LMFDB - Embedded newform 2100.2.bc.e.1549.2

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:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.49787136.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 3x^{6} + 5x^{4} + 12x^{2} + 16 $ x^8 + 3x^6 + 5x^4 + 12*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 420)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1549.2
Root			$-0.228425 + 1.39564i$ of defining polynomial
Character	$\chi$	$=$	2100.1549
Dual form			2100.2.bc.e.949.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{3} +(2.29129 + 1.32288i) q^{7} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	$q+(-0.866025 + 0.500000i) q^{3} +(2.29129 + 1.32288i) q^{7} +(0.500000 - 0.866025i) q^{9} +(-1.82288 - 3.15731i) q^{11} -2.64575i q^{13} +(3.15731 - 1.82288i) q^{17} +(-1.14575 + 1.98450i) q^{19} -2.64575 q^{21} +(-3.15731 - 1.82288i) q^{23} +1.00000i q^{27} -2.35425 q^{29} +(-3.14575 - 5.44860i) q^{31} +(3.15731 + 1.82288i) q^{33} +(4.02334 + 2.32288i) q^{37} +(1.32288 + 2.29129i) q^{39} -10.9373 q^{41} -9.93725i q^{43} +(-5.19615 - 3.00000i) q^{47} +(3.50000 + 6.06218i) q^{49} +(-1.82288 + 3.15731i) q^{51} +(6.31463 - 3.64575i) q^{53} -2.29150i q^{57} +(-2.46863 - 4.27579i) q^{59} +(-4.00000 + 6.92820i) q^{61} +(2.29129 - 1.32288i) q^{63} +(-4.02334 + 2.32288i) q^{67} +3.64575 q^{69} +8.35425 q^{71} +(11.4564 - 6.61438i) q^{73} -9.64575i q^{77} +(-4.14575 + 7.18065i) q^{79} +(-0.500000 - 0.866025i) q^{81} -4.93725i q^{83} +(2.03884 - 1.17712i) q^{87} +(6.11438 - 10.5904i) q^{89} +(3.50000 - 6.06218i) q^{91} +(5.44860 + 3.14575i) q^{93} +8.00000i q^{97} -3.64575 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{9}+O(q^{10}) $ 8 * q + 4 * q^9	$ 8 q + 4 q^{9} - 4 q^{11} + 12 q^{19} - 40 q^{29} - 4 q^{31} - 24 q^{41} + 28 q^{49} - 4 q^{51} + 12 q^{59} - 32 q^{61} + 8 q^{69} + 88 q^{71} - 12 q^{79} - 4 q^{81} - 4 q^{89} + 28 q^{91} - 8 q^{99}+O(q^{100}) $ 8 * q + 4 * q^9 - 4 * q^11 + 12 * q^19 - 40 * q^29 - 4 * q^31 - 24 * q^41 + 28 * q^49 - 4 * q^51 + 12 * q^59 - 32 * q^61 + 8 * q^69 + 88 * q^71 - 12 * q^79 - 4 * q^81 - 4 * q^89 + 28 * q^91 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	−0.866025	+	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
$7$	2.29129	+	1.32288i	0.866025	+	0.500000i
$7$	2.29129	+	1.32288i	0.866025	+	0.500000i
$8$		0			0
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$		0			0
$11$	−1.82288	−	3.15731i	−0.549618	−	0.951966i	−0.998301	−	0.0582747i	$-0.981440\pi$
$11$	−1.82288	−	3.15731i	−0.549618	−	0.951966i	0.448683	−	0.893691i	$-0.351893\pi$
$12$		0			0
$13$		−	2.64575i		−	0.733799i	−0.930261	−	0.366900i	$-0.880419\pi$
$13$		−	2.64575i		−	0.733799i	0.930261	−	0.366900i	$-0.119581\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	3.15731	−	1.82288i	0.765761	−	0.442112i	−0.0655994	−	0.997846i	$-0.520896\pi$
$17$	3.15731	−	1.82288i	0.765761	−	0.442112i	0.831360	+	0.555734i	$0.187563\pi$
$18$		0			0
$19$	−1.14575	+	1.98450i	−0.262853	+	0.455275i	−0.966999	−	0.254780i	$-0.917997\pi$
$19$	−1.14575	+	1.98450i	−0.262853	+	0.455275i	0.704146	+	0.710056i	$0.251330\pi$
$20$		0			0
$21$	−2.64575			−0.577350
$22$		0			0
$23$	−3.15731	−	1.82288i	−0.658345	−	0.380096i	0.133301	−	0.991076i	$-0.457442\pi$
$23$	−3.15731	−	1.82288i	−0.658345	−	0.380096i	−0.791646	+	0.610980i	$0.790776\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$			1.00000i			0.192450i
$28$		0			0
$29$	−2.35425			−0.437173			−0.218587	−	0.975818i	$-0.570145\pi$
$29$	−2.35425			−0.437173			−0.218587	+	0.975818i	$0.570145\pi$
$30$		0			0
$31$	−3.14575	−	5.44860i	−0.564994	−	0.978598i	−0.997050	−	0.0767512i	$-0.975545\pi$
$31$	−3.14575	−	5.44860i	−0.564994	−	0.978598i	0.432057	−	0.901846i	$-0.357788\pi$
$32$		0			0
$33$	3.15731	+	1.82288i	0.549618	+	0.317322i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	4.02334	+	2.32288i	0.661433	+	0.381878i	0.792823	−	0.609452i	$-0.208611\pi$
$37$	4.02334	+	2.32288i	0.661433	+	0.381878i	−0.131390	+	0.991331i	$0.541944\pi$
$38$		0			0
$39$	1.32288	+	2.29129i	0.211830	+	0.366900i
$40$		0			0
$41$	−10.9373			−1.70811			−0.854056	−	0.520181i	$-0.825864\pi$
$41$	−10.9373			−1.70811			−0.854056	+	0.520181i	$0.825864\pi$
$42$		0			0
$43$		−	9.93725i		−	1.51542i	−0.652593	−	0.757709i	$-0.726319\pi$
$43$		−	9.93725i		−	1.51542i	0.652593	−	0.757709i	$-0.273681\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−5.19615	−	3.00000i	−0.757937	−	0.437595i	0.0706177	−	0.997503i	$-0.477503\pi$
$47$	−5.19615	−	3.00000i	−0.757937	−	0.437595i	−0.828554	+	0.559908i	$0.810836\pi$
$48$		0			0
$49$	3.50000	+	6.06218i	0.500000	+	0.866025i
$50$		0			0
$51$	−1.82288	+	3.15731i	−0.255254	+	0.442112i
$52$		0			0
$53$	6.31463	−	3.64575i	0.867381	−	0.500782i	0.000903738	−	1.00000i	$-0.499712\pi$
$53$	6.31463	−	3.64575i	0.867381	−	0.500782i	0.866477	+	0.499217i	$0.166379\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		−	2.29150i		−	0.303517i
$58$		0			0
$59$	−2.46863	−	4.27579i	−0.321388	−	0.556660i	0.659387	−	0.751804i	$-0.270816\pi$
$59$	−2.46863	−	4.27579i	−0.321388	−	0.556660i	−0.980775	+	0.195144i	$0.937483\pi$
$60$		0			0
$61$	−4.00000	+	6.92820i	−0.512148	+	0.887066i	0.487753	+	0.872982i	$0.337817\pi$
$61$	−4.00000	+	6.92820i	−0.512148	+	0.887066i	−0.999901	+	0.0140840i	$0.995517\pi$
$62$		0			0
$63$	2.29129	−	1.32288i	0.288675	−	0.166667i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−4.02334	+	2.32288i	−0.491529	+	0.283784i	−0.725209	−	0.688529i	$-0.758257\pi$
$67$	−4.02334	+	2.32288i	−0.491529	+	0.283784i	0.233680	+	0.972314i	$0.424923\pi$
$68$		0			0
$69$	3.64575			0.438897
$70$		0			0
$71$	8.35425			0.991467			0.495733	−	0.868475i	$-0.334899\pi$
$71$	8.35425			0.991467			0.495733	+	0.868475i	$0.334899\pi$
$72$		0			0
$73$	11.4564	−	6.61438i	1.34087	−	0.774154i	0.353939	−	0.935269i	$-0.384842\pi$
$73$	11.4564	−	6.61438i	1.34087	−	0.774154i	0.986936	+	0.161114i	$0.0515087\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$		−	9.64575i		−	1.09924i
$78$		0			0
$79$	−4.14575	+	7.18065i	−0.466433	+	0.807886i	−0.999265	−	0.0383349i	$-0.987795\pi$
$79$	−4.14575	+	7.18065i	−0.466433	+	0.807886i	0.532831	+	0.846221i	$0.321128\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$		−	4.93725i		−	0.541934i	−0.962589	−	0.270967i	$-0.912657\pi$
$83$		−	4.93725i		−	0.541934i	0.962589	−	0.270967i	$-0.0873434\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	2.03884	−	1.17712i	0.218587	−	0.126201i
$88$		0			0
$89$	6.11438	−	10.5904i	0.648123	−	1.12258i	−0.335448	−	0.942059i	$-0.608888\pi$
$89$	6.11438	−	10.5904i	0.648123	−	1.12258i	0.983571	−	0.180523i	$-0.0577790\pi$
$90$		0			0
$91$	3.50000	−	6.06218i	0.366900	−	0.635489i
$92$		0			0
$93$	5.44860	+	3.14575i	0.564994	+	0.326199i
$94$		0			0
$95$		0			0
$96$		0			0
$97$			8.00000i			0.812277i	0.913812	+	0.406138i	$0.133125\pi$
$97$			8.00000i			0.812277i	−0.913812	+	0.406138i	$0.866875\pi$
$98$		0			0
$99$	−3.64575			−0.366412
$100$		0			0
$101$	−5.46863	−	9.47194i	−0.544149	−	0.942493i	−0.998660	−	0.0517522i	$-0.983519\pi$
$101$	−5.46863	−	9.47194i	−0.544149	−	0.942493i	0.454511	−	0.890741i	$-0.349814\pi$
$102$		0			0
$103$	12.6836	+	7.32288i	1.24975	+	0.721544i	0.971060	−	0.238836i	$-0.0767659\pi$
$103$	12.6836	+	7.32288i	1.24975	+	0.721544i	0.278692	+	0.960381i	$0.410099\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	0.920365	+	0.531373i	0.0889751	+	0.0513698i	0.543827	−	0.839197i	$-0.316975\pi$
$107$	0.920365	+	0.531373i	0.0889751	+	0.0513698i	−0.454852	+	0.890567i	$0.650308\pi$
$108$		0			0
$109$	−6.50000	−	11.2583i	−0.622587	−	1.07835i	−0.989002	−	0.147901i	$-0.952748\pi$
$109$	−6.50000	−	11.2583i	−0.622587	−	1.07835i	0.366415	−	0.930451i	$-0.380585\pi$
$110$		0			0
$111$	−4.64575			−0.440955
$112$		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
$117$	−2.29129	−	1.32288i	−0.211830	−	0.122300i
$118$		0			0
$119$	9.64575			0.884225
$120$		0			0
$121$	−1.14575	+	1.98450i	−0.104159	+	0.180409i
$122$		0			0
$123$	9.47194	−	5.46863i	0.854056	−	0.493089i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		−	17.9373i		−	1.59167i	−0.605511	−	0.795837i	$-0.707031\pi$
$127$		−	17.9373i		−	1.59167i	0.605511	−	0.795837i	$-0.292969\pi$
$128$		0			0
$129$	4.96863	+	8.60591i	0.437463	+	0.757709i
$130$		0			0
$131$	−5.35425	+	9.27383i	−0.467803	+	0.810258i	−0.999323	−	0.0367872i	$-0.988288\pi$
$131$	−5.35425	+	9.27383i	−0.467803	+	0.810258i	0.531520	+	0.847046i	$0.321621\pi$
$132$		0			0
$133$	−5.25049	+	3.03137i	−0.455275	+	0.262853i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	5.39426	−	3.11438i	0.460863	−	0.266079i	−0.251544	−	0.967846i	$-0.580938\pi$
$137$	5.39426	−	3.11438i	0.460863	−	0.266079i	0.712407	+	0.701767i	$0.247605\pi$
$138$		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
$143$	−8.35347	+	4.82288i	−0.698552	+	0.403309i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−6.06218	−	3.50000i	−0.500000	−	0.288675i
$148$		0			0
$149$	7.29150	−	12.6293i	0.597343	−	1.03463i	−0.395868	−	0.918307i	$-0.629556\pi$
$149$	7.29150	−	12.6293i	0.597343	−	1.03463i	0.993212	−	0.116321i	$-0.0371103\pi$
$150$		0			0
$151$	−8.29150	−	14.3613i	−0.674753	−	1.16871i	−0.976541	−	0.215331i	$-0.930917\pi$
$151$	−8.29150	−	14.3613i	−0.674753	−	1.16871i	0.301788	−	0.953375i	$-0.402416\pi$
$152$		0			0
$153$		−	3.64575i		−	0.294742i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	8.04668	−	4.64575i	0.642195	−	0.370771i	−0.143265	−	0.989684i	$-0.545760\pi$
$157$	8.04668	−	4.64575i	0.642195	−	0.370771i	0.785459	+	0.618913i	$0.212427\pi$
$158$		0			0
$159$	−3.64575	+	6.31463i	−0.289127	+	0.500782i
$160$		0			0
$161$	−4.82288	−	8.35347i	−0.380096	−	0.658345i
$162$		0			0
$163$	−13.8564	−	8.00000i	−1.08532	−	0.626608i	−0.152992	−	0.988227i	$-0.548891\pi$
$163$	−13.8564	−	8.00000i	−1.08532	−	0.626608i	−0.932326	+	0.361619i	$0.882224\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$			14.3542i			1.11077i	0.831595	+	0.555383i	$0.187428\pi$
$167$			14.3542i			1.11077i	−0.831595	+	0.555383i	$0.812572\pi$
$168$		0			0
$169$	6.00000			0.461538
$170$		0			0
$171$	1.14575	+	1.98450i	0.0876178	+	0.151758i
$172$		0			0
$173$	−18.9439	−	10.9373i	−1.44028	−	0.831544i	−0.442409	−	0.896813i	$-0.645876\pi$
$173$	−18.9439	−	10.9373i	−1.44028	−	0.831544i	−0.997868	+	0.0652695i	$0.979209\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	4.27579	+	2.46863i	0.321388	+	0.185553i
$178$		0			0
$179$	−10.2915	−	17.8254i	−0.769223	−	1.33233i	−0.937985	−	0.346676i	$-0.887310\pi$
$179$	−10.2915	−	17.8254i	−0.769223	−	1.33233i	0.168762	−	0.985657i	$-0.446023\pi$
$180$		0			0
$181$	6.29150			0.467644			0.233822	−	0.972279i	$-0.424877\pi$
$181$	6.29150			0.467644			0.233822	+	0.972279i	$0.424877\pi$
$182$		0			0
$183$		−	8.00000i		−	0.591377i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−11.5108	−	6.64575i	−0.841752	−	0.485985i
$188$		0			0
$189$	−1.32288	+	2.29129i	−0.0962250	+	0.166667i
$190$		0			0
$191$	11.5830	−	20.0624i	0.838117	−	1.45166i	−0.0533504	−	0.998576i	$-0.516990\pi$
$191$	11.5830	−	20.0624i	0.838117	−	1.45166i	0.891467	−	0.453085i	$-0.149677\pi$
$192$		0			0
$193$	20.7303	−	11.9686i	1.49220	−	0.861521i	0.492237	−	0.870461i	$-0.336179\pi$
$193$	20.7303	−	11.9686i	1.49220	−	0.861521i	0.999960	+	0.00894034i	$0.00284584\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			10.9373i			0.779247i	0.920974	+	0.389624i	$0.127395\pi$
$197$			10.9373i			0.779247i	−0.920974	+	0.389624i	$0.872605\pi$
$198$		0			0
$199$	9.58301	+	16.5983i	0.679321	+	1.17662i	0.975186	+	0.221389i	$0.0710590\pi$
$199$	9.58301	+	16.5983i	0.679321	+	1.17662i	−0.295864	+	0.955230i	$0.595608\pi$
$200$		0			0
$201$	2.32288	−	4.02334i	0.163843	−	0.283784i
$202$		0			0
$203$	−5.39426	−	3.11438i	−0.378603	−	0.218587i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−3.15731	+	1.82288i	−0.219448	+	0.126699i
$208$		0			0
$209$	8.35425			0.577875
$210$		0			0
$211$	−12.5830			−0.866250			−0.433125	−	0.901334i	$-0.642589\pi$
$211$	−12.5830			−0.866250			−0.433125	+	0.901334i	$0.642589\pi$
$212$		0			0
$213$	−7.23499	+	4.17712i	−0.495733	+	0.286212i
$214$		0			0
$215$		0			0
$216$		0			0
$217$		−	16.6458i		−	1.12999i
$218$		0			0
$219$	−6.61438	+	11.4564i	−0.446958	+	0.774154i
$220$		0			0
$221$	−4.82288	−	8.35347i	−0.324422	−	0.561915i
$222$		0			0
$223$			13.8745i			0.929106i	0.885545	+	0.464553i	$0.153785\pi$
$223$			13.8745i			0.929106i	−0.885545	+	0.464553i	$0.846215\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	12.4311	−	7.17712i	0.825084	−	0.476362i	−0.0270825	−	0.999633i	$-0.508622\pi$
$227$	12.4311	−	7.17712i	0.825084	−	0.476362i	0.852167	+	0.523271i	$0.175288\pi$
$228$		0			0
$229$	−3.50000	+	6.06218i	−0.231287	+	0.400600i	−0.958187	−	0.286143i	$-0.907627\pi$
$229$	−3.50000	+	6.06218i	−0.231287	+	0.400600i	0.726900	+	0.686743i	$0.240960\pi$
$230$		0			0
$231$	4.82288	+	8.35347i	0.317322	+	0.549618i
$232$		0			0
$233$	9.27383	+	5.35425i	0.607549	+	0.350768i	0.772006	−	0.635616i	$-0.219254\pi$
$233$	9.27383	+	5.35425i	0.607549	+	0.350768i	−0.164457	+	0.986384i	$0.552587\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		−	8.29150i		−	0.538591i
$238$		0			0
$239$	−6.00000			−0.388108			−0.194054	−	0.980991i	$-0.562164\pi$
$239$	−6.00000			−0.388108			−0.194054	+	0.980991i	$0.562164\pi$
$240$		0			0
$241$	11.6458	+	20.1710i	0.750169	+	1.29933i	0.947741	+	0.319042i	$0.103361\pi$
$241$	11.6458	+	20.1710i	0.750169	+	1.29933i	−0.197572	+	0.980288i	$0.563306\pi$
$242$		0			0
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	5.25049	+	3.03137i	0.334081	+	0.192882i
$248$		0			0
$249$	2.46863	+	4.27579i	0.156443	+	0.270967i
$250$		0			0
$251$	4.93725			0.311637			0.155818	−	0.987786i	$-0.450199\pi$
$251$	4.93725			0.311637			0.155818	+	0.987786i	$0.450199\pi$
$252$		0			0
$253$			13.2915i			0.835630i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	27.2973	+	15.7601i	1.70276	+	0.983090i	0.942943	+	0.332955i	$0.108046\pi$
$257$	27.2973	+	15.7601i	1.70276	+	0.983090i	0.759819	+	0.650135i	$0.225288\pi$
$258$		0			0
$259$	6.14575	+	10.6448i	0.381878	+	0.661433i
$260$		0			0
$261$	−1.17712	+	2.03884i	−0.0728622	+	0.126201i
$262$		0			0
$263$	−21.1808	+	12.2288i	−1.30607	+	0.754057i	−0.981437	−	0.191784i	$-0.938573\pi$
$263$	−21.1808	+	12.2288i	−1.30607	+	0.754057i	−0.324629	+	0.945842i	$0.605239\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$			12.2288i			0.748388i
$268$		0			0
$269$	−1.93725	−	3.35542i	−0.118116	−	0.204584i	0.800905	−	0.598792i	$-0.204352\pi$
$269$	−1.93725	−	3.35542i	−0.118116	−	0.204584i	−0.919021	+	0.394208i	$0.871019\pi$
$270$		0			0
$271$	−14.2915	+	24.7536i	−0.868147	+	1.50367i	−0.00425882	+	0.999991i	$0.501356\pi$
$271$	−14.2915	+	24.7536i	−0.868147	+	1.50367i	−0.863888	+	0.503684i	$0.831978\pi$
$272$		0			0
$273$			7.00000i			0.423659i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−13.2972	+	7.67712i	−0.798949	+	0.461274i	−0.843104	−	0.537751i	$-0.819274\pi$
$277$	−13.2972	+	7.67712i	−0.798949	+	0.461274i	0.0441542	+	0.999025i	$0.485941\pi$
$278$		0			0
$279$	−6.29150			−0.376662
$280$		0			0
$281$	24.0000			1.43172			0.715860	−	0.698244i	$-0.246035\pi$
$281$	24.0000			1.43172			0.715860	+	0.698244i	$0.246035\pi$
$282$		0			0
$283$	8.10102	−	4.67712i	0.481555	−	0.278026i	−0.239509	−	0.970894i	$-0.576986\pi$
$283$	8.10102	−	4.67712i	0.481555	−	0.278026i	0.721064	+	0.692868i	$0.243653\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−25.0604	−	14.4686i	−1.47927	−	0.854056i
$288$		0			0
$289$	−1.85425	+	3.21165i	−0.109073	+	0.188921i
$290$		0			0
$291$	−4.00000	−	6.92820i	−0.234484	−	0.406138i
$292$		0			0
$293$		0			0		1.00000			$0$
$293$		0			0		−1.00000			$\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	3.15731	−	1.82288i	0.183206	−	0.105774i
$298$		0			0
$299$	−4.82288	+	8.35347i	−0.278914	+	0.483093i
$300$		0			0
$301$	13.1458	−	22.7691i	0.757709	−	1.31239i
$302$		0			0
$303$	9.47194	+	5.46863i	0.544149	+	0.314164i
$304$		0			0
$305$		0			0
$306$		0			0
$307$			12.0627i			0.688457i	0.938886	+	0.344229i	$0.111860\pi$
$307$			12.0627i			0.688457i	−0.938886	+	0.344229i	$0.888140\pi$
$308$		0			0
$309$	−14.6458			−0.833168
$310$		0			0
$311$	−4.17712	−	7.23499i	−0.236863	−	0.410259i	0.722949	−	0.690901i	$-0.242786\pi$
$311$	−4.17712	−	7.23499i	−0.236863	−	0.410259i	−0.959812	+	0.280642i	$0.909453\pi$
$312$		0			0
$313$	4.52824	+	2.61438i	0.255951	+	0.147773i	0.622486	−	0.782631i	$-0.286123\pi$
$313$	4.52824	+	2.61438i	0.255951	+	0.147773i	−0.366535	+	0.930404i	$0.619456\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	11.7089	+	6.76013i	0.657637	+	0.379687i	0.791376	−	0.611330i	$-0.209365\pi$
$317$	11.7089	+	6.76013i	0.657637	+	0.379687i	−0.133739	+	0.991017i	$0.542698\pi$
$318$		0			0
$319$	4.29150	+	7.43310i	0.240278	+	0.416174i
$320$		0			0
$321$	−1.06275			−0.0593167
$322$		0			0
$323$			8.35425i			0.464843i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	11.2583	+	6.50000i	0.622587	+	0.359451i
$328$		0			0
$329$	−7.93725	−	13.7477i	−0.437595	−	0.757937i
$330$		0			0
$331$	−11.0830	+	19.1963i	−0.609177	+	1.05513i	0.382199	+	0.924080i	$0.375167\pi$
$331$	−11.0830	+	19.1963i	−0.609177	+	1.05513i	−0.991376	+	0.131046i	$0.958167\pi$
$332$		0			0
$333$	4.02334	−	2.32288i	0.220478	−	0.127293i
$334$		0			0
$335$		0			0
$336$		0			0
$337$		−	6.77124i		−	0.368853i	−0.982846	−	0.184427i	$-0.940957\pi$
$337$		−	6.77124i		−	0.368853i	0.982846	−	0.184427i	$-0.0590428\pi$
$338$		0			0
$339$	3.00000	+	5.19615i	0.162938	+	0.282216i
$340$		0			0
$341$	−11.4686	+	19.8642i	−0.621061	+	1.07571i
$342$		0			0
$343$			18.5203i			1.00000i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−25.2585	+	14.5830i	−1.35595	+	0.782857i	−0.989075	−	0.147414i	$-0.952905\pi$
$347$	−25.2585	+	14.5830i	−1.35595	+	0.782857i	−0.366873	+	0.930271i	$0.619572\pi$
$348$		0			0
$349$	10.0000			0.535288			0.267644	−	0.963518i	$-0.413755\pi$
$349$	10.0000			0.535288			0.267644	+	0.963518i	$0.413755\pi$
$350$		0			0
$351$	2.64575			0.141220
$352$		0			0
$353$	−19.1420	+	11.0516i	−1.01883	+	0.588219i	−0.913763	−	0.406247i	$-0.866837\pi$
$353$	−19.1420	+	11.0516i	−1.01883	+	0.588219i	−0.105062	+	0.994466i	$0.533504\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−8.35347	+	4.82288i	−0.442112	+	0.255254i
$358$		0			0
$359$	13.4059	−	23.2197i	0.707535	−	1.22549i	−0.258233	−	0.966083i	$-0.583140\pi$
$359$	13.4059	−	23.2197i	0.707535	−	1.22549i	0.965769	−	0.259405i	$-0.0835263\pi$
$360$		0			0
$361$	6.87451	+	11.9070i	0.361816	+	0.626684i
$362$		0			0
$363$		−	2.29150i		−	0.120273i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−16.6526	+	9.61438i	−0.869258	+	0.501866i	−0.867102	−	0.498131i	$-0.834020\pi$
$367$	−16.6526	+	9.61438i	−0.869258	+	0.501866i	−0.00215655	+	0.999998i	$0.500686\pi$
$368$		0			0
$369$	−5.46863	+	9.47194i	−0.284685	+	0.493089i
$370$		0			0
$371$	19.2915			1.00156
$372$		0			0
$373$	13.8021	+	7.96863i	0.714644	+	0.412600i	0.812778	−	0.582573i	$-0.197954\pi$
$373$	13.8021	+	7.96863i	0.714644	+	0.412600i	−0.0981342	+	0.995173i	$0.531287\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			6.22876i			0.320797i
$378$		0			0
$379$	26.2915			1.35050			0.675252	−	0.737587i	$-0.264035\pi$
$379$	26.2915			1.35050			0.675252	+	0.737587i	$0.264035\pi$
$380$		0			0
$381$	8.96863	+	15.5341i	0.459477	+	0.795837i
$382$		0			0
$383$	−14.4700	−	8.35425i	−0.739382	−	0.426882i	0.0824628	−	0.996594i	$-0.473721\pi$
$383$	−14.4700	−	8.35425i	−0.739382	−	0.426882i	−0.821844	+	0.569712i	$0.807055\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−8.60591	−	4.96863i	−0.437463	−	0.252570i
$388$		0			0
$389$	−18.7601	−	32.4935i	−0.951176	−	1.64749i	−0.742885	−	0.669419i	$-0.766543\pi$
$389$	−18.7601	−	32.4935i	−0.951176	−	1.64749i	−0.208291	−	0.978067i	$-0.566790\pi$
$390$		0			0
$391$	−13.2915			−0.672180
$392$		0			0
$393$		−	10.7085i		−	0.540172i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	14.4156	+	8.32288i	0.723500	+	0.417713i	0.816040	−	0.577996i	$-0.196165\pi$
$397$	14.4156	+	8.32288i	0.723500	+	0.417713i	−0.0925393	+	0.995709i	$0.529498\pi$
$398$		0			0
$399$	3.03137	−	5.25049i	0.151758	−	0.262853i
$400$		0			0
$401$	−9.64575	+	16.7069i	−0.481686	+	0.834304i	−0.999779	−	0.0210198i	$-0.993309\pi$
$401$	−9.64575	+	16.7069i	−0.481686	+	0.834304i	0.518093	+	0.855324i	$0.326642\pi$
$402$		0			0
$403$	−14.4156	+	8.32288i	−0.718094	+	0.414592i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		−	16.9373i		−	0.839549i
$408$		0			0
$409$	−18.0830	−	31.3207i	−0.894147	−	1.54871i	−0.834857	−	0.550467i	$-0.814450\pi$
$409$	−18.0830	−	31.3207i	−0.894147	−	1.54871i	−0.0592904	−	0.998241i	$-0.518884\pi$
$410$		0			0
$411$	−3.11438	+	5.39426i	−0.153621	+	0.266079i
$412$		0			0
$413$		−	13.0627i		−	0.642776i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	4.33013	−	2.50000i	0.212047	−	0.122426i
$418$		0			0
$419$	−10.7085			−0.523144			−0.261572	−	0.965184i	$-0.584241\pi$
$419$	−10.7085			−0.523144			−0.261572	+	0.965184i	$0.584241\pi$
$420$		0			0
$421$	1.58301			0.0771510			0.0385755	−	0.999256i	$-0.487718\pi$
$421$	1.58301			0.0771510			0.0385755	+	0.999256i	$0.487718\pi$
$422$		0			0
$423$	−5.19615	+	3.00000i	−0.252646	+	0.145865i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−18.3303	+	10.5830i	−0.887066	+	0.512148i
$428$		0			0
$429$	4.82288	−	8.35347i	0.232851	−	0.403309i
$430$		0			0
$431$	−4.06275	−	7.03688i	−0.195696	−	0.338955i	0.751433	−	0.659810i	$-0.229363\pi$
$431$	−4.06275	−	7.03688i	−0.195696	−	0.338955i	−0.947128	+	0.320855i	$0.896030\pi$
$432$		0			0
$433$		−	8.64575i		−	0.415488i	−0.978183	−	0.207744i	$-0.933388\pi$
$433$		−	8.64575i		−	0.415488i	0.978183	−	0.207744i	$-0.0666121\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	7.23499	−	4.17712i	0.346097	−	0.199819i
$438$		0			0
$439$	−2.64575	+	4.58258i	−0.126275	+	0.218714i	−0.922231	−	0.386640i	$-0.873635\pi$
$439$	−2.64575	+	4.58258i	−0.126275	+	0.218714i	0.795956	+	0.605355i	$0.206969\pi$
$440$		0			0
$441$	7.00000			0.333333
$442$		0			0
$443$	−18.9439	−	10.9373i	−0.900051	−	0.519645i	−0.0228342	−	0.999739i	$-0.507269\pi$
$443$	−18.9439	−	10.9373i	−0.900051	−	0.519645i	−0.877217	+	0.480095i	$0.840602\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$			14.5830i			0.689752i
$448$		0			0
$449$	−8.58301			−0.405057			−0.202529	−	0.979276i	$-0.564916\pi$
$449$	−8.58301			−0.405057			−0.202529	+	0.979276i	$0.564916\pi$
$450$		0			0
$451$	19.9373	+	34.5323i	0.938809	+	1.62606i
$452$		0			0
$453$	14.3613	+	8.29150i	0.674753	+	0.389569i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	8.10102	+	4.67712i	0.378950	+	0.218787i	0.677361	−	0.735651i	$-0.263123\pi$
$457$	8.10102	+	4.67712i	0.378950	+	0.218787i	−0.298412	+	0.954437i	$0.596457\pi$
$458$		0			0
$459$	1.82288	+	3.15731i	0.0850845	+	0.147371i
$460$		0			0
$461$	−14.3542			−0.668544			−0.334272	−	0.942477i	$-0.608490\pi$
$461$	−14.3542			−0.668544			−0.334272	+	0.942477i	$0.608490\pi$
$462$		0			0
$463$			26.5203i			1.23250i	0.787550	+	0.616250i	$0.211349\pi$
$463$			26.5203i			1.23250i	−0.787550	+	0.616250i	$0.788651\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−22.2993	−	12.8745i	−1.03189	−	0.595761i	−0.114363	−	0.993439i	$-0.536483\pi$
$467$	−22.2993	−	12.8745i	−1.03189	−	0.595761i	−0.917525	+	0.397678i	$0.869816\pi$
$468$		0			0
$469$	−12.2915			−0.567569
$470$		0			0
$471$	−4.64575	+	8.04668i	−0.214065	+	0.370771i
$472$		0			0
$473$	−31.3750	+	18.1144i	−1.44263	+	0.832900i
$474$		0			0
$475$		0			0
$476$		0			0
$477$		−	7.29150i		−	0.333855i
$478$		0			0
$479$	7.29150	+	12.6293i	0.333157	+	0.577045i	0.983129	−	0.182913i	$-0.0585527\pi$
$479$	7.29150	+	12.6293i	0.333157	+	0.577045i	−0.649972	+	0.759958i	$0.725219\pi$
$480$		0			0
$481$	6.14575	−	10.6448i	0.280222	−	0.485359i
$482$		0			0
$483$	8.35347	+	4.82288i	0.380096	+	0.219448i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	2.29129	−	1.32288i	0.103828	−	0.0599452i	−0.447187	−	0.894441i	$-0.647574\pi$
$487$	2.29129	−	1.32288i	0.103828	−	0.0599452i	0.551015	+	0.834495i	$0.314241\pi$
$488$		0			0
$489$	16.0000			0.723545
$490$		0			0
$491$	33.8745			1.52874			0.764368	−	0.644781i	$-0.223051\pi$
$491$	33.8745			1.52874			0.764368	+	0.644781i	$0.223051\pi$
$492$		0			0
$493$	−7.43310	+	4.29150i	−0.334770	+	0.193280i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	19.1420	+	11.0516i	0.858636	+	0.495733i
$498$		0			0
$499$	−12.7288	+	22.0469i	−0.569817	+	0.986953i	0.426766	+	0.904362i	$0.359653\pi$
$499$	−12.7288	+	22.0469i	−0.569817	+	0.986953i	−0.996584	+	0.0825907i	$0.973681\pi$
$500$		0			0
$501$	−7.17712	−	12.4311i	−0.320650	−	0.555383i
$502$		0			0
$503$			30.4575i			1.35803i	0.734123	+	0.679017i	$0.237594\pi$
$503$			30.4575i			1.35803i	−0.734123	+	0.679017i	$0.762406\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−5.19615	+	3.00000i	−0.230769	+	0.133235i
$508$		0			0
$509$	1.93725	−	3.35542i	0.0858673	−	0.148726i	−0.819893	−	0.572517i	$-0.805967\pi$
$509$	1.93725	−	3.35542i	0.0858673	−	0.148726i	0.905760	+	0.423790i	$0.139301\pi$
$510$		0			0
$511$	35.0000			1.54831
$512$		0			0
$513$	−1.98450	−	1.14575i	−0.0876178	−	0.0505862i
$514$		0			0
$515$		0			0
$516$		0			0
$517$			21.8745i			0.962040i
$518$		0			0
$519$	21.8745			0.960184
$520$		0			0
$521$	16.9373	+	29.3362i	0.742035	+	1.28524i	0.951567	+	0.307440i	$0.0994723\pi$
$521$	16.9373	+	29.3362i	0.742035	+	1.28524i	−0.209533	+	0.977802i	$0.567194\pi$
$522$		0			0
$523$	4.13202	+	2.38562i	0.180681	+	0.104316i	0.587612	−	0.809143i	$-0.300068\pi$
$523$	4.13202	+	2.38562i	0.180681	+	0.104316i	−0.406932	+	0.913459i	$0.633401\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−19.8642	−	11.4686i	−0.865300	−	0.499581i
$528$		0			0
$529$	−4.85425	−	8.40781i	−0.211054	−	0.365557i
$530$		0			0
$531$	−4.93725			−0.214259
$532$		0			0
$533$			28.9373i			1.25341i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	17.8254	+	10.2915i	0.769223	+	0.444111i
$538$		0			0
$539$	12.7601	−	22.1012i	0.549618	−	0.951966i
$540$		0			0
$541$	13.3745	−	23.1653i	0.575015	−	0.995955i	−0.421025	−	0.907049i	$-0.638330\pi$
$541$	13.3745	−	23.1653i	0.575015	−	0.995955i	0.996040	−	0.0889062i	$-0.0283371\pi$
$542$		0			0
$543$	−5.44860	+	3.14575i	−0.233822	+	0.134997i
$544$		0			0
$545$		0			0
$546$		0			0
$547$		−	32.7085i		−	1.39851i	−0.714870	−	0.699257i	$-0.753514\pi$
$547$		−	32.7085i		−	1.39851i	0.714870	−	0.699257i	$-0.246486\pi$
$548$		0			0
$549$	4.00000	+	6.92820i	0.170716	+	0.295689i
$550$		0			0
$551$	2.69738	−	4.67201i	0.114912	−	0.199034i
$552$		0			0
$553$	−18.9982	+	10.9686i	−0.807886	+	0.466433i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−15.5885	+	9.00000i	−0.660504	+	0.381342i	−0.792469	−	0.609912i	$-0.791205\pi$
$557$	−15.5885	+	9.00000i	−0.660504	+	0.381342i	0.131965	+	0.991254i	$0.457871\pi$
$558$		0			0
$559$	−26.2915			−1.11201
$560$		0			0
$561$	13.2915			0.561168
$562$		0			0
$563$	13.3515	−	7.70850i	0.562699	−	0.324874i	−0.191529	−	0.981487i	$-0.561345\pi$
$563$	13.3515	−	7.70850i	0.562699	−	0.324874i	0.754228	+	0.656613i	$0.228011\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$		−	2.64575i		−	0.111111i
$568$		0			0
$569$	−15.1144	+	26.1789i	−0.633628	+	1.09748i	0.353176	+	0.935557i	$0.385102\pi$
$569$	−15.1144	+	26.1789i	−0.633628	+	1.09748i	−0.986804	+	0.161919i	$0.948232\pi$
$570$		0			0
$571$	−16.8542	−	29.1924i	−0.705328	−	1.22166i	−0.966573	−	0.256392i	$-0.917466\pi$
$571$	−16.8542	−	29.1924i	−0.705328	−	1.22166i	0.261245	−	0.965273i	$-0.415867\pi$
$572$		0			0
$573$			23.1660i			0.967774i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−4.74559	+	2.73987i	−0.197562	+	0.114062i	−0.595518	−	0.803342i	$-0.703053\pi$
$577$	−4.74559	+	2.73987i	−0.197562	+	0.114062i	0.397956	+	0.917405i	$0.369720\pi$
$578$		0			0
$579$	−11.9686	+	20.7303i	−0.497399	+	0.861521i
$580$		0			0
$581$	6.53137	−	11.3127i	0.270967	−	0.469329i
$582$		0			0
$583$	−23.0216	−	13.2915i	−0.953456	−	0.550478i
$584$		0			0
$585$		0			0
$586$		0			0
$587$			1.06275i			0.0438642i	0.999759	+	0.0219321i	$0.00698177\pi$
$587$			1.06275i			0.0438642i	−0.999759	+	0.0219321i	$0.993018\pi$
$588$		0			0
$589$	14.4170			0.594042
$590$		0			0
$591$	−5.46863	−	9.47194i	−0.224949	−	0.389624i
$592$		0			0
$593$	−35.4527	−	20.4686i	−1.45587	−	0.840546i	−0.457064	−	0.889434i	$-0.651099\pi$
$593$	−35.4527	−	20.4686i	−1.45587	−	0.840546i	−0.998804	+	0.0488882i	$0.984432\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−16.5983	−	9.58301i	−0.679321	−	0.392206i
$598$		0			0
$599$	16.9373	+	29.3362i	0.692037	+	1.19864i	0.971169	+	0.238391i	$0.0766200\pi$
$599$	16.9373	+	29.3362i	0.692037	+	1.19864i	−0.279132	+	0.960253i	$0.590047\pi$
$600$		0			0
$601$	−16.4170			−0.669663			−0.334832	−	0.942278i	$-0.608679\pi$
$601$	−16.4170			−0.669663			−0.334832	+	0.942278i	$0.608679\pi$
$602$		0			0
$603$			4.64575i			0.189190i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	37.4372	+	21.6144i	1.51953	+	0.877301i	0.999735	+	0.0230088i	$0.00732459\pi$
$607$	37.4372	+	21.6144i	1.51953	+	0.877301i	0.519794	+	0.854292i	$0.326009\pi$
$608$		0			0
$609$	6.22876			0.252402
$610$		0			0
$611$	−7.93725	+	13.7477i	−0.321107	+	0.556174i
$612$		0			0
$613$	−1.00979	+	0.583005i	−0.0407852	+	0.0235474i	−0.520254	−	0.854012i	$-0.674163\pi$
$613$	−1.00979	+	0.583005i	−0.0407852	+	0.0235474i	0.479469	+	0.877559i	$0.340829\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		−	1.29150i		−	0.0519939i	−0.999662	−	0.0259970i	$-0.991724\pi$
$617$		−	1.29150i		−	0.0519939i	0.999662	−	0.0259970i	$-0.00827602\pi$
$618$		0			0
$619$	−9.50000	−	16.4545i	−0.381837	−	0.661361i	0.609488	−	0.792796i	$-0.291375\pi$
$619$	−9.50000	−	16.4545i	−0.381837	−	0.661361i	−0.991325	+	0.131434i	$0.958042\pi$
$620$		0			0
$621$	1.82288	−	3.15731i	0.0731495	−	0.126699i
$622$		0			0
$623$	28.0196	−	16.1771i	1.12258	−	0.648123i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−7.23499	+	4.17712i	−0.288938	+	0.166818i
$628$		0			0
$629$	16.9373			0.675333
$630$		0			0
$631$	27.7490			1.10467			0.552335	−	0.833622i	$-0.313737\pi$
$631$	27.7490			1.10467			0.552335	+	0.833622i	$0.313737\pi$
$632$		0			0
$633$	10.8972	−	6.29150i	0.433125	−	0.250065i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	16.0390	−	9.26013i	0.635489	−	0.366900i
$638$		0			0
$639$	4.17712	−	7.23499i	0.165244	−	0.286212i
$640$		0			0
$641$	−23.0516	−	39.9266i	−0.910485	−	1.57701i	−0.813381	−	0.581732i	$-0.802375\pi$
$641$	−23.0516	−	39.9266i	−0.910485	−	1.57701i	−0.0971039	−	0.995274i	$-0.530958\pi$
$642$		0			0
$643$		−	25.8118i		−	1.01792i	−0.860791	−	0.508958i	$-0.830031\pi$
$643$		−	25.8118i		−	1.01792i	0.860791	−	0.508958i	$-0.169969\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	6.11652	−	3.53137i	0.240465	−	0.138833i	−0.374925	−	0.927055i	$-0.622332\pi$
$647$	6.11652	−	3.53137i	0.240465	−	0.138833i	0.615390	+	0.788222i	$0.288998\pi$
$648$		0			0
$649$	−9.00000	+	15.5885i	−0.353281	+	0.611900i
$650$		0			0
$651$	8.32288	+	14.4156i	0.326199	+	0.564994i
$652$		0			0
$653$	29.1381	+	16.8229i	1.14026	+	0.658330i	0.946495	−	0.322718i	$-0.104596\pi$
$653$	29.1381	+	16.8229i	1.14026	+	0.658330i	0.193766	+	0.981048i	$0.437930\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		−	13.2288i		−	0.516103i
$658$		0			0
$659$	24.0000			0.934907			0.467454	−	0.884018i	$-0.345171\pi$
$659$	24.0000			0.934907			0.467454	+	0.884018i	$0.345171\pi$
$660$		0			0
$661$	4.56275	+	7.90291i	0.177470	+	0.307387i	0.941013	−	0.338369i	$-0.109875\pi$
$661$	4.56275	+	7.90291i	0.177470	+	0.307387i	−0.763543	+	0.645757i	$0.776542\pi$
$662$		0			0
$663$	8.35347	+	4.82288i	0.324422	+	0.187305i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	7.43310	+	4.29150i	0.287811	+	0.166168i
$668$		0			0
$669$	−6.93725	−	12.0157i	−0.268210	−	0.464553i
$670$		0			0
$671$	29.1660			1.12594
$672$		0			0
$673$			10.6458i			0.410364i	0.978724	+	0.205182i	$0.0657786\pi$
$673$			10.6458i			0.410364i	−0.978724	+	0.205182i	$0.934221\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	23.9419	+	13.8229i	0.920163	+	0.531256i	0.883687	−	0.468078i	$-0.155053\pi$
$677$	23.9419	+	13.8229i	0.920163	+	0.531256i	0.0364758	+	0.999335i	$0.488387\pi$
$678$		0			0
$679$	−10.5830	+	18.3303i	−0.406138	+	0.703452i
$680$		0			0
$681$	−7.17712	+	12.4311i	−0.275028	+	0.476362i
$682$		0			0
$683$	9.47194	−	5.46863i	0.362434	−	0.209251i	−0.307714	−	0.951479i	$-0.599564\pi$
$683$	9.47194	−	5.46863i	0.362434	−	0.209251i	0.670148	+	0.742228i	$0.266231\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$		−	7.00000i		−	0.267067i
$688$		0			0
$689$	−9.64575	−	16.7069i	−0.367474	−	0.636483i
$690$		0			0
$691$	−1.20850	+	2.09318i	−0.0459734	+	0.0796283i	−0.888096	−	0.459657i	$-0.847972\pi$
$691$	−1.20850	+	2.09318i	−0.0459734	+	0.0796283i	0.842123	+	0.539285i	$0.181306\pi$
$692$		0			0
$693$	−8.35347	−	4.82288i	−0.317322	−	0.183206i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−34.5323	+	19.9373i	−1.30801	+	0.755177i
$698$		0			0
$699$	−10.7085			−0.405033
$700$		0			0
$701$	19.0627			0.719990			0.359995	−	0.932954i	$-0.382778\pi$
$701$	19.0627			0.719990			0.359995	+	0.932954i	$0.382778\pi$
$702$		0			0
$703$	−9.21949	+	5.32288i	−0.347720	+	0.200756i
$704$		0			0
$705$		0			0
$706$		0			0
$707$		−	28.9373i		−	1.08830i
$708$		0			0
$709$	−0.708497	+	1.22715i	−0.0266082	+	0.0460867i	−0.879023	−	0.476780i	$-0.841804\pi$
$709$	−0.708497	+	1.22715i	−0.0266082	+	0.0460867i	0.852415	+	0.522866i	$0.175137\pi$
$710$		0			0
$711$	4.14575	+	7.18065i	0.155478	+	0.269295i
$712$		0			0
$713$			22.9373i			0.859007i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	5.19615	−	3.00000i	0.194054	−	0.112037i
$718$		0			0
$719$	−12.6458	+	21.9031i	−0.471607	+	0.816847i	−0.999472	−	0.0324808i	$-0.989659\pi$
$719$	−12.6458	+	21.9031i	−0.471607	+	0.816847i	0.527865	+	0.849328i	$0.322993\pi$
$720$		0			0
$721$	19.3745	+	33.5576i	0.721544	+	1.24975i
$722$		0			0
$723$	−20.1710	−	11.6458i	−0.750169	−	0.433110i
$724$		0			0
$725$		0			0
$726$		0			0
$727$			13.8118i			0.512250i	0.966644	+	0.256125i	$0.0824459\pi$
$727$			13.8118i			0.512250i	−0.966644	+	0.256125i	$0.917554\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	−18.1144	−	31.3750i	−0.669984	−	1.16045i
$732$		0			0
$733$	−16.6526	−	9.61438i	−0.615078	−	0.355115i	0.159873	−	0.987138i	$-0.448892\pi$
$733$	−16.6526	−	9.61438i	−0.615078	−	0.355115i	−0.774950	+	0.632023i	$0.782225\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	14.6681	+	8.46863i	0.540306	+	0.311946i
$738$		0			0
$739$	14.5000	+	25.1147i	0.533391	+	0.923861i	0.999239	+	0.0389959i	$0.0124159\pi$
$739$	14.5000	+	25.1147i	0.533391	+	0.923861i	−0.465848	+	0.884865i	$0.654251\pi$
$740$		0			0
$741$	−6.06275			−0.222721
$742$		0			0
$743$			28.9373i			1.06160i	0.847496	+	0.530802i	$0.178109\pi$
$743$			28.9373i			1.06160i	−0.847496	+	0.530802i	$0.821891\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−4.27579	−	2.46863i	−0.156443	−	0.0903223i
$748$		0			0
$749$	1.40588	+	2.43506i	0.0513698	+	0.0889751i
$750$		0			0
$751$	9.08301	−	15.7322i	0.331444	−	0.574077i	−0.651352	−	0.758776i	$-0.725798\pi$
$751$	9.08301	−	15.7322i	0.331444	−	0.574077i	0.982795	+	0.184699i	$0.0591310\pi$
$752$		0			0
$753$	−4.27579	+	2.46863i	−0.155818	+	0.0899618i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		−	51.1660i		−	1.85966i	−0.367989	−	0.929830i	$-0.619954\pi$
$757$		−	51.1660i		−	1.85966i	0.367989	−	0.929830i	$-0.380046\pi$
$758$		0			0
$759$	−6.64575	−	11.5108i	−0.241225	−	0.417815i
$760$		0			0
$761$	−23.0516	+	39.9266i	−0.835621	+	1.44734i	0.0579028	+	0.998322i	$0.481559\pi$
$761$	−23.0516	+	39.9266i	−0.835621	+	1.44734i	−0.893524	+	0.449016i	$0.851775\pi$
$762$		0			0
$763$		−	34.3948i		−	1.24517i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−11.3127	+	6.53137i	−0.408477	+	0.235834i
$768$		0			0
$769$	14.2915			0.515365			0.257682	−	0.966230i	$-0.417041\pi$
$769$	14.2915			0.515365			0.257682	+	0.966230i	$0.417041\pi$
$770$		0			0
$771$	−31.5203			−1.13517
$772$		0			0
$773$	35.8489	−	20.6974i	1.28940	−	0.744433i	0.310850	−	0.950459i	$-0.399386\pi$
$773$	35.8489	−	20.6974i	1.28940	−	0.744433i	0.978547	+	0.206026i	$0.0660531\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−10.6448	−	6.14575i	−0.381878	−	0.220478i
$778$		0			0
$779$	12.5314	−	21.7050i	0.448983	−	0.777661i
$780$		0			0
$781$	−15.2288	−	26.3770i	−0.544928	−	0.943843i
$782$		0			0
$783$		−	2.35425i		−	0.0841340i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−22.4080	+	12.9373i	−0.798758	+	0.461163i	−0.843037	−	0.537856i	$-0.819234\pi$
$787$	−22.4080	+	12.9373i	−0.798758	+	0.461163i	0.0442785	+	0.999019i	$0.485901\pi$
$788$		0			0
$789$	12.2288	−	21.1808i	0.435355	−	0.754057i
$790$		0			0
$791$	7.93725	−	13.7477i	0.282216	−	0.488813i
$792$		0			0
$793$	18.3303	+	10.5830i	0.650928	+	0.375814i
$794$		0			0
$795$		0			0
$796$		0			0
$797$		−	10.9373i		−	0.387417i	−0.981059	−	0.193709i	$-0.937948\pi$
$797$		−	10.9373i		−	0.387417i	0.981059	−	0.193709i	$-0.0620517\pi$
$798$		0			0
$799$	−21.8745			−0.773864
$800$		0			0
$801$	−6.11438	−	10.5904i	−0.216041	−	0.374194i
$802$		0			0
$803$	−41.7673	−	24.1144i	−1.47394	−	0.850978i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	3.35542	+	1.93725i	0.118116	+	0.0681946i
$808$		0			0
$809$	−11.5830	−	20.0624i	−0.407237	−	0.705355i	0.587342	−	0.809339i	$-0.300174\pi$
$809$	−11.5830	−	20.0624i	−0.407237	−	0.705355i	−0.994579	+	0.103984i	$0.966841\pi$
$810$		0			0
$811$	6.70850			0.235567			0.117784	−	0.993039i	$-0.462421\pi$
$811$	6.70850			0.235567			0.117784	+	0.993039i	$0.462421\pi$
$812$		0			0
$813$		−	28.5830i		−	1.00245i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	19.7205	+	11.3856i	0.689932	+	0.398332i
$818$		0			0
$819$	−3.50000	−	6.06218i	−0.122300	−	0.211830i
$820$		0			0
$821$	−18.9889	+	32.8897i	−0.662717	+	1.14786i	0.317182	+	0.948365i	$0.397263\pi$
$821$	−18.9889	+	32.8897i	−0.662717	+	1.14786i	−0.979899	+	0.199494i	$0.936070\pi$
$822$		0			0
$823$	29.8411	−	17.2288i	1.04019	−	0.600557i	0.120306	−	0.992737i	$-0.461612\pi$
$823$	29.8411	−	17.2288i	1.04019	−	0.600557i	0.919888	+	0.392180i	$0.128279\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	30.4575i		−	1.05911i	−0.848275	−	0.529556i	$-0.822359\pi$
$827$		−	30.4575i		−	1.05911i	0.848275	−	0.529556i	$-0.177641\pi$
$828$		0			0
$829$	15.1458	+	26.2332i	0.526034	+	0.911117i	0.999540	+	0.0303267i	$0.00965476\pi$
$829$	15.1458	+	26.2332i	0.526034	+	0.911117i	−0.473506	+	0.880790i	$0.657012\pi$
$830$		0			0
$831$	7.67712	−	13.2972i	0.266316	−	0.461274i
$832$		0			0
$833$	22.1012	+	12.7601i	0.765761	+	0.442112i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	5.44860	−	3.14575i	0.188331	−	0.108733i
$838$		0			0
$839$	−21.6458			−0.747294			−0.373647	−	0.927571i	$-0.621893\pi$
$839$	−21.6458			−0.747294			−0.373647	+	0.927571i	$0.621893\pi$
$840$		0			0
$841$	−23.4575			−0.808880
$842$		0			0
$843$	−20.7846	+	12.0000i	−0.715860	+	0.413302i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−5.25049	+	3.03137i	−0.180409	+	0.104159i
$848$		0			0
$849$	−4.67712	+	8.10102i	−0.160518	+	0.278026i
$850$		0			0
$851$	−8.46863	−	14.6681i	−0.290301	−	0.502816i
$852$		0			0
$853$		−	16.7712i		−	0.574236i	−0.957895	−	0.287118i	$-0.907303\pi$
$853$		−	16.7712i		−	0.574236i	0.957895	−	0.287118i	$-0.0926973\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−7.23499	+	4.17712i	−0.247143	+	0.142688i	−0.618455	−	0.785820i	$-0.712241\pi$
$857$	−7.23499	+	4.17712i	−0.247143	+	0.142688i	0.371313	+	0.928508i	$0.378908\pi$
$858$		0			0
$859$	13.2288	−	22.9129i	0.451359	−	0.781777i	−0.547111	−	0.837060i	$-0.684273\pi$
$859$	13.2288	−	22.9129i	0.451359	−	0.781777i	0.998471	+	0.0552825i	$0.0176059\pi$
$860$		0			0
$861$	28.9373			0.986179
$862$		0			0
$863$	15.9847	+	9.22876i	0.544125	+	0.314151i	0.746749	−	0.665106i	$-0.231614\pi$
$863$	15.9847	+	9.22876i	0.544125	+	0.314151i	−0.202624	+	0.979257i	$0.564947\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$		−	3.70850i		−	0.125947i
$868$		0			0
$869$	30.2288			1.02544
$870$		0			0
$871$	6.14575	+	10.6448i	0.208241	+	0.360684i
$872$		0			0
$873$	6.92820	+	4.00000i	0.234484	+	0.135379i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−12.1244	−	7.00000i	−0.409410	−	0.236373i	0.281126	−	0.959671i	$-0.409292\pi$
$877$	−12.1244	−	7.00000i	−0.409410	−	0.236373i	−0.690536	+	0.723298i	$0.742625\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−41.1660			−1.38692			−0.693459	−	0.720496i	$-0.743914\pi$
$881$	−41.1660			−1.38692			−0.693459	+	0.720496i	$0.743914\pi$
$882$		0			0
$883$		−	25.8118i		−	0.868635i	−0.900760	−	0.434317i	$-0.856990\pi$
$883$		−	25.8118i		−	0.868635i	0.900760	−	0.434317i	$-0.143010\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	12.4311	+	7.17712i	0.417397	+	0.240984i	0.693963	−	0.720011i	$-0.255863\pi$
$887$	12.4311	+	7.17712i	0.417397	+	0.240984i	−0.276566	+	0.960995i	$0.589196\pi$
$888$		0			0
$889$	23.7288	−	41.0994i	0.795837	−	1.37843i
$890$		0			0
$891$	−1.82288	+	3.15731i	−0.0610686	+	0.105774i
$892$		0			0
$893$	11.9070	−	6.87451i	0.398452	−	0.230047i
$894$		0			0
$895$		0			0
$896$		0			0
$897$		−	9.64575i		−	0.322062i
$898$		0			0
$899$	7.40588	+	12.8274i	0.247000	+	0.427816i
$900$		0			0
$901$	13.2915	−	23.0216i	0.442804	−	0.766959i
$902$		0			0
$903$			26.2915i			0.874926i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−13.2972	+	7.67712i	−0.441525	+	0.254915i	−0.704244	−	0.709958i	$-0.748714\pi$
$907$	−13.2972	+	7.67712i	−0.441525	+	0.254915i	0.262719	+	0.964872i	$0.415381\pi$
$908$		0			0
$909$	−10.9373			−0.362766
$910$		0			0
$911$	31.5203			1.04431			0.522156	−	0.852850i	$-0.325128\pi$
$911$	31.5203			1.04431			0.522156	+	0.852850i	$0.325128\pi$
$912$		0			0
$913$	−15.5885	+	9.00000i	−0.515903	+	0.297857i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−24.5362	+	14.1660i	−0.810258	+	0.467803i
$918$		0			0
$919$	15.7915	−	27.3517i	0.520914	−	0.902249i	−0.478791	−	0.877929i	$-0.658925\pi$
$919$	15.7915	−	27.3517i	0.520914	−	0.902249i	0.999704	−	0.0243197i	$-0.00774197\pi$
$920$		0			0
$921$	−6.03137	−	10.4466i	−0.198740	−	0.344229i
$922$		0			0
$923$		−	22.1033i		−	0.727538i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	12.6836	−	7.32288i	0.416584	−	0.240515i
$928$		0			0
$929$	−0.760130	+	1.31658i	−0.0249390	+	0.0431957i	−0.878226	−	0.478247i	$-0.841273\pi$
$929$	−0.760130	+	1.31658i	−0.0249390	+	0.0431957i	0.853287	+	0.521442i	$0.174606\pi$
$930$		0			0
$931$	−16.0405			−0.525707
$932$		0			0
$933$	7.23499	+	4.17712i	0.236863	+	0.136753i
$934$		0			0
$935$		0			0
$936$		0			0
$937$		−	50.9778i		−	1.66537i	−0.553746	−	0.832686i	$-0.686802\pi$
$937$		−	50.9778i		−	1.66537i	0.553746	−	0.832686i	$-0.313198\pi$
$938$		0			0
$939$	−5.22876			−0.170634
$940$		0			0
$941$	−2.46863	−	4.27579i	−0.0804749	−	0.139387i	0.822979	−	0.568072i	$-0.192310\pi$
$941$	−2.46863	−	4.27579i	−0.0804749	−	0.139387i	−0.903454	+	0.428685i	$0.858977\pi$
$942$		0			0
$943$	34.5323	+	19.9373i	1.12453	+	0.649246i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	39.5304	+	22.8229i	1.28456	+	0.741644i	0.977679	−	0.210103i	$-0.0673798\pi$
$947$	39.5304	+	22.8229i	1.28456	+	0.741644i	0.306885	+	0.951746i	$0.400713\pi$
$948$		0			0
$949$	−17.5000	−	30.3109i	−0.568074	−	0.983933i
$950$		0			0
$951$	−13.5203			−0.438424
$952$		0			0
$953$		−	0.457513i		−	0.0148203i	−0.999973	−	0.00741015i	$-0.997641\pi$
$953$		−	0.457513i		−	0.0148203i	0.999973	−	0.00741015i	$-0.00235875\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−7.43310	−	4.29150i	−0.240278	−	0.138725i
$958$		0			0
$959$	16.4797			0.532159
$960$		0			0
$961$	−4.29150	+	7.43310i	−0.138436	+	0.239777i
$962$		0			0
$963$	0.920365	−	0.531373i	0.0296584	−	0.0171233i
$964$		0			0
$965$		0			0
$966$		0			0
$967$			40.3948i			1.29901i	0.760358	+	0.649504i	$0.225023\pi$
$967$			40.3948i			1.29901i	−0.760358	+	0.649504i	$0.774977\pi$
$968$		0			0
$969$	−4.17712	−	7.23499i	−0.134189	−	0.232421i
$970$		0			0
$971$	−26.5830	+	46.0431i	−0.853089	+	1.47759i	0.0253172	+	0.999679i	$0.491940\pi$
$971$	−26.5830	+	46.0431i	−0.853089	+	1.47759i	−0.878406	+	0.477914i	$0.841393\pi$
$972$		0			0
$973$	−11.4564	−	6.61438i	−0.367277	−	0.212047i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−35.4527	+	20.4686i	−1.13423	+	0.654849i	−0.944996	−	0.327082i	$-0.893935\pi$
$977$	−35.4527	+	20.4686i	−1.13423	+	0.654849i	−0.189237	+	0.981932i	$0.560601\pi$
$978$		0			0
$979$	−44.5830			−1.42488
$980$		0			0
$981$	−13.0000			−0.415058
$982$		0			0
$983$	47.3597	−	27.3431i	1.51054	−	0.872111i	0.510615	−	0.859809i	$-0.329418\pi$
$983$	47.3597	−	27.3431i	1.51054	−	0.872111i	0.999924	−	0.0123014i	$-0.00391575\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	13.7477	+	7.93725i	0.437595	+	0.252646i
$988$		0			0
$989$	−18.1144	+	31.3750i	−0.576004	+	0.997668i
$990$		0			0
$991$	−16.8542	−	29.1924i	−0.535393	−	0.927328i	−0.999144	−	0.0413622i	$-0.986830\pi$
$991$	−16.8542	−	29.1924i	−0.535393	−	0.927328i	0.463751	−	0.885965i	$-0.346503\pi$
$992$		0			0
$993$		−	22.1660i		−	0.703417i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	14.5243	−	8.38562i	0.459990	−	0.265575i	−0.252050	−	0.967714i	$-0.581105\pi$
$997$	14.5243	−	8.38562i	0.459990	−	0.265575i	0.712040	+	0.702139i	$0.247771\pi$
$998$		0			0
$999$	−2.32288	+	4.02334i	−0.0734925	+	0.127293i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2100.2.bc.e.1549.2		8
5.2	odd	4		2100.2.q.h.1801.1		4
5.3	odd	4		420.2.q.c.121.2	✓	4
5.4	even	2	inner	2100.2.bc.e.1549.3		8
7.4	even	3	inner	2100.2.bc.e.949.3		8
15.8	even	4		1260.2.s.f.541.2		4
20.3	even	4		1680.2.bg.q.961.1		4
35.3	even	12		2940.2.q.t.361.1		4
35.4	even	6	inner	2100.2.bc.e.949.2		8
35.13	even	4		2940.2.q.t.961.1		4
35.18	odd	12		420.2.q.c.361.2	yes	4
35.23	odd	12		2940.2.a.s.1.2		2
35.32	odd	12		2100.2.q.h.1201.1		4
35.33	even	12		2940.2.a.m.1.2		2
105.23	even	12		8820.2.a.be.1.1		2
105.53	even	12		1260.2.s.f.361.2		4
105.68	odd	12		8820.2.a.bj.1.1		2
140.123	even	12		1680.2.bg.q.1201.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.q.c.121.2	✓	4	5.3	odd	4
420.2.q.c.361.2	yes	4	35.18	odd	12
1260.2.s.f.361.2		4	105.53	even	12
1260.2.s.f.541.2		4	15.8	even	4
1680.2.bg.q.961.1		4	20.3	even	4
1680.2.bg.q.1201.1		4	140.123	even	12
2100.2.q.h.1201.1		4	35.32	odd	12
2100.2.q.h.1801.1		4	5.2	odd	4
2100.2.bc.e.949.2		8	35.4	even	6	inner
2100.2.bc.e.949.3		8	7.4	even	3	inner
2100.2.bc.e.1549.2		8	1.1	even	1	trivial
2100.2.bc.e.1549.3		8	5.4	even	2	inner
2940.2.a.m.1.2		2	35.33	even	12
2940.2.a.s.1.2		2	35.23	odd	12
2940.2.q.t.361.1		4	35.3	even	12
2940.2.q.t.961.1		4	35.13	even	4
8820.2.a.be.1.1		2	105.23	even	12
8820.2.a.bj.1.1		2	105.68	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{3} +(2.29129 + 1.32288i) q^{7} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{3} +(2.29129 + 1.32288i) q^{7} +(0.500000 - 0.866025i) q^{9} +(-1.82288 - 3.15731i) q^{11} -2.64575i q^{13} +(3.15731 - 1.82288i) q^{17} +(-1.14575 + 1.98450i) q^{19} -2.64575 q^{21} +(-3.15731 - 1.82288i) q^{23} +1.00000i q^{27} -2.35425 q^{29} +(-3.14575 - 5.44860i) q^{31} +(3.15731 + 1.82288i) q^{33} +(4.02334 + 2.32288i) q^{37} +(1.32288 + 2.29129i) q^{39} -10.9373 q^{41} -9.93725i q^{43} +(-5.19615 - 3.00000i) q^{47} +(3.50000 + 6.06218i) q^{49} +(-1.82288 + 3.15731i) q^{51} +(6.31463 - 3.64575i) q^{53} -2.29150i q^{57} +(-2.46863 - 4.27579i) q^{59} +(-4.00000 + 6.92820i) q^{61} +(2.29129 - 1.32288i) q^{63} +(-4.02334 + 2.32288i) q^{67} +3.64575 q^{69} +8.35425 q^{71} +(11.4564 - 6.61438i) q^{73} -9.64575i q^{77} +(-4.14575 + 7.18065i) q^{79} +(-0.500000 - 0.866025i) q^{81} -4.93725i q^{83} +(2.03884 - 1.17712i) q^{87} +(6.11438 - 10.5904i) q^{89} +(3.50000 - 6.06218i) q^{91} +(5.44860 + 3.14575i) q^{93} +8.00000i q^{97} -3.64575 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{9}+O(q^{10}) \) 8 * q + 4 * q^9	\( 8 q + 4 q^{9} - 4 q^{11} + 12 q^{19} - 40 q^{29} - 4 q^{31} - 24 q^{41} + 28 q^{49} - 4 q^{51} + 12 q^{59} - 32 q^{61} + 8 q^{69} + 88 q^{71} - 12 q^{79} - 4 q^{81} - 4 q^{89} + 28 q^{91} - 8 q^{99}+O(q^{100}) \) 8 * q + 4 * q^9 - 4 * q^11 + 12 * q^19 - 40 * q^29 - 4 * q^31 - 24 * q^41 + 28 * q^49 - 4 * q^51 + 12 * q^59 - 32 * q^61 + 8 * q^69 + 88 * q^71 - 12 * q^79 - 4 * q^81 - 4 * q^89 + 28 * q^91 - 8 * q^99

Introduction

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