LMFDB - Embedded newform 2366.2.a.ba.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2366,2,Mod(1,2366)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2366, 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("2366.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2366 = 2 \cdot 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2366.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:	$18.8926051182$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	$\Q(\zeta_{14})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 2x + 1 $ x^3 - x^2 - 2*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$0.445042$ of defining polynomial
Character	$\chi$	$=$	2366.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.44504 q^{3} +1.00000 q^{4} +2.24698 q^{5} -1.44504 q^{6} +1.00000 q^{7} +1.00000 q^{8} -0.911854 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.44504 q^{3} +1.00000 q^{4} +2.24698 q^{5} -1.44504 q^{6} +1.00000 q^{7} +1.00000 q^{8} -0.911854 q^{9} +2.24698 q^{10} -2.19806 q^{11} -1.44504 q^{12} +1.00000 q^{14} -3.24698 q^{15} +1.00000 q^{16} -8.00969 q^{17} -0.911854 q^{18} -4.44504 q^{19} +2.24698 q^{20} -1.44504 q^{21} -2.19806 q^{22} -4.13706 q^{23} -1.44504 q^{24} +0.0489173 q^{25} +5.65279 q^{27} +1.00000 q^{28} -8.45473 q^{29} -3.24698 q^{30} -4.96077 q^{31} +1.00000 q^{32} +3.17629 q^{33} -8.00969 q^{34} +2.24698 q^{35} -0.911854 q^{36} +4.74094 q^{37} -4.44504 q^{38} +2.24698 q^{40} +8.72886 q^{41} -1.44504 q^{42} -8.93900 q^{43} -2.19806 q^{44} -2.04892 q^{45} -4.13706 q^{46} -0.472189 q^{47} -1.44504 q^{48} +1.00000 q^{49} +0.0489173 q^{50} +11.5743 q^{51} +5.76271 q^{53} +5.65279 q^{54} -4.93900 q^{55} +1.00000 q^{56} +6.42327 q^{57} -8.45473 q^{58} -4.19806 q^{59} -3.24698 q^{60} -0.0217703 q^{61} -4.96077 q^{62} -0.911854 q^{63} +1.00000 q^{64} +3.17629 q^{66} -6.66487 q^{67} -8.00969 q^{68} +5.97823 q^{69} +2.24698 q^{70} +13.5700 q^{71} -0.911854 q^{72} +3.15883 q^{73} +4.74094 q^{74} -0.0706876 q^{75} -4.44504 q^{76} -2.19806 q^{77} +2.77479 q^{79} +2.24698 q^{80} -5.43296 q^{81} +8.72886 q^{82} +1.91723 q^{83} -1.44504 q^{84} -17.9976 q^{85} -8.93900 q^{86} +12.2174 q^{87} -2.19806 q^{88} -9.72886 q^{89} -2.04892 q^{90} -4.13706 q^{92} +7.16852 q^{93} -0.472189 q^{94} -9.98792 q^{95} -1.44504 q^{96} +4.05861 q^{97} +1.00000 q^{98} +2.00431 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{2} - 4 q^{3} + 3 q^{4} + 2 q^{5} - 4 q^{6} + 3 q^{7} + 3 q^{8} + q^{9}+O(q^{10}) $ 3 * q + 3 * q^2 - 4 * q^3 + 3 * q^4 + 2 * q^5 - 4 * q^6 + 3 * q^7 + 3 * q^8 + q^9	$ 3 q + 3 q^{2} - 4 q^{3} + 3 q^{4} + 2 q^{5} - 4 q^{6} + 3 q^{7} + 3 q^{8} + q^{9} + 2 q^{10} - 11 q^{11} - 4 q^{12} + 3 q^{14} - 5 q^{15} + 3 q^{16} - 2 q^{17} + q^{18} - 13 q^{19} + 2 q^{20} - 4 q^{21} - 11 q^{22} - 7 q^{23} - 4 q^{24} - 9 q^{25} - q^{27} + 3 q^{28} - 3 q^{29} - 5 q^{30} - 2 q^{31} + 3 q^{32} + 17 q^{33} - 2 q^{34} + 2 q^{35} + q^{36} - 13 q^{38} + 2 q^{40} - 7 q^{41} - 4 q^{42} - 17 q^{43} - 11 q^{44} + 3 q^{45} - 7 q^{46} + 5 q^{47} - 4 q^{48} + 3 q^{49} - 9 q^{50} - 9 q^{51} - q^{54} - 5 q^{55} + 3 q^{56} + 22 q^{57} - 3 q^{58} - 17 q^{59} - 5 q^{60} + 3 q^{61} - 2 q^{62} + q^{63} + 3 q^{64} + 17 q^{66} - 21 q^{67} - 2 q^{68} + 21 q^{69} + 2 q^{70} + 16 q^{71} + q^{72} + q^{73} + 12 q^{75} - 13 q^{76} - 11 q^{77} + 10 q^{79} + 2 q^{80} + 3 q^{81} - 7 q^{82} - q^{83} - 4 q^{84} - 13 q^{85} - 17 q^{86} - 3 q^{87} - 11 q^{88} + 4 q^{89} + 3 q^{90} - 7 q^{92} - 9 q^{93} + 5 q^{94} - 11 q^{95} - 4 q^{96} - 19 q^{97} + 3 q^{98} - 13 q^{99}+O(q^{100}) $ 3 * q + 3 * q^2 - 4 * q^3 + 3 * q^4 + 2 * q^5 - 4 * q^6 + 3 * q^7 + 3 * q^8 + q^9 + 2 * q^10 - 11 * q^11 - 4 * q^12 + 3 * q^14 - 5 * q^15 + 3 * q^16 - 2 * q^17 + q^18 - 13 * q^19 + 2 * q^20 - 4 * q^21 - 11 * q^22 - 7 * q^23 - 4 * q^24 - 9 * q^25 - q^27 + 3 * q^28 - 3 * q^29 - 5 * q^30 - 2 * q^31 + 3 * q^32 + 17 * q^33 - 2 * q^34 + 2 * q^35 + q^36 - 13 * q^38 + 2 * q^40 - 7 * q^41 - 4 * q^42 - 17 * q^43 - 11 * q^44 + 3 * q^45 - 7 * q^46 + 5 * q^47 - 4 * q^48 + 3 * q^49 - 9 * q^50 - 9 * q^51 - q^54 - 5 * q^55 + 3 * q^56 + 22 * q^57 - 3 * q^58 - 17 * q^59 - 5 * q^60 + 3 * q^61 - 2 * q^62 + q^63 + 3 * q^64 + 17 * q^66 - 21 * q^67 - 2 * q^68 + 21 * q^69 + 2 * q^70 + 16 * q^71 + q^72 + q^73 + 12 * q^75 - 13 * q^76 - 11 * q^77 + 10 * q^79 + 2 * q^80 + 3 * q^81 - 7 * q^82 - q^83 - 4 * q^84 - 13 * q^85 - 17 * q^86 - 3 * q^87 - 11 * q^88 + 4 * q^89 + 3 * q^90 - 7 * q^92 - 9 * q^93 + 5 * q^94 - 11 * q^95 - 4 * q^96 - 19 * q^97 + 3 * q^98 - 13 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.44504	−0.834295	−0.417148	−	0.908839i	$-0.636970\pi$
$3$	−1.44504	−0.834295	−0.417148	+	0.908839i	$0.636970\pi$
$4$	1.00000	0.500000
$5$	2.24698	1.00488	0.502440	−	0.864612i	$-0.332436\pi$
$5$	2.24698	1.00488	0.502440	+	0.864612i	$0.332436\pi$
$6$	−1.44504	−0.589936
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	−0.911854	−0.303951
$10$	2.24698	0.710557
$11$	−2.19806	−0.662741	−0.331370	−	0.943501i	$-0.607511\pi$
$11$	−2.19806	−0.662741	−0.331370	+	0.943501i	$0.607511\pi$
$12$	−1.44504	−0.417148
$13$	0	0
$13$	0	0
$14$	1.00000	0.267261
$15$	−3.24698	−0.838367
$16$	1.00000	0.250000
$17$	−8.00969	−1.94263	−0.971317	−	0.237787i	$-0.923578\pi$
$17$	−8.00969	−1.94263	−0.971317	+	0.237787i	$0.923578\pi$
$18$	−0.911854	−0.214926
$19$	−4.44504	−1.01976	−0.509881	−	0.860245i	$-0.670311\pi$
$19$	−4.44504	−1.01976	−0.509881	+	0.860245i	$0.670311\pi$
$20$	2.24698	0.502440
$21$	−1.44504	−0.315334
$22$	−2.19806	−0.468628
$23$	−4.13706	−0.862637	−0.431319	−	0.902200i	$-0.641952\pi$
$23$	−4.13706	−0.862637	−0.431319	+	0.902200i	$0.641952\pi$
$24$	−1.44504	−0.294968
$25$	0.0489173	0.00978347
$26$	0	0
$27$	5.65279	1.08788
$28$	1.00000	0.188982
$29$	−8.45473	−1.57000	−0.785002	−	0.619493i	$-0.787338\pi$
$29$	−8.45473	−1.57000	−0.785002	+	0.619493i	$0.787338\pi$
$30$	−3.24698	−0.592815
$31$	−4.96077	−0.890981	−0.445490	−	0.895287i	$-0.646971\pi$
$31$	−4.96077	−0.890981	−0.445490	+	0.895287i	$0.646971\pi$
$32$	1.00000	0.176777
$33$	3.17629	0.552921
$34$	−8.00969	−1.37365
$35$	2.24698	0.379809
$36$	−0.911854	−0.151976
$37$	4.74094	0.779406	0.389703	−	0.920941i	$-0.372578\pi$
$37$	4.74094	0.779406	0.389703	+	0.920941i	$0.372578\pi$
$38$	−4.44504	−0.721081
$39$	0	0
$40$	2.24698	0.355279
$41$	8.72886	1.36322	0.681609	−	0.731716i	$-0.261280\pi$
$41$	8.72886	1.36322	0.681609	+	0.731716i	$0.261280\pi$
$42$	−1.44504	−0.222975
$43$	−8.93900	−1.36318	−0.681592	−	0.731732i	$-0.738712\pi$
$43$	−8.93900	−1.36318	−0.681592	+	0.731732i	$0.738712\pi$
$44$	−2.19806	−0.331370
$45$	−2.04892	−0.305435
$46$	−4.13706	−0.609977
$47$	−0.472189	−0.0688758	−0.0344379	−	0.999407i	$-0.510964\pi$
$47$	−0.472189	−0.0688758	−0.0344379	+	0.999407i	$0.510964\pi$
$48$	−1.44504	−0.208574
$49$	1.00000	0.142857
$50$	0.0489173	0.00691796
$51$	11.5743	1.62073
$52$	0	0
$53$	5.76271	0.791569	0.395784	−	0.918343i	$-0.370473\pi$
$53$	5.76271	0.791569	0.395784	+	0.918343i	$0.370473\pi$
$54$	5.65279	0.769248
$55$	−4.93900	−0.665975
$56$	1.00000	0.133631
$57$	6.42327	0.850783
$58$	−8.45473	−1.11016
$59$	−4.19806	−0.546541	−0.273271	−	0.961937i	$-0.588105\pi$
$59$	−4.19806	−0.546541	−0.273271	+	0.961937i	$0.588105\pi$
$60$	−3.24698	−0.419183
$61$	−0.0217703	−0.00278740	−0.00139370	−	0.999999i	$-0.500444\pi$
$61$	−0.0217703	−0.00278740	−0.00139370	+	0.999999i	$0.500444\pi$
$62$	−4.96077	−0.630019
$63$	−0.911854	−0.114883
$64$	1.00000	0.125000
$65$	0	0
$66$	3.17629	0.390975
$67$	−6.66487	−0.814244	−0.407122	−	0.913374i	$-0.633468\pi$
$67$	−6.66487	−0.814244	−0.407122	+	0.913374i	$0.633468\pi$
$68$	−8.00969	−0.971317
$69$	5.97823	0.719694
$70$	2.24698	0.268565
$71$	13.5700	1.61047	0.805233	−	0.592959i	$-0.202040\pi$
$71$	13.5700	1.61047	0.805233	+	0.592959i	$0.202040\pi$
$72$	−0.911854	−0.107463
$73$	3.15883	0.369714	0.184857	−	0.982765i	$-0.440818\pi$
$73$	3.15883	0.369714	0.184857	+	0.982765i	$0.440818\pi$
$74$	4.74094	0.551123
$75$	−0.0706876	−0.00816230
$76$	−4.44504	−0.509881
$77$	−2.19806	−0.250492
$78$	0	0
$79$	2.77479	0.312188	0.156094	−	0.987742i	$-0.450110\pi$
$79$	2.77479	0.312188	0.156094	+	0.987742i	$0.450110\pi$
$80$	2.24698	0.251220
$81$	−5.43296	−0.603662
$82$	8.72886	0.963941
$83$	1.91723	0.210443	0.105222	−	0.994449i	$-0.466445\pi$
$83$	1.91723	0.210443	0.105222	+	0.994449i	$0.466445\pi$
$84$	−1.44504	−0.157667
$85$	−17.9976	−1.95211
$86$	−8.93900	−0.963917
$87$	12.2174	1.30985
$88$	−2.19806	−0.234314
$89$	−9.72886	−1.03126	−0.515628	−	0.856812i	$-0.672441\pi$
$89$	−9.72886	−1.03126	−0.515628	+	0.856812i	$0.672441\pi$
$90$	−2.04892	−0.215975
$91$	0	0
$92$	−4.13706	−0.431319
$93$	7.16852	0.743341
$94$	−0.472189	−0.0487026
$95$	−9.98792	−1.02474
$96$	−1.44504	−0.147484
$97$	4.05861	0.412089	0.206045	−	0.978543i	$-0.433941\pi$
$97$	4.05861	0.412089	0.206045	+	0.978543i	$0.433941\pi$
$98$	1.00000	0.101015
$99$	2.00431	0.201441
$100$	0.0489173	0.00489173
$101$	16.3884	1.63070	0.815351	−	0.578967i	$-0.196544\pi$
$101$	16.3884	1.63070	0.815351	+	0.578967i	$0.196544\pi$
$102$	11.5743	1.14603
$103$	−1.25667	−0.123823	−0.0619116	−	0.998082i	$-0.519720\pi$
$103$	−1.25667	−0.123823	−0.0619116	+	0.998082i	$0.519720\pi$
$104$	0	0
$105$	−3.24698	−0.316873
$106$	5.76271	0.559724
$107$	−10.6920	−1.03364	−0.516818	−	0.856095i	$-0.672884\pi$
$107$	−10.6920	−1.03364	−0.516818	+	0.856095i	$0.672884\pi$
$108$	5.65279	0.543940
$109$	−10.5332	−1.00890	−0.504448	−	0.863442i	$-0.668304\pi$
$109$	−10.5332	−1.00890	−0.504448	+	0.863442i	$0.668304\pi$
$110$	−4.93900	−0.470915
$111$	−6.85086	−0.650254
$112$	1.00000	0.0944911
$113$	13.6504	1.28412	0.642061	−	0.766654i	$-0.278080\pi$
$113$	13.6504	1.28412	0.642061	+	0.766654i	$0.278080\pi$
$114$	6.42327	0.601595
$115$	−9.29590	−0.866847
$116$	−8.45473	−0.785002
$117$	0	0
$118$	−4.19806	−0.386463
$119$	−8.00969	−0.734247
$120$	−3.24698	−0.296407
$121$	−6.16852	−0.560775
$122$	−0.0217703	−0.00197099
$123$	−12.6136	−1.13733
$124$	−4.96077	−0.445490
$125$	−11.1250	−0.995049
$126$	−0.911854	−0.0812344
$127$	−13.1588	−1.16766	−0.583829	−	0.811877i	$-0.698446\pi$
$127$	−13.1588	−1.16766	−0.583829	+	0.811877i	$0.698446\pi$
$128$	1.00000	0.0883883
$129$	12.9172	1.13730
$130$	0	0
$131$	17.4373	1.52350	0.761751	−	0.647870i	$-0.224340\pi$
$131$	17.4373	1.52350	0.761751	+	0.647870i	$0.224340\pi$
$132$	3.17629	0.276461
$133$	−4.44504	−0.385434
$134$	−6.66487	−0.575757
$135$	12.7017	1.09319
$136$	−8.00969	−0.686825
$137$	−7.67025	−0.655314	−0.327657	−	0.944797i	$-0.606259\pi$
$137$	−7.67025	−0.655314	−0.327657	+	0.944797i	$0.606259\pi$
$138$	5.97823	0.508901
$139$	4.98792	0.423070	0.211535	−	0.977370i	$-0.432154\pi$
$139$	4.98792	0.423070	0.211535	+	0.977370i	$0.432154\pi$
$140$	2.24698	0.189904
$141$	0.682333	0.0574628
$142$	13.5700	1.13877
$143$	0	0
$144$	−0.911854	−0.0759878
$145$	−18.9976	−1.57767
$146$	3.15883	0.261427
$147$	−1.44504	−0.119185
$148$	4.74094	0.389703
$149$	7.62565	0.624717	0.312359	−	0.949964i	$-0.398881\pi$
$149$	7.62565	0.624717	0.312359	+	0.949964i	$0.398881\pi$
$150$	−0.0706876	−0.00577162
$151$	−15.7463	−1.28142	−0.640708	−	0.767784i	$-0.721359\pi$
$151$	−15.7463	−1.28142	−0.640708	+	0.767784i	$0.721359\pi$
$152$	−4.44504	−0.360541
$153$	7.30367	0.590466
$154$	−2.19806	−0.177125
$155$	−11.1468	−0.895329
$156$	0	0
$157$	−12.1129	−0.966715	−0.483357	−	0.875423i	$-0.660583\pi$
$157$	−12.1129	−0.966715	−0.483357	+	0.875423i	$0.660583\pi$
$158$	2.77479	0.220750
$159$	−8.32736	−0.660402
$160$	2.24698	0.177639
$161$	−4.13706	−0.326046
$162$	−5.43296	−0.426854
$163$	1.01507	0.0795061	0.0397530	−	0.999210i	$-0.487343\pi$
$163$	1.01507	0.0795061	0.0397530	+	0.999210i	$0.487343\pi$
$164$	8.72886	0.681609
$165$	7.13706	0.555620
$166$	1.91723	0.148806
$167$	−10.5700	−0.817933	−0.408966	−	0.912549i	$-0.634111\pi$
$167$	−10.5700	−0.817933	−0.408966	+	0.912549i	$0.634111\pi$
$168$	−1.44504	−0.111487
$169$	0	0
$170$	−17.9976	−1.38035
$171$	4.05323	0.309958
$172$	−8.93900	−0.681592
$173$	12.1424	0.923173	0.461586	−	0.887095i	$-0.347280\pi$
$173$	12.1424	0.923173	0.461586	+	0.887095i	$0.347280\pi$
$174$	12.2174	0.926202
$175$	0.0489173	0.00369780
$176$	−2.19806	−0.165685
$177$	6.06638	0.455977
$178$	−9.72886	−0.729209
$179$	−23.5676	−1.76153	−0.880764	−	0.473556i	$-0.842970\pi$
$179$	−23.5676	−1.76153	−0.880764	+	0.473556i	$0.842970\pi$
$180$	−2.04892	−0.152717
$181$	17.5254	1.30265	0.651327	−	0.758797i	$-0.274213\pi$
$181$	17.5254	1.30265	0.651327	+	0.758797i	$0.274213\pi$
$182$	0	0
$183$	0.0314589	0.00232551
$184$	−4.13706	−0.304988
$185$	10.6528	0.783209
$186$	7.16852	0.525622
$187$	17.6058	1.28746
$188$	−0.472189	−0.0344379
$189$	5.65279	0.411180
$190$	−9.98792	−0.724600
$191$	−22.7482	−1.64600	−0.823002	−	0.568038i	$-0.807703\pi$
$191$	−22.7482	−1.64600	−0.823002	+	0.568038i	$0.807703\pi$
$192$	−1.44504	−0.104287
$193$	−24.1196	−1.73617	−0.868084	−	0.496418i	$-0.834648\pi$
$193$	−24.1196	−1.73617	−0.868084	+	0.496418i	$0.834648\pi$
$194$	4.05861	0.291391
$195$	0	0
$196$	1.00000	0.0714286
$197$	19.0127	1.35460	0.677298	−	0.735708i	$-0.263151\pi$
$197$	19.0127	1.35460	0.677298	+	0.735708i	$0.263151\pi$
$198$	2.00431	0.142440
$199$	17.6461	1.25090	0.625449	−	0.780265i	$-0.284916\pi$
$199$	17.6461	1.25090	0.625449	+	0.780265i	$0.284916\pi$
$200$	0.0489173	0.00345898
$201$	9.63102	0.679320
$202$	16.3884	1.15308
$203$	−8.45473	−0.593406
$204$	11.5743	0.810366
$205$	19.6136	1.36987
$206$	−1.25667	−0.0875562
$207$	3.77240	0.262200
$208$	0	0
$209$	9.77048	0.675838
$210$	−3.24698	−0.224063
$211$	14.8213	1.02034	0.510171	−	0.860073i	$-0.329582\pi$
$211$	14.8213	1.02034	0.510171	+	0.860073i	$0.329582\pi$
$212$	5.76271	0.395784
$213$	−19.6093	−1.34360
$214$	−10.6920	−0.730892
$215$	−20.0858	−1.36984
$216$	5.65279	0.384624
$217$	−4.96077	−0.336759
$218$	−10.5332	−0.713398
$219$	−4.56465	−0.308450
$220$	−4.93900	−0.332987
$221$	0	0
$222$	−6.85086	−0.459799
$223$	5.40150	0.361711	0.180856	−	0.983510i	$-0.442113\pi$
$223$	5.40150	0.361711	0.180856	+	0.983510i	$0.442113\pi$
$224$	1.00000	0.0668153
$225$	−0.0446055	−0.00297370
$226$	13.6504	0.908011
$227$	−16.3327	−1.08404	−0.542021	−	0.840365i	$-0.682341\pi$
$227$	−16.3327	−1.08404	−0.542021	+	0.840365i	$0.682341\pi$
$228$	6.42327	0.425392
$229$	27.1105	1.79151	0.895756	−	0.444545i	$-0.146635\pi$
$229$	27.1105	1.79151	0.895756	+	0.444545i	$0.146635\pi$
$230$	−9.29590	−0.612953
$231$	3.17629	0.208985
$232$	−8.45473	−0.555080
$233$	19.2403	1.26047	0.630236	−	0.776403i	$-0.282958\pi$
$233$	19.2403	1.26047	0.630236	+	0.776403i	$0.282958\pi$
$234$	0	0
$235$	−1.06100	−0.0692119
$236$	−4.19806	−0.273271
$237$	−4.00969	−0.260457
$238$	−8.00969	−0.519191
$239$	−18.6601	−1.20702	−0.603510	−	0.797355i	$-0.706232\pi$
$239$	−18.6601	−1.20702	−0.603510	+	0.797355i	$0.706232\pi$
$240$	−3.24698	−0.209592
$241$	−21.0489	−1.35588	−0.677940	−	0.735117i	$-0.737127\pi$
$241$	−21.0489	−1.35588	−0.677940	+	0.735117i	$0.737127\pi$
$242$	−6.16852	−0.396528
$243$	−9.10752	−0.584248
$244$	−0.0217703	−0.00139370
$245$	2.24698	0.143554
$246$	−12.6136	−0.804211
$247$	0	0
$248$	−4.96077	−0.315009
$249$	−2.77048	−0.175572
$250$	−11.1250	−0.703606
$251$	−13.5646	−0.856193	−0.428096	−	0.903733i	$-0.640816\pi$
$251$	−13.5646	−0.856193	−0.428096	+	0.903733i	$0.640816\pi$
$252$	−0.911854	−0.0574414
$253$	9.09352	0.571705
$254$	−13.1588	−0.825659
$255$	26.0073	1.62864
$256$	1.00000	0.0625000
$257$	2.14914	0.134060	0.0670300	−	0.997751i	$-0.478648\pi$
$257$	2.14914	0.134060	0.0670300	+	0.997751i	$0.478648\pi$
$258$	12.9172	0.804192
$259$	4.74094	0.294588
$260$	0	0
$261$	7.70948	0.477205
$262$	17.4373	1.07728
$263$	21.1129	1.30188	0.650939	−	0.759130i	$-0.274376\pi$
$263$	21.1129	1.30188	0.650939	+	0.759130i	$0.274376\pi$
$264$	3.17629	0.195487
$265$	12.9487	0.795432
$266$	−4.44504	−0.272543
$267$	14.0586	0.860373
$268$	−6.66487	−0.407122
$269$	17.4711	1.06523	0.532617	−	0.846357i	$-0.321209\pi$
$269$	17.4711	1.06523	0.532617	+	0.846357i	$0.321209\pi$
$270$	12.7017	0.773001
$271$	−24.7222	−1.50176	−0.750882	−	0.660436i	$-0.770371\pi$
$271$	−24.7222	−1.50176	−0.750882	+	0.660436i	$0.770371\pi$
$272$	−8.00969	−0.485659
$273$	0	0
$274$	−7.67025	−0.463377
$275$	−0.107523	−0.00648390
$276$	5.97823	0.359847
$277$	−13.3502	−0.802135	−0.401068	−	0.916048i	$-0.631361\pi$
$277$	−13.3502	−0.802135	−0.401068	+	0.916048i	$0.631361\pi$
$278$	4.98792	0.299155
$279$	4.52350	0.270815
$280$	2.24698	0.134283
$281$	−6.91185	−0.412327	−0.206163	−	0.978518i	$-0.566098\pi$
$281$	−6.91185	−0.412327	−0.206163	+	0.978518i	$0.566098\pi$
$282$	0.682333	0.0406323
$283$	1.53989	0.0915371	0.0457686	−	0.998952i	$-0.485426\pi$
$283$	1.53989	0.0915371	0.0457686	+	0.998952i	$0.485426\pi$
$284$	13.5700	0.805233
$285$	14.4330	0.854935
$286$	0	0
$287$	8.72886	0.515248
$288$	−0.911854	−0.0537315
$289$	47.1551	2.77383
$290$	−18.9976	−1.11558
$291$	−5.86486	−0.343804
$292$	3.15883	0.184857
$293$	18.4722	1.07916	0.539578	−	0.841935i	$-0.318584\pi$
$293$	18.4722	1.07916	0.539578	+	0.841935i	$0.318584\pi$
$294$	−1.44504	−0.0842766
$295$	−9.43296	−0.549208
$296$	4.74094	0.275561
$297$	−12.4252	−0.720983
$298$	7.62565	0.441742
$299$	0	0
$300$	−0.0706876	−0.00408115
$301$	−8.93900	−0.515235
$302$	−15.7463	−0.906099
$303$	−23.6819	−1.36049
$304$	−4.44504	−0.254941
$305$	−0.0489173	−0.00280100
$306$	7.30367	0.417523
$307$	−13.6286	−0.777827	−0.388913	−	0.921274i	$-0.627150\pi$
$307$	−13.6286	−0.777827	−0.388913	+	0.921274i	$0.627150\pi$
$308$	−2.19806	−0.125246
$309$	1.81594	0.103305
$310$	−11.1468	−0.633093
$311$	−10.5797	−0.599920	−0.299960	−	0.953952i	$-0.596973\pi$
$311$	−10.5797	−0.599920	−0.299960	+	0.953952i	$0.596973\pi$
$312$	0	0
$313$	−10.5187	−0.594553	−0.297276	−	0.954791i	$-0.596078\pi$
$313$	−10.5187	−0.594553	−0.297276	+	0.954791i	$0.596078\pi$
$314$	−12.1129	−0.683571
$315$	−2.04892	−0.115443
$316$	2.77479	0.156094
$317$	−29.1269	−1.63593	−0.817965	−	0.575268i	$-0.804898\pi$
$317$	−29.1269	−1.63593	−0.817965	+	0.575268i	$0.804898\pi$
$318$	−8.32736	−0.466975
$319$	18.5840	1.04051
$320$	2.24698	0.125610
$321$	15.4504	0.862358
$322$	−4.13706	−0.230550
$323$	35.6034	1.98103
$324$	−5.43296	−0.301831
$325$	0	0
$326$	1.01507	0.0562193
$327$	15.2209	0.841718
$328$	8.72886	0.481971
$329$	−0.472189	−0.0260326
$330$	7.13706	0.392882
$331$	−15.5670	−0.855642	−0.427821	−	0.903864i	$-0.640719\pi$
$331$	−15.5670	−0.855642	−0.427821	+	0.903864i	$0.640719\pi$
$332$	1.91723	0.105222
$333$	−4.32304	−0.236901
$334$	−10.5700	−0.578366
$335$	−14.9758	−0.818217
$336$	−1.44504	−0.0788335
$337$	−28.2368	−1.53816	−0.769079	−	0.639154i	$-0.779285\pi$
$337$	−28.2368	−1.53816	−0.769079	+	0.639154i	$0.779285\pi$
$338$	0	0
$339$	−19.7254	−1.07134
$340$	−17.9976	−0.976057
$341$	10.9041	0.590489
$342$	4.05323	0.219174
$343$	1.00000	0.0539949
$344$	−8.93900	−0.481959
$345$	13.4330	0.723206
$346$	12.1424	0.652782
$347$	8.38165	0.449951	0.224975	−	0.974364i	$-0.427770\pi$
$347$	8.38165	0.449951	0.224975	+	0.974364i	$0.427770\pi$
$348$	12.2174	0.654924
$349$	16.8810	0.903618	0.451809	−	0.892115i	$-0.350779\pi$
$349$	16.8810	0.903618	0.451809	+	0.892115i	$0.350779\pi$
$350$	0.0489173	0.00261474
$351$	0	0
$352$	−2.19806	−0.117157
$353$	12.6420	0.672868	0.336434	−	0.941707i	$-0.390779\pi$
$353$	12.6420	0.672868	0.336434	+	0.941707i	$0.390779\pi$
$354$	6.06638	0.322424
$355$	30.4916	1.61832
$356$	−9.72886	−0.515628
$357$	11.5743	0.612579
$358$	−23.5676	−1.24559
$359$	27.3870	1.44543	0.722716	−	0.691145i	$-0.242893\pi$
$359$	27.3870	1.44543	0.722716	+	0.691145i	$0.242893\pi$
$360$	−2.04892	−0.107987
$361$	0.758397	0.0399156
$362$	17.5254	0.921116
$363$	8.91377	0.467852
$364$	0	0
$365$	7.09783	0.371518
$366$	0.0314589	0.00164439
$367$	28.2204	1.47309	0.736547	−	0.676386i	$-0.236455\pi$
$367$	28.2204	1.47309	0.736547	+	0.676386i	$0.236455\pi$
$368$	−4.13706	−0.215659
$369$	−7.95944	−0.414352
$370$	10.6528	0.553812
$371$	5.76271	0.299185
$372$	7.16852	0.371671
$373$	14.0339	0.726645	0.363323	−	0.931663i	$-0.381642\pi$
$373$	14.0339	0.726645	0.363323	+	0.931663i	$0.381642\pi$
$374$	17.6058	0.910374
$375$	16.0761	0.830164
$376$	−0.472189	−0.0243513
$377$	0	0
$378$	5.65279	0.290748
$379$	−17.1075	−0.878754	−0.439377	−	0.898303i	$-0.644801\pi$
$379$	−17.1075	−0.878754	−0.439377	+	0.898303i	$0.644801\pi$
$380$	−9.98792	−0.512369
$381$	19.0151	0.974171
$382$	−22.7482	−1.16390
$383$	20.8509	1.06543	0.532714	−	0.846295i	$-0.321172\pi$
$383$	20.8509	1.06543	0.532714	+	0.846295i	$0.321172\pi$
$384$	−1.44504	−0.0737420
$385$	−4.93900	−0.251715
$386$	−24.1196	−1.22766
$387$	8.15106	0.414342
$388$	4.05861	0.206045
$389$	−24.9801	−1.26654	−0.633272	−	0.773929i	$-0.718289\pi$
$389$	−24.9801	−1.26654	−0.633272	+	0.773929i	$0.718289\pi$
$390$	0	0
$391$	33.1366	1.67579
$392$	1.00000	0.0505076
$393$	−25.1976	−1.27105
$394$	19.0127	0.957845
$395$	6.23490	0.313712
$396$	2.00431	0.100720
$397$	12.5321	0.628969	0.314485	−	0.949263i	$-0.398168\pi$
$397$	12.5321	0.628969	0.314485	+	0.949263i	$0.398168\pi$
$398$	17.6461	0.884518
$399$	6.42327	0.321566
$400$	0.0489173	0.00244587
$401$	20.5080	1.02412	0.512059	−	0.858950i	$-0.328883\pi$
$401$	20.5080	1.02412	0.512059	+	0.858950i	$0.328883\pi$
$402$	9.63102	0.480352
$403$	0	0
$404$	16.3884	0.815351
$405$	−12.2078	−0.606608
$406$	−8.45473	−0.419601
$407$	−10.4209	−0.516544
$408$	11.5743	0.573015
$409$	9.83446	0.486283	0.243141	−	0.969991i	$-0.421822\pi$
$409$	9.83446	0.486283	0.243141	+	0.969991i	$0.421822\pi$
$410$	19.6136	0.968645
$411$	11.0838	0.546725
$412$	−1.25667	−0.0619116
$413$	−4.19806	−0.206573
$414$	3.77240	0.185403
$415$	4.30798	0.211470
$416$	0	0
$417$	−7.20775	−0.352965
$418$	9.77048	0.477890
$419$	−30.9138	−1.51024	−0.755118	−	0.655589i	$-0.772421\pi$
$419$	−30.9138	−1.51024	−0.755118	+	0.655589i	$0.772421\pi$
$420$	−3.24698	−0.158436
$421$	15.3690	0.749038	0.374519	−	0.927219i	$-0.377808\pi$
$421$	15.3690	0.749038	0.374519	+	0.927219i	$0.377808\pi$
$422$	14.8213	0.721490
$423$	0.430567	0.0209349
$424$	5.76271	0.279862
$425$	−0.391813	−0.0190057
$426$	−19.6093	−0.950071
$427$	−0.0217703	−0.00105354
$428$	−10.6920	−0.516818
$429$	0	0
$430$	−20.0858	−0.968621
$431$	12.6703	0.610305	0.305152	−	0.952304i	$-0.401293\pi$
$431$	12.6703	0.610305	0.305152	+	0.952304i	$0.401293\pi$
$432$	5.65279	0.271970
$433$	32.2446	1.54958	0.774788	−	0.632221i	$-0.217857\pi$
$433$	32.2446	1.54958	0.774788	+	0.632221i	$0.217857\pi$
$434$	−4.96077	−0.238125
$435$	27.4523	1.31624
$436$	−10.5332	−0.504448
$437$	18.3894	0.879685
$438$	−4.56465	−0.218107
$439$	−4.28860	−0.204684	−0.102342	−	0.994749i	$-0.532634\pi$
$439$	−4.28860	−0.204684	−0.102342	+	0.994749i	$0.532634\pi$
$440$	−4.93900	−0.235458
$441$	−0.911854	−0.0434216
$442$	0	0
$443$	−3.29722	−0.156656	−0.0783279	−	0.996928i	$-0.524958\pi$
$443$	−3.29722	−0.156656	−0.0783279	+	0.996928i	$0.524958\pi$
$444$	−6.85086	−0.325127
$445$	−21.8605	−1.03629
$446$	5.40150	0.255769
$447$	−11.0194	−0.521199
$448$	1.00000	0.0472456
$449$	−19.2379	−0.907892	−0.453946	−	0.891029i	$-0.649984\pi$
$449$	−19.2379	−0.907892	−0.453946	+	0.891029i	$0.649984\pi$
$450$	−0.0446055	−0.00210272
$451$	−19.1866	−0.903460
$452$	13.6504	0.642061
$453$	22.7541	1.06908
$454$	−16.3327	−0.766533
$455$	0	0
$456$	6.42327	0.300797
$457$	−13.6146	−0.636865	−0.318433	−	0.947945i	$-0.603157\pi$
$457$	−13.6146	−0.636865	−0.318433	+	0.947945i	$0.603157\pi$
$458$	27.1105	1.26679
$459$	−45.2771	−2.11335
$460$	−9.29590	−0.433423
$461$	−12.1521	−0.565981	−0.282991	−	0.959123i	$-0.591327\pi$
$461$	−12.1521	−0.565981	−0.282991	+	0.959123i	$0.591327\pi$
$462$	3.17629	0.147774
$463$	−9.76032	−0.453600	−0.226800	−	0.973941i	$-0.572826\pi$
$463$	−9.76032	−0.453600	−0.226800	+	0.973941i	$0.572826\pi$
$464$	−8.45473	−0.392501
$465$	16.1075	0.746969
$466$	19.2403	0.891289
$467$	−20.8562	−0.965111	−0.482556	−	0.875865i	$-0.660291\pi$
$467$	−20.8562	−0.965111	−0.482556	+	0.875865i	$0.660291\pi$
$468$	0	0
$469$	−6.66487	−0.307755
$470$	−1.06100	−0.0489402
$471$	17.5036	0.806526
$472$	−4.19806	−0.193231
$473$	19.6485	0.903438
$474$	−4.00969	−0.184171
$475$	−0.217440	−0.00997681
$476$	−8.00969	−0.367123
$477$	−5.25475	−0.240598
$478$	−18.6601	−0.853493
$479$	−0.140047	−0.00639892	−0.00319946	−	0.999995i	$-0.501018\pi$
$479$	−0.140047	−0.00639892	−0.00319946	+	0.999995i	$0.501018\pi$
$480$	−3.24698	−0.148204
$481$	0	0
$482$	−21.0489	−0.958752
$483$	5.97823	0.272019
$484$	−6.16852	−0.280387
$485$	9.11960	0.414100
$486$	−9.10752	−0.413126
$487$	33.0930	1.49959	0.749795	−	0.661671i	$-0.230152\pi$
$487$	33.0930	1.49959	0.749795	+	0.661671i	$0.230152\pi$
$488$	−0.0217703	−0.000985494 0
$489$	−1.46681	−0.0663315
$490$	2.24698	0.101508
$491$	−22.6353	−1.02152	−0.510759	−	0.859724i	$-0.670636\pi$
$491$	−22.6353	−1.02152	−0.510759	+	0.859724i	$0.670636\pi$
$492$	−12.6136	−0.568663
$493$	67.7198	3.04994
$494$	0	0
$495$	4.50365	0.202424
$496$	−4.96077	−0.222745
$497$	13.5700	0.608699
$498$	−2.77048	−0.124148
$499$	−44.4456	−1.98966	−0.994830	−	0.101555i	$-0.967618\pi$
$499$	−44.4456	−1.98966	−0.994830	+	0.101555i	$0.967618\pi$
$500$	−11.1250	−0.497524
$501$	15.2741	0.682398
$502$	−13.5646	−0.605420
$503$	14.0180	0.625034	0.312517	−	0.949912i	$-0.398828\pi$
$503$	14.0180	0.625034	0.312517	+	0.949912i	$0.398828\pi$
$504$	−0.911854	−0.0406172
$505$	36.8243	1.63866
$506$	9.09352	0.404256
$507$	0	0
$508$	−13.1588	−0.583829
$509$	22.2107	0.984474	0.492237	−	0.870461i	$-0.336179\pi$
$509$	22.2107	0.984474	0.492237	+	0.870461i	$0.336179\pi$
$510$	26.0073	1.15162
$511$	3.15883	0.139739
$512$	1.00000	0.0441942
$513$	−25.1269	−1.10938
$514$	2.14914	0.0947947
$515$	−2.82371	−0.124427
$516$	12.9172	0.568649
$517$	1.03790	0.0456468
$518$	4.74094	0.208305
$519$	−17.5463	−0.770199
$520$	0	0
$521$	−28.0834	−1.23035	−0.615177	−	0.788389i	$-0.710916\pi$
$521$	−28.0834	−1.23035	−0.615177	+	0.788389i	$0.710916\pi$
$522$	7.70948	0.337435
$523$	31.6655	1.38463	0.692317	−	0.721593i	$-0.256590\pi$
$523$	31.6655	1.38463	0.692317	+	0.721593i	$0.256590\pi$
$524$	17.4373	0.761751
$525$	−0.0706876	−0.00308506
$526$	21.1129	0.920566
$527$	39.7342	1.73085
$528$	3.17629	0.138230
$529$	−5.88471	−0.255857
$530$	12.9487	0.562455
$531$	3.82802	0.166122
$532$	−4.44504	−0.192717
$533$	0	0
$534$	14.0586	0.608375
$535$	−24.0248	−1.03868
$536$	−6.66487	−0.287879
$537$	34.0562	1.46963
$538$	17.4711	0.753234
$539$	−2.19806	−0.0946772
$540$	12.7017	0.546595
$541$	−1.30260	−0.0560032	−0.0280016	−	0.999608i	$-0.508914\pi$
$541$	−1.30260	−0.0560032	−0.0280016	+	0.999608i	$0.508914\pi$
$542$	−24.7222	−1.06191
$543$	−25.3250	−1.08680
$544$	−8.00969	−0.343413
$545$	−23.6679	−1.01382
$546$	0	0
$547$	−14.2808	−0.610604	−0.305302	−	0.952256i	$-0.598757\pi$
$547$	−14.2808	−0.610604	−0.305302	+	0.952256i	$0.598757\pi$
$548$	−7.67025	−0.327657
$549$	0.0198513	0.000847233 0
$550$	−0.107523	−0.00458481
$551$	37.5816	1.60103
$552$	5.97823	0.254450
$553$	2.77479	0.117996
$554$	−13.3502	−0.567195
$555$	−15.3937	−0.653428
$556$	4.98792	0.211535
$557$	26.0127	1.10219	0.551096	−	0.834442i	$-0.314210\pi$
$557$	26.0127	1.10219	0.551096	+	0.834442i	$0.314210\pi$
$558$	4.52350	0.191495
$559$	0	0
$560$	2.24698	0.0949522
$561$	−25.4411	−1.07412
$562$	−6.91185	−0.291559
$563$	−15.2916	−0.644463	−0.322232	−	0.946661i	$-0.604433\pi$
$563$	−15.2916	−0.644463	−0.322232	+	0.946661i	$0.604433\pi$
$564$	0.682333	0.0287314
$565$	30.6722	1.29039
$566$	1.53989	0.0647265
$567$	−5.43296	−0.228163
$568$	13.5700	0.569386
$569$	29.2924	1.22800	0.614001	−	0.789305i	$-0.289559\pi$
$569$	29.2924	1.22800	0.614001	+	0.789305i	$0.289559\pi$
$570$	14.4330	0.604530
$571$	−35.9560	−1.50471	−0.752356	−	0.658757i	$-0.771082\pi$
$571$	−35.9560	−1.50471	−0.752356	+	0.658757i	$0.771082\pi$
$572$	0	0
$573$	32.8722	1.37325
$574$	8.72886	0.364335
$575$	−0.202374	−0.00843958
$576$	−0.911854	−0.0379939
$577$	16.5840	0.690402	0.345201	−	0.938529i	$-0.387811\pi$
$577$	16.5840	0.690402	0.345201	+	0.938529i	$0.387811\pi$
$578$	47.1551	1.96139
$579$	34.8538	1.44848
$580$	−18.9976	−0.788833
$581$	1.91723	0.0795401
$582$	−5.86486	−0.243106
$583$	−12.6668	−0.524605
$584$	3.15883	0.130713
$585$	0	0
$586$	18.4722	0.763079
$587$	9.86592	0.407210	0.203605	−	0.979053i	$-0.434734\pi$
$587$	9.86592	0.407210	0.203605	+	0.979053i	$0.434734\pi$
$588$	−1.44504	−0.0595925
$589$	22.0508	0.908589
$590$	−9.43296	−0.388349
$591$	−27.4741	−1.13013
$592$	4.74094	0.194851
$593$	4.57971	0.188066	0.0940331	−	0.995569i	$-0.470024\pi$
$593$	4.57971	0.188066	0.0940331	+	0.995569i	$0.470024\pi$
$594$	−12.4252	−0.509812
$595$	−17.9976	−0.737830
$596$	7.62565	0.312359
$597$	−25.4993	−1.04362
$598$	0	0
$599$	27.6980	1.13171	0.565855	−	0.824505i	$-0.308546\pi$
$599$	27.6980	1.13171	0.565855	+	0.824505i	$0.308546\pi$
$600$	−0.0706876	−0.00288581
$601$	−11.4534	−0.467194	−0.233597	−	0.972333i	$-0.575050\pi$
$601$	−11.4534	−0.467194	−0.233597	+	0.972333i	$0.575050\pi$
$602$	−8.93900	−0.364326
$603$	6.07739	0.247491
$604$	−15.7463	−0.640708
$605$	−13.8605	−0.563511
$606$	−23.6819	−0.962010
$607$	2.90887	0.118067	0.0590337	−	0.998256i	$-0.481198\pi$
$607$	2.90887	0.118067	0.0590337	+	0.998256i	$0.481198\pi$
$608$	−4.44504	−0.180270
$609$	12.2174	0.495076
$610$	−0.0489173	−0.00198061
$611$	0	0
$612$	7.30367	0.295233
$613$	−19.9530	−0.805894	−0.402947	−	0.915223i	$-0.632014\pi$
$613$	−19.9530	−0.805894	−0.402947	+	0.915223i	$0.632014\pi$
$614$	−13.6286	−0.550007
$615$	−28.3424	−1.14288
$616$	−2.19806	−0.0885625
$617$	6.69873	0.269681	0.134840	−	0.990867i	$-0.456948\pi$
$617$	6.69873	0.269681	0.134840	+	0.990867i	$0.456948\pi$
$618$	1.81594	0.0730478
$619$	0.863528	0.0347081	0.0173541	−	0.999849i	$-0.494476\pi$
$619$	0.863528	0.0347081	0.0173541	+	0.999849i	$0.494476\pi$
$620$	−11.1468	−0.447664
$621$	−23.3860	−0.938446
$622$	−10.5797	−0.424208
$623$	−9.72886	−0.389778
$624$	0	0
$625$	−25.2422	−1.00969
$626$	−10.5187	−0.420412
$627$	−14.1188	−0.563849
$628$	−12.1129	−0.483357
$629$	−37.9734	−1.51410
$630$	−2.04892	−0.0816308
$631$	41.2261	1.64118	0.820592	−	0.571515i	$-0.193644\pi$
$631$	41.2261	1.64118	0.820592	+	0.571515i	$0.193644\pi$
$632$	2.77479	0.110375
$633$	−21.4174	−0.851266
$634$	−29.1269	−1.15678
$635$	−29.5676	−1.17336
$636$	−8.32736	−0.330201
$637$	0	0
$638$	18.5840	0.735749
$639$	−12.3739	−0.489503
$640$	2.24698	0.0888197
$641$	15.7423	0.621782	0.310891	−	0.950446i	$-0.399373\pi$
$641$	15.7423	0.621782	0.310891	+	0.950446i	$0.399373\pi$
$642$	15.4504	0.609779
$643$	5.75361	0.226900	0.113450	−	0.993544i	$-0.463810\pi$
$643$	5.75361	0.226900	0.113450	+	0.993544i	$0.463810\pi$
$644$	−4.13706	−0.163023
$645$	29.0248	1.14285
$646$	35.6034	1.40080
$647$	44.1323	1.73502	0.867509	−	0.497421i	$-0.165719\pi$
$647$	44.1323	1.73502	0.867509	+	0.497421i	$0.165719\pi$
$648$	−5.43296	−0.213427
$649$	9.22760	0.362215
$650$	0	0
$651$	7.16852	0.280957
$652$	1.01507	0.0397530
$653$	22.4601	0.878932	0.439466	−	0.898259i	$-0.355168\pi$
$653$	22.4601	0.878932	0.439466	+	0.898259i	$0.355168\pi$
$654$	15.2209	0.595184
$655$	39.1812	1.53094
$656$	8.72886	0.340805
$657$	−2.88040	−0.112375
$658$	−0.472189	−0.0184078
$659$	−8.25560	−0.321593	−0.160796	−	0.986988i	$-0.551406\pi$
$659$	−8.25560	−0.321593	−0.160796	+	0.986988i	$0.551406\pi$
$660$	7.13706	0.277810
$661$	−7.81163	−0.303837	−0.151919	−	0.988393i	$-0.548545\pi$
$661$	−7.81163	−0.303837	−0.151919	+	0.988393i	$0.548545\pi$
$662$	−15.5670	−0.605030
$663$	0	0
$664$	1.91723	0.0744030
$665$	−9.98792	−0.387315
$666$	−4.32304	−0.167515
$667$	34.9778	1.35434
$668$	−10.5700	−0.408966
$669$	−7.80540	−0.301774
$670$	−14.9758	−0.578567
$671$	0.0478524	0.00184732
$672$	−1.44504	−0.0557437
$673$	−41.7157	−1.60802	−0.804011	−	0.594614i	$-0.797305\pi$
$673$	−41.7157	−1.60802	−0.804011	+	0.594614i	$0.797305\pi$
$674$	−28.2368	−1.08764
$675$	0.276520	0.0106432
$676$	0	0
$677$	−29.7603	−1.14378	−0.571891	−	0.820330i	$-0.693790\pi$
$677$	−29.7603	−1.14378	−0.571891	+	0.820330i	$0.693790\pi$
$678$	−19.7254	−0.757549
$679$	4.05861	0.155755
$680$	−17.9976	−0.690177
$681$	23.6015	0.904411
$682$	10.9041	0.417539
$683$	−15.9323	−0.609632	−0.304816	−	0.952411i	$-0.598595\pi$
$683$	−15.9323	−0.609632	−0.304816	+	0.952411i	$0.598595\pi$
$684$	4.05323	0.154979
$685$	−17.2349	−0.658512
$686$	1.00000	0.0381802
$687$	−39.1758	−1.49465
$688$	−8.93900	−0.340796
$689$	0	0
$690$	13.4330	0.511384
$691$	−13.9855	−0.532034	−0.266017	−	0.963968i	$-0.585708\pi$
$691$	−13.9855	−0.532034	−0.266017	+	0.963968i	$0.585708\pi$
$692$	12.1424	0.461586
$693$	2.00431	0.0761375
$694$	8.38165	0.318163
$695$	11.2078	0.425134
$696$	12.2174	0.463101
$697$	−69.9154	−2.64824
$698$	16.8810	0.638955
$699$	−27.8030	−1.05161
$700$	0.0489173	0.00184890
$701$	−4.52542	−0.170923	−0.0854613	−	0.996341i	$-0.527236\pi$
$701$	−4.52542	−0.170923	−0.0854613	+	0.996341i	$0.527236\pi$
$702$	0	0
$703$	−21.0737	−0.794809
$704$	−2.19806	−0.0828426
$705$	1.53319	0.0577432
$706$	12.6420	0.475789
$707$	16.3884	0.616348
$708$	6.06638	0.227988
$709$	−9.15751	−0.343917	−0.171959	−	0.985104i	$-0.555010\pi$
$709$	−9.15751	−0.343917	−0.171959	+	0.985104i	$0.555010\pi$
$710$	30.4916	1.14433
$711$	−2.53020	−0.0948901
$712$	−9.72886	−0.364604
$713$	20.5230	0.768593
$714$	11.5743	0.433159
$715$	0	0
$716$	−23.5676	−0.880764
$717$	26.9646	1.00701
$718$	27.3870	1.02207
$719$	−3.00670	−0.112131	−0.0560656	−	0.998427i	$-0.517856\pi$
$719$	−3.00670	−0.112131	−0.0560656	+	0.998427i	$0.517856\pi$
$720$	−2.04892	−0.0763586
$721$	−1.25667	−0.0468008
$722$	0.758397	0.0282246
$723$	30.4166	1.13120
$724$	17.5254	0.651327
$725$	−0.413583	−0.0153601
$726$	8.91377	0.330821
$727$	−34.0890	−1.26429	−0.632146	−	0.774850i	$-0.717826\pi$
$727$	−34.0890	−1.26429	−0.632146	+	0.774850i	$0.717826\pi$
$728$	0	0
$729$	29.4596	1.09110
$730$	7.09783	0.262703
$731$	71.5986	2.64817
$732$	0.0314589	0.00116276
$733$	−3.17821	−0.117390	−0.0586950	−	0.998276i	$-0.518694\pi$
$733$	−3.17821	−0.117390	−0.0586950	+	0.998276i	$0.518694\pi$
$734$	28.2204	1.04163
$735$	−3.24698	−0.119767
$736$	−4.13706	−0.152494
$737$	14.6498	0.539633
$738$	−7.95944	−0.292991
$739$	−46.9487	−1.72704	−0.863518	−	0.504318i	$-0.831744\pi$
$739$	−46.9487	−1.72704	−0.863518	+	0.504318i	$0.831744\pi$
$740$	10.6528	0.391604
$741$	0	0
$742$	5.76271	0.211556
$743$	−16.9565	−0.622072	−0.311036	−	0.950398i	$-0.600676\pi$
$743$	−16.9565	−0.622072	−0.311036	+	0.950398i	$0.600676\pi$
$744$	7.16852	0.262811
$745$	17.1347	0.627766
$746$	14.0339	0.513816
$747$	−1.74823	−0.0639646
$748$	17.6058	0.643732
$749$	−10.6920	−0.390678
$750$	16.0761	0.587015
$751$	1.31336	0.0479250	0.0239625	−	0.999713i	$-0.492372\pi$
$751$	1.31336	0.0479250	0.0239625	+	0.999713i	$0.492372\pi$
$752$	−0.472189	−0.0172190
$753$	19.6015	0.714318
$754$	0	0
$755$	−35.3817	−1.28767
$756$	5.65279	0.205590
$757$	−15.2929	−0.555830	−0.277915	−	0.960606i	$-0.589643\pi$
$757$	−15.2929	−0.555830	−0.277915	+	0.960606i	$0.589643\pi$
$758$	−17.1075	−0.621373
$759$	−13.1405	−0.476971
$760$	−9.98792	−0.362300
$761$	−34.0465	−1.23419	−0.617093	−	0.786890i	$-0.711690\pi$
$761$	−34.0465	−1.23419	−0.617093	+	0.786890i	$0.711690\pi$
$762$	19.0151	0.688843
$763$	−10.5332	−0.381327
$764$	−22.7482	−0.823002
$765$	16.4112	0.593348
$766$	20.8509	0.753372
$767$	0	0
$768$	−1.44504	−0.0521435
$769$	−46.5284	−1.67786	−0.838929	−	0.544242i	$-0.816817\pi$
$769$	−46.5284	−1.67786	−0.838929	+	0.544242i	$0.816817\pi$
$770$	−4.93900	−0.177989
$771$	−3.10560	−0.111846
$772$	−24.1196	−0.868084
$773$	−9.62624	−0.346232	−0.173116	−	0.984901i	$-0.555383\pi$
$773$	−9.62624	−0.346232	−0.173116	+	0.984901i	$0.555383\pi$
$774$	8.15106	0.292984
$775$	−0.242668	−0.00871688
$776$	4.05861	0.145695
$777$	−6.85086	−0.245773
$778$	−24.9801	−0.895582
$779$	−38.8001	−1.39016
$780$	0	0
$781$	−29.8278	−1.06732
$782$	33.1366	1.18496
$783$	−47.7928	−1.70798
$784$	1.00000	0.0357143
$785$	−27.2174	−0.971432
$786$	−25.1976	−0.898768
$787$	−31.6420	−1.12792	−0.563958	−	0.825803i	$-0.690722\pi$
$787$	−31.6420	−1.12792	−0.563958	+	0.825803i	$0.690722\pi$
$788$	19.0127	0.677298
$789$	−30.5090	−1.08615
$790$	6.23490	0.221828
$791$	13.6504	0.485352
$792$	2.00431	0.0712201
$793$	0	0
$794$	12.5321	0.444748
$795$	−18.7114	−0.663625
$796$	17.6461	0.625449
$797$	−49.7603	−1.76260	−0.881300	−	0.472556i	$-0.843331\pi$
$797$	−49.7603	−1.76260	−0.881300	+	0.472556i	$0.843331\pi$
$798$	6.42327	0.227381
$799$	3.78209	0.133801
$800$	0.0489173	0.00172949
$801$	8.87130	0.313452
$802$	20.5080	0.724161
$803$	−6.94331	−0.245024
$804$	9.63102	0.339660
$805$	−9.29590	−0.327637
$806$	0	0
$807$	−25.2465	−0.888719
$808$	16.3884	0.576540
$809$	−23.3303	−0.820251	−0.410126	−	0.912029i	$-0.634515\pi$
$809$	−23.3303	−0.820251	−0.410126	+	0.912029i	$0.634515\pi$
$810$	−12.2078	−0.428937
$811$	41.4922	1.45699	0.728493	−	0.685053i	$-0.240221\pi$
$811$	41.4922	1.45699	0.728493	+	0.685053i	$0.240221\pi$
$812$	−8.45473	−0.296703
$813$	35.7245	1.25291
$814$	−10.4209	−0.365252
$815$	2.28083	0.0798940
$816$	11.5743	0.405183
$817$	39.7342	1.39012
$818$	9.83446	0.343854
$819$	0	0
$820$	19.6136	0.684935
$821$	17.5375	0.612063	0.306031	−	0.952021i	$-0.400999\pi$
$821$	17.5375	0.612063	0.306031	+	0.952021i	$0.400999\pi$
$822$	11.0838	0.386593
$823$	−28.3752	−0.989098	−0.494549	−	0.869150i	$-0.664667\pi$
$823$	−28.3752	−0.989098	−0.494549	+	0.869150i	$0.664667\pi$
$824$	−1.25667	−0.0437781
$825$	0.155376	0.00540949
$826$	−4.19806	−0.146069
$827$	−33.0863	−1.15052	−0.575262	−	0.817969i	$-0.695100\pi$
$827$	−33.0863	−1.15052	−0.575262	+	0.817969i	$0.695100\pi$
$828$	3.77240	0.131100
$829$	−19.2519	−0.668646	−0.334323	−	0.942459i	$-0.608508\pi$
$829$	−19.2519	−0.668646	−0.334323	+	0.942459i	$0.608508\pi$
$830$	4.30798	0.149532
$831$	19.2916	0.669218
$832$	0	0
$833$	−8.00969	−0.277519
$834$	−7.20775	−0.249584
$835$	−23.7506	−0.821924
$836$	9.77048	0.337919
$837$	−28.0422	−0.969281
$838$	−30.9138	−1.06790
$839$	−34.9541	−1.20675	−0.603374	−	0.797458i	$-0.706177\pi$
$839$	−34.9541	−1.20675	−0.603374	+	0.797458i	$0.706177\pi$
$840$	−3.24698	−0.112031
$841$	42.4825	1.46491
$842$	15.3690	0.529650
$843$	9.98792	0.344002
$844$	14.8213	0.510171
$845$	0	0
$846$	0.430567	0.0148032
$847$	−6.16852	−0.211953
$848$	5.76271	0.197892
$849$	−2.22521	−0.0763690
$850$	−0.391813	−0.0134391
$851$	−19.6136	−0.672344
$852$	−19.6093	−0.671802
$853$	−31.4849	−1.07802	−0.539011	−	0.842299i	$-0.681202\pi$
$853$	−31.4849	−1.07802	−0.539011	+	0.842299i	$0.681202\pi$
$854$	−0.0217703	−0.000744963 0
$855$	9.10752	0.311471
$856$	−10.6920	−0.365446
$857$	37.9939	1.29785	0.648923	−	0.760854i	$-0.275220\pi$
$857$	37.9939	1.29785	0.648923	+	0.760854i	$0.275220\pi$
$858$	0	0
$859$	−45.4034	−1.54914	−0.774572	−	0.632485i	$-0.782035\pi$
$859$	−45.4034	−1.54914	−0.774572	+	0.632485i	$0.782035\pi$
$860$	−20.0858	−0.684918
$861$	−12.6136	−0.429869
$862$	12.6703	0.431550
$863$	−24.0388	−0.818289	−0.409144	−	0.912470i	$-0.634173\pi$
$863$	−24.0388	−0.818289	−0.409144	+	0.912470i	$0.634173\pi$
$864$	5.65279	0.192312
$865$	27.2838	0.927678
$866$	32.2446	1.09572
$867$	−68.1411	−2.31419
$868$	−4.96077	−0.168380
$869$	−6.09916	−0.206900
$870$	27.4523	0.930721
$871$	0	0
$872$	−10.5332	−0.356699
$873$	−3.70086	−0.125255
$874$	18.3894	0.622031
$875$	−11.1250	−0.376093
$876$	−4.56465	−0.154225
$877$	12.2101	0.412307	0.206154	−	0.978520i	$-0.433905\pi$
$877$	12.2101	0.412307	0.206154	+	0.978520i	$0.433905\pi$
$878$	−4.28860	−0.144733
$879$	−26.6931	−0.900335
$880$	−4.93900	−0.166494
$881$	33.7036	1.13550	0.567752	−	0.823200i	$-0.307813\pi$
$881$	33.7036	1.13550	0.567752	+	0.823200i	$0.307813\pi$
$882$	−0.911854	−0.0307037
$883$	−7.31096	−0.246033	−0.123017	−	0.992405i	$-0.539257\pi$
$883$	−7.31096	−0.246033	−0.123017	+	0.992405i	$0.539257\pi$
$884$	0	0
$885$	13.6310	0.458202
$886$	−3.29722	−0.110772
$887$	−1.55927	−0.0523552	−0.0261776	−	0.999657i	$-0.508334\pi$
$887$	−1.55927	−0.0523552	−0.0261776	+	0.999657i	$0.508334\pi$
$888$	−6.85086	−0.229900
$889$	−13.1588	−0.441333
$890$	−21.8605	−0.732767
$891$	11.9420	0.400072
$892$	5.40150	0.180856
$893$	2.09890	0.0702370
$894$	−11.0194	−0.368543
$895$	−52.9560	−1.77012
$896$	1.00000	0.0334077
$897$	0	0
$898$	−19.2379	−0.641976
$899$	41.9420	1.39884
$900$	−0.0446055	−0.00148685
$901$	−46.1575	−1.53773
$902$	−19.1866	−0.638843
$903$	12.9172	0.429859
$904$	13.6504	0.454006
$905$	39.3793	1.30901
$906$	22.7541	0.755954
$907$	48.0404	1.59516	0.797578	−	0.603216i	$-0.206114\pi$
$907$	48.0404	1.59516	0.797578	+	0.603216i	$0.206114\pi$
$908$	−16.3327	−0.542021
$909$	−14.9438	−0.495654
$910$	0	0
$911$	34.4336	1.14083	0.570417	−	0.821355i	$-0.306782\pi$
$911$	34.4336	1.14083	0.570417	+	0.821355i	$0.306782\pi$
$912$	6.42327	0.212696
$913$	−4.21419	−0.139469
$914$	−13.6146	−0.450332
$915$	0.0706876	0.00233686
$916$	27.1105	0.895756
$917$	17.4373	0.575829
$918$	−45.2771	−1.49437
$919$	4.11423	0.135716	0.0678579	−	0.997695i	$-0.478384\pi$
$919$	4.11423	0.135716	0.0678579	+	0.997695i	$0.478384\pi$
$920$	−9.29590	−0.306477
$921$	19.6939	0.648937
$922$	−12.1521	−0.400209
$923$	0	0
$924$	3.17629	0.104492
$925$	0.231914	0.00762529
$926$	−9.76032	−0.320744
$927$	1.14590	0.0376362
$928$	−8.45473	−0.277540
$929$	−37.9148	−1.24395	−0.621973	−	0.783039i	$-0.713669\pi$
$929$	−37.9148	−1.24395	−0.621973	+	0.783039i	$0.713669\pi$
$930$	16.1075	0.528186
$931$	−4.44504	−0.145680
$932$	19.2403	0.630236
$933$	15.2881	0.500511
$934$	−20.8562	−0.682437
$935$	39.5599	1.29375
$936$	0	0
$937$	−16.3618	−0.534517	−0.267258	−	0.963625i	$-0.586118\pi$
$937$	−16.3618	−0.534517	−0.267258	+	0.963625i	$0.586118\pi$
$938$	−6.66487	−0.217616
$939$	15.2000	0.496033
$940$	−1.06100	−0.0346060
$941$	−3.51275	−0.114512	−0.0572561	−	0.998360i	$-0.518235\pi$
$941$	−3.51275	−0.114512	−0.0572561	+	0.998360i	$0.518235\pi$
$942$	17.5036	0.570300
$943$	−36.1118	−1.17596
$944$	−4.19806	−0.136635
$945$	12.7017	0.413187
$946$	19.6485	0.638827
$947$	−17.0616	−0.554427	−0.277214	−	0.960808i	$-0.589411\pi$
$947$	−17.0616	−0.554427	−0.277214	+	0.960808i	$0.589411\pi$
$948$	−4.00969	−0.130229
$949$	0	0
$950$	−0.217440	−0.00705467
$951$	42.0896	1.36485
$952$	−8.00969	−0.259596
$953$	43.9463	1.42356	0.711780	−	0.702402i	$-0.247889\pi$
$953$	43.9463	1.42356	0.711780	+	0.702402i	$0.247889\pi$
$954$	−5.25475	−0.170129
$955$	−51.1148	−1.65404
$956$	−18.6601	−0.603510
$957$	−26.8547	−0.868089
$958$	−0.140047	−0.00452472
$959$	−7.67025	−0.247685
$960$	−3.24698	−0.104796
$961$	−6.39075	−0.206153
$962$	0	0
$963$	9.74956	0.314175
$964$	−21.0489	−0.677940
$965$	−54.1963	−1.74464
$966$	5.97823	0.192346
$967$	36.2898	1.16700	0.583500	−	0.812113i	$-0.301683\pi$
$967$	36.2898	1.16700	0.583500	+	0.812113i	$0.301683\pi$
$968$	−6.16852	−0.198264
$969$	−51.4484	−1.65276
$970$	9.11960	0.292813
$971$	−18.0718	−0.579950	−0.289975	−	0.957034i	$-0.593647\pi$
$971$	−18.0718	−0.579950	−0.289975	+	0.957034i	$0.593647\pi$
$972$	−9.10752	−0.292124
$973$	4.98792	0.159905
$974$	33.0930	1.06037
$975$	0	0
$976$	−0.0217703	−0.000696849 0
$977$	11.2306	0.359298	0.179649	−	0.983731i	$-0.442504\pi$
$977$	11.2306	0.359298	0.179649	+	0.983731i	$0.442504\pi$
$978$	−1.46681	−0.0469035
$979$	21.3846	0.683456
$980$	2.24698	0.0717771
$981$	9.60473	0.306655
$982$	−22.6353	−0.722323
$983$	13.6364	0.434934	0.217467	−	0.976068i	$-0.430221\pi$
$983$	13.6364	0.434934	0.217467	+	0.976068i	$0.430221\pi$
$984$	−12.6136	−0.402106
$985$	42.7211	1.36121
$986$	67.7198	2.15664
$987$	0.682333	0.0217189
$988$	0	0
$989$	36.9812	1.17593
$990$	4.50365	0.143135
$991$	−4.51248	−0.143344	−0.0716719	−	0.997428i	$-0.522833\pi$
$991$	−4.51248	−0.143344	−0.0716719	+	0.997428i	$0.522833\pi$
$992$	−4.96077	−0.157505
$993$	22.4950	0.713858
$994$	13.5700	0.430415
$995$	39.6504	1.25700
$996$	−2.77048	−0.0877860
$997$	−24.5271	−0.776780	−0.388390	−	0.921495i	$-0.626969\pi$
$997$	−24.5271	−0.776780	−0.388390	+	0.921495i	$0.626969\pi$
$998$	−44.4456	−1.40690
$999$	26.7995	0.847900

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2366.2.a.ba.1.2	yes	3
13.5	odd	4		2366.2.d.n.337.2		6
13.8	odd	4		2366.2.d.n.337.5		6
13.12	even	2		2366.2.a.v.1.2	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2366.2.a.v.1.2	✓	3	13.12	even	2
2366.2.a.ba.1.2	yes	3	1.1	even	1	trivial
2366.2.d.n.337.2		6	13.5	odd	4
2366.2.d.n.337.5		6	13.8	odd	4

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:	\( N \)	\(=\)	\( 2366 = 2 \cdot 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2366.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.44504 q^{3} +1.00000 q^{4} +2.24698 q^{5} -1.44504 q^{6} +1.00000 q^{7} +1.00000 q^{8} -0.911854 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.44504 q^{3} +1.00000 q^{4} +2.24698 q^{5} -1.44504 q^{6} +1.00000 q^{7} +1.00000 q^{8} -0.911854 q^{9} +2.24698 q^{10} -2.19806 q^{11} -1.44504 q^{12} +1.00000 q^{14} -3.24698 q^{15} +1.00000 q^{16} -8.00969 q^{17} -0.911854 q^{18} -4.44504 q^{19} +2.24698 q^{20} -1.44504 q^{21} -2.19806 q^{22} -4.13706 q^{23} -1.44504 q^{24} +0.0489173 q^{25} +5.65279 q^{27} +1.00000 q^{28} -8.45473 q^{29} -3.24698 q^{30} -4.96077 q^{31} +1.00000 q^{32} +3.17629 q^{33} -8.00969 q^{34} +2.24698 q^{35} -0.911854 q^{36} +4.74094 q^{37} -4.44504 q^{38} +2.24698 q^{40} +8.72886 q^{41} -1.44504 q^{42} -8.93900 q^{43} -2.19806 q^{44} -2.04892 q^{45} -4.13706 q^{46} -0.472189 q^{47} -1.44504 q^{48} +1.00000 q^{49} +0.0489173 q^{50} +11.5743 q^{51} +5.76271 q^{53} +5.65279 q^{54} -4.93900 q^{55} +1.00000 q^{56} +6.42327 q^{57} -8.45473 q^{58} -4.19806 q^{59} -3.24698 q^{60} -0.0217703 q^{61} -4.96077 q^{62} -0.911854 q^{63} +1.00000 q^{64} +3.17629 q^{66} -6.66487 q^{67} -8.00969 q^{68} +5.97823 q^{69} +2.24698 q^{70} +13.5700 q^{71} -0.911854 q^{72} +3.15883 q^{73} +4.74094 q^{74} -0.0706876 q^{75} -4.44504 q^{76} -2.19806 q^{77} +2.77479 q^{79} +2.24698 q^{80} -5.43296 q^{81} +8.72886 q^{82} +1.91723 q^{83} -1.44504 q^{84} -17.9976 q^{85} -8.93900 q^{86} +12.2174 q^{87} -2.19806 q^{88} -9.72886 q^{89} -2.04892 q^{90} -4.13706 q^{92} +7.16852 q^{93} -0.472189 q^{94} -9.98792 q^{95} -1.44504 q^{96} +4.05861 q^{97} +1.00000 q^{98} +2.00431 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} - 4 q^{3} + 3 q^{4} + 2 q^{5} - 4 q^{6} + 3 q^{7} + 3 q^{8} + q^{9}+O(q^{10}) \) 3 * q + 3 * q^2 - 4 * q^3 + 3 * q^4 + 2 * q^5 - 4 * q^6 + 3 * q^7 + 3 * q^8 + q^9	\( 3 q + 3 q^{2} - 4 q^{3} + 3 q^{4} + 2 q^{5} - 4 q^{6} + 3 q^{7} + 3 q^{8} + q^{9} + 2 q^{10} - 11 q^{11} - 4 q^{12} + 3 q^{14} - 5 q^{15} + 3 q^{16} - 2 q^{17} + q^{18} - 13 q^{19} + 2 q^{20} - 4 q^{21} - 11 q^{22} - 7 q^{23} - 4 q^{24} - 9 q^{25} - q^{27} + 3 q^{28} - 3 q^{29} - 5 q^{30} - 2 q^{31} + 3 q^{32} + 17 q^{33} - 2 q^{34} + 2 q^{35} + q^{36} - 13 q^{38} + 2 q^{40} - 7 q^{41} - 4 q^{42} - 17 q^{43} - 11 q^{44} + 3 q^{45} - 7 q^{46} + 5 q^{47} - 4 q^{48} + 3 q^{49} - 9 q^{50} - 9 q^{51} - q^{54} - 5 q^{55} + 3 q^{56} + 22 q^{57} - 3 q^{58} - 17 q^{59} - 5 q^{60} + 3 q^{61} - 2 q^{62} + q^{63} + 3 q^{64} + 17 q^{66} - 21 q^{67} - 2 q^{68} + 21 q^{69} + 2 q^{70} + 16 q^{71} + q^{72} + q^{73} + 12 q^{75} - 13 q^{76} - 11 q^{77} + 10 q^{79} + 2 q^{80} + 3 q^{81} - 7 q^{82} - q^{83} - 4 q^{84} - 13 q^{85} - 17 q^{86} - 3 q^{87} - 11 q^{88} + 4 q^{89} + 3 q^{90} - 7 q^{92} - 9 q^{93} + 5 q^{94} - 11 q^{95} - 4 q^{96} - 19 q^{97} + 3 q^{98} - 13 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 - 4 * q^3 + 3 * q^4 + 2 * q^5 - 4 * q^6 + 3 * q^7 + 3 * q^8 + q^9 + 2 * q^10 - 11 * q^11 - 4 * q^12 + 3 * q^14 - 5 * q^15 + 3 * q^16 - 2 * q^17 + q^18 - 13 * q^19 + 2 * q^20 - 4 * q^21 - 11 * q^22 - 7 * q^23 - 4 * q^24 - 9 * q^25 - q^27 + 3 * q^28 - 3 * q^29 - 5 * q^30 - 2 * q^31 + 3 * q^32 + 17 * q^33 - 2 * q^34 + 2 * q^35 + q^36 - 13 * q^38 + 2 * q^40 - 7 * q^41 - 4 * q^42 - 17 * q^43 - 11 * q^44 + 3 * q^45 - 7 * q^46 + 5 * q^47 - 4 * q^48 + 3 * q^49 - 9 * q^50 - 9 * q^51 - q^54 - 5 * q^55 + 3 * q^56 + 22 * q^57 - 3 * q^58 - 17 * q^59 - 5 * q^60 + 3 * q^61 - 2 * q^62 + q^63 + 3 * q^64 + 17 * q^66 - 21 * q^67 - 2 * q^68 + 21 * q^69 + 2 * q^70 + 16 * q^71 + q^72 + q^73 + 12 * q^75 - 13 * q^76 - 11 * q^77 + 10 * q^79 + 2 * q^80 + 3 * q^81 - 7 * q^82 - q^83 - 4 * q^84 - 13 * q^85 - 17 * q^86 - 3 * q^87 - 11 * q^88 + 4 * q^89 + 3 * q^90 - 7 * q^92 - 9 * q^93 + 5 * q^94 - 11 * q^95 - 4 * q^96 - 19 * q^97 + 3 * q^98 - 13 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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