LMFDB - Embedded newform 2100.2.bc.b.949.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("2100.949");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$16.7685844245$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

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

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{3} +(-1.73205 - 2.00000i) q^{7} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{3} +(-1.73205 - 2.00000i) q^{7} +(0.500000 + 0.866025i) q^{9} +(-1.00000 + 1.73205i) q^{11} -2.00000i q^{13} +(1.73205 + 1.00000i) q^{17} +(2.00000 + 3.46410i) q^{19} +(0.500000 + 2.59808i) q^{21} +(-6.92820 + 4.00000i) q^{23} -1.00000i q^{27} -4.00000 q^{29} +(-1.50000 + 2.59808i) q^{31} +(1.73205 - 1.00000i) q^{33} +(7.79423 - 4.50000i) q^{37} +(-1.00000 + 1.73205i) q^{39} +6.00000 q^{41} -1.00000i q^{43} +(5.19615 - 3.00000i) q^{47} +(-1.00000 + 6.92820i) q^{49} +(-1.00000 - 1.73205i) q^{51} +(-1.73205 - 1.00000i) q^{53} -4.00000i q^{57} +(-3.00000 + 5.19615i) q^{59} +(0.500000 + 0.866025i) q^{61} +(0.866025 - 2.50000i) q^{63} +(10.3923 + 6.00000i) q^{67} +8.00000 q^{69} +10.0000 q^{71} +(-0.866025 - 0.500000i) q^{73} +(5.19615 - 1.00000i) q^{77} +(3.50000 + 6.06218i) q^{79} +(-0.500000 + 0.866025i) q^{81} +18.0000i q^{83} +(3.46410 + 2.00000i) q^{87} +(5.00000 + 8.66025i) q^{89} +(-4.00000 + 3.46410i) q^{91} +(2.59808 - 1.50000i) q^{93} -5.00000i q^{97} -2.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^9	$ 4 q + 2 q^{9} - 4 q^{11} + 8 q^{19} + 2 q^{21} - 16 q^{29} - 6 q^{31} - 4 q^{39} + 24 q^{41} - 4 q^{49} - 4 q^{51} - 12 q^{59} + 2 q^{61} + 32 q^{69} + 40 q^{71} + 14 q^{79} - 2 q^{81} + 20 q^{89} - 16 q^{91} - 8 q^{99}+O(q^{100}) $ 4 * q + 2 * q^9 - 4 * q^11 + 8 * q^19 + 2 * q^21 - 16 * q^29 - 6 * q^31 - 4 * q^39 + 24 * q^41 - 4 * q^49 - 4 * q^51 - 12 * q^59 + 2 * q^61 + 32 * q^69 + 40 * q^71 + 14 * q^79 - 2 * q^81 + 20 * q^89 - 16 * q^91 - 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
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−1.73205	−	2.00000i	−0.654654	−	0.755929i
$7$	−1.73205	−	2.00000i	−0.654654	−	0.755929i
$8$		0			0
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$		0			0
$11$	−1.00000	+	1.73205i	−0.301511	+	0.522233i	−0.976478	−	0.215615i	$-0.930824\pi$
$11$	−1.00000	+	1.73205i	−0.301511	+	0.522233i	0.674967	+	0.737848i	$0.264158\pi$
$12$		0			0
$13$		−	2.00000i		−	0.554700i	−0.960769	−	0.277350i	$-0.910544\pi$
$13$		−	2.00000i		−	0.554700i	0.960769	−	0.277350i	$-0.0894562\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	1.73205	+	1.00000i	0.420084	+	0.242536i	0.695113	−	0.718900i	$-0.255354\pi$
$17$	1.73205	+	1.00000i	0.420084	+	0.242536i	−0.275029	+	0.961436i	$0.588688\pi$
$18$		0			0
$19$	2.00000	+	3.46410i	0.458831	+	0.794719i	0.998899	−	0.0469020i	$-0.0149348\pi$
$19$	2.00000	+	3.46410i	0.458831	+	0.794719i	−0.540068	+	0.841621i	$0.681602\pi$
$20$		0			0
$21$	0.500000	+	2.59808i	0.109109	+	0.566947i
$22$		0			0
$23$	−6.92820	+	4.00000i	−1.44463	+	0.834058i	−0.998154	−	0.0607377i	$-0.980655\pi$
$23$	−6.92820	+	4.00000i	−1.44463	+	0.834058i	−0.446476	+	0.894795i	$0.647321\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$		−	1.00000i		−	0.192450i
$28$		0			0
$29$	−4.00000			−0.742781			−0.371391	−	0.928477i	$-0.621119\pi$
$29$	−4.00000			−0.742781			−0.371391	+	0.928477i	$0.621119\pi$
$30$		0			0
$31$	−1.50000	+	2.59808i	−0.269408	+	0.466628i	−0.968709	−	0.248199i	$-0.920161\pi$
$31$	−1.50000	+	2.59808i	−0.269408	+	0.466628i	0.699301	+	0.714827i	$0.253495\pi$
$32$		0			0
$33$	1.73205	−	1.00000i	0.301511	−	0.174078i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	7.79423	−	4.50000i	1.28136	−	0.739795i	0.304266	−	0.952587i	$-0.401589\pi$
$37$	7.79423	−	4.50000i	1.28136	−	0.739795i	0.977098	+	0.212792i	$0.0682556\pi$
$38$		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
$43$		−	1.00000i		−	0.152499i	−0.997089	−	0.0762493i	$-0.975706\pi$
$43$		−	1.00000i		−	0.152499i	0.997089	−	0.0762493i	$-0.0242945\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	5.19615	−	3.00000i	0.757937	−	0.437595i	−0.0706177	−	0.997503i	$-0.522497\pi$
$47$	5.19615	−	3.00000i	0.757937	−	0.437595i	0.828554	+	0.559908i	$0.189164\pi$
$48$		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
$53$	−1.73205	−	1.00000i	−0.237915	−	0.137361i	0.376303	−	0.926497i	$-0.377195\pi$
$53$	−1.73205	−	1.00000i	−0.237915	−	0.137361i	−0.614218	+	0.789136i	$0.710529\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		−	4.00000i		−	0.529813i
$58$		0			0
$59$	−3.00000	+	5.19615i	−0.390567	+	0.676481i	−0.992524	−	0.122047i	$-0.961054\pi$
$59$	−3.00000	+	5.19615i	−0.390567	+	0.676481i	0.601958	+	0.798528i	$0.294388\pi$
$60$		0			0
$61$	0.500000	+	0.866025i	0.0640184	+	0.110883i	0.896258	−	0.443533i	$-0.146275\pi$
$61$	0.500000	+	0.866025i	0.0640184	+	0.110883i	−0.832240	+	0.554416i	$0.812942\pi$
$62$		0			0
$63$	0.866025	−	2.50000i	0.109109	−	0.314970i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	10.3923	+	6.00000i	1.26962	+	0.733017i	0.974916	−	0.222571i	$-0.0714450\pi$
$67$	10.3923	+	6.00000i	1.26962	+	0.733017i	0.294706	+	0.955588i	$0.404778\pi$
$68$		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
$73$	−0.866025	−	0.500000i	−0.101361	−	0.0585206i	0.448463	−	0.893801i	$-0.351972\pi$
$73$	−0.866025	−	0.500000i	−0.101361	−	0.0585206i	−0.549823	+	0.835281i	$0.685305\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	5.19615	−	1.00000i	0.592157	−	0.113961i
$78$		0			0
$79$	3.50000	+	6.06218i	0.393781	+	0.682048i	0.992945	−	0.118578i	$-0.0378336\pi$
$79$	3.50000	+	6.06218i	0.393781	+	0.682048i	−0.599164	+	0.800626i	$0.704500\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$			18.0000i			1.97576i	0.155230	+	0.987878i	$0.450388\pi$
$83$			18.0000i			1.97576i	−0.155230	+	0.987878i	$0.549612\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	3.46410	+	2.00000i	0.371391	+	0.214423i
$88$		0			0
$89$	5.00000	+	8.66025i	0.529999	+	0.917985i	0.999388	+	0.0349934i	$0.0111410\pi$
$89$	5.00000	+	8.66025i	0.529999	+	0.917985i	−0.469389	+	0.882992i	$0.655526\pi$
$90$		0			0
$91$	−4.00000	+	3.46410i	−0.419314	+	0.363137i
$92$		0			0
$93$	2.59808	−	1.50000i	0.269408	−	0.155543i
$94$		0			0
$95$		0			0
$96$		0			0
$97$		−	5.00000i		−	0.507673i	−0.967247	−	0.253837i	$-0.918307\pi$
$97$		−	5.00000i		−	0.507673i	0.967247	−	0.253837i	$-0.0816925\pi$
$98$		0			0
$99$	−2.00000			−0.201008
$100$		0			0
$101$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$101$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$102$		0			0
$103$	−9.52628	+	5.50000i	−0.938652	+	0.541931i	−0.889538	−	0.456862i	$-0.848973\pi$
$103$	−9.52628	+	5.50000i	−0.938652	+	0.541931i	−0.0491146	+	0.998793i	$0.515640\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$107$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$108$		0			0
$109$	7.00000	−	12.1244i	0.670478	−	1.16130i	−0.307290	−	0.951616i	$-0.599422\pi$
$109$	7.00000	−	12.1244i	0.670478	−	1.16130i	0.977769	−	0.209687i	$-0.0672444\pi$
$110$		0			0
$111$	−9.00000			−0.854242
$112$		0			0
$113$		−	6.00000i		−	0.564433i	−0.959351	−	0.282216i	$-0.908930\pi$
$113$		−	6.00000i		−	0.564433i	0.959351	−	0.282216i	$-0.0910696\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	1.73205	−	1.00000i	0.160128	−	0.0924500i
$118$		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
$123$	−5.19615	−	3.00000i	−0.468521	−	0.270501i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		−	17.0000i		−	1.50851i	−0.656584	−	0.754253i	$-0.727999\pi$
$127$		−	17.0000i		−	1.50851i	0.656584	−	0.754253i	$-0.272001\pi$
$128$		0			0
$129$	−0.500000	+	0.866025i	−0.0440225	+	0.0762493i
$130$		0			0
$131$	11.0000	+	19.0526i	0.961074	+	1.66463i	0.719811	+	0.694170i	$0.244228\pi$
$131$	11.0000	+	19.0526i	0.961074	+	1.66463i	0.241264	+	0.970460i	$0.422438\pi$
$132$		0			0
$133$	3.46410	−	10.0000i	0.300376	−	0.867110i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	13.8564	+	8.00000i	1.18383	+	0.683486i	0.956898	−	0.290424i	$-0.0937963\pi$
$137$	13.8564	+	8.00000i	1.18383	+	0.683486i	0.226935	+	0.973910i	$0.427130\pi$
$138$		0			0
$139$	−5.00000			−0.424094			−0.212047	−	0.977259i	$-0.568013\pi$
$139$	−5.00000			−0.424094			−0.212047	+	0.977259i	$0.568013\pi$
$140$		0			0
$141$	−6.00000			−0.505291
$142$		0			0
$143$	3.46410	+	2.00000i	0.289683	+	0.167248i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	4.33013	−	5.50000i	0.357143	−	0.453632i
$148$		0			0
$149$	4.00000	+	6.92820i	0.327693	+	0.567581i	0.982054	−	0.188602i	$-0.0603956\pi$
$149$	4.00000	+	6.92820i	0.327693	+	0.567581i	−0.654361	+	0.756182i	$0.727062\pi$
$150$		0			0
$151$	−3.50000	+	6.06218i	−0.284826	+	0.493333i	−0.972567	−	0.232623i	$-0.925269\pi$
$151$	−3.50000	+	6.06218i	−0.284826	+	0.493333i	0.687741	+	0.725956i	$0.258602\pi$
$152$		0			0
$153$			2.00000i			0.161690i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	2.59808	+	1.50000i	0.207349	+	0.119713i	0.600079	−	0.799941i	$-0.295136\pi$
$157$	2.59808	+	1.50000i	0.207349	+	0.119713i	−0.392730	+	0.919654i	$0.628469\pi$
$158$		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
$163$	−0.866025	+	0.500000i	−0.0678323	+	0.0391630i	−0.533533	−	0.845780i	$-0.679136\pi$
$163$	−0.866025	+	0.500000i	−0.0678323	+	0.0391630i	0.465700	+	0.884943i	$0.345802\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$			8.00000i			0.619059i	0.950890	+	0.309529i	$0.100171\pi$
$167$			8.00000i			0.619059i	−0.950890	+	0.309529i	$0.899829\pi$
$168$		0			0
$169$	9.00000			0.692308
$170$		0			0
$171$	−2.00000	+	3.46410i	−0.152944	+	0.264906i
$172$		0			0
$173$	−5.19615	+	3.00000i	−0.395056	+	0.228086i	−0.684349	−	0.729155i	$-0.739913\pi$
$173$	−5.19615	+	3.00000i	−0.395056	+	0.228086i	0.289292	+	0.957241i	$0.406580\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	5.19615	−	3.00000i	0.390567	−	0.225494i
$178$		0			0
$179$	8.00000	−	13.8564i	0.597948	−	1.03568i	−0.395175	−	0.918606i	$-0.629316\pi$
$179$	8.00000	−	13.8564i	0.597948	−	1.03568i	0.993124	−	0.117071i	$-0.0373504\pi$
$180$		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
$183$		−	1.00000i		−	0.0739221i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−3.46410	+	2.00000i	−0.253320	+	0.146254i
$188$		0			0
$189$	−2.00000	+	1.73205i	−0.145479	+	0.125988i
$190$		0			0
$191$	2.00000	+	3.46410i	0.144715	+	0.250654i	0.929267	−	0.369410i	$-0.120440\pi$
$191$	2.00000	+	3.46410i	0.144715	+	0.250654i	−0.784552	+	0.620063i	$0.787107\pi$
$192$		0			0
$193$	0.866025	+	0.500000i	0.0623379	+	0.0359908i	0.530845	−	0.847469i	$-0.321875\pi$
$193$	0.866025	+	0.500000i	0.0623379	+	0.0359908i	−0.468507	+	0.883460i	$0.655208\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			18.0000i			1.28245i	0.767354	+	0.641223i	$0.221573\pi$
$197$			18.0000i			1.28245i	−0.767354	+	0.641223i	$0.778427\pi$
$198$		0			0
$199$	1.50000	−	2.59808i	0.106332	−	0.184173i	−0.807950	−	0.589252i	$-0.799423\pi$
$199$	1.50000	−	2.59808i	0.106332	−	0.184173i	0.914282	+	0.405079i	$0.132756\pi$
$200$		0			0
$201$	−6.00000	−	10.3923i	−0.423207	−	0.733017i
$202$		0			0
$203$	6.92820	+	8.00000i	0.486265	+	0.561490i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−6.92820	−	4.00000i	−0.481543	−	0.278019i
$208$		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
$213$	−8.66025	−	5.00000i	−0.593391	−	0.342594i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	7.79423	−	1.50000i	0.529107	−	0.101827i
$218$		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
$223$			17.0000i			1.13840i	0.822198	+	0.569202i	$0.192748\pi$
$223$			17.0000i			1.13840i	−0.822198	+	0.569202i	$0.807252\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−1.73205	−	1.00000i	−0.114960	−	0.0663723i	0.441417	−	0.897302i	$-0.354476\pi$
$227$	−1.73205	−	1.00000i	−0.114960	−	0.0663723i	−0.556378	+	0.830930i	$0.687809\pi$
$228$		0			0
$229$	13.0000	+	22.5167i	0.859064	+	1.48794i	0.872823	+	0.488037i	$0.162287\pi$
$229$	13.0000	+	22.5167i	0.859064	+	1.48794i	−0.0137585	+	0.999905i	$0.504380\pi$
$230$		0			0
$231$	−5.00000	−	1.73205i	−0.328976	−	0.113961i
$232$		0			0
$233$	−3.46410	+	2.00000i	−0.226941	+	0.131024i	−0.609160	−	0.793047i	$-0.708493\pi$
$233$	−3.46410	+	2.00000i	−0.226941	+	0.131024i	0.382219	+	0.924072i	$0.375160\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		−	7.00000i		−	0.454699i
$238$		0			0
$239$	−18.0000			−1.16432			−0.582162	−	0.813073i	$-0.697793\pi$
$239$	−18.0000			−1.16432			−0.582162	+	0.813073i	$0.697793\pi$
$240$		0			0
$241$	5.50000	−	9.52628i	0.354286	−	0.613642i	−0.632709	−	0.774389i	$-0.718057\pi$
$241$	5.50000	−	9.52628i	0.354286	−	0.613642i	0.986996	+	0.160748i	$0.0513906\pi$
$242$		0			0
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	6.92820	−	4.00000i	0.440831	−	0.254514i
$248$		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
$253$		−	16.0000i		−	1.00591i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−19.0526	+	11.0000i	−1.18847	+	0.686161i	−0.957958	−	0.286909i	$-0.907372\pi$
$257$	−19.0526	+	11.0000i	−1.18847	+	0.686161i	−0.230508	+	0.973070i	$0.574039\pi$
$258$		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
$263$	19.0526	+	11.0000i	1.17483	+	0.678289i	0.954813	−	0.297207i	$-0.0960551\pi$
$263$	19.0526	+	11.0000i	1.17483	+	0.678289i	0.220018	+	0.975496i	$0.429388\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		−	10.0000i		−	0.611990i
$268$		0			0
$269$	−6.00000	+	10.3923i	−0.365826	+	0.633630i	−0.988908	−	0.148527i	$-0.952547\pi$
$269$	−6.00000	+	10.3923i	−0.365826	+	0.633630i	0.623082	+	0.782157i	$0.285880\pi$
$270$		0			0
$271$	−8.00000	−	13.8564i	−0.485965	−	0.841717i	0.513905	−	0.857847i	$-0.328199\pi$
$271$	−8.00000	−	13.8564i	−0.485965	−	0.841717i	−0.999870	+	0.0161307i	$0.994865\pi$
$272$		0			0
$273$	5.19615	−	1.00000i	0.314485	−	0.0605228i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−1.73205	−	1.00000i	−0.104069	−	0.0600842i	0.447062	−	0.894503i	$-0.352470\pi$
$277$	−1.73205	−	1.00000i	−0.104069	−	0.0600842i	−0.551131	+	0.834419i	$0.685804\pi$
$278$		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
$283$	−13.8564	−	8.00000i	−0.823678	−	0.475551i	0.0280052	−	0.999608i	$-0.491084\pi$
$283$	−13.8564	−	8.00000i	−0.823678	−	0.475551i	−0.851683	+	0.524057i	$0.824418\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−10.3923	−	12.0000i	−0.613438	−	0.708338i
$288$		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
$293$		−	6.00000i		−	0.350524i	−0.984522	−	0.175262i	$-0.943923\pi$
$293$		−	6.00000i		−	0.350524i	0.984522	−	0.175262i	$-0.0560772\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	1.73205	+	1.00000i	0.100504	+	0.0580259i
$298$		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
$307$			7.00000i			0.399511i	0.979846	+	0.199756i	$0.0640148\pi$
$307$			7.00000i			0.399511i	−0.979846	+	0.199756i	$0.935985\pi$
$308$		0			0
$309$	11.0000			0.625768
$310$		0			0
$311$	16.0000	−	27.7128i	0.907277	−	1.57145i	0.0894452	−	0.995992i	$-0.471491\pi$
$311$	16.0000	−	27.7128i	0.907277	−	1.57145i	0.817832	−	0.575458i	$-0.195176\pi$
$312$		0			0
$313$	23.3827	−	13.5000i	1.32167	−	0.763065i	0.337673	−	0.941263i	$-0.390360\pi$
$313$	23.3827	−	13.5000i	1.32167	−	0.763065i	0.983995	+	0.178198i	$0.0570269\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−29.4449	+	17.0000i	−1.65379	+	0.954815i	−0.678294	+	0.734791i	$0.737280\pi$
$317$	−29.4449	+	17.0000i	−1.65379	+	0.954815i	−0.975494	+	0.220024i	$0.929386\pi$
$318$		0			0
$319$	4.00000	−	6.92820i	0.223957	−	0.387905i
$320$		0			0
$321$		0			0
$322$		0			0
$323$			8.00000i			0.445132i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−12.1244	+	7.00000i	−0.670478	+	0.387101i
$328$		0			0
$329$	−15.0000	−	5.19615i	−0.826977	−	0.286473i
$330$		0			0
$331$	−13.5000	−	23.3827i	−0.742027	−	1.28523i	−0.951571	−	0.307429i	$-0.900531\pi$
$331$	−13.5000	−	23.3827i	−0.742027	−	1.28523i	0.209544	−	0.977799i	$-0.432802\pi$
$332$		0			0
$333$	7.79423	+	4.50000i	0.427121	+	0.246598i
$334$		0			0
$335$		0			0
$336$		0			0
$337$		−	9.00000i		−	0.490261i	−0.969490	−	0.245131i	$-0.921169\pi$
$337$		−	9.00000i		−	0.490261i	0.969490	−	0.245131i	$-0.0788309\pi$
$338$		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
$343$	15.5885	−	10.0000i	0.841698	−	0.539949i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	22.5167	+	13.0000i	1.20876	+	0.697877i	0.962488	−	0.271325i	$-0.0874617\pi$
$347$	22.5167	+	13.0000i	1.20876	+	0.697877i	0.246270	+	0.969201i	$0.420795\pi$
$348$		0			0
$349$	34.0000			1.81998			0.909989	−	0.414632i	$-0.136090\pi$
$349$	34.0000			1.81998			0.909989	+	0.414632i	$0.136090\pi$
$350$		0			0
$351$	−2.00000			−0.106752
$352$		0			0
$353$	−13.8564	−	8.00000i	−0.737502	−	0.425797i	0.0836583	−	0.996495i	$-0.473340\pi$
$353$	−13.8564	−	8.00000i	−0.737502	−	0.425797i	−0.821160	+	0.570697i	$0.806673\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−1.73205	+	5.00000i	−0.0916698	+	0.264628i
$358$		0			0
$359$	−15.0000	−	25.9808i	−0.791670	−	1.37121i	−0.924932	−	0.380131i	$-0.875879\pi$
$359$	−15.0000	−	25.9808i	−0.791670	−	1.37121i	0.133263	−	0.991081i	$-0.457455\pi$
$360$		0			0
$361$	1.50000	−	2.59808i	0.0789474	−	0.136741i
$362$		0			0
$363$		−	7.00000i		−	0.367405i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−30.3109	−	17.5000i	−1.58222	−	0.913493i	−0.994535	−	0.104399i	$-0.966708\pi$
$367$	−30.3109	−	17.5000i	−1.58222	−	0.913493i	−0.587680	−	0.809093i	$-0.699959\pi$
$368$		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
$373$	−8.66025	+	5.00000i	−0.448411	+	0.258890i	−0.707159	−	0.707055i	$-0.750023\pi$
$373$	−8.66025	+	5.00000i	−0.448411	+	0.258890i	0.258748	+	0.965945i	$0.416690\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			8.00000i			0.412021i
$378$		0			0
$379$	−28.0000			−1.43826			−0.719132	−	0.694874i	$-0.755460\pi$
$379$	−28.0000			−1.43826			−0.719132	+	0.694874i	$0.755460\pi$
$380$		0			0
$381$	−8.50000	+	14.7224i	−0.435468	+	0.754253i
$382$		0			0
$383$	−27.7128	+	16.0000i	−1.41606	+	0.817562i	−0.995950	−	0.0899119i	$-0.971341\pi$
$383$	−27.7128	+	16.0000i	−1.41606	+	0.817562i	−0.420109	+	0.907474i	$0.638008\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	0.866025	−	0.500000i	0.0440225	−	0.0254164i
$388$		0			0
$389$	5.00000	−	8.66025i	0.253510	−	0.439092i	−0.710980	−	0.703213i	$-0.751748\pi$
$389$	5.00000	−	8.66025i	0.253510	−	0.439092i	0.964490	+	0.264120i	$0.0850816\pi$
$390$		0			0
$391$	−16.0000			−0.809155
$392$		0			0
$393$		−	22.0000i		−	1.10975i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−23.3827	+	13.5000i	−1.17354	+	0.677546i	−0.954512	−	0.298172i	$-0.903623\pi$
$397$	−23.3827	+	13.5000i	−1.17354	+	0.677546i	−0.219031	+	0.975718i	$0.570290\pi$
$398$		0			0
$399$	−8.00000	+	6.92820i	−0.400501	+	0.346844i
$400$		0			0
$401$	1.00000	+	1.73205i	0.0499376	+	0.0864945i	0.889914	−	0.456129i	$-0.150764\pi$
$401$	1.00000	+	1.73205i	0.0499376	+	0.0864945i	−0.839976	+	0.542623i	$0.817431\pi$
$402$		0			0
$403$	5.19615	+	3.00000i	0.258839	+	0.149441i
$404$		0			0
$405$		0			0
$406$		0			0
$407$			18.0000i			0.892227i
$408$		0			0
$409$	−7.00000	+	12.1244i	−0.346128	+	0.599511i	−0.985558	−	0.169338i	$-0.945837\pi$
$409$	−7.00000	+	12.1244i	−0.346128	+	0.599511i	0.639430	+	0.768849i	$0.279170\pi$
$410$		0			0
$411$	−8.00000	−	13.8564i	−0.394611	−	0.683486i
$412$		0			0
$413$	15.5885	−	3.00000i	0.767058	−	0.147620i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	4.33013	+	2.50000i	0.212047	+	0.122426i
$418$		0			0
$419$	−8.00000			−0.390826			−0.195413	−	0.980721i	$-0.562605\pi$
$419$	−8.00000			−0.390826			−0.195413	+	0.980721i	$0.562605\pi$
$420$		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
$423$	5.19615	+	3.00000i	0.252646	+	0.145865i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	0.866025	−	2.50000i	0.0419099	−	0.120983i
$428$		0			0
$429$	−2.00000	−	3.46410i	−0.0965609	−	0.167248i
$430$		0			0
$431$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$431$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$432$		0			0
$433$		−	5.00000i		−	0.240285i	−0.992757	−	0.120142i	$-0.961665\pi$
$433$		−	5.00000i		−	0.240285i	0.992757	−	0.120142i	$-0.0383351\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−27.7128	−	16.0000i	−1.32568	−	0.765384i
$438$		0			0
$439$	−5.50000	−	9.52628i	−0.262501	−	0.454665i	0.704405	−	0.709798i	$-0.251214\pi$
$439$	−5.50000	−	9.52628i	−0.262501	−	0.454665i	−0.966906	+	0.255134i	$0.917881\pi$
$440$		0			0
$441$	−6.50000	+	2.59808i	−0.309524	+	0.123718i
$442$		0			0
$443$	−5.19615	+	3.00000i	−0.246877	+	0.142534i	−0.618333	−	0.785916i	$-0.712192\pi$
$443$	−5.19615	+	3.00000i	−0.246877	+	0.142534i	0.371457	+	0.928450i	$0.378858\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		−	8.00000i		−	0.378387i
$448$		0			0
$449$	−32.0000			−1.51017			−0.755087	−	0.655625i	$-0.772405\pi$
$449$	−32.0000			−1.51017			−0.755087	+	0.655625i	$0.772405\pi$
$450$		0			0
$451$	−6.00000	+	10.3923i	−0.282529	+	0.489355i
$452$		0			0
$453$	6.06218	−	3.50000i	0.284826	−	0.164444i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−32.0429	+	18.5000i	−1.49891	+	0.865393i	−0.999999	−	0.00126243i	$-0.999598\pi$
$457$	−32.0429	+	18.5000i	−1.49891	+	0.865393i	−0.498906	+	0.866656i	$0.666265\pi$
$458$		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
$463$		−	9.00000i		−	0.418265i	−0.977887	−	0.209133i	$-0.932936\pi$
$463$		−	9.00000i		−	0.418265i	0.977887	−	0.209133i	$-0.0670641\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−5.19615	+	3.00000i	−0.240449	+	0.138823i	−0.615383	−	0.788228i	$-0.710999\pi$
$467$	−5.19615	+	3.00000i	−0.240449	+	0.138823i	0.374934	+	0.927052i	$0.377665\pi$
$468$		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
$473$	1.73205	+	1.00000i	0.0796398	+	0.0459800i
$474$		0			0
$475$		0			0
$476$		0			0
$477$		−	2.00000i		−	0.0915737i
$478$		0			0
$479$	16.0000	−	27.7128i	0.731059	−	1.26623i	−0.225372	−	0.974273i	$-0.572360\pi$
$479$	16.0000	−	27.7128i	0.731059	−	1.26623i	0.956431	−	0.291958i	$-0.0943068\pi$
$480$		0			0
$481$	−9.00000	−	15.5885i	−0.410365	−	0.710772i
$482$		0			0
$483$	−13.8564	−	16.0000i	−0.630488	−	0.728025i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−9.52628	−	5.50000i	−0.431677	−	0.249229i	0.268384	−	0.963312i	$-0.413510\pi$
$487$	−9.52628	−	5.50000i	−0.431677	−	0.249229i	−0.700061	+	0.714083i	$0.746844\pi$
$488$		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
$493$	−6.92820	−	4.00000i	−0.312031	−	0.180151i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−17.3205	−	20.0000i	−0.776931	−	0.897123i
$498$		0			0
$499$	18.0000	+	31.1769i	0.805791	+	1.39567i	0.915756	+	0.401735i	$0.131593\pi$
$499$	18.0000	+	31.1769i	0.805791	+	1.39567i	−0.109965	+	0.993935i	$0.535074\pi$
$500$		0			0
$501$	4.00000	−	6.92820i	0.178707	−	0.309529i
$502$		0			0
$503$			40.0000i			1.78351i	0.452517	+	0.891756i	$0.350526\pi$
$503$			40.0000i			1.78351i	−0.452517	+	0.891756i	$0.649474\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−7.79423	−	4.50000i	−0.346154	−	0.199852i
$508$		0			0
$509$	9.00000	+	15.5885i	0.398918	+	0.690946i	0.993593	−	0.113020i	$-0.0360525\pi$
$509$	9.00000	+	15.5885i	0.398918	+	0.690946i	−0.594675	+	0.803966i	$0.702719\pi$
$510$		0			0
$511$	0.500000	+	2.59808i	0.0221187	+	0.114932i
$512$		0			0
$513$	3.46410	−	2.00000i	0.152944	−	0.0883022i
$514$		0			0
$515$		0			0
$516$		0			0
$517$			12.0000i			0.527759i
$518$		0			0
$519$	6.00000			0.263371
$520$		0			0
$521$	3.00000	−	5.19615i	0.131432	−	0.227648i	−0.792797	−	0.609486i	$-0.791376\pi$
$521$	3.00000	−	5.19615i	0.131432	−	0.227648i	0.924229	+	0.381839i	$0.124709\pi$
$522$		0			0
$523$	0.866025	−	0.500000i	0.0378686	−	0.0218635i	−0.480946	−	0.876750i	$-0.659707\pi$
$523$	0.866025	−	0.500000i	0.0378686	−	0.0218635i	0.518815	+	0.854887i	$0.326373\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−5.19615	+	3.00000i	−0.226348	+	0.130682i
$528$		0			0
$529$	20.5000	−	35.5070i	0.891304	−	1.54378i
$530$		0			0
$531$	−6.00000			−0.260378
$532$		0			0
$533$		−	12.0000i		−	0.519778i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−13.8564	+	8.00000i	−0.597948	+	0.345225i
$538$		0			0
$539$	−11.0000	−	8.66025i	−0.473804	−	0.373024i
$540$		0			0
$541$	5.00000	+	8.66025i	0.214967	+	0.372333i	0.953262	−	0.302144i	$-0.0977023\pi$
$541$	5.00000	+	8.66025i	0.214967	+	0.372333i	−0.738296	+	0.674477i	$0.764369\pi$
$542$		0			0
$543$	12.9904	+	7.50000i	0.557471	+	0.321856i
$544$		0			0
$545$		0			0
$546$		0			0
$547$		−	12.0000i		−	0.513083i	−0.966533	−	0.256541i	$-0.917417\pi$
$547$		−	12.0000i		−	0.513083i	0.966533	−	0.256541i	$-0.0825830\pi$
$548$		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
$553$	6.06218	−	17.5000i	0.257790	−	0.744176i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	15.5885	+	9.00000i	0.660504	+	0.381342i	0.792469	−	0.609912i	$-0.208795\pi$
$557$	15.5885	+	9.00000i	0.660504	+	0.381342i	−0.131965	+	0.991254i	$0.542129\pi$
$558$		0			0
$559$	−2.00000			−0.0845910
$560$		0			0
$561$	4.00000			0.168880
$562$		0			0
$563$	29.4449	+	17.0000i	1.24095	+	0.716465i	0.969288	−	0.245927i	$-0.0790925\pi$
$563$	29.4449	+	17.0000i	1.24095	+	0.716465i	0.271665	+	0.962392i	$0.412426\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	2.59808	−	0.500000i	0.109109	−	0.0209980i
$568$		0			0
$569$	−2.00000	−	3.46410i	−0.0838444	−	0.145223i	0.821054	−	0.570851i	$-0.193387\pi$
$569$	−2.00000	−	3.46410i	−0.0838444	−	0.145223i	−0.904898	+	0.425628i	$0.860053\pi$
$570$		0			0
$571$	−2.00000	+	3.46410i	−0.0836974	+	0.144968i	−0.904835	−	0.425762i	$-0.860006\pi$
$571$	−2.00000	+	3.46410i	−0.0836974	+	0.144968i	0.821138	+	0.570730i	$0.193340\pi$
$572$		0			0
$573$		−	4.00000i		−	0.167102i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	26.8468	+	15.5000i	1.11765	+	0.645273i	0.940799	−	0.338965i	$-0.110077\pi$
$577$	26.8468	+	15.5000i	1.11765	+	0.645273i	0.176847	+	0.984238i	$0.443410\pi$
$578$		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
$583$	3.46410	−	2.00000i	0.143468	−	0.0828315i
$584$		0			0
$585$		0			0
$586$		0			0
$587$			42.0000i			1.73353i	0.498721	+	0.866763i	$0.333803\pi$
$587$			42.0000i			1.73353i	−0.498721	+	0.866763i	$0.666197\pi$
$588$		0			0
$589$	−12.0000			−0.494451
$590$		0			0
$591$	9.00000	−	15.5885i	0.370211	−	0.641223i
$592$		0			0
$593$	−20.7846	+	12.0000i	−0.853522	+	0.492781i	−0.861838	−	0.507184i	$-0.830686\pi$
$593$	−20.7846	+	12.0000i	−0.853522	+	0.492781i	0.00831589	+	0.999965i	$0.497353\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−2.59808	+	1.50000i	−0.106332	+	0.0613909i
$598$		0			0
$599$	24.0000	−	41.5692i	0.980613	−	1.69847i	0.320607	−	0.947212i	$-0.396113\pi$
$599$	24.0000	−	41.5692i	0.980613	−	1.69847i	0.660006	−	0.751260i	$-0.270554\pi$
$600$		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
$603$			12.0000i			0.488678i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−37.2391	+	21.5000i	−1.51149	+	0.872658i	−0.511578	+	0.859237i	$0.670939\pi$
$607$	−37.2391	+	21.5000i	−1.51149	+	0.872658i	−0.999910	+	0.0134214i	$0.995728\pi$
$608$		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
$613$	25.9808	+	15.0000i	1.04935	+	0.605844i	0.922468	−	0.386073i	$-0.126169\pi$
$613$	25.9808	+	15.0000i	1.04935	+	0.605844i	0.126885	+	0.991917i	$0.459502\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		−	14.0000i		−	0.563619i	−0.959470	−	0.281809i	$-0.909065\pi$
$617$		−	14.0000i		−	0.563619i	0.959470	−	0.281809i	$-0.0909346\pi$
$618$		0			0
$619$	−15.5000	+	26.8468i	−0.622998	+	1.07906i	0.365927	+	0.930644i	$0.380752\pi$
$619$	−15.5000	+	26.8468i	−0.622998	+	1.07906i	−0.988924	+	0.148420i	$0.952581\pi$
$620$		0			0
$621$	4.00000	+	6.92820i	0.160514	+	0.278019i
$622$		0			0
$623$	8.66025	−	25.0000i	0.346966	−	1.00160i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	6.92820	+	4.00000i	0.276686	+	0.159745i
$628$		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
$633$	7.79423	+	4.50000i	0.309793	+	0.178859i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	13.8564	+	2.00000i	0.549011	+	0.0792429i
$638$		0			0
$639$	5.00000	+	8.66025i	0.197797	+	0.342594i
$640$		0			0
$641$	−5.00000	+	8.66025i	−0.197488	+	0.342059i	−0.947713	−	0.319123i	$-0.896612\pi$
$641$	−5.00000	+	8.66025i	−0.197488	+	0.342059i	0.750225	+	0.661182i	$0.229945\pi$
$642$		0			0
$643$			5.00000i			0.197181i	0.995128	+	0.0985904i	$0.0314334\pi$
$643$			5.00000i			0.197181i	−0.995128	+	0.0985904i	$0.968567\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−5.19615	−	3.00000i	−0.204282	−	0.117942i	0.394369	−	0.918952i	$-0.370963\pi$
$647$	−5.19615	−	3.00000i	−0.204282	−	0.117942i	−0.598651	+	0.801010i	$0.704296\pi$
$648$		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
$653$	22.5167	−	13.0000i	0.881145	−	0.508729i	0.0101092	−	0.999949i	$-0.496782\pi$
$653$	22.5167	−	13.0000i	0.881145	−	0.508729i	0.871036	+	0.491220i	$0.163449\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		−	1.00000i		−	0.0390137i
$658$		0			0
$659$	−42.0000			−1.63609			−0.818044	−	0.575156i	$-0.804941\pi$
$659$	−42.0000			−1.63609			−0.818044	+	0.575156i	$0.804941\pi$
$660$		0			0
$661$	−5.50000	+	9.52628i	−0.213925	+	0.370529i	−0.952940	−	0.303160i	$-0.901958\pi$
$661$	−5.50000	+	9.52628i	−0.213925	+	0.370529i	0.739014	+	0.673690i	$0.235292\pi$
$662$		0			0
$663$	−3.46410	+	2.00000i	−0.134535	+	0.0776736i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	27.7128	−	16.0000i	1.07304	−	0.619522i
$668$		0			0
$669$	8.50000	−	14.7224i	0.328629	−	0.569202i
$670$		0			0
$671$	−2.00000			−0.0772091
$672$		0			0
$673$		−	9.00000i		−	0.346925i	−0.984841	−	0.173462i	$-0.944505\pi$
$673$		−	9.00000i		−	0.346925i	0.984841	−	0.173462i	$-0.0554955\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	27.7128	−	16.0000i	1.06509	−	0.614930i	0.138254	−	0.990397i	$-0.455851\pi$
$677$	27.7128	−	16.0000i	1.06509	−	0.614930i	0.926836	+	0.375467i	$0.122518\pi$
$678$		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
$683$	5.19615	+	3.00000i	0.198825	+	0.114792i	0.596107	−	0.802905i	$-0.296713\pi$
$683$	5.19615	+	3.00000i	0.198825	+	0.114792i	−0.397282	+	0.917697i	$0.630047\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$		−	26.0000i		−	0.991962i
$688$		0			0
$689$	−2.00000	+	3.46410i	−0.0761939	+	0.131972i
$690$		0			0
$691$	−13.5000	−	23.3827i	−0.513564	−	0.889519i	−0.999876	−	0.0157341i	$-0.994991\pi$
$691$	−13.5000	−	23.3827i	−0.513564	−	0.889519i	0.486312	−	0.873785i	$-0.338342\pi$
$692$		0			0
$693$	3.46410	+	4.00000i	0.131590	+	0.151947i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	10.3923	+	6.00000i	0.393637	+	0.227266i
$698$		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
$703$	31.1769	+	18.0000i	1.17586	+	0.678883i
$704$		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	$-0.232892\pi$
$709$	−5.50000	−	9.52628i	−0.206557	−	0.357767i	−0.950628	+	0.310334i	$0.899559\pi$
$710$		0			0
$711$	−3.50000	+	6.06218i	−0.131260	+	0.227349i
$712$		0			0
$713$		−	24.0000i		−	0.898807i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	15.5885	+	9.00000i	0.582162	+	0.336111i
$718$		0			0
$719$	22.0000	+	38.1051i	0.820462	+	1.42108i	0.905339	+	0.424690i	$0.139617\pi$
$719$	22.0000	+	38.1051i	0.820462	+	1.42108i	−0.0848774	+	0.996391i	$0.527050\pi$
$720$		0			0
$721$	27.5000	+	9.52628i	1.02415	+	0.354777i
$722$		0			0
$723$	−9.52628	+	5.50000i	−0.354286	+	0.204547i
$724$		0			0
$725$		0			0
$726$		0			0
$727$		−	8.00000i		−	0.296704i	−0.988935	−	0.148352i	$-0.952603\pi$
$727$		−	8.00000i		−	0.296704i	0.988935	−	0.148352i	$-0.0473968\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	1.00000	−	1.73205i	0.0369863	−	0.0640622i
$732$		0			0
$733$	−30.3109	+	17.5000i	−1.11956	+	0.646377i	−0.941288	−	0.337604i	$-0.890383\pi$
$733$	−30.3109	+	17.5000i	−1.11956	+	0.646377i	−0.178270	+	0.983982i	$0.557050\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−20.7846	+	12.0000i	−0.765611	+	0.442026i
$738$		0			0
$739$	20.5000	−	35.5070i	0.754105	−	1.30615i	−0.191714	−	0.981451i	$-0.561404\pi$
$739$	20.5000	−	35.5070i	0.754105	−	1.30615i	0.945818	−	0.324697i	$-0.105262\pi$
$740$		0			0
$741$	−8.00000			−0.293887
$742$		0			0
$743$		−	12.0000i		−	0.440237i	−0.975473	−	0.220119i	$-0.929356\pi$
$743$		−	12.0000i		−	0.440237i	0.975473	−	0.220119i	$-0.0706445\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−15.5885	+	9.00000i	−0.570352	+	0.329293i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−12.5000	−	21.6506i	−0.456131	−	0.790043i	0.542621	−	0.839978i	$-0.317432\pi$
$751$	−12.5000	−	21.6506i	−0.456131	−	0.790043i	−0.998752	+	0.0499348i	$0.984099\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$		−	13.0000i		−	0.472493i	−0.971693	−	0.236247i	$-0.924083\pi$
$757$		−	13.0000i		−	0.472493i	0.971693	−	0.236247i	$-0.0759173\pi$
$758$		0			0
$759$	−8.00000	+	13.8564i	−0.290382	+	0.502956i
$760$		0			0
$761$	16.0000	+	27.7128i	0.580000	+	1.00459i	0.995479	+	0.0949859i	$0.0302806\pi$
$761$	16.0000	+	27.7128i	0.580000	+	1.00459i	−0.415479	+	0.909603i	$0.636386\pi$
$762$		0			0
$763$	−36.3731	+	7.00000i	−1.31679	+	0.253417i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	10.3923	+	6.00000i	0.375244	+	0.216647i
$768$		0			0
$769$	29.0000			1.04577			0.522883	−	0.852404i	$-0.324856\pi$
$769$	29.0000			1.04577			0.522883	+	0.852404i	$0.324856\pi$
$770$		0			0
$771$	22.0000			0.792311
$772$		0			0
$773$	−24.2487	−	14.0000i	−0.872166	−	0.503545i	−0.00409826	−	0.999992i	$-0.501305\pi$
$773$	−24.2487	−	14.0000i	−0.872166	−	0.503545i	−0.868067	+	0.496447i	$0.834638\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	15.5885	+	18.0000i	0.559233	+	0.645746i
$778$		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
$783$			4.00000i			0.142948i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	9.52628	+	5.50000i	0.339575	+	0.196054i	0.660084	−	0.751192i	$-0.270521\pi$
$787$	9.52628	+	5.50000i	0.339575	+	0.196054i	−0.320509	+	0.947245i	$0.603854\pi$
$788$		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
$793$	1.73205	−	1.00000i	0.0615069	−	0.0355110i
$794$		0			0
$795$		0			0
$796$		0			0
$797$			12.0000i			0.425062i	0.977154	+	0.212531i	$0.0681706\pi$
$797$			12.0000i			0.425062i	−0.977154	+	0.212531i	$0.931829\pi$
$798$		0			0
$799$	12.0000			0.424529
$800$		0			0
$801$	−5.00000	+	8.66025i	−0.176666	+	0.305995i
$802$		0			0
$803$	1.73205	−	1.00000i	0.0611227	−	0.0352892i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	10.3923	−	6.00000i	0.365826	−	0.211210i
$808$		0			0
$809$	−14.0000	+	24.2487i	−0.492214	+	0.852539i	−0.999960	−	0.00896753i	$-0.997146\pi$
$809$	−14.0000	+	24.2487i	−0.492214	+	0.852539i	0.507746	+	0.861507i	$0.330479\pi$
$810$		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
$813$			16.0000i			0.561144i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	3.46410	−	2.00000i	0.121194	−	0.0699711i
$818$		0			0
$819$	−5.00000	−	1.73205i	−0.174714	−	0.0605228i
$820$		0			0
$821$	4.00000	+	6.92820i	0.139601	+	0.241796i	0.927346	−	0.374206i	$-0.122085\pi$
$821$	4.00000	+	6.92820i	0.139601	+	0.241796i	−0.787745	+	0.616002i	$0.788751\pi$
$822$		0			0
$823$	12.9904	+	7.50000i	0.452816	+	0.261434i	0.709019	−	0.705190i	$-0.249138\pi$
$823$	12.9904	+	7.50000i	0.452816	+	0.261434i	−0.256203	+	0.966623i	$0.582471\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			14.0000i			0.486828i	0.969923	+	0.243414i	$0.0782673\pi$
$827$			14.0000i			0.486828i	−0.969923	+	0.243414i	$0.921733\pi$
$828$		0			0
$829$	4.50000	−	7.79423i	0.156291	−	0.270705i	−0.777237	−	0.629208i	$-0.783379\pi$
$829$	4.50000	−	7.79423i	0.156291	−	0.270705i	0.933529	+	0.358503i	$0.116713\pi$
$830$		0			0
$831$	1.00000	+	1.73205i	0.0346896	+	0.0600842i
$832$		0			0
$833$	−8.66025	+	11.0000i	−0.300060	+	0.381127i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	2.59808	+	1.50000i	0.0898027	+	0.0518476i
$838$		0			0
$839$	34.0000			1.17381			0.586905	−	0.809656i	$-0.300346\pi$
$839$	34.0000			1.17381			0.586905	+	0.809656i	$0.300346\pi$
$840$		0			0
$841$	−13.0000			−0.448276
$842$		0			0
$843$	−25.9808	−	15.0000i	−0.894825	−	0.516627i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	6.06218	−	17.5000i	0.208299	−	0.601307i
$848$		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
$853$			7.00000i			0.239675i	0.992793	+	0.119838i	$0.0382374\pi$
$853$			7.00000i			0.239675i	−0.992793	+	0.119838i	$0.961763\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−34.6410	−	20.0000i	−1.18331	−	0.683187i	−0.226536	−	0.974003i	$-0.572740\pi$
$857$	−34.6410	−	20.0000i	−1.18331	−	0.683187i	−0.956779	+	0.290816i	$0.906073\pi$
$858$		0			0
$859$	14.0000	+	24.2487i	0.477674	+	0.827355i	0.999672	−	0.0255910i	$-0.00814674\pi$
$859$	14.0000	+	24.2487i	0.477674	+	0.827355i	−0.521999	+	0.852946i	$0.674813\pi$
$860$		0			0
$861$	3.00000	+	15.5885i	0.102240	+	0.531253i
$862$		0			0
$863$	12.1244	−	7.00000i	0.412718	−	0.238283i	−0.279239	−	0.960222i	$-0.590082\pi$
$863$	12.1244	−	7.00000i	0.412718	−	0.238283i	0.691957	+	0.721939i	$0.256749\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$			13.0000i			0.441503i
$868$		0			0
$869$	−14.0000			−0.474917
$870$		0			0
$871$	12.0000	−	20.7846i	0.406604	−	0.704260i
$872$		0			0
$873$	4.33013	−	2.50000i	0.146553	−	0.0846122i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−19.9186	+	11.5000i	−0.672603	+	0.388327i	−0.797062	−	0.603897i	$-0.793614\pi$
$877$	−19.9186	+	11.5000i	−0.672603	+	0.388327i	0.124459	+	0.992225i	$0.460280\pi$
$878$		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
$883$		−	4.00000i		−	0.134611i	−0.997732	−	0.0673054i	$-0.978560\pi$
$883$		−	4.00000i		−	0.134611i	0.997732	−	0.0673054i	$-0.0214402\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	29.4449	−	17.0000i	0.988662	−	0.570804i	0.0837878	−	0.996484i	$-0.473298\pi$
$887$	29.4449	−	17.0000i	0.988662	−	0.570804i	0.904874	+	0.425679i	$0.139965\pi$
$888$		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
$893$	20.7846	+	12.0000i	0.695530	+	0.401565i
$894$		0			0
$895$		0			0
$896$		0			0
$897$		−	16.0000i		−	0.534224i
$898$		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
$903$	2.59808	−	0.500000i	0.0864586	−	0.0166390i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	16.4545	+	9.50000i	0.546362	+	0.315442i	0.747653	−	0.664089i	$-0.231180\pi$
$907$	16.4545	+	9.50000i	0.546362	+	0.315442i	−0.201291	+	0.979531i	$0.564514\pi$
$908$		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
$913$	−31.1769	−	18.0000i	−1.03181	−	0.595713i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	19.0526	−	55.0000i	0.629171	−	1.81626i
$918$		0			0
$919$	−5.50000	−	9.52628i	−0.181428	−	0.314243i	0.760939	−	0.648824i	$-0.224739\pi$
$919$	−5.50000	−	9.52628i	−0.181428	−	0.314243i	−0.942367	+	0.334581i	$0.891405\pi$
$920$		0			0
$921$	3.50000	−	6.06218i	0.115329	−	0.199756i
$922$		0			0
$923$		−	20.0000i		−	0.658308i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−9.52628	−	5.50000i	−0.312884	−	0.180644i
$928$		0			0
$929$	23.0000	+	39.8372i	0.754606	+	1.30702i	0.945570	+	0.325418i	$0.105505\pi$
$929$	23.0000	+	39.8372i	0.754606	+	1.30702i	−0.190965	+	0.981597i	$0.561162\pi$
$930$		0			0
$931$	−26.0000	+	10.3923i	−0.852116	+	0.340594i
$932$		0			0
$933$	−27.7128	+	16.0000i	−0.907277	+	0.523816i
$934$		0			0
$935$		0			0
$936$		0			0
$937$		−	19.0000i		−	0.620703i	−0.950622	−	0.310351i	$-0.899553\pi$
$937$		−	19.0000i		−	0.620703i	0.950622	−	0.310351i	$-0.100447\pi$
$938$		0			0
$939$	−27.0000			−0.881112
$940$		0			0
$941$	9.00000	−	15.5885i	0.293392	−	0.508169i	−0.681218	−	0.732081i	$-0.738549\pi$
$941$	9.00000	−	15.5885i	0.293392	−	0.508169i	0.974609	+	0.223912i	$0.0718827\pi$
$942$		0			0
$943$	−41.5692	+	24.0000i	−1.35368	+	0.781548i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	43.3013	−	25.0000i	1.40710	−	0.812391i	0.411994	−	0.911186i	$-0.364832\pi$
$947$	43.3013	−	25.0000i	1.40710	−	0.812391i	0.995108	+	0.0987955i	$0.0314990\pi$
$948$		0			0
$949$	−1.00000	+	1.73205i	−0.0324614	+	0.0562247i
$950$		0			0
$951$	34.0000			1.10253
$952$		0			0
$953$		−	52.0000i		−	1.68445i	−0.539130	−	0.842223i	$-0.681247\pi$
$953$		−	52.0000i		−	1.68445i	0.539130	−	0.842223i	$-0.318753\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−6.92820	+	4.00000i	−0.223957	+	0.129302i
$958$		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
$967$		−	31.0000i		−	0.996893i	−0.866921	−	0.498446i	$-0.833904\pi$
$967$		−	31.0000i		−	0.996893i	0.866921	−	0.498446i	$-0.166096\pi$
$968$		0			0
$969$	4.00000	−	6.92820i	0.128499	−	0.222566i
$970$		0			0
$971$	22.0000	+	38.1051i	0.706014	+	1.22285i	0.966324	+	0.257327i	$0.0828416\pi$
$971$	22.0000	+	38.1051i	0.706014	+	1.22285i	−0.260311	+	0.965525i	$0.583825\pi$
$972$		0			0
$973$	8.66025	+	10.0000i	0.277635	+	0.320585i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−10.3923	−	6.00000i	−0.332479	−	0.191957i	0.324462	−	0.945899i	$-0.394817\pi$
$977$	−10.3923	−	6.00000i	−0.332479	−	0.191957i	−0.656941	+	0.753942i	$0.728150\pi$
$978$		0			0
$979$	−20.0000			−0.639203
$980$		0			0
$981$	14.0000			0.446986
$982$		0			0
$983$	15.5885	+	9.00000i	0.497195	+	0.287055i	0.727554	−	0.686050i	$-0.240657\pi$
$983$	15.5885	+	9.00000i	0.497195	+	0.287055i	−0.230360	+	0.973106i	$0.573990\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	10.3923	+	12.0000i	0.330791	+	0.381964i
$988$		0			0
$989$	4.00000	+	6.92820i	0.127193	+	0.220304i
$990$		0			0
$991$	−15.5000	+	26.8468i	−0.492374	+	0.852816i	−0.999961	−	0.00878379i	$-0.997204\pi$
$991$	−15.5000	+	26.8468i	−0.492374	+	0.852816i	0.507588	+	0.861600i	$0.330537\pi$
$992$		0			0
$993$			27.0000i			0.856819i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	26.8468	+	15.5000i	0.850246	+	0.490890i	0.860734	−	0.509055i	$-0.170005\pi$
$997$	26.8468	+	15.5000i	0.850246	+	0.490890i	−0.0104877	+	0.999945i	$0.503338\pi$
$998$		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.bc.b.949.1		4
5.2	odd	4		2100.2.q.c.1201.1	✓	2
5.3	odd	4		2100.2.q.e.1201.1	yes	2
5.4	even	2	inner	2100.2.bc.b.949.2		4
7.2	even	3	inner	2100.2.bc.b.1549.2		4
35.2	odd	12		2100.2.q.c.1801.1	yes	2
35.9	even	6	inner	2100.2.bc.b.1549.1		4
35.23	odd	12		2100.2.q.e.1801.1	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2100.2.q.c.1201.1	✓	2	5.2	odd	4
2100.2.q.c.1801.1	yes	2	35.2	odd	12
2100.2.q.e.1201.1	yes	2	5.3	odd	4
2100.2.q.e.1801.1	yes	2	35.23	odd	12
2100.2.bc.b.949.1		4	1.1	even	1	trivial
2100.2.bc.b.949.2		4	5.4	even	2	inner
2100.2.bc.b.1549.1		4	35.9	even	6	inner
2100.2.bc.b.1549.2		4	7.2	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{3} +(-1.73205 - 2.00000i) q^{7} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{3} +(-1.73205 - 2.00000i) q^{7} +(0.500000 + 0.866025i) q^{9} +(-1.00000 + 1.73205i) q^{11} -2.00000i q^{13} +(1.73205 + 1.00000i) q^{17} +(2.00000 + 3.46410i) q^{19} +(0.500000 + 2.59808i) q^{21} +(-6.92820 + 4.00000i) q^{23} -1.00000i q^{27} -4.00000 q^{29} +(-1.50000 + 2.59808i) q^{31} +(1.73205 - 1.00000i) q^{33} +(7.79423 - 4.50000i) q^{37} +(-1.00000 + 1.73205i) q^{39} +6.00000 q^{41} -1.00000i q^{43} +(5.19615 - 3.00000i) q^{47} +(-1.00000 + 6.92820i) q^{49} +(-1.00000 - 1.73205i) q^{51} +(-1.73205 - 1.00000i) q^{53} -4.00000i q^{57} +(-3.00000 + 5.19615i) q^{59} +(0.500000 + 0.866025i) q^{61} +(0.866025 - 2.50000i) q^{63} +(10.3923 + 6.00000i) q^{67} +8.00000 q^{69} +10.0000 q^{71} +(-0.866025 - 0.500000i) q^{73} +(5.19615 - 1.00000i) q^{77} +(3.50000 + 6.06218i) q^{79} +(-0.500000 + 0.866025i) q^{81} +18.0000i q^{83} +(3.46410 + 2.00000i) q^{87} +(5.00000 + 8.66025i) q^{89} +(-4.00000 + 3.46410i) q^{91} +(2.59808 - 1.50000i) q^{93} -5.00000i q^{97} -2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^9	\( 4 q + 2 q^{9} - 4 q^{11} + 8 q^{19} + 2 q^{21} - 16 q^{29} - 6 q^{31} - 4 q^{39} + 24 q^{41} - 4 q^{49} - 4 q^{51} - 12 q^{59} + 2 q^{61} + 32 q^{69} + 40 q^{71} + 14 q^{79} - 2 q^{81} + 20 q^{89} - 16 q^{91} - 8 q^{99}+O(q^{100}) \) 4 * q + 2 * q^9 - 4 * q^11 + 8 * q^19 + 2 * q^21 - 16 * q^29 - 6 * q^31 - 4 * q^39 + 24 * q^41 - 4 * q^49 - 4 * q^51 - 12 * q^59 + 2 * q^61 + 32 * q^69 + 40 * q^71 + 14 * q^79 - 2 * q^81 + 20 * q^89 - 16 * q^91 - 8 * q^99

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