LMFDB - Embedded newform 4598.2.a.bx.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4598,2,Mod(1,4598)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4598, 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("4598.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4598 = 2 \cdot 11^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4598.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:	$36.7152148494$
Analytic rank:	$1$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} - 10x^{6} + 16x^{5} + 26x^{4} - 32x^{3} - 16x^{2} + 20x - 4 $ x^8 - 2x^7 - 10x^6 + 16x^5 + 26x^4 - 32x^3 - 16x^2 + 20*x - 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 418)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-2.40747$ of defining polynomial
Character	$\chi$	$=$	4598.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -3.37266 q^{3} +1.00000 q^{4} -0.689994 q^{5} +3.37266 q^{6} -0.481411 q^{7} -1.00000 q^{8} +8.37481 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -3.37266 q^{3} +1.00000 q^{4} -0.689994 q^{5} +3.37266 q^{6} -0.481411 q^{7} -1.00000 q^{8} +8.37481 q^{9} +0.689994 q^{10} -3.37266 q^{12} +3.54995 q^{13} +0.481411 q^{14} +2.32711 q^{15} +1.00000 q^{16} -5.33724 q^{17} -8.37481 q^{18} +1.00000 q^{19} -0.689994 q^{20} +1.62363 q^{21} +8.97883 q^{23} +3.37266 q^{24} -4.52391 q^{25} -3.54995 q^{26} -18.1274 q^{27} -0.481411 q^{28} -5.75032 q^{29} -2.32711 q^{30} -3.56318 q^{31} -1.00000 q^{32} +5.33724 q^{34} +0.332171 q^{35} +8.37481 q^{36} -3.61060 q^{37} -1.00000 q^{38} -11.9728 q^{39} +0.689994 q^{40} +2.97333 q^{41} -1.62363 q^{42} -2.54548 q^{43} -5.77857 q^{45} -8.97883 q^{46} +10.4385 q^{47} -3.37266 q^{48} -6.76824 q^{49} +4.52391 q^{50} +18.0007 q^{51} +3.54995 q^{52} -8.44790 q^{53} +18.1274 q^{54} +0.481411 q^{56} -3.37266 q^{57} +5.75032 q^{58} +7.38112 q^{59} +2.32711 q^{60} +11.0950 q^{61} +3.56318 q^{62} -4.03173 q^{63} +1.00000 q^{64} -2.44945 q^{65} -5.10791 q^{67} -5.33724 q^{68} -30.2825 q^{69} -0.332171 q^{70} +5.42351 q^{71} -8.37481 q^{72} -1.41839 q^{73} +3.61060 q^{74} +15.2576 q^{75} +1.00000 q^{76} +11.9728 q^{78} +4.39034 q^{79} -0.689994 q^{80} +36.0130 q^{81} -2.97333 q^{82} -11.4373 q^{83} +1.62363 q^{84} +3.68267 q^{85} +2.54548 q^{86} +19.3938 q^{87} +7.61220 q^{89} +5.77857 q^{90} -1.70899 q^{91} +8.97883 q^{92} +12.0174 q^{93} -10.4385 q^{94} -0.689994 q^{95} +3.37266 q^{96} -3.25227 q^{97} +6.76824 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} + 8 q^{4} + 2 q^{5} - 8 q^{7} - 8 q^{8} + 20 q^{9}+O(q^{10}) $ 8 * q - 8 * q^2 + 8 * q^4 + 2 * q^5 - 8 * q^7 - 8 * q^8 + 20 * q^9	$ 8 q - 8 q^{2} + 8 q^{4} + 2 q^{5} - 8 q^{7} - 8 q^{8} + 20 q^{9} - 2 q^{10} - 18 q^{13} + 8 q^{14} + 10 q^{15} + 8 q^{16} - 4 q^{17} - 20 q^{18} + 8 q^{19} + 2 q^{20} - 14 q^{21} + 12 q^{23} + 18 q^{26} - 24 q^{27} - 8 q^{28} - 14 q^{29} - 10 q^{30} - 2 q^{31} - 8 q^{32} + 4 q^{34} - 40 q^{35} + 20 q^{36} - 22 q^{37} - 8 q^{38} + 4 q^{39} - 2 q^{40} - 8 q^{41} + 14 q^{42} - 28 q^{43} - 28 q^{45} - 12 q^{46} + 6 q^{47} + 32 q^{49} + 12 q^{51} - 18 q^{52} - 24 q^{53} + 24 q^{54} + 8 q^{56} + 14 q^{58} + 46 q^{59} + 10 q^{60} + 24 q^{61} + 2 q^{62} - 30 q^{63} + 8 q^{64} + 16 q^{65} - 22 q^{67} - 4 q^{68} - 38 q^{69} + 40 q^{70} + 8 q^{71} - 20 q^{72} - 16 q^{73} + 22 q^{74} + 6 q^{75} + 8 q^{76} - 4 q^{78} - 4 q^{79} + 2 q^{80} + 28 q^{81} + 8 q^{82} - 12 q^{83} - 14 q^{84} - 48 q^{85} + 28 q^{86} - 42 q^{87} - 28 q^{89} + 28 q^{90} - 12 q^{91} + 12 q^{92} + 22 q^{93} - 6 q^{94} + 2 q^{95} - 22 q^{97} - 32 q^{98}+O(q^{100}) $ 8 * q - 8 * q^2 + 8 * q^4 + 2 * q^5 - 8 * q^7 - 8 * q^8 + 20 * q^9 - 2 * q^10 - 18 * q^13 + 8 * q^14 + 10 * q^15 + 8 * q^16 - 4 * q^17 - 20 * q^18 + 8 * q^19 + 2 * q^20 - 14 * q^21 + 12 * q^23 + 18 * q^26 - 24 * q^27 - 8 * q^28 - 14 * q^29 - 10 * q^30 - 2 * q^31 - 8 * q^32 + 4 * q^34 - 40 * q^35 + 20 * q^36 - 22 * q^37 - 8 * q^38 + 4 * q^39 - 2 * q^40 - 8 * q^41 + 14 * q^42 - 28 * q^43 - 28 * q^45 - 12 * q^46 + 6 * q^47 + 32 * q^49 + 12 * q^51 - 18 * q^52 - 24 * q^53 + 24 * q^54 + 8 * q^56 + 14 * q^58 + 46 * q^59 + 10 * q^60 + 24 * q^61 + 2 * q^62 - 30 * q^63 + 8 * q^64 + 16 * q^65 - 22 * q^67 - 4 * q^68 - 38 * q^69 + 40 * q^70 + 8 * q^71 - 20 * q^72 - 16 * q^73 + 22 * q^74 + 6 * q^75 + 8 * q^76 - 4 * q^78 - 4 * q^79 + 2 * q^80 + 28 * q^81 + 8 * q^82 - 12 * q^83 - 14 * q^84 - 48 * q^85 + 28 * q^86 - 42 * q^87 - 28 * q^89 + 28 * q^90 - 12 * q^91 + 12 * q^92 + 22 * q^93 - 6 * q^94 + 2 * q^95 - 22 * q^97 - 32 * q^98

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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−3.37266	−1.94720	−0.973602	−	0.228253i	$-0.926699\pi$
$3$	−3.37266	−1.94720	−0.973602	+	0.228253i	$0.926699\pi$
$4$	1.00000	0.500000
$5$	−0.689994	−0.308575	−0.154287	−	0.988026i	$-0.549308\pi$
$5$	−0.689994	−0.308575	−0.154287	+	0.988026i	$0.549308\pi$
$6$	3.37266	1.37688
$7$	−0.481411	−0.181956	−0.0909782	−	0.995853i	$-0.528999\pi$
$7$	−0.481411	−0.181956	−0.0909782	+	0.995853i	$0.528999\pi$
$8$	−1.00000	−0.353553
$9$	8.37481	2.79160
$10$	0.689994	0.218195
$11$	0	0
$11$	0	0
$12$	−3.37266	−0.973602
$13$	3.54995	0.984580	0.492290	−	0.870431i	$-0.336160\pi$
$13$	3.54995	0.984580	0.492290	+	0.870431i	$0.336160\pi$
$14$	0.481411	0.128663
$15$	2.32711	0.600858
$16$	1.00000	0.250000
$17$	−5.33724	−1.29447	−0.647236	−	0.762290i	$-0.724075\pi$
$17$	−5.33724	−1.29447	−0.647236	+	0.762290i	$0.724075\pi$
$18$	−8.37481	−1.97396
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−0.689994	−0.154287
$21$	1.62363	0.354306
$22$	0	0
$23$	8.97883	1.87222	0.936108	−	0.351714i	$-0.114401\pi$
$23$	8.97883	1.87222	0.936108	+	0.351714i	$0.114401\pi$
$24$	3.37266	0.688441
$25$	−4.52391	−0.904782
$26$	−3.54995	−0.696203
$27$	−18.1274	−3.48862
$28$	−0.481411	−0.0909782
$29$	−5.75032	−1.06781	−0.533904	−	0.845545i	$-0.679276\pi$
$29$	−5.75032	−1.06781	−0.533904	+	0.845545i	$0.679276\pi$
$30$	−2.32711	−0.424871
$31$	−3.56318	−0.639966	−0.319983	−	0.947423i	$-0.603677\pi$
$31$	−3.56318	−0.639966	−0.319983	+	0.947423i	$0.603677\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	5.33724	0.915329
$35$	0.332171	0.0561471
$36$	8.37481	1.39580
$37$	−3.61060	−0.593579	−0.296789	−	0.954943i	$-0.595916\pi$
$37$	−3.61060	−0.593579	−0.296789	+	0.954943i	$0.595916\pi$
$38$	−1.00000	−0.162221
$39$	−11.9728	−1.91718
$40$	0.689994	0.109098
$41$	2.97333	0.464356	0.232178	−	0.972673i	$-0.425415\pi$
$41$	2.97333	0.464356	0.232178	+	0.972673i	$0.425415\pi$
$42$	−1.62363	−0.250532
$43$	−2.54548	−0.388182	−0.194091	−	0.980984i	$-0.562176\pi$
$43$	−2.54548	−0.388182	−0.194091	+	0.980984i	$0.562176\pi$
$44$	0	0
$45$	−5.77857	−0.861418
$46$	−8.97883	−1.32386
$47$	10.4385	1.52261	0.761306	−	0.648392i	$-0.224558\pi$
$47$	10.4385	1.52261	0.761306	+	0.648392i	$0.224558\pi$
$48$	−3.37266	−0.486801
$49$	−6.76824	−0.966892
$50$	4.52391	0.639777
$51$	18.0007	2.52060
$52$	3.54995	0.492290
$53$	−8.44790	−1.16041	−0.580204	−	0.814471i	$-0.697027\pi$
$53$	−8.44790	−1.16041	−0.580204	+	0.814471i	$0.697027\pi$
$54$	18.1274	2.46682
$55$	0	0
$56$	0.481411	0.0643313
$57$	−3.37266	−0.446719
$58$	5.75032	0.755054
$59$	7.38112	0.960940	0.480470	−	0.877011i	$-0.340466\pi$
$59$	7.38112	0.960940	0.480470	+	0.877011i	$0.340466\pi$
$60$	2.32711	0.300429
$61$	11.0950	1.42057	0.710283	−	0.703916i	$-0.248567\pi$
$61$	11.0950	1.42057	0.710283	+	0.703916i	$0.248567\pi$
$62$	3.56318	0.452524
$63$	−4.03173	−0.507950
$64$	1.00000	0.125000
$65$	−2.44945	−0.303817
$66$	0	0
$67$	−5.10791	−0.624031	−0.312016	−	0.950077i	$-0.601004\pi$
$67$	−5.10791	−0.624031	−0.312016	+	0.950077i	$0.601004\pi$
$68$	−5.33724	−0.647236
$69$	−30.2825	−3.64558
$70$	−0.332171	−0.0397020
$71$	5.42351	0.643653	0.321826	−	0.946799i	$-0.395703\pi$
$71$	5.42351	0.643653	0.321826	+	0.946799i	$0.395703\pi$
$72$	−8.37481	−0.986981
$73$	−1.41839	−0.166010	−0.0830052	−	0.996549i	$-0.526452\pi$
$73$	−1.41839	−0.166010	−0.0830052	+	0.996549i	$0.526452\pi$
$74$	3.61060	0.419724
$75$	15.2576	1.76179
$76$	1.00000	0.114708
$77$	0	0
$78$	11.9728	1.35565
$79$	4.39034	0.493952	0.246976	−	0.969022i	$-0.420563\pi$
$79$	4.39034	0.493952	0.246976	+	0.969022i	$0.420563\pi$
$80$	−0.689994	−0.0771437
$81$	36.0130	4.00144
$82$	−2.97333	−0.328349
$83$	−11.4373	−1.25540	−0.627701	−	0.778454i	$-0.716004\pi$
$83$	−11.4373	−1.25540	−0.627701	+	0.778454i	$0.716004\pi$
$84$	1.62363	0.177153
$85$	3.68267	0.399441
$86$	2.54548	0.274486
$87$	19.3938	2.07924
$88$	0	0
$89$	7.61220	0.806892	0.403446	−	0.915003i	$-0.367812\pi$
$89$	7.61220	0.806892	0.403446	+	0.915003i	$0.367812\pi$
$90$	5.77857	0.609115
$91$	−1.70899	−0.179151
$92$	8.97883	0.936108
$93$	12.0174	1.24614
$94$	−10.4385	−1.07665
$95$	−0.689994	−0.0707919
$96$	3.37266	0.344220
$97$	−3.25227	−0.330218	−0.165109	−	0.986275i	$-0.552798\pi$
$97$	−3.25227	−0.330218	−0.165109	+	0.986275i	$0.552798\pi$
$98$	6.76824	0.683696
$99$	0	0
$100$	−4.52391	−0.452391
$101$	7.75446	0.771598	0.385799	−	0.922583i	$-0.373926\pi$
$101$	7.75446	0.771598	0.385799	+	0.922583i	$0.373926\pi$
$102$	−18.0007	−1.78233
$103$	1.34160	0.132192	0.0660961	−	0.997813i	$-0.478946\pi$
$103$	1.34160	0.132192	0.0660961	+	0.997813i	$0.478946\pi$
$104$	−3.54995	−0.348102
$105$	−1.12030	−0.109330
$106$	8.44790	0.820533
$107$	5.50853	0.532530	0.266265	−	0.963900i	$-0.414210\pi$
$107$	5.50853	0.532530	0.266265	+	0.963900i	$0.414210\pi$
$108$	−18.1274	−1.74431
$109$	−7.73897	−0.741259	−0.370630	−	0.928781i	$-0.620858\pi$
$109$	−7.73897	−0.741259	−0.370630	+	0.928781i	$0.620858\pi$
$110$	0	0
$111$	12.1773	1.15582
$112$	−0.481411	−0.0454891
$113$	1.87987	0.176844	0.0884218	−	0.996083i	$-0.471818\pi$
$113$	1.87987	0.176844	0.0884218	+	0.996083i	$0.471818\pi$
$114$	3.37266	0.315878
$115$	−6.19534	−0.577718
$116$	−5.75032	−0.533904
$117$	29.7302	2.74856
$118$	−7.38112	−0.679487
$119$	2.56941	0.235537
$120$	−2.32711	−0.212435
$121$	0	0
$122$	−11.0950	−1.00449
$123$	−10.0280	−0.904196
$124$	−3.56318	−0.319983
$125$	6.57144	0.587768
$126$	4.03173	0.359175
$127$	−12.5300	−1.11186	−0.555928	−	0.831230i	$-0.687637\pi$
$127$	−12.5300	−1.11186	−0.555928	+	0.831230i	$0.687637\pi$
$128$	−1.00000	−0.0883883
$129$	8.58502	0.755869
$130$	2.44945	0.214831
$131$	17.4721	1.52654	0.763272	−	0.646077i	$-0.223592\pi$
$131$	17.4721	1.52654	0.763272	+	0.646077i	$0.223592\pi$
$132$	0	0
$133$	−0.481411	−0.0417436
$134$	5.10791	0.441257
$135$	12.5078	1.07650
$136$	5.33724	0.457665
$137$	6.56176	0.560609	0.280305	−	0.959911i	$-0.409565\pi$
$137$	6.56176	0.560609	0.280305	+	0.959911i	$0.409565\pi$
$138$	30.2825	2.57782
$139$	−2.83346	−0.240331	−0.120166	−	0.992754i	$-0.538343\pi$
$139$	−2.83346	−0.240331	−0.120166	+	0.992754i	$0.538343\pi$
$140$	0.332171	0.0280736
$141$	−35.2055	−2.96484
$142$	−5.42351	−0.455131
$143$	0	0
$144$	8.37481	0.697901
$145$	3.96769	0.329499
$146$	1.41839	0.117387
$147$	22.8270	1.88274
$148$	−3.61060	−0.296789
$149$	−20.5150	−1.68065	−0.840327	−	0.542079i	$-0.817637\pi$
$149$	−20.5150	−1.68065	−0.840327	+	0.542079i	$0.817637\pi$
$150$	−15.2576	−1.24578
$151$	−3.58680	−0.291890	−0.145945	−	0.989293i	$-0.546622\pi$
$151$	−3.58680	−0.291890	−0.145945	+	0.989293i	$0.546622\pi$
$152$	−1.00000	−0.0811107
$153$	−44.6984	−3.61365
$154$	0	0
$155$	2.45858	0.197477
$156$	−11.9728	−0.958589
$157$	−3.93646	−0.314164	−0.157082	−	0.987586i	$-0.550209\pi$
$157$	−3.93646	−0.314164	−0.157082	+	0.987586i	$0.550209\pi$
$158$	−4.39034	−0.349277
$159$	28.4919	2.25955
$160$	0.689994	0.0545488
$161$	−4.32251	−0.340661
$162$	−36.0130	−2.82945
$163$	17.9571	1.40651	0.703254	−	0.710938i	$-0.251730\pi$
$163$	17.9571	1.40651	0.703254	+	0.710938i	$0.251730\pi$
$164$	2.97333	0.232178
$165$	0	0
$166$	11.4373	0.887704
$167$	6.52452	0.504883	0.252441	−	0.967612i	$-0.418767\pi$
$167$	6.52452	0.504883	0.252441	+	0.967612i	$0.418767\pi$
$168$	−1.62363	−0.125266
$169$	−0.397823	−0.0306018
$170$	−3.68267	−0.282448
$171$	8.37481	0.640438
$172$	−2.54548	−0.194091
$173$	−5.34025	−0.406012	−0.203006	−	0.979178i	$-0.565071\pi$
$173$	−5.34025	−0.406012	−0.203006	+	0.979178i	$0.565071\pi$
$174$	−19.3938	−1.47024
$175$	2.17786	0.164631
$176$	0	0
$177$	−24.8940	−1.87115
$178$	−7.61220	−0.570559
$179$	20.4311	1.52709	0.763547	−	0.645752i	$-0.223456\pi$
$179$	20.4311	1.52709	0.763547	+	0.645752i	$0.223456\pi$
$180$	−5.77857	−0.430709
$181$	0.000611695 0	4.54670e−5 0	2.27335e−5	−	1.00000i	$-0.499993\pi$
$181$	0.000611695 0	4.54670e−5 0	2.27335e−5		1.00000i	$0.499993\pi$
$182$	1.70899	0.126679
$183$	−37.4196	−2.76613
$184$	−8.97883	−0.661928
$185$	2.49129	0.183163
$186$	−12.0174	−0.881157
$187$	0	0
$188$	10.4385	0.761306
$189$	8.72672	0.634776
$190$	0.689994	0.0500575
$191$	23.7760	1.72037	0.860184	−	0.509983i	$-0.170348\pi$
$191$	23.7760	1.72037	0.860184	+	0.509983i	$0.170348\pi$
$192$	−3.37266	−0.243400
$193$	4.36281	0.314042	0.157021	−	0.987595i	$-0.449811\pi$
$193$	4.36281	0.314042	0.157021	+	0.987595i	$0.449811\pi$
$194$	3.25227	0.233500
$195$	8.26115	0.591593
$196$	−6.76824	−0.483446
$197$	13.0801	0.931917	0.465959	−	0.884807i	$-0.345710\pi$
$197$	13.0801	0.931917	0.465959	+	0.884807i	$0.345710\pi$
$198$	0	0
$199$	15.0436	1.06641	0.533205	−	0.845986i	$-0.320987\pi$
$199$	15.0436	1.06641	0.533205	+	0.845986i	$0.320987\pi$
$200$	4.52391	0.319889
$201$	17.2272	1.21512
$202$	−7.75446	−0.545602
$203$	2.76827	0.194294
$204$	18.0007	1.26030
$205$	−2.05158	−0.143289
$206$	−1.34160	−0.0934739
$207$	75.1960	5.22648
$208$	3.54995	0.246145
$209$	0	0
$210$	1.12030	0.0773079
$211$	−12.5052	−0.860896	−0.430448	−	0.902615i	$-0.641644\pi$
$211$	−12.5052	−0.860896	−0.430448	+	0.902615i	$0.641644\pi$
$212$	−8.44790	−0.580204
$213$	−18.2916	−1.25332
$214$	−5.50853	−0.376555
$215$	1.75637	0.119783
$216$	18.1274	1.23341
$217$	1.71536	0.116446
$218$	7.73897	0.524149
$219$	4.78375	0.323256
$220$	0	0
$221$	−18.9470	−1.27451
$222$	−12.1773	−0.817287
$223$	−7.13128	−0.477546	−0.238773	−	0.971075i	$-0.576745\pi$
$223$	−7.13128	−0.477546	−0.238773	+	0.971075i	$0.576745\pi$
$224$	0.481411	0.0321656
$225$	−37.8869	−2.52579
$226$	−1.87987	−0.125047
$227$	−22.0665	−1.46460	−0.732301	−	0.680981i	$-0.761554\pi$
$227$	−22.0665	−1.46460	−0.732301	+	0.680981i	$0.761554\pi$
$228$	−3.37266	−0.223360
$229$	−3.84131	−0.253841	−0.126920	−	0.991913i	$-0.540509\pi$
$229$	−3.84131	−0.253841	−0.126920	+	0.991913i	$0.540509\pi$
$230$	6.19534	0.408509
$231$	0	0
$232$	5.75032	0.377527
$233$	−28.1917	−1.84690	−0.923450	−	0.383720i	$-0.874643\pi$
$233$	−28.1917	−1.84690	−0.923450	+	0.383720i	$0.874643\pi$
$234$	−29.7302	−1.94352
$235$	−7.20251	−0.469840
$236$	7.38112	0.480470
$237$	−14.8071	−0.961826
$238$	−2.56941	−0.166550
$239$	−3.48744	−0.225584	−0.112792	−	0.993619i	$-0.535979\pi$
$239$	−3.48744	−0.225584	−0.112792	+	0.993619i	$0.535979\pi$
$240$	2.32711	0.150215
$241$	−10.3598	−0.667336	−0.333668	−	0.942691i	$-0.608286\pi$
$241$	−10.3598	−0.667336	−0.333668	+	0.942691i	$0.608286\pi$
$242$	0	0
$243$	−67.0773	−4.30301
$244$	11.0950	0.710283
$245$	4.67005	0.298359
$246$	10.0280	0.639363
$247$	3.54995	0.225878
$248$	3.56318	0.226262
$249$	38.5739	2.44452
$250$	−6.57144	−0.415615
$251$	5.01833	0.316754	0.158377	−	0.987379i	$-0.449374\pi$
$251$	5.01833	0.316754	0.158377	+	0.987379i	$0.449374\pi$
$252$	−4.03173	−0.253975
$253$	0	0
$254$	12.5300	0.786201
$255$	−12.4204	−0.777794
$256$	1.00000	0.0625000
$257$	−26.1506	−1.63123	−0.815615	−	0.578595i	$-0.803601\pi$
$257$	−26.1506	−1.63123	−0.815615	+	0.578595i	$0.803601\pi$
$258$	−8.58502	−0.534480
$259$	1.73818	0.108005
$260$	−2.44945	−0.151908
$261$	−48.1578	−2.98089
$262$	−17.4721	−1.07943
$263$	10.3332	0.637171	0.318586	−	0.947894i	$-0.396792\pi$
$263$	10.3332	0.637171	0.318586	+	0.947894i	$0.396792\pi$
$264$	0	0
$265$	5.82900	0.358073
$266$	0.481411	0.0295172
$267$	−25.6733	−1.57118
$268$	−5.10791	−0.312016
$269$	13.2646	0.808754	0.404377	−	0.914592i	$-0.367488\pi$
$269$	13.2646	0.808754	0.404377	+	0.914592i	$0.367488\pi$
$270$	−12.5078	−0.761200
$271$	−10.5064	−0.638218	−0.319109	−	0.947718i	$-0.603384\pi$
$271$	−10.5064	−0.638218	−0.319109	+	0.947718i	$0.603384\pi$
$272$	−5.33724	−0.323618
$273$	5.76383	0.348843
$274$	−6.56176	−0.396411
$275$	0	0
$276$	−30.2825	−1.82279
$277$	−29.2272	−1.75609	−0.878046	−	0.478577i	$-0.841153\pi$
$277$	−29.2272	−1.75609	−0.878046	+	0.478577i	$0.841153\pi$
$278$	2.83346	0.169940
$279$	−29.8410	−1.78653
$280$	−0.332171	−0.0198510
$281$	14.1571	0.844543	0.422272	−	0.906469i	$-0.361233\pi$
$281$	14.1571	0.844543	0.422272	+	0.906469i	$0.361233\pi$
$282$	35.2055	2.09646
$283$	−27.0388	−1.60729	−0.803645	−	0.595109i	$-0.797109\pi$
$283$	−27.0388	−1.60729	−0.803645	+	0.595109i	$0.797109\pi$
$284$	5.42351	0.321826
$285$	2.32711	0.137846
$286$	0	0
$287$	−1.43139	−0.0844926
$288$	−8.37481	−0.493490
$289$	11.4862	0.675656
$290$	−3.96769	−0.232991
$291$	10.9688	0.643002
$292$	−1.41839	−0.0830052
$293$	−18.1121	−1.05812	−0.529059	−	0.848585i	$-0.677455\pi$
$293$	−18.1121	−1.05812	−0.529059	+	0.848585i	$0.677455\pi$
$294$	−22.8270	−1.33130
$295$	−5.09293	−0.296522
$296$	3.61060	0.209862
$297$	0	0
$298$	20.5150	1.18840
$299$	31.8744	1.84335
$300$	15.2576	0.880897
$301$	1.22542	0.0706322
$302$	3.58680	0.206397
$303$	−26.1531	−1.50246
$304$	1.00000	0.0573539
$305$	−7.65547	−0.438351
$306$	44.6984	2.55524
$307$	2.68997	0.153525	0.0767624	−	0.997049i	$-0.475542\pi$
$307$	2.68997	0.153525	0.0767624	+	0.997049i	$0.475542\pi$
$308$	0	0
$309$	−4.52477	−0.257405
$310$	−2.45858	−0.139638
$311$	7.93436	0.449916	0.224958	−	0.974368i	$-0.427775\pi$
$311$	7.93436	0.449916	0.224958	+	0.974368i	$0.427775\pi$
$312$	11.9728	0.677825
$313$	−16.1969	−0.915505	−0.457752	−	0.889080i	$-0.651345\pi$
$313$	−16.1969	−0.915505	−0.457752	+	0.889080i	$0.651345\pi$
$314$	3.93646	0.222147
$315$	2.78187	0.156741
$316$	4.39034	0.246976
$317$	15.2129	0.854441	0.427221	−	0.904147i	$-0.359493\pi$
$317$	15.2129	0.854441	0.427221	+	0.904147i	$0.359493\pi$
$318$	−28.4919	−1.59774
$319$	0	0
$320$	−0.689994	−0.0385719
$321$	−18.5784	−1.03694
$322$	4.32251	0.240884
$323$	−5.33724	−0.296972
$324$	36.0130	2.00072
$325$	−16.0597	−0.890830
$326$	−17.9571	−0.994552
$327$	26.1009	1.44338
$328$	−2.97333	−0.164175
$329$	−5.02521	−0.277049
$330$	0	0
$331$	−24.0923	−1.32423	−0.662117	−	0.749400i	$-0.730342\pi$
$331$	−24.0923	−1.32423	−0.662117	+	0.749400i	$0.730342\pi$
$332$	−11.4373	−0.627701
$333$	−30.2381	−1.65704
$334$	−6.52452	−0.357006
$335$	3.52443	0.192560
$336$	1.62363	0.0885765
$337$	−1.74980	−0.0953174	−0.0476587	−	0.998864i	$-0.515176\pi$
$337$	−1.74980	−0.0953174	−0.0476587	+	0.998864i	$0.515176\pi$
$338$	0.397823	0.0216387
$339$	−6.34016	−0.344350
$340$	3.68267	0.199721
$341$	0	0
$342$	−8.37481	−0.452858
$343$	6.62819	0.357888
$344$	2.54548	0.137243
$345$	20.8948	1.12494
$346$	5.34025	0.287094
$347$	−24.0766	−1.29250	−0.646250	−	0.763126i	$-0.723664\pi$
$347$	−24.0766	−1.29250	−0.646250	+	0.763126i	$0.723664\pi$
$348$	19.3938	1.03962
$349$	27.1978	1.45586	0.727932	−	0.685649i	$-0.240482\pi$
$349$	27.1978	1.45586	0.727932	+	0.685649i	$0.240482\pi$
$350$	−2.17786	−0.116412
$351$	−64.3514	−3.43482
$352$	0	0
$353$	9.07144	0.482824	0.241412	−	0.970423i	$-0.422389\pi$
$353$	9.07144	0.482824	0.241412	+	0.970423i	$0.422389\pi$
$354$	24.8940	1.32310
$355$	−3.74219	−0.198615
$356$	7.61220	0.403446
$357$	−8.66573	−0.458639
$358$	−20.4311	−1.07982
$359$	−12.0734	−0.637210	−0.318605	−	0.947888i	$-0.603214\pi$
$359$	−12.0734	−0.637210	−0.318605	+	0.947888i	$0.603214\pi$
$360$	5.77857	0.304557
$361$	1.00000	0.0526316
$362$	−0.000611695 0	−3.21500e−5 0
$363$	0	0
$364$	−1.70899	−0.0895753
$365$	0.978684	0.0512266
$366$	37.4196	1.95595
$367$	21.5024	1.12242	0.561209	−	0.827674i	$-0.310336\pi$
$367$	21.5024	1.12242	0.561209	+	0.827674i	$0.310336\pi$
$368$	8.97883	0.468054
$369$	24.9011	1.29630
$370$	−2.49129	−0.129516
$371$	4.06691	0.211144
$372$	12.0174	0.623072
$373$	−35.0210	−1.81332	−0.906660	−	0.421863i	$-0.861376\pi$
$373$	−35.0210	−1.81332	−0.906660	+	0.421863i	$0.861376\pi$
$374$	0	0
$375$	−22.1632	−1.14450
$376$	−10.4385	−0.538325
$377$	−20.4134	−1.05134
$378$	−8.72672	−0.448854
$379$	−9.32660	−0.479075	−0.239538	−	0.970887i	$-0.576996\pi$
$379$	−9.32660	−0.479075	−0.239538	+	0.970887i	$0.576996\pi$
$380$	−0.689994	−0.0353960
$381$	42.2593	2.16501
$382$	−23.7760	−1.21648
$383$	−2.47805	−0.126622	−0.0633111	−	0.997994i	$-0.520166\pi$
$383$	−2.47805	−0.126622	−0.0633111	+	0.997994i	$0.520166\pi$
$384$	3.37266	0.172110
$385$	0	0
$386$	−4.36281	−0.222061
$387$	−21.3179	−1.08365
$388$	−3.25227	−0.165109
$389$	−8.02983	−0.407128	−0.203564	−	0.979062i	$-0.565253\pi$
$389$	−8.02983	−0.407128	−0.203564	+	0.979062i	$0.565253\pi$
$390$	−8.26115	−0.418319
$391$	−47.9222	−2.42353
$392$	6.76824	0.341848
$393$	−58.9274	−2.97249
$394$	−13.0801	−0.658965
$395$	−3.02931	−0.152421
$396$	0	0
$397$	16.4964	0.827931	0.413966	−	0.910292i	$-0.364143\pi$
$397$	16.4964	0.827931	0.413966	+	0.910292i	$0.364143\pi$
$398$	−15.0436	−0.754066
$399$	1.62363	0.0812834
$400$	−4.52391	−0.226195
$401$	6.07123	0.303183	0.151591	−	0.988443i	$-0.451560\pi$
$401$	6.07123	0.303183	0.151591	+	0.988443i	$0.451560\pi$
$402$	−17.2272	−0.859217
$403$	−12.6491	−0.630098
$404$	7.75446	0.385799
$405$	−24.8488	−1.23474
$406$	−2.76827	−0.137387
$407$	0	0
$408$	−18.0007	−0.891166
$409$	−34.3631	−1.69915	−0.849574	−	0.527470i	$-0.823141\pi$
$409$	−34.3631	−1.69915	−0.849574	+	0.527470i	$0.823141\pi$
$410$	2.05158	0.101320
$411$	−22.1306	−1.09162
$412$	1.34160	0.0660961
$413$	−3.55336	−0.174849
$414$	−75.1960	−3.69568
$415$	7.89165	0.387386
$416$	−3.54995	−0.174051
$417$	9.55629	0.467974
$418$	0	0
$419$	−12.7191	−0.621367	−0.310683	−	0.950513i	$-0.600558\pi$
$419$	−12.7191	−0.621367	−0.310683	+	0.950513i	$0.600558\pi$
$420$	−1.12030	−0.0546650
$421$	3.26505	0.159129	0.0795644	−	0.996830i	$-0.474647\pi$
$421$	3.26505	0.159129	0.0795644	+	0.996830i	$0.474647\pi$
$422$	12.5052	0.608745
$423$	87.4205	4.25053
$424$	8.44790	0.410266
$425$	24.1452	1.17121
$426$	18.2916	0.886233
$427$	−5.34125	−0.258481
$428$	5.50853	0.266265
$429$	0	0
$430$	−1.75637	−0.0846995
$431$	−22.9868	−1.10723	−0.553617	−	0.832772i	$-0.686753\pi$
$431$	−22.9868	−1.10723	−0.553617	+	0.832772i	$0.686753\pi$
$432$	−18.1274	−0.872154
$433$	25.1177	1.20708	0.603539	−	0.797333i	$-0.293757\pi$
$433$	25.1177	1.20708	0.603539	+	0.797333i	$0.293757\pi$
$434$	−1.71536	−0.0823397
$435$	−13.3816	−0.641601
$436$	−7.73897	−0.370630
$437$	8.97883	0.429516
$438$	−4.78375	−0.228577
$439$	21.0569	1.00499	0.502496	−	0.864579i	$-0.332415\pi$
$439$	21.0569	1.00499	0.502496	+	0.864579i	$0.332415\pi$
$440$	0	0
$441$	−56.6827	−2.69918
$442$	18.9470	0.901215
$443$	−35.3200	−1.67810	−0.839051	−	0.544053i	$-0.816889\pi$
$443$	−35.3200	−1.67810	−0.839051	+	0.544053i	$0.816889\pi$
$444$	12.1773	0.577909
$445$	−5.25238	−0.248987
$446$	7.13128	0.337676
$447$	69.1900	3.27258
$448$	−0.481411	−0.0227445
$449$	−40.3602	−1.90472	−0.952359	−	0.304979i	$-0.901350\pi$
$449$	−40.3602	−1.90472	−0.952359	+	0.304979i	$0.901350\pi$
$450$	37.8869	1.78600
$451$	0	0
$452$	1.87987	0.0884218
$453$	12.0971	0.568369
$454$	22.0665	1.03563
$455$	1.17919	0.0552814
$456$	3.37266	0.157939
$457$	−2.69285	−0.125966	−0.0629831	−	0.998015i	$-0.520061\pi$
$457$	−2.69285	−0.125966	−0.0629831	+	0.998015i	$0.520061\pi$
$458$	3.84131	0.179493
$459$	96.7502	4.51591
$460$	−6.19534	−0.288859
$461$	15.9820	0.744358	0.372179	−	0.928161i	$-0.378611\pi$
$461$	15.9820	0.744358	0.372179	+	0.928161i	$0.378611\pi$
$462$	0	0
$463$	2.32451	0.108029	0.0540145	−	0.998540i	$-0.482798\pi$
$463$	2.32451	0.108029	0.0540145	+	0.998540i	$0.482798\pi$
$464$	−5.75032	−0.266952
$465$	−8.29193	−0.384529
$466$	28.1917	1.30595
$467$	5.97041	0.276278	0.138139	−	0.990413i	$-0.455888\pi$
$467$	5.97041	0.276278	0.138139	+	0.990413i	$0.455888\pi$
$468$	29.7302	1.37428
$469$	2.45901	0.113546
$470$	7.20251	0.332227
$471$	13.2763	0.611740
$472$	−7.38112	−0.339744
$473$	0	0
$474$	14.8071	0.680114
$475$	−4.52391	−0.207571
$476$	2.56941	0.117769
$477$	−70.7496	−3.23940
$478$	3.48744	0.159512
$479$	36.4012	1.66321	0.831607	−	0.555364i	$-0.187421\pi$
$479$	36.4012	1.66321	0.831607	+	0.555364i	$0.187421\pi$
$480$	−2.32711	−0.106218
$481$	−12.8175	−0.584426
$482$	10.3598	0.471878
$483$	14.5783	0.663337
$484$	0	0
$485$	2.24405	0.101897
$486$	67.0773	3.04269
$487$	16.7032	0.756894	0.378447	−	0.925623i	$-0.376458\pi$
$487$	16.7032	0.756894	0.378447	+	0.925623i	$0.376458\pi$
$488$	−11.0950	−0.502246
$489$	−60.5631	−2.73876
$490$	−4.67005	−0.210971
$491$	13.0552	0.589175	0.294587	−	0.955625i	$-0.404818\pi$
$491$	13.0552	0.589175	0.294587	+	0.955625i	$0.404818\pi$
$492$	−10.0280	−0.452098
$493$	30.6908	1.38225
$494$	−3.54995	−0.159720
$495$	0	0
$496$	−3.56318	−0.159992
$497$	−2.61094	−0.117117
$498$	−38.5739	−1.72854
$499$	−35.1265	−1.57248	−0.786239	−	0.617923i	$-0.787974\pi$
$499$	−35.1265	−1.57248	−0.786239	+	0.617923i	$0.787974\pi$
$500$	6.57144	0.293884
$501$	−22.0050	−0.983110
$502$	−5.01833	−0.223979
$503$	29.8108	1.32920	0.664599	−	0.747200i	$-0.268602\pi$
$503$	29.8108	1.32920	0.664599	+	0.747200i	$0.268602\pi$
$504$	4.03173	0.179587
$505$	−5.35054	−0.238096
$506$	0	0
$507$	1.34172	0.0595879
$508$	−12.5300	−0.555928
$509$	−15.8554	−0.702777	−0.351389	−	0.936230i	$-0.614290\pi$
$509$	−15.8554	−0.702777	−0.351389	+	0.936230i	$0.614290\pi$
$510$	12.4204	0.549983
$511$	0.682831	0.0302067
$512$	−1.00000	−0.0441942
$513$	−18.1274	−0.800343
$514$	26.1506	1.15345
$515$	−0.925699	−0.0407912
$516$	8.58502	0.377935
$517$	0	0
$518$	−1.73818	−0.0763714
$519$	18.0108	0.790588
$520$	2.44945	0.107415
$521$	−27.3098	−1.19646	−0.598232	−	0.801323i	$-0.704130\pi$
$521$	−27.3098	−1.19646	−0.598232	+	0.801323i	$0.704130\pi$
$522$	48.1578	2.10781
$523$	−2.93591	−0.128378	−0.0641892	−	0.997938i	$-0.520446\pi$
$523$	−2.93591	−0.128378	−0.0641892	+	0.997938i	$0.520446\pi$
$524$	17.4721	0.763272
$525$	−7.34517	−0.320570
$526$	−10.3332	−0.450548
$527$	19.0176	0.828418
$528$	0	0
$529$	57.6193	2.50519
$530$	−5.82900	−0.253196
$531$	61.8155	2.68256
$532$	−0.481411	−0.0208718
$533$	10.5552	0.457196
$534$	25.6733	1.11099
$535$	−3.80086	−0.164325
$536$	5.10791	0.220628
$537$	−68.9071	−2.97356
$538$	−13.2646	−0.571875
$539$	0	0
$540$	12.5078	0.538249
$541$	32.8834	1.41377	0.706884	−	0.707329i	$-0.250100\pi$
$541$	32.8834	1.41377	0.706884	+	0.707329i	$0.250100\pi$
$542$	10.5064	0.451288
$543$	−0.00206304	−8.85334e−5 0
$544$	5.33724	0.228832
$545$	5.33985	0.228734
$546$	−5.76383	−0.246669
$547$	−14.3334	−0.612852	−0.306426	−	0.951895i	$-0.599133\pi$
$547$	−14.3334	−0.612852	−0.306426	+	0.951895i	$0.599133\pi$
$548$	6.56176	0.280305
$549$	92.9183	3.96566
$550$	0	0
$551$	−5.75032	−0.244972
$552$	30.2825	1.28891
$553$	−2.11356	−0.0898777
$554$	29.2272	1.24174
$555$	−8.40227	−0.356657
$556$	−2.83346	−0.120166
$557$	−28.1749	−1.19381	−0.596905	−	0.802312i	$-0.703603\pi$
$557$	−28.1749	−1.19381	−0.596905	+	0.802312i	$0.703603\pi$
$558$	29.8410	1.26327
$559$	−9.03633	−0.382196
$560$	0.332171	0.0140368
$561$	0	0
$562$	−14.1571	−0.597182
$563$	−38.7673	−1.63385	−0.816923	−	0.576747i	$-0.804322\pi$
$563$	−38.7673	−1.63385	−0.816923	+	0.576747i	$0.804322\pi$
$564$	−35.2055	−1.48242
$565$	−1.29710	−0.0545695
$566$	27.0388	1.13653
$567$	−17.3371	−0.728088
$568$	−5.42351	−0.227566
$569$	−15.8745	−0.665494	−0.332747	−	0.943016i	$-0.607976\pi$
$569$	−15.8745	−0.665494	−0.332747	+	0.943016i	$0.607976\pi$
$570$	−2.32711	−0.0974721
$571$	20.3701	0.852462	0.426231	−	0.904614i	$-0.359841\pi$
$571$	20.3701	0.852462	0.426231	+	0.904614i	$0.359841\pi$
$572$	0	0
$573$	−80.1881	−3.34991
$574$	1.43139	0.0597453
$575$	−40.6194	−1.69395
$576$	8.37481	0.348950
$577$	−3.38112	−0.140758	−0.0703789	−	0.997520i	$-0.522421\pi$
$577$	−3.38112	−0.140758	−0.0703789	+	0.997520i	$0.522421\pi$
$578$	−11.4862	−0.477761
$579$	−14.7142	−0.611503
$580$	3.96769	0.164749
$581$	5.50603	0.228428
$582$	−10.9688	−0.454671
$583$	0	0
$584$	1.41839	0.0586936
$585$	−20.5137	−0.848135
$586$	18.1121	0.748202
$587$	−9.16335	−0.378212	−0.189106	−	0.981957i	$-0.560559\pi$
$587$	−9.16335	−0.378212	−0.189106	+	0.981957i	$0.560559\pi$
$588$	22.8270	0.941368
$589$	−3.56318	−0.146818
$590$	5.09293	0.209673
$591$	−44.1146	−1.81463
$592$	−3.61060	−0.148395
$593$	−22.7485	−0.934168	−0.467084	−	0.884213i	$-0.654695\pi$
$593$	−22.7485	−0.934168	−0.467084	+	0.884213i	$0.654695\pi$
$594$	0	0
$595$	−1.77288	−0.0726809
$596$	−20.5150	−0.840327
$597$	−50.7368	−2.07652
$598$	−31.8744	−1.30344
$599$	−34.3303	−1.40270	−0.701349	−	0.712818i	$-0.747419\pi$
$599$	−34.3303	−1.40270	−0.701349	+	0.712818i	$0.747419\pi$
$600$	−15.2576	−0.622888
$601$	12.6496	0.515987	0.257994	−	0.966147i	$-0.416939\pi$
$601$	12.6496	0.515987	0.257994	+	0.966147i	$0.416939\pi$
$602$	−1.22542	−0.0499445
$603$	−42.7778	−1.74205
$604$	−3.58680	−0.145945
$605$	0	0
$606$	26.1531	1.06240
$607$	8.78502	0.356573	0.178286	−	0.983979i	$-0.442945\pi$
$607$	8.78502	0.356573	0.178286	+	0.983979i	$0.442945\pi$
$608$	−1.00000	−0.0405554
$609$	−9.33642	−0.378331
$610$	7.65547	0.309961
$611$	37.0562	1.49913
$612$	−44.6984	−1.80682
$613$	11.4054	0.460661	0.230331	−	0.973112i	$-0.426019\pi$
$613$	11.4054	0.460661	0.230331	+	0.973112i	$0.426019\pi$
$614$	−2.68997	−0.108558
$615$	6.91928	0.279012
$616$	0	0
$617$	11.1186	0.447616	0.223808	−	0.974633i	$-0.428151\pi$
$617$	11.1186	0.447616	0.223808	+	0.974633i	$0.428151\pi$
$618$	4.52477	0.182013
$619$	−18.4608	−0.742002	−0.371001	−	0.928633i	$-0.620985\pi$
$619$	−18.4608	−0.742002	−0.371001	+	0.928633i	$0.620985\pi$
$620$	2.45858	0.0987387
$621$	−162.763	−6.53144
$622$	−7.93436	−0.318139
$623$	−3.66460	−0.146819
$624$	−11.9728	−0.479295
$625$	18.0853	0.723411
$626$	16.1969	0.647360
$627$	0	0
$628$	−3.93646	−0.157082
$629$	19.2706	0.768371
$630$	−2.78187	−0.110832
$631$	−12.9830	−0.516846	−0.258423	−	0.966032i	$-0.583203\pi$
$631$	−12.9830	−0.516846	−0.258423	+	0.966032i	$0.583203\pi$
$632$	−4.39034	−0.174639
$633$	42.1759	1.67634
$634$	−15.2129	−0.604181
$635$	8.64561	0.343091
$636$	28.4919	1.12978
$637$	−24.0270	−0.951983
$638$	0	0
$639$	45.4209	1.79682
$640$	0.689994	0.0272744
$641$	−30.1532	−1.19098	−0.595490	−	0.803363i	$-0.703042\pi$
$641$	−30.1532	−1.19098	−0.595490	+	0.803363i	$0.703042\pi$
$642$	18.5784	0.733230
$643$	16.3249	0.643793	0.321896	−	0.946775i	$-0.395680\pi$
$643$	16.3249	0.643793	0.321896	+	0.946775i	$0.395680\pi$
$644$	−4.32251	−0.170331
$645$	−5.92362	−0.233242
$646$	5.33724	0.209991
$647$	−5.58327	−0.219501	−0.109751	−	0.993959i	$-0.535005\pi$
$647$	−5.58327	−0.219501	−0.109751	+	0.993959i	$0.535005\pi$
$648$	−36.0130	−1.41472
$649$	0	0
$650$	16.0597	0.629912
$651$	−5.78530	−0.226744
$652$	17.9571	0.703254
$653$	7.97061	0.311914	0.155957	−	0.987764i	$-0.450154\pi$
$653$	7.97061	0.311914	0.155957	+	0.987764i	$0.450154\pi$
$654$	−26.1009	−1.02063
$655$	−12.0556	−0.471053
$656$	2.97333	0.116089
$657$	−11.8788	−0.463435
$658$	5.02521	0.195903
$659$	−48.7876	−1.90050	−0.950248	−	0.311496i	$-0.899170\pi$
$659$	−48.7876	−1.90050	−0.950248	+	0.311496i	$0.899170\pi$
$660$	0	0
$661$	4.62199	0.179774	0.0898872	−	0.995952i	$-0.471349\pi$
$661$	4.62199	0.179774	0.0898872	+	0.995952i	$0.471349\pi$
$662$	24.0923	0.936375
$663$	63.9016	2.48173
$664$	11.4373	0.443852
$665$	0.332171	0.0128810
$666$	30.2381	1.17170
$667$	−51.6311	−1.99917
$668$	6.52452	0.252441
$669$	24.0514	0.929879
$670$	−3.52443	−0.136161
$671$	0	0
$672$	−1.62363	−0.0626331
$673$	27.4064	1.05644	0.528219	−	0.849108i	$-0.322860\pi$
$673$	27.4064	1.05644	0.528219	+	0.849108i	$0.322860\pi$
$674$	1.74980	0.0673996
$675$	82.0066	3.15643
$676$	−0.397823	−0.0153009
$677$	3.46731	0.133260	0.0666298	−	0.997778i	$-0.478775\pi$
$677$	3.46731	0.133260	0.0666298	+	0.997778i	$0.478775\pi$
$678$	6.34016	0.243493
$679$	1.56568	0.0600853
$680$	−3.68267	−0.141224
$681$	74.4226	2.85188
$682$	0	0
$683$	29.8195	1.14101	0.570506	−	0.821294i	$-0.306747\pi$
$683$	29.8195	1.14101	0.570506	+	0.821294i	$0.306747\pi$
$684$	8.37481	0.320219
$685$	−4.52758	−0.172990
$686$	−6.62819	−0.253065
$687$	12.9554	0.494280
$688$	−2.54548	−0.0970455
$689$	−29.9897	−1.14252
$690$	−20.8948	−0.795450
$691$	−7.20626	−0.274139	−0.137070	−	0.990561i	$-0.543768\pi$
$691$	−7.20626	−0.274139	−0.137070	+	0.990561i	$0.543768\pi$
$692$	−5.34025	−0.203006
$693$	0	0
$694$	24.0766	0.913935
$695$	1.95507	0.0741601
$696$	−19.3938	−0.735122
$697$	−15.8694	−0.601096
$698$	−27.1978	−1.02945
$699$	95.0809	3.59629
$700$	2.17786	0.0823154
$701$	26.1771	0.988694	0.494347	−	0.869265i	$-0.335407\pi$
$701$	26.1771	0.988694	0.494347	+	0.869265i	$0.335407\pi$
$702$	64.3514	2.42879
$703$	−3.61060	−0.136176
$704$	0	0
$705$	24.2916	0.914874
$706$	−9.07144	−0.341408
$707$	−3.73309	−0.140397
$708$	−24.8940	−0.935573
$709$	−41.9357	−1.57493	−0.787463	−	0.616361i	$-0.788606\pi$
$709$	−41.9357	−1.57493	−0.787463	+	0.616361i	$0.788606\pi$
$710$	3.74219	0.140442
$711$	36.7683	1.37892
$712$	−7.61220	−0.285279
$713$	−31.9932	−1.19815
$714$	8.66573	0.324307
$715$	0	0
$716$	20.4311	0.763547
$717$	11.7619	0.439257
$718$	12.0734	0.450575
$719$	−14.9458	−0.557385	−0.278693	−	0.960380i	$-0.589901\pi$
$719$	−14.9458	−0.557385	−0.278693	+	0.960380i	$0.589901\pi$
$720$	−5.77857	−0.215355
$721$	−0.645863	−0.0240532
$722$	−1.00000	−0.0372161
$723$	34.9402	1.29944
$724$	0.000611695 0	2.27335e−5 0
$725$	26.0139	0.966133
$726$	0	0
$727$	−17.2746	−0.640681	−0.320341	−	0.947302i	$-0.603797\pi$
$727$	−17.2746	−0.640681	−0.320341	+	0.947302i	$0.603797\pi$
$728$	1.70899	0.0633393
$729$	118.190	4.37739
$730$	−0.978684	−0.0362227
$731$	13.5858	0.502490
$732$	−37.4196	−1.38307
$733$	−10.6775	−0.394384	−0.197192	−	0.980365i	$-0.563182\pi$
$733$	−10.6775	−0.394384	−0.197192	+	0.980365i	$0.563182\pi$
$734$	−21.5024	−0.793669
$735$	−15.7505	−0.580965
$736$	−8.97883	−0.330964
$737$	0	0
$738$	−24.9011	−0.916621
$739$	9.17543	0.337524	0.168762	−	0.985657i	$-0.446023\pi$
$739$	9.17543	0.337524	0.168762	+	0.985657i	$0.446023\pi$
$740$	2.49129	0.0915817
$741$	−11.9728	−0.439831
$742$	−4.06691	−0.149301
$743$	−47.8824	−1.75664	−0.878318	−	0.478078i	$-0.841334\pi$
$743$	−47.8824	−1.75664	−0.878318	+	0.478078i	$0.841334\pi$
$744$	−12.0174	−0.440579
$745$	14.1552	0.518608
$746$	35.0210	1.28221
$747$	−95.7849	−3.50459
$748$	0	0
$749$	−2.65187	−0.0968972
$750$	22.1632	0.809286
$751$	6.08876	0.222182	0.111091	−	0.993810i	$-0.464566\pi$
$751$	6.08876	0.222182	0.111091	+	0.993810i	$0.464566\pi$
$752$	10.4385	0.380653
$753$	−16.9251	−0.616785
$754$	20.4134	0.743411
$755$	2.47487	0.0900699
$756$	8.72672	0.317388
$757$	−13.9195	−0.505912	−0.252956	−	0.967478i	$-0.581403\pi$
$757$	−13.9195	−0.505912	−0.252956	+	0.967478i	$0.581403\pi$
$758$	9.32660	0.338757
$759$	0	0
$760$	0.689994	0.0250287
$761$	−18.7638	−0.680186	−0.340093	−	0.940392i	$-0.610459\pi$
$761$	−18.7638	−0.680186	−0.340093	+	0.940392i	$0.610459\pi$
$762$	−42.2593	−1.53089
$763$	3.72563	0.134877
$764$	23.7760	0.860184
$765$	30.8416	1.11508
$766$	2.47805	0.0895354
$767$	26.2026	0.946123
$768$	−3.37266	−0.121700
$769$	11.9985	0.432677	0.216338	−	0.976318i	$-0.430589\pi$
$769$	11.9985	0.432677	0.216338	+	0.976318i	$0.430589\pi$
$770$	0	0
$771$	88.1970	3.17634
$772$	4.36281	0.157021
$773$	−15.5924	−0.560820	−0.280410	−	0.959880i	$-0.590470\pi$
$773$	−15.5924	−0.560820	−0.280410	+	0.959880i	$0.590470\pi$
$774$	21.3179	0.766256
$775$	16.1195	0.579030
$776$	3.25227	0.116750
$777$	−5.86229	−0.210309
$778$	8.02983	0.287883
$779$	2.97333	0.106531
$780$	8.26115	0.295797
$781$	0	0
$782$	47.9222	1.71369
$783$	104.238	3.72517
$784$	−6.76824	−0.241723
$785$	2.71613	0.0969430
$786$	58.9274	2.10187
$787$	−20.2661	−0.722409	−0.361205	−	0.932487i	$-0.617634\pi$
$787$	−20.2661	−0.722409	−0.361205	+	0.932487i	$0.617634\pi$
$788$	13.0801	0.465959
$789$	−34.8503	−1.24070
$790$	3.02931	0.107778
$791$	−0.904992	−0.0321778
$792$	0	0
$793$	39.3867	1.39866
$794$	−16.4964	−0.585436
$795$	−19.6592	−0.697241
$796$	15.0436	0.533205
$797$	46.8057	1.65794	0.828972	−	0.559291i	$-0.188926\pi$
$797$	46.8057	1.65794	0.828972	+	0.559291i	$0.188926\pi$
$798$	−1.62363	−0.0574760
$799$	−55.7128	−1.97098
$800$	4.52391	0.159944
$801$	63.7508	2.25252
$802$	−6.07123	−0.214382
$803$	0	0
$804$	17.2272	0.607558
$805$	2.98251	0.105120
$806$	12.6491	0.445547
$807$	−44.7368	−1.57481
$808$	−7.75446	−0.272801
$809$	−15.2078	−0.534678	−0.267339	−	0.963603i	$-0.586144\pi$
$809$	−15.2078	−0.534678	−0.267339	+	0.963603i	$0.586144\pi$
$810$	24.8488	0.873096
$811$	−49.9979	−1.75566	−0.877832	−	0.478968i	$-0.841011\pi$
$811$	−49.9979	−1.75566	−0.877832	+	0.478968i	$0.841011\pi$
$812$	2.76827	0.0971472
$813$	35.4345	1.24274
$814$	0	0
$815$	−12.3903	−0.434013
$816$	18.0007	0.630150
$817$	−2.54548	−0.0890550
$818$	34.3631	1.20148
$819$	−14.3124	−0.500117
$820$	−2.05158	−0.0716443
$821$	−33.5639	−1.17139	−0.585695	−	0.810532i	$-0.699178\pi$
$821$	−33.5639	−1.17139	−0.585695	+	0.810532i	$0.699178\pi$
$822$	22.1306	0.771892
$823$	−9.53996	−0.332542	−0.166271	−	0.986080i	$-0.553173\pi$
$823$	−9.53996	−0.332542	−0.166271	+	0.986080i	$0.553173\pi$
$824$	−1.34160	−0.0467370
$825$	0	0
$826$	3.55336	0.123637
$827$	3.98579	0.138600	0.0692998	−	0.997596i	$-0.477924\pi$
$827$	3.98579	0.138600	0.0692998	+	0.997596i	$0.477924\pi$
$828$	75.1960	2.61324
$829$	2.43722	0.0846480	0.0423240	−	0.999104i	$-0.486524\pi$
$829$	2.43722	0.0846480	0.0423240	+	0.999104i	$0.486524\pi$
$830$	−7.89165	−0.273923
$831$	98.5732	3.41947
$832$	3.54995	0.123073
$833$	36.1238	1.25161
$834$	−9.55629	−0.330907
$835$	−4.50188	−0.155794
$836$	0	0
$837$	64.5911	2.23260
$838$	12.7191	0.439373
$839$	39.0836	1.34932	0.674658	−	0.738131i	$-0.264291\pi$
$839$	39.0836	1.34932	0.674658	+	0.738131i	$0.264291\pi$
$840$	1.12030	0.0386540
$841$	4.06617	0.140213
$842$	−3.26505	−0.112521
$843$	−47.7471	−1.64450
$844$	−12.5052	−0.430448
$845$	0.274496	0.00944294
$846$	−87.4205	−3.00558
$847$	0	0
$848$	−8.44790	−0.290102
$849$	91.1926	3.12972
$850$	−24.1452	−0.828173
$851$	−32.4189	−1.11131
$852$	−18.2916	−0.626661
$853$	31.1322	1.06595	0.532973	−	0.846132i	$-0.321075\pi$
$853$	31.1322	1.06595	0.532973	+	0.846132i	$0.321075\pi$
$854$	5.34125	0.182774
$855$	−5.77857	−0.197623
$856$	−5.50853	−0.188278
$857$	37.3236	1.27495	0.637476	−	0.770470i	$-0.279979\pi$
$857$	37.3236	1.27495	0.637476	+	0.770470i	$0.279979\pi$
$858$	0	0
$859$	−17.9737	−0.613255	−0.306628	−	0.951830i	$-0.599201\pi$
$859$	−17.9737	−0.613255	−0.306628	+	0.951830i	$0.599201\pi$
$860$	1.75637	0.0598916
$861$	4.82760	0.164524
$862$	22.9868	0.782932
$863$	45.4858	1.54836	0.774178	−	0.632968i	$-0.218164\pi$
$863$	45.4858	1.54836	0.774178	+	0.632968i	$0.218164\pi$
$864$	18.1274	0.616706
$865$	3.68474	0.125285
$866$	−25.1177	−0.853534
$867$	−38.7388	−1.31564
$868$	1.71536	0.0582230
$869$	0	0
$870$	13.3816	0.453680
$871$	−18.1329	−0.614409
$872$	7.73897	0.262075
$873$	−27.2372	−0.921839
$874$	−8.97883	−0.303713
$875$	−3.16357	−0.106948
$876$	4.78375	0.161628
$877$	−45.9405	−1.55130	−0.775650	−	0.631163i	$-0.782578\pi$
$877$	−45.9405	−1.55130	−0.775650	+	0.631163i	$0.782578\pi$
$878$	−21.0569	−0.710637
$879$	61.0857	2.06037
$880$	0	0
$881$	37.6433	1.26823	0.634117	−	0.773237i	$-0.281364\pi$
$881$	37.6433	1.26823	0.634117	+	0.773237i	$0.281364\pi$
$882$	56.6827	1.90861
$883$	−12.8430	−0.432203	−0.216101	−	0.976371i	$-0.569334\pi$
$883$	−12.8430	−0.432203	−0.216101	+	0.976371i	$0.569334\pi$
$884$	−18.9470	−0.637255
$885$	17.1767	0.577389
$886$	35.3200	1.18660
$887$	50.8087	1.70599	0.852995	−	0.521919i	$-0.174784\pi$
$887$	50.8087	1.70599	0.852995	+	0.521919i	$0.174784\pi$
$888$	−12.1773	−0.408644
$889$	6.03207	0.202309
$890$	5.25238	0.176060
$891$	0	0
$892$	−7.13128	−0.238773
$893$	10.4385	0.349311
$894$	−69.1900	−2.31406
$895$	−14.0974	−0.471223
$896$	0.481411	0.0160828
$897$	−107.501	−3.58937
$898$	40.3602	1.34684
$899$	20.4894	0.683361
$900$	−37.8869	−1.26290
$901$	45.0885	1.50212
$902$	0	0
$903$	−4.13293	−0.137535
$904$	−1.87987	−0.0625236
$905$	−0.000422066 0	−1.40300e−5 0
$906$	−12.0971	−0.401898
$907$	−28.1948	−0.936194	−0.468097	−	0.883677i	$-0.655060\pi$
$907$	−28.1948	−0.936194	−0.468097	+	0.883677i	$0.655060\pi$
$908$	−22.0665	−0.732301
$909$	64.9421	2.15399
$910$	−1.17919	−0.0390898
$911$	23.8832	0.791286	0.395643	−	0.918404i	$-0.370522\pi$
$911$	23.8832	0.791286	0.395643	+	0.918404i	$0.370522\pi$
$912$	−3.37266	−0.111680
$913$	0	0
$914$	2.69285	0.0890716
$915$	25.8193	0.853559
$916$	−3.84131	−0.126920
$917$	−8.41126	−0.277764
$918$	−96.7502	−3.19323
$919$	−30.5252	−1.00693	−0.503466	−	0.864015i	$-0.667942\pi$
$919$	−30.5252	−1.00693	−0.503466	+	0.864015i	$0.667942\pi$
$920$	6.19534	0.204254
$921$	−9.07235	−0.298944
$922$	−15.9820	−0.526341
$923$	19.2532	0.633728
$924$	0	0
$925$	16.3340	0.537059
$926$	−2.32451	−0.0763881
$927$	11.2357	0.369028
$928$	5.75032	0.188763
$929$	31.8902	1.04628	0.523142	−	0.852246i	$-0.324760\pi$
$929$	31.8902	1.04628	0.523142	+	0.852246i	$0.324760\pi$
$930$	8.29193	0.271903
$931$	−6.76824	−0.221820
$932$	−28.1917	−0.923450
$933$	−26.7599	−0.876078
$934$	−5.97041	−0.195358
$935$	0	0
$936$	−29.7302	−0.971762
$937$	−6.68941	−0.218534	−0.109267	−	0.994012i	$-0.534850\pi$
$937$	−6.68941	−0.218534	−0.109267	+	0.994012i	$0.534850\pi$
$938$	−2.45901	−0.0802894
$939$	54.6267	1.78267
$940$	−7.20251	−0.234920
$941$	15.8836	0.517792	0.258896	−	0.965905i	$-0.416641\pi$
$941$	15.8836	0.517792	0.258896	+	0.965905i	$0.416641\pi$
$942$	−13.2763	−0.432566
$943$	26.6970	0.869375
$944$	7.38112	0.240235
$945$	−6.02139	−0.195876
$946$	0	0
$947$	−33.3786	−1.08466	−0.542329	−	0.840166i	$-0.682457\pi$
$947$	−33.3786	−1.08466	−0.542329	+	0.840166i	$0.682457\pi$
$948$	−14.8071	−0.480913
$949$	−5.03523	−0.163451
$950$	4.52391	0.146775
$951$	−51.3079	−1.66377
$952$	−2.56941	−0.0832750
$953$	10.4220	0.337603	0.168802	−	0.985650i	$-0.446010\pi$
$953$	10.4220	0.337603	0.168802	+	0.985650i	$0.446010\pi$
$954$	70.7496	2.29060
$955$	−16.4053	−0.530862
$956$	−3.48744	−0.112792
$957$	0	0
$958$	−36.4012	−1.17607
$959$	−3.15891	−0.102006
$960$	2.32711	0.0751073
$961$	−18.3037	−0.590443
$962$	12.8175	0.413252
$963$	46.1329	1.48661
$964$	−10.3598	−0.333668
$965$	−3.01031	−0.0969054
$966$	−14.5783	−0.469050
$967$	−1.09451	−0.0351972	−0.0175986	−	0.999845i	$-0.505602\pi$
$967$	−1.09451	−0.0351972	−0.0175986	+	0.999845i	$0.505602\pi$
$968$	0	0
$969$	18.0007	0.578265
$970$	−2.24405	−0.0720521
$971$	42.3231	1.35821	0.679106	−	0.734040i	$-0.262367\pi$
$971$	42.3231	1.35821	0.679106	+	0.734040i	$0.262367\pi$
$972$	−67.0773	−2.15150
$973$	1.36406	0.0437298
$974$	−16.7032	−0.535205
$975$	54.1637	1.73463
$976$	11.0950	0.355142
$977$	−2.58181	−0.0825996	−0.0412998	−	0.999147i	$-0.513150\pi$
$977$	−2.58181	−0.0825996	−0.0412998	+	0.999147i	$0.513150\pi$
$978$	60.5631	1.93659
$979$	0	0
$980$	4.67005	0.149179
$981$	−64.8124	−2.06930
$982$	−13.0552	−0.416609
$983$	−33.2910	−1.06182	−0.530909	−	0.847429i	$-0.678149\pi$
$983$	−33.2910	−1.06182	−0.530909	+	0.847429i	$0.678149\pi$
$984$	10.0280	0.319682
$985$	−9.02518	−0.287566
$986$	−30.6908	−0.977396
$987$	16.9483	0.539471
$988$	3.54995	0.112939
$989$	−22.8554	−0.726760
$990$	0	0
$991$	6.33308	0.201177	0.100588	−	0.994928i	$-0.467927\pi$
$991$	6.33308	0.201177	0.100588	+	0.994928i	$0.467927\pi$
$992$	3.56318	0.113131
$993$	81.2551	2.57855
$994$	2.61094	0.0828140
$995$	−10.3800	−0.329068
$996$	38.5739	1.22226
$997$	−49.9406	−1.58163	−0.790817	−	0.612052i	$-0.790344\pi$
$997$	−49.9406	−1.58163	−0.790817	+	0.612052i	$0.790344\pi$
$998$	35.1265	1.11191
$999$	65.4507	2.07077

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4598.2.a.bx.1.1		8
11.7	odd	10		418.2.f.f.115.4	✓	16
11.8	odd	10		418.2.f.f.229.4	yes	16
11.10	odd	2		4598.2.a.ca.1.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.f.f.115.4	✓	16	11.7	odd	10
418.2.f.f.229.4	yes	16	11.8	odd	10
4598.2.a.bx.1.1		8	1.1	even	1	trivial
4598.2.a.ca.1.1		8	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:	\( N \)	\(=\)	\( 4598 = 2 \cdot 11^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4598.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -3.37266 q^{3} +1.00000 q^{4} -0.689994 q^{5} +3.37266 q^{6} -0.481411 q^{7} -1.00000 q^{8} +8.37481 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -3.37266 q^{3} +1.00000 q^{4} -0.689994 q^{5} +3.37266 q^{6} -0.481411 q^{7} -1.00000 q^{8} +8.37481 q^{9} +0.689994 q^{10} -3.37266 q^{12} +3.54995 q^{13} +0.481411 q^{14} +2.32711 q^{15} +1.00000 q^{16} -5.33724 q^{17} -8.37481 q^{18} +1.00000 q^{19} -0.689994 q^{20} +1.62363 q^{21} +8.97883 q^{23} +3.37266 q^{24} -4.52391 q^{25} -3.54995 q^{26} -18.1274 q^{27} -0.481411 q^{28} -5.75032 q^{29} -2.32711 q^{30} -3.56318 q^{31} -1.00000 q^{32} +5.33724 q^{34} +0.332171 q^{35} +8.37481 q^{36} -3.61060 q^{37} -1.00000 q^{38} -11.9728 q^{39} +0.689994 q^{40} +2.97333 q^{41} -1.62363 q^{42} -2.54548 q^{43} -5.77857 q^{45} -8.97883 q^{46} +10.4385 q^{47} -3.37266 q^{48} -6.76824 q^{49} +4.52391 q^{50} +18.0007 q^{51} +3.54995 q^{52} -8.44790 q^{53} +18.1274 q^{54} +0.481411 q^{56} -3.37266 q^{57} +5.75032 q^{58} +7.38112 q^{59} +2.32711 q^{60} +11.0950 q^{61} +3.56318 q^{62} -4.03173 q^{63} +1.00000 q^{64} -2.44945 q^{65} -5.10791 q^{67} -5.33724 q^{68} -30.2825 q^{69} -0.332171 q^{70} +5.42351 q^{71} -8.37481 q^{72} -1.41839 q^{73} +3.61060 q^{74} +15.2576 q^{75} +1.00000 q^{76} +11.9728 q^{78} +4.39034 q^{79} -0.689994 q^{80} +36.0130 q^{81} -2.97333 q^{82} -11.4373 q^{83} +1.62363 q^{84} +3.68267 q^{85} +2.54548 q^{86} +19.3938 q^{87} +7.61220 q^{89} +5.77857 q^{90} -1.70899 q^{91} +8.97883 q^{92} +12.0174 q^{93} -10.4385 q^{94} -0.689994 q^{95} +3.37266 q^{96} -3.25227 q^{97} +6.76824 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} + 8 q^{4} + 2 q^{5} - 8 q^{7} - 8 q^{8} + 20 q^{9}+O(q^{10}) \) 8 * q - 8 * q^2 + 8 * q^4 + 2 * q^5 - 8 * q^7 - 8 * q^8 + 20 * q^9	\( 8 q - 8 q^{2} + 8 q^{4} + 2 q^{5} - 8 q^{7} - 8 q^{8} + 20 q^{9} - 2 q^{10} - 18 q^{13} + 8 q^{14} + 10 q^{15} + 8 q^{16} - 4 q^{17} - 20 q^{18} + 8 q^{19} + 2 q^{20} - 14 q^{21} + 12 q^{23} + 18 q^{26} - 24 q^{27} - 8 q^{28} - 14 q^{29} - 10 q^{30} - 2 q^{31} - 8 q^{32} + 4 q^{34} - 40 q^{35} + 20 q^{36} - 22 q^{37} - 8 q^{38} + 4 q^{39} - 2 q^{40} - 8 q^{41} + 14 q^{42} - 28 q^{43} - 28 q^{45} - 12 q^{46} + 6 q^{47} + 32 q^{49} + 12 q^{51} - 18 q^{52} - 24 q^{53} + 24 q^{54} + 8 q^{56} + 14 q^{58} + 46 q^{59} + 10 q^{60} + 24 q^{61} + 2 q^{62} - 30 q^{63} + 8 q^{64} + 16 q^{65} - 22 q^{67} - 4 q^{68} - 38 q^{69} + 40 q^{70} + 8 q^{71} - 20 q^{72} - 16 q^{73} + 22 q^{74} + 6 q^{75} + 8 q^{76} - 4 q^{78} - 4 q^{79} + 2 q^{80} + 28 q^{81} + 8 q^{82} - 12 q^{83} - 14 q^{84} - 48 q^{85} + 28 q^{86} - 42 q^{87} - 28 q^{89} + 28 q^{90} - 12 q^{91} + 12 q^{92} + 22 q^{93} - 6 q^{94} + 2 q^{95} - 22 q^{97} - 32 q^{98}+O(q^{100}) \) 8 * q - 8 * q^2 + 8 * q^4 + 2 * q^5 - 8 * q^7 - 8 * q^8 + 20 * q^9 - 2 * q^10 - 18 * q^13 + 8 * q^14 + 10 * q^15 + 8 * q^16 - 4 * q^17 - 20 * q^18 + 8 * q^19 + 2 * q^20 - 14 * q^21 + 12 * q^23 + 18 * q^26 - 24 * q^27 - 8 * q^28 - 14 * q^29 - 10 * q^30 - 2 * q^31 - 8 * q^32 + 4 * q^34 - 40 * q^35 + 20 * q^36 - 22 * q^37 - 8 * q^38 + 4 * q^39 - 2 * q^40 - 8 * q^41 + 14 * q^42 - 28 * q^43 - 28 * q^45 - 12 * q^46 + 6 * q^47 + 32 * q^49 + 12 * q^51 - 18 * q^52 - 24 * q^53 + 24 * q^54 + 8 * q^56 + 14 * q^58 + 46 * q^59 + 10 * q^60 + 24 * q^61 + 2 * q^62 - 30 * q^63 + 8 * q^64 + 16 * q^65 - 22 * q^67 - 4 * q^68 - 38 * q^69 + 40 * q^70 + 8 * q^71 - 20 * q^72 - 16 * q^73 + 22 * q^74 + 6 * q^75 + 8 * q^76 - 4 * q^78 - 4 * q^79 + 2 * q^80 + 28 * q^81 + 8 * q^82 - 12 * q^83 - 14 * q^84 - 48 * q^85 + 28 * q^86 - 42 * q^87 - 28 * q^89 + 28 * q^90 - 12 * q^91 + 12 * q^92 + 22 * q^93 - 6 * q^94 + 2 * q^95 - 22 * q^97 - 32 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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