LMFDB - Embedded newform 1859.2.a.t.1.16

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			1.16
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)

$f(q)$	$=$	$q+2.13563 q^{2} -2.20961 q^{3} +2.56090 q^{4} -1.38469 q^{5} -4.71890 q^{6} +5.12151 q^{7} +1.19787 q^{8} +1.88237 q^{9} +O(q^{10})$	\(q+2.13563 q^{2} -2.20961 q^{3} +2.56090 q^{4} -1.38469 q^{5} -4.71890 q^{6} +5.12151 q^{7} +1.19787 q^{8} +1.88237 q^{9} -2.95718 q^{10} +1.00000 q^{11} -5.65858 q^{12} +10.9376 q^{14} +3.05962 q^{15} -2.56360 q^{16} -0.645800 q^{17} +4.02004 q^{18} +5.71986 q^{19} -3.54604 q^{20} -11.3165 q^{21} +2.13563 q^{22} -2.41000 q^{23} -2.64682 q^{24} -3.08264 q^{25} +2.46952 q^{27} +13.1157 q^{28} +2.88360 q^{29} +6.53420 q^{30} +3.43199 q^{31} -7.87062 q^{32} -2.20961 q^{33} -1.37919 q^{34} -7.09169 q^{35} +4.82056 q^{36} +10.2685 q^{37} +12.2155 q^{38} -1.65867 q^{40} -3.99879 q^{41} -24.1679 q^{42} +7.08446 q^{43} +2.56090 q^{44} -2.60650 q^{45} -5.14686 q^{46} +11.7099 q^{47} +5.66455 q^{48} +19.2298 q^{49} -6.58337 q^{50} +1.42697 q^{51} -12.7035 q^{53} +5.27398 q^{54} -1.38469 q^{55} +6.13489 q^{56} -12.6387 q^{57} +6.15828 q^{58} -0.0415150 q^{59} +7.83537 q^{60} -4.29284 q^{61} +7.32946 q^{62} +9.64058 q^{63} -11.6815 q^{64} -4.71890 q^{66} +14.4565 q^{67} -1.65383 q^{68} +5.32515 q^{69} -15.1452 q^{70} +4.10847 q^{71} +2.25483 q^{72} +4.85130 q^{73} +21.9297 q^{74} +6.81143 q^{75} +14.6480 q^{76} +5.12151 q^{77} +3.30530 q^{79} +3.54978 q^{80} -11.1038 q^{81} -8.53993 q^{82} +3.87295 q^{83} -28.9805 q^{84} +0.894231 q^{85} +15.1298 q^{86} -6.37162 q^{87} +1.19787 q^{88} +5.70850 q^{89} -5.56650 q^{90} -6.17176 q^{92} -7.58337 q^{93} +25.0080 q^{94} -7.92022 q^{95} +17.3910 q^{96} -0.622364 q^{97} +41.0677 q^{98} +1.88237 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.13563	1.51012	0.755058	−	0.655658i	$-0.227609\pi$
$2$	2.13563	1.51012	0.755058	+	0.655658i	$0.227609\pi$
$3$	−2.20961	−1.27572	−0.637859	−	0.770153i	$-0.720180\pi$
$3$	−2.20961	−1.27572	−0.637859	+	0.770153i	$0.720180\pi$
$4$	2.56090	1.28045
$5$	−1.38469	−0.619251	−0.309626	−	0.950859i	$-0.600204\pi$
$5$	−1.38469	−0.619251	−0.309626	+	0.950859i	$0.600204\pi$
$6$	−4.71890	−1.92648
$7$	5.12151	1.93575	0.967874	−	0.251436i	$-0.0809030\pi$
$7$	5.12151	1.93575	0.967874	+	0.251436i	$0.0809030\pi$
$8$	1.19787	0.423510
$9$	1.88237	0.627457
$10$	−2.95718	−0.935141
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−5.65858	−1.63349
$13$	0	0
$13$	0	0
$14$	10.9376	2.92320
$15$	3.05962	0.789990
$16$	−2.56360	−0.640899
$17$	−0.645800	−0.156629	−0.0783147	−	0.996929i	$-0.524954\pi$
$17$	−0.645800	−0.156629	−0.0783147	+	0.996929i	$0.524954\pi$
$18$	4.02004	0.947533
$19$	5.71986	1.31223	0.656113	−	0.754663i	$-0.272199\pi$
$19$	5.71986	1.31223	0.656113	+	0.754663i	$0.272199\pi$
$20$	−3.54604	−0.792920
$21$	−11.3165	−2.46947
$22$	2.13563	0.455317
$23$	−2.41000	−0.502519	−0.251260	−	0.967920i	$-0.580845\pi$
$23$	−2.41000	−0.502519	−0.251260	+	0.967920i	$0.580845\pi$
$24$	−2.64682	−0.540280
$25$	−3.08264	−0.616528
$26$	0	0
$27$	2.46952	0.475260
$28$	13.1157	2.47863
$29$	2.88360	0.535471	0.267735	−	0.963493i	$-0.413725\pi$
$29$	2.88360	0.535471	0.267735	+	0.963493i	$0.413725\pi$
$30$	6.53420	1.19298
$31$	3.43199	0.616404	0.308202	−	0.951321i	$-0.400273\pi$
$31$	3.43199	0.616404	0.308202	+	0.951321i	$0.400273\pi$
$32$	−7.87062	−1.39134
$33$	−2.20961	−0.384644
$34$	−1.37919	−0.236529
$35$	−7.09169	−1.19871
$36$	4.82056	0.803427
$37$	10.2685	1.68813	0.844067	−	0.536238i	$-0.180155\pi$
$37$	10.2685	1.68813	0.844067	+	0.536238i	$0.180155\pi$
$38$	12.2155	1.98161
$39$	0	0
$40$	−1.65867	−0.262259
$41$	−3.99879	−0.624507	−0.312253	−	0.949999i	$-0.601084\pi$
$41$	−3.99879	−0.624507	−0.312253	+	0.949999i	$0.601084\pi$
$42$	−24.1679	−3.72918
$43$	7.08446	1.08037	0.540185	−	0.841546i	$-0.318354\pi$
$43$	7.08446	1.08037	0.540185	+	0.841546i	$0.318354\pi$
$44$	2.56090	0.386070
$45$	−2.60650	−0.388554
$46$	−5.14686	−0.758862
$47$	11.7099	1.70807	0.854033	−	0.520219i	$-0.174150\pi$
$47$	11.7099	1.70807	0.854033	+	0.520219i	$0.174150\pi$
$48$	5.66455	0.817607
$49$	19.2298	2.74712
$50$	−6.58337	−0.931028
$51$	1.42697	0.199815
$52$	0	0
$53$	−12.7035	−1.74496	−0.872479	−	0.488651i	$-0.837489\pi$
$53$	−12.7035	−1.74496	−0.872479	+	0.488651i	$0.837489\pi$
$54$	5.27398	0.717697
$55$	−1.38469	−0.186711
$56$	6.13489	0.819809
$57$	−12.6387	−1.67403
$58$	6.15828	0.808622
$59$	−0.0415150	−0.00540480	−0.00270240	−	0.999996i	$-0.500860\pi$
$59$	−0.0415150	−0.00540480	−0.00270240	+	0.999996i	$0.500860\pi$
$60$	7.83537	1.01154
$61$	−4.29284	−0.549641	−0.274821	−	0.961495i	$-0.588619\pi$
$61$	−4.29284	−0.549641	−0.274821	+	0.961495i	$0.588619\pi$
$62$	7.32946	0.930842
$63$	9.64058	1.21460
$64$	−11.6815	−1.46019
$65$	0	0
$66$	−4.71890	−0.580856
$67$	14.4565	1.76614	0.883071	−	0.469239i	$-0.155472\pi$
$67$	14.4565	1.76614	0.883071	+	0.469239i	$0.155472\pi$
$68$	−1.65383	−0.200556
$69$	5.32515	0.641073
$70$	−15.1452	−1.81020
$71$	4.10847	0.487586	0.243793	−	0.969827i	$-0.421608\pi$
$71$	4.10847	0.487586	0.243793	+	0.969827i	$0.421608\pi$
$72$	2.25483	0.265735
$73$	4.85130	0.567802	0.283901	−	0.958854i	$-0.408371\pi$
$73$	4.85130	0.567802	0.283901	+	0.958854i	$0.408371\pi$
$74$	21.9297	2.54928
$75$	6.81143	0.786516
$76$	14.6480	1.68024
$77$	5.12151	0.583650
$78$	0	0
$79$	3.30530	0.371875	0.185938	−	0.982562i	$-0.440468\pi$
$79$	3.30530	0.371875	0.185938	+	0.982562i	$0.440468\pi$
$80$	3.54978	0.396878
$81$	−11.1038	−1.23375
$82$	−8.53993	−0.943077
$83$	3.87295	0.425111	0.212556	−	0.977149i	$-0.431821\pi$
$83$	3.87295	0.425111	0.212556	+	0.977149i	$0.431821\pi$
$84$	−28.9805	−3.16203
$85$	0.894231	0.0969930
$86$	15.1298	1.63148
$87$	−6.37162	−0.683110
$88$	1.19787	0.127693
$89$	5.70850	0.605100	0.302550	−	0.953133i	$-0.402162\pi$
$89$	5.70850	0.605100	0.302550	+	0.953133i	$0.402162\pi$
$90$	−5.56650	−0.586761
$91$	0	0
$92$	−6.17176	−0.643450
$93$	−7.58337	−0.786358
$94$	25.0080	2.57938
$95$	−7.92022	−0.812598
$96$	17.3910	1.77496
$97$	−0.622364	−0.0631915	−0.0315957	−	0.999501i	$-0.510059\pi$
$97$	−0.622364	−0.0631915	−0.0315957	+	0.999501i	$0.510059\pi$
$98$	41.0677	4.14847
$99$	1.88237	0.189185
$100$	−7.89433	−0.789433
$101$	17.8839	1.77951	0.889757	−	0.456435i	$-0.150874\pi$
$101$	17.8839	1.77951	0.889757	+	0.456435i	$0.150874\pi$
$102$	3.04746	0.301744
$103$	−3.48136	−0.343029	−0.171515	−	0.985182i	$-0.554866\pi$
$103$	−3.48136	−0.343029	−0.171515	+	0.985182i	$0.554866\pi$
$104$	0	0
$105$	15.6699	1.52922
$106$	−27.1299	−2.63509
$107$	0.270944	0.0261932	0.0130966	−	0.999914i	$-0.495831\pi$
$107$	0.270944	0.0261932	0.0130966	+	0.999914i	$0.495831\pi$
$108$	6.32419	0.608546
$109$	−11.2913	−1.08151	−0.540756	−	0.841179i	$-0.681862\pi$
$109$	−11.2913	−1.08151	−0.540756	+	0.841179i	$0.681862\pi$
$110$	−2.95718	−0.281956
$111$	−22.6894	−2.15358
$112$	−13.1295	−1.24062
$113$	−12.2758	−1.15481	−0.577407	−	0.816456i	$-0.695935\pi$
$113$	−12.2758	−1.15481	−0.577407	+	0.816456i	$0.695935\pi$
$114$	−26.9914	−2.52798
$115$	3.33710	0.311186
$116$	7.38460	0.685643
$117$	0	0
$118$	−0.0886606	−0.00816187
$119$	−3.30747	−0.303195
$120$	3.66502	0.334569
$121$	1.00000	0.0909091
$122$	−9.16789	−0.830022
$123$	8.83577	0.796694
$124$	8.78899	0.789274
$125$	11.1919	1.00104
$126$	20.5887	1.83418
$127$	−2.37725	−0.210947	−0.105473	−	0.994422i	$-0.533636\pi$
$127$	−2.37725	−0.210947	−0.105473	+	0.994422i	$0.533636\pi$
$128$	−9.20609	−0.813711
$129$	−15.6539	−1.37825
$130$	0	0
$131$	−19.2094	−1.67834	−0.839168	−	0.543872i	$-0.816958\pi$
$131$	−19.2094	−1.67834	−0.839168	+	0.543872i	$0.816958\pi$
$132$	−5.65858	−0.492516
$133$	29.2943	2.54014
$134$	30.8737	2.66708
$135$	−3.41952	−0.294305
$136$	−0.773583	−0.0663342
$137$	−18.7695	−1.60359	−0.801793	−	0.597602i	$-0.796120\pi$
$137$	−18.7695	−1.60359	−0.801793	+	0.597602i	$0.796120\pi$
$138$	11.3725	0.968095
$139$	−0.0825625	−0.00700286	−0.00350143	−	0.999994i	$-0.501115\pi$
$139$	−0.0825625	−0.00700286	−0.00350143	+	0.999994i	$0.501115\pi$
$140$	−18.1611	−1.53489
$141$	−25.8743	−2.17901
$142$	8.77415	0.736311
$143$	0	0
$144$	−4.82564	−0.402137
$145$	−3.99288	−0.331591
$146$	10.3606	0.857446
$147$	−42.4904	−3.50455
$148$	26.2966	2.16157
$149$	3.42408	0.280512	0.140256	−	0.990115i	$-0.455207\pi$
$149$	3.42408	0.280512	0.140256	+	0.990115i	$0.455207\pi$
$150$	14.5467	1.18773
$151$	−14.8265	−1.20656	−0.603282	−	0.797528i	$-0.706141\pi$
$151$	−14.8265	−1.20656	−0.603282	+	0.797528i	$0.706141\pi$
$152$	6.85164	0.555741
$153$	−1.21564	−0.0982783
$154$	10.9376	0.881379
$155$	−4.75224	−0.381709
$156$	0	0
$157$	2.57432	0.205453	0.102727	−	0.994710i	$-0.467243\pi$
$157$	2.57432	0.205453	0.102727	+	0.994710i	$0.467243\pi$
$158$	7.05888	0.561575
$159$	28.0697	2.22608
$160$	10.8984	0.861591
$161$	−12.3428	−0.972751
$162$	−23.7135	−1.86311
$163$	−12.5648	−0.984151	−0.492076	−	0.870552i	$-0.663762\pi$
$163$	−12.5648	−0.984151	−0.492076	+	0.870552i	$0.663762\pi$
$164$	−10.2405	−0.799649
$165$	3.05962	0.238191
$166$	8.27116	0.641967
$167$	−6.24946	−0.483598	−0.241799	−	0.970326i	$-0.577737\pi$
$167$	−6.24946	−0.483598	−0.241799	+	0.970326i	$0.577737\pi$
$168$	−13.5557	−1.04585
$169$	0	0
$170$	1.90974	0.146471
$171$	10.7669	0.823366
$172$	18.1426	1.38336
$173$	7.40017	0.562624	0.281312	−	0.959616i	$-0.409230\pi$
$173$	7.40017	0.562624	0.281312	+	0.959616i	$0.409230\pi$
$174$	−13.6074	−1.03157
$175$	−15.7878	−1.19344
$176$	−2.56360	−0.193238
$177$	0.0917320	0.00689500
$178$	12.1912	0.913771
$179$	13.5994	1.01647	0.508233	−	0.861220i	$-0.330299\pi$
$179$	13.5994	1.01647	0.508233	+	0.861220i	$0.330299\pi$
$180$	−6.67497	−0.497523
$181$	5.41011	0.402130	0.201065	−	0.979578i	$-0.435560\pi$
$181$	5.41011	0.402130	0.201065	+	0.979578i	$0.435560\pi$
$182$	0	0
$183$	9.48549	0.701188
$184$	−2.88686	−0.212822
$185$	−14.2187	−1.04538
$186$	−16.1952	−1.18749
$187$	−0.645800	−0.0472256
$188$	29.9879	2.18709
$189$	12.6477	0.919983
$190$	−16.9146	−1.22712
$191$	3.73932	0.270568	0.135284	−	0.990807i	$-0.456805\pi$
$191$	3.73932	0.270568	0.135284	+	0.990807i	$0.456805\pi$
$192$	25.8116	1.86279
$193$	−8.49207	−0.611273	−0.305636	−	0.952148i	$-0.598869\pi$
$193$	−8.49207	−0.611273	−0.305636	+	0.952148i	$0.598869\pi$
$194$	−1.32914	−0.0954265
$195$	0	0
$196$	49.2456	3.51755
$197$	−17.5966	−1.25371	−0.626855	−	0.779136i	$-0.715658\pi$
$197$	−17.5966	−1.25371	−0.626855	+	0.779136i	$0.715658\pi$
$198$	4.02004	0.285692
$199$	15.1611	1.07474	0.537372	−	0.843346i	$-0.319417\pi$
$199$	15.1611	1.07474	0.537372	+	0.843346i	$0.319417\pi$
$200$	−3.69260	−0.261106
$201$	−31.9432	−2.25310
$202$	38.1933	2.68727
$203$	14.7684	1.03654
$204$	3.65431	0.255853
$205$	5.53708	0.386726
$206$	−7.43489	−0.518014
$207$	−4.53651	−0.315309
$208$	0	0
$209$	5.71986	0.395651
$210$	33.4650	2.30930
$211$	−11.0003	−0.757295	−0.378648	−	0.925541i	$-0.623611\pi$
$211$	−11.0003	−0.757295	−0.378648	+	0.925541i	$0.623611\pi$
$212$	−32.5323	−2.23433
$213$	−9.07811	−0.622022
$214$	0.578636	0.0395547
$215$	−9.80977	−0.669021
$216$	2.95816	0.201277
$217$	17.5770	1.19320
$218$	−24.1140	−1.63321
$219$	−10.7195	−0.724355
$220$	−3.54604	−0.239074
$221$	0	0
$222$	−48.4561	−3.25216
$223$	−16.6700	−1.11631	−0.558153	−	0.829738i	$-0.688490\pi$
$223$	−16.6700	−1.11631	−0.558153	+	0.829738i	$0.688490\pi$
$224$	−40.3094	−2.69329
$225$	−5.80267	−0.386845
$226$	−26.2166	−1.74390
$227$	18.4415	1.22401	0.612003	−	0.790856i	$-0.290364\pi$
$227$	18.4415	1.22401	0.612003	+	0.790856i	$0.290364\pi$
$228$	−32.3663	−2.14351
$229$	−26.5377	−1.75366	−0.876829	−	0.480803i	$-0.840345\pi$
$229$	−26.5377	−1.75366	−0.876829	+	0.480803i	$0.840345\pi$
$230$	7.12679	0.469926
$231$	−11.3165	−0.744573
$232$	3.45417	0.226777
$233$	2.00904	0.131617	0.0658084	−	0.997832i	$-0.479037\pi$
$233$	2.00904	0.131617	0.0658084	+	0.997832i	$0.479037\pi$
$234$	0	0
$235$	−16.2146	−1.05772
$236$	−0.106316	−0.00692056
$237$	−7.30342	−0.474408
$238$	−7.06352	−0.457860
$239$	−24.3230	−1.57333	−0.786663	−	0.617383i	$-0.788193\pi$
$239$	−24.3230	−1.57333	−0.786663	+	0.617383i	$0.788193\pi$
$240$	−7.84363	−0.506304
$241$	−14.0789	−0.906905	−0.453452	−	0.891280i	$-0.649808\pi$
$241$	−14.0789	−0.906905	−0.453452	+	0.891280i	$0.649808\pi$
$242$	2.13563	0.137283
$243$	17.1265	1.09866
$244$	−10.9935	−0.703788
$245$	−26.6273	−1.70116
$246$	18.8699	1.20310
$247$	0	0
$248$	4.11108	0.261054
$249$	−8.55770	−0.542322
$250$	23.9018	1.51168
$251$	−10.8501	−0.684853	−0.342427	−	0.939545i	$-0.611249\pi$
$251$	−10.8501	−0.684853	−0.342427	+	0.939545i	$0.611249\pi$
$252$	24.6885	1.55523
$253$	−2.41000	−0.151515
$254$	−5.07692	−0.318554
$255$	−1.97590	−0.123736
$256$	3.70226	0.231391
$257$	−11.5040	−0.717600	−0.358800	−	0.933415i	$-0.616814\pi$
$257$	−11.5040	−0.717600	−0.358800	+	0.933415i	$0.616814\pi$
$258$	−33.4309	−2.08131
$259$	52.5903	3.26780
$260$	0	0
$261$	5.42800	0.335985
$262$	−41.0242	−2.53448
$263$	−16.7453	−1.03256	−0.516281	−	0.856419i	$-0.672684\pi$
$263$	−16.7453	−1.03256	−0.516281	+	0.856419i	$0.672684\pi$
$264$	−2.64682	−0.162901
$265$	17.5904	1.08057
$266$	62.5617	3.83590
$267$	−12.6136	−0.771937
$268$	37.0216	2.26146
$269$	−4.08991	−0.249366	−0.124683	−	0.992197i	$-0.539791\pi$
$269$	−4.08991	−0.249366	−0.124683	+	0.992197i	$0.539791\pi$
$270$	−7.30281	−0.444435
$271$	10.5903	0.643316	0.321658	−	0.946856i	$-0.395760\pi$
$271$	10.5903	0.643316	0.321658	+	0.946856i	$0.395760\pi$
$272$	1.65557	0.100384
$273$	0	0
$274$	−40.0846	−2.42160
$275$	−3.08264	−0.185890
$276$	13.6372	0.820862
$277$	11.8675	0.713047	0.356524	−	0.934286i	$-0.383962\pi$
$277$	11.8675	0.713047	0.356524	+	0.934286i	$0.383962\pi$
$278$	−0.176323	−0.0105751
$279$	6.46029	0.386767
$280$	−8.49491	−0.507668
$281$	11.6973	0.697803	0.348901	−	0.937159i	$-0.386555\pi$
$281$	11.6973	0.697803	0.348901	+	0.937159i	$0.386555\pi$
$282$	−55.2579	−3.29056
$283$	−9.31846	−0.553925	−0.276963	−	0.960881i	$-0.589328\pi$
$283$	−9.31846	−0.553925	−0.276963	+	0.960881i	$0.589328\pi$
$284$	10.5214	0.624328
$285$	17.5006	1.03665
$286$	0	0
$287$	−20.4798	−1.20889
$288$	−14.8154	−0.873008
$289$	−16.5829	−0.975467
$290$	−8.52730	−0.500740
$291$	1.37518	0.0806145
$292$	12.4237	0.727041
$293$	14.4492	0.844130	0.422065	−	0.906566i	$-0.361305\pi$
$293$	14.4492	0.844130	0.422065	+	0.906566i	$0.361305\pi$
$294$	−90.7436	−5.29227
$295$	0.0574853	0.00334693
$296$	12.3003	0.714942
$297$	2.46952	0.143296
$298$	7.31256	0.423605
$299$	0	0
$300$	17.4434	1.00709
$301$	36.2831	2.09132
$302$	−31.6639	−1.82205
$303$	−39.5164	−2.27016
$304$	−14.6634	−0.841005
$305$	5.94424	0.340366
$306$	−2.59614	−0.148412
$307$	8.18391	0.467081	0.233540	−	0.972347i	$-0.424969\pi$
$307$	8.18391	0.467081	0.233540	+	0.972347i	$0.424969\pi$
$308$	13.1157	0.747334
$309$	7.69245	0.437608
$310$	−10.1490	−0.576425
$311$	−0.0504367	−0.00286000	−0.00143000	−	0.999999i	$-0.500455\pi$
$311$	−0.0504367	−0.00286000	−0.00143000	+	0.999999i	$0.500455\pi$
$312$	0	0
$313$	15.6601	0.885162	0.442581	−	0.896729i	$-0.354063\pi$
$313$	15.6601	0.885162	0.442581	+	0.896729i	$0.354063\pi$
$314$	5.49779	0.310258
$315$	−13.3492	−0.752142
$316$	8.46454	0.476167
$317$	5.10412	0.286676	0.143338	−	0.989674i	$-0.454216\pi$
$317$	5.10412	0.286676	0.143338	+	0.989674i	$0.454216\pi$
$318$	59.9465	3.36163
$319$	2.88360	0.161450
$320$	16.1752	0.904223
$321$	−0.598681	−0.0334151
$322$	−26.3597	−1.46897
$323$	−3.69389	−0.205533
$324$	−28.4357	−1.57976
$325$	0	0
$326$	−26.8337	−1.48618
$327$	24.9494	1.37970
$328$	−4.79003	−0.264485
$329$	59.9724	3.30638
$330$	6.53420	0.359696
$331$	27.0938	1.48921	0.744604	−	0.667507i	$-0.232638\pi$
$331$	27.0938	1.48921	0.744604	+	0.667507i	$0.232638\pi$
$332$	9.91822	0.544333
$333$	19.3292	1.05923
$334$	−13.3465	−0.730289
$335$	−20.0177	−1.09369
$336$	29.0110	1.58268
$337$	−14.5894	−0.794735	−0.397368	−	0.917660i	$-0.630076\pi$
$337$	−14.5894	−0.794735	−0.397368	+	0.917660i	$0.630076\pi$
$338$	0	0
$339$	27.1248	1.47322
$340$	2.29003	0.124195
$341$	3.43199	0.185853
$342$	22.9941	1.24338
$343$	62.6352	3.38198
$344$	8.48625	0.457548
$345$	−7.37368	−0.396985
$346$	15.8040	0.849628
$347$	0.368012	0.0197559	0.00987796	−	0.999951i	$-0.496856\pi$
$347$	0.368012	0.0197559	0.00987796	+	0.999951i	$0.496856\pi$
$348$	−16.3171	−0.874687
$349$	36.4344	1.95029	0.975145	−	0.221566i	$-0.0711168\pi$
$349$	36.4344	1.95029	0.975145	+	0.221566i	$0.0711168\pi$
$350$	−33.7168	−1.80224
$351$	0	0
$352$	−7.87062	−0.419506
$353$	−21.6896	−1.15442	−0.577210	−	0.816596i	$-0.695859\pi$
$353$	−21.6896	−1.15442	−0.577210	+	0.816596i	$0.695859\pi$
$354$	0.195905	0.0104122
$355$	−5.68895	−0.301938
$356$	14.6189	0.774800
$357$	7.30821	0.386792
$358$	29.0432	1.53498
$359$	−15.7429	−0.830881	−0.415440	−	0.909620i	$-0.636373\pi$
$359$	−15.7429	−0.830881	−0.415440	+	0.909620i	$0.636373\pi$
$360$	−3.12224	−0.164556
$361$	13.7168	0.721937
$362$	11.5540	0.607263
$363$	−2.20961	−0.115974
$364$	0	0
$365$	−6.71754	−0.351612
$366$	20.2575	1.05887
$367$	8.24346	0.430305	0.215153	−	0.976580i	$-0.430975\pi$
$367$	8.24346	0.430305	0.215153	+	0.976580i	$0.430975\pi$
$368$	6.17827	0.322064
$369$	−7.52721	−0.391851
$370$	−30.3658	−1.57864
$371$	−65.0610	−3.37780
$372$	−19.4202	−1.00689
$373$	2.74984	0.142382	0.0711908	−	0.997463i	$-0.477320\pi$
$373$	2.74984	0.142382	0.0711908	+	0.997463i	$0.477320\pi$
$374$	−1.37919	−0.0713161
$375$	−24.7298	−1.27704
$376$	14.0269	0.723384
$377$	0	0
$378$	27.0107	1.38928
$379$	−21.1587	−1.08685	−0.543424	−	0.839458i	$-0.682872\pi$
$379$	−21.1587	−1.08685	−0.543424	+	0.839458i	$0.682872\pi$
$380$	−20.2829	−1.04049
$381$	5.25280	0.269109
$382$	7.98580	0.408589
$383$	−27.9252	−1.42691	−0.713457	−	0.700699i	$-0.752872\pi$
$383$	−27.9252	−1.42691	−0.713457	+	0.700699i	$0.752872\pi$
$384$	20.3419	1.03807
$385$	−7.09169	−0.361426
$386$	−18.1359	−0.923093
$387$	13.3356	0.677886
$388$	−1.59381	−0.0809135
$389$	−20.4825	−1.03850	−0.519251	−	0.854622i	$-0.673789\pi$
$389$	−20.4825	−1.03850	−0.519251	+	0.854622i	$0.673789\pi$
$390$	0	0
$391$	1.55638	0.0787094
$392$	23.0348	1.16343
$393$	42.4454	2.14108
$394$	−37.5799	−1.89325
$395$	−4.57681	−0.230284
$396$	4.82056	0.242242
$397$	3.57380	0.179364	0.0896821	−	0.995970i	$-0.471415\pi$
$397$	3.57380	0.179364	0.0896821	+	0.995970i	$0.471415\pi$
$398$	32.3785	1.62299
$399$	−64.7290	−3.24050
$400$	7.90265	0.395132
$401$	14.8809	0.743119	0.371559	−	0.928409i	$-0.378823\pi$
$401$	14.8809	0.743119	0.371559	+	0.928409i	$0.378823\pi$
$402$	−68.2188	−3.40244
$403$	0	0
$404$	45.7988	2.27858
$405$	15.3753	0.764004
$406$	31.5397	1.56529
$407$	10.2685	0.508991
$408$	1.70932	0.0846238
$409$	−21.5122	−1.06371	−0.531854	−	0.846836i	$-0.678504\pi$
$409$	−21.5122	−1.06371	−0.531854	+	0.846836i	$0.678504\pi$
$410$	11.8251	0.584002
$411$	41.4732	2.04572
$412$	−8.91542	−0.439231
$413$	−0.212619	−0.0104623
$414$	−9.68829	−0.476154
$415$	−5.36282	−0.263251
$416$	0	0
$417$	0.182431	0.00893368
$418$	12.2155	0.597479
$419$	3.78497	0.184908	0.0924539	−	0.995717i	$-0.470529\pi$
$419$	3.78497	0.184908	0.0924539	+	0.995717i	$0.470529\pi$
$420$	40.1289	1.95809
$421$	−37.4751	−1.82643	−0.913213	−	0.407483i	$-0.866407\pi$
$421$	−37.4751	−1.82643	−0.913213	+	0.407483i	$0.866407\pi$
$422$	−23.4926	−1.14360
$423$	22.0424	1.07174
$424$	−15.2171	−0.739008
$425$	1.99077	0.0965665
$426$	−19.3874	−0.939325
$427$	−21.9858	−1.06397
$428$	0.693861	0.0335390
$429$	0	0
$430$	−20.9500	−1.01030
$431$	13.9068	0.669867	0.334934	−	0.942242i	$-0.391286\pi$
$431$	13.9068	0.669867	0.334934	+	0.942242i	$0.391286\pi$
$432$	−6.33086	−0.304594
$433$	−8.39781	−0.403573	−0.201787	−	0.979430i	$-0.564675\pi$
$433$	−8.39781	−0.403573	−0.201787	+	0.979430i	$0.564675\pi$
$434$	37.5379	1.80188
$435$	8.82271	0.423016
$436$	−28.9159	−1.38482
$437$	−13.7849	−0.659419
$438$	−22.8928	−1.09386
$439$	−3.77193	−0.180024	−0.0900122	−	0.995941i	$-0.528691\pi$
$439$	−3.77193	−0.180024	−0.0900122	+	0.995941i	$0.528691\pi$
$440$	−1.65867	−0.0790741
$441$	36.1977	1.72370
$442$	0	0
$443$	−5.55546	−0.263948	−0.131974	−	0.991253i	$-0.542132\pi$
$443$	−5.55546	−0.263948	−0.131974	+	0.991253i	$0.542132\pi$
$444$	−58.1053	−2.75755
$445$	−7.90450	−0.374709
$446$	−35.6009	−1.68575
$447$	−7.56588	−0.357854
$448$	−59.8269	−2.82656
$449$	25.3384	1.19579	0.597896	−	0.801574i	$-0.296004\pi$
$449$	25.3384	1.19579	0.597896	+	0.801574i	$0.296004\pi$
$450$	−12.3923	−0.584180
$451$	−3.99879	−0.188296
$452$	−31.4372	−1.47868
$453$	32.7608	1.53924
$454$	39.3841	1.84839
$455$	0	0
$456$	−15.1394	−0.708969
$457$	30.4784	1.42572	0.712859	−	0.701308i	$-0.247400\pi$
$457$	30.4784	1.42572	0.712859	+	0.701308i	$0.247400\pi$
$458$	−56.6745	−2.64823
$459$	−1.59482	−0.0744397
$460$	8.54596	0.398457
$461$	33.7216	1.57057	0.785285	−	0.619134i	$-0.212516\pi$
$461$	33.7216	1.57057	0.785285	+	0.619134i	$0.212516\pi$
$462$	−24.1679	−1.12439
$463$	−24.1398	−1.12187	−0.560935	−	0.827860i	$-0.689558\pi$
$463$	−24.1398	−1.12187	−0.560935	+	0.827860i	$0.689558\pi$
$464$	−7.39238	−0.343183
$465$	10.5006	0.486953
$466$	4.29057	0.198757
$467$	22.4626	1.03945	0.519723	−	0.854335i	$-0.326035\pi$
$467$	22.4626	1.03945	0.519723	+	0.854335i	$0.326035\pi$
$468$	0	0
$469$	74.0391	3.41881
$470$	−34.6283	−1.59728
$471$	−5.68824	−0.262100
$472$	−0.0497295	−0.00228899
$473$	7.08446	0.325744
$474$	−15.5974	−0.716411
$475$	−17.6323	−0.809024
$476$	−8.47009	−0.388226
$477$	−23.9127	−1.09489
$478$	−51.9449	−2.37590
$479$	−9.61420	−0.439284	−0.219642	−	0.975581i	$-0.570489\pi$
$479$	−9.61420	−0.439284	−0.219642	+	0.975581i	$0.570489\pi$
$480$	−24.0811	−1.09915
$481$	0	0
$482$	−30.0674	−1.36953
$483$	27.2728	1.24096
$484$	2.56090	0.116404
$485$	0.861780	0.0391314
$486$	36.5757	1.65911
$487$	−18.7202	−0.848295	−0.424147	−	0.905593i	$-0.639426\pi$
$487$	−18.7202	−0.848295	−0.424147	+	0.905593i	$0.639426\pi$
$488$	−5.14225	−0.232779
$489$	27.7633	1.25550
$490$	−56.8660	−2.56894
$491$	18.5850	0.838728	0.419364	−	0.907818i	$-0.362253\pi$
$491$	18.5850	0.838728	0.419364	+	0.907818i	$0.362253\pi$
$492$	22.6275	1.02013
$493$	−1.86223	−0.0838705
$494$	0	0
$495$	−2.60650	−0.117153
$496$	−8.79825	−0.395053
$497$	21.0416	0.943843
$498$	−18.2760	−0.818969
$499$	16.2463	0.727285	0.363642	−	0.931539i	$-0.381533\pi$
$499$	16.2463	0.727285	0.363642	+	0.931539i	$0.381533\pi$
$500$	28.6614	1.28178
$501$	13.8089	0.616935
$502$	−23.1718	−1.03421
$503$	−14.9137	−0.664971	−0.332485	−	0.943108i	$-0.607887\pi$
$503$	−14.9137	−0.664971	−0.332485	+	0.943108i	$0.607887\pi$
$504$	11.5481	0.514395
$505$	−24.7636	−1.10197
$506$	−5.14686	−0.228806
$507$	0	0
$508$	−6.08790	−0.270107
$509$	−1.60613	−0.0711904	−0.0355952	−	0.999366i	$-0.511333\pi$
$509$	−1.60613	−0.0711904	−0.0355952	+	0.999366i	$0.511333\pi$
$510$	−4.21979	−0.186855
$511$	24.8460	1.09912
$512$	26.3188	1.16314
$513$	14.1253	0.623648
$514$	−24.5682	−1.08366
$515$	4.82060	0.212421
$516$	−40.0880	−1.76478
$517$	11.7099	0.515001
$518$	112.313	4.93476
$519$	−16.3515	−0.717750
$520$	0	0
$521$	15.5845	0.682769	0.341385	−	0.939924i	$-0.389104\pi$
$521$	15.5845	0.682769	0.341385	+	0.939924i	$0.389104\pi$
$522$	11.5922	0.507376
$523$	30.1082	1.31654	0.658269	−	0.752783i	$-0.271289\pi$
$523$	30.1082	1.31654	0.658269	+	0.752783i	$0.271289\pi$
$524$	−49.1934	−2.14902
$525$	34.8848	1.52250
$526$	−35.7618	−1.55929
$527$	−2.21638	−0.0965471
$528$	5.66455	0.246518
$529$	−17.1919	−0.747474
$530$	37.5664	1.63178
$531$	−0.0781467	−0.00339128
$532$	75.0197	3.25252
$533$	0	0
$534$	−26.9378	−1.16571
$535$	−0.375173	−0.0162202
$536$	17.3170	0.747980
$537$	−30.0493	−1.29672
$538$	−8.73452	−0.376572
$539$	19.2298	0.828287
$540$	−8.75703	−0.376843
$541$	−7.07231	−0.304062	−0.152031	−	0.988376i	$-0.548581\pi$
$541$	−7.07231	−0.304062	−0.152031	+	0.988376i	$0.548581\pi$
$542$	22.6170	0.971482
$543$	−11.9542	−0.513005
$544$	5.08285	0.217925
$545$	15.6350	0.669728
$546$	0	0
$547$	3.83951	0.164166	0.0820828	−	0.996626i	$-0.473843\pi$
$547$	3.83951	0.164166	0.0820828	+	0.996626i	$0.473843\pi$
$548$	−48.0668	−2.05331
$549$	−8.08071	−0.344876
$550$	−6.58337	−0.280716
$551$	16.4938	0.702658
$552$	6.37883	0.271501
$553$	16.9281	0.719857
$554$	25.3445	1.07678
$555$	31.4177	1.33361
$556$	−0.211434	−0.00896680
$557$	−9.17155	−0.388611	−0.194305	−	0.980941i	$-0.562245\pi$
$557$	−9.17155	−0.388611	−0.194305	+	0.980941i	$0.562245\pi$
$558$	13.7968	0.584063
$559$	0	0
$560$	18.1802	0.768255
$561$	1.42697	0.0602465
$562$	24.9811	1.05376
$563$	−17.3419	−0.730872	−0.365436	−	0.930836i	$-0.619080\pi$
$563$	−17.3419	−0.730872	−0.365436	+	0.930836i	$0.619080\pi$
$564$	−66.2615	−2.79011
$565$	16.9982	0.715120
$566$	−19.9008	−0.836491
$567$	−56.8681	−2.38824
$568$	4.92140	0.206498
$569$	26.9476	1.12970	0.564851	−	0.825193i	$-0.308934\pi$
$569$	26.9476	1.12970	0.564851	+	0.825193i	$0.308934\pi$
$570$	37.3747	1.56545
$571$	−29.1884	−1.22149	−0.610747	−	0.791825i	$-0.709131\pi$
$571$	−29.1884	−1.22149	−0.610747	+	0.791825i	$0.709131\pi$
$572$	0	0
$573$	−8.26244	−0.345169
$574$	−43.7373	−1.82556
$575$	7.42916	0.309817
$576$	−21.9889	−0.916206
$577$	−16.7437	−0.697049	−0.348524	−	0.937300i	$-0.613317\pi$
$577$	−16.7437	−0.697049	−0.348524	+	0.937300i	$0.613317\pi$
$578$	−35.4150	−1.47307
$579$	18.7642	0.779812
$580$	−10.2254	−0.424585
$581$	19.8353	0.822908
$582$	2.93687	0.121737
$583$	−12.7035	−0.526125
$584$	5.81122	0.240470
$585$	0	0
$586$	30.8580	1.27473
$587$	−2.05072	−0.0846423	−0.0423212	−	0.999104i	$-0.513475\pi$
$587$	−2.05072	−0.0846423	−0.0423212	+	0.999104i	$0.513475\pi$
$588$	−108.814	−4.48740
$589$	19.6305	0.808862
$590$	0.122767	0.00505425
$591$	38.8817	1.59938
$592$	−26.3243	−1.08192
$593$	21.3813	0.878023	0.439012	−	0.898481i	$-0.355329\pi$
$593$	21.3813	0.878023	0.439012	+	0.898481i	$0.355329\pi$
$594$	5.27398	0.216394
$595$	4.57981	0.187754
$596$	8.76873	0.359181
$597$	−33.5001	−1.37107
$598$	0	0
$599$	−18.8361	−0.769624	−0.384812	−	0.922995i	$-0.625734\pi$
$599$	−18.8361	−0.769624	−0.384812	+	0.922995i	$0.625734\pi$
$600$	8.15919	0.333098
$601$	−8.56448	−0.349352	−0.174676	−	0.984626i	$-0.555888\pi$
$601$	−8.56448	−0.349352	−0.174676	+	0.984626i	$0.555888\pi$
$602$	77.4872	3.15814
$603$	27.2125	1.10818
$604$	−37.9692	−1.54494
$605$	−1.38469	−0.0562956
$606$	−84.3923	−3.42820
$607$	35.0755	1.42367	0.711836	−	0.702345i	$-0.247864\pi$
$607$	35.0755	1.42367	0.711836	+	0.702345i	$0.247864\pi$
$608$	−45.0189	−1.82576
$609$	−32.6323	−1.32233
$610$	12.6947	0.513992
$611$	0	0
$612$	−3.11312	−0.125840
$613$	13.5499	0.547276	0.273638	−	0.961833i	$-0.411773\pi$
$613$	13.5499	0.547276	0.273638	+	0.961833i	$0.411773\pi$
$614$	17.4778	0.705346
$615$	−12.2348	−0.493354
$616$	6.13489	0.247182
$617$	−21.5419	−0.867243	−0.433621	−	0.901095i	$-0.642764\pi$
$617$	−21.5419	−0.867243	−0.433621	+	0.901095i	$0.642764\pi$
$618$	16.4282	0.660839
$619$	−33.1911	−1.33406	−0.667031	−	0.745030i	$-0.732435\pi$
$619$	−33.1911	−1.33406	−0.667031	+	0.745030i	$0.732435\pi$
$620$	−12.1700	−0.488759
$621$	−5.95154	−0.238827
$622$	−0.107714	−0.00431893
$623$	29.2361	1.17132
$624$	0	0
$625$	−0.0841326	−0.00336530
$626$	33.4441	1.33670
$627$	−12.6387	−0.504739
$628$	6.59257	0.263072
$629$	−6.63141	−0.264412
$630$	−28.5089	−1.13582
$631$	40.7567	1.62250	0.811250	−	0.584700i	$-0.198788\pi$
$631$	40.7567	1.62250	0.811250	+	0.584700i	$0.198788\pi$
$632$	3.95931	0.157493
$633$	24.3065	0.966095
$634$	10.9005	0.432914
$635$	3.29175	0.130629
$636$	71.8838	2.85038
$637$	0	0
$638$	6.15828	0.243809
$639$	7.73366	0.305939
$640$	12.7476	0.503891
$641$	21.9440	0.866737	0.433368	−	0.901217i	$-0.357325\pi$
$641$	21.9440	0.866737	0.433368	+	0.901217i	$0.357325\pi$
$642$	−1.27856	−0.0504607
$643$	−3.60153	−0.142031	−0.0710153	−	0.997475i	$-0.522624\pi$
$643$	−3.60153	−0.142031	−0.0710153	+	0.997475i	$0.522624\pi$
$644$	−31.6087	−1.24556
$645$	21.6758	0.853482
$646$	−7.88876	−0.310379
$647$	32.3457	1.27164	0.635821	−	0.771837i	$-0.280662\pi$
$647$	32.3457	1.27164	0.635821	+	0.771837i	$0.280662\pi$
$648$	−13.3009	−0.522508
$649$	−0.0415150	−0.00162961
$650$	0	0
$651$	−38.8383	−1.52219
$652$	−32.1772	−1.26016
$653$	−18.5689	−0.726659	−0.363330	−	0.931661i	$-0.618360\pi$
$653$	−18.5689	−0.726659	−0.363330	+	0.931661i	$0.618360\pi$
$654$	53.2826	2.08351
$655$	26.5991	1.03931
$656$	10.2513	0.400246
$657$	9.13195	0.356271
$658$	128.079	4.99302
$659$	−25.7325	−1.00240	−0.501198	−	0.865332i	$-0.667107\pi$
$659$	−25.7325	−1.00240	−0.501198	+	0.865332i	$0.667107\pi$
$660$	7.83537	0.304991
$661$	18.7214	0.728179	0.364090	−	0.931364i	$-0.381380\pi$
$661$	18.7214	0.728179	0.364090	+	0.931364i	$0.381380\pi$
$662$	57.8621	2.24888
$663$	0	0
$664$	4.63928	0.180039
$665$	−40.5635	−1.57298
$666$	41.2799	1.59956
$667$	−6.94946	−0.269084
$668$	−16.0042	−0.619222
$669$	36.8342	1.42409
$670$	−42.7504	−1.65159
$671$	−4.29284	−0.165723
$672$	89.0681	3.43588
$673$	23.4403	0.903558	0.451779	−	0.892130i	$-0.350790\pi$
$673$	23.4403	0.903558	0.451779	+	0.892130i	$0.350790\pi$
$674$	−31.1575	−1.20014
$675$	−7.61265	−0.293011
$676$	0	0
$677$	13.1583	0.505714	0.252857	−	0.967504i	$-0.418630\pi$
$677$	13.1583	0.505714	0.252857	+	0.967504i	$0.418630\pi$
$678$	57.9285	2.22473
$679$	−3.18744	−0.122323
$680$	1.07117	0.0410775
$681$	−40.7485	−1.56149
$682$	7.32946	0.280659
$683$	19.3245	0.739432	0.369716	−	0.929145i	$-0.379455\pi$
$683$	19.3245	0.739432	0.369716	+	0.929145i	$0.379455\pi$
$684$	27.5729	1.05428
$685$	25.9899	0.993022
$686$	133.765	5.10718
$687$	58.6378	2.23717
$688$	−18.1617	−0.692409
$689$	0	0
$690$	−15.7474	−0.599494
$691$	−28.1049	−1.06916	−0.534581	−	0.845117i	$-0.679530\pi$
$691$	−28.1049	−1.06916	−0.534581	+	0.845117i	$0.679530\pi$
$692$	18.9511	0.720412
$693$	9.64058	0.366215
$694$	0.785936	0.0298337
$695$	0.114323	0.00433653
$696$	−7.63236	−0.289304
$697$	2.58242	0.0978161
$698$	77.8103	2.94516
$699$	−4.43920	−0.167906
$700$	−40.4308	−1.52814
$701$	8.63821	0.326261	0.163130	−	0.986605i	$-0.447841\pi$
$701$	8.63821	0.326261	0.163130	+	0.986605i	$0.447841\pi$
$702$	0	0
$703$	58.7345	2.21521
$704$	−11.6815	−0.440263
$705$	35.8279	1.34936
$706$	−46.3208	−1.74331
$707$	91.5925	3.44469
$708$	0.234916	0.00882869
$709$	22.7877	0.855811	0.427905	−	0.903823i	$-0.359252\pi$
$709$	22.7877	0.855811	0.427905	+	0.903823i	$0.359252\pi$
$710$	−12.1495	−0.455961
$711$	6.22180	0.233336
$712$	6.83804	0.256266
$713$	−8.27110	−0.309755
$714$	15.6076	0.584100
$715$	0	0
$716$	34.8266	1.30153
$717$	53.7444	2.00712
$718$	−33.6210	−1.25473
$719$	−23.4448	−0.874343	−0.437171	−	0.899378i	$-0.644020\pi$
$719$	−23.4448	−0.874343	−0.437171	+	0.899378i	$0.644020\pi$
$720$	6.68201	0.249024
$721$	−17.8298	−0.664018
$722$	29.2940	1.09021
$723$	31.1090	1.15696
$724$	13.8547	0.514908
$725$	−8.88909	−0.330133
$726$	−4.71890	−0.175135
$727$	−29.4337	−1.09164	−0.545818	−	0.837904i	$-0.683781\pi$
$727$	−29.4337	−1.09164	−0.545818	+	0.837904i	$0.683781\pi$
$728$	0	0
$729$	−4.53143	−0.167831
$730$	−14.3461	−0.530975
$731$	−4.57515	−0.169218
$732$	24.2914	0.897835
$733$	−23.7507	−0.877253	−0.438627	−	0.898669i	$-0.644535\pi$
$733$	−23.7507	−0.877253	−0.438627	+	0.898669i	$0.644535\pi$
$734$	17.6049	0.649810
$735$	58.8359	2.17020
$736$	18.9682	0.699177
$737$	14.4565	0.532512
$738$	−16.0753	−0.591740
$739$	−34.0665	−1.25316	−0.626578	−	0.779359i	$-0.715545\pi$
$739$	−34.0665	−1.25316	−0.626578	+	0.779359i	$0.715545\pi$
$740$	−36.4126	−1.33855
$741$	0	0
$742$	−138.946	−5.10087
$743$	−11.5487	−0.423681	−0.211840	−	0.977304i	$-0.567946\pi$
$743$	−11.5487	−0.423681	−0.211840	+	0.977304i	$0.567946\pi$
$744$	−9.08387	−0.333031
$745$	−4.74129	−0.173707
$746$	5.87264	0.215013
$747$	7.29032	0.266739
$748$	−1.65383	−0.0604699
$749$	1.38764	0.0507034
$750$	−52.8136	−1.92848
$751$	−5.63835	−0.205746	−0.102873	−	0.994694i	$-0.532804\pi$
$751$	−5.63835	−0.205746	−0.102873	+	0.994694i	$0.532804\pi$
$752$	−30.0195	−1.09470
$753$	23.9745	0.873680
$754$	0	0
$755$	20.5301	0.747166
$756$	32.3894	1.17799
$757$	−22.7592	−0.827197	−0.413599	−	0.910459i	$-0.635728\pi$
$757$	−22.7592	−0.827197	−0.413599	+	0.910459i	$0.635728\pi$
$758$	−45.1870	−1.64127
$759$	5.32515	0.193291
$760$	−9.48738	−0.344143
$761$	−3.78582	−0.137236	−0.0686180	−	0.997643i	$-0.521859\pi$
$761$	−3.78582	−0.137236	−0.0686180	+	0.997643i	$0.521859\pi$
$762$	11.2180	0.406385
$763$	−57.8286	−2.09353
$764$	9.57603	0.346449
$765$	1.68328	0.0608589
$766$	−59.6379	−2.15480
$767$	0	0
$768$	−8.18054	−0.295190
$769$	−13.7937	−0.497412	−0.248706	−	0.968579i	$-0.580005\pi$
$769$	−13.7937	−0.497412	−0.248706	+	0.968579i	$0.580005\pi$
$770$	−15.1452	−0.545795
$771$	25.4193	0.915455
$772$	−21.7473	−0.782704
$773$	1.79049	0.0643995	0.0321998	−	0.999481i	$-0.489749\pi$
$773$	1.79049	0.0643995	0.0321998	+	0.999481i	$0.489749\pi$
$774$	28.4798	1.02369
$775$	−10.5796	−0.380031
$776$	−0.745510	−0.0267623
$777$	−116.204	−4.16879
$778$	−43.7429	−1.56826
$779$	−22.8725	−0.819494
$780$	0	0
$781$	4.10847	0.147013
$782$	3.32384	0.118860
$783$	7.12111	0.254488
$784$	−49.2976	−1.76063
$785$	−3.56463	−0.127227
$786$	90.6474	3.23329
$787$	35.3418	1.25980	0.629899	−	0.776677i	$-0.283096\pi$
$787$	35.3418	1.25980	0.629899	+	0.776677i	$0.283096\pi$
$788$	−45.0632	−1.60531
$789$	37.0007	1.31726
$790$	−9.77435	−0.347756
$791$	−62.8708	−2.23543
$792$	2.25483	0.0801220
$793$	0	0
$794$	7.63231	0.270861
$795$	−38.8678	−1.37850
$796$	38.8261	1.37615
$797$	−28.5171	−1.01013	−0.505063	−	0.863082i	$-0.668531\pi$
$797$	−28.5171	−1.01013	−0.505063	+	0.863082i	$0.668531\pi$
$798$	−138.237	−4.89353
$799$	−7.56226	−0.267533
$800$	24.2623	0.857802
$801$	10.7455	0.379674
$802$	31.7801	1.12220
$803$	4.85130	0.171199
$804$	−81.8033	−2.88498
$805$	17.0910	0.602377
$806$	0	0
$807$	9.03711	0.318121
$808$	21.4225	0.753643
$809$	−30.2037	−1.06190	−0.530952	−	0.847402i	$-0.678166\pi$
$809$	−30.2037	−1.06190	−0.530952	+	0.847402i	$0.678166\pi$
$810$	32.8359	1.15373
$811$	34.1934	1.20069	0.600347	−	0.799740i	$-0.295029\pi$
$811$	34.1934	1.20069	0.600347	+	0.799740i	$0.295029\pi$
$812$	37.8203	1.32723
$813$	−23.4005	−0.820690
$814$	21.9297	0.768636
$815$	17.3983	0.609437
$816$	−3.65816	−0.128061
$817$	40.5221	1.41769
$818$	−45.9419	−1.60632
$819$	0	0
$820$	14.1799	0.495183
$821$	45.9333	1.60308	0.801541	−	0.597939i	$-0.204014\pi$
$821$	45.9333	1.60308	0.801541	+	0.597939i	$0.204014\pi$
$822$	88.5713	3.08928
$823$	−30.1187	−1.04987	−0.524936	−	0.851142i	$-0.675911\pi$
$823$	−30.1187	−1.04987	−0.524936	+	0.851142i	$0.675911\pi$
$824$	−4.17022	−0.145276
$825$	6.81143	0.237143
$826$	−0.454076	−0.0157993
$827$	−27.8723	−0.969214	−0.484607	−	0.874732i	$-0.661037\pi$
$827$	−27.8723	−0.969214	−0.484607	+	0.874732i	$0.661037\pi$
$828$	−11.6175	−0.403738
$829$	−7.33079	−0.254609	−0.127304	−	0.991864i	$-0.540633\pi$
$829$	−7.33079	−0.254609	−0.127304	+	0.991864i	$0.540633\pi$
$830$	−11.4530	−0.397539
$831$	−26.2225	−0.909647
$832$	0	0
$833$	−12.4186	−0.430280
$834$	0.389604	0.0134909
$835$	8.65355	0.299469
$836$	14.6480	0.506611
$837$	8.47539	0.292952
$838$	8.08328	0.279232
$839$	40.2027	1.38795	0.693975	−	0.719999i	$-0.255858\pi$
$839$	40.2027	1.38795	0.693975	+	0.719999i	$0.255858\pi$
$840$	18.7704	0.647641
$841$	−20.6849	−0.713271
$842$	−80.0328	−2.75811
$843$	−25.8465	−0.890200
$844$	−28.1708	−0.969678
$845$	0	0
$846$	47.0743	1.61845
$847$	5.12151	0.175977
$848$	32.5666	1.11834
$849$	20.5902	0.706653
$850$	4.25154	0.145826
$851$	−24.7471	−0.848320
$852$	−23.2481	−0.796467
$853$	−8.07861	−0.276606	−0.138303	−	0.990390i	$-0.544165\pi$
$853$	−8.07861	−0.276606	−0.138303	+	0.990390i	$0.544165\pi$
$854$	−46.9534	−1.60671
$855$	−14.9088	−0.509870
$856$	0.324556	0.0110931
$857$	−46.1547	−1.57661	−0.788307	−	0.615282i	$-0.789042\pi$
$857$	−46.1547	−1.57661	−0.788307	+	0.615282i	$0.789042\pi$
$858$	0	0
$859$	−30.1760	−1.02959	−0.514796	−	0.857313i	$-0.672132\pi$
$859$	−30.1760	−1.02959	−0.514796	+	0.857313i	$0.672132\pi$
$860$	−25.1218	−0.856647
$861$	45.2524	1.54220
$862$	29.6997	1.01158
$863$	−24.3157	−0.827715	−0.413858	−	0.910342i	$-0.635819\pi$
$863$	−24.3157	−0.827715	−0.413858	+	0.910342i	$0.635819\pi$
$864$	−19.4367	−0.661249
$865$	−10.2469	−0.348406
$866$	−17.9346	−0.609442
$867$	36.6418	1.24442
$868$	45.0129	1.52784
$869$	3.30530	0.112125
$870$	18.8420	0.638804
$871$	0	0
$872$	−13.5255	−0.458032
$873$	−1.17152	−0.0396500
$874$	−29.4393	−0.995799
$875$	57.3196	1.93775
$876$	−27.4515	−0.927500
$877$	−15.6622	−0.528876	−0.264438	−	0.964403i	$-0.585186\pi$
$877$	−15.6622	−0.528876	−0.264438	+	0.964403i	$0.585186\pi$
$878$	−8.05543	−0.271858
$879$	−31.9270	−1.07687
$880$	3.54978	0.119663
$881$	−39.6536	−1.33596	−0.667981	−	0.744178i	$-0.732841\pi$
$881$	−39.6536	−1.33596	−0.667981	+	0.744178i	$0.732841\pi$
$882$	77.3047	2.60299
$883$	−1.49267	−0.0502323	−0.0251161	−	0.999685i	$-0.507996\pi$
$883$	−1.49267	−0.0502323	−0.0251161	+	0.999685i	$0.507996\pi$
$884$	0	0
$885$	−0.127020	−0.00426973
$886$	−11.8644	−0.398592
$887$	26.5235	0.890573	0.445287	−	0.895388i	$-0.353102\pi$
$887$	26.5235	0.890573	0.445287	+	0.895388i	$0.353102\pi$
$888$	−27.1789	−0.912065
$889$	−12.1751	−0.408340
$890$	−16.8810	−0.565854
$891$	−11.1038	−0.371991
$892$	−42.6902	−1.42937
$893$	66.9791	2.24137
$894$	−16.1579	−0.540401
$895$	−18.8309	−0.629448
$896$	−47.1490	−1.57514
$897$	0	0
$898$	54.1133	1.80578
$899$	9.89649	0.330066
$900$	−14.8601	−0.495335
$901$	8.20391	0.273312
$902$	−8.53993	−0.284348
$903$	−80.1715	−2.66794
$904$	−14.7048	−0.489076
$905$	−7.49132	−0.249020
$906$	69.9648	2.32442
$907$	48.7847	1.61987	0.809935	−	0.586519i	$-0.199502\pi$
$907$	48.7847	1.61987	0.809935	+	0.586519i	$0.199502\pi$
$908$	47.2268	1.56728
$909$	33.6641	1.11657
$910$	0	0
$911$	−36.7550	−1.21775	−0.608874	−	0.793267i	$-0.708379\pi$
$911$	−36.7550	−1.21775	−0.608874	+	0.793267i	$0.708379\pi$
$912$	32.4004	1.07289
$913$	3.87295	0.128176
$914$	65.0904	2.15300
$915$	−13.1344	−0.434211
$916$	−67.9602	−2.24547
$917$	−98.3813	−3.24884
$918$	−3.40593	−0.112413
$919$	−31.1775	−1.02845	−0.514225	−	0.857655i	$-0.671920\pi$
$919$	−31.1775	−1.02845	−0.514225	+	0.857655i	$0.671920\pi$
$920$	3.99740	0.131790
$921$	−18.0832	−0.595863
$922$	72.0167	2.37174
$923$	0	0
$924$	−28.9805	−0.953387
$925$	−31.6541	−1.04078
$926$	−51.5535	−1.69415
$927$	−6.55322	−0.215236
$928$	−22.6957	−0.745023
$929$	22.0105	0.722141	0.361071	−	0.932538i	$-0.382411\pi$
$929$	22.0105	0.722141	0.361071	+	0.932538i	$0.382411\pi$
$930$	22.4253	0.735356
$931$	109.992	3.60484
$932$	5.14495	0.168529
$933$	0.111445	0.00364856
$934$	47.9717	1.56968
$935$	0.894231	0.0292445
$936$	0	0
$937$	−9.10082	−0.297311	−0.148655	−	0.988889i	$-0.547495\pi$
$937$	−9.10082	−0.297311	−0.148655	+	0.988889i	$0.547495\pi$
$938$	158.120	5.16279
$939$	−34.6027	−1.12922
$940$	−41.5239	−1.35436
$941$	−10.7409	−0.350142	−0.175071	−	0.984556i	$-0.556015\pi$
$941$	−10.7409	−0.350142	−0.175071	+	0.984556i	$0.556015\pi$
$942$	−12.1480	−0.395802
$943$	9.63708	0.313827
$944$	0.106428	0.00346393
$945$	−17.5131	−0.569701
$946$	15.1298	0.491911
$947$	−22.9686	−0.746379	−0.373190	−	0.927755i	$-0.621736\pi$
$947$	−22.9686	−0.746379	−0.373190	+	0.927755i	$0.621736\pi$
$948$	−18.7033	−0.607455
$949$	0	0
$950$	−37.6559	−1.22172
$951$	−11.2781	−0.365718
$952$	−3.96191	−0.128406
$953$	11.3117	0.366421	0.183211	−	0.983074i	$-0.441351\pi$
$953$	11.3117	0.366421	0.183211	+	0.983074i	$0.441351\pi$
$954$	−51.0686	−1.65341
$955$	−5.17780	−0.167550
$956$	−62.2888	−2.01456
$957$	−6.37162	−0.205965
$958$	−20.5323	−0.663370
$959$	−96.1281	−3.10414
$960$	−35.7410	−1.15353
$961$	−19.2214	−0.620046
$962$	0	0
$963$	0.510018	0.0164351
$964$	−36.0547	−1.16125
$965$	11.7589	0.378531
$966$	58.2445	1.87399
$967$	−28.6154	−0.920211	−0.460105	−	0.887864i	$-0.652188\pi$
$967$	−28.6154	−0.920211	−0.460105	+	0.887864i	$0.652188\pi$
$968$	1.19787	0.0385009
$969$	8.16204	0.262203
$970$	1.84044	0.0590929
$971$	14.1652	0.454583	0.227292	−	0.973827i	$-0.427013\pi$
$971$	14.1652	0.454583	0.227292	+	0.973827i	$0.427013\pi$
$972$	43.8591	1.40678
$973$	−0.422844	−0.0135558
$974$	−39.9794	−1.28102
$975$	0	0
$976$	11.0051	0.352265
$977$	33.7336	1.07923	0.539617	−	0.841910i	$-0.318569\pi$
$977$	33.7336	1.07923	0.539617	+	0.841910i	$0.318569\pi$
$978$	59.2920	1.89595
$979$	5.70850	0.182445
$980$	−68.1898	−2.17824
$981$	−21.2545	−0.678603
$982$	39.6906	1.26658
$983$	−39.6732	−1.26538	−0.632689	−	0.774406i	$-0.718049\pi$
$983$	−39.6732	−1.26538	−0.632689	+	0.774406i	$0.718049\pi$
$984$	10.5841	0.337408
$985$	24.3659	0.776361
$986$	−3.97702	−0.126654
$987$	−132.516	−4.21802
$988$	0	0
$989$	−17.0735	−0.542907
$990$	−5.56650	−0.176915
$991$	−21.8300	−0.693453	−0.346726	−	0.937966i	$-0.612707\pi$
$991$	−21.8300	−0.693453	−0.346726	+	0.937966i	$0.612707\pi$
$992$	−27.0119	−0.857630
$993$	−59.8666	−1.89981
$994$	44.9369	1.42531
$995$	−20.9934	−0.665536
$996$	−21.9154	−0.694416
$997$	40.9743	1.29767	0.648834	−	0.760930i	$-0.275257\pi$
$997$	40.9743	1.29767	0.648834	+	0.760930i	$0.275257\pi$
$998$	34.6960	1.09828
$999$	25.3583	0.802302

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.2.a.t.1.16	yes	21
13.12	even	2		1859.2.a.s.1.6	✓	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1859.2.a.s.1.6	✓	21	13.12	even	2
1859.2.a.t.1.16	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)

\(f(q)\)	\(=\)	\(q+2.13563 q^{2} -2.20961 q^{3} +2.56090 q^{4} -1.38469 q^{5} -4.71890 q^{6} +5.12151 q^{7} +1.19787 q^{8} +1.88237 q^{9} +O(q^{10})\)	\(q+2.13563 q^{2} -2.20961 q^{3} +2.56090 q^{4} -1.38469 q^{5} -4.71890 q^{6} +5.12151 q^{7} +1.19787 q^{8} +1.88237 q^{9} -2.95718 q^{10} +1.00000 q^{11} -5.65858 q^{12} +10.9376 q^{14} +3.05962 q^{15} -2.56360 q^{16} -0.645800 q^{17} +4.02004 q^{18} +5.71986 q^{19} -3.54604 q^{20} -11.3165 q^{21} +2.13563 q^{22} -2.41000 q^{23} -2.64682 q^{24} -3.08264 q^{25} +2.46952 q^{27} +13.1157 q^{28} +2.88360 q^{29} +6.53420 q^{30} +3.43199 q^{31} -7.87062 q^{32} -2.20961 q^{33} -1.37919 q^{34} -7.09169 q^{35} +4.82056 q^{36} +10.2685 q^{37} +12.2155 q^{38} -1.65867 q^{40} -3.99879 q^{41} -24.1679 q^{42} +7.08446 q^{43} +2.56090 q^{44} -2.60650 q^{45} -5.14686 q^{46} +11.7099 q^{47} +5.66455 q^{48} +19.2298 q^{49} -6.58337 q^{50} +1.42697 q^{51} -12.7035 q^{53} +5.27398 q^{54} -1.38469 q^{55} +6.13489 q^{56} -12.6387 q^{57} +6.15828 q^{58} -0.0415150 q^{59} +7.83537 q^{60} -4.29284 q^{61} +7.32946 q^{62} +9.64058 q^{63} -11.6815 q^{64} -4.71890 q^{66} +14.4565 q^{67} -1.65383 q^{68} +5.32515 q^{69} -15.1452 q^{70} +4.10847 q^{71} +2.25483 q^{72} +4.85130 q^{73} +21.9297 q^{74} +6.81143 q^{75} +14.6480 q^{76} +5.12151 q^{77} +3.30530 q^{79} +3.54978 q^{80} -11.1038 q^{81} -8.53993 q^{82} +3.87295 q^{83} -28.9805 q^{84} +0.894231 q^{85} +15.1298 q^{86} -6.37162 q^{87} +1.19787 q^{88} +5.70850 q^{89} -5.56650 q^{90} -6.17176 q^{92} -7.58337 q^{93} +25.0080 q^{94} -7.92022 q^{95} +17.3910 q^{96} -0.622364 q^{97} +41.0677 q^{98} +1.88237 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 6 q^{3} + 32 q^{4} + 7 q^{5} - 19 q^{6} + q^{7} - 3 q^{8} + 33 q^{9}+O(q^{10}) \) 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

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Database

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