LMFDB - Embedded newform 7569.2.a.ba.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7569,2,Mod(1,7569)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7569, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("7569.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7569 = 3^{2} \cdot 29^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7569.a (trivial)

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:	yes
Analytic conductor:	$60.4387692899$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.160016229.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 12x^{4} + 36x^{2} - 29 $ x^6 - 12x^4 + 36x^2 - 29
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	no (minimal twist has level 261)
Fricke sign:	$-1$
Sato-Tate group:	$N(\mathrm{U}(1))$

Embedding invariants

Embedding label			1.2
Root			$-1.66024$ of defining polynomial
Character	$\chi$	$=$	7569.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.66024 q^{2} +0.756389 q^{4} +5.20982 q^{7} +2.06469 q^{8} +4.92462 q^{11} +2.72260 q^{13} -8.64954 q^{14} -4.94065 q^{16} -8.24509 q^{17} -8.17603 q^{22} -5.00000 q^{25} -4.52016 q^{26} +3.94065 q^{28} +4.07328 q^{32} +13.6888 q^{34} -10.7703 q^{41} +3.72493 q^{44} -1.71634 q^{47} +20.1422 q^{49} +8.30119 q^{50} +2.05935 q^{52} +10.7567 q^{56} +3.11869 q^{64} +10.6550 q^{67} -6.23650 q^{68} +25.6564 q^{77} +17.8813 q^{82} +10.1678 q^{88} -5.03681 q^{89} +14.1843 q^{91} +2.84952 q^{94} -33.4409 q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 12 q^{4} + 24 q^{16} + 6 q^{22} - 30 q^{25} - 30 q^{28} + 42 q^{34} + 42 q^{49} + 66 q^{52} + 126 q^{64} + 12 q^{88} + 24 q^{91} + 102 q^{94}+O(q^{100}) $ 6 * q + 12 * q^4 + 24 * q^16 + 6 * q^22 - 30 * q^25 - 30 * q^28 + 42 * q^34 + 42 * q^49 + 66 * q^52 + 126 * q^64 + 12 * q^88 + 24 * q^91 + 102 * q^94

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 $

$2$	−1.66024	−1.17397	−0.586983	−	0.809599i	$-0.699684\pi$
$2$	−1.66024	−1.17397	−0.586983	+	0.809599i	$0.699684\pi$
$3$	0	0
$3$	0	0
$4$	0.756389	0.378195
$5$	0	0		−	1.00000i	$-0.5\pi$
$5$	0	0			1.00000i	$0.5\pi$
$6$	0	0
$7$	5.20982	1.96913	0.984564	−	0.175026i	$-0.0560010\pi$
$7$	5.20982	1.96913	0.984564	+	0.175026i	$0.0560010\pi$
$8$	2.06469	0.729978
$9$	0	0
$10$	0	0
$11$	4.92462	1.48483	0.742414	−	0.669942i	$-0.233681\pi$
$11$	4.92462	1.48483	0.742414	+	0.669942i	$0.233681\pi$
$12$	0	0
$13$	2.72260	0.755114	0.377557	−	0.925986i	$-0.376764\pi$
$13$	2.72260	0.755114	0.377557	+	0.925986i	$0.376764\pi$
$14$	−8.64954	−2.31169
$15$	0	0
$16$	−4.94065	−1.23516
$17$	−8.24509	−1.99973	−0.999864	−	0.0164799i	$-0.994754\pi$
$17$	−8.24509	−1.99973	−0.999864	+	0.0164799i	$0.994754\pi$
$18$	0	0
$19$	0	0		−	1.00000i	$-0.5\pi$
$19$	0	0			1.00000i	$0.5\pi$
$20$	0	0
$21$	0	0
$22$	−8.17603	−1.74314
$23$	0	0		−	1.00000i	$-0.5\pi$
$23$	0	0			1.00000i	$0.5\pi$
$24$	0	0
$25$	−5.00000	−1.00000
$26$	−4.52016	−0.886477
$27$	0	0
$28$	3.94065	0.744714
$29$	0	0
$29$	0	0
$30$	0	0
$31$	0	0		−	1.00000i	$-0.5\pi$
$31$	0	0			1.00000i	$0.5\pi$
$32$	4.07328	0.720061
$33$	0	0
$34$	13.6888	2.34761
$35$	0	0
$36$	0	0
$37$	0	0		−	1.00000i	$-0.5\pi$
$37$	0	0			1.00000i	$0.5\pi$
$38$	0	0
$39$	0	0
$40$	0	0
$41$	−10.7703	−1.68204	−0.841021	−	0.541002i	$-0.818045\pi$
$41$	−10.7703	−1.68204	−0.841021	+	0.541002i	$0.818045\pi$
$42$	0	0
$43$	0	0		−	1.00000i	$-0.5\pi$
$43$	0	0			1.00000i	$0.5\pi$
$44$	3.72493	0.561554
$45$	0	0
$46$	0	0
$47$	−1.71634	−0.250353	−0.125177	−	0.992134i	$-0.539950\pi$
$47$	−1.71634	−0.250353	−0.125177	+	0.992134i	$0.539950\pi$
$48$	0	0
$49$	20.1422	2.87746
$50$	8.30119	1.17397
$51$	0	0
$52$	2.05935	0.285580
$53$	0	0		−	1.00000i	$-0.5\pi$
$53$	0	0			1.00000i	$0.5\pi$
$54$	0	0
$55$	0	0
$56$	10.7567	1.43742
$57$	0	0
$58$	0	0
$59$	0	0		−	1.00000i	$-0.5\pi$
$59$	0	0			1.00000i	$0.5\pi$
$60$	0	0
$61$	0	0		−	1.00000i	$-0.5\pi$
$61$	0	0			1.00000i	$0.5\pi$
$62$	0	0
$63$	0	0
$64$	3.11869	0.389837
$65$	0	0
$66$	0	0
$67$	10.6550	1.30172	0.650859	−	0.759199i	$-0.274409\pi$
$67$	10.6550	1.30172	0.650859	+	0.759199i	$0.274409\pi$
$68$	−6.23650	−0.756287
$69$	0	0
$70$	0	0
$71$	0	0		−	1.00000i	$-0.5\pi$
$71$	0	0			1.00000i	$0.5\pi$
$72$	0	0
$73$	0	0		−	1.00000i	$-0.5\pi$
$73$	0	0			1.00000i	$0.5\pi$
$74$	0	0
$75$	0	0
$76$	0	0
$77$	25.6564	2.92381
$78$	0	0
$79$	0	0		−	1.00000i	$-0.5\pi$
$79$	0	0			1.00000i	$0.5\pi$
$80$	0	0
$81$	0	0
$82$	17.8813	1.97466
$83$	0	0		−	1.00000i	$-0.5\pi$
$83$	0	0			1.00000i	$0.5\pi$
$84$	0	0
$85$	0	0
$86$	0	0
$87$	0	0
$88$	10.1678	1.08389
$89$	−5.03681	−0.533901	−0.266950	−	0.963710i	$-0.586016\pi$
$89$	−5.03681	−0.533901	−0.266950	+	0.963710i	$0.586016\pi$
$90$	0	0
$91$	14.1843	1.48691
$92$	0	0
$93$	0	0
$94$	2.84952	0.293906
$95$	0	0
$96$	0	0
$97$	0	0		−	1.00000i	$-0.5\pi$
$97$	0	0			1.00000i	$0.5\pi$
$98$	−33.4409	−3.37804
$99$	0	0
$100$	−3.78195	−0.378195
$101$	18.0943	1.80045	0.900226	−	0.435422i	$-0.143401\pi$
$101$	18.0943	1.80045	0.900226	+	0.435422i	$0.143401\pi$
$102$	0	0
$103$	8.00000	0.788263	0.394132	−	0.919054i	$-0.371045\pi$
$103$	8.00000	0.788263	0.394132	+	0.919054i	$0.371045\pi$
$104$	5.62132	0.551216
$105$	0	0
$106$	0	0
$107$	0	0		−	1.00000i	$-0.5\pi$
$107$	0	0			1.00000i	$0.5\pi$
$108$	0	0
$109$	18.1167	1.73526	0.867632	−	0.497207i	$-0.165641\pi$
$109$	18.1167	1.73526	0.867632	+	0.497207i	$0.165641\pi$
$110$	0	0
$111$	0	0
$112$	−25.7399	−2.43219
$113$	11.4534	1.07744	0.538721	−	0.842484i	$-0.318908\pi$
$113$	11.4534	1.07744	0.538721	+	0.842484i	$0.318908\pi$
$114$	0	0
$115$	0	0
$116$	0	0
$117$	0	0
$118$	0	0
$119$	−42.9555	−3.93772
$120$	0	0
$121$	13.2518	1.20471
$122$	0	0
$123$	0	0
$124$	0	0
$125$	0	0
$126$	0	0
$127$	0	0		−	1.00000i	$-0.5\pi$
$127$	0	0			1.00000i	$0.5\pi$
$128$	−13.3243	−1.17772
$129$	0	0
$130$	0	0
$131$	18.2065	1.59071	0.795355	−	0.606143i	$-0.207284\pi$
$131$	18.2065	1.59071	0.795355	+	0.606143i	$0.207284\pi$
$132$	0	0
$133$	0	0
$134$	−17.6899	−1.52817
$135$	0	0
$136$	−17.0236	−1.45976
$137$	10.7703	0.920171	0.460086	−	0.887875i	$-0.347819\pi$
$137$	10.7703	0.920171	0.460086	+	0.887875i	$0.347819\pi$
$138$	0	0
$139$	21.0747	1.78753	0.893765	−	0.448536i	$-0.148054\pi$
$139$	21.0747	1.78753	0.893765	+	0.448536i	$0.148054\pi$
$140$	0	0
$141$	0	0
$142$	0	0
$143$	13.4078	1.12121
$144$	0	0
$145$	0	0
$146$	0	0
$147$	0	0
$148$	0	0
$149$	0	0		−	1.00000i	$-0.5\pi$
$149$	0	0			1.00000i	$0.5\pi$
$150$	0	0
$151$	16.0000	1.30206	0.651031	−	0.759051i	$-0.274337\pi$
$151$	16.0000	1.30206	0.651031	+	0.759051i	$0.274337\pi$
$152$	0	0
$153$	0	0
$154$	−42.5957	−3.43246
$155$	0	0
$156$	0	0
$157$	0	0		−	1.00000i	$-0.5\pi$
$157$	0	0			1.00000i	$0.5\pi$
$158$	0	0
$159$	0	0
$160$	0	0
$161$	0	0
$162$	0	0
$163$	0	0		−	1.00000i	$-0.5\pi$
$163$	0	0			1.00000i	$0.5\pi$
$164$	−8.14656	−0.636140
$165$	0	0
$166$	0	0
$167$	0	0		−	1.00000i	$-0.5\pi$
$167$	0	0			1.00000i	$0.5\pi$
$168$	0	0
$169$	−5.58745	−0.429804
$170$	0	0
$171$	0	0
$172$	0	0
$173$	0	0		−	1.00000i	$-0.5\pi$
$173$	0	0			1.00000i	$0.5\pi$
$174$	0	0
$175$	−26.0491	−1.96913
$176$	−24.3308	−1.83400
$177$	0	0
$178$	8.36230	0.626781
$179$	0	0		−	1.00000i	$-0.5\pi$
$179$	0	0			1.00000i	$0.5\pi$
$180$	0	0
$181$	12.6715	0.941864	0.470932	−	0.882169i	$-0.343918\pi$
$181$	12.6715	0.941864	0.470932	+	0.882169i	$0.343918\pi$
$182$	−23.5493	−1.74559
$183$	0	0
$184$	0	0
$185$	0	0
$186$	0	0
$187$	−40.6039	−2.96925
$188$	−1.29822	−0.0946822
$189$	0	0
$190$	0	0
$191$	−21.5407	−1.55863	−0.779314	−	0.626634i	$-0.784432\pi$
$191$	−21.5407	−1.55863	−0.779314	+	0.626634i	$0.784432\pi$
$192$	0	0
$193$	0	0		−	1.00000i	$-0.5\pi$
$193$	0	0			1.00000i	$0.5\pi$
$194$	0	0
$195$	0	0
$196$	15.2354	1.08824
$197$	0	0		−	1.00000i	$-0.5\pi$
$197$	0	0			1.00000i	$0.5\pi$
$198$	0	0
$199$	5.68058	0.402686	0.201343	−	0.979521i	$-0.435469\pi$
$199$	5.68058	0.402686	0.201343	+	0.979521i	$0.435469\pi$
$200$	−10.3234	−0.729978
$201$	0	0
$202$	−30.0409	−2.11367
$203$	0	0
$204$	0	0
$205$	0	0
$206$	−13.2819	−0.925394
$207$	0	0
$208$	−13.4514	−0.932689
$209$	0	0
$210$	0	0
$211$	0	0		−	1.00000i	$-0.5\pi$
$211$	0	0			1.00000i	$0.5\pi$
$212$	0	0
$213$	0	0
$214$	0	0
$215$	0	0
$216$	0	0
$217$	0	0
$218$	−30.0780	−2.03714
$219$	0	0
$220$	0	0
$221$	−22.4481	−1.51002
$222$	0	0
$223$	4.73906	0.317351	0.158676	−	0.987331i	$-0.449278\pi$
$223$	4.73906	0.317351	0.158676	+	0.987331i	$0.449278\pi$
$224$	21.2211	1.41789
$225$	0	0
$226$	−19.0153	−1.26488
$227$	0	0		−	1.00000i	$-0.5\pi$
$227$	0	0			1.00000i	$0.5\pi$
$228$	0	0
$229$	0	0		−	1.00000i	$-0.5\pi$
$229$	0	0			1.00000i	$0.5\pi$
$230$	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
$237$	0	0
$238$	71.3163	4.62275
$239$	0	0		−	1.00000i	$-0.5\pi$
$239$	0	0			1.00000i	$0.5\pi$
$240$	0	0
$241$	−28.5363	−1.83819	−0.919093	−	0.394040i	$-0.871077\pi$
$241$	−28.5363	−1.83819	−0.919093	+	0.394040i	$0.871077\pi$
$242$	−22.0012	−1.41429
$243$	0	0
$244$	0	0
$245$	0	0
$246$	0	0
$247$	0	0
$248$	0	0
$249$	0	0
$250$	0	0
$251$	−1.49195	−0.0941708	−0.0470854	−	0.998891i	$-0.514993\pi$
$251$	−1.49195	−0.0941708	−0.0470854	+	0.998891i	$0.514993\pi$
$252$	0	0
$253$	0	0
$254$	0	0
$255$	0	0
$256$	15.8842	0.992761
$257$	0	0		−	1.00000i	$-0.5\pi$
$257$	0	0			1.00000i	$0.5\pi$
$258$	0	0
$259$	0	0
$260$	0	0
$261$	0	0
$262$	−30.2271	−1.86744
$263$	−21.5407	−1.32825	−0.664127	−	0.747620i	$-0.731197\pi$
$263$	−21.5407	−1.32825	−0.664127	+	0.747620i	$0.731197\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	0	0
$268$	8.05935	0.492303
$269$	31.3762	1.91304	0.956521	−	0.291663i	$-0.0942086\pi$
$269$	31.3762	1.91304	0.956521	+	0.291663i	$0.0942086\pi$
$270$	0	0
$271$	0	0		−	1.00000i	$-0.5\pi$
$271$	0	0			1.00000i	$0.5\pi$
$272$	40.7361	2.46999
$273$	0	0
$274$	−17.8813	−1.08025
$275$	−24.6231	−1.48483
$276$	0	0
$277$	29.0071	1.74287	0.871434	−	0.490514i	$-0.163191\pi$
$277$	29.0071	1.74287	0.871434	+	0.490514i	$0.163191\pi$
$278$	−34.9890	−2.09850
$279$	0	0
$280$	0	0
$281$	0	0		−	1.00000i	$-0.5\pi$
$281$	0	0			1.00000i	$0.5\pi$
$282$	0	0
$283$	28.0000	1.66443	0.832214	−	0.554455i	$-0.187073\pi$
$283$	28.0000	1.66443	0.832214	+	0.554455i	$0.187073\pi$
$284$	0	0
$285$	0	0
$286$	−22.2601	−1.31627
$287$	−56.1115	−3.31216
$288$	0	0
$289$	50.9815	2.99891
$290$	0	0
$291$	0	0
$292$	0	0
$293$	21.3026	1.24451	0.622256	−	0.782814i	$-0.286216\pi$
$293$	21.3026	1.24451	0.622256	+	0.782814i	$0.286216\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	0	0
$298$	0	0
$299$	0	0
$300$	0	0
$301$	0	0
$302$	−26.5638	−1.52858
$303$	0	0
$304$	0	0
$305$	0	0
$306$	0	0
$307$	0	0		−	1.00000i	$-0.5\pi$
$307$	0	0			1.00000i	$0.5\pi$
$308$	19.4062	1.10577
$309$	0	0
$310$	0	0
$311$	−14.9982	−0.850472	−0.425236	−	0.905083i	$-0.639809\pi$
$311$	−14.9982	−0.850472	−0.425236	+	0.905083i	$0.639809\pi$
$312$	0	0
$313$	−3.19336	−0.180499	−0.0902497	−	0.995919i	$-0.528767\pi$
$313$	−3.19336	−0.180499	−0.0902497	+	0.995919i	$0.528767\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	34.5845	1.94246	0.971230	−	0.238145i	$-0.0765392\pi$
$317$	34.5845	1.94246	0.971230	+	0.238145i	$0.0765392\pi$
$318$	0	0
$319$	0	0
$320$	0	0
$321$	0	0
$322$	0	0
$323$	0	0
$324$	0	0
$325$	−13.6130	−0.755114
$326$	0	0
$327$	0	0
$328$	−22.2374	−1.22785
$329$	−8.94180	−0.492977
$330$	0	0
$331$	0	0		−	1.00000i	$-0.5\pi$
$331$	0	0			1.00000i	$0.5\pi$
$332$	0	0
$333$	0	0
$334$	0	0
$335$	0	0
$336$	0	0
$337$	0	0		−	1.00000i	$-0.5\pi$
$337$	0	0			1.00000i	$0.5\pi$
$338$	9.27649	0.504574
$339$	0	0
$340$	0	0
$341$	0	0
$342$	0	0
$343$	68.4688	3.69697
$344$	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
$349$	2.00000	0.107058	0.0535288	−	0.998566i	$-0.482953\pi$
$349$	2.00000	0.107058	0.0535288	+	0.998566i	$0.482953\pi$
$350$	43.2477	2.31169
$351$	0	0
$352$	20.0593	1.06917
$353$	0	0		−	1.00000i	$-0.5\pi$
$353$	0	0			1.00000i	$0.5\pi$
$354$	0	0
$355$	0	0
$356$	−3.80979	−0.201918
$357$	0	0
$358$	0	0
$359$	−21.5407	−1.13687	−0.568436	−	0.822727i	$-0.692451\pi$
$359$	−21.5407	−1.13687	−0.568436	+	0.822727i	$0.692451\pi$
$360$	0	0
$361$	−19.0000	−1.00000
$362$	−21.0377	−1.10572
$363$	0	0
$364$	10.7288	0.562343
$365$	0	0
$366$	0	0
$367$	0	0		−	1.00000i	$-0.5\pi$
$367$	0	0			1.00000i	$0.5\pi$
$368$	0	0
$369$	0	0
$370$	0	0
$371$	0	0
$372$	0	0
$373$	−10.0000	−0.517780	−0.258890	−	0.965907i	$-0.583357\pi$
$373$	−10.0000	−0.517780	−0.258890	+	0.965907i	$0.583357\pi$
$374$	67.4121	3.48580
$375$	0	0
$376$	−3.54370	−0.182752
$377$	0	0
$378$	0	0
$379$	0	0		−	1.00000i	$-0.5\pi$
$379$	0	0			1.00000i	$0.5\pi$
$380$	0	0
$381$	0	0
$382$	35.7626	1.82977
$383$	0	0		−	1.00000i	$-0.5\pi$
$383$	0	0			1.00000i	$0.5\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	0	0
$388$	0	0
$389$	28.1679	1.42817	0.714086	−	0.700058i	$-0.246843\pi$
$389$	28.1679	1.42817	0.714086	+	0.700058i	$0.246843\pi$
$390$	0	0
$391$	0	0
$392$	41.5875	2.10048
$393$	0	0
$394$	0	0
$395$	0	0
$396$	0	0
$397$	14.0000	0.702640	0.351320	−	0.936255i	$-0.385733\pi$
$397$	14.0000	0.702640	0.351320	+	0.936255i	$0.385733\pi$
$398$	−9.43111	−0.472739
$399$	0	0
$400$	24.7033	1.23516
$401$	0	0		−	1.00000i	$-0.5\pi$
$401$	0	0			1.00000i	$0.5\pi$
$402$	0	0
$403$	0	0
$404$	13.6864	0.680922
$405$	0	0
$406$	0	0
$407$	0	0
$408$	0	0
$409$	0	0		−	1.00000i	$-0.5\pi$
$409$	0	0			1.00000i	$0.5\pi$
$410$	0	0
$411$	0	0
$412$	6.05111	0.298117
$413$	0	0
$414$	0	0
$415$	0	0
$416$	11.0899	0.543728
$417$	0	0
$418$	0	0
$419$	0	0		−	1.00000i	$-0.5\pi$
$419$	0	0			1.00000i	$0.5\pi$
$420$	0	0
$421$	0	0		−	1.00000i	$-0.5\pi$
$421$	0	0			1.00000i	$0.5\pi$
$422$	0	0
$423$	0	0
$424$	0	0
$425$	41.2255	1.99973
$426$	0	0
$427$	0	0
$428$	0	0
$429$	0	0
$430$	0	0
$431$	0	0		−	1.00000i	$-0.5\pi$
$431$	0	0			1.00000i	$0.5\pi$
$432$	0	0
$433$	0	0		−	1.00000i	$-0.5\pi$
$433$	0	0			1.00000i	$0.5\pi$
$434$	0	0
$435$	0	0
$436$	13.7033	0.656268
$437$	0	0
$438$	0	0
$439$	25.5784	1.22079	0.610394	−	0.792098i	$-0.291011\pi$
$439$	25.5784	1.22079	0.610394	+	0.792098i	$0.291011\pi$
$440$	0	0
$441$	0	0
$442$	37.2692	1.77271
$443$	−11.3412	−0.538836	−0.269418	−	0.963023i	$-0.586831\pi$
$443$	−11.3412	−0.538836	−0.269418	+	0.963023i	$0.586831\pi$
$444$	0	0
$445$	0	0
$446$	−7.86797	−0.372559
$447$	0	0
$448$	16.2478	0.767638
$449$	38.0172	1.79414	0.897071	−	0.441887i	$-0.145691\pi$
$449$	38.0172	1.79414	0.897071	+	0.441887i	$0.145691\pi$
$450$	0	0
$451$	−53.0397	−2.49754
$452$	8.66321	0.407483
$453$	0	0
$454$	0	0
$455$	0	0
$456$	0	0
$457$	17.6459	0.825442	0.412721	−	0.910858i	$-0.364579\pi$
$457$	17.6459	0.825442	0.412721	+	0.910858i	$0.364579\pi$
$458$	0	0
$459$	0	0
$460$	0	0
$461$	−10.7703	−0.501624	−0.250812	−	0.968036i	$-0.580698\pi$
$461$	−10.7703	−0.501624	−0.250812	+	0.968036i	$0.580698\pi$
$462$	0	0
$463$	−36.9395	−1.71672	−0.858362	−	0.513044i	$-0.828518\pi$
$463$	−36.9395	−1.71672	−0.858362	+	0.513044i	$0.828518\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	43.0813	1.99357	0.996783	−	0.0801498i	$-0.0255399\pi$
$467$	43.0813	1.99357	0.996783	+	0.0801498i	$0.0255399\pi$
$468$	0	0
$469$	55.5108	2.56325
$470$	0	0
$471$	0	0
$472$	0	0
$473$	0	0
$474$	0	0
$475$	0	0
$476$	−32.4911	−1.48922
$477$	0	0
$478$	0	0
$479$	21.5407	0.984218	0.492109	−	0.870534i	$-0.336226\pi$
$479$	21.5407	0.984218	0.492109	+	0.870534i	$0.336226\pi$
$480$	0	0
$481$	0	0
$482$	47.3771	2.15797
$483$	0	0
$484$	10.0236	0.455616
$485$	0	0
$486$	0	0
$487$	−40.0000	−1.81257	−0.906287	−	0.422664i	$-0.861095\pi$
$487$	−40.0000	−1.81257	−0.906287	+	0.422664i	$0.861095\pi$
$488$	0	0
$489$	0	0
$490$	0	0
$491$	−43.0813	−1.94423	−0.972116	−	0.234499i	$-0.924655\pi$
$491$	−43.0813	−1.94423	−0.972116	+	0.234499i	$0.924655\pi$
$492$	0	0
$493$	0	0
$494$	0	0
$495$	0	0
$496$	0	0
$497$	0	0
$498$	0	0
$499$	−21.5454	−0.964506	−0.482253	−	0.876032i	$-0.660181\pi$
$499$	−21.5454	−0.964506	−0.482253	+	0.876032i	$0.660181\pi$
$500$	0	0
$501$	0	0
$502$	2.47698	0.110553
$503$	44.5459	1.98620	0.993102	−	0.117250i	$-0.0374077\pi$
$503$	44.5459	1.98620	0.993102	+	0.117250i	$0.0374077\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	0	0
$508$	0	0
$509$	0	0		−	1.00000i	$-0.5\pi$
$509$	0	0			1.00000i	$0.5\pi$
$510$	0	0
$511$	0	0
$512$	0.277157	0.0122487
$513$	0	0
$514$	0	0
$515$	0	0
$516$	0	0
$517$	−8.45229	−0.371731
$518$	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
$523$	−9.71351	−0.424742	−0.212371	−	0.977189i	$-0.568119\pi$
$523$	−9.71351	−0.424742	−0.212371	+	0.977189i	$0.568119\pi$
$524$	13.7712	0.601598
$525$	0	0
$526$	35.7626	1.55932
$527$	0	0
$528$	0	0
$529$	−23.0000	−1.00000
$530$	0	0
$531$	0	0
$532$	0	0
$533$	−29.3233	−1.27013
$534$	0	0
$535$	0	0
$536$	21.9993	0.950226
$537$	0	0
$538$	−52.0920	−2.24585
$539$	99.1928	4.27254
$540$	0	0
$541$	0	0		−	1.00000i	$-0.5\pi$
$541$	0	0			1.00000i	$0.5\pi$
$542$	0	0
$543$	0	0
$544$	−33.5846	−1.43993
$545$	0	0
$546$	0	0
$547$	−41.4432	−1.77198	−0.885992	−	0.463701i	$-0.846521\pi$
$547$	−41.4432	−1.77198	−0.885992	+	0.463701i	$0.846521\pi$
$548$	8.14656	0.348004
$549$	0	0
$550$	40.8802	1.74314
$551$	0	0
$552$	0	0
$553$	0	0
$554$	−48.1587	−2.04607
$555$	0	0
$556$	15.9407	0.676034
$557$	0	0		−	1.00000i	$-0.5\pi$
$557$	0	0			1.00000i	$0.5\pi$
$558$	0	0
$559$	0	0
$560$	0	0
$561$	0	0
$562$	0	0
$563$	41.3377	1.74217	0.871087	−	0.491128i	$-0.163415\pi$
$563$	41.3377	1.74217	0.871087	+	0.491128i	$0.163415\pi$
$564$	0	0
$565$	0	0
$566$	−46.4867	−1.95398
$567$	0	0
$568$	0	0
$569$	−44.4337	−1.86276	−0.931380	−	0.364050i	$-0.881394\pi$
$569$	−44.4337	−1.86276	−0.931380	+	0.364050i	$0.881394\pi$
$570$	0	0
$571$	44.0000	1.84134	0.920671	−	0.390339i	$-0.127642\pi$
$571$	44.0000	1.84134	0.920671	+	0.390339i	$0.127642\pi$
$572$	10.1415	0.424037
$573$	0	0
$574$	93.1584	3.88836
$575$	0	0
$576$	0	0
$577$	0	0		−	1.00000i	$-0.5\pi$
$577$	0	0			1.00000i	$0.5\pi$
$578$	−84.6415	−3.52062
$579$	0	0
$580$	0	0
$581$	0	0
$582$	0	0
$583$	0	0
$584$	0	0
$585$	0	0
$586$	−35.3674	−1.46101
$587$	0	0		−	1.00000i	$-0.5\pi$
$587$	0	0			1.00000i	$0.5\pi$
$588$	0	0
$589$	0	0
$590$	0	0
$591$	0	0
$592$	0	0
$593$	0	0		−	1.00000i	$-0.5\pi$
$593$	0	0			1.00000i	$0.5\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	0	0
$598$	0	0
$599$	−27.8314	−1.13716	−0.568579	−	0.822628i	$-0.692507\pi$
$599$	−27.8314	−1.13716	−0.568579	+	0.822628i	$0.692507\pi$
$600$	0	0
$601$	0	0		−	1.00000i	$-0.5\pi$
$601$	0	0			1.00000i	$0.5\pi$
$602$	0	0
$603$	0	0
$604$	12.1022	0.492433
$605$	0	0
$606$	0	0
$607$	0	0		−	1.00000i	$-0.5\pi$
$607$	0	0			1.00000i	$0.5\pi$
$608$	0	0
$609$	0	0
$610$	0	0
$611$	−4.67289	−0.189045
$612$	0	0
$613$	−28.0656	−1.13356	−0.566779	−	0.823870i	$-0.691811\pi$
$613$	−28.0656	−1.13356	−0.566779	+	0.823870i	$0.691811\pi$
$614$	0	0
$615$	0	0
$616$	52.9724	2.13432
$617$	−10.7703	−0.433597	−0.216799	−	0.976216i	$-0.569561\pi$
$617$	−10.7703	−0.433597	−0.216799	+	0.976216i	$0.569561\pi$
$618$	0	0
$619$	0	0		−	1.00000i	$-0.5\pi$
$619$	0	0			1.00000i	$0.5\pi$
$620$	0	0
$621$	0	0
$622$	24.9006	0.998425
$623$	−26.2409	−1.05132
$624$	0	0
$625$	25.0000	1.00000
$626$	5.30174	0.211900
$627$	0	0
$628$	0	0
$629$	0	0
$630$	0	0
$631$	−35.9980	−1.43306	−0.716529	−	0.697558i	$-0.754270\pi$
$631$	−35.9980	−1.43306	−0.716529	+	0.697558i	$0.754270\pi$
$632$	0	0
$633$	0	0
$634$	−57.4185	−2.28038
$635$	0	0
$636$	0	0
$637$	54.8393	2.17281
$638$	0	0
$639$	0	0
$640$	0	0
$641$	34.8089	1.37487	0.687434	−	0.726247i	$-0.258737\pi$
$641$	34.8089	1.37487	0.687434	+	0.726247i	$0.258737\pi$
$642$	0	0
$643$	−20.1331	−0.793974	−0.396987	−	0.917824i	$-0.629944\pi$
$643$	−20.1331	−0.793974	−0.396987	+	0.917824i	$0.629944\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	0	0		−	1.00000i	$-0.5\pi$
$647$	0	0			1.00000i	$0.5\pi$
$648$	0	0
$649$	0	0
$650$	22.6008	0.886477
$651$	0	0
$652$	0	0
$653$	−24.5109	−0.959185	−0.479593	−	0.877491i	$-0.659216\pi$
$653$	−24.5109	−0.959185	−0.479593	+	0.877491i	$0.659216\pi$
$654$	0	0
$655$	0	0
$656$	53.2125	2.07760
$657$	0	0
$658$	14.8455	0.578738
$659$	−11.7900	−0.459271	−0.229636	−	0.973277i	$-0.573753\pi$
$659$	−11.7900	−0.459271	−0.229636	+	0.973277i	$0.573753\pi$
$660$	0	0
$661$	−49.8464	−1.93880	−0.969400	−	0.245488i	$-0.921052\pi$
$661$	−49.8464	−1.93880	−0.969400	+	0.245488i	$0.921052\pi$
$662$	0	0
$663$	0	0
$664$	0	0
$665$	0	0
$666$	0	0
$667$	0	0
$668$	0	0
$669$	0	0
$670$	0	0
$671$	0	0
$672$	0	0
$673$	49.3756	1.90329	0.951645	−	0.307200i	$-0.0993919\pi$
$673$	49.3756	1.90329	0.951645	+	0.307200i	$0.0993919\pi$
$674$	0	0
$675$	0	0
$676$	−4.22628	−0.162549
$677$	24.9597	0.959278	0.479639	−	0.877466i	$-0.340768\pi$
$677$	24.9597	0.959278	0.479639	+	0.877466i	$0.340768\pi$
$678$	0	0
$679$	0	0
$680$	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
$686$	−113.674	−4.34011
$687$	0	0
$688$	0	0
$689$	0	0
$690$	0	0
$691$	52.3336	1.99086	0.995432	−	0.0954736i	$-0.0304366\pi$
$691$	52.3336	1.99086	0.995432	+	0.0954736i	$0.0304366\pi$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	0	0
$696$	0	0
$697$	88.8024	3.36363
$698$	−3.32048	−0.125682
$699$	0	0
$700$	−19.7033	−0.744714
$701$	0	0		−	1.00000i	$-0.5\pi$
$701$	0	0			1.00000i	$0.5\pi$
$702$	0	0
$703$	0	0
$704$	15.3584	0.578840
$705$	0	0
$706$	0	0
$707$	94.2682	3.54532
$708$	0	0
$709$	−38.0000	−1.42712	−0.713560	−	0.700594i	$-0.752918\pi$
$709$	−38.0000	−1.42712	−0.713560	+	0.700594i	$0.752918\pi$
$710$	0	0
$711$	0	0
$712$	−10.3994	−0.389736
$713$	0	0
$714$	0	0
$715$	0	0
$716$	0	0
$717$	0	0
$718$	35.7626	1.33465
$719$	0	0		−	1.00000i	$-0.5\pi$
$719$	0	0			1.00000i	$0.5\pi$
$720$	0	0
$721$	41.6786	1.55219
$722$	31.5445	1.17397
$723$	0	0
$724$	9.58458	0.356208
$725$	0	0
$726$	0	0
$727$	0	0		−	1.00000i	$-0.5\pi$
$727$	0	0			1.00000i	$0.5\pi$
$728$	29.2861	1.08542
$729$	0	0
$730$	0	0
$731$	0	0
$732$	0	0
$733$	0	0		−	1.00000i	$-0.5\pi$
$733$	0	0			1.00000i	$0.5\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	52.4719	1.93283
$738$	0	0
$739$	0	0		−	1.00000i	$-0.5\pi$
$739$	0	0			1.00000i	$0.5\pi$
$740$	0	0
$741$	0	0
$742$	0	0
$743$	−54.3952	−1.99557	−0.997783	−	0.0665586i	$-0.978798\pi$
$743$	−54.3952	−1.99557	−0.997783	+	0.0665586i	$0.978798\pi$
$744$	0	0
$745$	0	0
$746$	16.6024	0.607856
$747$	0	0
$748$	−30.7124	−1.12296
$749$	0	0
$750$	0	0
$751$	0	0		−	1.00000i	$-0.5\pi$
$751$	0	0			1.00000i	$0.5\pi$
$752$	8.47982	0.309227
$753$	0	0
$754$	0	0
$755$	0	0
$756$	0	0
$757$	0	0		−	1.00000i	$-0.5\pi$
$757$	0	0			1.00000i	$0.5\pi$
$758$	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
$763$	94.3847	3.41696
$764$	−16.2931	−0.589465
$765$	0	0
$766$	0	0
$767$	0	0
$768$	0	0
$769$	0	0		−	1.00000i	$-0.5\pi$
$769$	0	0			1.00000i	$0.5\pi$
$770$	0	0
$771$	0	0
$772$	0	0
$773$	−53.8516	−1.93691	−0.968455	−	0.249190i	$-0.919836\pi$
$773$	−53.8516	−1.93691	−0.968455	+	0.249190i	$0.919836\pi$
$774$	0	0
$775$	0	0
$776$	0	0
$777$	0	0
$778$	−46.7655	−1.67662
$779$	0	0
$780$	0	0
$781$	0	0
$782$	0	0
$783$	0	0
$784$	−99.5159	−3.55414
$785$	0	0
$786$	0	0
$787$	4.00000	0.142585	0.0712923	−	0.997455i	$-0.477288\pi$
$787$	4.00000	0.142585	0.0712923	+	0.997455i	$0.477288\pi$
$788$	0	0
$789$	0	0
$790$	0	0
$791$	59.6700	2.12162
$792$	0	0
$793$	0	0
$794$	−23.2433	−0.824875
$795$	0	0
$796$	4.29673	0.152294
$797$	10.7703	0.381505	0.190752	−	0.981638i	$-0.438907\pi$
$797$	10.7703	0.381505	0.190752	+	0.981638i	$0.438907\pi$
$798$	0	0
$799$	14.1513	0.500638
$800$	−20.3664	−0.720061
$801$	0	0
$802$	0	0
$803$	0	0
$804$	0	0
$805$	0	0
$806$	0	0
$807$	0	0
$808$	37.3592	1.31429
$809$	17.8699	0.628273	0.314137	−	0.949378i	$-0.398285\pi$
$809$	17.8699	0.628273	0.314137	+	0.949378i	$0.398285\pi$
$810$	0	0
$811$	−51.8628	−1.82115	−0.910575	−	0.413343i	$-0.864361\pi$
$811$	−51.8628	−1.82115	−0.910575	+	0.413343i	$0.864361\pi$
$812$	0	0
$813$	0	0
$814$	0	0
$815$	0	0
$816$	0	0
$817$	0	0
$818$	0	0
$819$	0	0
$820$	0	0
$821$	0	0		−	1.00000i	$-0.5\pi$
$821$	0	0			1.00000i	$0.5\pi$
$822$	0	0
$823$	0	0		−	1.00000i	$-0.5\pi$
$823$	0	0			1.00000i	$0.5\pi$
$824$	16.5175	0.575415
$825$	0	0
$826$	0	0
$827$	−43.0813	−1.49808	−0.749042	−	0.662522i	$-0.769486\pi$
$827$	−43.0813	−1.49808	−0.749042	+	0.662522i	$0.769486\pi$
$828$	0	0
$829$	0	0		−	1.00000i	$-0.5\pi$
$829$	0	0			1.00000i	$0.5\pi$
$830$	0	0
$831$	0	0
$832$	8.49095	0.294371
$833$	−166.075	−5.75415
$834$	0	0
$835$	0	0
$836$	0	0
$837$	0	0
$838$	0	0
$839$	−47.9786	−1.65641	−0.828203	−	0.560429i	$-0.810636\pi$
$839$	−47.9786	−1.65641	−0.828203	+	0.560429i	$0.810636\pi$
$840$	0	0
$841$	0	0
$842$	0	0
$843$	0	0
$844$	0	0
$845$	0	0
$846$	0	0
$847$	69.0397	2.37223
$848$	0	0
$849$	0	0
$850$	−68.4441	−2.34761
$851$	0	0
$852$	0	0
$853$	0	0		−	1.00000i	$-0.5\pi$
$853$	0	0			1.00000i	$0.5\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	0	0		−	1.00000i	$-0.5\pi$
$857$	0	0			1.00000i	$0.5\pi$
$858$	0	0
$859$	0	0		−	1.00000i	$-0.5\pi$
$859$	0	0			1.00000i	$0.5\pi$
$860$	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
$867$	0	0
$868$	0	0
$869$	0	0
$870$	0	0
$871$	29.0094	0.982945
$872$	37.4053	1.26670
$873$	0	0
$874$	0	0
$875$	0	0
$876$	0	0
$877$	−46.0000	−1.55331	−0.776655	−	0.629926i	$-0.783085\pi$
$877$	−46.0000	−1.55331	−0.776655	+	0.629926i	$0.783085\pi$
$878$	−42.4661	−1.43316
$879$	0	0
$880$	0	0
$881$	47.6420	1.60510	0.802550	−	0.596585i	$-0.203476\pi$
$881$	47.6420	1.60510	0.802550	+	0.596585i	$0.203476\pi$
$882$	0	0
$883$	−20.0000	−0.673054	−0.336527	−	0.941674i	$-0.609252\pi$
$883$	−20.0000	−0.673054	−0.336527	+	0.941674i	$0.609252\pi$
$884$	−16.9795	−0.571082
$885$	0	0
$886$	18.8291	0.632574
$887$	−50.9625	−1.71115	−0.855577	−	0.517676i	$-0.826797\pi$
$887$	−50.9625	−1.71115	−0.855577	+	0.517676i	$0.826797\pi$
$888$	0	0
$889$	0	0
$890$	0	0
$891$	0	0
$892$	3.58458	0.120021
$893$	0	0
$894$	0	0
$895$	0	0
$896$	−69.4174	−2.31907
$897$	0	0
$898$	−63.1176	−2.10626
$899$	0	0
$900$	0	0
$901$	0	0
$902$	88.0586	2.93203
$903$	0	0
$904$	23.6477	0.786509
$905$	0	0
$906$	0	0
$907$	0	0		−	1.00000i	$-0.5\pi$
$907$	0	0			1.00000i	$0.5\pi$
$908$	0	0
$909$	0	0
$910$	0	0
$911$	−14.5495	−0.482045	−0.241023	−	0.970520i	$-0.577483\pi$
$911$	−14.5495	−0.482045	−0.241023	+	0.970520i	$0.577483\pi$
$912$	0	0
$913$	0	0
$914$	−29.2964	−0.969040
$915$	0	0
$916$	0	0
$917$	94.8527	3.13231
$918$	0	0
$919$	−57.7788	−1.90595	−0.952973	−	0.303054i	$-0.901994\pi$
$919$	−57.7788	−1.90595	−0.952973	+	0.303054i	$0.901994\pi$
$920$	0	0
$921$	0	0
$922$	17.8813	0.588890
$923$	0	0
$924$	0	0
$925$	0	0
$926$	61.3284	2.01538
$927$	0	0
$928$	0	0
$929$	0	0		−	1.00000i	$-0.5\pi$
$929$	0	0			1.00000i	$0.5\pi$
$930$	0	0
$931$	0	0
$932$	0	0
$933$	0	0
$934$	−71.5252	−2.34038
$935$	0	0
$936$	0	0
$937$	−60.2660	−1.96881	−0.984403	−	0.175931i	$-0.943707\pi$
$937$	−60.2660	−1.96881	−0.984403	+	0.175931i	$0.943707\pi$
$938$	−92.1611	−3.00917
$939$	0	0
$940$	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
$947$	57.6034	1.87186	0.935930	−	0.352185i	$-0.114561\pi$
$947$	57.6034	1.87186	0.935930	+	0.352185i	$0.114561\pi$
$948$	0	0
$949$	0	0
$950$	0	0
$951$	0	0
$952$	−88.6897	−2.87445
$953$	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
$958$	−35.7626	−1.15544
$959$	56.1115	1.81193
$960$	0	0
$961$	−31.0000	−1.00000
$962$	0	0
$963$	0	0
$964$	−21.5846	−0.695192
$965$	0	0
$966$	0	0
$967$	0	0		−	1.00000i	$-0.5\pi$
$967$	0	0			1.00000i	$0.5\pi$
$968$	27.3609	0.879414
$969$	0	0
$970$	0	0
$971$	43.0813	1.38255	0.691273	−	0.722594i	$-0.257050\pi$
$971$	43.0813	1.38255	0.691273	+	0.722594i	$0.257050\pi$
$972$	0	0
$973$	109.795	3.51987
$974$	66.4095	2.12790
$975$	0	0
$976$	0	0
$977$	0	0		−	1.00000i	$-0.5\pi$
$977$	0	0			1.00000i	$0.5\pi$
$978$	0	0
$979$	−24.8044	−0.792751
$980$	0	0
$981$	0	0
$982$	71.5252	2.28246
$983$	21.5407	0.687040	0.343520	−	0.939145i	$-0.388381\pi$
$983$	21.5407	0.687040	0.343520	+	0.939145i	$0.388381\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	0	0
$988$	0	0
$989$	0	0
$990$	0	0
$991$	−37.4103	−1.18838	−0.594188	−	0.804326i	$-0.702527\pi$
$991$	−37.4103	−1.18838	−0.594188	+	0.804326i	$0.702527\pi$
$992$	0	0
$993$	0	0
$994$	0	0
$995$	0	0
$996$	0	0
$997$	0	0		−	1.00000i	$-0.5\pi$
$997$	0	0			1.00000i	$0.5\pi$
$998$	35.7705	1.13230
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7569.2.a.ba.1.2		6
3.2	odd	2	inner	7569.2.a.ba.1.5		6
29.12	odd	4		261.2.c.c.28.2	✓	6
29.17	odd	4		261.2.c.c.28.5	yes	6
29.28	even	2	inner	7569.2.a.ba.1.5		6
87.17	even	4		261.2.c.c.28.2	✓	6
87.41	even	4		261.2.c.c.28.5	yes	6
87.86	odd	2	CM	7569.2.a.ba.1.2		6
116.75	even	4		4176.2.o.p.289.2		6
116.99	even	4		4176.2.o.p.289.1		6
348.191	odd	4		4176.2.o.p.289.1		6
348.215	odd	4		4176.2.o.p.289.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
261.2.c.c.28.2	✓	6	29.12	odd	4
261.2.c.c.28.2	✓	6	87.17	even	4
261.2.c.c.28.5	yes	6	29.17	odd	4
261.2.c.c.28.5	yes	6	87.41	even	4
4176.2.o.p.289.1		6	116.99	even	4
4176.2.o.p.289.1		6	348.191	odd	4
4176.2.o.p.289.2		6	116.75	even	4
4176.2.o.p.289.2		6	348.215	odd	4
7569.2.a.ba.1.2		6	1.1	even	1	trivial
7569.2.a.ba.1.2		6	87.86	odd	2	CM
7569.2.a.ba.1.5		6	3.2	odd	2	inner
7569.2.a.ba.1.5		6	29.28	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:	\( N \)	\(=\)	\( 7569 = 3^{2} \cdot 29^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7569.a (trivial)

\(f(q)\)	\(=\)	\(q-1.66024 q^{2} +0.756389 q^{4} +5.20982 q^{7} +2.06469 q^{8} +4.92462 q^{11} +2.72260 q^{13} -8.64954 q^{14} -4.94065 q^{16} -8.24509 q^{17} -8.17603 q^{22} -5.00000 q^{25} -4.52016 q^{26} +3.94065 q^{28} +4.07328 q^{32} +13.6888 q^{34} -10.7703 q^{41} +3.72493 q^{44} -1.71634 q^{47} +20.1422 q^{49} +8.30119 q^{50} +2.05935 q^{52} +10.7567 q^{56} +3.11869 q^{64} +10.6550 q^{67} -6.23650 q^{68} +25.6564 q^{77} +17.8813 q^{82} +10.1678 q^{88} -5.03681 q^{89} +14.1843 q^{91} +2.84952 q^{94} -33.4409 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 12 q^{4} + 24 q^{16} + 6 q^{22} - 30 q^{25} - 30 q^{28} + 42 q^{34} + 42 q^{49} + 66 q^{52} + 126 q^{64} + 12 q^{88} + 24 q^{91} + 102 q^{94}+O(q^{100}) \) 6 * q + 12 * q^4 + 24 * q^16 + 6 * q^22 - 30 * q^25 - 30 * q^28 + 42 * q^34 + 42 * q^49 + 66 * q^52 + 126 * q^64 + 12 * q^88 + 24 * q^91 + 102 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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