LMFDB - Embedded newform 2100.2.f.e.1049.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2100,2,Mod(1049,2100)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2100, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 1, 1]))

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

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

chi := DirichletCharacter("2100.1049");

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.f (of order $2$, degree $1$, 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:	$4$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 84)
Sato-Tate group:	$\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label			1049.2
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	2100.1049
Dual form			2100.2.f.e.1049.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.73205 q^{3} +(1.73205 + 2.00000i) q^{7} +3.00000 q^{9} +O(q^{10})$	$q-1.73205 q^{3} +(1.73205 + 2.00000i) q^{7} +3.00000 q^{9} +6.92820 q^{13} -3.46410i q^{19} +(-3.00000 - 3.46410i) q^{21} -5.19615 q^{27} -10.3923i q^{31} +10.0000i q^{37} -12.0000 q^{39} +8.00000i q^{43} +(-1.00000 + 6.92820i) q^{49} +6.00000i q^{57} -6.92820i q^{61} +(5.19615 + 6.00000i) q^{63} -16.0000i q^{67} +13.8564 q^{73} +4.00000 q^{79} +9.00000 q^{81} +(12.0000 + 13.8564i) q^{91} +18.0000i q^{93} +13.8564 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 12 q^{9}+O(q^{10}) $ 4 * q + 12 * q^9	$ 4 q + 12 q^{9} - 12 q^{21} - 48 q^{39} - 4 q^{49} + 16 q^{79} + 36 q^{81} + 48 q^{91}+O(q^{100}) $ 4 * q + 12 * q^9 - 12 * q^21 - 48 * q^39 - 4 * q^49 + 16 * q^79 + 36 * q^81 + 48 * q^91

Display 100 coefficients 10 coefficients

Character values

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

$n$	$701$	$1051$	$1177$	$1501$
$\chi(n)$	$-1$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.73205			−1.00000
$3$	−1.73205			−1.00000
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	1.73205	+	2.00000i	0.654654	+	0.755929i
$7$	1.73205	+	2.00000i	0.654654	+	0.755929i
$8$		0			0
$9$	3.00000			1.00000
$10$		0			0
$11$		0			0		1.00000			$0$
$11$		0			0		−1.00000			$\pi$
$12$		0			0
$13$	6.92820			1.92154			0.960769	−	0.277350i	$-0.0894562\pi$
$13$	6.92820			1.92154			0.960769	+	0.277350i	$0.0894562\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$		0			0		1.00000			$0$
$17$		0			0		−1.00000			$\pi$
$18$		0			0
$19$		−	3.46410i		−	0.794719i	−0.917663	−	0.397360i	$-0.869927\pi$
$19$		−	3.46410i		−	0.794719i	0.917663	−	0.397360i	$-0.130073\pi$
$20$		0			0
$21$	−3.00000	−	3.46410i	−0.654654	−	0.755929i
$22$		0			0
$23$		0			0			−	1.00000i	$-0.5\pi$
$23$		0			0				1.00000i	$0.5\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−5.19615			−1.00000
$28$		0			0
$29$		0			0		1.00000			$0$
$29$		0			0		−1.00000			$\pi$
$30$		0			0
$31$		−	10.3923i		−	1.86651i	−0.359211	−	0.933257i	$-0.616954\pi$
$31$		−	10.3923i		−	1.86651i	0.359211	−	0.933257i	$-0.383046\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$		0			0
$36$		0			0
$37$			10.0000i			1.64399i	0.569495	+	0.821995i	$0.307139\pi$
$37$			10.0000i			1.64399i	−0.569495	+	0.821995i	$0.692861\pi$
$38$		0			0
$39$	−12.0000			−1.92154
$40$		0			0
$41$		0			0			−	1.00000i	$-0.5\pi$
$41$		0			0				1.00000i	$0.5\pi$
$42$		0			0
$43$			8.00000i			1.21999i	0.792406	+	0.609994i	$0.208828\pi$
$43$			8.00000i			1.21999i	−0.792406	+	0.609994i	$0.791172\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$		0			0		1.00000			$0$
$47$		0			0		−1.00000			$\pi$
$48$		0			0
$49$	−1.00000	+	6.92820i	−0.142857	+	0.989743i
$50$		0			0
$51$		0			0
$52$		0			0
$53$		0			0			−	1.00000i	$-0.5\pi$
$53$		0			0				1.00000i	$0.5\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$			6.00000i			0.794719i
$58$		0			0
$59$		0			0			−	1.00000i	$-0.5\pi$
$59$		0			0				1.00000i	$0.5\pi$
$60$		0			0
$61$		−	6.92820i		−	0.887066i	−0.896258	−	0.443533i	$-0.853725\pi$
$61$		−	6.92820i		−	0.887066i	0.896258	−	0.443533i	$-0.146275\pi$
$62$		0			0
$63$	5.19615	+	6.00000i	0.654654	+	0.755929i
$64$		0			0
$65$		0			0
$66$		0			0
$67$		−	16.0000i		−	1.95471i	−0.211604	−	0.977356i	$-0.567869\pi$
$67$		−	16.0000i		−	1.95471i	0.211604	−	0.977356i	$-0.432131\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		0			0		1.00000			$0$
$71$		0			0		−1.00000			$\pi$
$72$		0			0
$73$	13.8564			1.62177			0.810885	−	0.585206i	$-0.198986\pi$
$73$	13.8564			1.62177			0.810885	+	0.585206i	$0.198986\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$		0			0
$78$		0			0
$79$	4.00000			0.450035			0.225018	−	0.974355i	$-0.427756\pi$
$79$	4.00000			0.450035			0.225018	+	0.974355i	$0.427756\pi$
$80$		0			0
$81$	9.00000			1.00000
$82$		0			0
$83$		0			0		1.00000			$0$
$83$		0			0		−1.00000			$\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		0			0
$88$		0			0
$89$		0			0			−	1.00000i	$-0.5\pi$
$89$		0			0				1.00000i	$0.5\pi$
$90$		0			0
$91$	12.0000	+	13.8564i	1.25794	+	1.45255i
$92$		0			0
$93$			18.0000i			1.86651i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	13.8564			1.40690			0.703452	−	0.710742i	$-0.251641\pi$
$97$	13.8564			1.40690			0.703452	+	0.710742i	$0.251641\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$		0			0			−	1.00000i	$-0.5\pi$
$101$		0			0				1.00000i	$0.5\pi$
$102$		0			0
$103$	3.46410			0.341328			0.170664	−	0.985329i	$-0.445409\pi$
$103$	3.46410			0.341328			0.170664	+	0.985329i	$0.445409\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		0			0			−	1.00000i	$-0.5\pi$
$107$		0			0				1.00000i	$0.5\pi$
$108$		0			0
$109$	2.00000			0.191565			0.0957826	−	0.995402i	$-0.469465\pi$
$109$	2.00000			0.191565			0.0957826	+	0.995402i	$0.469465\pi$
$110$		0			0
$111$		−	17.3205i		−	1.64399i
$112$		0			0
$113$		0			0			−	1.00000i	$-0.5\pi$
$113$		0			0				1.00000i	$0.5\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	20.7846			1.92154
$118$		0			0
$119$		0			0
$120$		0			0
$121$	11.0000			1.00000
$122$		0			0
$123$		0			0
$124$		0			0
$125$		0			0
$126$		0			0
$127$			20.0000i			1.77471i	0.461084	+	0.887357i	$0.347461\pi$
$127$			20.0000i			1.77471i	−0.461084	+	0.887357i	$0.652539\pi$
$128$		0			0
$129$		−	13.8564i		−	1.21999i
$130$		0			0
$131$		0			0			−	1.00000i	$-0.5\pi$
$131$		0			0				1.00000i	$0.5\pi$
$132$		0			0
$133$	6.92820	−	6.00000i	0.600751	−	0.520266i
$134$		0			0
$135$		0			0
$136$		0			0
$137$		0			0			−	1.00000i	$-0.5\pi$
$137$		0			0				1.00000i	$0.5\pi$
$138$		0			0
$139$			17.3205i			1.46911i	0.678551	+	0.734553i	$0.262608\pi$
$139$			17.3205i			1.46911i	−0.678551	+	0.734553i	$0.737392\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$		0			0
$145$		0			0
$146$		0			0
$147$	1.73205	−	12.0000i	0.142857	−	0.989743i
$148$		0			0
$149$		0			0		1.00000			$0$
$149$		0			0		−1.00000			$\pi$
$150$		0			0
$151$	4.00000			0.325515			0.162758	−	0.986666i	$-0.447961\pi$
$151$	4.00000			0.325515			0.162758	+	0.986666i	$0.447961\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−20.7846			−1.65879			−0.829396	−	0.558661i	$-0.811315\pi$
$157$	−20.7846			−1.65879			−0.829396	+	0.558661i	$0.811315\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$		0			0
$163$		−	8.00000i		−	0.626608i	−0.949653	−	0.313304i	$-0.898564\pi$
$163$		−	8.00000i		−	0.626608i	0.949653	−	0.313304i	$-0.101436\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		0			0		1.00000			$0$
$167$		0			0		−1.00000			$\pi$
$168$		0			0
$169$	35.0000			2.69231
$170$		0			0
$171$		−	10.3923i		−	0.794719i
$172$		0			0
$173$		0			0		1.00000			$0$
$173$		0			0		−1.00000			$\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$		0			0
$179$		0			0		1.00000			$0$
$179$		0			0		−1.00000			$\pi$
$180$		0			0
$181$			6.92820i			0.514969i	0.966282	+	0.257485i	$0.0828937\pi$
$181$			6.92820i			0.514969i	−0.966282	+	0.257485i	$0.917106\pi$
$182$		0			0
$183$			12.0000i			0.887066i
$184$		0			0
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$	−9.00000	−	10.3923i	−0.654654	−	0.755929i
$190$		0			0
$191$		0			0		1.00000			$0$
$191$		0			0		−1.00000			$\pi$
$192$		0			0
$193$			2.00000i			0.143963i	0.997406	+	0.0719816i	$0.0229323\pi$
$193$			2.00000i			0.143963i	−0.997406	+	0.0719816i	$0.977068\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		0			0			−	1.00000i	$-0.5\pi$
$197$		0			0				1.00000i	$0.5\pi$
$198$		0			0
$199$			3.46410i			0.245564i	0.992434	+	0.122782i	$0.0391815\pi$
$199$			3.46410i			0.245564i	−0.992434	+	0.122782i	$0.960818\pi$
$200$		0			0
$201$			27.7128i			1.95471i
$202$		0			0
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$		0			0
$210$		0			0
$211$	16.0000			1.10149			0.550743	−	0.834675i	$-0.314345\pi$
$211$	16.0000			1.10149			0.550743	+	0.834675i	$0.314345\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$		0			0
$216$		0			0
$217$	20.7846	−	18.0000i	1.41095	−	1.22192i
$218$		0			0
$219$	−24.0000			−1.62177
$220$		0			0
$221$		0			0
$222$		0			0
$223$	10.3923			0.695920			0.347960	−	0.937509i	$-0.386874\pi$
$223$	10.3923			0.695920			0.347960	+	0.937509i	$0.386874\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$		0			0		1.00000			$0$
$227$		0			0		−1.00000			$\pi$
$228$		0			0
$229$			20.7846i			1.37349i	0.726900	+	0.686743i	$0.240960\pi$
$229$			20.7846i			1.37349i	−0.726900	+	0.686743i	$0.759040\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		0			0			−	1.00000i	$-0.5\pi$
$233$		0			0				1.00000i	$0.5\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−6.92820			−0.450035
$238$		0			0
$239$		0			0		1.00000			$0$
$239$		0			0		−1.00000			$\pi$
$240$		0			0
$241$		−	27.7128i		−	1.78514i	−0.450910	−	0.892570i	$-0.648900\pi$
$241$		−	27.7128i		−	1.78514i	0.450910	−	0.892570i	$-0.351100\pi$
$242$		0			0
$243$	−15.5885			−1.00000
$244$		0			0
$245$		0			0
$246$		0			0
$247$		−	24.0000i		−	1.52708i
$248$		0			0
$249$		0			0
$250$		0			0
$251$		0			0			−	1.00000i	$-0.5\pi$
$251$		0			0				1.00000i	$0.5\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$		0			0
$257$		0			0		1.00000			$0$
$257$		0			0		−1.00000			$\pi$
$258$		0			0
$259$	−20.0000	+	17.3205i	−1.24274	+	1.07624i
$260$		0			0
$261$		0			0
$262$		0			0
$263$		0			0			−	1.00000i	$-0.5\pi$
$263$		0			0				1.00000i	$0.5\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$		0			0
$269$		0			0			−	1.00000i	$-0.5\pi$
$269$		0			0				1.00000i	$0.5\pi$
$270$		0			0
$271$			17.3205i			1.05215i	0.850439	+	0.526073i	$0.176336\pi$
$271$			17.3205i			1.05215i	−0.850439	+	0.526073i	$0.823664\pi$
$272$		0			0
$273$	−20.7846	−	24.0000i	−1.25794	−	1.45255i
$274$		0			0
$275$		0			0
$276$		0			0
$277$			26.0000i			1.56219i	0.624413	+	0.781094i	$0.285338\pi$
$277$			26.0000i			1.56219i	−0.624413	+	0.781094i	$0.714662\pi$
$278$		0			0
$279$		−	31.1769i		−	1.86651i
$280$		0			0
$281$		0			0		1.00000			$0$
$281$		0			0		−1.00000			$\pi$
$282$		0			0
$283$	−10.3923			−0.617758			−0.308879	−	0.951101i	$-0.599954\pi$
$283$	−10.3923			−0.617758			−0.308879	+	0.951101i	$0.599954\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$		0			0
$289$	17.0000			1.00000
$290$		0			0
$291$	−24.0000			−1.40690
$292$		0			0
$293$		0			0		1.00000			$0$
$293$		0			0		−1.00000			$\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$		0			0
$298$		0			0
$299$		0			0
$300$		0			0
$301$	−16.0000	+	13.8564i	−0.922225	+	0.798670i
$302$		0			0
$303$		0			0
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−31.1769			−1.77936			−0.889680	−	0.456584i	$-0.849073\pi$
$307$	−31.1769			−1.77936			−0.889680	+	0.456584i	$0.849073\pi$
$308$		0			0
$309$	−6.00000			−0.341328
$310$		0			0
$311$		0			0			−	1.00000i	$-0.5\pi$
$311$		0			0				1.00000i	$0.5\pi$
$312$		0			0
$313$	27.7128			1.56642			0.783210	−	0.621757i	$-0.213581\pi$
$313$	27.7128			1.56642			0.783210	+	0.621757i	$0.213581\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0			−	1.00000i	$-0.5\pi$
$317$		0			0				1.00000i	$0.5\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$		0			0
$322$		0			0
$323$		0			0
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−3.46410			−0.191565
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−32.0000			−1.75888			−0.879440	−	0.476011i	$-0.842082\pi$
$331$	−32.0000			−1.75888			−0.879440	+	0.476011i	$0.842082\pi$
$332$		0			0
$333$			30.0000i			1.64399i
$334$		0			0
$335$		0			0
$336$		0			0
$337$			34.0000i			1.85210i	0.377403	+	0.926049i	$0.376817\pi$
$337$			34.0000i			1.85210i	−0.377403	+	0.926049i	$0.623183\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−15.5885	+	10.0000i	−0.841698	+	0.539949i
$344$		0			0
$345$		0			0
$346$		0			0
$347$		0			0			−	1.00000i	$-0.5\pi$
$347$		0			0				1.00000i	$0.5\pi$
$348$		0			0
$349$		−	34.6410i		−	1.85429i	−0.374701	−	0.927146i	$-0.622255\pi$
$349$		−	34.6410i		−	1.85429i	0.374701	−	0.927146i	$-0.377745\pi$
$350$		0			0
$351$	−36.0000			−1.92154
$352$		0			0
$353$		0			0		1.00000			$0$
$353$		0			0		−1.00000			$\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$		0			0
$359$		0			0		1.00000			$0$
$359$		0			0		−1.00000			$\pi$
$360$		0			0
$361$	7.00000			0.368421
$362$		0			0
$363$	−19.0526			−1.00000
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−38.1051			−1.98907			−0.994535	−	0.104399i	$-0.966708\pi$
$367$	−38.1051			−1.98907			−0.994535	+	0.104399i	$0.966708\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$		−	38.0000i		−	1.96757i	−0.179364	−	0.983783i	$-0.557404\pi$
$373$		−	38.0000i		−	1.96757i	0.179364	−	0.983783i	$-0.442596\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	8.00000			0.410932			0.205466	−	0.978664i	$-0.434129\pi$
$379$	8.00000			0.410932			0.205466	+	0.978664i	$0.434129\pi$
$380$		0			0
$381$		−	34.6410i		−	1.77471i
$382$		0			0
$383$		0			0		1.00000			$0$
$383$		0			0		−1.00000			$\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$			24.0000i			1.21999i
$388$		0			0
$389$		0			0		1.00000			$0$
$389$		0			0		−1.00000			$\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$		0			0
$394$		0			0
$395$		0			0
$396$		0			0
$397$	20.7846			1.04315			0.521575	−	0.853206i	$-0.325345\pi$
$397$	20.7846			1.04315			0.521575	+	0.853206i	$0.325345\pi$
$398$		0			0
$399$	−12.0000	+	10.3923i	−0.600751	+	0.520266i
$400$		0			0
$401$		0			0		1.00000			$0$
$401$		0			0		−1.00000			$\pi$
$402$		0			0
$403$		−	72.0000i		−	3.58658i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$		0			0
$409$		−	13.8564i		−	0.685155i	−0.939490	−	0.342578i	$-0.888700\pi$
$409$		−	13.8564i		−	0.685155i	0.939490	−	0.342578i	$-0.111300\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$		−	30.0000i		−	1.46911i
$418$		0			0
$419$		0			0			−	1.00000i	$-0.5\pi$
$419$		0			0				1.00000i	$0.5\pi$
$420$		0			0
$421$	−22.0000			−1.07221			−0.536107	−	0.844150i	$-0.680106\pi$
$421$	−22.0000			−1.07221			−0.536107	+	0.844150i	$0.680106\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$		0			0
$426$		0			0
$427$	13.8564	−	12.0000i	0.670559	−	0.580721i
$428$		0			0
$429$		0			0
$430$		0			0
$431$		0			0		1.00000			$0$
$431$		0			0		−1.00000			$\pi$
$432$		0			0
$433$	−41.5692			−1.99769			−0.998845	−	0.0480569i	$-0.984697\pi$
$433$	−41.5692			−1.99769			−0.998845	+	0.0480569i	$0.984697\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$		0			0
$439$			31.1769i			1.48799i	0.668184	+	0.743996i	$0.267072\pi$
$439$			31.1769i			1.48799i	−0.668184	+	0.743996i	$0.732928\pi$
$440$		0			0
$441$	−3.00000	+	20.7846i	−0.142857	+	0.989743i
$442$		0			0
$443$		0			0			−	1.00000i	$-0.5\pi$
$443$		0			0				1.00000i	$0.5\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$		0			0		1.00000			$0$
$449$		0			0		−1.00000			$\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$	−6.92820			−0.325515
$454$		0			0
$455$		0			0
$456$		0			0
$457$			10.0000i			0.467780i	0.972263	+	0.233890i	$0.0751456\pi$
$457$			10.0000i			0.467780i	−0.972263	+	0.233890i	$0.924854\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$		0			0			−	1.00000i	$-0.5\pi$
$461$		0			0				1.00000i	$0.5\pi$
$462$		0			0
$463$		−	20.0000i		−	0.929479i	−0.885448	−	0.464739i	$-0.846148\pi$
$463$		−	20.0000i		−	0.929479i	0.885448	−	0.464739i	$-0.153852\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		0			0		1.00000			$0$
$467$		0			0		−1.00000			$\pi$
$468$		0			0
$469$	32.0000	−	27.7128i	1.47762	−	1.27966i
$470$		0			0
$471$	36.0000			1.65879
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0			−	1.00000i	$-0.5\pi$
$479$		0			0				1.00000i	$0.5\pi$
$480$		0			0
$481$			69.2820i			3.15899i
$482$		0			0
$483$		0			0
$484$		0			0
$485$		0			0
$486$		0			0
$487$		−	44.0000i		−	1.99383i	−0.0784867	−	0.996915i	$-0.525009\pi$
$487$		−	44.0000i		−	1.99383i	0.0784867	−	0.996915i	$-0.474991\pi$
$488$		0			0
$489$			13.8564i			0.626608i
$490$		0			0
$491$		0			0		1.00000			$0$
$491$		0			0		−1.00000			$\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$	32.0000			1.43252			0.716258	−	0.697835i	$-0.245853\pi$
$499$	32.0000			1.43252			0.716258	+	0.697835i	$0.245853\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		0			0		1.00000			$0$
$503$		0			0		−1.00000			$\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−60.6218			−2.69231
$508$		0			0
$509$		0			0			−	1.00000i	$-0.5\pi$
$509$		0			0				1.00000i	$0.5\pi$
$510$		0			0
$511$	24.0000	+	27.7128i	1.06170	+	1.22594i
$512$		0			0
$513$			18.0000i			0.794719i
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$		0			0			−	1.00000i	$-0.5\pi$
$521$		0			0				1.00000i	$0.5\pi$
$522$		0			0
$523$	−45.0333			−1.96917			−0.984585	−	0.174908i	$-0.944037\pi$
$523$	−45.0333			−1.96917			−0.984585	+	0.174908i	$0.944037\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		0			0
$528$		0			0
$529$	−23.0000			−1.00000
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−46.0000			−1.97769			−0.988847	−	0.148933i	$-0.952416\pi$
$541$	−46.0000			−1.97769			−0.988847	+	0.148933i	$0.952416\pi$
$542$		0			0
$543$		−	12.0000i		−	0.514969i
$544$		0			0
$545$		0			0
$546$		0			0
$547$		−	40.0000i		−	1.71028i	−0.518400	−	0.855138i	$-0.673472\pi$
$547$		−	40.0000i		−	1.71028i	0.518400	−	0.855138i	$-0.326528\pi$
$548$		0			0
$549$		−	20.7846i		−	0.887066i
$550$		0			0
$551$		0			0
$552$		0			0
$553$	6.92820	+	8.00000i	0.294617	+	0.340195i
$554$		0			0
$555$		0			0
$556$		0			0
$557$		0			0			−	1.00000i	$-0.5\pi$
$557$		0			0				1.00000i	$0.5\pi$
$558$		0			0
$559$			55.4256i			2.34425i
$560$		0			0
$561$		0			0
$562$		0			0
$563$		0			0		1.00000			$0$
$563$		0			0		−1.00000			$\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	15.5885	+	18.0000i	0.654654	+	0.755929i
$568$		0			0
$569$		0			0		1.00000			$0$
$569$		0			0		−1.00000			$\pi$
$570$		0			0
$571$	−16.0000			−0.669579			−0.334790	−	0.942293i	$-0.608665\pi$
$571$	−16.0000			−0.669579			−0.334790	+	0.942293i	$0.608665\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−13.8564			−0.576850			−0.288425	−	0.957503i	$-0.593132\pi$
$577$	−13.8564			−0.576850			−0.288425	+	0.957503i	$0.593132\pi$
$578$		0			0
$579$		−	3.46410i		−	0.143963i
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$		0			0		1.00000			$0$
$587$		0			0		−1.00000			$\pi$
$588$		0			0
$589$	−36.0000			−1.48335
$590$		0			0
$591$		0			0
$592$		0			0
$593$		0			0		1.00000			$0$
$593$		0			0		−1.00000			$\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		−	6.00000i		−	0.245564i
$598$		0			0
$599$		0			0		1.00000			$0$
$599$		0			0		−1.00000			$\pi$
$600$		0			0
$601$		−	41.5692i		−	1.69564i	−0.530281	−	0.847822i	$-0.677914\pi$
$601$		−	41.5692i		−	1.69564i	0.530281	−	0.847822i	$-0.322086\pi$
$602$		0			0
$603$		−	48.0000i		−	1.95471i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	45.0333			1.82785			0.913923	−	0.405887i	$-0.133038\pi$
$607$	45.0333			1.82785			0.913923	+	0.405887i	$0.133038\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$			10.0000i			0.403896i	0.979396	+	0.201948i	$0.0647272\pi$
$613$			10.0000i			0.403896i	−0.979396	+	0.201948i	$0.935273\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		0			0			−	1.00000i	$-0.5\pi$
$617$		0			0				1.00000i	$0.5\pi$
$618$		0			0
$619$		−	38.1051i		−	1.53157i	−0.643094	−	0.765787i	$-0.722350\pi$
$619$		−	38.1051i		−	1.53157i	0.643094	−	0.765787i	$-0.277650\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$		0			0
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$	44.0000			1.75161			0.875806	−	0.482663i	$-0.160330\pi$
$631$	44.0000			1.75161			0.875806	+	0.482663i	$0.160330\pi$
$632$		0			0
$633$	−27.7128			−1.10149
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−6.92820	+	48.0000i	−0.274505	+	1.90183i
$638$		0			0
$639$		0			0
$640$		0			0
$641$		0			0		1.00000			$0$
$641$		0			0		−1.00000			$\pi$
$642$		0			0
$643$	31.1769			1.22950			0.614749	−	0.788723i	$-0.289257\pi$
$643$	31.1769			1.22950			0.614749	+	0.788723i	$0.289257\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		1.00000			$0$
$647$		0			0		−1.00000			$\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$	−36.0000	+	31.1769i	−1.41095	+	1.22192i
$652$		0			0
$653$		0			0			−	1.00000i	$-0.5\pi$
$653$		0			0				1.00000i	$0.5\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	41.5692			1.62177
$658$		0			0
$659$		0			0		1.00000			$0$
$659$		0			0		−1.00000			$\pi$
$660$		0			0
$661$		−	34.6410i		−	1.34738i	−0.739014	−	0.673690i	$-0.764708\pi$
$661$		−	34.6410i		−	1.34738i	0.739014	−	0.673690i	$-0.235292\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$	−18.0000			−0.695920
$670$		0			0
$671$		0			0
$672$		0			0
$673$			50.0000i			1.92736i	0.267063	+	0.963679i	$0.413947\pi$
$673$			50.0000i			1.92736i	−0.267063	+	0.963679i	$0.586053\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$		0			0		1.00000			$0$
$677$		0			0		−1.00000			$\pi$
$678$		0			0
$679$	24.0000	+	27.7128i	0.921035	+	1.06352i
$680$		0			0
$681$		0			0
$682$		0			0
$683$		0			0			−	1.00000i	$-0.5\pi$
$683$		0			0				1.00000i	$0.5\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$		−	36.0000i		−	1.37349i
$688$		0			0
$689$		0			0
$690$		0			0
$691$			51.9615i			1.97671i	0.152167	+	0.988355i	$0.451375\pi$
$691$			51.9615i			1.97671i	−0.152167	+	0.988355i	$0.548625\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$		0			0
$701$		0			0		1.00000			$0$
$701$		0			0		−1.00000			$\pi$
$702$		0			0
$703$	34.6410			1.30651
$704$		0			0
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−22.0000			−0.826227			−0.413114	−	0.910679i	$-0.635559\pi$
$709$	−22.0000			−0.826227			−0.413114	+	0.910679i	$0.635559\pi$
$710$		0			0
$711$	12.0000			0.450035
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0			−	1.00000i	$-0.5\pi$
$719$		0			0				1.00000i	$0.5\pi$
$720$		0			0
$721$	6.00000	+	6.92820i	0.223452	+	0.258020i
$722$		0			0
$723$			48.0000i			1.78514i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−31.1769			−1.15629			−0.578144	−	0.815935i	$-0.696223\pi$
$727$	−31.1769			−1.15629			−0.578144	+	0.815935i	$0.696223\pi$
$728$		0			0
$729$	27.0000			1.00000
$730$		0			0
$731$		0			0
$732$		0			0
$733$	−20.7846			−0.767697			−0.383849	−	0.923396i	$-0.625402\pi$
$733$	−20.7846			−0.767697			−0.383849	+	0.923396i	$0.625402\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		0			0
$738$		0			0
$739$	16.0000			0.588570			0.294285	−	0.955718i	$-0.404919\pi$
$739$	16.0000			0.588570			0.294285	+	0.955718i	$0.404919\pi$
$740$		0			0
$741$			41.5692i			1.52708i
$742$		0			0
$743$		0			0			−	1.00000i	$-0.5\pi$
$743$		0			0				1.00000i	$0.5\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$	52.0000			1.89751			0.948753	−	0.316017i	$-0.102346\pi$
$751$	52.0000			1.89751			0.948753	+	0.316017i	$0.102346\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$		−	26.0000i		−	0.944986i	−0.881334	−	0.472493i	$-0.843354\pi$
$757$		−	26.0000i		−	0.944986i	0.881334	−	0.472493i	$-0.156646\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$		0			0			−	1.00000i	$-0.5\pi$
$761$		0			0				1.00000i	$0.5\pi$
$762$		0			0
$763$	3.46410	+	4.00000i	0.125409	+	0.144810i
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$		0			0
$769$		−	55.4256i		−	1.99870i	−0.0360609	−	0.999350i	$-0.511481\pi$
$769$		−	55.4256i		−	1.99870i	0.0360609	−	0.999350i	$-0.488519\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		0			0		1.00000			$0$
$773$		0			0		−1.00000			$\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	34.6410	−	30.0000i	1.24274	−	1.07624i
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$		0			0
$785$		0			0
$786$		0			0
$787$	3.46410			0.123482			0.0617409	−	0.998092i	$-0.480335\pi$
$787$	3.46410			0.123482			0.0617409	+	0.998092i	$0.480335\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$		−	48.0000i		−	1.70453i
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		1.00000			$0$
$797$		0			0		−1.00000			$\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$		0			0
$802$		0			0
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$		0			0		1.00000			$0$
$809$		0			0		−1.00000			$\pi$
$810$		0			0
$811$			10.3923i			0.364923i	0.983213	+	0.182462i	$0.0584065\pi$
$811$			10.3923i			0.364923i	−0.983213	+	0.182462i	$0.941593\pi$
$812$		0			0
$813$		−	30.0000i		−	1.05215i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	27.7128			0.969549
$818$		0			0
$819$	36.0000	+	41.5692i	1.25794	+	1.45255i
$820$		0			0
$821$		0			0		1.00000			$0$
$821$		0			0		−1.00000			$\pi$
$822$		0			0
$823$			52.0000i			1.81261i	0.422628	+	0.906303i	$0.361108\pi$
$823$			52.0000i			1.81261i	−0.422628	+	0.906303i	$0.638892\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		0			0			−	1.00000i	$-0.5\pi$
$827$		0			0				1.00000i	$0.5\pi$
$828$		0			0
$829$			34.6410i			1.20313i	0.798823	+	0.601566i	$0.205456\pi$
$829$			34.6410i			1.20313i	−0.798823	+	0.601566i	$0.794544\pi$
$830$		0			0
$831$		−	45.0333i		−	1.56219i
$832$		0			0
$833$		0			0
$834$		0			0
$835$		0			0
$836$		0			0
$837$			54.0000i			1.86651i
$838$		0			0
$839$		0			0			−	1.00000i	$-0.5\pi$
$839$		0			0				1.00000i	$0.5\pi$
$840$		0			0
$841$	29.0000			1.00000
$842$		0			0
$843$		0			0
$844$		0			0
$845$		0			0
$846$		0			0
$847$	19.0526	+	22.0000i	0.654654	+	0.755929i
$848$		0			0
$849$	18.0000			0.617758
$850$		0			0
$851$		0			0
$852$		0			0
$853$	6.92820			0.237217			0.118609	−	0.992941i	$-0.462157\pi$
$853$	6.92820			0.237217			0.118609	+	0.992941i	$0.462157\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		0			0		1.00000			$0$
$857$		0			0		−1.00000			$\pi$
$858$		0			0
$859$		−	17.3205i		−	0.590968i	−0.955348	−	0.295484i	$-0.904519\pi$
$859$		−	17.3205i		−	0.590968i	0.955348	−	0.295484i	$-0.0954809\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0			−	1.00000i	$-0.5\pi$
$863$		0			0				1.00000i	$0.5\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−29.4449			−1.00000
$868$		0			0
$869$		0			0
$870$		0			0
$871$		−	110.851i		−	3.75605i
$872$		0			0
$873$	41.5692			1.40690
$874$		0			0
$875$		0			0
$876$		0			0
$877$		−	34.0000i		−	1.14810i	−0.818821	−	0.574049i	$-0.805372\pi$
$877$		−	34.0000i		−	1.14810i	0.818821	−	0.574049i	$-0.194628\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		0			0			−	1.00000i	$-0.5\pi$
$881$		0			0				1.00000i	$0.5\pi$
$882$		0			0
$883$			8.00000i			0.269221i	0.990899	+	0.134611i	$0.0429784\pi$
$883$			8.00000i			0.269221i	−0.990899	+	0.134611i	$0.957022\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$		0			0		1.00000			$0$
$887$		0			0		−1.00000			$\pi$
$888$		0			0
$889$	−40.0000	+	34.6410i	−1.34156	+	1.16182i
$890$		0			0
$891$		0			0
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$		0			0
$899$		0			0
$900$		0			0
$901$		0			0
$902$		0			0
$903$	27.7128	−	24.0000i	0.922225	−	0.798670i
$904$		0			0
$905$		0			0
$906$		0			0
$907$			40.0000i			1.32818i	0.747653	+	0.664089i	$0.231180\pi$
$907$			40.0000i			1.32818i	−0.747653	+	0.664089i	$0.768820\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$		0			0		1.00000			$0$
$911$		0			0		−1.00000			$\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−52.0000			−1.71532			−0.857661	−	0.514216i	$-0.828083\pi$
$919$	−52.0000			−1.71532			−0.857661	+	0.514216i	$0.828083\pi$
$920$		0			0
$921$	54.0000			1.77936
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$	10.3923			0.341328
$928$		0			0
$929$		0			0			−	1.00000i	$-0.5\pi$
$929$		0			0				1.00000i	$0.5\pi$
$930$		0			0
$931$	24.0000	+	3.46410i	0.786568	+	0.113531i
$932$		0			0
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−55.4256			−1.81068			−0.905338	−	0.424691i	$-0.860383\pi$
$937$	−55.4256			−1.81068			−0.905338	+	0.424691i	$0.860383\pi$
$938$		0			0
$939$	−48.0000			−1.56642
$940$		0			0
$941$		0			0			−	1.00000i	$-0.5\pi$
$941$		0			0				1.00000i	$0.5\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$		0			0			−	1.00000i	$-0.5\pi$
$947$		0			0				1.00000i	$0.5\pi$
$948$		0			0
$949$	96.0000			3.11629
$950$		0			0
$951$		0			0
$952$		0			0
$953$		0			0			−	1.00000i	$-0.5\pi$
$953$		0			0				1.00000i	$0.5\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−77.0000			−2.48387
$962$		0			0
$963$		0			0
$964$		0			0
$965$		0			0
$966$		0			0
$967$			20.0000i			0.643157i	0.946883	+	0.321578i	$0.104213\pi$
$967$			20.0000i			0.643157i	−0.946883	+	0.321578i	$0.895787\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$		0			0			−	1.00000i	$-0.5\pi$
$971$		0			0				1.00000i	$0.5\pi$
$972$		0			0
$973$	−34.6410	+	30.0000i	−1.11054	+	0.961756i
$974$		0			0
$975$		0			0
$976$		0			0
$977$		0			0			−	1.00000i	$-0.5\pi$
$977$		0			0				1.00000i	$0.5\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	6.00000			0.191565
$982$		0			0
$983$		0			0		1.00000			$0$
$983$		0			0		−1.00000			$\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	−44.0000			−1.39771			−0.698853	−	0.715265i	$-0.746306\pi$
$991$	−44.0000			−1.39771			−0.698853	+	0.715265i	$0.746306\pi$
$992$		0			0
$993$	55.4256			1.75888
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−62.3538			−1.97477			−0.987383	−	0.158352i	$-0.949382\pi$
$997$	−62.3538			−1.97477			−0.987383	+	0.158352i	$0.949382\pi$
$998$		0			0
$999$		−	51.9615i		−	1.64399i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2100.2.f.e.1049.2		4
3.2	odd	2	CM	2100.2.f.e.1049.2		4
5.2	odd	4		2100.2.d.b.1301.2		2
5.3	odd	4		84.2.f.a.41.1	✓	2
5.4	even	2	inner	2100.2.f.e.1049.3		4
7.6	odd	2	inner	2100.2.f.e.1049.4		4
15.2	even	4		2100.2.d.b.1301.2		2
15.8	even	4		84.2.f.a.41.1	✓	2
15.14	odd	2	inner	2100.2.f.e.1049.3		4
20.3	even	4		336.2.k.a.209.2		2
21.20	even	2	inner	2100.2.f.e.1049.4		4
35.3	even	12		588.2.k.e.509.1		2
35.13	even	4		84.2.f.a.41.2	yes	2
35.18	odd	12		588.2.k.a.509.1		2
35.23	odd	12		588.2.k.e.521.1		2
35.27	even	4		2100.2.d.b.1301.1		2
35.33	even	12		588.2.k.a.521.1		2
35.34	odd	2	inner	2100.2.f.e.1049.1		4
40.3	even	4		1344.2.k.a.1217.1		2
40.13	odd	4		1344.2.k.b.1217.2		2
45.13	odd	12		2268.2.x.e.1889.1		2
45.23	even	12		2268.2.x.e.1889.1		2
45.38	even	12		2268.2.x.c.377.1		2
45.43	odd	12		2268.2.x.c.377.1		2
60.23	odd	4		336.2.k.a.209.2		2
105.23	even	12		588.2.k.e.521.1		2
105.38	odd	12		588.2.k.e.509.1		2
105.53	even	12		588.2.k.a.509.1		2
105.62	odd	4		2100.2.d.b.1301.1		2
105.68	odd	12		588.2.k.a.521.1		2
105.83	odd	4		84.2.f.a.41.2	yes	2
105.104	even	2	inner	2100.2.f.e.1049.1		4
120.53	even	4		1344.2.k.b.1217.2		2
120.83	odd	4		1344.2.k.a.1217.1		2
140.83	odd	4		336.2.k.a.209.1		2
280.13	even	4		1344.2.k.b.1217.1		2
280.83	odd	4		1344.2.k.a.1217.2		2
315.13	even	12		2268.2.x.c.1889.1		2
315.83	odd	12		2268.2.x.e.377.1		2
315.223	even	12		2268.2.x.e.377.1		2
315.293	odd	12		2268.2.x.c.1889.1		2
420.83	even	4		336.2.k.a.209.1		2
840.83	even	4		1344.2.k.a.1217.2		2
840.293	odd	4		1344.2.k.b.1217.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.2.f.a.41.1	✓	2	5.3	odd	4
84.2.f.a.41.1	✓	2	15.8	even	4
84.2.f.a.41.2	yes	2	35.13	even	4
84.2.f.a.41.2	yes	2	105.83	odd	4
336.2.k.a.209.1		2	140.83	odd	4
336.2.k.a.209.1		2	420.83	even	4
336.2.k.a.209.2		2	20.3	even	4
336.2.k.a.209.2		2	60.23	odd	4
588.2.k.a.509.1		2	35.18	odd	12
588.2.k.a.509.1		2	105.53	even	12
588.2.k.a.521.1		2	35.33	even	12
588.2.k.a.521.1		2	105.68	odd	12
588.2.k.e.509.1		2	35.3	even	12
588.2.k.e.509.1		2	105.38	odd	12
588.2.k.e.521.1		2	35.23	odd	12
588.2.k.e.521.1		2	105.23	even	12
1344.2.k.a.1217.1		2	40.3	even	4
1344.2.k.a.1217.1		2	120.83	odd	4
1344.2.k.a.1217.2		2	280.83	odd	4
1344.2.k.a.1217.2		2	840.83	even	4
1344.2.k.b.1217.1		2	280.13	even	4
1344.2.k.b.1217.1		2	840.293	odd	4
1344.2.k.b.1217.2		2	40.13	odd	4
1344.2.k.b.1217.2		2	120.53	even	4
2100.2.d.b.1301.1		2	35.27	even	4
2100.2.d.b.1301.1		2	105.62	odd	4
2100.2.d.b.1301.2		2	5.2	odd	4
2100.2.d.b.1301.2		2	15.2	even	4
2100.2.f.e.1049.1		4	35.34	odd	2	inner
2100.2.f.e.1049.1		4	105.104	even	2	inner
2100.2.f.e.1049.2		4	1.1	even	1	trivial
2100.2.f.e.1049.2		4	3.2	odd	2	CM
2100.2.f.e.1049.3		4	5.4	even	2	inner
2100.2.f.e.1049.3		4	15.14	odd	2	inner
2100.2.f.e.1049.4		4	7.6	odd	2	inner
2100.2.f.e.1049.4		4	21.20	even	2	inner
2268.2.x.c.377.1		2	45.38	even	12
2268.2.x.c.377.1		2	45.43	odd	12
2268.2.x.c.1889.1		2	315.13	even	12
2268.2.x.c.1889.1		2	315.293	odd	12
2268.2.x.e.377.1		2	315.83	odd	12
2268.2.x.e.377.1		2	315.223	even	12
2268.2.x.e.1889.1		2	45.13	odd	12
2268.2.x.e.1889.1		2	45.23	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2100.f (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-1.73205 q^{3} +(1.73205 + 2.00000i) q^{7} +3.00000 q^{9} +O(q^{10})\)	\(q-1.73205 q^{3} +(1.73205 + 2.00000i) q^{7} +3.00000 q^{9} +6.92820 q^{13} -3.46410i q^{19} +(-3.00000 - 3.46410i) q^{21} -5.19615 q^{27} -10.3923i q^{31} +10.0000i q^{37} -12.0000 q^{39} +8.00000i q^{43} +(-1.00000 + 6.92820i) q^{49} +6.00000i q^{57} -6.92820i q^{61} +(5.19615 + 6.00000i) q^{63} -16.0000i q^{67} +13.8564 q^{73} +4.00000 q^{79} +9.00000 q^{81} +(12.0000 + 13.8564i) q^{91} +18.0000i q^{93} +13.8564 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 12 q^{9}+O(q^{10}) \) 4 * q + 12 * q^9	\( 4 q + 12 q^{9} - 12 q^{21} - 48 q^{39} - 4 q^{49} + 16 q^{79} + 36 q^{81} + 48 q^{91}+O(q^{100}) \) 4 * q + 12 * q^9 - 12 * q^21 - 48 * q^39 - 4 * q^49 + 16 * q^79 + 36 * q^81 + 48 * q^91

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