LMFDB - Embedded newform 1859.2.a.t.1.11

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			1.11
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)

$f(q)$	$=$	$q-0.340522 q^{2} -1.21327 q^{3} -1.88404 q^{4} -3.18769 q^{5} +0.413146 q^{6} +4.05402 q^{7} +1.32260 q^{8} -1.52797 q^{9} +O(q^{10})$	\(q-0.340522 q^{2} -1.21327 q^{3} -1.88404 q^{4} -3.18769 q^{5} +0.413146 q^{6} +4.05402 q^{7} +1.32260 q^{8} -1.52797 q^{9} +1.08548 q^{10} +1.00000 q^{11} +2.28586 q^{12} -1.38048 q^{14} +3.86754 q^{15} +3.31771 q^{16} -2.34667 q^{17} +0.520307 q^{18} -6.23610 q^{19} +6.00575 q^{20} -4.91864 q^{21} -0.340522 q^{22} -8.20474 q^{23} -1.60468 q^{24} +5.16137 q^{25} +5.49366 q^{27} -7.63796 q^{28} -4.01420 q^{29} -1.31698 q^{30} +0.723646 q^{31} -3.77496 q^{32} -1.21327 q^{33} +0.799091 q^{34} -12.9230 q^{35} +2.87876 q^{36} -10.0577 q^{37} +2.12353 q^{38} -4.21605 q^{40} -4.40518 q^{41} +1.67490 q^{42} +9.58073 q^{43} -1.88404 q^{44} +4.87069 q^{45} +2.79390 q^{46} +4.76081 q^{47} -4.02529 q^{48} +9.43510 q^{49} -1.75756 q^{50} +2.84714 q^{51} +5.18522 q^{53} -1.87071 q^{54} -3.18769 q^{55} +5.36186 q^{56} +7.56609 q^{57} +1.36692 q^{58} -0.694630 q^{59} -7.28661 q^{60} +10.3413 q^{61} -0.246418 q^{62} -6.19442 q^{63} -5.34997 q^{64} +0.413146 q^{66} +7.17195 q^{67} +4.42122 q^{68} +9.95459 q^{69} +4.40056 q^{70} +2.32931 q^{71} -2.02090 q^{72} -2.44069 q^{73} +3.42485 q^{74} -6.26215 q^{75} +11.7491 q^{76} +4.05402 q^{77} -2.59565 q^{79} -10.5758 q^{80} -2.08140 q^{81} +1.50006 q^{82} +13.6065 q^{83} +9.26693 q^{84} +7.48044 q^{85} -3.26245 q^{86} +4.87032 q^{87} +1.32260 q^{88} -15.3302 q^{89} -1.65858 q^{90} +15.4581 q^{92} -0.877980 q^{93} -1.62116 q^{94} +19.8788 q^{95} +4.58006 q^{96} -12.7385 q^{97} -3.21286 q^{98} -1.52797 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.340522	−0.240786	−0.120393	−	0.992726i	$-0.538415\pi$
$2$	−0.340522	−0.240786	−0.120393	+	0.992726i	$0.538415\pi$
$3$	−1.21327	−0.700483	−0.350242	−	0.936659i	$-0.613901\pi$
$3$	−1.21327	−0.700483	−0.350242	+	0.936659i	$0.613901\pi$
$4$	−1.88404	−0.942022
$5$	−3.18769	−1.42558	−0.712789	−	0.701378i	$-0.752568\pi$
$5$	−3.18769	−1.42558	−0.712789	+	0.701378i	$0.752568\pi$
$6$	0.413146	0.168666
$7$	4.05402	1.53228	0.766138	−	0.642676i	$-0.222176\pi$
$7$	4.05402	1.53228	0.766138	+	0.642676i	$0.222176\pi$
$8$	1.32260	0.467611
$9$	−1.52797	−0.509323
$10$	1.08548	0.343259
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	2.28586	0.659871
$13$	0	0
$13$	0	0
$14$	−1.38048	−0.368950
$15$	3.86754	0.998594
$16$	3.31771	0.829428
$17$	−2.34667	−0.569150	−0.284575	−	0.958654i	$-0.591852\pi$
$17$	−2.34667	−0.569150	−0.284575	+	0.958654i	$0.591852\pi$
$18$	0.520307	0.122638
$19$	−6.23610	−1.43066	−0.715330	−	0.698787i	$-0.753723\pi$
$19$	−6.23610	−1.43066	−0.715330	+	0.698787i	$0.753723\pi$
$20$	6.00575	1.34293
$21$	−4.91864	−1.07333
$22$	−0.340522	−0.0725996
$23$	−8.20474	−1.71081	−0.855403	−	0.517963i	$-0.826691\pi$
$23$	−8.20474	−1.71081	−0.855403	+	0.517963i	$0.826691\pi$
$24$	−1.60468	−0.327554
$25$	5.16137	1.03227
$26$	0	0
$27$	5.49366	1.05726
$28$	−7.63796	−1.44344
$29$	−4.01420	−0.745419	−0.372709	−	0.927948i	$-0.621571\pi$
$29$	−4.01420	−0.745419	−0.372709	+	0.927948i	$0.621571\pi$
$30$	−1.31698	−0.240447
$31$	0.723646	0.129971	0.0649854	−	0.997886i	$-0.479300\pi$
$31$	0.723646	0.129971	0.0649854	+	0.997886i	$0.479300\pi$
$32$	−3.77496	−0.667325
$33$	−1.21327	−0.211204
$34$	0.799091	0.137043
$35$	−12.9230	−2.18438
$36$	2.87876	0.479794
$37$	−10.0577	−1.65347	−0.826734	−	0.562593i	$-0.809804\pi$
$37$	−10.0577	−1.65347	−0.826734	+	0.562593i	$0.809804\pi$
$38$	2.12353	0.344482
$39$	0	0
$40$	−4.21605	−0.666616
$41$	−4.40518	−0.687974	−0.343987	−	0.938974i	$-0.611778\pi$
$41$	−4.40518	−0.687974	−0.343987	+	0.938974i	$0.611778\pi$
$42$	1.67490	0.258443
$43$	9.58073	1.46105	0.730524	−	0.682887i	$-0.239276\pi$
$43$	9.58073	1.46105	0.730524	+	0.682887i	$0.239276\pi$
$44$	−1.88404	−0.284030
$45$	4.87069	0.726080
$46$	2.79390	0.411937
$47$	4.76081	0.694435	0.347217	−	0.937785i	$-0.387127\pi$
$47$	4.76081	0.694435	0.347217	+	0.937785i	$0.387127\pi$
$48$	−4.02529	−0.581001
$49$	9.43510	1.34787
$50$	−1.75756	−0.248557
$51$	2.84714	0.398680
$52$	0	0
$53$	5.18522	0.712245	0.356122	−	0.934439i	$-0.384099\pi$
$53$	5.18522	0.712245	0.356122	+	0.934439i	$0.384099\pi$
$54$	−1.87071	−0.254572
$55$	−3.18769	−0.429828
$56$	5.36186	0.716509
$57$	7.56609	1.00215
$58$	1.36692	0.179486
$59$	−0.694630	−0.0904331	−0.0452166	−	0.998977i	$-0.514398\pi$
$59$	−0.694630	−0.0904331	−0.0452166	+	0.998977i	$0.514398\pi$
$60$	−7.28661	−0.940698
$61$	10.3413	1.32407	0.662033	−	0.749475i	$-0.269694\pi$
$61$	10.3413	1.32407	0.662033	+	0.749475i	$0.269694\pi$
$62$	−0.246418	−0.0312951
$63$	−6.19442	−0.780424
$64$	−5.34997	−0.668746
$65$	0	0
$66$	0.413146	0.0508548
$67$	7.17195	0.876193	0.438097	−	0.898928i	$-0.355653\pi$
$67$	7.17195	0.876193	0.438097	+	0.898928i	$0.355653\pi$
$68$	4.42122	0.536152
$69$	9.95459	1.19839
$70$	4.40056	0.525967
$71$	2.32931	0.276438	0.138219	−	0.990402i	$-0.455862\pi$
$71$	2.32931	0.276438	0.138219	+	0.990402i	$0.455862\pi$
$72$	−2.02090	−0.238165
$73$	−2.44069	−0.285662	−0.142831	−	0.989747i	$-0.545620\pi$
$73$	−2.44069	−0.285662	−0.142831	+	0.989747i	$0.545620\pi$
$74$	3.42485	0.398131
$75$	−6.26215	−0.723091
$76$	11.7491	1.34771
$77$	4.05402	0.461999
$78$	0	0
$79$	−2.59565	−0.292034	−0.146017	−	0.989282i	$-0.546645\pi$
$79$	−2.59565	−0.292034	−0.146017	+	0.989282i	$0.546645\pi$
$80$	−10.5758	−1.18242
$81$	−2.08140	−0.231267
$82$	1.50006	0.165654
$83$	13.6065	1.49351	0.746756	−	0.665098i	$-0.231610\pi$
$83$	13.6065	1.49351	0.746756	+	0.665098i	$0.231610\pi$
$84$	9.26693	1.01110
$85$	7.48044	0.811368
$86$	−3.26245	−0.351799
$87$	4.87032	0.522153
$88$	1.32260	0.140990
$89$	−15.3302	−1.62500	−0.812498	−	0.582964i	$-0.801893\pi$
$89$	−15.3302	−1.62500	−0.812498	+	0.582964i	$0.801893\pi$
$90$	−1.65858	−0.174830
$91$	0	0
$92$	15.4581	1.61162
$93$	−0.877980	−0.0910423
$94$	−1.62116	−0.167210
$95$	19.8788	2.03952
$96$	4.58006	0.467450
$97$	−12.7385	−1.29340	−0.646700	−	0.762744i	$-0.723852\pi$
$97$	−12.7385	−1.29340	−0.646700	+	0.762744i	$0.723852\pi$
$98$	−3.21286	−0.324548
$99$	−1.52797	−0.153567
$100$	−9.72425	−0.972425
$101$	0.398607	0.0396629	0.0198315	−	0.999803i	$-0.493687\pi$
$101$	0.398607	0.0396629	0.0198315	+	0.999803i	$0.493687\pi$
$102$	−0.969516	−0.0959964
$103$	13.6068	1.34072	0.670360	−	0.742036i	$-0.266140\pi$
$103$	13.6068	1.34072	0.670360	+	0.742036i	$0.266140\pi$
$104$	0	0
$105$	15.6791	1.53012
$106$	−1.76568	−0.171498
$107$	7.75320	0.749530	0.374765	−	0.927120i	$-0.377723\pi$
$107$	7.75320	0.749530	0.374765	+	0.927120i	$0.377723\pi$
$108$	−10.3503	−0.995958
$109$	9.30888	0.891629	0.445815	−	0.895125i	$-0.352914\pi$
$109$	9.30888	0.891629	0.445815	+	0.895125i	$0.352914\pi$
$110$	1.08548	0.103496
$111$	12.2027	1.15823
$112$	13.4501	1.27091
$113$	−8.75929	−0.824005	−0.412003	−	0.911183i	$-0.635171\pi$
$113$	−8.75929	−0.824005	−0.412003	+	0.911183i	$0.635171\pi$
$114$	−2.57642	−0.241304
$115$	26.1542	2.43889
$116$	7.56294	0.702201
$117$	0	0
$118$	0.236537	0.0217750
$119$	−9.51343	−0.872095
$120$	5.11522	0.466953
$121$	1.00000	0.0909091
$122$	−3.52144	−0.318816
$123$	5.34469	0.481914
$124$	−1.36338	−0.122435
$125$	−0.514399	−0.0460093
$126$	2.10934	0.187915
$127$	16.8374	1.49408	0.747040	−	0.664779i	$-0.231474\pi$
$127$	16.8374	1.49408	0.747040	+	0.664779i	$0.231474\pi$
$128$	9.37171	0.828350
$129$	−11.6240	−1.02344
$130$	0	0
$131$	14.5768	1.27358	0.636792	−	0.771035i	$-0.280261\pi$
$131$	14.5768	1.27358	0.636792	+	0.771035i	$0.280261\pi$
$132$	2.28586	0.198959
$133$	−25.2813	−2.19217
$134$	−2.44221	−0.210975
$135$	−17.5121	−1.50720
$136$	−3.10371	−0.266141
$137$	−2.47456	−0.211416	−0.105708	−	0.994397i	$-0.533711\pi$
$137$	−2.47456	−0.211416	−0.105708	+	0.994397i	$0.533711\pi$
$138$	−3.38976	−0.288555
$139$	8.57679	0.727474	0.363737	−	0.931502i	$-0.381501\pi$
$139$	8.57679	0.727474	0.363737	+	0.931502i	$0.381501\pi$
$140$	24.3475	2.05774
$141$	−5.77616	−0.486440
$142$	−0.793180	−0.0665622
$143$	0	0
$144$	−5.06937	−0.422447
$145$	12.7960	1.06265
$146$	0.831110	0.0687832
$147$	−11.4474	−0.944162
$148$	18.9491	1.55760
$149$	−18.2363	−1.49398	−0.746989	−	0.664837i	$-0.768501\pi$
$149$	−18.2363	−1.49398	−0.746989	+	0.664837i	$0.768501\pi$
$150$	2.13240	0.174110
$151$	−16.5757	−1.34891	−0.674455	−	0.738316i	$-0.735621\pi$
$151$	−16.5757	−1.34891	−0.674455	+	0.738316i	$0.735621\pi$
$152$	−8.24789	−0.668992
$153$	3.58563	0.289881
$154$	−1.38048	−0.111243
$155$	−2.30676	−0.185283
$156$	0	0
$157$	−3.20959	−0.256153	−0.128077	−	0.991764i	$-0.540880\pi$
$157$	−3.20959	−0.256153	−0.128077	+	0.991764i	$0.540880\pi$
$158$	0.883878	0.0703176
$159$	−6.29109	−0.498916
$160$	12.0334	0.951324
$161$	−33.2622	−2.62143
$162$	0.708763	0.0556857
$163$	11.8715	0.929850	0.464925	−	0.885350i	$-0.346081\pi$
$163$	11.8715	0.929850	0.464925	+	0.885350i	$0.346081\pi$
$164$	8.29956	0.648087
$165$	3.86754	0.301087
$166$	−4.63333	−0.359616
$167$	12.1933	0.943545	0.471773	−	0.881720i	$-0.343614\pi$
$167$	12.1933	0.943545	0.471773	+	0.881720i	$0.343614\pi$
$168$	−6.50540	−0.501903
$169$	0	0
$170$	−2.54726	−0.195366
$171$	9.52857	0.728668
$172$	−18.0505	−1.37634
$173$	−0.995436	−0.0756816	−0.0378408	−	0.999284i	$-0.512048\pi$
$173$	−0.995436	−0.0756816	−0.0378408	+	0.999284i	$0.512048\pi$
$174$	−1.65845	−0.125727
$175$	20.9243	1.58173
$176$	3.31771	0.250082
$177$	0.842776	0.0633469
$178$	5.22027	0.391276
$179$	−13.8360	−1.03415	−0.517077	−	0.855939i	$-0.672980\pi$
$179$	−13.8360	−1.03415	−0.517077	+	0.855939i	$0.672980\pi$
$180$	−9.17660	−0.683984
$181$	19.6335	1.45935	0.729673	−	0.683796i	$-0.239672\pi$
$181$	19.6335	1.45935	0.729673	+	0.683796i	$0.239672\pi$
$182$	0	0
$183$	−12.5468	−0.927486
$184$	−10.8516	−0.799992
$185$	32.0607	2.35715
$186$	0.298972	0.0219217
$187$	−2.34667	−0.171605
$188$	−8.96957	−0.654173
$189$	22.2714	1.62001
$190$	−6.76916	−0.491086
$191$	9.98283	0.722332	0.361166	−	0.932501i	$-0.382379\pi$
$191$	9.98283	0.722332	0.361166	+	0.932501i	$0.382379\pi$
$192$	6.49097	0.468446
$193$	−2.95160	−0.212461	−0.106230	−	0.994342i	$-0.533878\pi$
$193$	−2.95160	−0.212461	−0.106230	+	0.994342i	$0.533878\pi$
$194$	4.33775	0.311432
$195$	0	0
$196$	−17.7762	−1.26973
$197$	−1.96116	−0.139727	−0.0698635	−	0.997557i	$-0.522256\pi$
$197$	−1.96116	−0.139727	−0.0698635	+	0.997557i	$0.522256\pi$
$198$	0.520307	0.0369766
$199$	−8.54240	−0.605555	−0.302777	−	0.953061i	$-0.597914\pi$
$199$	−8.54240	−0.605555	−0.302777	+	0.953061i	$0.597914\pi$
$200$	6.82645	0.482703
$201$	−8.70153	−0.613759
$202$	−0.135735	−0.00955025
$203$	−16.2737	−1.14219
$204$	−5.36415	−0.375565
$205$	14.0424	0.980761
$206$	−4.63342	−0.322826
$207$	12.5366	0.871353
$208$	0	0
$209$	−6.23610	−0.431360
$210$	−5.33908	−0.368431
$211$	23.0336	1.58570	0.792848	−	0.609420i	$-0.208598\pi$
$211$	23.0336	1.58570	0.792848	+	0.609420i	$0.208598\pi$
$212$	−9.76919	−0.670950
$213$	−2.82608	−0.193640
$214$	−2.64014	−0.180476
$215$	−30.5404	−2.08284
$216$	7.26593	0.494384
$217$	2.93368	0.199151
$218$	−3.16988	−0.214691
$219$	2.96123	0.200101
$220$	6.00575	0.404908
$221$	0	0
$222$	−4.15528	−0.278884
$223$	8.80848	0.589860	0.294930	−	0.955519i	$-0.404704\pi$
$223$	8.80848	0.589860	0.294930	+	0.955519i	$0.404704\pi$
$224$	−15.3038	−1.02253
$225$	−7.88642	−0.525761
$226$	2.98273	0.198408
$227$	20.6166	1.36837	0.684185	−	0.729309i	$-0.260158\pi$
$227$	20.6166	1.36837	0.684185	+	0.729309i	$0.260158\pi$
$228$	−14.2549	−0.944051
$229$	6.88948	0.455269	0.227635	−	0.973747i	$-0.426901\pi$
$229$	6.88948	0.455269	0.227635	+	0.973747i	$0.426901\pi$
$230$	−8.90607	−0.587249
$231$	−4.91864	−0.323622
$232$	−5.30920	−0.348566
$233$	10.1842	0.667186	0.333593	−	0.942717i	$-0.391739\pi$
$233$	10.1842	0.667186	0.333593	+	0.942717i	$0.391739\pi$
$234$	0	0
$235$	−15.1760	−0.989971
$236$	1.30871	0.0851900
$237$	3.14924	0.204565
$238$	3.23954	0.209988
$239$	−18.7944	−1.21571	−0.607854	−	0.794049i	$-0.707969\pi$
$239$	−18.7944	−1.21571	−0.607854	+	0.794049i	$0.707969\pi$
$240$	12.8314	0.828262
$241$	1.23448	0.0795200	0.0397600	−	0.999209i	$-0.487341\pi$
$241$	1.23448	0.0795200	0.0397600	+	0.999209i	$0.487341\pi$
$242$	−0.340522	−0.0218896
$243$	−13.9557	−0.895257
$244$	−19.4834	−1.24730
$245$	−30.0762	−1.92150
$246$	−1.81998	−0.116038
$247$	0	0
$248$	0.957097	0.0607757
$249$	−16.5084	−1.04618
$250$	0.175164	0.0110784
$251$	−24.5319	−1.54844	−0.774220	−	0.632916i	$-0.781858\pi$
$251$	−24.5319	−1.54844	−0.774220	+	0.632916i	$0.781858\pi$
$252$	11.6706	0.735177
$253$	−8.20474	−0.515828
$254$	−5.73352	−0.359753
$255$	−9.07582	−0.568350
$256$	7.50867	0.469292
$257$	−12.8523	−0.801706	−0.400853	−	0.916142i	$-0.631286\pi$
$257$	−12.8523	−0.801706	−0.400853	+	0.916142i	$0.631286\pi$
$258$	3.95824	0.246429
$259$	−40.7739	−2.53357
$260$	0	0
$261$	6.13358	0.379659
$262$	−4.96374	−0.306661
$263$	7.20748	0.444432	0.222216	−	0.974997i	$-0.428671\pi$
$263$	7.20748	0.444432	0.222216	+	0.974997i	$0.428671\pi$
$264$	−1.60468	−0.0987611
$265$	−16.5289	−1.01536
$266$	8.60884	0.527842
$267$	18.5997	1.13828
$268$	−13.5123	−0.825394
$269$	12.9503	0.789592	0.394796	−	0.918769i	$-0.370815\pi$
$269$	12.9503	0.789592	0.394796	+	0.918769i	$0.370815\pi$
$270$	5.96326	0.362912
$271$	−6.05682	−0.367926	−0.183963	−	0.982933i	$-0.558893\pi$
$271$	−6.05682	−0.367926	−0.183963	+	0.982933i	$0.558893\pi$
$272$	−7.78556	−0.472069
$273$	0	0
$274$	0.842642	0.0509059
$275$	5.16137	0.311242
$276$	−18.7549	−1.12891
$277$	26.3488	1.58314	0.791572	−	0.611076i	$-0.209263\pi$
$277$	26.3488	1.58314	0.791572	+	0.611076i	$0.209263\pi$
$278$	−2.92059	−0.175165
$279$	−1.10571	−0.0661971
$280$	−17.0920	−1.02144
$281$	14.3133	0.853863	0.426931	−	0.904284i	$-0.359595\pi$
$281$	14.3133	0.853863	0.426931	+	0.904284i	$0.359595\pi$
$282$	1.96691	0.117128
$283$	−13.4251	−0.798040	−0.399020	−	0.916942i	$-0.630650\pi$
$283$	−13.4251	−0.798040	−0.399020	+	0.916942i	$0.630650\pi$
$284$	−4.38852	−0.260410
$285$	−24.1184	−1.42865
$286$	0	0
$287$	−17.8587	−1.05417
$288$	5.76803	0.339884
$289$	−11.4932	−0.676068
$290$	−4.35733	−0.255871
$291$	15.4553	0.906005
$292$	4.59838	0.269100
$293$	19.2112	1.12233	0.561165	−	0.827704i	$-0.310353\pi$
$293$	19.2112	1.12233	0.561165	+	0.827704i	$0.310353\pi$
$294$	3.89808	0.227340
$295$	2.21427	0.128920
$296$	−13.3023	−0.773179
$297$	5.49366	0.318775
$298$	6.20987	0.359728
$299$	0	0
$300$	11.7982	0.681168
$301$	38.8405	2.23873
$302$	5.64439	0.324798
$303$	−0.483619	−0.0277832
$304$	−20.6896	−1.18663
$305$	−32.9648	−1.88756
$306$	−1.22099	−0.0697992
$307$	17.1911	0.981146	0.490573	−	0.871400i	$-0.336788\pi$
$307$	17.1911	0.981146	0.490573	+	0.871400i	$0.336788\pi$
$308$	−7.63796	−0.435213
$309$	−16.5088	−0.939151
$310$	0.785503	0.0446136
$311$	−13.4197	−0.760960	−0.380480	−	0.924789i	$-0.624241\pi$
$311$	−13.4197	−0.760960	−0.380480	+	0.924789i	$0.624241\pi$
$312$	0	0
$313$	−13.0687	−0.738684	−0.369342	−	0.929293i	$-0.620417\pi$
$313$	−13.0687	−0.738684	−0.369342	+	0.929293i	$0.620417\pi$
$314$	1.09294	0.0616780
$315$	19.7459	1.11256
$316$	4.89033	0.275103
$317$	11.3044	0.634918	0.317459	−	0.948272i	$-0.397170\pi$
$317$	11.3044	0.634918	0.317459	+	0.948272i	$0.397170\pi$
$318$	2.14225	0.120132
$319$	−4.01420	−0.224752
$320$	17.0540	0.953350
$321$	−9.40675	−0.525034
$322$	11.3265	0.631202
$323$	14.6340	0.814260
$324$	3.92145	0.217858
$325$	0	0
$326$	−4.04252	−0.223894
$327$	−11.2942	−0.624571
$328$	−5.82631	−0.321704
$329$	19.3004	1.06407
$330$	−1.31698	−0.0724975
$331$	5.18040	0.284740	0.142370	−	0.989813i	$-0.454528\pi$
$331$	5.18040	0.284740	0.142370	+	0.989813i	$0.454528\pi$
$332$	−25.6353	−1.40692
$333$	15.3678	0.842149
$334$	−4.15209	−0.227192
$335$	−22.8620	−1.24908
$336$	−16.3186	−0.890254
$337$	−7.41964	−0.404174	−0.202087	−	0.979368i	$-0.564772\pi$
$337$	−7.41964	−0.404174	−0.202087	+	0.979368i	$0.564772\pi$
$338$	0	0
$339$	10.6274	0.577202
$340$	−14.0935	−0.764327
$341$	0.723646	0.0391876
$342$	−3.24469	−0.175453
$343$	9.87196	0.533036
$344$	12.6715	0.683202
$345$	−31.7321	−1.70840
$346$	0.338968	0.0182230
$347$	23.8714	1.28149	0.640743	−	0.767755i	$-0.278626\pi$
$347$	23.8714	1.28149	0.640743	+	0.767755i	$0.278626\pi$
$348$	−9.17590	−0.491880
$349$	22.7399	1.21724	0.608620	−	0.793462i	$-0.291724\pi$
$349$	22.7399	1.21724	0.608620	+	0.793462i	$0.291724\pi$
$350$	−7.12519	−0.380858
$351$	0	0
$352$	−3.77496	−0.201206
$353$	19.7394	1.05062	0.525312	−	0.850910i	$-0.323949\pi$
$353$	19.7394	1.05062	0.525312	+	0.850910i	$0.323949\pi$
$354$	−0.286984	−0.0152530
$355$	−7.42510	−0.394084
$356$	28.8828	1.53078
$357$	11.5424	0.610888
$358$	4.71148	0.249009
$359$	10.7299	0.566302	0.283151	−	0.959075i	$-0.408620\pi$
$359$	10.7299	0.566302	0.283151	+	0.959075i	$0.408620\pi$
$360$	6.44200	0.339523
$361$	19.8889	1.04679
$362$	−6.68564	−0.351390
$363$	−1.21327	−0.0636803
$364$	0	0
$365$	7.78018	0.407233
$366$	4.27246	0.223325
$367$	4.36648	0.227928	0.113964	−	0.993485i	$-0.463645\pi$
$367$	4.36648	0.227928	0.113964	+	0.993485i	$0.463645\pi$
$368$	−27.2210	−1.41899
$369$	6.73098	0.350401
$370$	−10.9174	−0.567567
$371$	21.0210	1.09136
$372$	1.65415	0.0857639
$373$	1.64386	0.0851161	0.0425580	−	0.999094i	$-0.486449\pi$
$373$	1.64386	0.0851161	0.0425580	+	0.999094i	$0.486449\pi$
$374$	0.799091	0.0413200
$375$	0.624107	0.0322287
$376$	6.29666	0.324725
$377$	0	0
$378$	−7.58392	−0.390075
$379$	27.3618	1.40548	0.702741	−	0.711446i	$-0.251959\pi$
$379$	27.3618	1.40548	0.702741	+	0.711446i	$0.251959\pi$
$380$	−37.4525	−1.92127
$381$	−20.4284	−1.04658
$382$	−3.39938	−0.173927
$383$	8.65412	0.442205	0.221102	−	0.975251i	$-0.429034\pi$
$383$	8.65412	0.442205	0.221102	+	0.975251i	$0.429034\pi$
$384$	−11.3704	−0.580245
$385$	−12.9230	−0.658616
$386$	1.00508	0.0511575
$387$	−14.6391	−0.744145
$388$	23.9999	1.21841
$389$	−3.91452	−0.198474	−0.0992369	−	0.995064i	$-0.531640\pi$
$389$	−3.91452	−0.198474	−0.0992369	+	0.995064i	$0.531640\pi$
$390$	0	0
$391$	19.2538	0.973705
$392$	12.4789	0.630279
$393$	−17.6857	−0.892125
$394$	0.667819	0.0336442
$395$	8.27414	0.416317
$396$	2.87876	0.144663
$397$	−33.0114	−1.65680	−0.828398	−	0.560140i	$-0.810747\pi$
$397$	−33.0114	−1.65680	−0.828398	+	0.560140i	$0.810747\pi$
$398$	2.90888	0.145809
$399$	30.6731	1.53558
$400$	17.1239	0.856197
$401$	−3.51309	−0.175435	−0.0877177	−	0.996145i	$-0.527957\pi$
$401$	−3.51309	−0.175435	−0.0877177	+	0.996145i	$0.527957\pi$
$402$	2.96306	0.147784
$403$	0	0
$404$	−0.750994	−0.0373633
$405$	6.63486	0.329689
$406$	5.54154	0.275022
$407$	−10.0577	−0.498539
$408$	3.76564	0.186427
$409$	34.1687	1.68953	0.844766	−	0.535136i	$-0.179740\pi$
$409$	34.1687	1.68953	0.844766	+	0.535136i	$0.179740\pi$
$410$	−4.78173	−0.236153
$411$	3.00232	0.148093
$412$	−25.6358	−1.26299
$413$	−2.81605	−0.138569
$414$	−4.26899	−0.209809
$415$	−43.3734	−2.12912
$416$	0	0
$417$	−10.4060	−0.509583
$418$	2.12353	0.103865
$419$	19.2903	0.942391	0.471196	−	0.882029i	$-0.343823\pi$
$419$	19.2903	0.942391	0.471196	+	0.882029i	$0.343823\pi$
$420$	−29.5401	−1.44141
$421$	−19.0828	−0.930038	−0.465019	−	0.885301i	$-0.653952\pi$
$421$	−19.0828	−0.930038	−0.465019	+	0.885301i	$0.653952\pi$
$422$	−7.84343	−0.381812
$423$	−7.27437	−0.353692
$424$	6.85799	0.333053
$425$	−12.1120	−0.587519
$426$	0.962344	0.0466257
$427$	41.9238	2.02883
$428$	−14.6074	−0.706074
$429$	0	0
$430$	10.3997	0.501517
$431$	−1.54727	−0.0745295	−0.0372647	−	0.999305i	$-0.511864\pi$
$431$	−1.54727	−0.0745295	−0.0372647	+	0.999305i	$0.511864\pi$
$432$	18.2264	0.876918
$433$	7.28913	0.350293	0.175147	−	0.984542i	$-0.443960\pi$
$433$	7.28913	0.350293	0.175147	+	0.984542i	$0.443960\pi$
$434$	−0.998983	−0.0479527
$435$	−15.5251	−0.744371
$436$	−17.5384	−0.839935
$437$	51.1656	2.44758
$438$	−1.00836	−0.0481815
$439$	14.1267	0.674229	0.337114	−	0.941464i	$-0.390549\pi$
$439$	14.1267	0.674229	0.337114	+	0.941464i	$0.390549\pi$
$440$	−4.21605	−0.200992
$441$	−14.4165	−0.686502
$442$	0	0
$443$	−13.3152	−0.632624	−0.316312	−	0.948655i	$-0.602445\pi$
$443$	−13.3152	−0.632624	−0.316312	+	0.948655i	$0.602445\pi$
$444$	−22.9904	−1.09108
$445$	48.8679	2.31656
$446$	−2.99948	−0.142030
$447$	22.1256	1.04651
$448$	−21.6889	−1.02470
$449$	−3.03021	−0.143004	−0.0715022	−	0.997440i	$-0.522779\pi$
$449$	−3.03021	−0.143004	−0.0715022	+	0.997440i	$0.522779\pi$
$450$	2.68550	0.126596
$451$	−4.40518	−0.207432
$452$	16.5029	0.776231
$453$	20.1108	0.944889
$454$	−7.02040	−0.329484
$455$	0	0
$456$	10.0069	0.468618
$457$	−23.8096	−1.11376	−0.556882	−	0.830592i	$-0.688002\pi$
$457$	−23.8096	−1.11376	−0.556882	+	0.830592i	$0.688002\pi$
$458$	−2.34602	−0.109622
$459$	−12.8918	−0.601737
$460$	−49.2756	−2.29749
$461$	−15.5141	−0.722565	−0.361283	−	0.932456i	$-0.617661\pi$
$461$	−15.5141	−0.722565	−0.361283	+	0.932456i	$0.617661\pi$
$462$	1.67490	0.0779236
$463$	−18.3059	−0.850748	−0.425374	−	0.905018i	$-0.639857\pi$
$463$	−18.3059	−0.850748	−0.425374	+	0.905018i	$0.639857\pi$
$464$	−13.3180	−0.618271
$465$	2.79873	0.129788
$466$	−3.46793	−0.160649
$467$	27.5553	1.27511	0.637553	−	0.770407i	$-0.279947\pi$
$467$	27.5553	1.27511	0.637553	+	0.770407i	$0.279947\pi$
$468$	0	0
$469$	29.0753	1.34257
$470$	5.16776	0.238371
$471$	3.89411	0.179431
$472$	−0.918720	−0.0422875
$473$	9.58073	0.440522
$474$	−1.07238	−0.0492563
$475$	−32.1868	−1.47683
$476$	17.9237	0.821533
$477$	−7.92286	−0.362763
$478$	6.39990	0.292725
$479$	−8.86209	−0.404919	−0.202460	−	0.979291i	$-0.564893\pi$
$479$	−8.86209	−0.404919	−0.202460	+	0.979291i	$0.564893\pi$
$480$	−14.5998	−0.666387
$481$	0	0
$482$	−0.420368	−0.0191473
$483$	40.3561	1.83627
$484$	−1.88404	−0.0856384
$485$	40.6064	1.84384
$486$	4.75222	0.215565
$487$	−1.95588	−0.0886296	−0.0443148	−	0.999018i	$-0.514110\pi$
$487$	−1.95588	−0.0886296	−0.0443148	+	0.999018i	$0.514110\pi$
$488$	13.6774	0.619147
$489$	−14.4034	−0.651344
$490$	10.2416	0.462669
$491$	−41.7444	−1.88390	−0.941949	−	0.335755i	$-0.891008\pi$
$491$	−41.7444	−1.88390	−0.941949	+	0.335755i	$0.891008\pi$
$492$	−10.0696	−0.453974
$493$	9.41999	0.424255
$494$	0	0
$495$	4.87069	0.218921
$496$	2.40085	0.107801
$497$	9.44306	0.423579
$498$	5.62149	0.251905
$499$	−27.7777	−1.24350	−0.621749	−	0.783216i	$-0.713578\pi$
$499$	−27.7777	−1.24350	−0.621749	+	0.783216i	$0.713578\pi$
$500$	0.969151	0.0433418
$501$	−14.7938	−0.660938
$502$	8.35366	0.372842
$503$	24.6062	1.09714	0.548569	−	0.836106i	$-0.315173\pi$
$503$	24.6062	1.09714	0.548569	+	0.836106i	$0.315173\pi$
$504$	−8.19276	−0.364935
$505$	−1.27064	−0.0565426
$506$	2.79390	0.124204
$507$	0	0
$508$	−31.7225	−1.40746
$509$	−40.3334	−1.78775	−0.893874	−	0.448318i	$-0.852023\pi$
$509$	−40.3334	−1.78775	−0.893874	+	0.448318i	$0.852023\pi$
$510$	3.09052	0.136850
$511$	−9.89463	−0.437713
$512$	−21.3003	−0.941348
$513$	−34.2590	−1.51257
$514$	4.37650	0.193039
$515$	−43.3743	−1.91130
$516$	21.9002	0.964103
$517$	4.76081	0.209380
$518$	13.8844	0.610047
$519$	1.20773	0.0530137
$520$	0	0
$521$	16.8953	0.740198	0.370099	−	0.928992i	$-0.379324\pi$
$521$	16.8953	0.740198	0.370099	+	0.928992i	$0.379324\pi$
$522$	−2.08862	−0.0914164
$523$	4.22744	0.184853	0.0924265	−	0.995720i	$-0.470538\pi$
$523$	4.22744	0.184853	0.0924265	+	0.995720i	$0.470538\pi$
$524$	−27.4634	−1.19975
$525$	−25.3869	−1.10798
$526$	−2.45431	−0.107013
$527$	−1.69816	−0.0739728
$528$	−4.02529	−0.175178
$529$	44.3177	1.92686
$530$	5.62845	0.244484
$531$	1.06137	0.0460597
$532$	47.6311	2.06507
$533$	0	0
$534$	−6.33361	−0.274082
$535$	−24.7148	−1.06851
$536$	9.48564	0.409717
$537$	16.7869	0.724408
$538$	−4.40985	−0.190122
$539$	9.43510	0.406399
$540$	32.9936	1.41982
$541$	−34.1415	−1.46786	−0.733929	−	0.679227i	$-0.762315\pi$
$541$	−34.1415	−1.46786	−0.733929	+	0.679227i	$0.762315\pi$
$542$	2.06248	0.0885912
$543$	−23.8208	−1.02225
$544$	8.85857	0.379808
$545$	−29.6738	−1.27109
$546$	0	0
$547$	−26.3451	−1.12644	−0.563218	−	0.826309i	$-0.690437\pi$
$547$	−26.3451	−1.12644	−0.563218	+	0.826309i	$0.690437\pi$
$548$	4.66218	0.199159
$549$	−15.8012	−0.674377
$550$	−1.75756	−0.0749427
$551$	25.0330	1.06644
$552$	13.1660	0.560381
$553$	−10.5228	−0.447477
$554$	−8.97234	−0.381198
$555$	−38.8983	−1.65114
$556$	−16.1591	−0.685297
$557$	−30.8796	−1.30841	−0.654205	−	0.756317i	$-0.726997\pi$
$557$	−30.8796	−1.30841	−0.654205	+	0.756317i	$0.726997\pi$
$558$	0.376519	0.0159393
$559$	0	0
$560$	−42.8747	−1.81179
$561$	2.84714	0.120207
$562$	−4.87401	−0.205598
$563$	2.54576	0.107291	0.0536456	−	0.998560i	$-0.482916\pi$
$563$	2.54576	0.107291	0.0536456	+	0.998560i	$0.482916\pi$
$564$	10.8825	0.458237
$565$	27.9219	1.17468
$566$	4.57155	0.192156
$567$	−8.43805	−0.354365
$568$	3.08075	0.129265
$569$	45.7155	1.91649	0.958247	−	0.285942i	$-0.0923063\pi$
$569$	45.7155	1.91649	0.958247	+	0.285942i	$0.0923063\pi$
$570$	8.21283	0.343998
$571$	33.6349	1.40758	0.703788	−	0.710410i	$-0.251491\pi$
$571$	33.6349	1.40758	0.703788	+	0.710410i	$0.251491\pi$
$572$	0	0
$573$	−12.1119	−0.505982
$574$	6.08129	0.253828
$575$	−42.3477	−1.76602
$576$	8.17459	0.340608
$577$	6.91915	0.288048	0.144024	−	0.989574i	$-0.453996\pi$
$577$	6.91915	0.288048	0.144024	+	0.989574i	$0.453996\pi$
$578$	3.91368	0.162787
$579$	3.58109	0.148825
$580$	−24.1083	−1.00104
$581$	55.1612	2.28847
$582$	−5.26287	−0.218153
$583$	5.18522	0.214750
$584$	−3.22807	−0.133578
$585$	0	0
$586$	−6.54184	−0.270241
$587$	−7.84590	−0.323835	−0.161917	−	0.986804i	$-0.551768\pi$
$587$	−7.84590	−0.323835	−0.161917	+	0.986804i	$0.551768\pi$
$588$	21.5673	0.889421
$589$	−4.51273	−0.185944
$590$	−0.754007	−0.0310420
$591$	2.37942	0.0978764
$592$	−33.3684	−1.37143
$593$	−20.0657	−0.823999	−0.411999	−	0.911184i	$-0.635169\pi$
$593$	−20.0657	−0.823999	−0.411999	+	0.911184i	$0.635169\pi$
$594$	−1.87071	−0.0767563
$595$	30.3259	1.24324
$596$	34.3580	1.40736
$597$	10.3643	0.424181
$598$	0	0
$599$	−27.3966	−1.11940	−0.559698	−	0.828697i	$-0.689083\pi$
$599$	−27.3966	−1.11940	−0.559698	+	0.828697i	$0.689083\pi$
$600$	−8.28234	−0.338125
$601$	22.6514	0.923970	0.461985	−	0.886888i	$-0.347137\pi$
$601$	22.6514	0.923970	0.461985	+	0.886888i	$0.347137\pi$
$602$	−13.2261	−0.539054
$603$	−10.9585	−0.446265
$604$	31.2293	1.27070
$605$	−3.18769	−0.129598
$606$	0.164683	0.00668979
$607$	−11.6319	−0.472124	−0.236062	−	0.971738i	$-0.575857\pi$
$607$	−11.6319	−0.472124	−0.236062	+	0.971738i	$0.575857\pi$
$608$	23.5410	0.954715
$609$	19.7444	0.800083
$610$	11.2252	0.454497
$611$	0	0
$612$	−6.75549	−0.273075
$613$	−27.6162	−1.11541	−0.557704	−	0.830040i	$-0.688318\pi$
$613$	−27.6162	−1.11541	−0.557704	+	0.830040i	$0.688318\pi$
$614$	−5.85394	−0.236246
$615$	−17.0372	−0.687006
$616$	5.36186	0.216036
$617$	−13.4667	−0.542150	−0.271075	−	0.962558i	$-0.587379\pi$
$617$	−13.4667	−0.542150	−0.271075	+	0.962558i	$0.587379\pi$
$618$	5.62160	0.226134
$619$	1.79201	0.0720271	0.0360136	−	0.999351i	$-0.488534\pi$
$619$	1.79201	0.0720271	0.0360136	+	0.999351i	$0.488534\pi$
$620$	4.34604	0.174541
$621$	−45.0741	−1.80876
$622$	4.56970	0.183228
$623$	−62.1489	−2.48994
$624$	0	0
$625$	−24.1671	−0.966684
$626$	4.45017	0.177865
$627$	7.56609	0.302160
$628$	6.04702	0.241302
$629$	23.6019	0.941071
$630$	−6.72392	−0.267887
$631$	−34.8888	−1.38890	−0.694451	−	0.719540i	$-0.744353\pi$
$631$	−34.8888	−1.38890	−0.694451	+	0.719540i	$0.744353\pi$
$632$	−3.43302	−0.136558
$633$	−27.9460	−1.11075
$634$	−3.84940	−0.152879
$635$	−53.6725	−2.12993
$636$	11.8527	0.469990
$637$	0	0
$638$	1.36692	0.0541171
$639$	−3.55911	−0.140796
$640$	−29.8741	−1.18088
$641$	3.84384	0.151823	0.0759114	−	0.997115i	$-0.475813\pi$
$641$	3.84384	0.151823	0.0759114	+	0.997115i	$0.475813\pi$
$642$	3.20321	0.126420
$643$	−7.25080	−0.285944	−0.142972	−	0.989727i	$-0.545666\pi$
$643$	−7.25080	−0.285944	−0.142972	+	0.989727i	$0.545666\pi$
$644$	62.6675	2.46944
$645$	37.0538	1.45899
$646$	−4.98321	−0.196062
$647$	27.5012	1.08118	0.540592	−	0.841285i	$-0.318200\pi$
$647$	27.5012	1.08118	0.540592	+	0.841285i	$0.318200\pi$
$648$	−2.75287	−0.108143
$649$	−0.694630	−0.0272666
$650$	0	0
$651$	−3.55935	−0.139502
$652$	−22.3665	−0.875940
$653$	9.21600	0.360650	0.180325	−	0.983607i	$-0.442285\pi$
$653$	9.21600	0.360650	0.180325	+	0.983607i	$0.442285\pi$
$654$	3.84593	0.150388
$655$	−46.4665	−1.81559
$656$	−14.6151	−0.570625
$657$	3.72931	0.145494
$658$	−6.57222	−0.256212
$659$	−29.7952	−1.16066	−0.580328	−	0.814383i	$-0.697075\pi$
$659$	−29.7952	−1.16066	−0.580328	+	0.814383i	$0.697075\pi$
$660$	−7.28661	−0.283631
$661$	15.5749	0.605793	0.302896	−	0.953024i	$-0.402046\pi$
$661$	15.5749	0.605793	0.302896	+	0.953024i	$0.402046\pi$
$662$	−1.76404	−0.0685614
$663$	0	0
$664$	17.9961	0.698382
$665$	80.5889	3.12510
$666$	−5.23307	−0.202777
$667$	32.9355	1.27527
$668$	−22.9727	−0.888841
$669$	−10.6871	−0.413187
$670$	7.78500	0.300761
$671$	10.3413	0.399221
$672$	18.5677	0.716263
$673$	0.147971	0.00570386	0.00285193	−	0.999996i	$-0.499092\pi$
$673$	0.147971	0.00570386	0.00285193	+	0.999996i	$0.499092\pi$
$674$	2.52655	0.0973192
$675$	28.3548	1.09138
$676$	0	0
$677$	−13.5263	−0.519857	−0.259928	−	0.965628i	$-0.583699\pi$
$677$	−13.5263	−0.519857	−0.259928	+	0.965628i	$0.583699\pi$
$678$	−3.61887	−0.138982
$679$	−51.6422	−1.98185
$680$	9.89366	0.379404
$681$	−25.0135	−0.958520
$682$	−0.246418	−0.00943582
$683$	−28.2401	−1.08058	−0.540289	−	0.841480i	$-0.681685\pi$
$683$	−28.2401	−1.08058	−0.540289	+	0.841480i	$0.681685\pi$
$684$	−17.9523	−0.686422
$685$	7.88813	0.301390
$686$	−3.36162	−0.128347
$687$	−8.35881	−0.318909
$688$	31.7861	1.21183
$689$	0	0
$690$	10.8055	0.411358
$691$	4.75615	0.180932	0.0904662	−	0.995900i	$-0.471164\pi$
$691$	4.75615	0.180932	0.0904662	+	0.995900i	$0.471164\pi$
$692$	1.87545	0.0712937
$693$	−6.19442	−0.235307
$694$	−8.12875	−0.308563
$695$	−27.3402	−1.03707
$696$	6.44150	0.244165
$697$	10.3375	0.391560
$698$	−7.74344	−0.293094
$699$	−12.3562	−0.467353
$700$	−39.4223	−1.49002
$701$	13.5172	0.510536	0.255268	−	0.966870i	$-0.417836\pi$
$701$	13.5172	0.510536	0.255268	+	0.966870i	$0.417836\pi$
$702$	0	0
$703$	62.7205	2.36555
$704$	−5.34997	−0.201635
$705$	18.4126	0.693458
$706$	−6.72171	−0.252975
$707$	1.61596	0.0607745
$708$	−1.58783	−0.0596742
$709$	37.1430	1.39493	0.697466	−	0.716617i	$-0.254311\pi$
$709$	37.1430	1.39493	0.697466	+	0.716617i	$0.254311\pi$
$710$	2.52841	0.0948896
$711$	3.96608	0.148740
$712$	−20.2758	−0.759866
$713$	−5.93733	−0.222355
$714$	−3.93044	−0.147093
$715$	0	0
$716$	26.0677	0.974196
$717$	22.8027	0.851583
$718$	−3.65377	−0.136357
$719$	−33.2422	−1.23973	−0.619863	−	0.784710i	$-0.712812\pi$
$719$	−33.2422	−1.23973	−0.619863	+	0.784710i	$0.712812\pi$
$720$	16.1596	0.602232
$721$	55.1623	2.05435
$722$	−6.77262	−0.252051
$723$	−1.49776	−0.0557024
$724$	−36.9904	−1.37474
$725$	−20.7188	−0.769476
$726$	0.413146	0.0153333
$727$	−23.9978	−0.890029	−0.445015	−	0.895523i	$-0.646802\pi$
$727$	−23.9978	−0.890029	−0.445015	+	0.895523i	$0.646802\pi$
$728$	0	0
$729$	23.1762	0.858379
$730$	−2.64932	−0.0980558
$731$	−22.4828	−0.831555
$732$	23.6387	0.873712
$733$	46.2211	1.70721	0.853607	−	0.520918i	$-0.174410\pi$
$733$	46.2211	1.70721	0.853607	+	0.520918i	$0.174410\pi$
$734$	−1.48688	−0.0548818
$735$	36.4906	1.34598
$736$	30.9726	1.14166
$737$	7.17195	0.264182
$738$	−2.29205	−0.0843715
$739$	38.6098	1.42028	0.710142	−	0.704058i	$-0.248631\pi$
$739$	38.6098	1.42028	0.710142	+	0.704058i	$0.248631\pi$
$740$	−60.4037	−2.22049
$741$	0	0
$742$	−7.15812	−0.262783
$743$	−4.54400	−0.166703	−0.0833517	−	0.996520i	$-0.526562\pi$
$743$	−4.54400	−0.166703	−0.0833517	+	0.996520i	$0.526562\pi$
$744$	−1.16122	−0.0425724
$745$	58.1317	2.12978
$746$	−0.559772	−0.0204947
$747$	−20.7904	−0.760680
$748$	4.42122	0.161656
$749$	31.4317	1.14849
$750$	−0.212522	−0.00776021
$751$	15.0106	0.547744	0.273872	−	0.961766i	$-0.411696\pi$
$751$	15.0106	0.547744	0.273872	+	0.961766i	$0.411696\pi$
$752$	15.7950	0.575984
$753$	29.7639	1.08466
$754$	0	0
$755$	52.8381	1.92298
$756$	−41.9604	−1.52608
$757$	−24.8517	−0.903251	−0.451625	−	0.892208i	$-0.649156\pi$
$757$	−24.8517	−0.903251	−0.451625	+	0.892208i	$0.649156\pi$
$758$	−9.31730	−0.338420
$759$	9.95459	0.361329
$760$	26.2917	0.953700
$761$	34.4446	1.24862	0.624308	−	0.781178i	$-0.285381\pi$
$761$	34.4446	1.24862	0.624308	+	0.781178i	$0.285381\pi$
$762$	6.95632	0.252001
$763$	37.7384	1.36622
$764$	−18.8081	−0.680453
$765$	−11.4299	−0.413248
$766$	−2.94692	−0.106477
$767$	0	0
$768$	−9.11006	−0.328731
$769$	−1.69417	−0.0610935	−0.0305467	−	0.999533i	$-0.509725\pi$
$769$	−1.69417	−0.0610935	−0.0305467	+	0.999533i	$0.509725\pi$
$770$	4.40056	0.158585
$771$	15.5934	0.561582
$772$	5.56094	0.200143
$773$	−3.09763	−0.111414	−0.0557071	−	0.998447i	$-0.517741\pi$
$773$	−3.09763	−0.111414	−0.0557071	+	0.998447i	$0.517741\pi$
$774$	4.98493	0.179179
$775$	3.73501	0.134165
$776$	−16.8480	−0.604808
$777$	49.4699	1.77472
$778$	1.33298	0.0477896
$779$	27.4712	0.984256
$780$	0	0
$781$	2.32931	0.0833491
$782$	−6.55634	−0.234454
$783$	−22.0527	−0.788098
$784$	31.3030	1.11796
$785$	10.2312	0.365167
$786$	6.02237	0.214811
$787$	1.37743	0.0491000	0.0245500	−	0.999699i	$-0.492185\pi$
$787$	1.37743	0.0491000	0.0245500	+	0.999699i	$0.492185\pi$
$788$	3.69492	0.131626
$789$	−8.74463	−0.311317
$790$	−2.81753	−0.100243
$791$	−35.5104	−1.26260
$792$	−2.02090	−0.0718095
$793$	0	0
$794$	11.2411	0.398932
$795$	20.0540	0.711243
$796$	16.0943	0.570446
$797$	−50.0186	−1.77175	−0.885875	−	0.463925i	$-0.846441\pi$
$797$	−50.0186	−1.77175	−0.885875	+	0.463925i	$0.846441\pi$
$798$	−10.4449	−0.369744
$799$	−11.1720	−0.395238
$800$	−19.4840	−0.688863
$801$	23.4241	0.827648
$802$	1.19629	0.0422423
$803$	−2.44069	−0.0861302
$804$	16.3941	0.578174
$805$	106.030	3.73705
$806$	0	0
$807$	−15.7122	−0.553096
$808$	0.527199	0.0185468
$809$	20.9847	0.737784	0.368892	−	0.929472i	$-0.379737\pi$
$809$	20.9847	0.737784	0.368892	+	0.929472i	$0.379737\pi$
$810$	−2.25932	−0.0793843
$811$	−36.4314	−1.27928	−0.639641	−	0.768674i	$-0.720917\pi$
$811$	−36.4314	−1.27928	−0.639641	+	0.768674i	$0.720917\pi$
$812$	30.6603	1.07597
$813$	7.34858	0.257726
$814$	3.42485	0.120041
$815$	−37.8428	−1.32557
$816$	9.44601	0.330677
$817$	−59.7464	−2.09026
$818$	−11.6352	−0.406815
$819$	0	0
$820$	−26.4564	−0.923898
$821$	−18.3895	−0.641799	−0.320899	−	0.947113i	$-0.603985\pi$
$821$	−18.3895	−0.641799	−0.320899	+	0.947113i	$0.603985\pi$
$822$	−1.02235	−0.0356587
$823$	30.3408	1.05761	0.528807	−	0.848742i	$-0.322640\pi$
$823$	30.3408	1.05761	0.528807	+	0.848742i	$0.322640\pi$
$824$	17.9964	0.626935
$825$	−6.26215	−0.218020
$826$	0.958926	0.0333653
$827$	−3.11611	−0.108358	−0.0541788	−	0.998531i	$-0.517254\pi$
$827$	−3.11611	−0.108358	−0.0541788	+	0.998531i	$0.517254\pi$
$828$	−23.6195	−0.820834
$829$	23.6630	0.821850	0.410925	−	0.911669i	$-0.365206\pi$
$829$	23.6630	0.821850	0.410925	+	0.911669i	$0.365206\pi$
$830$	14.7696	0.512661
$831$	−31.9682	−1.10897
$832$	0	0
$833$	−22.1410	−0.767141
$834$	3.54347	0.122700
$835$	−38.8684	−1.34510
$836$	11.7491	0.406351
$837$	3.97547	0.137412
$838$	−6.56876	−0.226914
$839$	−1.11574	−0.0385195	−0.0192598	−	0.999815i	$-0.506131\pi$
$839$	−1.11574	−0.0385195	−0.0192598	+	0.999815i	$0.506131\pi$
$840$	20.7372	0.715502
$841$	−12.8862	−0.444351
$842$	6.49811	0.223940
$843$	−17.3660	−0.598116
$844$	−43.3962	−1.49376
$845$	0	0
$846$	2.47708	0.0851639
$847$	4.05402	0.139298
$848$	17.2031	0.590756
$849$	16.2883	0.559014
$850$	4.12441	0.141466
$851$	82.5204	2.82876
$852$	5.32447	0.182413
$853$	31.0297	1.06244	0.531219	−	0.847235i	$-0.321734\pi$
$853$	31.0297	1.06244	0.531219	+	0.847235i	$0.321734\pi$
$854$	−14.2760	−0.488514
$855$	−30.3741	−1.03877
$856$	10.2544	0.350489
$857$	42.0441	1.43620	0.718099	−	0.695941i	$-0.245012\pi$
$857$	42.0441	1.43620	0.718099	+	0.695941i	$0.245012\pi$
$858$	0	0
$859$	44.7236	1.52595	0.762975	−	0.646428i	$-0.223738\pi$
$859$	44.7236	1.52595	0.762975	+	0.646428i	$0.223738\pi$
$860$	57.5395	1.96208
$861$	21.6675	0.738426
$862$	0.526880	0.0179456
$863$	41.5738	1.41519	0.707594	−	0.706619i	$-0.249781\pi$
$863$	41.5738	1.41519	0.707594	+	0.706619i	$0.249781\pi$
$864$	−20.7384	−0.705533
$865$	3.17314	0.107890
$866$	−2.48211	−0.0843456
$867$	13.9443	0.473575
$868$	−5.52718	−0.187605
$869$	−2.59565	−0.0880516
$870$	5.28663	0.179234
$871$	0	0
$872$	12.3120	0.416936
$873$	19.4641	0.658759
$874$	−17.4230	−0.589342
$875$	−2.08539	−0.0704989
$876$	−5.57908	−0.188500
$877$	−2.69580	−0.0910306	−0.0455153	−	0.998964i	$-0.514493\pi$
$877$	−2.69580	−0.0910306	−0.0455153	+	0.998964i	$0.514493\pi$
$878$	−4.81044	−0.162345
$879$	−23.3084	−0.786174
$880$	−10.5758	−0.356512
$881$	45.7371	1.54092	0.770461	−	0.637487i	$-0.220026\pi$
$881$	45.7371	1.54092	0.770461	+	0.637487i	$0.220026\pi$
$882$	4.90915	0.165300
$883$	−43.7239	−1.47143	−0.735713	−	0.677293i	$-0.763153\pi$
$883$	−43.7239	−1.47143	−0.735713	+	0.677293i	$0.763153\pi$
$884$	0	0
$885$	−2.68651	−0.0903060
$886$	4.53412	0.152327
$887$	−13.1632	−0.441977	−0.220989	−	0.975276i	$-0.570928\pi$
$887$	−13.1632	−0.441977	−0.220989	+	0.975276i	$0.570928\pi$
$888$	16.1393	0.541599
$889$	68.2593	2.28934
$890$	−16.6406	−0.557794
$891$	−2.08140	−0.0697295
$892$	−16.5956	−0.555661
$893$	−29.6889	−0.993500
$894$	−7.53427	−0.251984
$895$	44.1050	1.47427
$896$	37.9931	1.26926
$897$	0	0
$898$	1.03185	0.0344334
$899$	−2.90486	−0.0968826
$900$	14.8584	0.495279
$901$	−12.1680	−0.405374
$902$	1.50006	0.0499466
$903$	−47.1241	−1.56819
$904$	−11.5851	−0.385314
$905$	−62.5855	−2.08041
$906$	−6.84818	−0.227516
$907$	−31.6975	−1.05250	−0.526250	−	0.850330i	$-0.676402\pi$
$907$	−31.6975	−1.05250	−0.526250	+	0.850330i	$0.676402\pi$
$908$	−38.8425	−1.28903
$909$	−0.609060	−0.0202012
$910$	0	0
$911$	23.6450	0.783393	0.391696	−	0.920094i	$-0.371888\pi$
$911$	23.6450	0.783393	0.391696	+	0.920094i	$0.371888\pi$
$912$	25.1021	0.831214
$913$	13.6065	0.450311
$914$	8.10768	0.268178
$915$	39.9953	1.32220
$916$	−12.9801	−0.428874
$917$	59.0949	1.95148
$918$	4.38994	0.144890
$919$	27.0043	0.890788	0.445394	−	0.895335i	$-0.353064\pi$
$919$	27.0043	0.890788	0.445394	+	0.895335i	$0.353064\pi$
$920$	34.5916	1.14045
$921$	−20.8574	−0.687276
$922$	5.28290	0.173983
$923$	0	0
$924$	9.26693	0.304860
$925$	−51.9113	−1.70683
$926$	6.23357	0.204848
$927$	−20.7908	−0.682859
$928$	15.1535	0.497437
$929$	30.8019	1.01058	0.505288	−	0.862951i	$-0.331386\pi$
$929$	30.8019	1.01058	0.505288	+	0.862951i	$0.331386\pi$
$930$	−0.953029	−0.0312511
$931$	−58.8382	−1.92835
$932$	−19.1874	−0.628505
$933$	16.2817	0.533040
$934$	−9.38318	−0.307027
$935$	7.48044	0.244637
$936$	0	0
$937$	51.5301	1.68342	0.841708	−	0.539933i	$-0.181550\pi$
$937$	51.5301	1.68342	0.841708	+	0.539933i	$0.181550\pi$
$938$	−9.90077	−0.323272
$939$	15.8559	0.517436
$940$	28.5922	0.932575
$941$	−43.8944	−1.43092	−0.715459	−	0.698655i	$-0.753782\pi$
$941$	−43.8944	−1.43092	−0.715459	+	0.698655i	$0.753782\pi$
$942$	−1.32603	−0.0432044
$943$	36.1434	1.17699
$944$	−2.30458	−0.0750078
$945$	−70.9944	−2.30945
$946$	−3.26245	−0.106071
$947$	−0.525148	−0.0170650	−0.00853251	−	0.999964i	$-0.502716\pi$
$947$	−0.525148	−0.0170650	−0.00853251	+	0.999964i	$0.502716\pi$
$948$	−5.93330	−0.192705
$949$	0	0
$950$	10.9603	0.355600
$951$	−13.7153	−0.444749
$952$	−12.5825	−0.407801
$953$	−6.98333	−0.226212	−0.113106	−	0.993583i	$-0.536080\pi$
$953$	−6.98333	−0.226212	−0.113106	+	0.993583i	$0.536080\pi$
$954$	2.69791	0.0873480
$955$	−31.8222	−1.02974
$956$	35.4095	1.14522
$957$	4.87032	0.157435
$958$	3.01774	0.0974987
$959$	−10.0319	−0.323948
$960$	−20.6912	−0.667806
$961$	−30.4763	−0.983108
$962$	0	0
$963$	−11.8467	−0.381753
$964$	−2.32582	−0.0749096
$965$	9.40878	0.302879
$966$	−13.7422	−0.442146
$967$	−12.2724	−0.394652	−0.197326	−	0.980338i	$-0.563226\pi$
$967$	−12.2724	−0.394652	−0.197326	+	0.980338i	$0.563226\pi$
$968$	1.32260	0.0425101
$969$	−17.7551	−0.570375
$970$	−13.8274	−0.443971
$971$	39.1865	1.25755	0.628777	−	0.777586i	$-0.283556\pi$
$971$	39.1865	1.25755	0.628777	+	0.777586i	$0.283556\pi$
$972$	26.2931	0.843352
$973$	34.7705	1.11469
$974$	0.666022	0.0213407
$975$	0	0
$976$	34.3094	1.09822
$977$	−32.7362	−1.04733	−0.523663	−	0.851926i	$-0.675435\pi$
$977$	−32.7362	−1.04733	−0.523663	+	0.851926i	$0.675435\pi$
$978$	4.90468	0.156834
$979$	−15.3302	−0.489955
$980$	56.6649	1.81009
$981$	−14.2237	−0.454127
$982$	14.2149	0.453615
$983$	−47.8968	−1.52767	−0.763836	−	0.645411i	$-0.776686\pi$
$983$	−47.8968	−1.52767	−0.763836	+	0.645411i	$0.776686\pi$
$984$	7.06890	0.225348
$985$	6.25158	0.199192
$986$	−3.20771	−0.102154
$987$	−23.4167	−0.745361
$988$	0	0
$989$	−78.6074	−2.49957
$990$	−1.65858	−0.0527131
$991$	39.8530	1.26597	0.632986	−	0.774163i	$-0.281829\pi$
$991$	39.8530	1.26597	0.632986	+	0.774163i	$0.281829\pi$
$992$	−2.73174	−0.0867327
$993$	−6.28523	−0.199456
$994$	−3.21557	−0.101992
$995$	27.2305	0.863266
$996$	31.1026	0.985525
$997$	35.4976	1.12422	0.562110	−	0.827062i	$-0.309990\pi$
$997$	35.4976	1.12422	0.562110	+	0.827062i	$0.309990\pi$
$998$	9.45891	0.299416
$999$	−55.2533	−1.74814

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.2.a.t.1.11	yes	21
13.12	even	2		1859.2.a.s.1.11	✓	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1859.2.a.s.1.11	✓	21	13.12	even	2
1859.2.a.t.1.11	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)

\(f(q)\)	\(=\)	\(q-0.340522 q^{2} -1.21327 q^{3} -1.88404 q^{4} -3.18769 q^{5} +0.413146 q^{6} +4.05402 q^{7} +1.32260 q^{8} -1.52797 q^{9} +O(q^{10})\)	\(q-0.340522 q^{2} -1.21327 q^{3} -1.88404 q^{4} -3.18769 q^{5} +0.413146 q^{6} +4.05402 q^{7} +1.32260 q^{8} -1.52797 q^{9} +1.08548 q^{10} +1.00000 q^{11} +2.28586 q^{12} -1.38048 q^{14} +3.86754 q^{15} +3.31771 q^{16} -2.34667 q^{17} +0.520307 q^{18} -6.23610 q^{19} +6.00575 q^{20} -4.91864 q^{21} -0.340522 q^{22} -8.20474 q^{23} -1.60468 q^{24} +5.16137 q^{25} +5.49366 q^{27} -7.63796 q^{28} -4.01420 q^{29} -1.31698 q^{30} +0.723646 q^{31} -3.77496 q^{32} -1.21327 q^{33} +0.799091 q^{34} -12.9230 q^{35} +2.87876 q^{36} -10.0577 q^{37} +2.12353 q^{38} -4.21605 q^{40} -4.40518 q^{41} +1.67490 q^{42} +9.58073 q^{43} -1.88404 q^{44} +4.87069 q^{45} +2.79390 q^{46} +4.76081 q^{47} -4.02529 q^{48} +9.43510 q^{49} -1.75756 q^{50} +2.84714 q^{51} +5.18522 q^{53} -1.87071 q^{54} -3.18769 q^{55} +5.36186 q^{56} +7.56609 q^{57} +1.36692 q^{58} -0.694630 q^{59} -7.28661 q^{60} +10.3413 q^{61} -0.246418 q^{62} -6.19442 q^{63} -5.34997 q^{64} +0.413146 q^{66} +7.17195 q^{67} +4.42122 q^{68} +9.95459 q^{69} +4.40056 q^{70} +2.32931 q^{71} -2.02090 q^{72} -2.44069 q^{73} +3.42485 q^{74} -6.26215 q^{75} +11.7491 q^{76} +4.05402 q^{77} -2.59565 q^{79} -10.5758 q^{80} -2.08140 q^{81} +1.50006 q^{82} +13.6065 q^{83} +9.26693 q^{84} +7.48044 q^{85} -3.26245 q^{86} +4.87032 q^{87} +1.32260 q^{88} -15.3302 q^{89} -1.65858 q^{90} +15.4581 q^{92} -0.877980 q^{93} -1.62116 q^{94} +19.8788 q^{95} +4.58006 q^{96} -12.7385 q^{97} -3.21286 q^{98} -1.52797 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 6 q^{3} + 32 q^{4} + 7 q^{5} - 19 q^{6} + q^{7} - 3 q^{8} + 33 q^{9}+O(q^{10}) \) 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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