LMFDB - Embedded newform 2100.2.bc.h.1549.1

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:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.49787136.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 3x^{6} + 5x^{4} + 12x^{2} + 16 $ x^8 + 3x^6 + 5x^4 + 12*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1549.1
Root			$1.09445 - 0.895644i$ of defining polynomial
Character	$\chi$	$=$	2100.1549
Dual form			2100.2.bc.h.949.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{3} +(-2.29129 + 1.32288i) q^{7} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{3} +(-2.29129 + 1.32288i) q^{7} +(0.500000 - 0.866025i) q^{9} +(0.177124 + 0.306788i) q^{11} +1.00000i q^{13} +(-3.15731 + 1.82288i) q^{17} +(0.322876 - 0.559237i) q^{19} +(1.32288 - 2.29129i) q^{21} +(1.73205 + 1.00000i) q^{23} +1.00000i q^{27} +3.29150 q^{29} +(-2.00000 - 3.46410i) q^{31} +(-0.306788 - 0.177124i) q^{33} +(-1.98450 - 1.14575i) q^{37} +(-0.500000 - 0.866025i) q^{39} -5.64575 q^{41} +3.29150i q^{43} +(-11.2040 - 6.46863i) q^{47} +(3.50000 - 6.06218i) q^{49} +(1.82288 - 3.15731i) q^{51} +(6.62141 - 3.82288i) q^{53} +0.645751i q^{57} +(-0.468627 - 0.811686i) q^{59} +(5.79150 - 10.0312i) q^{61} +2.64575i q^{63} +(-6.87386 + 3.96863i) q^{67} -2.00000 q^{69} -7.29150 q^{71} +(3.71655 - 2.14575i) q^{73} +(-0.811686 - 0.468627i) q^{77} +(-0.677124 + 1.17281i) q^{79} +(-0.500000 - 0.866025i) q^{81} -1.64575i q^{83} +(-2.85052 + 1.64575i) q^{87} +(3.46863 - 6.00784i) q^{89} +(-1.32288 - 2.29129i) q^{91} +(3.46410 + 2.00000i) q^{93} -3.70850i q^{97} +0.354249 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{9}+O(q^{10}) $ 8 * q + 4 * q^9	$ 8 q + 4 q^{9} + 12 q^{11} - 8 q^{19} - 16 q^{29} - 16 q^{31} - 4 q^{39} - 24 q^{41} + 28 q^{49} + 4 q^{51} + 28 q^{59} + 4 q^{61} - 16 q^{69} - 16 q^{71} - 16 q^{79} - 4 q^{81} - 4 q^{89} + 24 q^{99}+O(q^{100}) $ 8 * q + 4 * q^9 + 12 * q^11 - 8 * q^19 - 16 * q^29 - 16 * q^31 - 4 * q^39 - 24 * q^41 + 28 * q^49 + 4 * q^51 + 28 * q^59 + 4 * q^61 - 16 * q^69 - 16 * q^71 - 16 * q^79 - 4 * q^81 - 4 * q^89 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−2.29129	+	1.32288i	−0.866025	+	0.500000i
$7$	−2.29129	+	1.32288i	−0.866025	+	0.500000i
$8$		0			0
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$		0			0
$11$	0.177124	+	0.306788i	0.0534050	+	0.0925002i	0.891492	−	0.453036i	$-0.149659\pi$
$11$	0.177124	+	0.306788i	0.0534050	+	0.0925002i	−0.838087	+	0.545537i	$0.816326\pi$
$12$		0			0
$13$			1.00000i			0.277350i	0.990338	+	0.138675i	$0.0442844\pi$
$13$			1.00000i			0.277350i	−0.990338	+	0.138675i	$0.955716\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−3.15731	+	1.82288i	−0.765761	+	0.442112i	−0.831360	−	0.555734i	$-0.812437\pi$
$17$	−3.15731	+	1.82288i	−0.765761	+	0.442112i	0.0655994	+	0.997846i	$0.479104\pi$
$18$		0			0
$19$	0.322876	−	0.559237i	0.0740728	−	0.128298i	−0.826610	−	0.562775i	$-0.809734\pi$
$19$	0.322876	−	0.559237i	0.0740728	−	0.128298i	0.900683	+	0.434478i	$0.143067\pi$
$20$		0			0
$21$	1.32288	−	2.29129i	0.288675	−	0.500000i
$22$		0			0
$23$	1.73205	+	1.00000i	0.361158	+	0.208514i	0.669588	−	0.742732i	$-0.266471\pi$
$23$	1.73205	+	1.00000i	0.361158	+	0.208514i	−0.308431	+	0.951247i	$0.599804\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$			1.00000i			0.192450i
$28$		0			0
$29$	3.29150			0.611217			0.305608	−	0.952157i	$-0.401140\pi$
$29$	3.29150			0.611217			0.305608	+	0.952157i	$0.401140\pi$
$30$		0			0
$31$	−2.00000	−	3.46410i	−0.359211	−	0.622171i	0.628619	−	0.777714i	$-0.283621\pi$
$31$	−2.00000	−	3.46410i	−0.359211	−	0.622171i	−0.987829	+	0.155543i	$0.950287\pi$
$32$		0			0
$33$	−0.306788	−	0.177124i	−0.0534050	−	0.0308334i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−1.98450	−	1.14575i	−0.326250	−	0.188360i	0.327925	−	0.944704i	$-0.393651\pi$
$37$	−1.98450	−	1.14575i	−0.326250	−	0.188360i	−0.654175	+	0.756343i	$0.726984\pi$
$38$		0			0
$39$	−0.500000	−	0.866025i	−0.0800641	−	0.138675i
$40$		0			0
$41$	−5.64575			−0.881718			−0.440859	−	0.897576i	$-0.645326\pi$
$41$	−5.64575			−0.881718			−0.440859	+	0.897576i	$0.645326\pi$
$42$		0			0
$43$			3.29150i			0.501949i	0.967994	+	0.250975i	$0.0807511\pi$
$43$			3.29150i			0.501949i	−0.967994	+	0.250975i	$0.919249\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−11.2040	−	6.46863i	−1.63427	−	0.943546i	−0.982755	−	0.184910i	$-0.940801\pi$
$47$	−11.2040	−	6.46863i	−1.63427	−	0.943546i	−0.651515	−	0.758636i	$-0.725866\pi$
$48$		0			0
$49$	3.50000	−	6.06218i	0.500000	−	0.866025i
$50$		0			0
$51$	1.82288	−	3.15731i	0.255254	−	0.442112i
$52$		0			0
$53$	6.62141	−	3.82288i	0.909521	−	0.525112i	0.0292442	−	0.999572i	$-0.490690\pi$
$53$	6.62141	−	3.82288i	0.909521	−	0.525112i	0.880277	+	0.474460i	$0.157357\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$			0.645751i			0.0855319i
$58$		0			0
$59$	−0.468627	−	0.811686i	−0.0610100	−	0.105672i	0.833907	−	0.551905i	$-0.186099\pi$
$59$	−0.468627	−	0.811686i	−0.0610100	−	0.105672i	−0.894917	+	0.446232i	$0.852765\pi$
$60$		0			0
$61$	5.79150	−	10.0312i	0.741526	−	1.28436i	−0.210274	−	0.977642i	$-0.567436\pi$
$61$	5.79150	−	10.0312i	0.741526	−	1.28436i	0.951800	−	0.306718i	$-0.0992309\pi$
$62$		0			0
$63$			2.64575i			0.333333i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−6.87386	+	3.96863i	−0.839776	+	0.484845i	−0.857188	−	0.515003i	$-0.827791\pi$
$67$	−6.87386	+	3.96863i	−0.839776	+	0.484845i	0.0174120	+	0.999848i	$0.494457\pi$
$68$		0			0
$69$	−2.00000			−0.240772
$70$		0			0
$71$	−7.29150			−0.865342			−0.432671	−	0.901552i	$-0.642429\pi$
$71$	−7.29150			−0.865342			−0.432671	+	0.901552i	$0.642429\pi$
$72$		0			0
$73$	3.71655	−	2.14575i	0.434989	−	0.251141i	−0.266481	−	0.963840i	$-0.585861\pi$
$73$	3.71655	−	2.14575i	0.434989	−	0.251141i	0.701470	+	0.712699i	$0.252527\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−0.811686	−	0.468627i	−0.0925002	−	0.0534050i
$78$		0			0
$79$	−0.677124	+	1.17281i	−0.0761824	+	0.131952i	−0.901600	−	0.432571i	$-0.857606\pi$
$79$	−0.677124	+	1.17281i	−0.0761824	+	0.131952i	0.825417	+	0.564523i	$0.190940\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$		−	1.64575i		−	0.180645i	−0.995913	−	0.0903223i	$-0.971210\pi$
$83$		−	1.64575i		−	0.180645i	0.995913	−	0.0903223i	$-0.0287897\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−2.85052	+	1.64575i	−0.305608	+	0.176443i
$88$		0			0
$89$	3.46863	−	6.00784i	0.367674	−	0.636830i	−0.621528	−	0.783392i	$-0.713488\pi$
$89$	3.46863	−	6.00784i	0.367674	−	0.636830i	0.989201	+	0.146563i	$0.0468210\pi$
$90$		0			0
$91$	−1.32288	−	2.29129i	−0.138675	−	0.240192i
$92$		0			0
$93$	3.46410	+	2.00000i	0.359211	+	0.207390i
$94$		0			0
$95$		0			0
$96$		0			0
$97$		−	3.70850i		−	0.376541i	−0.982117	−	0.188270i	$-0.939712\pi$
$97$		−	3.70850i		−	0.376541i	0.982117	−	0.188270i	$-0.0602881\pi$
$98$		0			0
$99$	0.354249			0.0356033
$100$		0			0
$101$	−2.46863	−	4.27579i	−0.245638	−	0.425457i	0.716673	−	0.697409i	$-0.245664\pi$
$101$	−2.46863	−	4.27579i	−0.245638	−	0.425457i	−0.962311	+	0.271953i	$0.912331\pi$
$102$		0			0
$103$	−0.0543397	−	0.0313730i	−0.00535425	−	0.00309128i	0.497320	−	0.867567i	$-0.334317\pi$
$103$	−0.0543397	−	0.0313730i	−0.00535425	−	0.00309128i	−0.502675	+	0.864476i	$0.667651\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−14.0545	−	8.11438i	−1.35870	−	0.784447i	−0.369252	−	0.929329i	$-0.620386\pi$
$107$	−14.0545	−	8.11438i	−1.35870	−	0.784447i	−0.989449	+	0.144883i	$0.953720\pi$
$108$		0			0
$109$	−5.79150	−	10.0312i	−0.554725	−	0.960812i	−0.997925	−	0.0643895i	$-0.979490\pi$
$109$	−5.79150	−	10.0312i	−0.554725	−	0.960812i	0.443200	−	0.896423i	$-0.353843\pi$
$110$		0			0
$111$	2.29150			0.217500
$112$		0			0
$113$		−	8.58301i		−	0.807421i	−0.914887	−	0.403711i	$-0.867720\pi$
$113$		−	8.58301i		−	0.807421i	0.914887	−	0.403711i	$-0.132280\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	0.866025	+	0.500000i	0.0800641	+	0.0462250i
$118$		0			0
$119$	4.82288	−	8.35347i	0.442112	−	0.765761i
$120$		0			0
$121$	5.43725	−	9.41760i	0.494296	−	0.856145i
$122$		0			0
$123$	4.88936	−	2.82288i	0.440859	−	0.254530i
$124$		0			0
$125$		0			0
$126$		0			0
$127$			1.35425i			0.120170i	0.998193	+	0.0600851i	$0.0191372\pi$
$127$			1.35425i			0.120170i	−0.998193	+	0.0600851i	$0.980863\pi$
$128$		0			0
$129$	−1.64575	−	2.85052i	−0.144900	−	0.250975i
$130$		0			0
$131$	−0.291503	+	0.504897i	−0.0254687	+	0.0441131i	−0.878479	−	0.477781i	$-0.841441\pi$
$131$	−0.291503	+	0.504897i	−0.0254687	+	0.0441131i	0.853010	+	0.521894i	$0.174774\pi$
$132$		0			0
$133$			1.70850i			0.148146i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−1.11847	+	0.645751i	−0.0955577	+	0.0551703i	−0.547017	−	0.837121i	$-0.684237\pi$
$137$	−1.11847	+	0.645751i	−0.0955577	+	0.0551703i	0.451460	+	0.892292i	$0.350903\pi$
$138$		0			0
$139$	−15.9373			−1.35178			−0.675890	−	0.737002i	$-0.736241\pi$
$139$	−15.9373			−1.35178			−0.675890	+	0.737002i	$0.736241\pi$
$140$		0			0
$141$	12.9373			1.08951
$142$		0			0
$143$	−0.306788	+	0.177124i	−0.0256549	+	0.0148119i
$144$		0			0
$145$		0			0
$146$		0			0
$147$			7.00000i			0.577350i
$148$		0			0
$149$	2.46863	−	4.27579i	0.202238	−	0.350286i	−0.747011	−	0.664811i	$-0.768512\pi$
$149$	2.46863	−	4.27579i	0.202238	−	0.350286i	0.949249	+	0.314525i	$0.101845\pi$
$150$		0			0
$151$	5.67712	+	9.83307i	0.461998	+	0.800204i	0.999060	−	0.0433387i	$-0.0137995\pi$
$151$	5.67712	+	9.83307i	0.461998	+	0.800204i	−0.537063	+	0.843542i	$0.680466\pi$
$152$		0			0
$153$			3.64575i			0.294742i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−14.7224	+	8.50000i	−1.17498	+	0.678374i	−0.954847	−	0.297097i	$-0.903982\pi$
$157$	−14.7224	+	8.50000i	−1.17498	+	0.678374i	−0.220131	+	0.975470i	$0.570648\pi$
$158$		0			0
$159$	−3.82288	+	6.62141i	−0.303174	+	0.525112i
$160$		0			0
$161$	−5.29150			−0.417029
$162$		0			0
$163$	14.9205	+	8.61438i	1.16867	+	0.674730i	0.953366	−	0.301818i	$-0.0975933\pi$
$163$	14.9205	+	8.61438i	1.16867	+	0.674730i	0.215301	+	0.976548i	$0.430927\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		−	19.5203i		−	1.51052i	−0.655424	−	0.755262i	$-0.727510\pi$
$167$		−	19.5203i		−	1.51052i	0.655424	−	0.755262i	$-0.272490\pi$
$168$		0			0
$169$	12.0000			0.923077
$170$		0			0
$171$	−0.322876	−	0.559237i	−0.0246909	−	0.0427659i
$172$		0			0
$173$	−17.8254	−	10.2915i	−1.35524	−	0.782448i	−0.366263	−	0.930512i	$-0.619363\pi$
$173$	−17.8254	−	10.2915i	−1.35524	−	0.782448i	−0.988978	+	0.148063i	$0.952696\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	0.811686	+	0.468627i	0.0610100	+	0.0352242i
$178$		0			0
$179$	−11.6458	−	20.1710i	−0.870444	−	1.50765i	−0.861538	−	0.507693i	$-0.830498\pi$
$179$	−11.6458	−	20.1710i	−0.870444	−	1.50765i	−0.00890653	−	0.999960i	$-0.502835\pi$
$180$		0			0
$181$	14.5830			1.08395			0.541973	−	0.840396i	$-0.317677\pi$
$181$	14.5830			1.08395			0.541973	+	0.840396i	$0.317677\pi$
$182$		0			0
$183$			11.5830i			0.856240i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−1.11847	−	0.645751i	−0.0817909	−	0.0472220i
$188$		0			0
$189$	−1.32288	−	2.29129i	−0.0962250	−	0.166667i
$190$		0			0
$191$	−6.76013	+	11.7089i	−0.489146	+	0.847225i	−0.999922	−	0.0124883i	$-0.996025\pi$
$191$	−6.76013	+	11.7089i	−0.489146	+	0.847225i	0.510776	+	0.859714i	$0.329358\pi$
$192$		0			0
$193$	13.8564	−	8.00000i	0.997406	−	0.575853i	0.0899262	−	0.995948i	$-0.471337\pi$
$193$	13.8564	−	8.00000i	0.997406	−	0.575853i	0.907480	+	0.420096i	$0.138004\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			8.70850i			0.620455i	0.950662	+	0.310227i	$0.100405\pi$
$197$			8.70850i			0.620455i	−0.950662	+	0.310227i	$0.899595\pi$
$198$		0			0
$199$	0.322876	+	0.559237i	0.0228880	+	0.0396433i	0.877243	−	0.480047i	$-0.159381\pi$
$199$	0.322876	+	0.559237i	0.0228880	+	0.0396433i	−0.854355	+	0.519691i	$0.826047\pi$
$200$		0			0
$201$	3.96863	−	6.87386i	0.279925	−	0.484845i
$202$		0			0
$203$	−7.54178	+	4.35425i	−0.529329	+	0.305608i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	1.73205	−	1.00000i	0.120386	−	0.0695048i
$208$		0			0
$209$	0.228757			0.0158234
$210$		0			0
$211$	−2.06275			−0.142005			−0.0710026	−	0.997476i	$-0.522620\pi$
$211$	−2.06275			−0.142005			−0.0710026	+	0.997476i	$0.522620\pi$
$212$		0			0
$213$	6.31463	−	3.64575i	0.432671	−	0.249803i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	9.16515	+	5.29150i	0.622171	+	0.359211i
$218$		0			0
$219$	−2.14575	+	3.71655i	−0.144996	+	0.251141i
$220$		0			0
$221$	−1.82288	−	3.15731i	−0.122620	−	0.212384i
$222$		0			0
$223$			13.9373i			0.933308i	0.884440	+	0.466654i	$0.154541\pi$
$223$			13.9373i			0.933308i	−0.884440	+	0.466654i	$0.845459\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	7.54178	−	4.35425i	0.500566	−	0.289002i	−0.228382	−	0.973572i	$-0.573343\pi$
$227$	7.54178	−	4.35425i	0.500566	−	0.289002i	0.728947	+	0.684570i	$0.240010\pi$
$228$		0			0
$229$	−10.1458	+	17.5730i	−0.670450	+	1.16125i	0.307326	+	0.951604i	$0.400566\pi$
$229$	−10.1458	+	17.5730i	−0.670450	+	1.16125i	−0.977777	+	0.209650i	$0.932768\pi$
$230$		0			0
$231$	0.937254			0.0616668
$232$		0			0
$233$	−20.9827	−	12.1144i	−1.37462	−	0.793639i	−0.383118	−	0.923700i	$-0.625150\pi$
$233$	−20.9827	−	12.1144i	−1.37462	−	0.793639i	−0.991506	+	0.130060i	$0.958483\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		−	1.35425i		−	0.0879679i
$238$		0			0
$239$	9.41699			0.609135			0.304567	−	0.952491i	$-0.401488\pi$
$239$	9.41699			0.609135			0.304567	+	0.952491i	$0.401488\pi$
$240$		0			0
$241$	0.145751	+	0.252449i	0.00938867	+	0.0162616i	0.870682	−	0.491847i	$-0.163678\pi$
$241$	0.145751	+	0.252449i	0.00938867	+	0.0162616i	−0.861293	+	0.508109i	$0.830345\pi$
$242$		0			0
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	0.559237	+	0.322876i	0.0355834	+	0.0205441i
$248$		0			0
$249$	0.822876	+	1.42526i	0.0521476	+	0.0903223i
$250$		0			0
$251$	−28.8118			−1.81858			−0.909291	−	0.416161i	$-0.863375\pi$
$251$	−28.8118			−1.81858			−0.909291	+	0.416161i	$0.863375\pi$
$252$		0			0
$253$			0.708497i			0.0445428i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−15.2817	−	8.82288i	−0.953244	−	0.550356i	−0.0591571	−	0.998249i	$-0.518841\pi$
$257$	−15.2817	−	8.82288i	−0.953244	−	0.550356i	−0.894087	+	0.447893i	$0.852175\pi$
$258$		0			0
$259$	6.06275			0.376721
$260$		0			0
$261$	1.64575	−	2.85052i	0.101869	−	0.176443i
$262$		0			0
$263$	20.7846	−	12.0000i	1.28163	−	0.739952i	0.304487	−	0.952517i	$-0.401515\pi$
$263$	20.7846	−	12.0000i	1.28163	−	0.739952i	0.977147	+	0.212565i	$0.0681817\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$			6.93725i			0.424553i
$268$		0			0
$269$	10.1144	+	17.5186i	0.616685	+	1.06813i	0.990086	+	0.140459i	$0.0448579\pi$
$269$	10.1144	+	17.5186i	0.616685	+	1.06813i	−0.373402	+	0.927670i	$0.621809\pi$
$270$		0			0
$271$	1.35425	−	2.34563i	0.0822647	−	0.142487i	−0.821958	−	0.569549i	$-0.807118\pi$
$271$	1.35425	−	2.34563i	0.0822647	−	0.142487i	0.904222	+	0.427062i	$0.140451\pi$
$272$		0			0
$273$	2.29129	+	1.32288i	0.138675	+	0.0800641i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	21.6506	−	12.5000i	1.30086	−	0.751052i	0.320309	−	0.947313i	$-0.396213\pi$
$277$	21.6506	−	12.5000i	1.30086	−	0.751052i	0.980552	+	0.196261i	$0.0628800\pi$
$278$		0			0
$279$	−4.00000			−0.239474
$280$		0			0
$281$	−22.2288			−1.32606			−0.663028	−	0.748594i	$-0.730729\pi$
$281$	−22.2288			−1.32606			−0.663028	+	0.748594i	$0.730729\pi$
$282$		0			0
$283$	−5.64671	+	3.26013i	−0.335662	+	0.193795i	−0.658352	−	0.752710i	$-0.728746\pi$
$283$	−5.64671	+	3.26013i	−0.335662	+	0.193795i	0.322690	+	0.946505i	$0.395413\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	12.9360	−	7.46863i	0.763590	−	0.440859i
$288$		0			0
$289$	−1.85425	+	3.21165i	−0.109073	+	0.188921i
$290$		0			0
$291$	1.85425	+	3.21165i	0.108698	+	0.188270i
$292$		0			0
$293$		−	9.87451i		−	0.576875i	−0.957499	−	0.288437i	$-0.906864\pi$
$293$		−	9.87451i		−	0.576875i	0.957499	−	0.288437i	$-0.0931357\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−0.306788	+	0.177124i	−0.0178017	+	0.0102778i
$298$		0			0
$299$	−1.00000	+	1.73205i	−0.0578315	+	0.100167i
$300$		0			0
$301$	−4.35425	−	7.54178i	−0.250975	−	0.434701i
$302$		0			0
$303$	4.27579	+	2.46863i	0.245638	+	0.141819i
$304$		0			0
$305$		0			0
$306$		0			0
$307$			1.87451i			0.106984i	0.998568	+	0.0534919i	$0.0170351\pi$
$307$			1.87451i			0.106984i	−0.998568	+	0.0534919i	$0.982965\pi$
$308$		0			0
$309$	0.0627461			0.00356950
$310$		0			0
$311$	6.64575	+	11.5108i	0.376846	+	0.652716i	0.990601	−	0.136780i	$-0.0436753\pi$
$311$	6.64575	+	11.5108i	0.376846	+	0.652716i	−0.613755	+	0.789496i	$0.710342\pi$
$312$		0			0
$313$	−16.7069	−	9.64575i	−0.944332	−	0.545210i	−0.0530161	−	0.998594i	$-0.516883\pi$
$313$	−16.7069	−	9.64575i	−0.944332	−	0.545210i	−0.891316	+	0.453384i	$0.850217\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	7.43310	+	4.29150i	0.417485	+	0.241035i	0.694000	−	0.719975i	$-0.255847\pi$
$317$	7.43310	+	4.29150i	0.417485	+	0.241035i	−0.276516	+	0.961009i	$0.589180\pi$
$318$		0			0
$319$	0.583005	+	1.00979i	0.0326420	+	0.0565376i
$320$		0			0
$321$	16.2288			0.905801
$322$		0			0
$323$			2.35425i			0.130994i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	10.0312	+	5.79150i	0.554725	+	0.320271i
$328$		0			0
$329$	34.2288			1.88709
$330$		0			0
$331$	1.67712	−	2.90486i	0.0921831	−	0.159666i	−0.816246	−	0.577704i	$-0.803949\pi$
$331$	1.67712	−	2.90486i	0.0921831	−	0.159666i	0.908429	+	0.418038i	$0.137282\pi$
$332$		0			0
$333$	−1.98450	+	1.14575i	−0.108750	+	0.0627868i
$334$		0			0
$335$		0			0
$336$		0			0
$337$			19.2915i			1.05088i	0.850832	+	0.525438i	$0.176098\pi$
$337$			19.2915i			1.05088i	−0.850832	+	0.525438i	$0.823902\pi$
$338$		0			0
$339$	4.29150	+	7.43310i	0.233082	+	0.403711i
$340$		0			0
$341$	0.708497	−	1.22715i	0.0383673	−	0.0664541i
$342$		0			0
$343$			18.5203i			1.00000i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	9.97684	−	5.76013i	0.535585	−	0.309220i	−0.207703	−	0.978192i	$-0.566599\pi$
$347$	9.97684	−	5.76013i	0.535585	−	0.309220i	0.743288	+	0.668972i	$0.233265\pi$
$348$		0			0
$349$	−4.70850			−0.252040			−0.126020	−	0.992028i	$-0.540220\pi$
$349$	−4.70850			−0.252040			−0.126020	+	0.992028i	$0.540220\pi$
$350$		0			0
$351$	−1.00000			−0.0533761
$352$		0			0
$353$	−14.6681	+	8.46863i	−0.780704	+	0.450740i	−0.836680	−	0.547693i	$-0.815506\pi$
$353$	−14.6681	+	8.46863i	−0.780704	+	0.450740i	0.0559759	+	0.998432i	$0.482173\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$			9.64575i			0.510507i
$358$		0			0
$359$	−12.4686	+	21.5963i	−0.658069	+	1.13981i	0.323046	+	0.946383i	$0.395293\pi$
$359$	−12.4686	+	21.5963i	−0.658069	+	1.13981i	−0.981115	+	0.193426i	$0.938040\pi$
$360$		0			0
$361$	9.29150	+	16.0934i	0.489026	+	0.847019i
$362$		0			0
$363$			10.8745i			0.570764i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	10.2836	−	5.93725i	0.536801	−	0.309922i	−0.206981	−	0.978345i	$-0.566364\pi$
$367$	10.2836	−	5.93725i	0.536801	−	0.309922i	0.743781	+	0.668423i	$0.233030\pi$
$368$		0			0
$369$	−2.82288	+	4.88936i	−0.146953	+	0.254530i
$370$		0			0
$371$	−10.1144	+	17.5186i	−0.525112	+	0.909521i
$372$		0			0
$373$	−20.4235	−	11.7915i	−1.05749	−	0.610541i	−0.132752	−	0.991149i	$-0.542381\pi$
$373$	−20.4235	−	11.7915i	−1.05749	−	0.610541i	−0.924736	+	0.380608i	$0.875715\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			3.29150i			0.169521i
$378$		0			0
$379$	15.3542			0.788695			0.394347	−	0.918961i	$-0.370971\pi$
$379$	15.3542			0.788695			0.394347	+	0.918961i	$0.370971\pi$
$380$		0			0
$381$	−0.677124	−	1.17281i	−0.0346901	−	0.0600851i
$382$		0			0
$383$	−8.04668	−	4.64575i	−0.411166	−	0.237387i	0.280125	−	0.959964i	$-0.409624\pi$
$383$	−8.04668	−	4.64575i	−0.411166	−	0.237387i	−0.691291	+	0.722577i	$0.742958\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	2.85052	+	1.64575i	0.144900	+	0.0836582i
$388$		0			0
$389$	−0.239870	−	0.415468i	−0.0121619	−	0.0210651i	0.859880	−	0.510496i	$-0.170538\pi$
$389$	−0.239870	−	0.415468i	−0.0121619	−	0.0210651i	−0.872042	+	0.489430i	$0.837205\pi$
$390$		0			0
$391$	−7.29150			−0.368747
$392$		0			0
$393$		−	0.583005i		−	0.0294087i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	17.7167	+	10.2288i	0.889177	+	0.513367i	0.873673	−	0.486513i	$-0.161731\pi$
$397$	17.7167	+	10.2288i	0.889177	+	0.513367i	0.0155038	+	0.999880i	$0.495065\pi$
$398$		0			0
$399$	−0.854249	−	1.47960i	−0.0427659	−	0.0740728i
$400$		0			0
$401$	−17.7601	+	30.7614i	−0.886899	+	1.53615i	−0.0433765	+	0.999059i	$0.513812\pi$
$401$	−17.7601	+	30.7614i	−0.886899	+	1.53615i	−0.843522	+	0.537095i	$0.819522\pi$
$402$		0			0
$403$	3.46410	−	2.00000i	0.172559	−	0.0996271i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		−	0.811762i		−	0.0402375i
$408$		0			0
$409$	3.79150	+	6.56708i	0.187478	+	0.324721i	0.944409	−	0.328774i	$-0.106635\pi$
$409$	3.79150	+	6.56708i	0.187478	+	0.324721i	−0.756931	+	0.653495i	$0.773302\pi$
$410$		0			0
$411$	0.645751	−	1.11847i	0.0318526	−	0.0551703i
$412$		0			0
$413$	2.14752	+	1.23987i	0.105672	+	0.0610100i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	13.8021	−	7.96863i	0.675890	−	0.390225i
$418$		0			0
$419$	−31.6458			−1.54600			−0.772998	−	0.634408i	$-0.781244\pi$
$419$	−31.6458			−1.54600			−0.772998	+	0.634408i	$0.781244\pi$
$420$		0			0
$421$	28.8745			1.40726			0.703629	−	0.710568i	$-0.251562\pi$
$421$	28.8745			1.40726			0.703629	+	0.710568i	$0.251562\pi$
$422$		0			0
$423$	−11.2040	+	6.46863i	−0.544757	+	0.314515i
$424$		0			0
$425$		0			0
$426$		0			0
$427$			30.6458i			1.48305i
$428$		0			0
$429$	0.177124	−	0.306788i	0.00855164	−	0.0148119i
$430$		0			0
$431$	13.9373	+	24.1400i	0.671334	+	1.16278i	0.977526	+	0.210815i	$0.0676117\pi$
$431$	13.9373	+	24.1400i	0.671334	+	1.16278i	−0.306192	+	0.951970i	$0.599055\pi$
$432$		0			0
$433$		−	3.29150i		−	0.158180i	−0.996867	−	0.0790898i	$-0.974799\pi$
$433$		−	3.29150i		−	0.158180i	0.996867	−	0.0790898i	$-0.0252014\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	1.11847	−	0.645751i	0.0535039	−	0.0308905i
$438$		0			0
$439$	−19.9059	+	34.4780i	−0.950056	+	1.64555i	−0.204759	+	0.978812i	$0.565641\pi$
$439$	−19.9059	+	34.4780i	−0.950056	+	1.64555i	−0.745297	+	0.666733i	$0.767692\pi$
$440$		0			0
$441$	−3.50000	−	6.06218i	−0.166667	−	0.288675i
$442$		0			0
$443$	5.80973	+	3.35425i	0.276029	+	0.159365i	0.631624	−	0.775275i	$-0.282389\pi$
$443$	5.80973	+	3.35425i	0.276029	+	0.159365i	−0.355596	+	0.934640i	$0.615722\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$			4.93725i			0.233524i
$448$		0			0
$449$	32.1033			1.51505			0.757523	−	0.652808i	$-0.226409\pi$
$449$	32.1033			1.51505			0.757523	+	0.652808i	$0.226409\pi$
$450$		0			0
$451$	−1.00000	−	1.73205i	−0.0470882	−	0.0815591i
$452$		0			0
$453$	−9.83307	−	5.67712i	−0.461998	−	0.266735i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	7.07197	+	4.08301i	0.330813	+	0.190995i	0.656202	−	0.754585i	$-0.272162\pi$
$457$	7.07197	+	4.08301i	0.330813	+	0.190995i	−0.325389	+	0.945580i	$0.605495\pi$
$458$		0			0
$459$	−1.82288	−	3.15731i	−0.0850845	−	0.147371i
$460$		0			0
$461$	10.7085			0.498744			0.249372	−	0.968408i	$-0.419776\pi$
$461$	10.7085			0.498744			0.249372	+	0.968408i	$0.419776\pi$
$462$		0			0
$463$			33.9373i			1.57720i	0.614908	+	0.788599i	$0.289193\pi$
$463$			33.9373i			1.57720i	−0.614908	+	0.788599i	$0.710807\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−19.6661	−	11.3542i	−0.910040	−	0.525412i	−0.0295961	−	0.999562i	$-0.509422\pi$
$467$	−19.6661	−	11.3542i	−0.910040	−	0.525412i	−0.880444	+	0.474150i	$0.842755\pi$
$468$		0			0
$469$	10.5000	−	18.1865i	0.484845	−	0.839776i
$470$		0			0
$471$	8.50000	−	14.7224i	0.391659	−	0.678374i
$472$		0			0
$473$	−1.00979	+	0.583005i	−0.0464304	+	0.0268066i
$474$		0			0
$475$		0			0
$476$		0			0
$477$		−	7.64575i		−	0.350075i
$478$		0			0
$479$	12.8229	+	22.2099i	0.585892	+	1.01479i	0.994764	+	0.102203i	$0.0325891\pi$
$479$	12.8229	+	22.2099i	0.585892	+	1.01479i	−0.408871	+	0.912592i	$0.634078\pi$
$480$		0			0
$481$	1.14575	−	1.98450i	0.0522418	−	0.0904854i
$482$		0			0
$483$	4.58258	−	2.64575i	0.208514	−	0.120386i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	35.0372	−	20.2288i	1.58769	−	0.916652i	0.594002	−	0.804464i	$-0.297547\pi$
$487$	35.0372	−	20.2288i	1.58769	−	0.916652i	0.993687	−	0.112189i	$-0.0357861\pi$
$488$		0			0
$489$	−17.2288			−0.779111
$490$		0			0
$491$	−34.4575			−1.55505			−0.777523	−	0.628855i	$-0.783524\pi$
$491$	−34.4575			−1.55505			−0.777523	+	0.628855i	$0.783524\pi$
$492$		0			0
$493$	−10.3923	+	6.00000i	−0.468046	+	0.270226i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	16.7069	−	9.64575i	0.749408	−	0.432671i
$498$		0			0
$499$	−9.90588	+	17.1575i	−0.443448	+	0.768075i	−0.997943	−	0.0641127i	$-0.979578\pi$
$499$	−9.90588	+	17.1575i	−0.443448	+	0.768075i	0.554495	+	0.832187i	$0.312912\pi$
$500$		0			0
$501$	9.76013	+	16.9050i	0.436050	+	0.755262i
$502$		0			0
$503$		−	16.7085i		−	0.744995i	−0.928033	−	0.372498i	$-0.878502\pi$
$503$		−	16.7085i		−	0.744995i	0.928033	−	0.372498i	$-0.121498\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−10.3923	+	6.00000i	−0.461538	+	0.266469i
$508$		0			0
$509$	−12.9373	+	22.4080i	−0.573434	+	0.993216i	0.422776	+	0.906234i	$0.361056\pi$
$509$	−12.9373	+	22.4080i	−0.573434	+	0.993216i	−0.996210	+	0.0869822i	$0.972278\pi$
$510$		0			0
$511$	−5.67712	+	9.83307i	−0.251141	+	0.434989i
$512$		0			0
$513$	0.559237	+	0.322876i	0.0246909	+	0.0142553i
$514$		0			0
$515$		0			0
$516$		0			0
$517$		−	4.58301i		−	0.201560i
$518$		0			0
$519$	20.5830			0.903494
$520$		0			0
$521$	7.93725	+	13.7477i	0.347737	+	0.602299i	0.985847	−	0.167647i	$-0.0536167\pi$
$521$	7.93725	+	13.7477i	0.347737	+	0.602299i	−0.638110	+	0.769945i	$0.720283\pi$
$522$		0			0
$523$	−8.76893	−	5.06275i	−0.383439	−	0.221378i	0.295875	−	0.955227i	$-0.404389\pi$
$523$	−8.76893	−	5.06275i	−0.383439	−	0.221378i	−0.679313	+	0.733848i	$0.737722\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	12.6293	+	7.29150i	0.550139	+	0.317623i
$528$		0			0
$529$	−9.50000	−	16.4545i	−0.413043	−	0.715412i
$530$		0			0
$531$	−0.937254			−0.0406734
$532$		0			0
$533$		−	5.64575i		−	0.244545i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	20.1710	+	11.6458i	0.870444	+	0.502551i
$538$		0			0
$539$	2.47974			0.106810
$540$		0			0
$541$	−13.4373	+	23.2740i	−0.577713	+	1.00063i	0.418028	+	0.908434i	$0.362721\pi$
$541$	−13.4373	+	23.2740i	−0.577713	+	1.00063i	−0.995741	+	0.0921937i	$0.970612\pi$
$542$		0			0
$543$	−12.6293	+	7.29150i	−0.541973	+	0.312908i
$544$		0			0
$545$		0			0
$546$		0			0
$547$		−	0.125492i		−	0.00536566i	−0.999996	−	0.00268283i	$-0.999146\pi$
$547$		−	0.125492i		−	0.00536566i	0.999996	−	0.00268283i	$-0.000853972\pi$
$548$		0			0
$549$	−5.79150	−	10.0312i	−0.247175	−	0.428120i
$550$		0			0
$551$	1.06275	−	1.84073i	0.0452745	−	0.0784177i
$552$		0			0
$553$		−	3.58301i		−	0.152365i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	14.4700	−	8.35425i	0.613113	−	0.353981i	−0.161070	−	0.986943i	$-0.551494\pi$
$557$	14.4700	−	8.35425i	0.613113	−	0.353981i	0.774183	+	0.632962i	$0.218161\pi$
$558$		0			0
$559$	−3.29150			−0.139216
$560$		0			0
$561$	1.29150			0.0545273
$562$		0			0
$563$	4.78068	−	2.76013i	0.201482	−	0.116326i	−0.395865	−	0.918309i	$-0.629555\pi$
$563$	4.78068	−	2.76013i	0.201482	−	0.116326i	0.597346	+	0.801983i	$0.296222\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	2.29129	+	1.32288i	0.0962250	+	0.0555556i
$568$		0			0
$569$	2.46863	−	4.27579i	0.103490	−	0.179250i	−0.809630	−	0.586940i	$-0.800332\pi$
$569$	2.46863	−	4.27579i	0.103490	−	0.179250i	0.913120	+	0.407690i	$0.133666\pi$
$570$		0			0
$571$	−2.96863	−	5.14181i	−0.124233	−	0.215178i	0.797200	−	0.603716i	$-0.206314\pi$
$571$	−2.96863	−	5.14181i	−0.124233	−	0.215178i	−0.921433	+	0.388537i	$0.872980\pi$
$572$		0			0
$573$		−	13.5203i		−	0.564817i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	3.96900	−	2.29150i	0.165232	−	0.0953965i	−0.415104	−	0.909774i	$-0.636255\pi$
$577$	3.96900	−	2.29150i	0.165232	−	0.0953965i	0.580335	+	0.814378i	$0.302921\pi$
$578$		0			0
$579$	−8.00000	+	13.8564i	−0.332469	+	0.575853i
$580$		0			0
$581$	2.17712	+	3.77089i	0.0903223	+	0.156443i
$582$		0			0
$583$	2.34563	+	1.35425i	0.0971460	+	0.0560872i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		−	6.00000i		−	0.247647i	−0.992304	−	0.123823i	$-0.960484\pi$
$587$		−	6.00000i		−	0.247647i	0.992304	−	0.123823i	$-0.0395156\pi$
$588$		0			0
$589$	−2.58301			−0.106431
$590$		0			0
$591$	−4.35425	−	7.54178i	−0.179110	−	0.310227i
$592$		0			0
$593$	−0.504897	−	0.291503i	−0.0207336	−	0.0119706i	0.489597	−	0.871949i	$-0.337144\pi$
$593$	−0.504897	−	0.291503i	−0.0207336	−	0.0119706i	−0.510331	+	0.859978i	$0.670477\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−0.559237	−	0.322876i	−0.0228880	−	0.0132144i
$598$		0			0
$599$	−16.4686	−	28.5245i	−0.672890	−	1.16548i	−0.977081	−	0.212868i	$-0.931719\pi$
$599$	−16.4686	−	28.5245i	−0.672890	−	1.16548i	0.304191	−	0.952611i	$-0.401614\pi$
$600$		0			0
$601$	14.2915			0.582963			0.291481	−	0.956577i	$-0.405852\pi$
$601$	14.2915			0.582963			0.291481	+	0.956577i	$0.405852\pi$
$602$		0			0
$603$			7.93725i			0.323230i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−14.4156	−	8.32288i	−0.585113	−	0.337815i	0.178050	−	0.984021i	$-0.443021\pi$
$607$	−14.4156	−	8.32288i	−0.585113	−	0.337815i	−0.763163	+	0.646206i	$0.776355\pi$
$608$		0			0
$609$	4.35425	−	7.54178i	0.176443	−	0.305608i
$610$		0			0
$611$	6.46863	−	11.2040i	0.261693	−	0.453265i
$612$		0			0
$613$	30.5633	−	17.6458i	1.23444	−	0.712705i	0.266489	−	0.963838i	$-0.414136\pi$
$613$	30.5633	−	17.6458i	1.23444	−	0.712705i	0.967953	+	0.251133i	$0.0808031\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$			41.8745i			1.68580i	0.538067	+	0.842902i	$0.319155\pi$
$617$			41.8745i			1.68580i	−0.538067	+	0.842902i	$0.680845\pi$
$618$		0			0
$619$	12.3542	+	21.3982i	0.496559	+	0.860066i	0.999992	−	0.00396857i	$-0.00126324\pi$
$619$	12.3542	+	21.3982i	0.496559	+	0.860066i	−0.503433	+	0.864034i	$0.667930\pi$
$620$		0			0
$621$	−1.00000	+	1.73205i	−0.0401286	+	0.0695048i
$622$		0			0
$623$			18.3542i			0.735347i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−0.198109	+	0.114378i	−0.00791171	+	0.00456783i
$628$		0			0
$629$	8.35425			0.333106
$630$		0			0
$631$	−1.35425			−0.0539118			−0.0269559	−	0.999637i	$-0.508581\pi$
$631$	−1.35425			−0.0539118			−0.0269559	+	0.999637i	$0.508581\pi$
$632$		0			0
$633$	1.78639	−	1.03137i	0.0710026	−	0.0409934i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	6.06218	+	3.50000i	0.240192	+	0.138675i
$638$		0			0
$639$	−3.64575	+	6.31463i	−0.144224	+	0.249803i
$640$		0			0
$641$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$641$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$642$		0			0
$643$		−	27.3542i		−	1.07875i	−0.842067	−	0.539373i	$-0.818661\pi$
$643$		−	27.3542i		−	1.07875i	0.842067	−	0.539373i	$-0.181339\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	43.8956	−	25.3431i	1.72571	−	0.996341i	0.820126	−	0.572183i	$-0.193903\pi$
$647$	43.8956	−	25.3431i	1.72571	−	0.996341i	0.905588	−	0.424159i	$-0.139430\pi$
$648$		0			0
$649$	0.166010	−	0.287539i	0.00651648	−	0.0112869i
$650$		0			0
$651$	−10.5830			−0.414781
$652$		0			0
$653$	−14.0545	−	8.11438i	−0.549996	−	0.317540i	0.199125	−	0.979974i	$-0.436190\pi$
$653$	−14.0545	−	8.11438i	−0.549996	−	0.317540i	−0.749120	+	0.662434i	$0.769523\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		−	4.29150i		−	0.167427i
$658$		0			0
$659$	−40.1033			−1.56220			−0.781101	−	0.624405i	$-0.785341\pi$
$659$	−40.1033			−1.56220			−0.781101	+	0.624405i	$0.785341\pi$
$660$		0			0
$661$	−0.854249	−	1.47960i	−0.0332264	−	0.0575499i	0.848934	−	0.528499i	$-0.177245\pi$
$661$	−0.854249	−	1.47960i	−0.0332264	−	0.0575499i	−0.882160	+	0.470949i	$0.843912\pi$
$662$		0			0
$663$	3.15731	+	1.82288i	0.122620	+	0.0707946i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	5.70105	+	3.29150i	0.220746	+	0.127447i
$668$		0			0
$669$	−6.96863	−	12.0700i	−0.269423	−	0.466654i
$670$		0			0
$671$	4.10326			0.158405
$672$		0			0
$673$			2.29150i			0.0883309i	0.999024	+	0.0441655i	$0.0140629\pi$
$673$			2.29150i			0.0883309i	−0.999024	+	0.0441655i	$0.985937\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−33.5225	−	19.3542i	−1.28838	−	0.743844i	−0.310011	−	0.950733i	$-0.600333\pi$
$677$	−33.5225	−	19.3542i	−1.28838	−	0.743844i	−0.978365	+	0.206889i	$0.933666\pi$
$678$		0			0
$679$	4.90588	+	8.49723i	0.188270	+	0.326094i
$680$		0			0
$681$	−4.35425	+	7.54178i	−0.166855	+	0.289002i
$682$		0			0
$683$	17.4099	−	10.0516i	0.666173	−	0.384615i	−0.128452	−	0.991716i	$-0.541001\pi$
$683$	17.4099	−	10.0516i	0.666173	−	0.384615i	0.794625	+	0.607101i	$0.207668\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$		−	20.2915i		−	0.774169i
$688$		0			0
$689$	3.82288	+	6.62141i	0.145640	+	0.252256i
$690$		0			0
$691$	−7.61438	+	13.1885i	−0.289665	+	0.501714i	−0.973730	−	0.227707i	$-0.926877\pi$
$691$	−7.61438	+	13.1885i	−0.289665	+	0.501714i	0.684065	+	0.729421i	$0.260210\pi$
$692$		0			0
$693$	−0.811686	+	0.468627i	−0.0308334	+	0.0178017i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	17.8254	−	10.2915i	0.675185	−	0.389818i
$698$		0			0
$699$	24.2288			0.916416
$700$		0			0
$701$	−25.0627			−0.946607			−0.473303	−	0.880899i	$-0.656939\pi$
$701$	−25.0627			−0.946607			−0.473303	+	0.880899i	$0.656939\pi$
$702$		0			0
$703$	−1.28149	+	0.739870i	−0.0483324	+	0.0279047i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	11.3127	+	6.53137i	0.425457	+	0.245638i
$708$		0			0
$709$	−3.08301	+	5.33992i	−0.115785	+	0.200545i	−0.918093	−	0.396365i	$-0.870272\pi$
$709$	−3.08301	+	5.33992i	−0.115785	+	0.200545i	0.802308	+	0.596910i	$0.203605\pi$
$710$		0			0
$711$	0.677124	+	1.17281i	0.0253941	+	0.0439840i
$712$		0			0
$713$		−	8.00000i		−	0.299602i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−8.15536	+	4.70850i	−0.304567	+	0.175842i
$718$		0			0
$719$	1.11438	−	1.93016i	0.0415593	−	0.0719828i	−0.844498	−	0.535559i	$-0.820101\pi$
$719$	1.11438	−	1.93016i	0.0415593	−	0.0719828i	0.886057	+	0.463577i	$0.153434\pi$
$720$		0			0
$721$	0.166010			0.00618255
$722$		0			0
$723$	−0.252449	−	0.145751i	−0.00938867	−	0.00542055i
$724$		0			0
$725$		0			0
$726$		0			0
$727$		−	27.1033i		−	1.00520i	−0.864518	−	0.502602i	$-0.832376\pi$
$727$		−	27.1033i		−	1.00520i	0.864518	−	0.502602i	$-0.167624\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	−6.00000	−	10.3923i	−0.221918	−	0.384373i
$732$		0			0
$733$	−27.7479	−	16.0203i	−1.02489	−	0.591722i	−0.109375	−	0.994001i	$-0.534885\pi$
$733$	−27.7479	−	16.0203i	−1.02489	−	0.591722i	−0.915517	+	0.402279i	$0.868218\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−2.43506	−	1.40588i	−0.0896965	−	0.0517863i
$738$		0			0
$739$	−25.2601	−	43.7518i	−0.929209	−	1.60944i	−0.784648	−	0.619941i	$-0.787157\pi$
$739$	−25.2601	−	43.7518i	−0.929209	−	1.60944i	−0.144560	−	0.989496i	$-0.546177\pi$
$740$		0			0
$741$	−0.645751			−0.0237223
$742$		0			0
$743$		−	11.4170i		−	0.418849i	−0.977825	−	0.209424i	$-0.932841\pi$
$743$		−	11.4170i		−	0.418849i	0.977825	−	0.209424i	$-0.0671590\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−1.42526	−	0.822876i	−0.0521476	−	0.0301074i
$748$		0			0
$749$	42.9373			1.56889
$750$		0			0
$751$	16.6771	−	28.8856i	0.608557	−	1.05405i	−0.382922	−	0.923781i	$-0.625082\pi$
$751$	16.6771	−	28.8856i	0.608557	−	1.05405i	0.991478	−	0.130271i	$-0.0415846\pi$
$752$		0			0
$753$	24.9517	−	14.4059i	0.909291	−	0.524979i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		−	11.0000i		−	0.399802i	−0.979816	−	0.199901i	$-0.935938\pi$
$757$		−	11.0000i		−	0.399802i	0.979816	−	0.199901i	$-0.0640620\pi$
$758$		0			0
$759$	−0.354249	−	0.613577i	−0.0128584	−	0.0222714i
$760$		0			0
$761$	22.1771	−	38.4119i	0.803920	−	1.39243i	−0.113098	−	0.993584i	$-0.536077\pi$
$761$	22.1771	−	38.4119i	0.803920	−	1.39243i	0.917018	−	0.398847i	$-0.130589\pi$
$762$		0			0
$763$	26.5400	+	15.3229i	0.960812	+	0.554725i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	0.811686	−	0.468627i	0.0293083	−	0.0169211i
$768$		0			0
$769$	−4.00000			−0.144244			−0.0721218	−	0.997396i	$-0.522977\pi$
$769$	−4.00000			−0.144244			−0.0721218	+	0.997396i	$0.522977\pi$
$770$		0			0
$771$	17.6458			0.635496
$772$		0			0
$773$	−23.0216	+	13.2915i	−0.828028	+	0.478062i	−0.853177	−	0.521622i	$-0.825327\pi$
$773$	−23.0216	+	13.2915i	−0.828028	+	0.478062i	0.0251491	+	0.999684i	$0.491994\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−5.25049	+	3.03137i	−0.188360	+	0.108750i
$778$		0			0
$779$	−1.82288	+	3.15731i	−0.0653113	+	0.113122i
$780$		0			0
$781$	−1.29150	−	2.23695i	−0.0462136	−	0.0800443i
$782$		0			0
$783$			3.29150i			0.117629i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−38.9519	+	22.4889i	−1.38849	+	0.801642i	−0.993145	−	0.116892i	$-0.962707\pi$
$787$	−38.9519	+	22.4889i	−1.38849	+	0.801642i	−0.395340	+	0.918535i	$0.629373\pi$
$788$		0			0
$789$	−12.0000	+	20.7846i	−0.427211	+	0.739952i
$790$		0			0
$791$	11.3542	+	19.6661i	0.403711	+	0.699247i
$792$		0			0
$793$	10.0312	+	5.79150i	0.356218	+	0.205662i
$794$		0			0
$795$		0			0
$796$		0			0
$797$			3.87451i			0.137242i	0.997643	+	0.0686211i	$0.0218599\pi$
$797$			3.87451i			0.137242i	−0.997643	+	0.0686211i	$0.978140\pi$
$798$		0			0
$799$	47.1660			1.66861
$800$		0			0
$801$	−3.46863	−	6.00784i	−0.122558	−	0.212277i
$802$		0			0
$803$	1.31658	+	0.760130i	0.0464612	+	0.0268244i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−17.5186	−	10.1144i	−0.616685	−	0.356043i
$808$		0			0
$809$	−17.3542	−	30.0584i	−0.610143	−	1.05680i	−0.991216	−	0.132254i	$-0.957779\pi$
$809$	−17.3542	−	30.0584i	−0.610143	−	1.05680i	0.381073	−	0.924545i	$-0.375555\pi$
$810$		0			0
$811$	−7.93725			−0.278715			−0.139357	−	0.990242i	$-0.544504\pi$
$811$	−7.93725			−0.278715			−0.139357	+	0.990242i	$0.544504\pi$
$812$		0			0
$813$			2.70850i			0.0949912i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	1.84073	+	1.06275i	0.0643990	+	0.0371808i
$818$		0			0
$819$	−2.64575			−0.0924500
$820$		0			0
$821$	8.69738	−	15.0643i	0.303541	−	0.525748i	−0.673395	−	0.739283i	$-0.735164\pi$
$821$	8.69738	−	15.0643i	0.303541	−	0.525748i	0.976935	+	0.213535i	$0.0684978\pi$
$822$		0			0
$823$	−14.3070	+	8.26013i	−0.498709	+	0.287930i	−0.728180	−	0.685385i	$-0.759634\pi$
$823$	−14.3070	+	8.26013i	−0.498709	+	0.287930i	0.229471	+	0.973315i	$0.426300\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			42.5830i			1.48076i	0.672191	+	0.740378i	$0.265354\pi$
$827$			42.5830i			1.48076i	−0.672191	+	0.740378i	$0.734646\pi$
$828$		0			0
$829$	−19.6660	−	34.0625i	−0.683029	−	1.18304i	−0.974052	−	0.226325i	$-0.927329\pi$
$829$	−19.6660	−	34.0625i	−0.683029	−	1.18304i	0.291023	−	0.956716i	$-0.406004\pi$
$830$		0			0
$831$	−12.5000	+	21.6506i	−0.433620	+	0.751052i
$832$		0			0
$833$			25.5203i			0.884225i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	3.46410	−	2.00000i	0.119737	−	0.0691301i
$838$		0			0
$839$	−19.1660			−0.661684			−0.330842	−	0.943686i	$-0.607333\pi$
$839$	−19.1660			−0.661684			−0.330842	+	0.943686i	$0.607333\pi$
$840$		0			0
$841$	−18.1660			−0.626414
$842$		0			0
$843$	19.2507	−	11.1144i	0.663028	−	0.382800i
$844$		0			0
$845$		0			0
$846$		0			0
$847$			28.7712i			0.988592i
$848$		0			0
$849$	3.26013	−	5.64671i	0.111887	−	0.193795i
$850$		0			0
$851$	−2.29150	−	3.96900i	−0.0785517	−	0.136056i
$852$		0			0
$853$		−	2.00000i		−	0.0684787i	−0.999414	−	0.0342393i	$-0.989099\pi$
$853$		−	2.00000i		−	0.0684787i	0.999414	−	0.0342393i	$-0.0109009\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−23.5265	+	13.5830i	−0.803648	+	0.463987i	−0.844745	−	0.535169i	$-0.820248\pi$
$857$	−23.5265	+	13.5830i	−0.803648	+	0.463987i	0.0410969	+	0.999155i	$0.486915\pi$
$858$		0			0
$859$	−20.5830	+	35.6508i	−0.702283	+	1.21639i	0.265380	+	0.964144i	$0.414503\pi$
$859$	−20.5830	+	35.6508i	−0.702283	+	1.21639i	−0.967663	+	0.252246i	$0.918831\pi$
$860$		0			0
$861$	−7.46863	+	12.9360i	−0.254530	+	0.440859i
$862$		0			0
$863$	5.28558	+	3.05163i	0.179923	+	0.103879i	0.587257	−	0.809401i	$-0.300208\pi$
$863$	5.28558	+	3.05163i	0.179923	+	0.103879i	−0.407333	+	0.913280i	$0.633541\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$		−	3.70850i		−	0.125947i
$868$		0			0
$869$	−0.479741			−0.0162741
$870$		0			0
$871$	−3.96863	−	6.87386i	−0.134472	−	0.232912i
$872$		0			0
$873$	−3.21165	−	1.85425i	−0.108698	−	0.0627568i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−38.7538	−	22.3745i	−1.30862	−	0.755533i	−0.326756	−	0.945109i	$-0.605956\pi$
$877$	−38.7538	−	22.3745i	−1.30862	−	0.755533i	−0.981866	+	0.189575i	$0.939289\pi$
$878$		0			0
$879$	4.93725	+	8.55157i	0.166529	+	0.288437i
$880$		0			0
$881$	44.7085			1.50627			0.753134	−	0.657867i	$-0.228541\pi$
$881$	44.7085			1.50627			0.753134	+	0.657867i	$0.228541\pi$
$882$		0			0
$883$			23.3542i			0.785933i	0.919553	+	0.392967i	$0.128551\pi$
$883$			23.3542i			0.785933i	−0.919553	+	0.392967i	$0.871449\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−35.7595	−	20.6458i	−1.20069	−	0.693216i	−0.239978	−	0.970778i	$-0.577140\pi$
$887$	−35.7595	−	20.6458i	−1.20069	−	0.693216i	−0.960708	+	0.277562i	$0.910474\pi$
$888$		0			0
$889$	−1.79150	−	3.10297i	−0.0600851	−	0.104070i
$890$		0			0
$891$	0.177124	−	0.306788i	0.00593389	−	0.0102778i
$892$		0			0
$893$	−7.23499	+	4.17712i	−0.242110	+	0.139782i
$894$		0			0
$895$		0			0
$896$		0			0
$897$		−	2.00000i		−	0.0667781i
$898$		0			0
$899$	−6.58301	−	11.4021i	−0.219556	−	0.380281i
$900$		0			0
$901$	−13.9373	+	24.1400i	−0.464317	+	0.804221i
$902$		0			0
$903$	7.54178	+	4.35425i	0.250975	+	0.144900i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−26.8275	+	15.4889i	−0.890794	+	0.514300i	−0.874202	−	0.485562i	$-0.838615\pi$
$907$	−26.8275	+	15.4889i	−0.890794	+	0.514300i	−0.0165917	+	0.999862i	$0.505282\pi$
$908$		0			0
$909$	−4.93725			−0.163758
$910$		0			0
$911$	32.3320			1.07121			0.535604	−	0.844469i	$-0.320084\pi$
$911$	32.3320			1.07121			0.535604	+	0.844469i	$0.320084\pi$
$912$		0			0
$913$	0.504897	−	0.291503i	0.0167097	−	0.00964733i
$914$		0			0
$915$		0			0
$916$		0			0
$917$		−	1.54249i		−	0.0509374i
$918$		0			0
$919$	24.4575	−	42.3617i	0.806779	−	1.39738i	−0.108305	−	0.994118i	$-0.534542\pi$
$919$	24.4575	−	42.3617i	0.806779	−	1.39738i	0.915084	−	0.403264i	$-0.132124\pi$
$920$		0			0
$921$	−0.937254	−	1.62337i	−0.0308836	−	0.0534919i
$922$		0			0
$923$		−	7.29150i		−	0.240003i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−0.0543397	+	0.0313730i	−0.00178475	+	0.00103043i
$928$		0			0
$929$	1.17712	−	2.03884i	0.0386202	−	0.0668921i	−0.846069	−	0.533073i	$-0.821037\pi$
$929$	1.17712	−	2.03884i	0.0386202	−	0.0668921i	0.884689	+	0.466181i	$0.154370\pi$
$930$		0			0
$931$	−2.26013	−	3.91466i	−0.0740728	−	0.128298i
$932$		0			0
$933$	−11.5108	−	6.64575i	−0.376846	−	0.217572i
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		1.00000			$0$
$937$		0			0		−1.00000			$\pi$
$938$		0			0
$939$	19.2915			0.629554
$940$		0			0
$941$	−6.87451	−	11.9070i	−0.224103	−	0.388157i	0.731947	−	0.681361i	$-0.238612\pi$
$941$	−6.87451	−	11.9070i	−0.224103	−	0.388157i	−0.956050	+	0.293204i	$0.905278\pi$
$942$		0			0
$943$	−9.77873	−	5.64575i	−0.318439	−	0.183851i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	23.1302	+	13.3542i	0.751632	+	0.433955i	0.826283	−	0.563255i	$-0.190451\pi$
$947$	23.1302	+	13.3542i	0.751632	+	0.433955i	−0.0746515	+	0.997210i	$0.523784\pi$
$948$		0			0
$949$	2.14575	+	3.71655i	0.0696540	+	0.120644i
$950$		0			0
$951$	−8.58301			−0.278323
$952$		0			0
$953$			47.5203i			1.53933i	0.638447	+	0.769666i	$0.279577\pi$
$953$			47.5203i			1.53933i	−0.638447	+	0.769666i	$0.720423\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−1.00979	−	0.583005i	−0.0326420	−	0.0188459i
$958$		0			0
$959$	1.70850	−	2.95920i	0.0551703	−	0.0955577i
$960$		0			0
$961$	7.50000	−	12.9904i	0.241935	−	0.419045i
$962$		0			0
$963$	−14.0545	+	8.11438i	−0.452900	+	0.261482i
$964$		0			0
$965$		0			0
$966$		0			0
$967$		−	29.9373i		−	0.962717i	−0.876524	−	0.481359i	$-0.840143\pi$
$967$		−	29.9373i		−	0.962717i	0.876524	−	0.481359i	$-0.159857\pi$
$968$		0			0
$969$	−1.17712	−	2.03884i	−0.0378147	−	0.0654970i
$970$		0			0
$971$	26.2804	−	45.5190i	0.843378	−	1.46077i	−0.0436447	−	0.999047i	$-0.513897\pi$
$971$	26.2804	−	45.5190i	0.843378	−	1.46077i	0.887023	−	0.461726i	$-0.152770\pi$
$972$		0			0
$973$	36.5168	−	21.0830i	1.17068	−	0.675890i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−21.3789	+	12.3431i	−0.683973	+	0.394892i	−0.801350	−	0.598196i	$-0.795885\pi$
$977$	−21.3789	+	12.3431i	−0.683973	+	0.394892i	0.117377	+	0.993087i	$0.462551\pi$
$978$		0			0
$979$	2.45751			0.0785425
$980$		0			0
$981$	−11.5830			−0.369817
$982$		0			0
$983$	−4.88936	+	2.82288i	−0.155946	+	0.0900358i	−0.575943	−	0.817490i	$-0.695365\pi$
$983$	−4.88936	+	2.82288i	−0.155946	+	0.0900358i	0.419996	+	0.907526i	$0.362031\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−29.6430	+	17.1144i	−0.943546	+	0.544757i
$988$		0			0
$989$	−3.29150	+	5.70105i	−0.104664	+	0.181283i
$990$		0			0
$991$	11.9373	+	20.6759i	0.379199	+	0.656793i	0.990946	−	0.134261i	$-0.0428661\pi$
$991$	11.9373	+	20.6759i	0.379199	+	0.656793i	−0.611747	+	0.791054i	$0.709533\pi$
$992$		0			0
$993$			3.35425i			0.106444i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−42.2179	+	24.3745i	−1.33705	+	0.771948i	−0.986370	−	0.164545i	$-0.947384\pi$
$997$	−42.2179	+	24.3745i	−1.33705	+	0.771948i	−0.350684	+	0.936494i	$0.614051\pi$
$998$		0			0
$999$	1.14575	−	1.98450i	0.0362500	−	0.0627868i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2100.2.bc.h.1549.1		8
5.2	odd	4		2100.2.q.i.1801.1	yes	4
5.3	odd	4		2100.2.q.g.1801.2	yes	4
5.4	even	2	inner	2100.2.bc.h.1549.4		8
7.4	even	3	inner	2100.2.bc.h.949.4		8
35.4	even	6	inner	2100.2.bc.h.949.1		8
35.18	odd	12		2100.2.q.g.1201.2	✓	4
35.32	odd	12		2100.2.q.i.1201.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2100.2.q.g.1201.2	✓	4	35.18	odd	12
2100.2.q.g.1801.2	yes	4	5.3	odd	4
2100.2.q.i.1201.1	yes	4	35.32	odd	12
2100.2.q.i.1801.1	yes	4	5.2	odd	4
2100.2.bc.h.949.1		8	35.4	even	6	inner
2100.2.bc.h.949.4		8	7.4	even	3	inner
2100.2.bc.h.1549.1		8	1.1	even	1	trivial
2100.2.bc.h.1549.4		8	5.4	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{3} +(-2.29129 + 1.32288i) q^{7} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{3} +(-2.29129 + 1.32288i) q^{7} +(0.500000 - 0.866025i) q^{9} +(0.177124 + 0.306788i) q^{11} +1.00000i q^{13} +(-3.15731 + 1.82288i) q^{17} +(0.322876 - 0.559237i) q^{19} +(1.32288 - 2.29129i) q^{21} +(1.73205 + 1.00000i) q^{23} +1.00000i q^{27} +3.29150 q^{29} +(-2.00000 - 3.46410i) q^{31} +(-0.306788 - 0.177124i) q^{33} +(-1.98450 - 1.14575i) q^{37} +(-0.500000 - 0.866025i) q^{39} -5.64575 q^{41} +3.29150i q^{43} +(-11.2040 - 6.46863i) q^{47} +(3.50000 - 6.06218i) q^{49} +(1.82288 - 3.15731i) q^{51} +(6.62141 - 3.82288i) q^{53} +0.645751i q^{57} +(-0.468627 - 0.811686i) q^{59} +(5.79150 - 10.0312i) q^{61} +2.64575i q^{63} +(-6.87386 + 3.96863i) q^{67} -2.00000 q^{69} -7.29150 q^{71} +(3.71655 - 2.14575i) q^{73} +(-0.811686 - 0.468627i) q^{77} +(-0.677124 + 1.17281i) q^{79} +(-0.500000 - 0.866025i) q^{81} -1.64575i q^{83} +(-2.85052 + 1.64575i) q^{87} +(3.46863 - 6.00784i) q^{89} +(-1.32288 - 2.29129i) q^{91} +(3.46410 + 2.00000i) q^{93} -3.70850i q^{97} +0.354249 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{9}+O(q^{10}) \) 8 * q + 4 * q^9	\( 8 q + 4 q^{9} + 12 q^{11} - 8 q^{19} - 16 q^{29} - 16 q^{31} - 4 q^{39} - 24 q^{41} + 28 q^{49} + 4 q^{51} + 28 q^{59} + 4 q^{61} - 16 q^{69} - 16 q^{71} - 16 q^{79} - 4 q^{81} - 4 q^{89} + 24 q^{99}+O(q^{100}) \) 8 * q + 4 * q^9 + 12 * q^11 - 8 * q^19 - 16 * q^29 - 16 * q^31 - 4 * q^39 - 24 * q^41 + 28 * q^49 + 4 * q^51 + 28 * q^59 + 4 * q^61 - 16 * q^69 - 16 * q^71 - 16 * q^79 - 4 * q^81 - 4 * q^89 + 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more