LMFDB - Embedded newform 2100.2.bc.c.949.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("2100.949");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$16.7685844245$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 420)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

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

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{3} +(-0.866025 + 2.50000i) q^{7} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	$q+(-0.866025 - 0.500000i) q^{3} +(-0.866025 + 2.50000i) q^{7} +(0.500000 + 0.866025i) q^{9} +(1.00000 - 1.73205i) q^{11} -1.00000i q^{13} +(3.46410 + 2.00000i) q^{17} +(-0.500000 - 0.866025i) q^{19} +(2.00000 - 1.73205i) q^{21} +(-3.46410 + 2.00000i) q^{23} -1.00000i q^{27} +(2.50000 - 4.33013i) q^{31} +(-1.73205 + 1.00000i) q^{33} +(-4.33013 + 2.50000i) q^{37} +(-0.500000 + 0.866025i) q^{39} +2.00000 q^{41} +9.00000i q^{43} +(-1.73205 + 1.00000i) q^{47} +(-5.50000 - 4.33013i) q^{49} +(-2.00000 - 3.46410i) q^{51} +(10.3923 + 6.00000i) q^{53} +1.00000i q^{57} +(-4.00000 + 6.92820i) q^{59} +(7.00000 + 12.1244i) q^{61} +(-2.59808 + 0.500000i) q^{63} +(-7.79423 - 4.50000i) q^{67} +4.00000 q^{69} +2.00000 q^{71} +(0.866025 + 0.500000i) q^{73} +(3.46410 + 4.00000i) q^{77} +(-1.50000 - 2.59808i) q^{79} +(-0.500000 + 0.866025i) q^{81} +18.0000i q^{83} +(-2.00000 - 3.46410i) q^{89} +(2.50000 + 0.866025i) q^{91} +(-4.33013 + 2.50000i) q^{93} +10.0000i q^{97} +2.00000 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^9	$ 4 q + 2 q^{9} + 4 q^{11} - 2 q^{19} + 8 q^{21} + 10 q^{31} - 2 q^{39} + 8 q^{41} - 22 q^{49} - 8 q^{51} - 16 q^{59} + 28 q^{61} + 16 q^{69} + 8 q^{71} - 6 q^{79} - 2 q^{81} - 8 q^{89} + 10 q^{91} + 8 q^{99}+O(q^{100}) $ 4 * q + 2 * q^9 + 4 * q^11 - 2 * q^19 + 8 * q^21 + 10 * q^31 - 2 * q^39 + 8 * q^41 - 22 * q^49 - 8 * q^51 - 16 * q^59 + 28 * q^61 + 16 * q^69 + 8 * q^71 - 6 * q^79 - 2 * q^81 - 8 * q^89 + 10 * 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
$7$	−0.866025	+	2.50000i	−0.327327	+	0.944911i
$7$	−0.866025	+	2.50000i	−0.327327	+	0.944911i
$8$		0			0
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$		0			0
$11$	1.00000	−	1.73205i	0.301511	−	0.522233i	−0.674967	−	0.737848i	$-0.735842\pi$
$11$	1.00000	−	1.73205i	0.301511	−	0.522233i	0.976478	+	0.215615i	$0.0691756\pi$
$12$		0			0
$13$		−	1.00000i		−	0.277350i	−0.990338	−	0.138675i	$-0.955716\pi$
$13$		−	1.00000i		−	0.277350i	0.990338	−	0.138675i	$-0.0442844\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	3.46410	+	2.00000i	0.840168	+	0.485071i	0.857321	−	0.514782i	$-0.172127\pi$
$17$	3.46410	+	2.00000i	0.840168	+	0.485071i	−0.0171533	+	0.999853i	$0.505460\pi$
$18$		0			0
$19$	−0.500000	−	0.866025i	−0.114708	−	0.198680i	0.802955	−	0.596040i	$-0.203260\pi$
$19$	−0.500000	−	0.866025i	−0.114708	−	0.198680i	−0.917663	+	0.397360i	$0.869927\pi$
$20$		0			0
$21$	2.00000	−	1.73205i	0.436436	−	0.377964i
$22$		0			0
$23$	−3.46410	+	2.00000i	−0.722315	+	0.417029i	−0.815604	−	0.578610i	$-0.803595\pi$
$23$	−3.46410	+	2.00000i	−0.722315	+	0.417029i	0.0932891	+	0.995639i	$0.470262\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$		−	1.00000i		−	0.192450i
$28$		0			0
$29$		0			0			−	1.00000i	$-0.5\pi$
$29$		0			0				1.00000i	$0.5\pi$
$30$		0			0
$31$	2.50000	−	4.33013i	0.449013	−	0.777714i	−0.549309	−	0.835619i	$-0.685109\pi$
$31$	2.50000	−	4.33013i	0.449013	−	0.777714i	0.998322	+	0.0579057i	$0.0184423\pi$
$32$		0			0
$33$	−1.73205	+	1.00000i	−0.301511	+	0.174078i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−4.33013	+	2.50000i	−0.711868	+	0.410997i	−0.811752	−	0.584002i	$-0.801486\pi$
$37$	−4.33013	+	2.50000i	−0.711868	+	0.410997i	0.0998840	+	0.994999i	$0.468153\pi$
$38$		0			0
$39$	−0.500000	+	0.866025i	−0.0800641	+	0.138675i
$40$		0			0
$41$	2.00000			0.312348			0.156174	−	0.987730i	$-0.450084\pi$
$41$	2.00000			0.312348			0.156174	+	0.987730i	$0.450084\pi$
$42$		0			0
$43$			9.00000i			1.37249i	0.727372	+	0.686244i	$0.240742\pi$
$43$			9.00000i			1.37249i	−0.727372	+	0.686244i	$0.759258\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−1.73205	+	1.00000i	−0.252646	+	0.145865i	−0.620975	−	0.783830i	$-0.713263\pi$
$47$	−1.73205	+	1.00000i	−0.252646	+	0.145865i	0.368329	+	0.929695i	$0.379930\pi$
$48$		0			0
$49$	−5.50000	−	4.33013i	−0.785714	−	0.618590i
$50$		0			0
$51$	−2.00000	−	3.46410i	−0.280056	−	0.485071i
$52$		0			0
$53$	10.3923	+	6.00000i	1.42749	+	0.824163i	0.996922	−	0.0783936i	$-0.0249791\pi$
$53$	10.3923	+	6.00000i	1.42749	+	0.824163i	0.430570	+	0.902557i	$0.358312\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$			1.00000i			0.132453i
$58$		0			0
$59$	−4.00000	+	6.92820i	−0.520756	+	0.901975i	0.478953	+	0.877841i	$0.341016\pi$
$59$	−4.00000	+	6.92820i	−0.520756	+	0.901975i	−0.999709	+	0.0241347i	$0.992317\pi$
$60$		0			0
$61$	7.00000	+	12.1244i	0.896258	+	1.55236i	0.832240	+	0.554416i	$0.187058\pi$
$61$	7.00000	+	12.1244i	0.896258	+	1.55236i	0.0640184	+	0.997949i	$0.479608\pi$
$62$		0			0
$63$	−2.59808	+	0.500000i	−0.327327	+	0.0629941i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−7.79423	−	4.50000i	−0.952217	−	0.549762i	−0.0584478	−	0.998290i	$-0.518615\pi$
$67$	−7.79423	−	4.50000i	−0.952217	−	0.549762i	−0.893769	+	0.448528i	$0.851948\pi$
$68$		0			0
$69$	4.00000			0.481543
$70$		0			0
$71$	2.00000			0.237356			0.118678	−	0.992933i	$-0.462134\pi$
$71$	2.00000			0.237356			0.118678	+	0.992933i	$0.462134\pi$
$72$		0			0
$73$	0.866025	+	0.500000i	0.101361	+	0.0585206i	0.549823	−	0.835281i	$-0.314695\pi$
$73$	0.866025	+	0.500000i	0.101361	+	0.0585206i	−0.448463	+	0.893801i	$0.648028\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	3.46410	+	4.00000i	0.394771	+	0.455842i
$78$		0			0
$79$	−1.50000	−	2.59808i	−0.168763	−	0.292306i	0.769222	−	0.638982i	$-0.220644\pi$
$79$	−1.50000	−	2.59808i	−0.168763	−	0.292306i	−0.937985	+	0.346675i	$0.887311\pi$
$80$		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
$87$		0			0
$88$		0			0
$89$	−2.00000	−	3.46410i	−0.212000	−	0.367194i	0.740341	−	0.672232i	$-0.234664\pi$
$89$	−2.00000	−	3.46410i	−0.212000	−	0.367194i	−0.952340	+	0.305038i	$0.901331\pi$
$90$		0			0
$91$	2.50000	+	0.866025i	0.262071	+	0.0907841i
$92$		0			0
$93$	−4.33013	+	2.50000i	−0.449013	+	0.259238i
$94$		0			0
$95$		0			0
$96$		0			0
$97$			10.0000i			1.01535i	0.861550	+	0.507673i	$0.169494\pi$
$97$			10.0000i			1.01535i	−0.861550	+	0.507673i	$0.830506\pi$
$98$		0			0
$99$	2.00000			0.201008
$100$		0			0
$101$	−3.00000	+	5.19615i	−0.298511	+	0.517036i	−0.975796	−	0.218685i	$-0.929823\pi$
$101$	−3.00000	+	5.19615i	−0.298511	+	0.517036i	0.677284	+	0.735721i	$0.263157\pi$
$102$		0			0
$103$	0.866025	−	0.500000i	0.0853320	−	0.0492665i	−0.456727	−	0.889607i	$-0.650978\pi$
$103$	0.866025	−	0.500000i	0.0853320	−	0.0492665i	0.542059	+	0.840341i	$0.317645\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	3.46410	−	2.00000i	0.334887	−	0.193347i	−0.323122	−	0.946357i	$-0.604732\pi$
$107$	3.46410	−	2.00000i	0.334887	−	0.193347i	0.658009	+	0.753010i	$0.271399\pi$
$108$		0			0
$109$	6.50000	−	11.2583i	0.622587	−	1.07835i	−0.366415	−	0.930451i	$-0.619415\pi$
$109$	6.50000	−	11.2583i	0.622587	−	1.07835i	0.989002	−	0.147901i	$-0.0472517\pi$
$110$		0			0
$111$	5.00000			0.474579
$112$		0			0
$113$			14.0000i			1.31701i	0.752577	+	0.658505i	$0.228811\pi$
$113$			14.0000i			1.31701i	−0.752577	+	0.658505i	$0.771189\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	0.866025	−	0.500000i	0.0800641	−	0.0462250i
$118$		0			0
$119$	−8.00000	+	6.92820i	−0.733359	+	0.635107i
$120$		0			0
$121$	3.50000	+	6.06218i	0.318182	+	0.551107i
$122$		0			0
$123$	−1.73205	−	1.00000i	−0.156174	−	0.0901670i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		−	9.00000i		−	0.798621i	−0.916816	−	0.399310i	$-0.869250\pi$
$127$		−	9.00000i		−	0.798621i	0.916816	−	0.399310i	$-0.130750\pi$
$128$		0			0
$129$	4.50000	−	7.79423i	0.396203	−	0.686244i
$130$		0			0
$131$	9.00000	+	15.5885i	0.786334	+	1.36197i	0.928199	+	0.372084i	$0.121357\pi$
$131$	9.00000	+	15.5885i	0.786334	+	1.36197i	−0.141865	+	0.989886i	$0.545310\pi$
$132$		0			0
$133$	2.59808	−	0.500000i	0.225282	−	0.0433555i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−13.8564	−	8.00000i	−1.18383	−	0.683486i	−0.226935	−	0.973910i	$-0.572870\pi$
$137$	−13.8564	−	8.00000i	−1.18383	−	0.683486i	−0.956898	+	0.290424i	$0.906204\pi$
$138$		0			0
$139$	13.0000			1.10265			0.551323	−	0.834292i	$-0.314123\pi$
$139$	13.0000			1.10265			0.551323	+	0.834292i	$0.314123\pi$
$140$		0			0
$141$	2.00000			0.168430
$142$		0			0
$143$	−1.73205	−	1.00000i	−0.144841	−	0.0836242i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	2.59808	+	6.50000i	0.214286	+	0.536111i
$148$		0			0
$149$	6.00000	+	10.3923i	0.491539	+	0.851371i	0.999953	−	0.00974235i	$-0.00310113\pi$
$149$	6.00000	+	10.3923i	0.491539	+	0.851371i	−0.508413	+	0.861113i	$0.669768\pi$
$150$		0			0
$151$	8.00000	−	13.8564i	0.651031	−	1.12762i	−0.331842	−	0.943335i	$-0.607670\pi$
$151$	8.00000	−	13.8564i	0.651031	−	1.12762i	0.982873	−	0.184284i	$-0.0589965\pi$
$152$		0			0
$153$			4.00000i			0.323381i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	19.0526	+	11.0000i	1.52056	+	0.877896i	0.999706	+	0.0242497i	$0.00771967\pi$
$157$	19.0526	+	11.0000i	1.52056	+	0.877896i	0.520854	+	0.853646i	$0.325614\pi$
$158$		0			0
$159$	−6.00000	−	10.3923i	−0.475831	−	0.824163i
$160$		0			0
$161$	−2.00000	−	10.3923i	−0.157622	−	0.819028i
$162$		0			0
$163$	−10.3923	+	6.00000i	−0.813988	+	0.469956i	−0.848339	−	0.529454i	$-0.822397\pi$
$163$	−10.3923	+	6.00000i	−0.813988	+	0.469956i	0.0343508	+	0.999410i	$0.489064\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$			2.00000i			0.154765i	0.997001	+	0.0773823i	$0.0246562\pi$
$167$			2.00000i			0.154765i	−0.997001	+	0.0773823i	$0.975344\pi$
$168$		0			0
$169$	12.0000			0.923077
$170$		0			0
$171$	0.500000	−	0.866025i	0.0382360	−	0.0662266i
$172$		0			0
$173$	13.8564	−	8.00000i	1.05348	−	0.608229i	0.129861	−	0.991532i	$-0.458547\pi$
$173$	13.8564	−	8.00000i	1.05348	−	0.608229i	0.923622	+	0.383304i	$0.125214\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	6.92820	−	4.00000i	0.520756	−	0.300658i
$178$		0			0
$179$	−13.0000	+	22.5167i	−0.971666	+	1.68297i	−0.281139	+	0.959667i	$0.590712\pi$
$179$	−13.0000	+	22.5167i	−0.971666	+	1.68297i	−0.690526	+	0.723307i	$0.742621\pi$
$180$		0			0
$181$	17.0000			1.26360			0.631800	−	0.775131i	$-0.282316\pi$
$181$	17.0000			1.26360			0.631800	+	0.775131i	$0.282316\pi$
$182$		0			0
$183$		−	14.0000i		−	1.03491i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	6.92820	−	4.00000i	0.506640	−	0.292509i
$188$		0			0
$189$	2.50000	+	0.866025i	0.181848	+	0.0629941i
$190$		0			0
$191$	5.00000	+	8.66025i	0.361787	+	0.626634i	0.988255	−	0.152813i	$-0.0488333\pi$
$191$	5.00000	+	8.66025i	0.361787	+	0.626634i	−0.626468	+	0.779447i	$0.715500\pi$
$192$		0			0
$193$	−14.7224	−	8.50000i	−1.05974	−	0.611843i	−0.134382	−	0.990930i	$-0.542905\pi$
$193$	−14.7224	−	8.50000i	−1.05974	−	0.611843i	−0.925361	+	0.379086i	$0.876238\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			12.0000i			0.854965i	0.904024	+	0.427482i	$0.140599\pi$
$197$			12.0000i			0.854965i	−0.904024	+	0.427482i	$0.859401\pi$
$198$		0			0
$199$	−8.00000	+	13.8564i	−0.567105	+	0.982255i	0.429745	+	0.902950i	$0.358603\pi$
$199$	−8.00000	+	13.8564i	−0.567105	+	0.982255i	−0.996850	+	0.0793045i	$0.974730\pi$
$200$		0			0
$201$	4.50000	+	7.79423i	0.317406	+	0.549762i
$202$		0			0
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−3.46410	−	2.00000i	−0.240772	−	0.139010i
$208$		0			0
$209$	−2.00000			−0.138343
$210$		0			0
$211$	−28.0000			−1.92760			−0.963800	−	0.266627i	$-0.914091\pi$
$211$	−28.0000			−1.92760			−0.963800	+	0.266627i	$0.914091\pi$
$212$		0			0
$213$	−1.73205	−	1.00000i	−0.118678	−	0.0685189i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	8.66025	+	10.0000i	0.587896	+	0.678844i
$218$		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
$223$		0			0		1.00000			$0$
$223$		0			0		−1.00000			$\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−15.5885	−	9.00000i	−1.03464	−	0.597351i	−0.116331	−	0.993210i	$-0.537113\pi$
$227$	−15.5885	−	9.00000i	−1.03464	−	0.597351i	−0.918311	+	0.395860i	$0.870447\pi$
$228$		0			0
$229$	0.500000	+	0.866025i	0.0330409	+	0.0572286i	0.882073	−	0.471113i	$-0.156147\pi$
$229$	0.500000	+	0.866025i	0.0330409	+	0.0572286i	−0.849032	+	0.528341i	$0.822814\pi$
$230$		0			0
$231$	−1.00000	−	5.19615i	−0.0657952	−	0.341882i
$232$		0			0
$233$	1.73205	−	1.00000i	0.113470	−	0.0655122i	−0.442191	−	0.896921i	$-0.645799\pi$
$233$	1.73205	−	1.00000i	0.113470	−	0.0655122i	0.555661	+	0.831409i	$0.312465\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$			3.00000i			0.194871i
$238$		0			0
$239$	−26.0000			−1.68180			−0.840900	−	0.541190i	$-0.817974\pi$
$239$	−26.0000			−1.68180			−0.840900	+	0.541190i	$0.817974\pi$
$240$		0			0
$241$	9.00000	−	15.5885i	0.579741	−	1.00414i	−0.415768	−	0.909471i	$-0.636487\pi$
$241$	9.00000	−	15.5885i	0.579741	−	1.00414i	0.995509	−	0.0946700i	$-0.0301796\pi$
$242$		0			0
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−0.866025	+	0.500000i	−0.0551039	+	0.0318142i
$248$		0			0
$249$	9.00000	−	15.5885i	0.570352	−	0.987878i
$250$		0			0
$251$	4.00000			0.252478			0.126239	−	0.992000i	$-0.459709\pi$
$251$	4.00000			0.252478			0.126239	+	0.992000i	$0.459709\pi$
$252$		0			0
$253$			8.00000i			0.502956i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	12.1244	−	7.00000i	0.756297	−	0.436648i	−0.0716680	−	0.997429i	$-0.522832\pi$
$257$	12.1244	−	7.00000i	0.756297	−	0.436648i	0.827964	+	0.560781i	$0.189499\pi$
$258$		0			0
$259$	−2.50000	−	12.9904i	−0.155342	−	0.807183i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	10.3923	+	6.00000i	0.640817	+	0.369976i	0.784929	−	0.619586i	$-0.212699\pi$
$263$	10.3923	+	6.00000i	0.640817	+	0.369976i	−0.144112	+	0.989561i	$0.546033\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$			4.00000i			0.244796i
$268$		0			0
$269$	−9.00000	+	15.5885i	−0.548740	+	0.950445i	0.449622	+	0.893219i	$0.351559\pi$
$269$	−9.00000	+	15.5885i	−0.548740	+	0.950445i	−0.998361	+	0.0572259i	$0.981774\pi$
$270$		0			0
$271$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$271$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$272$		0			0
$273$	−1.73205	−	2.00000i	−0.104828	−	0.121046i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−4.33013	−	2.50000i	−0.260172	−	0.150210i	0.364241	−	0.931305i	$-0.381328\pi$
$277$	−4.33013	−	2.50000i	−0.260172	−	0.150210i	−0.624413	+	0.781094i	$0.714662\pi$
$278$		0			0
$279$	5.00000			0.299342
$280$		0			0
$281$	−20.0000			−1.19310			−0.596550	−	0.802576i	$-0.703462\pi$
$281$	−20.0000			−1.19310			−0.596550	+	0.802576i	$0.703462\pi$
$282$		0			0
$283$	−21.6506	−	12.5000i	−1.28700	−	0.743048i	−0.308879	−	0.951101i	$-0.599954\pi$
$283$	−21.6506	−	12.5000i	−1.28700	−	0.743048i	−0.978117	+	0.208053i	$0.933287\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−1.73205	+	5.00000i	−0.102240	+	0.295141i
$288$		0			0
$289$	−0.500000	−	0.866025i	−0.0294118	−	0.0509427i
$290$		0			0
$291$	5.00000	−	8.66025i	0.293105	−	0.507673i
$292$		0			0
$293$		0			0		1.00000			$0$
$293$		0			0		−1.00000			$\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−1.73205	−	1.00000i	−0.100504	−	0.0580259i
$298$		0			0
$299$	2.00000	+	3.46410i	0.115663	+	0.200334i
$300$		0			0
$301$	−22.5000	−	7.79423i	−1.29688	−	0.449252i
$302$		0			0
$303$	5.19615	−	3.00000i	0.298511	−	0.172345i
$304$		0			0
$305$		0			0
$306$		0			0
$307$		−	19.0000i		−	1.08439i	−0.840254	−	0.542194i	$-0.817594\pi$
$307$		−	19.0000i		−	1.08439i	0.840254	−	0.542194i	$-0.182406\pi$
$308$		0			0
$309$	−1.00000			−0.0568880
$310$		0			0
$311$	−13.0000	+	22.5167i	−0.737162	+	1.27680i	0.216606	+	0.976259i	$0.430501\pi$
$311$	−13.0000	+	22.5167i	−0.737162	+	1.27680i	−0.953768	+	0.300544i	$0.902832\pi$
$312$		0			0
$313$	−16.4545	+	9.50000i	−0.930062	+	0.536972i	−0.886831	−	0.462093i	$-0.847098\pi$
$313$	−16.4545	+	9.50000i	−0.930062	+	0.536972i	−0.0432311	+	0.999065i	$0.513765\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−3.46410	+	2.00000i	−0.194563	+	0.112331i	−0.594117	−	0.804379i	$-0.702498\pi$
$317$	−3.46410	+	2.00000i	−0.194563	+	0.112331i	0.399554	+	0.916710i	$0.369165\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	−4.00000			−0.223258
$322$		0			0
$323$		−	4.00000i		−	0.222566i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−11.2583	+	6.50000i	−0.622587	+	0.359451i
$328$		0			0
$329$	−1.00000	−	5.19615i	−0.0551318	−	0.286473i
$330$		0			0
$331$	−0.500000	−	0.866025i	−0.0274825	−	0.0476011i	0.851957	−	0.523612i	$-0.175416\pi$
$331$	−0.500000	−	0.866025i	−0.0274825	−	0.0476011i	−0.879440	+	0.476011i	$0.842082\pi$
$332$		0			0
$333$	−4.33013	−	2.50000i	−0.237289	−	0.136999i
$334$		0			0
$335$		0			0
$336$		0			0
$337$		−	7.00000i		−	0.381314i	−0.981657	−	0.190657i	$-0.938938\pi$
$337$		−	7.00000i		−	0.381314i	0.981657	−	0.190657i	$-0.0610619\pi$
$338$		0			0
$339$	7.00000	−	12.1244i	0.380188	−	0.658505i
$340$		0			0
$341$	−5.00000	−	8.66025i	−0.270765	−	0.468979i
$342$		0			0
$343$	15.5885	−	10.0000i	0.841698	−	0.539949i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−20.7846	−	12.0000i	−1.11578	−	0.644194i	−0.175457	−	0.984487i	$-0.556140\pi$
$347$	−20.7846	−	12.0000i	−1.11578	−	0.644194i	−0.940319	+	0.340293i	$0.889474\pi$
$348$		0			0
$349$	−2.00000			−0.107058			−0.0535288	−	0.998566i	$-0.517047\pi$
$349$	−2.00000			−0.107058			−0.0535288	+	0.998566i	$0.517047\pi$
$350$		0			0
$351$	−1.00000			−0.0533761
$352$		0			0
$353$	25.9808	+	15.0000i	1.38282	+	0.798369i	0.992492	−	0.122308i	$-0.0390296\pi$
$353$	25.9808	+	15.0000i	1.38282	+	0.798369i	0.390324	+	0.920677i	$0.372363\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	10.3923	−	2.00000i	0.550019	−	0.105851i
$358$		0			0
$359$	8.00000	+	13.8564i	0.422224	+	0.731313i	0.996157	−	0.0875892i	$-0.0279163\pi$
$359$	8.00000	+	13.8564i	0.422224	+	0.731313i	−0.573933	+	0.818902i	$0.694583\pi$
$360$		0			0
$361$	9.00000	−	15.5885i	0.473684	−	0.820445i
$362$		0			0
$363$		−	7.00000i		−	0.367405i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−0.866025	−	0.500000i	−0.0452062	−	0.0260998i	0.477227	−	0.878780i	$-0.341642\pi$
$367$	−0.866025	−	0.500000i	−0.0452062	−	0.0260998i	−0.522433	+	0.852680i	$0.674975\pi$
$368$		0			0
$369$	1.00000	+	1.73205i	0.0520579	+	0.0901670i
$370$		0			0
$371$	−24.0000	+	20.7846i	−1.24602	+	1.07908i
$372$		0			0
$373$	21.6506	−	12.5000i	1.12103	−	0.647225i	0.179364	−	0.983783i	$-0.442596\pi$
$373$	21.6506	−	12.5000i	1.12103	−	0.647225i	0.941663	+	0.336557i	$0.109263\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	11.0000			0.565032			0.282516	−	0.959263i	$-0.408831\pi$
$379$	11.0000			0.565032			0.282516	+	0.959263i	$0.408831\pi$
$380$		0			0
$381$	−4.50000	+	7.79423i	−0.230542	+	0.399310i
$382$		0			0
$383$	31.1769	−	18.0000i	1.59307	−	0.919757i	0.600289	−	0.799783i	$-0.295052\pi$
$383$	31.1769	−	18.0000i	1.59307	−	0.919757i	0.992777	−	0.119974i	$-0.0382810\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−7.79423	+	4.50000i	−0.396203	+	0.228748i
$388$		0			0
$389$	15.0000	−	25.9808i	0.760530	−	1.31728i	−0.182047	−	0.983290i	$-0.558272\pi$
$389$	15.0000	−	25.9808i	0.760530	−	1.31728i	0.942578	−	0.333987i	$-0.108394\pi$
$390$		0			0
$391$	−16.0000			−0.809155
$392$		0			0
$393$		−	18.0000i		−	0.907980i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	26.8468	−	15.5000i	1.34740	−	0.777923i	0.359521	−	0.933137i	$-0.382940\pi$
$397$	26.8468	−	15.5000i	1.34740	−	0.777923i	0.987881	+	0.155214i	$0.0496068\pi$
$398$		0			0
$399$	−2.50000	−	0.866025i	−0.125157	−	0.0433555i
$400$		0			0
$401$	−6.00000	−	10.3923i	−0.299626	−	0.518967i	0.676425	−	0.736512i	$-0.263528\pi$
$401$	−6.00000	−	10.3923i	−0.299626	−	0.518967i	−0.976050	+	0.217545i	$0.930195\pi$
$402$		0			0
$403$	−4.33013	−	2.50000i	−0.215699	−	0.124534i
$404$		0			0
$405$		0			0
$406$		0			0
$407$			10.0000i			0.495682i
$408$		0			0
$409$	6.50000	−	11.2583i	0.321404	−	0.556689i	−0.659374	−	0.751815i	$-0.729178\pi$
$409$	6.50000	−	11.2583i	0.321404	−	0.556689i	0.980778	+	0.195127i	$0.0625118\pi$
$410$		0			0
$411$	8.00000	+	13.8564i	0.394611	+	0.683486i
$412$		0			0
$413$	−13.8564	−	16.0000i	−0.681829	−	0.787309i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−11.2583	−	6.50000i	−0.551323	−	0.318306i
$418$		0			0
$419$	6.00000			0.293119			0.146560	−	0.989202i	$-0.453180\pi$
$419$	6.00000			0.293119			0.146560	+	0.989202i	$0.453180\pi$
$420$		0			0
$421$	−35.0000			−1.70580			−0.852898	−	0.522078i	$-0.825157\pi$
$421$	−35.0000			−1.70580			−0.852898	+	0.522078i	$0.825157\pi$
$422$		0			0
$423$	−1.73205	−	1.00000i	−0.0842152	−	0.0486217i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−36.3731	+	7.00000i	−1.76022	+	0.338754i
$428$		0			0
$429$	1.00000	+	1.73205i	0.0482805	+	0.0836242i
$430$		0			0
$431$	15.0000	−	25.9808i	0.722525	−	1.25145i	−0.237460	−	0.971397i	$-0.576315\pi$
$431$	15.0000	−	25.9808i	0.722525	−	1.25145i	0.959985	−	0.280052i	$-0.0903517\pi$
$432$		0			0
$433$		−	27.0000i		−	1.29754i	−0.760986	−	0.648769i	$-0.775284\pi$
$433$		−	27.0000i		−	1.29754i	0.760986	−	0.648769i	$-0.224716\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	3.46410	+	2.00000i	0.165710	+	0.0956730i
$438$		0			0
$439$	4.00000	+	6.92820i	0.190910	+	0.330665i	0.945552	−	0.325471i	$-0.105523\pi$
$439$	4.00000	+	6.92820i	0.190910	+	0.330665i	−0.754642	+	0.656136i	$0.772190\pi$
$440$		0			0
$441$	1.00000	−	6.92820i	0.0476190	−	0.329914i
$442$		0			0
$443$	3.46410	−	2.00000i	0.164584	−	0.0950229i	−0.415445	−	0.909618i	$-0.636374\pi$
$443$	3.46410	−	2.00000i	0.164584	−	0.0950229i	0.580030	+	0.814595i	$0.303041\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		−	12.0000i		−	0.567581i
$448$		0			0
$449$	−22.0000			−1.03824			−0.519122	−	0.854700i	$-0.673741\pi$
$449$	−22.0000			−1.03824			−0.519122	+	0.854700i	$0.673741\pi$
$450$		0			0
$451$	2.00000	−	3.46410i	0.0941763	−	0.163118i
$452$		0			0
$453$	−13.8564	+	8.00000i	−0.651031	+	0.375873i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	0.866025	−	0.500000i	0.0405110	−	0.0233890i	−0.479608	−	0.877483i	$-0.659221\pi$
$457$	0.866025	−	0.500000i	0.0405110	−	0.0233890i	0.520119	+	0.854094i	$0.325888\pi$
$458$		0			0
$459$	2.00000	−	3.46410i	0.0933520	−	0.161690i
$460$		0			0
$461$	−16.0000			−0.745194			−0.372597	−	0.927993i	$-0.621533\pi$
$461$	−16.0000			−0.745194			−0.372597	+	0.927993i	$0.621533\pi$
$462$		0			0
$463$		−	41.0000i		−	1.90543i	−0.303863	−	0.952716i	$-0.598276\pi$
$463$		−	41.0000i		−	1.90543i	0.303863	−	0.952716i	$-0.401724\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	29.4449	−	17.0000i	1.36255	−	0.786666i	0.372584	−	0.927999i	$-0.378472\pi$
$467$	29.4449	−	17.0000i	1.36255	−	0.786666i	0.989962	+	0.141332i	$0.0451386\pi$
$468$		0			0
$469$	18.0000	−	15.5885i	0.831163	−	0.719808i
$470$		0			0
$471$	−11.0000	−	19.0526i	−0.506853	−	0.877896i
$472$		0			0
$473$	15.5885	+	9.00000i	0.716758	+	0.413820i
$474$		0			0
$475$		0			0
$476$		0			0
$477$			12.0000i			0.549442i
$478$		0			0
$479$	6.00000	−	10.3923i	0.274147	−	0.474837i	−0.695773	−	0.718262i	$-0.744938\pi$
$479$	6.00000	−	10.3923i	0.274147	−	0.474837i	0.969920	+	0.243426i	$0.0782712\pi$
$480$		0			0
$481$	2.50000	+	4.33013i	0.113990	+	0.197437i
$482$		0			0
$483$	−3.46410	+	10.0000i	−0.157622	+	0.455016i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−28.5788	−	16.5000i	−1.29503	−	0.747686i	−0.315489	−	0.948929i	$-0.602169\pi$
$487$	−28.5788	−	16.5000i	−1.29503	−	0.747686i	−0.979541	+	0.201243i	$0.935502\pi$
$488$		0			0
$489$	12.0000			0.542659
$490$		0			0
$491$	12.0000			0.541552			0.270776	−	0.962642i	$-0.412720\pi$
$491$	12.0000			0.541552			0.270776	+	0.962642i	$0.412720\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−1.73205	+	5.00000i	−0.0776931	+	0.224281i
$498$		0			0
$499$	−2.50000	−	4.33013i	−0.111915	−	0.193843i	0.804627	−	0.593780i	$-0.202365\pi$
$499$	−2.50000	−	4.33013i	−0.111915	−	0.193843i	−0.916542	+	0.399937i	$0.869032\pi$
$500$		0			0
$501$	1.00000	−	1.73205i	0.0446767	−	0.0773823i
$502$		0			0
$503$		−	10.0000i		−	0.445878i	−0.974832	−	0.222939i	$-0.928435\pi$
$503$		−	10.0000i		−	0.445878i	0.974832	−	0.222939i	$-0.0715651\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−10.3923	−	6.00000i	−0.461538	−	0.266469i
$508$		0			0
$509$	13.0000	+	22.5167i	0.576215	+	0.998033i	0.995908	+	0.0903676i	$0.0288042\pi$
$509$	13.0000	+	22.5167i	0.576215	+	0.998033i	−0.419694	+	0.907666i	$0.637862\pi$
$510$		0			0
$511$	−2.00000	+	1.73205i	−0.0884748	+	0.0766214i
$512$		0			0
$513$	−0.866025	+	0.500000i	−0.0382360	+	0.0220755i
$514$		0			0
$515$		0			0
$516$		0			0
$517$			4.00000i			0.175920i
$518$		0			0
$519$	−16.0000			−0.702322
$520$		0			0
$521$	−18.0000	+	31.1769i	−0.788594	+	1.36589i	0.138234	+	0.990400i	$0.455857\pi$
$521$	−18.0000	+	31.1769i	−0.788594	+	1.36589i	−0.926828	+	0.375486i	$0.877476\pi$
$522$		0			0
$523$	−25.1147	+	14.5000i	−1.09819	+	0.634041i	−0.935745	−	0.352677i	$-0.885272\pi$
$523$	−25.1147	+	14.5000i	−1.09819	+	0.634041i	−0.162446	+	0.986718i	$0.551938\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	17.3205	−	10.0000i	0.754493	−	0.435607i
$528$		0			0
$529$	−3.50000	+	6.06218i	−0.152174	+	0.263573i
$530$		0			0
$531$	−8.00000			−0.347170
$532$		0			0
$533$		−	2.00000i		−	0.0866296i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	22.5167	−	13.0000i	0.971666	−	0.560991i
$538$		0			0
$539$	−13.0000	+	5.19615i	−0.559950	+	0.223814i
$540$		0			0
$541$	15.5000	+	26.8468i	0.666397	+	1.15423i	0.978905	+	0.204318i	$0.0654977\pi$
$541$	15.5000	+	26.8468i	0.666397	+	1.15423i	−0.312507	+	0.949915i	$0.601169\pi$
$542$		0			0
$543$	−14.7224	−	8.50000i	−0.631800	−	0.364770i
$544$		0			0
$545$		0			0
$546$		0			0
$547$			28.0000i			1.19719i	0.801050	+	0.598597i	$0.204275\pi$
$547$			28.0000i			1.19719i	−0.801050	+	0.598597i	$0.795725\pi$
$548$		0			0
$549$	−7.00000	+	12.1244i	−0.298753	+	0.517455i
$550$		0			0
$551$		0			0
$552$		0			0
$553$	7.79423	−	1.50000i	0.331444	−	0.0637865i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	1.73205	+	1.00000i	0.0733893	+	0.0423714i	0.536246	−	0.844062i	$-0.319842\pi$
$557$	1.73205	+	1.00000i	0.0733893	+	0.0423714i	−0.462856	+	0.886433i	$0.653175\pi$
$558$		0			0
$559$	9.00000			0.380659
$560$		0			0
$561$	−8.00000			−0.337760
$562$		0			0
$563$	−25.9808	−	15.0000i	−1.09496	−	0.632175i	−0.160066	−	0.987106i	$-0.551171\pi$
$563$	−25.9808	−	15.0000i	−1.09496	−	0.632175i	−0.934892	+	0.354932i	$0.884504\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−1.73205	−	2.00000i	−0.0727393	−	0.0839921i
$568$		0			0
$569$	−3.00000	−	5.19615i	−0.125767	−	0.217834i	0.796266	−	0.604947i	$-0.206806\pi$
$569$	−3.00000	−	5.19615i	−0.125767	−	0.217834i	−0.922032	+	0.387113i	$0.873472\pi$
$570$		0			0
$571$	2.50000	−	4.33013i	0.104622	−	0.181210i	−0.808962	−	0.587861i	$-0.799970\pi$
$571$	2.50000	−	4.33013i	0.104622	−	0.181210i	0.913584	+	0.406651i	$0.133303\pi$
$572$		0			0
$573$		−	10.0000i		−	0.417756i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	11.2583	+	6.50000i	0.468690	+	0.270599i	0.715691	−	0.698417i	$-0.246112\pi$
$577$	11.2583	+	6.50000i	0.468690	+	0.270599i	−0.247001	+	0.969015i	$0.579445\pi$
$578$		0			0
$579$	8.50000	+	14.7224i	0.353248	+	0.611843i
$580$		0			0
$581$	−45.0000	−	15.5885i	−1.86691	−	0.646718i
$582$		0			0
$583$	20.7846	−	12.0000i	0.860811	−	0.496989i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		−	36.0000i		−	1.48588i	−0.669359	−	0.742940i	$-0.733431\pi$
$587$		−	36.0000i		−	1.48588i	0.669359	−	0.742940i	$-0.266569\pi$
$588$		0			0
$589$	−5.00000			−0.206021
$590$		0			0
$591$	6.00000	−	10.3923i	0.246807	−	0.427482i
$592$		0			0
$593$	−5.19615	+	3.00000i	−0.213380	+	0.123195i	−0.602881	−	0.797831i	$-0.705981\pi$
$593$	−5.19615	+	3.00000i	−0.213380	+	0.123195i	0.389501	+	0.921026i	$0.372647\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	13.8564	−	8.00000i	0.567105	−	0.327418i
$598$		0			0
$599$	−14.0000	+	24.2487i	−0.572024	+	0.990775i	0.424333	+	0.905506i	$0.360508\pi$
$599$	−14.0000	+	24.2487i	−0.572024	+	0.990775i	−0.996358	+	0.0852695i	$0.972825\pi$
$600$		0			0
$601$	23.0000			0.938190			0.469095	−	0.883148i	$-0.344580\pi$
$601$	23.0000			0.938190			0.469095	+	0.883148i	$0.344580\pi$
$602$		0			0
$603$		−	9.00000i		−	0.366508i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	7.79423	−	4.50000i	0.316358	−	0.182649i	−0.333410	−	0.942782i	$-0.608199\pi$
$607$	7.79423	−	4.50000i	0.316358	−	0.182649i	0.649768	+	0.760133i	$0.274866\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	1.00000	+	1.73205i	0.0404557	+	0.0700713i
$612$		0			0
$613$	1.73205	+	1.00000i	0.0699569	+	0.0403896i	0.534570	−	0.845124i	$-0.320473\pi$
$613$	1.73205	+	1.00000i	0.0699569	+	0.0403896i	−0.464614	+	0.885514i	$0.653807\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$			34.0000i			1.36879i	0.729112	+	0.684394i	$0.239933\pi$
$617$			34.0000i			1.36879i	−0.729112	+	0.684394i	$0.760067\pi$
$618$		0			0
$619$	−5.50000	+	9.52628i	−0.221064	+	0.382893i	−0.955131	−	0.296183i	$-0.904286\pi$
$619$	−5.50000	+	9.52628i	−0.221064	+	0.382893i	0.734068	+	0.679076i	$0.237620\pi$
$620$		0			0
$621$	2.00000	+	3.46410i	0.0802572	+	0.139010i
$622$		0			0
$623$	10.3923	−	2.00000i	0.416359	−	0.0801283i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	1.73205	+	1.00000i	0.0691714	+	0.0399362i
$628$		0			0
$629$	−20.0000			−0.797452
$630$		0			0
$631$		0			0			−	1.00000i	$-0.5\pi$
$631$		0			0				1.00000i	$0.5\pi$
$632$		0			0
$633$	24.2487	+	14.0000i	0.963800	+	0.556450i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−4.33013	+	5.50000i	−0.171566	+	0.217918i
$638$		0			0
$639$	1.00000	+	1.73205i	0.0395594	+	0.0685189i
$640$		0			0
$641$	18.0000	−	31.1769i	0.710957	−	1.23141i	−0.253541	−	0.967325i	$-0.581595\pi$
$641$	18.0000	−	31.1769i	0.710957	−	1.23141i	0.964498	−	0.264089i	$-0.0850714\pi$
$642$		0			0
$643$		−	7.00000i		−	0.276053i	−0.990429	−	0.138027i	$-0.955924\pi$
$643$		−	7.00000i		−	0.276053i	0.990429	−	0.138027i	$-0.0440759\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	12.1244	+	7.00000i	0.476658	+	0.275198i	0.719023	−	0.694987i	$-0.244590\pi$
$647$	12.1244	+	7.00000i	0.476658	+	0.275198i	−0.242365	+	0.970185i	$0.577923\pi$
$648$		0			0
$649$	8.00000	+	13.8564i	0.314027	+	0.543912i
$650$		0			0
$651$	−2.50000	−	12.9904i	−0.0979827	−	0.509133i
$652$		0			0
$653$	−12.1244	+	7.00000i	−0.474463	+	0.273931i	−0.718106	−	0.695934i	$-0.754991\pi$
$653$	−12.1244	+	7.00000i	−0.474463	+	0.273931i	0.243643	+	0.969865i	$0.421657\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$			1.00000i			0.0390137i
$658$		0			0
$659$	−4.00000			−0.155818			−0.0779089	−	0.996960i	$-0.524824\pi$
$659$	−4.00000			−0.155818			−0.0779089	+	0.996960i	$0.524824\pi$
$660$		0			0
$661$	−17.5000	+	30.3109i	−0.680671	+	1.17896i	0.294105	+	0.955773i	$0.404978\pi$
$661$	−17.5000	+	30.3109i	−0.680671	+	1.17896i	−0.974776	+	0.223184i	$0.928355\pi$
$662$		0			0
$663$	−3.46410	+	2.00000i	−0.134535	+	0.0776736i
$664$		0			0
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$	28.0000			1.08093
$672$		0			0
$673$		−	11.0000i		−	0.424019i	−0.977268	−	0.212009i	$-0.931999\pi$
$673$		−	11.0000i		−	0.424019i	0.977268	−	0.212009i	$-0.0680008\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	20.7846	−	12.0000i	0.798817	−	0.461197i	−0.0442400	−	0.999021i	$-0.514087\pi$
$677$	20.7846	−	12.0000i	0.798817	−	0.461197i	0.843057	+	0.537823i	$0.180753\pi$
$678$		0			0
$679$	−25.0000	−	8.66025i	−0.959412	−	0.332350i
$680$		0			0
$681$	9.00000	+	15.5885i	0.344881	+	0.597351i
$682$		0			0
$683$	−13.8564	−	8.00000i	−0.530201	−	0.306111i	0.210898	−	0.977508i	$-0.432361\pi$
$683$	−13.8564	−	8.00000i	−0.530201	−	0.306111i	−0.741098	+	0.671397i	$0.765695\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$		−	1.00000i		−	0.0381524i
$688$		0			0
$689$	6.00000	−	10.3923i	0.228582	−	0.395915i
$690$		0			0
$691$	5.50000	+	9.52628i	0.209230	+	0.362397i	0.951472	−	0.307735i	$-0.0995710\pi$
$691$	5.50000	+	9.52628i	0.209230	+	0.362397i	−0.742242	+	0.670132i	$0.766238\pi$
$692$		0			0
$693$	−1.73205	+	5.00000i	−0.0657952	+	0.189934i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	6.92820	+	4.00000i	0.262424	+	0.151511i
$698$		0			0
$699$	−2.00000			−0.0756469
$700$		0			0
$701$	36.0000			1.35970			0.679851	−	0.733351i	$-0.262045\pi$
$701$	36.0000			1.35970			0.679851	+	0.733351i	$0.262045\pi$
$702$		0			0
$703$	4.33013	+	2.50000i	0.163314	+	0.0942893i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−10.3923	−	12.0000i	−0.390843	−	0.451306i
$708$		0			0
$709$	−13.0000	−	22.5167i	−0.488225	−	0.845631i	0.511683	−	0.859174i	$-0.329022\pi$
$709$	−13.0000	−	22.5167i	−0.488225	−	0.845631i	−0.999908	+	0.0135434i	$0.995689\pi$
$710$		0			0
$711$	1.50000	−	2.59808i	0.0562544	−	0.0974355i
$712$		0			0
$713$			20.0000i			0.749006i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	22.5167	+	13.0000i	0.840900	+	0.485494i
$718$		0			0
$719$	21.0000	+	36.3731i	0.783168	+	1.35649i	0.930087	+	0.367338i	$0.119731\pi$
$719$	21.0000	+	36.3731i	0.783168	+	1.35649i	−0.146920	+	0.989148i	$0.546936\pi$
$720$		0			0
$721$	0.500000	+	2.59808i	0.0186210	+	0.0967574i
$722$		0			0
$723$	−15.5885	+	9.00000i	−0.579741	+	0.334714i
$724$		0			0
$725$		0			0
$726$		0			0
$727$		−	3.00000i		−	0.111264i	−0.998451	−	0.0556319i	$-0.982283\pi$
$727$		−	3.00000i		−	0.111264i	0.998451	−	0.0556319i	$-0.0177173\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	−18.0000	+	31.1769i	−0.665754	+	1.15312i
$732$		0			0
$733$	−7.79423	+	4.50000i	−0.287886	+	0.166211i	−0.636988	−	0.770873i	$-0.719820\pi$
$733$	−7.79423	+	4.50000i	−0.287886	+	0.166211i	0.349102	+	0.937085i	$0.386487\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−15.5885	+	9.00000i	−0.574208	+	0.331519i
$738$		0			0
$739$	7.50000	−	12.9904i	0.275892	−	0.477859i	−0.694468	−	0.719524i	$-0.744360\pi$
$739$	7.50000	−	12.9904i	0.275892	−	0.477859i	0.970360	+	0.241665i	$0.0776935\pi$
$740$		0			0
$741$	1.00000			0.0367359
$742$		0			0
$743$			6.00000i			0.220119i	0.993925	+	0.110059i	$0.0351041\pi$
$743$			6.00000i			0.220119i	−0.993925	+	0.110059i	$0.964896\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−15.5885	+	9.00000i	−0.570352	+	0.329293i
$748$		0			0
$749$	2.00000	+	10.3923i	0.0730784	+	0.379727i
$750$		0			0
$751$	−15.5000	−	26.8468i	−0.565603	−	0.979653i	−0.996993	−	0.0774878i	$-0.975310\pi$
$751$	−15.5000	−	26.8468i	−0.565603	−	0.979653i	0.431390	−	0.902165i	$-0.358023\pi$
$752$		0			0
$753$	−3.46410	−	2.00000i	−0.126239	−	0.0728841i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		−	22.0000i		−	0.799604i	−0.916602	−	0.399802i	$-0.869079\pi$
$757$		−	22.0000i		−	0.799604i	0.916602	−	0.399802i	$-0.130921\pi$
$758$		0			0
$759$	4.00000	−	6.92820i	0.145191	−	0.251478i
$760$		0			0
$761$	−10.0000	−	17.3205i	−0.362500	−	0.627868i	0.625872	−	0.779926i	$-0.284743\pi$
$761$	−10.0000	−	17.3205i	−0.362500	−	0.627868i	−0.988372	+	0.152058i	$0.951410\pi$
$762$		0			0
$763$	22.5167	+	26.0000i	0.815158	+	0.941263i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	6.92820	+	4.00000i	0.250163	+	0.144432i
$768$		0			0
$769$	−31.0000			−1.11789			−0.558944	−	0.829205i	$-0.688793\pi$
$769$	−31.0000			−1.11789			−0.558944	+	0.829205i	$0.688793\pi$
$770$		0			0
$771$	−14.0000			−0.504198
$772$		0			0
$773$	−12.1244	−	7.00000i	−0.436083	−	0.251773i	0.265852	−	0.964014i	$-0.414347\pi$
$773$	−12.1244	−	7.00000i	−0.436083	−	0.251773i	−0.701935	+	0.712241i	$0.747680\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−4.33013	+	12.5000i	−0.155342	+	0.448435i
$778$		0			0
$779$	−1.00000	−	1.73205i	−0.0358287	−	0.0620572i
$780$		0			0
$781$	2.00000	−	3.46410i	0.0715656	−	0.123955i
$782$		0			0
$783$		0			0
$784$		0			0
$785$		0			0
$786$		0			0
$787$	13.8564	+	8.00000i	0.493928	+	0.285169i	0.726202	−	0.687481i	$-0.241284\pi$
$787$	13.8564	+	8.00000i	0.493928	+	0.285169i	−0.232275	+	0.972650i	$0.574617\pi$
$788$		0			0
$789$	−6.00000	−	10.3923i	−0.213606	−	0.369976i
$790$		0			0
$791$	−35.0000	−	12.1244i	−1.24446	−	0.431092i
$792$		0			0
$793$	12.1244	−	7.00000i	0.430548	−	0.248577i
$794$		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
$799$	−8.00000			−0.283020
$800$		0			0
$801$	2.00000	−	3.46410i	0.0706665	−	0.122398i
$802$		0			0
$803$	1.73205	−	1.00000i	0.0611227	−	0.0352892i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	15.5885	−	9.00000i	0.548740	−	0.316815i
$808$		0			0
$809$	23.0000	−	39.8372i	0.808637	−	1.40060i	−0.105171	−	0.994454i	$-0.533539\pi$
$809$	23.0000	−	39.8372i	0.808637	−	1.40060i	0.913808	−	0.406146i	$-0.133128\pi$
$810$		0			0
$811$	48.0000			1.68551			0.842754	−	0.538299i	$-0.180933\pi$
$811$	48.0000			1.68551			0.842754	+	0.538299i	$0.180933\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$	7.79423	−	4.50000i	0.272686	−	0.157435i
$818$		0			0
$819$	0.500000	+	2.59808i	0.0174714	+	0.0907841i
$820$		0			0
$821$	25.0000	+	43.3013i	0.872506	+	1.51122i	0.859396	+	0.511311i	$0.170840\pi$
$821$	25.0000	+	43.3013i	0.872506	+	1.51122i	0.0131101	+	0.999914i	$0.495827\pi$
$822$		0			0
$823$	13.8564	+	8.00000i	0.483004	+	0.278862i	0.721668	−	0.692240i	$-0.243376\pi$
$823$	13.8564	+	8.00000i	0.483004	+	0.278862i	−0.238664	+	0.971102i	$0.576709\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			6.00000i			0.208640i	0.994544	+	0.104320i	$0.0332667\pi$
$827$			6.00000i			0.208640i	−0.994544	+	0.104320i	$0.966733\pi$
$828$		0			0
$829$	2.50000	−	4.33013i	0.0868286	−	0.150392i	−0.819340	−	0.573307i	$-0.805660\pi$
$829$	2.50000	−	4.33013i	0.0868286	−	0.150392i	0.906169	+	0.422916i	$0.138993\pi$
$830$		0			0
$831$	2.50000	+	4.33013i	0.0867240	+	0.150210i
$832$		0			0
$833$	−10.3923	−	26.0000i	−0.360072	−	0.900847i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−4.33013	−	2.50000i	−0.149671	−	0.0864126i
$838$		0			0
$839$	48.0000			1.65714			0.828572	−	0.559883i	$-0.189154\pi$
$839$	48.0000			1.65714			0.828572	+	0.559883i	$0.189154\pi$
$840$		0			0
$841$	−29.0000			−1.00000
$842$		0			0
$843$	17.3205	+	10.0000i	0.596550	+	0.344418i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−18.1865	+	3.50000i	−0.624897	+	0.120261i
$848$		0			0
$849$	12.5000	+	21.6506i	0.428999	+	0.743048i
$850$		0			0
$851$	10.0000	−	17.3205i	0.342796	−	0.593739i
$852$		0			0
$853$			29.0000i			0.992941i	0.868054	+	0.496471i	$0.165371\pi$
$853$			29.0000i			0.992941i	−0.868054	+	0.496471i	$0.834629\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−38.1051	−	22.0000i	−1.30165	−	0.751506i	−0.320960	−	0.947093i	$-0.604005\pi$
$857$	−38.1051	−	22.0000i	−1.30165	−	0.751506i	−0.980686	+	0.195587i	$0.937339\pi$
$858$		0			0
$859$	4.00000	+	6.92820i	0.136478	+	0.236387i	0.926161	−	0.377128i	$-0.123088\pi$
$859$	4.00000	+	6.92820i	0.136478	+	0.236387i	−0.789683	+	0.613515i	$0.789755\pi$
$860$		0			0
$861$	4.00000	−	3.46410i	0.136320	−	0.118056i
$862$		0			0
$863$	−25.9808	+	15.0000i	−0.884395	+	0.510606i	−0.872105	−	0.489319i	$-0.837246\pi$
$863$	−25.9808	+	15.0000i	−0.884395	+	0.510606i	−0.0122903	+	0.999924i	$0.503912\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$			1.00000i			0.0339618i
$868$		0			0
$869$	−6.00000			−0.203536
$870$		0			0
$871$	−4.50000	+	7.79423i	−0.152477	+	0.264097i
$872$		0			0
$873$	−8.66025	+	5.00000i	−0.293105	+	0.169224i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−19.0526	+	11.0000i	−0.643359	+	0.371444i	−0.785907	−	0.618344i	$-0.787804\pi$
$877$	−19.0526	+	11.0000i	−0.643359	+	0.371444i	0.142548	+	0.989788i	$0.454470\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	24.0000			0.808581			0.404290	−	0.914631i	$-0.367519\pi$
$881$	24.0000			0.808581			0.404290	+	0.914631i	$0.367519\pi$
$882$		0			0
$883$		−	1.00000i		−	0.0336527i	−0.999858	−	0.0168263i	$-0.994644\pi$
$883$		−	1.00000i		−	0.0336527i	0.999858	−	0.0168263i	$-0.00535624\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	19.0526	−	11.0000i	0.639722	−	0.369344i	−0.144785	−	0.989463i	$-0.546249\pi$
$887$	19.0526	−	11.0000i	0.639722	−	0.369344i	0.784508	+	0.620119i	$0.212916\pi$
$888$		0			0
$889$	22.5000	+	7.79423i	0.754626	+	0.261410i
$890$		0			0
$891$	1.00000	+	1.73205i	0.0335013	+	0.0580259i
$892$		0			0
$893$	1.73205	+	1.00000i	0.0579609	+	0.0334637i
$894$		0			0
$895$		0			0
$896$		0			0
$897$		−	4.00000i		−	0.133556i
$898$		0			0
$899$		0			0
$900$		0			0
$901$	24.0000	+	41.5692i	0.799556	+	1.38487i
$902$		0			0
$903$	15.5885	+	18.0000i	0.518751	+	0.599002i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−7.79423	−	4.50000i	−0.258803	−	0.149420i	0.364985	−	0.931013i	$-0.381074\pi$
$907$	−7.79423	−	4.50000i	−0.258803	−	0.149420i	−0.623788	+	0.781593i	$0.714407\pi$
$908$		0			0
$909$	−6.00000			−0.199007
$910$		0			0
$911$	−12.0000			−0.397578			−0.198789	−	0.980042i	$-0.563701\pi$
$911$	−12.0000			−0.397578			−0.198789	+	0.980042i	$0.563701\pi$
$912$		0			0
$913$	31.1769	+	18.0000i	1.03181	+	0.595713i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−46.7654	+	9.00000i	−1.54433	+	0.297206i
$918$		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
$921$	−9.50000	+	16.4545i	−0.313036	+	0.542194i
$922$		0			0
$923$		−	2.00000i		−	0.0658308i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	0.866025	+	0.500000i	0.0284440	+	0.0164222i
$928$		0			0
$929$	−7.00000	−	12.1244i	−0.229663	−	0.397787i	0.728046	−	0.685529i	$-0.240429\pi$
$929$	−7.00000	−	12.1244i	−0.229663	−	0.397787i	−0.957708	+	0.287742i	$0.907096\pi$
$930$		0			0
$931$	−1.00000	+	6.92820i	−0.0327737	+	0.227063i
$932$		0			0
$933$	22.5167	−	13.0000i	0.737162	−	0.425601i
$934$		0			0
$935$		0			0
$936$		0			0
$937$		−	21.0000i		−	0.686040i	−0.939328	−	0.343020i	$-0.888550\pi$
$937$		−	21.0000i		−	0.686040i	0.939328	−	0.343020i	$-0.111450\pi$
$938$		0			0
$939$	19.0000			0.620042
$940$		0			0
$941$	24.0000	−	41.5692i	0.782378	−	1.35512i	−0.148176	−	0.988961i	$-0.547340\pi$
$941$	24.0000	−	41.5692i	0.782378	−	1.35512i	0.930553	−	0.366157i	$-0.119327\pi$
$942$		0			0
$943$	−6.92820	+	4.00000i	−0.225613	+	0.130258i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−15.5885	+	9.00000i	−0.506557	+	0.292461i	−0.731417	−	0.681930i	$-0.761141\pi$
$947$	−15.5885	+	9.00000i	−0.506557	+	0.292461i	0.224860	+	0.974391i	$0.427807\pi$
$948$		0			0
$949$	0.500000	−	0.866025i	0.0162307	−	0.0281124i
$950$		0			0
$951$	4.00000			0.129709
$952$		0			0
$953$			36.0000i			1.16615i	0.812417	+	0.583077i	$0.198151\pi$
$953$			36.0000i			1.16615i	−0.812417	+	0.583077i	$0.801849\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$	32.0000	−	27.7128i	1.03333	−	0.894893i
$960$		0			0
$961$	3.00000	+	5.19615i	0.0967742	+	0.167618i
$962$		0			0
$963$	3.46410	+	2.00000i	0.111629	+	0.0644491i
$964$		0			0
$965$		0			0
$966$		0			0
$967$			37.0000i			1.18984i	0.803785	+	0.594920i	$0.202816\pi$
$967$			37.0000i			1.18984i	−0.803785	+	0.594920i	$0.797184\pi$
$968$		0			0
$969$	−2.00000	+	3.46410i	−0.0642493	+	0.111283i
$970$		0			0
$971$	18.0000	+	31.1769i	0.577647	+	1.00051i	0.995748	+	0.0921142i	$0.0293625\pi$
$971$	18.0000	+	31.1769i	0.577647	+	1.00051i	−0.418101	+	0.908401i	$0.637304\pi$
$972$		0			0
$973$	−11.2583	+	32.5000i	−0.360925	+	1.04190i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−15.5885	−	9.00000i	−0.498719	−	0.287936i	0.229465	−	0.973317i	$-0.426302\pi$
$977$	−15.5885	−	9.00000i	−0.498719	−	0.287936i	−0.728184	+	0.685381i	$0.759636\pi$
$978$		0			0
$979$	−8.00000			−0.255681
$980$		0			0
$981$	13.0000			0.415058
$982$		0			0
$983$	−13.8564	−	8.00000i	−0.441951	−	0.255160i	0.262474	−	0.964939i	$-0.415462\pi$
$983$	−13.8564	−	8.00000i	−0.441951	−	0.255160i	−0.704425	+	0.709779i	$0.748795\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−1.73205	+	5.00000i	−0.0551318	+	0.159152i
$988$		0			0
$989$	−18.0000	−	31.1769i	−0.572367	−	0.991368i
$990$		0			0
$991$	26.5000	−	45.8993i	0.841800	−	1.45804i	−0.0465710	−	0.998915i	$-0.514829\pi$
$991$	26.5000	−	45.8993i	0.841800	−	1.45804i	0.888371	−	0.459126i	$-0.151837\pi$
$992$		0			0
$993$			1.00000i			0.0317340i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−9.52628	−	5.50000i	−0.301700	−	0.174187i	0.341506	−	0.939880i	$-0.389063\pi$
$997$	−9.52628	−	5.50000i	−0.301700	−	0.174187i	−0.643206	+	0.765693i	$0.722396\pi$
$998$		0			0
$999$	2.50000	+	4.33013i	0.0790965	+	0.136999i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{3} +(-0.866025 + 2.50000i) q^{7} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{3} +(-0.866025 + 2.50000i) q^{7} +(0.500000 + 0.866025i) q^{9} +(1.00000 - 1.73205i) q^{11} -1.00000i q^{13} +(3.46410 + 2.00000i) q^{17} +(-0.500000 - 0.866025i) q^{19} +(2.00000 - 1.73205i) q^{21} +(-3.46410 + 2.00000i) q^{23} -1.00000i q^{27} +(2.50000 - 4.33013i) q^{31} +(-1.73205 + 1.00000i) q^{33} +(-4.33013 + 2.50000i) q^{37} +(-0.500000 + 0.866025i) q^{39} +2.00000 q^{41} +9.00000i q^{43} +(-1.73205 + 1.00000i) q^{47} +(-5.50000 - 4.33013i) q^{49} +(-2.00000 - 3.46410i) q^{51} +(10.3923 + 6.00000i) q^{53} +1.00000i q^{57} +(-4.00000 + 6.92820i) q^{59} +(7.00000 + 12.1244i) q^{61} +(-2.59808 + 0.500000i) q^{63} +(-7.79423 - 4.50000i) q^{67} +4.00000 q^{69} +2.00000 q^{71} +(0.866025 + 0.500000i) q^{73} +(3.46410 + 4.00000i) q^{77} +(-1.50000 - 2.59808i) q^{79} +(-0.500000 + 0.866025i) q^{81} +18.0000i q^{83} +(-2.00000 - 3.46410i) q^{89} +(2.50000 + 0.866025i) q^{91} +(-4.33013 + 2.50000i) q^{93} +10.0000i q^{97} +2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^9	\( 4 q + 2 q^{9} + 4 q^{11} - 2 q^{19} + 8 q^{21} + 10 q^{31} - 2 q^{39} + 8 q^{41} - 22 q^{49} - 8 q^{51} - 16 q^{59} + 28 q^{61} + 16 q^{69} + 8 q^{71} - 6 q^{79} - 2 q^{81} - 8 q^{89} + 10 q^{91} + 8 q^{99}+O(q^{100}) \) 4 * q + 2 * q^9 + 4 * q^11 - 2 * q^19 + 8 * q^21 + 10 * q^31 - 2 * q^39 + 8 * q^41 - 22 * q^49 - 8 * q^51 - 16 * q^59 + 28 * q^61 + 16 * q^69 + 8 * q^71 - 6 * q^79 - 2 * q^81 - 8 * q^89 + 10 * q^91 + 8 * q^99

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