LMFDB - Embedded newform 4598.2.a.y.1.2

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:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{21}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 5 $ x^2 - x - 5
Coefficient ring:	$\Z[a_1, a_2, a_3]$
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			1.2
Root			$-1.79129$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +1.79129 q^{3} +1.00000 q^{4} +3.79129 q^{5} -1.79129 q^{6} +4.79129 q^{7} -1.00000 q^{8} +0.208712 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.79129 q^{3} +1.00000 q^{4} +3.79129 q^{5} -1.79129 q^{6} +4.79129 q^{7} -1.00000 q^{8} +0.208712 q^{9} -3.79129 q^{10} +1.79129 q^{12} -1.20871 q^{13} -4.79129 q^{14} +6.79129 q^{15} +1.00000 q^{16} +7.58258 q^{17} -0.208712 q^{18} -1.00000 q^{19} +3.79129 q^{20} +8.58258 q^{21} -1.58258 q^{23} -1.79129 q^{24} +9.37386 q^{25} +1.20871 q^{26} -5.00000 q^{27} +4.79129 q^{28} -2.20871 q^{29} -6.79129 q^{30} -10.7913 q^{31} -1.00000 q^{32} -7.58258 q^{34} +18.1652 q^{35} +0.208712 q^{36} +8.00000 q^{37} +1.00000 q^{38} -2.16515 q^{39} -3.79129 q^{40} +0.791288 q^{41} -8.58258 q^{42} -7.37386 q^{43} +0.791288 q^{45} +1.58258 q^{46} +9.16515 q^{47} +1.79129 q^{48} +15.9564 q^{49} -9.37386 q^{50} +13.5826 q^{51} -1.20871 q^{52} -1.58258 q^{53} +5.00000 q^{54} -4.79129 q^{56} -1.79129 q^{57} +2.20871 q^{58} +6.79129 q^{60} -2.00000 q^{61} +10.7913 q^{62} +1.00000 q^{63} +1.00000 q^{64} -4.58258 q^{65} -4.79129 q^{67} +7.58258 q^{68} -2.83485 q^{69} -18.1652 q^{70} -11.3739 q^{71} -0.208712 q^{72} -9.58258 q^{73} -8.00000 q^{74} +16.7913 q^{75} -1.00000 q^{76} +2.16515 q^{78} +5.58258 q^{79} +3.79129 q^{80} -9.58258 q^{81} -0.791288 q^{82} +3.79129 q^{83} +8.58258 q^{84} +28.7477 q^{85} +7.37386 q^{86} -3.95644 q^{87} -4.41742 q^{89} -0.791288 q^{90} -5.79129 q^{91} -1.58258 q^{92} -19.3303 q^{93} -9.16515 q^{94} -3.79129 q^{95} -1.79129 q^{96} +8.00000 q^{97} -15.9564 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - q^{3} + 2 q^{4} + 3 q^{5} + q^{6} + 5 q^{7} - 2 q^{8} + 5 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 - q^3 + 2 * q^4 + 3 * q^5 + q^6 + 5 * q^7 - 2 * q^8 + 5 * q^9	$ 2 q - 2 q^{2} - q^{3} + 2 q^{4} + 3 q^{5} + q^{6} + 5 q^{7} - 2 q^{8} + 5 q^{9} - 3 q^{10} - q^{12} - 7 q^{13} - 5 q^{14} + 9 q^{15} + 2 q^{16} + 6 q^{17} - 5 q^{18} - 2 q^{19} + 3 q^{20} + 8 q^{21} + 6 q^{23} + q^{24} + 5 q^{25} + 7 q^{26} - 10 q^{27} + 5 q^{28} - 9 q^{29} - 9 q^{30} - 17 q^{31} - 2 q^{32} - 6 q^{34} + 18 q^{35} + 5 q^{36} + 16 q^{37} + 2 q^{38} + 14 q^{39} - 3 q^{40} - 3 q^{41} - 8 q^{42} - q^{43} - 3 q^{45} - 6 q^{46} - q^{48} + 9 q^{49} - 5 q^{50} + 18 q^{51} - 7 q^{52} + 6 q^{53} + 10 q^{54} - 5 q^{56} + q^{57} + 9 q^{58} + 9 q^{60} - 4 q^{61} + 17 q^{62} + 2 q^{63} + 2 q^{64} - 5 q^{67} + 6 q^{68} - 24 q^{69} - 18 q^{70} - 9 q^{71} - 5 q^{72} - 10 q^{73} - 16 q^{74} + 29 q^{75} - 2 q^{76} - 14 q^{78} + 2 q^{79} + 3 q^{80} - 10 q^{81} + 3 q^{82} + 3 q^{83} + 8 q^{84} + 30 q^{85} + q^{86} + 15 q^{87} - 18 q^{89} + 3 q^{90} - 7 q^{91} + 6 q^{92} - 2 q^{93} - 3 q^{95} + q^{96} + 16 q^{97} - 9 q^{98}+O(q^{100}) $ 2 * q - 2 * q^2 - q^3 + 2 * q^4 + 3 * q^5 + q^6 + 5 * q^7 - 2 * q^8 + 5 * q^9 - 3 * q^10 - q^12 - 7 * q^13 - 5 * q^14 + 9 * q^15 + 2 * q^16 + 6 * q^17 - 5 * q^18 - 2 * q^19 + 3 * q^20 + 8 * q^21 + 6 * q^23 + q^24 + 5 * q^25 + 7 * q^26 - 10 * q^27 + 5 * q^28 - 9 * q^29 - 9 * q^30 - 17 * q^31 - 2 * q^32 - 6 * q^34 + 18 * q^35 + 5 * q^36 + 16 * q^37 + 2 * q^38 + 14 * q^39 - 3 * q^40 - 3 * q^41 - 8 * q^42 - q^43 - 3 * q^45 - 6 * q^46 - q^48 + 9 * q^49 - 5 * q^50 + 18 * q^51 - 7 * q^52 + 6 * q^53 + 10 * q^54 - 5 * q^56 + q^57 + 9 * q^58 + 9 * q^60 - 4 * q^61 + 17 * q^62 + 2 * q^63 + 2 * q^64 - 5 * q^67 + 6 * q^68 - 24 * q^69 - 18 * q^70 - 9 * q^71 - 5 * q^72 - 10 * q^73 - 16 * q^74 + 29 * q^75 - 2 * q^76 - 14 * q^78 + 2 * q^79 + 3 * q^80 - 10 * q^81 + 3 * q^82 + 3 * q^83 + 8 * q^84 + 30 * q^85 + q^86 + 15 * q^87 - 18 * q^89 + 3 * q^90 - 7 * q^91 + 6 * q^92 - 2 * q^93 - 3 * q^95 + q^96 + 16 * q^97 - 9 * 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
$3$	1.79129	1.03420	0.517100	−	0.855925i	$-0.327011\pi$
$3$	1.79129	1.03420	0.517100	+	0.855925i	$0.327011\pi$
$4$	1.00000	0.500000
$5$	3.79129	1.69552	0.847758	−	0.530384i	$-0.177952\pi$
$5$	3.79129	1.69552	0.847758	+	0.530384i	$0.177952\pi$
$6$	−1.79129	−0.731290
$7$	4.79129	1.81094	0.905468	−	0.424414i	$-0.139520\pi$
$7$	4.79129	1.81094	0.905468	+	0.424414i	$0.139520\pi$
$8$	−1.00000	−0.353553
$9$	0.208712	0.0695707
$10$	−3.79129	−1.19891
$11$	0	0
$11$	0	0
$12$	1.79129	0.517100
$13$	−1.20871	−0.335236	−0.167618	−	0.985852i	$-0.553608\pi$
$13$	−1.20871	−0.335236	−0.167618	+	0.985852i	$0.553608\pi$
$14$	−4.79129	−1.28053
$15$	6.79129	1.75350
$16$	1.00000	0.250000
$17$	7.58258	1.83904	0.919522	−	0.393038i	$-0.128576\pi$
$17$	7.58258	1.83904	0.919522	+	0.393038i	$0.128576\pi$
$18$	−0.208712	−0.0491939
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	3.79129	0.847758
$21$	8.58258	1.87287
$22$	0	0
$23$	−1.58258	−0.329990	−0.164995	−	0.986294i	$-0.552761\pi$
$23$	−1.58258	−0.329990	−0.164995	+	0.986294i	$0.552761\pi$
$24$	−1.79129	−0.365645
$25$	9.37386	1.87477
$26$	1.20871	0.237048
$27$	−5.00000	−0.962250
$28$	4.79129	0.905468
$29$	−2.20871	−0.410148	−0.205074	−	0.978747i	$-0.565743\pi$
$29$	−2.20871	−0.410148	−0.205074	+	0.978747i	$0.565743\pi$
$30$	−6.79129	−1.23991
$31$	−10.7913	−1.93817	−0.969086	−	0.246722i	$-0.920646\pi$
$31$	−10.7913	−1.93817	−0.969086	+	0.246722i	$0.920646\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	−7.58258	−1.30040
$35$	18.1652	3.07047
$36$	0.208712	0.0347854
$37$	8.00000	1.31519	0.657596	−	0.753371i	$-0.271573\pi$
$37$	8.00000	1.31519	0.657596	+	0.753371i	$0.271573\pi$
$38$	1.00000	0.162221
$39$	−2.16515	−0.346702
$40$	−3.79129	−0.599455
$41$	0.791288	0.123578	0.0617892	−	0.998089i	$-0.480319\pi$
$41$	0.791288	0.123578	0.0617892	+	0.998089i	$0.480319\pi$
$42$	−8.58258	−1.32432
$43$	−7.37386	−1.12450	−0.562252	−	0.826966i	$-0.690065\pi$
$43$	−7.37386	−1.12450	−0.562252	+	0.826966i	$0.690065\pi$
$44$	0	0
$45$	0.791288	0.117958
$46$	1.58258	0.233338
$47$	9.16515	1.33687	0.668437	−	0.743768i	$-0.266963\pi$
$47$	9.16515	1.33687	0.668437	+	0.743768i	$0.266963\pi$
$48$	1.79129	0.258550
$49$	15.9564	2.27949
$50$	−9.37386	−1.32566
$51$	13.5826	1.90194
$52$	−1.20871	−0.167618
$53$	−1.58258	−0.217383	−0.108692	−	0.994076i	$-0.534666\pi$
$53$	−1.58258	−0.217383	−0.108692	+	0.994076i	$0.534666\pi$
$54$	5.00000	0.680414
$55$	0	0
$56$	−4.79129	−0.640263
$57$	−1.79129	−0.237262
$58$	2.20871	0.290018
$59$	0	0		−	1.00000i	$-0.5\pi$
$59$	0	0			1.00000i	$0.5\pi$
$60$	6.79129	0.876751
$61$	−2.00000	−0.256074	−0.128037	−	0.991769i	$-0.540868\pi$
$61$	−2.00000	−0.256074	−0.128037	+	0.991769i	$0.540868\pi$
$62$	10.7913	1.37049
$63$	1.00000	0.125988
$64$	1.00000	0.125000
$65$	−4.58258	−0.568399
$66$	0	0
$67$	−4.79129	−0.585349	−0.292674	−	0.956212i	$-0.594545\pi$
$67$	−4.79129	−0.585349	−0.292674	+	0.956212i	$0.594545\pi$
$68$	7.58258	0.919522
$69$	−2.83485	−0.341276
$70$	−18.1652	−2.17115
$71$	−11.3739	−1.34983	−0.674915	−	0.737896i	$-0.735820\pi$
$71$	−11.3739	−1.34983	−0.674915	+	0.737896i	$0.735820\pi$
$72$	−0.208712	−0.0245970
$73$	−9.58258	−1.12156	−0.560778	−	0.827966i	$-0.689498\pi$
$73$	−9.58258	−1.12156	−0.560778	+	0.827966i	$0.689498\pi$
$74$	−8.00000	−0.929981
$75$	16.7913	1.93889
$76$	−1.00000	−0.114708
$77$	0	0
$78$	2.16515	0.245155
$79$	5.58258	0.628089	0.314044	−	0.949408i	$-0.398316\pi$
$79$	5.58258	0.628089	0.314044	+	0.949408i	$0.398316\pi$
$80$	3.79129	0.423879
$81$	−9.58258	−1.06473
$82$	−0.791288	−0.0873831
$83$	3.79129	0.416148	0.208074	−	0.978113i	$-0.433281\pi$
$83$	3.79129	0.416148	0.208074	+	0.978113i	$0.433281\pi$
$84$	8.58258	0.936436
$85$	28.7477	3.11813
$86$	7.37386	0.795144
$87$	−3.95644	−0.424175
$88$	0	0
$89$	−4.41742	−0.468246	−0.234123	−	0.972207i	$-0.575222\pi$
$89$	−4.41742	−0.468246	−0.234123	+	0.972207i	$0.575222\pi$
$90$	−0.791288	−0.0834091
$91$	−5.79129	−0.607092
$92$	−1.58258	−0.164995
$93$	−19.3303	−2.00446
$94$	−9.16515	−0.945313
$95$	−3.79129	−0.388978
$96$	−1.79129	−0.182823
$97$	8.00000	0.812277	0.406138	−	0.913812i	$-0.366875\pi$
$97$	8.00000	0.812277	0.406138	+	0.913812i	$0.366875\pi$
$98$	−15.9564	−1.61184
$99$	0	0
$100$	9.37386	0.937386
$101$	13.5826	1.35152	0.675758	−	0.737123i	$-0.263816\pi$
$101$	13.5826	1.35152	0.675758	+	0.737123i	$0.263816\pi$
$102$	−13.5826	−1.34488
$103$	2.95644	0.291307	0.145653	−	0.989336i	$-0.453472\pi$
$103$	2.95644	0.291307	0.145653	+	0.989336i	$0.453472\pi$
$104$	1.20871	0.118524
$105$	32.5390	3.17548
$106$	1.58258	0.153713
$107$	−18.0000	−1.74013	−0.870063	−	0.492941i	$-0.835922\pi$
$107$	−18.0000	−1.74013	−0.870063	+	0.492941i	$0.835922\pi$
$108$	−5.00000	−0.481125
$109$	10.0000	0.957826	0.478913	−	0.877862i	$-0.341031\pi$
$109$	10.0000	0.957826	0.478913	+	0.877862i	$0.341031\pi$
$110$	0	0
$111$	14.3303	1.36017
$112$	4.79129	0.452734
$113$	15.1652	1.42662	0.713309	−	0.700850i	$-0.247196\pi$
$113$	15.1652	1.42662	0.713309	+	0.700850i	$0.247196\pi$
$114$	1.79129	0.167769
$115$	−6.00000	−0.559503
$116$	−2.20871	−0.205074
$117$	−0.252273	−0.0233226
$118$	0	0
$119$	36.3303	3.33039
$120$	−6.79129	−0.619957
$121$	0	0
$122$	2.00000	0.181071
$123$	1.41742	0.127805
$124$	−10.7913	−0.969086
$125$	16.5826	1.48319
$126$	−1.00000	−0.0890871
$127$	8.74773	0.776235	0.388118	−	0.921610i	$-0.373125\pi$
$127$	8.74773	0.776235	0.388118	+	0.921610i	$0.373125\pi$
$128$	−1.00000	−0.0883883
$129$	−13.2087	−1.16296
$130$	4.58258	0.401918
$131$	−3.62614	−0.316817	−0.158409	−	0.987374i	$-0.550636\pi$
$131$	−3.62614	−0.316817	−0.158409	+	0.987374i	$0.550636\pi$
$132$	0	0
$133$	−4.79129	−0.415457
$134$	4.79129	0.413904
$135$	−18.9564	−1.63151
$136$	−7.58258	−0.650201
$137$	5.20871	0.445010	0.222505	−	0.974932i	$-0.428577\pi$
$137$	5.20871	0.445010	0.222505	+	0.974932i	$0.428577\pi$
$138$	2.83485	0.241318
$139$	12.2087	1.03553	0.517765	−	0.855523i	$-0.326764\pi$
$139$	12.2087	1.03553	0.517765	+	0.855523i	$0.326764\pi$
$140$	18.1652	1.53524
$141$	16.4174	1.38260
$142$	11.3739	0.954473
$143$	0	0
$144$	0.208712	0.0173927
$145$	−8.37386	−0.695412
$146$	9.58258	0.793060
$147$	28.5826	2.35745
$148$	8.00000	0.657596
$149$	0	0		−	1.00000i	$-0.5\pi$
$149$	0	0			1.00000i	$0.5\pi$
$150$	−16.7913	−1.37100
$151$	−2.00000	−0.162758	−0.0813788	−	0.996683i	$-0.525932\pi$
$151$	−2.00000	−0.162758	−0.0813788	+	0.996683i	$0.525932\pi$
$152$	1.00000	0.0811107
$153$	1.58258	0.127944
$154$	0	0
$155$	−40.9129	−3.28620
$156$	−2.16515	−0.173351
$157$	−10.9564	−0.874419	−0.437210	−	0.899360i	$-0.644033\pi$
$157$	−10.9564	−0.874419	−0.437210	+	0.899360i	$0.644033\pi$
$158$	−5.58258	−0.444126
$159$	−2.83485	−0.224818
$160$	−3.79129	−0.299728
$161$	−7.58258	−0.597591
$162$	9.58258	0.752878
$163$	−11.5826	−0.907217	−0.453609	−	0.891201i	$-0.649864\pi$
$163$	−11.5826	−0.907217	−0.453609	+	0.891201i	$0.649864\pi$
$164$	0.791288	0.0617892
$165$	0	0
$166$	−3.79129	−0.294261
$167$	−18.0000	−1.39288	−0.696441	−	0.717614i	$-0.745234\pi$
$167$	−18.0000	−1.39288	−0.696441	+	0.717614i	$0.745234\pi$
$168$	−8.58258	−0.662160
$169$	−11.5390	−0.887617
$170$	−28.7477	−2.20485
$171$	−0.208712	−0.0159606
$172$	−7.37386	−0.562252
$173$	−12.9564	−0.985060	−0.492530	−	0.870296i	$-0.663928\pi$
$173$	−12.9564	−0.985060	−0.492530	+	0.870296i	$0.663928\pi$
$174$	3.95644	0.299937
$175$	44.9129	3.39509
$176$	0	0
$177$	0	0
$178$	4.41742	0.331100
$179$	3.95644	0.295718	0.147859	−	0.989008i	$-0.452762\pi$
$179$	3.95644	0.295718	0.147859	+	0.989008i	$0.452762\pi$
$180$	0.791288	0.0589791
$181$	18.7477	1.39351	0.696754	−	0.717310i	$-0.254627\pi$
$181$	18.7477	1.39351	0.696754	+	0.717310i	$0.254627\pi$
$182$	5.79129	0.429279
$183$	−3.58258	−0.264832
$184$	1.58258	0.116669
$185$	30.3303	2.22993
$186$	19.3303	1.41737
$187$	0	0
$188$	9.16515	0.668437
$189$	−23.9564	−1.74257
$190$	3.79129	0.275049
$191$	−18.0000	−1.30243	−0.651217	−	0.758891i	$-0.725741\pi$
$191$	−18.0000	−1.30243	−0.651217	+	0.758891i	$0.725741\pi$
$192$	1.79129	0.129275
$193$	−7.37386	−0.530782	−0.265391	−	0.964141i	$-0.585501\pi$
$193$	−7.37386	−0.530782	−0.265391	+	0.964141i	$0.585501\pi$
$194$	−8.00000	−0.574367
$195$	−8.20871	−0.587838
$196$	15.9564	1.13975
$197$	−9.16515	−0.652990	−0.326495	−	0.945199i	$-0.605868\pi$
$197$	−9.16515	−0.652990	−0.326495	+	0.945199i	$0.605868\pi$
$198$	0	0
$199$	6.74773	0.478334	0.239167	−	0.970978i	$-0.423126\pi$
$199$	6.74773	0.478334	0.239167	+	0.970978i	$0.423126\pi$
$200$	−9.37386	−0.662832
$201$	−8.58258	−0.605368
$202$	−13.5826	−0.955667
$203$	−10.5826	−0.742751
$204$	13.5826	0.950971
$205$	3.00000	0.209529
$206$	−2.95644	−0.205985
$207$	−0.330303	−0.0229576
$208$	−1.20871	−0.0838091
$209$	0	0
$210$	−32.5390	−2.24541
$211$	−18.7477	−1.29065	−0.645323	−	0.763910i	$-0.723277\pi$
$211$	−18.7477	−1.29065	−0.645323	+	0.763910i	$0.723277\pi$
$212$	−1.58258	−0.108692
$213$	−20.3739	−1.39599
$214$	18.0000	1.23045
$215$	−27.9564	−1.90661
$216$	5.00000	0.340207
$217$	−51.7042	−3.50991
$218$	−10.0000	−0.677285
$219$	−17.1652	−1.15991
$220$	0	0
$221$	−9.16515	−0.616515
$222$	−14.3303	−0.961787
$223$	−7.16515	−0.479814	−0.239907	−	0.970796i	$-0.577117\pi$
$223$	−7.16515	−0.479814	−0.239907	+	0.970796i	$0.577117\pi$
$224$	−4.79129	−0.320131
$225$	1.95644	0.130429
$226$	−15.1652	−1.00877
$227$	7.58258	0.503273	0.251637	−	0.967822i	$-0.419031\pi$
$227$	7.58258	0.503273	0.251637	+	0.967822i	$0.419031\pi$
$228$	−1.79129	−0.118631
$229$	−18.3739	−1.21418	−0.607090	−	0.794633i	$-0.707663\pi$
$229$	−18.3739	−1.21418	−0.607090	+	0.794633i	$0.707663\pi$
$230$	6.00000	0.395628
$231$	0	0
$232$	2.20871	0.145009
$233$	−15.1652	−0.993502	−0.496751	−	0.867893i	$-0.665474\pi$
$233$	−15.1652	−0.993502	−0.496751	+	0.867893i	$0.665474\pi$
$234$	0.252273	0.0164916
$235$	34.7477	2.26669
$236$	0	0
$237$	10.0000	0.649570
$238$	−36.3303	−2.35494
$239$	2.20871	0.142870	0.0714349	−	0.997445i	$-0.477242\pi$
$239$	2.20871	0.142870	0.0714349	+	0.997445i	$0.477242\pi$
$240$	6.79129	0.438376
$241$	0.208712	0.0134443	0.00672217	−	0.999977i	$-0.497860\pi$
$241$	0.208712	0.0134443	0.00672217	+	0.999977i	$0.497860\pi$
$242$	0	0
$243$	−2.16515	−0.138895
$244$	−2.00000	−0.128037
$245$	60.4955	3.86491
$246$	−1.41742	−0.0903717
$247$	1.20871	0.0769085
$248$	10.7913	0.685247
$249$	6.79129	0.430380
$250$	−16.5826	−1.04877
$251$	12.0000	0.757433	0.378717	−	0.925513i	$-0.376365\pi$
$251$	12.0000	0.757433	0.378717	+	0.925513i	$0.376365\pi$
$252$	1.00000	0.0629941
$253$	0	0
$254$	−8.74773	−0.548881
$255$	51.4955	3.22477
$256$	1.00000	0.0625000
$257$	−7.58258	−0.472988	−0.236494	−	0.971633i	$-0.575998\pi$
$257$	−7.58258	−0.472988	−0.236494	+	0.971633i	$0.575998\pi$
$258$	13.2087	0.822338
$259$	38.3303	2.38173
$260$	−4.58258	−0.284199
$261$	−0.460985	−0.0285343
$262$	3.62614	0.224023
$263$	−12.9564	−0.798928	−0.399464	−	0.916749i	$-0.630804\pi$
$263$	−12.9564	−0.798928	−0.399464	+	0.916749i	$0.630804\pi$
$264$	0	0
$265$	−6.00000	−0.368577
$266$	4.79129	0.293773
$267$	−7.91288	−0.484260
$268$	−4.79129	−0.292674
$269$	−16.7477	−1.02113	−0.510563	−	0.859840i	$-0.670563\pi$
$269$	−16.7477	−1.02113	−0.510563	+	0.859840i	$0.670563\pi$
$270$	18.9564	1.15365
$271$	6.37386	0.387185	0.193592	−	0.981082i	$-0.437986\pi$
$271$	6.37386	0.387185	0.193592	+	0.981082i	$0.437986\pi$
$272$	7.58258	0.459761
$273$	−10.3739	−0.627855
$274$	−5.20871	−0.314670
$275$	0	0
$276$	−2.83485	−0.170638
$277$	22.0000	1.32185	0.660926	−	0.750451i	$-0.270164\pi$
$277$	22.0000	1.32185	0.660926	+	0.750451i	$0.270164\pi$
$278$	−12.2087	−0.732230
$279$	−2.25227	−0.134840
$280$	−18.1652	−1.08558
$281$	−22.1216	−1.31966	−0.659832	−	0.751413i	$-0.729372\pi$
$281$	−22.1216	−1.31966	−0.659832	+	0.751413i	$0.729372\pi$
$282$	−16.4174	−0.977643
$283$	−9.12159	−0.542222	−0.271111	−	0.962548i	$-0.587391\pi$
$283$	−9.12159	−0.542222	−0.271111	+	0.962548i	$0.587391\pi$
$284$	−11.3739	−0.674915
$285$	−6.79129	−0.402281
$286$	0	0
$287$	3.79129	0.223793
$288$	−0.208712	−0.0122985
$289$	40.4955	2.38209
$290$	8.37386	0.491730
$291$	14.3303	0.840057
$292$	−9.58258	−0.560778
$293$	−6.79129	−0.396751	−0.198376	−	0.980126i	$-0.563567\pi$
$293$	−6.79129	−0.396751	−0.198376	+	0.980126i	$0.563567\pi$
$294$	−28.5826	−1.66697
$295$	0	0
$296$	−8.00000	−0.464991
$297$	0	0
$298$	0	0
$299$	1.91288	0.110625
$300$	16.7913	0.969445
$301$	−35.3303	−2.03640
$302$	2.00000	0.115087
$303$	24.3303	1.39774
$304$	−1.00000	−0.0573539
$305$	−7.58258	−0.434177
$306$	−1.58258	−0.0904698
$307$	5.25227	0.299763	0.149882	−	0.988704i	$-0.452111\pi$
$307$	5.25227	0.299763	0.149882	+	0.988704i	$0.452111\pi$
$308$	0	0
$309$	5.29583	0.301269
$310$	40.9129	2.32370
$311$	−25.9129	−1.46938	−0.734692	−	0.678401i	$-0.762673\pi$
$311$	−25.9129	−1.46938	−0.734692	+	0.678401i	$0.762673\pi$
$312$	2.16515	0.122578
$313$	−9.37386	−0.529842	−0.264921	−	0.964270i	$-0.585346\pi$
$313$	−9.37386	−0.529842	−0.264921	+	0.964270i	$0.585346\pi$
$314$	10.9564	0.618308
$315$	3.79129	0.213615
$316$	5.58258	0.314044
$317$	1.25227	0.0703347	0.0351673	−	0.999381i	$-0.488804\pi$
$317$	1.25227	0.0703347	0.0351673	+	0.999381i	$0.488804\pi$
$318$	2.83485	0.158970
$319$	0	0
$320$	3.79129	0.211939
$321$	−32.2432	−1.79964
$322$	7.58258	0.422560
$323$	−7.58258	−0.421906
$324$	−9.58258	−0.532365
$325$	−11.3303	−0.628492
$326$	11.5826	0.641500
$327$	17.9129	0.990584
$328$	−0.791288	−0.0436916
$329$	43.9129	2.42100
$330$	0	0
$331$	29.7913	1.63748	0.818739	−	0.574166i	$-0.194674\pi$
$331$	29.7913	1.63748	0.818739	+	0.574166i	$0.194674\pi$
$332$	3.79129	0.208074
$333$	1.66970	0.0914988
$334$	18.0000	0.984916
$335$	−18.1652	−0.992468
$336$	8.58258	0.468218
$337$	13.6261	0.742263	0.371131	−	0.928580i	$-0.378970\pi$
$337$	13.6261	0.742263	0.371131	+	0.928580i	$0.378970\pi$
$338$	11.5390	0.627640
$339$	27.1652	1.47541
$340$	28.7477	1.55906
$341$	0	0
$342$	0.208712	0.0112859
$343$	42.9129	2.31708
$344$	7.37386	0.397572
$345$	−10.7477	−0.578638
$346$	12.9564	0.696542
$347$	3.16515	0.169914	0.0849571	−	0.996385i	$-0.472925\pi$
$347$	3.16515	0.169914	0.0849571	+	0.996385i	$0.472925\pi$
$348$	−3.95644	−0.212087
$349$	−23.4955	−1.25768	−0.628841	−	0.777534i	$-0.716471\pi$
$349$	−23.4955	−1.25768	−0.628841	+	0.777534i	$0.716471\pi$
$350$	−44.9129	−2.40069
$351$	6.04356	0.322581
$352$	0	0
$353$	−14.8348	−0.789579	−0.394790	−	0.918772i	$-0.629183\pi$
$353$	−14.8348	−0.789579	−0.394790	+	0.918772i	$0.629183\pi$
$354$	0	0
$355$	−43.1216	−2.28866
$356$	−4.41742	−0.234123
$357$	65.0780	3.44429
$358$	−3.95644	−0.209104
$359$	−20.7042	−1.09272	−0.546362	−	0.837549i	$-0.683988\pi$
$359$	−20.7042	−1.09272	−0.546362	+	0.837549i	$0.683988\pi$
$360$	−0.791288	−0.0417045
$361$	1.00000	0.0526316
$362$	−18.7477	−0.985359
$363$	0	0
$364$	−5.79129	−0.303546
$365$	−36.3303	−1.90161
$366$	3.58258	0.187264
$367$	20.3303	1.06123	0.530617	−	0.847612i	$-0.321960\pi$
$367$	20.3303	1.06123	0.530617	+	0.847612i	$0.321960\pi$
$368$	−1.58258	−0.0824975
$369$	0.165151	0.00859744
$370$	−30.3303	−1.57680
$371$	−7.58258	−0.393668
$372$	−19.3303	−1.00223
$373$	9.37386	0.485360	0.242680	−	0.970106i	$-0.421973\pi$
$373$	9.37386	0.485360	0.242680	+	0.970106i	$0.421973\pi$
$374$	0	0
$375$	29.7042	1.53392
$376$	−9.16515	−0.472657
$377$	2.66970	0.137496
$378$	23.9564	1.23219
$379$	32.7913	1.68438	0.842188	−	0.539185i	$-0.181267\pi$
$379$	32.7913	1.68438	0.842188	+	0.539185i	$0.181267\pi$
$380$	−3.79129	−0.194489
$381$	15.6697	0.802783
$382$	18.0000	0.920960
$383$	−9.95644	−0.508750	−0.254375	−	0.967106i	$-0.581870\pi$
$383$	−9.95644	−0.508750	−0.254375	+	0.967106i	$0.581870\pi$
$384$	−1.79129	−0.0914113
$385$	0	0
$386$	7.37386	0.375320
$387$	−1.53901	−0.0782325
$388$	8.00000	0.406138
$389$	10.1216	0.513185	0.256593	−	0.966520i	$-0.417400\pi$
$389$	10.1216	0.513185	0.256593	+	0.966520i	$0.417400\pi$
$390$	8.20871	0.415664
$391$	−12.0000	−0.606866
$392$	−15.9564	−0.805922
$393$	−6.49545	−0.327652
$394$	9.16515	0.461734
$395$	21.1652	1.06493
$396$	0	0
$397$	4.04356	0.202940	0.101470	−	0.994839i	$-0.467645\pi$
$397$	4.04356	0.202940	0.101470	+	0.994839i	$0.467645\pi$
$398$	−6.74773	−0.338233
$399$	−8.58258	−0.429666
$400$	9.37386	0.468693
$401$	−13.5826	−0.678281	−0.339141	−	0.940736i	$-0.610136\pi$
$401$	−13.5826	−0.678281	−0.339141	+	0.940736i	$0.610136\pi$
$402$	8.58258	0.428060
$403$	13.0436	0.649746
$404$	13.5826	0.675758
$405$	−36.3303	−1.80527
$406$	10.5826	0.525204
$407$	0	0
$408$	−13.5826	−0.672438
$409$	3.37386	0.166827	0.0834134	−	0.996515i	$-0.473418\pi$
$409$	3.37386	0.166827	0.0834134	+	0.996515i	$0.473418\pi$
$410$	−3.00000	−0.148159
$411$	9.33030	0.460230
$412$	2.95644	0.145653
$413$	0	0
$414$	0.330303	0.0162335
$415$	14.3739	0.705585
$416$	1.20871	0.0592620
$417$	21.8693	1.07095
$418$	0	0
$419$	12.3303	0.602375	0.301187	−	0.953565i	$-0.402617\pi$
$419$	12.3303	0.602375	0.301187	+	0.953565i	$0.402617\pi$
$420$	32.5390	1.58774
$421$	−11.2523	−0.548402	−0.274201	−	0.961672i	$-0.588413\pi$
$421$	−11.2523	−0.548402	−0.274201	+	0.961672i	$0.588413\pi$
$422$	18.7477	0.912625
$423$	1.91288	0.0930073
$424$	1.58258	0.0768567
$425$	71.0780	3.44779
$426$	20.3739	0.987117
$427$	−9.58258	−0.463733
$428$	−18.0000	−0.870063
$429$	0	0
$430$	27.9564	1.34818
$431$	21.4955	1.03540	0.517700	−	0.855562i	$-0.326788\pi$
$431$	21.4955	1.03540	0.517700	+	0.855562i	$0.326788\pi$
$432$	−5.00000	−0.240563
$433$	−11.5826	−0.556623	−0.278312	−	0.960491i	$-0.589775\pi$
$433$	−11.5826	−0.556623	−0.278312	+	0.960491i	$0.589775\pi$
$434$	51.7042	2.48188
$435$	−15.0000	−0.719195
$436$	10.0000	0.478913
$437$	1.58258	0.0757049
$438$	17.1652	0.820183
$439$	31.1652	1.48743	0.743716	−	0.668496i	$-0.233062\pi$
$439$	31.1652	1.48743	0.743716	+	0.668496i	$0.233062\pi$
$440$	0	0
$441$	3.33030	0.158586
$442$	9.16515	0.435942
$443$	−18.3303	−0.870899	−0.435449	−	0.900213i	$-0.643411\pi$
$443$	−18.3303	−0.870899	−0.435449	+	0.900213i	$0.643411\pi$
$444$	14.3303	0.680086
$445$	−16.7477	−0.793918
$446$	7.16515	0.339280
$447$	0	0
$448$	4.79129	0.226367
$449$	16.7477	0.790374	0.395187	−	0.918601i	$-0.370680\pi$
$449$	16.7477	0.790374	0.395187	+	0.918601i	$0.370680\pi$
$450$	−1.95644	−0.0922274
$451$	0	0
$452$	15.1652	0.713309
$453$	−3.58258	−0.168324
$454$	−7.58258	−0.355868
$455$	−21.9564	−1.02933
$456$	1.79129	0.0838847
$457$	5.25227	0.245691	0.122845	−	0.992426i	$-0.460798\pi$
$457$	5.25227	0.245691	0.122845	+	0.992426i	$0.460798\pi$
$458$	18.3739	0.858554
$459$	−37.9129	−1.76962
$460$	−6.00000	−0.279751
$461$	30.3303	1.41262	0.706312	−	0.707901i	$-0.250358\pi$
$461$	30.3303	1.41262	0.706312	+	0.707901i	$0.250358\pi$
$462$	0	0
$463$	−40.6606	−1.88966	−0.944829	−	0.327563i	$-0.893773\pi$
$463$	−40.6606	−1.88966	−0.944829	+	0.327563i	$0.893773\pi$
$464$	−2.20871	−0.102537
$465$	−73.2867	−3.39859
$466$	15.1652	0.702512
$467$	13.5826	0.628527	0.314263	−	0.949336i	$-0.398243\pi$
$467$	13.5826	0.628527	0.314263	+	0.949336i	$0.398243\pi$
$468$	−0.252273	−0.0116613
$469$	−22.9564	−1.06003
$470$	−34.7477	−1.60279
$471$	−19.6261	−0.904325
$472$	0	0
$473$	0	0
$474$	−10.0000	−0.459315
$475$	−9.37386	−0.430102
$476$	36.3303	1.66520
$477$	−0.330303	−0.0151235
$478$	−2.20871	−0.101024
$479$	12.7913	0.584449	0.292224	−	0.956350i	$-0.405605\pi$
$479$	12.7913	0.584449	0.292224	+	0.956350i	$0.405605\pi$
$480$	−6.79129	−0.309978
$481$	−9.66970	−0.440900
$482$	−0.208712	−0.00950658
$483$	−13.5826	−0.618029
$484$	0	0
$485$	30.3303	1.37723
$486$	2.16515	0.0982133
$487$	18.1216	0.821168	0.410584	−	0.911823i	$-0.365325\pi$
$487$	18.1216	0.821168	0.410584	+	0.911823i	$0.365325\pi$
$488$	2.00000	0.0905357
$489$	−20.7477	−0.938245
$490$	−60.4955	−2.73291
$491$	29.8693	1.34798	0.673992	−	0.738739i	$-0.264578\pi$
$491$	29.8693	1.34798	0.673992	+	0.738739i	$0.264578\pi$
$492$	1.41742	0.0639024
$493$	−16.7477	−0.754280
$494$	−1.20871	−0.0543825
$495$	0	0
$496$	−10.7913	−0.484543
$497$	−54.4955	−2.44446
$498$	−6.79129	−0.304325
$499$	−1.16515	−0.0521593	−0.0260797	−	0.999660i	$-0.508302\pi$
$499$	−1.16515	−0.0521593	−0.0260797	+	0.999660i	$0.508302\pi$
$500$	16.5826	0.741595
$501$	−32.2432	−1.44052
$502$	−12.0000	−0.535586
$503$	−12.9564	−0.577699	−0.288850	−	0.957375i	$-0.593273\pi$
$503$	−12.9564	−0.577699	−0.288850	+	0.957375i	$0.593273\pi$
$504$	−1.00000	−0.0445435
$505$	51.4955	2.29152
$506$	0	0
$507$	−20.6697	−0.917973
$508$	8.74773	0.388118
$509$	−8.83485	−0.391598	−0.195799	−	0.980644i	$-0.562730\pi$
$509$	−8.83485	−0.391598	−0.195799	+	0.980644i	$0.562730\pi$
$510$	−51.4955	−2.28026
$511$	−45.9129	−2.03107
$512$	−1.00000	−0.0441942
$513$	5.00000	0.220755
$514$	7.58258	0.334453
$515$	11.2087	0.493915
$516$	−13.2087	−0.581481
$517$	0	0
$518$	−38.3303	−1.68414
$519$	−23.2087	−1.01875
$520$	4.58258	0.200959
$521$	33.1652	1.45299	0.726496	−	0.687171i	$-0.241148\pi$
$521$	33.1652	1.45299	0.726496	+	0.687171i	$0.241148\pi$
$522$	0.460985	0.0201768
$523$	2.74773	0.120150	0.0600749	−	0.998194i	$-0.480866\pi$
$523$	2.74773	0.120150	0.0600749	+	0.998194i	$0.480866\pi$
$524$	−3.62614	−0.158409
$525$	80.4519	3.51121
$526$	12.9564	0.564928
$527$	−81.8258	−3.56439
$528$	0	0
$529$	−20.4955	−0.891107
$530$	6.00000	0.260623
$531$	0	0
$532$	−4.79129	−0.207729
$533$	−0.956439	−0.0414280
$534$	7.91288	0.342424
$535$	−68.2432	−2.95041
$536$	4.79129	0.206952
$537$	7.08712	0.305832
$538$	16.7477	0.722046
$539$	0	0
$540$	−18.9564	−0.815755
$541$	35.9129	1.54402	0.772008	−	0.635613i	$-0.219253\pi$
$541$	35.9129	1.54402	0.772008	+	0.635613i	$0.219253\pi$
$542$	−6.37386	−0.273781
$543$	33.5826	1.44117
$544$	−7.58258	−0.325100
$545$	37.9129	1.62401
$546$	10.3739	0.443960
$547$	43.1652	1.84561	0.922804	−	0.385269i	$-0.125891\pi$
$547$	43.1652	1.84561	0.922804	+	0.385269i	$0.125891\pi$
$548$	5.20871	0.222505
$549$	−0.417424	−0.0178152
$550$	0	0
$551$	2.20871	0.0940943
$552$	2.83485	0.120659
$553$	26.7477	1.13743
$554$	−22.0000	−0.934690
$555$	54.3303	2.30619
$556$	12.2087	0.517765
$557$	20.8348	0.882801	0.441400	−	0.897310i	$-0.354482\pi$
$557$	20.8348	0.882801	0.441400	+	0.897310i	$0.354482\pi$
$558$	2.25227	0.0953463
$559$	8.91288	0.376975
$560$	18.1652	0.767618
$561$	0	0
$562$	22.1216	0.933143
$563$	30.6606	1.29219	0.646095	−	0.763257i	$-0.276401\pi$
$563$	30.6606	1.29219	0.646095	+	0.763257i	$0.276401\pi$
$564$	16.4174	0.691298
$565$	57.4955	2.41885
$566$	9.12159	0.383409
$567$	−45.9129	−1.92816
$568$	11.3739	0.477237
$569$	3.95644	0.165863	0.0829313	−	0.996555i	$-0.473572\pi$
$569$	3.95644	0.165863	0.0829313	+	0.996555i	$0.473572\pi$
$570$	6.79129	0.284456
$571$	−14.7913	−0.618996	−0.309498	−	0.950900i	$-0.600161\pi$
$571$	−14.7913	−0.618996	−0.309498	+	0.950900i	$0.600161\pi$
$572$	0	0
$573$	−32.2432	−1.34698
$574$	−3.79129	−0.158245
$575$	−14.8348	−0.618656
$576$	0.208712	0.00869634
$577$	−33.8693	−1.41000	−0.704999	−	0.709208i	$-0.749053\pi$
$577$	−33.8693	−1.41000	−0.704999	+	0.709208i	$0.749053\pi$
$578$	−40.4955	−1.68439
$579$	−13.2087	−0.548935
$580$	−8.37386	−0.347706
$581$	18.1652	0.753617
$582$	−14.3303	−0.594010
$583$	0	0
$584$	9.58258	0.396530
$585$	−0.956439	−0.0395439
$586$	6.79129	0.280546
$587$	−3.16515	−0.130640	−0.0653199	−	0.997864i	$-0.520807\pi$
$587$	−3.16515	−0.130640	−0.0653199	+	0.997864i	$0.520807\pi$
$588$	28.5826	1.17873
$589$	10.7913	0.444647
$590$	0	0
$591$	−16.4174	−0.675323
$592$	8.00000	0.328798
$593$	−2.83485	−0.116413	−0.0582066	−	0.998305i	$-0.518538\pi$
$593$	−2.83485	−0.116413	−0.0582066	+	0.998305i	$0.518538\pi$
$594$	0	0
$595$	137.739	5.64673
$596$	0	0
$597$	12.0871	0.494693
$598$	−1.91288	−0.0782234
$599$	−18.9564	−0.774539	−0.387270	−	0.921967i	$-0.626582\pi$
$599$	−18.9564	−0.774539	−0.387270	+	0.921967i	$0.626582\pi$
$600$	−16.7913	−0.685501
$601$	15.2087	0.620376	0.310188	−	0.950675i	$-0.399608\pi$
$601$	15.2087	0.620376	0.310188	+	0.950675i	$0.399608\pi$
$602$	35.3303	1.43996
$603$	−1.00000	−0.0407231
$604$	−2.00000	−0.0813788
$605$	0	0
$606$	−24.3303	−0.988351
$607$	−15.9129	−0.645884	−0.322942	−	0.946419i	$-0.604672\pi$
$607$	−15.9129	−0.645884	−0.322942	+	0.946419i	$0.604672\pi$
$608$	1.00000	0.0405554
$609$	−18.9564	−0.768154
$610$	7.58258	0.307010
$611$	−11.0780	−0.448169
$612$	1.58258	0.0639718
$613$	−14.0000	−0.565455	−0.282727	−	0.959200i	$-0.591239\pi$
$613$	−14.0000	−0.565455	−0.282727	+	0.959200i	$0.591239\pi$
$614$	−5.25227	−0.211964
$615$	5.37386	0.216695
$616$	0	0
$617$	5.20871	0.209695	0.104847	−	0.994488i	$-0.466565\pi$
$617$	5.20871	0.209695	0.104847	+	0.994488i	$0.466565\pi$
$618$	−5.29583	−0.213030
$619$	−1.16515	−0.0468314	−0.0234157	−	0.999726i	$-0.507454\pi$
$619$	−1.16515	−0.0468314	−0.0234157	+	0.999726i	$0.507454\pi$
$620$	−40.9129	−1.64310
$621$	7.91288	0.317533
$622$	25.9129	1.03901
$623$	−21.1652	−0.847964
$624$	−2.16515	−0.0866754
$625$	16.0000	0.640000
$626$	9.37386	0.374655
$627$	0	0
$628$	−10.9564	−0.437210
$629$	60.6606	2.41870
$630$	−3.79129	−0.151049
$631$	−35.9129	−1.42967	−0.714835	−	0.699294i	$-0.753498\pi$
$631$	−35.9129	−1.42967	−0.714835	+	0.699294i	$0.753498\pi$
$632$	−5.58258	−0.222063
$633$	−33.5826	−1.33479
$634$	−1.25227	−0.0497341
$635$	33.1652	1.31612
$636$	−2.83485	−0.112409
$637$	−19.2867	−0.764169
$638$	0	0
$639$	−2.37386	−0.0939086
$640$	−3.79129	−0.149864
$641$	16.4174	0.648449	0.324225	−	0.945980i	$-0.394897\pi$
$641$	16.4174	0.648449	0.324225	+	0.945980i	$0.394897\pi$
$642$	32.2432	1.27254
$643$	26.3303	1.03837	0.519183	−	0.854663i	$-0.326236\pi$
$643$	26.3303	1.03837	0.519183	+	0.854663i	$0.326236\pi$
$644$	−7.58258	−0.298795
$645$	−50.0780	−1.97182
$646$	7.58258	0.298332
$647$	25.9129	1.01874	0.509370	−	0.860548i	$-0.329878\pi$
$647$	25.9129	1.01874	0.509370	+	0.860548i	$0.329878\pi$
$648$	9.58258	0.376439
$649$	0	0
$650$	11.3303	0.444411
$651$	−92.6170	−3.62995
$652$	−11.5826	−0.453609
$653$	10.2867	0.402551	0.201276	−	0.979535i	$-0.435491\pi$
$653$	10.2867	0.402551	0.201276	+	0.979535i	$0.435491\pi$
$654$	−17.9129	−0.700449
$655$	−13.7477	−0.537168
$656$	0.791288	0.0308946
$657$	−2.00000	−0.0780274
$658$	−43.9129	−1.71190
$659$	−7.91288	−0.308242	−0.154121	−	0.988052i	$-0.549255\pi$
$659$	−7.91288	−0.308242	−0.154121	+	0.988052i	$0.549255\pi$
$660$	0	0
$661$	32.0000	1.24466	0.622328	−	0.782757i	$-0.286187\pi$
$661$	32.0000	1.24466	0.622328	+	0.782757i	$0.286187\pi$
$662$	−29.7913	−1.15787
$663$	−16.4174	−0.637600
$664$	−3.79129	−0.147131
$665$	−18.1652	−0.704414
$666$	−1.66970	−0.0646995
$667$	3.49545	0.135345
$668$	−18.0000	−0.696441
$669$	−12.8348	−0.496224
$670$	18.1652	0.701781
$671$	0	0
$672$	−8.58258	−0.331080
$673$	12.0436	0.464245	0.232123	−	0.972687i	$-0.425433\pi$
$673$	12.0436	0.464245	0.232123	+	0.972687i	$0.425433\pi$
$674$	−13.6261	−0.524859
$675$	−46.8693	−1.80400
$676$	−11.5390	−0.443808
$677$	−32.5390	−1.25058	−0.625288	−	0.780394i	$-0.715018\pi$
$677$	−32.5390	−1.25058	−0.625288	+	0.780394i	$0.715018\pi$
$678$	−27.1652	−1.04327
$679$	38.3303	1.47098
$680$	−28.7477	−1.10243
$681$	13.5826	0.520485
$682$	0	0
$683$	48.6606	1.86195	0.930973	−	0.365088i	$-0.118961\pi$
$683$	48.6606	1.86195	0.930973	+	0.365088i	$0.118961\pi$
$684$	−0.208712	−0.00798031
$685$	19.7477	0.754522
$686$	−42.9129	−1.63842
$687$	−32.9129	−1.25570
$688$	−7.37386	−0.281126
$689$	1.91288	0.0728749
$690$	10.7477	0.409159
$691$	−31.4955	−1.19814	−0.599072	−	0.800695i	$-0.704464\pi$
$691$	−31.4955	−1.19814	−0.599072	+	0.800695i	$0.704464\pi$
$692$	−12.9564	−0.492530
$693$	0	0
$694$	−3.16515	−0.120148
$695$	46.2867	1.75576
$696$	3.95644	0.149968
$697$	6.00000	0.227266
$698$	23.4955	0.889316
$699$	−27.1652	−1.02748
$700$	44.9129	1.69755
$701$	5.66970	0.214142	0.107071	−	0.994251i	$-0.465853\pi$
$701$	5.66970	0.214142	0.107071	+	0.994251i	$0.465853\pi$
$702$	−6.04356	−0.228100
$703$	−8.00000	−0.301726
$704$	0	0
$705$	62.2432	2.34421
$706$	14.8348	0.558317
$707$	65.0780	2.44751
$708$	0	0
$709$	32.7913	1.23150	0.615751	−	0.787941i	$-0.288853\pi$
$709$	32.7913	1.23150	0.615751	+	0.787941i	$0.288853\pi$
$710$	43.1216	1.61832
$711$	1.16515	0.0436966
$712$	4.41742	0.165550
$713$	17.0780	0.639577
$714$	−65.0780	−2.43548
$715$	0	0
$716$	3.95644	0.147859
$717$	3.95644	0.147756
$718$	20.7042	0.772673
$719$	−29.0780	−1.08443	−0.542214	−	0.840241i	$-0.682414\pi$
$719$	−29.0780	−1.08443	−0.542214	+	0.840241i	$0.682414\pi$
$720$	0.791288	0.0294896
$721$	14.1652	0.527538
$722$	−1.00000	−0.0372161
$723$	0.373864	0.0139041
$724$	18.7477	0.696754
$725$	−20.7042	−0.768933
$726$	0	0
$727$	−25.4955	−0.945574	−0.472787	−	0.881177i	$-0.656752\pi$
$727$	−25.4955	−0.945574	−0.472787	+	0.881177i	$0.656752\pi$
$728$	5.79129	0.214639
$729$	24.8693	0.921086
$730$	36.3303	1.34464
$731$	−55.9129	−2.06801
$732$	−3.58258	−0.132416
$733$	19.4955	0.720081	0.360041	−	0.932937i	$-0.382763\pi$
$733$	19.4955	0.720081	0.360041	+	0.932937i	$0.382763\pi$
$734$	−20.3303	−0.750405
$735$	108.365	3.99709
$736$	1.58258	0.0583345
$737$	0	0
$738$	−0.165151	−0.00607931
$739$	−38.9564	−1.43304	−0.716518	−	0.697569i	$-0.754265\pi$
$739$	−38.9564	−1.43304	−0.716518	+	0.697569i	$0.754265\pi$
$740$	30.3303	1.11496
$741$	2.16515	0.0795388
$742$	7.58258	0.278365
$743$	−45.1652	−1.65695	−0.828474	−	0.560027i	$-0.810791\pi$
$743$	−45.1652	−1.65695	−0.828474	+	0.560027i	$0.810791\pi$
$744$	19.3303	0.708683
$745$	0	0
$746$	−9.37386	−0.343202
$747$	0.791288	0.0289517
$748$	0	0
$749$	−86.2432	−3.15126
$750$	−29.7042	−1.08464
$751$	−10.3303	−0.376958	−0.188479	−	0.982077i	$-0.560356\pi$
$751$	−10.3303	−0.376958	−0.188479	+	0.982077i	$0.560356\pi$
$752$	9.16515	0.334219
$753$	21.4955	0.783338
$754$	−2.66970	−0.0972246
$755$	−7.58258	−0.275958
$756$	−23.9564	−0.871287
$757$	−24.2087	−0.879881	−0.439940	−	0.898027i	$-0.645000\pi$
$757$	−24.2087	−0.879881	−0.439940	+	0.898027i	$0.645000\pi$
$758$	−32.7913	−1.19103
$759$	0	0
$760$	3.79129	0.137524
$761$	−49.9129	−1.80934	−0.904670	−	0.426112i	$-0.859883\pi$
$761$	−49.9129	−1.80934	−0.904670	+	0.426112i	$0.859883\pi$
$762$	−15.6697	−0.567653
$763$	47.9129	1.73456
$764$	−18.0000	−0.651217
$765$	6.00000	0.216930
$766$	9.95644	0.359741
$767$	0	0
$768$	1.79129	0.0646375
$769$	−7.66970	−0.276576	−0.138288	−	0.990392i	$-0.544160\pi$
$769$	−7.66970	−0.276576	−0.138288	+	0.990392i	$0.544160\pi$
$770$	0	0
$771$	−13.5826	−0.489165
$772$	−7.37386	−0.265391
$773$	−39.4955	−1.42055	−0.710276	−	0.703923i	$-0.751430\pi$
$773$	−39.4955	−1.42055	−0.710276	+	0.703923i	$0.751430\pi$
$774$	1.53901	0.0553187
$775$	−101.156	−3.63363
$776$	−8.00000	−0.287183
$777$	68.6606	2.46319
$778$	−10.1216	−0.362877
$779$	−0.791288	−0.0283508
$780$	−8.20871	−0.293919
$781$	0	0
$782$	12.0000	0.429119
$783$	11.0436	0.394665
$784$	15.9564	0.569873
$785$	−41.5390	−1.48259
$786$	6.49545	0.231685
$787$	−3.58258	−0.127705	−0.0638525	−	0.997959i	$-0.520339\pi$
$787$	−3.58258	−0.127705	−0.0638525	+	0.997959i	$0.520339\pi$
$788$	−9.16515	−0.326495
$789$	−23.2087	−0.826252
$790$	−21.1652	−0.753022
$791$	72.6606	2.58351
$792$	0	0
$793$	2.41742	0.0858453
$794$	−4.04356	−0.143501
$795$	−10.7477	−0.381183
$796$	6.74773	0.239167
$797$	−32.2432	−1.14211	−0.571056	−	0.820911i	$-0.693466\pi$
$797$	−32.2432	−1.14211	−0.571056	+	0.820911i	$0.693466\pi$
$798$	8.58258	0.303820
$799$	69.4955	2.45857
$800$	−9.37386	−0.331416
$801$	−0.921970	−0.0325762
$802$	13.5826	0.479617
$803$	0	0
$804$	−8.58258	−0.302684
$805$	−28.7477	−1.01322
$806$	−13.0436	−0.459440
$807$	−30.0000	−1.05605
$808$	−13.5826	−0.477833
$809$	42.3303	1.48825	0.744127	−	0.668038i	$-0.232866\pi$
$809$	42.3303	1.48825	0.744127	+	0.668038i	$0.232866\pi$
$810$	36.3303	1.27652
$811$	31.4955	1.10595	0.552977	−	0.833196i	$-0.313492\pi$
$811$	31.4955	1.10595	0.552977	+	0.833196i	$0.313492\pi$
$812$	−10.5826	−0.371376
$813$	11.4174	0.400427
$814$	0	0
$815$	−43.9129	−1.53820
$816$	13.5826	0.475485
$817$	7.37386	0.257979
$818$	−3.37386	−0.117964
$819$	−1.20871	−0.0422358
$820$	3.00000	0.104765
$821$	47.0780	1.64303	0.821517	−	0.570184i	$-0.193128\pi$
$821$	47.0780	1.64303	0.821517	+	0.570184i	$0.193128\pi$
$822$	−9.33030	−0.325432
$823$	17.4955	0.609853	0.304927	−	0.952376i	$-0.401368\pi$
$823$	17.4955	0.609853	0.304927	+	0.952376i	$0.401368\pi$
$824$	−2.95644	−0.102992
$825$	0	0
$826$	0	0
$827$	−48.0000	−1.66912	−0.834562	−	0.550914i	$-0.814279\pi$
$827$	−48.0000	−1.66912	−0.834562	+	0.550914i	$0.814279\pi$
$828$	−0.330303	−0.0114788
$829$	−10.0000	−0.347314	−0.173657	−	0.984806i	$-0.555558\pi$
$829$	−10.0000	−0.347314	−0.173657	+	0.984806i	$0.555558\pi$
$830$	−14.3739	−0.498924
$831$	39.4083	1.36706
$832$	−1.20871	−0.0419046
$833$	120.991	4.19209
$834$	−21.8693	−0.757273
$835$	−68.2432	−2.36165
$836$	0	0
$837$	53.9564	1.86501
$838$	−12.3303	−0.425943
$839$	18.9564	0.654449	0.327224	−	0.944947i	$-0.393887\pi$
$839$	18.9564	0.654449	0.327224	+	0.944947i	$0.393887\pi$
$840$	−32.5390	−1.12270
$841$	−24.1216	−0.831779
$842$	11.2523	0.387779
$843$	−39.6261	−1.36480
$844$	−18.7477	−0.645323
$845$	−43.7477	−1.50497
$846$	−1.91288	−0.0657661
$847$	0	0
$848$	−1.58258	−0.0543459
$849$	−16.3394	−0.560767
$850$	−71.0780	−2.43796
$851$	−12.6606	−0.434000
$852$	−20.3739	−0.697997
$853$	7.16515	0.245330	0.122665	−	0.992448i	$-0.460856\pi$
$853$	7.16515	0.245330	0.122665	+	0.992448i	$0.460856\pi$
$854$	9.58258	0.327909
$855$	−0.791288	−0.0270615
$856$	18.0000	0.615227
$857$	−34.2867	−1.17121	−0.585606	−	0.810596i	$-0.699144\pi$
$857$	−34.2867	−1.17121	−0.585606	+	0.810596i	$0.699144\pi$
$858$	0	0
$859$	−13.4955	−0.460459	−0.230229	−	0.973136i	$-0.573948\pi$
$859$	−13.4955	−0.460459	−0.230229	+	0.973136i	$0.573948\pi$
$860$	−27.9564	−0.953307
$861$	6.79129	0.231446
$862$	−21.4955	−0.732138
$863$	23.5390	0.801277	0.400639	−	0.916236i	$-0.368788\pi$
$863$	23.5390	0.801277	0.400639	+	0.916236i	$0.368788\pi$
$864$	5.00000	0.170103
$865$	−49.1216	−1.67018
$866$	11.5826	0.393592
$867$	72.5390	2.46355
$868$	−51.7042	−1.75495
$869$	0	0
$870$	15.0000	0.508548
$871$	5.79129	0.196230
$872$	−10.0000	−0.338643
$873$	1.66970	0.0565107
$874$	−1.58258	−0.0535314
$875$	79.4519	2.68596
$876$	−17.1652	−0.579957
$877$	11.8784	0.401105	0.200553	−	0.979683i	$-0.435726\pi$
$877$	11.8784	0.401105	0.200553	+	0.979683i	$0.435726\pi$
$878$	−31.1652	−1.05177
$879$	−12.1652	−0.410320
$880$	0	0
$881$	−13.1216	−0.442078	−0.221039	−	0.975265i	$-0.570945\pi$
$881$	−13.1216	−0.442078	−0.221039	+	0.975265i	$0.570945\pi$
$882$	−3.33030	−0.112137
$883$	21.9129	0.737427	0.368714	−	0.929543i	$-0.379798\pi$
$883$	21.9129	0.737427	0.368714	+	0.929543i	$0.379798\pi$
$884$	−9.16515	−0.308257
$885$	0	0
$886$	18.3303	0.615819
$887$	−21.4955	−0.721747	−0.360873	−	0.932615i	$-0.617521\pi$
$887$	−21.4955	−0.721747	−0.360873	+	0.932615i	$0.617521\pi$
$888$	−14.3303	−0.480893
$889$	41.9129	1.40571
$890$	16.7477	0.561385
$891$	0	0
$892$	−7.16515	−0.239907
$893$	−9.16515	−0.306700
$894$	0	0
$895$	15.0000	0.501395
$896$	−4.79129	−0.160066
$897$	3.42652	0.114408
$898$	−16.7477	−0.558879
$899$	23.8348	0.794937
$900$	1.95644	0.0652146
$901$	−12.0000	−0.399778
$902$	0	0
$903$	−63.2867	−2.10605
$904$	−15.1652	−0.504385
$905$	71.0780	2.36271
$906$	3.58258	0.119023
$907$	8.00000	0.265636	0.132818	−	0.991140i	$-0.457597\pi$
$907$	8.00000	0.265636	0.132818	+	0.991140i	$0.457597\pi$
$908$	7.58258	0.251637
$909$	2.83485	0.0940260
$910$	21.9564	0.727849
$911$	−39.1652	−1.29760	−0.648800	−	0.760959i	$-0.724729\pi$
$911$	−39.1652	−1.29760	−0.648800	+	0.760959i	$0.724729\pi$
$912$	−1.79129	−0.0593155
$913$	0	0
$914$	−5.25227	−0.173730
$915$	−13.5826	−0.449026
$916$	−18.3739	−0.607090
$917$	−17.3739	−0.573736
$918$	37.9129	1.25131
$919$	−51.2867	−1.69179	−0.845897	−	0.533347i	$-0.820934\pi$
$919$	−51.2867	−1.69179	−0.845897	+	0.533347i	$0.820934\pi$
$920$	6.00000	0.197814
$921$	9.40833	0.310015
$922$	−30.3303	−0.998875
$923$	13.7477	0.452512
$924$	0	0
$925$	74.9909	2.46569
$926$	40.6606	1.33619
$927$	0.617045	0.0202664
$928$	2.20871	0.0725045
$929$	−17.2087	−0.564600	−0.282300	−	0.959326i	$-0.591097\pi$
$929$	−17.2087	−0.564600	−0.282300	+	0.959326i	$0.591097\pi$
$930$	73.2867	2.40317
$931$	−15.9564	−0.522951
$932$	−15.1652	−0.496751
$933$	−46.4174	−1.51964
$934$	−13.5826	−0.444435
$935$	0	0
$936$	0.252273	0.00824580
$937$	37.8258	1.23571	0.617857	−	0.786291i	$-0.288001\pi$
$937$	37.8258	1.23571	0.617857	+	0.786291i	$0.288001\pi$
$938$	22.9564	0.749554
$939$	−16.7913	−0.547963
$940$	34.7477	1.13335
$941$	26.8348	0.874791	0.437396	−	0.899269i	$-0.355901\pi$
$941$	26.8348	0.874791	0.437396	+	0.899269i	$0.355901\pi$
$942$	19.6261	0.639454
$943$	−1.25227	−0.0407796
$944$	0	0
$945$	−90.8258	−2.95456
$946$	0	0
$947$	17.0780	0.554961	0.277481	−	0.960731i	$-0.410501\pi$
$947$	17.0780	0.554961	0.277481	+	0.960731i	$0.410501\pi$
$948$	10.0000	0.324785
$949$	11.5826	0.375986
$950$	9.37386	0.304128
$951$	2.24318	0.0727401
$952$	−36.3303	−1.17747
$953$	14.8348	0.480548	0.240274	−	0.970705i	$-0.422763\pi$
$953$	14.8348	0.480548	0.240274	+	0.970705i	$0.422763\pi$
$954$	0.330303	0.0106939
$955$	−68.2432	−2.20830
$956$	2.20871	0.0714349
$957$	0	0
$958$	−12.7913	−0.413268
$959$	24.9564	0.805885
$960$	6.79129	0.219188
$961$	85.4519	2.75651
$962$	9.66970	0.311764
$963$	−3.75682	−0.121062
$964$	0.208712	0.00672217
$965$	−27.9564	−0.899950
$966$	13.5826	0.437012
$967$	−41.4955	−1.33440	−0.667202	−	0.744877i	$-0.732508\pi$
$967$	−41.4955	−1.33440	−0.667202	+	0.744877i	$0.732508\pi$
$968$	0	0
$969$	−13.5826	−0.436335
$970$	−30.3303	−0.973847
$971$	−19.2867	−0.618941	−0.309471	−	0.950909i	$-0.600152\pi$
$971$	−19.2867	−0.618941	−0.309471	+	0.950909i	$0.600152\pi$
$972$	−2.16515	−0.0694473
$973$	58.4955	1.87528
$974$	−18.1216	−0.580653
$975$	−20.2958	−0.649987
$976$	−2.00000	−0.0640184
$977$	−20.8348	−0.666566	−0.333283	−	0.942827i	$-0.608156\pi$
$977$	−20.8348	−0.666566	−0.333283	+	0.942827i	$0.608156\pi$
$978$	20.7477	0.663439
$979$	0	0
$980$	60.4955	1.93246
$981$	2.08712	0.0666367
$982$	−29.8693	−0.953168
$983$	6.79129	0.216608	0.108304	−	0.994118i	$-0.465458\pi$
$983$	6.79129	0.216608	0.108304	+	0.994118i	$0.465458\pi$
$984$	−1.41742	−0.0451858
$985$	−34.7477	−1.10715
$986$	16.7477	0.533356
$987$	78.6606	2.50379
$988$	1.20871	0.0384543
$989$	11.6697	0.371075
$990$	0	0
$991$	5.95644	0.189213	0.0946063	−	0.995515i	$-0.469841\pi$
$991$	5.95644	0.189213	0.0946063	+	0.995515i	$0.469841\pi$
$992$	10.7913	0.342624
$993$	53.3648	1.69348
$994$	54.4955	1.72849
$995$	25.5826	0.811022
$996$	6.79129	0.215190
$997$	59.9129	1.89746	0.948730	−	0.316088i	$-0.102369\pi$
$997$	59.9129	1.89746	0.948730	+	0.316088i	$0.102369\pi$
$998$	1.16515	0.0368822
$999$	−40.0000	−1.26554

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4598.2.a.y.1.2		2
11.10	odd	2		418.2.a.f.1.2	✓	2
33.32	even	2		3762.2.a.s.1.1		2
44.43	even	2		3344.2.a.l.1.1		2
209.208	even	2		7942.2.a.w.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.a.f.1.2	✓	2	11.10	odd	2
3344.2.a.l.1.1		2	44.43	even	2
3762.2.a.s.1.1		2	33.32	even	2
4598.2.a.y.1.2		2	1.1	even	1	trivial
7942.2.a.w.1.1		2	209.208	even	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.79129 q^{3} +1.00000 q^{4} +3.79129 q^{5} -1.79129 q^{6} +4.79129 q^{7} -1.00000 q^{8} +0.208712 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.79129 q^{3} +1.00000 q^{4} +3.79129 q^{5} -1.79129 q^{6} +4.79129 q^{7} -1.00000 q^{8} +0.208712 q^{9} -3.79129 q^{10} +1.79129 q^{12} -1.20871 q^{13} -4.79129 q^{14} +6.79129 q^{15} +1.00000 q^{16} +7.58258 q^{17} -0.208712 q^{18} -1.00000 q^{19} +3.79129 q^{20} +8.58258 q^{21} -1.58258 q^{23} -1.79129 q^{24} +9.37386 q^{25} +1.20871 q^{26} -5.00000 q^{27} +4.79129 q^{28} -2.20871 q^{29} -6.79129 q^{30} -10.7913 q^{31} -1.00000 q^{32} -7.58258 q^{34} +18.1652 q^{35} +0.208712 q^{36} +8.00000 q^{37} +1.00000 q^{38} -2.16515 q^{39} -3.79129 q^{40} +0.791288 q^{41} -8.58258 q^{42} -7.37386 q^{43} +0.791288 q^{45} +1.58258 q^{46} +9.16515 q^{47} +1.79129 q^{48} +15.9564 q^{49} -9.37386 q^{50} +13.5826 q^{51} -1.20871 q^{52} -1.58258 q^{53} +5.00000 q^{54} -4.79129 q^{56} -1.79129 q^{57} +2.20871 q^{58} +6.79129 q^{60} -2.00000 q^{61} +10.7913 q^{62} +1.00000 q^{63} +1.00000 q^{64} -4.58258 q^{65} -4.79129 q^{67} +7.58258 q^{68} -2.83485 q^{69} -18.1652 q^{70} -11.3739 q^{71} -0.208712 q^{72} -9.58258 q^{73} -8.00000 q^{74} +16.7913 q^{75} -1.00000 q^{76} +2.16515 q^{78} +5.58258 q^{79} +3.79129 q^{80} -9.58258 q^{81} -0.791288 q^{82} +3.79129 q^{83} +8.58258 q^{84} +28.7477 q^{85} +7.37386 q^{86} -3.95644 q^{87} -4.41742 q^{89} -0.791288 q^{90} -5.79129 q^{91} -1.58258 q^{92} -19.3303 q^{93} -9.16515 q^{94} -3.79129 q^{95} -1.79129 q^{96} +8.00000 q^{97} -15.9564 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - q^{3} + 2 q^{4} + 3 q^{5} + q^{6} + 5 q^{7} - 2 q^{8} + 5 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 - q^3 + 2 * q^4 + 3 * q^5 + q^6 + 5 * q^7 - 2 * q^8 + 5 * q^9	\( 2 q - 2 q^{2} - q^{3} + 2 q^{4} + 3 q^{5} + q^{6} + 5 q^{7} - 2 q^{8} + 5 q^{9} - 3 q^{10} - q^{12} - 7 q^{13} - 5 q^{14} + 9 q^{15} + 2 q^{16} + 6 q^{17} - 5 q^{18} - 2 q^{19} + 3 q^{20} + 8 q^{21} + 6 q^{23} + q^{24} + 5 q^{25} + 7 q^{26} - 10 q^{27} + 5 q^{28} - 9 q^{29} - 9 q^{30} - 17 q^{31} - 2 q^{32} - 6 q^{34} + 18 q^{35} + 5 q^{36} + 16 q^{37} + 2 q^{38} + 14 q^{39} - 3 q^{40} - 3 q^{41} - 8 q^{42} - q^{43} - 3 q^{45} - 6 q^{46} - q^{48} + 9 q^{49} - 5 q^{50} + 18 q^{51} - 7 q^{52} + 6 q^{53} + 10 q^{54} - 5 q^{56} + q^{57} + 9 q^{58} + 9 q^{60} - 4 q^{61} + 17 q^{62} + 2 q^{63} + 2 q^{64} - 5 q^{67} + 6 q^{68} - 24 q^{69} - 18 q^{70} - 9 q^{71} - 5 q^{72} - 10 q^{73} - 16 q^{74} + 29 q^{75} - 2 q^{76} - 14 q^{78} + 2 q^{79} + 3 q^{80} - 10 q^{81} + 3 q^{82} + 3 q^{83} + 8 q^{84} + 30 q^{85} + q^{86} + 15 q^{87} - 18 q^{89} + 3 q^{90} - 7 q^{91} + 6 q^{92} - 2 q^{93} - 3 q^{95} + q^{96} + 16 q^{97} - 9 q^{98}+O(q^{100}) \) 2 * q - 2 * q^2 - q^3 + 2 * q^4 + 3 * q^5 + q^6 + 5 * q^7 - 2 * q^8 + 5 * q^9 - 3 * q^10 - q^12 - 7 * q^13 - 5 * q^14 + 9 * q^15 + 2 * q^16 + 6 * q^17 - 5 * q^18 - 2 * q^19 + 3 * q^20 + 8 * q^21 + 6 * q^23 + q^24 + 5 * q^25 + 7 * q^26 - 10 * q^27 + 5 * q^28 - 9 * q^29 - 9 * q^30 - 17 * q^31 - 2 * q^32 - 6 * q^34 + 18 * q^35 + 5 * q^36 + 16 * q^37 + 2 * q^38 + 14 * q^39 - 3 * q^40 - 3 * q^41 - 8 * q^42 - q^43 - 3 * q^45 - 6 * q^46 - q^48 + 9 * q^49 - 5 * q^50 + 18 * q^51 - 7 * q^52 + 6 * q^53 + 10 * q^54 - 5 * q^56 + q^57 + 9 * q^58 + 9 * q^60 - 4 * q^61 + 17 * q^62 + 2 * q^63 + 2 * q^64 - 5 * q^67 + 6 * q^68 - 24 * q^69 - 18 * q^70 - 9 * q^71 - 5 * q^72 - 10 * q^73 - 16 * q^74 + 29 * q^75 - 2 * q^76 - 14 * q^78 + 2 * q^79 + 3 * q^80 - 10 * q^81 + 3 * q^82 + 3 * q^83 + 8 * q^84 + 30 * q^85 + q^86 + 15 * q^87 - 18 * q^89 + 3 * q^90 - 7 * q^91 + 6 * q^92 - 2 * q^93 - 3 * q^95 + q^96 + 16 * q^97 - 9 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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