	+	1.51149i	−0.859237	+	0.511578i	$0.829061\pi$
$608$		0			0
$609$	2.00000	−	10.3923i	0.0810441	−	0.421117i
$610$		0			0
$611$	−6.00000	+	10.3923i	−0.242734	+	0.420428i
$612$		0			0
$613$	15.0000	+	25.9808i	0.605844	+	1.04935i	0.991917	+	0.126885i	$0.0404979\pi$
$613$	15.0000	+	25.9808i	0.605844	+	1.04935i	−0.386073	+	0.922468i	$0.626169\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	14.0000			0.563619			0.281809	−	0.959470i	$-0.409065\pi$
$617$	14.0000			0.563619			0.281809	+	0.959470i	$0.409065\pi$
$618$		0			0
$619$	15.5000	+	26.8468i	0.622998	+	1.07906i	0.988924	+	0.148420i	$0.0474187\pi$
$619$	15.5000	+	26.8468i	0.622998	+	1.07906i	−0.365927	+	0.930644i	$0.619248\pi$
$620$		0			0
$621$	4.00000	−	6.92820i	0.160514	−	0.278019i
$622$		0			0
$623$	−25.0000	+	8.66025i	−1.00160	+	0.346966i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−4.00000	−	6.92820i	−0.159745	−	0.276686i
$628$		0			0
$629$	−18.0000			−0.717707
$630$		0			0
$631$	29.0000			1.15447			0.577236	−	0.816577i	$-0.304131\pi$
$631$	29.0000			1.15447			0.577236	+	0.816577i	$0.304131\pi$
$632$		0			0
$633$	4.50000	+	7.79423i	0.178859	+	0.309793i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−2.00000	−	13.8564i	−0.0792429	−	0.549011i
$638$		0			0
$639$	−5.00000	+	8.66025i	−0.197797	+	0.342594i
$640$		0			0
$641$	−5.00000	−	8.66025i	−0.197488	−	0.342059i	0.750225	−	0.661182i	$-0.229945\pi$
$641$	−5.00000	−	8.66025i	−0.197488	−	0.342059i	−0.947713	+	0.319123i	$0.896612\pi$
$642$		0			0
$643$	5.00000			0.197181			0.0985904	−	0.995128i	$-0.468567\pi$
$643$	5.00000			0.197181			0.0985904	+	0.995128i	$0.468567\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	3.00000	+	5.19615i	0.117942	+	0.204282i	0.918952	−	0.394369i	$-0.129037\pi$
$647$	3.00000	+	5.19615i	0.117942	+	0.204282i	−0.801010	+	0.598651i	$0.795704\pi$
$648$		0			0
$649$	6.00000	−	10.3923i	0.235521	−	0.407934i
$650$		0			0
$651$	−7.50000	+	2.59808i	−0.293948	+	0.101827i
$652$		0			0
$653$	−13.0000	+	22.5167i	−0.508729	+	0.881145i	0.491220	+	0.871036i	$0.336551\pi$
$653$	−13.0000	+	22.5167i	−0.508729	+	0.881145i	−0.999949	+	0.0101092i	$0.996782\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	1.00000			0.0390137
$658$		0			0
$659$	42.0000			1.63609			0.818044	−	0.575156i	$-0.195059\pi$
$659$	42.0000			1.63609			0.818044	+	0.575156i	$0.195059\pi$
$660$		0			0
$661$	−5.50000	−	9.52628i	−0.213925	−	0.370529i	0.739014	−	0.673690i	$-0.235292\pi$
$661$	−5.50000	−	9.52628i	−0.213925	−	0.370529i	−0.952940	+	0.303160i	$0.901958\pi$
$662$		0			0
$663$	2.00000	−	3.46410i	0.0776736	−	0.134535i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	16.0000	−	27.7128i	0.619522	−	1.07304i
$668$		0			0
$669$	−8.50000	−	14.7224i	−0.328629	−	0.569202i
$670$		0			0
$671$	−2.00000			−0.0772091
$672$		0			0
$673$	−9.00000			−0.346925			−0.173462	−	0.984841i	$-0.555495\pi$
$673$	−9.00000			−0.346925			−0.173462	+	0.984841i	$0.555495\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	16.0000	−	27.7128i	0.614930	−	1.06509i	−0.375467	−	0.926836i	$-0.622518\pi$
$677$	16.0000	−	27.7128i	0.614930	−	1.06509i	0.990397	−	0.138254i	$-0.0441491\pi$
$678$		0			0
$679$	10.0000	+	8.66025i	0.383765	+	0.332350i
$680$		0			0
$681$	1.00000	−	1.73205i	0.0383201	−	0.0663723i
$682$		0			0
$683$	3.00000	+	5.19615i	0.114792	+	0.198825i	0.917697	−	0.397282i	$-0.130047\pi$
$683$	3.00000	+	5.19615i	0.114792	+	0.198825i	−0.802905	+	0.596107i	$0.796713\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	26.0000			0.991962
$688$		0			0
$689$	2.00000	+	3.46410i	0.0761939	+	0.131972i
$690$		0			0
$691$	−13.5000	+	23.3827i	−0.513564	+	0.889519i	0.486312	+	0.873785i	$0.338342\pi$
$691$	−13.5000	+	23.3827i	−0.513564	+	0.889519i	−0.999876	+	0.0157341i	$0.994991\pi$
$692$		0			0
$693$	4.00000	+	3.46410i	0.151947	+	0.131590i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−6.00000	−	10.3923i	−0.227266	−	0.393637i
$698$		0			0
$699$	−4.00000			−0.151294
$700$		0			0
$701$	−18.0000			−0.679851			−0.339925	−	0.940452i	$-0.610402\pi$
$701$	−18.0000			−0.679851			−0.339925	+	0.940452i	$0.610402\pi$
$702$		0			0
$703$	18.0000	+	31.1769i	0.678883	+	1.17586i
$704$		0			0
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	5.50000	−	9.52628i	0.206557	−	0.357767i	−0.744071	−	0.668101i	$-0.767108\pi$
$709$	5.50000	−	9.52628i	0.206557	−	0.357767i	0.950628	+	0.310334i	$0.100441\pi$
$710$		0			0
$711$	−3.50000	−	6.06218i	−0.131260	−	0.227349i
$712$		0			0
$713$	−24.0000			−0.898807
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−9.00000	−	15.5885i	−0.336111	−	0.582162i
$718$		0			0
$719$	−22.0000	+	38.1051i	−0.820462	+	1.42108i	0.0848774	+	0.996391i	$0.472950\pi$
$719$	−22.0000	+	38.1051i	−0.820462	+	1.42108i	−0.905339	+	0.424690i	$0.860383\pi$
$720$		0			0
$721$	27.5000	−	9.52628i	1.02415	−	0.354777i
$722$		0			0
$723$	5.50000	−	9.52628i	0.204547	−	0.354286i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	8.00000			0.296704			0.148352	−	0.988935i	$-0.452603\pi$
$727$	8.00000			0.296704			0.148352	+	0.988935i	$0.452603\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	1.00000	+	1.73205i	0.0369863	+	0.0640622i
$732$		0			0
$733$	17.5000	−	30.3109i	0.646377	−	1.11956i	−0.337604	−	0.941288i	$-0.609617\pi$
$733$	17.5000	−	30.3109i	0.646377	−	1.11956i	0.983982	−	0.178270i	$-0.0570501\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−12.0000	+	20.7846i	−0.442026	+	0.765611i
$738$		0			0
$739$	−20.5000	−	35.5070i	−0.754105	−	1.30615i	−0.945818	−	0.324697i	$-0.894738\pi$
$739$	−20.5000	−	35.5070i	−0.754105	−	1.30615i	0.191714	−	0.981451i	$-0.438596\pi$
$740$		0			0
$741$	−8.00000			−0.293887
$742$		0			0
$743$	−12.0000			−0.440237			−0.220119	−	0.975473i	$-0.570644\pi$
$743$	−12.0000			−0.440237			−0.220119	+	0.975473i	$0.570644\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−9.00000	+	15.5885i	−0.329293	+	0.570352i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−12.5000	+	21.6506i	−0.456131	+	0.790043i	−0.998752	−	0.0499348i	$-0.984099\pi$
$751$	−12.5000	+	21.6506i	−0.456131	+	0.790043i	0.542621	+	0.839978i	$0.317432\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$	13.0000			0.472493			0.236247	−	0.971693i	$-0.424083\pi$
$757$	13.0000			0.472493			0.236247	+	0.971693i	$0.424083\pi$
$758$		0			0
$759$	8.00000	+	13.8564i	0.290382	+	0.502956i
$760$		0			0
$761$	16.0000	−	27.7128i	0.580000	−	1.00459i	−0.415479	−	0.909603i	$-0.636386\pi$
$761$	16.0000	−	27.7128i	0.580000	−	1.00459i	0.995479	−	0.0949859i	$-0.0302806\pi$
$762$		0			0
$763$	7.00000	−	36.3731i	0.253417	−	1.31679i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−6.00000	−	10.3923i	−0.216647	−	0.375244i
$768$		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
$771$	22.0000			0.792311
$772$		0			0
$773$	−14.0000	−	24.2487i	−0.503545	−	0.872166i	−0.999992	−	0.00409826i	$-0.998695\pi$
$773$	−14.0000	−	24.2487i	−0.503545	−	0.872166i	0.496447	−	0.868067i	$-0.334638\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−18.0000	−	15.5885i	−0.645746	−	0.559233i
$778$		0			0
$779$	−12.0000	+	20.7846i	−0.429945	+	0.744686i
$780$		0			0
$781$	−10.0000	−	17.3205i	−0.357828	−	0.619777i
$782$		0			0
$783$	4.00000			0.142948
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−5.50000	−	9.52628i	−0.196054	−	0.339575i	0.751192	−	0.660084i	$-0.229479\pi$
$787$	−5.50000	−	9.52628i	−0.196054	−	0.339575i	−0.947245	+	0.320509i	$0.896146\pi$
$788$		0			0
$789$	11.0000	−	19.0526i	0.391610	−	0.678289i
$790$		0			0
$791$	−12.0000	−	10.3923i	−0.426671	−	0.369508i
$792$		0			0
$793$	−1.00000	+	1.73205i	−0.0355110	+	0.0615069i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−12.0000			−0.425062			−0.212531	−	0.977154i	$-0.568171\pi$
$797$	−12.0000			−0.425062			−0.212531	+	0.977154i	$0.568171\pi$
$798$		0			0
$799$	−12.0000			−0.424529
$800$		0			0
$801$	−5.00000	−	8.66025i	−0.176666	−	0.305995i
$802$		0			0
$803$	−1.00000	+	1.73205i	−0.0352892	+	0.0611227i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	6.00000	−	10.3923i	0.211210	−	0.365826i
$808$		0			0
$809$	14.0000	+	24.2487i	0.492214	+	0.852539i	0.999960	−	0.00896753i	$-0.00285449\pi$
$809$	14.0000	+	24.2487i	0.492214	+	0.852539i	−0.507746	+	0.861507i	$0.669521\pi$
$810$		0			0
$811$	43.0000			1.50993			0.754967	−	0.655763i	$-0.227653\pi$
$811$	43.0000			1.50993			0.754967	+	0.655763i	$0.227653\pi$
$812$		0			0
$813$	16.0000			0.561144
$814$		0			0
$815$		0			0
$816$		0			0
$817$	2.00000	−	3.46410i	0.0699711	−	0.121194i
$818$		0			0
$819$	5.00000	−	1.73205i	0.174714	−	0.0605228i
$820$		0			0
$821$	4.00000	−	6.92820i	0.139601	−	0.241796i	−0.787745	−	0.616002i	$-0.788751\pi$
$821$	4.00000	−	6.92820i	0.139601	−	0.241796i	0.927346	+	0.374206i	$0.122085\pi$
$822$		0			0
$823$	7.50000	+	12.9904i	0.261434	+	0.452816i	0.966623	−	0.256203i	$-0.0824714\pi$
$823$	7.50000	+	12.9904i	0.261434	+	0.452816i	−0.705190	+	0.709019i	$0.749138\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−14.0000			−0.486828			−0.243414	−	0.969923i	$-0.578267\pi$
$827$	−14.0000			−0.486828			−0.243414	+	0.969923i	$0.578267\pi$
$828$		0			0
$829$	−4.50000	−	7.79423i	−0.156291	−	0.270705i	0.777237	−	0.629208i	$-0.216621\pi$
$829$	−4.50000	−	7.79423i	−0.156291	−	0.270705i	−0.933529	+	0.358503i	$0.883287\pi$
$830$		0			0
$831$	1.00000	−	1.73205i	0.0346896	−	0.0600842i
$832$		0			0
$833$	11.0000	−	8.66025i	0.381127	−	0.300060i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−1.50000	−	2.59808i	−0.0518476	−	0.0898027i
$838$		0			0
$839$	−34.0000			−1.17381			−0.586905	−	0.809656i	$-0.699654\pi$
$839$	−34.0000			−1.17381			−0.586905	+	0.809656i	$0.699654\pi$
$840$		0			0
$841$	−13.0000			−0.448276
$842$		0			0
$843$	−15.0000	−	25.9808i	−0.516627	−	0.894825i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	17.5000	−	6.06218i	0.601307	−	0.208299i
$848$		0			0
$849$	−8.00000	+	13.8564i	−0.274559	+	0.475551i
$850$		0			0
$851$	−36.0000	−	62.3538i	−1.23406	−	2.13746i
$852$		0			0
$853$	7.00000			0.239675			0.119838	−	0.992793i	$-0.461763\pi$
$853$	7.00000			0.239675			0.119838	+	0.992793i	$0.461763\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	20.0000	+	34.6410i	0.683187	+	1.18331i	0.974003	+	0.226536i	$0.0727399\pi$
$857$	20.0000	+	34.6410i	0.683187	+	1.18331i	−0.290816	+	0.956779i	$0.593927\pi$
$858$		0			0
$859$	−14.0000	+	24.2487i	−0.477674	+	0.827355i	−0.999672	−	0.0255910i	$-0.991853\pi$
$859$	−14.0000	+	24.2487i	−0.477674	+	0.827355i	0.521999	+	0.852946i	$0.325187\pi$
$860$		0			0
$861$	3.00000	−	15.5885i	0.102240	−	0.531253i
$862$		0			0
$863$	−7.00000	+	12.1244i	−0.238283	+	0.412718i	−0.960222	−	0.279239i	$-0.909918\pi$
$863$	−7.00000	+	12.1244i	−0.238283	+	0.412718i	0.721939	+	0.691957i	$0.243251\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−13.0000			−0.441503
$868$		0			0
$869$	14.0000			0.474917
$870$		0			0
$871$	12.0000	+	20.7846i	0.406604	+	0.704260i
$872$		0			0
$873$	−2.50000	+	4.33013i	−0.0846122	+	0.146553i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−11.5000	+	19.9186i	−0.388327	+	0.672603i	−0.992225	−	0.124459i	$-0.960280\pi$
$877$	−11.5000	+	19.9186i	−0.388327	+	0.672603i	0.603897	+	0.797062i	$0.293614\pi$
$878$		0			0
$879$	3.00000	+	5.19615i	0.101187	+	0.175262i
$880$		0			0
$881$	−22.0000			−0.741199			−0.370599	−	0.928793i	$-0.620848\pi$
$881$	−22.0000			−0.741199			−0.370599	+	0.928793i	$0.620848\pi$
$882$		0			0
$883$	−4.00000			−0.134611			−0.0673054	−	0.997732i	$-0.521440\pi$
$883$	−4.00000			−0.134611			−0.0673054	+	0.997732i	$0.521440\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	17.0000	−	29.4449i	0.570804	−	0.988662i	−0.425679	−	0.904874i	$-0.639965\pi$
$887$	17.0000	−	29.4449i	0.570804	−	0.988662i	0.996484	−	0.0837878i	$-0.0267018\pi$
$888$		0			0
$889$	34.0000	+	29.4449i	1.14032	+	0.987549i
$890$		0			0
$891$	−1.00000	+	1.73205i	−0.0335013	+	0.0580259i
$892$		0			0
$893$	12.0000	+	20.7846i	0.401565	+	0.695530i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	16.0000			0.534224
$898$		0			0
$899$	−6.00000	−	10.3923i	−0.200111	−	0.346603i
$900$		0			0
$901$	−2.00000	+	3.46410i	−0.0666297	+	0.115406i
$902$		0			0
$903$	−0.500000	+	2.59808i	−0.0166390	+	0.0864586i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−9.50000	−	16.4545i	−0.315442	−	0.546362i	0.664089	−	0.747653i	$-0.268820\pi$
$907$	−9.50000	−	16.4545i	−0.315442	−	0.546362i	−0.979531	+	0.201291i	$0.935486\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	8.00000			0.265052			0.132526	−	0.991180i	$-0.457691\pi$
$911$	8.00000			0.265052			0.132526	+	0.991180i	$0.457691\pi$
$912$		0			0
$913$	−18.0000	−	31.1769i	−0.595713	−	1.03181i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	55.0000	−	19.0526i	1.81626	−	0.629171i
$918$		0			0
$919$	5.50000	−	9.52628i	0.181428	−	0.314243i	−0.760939	−	0.648824i	$-0.775261\pi$
$919$	5.50000	−	9.52628i	0.181428	−	0.314243i	0.942367	+	0.334581i	$0.108595\pi$
$920$		0			0
$921$	3.50000	+	6.06218i	0.115329	+	0.199756i
$922$		0			0
$923$	−20.0000			−0.658308
$924$		0			0
$925$		0			0
$926$		0			0
$927$	5.50000	+	9.52628i	0.180644	+	0.312884i
$928$		0			0
$929$	−23.0000	+	39.8372i	−0.754606	+	1.30702i	0.190965	+	0.981597i	$0.438838\pi$
$929$	−23.0000	+	39.8372i	−0.754606	+	1.30702i	−0.945570	+	0.325418i	$0.894495\pi$
$930$		0			0
$931$	−26.0000	−	10.3923i	−0.852116	−	0.340594i
$932$		0			0
$933$	16.0000	−	27.7128i	0.523816	−	0.907277i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	19.0000			0.620703			0.310351	−	0.950622i	$-0.399553\pi$
$937$	19.0000			0.620703			0.310351	+	0.950622i	$0.399553\pi$
$938$		0			0
$939$	27.0000			0.881112
$940$		0			0
$941$	9.00000	+	15.5885i	0.293392	+	0.508169i	0.974609	−	0.223912i	$-0.0718827\pi$
$941$	9.00000	+	15.5885i	0.293392	+	0.508169i	−0.681218	+	0.732081i	$0.738549\pi$
$942$		0			0
$943$	24.0000	−	41.5692i	0.781548	−	1.35368i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	25.0000	−	43.3013i	0.812391	−	1.40710i	−0.0987955	−	0.995108i	$-0.531499\pi$
$947$	25.0000	−	43.3013i	0.812391	−	1.40710i	0.911186	−	0.411994i	$-0.135168\pi$
$948$		0			0
$949$	1.00000	+	1.73205i	0.0324614	+	0.0562247i
$950$		0			0
$951$	34.0000			1.10253
$952$		0			0
$953$	−52.0000			−1.68445			−0.842223	−	0.539130i	$-0.818753\pi$
$953$	−52.0000			−1.68445			−0.842223	+	0.539130i	$0.818753\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−4.00000	+	6.92820i	−0.129302	+	0.223957i
$958$		0			0
$959$	8.00000	−	41.5692i	0.258333	−	1.34234i
$960$		0			0
$961$	11.0000	−	19.0526i	0.354839	−	0.614599i
$962$		0			0
$963$		0			0
$964$		0			0
$965$		0			0
$966$		0			0
$967$	31.0000			0.996893			0.498446	−	0.866921i	$-0.333904\pi$
$967$	31.0000			0.996893			0.498446	+	0.866921i	$0.333904\pi$
$968$		0			0
$969$	−4.00000	−	6.92820i	−0.128499	−	0.222566i
$970$		0			0
$971$	22.0000	−	38.1051i	0.706014	−	1.22285i	−0.260311	−	0.965525i	$-0.583825\pi$
$971$	22.0000	−	38.1051i	0.706014	−	1.22285i	0.966324	−	0.257327i	$-0.0828416\pi$
$972$		0			0
$973$	10.0000	+	8.66025i	0.320585	+	0.277635i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	6.00000	+	10.3923i	0.191957	+	0.332479i	0.945899	−	0.324462i	$-0.105183\pi$
$977$	6.00000	+	10.3923i	0.191957	+	0.332479i	−0.753942	+	0.656941i	$0.771850\pi$
$978$		0			0
$979$	20.0000			0.639203
$980$		0			0
$981$	14.0000			0.446986
$982$		0			0
$983$	9.00000	+	15.5885i	0.287055	+	0.497195i	0.973106	−	0.230360i	$-0.0739903\pi$
$983$	9.00000	+	15.5885i	0.287055	+	0.497195i	−0.686050	+	0.727554i	$0.740657\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−12.0000	−	10.3923i	−0.381964	−	0.330791i
$988$		0			0
$989$	−4.00000	+	6.92820i	−0.127193	+	0.220304i
$990$		0			0
$991$	−15.5000	−	26.8468i	−0.492374	−	0.852816i	0.507588	−	0.861600i	$-0.330537\pi$
$991$	−15.5000	−	26.8468i	−0.492374	−	0.852816i	−0.999961	+	0.00878379i	$0.997204\pi$
$992$		0			0
$993$	27.0000			0.856819
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−15.5000	−	26.8468i	−0.490890	−	0.850246i	0.509055	−	0.860734i	$-0.329995\pi$
$997$	−15.5000	−	26.8468i	−0.490890	−	0.850246i	−0.999945	+	0.0104877i	$0.996662\pi$
$998$		0			0
$999$	4.50000	−	7.79423i	0.142374	−	0.246598i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2100.2.q.c.1801.1	yes	2
5.2	odd	4		2100.2.bc.b.1549.1		4
5.3	odd	4		2100.2.bc.b.1549.2		4
5.4	even	2		2100.2.q.e.1801.1	yes	2
7.4	even	3	inner	2100.2.q.c.1201.1	✓	2
35.4	even	6		2100.2.q.e.1201.1	yes	2
35.18	odd	12		2100.2.bc.b.949.1		4
35.32	odd	12		2100.2.bc.b.949.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2100.2.q.c.1201.1	✓	2	7.4	even	3	inner
2100.2.q.c.1801.1	yes	2	1.1	even	1	trivial
2100.2.q.e.1201.1	yes	2	35.4	even	6
2100.2.q.e.1801.1	yes	2	5.4	even	2
2100.2.bc.b.949.1		4	35.18	odd	12
2100.2.bc.b.949.2		4	35.32	odd	12
2100.2.bc.b.1549.1		4	5.2	odd	4
2100.2.bc.b.1549.2		4	5.3	odd	4

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)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{3} +(2.00000 + 1.73205i) q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{3} +(2.00000 + 1.73205i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(-1.00000 - 1.73205i) q^{11} -2.00000 q^{13} +(-1.00000 - 1.73205i) q^{17} +(-2.00000 + 3.46410i) q^{19} +(0.500000 - 2.59808i) q^{21} +(4.00000 - 6.92820i) q^{23} +1.00000 q^{27} +4.00000 q^{29} +(-1.50000 - 2.59808i) q^{31} +(-1.00000 + 1.73205i) q^{33} +(4.50000 - 7.79423i) q^{37} +(1.00000 + 1.73205i) q^{39} +6.00000 q^{41} -1.00000 q^{43} +(3.00000 - 5.19615i) q^{47} +(1.00000 + 6.92820i) q^{49} +(-1.00000 + 1.73205i) q^{51} +(-1.00000 - 1.73205i) q^{53} +4.00000 q^{57} +(3.00000 + 5.19615i) q^{59} +(0.500000 - 0.866025i) q^{61} +(-2.50000 + 0.866025i) q^{63} +(-6.00000 - 10.3923i) q^{67} -8.00000 q^{69} +10.0000 q^{71} +(-0.500000 - 0.866025i) q^{73} +(1.00000 - 5.19615i) q^{77} +(-3.50000 + 6.06218i) q^{79} +(-0.500000 - 0.866025i) q^{81} +18.0000 q^{83} +(-2.00000 - 3.46410i) q^{87} +(-5.00000 + 8.66025i) q^{89} +(-4.00000 - 3.46410i) q^{91} +(-1.50000 + 2.59808i) q^{93} +5.00000 q^{97} +2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{3} + 4 q^{7} - q^{9}+O(q^{10}) \) 2 * q - q^3 + 4 * q^7 - q^9	\( 2 q - q^{3} + 4 q^{7} - q^{9} - 2 q^{11} - 4 q^{13} - 2 q^{17} - 4 q^{19} + q^{21} + 8 q^{23} + 2 q^{27} + 8 q^{29} - 3 q^{31} - 2 q^{33} + 9 q^{37} + 2 q^{39} + 12 q^{41} - 2 q^{43} + 6 q^{47} + 2 q^{49} - 2 q^{51} - 2 q^{53} + 8 q^{57} + 6 q^{59} + q^{61} - 5 q^{63} - 12 q^{67} - 16 q^{69} + 20 q^{71} - q^{73} + 2 q^{77} - 7 q^{79} - q^{81} + 36 q^{83} - 4 q^{87} - 10 q^{89} - 8 q^{91} - 3 q^{93} + 10 q^{97} + 4 q^{99}+O(q^{100}) \) 2 * q - q^3 + 4 * q^7 - q^9 - 2 * q^11 - 4 * q^13 - 2 * q^17 - 4 * q^19 + q^21 + 8 * q^23 + 2 * q^27 + 8 * q^29 - 3 * q^31 - 2 * q^33 + 9 * q^37 + 2 * q^39 + 12 * q^41 - 2 * q^43 + 6 * q^47 + 2 * q^49 - 2 * q^51 - 2 * q^53 + 8 * q^57 + 6 * q^59 + q^61 - 5 * q^63 - 12 * q^67 - 16 * q^69 + 20 * q^71 - q^73 + 2 * q^77 - 7 * q^79 - q^81 + 36 * q^83 - 4 * q^87 - 10 * q^89 - 8 * q^91 - 3 * q^93 + 10 * q^97 + 4 * q^99

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