LMFDB - Embedded newform 3381.2.a.bi.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3381,2,Mod(1,3381)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3381, 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("3381.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3381 = 3 \cdot 7^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3381.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:	$26.9974209234$
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} - 3x^{9} - 13x^{8} + 41x^{7} + 47x^{6} - 165x^{5} - 45x^{4} + 207x^{3} + 12x^{2} - 76x - 2 $ x^10 - 3x^9 - 13x^8 + 41x^7 + 47x^6 - 165x^5 - 45x^4 + 207x^3 + 12x^2 - 76*x - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 483)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-1.05351$ of defining polynomial
Character	$\chi$	$=$	3381.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.05351 q^{2} -1.00000 q^{3} -0.890116 q^{4} +2.17612 q^{5} +1.05351 q^{6} +3.04477 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.05351 q^{2} -1.00000 q^{3} -0.890116 q^{4} +2.17612 q^{5} +1.05351 q^{6} +3.04477 q^{8} +1.00000 q^{9} -2.29256 q^{10} -2.62243 q^{11} +0.890116 q^{12} -3.30704 q^{13} -2.17612 q^{15} -1.42746 q^{16} -2.96912 q^{17} -1.05351 q^{18} +0.697769 q^{19} -1.93700 q^{20} +2.76276 q^{22} +1.00000 q^{23} -3.04477 q^{24} -0.264516 q^{25} +3.48400 q^{26} -1.00000 q^{27} +7.31827 q^{29} +2.29256 q^{30} +5.60209 q^{31} -4.58569 q^{32} +2.62243 q^{33} +3.12800 q^{34} -0.890116 q^{36} -4.52695 q^{37} -0.735106 q^{38} +3.30704 q^{39} +6.62577 q^{40} +2.28774 q^{41} -7.79527 q^{43} +2.33427 q^{44} +2.17612 q^{45} -1.05351 q^{46} -3.81394 q^{47} +1.42746 q^{48} +0.278671 q^{50} +2.96912 q^{51} +2.94365 q^{52} +3.13059 q^{53} +1.05351 q^{54} -5.70671 q^{55} -0.697769 q^{57} -7.70988 q^{58} +12.1628 q^{59} +1.93700 q^{60} +1.48459 q^{61} -5.90186 q^{62} +7.68599 q^{64} -7.19650 q^{65} -2.76276 q^{66} +11.2755 q^{67} +2.64286 q^{68} -1.00000 q^{69} +13.8643 q^{71} +3.04477 q^{72} +0.705829 q^{73} +4.76919 q^{74} +0.264516 q^{75} -0.621095 q^{76} -3.48400 q^{78} -8.60406 q^{79} -3.10632 q^{80} +1.00000 q^{81} -2.41016 q^{82} -11.5918 q^{83} -6.46115 q^{85} +8.21240 q^{86} -7.31827 q^{87} -7.98469 q^{88} -0.333776 q^{89} -2.29256 q^{90} -0.890116 q^{92} -5.60209 q^{93} +4.01803 q^{94} +1.51843 q^{95} +4.58569 q^{96} +0.124876 q^{97} -2.62243 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 3 q^{2} - 10 q^{3} + 15 q^{4} - 5 q^{5} - 3 q^{6} + 9 q^{8} + 10 q^{9}+O(q^{10}) $ 10 * q + 3 * q^2 - 10 * q^3 + 15 * q^4 - 5 * q^5 - 3 * q^6 + 9 * q^8 + 10 * q^9	$ 10 q + 3 q^{2} - 10 q^{3} + 15 q^{4} - 5 q^{5} - 3 q^{6} + 9 q^{8} + 10 q^{9} + 11 q^{10} + 8 q^{11} - 15 q^{12} + 5 q^{15} + 37 q^{16} - 11 q^{17} + 3 q^{18} + q^{19} - 15 q^{20} + 6 q^{22} + 10 q^{23} - 9 q^{24} + 21 q^{25} + q^{26} - 10 q^{27} + 22 q^{29} - 11 q^{30} - 3 q^{31} + 11 q^{32} - 8 q^{33} - 3 q^{34} + 15 q^{36} - 3 q^{37} + 16 q^{38} + 39 q^{40} - 26 q^{41} + 27 q^{43} + 16 q^{44} - 5 q^{45} + 3 q^{46} + 11 q^{47} - 37 q^{48} + 2 q^{50} + 11 q^{51} + 29 q^{52} + 5 q^{53} - 3 q^{54} - 18 q^{55} - q^{57} + 16 q^{58} - 10 q^{59} + 15 q^{60} + 22 q^{61} - 32 q^{62} + 69 q^{64} - 11 q^{65} - 6 q^{66} - 2 q^{67} - 21 q^{68} - 10 q^{69} + 27 q^{71} + 9 q^{72} - 8 q^{73} + 14 q^{74} - 21 q^{75} - 22 q^{76} - q^{78} + 21 q^{79} - 53 q^{80} + 10 q^{81} + 36 q^{82} - 12 q^{83} + 23 q^{85} + 18 q^{86} - 22 q^{87} - 10 q^{88} + 6 q^{89} + 11 q^{90} + 15 q^{92} + 3 q^{93} + 35 q^{94} + 44 q^{95} - 11 q^{96} + 6 q^{97} + 8 q^{99}+O(q^{100}) $ 10 * q + 3 * q^2 - 10 * q^3 + 15 * q^4 - 5 * q^5 - 3 * q^6 + 9 * q^8 + 10 * q^9 + 11 * q^10 + 8 * q^11 - 15 * q^12 + 5 * q^15 + 37 * q^16 - 11 * q^17 + 3 * q^18 + q^19 - 15 * q^20 + 6 * q^22 + 10 * q^23 - 9 * q^24 + 21 * q^25 + q^26 - 10 * q^27 + 22 * q^29 - 11 * q^30 - 3 * q^31 + 11 * q^32 - 8 * q^33 - 3 * q^34 + 15 * q^36 - 3 * q^37 + 16 * q^38 + 39 * q^40 - 26 * q^41 + 27 * q^43 + 16 * q^44 - 5 * q^45 + 3 * q^46 + 11 * q^47 - 37 * q^48 + 2 * q^50 + 11 * q^51 + 29 * q^52 + 5 * q^53 - 3 * q^54 - 18 * q^55 - q^57 + 16 * q^58 - 10 * q^59 + 15 * q^60 + 22 * q^61 - 32 * q^62 + 69 * q^64 - 11 * q^65 - 6 * q^66 - 2 * q^67 - 21 * q^68 - 10 * q^69 + 27 * q^71 + 9 * q^72 - 8 * q^73 + 14 * q^74 - 21 * q^75 - 22 * q^76 - q^78 + 21 * q^79 - 53 * q^80 + 10 * q^81 + 36 * q^82 - 12 * q^83 + 23 * q^85 + 18 * q^86 - 22 * q^87 - 10 * q^88 + 6 * q^89 + 11 * q^90 + 15 * q^92 + 3 * q^93 + 35 * q^94 + 44 * q^95 - 11 * q^96 + 6 * q^97 + 8 * 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 $

$2$	−1.05351	−0.744944	−0.372472	−	0.928043i	$-0.621490\pi$
$2$	−1.05351	−0.744944	−0.372472	+	0.928043i	$0.621490\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−0.890116	−0.445058
$5$	2.17612	0.973189	0.486594	−	0.873628i	$-0.338239\pi$
$5$	2.17612	0.973189	0.486594	+	0.873628i	$0.338239\pi$
$6$	1.05351	0.430094
$7$	0	0
$7$	0	0
$8$	3.04477	1.07649
$9$	1.00000	0.333333
$10$	−2.29256	−0.724972
$11$	−2.62243	−0.790692	−0.395346	−	0.918532i	$-0.629375\pi$
$11$	−2.62243	−0.790692	−0.395346	+	0.918532i	$0.629375\pi$
$12$	0.890116	0.256954
$13$	−3.30704	−0.917208	−0.458604	−	0.888641i	$-0.651650\pi$
$13$	−3.30704	−0.917208	−0.458604	+	0.888641i	$0.651650\pi$
$14$	0	0
$15$	−2.17612	−0.561871
$16$	−1.42746	−0.356865
$17$	−2.96912	−0.720118	−0.360059	−	0.932930i	$-0.617243\pi$
$17$	−2.96912	−0.720118	−0.360059	+	0.932930i	$0.617243\pi$
$18$	−1.05351	−0.248315
$19$	0.697769	0.160079	0.0800396	−	0.996792i	$-0.474495\pi$
$19$	0.697769	0.160079	0.0800396	+	0.996792i	$0.474495\pi$
$20$	−1.93700	−0.433126
$21$	0	0
$22$	2.76276	0.589022
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−3.04477	−0.621510
$25$	−0.264516	−0.0529033
$26$	3.48400	0.683269
$27$	−1.00000	−0.192450
$28$	0	0
$29$	7.31827	1.35897	0.679485	−	0.733690i	$-0.262203\pi$
$29$	7.31827	1.35897	0.679485	+	0.733690i	$0.262203\pi$
$30$	2.29256	0.418563
$31$	5.60209	1.00617	0.503083	−	0.864238i	$-0.332199\pi$
$31$	5.60209	1.00617	0.503083	+	0.864238i	$0.332199\pi$
$32$	−4.58569	−0.810643
$33$	2.62243	0.456506
$34$	3.12800	0.536448
$35$	0	0
$36$	−0.890116	−0.148353
$37$	−4.52695	−0.744226	−0.372113	−	0.928187i	$-0.621367\pi$
$37$	−4.52695	−0.744226	−0.372113	+	0.928187i	$0.621367\pi$
$38$	−0.735106	−0.119250
$39$	3.30704	0.529550
$40$	6.62577	1.04763
$41$	2.28774	0.357285	0.178643	−	0.983914i	$-0.442829\pi$
$41$	2.28774	0.357285	0.178643	+	0.983914i	$0.442829\pi$
$42$	0	0
$43$	−7.79527	−1.18877	−0.594384	−	0.804182i	$-0.702604\pi$
$43$	−7.79527	−1.18877	−0.594384	+	0.804182i	$0.702604\pi$
$44$	2.33427	0.351904
$45$	2.17612	0.324396
$46$	−1.05351	−0.155332
$47$	−3.81394	−0.556321	−0.278160	−	0.960535i	$-0.589725\pi$
$47$	−3.81394	−0.556321	−0.278160	+	0.960535i	$0.589725\pi$
$48$	1.42746	0.206036
$49$	0	0
$50$	0.278671	0.0394100
$51$	2.96912	0.415760
$52$	2.94365	0.408211
$53$	3.13059	0.430020	0.215010	−	0.976612i	$-0.431022\pi$
$53$	3.13059	0.430020	0.215010	+	0.976612i	$0.431022\pi$
$54$	1.05351	0.143365
$55$	−5.70671	−0.769493
$56$	0	0
$57$	−0.697769	−0.0924217
$58$	−7.70988	−1.01236
$59$	12.1628	1.58347	0.791733	−	0.610868i	$-0.209179\pi$
$59$	12.1628	1.58347	0.791733	+	0.610868i	$0.209179\pi$
$60$	1.93700	0.250065
$61$	1.48459	0.190082	0.0950412	−	0.995473i	$-0.469702\pi$
$61$	1.48459	0.190082	0.0950412	+	0.995473i	$0.469702\pi$
$62$	−5.90186	−0.749537
$63$	0	0
$64$	7.68599	0.960749
$65$	−7.19650	−0.892617
$66$	−2.76276	−0.340072
$67$	11.2755	1.37753	0.688763	−	0.724986i	$-0.258154\pi$
$67$	11.2755	1.37753	0.688763	+	0.724986i	$0.258154\pi$
$68$	2.64286	0.320494
$69$	−1.00000	−0.120386
$70$	0	0
$71$	13.8643	1.64539	0.822693	−	0.568486i	$-0.192471\pi$
$71$	13.8643	1.64539	0.822693	+	0.568486i	$0.192471\pi$
$72$	3.04477	0.358829
$73$	0.705829	0.0826111	0.0413055	−	0.999147i	$-0.486848\pi$
$73$	0.705829	0.0826111	0.0413055	+	0.999147i	$0.486848\pi$
$74$	4.76919	0.554407
$75$	0.264516	0.0305437
$76$	−0.621095	−0.0712445
$77$	0	0
$78$	−3.48400	−0.394485
$79$	−8.60406	−0.968033	−0.484016	−	0.875059i	$-0.660822\pi$
$79$	−8.60406	−0.968033	−0.484016	+	0.875059i	$0.660822\pi$
$80$	−3.10632	−0.347297
$81$	1.00000	0.111111
$82$	−2.41016	−0.266157
$83$	−11.5918	−1.27237	−0.636185	−	0.771537i	$-0.719489\pi$
$83$	−11.5918	−1.27237	−0.636185	+	0.771537i	$0.719489\pi$
$84$	0	0
$85$	−6.46115	−0.700811
$86$	8.21240	0.885566
$87$	−7.31827	−0.784601
$88$	−7.98469	−0.851170
$89$	−0.333776	−0.0353802	−0.0176901	−	0.999844i	$-0.505631\pi$
$89$	−0.333776	−0.0353802	−0.0176901	+	0.999844i	$0.505631\pi$
$90$	−2.29256	−0.241657
$91$	0	0
$92$	−0.890116	−0.0928010
$93$	−5.60209	−0.580910
$94$	4.01803	0.414428
$95$	1.51843	0.155787
$96$	4.58569	0.468025
$97$	0.124876	0.0126793	0.00633963	−	0.999980i	$-0.497982\pi$
$97$	0.124876	0.0126793	0.00633963	+	0.999980i	$0.497982\pi$
$98$	0	0
$99$	−2.62243	−0.263564
$100$	0.235450	0.0235450
$101$	−8.77972	−0.873615	−0.436807	−	0.899555i	$-0.643891\pi$
$101$	−8.77972	−0.873615	−0.436807	+	0.899555i	$0.643891\pi$
$102$	−3.12800	−0.309718
$103$	−5.46482	−0.538465	−0.269232	−	0.963075i	$-0.586770\pi$
$103$	−5.46482	−0.538465	−0.269232	+	0.963075i	$0.586770\pi$
$104$	−10.0692	−0.987363
$105$	0	0
$106$	−3.29811	−0.320341
$107$	10.8427	1.04820	0.524100	−	0.851657i	$-0.324402\pi$
$107$	10.8427	1.04820	0.524100	+	0.851657i	$0.324402\pi$
$108$	0.890116	0.0856515
$109$	−1.05736	−0.101277	−0.0506384	−	0.998717i	$-0.516126\pi$
$109$	−1.05736	−0.101277	−0.0506384	+	0.998717i	$0.516126\pi$
$110$	6.01208	0.573229
$111$	4.52695	0.429679
$112$	0	0
$113$	−14.0938	−1.32584	−0.662918	−	0.748692i	$-0.730682\pi$
$113$	−14.0938	−1.32584	−0.662918	+	0.748692i	$0.730682\pi$
$114$	0.735106	0.0688490
$115$	2.17612	0.202924
$116$	−6.51411	−0.604820
$117$	−3.30704	−0.305736
$118$	−12.8137	−1.17959
$119$	0	0
$120$	−6.62577	−0.604847
$121$	−4.12286	−0.374806
$122$	−1.56403	−0.141601
$123$	−2.28774	−0.206279
$124$	−4.98651	−0.447802
$125$	−11.4562	−1.02467
$126$	0	0
$127$	15.7177	1.39472	0.697360	−	0.716721i	$-0.254358\pi$
$127$	15.7177	1.39472	0.697360	+	0.716721i	$0.254358\pi$
$128$	1.07410	0.0949383
$129$	7.79527	0.686335
$130$	7.58159	0.664950
$131$	−10.0029	−0.873960	−0.436980	−	0.899471i	$-0.643952\pi$
$131$	−10.0029	−0.873960	−0.436980	+	0.899471i	$0.643952\pi$
$132$	−2.33427	−0.203172
$133$	0	0
$134$	−11.8789	−1.02618
$135$	−2.17612	−0.187290
$136$	−9.04028	−0.775198
$137$	6.06773	0.518401	0.259201	−	0.965823i	$-0.416541\pi$
$137$	6.06773	0.518401	0.259201	+	0.965823i	$0.416541\pi$
$138$	1.05351	0.0896808
$139$	14.1199	1.19763	0.598815	−	0.800887i	$-0.295638\pi$
$139$	14.1199	1.19763	0.598815	+	0.800887i	$0.295638\pi$
$140$	0	0
$141$	3.81394	0.321192
$142$	−14.6061	−1.22572
$143$	8.67248	0.725229
$144$	−1.42746	−0.118955
$145$	15.9254	1.32253
$146$	−0.743598	−0.0615406
$147$	0	0
$148$	4.02951	0.331224
$149$	1.01590	0.0832261	0.0416131	−	0.999134i	$-0.486750\pi$
$149$	1.01590	0.0832261	0.0416131	+	0.999134i	$0.486750\pi$
$150$	−0.278671	−0.0227534
$151$	22.5385	1.83416	0.917080	−	0.398702i	$-0.130539\pi$
$151$	22.5385	1.83416	0.917080	+	0.398702i	$0.130539\pi$
$152$	2.12454	0.172323
$153$	−2.96912	−0.240039
$154$	0	0
$155$	12.1908	0.979189
$156$	−2.94365	−0.235681
$157$	−11.3661	−0.907114	−0.453557	−	0.891227i	$-0.649845\pi$
$157$	−11.3661	−0.907114	−0.453557	+	0.891227i	$0.649845\pi$
$158$	9.06447	0.721131
$159$	−3.13059	−0.248272
$160$	−9.97899	−0.788909
$161$	0	0
$162$	−1.05351	−0.0827716
$163$	14.7670	1.15664	0.578322	−	0.815809i	$-0.303708\pi$
$163$	14.7670	1.15664	0.578322	+	0.815809i	$0.303708\pi$
$164$	−2.03635	−0.159013
$165$	5.70671	0.444267
$166$	12.2121	0.947845
$167$	−8.85336	−0.685093	−0.342547	−	0.939501i	$-0.611290\pi$
$167$	−8.85336	−0.685093	−0.342547	+	0.939501i	$0.611290\pi$
$168$	0	0
$169$	−2.06349	−0.158730
$170$	6.80689	0.522065
$171$	0.697769	0.0533597
$172$	6.93869	0.529070
$173$	15.7040	1.19396	0.596978	−	0.802258i	$-0.296368\pi$
$173$	15.7040	1.19396	0.596978	+	0.802258i	$0.296368\pi$
$174$	7.70988	0.584484
$175$	0	0
$176$	3.74342	0.282171
$177$	−12.1628	−0.914214
$178$	0.351636	0.0263562
$179$	−5.30752	−0.396703	−0.198351	−	0.980131i	$-0.563559\pi$
$179$	−5.30752	−0.396703	−0.198351	+	0.980131i	$0.563559\pi$
$180$	−1.93700	−0.144375
$181$	1.93050	0.143493	0.0717463	−	0.997423i	$-0.477143\pi$
$181$	1.93050	0.143493	0.0717463	+	0.997423i	$0.477143\pi$
$182$	0	0
$183$	−1.48459	−0.109744
$184$	3.04477	0.224463
$185$	−9.85117	−0.724273
$186$	5.90186	0.432745
$187$	7.78631	0.569391
$188$	3.39485	0.247595
$189$	0	0
$190$	−1.59968	−0.116053
$191$	10.4418	0.755540	0.377770	−	0.925899i	$-0.376691\pi$
$191$	10.4418	0.755540	0.377770	+	0.925899i	$0.376691\pi$
$192$	−7.68599	−0.554689
$193$	24.6163	1.77192	0.885959	−	0.463763i	$-0.153501\pi$
$193$	24.6163	1.77192	0.885959	+	0.463763i	$0.153501\pi$
$194$	−0.131558	−0.00944534
$195$	7.19650	0.515352
$196$	0	0
$197$	5.17797	0.368915	0.184458	−	0.982840i	$-0.440947\pi$
$197$	5.17797	0.368915	0.184458	+	0.982840i	$0.440947\pi$
$198$	2.76276	0.196341
$199$	−16.6371	−1.17937	−0.589687	−	0.807632i	$-0.700749\pi$
$199$	−16.6371	−1.17937	−0.589687	+	0.807632i	$0.700749\pi$
$200$	−0.805391	−0.0569497
$201$	−11.2755	−0.795315
$202$	9.24952	0.650794
$203$	0	0
$204$	−2.64286	−0.185037
$205$	4.97839	0.347706
$206$	5.75724	0.401126
$207$	1.00000	0.0695048
$208$	4.72067	0.327320
$209$	−1.82985	−0.126573
$210$	0	0
$211$	28.5995	1.96887	0.984435	−	0.175751i	$-0.0562354\pi$
$211$	28.5995	1.96887	0.984435	+	0.175751i	$0.0562354\pi$
$212$	−2.78659	−0.191384
$213$	−13.8643	−0.949964
$214$	−11.4229	−0.780850
$215$	−16.9634	−1.15690
$216$	−3.04477	−0.207170
$217$	0	0
$218$	1.11394	0.0754456
$219$	−0.705829	−0.0476955
$220$	5.07964	0.342469
$221$	9.81900	0.660498
$222$	−4.76919	−0.320087
$223$	16.5464	1.10803	0.554016	−	0.832506i	$-0.313095\pi$
$223$	16.5464	1.10803	0.554016	+	0.832506i	$0.313095\pi$
$224$	0	0
$225$	−0.264516	−0.0176344
$226$	14.8480	0.987674
$227$	−17.9650	−1.19238	−0.596189	−	0.802844i	$-0.703319\pi$
$227$	−17.9650	−1.19238	−0.596189	+	0.802844i	$0.703319\pi$
$228$	0.621095	0.0411330
$229$	28.0061	1.85070	0.925348	−	0.379120i	$-0.123773\pi$
$229$	28.0061	1.85070	0.925348	+	0.379120i	$0.123773\pi$
$230$	−2.29256	−0.151167
$231$	0	0
$232$	22.2824	1.46291
$233$	23.2462	1.52291	0.761454	−	0.648219i	$-0.224486\pi$
$233$	23.2462	1.52291	0.761454	+	0.648219i	$0.224486\pi$
$234$	3.48400	0.227756
$235$	−8.29958	−0.541405
$236$	−10.8263	−0.704734
$237$	8.60406	0.558894
$238$	0	0
$239$	6.43482	0.416234	0.208117	−	0.978104i	$-0.433267\pi$
$239$	6.43482	0.416234	0.208117	+	0.978104i	$0.433267\pi$
$240$	3.10632	0.200512
$241$	23.5177	1.51491	0.757455	−	0.652888i	$-0.226443\pi$
$241$	23.5177	1.51491	0.757455	+	0.652888i	$0.226443\pi$
$242$	4.34348	0.279209
$243$	−1.00000	−0.0641500
$244$	−1.32146	−0.0845977
$245$	0	0
$246$	2.41016	0.153666
$247$	−2.30755	−0.146826
$248$	17.0571	1.08312
$249$	11.5918	0.734603
$250$	12.0692	0.763325
$251$	−3.12594	−0.197307	−0.0986537	−	0.995122i	$-0.531454\pi$
$251$	−3.12594	−0.197307	−0.0986537	+	0.995122i	$0.531454\pi$
$252$	0	0
$253$	−2.62243	−0.164871
$254$	−16.5587	−1.03899
$255$	6.46115	0.404613
$256$	−16.5036	−1.03147
$257$	−20.5336	−1.28085	−0.640426	−	0.768020i	$-0.721242\pi$
$257$	−20.5336	−1.28085	−0.640426	+	0.768020i	$0.721242\pi$
$258$	−8.21240	−0.511282
$259$	0	0
$260$	6.40572	0.397266
$261$	7.31827	0.452990
$262$	10.5382	0.651052
$263$	19.4476	1.19919	0.599594	−	0.800304i	$-0.295329\pi$
$263$	19.4476	1.19919	0.599594	+	0.800304i	$0.295329\pi$
$264$	7.98469	0.491424
$265$	6.81254	0.418491
$266$	0	0
$267$	0.333776	0.0204267
$268$	−10.0365	−0.613079
$269$	7.71940	0.470660	0.235330	−	0.971916i	$-0.424383\pi$
$269$	7.71940	0.470660	0.235330	+	0.971916i	$0.424383\pi$
$270$	2.29256	0.139521
$271$	30.8637	1.87484	0.937418	−	0.348205i	$-0.113209\pi$
$271$	30.8637	1.87484	0.937418	+	0.348205i	$0.113209\pi$
$272$	4.23831	0.256985
$273$	0	0
$274$	−6.39242	−0.386180
$275$	0.693675	0.0418302
$276$	0.890116	0.0535787
$277$	6.40144	0.384625	0.192313	−	0.981334i	$-0.438401\pi$
$277$	6.40144	0.384625	0.192313	+	0.981334i	$0.438401\pi$
$278$	−14.8754	−0.892168
$279$	5.60209	0.335388
$280$	0	0
$281$	−4.79227	−0.285883	−0.142941	−	0.989731i	$-0.545656\pi$
$281$	−4.79227	−0.285883	−0.142941	+	0.989731i	$0.545656\pi$
$282$	−4.01803	−0.239270
$283$	−11.7015	−0.695579	−0.347790	−	0.937573i	$-0.613068\pi$
$283$	−11.7015	−0.695579	−0.347790	+	0.937573i	$0.613068\pi$
$284$	−12.3408	−0.732292
$285$	−1.51843	−0.0899438
$286$	−9.13655	−0.540255
$287$	0	0
$288$	−4.58569	−0.270214
$289$	−8.18432	−0.481431
$290$	−16.7776	−0.985214
$291$	−0.124876	−0.00732038
$292$	−0.628270	−0.0367667
$293$	19.9031	1.16275	0.581376	−	0.813635i	$-0.302515\pi$
$293$	19.9031	1.16275	0.581376	+	0.813635i	$0.302515\pi$
$294$	0	0
$295$	26.4677	1.54101
$296$	−13.7835	−0.801150
$297$	2.62243	0.152169
$298$	−1.07027	−0.0619988
$299$	−3.30704	−0.191251
$300$	−0.235450	−0.0135937
$301$	0	0
$302$	−23.7446	−1.36635
$303$	8.77972	0.504382
$304$	−0.996038	−0.0571267
$305$	3.23064	0.184986
$306$	3.12800	0.178816
$307$	21.7588	1.24184	0.620920	−	0.783874i	$-0.286759\pi$
$307$	21.7588	1.24184	0.620920	+	0.783874i	$0.286759\pi$
$308$	0	0
$309$	5.46482	0.310883
$310$	−12.8431	−0.729441
$311$	−8.14345	−0.461773	−0.230886	−	0.972981i	$-0.574163\pi$
$311$	−8.14345	−0.461773	−0.230886	+	0.972981i	$0.574163\pi$
$312$	10.0692	0.570054
$313$	1.05044	0.0593743	0.0296871	−	0.999559i	$-0.490549\pi$
$313$	1.05044	0.0593743	0.0296871	+	0.999559i	$0.490549\pi$
$314$	11.9743	0.675749
$315$	0	0
$316$	7.65861	0.430831
$317$	16.3680	0.919317	0.459658	−	0.888096i	$-0.347972\pi$
$317$	16.3680	0.919317	0.459658	+	0.888096i	$0.347972\pi$
$318$	3.29811	0.184949
$319$	−19.1917	−1.07453
$320$	16.7256	0.934990
$321$	−10.8427	−0.605178
$322$	0	0
$323$	−2.07176	−0.115276
$324$	−0.890116	−0.0494509
$325$	0.874766	0.0485233
$326$	−15.5572	−0.861635
$327$	1.05736	0.0584722
$328$	6.96564	0.384613
$329$	0	0
$330$	−6.01208	−0.330954
$331$	29.2929	1.61008	0.805042	−	0.593218i	$-0.202143\pi$
$331$	29.2929	1.61008	0.805042	+	0.593218i	$0.202143\pi$
$332$	10.3181	0.566278
$333$	−4.52695	−0.248075
$334$	9.32711	0.510356
$335$	24.5369	1.34059
$336$	0	0
$337$	−4.27417	−0.232829	−0.116414	−	0.993201i	$-0.537140\pi$
$337$	−4.27417	−0.232829	−0.116414	+	0.993201i	$0.537140\pi$
$338$	2.17391	0.118245
$339$	14.0938	0.765472
$340$	5.75118	0.311901
$341$	−14.6911	−0.795567
$342$	−0.735106	−0.0397500
$343$	0	0
$344$	−23.7348	−1.27969
$345$	−2.17612	−0.117158
$346$	−16.5444	−0.889430
$347$	18.4439	0.990120	0.495060	−	0.868859i	$-0.335146\pi$
$347$	18.4439	0.990120	0.495060	+	0.868859i	$0.335146\pi$
$348$	6.51411	0.349193
$349$	−19.9398	−1.06736	−0.533678	−	0.845688i	$-0.679190\pi$
$349$	−19.9398	−1.06736	−0.533678	+	0.845688i	$0.679190\pi$
$350$	0	0
$351$	3.30704	0.176517
$352$	12.0256	0.640969
$353$	−22.0855	−1.17549	−0.587746	−	0.809046i	$-0.699985\pi$
$353$	−22.0855	−1.17549	−0.587746	+	0.809046i	$0.699985\pi$
$354$	12.8137	0.681038
$355$	30.1703	1.60127
$356$	0.297099	0.0157462
$357$	0	0
$358$	5.59153	0.295521
$359$	−12.0390	−0.635392	−0.317696	−	0.948193i	$-0.602909\pi$
$359$	−12.0390	−0.635392	−0.317696	+	0.948193i	$0.602909\pi$
$360$	6.62577	0.349209
$361$	−18.5131	−0.974375
$362$	−2.03380	−0.106894
$363$	4.12286	0.216394
$364$	0	0
$365$	1.53597	0.0803962
$366$	1.56403	0.0817533
$367$	21.6477	1.13000	0.565000	−	0.825091i	$-0.308876\pi$
$367$	21.6477	1.13000	0.565000	+	0.825091i	$0.308876\pi$
$368$	−1.42746	−0.0744116
$369$	2.28774	0.119095
$370$	10.3783	0.539543
$371$	0	0
$372$	4.98651	0.258539
$373$	21.9427	1.13615	0.568074	−	0.822977i	$-0.307689\pi$
$373$	21.9427	1.13615	0.568074	+	0.822977i	$0.307689\pi$
$374$	−8.20296	−0.424165
$375$	11.4562	0.591596
$376$	−11.6126	−0.598872
$377$	−24.2018	−1.24646
$378$	0	0
$379$	11.8759	0.610026	0.305013	−	0.952348i	$-0.401339\pi$
$379$	11.8759	0.610026	0.305013	+	0.952348i	$0.401339\pi$
$380$	−1.35158	−0.0693343
$381$	−15.7177	−0.805242
$382$	−11.0005	−0.562835
$383$	−4.46691	−0.228248	−0.114124	−	0.993466i	$-0.536406\pi$
$383$	−4.46691	−0.228248	−0.114124	+	0.993466i	$0.536406\pi$
$384$	−1.07410	−0.0548126
$385$	0	0
$386$	−25.9335	−1.31998
$387$	−7.79527	−0.396256
$388$	−0.111154	−0.00564301
$389$	−2.71425	−0.137618	−0.0688089	−	0.997630i	$-0.521920\pi$
$389$	−2.71425	−0.137618	−0.0688089	+	0.997630i	$0.521920\pi$
$390$	−7.58159	−0.383909
$391$	−2.96912	−0.150155
$392$	0	0
$393$	10.0029	0.504581
$394$	−5.45505	−0.274821
$395$	−18.7234	−0.942079
$396$	2.33427	0.117301
$397$	−7.38176	−0.370480	−0.185240	−	0.982693i	$-0.559306\pi$
$397$	−7.38176	−0.370480	−0.185240	+	0.982693i	$0.559306\pi$
$398$	17.5274	0.878567
$399$	0	0
$400$	0.377587	0.0188793
$401$	2.70191	0.134927	0.0674634	−	0.997722i	$-0.478509\pi$
$401$	2.70191	0.134927	0.0674634	+	0.997722i	$0.478509\pi$
$402$	11.8789	0.592466
$403$	−18.5263	−0.922863
$404$	7.81497	0.388809
$405$	2.17612	0.108132
$406$	0	0
$407$	11.8716	0.588454
$408$	9.04028	0.447561
$409$	24.8095	1.22675	0.613376	−	0.789791i	$-0.289811\pi$
$409$	24.8095	1.22675	0.613376	+	0.789791i	$0.289811\pi$
$410$	−5.24479	−0.259021
$411$	−6.06773	−0.299299
$412$	4.86432	0.239648
$413$	0	0
$414$	−1.05351	−0.0517772
$415$	−25.2252	−1.23826
$416$	15.1651	0.743528
$417$	−14.1199	−0.691452
$418$	1.92776	0.0942901
$419$	−20.0785	−0.980899	−0.490450	−	0.871470i	$-0.663167\pi$
$419$	−20.0785	−0.980899	−0.490450	+	0.871470i	$0.663167\pi$
$420$	0	0
$421$	−26.5979	−1.29630	−0.648151	−	0.761512i	$-0.724458\pi$
$421$	−26.5979	−1.29630	−0.648151	+	0.761512i	$0.724458\pi$
$422$	−30.1298	−1.46670
$423$	−3.81394	−0.185440
$424$	9.53193	0.462911
$425$	0.785381	0.0380966
$426$	14.6061	0.707670
$427$	0	0
$428$	−9.65122	−0.466509
$429$	−8.67248	−0.418711
$430$	17.8711	0.861823
$431$	−24.0219	−1.15710	−0.578548	−	0.815649i	$-0.696380\pi$
$431$	−24.0219	−1.15710	−0.578548	+	0.815649i	$0.696380\pi$
$432$	1.42746	0.0686788
$433$	−14.0909	−0.677165	−0.338582	−	0.940937i	$-0.609947\pi$
$433$	−14.0909	−0.677165	−0.338582	+	0.940937i	$0.609947\pi$
$434$	0	0
$435$	−15.9254	−0.763565
$436$	0.941174	0.0450740
$437$	0.697769	0.0333788
$438$	0.743598	0.0355305
$439$	2.89952	0.138387	0.0691933	−	0.997603i	$-0.477957\pi$
$439$	2.89952	0.138387	0.0691933	+	0.997603i	$0.477957\pi$
$440$	−17.3756	−0.828350
$441$	0	0
$442$	−10.3444	−0.492034
$443$	13.9959	0.664965	0.332482	−	0.943109i	$-0.392114\pi$
$443$	13.9959	0.664965	0.332482	+	0.943109i	$0.392114\pi$
$444$	−4.02951	−0.191232
$445$	−0.726335	−0.0344316
$446$	−17.4319	−0.825422
$447$	−1.01590	−0.0480506
$448$	0	0
$449$	12.6648	0.597690	0.298845	−	0.954302i	$-0.403399\pi$
$449$	12.6648	0.597690	0.298845	+	0.954302i	$0.403399\pi$
$450$	0.278671	0.0131367
$451$	−5.99944	−0.282502
$452$	12.5451	0.590074
$453$	−22.5385	−1.05895
$454$	18.9263	0.888256
$455$	0	0
$456$	−2.12454	−0.0994908
$457$	−3.55672	−0.166376	−0.0831881	−	0.996534i	$-0.526510\pi$
$457$	−3.55672	−0.166376	−0.0831881	+	0.996534i	$0.526510\pi$
$458$	−29.5047	−1.37866
$459$	2.96912	0.138587
$460$	−1.93700	−0.0903129
$461$	16.1441	0.751904	0.375952	−	0.926639i	$-0.377316\pi$
$461$	16.1441	0.751904	0.375952	+	0.926639i	$0.377316\pi$
$462$	0	0
$463$	9.78687	0.454834	0.227417	−	0.973797i	$-0.426972\pi$
$463$	9.78687	0.454834	0.227417	+	0.973797i	$0.426972\pi$
$464$	−10.4466	−0.484969
$465$	−12.1908	−0.565335
$466$	−24.4901	−1.13448
$467$	−30.1576	−1.39553	−0.697763	−	0.716329i	$-0.745821\pi$
$467$	−30.1576	−1.39553	−0.697763	+	0.716329i	$0.745821\pi$
$468$	2.94365	0.136070
$469$	0	0
$470$	8.74370	0.403317
$471$	11.3661	0.523722
$472$	37.0330	1.70458
$473$	20.4425	0.939949
$474$	−9.06447	−0.416345
$475$	−0.184571	−0.00846871
$476$	0	0
$477$	3.13059	0.143340
$478$	−6.77914	−0.310071
$479$	2.92167	0.133494	0.0667471	−	0.997770i	$-0.478738\pi$
$479$	2.92167	0.133494	0.0667471	+	0.997770i	$0.478738\pi$
$480$	9.97899	0.455477
$481$	14.9708	0.682610
$482$	−24.7762	−1.12852
$483$	0	0
$484$	3.66983	0.166810
$485$	0.271745	0.0123393
$486$	1.05351	0.0477882
$487$	32.2382	1.46085	0.730427	−	0.682991i	$-0.239321\pi$
$487$	32.2382	1.46085	0.730427	+	0.682991i	$0.239321\pi$
$488$	4.52023	0.204621
$489$	−14.7670	−0.667789
$490$	0	0
$491$	−12.1670	−0.549091	−0.274546	−	0.961574i	$-0.588527\pi$
$491$	−12.1670	−0.549091	−0.274546	+	0.961574i	$0.588527\pi$
$492$	2.03635	0.0918059
$493$	−21.7288	−0.978618
$494$	2.43103	0.109377
$495$	−5.70671	−0.256498
$496$	−7.99677	−0.359066
$497$	0	0
$498$	−12.2121	−0.547238
$499$	31.8296	1.42489	0.712444	−	0.701729i	$-0.247588\pi$
$499$	31.8296	1.42489	0.712444	+	0.701729i	$0.247588\pi$
$500$	10.1973	0.456039
$501$	8.85336	0.395539
$502$	3.29321	0.146983
$503$	0.217299	0.00968890	0.00484445	−	0.999988i	$-0.498458\pi$
$503$	0.217299	0.00968890	0.00484445	+	0.999988i	$0.498458\pi$
$504$	0	0
$505$	−19.1057	−0.850192
$506$	2.76276	0.122820
$507$	2.06349	0.0916427
$508$	−13.9906	−0.620731
$509$	15.1597	0.671942	0.335971	−	0.941872i	$-0.390936\pi$
$509$	15.1597	0.671942	0.335971	+	0.941872i	$0.390936\pi$
$510$	−6.80689	−0.301414
$511$	0	0
$512$	15.2385	0.673452
$513$	−0.697769	−0.0308072
$514$	21.6324	0.954164
$515$	−11.8921	−0.524028
$516$	−6.93869	−0.305459
$517$	10.0018	0.439878
$518$	0	0
$519$	−15.7040	−0.689330
$520$	−21.9117	−0.960891
$521$	−26.5770	−1.16436	−0.582179	−	0.813060i	$-0.697800\pi$
$521$	−26.5770	−1.16436	−0.582179	+	0.813060i	$0.697800\pi$
$522$	−7.70988	−0.337452
$523$	−36.5361	−1.59761	−0.798807	−	0.601588i	$-0.794535\pi$
$523$	−36.5361	−1.59761	−0.798807	+	0.601588i	$0.794535\pi$
$524$	8.90377	0.388963
$525$	0	0
$526$	−20.4882	−0.893328
$527$	−16.6333	−0.724557
$528$	−3.74342	−0.162911
$529$	1.00000	0.0434783
$530$	−7.17708	−0.311752
$531$	12.1628	0.527822
$532$	0	0
$533$	−7.56565	−0.327705
$534$	−0.351636	−0.0152168
$535$	23.5949	1.02010
$536$	34.3314	1.48289
$537$	5.30752	0.229036
$538$	−8.13247	−0.350616
$539$	0	0
$540$	1.93700	0.0833550
$541$	9.94639	0.427629	0.213814	−	0.976874i	$-0.431411\pi$
$541$	9.94639	0.427629	0.213814	+	0.976874i	$0.431411\pi$
$542$	−32.5152	−1.39665
$543$	−1.93050	−0.0828455
$544$	13.6155	0.583758
$545$	−2.30094	−0.0985614
$546$	0	0
$547$	−35.8124	−1.53123	−0.765614	−	0.643300i	$-0.777565\pi$
$547$	−35.8124	−1.53123	−0.765614	+	0.643300i	$0.777565\pi$
$548$	−5.40099	−0.230719
$549$	1.48459	0.0633608
$550$	−0.730794	−0.0311612
$551$	5.10646	0.217543
$552$	−3.04477	−0.129594
$553$	0	0
$554$	−6.74398	−0.286524
$555$	9.85117	0.418159
$556$	−12.5683	−0.533015
$557$	−13.5026	−0.572124	−0.286062	−	0.958211i	$-0.592346\pi$
$557$	−13.5026	−0.572124	−0.286062	+	0.958211i	$0.592346\pi$
$558$	−5.90186	−0.249846
$559$	25.7793	1.09035
$560$	0	0
$561$	−7.78631	−0.328738
$562$	5.04871	0.212967
$563$	37.4182	1.57699	0.788495	−	0.615041i	$-0.210861\pi$
$563$	37.4182	1.57699	0.788495	+	0.615041i	$0.210861\pi$
$564$	−3.39485	−0.142949
$565$	−30.6698	−1.29029
$566$	12.3276	0.518168
$567$	0	0
$568$	42.2135	1.77124
$569$	42.9853	1.80204	0.901019	−	0.433779i	$-0.142820\pi$
$569$	42.9853	1.80204	0.901019	+	0.433779i	$0.142820\pi$
$570$	1.59968	0.0670031
$571$	−20.7497	−0.868349	−0.434175	−	0.900829i	$-0.642960\pi$
$571$	−20.7497	−0.868349	−0.434175	+	0.900829i	$0.642960\pi$
$572$	−7.71951	−0.322769
$573$	−10.4418	−0.436211
$574$	0	0
$575$	−0.264516	−0.0110311
$576$	7.68599	0.320250
$577$	−38.3634	−1.59709	−0.798544	−	0.601936i	$-0.794396\pi$
$577$	−38.3634	−1.59709	−0.798544	+	0.601936i	$0.794396\pi$
$578$	8.62227	0.358639
$579$	−24.6163	−1.02302
$580$	−14.1755	−0.588604
$581$	0	0
$582$	0.131558	0.00545327
$583$	−8.20976	−0.340014
$584$	2.14909	0.0889298
$585$	−7.19650	−0.297539
$586$	−20.9681	−0.866185
$587$	−21.7316	−0.896958	−0.448479	−	0.893793i	$-0.648034\pi$
$587$	−21.7316	−0.896958	−0.448479	+	0.893793i	$0.648034\pi$
$588$	0	0
$589$	3.90896	0.161066
$590$	−27.8840	−1.14797
$591$	−5.17797	−0.212993
$592$	6.46205	0.265589
$593$	−0.868007	−0.0356448	−0.0178224	−	0.999841i	$-0.505673\pi$
$593$	−0.868007	−0.0356448	−0.0178224	+	0.999841i	$0.505673\pi$
$594$	−2.76276	−0.113357
$595$	0	0
$596$	−0.904273	−0.0370404
$597$	16.6371	0.680911
$598$	3.48400	0.142471
$599$	−13.0652	−0.533829	−0.266914	−	0.963720i	$-0.586004\pi$
$599$	−13.0652	−0.533829	−0.266914	+	0.963720i	$0.586004\pi$
$600$	0.805391	0.0328799
$601$	−14.4244	−0.588385	−0.294192	−	0.955746i	$-0.595051\pi$
$601$	−14.4244	−0.588385	−0.294192	+	0.955746i	$0.595051\pi$
$602$	0	0
$603$	11.2755	0.459176
$604$	−20.0619	−0.816308
$605$	−8.97183	−0.364757
$606$	−9.24952	−0.375736
$607$	28.9832	1.17639	0.588195	−	0.808719i	$-0.299839\pi$
$607$	28.9832	1.17639	0.588195	+	0.808719i	$0.299839\pi$
$608$	−3.19975	−0.129767
$609$	0	0
$610$	−3.40352	−0.137804
$611$	12.6129	0.510262
$612$	2.64286	0.106831
$613$	−5.95694	−0.240598	−0.120299	−	0.992738i	$-0.538385\pi$
$613$	−5.95694	−0.240598	−0.120299	+	0.992738i	$0.538385\pi$
$614$	−22.9231	−0.925101
$615$	−4.97839	−0.200748
$616$	0	0
$617$	−40.0363	−1.61180	−0.805901	−	0.592050i	$-0.798319\pi$
$617$	−40.0363	−1.61180	−0.805901	+	0.592050i	$0.798319\pi$
$618$	−5.75724	−0.231590
$619$	10.5175	0.422734	0.211367	−	0.977407i	$-0.432209\pi$
$619$	10.5175	0.422734	0.211367	+	0.977407i	$0.432209\pi$
$620$	−10.8512	−0.435796
$621$	−1.00000	−0.0401286
$622$	8.57921	0.343995
$623$	0	0
$624$	−4.72067	−0.188978
$625$	−23.6074	−0.944298
$626$	−1.10665	−0.0442305
$627$	1.82985	0.0730771
$628$	10.1172	0.403718
$629$	13.4411	0.535930
$630$	0	0
$631$	44.9392	1.78900	0.894501	−	0.447065i	$-0.147531\pi$
$631$	44.9392	1.78900	0.894501	+	0.447065i	$0.147531\pi$
$632$	−26.1974	−1.04208
$633$	−28.5995	−1.13673
$634$	−17.2438	−0.684840
$635$	34.2035	1.35733
$636$	2.78659	0.110496
$637$	0	0
$638$	20.2186	0.800462
$639$	13.8643	0.548462
$640$	2.33738	0.0923929
$641$	−32.0409	−1.26554	−0.632769	−	0.774341i	$-0.718082\pi$
$641$	−32.0409	−1.26554	−0.632769	+	0.774341i	$0.718082\pi$
$642$	11.4229	0.450824
$643$	38.5772	1.52134	0.760669	−	0.649140i	$-0.224871\pi$
$643$	38.5772	1.52134	0.760669	+	0.649140i	$0.224871\pi$
$644$	0	0
$645$	16.9634	0.667934
$646$	2.18262	0.0858740
$647$	30.9334	1.21612	0.608058	−	0.793892i	$-0.291949\pi$
$647$	30.9334	1.21612	0.608058	+	0.793892i	$0.291949\pi$
$648$	3.04477	0.119610
$649$	−31.8962	−1.25203
$650$	−0.921575	−0.0361472
$651$	0	0
$652$	−13.1444	−0.514774
$653$	42.5576	1.66541	0.832704	−	0.553718i	$-0.186792\pi$
$653$	42.5576	1.66541	0.832704	+	0.553718i	$0.186792\pi$
$654$	−1.11394	−0.0435585
$655$	−21.7676	−0.850529
$656$	−3.26566	−0.127503
$657$	0.705829	0.0275370
$658$	0	0
$659$	32.5053	1.26623	0.633113	−	0.774059i	$-0.281777\pi$
$659$	32.5053	1.26623	0.633113	+	0.774059i	$0.281777\pi$
$660$	−5.07964	−0.197725
$661$	33.5828	1.30622	0.653109	−	0.757264i	$-0.273464\pi$
$661$	33.5828	1.30622	0.653109	+	0.757264i	$0.273464\pi$
$662$	−30.8604	−1.19942
$663$	−9.81900	−0.381338
$664$	−35.2945	−1.36969
$665$	0	0
$666$	4.76919	0.184802
$667$	7.31827	0.283365
$668$	7.88052	0.304906
$669$	−16.5464	−0.639723
$670$	−25.8499	−0.998668
$671$	−3.89324	−0.150297
$672$	0	0
$673$	−1.23960	−0.0477832	−0.0238916	−	0.999715i	$-0.507606\pi$
$673$	−1.23960	−0.0477832	−0.0238916	+	0.999715i	$0.507606\pi$
$674$	4.50288	0.173444
$675$	0.264516	0.0101812
$676$	1.83674	0.0706440
$677$	5.69833	0.219004	0.109502	−	0.993987i	$-0.465074\pi$
$677$	5.69833	0.219004	0.109502	+	0.993987i	$0.465074\pi$
$678$	−14.8480	−0.570234
$679$	0	0
$680$	−19.6727	−0.754414
$681$	17.9650	0.688420
$682$	15.4772	0.592653
$683$	27.2518	1.04276	0.521380	−	0.853325i	$-0.325418\pi$
$683$	27.2518	1.04276	0.521380	+	0.853325i	$0.325418\pi$
$684$	−0.621095	−0.0237482
$685$	13.2041	0.504503
$686$	0	0
$687$	−28.0061	−1.06850
$688$	11.1274	0.424230
$689$	−10.3530	−0.394418
$690$	2.29256	0.0872763
$691$	−45.1514	−1.71764	−0.858820	−	0.512277i	$-0.828802\pi$
$691$	−45.1514	−1.71764	−0.858820	+	0.512277i	$0.828802\pi$
$692$	−13.9784	−0.531379
$693$	0	0
$694$	−19.4308	−0.737584
$695$	30.7264	1.16552
$696$	−22.2824	−0.844614
$697$	−6.79258	−0.257287
$698$	21.0068	0.795120
$699$	−23.2462	−0.879251
$700$	0	0
$701$	−0.456514	−0.0172423	−0.00862116	−	0.999963i	$-0.502744\pi$
$701$	−0.456514	−0.0172423	−0.00862116	+	0.999963i	$0.502744\pi$
$702$	−3.48400	−0.131495
$703$	−3.15876	−0.119135
$704$	−20.1560	−0.759657
$705$	8.29958	0.312580
$706$	23.2673	0.875676
$707$	0	0
$708$	10.8263	0.406878
$709$	−9.90247	−0.371895	−0.185948	−	0.982560i	$-0.559535\pi$
$709$	−9.90247	−0.371895	−0.185948	+	0.982560i	$0.559535\pi$
$710$	−31.7847	−1.19286
$711$	−8.60406	−0.322678
$712$	−1.01627	−0.0380863
$713$	5.60209	0.209800
$714$	0	0
$715$	18.8723	0.705785
$716$	4.72431	0.176556
$717$	−6.43482	−0.240313
$718$	12.6832	0.473332
$719$	−27.2086	−1.01471	−0.507355	−	0.861737i	$-0.669377\pi$
$719$	−27.2086	−1.01471	−0.507355	+	0.861737i	$0.669377\pi$
$720$	−3.10632	−0.115766
$721$	0	0
$722$	19.5038	0.725855
$723$	−23.5177	−0.874633
$724$	−1.71837	−0.0638626
$725$	−1.93580	−0.0718939
$726$	−4.34348	−0.161202
$727$	−29.0386	−1.07698	−0.538491	−	0.842631i	$-0.681006\pi$
$727$	−29.0386	−1.07698	−0.538491	+	0.842631i	$0.681006\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−1.61816	−0.0598907
$731$	23.1451	0.856052
$732$	1.32146	0.0488425
$733$	−20.7986	−0.768215	−0.384108	−	0.923288i	$-0.625491\pi$
$733$	−20.7986	−0.768215	−0.384108	+	0.923288i	$0.625491\pi$
$734$	−22.8060	−0.841786
$735$	0	0
$736$	−4.58569	−0.169031
$737$	−29.5693	−1.08920
$738$	−2.41016	−0.0887191
$739$	16.8470	0.619727	0.309864	−	0.950781i	$-0.399717\pi$
$739$	16.8470	0.619727	0.309864	+	0.950781i	$0.399717\pi$
$740$	8.76869	0.322343
$741$	2.30755	0.0847699
$742$	0	0
$743$	−38.5982	−1.41603	−0.708016	−	0.706197i	$-0.750409\pi$
$743$	−38.5982	−1.41603	−0.708016	+	0.706197i	$0.750409\pi$
$744$	−17.0571	−0.625342
$745$	2.21073	0.0809947
$746$	−23.1168	−0.846367
$747$	−11.5918	−0.424123
$748$	−6.93072	−0.253412
$749$	0	0
$750$	−12.0692	−0.440706
$751$	24.0032	0.875889	0.437945	−	0.899002i	$-0.355707\pi$
$751$	24.0032	0.875889	0.437945	+	0.899002i	$0.355707\pi$
$752$	5.44426	0.198532
$753$	3.12594	0.113915
$754$	25.4969	0.928541
$755$	49.0465	1.78498
$756$	0	0
$757$	−6.54398	−0.237845	−0.118923	−	0.992904i	$-0.537944\pi$
$757$	−6.54398	−0.237845	−0.118923	+	0.992904i	$0.537944\pi$
$758$	−12.5114	−0.454436
$759$	2.62243	0.0951882
$760$	4.62325	0.167703
$761$	16.0091	0.580328	0.290164	−	0.956977i	$-0.406290\pi$
$761$	16.0091	0.580328	0.290164	+	0.956977i	$0.406290\pi$
$762$	16.5587	0.599860
$763$	0	0
$764$	−9.29439	−0.336259
$765$	−6.46115	−0.233604
$766$	4.70593	0.170032
$767$	−40.2229	−1.45237
$768$	16.5036	0.595521
$769$	35.3103	1.27332	0.636661	−	0.771144i	$-0.280315\pi$
$769$	35.3103	1.27332	0.636661	+	0.771144i	$0.280315\pi$
$770$	0	0
$771$	20.5336	0.739500
$772$	−21.9113	−0.788607
$773$	−54.2901	−1.95268	−0.976339	−	0.216246i	$-0.930619\pi$
$773$	−54.2901	−1.95268	−0.976339	+	0.216246i	$0.930619\pi$
$774$	8.21240	0.295189
$775$	−1.48184	−0.0532294
$776$	0.380219	0.0136491
$777$	0	0
$778$	2.85949	0.102518
$779$	1.59631	0.0571939
$780$	−6.40572	−0.229362
$781$	−36.3581	−1.30099
$782$	3.12800	0.111857
$783$	−7.31827	−0.261534
$784$	0	0
$785$	−24.7340	−0.882793
$786$	−10.5382	−0.375885
$787$	51.9594	1.85215	0.926077	−	0.377335i	$-0.123159\pi$
$787$	51.9594	1.85215	0.926077	+	0.377335i	$0.123159\pi$
$788$	−4.60900	−0.164189
$789$	−19.4476	−0.692352
$790$	19.7253	0.701796
$791$	0	0
$792$	−7.98469	−0.283723
$793$	−4.90960	−0.174345
$794$	7.77677	0.275987
$795$	−6.81254	−0.241616
$796$	14.8090	0.524889
$797$	24.3737	0.863361	0.431680	−	0.902027i	$-0.357921\pi$
$797$	24.3737	0.863361	0.431680	+	0.902027i	$0.357921\pi$
$798$	0	0
$799$	11.3241	0.400616
$800$	1.21299	0.0428857
$801$	−0.333776	−0.0117934
$802$	−2.84649	−0.100513
$803$	−1.85099	−0.0653199
$804$	10.0365	0.353961
$805$	0	0
$806$	19.5177	0.687481
$807$	−7.71940	−0.271736
$808$	−26.7322	−0.940435
$809$	9.43223	0.331619	0.165810	−	0.986158i	$-0.446976\pi$
$809$	9.43223	0.331619	0.165810	+	0.986158i	$0.446976\pi$
$810$	−2.29256	−0.0805524
$811$	26.7248	0.938436	0.469218	−	0.883082i	$-0.344536\pi$
$811$	26.7248	0.938436	0.469218	+	0.883082i	$0.344536\pi$
$812$	0	0
$813$	−30.8637	−1.08244
$814$	−12.5069	−0.438365
$815$	32.1348	1.12563
$816$	−4.23831	−0.148370
$817$	−5.43929	−0.190297
$818$	−26.1371	−0.913861
$819$	0	0
$820$	−4.43134	−0.154749
$821$	−44.1164	−1.53967	−0.769837	−	0.638240i	$-0.779663\pi$
$821$	−44.1164	−1.53967	−0.769837	+	0.638240i	$0.779663\pi$
$822$	6.39242	0.222961
$823$	1.47720	0.0514921	0.0257461	−	0.999669i	$-0.491804\pi$
$823$	1.47720	0.0514921	0.0257461	+	0.999669i	$0.491804\pi$
$824$	−16.6391	−0.579650
$825$	−0.693675	−0.0241507
$826$	0	0
$827$	−39.6798	−1.37980	−0.689900	−	0.723904i	$-0.742346\pi$
$827$	−39.6798	−1.37980	−0.689900	+	0.723904i	$0.742346\pi$
$828$	−0.890116	−0.0309337
$829$	−3.10798	−0.107945	−0.0539724	−	0.998542i	$-0.517188\pi$
$829$	−3.10798	−0.107945	−0.0539724	+	0.998542i	$0.517188\pi$
$830$	26.5750	0.922432
$831$	−6.40144	−0.222063
$832$	−25.4179	−0.881207
$833$	0	0
$834$	14.8754	0.515093
$835$	−19.2659	−0.666725
$836$	1.62878	0.0563325
$837$	−5.60209	−0.193637
$838$	21.1529	0.730715
$839$	52.8937	1.82609	0.913046	−	0.407856i	$-0.133724\pi$
$839$	52.8937	1.82609	0.913046	+	0.407856i	$0.133724\pi$
$840$	0	0
$841$	24.5571	0.846798
$842$	28.0212	0.965673
$843$	4.79227	0.165055
$844$	−25.4569	−0.876261
$845$	−4.49039	−0.154474
$846$	4.01803	0.138143
$847$	0	0
$848$	−4.46880	−0.153459
$849$	11.7015	0.401593
$850$	−0.827407	−0.0283798
$851$	−4.52695	−0.155182
$852$	12.3408	0.422789
$853$	14.0250	0.480205	0.240103	−	0.970748i	$-0.422819\pi$
$853$	14.0250	0.480205	0.240103	+	0.970748i	$0.422819\pi$
$854$	0	0
$855$	1.51843	0.0519291
$856$	33.0134	1.12837
$857$	22.1856	0.757845	0.378923	−	0.925428i	$-0.376295\pi$
$857$	22.1856	0.757845	0.378923	+	0.925428i	$0.376295\pi$
$858$	9.13655	0.311917
$859$	6.51983	0.222454	0.111227	−	0.993795i	$-0.464522\pi$
$859$	6.51983	0.222454	0.111227	+	0.993795i	$0.464522\pi$
$860$	15.0994	0.514886
$861$	0	0
$862$	25.3073	0.861972
$863$	−15.8555	−0.539726	−0.269863	−	0.962899i	$-0.586978\pi$
$863$	−15.8555	−0.539726	−0.269863	+	0.962899i	$0.586978\pi$
$864$	4.58569	0.156008
$865$	34.1738	1.16194
$866$	14.8449	0.504450
$867$	8.18432	0.277954
$868$	0	0
$869$	22.5636	0.765416
$870$	16.7776	0.568814
$871$	−37.2887	−1.26348
$872$	−3.21942	−0.109023
$873$	0.124876	0.00422642
$874$	−0.735106	−0.0248653
$875$	0	0
$876$	0.628270	0.0212273
$877$	−34.2400	−1.15620	−0.578102	−	0.815965i	$-0.696206\pi$
$877$	−34.2400	−1.15620	−0.578102	+	0.815965i	$0.696206\pi$
$878$	−3.05467	−0.103090
$879$	−19.9031	−0.671315
$880$	8.14611	0.274605
$881$	−41.1806	−1.38741	−0.693704	−	0.720260i	$-0.744023\pi$
$881$	−41.1806	−1.38741	−0.693704	+	0.720260i	$0.744023\pi$
$882$	0	0
$883$	43.6733	1.46972	0.734862	−	0.678216i	$-0.237247\pi$
$883$	43.6733	1.46972	0.734862	+	0.678216i	$0.237247\pi$
$884$	−8.74005	−0.293960
$885$	−26.4677	−0.889703
$886$	−14.7448	−0.495362
$887$	−12.3397	−0.414327	−0.207164	−	0.978306i	$-0.566423\pi$
$887$	−12.3397	−0.414327	−0.207164	+	0.978306i	$0.566423\pi$
$888$	13.7835	0.462544
$889$	0	0
$890$	0.765201	0.0256496
$891$	−2.62243	−0.0878547
$892$	−14.7283	−0.493139
$893$	−2.66125	−0.0890553
$894$	1.07027	0.0357950
$895$	−11.5498	−0.386067
$896$	0	0
$897$	3.30704	0.110419
$898$	−13.3425	−0.445246
$899$	40.9976	1.36735
$900$	0.235450	0.00784834
$901$	−9.29511	−0.309665
$902$	6.32047	0.210449
$903$	0	0
$904$	−42.9124	−1.42725
$905$	4.20099	0.139645
$906$	23.7446	0.788861
$907$	−23.5472	−0.781873	−0.390936	−	0.920418i	$-0.627849\pi$
$907$	−23.5472	−0.781873	−0.390936	+	0.920418i	$0.627849\pi$
$908$	15.9909	0.530678
$909$	−8.77972	−0.291205
$910$	0	0
$911$	19.5967	0.649268	0.324634	−	0.945840i	$-0.394759\pi$
$911$	19.5967	0.649268	0.324634	+	0.945840i	$0.394759\pi$
$912$	0.996038	0.0329821
$913$	30.3988	1.00605
$914$	3.74704	0.123941
$915$	−3.23064	−0.106802
$916$	−24.9287	−0.823667
$917$	0	0
$918$	−3.12800	−0.103239
$919$	−38.2527	−1.26184	−0.630920	−	0.775848i	$-0.717323\pi$
$919$	−38.2527	−1.26184	−0.630920	+	0.775848i	$0.717323\pi$
$920$	6.62577	0.218445
$921$	−21.7588	−0.716976
$922$	−17.0079	−0.560127
$923$	−45.8497	−1.50916
$924$	0	0
$925$	1.19745	0.0393720
$926$	−10.3106	−0.338826
$927$	−5.46482	−0.179488
$928$	−33.5593	−1.10164
$929$	−32.7683	−1.07509	−0.537546	−	0.843235i	$-0.680648\pi$
$929$	−32.7683	−1.07509	−0.537546	+	0.843235i	$0.680648\pi$
$930$	12.8431	0.421143
$931$	0	0
$932$	−20.6918	−0.677782
$933$	8.14345	0.266605
$934$	31.7713	1.03959
$935$	16.9439	0.554125
$936$	−10.0692	−0.329121
$937$	−49.1394	−1.60531	−0.802657	−	0.596441i	$-0.796581\pi$
$937$	−49.1394	−1.60531	−0.802657	+	0.596441i	$0.796581\pi$
$938$	0	0
$939$	−1.05044	−0.0342797
$940$	7.38759	0.240957
$941$	59.6840	1.94564	0.972821	−	0.231557i	$-0.0743820\pi$
$941$	59.6840	1.94564	0.972821	+	0.231557i	$0.0743820\pi$
$942$	−11.9743	−0.390144
$943$	2.28774	0.0744991
$944$	−17.3620	−0.565084
$945$	0	0
$946$	−21.5364	−0.700210
$947$	−2.66069	−0.0864608	−0.0432304	−	0.999065i	$-0.513765\pi$
$947$	−2.66069	−0.0864608	−0.0432304	+	0.999065i	$0.513765\pi$
$948$	−7.65861	−0.248740
$949$	−2.33421	−0.0757715
$950$	0.194448	0.00630872
$951$	−16.3680	−0.530768
$952$	0	0
$953$	−23.2051	−0.751686	−0.375843	−	0.926683i	$-0.622647\pi$
$953$	−23.2051	−0.751686	−0.375843	+	0.926683i	$0.622647\pi$
$954$	−3.29811	−0.106780
$955$	22.7225	0.735284
$956$	−5.72773	−0.185248
$957$	19.1917	0.620378
$958$	−3.07800	−0.0994458
$959$	0	0
$960$	−16.7256	−0.539817
$961$	0.383420	0.0123684
$962$	−15.7719	−0.508506
$963$	10.8427	0.349400
$964$	−20.9335	−0.674223
$965$	53.5679	1.72441
$966$	0	0
$967$	−6.58436	−0.211739	−0.105869	−	0.994380i	$-0.533763\pi$
$967$	−6.58436	−0.211739	−0.105869	+	0.994380i	$0.533763\pi$
$968$	−12.5532	−0.403474
$969$	2.07176	0.0665545
$970$	−0.286286	−0.00919210
$971$	41.8221	1.34213	0.671067	−	0.741397i	$-0.265836\pi$
$971$	41.8221	1.34213	0.671067	+	0.741397i	$0.265836\pi$
$972$	0.890116	0.0285505
$973$	0	0
$974$	−33.9633	−1.08825
$975$	−0.874766	−0.0280149
$976$	−2.11920	−0.0678338
$977$	−17.2560	−0.552067	−0.276033	−	0.961148i	$-0.589020\pi$
$977$	−17.2560	−0.552067	−0.276033	+	0.961148i	$0.589020\pi$
$978$	15.5572	0.497465
$979$	0.875303	0.0279748
$980$	0	0
$981$	−1.05736	−0.0337589
$982$	12.8181	0.409042
$983$	61.1190	1.94939	0.974697	−	0.223531i	$-0.0717586\pi$
$983$	61.1190	1.94939	0.974697	+	0.223531i	$0.0717586\pi$
$984$	−6.96564	−0.222056
$985$	11.2679	0.359024
$986$	22.8916	0.729016
$987$	0	0
$988$	2.05399	0.0653460
$989$	−7.79527	−0.247875
$990$	6.01208	0.191076
$991$	27.6963	0.879802	0.439901	−	0.898046i	$-0.355013\pi$
$991$	27.6963	0.879802	0.439901	+	0.898046i	$0.355013\pi$
$992$	−25.6894	−0.815641
$993$	−29.2929	−0.929582
$994$	0	0
$995$	−36.2043	−1.14775
$996$	−10.3181	−0.326941
$997$	15.6408	0.495350	0.247675	−	0.968843i	$-0.420334\pi$
$997$	15.6408	0.495350	0.247675	+	0.968843i	$0.420334\pi$
$998$	−33.5328	−1.06146
$999$	4.52695	0.143226

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3381.2.a.bi.1.3		10
7.2	even	3		483.2.i.h.277.8	✓	20
7.4	even	3		483.2.i.h.415.8	yes	20
7.6	odd	2		3381.2.a.bj.1.3		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.i.h.277.8	✓	20	7.2	even	3
483.2.i.h.415.8	yes	20	7.4	even	3
3381.2.a.bi.1.3		10	1.1	even	1	trivial
3381.2.a.bj.1.3		10	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:	\( N \)	\(=\)	\( 3381 = 3 \cdot 7^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3381.a (trivial)

\(f(q)\)	\(=\)	\(q-1.05351 q^{2} -1.00000 q^{3} -0.890116 q^{4} +2.17612 q^{5} +1.05351 q^{6} +3.04477 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.05351 q^{2} -1.00000 q^{3} -0.890116 q^{4} +2.17612 q^{5} +1.05351 q^{6} +3.04477 q^{8} +1.00000 q^{9} -2.29256 q^{10} -2.62243 q^{11} +0.890116 q^{12} -3.30704 q^{13} -2.17612 q^{15} -1.42746 q^{16} -2.96912 q^{17} -1.05351 q^{18} +0.697769 q^{19} -1.93700 q^{20} +2.76276 q^{22} +1.00000 q^{23} -3.04477 q^{24} -0.264516 q^{25} +3.48400 q^{26} -1.00000 q^{27} +7.31827 q^{29} +2.29256 q^{30} +5.60209 q^{31} -4.58569 q^{32} +2.62243 q^{33} +3.12800 q^{34} -0.890116 q^{36} -4.52695 q^{37} -0.735106 q^{38} +3.30704 q^{39} +6.62577 q^{40} +2.28774 q^{41} -7.79527 q^{43} +2.33427 q^{44} +2.17612 q^{45} -1.05351 q^{46} -3.81394 q^{47} +1.42746 q^{48} +0.278671 q^{50} +2.96912 q^{51} +2.94365 q^{52} +3.13059 q^{53} +1.05351 q^{54} -5.70671 q^{55} -0.697769 q^{57} -7.70988 q^{58} +12.1628 q^{59} +1.93700 q^{60} +1.48459 q^{61} -5.90186 q^{62} +7.68599 q^{64} -7.19650 q^{65} -2.76276 q^{66} +11.2755 q^{67} +2.64286 q^{68} -1.00000 q^{69} +13.8643 q^{71} +3.04477 q^{72} +0.705829 q^{73} +4.76919 q^{74} +0.264516 q^{75} -0.621095 q^{76} -3.48400 q^{78} -8.60406 q^{79} -3.10632 q^{80} +1.00000 q^{81} -2.41016 q^{82} -11.5918 q^{83} -6.46115 q^{85} +8.21240 q^{86} -7.31827 q^{87} -7.98469 q^{88} -0.333776 q^{89} -2.29256 q^{90} -0.890116 q^{92} -5.60209 q^{93} +4.01803 q^{94} +1.51843 q^{95} +4.58569 q^{96} +0.124876 q^{97} -2.62243 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 3 q^{2} - 10 q^{3} + 15 q^{4} - 5 q^{5} - 3 q^{6} + 9 q^{8} + 10 q^{9}+O(q^{10}) \) 10 * q + 3 * q^2 - 10 * q^3 + 15 * q^4 - 5 * q^5 - 3 * q^6 + 9 * q^8 + 10 * q^9	\( 10 q + 3 q^{2} - 10 q^{3} + 15 q^{4} - 5 q^{5} - 3 q^{6} + 9 q^{8} + 10 q^{9} + 11 q^{10} + 8 q^{11} - 15 q^{12} + 5 q^{15} + 37 q^{16} - 11 q^{17} + 3 q^{18} + q^{19} - 15 q^{20} + 6 q^{22} + 10 q^{23} - 9 q^{24} + 21 q^{25} + q^{26} - 10 q^{27} + 22 q^{29} - 11 q^{30} - 3 q^{31} + 11 q^{32} - 8 q^{33} - 3 q^{34} + 15 q^{36} - 3 q^{37} + 16 q^{38} + 39 q^{40} - 26 q^{41} + 27 q^{43} + 16 q^{44} - 5 q^{45} + 3 q^{46} + 11 q^{47} - 37 q^{48} + 2 q^{50} + 11 q^{51} + 29 q^{52} + 5 q^{53} - 3 q^{54} - 18 q^{55} - q^{57} + 16 q^{58} - 10 q^{59} + 15 q^{60} + 22 q^{61} - 32 q^{62} + 69 q^{64} - 11 q^{65} - 6 q^{66} - 2 q^{67} - 21 q^{68} - 10 q^{69} + 27 q^{71} + 9 q^{72} - 8 q^{73} + 14 q^{74} - 21 q^{75} - 22 q^{76} - q^{78} + 21 q^{79} - 53 q^{80} + 10 q^{81} + 36 q^{82} - 12 q^{83} + 23 q^{85} + 18 q^{86} - 22 q^{87} - 10 q^{88} + 6 q^{89} + 11 q^{90} + 15 q^{92} + 3 q^{93} + 35 q^{94} + 44 q^{95} - 11 q^{96} + 6 q^{97} + 8 q^{99}+O(q^{100}) \) 10 * q + 3 * q^2 - 10 * q^3 + 15 * q^4 - 5 * q^5 - 3 * q^6 + 9 * q^8 + 10 * q^9 + 11 * q^10 + 8 * q^11 - 15 * q^12 + 5 * q^15 + 37 * q^16 - 11 * q^17 + 3 * q^18 + q^19 - 15 * q^20 + 6 * q^22 + 10 * q^23 - 9 * q^24 + 21 * q^25 + q^26 - 10 * q^27 + 22 * q^29 - 11 * q^30 - 3 * q^31 + 11 * q^32 - 8 * q^33 - 3 * q^34 + 15 * q^36 - 3 * q^37 + 16 * q^38 + 39 * q^40 - 26 * q^41 + 27 * q^43 + 16 * q^44 - 5 * q^45 + 3 * q^46 + 11 * q^47 - 37 * q^48 + 2 * q^50 + 11 * q^51 + 29 * q^52 + 5 * q^53 - 3 * q^54 - 18 * q^55 - q^57 + 16 * q^58 - 10 * q^59 + 15 * q^60 + 22 * q^61 - 32 * q^62 + 69 * q^64 - 11 * q^65 - 6 * q^66 - 2 * q^67 - 21 * q^68 - 10 * q^69 + 27 * q^71 + 9 * q^72 - 8 * q^73 + 14 * q^74 - 21 * q^75 - 22 * q^76 - q^78 + 21 * q^79 - 53 * q^80 + 10 * q^81 + 36 * q^82 - 12 * q^83 + 23 * q^85 + 18 * q^86 - 22 * q^87 - 10 * q^88 + 6 * q^89 + 11 * q^90 + 15 * q^92 + 3 * q^93 + 35 * q^94 + 44 * q^95 - 11 * q^96 + 6 * q^97 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more