LMFDB - Embedded newform 4235.2.a.ba.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4235,2,Mod(1,4235)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4235, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("4235.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4235 = 5 \cdot 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4235.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:	$33.8166452560$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.580017.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 7x^{3} - 4x^{2} + 6x + 3 $ x^5 - 7x^3 - 4x^2 + 6*x + 3
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.93511$ of defining polynomial
Character	$\chi$	$=$	4235.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.93511 q^{2} -2.61037 q^{3} +1.74465 q^{4} -1.00000 q^{5} +5.05136 q^{6} -1.00000 q^{7} +0.494123 q^{8} +3.81405 q^{9} +O(q^{10})$	\(q-1.93511 q^{2} -2.61037 q^{3} +1.74465 q^{4} -1.00000 q^{5} +5.05136 q^{6} -1.00000 q^{7} +0.494123 q^{8} +3.81405 q^{9} +1.93511 q^{10} -4.55420 q^{12} -2.11625 q^{13} +1.93511 q^{14} +2.61037 q^{15} -4.44549 q^{16} +5.18564 q^{17} -7.38060 q^{18} -5.34181 q^{19} -1.74465 q^{20} +2.61037 q^{21} +5.31060 q^{23} -1.28985 q^{24} +1.00000 q^{25} +4.09518 q^{26} -2.12496 q^{27} -1.74465 q^{28} +2.45420 q^{29} -5.05136 q^{30} -6.26825 q^{31} +7.61427 q^{32} -10.0348 q^{34} +1.00000 q^{35} +6.65419 q^{36} +6.82305 q^{37} +10.3370 q^{38} +5.52420 q^{39} -0.494123 q^{40} -1.91014 q^{41} -5.05136 q^{42} +5.23006 q^{43} -3.81405 q^{45} -10.2766 q^{46} -5.48510 q^{47} +11.6044 q^{48} +1.00000 q^{49} -1.93511 q^{50} -13.5365 q^{51} -3.69212 q^{52} +11.6350 q^{53} +4.11204 q^{54} -0.494123 q^{56} +13.9441 q^{57} -4.74916 q^{58} -11.1856 q^{59} +4.55420 q^{60} +9.29495 q^{61} +12.1298 q^{62} -3.81405 q^{63} -5.84348 q^{64} +2.11625 q^{65} -7.45806 q^{67} +9.04715 q^{68} -13.8627 q^{69} -1.93511 q^{70} +7.38000 q^{71} +1.88461 q^{72} +6.61877 q^{73} -13.2034 q^{74} -2.61037 q^{75} -9.31961 q^{76} -10.6899 q^{78} -9.28593 q^{79} +4.44549 q^{80} -5.89519 q^{81} +3.69633 q^{82} +2.17213 q^{83} +4.55420 q^{84} -5.18564 q^{85} -10.1208 q^{86} -6.40639 q^{87} -8.52745 q^{89} +7.38060 q^{90} +2.11625 q^{91} +9.26517 q^{92} +16.3625 q^{93} +10.6143 q^{94} +5.34181 q^{95} -19.8761 q^{96} -0.130383 q^{97} -1.93511 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 2 q^{3} + 4 q^{4} - 5 q^{5} - 5 q^{6} - 5 q^{7} + 12 q^{8} + 11 q^{9}+O(q^{10}) $ 5 * q - 2 * q^3 + 4 * q^4 - 5 * q^5 - 5 * q^6 - 5 * q^7 + 12 * q^8 + 11 * q^9	$ 5 q - 2 q^{3} + 4 q^{4} - 5 q^{5} - 5 q^{6} - 5 q^{7} + 12 q^{8} + 11 q^{9} - 23 q^{12} + 10 q^{13} + 2 q^{15} + 10 q^{16} + 2 q^{17} + 5 q^{18} - 3 q^{19} - 4 q^{20} + 2 q^{21} + 3 q^{23} - 28 q^{24} + 5 q^{25} + 13 q^{26} - 11 q^{27} - 4 q^{28} + q^{29} + 5 q^{30} - 12 q^{31} + 29 q^{32} - 20 q^{34} + 5 q^{35} + 45 q^{36} + 9 q^{38} - 2 q^{39} - 12 q^{40} - 11 q^{41} + 5 q^{42} + 10 q^{43} - 11 q^{45} + 14 q^{46} + 16 q^{47} - 46 q^{48} + 5 q^{49} + 6 q^{51} + 30 q^{52} + 4 q^{53} - 34 q^{54} - 12 q^{56} + 34 q^{57} - 6 q^{58} - 32 q^{59} + 23 q^{60} + 40 q^{61} + q^{62} - 11 q^{63} + 38 q^{64} - 10 q^{65} + 7 q^{67} - 19 q^{68} - 24 q^{69} + 10 q^{71} + 72 q^{72} + 11 q^{73} - 37 q^{74} - 2 q^{75} + 3 q^{76} - 87 q^{78} + 13 q^{79} - 10 q^{80} + q^{81} + 4 q^{82} + 26 q^{83} + 23 q^{84} - 2 q^{85} - 17 q^{86} + 14 q^{87} + 5 q^{89} - 5 q^{90} - 10 q^{91} + 32 q^{92} + 3 q^{93} + 44 q^{94} + 3 q^{95} - 84 q^{96} - 5 q^{97}+O(q^{100}) $ 5 * q - 2 * q^3 + 4 * q^4 - 5 * q^5 - 5 * q^6 - 5 * q^7 + 12 * q^8 + 11 * q^9 - 23 * q^12 + 10 * q^13 + 2 * q^15 + 10 * q^16 + 2 * q^17 + 5 * q^18 - 3 * q^19 - 4 * q^20 + 2 * q^21 + 3 * q^23 - 28 * q^24 + 5 * q^25 + 13 * q^26 - 11 * q^27 - 4 * q^28 + q^29 + 5 * q^30 - 12 * q^31 + 29 * q^32 - 20 * q^34 + 5 * q^35 + 45 * q^36 + 9 * q^38 - 2 * q^39 - 12 * q^40 - 11 * q^41 + 5 * q^42 + 10 * q^43 - 11 * q^45 + 14 * q^46 + 16 * q^47 - 46 * q^48 + 5 * q^49 + 6 * q^51 + 30 * q^52 + 4 * q^53 - 34 * q^54 - 12 * q^56 + 34 * q^57 - 6 * q^58 - 32 * q^59 + 23 * q^60 + 40 * q^61 + q^62 - 11 * q^63 + 38 * q^64 - 10 * q^65 + 7 * q^67 - 19 * q^68 - 24 * q^69 + 10 * q^71 + 72 * q^72 + 11 * q^73 - 37 * q^74 - 2 * q^75 + 3 * q^76 - 87 * q^78 + 13 * q^79 - 10 * q^80 + q^81 + 4 * q^82 + 26 * q^83 + 23 * q^84 - 2 * q^85 - 17 * q^86 + 14 * q^87 + 5 * q^89 - 5 * q^90 - 10 * q^91 + 32 * q^92 + 3 * q^93 + 44 * q^94 + 3 * q^95 - 84 * q^96 - 5 * q^97

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.93511	−1.36833	−0.684165	−	0.729327i	$-0.739833\pi$
$2$	−1.93511	−1.36833	−0.684165	+	0.729327i	$0.739833\pi$
$3$	−2.61037	−1.50710	−0.753550	−	0.657391i	$-0.771660\pi$
$3$	−2.61037	−1.50710	−0.753550	+	0.657391i	$0.771660\pi$
$4$	1.74465	0.872327
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	5.05136	2.06221
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	0.494123	0.174699
$9$	3.81405	1.27135
$10$	1.93511	0.611936
$11$	0	0
$11$	0	0
$12$	−4.55420	−1.31468
$13$	−2.11625	−0.586942	−0.293471	−	0.955968i	$-0.594810\pi$
$13$	−2.11625	−0.586942	−0.293471	+	0.955968i	$0.594810\pi$
$14$	1.93511	0.517180
$15$	2.61037	0.673995
$16$	−4.44549	−1.11137
$17$	5.18564	1.25770	0.628851	−	0.777525i	$-0.283525\pi$
$17$	5.18564	1.25770	0.628851	+	0.777525i	$0.283525\pi$
$18$	−7.38060	−1.73962
$19$	−5.34181	−1.22550	−0.612748	−	0.790279i	$-0.709936\pi$
$19$	−5.34181	−1.22550	−0.612748	+	0.790279i	$0.709936\pi$
$20$	−1.74465	−0.390116
$21$	2.61037	0.569630
$22$	0	0
$23$	5.31060	1.10734	0.553669	−	0.832737i	$-0.313227\pi$
$23$	5.31060	1.10734	0.553669	+	0.832737i	$0.313227\pi$
$24$	−1.28985	−0.263289
$25$	1.00000	0.200000
$26$	4.09518	0.803130
$27$	−2.12496	−0.408949
$28$	−1.74465	−0.329709
$29$	2.45420	0.455734	0.227867	−	0.973692i	$-0.426825\pi$
$29$	2.45420	0.455734	0.227867	+	0.973692i	$0.426825\pi$
$30$	−5.05136	−0.922248
$31$	−6.26825	−1.12581	−0.562905	−	0.826521i	$-0.690316\pi$
$31$	−6.26825	−1.12581	−0.562905	+	0.826521i	$0.690316\pi$
$32$	7.61427	1.34603
$33$	0	0
$34$	−10.0348	−1.72095
$35$	1.00000	0.169031
$36$	6.65419	1.10903
$37$	6.82305	1.12170	0.560851	−	0.827917i	$-0.310474\pi$
$37$	6.82305	1.12170	0.560851	+	0.827917i	$0.310474\pi$
$38$	10.3370	1.67688
$39$	5.52420	0.884580
$40$	−0.494123	−0.0781277
$41$	−1.91014	−0.298314	−0.149157	−	0.988814i	$-0.547656\pi$
$41$	−1.91014	−0.298314	−0.149157	+	0.988814i	$0.547656\pi$
$42$	−5.05136	−0.779442
$43$	5.23006	0.797577	0.398789	−	0.917043i	$-0.369431\pi$
$43$	5.23006	0.797577	0.398789	+	0.917043i	$0.369431\pi$
$44$	0	0
$45$	−3.81405	−0.568564
$46$	−10.2766	−1.51520
$47$	−5.48510	−0.800084	−0.400042	−	0.916497i	$-0.631004\pi$
$47$	−5.48510	−0.800084	−0.400042	+	0.916497i	$0.631004\pi$
$48$	11.6044	1.67495
$49$	1.00000	0.142857
$50$	−1.93511	−0.273666
$51$	−13.5365	−1.89548
$52$	−3.69212	−0.512005
$53$	11.6350	1.59819	0.799097	−	0.601202i	$-0.205311\pi$
$53$	11.6350	1.59819	0.799097	+	0.601202i	$0.205311\pi$
$54$	4.11204	0.559578
$55$	0	0
$56$	−0.494123	−0.0660300
$57$	13.9441	1.84694
$58$	−4.74916	−0.623595
$59$	−11.1856	−1.45625	−0.728123	−	0.685446i	$-0.759607\pi$
$59$	−11.1856	−1.45625	−0.728123	+	0.685446i	$0.759607\pi$
$60$	4.55420	0.587944
$61$	9.29495	1.19010	0.595048	−	0.803690i	$-0.297133\pi$
$61$	9.29495	1.19010	0.595048	+	0.803690i	$0.297133\pi$
$62$	12.1298	1.54048
$63$	−3.81405	−0.480525
$64$	−5.84348	−0.730435
$65$	2.11625	0.262488
$66$	0	0
$67$	−7.45806	−0.911147	−0.455574	−	0.890198i	$-0.650566\pi$
$67$	−7.45806	−0.911147	−0.455574	+	0.890198i	$0.650566\pi$
$68$	9.04715	1.09713
$69$	−13.8627	−1.66887
$70$	−1.93511	−0.231290
$71$	7.38000	0.875844	0.437922	−	0.899013i	$-0.355715\pi$
$71$	7.38000	0.875844	0.437922	+	0.899013i	$0.355715\pi$
$72$	1.88461	0.222103
$73$	6.61877	0.774669	0.387334	−	0.921939i	$-0.373396\pi$
$73$	6.61877	0.774669	0.387334	+	0.921939i	$0.373396\pi$
$74$	−13.2034	−1.53486
$75$	−2.61037	−0.301420
$76$	−9.31961	−1.06903
$77$	0	0
$78$	−10.6899	−1.21040
$79$	−9.28593	−1.04475	−0.522374	−	0.852716i	$-0.674954\pi$
$79$	−9.28593	−1.04475	−0.522374	+	0.852716i	$0.674954\pi$
$80$	4.44549	0.497021
$81$	−5.89519	−0.655021
$82$	3.69633	0.408192
$83$	2.17213	0.238423	0.119211	−	0.992869i	$-0.461963\pi$
$83$	2.17213	0.238423	0.119211	+	0.992869i	$0.461963\pi$
$84$	4.55420	0.496904
$85$	−5.18564	−0.562462
$86$	−10.1208	−1.09135
$87$	−6.40639	−0.686837
$88$	0	0
$89$	−8.52745	−0.903908	−0.451954	−	0.892041i	$-0.649273\pi$
$89$	−8.52745	−0.903908	−0.451954	+	0.892041i	$0.649273\pi$
$90$	7.38060	0.777984
$91$	2.11625	0.221843
$92$	9.26517	0.965960
$93$	16.3625	1.69671
$94$	10.6143	1.09478
$95$	5.34181	0.548058
$96$	−19.8761	−2.02859
$97$	−0.130383	−0.0132384	−0.00661919	−	0.999978i	$-0.502107\pi$
$97$	−0.130383	−0.0132384	−0.00661919	+	0.999978i	$0.502107\pi$
$98$	−1.93511	−0.195476
$99$	0	0
$100$	1.74465	0.174465
$101$	−10.4929	−1.04408	−0.522039	−	0.852922i	$-0.674828\pi$
$101$	−10.4929	−1.04408	−0.522039	+	0.852922i	$0.674828\pi$
$102$	26.1945	2.59365
$103$	−16.7755	−1.65294	−0.826472	−	0.562978i	$-0.809656\pi$
$103$	−16.7755	−1.65294	−0.826472	+	0.562978i	$0.809656\pi$
$104$	−1.04569	−0.102538
$105$	−2.61037	−0.254746
$106$	−22.5151	−2.18686
$107$	1.19679	0.115698	0.0578491	−	0.998325i	$-0.481576\pi$
$107$	1.19679	0.115698	0.0578491	+	0.998325i	$0.481576\pi$
$108$	−3.70733	−0.356738
$109$	16.8651	1.61538	0.807692	−	0.589605i	$-0.200717\pi$
$109$	16.8651	1.61538	0.807692	+	0.589605i	$0.200717\pi$
$110$	0	0
$111$	−17.8107	−1.69052
$112$	4.44549	0.420059
$113$	−14.9218	−1.40372	−0.701861	−	0.712314i	$-0.747647\pi$
$113$	−14.9218	−1.40372	−0.701861	+	0.712314i	$0.747647\pi$
$114$	−26.9834	−2.52723
$115$	−5.31060	−0.495216
$116$	4.28174	0.397549
$117$	−8.07147	−0.746208
$118$	21.6455	1.99263
$119$	−5.18564	−0.475367
$120$	1.28985	0.117746
$121$	0	0
$122$	−17.9868	−1.62845
$123$	4.98618	0.449589
$124$	−10.9359	−0.982075
$125$	−1.00000	−0.0894427
$126$	7.38060	0.657516
$127$	9.45141	0.838677	0.419339	−	0.907830i	$-0.362262\pi$
$127$	9.45141	0.838677	0.419339	+	0.907830i	$0.362262\pi$
$128$	−3.92077	−0.346550
$129$	−13.6524	−1.20203
$130$	−4.09518	−0.359171
$131$	−1.60729	−0.140430	−0.0702148	−	0.997532i	$-0.522368\pi$
$131$	−1.60729	−0.140430	−0.0702148	+	0.997532i	$0.522368\pi$
$132$	0	0
$133$	5.34181	0.463194
$134$	14.4322	1.24675
$135$	2.12496	0.182888
$136$	2.56234	0.219719
$137$	−16.0222	−1.36887	−0.684435	−	0.729074i	$-0.739951\pi$
$137$	−16.0222	−1.36887	−0.684435	+	0.729074i	$0.739951\pi$
$138$	26.8258	2.28356
$139$	13.1922	1.11895	0.559476	−	0.828847i	$-0.311002\pi$
$139$	13.1922	1.11895	0.559476	+	0.828847i	$0.311002\pi$
$140$	1.74465	0.147450
$141$	14.3181	1.20581
$142$	−14.2811	−1.19844
$143$	0	0
$144$	−16.9553	−1.41294
$145$	−2.45420	−0.203811
$146$	−12.8081	−1.06000
$147$	−2.61037	−0.215300
$148$	11.9039	0.978492
$149$	−16.9026	−1.38472	−0.692359	−	0.721553i	$-0.743428\pi$
$149$	−16.9026	−1.38472	−0.692359	+	0.721553i	$0.743428\pi$
$150$	5.05136	0.412442
$151$	−9.89695	−0.805402	−0.402701	−	0.915332i	$-0.631929\pi$
$151$	−9.89695	−0.805402	−0.402701	+	0.915332i	$0.631929\pi$
$152$	−2.63951	−0.214093
$153$	19.7783	1.59898
$154$	0	0
$155$	6.26825	0.503478
$156$	9.63782	0.771643
$157$	−22.0507	−1.75984	−0.879920	−	0.475122i	$-0.842404\pi$
$157$	−22.0507	−1.75984	−0.879920	+	0.475122i	$0.842404\pi$
$158$	17.9693	1.42956
$159$	−30.3718	−2.40864
$160$	−7.61427	−0.601961
$161$	−5.31060	−0.418534
$162$	11.4078	0.896285
$163$	−19.1878	−1.50290	−0.751451	−	0.659789i	$-0.770646\pi$
$163$	−19.1878	−1.50290	−0.751451	+	0.659789i	$0.770646\pi$
$164$	−3.33253	−0.260227
$165$	0	0
$166$	−4.20332	−0.326241
$167$	8.73801	0.676167	0.338084	−	0.941116i	$-0.390221\pi$
$167$	8.73801	0.676167	0.338084	+	0.941116i	$0.390221\pi$
$168$	1.28985	0.0995137
$169$	−8.52149	−0.655499
$170$	10.0348	0.769633
$171$	−20.3739	−1.55803
$172$	9.12465	0.695748
$173$	−0.733192	−0.0557436	−0.0278718	−	0.999612i	$-0.508873\pi$
$173$	−0.733192	−0.0557436	−0.0278718	+	0.999612i	$0.508873\pi$
$174$	12.3971	0.939819
$175$	−1.00000	−0.0755929
$176$	0	0
$177$	29.1987	2.19471
$178$	16.5016	1.23684
$179$	7.70676	0.576030	0.288015	−	0.957626i	$-0.407005\pi$
$179$	7.70676	0.576030	0.288015	+	0.957626i	$0.407005\pi$
$180$	−6.65419	−0.495974
$181$	18.2163	1.35400	0.677002	−	0.735981i	$-0.263279\pi$
$181$	18.2163	1.35400	0.677002	+	0.735981i	$0.263279\pi$
$182$	−4.09518	−0.303555
$183$	−24.2633	−1.79359
$184$	2.62409	0.193451
$185$	−6.82305	−0.501641
$186$	−31.6632	−2.32166
$187$	0	0
$188$	−9.56960	−0.697935
$189$	2.12496	0.154568
$190$	−10.3370	−0.749924
$191$	−4.90357	−0.354810	−0.177405	−	0.984138i	$-0.556770\pi$
$191$	−4.90357	−0.354810	−0.177405	+	0.984138i	$0.556770\pi$
$192$	15.2537	1.10084
$193$	10.7952	0.777055	0.388528	−	0.921437i	$-0.372984\pi$
$193$	10.7952	0.777055	0.388528	+	0.921437i	$0.372984\pi$
$194$	0.252306	0.0181145
$195$	−5.52420	−0.395596
$196$	1.74465	0.124618
$197$	−8.66532	−0.617378	−0.308689	−	0.951163i	$-0.599890\pi$
$197$	−8.66532	−0.617378	−0.308689	+	0.951163i	$0.599890\pi$
$198$	0	0
$199$	16.9008	1.19807	0.599033	−	0.800724i	$-0.295552\pi$
$199$	16.9008	1.19807	0.599033	+	0.800724i	$0.295552\pi$
$200$	0.494123	0.0349398
$201$	19.4683	1.37319
$202$	20.3048	1.42864
$203$	−2.45420	−0.172251
$204$	−23.6164	−1.65348
$205$	1.91014	0.133410
$206$	32.4625	2.26177
$207$	20.2549	1.40781
$208$	9.40777	0.652311
$209$	0	0
$210$	5.05136	0.348577
$211$	21.1775	1.45792	0.728961	−	0.684555i	$-0.240004\pi$
$211$	21.1775	1.45792	0.728961	+	0.684555i	$0.240004\pi$
$212$	20.2991	1.39415
$213$	−19.2645	−1.31998
$214$	−2.31592	−0.158313
$215$	−5.23006	−0.356687
$216$	−1.04999	−0.0714430
$217$	6.26825	0.425517
$218$	−32.6358	−2.21038
$219$	−17.2775	−1.16750
$220$	0	0
$221$	−10.9741	−0.738199
$222$	34.4657	2.31319
$223$	−6.07467	−0.406790	−0.203395	−	0.979097i	$-0.565198\pi$
$223$	−6.07467	−0.406790	−0.203395	+	0.979097i	$0.565198\pi$
$224$	−7.61427	−0.508750
$225$	3.81405	0.254270
$226$	28.8753	1.92076
$227$	18.7791	1.24641	0.623206	−	0.782058i	$-0.285830\pi$
$227$	18.7791	1.24641	0.623206	+	0.782058i	$0.285830\pi$
$228$	24.3277	1.61114
$229$	−8.95710	−0.591902	−0.295951	−	0.955203i	$-0.595636\pi$
$229$	−8.95710	−0.591902	−0.295951	+	0.955203i	$0.595636\pi$
$230$	10.2766	0.677620
$231$	0	0
$232$	1.21268	0.0796163
$233$	−21.2610	−1.39286	−0.696428	−	0.717627i	$-0.745228\pi$
$233$	−21.2610	−1.39286	−0.696428	+	0.717627i	$0.745228\pi$
$234$	15.6192	1.02106
$235$	5.48510	0.357808
$236$	−19.5151	−1.27032
$237$	24.2397	1.57454
$238$	10.0348	0.650459
$239$	−20.7948	−1.34510	−0.672551	−	0.740051i	$-0.734801\pi$
$239$	−20.7948	−1.34510	−0.672551	+	0.740051i	$0.734801\pi$
$240$	−11.6044	−0.749060
$241$	25.8494	1.66511	0.832554	−	0.553943i	$-0.186878\pi$
$241$	25.8494	1.66511	0.832554	+	0.553943i	$0.186878\pi$
$242$	0	0
$243$	21.7635	1.39613
$244$	16.2165	1.03815
$245$	−1.00000	−0.0638877
$246$	−9.64881	−0.615186
$247$	11.3046	0.719295
$248$	−3.09729	−0.196678
$249$	−5.67008	−0.359327
$250$	1.93511	0.122387
$251$	18.1414	1.14507	0.572537	−	0.819879i	$-0.305959\pi$
$251$	18.1414	1.14507	0.572537	+	0.819879i	$0.305959\pi$
$252$	−6.65419	−0.419175
$253$	0	0
$254$	−18.2895	−1.14759
$255$	13.5365	0.847686
$256$	19.2741	1.20463
$257$	−5.56328	−0.347028	−0.173514	−	0.984831i	$-0.555512\pi$
$257$	−5.56328	−0.347028	−0.173514	+	0.984831i	$0.555512\pi$
$258$	26.4189	1.64477
$259$	−6.82305	−0.423964
$260$	3.69212	0.228976
$261$	9.36045	0.579397
$262$	3.11028	0.192154
$263$	−4.89215	−0.301663	−0.150831	−	0.988559i	$-0.548195\pi$
$263$	−4.89215	−0.301663	−0.150831	+	0.988559i	$0.548195\pi$
$264$	0	0
$265$	−11.6350	−0.714734
$266$	−10.3370	−0.633802
$267$	22.2598	1.36228
$268$	−13.0117	−0.794818
$269$	−20.3451	−1.24046	−0.620231	−	0.784419i	$-0.712961\pi$
$269$	−20.3451	−1.24046	−0.620231	+	0.784419i	$0.712961\pi$
$270$	−4.11204	−0.250251
$271$	−27.6372	−1.67884	−0.839422	−	0.543481i	$-0.817106\pi$
$271$	−27.6372	−1.67884	−0.839422	+	0.543481i	$0.817106\pi$
$272$	−23.0527	−1.39778
$273$	−5.52420	−0.334340
$274$	31.0047	1.87306
$275$	0	0
$276$	−24.1855	−1.45580
$277$	−3.10804	−0.186744	−0.0933720	−	0.995631i	$-0.529765\pi$
$277$	−3.10804	−0.186744	−0.0933720	+	0.995631i	$0.529765\pi$
$278$	−25.5285	−1.53110
$279$	−23.9074	−1.43130
$280$	0.494123	0.0295295
$281$	2.78670	0.166240	0.0831202	−	0.996540i	$-0.473511\pi$
$281$	2.78670	0.166240	0.0831202	+	0.996540i	$0.473511\pi$
$282$	−27.7072	−1.64994
$283$	29.3075	1.74215	0.871075	−	0.491150i	$-0.163423\pi$
$283$	29.3075	1.74215	0.871075	+	0.491150i	$0.163423\pi$
$284$	12.8755	0.764023
$285$	−13.9441	−0.825978
$286$	0	0
$287$	1.91014	0.112752
$288$	29.0412	1.71127
$289$	9.89088	0.581816
$290$	4.74916	0.278880
$291$	0.340348	0.0199516
$292$	11.5475	0.675765
$293$	14.4165	0.842222	0.421111	−	0.907009i	$-0.361640\pi$
$293$	14.4165	0.842222	0.421111	+	0.907009i	$0.361640\pi$
$294$	5.05136	0.294601
$295$	11.1856	0.651253
$296$	3.37143	0.195960
$297$	0	0
$298$	32.7085	1.89475
$299$	−11.2386	−0.649943
$300$	−4.55420	−0.262937
$301$	−5.23006	−0.301456
$302$	19.1517	1.10206
$303$	27.3903	1.57353
$304$	23.7470	1.36198
$305$	−9.29495	−0.532227
$306$	−38.2732	−2.18793
$307$	−9.75383	−0.556680	−0.278340	−	0.960483i	$-0.589784\pi$
$307$	−9.75383	−0.556680	−0.278340	+	0.960483i	$0.589784\pi$
$308$	0	0
$309$	43.7904	2.49115
$310$	−12.1298	−0.688924
$311$	22.8777	1.29727	0.648637	−	0.761098i	$-0.275340\pi$
$311$	22.8777	1.29727	0.648637	+	0.761098i	$0.275340\pi$
$312$	2.72963	0.154535
$313$	−24.7659	−1.39985	−0.699926	−	0.714215i	$-0.746784\pi$
$313$	−24.7659	−1.39985	−0.699926	+	0.714215i	$0.746784\pi$
$314$	42.6706	2.40804
$315$	3.81405	0.214897
$316$	−16.2007	−0.911362
$317$	27.8136	1.56217	0.781084	−	0.624426i	$-0.214667\pi$
$317$	27.8136	1.56217	0.781084	+	0.624426i	$0.214667\pi$
$318$	58.7727	3.29581
$319$	0	0
$320$	5.84348	0.326660
$321$	−3.12407	−0.174369
$322$	10.2766	0.572693
$323$	−27.7007	−1.54131
$324$	−10.2851	−0.571393
$325$	−2.11625	−0.117388
$326$	37.1305	2.05647
$327$	−44.0242	−2.43454
$328$	−0.943844	−0.0521151
$329$	5.48510	0.302403
$330$	0	0
$331$	19.5064	1.07217	0.536085	−	0.844164i	$-0.319903\pi$
$331$	19.5064	1.07217	0.536085	+	0.844164i	$0.319903\pi$
$332$	3.78962	0.207982
$333$	26.0234	1.42608
$334$	−16.9090	−0.925220
$335$	7.45806	0.407477
$336$	−11.6044	−0.633071
$337$	18.0283	0.982065	0.491032	−	0.871141i	$-0.336620\pi$
$337$	18.0283	0.982065	0.491032	+	0.871141i	$0.336620\pi$
$338$	16.4900	0.896939
$339$	38.9514	2.11555
$340$	−9.04715	−0.490651
$341$	0	0
$342$	39.4258	2.13190
$343$	−1.00000	−0.0539949
$344$	2.58429	0.139336
$345$	13.8627	0.746340
$346$	1.41881	0.0762756
$347$	8.95676	0.480824	0.240412	−	0.970671i	$-0.422717\pi$
$347$	8.95676	0.480824	0.240412	+	0.970671i	$0.422717\pi$
$348$	−11.1769	−0.599146
$349$	32.5926	1.74464	0.872320	−	0.488936i	$-0.162615\pi$
$349$	32.5926	1.74464	0.872320	+	0.488936i	$0.162615\pi$
$350$	1.93511	0.103436
$351$	4.49695	0.240030
$352$	0	0
$353$	27.6577	1.47207	0.736035	−	0.676944i	$-0.236696\pi$
$353$	27.6577	1.47207	0.736035	+	0.676944i	$0.236696\pi$
$354$	−56.5027	−3.00309
$355$	−7.38000	−0.391690
$356$	−14.8775	−0.788503
$357$	13.5365	0.716425
$358$	−14.9134	−0.788199
$359$	2.91864	0.154040	0.0770200	−	0.997030i	$-0.475459\pi$
$359$	2.91864	0.154040	0.0770200	+	0.997030i	$0.475459\pi$
$360$	−1.88461	−0.0993276
$361$	9.53494	0.501839
$362$	−35.2505	−1.85272
$363$	0	0
$364$	3.69212	0.193520
$365$	−6.61877	−0.346442
$366$	46.9522	2.45423
$367$	9.77009	0.509994	0.254997	−	0.966942i	$-0.417925\pi$
$367$	9.77009	0.509994	0.254997	+	0.966942i	$0.417925\pi$
$368$	−23.6082	−1.23066
$369$	−7.28536	−0.379261
$370$	13.2034	0.686410
$371$	−11.6350	−0.604061
$372$	28.5468	1.48008
$373$	12.2693	0.635282	0.317641	−	0.948211i	$-0.397109\pi$
$373$	12.2693	0.635282	0.317641	+	0.948211i	$0.397109\pi$
$374$	0	0
$375$	2.61037	0.134799
$376$	−2.71031	−0.139774
$377$	−5.19371	−0.267490
$378$	−4.11204	−0.211500
$379$	−25.5799	−1.31395	−0.656977	−	0.753911i	$-0.728165\pi$
$379$	−25.5799	−1.31395	−0.656977	+	0.753911i	$0.728165\pi$
$380$	9.31961	0.478086
$381$	−24.6717	−1.26397
$382$	9.48895	0.485497
$383$	2.82570	0.144386	0.0721932	−	0.997391i	$-0.477000\pi$
$383$	2.82570	0.144386	0.0721932	+	0.997391i	$0.477000\pi$
$384$	10.2347	0.522285
$385$	0	0
$386$	−20.8899	−1.06327
$387$	19.9477	1.01400
$388$	−0.227473	−0.0115482
$389$	−18.5961	−0.942861	−0.471430	−	0.881903i	$-0.656262\pi$
$389$	−18.5961	−0.942861	−0.471430	+	0.881903i	$0.656262\pi$
$390$	10.6899	0.541306
$391$	27.5389	1.39270
$392$	0.494123	0.0249570
$393$	4.19563	0.211641
$394$	16.7684	0.844777
$395$	9.28593	0.467226
$396$	0	0
$397$	3.16356	0.158775	0.0793873	−	0.996844i	$-0.474704\pi$
$397$	3.16356	0.158775	0.0793873	+	0.996844i	$0.474704\pi$
$398$	−32.7049	−1.63935
$399$	−13.9441	−0.698079
$400$	−4.44549	−0.222275
$401$	−13.7210	−0.685193	−0.342596	−	0.939483i	$-0.611306\pi$
$401$	−13.7210	−0.685193	−0.342596	+	0.939483i	$0.611306\pi$
$402$	−37.6734	−1.87898
$403$	13.2652	0.660786
$404$	−18.3064	−0.910777
$405$	5.89519	0.292934
$406$	4.74916	0.235697
$407$	0	0
$408$	−6.68868	−0.331139
$409$	−18.6233	−0.920861	−0.460430	−	0.887696i	$-0.652305\pi$
$409$	−18.6233	−0.920861	−0.460430	+	0.887696i	$0.652305\pi$
$410$	−3.69633	−0.182549
$411$	41.8239	2.06302
$412$	−29.2675	−1.44191
$413$	11.1856	0.550409
$414$	−39.1955	−1.92635
$415$	−2.17213	−0.106626
$416$	−16.1137	−0.790039
$417$	−34.4367	−1.68637
$418$	0	0
$419$	0.644703	0.0314958	0.0157479	−	0.999876i	$-0.494987\pi$
$419$	0.644703	0.0314958	0.0157479	+	0.999876i	$0.494987\pi$
$420$	−4.55420	−0.222222
$421$	6.14960	0.299713	0.149857	−	0.988708i	$-0.452119\pi$
$421$	6.14960	0.299713	0.149857	+	0.988708i	$0.452119\pi$
$422$	−40.9809	−1.99492
$423$	−20.9204	−1.01719
$424$	5.74914	0.279203
$425$	5.18564	0.251541
$426$	37.2790	1.80617
$427$	−9.29495	−0.449814
$428$	2.08799	0.100927
$429$	0	0
$430$	10.1208	0.488066
$431$	−19.7680	−0.952190	−0.476095	−	0.879394i	$-0.657948\pi$
$431$	−19.7680	−0.952190	−0.476095	+	0.879394i	$0.657948\pi$
$432$	9.44650	0.454495
$433$	31.5980	1.51850	0.759251	−	0.650798i	$-0.225565\pi$
$433$	31.5980	1.51850	0.759251	+	0.650798i	$0.225565\pi$
$434$	−12.1298	−0.582247
$435$	6.40639	0.307163
$436$	29.4238	1.40914
$437$	−28.3682	−1.35704
$438$	33.4338	1.59753
$439$	−21.4299	−1.02279	−0.511397	−	0.859345i	$-0.670872\pi$
$439$	−21.4299	−1.02279	−0.511397	+	0.859345i	$0.670872\pi$
$440$	0	0
$441$	3.81405	0.181621
$442$	21.2361	1.01010
$443$	28.4261	1.35057	0.675283	−	0.737559i	$-0.264021\pi$
$443$	28.4261	1.35057	0.675283	+	0.737559i	$0.264021\pi$
$444$	−31.0735	−1.47468
$445$	8.52745	0.404240
$446$	11.7552	0.556623
$447$	44.1222	2.08691
$448$	5.84348	0.276078
$449$	14.5702	0.687611	0.343806	−	0.939041i	$-0.388284\pi$
$449$	14.5702	0.687611	0.343806	+	0.939041i	$0.388284\pi$
$450$	−7.38060	−0.347925
$451$	0	0
$452$	−26.0333	−1.22450
$453$	25.8347	1.21382
$454$	−36.3396	−1.70550
$455$	−2.11625	−0.0992113
$456$	6.89011	0.322659
$457$	13.5385	0.633305	0.316653	−	0.948542i	$-0.397441\pi$
$457$	13.5385	0.633305	0.316653	+	0.948542i	$0.397441\pi$
$458$	17.3330	0.809917
$459$	−11.0193	−0.514337
$460$	−9.26517	−0.431991
$461$	0.632553	0.0294609	0.0147305	−	0.999892i	$-0.495311\pi$
$461$	0.632553	0.0294609	0.0147305	+	0.999892i	$0.495311\pi$
$462$	0	0
$463$	−18.7924	−0.873358	−0.436679	−	0.899617i	$-0.643845\pi$
$463$	−18.7924	−0.873358	−0.436679	+	0.899617i	$0.643845\pi$
$464$	−10.9101	−0.506491
$465$	−16.3625	−0.758791
$466$	41.1424	1.90589
$467$	−4.84156	−0.224041	−0.112020	−	0.993706i	$-0.535732\pi$
$467$	−4.84156	−0.224041	−0.112020	+	0.993706i	$0.535732\pi$
$468$	−14.0819	−0.650937
$469$	7.45806	0.344381
$470$	−10.6143	−0.489600
$471$	57.5606	2.65225
$472$	−5.52708	−0.254405
$473$	0	0
$474$	−46.9066	−2.15449
$475$	−5.34181	−0.245099
$476$	−9.04715	−0.414675
$477$	44.3765	2.03186
$478$	40.2402	1.84054
$479$	−29.5812	−1.35160	−0.675799	−	0.737086i	$-0.736201\pi$
$479$	−29.5812	−1.35160	−0.675799	+	0.737086i	$0.736201\pi$
$480$	19.8761	0.907215
$481$	−14.4393	−0.658375
$482$	−50.0215	−2.27842
$483$	13.8627	0.630773
$484$	0	0
$485$	0.130383	0.00592039
$486$	−42.1149	−1.91037
$487$	31.4134	1.42348	0.711739	−	0.702444i	$-0.247908\pi$
$487$	31.4134	1.42348	0.711739	+	0.702444i	$0.247908\pi$
$488$	4.59285	0.207909
$489$	50.0872	2.26502
$490$	1.93511	0.0874194
$491$	19.6476	0.886685	0.443342	−	0.896352i	$-0.353793\pi$
$491$	19.6476	0.886685	0.443342	+	0.896352i	$0.353793\pi$
$492$	8.69916	0.392188
$493$	12.7266	0.573178
$494$	−21.8757	−0.984233
$495$	0	0
$496$	27.8654	1.25120
$497$	−7.38000	−0.331038
$498$	10.9722	0.491677
$499$	14.7187	0.658902	0.329451	−	0.944173i	$-0.393136\pi$
$499$	14.7187	0.658902	0.329451	+	0.944173i	$0.393136\pi$
$500$	−1.74465	−0.0780233
$501$	−22.8095	−1.01905
$502$	−35.1056	−1.56684
$503$	−27.7740	−1.23838	−0.619191	−	0.785241i	$-0.712539\pi$
$503$	−27.7740	−1.23838	−0.619191	+	0.785241i	$0.712539\pi$
$504$	−1.88461	−0.0839471
$505$	10.4929	0.466926
$506$	0	0
$507$	22.2443	0.987902
$508$	16.4894	0.731601
$509$	−5.57965	−0.247314	−0.123657	−	0.992325i	$-0.539462\pi$
$509$	−5.57965	−0.247314	−0.123657	+	0.992325i	$0.539462\pi$
$510$	−26.1945	−1.15991
$511$	−6.61877	−0.292797
$512$	−29.4559	−1.30178
$513$	11.3512	0.501166
$514$	10.7656	0.474849
$515$	16.7755	0.739219
$516$	−23.8187	−1.04856
$517$	0	0
$518$	13.2034	0.580122
$519$	1.91390	0.0840111
$520$	1.04569	0.0458564
$521$	35.0479	1.53547	0.767737	−	0.640765i	$-0.221383\pi$
$521$	35.0479	1.53547	0.767737	+	0.640765i	$0.221383\pi$
$522$	−18.1135	−0.792806
$523$	−9.87639	−0.431864	−0.215932	−	0.976408i	$-0.569279\pi$
$523$	−9.87639	−0.431864	−0.215932	+	0.976408i	$0.569279\pi$
$524$	−2.80417	−0.122501
$525$	2.61037	0.113926
$526$	9.46685	0.412774
$527$	−32.5049	−1.41594
$528$	0	0
$529$	5.20252	0.226197
$530$	22.5151	0.977992
$531$	−42.6626	−1.85140
$532$	9.31961	0.404056
$533$	4.04233	0.175093
$534$	−43.0752	−1.86405
$535$	−1.19679	−0.0517418
$536$	−3.68520	−0.159176
$537$	−20.1175	−0.868135
$538$	39.3700	1.69736
$539$	0	0
$540$	3.70733	0.159538
$541$	31.8306	1.36850	0.684252	−	0.729246i	$-0.260129\pi$
$541$	31.8306	1.36850	0.684252	+	0.729246i	$0.260129\pi$
$542$	53.4811	2.29721
$543$	−47.5512	−2.04062
$544$	39.4849	1.69290
$545$	−16.8651	−0.722421
$546$	10.6899	0.457487
$547$	27.8543	1.19097	0.595483	−	0.803368i	$-0.296961\pi$
$547$	27.8543	1.19097	0.595483	+	0.803368i	$0.296961\pi$
$548$	−27.9532	−1.19410
$549$	35.4514	1.51303
$550$	0	0
$551$	−13.1099	−0.558500
$552$	−6.84986	−0.291549
$553$	9.28593	0.394878
$554$	6.01440	0.255527
$555$	17.8107	0.756022
$556$	23.0159	0.976092
$557$	31.0152	1.31416	0.657078	−	0.753822i	$-0.271792\pi$
$557$	31.0152	1.31416	0.657078	+	0.753822i	$0.271792\pi$
$558$	46.2635	1.95849
$559$	−11.0681	−0.468132
$560$	−4.44549	−0.187856
$561$	0	0
$562$	−5.39257	−0.227472
$563$	7.71505	0.325150	0.162575	−	0.986696i	$-0.448020\pi$
$563$	7.71505	0.325150	0.162575	+	0.986696i	$0.448020\pi$
$564$	24.9802	1.05186
$565$	14.9218	0.627764
$566$	−56.7133	−2.38384
$567$	5.89519	0.247575
$568$	3.64663	0.153009
$569$	47.4522	1.98930	0.994649	−	0.103311i	$-0.0329437\pi$
$569$	47.4522	1.98930	0.994649	+	0.103311i	$0.0329437\pi$
$570$	26.9834	1.13021
$571$	−46.0258	−1.92612	−0.963061	−	0.269284i	$-0.913213\pi$
$571$	−46.0258	−1.92612	−0.963061	+	0.269284i	$0.913213\pi$
$572$	0	0
$573$	12.8001	0.534734
$574$	−3.69633	−0.154282
$575$	5.31060	0.221468
$576$	−22.2873	−0.928637
$577$	10.5594	0.439595	0.219797	−	0.975546i	$-0.429460\pi$
$577$	10.5594	0.439595	0.219797	+	0.975546i	$0.429460\pi$
$578$	−19.1399	−0.796117
$579$	−28.1795	−1.17110
$580$	−4.28174	−0.177789
$581$	−2.17213	−0.0901153
$582$	−0.658612	−0.0273003
$583$	0	0
$584$	3.27049	0.135334
$585$	8.07147	0.333714
$586$	−27.8976	−1.15244
$587$	6.86408	0.283311	0.141655	−	0.989916i	$-0.454758\pi$
$587$	6.86408	0.283311	0.141655	+	0.989916i	$0.454758\pi$
$588$	−4.55420	−0.187812
$589$	33.4838	1.37968
$590$	−21.6455	−0.891129
$591$	22.6197	0.930451
$592$	−30.3318	−1.24663
$593$	10.5379	0.432740	0.216370	−	0.976311i	$-0.430578\pi$
$593$	10.5379	0.432740	0.216370	+	0.976311i	$0.430578\pi$
$594$	0	0
$595$	5.18564	0.212591
$596$	−29.4892	−1.20793
$597$	−44.1174	−1.80560
$598$	21.7479	0.889337
$599$	20.7953	0.849671	0.424836	−	0.905271i	$-0.360332\pi$
$599$	20.7953	0.849671	0.424836	+	0.905271i	$0.360332\pi$
$600$	−1.28985	−0.0526577
$601$	9.79763	0.399654	0.199827	−	0.979831i	$-0.435962\pi$
$601$	9.79763	0.399654	0.199827	+	0.979831i	$0.435962\pi$
$602$	10.1208	0.412491
$603$	−28.4454	−1.15839
$604$	−17.2667	−0.702574
$605$	0	0
$606$	−53.0032	−2.15311
$607$	−45.8028	−1.85908	−0.929539	−	0.368724i	$-0.879795\pi$
$607$	−45.8028	−1.85908	−0.929539	+	0.368724i	$0.879795\pi$
$608$	−40.6740	−1.64955
$609$	6.40639	0.259600
$610$	17.9868	0.728263
$611$	11.6078	0.469603
$612$	34.5062	1.39483
$613$	30.9633	1.25060	0.625299	−	0.780386i	$-0.284977\pi$
$613$	30.9633	1.25060	0.625299	+	0.780386i	$0.284977\pi$
$614$	18.8747	0.761722
$615$	−4.98618	−0.201062
$616$	0	0
$617$	−7.61596	−0.306607	−0.153304	−	0.988179i	$-0.548991\pi$
$617$	−7.61596	−0.306607	−0.153304	+	0.988179i	$0.548991\pi$
$618$	−84.7393	−3.40872
$619$	−23.1635	−0.931021	−0.465510	−	0.885042i	$-0.654129\pi$
$619$	−23.1635	−0.931021	−0.465510	+	0.885042i	$0.654129\pi$
$620$	10.9359	0.439197
$621$	−11.2848	−0.452845
$622$	−44.2708	−1.77510
$623$	8.52745	0.341645
$624$	−24.5578	−0.983098
$625$	1.00000	0.0400000
$626$	47.9248	1.91546
$627$	0	0
$628$	−38.4709	−1.53516
$629$	35.3819	1.41077
$630$	−7.38060	−0.294050
$631$	−20.1350	−0.801561	−0.400780	−	0.916174i	$-0.631261\pi$
$631$	−20.1350	−0.801561	−0.400780	+	0.916174i	$0.631261\pi$
$632$	−4.58839	−0.182516
$633$	−55.2813	−2.19723
$634$	−53.8224	−2.13756
$635$	−9.45141	−0.375068
$636$	−52.9882	−2.10112
$637$	−2.11625	−0.0838489
$638$	0	0
$639$	28.1476	1.11350
$640$	3.92077	0.154982
$641$	44.4009	1.75373	0.876864	−	0.480738i	$-0.159631\pi$
$641$	44.4009	1.75373	0.876864	+	0.480738i	$0.159631\pi$
$642$	6.04542	0.238594
$643$	13.9804	0.551334	0.275667	−	0.961253i	$-0.411101\pi$
$643$	13.9804	0.551334	0.275667	+	0.961253i	$0.411101\pi$
$644$	−9.26517	−0.365099
$645$	13.6524	0.537563
$646$	53.6040	2.10902
$647$	−17.8031	−0.699914	−0.349957	−	0.936766i	$-0.613804\pi$
$647$	−17.8031	−0.699914	−0.349957	+	0.936766i	$0.613804\pi$
$648$	−2.91295	−0.114431
$649$	0	0
$650$	4.09518	0.160626
$651$	−16.3625	−0.641296
$652$	−33.4760	−1.31102
$653$	46.0439	1.80184	0.900918	−	0.433990i	$-0.142895\pi$
$653$	46.0439	1.80184	0.900918	+	0.433990i	$0.142895\pi$
$654$	85.1917	3.33126
$655$	1.60729	0.0628020
$656$	8.49151	0.331538
$657$	25.2443	0.984874
$658$	−10.6143	−0.413787
$659$	5.12070	0.199474	0.0997370	−	0.995014i	$-0.468200\pi$
$659$	5.12070	0.199474	0.0997370	+	0.995014i	$0.468200\pi$
$660$	0	0
$661$	−24.7725	−0.963538	−0.481769	−	0.876298i	$-0.660006\pi$
$661$	−24.7725	−0.963538	−0.481769	+	0.876298i	$0.660006\pi$
$662$	−37.7471	−1.46708
$663$	28.6465	1.11254
$664$	1.07330	0.0416522
$665$	−5.34181	−0.207147
$666$	−50.3582	−1.95134
$667$	13.0333	0.504652
$668$	15.2448	0.589839
$669$	15.8571	0.613073
$670$	−14.4322	−0.557563
$671$	0	0
$672$	19.8761	0.766737
$673$	22.0099	0.848420	0.424210	−	0.905564i	$-0.360552\pi$
$673$	22.0099	0.848420	0.424210	+	0.905564i	$0.360552\pi$
$674$	−34.8868	−1.34379
$675$	−2.12496	−0.0817899
$676$	−14.8670	−0.571809
$677$	21.2781	0.817783	0.408891	−	0.912583i	$-0.365915\pi$
$677$	21.2781	0.817783	0.408891	+	0.912583i	$0.365915\pi$
$678$	−75.3753	−2.89477
$679$	0.130383	0.00500364
$680$	−2.56234	−0.0982614
$681$	−49.0204	−1.87847
$682$	0	0
$683$	−48.9094	−1.87146	−0.935732	−	0.352711i	$-0.885260\pi$
$683$	−48.9094	−1.87146	−0.935732	+	0.352711i	$0.885260\pi$
$684$	−35.5454	−1.35911
$685$	16.0222	0.612177
$686$	1.93511	0.0738829
$687$	23.3814	0.892055
$688$	−23.2502	−0.886405
$689$	−24.6226	−0.938047
$690$	−26.8258	−1.02124
$691$	29.9813	1.14054	0.570272	−	0.821456i	$-0.306838\pi$
$691$	29.9813	1.14054	0.570272	+	0.821456i	$0.306838\pi$
$692$	−1.27917	−0.0486266
$693$	0	0
$694$	−17.3323	−0.657926
$695$	−13.1922	−0.500410
$696$	−3.16554	−0.119990
$697$	−9.90531	−0.375190
$698$	−63.0702	−2.38724
$699$	55.4992	2.09917
$700$	−1.74465	−0.0659417
$701$	−21.8160	−0.823979	−0.411989	−	0.911189i	$-0.635166\pi$
$701$	−21.8160	−0.823979	−0.411989	+	0.911189i	$0.635166\pi$
$702$	−8.70210	−0.328440
$703$	−36.4474	−1.37464
$704$	0	0
$705$	−14.3181	−0.539253
$706$	−53.5207	−2.01428
$707$	10.4929	0.394624
$708$	50.9416	1.91450
$709$	−3.52064	−0.132220	−0.0661101	−	0.997812i	$-0.521059\pi$
$709$	−3.52064	−0.132220	−0.0661101	+	0.997812i	$0.521059\pi$
$710$	14.2811	0.535961
$711$	−35.4170	−1.32824
$712$	−4.21361	−0.157912
$713$	−33.2882	−1.24665
$714$	−26.1945	−0.980306
$715$	0	0
$716$	13.4456	0.502487
$717$	54.2821	2.02720
$718$	−5.64790	−0.210778
$719$	−51.1706	−1.90834	−0.954170	−	0.299265i	$-0.903259\pi$
$719$	−51.1706	−1.90834	−0.954170	+	0.299265i	$0.903259\pi$
$720$	16.9553	0.631887
$721$	16.7755	0.624754
$722$	−18.4512	−0.686681
$723$	−67.4767	−2.50948
$724$	31.7811	1.18113
$725$	2.45420	0.0911468
$726$	0	0
$727$	6.33549	0.234970	0.117485	−	0.993075i	$-0.462517\pi$
$727$	6.33549	0.234970	0.117485	+	0.993075i	$0.462517\pi$
$728$	1.04569	0.0387558
$729$	−39.1254	−1.44909
$730$	12.8081	0.474048
$731$	27.1212	1.00312
$732$	−42.3310	−1.56460
$733$	40.9406	1.51217	0.756087	−	0.654471i	$-0.227109\pi$
$733$	40.9406	1.51217	0.756087	+	0.654471i	$0.227109\pi$
$734$	−18.9062	−0.697840
$735$	2.61037	0.0962850
$736$	40.4364	1.49050
$737$	0	0
$738$	14.0980	0.518954
$739$	0.612851	0.0225441	0.0112720	−	0.999936i	$-0.496412\pi$
$739$	0.612851	0.0225441	0.0112720	+	0.999936i	$0.496412\pi$
$740$	−11.9039	−0.437595
$741$	−29.5092	−1.08405
$742$	22.5151	0.826554
$743$	−20.2191	−0.741767	−0.370883	−	0.928679i	$-0.620945\pi$
$743$	−20.2191	−0.741767	−0.370883	+	0.928679i	$0.620945\pi$
$744$	8.08507	0.296413
$745$	16.9026	0.619265
$746$	−23.7425	−0.869276
$747$	8.28462	0.303118
$748$	0	0
$749$	−1.19679	−0.0437298
$750$	−5.05136	−0.184450
$751$	23.5949	0.860992	0.430496	−	0.902593i	$-0.358339\pi$
$751$	23.5949	0.860992	0.430496	+	0.902593i	$0.358339\pi$
$752$	24.3839	0.889191
$753$	−47.3557	−1.72574
$754$	10.0504	0.366014
$755$	9.89695	0.360187
$756$	3.70733	0.134834
$757$	−24.4568	−0.888898	−0.444449	−	0.895804i	$-0.646600\pi$
$757$	−24.4568	−0.888898	−0.444449	+	0.895804i	$0.646600\pi$
$758$	49.5000	1.79792
$759$	0	0
$760$	2.63951	0.0957451
$761$	−17.4005	−0.630767	−0.315384	−	0.948964i	$-0.602133\pi$
$761$	−17.4005	−0.630767	−0.315384	+	0.948964i	$0.602133\pi$
$762$	47.7425	1.72953
$763$	−16.8651	−0.610557
$764$	−8.55503	−0.309510
$765$	−19.7783	−0.715085
$766$	−5.46804	−0.197568
$767$	23.6716	0.854732
$768$	−50.3125	−1.81550
$769$	−42.5038	−1.53273	−0.766363	−	0.642408i	$-0.777936\pi$
$769$	−42.5038	−1.53273	−0.766363	+	0.642408i	$0.777936\pi$
$770$	0	0
$771$	14.5222	0.523005
$772$	18.8339	0.677846
$773$	0.514790	0.0185157	0.00925786	−	0.999957i	$-0.497053\pi$
$773$	0.514790	0.0185157	0.00925786	+	0.999957i	$0.497053\pi$
$774$	−38.6010	−1.38748
$775$	−6.26825	−0.225162
$776$	−0.0644252	−0.00231273
$777$	17.8107	0.638956
$778$	35.9856	1.29014
$779$	10.2036	0.365582
$780$	−9.63782	−0.345089
$781$	0	0
$782$	−53.2908	−1.90568
$783$	−5.21509	−0.186372
$784$	−4.44549	−0.158768
$785$	22.0507	0.787025
$786$	−8.11900	−0.289595
$787$	2.53847	0.0904865	0.0452433	−	0.998976i	$-0.485594\pi$
$787$	2.53847	0.0904865	0.0452433	+	0.998976i	$0.485594\pi$
$788$	−15.1180	−0.538556
$789$	12.7703	0.454636
$790$	−17.9693	−0.639319
$791$	14.9218	0.530557
$792$	0	0
$793$	−19.6704	−0.698518
$794$	−6.12185	−0.217256
$795$	30.3718	1.07718
$796$	29.4861	1.04511
$797$	15.7444	0.557695	0.278847	−	0.960335i	$-0.410048\pi$
$797$	15.7444	0.557695	0.278847	+	0.960335i	$0.410048\pi$
$798$	26.9834	0.955202
$799$	−28.4437	−1.00627
$800$	7.61427	0.269205
$801$	−32.5241	−1.14918
$802$	26.5516	0.937569
$803$	0	0
$804$	33.9655	1.19787
$805$	5.31060	0.187174
$806$	−25.6696	−0.904173
$807$	53.1083	1.86950
$808$	−5.18476	−0.182399
$809$	−10.7422	−0.377676	−0.188838	−	0.982008i	$-0.560472\pi$
$809$	−10.7422	−0.377676	−0.188838	+	0.982008i	$0.560472\pi$
$810$	−11.4078	−0.400831
$811$	3.98623	0.139975	0.0699877	−	0.997548i	$-0.477704\pi$
$811$	3.98623	0.139975	0.0699877	+	0.997548i	$0.477704\pi$
$812$	−4.28174	−0.150259
$813$	72.1435	2.53018
$814$	0	0
$815$	19.1878	0.672118
$816$	60.1762	2.10659
$817$	−27.9380	−0.977427
$818$	36.0381	1.26004
$819$	8.07147	0.282040
$820$	3.33253	0.116377
$821$	34.9024	1.21810	0.609051	−	0.793131i	$-0.291551\pi$
$821$	34.9024	1.21810	0.609051	+	0.793131i	$0.291551\pi$
$822$	−80.9339	−2.82289
$823$	1.71816	0.0598915	0.0299457	−	0.999552i	$-0.490467\pi$
$823$	1.71816	0.0598915	0.0299457	+	0.999552i	$0.490467\pi$
$824$	−8.28918	−0.288767
$825$	0	0
$826$	−21.6455	−0.753142
$827$	−11.4733	−0.398967	−0.199484	−	0.979901i	$-0.563926\pi$
$827$	−11.4733	−0.398967	−0.199484	+	0.979901i	$0.563926\pi$
$828$	35.3378	1.22807
$829$	−29.4687	−1.02349	−0.511745	−	0.859137i	$-0.671001\pi$
$829$	−29.4687	−1.02349	−0.511745	+	0.859137i	$0.671001\pi$
$830$	4.20332	0.145899
$831$	8.11314	0.281442
$832$	12.3663	0.428723
$833$	5.18564	0.179672
$834$	66.6388	2.30751
$835$	−8.73801	−0.302391
$836$	0	0
$837$	13.3198	0.460400
$838$	−1.24757	−0.0430966
$839$	19.4945	0.673024	0.336512	−	0.941679i	$-0.390753\pi$
$839$	19.4945	0.673024	0.336512	+	0.941679i	$0.390753\pi$
$840$	−1.28985	−0.0445039
$841$	−22.9769	−0.792306
$842$	−11.9002	−0.410106
$843$	−7.27432	−0.250541
$844$	36.9475	1.27178
$845$	8.52149	0.293148
$846$	40.4833	1.39185
$847$	0	0
$848$	−51.7234	−1.77619
$849$	−76.5035	−2.62559
$850$	−10.0348	−0.344191
$851$	36.2345	1.24210
$852$	−33.6100	−1.15146
$853$	−49.0267	−1.67864	−0.839321	−	0.543636i	$-0.817047\pi$
$853$	−49.0267	−1.67864	−0.839321	+	0.543636i	$0.817047\pi$
$854$	17.9868	0.615494
$855$	20.3739	0.696773
$856$	0.591362	0.0202123
$857$	29.9707	1.02378	0.511890	−	0.859051i	$-0.328945\pi$
$857$	29.9707	1.02378	0.511890	+	0.859051i	$0.328945\pi$
$858$	0	0
$859$	−19.3492	−0.660187	−0.330093	−	0.943948i	$-0.607080\pi$
$859$	−19.3492	−0.660187	−0.330093	+	0.943948i	$0.607080\pi$
$860$	−9.12465	−0.311148
$861$	−4.98618	−0.169929
$862$	38.2532	1.30291
$863$	−55.3688	−1.88477	−0.942387	−	0.334524i	$-0.891425\pi$
$863$	−55.3688	−1.88477	−0.942387	+	0.334524i	$0.891425\pi$
$864$	−16.1800	−0.550456
$865$	0.733192	0.0249293
$866$	−61.1456	−2.07781
$867$	−25.8189	−0.876855
$868$	10.9359	0.371190
$869$	0	0
$870$	−12.3971	−0.420300
$871$	15.7831	0.534791
$872$	8.33343	0.282206
$873$	−0.497287	−0.0168306
$874$	54.8957	1.85687
$875$	1.00000	0.0338062
$876$	−30.1432	−1.01844
$877$	34.9381	1.17978	0.589888	−	0.807485i	$-0.299172\pi$
$877$	34.9381	1.17978	0.589888	+	0.807485i	$0.299172\pi$
$878$	41.4692	1.39952
$879$	−37.6325	−1.26931
$880$	0	0
$881$	49.8267	1.67870	0.839352	−	0.543589i	$-0.182935\pi$
$881$	49.8267	1.67870	0.839352	+	0.543589i	$0.182935\pi$
$882$	−7.38060	−0.248518
$883$	1.97099	0.0663290	0.0331645	−	0.999450i	$-0.489441\pi$
$883$	1.97099	0.0663290	0.0331645	+	0.999450i	$0.489441\pi$
$884$	−19.1460	−0.643951
$885$	−29.1987	−0.981503
$886$	−55.0077	−1.84802
$887$	12.2833	0.412434	0.206217	−	0.978506i	$-0.433885\pi$
$887$	12.2833	0.412434	0.206217	+	0.978506i	$0.433885\pi$
$888$	−8.80068	−0.295332
$889$	−9.45141	−0.316990
$890$	−16.5016	−0.553134
$891$	0	0
$892$	−10.5982	−0.354854
$893$	29.3003	0.980499
$894$	−85.3813	−2.85558
$895$	−7.70676	−0.257609
$896$	3.92077	0.130984
$897$	29.3368	0.979529
$898$	−28.1950	−0.940879
$899$	−15.3836	−0.513071
$900$	6.65419	0.221806
$901$	60.3351	2.01005
$902$	0	0
$903$	13.6524	0.454324
$904$	−7.37319	−0.245229
$905$	−18.2163	−0.605529
$906$	−49.9930	−1.66091
$907$	4.42343	0.146878	0.0734389	−	0.997300i	$-0.476603\pi$
$907$	4.42343	0.146878	0.0734389	+	0.997300i	$0.476603\pi$
$908$	32.7630	1.08728
$909$	−40.0202	−1.32739
$910$	4.09518	0.135754
$911$	36.9229	1.22331	0.611655	−	0.791125i	$-0.290504\pi$
$911$	36.9229	1.22331	0.611655	+	0.791125i	$0.290504\pi$
$912$	−61.9884	−2.05264
$913$	0	0
$914$	−26.1985	−0.866571
$915$	24.2633	0.802120
$916$	−15.6270	−0.516332
$917$	1.60729	0.0530774
$918$	21.3236	0.703782
$919$	13.5929	0.448388	0.224194	−	0.974544i	$-0.428025\pi$
$919$	13.5929	0.448388	0.224194	+	0.974544i	$0.428025\pi$
$920$	−2.62409	−0.0865138
$921$	25.4611	0.838973
$922$	−1.22406	−0.0403122
$923$	−15.6179	−0.514070
$924$	0	0
$925$	6.82305	0.224341
$926$	36.3654	1.19504
$927$	−63.9827	−2.10147
$928$	18.6870	0.613430
$929$	−27.7752	−0.911275	−0.455638	−	0.890165i	$-0.650589\pi$
$929$	−27.7752	−0.911275	−0.455638	+	0.890165i	$0.650589\pi$
$930$	31.6632	1.03828
$931$	−5.34181	−0.175071
$932$	−37.0931	−1.21503
$933$	−59.7192	−1.95512
$934$	9.36896	0.306562
$935$	0	0
$936$	−3.98830	−0.130362
$937$	53.2768	1.74048	0.870238	−	0.492632i	$-0.163965\pi$
$937$	53.2768	1.74048	0.870238	+	0.492632i	$0.163965\pi$
$938$	−14.4322	−0.471227
$939$	64.6483	2.10972
$940$	9.56960	0.312126
$941$	−44.2295	−1.44184	−0.720921	−	0.693018i	$-0.756281\pi$
$941$	−44.2295	−1.44184	−0.720921	+	0.693018i	$0.756281\pi$
$942$	−111.386	−3.62916
$943$	−10.1440	−0.330334
$944$	49.7257	1.61843
$945$	−2.12496	−0.0691251
$946$	0	0
$947$	−29.2344	−0.949991	−0.474996	−	0.879988i	$-0.657550\pi$
$947$	−29.2344	−0.949991	−0.474996	+	0.879988i	$0.657550\pi$
$948$	42.2899	1.37351
$949$	−14.0070	−0.454686
$950$	10.3370	0.335376
$951$	−72.6039	−2.35434
$952$	−2.56234	−0.0830461
$953$	40.1422	1.30033	0.650166	−	0.759792i	$-0.274699\pi$
$953$	40.1422	1.30033	0.650166	+	0.759792i	$0.274699\pi$
$954$	−85.8735	−2.78026
$955$	4.90357	0.158676
$956$	−36.2797	−1.17337
$957$	0	0
$958$	57.2428	1.84943
$959$	16.0222	0.517384
$960$	−15.2537	−0.492310
$961$	8.29096	0.267450
$962$	27.9416	0.900874
$963$	4.56462	0.147093
$964$	45.0983	1.45252
$965$	−10.7952	−0.347510
$966$	−26.8258	−0.863105
$967$	32.2412	1.03681	0.518404	−	0.855136i	$-0.326526\pi$
$967$	32.2412	1.03681	0.518404	+	0.855136i	$0.326526\pi$
$968$	0	0
$969$	72.3092	2.32291
$970$	−0.252306	−0.00810104
$971$	13.3210	0.427490	0.213745	−	0.976889i	$-0.431434\pi$
$971$	13.3210	0.427490	0.213745	+	0.976889i	$0.431434\pi$
$972$	37.9698	1.21788
$973$	−13.1922	−0.422924
$974$	−60.7885	−1.94779
$975$	5.52420	0.176916
$976$	−41.3206	−1.32264
$977$	−33.7803	−1.08073	−0.540364	−	0.841432i	$-0.681713\pi$
$977$	−33.7803	−1.08073	−0.540364	+	0.841432i	$0.681713\pi$
$978$	−96.9243	−3.09930
$979$	0	0
$980$	−1.74465	−0.0557309
$981$	64.3242	2.05371
$982$	−38.0203	−1.21328
$983$	6.79497	0.216726	0.108363	−	0.994111i	$-0.465439\pi$
$983$	6.79497	0.216726	0.108363	+	0.994111i	$0.465439\pi$
$984$	2.46379	0.0785426
$985$	8.66532	0.276100
$986$	−24.6274	−0.784297
$987$	−14.3181	−0.455752
$988$	19.7226	0.627460
$989$	27.7748	0.883187
$990$	0	0
$991$	38.6289	1.22709	0.613543	−	0.789661i	$-0.289744\pi$
$991$	38.6289	1.22709	0.613543	+	0.789661i	$0.289744\pi$
$992$	−47.7282	−1.51537
$993$	−50.9191	−1.61587
$994$	14.2811	0.452969
$995$	−16.9008	−0.535791
$996$	−9.89232	−0.313450
$997$	−28.5439	−0.903994	−0.451997	−	0.892019i	$-0.649288\pi$
$997$	−28.5439	−0.903994	−0.451997	+	0.892019i	$0.649288\pi$
$998$	−28.4824	−0.901595
$999$	−14.4987	−0.458720

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4235.2.a.ba.1.1	✓	5
11.10	odd	2		4235.2.a.bb.1.5	yes	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4235.2.a.ba.1.1	✓	5	1.1	even	1	trivial
4235.2.a.bb.1.5	yes	5	11.10	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 4235 = 5 \cdot 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4235.a (trivial)

\(f(q)\)	\(=\)	\(q-1.93511 q^{2} -2.61037 q^{3} +1.74465 q^{4} -1.00000 q^{5} +5.05136 q^{6} -1.00000 q^{7} +0.494123 q^{8} +3.81405 q^{9} +O(q^{10})\)	\(q-1.93511 q^{2} -2.61037 q^{3} +1.74465 q^{4} -1.00000 q^{5} +5.05136 q^{6} -1.00000 q^{7} +0.494123 q^{8} +3.81405 q^{9} +1.93511 q^{10} -4.55420 q^{12} -2.11625 q^{13} +1.93511 q^{14} +2.61037 q^{15} -4.44549 q^{16} +5.18564 q^{17} -7.38060 q^{18} -5.34181 q^{19} -1.74465 q^{20} +2.61037 q^{21} +5.31060 q^{23} -1.28985 q^{24} +1.00000 q^{25} +4.09518 q^{26} -2.12496 q^{27} -1.74465 q^{28} +2.45420 q^{29} -5.05136 q^{30} -6.26825 q^{31} +7.61427 q^{32} -10.0348 q^{34} +1.00000 q^{35} +6.65419 q^{36} +6.82305 q^{37} +10.3370 q^{38} +5.52420 q^{39} -0.494123 q^{40} -1.91014 q^{41} -5.05136 q^{42} +5.23006 q^{43} -3.81405 q^{45} -10.2766 q^{46} -5.48510 q^{47} +11.6044 q^{48} +1.00000 q^{49} -1.93511 q^{50} -13.5365 q^{51} -3.69212 q^{52} +11.6350 q^{53} +4.11204 q^{54} -0.494123 q^{56} +13.9441 q^{57} -4.74916 q^{58} -11.1856 q^{59} +4.55420 q^{60} +9.29495 q^{61} +12.1298 q^{62} -3.81405 q^{63} -5.84348 q^{64} +2.11625 q^{65} -7.45806 q^{67} +9.04715 q^{68} -13.8627 q^{69} -1.93511 q^{70} +7.38000 q^{71} +1.88461 q^{72} +6.61877 q^{73} -13.2034 q^{74} -2.61037 q^{75} -9.31961 q^{76} -10.6899 q^{78} -9.28593 q^{79} +4.44549 q^{80} -5.89519 q^{81} +3.69633 q^{82} +2.17213 q^{83} +4.55420 q^{84} -5.18564 q^{85} -10.1208 q^{86} -6.40639 q^{87} -8.52745 q^{89} +7.38060 q^{90} +2.11625 q^{91} +9.26517 q^{92} +16.3625 q^{93} +10.6143 q^{94} +5.34181 q^{95} -19.8761 q^{96} -0.130383 q^{97} -1.93511 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 2 q^{3} + 4 q^{4} - 5 q^{5} - 5 q^{6} - 5 q^{7} + 12 q^{8} + 11 q^{9}+O(q^{10}) \) 5 * q - 2 * q^3 + 4 * q^4 - 5 * q^5 - 5 * q^6 - 5 * q^7 + 12 * q^8 + 11 * q^9	\( 5 q - 2 q^{3} + 4 q^{4} - 5 q^{5} - 5 q^{6} - 5 q^{7} + 12 q^{8} + 11 q^{9} - 23 q^{12} + 10 q^{13} + 2 q^{15} + 10 q^{16} + 2 q^{17} + 5 q^{18} - 3 q^{19} - 4 q^{20} + 2 q^{21} + 3 q^{23} - 28 q^{24} + 5 q^{25} + 13 q^{26} - 11 q^{27} - 4 q^{28} + q^{29} + 5 q^{30} - 12 q^{31} + 29 q^{32} - 20 q^{34} + 5 q^{35} + 45 q^{36} + 9 q^{38} - 2 q^{39} - 12 q^{40} - 11 q^{41} + 5 q^{42} + 10 q^{43} - 11 q^{45} + 14 q^{46} + 16 q^{47} - 46 q^{48} + 5 q^{49} + 6 q^{51} + 30 q^{52} + 4 q^{53} - 34 q^{54} - 12 q^{56} + 34 q^{57} - 6 q^{58} - 32 q^{59} + 23 q^{60} + 40 q^{61} + q^{62} - 11 q^{63} + 38 q^{64} - 10 q^{65} + 7 q^{67} - 19 q^{68} - 24 q^{69} + 10 q^{71} + 72 q^{72} + 11 q^{73} - 37 q^{74} - 2 q^{75} + 3 q^{76} - 87 q^{78} + 13 q^{79} - 10 q^{80} + q^{81} + 4 q^{82} + 26 q^{83} + 23 q^{84} - 2 q^{85} - 17 q^{86} + 14 q^{87} + 5 q^{89} - 5 q^{90} - 10 q^{91} + 32 q^{92} + 3 q^{93} + 44 q^{94} + 3 q^{95} - 84 q^{96} - 5 q^{97}+O(q^{100}) \) 5 * q - 2 * q^3 + 4 * q^4 - 5 * q^5 - 5 * q^6 - 5 * q^7 + 12 * q^8 + 11 * q^9 - 23 * q^12 + 10 * q^13 + 2 * q^15 + 10 * q^16 + 2 * q^17 + 5 * q^18 - 3 * q^19 - 4 * q^20 + 2 * q^21 + 3 * q^23 - 28 * q^24 + 5 * q^25 + 13 * q^26 - 11 * q^27 - 4 * q^28 + q^29 + 5 * q^30 - 12 * q^31 + 29 * q^32 - 20 * q^34 + 5 * q^35 + 45 * q^36 + 9 * q^38 - 2 * q^39 - 12 * q^40 - 11 * q^41 + 5 * q^42 + 10 * q^43 - 11 * q^45 + 14 * q^46 + 16 * q^47 - 46 * q^48 + 5 * q^49 + 6 * q^51 + 30 * q^52 + 4 * q^53 - 34 * q^54 - 12 * q^56 + 34 * q^57 - 6 * q^58 - 32 * q^59 + 23 * q^60 + 40 * q^61 + q^62 - 11 * q^63 + 38 * q^64 - 10 * q^65 + 7 * q^67 - 19 * q^68 - 24 * q^69 + 10 * q^71 + 72 * q^72 + 11 * q^73 - 37 * q^74 - 2 * q^75 + 3 * q^76 - 87 * q^78 + 13 * q^79 - 10 * q^80 + q^81 + 4 * q^82 + 26 * q^83 + 23 * q^84 - 2 * q^85 - 17 * q^86 + 14 * q^87 + 5 * q^89 - 5 * q^90 - 10 * q^91 + 32 * q^92 + 3 * q^93 + 44 * q^94 + 3 * q^95 - 84 * q^96 - 5 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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