LMFDB - Embedded newform 195.3.e.a.194.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [195,3,Mod(194,195)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("195.194"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(195, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 1])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 195 = 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	195.e (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [1,0,-3,4,-5] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	yes
Analytic conductor:	$5.31336515503$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label			194.1
Character	$\chi$	$=$	195.194

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$

$=$

$q-3.00000 q^{3} +4.00000 q^{4} -5.00000 q^{5} +1.00000 q^{7} +9.00000 q^{9} +17.0000 q^{11} -12.0000 q^{12} -13.0000 q^{13} +15.0000 q^{15} +16.0000 q^{16} +31.0000 q^{17} -20.0000 q^{20} -3.00000 q^{21} +19.0000 q^{23} +25.0000 q^{25} -27.0000 q^{27} +4.00000 q^{28} -51.0000 q^{33} -5.00000 q^{35} +36.0000 q^{36} +61.0000 q^{37} +39.0000 q^{39} -43.0000 q^{41} +68.0000 q^{44} -45.0000 q^{45} -48.0000 q^{48} -48.0000 q^{49} -93.0000 q^{51} -52.0000 q^{52} -41.0000 q^{53} -85.0000 q^{55} +38.0000 q^{59} +60.0000 q^{60} -73.0000 q^{61} +9.00000 q^{63} +64.0000 q^{64} +65.0000 q^{65} -74.0000 q^{67} +124.000 q^{68} -57.0000 q^{69} -103.000 q^{71} +94.0000 q^{73} -75.0000 q^{75} +17.0000 q^{77} -37.0000 q^{79} -80.0000 q^{80} +81.0000 q^{81} -12.0000 q^{84} -155.000 q^{85} +173.000 q^{89} -13.0000 q^{91} +76.0000 q^{92} +181.000 q^{97} +153.000 q^{99} +O(q^{100})$

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/195\mathbb{Z}\right)^\times$.

$n$	$106$	$131$	$157$
$\chi(n)$	$-1$	$-1$	$-1$

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	1.00000			$0$
$2$	0	0	−1.00000			$\pi$
$3$	−3.00000	−1.00000
$3$	−3.00000	−1.00000
$4$	4.00000	1.00000
$5$	−5.00000	−1.00000
$5$	−5.00000	−1.00000
$6$	0	0
$7$	1.00000	0.142857	0.0714286	−	0.997446i	$-0.477244\pi$
$7$	1.00000	0.142857	0.0714286	+	0.997446i	$0.477244\pi$
$8$	0	0
$9$	9.00000	1.00000
$10$	0	0
$11$	17.0000	1.54545	0.772727	−	0.634738i	$-0.218892\pi$
$11$	17.0000	1.54545	0.772727	+	0.634738i	$0.218892\pi$
$12$	−12.0000	−1.00000
$13$	−13.0000	−1.00000
$13$	−13.0000	−1.00000
$14$	0	0
$15$	15.0000	1.00000
$16$	16.0000	1.00000
$17$	31.0000	1.82353	0.911765	−	0.410713i	$-0.134720\pi$
$17$	31.0000	1.82353	0.911765	+	0.410713i	$0.134720\pi$
$18$	0	0
$19$	0	0	1.00000			$0$
$19$	0	0	−1.00000			$\pi$
$20$	−20.0000	−1.00000
$21$	−3.00000	−0.142857
$22$	0	0
$23$	19.0000	0.826087	0.413043	−	0.910711i	$-0.364466\pi$
$23$	19.0000	0.826087	0.413043	+	0.910711i	$0.364466\pi$
$24$	0	0
$25$	25.0000	1.00000
$26$	0	0
$27$	−27.0000	−1.00000
$28$	4.00000	0.142857
$29$	0	0	1.00000			$0$
$29$	0	0	−1.00000			$\pi$
$30$	0	0
$31$	0	0	1.00000			$0$
$31$	0	0	−1.00000			$\pi$
$32$	0	0
$33$	−51.0000	−1.54545
$34$	0	0
$35$	−5.00000	−0.142857
$36$	36.0000	1.00000
$37$	61.0000	1.64865	0.824324	−	0.566118i	$-0.191555\pi$
$37$	61.0000	1.64865	0.824324	+	0.566118i	$0.191555\pi$
$38$	0	0
$39$	39.0000	1.00000
$40$	0	0
$41$	−43.0000	−1.04878	−0.524390	−	0.851478i	$-0.675707\pi$
$41$	−43.0000	−1.04878	−0.524390	+	0.851478i	$0.675707\pi$
$42$	0	0
$43$	0	0	1.00000			$0$
$43$	0	0	−1.00000			$\pi$
$44$	68.0000	1.54545
$45$	−45.0000	−1.00000
$46$	0	0
$47$	0	0	1.00000			$0$
$47$	0	0	−1.00000			$\pi$
$48$	−48.0000	−1.00000
$49$	−48.0000	−0.979592
$50$	0	0
$51$	−93.0000	−1.82353
$52$	−52.0000	−1.00000
$53$	−41.0000	−0.773585	−0.386792	−	0.922167i	$-0.626417\pi$
$53$	−41.0000	−0.773585	−0.386792	+	0.922167i	$0.626417\pi$
$54$	0	0
$55$	−85.0000	−1.54545
$56$	0	0
$57$	0	0
$58$	0	0
$59$	38.0000	0.644068	0.322034	−	0.946728i	$-0.395633\pi$
$59$	38.0000	0.644068	0.322034	+	0.946728i	$0.395633\pi$
$60$	60.0000	1.00000
$61$	−73.0000	−1.19672	−0.598361	−	0.801227i	$-0.704181\pi$
$61$	−73.0000	−1.19672	−0.598361	+	0.801227i	$0.704181\pi$
$62$	0	0
$63$	9.00000	0.142857
$64$	64.0000	1.00000
$65$	65.0000	1.00000
$66$	0	0
$67$	−74.0000	−1.10448	−0.552239	−	0.833686i	$-0.686226\pi$
$67$	−74.0000	−1.10448	−0.552239	+	0.833686i	$0.686226\pi$
$68$	124.000	1.82353
$69$	−57.0000	−0.826087
$70$	0	0
$71$	−103.000	−1.45070	−0.725352	−	0.688378i	$-0.758323\pi$
$71$	−103.000	−1.45070	−0.725352	+	0.688378i	$0.758323\pi$
$72$	0	0
$73$	94.0000	1.28767	0.643836	−	0.765164i	$-0.277342\pi$
$73$	94.0000	1.28767	0.643836	+	0.765164i	$0.277342\pi$
$74$	0	0
$75$	−75.0000	−1.00000
$76$	0	0
$77$	17.0000	0.220779
$78$	0	0
$79$	−37.0000	−0.468354	−0.234177	−	0.972194i	$-0.575240\pi$
$79$	−37.0000	−0.468354	−0.234177	+	0.972194i	$0.575240\pi$
$80$	−80.0000	−1.00000
$81$	81.0000	1.00000
$82$	0	0
$83$	0	0	1.00000			$0$
$83$	0	0	−1.00000			$\pi$
$84$	−12.0000	−0.142857
$85$	−155.000	−1.82353
$86$	0	0
$87$	0	0
$88$	0	0
$89$	173.000	1.94382	0.971910	−	0.235352i	$-0.0756244\pi$
$89$	173.000	1.94382	0.971910	+	0.235352i	$0.0756244\pi$
$90$	0	0
$91$	−13.0000	−0.142857
$92$	76.0000	0.826087
$93$	0	0
$94$	0	0
$95$	0	0
$96$	0	0
$97$	181.000	1.86598	0.932990	−	0.359903i	$-0.117190\pi$
$97$	181.000	1.86598	0.932990	+	0.359903i	$0.117190\pi$
$98$	0	0
$99$	153.000	1.54545
$100$	100.000	1.00000
$101$	0	0	1.00000			$0$
$101$	0	0	−1.00000			$\pi$
$102$	0	0
$103$	0	0	1.00000			$0$
$103$	0	0	−1.00000			$\pi$
$104$	0	0
$105$	15.0000	0.142857
$106$	0	0
$107$	−149.000	−1.39252	−0.696262	−	0.717788i	$-0.745155\pi$
$107$	−149.000	−1.39252	−0.696262	+	0.717788i	$0.745155\pi$
$108$	−108.000	−1.00000
$109$	0	0	1.00000			$0$
$109$	0	0	−1.00000			$\pi$
$110$	0	0
$111$	−183.000	−1.64865
$112$	16.0000	0.142857
$113$	34.0000	0.300885	0.150442	−	0.988619i	$-0.451930\pi$
$113$	34.0000	0.300885	0.150442	+	0.988619i	$0.451930\pi$
$114$	0	0
$115$	−95.0000	−0.826087
$116$	0	0
$117$	−117.000	−1.00000
$118$	0	0
$119$	31.0000	0.260504
$120$	0	0
$121$	168.000	1.38843
$122$	0	0
$123$	129.000	1.04878
$124$	0	0
$125$	−125.000	−1.00000
$126$	0	0
$127$	0	0	1.00000			$0$
$127$	0	0	−1.00000			$\pi$
$128$	0	0
$129$	0	0
$130$	0	0
$131$	0	0	1.00000			$0$
$131$	0	0	−1.00000			$\pi$
$132$	−204.000	−1.54545
$133$	0	0
$134$	0	0
$135$	135.000	1.00000
$136$	0	0
$137$	0	0	1.00000			$0$
$137$	0	0	−1.00000			$\pi$
$138$	0	0
$139$	83.0000	0.597122	0.298561	−	0.954391i	$-0.403493\pi$
$139$	83.0000	0.597122	0.298561	+	0.954391i	$0.403493\pi$
$140$	−20.0000	−0.142857
$141$	0	0
$142$	0	0
$143$	−221.000	−1.54545
$144$	144.000	1.00000
$145$	0	0
$146$	0	0
$147$	144.000	0.979592
$148$	244.000	1.64865
$149$	53.0000	0.355705	0.177852	−	0.984057i	$-0.443085\pi$
$149$	53.0000	0.355705	0.177852	+	0.984057i	$0.443085\pi$
$150$	0	0
$151$	0	0	1.00000			$0$
$151$	0	0	−1.00000			$\pi$
$152$	0	0
$153$	279.000	1.82353
$154$	0	0
$155$	0	0
$156$	156.000	1.00000
$157$	0	0	1.00000			$0$
$157$	0	0	−1.00000			$\pi$
$158$	0	0
$159$	123.000	0.773585
$160$	0	0
$161$	19.0000	0.118012
$162$	0	0
$163$	−311.000	−1.90798	−0.953988	−	0.299846i	$-0.903065\pi$
$163$	−311.000	−1.90798	−0.953988	+	0.299846i	$0.903065\pi$
$164$	−172.000	−1.04878
$165$	255.000	1.54545
$166$	0	0
$167$	0	0	1.00000			$0$
$167$	0	0	−1.00000			$\pi$
$168$	0	0
$169$	169.000	1.00000
$170$	0	0
$171$	0	0
$172$	0	0
$173$	−86.0000	−0.497110	−0.248555	−	0.968618i	$-0.579956\pi$
$173$	−86.0000	−0.497110	−0.248555	+	0.968618i	$0.579956\pi$
$174$	0	0
$175$	25.0000	0.142857
$176$	272.000	1.54545
$177$	−114.000	−0.644068
$178$	0	0
$179$	0	0	1.00000			$0$
$179$	0	0	−1.00000			$\pi$
$180$	−180.000	−1.00000
$181$	167.000	0.922652	0.461326	−	0.887231i	$-0.347374\pi$
$181$	167.000	0.922652	0.461326	+	0.887231i	$0.347374\pi$
$182$	0	0
$183$	219.000	1.19672
$184$	0	0
$185$	−305.000	−1.64865
$186$	0	0
$187$	527.000	2.81818
$188$	0	0
$189$	−27.0000	−0.142857
$190$	0	0
$191$	0	0	1.00000			$0$
$191$	0	0	−1.00000			$\pi$
$192$	−192.000	−1.00000
$193$	−251.000	−1.30052	−0.650259	−	0.759713i	$-0.725340\pi$
$193$	−251.000	−1.30052	−0.650259	+	0.759713i	$0.725340\pi$
$194$	0	0
$195$	−195.000	−1.00000
$196$	−192.000	−0.979592
$197$	0	0	1.00000			$0$
$197$	0	0	−1.00000			$\pi$
$198$	0	0
$199$	−382.000	−1.91960	−0.959799	−	0.280688i	$-0.909437\pi$
$199$	−382.000	−1.91960	−0.959799	+	0.280688i	$0.909437\pi$
$200$	0	0
$201$	222.000	1.10448
$202$	0	0
$203$	0	0
$204$	−372.000	−1.82353
$205$	215.000	1.04878
$206$	0	0
$207$	171.000	0.826087
$208$	−208.000	−1.00000
$209$	0	0
$210$	0	0
$211$	−358.000	−1.69668	−0.848341	−	0.529450i	$-0.822398\pi$
$211$	−358.000	−1.69668	−0.848341	+	0.529450i	$0.822398\pi$
$212$	−164.000	−0.773585
$213$	309.000	1.45070
$214$	0	0
$215$	0	0
$216$	0	0
$217$	0	0
$218$	0	0
$219$	−282.000	−1.28767
$220$	−340.000	−1.54545
$221$	−403.000	−1.82353
$222$	0	0
$223$	−386.000	−1.73094	−0.865471	−	0.500959i	$-0.832981\pi$
$223$	−386.000	−1.73094	−0.865471	+	0.500959i	$0.832981\pi$
$224$	0	0
$225$	225.000	1.00000
$226$	0	0
$227$	0	0	1.00000			$0$
$227$	0	0	−1.00000			$\pi$
$228$	0	0
$229$	0	0	1.00000			$0$
$229$	0	0	−1.00000			$\pi$
$230$	0	0
$231$	−51.0000	−0.220779
$232$	0	0
$233$	−401.000	−1.72103	−0.860515	−	0.509425i	$-0.829858\pi$
$233$	−401.000	−1.72103	−0.860515	+	0.509425i	$0.829858\pi$
$234$	0	0
$235$	0	0
$236$	152.000	0.644068
$237$	111.000	0.468354
$238$	0	0
$239$	−127.000	−0.531381	−0.265690	−	0.964058i	$-0.585600\pi$
$239$	−127.000	−0.531381	−0.265690	+	0.964058i	$0.585600\pi$
$240$	240.000	1.00000
$241$	0	0	1.00000			$0$
$241$	0	0	−1.00000			$\pi$
$242$	0	0
$243$	−243.000	−1.00000
$244$	−292.000	−1.19672
$245$	240.000	0.979592
$246$	0	0
$247$	0	0
$248$	0	0
$249$	0	0
$250$	0	0
$251$	0	0	1.00000			$0$
$251$	0	0	−1.00000			$\pi$
$252$	36.0000	0.142857
$253$	323.000	1.27668
$254$	0	0
$255$	465.000	1.82353
$256$	256.000	1.00000
$257$	−254.000	−0.988327	−0.494163	−	0.869369i	$-0.664526\pi$
$257$	−254.000	−0.988327	−0.494163	+	0.869369i	$0.664526\pi$
$258$	0	0
$259$	61.0000	0.235521
$260$	260.000	1.00000
$261$	0	0
$262$	0	0
$263$	514.000	1.95437	0.977186	−	0.212384i	$-0.0681227\pi$
$263$	514.000	1.95437	0.977186	+	0.212384i	$0.0681227\pi$
$264$	0	0
$265$	205.000	0.773585
$266$	0	0
$267$	−519.000	−1.94382
$268$	−296.000	−1.10448
$269$	0	0	1.00000			$0$
$269$	0	0	−1.00000			$\pi$
$270$	0	0
$271$	0	0	1.00000			$0$
$271$	0	0	−1.00000			$\pi$
$272$	496.000	1.82353
$273$	39.0000	0.142857
$274$	0	0
$275$	425.000	1.54545
$276$	−228.000	−0.826087
$277$	0	0	1.00000			$0$
$277$	0	0	−1.00000			$\pi$
$278$	0	0
$279$	0	0
$280$	0	0
$281$	62.0000	0.220641	0.110320	−	0.993896i	$-0.464812\pi$
$281$	62.0000	0.220641	0.110320	+	0.993896i	$0.464812\pi$
$282$	0	0
$283$	0	0	1.00000			$0$
$283$	0	0	−1.00000			$\pi$
$284$	−412.000	−1.45070
$285$	0	0
$286$	0	0
$287$	−43.0000	−0.149826
$288$	0	0
$289$	672.000	2.32526
$290$	0	0
$291$	−543.000	−1.86598
$292$	376.000	1.28767
$293$	0	0	1.00000			$0$
$293$	0	0	−1.00000			$\pi$
$294$	0	0
$295$	−190.000	−0.644068
$296$	0	0
$297$	−459.000	−1.54545
$298$	0	0
$299$	−247.000	−0.826087
$300$	−300.000	−1.00000
$301$	0	0
$302$	0	0
$303$	0	0
$304$	0	0
$305$	365.000	1.19672
$306$	0	0
$307$	601.000	1.95765	0.978827	−	0.204688i	$-0.0656178\pi$
$307$	601.000	1.95765	0.978827	+	0.204688i	$0.0656178\pi$
$308$	68.0000	0.220779
$309$	0	0
$310$	0	0
$311$	0	0	1.00000			$0$
$311$	0	0	−1.00000			$\pi$
$312$	0	0
$313$	0	0	1.00000			$0$
$313$	0	0	−1.00000			$\pi$
$314$	0	0
$315$	−45.0000	−0.142857
$316$	−148.000	−0.468354
$317$	0	0	1.00000			$0$
$317$	0	0	−1.00000			$\pi$
$318$	0	0
$319$	0	0
$320$	−320.000	−1.00000
$321$	447.000	1.39252
$322$	0	0
$323$	0	0
$324$	324.000	1.00000
$325$	−325.000	−1.00000
$326$	0	0
$327$	0	0
$328$	0	0
$329$	0	0
$330$	0	0
$331$	0	0	1.00000			$0$
$331$	0	0	−1.00000			$\pi$
$332$	0	0
$333$	549.000	1.64865
$334$	0	0
$335$	370.000	1.10448
$336$	−48.0000	−0.142857
$337$	0	0	1.00000			$0$
$337$	0	0	−1.00000			$\pi$
$338$	0	0
$339$	−102.000	−0.300885
$340$	−620.000	−1.82353
$341$	0	0
$342$	0	0
$343$	−97.0000	−0.282799
$344$	0	0
$345$	285.000	0.826087
$346$	0	0
$347$	−629.000	−1.81268	−0.906340	−	0.422549i	$-0.861135\pi$
$347$	−629.000	−1.81268	−0.906340	+	0.422549i	$0.861135\pi$
$348$	0	0
$349$	0	0	1.00000			$0$
$349$	0	0	−1.00000			$\pi$
$350$	0	0
$351$	351.000	1.00000
$352$	0	0
$353$	0	0	1.00000			$0$
$353$	0	0	−1.00000			$\pi$
$354$	0	0
$355$	515.000	1.45070
$356$	692.000	1.94382
$357$	−93.0000	−0.260504
$358$	0	0
$359$	−562.000	−1.56546	−0.782730	−	0.622362i	$-0.786173\pi$
$359$	−562.000	−1.56546	−0.782730	+	0.622362i	$0.786173\pi$
$360$	0	0
$361$	361.000	1.00000
$362$	0	0
$363$	−504.000	−1.38843
$364$	−52.0000	−0.142857
$365$	−470.000	−1.28767
$366$	0	0
$367$	0	0	1.00000			$0$
$367$	0	0	−1.00000			$\pi$
$368$	304.000	0.826087
$369$	−387.000	−1.04878
$370$	0	0
$371$	−41.0000	−0.110512
$372$	0	0
$373$	0	0	1.00000			$0$
$373$	0	0	−1.00000			$\pi$
$374$	0	0
$375$	375.000	1.00000
$376$	0	0
$377$	0	0
$378$	0	0
$379$	0	0	1.00000			$0$
$379$	0	0	−1.00000			$\pi$
$380$	0	0
$381$	0	0
$382$	0	0
$383$	0	0	1.00000			$0$
$383$	0	0	−1.00000			$\pi$
$384$	0	0
$385$	−85.0000	−0.220779
$386$	0	0
$387$	0	0
$388$	724.000	1.86598
$389$	0	0	1.00000			$0$
$389$	0	0	−1.00000			$\pi$
$390$	0	0
$391$	589.000	1.50639
$392$	0	0
$393$	0	0
$394$	0	0
$395$	185.000	0.468354
$396$	612.000	1.54545
$397$	−779.000	−1.96222	−0.981108	−	0.193459i	$-0.938029\pi$
$397$	−779.000	−1.96222	−0.981108	+	0.193459i	$0.938029\pi$
$398$	0	0
$399$	0	0
$400$	400.000	1.00000
$401$	−178.000	−0.443890	−0.221945	−	0.975059i	$-0.571241\pi$
$401$	−178.000	−0.443890	−0.221945	+	0.975059i	$0.571241\pi$
$402$	0	0
$403$	0	0
$404$	0	0
$405$	−405.000	−1.00000
$406$	0	0
$407$	1037.00	2.54791
$408$	0	0
$409$	0	0	1.00000			$0$
$409$	0	0	−1.00000			$\pi$
$410$	0	0
$411$	0	0
$412$	0	0
$413$	38.0000	0.0920097
$414$	0	0
$415$	0	0
$416$	0	0
$417$	−249.000	−0.597122
$418$	0	0
$419$	0	0	1.00000			$0$
$419$	0	0	−1.00000			$\pi$
$420$	60.0000	0.142857
$421$	0	0	1.00000			$0$
$421$	0	0	−1.00000			$\pi$
$422$	0	0
$423$	0	0
$424$	0	0
$425$	775.000	1.82353
$426$	0	0
$427$	−73.0000	−0.170960
$428$	−596.000	−1.39252
$429$	663.000	1.54545
$430$	0	0
$431$	542.000	1.25754	0.628770	−	0.777591i	$-0.283559\pi$
$431$	542.000	1.25754	0.628770	+	0.777591i	$0.283559\pi$
$432$	−432.000	−1.00000
$433$	0	0	1.00000			$0$
$433$	0	0	−1.00000			$\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	0	0
$438$	0	0
$439$	−877.000	−1.99772	−0.998861	−	0.0477138i	$-0.984806\pi$
$439$	−877.000	−1.99772	−0.998861	+	0.0477138i	$0.984806\pi$
$440$	0	0
$441$	−432.000	−0.979592
$442$	0	0
$443$	739.000	1.66817	0.834086	−	0.551635i	$-0.185996\pi$
$443$	739.000	1.66817	0.834086	+	0.551635i	$0.185996\pi$
$444$	−732.000	−1.64865
$445$	−865.000	−1.94382
$446$	0	0
$447$	−159.000	−0.355705
$448$	64.0000	0.142857
$449$	−547.000	−1.21826	−0.609131	−	0.793069i	$-0.708482\pi$
$449$	−547.000	−1.21826	−0.609131	+	0.793069i	$0.708482\pi$
$450$	0	0
$451$	−731.000	−1.62084
$452$	136.000	0.300885
$453$	0	0
$454$	0	0
$455$	65.0000	0.142857
$456$	0	0
$457$	901.000	1.97155	0.985777	−	0.168060i	$-0.0537502\pi$
$457$	901.000	1.97155	0.985777	+	0.168060i	$0.0537502\pi$
$458$	0	0
$459$	−837.000	−1.82353
$460$	−380.000	−0.826087
$461$	−883.000	−1.91540	−0.957701	−	0.287766i	$-0.907087\pi$
$461$	−883.000	−1.91540	−0.957701	+	0.287766i	$0.907087\pi$
$462$	0	0
$463$	289.000	0.624190	0.312095	−	0.950051i	$-0.398969\pi$
$463$	289.000	0.624190	0.312095	+	0.950051i	$0.398969\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	691.000	1.47966	0.739829	−	0.672795i	$-0.234907\pi$
$467$	691.000	1.47966	0.739829	+	0.672795i	$0.234907\pi$
$468$	−468.000	−1.00000
$469$	−74.0000	−0.157783
$470$	0	0
$471$	0	0
$472$	0	0
$473$	0	0
$474$	0	0
$475$	0	0
$476$	124.000	0.260504
$477$	−369.000	−0.773585
$478$	0	0
$479$	953.000	1.98956	0.994781	−	0.102035i	$-0.0325354\pi$
$479$	953.000	1.98956	0.994781	+	0.102035i	$0.0325354\pi$
$480$	0	0
$481$	−793.000	−1.64865
$482$	0	0
$483$	−57.0000	−0.118012
$484$	672.000	1.38843
$485$	−905.000	−1.86598
$486$	0	0
$487$	−599.000	−1.22998	−0.614990	−	0.788535i	$-0.710840\pi$
$487$	−599.000	−1.22998	−0.614990	+	0.788535i	$0.710840\pi$
$488$	0	0
$489$	933.000	1.90798
$490$	0	0
$491$	0	0	1.00000			$0$
$491$	0	0	−1.00000			$\pi$
$492$	516.000	1.04878
$493$	0	0
$494$	0	0
$495$	−765.000	−1.54545
$496$	0	0
$497$	−103.000	−0.207243
$498$	0	0
$499$	0	0	1.00000			$0$
$499$	0	0	−1.00000			$\pi$
$500$	−500.000	−1.00000
$501$	0	0
$502$	0	0
$503$	34.0000	0.0675944	0.0337972	−	0.999429i	$-0.489240\pi$
$503$	34.0000	0.0675944	0.0337972	+	0.999429i	$0.489240\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	−507.000	−1.00000
$508$	0	0
$509$	893.000	1.75442	0.877210	−	0.480106i	$-0.159402\pi$
$509$	893.000	1.75442	0.877210	+	0.480106i	$0.159402\pi$
$510$	0	0
$511$	94.0000	0.183953
$512$	0	0
$513$	0	0
$514$	0	0
$515$	0	0
$516$	0	0
$517$	0	0
$518$	0	0
$519$	258.000	0.497110
$520$	0	0
$521$	0	0	1.00000			$0$
$521$	0	0	−1.00000			$\pi$
$522$	0	0
$523$	0	0	1.00000			$0$
$523$	0	0	−1.00000			$\pi$
$524$	0	0
$525$	−75.0000	−0.142857
$526$	0	0
$527$	0	0
$528$	−816.000	−1.54545
$529$	−168.000	−0.317580
$530$	0	0
$531$	342.000	0.644068
$532$	0	0
$533$	559.000	1.04878
$534$	0	0
$535$	745.000	1.39252
$536$	0	0
$537$	0	0
$538$	0	0
$539$	−816.000	−1.51391
$540$	540.000	1.00000
$541$	0	0	1.00000			$0$
$541$	0	0	−1.00000			$\pi$
$542$	0	0
$543$	−501.000	−0.922652
$544$	0	0
$545$	0	0
$546$	0	0
$547$	0	0	1.00000			$0$
$547$	0	0	−1.00000			$\pi$
$548$	0	0
$549$	−657.000	−1.19672
$550$	0	0
$551$	0	0
$552$	0	0
$553$	−37.0000	−0.0669078
$554$	0	0
$555$	915.000	1.64865
$556$	332.000	0.597122
$557$	0	0	1.00000			$0$
$557$	0	0	−1.00000			$\pi$
$558$	0	0
$559$	0	0
$560$	−80.0000	−0.142857
$561$	−1581.00	−2.81818
$562$	0	0
$563$	−1061.00	−1.88455	−0.942274	−	0.334844i	$-0.891316\pi$
$563$	−1061.00	−1.88455	−0.942274	+	0.334844i	$0.891316\pi$
$564$	0	0
$565$	−170.000	−0.300885
$566$	0	0
$567$	81.0000	0.142857
$568$	0	0
$569$	0	0	1.00000			$0$
$569$	0	0	−1.00000			$\pi$
$570$	0	0
$571$	−613.000	−1.07356	−0.536778	−	0.843724i	$-0.680359\pi$
$571$	−613.000	−1.07356	−0.536778	+	0.843724i	$0.680359\pi$
$572$	−884.000	−1.54545
$573$	0	0
$574$	0	0
$575$	475.000	0.826087
$576$	576.000	1.00000
$577$	−419.000	−0.726170	−0.363085	−	0.931756i	$-0.618277\pi$
$577$	−419.000	−0.726170	−0.363085	+	0.931756i	$0.618277\pi$
$578$	0	0
$579$	753.000	1.30052
$580$	0	0
$581$	0	0
$582$	0	0
$583$	−697.000	−1.19554
$584$	0	0
$585$	585.000	1.00000
$586$	0	0
$587$	0	0	1.00000			$0$
$587$	0	0	−1.00000			$\pi$
$588$	576.000	0.979592
$589$	0	0
$590$	0	0
$591$	0	0
$592$	976.000	1.64865
$593$	0	0	1.00000			$0$
$593$	0	0	−1.00000			$\pi$
$594$	0	0
$595$	−155.000	−0.260504
$596$	212.000	0.355705
$597$	1146.00	1.91960
$598$	0	0
$599$	0	0	1.00000			$0$
$599$	0	0	−1.00000			$\pi$
$600$	0	0
$601$	1007.00	1.67554	0.837770	−	0.546023i	$-0.183859\pi$
$601$	1007.00	1.67554	0.837770	+	0.546023i	$0.183859\pi$
$602$	0	0
$603$	−666.000	−1.10448
$604$	0	0
$605$	−840.000	−1.38843
$606$	0	0
$607$	0	0	1.00000			$0$
$607$	0	0	−1.00000			$\pi$
$608$	0	0
$609$	0	0
$610$	0	0
$611$	0	0
$612$	1116.00	1.82353
$613$	589.000	0.960848	0.480424	−	0.877036i	$-0.340483\pi$
$613$	589.000	0.960848	0.480424	+	0.877036i	$0.340483\pi$
$614$	0	0
$615$	−645.000	−1.04878
$616$	0	0
$617$	0	0	1.00000			$0$
$617$	0	0	−1.00000			$\pi$
$618$	0	0
$619$	0	0	1.00000			$0$
$619$	0	0	−1.00000			$\pi$
$620$	0	0
$621$	−513.000	−0.826087
$622$	0	0
$623$	173.000	0.277689
$624$	624.000	1.00000
$625$	625.000	1.00000
$626$	0	0
$627$	0	0
$628$	0	0
$629$	1891.00	3.00636
$630$	0	0
$631$	0	0	1.00000			$0$
$631$	0	0	−1.00000			$\pi$
$632$	0	0
$633$	1074.00	1.69668
$634$	0	0
$635$	0	0
$636$	492.000	0.773585
$637$	624.000	0.979592
$638$	0	0
$639$	−927.000	−1.45070
$640$	0	0
$641$	0	0	1.00000			$0$
$641$	0	0	−1.00000			$\pi$
$642$	0	0
$643$	−911.000	−1.41680	−0.708398	−	0.705813i	$-0.750582\pi$
$643$	−911.000	−1.41680	−0.708398	+	0.705813i	$0.750582\pi$
$644$	76.0000	0.118012
$645$	0	0
$646$	0	0
$647$	−1229.00	−1.89954	−0.949768	−	0.312954i	$-0.898681\pi$
$647$	−1229.00	−1.89954	−0.949768	+	0.312954i	$0.898681\pi$
$648$	0	0
$649$	646.000	0.995378
$650$	0	0
$651$	0	0
$652$	−1244.00	−1.90798
$653$	−1046.00	−1.60184	−0.800919	−	0.598773i	$-0.795655\pi$
$653$	−1046.00	−1.60184	−0.800919	+	0.598773i	$0.795655\pi$
$654$	0	0
$655$	0	0
$656$	−688.000	−1.04878
$657$	846.000	1.28767
$658$	0	0
$659$	0	0	1.00000			$0$
$659$	0	0	−1.00000			$\pi$
$660$	1020.00	1.54545
$661$	0	0	1.00000			$0$
$661$	0	0	−1.00000			$\pi$
$662$	0	0
$663$	1209.00	1.82353
$664$	0	0
$665$	0	0
$666$	0	0
$667$	0	0
$668$	0	0
$669$	1158.00	1.73094
$670$	0	0
$671$	−1241.00	−1.84948
$672$	0	0
$673$	0	0	1.00000			$0$
$673$	0	0	−1.00000			$\pi$
$674$	0	0
$675$	−675.000	−1.00000
$676$	676.000	1.00000
$677$	271.000	0.400295	0.200148	−	0.979766i	$-0.435858\pi$
$677$	271.000	0.400295	0.200148	+	0.979766i	$0.435858\pi$
$678$	0	0
$679$	181.000	0.266568
$680$	0	0
$681$	0	0
$682$	0	0
$683$	0	0	1.00000			$0$
$683$	0	0	−1.00000			$\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	0	0
$688$	0	0
$689$	533.000	0.773585
$690$	0	0
$691$	0	0	1.00000			$0$
$691$	0	0	−1.00000			$\pi$
$692$	−344.000	−0.497110
$693$	153.000	0.220779
$694$	0	0
$695$	−415.000	−0.597122
$696$	0	0
$697$	−1333.00	−1.91248
$698$	0	0
$699$	1203.00	1.72103
$700$	100.000	0.142857
$701$	0	0	1.00000			$0$
$701$	0	0	−1.00000			$\pi$
$702$	0	0
$703$	0	0
$704$	1088.00	1.54545
$705$	0	0
$706$	0	0
$707$	0	0
$708$	−456.000	−0.644068
$709$	0	0	1.00000			$0$
$709$	0	0	−1.00000			$\pi$
$710$	0	0
$711$	−333.000	−0.468354
$712$	0	0
$713$	0	0
$714$	0	0
$715$	1105.00	1.54545
$716$	0	0
$717$	381.000	0.531381
$718$	0	0
$719$	0	0	1.00000			$0$
$719$	0	0	−1.00000			$\pi$
$720$	−720.000	−1.00000
$721$	0	0
$722$	0	0
$723$	0	0
$724$	668.000	0.922652
$725$	0	0
$726$	0	0
$727$	0	0	1.00000			$0$
$727$	0	0	−1.00000			$\pi$
$728$	0	0
$729$	729.000	1.00000
$730$	0	0
$731$	0	0
$732$	876.000	1.19672
$733$	−731.000	−0.997271	−0.498636	−	0.866812i	$-0.666165\pi$
$733$	−731.000	−0.997271	−0.498636	+	0.866812i	$0.666165\pi$
$734$	0	0
$735$	−720.000	−0.979592
$736$	0	0
$737$	−1258.00	−1.70692
$738$	0	0
$739$	0	0	1.00000			$0$
$739$	0	0	−1.00000			$\pi$
$740$	−1220.00	−1.64865
$741$	0	0
$742$	0	0
$743$	0	0	1.00000			$0$
$743$	0	0	−1.00000			$\pi$
$744$	0	0
$745$	−265.000	−0.355705
$746$	0	0
$747$	0	0
$748$	2108.00	2.81818
$749$	−149.000	−0.198932
$750$	0	0
$751$	1307.00	1.74035	0.870173	−	0.492746i	$-0.164007\pi$
$751$	1307.00	1.74035	0.870173	+	0.492746i	$0.164007\pi$
$752$	0	0
$753$	0	0
$754$	0	0
$755$	0	0
$756$	−108.000	−0.142857
$757$	0	0	1.00000			$0$
$757$	0	0	−1.00000			$\pi$
$758$	0	0
$759$	−969.000	−1.27668
$760$	0	0
$761$	−898.000	−1.18003	−0.590013	−	0.807394i	$-0.700877\pi$
$761$	−898.000	−1.18003	−0.590013	+	0.807394i	$0.700877\pi$
$762$	0	0
$763$	0	0
$764$	0	0
$765$	−1395.00	−1.82353
$766$	0	0
$767$	−494.000	−0.644068
$768$	−768.000	−1.00000
$769$	0	0	1.00000			$0$
$769$	0	0	−1.00000			$\pi$
$770$	0	0
$771$	762.000	0.988327
$772$	−1004.00	−1.30052
$773$	0	0	1.00000			$0$
$773$	0	0	−1.00000			$\pi$
$774$	0	0
$775$	0	0
$776$	0	0
$777$	−183.000	−0.235521
$778$	0	0
$779$	0	0
$780$	−780.000	−1.00000
$781$	−1751.00	−2.24200
$782$	0	0
$783$	0	0
$784$	−768.000	−0.979592
$785$	0	0
$786$	0	0
$787$	1366.00	1.73571	0.867853	−	0.496822i	$-0.165500\pi$
$787$	1366.00	1.73571	0.867853	+	0.496822i	$0.165500\pi$
$788$	0	0
$789$	−1542.00	−1.95437
$790$	0	0
$791$	34.0000	0.0429836
$792$	0	0
$793$	949.000	1.19672
$794$	0	0
$795$	−615.000	−0.773585
$796$	−1528.00	−1.91960
$797$	1591.00	1.99624	0.998118	−	0.0613235i	$-0.0195321\pi$
$797$	1591.00	1.99624	0.998118	+	0.0613235i	$0.0195321\pi$
$798$	0	0
$799$	0	0
$800$	0	0
$801$	1557.00	1.94382
$802$	0	0
$803$	1598.00	1.99004
$804$	888.000	1.10448
$805$	−95.0000	−0.118012
$806$	0	0
$807$	0	0
$808$	0	0
$809$	0	0	1.00000			$0$
$809$	0	0	−1.00000			$\pi$
$810$	0	0
$811$	0	0	1.00000			$0$
$811$	0	0	−1.00000			$\pi$
$812$	0	0
$813$	0	0
$814$	0	0
$815$	1555.00	1.90798
$816$	−1488.00	−1.82353
$817$	0	0
$818$	0	0
$819$	−117.000	−0.142857
$820$	860.000	1.04878
$821$	1517.00	1.84775	0.923873	−	0.382698i	$-0.125005\pi$
$821$	1517.00	1.84775	0.923873	+	0.382698i	$0.125005\pi$
$822$	0	0
$823$	0	0	1.00000			$0$
$823$	0	0	−1.00000			$\pi$
$824$	0	0
$825$	−1275.00	−1.54545
$826$	0	0
$827$	0	0	1.00000			$0$
$827$	0	0	−1.00000			$\pi$
$828$	684.000	0.826087
$829$	−1462.00	−1.76357	−0.881785	−	0.471651i	$-0.843658\pi$
$829$	−1462.00	−1.76357	−0.881785	+	0.471651i	$0.843658\pi$
$830$	0	0
$831$	0	0
$832$	−832.000	−1.00000
$833$	−1488.00	−1.78631
$834$	0	0
$835$	0	0
$836$	0	0
$837$	0	0
$838$	0	0
$839$	233.000	0.277712	0.138856	−	0.990313i	$-0.455658\pi$
$839$	233.000	0.277712	0.138856	+	0.990313i	$0.455658\pi$
$840$	0	0
$841$	841.000	1.00000
$842$	0	0
$843$	−186.000	−0.220641
$844$	−1432.00	−1.69668
$845$	−845.000	−1.00000
$846$	0	0
$847$	168.000	0.198347
$848$	−656.000	−0.773585
$849$	0	0
$850$	0	0
$851$	1159.00	1.36193
$852$	1236.00	1.45070
$853$	−491.000	−0.575615	−0.287808	−	0.957688i	$-0.592926\pi$
$853$	−491.000	−0.575615	−0.287808	+	0.957688i	$0.592926\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	1471.00	1.71645	0.858226	−	0.513271i	$-0.171567\pi$
$857$	1471.00	1.71645	0.858226	+	0.513271i	$0.171567\pi$
$858$	0	0
$859$	−37.0000	−0.0430733	−0.0215367	−	0.999768i	$-0.506856\pi$
$859$	−37.0000	−0.0430733	−0.0215367	+	0.999768i	$0.506856\pi$
$860$	0	0
$861$	129.000	0.149826
$862$	0	0
$863$	0	0	1.00000			$0$
$863$	0	0	−1.00000			$\pi$
$864$	0	0
$865$	430.000	0.497110
$866$	0	0
$867$	−2016.00	−2.32526
$868$	0	0
$869$	−629.000	−0.723820
$870$	0	0
$871$	962.000	1.10448
$872$	0	0
$873$	1629.00	1.86598
$874$	0	0
$875$	−125.000	−0.142857
$876$	−1128.00	−1.28767
$877$	−794.000	−0.905359	−0.452680	−	0.891673i	$-0.649532\pi$
$877$	−794.000	−0.905359	−0.452680	+	0.891673i	$0.649532\pi$
$878$	0	0
$879$	0	0
$880$	−1360.00	−1.54545
$881$	0	0	1.00000			$0$
$881$	0	0	−1.00000			$\pi$
$882$	0	0
$883$	0	0	1.00000			$0$
$883$	0	0	−1.00000			$\pi$
$884$	−1612.00	−1.82353
$885$	570.000	0.644068
$886$	0	0
$887$	1411.00	1.59076	0.795378	−	0.606114i	$-0.207273\pi$
$887$	1411.00	1.59076	0.795378	+	0.606114i	$0.207273\pi$
$888$	0	0
$889$	0	0
$890$	0	0
$891$	1377.00	1.54545
$892$	−1544.00	−1.73094
$893$	0	0
$894$	0	0
$895$	0	0
$896$	0	0
$897$	741.000	0.826087
$898$	0	0
$899$	0	0
$900$	900.000	1.00000
$901$	−1271.00	−1.41065
$902$	0	0
$903$	0	0
$904$	0	0
$905$	−835.000	−0.922652
$906$	0	0
$907$	0	0	1.00000			$0$
$907$	0	0	−1.00000			$\pi$
$908$	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
$915$	−1095.00	−1.19672
$916$	0	0
$917$	0	0
$918$	0	0
$919$	1643.00	1.78781	0.893906	−	0.448254i	$-0.147954\pi$
$919$	1643.00	1.78781	0.893906	+	0.448254i	$0.147954\pi$
$920$	0	0
$921$	−1803.00	−1.95765
$922$	0	0
$923$	1339.00	1.45070
$924$	−204.000	−0.220779
$925$	1525.00	1.64865
$926$	0	0
$927$	0	0
$928$	0	0
$929$	53.0000	0.0570506	0.0285253	−	0.999593i	$-0.490919\pi$
$929$	53.0000	0.0570506	0.0285253	+	0.999593i	$0.490919\pi$
$930$	0	0
$931$	0	0
$932$	−1604.00	−1.72103
$933$	0	0
$934$	0	0
$935$	−2635.00	−2.81818
$936$	0	0
$937$	0	0	1.00000			$0$
$937$	0	0	−1.00000			$\pi$
$938$	0	0
$939$	0	0
$940$	0	0
$941$	1277.00	1.35707	0.678533	−	0.734569i	$-0.262616\pi$
$941$	1277.00	1.35707	0.678533	+	0.734569i	$0.262616\pi$
$942$	0	0
$943$	−817.000	−0.866384
$944$	608.000	0.644068
$945$	135.000	0.142857
$946$	0	0
$947$	0	0	1.00000			$0$
$947$	0	0	−1.00000			$\pi$
$948$	444.000	0.468354
$949$	−1222.00	−1.28767
$950$	0	0
$951$	0	0
$952$	0	0
$953$	−281.000	−0.294858	−0.147429	−	0.989073i	$-0.547100\pi$
$953$	−281.000	−0.294858	−0.147429	+	0.989073i	$0.547100\pi$
$954$	0	0
$955$	0	0
$956$	−508.000	−0.531381
$957$	0	0
$958$	0	0
$959$	0	0
$960$	960.000	1.00000
$961$	961.000	1.00000
$962$	0	0
$963$	−1341.00	−1.39252
$964$	0	0
$965$	1255.00	1.30052
$966$	0	0
$967$	−1394.00	−1.44157	−0.720786	−	0.693158i	$-0.756219\pi$
$967$	−1394.00	−1.44157	−0.720786	+	0.693158i	$0.756219\pi$
$968$	0	0
$969$	0	0
$970$	0	0
$971$	0	0	1.00000			$0$
$971$	0	0	−1.00000			$\pi$
$972$	−972.000	−1.00000
$973$	83.0000	0.0853032
$974$	0	0
$975$	975.000	1.00000
$976$	−1168.00	−1.19672
$977$	0	0	1.00000			$0$
$977$	0	0	−1.00000			$\pi$
$978$	0	0
$979$	2941.00	3.00409
$980$	960.000	0.979592
$981$	0	0
$982$	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
$991$	227.000	0.229062	0.114531	−	0.993420i	$-0.463464\pi$
$991$	227.000	0.229062	0.114531	+	0.993420i	$0.463464\pi$
$992$	0	0
$993$	0	0
$994$	0	0
$995$	1910.00	1.91960
$996$	0	0
$997$	0	0	1.00000			$0$
$997$	0	0	−1.00000			$\pi$
$998$	0	0
$999$	−1647.00	−1.64865

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	195.3.e.a.194.1	✓	1
3.2	odd	2		195.3.e.d.194.1	yes	1
5.4	even	2		195.3.e.c.194.1	yes	1
13.12	even	2		195.3.e.b.194.1	yes	1
15.14	odd	2		195.3.e.b.194.1	yes	1
39.38	odd	2		195.3.e.c.194.1	yes	1
65.64	even	2		195.3.e.d.194.1	yes	1
195.194	odd	2	CM	195.3.e.a.194.1	✓	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.3.e.a.194.1	✓	1	1.1	even	1	trivial
195.3.e.a.194.1	✓	1	195.194	odd	2	CM
195.3.e.b.194.1	yes	1	13.12	even	2
195.3.e.b.194.1	yes	1	15.14	odd	2
195.3.e.c.194.1	yes	1	5.4	even	2
195.3.e.c.194.1	yes	1	39.38	odd	2
195.3.e.d.194.1	yes	1	3.2	odd	2
195.3.e.d.194.1	yes	1	65.64	even	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 195 = 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	195.e (of order \(2\), degree \(1\), minimal)

\(n\)	\(106\)	\(131\)	\(157\)
\(\chi(n)\)	\(-1\)	\(-1\)	\(-1\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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