LMFDB - Embedded newform 2100.2.bo.f.1949.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2100,2,Mod(1349,2100)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2100.1349"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2100, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 3, 5])) N = Newforms(chi, 2, names="a")

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

Newform invariants

comment:select newform

sage:traces = [4,0,0,0,0,0,0,0,12,0,18,0,0,0,0,0,0,0,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(19)] == traces)

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:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 84)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1949.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	2100.1949
Dual form			2100.2.bo.f.1349.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q-1.73205 q^{3} +(-1.73205 + 2.00000i) q^{7} +3.00000 q^{9} +(4.50000 + 2.59808i) q^{11} +(-2.59808 - 1.50000i) q^{17} +(-1.50000 + 0.866025i) q^{19} +(3.00000 - 3.46410i) q^{21} +(2.59808 + 4.50000i) q^{23} -5.19615 q^{27} +(-1.50000 - 0.866025i) q^{31} +(-7.79423 - 4.50000i) q^{33} +(6.06218 - 3.50000i) q^{37} +6.00000 q^{41} -4.00000i q^{43} +(2.59808 - 1.50000i) q^{47} +(-1.00000 - 6.92820i) q^{49} +(4.50000 + 2.59808i) q^{51} +(-2.59808 + 4.50000i) q^{53} +(2.59808 - 1.50000i) q^{57} +(-1.50000 + 2.59808i) q^{59} +(-10.5000 + 6.06218i) q^{61} +(-5.19615 + 6.00000i) q^{63} +(-4.33013 - 2.50000i) q^{67} +(-4.50000 - 7.79423i) q^{69} +10.3923i q^{71} +(-6.06218 + 10.5000i) q^{73} +(-12.9904 + 4.50000i) q^{77} +(-0.500000 - 0.866025i) q^{79} +9.00000 q^{81} +12.0000i q^{83} +(-4.50000 - 7.79423i) q^{89} +(2.59808 + 1.50000i) q^{93} -6.92820 q^{97} +(13.5000 + 7.79423i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 12 q^{9} + 18 q^{11} - 6 q^{19} + 12 q^{21} - 6 q^{31} + 24 q^{41} - 4 q^{49} + 18 q^{51} - 6 q^{59} - 42 q^{61} - 18 q^{69} - 2 q^{79} + 36 q^{81} - 18 q^{89} + 54 q^{99}+O(q^{100}) $ 4 * q + 12 * q^9 + 18 * q^11 - 6 * q^19 + 12 * q^21 - 6 * q^31 + 24 * q^41 - 4 * q^49 + 18 * q^51 - 6 * q^59 - 42 * q^61 - 18 * q^69 - 2 * q^79 + 36 * q^81 - 18 * q^89 + 54 * q^99

Character values

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

$n$	$701$	$1051$	$1177$	$1501$
$\chi(n)$	$-1$	$1$	$-1$	$e\left(\frac{1}{6}\right)$

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
$3$	−1.73205			−1.00000
$3$	−1.73205			−1.00000
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−1.73205	+	2.00000i	−0.654654	+	0.755929i
$7$	−1.73205	+	2.00000i	−0.654654	+	0.755929i
$8$		0			0
$9$	3.00000			1.00000
$10$		0			0
$11$	4.50000	+	2.59808i	1.35680	+	0.783349i	0.989191	−	0.146631i	$-0.0468429\pi$
$11$	4.50000	+	2.59808i	1.35680	+	0.783349i	0.367610	+	0.929980i	$0.380176\pi$
$12$		0			0
$13$		0			0			−	1.00000i	$-0.5\pi$
$13$		0			0				1.00000i	$0.5\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−2.59808	−	1.50000i	−0.630126	−	0.363803i	0.150675	−	0.988583i	$-0.451855\pi$
$17$	−2.59808	−	1.50000i	−0.630126	−	0.363803i	−0.780801	+	0.624780i	$0.785189\pi$
$18$		0			0
$19$	−1.50000	+	0.866025i	−0.344124	+	0.198680i	−0.662094	−	0.749421i	$-0.730332\pi$
$19$	−1.50000	+	0.866025i	−0.344124	+	0.198680i	0.317970	+	0.948101i	$0.396999\pi$
$20$		0			0
$21$	3.00000	−	3.46410i	0.654654	−	0.755929i
$22$		0			0
$23$	2.59808	+	4.50000i	0.541736	+	0.938315i	0.998805	+	0.0488832i	$0.0155662\pi$
$23$	2.59808	+	4.50000i	0.541736	+	0.938315i	−0.457068	+	0.889432i	$0.651100\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−5.19615			−1.00000
$28$		0			0
$29$		0			0		1.00000			$0$
$29$		0			0		−1.00000			$\pi$
$30$		0			0
$31$	−1.50000	−	0.866025i	−0.269408	−	0.155543i	0.359211	−	0.933257i	$-0.383046\pi$
$31$	−1.50000	−	0.866025i	−0.269408	−	0.155543i	−0.628619	+	0.777714i	$0.716379\pi$
$32$		0			0
$33$	−7.79423	−	4.50000i	−1.35680	−	0.783349i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	6.06218	−	3.50000i	0.996616	−	0.575396i	0.0893706	−	0.995998i	$-0.471514\pi$
$37$	6.06218	−	3.50000i	0.996616	−	0.575396i	0.907245	+	0.420602i	$0.138181\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	6.00000			0.937043			0.468521	−	0.883452i	$-0.344787\pi$
$41$	6.00000			0.937043			0.468521	+	0.883452i	$0.344787\pi$
$42$		0			0
$43$		−	4.00000i		−	0.609994i	−0.952353	−	0.304997i	$-0.901344\pi$
$43$		−	4.00000i		−	0.609994i	0.952353	−	0.304997i	$-0.0986555\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	2.59808	−	1.50000i	0.378968	−	0.218797i	−0.298401	−	0.954441i	$-0.596453\pi$
$47$	2.59808	−	1.50000i	0.378968	−	0.218797i	0.677369	+	0.735643i	$0.263120\pi$
$48$		0			0
$49$	−1.00000	−	6.92820i	−0.142857	−	0.989743i
$50$		0			0
$51$	4.50000	+	2.59808i	0.630126	+	0.363803i
$52$		0			0
$53$	−2.59808	+	4.50000i	−0.356873	+	0.618123i	−0.987437	−	0.158015i	$-0.949491\pi$
$53$	−2.59808	+	4.50000i	−0.356873	+	0.618123i	0.630563	+	0.776138i	$0.282824\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	2.59808	−	1.50000i	0.344124	−	0.198680i
$58$		0			0
$59$	−1.50000	+	2.59808i	−0.195283	+	0.338241i	−0.946993	−	0.321253i	$-0.895896\pi$
$59$	−1.50000	+	2.59808i	−0.195283	+	0.338241i	0.751710	+	0.659494i	$0.229229\pi$
$60$		0			0
$61$	−10.5000	+	6.06218i	−1.34439	+	0.776182i	−0.987448	−	0.157945i	$-0.949513\pi$
$61$	−10.5000	+	6.06218i	−1.34439	+	0.776182i	−0.356939	+	0.934128i	$0.616180\pi$
$62$		0			0
$63$	−5.19615	+	6.00000i	−0.654654	+	0.755929i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−4.33013	−	2.50000i	−0.529009	−	0.305424i	0.211604	−	0.977356i	$-0.432131\pi$
$67$	−4.33013	−	2.50000i	−0.529009	−	0.305424i	−0.740613	+	0.671932i	$0.765465\pi$
$68$		0			0
$69$	−4.50000	−	7.79423i	−0.541736	−	0.938315i
$70$		0			0
$71$			10.3923i			1.23334i	0.787222	+	0.616670i	$0.211519\pi$
$71$			10.3923i			1.23334i	−0.787222	+	0.616670i	$0.788481\pi$
$72$		0			0
$73$	−6.06218	+	10.5000i	−0.709524	+	1.22893i	0.255510	+	0.966807i	$0.417757\pi$
$73$	−6.06218	+	10.5000i	−0.709524	+	1.22893i	−0.965034	+	0.262126i	$0.915577\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−12.9904	+	4.50000i	−1.48039	+	0.512823i
$78$		0			0
$79$	−0.500000	−	0.866025i	−0.0562544	−	0.0974355i	0.836527	−	0.547926i	$-0.184582\pi$
$79$	−0.500000	−	0.866025i	−0.0562544	−	0.0974355i	−0.892781	+	0.450490i	$0.851249\pi$
$80$		0			0
$81$	9.00000			1.00000
$82$		0			0
$83$			12.0000i			1.31717i	0.752506	+	0.658586i	$0.228845\pi$
$83$			12.0000i			1.31717i	−0.752506	+	0.658586i	$0.771155\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−4.50000	−	7.79423i	−0.476999	−	0.826187i	0.522654	−	0.852545i	$-0.324942\pi$
$89$	−4.50000	−	7.79423i	−0.476999	−	0.826187i	−0.999653	+	0.0263586i	$0.991609\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	2.59808	+	1.50000i	0.269408	+	0.155543i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−6.92820			−0.703452			−0.351726	−	0.936103i	$-0.614405\pi$
$97$	−6.92820			−0.703452			−0.351726	+	0.936103i	$0.614405\pi$
$98$		0			0
$99$	13.5000	+	7.79423i	1.35680	+	0.783349i
$100$		0			0
$101$	4.50000	−	7.79423i	0.447767	−	0.775555i	−0.550474	−	0.834853i	$-0.685553\pi$
$101$	4.50000	−	7.79423i	0.447767	−	0.775555i	0.998240	+	0.0592978i	$0.0188862\pi$
$102$		0			0
$103$	2.59808	+	4.50000i	0.255996	+	0.443398i	0.965166	−	0.261640i	$-0.0842633\pi$
$103$	2.59808	+	4.50000i	0.255996	+	0.443398i	−0.709170	+	0.705038i	$0.750930\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	7.79423	+	13.5000i	0.753497	+	1.30509i	0.946118	+	0.323821i	$0.104968\pi$
$107$	7.79423	+	13.5000i	0.753497	+	1.30509i	−0.192622	+	0.981273i	$0.561699\pi$
$108$		0			0
$109$	−8.50000	+	14.7224i	−0.814152	+	1.41015i	0.0957826	+	0.995402i	$0.469465\pi$
$109$	−8.50000	+	14.7224i	−0.814152	+	1.41015i	−0.909935	+	0.414751i	$0.863869\pi$
$110$		0			0
$111$	−10.5000	+	6.06218i	−0.996616	+	0.575396i
$112$		0			0
$113$	−20.7846			−1.95525			−0.977626	−	0.210352i	$-0.932539\pi$
$113$	−20.7846			−1.95525			−0.977626	+	0.210352i	$0.932539\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$		0			0
$118$		0			0
$119$	7.50000	−	2.59808i	0.687524	−	0.238165i
$120$		0			0
$121$	8.00000	+	13.8564i	0.727273	+	1.25967i
$122$		0			0
$123$	−10.3923			−0.937043
$124$		0			0
$125$		0			0
$126$		0			0
$127$			8.00000i			0.709885i	0.934888	+	0.354943i	$0.115500\pi$
$127$			8.00000i			0.709885i	−0.934888	+	0.354943i	$0.884500\pi$
$128$		0			0
$129$			6.92820i			0.609994i
$130$		0			0
$131$	4.50000	+	7.79423i	0.393167	+	0.680985i	0.992865	−	0.119241i	$-0.0380462\pi$
$131$	4.50000	+	7.79423i	0.393167	+	0.680985i	−0.599699	+	0.800226i	$0.704713\pi$
$132$		0			0
$133$	0.866025	−	4.50000i	0.0750939	−	0.390199i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	2.59808	−	4.50000i	0.221969	−	0.384461i	−0.733437	−	0.679757i	$-0.762085\pi$
$137$	2.59808	−	4.50000i	0.221969	−	0.384461i	0.955406	+	0.295296i	$0.0954184\pi$
$138$		0			0
$139$			10.3923i			0.881464i	0.897639	+	0.440732i	$0.145281\pi$
$139$			10.3923i			0.881464i	−0.897639	+	0.440732i	$0.854719\pi$
$140$		0			0
$141$	−4.50000	+	2.59808i	−0.378968	+	0.218797i
$142$		0			0
$143$		0			0
$144$		0			0
$145$		0			0
$146$		0			0
$147$	1.73205	+	12.0000i	0.142857	+	0.989743i
$148$		0			0
$149$	4.50000	−	2.59808i	0.368654	−	0.212843i	−0.304216	−	0.952603i	$-0.598394\pi$
$149$	4.50000	−	2.59808i	0.368654	−	0.212843i	0.672870	+	0.739760i	$0.265061\pi$
$150$		0			0
$151$	−6.50000	+	11.2583i	−0.528962	+	0.916190i	0.470467	+	0.882418i	$0.344085\pi$
$151$	−6.50000	+	11.2583i	−0.528962	+	0.916190i	−0.999430	+	0.0337724i	$0.989248\pi$
$152$		0			0
$153$	−7.79423	−	4.50000i	−0.630126	−	0.363803i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	2.59808	−	4.50000i	0.207349	−	0.359139i	−0.743530	−	0.668703i	$-0.766850\pi$
$157$	2.59808	−	4.50000i	0.207349	−	0.359139i	0.950879	+	0.309564i	$0.100183\pi$
$158$		0			0
$159$	4.50000	−	7.79423i	0.356873	−	0.618123i
$160$		0			0
$161$	−13.5000	−	2.59808i	−1.06395	−	0.204757i
$162$		0			0
$163$	0.866025	−	0.500000i	0.0678323	−	0.0391630i	−0.465700	−	0.884943i	$-0.654198\pi$
$163$	0.866025	−	0.500000i	0.0678323	−	0.0391630i	0.533533	+	0.845780i	$0.320864\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$			12.0000i			0.928588i	0.885681	+	0.464294i	$0.153692\pi$
$167$			12.0000i			0.928588i	−0.885681	+	0.464294i	$0.846308\pi$
$168$		0			0
$169$	−13.0000			−1.00000
$170$		0			0
$171$	−4.50000	+	2.59808i	−0.344124	+	0.198680i
$172$		0			0
$173$	7.79423	−	4.50000i	0.592584	−	0.342129i	−0.173534	−	0.984828i	$-0.555519\pi$
$173$	7.79423	−	4.50000i	0.592584	−	0.342129i	0.766119	+	0.642699i	$0.222185\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	2.59808	−	4.50000i	0.195283	−	0.338241i
$178$		0			0
$179$	−4.50000	−	2.59808i	−0.336346	−	0.194189i	0.322309	−	0.946634i	$-0.395541\pi$
$179$	−4.50000	−	2.59808i	−0.336346	−	0.194189i	−0.658655	+	0.752445i	$0.728874\pi$
$180$		0			0
$181$		−	6.92820i		−	0.514969i	−0.966282	−	0.257485i	$-0.917106\pi$
$181$		−	6.92820i		−	0.514969i	0.966282	−	0.257485i	$-0.0828937\pi$
$182$		0			0
$183$	18.1865	−	10.5000i	1.34439	−	0.776182i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−7.79423	−	13.5000i	−0.569970	−	0.987218i
$188$		0			0
$189$	9.00000	−	10.3923i	0.654654	−	0.755929i
$190$		0			0
$191$	13.5000	−	7.79423i	0.976826	−	0.563971i	0.0755154	−	0.997145i	$-0.475940\pi$
$191$	13.5000	−	7.79423i	0.976826	−	0.563971i	0.901310	+	0.433174i	$0.142606\pi$
$192$		0			0
$193$	−4.33013	−	2.50000i	−0.311689	−	0.179954i	0.335993	−	0.941865i	$-0.390928\pi$
$193$	−4.33013	−	2.50000i	−0.311689	−	0.179954i	−0.647682	+	0.761911i	$0.724262\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		0			0			−	1.00000i	$-0.5\pi$
$197$		0			0				1.00000i	$0.5\pi$
$198$		0			0
$199$	1.50000	+	0.866025i	0.106332	+	0.0613909i	0.552223	−	0.833696i	$-0.313780\pi$
$199$	1.50000	+	0.866025i	0.106332	+	0.0613909i	−0.445891	+	0.895087i	$0.647113\pi$
$200$		0			0
$201$	7.50000	+	4.33013i	0.529009	+	0.305424i
$202$		0			0
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$	7.79423	+	13.5000i	0.541736	+	0.938315i
$208$		0			0
$209$	−9.00000			−0.622543
$210$		0			0
$211$	−20.0000			−1.37686			−0.688428	−	0.725304i	$-0.741699\pi$
$211$	−20.0000			−1.37686			−0.688428	+	0.725304i	$0.741699\pi$
$212$		0			0
$213$		−	18.0000i		−	1.23334i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	4.33013	−	1.50000i	0.293948	−	0.101827i
$218$		0			0
$219$	10.5000	−	18.1865i	0.709524	−	1.22893i
$220$		0			0
$221$		0			0
$222$		0			0
$223$	10.3923			0.695920			0.347960	−	0.937509i	$-0.386874\pi$
$223$	10.3923			0.695920			0.347960	+	0.937509i	$0.386874\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−7.79423	−	4.50000i	−0.517321	−	0.298675i	0.218517	−	0.975833i	$-0.429878\pi$
$227$	−7.79423	−	4.50000i	−0.517321	−	0.298675i	−0.735838	+	0.677158i	$0.763211\pi$
$228$		0			0
$229$	−19.5000	+	11.2583i	−1.28860	+	0.743971i	−0.978404	−	0.206702i	$-0.933727\pi$
$229$	−19.5000	+	11.2583i	−1.28860	+	0.743971i	−0.310192	+	0.950674i	$0.600393\pi$
$230$		0			0
$231$	22.5000	−	7.79423i	1.48039	−	0.512823i
$232$		0			0
$233$	2.59808	+	4.50000i	0.170206	+	0.294805i	0.938492	−	0.345302i	$-0.112223\pi$
$233$	2.59808	+	4.50000i	0.170206	+	0.294805i	−0.768286	+	0.640107i	$0.778890\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	0.866025	+	1.50000i	0.0562544	+	0.0974355i
$238$		0			0
$239$			10.3923i			0.672222i	0.941822	+	0.336111i	$0.109112\pi$
$239$			10.3923i			0.672222i	−0.941822	+	0.336111i	$0.890888\pi$
$240$		0			0
$241$	1.50000	+	0.866025i	0.0966235	+	0.0557856i	0.547533	−	0.836784i	$-0.315567\pi$
$241$	1.50000	+	0.866025i	0.0966235	+	0.0557856i	−0.450910	+	0.892570i	$0.648900\pi$
$242$		0			0
$243$	−15.5885			−1.00000
$244$		0			0
$245$		0			0
$246$		0			0
$247$		0			0
$248$		0			0
$249$		−	20.7846i		−	1.31717i
$250$		0			0
$251$	−24.0000			−1.51487			−0.757433	−	0.652913i	$-0.773547\pi$
$251$	−24.0000			−1.51487			−0.757433	+	0.652913i	$0.773547\pi$
$252$		0			0
$253$			27.0000i			1.69748i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	23.3827	−	13.5000i	1.45857	−	0.842107i	0.459631	−	0.888110i	$-0.347982\pi$
$257$	23.3827	−	13.5000i	1.45857	−	0.842107i	0.998941	+	0.0460033i	$0.0146485\pi$
$258$		0			0
$259$	−3.50000	+	18.1865i	−0.217479	+	1.13006i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	2.59808	−	4.50000i	0.160204	−	0.277482i	−0.774738	−	0.632283i	$-0.782118\pi$
$263$	2.59808	−	4.50000i	0.160204	−	0.277482i	0.934942	+	0.354801i	$0.115451\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	7.79423	+	13.5000i	0.476999	+	0.826187i
$268$		0			0
$269$	−10.5000	+	18.1865i	−0.640196	+	1.10885i	0.345192	+	0.938532i	$0.387814\pi$
$269$	−10.5000	+	18.1865i	−0.640196	+	1.10885i	−0.985389	+	0.170321i	$0.945520\pi$
$270$		0			0
$271$	19.5000	−	11.2583i	1.18454	−	0.683895i	0.227480	−	0.973783i	$-0.426951\pi$
$271$	19.5000	−	11.2583i	1.18454	−	0.683895i	0.957061	+	0.289888i	$0.0936180\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$		0			0
$277$	11.2583	+	6.50000i	0.676448	+	0.390547i	0.798515	−	0.601975i	$-0.205619\pi$
$277$	11.2583	+	6.50000i	0.676448	+	0.390547i	−0.122068	+	0.992522i	$0.538953\pi$
$278$		0			0
$279$	−4.50000	−	2.59808i	−0.269408	−	0.155543i
$280$		0			0
$281$			20.7846i			1.23991i	0.784639	+	0.619953i	$0.212848\pi$
$281$			20.7846i			1.23991i	−0.784639	+	0.619953i	$0.787152\pi$
$282$		0			0
$283$	−4.33013	+	7.50000i	−0.257399	+	0.445829i	−0.965544	−	0.260238i	$-0.916199\pi$
$283$	−4.33013	+	7.50000i	−0.257399	+	0.445829i	0.708145	+	0.706067i	$0.249532\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−10.3923	+	12.0000i	−0.613438	+	0.708338i
$288$		0			0
$289$	−4.00000	−	6.92820i	−0.235294	−	0.407541i
$290$		0			0
$291$	12.0000			0.703452
$292$		0			0
$293$		−	6.00000i		−	0.350524i	−0.984522	−	0.175262i	$-0.943923\pi$
$293$		−	6.00000i		−	0.350524i	0.984522	−	0.175262i	$-0.0560772\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−23.3827	−	13.5000i	−1.35680	−	0.783349i
$298$		0			0
$299$		0			0
$300$		0			0
$301$	8.00000	+	6.92820i	0.461112	+	0.399335i
$302$		0			0
$303$	−7.79423	+	13.5000i	−0.447767	+	0.775555i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−17.3205			−0.988534			−0.494267	−	0.869310i	$-0.664563\pi$
$307$	−17.3205			−0.988534			−0.494267	+	0.869310i	$0.664563\pi$
$308$		0			0
$309$	−4.50000	−	7.79423i	−0.255996	−	0.443398i
$310$		0			0
$311$	7.50000	−	12.9904i	0.425286	−	0.736617i	−0.571161	−	0.820838i	$-0.693507\pi$
$311$	7.50000	−	12.9904i	0.425286	−	0.736617i	0.996447	+	0.0842210i	$0.0268402\pi$
$312$		0			0
$313$	6.06218	+	10.5000i	0.342655	+	0.593495i	0.984925	−	0.172983i	$-0.0553406\pi$
$313$	6.06218	+	10.5000i	0.342655	+	0.593495i	−0.642270	+	0.766478i	$0.722007\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−12.9904	−	22.5000i	−0.729612	−	1.26373i	−0.957047	−	0.289933i	$-0.906367\pi$
$317$	−12.9904	−	22.5000i	−0.729612	−	1.26373i	0.227435	−	0.973793i	$-0.426966\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	−13.5000	−	23.3827i	−0.753497	−	1.30509i
$322$		0			0
$323$	5.19615			0.289122
$324$		0			0
$325$		0			0
$326$		0			0
$327$	14.7224	−	25.5000i	0.814152	−	1.41015i
$328$		0			0
$329$	−1.50000	+	7.79423i	−0.0826977	+	0.429710i
$330$		0			0
$331$	−15.5000	−	26.8468i	−0.851957	−	1.47563i	−0.879440	−	0.476011i	$-0.842082\pi$
$331$	−15.5000	−	26.8468i	−0.851957	−	1.47563i	0.0274825	−	0.999622i	$-0.491251\pi$
$332$		0			0
$333$	18.1865	−	10.5000i	0.996616	−	0.575396i
$334$		0			0
$335$		0			0
$336$		0			0
$337$		−	2.00000i		−	0.108947i	−0.998515	−	0.0544735i	$-0.982652\pi$
$337$		−	2.00000i		−	0.108947i	0.998515	−	0.0544735i	$-0.0173480\pi$
$338$		0			0
$339$	36.0000			1.95525
$340$		0			0
$341$	−4.50000	−	7.79423i	−0.243689	−	0.422081i
$342$		0			0
$343$	15.5885	+	10.0000i	0.841698	+	0.539949i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	7.79423	−	13.5000i	0.418416	−	0.724718i	−0.577364	−	0.816487i	$-0.695919\pi$
$347$	7.79423	−	13.5000i	0.418416	−	0.724718i	0.995780	+	0.0917687i	$0.0292521\pi$
$348$		0			0
$349$		−	13.8564i		−	0.741716i	−0.928689	−	0.370858i	$-0.879064\pi$
$349$		−	13.8564i		−	0.741716i	0.928689	−	0.370858i	$-0.120936\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	2.59808	+	1.50000i	0.138282	+	0.0798369i	0.567545	−	0.823343i	$-0.307893\pi$
$353$	2.59808	+	1.50000i	0.138282	+	0.0798369i	−0.429263	+	0.903179i	$0.641227\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−12.9904	+	4.50000i	−0.687524	+	0.238165i
$358$		0			0
$359$	22.5000	−	12.9904i	1.18750	−	0.685606i	0.229766	−	0.973246i	$-0.426204\pi$
$359$	22.5000	−	12.9904i	1.18750	−	0.685606i	0.957739	+	0.287640i	$0.0928706\pi$
$360$		0			0
$361$	−8.00000	+	13.8564i	−0.421053	+	0.729285i
$362$		0			0
$363$	−13.8564	−	24.0000i	−0.727273	−	1.25967i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−16.4545	+	28.5000i	−0.858917	+	1.48769i	0.0140459	+	0.999901i	$0.495529\pi$
$367$	−16.4545	+	28.5000i	−0.858917	+	1.48769i	−0.872963	+	0.487787i	$0.837804\pi$
$368$		0			0
$369$	18.0000			0.937043
$370$		0			0
$371$	−4.50000	−	12.9904i	−0.233628	−	0.674427i
$372$		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
$379$	−16.0000			−0.821865			−0.410932	−	0.911666i	$-0.634797\pi$
$379$	−16.0000			−0.821865			−0.410932	+	0.911666i	$0.634797\pi$
$380$		0			0
$381$		−	13.8564i		−	0.709885i
$382$		0			0
$383$	18.1865	−	10.5000i	0.929288	−	0.536525i	0.0427020	−	0.999088i	$-0.486403\pi$
$383$	18.1865	−	10.5000i	0.929288	−	0.536525i	0.886586	+	0.462563i	$0.153070\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$		−	12.0000i		−	0.609994i
$388$		0			0
$389$	22.5000	+	12.9904i	1.14080	+	0.658638i	0.946627	−	0.322330i	$-0.104466\pi$
$389$	22.5000	+	12.9904i	1.14080	+	0.658638i	0.194168	+	0.980968i	$0.437799\pi$
$390$		0			0
$391$		−	15.5885i		−	0.788342i
$392$		0			0
$393$	−7.79423	−	13.5000i	−0.393167	−	0.680985i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	4.33013	+	7.50000i	0.217323	+	0.376414i	0.953989	−	0.299843i	$-0.0969342\pi$
$397$	4.33013	+	7.50000i	0.217323	+	0.376414i	−0.736666	+	0.676257i	$0.763601\pi$
$398$		0			0
$399$	−1.50000	+	7.79423i	−0.0750939	+	0.390199i
$400$		0			0
$401$	31.5000	−	18.1865i	1.57303	−	0.908192i	0.577241	−	0.816574i	$-0.304129\pi$
$401$	31.5000	−	18.1865i	1.57303	−	0.908192i	0.995794	−	0.0916181i	$-0.0292039\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$	36.3731			1.80295
$408$		0			0
$409$	4.50000	+	2.59808i	0.222511	+	0.128467i	0.607112	−	0.794616i	$-0.292328\pi$
$409$	4.50000	+	2.59808i	0.222511	+	0.128467i	−0.384602	+	0.923083i	$0.625661\pi$
$410$		0			0
$411$	−4.50000	+	7.79423i	−0.221969	+	0.384461i
$412$		0			0
$413$	−2.59808	−	7.50000i	−0.127843	−	0.369051i
$414$		0			0
$415$		0			0
$416$		0			0
$417$		−	18.0000i		−	0.881464i
$418$		0			0
$419$	−12.0000			−0.586238			−0.293119	−	0.956076i	$-0.594693\pi$
$419$	−12.0000			−0.586238			−0.293119	+	0.956076i	$0.594693\pi$
$420$		0			0
$421$	−22.0000			−1.07221			−0.536107	−	0.844150i	$-0.680106\pi$
$421$	−22.0000			−1.07221			−0.536107	+	0.844150i	$0.680106\pi$
$422$		0			0
$423$	7.79423	−	4.50000i	0.378968	−	0.218797i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	6.06218	−	31.5000i	0.293369	−	1.52439i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−13.5000	−	7.79423i	−0.650272	−	0.375435i	0.138288	−	0.990392i	$-0.455840\pi$
$431$	−13.5000	−	7.79423i	−0.650272	−	0.375435i	−0.788560	+	0.614957i	$0.789173\pi$
$432$		0			0
$433$	34.6410			1.66474			0.832370	−	0.554220i	$-0.186983\pi$
$433$	34.6410			1.66474			0.832370	+	0.554220i	$0.186983\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−7.79423	−	4.50000i	−0.372849	−	0.215264i
$438$		0			0
$439$	−13.5000	+	7.79423i	−0.644320	+	0.371998i	−0.786277	−	0.617875i	$-0.787994\pi$
$439$	−13.5000	+	7.79423i	−0.644320	+	0.371998i	0.141957	+	0.989873i	$0.454661\pi$
$440$		0			0
$441$	−3.00000	−	20.7846i	−0.142857	−	0.989743i
$442$		0			0
$443$	−7.79423	−	13.5000i	−0.370315	−	0.641404i	0.619299	−	0.785155i	$-0.287417\pi$
$443$	−7.79423	−	13.5000i	−0.370315	−	0.641404i	−0.989614	+	0.143751i	$0.954084\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−7.79423	+	4.50000i	−0.368654	+	0.212843i
$448$		0			0
$449$			20.7846i			0.980886i	0.871473	+	0.490443i	$0.163165\pi$
$449$			20.7846i			0.980886i	−0.871473	+	0.490443i	$0.836835\pi$
$450$		0			0
$451$	27.0000	+	15.5885i	1.27138	+	0.734032i
$452$		0			0
$453$	11.2583	−	19.5000i	0.528962	−	0.916190i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	26.8468	−	15.5000i	1.25584	−	0.725059i	0.283577	−	0.958950i	$-0.408479\pi$
$457$	26.8468	−	15.5000i	1.25584	−	0.725059i	0.972263	+	0.233890i	$0.0751456\pi$
$458$		0			0
$459$	13.5000	+	7.79423i	0.630126	+	0.363803i
$460$		0			0
$461$	−30.0000			−1.39724			−0.698620	−	0.715493i	$-0.746202\pi$
$461$	−30.0000			−1.39724			−0.698620	+	0.715493i	$0.746202\pi$
$462$		0			0
$463$			16.0000i			0.743583i	0.928316	+	0.371792i	$0.121256\pi$
$463$			16.0000i			0.743583i	−0.928316	+	0.371792i	$0.878744\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−7.79423	+	4.50000i	−0.360674	+	0.208235i	−0.669376	−	0.742923i	$-0.733439\pi$
$467$	−7.79423	+	4.50000i	−0.360674	+	0.208235i	0.308702	+	0.951159i	$0.400105\pi$
$468$		0			0
$469$	12.5000	−	4.33013i	0.577196	−	0.199947i
$470$		0			0
$471$	−4.50000	+	7.79423i	−0.207349	+	0.359139i
$472$		0			0
$473$	10.3923	−	18.0000i	0.477839	−	0.827641i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−7.79423	+	13.5000i	−0.356873	+	0.618123i
$478$		0			0
$479$	16.5000	−	28.5788i	0.753904	−	1.30580i	−0.192013	−	0.981392i	$-0.561502\pi$
$479$	16.5000	−	28.5788i	0.753904	−	1.30580i	0.945917	−	0.324408i	$-0.105165\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$	23.3827	+	4.50000i	1.06395	+	0.204757i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−0.866025	−	0.500000i	−0.0392434	−	0.0226572i	0.480250	−	0.877132i	$-0.340546\pi$
$487$	−0.866025	−	0.500000i	−0.0392434	−	0.0226572i	−0.519493	+	0.854475i	$0.673879\pi$
$488$		0			0
$489$	−1.50000	+	0.866025i	−0.0678323	+	0.0391630i
$490$		0			0
$491$			10.3923i			0.468998i	0.972116	+	0.234499i	$0.0753450\pi$
$491$			10.3923i			0.468998i	−0.972116	+	0.234499i	$0.924655\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−20.7846	−	18.0000i	−0.932317	−	0.807410i
$498$		0			0
$499$	3.50000	+	6.06218i	0.156682	+	0.271380i	0.933670	−	0.358134i	$-0.116587\pi$
$499$	3.50000	+	6.06218i	0.156682	+	0.271380i	−0.776989	+	0.629515i	$0.783254\pi$
$500$		0			0
$501$		−	20.7846i		−	0.928588i
$502$		0			0
$503$		−	24.0000i		−	1.07011i	−0.844818	−	0.535054i	$-0.820291\pi$
$503$		−	24.0000i		−	1.07011i	0.844818	−	0.535054i	$-0.179709\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	22.5167			1.00000
$508$		0			0
$509$	−10.5000	−	18.1865i	−0.465404	−	0.806104i	0.533815	−	0.845601i	$-0.320758\pi$
$509$	−10.5000	−	18.1865i	−0.465404	−	0.806104i	−0.999220	+	0.0394971i	$0.987424\pi$
$510$		0			0
$511$	−10.5000	−	30.3109i	−0.464493	−	1.34087i
$512$		0			0
$513$	7.79423	−	4.50000i	0.344124	−	0.198680i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	15.5885			0.685580
$518$		0			0
$519$	−13.5000	+	7.79423i	−0.592584	+	0.342129i
$520$		0			0
$521$	−7.50000	+	12.9904i	−0.328581	+	0.569119i	−0.982231	−	0.187678i	$-0.939904\pi$
$521$	−7.50000	+	12.9904i	−0.328581	+	0.569119i	0.653650	+	0.756797i	$0.273237\pi$
$522$		0			0
$523$	12.9904	+	22.5000i	0.568030	+	0.983856i	0.996761	+	0.0804241i	$0.0256275\pi$
$523$	12.9904	+	22.5000i	0.568030	+	0.983856i	−0.428731	+	0.903432i	$0.641039\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	2.59808	+	4.50000i	0.113174	+	0.196023i
$528$		0			0
$529$	−2.00000	+	3.46410i	−0.0869565	+	0.150613i
$530$		0			0
$531$	−4.50000	+	7.79423i	−0.195283	+	0.338241i
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$		0			0
$537$	7.79423	+	4.50000i	0.336346	+	0.194189i
$538$		0			0
$539$	13.5000	−	33.7750i	0.581486	−	1.45479i
$540$		0			0
$541$	18.5000	+	32.0429i	0.795377	+	1.37763i	0.922599	+	0.385759i	$0.126061\pi$
$541$	18.5000	+	32.0429i	0.795377	+	1.37763i	−0.127222	+	0.991874i	$0.540606\pi$
$542$		0			0
$543$			12.0000i			0.514969i
$544$		0			0
$545$		0			0
$546$		0			0
$547$			32.0000i			1.36822i	0.729378	+	0.684111i	$0.239809\pi$
$547$			32.0000i			1.36822i	−0.729378	+	0.684111i	$0.760191\pi$
$548$		0			0
$549$	−31.5000	+	18.1865i	−1.34439	+	0.776182i
$550$		0			0
$551$		0			0
$552$		0			0
$553$	2.59808	+	0.500000i	0.110481	+	0.0212622i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	12.9904	−	22.5000i	0.550420	−	0.953356i	−0.447824	−	0.894122i	$-0.647801\pi$
$557$	12.9904	−	22.5000i	0.550420	−	0.953356i	0.998244	−	0.0592339i	$-0.0188658\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	13.5000	+	23.3827i	0.569970	+	0.987218i
$562$		0			0
$563$	−23.3827	−	13.5000i	−0.985463	−	0.568957i	−0.0815478	−	0.996669i	$-0.525986\pi$
$563$	−23.3827	−	13.5000i	−0.985463	−	0.568957i	−0.903915	+	0.427712i	$0.859320\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−15.5885	+	18.0000i	−0.654654	+	0.755929i
$568$		0			0
$569$	−13.5000	+	7.79423i	−0.565949	+	0.326751i	−0.755530	−	0.655114i	$-0.772621\pi$
$569$	−13.5000	+	7.79423i	−0.565949	+	0.326751i	0.189580	+	0.981865i	$0.439287\pi$
$570$		0			0
$571$	3.50000	−	6.06218i	0.146470	−	0.253694i	−0.783450	−	0.621455i	$-0.786542\pi$
$571$	3.50000	−	6.06218i	0.146470	−	0.253694i	0.929921	+	0.367760i	$0.119875\pi$
$572$		0			0
$573$	−23.3827	+	13.5000i	−0.976826	+	0.563971i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	12.9904	−	22.5000i	0.540797	−	0.936687i	−0.458062	−	0.888920i	$-0.651456\pi$
$577$	12.9904	−	22.5000i	0.540797	−	0.936687i	0.998859	−	0.0477669i	$-0.0152105\pi$
$578$		0			0
$579$	7.50000	+	4.33013i	0.311689	+	0.179954i
$580$		0			0
$581$	−24.0000	−	20.7846i	−0.995688	−	0.862291i
$582$		0			0
$583$	−23.3827	+	13.5000i	−0.968412	+	0.559113i
$584$		0			0
$585$		0			0
$586$		0			0
$587$			36.0000i			1.48588i	0.669359	+	0.742940i	$0.266569\pi$
$587$			36.0000i			1.48588i	−0.669359	+	0.742940i	$0.733431\pi$
$588$		0			0
$589$	3.00000			0.123613
$590$		0			0
$591$		0			0
$592$		0			0
$593$	18.1865	−	10.5000i	0.746831	−	0.431183i	−0.0777165	−	0.996976i	$-0.524763\pi$
$593$	18.1865	−	10.5000i	0.746831	−	0.431183i	0.824548	+	0.565792i	$0.191430\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−2.59808	−	1.50000i	−0.106332	−	0.0613909i
$598$		0			0
$599$	−4.50000	−	2.59808i	−0.183865	−	0.106155i	0.405242	−	0.914209i	$-0.367187\pi$
$599$	−4.50000	−	2.59808i	−0.183865	−	0.106155i	−0.589107	+	0.808055i	$0.700520\pi$
$600$		0			0
$601$		−	34.6410i		−	1.41304i	−0.707695	−	0.706518i	$-0.750265\pi$
$601$		−	34.6410i		−	1.41304i	0.707695	−	0.706518i	$-0.249735\pi$
$602$		0			0
$603$	−12.9904	−	7.50000i	−0.529009	−	0.305424i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	14.7224	+	25.5000i	0.597565	+	1.03501i	0.993179	+	0.116596i	$0.0371984\pi$
$607$	14.7224	+	25.5000i	0.597565	+	1.03501i	−0.395614	+	0.918417i	$0.629468\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−0.866025	−	0.500000i	−0.0349784	−	0.0201948i	0.482409	−	0.875946i	$-0.339762\pi$
$613$	−0.866025	−	0.500000i	−0.0349784	−	0.0201948i	−0.517387	+	0.855751i	$0.673095\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	20.7846			0.836757			0.418378	−	0.908273i	$-0.362599\pi$
$617$	20.7846			0.836757			0.418378	+	0.908273i	$0.362599\pi$
$618$		0			0
$619$	−22.5000	−	12.9904i	−0.904351	−	0.522127i	−0.0257420	−	0.999669i	$-0.508195\pi$
$619$	−22.5000	−	12.9904i	−0.904351	−	0.522127i	−0.878609	+	0.477541i	$0.841528\pi$
$620$		0			0
$621$	−13.5000	−	23.3827i	−0.541736	−	0.938315i
$622$		0			0
$623$	23.3827	+	4.50000i	0.936808	+	0.180289i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	15.5885			0.622543
$628$		0			0
$629$	−21.0000			−0.837325
$630$		0			0
$631$	8.00000			0.318475			0.159237	−	0.987240i	$-0.449096\pi$
$631$	8.00000			0.318475			0.159237	+	0.987240i	$0.449096\pi$
$632$		0			0
$633$	34.6410			1.37686
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$			31.1769i			1.23334i
$640$		0			0
$641$	13.5000	+	7.79423i	0.533218	+	0.307854i	0.742326	−	0.670039i	$-0.233723\pi$
$641$	13.5000	+	7.79423i	0.533218	+	0.307854i	−0.209108	+	0.977893i	$0.567056\pi$
$642$		0			0
$643$	3.46410			0.136611			0.0683054	−	0.997664i	$-0.478241\pi$
$643$	3.46410			0.136611			0.0683054	+	0.997664i	$0.478241\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−7.79423	−	4.50000i	−0.306423	−	0.176913i	0.338902	−	0.940822i	$-0.389945\pi$
$647$	−7.79423	−	4.50000i	−0.306423	−	0.176913i	−0.645325	+	0.763908i	$0.723278\pi$
$648$		0			0
$649$	−13.5000	+	7.79423i	−0.529921	+	0.305950i
$650$		0			0
$651$	−7.50000	+	2.59808i	−0.293948	+	0.101827i
$652$		0			0
$653$	−7.79423	−	13.5000i	−0.305012	−	0.528296i	0.672252	−	0.740322i	$-0.265327\pi$
$653$	−7.79423	−	13.5000i	−0.305012	−	0.528296i	−0.977264	+	0.212026i	$0.931994\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−18.1865	+	31.5000i	−0.709524	+	1.22893i
$658$		0			0
$659$			10.3923i			0.404827i	0.979300	+	0.202413i	$0.0648785\pi$
$659$			10.3923i			0.404827i	−0.979300	+	0.202413i	$0.935122\pi$
$660$		0			0
$661$	19.5000	+	11.2583i	0.758462	+	0.437898i	0.828743	−	0.559629i	$-0.189056\pi$
$661$	19.5000	+	11.2583i	0.758462	+	0.437898i	−0.0702812	+	0.997527i	$0.522390\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$	−18.0000			−0.695920
$670$		0			0
$671$	−63.0000			−2.43209
$672$		0			0
$673$		−	22.0000i		−	0.848038i	−0.905653	−	0.424019i	$-0.860619\pi$
$673$		−	22.0000i		−	0.848038i	0.905653	−	0.424019i	$-0.139381\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−38.9711	+	22.5000i	−1.49778	+	0.864745i	−0.999997	−	0.00255466i	$-0.999187\pi$
$677$	−38.9711	+	22.5000i	−1.49778	+	0.864745i	−0.497786	+	0.867300i	$0.665853\pi$
$678$		0			0
$679$	12.0000	−	13.8564i	0.460518	−	0.531760i
$680$		0			0
$681$	13.5000	+	7.79423i	0.517321	+	0.298675i
$682$		0			0
$683$	−18.1865	+	31.5000i	−0.695888	+	1.20531i	0.273992	+	0.961732i	$0.411656\pi$
$683$	−18.1865	+	31.5000i	−0.695888	+	1.20531i	−0.969880	+	0.243582i	$0.921677\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	33.7750	−	19.5000i	1.28860	−	0.743971i
$688$		0			0
$689$		0			0
$690$		0			0
$691$	−28.5000	+	16.4545i	−1.08419	+	0.625958i	−0.932024	−	0.362397i	$-0.881959\pi$
$691$	−28.5000	+	16.4545i	−1.08419	+	0.625958i	−0.152167	+	0.988355i	$0.548625\pi$
$692$		0			0
$693$	−38.9711	+	13.5000i	−1.48039	+	0.512823i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−15.5885	−	9.00000i	−0.590455	−	0.340899i
$698$		0			0
$699$	−4.50000	−	7.79423i	−0.170206	−	0.294805i
$700$		0			0
$701$			20.7846i			0.785024i	0.919747	+	0.392512i	$0.128394\pi$
$701$			20.7846i			0.785024i	−0.919747	+	0.392512i	$0.871606\pi$
$702$		0			0
$703$	−6.06218	+	10.5000i	−0.228639	+	0.396015i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	7.79423	+	22.5000i	0.293132	+	0.846200i
$708$		0			0
$709$	15.5000	+	26.8468i	0.582115	+	1.00825i	0.995228	+	0.0975728i	$0.0311079\pi$
$709$	15.5000	+	26.8468i	0.582115	+	1.00825i	−0.413114	+	0.910679i	$0.635559\pi$
$710$		0			0
$711$	−1.50000	−	2.59808i	−0.0562544	−	0.0974355i
$712$		0			0
$713$		−	9.00000i		−	0.337053i
$714$		0			0
$715$		0			0
$716$		0			0
$717$		−	18.0000i		−	0.672222i
$718$		0			0
$719$	7.50000	+	12.9904i	0.279703	+	0.484459i	0.971311	−	0.237814i	$-0.0764307\pi$
$719$	7.50000	+	12.9904i	0.279703	+	0.484459i	−0.691608	+	0.722273i	$0.743097\pi$
$720$		0			0
$721$	−13.5000	−	2.59808i	−0.502766	−	0.0967574i
$722$		0			0
$723$	−2.59808	−	1.50000i	−0.0966235	−	0.0557856i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−24.2487			−0.899335			−0.449667	−	0.893196i	$-0.648458\pi$
$727$	−24.2487			−0.899335			−0.449667	+	0.893196i	$0.648458\pi$
$728$		0			0
$729$	27.0000			1.00000
$730$		0			0
$731$	−6.00000	+	10.3923i	−0.221918	+	0.384373i
$732$		0			0
$733$	−14.7224	−	25.5000i	−0.543785	−	0.941864i	−0.998682	−	0.0513199i	$-0.983657\pi$
$733$	−14.7224	−	25.5000i	−0.543785	−	0.941864i	0.454897	−	0.890544i	$-0.349676\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−12.9904	−	22.5000i	−0.478507	−	0.828798i
$738$		0			0
$739$	8.50000	−	14.7224i	0.312678	−	0.541573i	−0.666264	−	0.745716i	$-0.732107\pi$
$739$	8.50000	−	14.7224i	0.312678	−	0.541573i	0.978941	+	0.204143i	$0.0654407\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	51.9615			1.90628			0.953142	−	0.302524i	$-0.0978293\pi$
$743$	51.9615			1.90628			0.953142	+	0.302524i	$0.0978293\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$			36.0000i			1.31717i
$748$		0			0
$749$	−40.5000	−	7.79423i	−1.47984	−	0.284795i
$750$		0			0
$751$	14.5000	+	25.1147i	0.529113	+	0.916450i	0.999424	+	0.0339490i	$0.0108084\pi$
$751$	14.5000	+	25.1147i	0.529113	+	0.916450i	−0.470311	+	0.882501i	$0.655858\pi$
$752$		0			0
$753$	41.5692			1.51487
$754$		0			0
$755$		0			0
$756$		0			0
$757$			10.0000i			0.363456i	0.983349	+	0.181728i	$0.0581691\pi$
$757$			10.0000i			0.363456i	−0.983349	+	0.181728i	$0.941831\pi$
$758$		0			0
$759$		−	46.7654i		−	1.69748i
$760$		0			0
$761$	10.5000	+	18.1865i	0.380625	+	0.659261i	0.991152	−	0.132734i	$-0.0423756\pi$
$761$	10.5000	+	18.1865i	0.380625	+	0.659261i	−0.610527	+	0.791995i	$0.709042\pi$
$762$		0			0
$763$	−14.7224	−	42.5000i	−0.532988	−	1.53860i
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$		0			0
$769$			34.6410i			1.24919i	0.780950	+	0.624593i	$0.214735\pi$
$769$			34.6410i			1.24919i	−0.780950	+	0.624593i	$0.785265\pi$
$770$		0			0
$771$	−40.5000	+	23.3827i	−1.45857	+	0.842107i
$772$		0			0
$773$	33.7750	+	19.5000i	1.21480	+	0.701366i	0.963802	−	0.266621i	$-0.0859071\pi$
$773$	33.7750	+	19.5000i	1.21480	+	0.701366i	0.251000	+	0.967987i	$0.419240\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	6.06218	−	31.5000i	0.217479	−	1.13006i
$778$		0			0
$779$	−9.00000	+	5.19615i	−0.322458	+	0.186171i
$780$		0			0
$781$	−27.0000	+	46.7654i	−0.966136	+	1.67340i
$782$		0			0
$783$		0			0
$784$		0			0
$785$		0			0
$786$		0			0
$787$	0.866025	−	1.50000i	0.0308705	−	0.0534692i	−0.850177	−	0.526496i	$-0.823505\pi$
$787$	0.866025	−	1.50000i	0.0308705	−	0.0534692i	0.881048	+	0.473027i	$0.156839\pi$
$788$		0			0
$789$	−4.50000	+	7.79423i	−0.160204	+	0.277482i
$790$		0			0
$791$	36.0000	−	41.5692i	1.28001	−	1.47803i
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$			18.0000i			0.637593i	0.947823	+	0.318796i	$0.103279\pi$
$797$			18.0000i			0.637593i	−0.947823	+	0.318796i	$0.896721\pi$
$798$		0			0
$799$	−9.00000			−0.318397
$800$		0			0
$801$	−13.5000	−	23.3827i	−0.476999	−	0.826187i
$802$		0			0
$803$	−54.5596	+	31.5000i	−1.92537	+	1.11161i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	18.1865	−	31.5000i	0.640196	−	1.10885i
$808$		0			0
$809$	22.5000	+	12.9904i	0.791058	+	0.456717i	0.840335	−	0.542068i	$-0.182358\pi$
$809$	22.5000	+	12.9904i	0.791058	+	0.456717i	−0.0492770	+	0.998785i	$0.515692\pi$
$810$		0			0
$811$		−	51.9615i		−	1.82462i	−0.409505	−	0.912308i	$-0.634299\pi$
$811$		−	51.9615i		−	1.82462i	0.409505	−	0.912308i	$-0.365701\pi$
$812$		0			0
$813$	−33.7750	+	19.5000i	−1.18454	+	0.683895i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	3.46410	+	6.00000i	0.121194	+	0.209913i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−4.50000	+	2.59808i	−0.157051	+	0.0906735i	−0.576466	−	0.817121i	$-0.695569\pi$
$821$	−4.50000	+	2.59808i	−0.157051	+	0.0906735i	0.419415	+	0.907795i	$0.362235\pi$
$822$		0			0
$823$	−6.06218	−	3.50000i	−0.211314	−	0.122002i	0.390608	−	0.920557i	$-0.372265\pi$
$823$	−6.06218	−	3.50000i	−0.211314	−	0.122002i	−0.601922	+	0.798555i	$0.705598\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	10.3923			0.361376			0.180688	−	0.983540i	$-0.442168\pi$
$827$	10.3923			0.361376			0.180688	+	0.983540i	$0.442168\pi$
$828$		0			0
$829$	−1.50000	−	0.866025i	−0.0520972	−	0.0300783i	0.473725	−	0.880673i	$-0.342909\pi$
$829$	−1.50000	−	0.866025i	−0.0520972	−	0.0300783i	−0.525822	+	0.850594i	$0.676242\pi$
$830$		0			0
$831$	−19.5000	−	11.2583i	−0.676448	−	0.390547i
$832$		0			0
$833$	−7.79423	+	19.5000i	−0.270054	+	0.675635i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	7.79423	+	4.50000i	0.269408	+	0.155543i
$838$		0			0
$839$	24.0000			0.828572			0.414286	−	0.910147i	$-0.364031\pi$
$839$	24.0000			0.828572			0.414286	+	0.910147i	$0.364031\pi$
$840$		0			0
$841$	29.0000			1.00000
$842$		0			0
$843$		−	36.0000i		−	1.23991i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−41.5692	−	8.00000i	−1.42834	−	0.274883i
$848$		0			0
$849$	7.50000	−	12.9904i	0.257399	−	0.445829i
$850$		0			0
$851$	31.5000	+	18.1865i	1.07981	+	0.623426i
$852$		0			0
$853$	13.8564			0.474434			0.237217	−	0.971457i	$-0.423765\pi$
$853$	13.8564			0.474434			0.237217	+	0.971457i	$0.423765\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	28.5788	+	16.5000i	0.976235	+	0.563629i	0.901131	−	0.433546i	$-0.142738\pi$
$857$	28.5788	+	16.5000i	0.976235	+	0.563629i	0.0751033	+	0.997176i	$0.476071\pi$
$858$		0			0
$859$	34.5000	−	19.9186i	1.17712	−	0.679613i	0.221777	−	0.975097i	$-0.428814\pi$
$859$	34.5000	−	19.9186i	1.17712	−	0.679613i	0.955348	+	0.295484i	$0.0954809\pi$
$860$		0			0
$861$	18.0000	−	20.7846i	0.613438	−	0.708338i
$862$		0			0
$863$	2.59808	+	4.50000i	0.0884395	+	0.153182i	0.906852	−	0.421450i	$-0.138479\pi$
$863$	2.59808	+	4.50000i	0.0884395	+	0.153182i	−0.818412	+	0.574632i	$0.805145\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	6.92820	+	12.0000i	0.235294	+	0.407541i
$868$		0			0
$869$		−	5.19615i		−	0.176267i
$870$		0			0
$871$		0			0
$872$		0			0
$873$	−20.7846			−0.703452
$874$		0			0
$875$		0			0
$876$		0			0
$877$	9.52628	−	5.50000i	0.321680	−	0.185722i	−0.330461	−	0.943820i	$-0.607204\pi$
$877$	9.52628	−	5.50000i	0.321680	−	0.185722i	0.652141	+	0.758098i	$0.273871\pi$
$878$		0			0
$879$			10.3923i			0.350524i
$880$		0			0
$881$	18.0000			0.606435			0.303218	−	0.952921i	$-0.401939\pi$
$881$	18.0000			0.606435			0.303218	+	0.952921i	$0.401939\pi$
$882$		0			0
$883$		−	28.0000i		−	0.942275i	−0.882060	−	0.471138i	$-0.843844\pi$
$883$		−	28.0000i		−	0.942275i	0.882060	−	0.471138i	$-0.156156\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	2.59808	−	1.50000i	0.0872349	−	0.0503651i	−0.455748	−	0.890109i	$-0.650628\pi$
$887$	2.59808	−	1.50000i	0.0872349	−	0.0503651i	0.542983	+	0.839744i	$0.317295\pi$
$888$		0			0
$889$	−16.0000	−	13.8564i	−0.536623	−	0.464729i
$890$		0			0
$891$	40.5000	+	23.3827i	1.35680	+	0.783349i
$892$		0			0
$893$	−2.59808	+	4.50000i	−0.0869413	+	0.150587i
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$		0			0
$899$		0			0
$900$		0			0
$901$	13.5000	−	7.79423i	0.449750	−	0.259663i
$902$		0			0
$903$	−13.8564	−	12.0000i	−0.461112	−	0.399335i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−32.0429	−	18.5000i	−1.06397	−	0.614282i	−0.137441	−	0.990510i	$-0.543888\pi$
$907$	−32.0429	−	18.5000i	−1.06397	−	0.614282i	−0.926527	+	0.376228i	$0.877221\pi$
$908$		0			0
$909$	13.5000	−	23.3827i	0.447767	−	0.775555i
$910$		0			0
$911$			10.3923i			0.344312i	0.985070	+	0.172156i	$0.0550734\pi$
$911$			10.3923i			0.344312i	−0.985070	+	0.172156i	$0.944927\pi$
$912$		0			0
$913$	−31.1769	+	54.0000i	−1.03181	+	1.78714i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−23.3827	−	4.50000i	−0.772164	−	0.148603i
$918$		0			0
$919$	9.50000	+	16.4545i	0.313376	+	0.542783i	0.979091	−	0.203423i	$-0.0652066\pi$
$919$	9.50000	+	16.4545i	0.313376	+	0.542783i	−0.665715	+	0.746206i	$0.731873\pi$
$920$		0			0
$921$	30.0000			0.988534
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$	7.79423	+	13.5000i	0.255996	+	0.443398i
$928$		0			0
$929$	19.5000	+	33.7750i	0.639774	+	1.10812i	0.985482	+	0.169779i	$0.0543055\pi$
$929$	19.5000	+	33.7750i	0.639774	+	1.10812i	−0.345708	+	0.938342i	$0.612361\pi$
$930$		0			0
$931$	7.50000	+	9.52628i	0.245803	+	0.312211i
$932$		0			0
$933$	−12.9904	+	22.5000i	−0.425286	+	0.736617i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	41.5692			1.35801			0.679004	−	0.734135i	$-0.262412\pi$
$937$	41.5692			1.35801			0.679004	+	0.734135i	$0.262412\pi$
$938$		0			0
$939$	−10.5000	−	18.1865i	−0.342655	−	0.593495i
$940$		0			0
$941$	10.5000	−	18.1865i	0.342290	−	0.592864i	−0.642567	−	0.766229i	$-0.722131\pi$
$941$	10.5000	−	18.1865i	0.342290	−	0.592864i	0.984858	+	0.173365i	$0.0554641\pi$
$942$		0			0
$943$	15.5885	+	27.0000i	0.507630	+	0.879241i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−23.3827	−	40.5000i	−0.759835	−	1.31607i	−0.942934	−	0.332979i	$-0.891946\pi$
$947$	−23.3827	−	40.5000i	−0.759835	−	1.31607i	0.183099	−	0.983094i	$-0.441387\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$	22.5000	+	38.9711i	0.729612	+	1.26373i
$952$		0			0
$953$	−20.7846			−0.673280			−0.336640	−	0.941634i	$-0.609290\pi$
$953$	−20.7846			−0.673280			−0.336640	+	0.941634i	$0.609290\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$	4.50000	+	12.9904i	0.145313	+	0.419481i
$960$		0			0
$961$	−14.0000	−	24.2487i	−0.451613	−	0.782216i
$962$		0			0
$963$	23.3827	+	40.5000i	0.753497	+	1.30509i
$964$		0			0
$965$		0			0
$966$		0			0
$967$		−	40.0000i		−	1.28631i	−0.765735	−	0.643157i	$-0.777624\pi$
$967$		−	40.0000i		−	1.28631i	0.765735	−	0.643157i	$-0.222376\pi$
$968$		0			0
$969$	−9.00000			−0.289122
$970$		0			0
$971$	28.5000	+	49.3634i	0.914609	+	1.58415i	0.807473	+	0.589904i	$0.200834\pi$
$971$	28.5000	+	49.3634i	0.914609	+	1.58415i	0.107135	+	0.994244i	$0.465832\pi$
$972$		0			0
$973$	−20.7846	−	18.0000i	−0.666324	−	0.577054i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−18.1865	+	31.5000i	−0.581839	+	1.00777i	0.413423	+	0.910539i	$0.364333\pi$
$977$	−18.1865	+	31.5000i	−0.581839	+	1.00777i	−0.995261	+	0.0972351i	$0.969000\pi$
$978$		0			0
$979$		−	46.7654i		−	1.49463i
$980$		0			0
$981$	−25.5000	+	44.1673i	−0.814152	+	1.41015i
$982$		0			0
$983$	−2.59808	−	1.50000i	−0.0828658	−	0.0478426i	0.457995	−	0.888955i	$-0.348568\pi$
$983$	−2.59808	−	1.50000i	−0.0828658	−	0.0478426i	−0.540860	+	0.841112i	$0.681901\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	2.59808	−	13.5000i	0.0826977	−	0.429710i
$988$		0			0
$989$	18.0000	−	10.3923i	0.572367	−	0.330456i
$990$		0			0
$991$	−12.5000	+	21.6506i	−0.397076	+	0.687755i	−0.993364	−	0.115015i	$-0.963308\pi$
$991$	−12.5000	+	21.6506i	−0.397076	+	0.687755i	0.596288	+	0.802771i	$0.296642\pi$
$992$		0			0
$993$	26.8468	+	46.5000i	0.851957	+	1.47563i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−11.2583	+	19.5000i	−0.356555	+	0.617571i	−0.987383	−	0.158352i	$-0.949382\pi$
$997$	−11.2583	+	19.5000i	−0.356555	+	0.617571i	0.630828	+	0.775923i	$0.282715\pi$
$998$		0			0
$999$	−31.5000	+	18.1865i	−0.996616	+	0.575396i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2100.2.bo.f.1949.1		4
3.2	odd	2		2100.2.bo.a.1949.2		4
5.2	odd	4		2100.2.bi.e.101.1		2
5.3	odd	4		84.2.k.b.17.1	yes	2
5.4	even	2	inner	2100.2.bo.f.1949.2		4
7.5	odd	6		2100.2.bo.a.1349.1		4
15.2	even	4		2100.2.bi.f.101.1		2
15.8	even	4		84.2.k.a.17.1	yes	2
15.14	odd	2		2100.2.bo.a.1949.1		4
20.3	even	4		336.2.bc.b.17.1		2
21.5	even	6	inner	2100.2.bo.f.1349.2		4
35.3	even	12		588.2.f.c.293.1		2
35.12	even	12		2100.2.bi.f.1601.1		2
35.13	even	4		588.2.k.c.521.1		2
35.18	odd	12		588.2.f.a.293.2		2
35.19	odd	6		2100.2.bo.a.1349.2		4
35.23	odd	12		588.2.k.d.509.1		2
35.33	even	12		84.2.k.a.5.1	✓	2
45.13	odd	12		2268.2.w.a.269.1		2
45.23	even	12		2268.2.w.f.269.1		2
45.38	even	12		2268.2.bm.a.1025.1		2
45.43	odd	12		2268.2.bm.f.1025.1		2
60.23	odd	4		336.2.bc.d.17.1		2
105.23	even	12		588.2.k.c.509.1		2
105.38	odd	12		588.2.f.a.293.1		2
105.47	odd	12		2100.2.bi.e.1601.1		2
105.53	even	12		588.2.f.c.293.2		2
105.68	odd	12		84.2.k.b.5.1	yes	2
105.83	odd	4		588.2.k.d.521.1		2
105.89	even	6	inner	2100.2.bo.f.1349.1		4
140.3	odd	12		2352.2.k.a.881.2		2
140.103	odd	12		336.2.bc.d.257.1		2
140.123	even	12		2352.2.k.d.881.1		2
315.68	odd	12		2268.2.bm.f.593.1		2
315.103	even	12		2268.2.bm.a.593.1		2
315.173	odd	12		2268.2.w.a.1349.1		2
315.313	even	12		2268.2.w.f.1349.1		2
420.143	even	12		2352.2.k.d.881.2		2
420.263	odd	12		2352.2.k.a.881.1		2
420.383	even	12		336.2.bc.b.257.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.2.k.a.5.1	✓	2	35.33	even	12
84.2.k.a.17.1	yes	2	15.8	even	4
84.2.k.b.5.1	yes	2	105.68	odd	12
84.2.k.b.17.1	yes	2	5.3	odd	4
336.2.bc.b.17.1		2	20.3	even	4
336.2.bc.b.257.1		2	420.383	even	12
336.2.bc.d.17.1		2	60.23	odd	4
336.2.bc.d.257.1		2	140.103	odd	12
588.2.f.a.293.1		2	105.38	odd	12
588.2.f.a.293.2		2	35.18	odd	12
588.2.f.c.293.1		2	35.3	even	12
588.2.f.c.293.2		2	105.53	even	12
588.2.k.c.509.1		2	105.23	even	12
588.2.k.c.521.1		2	35.13	even	4
588.2.k.d.509.1		2	35.23	odd	12
588.2.k.d.521.1		2	105.83	odd	4
2100.2.bi.e.101.1		2	5.2	odd	4
2100.2.bi.e.1601.1		2	105.47	odd	12
2100.2.bi.f.101.1		2	15.2	even	4
2100.2.bi.f.1601.1		2	35.12	even	12
2100.2.bo.a.1349.1		4	7.5	odd	6
2100.2.bo.a.1349.2		4	35.19	odd	6
2100.2.bo.a.1949.1		4	15.14	odd	2
2100.2.bo.a.1949.2		4	3.2	odd	2
2100.2.bo.f.1349.1		4	105.89	even	6	inner
2100.2.bo.f.1349.2		4	21.5	even	6	inner
2100.2.bo.f.1949.1		4	1.1	even	1	trivial
2100.2.bo.f.1949.2		4	5.4	even	2	inner
2268.2.w.a.269.1		2	45.13	odd	12
2268.2.w.a.1349.1		2	315.173	odd	12
2268.2.w.f.269.1		2	45.23	even	12
2268.2.w.f.1349.1		2	315.313	even	12
2268.2.bm.a.593.1		2	315.103	even	12
2268.2.bm.a.1025.1		2	45.38	even	12
2268.2.bm.f.593.1		2	315.68	odd	12
2268.2.bm.f.1025.1		2	45.43	odd	12
2352.2.k.a.881.1		2	420.263	odd	12
2352.2.k.a.881.2		2	140.3	odd	12
2352.2.k.d.881.1		2	140.123	even	12
2352.2.k.d.881.2		2	420.143	even	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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q-1.73205 q^{3} +(-1.73205 + 2.00000i) q^{7} +3.00000 q^{9} +(4.50000 + 2.59808i) q^{11} +(-2.59808 - 1.50000i) q^{17} +(-1.50000 + 0.866025i) q^{19} +(3.00000 - 3.46410i) q^{21} +(2.59808 + 4.50000i) q^{23} -5.19615 q^{27} +(-1.50000 - 0.866025i) q^{31} +(-7.79423 - 4.50000i) q^{33} +(6.06218 - 3.50000i) q^{37} +6.00000 q^{41} -4.00000i q^{43} +(2.59808 - 1.50000i) q^{47} +(-1.00000 - 6.92820i) q^{49} +(4.50000 + 2.59808i) q^{51} +(-2.59808 + 4.50000i) q^{53} +(2.59808 - 1.50000i) q^{57} +(-1.50000 + 2.59808i) q^{59} +(-10.5000 + 6.06218i) q^{61} +(-5.19615 + 6.00000i) q^{63} +(-4.33013 - 2.50000i) q^{67} +(-4.50000 - 7.79423i) q^{69} +10.3923i q^{71} +(-6.06218 + 10.5000i) q^{73} +(-12.9904 + 4.50000i) q^{77} +(-0.500000 - 0.866025i) q^{79} +9.00000 q^{81} +12.0000i q^{83} +(-4.50000 - 7.79423i) q^{89} +(2.59808 + 1.50000i) q^{93} -6.92820 q^{97} +(13.5000 + 7.79423i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 12 q^{9} + 18 q^{11} - 6 q^{19} + 12 q^{21} - 6 q^{31} + 24 q^{41} - 4 q^{49} + 18 q^{51} - 6 q^{59} - 42 q^{61} - 18 q^{69} - 2 q^{79} + 36 q^{81} - 18 q^{89} + 54 q^{99}+O(q^{100}) \) 4 * q + 12 * q^9 + 18 * q^11 - 6 * q^19 + 12 * q^21 - 6 * q^31 + 24 * q^41 - 4 * q^49 + 18 * q^51 - 6 * q^59 - 42 * q^61 - 18 * q^69 - 2 * q^79 + 36 * q^81 - 18 * q^89 + 54 * q^99

Introduction

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