LMFDB - Embedded newform 6762.2.a.ci.1.1

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:	$4$
Coefficient field:	4.4.2624.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 3x^{2} + 2x + 1 $ x^4 - 2x^3 - 3x^2 + 2*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-0.360409$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.41421 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.41421 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} -3.41421 q^{10} -0.298573 q^{11} -1.00000 q^{12} -4.72082 q^{13} +3.41421 q^{15} +1.00000 q^{16} -3.54925 q^{17} +1.00000 q^{18} +7.98285 q^{19} -3.41421 q^{20} -0.298573 q^{22} +1.00000 q^{23} -1.00000 q^{24} +6.65685 q^{25} -4.72082 q^{26} -1.00000 q^{27} +8.03878 q^{29} +3.41421 q^{30} +9.98285 q^{31} +1.00000 q^{32} +0.298573 q^{33} -3.54925 q^{34} +1.00000 q^{36} -3.54925 q^{37} +7.98285 q^{38} +4.72082 q^{39} -3.41421 q^{40} +0.817068 q^{41} -6.99088 q^{43} -0.298573 q^{44} -3.41421 q^{45} +1.00000 q^{46} -9.38571 q^{47} -1.00000 q^{48} +6.65685 q^{50} +3.54925 q^{51} -4.72082 q^{52} +8.14639 q^{53} -1.00000 q^{54} +1.01939 q^{55} -7.98285 q^{57} +8.03878 q^{58} -10.0388 q^{59} +3.41421 q^{60} -5.18293 q^{61} +9.98285 q^{62} +1.00000 q^{64} +16.1179 q^{65} +0.298573 q^{66} +15.2061 q^{67} -3.54925 q^{68} -1.00000 q^{69} -5.57775 q^{71} +1.00000 q^{72} -0.776751 q^{73} -3.54925 q^{74} -6.65685 q^{75} +7.98285 q^{76} +4.72082 q^{78} -14.0791 q^{79} -3.41421 q^{80} +1.00000 q^{81} +0.817068 q^{82} +0.884359 q^{83} +12.1179 q^{85} -6.99088 q^{86} -8.03878 q^{87} -0.298573 q^{88} -2.43469 q^{89} -3.41421 q^{90} +1.00000 q^{92} -9.98285 q^{93} -9.38571 q^{94} -27.2552 q^{95} -1.00000 q^{96} +12.0345 q^{97} -0.298573 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} - 8 q^{5} - 4 q^{6} + 4 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 - 8 * q^5 - 4 * q^6 + 4 * q^8 + 4 * q^9	$ 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} - 8 q^{5} - 4 q^{6} + 4 q^{8} + 4 q^{9} - 8 q^{10} + 4 q^{11} - 4 q^{12} - 12 q^{13} + 8 q^{15} + 4 q^{16} + 4 q^{17} + 4 q^{18} - 4 q^{19} - 8 q^{20} + 4 q^{22} + 4 q^{23} - 4 q^{24} + 4 q^{25} - 12 q^{26} - 4 q^{27} + 8 q^{29} + 8 q^{30} + 4 q^{31} + 4 q^{32} - 4 q^{33} + 4 q^{34} + 4 q^{36} + 4 q^{37} - 4 q^{38} + 12 q^{39} - 8 q^{40} + 8 q^{41} + 4 q^{43} + 4 q^{44} - 8 q^{45} + 4 q^{46} - 12 q^{47} - 4 q^{48} + 4 q^{50} - 4 q^{51} - 12 q^{52} + 4 q^{53} - 4 q^{54} - 8 q^{55} + 4 q^{57} + 8 q^{58} - 16 q^{59} + 8 q^{60} - 16 q^{61} + 4 q^{62} + 4 q^{64} + 16 q^{65} - 4 q^{66} + 20 q^{67} + 4 q^{68} - 4 q^{69} - 24 q^{71} + 4 q^{72} - 8 q^{73} + 4 q^{74} - 4 q^{75} - 4 q^{76} + 12 q^{78} - 32 q^{79} - 8 q^{80} + 4 q^{81} + 8 q^{82} + 4 q^{83} + 4 q^{86} - 8 q^{87} + 4 q^{88} - 20 q^{89} - 8 q^{90} + 4 q^{92} - 4 q^{93} - 12 q^{94} - 4 q^{96} - 4 q^{97} + 4 q^{99}+O(q^{100}) $ 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 - 8 * q^5 - 4 * q^6 + 4 * q^8 + 4 * q^9 - 8 * q^10 + 4 * q^11 - 4 * q^12 - 12 * q^13 + 8 * q^15 + 4 * q^16 + 4 * q^17 + 4 * q^18 - 4 * q^19 - 8 * q^20 + 4 * q^22 + 4 * q^23 - 4 * q^24 + 4 * q^25 - 12 * q^26 - 4 * q^27 + 8 * q^29 + 8 * q^30 + 4 * q^31 + 4 * q^32 - 4 * q^33 + 4 * q^34 + 4 * q^36 + 4 * q^37 - 4 * q^38 + 12 * q^39 - 8 * q^40 + 8 * q^41 + 4 * q^43 + 4 * q^44 - 8 * q^45 + 4 * q^46 - 12 * q^47 - 4 * q^48 + 4 * q^50 - 4 * q^51 - 12 * q^52 + 4 * q^53 - 4 * q^54 - 8 * q^55 + 4 * q^57 + 8 * q^58 - 16 * q^59 + 8 * q^60 - 16 * q^61 + 4 * q^62 + 4 * q^64 + 16 * q^65 - 4 * q^66 + 20 * q^67 + 4 * q^68 - 4 * q^69 - 24 * q^71 + 4 * q^72 - 8 * q^73 + 4 * q^74 - 4 * q^75 - 4 * q^76 + 12 * q^78 - 32 * q^79 - 8 * q^80 + 4 * q^81 + 8 * q^82 + 4 * q^83 + 4 * q^86 - 8 * q^87 + 4 * q^88 - 20 * q^89 - 8 * q^90 + 4 * q^92 - 4 * q^93 - 12 * q^94 - 4 * q^96 - 4 * q^97 + 4 * q^99

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
$5$	−3.41421	−1.52688	−0.763441	−	0.645877i	$-0.776492\pi$
$5$	−3.41421	−1.52688	−0.763441	+	0.645877i	$0.776492\pi$
$6$	−1.00000	−0.408248
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−3.41421	−1.07967
$11$	−0.298573	−0.0900231	−0.0450116	−	0.998986i	$-0.514332\pi$
$11$	−0.298573	−0.0900231	−0.0450116	+	0.998986i	$0.514332\pi$
$12$	−1.00000	−0.288675
$13$	−4.72082	−1.30932	−0.654660	−	0.755924i	$-0.727188\pi$
$13$	−4.72082	−1.30932	−0.654660	+	0.755924i	$0.727188\pi$
$14$	0	0
$15$	3.41421	0.881546
$16$	1.00000	0.250000
$17$	−3.54925	−0.860819	−0.430409	−	0.902634i	$-0.641631\pi$
$17$	−3.54925	−0.860819	−0.430409	+	0.902634i	$0.641631\pi$
$18$	1.00000	0.235702
$19$	7.98285	1.83139	0.915696	−	0.401872i	$-0.131640\pi$
$19$	7.98285	1.83139	0.915696	+	0.401872i	$0.131640\pi$
$20$	−3.41421	−0.763441
$21$	0	0
$22$	−0.298573	−0.0636559
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−1.00000	−0.204124
$25$	6.65685	1.33137
$26$	−4.72082	−0.925829
$27$	−1.00000	−0.192450
$28$	0	0
$29$	8.03878	1.49276	0.746382	−	0.665517i	$-0.231789\pi$
$29$	8.03878	1.49276	0.746382	+	0.665517i	$0.231789\pi$
$30$	3.41421	0.623347
$31$	9.98285	1.79297	0.896486	−	0.443071i	$-0.146111\pi$
$31$	9.98285	1.79297	0.896486	+	0.443071i	$0.146111\pi$
$32$	1.00000	0.176777
$33$	0.298573	0.0519749
$34$	−3.54925	−0.608691
$35$	0	0
$36$	1.00000	0.166667
$37$	−3.54925	−0.583492	−0.291746	−	0.956496i	$-0.594236\pi$
$37$	−3.54925	−0.583492	−0.291746	+	0.956496i	$0.594236\pi$
$38$	7.98285	1.29499
$39$	4.72082	0.755936
$40$	−3.41421	−0.539835
$41$	0.817068	0.127605	0.0638023	−	0.997963i	$-0.479677\pi$
$41$	0.817068	0.127605	0.0638023	+	0.997963i	$0.479677\pi$
$42$	0	0
$43$	−6.99088	−1.06610	−0.533050	−	0.846084i	$-0.678954\pi$
$43$	−6.99088	−1.06610	−0.533050	+	0.846084i	$0.678954\pi$
$44$	−0.298573	−0.0450116
$45$	−3.41421	−0.508961
$46$	1.00000	0.147442
$47$	−9.38571	−1.36905	−0.684523	−	0.728991i	$-0.739989\pi$
$47$	−9.38571	−1.36905	−0.684523	+	0.728991i	$0.739989\pi$
$48$	−1.00000	−0.144338
$49$	0	0
$50$	6.65685	0.941421
$51$	3.54925	0.496994
$52$	−4.72082	−0.654660
$53$	8.14639	1.11899	0.559496	−	0.828833i	$-0.310995\pi$
$53$	8.14639	1.11899	0.559496	+	0.828833i	$0.310995\pi$
$54$	−1.00000	−0.136083
$55$	1.01939	0.137455
$56$	0	0
$57$	−7.98285	−1.05735
$58$	8.03878	1.05554
$59$	−10.0388	−1.30694	−0.653469	−	0.756953i	$-0.726687\pi$
$59$	−10.0388	−1.30694	−0.653469	+	0.756953i	$0.726687\pi$
$60$	3.41421	0.440773
$61$	−5.18293	−0.663606	−0.331803	−	0.943349i	$-0.607657\pi$
$61$	−5.18293	−0.663606	−0.331803	+	0.943349i	$0.607657\pi$
$62$	9.98285	1.26782
$63$	0	0
$64$	1.00000	0.125000
$65$	16.1179	1.99918
$66$	0.298573	0.0367518
$67$	15.2061	1.85772	0.928860	−	0.370430i	$-0.120790\pi$
$67$	15.2061	1.85772	0.928860	+	0.370430i	$0.120790\pi$
$68$	−3.54925	−0.430409
$69$	−1.00000	−0.120386
$70$	0	0
$71$	−5.57775	−0.661958	−0.330979	−	0.943638i	$-0.607379\pi$
$71$	−5.57775	−0.661958	−0.330979	+	0.943638i	$0.607379\pi$
$72$	1.00000	0.117851
$73$	−0.776751	−0.0909118	−0.0454559	−	0.998966i	$-0.514474\pi$
$73$	−0.776751	−0.0909118	−0.0454559	+	0.998966i	$0.514474\pi$
$74$	−3.54925	−0.412591
$75$	−6.65685	−0.768667
$76$	7.98285	0.915696
$77$	0	0
$78$	4.72082	0.534527
$79$	−14.0791	−1.58402	−0.792011	−	0.610506i	$-0.790966\pi$
$79$	−14.0791	−1.58402	−0.792011	+	0.610506i	$0.790966\pi$
$80$	−3.41421	−0.381721
$81$	1.00000	0.111111
$82$	0.817068	0.0902300
$83$	0.884359	0.0970710	0.0485355	−	0.998821i	$-0.484545\pi$
$83$	0.884359	0.0970710	0.0485355	+	0.998821i	$0.484545\pi$
$84$	0	0
$85$	12.1179	1.31437
$86$	−6.99088	−0.753846
$87$	−8.03878	−0.861848
$88$	−0.298573	−0.0318280
$89$	−2.43469	−0.258077	−0.129038	−	0.991640i	$-0.541189\pi$
$89$	−2.43469	−0.258077	−0.129038	+	0.991640i	$0.541189\pi$
$90$	−3.41421	−0.359890
$91$	0	0
$92$	1.00000	0.104257
$93$	−9.98285	−1.03517
$94$	−9.38571	−0.968062
$95$	−27.2552	−2.79632
$96$	−1.00000	−0.102062
$97$	12.0345	1.22192	0.610961	−	0.791661i	$-0.290783\pi$
$97$	12.0345	1.22192	0.610961	+	0.791661i	$0.290783\pi$
$98$	0	0
$99$	−0.298573	−0.0300077
$100$	6.65685	0.665685
$101$	4.99088	0.496611	0.248306	−	0.968682i	$-0.420126\pi$
$101$	4.99088	0.496611	0.248306	+	0.968682i	$0.420126\pi$
$102$	3.54925	0.351428
$103$	8.86721	0.873712	0.436856	−	0.899531i	$-0.356092\pi$
$103$	8.86721	0.873712	0.436856	+	0.899531i	$0.356092\pi$
$104$	−4.72082	−0.462914
$105$	0	0
$106$	8.14639	0.791247
$107$	−14.4956	−1.40134	−0.700669	−	0.713486i	$-0.747115\pi$
$107$	−14.4956	−1.40134	−0.700669	+	0.713486i	$0.747115\pi$
$108$	−1.00000	−0.0962250
$109$	10.0345	0.961133	0.480567	−	0.876958i	$-0.340431\pi$
$109$	10.0345	0.961133	0.480567	+	0.876958i	$0.340431\pi$
$110$	1.01939	0.0971952
$111$	3.54925	0.336880
$112$	0	0
$113$	−15.0194	−1.41291	−0.706453	−	0.707760i	$-0.749706\pi$
$113$	−15.0194	−1.41291	−0.706453	+	0.707760i	$0.749706\pi$
$114$	−7.98285	−0.747662
$115$	−3.41421	−0.318377
$116$	8.03878	0.746382
$117$	−4.72082	−0.436440
$118$	−10.0388	−0.924145
$119$	0	0
$120$	3.41421	0.311674
$121$	−10.9109	−0.991896
$122$	−5.18293	−0.469241
$123$	−0.817068	−0.0736725
$124$	9.98285	0.896486
$125$	−5.65685	−0.505964
$126$	0	0
$127$	−11.4820	−1.01886	−0.509429	−	0.860512i	$-0.670143\pi$
$127$	−11.4820	−1.01886	−0.509429	+	0.860512i	$0.670143\pi$
$128$	1.00000	0.0883883
$129$	6.99088	0.615513
$130$	16.1179	1.41363
$131$	−14.7941	−1.29257	−0.646285	−	0.763097i	$-0.723678\pi$
$131$	−14.7941	−1.29257	−0.646285	+	0.763097i	$0.723678\pi$
$132$	0.298573	0.0259874
$133$	0	0
$134$	15.2061	1.31361
$135$	3.41421	0.293849
$136$	−3.54925	−0.304345
$137$	−2.90151	−0.247893	−0.123946	−	0.992289i	$-0.539555\pi$
$137$	−2.90151	−0.247893	−0.123946	+	0.992289i	$0.539555\pi$
$138$	−1.00000	−0.0851257
$139$	−5.17157	−0.438647	−0.219324	−	0.975652i	$-0.570385\pi$
$139$	−5.17157	−0.438647	−0.219324	+	0.975652i	$0.570385\pi$
$140$	0	0
$141$	9.38571	0.790419
$142$	−5.57775	−0.468075
$143$	1.40951	0.117869
$144$	1.00000	0.0833333
$145$	−27.4461	−2.27928
$146$	−0.776751	−0.0642844
$147$	0	0
$148$	−3.54925	−0.291746
$149$	7.78053	0.637406	0.318703	−	0.947855i	$-0.396753\pi$
$149$	7.78053	0.637406	0.318703	+	0.947855i	$0.396753\pi$
$150$	−6.65685	−0.543530
$151$	−20.6192	−1.67797	−0.838985	−	0.544155i	$-0.816850\pi$
$151$	−20.6192	−1.67797	−0.838985	+	0.544155i	$0.816850\pi$
$152$	7.98285	0.647495
$153$	−3.54925	−0.286940
$154$	0	0
$155$	−34.0836	−2.73766
$156$	4.72082	0.377968
$157$	−22.9577	−1.83222	−0.916111	−	0.400925i	$-0.868689\pi$
$157$	−22.9577	−1.83222	−0.916111	+	0.400925i	$0.868689\pi$
$158$	−14.0791	−1.12007
$159$	−8.14639	−0.646051
$160$	−3.41421	−0.269917
$161$	0	0
$162$	1.00000	0.0785674
$163$	−4.63746	−0.363234	−0.181617	−	0.983369i	$-0.558133\pi$
$163$	−4.63746	−0.363234	−0.181617	+	0.983369i	$0.558133\pi$
$164$	0.817068	0.0638023
$165$	−1.01939	−0.0793595
$166$	0.884359	0.0686396
$167$	−22.1981	−1.71774	−0.858869	−	0.512195i	$-0.828832\pi$
$167$	−22.1981	−1.71774	−0.858869	+	0.512195i	$0.828832\pi$
$168$	0	0
$169$	9.28613	0.714318
$170$	12.1179	0.929399
$171$	7.98285	0.610464
$172$	−6.99088	−0.533050
$173$	−3.16732	−0.240807	−0.120403	−	0.992725i	$-0.538419\pi$
$173$	−3.16732	−0.240807	−0.120403	+	0.992725i	$0.538419\pi$
$174$	−8.03878	−0.609419
$175$	0	0
$176$	−0.298573	−0.0225058
$177$	10.0388	0.754561
$178$	−2.43469	−0.182488
$179$	13.5998	1.01650	0.508250	−	0.861210i	$-0.330293\pi$
$179$	13.5998	1.01650	0.508250	+	0.861210i	$0.330293\pi$
$180$	−3.41421	−0.254480
$181$	−9.64549	−0.716944	−0.358472	−	0.933540i	$-0.616702\pi$
$181$	−9.64549	−0.716944	−0.358472	+	0.933540i	$0.616702\pi$
$182$	0	0
$183$	5.18293	0.383133
$184$	1.00000	0.0737210
$185$	12.1179	0.890924
$186$	−9.98285	−0.731978
$187$	1.05971	0.0774936
$188$	−9.38571	−0.684523
$189$	0	0
$190$	−27.2552	−1.97730
$191$	−2.13612	−0.154564	−0.0772820	−	0.997009i	$-0.524624\pi$
$191$	−2.13612	−0.154564	−0.0772820	+	0.997009i	$0.524624\pi$
$192$	−1.00000	−0.0721688
$193$	21.9496	1.57997	0.789985	−	0.613127i	$-0.210088\pi$
$193$	21.9496	1.57997	0.789985	+	0.613127i	$0.210088\pi$
$194$	12.0345	0.864029
$195$	−16.1179	−1.15423
$196$	0	0
$197$	6.17490	0.439943	0.219972	−	0.975506i	$-0.429403\pi$
$197$	6.17490	0.439943	0.219972	+	0.975506i	$0.429403\pi$
$198$	−0.298573	−0.0212186
$199$	21.4644	1.52157	0.760784	−	0.649005i	$-0.224815\pi$
$199$	21.4644	1.52157	0.760784	+	0.649005i	$0.224815\pi$
$200$	6.65685	0.470711
$201$	−15.2061	−1.07256
$202$	4.99088	0.351157
$203$	0	0
$204$	3.54925	0.248497
$205$	−2.78964	−0.194837
$206$	8.86721	0.617808
$207$	1.00000	0.0695048
$208$	−4.72082	−0.327330
$209$	−2.38346	−0.164868
$210$	0	0
$211$	−9.23461	−0.635737	−0.317868	−	0.948135i	$-0.602967\pi$
$211$	−9.23461	−0.635737	−0.317868	+	0.948135i	$0.602967\pi$
$212$	8.14639	0.559496
$213$	5.57775	0.382181
$214$	−14.4956	−0.990896
$215$	23.8684	1.62781
$216$	−1.00000	−0.0680414
$217$	0	0
$218$	10.0345	0.679624
$219$	0.776751	0.0524880
$220$	1.01939	0.0687274
$221$	16.7553	1.12709
$222$	3.54925	0.238210
$223$	−17.0265	−1.14018	−0.570089	−	0.821583i	$-0.693091\pi$
$223$	−17.0265	−1.14018	−0.570089	+	0.821583i	$0.693091\pi$
$224$	0	0
$225$	6.65685	0.443790
$226$	−15.0194	−0.999075
$227$	24.3563	1.61658	0.808291	−	0.588783i	$-0.200393\pi$
$227$	24.3563	1.61658	0.808291	+	0.588783i	$0.200393\pi$
$228$	−7.98285	−0.528677
$229$	24.1923	1.59867	0.799335	−	0.600885i	$-0.205185\pi$
$229$	24.1923	1.59867	0.799335	+	0.600885i	$0.205185\pi$
$230$	−3.41421	−0.225127
$231$	0	0
$232$	8.03878	0.527772
$233$	−21.9109	−1.43543	−0.717714	−	0.696338i	$-0.754811\pi$
$233$	−21.9109	−1.43543	−0.717714	+	0.696338i	$0.754811\pi$
$234$	−4.72082	−0.308610
$235$	32.0448	2.09037
$236$	−10.0388	−0.653469
$237$	14.0791	0.914536
$238$	0	0
$239$	−6.47926	−0.419109	−0.209554	−	0.977797i	$-0.567201\pi$
$239$	−6.47926	−0.419109	−0.209554	+	0.977797i	$0.567201\pi$
$240$	3.41421	0.220387
$241$	8.52832	0.549357	0.274679	−	0.961536i	$-0.411429\pi$
$241$	8.52832	0.549357	0.274679	+	0.961536i	$0.411429\pi$
$242$	−10.9109	−0.701376
$243$	−1.00000	−0.0641500
$244$	−5.18293	−0.331803
$245$	0	0
$246$	−0.817068	−0.0520943
$247$	−37.6856	−2.39788
$248$	9.98285	0.633912
$249$	−0.884359	−0.0560440
$250$	−5.65685	−0.357771
$251$	−12.5024	−0.789146	−0.394573	−	0.918865i	$-0.629108\pi$
$251$	−12.5024	−0.789146	−0.394573	+	0.918865i	$0.629108\pi$
$252$	0	0
$253$	−0.298573	−0.0187711
$254$	−11.4820	−0.720442
$255$	−12.1179	−0.758851
$256$	1.00000	0.0625000
$257$	−5.79614	−0.361553	−0.180777	−	0.983524i	$-0.557861\pi$
$257$	−5.79614	−0.361553	−0.180777	+	0.983524i	$0.557861\pi$
$258$	6.99088	0.435233
$259$	0	0
$260$	16.1179	0.999589
$261$	8.03878	0.497588
$262$	−14.7941	−0.913984
$263$	−8.68629	−0.535620	−0.267810	−	0.963472i	$-0.586300\pi$
$263$	−8.68629	−0.535620	−0.267810	+	0.963472i	$0.586300\pi$
$264$	0.298573	0.0183759
$265$	−27.8135	−1.70857
$266$	0	0
$267$	2.43469	0.149001
$268$	15.2061	0.928860
$269$	−28.4713	−1.73593	−0.867963	−	0.496629i	$-0.834571\pi$
$269$	−28.4713	−1.73593	−0.867963	+	0.496629i	$0.834571\pi$
$270$	3.41421	0.207782
$271$	2.46211	0.149563	0.0747814	−	0.997200i	$-0.476174\pi$
$271$	2.46211	0.149563	0.0747814	+	0.997200i	$0.476174\pi$
$272$	−3.54925	−0.215205
$273$	0	0
$274$	−2.90151	−0.175287
$275$	−1.98756	−0.119854
$276$	−1.00000	−0.0601929
$277$	−23.5192	−1.41313	−0.706566	−	0.707647i	$-0.749757\pi$
$277$	−23.5192	−1.41313	−0.706566	+	0.707647i	$0.749757\pi$
$278$	−5.17157	−0.310170
$279$	9.98285	0.597658
$280$	0	0
$281$	−2.81236	−0.167771	−0.0838857	−	0.996475i	$-0.526733\pi$
$281$	−2.81236	−0.167771	−0.0838857	+	0.996475i	$0.526733\pi$
$282$	9.38571	0.558911
$283$	17.6800	1.05097	0.525484	−	0.850803i	$-0.323884\pi$
$283$	17.6800	1.05097	0.525484	+	0.850803i	$0.323884\pi$
$284$	−5.57775	−0.330979
$285$	27.2552	1.61446
$286$	1.40951	0.0833460
$287$	0	0
$288$	1.00000	0.0589256
$289$	−4.40285	−0.258991
$290$	−27.4461	−1.61169
$291$	−12.0345	−0.705476
$292$	−0.776751	−0.0454559
$293$	8.97373	0.524251	0.262126	−	0.965034i	$-0.415577\pi$
$293$	8.97373	0.524251	0.262126	+	0.965034i	$0.415577\pi$
$294$	0	0
$295$	34.2745	1.99554
$296$	−3.54925	−0.206296
$297$	0.298573	0.0173250
$298$	7.78053	0.450714
$299$	−4.72082	−0.273012
$300$	−6.65685	−0.384334
$301$	0	0
$302$	−20.6192	−1.18650
$303$	−4.99088	−0.286719
$304$	7.98285	0.457848
$305$	17.6956	1.01325
$306$	−3.54925	−0.202897
$307$	−5.49648	−0.313701	−0.156850	−	0.987622i	$-0.550134\pi$
$307$	−5.49648	−0.313701	−0.156850	+	0.987622i	$0.550134\pi$
$308$	0	0
$309$	−8.86721	−0.504438
$310$	−34.0836	−1.93582
$311$	20.0277	1.13566	0.567832	−	0.823144i	$-0.307782\pi$
$311$	20.0277	1.13566	0.567832	+	0.823144i	$0.307782\pi$
$312$	4.72082	0.267264
$313$	18.4004	1.04005	0.520026	−	0.854151i	$-0.325922\pi$
$313$	18.4004	1.04005	0.520026	+	0.854151i	$0.325922\pi$
$314$	−22.9577	−1.29558
$315$	0	0
$316$	−14.0791	−0.792011
$317$	−21.6468	−1.21581	−0.607903	−	0.794011i	$-0.707989\pi$
$317$	−21.6468	−1.21581	−0.607903	+	0.794011i	$0.707989\pi$
$318$	−8.14639	−0.456827
$319$	−2.40016	−0.134383
$320$	−3.41421	−0.190860
$321$	14.4956	0.809063
$322$	0	0
$323$	−28.3331	−1.57650
$324$	1.00000	0.0555556
$325$	−31.4258	−1.74319
$326$	−4.63746	−0.256845
$327$	−10.0345	−0.554911
$328$	0.817068	0.0451150
$329$	0	0
$330$	−1.01939	−0.0561157
$331$	6.34315	0.348651	0.174325	−	0.984688i	$-0.444226\pi$
$331$	6.34315	0.348651	0.174325	+	0.984688i	$0.444226\pi$
$332$	0.884359	0.0485355
$333$	−3.54925	−0.194497
$334$	−22.1981	−1.21462
$335$	−51.9169	−2.83652
$336$	0	0
$337$	−10.7150	−0.583685	−0.291842	−	0.956466i	$-0.594268\pi$
$337$	−10.7150	−0.583685	−0.291842	+	0.956466i	$0.594268\pi$
$338$	9.28613	0.505099
$339$	15.0194	0.815741
$340$	12.1179	0.657184
$341$	−2.98061	−0.161409
$342$	7.98285	0.431663
$343$	0	0
$344$	−6.99088	−0.376923
$345$	3.41421	0.183815
$346$	−3.16732	−0.170276
$347$	22.9120	1.22998	0.614991	−	0.788534i	$-0.289160\pi$
$347$	22.9120	1.22998	0.614991	+	0.788534i	$0.289160\pi$
$348$	−8.03878	−0.430924
$349$	11.4922	0.615165	0.307582	−	0.951521i	$-0.400480\pi$
$349$	11.4922	0.615165	0.307582	+	0.951521i	$0.400480\pi$
$350$	0	0
$351$	4.72082	0.251979
$352$	−0.298573	−0.0159140
$353$	−10.9510	−0.582864	−0.291432	−	0.956592i	$-0.594132\pi$
$353$	−10.9510	−0.582864	−0.291432	+	0.956592i	$0.594132\pi$
$354$	10.0388	0.533555
$355$	19.0436	1.01073
$356$	−2.43469	−0.129038
$357$	0	0
$358$	13.5998	0.718774
$359$	−4.63746	−0.244756	−0.122378	−	0.992484i	$-0.539052\pi$
$359$	−4.63746	−0.244756	−0.122378	+	0.992484i	$0.539052\pi$
$360$	−3.41421	−0.179945
$361$	44.7259	2.35400
$362$	−9.64549	−0.506956
$363$	10.9109	0.572671
$364$	0	0
$365$	2.65199	0.138812
$366$	5.18293	0.270916
$367$	−15.5838	−0.813466	−0.406733	−	0.913547i	$-0.633332\pi$
$367$	−15.5838	−0.813466	−0.406733	+	0.913547i	$0.633332\pi$
$368$	1.00000	0.0521286
$369$	0.817068	0.0425349
$370$	12.1179	0.629979
$371$	0	0
$372$	−9.98285	−0.517587
$373$	−18.4650	−0.956079	−0.478040	−	0.878338i	$-0.658653\pi$
$373$	−18.4650	−0.956079	−0.478040	+	0.878338i	$0.658653\pi$
$374$	1.05971	0.0547962
$375$	5.65685	0.292119
$376$	−9.38571	−0.484031
$377$	−37.9496	−1.95451
$378$	0	0
$379$	25.2691	1.29799	0.648994	−	0.760793i	$-0.275190\pi$
$379$	25.2691	1.29799	0.648994	+	0.760793i	$0.275190\pi$
$380$	−27.2552	−1.39816
$381$	11.4820	0.588238
$382$	−2.13612	−0.109293
$383$	−20.6983	−1.05764	−0.528818	−	0.848735i	$-0.677364\pi$
$383$	−20.6983	−1.05764	−0.528818	+	0.848735i	$0.677364\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	21.9496	1.11721
$387$	−6.99088	−0.355367
$388$	12.0345	0.610961
$389$	−18.6638	−0.946292	−0.473146	−	0.880984i	$-0.656882\pi$
$389$	−18.6638	−0.946292	−0.473146	+	0.880984i	$0.656882\pi$
$390$	−16.1179	−0.816161
$391$	−3.54925	−0.179493
$392$	0	0
$393$	14.7941	0.746265
$394$	6.17490	0.311087
$395$	48.0691	2.41862
$396$	−0.298573	−0.0150039
$397$	23.4374	1.17629	0.588144	−	0.808756i	$-0.299859\pi$
$397$	23.4374	1.17629	0.588144	+	0.808756i	$0.299859\pi$
$398$	21.4644	1.07591
$399$	0	0
$400$	6.65685	0.332843
$401$	−6.24735	−0.311978	−0.155989	−	0.987759i	$-0.549856\pi$
$401$	−6.24735	−0.311978	−0.155989	+	0.987759i	$0.549856\pi$
$402$	−15.2061	−0.758411
$403$	−47.1272	−2.34757
$404$	4.99088	0.248306
$405$	−3.41421	−0.169654
$406$	0	0
$407$	1.05971	0.0525278
$408$	3.54925	0.175714
$409$	−29.9222	−1.47956	−0.739779	−	0.672850i	$-0.765070\pi$
$409$	−29.9222	−1.47956	−0.739779	+	0.672850i	$0.765070\pi$
$410$	−2.78964	−0.137771
$411$	2.90151	0.143121
$412$	8.86721	0.436856
$413$	0	0
$414$	1.00000	0.0491473
$415$	−3.01939	−0.148216
$416$	−4.72082	−0.231457
$417$	5.17157	0.253253
$418$	−2.38346	−0.116579
$419$	−29.5827	−1.44521	−0.722604	−	0.691262i	$-0.757055\pi$
$419$	−29.5827	−1.44521	−0.722604	+	0.691262i	$0.757055\pi$
$420$	0	0
$421$	0.970334	0.0472912	0.0236456	−	0.999720i	$-0.492473\pi$
$421$	0.970334	0.0472912	0.0236456	+	0.999720i	$0.492473\pi$
$422$	−9.23461	−0.449534
$423$	−9.38571	−0.456349
$424$	8.14639	0.395624
$425$	−23.6268	−1.14607
$426$	5.57775	0.270243
$427$	0	0
$428$	−14.4956	−0.700669
$429$	−1.40951	−0.0680517
$430$	23.8684	1.15103
$431$	23.2246	1.11869	0.559344	−	0.828936i	$-0.311053\pi$
$431$	23.2246	1.11869	0.559344	+	0.828936i	$0.311053\pi$
$432$	−1.00000	−0.0481125
$433$	−5.94724	−0.285806	−0.142903	−	0.989737i	$-0.545644\pi$
$433$	−5.94724	−0.285806	−0.142903	+	0.989737i	$0.545644\pi$
$434$	0	0
$435$	27.4461	1.31594
$436$	10.0345	0.480567
$437$	7.98285	0.381872
$438$	0.776751	0.0371146
$439$	17.8080	0.849927	0.424964	−	0.905210i	$-0.360287\pi$
$439$	17.8080	0.849927	0.424964	+	0.905210i	$0.360287\pi$
$440$	1.01939	0.0485976
$441$	0	0
$442$	16.7553	0.796971
$443$	27.5983	1.31123	0.655617	−	0.755093i	$-0.272408\pi$
$443$	27.5983	1.31123	0.655617	+	0.755093i	$0.272408\pi$
$444$	3.54925	0.168440
$445$	8.31255	0.394053
$446$	−17.0265	−0.806228
$447$	−7.78053	−0.368006
$448$	0	0
$449$	−36.9221	−1.74246	−0.871230	−	0.490875i	$-0.836677\pi$
$449$	−36.9221	−1.74246	−0.871230	+	0.490875i	$0.836677\pi$
$450$	6.65685	0.313807
$451$	−0.243954	−0.0114874
$452$	−15.0194	−0.706453
$453$	20.6192	0.968776
$454$	24.3563	1.14310
$455$	0	0
$456$	−7.98285	−0.373831
$457$	−14.5971	−0.682826	−0.341413	−	0.939913i	$-0.610905\pi$
$457$	−14.5971	−0.682826	−0.341413	+	0.939913i	$0.610905\pi$
$458$	24.1923	1.13043
$459$	3.54925	0.165665
$460$	−3.41421	−0.159189
$461$	3.08668	0.143761	0.0718806	−	0.997413i	$-0.477100\pi$
$461$	3.08668	0.143761	0.0718806	+	0.997413i	$0.477100\pi$
$462$	0	0
$463$	−35.1190	−1.63212	−0.816060	−	0.577967i	$-0.803846\pi$
$463$	−35.1190	−1.63212	−0.816060	+	0.577967i	$0.803846\pi$
$464$	8.03878	0.373191
$465$	34.0836	1.58059
$466$	−21.9109	−1.01500
$467$	−0.462114	−0.0213841	−0.0106920	−	0.999943i	$-0.503403\pi$
$467$	−0.462114	−0.0213841	−0.0106920	+	0.999943i	$0.503403\pi$
$468$	−4.72082	−0.218220
$469$	0	0
$470$	32.0448	1.47812
$471$	22.9577	1.05783
$472$	−10.0388	−0.462072
$473$	2.08729	0.0959736
$474$	14.0791	0.646674
$475$	53.1407	2.43826
$476$	0	0
$477$	8.14639	0.372998
$478$	−6.47926	−0.296355
$479$	−19.3115	−0.882367	−0.441183	−	0.897417i	$-0.645441\pi$
$479$	−19.3115	−0.882367	−0.441183	+	0.897417i	$0.645441\pi$
$480$	3.41421	0.155837
$481$	16.7553	0.763978
$482$	8.52832	0.388454
$483$	0	0
$484$	−10.9109	−0.495948
$485$	−41.0884	−1.86573
$486$	−1.00000	−0.0453609
$487$	−10.4692	−0.474406	−0.237203	−	0.971460i	$-0.576231\pi$
$487$	−10.4692	−0.474406	−0.237203	+	0.971460i	$0.576231\pi$
$488$	−5.18293	−0.234620
$489$	4.63746	0.209713
$490$	0	0
$491$	12.2846	0.554396	0.277198	−	0.960813i	$-0.410594\pi$
$491$	12.2846	0.554396	0.277198	+	0.960813i	$0.410594\pi$
$492$	−0.817068	−0.0368363
$493$	−28.5316	−1.28500
$494$	−37.6856	−1.69555
$495$	1.01939	0.0458182
$496$	9.98285	0.448243
$497$	0	0
$498$	−0.884359	−0.0396291
$499$	−6.37188	−0.285245	−0.142622	−	0.989777i	$-0.545553\pi$
$499$	−6.37188	−0.285245	−0.142622	+	0.989777i	$0.545553\pi$
$500$	−5.65685	−0.252982
$501$	22.1981	0.991737
$502$	−12.5024	−0.558011
$503$	−9.94964	−0.443632	−0.221816	−	0.975088i	$-0.571198\pi$
$503$	−9.94964	−0.443632	−0.221816	+	0.975088i	$0.571198\pi$
$504$	0	0
$505$	−17.0399	−0.758267
$506$	−0.298573	−0.0132732
$507$	−9.28613	−0.412411
$508$	−11.4820	−0.509429
$509$	0.743537	0.0329567	0.0164784	−	0.999864i	$-0.494755\pi$
$509$	0.743537	0.0329567	0.0164784	+	0.999864i	$0.494755\pi$
$510$	−12.1179	−0.536589
$511$	0	0
$512$	1.00000	0.0441942
$513$	−7.98285	−0.352451
$514$	−5.79614	−0.255657
$515$	−30.2745	−1.33406
$516$	6.99088	0.307756
$517$	2.80232	0.123246
$518$	0	0
$519$	3.16732	0.139030
$520$	16.1179	0.706816
$521$	−12.6317	−0.553404	−0.276702	−	0.960956i	$-0.589241\pi$
$521$	−12.6317	−0.553404	−0.276702	+	0.960956i	$0.589241\pi$
$522$	8.03878	0.351848
$523$	−13.9441	−0.609732	−0.304866	−	0.952395i	$-0.598612\pi$
$523$	−13.9441	−0.609732	−0.304866	+	0.952395i	$0.598612\pi$
$524$	−14.7941	−0.646285
$525$	0	0
$526$	−8.68629	−0.378740
$527$	−35.4316	−1.54342
$528$	0.298573	0.0129937
$529$	1.00000	0.0434783
$530$	−27.8135	−1.20814
$531$	−10.0388	−0.435646
$532$	0	0
$533$	−3.85723	−0.167075
$534$	2.43469	0.105359
$535$	49.4909	2.13968
$536$	15.2061	0.656803
$537$	−13.5998	−0.586876
$538$	−28.4713	−1.22749
$539$	0	0
$540$	3.41421	0.146924
$541$	12.8263	0.551444	0.275722	−	0.961237i	$-0.411083\pi$
$541$	12.8263	0.551444	0.275722	+	0.961237i	$0.411083\pi$
$542$	2.46211	0.105757
$543$	9.64549	0.413928
$544$	−3.54925	−0.152173
$545$	−34.2600	−1.46754
$546$	0	0
$547$	−11.4234	−0.488429	−0.244215	−	0.969721i	$-0.578530\pi$
$547$	−11.4234	−0.488429	−0.244215	+	0.969721i	$0.578530\pi$
$548$	−2.90151	−0.123946
$549$	−5.18293	−0.221202
$550$	−1.98756	−0.0847497
$551$	64.1724	2.73384
$552$	−1.00000	−0.0425628
$553$	0	0
$554$	−23.5192	−0.999235
$555$	−12.1179	−0.514375
$556$	−5.17157	−0.219324
$557$	−24.7026	−1.04668	−0.523341	−	0.852123i	$-0.675315\pi$
$557$	−24.7026	−1.04668	−0.523341	+	0.852123i	$0.675315\pi$
$558$	9.98285	0.422608
$559$	33.0027	1.39587
$560$	0	0
$561$	−1.05971	−0.0447409
$562$	−2.81236	−0.118632
$563$	−36.6658	−1.54528	−0.772639	−	0.634846i	$-0.781063\pi$
$563$	−36.6658	−1.54528	−0.772639	+	0.634846i	$0.781063\pi$
$564$	9.38571	0.395209
$565$	51.2794	2.15734
$566$	17.6800	0.743147
$567$	0	0
$568$	−5.57775	−0.234037
$569$	−29.9430	−1.25528	−0.627638	−	0.778506i	$-0.715978\pi$
$569$	−29.9430	−1.25528	−0.627638	+	0.778506i	$0.715978\pi$
$570$	27.2552	1.14159
$571$	27.2837	1.14179	0.570893	−	0.821025i	$-0.306597\pi$
$571$	27.2837	1.14179	0.570893	+	0.821025i	$0.306597\pi$
$572$	1.40951	0.0589345
$573$	2.13612	0.0892376
$574$	0	0
$575$	6.65685	0.277610
$576$	1.00000	0.0416667
$577$	6.84766	0.285072	0.142536	−	0.989790i	$-0.454474\pi$
$577$	6.84766	0.285072	0.142536	+	0.989790i	$0.454474\pi$
$578$	−4.40285	−0.183135
$579$	−21.9496	−0.912196
$580$	−27.4461	−1.13964
$581$	0	0
$582$	−12.0345	−0.498847
$583$	−2.43229	−0.100735
$584$	−0.776751	−0.0321422
$585$	16.1179	0.666392
$586$	8.97373	0.370702
$587$	−3.17823	−0.131179	−0.0655897	−	0.997847i	$-0.520893\pi$
$587$	−3.17823	−0.131179	−0.0655897	+	0.997847i	$0.520893\pi$
$588$	0	0
$589$	79.6916	3.28364
$590$	34.2745	1.41106
$591$	−6.17490	−0.254001
$592$	−3.54925	−0.145873
$593$	11.6433	0.478134	0.239067	−	0.971003i	$-0.423158\pi$
$593$	11.6433	0.478134	0.239067	+	0.971003i	$0.423158\pi$
$594$	0.298573	0.0122506
$595$	0	0
$596$	7.78053	0.318703
$597$	−21.4644	−0.878478
$598$	−4.72082	−0.193049
$599$	−21.0027	−0.858147	−0.429073	−	0.903270i	$-0.641160\pi$
$599$	−21.0027	−0.858147	−0.429073	+	0.903270i	$0.641160\pi$
$600$	−6.65685	−0.271765
$601$	25.5236	1.04113	0.520564	−	0.853822i	$-0.325722\pi$
$601$	25.5236	1.04113	0.520564	+	0.853822i	$0.325722\pi$
$602$	0	0
$603$	15.2061	0.619240
$604$	−20.6192	−0.838985
$605$	37.2520	1.51451
$606$	−4.99088	−0.202741
$607$	−38.7124	−1.57129	−0.785644	−	0.618679i	$-0.787668\pi$
$607$	−38.7124	−1.57129	−0.785644	+	0.618679i	$0.787668\pi$
$608$	7.98285	0.323747
$609$	0	0
$610$	17.6956	0.716475
$611$	44.3082	1.79252
$612$	−3.54925	−0.143470
$613$	−4.91780	−0.198628	−0.0993141	−	0.995056i	$-0.531665\pi$
$613$	−4.91780	−0.198628	−0.0993141	+	0.995056i	$0.531665\pi$
$614$	−5.49648	−0.221820
$615$	2.78964	0.112489
$616$	0	0
$617$	0.196983	0.00793024	0.00396512	−	0.999992i	$-0.498738\pi$
$617$	0.196983	0.00793024	0.00396512	+	0.999992i	$0.498738\pi$
$618$	−8.86721	−0.356692
$619$	−11.2623	−0.452668	−0.226334	−	0.974050i	$-0.572674\pi$
$619$	−11.2623	−0.452668	−0.226334	+	0.974050i	$0.572674\pi$
$620$	−34.0836	−1.36883
$621$	−1.00000	−0.0401286
$622$	20.0277	0.803036
$623$	0	0
$624$	4.72082	0.188984
$625$	−13.9706	−0.558823
$626$	18.4004	0.735428
$627$	2.38346	0.0951863
$628$	−22.9577	−0.916111
$629$	12.5971	0.502281
$630$	0	0
$631$	31.4067	1.25028	0.625141	−	0.780512i	$-0.285042\pi$
$631$	31.4067	1.25028	0.625141	+	0.780512i	$0.285042\pi$
$632$	−14.0791	−0.560037
$633$	9.23461	0.367043
$634$	−21.6468	−0.859705
$635$	39.2018	1.55568
$636$	−8.14639	−0.323025
$637$	0	0
$638$	−2.40016	−0.0950233
$639$	−5.57775	−0.220653
$640$	−3.41421	−0.134959
$641$	−7.71387	−0.304680	−0.152340	−	0.988328i	$-0.548681\pi$
$641$	−7.71387	−0.304680	−0.152340	+	0.988328i	$0.548681\pi$
$642$	14.4956	0.572094
$643$	10.3260	0.407218	0.203609	−	0.979052i	$-0.434733\pi$
$643$	10.3260	0.407218	0.203609	+	0.979052i	$0.434733\pi$
$644$	0	0
$645$	−23.8684	−0.939816
$646$	−28.3331	−1.11475
$647$	−11.4897	−0.451706	−0.225853	−	0.974161i	$-0.572517\pi$
$647$	−11.4897	−0.451706	−0.225853	+	0.974161i	$0.572517\pi$
$648$	1.00000	0.0392837
$649$	2.99731	0.117655
$650$	−31.4258	−1.23262
$651$	0	0
$652$	−4.63746	−0.181617
$653$	−36.4898	−1.42795	−0.713977	−	0.700169i	$-0.753108\pi$
$653$	−36.4898	−1.42795	−0.713977	+	0.700169i	$0.753108\pi$
$654$	−10.0345	−0.392381
$655$	50.5103	1.97360
$656$	0.817068	0.0319011
$657$	−0.776751	−0.0303039
$658$	0	0
$659$	16.5702	0.645482	0.322741	−	0.946487i	$-0.395396\pi$
$659$	16.5702	0.645482	0.322741	+	0.946487i	$0.395396\pi$
$660$	−1.01939	−0.0396798
$661$	−43.7190	−1.70047	−0.850237	−	0.526401i	$-0.823541\pi$
$661$	−43.7190	−1.70047	−0.850237	+	0.526401i	$0.823541\pi$
$662$	6.34315	0.246533
$663$	−16.7553	−0.650724
$664$	0.884359	0.0343198
$665$	0	0
$666$	−3.54925	−0.137530
$667$	8.03878	0.311263
$668$	−22.1981	−0.858869
$669$	17.0265	0.658282
$670$	−51.9169	−2.00572
$671$	1.54748	0.0597399
$672$	0	0
$673$	40.2745	1.55247	0.776235	−	0.630444i	$-0.217127\pi$
$673$	40.2745	1.55247	0.776235	+	0.630444i	$0.217127\pi$
$674$	−10.7150	−0.412727
$675$	−6.65685	−0.256222
$676$	9.28613	0.357159
$677$	27.9543	1.07437	0.537186	−	0.843464i	$-0.319487\pi$
$677$	27.9543	1.07437	0.537186	+	0.843464i	$0.319487\pi$
$678$	15.0194	0.576816
$679$	0	0
$680$	12.1179	0.464700
$681$	−24.3563	−0.933334
$682$	−2.98061	−0.114133
$683$	25.8554	0.989328	0.494664	−	0.869084i	$-0.335291\pi$
$683$	25.8554	0.989328	0.494664	+	0.869084i	$0.335291\pi$
$684$	7.98285	0.305232
$685$	9.90637	0.378503
$686$	0	0
$687$	−24.1923	−0.922993
$688$	−6.99088	−0.266525
$689$	−38.4576	−1.46512
$690$	3.41421	0.129977
$691$	5.83777	0.222079	0.111040	−	0.993816i	$-0.464582\pi$
$691$	5.83777	0.222079	0.111040	+	0.993816i	$0.464582\pi$
$692$	−3.16732	−0.120403
$693$	0	0
$694$	22.9120	0.869728
$695$	17.6569	0.669763
$696$	−8.03878	−0.304709
$697$	−2.89997	−0.109844
$698$	11.4922	0.434987
$699$	21.9109	0.828745
$700$	0	0
$701$	25.0394	0.945725	0.472862	−	0.881136i	$-0.343221\pi$
$701$	25.0394	0.945725	0.472862	+	0.881136i	$0.343221\pi$
$702$	4.72082	0.178176
$703$	−28.3331	−1.06860
$704$	−0.298573	−0.0112529
$705$	−32.0448	−1.20688
$706$	−10.9510	−0.412147
$707$	0	0
$708$	10.0388	0.377281
$709$	6.97699	0.262026	0.131013	−	0.991381i	$-0.458177\pi$
$709$	6.97699	0.262026	0.131013	+	0.991381i	$0.458177\pi$
$710$	19.0436	0.714695
$711$	−14.0791	−0.528008
$712$	−2.43469	−0.0912439
$713$	9.98285	0.373861
$714$	0	0
$715$	−4.81236	−0.179972
$716$	13.5998	0.508250
$717$	6.47926	0.241972
$718$	−4.63746	−0.173069
$719$	7.63369	0.284688	0.142344	−	0.989817i	$-0.454536\pi$
$719$	7.63369	0.284688	0.142344	+	0.989817i	$0.454536\pi$
$720$	−3.41421	−0.127240
$721$	0	0
$722$	44.7259	1.66453
$723$	−8.52832	−0.317172
$724$	−9.64549	−0.358472
$725$	53.5130	1.98742
$726$	10.9109	0.404940
$727$	−9.08243	−0.336849	−0.168424	−	0.985715i	$-0.553868\pi$
$727$	−9.08243	−0.336849	−0.168424	+	0.985715i	$0.553868\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	2.65199	0.0981547
$731$	24.8124	0.917718
$732$	5.18293	0.191567
$733$	−39.1874	−1.44742	−0.723710	−	0.690104i	$-0.757565\pi$
$733$	−39.1874	−1.44742	−0.723710	+	0.690104i	$0.757565\pi$
$734$	−15.5838	−0.575208
$735$	0	0
$736$	1.00000	0.0368605
$737$	−4.54013	−0.167238
$738$	0.817068	0.0300767
$739$	5.78325	0.212740	0.106370	−	0.994327i	$-0.466077\pi$
$739$	5.78325	0.212740	0.106370	+	0.994327i	$0.466077\pi$
$740$	12.1179	0.445462
$741$	37.6856	1.38441
$742$	0	0
$743$	−30.6192	−1.12331	−0.561655	−	0.827371i	$-0.689835\pi$
$743$	−30.6192	−1.12331	−0.561655	+	0.827371i	$0.689835\pi$
$744$	−9.98285	−0.365989
$745$	−26.5644	−0.973244
$746$	−18.4650	−0.676050
$747$	0.884359	0.0323570
$748$	1.05971	0.0387468
$749$	0	0
$750$	5.65685	0.206559
$751$	7.75265	0.282898	0.141449	−	0.989946i	$-0.454824\pi$
$751$	7.75265	0.282898	0.141449	+	0.989946i	$0.454824\pi$
$752$	−9.38571	−0.342261
$753$	12.5024	0.455614
$754$	−37.9496	−1.38204
$755$	70.3985	2.56206
$756$	0	0
$757$	−32.0617	−1.16530	−0.582652	−	0.812722i	$-0.697985\pi$
$757$	−32.0617	−1.16530	−0.582652	+	0.812722i	$0.697985\pi$
$758$	25.2691	0.917816
$759$	0.298573	0.0108375
$760$	−27.2552	−0.988648
$761$	−27.4933	−0.996632	−0.498316	−	0.866996i	$-0.666048\pi$
$761$	−27.4933	−0.996632	−0.498316	+	0.866996i	$0.666048\pi$
$762$	11.4820	0.415947
$763$	0	0
$764$	−2.13612	−0.0772820
$765$	12.1179	0.438123
$766$	−20.6983	−0.747861
$767$	47.3913	1.71120
$768$	−1.00000	−0.0360844
$769$	30.3755	1.09537	0.547684	−	0.836685i	$-0.315509\pi$
$769$	30.3755	1.09537	0.547684	+	0.836685i	$0.315509\pi$
$770$	0	0
$771$	5.79614	0.208743
$772$	21.9496	0.789985
$773$	31.6645	1.13889	0.569447	−	0.822028i	$-0.307158\pi$
$773$	31.6645	1.13889	0.569447	+	0.822028i	$0.307158\pi$
$774$	−6.99088	−0.251282
$775$	66.4544	2.38711
$776$	12.0345	0.432014
$777$	0	0
$778$	−18.6638	−0.669130
$779$	6.52253	0.233694
$780$	−16.1179	−0.577113
$781$	1.66537	0.0595915
$782$	−3.54925	−0.126921
$783$	−8.03878	−0.287283
$784$	0	0
$785$	78.3824	2.79759
$786$	14.7941	0.527689
$787$	−15.0586	−0.536782	−0.268391	−	0.963310i	$-0.586492\pi$
$787$	−15.0586	−0.536782	−0.268391	+	0.963310i	$0.586492\pi$
$788$	6.17490	0.219972
$789$	8.68629	0.309240
$790$	48.0691	1.71022
$791$	0	0
$792$	−0.298573	−0.0106093
$793$	24.4677	0.868873
$794$	23.4374	0.831762
$795$	27.8135	0.986444
$796$	21.4644	0.760784
$797$	9.68491	0.343057	0.171529	−	0.985179i	$-0.445129\pi$
$797$	9.68491	0.343057	0.171529	+	0.985179i	$0.445129\pi$
$798$	0	0
$799$	33.3122	1.17850
$800$	6.65685	0.235355
$801$	−2.43469	−0.0860255
$802$	−6.24735	−0.220601
$803$	0.231917	0.00818416
$804$	−15.2061	−0.536278
$805$	0	0
$806$	−47.1272	−1.65999
$807$	28.4713	1.00224
$808$	4.99088	0.175579
$809$	−34.1649	−1.20117	−0.600586	−	0.799560i	$-0.705066\pi$
$809$	−34.1649	−1.20117	−0.600586	+	0.799560i	$0.705066\pi$
$810$	−3.41421	−0.119963
$811$	18.1649	0.637854	0.318927	−	0.947779i	$-0.396677\pi$
$811$	18.1649	0.637854	0.318927	+	0.947779i	$0.396677\pi$
$812$	0	0
$813$	−2.46211	−0.0863501
$814$	1.05971	0.0371428
$815$	15.8333	0.554616
$816$	3.54925	0.124248
$817$	−55.8072	−1.95245
$818$	−29.9222	−1.04621
$819$	0	0
$820$	−2.78964	−0.0974186
$821$	7.18610	0.250797	0.125398	−	0.992106i	$-0.459979\pi$
$821$	7.18610	0.250797	0.125398	+	0.992106i	$0.459979\pi$
$822$	2.90151	0.101202
$823$	−31.5189	−1.09868	−0.549340	−	0.835599i	$-0.685121\pi$
$823$	−31.5189	−1.09868	−0.549340	+	0.835599i	$0.685121\pi$
$824$	8.86721	0.308904
$825$	1.98756	0.0691978
$826$	0	0
$827$	31.2594	1.08700	0.543498	−	0.839410i	$-0.317099\pi$
$827$	31.2594	1.08700	0.543498	+	0.839410i	$0.317099\pi$
$828$	1.00000	0.0347524
$829$	55.9338	1.94266	0.971331	−	0.237733i	$-0.0764042\pi$
$829$	55.9338	1.94266	0.971331	+	0.237733i	$0.0764042\pi$
$830$	−3.01939	−0.104805
$831$	23.5192	0.815872
$832$	−4.72082	−0.163665
$833$	0	0
$834$	5.17157	0.179077
$835$	75.7889	2.62278
$836$	−2.38346	−0.0824338
$837$	−9.98285	−0.345058
$838$	−29.5827	−1.02192
$839$	28.3249	0.977885	0.488942	−	0.872316i	$-0.337383\pi$
$839$	28.3249	0.977885	0.488942	+	0.872316i	$0.337383\pi$
$840$	0	0
$841$	35.6220	1.22835
$842$	0.970334	0.0334399
$843$	2.81236	0.0968629
$844$	−9.23461	−0.317868
$845$	−31.7048	−1.09068
$846$	−9.38571	−0.322687
$847$	0	0
$848$	8.14639	0.279748
$849$	−17.6800	−0.606777
$850$	−23.6268	−0.810393
$851$	−3.54925	−0.121667
$852$	5.57775	0.191091
$853$	29.6914	1.01661	0.508307	−	0.861176i	$-0.330272\pi$
$853$	29.6914	1.01661	0.508307	+	0.861176i	$0.330272\pi$
$854$	0	0
$855$	−27.2552	−0.932107
$856$	−14.4956	−0.495448
$857$	26.6467	0.910232	0.455116	−	0.890432i	$-0.349598\pi$
$857$	26.6467	0.910232	0.455116	+	0.890432i	$0.349598\pi$
$858$	−1.40951	−0.0481198
$859$	−28.5543	−0.974261	−0.487131	−	0.873329i	$-0.661956\pi$
$859$	−28.5543	−0.974261	−0.487131	+	0.873329i	$0.661956\pi$
$860$	23.8684	0.813905
$861$	0	0
$862$	23.2246	0.791032
$863$	−6.82906	−0.232464	−0.116232	−	0.993222i	$-0.537082\pi$
$863$	−6.82906	−0.232464	−0.116232	+	0.993222i	$0.537082\pi$
$864$	−1.00000	−0.0340207
$865$	10.8139	0.367684
$866$	−5.94724	−0.202095
$867$	4.40285	0.149529
$868$	0	0
$869$	4.20364	0.142599
$870$	27.4461	0.930511
$871$	−71.7852	−2.43235
$872$	10.0345	0.339812
$873$	12.0345	0.407307
$874$	7.98285	0.270024
$875$	0	0
$876$	0.776751	0.0262440
$877$	−46.7034	−1.57706	−0.788532	−	0.614994i	$-0.789158\pi$
$877$	−46.7034	−1.57706	−0.788532	+	0.614994i	$0.789158\pi$
$878$	17.8080	0.600989
$879$	−8.97373	−0.302677
$880$	1.01939	0.0343637
$881$	−29.0805	−0.979746	−0.489873	−	0.871794i	$-0.662957\pi$
$881$	−29.0805	−0.979746	−0.489873	+	0.871794i	$0.662957\pi$
$882$	0	0
$883$	24.0858	0.810550	0.405275	−	0.914195i	$-0.367176\pi$
$883$	24.0858	0.810550	0.405275	+	0.914195i	$0.367176\pi$
$884$	16.7553	0.563543
$885$	−34.2745	−1.15213
$886$	27.5983	0.927183
$887$	48.3629	1.62387	0.811934	−	0.583749i	$-0.198415\pi$
$887$	48.3629	1.62387	0.811934	+	0.583749i	$0.198415\pi$
$888$	3.54925	0.119105
$889$	0	0
$890$	8.31255	0.278637
$891$	−0.298573	−0.0100026
$892$	−17.0265	−0.570089
$893$	−74.9247	−2.50726
$894$	−7.78053	−0.260220
$895$	−46.4327	−1.55208
$896$	0	0
$897$	4.72082	0.157624
$898$	−36.9221	−1.23211
$899$	80.2500	2.67649
$900$	6.65685	0.221895
$901$	−28.9135	−0.963250
$902$	−0.243954	−0.00812279
$903$	0	0
$904$	−15.0194	−0.499538
$905$	32.9318	1.09469
$906$	20.6192	0.685028
$907$	−35.3606	−1.17413	−0.587065	−	0.809540i	$-0.699717\pi$
$907$	−35.3606	−1.17413	−0.587065	+	0.809540i	$0.699717\pi$
$908$	24.3563	0.808291
$909$	4.99088	0.165537
$910$	0	0
$911$	−30.9926	−1.02683	−0.513416	−	0.858140i	$-0.671620\pi$
$911$	−30.9926	−1.02683	−0.513416	+	0.858140i	$0.671620\pi$
$912$	−7.98285	−0.264339
$913$	−0.264046	−0.00873864
$914$	−14.5971	−0.482831
$915$	−17.6956	−0.585000
$916$	24.1923	0.799335
$917$	0	0
$918$	3.54925	0.117143
$919$	27.9717	0.922702	0.461351	−	0.887218i	$-0.347365\pi$
$919$	27.9717	0.922702	0.461351	+	0.887218i	$0.347365\pi$
$920$	−3.41421	−0.112563
$921$	5.49648	0.181115
$922$	3.08668	0.101654
$923$	26.3316	0.866714
$924$	0	0
$925$	−23.6268	−0.776845
$926$	−35.1190	−1.15408
$927$	8.86721	0.291237
$928$	8.03878	0.263886
$929$	22.1696	0.727360	0.363680	−	0.931524i	$-0.381520\pi$
$929$	22.1696	0.727360	0.363680	+	0.931524i	$0.381520\pi$
$930$	34.0836	1.11764
$931$	0	0
$932$	−21.9109	−0.717714
$933$	−20.0277	−0.655676
$934$	−0.462114	−0.0151208
$935$	−3.61807	−0.118324
$936$	−4.72082	−0.154305
$937$	32.8696	1.07380	0.536902	−	0.843645i	$-0.319595\pi$
$937$	32.8696	1.07380	0.536902	+	0.843645i	$0.319595\pi$
$938$	0	0
$939$	−18.4004	−0.600474
$940$	32.0448	1.04519
$941$	6.11920	0.199480	0.0997401	−	0.995014i	$-0.468199\pi$
$941$	6.11920	0.199480	0.0997401	+	0.995014i	$0.468199\pi$
$942$	22.9577	0.748001
$943$	0.817068	0.0266074
$944$	−10.0388	−0.326735
$945$	0	0
$946$	2.08729	0.0678636
$947$	14.2943	0.464503	0.232251	−	0.972656i	$-0.425391\pi$
$947$	14.2943	0.464503	0.232251	+	0.972656i	$0.425391\pi$
$948$	14.0791	0.457268
$949$	3.66690	0.119033
$950$	53.1407	1.72411
$951$	21.6468	0.701946
$952$	0	0
$953$	8.54166	0.276692	0.138346	−	0.990384i	$-0.455821\pi$
$953$	8.54166	0.276692	0.138346	+	0.990384i	$0.455821\pi$
$954$	8.14639	0.263749
$955$	7.29316	0.236001
$956$	−6.47926	−0.209554
$957$	2.40016	0.0775862
$958$	−19.3115	−0.623928
$959$	0	0
$960$	3.41421	0.110193
$961$	68.6573	2.21475
$962$	16.7553	0.540214
$963$	−14.4956	−0.467113
$964$	8.52832	0.274679
$965$	−74.9407	−2.41243
$966$	0	0
$967$	35.5816	1.14423	0.572114	−	0.820174i	$-0.306124\pi$
$967$	35.5816	1.14423	0.572114	+	0.820174i	$0.306124\pi$
$968$	−10.9109	−0.350688
$969$	28.3331	0.910190
$970$	−41.0884	−1.31927
$971$	39.0732	1.25392	0.626959	−	0.779053i	$-0.284300\pi$
$971$	39.0732	1.25392	0.626959	+	0.779053i	$0.284300\pi$
$972$	−1.00000	−0.0320750
$973$	0	0
$974$	−10.4692	−0.335455
$975$	31.4258	1.00643
$976$	−5.18293	−0.165902
$977$	−12.1400	−0.388392	−0.194196	−	0.980963i	$-0.562210\pi$
$977$	−12.1400	−0.388392	−0.194196	+	0.980963i	$0.562210\pi$
$978$	4.63746	0.148290
$979$	0.726932	0.0232329
$980$	0	0
$981$	10.0345	0.320378
$982$	12.2846	0.392017
$983$	56.4746	1.80126	0.900630	−	0.434587i	$-0.143106\pi$
$983$	56.4746	1.80126	0.900630	+	0.434587i	$0.143106\pi$
$984$	−0.817068	−0.0260472
$985$	−21.0824	−0.671742
$986$	−28.5316	−0.908632
$987$	0	0
$988$	−37.6856	−1.19894
$989$	−6.99088	−0.222297
$990$	1.01939	0.0323984
$991$	−48.3603	−1.53622	−0.768108	−	0.640321i	$-0.778802\pi$
$991$	−48.3603	−1.53622	−0.768108	+	0.640321i	$0.778802\pi$
$992$	9.98285	0.316956
$993$	−6.34315	−0.201294
$994$	0	0
$995$	−73.2839	−2.32326
$996$	−0.884359	−0.0280220
$997$	13.6999	0.433880	0.216940	−	0.976185i	$-0.430392\pi$
$997$	13.6999	0.433880	0.216940	+	0.976185i	$0.430392\pi$
$998$	−6.37188	−0.201698
$999$	3.54925	0.112293

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6762.2.a.ci.1.1	✓	4
7.6	odd	2		6762.2.a.ct.1.3	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6762.2.a.ci.1.1	✓	4	1.1	even	1	trivial
6762.2.a.ct.1.3	yes	4	7.6	odd	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.41421 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.41421 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} -3.41421 q^{10} -0.298573 q^{11} -1.00000 q^{12} -4.72082 q^{13} +3.41421 q^{15} +1.00000 q^{16} -3.54925 q^{17} +1.00000 q^{18} +7.98285 q^{19} -3.41421 q^{20} -0.298573 q^{22} +1.00000 q^{23} -1.00000 q^{24} +6.65685 q^{25} -4.72082 q^{26} -1.00000 q^{27} +8.03878 q^{29} +3.41421 q^{30} +9.98285 q^{31} +1.00000 q^{32} +0.298573 q^{33} -3.54925 q^{34} +1.00000 q^{36} -3.54925 q^{37} +7.98285 q^{38} +4.72082 q^{39} -3.41421 q^{40} +0.817068 q^{41} -6.99088 q^{43} -0.298573 q^{44} -3.41421 q^{45} +1.00000 q^{46} -9.38571 q^{47} -1.00000 q^{48} +6.65685 q^{50} +3.54925 q^{51} -4.72082 q^{52} +8.14639 q^{53} -1.00000 q^{54} +1.01939 q^{55} -7.98285 q^{57} +8.03878 q^{58} -10.0388 q^{59} +3.41421 q^{60} -5.18293 q^{61} +9.98285 q^{62} +1.00000 q^{64} +16.1179 q^{65} +0.298573 q^{66} +15.2061 q^{67} -3.54925 q^{68} -1.00000 q^{69} -5.57775 q^{71} +1.00000 q^{72} -0.776751 q^{73} -3.54925 q^{74} -6.65685 q^{75} +7.98285 q^{76} +4.72082 q^{78} -14.0791 q^{79} -3.41421 q^{80} +1.00000 q^{81} +0.817068 q^{82} +0.884359 q^{83} +12.1179 q^{85} -6.99088 q^{86} -8.03878 q^{87} -0.298573 q^{88} -2.43469 q^{89} -3.41421 q^{90} +1.00000 q^{92} -9.98285 q^{93} -9.38571 q^{94} -27.2552 q^{95} -1.00000 q^{96} +12.0345 q^{97} -0.298573 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} - 8 q^{5} - 4 q^{6} + 4 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 - 8 * q^5 - 4 * q^6 + 4 * q^8 + 4 * q^9	\( 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} - 8 q^{5} - 4 q^{6} + 4 q^{8} + 4 q^{9} - 8 q^{10} + 4 q^{11} - 4 q^{12} - 12 q^{13} + 8 q^{15} + 4 q^{16} + 4 q^{17} + 4 q^{18} - 4 q^{19} - 8 q^{20} + 4 q^{22} + 4 q^{23} - 4 q^{24} + 4 q^{25} - 12 q^{26} - 4 q^{27} + 8 q^{29} + 8 q^{30} + 4 q^{31} + 4 q^{32} - 4 q^{33} + 4 q^{34} + 4 q^{36} + 4 q^{37} - 4 q^{38} + 12 q^{39} - 8 q^{40} + 8 q^{41} + 4 q^{43} + 4 q^{44} - 8 q^{45} + 4 q^{46} - 12 q^{47} - 4 q^{48} + 4 q^{50} - 4 q^{51} - 12 q^{52} + 4 q^{53} - 4 q^{54} - 8 q^{55} + 4 q^{57} + 8 q^{58} - 16 q^{59} + 8 q^{60} - 16 q^{61} + 4 q^{62} + 4 q^{64} + 16 q^{65} - 4 q^{66} + 20 q^{67} + 4 q^{68} - 4 q^{69} - 24 q^{71} + 4 q^{72} - 8 q^{73} + 4 q^{74} - 4 q^{75} - 4 q^{76} + 12 q^{78} - 32 q^{79} - 8 q^{80} + 4 q^{81} + 8 q^{82} + 4 q^{83} + 4 q^{86} - 8 q^{87} + 4 q^{88} - 20 q^{89} - 8 q^{90} + 4 q^{92} - 4 q^{93} - 12 q^{94} - 4 q^{96} - 4 q^{97} + 4 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 - 8 * q^5 - 4 * q^6 + 4 * q^8 + 4 * q^9 - 8 * q^10 + 4 * q^11 - 4 * q^12 - 12 * q^13 + 8 * q^15 + 4 * q^16 + 4 * q^17 + 4 * q^18 - 4 * q^19 - 8 * q^20 + 4 * q^22 + 4 * q^23 - 4 * q^24 + 4 * q^25 - 12 * q^26 - 4 * q^27 + 8 * q^29 + 8 * q^30 + 4 * q^31 + 4 * q^32 - 4 * q^33 + 4 * q^34 + 4 * q^36 + 4 * q^37 - 4 * q^38 + 12 * q^39 - 8 * q^40 + 8 * q^41 + 4 * q^43 + 4 * q^44 - 8 * q^45 + 4 * q^46 - 12 * q^47 - 4 * q^48 + 4 * q^50 - 4 * q^51 - 12 * q^52 + 4 * q^53 - 4 * q^54 - 8 * q^55 + 4 * q^57 + 8 * q^58 - 16 * q^59 + 8 * q^60 - 16 * q^61 + 4 * q^62 + 4 * q^64 + 16 * q^65 - 4 * q^66 + 20 * q^67 + 4 * q^68 - 4 * q^69 - 24 * q^71 + 4 * q^72 - 8 * q^73 + 4 * q^74 - 4 * q^75 - 4 * q^76 + 12 * q^78 - 32 * q^79 - 8 * q^80 + 4 * q^81 + 8 * q^82 + 4 * q^83 + 4 * q^86 - 8 * q^87 + 4 * q^88 - 20 * q^89 - 8 * q^90 + 4 * q^92 - 4 * q^93 - 12 * q^94 - 4 * q^96 - 4 * q^97 + 4 * q^99

Introduction

L-functions

Modular forms

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Database

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