LMFDB - Embedded newform 1859.2.a.t.1.21

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:	$0$
Dimension:	$21$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.21
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)

$f(q)$	$=$	$q+2.68791 q^{2} -2.90985 q^{3} +5.22486 q^{4} +3.09378 q^{5} -7.82142 q^{6} +1.70397 q^{7} +8.66813 q^{8} +5.46725 q^{9} +O(q^{10})$	\(q+2.68791 q^{2} -2.90985 q^{3} +5.22486 q^{4} +3.09378 q^{5} -7.82142 q^{6} +1.70397 q^{7} +8.66813 q^{8} +5.46725 q^{9} +8.31580 q^{10} +1.00000 q^{11} -15.2036 q^{12} +4.58011 q^{14} -9.00245 q^{15} +12.8494 q^{16} +1.04237 q^{17} +14.6955 q^{18} -0.291109 q^{19} +16.1646 q^{20} -4.95829 q^{21} +2.68791 q^{22} -7.88320 q^{23} -25.2230 q^{24} +4.57148 q^{25} -7.17933 q^{27} +8.90299 q^{28} -0.935722 q^{29} -24.1978 q^{30} +1.01935 q^{31} +17.2019 q^{32} -2.90985 q^{33} +2.80179 q^{34} +5.27170 q^{35} +28.5656 q^{36} -6.79609 q^{37} -0.782475 q^{38} +26.8173 q^{40} +4.76040 q^{41} -13.3274 q^{42} -10.1591 q^{43} +5.22486 q^{44} +16.9145 q^{45} -21.1893 q^{46} +2.04588 q^{47} -37.3900 q^{48} -4.09650 q^{49} +12.2877 q^{50} -3.03314 q^{51} -4.76011 q^{53} -19.2974 q^{54} +3.09378 q^{55} +14.7702 q^{56} +0.847085 q^{57} -2.51514 q^{58} +11.6149 q^{59} -47.0365 q^{60} +9.48390 q^{61} +2.73991 q^{62} +9.31601 q^{63} +20.5382 q^{64} -7.82142 q^{66} +9.43031 q^{67} +5.44623 q^{68} +22.9389 q^{69} +14.1699 q^{70} +0.582928 q^{71} +47.3908 q^{72} +15.8198 q^{73} -18.2673 q^{74} -13.3023 q^{75} -1.52100 q^{76} +1.70397 q^{77} -12.2976 q^{79} +39.7533 q^{80} +4.48905 q^{81} +12.7955 q^{82} -10.5008 q^{83} -25.9064 q^{84} +3.22486 q^{85} -27.3069 q^{86} +2.72281 q^{87} +8.66813 q^{88} +5.79180 q^{89} +45.4646 q^{90} -41.1886 q^{92} -2.96615 q^{93} +5.49914 q^{94} -0.900628 q^{95} -50.0549 q^{96} -0.922801 q^{97} -11.0110 q^{98} +5.46725 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q + 6 q^{3} + 32 q^{4} + 7 q^{5} - 19 q^{6} + q^{7} - 3 q^{8} + 33 q^{9}+O(q^{10}) $ 21 * q + 6 * q^3 + 32 * q^4 + 7 * q^5 - 19 * q^6 + q^7 - 3 * q^8 + 33 * q^9	\( 21 q + 6 q^{3} + 32 q^{4} + 7 q^{5} - 19 q^{6} + q^{7} - 3 q^{8} + 33 q^{9} + 18 q^{10} + 21 q^{11} + 23 q^{12} + 20 q^{14} + 16 q^{15} + 50 q^{16} + 16 q^{17} + 3 q^{18} - 11 q^{19} + 24 q^{20} - 5 q^{21} - 9 q^{23} - 54 q^{24} + 36 q^{25} - 11 q^{28} + 28 q^{29} + 21 q^{30} + 15 q^{31} - 61 q^{32} + 6 q^{33} - 6 q^{34} - 3 q^{35} + 45 q^{36} - 12 q^{37} + q^{38} + 55 q^{40} - 4 q^{41} - 34 q^{42} + 17 q^{43} + 32 q^{44} + 9 q^{45} + 11 q^{46} + 36 q^{47} + 24 q^{48} + 72 q^{49} - 9 q^{50} + 2 q^{51} + 19 q^{53} + q^{54} + 7 q^{55} + 44 q^{56} - 4 q^{57} - 33 q^{58} + 54 q^{59} + 64 q^{60} + 98 q^{61} - 29 q^{62} - 81 q^{63} + 63 q^{64} - 19 q^{66} + 25 q^{67} + 4 q^{68} + 89 q^{69} + 65 q^{70} + 37 q^{71} + 55 q^{72} + 8 q^{73} - 11 q^{74} + 24 q^{75} + 13 q^{76} + q^{77} + 24 q^{79} + 26 q^{80} + 81 q^{81} + 26 q^{82} - 34 q^{83} - 103 q^{84} - 11 q^{85} + 30 q^{86} + 32 q^{87} - 3 q^{88} + 6 q^{89} + 47 q^{90} - 80 q^{92} + 41 q^{93} + 40 q^{94} + 20 q^{95} - 98 q^{96} - 5 q^{98} + 33 q^{99}+O(q^{100}) \) 21 * q + 6 * q^3 + 32 * q^4 + 7 * q^5 - 19 * q^6 + q^7 - 3 * q^8 + 33 * q^9 + 18 * q^10 + 21 * q^11 + 23 * q^12 + 20 * q^14 + 16 * q^15 + 50 * q^16 + 16 * q^17 + 3 * q^18 - 11 * q^19 + 24 * q^20 - 5 * q^21 - 9 * q^23 - 54 * q^24 + 36 * q^25 - 11 * q^28 + 28 * q^29 + 21 * q^30 + 15 * q^31 - 61 * q^32 + 6 * q^33 - 6 * q^34 - 3 * q^35 + 45 * q^36 - 12 * q^37 + q^38 + 55 * q^40 - 4 * q^41 - 34 * q^42 + 17 * q^43 + 32 * q^44 + 9 * q^45 + 11 * q^46 + 36 * q^47 + 24 * q^48 + 72 * q^49 - 9 * q^50 + 2 * q^51 + 19 * q^53 + q^54 + 7 * q^55 + 44 * q^56 - 4 * q^57 - 33 * q^58 + 54 * q^59 + 64 * q^60 + 98 * q^61 - 29 * q^62 - 81 * q^63 + 63 * q^64 - 19 * q^66 + 25 * q^67 + 4 * q^68 + 89 * q^69 + 65 * q^70 + 37 * q^71 + 55 * q^72 + 8 * q^73 - 11 * q^74 + 24 * q^75 + 13 * q^76 + q^77 + 24 * q^79 + 26 * q^80 + 81 * q^81 + 26 * q^82 - 34 * q^83 - 103 * q^84 - 11 * q^85 + 30 * q^86 + 32 * q^87 - 3 * q^88 + 6 * q^89 + 47 * q^90 - 80 * q^92 + 41 * q^93 + 40 * q^94 + 20 * q^95 - 98 * q^96 - 5 * q^98 + 33 * 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 $

$2$	2.68791	1.90064	0.950320	−	0.311276i	$-0.100756\pi$
$2$	2.68791	1.90064	0.950320	+	0.311276i	$0.100756\pi$
$3$	−2.90985	−1.68000	−0.840002	−	0.542583i	$-0.817446\pi$
$3$	−2.90985	−1.68000	−0.840002	+	0.542583i	$0.817446\pi$
$4$	5.22486	2.61243
$5$	3.09378	1.38358	0.691790	−	0.722098i	$-0.256822\pi$
$5$	3.09378	1.38358	0.691790	+	0.722098i	$0.256822\pi$
$6$	−7.82142	−3.19308
$7$	1.70397	0.644039	0.322020	−	0.946733i	$-0.395638\pi$
$7$	1.70397	0.644039	0.322020	+	0.946733i	$0.395638\pi$
$8$	8.66813	3.06465
$9$	5.46725	1.82242
$10$	8.31580	2.62969
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−15.2036	−4.38889
$13$	0	0
$13$	0	0
$14$	4.58011	1.22409
$15$	−9.00245	−2.32442
$16$	12.8494	3.21236
$17$	1.04237	0.252811	0.126406	−	0.991979i	$-0.459656\pi$
$17$	1.04237	0.252811	0.126406	+	0.991979i	$0.459656\pi$
$18$	14.6955	3.46375
$19$	−0.291109	−0.0667850	−0.0333925	−	0.999442i	$-0.510631\pi$
$19$	−0.291109	−0.0667850	−0.0333925	+	0.999442i	$0.510631\pi$
$20$	16.1646	3.61451
$21$	−4.95829	−1.08199
$22$	2.68791	0.573064
$23$	−7.88320	−1.64376	−0.821880	−	0.569661i	$-0.807075\pi$
$23$	−7.88320	−1.64376	−0.821880	+	0.569661i	$0.807075\pi$
$24$	−25.2230	−5.14862
$25$	4.57148	0.914296
$26$	0	0
$27$	−7.17933	−1.38166
$28$	8.90299	1.68251
$29$	−0.935722	−0.173759	−0.0868796	−	0.996219i	$-0.527690\pi$
$29$	−0.935722	−0.173759	−0.0868796	+	0.996219i	$0.527690\pi$
$30$	−24.1978	−4.41789
$31$	1.01935	0.183080	0.0915399	−	0.995801i	$-0.470821\pi$
$31$	1.01935	0.183080	0.0915399	+	0.995801i	$0.470821\pi$
$32$	17.2019	3.04089
$33$	−2.90985	−0.506540
$34$	2.80179	0.480503
$35$	5.27170	0.891080
$36$	28.5656	4.76093
$37$	−6.79609	−1.11727	−0.558635	−	0.829414i	$-0.688675\pi$
$37$	−6.79609	−1.11727	−0.558635	+	0.829414i	$0.688675\pi$
$38$	−0.782475	−0.126934
$39$	0	0
$40$	26.8173	4.24019
$41$	4.76040	0.743450	0.371725	−	0.928343i	$-0.378766\pi$
$41$	4.76040	0.743450	0.371725	+	0.928343i	$0.378766\pi$
$42$	−13.3274	−2.05647
$43$	−10.1591	−1.54926	−0.774628	−	0.632418i	$-0.782063\pi$
$43$	−10.1591	−1.54926	−0.774628	+	0.632418i	$0.782063\pi$
$44$	5.22486	0.787677
$45$	16.9145	2.52146
$46$	−21.1893	−3.12419
$47$	2.04588	0.298422	0.149211	−	0.988805i	$-0.452327\pi$
$47$	2.04588	0.298422	0.149211	+	0.988805i	$0.452327\pi$
$48$	−37.3900	−5.39678
$49$	−4.09650	−0.585214
$50$	12.2877	1.73775
$51$	−3.03314	−0.424724
$52$	0	0
$53$	−4.76011	−0.653851	−0.326926	−	0.945050i	$-0.606013\pi$
$53$	−4.76011	−0.653851	−0.326926	+	0.945050i	$0.606013\pi$
$54$	−19.2974	−2.62604
$55$	3.09378	0.417165
$56$	14.7702	1.97375
$57$	0.847085	0.112199
$58$	−2.51514	−0.330254
$59$	11.6149	1.51212	0.756062	−	0.654500i	$-0.227121\pi$
$59$	11.6149	1.51212	0.756062	+	0.654500i	$0.227121\pi$
$60$	−47.0365	−6.07239
$61$	9.48390	1.21429	0.607145	−	0.794591i	$-0.292315\pi$
$61$	9.48390	1.21429	0.607145	+	0.794591i	$0.292315\pi$
$62$	2.73991	0.347969
$63$	9.31601	1.17371
$64$	20.5382	2.56727
$65$	0	0
$66$	−7.82142	−0.962751
$67$	9.43031	1.15210	0.576048	−	0.817416i	$-0.304594\pi$
$67$	9.43031	1.15210	0.576048	+	0.817416i	$0.304594\pi$
$68$	5.44623	0.660452
$69$	22.9389	2.76152
$70$	14.1699	1.69362
$71$	0.582928	0.0691808	0.0345904	−	0.999402i	$-0.488987\pi$
$71$	0.582928	0.0691808	0.0345904	+	0.999402i	$0.488987\pi$
$72$	47.3908	5.58506
$73$	15.8198	1.85157	0.925784	−	0.378053i	$-0.123406\pi$
$73$	15.8198	1.85157	0.925784	+	0.378053i	$0.123406\pi$
$74$	−18.2673	−2.12353
$75$	−13.3023	−1.53602
$76$	−1.52100	−0.174471
$77$	1.70397	0.194185
$78$	0	0
$79$	−12.2976	−1.38358	−0.691792	−	0.722097i	$-0.743179\pi$
$79$	−12.2976	−1.38358	−0.691792	+	0.722097i	$0.743179\pi$
$80$	39.7533	4.44456
$81$	4.48905	0.498783
$82$	12.7955	1.41303
$83$	−10.5008	−1.15261	−0.576305	−	0.817235i	$-0.695506\pi$
$83$	−10.5008	−1.15261	−0.576305	+	0.817235i	$0.695506\pi$
$84$	−25.9064	−2.82662
$85$	3.22486	0.349785
$86$	−27.3069	−2.94458
$87$	2.72281	0.291916
$88$	8.66813	0.924026
$89$	5.79180	0.613930	0.306965	−	0.951721i	$-0.400687\pi$
$89$	5.79180	0.613930	0.306965	+	0.951721i	$0.400687\pi$
$90$	45.4646	4.79238
$91$	0	0
$92$	−41.1886	−4.29421
$93$	−2.96615	−0.307575
$94$	5.49914	0.567193
$95$	−0.900628	−0.0924025
$96$	−50.0549	−5.10870
$97$	−0.922801	−0.0936963	−0.0468481	−	0.998902i	$-0.514918\pi$
$97$	−0.922801	−0.0936963	−0.0468481	+	0.998902i	$0.514918\pi$
$98$	−11.0110	−1.11228
$99$	5.46725	0.549479
$100$	23.8853	2.38853
$101$	−12.8629	−1.27990	−0.639951	−	0.768415i	$-0.721046\pi$
$101$	−12.8629	−1.27990	−0.639951	+	0.768415i	$0.721046\pi$
$102$	−8.15280	−0.807248
$103$	−16.8954	−1.66475	−0.832377	−	0.554210i	$-0.813021\pi$
$103$	−16.8954	−1.66475	−0.832377	+	0.554210i	$0.813021\pi$
$104$	0	0
$105$	−15.3399	−1.49702
$106$	−12.7947	−1.24274
$107$	4.69227	0.453619	0.226809	−	0.973939i	$-0.427171\pi$
$107$	4.69227	0.453619	0.226809	+	0.973939i	$0.427171\pi$
$108$	−37.5110	−3.60949
$109$	13.7724	1.31916	0.659580	−	0.751634i	$-0.270734\pi$
$109$	13.7724	1.31916	0.659580	+	0.751634i	$0.270734\pi$
$110$	8.31580	0.792881
$111$	19.7756	1.87702
$112$	21.8950	2.06888
$113$	−8.36051	−0.786491	−0.393245	−	0.919434i	$-0.628648\pi$
$113$	−8.36051	−0.786491	−0.393245	+	0.919434i	$0.628648\pi$
$114$	2.27689	0.213250
$115$	−24.3889	−2.27428
$116$	−4.88902	−0.453934
$117$	0	0
$118$	31.2197	2.87400
$119$	1.77616	0.162820
$120$	−78.0344	−7.12353
$121$	1.00000	0.0909091
$122$	25.4919	2.30793
$123$	−13.8521	−1.24900
$124$	5.32594	0.478283
$125$	−1.32574	−0.118578
$126$	25.0406	2.23079
$127$	−4.09166	−0.363076	−0.181538	−	0.983384i	$-0.558107\pi$
$127$	−4.09166	−0.363076	−0.181538	+	0.983384i	$0.558107\pi$
$128$	20.8010	1.83857
$129$	29.5616	2.60276
$130$	0	0
$131$	−1.63924	−0.143221	−0.0716104	−	0.997433i	$-0.522814\pi$
$131$	−1.63924	−0.143221	−0.0716104	+	0.997433i	$0.522814\pi$
$132$	−15.2036	−1.32330
$133$	−0.496041	−0.0430122
$134$	25.3478	2.18972
$135$	−22.2113	−1.91164
$136$	9.03538	0.774778
$137$	7.27779	0.621783	0.310892	−	0.950445i	$-0.399372\pi$
$137$	7.27779	0.621783	0.310892	+	0.950445i	$0.399372\pi$
$138$	61.6578	5.24866
$139$	11.0849	0.940212	0.470106	−	0.882610i	$-0.344216\pi$
$139$	11.0849	0.940212	0.470106	+	0.882610i	$0.344216\pi$
$140$	27.5439	2.32788
$141$	−5.95321	−0.501351
$142$	1.56686	0.131488
$143$	0	0
$144$	70.2510	5.85425
$145$	−2.89492	−0.240410
$146$	42.5222	3.51916
$147$	11.9202	0.983162
$148$	−35.5086	−2.91879
$149$	0.116636	0.00955523	0.00477761	−	0.999989i	$-0.498479\pi$
$149$	0.116636	0.00955523	0.00477761	+	0.999989i	$0.498479\pi$
$150$	−35.7555	−2.91942
$151$	−9.89456	−0.805208	−0.402604	−	0.915374i	$-0.631895\pi$
$151$	−9.89456	−0.805208	−0.402604	+	0.915374i	$0.631895\pi$
$152$	−2.52337	−0.204673
$153$	5.69888	0.460727
$154$	4.58011	0.369076
$155$	3.15363	0.253306
$156$	0	0
$157$	7.33594	0.585472	0.292736	−	0.956193i	$-0.405434\pi$
$157$	7.33594	0.585472	0.292736	+	0.956193i	$0.405434\pi$
$158$	−33.0547	−2.62969
$159$	13.8512	1.09847
$160$	53.2188	4.20731
$161$	−13.4327	−1.05865
$162$	12.0661	0.948006
$163$	−20.1802	−1.58064	−0.790318	−	0.612696i	$-0.790085\pi$
$163$	−20.1802	−1.58064	−0.790318	+	0.612696i	$0.790085\pi$
$164$	24.8724	1.94221
$165$	−9.00245	−0.700840
$166$	−28.2251	−2.19069
$167$	−4.95156	−0.383163	−0.191582	−	0.981477i	$-0.561362\pi$
$167$	−4.95156	−0.383163	−0.191582	+	0.981477i	$0.561362\pi$
$168$	−42.9791	−3.31591
$169$	0	0
$170$	8.66813	0.664815
$171$	−1.59157	−0.121710
$172$	−53.0801	−4.04732
$173$	21.1077	1.60479	0.802394	−	0.596795i	$-0.203560\pi$
$173$	21.1077	1.60479	0.802394	+	0.596795i	$0.203560\pi$
$174$	7.31868	0.554828
$175$	7.78965	0.588842
$176$	12.8494	0.968562
$177$	−33.7975	−2.54038
$178$	15.5678	1.16686
$179$	1.06432	0.0795513	0.0397757	−	0.999209i	$-0.487336\pi$
$179$	1.06432	0.0795513	0.0397757	+	0.999209i	$0.487336\pi$
$180$	88.3757	6.58713
$181$	18.7869	1.39642	0.698210	−	0.715893i	$-0.253980\pi$
$181$	18.7869	1.39642	0.698210	+	0.715893i	$0.253980\pi$
$182$	0	0
$183$	−27.5968	−2.04001
$184$	−68.3326	−5.03754
$185$	−21.0256	−1.54583
$186$	−7.97273	−0.584589
$187$	1.04237	0.0762255
$188$	10.6894	0.779608
$189$	−12.2333	−0.889844
$190$	−2.42081	−0.175624
$191$	−19.2897	−1.39575	−0.697876	−	0.716219i	$-0.745871\pi$
$191$	−19.2897	−1.39575	−0.697876	+	0.716219i	$0.745871\pi$
$192$	−59.7630	−4.31303
$193$	10.4036	0.748864	0.374432	−	0.927254i	$-0.377838\pi$
$193$	10.4036	0.748864	0.374432	+	0.927254i	$0.377838\pi$
$194$	−2.48041	−0.178083
$195$	0	0
$196$	−21.4036	−1.52883
$197$	9.93369	0.707746	0.353873	−	0.935293i	$-0.384864\pi$
$197$	9.93369	0.707746	0.353873	+	0.935293i	$0.384864\pi$
$198$	14.6955	1.04436
$199$	−12.7227	−0.901886	−0.450943	−	0.892553i	$-0.648912\pi$
$199$	−12.7227	−0.901886	−0.450943	+	0.892553i	$0.648912\pi$
$200$	39.6262	2.80199
$201$	−27.4408	−1.93553
$202$	−34.5742	−2.43263
$203$	−1.59444	−0.111908
$204$	−15.8477	−1.10956
$205$	14.7276	1.02862
$206$	−45.4133	−3.16410
$207$	−43.0994	−2.99561
$208$	0	0
$209$	−0.291109	−0.0201364
$210$	−41.2322	−2.84529
$211$	2.00015	0.137696	0.0688480	−	0.997627i	$-0.478068\pi$
$211$	2.00015	0.137696	0.0688480	+	0.997627i	$0.478068\pi$
$212$	−24.8709	−1.70814
$213$	−1.69623	−0.116224
$214$	12.6124	0.862166
$215$	−31.4302	−2.14352
$216$	−62.2313	−4.23431
$217$	1.73693	0.117911
$218$	37.0191	2.50725
$219$	−46.0333	−3.11064
$220$	16.1646	1.08981
$221$	0	0
$222$	53.1551	3.56753
$223$	−3.25053	−0.217672	−0.108836	−	0.994060i	$-0.534712\pi$
$223$	−3.25053	−0.217672	−0.108836	+	0.994060i	$0.534712\pi$
$224$	29.3114	1.95845
$225$	24.9934	1.66623
$226$	−22.4723	−1.49483
$227$	−17.3081	−1.14878	−0.574388	−	0.818583i	$-0.694760\pi$
$227$	−17.3081	−1.14878	−0.574388	+	0.818583i	$0.694760\pi$
$228$	4.42590	0.293112
$229$	−12.2229	−0.807712	−0.403856	−	0.914822i	$-0.632330\pi$
$229$	−12.2229	−0.807712	−0.403856	+	0.914822i	$0.632330\pi$
$230$	−65.5551	−4.32258
$231$	−4.95829	−0.326232
$232$	−8.11096	−0.532511
$233$	0.275611	0.0180558	0.00902792	−	0.999959i	$-0.497126\pi$
$233$	0.275611	0.0180558	0.00902792	+	0.999959i	$0.497126\pi$
$234$	0	0
$235$	6.32951	0.412892
$236$	60.6860	3.95032
$237$	35.7841	2.32443
$238$	4.77416	0.309463
$239$	22.4425	1.45168	0.725841	−	0.687863i	$-0.241451\pi$
$239$	22.4425	1.45168	0.725841	+	0.687863i	$0.241451\pi$
$240$	−115.676	−7.46688
$241$	−17.7396	−1.14271	−0.571353	−	0.820705i	$-0.693581\pi$
$241$	−17.7396	−1.14271	−0.571353	+	0.820705i	$0.693581\pi$
$242$	2.68791	0.172785
$243$	8.47551	0.543704
$244$	49.5521	3.17225
$245$	−12.6737	−0.809691
$246$	−37.2331	−2.37390
$247$	0	0
$248$	8.83582	0.561075
$249$	30.5557	1.93639
$250$	−3.56348	−0.225374
$251$	−20.5224	−1.29537	−0.647683	−	0.761910i	$-0.724262\pi$
$251$	−20.5224	−1.29537	−0.647683	+	0.761910i	$0.724262\pi$
$252$	48.6748	3.06623
$253$	−7.88320	−0.495612
$254$	−10.9980	−0.690076
$255$	−9.38387	−0.587641
$256$	14.8350	0.927185
$257$	−10.1295	−0.631862	−0.315931	−	0.948782i	$-0.602317\pi$
$257$	−10.1295	−0.631862	−0.315931	+	0.948782i	$0.602317\pi$
$258$	79.4590	4.94690
$259$	−11.5803	−0.719565
$260$	0	0
$261$	−5.11583	−0.316662
$262$	−4.40612	−0.272211
$263$	0.0974277	0.00600765	0.00300383	−	0.999995i	$-0.499044\pi$
$263$	0.0974277	0.00600765	0.00300383	+	0.999995i	$0.499044\pi$
$264$	−25.2230	−1.55237
$265$	−14.7267	−0.904656
$266$	−1.33331	−0.0817506
$267$	−16.8533	−1.03140
$268$	49.2721	3.00977
$269$	−3.50796	−0.213884	−0.106942	−	0.994265i	$-0.534106\pi$
$269$	−3.50796	−0.213884	−0.106942	+	0.994265i	$0.534106\pi$
$270$	−59.7019	−3.63334
$271$	15.3135	0.930230	0.465115	−	0.885250i	$-0.346013\pi$
$271$	15.3135	0.930230	0.465115	+	0.885250i	$0.346013\pi$
$272$	13.3938	0.812121
$273$	0	0
$274$	19.5620	1.18179
$275$	4.57148	0.275671
$276$	119.853	7.21429
$277$	−20.6695	−1.24191	−0.620954	−	0.783847i	$-0.713255\pi$
$277$	−20.6695	−1.24191	−0.620954	+	0.783847i	$0.713255\pi$
$278$	29.7953	1.78700
$279$	5.57301	0.333648
$280$	45.6958	2.73085
$281$	−28.7750	−1.71657	−0.858286	−	0.513172i	$-0.828470\pi$
$281$	−28.7750	−1.71657	−0.858286	+	0.513172i	$0.828470\pi$
$282$	−16.0017	−0.952887
$283$	−30.2757	−1.79971	−0.899853	−	0.436193i	$-0.856326\pi$
$283$	−30.2757	−1.79971	−0.899853	+	0.436193i	$0.856326\pi$
$284$	3.04571	0.180730
$285$	2.62070	0.155237
$286$	0	0
$287$	8.11157	0.478811
$288$	94.0468	5.54176
$289$	−15.9135	−0.936086
$290$	−7.78128	−0.456933
$291$	2.68522	0.157410
$292$	82.6562	4.83709
$293$	−11.0766	−0.647100	−0.323550	−	0.946211i	$-0.604876\pi$
$293$	−11.0766	−0.647100	−0.323550	+	0.946211i	$0.604876\pi$
$294$	32.0404	1.86864
$295$	35.9338	2.09215
$296$	−58.9094	−3.42404
$297$	−7.17933	−0.416587
$298$	0.313508	0.0181610
$299$	0	0
$300$	−69.5028	−4.01275
$301$	−17.3108	−0.997781
$302$	−26.5957	−1.53041
$303$	37.4291	2.15024
$304$	−3.74059	−0.214537
$305$	29.3411	1.68007
$306$	15.3181	0.875677
$307$	−5.13474	−0.293055	−0.146528	−	0.989207i	$-0.546810\pi$
$307$	−5.13474	−0.293055	−0.146528	+	0.989207i	$0.546810\pi$
$308$	8.90299	0.507295
$309$	49.1632	2.79679
$310$	8.47668	0.481443
$311$	21.3788	1.21228	0.606141	−	0.795357i	$-0.292717\pi$
$311$	21.3788	1.21228	0.606141	+	0.795357i	$0.292717\pi$
$312$	0	0
$313$	1.92078	0.108569	0.0542845	−	0.998526i	$-0.482712\pi$
$313$	1.92078	0.108569	0.0542845	+	0.998526i	$0.482712\pi$
$314$	19.7183	1.11277
$315$	28.8217	1.62392
$316$	−64.2530	−3.61452
$317$	8.45359	0.474801	0.237400	−	0.971412i	$-0.423705\pi$
$317$	8.45359	0.474801	0.237400	+	0.971412i	$0.423705\pi$
$318$	37.2308	2.08780
$319$	−0.935722	−0.0523904
$320$	63.5406	3.55203
$321$	−13.6538	−0.762082
$322$	−36.1059	−2.01210
$323$	−0.303443	−0.0168840
$324$	23.4546	1.30303
$325$	0	0
$326$	−54.2426	−3.00422
$327$	−40.0758	−2.21619
$328$	41.2638	2.27841
$329$	3.48611	0.192196
$330$	−24.1978	−1.33204
$331$	24.7021	1.35775	0.678874	−	0.734255i	$-0.262468\pi$
$331$	24.7021	1.35775	0.678874	+	0.734255i	$0.262468\pi$
$332$	−54.8651	−3.01111
$333$	−37.1559	−2.03613
$334$	−13.3093	−0.728255
$335$	29.1753	1.59402
$336$	−63.7113	−3.47573
$337$	25.8404	1.40762	0.703809	−	0.710389i	$-0.251481\pi$
$337$	25.8404	1.40762	0.703809	+	0.710389i	$0.251481\pi$
$338$	0	0
$339$	24.3279	1.32131
$340$	16.8494	0.913789
$341$	1.01935	0.0552007
$342$	−4.27799	−0.231327
$343$	−18.9081	−1.02094
$344$	−88.0608	−4.74792
$345$	70.9681	3.82079
$346$	56.7355	3.05012
$347$	1.98790	0.106716	0.0533580	−	0.998575i	$-0.483008\pi$
$347$	1.98790	0.106716	0.0533580	+	0.998575i	$0.483008\pi$
$348$	14.2263	0.762611
$349$	−9.65372	−0.516752	−0.258376	−	0.966044i	$-0.583187\pi$
$349$	−9.65372	−0.516752	−0.258376	+	0.966044i	$0.583187\pi$
$350$	20.9379	1.11918
$351$	0	0
$352$	17.2019	0.916862
$353$	4.97653	0.264874	0.132437	−	0.991191i	$-0.457720\pi$
$353$	4.97653	0.264874	0.132437	+	0.991191i	$0.457720\pi$
$354$	−90.8447	−4.82834
$355$	1.80345	0.0957172
$356$	30.2614	1.60385
$357$	−5.16837	−0.273539
$358$	2.86081	0.151198
$359$	15.8428	0.836149	0.418075	−	0.908413i	$-0.362705\pi$
$359$	15.8428	0.836149	0.418075	+	0.908413i	$0.362705\pi$
$360$	146.617	7.72738
$361$	−18.9153	−0.995540
$362$	50.4975	2.65409
$363$	−2.90985	−0.152728
$364$	0	0
$365$	48.9430	2.56179
$366$	−74.1776	−3.87733
$367$	−4.23360	−0.220992	−0.110496	−	0.993877i	$-0.535244\pi$
$367$	−4.23360	−0.220992	−0.110496	+	0.993877i	$0.535244\pi$
$368$	−101.295	−5.28035
$369$	26.0263	1.35488
$370$	−56.5149	−2.93807
$371$	−8.11107	−0.421106
$372$	−15.4977	−0.803518
$373$	−3.24566	−0.168054	−0.0840269	−	0.996463i	$-0.526778\pi$
$373$	−3.24566	−0.168054	−0.0840269	+	0.996463i	$0.526778\pi$
$374$	2.80179	0.144877
$375$	3.85772	0.199212
$376$	17.7340	0.914559
$377$	0	0
$378$	−32.8821	−1.69127
$379$	20.8566	1.07133	0.535666	−	0.844430i	$-0.320060\pi$
$379$	20.8566	1.07133	0.535666	+	0.844430i	$0.320060\pi$
$380$	−4.70565	−0.241395
$381$	11.9061	0.609969
$382$	−51.8489	−2.65282
$383$	25.6788	1.31213	0.656063	−	0.754706i	$-0.272220\pi$
$383$	25.6788	1.31213	0.656063	+	0.754706i	$0.272220\pi$
$384$	−60.5279	−3.08880
$385$	5.27170	0.268671
$386$	27.9638	1.42332
$387$	−55.5426	−2.82339
$388$	−4.82151	−0.244775
$389$	16.8280	0.853214	0.426607	−	0.904437i	$-0.359709\pi$
$389$	16.8280	0.853214	0.426607	+	0.904437i	$0.359709\pi$
$390$	0	0
$391$	−8.21719	−0.415561
$392$	−35.5090	−1.79347
$393$	4.76994	0.240611
$394$	26.7009	1.34517
$395$	−38.0460	−1.91430
$396$	28.5656	1.43547
$397$	3.41837	0.171563	0.0857817	−	0.996314i	$-0.472661\pi$
$397$	3.41837	0.171563	0.0857817	+	0.996314i	$0.472661\pi$
$398$	−34.1974	−1.71416
$399$	1.44341	0.0722606
$400$	58.7409	2.93705
$401$	−5.82738	−0.291005	−0.145503	−	0.989358i	$-0.546480\pi$
$401$	−5.82738	−0.291005	−0.145503	+	0.989358i	$0.546480\pi$
$402$	−73.7585	−3.67874
$403$	0	0
$404$	−67.2067	−3.34366
$405$	13.8881	0.690106
$406$	−4.28571	−0.212696
$407$	−6.79609	−0.336870
$408$	−26.2916	−1.30163
$409$	−13.4473	−0.664927	−0.332464	−	0.943116i	$-0.607880\pi$
$409$	−13.4473	−0.664927	−0.332464	+	0.943116i	$0.607880\pi$
$410$	39.5866	1.95504
$411$	−21.1773	−1.04460
$412$	−88.2761	−4.34905
$413$	19.7913	0.973867
$414$	−115.847	−5.69358
$415$	−32.4871	−1.59473
$416$	0	0
$417$	−32.2555	−1.57956
$418$	−0.782475	−0.0382721
$419$	−25.5596	−1.24867	−0.624335	−	0.781157i	$-0.714630\pi$
$419$	−25.5596	−1.24867	−0.624335	+	0.781157i	$0.714630\pi$
$420$	−80.1487	−3.91086
$421$	30.5005	1.48650	0.743251	−	0.669013i	$-0.233283\pi$
$421$	30.5005	1.48650	0.743251	+	0.669013i	$0.233283\pi$
$422$	5.37622	0.261710
$423$	11.1853	0.543850
$424$	−41.2613	−2.00382
$425$	4.76517	0.231145
$426$	−4.55932	−0.220900
$427$	16.1603	0.782050
$428$	24.5164	1.18505
$429$	0	0
$430$	−84.4815	−4.07406
$431$	−9.03274	−0.435092	−0.217546	−	0.976050i	$-0.569805\pi$
$431$	−9.03274	−0.435092	−0.217546	+	0.976050i	$0.569805\pi$
$432$	−92.2503	−4.43839
$433$	−20.8135	−1.00023	−0.500116	−	0.865958i	$-0.666709\pi$
$433$	−20.8135	−1.00023	−0.500116	+	0.865958i	$0.666709\pi$
$434$	4.66872	0.224106
$435$	8.42379	0.403890
$436$	71.9590	3.44621
$437$	2.29487	0.109779
$438$	−123.733	−5.91221
$439$	25.1827	1.20191	0.600953	−	0.799284i	$-0.294788\pi$
$439$	25.1827	1.20191	0.600953	+	0.799284i	$0.294788\pi$
$440$	26.8173	1.27846
$441$	−22.3966	−1.06650
$442$	0	0
$443$	37.6126	1.78703	0.893513	−	0.449037i	$-0.148233\pi$
$443$	37.6126	1.78703	0.893513	+	0.449037i	$0.148233\pi$
$444$	103.325	4.90358
$445$	17.9186	0.849422
$446$	−8.73714	−0.413715
$447$	−0.339395	−0.0160528
$448$	34.9964	1.65342
$449$	9.31247	0.439482	0.219741	−	0.975558i	$-0.429479\pi$
$449$	9.31247	0.439482	0.219741	+	0.975558i	$0.429479\pi$
$450$	67.1800	3.16690
$451$	4.76040	0.224159
$452$	−43.6825	−2.05465
$453$	28.7917	1.35275
$454$	−46.5225	−2.18341
$455$	0	0
$456$	7.34264	0.343851
$457$	−24.0367	−1.12439	−0.562194	−	0.827005i	$-0.690043\pi$
$457$	−24.0367	−1.12439	−0.562194	+	0.827005i	$0.690043\pi$
$458$	−32.8541	−1.53517
$459$	−7.48350	−0.349300
$460$	−127.428	−5.94138
$461$	−26.9815	−1.25665	−0.628327	−	0.777949i	$-0.716260\pi$
$461$	−26.9815	−1.25665	−0.628327	+	0.777949i	$0.716260\pi$
$462$	−13.3274	−0.620049
$463$	32.5496	1.51271	0.756355	−	0.654161i	$-0.226978\pi$
$463$	32.5496	1.51271	0.756355	+	0.654161i	$0.226978\pi$
$464$	−12.0235	−0.558177
$465$	−9.17661	−0.425555
$466$	0.740816	0.0343177
$467$	−20.5962	−0.953077	−0.476538	−	0.879154i	$-0.658109\pi$
$467$	−20.5962	−0.953077	−0.476538	+	0.879154i	$0.658109\pi$
$468$	0	0
$469$	16.0689	0.741995
$470$	17.0131	0.784758
$471$	−21.3465	−0.983595
$472$	100.679	4.63413
$473$	−10.1591	−0.467118
$474$	96.1845	4.41790
$475$	−1.33080	−0.0610613
$476$	9.28019	0.425357
$477$	−26.0247	−1.19159
$478$	60.3233	2.75912
$479$	11.7511	0.536923	0.268461	−	0.963290i	$-0.413485\pi$
$479$	11.7511	0.536923	0.268461	+	0.963290i	$0.413485\pi$
$480$	−154.859	−7.06830
$481$	0	0
$482$	−47.6823	−2.17187
$483$	39.0872	1.77853
$484$	5.22486	0.237494
$485$	−2.85495	−0.129636
$486$	22.7814	1.03339
$487$	9.45558	0.428473	0.214237	−	0.976782i	$-0.431274\pi$
$487$	9.45558	0.428473	0.214237	+	0.976782i	$0.431274\pi$
$488$	82.2077	3.72137
$489$	58.7215	2.65548
$490$	−34.0657	−1.53893
$491$	16.0978	0.726482	0.363241	−	0.931695i	$-0.381670\pi$
$491$	16.0978	0.726482	0.363241	+	0.931695i	$0.381670\pi$
$492$	−72.3751	−3.26292
$493$	−0.975367	−0.0439283
$494$	0	0
$495$	16.9145	0.760249
$496$	13.0980	0.588118
$497$	0.993290	0.0445551
$498$	82.1310	3.68038
$499$	30.5933	1.36954	0.684772	−	0.728758i	$-0.259902\pi$
$499$	30.5933	1.36954	0.684772	+	0.728758i	$0.259902\pi$
$500$	−6.92683	−0.309777
$501$	14.4083	0.643716
$502$	−55.1625	−2.46202
$503$	26.5348	1.18313	0.591563	−	0.806259i	$-0.298511\pi$
$503$	26.5348	1.18313	0.591563	+	0.806259i	$0.298511\pi$
$504$	80.7524	3.59700
$505$	−39.7949	−1.77085
$506$	−21.1893	−0.941980
$507$	0	0
$508$	−21.3783	−0.948510
$509$	22.5513	0.999570	0.499785	−	0.866149i	$-0.333412\pi$
$509$	22.5513	0.999570	0.499785	+	0.866149i	$0.333412\pi$
$510$	−25.2230	−1.11689
$511$	26.9564	1.19248
$512$	−1.72704	−0.0763250
$513$	2.08997	0.0922743
$514$	−27.2272	−1.20094
$515$	−52.2707	−2.30332
$516$	154.455	6.79952
$517$	2.04588	0.0899777
$518$	−31.1268	−1.36763
$519$	−61.4203	−2.69605
$520$	0	0
$521$	16.4510	0.720732	0.360366	−	0.932811i	$-0.382652\pi$
$521$	16.4510	0.720732	0.360366	+	0.932811i	$0.382652\pi$
$522$	−13.7509	−0.601859
$523$	−10.0678	−0.440234	−0.220117	−	0.975473i	$-0.570644\pi$
$523$	−10.0678	−0.440234	−0.220117	+	0.975473i	$0.570644\pi$
$524$	−8.56478	−0.374154
$525$	−22.6667	−0.989258
$526$	0.261877	0.0114184
$527$	1.06253	0.0462847
$528$	−37.3900	−1.62719
$529$	39.1448	1.70195
$530$	−39.5841	−1.71943
$531$	63.5013	2.75572
$532$	−2.59174	−0.112366
$533$	0	0
$534$	−45.3001	−1.96033
$535$	14.5169	0.627618
$536$	81.7432	3.53077
$537$	−3.09703	−0.133647
$538$	−9.42909	−0.406517
$539$	−4.09650	−0.176449
$540$	−116.051	−4.99403
$541$	3.30312	0.142012	0.0710060	−	0.997476i	$-0.477379\pi$
$541$	3.30312	0.142012	0.0710060	+	0.997476i	$0.477379\pi$
$542$	41.1614	1.76803
$543$	−54.6672	−2.34599
$544$	17.9307	0.768771
$545$	42.6089	1.82516
$546$	0	0
$547$	4.05777	0.173498	0.0867489	−	0.996230i	$-0.472352\pi$
$547$	4.05777	0.173498	0.0867489	+	0.996230i	$0.472352\pi$
$548$	38.0254	1.62436
$549$	51.8508	2.21294
$550$	12.2877	0.523950
$551$	0.272397	0.0116045
$552$	198.838	8.46310
$553$	−20.9546	−0.891082
$554$	−55.5577	−2.36042
$555$	61.1814	2.59701
$556$	57.9172	2.45624
$557$	−6.10464	−0.258662	−0.129331	−	0.991601i	$-0.541283\pi$
$557$	−6.10464	−0.258662	−0.129331	+	0.991601i	$0.541283\pi$
$558$	14.9798	0.634144
$559$	0	0
$560$	67.7384	2.86247
$561$	−3.03314	−0.128059
$562$	−77.3446	−3.26258
$563$	−17.0418	−0.718225	−0.359112	−	0.933294i	$-0.616921\pi$
$563$	−17.0418	−0.718225	−0.359112	+	0.933294i	$0.616921\pi$
$564$	−31.1047	−1.30974
$565$	−25.8656	−1.08817
$566$	−81.3785	−3.42059
$567$	7.64919	0.321236
$568$	5.05289	0.212015
$569$	−7.42389	−0.311226	−0.155613	−	0.987818i	$-0.549735\pi$
$569$	−7.42389	−0.311226	−0.155613	+	0.987818i	$0.549735\pi$
$570$	7.04419	0.295049
$571$	10.9772	0.459382	0.229691	−	0.973264i	$-0.426228\pi$
$571$	10.9772	0.459382	0.229691	+	0.973264i	$0.426228\pi$
$572$	0	0
$573$	56.1301	2.34487
$574$	21.8032	0.910047
$575$	−36.0379	−1.50288
$576$	112.287	4.67863
$577$	−3.74826	−0.156042	−0.0780211	−	0.996952i	$-0.524860\pi$
$577$	−3.74826	−0.156042	−0.0780211	+	0.996952i	$0.524860\pi$
$578$	−42.7740	−1.77916
$579$	−30.2728	−1.25810
$580$	−15.1255	−0.628054
$581$	−17.8930	−0.742326
$582$	7.21762	0.299180
$583$	−4.76011	−0.197144
$584$	137.128	5.67440
$585$	0	0
$586$	−29.7728	−1.22990
$587$	20.5788	0.849377	0.424688	−	0.905340i	$-0.360384\pi$
$587$	20.5788	0.849377	0.424688	+	0.905340i	$0.360384\pi$
$588$	62.2814	2.56844
$589$	−0.296741	−0.0122270
$590$	96.5868	3.97642
$591$	−28.9056	−1.18902
$592$	−87.3258	−3.58907
$593$	6.50155	0.266986	0.133493	−	0.991050i	$-0.457381\pi$
$593$	6.50155	0.266986	0.133493	+	0.991050i	$0.457381\pi$
$594$	−19.2974	−0.791781
$595$	5.49505	0.225275
$596$	0.609409	0.0249624
$597$	37.0211	1.51517
$598$	0	0
$599$	−22.5421	−0.921045	−0.460522	−	0.887648i	$-0.652338\pi$
$599$	−22.5421	−0.921045	−0.460522	+	0.887648i	$0.652338\pi$
$600$	−115.306	−4.70736
$601$	42.5783	1.73680	0.868402	−	0.495860i	$-0.165147\pi$
$601$	42.5783	1.73680	0.868402	+	0.495860i	$0.165147\pi$
$602$	−46.5300	−1.89642
$603$	51.5578	2.09960
$604$	−51.6977	−2.10355
$605$	3.09378	0.125780
$606$	100.606	4.08684
$607$	25.3486	1.02887	0.514434	−	0.857530i	$-0.328002\pi$
$607$	25.3486	1.02887	0.514434	+	0.857530i	$0.328002\pi$
$608$	−5.00762	−0.203086
$609$	4.63959	0.188006
$610$	78.8663	3.19320
$611$	0	0
$612$	29.7759	1.20362
$613$	16.9842	0.685985	0.342992	−	0.939338i	$-0.388559\pi$
$613$	16.9842	0.685985	0.342992	+	0.939338i	$0.388559\pi$
$614$	−13.8017	−0.556992
$615$	−42.8553	−1.72809
$616$	14.7702	0.595109
$617$	−44.9940	−1.81139	−0.905695	−	0.423929i	$-0.860650\pi$
$617$	−44.9940	−1.81139	−0.905695	+	0.423929i	$0.860650\pi$
$618$	132.146	5.31570
$619$	−11.3275	−0.455292	−0.227646	−	0.973744i	$-0.573103\pi$
$619$	−11.3275	−0.455292	−0.227646	+	0.973744i	$0.573103\pi$
$620$	16.4773	0.661744
$621$	56.5960	2.27112
$622$	57.4644	2.30411
$623$	9.86904	0.395395
$624$	0	0
$625$	−26.9590	−1.07836
$626$	5.16289	0.206351
$627$	0.847085	0.0338293
$628$	38.3293	1.52950
$629$	−7.08402	−0.282459
$630$	77.4701	3.08648
$631$	−3.00798	−0.119746	−0.0598730	−	0.998206i	$-0.519070\pi$
$631$	−3.00798	−0.119746	−0.0598730	+	0.998206i	$0.519070\pi$
$632$	−106.597	−4.24020
$633$	−5.82014	−0.231330
$634$	22.7225	0.902425
$635$	−12.6587	−0.502345
$636$	72.3707	2.86968
$637$	0	0
$638$	−2.51514	−0.0995752
$639$	3.18701	0.126076
$640$	64.3538	2.54381
$641$	−15.0695	−0.595208	−0.297604	−	0.954689i	$-0.596188\pi$
$641$	−15.0695	−0.595208	−0.297604	+	0.954689i	$0.596188\pi$
$642$	−36.7002	−1.44844
$643$	−16.4528	−0.648833	−0.324417	−	0.945914i	$-0.605168\pi$
$643$	−16.4528	−0.648833	−0.324417	+	0.945914i	$0.605168\pi$
$644$	−70.1840	−2.76564
$645$	91.4572	3.60112
$646$	−0.815627	−0.0320904
$647$	30.2788	1.19038	0.595191	−	0.803585i	$-0.297077\pi$
$647$	30.2788	1.19038	0.595191	+	0.803585i	$0.297077\pi$
$648$	38.9116	1.52859
$649$	11.6149	0.455923
$650$	0	0
$651$	−5.05422	−0.198090
$652$	−105.439	−4.12930
$653$	23.8518	0.933394	0.466697	−	0.884417i	$-0.345444\pi$
$653$	23.8518	0.933394	0.466697	+	0.884417i	$0.345444\pi$
$654$	−107.720	−4.21219
$655$	−5.07144	−0.198157
$656$	61.1685	2.38823
$657$	86.4908	3.37433
$658$	9.37036	0.365295
$659$	−11.9043	−0.463727	−0.231863	−	0.972748i	$-0.574482\pi$
$659$	−11.9043	−0.463727	−0.231863	+	0.972748i	$0.574482\pi$
$660$	−47.0365	−1.83089
$661$	−4.50059	−0.175053	−0.0875263	−	0.996162i	$-0.527896\pi$
$661$	−4.50059	−0.175053	−0.0875263	+	0.996162i	$0.527896\pi$
$662$	66.3969	2.58059
$663$	0	0
$664$	−91.0221	−3.53234
$665$	−1.53464	−0.0595108
$666$	−99.8717	−3.86995
$667$	7.37648	0.285619
$668$	−25.8712	−1.00099
$669$	9.45857	0.365690
$670$	78.4206	3.02965
$671$	9.48390	0.366122
$672$	−85.2918	−3.29020
$673$	−9.30191	−0.358562	−0.179281	−	0.983798i	$-0.557377\pi$
$673$	−9.30191	−0.358562	−0.179281	+	0.983798i	$0.557377\pi$
$674$	69.4568	2.67538
$675$	−32.8202	−1.26325
$676$	0	0
$677$	44.0200	1.69183	0.845913	−	0.533322i	$-0.179056\pi$
$677$	44.0200	1.69183	0.845913	+	0.533322i	$0.179056\pi$
$678$	65.3911	2.51133
$679$	−1.57242	−0.0603441
$680$	27.9535	1.07197
$681$	50.3639	1.92995
$682$	2.73991	0.104917
$683$	17.7684	0.679891	0.339945	−	0.940445i	$-0.389591\pi$
$683$	17.7684	0.679891	0.339945	+	0.940445i	$0.389591\pi$
$684$	−8.31571	−0.317959
$685$	22.5159	0.860287
$686$	−50.8232	−1.94044
$687$	35.5669	1.35696
$688$	−130.539	−4.97676
$689$	0	0
$690$	190.756	7.26195
$691$	6.75142	0.256836	0.128418	−	0.991720i	$-0.459010\pi$
$691$	6.75142	0.256836	0.128418	+	0.991720i	$0.459010\pi$
$692$	110.285	4.19239
$693$	9.31601	0.353886
$694$	5.34329	0.202829
$695$	34.2943	1.30086
$696$	23.6017	0.894621
$697$	4.96209	0.187953
$698$	−25.9483	−0.982159
$699$	−0.801986	−0.0303339
$700$	40.6998	1.53831
$701$	−10.2838	−0.388412	−0.194206	−	0.980961i	$-0.562213\pi$
$701$	−10.2838	−0.388412	−0.194206	+	0.980961i	$0.562213\pi$
$702$	0	0
$703$	1.97840	0.0746169
$704$	20.5382	0.774061
$705$	−18.4179	−0.693660
$706$	13.3765	0.503430
$707$	−21.9179	−0.824307
$708$	−176.587	−6.63655
$709$	−26.3616	−0.990029	−0.495015	−	0.868885i	$-0.664837\pi$
$709$	−26.3616	−0.990029	−0.495015	+	0.868885i	$0.664837\pi$
$710$	4.84751	0.181924
$711$	−67.2338	−2.52147
$712$	50.2041	1.88148
$713$	−8.03570	−0.300939
$714$	−13.8921	−0.519899
$715$	0	0
$716$	5.56094	0.207822
$717$	−65.3043	−2.43883
$718$	42.5839	1.58922
$719$	31.9625	1.19200	0.596000	−	0.802984i	$-0.296756\pi$
$719$	31.9625	1.19200	0.596000	+	0.802984i	$0.296756\pi$
$720$	217.341	8.09983
$721$	−28.7892	−1.07217
$722$	−50.8425	−1.89216
$723$	51.6195	1.91975
$724$	98.1590	3.64805
$725$	−4.27764	−0.158867
$726$	−7.82142	−0.290280
$727$	−6.35132	−0.235557	−0.117779	−	0.993040i	$-0.537577\pi$
$727$	−6.35132	−0.235557	−0.117779	+	0.993040i	$0.537577\pi$
$728$	0	0
$729$	−38.1296	−1.41221
$730$	131.554	4.86905
$731$	−10.5896	−0.391669
$732$	−144.189	−5.32939
$733$	33.9768	1.25496	0.627481	−	0.778632i	$-0.284086\pi$
$733$	33.9768	1.25496	0.627481	+	0.778632i	$0.284086\pi$
$734$	−11.3795	−0.420026
$735$	36.8785	1.36028
$736$	−135.606	−4.99849
$737$	9.43031	0.347370
$738$	69.9563	2.57513
$739$	31.1540	1.14602	0.573009	−	0.819549i	$-0.305776\pi$
$739$	31.1540	1.14602	0.573009	+	0.819549i	$0.305776\pi$
$740$	−109.856	−4.03838
$741$	0	0
$742$	−21.8018	−0.800370
$743$	−39.1173	−1.43507	−0.717537	−	0.696520i	$-0.754731\pi$
$743$	−39.1173	−1.43507	−0.717537	+	0.696520i	$0.754731\pi$
$744$	−25.7109	−0.942609
$745$	0.360847	0.0132204
$746$	−8.72403	−0.319410
$747$	−57.4103	−2.10053
$748$	5.44623	0.199134
$749$	7.99547	0.292148
$750$	10.3692	0.378630
$751$	−2.15947	−0.0788001	−0.0394000	−	0.999224i	$-0.512545\pi$
$751$	−2.15947	−0.0788001	−0.0394000	+	0.999224i	$0.512545\pi$
$752$	26.2884	0.958640
$753$	59.7173	2.17622
$754$	0	0
$755$	−30.6116	−1.11407
$756$	−63.9174	−2.32466
$757$	−0.315358	−0.0114619	−0.00573094	−	0.999984i	$-0.501824\pi$
$757$	−0.315358	−0.0114619	−0.00573094	+	0.999984i	$0.501824\pi$
$758$	56.0607	2.03622
$759$	22.9389	0.832631
$760$	−7.80676	−0.283181
$761$	−20.6516	−0.748622	−0.374311	−	0.927303i	$-0.622121\pi$
$761$	−20.6516	−0.748622	−0.374311	+	0.927303i	$0.622121\pi$
$762$	32.0026	1.15933
$763$	23.4678	0.849590
$764$	−100.786	−3.64630
$765$	17.6311	0.637454
$766$	69.0223	2.49388
$767$	0	0
$768$	−43.1675	−1.55767
$769$	12.7162	0.458559	0.229280	−	0.973361i	$-0.426363\pi$
$769$	12.7162	0.458559	0.229280	+	0.973361i	$0.426363\pi$
$770$	14.1699	0.510646
$771$	29.4754	1.06153
$772$	54.3571	1.95635
$773$	−8.70103	−0.312954	−0.156477	−	0.987682i	$-0.550014\pi$
$773$	−8.70103	−0.312954	−0.156477	+	0.987682i	$0.550014\pi$
$774$	−149.293	−5.36624
$775$	4.65992	0.167389
$776$	−7.99896	−0.287146
$777$	33.6970	1.20887
$778$	45.2322	1.62165
$779$	−1.38580	−0.0496513
$780$	0	0
$781$	0.582928	0.0208588
$782$	−22.0871	−0.789832
$783$	6.71786	0.240077
$784$	−52.6376	−1.87992
$785$	22.6958	0.810048
$786$	12.8212	0.457316
$787$	36.4098	1.29787	0.648934	−	0.760845i	$-0.275215\pi$
$787$	36.4098	1.29787	0.648934	+	0.760845i	$0.275215\pi$
$788$	51.9021	1.84894
$789$	−0.283500	−0.0100929
$790$	−102.264	−3.63840
$791$	−14.2460	−0.506531
$792$	47.3908	1.68396
$793$	0	0
$794$	9.18828	0.326080
$795$	42.8527	1.51983
$796$	−66.4741	−2.35611
$797$	3.32151	0.117654	0.0588270	−	0.998268i	$-0.481264\pi$
$797$	3.32151	0.117654	0.0588270	+	0.998268i	$0.481264\pi$
$798$	3.87974	0.137341
$799$	2.13256	0.0754446
$800$	78.6379	2.78027
$801$	31.6652	1.11884
$802$	−15.6635	−0.553096
$803$	15.8198	0.558269
$804$	−143.374	−5.05643
$805$	−41.5579	−1.46472
$806$	0	0
$807$	10.2077	0.359327
$808$	−111.497	−3.92245
$809$	7.94177	0.279218	0.139609	−	0.990207i	$-0.455415\pi$
$809$	7.94177	0.279218	0.139609	+	0.990207i	$0.455415\pi$
$810$	37.3300	1.31164
$811$	18.5407	0.651052	0.325526	−	0.945533i	$-0.394459\pi$
$811$	18.5407	0.651052	0.325526	+	0.945533i	$0.394459\pi$
$812$	−8.33072	−0.292351
$813$	−44.5601	−1.56279
$814$	−18.2673	−0.640267
$815$	−62.4332	−2.18694
$816$	−38.9741	−1.36437
$817$	2.95742	0.103467
$818$	−36.1452	−1.26379
$819$	0	0
$820$	76.9499	2.68721
$821$	26.9214	0.939565	0.469782	−	0.882782i	$-0.344332\pi$
$821$	26.9214	0.939565	0.469782	+	0.882782i	$0.344332\pi$
$822$	−56.9226	−1.98541
$823$	−48.5760	−1.69325	−0.846626	−	0.532188i	$-0.821370\pi$
$823$	−48.5760	−1.69325	−0.846626	+	0.532188i	$0.821370\pi$
$824$	−146.452	−5.10188
$825$	−13.3023	−0.463128
$826$	53.1973	1.85097
$827$	−47.6008	−1.65524	−0.827621	−	0.561287i	$-0.810306\pi$
$827$	−47.6008	−1.65524	−0.827621	+	0.561287i	$0.810306\pi$
$828$	−225.188	−7.82583
$829$	−3.40020	−0.118094	−0.0590470	−	0.998255i	$-0.518806\pi$
$829$	−3.40020	−0.118094	−0.0590470	+	0.998255i	$0.518806\pi$
$830$	−87.3224	−3.03100
$831$	60.1451	2.08641
$832$	0	0
$833$	−4.27006	−0.147949
$834$	−86.6999	−3.00217
$835$	−15.3190	−0.530137
$836$	−1.52100	−0.0526050
$837$	−7.31822	−0.252955
$838$	−68.7020	−2.37327
$839$	−42.8825	−1.48047	−0.740233	−	0.672350i	$-0.765285\pi$
$839$	−42.8825	−1.48047	−0.740233	+	0.672350i	$0.765285\pi$
$840$	−132.968	−4.58783
$841$	−28.1244	−0.969808
$842$	81.9825	2.82530
$843$	83.7310	2.88385
$844$	10.4505	0.359721
$845$	0	0
$846$	30.0652	1.03366
$847$	1.70397	0.0585490
$848$	−61.1647	−2.10040
$849$	88.0980	3.02351
$850$	12.8083	0.439322
$851$	53.5749	1.83652
$852$	−8.86258	−0.303627
$853$	−41.0285	−1.40479	−0.702395	−	0.711787i	$-0.747886\pi$
$853$	−41.0285	−1.40479	−0.702395	+	0.711787i	$0.747886\pi$
$854$	43.4373	1.48639
$855$	−4.92396	−0.168396
$856$	40.6732	1.39018
$857$	−46.7316	−1.59632	−0.798161	−	0.602444i	$-0.794194\pi$
$857$	−46.7316	−1.59632	−0.798161	+	0.602444i	$0.794194\pi$
$858$	0	0
$859$	5.18746	0.176994	0.0884970	−	0.996076i	$-0.471794\pi$
$859$	5.18746	0.176994	0.0884970	+	0.996076i	$0.471794\pi$
$860$	−164.218	−5.59979
$861$	−23.6035	−0.804405
$862$	−24.2792	−0.826953
$863$	−44.3316	−1.50907	−0.754533	−	0.656262i	$-0.772136\pi$
$863$	−44.3316	−1.50907	−0.754533	+	0.656262i	$0.772136\pi$
$864$	−123.498	−4.20148
$865$	65.3025	2.22035
$866$	−55.9448	−1.90108
$867$	46.3059	1.57263
$868$	9.07522	0.308033
$869$	−12.2976	−0.417166
$870$	22.6424	0.767649
$871$	0	0
$872$	119.381	4.04276
$873$	−5.04518	−0.170754
$874$	6.16841	0.208649
$875$	−2.25902	−0.0763690
$876$	−240.518	−8.12633
$877$	28.7343	0.970288	0.485144	−	0.874434i	$-0.338767\pi$
$877$	28.7343	0.970288	0.485144	+	0.874434i	$0.338767\pi$
$878$	67.6889	2.28439
$879$	32.2312	1.08713
$880$	39.7533	1.34008
$881$	3.46294	0.116669	0.0583347	−	0.998297i	$-0.481421\pi$
$881$	3.46294	0.116669	0.0583347	+	0.998297i	$0.481421\pi$
$882$	−60.1999	−2.02704
$883$	−25.7431	−0.866326	−0.433163	−	0.901316i	$-0.642602\pi$
$883$	−25.7431	−0.866326	−0.433163	+	0.901316i	$0.642602\pi$
$884$	0	0
$885$	−104.562	−3.51482
$886$	101.099	3.39649
$887$	56.3033	1.89048	0.945240	−	0.326375i	$-0.105827\pi$
$887$	56.3033	1.89048	0.945240	+	0.326375i	$0.105827\pi$
$888$	171.418	5.75240
$889$	−6.97205	−0.233835
$890$	48.1635	1.61444
$891$	4.48905	0.150389
$892$	−16.9836	−0.568652
$893$	−0.595575	−0.0199302
$894$	−0.912263	−0.0305106
$895$	3.29279	0.110066
$896$	35.4443	1.18411
$897$	0	0
$898$	25.0311	0.835298
$899$	−0.953825	−0.0318118
$900$	130.587	4.35290
$901$	−4.96179	−0.165301
$902$	12.7955	0.426045
$903$	50.3720	1.67628
$904$	−72.4700	−2.41032
$905$	58.1226	1.93206
$906$	77.3896	2.57110
$907$	25.6494	0.851676	0.425838	−	0.904799i	$-0.359979\pi$
$907$	25.6494	0.851676	0.425838	+	0.904799i	$0.359979\pi$
$908$	−90.4322	−3.00110
$909$	−70.3245	−2.33251
$910$	0	0
$911$	35.7349	1.18395	0.591975	−	0.805957i	$-0.298349\pi$
$911$	35.7349	1.18395	0.591975	+	0.805957i	$0.298349\pi$
$912$	10.8846	0.360424
$913$	−10.5008	−0.347525
$914$	−64.6084	−2.13706
$915$	−85.3784	−2.82252
$916$	−63.8630	−2.11009
$917$	−2.79320	−0.0922397
$918$	−20.1150	−0.663893
$919$	−7.42382	−0.244889	−0.122445	−	0.992475i	$-0.539073\pi$
$919$	−7.42382	−0.244889	−0.122445	+	0.992475i	$0.539073\pi$
$920$	−211.406	−6.96985
$921$	14.9414	0.492334
$922$	−72.5238	−2.38845
$923$	0	0
$924$	−25.9064	−0.852258
$925$	−31.0682	−1.02152
$926$	87.4905	2.87512
$927$	−92.3714	−3.03387
$928$	−16.0962	−0.528382
$929$	28.5106	0.935403	0.467702	−	0.883886i	$-0.345082\pi$
$929$	28.5106	0.935403	0.467702	+	0.883886i	$0.345082\pi$
$930$	−24.6659	−0.808827
$931$	1.19253	0.0390835
$932$	1.44003	0.0471696
$933$	−62.2093	−2.03664
$934$	−55.3606	−1.81146
$935$	3.22486	0.105464
$936$	0	0
$937$	14.3343	0.468280	0.234140	−	0.972203i	$-0.424773\pi$
$937$	14.3343	0.468280	0.234140	+	0.972203i	$0.424773\pi$
$938$	43.1919	1.41026
$939$	−5.58920	−0.182396
$940$	33.0708	1.07865
$941$	−26.5519	−0.865568	−0.432784	−	0.901498i	$-0.642469\pi$
$941$	−26.5519	−0.865568	−0.432784	+	0.901498i	$0.642469\pi$
$942$	−57.3775	−1.86946
$943$	−37.5272	−1.22205
$944$	149.244	4.85749
$945$	−37.8473	−1.23117
$946$	−27.3069	−0.887823
$947$	51.3198	1.66767	0.833835	−	0.552013i	$-0.186140\pi$
$947$	51.3198	1.66767	0.833835	+	0.552013i	$0.186140\pi$
$948$	186.967	6.07240
$949$	0	0
$950$	−3.57707	−0.116055
$951$	−24.5987	−0.797668
$952$	15.3960	0.498987
$953$	32.8316	1.06352	0.531759	−	0.846895i	$-0.321531\pi$
$953$	32.8316	1.06352	0.531759	+	0.846895i	$0.321531\pi$
$954$	−69.9520	−2.26478
$955$	−59.6780	−1.93113
$956$	117.259	3.79242
$957$	2.72281	0.0880161
$958$	31.5860	1.02050
$959$	12.4011	0.400453
$960$	−184.894	−5.96742
$961$	−29.9609	−0.966482
$962$	0	0
$963$	25.6538	0.826682
$964$	−92.6867	−2.98524
$965$	32.1863	1.03611
$966$	105.063	3.38034
$967$	−26.5335	−0.853259	−0.426630	−	0.904426i	$-0.640299\pi$
$967$	−26.5335	−0.853259	−0.426630	+	0.904426i	$0.640299\pi$
$968$	8.66813	0.278604
$969$	0.882975	0.0283652
$970$	−7.67384	−0.246392
$971$	0.504385	0.0161865	0.00809324	−	0.999967i	$-0.497424\pi$
$971$	0.504385	0.0161865	0.00809324	+	0.999967i	$0.497424\pi$
$972$	44.2834	1.42039
$973$	18.8884	0.605533
$974$	25.4157	0.814373
$975$	0	0
$976$	121.863	3.90073
$977$	19.3758	0.619886	0.309943	−	0.950755i	$-0.399690\pi$
$977$	19.3758	0.619886	0.309943	+	0.950755i	$0.399690\pi$
$978$	157.838	5.04710
$979$	5.79180	0.185107
$980$	−66.2181	−2.11526
$981$	75.2973	2.40406
$982$	43.2693	1.38078
$983$	−10.6735	−0.340432	−0.170216	−	0.985407i	$-0.554446\pi$
$983$	−10.6735	−0.340432	−0.170216	+	0.985407i	$0.554446\pi$
$984$	−120.072	−3.82774
$985$	30.7327	0.979224
$986$	−2.62170	−0.0834919
$987$	−10.1441	−0.322890
$988$	0	0
$989$	80.0865	2.54660
$990$	45.4646	1.44496
$991$	−8.52193	−0.270708	−0.135354	−	0.990797i	$-0.543217\pi$
$991$	−8.52193	−0.270708	−0.135354	+	0.990797i	$0.543217\pi$
$992$	17.5346	0.556725
$993$	−71.8794	−2.28102
$994$	2.66987	0.0846832
$995$	−39.3611	−1.24783
$996$	159.649	5.05868
$997$	−35.8287	−1.13471	−0.567354	−	0.823474i	$-0.692033\pi$
$997$	−35.8287	−1.13471	−0.567354	+	0.823474i	$0.692033\pi$
$998$	82.2320	2.60301
$999$	48.7913	1.54369

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.2.a.t.1.21	yes	21
13.12	even	2		1859.2.a.s.1.1	✓	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1859.2.a.s.1.1	✓	21	13.12	even	2
1859.2.a.t.1.21	yes	21	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+2.68791 q^{2} -2.90985 q^{3} +5.22486 q^{4} +3.09378 q^{5} -7.82142 q^{6} +1.70397 q^{7} +8.66813 q^{8} +5.46725 q^{9} +O(q^{10})\)	\(q+2.68791 q^{2} -2.90985 q^{3} +5.22486 q^{4} +3.09378 q^{5} -7.82142 q^{6} +1.70397 q^{7} +8.66813 q^{8} +5.46725 q^{9} +8.31580 q^{10} +1.00000 q^{11} -15.2036 q^{12} +4.58011 q^{14} -9.00245 q^{15} +12.8494 q^{16} +1.04237 q^{17} +14.6955 q^{18} -0.291109 q^{19} +16.1646 q^{20} -4.95829 q^{21} +2.68791 q^{22} -7.88320 q^{23} -25.2230 q^{24} +4.57148 q^{25} -7.17933 q^{27} +8.90299 q^{28} -0.935722 q^{29} -24.1978 q^{30} +1.01935 q^{31} +17.2019 q^{32} -2.90985 q^{33} +2.80179 q^{34} +5.27170 q^{35} +28.5656 q^{36} -6.79609 q^{37} -0.782475 q^{38} +26.8173 q^{40} +4.76040 q^{41} -13.3274 q^{42} -10.1591 q^{43} +5.22486 q^{44} +16.9145 q^{45} -21.1893 q^{46} +2.04588 q^{47} -37.3900 q^{48} -4.09650 q^{49} +12.2877 q^{50} -3.03314 q^{51} -4.76011 q^{53} -19.2974 q^{54} +3.09378 q^{55} +14.7702 q^{56} +0.847085 q^{57} -2.51514 q^{58} +11.6149 q^{59} -47.0365 q^{60} +9.48390 q^{61} +2.73991 q^{62} +9.31601 q^{63} +20.5382 q^{64} -7.82142 q^{66} +9.43031 q^{67} +5.44623 q^{68} +22.9389 q^{69} +14.1699 q^{70} +0.582928 q^{71} +47.3908 q^{72} +15.8198 q^{73} -18.2673 q^{74} -13.3023 q^{75} -1.52100 q^{76} +1.70397 q^{77} -12.2976 q^{79} +39.7533 q^{80} +4.48905 q^{81} +12.7955 q^{82} -10.5008 q^{83} -25.9064 q^{84} +3.22486 q^{85} -27.3069 q^{86} +2.72281 q^{87} +8.66813 q^{88} +5.79180 q^{89} +45.4646 q^{90} -41.1886 q^{92} -2.96615 q^{93} +5.49914 q^{94} -0.900628 q^{95} -50.0549 q^{96} -0.922801 q^{97} -11.0110 q^{98} +5.46725 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 6 q^{3} + 32 q^{4} + 7 q^{5} - 19 q^{6} + q^{7} - 3 q^{8} + 33 q^{9}+O(q^{10}) \) 21 * q + 6 * q^3 + 32 * q^4 + 7 * q^5 - 19 * q^6 + q^7 - 3 * q^8 + 33 * q^9	\( 21 q + 6 q^{3} + 32 q^{4} + 7 q^{5} - 19 q^{6} + q^{7} - 3 q^{8} + 33 q^{9} + 18 q^{10} + 21 q^{11} + 23 q^{12} + 20 q^{14} + 16 q^{15} + 50 q^{16} + 16 q^{17} + 3 q^{18} - 11 q^{19} + 24 q^{20} - 5 q^{21} - 9 q^{23} - 54 q^{24} + 36 q^{25} - 11 q^{28} + 28 q^{29} + 21 q^{30} + 15 q^{31} - 61 q^{32} + 6 q^{33} - 6 q^{34} - 3 q^{35} + 45 q^{36} - 12 q^{37} + q^{38} + 55 q^{40} - 4 q^{41} - 34 q^{42} + 17 q^{43} + 32 q^{44} + 9 q^{45} + 11 q^{46} + 36 q^{47} + 24 q^{48} + 72 q^{49} - 9 q^{50} + 2 q^{51} + 19 q^{53} + q^{54} + 7 q^{55} + 44 q^{56} - 4 q^{57} - 33 q^{58} + 54 q^{59} + 64 q^{60} + 98 q^{61} - 29 q^{62} - 81 q^{63} + 63 q^{64} - 19 q^{66} + 25 q^{67} + 4 q^{68} + 89 q^{69} + 65 q^{70} + 37 q^{71} + 55 q^{72} + 8 q^{73} - 11 q^{74} + 24 q^{75} + 13 q^{76} + q^{77} + 24 q^{79} + 26 q^{80} + 81 q^{81} + 26 q^{82} - 34 q^{83} - 103 q^{84} - 11 q^{85} + 30 q^{86} + 32 q^{87} - 3 q^{88} + 6 q^{89} + 47 q^{90} - 80 q^{92} + 41 q^{93} + 40 q^{94} + 20 q^{95} - 98 q^{96} - 5 q^{98} + 33 q^{99}+O(q^{100}) \) 21 * q + 6 * q^3 + 32 * q^4 + 7 * q^5 - 19 * q^6 + q^7 - 3 * q^8 + 33 * q^9 + 18 * q^10 + 21 * q^11 + 23 * q^12 + 20 * q^14 + 16 * q^15 + 50 * q^16 + 16 * q^17 + 3 * q^18 - 11 * q^19 + 24 * q^20 - 5 * q^21 - 9 * q^23 - 54 * q^24 + 36 * q^25 - 11 * q^28 + 28 * q^29 + 21 * q^30 + 15 * q^31 - 61 * q^32 + 6 * q^33 - 6 * q^34 - 3 * q^35 + 45 * q^36 - 12 * q^37 + q^38 + 55 * q^40 - 4 * q^41 - 34 * q^42 + 17 * q^43 + 32 * q^44 + 9 * q^45 + 11 * q^46 + 36 * q^47 + 24 * q^48 + 72 * q^49 - 9 * q^50 + 2 * q^51 + 19 * q^53 + q^54 + 7 * q^55 + 44 * q^56 - 4 * q^57 - 33 * q^58 + 54 * q^59 + 64 * q^60 + 98 * q^61 - 29 * q^62 - 81 * q^63 + 63 * q^64 - 19 * q^66 + 25 * q^67 + 4 * q^68 + 89 * q^69 + 65 * q^70 + 37 * q^71 + 55 * q^72 + 8 * q^73 - 11 * q^74 + 24 * q^75 + 13 * q^76 + q^77 + 24 * q^79 + 26 * q^80 + 81 * q^81 + 26 * q^82 - 34 * q^83 - 103 * q^84 - 11 * q^85 + 30 * q^86 + 32 * q^87 - 3 * q^88 + 6 * q^89 + 47 * q^90 - 80 * q^92 + 41 * q^93 + 40 * q^94 + 20 * q^95 - 98 * q^96 - 5 * q^98 + 33 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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