LMFDB - Embedded newform 5566.2.a.bt.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5566,2,Mod(1,5566)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5566, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("5566.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5566 = 2 \cdot 11^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5566.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:	$44.4447337650$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 4x^{9} - 14x^{8} + 50x^{7} + 85x^{6} - 188x^{5} - 248x^{4} + 186x^{3} + 260x^{2} + 52x - 4 $ x^10 - 4x^9 - 14x^8 + 50x^7 + 85x^6 - 188x^5 - 248x^4 + 186x^3 + 260x^2 + 52*x - 4
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 506)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$3.32445$ of defining polynomial
Character	$\chi$	$=$	5566.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.32445 q^{3} +1.00000 q^{4} +4.41136 q^{5} +2.32445 q^{6} -3.63075 q^{7} -1.00000 q^{8} +2.40306 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.32445 q^{3} +1.00000 q^{4} +4.41136 q^{5} +2.32445 q^{6} -3.63075 q^{7} -1.00000 q^{8} +2.40306 q^{9} -4.41136 q^{10} -2.32445 q^{12} +2.24393 q^{13} +3.63075 q^{14} -10.2540 q^{15} +1.00000 q^{16} +1.32702 q^{17} -2.40306 q^{18} +4.62146 q^{19} +4.41136 q^{20} +8.43950 q^{21} -1.00000 q^{23} +2.32445 q^{24} +14.4601 q^{25} -2.24393 q^{26} +1.38755 q^{27} -3.63075 q^{28} +5.36358 q^{29} +10.2540 q^{30} -2.63994 q^{31} -1.00000 q^{32} -1.32702 q^{34} -16.0165 q^{35} +2.40306 q^{36} -0.353494 q^{37} -4.62146 q^{38} -5.21590 q^{39} -4.41136 q^{40} -1.79752 q^{41} -8.43950 q^{42} -12.1408 q^{43} +10.6008 q^{45} +1.00000 q^{46} +9.34759 q^{47} -2.32445 q^{48} +6.18237 q^{49} -14.4601 q^{50} -3.08460 q^{51} +2.24393 q^{52} -4.78338 q^{53} -1.38755 q^{54} +3.63075 q^{56} -10.7424 q^{57} -5.36358 q^{58} +3.47451 q^{59} -10.2540 q^{60} -4.10444 q^{61} +2.63994 q^{62} -8.72493 q^{63} +1.00000 q^{64} +9.89877 q^{65} +15.1202 q^{67} +1.32702 q^{68} +2.32445 q^{69} +16.0165 q^{70} +11.6332 q^{71} -2.40306 q^{72} -8.22022 q^{73} +0.353494 q^{74} -33.6117 q^{75} +4.62146 q^{76} +5.21590 q^{78} +3.32224 q^{79} +4.41136 q^{80} -10.4345 q^{81} +1.79752 q^{82} -11.5710 q^{83} +8.43950 q^{84} +5.85397 q^{85} +12.1408 q^{86} -12.4674 q^{87} +7.54740 q^{89} -10.6008 q^{90} -8.14715 q^{91} -1.00000 q^{92} +6.13640 q^{93} -9.34759 q^{94} +20.3869 q^{95} +2.32445 q^{96} -4.79207 q^{97} -6.18237 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 10 q^{2} + 6 q^{3} + 10 q^{4} + 12 q^{5} - 6 q^{6} - 4 q^{7} - 10 q^{8} + 16 q^{9}+O(q^{10}) $ 10 * q - 10 * q^2 + 6 * q^3 + 10 * q^4 + 12 * q^5 - 6 * q^6 - 4 * q^7 - 10 * q^8 + 16 * q^9	$ 10 q - 10 q^{2} + 6 q^{3} + 10 q^{4} + 12 q^{5} - 6 q^{6} - 4 q^{7} - 10 q^{8} + 16 q^{9} - 12 q^{10} + 6 q^{12} + 3 q^{13} + 4 q^{14} + 6 q^{15} + 10 q^{16} + 4 q^{17} - 16 q^{18} - 8 q^{19} + 12 q^{20} - 8 q^{21} - 10 q^{23} - 6 q^{24} + 34 q^{25} - 3 q^{26} + 12 q^{27} - 4 q^{28} + 15 q^{29} - 6 q^{30} - 10 q^{32} - 4 q^{34} - 8 q^{35} + 16 q^{36} + 18 q^{37} + 8 q^{38} - 29 q^{39} - 12 q^{40} - 3 q^{41} + 8 q^{42} - 4 q^{43} + 72 q^{45} + 10 q^{46} + 42 q^{47} + 6 q^{48} + 12 q^{49} - 34 q^{50} - 18 q^{51} + 3 q^{52} + 11 q^{53} - 12 q^{54} + 4 q^{56} - 16 q^{57} - 15 q^{58} + 54 q^{59} + 6 q^{60} - 6 q^{61} + 10 q^{64} + 31 q^{65} + 24 q^{67} + 4 q^{68} - 6 q^{69} + 8 q^{70} + 37 q^{71} - 16 q^{72} + 42 q^{73} - 18 q^{74} - 12 q^{75} - 8 q^{76} + 29 q^{78} - 37 q^{79} + 12 q^{80} + 10 q^{81} + 3 q^{82} - 21 q^{83} - 8 q^{84} + 20 q^{85} + 4 q^{86} - 15 q^{87} + 63 q^{89} - 72 q^{90} + 11 q^{91} - 10 q^{92} + 8 q^{93} - 42 q^{94} + 30 q^{95} - 6 q^{96} + 2 q^{97} - 12 q^{98}+O(q^{100}) $ 10 * q - 10 * q^2 + 6 * q^3 + 10 * q^4 + 12 * q^5 - 6 * q^6 - 4 * q^7 - 10 * q^8 + 16 * q^9 - 12 * q^10 + 6 * q^12 + 3 * q^13 + 4 * q^14 + 6 * q^15 + 10 * q^16 + 4 * q^17 - 16 * q^18 - 8 * q^19 + 12 * q^20 - 8 * q^21 - 10 * q^23 - 6 * q^24 + 34 * q^25 - 3 * q^26 + 12 * q^27 - 4 * q^28 + 15 * q^29 - 6 * q^30 - 10 * q^32 - 4 * q^34 - 8 * q^35 + 16 * q^36 + 18 * q^37 + 8 * q^38 - 29 * q^39 - 12 * q^40 - 3 * q^41 + 8 * q^42 - 4 * q^43 + 72 * q^45 + 10 * q^46 + 42 * q^47 + 6 * q^48 + 12 * q^49 - 34 * q^50 - 18 * q^51 + 3 * q^52 + 11 * q^53 - 12 * q^54 + 4 * q^56 - 16 * q^57 - 15 * q^58 + 54 * q^59 + 6 * q^60 - 6 * q^61 + 10 * q^64 + 31 * q^65 + 24 * q^67 + 4 * q^68 - 6 * q^69 + 8 * q^70 + 37 * q^71 - 16 * q^72 + 42 * q^73 - 18 * q^74 - 12 * q^75 - 8 * q^76 + 29 * q^78 - 37 * q^79 + 12 * q^80 + 10 * q^81 + 3 * q^82 - 21 * q^83 - 8 * q^84 + 20 * q^85 + 4 * q^86 - 15 * q^87 + 63 * q^89 - 72 * q^90 + 11 * q^91 - 10 * q^92 + 8 * q^93 - 42 * q^94 + 30 * q^95 - 6 * q^96 + 2 * q^97 - 12 * q^98

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
$3$	−2.32445	−1.34202	−0.671011	−	0.741448i	$-0.734140\pi$
$3$	−2.32445	−1.34202	−0.671011	+	0.741448i	$0.734140\pi$
$4$	1.00000	0.500000
$5$	4.41136	1.97282	0.986410	−	0.164305i	$-0.0525380\pi$
$5$	4.41136	1.97282	0.986410	+	0.164305i	$0.0525380\pi$
$6$	2.32445	0.948952
$7$	−3.63075	−1.37230	−0.686148	−	0.727462i	$-0.740700\pi$
$7$	−3.63075	−1.37230	−0.686148	+	0.727462i	$0.740700\pi$
$8$	−1.00000	−0.353553
$9$	2.40306	0.801021
$10$	−4.41136	−1.39499
$11$	0	0
$11$	0	0
$12$	−2.32445	−0.671011
$13$	2.24393	0.622354	0.311177	−	0.950352i	$-0.399277\pi$
$13$	2.24393	0.622354	0.311177	+	0.950352i	$0.399277\pi$
$14$	3.63075	0.970359
$15$	−10.2540	−2.64757
$16$	1.00000	0.250000
$17$	1.32702	0.321850	0.160925	−	0.986967i	$-0.448552\pi$
$17$	1.32702	0.321850	0.160925	+	0.986967i	$0.448552\pi$
$18$	−2.40306	−0.566408
$19$	4.62146	1.06024	0.530118	−	0.847924i	$-0.322148\pi$
$19$	4.62146	1.06024	0.530118	+	0.847924i	$0.322148\pi$
$20$	4.41136	0.986410
$21$	8.43950	1.84165
$22$	0	0
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	2.32445	0.474476
$25$	14.4601	2.89202
$26$	−2.24393	−0.440071
$27$	1.38755	0.267034
$28$	−3.63075	−0.686148
$29$	5.36358	0.995993	0.497996	−	0.867179i	$-0.334069\pi$
$29$	5.36358	0.995993	0.497996	+	0.867179i	$0.334069\pi$
$30$	10.2540	1.87211
$31$	−2.63994	−0.474147	−0.237073	−	0.971492i	$-0.576188\pi$
$31$	−2.63994	−0.474147	−0.237073	+	0.971492i	$0.576188\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	−1.32702	−0.227583
$35$	−16.0165	−2.70729
$36$	2.40306	0.400511
$37$	−0.353494	−0.0581141	−0.0290571	−	0.999578i	$-0.509250\pi$
$37$	−0.353494	−0.0581141	−0.0290571	+	0.999578i	$0.509250\pi$
$38$	−4.62146	−0.749700
$39$	−5.21590	−0.835212
$40$	−4.41136	−0.697497
$41$	−1.79752	−0.280725	−0.140362	−	0.990100i	$-0.544827\pi$
$41$	−1.79752	−0.280725	−0.140362	+	0.990100i	$0.544827\pi$
$42$	−8.43950	−1.30224
$43$	−12.1408	−1.85145	−0.925727	−	0.378194i	$-0.876545\pi$
$43$	−12.1408	−1.85145	−0.925727	+	0.378194i	$0.876545\pi$
$44$	0	0
$45$	10.6008	1.58027
$46$	1.00000	0.147442
$47$	9.34759	1.36349	0.681743	−	0.731592i	$-0.261222\pi$
$47$	9.34759	1.36349	0.681743	+	0.731592i	$0.261222\pi$
$48$	−2.32445	−0.335505
$49$	6.18237	0.883195
$50$	−14.4601	−2.04496
$51$	−3.08460	−0.431930
$52$	2.24393	0.311177
$53$	−4.78338	−0.657048	−0.328524	−	0.944496i	$-0.606551\pi$
$53$	−4.78338	−0.657048	−0.328524	+	0.944496i	$0.606551\pi$
$54$	−1.38755	−0.188821
$55$	0	0
$56$	3.63075	0.485180
$57$	−10.7424	−1.42286
$58$	−5.36358	−0.704273
$59$	3.47451	0.452343	0.226171	−	0.974088i	$-0.427379\pi$
$59$	3.47451	0.452343	0.226171	+	0.974088i	$0.427379\pi$
$60$	−10.2540	−1.32378
$61$	−4.10444	−0.525520	−0.262760	−	0.964861i	$-0.584633\pi$
$61$	−4.10444	−0.525520	−0.262760	+	0.964861i	$0.584633\pi$
$62$	2.63994	0.335272
$63$	−8.72493	−1.09924
$64$	1.00000	0.125000
$65$	9.89877	1.22779
$66$	0	0
$67$	15.1202	1.84722	0.923611	−	0.383331i	$-0.125223\pi$
$67$	15.1202	1.84722	0.923611	+	0.383331i	$0.125223\pi$
$68$	1.32702	0.160925
$69$	2.32445	0.279831
$70$	16.0165	1.91434
$71$	11.6332	1.38061	0.690303	−	0.723520i	$-0.257477\pi$
$71$	11.6332	1.38061	0.690303	+	0.723520i	$0.257477\pi$
$72$	−2.40306	−0.283204
$73$	−8.22022	−0.962104	−0.481052	−	0.876692i	$-0.659745\pi$
$73$	−8.22022	−0.962104	−0.481052	+	0.876692i	$0.659745\pi$
$74$	0.353494	0.0410929
$75$	−33.6117	−3.88115
$76$	4.62146	0.530118
$77$	0	0
$78$	5.21590	0.590584
$79$	3.32224	0.373781	0.186891	−	0.982381i	$-0.440159\pi$
$79$	3.32224	0.373781	0.186891	+	0.982381i	$0.440159\pi$
$80$	4.41136	0.493205
$81$	−10.4345	−1.15939
$82$	1.79752	0.198502
$83$	−11.5710	−1.27008	−0.635040	−	0.772479i	$-0.719017\pi$
$83$	−11.5710	−1.27008	−0.635040	+	0.772479i	$0.719017\pi$
$84$	8.43950	0.920825
$85$	5.85397	0.634952
$86$	12.1408	1.30917
$87$	−12.4674	−1.33664
$88$	0	0
$89$	7.54740	0.800023	0.400012	−	0.916510i	$-0.369006\pi$
$89$	7.54740	0.800023	0.400012	+	0.916510i	$0.369006\pi$
$90$	−10.6008	−1.11742
$91$	−8.14715	−0.854053
$92$	−1.00000	−0.104257
$93$	6.13640	0.636315
$94$	−9.34759	−0.964131
$95$	20.3869	2.09165
$96$	2.32445	0.237238
$97$	−4.79207	−0.486561	−0.243281	−	0.969956i	$-0.578224\pi$
$97$	−4.79207	−0.486561	−0.243281	+	0.969956i	$0.578224\pi$
$98$	−6.18237	−0.624513
$99$	0	0
$100$	14.4601	1.44601
$101$	6.50698	0.647469	0.323734	−	0.946148i	$-0.395062\pi$
$101$	6.50698	0.647469	0.323734	+	0.946148i	$0.395062\pi$
$102$	3.08460	0.305421
$103$	−5.64989	−0.556700	−0.278350	−	0.960480i	$-0.589788\pi$
$103$	−5.64989	−0.556700	−0.278350	+	0.960480i	$0.589788\pi$
$104$	−2.24393	−0.220035
$105$	37.2297	3.63324
$106$	4.78338	0.464603
$107$	−19.7757	−1.91179	−0.955896	−	0.293706i	$-0.905111\pi$
$107$	−19.7757	−1.91179	−0.955896	+	0.293706i	$0.905111\pi$
$108$	1.38755	0.133517
$109$	17.0910	1.63703	0.818513	−	0.574489i	$-0.194799\pi$
$109$	17.0910	1.63703	0.818513	+	0.574489i	$0.194799\pi$
$110$	0	0
$111$	0.821680	0.0779904
$112$	−3.63075	−0.343074
$113$	−4.84677	−0.455946	−0.227973	−	0.973668i	$-0.573210\pi$
$113$	−4.84677	−0.455946	−0.227973	+	0.973668i	$0.573210\pi$
$114$	10.7424	1.00611
$115$	−4.41136	−0.411361
$116$	5.36358	0.497996
$117$	5.39230	0.498519
$118$	−3.47451	−0.319855
$119$	−4.81809	−0.441674
$120$	10.2540	0.936056
$121$	0	0
$122$	4.10444	0.371599
$123$	4.17823	0.376739
$124$	−2.63994	−0.237073
$125$	41.7318	3.73261
$126$	8.72493	0.777279
$127$	13.6669	1.21274	0.606370	−	0.795183i	$-0.292625\pi$
$127$	13.6669	1.21274	0.606370	+	0.795183i	$0.292625\pi$
$128$	−1.00000	−0.0883883
$129$	28.2206	2.48469
$130$	−9.89877	−0.868180
$131$	−6.80788	−0.594807	−0.297404	−	0.954752i	$-0.596121\pi$
$131$	−6.80788	−0.594807	−0.297404	+	0.954752i	$0.596121\pi$
$132$	0	0
$133$	−16.7794	−1.45496
$134$	−15.1202	−1.30618
$135$	6.12097	0.526809
$136$	−1.32702	−0.113791
$137$	−2.52809	−0.215989	−0.107995	−	0.994151i	$-0.534443\pi$
$137$	−2.52809	−0.215989	−0.107995	+	0.994151i	$0.534443\pi$
$138$	−2.32445	−0.197870
$139$	11.0625	0.938306	0.469153	−	0.883117i	$-0.344559\pi$
$139$	11.0625	0.938306	0.469153	+	0.883117i	$0.344559\pi$
$140$	−16.0165	−1.35365
$141$	−21.7280	−1.82983
$142$	−11.6332	−0.976236
$143$	0	0
$144$	2.40306	0.200255
$145$	23.6607	1.96491
$146$	8.22022	0.680310
$147$	−14.3706	−1.18527
$148$	−0.353494	−0.0290571
$149$	−2.20045	−0.180268	−0.0901338	−	0.995930i	$-0.528729\pi$
$149$	−2.20045	−0.180268	−0.0901338	+	0.995930i	$0.528729\pi$
$150$	33.6117	2.74439
$151$	−7.59832	−0.618343	−0.309171	−	0.951006i	$-0.600052\pi$
$151$	−7.59832	−0.618343	−0.309171	+	0.951006i	$0.600052\pi$
$152$	−4.62146	−0.374850
$153$	3.18892	0.257809
$154$	0	0
$155$	−11.6457	−0.935406
$156$	−5.21590	−0.417606
$157$	17.3025	1.38089	0.690445	−	0.723385i	$-0.257415\pi$
$157$	17.3025	1.38089	0.690445	+	0.723385i	$0.257415\pi$
$158$	−3.32224	−0.264303
$159$	11.1187	0.881773
$160$	−4.41136	−0.348748
$161$	3.63075	0.286143
$162$	10.4345	0.819810
$163$	13.2435	1.03731	0.518655	−	0.854984i	$-0.326433\pi$
$163$	13.2435	1.03731	0.518655	+	0.854984i	$0.326433\pi$
$164$	−1.79752	−0.140362
$165$	0	0
$166$	11.5710	0.898083
$167$	−3.51506	−0.272004	−0.136002	−	0.990709i	$-0.543425\pi$
$167$	−3.51506	−0.272004	−0.136002	+	0.990709i	$0.543425\pi$
$168$	−8.43950	−0.651122
$169$	−7.96478	−0.612676
$170$	−5.85397	−0.448979
$171$	11.1057	0.849272
$172$	−12.1408	−0.925727
$173$	16.2910	1.23858	0.619290	−	0.785162i	$-0.287420\pi$
$173$	16.2910	1.23858	0.619290	+	0.785162i	$0.287420\pi$
$174$	12.4674	0.945150
$175$	−52.5010	−3.96870
$176$	0	0
$177$	−8.07633	−0.607054
$178$	−7.54740	−0.565702
$179$	−24.6494	−1.84239	−0.921193	−	0.389106i	$-0.872784\pi$
$179$	−24.6494	−1.84239	−0.921193	+	0.389106i	$0.872784\pi$
$180$	10.6008	0.790135
$181$	14.5515	1.08160	0.540802	−	0.841150i	$-0.318121\pi$
$181$	14.5515	1.08160	0.540802	+	0.841150i	$0.318121\pi$
$182$	8.14715	0.603907
$183$	9.54057	0.705259
$184$	1.00000	0.0737210
$185$	−1.55939	−0.114649
$186$	−6.13640	−0.449943
$187$	0	0
$188$	9.34759	0.681743
$189$	−5.03784	−0.366449
$190$	−20.3869	−1.47902
$191$	−13.8806	−1.00436	−0.502182	−	0.864762i	$-0.667469\pi$
$191$	−13.8806	−1.00436	−0.502182	+	0.864762i	$0.667469\pi$
$192$	−2.32445	−0.167753
$193$	−4.94031	−0.355611	−0.177806	−	0.984066i	$-0.556900\pi$
$193$	−4.94031	−0.355611	−0.177806	+	0.984066i	$0.556900\pi$
$194$	4.79207	0.344051
$195$	−23.0092	−1.64772
$196$	6.18237	0.441598
$197$	−3.13309	−0.223223	−0.111612	−	0.993752i	$-0.535601\pi$
$197$	−3.13309	−0.223223	−0.111612	+	0.993752i	$0.535601\pi$
$198$	0	0
$199$	−0.829942	−0.0588330	−0.0294165	−	0.999567i	$-0.509365\pi$
$199$	−0.829942	−0.0588330	−0.0294165	+	0.999567i	$0.509365\pi$
$200$	−14.4601	−1.02248
$201$	−35.1461	−2.47901
$202$	−6.50698	−0.457829
$203$	−19.4738	−1.36680
$204$	−3.08460	−0.215965
$205$	−7.92949	−0.553819
$206$	5.64989	0.393646
$207$	−2.40306	−0.167024
$208$	2.24393	0.155588
$209$	0	0
$210$	−37.2297	−2.56909
$211$	0.100035	0.00688668	0.00344334	−	0.999994i	$-0.498904\pi$
$211$	0.100035	0.00688668	0.00344334	+	0.999994i	$0.498904\pi$
$212$	−4.78338	−0.328524
$213$	−27.0408	−1.85280
$214$	19.7757	1.35184
$215$	−53.5574	−3.65258
$216$	−1.38755	−0.0944106
$217$	9.58496	0.650669
$218$	−17.0910	−1.15755
$219$	19.1075	1.29116
$220$	0	0
$221$	2.97774	0.200305
$222$	−0.821680	−0.0551475
$223$	−7.36589	−0.493256	−0.246628	−	0.969110i	$-0.579323\pi$
$223$	−7.36589	−0.493256	−0.246628	+	0.969110i	$0.579323\pi$
$224$	3.63075	0.242590
$225$	34.7485	2.31657
$226$	4.84677	0.322402
$227$	−10.8863	−0.722548	−0.361274	−	0.932460i	$-0.617658\pi$
$227$	−10.8863	−0.722548	−0.361274	+	0.932460i	$0.617658\pi$
$228$	−10.7424	−0.711430
$229$	12.2809	0.811542	0.405771	−	0.913975i	$-0.367003\pi$
$229$	12.2809	0.811542	0.405771	+	0.913975i	$0.367003\pi$
$230$	4.41136	0.290876
$231$	0	0
$232$	−5.36358	−0.352137
$233$	−1.54550	−0.101249	−0.0506244	−	0.998718i	$-0.516121\pi$
$233$	−1.54550	−0.101249	−0.0506244	+	0.998718i	$0.516121\pi$
$234$	−5.39230	−0.352506
$235$	41.2356	2.68991
$236$	3.47451	0.226171
$237$	−7.72238	−0.501622
$238$	4.81809	0.312310
$239$	9.97099	0.644970	0.322485	−	0.946575i	$-0.395482\pi$
$239$	9.97099	0.644970	0.322485	+	0.946575i	$0.395482\pi$
$240$	−10.2540	−0.661891
$241$	15.4129	0.992829	0.496415	−	0.868085i	$-0.334650\pi$
$241$	15.4129	0.992829	0.496415	+	0.868085i	$0.334650\pi$
$242$	0	0
$243$	20.0918	1.28889
$244$	−4.10444	−0.262760
$245$	27.2726	1.74238
$246$	−4.17823	−0.266395
$247$	10.3702	0.659842
$248$	2.63994	0.167636
$249$	26.8962	1.70448
$250$	−41.7318	−2.63935
$251$	−12.0786	−0.762397	−0.381198	−	0.924493i	$-0.624488\pi$
$251$	−12.0786	−0.762397	−0.381198	+	0.924493i	$0.624488\pi$
$252$	−8.72493	−0.549619
$253$	0	0
$254$	−13.6669	−0.857537
$255$	−13.6073	−0.852120
$256$	1.00000	0.0625000
$257$	−17.1291	−1.06848	−0.534241	−	0.845332i	$-0.679403\pi$
$257$	−17.1291	−1.06848	−0.534241	+	0.845332i	$0.679403\pi$
$258$	−28.2206	−1.75694
$259$	1.28345	0.0797497
$260$	9.89877	0.613896
$261$	12.8890	0.797811
$262$	6.80788	0.420592
$263$	11.2050	0.690927	0.345464	−	0.938432i	$-0.387722\pi$
$263$	11.2050	0.690927	0.345464	+	0.938432i	$0.387722\pi$
$264$	0	0
$265$	−21.1012	−1.29624
$266$	16.7794	1.02881
$267$	−17.5436	−1.07365
$268$	15.1202	0.923611
$269$	−3.94935	−0.240796	−0.120398	−	0.992726i	$-0.538417\pi$
$269$	−3.94935	−0.240796	−0.120398	+	0.992726i	$0.538417\pi$
$270$	−6.12097	−0.372510
$271$	−23.0116	−1.39786	−0.698928	−	0.715192i	$-0.746339\pi$
$271$	−23.0116	−1.39786	−0.698928	+	0.715192i	$0.746339\pi$
$272$	1.32702	0.0804626
$273$	18.9376	1.14616
$274$	2.52809	0.152728
$275$	0	0
$276$	2.32445	0.139915
$277$	8.73760	0.524992	0.262496	−	0.964933i	$-0.415454\pi$
$277$	8.73760	0.524992	0.262496	+	0.964933i	$0.415454\pi$
$278$	−11.0625	−0.663482
$279$	−6.34394	−0.379802
$280$	16.0165	0.957172
$281$	−8.54349	−0.509662	−0.254831	−	0.966986i	$-0.582020\pi$
$281$	−8.54349	−0.509662	−0.254831	+	0.966986i	$0.582020\pi$
$282$	21.7280	1.29388
$283$	−0.942069	−0.0560002	−0.0280001	−	0.999608i	$-0.508914\pi$
$283$	−0.942069	−0.0560002	−0.0280001	+	0.999608i	$0.508914\pi$
$284$	11.6332	0.690303
$285$	−47.3884	−2.80704
$286$	0	0
$287$	6.52634	0.385237
$288$	−2.40306	−0.141602
$289$	−15.2390	−0.896412
$290$	−23.6607	−1.38940
$291$	11.1389	0.652976
$292$	−8.22022	−0.481052
$293$	14.1061	0.824088	0.412044	−	0.911164i	$-0.364815\pi$
$293$	14.1061	0.824088	0.412044	+	0.911164i	$0.364815\pi$
$294$	14.3706	0.838110
$295$	15.3273	0.892391
$296$	0.353494	0.0205464
$297$	0	0
$298$	2.20045	0.127468
$299$	−2.24393	−0.129770
$300$	−33.6117	−1.94057
$301$	44.0802	2.54074
$302$	7.59832	0.437234
$303$	−15.1251	−0.868917
$304$	4.62146	0.265059
$305$	−18.1062	−1.03676
$306$	−3.18892	−0.182298
$307$	22.7739	1.29977	0.649886	−	0.760032i	$-0.274817\pi$
$307$	22.7739	1.29977	0.649886	+	0.760032i	$0.274817\pi$
$308$	0	0
$309$	13.1329	0.747103
$310$	11.6457	0.661432
$311$	23.9348	1.35722	0.678610	−	0.734499i	$-0.262583\pi$
$311$	23.9348	1.35722	0.678610	+	0.734499i	$0.262583\pi$
$312$	5.21590	0.295292
$313$	−20.3824	−1.15208	−0.576041	−	0.817421i	$-0.695403\pi$
$313$	−20.3824	−1.15208	−0.576041	+	0.817421i	$0.695403\pi$
$314$	−17.3025	−0.976436
$315$	−38.4888	−2.16860
$316$	3.32224	0.186891
$317$	8.88037	0.498771	0.249386	−	0.968404i	$-0.419771\pi$
$317$	8.88037	0.498771	0.249386	+	0.968404i	$0.419771\pi$
$318$	−11.1187	−0.623508
$319$	0	0
$320$	4.41136	0.246602
$321$	45.9677	2.56567
$322$	−3.63075	−0.202334
$323$	6.13279	0.341237
$324$	−10.4345	−0.579693
$325$	32.4474	1.79986
$326$	−13.2435	−0.733489
$327$	−39.7273	−2.19692
$328$	1.79752	0.0992512
$329$	−33.9388	−1.87111
$330$	0	0
$331$	34.5508	1.89909	0.949543	−	0.313637i	$-0.101548\pi$
$331$	34.5508	1.89909	0.949543	+	0.313637i	$0.101548\pi$
$332$	−11.5710	−0.635040
$333$	−0.849470	−0.0465506
$334$	3.51506	0.192336
$335$	66.7005	3.64424
$336$	8.43950	0.460412
$337$	2.04783	0.111552	0.0557761	−	0.998443i	$-0.482237\pi$
$337$	2.04783	0.111552	0.0557761	+	0.998443i	$0.482237\pi$
$338$	7.96478	0.433227
$339$	11.2661	0.611889
$340$	5.85397	0.317476
$341$	0	0
$342$	−11.1057	−0.600526
$343$	2.96863	0.160291
$344$	12.1408	0.654587
$345$	10.2540	0.552056
$346$	−16.2910	−0.875808
$347$	26.0542	1.39866	0.699332	−	0.714797i	$-0.253481\pi$
$347$	26.0542	1.39866	0.699332	+	0.714797i	$0.253481\pi$
$348$	−12.4674	−0.668322
$349$	6.05742	0.324246	0.162123	−	0.986771i	$-0.448166\pi$
$349$	6.05742	0.324246	0.162123	+	0.986771i	$0.448166\pi$
$350$	52.5010	2.80630
$351$	3.11356	0.166189
$352$	0	0
$353$	23.1057	1.22979	0.614896	−	0.788609i	$-0.289198\pi$
$353$	23.1057	1.22979	0.614896	+	0.788609i	$0.289198\pi$
$354$	8.07633	0.429252
$355$	51.3182	2.72369
$356$	7.54740	0.400012
$357$	11.1994	0.592736
$358$	24.6494	1.30276
$359$	20.1478	1.06336	0.531680	−	0.846945i	$-0.321561\pi$
$359$	20.1478	1.06336	0.531680	+	0.846945i	$0.321561\pi$
$360$	−10.6008	−0.558710
$361$	2.35792	0.124101
$362$	−14.5515	−0.764810
$363$	0	0
$364$	−8.14715	−0.427027
$365$	−36.2623	−1.89806
$366$	−9.54057	−0.498693
$367$	15.8506	0.827393	0.413697	−	0.910415i	$-0.364237\pi$
$367$	15.8506	0.827393	0.413697	+	0.910415i	$0.364237\pi$
$368$	−1.00000	−0.0521286
$369$	−4.31955	−0.224867
$370$	1.55939	0.0810688
$371$	17.3673	0.901664
$372$	6.13640	0.318157
$373$	30.5676	1.58273	0.791365	−	0.611344i	$-0.209371\pi$
$373$	30.5676	1.58273	0.791365	+	0.611344i	$0.209371\pi$
$374$	0	0
$375$	−97.0034	−5.00924
$376$	−9.34759	−0.482065
$377$	12.0355	0.619860
$378$	5.03784	0.259119
$379$	−5.85996	−0.301006	−0.150503	−	0.988610i	$-0.548089\pi$
$379$	−5.85996	−0.301006	−0.150503	+	0.988610i	$0.548089\pi$
$380$	20.3869	1.04583
$381$	−31.7680	−1.62752
$382$	13.8806	0.710193
$383$	−16.1540	−0.825431	−0.412716	−	0.910860i	$-0.635420\pi$
$383$	−16.1540	−0.825431	−0.412716	+	0.910860i	$0.635420\pi$
$384$	2.32445	0.118619
$385$	0	0
$386$	4.94031	0.251455
$387$	−29.1751	−1.48305
$388$	−4.79207	−0.243281
$389$	24.9890	1.26699	0.633496	−	0.773746i	$-0.281619\pi$
$389$	24.9890	1.26699	0.633496	+	0.773746i	$0.281619\pi$
$390$	23.0092	1.16512
$391$	−1.32702	−0.0671104
$392$	−6.18237	−0.312257
$393$	15.8246	0.798244
$394$	3.13309	0.157843
$395$	14.6556	0.737403
$396$	0	0
$397$	−2.71849	−0.136437	−0.0682185	−	0.997670i	$-0.521731\pi$
$397$	−2.71849	−0.136437	−0.0682185	+	0.997670i	$0.521731\pi$
$398$	0.829942	0.0416012
$399$	39.0028	1.95258
$400$	14.4601	0.723004
$401$	−17.3646	−0.867149	−0.433574	−	0.901118i	$-0.642748\pi$
$401$	−17.3646	−0.867149	−0.433574	+	0.901118i	$0.642748\pi$
$402$	35.1461	1.75293
$403$	−5.92383	−0.295087
$404$	6.50698	0.323734
$405$	−46.0302	−2.28726
$406$	19.4738	0.966471
$407$	0	0
$408$	3.08460	0.152710
$409$	−18.9748	−0.938242	−0.469121	−	0.883134i	$-0.655429\pi$
$409$	−18.9748	−0.938242	−0.469121	+	0.883134i	$0.655429\pi$
$410$	7.92949	0.391609
$411$	5.87642	0.289862
$412$	−5.64989	−0.278350
$413$	−12.6151	−0.620748
$414$	2.40306	0.118104
$415$	−51.0438	−2.50564
$416$	−2.24393	−0.110018
$417$	−25.7141	−1.25923
$418$	0	0
$419$	23.7347	1.15951	0.579757	−	0.814789i	$-0.303147\pi$
$419$	23.7347	1.15951	0.579757	+	0.814789i	$0.303147\pi$
$420$	37.2297	1.81662
$421$	33.0815	1.61229	0.806146	−	0.591716i	$-0.201549\pi$
$421$	33.0815	1.61229	0.806146	+	0.591716i	$0.201549\pi$
$422$	−0.100035	−0.00486962
$423$	22.4629	1.09218
$424$	4.78338	0.232302
$425$	19.1889	0.930796
$426$	27.0408	1.31013
$427$	14.9022	0.721169
$428$	−19.7757	−0.955896
$429$	0	0
$430$	53.5574	2.58277
$431$	2.74829	0.132380	0.0661902	−	0.997807i	$-0.478916\pi$
$431$	2.74829	0.132380	0.0661902	+	0.997807i	$0.478916\pi$
$432$	1.38755	0.0667584
$433$	−15.1958	−0.730265	−0.365133	−	0.930956i	$-0.618976\pi$
$433$	−15.1958	−0.730265	−0.365133	+	0.930956i	$0.618976\pi$
$434$	−9.58496	−0.460093
$435$	−54.9981	−2.63696
$436$	17.0910	0.818513
$437$	−4.62146	−0.221075
$438$	−19.1075	−0.912991
$439$	12.2481	0.584570	0.292285	−	0.956331i	$-0.405584\pi$
$439$	12.2481	0.584570	0.292285	+	0.956331i	$0.405584\pi$
$440$	0	0
$441$	14.8566	0.707458
$442$	−2.97774	−0.141637
$443$	27.4897	1.30608	0.653039	−	0.757325i	$-0.273494\pi$
$443$	27.4897	1.30608	0.653039	+	0.757325i	$0.273494\pi$
$444$	0.821680	0.0389952
$445$	33.2943	1.57830
$446$	7.36589	0.348785
$447$	5.11482	0.241923
$448$	−3.63075	−0.171537
$449$	−23.7187	−1.11935	−0.559677	−	0.828711i	$-0.689075\pi$
$449$	−23.7187	−1.11935	−0.559677	+	0.828711i	$0.689075\pi$
$450$	−34.7485	−1.63806
$451$	0	0
$452$	−4.84677	−0.227973
$453$	17.6619	0.829829
$454$	10.8863	0.510918
$455$	−35.9400	−1.68489
$456$	10.7424	0.503057
$457$	30.6685	1.43461	0.717305	−	0.696759i	$-0.245375\pi$
$457$	30.6685	1.43461	0.717305	+	0.696759i	$0.245375\pi$
$458$	−12.2809	−0.573847
$459$	1.84131	0.0859448
$460$	−4.41136	−0.205681
$461$	−1.19209	−0.0555210	−0.0277605	−	0.999615i	$-0.508838\pi$
$461$	−1.19209	−0.0555210	−0.0277605	+	0.999615i	$0.508838\pi$
$462$	0	0
$463$	−28.2091	−1.31099	−0.655494	−	0.755200i	$-0.727540\pi$
$463$	−28.2091	−1.31099	−0.655494	+	0.755200i	$0.727540\pi$
$464$	5.36358	0.248998
$465$	27.0699	1.25533
$466$	1.54550	0.0715937
$467$	5.71982	0.264682	0.132341	−	0.991204i	$-0.457751\pi$
$467$	5.71982	0.264682	0.132341	+	0.991204i	$0.457751\pi$
$468$	5.39230	0.249259
$469$	−54.8976	−2.53493
$470$	−41.2356	−1.90206
$471$	−40.2188	−1.85318
$472$	−3.47451	−0.159927
$473$	0	0
$474$	7.72238	0.354701
$475$	66.8267	3.06622
$476$	−4.81809	−0.220837
$477$	−11.4948	−0.526310
$478$	−9.97099	−0.456062
$479$	32.4299	1.48176	0.740880	−	0.671637i	$-0.234409\pi$
$479$	32.4299	1.48176	0.740880	+	0.671637i	$0.234409\pi$
$480$	10.2540	0.468028
$481$	−0.793216	−0.0361675
$482$	−15.4129	−0.702036
$483$	−8.43950	−0.384011
$484$	0	0
$485$	−21.1395	−0.959897
$486$	−20.0918	−0.911381
$487$	−32.7115	−1.48230	−0.741150	−	0.671340i	$-0.765719\pi$
$487$	−32.7115	−1.48230	−0.741150	+	0.671340i	$0.765719\pi$
$488$	4.10444	0.185799
$489$	−30.7838	−1.39209
$490$	−27.2726	−1.23205
$491$	24.8093	1.11963	0.559815	−	0.828618i	$-0.310872\pi$
$491$	24.8093	1.11963	0.559815	+	0.828618i	$0.310872\pi$
$492$	4.17823	0.188369
$493$	7.11760	0.320561
$494$	−10.3702	−0.466579
$495$	0	0
$496$	−2.63994	−0.118537
$497$	−42.2373	−1.89460
$498$	−26.8962	−1.20525
$499$	19.5325	0.874397	0.437198	−	0.899365i	$-0.355971\pi$
$499$	19.5325	0.874397	0.437198	+	0.899365i	$0.355971\pi$
$500$	41.7318	1.86630
$501$	8.17059	0.365035
$502$	12.0786	0.539096
$503$	33.7226	1.50362	0.751808	−	0.659382i	$-0.229182\pi$
$503$	33.7226	1.50362	0.751808	+	0.659382i	$0.229182\pi$
$504$	8.72493	0.388639
$505$	28.7046	1.27734
$506$	0	0
$507$	18.5137	0.822224
$508$	13.6669	0.606370
$509$	−28.5323	−1.26467	−0.632336	−	0.774694i	$-0.717904\pi$
$509$	−28.5323	−1.26467	−0.632336	+	0.774694i	$0.717904\pi$
$510$	13.6073	0.602540
$511$	29.8456	1.32029
$512$	−1.00000	−0.0441942
$513$	6.41250	0.283119
$514$	17.1291	0.755531
$515$	−24.9237	−1.09827
$516$	28.2206	1.24234
$517$	0	0
$518$	−1.28345	−0.0563916
$519$	−37.8676	−1.66220
$520$	−9.89877	−0.434090
$521$	14.7906	0.647988	0.323994	−	0.946059i	$-0.394974\pi$
$521$	14.7906	0.647988	0.323994	+	0.946059i	$0.394974\pi$
$522$	−12.8890	−0.564138
$523$	−3.40575	−0.148923	−0.0744616	−	0.997224i	$-0.523724\pi$
$523$	−3.40575	−0.148923	−0.0744616	+	0.997224i	$0.523724\pi$
$524$	−6.80788	−0.297404
$525$	122.036	5.32608
$526$	−11.2050	−0.488559
$527$	−3.50326	−0.152604
$528$	0	0
$529$	1.00000	0.0434783
$530$	21.1012	0.916578
$531$	8.34947	0.362336
$532$	−16.7794	−0.727479
$533$	−4.03350	−0.174710
$534$	17.5436	0.759184
$535$	−87.2378	−3.77162
$536$	−15.1202	−0.653092
$537$	57.2964	2.47252
$538$	3.94935	0.170268
$539$	0	0
$540$	6.12097	0.263405
$541$	−30.5179	−1.31207	−0.656034	−	0.754731i	$-0.727767\pi$
$541$	−30.5179	−1.31207	−0.656034	+	0.754731i	$0.727767\pi$
$542$	23.0116	0.988434
$543$	−33.8242	−1.45154
$544$	−1.32702	−0.0568956
$545$	75.3947	3.22955
$546$	−18.9376	−0.810456
$547$	−1.97295	−0.0843570	−0.0421785	−	0.999110i	$-0.513430\pi$
$547$	−1.97295	−0.0843570	−0.0421785	+	0.999110i	$0.513430\pi$
$548$	−2.52809	−0.107995
$549$	−9.86324	−0.420953
$550$	0	0
$551$	24.7876	1.05599
$552$	−2.32445	−0.0989351
$553$	−12.0622	−0.512938
$554$	−8.73760	−0.371225
$555$	3.62472	0.153861
$556$	11.0625	0.469153
$557$	−10.3175	−0.437164	−0.218582	−	0.975819i	$-0.570143\pi$
$557$	−10.3175	−0.437164	−0.218582	+	0.975819i	$0.570143\pi$
$558$	6.34394	0.268560
$559$	−27.2431	−1.15226
$560$	−16.0165	−0.676823
$561$	0	0
$562$	8.54349	0.360385
$563$	3.20443	0.135051	0.0675254	−	0.997718i	$-0.478490\pi$
$563$	3.20443	0.135051	0.0675254	+	0.997718i	$0.478490\pi$
$564$	−21.7280	−0.914914
$565$	−21.3808	−0.899498
$566$	0.942069	0.0395981
$567$	37.8850	1.59102
$568$	−11.6332	−0.488118
$569$	29.0200	1.21658	0.608291	−	0.793714i	$-0.291855\pi$
$569$	29.0200	1.21658	0.608291	+	0.793714i	$0.291855\pi$
$570$	47.3884	1.98488
$571$	37.6242	1.57452	0.787261	−	0.616619i	$-0.211498\pi$
$571$	37.6242	1.57452	0.787261	+	0.616619i	$0.211498\pi$
$572$	0	0
$573$	32.2647	1.34788
$574$	−6.52634	−0.272404
$575$	−14.4601	−0.603027
$576$	2.40306	0.100128
$577$	−22.9942	−0.957261	−0.478631	−	0.878016i	$-0.658867\pi$
$577$	−22.9942	−0.957261	−0.478631	+	0.878016i	$0.658867\pi$
$578$	15.2390	0.633859
$579$	11.4835	0.477238
$580$	23.6607	0.982457
$581$	42.0114	1.74293
$582$	−11.1389	−0.461723
$583$	0	0
$584$	8.22022	0.340155
$585$	23.7874	0.983487
$586$	−14.1061	−0.582719
$587$	−10.4411	−0.430951	−0.215475	−	0.976509i	$-0.569130\pi$
$587$	−10.4411	−0.430951	−0.215475	+	0.976509i	$0.569130\pi$
$588$	−14.3706	−0.592633
$589$	−12.2004	−0.502707
$590$	−15.3273	−0.631016
$591$	7.28271	0.299571
$592$	−0.353494	−0.0145285
$593$	−8.41640	−0.345620	−0.172810	−	0.984955i	$-0.555285\pi$
$593$	−8.41640	−0.345620	−0.172810	+	0.984955i	$0.555285\pi$
$594$	0	0
$595$	−21.2543	−0.871342
$596$	−2.20045	−0.0901338
$597$	1.92916	0.0789551
$598$	2.24393	0.0917611
$599$	−0.0574607	−0.00234778	−0.00117389	−	0.999999i	$-0.500374\pi$
$599$	−0.0574607	−0.00234778	−0.00117389	+	0.999999i	$0.500374\pi$
$600$	33.6117	1.37219
$601$	31.9799	1.30449	0.652244	−	0.758009i	$-0.273828\pi$
$601$	31.9799	1.30449	0.652244	+	0.758009i	$0.273828\pi$
$602$	−44.0802	−1.79657
$603$	36.3347	1.47966
$604$	−7.59832	−0.309171
$605$	0	0
$606$	15.1251	0.614417
$607$	−17.9587	−0.728923	−0.364461	−	0.931219i	$-0.618747\pi$
$607$	−17.9587	−0.728923	−0.364461	+	0.931219i	$0.618747\pi$
$608$	−4.62146	−0.187425
$609$	45.2660	1.83427
$610$	18.1062	0.733097
$611$	20.9753	0.848571
$612$	3.18892	0.128904
$613$	3.85636	0.155757	0.0778785	−	0.996963i	$-0.475185\pi$
$613$	3.85636	0.155757	0.0778785	+	0.996963i	$0.475185\pi$
$614$	−22.7739	−0.919078
$615$	18.4317	0.743237
$616$	0	0
$617$	14.9144	0.600429	0.300215	−	0.953872i	$-0.402942\pi$
$617$	14.9144	0.600429	0.300215	+	0.953872i	$0.402942\pi$
$618$	−13.1329	−0.528282
$619$	2.60123	0.104552	0.0522762	−	0.998633i	$-0.483352\pi$
$619$	2.60123	0.104552	0.0522762	+	0.998633i	$0.483352\pi$
$620$	−11.6457	−0.467703
$621$	−1.38755	−0.0556804
$622$	−23.9348	−0.959700
$623$	−27.4028	−1.09787
$624$	−5.21590	−0.208803
$625$	111.794	4.47174
$626$	20.3824	0.814646
$627$	0	0
$628$	17.3025	0.690445
$629$	−0.469095	−0.0187040
$630$	38.4888	1.53343
$631$	7.15779	0.284947	0.142474	−	0.989799i	$-0.454494\pi$
$631$	7.15779	0.284947	0.142474	+	0.989799i	$0.454494\pi$
$632$	−3.32224	−0.132152
$633$	−0.232526	−0.00924207
$634$	−8.88037	−0.352684
$635$	60.2895	2.39252
$636$	11.1187	0.440886
$637$	13.8728	0.549660
$638$	0	0
$639$	27.9553	1.10590
$640$	−4.41136	−0.174374
$641$	12.5141	0.494278	0.247139	−	0.968980i	$-0.420510\pi$
$641$	12.5141	0.494278	0.247139	+	0.968980i	$0.420510\pi$
$642$	−45.9677	−1.81420
$643$	−45.0083	−1.77495	−0.887477	−	0.460852i	$-0.847544\pi$
$643$	−45.0083	−1.77495	−0.887477	+	0.460852i	$0.847544\pi$
$644$	3.63075	0.143072
$645$	124.491	4.90184
$646$	−6.13279	−0.241291
$647$	9.38443	0.368940	0.184470	−	0.982838i	$-0.440943\pi$
$647$	9.38443	0.368940	0.184470	+	0.982838i	$0.440943\pi$
$648$	10.4345	0.409905
$649$	0	0
$650$	−32.4474	−1.27269
$651$	−22.2797	−0.873212
$652$	13.2435	0.518655
$653$	28.6356	1.12060	0.560299	−	0.828290i	$-0.310686\pi$
$653$	28.6356	1.12060	0.560299	+	0.828290i	$0.310686\pi$
$654$	39.7273	1.55346
$655$	−30.0320	−1.17345
$656$	−1.79752	−0.0701812
$657$	−19.7537	−0.770666
$658$	33.9388	1.32307
$659$	23.3523	0.909678	0.454839	−	0.890574i	$-0.349697\pi$
$659$	23.3523	0.909678	0.454839	+	0.890574i	$0.349697\pi$
$660$	0	0
$661$	−6.24290	−0.242820	−0.121410	−	0.992602i	$-0.538742\pi$
$661$	−6.24290	−0.242820	−0.121410	+	0.992602i	$0.538742\pi$
$662$	−34.5508	−1.34286
$663$	−6.92162	−0.268813
$664$	11.5710	0.449041
$665$	−74.0199	−2.87037
$666$	0.849470	0.0329163
$667$	−5.36358	−0.207679
$668$	−3.51506	−0.136002
$669$	17.1216	0.661961
$670$	−66.7005	−2.57686
$671$	0	0
$672$	−8.43950	−0.325561
$673$	17.4190	0.671454	0.335727	−	0.941959i	$-0.391018\pi$
$673$	17.4190	0.671454	0.335727	+	0.941959i	$0.391018\pi$
$674$	−2.04783	−0.0788794
$675$	20.0640	0.772265
$676$	−7.96478	−0.306338
$677$	−29.4330	−1.13120	−0.565602	−	0.824678i	$-0.691356\pi$
$677$	−29.4330	−1.13120	−0.565602	+	0.824678i	$0.691356\pi$
$678$	−11.2661	−0.432671
$679$	17.3988	0.667706
$680$	−5.85397	−0.224490
$681$	25.3046	0.969674
$682$	0	0
$683$	−2.35216	−0.0900028	−0.0450014	−	0.998987i	$-0.514329\pi$
$683$	−2.35216	−0.0900028	−0.0450014	+	0.998987i	$0.514329\pi$
$684$	11.1057	0.424636
$685$	−11.1523	−0.426108
$686$	−2.96863	−0.113343
$687$	−28.5462	−1.08911
$688$	−12.1408	−0.462863
$689$	−10.7336	−0.408917
$690$	−10.2540	−0.390362
$691$	−9.38510	−0.357026	−0.178513	−	0.983938i	$-0.557129\pi$
$691$	−9.38510	−0.357026	−0.178513	+	0.983938i	$0.557129\pi$
$692$	16.2910	0.619290
$693$	0	0
$694$	−26.0542	−0.989005
$695$	48.8005	1.85111
$696$	12.4674	0.472575
$697$	−2.38534	−0.0903514
$698$	−6.05742	−0.229277
$699$	3.59243	0.135878
$700$	−52.5010	−1.98435
$701$	30.7178	1.16020	0.580098	−	0.814547i	$-0.303014\pi$
$701$	30.7178	1.16020	0.580098	+	0.814547i	$0.303014\pi$
$702$	−3.11356	−0.117514
$703$	−1.63366	−0.0616147
$704$	0	0
$705$	−95.8500	−3.60992
$706$	−23.1057	−0.869594
$707$	−23.6252	−0.888518
$708$	−8.07633	−0.303527
$709$	−18.8961	−0.709657	−0.354828	−	0.934931i	$-0.615461\pi$
$709$	−18.8961	−0.709657	−0.354828	+	0.934931i	$0.615461\pi$
$710$	−51.3182	−1.92594
$711$	7.98356	0.299407
$712$	−7.54740	−0.282851
$713$	2.63994	0.0988664
$714$	−11.1994	−0.419127
$715$	0	0
$716$	−24.6494	−0.921193
$717$	−23.1771	−0.865563
$718$	−20.1478	−0.751909
$719$	−23.7632	−0.886218	−0.443109	−	0.896468i	$-0.646125\pi$
$719$	−23.7632	−0.886218	−0.443109	+	0.896468i	$0.646125\pi$
$720$	10.6008	0.395068
$721$	20.5133	0.763957
$722$	−2.35792	−0.0877526
$723$	−35.8264	−1.33240
$724$	14.5515	0.540802
$725$	77.5579	2.88043
$726$	0	0
$727$	43.9677	1.63067	0.815336	−	0.578989i	$-0.196552\pi$
$727$	43.9677	1.63067	0.815336	+	0.578989i	$0.196552\pi$
$728$	8.14715	0.301953
$729$	−15.3989	−0.570328
$730$	36.2623	1.34213
$731$	−16.1111	−0.595891
$732$	9.54057	0.352629
$733$	16.7099	0.617193	0.308597	−	0.951193i	$-0.400141\pi$
$733$	16.7099	0.617193	0.308597	+	0.951193i	$0.400141\pi$
$734$	−15.8506	−0.585055
$735$	−63.3938	−2.33832
$736$	1.00000	0.0368605
$737$	0	0
$738$	4.31955	0.159005
$739$	−3.88489	−0.142908	−0.0714540	−	0.997444i	$-0.522764\pi$
$739$	−3.88489	−0.142908	−0.0714540	+	0.997444i	$0.522764\pi$
$740$	−1.55939	−0.0573243
$741$	−24.1051	−0.885522
$742$	−17.3673	−0.637573
$743$	−26.5814	−0.975176	−0.487588	−	0.873074i	$-0.662123\pi$
$743$	−26.5814	−0.975176	−0.487588	+	0.873074i	$0.662123\pi$
$744$	−6.13640	−0.224971
$745$	−9.70695	−0.355635
$746$	−30.5676	−1.11916
$747$	−27.8058	−1.01736
$748$	0	0
$749$	71.8008	2.62354
$750$	97.0034	3.54206
$751$	−3.85806	−0.140783	−0.0703913	−	0.997519i	$-0.522425\pi$
$751$	−3.85806	−0.140783	−0.0703913	+	0.997519i	$0.522425\pi$
$752$	9.34759	0.340872
$753$	28.0762	1.02315
$754$	−12.0355	−0.438307
$755$	−33.5189	−1.21988
$756$	−5.03784	−0.183225
$757$	−30.6668	−1.11460	−0.557302	−	0.830310i	$-0.688163\pi$
$757$	−30.6668	−1.11460	−0.557302	+	0.830310i	$0.688163\pi$
$758$	5.85996	0.212843
$759$	0	0
$760$	−20.3869	−0.739512
$761$	−22.8196	−0.827208	−0.413604	−	0.910457i	$-0.635730\pi$
$761$	−22.8196	−0.827208	−0.413604	+	0.910457i	$0.635730\pi$
$762$	31.7680	1.15083
$763$	−62.0534	−2.24648
$764$	−13.8806	−0.502182
$765$	14.0675	0.508610
$766$	16.1540	0.583668
$767$	7.79656	0.281517
$768$	−2.32445	−0.0838763
$769$	6.42461	0.231677	0.115839	−	0.993268i	$-0.463044\pi$
$769$	6.42461	0.231677	0.115839	+	0.993268i	$0.463044\pi$
$770$	0	0
$771$	39.8157	1.43393
$772$	−4.94031	−0.177806
$773$	14.6290	0.526168	0.263084	−	0.964773i	$-0.415260\pi$
$773$	14.6290	0.526168	0.263084	+	0.964773i	$0.415260\pi$
$774$	29.1751	1.04868
$775$	−38.1737	−1.37124
$776$	4.79207	0.172025
$777$	−2.98332	−0.107026
$778$	−24.9890	−0.895898
$779$	−8.30715	−0.297635
$780$	−23.0092	−0.823861
$781$	0	0
$782$	1.32702	0.0474542
$783$	7.44223	0.265964
$784$	6.18237	0.220799
$785$	76.3275	2.72424
$786$	−15.8246	−0.564444
$787$	−7.55838	−0.269427	−0.134714	−	0.990885i	$-0.543011\pi$
$787$	−7.55838	−0.269427	−0.134714	+	0.990885i	$0.543011\pi$
$788$	−3.13309	−0.111612
$789$	−26.0454	−0.927239
$790$	−14.6556	−0.521423
$791$	17.5974	0.625692
$792$	0	0
$793$	−9.21007	−0.327059
$794$	2.71849	0.0964755
$795$	49.0487	1.73958
$796$	−0.829942	−0.0294165
$797$	−21.0705	−0.746356	−0.373178	−	0.927760i	$-0.621732\pi$
$797$	−21.0705	−0.746356	−0.373178	+	0.927760i	$0.621732\pi$
$798$	−39.0028	−1.38069
$799$	12.4045	0.438839
$800$	−14.4601	−0.511241
$801$	18.1369	0.640836
$802$	17.3646	0.613167
$803$	0	0
$804$	−35.1461	−1.23951
$805$	16.0165	0.564509
$806$	5.92383	0.208658
$807$	9.18006	0.323153
$808$	−6.50698	−0.228915
$809$	17.5774	0.617988	0.308994	−	0.951064i	$-0.400008\pi$
$809$	17.5774	0.617988	0.308994	+	0.951064i	$0.400008\pi$
$810$	46.0302	1.61734
$811$	−2.22943	−0.0782858	−0.0391429	−	0.999234i	$-0.512463\pi$
$811$	−2.22943	−0.0782858	−0.0391429	+	0.999234i	$0.512463\pi$
$812$	−19.4738	−0.683398
$813$	53.4893	1.87595
$814$	0	0
$815$	58.4218	2.04643
$816$	−3.08460	−0.107982
$817$	−56.1082	−1.96298
$818$	18.9748	0.663437
$819$	−19.5781	−0.684115
$820$	−7.92949	−0.276910
$821$	37.7040	1.31588	0.657939	−	0.753071i	$-0.271428\pi$
$821$	37.7040	1.31588	0.657939	+	0.753071i	$0.271428\pi$
$822$	−5.87642	−0.204964
$823$	26.9920	0.940881	0.470441	−	0.882432i	$-0.344095\pi$
$823$	26.9920	0.940881	0.470441	+	0.882432i	$0.344095\pi$
$824$	5.64989	0.196823
$825$	0	0
$826$	12.6151	0.438935
$827$	40.9195	1.42291	0.711455	−	0.702732i	$-0.248036\pi$
$827$	40.9195	1.42291	0.711455	+	0.702732i	$0.248036\pi$
$828$	−2.40306	−0.0835122
$829$	7.92737	0.275329	0.137664	−	0.990479i	$-0.456040\pi$
$829$	7.92737	0.275329	0.137664	+	0.990479i	$0.456040\pi$
$830$	51.0438	1.77175
$831$	−20.3101	−0.704550
$832$	2.24393	0.0777942
$833$	8.20414	0.284257
$834$	25.7141	0.890408
$835$	−15.5062	−0.536614
$836$	0	0
$837$	−3.66304	−0.126613
$838$	−23.7347	−0.819901
$839$	35.3181	1.21932	0.609658	−	0.792664i	$-0.291307\pi$
$839$	35.3181	1.21932	0.609658	+	0.792664i	$0.291307\pi$
$840$	−37.2297	−1.28455
$841$	−0.231959	−0.00799859
$842$	−33.0815	−1.14006
$843$	19.8589	0.683977
$844$	0.100035	0.00344334
$845$	−35.1355	−1.20870
$846$	−22.4629	−0.772289
$847$	0	0
$848$	−4.78338	−0.164262
$849$	2.18979	0.0751535
$850$	−19.1889	−0.658172
$851$	0.353494	0.0121176
$852$	−27.0408	−0.926402
$853$	−14.9643	−0.512368	−0.256184	−	0.966628i	$-0.582465\pi$
$853$	−14.9643	−0.512368	−0.256184	+	0.966628i	$0.582465\pi$
$854$	−14.9022	−0.509943
$855$	48.9911	1.67546
$856$	19.7757	0.675920
$857$	−6.38082	−0.217965	−0.108982	−	0.994044i	$-0.534759\pi$
$857$	−6.38082	−0.217965	−0.108982	+	0.994044i	$0.534759\pi$
$858$	0	0
$859$	−14.3879	−0.490907	−0.245454	−	0.969408i	$-0.578937\pi$
$859$	−14.3879	−0.490907	−0.245454	+	0.969408i	$0.578937\pi$
$860$	−53.5574	−1.82629
$861$	−15.1701	−0.516997
$862$	−2.74829	−0.0936071
$863$	−3.78180	−0.128734	−0.0643671	−	0.997926i	$-0.520503\pi$
$863$	−3.78180	−0.128734	−0.0643671	+	0.997926i	$0.520503\pi$
$864$	−1.38755	−0.0472053
$865$	71.8653	2.44349
$866$	15.1958	0.516376
$867$	35.4223	1.20300
$868$	9.58496	0.325335
$869$	0	0
$870$	54.9981	1.86461
$871$	33.9286	1.14963
$872$	−17.0910	−0.578776
$873$	−11.5157	−0.389746
$874$	4.62146	0.156323
$875$	−151.518	−5.12224
$876$	19.1075	0.645582
$877$	−48.9178	−1.65184	−0.825918	−	0.563790i	$-0.809343\pi$
$877$	−48.9178	−1.65184	−0.825918	+	0.563790i	$0.809343\pi$
$878$	−12.2481	−0.413353
$879$	−32.7890	−1.10594
$880$	0	0
$881$	−21.8410	−0.735843	−0.367921	−	0.929857i	$-0.619930\pi$
$881$	−21.8410	−0.735843	−0.367921	+	0.929857i	$0.619930\pi$
$882$	−14.8566	−0.500248
$883$	−0.0490473	−0.00165057	−0.000825286	−	1.00000i	$-0.500263\pi$
$883$	−0.0490473	−0.00165057	−0.000825286		1.00000i	$0.500263\pi$
$884$	2.97774	0.100152
$885$	−35.6276	−1.19761
$886$	−27.4897	−0.923536
$887$	−26.4993	−0.889759	−0.444879	−	0.895591i	$-0.646753\pi$
$887$	−26.4993	−0.889759	−0.444879	+	0.895591i	$0.646753\pi$
$888$	−0.821680	−0.0275738
$889$	−49.6211	−1.66424
$890$	−33.2943	−1.11603
$891$	0	0
$892$	−7.36589	−0.246628
$893$	43.1995	1.44562
$894$	−5.11482	−0.171065
$895$	−108.738	−3.63469
$896$	3.63075	0.121295
$897$	5.21590	0.174154
$898$	23.7187	0.791503
$899$	−14.1595	−0.472247
$900$	34.7485	1.15828
$901$	−6.34766	−0.211471
$902$	0	0
$903$	−102.462	−3.40973
$904$	4.84677	0.161201
$905$	64.1919	2.13381
$906$	−17.6619	−0.586778
$907$	30.1813	1.00215	0.501077	−	0.865403i	$-0.332937\pi$
$907$	30.1813	1.00215	0.501077	+	0.865403i	$0.332937\pi$
$908$	−10.8863	−0.361274
$909$	15.6367	0.518636
$910$	35.9400	1.19140
$911$	35.0594	1.16157	0.580785	−	0.814057i	$-0.302746\pi$
$911$	35.0594	1.16157	0.580785	+	0.814057i	$0.302746\pi$
$912$	−10.7424	−0.355715
$913$	0	0
$914$	−30.6685	−1.01442
$915$	42.0869	1.39135
$916$	12.2809	0.405771
$917$	24.7177	0.816251
$918$	−1.84131	−0.0607722
$919$	50.9349	1.68019	0.840094	−	0.542441i	$-0.182500\pi$
$919$	50.9349	1.68019	0.840094	+	0.542441i	$0.182500\pi$
$920$	4.41136	0.145438
$921$	−52.9367	−1.74432
$922$	1.19209	0.0392593
$923$	26.1041	0.859226
$924$	0	0
$925$	−5.11156	−0.168067
$926$	28.2091	0.927009
$927$	−13.5770	−0.445929
$928$	−5.36358	−0.176068
$929$	−17.7240	−0.581506	−0.290753	−	0.956798i	$-0.593906\pi$
$929$	−17.7240	−0.581506	−0.290753	+	0.956798i	$0.593906\pi$
$930$	−27.0699	−0.887656
$931$	28.5716	0.936395
$932$	−1.54550	−0.0506244
$933$	−55.6353	−1.82142
$934$	−5.71982	−0.187158
$935$	0	0
$936$	−5.39230	−0.176253
$937$	−23.3420	−0.762549	−0.381275	−	0.924462i	$-0.624515\pi$
$937$	−23.3420	−0.762549	−0.381275	+	0.924462i	$0.624515\pi$
$938$	54.8976	1.79247
$939$	47.3779	1.54612
$940$	41.2356	1.34496
$941$	0.224338	0.00731320	0.00365660	−	0.999993i	$-0.498836\pi$
$941$	0.224338	0.00731320	0.00365660	+	0.999993i	$0.498836\pi$
$942$	40.2188	1.31040
$943$	1.79752	0.0585352
$944$	3.47451	0.113086
$945$	−22.2237	−0.722938
$946$	0	0
$947$	34.7185	1.12820	0.564099	−	0.825707i	$-0.309223\pi$
$947$	34.7185	1.12820	0.564099	+	0.825707i	$0.309223\pi$
$948$	−7.72238	−0.250811
$949$	−18.4456	−0.598769
$950$	−66.8267	−2.16814
$951$	−20.6420	−0.669361
$952$	4.81809	0.156155
$953$	−1.87401	−0.0607051	−0.0303525	−	0.999539i	$-0.509663\pi$
$953$	−1.87401	−0.0607051	−0.0303525	+	0.999539i	$0.509663\pi$
$954$	11.4948	0.372157
$955$	−61.2323	−1.98143
$956$	9.97099	0.322485
$957$	0	0
$958$	−32.4299	−1.04776
$959$	9.17888	0.296401
$960$	−10.2540	−0.330946
$961$	−24.0307	−0.775185
$962$	0.793216	0.0255743
$963$	−47.5223	−1.53139
$964$	15.4129	0.496415
$965$	−21.7935	−0.701557
$966$	8.43950	0.271536
$967$	−31.1977	−1.00325	−0.501625	−	0.865085i	$-0.667264\pi$
$967$	−31.1977	−1.00325	−0.501625	+	0.865085i	$0.667264\pi$
$968$	0	0
$969$	−14.2553	−0.457948
$970$	21.1395	0.678750
$971$	−24.6184	−0.790042	−0.395021	−	0.918672i	$-0.629263\pi$
$971$	−24.6184	−0.790042	−0.395021	+	0.918672i	$0.629263\pi$
$972$	20.0918	0.644444
$973$	−40.1651	−1.28763
$974$	32.7115	1.04814
$975$	−75.4223	−2.41545
$976$	−4.10444	−0.131380
$977$	−36.5545	−1.16948	−0.584741	−	0.811220i	$-0.698804\pi$
$977$	−36.5545	−1.16948	−0.584741	+	0.811220i	$0.698804\pi$
$978$	30.7838	0.984358
$979$	0	0
$980$	27.2726	0.871192
$981$	41.0709	1.31129
$982$	−24.8093	−0.791697
$983$	32.0469	1.02214	0.511068	−	0.859540i	$-0.329250\pi$
$983$	32.0469	1.02214	0.511068	+	0.859540i	$0.329250\pi$
$984$	−4.17823	−0.133197
$985$	−13.8212	−0.440379
$986$	−7.11760	−0.226671
$987$	78.8890	2.51106
$988$	10.3702	0.329921
$989$	12.1408	0.386055
$990$	0	0
$991$	27.9008	0.886298	0.443149	−	0.896448i	$-0.353861\pi$
$991$	27.9008	0.886298	0.443149	+	0.896448i	$0.353861\pi$
$992$	2.63994	0.0838181
$993$	−80.3117	−2.54861
$994$	42.2373	1.33968
$995$	−3.66117	−0.116067
$996$	26.8962	0.852238
$997$	−30.8164	−0.975966	−0.487983	−	0.872853i	$-0.662267\pi$
$997$	−30.8164	−0.975966	−0.487983	+	0.872853i	$0.662267\pi$
$998$	−19.5325	−0.618292
$999$	−0.490490	−0.0155184

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5566.2.a.bt.1.2		10
11.2	odd	10		506.2.e.h.323.1	yes	20
11.6	odd	10		506.2.e.h.47.1	✓	20
11.10	odd	2		5566.2.a.bu.1.2		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
506.2.e.h.47.1	✓	20	11.6	odd	10
506.2.e.h.323.1	yes	20	11.2	odd	10
5566.2.a.bt.1.2		10	1.1	even	1	trivial
5566.2.a.bu.1.2		10	11.10	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:	\( N \)	\(=\)	\( 5566 = 2 \cdot 11^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5566.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.32445 q^{3} +1.00000 q^{4} +4.41136 q^{5} +2.32445 q^{6} -3.63075 q^{7} -1.00000 q^{8} +2.40306 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.32445 q^{3} +1.00000 q^{4} +4.41136 q^{5} +2.32445 q^{6} -3.63075 q^{7} -1.00000 q^{8} +2.40306 q^{9} -4.41136 q^{10} -2.32445 q^{12} +2.24393 q^{13} +3.63075 q^{14} -10.2540 q^{15} +1.00000 q^{16} +1.32702 q^{17} -2.40306 q^{18} +4.62146 q^{19} +4.41136 q^{20} +8.43950 q^{21} -1.00000 q^{23} +2.32445 q^{24} +14.4601 q^{25} -2.24393 q^{26} +1.38755 q^{27} -3.63075 q^{28} +5.36358 q^{29} +10.2540 q^{30} -2.63994 q^{31} -1.00000 q^{32} -1.32702 q^{34} -16.0165 q^{35} +2.40306 q^{36} -0.353494 q^{37} -4.62146 q^{38} -5.21590 q^{39} -4.41136 q^{40} -1.79752 q^{41} -8.43950 q^{42} -12.1408 q^{43} +10.6008 q^{45} +1.00000 q^{46} +9.34759 q^{47} -2.32445 q^{48} +6.18237 q^{49} -14.4601 q^{50} -3.08460 q^{51} +2.24393 q^{52} -4.78338 q^{53} -1.38755 q^{54} +3.63075 q^{56} -10.7424 q^{57} -5.36358 q^{58} +3.47451 q^{59} -10.2540 q^{60} -4.10444 q^{61} +2.63994 q^{62} -8.72493 q^{63} +1.00000 q^{64} +9.89877 q^{65} +15.1202 q^{67} +1.32702 q^{68} +2.32445 q^{69} +16.0165 q^{70} +11.6332 q^{71} -2.40306 q^{72} -8.22022 q^{73} +0.353494 q^{74} -33.6117 q^{75} +4.62146 q^{76} +5.21590 q^{78} +3.32224 q^{79} +4.41136 q^{80} -10.4345 q^{81} +1.79752 q^{82} -11.5710 q^{83} +8.43950 q^{84} +5.85397 q^{85} +12.1408 q^{86} -12.4674 q^{87} +7.54740 q^{89} -10.6008 q^{90} -8.14715 q^{91} -1.00000 q^{92} +6.13640 q^{93} -9.34759 q^{94} +20.3869 q^{95} +2.32445 q^{96} -4.79207 q^{97} -6.18237 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 10 q^{2} + 6 q^{3} + 10 q^{4} + 12 q^{5} - 6 q^{6} - 4 q^{7} - 10 q^{8} + 16 q^{9}+O(q^{10}) \) 10 * q - 10 * q^2 + 6 * q^3 + 10 * q^4 + 12 * q^5 - 6 * q^6 - 4 * q^7 - 10 * q^8 + 16 * q^9	\( 10 q - 10 q^{2} + 6 q^{3} + 10 q^{4} + 12 q^{5} - 6 q^{6} - 4 q^{7} - 10 q^{8} + 16 q^{9} - 12 q^{10} + 6 q^{12} + 3 q^{13} + 4 q^{14} + 6 q^{15} + 10 q^{16} + 4 q^{17} - 16 q^{18} - 8 q^{19} + 12 q^{20} - 8 q^{21} - 10 q^{23} - 6 q^{24} + 34 q^{25} - 3 q^{26} + 12 q^{27} - 4 q^{28} + 15 q^{29} - 6 q^{30} - 10 q^{32} - 4 q^{34} - 8 q^{35} + 16 q^{36} + 18 q^{37} + 8 q^{38} - 29 q^{39} - 12 q^{40} - 3 q^{41} + 8 q^{42} - 4 q^{43} + 72 q^{45} + 10 q^{46} + 42 q^{47} + 6 q^{48} + 12 q^{49} - 34 q^{50} - 18 q^{51} + 3 q^{52} + 11 q^{53} - 12 q^{54} + 4 q^{56} - 16 q^{57} - 15 q^{58} + 54 q^{59} + 6 q^{60} - 6 q^{61} + 10 q^{64} + 31 q^{65} + 24 q^{67} + 4 q^{68} - 6 q^{69} + 8 q^{70} + 37 q^{71} - 16 q^{72} + 42 q^{73} - 18 q^{74} - 12 q^{75} - 8 q^{76} + 29 q^{78} - 37 q^{79} + 12 q^{80} + 10 q^{81} + 3 q^{82} - 21 q^{83} - 8 q^{84} + 20 q^{85} + 4 q^{86} - 15 q^{87} + 63 q^{89} - 72 q^{90} + 11 q^{91} - 10 q^{92} + 8 q^{93} - 42 q^{94} + 30 q^{95} - 6 q^{96} + 2 q^{97} - 12 q^{98}+O(q^{100}) \) 10 * q - 10 * q^2 + 6 * q^3 + 10 * q^4 + 12 * q^5 - 6 * q^6 - 4 * q^7 - 10 * q^8 + 16 * q^9 - 12 * q^10 + 6 * q^12 + 3 * q^13 + 4 * q^14 + 6 * q^15 + 10 * q^16 + 4 * q^17 - 16 * q^18 - 8 * q^19 + 12 * q^20 - 8 * q^21 - 10 * q^23 - 6 * q^24 + 34 * q^25 - 3 * q^26 + 12 * q^27 - 4 * q^28 + 15 * q^29 - 6 * q^30 - 10 * q^32 - 4 * q^34 - 8 * q^35 + 16 * q^36 + 18 * q^37 + 8 * q^38 - 29 * q^39 - 12 * q^40 - 3 * q^41 + 8 * q^42 - 4 * q^43 + 72 * q^45 + 10 * q^46 + 42 * q^47 + 6 * q^48 + 12 * q^49 - 34 * q^50 - 18 * q^51 + 3 * q^52 + 11 * q^53 - 12 * q^54 + 4 * q^56 - 16 * q^57 - 15 * q^58 + 54 * q^59 + 6 * q^60 - 6 * q^61 + 10 * q^64 + 31 * q^65 + 24 * q^67 + 4 * q^68 - 6 * q^69 + 8 * q^70 + 37 * q^71 - 16 * q^72 + 42 * q^73 - 18 * q^74 - 12 * q^75 - 8 * q^76 + 29 * q^78 - 37 * q^79 + 12 * q^80 + 10 * q^81 + 3 * q^82 - 21 * q^83 - 8 * q^84 + 20 * q^85 + 4 * q^86 - 15 * q^87 + 63 * q^89 - 72 * q^90 + 11 * q^91 - 10 * q^92 + 8 * q^93 - 42 * q^94 + 30 * q^95 - 6 * q^96 + 2 * q^97 - 12 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more