LMFDB - Embedded newform 6762.2.a.cf.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6762,2,Mod(1,6762)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6762, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("6762.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6762 = 2 \cdot 3 \cdot 7^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6762.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:	$53.9948418468$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	3.3.3132.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 15x - 6 $ x^3 - 15*x - 6
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 966)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-0.404409$ of defining polynomial
Character	$\chi$	$=$	6762.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -0.404409 q^{11} +1.00000 q^{12} -4.12043 q^{13} -1.00000 q^{15} +1.00000 q^{16} -5.31161 q^{17} -1.00000 q^{18} +2.71602 q^{19} -1.00000 q^{20} +0.404409 q^{22} -1.00000 q^{23} -1.00000 q^{24} -4.00000 q^{25} +4.12043 q^{26} +1.00000 q^{27} +9.12043 q^{29} +1.00000 q^{30} +9.83645 q^{31} -1.00000 q^{32} -0.404409 q^{33} +5.31161 q^{34} +1.00000 q^{36} -7.90720 q^{37} -2.71602 q^{38} -4.12043 q^{39} +1.00000 q^{40} +10.7160 q^{41} +0.808819 q^{43} -0.404409 q^{44} -1.00000 q^{45} +1.00000 q^{46} +10.8365 q^{47} +1.00000 q^{48} +4.00000 q^{50} -5.31161 q^{51} -4.12043 q^{52} -0.191181 q^{53} -1.00000 q^{54} +0.404409 q^{55} +2.71602 q^{57} -9.12043 q^{58} +8.31161 q^{59} -1.00000 q^{60} -10.0000 q^{61} -9.83645 q^{62} +1.00000 q^{64} +4.12043 q^{65} +0.404409 q^{66} +2.83645 q^{67} -5.31161 q^{68} -1.00000 q^{69} -6.92925 q^{71} -1.00000 q^{72} -4.59559 q^{73} +7.90720 q^{74} -4.00000 q^{75} +2.71602 q^{76} +4.12043 q^{78} -9.92925 q^{79} -1.00000 q^{80} +1.00000 q^{81} -10.7160 q^{82} +4.40441 q^{83} +5.31161 q^{85} -0.808819 q^{86} +9.12043 q^{87} +0.404409 q^{88} -7.90720 q^{89} +1.00000 q^{90} -1.00000 q^{92} +9.83645 q^{93} -10.8365 q^{94} -2.71602 q^{95} -1.00000 q^{96} -15.3613 q^{97} -0.404409 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} - 3 q^{5} - 3 q^{6} - 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 - 3 * q^5 - 3 * q^6 - 3 * q^8 + 3 * q^9	$ 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} - 3 q^{5} - 3 q^{6} - 3 q^{8} + 3 q^{9} + 3 q^{10} + 3 q^{12} + 3 q^{13} - 3 q^{15} + 3 q^{16} - 3 q^{17} - 3 q^{18} - 6 q^{19} - 3 q^{20} - 3 q^{23} - 3 q^{24} - 12 q^{25} - 3 q^{26} + 3 q^{27} + 12 q^{29} + 3 q^{30} - 3 q^{32} + 3 q^{34} + 3 q^{36} - 12 q^{37} + 6 q^{38} + 3 q^{39} + 3 q^{40} + 18 q^{41} - 3 q^{45} + 3 q^{46} + 3 q^{47} + 3 q^{48} + 12 q^{50} - 3 q^{51} + 3 q^{52} - 3 q^{53} - 3 q^{54} - 6 q^{57} - 12 q^{58} + 12 q^{59} - 3 q^{60} - 30 q^{61} + 3 q^{64} - 3 q^{65} - 21 q^{67} - 3 q^{68} - 3 q^{69} - 3 q^{71} - 3 q^{72} - 15 q^{73} + 12 q^{74} - 12 q^{75} - 6 q^{76} - 3 q^{78} - 12 q^{79} - 3 q^{80} + 3 q^{81} - 18 q^{82} + 12 q^{83} + 3 q^{85} + 12 q^{87} - 12 q^{89} + 3 q^{90} - 3 q^{92} - 3 q^{94} + 6 q^{95} - 3 q^{96}+O(q^{100}) $ 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 - 3 * q^5 - 3 * q^6 - 3 * q^8 + 3 * q^9 + 3 * q^10 + 3 * q^12 + 3 * q^13 - 3 * q^15 + 3 * q^16 - 3 * q^17 - 3 * q^18 - 6 * q^19 - 3 * q^20 - 3 * q^23 - 3 * q^24 - 12 * q^25 - 3 * q^26 + 3 * q^27 + 12 * q^29 + 3 * q^30 - 3 * q^32 + 3 * q^34 + 3 * q^36 - 12 * q^37 + 6 * q^38 + 3 * q^39 + 3 * q^40 + 18 * q^41 - 3 * q^45 + 3 * q^46 + 3 * q^47 + 3 * q^48 + 12 * q^50 - 3 * q^51 + 3 * q^52 - 3 * q^53 - 3 * q^54 - 6 * q^57 - 12 * q^58 + 12 * q^59 - 3 * q^60 - 30 * q^61 + 3 * q^64 - 3 * q^65 - 21 * q^67 - 3 * q^68 - 3 * q^69 - 3 * q^71 - 3 * q^72 - 15 * q^73 + 12 * q^74 - 12 * q^75 - 6 * q^76 - 3 * q^78 - 12 * q^79 - 3 * q^80 + 3 * q^81 - 18 * q^82 + 12 * q^83 + 3 * q^85 + 12 * q^87 - 12 * q^89 + 3 * q^90 - 3 * q^92 - 3 * q^94 + 6 * q^95 - 3 * q^96

Display 100 coefficients 10 coefficients

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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214	−0.223607	−	0.974679i	$-0.571783\pi$
$5$	−1.00000	−0.447214	−0.223607	+	0.974679i	$0.571783\pi$
$6$	−1.00000	−0.408248
$7$	0	0
$7$	0	0
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	1.00000	0.316228
$11$	−0.404409	−0.121934	−0.0609670	−	0.998140i	$-0.519418\pi$
$11$	−0.404409	−0.121934	−0.0609670	+	0.998140i	$0.519418\pi$
$12$	1.00000	0.288675
$13$	−4.12043	−1.14280	−0.571401	−	0.820671i	$-0.693600\pi$
$13$	−4.12043	−1.14280	−0.571401	+	0.820671i	$0.693600\pi$
$14$	0	0
$15$	−1.00000	−0.258199
$16$	1.00000	0.250000
$17$	−5.31161	−1.28826	−0.644128	−	0.764918i	$-0.722779\pi$
$17$	−5.31161	−1.28826	−0.644128	+	0.764918i	$0.722779\pi$
$18$	−1.00000	−0.235702
$19$	2.71602	0.623098	0.311549	−	0.950230i	$-0.399152\pi$
$19$	2.71602	0.623098	0.311549	+	0.950230i	$0.399152\pi$
$20$	−1.00000	−0.223607
$21$	0	0
$22$	0.404409	0.0862204
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−1.00000	−0.204124
$25$	−4.00000	−0.800000
$26$	4.12043	0.808083
$27$	1.00000	0.192450
$28$	0	0
$29$	9.12043	1.69362	0.846811	−	0.531894i	$-0.178520\pi$
$29$	9.12043	1.69362	0.846811	+	0.531894i	$0.178520\pi$
$30$	1.00000	0.182574
$31$	9.83645	1.76668	0.883340	−	0.468734i	$-0.155290\pi$
$31$	9.83645	1.76668	0.883340	+	0.468734i	$0.155290\pi$
$32$	−1.00000	−0.176777
$33$	−0.404409	−0.0703986
$34$	5.31161	0.910934
$35$	0	0
$36$	1.00000	0.166667
$37$	−7.90720	−1.29994	−0.649968	−	0.759961i	$-0.725218\pi$
$37$	−7.90720	−1.29994	−0.649968	+	0.759961i	$0.725218\pi$
$38$	−2.71602	−0.440597
$39$	−4.12043	−0.659797
$40$	1.00000	0.158114
$41$	10.7160	1.67356	0.836781	−	0.547538i	$-0.184435\pi$
$41$	10.7160	1.67356	0.836781	+	0.547538i	$0.184435\pi$
$42$	0	0
$43$	0.808819	0.123344	0.0616718	−	0.998096i	$-0.480357\pi$
$43$	0.808819	0.123344	0.0616718	+	0.998096i	$0.480357\pi$
$44$	−0.404409	−0.0609670
$45$	−1.00000	−0.149071
$46$	1.00000	0.147442
$47$	10.8365	1.58066	0.790330	−	0.612682i	$-0.209909\pi$
$47$	10.8365	1.58066	0.790330	+	0.612682i	$0.209909\pi$
$48$	1.00000	0.144338
$49$	0	0
$50$	4.00000	0.565685
$51$	−5.31161	−0.743775
$52$	−4.12043	−0.571401
$53$	−0.191181	−0.0262608	−0.0131304	−	0.999914i	$-0.504180\pi$
$53$	−0.191181	−0.0262608	−0.0131304	+	0.999914i	$0.504180\pi$
$54$	−1.00000	−0.136083
$55$	0.404409	0.0545305
$56$	0	0
$57$	2.71602	0.359746
$58$	−9.12043	−1.19757
$59$	8.31161	1.08208	0.541040	−	0.840997i	$-0.318031\pi$
$59$	8.31161	1.08208	0.541040	+	0.840997i	$0.318031\pi$
$60$	−1.00000	−0.129099
$61$	−10.0000	−1.28037	−0.640184	−	0.768221i	$-0.721142\pi$
$61$	−10.0000	−1.28037	−0.640184	+	0.768221i	$0.721142\pi$
$62$	−9.83645	−1.24923
$63$	0	0
$64$	1.00000	0.125000
$65$	4.12043	0.511077
$66$	0.404409	0.0497793
$67$	2.83645	0.346528	0.173264	−	0.984875i	$-0.444569\pi$
$67$	2.83645	0.346528	0.173264	+	0.984875i	$0.444569\pi$
$68$	−5.31161	−0.644128
$69$	−1.00000	−0.120386
$70$	0	0
$71$	−6.92925	−0.822351	−0.411175	−	0.911556i	$-0.634882\pi$
$71$	−6.92925	−0.822351	−0.411175	+	0.911556i	$0.634882\pi$
$72$	−1.00000	−0.117851
$73$	−4.59559	−0.537873	−0.268937	−	0.963158i	$-0.586672\pi$
$73$	−4.59559	−0.537873	−0.268937	+	0.963158i	$0.586672\pi$
$74$	7.90720	0.919194
$75$	−4.00000	−0.461880
$76$	2.71602	0.311549
$77$	0	0
$78$	4.12043	0.466547
$79$	−9.92925	−1.11713	−0.558564	−	0.829461i	$-0.688647\pi$
$79$	−9.92925	−1.11713	−0.558564	+	0.829461i	$0.688647\pi$
$80$	−1.00000	−0.111803
$81$	1.00000	0.111111
$82$	−10.7160	−1.18339
$83$	4.40441	0.483447	0.241723	−	0.970345i	$-0.422287\pi$
$83$	4.40441	0.483447	0.241723	+	0.970345i	$0.422287\pi$
$84$	0	0
$85$	5.31161	0.576125
$86$	−0.808819	−0.0872172
$87$	9.12043	0.977813
$88$	0.404409	0.0431102
$89$	−7.90720	−0.838162	−0.419081	−	0.907949i	$-0.637648\pi$
$89$	−7.90720	−0.838162	−0.419081	+	0.907949i	$0.637648\pi$
$90$	1.00000	0.105409
$91$	0	0
$92$	−1.00000	−0.104257
$93$	9.83645	1.01999
$94$	−10.8365	−1.11769
$95$	−2.71602	−0.278658
$96$	−1.00000	−0.102062
$97$	−15.3613	−1.55970	−0.779852	−	0.625965i	$-0.784705\pi$
$97$	−15.3613	−1.55970	−0.779852	+	0.625965i	$0.784705\pi$
$98$	0	0
$99$	−0.404409	−0.0406447
$100$	−4.00000	−0.400000
$101$	5.19118	0.516542	0.258271	−	0.966073i	$-0.416847\pi$
$101$	5.19118	0.516542	0.258271	+	0.966073i	$0.416847\pi$
$102$	5.31161	0.525928
$103$	−16.8365	−1.65895	−0.829473	−	0.558548i	$-0.811359\pi$
$103$	−16.8365	−1.65895	−0.829473	+	0.558548i	$0.811359\pi$
$104$	4.12043	0.404042
$105$	0	0
$106$	0.191181	0.0185692
$107$	−9.59559	−0.927641	−0.463820	−	0.885929i	$-0.653522\pi$
$107$	−9.59559	−0.927641	−0.463820	+	0.885929i	$0.653522\pi$
$108$	1.00000	0.0962250
$109$	−3.19118	−0.305660	−0.152830	−	0.988253i	$-0.548839\pi$
$109$	−3.19118	−0.305660	−0.152830	+	0.988253i	$0.548839\pi$
$110$	−0.404409	−0.0385589
$111$	−7.90720	−0.750519
$112$	0	0
$113$	−18.7437	−1.76325	−0.881627	−	0.471946i	$-0.843552\pi$
$113$	−18.7437	−1.76325	−0.881627	+	0.471946i	$0.843552\pi$
$114$	−2.71602	−0.254379
$115$	1.00000	0.0932505
$116$	9.12043	0.846811
$117$	−4.12043	−0.380934
$118$	−8.31161	−0.765146
$119$	0	0
$120$	1.00000	0.0912871
$121$	−10.8365	−0.985132
$122$	10.0000	0.905357
$123$	10.7160	0.966231
$124$	9.83645	0.883340
$125$	9.00000	0.804984
$126$	0	0
$127$	−11.5956	−1.02894	−0.514471	−	0.857508i	$-0.672012\pi$
$127$	−11.5956	−1.02894	−0.514471	+	0.857508i	$0.672012\pi$
$128$	−1.00000	−0.0883883
$129$	0.808819	0.0712125
$130$	−4.12043	−0.361386
$131$	−16.7657	−1.46483	−0.732413	−	0.680860i	$-0.761606\pi$
$131$	−16.7657	−1.46483	−0.732413	+	0.680860i	$0.761606\pi$
$132$	−0.404409	−0.0351993
$133$	0	0
$134$	−2.83645	−0.245032
$135$	−1.00000	−0.0860663
$136$	5.31161	0.455467
$137$	−9.64527	−0.824051	−0.412026	−	0.911172i	$-0.635179\pi$
$137$	−9.64527	−0.824051	−0.412026	+	0.911172i	$0.635179\pi$
$138$	1.00000	0.0851257
$139$	16.8641	1.43039	0.715197	−	0.698923i	$-0.246337\pi$
$139$	16.8641	1.43039	0.715197	+	0.698923i	$0.246337\pi$
$140$	0	0
$141$	10.8365	0.912594
$142$	6.92925	0.581490
$143$	1.66634	0.139346
$144$	1.00000	0.0833333
$145$	−9.12043	−0.757411
$146$	4.59559	0.380334
$147$	0	0
$148$	−7.90720	−0.649968
$149$	−10.2132	−0.836700	−0.418350	−	0.908286i	$-0.637391\pi$
$149$	−10.2132	−0.836700	−0.418350	+	0.908286i	$0.637391\pi$
$150$	4.00000	0.326599
$151$	5.59559	0.455363	0.227681	−	0.973736i	$-0.426886\pi$
$151$	5.59559	0.455363	0.227681	+	0.973736i	$0.426886\pi$
$152$	−2.71602	−0.220298
$153$	−5.31161	−0.429418
$154$	0	0
$155$	−9.83645	−0.790083
$156$	−4.12043	−0.329899
$157$	−22.7713	−1.81735	−0.908673	−	0.417508i	$-0.862904\pi$
$157$	−22.7713	−1.81735	−0.908673	+	0.417508i	$0.862904\pi$
$158$	9.92925	0.789929
$159$	−0.191181	−0.0151617
$160$	1.00000	0.0790569
$161$	0	0
$162$	−1.00000	−0.0785674
$163$	24.7713	1.94024	0.970119	−	0.242631i	$-0.0780105\pi$
$163$	24.7713	1.94024	0.970119	+	0.242631i	$0.0780105\pi$
$164$	10.7160	0.836781
$165$	0.404409	0.0314832
$166$	−4.40441	−0.341848
$167$	19.0773	1.47625	0.738123	−	0.674666i	$-0.235712\pi$
$167$	19.0773	1.47625	0.738123	+	0.674666i	$0.235712\pi$
$168$	0	0
$169$	3.97795	0.305996
$170$	−5.31161	−0.407382
$171$	2.71602	0.207699
$172$	0.808819	0.0616718
$173$	−6.24086	−0.474484	−0.237242	−	0.971451i	$-0.576243\pi$
$173$	−6.24086	−0.474484	−0.237242	+	0.971451i	$0.576243\pi$
$174$	−9.12043	−0.691418
$175$	0	0
$176$	−0.404409	−0.0304835
$177$	8.31161	0.624739
$178$	7.90720	0.592670
$179$	−11.2188	−0.838534	−0.419267	−	0.907863i	$-0.637713\pi$
$179$	−11.2188	−0.838534	−0.419267	+	0.907863i	$0.637713\pi$
$180$	−1.00000	−0.0745356
$181$	−8.24086	−0.612538	−0.306269	−	0.951945i	$-0.599081\pi$
$181$	−8.24086	−0.612538	−0.306269	+	0.951945i	$0.599081\pi$
$182$	0	0
$183$	−10.0000	−0.739221
$184$	1.00000	0.0737210
$185$	7.90720	0.581349
$186$	−9.83645	−0.721244
$187$	2.14807	0.157082
$188$	10.8365	0.790330
$189$	0	0
$190$	2.71602	0.197041
$191$	24.7713	1.79239	0.896194	−	0.443663i	$-0.146321\pi$
$191$	24.7713	1.79239	0.896194	+	0.443663i	$0.146321\pi$
$192$	1.00000	0.0721688
$193$	−14.8585	−1.06954	−0.534769	−	0.844998i	$-0.679601\pi$
$193$	−14.8585	−1.06954	−0.534769	+	0.844998i	$0.679601\pi$
$194$	15.3613	1.10288
$195$	4.12043	0.295070
$196$	0	0
$197$	−11.4320	−0.814499	−0.407250	−	0.913317i	$-0.633512\pi$
$197$	−11.4320	−0.814499	−0.407250	+	0.913317i	$0.633512\pi$
$198$	0.404409	0.0287401
$199$	8.62323	0.611284	0.305642	−	0.952146i	$-0.401129\pi$
$199$	8.62323	0.611284	0.305642	+	0.952146i	$0.401129\pi$
$200$	4.00000	0.282843
$201$	2.83645	0.200068
$202$	−5.19118	−0.365250
$203$	0	0
$204$	−5.31161	−0.371887
$205$	−10.7160	−0.748439
$206$	16.8365	1.17305
$207$	−1.00000	−0.0695048
$208$	−4.12043	−0.285701
$209$	−1.09838	−0.0759769
$210$	0	0
$211$	7.43204	0.511643	0.255821	−	0.966724i	$-0.417654\pi$
$211$	7.43204	0.511643	0.255821	+	0.966724i	$0.417654\pi$
$212$	−0.191181	−0.0131304
$213$	−6.92925	−0.474784
$214$	9.59559	0.655941
$215$	−0.808819	−0.0551610
$216$	−1.00000	−0.0680414
$217$	0	0
$218$	3.19118	0.216134
$219$	−4.59559	−0.310541
$220$	0.404409	0.0272653
$221$	21.8861	1.47222
$222$	7.90720	0.530697
$223$	−10.2188	−0.684303	−0.342151	−	0.939645i	$-0.611156\pi$
$223$	−10.2188	−0.684303	−0.342151	+	0.939645i	$0.611156\pi$
$224$	0	0
$225$	−4.00000	−0.266667
$226$	18.7437	1.24681
$227$	−12.2188	−0.810991	−0.405496	−	0.914097i	$-0.632901\pi$
$227$	−12.2188	−0.810991	−0.405496	+	0.914097i	$0.632901\pi$
$228$	2.71602	0.179873
$229$	−3.85193	−0.254543	−0.127271	−	0.991868i	$-0.540622\pi$
$229$	−3.85193	−0.254543	−0.127271	+	0.991868i	$0.540622\pi$
$230$	−1.00000	−0.0659380
$231$	0	0
$232$	−9.12043	−0.598786
$233$	−26.5304	−1.73807	−0.869033	−	0.494754i	$-0.835258\pi$
$233$	−26.5304	−1.73807	−0.869033	+	0.494754i	$0.835258\pi$
$234$	4.12043	0.269361
$235$	−10.8365	−0.706892
$236$	8.31161	0.541040
$237$	−9.92925	−0.644974
$238$	0	0
$239$	−16.0000	−1.03495	−0.517477	−	0.855697i	$-0.673129\pi$
$239$	−16.0000	−1.03495	−0.517477	+	0.855697i	$0.673129\pi$
$240$	−1.00000	−0.0645497
$241$	14.7933	0.952923	0.476461	−	0.879195i	$-0.341919\pi$
$241$	14.7933	0.952923	0.476461	+	0.879195i	$0.341919\pi$
$242$	10.8365	0.696594
$243$	1.00000	0.0641500
$244$	−10.0000	−0.640184
$245$	0	0
$246$	−10.7160	−0.683229
$247$	−11.1912	−0.712078
$248$	−9.83645	−0.624615
$249$	4.40441	0.279118
$250$	−9.00000	−0.569210
$251$	−14.0220	−0.885064	−0.442532	−	0.896753i	$-0.645920\pi$
$251$	−14.0220	−0.885064	−0.442532	+	0.896753i	$0.645920\pi$
$252$	0	0
$253$	0.404409	0.0254250
$254$	11.5956	0.727572
$255$	5.31161	0.332626
$256$	1.00000	0.0625000
$257$	−7.09838	−0.442785	−0.221393	−	0.975185i	$-0.571060\pi$
$257$	−7.09838	−0.442785	−0.221393	+	0.975185i	$0.571060\pi$
$258$	−0.808819	−0.0503548
$259$	0	0
$260$	4.12043	0.255538
$261$	9.12043	0.564541
$262$	16.7657	1.03579
$263$	−8.80882	−0.543175	−0.271588	−	0.962414i	$-0.587549\pi$
$263$	−8.80882	−0.543175	−0.271588	+	0.962414i	$0.587549\pi$
$264$	0.404409	0.0248897
$265$	0.191181	0.0117442
$266$	0	0
$267$	−7.90720	−0.483913
$268$	2.83645	0.173264
$269$	4.49721	0.274199	0.137100	−	0.990557i	$-0.456222\pi$
$269$	4.49721	0.274199	0.137100	+	0.990557i	$0.456222\pi$
$270$	1.00000	0.0608581
$271$	−15.2685	−0.927495	−0.463748	−	0.885967i	$-0.653496\pi$
$271$	−15.2685	−0.927495	−0.463748	+	0.885967i	$0.653496\pi$
$272$	−5.31161	−0.322064
$273$	0	0
$274$	9.64527	0.582692
$275$	1.61764	0.0975472
$276$	−1.00000	−0.0601929
$277$	−2.21323	−0.132980	−0.0664900	−	0.997787i	$-0.521180\pi$
$277$	−2.21323	−0.132980	−0.0664900	+	0.997787i	$0.521180\pi$
$278$	−16.8641	−1.01144
$279$	9.83645	0.588893
$280$	0	0
$281$	29.4110	1.75451	0.877256	−	0.480023i	$-0.159372\pi$
$281$	29.4110	1.75451	0.877256	+	0.480023i	$0.159372\pi$
$282$	−10.8365	−0.645301
$283$	−27.0773	−1.60958	−0.804790	−	0.593560i	$-0.797722\pi$
$283$	−27.0773	−1.60958	−0.804790	+	0.593560i	$0.797722\pi$
$284$	−6.92925	−0.411175
$285$	−2.71602	−0.160883
$286$	−1.66634	−0.0985328
$287$	0	0
$288$	−1.00000	−0.0589256
$289$	11.2132	0.659602
$290$	9.12043	0.535570
$291$	−15.3613	−0.900495
$292$	−4.59559	−0.268937
$293$	19.8641	1.16047	0.580236	−	0.814448i	$-0.302960\pi$
$293$	19.8641	1.16047	0.580236	+	0.814448i	$0.302960\pi$
$294$	0	0
$295$	−8.31161	−0.483921
$296$	7.90720	0.459597
$297$	−0.404409	−0.0234662
$298$	10.2132	0.591636
$299$	4.12043	0.238291
$300$	−4.00000	−0.230940
$301$	0	0
$302$	−5.59559	−0.321990
$303$	5.19118	0.298226
$304$	2.71602	0.155775
$305$	10.0000	0.572598
$306$	5.31161	0.303645
$307$	30.5745	1.74498	0.872490	−	0.488632i	$-0.162504\pi$
$307$	30.5745	1.74498	0.872490	+	0.488632i	$0.162504\pi$
$308$	0	0
$309$	−16.8365	−0.957792
$310$	9.83645	0.558673
$311$	7.07075	0.400945	0.200473	−	0.979699i	$-0.435752\pi$
$311$	7.07075	0.400945	0.200473	+	0.979699i	$0.435752\pi$
$312$	4.12043	0.233273
$313$	−7.68839	−0.434573	−0.217287	−	0.976108i	$-0.569721\pi$
$313$	−7.68839	−0.434573	−0.217287	+	0.976108i	$0.569721\pi$
$314$	22.7713	1.28506
$315$	0	0
$316$	−9.92925	−0.558564
$317$	−22.7933	−1.28020	−0.640101	−	0.768291i	$-0.721107\pi$
$317$	−22.7933	−1.28020	−0.640101	+	0.768291i	$0.721107\pi$
$318$	0.191181	0.0107209
$319$	−3.68839	−0.206510
$320$	−1.00000	−0.0559017
$321$	−9.59559	−0.535574
$322$	0	0
$323$	−14.4265	−0.802709
$324$	1.00000	0.0555556
$325$	16.4817	0.914242
$326$	−24.7713	−1.37195
$327$	−3.19118	−0.176473
$328$	−10.7160	−0.591693
$329$	0	0
$330$	−0.404409	−0.0222620
$331$	−20.5304	−1.12845	−0.564227	−	0.825620i	$-0.690826\pi$
$331$	−20.5304	−1.12845	−0.564227	+	0.825620i	$0.690826\pi$
$332$	4.40441	0.241723
$333$	−7.90720	−0.433312
$334$	−19.0773	−1.04386
$335$	−2.83645	−0.154972
$336$	0	0
$337$	16.7933	0.914791	0.457396	−	0.889263i	$-0.348782\pi$
$337$	16.7933	0.914791	0.457396	+	0.889263i	$0.348782\pi$
$338$	−3.97795	−0.216372
$339$	−18.7437	−1.01802
$340$	5.31161	0.288063
$341$	−3.97795	−0.215418
$342$	−2.71602	−0.146866
$343$	0	0
$344$	−0.808819	−0.0436086
$345$	1.00000	0.0538382
$346$	6.24086	0.335511
$347$	0.354728	0.0190428	0.00952141	−	0.999955i	$-0.496969\pi$
$347$	0.354728	0.0190428	0.00952141	+	0.999955i	$0.496969\pi$
$348$	9.12043	0.488906
$349$	−20.9292	−1.12032	−0.560159	−	0.828385i	$-0.689260\pi$
$349$	−20.9292	−1.12032	−0.560159	+	0.828385i	$0.689260\pi$
$350$	0	0
$351$	−4.12043	−0.219932
$352$	0.404409	0.0215551
$353$	26.5304	1.41207	0.706036	−	0.708176i	$-0.250482\pi$
$353$	26.5304	1.41207	0.706036	+	0.708176i	$0.250482\pi$
$354$	−8.31161	−0.441757
$355$	6.92925	0.367766
$356$	−7.90720	−0.419081
$357$	0	0
$358$	11.2188	0.592933
$359$	4.86409	0.256717	0.128358	−	0.991728i	$-0.459029\pi$
$359$	4.86409	0.256717	0.128358	+	0.991728i	$0.459029\pi$
$360$	1.00000	0.0527046
$361$	−11.6232	−0.611749
$362$	8.24086	0.433130
$363$	−10.8365	−0.568766
$364$	0	0
$365$	4.59559	0.240544
$366$	10.0000	0.522708
$367$	25.9569	1.35494	0.677469	−	0.735551i	$-0.263077\pi$
$367$	25.9569	1.35494	0.677469	+	0.735551i	$0.263077\pi$
$368$	−1.00000	−0.0521286
$369$	10.7160	0.557854
$370$	−7.90720	−0.411076
$371$	0	0
$372$	9.83645	0.509996
$373$	−13.6729	−0.707956	−0.353978	−	0.935254i	$-0.615171\pi$
$373$	−13.6729	−0.707956	−0.353978	+	0.935254i	$0.615171\pi$
$374$	−2.14807	−0.111074
$375$	9.00000	0.464758
$376$	−10.8365	−0.558847
$377$	−37.5801	−1.93547
$378$	0	0
$379$	−22.4541	−1.15339	−0.576695	−	0.816960i	$-0.695658\pi$
$379$	−22.4541	−1.15339	−0.576695	+	0.816960i	$0.695658\pi$
$380$	−2.71602	−0.139329
$381$	−11.5956	−0.594060
$382$	−24.7713	−1.26741
$383$	−12.3889	−0.633045	−0.316522	−	0.948585i	$-0.602515\pi$
$383$	−12.3889	−0.633045	−0.316522	+	0.948585i	$0.602515\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	14.8585	0.756278
$387$	0.808819	0.0411146
$388$	−15.3613	−0.779852
$389$	28.5370	1.44688	0.723442	−	0.690386i	$-0.242559\pi$
$389$	28.5370	1.44688	0.723442	+	0.690386i	$0.242559\pi$
$390$	−4.12043	−0.208646
$391$	5.31161	0.268620
$392$	0	0
$393$	−16.7657	−0.845718
$394$	11.4320	0.575938
$395$	9.92925	0.499595
$396$	−0.404409	−0.0203223
$397$	−5.31161	−0.266582	−0.133291	−	0.991077i	$-0.542555\pi$
$397$	−5.31161	−0.266582	−0.133291	+	0.991077i	$0.542555\pi$
$398$	−8.62323	−0.432243
$399$	0	0
$400$	−4.00000	−0.200000
$401$	−6.21323	−0.310274	−0.155137	−	0.987893i	$-0.549582\pi$
$401$	−6.21323	−0.310274	−0.155137	+	0.987893i	$0.549582\pi$
$402$	−2.83645	−0.141469
$403$	−40.5304	−2.01896
$404$	5.19118	0.258271
$405$	−1.00000	−0.0496904
$406$	0	0
$407$	3.19775	0.158506
$408$	5.31161	0.262964
$409$	−28.1049	−1.38970	−0.694850	−	0.719155i	$-0.744529\pi$
$409$	−28.1049	−1.38970	−0.694850	+	0.719155i	$0.744529\pi$
$410$	10.7160	0.529227
$411$	−9.64527	−0.475766
$412$	−16.8365	−0.829473
$413$	0	0
$414$	1.00000	0.0491473
$415$	−4.40441	−0.216204
$416$	4.12043	0.202021
$417$	16.8641	0.825838
$418$	1.09838	0.0537237
$419$	11.0056	0.537658	0.268829	−	0.963188i	$-0.413363\pi$
$419$	11.0056	0.537658	0.268829	+	0.963188i	$0.413363\pi$
$420$	0	0
$421$	−23.4873	−1.14470	−0.572351	−	0.820009i	$-0.693968\pi$
$421$	−23.4873	−1.14470	−0.572351	+	0.820009i	$0.693968\pi$
$422$	−7.43204	−0.361786
$423$	10.8365	0.526886
$424$	0.191181	0.00928459
$425$	21.2465	1.03060
$426$	6.92925	0.335723
$427$	0	0
$428$	−9.59559	−0.463820
$429$	1.66634	0.0804517
$430$	0.808819	0.0390047
$431$	24.4817	1.17924	0.589622	−	0.807680i	$-0.299277\pi$
$431$	24.4817	1.17924	0.589622	+	0.807680i	$0.299277\pi$
$432$	1.00000	0.0481125
$433$	−1.23527	−0.0593635	−0.0296818	−	0.999559i	$-0.509449\pi$
$433$	−1.23527	−0.0593635	−0.0296818	+	0.999559i	$0.509449\pi$
$434$	0	0
$435$	−9.12043	−0.437291
$436$	−3.19118	−0.152830
$437$	−2.71602	−0.129925
$438$	4.59559	0.219586
$439$	22.6453	1.08080	0.540400	−	0.841408i	$-0.318273\pi$
$439$	22.6453	1.08080	0.540400	+	0.841408i	$0.318273\pi$
$440$	−0.404409	−0.0192795
$441$	0	0
$442$	−21.8861	−1.04102
$443$	−7.90162	−0.375417	−0.187709	−	0.982225i	$-0.560106\pi$
$443$	−7.90162	−0.375417	−0.187709	+	0.982225i	$0.560106\pi$
$444$	−7.90720	−0.375259
$445$	7.90720	0.374837
$446$	10.2188	0.483875
$447$	−10.2132	−0.483069
$448$	0	0
$449$	16.3889	0.773441	0.386721	−	0.922197i	$-0.373608\pi$
$449$	16.3889	0.773441	0.386721	+	0.922197i	$0.373608\pi$
$450$	4.00000	0.188562
$451$	−4.33366	−0.204064
$452$	−18.7437	−0.881627
$453$	5.59559	0.262904
$454$	12.2188	0.573457
$455$	0	0
$456$	−2.71602	−0.127189
$457$	−31.0342	−1.45172	−0.725859	−	0.687843i	$-0.758558\pi$
$457$	−31.0342	−1.45172	−0.725859	+	0.687843i	$0.758558\pi$
$458$	3.85193	0.179989
$459$	−5.31161	−0.247925
$460$	1.00000	0.0466252
$461$	−7.61764	−0.354789	−0.177394	−	0.984140i	$-0.556767\pi$
$461$	−7.61764	−0.354789	−0.177394	+	0.984140i	$0.556767\pi$
$462$	0	0
$463$	8.80882	0.409381	0.204690	−	0.978827i	$-0.434381\pi$
$463$	8.80882	0.409381	0.204690	+	0.978827i	$0.434381\pi$
$464$	9.12043	0.423405
$465$	−9.83645	−0.456155
$466$	26.5304	1.22900
$467$	−0.808819	−0.0374277	−0.0187138	−	0.999825i	$-0.505957\pi$
$467$	−0.808819	−0.0374277	−0.0187138	+	0.999825i	$0.505957\pi$
$468$	−4.12043	−0.190467
$469$	0	0
$470$	10.8365	0.499848
$471$	−22.7713	−1.04925
$472$	−8.31161	−0.382573
$473$	−0.327094	−0.0150398
$474$	9.92925	0.456066
$475$	−10.8641	−0.498479
$476$	0	0
$477$	−0.191181	−0.00875359
$478$	16.0000	0.731823
$479$	28.3337	1.29460	0.647299	−	0.762236i	$-0.275899\pi$
$479$	28.3337	1.29460	0.647299	+	0.762236i	$0.275899\pi$
$480$	1.00000	0.0456435
$481$	32.5811	1.48557
$482$	−14.7933	−0.673818
$483$	0	0
$484$	−10.8365	−0.492566
$485$	15.3613	0.697520
$486$	−1.00000	−0.0453609
$487$	18.7005	0.847402	0.423701	−	0.905802i	$-0.360731\pi$
$487$	18.7005	0.847402	0.423701	+	0.905802i	$0.360731\pi$
$488$	10.0000	0.452679
$489$	24.7713	1.12020
$490$	0	0
$491$	5.09280	0.229835	0.114917	−	0.993375i	$-0.463340\pi$
$491$	5.09280	0.229835	0.114917	+	0.993375i	$0.463340\pi$
$492$	10.7160	0.483116
$493$	−48.4442	−2.18182
$494$	11.1912	0.503515
$495$	0.404409	0.0181768
$496$	9.83645	0.441670
$497$	0	0
$498$	−4.40441	−0.197366
$499$	19.4873	0.872372	0.436186	−	0.899857i	$-0.356329\pi$
$499$	19.4873	0.872372	0.436186	+	0.899857i	$0.356329\pi$
$500$	9.00000	0.402492
$501$	19.0773	0.852312
$502$	14.0220	0.625835
$503$	2.99441	0.133514	0.0667571	−	0.997769i	$-0.478735\pi$
$503$	2.99441	0.133514	0.0667571	+	0.997769i	$0.478735\pi$
$504$	0	0
$505$	−5.19118	−0.231005
$506$	−0.404409	−0.0179782
$507$	3.97795	0.176667
$508$	−11.5956	−0.514471
$509$	11.7437	0.520528	0.260264	−	0.965537i	$-0.416190\pi$
$509$	11.7437	0.520528	0.260264	+	0.965537i	$0.416190\pi$
$510$	−5.31161	−0.235202
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	2.71602	0.119915
$514$	7.09838	0.313096
$515$	16.8365	0.741903
$516$	0.808819	0.0356063
$517$	−4.38236	−0.192736
$518$	0	0
$519$	−6.24086	−0.273943
$520$	−4.12043	−0.180693
$521$	−5.21882	−0.228640	−0.114320	−	0.993444i	$-0.536469\pi$
$521$	−5.21882	−0.228640	−0.114320	+	0.993444i	$0.536469\pi$
$522$	−9.12043	−0.399190
$523$	26.4541	1.15676	0.578378	−	0.815769i	$-0.303686\pi$
$523$	26.4541	1.15676	0.578378	+	0.815769i	$0.303686\pi$
$524$	−16.7657	−0.732413
$525$	0	0
$526$	8.80882	0.384083
$527$	−52.2474	−2.27593
$528$	−0.404409	−0.0175997
$529$	1.00000	0.0434783
$530$	−0.191181	−0.00830439
$531$	8.31161	0.360693
$532$	0	0
$533$	−44.1546	−1.91255
$534$	7.90720	0.342178
$535$	9.59559	0.414854
$536$	−2.83645	−0.122516
$537$	−11.2188	−0.484128
$538$	−4.49721	−0.193888
$539$	0	0
$540$	−1.00000	−0.0430331
$541$	−3.31161	−0.142377	−0.0711887	−	0.997463i	$-0.522679\pi$
$541$	−3.31161	−0.142377	−0.0711887	+	0.997463i	$0.522679\pi$
$542$	15.2685	0.655838
$543$	−8.24086	−0.353649
$544$	5.31161	0.227734
$545$	3.19118	0.136695
$546$	0	0
$547$	3.95130	0.168945	0.0844726	−	0.996426i	$-0.473079\pi$
$547$	3.95130	0.168945	0.0844726	+	0.996426i	$0.473079\pi$
$548$	−9.64527	−0.412026
$549$	−10.0000	−0.426790
$550$	−1.61764	−0.0689763
$551$	24.7713	1.05529
$552$	1.00000	0.0425628
$553$	0	0
$554$	2.21323	0.0940310
$555$	7.90720	0.335642
$556$	16.8641	0.715197
$557$	2.60118	0.110215	0.0551077	−	0.998480i	$-0.482450\pi$
$557$	2.60118	0.110215	0.0551077	+	0.998480i	$0.482450\pi$
$558$	−9.83645	−0.416410
$559$	−3.33268	−0.140957
$560$	0	0
$561$	2.14807	0.0906914
$562$	−29.4110	−1.24063
$563$	25.4100	1.07090	0.535452	−	0.844566i	$-0.320141\pi$
$563$	25.4100	1.07090	0.535452	+	0.844566i	$0.320141\pi$
$564$	10.8365	0.456297
$565$	18.7437	0.788552
$566$	27.0773	1.13814
$567$	0	0
$568$	6.92925	0.290745
$569$	−16.5956	−0.695723	−0.347862	−	0.937546i	$-0.613092\pi$
$569$	−16.5956	−0.695723	−0.347862	+	0.937546i	$0.613092\pi$
$570$	2.71602	0.113762
$571$	32.6574	1.36667	0.683335	−	0.730105i	$-0.260529\pi$
$571$	32.6574	1.36667	0.683335	+	0.730105i	$0.260529\pi$
$572$	1.66634	0.0696732
$573$	24.7713	1.03484
$574$	0	0
$575$	4.00000	0.166812
$576$	1.00000	0.0416667
$577$	−0.545910	−0.0227265	−0.0113633	−	0.999935i	$-0.503617\pi$
$577$	−0.545910	−0.0227265	−0.0113633	+	0.999935i	$0.503617\pi$
$578$	−11.2132	−0.466409
$579$	−14.8585	−0.617498
$580$	−9.12043	−0.378705
$581$	0	0
$582$	15.3613	0.636746
$583$	0.0773155	0.00320208
$584$	4.59559	0.190167
$585$	4.12043	0.170359
$586$	−19.8641	−0.820578
$587$	−8.82097	−0.364080	−0.182040	−	0.983291i	$-0.558270\pi$
$587$	−8.82097	−0.364080	−0.182040	+	0.983291i	$0.558270\pi$
$588$	0	0
$589$	26.7160	1.10081
$590$	8.31161	0.342184
$591$	−11.4320	−0.470251
$592$	−7.90720	−0.324984
$593$	40.0553	1.64487	0.822436	−	0.568857i	$-0.192614\pi$
$593$	40.0553	1.64487	0.822436	+	0.568857i	$0.192614\pi$
$594$	0.404409	0.0165931
$595$	0	0
$596$	−10.2132	−0.418350
$597$	8.62323	0.352925
$598$	−4.12043	−0.168497
$599$	−24.4166	−0.997634	−0.498817	−	0.866707i	$-0.666232\pi$
$599$	−24.4166	−0.997634	−0.498817	+	0.866707i	$0.666232\pi$
$600$	4.00000	0.163299
$601$	9.21323	0.375815	0.187908	−	0.982187i	$-0.439829\pi$
$601$	9.21323	0.375815	0.187908	+	0.982187i	$0.439829\pi$
$602$	0	0
$603$	2.83645	0.115509
$604$	5.59559	0.227681
$605$	10.8365	0.440564
$606$	−5.19118	−0.210877
$607$	−33.6950	−1.36764	−0.683818	−	0.729653i	$-0.739682\pi$
$607$	−33.6950	−1.36764	−0.683818	+	0.729653i	$0.739682\pi$
$608$	−2.71602	−0.110149
$609$	0	0
$610$	−10.0000	−0.404888
$611$	−44.6509	−1.80638
$612$	−5.31161	−0.214709
$613$	−24.4265	−0.986575	−0.493288	−	0.869866i	$-0.664205\pi$
$613$	−24.4265	−0.986575	−0.493288	+	0.869866i	$0.664205\pi$
$614$	−30.5745	−1.23389
$615$	−10.7160	−0.432112
$616$	0	0
$617$	−2.41000	−0.0970228	−0.0485114	−	0.998823i	$-0.515448\pi$
$617$	−2.41000	−0.0970228	−0.0485114	+	0.998823i	$0.515448\pi$
$618$	16.8365	0.677261
$619$	−45.8486	−1.84281	−0.921406	−	0.388602i	$-0.872958\pi$
$619$	−45.8486	−1.84281	−0.921406	+	0.388602i	$0.872958\pi$
$620$	−9.83645	−0.395041
$621$	−1.00000	−0.0401286
$622$	−7.07075	−0.283511
$623$	0	0
$624$	−4.12043	−0.164949
$625$	11.0000	0.440000
$626$	7.68839	0.307290
$627$	−1.09838	−0.0438653
$628$	−22.7713	−0.908673
$629$	42.0000	1.67465
$630$	0	0
$631$	−33.5745	−1.33658	−0.668290	−	0.743901i	$-0.732974\pi$
$631$	−33.5745	−1.33658	−0.668290	+	0.743901i	$0.732974\pi$
$632$	9.92925	0.394964
$633$	7.43204	0.295397
$634$	22.7933	0.905239
$635$	11.5956	0.460157
$636$	−0.191181	−0.00758083
$637$	0	0
$638$	3.68839	0.146025
$639$	−6.92925	−0.274117
$640$	1.00000	0.0395285
$641$	−33.4110	−1.31965	−0.659827	−	0.751417i	$-0.729370\pi$
$641$	−33.4110	−1.31965	−0.659827	+	0.751417i	$0.729370\pi$
$642$	9.59559	0.378708
$643$	−11.5248	−0.454495	−0.227248	−	0.973837i	$-0.572973\pi$
$643$	−11.5248	−0.454495	−0.227248	+	0.973837i	$0.572973\pi$
$644$	0	0
$645$	−0.808819	−0.0318472
$646$	14.4265	0.567601
$647$	48.3402	1.90045	0.950225	−	0.311564i	$-0.100853\pi$
$647$	48.3402	1.90045	0.950225	+	0.311564i	$0.100853\pi$
$648$	−1.00000	−0.0392837
$649$	−3.36129	−0.131942
$650$	−16.4817	−0.646466
$651$	0	0
$652$	24.7713	0.970119
$653$	25.7989	1.00959	0.504795	−	0.863239i	$-0.331568\pi$
$653$	25.7989	1.00959	0.504795	+	0.863239i	$0.331568\pi$
$654$	3.19118	0.124785
$655$	16.7657	0.655090
$656$	10.7160	0.418390
$657$	−4.59559	−0.179291
$658$	0	0
$659$	−14.1856	−0.552592	−0.276296	−	0.961073i	$-0.589107\pi$
$659$	−14.1856	−0.552592	−0.276296	+	0.961073i	$0.589107\pi$
$660$	0.404409	0.0157416
$661$	47.3017	1.83982	0.919912	−	0.392125i	$-0.128260\pi$
$661$	47.3017	1.83982	0.919912	+	0.392125i	$0.128260\pi$
$662$	20.5304	0.797938
$663$	21.8861	0.849987
$664$	−4.40441	−0.170924
$665$	0	0
$666$	7.90720	0.306398
$667$	−9.12043	−0.353145
$668$	19.0773	0.738123
$669$	−10.2188	−0.395082
$670$	2.83645	0.109582
$671$	4.04409	0.156120
$672$	0	0
$673$	0.448503	0.0172885	0.00864425	−	0.999963i	$-0.497248\pi$
$673$	0.448503	0.0172885	0.00864425	+	0.999963i	$0.497248\pi$
$674$	−16.7933	−0.646855
$675$	−4.00000	−0.153960
$676$	3.97795	0.152998
$677$	16.6176	0.638668	0.319334	−	0.947642i	$-0.396541\pi$
$677$	16.6176	0.638668	0.319334	+	0.947642i	$0.396541\pi$
$678$	18.7437	0.719846
$679$	0	0
$680$	−5.31161	−0.203691
$681$	−12.2188	−0.468226
$682$	3.97795	0.152324
$683$	−27.2033	−1.04091	−0.520453	−	0.853890i	$-0.674237\pi$
$683$	−27.2033	−1.04091	−0.520453	+	0.853890i	$0.674237\pi$
$684$	2.71602	0.103850
$685$	9.64527	0.368527
$686$	0	0
$687$	−3.85193	−0.146960
$688$	0.808819	0.0308359
$689$	0.787750	0.0300109
$690$	−1.00000	−0.0380693
$691$	−45.0122	−1.71234	−0.856172	−	0.516692i	$-0.827163\pi$
$691$	−45.0122	−1.71234	−0.856172	+	0.516692i	$0.827163\pi$
$692$	−6.24086	−0.237242
$693$	0	0
$694$	−0.354728	−0.0134653
$695$	−16.8641	−0.639691
$696$	−9.12043	−0.345709
$697$	−56.9194	−2.15597
$698$	20.9292	0.792184
$699$	−26.5304	−1.00347
$700$	0	0
$701$	−35.6232	−1.34547	−0.672735	−	0.739883i	$-0.734881\pi$
$701$	−35.6232	−1.34547	−0.672735	+	0.739883i	$0.734881\pi$
$702$	4.12043	0.155516
$703$	−21.4761	−0.809988
$704$	−0.404409	−0.0152417
$705$	−10.8365	−0.408124
$706$	−26.5304	−0.998486
$707$	0	0
$708$	8.31161	0.312370
$709$	−20.1922	−0.758332	−0.379166	−	0.925329i	$-0.623789\pi$
$709$	−20.1922	−0.758332	−0.379166	+	0.925329i	$0.623789\pi$
$710$	−6.92925	−0.260050
$711$	−9.92925	−0.372376
$712$	7.90720	0.296335
$713$	−9.83645	−0.368378
$714$	0	0
$715$	−1.66634	−0.0623176
$716$	−11.2188	−0.419267
$717$	−16.0000	−0.597531
$718$	−4.86409	−0.181526
$719$	−0.977953	−0.0364715	−0.0182358	−	0.999834i	$-0.505805\pi$
$719$	−0.977953	−0.0364715	−0.0182358	+	0.999834i	$0.505805\pi$
$720$	−1.00000	−0.0372678
$721$	0	0
$722$	11.6232	0.432572
$723$	14.7933	0.550170
$724$	−8.24086	−0.306269
$725$	−36.4817	−1.35490
$726$	10.8365	0.402178
$727$	36.9348	1.36984	0.684919	−	0.728620i	$-0.259838\pi$
$727$	36.9348	1.36984	0.684919	+	0.728620i	$0.259838\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−4.59559	−0.170090
$731$	−4.29613	−0.158898
$732$	−10.0000	−0.369611
$733$	35.6354	1.31622	0.658111	−	0.752921i	$-0.271356\pi$
$733$	35.6354	1.31622	0.658111	+	0.752921i	$0.271356\pi$
$734$	−25.9569	−0.958086
$735$	0	0
$736$	1.00000	0.0368605
$737$	−1.14709	−0.0422535
$738$	−10.7160	−0.394462
$739$	−33.8697	−1.24592	−0.622958	−	0.782255i	$-0.714069\pi$
$739$	−33.8697	−1.24592	−0.622958	+	0.782255i	$0.714069\pi$
$740$	7.90720	0.290675
$741$	−11.1912	−0.411118
$742$	0	0
$743$	21.1537	0.776052	0.388026	−	0.921648i	$-0.373157\pi$
$743$	21.1537	0.776052	0.388026	+	0.921648i	$0.373157\pi$
$744$	−9.83645	−0.360622
$745$	10.2132	0.374184
$746$	13.6729	0.500601
$747$	4.40441	0.161149
$748$	2.14807	0.0785411
$749$	0	0
$750$	−9.00000	−0.328634
$751$	20.9789	0.765532	0.382766	−	0.923845i	$-0.374972\pi$
$751$	20.9789	0.765532	0.382766	+	0.923845i	$0.374972\pi$
$752$	10.8365	0.395165
$753$	−14.0220	−0.510992
$754$	37.5801	1.36859
$755$	−5.59559	−0.203644
$756$	0	0
$757$	−4.95688	−0.180161	−0.0900805	−	0.995934i	$-0.528712\pi$
$757$	−4.95688	−0.180161	−0.0900805	+	0.995934i	$0.528712\pi$
$758$	22.4541	0.815569
$759$	0.404409	0.0146791
$760$	2.71602	0.0985205
$761$	−19.5689	−0.709373	−0.354687	−	0.934985i	$-0.615412\pi$
$761$	−19.5689	−0.709373	−0.354687	+	0.934985i	$0.615412\pi$
$762$	11.5956	0.420064
$763$	0	0
$764$	24.7713	0.896194
$765$	5.31161	0.192042
$766$	12.3889	0.447630
$767$	−34.2474	−1.23660
$768$	1.00000	0.0360844
$769$	−4.92366	−0.177552	−0.0887759	−	0.996052i	$-0.528295\pi$
$769$	−4.92366	−0.177552	−0.0887759	+	0.996052i	$0.528295\pi$
$770$	0	0
$771$	−7.09838	−0.255642
$772$	−14.8585	−0.534769
$773$	2.02763	0.0729289	0.0364645	−	0.999335i	$-0.488390\pi$
$773$	2.02763	0.0729289	0.0364645	+	0.999335i	$0.488390\pi$
$774$	−0.808819	−0.0290724
$775$	−39.3458	−1.41334
$776$	15.3613	0.551438
$777$	0	0
$778$	−28.5370	−1.02310
$779$	29.1049	1.04279
$780$	4.12043	0.147535
$781$	2.80225	0.100273
$782$	−5.31161	−0.189943
$783$	9.12043	0.325938
$784$	0	0
$785$	22.7713	0.812742
$786$	16.7657	0.598013
$787$	0.268497	0.00957088	0.00478544	−	0.999989i	$-0.498477\pi$
$787$	0.268497	0.00957088	0.00478544	+	0.999989i	$0.498477\pi$
$788$	−11.4320	−0.407250
$789$	−8.80882	−0.313602
$790$	−9.92925	−0.353267
$791$	0	0
$792$	0.404409	0.0143701
$793$	41.2043	1.46321
$794$	5.31161	0.188502
$795$	0.191181	0.00678050
$796$	8.62323	0.305642
$797$	16.0497	0.568509	0.284254	−	0.958749i	$-0.408254\pi$
$797$	16.0497	0.568509	0.284254	+	0.958749i	$0.408254\pi$
$798$	0	0
$799$	−57.5590	−2.03629
$800$	4.00000	0.141421
$801$	−7.90720	−0.279387
$802$	6.21323	0.219397
$803$	1.85850	0.0655850
$804$	2.83645	0.100034
$805$	0	0
$806$	40.5304	1.42762
$807$	4.49721	0.158309
$808$	−5.19118	−0.182625
$809$	−7.72161	−0.271477	−0.135739	−	0.990745i	$-0.543341\pi$
$809$	−7.72161	−0.271477	−0.135739	+	0.990745i	$0.543341\pi$
$810$	1.00000	0.0351364
$811$	23.2465	0.816293	0.408147	−	0.912916i	$-0.366175\pi$
$811$	23.2465	0.816293	0.408147	+	0.912916i	$0.366175\pi$
$812$	0	0
$813$	−15.2685	−0.535490
$814$	−3.19775	−0.112081
$815$	−24.7713	−0.867700
$816$	−5.31161	−0.185944
$817$	2.19677	0.0768552
$818$	28.1049	0.982667
$819$	0	0
$820$	−10.7160	−0.374220
$821$	−39.1204	−1.36531	−0.682656	−	0.730740i	$-0.739175\pi$
$821$	−39.1204	−1.36531	−0.682656	+	0.730740i	$0.739175\pi$
$822$	9.64527	0.336417
$823$	42.1546	1.46942	0.734709	−	0.678382i	$-0.237319\pi$
$823$	42.1546	1.46942	0.734709	+	0.678382i	$0.237319\pi$
$824$	16.8365	0.586526
$825$	1.61764	0.0563189
$826$	0	0
$827$	54.3294	1.88922	0.944608	−	0.328200i	$-0.106442\pi$
$827$	54.3294	1.88922	0.944608	+	0.328200i	$0.106442\pi$
$828$	−1.00000	−0.0347524
$829$	−18.6397	−0.647383	−0.323691	−	0.946163i	$-0.604924\pi$
$829$	−18.6397	−0.647383	−0.323691	+	0.946163i	$0.604924\pi$
$830$	4.40441	0.152879
$831$	−2.21323	−0.0767760
$832$	−4.12043	−0.142850
$833$	0	0
$834$	−16.8641	−0.583956
$835$	−19.0773	−0.660198
$836$	−1.09838	−0.0379884
$837$	9.83645	0.339998
$838$	−11.0056	−0.380182
$839$	−32.9569	−1.13780	−0.568899	−	0.822407i	$-0.692630\pi$
$839$	−32.9569	−1.13780	−0.568899	+	0.822407i	$0.692630\pi$
$840$	0	0
$841$	54.1823	1.86835
$842$	23.4873	0.809426
$843$	29.4110	1.01297
$844$	7.43204	0.255821
$845$	−3.97795	−0.136846
$846$	−10.8365	−0.372565
$847$	0	0
$848$	−0.191181	−0.00656519
$849$	−27.0773	−0.929291
$850$	−21.2465	−0.728747
$851$	7.90720	0.271055
$852$	−6.92925	−0.237392
$853$	25.0497	0.857685	0.428842	−	0.903379i	$-0.358922\pi$
$853$	25.0497	0.857685	0.428842	+	0.903379i	$0.358922\pi$
$854$	0	0
$855$	−2.71602	−0.0928860
$856$	9.59559	0.327971
$857$	4.04870	0.138301	0.0691505	−	0.997606i	$-0.477971\pi$
$857$	4.04870	0.138301	0.0691505	+	0.997606i	$0.477971\pi$
$858$	−1.66634	−0.0568879
$859$	−47.7769	−1.63013	−0.815063	−	0.579372i	$-0.803298\pi$
$859$	−47.7769	−1.63013	−0.815063	+	0.579372i	$0.803298\pi$
$860$	−0.808819	−0.0275805
$861$	0	0
$862$	−24.4817	−0.833851
$863$	−24.8852	−0.847101	−0.423550	−	0.905873i	$-0.639216\pi$
$863$	−24.8852	−0.847101	−0.423550	+	0.905873i	$0.639216\pi$
$864$	−1.00000	−0.0340207
$865$	6.24086	0.212196
$866$	1.23527	0.0419763
$867$	11.2132	0.380821
$868$	0	0
$869$	4.01548	0.136216
$870$	9.12043	0.309212
$871$	−11.6874	−0.396013
$872$	3.19118	0.108067
$873$	−15.3613	−0.519901
$874$	2.71602	0.0918708
$875$	0	0
$876$	−4.59559	−0.155271
$877$	−4.06516	−0.137271	−0.0686354	−	0.997642i	$-0.521865\pi$
$877$	−4.06516	−0.137271	−0.0686354	+	0.997642i	$0.521865\pi$
$878$	−22.6453	−0.764241
$879$	19.8641	0.669999
$880$	0.404409	0.0136326
$881$	12.2132	0.411474	0.205737	−	0.978607i	$-0.434041\pi$
$881$	12.2132	0.411474	0.205737	+	0.978607i	$0.434041\pi$
$882$	0	0
$883$	−5.14248	−0.173058	−0.0865291	−	0.996249i	$-0.527578\pi$
$883$	−5.14248	−0.173058	−0.0865291	+	0.996249i	$0.527578\pi$
$884$	21.8861	0.736110
$885$	−8.31161	−0.279392
$886$	7.90162	0.265460
$887$	−30.3824	−1.02014	−0.510070	−	0.860133i	$-0.670380\pi$
$887$	−30.3824	−1.02014	−0.510070	+	0.860133i	$0.670380\pi$
$888$	7.90720	0.265348
$889$	0	0
$890$	−7.90720	−0.265050
$891$	−0.404409	−0.0135482
$892$	−10.2188	−0.342151
$893$	29.4320	0.984906
$894$	10.2132	0.341581
$895$	11.2188	0.375004
$896$	0	0
$897$	4.12043	0.137577
$898$	−16.3889	−0.546906
$899$	89.7127	2.99209
$900$	−4.00000	−0.133333
$901$	1.01548	0.0338306
$902$	4.33366	0.144295
$903$	0	0
$904$	18.7437	0.623405
$905$	8.24086	0.273936
$906$	−5.59559	−0.185901
$907$	−13.8796	−0.460864	−0.230432	−	0.973088i	$-0.574014\pi$
$907$	−13.8796	−0.460864	−0.230432	+	0.973088i	$0.574014\pi$
$908$	−12.2188	−0.405496
$909$	5.19118	0.172181
$910$	0	0
$911$	−27.3017	−0.904546	−0.452273	−	0.891879i	$-0.649387\pi$
$911$	−27.3017	−0.904546	−0.452273	+	0.891879i	$0.649387\pi$
$912$	2.71602	0.0899365
$913$	−1.78118	−0.0589486
$914$	31.0342	1.02652
$915$	10.0000	0.330590
$916$	−3.85193	−0.127271
$917$	0	0
$918$	5.31161	0.175309
$919$	38.4541	1.26848	0.634242	−	0.773135i	$-0.281312\pi$
$919$	38.4541	1.26848	0.634242	+	0.773135i	$0.281312\pi$
$920$	−1.00000	−0.0329690
$921$	30.5745	1.00746
$922$	7.61764	0.250874
$923$	28.5515	0.939784
$924$	0	0
$925$	31.6288	1.03995
$926$	−8.80882	−0.289476
$927$	−16.8365	−0.552982
$928$	−9.12043	−0.299393
$929$	−53.0674	−1.74109	−0.870543	−	0.492093i	$-0.836232\pi$
$929$	−53.0674	−1.74109	−0.870543	+	0.492093i	$0.836232\pi$
$930$	9.83645	0.322550
$931$	0	0
$932$	−26.5304	−0.869033
$933$	7.07075	0.231486
$934$	0.808819	0.0264654
$935$	−2.14807	−0.0702493
$936$	4.12043	0.134681
$937$	29.1645	0.952763	0.476382	−	0.879239i	$-0.341948\pi$
$937$	29.1645	0.952763	0.476382	+	0.879239i	$0.341948\pi$
$938$	0	0
$939$	−7.68839	−0.250901
$940$	−10.8365	−0.353446
$941$	−26.0220	−0.848294	−0.424147	−	0.905593i	$-0.639426\pi$
$941$	−26.0220	−0.848294	−0.424147	+	0.905593i	$0.639426\pi$
$942$	22.7713	0.741929
$943$	−10.7160	−0.348962
$944$	8.31161	0.270520
$945$	0	0
$946$	0.327094	0.0106347
$947$	−12.9227	−0.419931	−0.209965	−	0.977709i	$-0.567335\pi$
$947$	−12.9227	−0.419931	−0.209965	+	0.977709i	$0.567335\pi$
$948$	−9.92925	−0.322487
$949$	18.9358	0.614683
$950$	10.8641	0.352478
$951$	−22.7933	−0.739125
$952$	0	0
$953$	12.5680	0.407116	0.203558	−	0.979063i	$-0.434749\pi$
$953$	12.5680	0.407116	0.203558	+	0.979063i	$0.434749\pi$
$954$	0.191181	0.00618972
$955$	−24.7713	−0.801580
$956$	−16.0000	−0.517477
$957$	−3.68839	−0.119229
$958$	−28.3337	−0.915419
$959$	0	0
$960$	−1.00000	−0.0322749
$961$	65.7558	2.12116
$962$	−32.5811	−1.05046
$963$	−9.59559	−0.309214
$964$	14.7933	0.476461
$965$	14.8585	0.478312
$966$	0	0
$967$	12.8309	0.412613	0.206306	−	0.978487i	$-0.433856\pi$
$967$	12.8309	0.412613	0.206306	+	0.978487i	$0.433856\pi$
$968$	10.8365	0.348297
$969$	−14.4265	−0.463445
$970$	−15.3613	−0.493221
$971$	22.4044	0.718992	0.359496	−	0.933147i	$-0.382949\pi$
$971$	22.4044	0.718992	0.359496	+	0.933147i	$0.382949\pi$
$972$	1.00000	0.0320750
$973$	0	0
$974$	−18.7005	−0.599204
$975$	16.4817	0.527838
$976$	−10.0000	−0.320092
$977$	−20.5094	−0.656153	−0.328076	−	0.944651i	$-0.606400\pi$
$977$	−20.5094	−0.656153	−0.328076	+	0.944651i	$0.606400\pi$
$978$	−24.7713	−0.792099
$979$	3.19775	0.102200
$980$	0	0
$981$	−3.19118	−0.101887
$982$	−5.09280	−0.162518
$983$	−4.53043	−0.144498	−0.0722491	−	0.997387i	$-0.523018\pi$
$983$	−4.53043	−0.144498	−0.0722491	+	0.997387i	$0.523018\pi$
$984$	−10.7160	−0.341614
$985$	11.4320	0.364255
$986$	48.4442	1.54278
$987$	0	0
$988$	−11.1912	−0.356039
$989$	−0.808819	−0.0257189
$990$	−0.404409	−0.0128530
$991$	−31.4100	−0.997771	−0.498886	−	0.866668i	$-0.666257\pi$
$991$	−31.4100	−0.997771	−0.498886	+	0.866668i	$0.666257\pi$
$992$	−9.83645	−0.312308
$993$	−20.5304	−0.651513
$994$	0	0
$995$	−8.62323	−0.273375
$996$	4.40441	0.139559
$997$	−18.4752	−0.585114	−0.292557	−	0.956248i	$-0.594506\pi$
$997$	−18.4752	−0.585114	−0.292557	+	0.956248i	$0.594506\pi$
$998$	−19.4873	−0.616860
$999$	−7.90720	−0.250173

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6762.2.a.cf.1.2		3
7.3	odd	6		966.2.i.k.415.3	yes	6
7.5	odd	6		966.2.i.k.277.3	✓	6
7.6	odd	2		6762.2.a.ce.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.i.k.277.3	✓	6	7.5	odd	6
966.2.i.k.415.3	yes	6	7.3	odd	6
6762.2.a.ce.1.2		3	7.6	odd	2
6762.2.a.cf.1.2		3	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 6762 = 2 \cdot 3 \cdot 7^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6762.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -0.404409 q^{11} +1.00000 q^{12} -4.12043 q^{13} -1.00000 q^{15} +1.00000 q^{16} -5.31161 q^{17} -1.00000 q^{18} +2.71602 q^{19} -1.00000 q^{20} +0.404409 q^{22} -1.00000 q^{23} -1.00000 q^{24} -4.00000 q^{25} +4.12043 q^{26} +1.00000 q^{27} +9.12043 q^{29} +1.00000 q^{30} +9.83645 q^{31} -1.00000 q^{32} -0.404409 q^{33} +5.31161 q^{34} +1.00000 q^{36} -7.90720 q^{37} -2.71602 q^{38} -4.12043 q^{39} +1.00000 q^{40} +10.7160 q^{41} +0.808819 q^{43} -0.404409 q^{44} -1.00000 q^{45} +1.00000 q^{46} +10.8365 q^{47} +1.00000 q^{48} +4.00000 q^{50} -5.31161 q^{51} -4.12043 q^{52} -0.191181 q^{53} -1.00000 q^{54} +0.404409 q^{55} +2.71602 q^{57} -9.12043 q^{58} +8.31161 q^{59} -1.00000 q^{60} -10.0000 q^{61} -9.83645 q^{62} +1.00000 q^{64} +4.12043 q^{65} +0.404409 q^{66} +2.83645 q^{67} -5.31161 q^{68} -1.00000 q^{69} -6.92925 q^{71} -1.00000 q^{72} -4.59559 q^{73} +7.90720 q^{74} -4.00000 q^{75} +2.71602 q^{76} +4.12043 q^{78} -9.92925 q^{79} -1.00000 q^{80} +1.00000 q^{81} -10.7160 q^{82} +4.40441 q^{83} +5.31161 q^{85} -0.808819 q^{86} +9.12043 q^{87} +0.404409 q^{88} -7.90720 q^{89} +1.00000 q^{90} -1.00000 q^{92} +9.83645 q^{93} -10.8365 q^{94} -2.71602 q^{95} -1.00000 q^{96} -15.3613 q^{97} -0.404409 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} - 3 q^{5} - 3 q^{6} - 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 - 3 * q^5 - 3 * q^6 - 3 * q^8 + 3 * q^9	\( 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} - 3 q^{5} - 3 q^{6} - 3 q^{8} + 3 q^{9} + 3 q^{10} + 3 q^{12} + 3 q^{13} - 3 q^{15} + 3 q^{16} - 3 q^{17} - 3 q^{18} - 6 q^{19} - 3 q^{20} - 3 q^{23} - 3 q^{24} - 12 q^{25} - 3 q^{26} + 3 q^{27} + 12 q^{29} + 3 q^{30} - 3 q^{32} + 3 q^{34} + 3 q^{36} - 12 q^{37} + 6 q^{38} + 3 q^{39} + 3 q^{40} + 18 q^{41} - 3 q^{45} + 3 q^{46} + 3 q^{47} + 3 q^{48} + 12 q^{50} - 3 q^{51} + 3 q^{52} - 3 q^{53} - 3 q^{54} - 6 q^{57} - 12 q^{58} + 12 q^{59} - 3 q^{60} - 30 q^{61} + 3 q^{64} - 3 q^{65} - 21 q^{67} - 3 q^{68} - 3 q^{69} - 3 q^{71} - 3 q^{72} - 15 q^{73} + 12 q^{74} - 12 q^{75} - 6 q^{76} - 3 q^{78} - 12 q^{79} - 3 q^{80} + 3 q^{81} - 18 q^{82} + 12 q^{83} + 3 q^{85} + 12 q^{87} - 12 q^{89} + 3 q^{90} - 3 q^{92} - 3 q^{94} + 6 q^{95} - 3 q^{96}+O(q^{100}) \) 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 - 3 * q^5 - 3 * q^6 - 3 * q^8 + 3 * q^9 + 3 * q^10 + 3 * q^12 + 3 * q^13 - 3 * q^15 + 3 * q^16 - 3 * q^17 - 3 * q^18 - 6 * q^19 - 3 * q^20 - 3 * q^23 - 3 * q^24 - 12 * q^25 - 3 * q^26 + 3 * q^27 + 12 * q^29 + 3 * q^30 - 3 * q^32 + 3 * q^34 + 3 * q^36 - 12 * q^37 + 6 * q^38 + 3 * q^39 + 3 * q^40 + 18 * q^41 - 3 * q^45 + 3 * q^46 + 3 * q^47 + 3 * q^48 + 12 * q^50 - 3 * q^51 + 3 * q^52 - 3 * q^53 - 3 * q^54 - 6 * q^57 - 12 * q^58 + 12 * q^59 - 3 * q^60 - 30 * q^61 + 3 * q^64 - 3 * q^65 - 21 * q^67 - 3 * q^68 - 3 * q^69 - 3 * q^71 - 3 * q^72 - 15 * q^73 + 12 * q^74 - 12 * q^75 - 6 * q^76 - 3 * q^78 - 12 * q^79 - 3 * q^80 + 3 * q^81 - 18 * q^82 + 12 * q^83 + 3 * q^85 + 12 * q^87 - 12 * q^89 + 3 * q^90 - 3 * q^92 - 3 * q^94 + 6 * q^95 - 3 * q^96

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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