LMFDB - Embedded newform 2100.2.bc.a.949.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("2100.949");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$16.7685844245$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 84)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

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

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{3} +(2.59808 + 0.500000i) q^{7} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	$q+(-0.866025 - 0.500000i) q^{3} +(2.59808 + 0.500000i) q^{7} +(0.500000 + 0.866025i) q^{9} +(-1.00000 + 1.73205i) q^{11} +3.00000i q^{13} +(-6.92820 - 4.00000i) q^{17} +(-0.500000 - 0.866025i) q^{19} +(-2.00000 - 1.73205i) q^{21} +(-6.92820 + 4.00000i) q^{23} -1.00000i q^{27} -4.00000 q^{29} +(-1.50000 + 2.59808i) q^{31} +(1.73205 - 1.00000i) q^{33} +(-0.866025 + 0.500000i) q^{37} +(1.50000 - 2.59808i) q^{39} +6.00000 q^{41} -11.0000i q^{43} +(5.19615 - 3.00000i) q^{47} +(6.50000 + 2.59808i) q^{49} +(4.00000 + 6.92820i) q^{51} +(-10.3923 - 6.00000i) q^{53} +1.00000i q^{57} +(2.00000 - 3.46410i) q^{59} +(3.00000 + 5.19615i) q^{61} +(0.866025 + 2.50000i) q^{63} +(-11.2583 - 6.50000i) q^{67} +8.00000 q^{69} -10.0000 q^{71} +(-9.52628 - 5.50000i) q^{73} +(-3.46410 + 4.00000i) q^{77} +(-1.50000 - 2.59808i) q^{79} +(-0.500000 + 0.866025i) q^{81} -2.00000i q^{83} +(3.46410 + 2.00000i) q^{87} +(-1.50000 + 7.79423i) q^{91} +(2.59808 - 1.50000i) q^{93} +10.0000i q^{97} -2.00000 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^9	$ 4 q + 2 q^{9} - 4 q^{11} - 2 q^{19} - 8 q^{21} - 16 q^{29} - 6 q^{31} + 6 q^{39} + 24 q^{41} + 26 q^{49} + 16 q^{51} + 8 q^{59} + 12 q^{61} + 32 q^{69} - 40 q^{71} - 6 q^{79} - 2 q^{81} - 6 q^{91} - 8 q^{99}+O(q^{100}) $ 4 * q + 2 * q^9 - 4 * q^11 - 2 * q^19 - 8 * q^21 - 16 * q^29 - 6 * q^31 + 6 * q^39 + 24 * q^41 + 26 * q^49 + 16 * q^51 + 8 * q^59 + 12 * q^61 + 32 * q^69 - 40 * q^71 - 6 * q^79 - 2 * q^81 - 6 * q^91 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$701$	$1051$	$1177$	$1501$
$\chi(n)$	$1$	$1$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	2.59808	+	0.500000i	0.981981	+	0.188982i
$7$	2.59808	+	0.500000i	0.981981	+	0.188982i
$8$		0			0
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$		0			0
$11$	−1.00000	+	1.73205i	−0.301511	+	0.522233i	−0.976478	−	0.215615i	$-0.930824\pi$
$11$	−1.00000	+	1.73205i	−0.301511	+	0.522233i	0.674967	+	0.737848i	$0.264158\pi$
$12$		0			0
$13$			3.00000i			0.832050i	0.909353	+	0.416025i	$0.136577\pi$
$13$			3.00000i			0.832050i	−0.909353	+	0.416025i	$0.863423\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−6.92820	−	4.00000i	−1.68034	−	0.970143i	−0.961436	−	0.275029i	$-0.911312\pi$
$17$	−6.92820	−	4.00000i	−1.68034	−	0.970143i	−0.718900	−	0.695113i	$-0.755354\pi$
$18$		0			0
$19$	−0.500000	−	0.866025i	−0.114708	−	0.198680i	0.802955	−	0.596040i	$-0.203260\pi$
$19$	−0.500000	−	0.866025i	−0.114708	−	0.198680i	−0.917663	+	0.397360i	$0.869927\pi$
$20$		0			0
$21$	−2.00000	−	1.73205i	−0.436436	−	0.377964i
$22$		0			0
$23$	−6.92820	+	4.00000i	−1.44463	+	0.834058i	−0.998154	−	0.0607377i	$-0.980655\pi$
$23$	−6.92820	+	4.00000i	−1.44463	+	0.834058i	−0.446476	+	0.894795i	$0.647321\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$		−	1.00000i		−	0.192450i
$28$		0			0
$29$	−4.00000			−0.742781			−0.371391	−	0.928477i	$-0.621119\pi$
$29$	−4.00000			−0.742781			−0.371391	+	0.928477i	$0.621119\pi$
$30$		0			0
$31$	−1.50000	+	2.59808i	−0.269408	+	0.466628i	−0.968709	−	0.248199i	$-0.920161\pi$
$31$	−1.50000	+	2.59808i	−0.269408	+	0.466628i	0.699301	+	0.714827i	$0.253495\pi$
$32$		0			0
$33$	1.73205	−	1.00000i	0.301511	−	0.174078i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−0.866025	+	0.500000i	−0.142374	+	0.0821995i	−0.569495	−	0.821995i	$-0.692861\pi$
$37$	−0.866025	+	0.500000i	−0.142374	+	0.0821995i	0.427121	+	0.904194i	$0.359528\pi$
$38$		0			0
$39$	1.50000	−	2.59808i	0.240192	−	0.416025i
$40$		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
$43$		−	11.0000i		−	1.67748i	−0.544529	−	0.838742i	$-0.683292\pi$
$43$		−	11.0000i		−	1.67748i	0.544529	−	0.838742i	$-0.316708\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	5.19615	−	3.00000i	0.757937	−	0.437595i	−0.0706177	−	0.997503i	$-0.522497\pi$
$47$	5.19615	−	3.00000i	0.757937	−	0.437595i	0.828554	+	0.559908i	$0.189164\pi$
$48$		0			0
$49$	6.50000	+	2.59808i	0.928571	+	0.371154i
$50$		0			0
$51$	4.00000	+	6.92820i	0.560112	+	0.970143i
$52$		0			0
$53$	−10.3923	−	6.00000i	−1.42749	−	0.824163i	−0.430570	−	0.902557i	$-0.641688\pi$
$53$	−10.3923	−	6.00000i	−1.42749	−	0.824163i	−0.996922	+	0.0783936i	$0.975021\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$			1.00000i			0.132453i
$58$		0			0
$59$	2.00000	−	3.46410i	0.260378	−	0.450988i	−0.705965	−	0.708247i	$-0.749486\pi$
$59$	2.00000	−	3.46410i	0.260378	−	0.450988i	0.966342	+	0.257260i	$0.0828195\pi$
$60$		0			0
$61$	3.00000	+	5.19615i	0.384111	+	0.665299i	0.991645	−	0.128994i	$-0.0411748\pi$
$61$	3.00000	+	5.19615i	0.384111	+	0.665299i	−0.607535	+	0.794293i	$0.707841\pi$
$62$		0			0
$63$	0.866025	+	2.50000i	0.109109	+	0.314970i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−11.2583	−	6.50000i	−1.37542	−	0.794101i	−0.383819	−	0.923408i	$-0.625391\pi$
$67$	−11.2583	−	6.50000i	−1.37542	−	0.794101i	−0.991605	+	0.129307i	$0.958725\pi$
$68$		0			0
$69$	8.00000			0.963087
$70$		0			0
$71$	−10.0000			−1.18678			−0.593391	−	0.804914i	$-0.702211\pi$
$71$	−10.0000			−1.18678			−0.593391	+	0.804914i	$0.702211\pi$
$72$		0			0
$73$	−9.52628	−	5.50000i	−1.11497	−	0.643726i	−0.174855	−	0.984594i	$-0.555946\pi$
$73$	−9.52628	−	5.50000i	−1.11497	−	0.643726i	−0.940111	+	0.340868i	$0.889279\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−3.46410	+	4.00000i	−0.394771	+	0.455842i
$78$		0			0
$79$	−1.50000	−	2.59808i	−0.168763	−	0.292306i	0.769222	−	0.638982i	$-0.220644\pi$
$79$	−1.50000	−	2.59808i	−0.168763	−	0.292306i	−0.937985	+	0.346675i	$0.887311\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$		−	2.00000i		−	0.219529i	−0.993958	−	0.109764i	$-0.964990\pi$
$83$		−	2.00000i		−	0.219529i	0.993958	−	0.109764i	$-0.0350096\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	3.46410	+	2.00000i	0.371391	+	0.214423i
$88$		0			0
$89$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$89$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$90$		0			0
$91$	−1.50000	+	7.79423i	−0.157243	+	0.817057i
$92$		0			0
$93$	2.59808	−	1.50000i	0.269408	−	0.155543i
$94$		0			0
$95$		0			0
$96$		0			0
$97$			10.0000i			1.01535i	0.861550	+	0.507673i	$0.169494\pi$
$97$			10.0000i			1.01535i	−0.861550	+	0.507673i	$0.830506\pi$
$98$		0			0
$99$	−2.00000			−0.201008
$100$		0			0
$101$	−5.00000	+	8.66025i	−0.497519	+	0.861727i	−0.999996	−	0.00286291i	$-0.999089\pi$
$101$	−5.00000	+	8.66025i	−0.497519	+	0.861727i	0.502477	+	0.864590i	$0.332422\pi$
$102$		0			0
$103$	−9.52628	+	5.50000i	−0.938652	+	0.541931i	−0.889538	−	0.456862i	$-0.848973\pi$
$103$	−9.52628	+	5.50000i	−0.938652	+	0.541931i	−0.0491146	+	0.998793i	$0.515640\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$107$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$108$		0			0
$109$	−5.50000	+	9.52628i	−0.526804	+	0.912452i	0.472708	+	0.881219i	$0.343277\pi$
$109$	−5.50000	+	9.52628i	−0.526804	+	0.912452i	−0.999512	+	0.0312328i	$0.990057\pi$
$110$		0			0
$111$	1.00000			0.0949158
$112$		0			0
$113$			14.0000i			1.31701i	0.752577	+	0.658505i	$0.228811\pi$
$113$			14.0000i			1.31701i	−0.752577	+	0.658505i	$0.771189\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−2.59808	+	1.50000i	−0.240192	+	0.138675i
$118$		0			0
$119$	−16.0000	−	13.8564i	−1.46672	−	1.27021i
$120$		0			0
$121$	3.50000	+	6.06218i	0.318182	+	0.551107i
$122$		0			0
$123$	−5.19615	−	3.00000i	−0.468521	−	0.270501i
$124$		0			0
$125$		0			0
$126$		0			0
$127$			3.00000i			0.266207i	0.991102	+	0.133103i	$0.0424943\pi$
$127$			3.00000i			0.266207i	−0.991102	+	0.133103i	$0.957506\pi$
$128$		0			0
$129$	−5.50000	+	9.52628i	−0.484248	+	0.838742i
$130$		0			0
$131$	1.00000	+	1.73205i	0.0873704	+	0.151330i	0.906399	−	0.422423i	$-0.138820\pi$
$131$	1.00000	+	1.73205i	0.0873704	+	0.151330i	−0.819028	+	0.573753i	$0.805487\pi$
$132$		0			0
$133$	−0.866025	−	2.50000i	−0.0750939	−	0.216777i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−3.46410	−	2.00000i	−0.295958	−	0.170872i	0.344668	−	0.938725i	$-0.387992\pi$
$137$	−3.46410	−	2.00000i	−0.295958	−	0.170872i	−0.640626	+	0.767853i	$0.721325\pi$
$138$		0			0
$139$	5.00000			0.424094			0.212047	−	0.977259i	$-0.431987\pi$
$139$	5.00000			0.424094			0.212047	+	0.977259i	$0.431987\pi$
$140$		0			0
$141$	−6.00000			−0.505291
$142$		0			0
$143$	−5.19615	−	3.00000i	−0.434524	−	0.250873i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−4.33013	−	5.50000i	−0.357143	−	0.453632i
$148$		0			0
$149$	−6.00000	−	10.3923i	−0.491539	−	0.851371i	0.508413	−	0.861113i	$-0.330232\pi$
$149$	−6.00000	−	10.3923i	−0.491539	−	0.851371i	−0.999953	+	0.00974235i	$0.996899\pi$
$150$		0			0
$151$	4.00000	−	6.92820i	0.325515	−	0.563809i	−0.656101	−	0.754673i	$-0.727796\pi$
$151$	4.00000	−	6.92820i	0.325515	−	0.563809i	0.981617	+	0.190864i	$0.0611289\pi$
$152$		0			0
$153$		−	8.00000i		−	0.646762i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−1.73205	−	1.00000i	−0.138233	−	0.0798087i	0.429289	−	0.903167i	$-0.358764\pi$
$157$	−1.73205	−	1.00000i	−0.138233	−	0.0798087i	−0.567521	+	0.823359i	$0.692098\pi$
$158$		0			0
$159$	6.00000	+	10.3923i	0.475831	+	0.824163i
$160$		0			0
$161$	−20.0000	+	6.92820i	−1.57622	+	0.546019i
$162$		0			0
$163$	3.46410	−	2.00000i	0.271329	−	0.156652i	−0.358162	−	0.933659i	$-0.616597\pi$
$163$	3.46410	−	2.00000i	0.271329	−	0.156652i	0.629492	+	0.777007i	$0.283263\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		−	2.00000i		−	0.154765i	−0.997001	−	0.0773823i	$-0.975344\pi$
$167$		−	2.00000i		−	0.154765i	0.997001	−	0.0773823i	$-0.0246562\pi$
$168$		0			0
$169$	4.00000			0.307692
$170$		0			0
$171$	0.500000	−	0.866025i	0.0382360	−	0.0662266i
$172$		0			0
$173$	−13.8564	+	8.00000i	−1.05348	+	0.608229i	−0.923622	−	0.383304i	$-0.874786\pi$
$173$	−13.8564	+	8.00000i	−1.05348	+	0.608229i	−0.129861	+	0.991532i	$0.541453\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−3.46410	+	2.00000i	−0.260378	+	0.150329i
$178$		0			0
$179$	3.00000	−	5.19615i	0.224231	−	0.388379i	−0.731858	−	0.681457i	$-0.761346\pi$
$179$	3.00000	−	5.19615i	0.224231	−	0.388379i	0.956088	+	0.293079i	$0.0946798\pi$
$180$		0			0
$181$	−15.0000			−1.11494			−0.557471	−	0.830197i	$-0.688228\pi$
$181$	−15.0000			−1.11494			−0.557471	+	0.830197i	$0.688228\pi$
$182$		0			0
$183$		−	6.00000i		−	0.443533i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	13.8564	−	8.00000i	1.01328	−	0.585018i
$188$		0			0
$189$	0.500000	−	2.59808i	0.0363696	−	0.188982i
$190$		0			0
$191$	−3.00000	−	5.19615i	−0.217072	−	0.375980i	0.736839	−	0.676068i	$-0.236317\pi$
$191$	−3.00000	−	5.19615i	−0.217072	−	0.375980i	−0.953912	+	0.300088i	$0.902984\pi$
$192$		0			0
$193$	9.52628	+	5.50000i	0.685717	+	0.395899i	0.802005	−	0.597317i	$-0.203766\pi$
$193$	9.52628	+	5.50000i	0.685717	+	0.395899i	−0.116289	+	0.993215i	$0.537100\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			8.00000i			0.569976i	0.958531	+	0.284988i	$0.0919897\pi$
$197$			8.00000i			0.569976i	−0.958531	+	0.284988i	$0.908010\pi$
$198$		0			0
$199$	4.00000	−	6.92820i	0.283552	−	0.491127i	−0.688705	−	0.725042i	$-0.741820\pi$
$199$	4.00000	−	6.92820i	0.283552	−	0.491127i	0.972257	+	0.233915i	$0.0751537\pi$
$200$		0			0
$201$	6.50000	+	11.2583i	0.458475	+	0.794101i
$202$		0			0
$203$	−10.3923	−	2.00000i	−0.729397	−	0.140372i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−6.92820	−	4.00000i	−0.481543	−	0.278019i
$208$		0			0
$209$	2.00000			0.138343
$210$		0			0
$211$	−4.00000			−0.275371			−0.137686	−	0.990476i	$-0.543966\pi$
$211$	−4.00000			−0.275371			−0.137686	+	0.990476i	$0.543966\pi$
$212$		0			0
$213$	8.66025	+	5.00000i	0.593391	+	0.342594i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−5.19615	+	6.00000i	−0.352738	+	0.407307i
$218$		0			0
$219$	5.50000	+	9.52628i	0.371656	+	0.643726i
$220$		0			0
$221$	12.0000	−	20.7846i	0.807207	−	1.39812i
$222$		0			0
$223$		−	8.00000i		−	0.535720i	−0.963458	−	0.267860i	$-0.913684\pi$
$223$		−	8.00000i		−	0.535720i	0.963458	−	0.267860i	$-0.0863164\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	15.5885	+	9.00000i	1.03464	+	0.597351i	0.918311	−	0.395860i	$-0.129553\pi$
$227$	15.5885	+	9.00000i	1.03464	+	0.597351i	0.116331	+	0.993210i	$0.462887\pi$
$228$		0			0
$229$	0.500000	+	0.866025i	0.0330409	+	0.0572286i	0.882073	−	0.471113i	$-0.156147\pi$
$229$	0.500000	+	0.866025i	0.0330409	+	0.0572286i	−0.849032	+	0.528341i	$0.822814\pi$
$230$		0			0
$231$	5.00000	−	1.73205i	0.328976	−	0.113961i
$232$		0			0
$233$	−12.1244	+	7.00000i	−0.794293	+	0.458585i	−0.841472	−	0.540301i	$-0.818310\pi$
$233$	−12.1244	+	7.00000i	−0.794293	+	0.458585i	0.0471787	+	0.998886i	$0.484977\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$			3.00000i			0.194871i
$238$		0			0
$239$	−18.0000			−1.16432			−0.582162	−	0.813073i	$-0.697793\pi$
$239$	−18.0000			−1.16432			−0.582162	+	0.813073i	$0.697793\pi$
$240$		0			0
$241$	−7.00000	+	12.1244i	−0.450910	+	0.780998i	−0.998443	−	0.0557856i	$-0.982234\pi$
$241$	−7.00000	+	12.1244i	−0.450910	+	0.780998i	0.547533	+	0.836784i	$0.315567\pi$
$242$		0			0
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	2.59808	−	1.50000i	0.165312	−	0.0954427i
$248$		0			0
$249$	−1.00000	+	1.73205i	−0.0633724	+	0.109764i
$250$		0			0
$251$		0			0			−	1.00000i	$-0.5\pi$
$251$		0			0				1.00000i	$0.5\pi$
$252$		0			0
$253$		−	16.0000i		−	1.00591i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	15.5885	−	9.00000i	0.972381	−	0.561405i	0.0724199	−	0.997374i	$-0.476928\pi$
$257$	15.5885	−	9.00000i	0.972381	−	0.561405i	0.899961	+	0.435970i	$0.143595\pi$
$258$		0			0
$259$	−2.50000	+	0.866025i	−0.155342	+	0.0538122i
$260$		0			0
$261$	−2.00000	−	3.46410i	−0.123797	−	0.214423i
$262$		0			0
$263$	10.3923	+	6.00000i	0.640817	+	0.369976i	0.784929	−	0.619586i	$-0.212699\pi$
$263$	10.3923	+	6.00000i	0.640817	+	0.369976i	−0.144112	+	0.989561i	$0.546033\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−1.00000	+	1.73205i	−0.0609711	+	0.105605i	−0.894900	−	0.446267i	$-0.852753\pi$
$269$	−1.00000	+	1.73205i	−0.0609711	+	0.105605i	0.833929	+	0.551872i	$0.186086\pi$
$270$		0			0
$271$	12.0000	+	20.7846i	0.728948	+	1.26258i	0.957328	+	0.289003i	$0.0933238\pi$
$271$	12.0000	+	20.7846i	0.728948	+	1.26258i	−0.228380	+	0.973572i	$0.573343\pi$
$272$		0			0
$273$	5.19615	−	6.00000i	0.314485	−	0.363137i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−14.7224	−	8.50000i	−0.884585	−	0.510716i	−0.0124177	−	0.999923i	$-0.503953\pi$
$277$	−14.7224	−	8.50000i	−0.884585	−	0.510716i	−0.872167	+	0.489207i	$0.837286\pi$
$278$		0			0
$279$	−3.00000			−0.179605
$280$		0			0
$281$	20.0000			1.19310			0.596550	−	0.802576i	$-0.296538\pi$
$281$	20.0000			1.19310			0.596550	+	0.802576i	$0.296538\pi$
$282$		0			0
$283$	16.4545	+	9.50000i	0.978117	+	0.564716i	0.901701	−	0.432360i	$-0.142319\pi$
$283$	16.4545	+	9.50000i	0.978117	+	0.564716i	0.0764162	+	0.997076i	$0.475652\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	15.5885	+	3.00000i	0.920158	+	0.177084i
$288$		0			0
$289$	23.5000	+	40.7032i	1.38235	+	2.39431i
$290$		0			0
$291$	5.00000	−	8.66025i	0.293105	−	0.507673i
$292$		0			0
$293$			24.0000i			1.40209i	0.713115	+	0.701047i	$0.247284\pi$
$293$			24.0000i			1.40209i	−0.713115	+	0.701047i	$0.752716\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	1.73205	+	1.00000i	0.100504	+	0.0580259i
$298$		0			0
$299$	−12.0000	−	20.7846i	−0.693978	−	1.20201i
$300$		0			0
$301$	5.50000	−	28.5788i	0.317015	−	1.64726i
$302$		0			0
$303$	8.66025	−	5.00000i	0.497519	−	0.287242i
$304$		0			0
$305$		0			0
$306$		0			0
$307$		−	23.0000i		−	1.31268i	−0.754466	−	0.656340i	$-0.772104\pi$
$307$		−	23.0000i		−	1.31268i	0.754466	−	0.656340i	$-0.227896\pi$
$308$		0			0
$309$	11.0000			0.625768
$310$		0			0
$311$	1.00000	−	1.73205i	0.0567048	−	0.0982156i	−0.836280	−	0.548303i	$-0.815274\pi$
$311$	1.00000	−	1.73205i	0.0567048	−	0.0982156i	0.892984	+	0.450088i	$0.148607\pi$
$312$		0			0
$313$	14.7224	−	8.50000i	0.832161	−	0.480448i	−0.0224310	−	0.999748i	$-0.507141\pi$
$313$	14.7224	−	8.50000i	0.832161	−	0.480448i	0.854592	+	0.519300i	$0.173807\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−20.7846	+	12.0000i	−1.16738	+	0.673987i	−0.953062	−	0.302777i	$-0.902086\pi$
$317$	−20.7846	+	12.0000i	−1.16738	+	0.673987i	−0.214318	+	0.976764i	$0.568753\pi$
$318$		0			0
$319$	4.00000	−	6.92820i	0.223957	−	0.387905i
$320$		0			0
$321$		0			0
$322$		0			0
$323$			8.00000i			0.445132i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	9.52628	−	5.50000i	0.526804	−	0.304151i
$328$		0			0
$329$	15.0000	−	5.19615i	0.826977	−	0.286473i
$330$		0			0
$331$	−8.50000	−	14.7224i	−0.467202	−	0.809218i	0.532096	−	0.846684i	$-0.321405\pi$
$331$	−8.50000	−	14.7224i	−0.467202	−	0.809218i	−0.999298	+	0.0374662i	$0.988071\pi$
$332$		0			0
$333$	−0.866025	−	0.500000i	−0.0474579	−	0.0273998i
$334$		0			0
$335$		0			0
$336$		0			0
$337$			21.0000i			1.14394i	0.820274	+	0.571971i	$0.193821\pi$
$337$			21.0000i			1.14394i	−0.820274	+	0.571971i	$0.806179\pi$
$338$		0			0
$339$	7.00000	−	12.1244i	0.380188	−	0.658505i
$340$		0			0
$341$	−3.00000	−	5.19615i	−0.162459	−	0.281387i
$342$		0			0
$343$	15.5885	+	10.0000i	0.841698	+	0.539949i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−20.7846	−	12.0000i	−1.11578	−	0.644194i	−0.175457	−	0.984487i	$-0.556140\pi$
$347$	−20.7846	−	12.0000i	−1.11578	−	0.644194i	−0.940319	+	0.340293i	$0.889474\pi$
$348$		0			0
$349$	14.0000			0.749403			0.374701	−	0.927146i	$-0.377745\pi$
$349$	14.0000			0.749403			0.374701	+	0.927146i	$0.377745\pi$
$350$		0			0
$351$	3.00000			0.160128
$352$		0			0
$353$	−5.19615	−	3.00000i	−0.276563	−	0.159674i	0.355303	−	0.934751i	$-0.384378\pi$
$353$	−5.19615	−	3.00000i	−0.276563	−	0.159674i	−0.631867	+	0.775077i	$0.717711\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	6.92820	+	20.0000i	0.366679	+	1.05851i
$358$		0			0
$359$	−10.0000	−	17.3205i	−0.527780	−	0.914141i	−0.999476	−	0.0323801i	$-0.989691\pi$
$359$	−10.0000	−	17.3205i	−0.527780	−	0.914141i	0.471696	−	0.881761i	$-0.343642\pi$
$360$		0			0
$361$	9.00000	−	15.5885i	0.473684	−	0.820445i
$362$		0			0
$363$		−	7.00000i		−	0.367405i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−4.33013	−	2.50000i	−0.226031	−	0.130499i	0.382709	−	0.923869i	$-0.374991\pi$
$367$	−4.33013	−	2.50000i	−0.226031	−	0.130499i	−0.608740	+	0.793370i	$0.708325\pi$
$368$		0			0
$369$	3.00000	+	5.19615i	0.156174	+	0.270501i
$370$		0			0
$371$	−24.0000	−	20.7846i	−1.24602	−	1.07908i
$372$		0			0
$373$	4.33013	−	2.50000i	0.224205	−	0.129445i	−0.383691	−	0.923462i	$-0.625347\pi$
$373$	4.33013	−	2.50000i	0.224205	−	0.129445i	0.607896	+	0.794017i	$0.292014\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	12.0000i		−	0.618031i
$378$		0			0
$379$	−13.0000			−0.667765			−0.333883	−	0.942615i	$-0.608359\pi$
$379$	−13.0000			−0.667765			−0.333883	+	0.942615i	$0.608359\pi$
$380$		0			0
$381$	1.50000	−	2.59808i	0.0768473	−	0.133103i
$382$		0			0
$383$	24.2487	−	14.0000i	1.23905	−	0.715367i	0.270151	−	0.962818i	$-0.412926\pi$
$383$	24.2487	−	14.0000i	1.23905	−	0.715367i	0.968900	+	0.247451i	$0.0795931\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	9.52628	−	5.50000i	0.484248	−	0.279581i
$388$		0			0
$389$	5.00000	−	8.66025i	0.253510	−	0.439092i	−0.710980	−	0.703213i	$-0.751748\pi$
$389$	5.00000	−	8.66025i	0.253510	−	0.439092i	0.964490	+	0.264120i	$0.0850816\pi$
$390$		0			0
$391$	64.0000			3.23662
$392$		0			0
$393$		−	2.00000i		−	0.100887i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	2.59808	−	1.50000i	0.130394	−	0.0752828i	−0.433384	−	0.901209i	$-0.642681\pi$
$397$	2.59808	−	1.50000i	0.130394	−	0.0752828i	0.563778	+	0.825926i	$0.309347\pi$
$398$		0			0
$399$	−0.500000	+	2.59808i	−0.0250313	+	0.130066i
$400$		0			0
$401$	6.00000	+	10.3923i	0.299626	+	0.518967i	0.976050	−	0.217545i	$-0.0698049\pi$
$401$	6.00000	+	10.3923i	0.299626	+	0.518967i	−0.676425	+	0.736512i	$0.736472\pi$
$402$		0			0
$403$	−7.79423	−	4.50000i	−0.388258	−	0.224161i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		−	2.00000i		−	0.0991363i
$408$		0			0
$409$	−9.50000	+	16.4545i	−0.469745	+	0.813622i	−0.999402	−	0.0345902i	$-0.988987\pi$
$409$	−9.50000	+	16.4545i	−0.469745	+	0.813622i	0.529657	+	0.848212i	$0.322321\pi$
$410$		0			0
$411$	2.00000	+	3.46410i	0.0986527	+	0.170872i
$412$		0			0
$413$	6.92820	−	8.00000i	0.340915	−	0.393654i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−4.33013	−	2.50000i	−0.212047	−	0.122426i
$418$		0			0
$419$	−18.0000			−0.879358			−0.439679	−	0.898155i	$-0.644908\pi$
$419$	−18.0000			−0.879358			−0.439679	+	0.898155i	$0.644908\pi$
$420$		0			0
$421$	−27.0000			−1.31590			−0.657950	−	0.753062i	$-0.728576\pi$
$421$	−27.0000			−1.31590			−0.657950	+	0.753062i	$0.728576\pi$
$422$		0			0
$423$	5.19615	+	3.00000i	0.252646	+	0.145865i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	5.19615	+	15.0000i	0.251459	+	0.725901i
$428$		0			0
$429$	3.00000	+	5.19615i	0.144841	+	0.250873i
$430$		0			0
$431$	15.0000	−	25.9808i	0.722525	−	1.25145i	−0.237460	−	0.971397i	$-0.576315\pi$
$431$	15.0000	−	25.9808i	0.722525	−	1.25145i	0.959985	−	0.280052i	$-0.0903517\pi$
$432$		0			0
$433$			25.0000i			1.20142i	0.799466	+	0.600712i	$0.205116\pi$
$433$			25.0000i			1.20142i	−0.799466	+	0.600712i	$0.794884\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	6.92820	+	4.00000i	0.331421	+	0.191346i
$438$		0			0
$439$	12.0000	+	20.7846i	0.572729	+	0.991995i	0.996284	+	0.0861252i	$0.0274485\pi$
$439$	12.0000	+	20.7846i	0.572729	+	0.991995i	−0.423556	+	0.905870i	$0.639218\pi$
$440$		0			0
$441$	1.00000	+	6.92820i	0.0476190	+	0.329914i
$442$		0			0
$443$	3.46410	−	2.00000i	0.164584	−	0.0950229i	−0.415445	−	0.909618i	$-0.636374\pi$
$443$	3.46410	−	2.00000i	0.164584	−	0.0950229i	0.580030	+	0.814595i	$0.303041\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$			12.0000i			0.567581i
$448$		0			0
$449$	−22.0000			−1.03824			−0.519122	−	0.854700i	$-0.673741\pi$
$449$	−22.0000			−1.03824			−0.519122	+	0.854700i	$0.673741\pi$
$450$		0			0
$451$	−6.00000	+	10.3923i	−0.282529	+	0.489355i
$452$		0			0
$453$	−6.92820	+	4.00000i	−0.325515	+	0.187936i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	11.2583	−	6.50000i	0.526642	−	0.304057i	−0.213006	−	0.977051i	$-0.568325\pi$
$457$	11.2583	−	6.50000i	0.526642	−	0.304057i	0.739648	+	0.672994i	$0.234992\pi$
$458$		0			0
$459$	−4.00000	+	6.92820i	−0.186704	+	0.323381i
$460$		0			0
$461$	4.00000			0.186299			0.0931493	−	0.995652i	$-0.470307\pi$
$461$	4.00000			0.186299			0.0931493	+	0.995652i	$0.470307\pi$
$462$		0			0
$463$			11.0000i			0.511213i	0.966781	+	0.255607i	$0.0822752\pi$
$463$			11.0000i			0.511213i	−0.966781	+	0.255607i	$0.917725\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	29.4449	−	17.0000i	1.36255	−	0.786666i	0.372584	−	0.927999i	$-0.378472\pi$
$467$	29.4449	−	17.0000i	1.36255	−	0.786666i	0.989962	+	0.141332i	$0.0451386\pi$
$468$		0			0
$469$	−26.0000	−	22.5167i	−1.20057	−	1.03972i
$470$		0			0
$471$	1.00000	+	1.73205i	0.0460776	+	0.0798087i
$472$		0			0
$473$	19.0526	+	11.0000i	0.876038	+	0.505781i
$474$		0			0
$475$		0			0
$476$		0			0
$477$		−	12.0000i		−	0.549442i
$478$		0			0
$479$	−14.0000	+	24.2487i	−0.639676	+	1.10795i	0.345827	+	0.938298i	$0.387598\pi$
$479$	−14.0000	+	24.2487i	−0.639676	+	1.10795i	−0.985504	+	0.169654i	$0.945735\pi$
$480$		0			0
$481$	−1.50000	−	2.59808i	−0.0683941	−	0.118462i
$482$		0			0
$483$	20.7846	+	4.00000i	0.945732	+	0.182006i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	16.4545	+	9.50000i	0.745624	+	0.430486i	0.824110	−	0.566429i	$-0.191675\pi$
$487$	16.4545	+	9.50000i	0.745624	+	0.430486i	−0.0784867	+	0.996915i	$0.525009\pi$
$488$		0			0
$489$	−4.00000			−0.180886
$490$		0			0
$491$	−36.0000			−1.62466			−0.812329	−	0.583200i	$-0.801800\pi$
$491$	−36.0000			−1.62466			−0.812329	+	0.583200i	$0.801800\pi$
$492$		0			0
$493$	27.7128	+	16.0000i	1.24812	+	0.720604i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−25.9808	−	5.00000i	−1.16540	−	0.224281i
$498$		0			0
$499$	−14.5000	−	25.1147i	−0.649109	−	1.12429i	−0.983336	−	0.181797i	$-0.941809\pi$
$499$	−14.5000	−	25.1147i	−0.649109	−	1.12429i	0.334227	−	0.942493i	$-0.391525\pi$
$500$		0			0
$501$	−1.00000	+	1.73205i	−0.0446767	+	0.0773823i
$502$		0			0
$503$			30.0000i			1.33763i	0.743427	+	0.668817i	$0.233199\pi$
$503$			30.0000i			1.33763i	−0.743427	+	0.668817i	$0.766801\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−3.46410	−	2.00000i	−0.153846	−	0.0888231i
$508$		0			0
$509$	9.00000	+	15.5885i	0.398918	+	0.690946i	0.993593	−	0.113020i	$-0.0360525\pi$
$509$	9.00000	+	15.5885i	0.398918	+	0.690946i	−0.594675	+	0.803966i	$0.702719\pi$
$510$		0			0
$511$	−22.0000	−	19.0526i	−0.973223	−	0.842836i
$512$		0			0
$513$	−0.866025	+	0.500000i	−0.0382360	+	0.0220755i
$514$		0			0
$515$		0			0
$516$		0			0
$517$			12.0000i			0.527759i
$518$		0			0
$519$	16.0000			0.702322
$520$		0			0
$521$	18.0000	−	31.1769i	0.788594	−	1.36589i	−0.138234	−	0.990400i	$-0.544143\pi$
$521$	18.0000	−	31.1769i	0.788594	−	1.36589i	0.926828	−	0.375486i	$-0.122524\pi$
$522$		0			0
$523$	26.8468	−	15.5000i	1.17393	−	0.677768i	0.219326	−	0.975652i	$-0.429614\pi$
$523$	26.8468	−	15.5000i	1.17393	−	0.677768i	0.954602	+	0.297884i	$0.0962809\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	20.7846	−	12.0000i	0.905392	−	0.522728i
$528$		0			0
$529$	20.5000	−	35.5070i	0.891304	−	1.54378i
$530$		0			0
$531$	4.00000			0.173585
$532$		0			0
$533$			18.0000i			0.779667i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−5.19615	+	3.00000i	−0.224231	+	0.129460i
$538$		0			0
$539$	−11.0000	+	8.66025i	−0.473804	+	0.373024i
$540$		0			0
$541$	7.50000	+	12.9904i	0.322450	+	0.558500i	0.980993	−	0.194043i	$-0.0621602\pi$
$541$	7.50000	+	12.9904i	0.322450	+	0.558500i	−0.658543	+	0.752543i	$0.728827\pi$
$542$		0			0
$543$	12.9904	+	7.50000i	0.557471	+	0.321856i
$544$		0			0
$545$		0			0
$546$		0			0
$547$		−	12.0000i		−	0.513083i	−0.966533	−	0.256541i	$-0.917417\pi$
$547$		−	12.0000i		−	0.513083i	0.966533	−	0.256541i	$-0.0825830\pi$
$548$		0			0
$549$	−3.00000	+	5.19615i	−0.128037	+	0.221766i
$550$		0			0
$551$	2.00000	+	3.46410i	0.0852029	+	0.147576i
$552$		0			0
$553$	−2.59808	−	7.50000i	−0.110481	−	0.318932i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−19.0526	−	11.0000i	−0.807283	−	0.466085i	0.0387286	−	0.999250i	$-0.487669\pi$
$557$	−19.0526	−	11.0000i	−0.807283	−	0.466085i	−0.846011	+	0.533165i	$0.821003\pi$
$558$		0			0
$559$	33.0000			1.39575
$560$		0			0
$561$	−16.0000			−0.675521
$562$		0			0
$563$	−39.8372	−	23.0000i	−1.67894	−	0.969334i	−0.962341	−	0.271846i	$-0.912366\pi$
$563$	−39.8372	−	23.0000i	−1.67894	−	0.969334i	−0.716596	−	0.697489i	$-0.754301\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−1.73205	+	2.00000i	−0.0727393	+	0.0839921i
$568$		0			0
$569$	3.00000	+	5.19615i	0.125767	+	0.217834i	0.922032	−	0.387113i	$-0.126528\pi$
$569$	3.00000	+	5.19615i	0.125767	+	0.217834i	−0.796266	+	0.604947i	$0.793194\pi$
$570$		0			0
$571$	10.5000	−	18.1865i	0.439411	−	0.761083i	−0.558233	−	0.829684i	$-0.688520\pi$
$571$	10.5000	−	18.1865i	0.439411	−	0.761083i	0.997644	+	0.0686016i	$0.0218537\pi$
$572$		0			0
$573$			6.00000i			0.250654i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	35.5070	+	20.5000i	1.47818	+	0.853426i	0.999696	−	0.0246713i	$-0.00785391\pi$
$577$	35.5070	+	20.5000i	1.47818	+	0.853426i	0.478482	+	0.878097i	$0.341187\pi$
$578$		0			0
$579$	−5.50000	−	9.52628i	−0.228572	−	0.395899i
$580$		0			0
$581$	1.00000	−	5.19615i	0.0414870	−	0.215573i
$582$		0			0
$583$	20.7846	−	12.0000i	0.860811	−	0.496989i
$584$		0			0
$585$		0			0
$586$		0			0
$587$			32.0000i			1.32078i	0.750922	+	0.660391i	$0.229609\pi$
$587$			32.0000i			1.32078i	−0.750922	+	0.660391i	$0.770391\pi$
$588$		0			0
$589$	3.00000			0.123613
$590$		0			0
$591$	4.00000	−	6.92820i	0.164538	−	0.284988i
$592$		0			0
$593$	5.19615	−	3.00000i	0.213380	−	0.123195i	−0.389501	−	0.921026i	$-0.627353\pi$
$593$	5.19615	−	3.00000i	0.213380	−	0.123195i	0.602881	+	0.797831i	$0.294019\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−6.92820	+	4.00000i	−0.283552	+	0.163709i
$598$		0			0
$599$	−6.00000	+	10.3923i	−0.245153	+	0.424618i	−0.962175	−	0.272433i	$-0.912172\pi$
$599$	−6.00000	+	10.3923i	−0.245153	+	0.424618i	0.717021	+	0.697051i	$0.245505\pi$
$600$		0			0
$601$	−1.00000			−0.0407909			−0.0203954	−	0.999792i	$-0.506493\pi$
$601$	−1.00000			−0.0407909			−0.0203954	+	0.999792i	$0.506493\pi$
$602$		0			0
$603$		−	13.0000i		−	0.529401i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−2.59808	+	1.50000i	−0.105453	+	0.0608831i	−0.551799	−	0.833977i	$-0.686058\pi$
$607$	−2.59808	+	1.50000i	−0.105453	+	0.0608831i	0.446346	+	0.894860i	$0.352725\pi$
$608$		0			0
$609$	8.00000	+	6.92820i	0.324176	+	0.280745i
$610$		0			0
$611$	9.00000	+	15.5885i	0.364101	+	0.630641i
$612$		0			0
$613$	−25.9808	−	15.0000i	−1.04935	−	0.605844i	−0.126885	−	0.991917i	$-0.540498\pi$
$613$	−25.9808	−	15.0000i	−1.04935	−	0.605844i	−0.922468	+	0.386073i	$0.873831\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$			26.0000i			1.04672i	0.852111	+	0.523360i	$0.175322\pi$
$617$			26.0000i			1.04672i	−0.852111	+	0.523360i	$0.824678\pi$
$618$		0			0
$619$	−5.50000	+	9.52628i	−0.221064	+	0.382893i	−0.955131	−	0.296183i	$-0.904286\pi$
$619$	−5.50000	+	9.52628i	−0.221064	+	0.382893i	0.734068	+	0.679076i	$0.237620\pi$
$620$		0			0
$621$	4.00000	+	6.92820i	0.160514	+	0.278019i
$622$		0			0
$623$		0			0
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−1.73205	−	1.00000i	−0.0691714	−	0.0399362i
$628$		0			0
$629$	8.00000			0.318981
$630$		0			0
$631$	−16.0000			−0.636950			−0.318475	−	0.947931i	$-0.603171\pi$
$631$	−16.0000			−0.636950			−0.318475	+	0.947931i	$0.603171\pi$
$632$		0			0
$633$	3.46410	+	2.00000i	0.137686	+	0.0794929i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−7.79423	+	19.5000i	−0.308819	+	0.772618i
$638$		0			0
$639$	−5.00000	−	8.66025i	−0.197797	−	0.342594i
$640$		0			0
$641$	20.0000	−	34.6410i	0.789953	−	1.36824i	−0.136043	−	0.990703i	$-0.543438\pi$
$641$	20.0000	−	34.6410i	0.789953	−	1.36824i	0.925995	−	0.377535i	$-0.123228\pi$
$642$		0			0
$643$		−	35.0000i		−	1.38027i	−0.723683	−	0.690133i	$-0.757552\pi$
$643$		−	35.0000i		−	1.38027i	0.723683	−	0.690133i	$-0.242448\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−5.19615	−	3.00000i	−0.204282	−	0.117942i	0.394369	−	0.918952i	$-0.370963\pi$
$647$	−5.19615	−	3.00000i	−0.204282	−	0.117942i	−0.598651	+	0.801010i	$0.704296\pi$
$648$		0			0
$649$	4.00000	+	6.92820i	0.157014	+	0.271956i
$650$		0			0
$651$	7.50000	−	2.59808i	0.293948	−	0.101827i
$652$		0			0
$653$	5.19615	−	3.00000i	0.203341	−	0.117399i	−0.394872	−	0.918736i	$-0.629211\pi$
$653$	5.19615	−	3.00000i	0.203341	−	0.117399i	0.598213	+	0.801337i	$0.295878\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		−	11.0000i		−	0.429151i
$658$		0			0
$659$	28.0000			1.09073			0.545363	−	0.838200i	$-0.316392\pi$
$659$	28.0000			1.09073			0.545363	+	0.838200i	$0.316392\pi$
$660$		0			0
$661$	14.5000	−	25.1147i	0.563985	−	0.976850i	−0.433159	−	0.901318i	$-0.642601\pi$
$661$	14.5000	−	25.1147i	0.563985	−	0.976850i	0.997143	−	0.0755324i	$-0.0240656\pi$
$662$		0			0
$663$	−20.7846	+	12.0000i	−0.807207	+	0.466041i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	27.7128	−	16.0000i	1.07304	−	0.619522i
$668$		0			0
$669$	−4.00000	+	6.92820i	−0.154649	+	0.267860i
$670$		0			0
$671$	−12.0000			−0.463255
$672$		0			0
$673$			1.00000i			0.0385472i	0.999814	+	0.0192736i	$0.00613535\pi$
$673$			1.00000i			0.0385472i	−0.999814	+	0.0192736i	$0.993865\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	10.3923	−	6.00000i	0.399409	−	0.230599i	−0.286820	−	0.957984i	$-0.592598\pi$
$677$	10.3923	−	6.00000i	0.399409	−	0.230599i	0.686229	+	0.727386i	$0.259265\pi$
$678$		0			0
$679$	−5.00000	+	25.9808i	−0.191882	+	0.997050i
$680$		0			0
$681$	−9.00000	−	15.5885i	−0.344881	−	0.597351i
$682$		0			0
$683$	31.1769	+	18.0000i	1.19295	+	0.688751i	0.958975	−	0.283491i	$-0.0914927\pi$
$683$	31.1769	+	18.0000i	1.19295	+	0.688751i	0.233977	+	0.972242i	$0.424826\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$		−	1.00000i		−	0.0381524i
$688$		0			0
$689$	18.0000	−	31.1769i	0.685745	−	1.18775i
$690$		0			0
$691$	21.5000	+	37.2391i	0.817899	+	1.41664i	0.907228	+	0.420640i	$0.138194\pi$
$691$	21.5000	+	37.2391i	0.817899	+	1.41664i	−0.0893292	+	0.996002i	$0.528472\pi$
$692$		0			0
$693$	−5.19615	−	1.00000i	−0.197386	−	0.0379869i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−41.5692	−	24.0000i	−1.57455	−	0.909065i
$698$		0			0
$699$	14.0000			0.529529
$700$		0			0
$701$	−8.00000			−0.302156			−0.151078	−	0.988522i	$-0.548274\pi$
$701$	−8.00000			−0.302156			−0.151078	+	0.988522i	$0.548274\pi$
$702$		0			0
$703$	0.866025	+	0.500000i	0.0326628	+	0.0188579i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−17.3205	+	20.0000i	−0.651405	+	0.752177i
$708$		0			0
$709$	7.00000	+	12.1244i	0.262891	+	0.455340i	0.967009	−	0.254743i	$-0.0819909\pi$
$709$	7.00000	+	12.1244i	0.262891	+	0.455340i	−0.704118	+	0.710083i	$0.748658\pi$
$710$		0			0
$711$	1.50000	−	2.59808i	0.0562544	−	0.0974355i
$712$		0			0
$713$		−	24.0000i		−	0.898807i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	15.5885	+	9.00000i	0.582162	+	0.336111i
$718$		0			0
$719$	−3.00000	−	5.19615i	−0.111881	−	0.193784i	0.804648	−	0.593753i	$-0.202354\pi$
$719$	−3.00000	−	5.19615i	−0.111881	−	0.193784i	−0.916529	+	0.399969i	$0.869021\pi$
$720$		0			0
$721$	−27.5000	+	9.52628i	−1.02415	+	0.354777i
$722$		0			0
$723$	12.1244	−	7.00000i	0.450910	−	0.260333i
$724$		0			0
$725$		0			0
$726$		0			0
$727$		−	23.0000i		−	0.853023i	−0.904482	−	0.426511i	$-0.859742\pi$
$727$		−	23.0000i		−	0.853023i	0.904482	−	0.426511i	$-0.140258\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	−44.0000	+	76.2102i	−1.62740	+	2.81874i
$732$		0			0
$733$	−38.9711	+	22.5000i	−1.43943	+	0.831056i	−0.997810	−	0.0661448i	$-0.978930\pi$
$733$	−38.9711	+	22.5000i	−1.43943	+	0.831056i	−0.441622	+	0.897201i	$0.645597\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	22.5167	−	13.0000i	0.829412	−	0.478861i
$738$		0			0
$739$	−4.50000	+	7.79423i	−0.165535	+	0.286715i	−0.936845	−	0.349744i	$-0.886268\pi$
$739$	−4.50000	+	7.79423i	−0.165535	+	0.286715i	0.771310	+	0.636460i	$0.219602\pi$
$740$		0			0
$741$	−3.00000			−0.110208
$742$		0			0
$743$			18.0000i			0.660356i	0.943919	+	0.330178i	$0.107109\pi$
$743$			18.0000i			0.660356i	−0.943919	+	0.330178i	$0.892891\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	1.73205	−	1.00000i	0.0633724	−	0.0365881i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−7.50000	−	12.9904i	−0.273679	−	0.474026i	0.696122	−	0.717923i	$-0.254907\pi$
$751$	−7.50000	−	12.9904i	−0.273679	−	0.474026i	−0.969801	+	0.243898i	$0.921574\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$			42.0000i			1.52652i	0.646094	+	0.763258i	$0.276401\pi$
$757$			42.0000i			1.52652i	−0.646094	+	0.763258i	$0.723599\pi$
$758$		0			0
$759$	−8.00000	+	13.8564i	−0.290382	+	0.502956i
$760$		0			0
$761$	−4.00000	−	6.92820i	−0.145000	−	0.251147i	0.784373	−	0.620289i	$-0.212985\pi$
$761$	−4.00000	−	6.92820i	−0.145000	−	0.251147i	−0.929373	+	0.369142i	$0.879652\pi$
$762$		0			0
$763$	−19.0526	+	22.0000i	−0.689749	+	0.796453i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	10.3923	+	6.00000i	0.375244	+	0.216647i
$768$		0			0
$769$	−31.0000			−1.11789			−0.558944	−	0.829205i	$-0.688793\pi$
$769$	−31.0000			−1.11789			−0.558944	+	0.829205i	$0.688793\pi$
$770$		0			0
$771$	−18.0000			−0.648254
$772$		0			0
$773$	19.0526	+	11.0000i	0.685273	+	0.395643i	0.801839	−	0.597540i	$-0.203855\pi$
$773$	19.0526	+	11.0000i	0.685273	+	0.395643i	−0.116566	+	0.993183i	$0.537189\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	2.59808	+	0.500000i	0.0932055	+	0.0179374i
$778$		0			0
$779$	−3.00000	−	5.19615i	−0.107486	−	0.186171i
$780$		0			0
$781$	10.0000	−	17.3205i	0.357828	−	0.619777i
$782$		0			0
$783$			4.00000i			0.142948i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−20.7846	−	12.0000i	−0.740891	−	0.427754i	0.0815020	−	0.996673i	$-0.474028\pi$
$787$	−20.7846	−	12.0000i	−0.740891	−	0.427754i	−0.822393	+	0.568919i	$0.807362\pi$
$788$		0			0
$789$	−6.00000	−	10.3923i	−0.213606	−	0.369976i
$790$		0			0
$791$	−7.00000	+	36.3731i	−0.248891	+	1.29328i
$792$		0			0
$793$	−15.5885	+	9.00000i	−0.553562	+	0.319599i
$794$		0			0
$795$		0			0
$796$		0			0
$797$		−	48.0000i		−	1.70025i	−0.526583	−	0.850124i	$-0.676527\pi$
$797$		−	48.0000i		−	1.70025i	0.526583	−	0.850124i	$-0.323473\pi$
$798$		0			0
$799$	−48.0000			−1.69812
$800$		0			0
$801$		0			0
$802$		0			0
$803$	19.0526	−	11.0000i	0.672350	−	0.388182i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	1.73205	−	1.00000i	0.0609711	−	0.0352017i
$808$		0			0
$809$	11.0000	−	19.0526i	0.386739	−	0.669852i	−0.605269	−	0.796021i	$-0.706935\pi$
$809$	11.0000	−	19.0526i	0.386739	−	0.669852i	0.992009	+	0.126168i	$0.0402680\pi$
$810$		0			0
$811$	−32.0000			−1.12367			−0.561836	−	0.827249i	$-0.689905\pi$
$811$	−32.0000			−1.12367			−0.561836	+	0.827249i	$0.689905\pi$
$812$		0			0
$813$		−	24.0000i		−	0.841717i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−9.52628	+	5.50000i	−0.333282	+	0.192421i
$818$		0			0
$819$	−7.50000	+	2.59808i	−0.262071	+	0.0907841i
$820$		0			0
$821$	−1.00000	−	1.73205i	−0.0349002	−	0.0604490i	0.848048	−	0.529920i	$-0.177778\pi$
$821$	−1.00000	−	1.73205i	−0.0349002	−	0.0604490i	−0.882948	+	0.469471i	$0.844445\pi$
$822$		0			0
$823$	34.6410	+	20.0000i	1.20751	+	0.697156i	0.962215	−	0.272292i	$-0.0877817\pi$
$823$	34.6410	+	20.0000i	1.20751	+	0.697156i	0.245295	+	0.969448i	$0.421115\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			54.0000i			1.87776i	0.344239	+	0.938882i	$0.388137\pi$
$827$			54.0000i			1.87776i	−0.344239	+	0.938882i	$0.611863\pi$
$828$		0			0
$829$	−5.50000	+	9.52628i	−0.191023	+	0.330861i	−0.945589	−	0.325362i	$-0.894514\pi$
$829$	−5.50000	+	9.52628i	−0.191023	+	0.330861i	0.754567	+	0.656223i	$0.227847\pi$
$830$		0			0
$831$	8.50000	+	14.7224i	0.294862	+	0.510716i
$832$		0			0
$833$	−34.6410	−	44.0000i	−1.20024	−	1.52451i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	2.59808	+	1.50000i	0.0898027	+	0.0518476i
$838$		0			0
$839$	4.00000			0.138095			0.0690477	−	0.997613i	$-0.478004\pi$
$839$	4.00000			0.138095			0.0690477	+	0.997613i	$0.478004\pi$
$840$		0			0
$841$	−13.0000			−0.448276
$842$		0			0
$843$	−17.3205	−	10.0000i	−0.596550	−	0.344418i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	6.06218	+	17.5000i	0.208299	+	0.601307i
$848$		0			0
$849$	−9.50000	−	16.4545i	−0.326039	−	0.564716i
$850$		0			0
$851$	4.00000	−	6.92820i	0.137118	−	0.237496i
$852$		0			0
$853$		−	23.0000i		−	0.787505i	−0.919216	−	0.393753i	$-0.871177\pi$
$853$		−	23.0000i		−	0.787505i	0.919216	−	0.393753i	$-0.128823\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$857$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$858$		0			0
$859$	4.00000	+	6.92820i	0.136478	+	0.236387i	0.926161	−	0.377128i	$-0.123088\pi$
$859$	4.00000	+	6.92820i	0.136478	+	0.236387i	−0.789683	+	0.613515i	$0.789755\pi$
$860$		0			0
$861$	−12.0000	−	10.3923i	−0.408959	−	0.354169i
$862$		0			0
$863$	−39.8372	+	23.0000i	−1.35607	+	0.782929i	−0.989092	−	0.147299i	$-0.952942\pi$
$863$	−39.8372	+	23.0000i	−1.35607	+	0.782929i	−0.366981	+	0.930228i	$0.619609\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$		−	47.0000i		−	1.59620i
$868$		0			0
$869$	6.00000			0.203536
$870$		0			0
$871$	19.5000	−	33.7750i	0.660732	−	1.14442i
$872$		0			0
$873$	−8.66025	+	5.00000i	−0.293105	+	0.169224i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−32.9090	+	19.0000i	−1.11126	+	0.641584i	−0.939155	−	0.343495i	$-0.888389\pi$
$877$	−32.9090	+	19.0000i	−1.11126	+	0.641584i	−0.172102	+	0.985079i	$0.555056\pi$
$878$		0			0
$879$	12.0000	−	20.7846i	0.404750	−	0.701047i
$880$		0			0
$881$	48.0000			1.61716			0.808581	−	0.588386i	$-0.200236\pi$
$881$	48.0000			1.61716			0.808581	+	0.588386i	$0.200236\pi$
$882$		0			0
$883$		−	29.0000i		−	0.975928i	−0.872864	−	0.487964i	$-0.837740\pi$
$883$		−	29.0000i		−	0.975928i	0.872864	−	0.487964i	$-0.162260\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−5.19615	+	3.00000i	−0.174470	+	0.100730i	−0.584692	−	0.811256i	$-0.698785\pi$
$887$	−5.19615	+	3.00000i	−0.174470	+	0.100730i	0.410222	+	0.911986i	$0.365451\pi$
$888$		0			0
$889$	−1.50000	+	7.79423i	−0.0503084	+	0.261410i
$890$		0			0
$891$	−1.00000	−	1.73205i	−0.0335013	−	0.0580259i
$892$		0			0
$893$	−5.19615	−	3.00000i	−0.173883	−	0.100391i
$894$		0			0
$895$		0			0
$896$		0			0
$897$			24.0000i			0.801337i
$898$		0			0
$899$	6.00000	−	10.3923i	0.200111	−	0.346603i
$900$		0			0
$901$	48.0000	+	83.1384i	1.59911	+	2.76974i
$902$		0			0
$903$	−19.0526	+	22.0000i	−0.634029	+	0.732114i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−18.1865	−	10.5000i	−0.603874	−	0.348647i	0.166690	−	0.986009i	$-0.446692\pi$
$907$	−18.1865	−	10.5000i	−0.603874	−	0.348647i	−0.770564	+	0.637363i	$0.780025\pi$
$908$		0			0
$909$	−10.0000			−0.331679
$910$		0			0
$911$	48.0000			1.59031			0.795155	−	0.606406i	$-0.207389\pi$
$911$	48.0000			1.59031			0.795155	+	0.606406i	$0.207389\pi$
$912$		0			0
$913$	3.46410	+	2.00000i	0.114645	+	0.0661903i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	1.73205	+	5.00000i	0.0571974	+	0.165115i
$918$		0			0
$919$	−5.50000	−	9.52628i	−0.181428	−	0.314243i	0.760939	−	0.648824i	$-0.224739\pi$
$919$	−5.50000	−	9.52628i	−0.181428	−	0.314243i	−0.942367	+	0.334581i	$0.891405\pi$
$920$		0			0
$921$	−11.5000	+	19.9186i	−0.378938	+	0.656340i
$922$		0			0
$923$		−	30.0000i		−	0.987462i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−9.52628	−	5.50000i	−0.312884	−	0.180644i
$928$		0			0
$929$	3.00000	+	5.19615i	0.0984268	+	0.170480i	0.911034	−	0.412332i	$-0.135286\pi$
$929$	3.00000	+	5.19615i	0.0984268	+	0.170480i	−0.812607	+	0.582812i	$0.801952\pi$
$930$		0			0
$931$	−1.00000	−	6.92820i	−0.0327737	−	0.227063i
$932$		0			0
$933$	−1.73205	+	1.00000i	−0.0567048	+	0.0327385i
$934$		0			0
$935$		0			0
$936$		0			0
$937$		−	49.0000i		−	1.60076i	−0.599493	−	0.800380i	$-0.704631\pi$
$937$		−	49.0000i		−	1.60076i	0.599493	−	0.800380i	$-0.295369\pi$
$938$		0			0
$939$	−17.0000			−0.554774
$940$		0			0
$941$	−26.0000	+	45.0333i	−0.847576	+	1.46804i	0.0357896	+	0.999359i	$0.488605\pi$
$941$	−26.0000	+	45.0333i	−0.847576	+	1.46804i	−0.883365	+	0.468685i	$0.844728\pi$
$942$		0			0
$943$	−41.5692	+	24.0000i	−1.35368	+	0.781548i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	8.66025	−	5.00000i	0.281420	−	0.162478i	−0.352646	−	0.935757i	$-0.614718\pi$
$947$	8.66025	−	5.00000i	0.281420	−	0.162478i	0.634066	+	0.773279i	$0.281385\pi$
$948$		0			0
$949$	16.5000	−	28.5788i	0.535613	−	0.927708i
$950$		0			0
$951$	24.0000			0.778253
$952$		0			0
$953$			28.0000i			0.907009i	0.891254	+	0.453504i	$0.149826\pi$
$953$			28.0000i			0.907009i	−0.891254	+	0.453504i	$0.850174\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−6.92820	+	4.00000i	−0.223957	+	0.129302i
$958$		0			0
$959$	−8.00000	−	6.92820i	−0.258333	−	0.223723i
$960$		0			0
$961$	11.0000	+	19.0526i	0.354839	+	0.614599i
$962$		0			0
$963$		0			0
$964$		0			0
$965$		0			0
$966$		0			0
$967$		−	31.0000i		−	0.996893i	−0.866921	−	0.498446i	$-0.833904\pi$
$967$		−	31.0000i		−	0.996893i	0.866921	−	0.498446i	$-0.166096\pi$
$968$		0			0
$969$	4.00000	−	6.92820i	0.128499	−	0.222566i
$970$		0			0
$971$	−18.0000	−	31.1769i	−0.577647	−	1.00051i	−0.995748	−	0.0921142i	$-0.970638\pi$
$971$	−18.0000	−	31.1769i	−0.577647	−	1.00051i	0.418101	−	0.908401i	$-0.362696\pi$
$972$		0			0
$973$	12.9904	+	2.50000i	0.416452	+	0.0801463i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	15.5885	+	9.00000i	0.498719	+	0.287936i	0.728184	−	0.685381i	$-0.240364\pi$
$977$	15.5885	+	9.00000i	0.498719	+	0.287936i	−0.229465	+	0.973317i	$0.573698\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	−11.0000			−0.351203
$982$		0			0
$983$	−10.3923	−	6.00000i	−0.331463	−	0.191370i	0.325027	−	0.945705i	$-0.394626\pi$
$983$	−10.3923	−	6.00000i	−0.331463	−	0.191370i	−0.656490	+	0.754334i	$0.727960\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−15.5885	−	3.00000i	−0.496186	−	0.0954911i
$988$		0			0
$989$	44.0000	+	76.2102i	1.39912	+	2.42334i
$990$		0			0
$991$	−5.50000	+	9.52628i	−0.174713	+	0.302612i	−0.940062	−	0.341004i	$-0.889233\pi$
$991$	−5.50000	+	9.52628i	−0.174713	+	0.302612i	0.765349	+	0.643616i	$0.222567\pi$
$992$		0			0
$993$			17.0000i			0.539479i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	0.866025	+	0.500000i	0.0274273	+	0.0158352i	0.513651	−	0.857999i	$-0.328293\pi$
$997$	0.866025	+	0.500000i	0.0274273	+	0.0158352i	−0.486224	+	0.873834i	$0.661626\pi$
$998$		0			0
$999$	0.500000	+	0.866025i	0.0158193	+	0.0273998i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2100.2.bc.a.949.1		4
5.2	odd	4		2100.2.q.b.1201.1		2
5.3	odd	4		84.2.i.a.25.1	✓	2
5.4	even	2	inner	2100.2.bc.a.949.2		4
7.2	even	3	inner	2100.2.bc.a.1549.2		4
15.8	even	4		252.2.k.a.109.1		2
20.3	even	4		336.2.q.c.193.1		2
35.2	odd	12		2100.2.q.b.1801.1		2
35.3	even	12		588.2.a.f.1.1		1
35.9	even	6	inner	2100.2.bc.a.1549.1		4
35.13	even	4		588.2.i.b.361.1		2
35.18	odd	12		588.2.a.a.1.1		1
35.23	odd	12		84.2.i.a.37.1	yes	2
35.33	even	12		588.2.i.b.373.1		2
40.3	even	4		1344.2.q.n.193.1		2
40.13	odd	4		1344.2.q.b.193.1		2
45.13	odd	12		2268.2.i.g.865.1		2
45.23	even	12		2268.2.i.b.865.1		2
45.38	even	12		2268.2.l.g.109.1		2
45.43	odd	12		2268.2.l.b.109.1		2
60.23	odd	4		1008.2.s.c.865.1		2
105.23	even	12		252.2.k.a.37.1		2
105.38	odd	12		1764.2.a.c.1.1		1
105.53	even	12		1764.2.a.h.1.1		1
105.68	odd	12		1764.2.k.j.1549.1		2
105.83	odd	4		1764.2.k.j.361.1		2
140.3	odd	12		2352.2.a.k.1.1		1
140.23	even	12		336.2.q.c.289.1		2
140.83	odd	4		2352.2.q.q.1537.1		2
140.103	odd	12		2352.2.q.q.961.1		2
140.123	even	12		2352.2.a.o.1.1		1
280.3	odd	12		9408.2.a.bx.1.1		1
280.53	odd	12		9408.2.a.cx.1.1		1
280.93	odd	12		1344.2.q.b.961.1		2
280.123	even	12		9408.2.a.bi.1.1		1
280.163	even	12		1344.2.q.n.961.1		2
280.213	even	12		9408.2.a.i.1.1		1
315.23	even	12		2268.2.l.g.541.1		2
315.58	odd	12		2268.2.l.b.541.1		2
315.128	even	12		2268.2.i.b.2053.1		2
315.268	odd	12		2268.2.i.g.2053.1		2
420.23	odd	12		1008.2.s.c.289.1		2
420.143	even	12		7056.2.a.o.1.1		1
420.263	odd	12		7056.2.a.bs.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.2.i.a.25.1	✓	2	5.3	odd	4
84.2.i.a.37.1	yes	2	35.23	odd	12
252.2.k.a.37.1		2	105.23	even	12
252.2.k.a.109.1		2	15.8	even	4
336.2.q.c.193.1		2	20.3	even	4
336.2.q.c.289.1		2	140.23	even	12
588.2.a.a.1.1		1	35.18	odd	12
588.2.a.f.1.1		1	35.3	even	12
588.2.i.b.361.1		2	35.13	even	4
588.2.i.b.373.1		2	35.33	even	12
1008.2.s.c.289.1		2	420.23	odd	12
1008.2.s.c.865.1		2	60.23	odd	4
1344.2.q.b.193.1		2	40.13	odd	4
1344.2.q.b.961.1		2	280.93	odd	12
1344.2.q.n.193.1		2	40.3	even	4
1344.2.q.n.961.1		2	280.163	even	12
1764.2.a.c.1.1		1	105.38	odd	12
1764.2.a.h.1.1		1	105.53	even	12
1764.2.k.j.361.1		2	105.83	odd	4
1764.2.k.j.1549.1		2	105.68	odd	12
2100.2.q.b.1201.1		2	5.2	odd	4
2100.2.q.b.1801.1		2	35.2	odd	12
2100.2.bc.a.949.1		4	1.1	even	1	trivial
2100.2.bc.a.949.2		4	5.4	even	2	inner
2100.2.bc.a.1549.1		4	35.9	even	6	inner
2100.2.bc.a.1549.2		4	7.2	even	3	inner
2268.2.i.b.865.1		2	45.23	even	12
2268.2.i.b.2053.1		2	315.128	even	12
2268.2.i.g.865.1		2	45.13	odd	12
2268.2.i.g.2053.1		2	315.268	odd	12
2268.2.l.b.109.1		2	45.43	odd	12
2268.2.l.b.541.1		2	315.58	odd	12
2268.2.l.g.109.1		2	45.38	even	12
2268.2.l.g.541.1		2	315.23	even	12
2352.2.a.k.1.1		1	140.3	odd	12
2352.2.a.o.1.1		1	140.123	even	12
2352.2.q.q.961.1		2	140.103	odd	12
2352.2.q.q.1537.1		2	140.83	odd	4
7056.2.a.o.1.1		1	420.143	even	12
7056.2.a.bs.1.1		1	420.263	odd	12
9408.2.a.i.1.1		1	280.213	even	12
9408.2.a.bi.1.1		1	280.123	even	12
9408.2.a.bx.1.1		1	280.3	odd	12
9408.2.a.cx.1.1		1	280.53	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{3} +(2.59808 + 0.500000i) q^{7} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{3} +(2.59808 + 0.500000i) q^{7} +(0.500000 + 0.866025i) q^{9} +(-1.00000 + 1.73205i) q^{11} +3.00000i q^{13} +(-6.92820 - 4.00000i) q^{17} +(-0.500000 - 0.866025i) q^{19} +(-2.00000 - 1.73205i) q^{21} +(-6.92820 + 4.00000i) q^{23} -1.00000i q^{27} -4.00000 q^{29} +(-1.50000 + 2.59808i) q^{31} +(1.73205 - 1.00000i) q^{33} +(-0.866025 + 0.500000i) q^{37} +(1.50000 - 2.59808i) q^{39} +6.00000 q^{41} -11.0000i q^{43} +(5.19615 - 3.00000i) q^{47} +(6.50000 + 2.59808i) q^{49} +(4.00000 + 6.92820i) q^{51} +(-10.3923 - 6.00000i) q^{53} +1.00000i q^{57} +(2.00000 - 3.46410i) q^{59} +(3.00000 + 5.19615i) q^{61} +(0.866025 + 2.50000i) q^{63} +(-11.2583 - 6.50000i) q^{67} +8.00000 q^{69} -10.0000 q^{71} +(-9.52628 - 5.50000i) q^{73} +(-3.46410 + 4.00000i) q^{77} +(-1.50000 - 2.59808i) q^{79} +(-0.500000 + 0.866025i) q^{81} -2.00000i q^{83} +(3.46410 + 2.00000i) q^{87} +(-1.50000 + 7.79423i) q^{91} +(2.59808 - 1.50000i) q^{93} +10.0000i q^{97} -2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^9	\( 4 q + 2 q^{9} - 4 q^{11} - 2 q^{19} - 8 q^{21} - 16 q^{29} - 6 q^{31} + 6 q^{39} + 24 q^{41} + 26 q^{49} + 16 q^{51} + 8 q^{59} + 12 q^{61} + 32 q^{69} - 40 q^{71} - 6 q^{79} - 2 q^{81} - 6 q^{91} - 8 q^{99}+O(q^{100}) \) 4 * q + 2 * q^9 - 4 * q^11 - 2 * q^19 - 8 * q^21 - 16 * q^29 - 6 * q^31 + 6 * q^39 + 24 * q^41 + 26 * q^49 + 16 * q^51 + 8 * q^59 + 12 * q^61 + 32 * q^69 - 40 * q^71 - 6 * q^79 - 2 * q^81 - 6 * q^91 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more