LMFDB - Embedded newform 2100.2.bi.e.1601.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2100,2,Mod(101,2100)]

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, 3, 0, 1]))

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

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

chi := DirichletCharacter("2100.101");

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.bi (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$16.7685844245$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 84)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1601.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	2100.1601
Dual form			2100.2.bi.e.101.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.73205i q^{3} +(-2.00000 + 1.73205i) q^{7} -3.00000 q^{9} +O(q^{10})$	$q-1.73205i q^{3} +(-2.00000 + 1.73205i) q^{7} -3.00000 q^{9} +(4.50000 - 2.59808i) q^{11} +(1.50000 + 2.59808i) q^{17} +(1.50000 + 0.866025i) q^{19} +(3.00000 + 3.46410i) q^{21} +(4.50000 + 2.59808i) q^{23} +5.19615i q^{27} +(-1.50000 + 0.866025i) q^{31} +(-4.50000 - 7.79423i) q^{33} +(3.50000 - 6.06218i) q^{37} +6.00000 q^{41} -4.00000 q^{43} +(1.50000 - 2.59808i) q^{47} +(1.00000 - 6.92820i) q^{49} +(4.50000 - 2.59808i) q^{51} +(4.50000 - 2.59808i) q^{53} +(1.50000 - 2.59808i) q^{57} +(1.50000 + 2.59808i) q^{59} +(-10.5000 - 6.06218i) q^{61} +(6.00000 - 5.19615i) q^{63} +(2.50000 + 4.33013i) q^{67} +(4.50000 - 7.79423i) q^{69} -10.3923i q^{71} +(10.5000 - 6.06218i) q^{73} +(-4.50000 + 12.9904i) q^{77} +(0.500000 - 0.866025i) q^{79} +9.00000 q^{81} +12.0000 q^{83} +(4.50000 - 7.79423i) q^{89} +(1.50000 + 2.59808i) q^{93} +6.92820i q^{97} +(-13.5000 + 7.79423i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 4 q^{7} - 6 q^{9}+O(q^{10}) $ 2 * q - 4 * q^7 - 6 * q^9	$ 2 q - 4 q^{7} - 6 q^{9} + 9 q^{11} + 3 q^{17} + 3 q^{19} + 6 q^{21} + 9 q^{23} - 3 q^{31} - 9 q^{33} + 7 q^{37} + 12 q^{41} - 8 q^{43} + 3 q^{47} + 2 q^{49} + 9 q^{51} + 9 q^{53} + 3 q^{57} + 3 q^{59} - 21 q^{61} + 12 q^{63} + 5 q^{67} + 9 q^{69} + 21 q^{73} - 9 q^{77} + q^{79} + 18 q^{81} + 24 q^{83} + 9 q^{89} + 3 q^{93} - 27 q^{99}+O(q^{100}) $ 2 * q - 4 * q^7 - 6 * q^9 + 9 * q^11 + 3 * q^17 + 3 * q^19 + 6 * q^21 + 9 * q^23 - 3 * q^31 - 9 * q^33 + 7 * q^37 + 12 * q^41 - 8 * q^43 + 3 * q^47 + 2 * q^49 + 9 * q^51 + 9 * q^53 + 3 * q^57 + 3 * q^59 - 21 * q^61 + 12 * q^63 + 5 * q^67 + 9 * q^69 + 21 * q^73 - 9 * q^77 + q^79 + 18 * q^81 + 24 * q^83 + 9 * q^89 + 3 * q^93 - 27 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$701$	$1051$	$1177$	$1501$
$\chi(n)$	$-1$	$1$	$1$	$e\left(\frac{5}{6}\right)$

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
$3$		−	1.73205i		−	1.00000i
$3$		−	1.73205i		−	1.00000i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−2.00000	+	1.73205i	−0.755929	+	0.654654i
$7$	−2.00000	+	1.73205i	−0.755929	+	0.654654i
$8$		0			0
$9$	−3.00000			−1.00000
$10$		0			0
$11$	4.50000	−	2.59808i	1.35680	−	0.783349i	0.367610	−	0.929980i	$-0.380176\pi$
$11$	4.50000	−	2.59808i	1.35680	−	0.783349i	0.989191	+	0.146631i	$0.0468429\pi$
$12$		0			0
$13$		0			0		1.00000			$0$
$13$		0			0		−1.00000			$\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	1.50000	+	2.59808i	0.363803	+	0.630126i	0.988583	−	0.150675i	$-0.0481447\pi$
$17$	1.50000	+	2.59808i	0.363803	+	0.630126i	−0.624780	+	0.780801i	$0.714811\pi$
$18$		0			0
$19$	1.50000	+	0.866025i	0.344124	+	0.198680i	0.662094	−	0.749421i	$-0.269668\pi$
$19$	1.50000	+	0.866025i	0.344124	+	0.198680i	−0.317970	+	0.948101i	$0.603001\pi$
$20$		0			0
$21$	3.00000	+	3.46410i	0.654654	+	0.755929i
$22$		0			0
$23$	4.50000	+	2.59808i	0.938315	+	0.541736i	0.889432	−	0.457068i	$-0.151100\pi$
$23$	4.50000	+	2.59808i	0.938315	+	0.541736i	0.0488832	+	0.998805i	$0.484434\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$			5.19615i			1.00000i
$28$		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	−0.628619	−	0.777714i	$-0.716379\pi$
$31$	−1.50000	+	0.866025i	−0.269408	+	0.155543i	0.359211	+	0.933257i	$0.383046\pi$
$32$		0			0
$33$	−4.50000	−	7.79423i	−0.783349	−	1.35680i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	3.50000	−	6.06218i	0.575396	−	0.996616i	−0.420602	−	0.907245i	$-0.638181\pi$
$37$	3.50000	−	6.06218i	0.575396	−	0.996616i	0.995998	−	0.0893706i	$-0.0284856\pi$
$38$		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
$43$	−4.00000			−0.609994			−0.304997	−	0.952353i	$-0.598656\pi$
$43$	−4.00000			−0.609994			−0.304997	+	0.952353i	$0.598656\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	1.50000	−	2.59808i	0.218797	−	0.378968i	−0.735643	−	0.677369i	$-0.763120\pi$
$47$	1.50000	−	2.59808i	0.218797	−	0.378968i	0.954441	+	0.298401i	$0.0964533\pi$
$48$		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
$53$	4.50000	−	2.59808i	0.618123	−	0.356873i	−0.158015	−	0.987437i	$-0.550509\pi$
$53$	4.50000	−	2.59808i	0.618123	−	0.356873i	0.776138	+	0.630563i	$0.217176\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	1.50000	−	2.59808i	0.198680	−	0.344124i
$58$		0			0
$59$	1.50000	+	2.59808i	0.195283	+	0.338241i	0.946993	−	0.321253i	$-0.104104\pi$
$59$	1.50000	+	2.59808i	0.195283	+	0.338241i	−0.751710	+	0.659494i	$0.770771\pi$
$60$		0			0
$61$	−10.5000	−	6.06218i	−1.34439	−	0.776182i	−0.356939	−	0.934128i	$-0.616180\pi$
$61$	−10.5000	−	6.06218i	−1.34439	−	0.776182i	−0.987448	+	0.157945i	$0.949513\pi$
$62$		0			0
$63$	6.00000	−	5.19615i	0.755929	−	0.654654i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	2.50000	+	4.33013i	0.305424	+	0.529009i	0.977356	−	0.211604i	$-0.0678686\pi$
$67$	2.50000	+	4.33013i	0.305424	+	0.529009i	−0.671932	+	0.740613i	$0.734535\pi$
$68$		0			0
$69$	4.50000	−	7.79423i	0.541736	−	0.938315i
$70$		0			0
$71$		−	10.3923i		−	1.23334i	−0.787222	−	0.616670i	$-0.788481\pi$
$71$		−	10.3923i		−	1.23334i	0.787222	−	0.616670i	$-0.211519\pi$
$72$		0			0
$73$	10.5000	−	6.06218i	1.22893	−	0.709524i	0.262126	−	0.965034i	$-0.415577\pi$
$73$	10.5000	−	6.06218i	1.22893	−	0.709524i	0.966807	+	0.255510i	$0.0822432\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−4.50000	+	12.9904i	−0.512823	+	1.48039i
$78$		0			0
$79$	0.500000	−	0.866025i	0.0562544	−	0.0974355i	−0.836527	−	0.547926i	$-0.815418\pi$
$79$	0.500000	−	0.866025i	0.0562544	−	0.0974355i	0.892781	+	0.450490i	$0.148751\pi$
$80$		0			0
$81$	9.00000			1.00000
$82$		0			0
$83$	12.0000			1.31717			0.658586	−	0.752506i	$-0.271155\pi$
$83$	12.0000			1.31717			0.658586	+	0.752506i	$0.271155\pi$
$84$		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	$-0.675058\pi$
$89$	4.50000	−	7.79423i	0.476999	−	0.826187i	0.999653	+	0.0263586i	$0.00839118\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	1.50000	+	2.59808i	0.155543	+	0.269408i
$94$		0			0
$95$		0			0
$96$		0			0
$97$			6.92820i			0.703452i	0.936103	+	0.351726i	$0.114405\pi$
$97$			6.92820i			0.703452i	−0.936103	+	0.351726i	$0.885595\pi$
$98$		0			0
$99$	−13.5000	+	7.79423i	−1.35680	+	0.783349i
$100$		0			0
$101$	4.50000	+	7.79423i	0.447767	+	0.775555i	0.998240	−	0.0592978i	$-0.0188862\pi$
$101$	4.50000	+	7.79423i	0.447767	+	0.775555i	−0.550474	+	0.834853i	$0.685553\pi$
$102$		0			0
$103$	4.50000	+	2.59808i	0.443398	+	0.255996i	0.705038	−	0.709170i	$-0.250930\pi$
$103$	4.50000	+	2.59808i	0.443398	+	0.255996i	−0.261640	+	0.965166i	$0.584263\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−13.5000	−	7.79423i	−1.30509	−	0.753497i	−0.323821	−	0.946118i	$-0.604968\pi$
$107$	−13.5000	−	7.79423i	−1.30509	−	0.753497i	−0.981273	+	0.192622i	$0.938301\pi$
$108$		0			0
$109$	8.50000	+	14.7224i	0.814152	+	1.41015i	0.909935	+	0.414751i	$0.136131\pi$
$109$	8.50000	+	14.7224i	0.814152	+	1.41015i	−0.0957826	+	0.995402i	$0.530535\pi$
$110$		0			0
$111$	−10.5000	−	6.06218i	−0.996616	−	0.575396i
$112$		0			0
$113$		−	20.7846i		−	1.95525i	−0.210352	−	0.977626i	$-0.567461\pi$
$113$		−	20.7846i		−	1.95525i	0.210352	−	0.977626i	$-0.432539\pi$
$114$		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
$123$		−	10.3923i		−	0.937043i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−8.00000			−0.709885			−0.354943	−	0.934888i	$-0.615500\pi$
$127$	−8.00000			−0.709885			−0.354943	+	0.934888i	$0.615500\pi$
$128$		0			0
$129$			6.92820i			0.609994i
$130$		0			0
$131$	4.50000	−	7.79423i	0.393167	−	0.680985i	−0.599699	−	0.800226i	$-0.704713\pi$
$131$	4.50000	−	7.79423i	0.393167	−	0.680985i	0.992865	+	0.119241i	$0.0380462\pi$
$132$		0			0
$133$	−4.50000	+	0.866025i	−0.390199	+	0.0750939i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	4.50000	−	2.59808i	0.384461	−	0.221969i	−0.295296	−	0.955406i	$-0.595418\pi$
$137$	4.50000	−	2.59808i	0.384461	−	0.221969i	0.679757	+	0.733437i	$0.262085\pi$
$138$		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
$147$	−12.0000	−	1.73205i	−0.989743	−	0.142857i
$148$		0			0
$149$	−4.50000	−	2.59808i	−0.368654	−	0.212843i	0.304216	−	0.952603i	$-0.401606\pi$
$149$	−4.50000	−	2.59808i	−0.368654	−	0.212843i	−0.672870	+	0.739760i	$0.734939\pi$
$150$		0			0
$151$	−6.50000	−	11.2583i	−0.528962	−	0.916190i	−0.999430	−	0.0337724i	$-0.989248\pi$
$151$	−6.50000	−	11.2583i	−0.528962	−	0.916190i	0.470467	−	0.882418i	$-0.344085\pi$
$152$		0			0
$153$	−4.50000	−	7.79423i	−0.363803	−	0.630126i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	4.50000	−	2.59808i	0.359139	−	0.207349i	−0.309564	−	0.950879i	$-0.600183\pi$
$157$	4.50000	−	2.59808i	0.359139	−	0.207349i	0.668703	+	0.743530i	$0.266850\pi$
$158$		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
$163$	−0.500000	+	0.866025i	−0.0391630	+	0.0678323i	−0.884943	−	0.465700i	$-0.845802\pi$
$163$	−0.500000	+	0.866025i	−0.0391630	+	0.0678323i	0.845780	+	0.533533i	$0.179136\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−12.0000			−0.928588			−0.464294	−	0.885681i	$-0.653692\pi$
$167$	−12.0000			−0.928588			−0.464294	+	0.885681i	$0.653692\pi$
$168$		0			0
$169$	13.0000			1.00000
$170$		0			0
$171$	−4.50000	−	2.59808i	−0.344124	−	0.198680i
$172$		0			0
$173$	−4.50000	+	7.79423i	−0.342129	+	0.592584i	−0.984828	−	0.173534i	$-0.944481\pi$
$173$	−4.50000	+	7.79423i	−0.342129	+	0.592584i	0.642699	+	0.766119i	$0.277815\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	4.50000	−	2.59808i	0.338241	−	0.195283i
$178$		0			0
$179$	4.50000	−	2.59808i	0.336346	−	0.194189i	−0.322309	−	0.946634i	$-0.604459\pi$
$179$	4.50000	−	2.59808i	0.336346	−	0.194189i	0.658655	+	0.752445i	$0.271126\pi$
$180$		0			0
$181$			6.92820i			0.514969i	0.966282	+	0.257485i	$0.0828937\pi$
$181$			6.92820i			0.514969i	−0.966282	+	0.257485i	$0.917106\pi$
$182$		0			0
$183$	−10.5000	+	18.1865i	−0.776182	+	1.34439i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	13.5000	+	7.79423i	0.987218	+	0.569970i
$188$		0			0
$189$	−9.00000	−	10.3923i	−0.654654	−	0.755929i
$190$		0			0
$191$	13.5000	+	7.79423i	0.976826	+	0.563971i	0.901310	−	0.433174i	$-0.142606\pi$
$191$	13.5000	+	7.79423i	0.976826	+	0.563971i	0.0755154	+	0.997145i	$0.475940\pi$
$192$		0			0
$193$	−2.50000	−	4.33013i	−0.179954	−	0.311689i	0.761911	−	0.647682i	$-0.224262\pi$
$193$	−2.50000	−	4.33013i	−0.179954	−	0.311689i	−0.941865	+	0.335993i	$0.890928\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		0			0		1.00000			$0$
$197$		0			0		−1.00000			$\pi$
$198$		0			0
$199$	−1.50000	+	0.866025i	−0.106332	+	0.0613909i	−0.552223	−	0.833696i	$-0.686220\pi$
$199$	−1.50000	+	0.866025i	−0.106332	+	0.0613909i	0.445891	+	0.895087i	$0.352887\pi$
$200$		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
$207$	−13.5000	−	7.79423i	−0.938315	−	0.541736i
$208$		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
$213$	−18.0000			−1.23334
$214$		0			0
$215$		0			0
$216$		0			0
$217$	1.50000	−	4.33013i	0.101827	−	0.293948i
$218$		0			0
$219$	−10.5000	−	18.1865i	−0.709524	−	1.22893i
$220$		0			0
$221$		0			0
$222$		0			0
$223$			10.3923i			0.695920i	0.937509	+	0.347960i	$0.113126\pi$
$223$			10.3923i			0.695920i	−0.937509	+	0.347960i	$0.886874\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	4.50000	+	7.79423i	0.298675	+	0.517321i	0.975833	−	0.218517i	$-0.0701218\pi$
$227$	4.50000	+	7.79423i	0.298675	+	0.517321i	−0.677158	+	0.735838i	$0.736789\pi$
$228$		0			0
$229$	19.5000	+	11.2583i	1.28860	+	0.743971i	0.978404	−	0.206702i	$-0.0662732\pi$
$229$	19.5000	+	11.2583i	1.28860	+	0.743971i	0.310192	+	0.950674i	$0.399607\pi$
$230$		0			0
$231$	22.5000	+	7.79423i	1.48039	+	0.512823i
$232$		0			0
$233$	4.50000	+	2.59808i	0.294805	+	0.170206i	0.640107	−	0.768286i	$-0.278890\pi$
$233$	4.50000	+	2.59808i	0.294805	+	0.170206i	−0.345302	+	0.938492i	$0.612223\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−1.50000	−	0.866025i	−0.0974355	−	0.0562544i
$238$		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	−0.450910	−	0.892570i	$-0.648900\pi$
$241$	1.50000	−	0.866025i	0.0966235	−	0.0557856i	0.547533	+	0.836784i	$0.315567\pi$
$242$		0			0
$243$		−	15.5885i		−	1.00000i
$244$		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
$253$	27.0000			1.69748
$254$		0			0
$255$		0			0
$256$		0			0
$257$	13.5000	−	23.3827i	0.842107	−	1.45857i	−0.0460033	−	0.998941i	$-0.514648\pi$
$257$	13.5000	−	23.3827i	0.842107	−	1.45857i	0.888110	−	0.459631i	$-0.152018\pi$
$258$		0			0
$259$	3.50000	+	18.1865i	0.217479	+	1.13006i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−4.50000	+	2.59808i	−0.277482	+	0.160204i	−0.632283	−	0.774738i	$-0.717882\pi$
$263$	−4.50000	+	2.59808i	−0.277482	+	0.160204i	0.354801	+	0.934942i	$0.384549\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−13.5000	−	7.79423i	−0.826187	−	0.476999i
$268$		0			0
$269$	10.5000	+	18.1865i	0.640196	+	1.10885i	0.985389	+	0.170321i	$0.0544803\pi$
$269$	10.5000	+	18.1865i	0.640196	+	1.10885i	−0.345192	+	0.938532i	$0.612186\pi$
$270$		0			0
$271$	19.5000	+	11.2583i	1.18454	+	0.683895i	0.957061	−	0.289888i	$-0.0936180\pi$
$271$	19.5000	+	11.2583i	1.18454	+	0.683895i	0.227480	+	0.973783i	$0.426951\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−6.50000	−	11.2583i	−0.390547	−	0.676448i	0.601975	−	0.798515i	$-0.294381\pi$
$277$	−6.50000	−	11.2583i	−0.390547	−	0.676448i	−0.992522	+	0.122068i	$0.961047\pi$
$278$		0			0
$279$	4.50000	−	2.59808i	0.269408	−	0.155543i
$280$		0			0
$281$		−	20.7846i		−	1.23991i	−0.784639	−	0.619953i	$-0.787152\pi$
$281$		−	20.7846i		−	1.23991i	0.784639	−	0.619953i	$-0.212848\pi$
$282$		0			0
$283$	7.50000	−	4.33013i	0.445829	−	0.257399i	−0.260238	−	0.965544i	$-0.583801\pi$
$283$	7.50000	−	4.33013i	0.445829	−	0.257399i	0.706067	+	0.708145i	$0.250468\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−12.0000	+	10.3923i	−0.708338	+	0.613438i
$288$		0			0
$289$	4.00000	−	6.92820i	0.235294	−	0.407541i
$290$		0			0
$291$	12.0000			0.703452
$292$		0			0
$293$	−6.00000			−0.350524			−0.175262	−	0.984522i	$-0.556077\pi$
$293$	−6.00000			−0.350524			−0.175262	+	0.984522i	$0.556077\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	13.5000	+	23.3827i	0.783349	+	1.35680i
$298$		0			0
$299$		0			0
$300$		0			0
$301$	8.00000	−	6.92820i	0.461112	−	0.399335i
$302$		0			0
$303$	13.5000	−	7.79423i	0.775555	−	0.447767i
$304$		0			0
$305$		0			0
$306$		0			0
$307$			17.3205i			0.988534i	0.869310	+	0.494267i	$0.164563\pi$
$307$			17.3205i			0.988534i	−0.869310	+	0.494267i	$0.835437\pi$
$308$		0			0
$309$	4.50000	−	7.79423i	0.255996	−	0.443398i
$310$		0			0
$311$	7.50000	+	12.9904i	0.425286	+	0.736617i	0.996447	−	0.0842210i	$-0.0268402\pi$
$311$	7.50000	+	12.9904i	0.425286	+	0.736617i	−0.571161	+	0.820838i	$0.693507\pi$
$312$		0			0
$313$	10.5000	+	6.06218i	0.593495	+	0.342655i	0.766478	−	0.642270i	$-0.222007\pi$
$313$	10.5000	+	6.06218i	0.593495	+	0.342655i	−0.172983	+	0.984925i	$0.555341\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	22.5000	+	12.9904i	1.26373	+	0.729612i	0.973793	−	0.227435i	$-0.0730338\pi$
$317$	22.5000	+	12.9904i	1.26373	+	0.729612i	0.289933	+	0.957047i	$0.406367\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	−13.5000	+	23.3827i	−0.753497	+	1.30509i
$322$		0			0
$323$			5.19615i			0.289122i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	25.5000	−	14.7224i	1.41015	−	0.814152i
$328$		0			0
$329$	1.50000	+	7.79423i	0.0826977	+	0.429710i
$330$		0			0
$331$	−15.5000	+	26.8468i	−0.851957	+	1.47563i	0.0274825	+	0.999622i	$0.491251\pi$
$331$	−15.5000	+	26.8468i	−0.851957	+	1.47563i	−0.879440	+	0.476011i	$0.842082\pi$
$332$		0			0
$333$	−10.5000	+	18.1865i	−0.575396	+	0.996616i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	2.00000			0.108947			0.0544735	−	0.998515i	$-0.482652\pi$
$337$	2.00000			0.108947			0.0544735	+	0.998515i	$0.482652\pi$
$338$		0			0
$339$	−36.0000			−1.95525
$340$		0			0
$341$	−4.50000	+	7.79423i	−0.243689	+	0.422081i
$342$		0			0
$343$	10.0000	+	15.5885i	0.539949	+	0.841698i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	13.5000	−	7.79423i	0.724718	−	0.418416i	−0.0917687	−	0.995780i	$-0.529252\pi$
$347$	13.5000	−	7.79423i	0.724718	−	0.418416i	0.816487	+	0.577364i	$0.195919\pi$
$348$		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
$353$	1.50000	+	2.59808i	0.0798369	+	0.138282i	0.903179	−	0.429263i	$-0.141227\pi$
$353$	1.50000	+	2.59808i	0.0798369	+	0.138282i	−0.823343	+	0.567545i	$0.807893\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−4.50000	+	12.9904i	−0.238165	+	0.687524i
$358$		0			0
$359$	−22.5000	−	12.9904i	−1.18750	−	0.685606i	−0.229766	−	0.973246i	$-0.573796\pi$
$359$	−22.5000	−	12.9904i	−1.18750	−	0.685606i	−0.957739	+	0.287640i	$0.907129\pi$
$360$		0			0
$361$	−8.00000	−	13.8564i	−0.421053	−	0.729285i
$362$		0			0
$363$	−24.0000	−	13.8564i	−1.25967	−	0.727273i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−28.5000	+	16.4545i	−1.48769	+	0.858917i	−0.999901	−	0.0140459i	$-0.995529\pi$
$367$	−28.5000	+	16.4545i	−1.48769	+	0.858917i	−0.487787	+	0.872963i	$0.662196\pi$
$368$		0			0
$369$	−18.0000			−0.937043
$370$		0			0
$371$	−4.50000	+	12.9904i	−0.233628	+	0.674427i
$372$		0			0
$373$	−12.5000	+	21.6506i	−0.647225	+	1.12103i	0.336557	+	0.941663i	$0.390737\pi$
$373$	−12.5000	+	21.6506i	−0.647225	+	1.12103i	−0.983783	+	0.179364i	$0.942596\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	16.0000			0.821865			0.410932	−	0.911666i	$-0.365203\pi$
$379$	16.0000			0.821865			0.410932	+	0.911666i	$0.365203\pi$
$380$		0			0
$381$			13.8564i			0.709885i
$382$		0			0
$383$	−10.5000	+	18.1865i	−0.536525	+	0.929288i	0.462563	+	0.886586i	$0.346930\pi$
$383$	−10.5000	+	18.1865i	−0.536525	+	0.929288i	−0.999088	+	0.0427020i	$0.986403\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	12.0000			0.609994
$388$		0			0
$389$	−22.5000	+	12.9904i	−1.14080	+	0.658638i	−0.946627	−	0.322330i	$-0.895534\pi$
$389$	−22.5000	+	12.9904i	−1.14080	+	0.658638i	−0.194168	+	0.980968i	$0.562201\pi$
$390$		0			0
$391$			15.5885i			0.788342i
$392$		0			0
$393$	−13.5000	−	7.79423i	−0.680985	−	0.393167i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−7.50000	−	4.33013i	−0.376414	−	0.217323i	0.299843	−	0.953989i	$-0.403066\pi$
$397$	−7.50000	−	4.33013i	−0.376414	−	0.217323i	−0.676257	+	0.736666i	$0.736399\pi$
$398$		0			0
$399$	1.50000	+	7.79423i	0.0750939	+	0.390199i
$400$		0			0
$401$	31.5000	+	18.1865i	1.57303	+	0.908192i	0.995794	+	0.0916181i	$0.0292039\pi$
$401$	31.5000	+	18.1865i	1.57303	+	0.908192i	0.577241	+	0.816574i	$0.304129\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		−	36.3731i		−	1.80295i
$408$		0			0
$409$	−4.50000	+	2.59808i	−0.222511	+	0.128467i	−0.607112	−	0.794616i	$-0.707672\pi$
$409$	−4.50000	+	2.59808i	−0.222511	+	0.128467i	0.384602	+	0.923083i	$0.374339\pi$
$410$		0			0
$411$	−4.50000	−	7.79423i	−0.221969	−	0.384461i
$412$		0			0
$413$	−7.50000	−	2.59808i	−0.369051	−	0.127843i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	18.0000			0.881464
$418$		0			0
$419$	12.0000			0.586238			0.293119	−	0.956076i	$-0.405307\pi$
$419$	12.0000			0.586238			0.293119	+	0.956076i	$0.405307\pi$
$420$		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
$423$	−4.50000	+	7.79423i	−0.218797	+	0.378968i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	31.5000	−	6.06218i	1.52439	−	0.293369i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−13.5000	+	7.79423i	−0.650272	+	0.375435i	−0.788560	−	0.614957i	$-0.789173\pi$
$431$	−13.5000	+	7.79423i	−0.650272	+	0.375435i	0.138288	+	0.990392i	$0.455840\pi$
$432$		0			0
$433$			34.6410i			1.66474i	0.554220	+	0.832370i	$0.313017\pi$
$433$			34.6410i			1.66474i	−0.554220	+	0.832370i	$0.686983\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	4.50000	+	7.79423i	0.215264	+	0.372849i
$438$		0			0
$439$	13.5000	+	7.79423i	0.644320	+	0.371998i	0.786277	−	0.617875i	$-0.212006\pi$
$439$	13.5000	+	7.79423i	0.644320	+	0.371998i	−0.141957	+	0.989873i	$0.545339\pi$
$440$		0			0
$441$	−3.00000	+	20.7846i	−0.142857	+	0.989743i
$442$		0			0
$443$	−13.5000	−	7.79423i	−0.641404	−	0.370315i	0.143751	−	0.989614i	$-0.454084\pi$
$443$	−13.5000	−	7.79423i	−0.641404	−	0.370315i	−0.785155	+	0.619299i	$0.787417\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−4.50000	+	7.79423i	−0.212843	+	0.368654i
$448$		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
$453$	−19.5000	+	11.2583i	−0.916190	+	0.528962i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	15.5000	−	26.8468i	0.725059	−	1.25584i	−0.233890	−	0.972263i	$-0.575146\pi$
$457$	15.5000	−	26.8468i	0.725059	−	1.25584i	0.958950	−	0.283577i	$-0.0915211\pi$
$458$		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
$463$	16.0000			0.743583			0.371792	−	0.928316i	$-0.378744\pi$
$463$	16.0000			0.743583			0.371792	+	0.928316i	$0.378744\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−4.50000	+	7.79423i	−0.208235	+	0.360674i	−0.951159	−	0.308702i	$-0.900105\pi$
$467$	−4.50000	+	7.79423i	−0.208235	+	0.360674i	0.742923	+	0.669376i	$0.233439\pi$
$468$		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
$473$	−18.0000	+	10.3923i	−0.827641	+	0.477839i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−13.5000	+	7.79423i	−0.618123	+	0.356873i
$478$		0			0
$479$	−16.5000	−	28.5788i	−0.753904	−	1.30580i	−0.945917	−	0.324408i	$-0.894835\pi$
$479$	−16.5000	−	28.5788i	−0.753904	−	1.30580i	0.192013	−	0.981392i	$-0.438498\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$	4.50000	+	23.3827i	0.204757	+	1.06395i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	0.500000	+	0.866025i	0.0226572	+	0.0392434i	0.877132	−	0.480250i	$-0.159454\pi$
$487$	0.500000	+	0.866025i	0.0226572	+	0.0392434i	−0.854475	+	0.519493i	$0.826121\pi$
$488$		0			0
$489$	1.50000	+	0.866025i	0.0678323	+	0.0391630i
$490$		0			0
$491$		−	10.3923i		−	0.468998i	−0.972116	−	0.234499i	$-0.924655\pi$
$491$		−	10.3923i		−	0.468998i	0.972116	−	0.234499i	$-0.0753450\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$	18.0000	+	20.7846i	0.807410	+	0.932317i
$498$		0			0
$499$	−3.50000	+	6.06218i	−0.156682	+	0.271380i	−0.933670	−	0.358134i	$-0.883413\pi$
$499$	−3.50000	+	6.06218i	−0.156682	+	0.271380i	0.776989	+	0.629515i	$0.216746\pi$
$500$		0			0
$501$			20.7846i			0.928588i
$502$		0			0
$503$	−24.0000			−1.07011			−0.535054	−	0.844818i	$-0.679709\pi$
$503$	−24.0000			−1.07011			−0.535054	+	0.844818i	$0.679709\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$		−	22.5167i		−	1.00000i
$508$		0			0
$509$	10.5000	−	18.1865i	0.465404	−	0.806104i	−0.533815	−	0.845601i	$-0.679242\pi$
$509$	10.5000	−	18.1865i	0.465404	−	0.806104i	0.999220	+	0.0394971i	$0.0125756\pi$
$510$		0			0
$511$	−10.5000	+	30.3109i	−0.464493	+	1.34087i
$512$		0			0
$513$	−4.50000	+	7.79423i	−0.198680	+	0.344124i
$514$		0			0
$515$		0			0
$516$		0			0
$517$		−	15.5885i		−	0.685580i
$518$		0			0
$519$	13.5000	+	7.79423i	0.592584	+	0.342129i
$520$		0			0
$521$	−7.50000	−	12.9904i	−0.328581	−	0.569119i	0.653650	−	0.756797i	$-0.273237\pi$
$521$	−7.50000	−	12.9904i	−0.328581	−	0.569119i	−0.982231	+	0.187678i	$0.939904\pi$
$522$		0			0
$523$	22.5000	+	12.9904i	0.983856	+	0.568030i	0.903432	−	0.428731i	$-0.141039\pi$
$523$	22.5000	+	12.9904i	0.983856	+	0.568030i	0.0804241	+	0.996761i	$0.474373\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−4.50000	−	2.59808i	−0.196023	−	0.113174i
$528$		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
$537$	−4.50000	−	7.79423i	−0.194189	−	0.336346i
$538$		0			0
$539$	−13.5000	−	33.7750i	−0.581486	−	1.45479i
$540$		0			0
$541$	18.5000	−	32.0429i	0.795377	−	1.37763i	−0.127222	−	0.991874i	$-0.540606\pi$
$541$	18.5000	−	32.0429i	0.795377	−	1.37763i	0.922599	−	0.385759i	$-0.126061\pi$
$542$		0			0
$543$	12.0000			0.514969
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−32.0000			−1.36822			−0.684111	−	0.729378i	$-0.739809\pi$
$547$	−32.0000			−1.36822			−0.684111	+	0.729378i	$0.739809\pi$
$548$		0			0
$549$	31.5000	+	18.1865i	1.34439	+	0.776182i
$550$		0			0
$551$		0			0
$552$		0			0
$553$	0.500000	+	2.59808i	0.0212622	+	0.110481i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	22.5000	−	12.9904i	0.953356	−	0.550420i	0.0592339	−	0.998244i	$-0.481134\pi$
$557$	22.5000	−	12.9904i	0.953356	−	0.550420i	0.894122	+	0.447824i	$0.147801\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	13.5000	−	23.3827i	0.569970	−	0.987218i
$562$		0			0
$563$	−13.5000	−	23.3827i	−0.568957	−	0.985463i	−0.996669	−	0.0815478i	$-0.974014\pi$
$563$	−13.5000	−	23.3827i	−0.568957	−	0.985463i	0.427712	−	0.903915i	$-0.359320\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−18.0000	+	15.5885i	−0.755929	+	0.654654i
$568$		0			0
$569$	13.5000	+	7.79423i	0.565949	+	0.326751i	0.755530	−	0.655114i	$-0.227379\pi$
$569$	13.5000	+	7.79423i	0.565949	+	0.326751i	−0.189580	+	0.981865i	$0.560713\pi$
$570$		0			0
$571$	3.50000	+	6.06218i	0.146470	+	0.253694i	0.929921	−	0.367760i	$-0.119875\pi$
$571$	3.50000	+	6.06218i	0.146470	+	0.253694i	−0.783450	+	0.621455i	$0.786542\pi$
$572$		0			0
$573$	13.5000	−	23.3827i	0.563971	−	0.976826i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	22.5000	−	12.9904i	0.936687	−	0.540797i	0.0477669	−	0.998859i	$-0.484790\pi$
$577$	22.5000	−	12.9904i	0.936687	−	0.540797i	0.888920	+	0.458062i	$0.151456\pi$
$578$		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
$583$	13.5000	−	23.3827i	0.559113	−	0.968412i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−36.0000			−1.48588			−0.742940	−	0.669359i	$-0.766569\pi$
$587$	−36.0000			−1.48588			−0.742940	+	0.669359i	$0.766569\pi$
$588$		0			0
$589$	−3.00000			−0.123613
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−10.5000	+	18.1865i	−0.431183	+	0.746831i	−0.996976	−	0.0777165i	$-0.975237\pi$
$593$	−10.5000	+	18.1865i	−0.431183	+	0.746831i	0.565792	+	0.824548i	$0.308570\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	1.50000	+	2.59808i	0.0613909	+	0.106332i
$598$		0			0
$599$	4.50000	−	2.59808i	0.183865	−	0.106155i	−0.405242	−	0.914209i	$-0.632813\pi$
$599$	4.50000	−	2.59808i	0.183865	−	0.106155i	0.589107	+	0.808055i	$0.299480\pi$
$600$		0			0
$601$			34.6410i			1.41304i	0.707695	+	0.706518i	$0.249735\pi$
$601$			34.6410i			1.41304i	−0.707695	+	0.706518i	$0.750265\pi$
$602$		0			0
$603$	−7.50000	−	12.9904i	−0.305424	−	0.529009i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−25.5000	−	14.7224i	−1.03501	−	0.597565i	−0.116596	−	0.993179i	$-0.537198\pi$
$607$	−25.5000	−	14.7224i	−1.03501	−	0.597565i	−0.918417	+	0.395614i	$0.870532\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−0.500000	−	0.866025i	−0.0201948	−	0.0349784i	0.855751	−	0.517387i	$-0.173095\pi$
$613$	−0.500000	−	0.866025i	−0.0201948	−	0.0349784i	−0.875946	+	0.482409i	$0.839762\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		−	20.7846i		−	0.836757i	−0.908273	−	0.418378i	$-0.862599\pi$
$617$		−	20.7846i		−	0.836757i	0.908273	−	0.418378i	$-0.137401\pi$
$618$		0			0
$619$	22.5000	−	12.9904i	0.904351	−	0.522127i	0.0257420	−	0.999669i	$-0.491805\pi$
$619$	22.5000	−	12.9904i	0.904351	−	0.522127i	0.878609	+	0.477541i	$0.158472\pi$
$620$		0			0
$621$	−13.5000	+	23.3827i	−0.541736	+	0.938315i
$622$		0			0
$623$	4.50000	+	23.3827i	0.180289	+	0.936808i
$624$		0			0
$625$		0			0
$626$		0			0
$627$		−	15.5885i		−	0.622543i
$628$		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
$633$			34.6410i			1.37686i
$634$		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	−0.209108	−	0.977893i	$-0.567056\pi$
$641$	13.5000	−	7.79423i	0.533218	−	0.307854i	0.742326	+	0.670039i	$0.233723\pi$
$642$		0			0
$643$			3.46410i			0.136611i	0.997664	+	0.0683054i	$0.0217592\pi$
$643$			3.46410i			0.136611i	−0.997664	+	0.0683054i	$0.978241\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	4.50000	+	7.79423i	0.176913	+	0.306423i	0.940822	−	0.338902i	$-0.110055\pi$
$647$	4.50000	+	7.79423i	0.176913	+	0.306423i	−0.763908	+	0.645325i	$0.776722\pi$
$648$		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
$653$	−13.5000	−	7.79423i	−0.528296	−	0.305012i	0.212026	−	0.977264i	$-0.431994\pi$
$653$	−13.5000	−	7.79423i	−0.528296	−	0.305012i	−0.740322	+	0.672252i	$0.765327\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−31.5000	+	18.1865i	−1.22893	+	0.709524i
$658$		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	−0.0702812	−	0.997527i	$-0.522390\pi$
$661$	19.5000	−	11.2583i	0.758462	−	0.437898i	0.828743	+	0.559629i	$0.189056\pi$
$662$		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
$673$	−22.0000			−0.848038			−0.424019	−	0.905653i	$-0.639381\pi$
$673$	−22.0000			−0.848038			−0.424019	+	0.905653i	$0.639381\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−22.5000	+	38.9711i	−0.864745	+	1.49778i	0.00255466	+	0.999997i	$0.499187\pi$
$677$	−22.5000	+	38.9711i	−0.864745	+	1.49778i	−0.867300	+	0.497786i	$0.834147\pi$
$678$		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
$683$	31.5000	−	18.1865i	1.20531	−	0.695888i	0.243582	−	0.969880i	$-0.421677\pi$
$683$	31.5000	−	18.1865i	1.20531	−	0.695888i	0.961732	+	0.273992i	$0.0883442\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	19.5000	−	33.7750i	0.743971	−	1.28860i
$688$		0			0
$689$		0			0
$690$		0			0
$691$	−28.5000	−	16.4545i	−1.08419	−	0.625958i	−0.152167	−	0.988355i	$-0.548625\pi$
$691$	−28.5000	−	16.4545i	−1.08419	−	0.625958i	−0.932024	+	0.362397i	$0.881959\pi$
$692$		0			0
$693$	13.5000	−	38.9711i	0.512823	−	1.48039i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	9.00000	+	15.5885i	0.340899	+	0.590455i
$698$		0			0
$699$	4.50000	−	7.79423i	0.170206	−	0.294805i
$700$		0			0
$701$		−	20.7846i		−	0.785024i	−0.919747	−	0.392512i	$-0.871606\pi$
$701$		−	20.7846i		−	0.785024i	0.919747	−	0.392512i	$-0.128394\pi$
$702$		0			0
$703$	10.5000	−	6.06218i	0.396015	−	0.228639i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−22.5000	−	7.79423i	−0.846200	−	0.293132i
$708$		0			0
$709$	−15.5000	+	26.8468i	−0.582115	+	1.00825i	0.413114	+	0.910679i	$0.364441\pi$
$709$	−15.5000	+	26.8468i	−0.582115	+	1.00825i	−0.995228	+	0.0975728i	$0.968892\pi$
$710$		0			0
$711$	−1.50000	+	2.59808i	−0.0562544	+	0.0974355i
$712$		0			0
$713$	−9.00000			−0.337053
$714$		0			0
$715$		0			0
$716$		0			0
$717$	18.0000			0.672222
$718$		0			0
$719$	−7.50000	+	12.9904i	−0.279703	+	0.484459i	−0.971311	−	0.237814i	$-0.923569\pi$
$719$	−7.50000	+	12.9904i	−0.279703	+	0.484459i	0.691608	+	0.722273i	$0.256903\pi$
$720$		0			0
$721$	−13.5000	+	2.59808i	−0.502766	+	0.0967574i
$722$		0			0
$723$	−1.50000	−	2.59808i	−0.0557856	−	0.0966235i
$724$		0			0
$725$		0			0
$726$		0			0
$727$			24.2487i			0.899335i	0.893196	+	0.449667i	$0.148458\pi$
$727$			24.2487i			0.899335i	−0.893196	+	0.449667i	$0.851542\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$		0			0
$731$	−6.00000	−	10.3923i	−0.221918	−	0.384373i
$732$		0			0
$733$	−25.5000	−	14.7224i	−0.941864	−	0.543785i	−0.0513199	−	0.998682i	$-0.516343\pi$
$733$	−25.5000	−	14.7224i	−0.941864	−	0.543785i	−0.890544	+	0.454897i	$0.849676\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	22.5000	+	12.9904i	0.828798	+	0.478507i
$738$		0			0
$739$	−8.50000	−	14.7224i	−0.312678	−	0.541573i	0.666264	−	0.745716i	$-0.267893\pi$
$739$	−8.50000	−	14.7224i	−0.312678	−	0.541573i	−0.978941	+	0.204143i	$0.934559\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$			51.9615i			1.90628i	0.302524	+	0.953142i	$0.402171\pi$
$743$			51.9615i			1.90628i	−0.302524	+	0.953142i	$0.597829\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−36.0000			−1.31717
$748$		0			0
$749$	40.5000	−	7.79423i	1.47984	−	0.284795i
$750$		0			0
$751$	14.5000	−	25.1147i	0.529113	−	0.916450i	−0.470311	−	0.882501i	$-0.655858\pi$
$751$	14.5000	−	25.1147i	0.529113	−	0.916450i	0.999424	−	0.0339490i	$-0.0108084\pi$
$752$		0			0
$753$			41.5692i			1.51487i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−10.0000			−0.363456			−0.181728	−	0.983349i	$-0.558169\pi$
$757$	−10.0000			−0.363456			−0.181728	+	0.983349i	$0.558169\pi$
$758$		0			0
$759$		−	46.7654i		−	1.69748i
$760$		0			0
$761$	10.5000	−	18.1865i	0.380625	−	0.659261i	−0.610527	−	0.791995i	$-0.709042\pi$
$761$	10.5000	−	18.1865i	0.380625	−	0.659261i	0.991152	+	0.132734i	$0.0423756\pi$
$762$		0			0
$763$	−42.5000	−	14.7224i	−1.53860	−	0.532988i
$764$		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
$773$	19.5000	+	33.7750i	0.701366	+	1.21480i	0.967987	+	0.251000i	$0.0807596\pi$
$773$	19.5000	+	33.7750i	0.701366	+	1.21480i	−0.266621	+	0.963802i	$0.585907\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	31.5000	−	6.06218i	1.13006	−	0.217479i
$778$		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
$787$	1.50000	−	0.866025i	0.0534692	−	0.0308705i	−0.473027	−	0.881048i	$-0.656839\pi$
$787$	1.50000	−	0.866025i	0.0534692	−	0.0308705i	0.526496	+	0.850177i	$0.323505\pi$
$788$		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
$797$	−18.0000			−0.637593			−0.318796	−	0.947823i	$-0.603279\pi$
$797$	−18.0000			−0.637593			−0.318796	+	0.947823i	$0.603279\pi$
$798$		0			0
$799$	9.00000			0.318397
$800$		0			0
$801$	−13.5000	+	23.3827i	−0.476999	+	0.826187i
$802$		0			0
$803$	31.5000	−	54.5596i	1.11161	−	1.92537i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	31.5000	−	18.1865i	1.10885	−	0.640196i
$808$		0			0
$809$	−22.5000	+	12.9904i	−0.791058	+	0.456717i	−0.840335	−	0.542068i	$-0.817642\pi$
$809$	−22.5000	+	12.9904i	−0.791058	+	0.456717i	0.0492770	+	0.998785i	$0.484308\pi$
$810$		0			0
$811$			51.9615i			1.82462i	0.409505	+	0.912308i	$0.365701\pi$
$811$			51.9615i			1.82462i	−0.409505	+	0.912308i	$0.634299\pi$
$812$		0			0
$813$	19.5000	−	33.7750i	0.683895	−	1.18454i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−6.00000	−	3.46410i	−0.209913	−	0.121194i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−4.50000	−	2.59808i	−0.157051	−	0.0906735i	0.419415	−	0.907795i	$-0.362235\pi$
$821$	−4.50000	−	2.59808i	−0.157051	−	0.0906735i	−0.576466	+	0.817121i	$0.695569\pi$
$822$		0			0
$823$	−3.50000	−	6.06218i	−0.122002	−	0.211314i	0.798555	−	0.601922i	$-0.205598\pi$
$823$	−3.50000	−	6.06218i	−0.122002	−	0.211314i	−0.920557	+	0.390608i	$0.872265\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	10.3923i		−	0.361376i	−0.983540	−	0.180688i	$-0.942168\pi$
$827$		−	10.3923i		−	0.361376i	0.983540	−	0.180688i	$-0.0578324\pi$
$828$		0			0
$829$	1.50000	−	0.866025i	0.0520972	−	0.0300783i	−0.473725	−	0.880673i	$-0.657091\pi$
$829$	1.50000	−	0.866025i	0.0520972	−	0.0300783i	0.525822	+	0.850594i	$0.323758\pi$
$830$		0			0
$831$	−19.5000	+	11.2583i	−0.676448	+	0.390547i
$832$		0			0
$833$	19.5000	−	7.79423i	0.675635	−	0.270054i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−4.50000	−	7.79423i	−0.155543	−	0.269408i
$838$		0			0
$839$	−24.0000			−0.828572			−0.414286	−	0.910147i	$-0.635969\pi$
$839$	−24.0000			−0.828572			−0.414286	+	0.910147i	$0.635969\pi$
$840$		0			0
$841$	29.0000			1.00000
$842$		0			0
$843$	−36.0000			−1.23991
$844$		0			0
$845$		0			0
$846$		0			0
$847$	8.00000	+	41.5692i	0.274883	+	1.42834i
$848$		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
$853$			13.8564i			0.474434i	0.971457	+	0.237217i	$0.0762353\pi$
$853$			13.8564i			0.474434i	−0.971457	+	0.237217i	$0.923765\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−16.5000	−	28.5788i	−0.563629	−	0.976235i	−0.997176	−	0.0751033i	$-0.976071\pi$
$857$	−16.5000	−	28.5788i	−0.563629	−	0.976235i	0.433546	−	0.901131i	$-0.357262\pi$
$858$		0			0
$859$	−34.5000	−	19.9186i	−1.17712	−	0.679613i	−0.221777	−	0.975097i	$-0.571186\pi$
$859$	−34.5000	−	19.9186i	−1.17712	−	0.679613i	−0.955348	+	0.295484i	$0.904519\pi$
$860$		0			0
$861$	18.0000	+	20.7846i	0.613438	+	0.708338i
$862$		0			0
$863$	4.50000	+	2.59808i	0.153182	+	0.0884395i	0.574632	−	0.818412i	$-0.305145\pi$
$863$	4.50000	+	2.59808i	0.153182	+	0.0884395i	−0.421450	+	0.906852i	$0.638479\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−12.0000	−	6.92820i	−0.407541	−	0.235294i
$868$		0			0
$869$		−	5.19615i		−	0.176267i
$870$		0			0
$871$		0			0
$872$		0			0
$873$		−	20.7846i		−	0.703452i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	5.50000	−	9.52628i	0.185722	−	0.321680i	−0.758098	−	0.652141i	$-0.773871\pi$
$877$	5.50000	−	9.52628i	0.185722	−	0.321680i	0.943820	+	0.330461i	$0.107204\pi$
$878$		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
$883$	−28.0000			−0.942275			−0.471138	−	0.882060i	$-0.656156\pi$
$883$	−28.0000			−0.942275			−0.471138	+	0.882060i	$0.656156\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	1.50000	−	2.59808i	0.0503651	−	0.0872349i	−0.839744	−	0.542983i	$-0.817295\pi$
$887$	1.50000	−	2.59808i	0.0503651	−	0.0872349i	0.890109	+	0.455748i	$0.150628\pi$
$888$		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
$893$	4.50000	−	2.59808i	0.150587	−	0.0869413i
$894$		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
$903$	−12.0000	−	13.8564i	−0.399335	−	0.461112i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	18.5000	+	32.0429i	0.614282	+	1.06397i	0.990510	+	0.137441i	$0.0438878\pi$
$907$	18.5000	+	32.0429i	0.614282	+	1.06397i	−0.376228	+	0.926527i	$0.622779\pi$
$908$		0			0
$909$	−13.5000	−	23.3827i	−0.447767	−	0.775555i
$910$		0			0
$911$		−	10.3923i		−	0.344312i	−0.985070	−	0.172156i	$-0.944927\pi$
$911$		−	10.3923i		−	0.344312i	0.985070	−	0.172156i	$-0.0550734\pi$
$912$		0			0
$913$	54.0000	−	31.1769i	1.78714	−	1.03181i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	4.50000	+	23.3827i	0.148603	+	0.772164i
$918$		0			0
$919$	−9.50000	+	16.4545i	−0.313376	+	0.542783i	−0.979091	−	0.203423i	$-0.934793\pi$
$919$	−9.50000	+	16.4545i	−0.313376	+	0.542783i	0.665715	+	0.746206i	$0.268127\pi$
$920$		0			0
$921$	30.0000			0.988534
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−13.5000	−	7.79423i	−0.443398	−	0.255996i
$928$		0			0
$929$	−19.5000	+	33.7750i	−0.639774	+	1.10812i	0.345708	+	0.938342i	$0.387639\pi$
$929$	−19.5000	+	33.7750i	−0.639774	+	1.10812i	−0.985482	+	0.169779i	$0.945695\pi$
$930$		0			0
$931$	7.50000	−	9.52628i	0.245803	−	0.312211i
$932$		0			0
$933$	22.5000	−	12.9904i	0.736617	−	0.425286i
$934$		0			0
$935$		0			0
$936$		0			0
$937$		−	41.5692i		−	1.35801i	−0.734135	−	0.679004i	$-0.762412\pi$
$937$		−	41.5692i		−	1.35801i	0.734135	−	0.679004i	$-0.237588\pi$
$938$		0			0
$939$	10.5000	−	18.1865i	0.342655	−	0.593495i
$940$		0			0
$941$	10.5000	+	18.1865i	0.342290	+	0.592864i	0.984858	−	0.173365i	$-0.0554641\pi$
$941$	10.5000	+	18.1865i	0.342290	+	0.592864i	−0.642567	+	0.766229i	$0.722131\pi$
$942$		0			0
$943$	27.0000	+	15.5885i	0.879241	+	0.507630i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	40.5000	+	23.3827i	1.31607	+	0.759835i	0.983094	−	0.183099i	$-0.0586129\pi$
$947$	40.5000	+	23.3827i	1.31607	+	0.759835i	0.332979	+	0.942934i	$0.391946\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$	22.5000	−	38.9711i	0.729612	−	1.26373i
$952$		0			0
$953$		−	20.7846i		−	0.673280i	−0.941634	−	0.336640i	$-0.890710\pi$
$953$		−	20.7846i		−	0.673280i	0.941634	−	0.336640i	$-0.109290\pi$
$954$		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
$963$	40.5000	+	23.3827i	1.30509	+	0.753497i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	40.0000			1.28631			0.643157	−	0.765735i	$-0.277624\pi$
$967$	40.0000			1.28631			0.643157	+	0.765735i	$0.277624\pi$
$968$		0			0
$969$	9.00000			0.289122
$970$		0			0
$971$	28.5000	−	49.3634i	0.914609	−	1.58415i	0.107135	−	0.994244i	$-0.465832\pi$
$971$	28.5000	−	49.3634i	0.914609	−	1.58415i	0.807473	−	0.589904i	$-0.200834\pi$
$972$		0			0
$973$	−18.0000	−	20.7846i	−0.577054	−	0.666324i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−31.5000	+	18.1865i	−1.00777	+	0.581839i	−0.910539	−	0.413423i	$-0.864333\pi$
$977$	−31.5000	+	18.1865i	−1.00777	+	0.581839i	−0.0972351	+	0.995261i	$0.531000\pi$
$978$		0			0
$979$		−	46.7654i		−	1.49463i
$980$		0			0
$981$	−25.5000	−	44.1673i	−0.814152	−	1.41015i
$982$		0			0
$983$	−1.50000	−	2.59808i	−0.0478426	−	0.0828658i	0.841112	−	0.540860i	$-0.181901\pi$
$983$	−1.50000	−	2.59808i	−0.0478426	−	0.0828658i	−0.888955	+	0.457995i	$0.848568\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	13.5000	−	2.59808i	0.429710	−	0.0826977i
$988$		0			0
$989$	−18.0000	−	10.3923i	−0.572367	−	0.330456i
$990$		0			0
$991$	−12.5000	−	21.6506i	−0.397076	−	0.687755i	0.596288	−	0.802771i	$-0.296642\pi$
$991$	−12.5000	−	21.6506i	−0.397076	−	0.687755i	−0.993364	+	0.115015i	$0.963308\pi$
$992$		0			0
$993$	46.5000	+	26.8468i	1.47563	+	0.851957i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−19.5000	+	11.2583i	−0.617571	+	0.356555i	−0.775923	−	0.630828i	$-0.782715\pi$
$997$	−19.5000	+	11.2583i	−0.617571	+	0.356555i	0.158352	+	0.987383i	$0.449382\pi$
$998$		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.bi.e.1601.1		2
3.2	odd	2		2100.2.bi.f.1601.1		2
5.2	odd	4		2100.2.bo.f.1349.1		4
5.3	odd	4		2100.2.bo.f.1349.2		4
5.4	even	2		84.2.k.b.5.1	yes	2
7.3	odd	6		2100.2.bi.f.101.1		2
15.2	even	4		2100.2.bo.a.1349.2		4
15.8	even	4		2100.2.bo.a.1349.1		4
15.14	odd	2		84.2.k.a.5.1	✓	2
20.19	odd	2		336.2.bc.b.257.1		2
21.17	even	6	inner	2100.2.bi.e.101.1		2
35.3	even	12		2100.2.bo.a.1949.2		4
35.4	even	6		588.2.k.d.521.1		2
35.9	even	6		588.2.f.a.293.1		2
35.17	even	12		2100.2.bo.a.1949.1		4
35.19	odd	6		588.2.f.c.293.2		2
35.24	odd	6		84.2.k.a.17.1	yes	2
35.34	odd	2		588.2.k.c.509.1		2
45.4	even	6		2268.2.bm.f.593.1		2
45.14	odd	6		2268.2.bm.a.593.1		2
45.29	odd	6		2268.2.w.f.1349.1		2
45.34	even	6		2268.2.w.a.1349.1		2
60.59	even	2		336.2.bc.d.257.1		2
105.17	odd	12		2100.2.bo.f.1949.2		4
105.38	odd	12		2100.2.bo.f.1949.1		4
105.44	odd	6		588.2.f.c.293.1		2
105.59	even	6		84.2.k.b.17.1	yes	2
105.74	odd	6		588.2.k.c.521.1		2
105.89	even	6		588.2.f.a.293.2		2
105.104	even	2		588.2.k.d.509.1		2
140.19	even	6		2352.2.k.a.881.1		2
140.59	even	6		336.2.bc.d.17.1		2
140.79	odd	6		2352.2.k.d.881.2		2
315.59	even	6		2268.2.w.a.269.1		2
315.94	odd	6		2268.2.w.f.269.1		2
315.164	even	6		2268.2.bm.f.1025.1		2
315.304	odd	6		2268.2.bm.a.1025.1		2
420.59	odd	6		336.2.bc.b.17.1		2
420.299	odd	6		2352.2.k.d.881.1		2
420.359	even	6		2352.2.k.a.881.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.2.k.a.5.1	✓	2	15.14	odd	2
84.2.k.a.17.1	yes	2	35.24	odd	6
84.2.k.b.5.1	yes	2	5.4	even	2
84.2.k.b.17.1	yes	2	105.59	even	6
336.2.bc.b.17.1		2	420.59	odd	6
336.2.bc.b.257.1		2	20.19	odd	2
336.2.bc.d.17.1		2	140.59	even	6
336.2.bc.d.257.1		2	60.59	even	2
588.2.f.a.293.1		2	35.9	even	6
588.2.f.a.293.2		2	105.89	even	6
588.2.f.c.293.1		2	105.44	odd	6
588.2.f.c.293.2		2	35.19	odd	6
588.2.k.c.509.1		2	35.34	odd	2
588.2.k.c.521.1		2	105.74	odd	6
588.2.k.d.509.1		2	105.104	even	2
588.2.k.d.521.1		2	35.4	even	6
2100.2.bi.e.101.1		2	21.17	even	6	inner
2100.2.bi.e.1601.1		2	1.1	even	1	trivial
2100.2.bi.f.101.1		2	7.3	odd	6
2100.2.bi.f.1601.1		2	3.2	odd	2
2100.2.bo.a.1349.1		4	15.8	even	4
2100.2.bo.a.1349.2		4	15.2	even	4
2100.2.bo.a.1949.1		4	35.17	even	12
2100.2.bo.a.1949.2		4	35.3	even	12
2100.2.bo.f.1349.1		4	5.2	odd	4
2100.2.bo.f.1349.2		4	5.3	odd	4
2100.2.bo.f.1949.1		4	105.38	odd	12
2100.2.bo.f.1949.2		4	105.17	odd	12
2268.2.w.a.269.1		2	315.59	even	6
2268.2.w.a.1349.1		2	45.34	even	6
2268.2.w.f.269.1		2	315.94	odd	6
2268.2.w.f.1349.1		2	45.29	odd	6
2268.2.bm.a.593.1		2	45.14	odd	6
2268.2.bm.a.1025.1		2	315.304	odd	6
2268.2.bm.f.593.1		2	45.4	even	6
2268.2.bm.f.1025.1		2	315.164	even	6
2352.2.k.a.881.1		2	140.19	even	6
2352.2.k.a.881.2		2	420.359	even	6
2352.2.k.d.881.1		2	420.299	odd	6
2352.2.k.d.881.2		2	140.79	odd	6

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.bi (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.73205i q^{3} +(-2.00000 + 1.73205i) q^{7} -3.00000 q^{9} +O(q^{10})\)	\(q-1.73205i q^{3} +(-2.00000 + 1.73205i) q^{7} -3.00000 q^{9} +(4.50000 - 2.59808i) q^{11} +(1.50000 + 2.59808i) q^{17} +(1.50000 + 0.866025i) q^{19} +(3.00000 + 3.46410i) q^{21} +(4.50000 + 2.59808i) q^{23} +5.19615i q^{27} +(-1.50000 + 0.866025i) q^{31} +(-4.50000 - 7.79423i) q^{33} +(3.50000 - 6.06218i) q^{37} +6.00000 q^{41} -4.00000 q^{43} +(1.50000 - 2.59808i) q^{47} +(1.00000 - 6.92820i) q^{49} +(4.50000 - 2.59808i) q^{51} +(4.50000 - 2.59808i) q^{53} +(1.50000 - 2.59808i) q^{57} +(1.50000 + 2.59808i) q^{59} +(-10.5000 - 6.06218i) q^{61} +(6.00000 - 5.19615i) q^{63} +(2.50000 + 4.33013i) q^{67} +(4.50000 - 7.79423i) q^{69} -10.3923i q^{71} +(10.5000 - 6.06218i) q^{73} +(-4.50000 + 12.9904i) q^{77} +(0.500000 - 0.866025i) q^{79} +9.00000 q^{81} +12.0000 q^{83} +(4.50000 - 7.79423i) q^{89} +(1.50000 + 2.59808i) q^{93} +6.92820i q^{97} +(-13.5000 + 7.79423i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 4 q^{7} - 6 q^{9}+O(q^{10}) \) 2 * q - 4 * q^7 - 6 * q^9	\( 2 q - 4 q^{7} - 6 q^{9} + 9 q^{11} + 3 q^{17} + 3 q^{19} + 6 q^{21} + 9 q^{23} - 3 q^{31} - 9 q^{33} + 7 q^{37} + 12 q^{41} - 8 q^{43} + 3 q^{47} + 2 q^{49} + 9 q^{51} + 9 q^{53} + 3 q^{57} + 3 q^{59} - 21 q^{61} + 12 q^{63} + 5 q^{67} + 9 q^{69} + 21 q^{73} - 9 q^{77} + q^{79} + 18 q^{81} + 24 q^{83} + 9 q^{89} + 3 q^{93} - 27 q^{99}+O(q^{100}) \) 2 * q - 4 * q^7 - 6 * q^9 + 9 * q^11 + 3 * q^17 + 3 * q^19 + 6 * q^21 + 9 * q^23 - 3 * q^31 - 9 * q^33 + 7 * q^37 + 12 * q^41 - 8 * q^43 + 3 * q^47 + 2 * q^49 + 9 * q^51 + 9 * q^53 + 3 * q^57 + 3 * q^59 - 21 * q^61 + 12 * q^63 + 5 * q^67 + 9 * q^69 + 21 * q^73 - 9 * q^77 + q^79 + 18 * q^81 + 24 * q^83 + 9 * q^89 + 3 * q^93 - 27 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more