LMFDB - Embedded newform 538.2.a.e.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [538,2,Mod(1,538)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(538, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("538.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 538 = 2 \cdot 269 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	538.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:	$4.29595162874$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - x^{6} - 15x^{5} + 16x^{4} + 49x^{3} - 53x^{2} - 44x + 48 $ x^7 - x^6 - 15x^5 + 16x^4 + 49x^3 - 53x^2 - 44*x + 48
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$-1.59223$ of defining polynomial
Character	$\chi$	$=$	538.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{2} +2.97499 q^{3} +1.00000 q^{4} +0.0316474 q^{5} +2.97499 q^{6} +1.08414 q^{7} +1.00000 q^{8} +5.85056 q^{9} +0.0316474 q^{10} -1.58058 q^{11} +2.97499 q^{12} -6.36076 q^{13} +1.08414 q^{14} +0.0941507 q^{15} +1.00000 q^{16} -5.53705 q^{17} +5.85056 q^{18} -3.17629 q^{19} +0.0316474 q^{20} +3.22531 q^{21} -1.58058 q^{22} -3.94998 q^{23} +2.97499 q^{24} -4.99900 q^{25} -6.36076 q^{26} +8.48039 q^{27} +1.08414 q^{28} +9.05434 q^{29} +0.0941507 q^{30} +6.51774 q^{31} +1.00000 q^{32} -4.70222 q^{33} -5.53705 q^{34} +0.0343103 q^{35} +5.85056 q^{36} +1.75269 q^{37} -3.17629 q^{38} -18.9232 q^{39} +0.0316474 q^{40} +1.61479 q^{41} +3.22531 q^{42} +11.5998 q^{43} -1.58058 q^{44} +0.185155 q^{45} -3.94998 q^{46} +7.88668 q^{47} +2.97499 q^{48} -5.82464 q^{49} -4.99900 q^{50} -16.4727 q^{51} -6.36076 q^{52} +9.57824 q^{53} +8.48039 q^{54} -0.0500214 q^{55} +1.08414 q^{56} -9.44943 q^{57} +9.05434 q^{58} -12.9416 q^{59} +0.0941507 q^{60} -6.40058 q^{61} +6.51774 q^{62} +6.34284 q^{63} +1.00000 q^{64} -0.201302 q^{65} -4.70222 q^{66} -3.38476 q^{67} -5.53705 q^{68} -11.7511 q^{69} +0.0343103 q^{70} +7.13600 q^{71} +5.85056 q^{72} -3.40593 q^{73} +1.75269 q^{74} -14.8720 q^{75} -3.17629 q^{76} -1.71358 q^{77} -18.9232 q^{78} +8.96616 q^{79} +0.0316474 q^{80} +7.67738 q^{81} +1.61479 q^{82} +7.05816 q^{83} +3.22531 q^{84} -0.175233 q^{85} +11.5998 q^{86} +26.9366 q^{87} -1.58058 q^{88} +11.3958 q^{89} +0.185155 q^{90} -6.89596 q^{91} -3.94998 q^{92} +19.3902 q^{93} +7.88668 q^{94} -0.100521 q^{95} +2.97499 q^{96} -7.66892 q^{97} -5.82464 q^{98} -9.24730 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 7 q^{2} + q^{3} + 7 q^{4} + 7 q^{5} + q^{6} + 6 q^{7} + 7 q^{8} + 12 q^{9} + 7 q^{10} - 3 q^{11} + q^{12} - 9 q^{13} + 6 q^{14} + 8 q^{15} + 7 q^{16} + 8 q^{17} + 12 q^{18} - 11 q^{19} + 7 q^{20}+ \cdots - 37 q^{99}+O(q^{100}) $ 7 * q + 7 * q^2 + q^3 + 7 * q^4 + 7 * q^5 + q^6 + 6 * q^7 + 7 * q^8 + 12 * q^9 + 7 * q^10 - 3 * q^11 + q^12 - 9 * q^13 + 6 * q^14 + 8 * q^15 + 7 * q^16 + 8 * q^17 + 12 * q^18 - 11 * q^19 + 7 * q^20 - 6 * q^21 - 3 * q^22 + 12 * q^23 + q^24 + 22 * q^25 - 9 * q^26 - 14 * q^27 + 6 * q^28 - 5 * q^29 + 8 * q^30 + 14 * q^31 + 7 * q^32 - 4 * q^33 + 8 * q^34 - 4 * q^35 + 12 * q^36 + 13 * q^37 - 11 * q^38 - 18 * q^39 + 7 * q^40 + 12 * q^41 - 6 * q^42 - 11 * q^43 - 3 * q^44 + 3 * q^45 + 12 * q^46 + 2 * q^47 + q^48 + 15 * q^49 + 22 * q^50 - 26 * q^51 - 9 * q^52 + 19 * q^53 - 14 * q^54 - 40 * q^55 + 6 * q^56 - 12 * q^57 - 5 * q^58 - 9 * q^59 + 8 * q^60 - 3 * q^61 + 14 * q^62 - 26 * q^63 + 7 * q^64 - 10 * q^65 - 4 * q^66 - 33 * q^67 + 8 * q^68 - 64 * q^69 - 4 * q^70 + 28 * q^71 + 12 * q^72 - 14 * q^73 + 13 * q^74 - 45 * q^75 - 11 * q^76 + 10 * q^77 - 18 * q^78 + 2 * q^79 + 7 * q^80 + 15 * q^81 + 12 * q^82 - 7 * q^83 - 6 * q^84 - 16 * q^85 - 11 * q^86 + 16 * q^87 - 3 * q^88 + 18 * q^89 + 3 * q^90 - 26 * q^91 + 12 * q^92 + 6 * q^93 + 2 * q^94 - 34 * q^95 + q^96 - 4 * q^97 + 15 * q^98 - 37 * q^99

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
$3$	2.97499	1.71761	0.858805	−	0.512302i	$-0.171207\pi$
$3$	2.97499	1.71761	0.858805	+	0.512302i	$0.171207\pi$
$4$	1.00000	0.500000
$5$	0.0316474	0.0141532	0.00707658	−	0.999975i	$-0.497747\pi$
$5$	0.0316474	0.0141532	0.00707658	+	0.999975i	$0.497747\pi$
$6$	2.97499	1.21453
$7$	1.08414	0.409767	0.204884	−	0.978786i	$-0.434318\pi$
$7$	1.08414	0.409767	0.204884	+	0.978786i	$0.434318\pi$
$8$	1.00000	0.353553
$9$	5.85056	1.95019
$10$	0.0316474	0.0100078
$11$	−1.58058	−0.476564	−0.238282	−	0.971196i	$-0.576584\pi$
$11$	−1.58058	−0.476564	−0.238282	+	0.971196i	$0.576584\pi$
$12$	2.97499	0.858805
$13$	−6.36076	−1.76416	−0.882078	−	0.471103i	$-0.843856\pi$
$13$	−6.36076	−1.76416	−0.882078	+	0.471103i	$0.843856\pi$
$14$	1.08414	0.289749
$15$	0.0941507	0.0243096
$16$	1.00000	0.250000
$17$	−5.53705	−1.34293	−0.671466	−	0.741036i	$-0.734335\pi$
$17$	−5.53705	−1.34293	−0.671466	+	0.741036i	$0.734335\pi$
$18$	5.85056	1.37899
$19$	−3.17629	−0.728691	−0.364346	−	0.931264i	$-0.618707\pi$
$19$	−3.17629	−0.728691	−0.364346	+	0.931264i	$0.618707\pi$
$20$	0.0316474	0.00707658
$21$	3.22531	0.703820
$22$	−1.58058	−0.336981
$23$	−3.94998	−0.823627	−0.411814	−	0.911268i	$-0.635105\pi$
$23$	−3.94998	−0.823627	−0.411814	+	0.911268i	$0.635105\pi$
$24$	2.97499	0.607267
$25$	−4.99900	−0.999800
$26$	−6.36076	−1.24745
$27$	8.48039	1.63205
$28$	1.08414	0.204884
$29$	9.05434	1.68135	0.840674	−	0.541542i	$-0.182159\pi$
$29$	9.05434	1.68135	0.840674	+	0.541542i	$0.182159\pi$
$30$	0.0941507	0.0171895
$31$	6.51774	1.17062	0.585310	−	0.810809i	$-0.300973\pi$
$31$	6.51774	1.17062	0.585310	+	0.810809i	$0.300973\pi$
$32$	1.00000	0.176777
$33$	−4.70222	−0.818551
$34$	−5.53705	−0.949596
$35$	0.0343103	0.00579950
$36$	5.85056	0.975094
$37$	1.75269	0.288141	0.144070	−	0.989567i	$-0.453981\pi$
$37$	1.75269	0.288141	0.144070	+	0.989567i	$0.453981\pi$
$38$	−3.17629	−0.515262
$39$	−18.9232	−3.03013
$40$	0.0316474	0.00500390
$41$	1.61479	0.252188	0.126094	−	0.992018i	$-0.459756\pi$
$41$	1.61479	0.252188	0.126094	+	0.992018i	$0.459756\pi$
$42$	3.22531	0.497676
$43$	11.5998	1.76895	0.884476	−	0.466585i	$-0.154516\pi$
$43$	11.5998	1.76895	0.884476	+	0.466585i	$0.154516\pi$
$44$	−1.58058	−0.238282
$45$	0.185155	0.0276013
$46$	−3.94998	−0.582393
$47$	7.88668	1.15039	0.575196	−	0.818016i	$-0.304926\pi$
$47$	7.88668	1.15039	0.575196	+	0.818016i	$0.304926\pi$
$48$	2.97499	0.429403
$49$	−5.82464	−0.832091
$50$	−4.99900	−0.706965
$51$	−16.4727	−2.30663
$52$	−6.36076	−0.882078
$53$	9.57824	1.31567	0.657836	−	0.753161i	$-0.271472\pi$
$53$	9.57824	1.31567	0.657836	+	0.753161i	$0.271472\pi$
$54$	8.48039	1.15403
$55$	−0.0500214	−0.00674488
$56$	1.08414	0.144875
$57$	−9.44943	−1.25161
$58$	9.05434	1.18889
$59$	−12.9416	−1.68485	−0.842424	−	0.538816i	$-0.818872\pi$
$59$	−12.9416	−1.68485	−0.842424	+	0.538816i	$0.818872\pi$
$60$	0.0941507	0.0121548
$61$	−6.40058	−0.819510	−0.409755	−	0.912196i	$-0.634386\pi$
$61$	−6.40058	−0.819510	−0.409755	+	0.912196i	$0.634386\pi$
$62$	6.51774	0.827754
$63$	6.34284	0.799123
$64$	1.00000	0.125000
$65$	−0.201302	−0.0249684
$66$	−4.70222	−0.578803
$67$	−3.38476	−0.413514	−0.206757	−	0.978392i	$-0.566291\pi$
$67$	−3.38476	−0.413514	−0.206757	+	0.978392i	$0.566291\pi$
$68$	−5.53705	−0.671466
$69$	−11.7511	−1.41467
$70$	0.0343103	0.00410086
$71$	7.13600	0.846888	0.423444	−	0.905922i	$-0.360821\pi$
$71$	7.13600	0.846888	0.423444	+	0.905922i	$0.360821\pi$
$72$	5.85056	0.689495
$73$	−3.40593	−0.398634	−0.199317	−	0.979935i	$-0.563872\pi$
$73$	−3.40593	−0.398634	−0.199317	+	0.979935i	$0.563872\pi$
$74$	1.75269	0.203746
$75$	−14.8720	−1.71727
$76$	−3.17629	−0.364346
$77$	−1.71358	−0.195280
$78$	−18.9232	−2.14263
$79$	8.96616	1.00877	0.504386	−	0.863478i	$-0.331719\pi$
$79$	8.96616	1.00877	0.504386	+	0.863478i	$0.331719\pi$
$80$	0.0316474	0.00353829
$81$	7.67738	0.853043
$82$	1.61479	0.178324
$83$	7.05816	0.774734	0.387367	−	0.921926i	$-0.373385\pi$
$83$	7.05816	0.774734	0.387367	+	0.921926i	$0.373385\pi$
$84$	3.22531	0.351910
$85$	−0.175233	−0.0190067
$86$	11.5998	1.25084
$87$	26.9366	2.88790
$88$	−1.58058	−0.168491
$89$	11.3958	1.20795	0.603976	−	0.797002i	$-0.293582\pi$
$89$	11.3958	1.20795	0.603976	+	0.797002i	$0.293582\pi$
$90$	0.185155	0.0195171
$91$	−6.89596	−0.722893
$92$	−3.94998	−0.411814
$93$	19.3902	2.01067
$94$	7.88668	0.813449
$95$	−0.100521	−0.0103133
$96$	2.97499	0.303634
$97$	−7.66892	−0.778661	−0.389330	−	0.921098i	$-0.627294\pi$
$97$	−7.66892	−0.778661	−0.389330	+	0.921098i	$0.627294\pi$
$98$	−5.82464	−0.588377
$99$	−9.24730	−0.929388
$100$	−4.99900	−0.499900
$101$	−11.1685	−1.11130	−0.555652	−	0.831415i	$-0.687531\pi$
$101$	−11.1685	−1.11130	−0.555652	+	0.831415i	$0.687531\pi$
$102$	−16.4727	−1.63104
$103$	1.16117	0.114413	0.0572065	−	0.998362i	$-0.481781\pi$
$103$	1.16117	0.114413	0.0572065	+	0.998362i	$0.481781\pi$
$104$	−6.36076	−0.623724
$105$	0.102073	0.00996128
$106$	9.57824	0.930321
$107$	4.01512	0.388157	0.194078	−	0.980986i	$-0.437828\pi$
$107$	4.01512	0.388157	0.194078	+	0.980986i	$0.437828\pi$
$108$	8.48039	0.816026
$109$	6.90453	0.661334	0.330667	−	0.943748i	$-0.392726\pi$
$109$	6.90453	0.661334	0.330667	+	0.943748i	$0.392726\pi$
$110$	−0.0500214	−0.00476935
$111$	5.21423	0.494913
$112$	1.08414	0.102442
$113$	3.23449	0.304275	0.152138	−	0.988359i	$-0.451384\pi$
$113$	3.23449	0.304275	0.152138	+	0.988359i	$0.451384\pi$
$114$	−9.44943	−0.885020
$115$	−0.125007	−0.0116569
$116$	9.05434	0.840674
$117$	−37.2140	−3.44044
$118$	−12.9416	−1.19137
$119$	−6.00295	−0.550289
$120$	0.0941507	0.00859475
$121$	−8.50176	−0.772887
$122$	−6.40058	−0.579481
$123$	4.80398	0.433161
$124$	6.51774	0.585310
$125$	−0.316442	−0.0283035
$126$	6.34284	0.565065
$127$	2.95984	0.262643	0.131322	−	0.991340i	$-0.458078\pi$
$127$	2.95984	0.262643	0.131322	+	0.991340i	$0.458078\pi$
$128$	1.00000	0.0883883
$129$	34.5093	3.03837
$130$	−0.201302	−0.0176553
$131$	1.33676	0.116793	0.0583965	−	0.998293i	$-0.481401\pi$
$131$	1.33676	0.116793	0.0583965	+	0.998293i	$0.481401\pi$
$132$	−4.70222	−0.409276
$133$	−3.44355	−0.298594
$134$	−3.38476	−0.292399
$135$	0.268382	0.0230987
$136$	−5.53705	−0.474798
$137$	7.93270	0.677736	0.338868	−	0.940834i	$-0.389956\pi$
$137$	7.93270	0.677736	0.338868	+	0.940834i	$0.389956\pi$
$138$	−11.7511	−1.00032
$139$	−21.0168	−1.78262	−0.891312	−	0.453391i	$-0.850214\pi$
$139$	−21.0168	−1.78262	−0.891312	+	0.453391i	$0.850214\pi$
$140$	0.0343103	0.00289975
$141$	23.4628	1.97592
$142$	7.13600	0.598840
$143$	10.0537	0.840733
$144$	5.85056	0.487547
$145$	0.286546	0.0237964
$146$	−3.40593	−0.281877
$147$	−17.3282	−1.42921
$148$	1.75269	0.144070
$149$	−9.83698	−0.805877	−0.402938	−	0.915227i	$-0.632011\pi$
$149$	−9.83698	−0.805877	−0.402938	+	0.915227i	$0.632011\pi$
$150$	−14.8720	−1.21429
$151$	−19.6011	−1.59511	−0.797557	−	0.603244i	$-0.793874\pi$
$151$	−19.6011	−1.59511	−0.797557	+	0.603244i	$0.793874\pi$
$152$	−3.17629	−0.257631
$153$	−32.3948	−2.61897
$154$	−1.71358	−0.138084
$155$	0.206270	0.0165680
$156$	−18.9232	−1.51507
$157$	13.1204	1.04712	0.523560	−	0.851989i	$-0.324604\pi$
$157$	13.1204	1.04712	0.523560	+	0.851989i	$0.324604\pi$
$158$	8.96616	0.713309
$159$	28.4952	2.25981
$160$	0.0316474	0.00250195
$161$	−4.28234	−0.337495
$162$	7.67738	0.603192
$163$	−8.72367	−0.683290	−0.341645	−	0.939829i	$-0.610984\pi$
$163$	−8.72367	−0.683290	−0.341645	+	0.939829i	$0.610984\pi$
$164$	1.61479	0.126094
$165$	−0.148813	−0.0115851
$166$	7.05816	0.547819
$167$	−8.02478	−0.620976	−0.310488	−	0.950577i	$-0.600492\pi$
$167$	−8.02478	−0.620976	−0.310488	+	0.950577i	$0.600492\pi$
$168$	3.22531	0.248838
$169$	27.4592	2.11225
$170$	−0.175233	−0.0134398
$171$	−18.5831	−1.42108
$172$	11.5998	0.884476
$173$	−10.2912	−0.782428	−0.391214	−	0.920300i	$-0.627945\pi$
$173$	−10.2912	−0.782428	−0.391214	+	0.920300i	$0.627945\pi$
$174$	26.9366	2.04205
$175$	−5.41962	−0.409685
$176$	−1.58058	−0.119141
$177$	−38.5010	−2.89391
$178$	11.3958	0.854151
$179$	2.95307	0.220723	0.110362	−	0.993892i	$-0.464799\pi$
$179$	2.95307	0.220723	0.110362	+	0.993892i	$0.464799\pi$
$180$	0.185155	0.0138006
$181$	−17.1817	−1.27711	−0.638555	−	0.769577i	$-0.720467\pi$
$181$	−17.1817	−1.27711	−0.638555	+	0.769577i	$0.720467\pi$
$182$	−6.89596	−0.511163
$183$	−19.0417	−1.40760
$184$	−3.94998	−0.291196
$185$	0.0554681	0.00407810
$186$	19.3902	1.42176
$187$	8.75176	0.639992
$188$	7.88668	0.575196
$189$	9.19395	0.668761
$190$	−0.100521	−0.00729259
$191$	5.35275	0.387311	0.193656	−	0.981070i	$-0.437966\pi$
$191$	5.35275	0.387311	0.193656	+	0.981070i	$0.437966\pi$
$192$	2.97499	0.214701
$193$	6.95289	0.500480	0.250240	−	0.968184i	$-0.419491\pi$
$193$	6.95289	0.500480	0.250240	+	0.968184i	$0.419491\pi$
$194$	−7.66892	−0.550596
$195$	−0.598870	−0.0428860
$196$	−5.82464	−0.416045
$197$	20.8427	1.48498	0.742489	−	0.669859i	$-0.233645\pi$
$197$	20.8427	1.48498	0.742489	+	0.669859i	$0.233645\pi$
$198$	−9.24730	−0.657177
$199$	20.2689	1.43682	0.718412	−	0.695618i	$-0.244869\pi$
$199$	20.2689	1.43682	0.718412	+	0.695618i	$0.244869\pi$
$200$	−4.99900	−0.353483
$201$	−10.0696	−0.710256
$202$	−11.1685	−0.785811
$203$	9.81619	0.688961
$204$	−16.4727	−1.15332
$205$	0.0511039	0.00356925
$206$	1.16117	0.0809023
$207$	−23.1096	−1.60623
$208$	−6.36076	−0.441039
$209$	5.02039	0.347268
$210$	0.102073	0.00704369
$211$	−23.8419	−1.64134	−0.820672	−	0.571400i	$-0.806400\pi$
$211$	−23.8419	−1.64134	−0.820672	+	0.571400i	$0.806400\pi$
$212$	9.57824	0.657836
$213$	21.2295	1.45462
$214$	4.01512	0.274468
$215$	0.367104	0.0250363
$216$	8.48039	0.577017
$217$	7.06615	0.479682
$218$	6.90453	0.467634
$219$	−10.1326	−0.684699
$220$	−0.0500214	−0.00337244
$221$	35.2198	2.36914
$222$	5.21423	0.349957
$223$	−3.53518	−0.236733	−0.118367	−	0.992970i	$-0.537766\pi$
$223$	−3.53518	−0.236733	−0.118367	+	0.992970i	$0.537766\pi$
$224$	1.08414	0.0724373
$225$	−29.2469	−1.94980
$226$	3.23449	0.215155
$227$	6.35473	0.421779	0.210889	−	0.977510i	$-0.432364\pi$
$227$	6.35473	0.421779	0.210889	+	0.977510i	$0.432364\pi$
$228$	−9.44943	−0.625804
$229$	25.6330	1.69388	0.846938	−	0.531691i	$-0.178443\pi$
$229$	25.6330	1.69388	0.846938	+	0.531691i	$0.178443\pi$
$230$	−0.125007	−0.00824269
$231$	−5.09787	−0.335415
$232$	9.05434	0.594446
$233$	−9.97660	−0.653589	−0.326794	−	0.945095i	$-0.605968\pi$
$233$	−9.97660	−0.653589	−0.326794	+	0.945095i	$0.605968\pi$
$234$	−37.2140	−2.43276
$235$	0.249593	0.0162817
$236$	−12.9416	−0.842424
$237$	26.6742	1.73268
$238$	−6.00295	−0.389113
$239$	−21.0659	−1.36264	−0.681319	−	0.731986i	$-0.738593\pi$
$239$	−21.0659	−1.36264	−0.681319	+	0.731986i	$0.738593\pi$
$240$	0.0941507	0.00607740
$241$	−7.70533	−0.496344	−0.248172	−	0.968716i	$-0.579830\pi$
$241$	−7.70533	−0.496344	−0.248172	+	0.968716i	$0.579830\pi$
$242$	−8.50176	−0.546514
$243$	−2.60103	−0.166856
$244$	−6.40058	−0.409755
$245$	−0.184335	−0.0117767
$246$	4.80398	0.306291
$247$	20.2036	1.28553
$248$	6.51774	0.413877
$249$	20.9979	1.33069
$250$	−0.316442	−0.0200136
$251$	1.90336	0.120139	0.0600696	−	0.998194i	$-0.480868\pi$
$251$	1.90336	0.120139	0.0600696	+	0.998194i	$0.480868\pi$
$252$	6.34284	0.399561
$253$	6.24327	0.392511
$254$	2.95984	0.185717
$255$	−0.521317	−0.0326461
$256$	1.00000	0.0625000
$257$	23.5548	1.46931	0.734655	−	0.678441i	$-0.237344\pi$
$257$	23.5548	1.46931	0.734655	+	0.678441i	$0.237344\pi$
$258$	34.5093	2.14845
$259$	1.90016	0.118071
$260$	−0.201302	−0.0124842
$261$	52.9729	3.27894
$262$	1.33676	0.0825851
$263$	−19.8442	−1.22364	−0.611822	−	0.790996i	$-0.709563\pi$
$263$	−19.8442	−1.22364	−0.611822	+	0.790996i	$0.709563\pi$
$264$	−4.70222	−0.289401
$265$	0.303127	0.0186209
$266$	−3.44355	−0.211138
$267$	33.9024	2.07479
$268$	−3.38476	−0.206757
$269$	−1.00000	−0.0609711
$269$	−1.00000	−0.0609711
$270$	0.268382	0.0163332
$271$	−13.4661	−0.818006	−0.409003	−	0.912533i	$-0.634124\pi$
$271$	−13.4661	−0.818006	−0.409003	+	0.912533i	$0.634124\pi$
$272$	−5.53705	−0.335733
$273$	−20.5154	−1.24165
$274$	7.93270	0.479232
$275$	7.90133	0.476468
$276$	−11.7511	−0.707336
$277$	0.456454	0.0274257	0.0137128	−	0.999906i	$-0.495635\pi$
$277$	0.456454	0.0274257	0.0137128	+	0.999906i	$0.495635\pi$
$278$	−21.0168	−1.26051
$279$	38.1324	2.28293
$280$	0.0343103	0.00205043
$281$	20.7243	1.23631	0.618153	−	0.786058i	$-0.287881\pi$
$281$	20.7243	1.23631	0.618153	+	0.786058i	$0.287881\pi$
$282$	23.4628	1.39719
$283$	2.38541	0.141798	0.0708989	−	0.997484i	$-0.477413\pi$
$283$	2.38541	0.141798	0.0708989	+	0.997484i	$0.477413\pi$
$284$	7.13600	0.423444
$285$	−0.299050	−0.0177142
$286$	10.0537	0.594488
$287$	1.75066	0.103338
$288$	5.85056	0.344748
$289$	13.6589	0.803465
$290$	0.286546	0.0168266
$291$	−22.8149	−1.33744
$292$	−3.40593	−0.199317
$293$	26.9825	1.57633	0.788167	−	0.615461i	$-0.211030\pi$
$293$	26.9825	1.57633	0.788167	+	0.615461i	$0.211030\pi$
$294$	−17.3282	−1.01060
$295$	−0.409567	−0.0238459
$296$	1.75269	0.101873
$297$	−13.4040	−0.777777
$298$	−9.83698	−0.569841
$299$	25.1249	1.45301
$300$	−14.8720	−0.858633
$301$	12.5758	0.724859
$302$	−19.6011	−1.12792
$303$	−33.2261	−1.90879
$304$	−3.17629	−0.182173
$305$	−0.202562	−0.0115987
$306$	−32.3948	−1.85189
$307$	−23.7098	−1.35319	−0.676594	−	0.736356i	$-0.736545\pi$
$307$	−23.7098	−1.35319	−0.676594	+	0.736356i	$0.736545\pi$
$308$	−1.71358	−0.0976401
$309$	3.45446	0.196517
$310$	0.206270	0.0117153
$311$	−11.2199	−0.636221	−0.318110	−	0.948054i	$-0.603048\pi$
$311$	−11.2199	−0.636221	−0.318110	+	0.948054i	$0.603048\pi$
$312$	−18.9232	−1.07131
$313$	21.7128	1.22728	0.613639	−	0.789587i	$-0.289705\pi$
$313$	21.7128	1.22728	0.613639	+	0.789587i	$0.289705\pi$
$314$	13.1204	0.740425
$315$	0.200734	0.0113101
$316$	8.96616	0.504386
$317$	−2.48557	−0.139604	−0.0698019	−	0.997561i	$-0.522237\pi$
$317$	−2.48557	−0.139604	−0.0698019	+	0.997561i	$0.522237\pi$
$318$	28.4952	1.59793
$319$	−14.3111	−0.801269
$320$	0.0316474	0.00176914
$321$	11.9450	0.666702
$322$	−4.28234	−0.238645
$323$	17.5873	0.978582
$324$	7.67738	0.426521
$325$	31.7974	1.76380
$326$	−8.72367	−0.483159
$327$	20.5409	1.13591
$328$	1.61479	0.0891619
$329$	8.55028	0.471392
$330$	−0.148813	−0.00819189
$331$	−4.81515	−0.264665	−0.132332	−	0.991205i	$-0.542247\pi$
$331$	−4.81515	−0.264665	−0.132332	+	0.991205i	$0.542247\pi$
$332$	7.05816	0.387367
$333$	10.2542	0.561928
$334$	−8.02478	−0.439096
$335$	−0.107119	−0.00585253
$336$	3.22531	0.175955
$337$	−15.4903	−0.843808	−0.421904	−	0.906640i	$-0.638638\pi$
$337$	−15.4903	−0.843808	−0.421904	+	0.906640i	$0.638638\pi$
$338$	27.4592	1.49359
$339$	9.62257	0.522626
$340$	−0.175233	−0.00950336
$341$	−10.3018	−0.557875
$342$	−18.5831	−1.00486
$343$	−13.9037	−0.750731
$344$	11.5998	0.625419
$345$	−0.371893	−0.0200221
$346$	−10.2912	−0.553260
$347$	−17.8412	−0.957767	−0.478884	−	0.877878i	$-0.658958\pi$
$347$	−17.8412	−0.957767	−0.478884	+	0.877878i	$0.658958\pi$
$348$	26.9366	1.44395
$349$	2.40201	0.128577	0.0642885	−	0.997931i	$-0.479522\pi$
$349$	2.40201	0.128577	0.0642885	+	0.997931i	$0.479522\pi$
$350$	−5.41962	−0.289691
$351$	−53.9417	−2.87919
$352$	−1.58058	−0.0842454
$353$	33.5276	1.78449	0.892246	−	0.451549i	$-0.149128\pi$
$353$	33.5276	1.78449	0.892246	+	0.451549i	$0.149128\pi$
$354$	−38.5010	−2.04630
$355$	0.225836	0.0119861
$356$	11.3958	0.603976
$357$	−17.8587	−0.945183
$358$	2.95307	0.156075
$359$	18.7359	0.988845	0.494422	−	0.869222i	$-0.335380\pi$
$359$	18.7359	0.988845	0.494422	+	0.869222i	$0.335380\pi$
$360$	0.185155	0.00975853
$361$	−8.91118	−0.469009
$362$	−17.1817	−0.903053
$363$	−25.2926	−1.32752
$364$	−6.89596	−0.361447
$365$	−0.107789	−0.00564193
$366$	−19.0417	−0.995323
$367$	−23.7327	−1.23884	−0.619419	−	0.785060i	$-0.712632\pi$
$367$	−23.7327	−1.23884	−0.619419	+	0.785060i	$0.712632\pi$
$368$	−3.94998	−0.205907
$369$	9.44743	0.491814
$370$	0.0554681	0.00288365
$371$	10.3842	0.539119
$372$	19.3902	1.00534
$373$	−36.8288	−1.90692	−0.953462	−	0.301513i	$-0.902508\pi$
$373$	−36.8288	−1.90692	−0.953462	+	0.301513i	$0.902508\pi$
$374$	8.75176	0.452543
$375$	−0.941413	−0.0486144
$376$	7.88668	0.406725
$377$	−57.5924	−2.96616
$378$	9.19395	0.472886
$379$	−22.7264	−1.16738	−0.583689	−	0.811977i	$-0.698391\pi$
$379$	−22.7264	−1.16738	−0.583689	+	0.811977i	$0.698391\pi$
$380$	−0.100521	−0.00515664
$381$	8.80548	0.451119
$382$	5.35275	0.273871
$383$	5.87594	0.300246	0.150123	−	0.988667i	$-0.452033\pi$
$383$	5.87594	0.300246	0.150123	+	0.988667i	$0.452033\pi$
$384$	2.97499	0.151817
$385$	−0.0542303	−0.00276383
$386$	6.95289	0.353893
$387$	67.8653	3.44979
$388$	−7.66892	−0.389330
$389$	14.9916	0.760103	0.380052	−	0.924965i	$-0.375906\pi$
$389$	14.9916	0.760103	0.380052	+	0.924965i	$0.375906\pi$
$390$	−0.598870	−0.0303250
$391$	21.8712	1.10608
$392$	−5.82464	−0.294189
$393$	3.97684	0.200605
$394$	20.8427	1.05004
$395$	0.283756	0.0142773
$396$	−9.24730	−0.464694
$397$	−25.2744	−1.26849	−0.634244	−	0.773133i	$-0.718689\pi$
$397$	−25.2744	−1.26849	−0.634244	+	0.773133i	$0.718689\pi$
$398$	20.2689	1.01599
$399$	−10.2445	−0.512868
$400$	−4.99900	−0.249950
$401$	11.8421	0.591366	0.295683	−	0.955286i	$-0.404453\pi$
$401$	11.8421	0.591366	0.295683	+	0.955286i	$0.404453\pi$
$402$	−10.0696	−0.502227
$403$	−41.4578	−2.06516
$404$	−11.1685	−0.555652
$405$	0.242969	0.0120732
$406$	9.81619	0.487169
$407$	−2.77027	−0.137317
$408$	−16.4727	−0.815518
$409$	25.6036	1.26602	0.633009	−	0.774145i	$-0.281820\pi$
$409$	25.6036	1.26602	0.633009	+	0.774145i	$0.281820\pi$
$410$	0.0511039	0.00252384
$411$	23.5997	1.16409
$412$	1.16117	0.0572065
$413$	−14.0305	−0.690395
$414$	−23.1096	−1.13577
$415$	0.223372	0.0109649
$416$	−6.36076	−0.311862
$417$	−62.5248	−3.06185
$418$	5.02039	0.245555
$419$	16.3173	0.797153	0.398576	−	0.917135i	$-0.369504\pi$
$419$	16.3173	0.797153	0.398576	+	0.917135i	$0.369504\pi$
$420$	0.102073	0.00498064
$421$	−16.7172	−0.814749	−0.407374	−	0.913261i	$-0.633556\pi$
$421$	−16.7172	−0.814749	−0.407374	+	0.913261i	$0.633556\pi$
$422$	−23.8419	−1.16060
$423$	46.1415	2.24348
$424$	9.57824	0.465161
$425$	27.6797	1.34266
$426$	21.2295	1.02857
$427$	−6.93914	−0.335808
$428$	4.01512	0.194078
$429$	29.9097	1.44405
$430$	0.367104	0.0177033
$431$	−23.6411	−1.13875	−0.569376	−	0.822077i	$-0.692815\pi$
$431$	−23.6411	−1.13875	−0.569376	+	0.822077i	$0.692815\pi$
$432$	8.48039	0.408013
$433$	−13.5895	−0.653070	−0.326535	−	0.945185i	$-0.605881\pi$
$433$	−13.5895	−0.653070	−0.326535	+	0.945185i	$0.605881\pi$
$434$	7.06615	0.339186
$435$	0.852472	0.0408729
$436$	6.90453	0.330667
$437$	12.5463	0.600170
$438$	−10.1326	−0.484155
$439$	35.3166	1.68557	0.842785	−	0.538251i	$-0.180915\pi$
$439$	35.3166	1.68557	0.842785	+	0.538251i	$0.180915\pi$
$440$	−0.0500214	−0.00238468
$441$	−34.0774	−1.62273
$442$	35.2198	1.67524
$443$	27.3334	1.29865	0.649324	−	0.760512i	$-0.275052\pi$
$443$	27.3334	1.29865	0.649324	+	0.760512i	$0.275052\pi$
$444$	5.21423	0.247457
$445$	0.360647	0.0170963
$446$	−3.53518	−0.167396
$447$	−29.2649	−1.38418
$448$	1.08414	0.0512209
$449$	−3.54747	−0.167415	−0.0837077	−	0.996490i	$-0.526676\pi$
$449$	−3.54747	−0.167415	−0.0837077	+	0.996490i	$0.526676\pi$
$450$	−29.2469	−1.37871
$451$	−2.55231	−0.120184
$452$	3.23449	0.152138
$453$	−58.3130	−2.73978
$454$	6.35473	0.298242
$455$	−0.218239	−0.0102312
$456$	−9.44943	−0.442510
$457$	25.2637	1.18178	0.590892	−	0.806750i	$-0.298776\pi$
$457$	25.2637	1.18178	0.590892	+	0.806750i	$0.298776\pi$
$458$	25.6330	1.19775
$459$	−46.9563	−2.19173
$460$	−0.125007	−0.00582846
$461$	13.5815	0.632553	0.316276	−	0.948667i	$-0.397567\pi$
$461$	13.5815	0.632553	0.316276	+	0.948667i	$0.397567\pi$
$462$	−5.09787	−0.237174
$463$	20.3739	0.946854	0.473427	−	0.880833i	$-0.343017\pi$
$463$	20.3739	0.946854	0.473427	+	0.880833i	$0.343017\pi$
$464$	9.05434	0.420337
$465$	0.613650	0.0284573
$466$	−9.97660	−0.462157
$467$	15.1522	0.701160	0.350580	−	0.936533i	$-0.385984\pi$
$467$	15.1522	0.701160	0.350580	+	0.936533i	$0.385984\pi$
$468$	−37.2140	−1.72022
$469$	−3.66956	−0.169444
$470$	0.249593	0.0115129
$471$	39.0330	1.79854
$472$	−12.9416	−0.595684
$473$	−18.3344	−0.843019
$474$	26.6742	1.22519
$475$	15.8783	0.728545
$476$	−6.00295	−0.275145
$477$	56.0381	2.56581
$478$	−21.0659	−0.963531
$479$	−33.3413	−1.52340	−0.761702	−	0.647928i	$-0.775636\pi$
$479$	−33.3413	−1.52340	−0.761702	+	0.647928i	$0.775636\pi$
$480$	0.0941507	0.00429737
$481$	−11.1484	−0.508325
$482$	−7.70533	−0.350968
$483$	−12.7399	−0.579686
$484$	−8.50176	−0.386444
$485$	−0.242701	−0.0110205
$486$	−2.60103	−0.117985
$487$	35.0213	1.58697	0.793484	−	0.608591i	$-0.208265\pi$
$487$	35.0213	1.58697	0.793484	+	0.608591i	$0.208265\pi$
$488$	−6.40058	−0.289741
$489$	−25.9528	−1.17363
$490$	−0.184335	−0.00832739
$491$	−0.715554	−0.0322925	−0.0161462	−	0.999870i	$-0.505140\pi$
$491$	−0.715554	−0.0322925	−0.0161462	+	0.999870i	$0.505140\pi$
$492$	4.80398	0.216580
$493$	−50.1343	−2.25793
$494$	20.2036	0.909004
$495$	−0.292653	−0.0131538
$496$	6.51774	0.292655
$497$	7.73644	0.347027
$498$	20.9979	0.940941
$499$	26.1873	1.17230	0.586152	−	0.810201i	$-0.300642\pi$
$499$	26.1873	1.17230	0.586152	+	0.810201i	$0.300642\pi$
$500$	−0.316442	−0.0141517
$501$	−23.8736	−1.06660
$502$	1.90336	0.0849513
$503$	35.1795	1.56857	0.784287	−	0.620398i	$-0.213029\pi$
$503$	35.1795	1.56857	0.784287	+	0.620398i	$0.213029\pi$
$504$	6.34284	0.282533
$505$	−0.353453	−0.0157285
$506$	6.24327	0.277547
$507$	81.6909	3.62802
$508$	2.95984	0.131322
$509$	−29.4653	−1.30603	−0.653014	−	0.757346i	$-0.726496\pi$
$509$	−29.4653	−1.30603	−0.653014	+	0.757346i	$0.726496\pi$
$510$	−0.521317	−0.0230843
$511$	−3.69252	−0.163347
$512$	1.00000	0.0441942
$513$	−26.9362	−1.18926
$514$	23.5548	1.03896
$515$	0.0367479	0.00161931
$516$	34.5093	1.51919
$517$	−12.4656	−0.548235
$518$	1.90016	0.0834885
$519$	−30.6163	−1.34391
$520$	−0.201302	−0.00882766
$521$	−42.1517	−1.84670	−0.923350	−	0.383960i	$-0.874560\pi$
$521$	−42.1517	−1.84670	−0.923350	+	0.383960i	$0.874560\pi$
$522$	52.9729	2.31856
$523$	−37.6271	−1.64532	−0.822660	−	0.568534i	$-0.807511\pi$
$523$	−37.6271	−1.64532	−0.822660	+	0.568534i	$0.807511\pi$
$524$	1.33676	0.0583965
$525$	−16.1233	−0.703679
$526$	−19.8442	−0.865247
$527$	−36.0890	−1.57206
$528$	−4.70222	−0.204638
$529$	−7.39767	−0.321638
$530$	0.303127	0.0131670
$531$	−75.7154	−3.28577
$532$	−3.44355	−0.149297
$533$	−10.2713	−0.444899
$534$	33.9024	1.46710
$535$	0.127068	0.00549364
$536$	−3.38476	−0.146199
$537$	8.78536	0.379116
$538$	−1.00000	−0.0431131
$539$	9.20632	0.396544
$540$	0.268382	0.0115493
$541$	14.5345	0.624887	0.312443	−	0.949936i	$-0.398853\pi$
$541$	14.5345	0.624887	0.312443	+	0.949936i	$0.398853\pi$
$542$	−13.4661	−0.578418
$543$	−51.1155	−2.19358
$544$	−5.53705	−0.237399
$545$	0.218510	0.00935996
$546$	−20.5154	−0.877979
$547$	−26.6331	−1.13875	−0.569374	−	0.822078i	$-0.692814\pi$
$547$	−26.6331	−1.13875	−0.569374	+	0.822078i	$0.692814\pi$
$548$	7.93270	0.338868
$549$	−37.4470	−1.59820
$550$	7.90133	0.336914
$551$	−28.7592	−1.22518
$552$	−11.7511	−0.500162
$553$	9.72059	0.413362
$554$	0.456454	0.0193929
$555$	0.165017	0.00700458
$556$	−21.0168	−0.891312
$557$	1.27322	0.0539480	0.0269740	−	0.999636i	$-0.491413\pi$
$557$	1.27322	0.0539480	0.0269740	+	0.999636i	$0.491413\pi$
$558$	38.1324	1.61427
$559$	−73.7835	−3.12071
$560$	0.0343103	0.00144987
$561$	26.0364	1.09926
$562$	20.7243	0.874200
$563$	−33.8825	−1.42798	−0.713989	−	0.700157i	$-0.753113\pi$
$563$	−33.8825	−1.42798	−0.713989	+	0.700157i	$0.753113\pi$
$564$	23.4628	0.987962
$565$	0.102363	0.00430645
$566$	2.38541	0.100266
$567$	8.32337	0.349549
$568$	7.13600	0.299420
$569$	−11.7954	−0.494487	−0.247244	−	0.968953i	$-0.579525\pi$
$569$	−11.7954	−0.494487	−0.247244	+	0.968953i	$0.579525\pi$
$570$	−0.299050	−0.0125258
$571$	5.32310	0.222765	0.111382	−	0.993778i	$-0.464472\pi$
$571$	5.32310	0.222765	0.111382	+	0.993778i	$0.464472\pi$
$572$	10.0537	0.420367
$573$	15.9244	0.665250
$574$	1.75066	0.0730712
$575$	19.7459	0.823462
$576$	5.85056	0.243773
$577$	19.7441	0.821958	0.410979	−	0.911645i	$-0.365187\pi$
$577$	19.7441	0.821958	0.410979	+	0.911645i	$0.365187\pi$
$578$	13.6589	0.568135
$579$	20.6848	0.859630
$580$	0.286546	0.0118982
$581$	7.65205	0.317460
$582$	−22.8149	−0.945710
$583$	−15.1392	−0.627002
$584$	−3.40593	−0.140939
$585$	−1.17773	−0.0486930
$586$	26.9825	1.11464
$587$	7.14170	0.294769	0.147385	−	0.989079i	$-0.452914\pi$
$587$	7.14170	0.294769	0.147385	+	0.989079i	$0.452914\pi$
$588$	−17.3282	−0.714604
$589$	−20.7022	−0.853021
$590$	−0.409567	−0.0168616
$591$	62.0067	2.55061
$592$	1.75269	0.0720351
$593$	10.5174	0.431897	0.215949	−	0.976405i	$-0.430716\pi$
$593$	10.5174	0.431897	0.215949	+	0.976405i	$0.430716\pi$
$594$	−13.4040	−0.549971
$595$	−0.189978	−0.00778833
$596$	−9.83698	−0.402938
$597$	60.2997	2.46790
$598$	25.1249	1.02743
$599$	−7.20868	−0.294539	−0.147269	−	0.989096i	$-0.547048\pi$
$599$	−7.20868	−0.294539	−0.147269	+	0.989096i	$0.547048\pi$
$600$	−14.8720	−0.607146
$601$	−32.6760	−1.33288	−0.666441	−	0.745558i	$-0.732183\pi$
$601$	−32.6760	−1.33288	−0.666441	+	0.745558i	$0.732183\pi$
$602$	12.5758	0.512552
$603$	−19.8027	−0.806430
$604$	−19.6011	−0.797557
$605$	−0.269059	−0.0109388
$606$	−33.2261	−1.34972
$607$	22.5267	0.914331	0.457165	−	0.889382i	$-0.348865\pi$
$607$	22.5267	0.914331	0.457165	+	0.889382i	$0.348865\pi$
$608$	−3.17629	−0.128816
$609$	29.2030	1.18337
$610$	−0.202562	−0.00820149
$611$	−50.1653	−2.02947
$612$	−32.3948	−1.30948
$613$	−12.1824	−0.492041	−0.246020	−	0.969265i	$-0.579123\pi$
$613$	−12.1824	−0.492041	−0.246020	+	0.969265i	$0.579123\pi$
$614$	−23.7098	−0.956849
$615$	0.152034	0.00613059
$616$	−1.71358	−0.0690420
$617$	29.3903	1.18321	0.591604	−	0.806228i	$-0.298495\pi$
$617$	29.3903	1.18321	0.591604	+	0.806228i	$0.298495\pi$
$618$	3.45446	0.138959
$619$	−3.19884	−0.128572	−0.0642861	−	0.997932i	$-0.520477\pi$
$619$	−3.19884	−0.128572	−0.0642861	+	0.997932i	$0.520477\pi$
$620$	0.206270	0.00828399
$621$	−33.4974	−1.34420
$622$	−11.2199	−0.449876
$623$	12.3547	0.494979
$624$	−18.9232	−0.757534
$625$	24.9850	0.999399
$626$	21.7128	0.867816
$627$	14.9356	0.596471
$628$	13.1204	0.523560
$629$	−9.70473	−0.386953
$630$	0.200734	0.00799745
$631$	−19.2578	−0.766640	−0.383320	−	0.923616i	$-0.625219\pi$
$631$	−19.2578	−0.766640	−0.383320	+	0.923616i	$0.625219\pi$
$632$	8.96616	0.356655
$633$	−70.9294	−2.81919
$634$	−2.48557	−0.0987148
$635$	0.0936712	0.00371723
$636$	28.4952	1.12991
$637$	37.0491	1.46794
$638$	−14.3111	−0.566583
$639$	41.7496	1.65159
$640$	0.0316474	0.00125097
$641$	24.0538	0.950068	0.475034	−	0.879967i	$-0.342436\pi$
$641$	24.0538	0.950068	0.475034	+	0.879967i	$0.342436\pi$
$642$	11.9450	0.471430
$643$	−36.2471	−1.42945	−0.714723	−	0.699407i	$-0.753447\pi$
$643$	−36.2471	−1.42945	−0.714723	+	0.699407i	$0.753447\pi$
$644$	−4.28234	−0.168748
$645$	1.09213	0.0430025
$646$	17.5873	0.691962
$647$	6.84549	0.269124	0.134562	−	0.990905i	$-0.457037\pi$
$647$	6.84549	0.269124	0.134562	+	0.990905i	$0.457037\pi$
$648$	7.67738	0.301596
$649$	20.4552	0.802937
$650$	31.7974	1.24720
$651$	21.0217	0.823907
$652$	−8.72367	−0.341645
$653$	24.7863	0.969964	0.484982	−	0.874524i	$-0.338826\pi$
$653$	24.7863	0.969964	0.484982	+	0.874524i	$0.338826\pi$
$654$	20.5409	0.803213
$655$	0.0423049	0.00165299
$656$	1.61479	0.0630470
$657$	−19.9266	−0.777412
$658$	8.55028	0.333325
$659$	−2.21313	−0.0862115	−0.0431057	−	0.999071i	$-0.513725\pi$
$659$	−2.21313	−0.0862115	−0.0431057	+	0.999071i	$0.513725\pi$
$660$	−0.148813	−0.00579254
$661$	1.73001	0.0672896	0.0336448	−	0.999434i	$-0.489289\pi$
$661$	1.73001	0.0672896	0.0336448	+	0.999434i	$0.489289\pi$
$662$	−4.81515	−0.187146
$663$	104.779	4.06926
$664$	7.05816	0.273910
$665$	−0.108979	−0.00422604
$666$	10.2542	0.397343
$667$	−35.7644	−1.38480
$668$	−8.02478	−0.310488
$669$	−10.5171	−0.406616
$670$	−0.107119	−0.00413836
$671$	10.1166	0.390549
$672$	3.22531	0.124419
$673$	−26.5381	−1.02297	−0.511484	−	0.859293i	$-0.670904\pi$
$673$	−26.5381	−1.02297	−0.511484	+	0.859293i	$0.670904\pi$
$674$	−15.4903	−0.596662
$675$	−42.3935	−1.63172
$676$	27.4592	1.05612
$677$	6.85812	0.263579	0.131789	−	0.991278i	$-0.457928\pi$
$677$	6.85812	0.263579	0.131789	+	0.991278i	$0.457928\pi$
$678$	9.62257	0.369552
$679$	−8.31419	−0.319069
$680$	−0.175233	−0.00671989
$681$	18.9053	0.724451
$682$	−10.3018	−0.394477
$683$	22.1665	0.848179	0.424089	−	0.905620i	$-0.360594\pi$
$683$	22.1665	0.848179	0.424089	+	0.905620i	$0.360594\pi$
$684$	−18.5831	−0.710542
$685$	0.251049	0.00959211
$686$	−13.9037	−0.530847
$687$	76.2579	2.90942
$688$	11.5998	0.442238
$689$	−60.9249	−2.32105
$690$	−0.371893	−0.0141577
$691$	−29.3696	−1.11727	−0.558636	−	0.829413i	$-0.688675\pi$
$691$	−29.3696	−1.11727	−0.558636	+	0.829413i	$0.688675\pi$
$692$	−10.2912	−0.391214
$693$	−10.0254	−0.380833
$694$	−17.8412	−0.677244
$695$	−0.665128	−0.0252297
$696$	26.9366	1.02103
$697$	−8.94117	−0.338671
$698$	2.40201	0.0909176
$699$	−29.6803	−1.12261
$700$	−5.41962	−0.204843
$701$	9.99997	0.377694	0.188847	−	0.982007i	$-0.439525\pi$
$701$	9.99997	0.377694	0.188847	+	0.982007i	$0.439525\pi$
$702$	−53.9417	−2.03590
$703$	−5.56705	−0.209965
$704$	−1.58058	−0.0595705
$705$	0.742537	0.0279656
$706$	33.5276	1.26183
$707$	−12.1082	−0.455376
$708$	−38.5010	−1.44696
$709$	8.26504	0.310400	0.155200	−	0.987883i	$-0.450398\pi$
$709$	8.26504	0.310400	0.155200	+	0.987883i	$0.450398\pi$
$710$	0.225836	0.00847548
$711$	52.4571	1.96729
$712$	11.3958	0.427076
$713$	−25.7449	−0.964155
$714$	−17.8587	−0.668345
$715$	0.318174	0.0118990
$716$	2.95307	0.110362
$717$	−62.6708	−2.34048
$718$	18.7359	0.699219
$719$	24.4853	0.913146	0.456573	−	0.889686i	$-0.349077\pi$
$719$	24.4853	0.913146	0.456573	+	0.889686i	$0.349077\pi$
$720$	0.185155	0.00690032
$721$	1.25887	0.0468827
$722$	−8.91118	−0.331640
$723$	−22.9233	−0.852526
$724$	−17.1817	−0.638555
$725$	−45.2626	−1.68101
$726$	−25.2926	−0.938698
$727$	5.22044	0.193615	0.0968077	−	0.995303i	$-0.469137\pi$
$727$	5.22044	0.193615	0.0968077	+	0.995303i	$0.469137\pi$
$728$	−6.89596	−0.255581
$729$	−30.7702	−1.13964
$730$	−0.107789	−0.00398945
$731$	−64.2286	−2.37558
$732$	−19.0417	−0.703800
$733$	13.1037	0.483997	0.241998	−	0.970277i	$-0.422197\pi$
$733$	13.1037	0.483997	0.241998	+	0.970277i	$0.422197\pi$
$734$	−23.7327	−0.875991
$735$	−0.548394	−0.0202278
$736$	−3.94998	−0.145598
$737$	5.34989	0.197066
$738$	9.44743	0.347765
$739$	23.4439	0.862398	0.431199	−	0.902257i	$-0.358091\pi$
$739$	23.4439	0.862398	0.431199	+	0.902257i	$0.358091\pi$
$740$	0.0554681	0.00203905
$741$	60.1055	2.20803
$742$	10.3842	0.381215
$743$	−26.2749	−0.963931	−0.481966	−	0.876190i	$-0.660077\pi$
$743$	−26.2749	−0.963931	−0.481966	+	0.876190i	$0.660077\pi$
$744$	19.3902	0.710879
$745$	−0.311315	−0.0114057
$746$	−36.8288	−1.34840
$747$	41.2942	1.51088
$748$	8.75176	0.319996
$749$	4.35297	0.159054
$750$	−0.941413	−0.0343755
$751$	13.6609	0.498493	0.249247	−	0.968440i	$-0.419817\pi$
$751$	13.6609	0.498493	0.249247	+	0.968440i	$0.419817\pi$
$752$	7.88668	0.287598
$753$	5.66249	0.206353
$754$	−57.5924	−2.09739
$755$	−0.620324	−0.0225759
$756$	9.19395	0.334381
$757$	17.9708	0.653160	0.326580	−	0.945170i	$-0.394104\pi$
$757$	17.9708	0.653160	0.326580	+	0.945170i	$0.394104\pi$
$758$	−22.7264	−0.825461
$759$	18.5737	0.674181
$760$	−0.100521	−0.00364629
$761$	−26.5465	−0.962311	−0.481155	−	0.876635i	$-0.659783\pi$
$761$	−26.5465	−0.962311	−0.481155	+	0.876635i	$0.659783\pi$
$762$	8.80548	0.318989
$763$	7.48549	0.270993
$764$	5.35275	0.193656
$765$	−1.02521	−0.0370667
$766$	5.87594	0.212306
$767$	82.3181	2.97233
$768$	2.97499	0.107351
$769$	17.2130	0.620718	0.310359	−	0.950619i	$-0.399551\pi$
$769$	17.2130	0.620718	0.310359	+	0.950619i	$0.399551\pi$
$770$	−0.0542303	−0.00195432
$771$	70.0753	2.52370
$772$	6.95289	0.250240
$773$	31.6287	1.13761	0.568803	−	0.822474i	$-0.307407\pi$
$773$	31.6287	1.13761	0.568803	+	0.822474i	$0.307407\pi$
$774$	67.8653	2.43937
$775$	−32.5822	−1.17039
$776$	−7.66892	−0.275298
$777$	5.65297	0.202799
$778$	14.9916	0.537474
$779$	−5.12904	−0.183767
$780$	−0.598870	−0.0214430
$781$	−11.2790	−0.403596
$782$	21.8712	0.782113
$783$	76.7843	2.74405
$784$	−5.82464	−0.208023
$785$	0.415226	0.0148200
$786$	3.97684	0.141849
$787$	−28.4125	−1.01280	−0.506399	−	0.862299i	$-0.669024\pi$
$787$	−28.4125	−1.01280	−0.506399	+	0.862299i	$0.669024\pi$
$788$	20.8427	0.742489
$789$	−59.0362	−2.10174
$790$	0.283756	0.0100956
$791$	3.50664	0.124682
$792$	−9.24730	−0.328588
$793$	40.7125	1.44574
$794$	−25.2744	−0.896956
$795$	0.901798	0.0319835
$796$	20.2689	0.718412
$797$	1.13199	0.0400971	0.0200486	−	0.999799i	$-0.493618\pi$
$797$	1.13199	0.0400971	0.0200486	+	0.999799i	$0.493618\pi$
$798$	−10.2445	−0.362652
$799$	−43.6689	−1.54490
$800$	−4.99900	−0.176741
$801$	66.6718	2.35573
$802$	11.8421	0.418159
$803$	5.38336	0.189975
$804$	−10.0696	−0.355128
$805$	−0.135525	−0.00477663
$806$	−41.4578	−1.46029
$807$	−2.97499	−0.104725
$808$	−11.1685	−0.392905
$809$	16.1496	0.567790	0.283895	−	0.958855i	$-0.408373\pi$
$809$	16.1496	0.567790	0.283895	+	0.958855i	$0.408373\pi$
$810$	0.242969	0.00853707
$811$	43.1152	1.51398	0.756990	−	0.653427i	$-0.226669\pi$
$811$	43.1152	1.51398	0.756990	+	0.653427i	$0.226669\pi$
$812$	9.81619	0.344481
$813$	−40.0615	−1.40502
$814$	−2.77027	−0.0970980
$815$	−0.276081	−0.00967071
$816$	−16.4727	−0.576658
$817$	−36.8443	−1.28902
$818$	25.6036	0.895210
$819$	−40.3453	−1.40978
$820$	0.0511039	0.00178463
$821$	13.5327	0.472296	0.236148	−	0.971717i	$-0.424115\pi$
$821$	13.5327	0.472296	0.236148	+	0.971717i	$0.424115\pi$
$822$	23.5997	0.823134
$823$	−6.64735	−0.231712	−0.115856	−	0.993266i	$-0.536961\pi$
$823$	−6.64735	−0.231712	−0.115856	+	0.993266i	$0.536961\pi$
$824$	1.16117	0.0404511
$825$	23.5064	0.818387
$826$	−14.0305	−0.488183
$827$	42.7988	1.48826	0.744130	−	0.668034i	$-0.232864\pi$
$827$	42.7988	1.48826	0.744130	+	0.668034i	$0.232864\pi$
$828$	−23.1096	−0.803114
$829$	−40.4386	−1.40449	−0.702246	−	0.711935i	$-0.747819\pi$
$829$	−40.4386	−1.40449	−0.702246	+	0.711935i	$0.747819\pi$
$830$	0.223372	0.00775337
$831$	1.35795	0.0471066
$832$	−6.36076	−0.220520
$833$	32.2513	1.11744
$834$	−62.5248	−2.16506
$835$	−0.253964	−0.00878877
$836$	5.02039	0.173634
$837$	55.2730	1.91051
$838$	16.3173	0.563672
$839$	50.8175	1.75441	0.877207	−	0.480112i	$-0.159404\pi$
$839$	50.8175	1.75441	0.877207	+	0.480112i	$0.159404\pi$
$840$	0.102073	0.00352184
$841$	52.9810	1.82693
$842$	−16.7172	−0.576114
$843$	61.6544	2.12349
$844$	−23.8419	−0.820672
$845$	0.869014	0.0298950
$846$	46.1415	1.58638
$847$	−9.21711	−0.316704
$848$	9.57824	0.328918
$849$	7.09657	0.243554
$850$	27.6797	0.949406
$851$	−6.92309	−0.237320
$852$	21.2295	0.727312
$853$	37.1567	1.27222	0.636110	−	0.771598i	$-0.280542\pi$
$853$	37.1567	1.27222	0.636110	+	0.771598i	$0.280542\pi$
$854$	−6.93914	−0.237452
$855$	−0.588107	−0.0201128
$856$	4.01512	0.137234
$857$	51.7474	1.76766	0.883829	−	0.467810i	$-0.154957\pi$
$857$	51.7474	1.76766	0.883829	+	0.467810i	$0.154957\pi$
$858$	29.9097	1.02110
$859$	17.1864	0.586394	0.293197	−	0.956052i	$-0.405281\pi$
$859$	17.1864	0.586394	0.293197	+	0.956052i	$0.405281\pi$
$860$	0.367104	0.0125181
$861$	5.20820	0.177495
$862$	−23.6411	−0.805219
$863$	−26.1350	−0.889647	−0.444823	−	0.895618i	$-0.646734\pi$
$863$	−26.1350	−0.889647	−0.444823	+	0.895618i	$0.646734\pi$
$864$	8.48039	0.288509
$865$	−0.325691	−0.0110738
$866$	−13.5895	−0.461790
$867$	40.6351	1.38004
$868$	7.06615	0.239841
$869$	−14.1718	−0.480744
$870$	0.852472	0.0289015
$871$	21.5296	0.729503
$872$	6.90453	0.233817
$873$	−44.8675	−1.51853
$874$	12.5463	0.424384
$875$	−0.343069	−0.0115978
$876$	−10.1326	−0.342349
$877$	−17.0807	−0.576774	−0.288387	−	0.957514i	$-0.593119\pi$
$877$	−17.0807	−0.576774	−0.288387	+	0.957514i	$0.593119\pi$
$878$	35.3166	1.19188
$879$	80.2726	2.70753
$880$	−0.0500214	−0.00168622
$881$	−19.1525	−0.645264	−0.322632	−	0.946524i	$-0.604568\pi$
$881$	−19.1525	−0.645264	−0.322632	+	0.946524i	$0.604568\pi$
$882$	−34.0774	−1.14745
$883$	−28.0553	−0.944136	−0.472068	−	0.881562i	$-0.656492\pi$
$883$	−28.0553	−0.944136	−0.472068	+	0.881562i	$0.656492\pi$
$884$	35.2198	1.18457
$885$	−1.21846	−0.0409580
$886$	27.3334	0.918283
$887$	−36.9015	−1.23903	−0.619515	−	0.784985i	$-0.712671\pi$
$887$	−36.9015	−1.23903	−0.619515	+	0.784985i	$0.712671\pi$
$888$	5.21423	0.174978
$889$	3.20888	0.107622
$890$	0.360647	0.0120889
$891$	−12.1347	−0.406529
$892$	−3.53518	−0.118367
$893$	−25.0504	−0.838280
$894$	−29.2649	−0.978765
$895$	0.0934571	0.00312393
$896$	1.08414	0.0362186
$897$	74.7462	2.49570
$898$	−3.54747	−0.118381
$899$	59.0138	1.96822
$900$	−29.2469	−0.974898
$901$	−53.0352	−1.76686
$902$	−2.55231	−0.0849826
$903$	37.4129	1.24502
$904$	3.23449	0.107577
$905$	−0.543758	−0.0180751
$906$	−58.3130	−1.93732
$907$	−18.4342	−0.612096	−0.306048	−	0.952016i	$-0.599007\pi$
$907$	−18.4342	−0.612096	−0.306048	+	0.952016i	$0.599007\pi$
$908$	6.35473	0.210889
$909$	−65.3418	−2.16725
$910$	−0.218239	−0.00723457
$911$	−11.9903	−0.397256	−0.198628	−	0.980075i	$-0.563649\pi$
$911$	−11.9903	−0.397256	−0.198628	+	0.980075i	$0.563649\pi$
$912$	−9.44943	−0.312902
$913$	−11.1560	−0.369210
$914$	25.2637	0.835648
$915$	−0.602619	−0.0199220
$916$	25.6330	0.846938
$917$	1.44923	0.0478579
$918$	−46.9563	−1.54979
$919$	13.6219	0.449345	0.224673	−	0.974434i	$-0.427869\pi$
$919$	13.6219	0.449345	0.224673	+	0.974434i	$0.427869\pi$
$920$	−0.125007	−0.00412135
$921$	−70.5363	−2.32425
$922$	13.5815	0.447282
$923$	−45.3904	−1.49404
$924$	−5.09787	−0.167708
$925$	−8.76170	−0.288083
$926$	20.3739	0.669527
$927$	6.79347	0.223127
$928$	9.05434	0.297223
$929$	−14.2112	−0.466253	−0.233127	−	0.972446i	$-0.574896\pi$
$929$	−14.2112	−0.466253	−0.233127	+	0.972446i	$0.574896\pi$
$930$	0.613650	0.0201224
$931$	18.5007	0.606337
$932$	−9.97660	−0.326794
$933$	−33.3790	−1.09278
$934$	15.1522	0.495795
$935$	0.276971	0.00905791
$936$	−37.2140	−1.21638
$937$	28.6353	0.935475	0.467737	−	0.883867i	$-0.345069\pi$
$937$	28.6353	0.935475	0.467737	+	0.883867i	$0.345069\pi$
$938$	−3.66956	−0.119815
$939$	64.5952	2.10799
$940$	0.249593	0.00814083
$941$	−28.6706	−0.934635	−0.467317	−	0.884090i	$-0.654779\pi$
$941$	−28.6706	−0.934635	−0.467317	+	0.884090i	$0.654779\pi$
$942$	39.0330	1.27176
$943$	−6.37839	−0.207709
$944$	−12.9416	−0.421212
$945$	0.290965	0.00946508
$946$	−18.3344	−0.596104
$947$	9.67565	0.314417	0.157208	−	0.987565i	$-0.449751\pi$
$947$	9.67565	0.314417	0.157208	+	0.987565i	$0.449751\pi$
$948$	26.6742	0.866339
$949$	21.6643	0.703253
$950$	15.8783	0.515159
$951$	−7.39456	−0.239785
$952$	−6.00295	−0.194557
$953$	−51.3712	−1.66408	−0.832039	−	0.554718i	$-0.812826\pi$
$953$	−51.3712	−1.66408	−0.832039	+	0.554718i	$0.812826\pi$
$954$	56.0381	1.81430
$955$	0.169401	0.00548168
$956$	−21.0659	−0.681319
$957$	−42.5755	−1.37627
$958$	−33.3413	−1.07721
$959$	8.60017	0.277714
$960$	0.0941507	0.00303870
$961$	11.4809	0.370353
$962$	−11.1484	−0.359440
$963$	23.4907	0.756978
$964$	−7.70533	−0.248172
$965$	0.220041	0.00708337
$966$	−12.7399	−0.409900
$967$	59.1220	1.90124	0.950618	−	0.310364i	$-0.100451\pi$
$967$	59.1220	1.90124	0.950618	+	0.310364i	$0.100451\pi$
$968$	−8.50176	−0.273257
$969$	52.3220	1.68082
$970$	−0.242701	−0.00779267
$971$	−45.5830	−1.46283	−0.731413	−	0.681934i	$-0.761139\pi$
$971$	−45.5830	−1.46283	−0.731413	+	0.681934i	$0.761139\pi$
$972$	−2.60103	−0.0834281
$973$	−22.7852	−0.730461
$974$	35.0213	1.12216
$975$	94.5970	3.02953
$976$	−6.40058	−0.204878
$977$	−56.3478	−1.80273	−0.901363	−	0.433065i	$-0.857432\pi$
$977$	−56.3478	−1.80273	−0.901363	+	0.433065i	$0.857432\pi$
$978$	−25.9528	−0.829879
$979$	−18.0120	−0.575666
$980$	−0.184335	−0.00588836
$981$	40.3954	1.28972
$982$	−0.715554	−0.0228342
$983$	12.1722	0.388233	0.194117	−	0.980978i	$-0.437816\pi$
$983$	12.1722	0.388233	0.194117	+	0.980978i	$0.437816\pi$
$984$	4.80398	0.153145
$985$	0.659616	0.0210171
$986$	−50.1343	−1.59660
$987$	25.4370	0.809669
$988$	20.2036	0.642763
$989$	−45.8190	−1.45696
$990$	−0.292653	−0.00930113
$991$	−25.4691	−0.809053	−0.404526	−	0.914526i	$-0.632564\pi$
$991$	−25.4691	−0.809053	−0.404526	+	0.914526i	$0.632564\pi$
$992$	6.51774	0.206938
$993$	−14.3250	−0.454591
$994$	7.73644	0.245385
$995$	0.641458	0.0203356
$996$	20.9979	0.665345
$997$	37.2793	1.18065	0.590324	−	0.807166i	$-0.299000\pi$
$997$	37.2793	1.18065	0.590324	+	0.807166i	$0.299000\pi$
$998$	26.1873	0.828945
$999$	14.8635	0.470260

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	538.2.a.e.1.7	✓	7
3.2	odd	2		4842.2.a.n.1.5		7
4.3	odd	2		4304.2.a.h.1.1		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
538.2.a.e.1.7	✓	7	1.1	even	1	trivial
4304.2.a.h.1.1		7	4.3	odd	2
4842.2.a.n.1.5		7	3.2	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:	\( N \)	\(=\)	\( 538 = 2 \cdot 269 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	538.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.97499 q^{3} +1.00000 q^{4} +0.0316474 q^{5} +2.97499 q^{6} +1.08414 q^{7} +1.00000 q^{8} +5.85056 q^{9} +0.0316474 q^{10} -1.58058 q^{11} +2.97499 q^{12} -6.36076 q^{13} +1.08414 q^{14} +0.0941507 q^{15} +1.00000 q^{16} -5.53705 q^{17} +5.85056 q^{18} -3.17629 q^{19} +0.0316474 q^{20} +3.22531 q^{21} -1.58058 q^{22} -3.94998 q^{23} +2.97499 q^{24} -4.99900 q^{25} -6.36076 q^{26} +8.48039 q^{27} +1.08414 q^{28} +9.05434 q^{29} +0.0941507 q^{30} +6.51774 q^{31} +1.00000 q^{32} -4.70222 q^{33} -5.53705 q^{34} +0.0343103 q^{35} +5.85056 q^{36} +1.75269 q^{37} -3.17629 q^{38} -18.9232 q^{39} +0.0316474 q^{40} +1.61479 q^{41} +3.22531 q^{42} +11.5998 q^{43} -1.58058 q^{44} +0.185155 q^{45} -3.94998 q^{46} +7.88668 q^{47} +2.97499 q^{48} -5.82464 q^{49} -4.99900 q^{50} -16.4727 q^{51} -6.36076 q^{52} +9.57824 q^{53} +8.48039 q^{54} -0.0500214 q^{55} +1.08414 q^{56} -9.44943 q^{57} +9.05434 q^{58} -12.9416 q^{59} +0.0941507 q^{60} -6.40058 q^{61} +6.51774 q^{62} +6.34284 q^{63} +1.00000 q^{64} -0.201302 q^{65} -4.70222 q^{66} -3.38476 q^{67} -5.53705 q^{68} -11.7511 q^{69} +0.0343103 q^{70} +7.13600 q^{71} +5.85056 q^{72} -3.40593 q^{73} +1.75269 q^{74} -14.8720 q^{75} -3.17629 q^{76} -1.71358 q^{77} -18.9232 q^{78} +8.96616 q^{79} +0.0316474 q^{80} +7.67738 q^{81} +1.61479 q^{82} +7.05816 q^{83} +3.22531 q^{84} -0.175233 q^{85} +11.5998 q^{86} +26.9366 q^{87} -1.58058 q^{88} +11.3958 q^{89} +0.185155 q^{90} -6.89596 q^{91} -3.94998 q^{92} +19.3902 q^{93} +7.88668 q^{94} -0.100521 q^{95} +2.97499 q^{96} -7.66892 q^{97} -5.82464 q^{98} -9.24730 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 7 q^{2} + q^{3} + 7 q^{4} + 7 q^{5} + q^{6} + 6 q^{7} + 7 q^{8} + 12 q^{9} + 7 q^{10} - 3 q^{11} + q^{12} - 9 q^{13} + 6 q^{14} + 8 q^{15} + 7 q^{16} + 8 q^{17} + 12 q^{18} - 11 q^{19} + 7 q^{20}+ \cdots - 37 q^{99}+O(q^{100}) \) 7 * q + 7 * q^2 + q^3 + 7 * q^4 + 7 * q^5 + q^6 + 6 * q^7 + 7 * q^8 + 12 * q^9 + 7 * q^10 - 3 * q^11 + q^12 - 9 * q^13 + 6 * q^14 + 8 * q^15 + 7 * q^16 + 8 * q^17 + 12 * q^18 - 11 * q^19 + 7 * q^20 - 6 * q^21 - 3 * q^22 + 12 * q^23 + q^24 + 22 * q^25 - 9 * q^26 - 14 * q^27 + 6 * q^28 - 5 * q^29 + 8 * q^30 + 14 * q^31 + 7 * q^32 - 4 * q^33 + 8 * q^34 - 4 * q^35 + 12 * q^36 + 13 * q^37 - 11 * q^38 - 18 * q^39 + 7 * q^40 + 12 * q^41 - 6 * q^42 - 11 * q^43 - 3 * q^44 + 3 * q^45 + 12 * q^46 + 2 * q^47 + q^48 + 15 * q^49 + 22 * q^50 - 26 * q^51 - 9 * q^52 + 19 * q^53 - 14 * q^54 - 40 * q^55 + 6 * q^56 - 12 * q^57 - 5 * q^58 - 9 * q^59 + 8 * q^60 - 3 * q^61 + 14 * q^62 - 26 * q^63 + 7 * q^64 - 10 * q^65 - 4 * q^66 - 33 * q^67 + 8 * q^68 - 64 * q^69 - 4 * q^70 + 28 * q^71 + 12 * q^72 - 14 * q^73 + 13 * q^74 - 45 * q^75 - 11 * q^76 + 10 * q^77 - 18 * q^78 + 2 * q^79 + 7 * q^80 + 15 * q^81 + 12 * q^82 - 7 * q^83 - 6 * q^84 - 16 * q^85 - 11 * q^86 + 16 * q^87 - 3 * q^88 + 18 * q^89 + 3 * q^90 - 26 * q^91 + 12 * q^92 + 6 * q^93 + 2 * q^94 - 34 * q^95 + q^96 - 4 * q^97 + 15 * q^98 - 37 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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