LMFDB - Embedded newform 1859.2.a.i.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1859,2,Mod(1,1859)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1859, 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("1859.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1859 = 11 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1859.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:	$14.8441897358$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	4.4.1957.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 4x^{2} - x + 1 $ x^4 - 4*x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 143)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.06150$ of defining polynomial
Character	$\chi$	$=$	1859.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.57641 q^{2} -0.188279 q^{3} +4.63791 q^{4} +4.12300 q^{5} +0.485084 q^{6} -2.15845 q^{7} -6.79636 q^{8} -2.96455 q^{9} +O(q^{10})$	\(q-2.57641 q^{2} -0.188279 q^{3} +4.63791 q^{4} +4.12300 q^{5} +0.485084 q^{6} -2.15845 q^{7} -6.79636 q^{8} -2.96455 q^{9} -10.6226 q^{10} -1.00000 q^{11} -0.873220 q^{12} +5.56105 q^{14} -0.776272 q^{15} +8.23442 q^{16} -3.09317 q^{17} +7.63791 q^{18} +2.68783 q^{19} +19.1221 q^{20} +0.406389 q^{21} +2.57641 q^{22} +3.31128 q^{23} +1.27961 q^{24} +11.9991 q^{25} +1.12300 q^{27} -10.0107 q^{28} -3.34673 q^{29} +2.00000 q^{30} -9.96928 q^{31} -7.62255 q^{32} +0.188279 q^{33} +7.96928 q^{34} -8.89927 q^{35} -13.7493 q^{36} -2.05966 q^{37} -6.92497 q^{38} -28.0214 q^{40} -9.49394 q^{41} -1.04703 q^{42} +2.84717 q^{43} -4.63791 q^{44} -12.2228 q^{45} -8.53122 q^{46} +9.46972 q^{47} -1.55036 q^{48} -2.34111 q^{49} -30.9147 q^{50} +0.582377 q^{51} -5.34111 q^{53} -2.89331 q^{54} -4.12300 q^{55} +14.6696 q^{56} -0.506062 q^{57} +8.62255 q^{58} -4.62255 q^{59} -3.60028 q^{60} -0.193895 q^{61} +25.6850 q^{62} +6.39883 q^{63} +3.17003 q^{64} -0.485084 q^{66} +5.78662 q^{67} -14.3458 q^{68} -0.623443 q^{69} +22.9282 q^{70} +3.78295 q^{71} +20.1482 q^{72} -7.47534 q^{73} +5.30655 q^{74} -2.25918 q^{75} +12.4659 q^{76} +2.15845 q^{77} -17.2049 q^{79} +33.9505 q^{80} +8.68222 q^{81} +24.4603 q^{82} +0.218111 q^{83} +1.88480 q^{84} -12.7531 q^{85} -7.33549 q^{86} +0.630117 q^{87} +6.79636 q^{88} +1.52939 q^{89} +31.4911 q^{90} +15.3574 q^{92} +1.87700 q^{93} -24.3979 q^{94} +11.0819 q^{95} +1.43516 q^{96} -12.1462 q^{97} +6.03167 q^{98} +2.96455 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 3 q^{2} + 3 q^{4} + q^{6} - 6 q^{7} - 9 q^{8} + 2 q^{9}+O(q^{10}) $ 4 * q - 3 * q^2 + 3 * q^4 + q^6 - 6 * q^7 - 9 * q^8 + 2 * q^9	$ 4 q - 3 q^{2} + 3 q^{4} + q^{6} - 6 q^{7} - 9 q^{8} + 2 q^{9} - 8 q^{10} - 4 q^{11} + 4 q^{12} - 4 q^{14} + 10 q^{15} + 5 q^{16} + 6 q^{17} + 15 q^{18} - 8 q^{19} + 24 q^{20} + 2 q^{21} + 3 q^{22} - 4 q^{23} - 2 q^{24} + 12 q^{25} - 12 q^{27} + q^{28} - 10 q^{29} + 8 q^{30} - 2 q^{31} + 4 q^{32} - 6 q^{34} - 6 q^{35} - 28 q^{36} - 12 q^{37} - 5 q^{38} - 30 q^{40} - 8 q^{41} - 13 q^{42} + 26 q^{43} - 3 q^{44} - 26 q^{45} - 6 q^{46} + 18 q^{47} - 21 q^{48} + 6 q^{49} - 29 q^{50} - 22 q^{51} - 6 q^{53} + q^{54} + 33 q^{56} - 32 q^{57} + 16 q^{59} - 26 q^{60} - 12 q^{61} + 12 q^{62} - 22 q^{63} + 5 q^{64} - q^{66} - 2 q^{67} - 18 q^{68} - 4 q^{69} + 28 q^{70} + 14 q^{71} + 6 q^{72} - 22 q^{73} + 28 q^{74} - 36 q^{75} + 6 q^{76} + 6 q^{77} - 10 q^{79} + 26 q^{80} + 4 q^{81} + 42 q^{82} + 2 q^{83} - 5 q^{84} - 48 q^{85} - 2 q^{86} + 16 q^{87} + 9 q^{88} - 10 q^{89} + 24 q^{90} + 17 q^{92} + 24 q^{93} - 14 q^{94} + 2 q^{95} + 8 q^{96} - 22 q^{97} + 14 q^{98} - 2 q^{99}+O(q^{100}) $ 4 * q - 3 * q^2 + 3 * q^4 + q^6 - 6 * q^7 - 9 * q^8 + 2 * q^9 - 8 * q^10 - 4 * q^11 + 4 * q^12 - 4 * q^14 + 10 * q^15 + 5 * q^16 + 6 * q^17 + 15 * q^18 - 8 * q^19 + 24 * q^20 + 2 * q^21 + 3 * q^22 - 4 * q^23 - 2 * q^24 + 12 * q^25 - 12 * q^27 + q^28 - 10 * q^29 + 8 * q^30 - 2 * q^31 + 4 * q^32 - 6 * q^34 - 6 * q^35 - 28 * q^36 - 12 * q^37 - 5 * q^38 - 30 * q^40 - 8 * q^41 - 13 * q^42 + 26 * q^43 - 3 * q^44 - 26 * q^45 - 6 * q^46 + 18 * q^47 - 21 * q^48 + 6 * q^49 - 29 * q^50 - 22 * q^51 - 6 * q^53 + q^54 + 33 * q^56 - 32 * q^57 + 16 * q^59 - 26 * q^60 - 12 * q^61 + 12 * q^62 - 22 * q^63 + 5 * q^64 - q^66 - 2 * q^67 - 18 * q^68 - 4 * q^69 + 28 * q^70 + 14 * q^71 + 6 * q^72 - 22 * q^73 + 28 * q^74 - 36 * q^75 + 6 * q^76 + 6 * q^77 - 10 * q^79 + 26 * q^80 + 4 * q^81 + 42 * q^82 + 2 * q^83 - 5 * q^84 - 48 * q^85 - 2 * q^86 + 16 * q^87 + 9 * q^88 - 10 * q^89 + 24 * q^90 + 17 * q^92 + 24 * q^93 - 14 * q^94 + 2 * q^95 + 8 * q^96 - 22 * q^97 + 14 * q^98 - 2 * 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 $

$2$	−2.57641	−1.82180	−0.910900	−	0.412627i	$-0.864611\pi$
$2$	−2.57641	−1.82180	−0.910900	+	0.412627i	$0.864611\pi$
$3$	−0.188279	−0.108703	−0.0543514	−	0.998522i	$-0.517309\pi$
$3$	−0.188279	−0.108703	−0.0543514	+	0.998522i	$0.517309\pi$
$4$	4.63791	2.31896
$5$	4.12300	1.84386	0.921930	−	0.387356i	$-0.126611\pi$
$5$	4.12300	1.84386	0.921930	+	0.387356i	$0.126611\pi$
$6$	0.485084	0.198035
$7$	−2.15845	−0.815816	−0.407908	−	0.913023i	$-0.633742\pi$
$7$	−2.15845	−0.815816	−0.407908	+	0.913023i	$0.633742\pi$
$8$	−6.79636	−2.40288
$9$	−2.96455	−0.988184
$10$	−10.6226	−3.35915
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−0.873220	−0.252077
$13$	0	0
$13$	0	0
$14$	5.56105	1.48625
$15$	−0.776272	−0.200433
$16$	8.23442	2.05860
$17$	−3.09317	−0.750203	−0.375101	−	0.926984i	$-0.622392\pi$
$17$	−3.09317	−0.750203	−0.375101	+	0.926984i	$0.622392\pi$
$18$	7.63791	1.80027
$19$	2.68783	0.616631	0.308316	−	0.951284i	$-0.400235\pi$
$19$	2.68783	0.616631	0.308316	+	0.951284i	$0.400235\pi$
$20$	19.1221	4.27583
$21$	0.406389	0.0886814
$22$	2.57641	0.549294
$23$	3.31128	0.690449	0.345224	−	0.938520i	$-0.387803\pi$
$23$	3.31128	0.690449	0.345224	+	0.938520i	$0.387803\pi$
$24$	1.27961	0.261199
$25$	11.9991	2.39982
$26$	0	0
$27$	1.12300	0.216121
$28$	−10.0107	−1.89184
$29$	−3.34673	−0.621471	−0.310736	−	0.950496i	$-0.600575\pi$
$29$	−3.34673	−0.621471	−0.310736	+	0.950496i	$0.600575\pi$
$30$	2.00000	0.365148
$31$	−9.96928	−1.79054	−0.895268	−	0.445529i	$-0.853016\pi$
$31$	−9.96928	−1.79054	−0.895268	+	0.445529i	$0.853016\pi$
$32$	−7.62255	−1.34749
$33$	0.188279	0.0327751
$34$	7.96928	1.36672
$35$	−8.89927	−1.50425
$36$	−13.7493	−2.29156
$37$	−2.05966	−0.338607	−0.169303	−	0.985564i	$-0.554152\pi$
$37$	−2.05966	−0.338607	−0.169303	+	0.985564i	$0.554152\pi$
$38$	−6.92497	−1.12338
$39$	0	0
$40$	−28.0214	−4.43057
$41$	−9.49394	−1.48270	−0.741352	−	0.671116i	$-0.765815\pi$
$41$	−9.49394	−1.48270	−0.741352	+	0.671116i	$0.765815\pi$
$42$	−1.04703	−0.161560
$43$	2.84717	0.434189	0.217095	−	0.976151i	$-0.430342\pi$
$43$	2.84717	0.434189	0.217095	+	0.976151i	$0.430342\pi$
$44$	−4.63791	−0.699192
$45$	−12.2228	−1.82207
$46$	−8.53122	−1.25786
$47$	9.46972	1.38130	0.690651	−	0.723189i	$-0.257324\pi$
$47$	9.46972	1.38130	0.690651	+	0.723189i	$0.257324\pi$
$48$	−1.55036	−0.223776
$49$	−2.34111	−0.334444
$50$	−30.9147	−4.37200
$51$	0.582377	0.0815491
$52$	0	0
$53$	−5.34111	−0.733658	−0.366829	−	0.930288i	$-0.619557\pi$
$53$	−5.34111	−0.733658	−0.366829	+	0.930288i	$0.619557\pi$
$54$	−2.89331	−0.393729
$55$	−4.12300	−0.555945
$56$	14.6696	1.96031
$57$	−0.506062	−0.0670295
$58$	8.62255	1.13220
$59$	−4.62255	−0.601805	−0.300903	−	0.953655i	$-0.597288\pi$
$59$	−4.62255	−0.601805	−0.300903	+	0.953655i	$0.597288\pi$
$60$	−3.60028	−0.464795
$61$	−0.193895	−0.0248258	−0.0124129	−	0.999923i	$-0.503951\pi$
$61$	−0.193895	−0.0248258	−0.0124129	+	0.999923i	$0.503951\pi$
$62$	25.6850	3.26200
$63$	6.39883	0.806176
$64$	3.17003	0.396253
$65$	0	0
$66$	−0.485084	−0.0597097
$67$	5.78662	0.706948	0.353474	−	0.935444i	$-0.385000\pi$
$67$	5.78662	0.706948	0.353474	+	0.935444i	$0.385000\pi$
$68$	−14.3458	−1.73969
$69$	−0.623443	−0.0750537
$70$	22.9282	2.74045
$71$	3.78295	0.448953	0.224477	−	0.974479i	$-0.427933\pi$
$71$	3.78295	0.448953	0.224477	+	0.974479i	$0.427933\pi$
$72$	20.1482	2.37448
$73$	−7.47534	−0.874922	−0.437461	−	0.899237i	$-0.644122\pi$
$73$	−7.47534	−0.874922	−0.437461	+	0.899237i	$0.644122\pi$
$74$	5.30655	0.616874
$75$	−2.25918	−0.260867
$76$	12.4659	1.42994
$77$	2.15845	0.245978
$78$	0	0
$79$	−17.2049	−1.93571	−0.967853	−	0.251517i	$-0.919071\pi$
$79$	−17.2049	−1.93571	−0.967853	+	0.251517i	$0.919071\pi$
$80$	33.9505	3.79578
$81$	8.68222	0.964691
$82$	24.4603	2.70119
$83$	0.218111	0.0239408	0.0119704	−	0.999928i	$-0.496190\pi$
$83$	0.218111	0.0239408	0.0119704	+	0.999928i	$0.496190\pi$
$84$	1.88480	0.205648
$85$	−12.7531	−1.38327
$86$	−7.33549	−0.791006
$87$	0.630117	0.0675556
$88$	6.79636	0.724494
$89$	1.52939	0.162115	0.0810574	−	0.996709i	$-0.474170\pi$
$89$	1.52939	0.162115	0.0810574	+	0.996709i	$0.474170\pi$
$90$	31.4911	3.31945
$91$	0	0
$92$	15.3574	1.60112
$93$	1.87700	0.194636
$94$	−24.3979	−2.51645
$95$	11.0819	1.13698
$96$	1.43516	0.146476
$97$	−12.1462	−1.23326	−0.616628	−	0.787255i	$-0.711502\pi$
$97$	−12.1462	−1.23326	−0.616628	+	0.787255i	$0.711502\pi$
$98$	6.03167	0.609290
$99$	2.96455	0.297949
$100$	55.6508	5.56508
$101$	−13.2162	−1.31506	−0.657529	−	0.753429i	$-0.728398\pi$
$101$	−13.2162	−1.31506	−0.657529	+	0.753429i	$0.728398\pi$
$102$	−1.50044	−0.148566
$103$	−4.61783	−0.455008	−0.227504	−	0.973777i	$-0.573056\pi$
$103$	−4.61783	−0.455008	−0.227504	+	0.973777i	$0.573056\pi$
$104$	0	0
$105$	1.67554	0.163516
$106$	13.7609	1.33658
$107$	10.3458	1.00017	0.500085	−	0.865976i	$-0.333302\pi$
$107$	10.3458	1.00017	0.500085	+	0.865976i	$0.333302\pi$
$108$	5.20837	0.501175
$109$	−6.83032	−0.654226	−0.327113	−	0.944985i	$-0.606076\pi$
$109$	−6.83032	−0.654226	−0.327113	+	0.944985i	$0.606076\pi$
$110$	10.6226	1.01282
$111$	0.387791	0.0368075
$112$	−17.7735	−1.67944
$113$	−7.40077	−0.696206	−0.348103	−	0.937456i	$-0.613174\pi$
$113$	−7.40077	−0.696206	−0.348103	+	0.937456i	$0.613174\pi$
$114$	1.30382	0.122114
$115$	13.6524	1.27309
$116$	−15.5218	−1.44117
$117$	0	0
$118$	11.9096	1.09637
$119$	6.67643	0.612028
$120$	5.27583	0.481615
$121$	1.00000	0.0909091
$122$	0.499555	0.0452276
$123$	1.78751	0.161174
$124$	−46.2367	−4.15217
$125$	28.8573	2.58108
$126$	−16.4860	−1.46869
$127$	8.40550	0.745867	0.372934	−	0.927858i	$-0.378352\pi$
$127$	8.40550	0.745867	0.372934	+	0.927858i	$0.378352\pi$
$128$	7.07780	0.625595
$129$	−0.536061	−0.0471976
$130$	0	0
$131$	−0.630117	−0.0550536	−0.0275268	−	0.999621i	$-0.508763\pi$
$131$	−0.630117	−0.0550536	−0.0275268	+	0.999621i	$0.508763\pi$
$132$	0.873220	0.0760041
$133$	−5.80155	−0.503058
$134$	−14.9087	−1.28792
$135$	4.63012	0.398497
$136$	21.0223	1.80264
$137$	−4.81645	−0.411497	−0.205748	−	0.978605i	$-0.565963\pi$
$137$	−4.81645	−0.411497	−0.205748	+	0.978605i	$0.565963\pi$
$138$	1.60625	0.136733
$139$	−10.5592	−0.895621	−0.447811	−	0.894128i	$-0.647796\pi$
$139$	−10.5592	−0.895621	−0.447811	+	0.894128i	$0.647796\pi$
$140$	−41.2740	−3.48829
$141$	−1.78295	−0.150151
$142$	−9.74644	−0.817903
$143$	0	0
$144$	−24.4113	−2.03428
$145$	−13.7985	−1.14591
$146$	19.2596	1.59393
$147$	0.440781	0.0363550
$148$	−9.55254	−0.785214
$149$	2.80049	0.229425	0.114712	−	0.993399i	$-0.463405\pi$
$149$	2.80049	0.229425	0.114712	+	0.993399i	$0.463405\pi$
$150$	5.82058	0.475248
$151$	8.24600	0.671050	0.335525	−	0.942031i	$-0.391086\pi$
$151$	8.24600	0.671050	0.335525	+	0.942031i	$0.391086\pi$
$152$	−18.2675	−1.48169
$153$	9.16985	0.741338
$154$	−5.56105	−0.448122
$155$	−41.1033	−3.30150
$156$	0	0
$157$	−13.2918	−1.06080	−0.530400	−	0.847747i	$-0.677958\pi$
$157$	−13.2918	−1.06080	−0.530400	+	0.847747i	$0.677958\pi$
$158$	44.3270	3.52647
$159$	1.00562	0.0797506
$160$	−31.4278	−2.48458
$161$	−7.14721	−0.563279
$162$	−22.3690	−1.75747
$163$	2.85084	0.223295	0.111647	−	0.993748i	$-0.464387\pi$
$163$	2.85084	0.223295	0.111647	+	0.993748i	$0.464387\pi$
$164$	−44.0321	−3.43833
$165$	0.776272	0.0604327
$166$	−0.561944	−0.0436153
$167$	1.30093	0.100669	0.0503346	−	0.998732i	$-0.483971\pi$
$167$	1.30093	0.100669	0.0503346	+	0.998732i	$0.483971\pi$
$168$	−2.76197	−0.213091
$169$	0	0
$170$	32.8573	2.52004
$171$	−7.96822	−0.609345
$172$	13.2049	1.00687
$173$	8.52850	0.648410	0.324205	−	0.945987i	$-0.394903\pi$
$173$	8.52850	0.648410	0.324205	+	0.945987i	$0.394903\pi$
$174$	−1.62344	−0.123073
$175$	−25.8994	−1.95781
$176$	−8.23442	−0.620692
$177$	0.870328	0.0654179
$178$	−3.94034	−0.295341
$179$	19.3048	1.44291	0.721453	−	0.692463i	$-0.243475\pi$
$179$	19.3048	1.44291	0.721453	+	0.692463i	$0.243475\pi$
$180$	−56.6885	−4.22531
$181$	−26.3402	−1.95785	−0.978927	−	0.204213i	$-0.934537\pi$
$181$	−26.3402	−1.95785	−0.978927	+	0.204213i	$0.934537\pi$
$182$	0	0
$183$	0.0365064	0.00269863
$184$	−22.5046	−1.65906
$185$	−8.49199	−0.624344
$186$	−4.83594	−0.354588
$187$	3.09317	0.226195
$188$	43.9198	3.20318
$189$	−2.42393	−0.176315
$190$	−28.5517	−2.07135
$191$	−1.86015	−0.134596	−0.0672979	−	0.997733i	$-0.521438\pi$
$191$	−1.86015	−0.134596	−0.0672979	+	0.997733i	$0.521438\pi$
$192$	−0.596848	−0.0430738
$193$	−16.4239	−1.18222	−0.591110	−	0.806591i	$-0.701310\pi$
$193$	−16.4239	−1.18222	−0.591110	+	0.806591i	$0.701310\pi$
$194$	31.2935	2.24674
$195$	0	0
$196$	−10.8579	−0.775561
$197$	17.5929	1.25344	0.626721	−	0.779244i	$-0.284397\pi$
$197$	17.5929	1.25344	0.626721	+	0.779244i	$0.284397\pi$
$198$	−7.63791	−0.542803
$199$	0.434274	0.0307849	0.0153924	−	0.999882i	$-0.495100\pi$
$199$	0.434274	0.0307849	0.0153924	+	0.999882i	$0.495100\pi$
$200$	−81.5503	−5.76648
$201$	−1.08950	−0.0768471
$202$	34.0503	2.39577
$203$	7.22373	0.507006
$204$	2.70101	0.189109
$205$	−39.1435	−2.73390
$206$	11.8974	0.828934
$207$	−9.81645	−0.682290
$208$	0	0
$209$	−2.68783	−0.185921
$210$	−4.31689	−0.297894
$211$	4.04018	0.278137	0.139069	−	0.990283i	$-0.455589\pi$
$211$	4.04018	0.278137	0.139069	+	0.990283i	$0.455589\pi$
$212$	−24.7716	−1.70132
$213$	−0.712248	−0.0488024
$214$	−26.6552	−1.82211
$215$	11.7389	0.800585
$216$	−7.63230	−0.519312
$217$	21.5182	1.46075
$218$	17.5977	1.19187
$219$	1.40745	0.0951065
$220$	−19.1221	−1.28921
$221$	0	0
$222$	−0.999110	−0.0670559
$223$	−21.4390	−1.43566	−0.717831	−	0.696218i	$-0.754865\pi$
$223$	−21.4390	−1.43566	−0.717831	+	0.696218i	$0.754865\pi$
$224$	16.4529	1.09930
$225$	−35.5720	−2.37147
$226$	19.0675	1.26835
$227$	−18.8647	−1.25209	−0.626047	−	0.779785i	$-0.715328\pi$
$227$	−18.8647	−1.25209	−0.626047	+	0.779785i	$0.715328\pi$
$228$	−2.34707	−0.155439
$229$	−13.3048	−0.879204	−0.439602	−	0.898193i	$-0.644880\pi$
$229$	−13.3048	−0.879204	−0.439602	+	0.898193i	$0.644880\pi$
$230$	−35.1742	−2.31932
$231$	−0.406389	−0.0267385
$232$	22.7456	1.49332
$233$	21.3160	1.39646	0.698229	−	0.715875i	$-0.253972\pi$
$233$	21.3160	1.39646	0.698229	+	0.715875i	$0.253972\pi$
$234$	0	0
$235$	39.0436	2.54693
$236$	−21.4390	−1.39556
$237$	3.23932	0.210417
$238$	−17.2013	−1.11499
$239$	−13.9123	−0.899909	−0.449954	−	0.893052i	$-0.648560\pi$
$239$	−13.9123	−0.899909	−0.449954	+	0.893052i	$0.648560\pi$
$240$	−6.39215	−0.412612
$241$	−0.565726	−0.0364416	−0.0182208	−	0.999834i	$-0.505800\pi$
$241$	−0.565726	−0.0364416	−0.0182208	+	0.999834i	$0.505800\pi$
$242$	−2.57641	−0.165618
$243$	−5.00367	−0.320986
$244$	−0.899270	−0.0575699
$245$	−9.65238	−0.616668
$246$	−4.60536	−0.293627
$247$	0	0
$248$	67.7548	4.30243
$249$	−0.0410656	−0.00260243
$250$	−74.3484	−4.70221
$251$	12.4985	0.788898	0.394449	−	0.918918i	$-0.370935\pi$
$251$	12.4985	0.788898	0.394449	+	0.918918i	$0.370935\pi$
$252$	29.6772	1.86949
$253$	−3.31128	−0.208178
$254$	−21.6561	−1.35882
$255$	2.40114	0.150365
$256$	−24.5754	−1.53596
$257$	14.7640	0.920952	0.460476	−	0.887672i	$-0.347679\pi$
$257$	14.7640	0.920952	0.460476	+	0.887672i	$0.347679\pi$
$258$	1.38112	0.0859846
$259$	4.44568	0.276241
$260$	0	0
$261$	9.92154	0.614128
$262$	1.62344	0.100297
$263$	−15.8445	−0.977014	−0.488507	−	0.872560i	$-0.662458\pi$
$263$	−15.8445	−0.977014	−0.488507	+	0.872560i	$0.662458\pi$
$264$	−1.27961	−0.0787545
$265$	−22.0214	−1.35276
$266$	14.9472	0.916471
$267$	−0.287951	−0.0176223
$268$	26.8378	1.63938
$269$	−2.34289	−0.142848	−0.0714242	−	0.997446i	$-0.522754\pi$
$269$	−2.34289	−0.142848	−0.0714242	+	0.997446i	$0.522754\pi$
$270$	−11.9291	−0.725982
$271$	−26.0038	−1.57962	−0.789810	−	0.613351i	$-0.789821\pi$
$271$	−26.0038	−1.57962	−0.789810	+	0.613351i	$0.789821\pi$
$272$	−25.4704	−1.54437
$273$	0	0
$274$	12.4092	0.749665
$275$	−11.9991	−0.723574
$276$	−2.89147	−0.174046
$277$	28.0019	1.68247	0.841235	−	0.540669i	$-0.181829\pi$
$277$	28.0019	1.68247	0.841235	+	0.540669i	$0.181829\pi$
$278$	27.2049	1.63164
$279$	29.5544	1.76938
$280$	60.4826	3.61453
$281$	20.4632	1.22073	0.610367	−	0.792119i	$-0.291022\pi$
$281$	20.4632	1.22073	0.610367	+	0.792119i	$0.291022\pi$
$282$	4.59361	0.273546
$283$	−9.17810	−0.545582	−0.272791	−	0.962073i	$-0.587947\pi$
$283$	−9.17810	−0.545582	−0.272791	+	0.962073i	$0.587947\pi$
$284$	17.5450	1.04110
$285$	−2.08649	−0.123593
$286$	0	0
$287$	20.4922	1.20961
$288$	22.5974	1.33157
$289$	−7.43233	−0.437196
$290$	35.5508	2.08761
$291$	2.28686	0.134058
$292$	−34.6700	−2.02891
$293$	−18.7380	−1.09468	−0.547342	−	0.836909i	$-0.684360\pi$
$293$	−18.7380	−1.09468	−0.547342	+	0.836909i	$0.684360\pi$
$294$	−1.13563	−0.0662315
$295$	−19.0588	−1.10964
$296$	13.9982	0.813630
$297$	−1.12300	−0.0651629
$298$	−7.21522	−0.417966
$299$	0	0
$300$	−10.4779	−0.604940
$301$	−6.14546	−0.354219
$302$	−21.2451	−1.22252
$303$	2.48832	0.142950
$304$	22.1327	1.26940
$305$	−0.799430	−0.0457752
$306$	−23.6253	−1.35057
$307$	−3.49288	−0.199349	−0.0996746	−	0.995020i	$-0.531780\pi$
$307$	−3.49288	−0.199349	−0.0996746	+	0.995020i	$0.531780\pi$
$308$	10.0107	0.570412
$309$	0.869438	0.0494606
$310$	105.899	6.01467
$311$	−4.19951	−0.238132	−0.119066	−	0.992886i	$-0.537990\pi$
$311$	−4.19951	−0.238132	−0.119066	+	0.992886i	$0.537990\pi$
$312$	0	0
$313$	−12.4678	−0.704720	−0.352360	−	0.935864i	$-0.614621\pi$
$313$	−12.4678	−0.704720	−0.352360	+	0.935864i	$0.614621\pi$
$314$	34.2452	1.93257
$315$	26.3823	1.48648
$316$	−79.7950	−4.48882
$317$	8.27494	0.464767	0.232383	−	0.972624i	$-0.425348\pi$
$317$	8.27494	0.464767	0.232383	+	0.972624i	$0.425348\pi$
$318$	−2.59089	−0.145290
$319$	3.34673	0.187381
$320$	13.0700	0.730636
$321$	−1.94790	−0.108721
$322$	18.4142	1.02618
$323$	−8.31391	−0.462599
$324$	40.2674	2.23708
$325$	0	0
$326$	−7.34495	−0.406799
$327$	1.28600	0.0711162
$328$	64.5242	3.56275
$329$	−20.4399	−1.12689
$330$	−2.00000	−0.110096
$331$	23.5852	1.29636	0.648179	−	0.761488i	$-0.275531\pi$
$331$	23.5852	1.29636	0.648179	+	0.761488i	$0.275531\pi$
$332$	1.01158	0.0555176
$333$	6.10598	0.334606
$334$	−3.35174	−0.183399
$335$	23.8582	1.30351
$336$	3.34638	0.182560
$337$	0.664508	0.0361981	0.0180990	−	0.999836i	$-0.494239\pi$
$337$	0.664508	0.0361981	0.0180990	+	0.999836i	$0.494239\pi$
$338$	0	0
$339$	1.39341	0.0756795
$340$	−59.1478	−3.20774
$341$	9.96928	0.539867
$342$	20.5294	1.11011
$343$	20.1623	1.08866
$344$	−19.3504	−1.04330
$345$	−2.57045	−0.138389
$346$	−21.9729	−1.18127
$347$	−1.33916	−0.0718899	−0.0359450	−	0.999354i	$-0.511444\pi$
$347$	−1.33916	−0.0718899	−0.0359450	+	0.999354i	$0.511444\pi$
$348$	2.92243	0.156659
$349$	1.48448	0.0794626	0.0397313	−	0.999210i	$-0.487350\pi$
$349$	1.48448	0.0794626	0.0397313	+	0.999210i	$0.487350\pi$
$350$	66.7277	3.56675
$351$	0	0
$352$	7.62255	0.406283
$353$	−6.04843	−0.321925	−0.160963	−	0.986960i	$-0.551460\pi$
$353$	−6.04843	−0.321925	−0.160963	+	0.986960i	$0.551460\pi$
$354$	−2.24233	−0.119178
$355$	15.5971	0.827807
$356$	7.09317	0.375937
$357$	−1.25703	−0.0665291
$358$	−49.7371	−2.62869
$359$	16.7101	0.881925	0.440963	−	0.897525i	$-0.354637\pi$
$359$	16.7101	0.881925	0.440963	+	0.897525i	$0.354637\pi$
$360$	83.0708	4.37822
$361$	−11.7756	−0.619766
$362$	67.8633	3.56682
$363$	−0.188279	−0.00988207
$364$	0	0
$365$	−30.8208	−1.61323
$366$	−0.0940556	−0.00491636
$367$	18.2943	0.954953	0.477476	−	0.878645i	$-0.341552\pi$
$367$	18.2943	0.954953	0.477476	+	0.878645i	$0.341552\pi$
$368$	27.2664	1.42136
$369$	28.1453	1.46518
$370$	21.8789	1.13743
$371$	11.5285	0.598530
$372$	8.70537	0.451353
$373$	16.5748	0.858211	0.429106	−	0.903254i	$-0.358829\pi$
$373$	16.5748	0.858211	0.429106	+	0.903254i	$0.358829\pi$
$374$	−7.96928	−0.412082
$375$	−5.43322	−0.280570
$376$	−64.3596	−3.31910
$377$	0	0
$378$	6.24505	0.321211
$379$	26.9952	1.38665	0.693326	−	0.720625i	$-0.256145\pi$
$379$	26.9952	1.38665	0.693326	+	0.720625i	$0.256145\pi$
$380$	51.3970	2.63661
$381$	−1.58258	−0.0810778
$382$	4.79252	0.245207
$383$	−9.35039	−0.477783	−0.238891	−	0.971046i	$-0.576784\pi$
$383$	−9.35039	−0.477783	−0.238891	+	0.971046i	$0.576784\pi$
$384$	−1.33260	−0.0680039
$385$	8.89927	0.453549
$386$	42.3149	2.15377
$387$	−8.44058	−0.429059
$388$	−56.3328	−2.85987
$389$	17.8258	0.903802	0.451901	−	0.892068i	$-0.350746\pi$
$389$	17.8258	0.903802	0.451901	+	0.892068i	$0.350746\pi$
$390$	0	0
$391$	−10.2423	−0.517977
$392$	15.9110	0.803628
$393$	0.118638	0.00598447
$394$	−45.3266	−2.28352
$395$	−70.9359	−3.56917
$396$	13.7493	0.690930
$397$	−36.0101	−1.80730	−0.903649	−	0.428275i	$-0.859122\pi$
$397$	−36.0101	−1.80730	−0.903649	+	0.428275i	$0.859122\pi$
$398$	−1.11887	−0.0560839
$399$	1.09231	0.0546838
$400$	98.8057	4.94028
$401$	−23.4604	−1.17156	−0.585778	−	0.810472i	$-0.699211\pi$
$401$	−23.4604	−1.17156	−0.585778	+	0.810472i	$0.699211\pi$
$402$	2.80699	0.140000
$403$	0	0
$404$	−61.2954	−3.04956
$405$	35.7968	1.77876
$406$	−18.6113	−0.923664
$407$	2.05966	0.102094
$408$	−3.95804	−0.195952
$409$	−14.8798	−0.735758	−0.367879	−	0.929874i	$-0.619916\pi$
$409$	−14.8798	−0.735758	−0.367879	+	0.929874i	$0.619916\pi$
$410$	100.850	4.98062
$411$	0.906834	0.0447308
$412$	−21.4171	−1.05514
$413$	9.97753	0.490962
$414$	25.2912	1.24300
$415$	0.899270	0.0441434
$416$	0	0
$417$	1.98808	0.0973565
$418$	6.92497	0.338712
$419$	−27.9935	−1.36757	−0.683786	−	0.729683i	$-0.739668\pi$
$419$	−27.9935	−1.36757	−0.683786	+	0.729683i	$0.739668\pi$
$420$	7.77102	0.379187
$421$	13.3185	0.649103	0.324551	−	0.945868i	$-0.394787\pi$
$421$	13.3185	0.649103	0.324551	+	0.945868i	$0.394787\pi$
$422$	−10.4092	−0.506710
$423$	−28.0735	−1.36498
$424$	36.3001	1.76289
$425$	−37.1152	−1.80035
$426$	1.83505	0.0889083
$427$	0.418513	0.0202533
$428$	47.9831	2.31935
$429$	0	0
$430$	−30.2442	−1.45851
$431$	−12.2181	−0.588526	−0.294263	−	0.955725i	$-0.595074\pi$
$431$	−12.2181	−0.588526	−0.294263	+	0.955725i	$0.595074\pi$
$432$	9.24723	0.444908
$433$	−27.2663	−1.31034	−0.655168	−	0.755483i	$-0.727402\pi$
$433$	−27.2663	−1.31034	−0.655168	+	0.755483i	$0.727402\pi$
$434$	−55.4397	−2.66119
$435$	2.59797	0.124563
$436$	−31.6784	−1.51712
$437$	8.90016	0.425752
$438$	−3.62617	−0.173265
$439$	−34.0428	−1.62477	−0.812386	−	0.583120i	$-0.801832\pi$
$439$	−34.0428	−1.62477	−0.812386	+	0.583120i	$0.801832\pi$
$440$	28.0214	1.33587
$441$	6.94034	0.330492
$442$	0	0
$443$	−39.2983	−1.86712	−0.933558	−	0.358425i	$-0.883314\pi$
$443$	−39.2983	−1.86712	−0.933558	+	0.358425i	$0.883314\pi$
$444$	1.79854	0.0853549
$445$	6.30566	0.298917
$446$	55.2358	2.61549
$447$	−0.527272	−0.0249391
$448$	−6.84233	−0.323270
$449$	−14.8508	−0.700854	−0.350427	−	0.936590i	$-0.613964\pi$
$449$	−14.8508	−0.700854	−0.350427	+	0.936590i	$0.613964\pi$
$450$	91.6482	4.32034
$451$	9.49394	0.447052
$452$	−34.3241	−1.61447
$453$	−1.55254	−0.0729449
$454$	48.6033	2.28107
$455$	0	0
$456$	3.43938	0.161064
$457$	−19.7213	−0.922525	−0.461263	−	0.887264i	$-0.652603\pi$
$457$	−19.7213	−0.922525	−0.461263	+	0.887264i	$0.652603\pi$
$458$	34.2786	1.60173
$459$	−3.47362	−0.162135
$460$	63.3186	2.95224
$461$	29.8161	1.38867	0.694337	−	0.719650i	$-0.255698\pi$
$461$	29.8161	1.38867	0.694337	+	0.719650i	$0.255698\pi$
$462$	1.04703	0.0487121
$463$	16.5769	0.770395	0.385198	−	0.922834i	$-0.374133\pi$
$463$	16.5769	0.770395	0.385198	+	0.922834i	$0.374133\pi$
$464$	−27.5583	−1.27936
$465$	7.73888	0.358882
$466$	−54.9189	−2.54407
$467$	−1.67187	−0.0773651	−0.0386825	−	0.999252i	$-0.512316\pi$
$467$	−1.67187	−0.0773651	−0.0386825	+	0.999252i	$0.512316\pi$
$468$	0	0
$469$	−12.4901	−0.576739
$470$	−100.593	−4.63999
$471$	2.50256	0.115312
$472$	31.4165	1.44606
$473$	−2.84717	−0.130913
$474$	−8.34584	−0.383337
$475$	32.2516	1.47981
$476$	30.9647	1.41927
$477$	15.8340	0.724989
$478$	35.8437	1.63945
$479$	20.0579	0.916468	0.458234	−	0.888832i	$-0.348482\pi$
$479$	20.0579	0.916468	0.458234	+	0.888832i	$0.348482\pi$
$480$	5.91718	0.270081
$481$	0	0
$482$	1.45754	0.0663893
$483$	1.34567	0.0612300
$484$	4.63791	0.210814
$485$	−50.0786	−2.27395
$486$	12.8915	0.584772
$487$	−4.74733	−0.215122	−0.107561	−	0.994198i	$-0.534304\pi$
$487$	−4.74733	−0.215122	−0.107561	+	0.994198i	$0.534304\pi$
$488$	1.31778	0.0596532
$489$	−0.536752	−0.0242728
$490$	24.8685	1.12345
$491$	42.4522	1.91584	0.957919	−	0.287037i	$-0.0926704\pi$
$491$	42.4522	1.91584	0.957919	+	0.287037i	$0.0926704\pi$
$492$	8.29030	0.373756
$493$	10.3520	0.466230
$494$	0	0
$495$	12.2228	0.549376
$496$	−82.0912	−3.68600
$497$	−8.16529	−0.366263
$498$	0.105802	0.00474110
$499$	20.6880	0.926122	0.463061	−	0.886326i	$-0.346751\pi$
$499$	20.6880	0.926122	0.463061	+	0.886326i	$0.346751\pi$
$500$	133.838	5.98541
$501$	−0.244938	−0.0109430
$502$	−32.2013	−1.43722
$503$	3.88526	0.173235	0.0866175	−	0.996242i	$-0.472394\pi$
$503$	3.88526	0.173235	0.0866175	+	0.996242i	$0.472394\pi$
$504$	−43.4887	−1.93714
$505$	−54.4902	−2.42478
$506$	8.53122	0.379259
$507$	0	0
$508$	38.9840	1.72963
$509$	−4.35776	−0.193154	−0.0965771	−	0.995326i	$-0.530789\pi$
$509$	−4.35776	−0.193154	−0.0965771	+	0.995326i	$0.530789\pi$
$510$	−6.18633	−0.273935
$511$	16.1351	0.713776
$512$	49.1608	2.17262
$513$	3.01843	0.133267
$514$	−38.0381	−1.67779
$515$	−19.0393	−0.838971
$516$	−2.48621	−0.109449
$517$	−9.46972	−0.416478
$518$	−11.4539	−0.503256
$519$	−1.60573	−0.0704839
$520$	0	0
$521$	−21.4185	−0.938360	−0.469180	−	0.883103i	$-0.655450\pi$
$521$	−21.4185	−0.938360	−0.469180	+	0.883103i	$0.655450\pi$
$522$	−25.5620	−1.11882
$523$	27.8835	1.21926	0.609630	−	0.792686i	$-0.291318\pi$
$523$	27.8835	1.21926	0.609630	+	0.792686i	$0.291318\pi$
$524$	−2.92243	−0.127667
$525$	4.87631	0.212820
$526$	40.8220	1.77992
$527$	30.8366	1.34326
$528$	1.55036	0.0674710
$529$	−12.0354	−0.523280
$530$	56.7362	2.46446
$531$	13.7038	0.594694
$532$	−26.9071	−1.16657
$533$	0	0
$534$	0.741881	0.0321043
$535$	42.6559	1.84417
$536$	−39.3279	−1.69871
$537$	−3.63468	−0.156848
$538$	6.03625	0.260241
$539$	2.34111	0.100839
$540$	21.4741	0.924097
$541$	−16.1874	−0.695950	−0.347975	−	0.937504i	$-0.613131\pi$
$541$	−16.1874	−0.695950	−0.347975	+	0.937504i	$0.613131\pi$
$542$	66.9967	2.87775
$543$	4.95930	0.212824
$544$	23.5778	1.01089
$545$	−28.1614	−1.20630
$546$	0	0
$547$	−16.5264	−0.706617	−0.353309	−	0.935507i	$-0.614943\pi$
$547$	−16.5264	−0.706617	−0.353309	+	0.935507i	$0.614943\pi$
$548$	−22.3383	−0.954244
$549$	0.574813	0.0245324
$550$	30.9147	1.31821
$551$	−8.99544	−0.383219
$552$	4.23714	0.180345
$553$	37.1359	1.57918
$554$	−72.1445	−3.06513
$555$	1.59886	0.0678679
$556$	−48.9727	−2.07691
$557$	27.0075	1.14434	0.572172	−	0.820133i	$-0.306101\pi$
$557$	27.0075	1.14434	0.572172	+	0.820133i	$0.306101\pi$
$558$	−76.1445	−3.22345
$559$	0	0
$560$	−73.2803	−3.09666
$561$	−0.582377	−0.0245880
$562$	−52.7217	−2.22393
$563$	37.7276	1.59003	0.795015	−	0.606589i	$-0.207463\pi$
$563$	37.7276	1.59003	0.795015	+	0.606589i	$0.207463\pi$
$564$	−8.26915	−0.348194
$565$	−30.5134	−1.28371
$566$	23.6466	0.993941
$567$	−18.7401	−0.787010
$568$	−25.7103	−1.07878
$569$	−7.39694	−0.310096	−0.155048	−	0.987907i	$-0.549553\pi$
$569$	−7.39694	−0.310096	−0.155048	+	0.987907i	$0.549553\pi$
$570$	5.37567	0.225162
$571$	24.3578	1.01934	0.509670	−	0.860370i	$-0.329767\pi$
$571$	24.3578	1.01934	0.509670	+	0.860370i	$0.329767\pi$
$572$	0	0
$573$	0.350227	0.0146309
$574$	−52.7963	−2.20368
$575$	39.7324	1.65695
$576$	−9.39770	−0.391571
$577$	−4.42797	−0.184339	−0.0921693	−	0.995743i	$-0.529380\pi$
$577$	−4.42797	−0.184339	−0.0921693	+	0.995743i	$0.529380\pi$
$578$	19.1488	0.796483
$579$	3.09228	0.128511
$580$	−63.9964	−2.65731
$581$	−0.470780	−0.0195313
$582$	−5.89191	−0.244227
$583$	5.34111	0.221206
$584$	50.8051	2.10233
$585$	0	0
$586$	48.2768	1.99430
$587$	−9.80799	−0.404819	−0.202410	−	0.979301i	$-0.564877\pi$
$587$	−9.80799	−0.404819	−0.202410	+	0.979301i	$0.564877\pi$
$588$	2.04430	0.0843056
$589$	−26.7958	−1.10410
$590$	49.1033	2.02155
$591$	−3.31237	−0.136253
$592$	−16.9601	−0.697057
$593$	−23.4213	−0.961796	−0.480898	−	0.876777i	$-0.659689\pi$
$593$	−23.4213	−0.961796	−0.480898	+	0.876777i	$0.659689\pi$
$594$	2.89331	0.118714
$595$	27.5269	1.12849
$596$	12.9884	0.532026
$597$	−0.0817645	−0.00334640
$598$	0	0
$599$	−2.61327	−0.106775	−0.0533876	−	0.998574i	$-0.517002\pi$
$599$	−2.61327	−0.106775	−0.0533876	+	0.998574i	$0.517002\pi$
$600$	15.3542	0.626832
$601$	−27.4904	−1.12136	−0.560679	−	0.828034i	$-0.689460\pi$
$601$	−27.4904	−1.12136	−0.560679	+	0.828034i	$0.689460\pi$
$602$	15.8333	0.645316
$603$	−17.1547	−0.698594
$604$	38.2442	1.55614
$605$	4.12300	0.167624
$606$	−6.41095	−0.260427
$607$	35.0458	1.42246	0.711232	−	0.702958i	$-0.248138\pi$
$607$	35.0458	1.42246	0.711232	+	0.702958i	$0.248138\pi$
$608$	−20.4882	−0.830904
$609$	−1.36007	−0.0551130
$610$	2.05966	0.0833934
$611$	0	0
$612$	42.5290	1.71913
$613$	15.8368	0.639641	0.319821	−	0.947478i	$-0.396377\pi$
$613$	15.8368	0.639641	0.319821	+	0.947478i	$0.396377\pi$
$614$	8.99911	0.363175
$615$	7.36988	0.297182
$616$	−14.6696	−0.591054
$617$	−19.0168	−0.765588	−0.382794	−	0.923834i	$-0.625038\pi$
$617$	−19.0168	−0.765588	−0.382794	+	0.923834i	$0.625038\pi$
$618$	−2.24003	−0.0901074
$619$	26.7417	1.07484	0.537419	−	0.843315i	$-0.319399\pi$
$619$	26.7417	1.07484	0.537419	+	0.843315i	$0.319399\pi$
$620$	−190.634	−7.65603
$621$	3.71856	0.149221
$622$	10.8197	0.433830
$623$	−3.30110	−0.132256
$624$	0	0
$625$	58.9831	2.35932
$626$	32.1222	1.28386
$627$	0.506062	0.0202102
$628$	−61.6462	−2.45995
$629$	6.37088	0.254024
$630$	−67.9719	−2.70806
$631$	39.8528	1.58651	0.793257	−	0.608888i	$-0.208384\pi$
$631$	39.8528	1.58651	0.793257	+	0.608888i	$0.208384\pi$
$632$	116.931	4.65126
$633$	−0.760679	−0.0302343
$634$	−21.3197	−0.846712
$635$	34.6559	1.37528
$636$	4.66396	0.184938
$637$	0	0
$638$	−8.62255	−0.341370
$639$	−11.2147	−0.443648
$640$	29.1818	1.15351
$641$	9.85468	0.389236	0.194618	−	0.980879i	$-0.437653\pi$
$641$	9.85468	0.389236	0.194618	+	0.980879i	$0.437653\pi$
$642$	5.01860	0.198068
$643$	−10.3078	−0.406499	−0.203249	−	0.979127i	$-0.565150\pi$
$643$	−10.3078	−0.406499	−0.203249	+	0.979127i	$0.565150\pi$
$644$	−33.1482	−1.30622
$645$	−2.21018	−0.0870257
$646$	21.4201	0.842762
$647$	−24.4455	−0.961052	−0.480526	−	0.876980i	$-0.659554\pi$
$647$	−24.4455	−0.961052	−0.480526	+	0.876980i	$0.659554\pi$
$648$	−59.0075	−2.31803
$649$	4.62255	0.181451
$650$	0	0
$651$	−4.05141	−0.158787
$652$	13.2219	0.517811
$653$	26.5723	1.03986	0.519928	−	0.854210i	$-0.325959\pi$
$653$	26.5723	1.03986	0.519928	+	0.854210i	$0.325959\pi$
$654$	−3.31328	−0.129559
$655$	−2.59797	−0.101511
$656$	−78.1770	−3.05230
$657$	22.1610	0.864584
$658$	52.6616	2.05296
$659$	22.5480	0.878345	0.439172	−	0.898403i	$-0.355272\pi$
$659$	22.5480	0.878345	0.439172	+	0.898403i	$0.355272\pi$
$660$	3.60028	0.140141
$661$	44.8824	1.74572	0.872861	−	0.487969i	$-0.162262\pi$
$661$	44.8824	1.74572	0.872861	+	0.487969i	$0.162262\pi$
$662$	−60.7651	−2.36170
$663$	0	0
$664$	−1.48236	−0.0575267
$665$	−23.9198	−0.927568
$666$	−15.7315	−0.609585
$667$	−11.0819	−0.429094
$668$	6.03361	0.233448
$669$	4.03651	0.156060
$670$	−61.4686	−2.37474
$671$	0.193895	0.00748525
$672$	−3.09772	−0.119497
$673$	−0.766928	−0.0295629	−0.0147815	−	0.999891i	$-0.504705\pi$
$673$	−0.766928	−0.0295629	−0.0147815	+	0.999891i	$0.504705\pi$
$674$	−1.71205	−0.0659457
$675$	13.4750	0.518652
$676$	0	0
$677$	22.6545	0.870682	0.435341	−	0.900266i	$-0.356628\pi$
$677$	22.6545	0.870682	0.435341	+	0.900266i	$0.356628\pi$
$678$	−3.59000	−0.137873
$679$	26.2168	1.00611
$680$	86.6748	3.32383
$681$	3.55182	0.136106
$682$	−25.6850	−0.983529
$683$	−6.69712	−0.256258	−0.128129	−	0.991757i	$-0.540897\pi$
$683$	−6.69712	−0.256258	−0.128129	+	0.991757i	$0.540897\pi$
$684$	−36.9559	−1.41304
$685$	−19.8582	−0.758743
$686$	−51.9464	−1.98332
$687$	2.50500	0.0955719
$688$	23.4448	0.893824
$689$	0	0
$690$	6.62255	0.252116
$691$	22.1563	0.842865	0.421433	−	0.906860i	$-0.361527\pi$
$691$	22.1563	0.842865	0.421433	+	0.906860i	$0.361527\pi$
$692$	39.5544	1.50363
$693$	−6.39883	−0.243071
$694$	3.45023	0.130969
$695$	−43.5356	−1.65140
$696$	−4.28250	−0.162328
$697$	29.3663	1.11233
$698$	−3.82465	−0.144765
$699$	−4.01335	−0.151799
$700$	−120.119	−4.54009
$701$	14.7084	0.555527	0.277763	−	0.960650i	$-0.410407\pi$
$701$	14.7084	0.555527	0.277763	+	0.960650i	$0.410407\pi$
$702$	0	0
$703$	−5.53603	−0.208796
$704$	−3.17003	−0.119475
$705$	−7.35109	−0.276858
$706$	15.5833	0.586484
$707$	28.5264	1.07285
$708$	4.03651	0.151701
$709$	−28.8284	−1.08267	−0.541336	−	0.840806i	$-0.682081\pi$
$709$	−28.8284	−1.08267	−0.541336	+	0.840806i	$0.682081\pi$
$710$	−40.1846	−1.50810
$711$	51.0049	1.91283
$712$	−10.3943	−0.389542
$713$	−33.0110	−1.23627
$714$	3.23863	0.121203
$715$	0	0
$716$	89.5339	3.34604
$717$	2.61938	0.0978225
$718$	−43.0522	−1.60669
$719$	−8.10420	−0.302236	−0.151118	−	0.988516i	$-0.548287\pi$
$719$	−8.10420	−0.302236	−0.151118	+	0.988516i	$0.548287\pi$
$720$	−100.648	−3.75093
$721$	9.96733	0.371203
$722$	30.3387	1.12909
$723$	0.106514	0.00396130
$724$	−122.164	−4.54018
$725$	−40.1577	−1.49142
$726$	0.485084	0.0180032
$727$	−19.1116	−0.708810	−0.354405	−	0.935092i	$-0.615317\pi$
$727$	−19.1116	−0.708810	−0.354405	+	0.935092i	$0.615317\pi$
$728$	0	0
$729$	−25.1046	−0.929799
$730$	79.4072	2.93899
$731$	−8.80677	−0.325730
$732$	0.169313	0.00625800
$733$	27.4827	1.01510	0.507548	−	0.861623i	$-0.330552\pi$
$733$	27.4827	1.01510	0.507548	+	0.861623i	$0.330552\pi$
$734$	−47.1336	−1.73973
$735$	1.81734	0.0670335
$736$	−25.2404	−0.930373
$737$	−5.78662	−0.213153
$738$	−72.5139	−2.66927
$739$	3.99458	0.146943	0.0734715	−	0.997297i	$-0.476592\pi$
$739$	3.99458	0.146943	0.0734715	+	0.997297i	$0.476592\pi$
$740$	−39.3851	−1.44783
$741$	0	0
$742$	−29.7022	−1.09040
$743$	−27.9386	−1.02497	−0.512483	−	0.858697i	$-0.671274\pi$
$743$	−27.9386	−1.02497	−0.512483	+	0.858697i	$0.671274\pi$
$744$	−12.7568	−0.467686
$745$	11.5464	0.423028
$746$	−42.7036	−1.56349
$747$	−0.646601	−0.0236579
$748$	14.3458	0.524536
$749$	−22.3309	−0.815955
$750$	13.9982	0.511143
$751$	−16.3149	−0.595341	−0.297670	−	0.954669i	$-0.596210\pi$
$751$	−16.3149	−0.595341	−0.297670	+	0.954669i	$0.596210\pi$
$752$	77.9776	2.84355
$753$	−2.35320	−0.0857554
$754$	0	0
$755$	33.9982	1.23732
$756$	−11.2420	−0.408867
$757$	50.8067	1.84660	0.923301	−	0.384077i	$-0.125480\pi$
$757$	50.8067	1.84660	0.923301	+	0.384077i	$0.125480\pi$
$758$	−69.5509	−2.52620
$759$	0.623443	0.0226295
$760$	−75.3168	−2.73203
$761$	7.06895	0.256249	0.128125	−	0.991758i	$-0.459104\pi$
$761$	7.06895	0.256249	0.128125	+	0.991758i	$0.459104\pi$
$762$	4.07737	0.147708
$763$	14.7429	0.533728
$764$	−8.62722	−0.312122
$765$	37.8073	1.36692
$766$	24.0905	0.870425
$767$	0	0
$768$	4.62703	0.166963
$769$	19.0465	0.686834	0.343417	−	0.939183i	$-0.388416\pi$
$769$	19.0465	0.686834	0.343417	+	0.939183i	$0.388416\pi$
$770$	−22.9282	−0.826275
$771$	−2.77974	−0.100110
$772$	−76.1728	−2.74152
$773$	34.6902	1.24772	0.623861	−	0.781536i	$-0.285563\pi$
$773$	34.6902	1.24772	0.623861	+	0.781536i	$0.285563\pi$
$774$	21.7464	0.781660
$775$	−119.622	−4.29697
$776$	82.5496	2.96336
$777$	−0.837026	−0.0300281
$778$	−45.9266	−1.64655
$779$	−25.5181	−0.914282
$780$	0	0
$781$	−3.78295	−0.135364
$782$	26.3885	0.943650
$783$	−3.75836	−0.134313
$784$	−19.2777	−0.688488
$785$	−54.8020	−1.95597
$786$	−0.305660	−0.0109025
$787$	29.2246	1.04174	0.520872	−	0.853635i	$-0.325607\pi$
$787$	29.2246	1.04174	0.520872	+	0.853635i	$0.325607\pi$
$788$	81.5943	2.90668
$789$	2.98318	0.106204
$790$	182.760	6.50232
$791$	15.9742	0.567976
$792$	−20.1482	−0.715934
$793$	0	0
$794$	92.7771	3.29254
$795$	4.14616	0.147049
$796$	2.01413	0.0713888
$797$	−3.30655	−0.117124	−0.0585620	−	0.998284i	$-0.518652\pi$
$797$	−3.30655	−0.117124	−0.0585620	+	0.998284i	$0.518652\pi$
$798$	−2.81424	−0.0996229
$799$	−29.2914	−1.03626
$800$	−91.4638	−3.23374
$801$	−4.53395	−0.160199
$802$	60.4437	2.13434
$803$	7.47534	0.263799
$804$	−5.05299	−0.178205
$805$	−29.4679	−1.03861
$806$	0	0
$807$	0.441116	0.0155280
$808$	89.8218	3.15992
$809$	−9.10142	−0.319989	−0.159994	−	0.987118i	$-0.551148\pi$
$809$	−9.10142	−0.319989	−0.159994	+	0.987118i	$0.551148\pi$
$810$	−92.2273	−3.24054
$811$	−25.0849	−0.880849	−0.440425	−	0.897790i	$-0.645172\pi$
$811$	−25.0849	−0.880849	−0.440425	+	0.897790i	$0.645172\pi$
$812$	33.5030	1.17573
$813$	4.89597	0.171709
$814$	−5.30655	−0.185994
$815$	11.7540	0.411725
$816$	4.79554	0.167877
$817$	7.65272	0.267735
$818$	38.3365	1.34040
$819$	0	0
$820$	−181.544	−6.33980
$821$	−6.29231	−0.219603	−0.109802	−	0.993954i	$-0.535022\pi$
$821$	−6.29231	−0.219603	−0.109802	+	0.993954i	$0.535022\pi$
$822$	−2.33638	−0.0814907
$823$	−32.7466	−1.14147	−0.570737	−	0.821133i	$-0.693343\pi$
$823$	−32.7466	−1.14147	−0.570737	+	0.821133i	$0.693343\pi$
$824$	31.3844	1.09333
$825$	2.25918	0.0786544
$826$	−25.7063	−0.894435
$827$	6.16948	0.214534	0.107267	−	0.994230i	$-0.465790\pi$
$827$	6.16948	0.214534	0.107267	+	0.994230i	$0.465790\pi$
$828$	−45.5278	−1.58220
$829$	16.0410	0.557127	0.278564	−	0.960418i	$-0.410142\pi$
$829$	16.0410	0.557127	0.278564	+	0.960418i	$0.410142\pi$
$830$	−2.31689	−0.0804205
$831$	−5.27216	−0.182889
$832$	0	0
$833$	7.24144	0.250901
$834$	−5.12211	−0.177364
$835$	5.36374	0.185620
$836$	−12.4659	−0.431144
$837$	−11.1955	−0.386972
$838$	72.1229	2.49144
$839$	−27.1837	−0.938484	−0.469242	−	0.883070i	$-0.655473\pi$
$839$	−27.1837	−0.938484	−0.469242	+	0.883070i	$0.655473\pi$
$840$	−11.3876	−0.392909
$841$	−17.7994	−0.613773
$842$	−34.3139	−1.18254
$843$	−3.85279	−0.132697
$844$	18.7380	0.644988
$845$	0	0
$846$	72.3289	2.48672
$847$	−2.15845	−0.0741651
$848$	−43.9809	−1.51031
$849$	1.72804	0.0593062
$850$	95.6242	3.27988
$851$	−6.82012	−0.233791
$852$	−3.30335	−0.113171
$853$	−24.2748	−0.831152	−0.415576	−	0.909558i	$-0.636420\pi$
$853$	−24.2748	−0.831152	−0.415576	+	0.909558i	$0.636420\pi$
$854$	−1.07826	−0.0368974
$855$	−32.8530	−1.12355
$856$	−70.3140	−2.40328
$857$	16.7036	0.570584	0.285292	−	0.958441i	$-0.407909\pi$
$857$	16.7036	0.570584	0.285292	+	0.958441i	$0.407909\pi$
$858$	0	0
$859$	−28.9414	−0.987468	−0.493734	−	0.869613i	$-0.664368\pi$
$859$	−28.9414	−0.987468	−0.493734	+	0.869613i	$0.664368\pi$
$860$	54.4439	1.85652
$861$	−3.85824	−0.131488
$862$	31.4789	1.07218
$863$	33.6601	1.14580	0.572901	−	0.819625i	$-0.305818\pi$
$863$	33.6601	1.14580	0.572901	+	0.819625i	$0.305818\pi$
$864$	−8.56011	−0.291221
$865$	35.1630	1.19558
$866$	70.2493	2.38717
$867$	1.39935	0.0475244
$868$	99.7993	3.38741
$869$	17.2049	0.583637
$870$	−6.69345	−0.226929
$871$	0	0
$872$	46.4213	1.57202
$873$	36.0079	1.21868
$874$	−22.9305	−0.775636
$875$	−62.2870	−2.10568
$876$	6.52762	0.220548
$877$	56.6214	1.91197	0.955985	−	0.293417i	$-0.0947925\pi$
$877$	56.6214	1.91197	0.955985	+	0.293417i	$0.0947925\pi$
$878$	87.7083	2.96001
$879$	3.52796	0.118995
$880$	−33.9505	−1.14447
$881$	35.8236	1.20693	0.603465	−	0.797390i	$-0.293786\pi$
$881$	35.8236	1.20693	0.603465	+	0.797390i	$0.293786\pi$
$882$	−17.8812	−0.602091
$883$	−29.2843	−0.985493	−0.492747	−	0.870173i	$-0.664007\pi$
$883$	−29.2843	−0.985493	−0.492747	+	0.870173i	$0.664007\pi$
$884$	0	0
$885$	3.58836	0.120621
$886$	101.249	3.40151
$887$	−36.8342	−1.23677	−0.618385	−	0.785875i	$-0.712213\pi$
$887$	−36.8342	−1.23677	−0.618385	+	0.785875i	$0.712213\pi$
$888$	−2.63557	−0.0884438
$889$	−18.1428	−0.608491
$890$	−16.2460	−0.544567
$891$	−8.68222	−0.290865
$892$	−99.4322	−3.32924
$893$	25.4530	0.851754
$894$	1.35847	0.0454341
$895$	79.5935	2.66052
$896$	−15.2771	−0.510371
$897$	0	0
$898$	38.2619	1.27682
$899$	33.3644	1.11277
$900$	−164.980	−5.49933
$901$	16.5209	0.550392
$902$	−24.4603	−0.814440
$903$	1.15706	0.0385045
$904$	50.2983	1.67290
$905$	−108.601	−3.61001
$906$	4.00000	0.132891
$907$	0.491159	0.0163087	0.00815433	−	0.999967i	$-0.497404\pi$
$907$	0.491159	0.0163087	0.00815433	+	0.999967i	$0.497404\pi$
$908$	−87.4929	−2.90355
$909$	39.1800	1.29952
$910$	0	0
$911$	−44.1275	−1.46201	−0.731005	−	0.682373i	$-0.760948\pi$
$911$	−44.1275	−1.46201	−0.731005	+	0.682373i	$0.760948\pi$
$912$	−4.16712	−0.137987
$913$	−0.218111	−0.00721841
$914$	50.8103	1.68066
$915$	0.150516	0.00497589
$916$	−61.7064	−2.03884
$917$	1.36007	0.0449136
$918$	8.94948	0.295377
$919$	−43.8564	−1.44669	−0.723345	−	0.690487i	$-0.757396\pi$
$919$	−43.8564	−1.44669	−0.723345	+	0.690487i	$0.757396\pi$
$920$	−92.7865	−3.05908
$921$	0.657635	0.0216698
$922$	−76.8186	−2.52989
$923$	0	0
$924$	−1.88480	−0.0620053
$925$	−24.7141	−0.812596
$926$	−42.7090	−1.40351
$927$	13.6898	0.449631
$928$	25.5106	0.837426
$929$	21.9917	0.721526	0.360763	−	0.932658i	$-0.382516\pi$
$929$	21.9917	0.721526	0.360763	+	0.932658i	$0.382516\pi$
$930$	−19.9386	−0.653811
$931$	−6.29251	−0.206229
$932$	98.8618	3.23833
$933$	0.790679	0.0258857
$934$	4.30744	0.140944
$935$	12.7531	0.417071
$936$	0	0
$937$	−15.9198	−0.520076	−0.260038	−	0.965598i	$-0.583735\pi$
$937$	−15.9198	−0.520076	−0.260038	+	0.965598i	$0.583735\pi$
$938$	32.1797	1.05070
$939$	2.34742	0.0766050
$940$	181.081	5.90621
$941$	−7.79435	−0.254088	−0.127044	−	0.991897i	$-0.540549\pi$
$941$	−7.79435	−0.254088	−0.127044	+	0.991897i	$0.540549\pi$
$942$	−6.44763	−0.210075
$943$	−31.4371	−1.02373
$944$	−38.0640	−1.23888
$945$	−9.99386	−0.325100
$946$	7.33549	0.238497
$947$	−37.4253	−1.21616	−0.608079	−	0.793876i	$-0.708060\pi$
$947$	−37.4253	−1.21616	−0.608079	+	0.793876i	$0.708060\pi$
$948$	15.0237	0.487947
$949$	0	0
$950$	−83.0935	−2.69591
$951$	−1.55799	−0.0505214
$952$	−45.3754	−1.47063
$953$	40.9457	1.32636	0.663181	−	0.748459i	$-0.269206\pi$
$953$	40.9457	1.32636	0.663181	+	0.748459i	$0.269206\pi$
$954$	−40.7949	−1.32078
$955$	−7.66940	−0.248176
$956$	−64.5238	−2.08685
$957$	−0.630117	−0.0203688
$958$	−51.6774	−1.66962
$959$	10.3960	0.335706
$960$	−2.46080	−0.0794221
$961$	68.3865	2.20602
$962$	0	0
$963$	−30.6708	−0.988351
$964$	−2.62379	−0.0845065
$965$	−67.7158	−2.17985
$966$	−3.46700	−0.111549
$967$	37.0738	1.19221	0.596107	−	0.802905i	$-0.296713\pi$
$967$	37.0738	1.19221	0.596107	+	0.802905i	$0.296713\pi$
$968$	−6.79636	−0.218443
$969$	1.56533	0.0502857
$970$	129.023	4.14268
$971$	−9.13718	−0.293226	−0.146613	−	0.989194i	$-0.546837\pi$
$971$	−9.13718	−0.293226	−0.146613	+	0.989194i	$0.546837\pi$
$972$	−23.2066	−0.744352
$973$	22.7915	0.730662
$974$	12.2311	0.391909
$975$	0	0
$976$	−1.59662	−0.0511064
$977$	−24.8647	−0.795491	−0.397745	−	0.917496i	$-0.630207\pi$
$977$	−24.8647	−0.795491	−0.397745	+	0.917496i	$0.630207\pi$
$978$	1.38290	0.0442202
$979$	−1.52939	−0.0488794
$980$	−44.7669	−1.43003
$981$	20.2488	0.646495
$982$	−109.374	−3.49028
$983$	22.0037	0.701808	0.350904	−	0.936411i	$-0.385874\pi$
$983$	22.0037	0.701808	0.350904	+	0.936411i	$0.385874\pi$
$984$	−12.1485	−0.387281
$985$	72.5354	2.31117
$986$	−26.6710	−0.849377
$987$	3.84840	0.122496
$988$	0	0
$989$	9.42777	0.299786
$990$	−31.4911	−1.00085
$991$	44.3616	1.40919	0.704596	−	0.709608i	$-0.251128\pi$
$991$	44.3616	1.40919	0.704596	+	0.709608i	$0.251128\pi$
$992$	75.9913	2.41273
$993$	−4.44058	−0.140918
$994$	21.0372	0.667259
$995$	1.79051	0.0567630
$996$	−0.190459	−0.00603492
$997$	−0.262678	−0.00831910	−0.00415955	−	0.999991i	$-0.501324\pi$
$997$	−0.262678	−0.00831910	−0.00415955	+	0.999991i	$0.501324\pi$
$998$	−53.3009	−1.68721
$999$	−2.31300	−0.0731800

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.2.a.i.1.1		4
13.12	even	2		143.2.a.b.1.4	✓	4
39.38	odd	2		1287.2.a.k.1.1		4
52.51	odd	2		2288.2.a.x.1.3		4
65.64	even	2		3575.2.a.k.1.1		4
91.90	odd	2		7007.2.a.n.1.4		4
104.51	odd	2		9152.2.a.cg.1.2		4
104.77	even	2		9152.2.a.ch.1.3		4
143.142	odd	2		1573.2.a.f.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.2.a.b.1.4	✓	4	13.12	even	2
1287.2.a.k.1.1		4	39.38	odd	2
1573.2.a.f.1.1		4	143.142	odd	2
1859.2.a.i.1.1		4	1.1	even	1	trivial
2288.2.a.x.1.3		4	52.51	odd	2
3575.2.a.k.1.1		4	65.64	even	2
7007.2.a.n.1.4		4	91.90	odd	2
9152.2.a.cg.1.2		4	104.51	odd	2
9152.2.a.ch.1.3		4	104.77	even	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:	\( N \)	\(=\)	\( 1859 = 11 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1859.a (trivial)

\(f(q)\)	\(=\)	\(q-2.57641 q^{2} -0.188279 q^{3} +4.63791 q^{4} +4.12300 q^{5} +0.485084 q^{6} -2.15845 q^{7} -6.79636 q^{8} -2.96455 q^{9} +O(q^{10})\)	\(q-2.57641 q^{2} -0.188279 q^{3} +4.63791 q^{4} +4.12300 q^{5} +0.485084 q^{6} -2.15845 q^{7} -6.79636 q^{8} -2.96455 q^{9} -10.6226 q^{10} -1.00000 q^{11} -0.873220 q^{12} +5.56105 q^{14} -0.776272 q^{15} +8.23442 q^{16} -3.09317 q^{17} +7.63791 q^{18} +2.68783 q^{19} +19.1221 q^{20} +0.406389 q^{21} +2.57641 q^{22} +3.31128 q^{23} +1.27961 q^{24} +11.9991 q^{25} +1.12300 q^{27} -10.0107 q^{28} -3.34673 q^{29} +2.00000 q^{30} -9.96928 q^{31} -7.62255 q^{32} +0.188279 q^{33} +7.96928 q^{34} -8.89927 q^{35} -13.7493 q^{36} -2.05966 q^{37} -6.92497 q^{38} -28.0214 q^{40} -9.49394 q^{41} -1.04703 q^{42} +2.84717 q^{43} -4.63791 q^{44} -12.2228 q^{45} -8.53122 q^{46} +9.46972 q^{47} -1.55036 q^{48} -2.34111 q^{49} -30.9147 q^{50} +0.582377 q^{51} -5.34111 q^{53} -2.89331 q^{54} -4.12300 q^{55} +14.6696 q^{56} -0.506062 q^{57} +8.62255 q^{58} -4.62255 q^{59} -3.60028 q^{60} -0.193895 q^{61} +25.6850 q^{62} +6.39883 q^{63} +3.17003 q^{64} -0.485084 q^{66} +5.78662 q^{67} -14.3458 q^{68} -0.623443 q^{69} +22.9282 q^{70} +3.78295 q^{71} +20.1482 q^{72} -7.47534 q^{73} +5.30655 q^{74} -2.25918 q^{75} +12.4659 q^{76} +2.15845 q^{77} -17.2049 q^{79} +33.9505 q^{80} +8.68222 q^{81} +24.4603 q^{82} +0.218111 q^{83} +1.88480 q^{84} -12.7531 q^{85} -7.33549 q^{86} +0.630117 q^{87} +6.79636 q^{88} +1.52939 q^{89} +31.4911 q^{90} +15.3574 q^{92} +1.87700 q^{93} -24.3979 q^{94} +11.0819 q^{95} +1.43516 q^{96} -12.1462 q^{97} +6.03167 q^{98} +2.96455 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 3 q^{2} + 3 q^{4} + q^{6} - 6 q^{7} - 9 q^{8} + 2 q^{9}+O(q^{10}) \) 4 * q - 3 * q^2 + 3 * q^4 + q^6 - 6 * q^7 - 9 * q^8 + 2 * q^9	\( 4 q - 3 q^{2} + 3 q^{4} + q^{6} - 6 q^{7} - 9 q^{8} + 2 q^{9} - 8 q^{10} - 4 q^{11} + 4 q^{12} - 4 q^{14} + 10 q^{15} + 5 q^{16} + 6 q^{17} + 15 q^{18} - 8 q^{19} + 24 q^{20} + 2 q^{21} + 3 q^{22} - 4 q^{23} - 2 q^{24} + 12 q^{25} - 12 q^{27} + q^{28} - 10 q^{29} + 8 q^{30} - 2 q^{31} + 4 q^{32} - 6 q^{34} - 6 q^{35} - 28 q^{36} - 12 q^{37} - 5 q^{38} - 30 q^{40} - 8 q^{41} - 13 q^{42} + 26 q^{43} - 3 q^{44} - 26 q^{45} - 6 q^{46} + 18 q^{47} - 21 q^{48} + 6 q^{49} - 29 q^{50} - 22 q^{51} - 6 q^{53} + q^{54} + 33 q^{56} - 32 q^{57} + 16 q^{59} - 26 q^{60} - 12 q^{61} + 12 q^{62} - 22 q^{63} + 5 q^{64} - q^{66} - 2 q^{67} - 18 q^{68} - 4 q^{69} + 28 q^{70} + 14 q^{71} + 6 q^{72} - 22 q^{73} + 28 q^{74} - 36 q^{75} + 6 q^{76} + 6 q^{77} - 10 q^{79} + 26 q^{80} + 4 q^{81} + 42 q^{82} + 2 q^{83} - 5 q^{84} - 48 q^{85} - 2 q^{86} + 16 q^{87} + 9 q^{88} - 10 q^{89} + 24 q^{90} + 17 q^{92} + 24 q^{93} - 14 q^{94} + 2 q^{95} + 8 q^{96} - 22 q^{97} + 14 q^{98} - 2 q^{99}+O(q^{100}) \) 4 * q - 3 * q^2 + 3 * q^4 + q^6 - 6 * q^7 - 9 * q^8 + 2 * q^9 - 8 * q^10 - 4 * q^11 + 4 * q^12 - 4 * q^14 + 10 * q^15 + 5 * q^16 + 6 * q^17 + 15 * q^18 - 8 * q^19 + 24 * q^20 + 2 * q^21 + 3 * q^22 - 4 * q^23 - 2 * q^24 + 12 * q^25 - 12 * q^27 + q^28 - 10 * q^29 + 8 * q^30 - 2 * q^31 + 4 * q^32 - 6 * q^34 - 6 * q^35 - 28 * q^36 - 12 * q^37 - 5 * q^38 - 30 * q^40 - 8 * q^41 - 13 * q^42 + 26 * q^43 - 3 * q^44 - 26 * q^45 - 6 * q^46 + 18 * q^47 - 21 * q^48 + 6 * q^49 - 29 * q^50 - 22 * q^51 - 6 * q^53 + q^54 + 33 * q^56 - 32 * q^57 + 16 * q^59 - 26 * q^60 - 12 * q^61 + 12 * q^62 - 22 * q^63 + 5 * q^64 - q^66 - 2 * q^67 - 18 * q^68 - 4 * q^69 + 28 * q^70 + 14 * q^71 + 6 * q^72 - 22 * q^73 + 28 * q^74 - 36 * q^75 + 6 * q^76 + 6 * q^77 - 10 * q^79 + 26 * q^80 + 4 * q^81 + 42 * q^82 + 2 * q^83 - 5 * q^84 - 48 * q^85 - 2 * q^86 + 16 * q^87 + 9 * q^88 - 10 * q^89 + 24 * q^90 + 17 * q^92 + 24 * q^93 - 14 * q^94 + 2 * q^95 + 8 * q^96 - 22 * q^97 + 14 * q^98 - 2 * q^99

Introduction

L-functions

Modular forms

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Database

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