LMFDB - Embedded newform 4598.2.a.bg.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4598, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4598.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4598 = 2 \cdot 11^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4598.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$36.7152148494$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$1.61803$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.61803 q^{3} +1.00000 q^{4} -1.61803 q^{5} -1.61803 q^{6} +3.85410 q^{7} +1.00000 q^{8} -0.381966 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.61803 q^{3} +1.00000 q^{4} -1.61803 q^{5} -1.61803 q^{6} +3.85410 q^{7} +1.00000 q^{8} -0.381966 q^{9} -1.61803 q^{10} -1.61803 q^{12} -0.618034 q^{13} +3.85410 q^{14} +2.61803 q^{15} +1.00000 q^{16} -3.23607 q^{17} -0.381966 q^{18} +1.00000 q^{19} -1.61803 q^{20} -6.23607 q^{21} -2.00000 q^{23} -1.61803 q^{24} -2.38197 q^{25} -0.618034 q^{26} +5.47214 q^{27} +3.85410 q^{28} +0.854102 q^{29} +2.61803 q^{30} -2.61803 q^{31} +1.00000 q^{32} -3.23607 q^{34} -6.23607 q^{35} -0.381966 q^{36} +1.23607 q^{37} +1.00000 q^{38} +1.00000 q^{39} -1.61803 q^{40} +0.618034 q^{41} -6.23607 q^{42} -12.0902 q^{43} +0.618034 q^{45} -2.00000 q^{46} -0.763932 q^{47} -1.61803 q^{48} +7.85410 q^{49} -2.38197 q^{50} +5.23607 q^{51} -0.618034 q^{52} -10.4721 q^{53} +5.47214 q^{54} +3.85410 q^{56} -1.61803 q^{57} +0.854102 q^{58} +12.9443 q^{59} +2.61803 q^{60} -5.70820 q^{61} -2.61803 q^{62} -1.47214 q^{63} +1.00000 q^{64} +1.00000 q^{65} +5.09017 q^{67} -3.23607 q^{68} +3.23607 q^{69} -6.23607 q^{70} +12.8541 q^{71} -0.381966 q^{72} -10.4721 q^{73} +1.23607 q^{74} +3.85410 q^{75} +1.00000 q^{76} +1.00000 q^{78} +4.47214 q^{79} -1.61803 q^{80} -7.70820 q^{81} +0.618034 q^{82} +2.38197 q^{83} -6.23607 q^{84} +5.23607 q^{85} -12.0902 q^{86} -1.38197 q^{87} +6.94427 q^{89} +0.618034 q^{90} -2.38197 q^{91} -2.00000 q^{92} +4.23607 q^{93} -0.763932 q^{94} -1.61803 q^{95} -1.61803 q^{96} -18.4721 q^{97} +7.85410 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - q^{3} + 2 q^{4} - q^{5} - q^{6} + q^{7} + 2 q^{8} - 3 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 - q^3 + 2 * q^4 - q^5 - q^6 + q^7 + 2 * q^8 - 3 * q^9	$ 2 q + 2 q^{2} - q^{3} + 2 q^{4} - q^{5} - q^{6} + q^{7} + 2 q^{8} - 3 q^{9} - q^{10} - q^{12} + q^{13} + q^{14} + 3 q^{15} + 2 q^{16} - 2 q^{17} - 3 q^{18} + 2 q^{19} - q^{20} - 8 q^{21} - 4 q^{23} - q^{24} - 7 q^{25} + q^{26} + 2 q^{27} + q^{28} - 5 q^{29} + 3 q^{30} - 3 q^{31} + 2 q^{32} - 2 q^{34} - 8 q^{35} - 3 q^{36} - 2 q^{37} + 2 q^{38} + 2 q^{39} - q^{40} - q^{41} - 8 q^{42} - 13 q^{43} - q^{45} - 4 q^{46} - 6 q^{47} - q^{48} + 9 q^{49} - 7 q^{50} + 6 q^{51} + q^{52} - 12 q^{53} + 2 q^{54} + q^{56} - q^{57} - 5 q^{58} + 8 q^{59} + 3 q^{60} + 2 q^{61} - 3 q^{62} + 6 q^{63} + 2 q^{64} + 2 q^{65} - q^{67} - 2 q^{68} + 2 q^{69} - 8 q^{70} + 19 q^{71} - 3 q^{72} - 12 q^{73} - 2 q^{74} + q^{75} + 2 q^{76} + 2 q^{78} - q^{80} - 2 q^{81} - q^{82} + 7 q^{83} - 8 q^{84} + 6 q^{85} - 13 q^{86} - 5 q^{87} - 4 q^{89} - q^{90} - 7 q^{91} - 4 q^{92} + 4 q^{93} - 6 q^{94} - q^{95} - q^{96} - 28 q^{97} + 9 q^{98}+O(q^{100}) $ 2 * q + 2 * q^2 - q^3 + 2 * q^4 - q^5 - q^6 + q^7 + 2 * q^8 - 3 * q^9 - q^10 - q^12 + q^13 + q^14 + 3 * q^15 + 2 * q^16 - 2 * q^17 - 3 * q^18 + 2 * q^19 - q^20 - 8 * q^21 - 4 * q^23 - q^24 - 7 * q^25 + q^26 + 2 * q^27 + q^28 - 5 * q^29 + 3 * q^30 - 3 * q^31 + 2 * q^32 - 2 * q^34 - 8 * q^35 - 3 * q^36 - 2 * q^37 + 2 * q^38 + 2 * q^39 - q^40 - q^41 - 8 * q^42 - 13 * q^43 - q^45 - 4 * q^46 - 6 * q^47 - q^48 + 9 * q^49 - 7 * q^50 + 6 * q^51 + q^52 - 12 * q^53 + 2 * q^54 + q^56 - q^57 - 5 * q^58 + 8 * q^59 + 3 * q^60 + 2 * q^61 - 3 * q^62 + 6 * q^63 + 2 * q^64 + 2 * q^65 - q^67 - 2 * q^68 + 2 * q^69 - 8 * q^70 + 19 * q^71 - 3 * q^72 - 12 * q^73 - 2 * q^74 + q^75 + 2 * q^76 + 2 * q^78 - q^80 - 2 * q^81 - q^82 + 7 * q^83 - 8 * q^84 + 6 * q^85 - 13 * q^86 - 5 * q^87 - 4 * q^89 - q^90 - 7 * q^91 - 4 * q^92 + 4 * q^93 - 6 * q^94 - q^95 - q^96 - 28 * 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
$3$	−1.61803	−0.934172	−0.467086	−	0.884212i	$-0.654696\pi$
$3$	−1.61803	−0.934172	−0.467086	+	0.884212i	$0.654696\pi$
$4$	1.00000	0.500000
$5$	−1.61803	−0.723607	−0.361803	−	0.932254i	$-0.617839\pi$
$5$	−1.61803	−0.723607	−0.361803	+	0.932254i	$0.617839\pi$
$6$	−1.61803	−0.660560
$7$	3.85410	1.45671	0.728357	−	0.685198i	$-0.240284\pi$
$7$	3.85410	1.45671	0.728357	+	0.685198i	$0.240284\pi$
$8$	1.00000	0.353553
$9$	−0.381966	−0.127322
$10$	−1.61803	−0.511667
$11$	0	0
$11$	0	0
$12$	−1.61803	−0.467086
$13$	−0.618034	−0.171412	−0.0857059	−	0.996320i	$-0.527315\pi$
$13$	−0.618034	−0.171412	−0.0857059	+	0.996320i	$0.527315\pi$
$14$	3.85410	1.03005
$15$	2.61803	0.675973
$16$	1.00000	0.250000
$17$	−3.23607	−0.784862	−0.392431	−	0.919781i	$-0.628366\pi$
$17$	−3.23607	−0.784862	−0.392431	+	0.919781i	$0.628366\pi$
$18$	−0.381966	−0.0900303
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−1.61803	−0.361803
$21$	−6.23607	−1.36082
$22$	0	0
$23$	−2.00000	−0.417029	−0.208514	−	0.978019i	$-0.566863\pi$
$23$	−2.00000	−0.417029	−0.208514	+	0.978019i	$0.566863\pi$
$24$	−1.61803	−0.330280
$25$	−2.38197	−0.476393
$26$	−0.618034	−0.121206
$27$	5.47214	1.05311
$28$	3.85410	0.728357
$29$	0.854102	0.158603	0.0793014	−	0.996851i	$-0.474731\pi$
$29$	0.854102	0.158603	0.0793014	+	0.996851i	$0.474731\pi$
$30$	2.61803	0.477985
$31$	−2.61803	−0.470213	−0.235106	−	0.971970i	$-0.575544\pi$
$31$	−2.61803	−0.470213	−0.235106	+	0.971970i	$0.575544\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	−3.23607	−0.554981
$35$	−6.23607	−1.05409
$36$	−0.381966	−0.0636610
$37$	1.23607	0.203208	0.101604	−	0.994825i	$-0.467602\pi$
$37$	1.23607	0.203208	0.101604	+	0.994825i	$0.467602\pi$
$38$	1.00000	0.162221
$39$	1.00000	0.160128
$40$	−1.61803	−0.255834
$41$	0.618034	0.0965207	0.0482603	−	0.998835i	$-0.484632\pi$
$41$	0.618034	0.0965207	0.0482603	+	0.998835i	$0.484632\pi$
$42$	−6.23607	−0.962246
$43$	−12.0902	−1.84373	−0.921867	−	0.387507i	$-0.873336\pi$
$43$	−12.0902	−1.84373	−0.921867	+	0.387507i	$0.873336\pi$
$44$	0	0
$45$	0.618034	0.0921311
$46$	−2.00000	−0.294884
$47$	−0.763932	−0.111431	−0.0557155	−	0.998447i	$-0.517744\pi$
$47$	−0.763932	−0.111431	−0.0557155	+	0.998447i	$0.517744\pi$
$48$	−1.61803	−0.233543
$49$	7.85410	1.12201
$50$	−2.38197	−0.336861
$51$	5.23607	0.733196
$52$	−0.618034	−0.0857059
$53$	−10.4721	−1.43846	−0.719229	−	0.694773i	$-0.755505\pi$
$53$	−10.4721	−1.43846	−0.719229	+	0.694773i	$0.755505\pi$
$54$	5.47214	0.744663
$55$	0	0
$56$	3.85410	0.515026
$57$	−1.61803	−0.214314
$58$	0.854102	0.112149
$59$	12.9443	1.68520	0.842600	−	0.538539i	$-0.181024\pi$
$59$	12.9443	1.68520	0.842600	+	0.538539i	$0.181024\pi$
$60$	2.61803	0.337987
$61$	−5.70820	−0.730861	−0.365430	−	0.930839i	$-0.619078\pi$
$61$	−5.70820	−0.730861	−0.365430	+	0.930839i	$0.619078\pi$
$62$	−2.61803	−0.332491
$63$	−1.47214	−0.185472
$64$	1.00000	0.125000
$65$	1.00000	0.124035
$66$	0	0
$67$	5.09017	0.621863	0.310932	−	0.950432i	$-0.399359\pi$
$67$	5.09017	0.621863	0.310932	+	0.950432i	$0.399359\pi$
$68$	−3.23607	−0.392431
$69$	3.23607	0.389577
$70$	−6.23607	−0.745353
$71$	12.8541	1.52550	0.762751	−	0.646693i	$-0.223848\pi$
$71$	12.8541	1.52550	0.762751	+	0.646693i	$0.223848\pi$
$72$	−0.381966	−0.0450151
$73$	−10.4721	−1.22567	−0.612835	−	0.790211i	$-0.709971\pi$
$73$	−10.4721	−1.22567	−0.612835	+	0.790211i	$0.709971\pi$
$74$	1.23607	0.143690
$75$	3.85410	0.445033
$76$	1.00000	0.114708
$77$	0	0
$78$	1.00000	0.113228
$79$	4.47214	0.503155	0.251577	−	0.967837i	$-0.419051\pi$
$79$	4.47214	0.503155	0.251577	+	0.967837i	$0.419051\pi$
$80$	−1.61803	−0.180902
$81$	−7.70820	−0.856467
$82$	0.618034	0.0682504
$83$	2.38197	0.261455	0.130727	−	0.991418i	$-0.458269\pi$
$83$	2.38197	0.261455	0.130727	+	0.991418i	$0.458269\pi$
$84$	−6.23607	−0.680411
$85$	5.23607	0.567931
$86$	−12.0902	−1.30372
$87$	−1.38197	−0.148162
$88$	0	0
$89$	6.94427	0.736091	0.368046	−	0.929808i	$-0.380027\pi$
$89$	6.94427	0.736091	0.368046	+	0.929808i	$0.380027\pi$
$90$	0.618034	0.0651465
$91$	−2.38197	−0.249698
$92$	−2.00000	−0.208514
$93$	4.23607	0.439260
$94$	−0.763932	−0.0787936
$95$	−1.61803	−0.166007
$96$	−1.61803	−0.165140
$97$	−18.4721	−1.87556	−0.937781	−	0.347228i	$-0.887123\pi$
$97$	−18.4721	−1.87556	−0.937781	+	0.347228i	$0.887123\pi$
$98$	7.85410	0.793384
$99$	0	0
$100$	−2.38197	−0.238197
$101$	−3.23607	−0.322001	−0.161000	−	0.986954i	$-0.551472\pi$
$101$	−3.23607	−0.322001	−0.161000	+	0.986954i	$0.551472\pi$
$102$	5.23607	0.518448
$103$	−7.14590	−0.704106	−0.352053	−	0.935980i	$-0.614516\pi$
$103$	−7.14590	−0.704106	−0.352053	+	0.935980i	$0.614516\pi$
$104$	−0.618034	−0.0606032
$105$	10.0902	0.984700
$106$	−10.4721	−1.01714
$107$	−6.18034	−0.597476	−0.298738	−	0.954335i	$-0.596566\pi$
$107$	−6.18034	−0.597476	−0.298738	+	0.954335i	$0.596566\pi$
$108$	5.47214	0.526557
$109$	−12.4721	−1.19461	−0.597307	−	0.802013i	$-0.703763\pi$
$109$	−12.4721	−1.19461	−0.597307	+	0.802013i	$0.703763\pi$
$110$	0	0
$111$	−2.00000	−0.189832
$112$	3.85410	0.364178
$113$	−13.7082	−1.28956	−0.644780	−	0.764368i	$-0.723051\pi$
$113$	−13.7082	−1.28956	−0.644780	+	0.764368i	$0.723051\pi$
$114$	−1.61803	−0.151543
$115$	3.23607	0.301765
$116$	0.854102	0.0793014
$117$	0.236068	0.0218245
$118$	12.9443	1.19162
$119$	−12.4721	−1.14332
$120$	2.61803	0.238993
$121$	0	0
$122$	−5.70820	−0.516797
$123$	−1.00000	−0.0901670
$124$	−2.61803	−0.235106
$125$	11.9443	1.06833
$126$	−1.47214	−0.131148
$127$	−6.00000	−0.532414	−0.266207	−	0.963916i	$-0.585770\pi$
$127$	−6.00000	−0.532414	−0.266207	+	0.963916i	$0.585770\pi$
$128$	1.00000	0.0883883
$129$	19.5623	1.72236
$130$	1.00000	0.0877058
$131$	−1.67376	−0.146237	−0.0731186	−	0.997323i	$-0.523295\pi$
$131$	−1.67376	−0.146237	−0.0731186	+	0.997323i	$0.523295\pi$
$132$	0	0
$133$	3.85410	0.334193
$134$	5.09017	0.439724
$135$	−8.85410	−0.762040
$136$	−3.23607	−0.277491
$137$	−0.326238	−0.0278724	−0.0139362	−	0.999903i	$-0.504436\pi$
$137$	−0.326238	−0.0278724	−0.0139362	+	0.999903i	$0.504436\pi$
$138$	3.23607	0.275472
$139$	−7.32624	−0.621403	−0.310702	−	0.950507i	$-0.600564\pi$
$139$	−7.32624	−0.621403	−0.310702	+	0.950507i	$0.600564\pi$
$140$	−6.23607	−0.527044
$141$	1.23607	0.104096
$142$	12.8541	1.07869
$143$	0	0
$144$	−0.381966	−0.0318305
$145$	−1.38197	−0.114766
$146$	−10.4721	−0.866680
$147$	−12.7082	−1.04815
$148$	1.23607	0.101604
$149$	6.47214	0.530218	0.265109	−	0.964218i	$-0.414592\pi$
$149$	6.47214	0.530218	0.265109	+	0.964218i	$0.414592\pi$
$150$	3.85410	0.314686
$151$	6.00000	0.488273	0.244137	−	0.969741i	$-0.421495\pi$
$151$	6.00000	0.488273	0.244137	+	0.969741i	$0.421495\pi$
$152$	1.00000	0.0811107
$153$	1.23607	0.0999302
$154$	0	0
$155$	4.23607	0.340249
$156$	1.00000	0.0800641
$157$	−12.8541	−1.02587	−0.512935	−	0.858428i	$-0.671442\pi$
$157$	−12.8541	−1.02587	−0.512935	+	0.858428i	$0.671442\pi$
$158$	4.47214	0.355784
$159$	16.9443	1.34377
$160$	−1.61803	−0.127917
$161$	−7.70820	−0.607492
$162$	−7.70820	−0.605614
$163$	2.94427	0.230613	0.115307	−	0.993330i	$-0.463215\pi$
$163$	2.94427	0.230613	0.115307	+	0.993330i	$0.463215\pi$
$164$	0.618034	0.0482603
$165$	0	0
$166$	2.38197	0.184876
$167$	0.944272	0.0730700	0.0365350	−	0.999332i	$-0.488368\pi$
$167$	0.944272	0.0730700	0.0365350	+	0.999332i	$0.488368\pi$
$168$	−6.23607	−0.481123
$169$	−12.6180	−0.970618
$170$	5.23607	0.401588
$171$	−0.381966	−0.0292097
$172$	−12.0902	−0.921867
$173$	12.0902	0.919199	0.459599	−	0.888126i	$-0.347993\pi$
$173$	12.0902	0.919199	0.459599	+	0.888126i	$0.347993\pi$
$174$	−1.38197	−0.104767
$175$	−9.18034	−0.693968
$176$	0	0
$177$	−20.9443	−1.57427
$178$	6.94427	0.520495
$179$	11.2705	0.842397	0.421199	−	0.906968i	$-0.361609\pi$
$179$	11.2705	0.842397	0.421199	+	0.906968i	$0.361609\pi$
$180$	0.618034	0.0460655
$181$	−19.8885	−1.47830	−0.739152	−	0.673539i	$-0.764773\pi$
$181$	−19.8885	−1.47830	−0.739152	+	0.673539i	$0.764773\pi$
$182$	−2.38197	−0.176563
$183$	9.23607	0.682750
$184$	−2.00000	−0.147442
$185$	−2.00000	−0.147043
$186$	4.23607	0.310604
$187$	0	0
$188$	−0.763932	−0.0557155
$189$	21.0902	1.53408
$190$	−1.61803	−0.117385
$191$	−10.0000	−0.723575	−0.361787	−	0.932261i	$-0.617833\pi$
$191$	−10.0000	−0.723575	−0.361787	+	0.932261i	$0.617833\pi$
$192$	−1.61803	−0.116772
$193$	−6.56231	−0.472365	−0.236183	−	0.971709i	$-0.575896\pi$
$193$	−6.56231	−0.472365	−0.236183	+	0.971709i	$0.575896\pi$
$194$	−18.4721	−1.32622
$195$	−1.61803	−0.115870
$196$	7.85410	0.561007
$197$	7.41641	0.528397	0.264199	−	0.964468i	$-0.414893\pi$
$197$	7.41641	0.528397	0.264199	+	0.964468i	$0.414893\pi$
$198$	0	0
$199$	−12.1803	−0.863441	−0.431721	−	0.902007i	$-0.642093\pi$
$199$	−12.1803	−0.863441	−0.431721	+	0.902007i	$0.642093\pi$
$200$	−2.38197	−0.168430
$201$	−8.23607	−0.580927
$202$	−3.23607	−0.227689
$203$	3.29180	0.231039
$204$	5.23607	0.366598
$205$	−1.00000	−0.0698430
$206$	−7.14590	−0.497878
$207$	0.763932	0.0530969
$208$	−0.618034	−0.0428529
$209$	0	0
$210$	10.0902	0.696288
$211$	−22.6525	−1.55946	−0.779730	−	0.626115i	$-0.784644\pi$
$211$	−22.6525	−1.55946	−0.779730	+	0.626115i	$0.784644\pi$
$212$	−10.4721	−0.719229
$213$	−20.7984	−1.42508
$214$	−6.18034	−0.422479
$215$	19.5623	1.33414
$216$	5.47214	0.372332
$217$	−10.0902	−0.684965
$218$	−12.4721	−0.844720
$219$	16.9443	1.14499
$220$	0	0
$221$	2.00000	0.134535
$222$	−2.00000	−0.134231
$223$	−10.4721	−0.701266	−0.350633	−	0.936513i	$-0.614034\pi$
$223$	−10.4721	−0.701266	−0.350633	+	0.936513i	$0.614034\pi$
$224$	3.85410	0.257513
$225$	0.909830	0.0606553
$226$	−13.7082	−0.911856
$227$	10.9443	0.726397	0.363198	−	0.931712i	$-0.381685\pi$
$227$	10.9443	0.726397	0.363198	+	0.931712i	$0.381685\pi$
$228$	−1.61803	−0.107157
$229$	−1.85410	−0.122523	−0.0612613	−	0.998122i	$-0.519512\pi$
$229$	−1.85410	−0.122523	−0.0612613	+	0.998122i	$0.519512\pi$
$230$	3.23607	0.213380
$231$	0	0
$232$	0.854102	0.0560745
$233$	−10.4721	−0.686052	−0.343026	−	0.939326i	$-0.611452\pi$
$233$	−10.4721	−0.686052	−0.343026	+	0.939326i	$0.611452\pi$
$234$	0.236068	0.0154322
$235$	1.23607	0.0806322
$236$	12.9443	0.842600
$237$	−7.23607	−0.470033
$238$	−12.4721	−0.808448
$239$	−28.2705	−1.82867	−0.914334	−	0.404962i	$-0.867285\pi$
$239$	−28.2705	−1.82867	−0.914334	+	0.404962i	$0.867285\pi$
$240$	2.61803	0.168993
$241$	−10.3820	−0.668761	−0.334381	−	0.942438i	$-0.608527\pi$
$241$	−10.3820	−0.668761	−0.334381	+	0.942438i	$0.608527\pi$
$242$	0	0
$243$	−3.94427	−0.253025
$244$	−5.70820	−0.365430
$245$	−12.7082	−0.811897
$246$	−1.00000	−0.0637577
$247$	−0.618034	−0.0393246
$248$	−2.61803	−0.166245
$249$	−3.85410	−0.244244
$250$	11.9443	0.755422
$251$	8.47214	0.534756	0.267378	−	0.963592i	$-0.413843\pi$
$251$	8.47214	0.534756	0.267378	+	0.963592i	$0.413843\pi$
$252$	−1.47214	−0.0927358
$253$	0	0
$254$	−6.00000	−0.376473
$255$	−8.47214	−0.530546
$256$	1.00000	0.0625000
$257$	−9.88854	−0.616830	−0.308415	−	0.951252i	$-0.599799\pi$
$257$	−9.88854	−0.616830	−0.308415	+	0.951252i	$0.599799\pi$
$258$	19.5623	1.21790
$259$	4.76393	0.296016
$260$	1.00000	0.0620174
$261$	−0.326238	−0.0201936
$262$	−1.67376	−0.103405
$263$	−25.7984	−1.59080	−0.795398	−	0.606088i	$-0.792738\pi$
$263$	−25.7984	−1.59080	−0.795398	+	0.606088i	$0.792738\pi$
$264$	0	0
$265$	16.9443	1.04088
$266$	3.85410	0.236310
$267$	−11.2361	−0.687636
$268$	5.09017	0.310932
$269$	−16.3607	−0.997528	−0.498764	−	0.866738i	$-0.666213\pi$
$269$	−16.3607	−0.997528	−0.498764	+	0.866738i	$0.666213\pi$
$270$	−8.85410	−0.538843
$271$	16.1459	0.980793	0.490397	−	0.871499i	$-0.336852\pi$
$271$	16.1459	0.980793	0.490397	+	0.871499i	$0.336852\pi$
$272$	−3.23607	−0.196215
$273$	3.85410	0.233261
$274$	−0.326238	−0.0197088
$275$	0	0
$276$	3.23607	0.194788
$277$	9.05573	0.544106	0.272053	−	0.962282i	$-0.412297\pi$
$277$	9.05573	0.544106	0.272053	+	0.962282i	$0.412297\pi$
$278$	−7.32624	−0.439399
$279$	1.00000	0.0598684
$280$	−6.23607	−0.372676
$281$	−29.2148	−1.74281	−0.871404	−	0.490566i	$-0.836790\pi$
$281$	−29.2148	−1.74281	−0.871404	+	0.490566i	$0.836790\pi$
$282$	1.23607	0.0736068
$283$	19.2705	1.14551	0.572756	−	0.819726i	$-0.305874\pi$
$283$	19.2705	1.14551	0.572756	+	0.819726i	$0.305874\pi$
$284$	12.8541	0.762751
$285$	2.61803	0.155079
$286$	0	0
$287$	2.38197	0.140603
$288$	−0.381966	−0.0225076
$289$	−6.52786	−0.383992
$290$	−1.38197	−0.0811518
$291$	29.8885	1.75210
$292$	−10.4721	−0.612835
$293$	20.0344	1.17042	0.585212	−	0.810880i	$-0.301011\pi$
$293$	20.0344	1.17042	0.585212	+	0.810880i	$0.301011\pi$
$294$	−12.7082	−0.741158
$295$	−20.9443	−1.21942
$296$	1.23607	0.0718450
$297$	0	0
$298$	6.47214	0.374921
$299$	1.23607	0.0714837
$300$	3.85410	0.222517
$301$	−46.5967	−2.68579
$302$	6.00000	0.345261
$303$	5.23607	0.300804
$304$	1.00000	0.0573539
$305$	9.23607	0.528856
$306$	1.23607	0.0706613
$307$	2.00000	0.114146	0.0570730	−	0.998370i	$-0.481823\pi$
$307$	2.00000	0.114146	0.0570730	+	0.998370i	$0.481823\pi$
$308$	0	0
$309$	11.5623	0.657757
$310$	4.23607	0.240592
$311$	21.1246	1.19787	0.598933	−	0.800799i	$-0.295591\pi$
$311$	21.1246	1.19787	0.598933	+	0.800799i	$0.295591\pi$
$312$	1.00000	0.0566139
$313$	11.3262	0.640197	0.320098	−	0.947384i	$-0.396284\pi$
$313$	11.3262	0.640197	0.320098	+	0.947384i	$0.396284\pi$
$314$	−12.8541	−0.725399
$315$	2.38197	0.134209
$316$	4.47214	0.251577
$317$	8.00000	0.449325	0.224662	−	0.974437i	$-0.427872\pi$
$317$	8.00000	0.449325	0.224662	+	0.974437i	$0.427872\pi$
$318$	16.9443	0.950188
$319$	0	0
$320$	−1.61803	−0.0904508
$321$	10.0000	0.558146
$322$	−7.70820	−0.429561
$323$	−3.23607	−0.180060
$324$	−7.70820	−0.428234
$325$	1.47214	0.0816594
$326$	2.94427	0.163068
$327$	20.1803	1.11598
$328$	0.618034	0.0341252
$329$	−2.94427	−0.162323
$330$	0	0
$331$	−33.9787	−1.86764	−0.933820	−	0.357744i	$-0.883546\pi$
$331$	−33.9787	−1.86764	−0.933820	+	0.357744i	$0.883546\pi$
$332$	2.38197	0.130727
$333$	−0.472136	−0.0258729
$334$	0.944272	0.0516683
$335$	−8.23607	−0.449984
$336$	−6.23607	−0.340205
$337$	19.0902	1.03991	0.519954	−	0.854194i	$-0.325949\pi$
$337$	19.0902	1.03991	0.519954	+	0.854194i	$0.325949\pi$
$338$	−12.6180	−0.686331
$339$	22.1803	1.20467
$340$	5.23607	0.283966
$341$	0	0
$342$	−0.381966	−0.0206544
$343$	3.29180	0.177740
$344$	−12.0902	−0.651858
$345$	−5.23607	−0.281900
$346$	12.0902	0.649972
$347$	22.4721	1.20637	0.603184	−	0.797602i	$-0.293899\pi$
$347$	22.4721	1.20637	0.603184	+	0.797602i	$0.293899\pi$
$348$	−1.38197	−0.0740812
$349$	20.6525	1.10550	0.552751	−	0.833347i	$-0.313578\pi$
$349$	20.6525	1.10550	0.552751	+	0.833347i	$0.313578\pi$
$350$	−9.18034	−0.490710
$351$	−3.38197	−0.180516
$352$	0	0
$353$	−15.8885	−0.845662	−0.422831	−	0.906209i	$-0.638964\pi$
$353$	−15.8885	−0.845662	−0.422831	+	0.906209i	$0.638964\pi$
$354$	−20.9443	−1.11318
$355$	−20.7984	−1.10386
$356$	6.94427	0.368046
$357$	20.1803	1.06806
$358$	11.2705	0.595665
$359$	35.2705	1.86151	0.930753	−	0.365648i	$-0.119153\pi$
$359$	35.2705	1.86151	0.930753	+	0.365648i	$0.119153\pi$
$360$	0.618034	0.0325733
$361$	1.00000	0.0526316
$362$	−19.8885	−1.04532
$363$	0	0
$364$	−2.38197	−0.124849
$365$	16.9443	0.886904
$366$	9.23607	0.482777
$367$	23.1246	1.20709	0.603547	−	0.797327i	$-0.293753\pi$
$367$	23.1246	1.20709	0.603547	+	0.797327i	$0.293753\pi$
$368$	−2.00000	−0.104257
$369$	−0.236068	−0.0122892
$370$	−2.00000	−0.103975
$371$	−40.3607	−2.09542
$372$	4.23607	0.219630
$373$	−22.7426	−1.17757	−0.588785	−	0.808290i	$-0.700393\pi$
$373$	−22.7426	−1.17757	−0.588785	+	0.808290i	$0.700393\pi$
$374$	0	0
$375$	−19.3262	−0.998003
$376$	−0.763932	−0.0393968
$377$	−0.527864	−0.0271864
$378$	21.0902	1.08476
$379$	−13.0902	−0.672397	−0.336198	−	0.941791i	$-0.609141\pi$
$379$	−13.0902	−0.672397	−0.336198	+	0.941791i	$0.609141\pi$
$380$	−1.61803	−0.0830034
$381$	9.70820	0.497366
$382$	−10.0000	−0.511645
$383$	−34.0344	−1.73908	−0.869539	−	0.493864i	$-0.835584\pi$
$383$	−34.0344	−1.73908	−0.869539	+	0.493864i	$0.835584\pi$
$384$	−1.61803	−0.0825700
$385$	0	0
$386$	−6.56231	−0.334013
$387$	4.61803	0.234748
$388$	−18.4721	−0.937781
$389$	13.7984	0.699605	0.349803	−	0.936823i	$-0.386249\pi$
$389$	13.7984	0.699605	0.349803	+	0.936823i	$0.386249\pi$
$390$	−1.61803	−0.0819323
$391$	6.47214	0.327310
$392$	7.85410	0.396692
$393$	2.70820	0.136611
$394$	7.41641	0.373633
$395$	−7.23607	−0.364086
$396$	0	0
$397$	−12.6180	−0.633281	−0.316640	−	0.948546i	$-0.602555\pi$
$397$	−12.6180	−0.633281	−0.316640	+	0.948546i	$0.602555\pi$
$398$	−12.1803	−0.610545
$399$	−6.23607	−0.312194
$400$	−2.38197	−0.119098
$401$	17.2361	0.860728	0.430364	−	0.902655i	$-0.358385\pi$
$401$	17.2361	0.860728	0.430364	+	0.902655i	$0.358385\pi$
$402$	−8.23607	−0.410778
$403$	1.61803	0.0806000
$404$	−3.23607	−0.161000
$405$	12.4721	0.619745
$406$	3.29180	0.163369
$407$	0	0
$408$	5.23607	0.259224
$409$	−0.270510	−0.0133759	−0.00668793	−	0.999978i	$-0.502129\pi$
$409$	−0.270510	−0.0133759	−0.00668793	+	0.999978i	$0.502129\pi$
$410$	−1.00000	−0.0493865
$411$	0.527864	0.0260376
$412$	−7.14590	−0.352053
$413$	49.8885	2.45485
$414$	0.763932	0.0375452
$415$	−3.85410	−0.189190
$416$	−0.618034	−0.0303016
$417$	11.8541	0.580498
$418$	0	0
$419$	−16.2918	−0.795906	−0.397953	−	0.917406i	$-0.630279\pi$
$419$	−16.2918	−0.795906	−0.397953	+	0.917406i	$0.630279\pi$
$420$	10.0902	0.492350
$421$	−8.18034	−0.398685	−0.199343	−	0.979930i	$-0.563881\pi$
$421$	−8.18034	−0.398685	−0.199343	+	0.979930i	$0.563881\pi$
$422$	−22.6525	−1.10271
$423$	0.291796	0.0141876
$424$	−10.4721	−0.508572
$425$	7.70820	0.373903
$426$	−20.7984	−1.00768
$427$	−22.0000	−1.06465
$428$	−6.18034	−0.298738
$429$	0	0
$430$	19.5623	0.943378
$431$	−37.4164	−1.80228	−0.901142	−	0.433523i	$-0.857270\pi$
$431$	−37.4164	−1.80228	−0.901142	+	0.433523i	$0.857270\pi$
$432$	5.47214	0.263278
$433$	6.18034	0.297008	0.148504	−	0.988912i	$-0.452554\pi$
$433$	6.18034	0.297008	0.148504	+	0.988912i	$0.452554\pi$
$434$	−10.0902	−0.484344
$435$	2.23607	0.107211
$436$	−12.4721	−0.597307
$437$	−2.00000	−0.0956730
$438$	16.9443	0.809629
$439$	−20.0000	−0.954548	−0.477274	−	0.878755i	$-0.658375\pi$
$439$	−20.0000	−0.954548	−0.477274	+	0.878755i	$0.658375\pi$
$440$	0	0
$441$	−3.00000	−0.142857
$442$	2.00000	0.0951303
$443$	17.7082	0.841342	0.420671	−	0.907213i	$-0.361795\pi$
$443$	17.7082	0.841342	0.420671	+	0.907213i	$0.361795\pi$
$444$	−2.00000	−0.0949158
$445$	−11.2361	−0.532641
$446$	−10.4721	−0.495870
$447$	−10.4721	−0.495315
$448$	3.85410	0.182089
$449$	16.1803	0.763597	0.381799	−	0.924245i	$-0.375305\pi$
$449$	16.1803	0.763597	0.381799	+	0.924245i	$0.375305\pi$
$450$	0.909830	0.0428898
$451$	0	0
$452$	−13.7082	−0.644780
$453$	−9.70820	−0.456131
$454$	10.9443	0.513640
$455$	3.85410	0.180683
$456$	−1.61803	−0.0757714
$457$	37.2361	1.74183	0.870915	−	0.491434i	$-0.163527\pi$
$457$	37.2361	1.74183	0.870915	+	0.491434i	$0.163527\pi$
$458$	−1.85410	−0.0866365
$459$	−17.7082	−0.826548
$460$	3.23607	0.150882
$461$	13.4164	0.624864	0.312432	−	0.949940i	$-0.398856\pi$
$461$	13.4164	0.624864	0.312432	+	0.949940i	$0.398856\pi$
$462$	0	0
$463$	−37.0132	−1.72015	−0.860074	−	0.510170i	$-0.829582\pi$
$463$	−37.0132	−1.72015	−0.860074	+	0.510170i	$0.829582\pi$
$464$	0.854102	0.0396507
$465$	−6.85410	−0.317851
$466$	−10.4721	−0.485112
$467$	26.8328	1.24167	0.620837	−	0.783939i	$-0.286793\pi$
$467$	26.8328	1.24167	0.620837	+	0.783939i	$0.286793\pi$
$468$	0.236068	0.0109122
$469$	19.6180	0.905877
$470$	1.23607	0.0570156
$471$	20.7984	0.958338
$472$	12.9443	0.595808
$473$	0	0
$474$	−7.23607	−0.332364
$475$	−2.38197	−0.109292
$476$	−12.4721	−0.571659
$477$	4.00000	0.183147
$478$	−28.2705	−1.29306
$479$	0.437694	0.0199988	0.00999938	−	0.999950i	$-0.496817\pi$
$479$	0.437694	0.0199988	0.00999938	+	0.999950i	$0.496817\pi$
$480$	2.61803	0.119496
$481$	−0.763932	−0.0348323
$482$	−10.3820	−0.472886
$483$	12.4721	0.567502
$484$	0	0
$485$	29.8885	1.35717
$486$	−3.94427	−0.178916
$487$	−23.5066	−1.06518	−0.532592	−	0.846372i	$-0.678782\pi$
$487$	−23.5066	−1.06518	−0.532592	+	0.846372i	$0.678782\pi$
$488$	−5.70820	−0.258398
$489$	−4.76393	−0.215432
$490$	−12.7082	−0.574098
$491$	−21.4508	−0.968063	−0.484032	−	0.875050i	$-0.660828\pi$
$491$	−21.4508	−0.968063	−0.484032	+	0.875050i	$0.660828\pi$
$492$	−1.00000	−0.0450835
$493$	−2.76393	−0.124481
$494$	−0.618034	−0.0278067
$495$	0	0
$496$	−2.61803	−0.117553
$497$	49.5410	2.22222
$498$	−3.85410	−0.172706
$499$	−25.1246	−1.12473	−0.562366	−	0.826888i	$-0.690109\pi$
$499$	−25.1246	−1.12473	−0.562366	+	0.826888i	$0.690109\pi$
$500$	11.9443	0.534164
$501$	−1.52786	−0.0682599
$502$	8.47214	0.378130
$503$	−15.3262	−0.683363	−0.341682	−	0.939816i	$-0.610996\pi$
$503$	−15.3262	−0.683363	−0.341682	+	0.939816i	$0.610996\pi$
$504$	−1.47214	−0.0655741
$505$	5.23607	0.233002
$506$	0	0
$507$	20.4164	0.906725
$508$	−6.00000	−0.266207
$509$	17.7082	0.784902	0.392451	−	0.919773i	$-0.371627\pi$
$509$	17.7082	0.784902	0.392451	+	0.919773i	$0.371627\pi$
$510$	−8.47214	−0.375152
$511$	−40.3607	−1.78545
$512$	1.00000	0.0441942
$513$	5.47214	0.241601
$514$	−9.88854	−0.436165
$515$	11.5623	0.509496
$516$	19.5623	0.861182
$517$	0	0
$518$	4.76393	0.209315
$519$	−19.5623	−0.858690
$520$	1.00000	0.0438529
$521$	31.1246	1.36359	0.681797	−	0.731541i	$-0.261199\pi$
$521$	31.1246	1.36359	0.681797	+	0.731541i	$0.261199\pi$
$522$	−0.326238	−0.0142790
$523$	21.8885	0.957119	0.478560	−	0.878055i	$-0.341159\pi$
$523$	21.8885	0.957119	0.478560	+	0.878055i	$0.341159\pi$
$524$	−1.67376	−0.0731186
$525$	14.8541	0.648286
$526$	−25.7984	−1.12486
$527$	8.47214	0.369052
$528$	0	0
$529$	−19.0000	−0.826087
$530$	16.9443	0.736012
$531$	−4.94427	−0.214563
$532$	3.85410	0.167097
$533$	−0.381966	−0.0165448
$534$	−11.2361	−0.486232
$535$	10.0000	0.432338
$536$	5.09017	0.219862
$537$	−18.2361	−0.786944
$538$	−16.3607	−0.705359
$539$	0	0
$540$	−8.85410	−0.381020
$541$	20.6525	0.887919	0.443960	−	0.896047i	$-0.353573\pi$
$541$	20.6525	0.887919	0.443960	+	0.896047i	$0.353573\pi$
$542$	16.1459	0.693526
$543$	32.1803	1.38099
$544$	−3.23607	−0.138745
$545$	20.1803	0.864431
$546$	3.85410	0.164940
$547$	22.6525	0.968550	0.484275	−	0.874916i	$-0.339083\pi$
$547$	22.6525	0.968550	0.484275	+	0.874916i	$0.339083\pi$
$548$	−0.326238	−0.0139362
$549$	2.18034	0.0930546
$550$	0	0
$551$	0.854102	0.0363860
$552$	3.23607	0.137736
$553$	17.2361	0.732952
$554$	9.05573	0.384741
$555$	3.23607	0.137363
$556$	−7.32624	−0.310702
$557$	−30.3607	−1.28642	−0.643212	−	0.765688i	$-0.722398\pi$
$557$	−30.3607	−1.28642	−0.643212	+	0.765688i	$0.722398\pi$
$558$	1.00000	0.0423334
$559$	7.47214	0.316038
$560$	−6.23607	−0.263522
$561$	0	0
$562$	−29.2148	−1.23235
$563$	−1.34752	−0.0567914	−0.0283957	−	0.999597i	$-0.509040\pi$
$563$	−1.34752	−0.0567914	−0.0283957	+	0.999597i	$0.509040\pi$
$564$	1.23607	0.0520479
$565$	22.1803	0.933134
$566$	19.2705	0.810000
$567$	−29.7082	−1.24763
$568$	12.8541	0.539346
$569$	15.4508	0.647733	0.323867	−	0.946103i	$-0.395017\pi$
$569$	15.4508	0.647733	0.323867	+	0.946103i	$0.395017\pi$
$570$	2.61803	0.109657
$571$	36.2148	1.51554	0.757771	−	0.652521i	$-0.226289\pi$
$571$	36.2148	1.51554	0.757771	+	0.652521i	$0.226289\pi$
$572$	0	0
$573$	16.1803	0.675943
$574$	2.38197	0.0994213
$575$	4.76393	0.198670
$576$	−0.381966	−0.0159153
$577$	23.1591	0.964124	0.482062	−	0.876137i	$-0.339888\pi$
$577$	23.1591	0.964124	0.482062	+	0.876137i	$0.339888\pi$
$578$	−6.52786	−0.271523
$579$	10.6180	0.441270
$580$	−1.38197	−0.0573830
$581$	9.18034	0.380865
$582$	29.8885	1.23892
$583$	0	0
$584$	−10.4721	−0.433340
$585$	−0.381966	−0.0157924
$586$	20.0344	0.827615
$587$	−3.23607	−0.133567	−0.0667834	−	0.997767i	$-0.521274\pi$
$587$	−3.23607	−0.133567	−0.0667834	+	0.997767i	$0.521274\pi$
$588$	−12.7082	−0.524077
$589$	−2.61803	−0.107874
$590$	−20.9443	−0.862262
$591$	−12.0000	−0.493614
$592$	1.23607	0.0508021
$593$	35.7082	1.46636	0.733180	−	0.680035i	$-0.238035\pi$
$593$	35.7082	1.46636	0.733180	+	0.680035i	$0.238035\pi$
$594$	0	0
$595$	20.1803	0.827313
$596$	6.47214	0.265109
$597$	19.7082	0.806603
$598$	1.23607	0.0505466
$599$	−25.2148	−1.03025	−0.515124	−	0.857116i	$-0.672254\pi$
$599$	−25.2148	−1.03025	−0.515124	+	0.857116i	$0.672254\pi$
$600$	3.85410	0.157343
$601$	−27.4508	−1.11974	−0.559872	−	0.828579i	$-0.689150\pi$
$601$	−27.4508	−1.11974	−0.559872	+	0.828579i	$0.689150\pi$
$602$	−46.5967	−1.89914
$603$	−1.94427	−0.0791769
$604$	6.00000	0.244137
$605$	0	0
$606$	5.23607	0.212701
$607$	37.1246	1.50684	0.753421	−	0.657539i	$-0.228402\pi$
$607$	37.1246	1.50684	0.753421	+	0.657539i	$0.228402\pi$
$608$	1.00000	0.0405554
$609$	−5.32624	−0.215830
$610$	9.23607	0.373957
$611$	0.472136	0.0191006
$612$	1.23607	0.0499651
$613$	42.9443	1.73450	0.867251	−	0.497870i	$-0.165885\pi$
$613$	42.9443	1.73450	0.867251	+	0.497870i	$0.165885\pi$
$614$	2.00000	0.0807134
$615$	1.61803	0.0652454
$616$	0	0
$617$	12.6180	0.507983	0.253991	−	0.967206i	$-0.418256\pi$
$617$	12.6180	0.507983	0.253991	+	0.967206i	$0.418256\pi$
$618$	11.5623	0.465104
$619$	49.0132	1.97001	0.985003	−	0.172540i	$-0.0551974\pi$
$619$	49.0132	1.97001	0.985003	+	0.172540i	$0.0551974\pi$
$620$	4.23607	0.170125
$621$	−10.9443	−0.439179
$622$	21.1246	0.847020
$623$	26.7639	1.07227
$624$	1.00000	0.0400320
$625$	−7.41641	−0.296656
$626$	11.3262	0.452688
$627$	0	0
$628$	−12.8541	−0.512935
$629$	−4.00000	−0.159490
$630$	2.38197	0.0948998
$631$	19.5967	0.780134	0.390067	−	0.920786i	$-0.372452\pi$
$631$	19.5967	0.780134	0.390067	+	0.920786i	$0.372452\pi$
$632$	4.47214	0.177892
$633$	36.6525	1.45681
$634$	8.00000	0.317721
$635$	9.70820	0.385258
$636$	16.9443	0.671884
$637$	−4.85410	−0.192327
$638$	0	0
$639$	−4.90983	−0.194230
$640$	−1.61803	−0.0639584
$641$	−18.9443	−0.748254	−0.374127	−	0.927378i	$-0.622058\pi$
$641$	−18.9443	−0.748254	−0.374127	+	0.927378i	$0.622058\pi$
$642$	10.0000	0.394669
$643$	−30.0000	−1.18308	−0.591542	−	0.806274i	$-0.701481\pi$
$643$	−30.0000	−1.18308	−0.591542	+	0.806274i	$0.701481\pi$
$644$	−7.70820	−0.303746
$645$	−31.6525	−1.24632
$646$	−3.23607	−0.127321
$647$	−26.8328	−1.05491	−0.527453	−	0.849584i	$-0.676853\pi$
$647$	−26.8328	−1.05491	−0.527453	+	0.849584i	$0.676853\pi$
$648$	−7.70820	−0.302807
$649$	0	0
$650$	1.47214	0.0577419
$651$	16.3262	0.639876
$652$	2.94427	0.115307
$653$	24.0344	0.940540	0.470270	−	0.882522i	$-0.344156\pi$
$653$	24.0344	0.940540	0.470270	+	0.882522i	$0.344156\pi$
$654$	20.1803	0.789114
$655$	2.70820	0.105818
$656$	0.618034	0.0241302
$657$	4.00000	0.156055
$658$	−2.94427	−0.114780
$659$	1.88854	0.0735672	0.0367836	−	0.999323i	$-0.488289\pi$
$659$	1.88854	0.0735672	0.0367836	+	0.999323i	$0.488289\pi$
$660$	0	0
$661$	41.2361	1.60390	0.801949	−	0.597393i	$-0.203797\pi$
$661$	41.2361	1.60390	0.801949	+	0.597393i	$0.203797\pi$
$662$	−33.9787	−1.32062
$663$	−3.23607	−0.125678
$664$	2.38197	0.0924382
$665$	−6.23607	−0.241824
$666$	−0.472136	−0.0182949
$667$	−1.70820	−0.0661419
$668$	0.944272	0.0365350
$669$	16.9443	0.655103
$670$	−8.23607	−0.318187
$671$	0	0
$672$	−6.23607	−0.240562
$673$	9.27051	0.357352	0.178676	−	0.983908i	$-0.442819\pi$
$673$	9.27051	0.357352	0.178676	+	0.983908i	$0.442819\pi$
$674$	19.0902	0.735326
$675$	−13.0344	−0.501696
$676$	−12.6180	−0.485309
$677$	−24.4508	−0.939722	−0.469861	−	0.882740i	$-0.655696\pi$
$677$	−24.4508	−0.939722	−0.469861	+	0.882740i	$0.655696\pi$
$678$	22.1803	0.851831
$679$	−71.1935	−2.73216
$680$	5.23607	0.200794
$681$	−17.7082	−0.678580
$682$	0	0
$683$	37.3050	1.42743	0.713717	−	0.700434i	$-0.247010\pi$
$683$	37.3050	1.42743	0.713717	+	0.700434i	$0.247010\pi$
$684$	−0.381966	−0.0146048
$685$	0.527864	0.0201686
$686$	3.29180	0.125681
$687$	3.00000	0.114457
$688$	−12.0902	−0.460933
$689$	6.47214	0.246569
$690$	−5.23607	−0.199334
$691$	25.7082	0.977986	0.488993	−	0.872288i	$-0.337364\pi$
$691$	25.7082	0.977986	0.488993	+	0.872288i	$0.337364\pi$
$692$	12.0902	0.459599
$693$	0	0
$694$	22.4721	0.853031
$695$	11.8541	0.449652
$696$	−1.38197	−0.0523833
$697$	−2.00000	−0.0757554
$698$	20.6525	0.781708
$699$	16.9443	0.640891
$700$	−9.18034	−0.346984
$701$	23.1246	0.873405	0.436702	−	0.899606i	$-0.356146\pi$
$701$	23.1246	0.873405	0.436702	+	0.899606i	$0.356146\pi$
$702$	−3.38197	−0.127644
$703$	1.23607	0.0466192
$704$	0	0
$705$	−2.00000	−0.0753244
$706$	−15.8885	−0.597973
$707$	−12.4721	−0.469063
$708$	−20.9443	−0.787134
$709$	−3.02129	−0.113467	−0.0567334	−	0.998389i	$-0.518069\pi$
$709$	−3.02129	−0.113467	−0.0567334	+	0.998389i	$0.518069\pi$
$710$	−20.7984	−0.780549
$711$	−1.70820	−0.0640627
$712$	6.94427	0.260248
$713$	5.23607	0.196092
$714$	20.1803	0.755230
$715$	0	0
$716$	11.2705	0.421199
$717$	45.7426	1.70829
$718$	35.2705	1.31628
$719$	20.2918	0.756756	0.378378	−	0.925651i	$-0.376482\pi$
$719$	20.2918	0.756756	0.378378	+	0.925651i	$0.376482\pi$
$720$	0.618034	0.0230328
$721$	−27.5410	−1.02568
$722$	1.00000	0.0372161
$723$	16.7984	0.624738
$724$	−19.8885	−0.739152
$725$	−2.03444	−0.0755573
$726$	0	0
$727$	45.8885	1.70191	0.850956	−	0.525237i	$-0.176023\pi$
$727$	45.8885	1.70191	0.850956	+	0.525237i	$0.176023\pi$
$728$	−2.38197	−0.0882815
$729$	29.5066	1.09284
$730$	16.9443	0.627136
$731$	39.1246	1.44708
$732$	9.23607	0.341375
$733$	4.36068	0.161065	0.0805327	−	0.996752i	$-0.474338\pi$
$733$	4.36068	0.161065	0.0805327	+	0.996752i	$0.474338\pi$
$734$	23.1246	0.853545
$735$	20.5623	0.758452
$736$	−2.00000	−0.0737210
$737$	0	0
$738$	−0.236068	−0.00868978
$739$	8.09017	0.297602	0.148801	−	0.988867i	$-0.452459\pi$
$739$	8.09017	0.297602	0.148801	+	0.988867i	$0.452459\pi$
$740$	−2.00000	−0.0735215
$741$	1.00000	0.0367359
$742$	−40.3607	−1.48169
$743$	18.3607	0.673588	0.336794	−	0.941578i	$-0.390657\pi$
$743$	18.3607	0.673588	0.336794	+	0.941578i	$0.390657\pi$
$744$	4.23607	0.155302
$745$	−10.4721	−0.383669
$746$	−22.7426	−0.832667
$747$	−0.909830	−0.0332889
$748$	0	0
$749$	−23.8197	−0.870351
$750$	−19.3262	−0.705694
$751$	11.0557	0.403429	0.201715	−	0.979444i	$-0.435349\pi$
$751$	11.0557	0.403429	0.201715	+	0.979444i	$0.435349\pi$
$752$	−0.763932	−0.0278577
$753$	−13.7082	−0.499555
$754$	−0.527864	−0.0192237
$755$	−9.70820	−0.353318
$756$	21.0902	0.767042
$757$	−41.3951	−1.50453	−0.752266	−	0.658860i	$-0.771039\pi$
$757$	−41.3951	−1.50453	−0.752266	+	0.658860i	$0.771039\pi$
$758$	−13.0902	−0.475456
$759$	0	0
$760$	−1.61803	−0.0586923
$761$	31.0557	1.12577	0.562885	−	0.826535i	$-0.309692\pi$
$761$	31.0557	1.12577	0.562885	+	0.826535i	$0.309692\pi$
$762$	9.70820	0.351691
$763$	−48.0689	−1.74021
$764$	−10.0000	−0.361787
$765$	−2.00000	−0.0723102
$766$	−34.0344	−1.22971
$767$	−8.00000	−0.288863
$768$	−1.61803	−0.0583858
$769$	28.1803	1.01621	0.508105	−	0.861295i	$-0.330346\pi$
$769$	28.1803	1.01621	0.508105	+	0.861295i	$0.330346\pi$
$770$	0	0
$771$	16.0000	0.576226
$772$	−6.56231	−0.236183
$773$	3.70820	0.133375	0.0666874	−	0.997774i	$-0.478757\pi$
$773$	3.70820	0.133375	0.0666874	+	0.997774i	$0.478757\pi$
$774$	4.61803	0.165992
$775$	6.23607	0.224006
$776$	−18.4721	−0.663111
$777$	−7.70820	−0.276530
$778$	13.7984	0.494696
$779$	0.618034	0.0221434
$780$	−1.61803	−0.0579349
$781$	0	0
$782$	6.47214	0.231443
$783$	4.67376	0.167027
$784$	7.85410	0.280504
$785$	20.7984	0.742326
$786$	2.70820	0.0965984
$787$	−45.2361	−1.61249	−0.806246	−	0.591581i	$-0.798504\pi$
$787$	−45.2361	−1.61249	−0.806246	+	0.591581i	$0.798504\pi$
$788$	7.41641	0.264199
$789$	41.7426	1.48608
$790$	−7.23607	−0.257448
$791$	−52.8328	−1.87852
$792$	0	0
$793$	3.52786	0.125278
$794$	−12.6180	−0.447797
$795$	−27.4164	−0.972360
$796$	−12.1803	−0.431721
$797$	−11.2361	−0.398002	−0.199001	−	0.979999i	$-0.563770\pi$
$797$	−11.2361	−0.398002	−0.199001	+	0.979999i	$0.563770\pi$
$798$	−6.23607	−0.220754
$799$	2.47214	0.0874579
$800$	−2.38197	−0.0842152
$801$	−2.65248	−0.0937206
$802$	17.2361	0.608627
$803$	0	0
$804$	−8.23607	−0.290464
$805$	12.4721	0.439585
$806$	1.61803	0.0569928
$807$	26.4721	0.931863
$808$	−3.23607	−0.113844
$809$	45.2361	1.59042	0.795208	−	0.606337i	$-0.207362\pi$
$809$	45.2361	1.59042	0.795208	+	0.606337i	$0.207362\pi$
$810$	12.4721	0.438226
$811$	−38.8328	−1.36360	−0.681802	−	0.731536i	$-0.738804\pi$
$811$	−38.8328	−1.36360	−0.681802	+	0.731536i	$0.738804\pi$
$812$	3.29180	0.115519
$813$	−26.1246	−0.916230
$814$	0	0
$815$	−4.76393	−0.166873
$816$	5.23607	0.183299
$817$	−12.0902	−0.422982
$818$	−0.270510	−0.00945815
$819$	0.909830	0.0317920
$820$	−1.00000	−0.0349215
$821$	−46.0000	−1.60541	−0.802706	−	0.596376i	$-0.796607\pi$
$821$	−46.0000	−1.60541	−0.802706	+	0.596376i	$0.796607\pi$
$822$	0.527864	0.0184114
$823$	−11.7082	−0.408122	−0.204061	−	0.978958i	$-0.565414\pi$
$823$	−11.7082	−0.408122	−0.204061	+	0.978958i	$0.565414\pi$
$824$	−7.14590	−0.248939
$825$	0	0
$826$	49.8885	1.73584
$827$	−46.0689	−1.60197	−0.800986	−	0.598683i	$-0.795691\pi$
$827$	−46.0689	−1.60197	−0.800986	+	0.598683i	$0.795691\pi$
$828$	0.763932	0.0265485
$829$	49.3050	1.71243	0.856216	−	0.516618i	$-0.172809\pi$
$829$	49.3050	1.71243	0.856216	+	0.516618i	$0.172809\pi$
$830$	−3.85410	−0.133778
$831$	−14.6525	−0.508289
$832$	−0.618034	−0.0214265
$833$	−25.4164	−0.880626
$834$	11.8541	0.410474
$835$	−1.52786	−0.0528739
$836$	0	0
$837$	−14.3262	−0.495187
$838$	−16.2918	−0.562791
$839$	43.3262	1.49579	0.747894	−	0.663818i	$-0.231065\pi$
$839$	43.3262	1.49579	0.747894	+	0.663818i	$0.231065\pi$
$840$	10.0902	0.348144
$841$	−28.2705	−0.974845
$842$	−8.18034	−0.281913
$843$	47.2705	1.62808
$844$	−22.6525	−0.779730
$845$	20.4164	0.702346
$846$	0.291796	0.0100322
$847$	0	0
$848$	−10.4721	−0.359615
$849$	−31.1803	−1.07011
$850$	7.70820	0.264389
$851$	−2.47214	−0.0847437
$852$	−20.7984	−0.712541
$853$	−25.5967	−0.876416	−0.438208	−	0.898874i	$-0.644387\pi$
$853$	−25.5967	−0.876416	−0.438208	+	0.898874i	$0.644387\pi$
$854$	−22.0000	−0.752825
$855$	0.618034	0.0211363
$856$	−6.18034	−0.211240
$857$	5.85410	0.199972	0.0999862	−	0.994989i	$-0.468120\pi$
$857$	5.85410	0.199972	0.0999862	+	0.994989i	$0.468120\pi$
$858$	0	0
$859$	35.1246	1.19844	0.599218	−	0.800586i	$-0.295478\pi$
$859$	35.1246	1.19844	0.599218	+	0.800586i	$0.295478\pi$
$860$	19.5623	0.667069
$861$	−3.85410	−0.131347
$862$	−37.4164	−1.27441
$863$	−39.5623	−1.34672	−0.673358	−	0.739316i	$-0.735149\pi$
$863$	−39.5623	−1.34672	−0.673358	+	0.739316i	$0.735149\pi$
$864$	5.47214	0.186166
$865$	−19.5623	−0.665138
$866$	6.18034	0.210016
$867$	10.5623	0.358715
$868$	−10.0902	−0.342483
$869$	0	0
$870$	2.23607	0.0758098
$871$	−3.14590	−0.106595
$872$	−12.4721	−0.422360
$873$	7.05573	0.238800
$874$	−2.00000	−0.0676510
$875$	46.0344	1.55625
$876$	16.9443	0.572494
$877$	−14.1591	−0.478117	−0.239059	−	0.971005i	$-0.576839\pi$
$877$	−14.1591	−0.478117	−0.239059	+	0.971005i	$0.576839\pi$
$878$	−20.0000	−0.674967
$879$	−32.4164	−1.09338
$880$	0	0
$881$	−3.74265	−0.126093	−0.0630465	−	0.998011i	$-0.520082\pi$
$881$	−3.74265	−0.126093	−0.0630465	+	0.998011i	$0.520082\pi$
$882$	−3.00000	−0.101015
$883$	−12.3607	−0.415970	−0.207985	−	0.978132i	$-0.566691\pi$
$883$	−12.3607	−0.415970	−0.207985	+	0.978132i	$0.566691\pi$
$884$	2.00000	0.0672673
$885$	33.8885	1.13915
$886$	17.7082	0.594919
$887$	−24.0689	−0.808154	−0.404077	−	0.914725i	$-0.632407\pi$
$887$	−24.0689	−0.808154	−0.404077	+	0.914725i	$0.632407\pi$
$888$	−2.00000	−0.0671156
$889$	−23.1246	−0.775575
$890$	−11.2361	−0.376634
$891$	0	0
$892$	−10.4721	−0.350633
$893$	−0.763932	−0.0255640
$894$	−10.4721	−0.350241
$895$	−18.2361	−0.609565
$896$	3.85410	0.128757
$897$	−2.00000	−0.0667781
$898$	16.1803	0.539945
$899$	−2.23607	−0.0745770
$900$	0.909830	0.0303277
$901$	33.8885	1.12899
$902$	0	0
$903$	75.3951	2.50899
$904$	−13.7082	−0.455928
$905$	32.1803	1.06971
$906$	−9.70820	−0.322533
$907$	−22.4721	−0.746175	−0.373088	−	0.927796i	$-0.621701\pi$
$907$	−22.4721	−0.746175	−0.373088	+	0.927796i	$0.621701\pi$
$908$	10.9443	0.363198
$909$	1.23607	0.0409978
$910$	3.85410	0.127762
$911$	35.0557	1.16145	0.580724	−	0.814100i	$-0.302770\pi$
$911$	35.0557	1.16145	0.580724	+	0.814100i	$0.302770\pi$
$912$	−1.61803	−0.0535785
$913$	0	0
$914$	37.2361	1.23166
$915$	−14.9443	−0.494042
$916$	−1.85410	−0.0612613
$917$	−6.45085	−0.213026
$918$	−17.7082	−0.584458
$919$	−30.3820	−1.00221	−0.501104	−	0.865387i	$-0.667073\pi$
$919$	−30.3820	−1.00221	−0.501104	+	0.865387i	$0.667073\pi$
$920$	3.23607	0.106690
$921$	−3.23607	−0.106632
$922$	13.4164	0.441846
$923$	−7.94427	−0.261489
$924$	0	0
$925$	−2.94427	−0.0968071
$926$	−37.0132	−1.21633
$927$	2.72949	0.0896482
$928$	0.854102	0.0280373
$929$	−14.1459	−0.464112	−0.232056	−	0.972702i	$-0.574545\pi$
$929$	−14.1459	−0.464112	−0.232056	+	0.972702i	$0.574545\pi$
$930$	−6.85410	−0.224755
$931$	7.85410	0.257408
$932$	−10.4721	−0.343026
$933$	−34.1803	−1.11901
$934$	26.8328	0.877997
$935$	0	0
$936$	0.236068	0.00771612
$937$	−36.5410	−1.19374	−0.596872	−	0.802337i	$-0.703590\pi$
$937$	−36.5410	−1.19374	−0.596872	+	0.802337i	$0.703590\pi$
$938$	19.6180	0.640552
$939$	−18.3262	−0.598054
$940$	1.23607	0.0403161
$941$	29.4164	0.958947	0.479474	−	0.877556i	$-0.340828\pi$
$941$	29.4164	0.958947	0.479474	+	0.877556i	$0.340828\pi$
$942$	20.7984	0.677648
$943$	−1.23607	−0.0402519
$944$	12.9443	0.421300
$945$	−34.1246	−1.11007
$946$	0	0
$947$	−49.7082	−1.61530	−0.807650	−	0.589662i	$-0.799261\pi$
$947$	−49.7082	−1.61530	−0.807650	+	0.589662i	$0.799261\pi$
$948$	−7.23607	−0.235017
$949$	6.47214	0.210094
$950$	−2.38197	−0.0772812
$951$	−12.9443	−0.419747
$952$	−12.4721	−0.404224
$953$	1.41641	0.0458820	0.0229410	−	0.999737i	$-0.492697\pi$
$953$	1.41641	0.0458820	0.0229410	+	0.999737i	$0.492697\pi$
$954$	4.00000	0.129505
$955$	16.1803	0.523584
$956$	−28.2705	−0.914334
$957$	0	0
$958$	0.437694	0.0141413
$959$	−1.25735	−0.0406021
$960$	2.61803	0.0844967
$961$	−24.1459	−0.778900
$962$	−0.763932	−0.0246302
$963$	2.36068	0.0760718
$964$	−10.3820	−0.334381
$965$	10.6180	0.341807
$966$	12.4721	0.401284
$967$	−6.11146	−0.196531	−0.0982656	−	0.995160i	$-0.531329\pi$
$967$	−6.11146	−0.196531	−0.0982656	+	0.995160i	$0.531329\pi$
$968$	0	0
$969$	5.23607	0.168207
$970$	29.8885	0.959663
$971$	41.6180	1.33559	0.667793	−	0.744347i	$-0.267239\pi$
$971$	41.6180	1.33559	0.667793	+	0.744347i	$0.267239\pi$
$972$	−3.94427	−0.126513
$973$	−28.2361	−0.905207
$974$	−23.5066	−0.753199
$975$	−2.38197	−0.0762840
$976$	−5.70820	−0.182715
$977$	20.4721	0.654962	0.327481	−	0.944858i	$-0.393800\pi$
$977$	20.4721	0.654962	0.327481	+	0.944858i	$0.393800\pi$
$978$	−4.76393	−0.152334
$979$	0	0
$980$	−12.7082	−0.405949
$981$	4.76393	0.152101
$982$	−21.4508	−0.684524
$983$	9.09017	0.289931	0.144966	−	0.989437i	$-0.453693\pi$
$983$	9.09017	0.289931	0.144966	+	0.989437i	$0.453693\pi$
$984$	−1.00000	−0.0318788
$985$	−12.0000	−0.382352
$986$	−2.76393	−0.0880215
$987$	4.76393	0.151638
$988$	−0.618034	−0.0196623
$989$	24.1803	0.768890
$990$	0	0
$991$	8.14590	0.258763	0.129381	−	0.991595i	$-0.458701\pi$
$991$	8.14590	0.258763	0.129381	+	0.991595i	$0.458701\pi$
$992$	−2.61803	−0.0831227
$993$	54.9787	1.74470
$994$	49.5410	1.57135
$995$	19.7082	0.624792
$996$	−3.85410	−0.122122
$997$	53.7771	1.70314	0.851569	−	0.524243i	$-0.175652\pi$
$997$	53.7771	1.70314	0.851569	+	0.524243i	$0.175652\pi$
$998$	−25.1246	−0.795306
$999$	6.76393	0.214001

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4598.2.a.bg.1.1	yes	2
11.10	odd	2		4598.2.a.x.1.1	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4598.2.a.x.1.1	✓	2	11.10	odd	2
4598.2.a.bg.1.1	yes	2	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4598 = 2 \cdot 11^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4598.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.61803 q^{3} +1.00000 q^{4} -1.61803 q^{5} -1.61803 q^{6} +3.85410 q^{7} +1.00000 q^{8} -0.381966 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.61803 q^{3} +1.00000 q^{4} -1.61803 q^{5} -1.61803 q^{6} +3.85410 q^{7} +1.00000 q^{8} -0.381966 q^{9} -1.61803 q^{10} -1.61803 q^{12} -0.618034 q^{13} +3.85410 q^{14} +2.61803 q^{15} +1.00000 q^{16} -3.23607 q^{17} -0.381966 q^{18} +1.00000 q^{19} -1.61803 q^{20} -6.23607 q^{21} -2.00000 q^{23} -1.61803 q^{24} -2.38197 q^{25} -0.618034 q^{26} +5.47214 q^{27} +3.85410 q^{28} +0.854102 q^{29} +2.61803 q^{30} -2.61803 q^{31} +1.00000 q^{32} -3.23607 q^{34} -6.23607 q^{35} -0.381966 q^{36} +1.23607 q^{37} +1.00000 q^{38} +1.00000 q^{39} -1.61803 q^{40} +0.618034 q^{41} -6.23607 q^{42} -12.0902 q^{43} +0.618034 q^{45} -2.00000 q^{46} -0.763932 q^{47} -1.61803 q^{48} +7.85410 q^{49} -2.38197 q^{50} +5.23607 q^{51} -0.618034 q^{52} -10.4721 q^{53} +5.47214 q^{54} +3.85410 q^{56} -1.61803 q^{57} +0.854102 q^{58} +12.9443 q^{59} +2.61803 q^{60} -5.70820 q^{61} -2.61803 q^{62} -1.47214 q^{63} +1.00000 q^{64} +1.00000 q^{65} +5.09017 q^{67} -3.23607 q^{68} +3.23607 q^{69} -6.23607 q^{70} +12.8541 q^{71} -0.381966 q^{72} -10.4721 q^{73} +1.23607 q^{74} +3.85410 q^{75} +1.00000 q^{76} +1.00000 q^{78} +4.47214 q^{79} -1.61803 q^{80} -7.70820 q^{81} +0.618034 q^{82} +2.38197 q^{83} -6.23607 q^{84} +5.23607 q^{85} -12.0902 q^{86} -1.38197 q^{87} +6.94427 q^{89} +0.618034 q^{90} -2.38197 q^{91} -2.00000 q^{92} +4.23607 q^{93} -0.763932 q^{94} -1.61803 q^{95} -1.61803 q^{96} -18.4721 q^{97} +7.85410 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - q^{3} + 2 q^{4} - q^{5} - q^{6} + q^{7} + 2 q^{8} - 3 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 - q^3 + 2 * q^4 - q^5 - q^6 + q^7 + 2 * q^8 - 3 * q^9	\( 2 q + 2 q^{2} - q^{3} + 2 q^{4} - q^{5} - q^{6} + q^{7} + 2 q^{8} - 3 q^{9} - q^{10} - q^{12} + q^{13} + q^{14} + 3 q^{15} + 2 q^{16} - 2 q^{17} - 3 q^{18} + 2 q^{19} - q^{20} - 8 q^{21} - 4 q^{23} - q^{24} - 7 q^{25} + q^{26} + 2 q^{27} + q^{28} - 5 q^{29} + 3 q^{30} - 3 q^{31} + 2 q^{32} - 2 q^{34} - 8 q^{35} - 3 q^{36} - 2 q^{37} + 2 q^{38} + 2 q^{39} - q^{40} - q^{41} - 8 q^{42} - 13 q^{43} - q^{45} - 4 q^{46} - 6 q^{47} - q^{48} + 9 q^{49} - 7 q^{50} + 6 q^{51} + q^{52} - 12 q^{53} + 2 q^{54} + q^{56} - q^{57} - 5 q^{58} + 8 q^{59} + 3 q^{60} + 2 q^{61} - 3 q^{62} + 6 q^{63} + 2 q^{64} + 2 q^{65} - q^{67} - 2 q^{68} + 2 q^{69} - 8 q^{70} + 19 q^{71} - 3 q^{72} - 12 q^{73} - 2 q^{74} + q^{75} + 2 q^{76} + 2 q^{78} - q^{80} - 2 q^{81} - q^{82} + 7 q^{83} - 8 q^{84} + 6 q^{85} - 13 q^{86} - 5 q^{87} - 4 q^{89} - q^{90} - 7 q^{91} - 4 q^{92} + 4 q^{93} - 6 q^{94} - q^{95} - q^{96} - 28 q^{97} + 9 q^{98}+O(q^{100}) \) 2 * q + 2 * q^2 - q^3 + 2 * q^4 - q^5 - q^6 + q^7 + 2 * q^8 - 3 * q^9 - q^10 - q^12 + q^13 + q^14 + 3 * q^15 + 2 * q^16 - 2 * q^17 - 3 * q^18 + 2 * q^19 - q^20 - 8 * q^21 - 4 * q^23 - q^24 - 7 * q^25 + q^26 + 2 * q^27 + q^28 - 5 * q^29 + 3 * q^30 - 3 * q^31 + 2 * q^32 - 2 * q^34 - 8 * q^35 - 3 * q^36 - 2 * q^37 + 2 * q^38 + 2 * q^39 - q^40 - q^41 - 8 * q^42 - 13 * q^43 - q^45 - 4 * q^46 - 6 * q^47 - q^48 + 9 * q^49 - 7 * q^50 + 6 * q^51 + q^52 - 12 * q^53 + 2 * q^54 + q^56 - q^57 - 5 * q^58 + 8 * q^59 + 3 * q^60 + 2 * q^61 - 3 * q^62 + 6 * q^63 + 2 * q^64 + 2 * q^65 - q^67 - 2 * q^68 + 2 * q^69 - 8 * q^70 + 19 * q^71 - 3 * q^72 - 12 * q^73 - 2 * q^74 + q^75 + 2 * q^76 + 2 * q^78 - q^80 - 2 * q^81 - q^82 + 7 * q^83 - 8 * q^84 + 6 * q^85 - 13 * q^86 - 5 * q^87 - 4 * q^89 - q^90 - 7 * q^91 - 4 * q^92 + 4 * q^93 - 6 * q^94 - q^95 - q^96 - 28 * q^97 + 9 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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