LMFDB - Embedded newform 830.2.a.k.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [830,2,Mod(1,830)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(830, 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("830.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 830 = 2 \cdot 5 \cdot 83 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	830.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:	$6.62758336777$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.887108.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 7x^{3} + 13x^{2} + 6x - 9 $ x^5 - 2x^4 - 7x^3 + 13x^2 + 6x - 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$1.90136$ of defining polynomial
Character	$\chi$	$=$	830.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.90136 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.90136 q^{6} +0.676454 q^{7} +1.00000 q^{8} +0.615178 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.90136 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.90136 q^{6} +0.676454 q^{7} +1.00000 q^{8} +0.615178 q^{9} +1.00000 q^{10} +3.66496 q^{11} +1.90136 q^{12} -4.18150 q^{13} +0.676454 q^{14} +1.90136 q^{15} +1.00000 q^{16} +1.93328 q^{17} +0.615178 q^{18} -3.24278 q^{19} +1.00000 q^{20} +1.28618 q^{21} +3.66496 q^{22} +2.41614 q^{23} +1.90136 q^{24} +1.00000 q^{25} -4.18150 q^{26} -4.53441 q^{27} +0.676454 q^{28} -0.713816 q^{29} +1.90136 q^{30} -6.46164 q^{31} +1.00000 q^{32} +6.96842 q^{33} +1.93328 q^{34} +0.676454 q^{35} +0.615178 q^{36} +11.1001 q^{37} -3.24278 q^{38} -7.95055 q^{39} +1.00000 q^{40} -1.26227 q^{41} +1.28618 q^{42} -11.5560 q^{43} +3.66496 q^{44} +0.615178 q^{45} +2.41614 q^{46} +5.69628 q^{47} +1.90136 q^{48} -6.54241 q^{49} +1.00000 q^{50} +3.67586 q^{51} -4.18150 q^{52} -6.76477 q^{53} -4.53441 q^{54} +3.66496 q^{55} +0.676454 q^{56} -6.16570 q^{57} -0.713816 q^{58} +12.3803 q^{59} +1.90136 q^{60} +10.8459 q^{61} -6.46164 q^{62} +0.416140 q^{63} +1.00000 q^{64} -4.18150 q^{65} +6.96842 q^{66} -13.1206 q^{67} +1.93328 q^{68} +4.59396 q^{69} +0.676454 q^{70} -13.6665 q^{71} +0.615178 q^{72} +2.40210 q^{73} +11.1001 q^{74} +1.90136 q^{75} -3.24278 q^{76} +2.47918 q^{77} -7.95055 q^{78} +4.25254 q^{79} +1.00000 q^{80} -10.4671 q^{81} -1.26227 q^{82} +1.00000 q^{83} +1.28618 q^{84} +1.93328 q^{85} -11.5560 q^{86} -1.35722 q^{87} +3.66496 q^{88} -6.64709 q^{89} +0.615178 q^{90} -2.82859 q^{91} +2.41614 q^{92} -12.2859 q^{93} +5.69628 q^{94} -3.24278 q^{95} +1.90136 q^{96} +0.225504 q^{97} -6.54241 q^{98} +2.25460 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 5 q^{2} + 2 q^{3} + 5 q^{4} + 5 q^{5} + 2 q^{6} + 5 q^{7} + 5 q^{8} + 3 q^{9}+O(q^{10}) $ 5 * q + 5 * q^2 + 2 * q^3 + 5 * q^4 + 5 * q^5 + 2 * q^6 + 5 * q^7 + 5 * q^8 + 3 * q^9	\( 5 q + 5 q^{2} + 2 q^{3} + 5 q^{4} + 5 q^{5} + 2 q^{6} + 5 q^{7} + 5 q^{8} + 3 q^{9} + 5 q^{10} + q^{11} + 2 q^{12} + 4 q^{13} + 5 q^{14} + 2 q^{15} + 5 q^{16} - q^{17} + 3 q^{18} + 7 q^{19} + 5 q^{20} - q^{21} + q^{22} + 8 q^{23} + 2 q^{24} + 5 q^{25} + 4 q^{26} - q^{27} + 5 q^{28} - 11 q^{29} + 2 q^{30} + 10 q^{31} + 5 q^{32} - 5 q^{33} - q^{34} + 5 q^{35} + 3 q^{36} + 8 q^{37} + 7 q^{38} - 14 q^{39} + 5 q^{40} - 3 q^{41} - q^{42} - 2 q^{43} + q^{44} + 3 q^{45} + 8 q^{46} + 7 q^{47} + 2 q^{48} - 12 q^{49} + 5 q^{50} + 19 q^{51} + 4 q^{52} - 12 q^{53} - q^{54} + q^{55} + 5 q^{56} - 6 q^{57} - 11 q^{58} - 3 q^{59} + 2 q^{60} + 11 q^{61} + 10 q^{62} - 2 q^{63} + 5 q^{64} + 4 q^{65} - 5 q^{66} + 4 q^{67} - q^{68} - 26 q^{69} + 5 q^{70} + 4 q^{71} + 3 q^{72} - 3 q^{73} + 8 q^{74} + 2 q^{75} + 7 q^{76} - q^{77} - 14 q^{78} - 12 q^{79} + 5 q^{80} - 19 q^{81} - 3 q^{82} + 5 q^{83} - q^{84} - q^{85} - 2 q^{86} + 9 q^{87} + q^{88} - 30 q^{89} + 3 q^{90} + 14 q^{91} + 8 q^{92} - 10 q^{93} + 7 q^{94} + 7 q^{95} + 2 q^{96} - 7 q^{97} - 12 q^{98} - 36 q^{99}+O(q^{100}) \) 5 * q + 5 * q^2 + 2 * q^3 + 5 * q^4 + 5 * q^5 + 2 * q^6 + 5 * q^7 + 5 * q^8 + 3 * q^9 + 5 * q^10 + q^11 + 2 * q^12 + 4 * q^13 + 5 * q^14 + 2 * q^15 + 5 * q^16 - q^17 + 3 * q^18 + 7 * q^19 + 5 * q^20 - q^21 + q^22 + 8 * q^23 + 2 * q^24 + 5 * q^25 + 4 * q^26 - q^27 + 5 * q^28 - 11 * q^29 + 2 * q^30 + 10 * q^31 + 5 * q^32 - 5 * q^33 - q^34 + 5 * q^35 + 3 * q^36 + 8 * q^37 + 7 * q^38 - 14 * q^39 + 5 * q^40 - 3 * q^41 - q^42 - 2 * q^43 + q^44 + 3 * q^45 + 8 * q^46 + 7 * q^47 + 2 * q^48 - 12 * q^49 + 5 * q^50 + 19 * q^51 + 4 * q^52 - 12 * q^53 - q^54 + q^55 + 5 * q^56 - 6 * q^57 - 11 * q^58 - 3 * q^59 + 2 * q^60 + 11 * q^61 + 10 * q^62 - 2 * q^63 + 5 * q^64 + 4 * q^65 - 5 * q^66 + 4 * q^67 - q^68 - 26 * q^69 + 5 * q^70 + 4 * q^71 + 3 * q^72 - 3 * q^73 + 8 * q^74 + 2 * q^75 + 7 * q^76 - q^77 - 14 * q^78 - 12 * q^79 + 5 * q^80 - 19 * q^81 - 3 * q^82 + 5 * q^83 - q^84 - q^85 - 2 * q^86 + 9 * q^87 + q^88 - 30 * q^89 + 3 * q^90 + 14 * q^91 + 8 * q^92 - 10 * q^93 + 7 * q^94 + 7 * q^95 + 2 * q^96 - 7 * q^97 - 12 * q^98 - 36 * q^99

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
$3$	1.90136	1.09775	0.548876	−	0.835904i	$-0.315056\pi$
$3$	1.90136	1.09775	0.548876	+	0.835904i	$0.315056\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	1.90136	0.776228
$7$	0.676454	0.255676	0.127838	−	0.991795i	$-0.459196\pi$
$7$	0.676454	0.255676	0.127838	+	0.991795i	$0.459196\pi$
$8$	1.00000	0.353553
$9$	0.615178	0.205059
$10$	1.00000	0.316228
$11$	3.66496	1.10503	0.552514	−	0.833504i	$-0.313669\pi$
$11$	3.66496	1.10503	0.552514	+	0.833504i	$0.313669\pi$
$12$	1.90136	0.548876
$13$	−4.18150	−1.15974	−0.579870	−	0.814709i	$-0.696897\pi$
$13$	−4.18150	−1.15974	−0.579870	+	0.814709i	$0.696897\pi$
$14$	0.676454	0.180790
$15$	1.90136	0.490930
$16$	1.00000	0.250000
$17$	1.93328	0.468888	0.234444	−	0.972130i	$-0.424673\pi$
$17$	1.93328	0.468888	0.234444	+	0.972130i	$0.424673\pi$
$18$	0.615178	0.144999
$19$	−3.24278	−0.743944	−0.371972	−	0.928244i	$-0.621318\pi$
$19$	−3.24278	−0.743944	−0.371972	+	0.928244i	$0.621318\pi$
$20$	1.00000	0.223607
$21$	1.28618	0.280668
$22$	3.66496	0.781373
$23$	2.41614	0.503800	0.251900	−	0.967753i	$-0.418945\pi$
$23$	2.41614	0.503800	0.251900	+	0.967753i	$0.418945\pi$
$24$	1.90136	0.388114
$25$	1.00000	0.200000
$26$	−4.18150	−0.820060
$27$	−4.53441	−0.872648
$28$	0.676454	0.127838
$29$	−0.713816	−0.132552	−0.0662761	−	0.997801i	$-0.521112\pi$
$29$	−0.713816	−0.132552	−0.0662761	+	0.997801i	$0.521112\pi$
$30$	1.90136	0.347140
$31$	−6.46164	−1.16055	−0.580273	−	0.814422i	$-0.697054\pi$
$31$	−6.46164	−1.16055	−0.580273	+	0.814422i	$0.697054\pi$
$32$	1.00000	0.176777
$33$	6.96842	1.21305
$34$	1.93328	0.331554
$35$	0.676454	0.114342
$36$	0.615178	0.102530
$37$	11.1001	1.82485	0.912426	−	0.409242i	$-0.134207\pi$
$37$	11.1001	1.82485	0.912426	+	0.409242i	$0.134207\pi$
$38$	−3.24278	−0.526048
$39$	−7.95055	−1.27311
$40$	1.00000	0.158114
$41$	−1.26227	−0.197133	−0.0985667	−	0.995130i	$-0.531426\pi$
$41$	−1.26227	−0.197133	−0.0985667	+	0.995130i	$0.531426\pi$
$42$	1.28618	0.198463
$43$	−11.5560	−1.76227	−0.881137	−	0.472862i	$-0.843221\pi$
$43$	−11.5560	−1.76227	−0.881137	+	0.472862i	$0.843221\pi$
$44$	3.66496	0.552514
$45$	0.615178	0.0917053
$46$	2.41614	0.356240
$47$	5.69628	0.830888	0.415444	−	0.909619i	$-0.363626\pi$
$47$	5.69628	0.830888	0.415444	+	0.909619i	$0.363626\pi$
$48$	1.90136	0.274438
$49$	−6.54241	−0.934630
$50$	1.00000	0.141421
$51$	3.67586	0.514723
$52$	−4.18150	−0.579870
$53$	−6.76477	−0.929212	−0.464606	−	0.885517i	$-0.653804\pi$
$53$	−6.76477	−0.929212	−0.464606	+	0.885517i	$0.653804\pi$
$54$	−4.53441	−0.617055
$55$	3.66496	0.494183
$56$	0.676454	0.0903950
$57$	−6.16570	−0.816666
$58$	−0.713816	−0.0937286
$59$	12.3803	1.61177	0.805887	−	0.592069i	$-0.201689\pi$
$59$	12.3803	1.61177	0.805887	+	0.592069i	$0.201689\pi$
$60$	1.90136	0.245465
$61$	10.8459	1.38867	0.694336	−	0.719651i	$-0.255698\pi$
$61$	10.8459	1.38867	0.694336	+	0.719651i	$0.255698\pi$
$62$	−6.46164	−0.820629
$63$	0.416140	0.0524287
$64$	1.00000	0.125000
$65$	−4.18150	−0.518652
$66$	6.96842	0.857753
$67$	−13.1206	−1.60293	−0.801466	−	0.598041i	$-0.795946\pi$
$67$	−13.1206	−1.60293	−0.801466	+	0.598041i	$0.795946\pi$
$68$	1.93328	0.234444
$69$	4.59396	0.553047
$70$	0.676454	0.0808517
$71$	−13.6665	−1.62191	−0.810955	−	0.585108i	$-0.801052\pi$
$71$	−13.6665	−1.62191	−0.810955	+	0.585108i	$0.801052\pi$
$72$	0.615178	0.0724994
$73$	2.40210	0.281144	0.140572	−	0.990070i	$-0.455106\pi$
$73$	2.40210	0.281144	0.140572	+	0.990070i	$0.455106\pi$
$74$	11.1001	1.29036
$75$	1.90136	0.219550
$76$	−3.24278	−0.371972
$77$	2.47918	0.282529
$78$	−7.95055	−0.900223
$79$	4.25254	0.478448	0.239224	−	0.970964i	$-0.423107\pi$
$79$	4.25254	0.478448	0.239224	+	0.970964i	$0.423107\pi$
$80$	1.00000	0.111803
$81$	−10.4671	−1.16301
$82$	−1.26227	−0.139394
$83$	1.00000	0.109764
$83$	1.00000	0.109764
$84$	1.28618	0.140334
$85$	1.93328	0.209693
$86$	−11.5560	−1.24612
$87$	−1.35722	−0.145510
$88$	3.66496	0.390686
$89$	−6.64709	−0.704590	−0.352295	−	0.935889i	$-0.614599\pi$
$89$	−6.64709	−0.704590	−0.352295	+	0.935889i	$0.614599\pi$
$90$	0.615178	0.0648455
$91$	−2.82859	−0.296517
$92$	2.41614	0.251900
$93$	−12.2859	−1.27399
$94$	5.69628	0.587526
$95$	−3.24278	−0.332702
$96$	1.90136	0.194057
$97$	0.225504	0.0228965	0.0114482	−	0.999934i	$-0.496356\pi$
$97$	0.225504	0.0228965	0.0114482	+	0.999934i	$0.496356\pi$
$98$	−6.54241	−0.660883
$99$	2.25460	0.226596
$100$	1.00000	0.100000
$101$	1.99827	0.198835	0.0994177	−	0.995046i	$-0.468302\pi$
$101$	1.99827	0.198835	0.0994177	+	0.995046i	$0.468302\pi$
$102$	3.67586	0.363964
$103$	8.00033	0.788296	0.394148	−	0.919047i	$-0.371040\pi$
$103$	8.00033	0.788296	0.394148	+	0.919047i	$0.371040\pi$
$104$	−4.18150	−0.410030
$105$	1.28618	0.125519
$106$	−6.76477	−0.657052
$107$	9.67855	0.935661	0.467830	−	0.883818i	$-0.345036\pi$
$107$	9.67855	0.935661	0.467830	+	0.883818i	$0.345036\pi$
$108$	−4.53441	−0.436324
$109$	−7.62760	−0.730592	−0.365296	−	0.930891i	$-0.619032\pi$
$109$	−7.62760	−0.730592	−0.365296	+	0.930891i	$0.619032\pi$
$110$	3.66496	0.349440
$111$	21.1054	2.00323
$112$	0.676454	0.0639189
$113$	−13.0659	−1.22914	−0.614569	−	0.788863i	$-0.710670\pi$
$113$	−13.0659	−1.22914	−0.614569	+	0.788863i	$0.710670\pi$
$114$	−6.16570	−0.577470
$115$	2.41614	0.225306
$116$	−0.713816	−0.0662761
$117$	−2.57237	−0.237816
$118$	12.3803	1.13970
$119$	1.30777	0.119883
$120$	1.90136	0.173570
$121$	2.43195	0.221086
$122$	10.8459	0.981939
$123$	−2.40003	−0.216404
$124$	−6.46164	−0.580273
$125$	1.00000	0.0894427
$126$	0.416140	0.0370727
$127$	13.6118	1.20785	0.603927	−	0.797040i	$-0.293602\pi$
$127$	13.6118	1.20785	0.603927	+	0.797040i	$0.293602\pi$
$128$	1.00000	0.0883883
$129$	−21.9721	−1.93454
$130$	−4.18150	−0.366742
$131$	3.64650	0.318596	0.159298	−	0.987231i	$-0.449077\pi$
$131$	3.64650	0.318596	0.159298	+	0.987231i	$0.449077\pi$
$132$	6.96842	0.606523
$133$	−2.19359	−0.190208
$134$	−13.1206	−1.13344
$135$	−4.53441	−0.390260
$136$	1.93328	0.165777
$137$	−7.63943	−0.652680	−0.326340	−	0.945252i	$-0.605815\pi$
$137$	−7.63943	−0.652680	−0.326340	+	0.945252i	$0.605815\pi$
$138$	4.59396	0.391064
$139$	13.3906	1.13578	0.567889	−	0.823105i	$-0.307760\pi$
$139$	13.3906	1.13578	0.567889	+	0.823105i	$0.307760\pi$
$140$	0.676454	0.0571708
$141$	10.8307	0.912109
$142$	−13.6665	−1.14686
$143$	−15.3250	−1.28154
$144$	0.615178	0.0512648
$145$	−0.713816	−0.0592792
$146$	2.40210	0.198799
$147$	−12.4395	−1.02599
$148$	11.1001	0.912426
$149$	−21.5526	−1.76566	−0.882829	−	0.469694i	$-0.844364\pi$
$149$	−21.5526	−1.76566	−0.882829	+	0.469694i	$0.844364\pi$
$150$	1.90136	0.155246
$151$	18.2521	1.48533	0.742667	−	0.669661i	$-0.233561\pi$
$151$	18.2521	1.48533	0.742667	+	0.669661i	$0.233561\pi$
$152$	−3.24278	−0.263024
$153$	1.18931	0.0961499
$154$	2.47918	0.199778
$155$	−6.46164	−0.519012
$156$	−7.95055	−0.636553
$157$	7.61634	0.607850	0.303925	−	0.952696i	$-0.401703\pi$
$157$	7.61634	0.607850	0.303925	+	0.952696i	$0.401703\pi$
$158$	4.25254	0.338314
$159$	−12.8623	−1.02004
$160$	1.00000	0.0790569
$161$	1.63441	0.128809
$162$	−10.4671	−0.822372
$163$	−19.1298	−1.49836	−0.749182	−	0.662364i	$-0.769553\pi$
$163$	−19.1298	−1.49836	−0.749182	+	0.662364i	$0.769553\pi$
$164$	−1.26227	−0.0985667
$165$	6.96842	0.542491
$166$	1.00000	0.0776151
$167$	−1.28131	−0.0991505	−0.0495752	−	0.998770i	$-0.515787\pi$
$167$	−1.28131	−0.0991505	−0.0495752	+	0.998770i	$0.515787\pi$
$168$	1.28618	0.0992313
$169$	4.48496	0.344997
$170$	1.93328	0.148276
$171$	−1.99489	−0.152553
$172$	−11.5560	−0.881137
$173$	1.64571	0.125121	0.0625604	−	0.998041i	$-0.480073\pi$
$173$	1.64571	0.125121	0.0625604	+	0.998041i	$0.480073\pi$
$174$	−1.35722	−0.102891
$175$	0.676454	0.0511351
$176$	3.66496	0.276257
$177$	23.5394	1.76933
$178$	−6.64709	−0.498221
$179$	−4.69850	−0.351182	−0.175591	−	0.984463i	$-0.556184\pi$
$179$	−4.69850	−0.351182	−0.175591	+	0.984463i	$0.556184\pi$
$180$	0.615178	0.0458527
$181$	8.38260	0.623074	0.311537	−	0.950234i	$-0.399156\pi$
$181$	8.38260	0.623074	0.311537	+	0.950234i	$0.399156\pi$
$182$	−2.82859	−0.209669
$183$	20.6219	1.52442
$184$	2.41614	0.178120
$185$	11.1001	0.816098
$186$	−12.2859	−0.900847
$187$	7.08538	0.518135
$188$	5.69628	0.415444
$189$	−3.06732	−0.223115
$190$	−3.24278	−0.235256
$191$	−1.46961	−0.106337	−0.0531686	−	0.998586i	$-0.516932\pi$
$191$	−1.46961	−0.106337	−0.0531686	+	0.998586i	$0.516932\pi$
$192$	1.90136	0.137219
$193$	−3.04517	−0.219196	−0.109598	−	0.993976i	$-0.534956\pi$
$193$	−3.04517	−0.219196	−0.109598	+	0.993976i	$0.534956\pi$
$194$	0.225504	0.0161903
$195$	−7.95055	−0.569351
$196$	−6.54241	−0.467315
$197$	26.7931	1.90893	0.954463	−	0.298328i	$-0.0964289\pi$
$197$	26.7931	1.90893	0.954463	+	0.298328i	$0.0964289\pi$
$198$	2.25460	0.160228
$199$	−16.1059	−1.14172	−0.570859	−	0.821048i	$-0.693390\pi$
$199$	−16.1059	−1.14172	−0.570859	+	0.821048i	$0.693390\pi$
$200$	1.00000	0.0707107
$201$	−24.9469	−1.75962
$202$	1.99827	0.140598
$203$	−0.482864	−0.0338904
$204$	3.67586	0.257362
$205$	−1.26227	−0.0881608
$206$	8.00033	0.557410
$207$	1.48636	0.103309
$208$	−4.18150	−0.289935
$209$	−11.8847	−0.822079
$210$	1.28618	0.0887551
$211$	−12.4698	−0.858455	−0.429228	−	0.903196i	$-0.641214\pi$
$211$	−12.4698	−0.858455	−0.429228	+	0.903196i	$0.641214\pi$
$212$	−6.76477	−0.464606
$213$	−25.9849	−1.78046
$214$	9.67855	0.661612
$215$	−11.5560	−0.788113
$216$	−4.53441	−0.308528
$217$	−4.37100	−0.296723
$218$	−7.62760	−0.516606
$219$	4.56725	0.308626
$220$	3.66496	0.247092
$221$	−8.08400	−0.543789
$222$	21.1054	1.41650
$223$	11.8562	0.793952	0.396976	−	0.917829i	$-0.370060\pi$
$223$	11.8562	0.793952	0.396976	+	0.917829i	$0.370060\pi$
$224$	0.676454	0.0451975
$225$	0.615178	0.0410119
$226$	−13.0659	−0.869132
$227$	−19.1281	−1.26958	−0.634788	−	0.772686i	$-0.718913\pi$
$227$	−19.1281	−1.26958	−0.634788	+	0.772686i	$0.718913\pi$
$228$	−6.16570	−0.408333
$229$	−21.0266	−1.38948	−0.694738	−	0.719263i	$-0.744480\pi$
$229$	−21.0266	−1.38948	−0.694738	+	0.719263i	$0.744480\pi$
$230$	2.41614	0.159316
$231$	4.71382	0.310146
$232$	−0.713816	−0.0468643
$233$	26.9296	1.76422	0.882110	−	0.471044i	$-0.156123\pi$
$233$	26.9296	1.76422	0.882110	+	0.471044i	$0.156123\pi$
$234$	−2.57237	−0.168161
$235$	5.69628	0.371584
$236$	12.3803	0.805887
$237$	8.08562	0.525217
$238$	1.30777	0.0847703
$239$	−2.85483	−0.184664	−0.0923319	−	0.995728i	$-0.529432\pi$
$239$	−2.85483	−0.184664	−0.0923319	+	0.995728i	$0.529432\pi$
$240$	1.90136	0.122732
$241$	14.5844	0.939465	0.469733	−	0.882809i	$-0.344350\pi$
$241$	14.5844	0.939465	0.469733	+	0.882809i	$0.344350\pi$
$242$	2.43195	0.156331
$243$	−6.29850	−0.404049
$244$	10.8459	0.694336
$245$	−6.54241	−0.417979
$246$	−2.40003	−0.153020
$247$	13.5597	0.862782
$248$	−6.46164	−0.410315
$249$	1.90136	0.120494
$250$	1.00000	0.0632456
$251$	10.6811	0.674183	0.337092	−	0.941472i	$-0.390557\pi$
$251$	10.6811	0.674183	0.337092	+	0.941472i	$0.390557\pi$
$252$	0.416140	0.0262143
$253$	8.85506	0.556713
$254$	13.6118	0.854082
$255$	3.67586	0.230191
$256$	1.00000	0.0625000
$257$	6.67532	0.416395	0.208198	−	0.978087i	$-0.433240\pi$
$257$	6.67532	0.416395	0.208198	+	0.978087i	$0.433240\pi$
$258$	−21.9721	−1.36793
$259$	7.50873	0.466570
$260$	−4.18150	−0.259326
$261$	−0.439124	−0.0271811
$262$	3.64650	0.225281
$263$	22.1289	1.36453	0.682263	−	0.731107i	$-0.260996\pi$
$263$	22.1289	1.36453	0.682263	+	0.731107i	$0.260996\pi$
$264$	6.96842	0.428877
$265$	−6.76477	−0.415556
$266$	−2.19359	−0.134498
$267$	−12.6385	−0.773465
$268$	−13.1206	−0.801466
$269$	−25.9955	−1.58497	−0.792486	−	0.609889i	$-0.791214\pi$
$269$	−25.9955	−1.58497	−0.792486	+	0.609889i	$0.791214\pi$
$270$	−4.53441	−0.275955
$271$	18.8894	1.14745	0.573724	−	0.819049i	$-0.305498\pi$
$271$	18.8894	1.14745	0.573724	+	0.819049i	$0.305498\pi$
$272$	1.93328	0.117222
$273$	−5.37818	−0.325502
$274$	−7.63943	−0.461515
$275$	3.66496	0.221006
$276$	4.59396	0.276524
$277$	−10.6147	−0.637773	−0.318886	−	0.947793i	$-0.603309\pi$
$277$	−10.6147	−0.637773	−0.318886	+	0.947793i	$0.603309\pi$
$278$	13.3906	0.803117
$279$	−3.97506	−0.237981
$280$	0.676454	0.0404259
$281$	−21.3410	−1.27310	−0.636550	−	0.771235i	$-0.719639\pi$
$281$	−21.3410	−1.27310	−0.636550	+	0.771235i	$0.719639\pi$
$282$	10.8307	0.644958
$283$	0.954875	0.0567614	0.0283807	−	0.999597i	$-0.490965\pi$
$283$	0.954875	0.0567614	0.0283807	+	0.999597i	$0.490965\pi$
$284$	−13.6665	−0.810955
$285$	−6.16570	−0.365224
$286$	−15.3250	−0.906189
$287$	−0.853868	−0.0504022
$288$	0.615178	0.0362497
$289$	−13.2624	−0.780144
$290$	−0.713816	−0.0419167
$291$	0.428765	0.0251347
$292$	2.40210	0.140572
$293$	−0.503318	−0.0294042	−0.0147021	−	0.999892i	$-0.504680\pi$
$293$	−0.503318	−0.0294042	−0.0147021	+	0.999892i	$0.504680\pi$
$294$	−12.4395	−0.725486
$295$	12.3803	0.720808
$296$	11.1001	0.645182
$297$	−16.6184	−0.964300
$298$	−21.5526	−1.24851
$299$	−10.1031	−0.584277
$300$	1.90136	0.109775
$301$	−7.81710	−0.450570
$302$	18.2521	1.05029
$303$	3.79944	0.218272
$304$	−3.24278	−0.185986
$305$	10.8459	0.621033
$306$	1.18931	0.0679883
$307$	24.8490	1.41821	0.709103	−	0.705105i	$-0.249100\pi$
$307$	24.8490	1.41821	0.709103	+	0.705105i	$0.249100\pi$
$308$	2.47918	0.141264
$309$	15.2115	0.865354
$310$	−6.46164	−0.366997
$311$	−8.40037	−0.476341	−0.238171	−	0.971223i	$-0.576548\pi$
$311$	−8.40037	−0.476341	−0.238171	+	0.971223i	$0.576548\pi$
$312$	−7.95055	−0.450111
$313$	−9.18012	−0.518891	−0.259445	−	0.965758i	$-0.583540\pi$
$313$	−9.18012	−0.518891	−0.259445	+	0.965758i	$0.583540\pi$
$314$	7.61634	0.429815
$315$	0.416140	0.0234468
$316$	4.25254	0.239224
$317$	13.7169	0.770417	0.385209	−	0.922830i	$-0.374130\pi$
$317$	13.7169	0.770417	0.385209	+	0.922830i	$0.374130\pi$
$318$	−12.8623	−0.721280
$319$	−2.61611	−0.146474
$320$	1.00000	0.0559017
$321$	18.4024	1.02712
$322$	1.63441	0.0910820
$323$	−6.26919	−0.348827
$324$	−10.4671	−0.581505
$325$	−4.18150	−0.231948
$326$	−19.1298	−1.05950
$327$	−14.5028	−0.802008
$328$	−1.26227	−0.0696972
$329$	3.85327	0.212438
$330$	6.96842	0.383599
$331$	19.0525	1.04722	0.523609	−	0.851958i	$-0.324585\pi$
$331$	19.0525	1.04722	0.523609	+	0.851958i	$0.324585\pi$
$332$	1.00000	0.0548821
$333$	6.82856	0.374203
$334$	−1.28131	−0.0701100
$335$	−13.1206	−0.716853
$336$	1.28618	0.0701671
$337$	−0.933610	−0.0508570	−0.0254285	−	0.999677i	$-0.508095\pi$
$337$	−0.933610	−0.0508570	−0.0254285	+	0.999677i	$0.508095\pi$
$338$	4.48496	0.243950
$339$	−24.8431	−1.34929
$340$	1.93328	0.104847
$341$	−23.6817	−1.28243
$342$	−1.99489	−0.107871
$343$	−9.16082	−0.494638
$344$	−11.5560	−0.623058
$345$	4.59396	0.247330
$346$	1.64571	0.0884737
$347$	8.09029	0.434310	0.217155	−	0.976137i	$-0.430322\pi$
$347$	8.09029	0.434310	0.217155	+	0.976137i	$0.430322\pi$
$348$	−1.35722	−0.0727548
$349$	21.1017	1.12955	0.564773	−	0.825246i	$-0.308964\pi$
$349$	21.1017	1.12955	0.564773	+	0.825246i	$0.308964\pi$
$350$	0.676454	0.0361580
$351$	18.9606	1.01204
$352$	3.66496	0.195343
$353$	17.0214	0.905955	0.452978	−	0.891522i	$-0.350362\pi$
$353$	17.0214	0.905955	0.452978	+	0.891522i	$0.350362\pi$
$354$	23.5394	1.25110
$355$	−13.6665	−0.725341
$356$	−6.64709	−0.352295
$357$	2.48655	0.131602
$358$	−4.69850	−0.248323
$359$	−10.4739	−0.552793	−0.276396	−	0.961044i	$-0.589140\pi$
$359$	−10.4739	−0.552793	−0.276396	+	0.961044i	$0.589140\pi$
$360$	0.615178	0.0324227
$361$	−8.48439	−0.446547
$362$	8.38260	0.440580
$363$	4.62401	0.242698
$364$	−2.82859	−0.148259
$365$	2.40210	0.125731
$366$	20.6219	1.07793
$367$	35.6683	1.86187	0.930934	−	0.365188i	$-0.118995\pi$
$367$	35.6683	1.86187	0.930934	+	0.365188i	$0.118995\pi$
$368$	2.41614	0.125950
$369$	−0.776521	−0.0404241
$370$	11.1001	0.577069
$371$	−4.57605	−0.237577
$372$	−12.2859	−0.636995
$373$	15.3023	0.792324	0.396162	−	0.918181i	$-0.370342\pi$
$373$	15.3023	0.792324	0.396162	+	0.918181i	$0.370342\pi$
$374$	7.08538	0.366376
$375$	1.90136	0.0981859
$376$	5.69628	0.293763
$377$	2.98482	0.153726
$378$	−3.06732	−0.157766
$379$	9.90264	0.508664	0.254332	−	0.967117i	$-0.418144\pi$
$379$	9.90264	0.508664	0.254332	+	0.967117i	$0.418144\pi$
$380$	−3.24278	−0.166351
$381$	25.8810	1.32592
$382$	−1.46961	−0.0751917
$383$	10.1907	0.520720	0.260360	−	0.965512i	$-0.416159\pi$
$383$	10.1907	0.520720	0.260360	+	0.965512i	$0.416159\pi$
$384$	1.90136	0.0970285
$385$	2.47918	0.126351
$386$	−3.04517	−0.154995
$387$	−7.10900	−0.361371
$388$	0.225504	0.0114482
$389$	20.8935	1.05934	0.529670	−	0.848204i	$-0.322316\pi$
$389$	20.8935	1.05934	0.529670	+	0.848204i	$0.322316\pi$
$390$	−7.95055	−0.402592
$391$	4.67106	0.236226
$392$	−6.54241	−0.330442
$393$	6.93331	0.349739
$394$	26.7931	1.34982
$395$	4.25254	0.213969
$396$	2.25460	0.113298
$397$	19.7012	0.988774	0.494387	−	0.869242i	$-0.335393\pi$
$397$	19.7012	0.988774	0.494387	+	0.869242i	$0.335393\pi$
$398$	−16.1059	−0.807317
$399$	−4.17081	−0.208802
$400$	1.00000	0.0500000
$401$	−8.55599	−0.427266	−0.213633	−	0.976914i	$-0.568530\pi$
$401$	−8.55599	−0.427266	−0.213633	+	0.976914i	$0.568530\pi$
$402$	−24.9469	−1.24424
$403$	27.0194	1.34593
$404$	1.99827	0.0994177
$405$	−10.4671	−0.520114
$406$	−0.482864	−0.0239641
$407$	40.6816	2.01651
$408$	3.67586	0.181982
$409$	19.7809	0.978103	0.489051	−	0.872255i	$-0.337343\pi$
$409$	19.7809	0.978103	0.489051	+	0.872255i	$0.337343\pi$
$410$	−1.26227	−0.0623391
$411$	−14.5253	−0.716481
$412$	8.00033	0.394148
$413$	8.37469	0.412092
$414$	1.48636	0.0730504
$415$	1.00000	0.0490881
$416$	−4.18150	−0.205015
$417$	25.4604	1.24680
$418$	−11.8847	−0.581298
$419$	−6.17741	−0.301786	−0.150893	−	0.988550i	$-0.548215\pi$
$419$	−6.17741	−0.301786	−0.150893	+	0.988550i	$0.548215\pi$
$420$	1.28618	0.0627594
$421$	−20.8153	−1.01447	−0.507237	−	0.861807i	$-0.669333\pi$
$421$	−20.8153	−1.01447	−0.507237	+	0.861807i	$0.669333\pi$
$422$	−12.4698	−0.607020
$423$	3.50423	0.170381
$424$	−6.76477	−0.328526
$425$	1.93328	0.0937777
$426$	−25.9849	−1.25897
$427$	7.33673	0.355049
$428$	9.67855	0.467830
$429$	−29.1385	−1.40682
$430$	−11.5560	−0.557280
$431$	26.8450	1.29308	0.646540	−	0.762880i	$-0.276215\pi$
$431$	26.8450	1.29308	0.646540	+	0.762880i	$0.276215\pi$
$432$	−4.53441	−0.218162
$433$	14.7687	0.709740	0.354870	−	0.934916i	$-0.384525\pi$
$433$	14.7687	0.709740	0.354870	+	0.934916i	$0.384525\pi$
$434$	−4.37100	−0.209815
$435$	−1.35722	−0.0650738
$436$	−7.62760	−0.365296
$437$	−7.83500	−0.374799
$438$	4.56725	0.218232
$439$	7.60197	0.362822	0.181411	−	0.983407i	$-0.441934\pi$
$439$	7.60197	0.362822	0.181411	+	0.983407i	$0.441934\pi$
$440$	3.66496	0.174720
$441$	−4.02475	−0.191655
$442$	−8.08400	−0.384517
$443$	27.9734	1.32906	0.664528	−	0.747263i	$-0.268632\pi$
$443$	27.9734	1.32906	0.664528	+	0.747263i	$0.268632\pi$
$444$	21.1054	1.00162
$445$	−6.64709	−0.315102
$446$	11.8562	0.561409
$447$	−40.9793	−1.93826
$448$	0.676454	0.0319594
$449$	−20.2209	−0.954285	−0.477142	−	0.878826i	$-0.658327\pi$
$449$	−20.2209	−0.954285	−0.477142	+	0.878826i	$0.658327\pi$
$450$	0.615178	0.0289998
$451$	−4.62617	−0.217838
$452$	−13.0659	−0.614569
$453$	34.7038	1.63053
$454$	−19.1281	−0.897726
$455$	−2.82859	−0.132607
$456$	−6.16570	−0.288735
$457$	−3.40867	−0.159451	−0.0797254	−	0.996817i	$-0.525404\pi$
$457$	−3.40867	−0.159451	−0.0797254	+	0.996817i	$0.525404\pi$
$458$	−21.0266	−0.982508
$459$	−8.76627	−0.409174
$460$	2.41614	0.112653
$461$	−18.4764	−0.860533	−0.430266	−	0.902702i	$-0.641580\pi$
$461$	−18.4764	−0.860533	−0.430266	+	0.902702i	$0.641580\pi$
$462$	4.71382	0.219307
$463$	13.7825	0.640526	0.320263	−	0.947329i	$-0.396229\pi$
$463$	13.7825	0.640526	0.320263	+	0.947329i	$0.396229\pi$
$464$	−0.713816	−0.0331381
$465$	−12.2859	−0.569746
$466$	26.9296	1.24749
$467$	32.6364	1.51023	0.755116	−	0.655591i	$-0.227581\pi$
$467$	32.6364	1.51023	0.755116	+	0.655591i	$0.227581\pi$
$468$	−2.57237	−0.118908
$469$	−8.87546	−0.409830
$470$	5.69628	0.262750
$471$	14.4814	0.667269
$472$	12.3803	0.569848
$473$	−42.3523	−1.94736
$474$	8.08562	0.371385
$475$	−3.24278	−0.148789
$476$	1.30777	0.0599416
$477$	−4.16154	−0.190544
$478$	−2.85483	−0.130577
$479$	27.4332	1.25346	0.626728	−	0.779238i	$-0.284394\pi$
$479$	27.4332	1.25346	0.626728	+	0.779238i	$0.284394\pi$
$480$	1.90136	0.0867849
$481$	−46.4153	−2.11635
$482$	14.5844	0.664302
$483$	3.10760	0.141401
$484$	2.43195	0.110543
$485$	0.225504	0.0102396
$486$	−6.29850	−0.285706
$487$	14.2221	0.644466	0.322233	−	0.946660i	$-0.395567\pi$
$487$	14.2221	0.644466	0.322233	+	0.946660i	$0.395567\pi$
$488$	10.8459	0.490969
$489$	−36.3727	−1.64483
$490$	−6.54241	−0.295556
$491$	−5.55428	−0.250661	−0.125331	−	0.992115i	$-0.539999\pi$
$491$	−5.55428	−0.250661	−0.125331	+	0.992115i	$0.539999\pi$
$492$	−2.40003	−0.108202
$493$	−1.38000	−0.0621522
$494$	13.5597	0.610079
$495$	2.25460	0.101337
$496$	−6.46164	−0.290136
$497$	−9.24473	−0.414683
$498$	1.90136	0.0852021
$499$	28.5067	1.27614	0.638069	−	0.769980i	$-0.279734\pi$
$499$	28.5067	1.27614	0.638069	+	0.769980i	$0.279734\pi$
$500$	1.00000	0.0447214
$501$	−2.43623	−0.108843
$502$	10.6811	0.476719
$503$	1.72926	0.0771037	0.0385518	−	0.999257i	$-0.487726\pi$
$503$	1.72926	0.0771037	0.0385518	+	0.999257i	$0.487726\pi$
$504$	0.416140	0.0185363
$505$	1.99827	0.0889219
$506$	8.85506	0.393655
$507$	8.52753	0.378721
$508$	13.6118	0.603927
$509$	−19.4684	−0.862922	−0.431461	−	0.902132i	$-0.642002\pi$
$509$	−19.4684	−0.862922	−0.431461	+	0.902132i	$0.642002\pi$
$510$	3.67586	0.162770
$511$	1.62491	0.0718817
$512$	1.00000	0.0441942
$513$	14.7041	0.649201
$514$	6.67532	0.294436
$515$	8.00033	0.352537
$516$	−21.9721	−0.967269
$517$	20.8766	0.918154
$518$	7.50873	0.329915
$519$	3.12908	0.137352
$520$	−4.18150	−0.183371
$521$	17.1975	0.753437	0.376719	−	0.926328i	$-0.377052\pi$
$521$	17.1975	0.753437	0.376719	+	0.926328i	$0.377052\pi$
$522$	−0.439124	−0.0192199
$523$	40.3732	1.76540	0.882699	−	0.469938i	$-0.155724\pi$
$523$	40.3732	1.76540	0.882699	+	0.469938i	$0.155724\pi$
$524$	3.64650	0.159298
$525$	1.28618	0.0561337
$526$	22.1289	0.964866
$527$	−12.4921	−0.544166
$528$	6.96842	0.303262
$529$	−17.1623	−0.746186
$530$	−6.76477	−0.293843
$531$	7.61608	0.330510
$532$	−2.19359	−0.0951042
$533$	5.27818	0.228624
$534$	−12.6385	−0.546923
$535$	9.67855	0.418440
$536$	−13.1206	−0.566722
$537$	−8.93355	−0.385511
$538$	−25.9955	−1.12075
$539$	−23.9777	−1.03279
$540$	−4.53441	−0.195130
$541$	−5.70138	−0.245122	−0.122561	−	0.992461i	$-0.539111\pi$
$541$	−5.70138	−0.245122	−0.122561	+	0.992461i	$0.539111\pi$
$542$	18.8894	0.811368
$543$	15.9384	0.683981
$544$	1.93328	0.0828885
$545$	−7.62760	−0.326730
$546$	−5.37818	−0.230165
$547$	−15.6918	−0.670933	−0.335467	−	0.942052i	$-0.608894\pi$
$547$	−15.6918	−0.670933	−0.335467	+	0.942052i	$0.608894\pi$
$548$	−7.63943	−0.326340
$549$	6.67214	0.284760
$550$	3.66496	0.156275
$551$	2.31475	0.0986115
$552$	4.59396	0.195532
$553$	2.87665	0.122328
$554$	−10.6147	−0.450973
$555$	21.1054	0.895874
$556$	13.3906	0.567889
$557$	−17.3131	−0.733580	−0.366790	−	0.930304i	$-0.619543\pi$
$557$	−17.3131	−0.733580	−0.366790	+	0.930304i	$0.619543\pi$
$558$	−3.97506	−0.168278
$559$	48.3214	2.04378
$560$	0.676454	0.0285854
$561$	13.4719	0.568783
$562$	−21.3410	−0.900218
$563$	20.2198	0.852163	0.426082	−	0.904685i	$-0.359894\pi$
$563$	20.2198	0.852163	0.426082	+	0.904685i	$0.359894\pi$
$564$	10.8307	0.456054
$565$	−13.0659	−0.549688
$566$	0.954875	0.0401364
$567$	−7.08051	−0.297353
$568$	−13.6665	−0.573432
$569$	24.1625	1.01294	0.506472	−	0.862256i	$-0.330949\pi$
$569$	24.1625	1.01294	0.506472	+	0.862256i	$0.330949\pi$
$570$	−6.16570	−0.258253
$571$	−5.04750	−0.211231	−0.105616	−	0.994407i	$-0.533681\pi$
$571$	−5.04750	−0.211231	−0.105616	+	0.994407i	$0.533681\pi$
$572$	−15.3250	−0.640772
$573$	−2.79426	−0.116732
$574$	−0.853868	−0.0356397
$575$	2.41614	0.100760
$576$	0.615178	0.0256324
$577$	29.1851	1.21499	0.607495	−	0.794324i	$-0.292175\pi$
$577$	29.1851	1.21499	0.607495	+	0.794324i	$0.292175\pi$
$578$	−13.2624	−0.551645
$579$	−5.78997	−0.240623
$580$	−0.713816	−0.0296396
$581$	0.676454	0.0280640
$582$	0.428765	0.0177729
$583$	−24.7926	−1.02681
$584$	2.40210	0.0993994
$585$	−2.57237	−0.106354
$586$	−0.503318	−0.0207919
$587$	−32.3034	−1.33330	−0.666651	−	0.745370i	$-0.732273\pi$
$587$	−32.3034	−1.33330	−0.666651	+	0.745370i	$0.732273\pi$
$588$	−12.4395	−0.512996
$589$	20.9537	0.863381
$590$	12.3803	0.509688
$591$	50.9433	2.09553
$592$	11.1001	0.456213
$593$	−40.4996	−1.66312	−0.831560	−	0.555436i	$-0.812552\pi$
$593$	−40.4996	−1.66312	−0.831560	+	0.555436i	$0.812552\pi$
$594$	−16.6184	−0.681863
$595$	1.30777	0.0536134
$596$	−21.5526	−0.882829
$597$	−30.6232	−1.25332
$598$	−10.1031	−0.413146
$599$	−10.3844	−0.424294	−0.212147	−	0.977238i	$-0.568046\pi$
$599$	−10.3844	−0.424294	−0.212147	+	0.977238i	$0.568046\pi$
$600$	1.90136	0.0776228
$601$	12.1056	0.493797	0.246899	−	0.969041i	$-0.420589\pi$
$601$	12.1056	0.493797	0.246899	+	0.969041i	$0.420589\pi$
$602$	−7.81710	−0.318601
$603$	−8.07148	−0.328696
$604$	18.2521	0.742667
$605$	2.43195	0.0988727
$606$	3.79944	0.154342
$607$	−35.1071	−1.42495	−0.712476	−	0.701696i	$-0.752426\pi$
$607$	−35.1071	−1.42495	−0.712476	+	0.701696i	$0.752426\pi$
$608$	−3.24278	−0.131512
$609$	−0.918099	−0.0372032
$610$	10.8459	0.439136
$611$	−23.8190	−0.963614
$612$	1.18931	0.0480750
$613$	16.5252	0.667447	0.333723	−	0.942671i	$-0.391695\pi$
$613$	16.5252	0.667447	0.333723	+	0.942671i	$0.391695\pi$
$614$	24.8490	1.00282
$615$	−2.40003	−0.0967786
$616$	2.47918	0.0998889
$617$	15.7815	0.635340	0.317670	−	0.948201i	$-0.397100\pi$
$617$	15.7815	0.635340	0.317670	+	0.948201i	$0.397100\pi$
$618$	15.2115	0.611898
$619$	29.1384	1.17117	0.585585	−	0.810611i	$-0.300865\pi$
$619$	29.1384	1.17117	0.585585	+	0.810611i	$0.300865\pi$
$620$	−6.46164	−0.259506
$621$	−10.9558	−0.439640
$622$	−8.40037	−0.336824
$623$	−4.49645	−0.180147
$624$	−7.95055	−0.318277
$625$	1.00000	0.0400000
$626$	−9.18012	−0.366911
$627$	−22.5970	−0.902439
$628$	7.61634	0.303925
$629$	21.4596	0.855652
$630$	0.416140	0.0165794
$631$	−29.0781	−1.15758	−0.578791	−	0.815476i	$-0.696475\pi$
$631$	−29.0781	−1.15758	−0.578791	+	0.815476i	$0.696475\pi$
$632$	4.25254	0.169157
$633$	−23.7096	−0.942371
$634$	13.7169	0.544767
$635$	13.6118	0.540169
$636$	−12.8623	−0.510022
$637$	27.3571	1.08393
$638$	−2.61611	−0.103573
$639$	−8.40731	−0.332588
$640$	1.00000	0.0395285
$641$	−46.4146	−1.83327	−0.916633	−	0.399730i	$-0.869104\pi$
$641$	−46.4146	−1.83327	−0.916633	+	0.399730i	$0.869104\pi$
$642$	18.4024	0.726286
$643$	−3.86264	−0.152328	−0.0761638	−	0.997095i	$-0.524267\pi$
$643$	−3.86264	−0.152328	−0.0761638	+	0.997095i	$0.524267\pi$
$644$	1.63441	0.0644047
$645$	−21.9721	−0.865152
$646$	−6.26919	−0.246658
$647$	13.1160	0.515644	0.257822	−	0.966192i	$-0.416995\pi$
$647$	13.1160	0.515644	0.257822	+	0.966192i	$0.416995\pi$
$648$	−10.4671	−0.411186
$649$	45.3732	1.78106
$650$	−4.18150	−0.164012
$651$	−8.31086	−0.325728
$652$	−19.1298	−0.749182
$653$	5.17260	0.202419	0.101210	−	0.994865i	$-0.467729\pi$
$653$	5.17260	0.202419	0.101210	+	0.994865i	$0.467729\pi$
$654$	−14.5028	−0.567106
$655$	3.64650	0.142480
$656$	−1.26227	−0.0492834
$657$	1.47772	0.0576512
$658$	3.85327	0.150216
$659$	−27.1920	−1.05925	−0.529626	−	0.848232i	$-0.677668\pi$
$659$	−27.1920	−1.05925	−0.529626	+	0.848232i	$0.677668\pi$
$660$	6.96842	0.271245
$661$	16.2686	0.632777	0.316388	−	0.948630i	$-0.397530\pi$
$661$	16.2686	0.632777	0.316388	+	0.948630i	$0.397530\pi$
$662$	19.0525	0.740496
$663$	−15.3706	−0.596945
$664$	1.00000	0.0388075
$665$	−2.19359	−0.0850638
$666$	6.82856	0.264601
$667$	−1.72468	−0.0667798
$668$	−1.28131	−0.0495752
$669$	22.5430	0.871562
$670$	−13.1206	−0.506891
$671$	39.7497	1.53452
$672$	1.28618	0.0496156
$673$	−7.76224	−0.299212	−0.149606	−	0.988746i	$-0.547801\pi$
$673$	−7.76224	−0.299212	−0.149606	+	0.988746i	$0.547801\pi$
$674$	−0.933610	−0.0359613
$675$	−4.53441	−0.174530
$676$	4.48496	0.172498
$677$	−22.2329	−0.854478	−0.427239	−	0.904139i	$-0.640514\pi$
$677$	−22.2329	−0.854478	−0.427239	+	0.904139i	$0.640514\pi$
$678$	−24.8431	−0.954092
$679$	0.152543	0.00585407
$680$	1.93328	0.0741378
$681$	−36.3695	−1.39368
$682$	−23.6817	−0.906818
$683$	12.6116	0.482571	0.241285	−	0.970454i	$-0.422431\pi$
$683$	12.6116	0.482571	0.241285	+	0.970454i	$0.422431\pi$
$684$	−1.99489	−0.0762764
$685$	−7.63943	−0.291887
$686$	−9.16082	−0.349762
$687$	−39.9791	−1.52530
$688$	−11.5560	−0.440568
$689$	28.2869	1.07764
$690$	4.59396	0.174889
$691$	−4.93392	−0.187695	−0.0938475	−	0.995587i	$-0.529917\pi$
$691$	−4.93392	−0.187695	−0.0938475	+	0.995587i	$0.529917\pi$
$692$	1.64571	0.0625604
$693$	1.52514	0.0579351
$694$	8.09029	0.307103
$695$	13.3906	0.507936
$696$	−1.35722	−0.0514454
$697$	−2.44032	−0.0924336
$698$	21.1017	0.798710
$699$	51.2030	1.93667
$700$	0.676454	0.0255676
$701$	−41.1971	−1.55599	−0.777997	−	0.628268i	$-0.783764\pi$
$701$	−41.1971	−1.55599	−0.777997	+	0.628268i	$0.783764\pi$
$702$	18.9606	0.715623
$703$	−35.9953	−1.35759
$704$	3.66496	0.138128
$705$	10.8307	0.407907
$706$	17.0214	0.640607
$707$	1.35174	0.0508373
$708$	23.5394	0.884665
$709$	4.73433	0.177802	0.0889008	−	0.996040i	$-0.471665\pi$
$709$	4.73433	0.177802	0.0889008	+	0.996040i	$0.471665\pi$
$710$	−13.6665	−0.512893
$711$	2.61607	0.0981103
$712$	−6.64709	−0.249110
$713$	−15.6122	−0.584683
$714$	2.48655	0.0930568
$715$	−15.3250	−0.573124
$716$	−4.69850	−0.175591
$717$	−5.42807	−0.202715
$718$	−10.4739	−0.390883
$719$	−41.1298	−1.53388	−0.766941	−	0.641717i	$-0.778222\pi$
$719$	−41.1298	−1.53388	−0.766941	+	0.641717i	$0.778222\pi$
$720$	0.615178	0.0229263
$721$	5.41186	0.201548
$722$	−8.48439	−0.315756
$723$	27.7303	1.03130
$724$	8.38260	0.311537
$725$	−0.713816	−0.0265105
$726$	4.62401	0.171613
$727$	−38.8338	−1.44027	−0.720133	−	0.693836i	$-0.755919\pi$
$727$	−38.8338	−1.44027	−0.720133	+	0.693836i	$0.755919\pi$
$728$	−2.82859	−0.104835
$729$	19.4255	0.719465
$730$	2.40210	0.0889056
$731$	−22.3409	−0.826309
$732$	20.6219	0.762208
$733$	−11.4181	−0.421737	−0.210868	−	0.977514i	$-0.567629\pi$
$733$	−11.4181	−0.421737	−0.210868	+	0.977514i	$0.567629\pi$
$734$	35.6683	1.31654
$735$	−12.4395	−0.458838
$736$	2.41614	0.0890601
$737$	−48.0864	−1.77128
$738$	−0.776521	−0.0285841
$739$	−0.0168706	−0.000620594 0	−0.000310297	−	1.00000i	$-0.500099\pi$
$739$	−0.0168706	−0.000620594 0	−0.000310297		1.00000i	$0.500099\pi$
$740$	11.1001	0.408049
$741$	25.7819	0.947121
$742$	−4.57605	−0.167992
$743$	22.2784	0.817316	0.408658	−	0.912688i	$-0.365997\pi$
$743$	22.2784	0.817316	0.408658	+	0.912688i	$0.365997\pi$
$744$	−12.2859	−0.450424
$745$	−21.5526	−0.789627
$746$	15.3023	0.560258
$747$	0.615178	0.0225082
$748$	7.08538	0.259067
$749$	6.54709	0.239226
$750$	1.90136	0.0694279
$751$	25.8159	0.942034	0.471017	−	0.882124i	$-0.343887\pi$
$751$	25.8159	0.942034	0.471017	+	0.882124i	$0.343887\pi$
$752$	5.69628	0.207722
$753$	20.3086	0.740086
$754$	2.98482	0.108701
$755$	18.2521	0.664261
$756$	−3.06732	−0.111557
$757$	−13.4878	−0.490223	−0.245111	−	0.969495i	$-0.578825\pi$
$757$	−13.4878	−0.490223	−0.245111	+	0.969495i	$0.578825\pi$
$758$	9.90264	0.359680
$759$	16.8367	0.611133
$760$	−3.24278	−0.117628
$761$	−39.8508	−1.44459	−0.722295	−	0.691585i	$-0.756913\pi$
$761$	−39.8508	−1.44459	−0.722295	+	0.691585i	$0.756913\pi$
$762$	25.8810	0.937570
$763$	−5.15972	−0.186794
$764$	−1.46961	−0.0531686
$765$	1.18931	0.0429996
$766$	10.1907	0.368205
$767$	−51.7682	−1.86924
$768$	1.90136	0.0686095
$769$	−17.8357	−0.643171	−0.321585	−	0.946881i	$-0.604216\pi$
$769$	−17.8357	−0.643171	−0.321585	+	0.946881i	$0.604216\pi$
$770$	2.47918	0.0893434
$771$	12.6922	0.457098
$772$	−3.04517	−0.109598
$773$	−4.63147	−0.166582	−0.0832912	−	0.996525i	$-0.526543\pi$
$773$	−4.63147	−0.166582	−0.0832912	+	0.996525i	$0.526543\pi$
$774$	−7.10900	−0.255528
$775$	−6.46164	−0.232109
$776$	0.225504	0.00809513
$777$	14.2768	0.512178
$778$	20.8935	0.749067
$779$	4.09326	0.146656
$780$	−7.95055	−0.284675
$781$	−50.0871	−1.79226
$782$	4.67106	0.167037
$783$	3.23673	0.115671
$784$	−6.54241	−0.233657
$785$	7.61634	0.271839
$786$	6.93331	0.247303
$787$	−22.1862	−0.790852	−0.395426	−	0.918498i	$-0.629403\pi$
$787$	−22.1862	−0.790852	−0.395426	+	0.918498i	$0.629403\pi$
$788$	26.7931	0.954463
$789$	42.0750	1.49791
$790$	4.25254	0.151299
$791$	−8.83850	−0.314261
$792$	2.25460	0.0801139
$793$	−45.3520	−1.61050
$794$	19.7012	0.699169
$795$	−12.8623	−0.456178
$796$	−16.1059	−0.570859
$797$	44.0369	1.55987	0.779934	−	0.625862i	$-0.215253\pi$
$797$	44.0369	1.55987	0.779934	+	0.625862i	$0.215253\pi$
$798$	−4.17081	−0.147645
$799$	11.0125	0.389594
$800$	1.00000	0.0353553
$801$	−4.08914	−0.144483
$802$	−8.55599	−0.302123
$803$	8.80359	0.310672
$804$	−24.9469	−0.879811
$805$	1.63441	0.0576053
$806$	27.0194	0.951717
$807$	−49.4268	−1.73991
$808$	1.99827	0.0702989
$809$	−36.9398	−1.29873	−0.649367	−	0.760475i	$-0.724966\pi$
$809$	−36.9398	−1.29873	−0.649367	+	0.760475i	$0.724966\pi$
$810$	−10.4671	−0.367776
$811$	−3.99794	−0.140387	−0.0701933	−	0.997533i	$-0.522362\pi$
$811$	−3.99794	−0.140387	−0.0701933	+	0.997533i	$0.522362\pi$
$812$	−0.482864	−0.0169452
$813$	35.9156	1.25961
$814$	40.6816	1.42589
$815$	−19.1298	−0.670089
$816$	3.67586	0.128681
$817$	37.4735	1.31103
$818$	19.7809	0.691623
$819$	−1.74009	−0.0608036
$820$	−1.26227	−0.0440804
$821$	56.5450	1.97343	0.986717	−	0.162447i	$-0.0519385\pi$
$821$	56.5450	1.97343	0.986717	+	0.162447i	$0.0519385\pi$
$822$	−14.5253	−0.506629
$823$	−45.4241	−1.58338	−0.791692	−	0.610921i	$-0.790799\pi$
$823$	−45.4241	−1.58338	−0.791692	+	0.610921i	$0.790799\pi$
$824$	8.00033	0.278705
$825$	6.96842	0.242609
$826$	8.37469	0.291393
$827$	−49.9030	−1.73530	−0.867648	−	0.497179i	$-0.834369\pi$
$827$	−49.9030	−1.73530	−0.867648	+	0.497179i	$0.834369\pi$
$828$	1.48636	0.0516544
$829$	−0.655282	−0.0227589	−0.0113794	−	0.999935i	$-0.503622\pi$
$829$	−0.655282	−0.0227589	−0.0113794	+	0.999935i	$0.503622\pi$
$830$	1.00000	0.0347105
$831$	−20.1823	−0.700116
$832$	−4.18150	−0.144968
$833$	−12.6483	−0.438237
$834$	25.4604	0.881623
$835$	−1.28131	−0.0443414
$836$	−11.8847	−0.411040
$837$	29.2997	1.01275
$838$	−6.17741	−0.213395
$839$	−1.17572	−0.0405904	−0.0202952	−	0.999794i	$-0.506461\pi$
$839$	−1.17572	−0.0405904	−0.0202952	+	0.999794i	$0.506461\pi$
$840$	1.28618	0.0443776
$841$	−28.4905	−0.982430
$842$	−20.8153	−0.717341
$843$	−40.5771	−1.39755
$844$	−12.4698	−0.429228
$845$	4.48496	0.154287
$846$	3.50423	0.120478
$847$	1.64510	0.0565263
$848$	−6.76477	−0.232303
$849$	1.81556	0.0623100
$850$	1.93328	0.0663108
$851$	26.8195	0.919360
$852$	−25.9849	−0.890228
$853$	8.01797	0.274530	0.137265	−	0.990534i	$-0.456169\pi$
$853$	8.01797	0.274530	0.137265	+	0.990534i	$0.456169\pi$
$854$	7.33673	0.251058
$855$	−1.99489	−0.0682237
$856$	9.67855	0.330806
$857$	−54.7273	−1.86945	−0.934725	−	0.355373i	$-0.884354\pi$
$857$	−54.7273	−1.86945	−0.934725	+	0.355373i	$0.884354\pi$
$858$	−29.1385	−0.994771
$859$	3.50130	0.119463	0.0597314	−	0.998214i	$-0.480976\pi$
$859$	3.50130	0.119463	0.0597314	+	0.998214i	$0.480976\pi$
$860$	−11.5560	−0.394056
$861$	−1.62351	−0.0553291
$862$	26.8450	0.914346
$863$	−10.0421	−0.341837	−0.170919	−	0.985285i	$-0.554674\pi$
$863$	−10.0421	−0.341837	−0.170919	+	0.985285i	$0.554674\pi$
$864$	−4.53441	−0.154264
$865$	1.64571	0.0559557
$866$	14.7687	0.501862
$867$	−25.2167	−0.856404
$868$	−4.37100	−0.148362
$869$	15.5854	0.528698
$870$	−1.35722	−0.0460142
$871$	54.8636	1.85898
$872$	−7.62760	−0.258303
$873$	0.138725	0.00469514
$874$	−7.83500	−0.265023
$875$	0.676454	0.0228683
$876$	4.56725	0.154313
$877$	0.842542	0.0284506	0.0142253	−	0.999899i	$-0.495472\pi$
$877$	0.842542	0.0284506	0.0142253	+	0.999899i	$0.495472\pi$
$878$	7.60197	0.256554
$879$	−0.956990	−0.0322785
$880$	3.66496	0.123546
$881$	−43.2206	−1.45614	−0.728069	−	0.685504i	$-0.759582\pi$
$881$	−43.2206	−1.45614	−0.728069	+	0.685504i	$0.759582\pi$
$882$	−4.02475	−0.135520
$883$	−53.3290	−1.79466	−0.897331	−	0.441357i	$-0.854497\pi$
$883$	−53.3290	−1.79466	−0.897331	+	0.441357i	$0.854497\pi$
$884$	−8.08400	−0.271894
$885$	23.5394	0.791268
$886$	27.9734	0.939785
$887$	−29.9794	−1.00661	−0.503306	−	0.864108i	$-0.667883\pi$
$887$	−29.9794	−1.00661	−0.503306	+	0.864108i	$0.667883\pi$
$888$	21.1054	0.708250
$889$	9.20778	0.308819
$890$	−6.64709	−0.222811
$891$	−38.3615	−1.28516
$892$	11.8562	0.396976
$893$	−18.4718	−0.618134
$894$	−40.9793	−1.37055
$895$	−4.69850	−0.157053
$896$	0.676454	0.0225987
$897$	−19.2096	−0.641391
$898$	−20.2209	−0.674781
$899$	4.61242	0.153833
$900$	0.615178	0.0205059
$901$	−13.0782	−0.435697
$902$	−4.62617	−0.154035
$903$	−14.8631	−0.494614
$904$	−13.0659	−0.434566
$905$	8.38260	0.278647
$906$	34.7038	1.15296
$907$	−29.3692	−0.975189	−0.487595	−	0.873070i	$-0.662126\pi$
$907$	−29.3692	−0.975189	−0.487595	+	0.873070i	$0.662126\pi$
$908$	−19.1281	−0.634788
$909$	1.22929	0.0407730
$910$	−2.82859	−0.0937670
$911$	−40.8914	−1.35479	−0.677397	−	0.735618i	$-0.736892\pi$
$911$	−40.8914	−1.35479	−0.677397	+	0.735618i	$0.736892\pi$
$912$	−6.16570	−0.204167
$913$	3.66496	0.121293
$914$	−3.40867	−0.112749
$915$	20.6219	0.681740
$916$	−21.0266	−0.694738
$917$	2.46669	0.0814572
$918$	−8.76627	−0.289330
$919$	24.1702	0.797303	0.398651	−	0.917103i	$-0.369478\pi$
$919$	24.1702	0.797303	0.398651	+	0.917103i	$0.369478\pi$
$920$	2.41614	0.0796578
$921$	47.2469	1.55684
$922$	−18.4764	−0.608489
$923$	57.1463	1.88099
$924$	4.71382	0.155073
$925$	11.1001	0.364970
$926$	13.7825	0.452920
$927$	4.92163	0.161648
$928$	−0.713816	−0.0234322
$929$	−49.7408	−1.63194	−0.815971	−	0.578092i	$-0.803797\pi$
$929$	−49.7408	−1.63194	−0.815971	+	0.578092i	$0.803797\pi$
$930$	−12.2859	−0.402871
$931$	21.2156	0.695313
$932$	26.9296	0.882110
$933$	−15.9721	−0.522904
$934$	32.6364	1.06790
$935$	7.08538	0.231717
$936$	−2.57237	−0.0840805
$937$	50.8620	1.66159	0.830794	−	0.556580i	$-0.187887\pi$
$937$	50.8620	1.66159	0.830794	+	0.556580i	$0.187887\pi$
$938$	−8.87546	−0.289794
$939$	−17.4547	−0.569613
$940$	5.69628	0.185792
$941$	−10.2878	−0.335374	−0.167687	−	0.985840i	$-0.553630\pi$
$941$	−10.2878	−0.335374	−0.167687	+	0.985840i	$0.553630\pi$
$942$	14.4814	0.471830
$943$	−3.04982	−0.0993158
$944$	12.3803	0.402944
$945$	−3.06732	−0.0997799
$946$	−42.3523	−1.37699
$947$	−39.6451	−1.28829	−0.644146	−	0.764902i	$-0.722787\pi$
$947$	−39.6451	−1.28829	−0.644146	+	0.764902i	$0.722787\pi$
$948$	8.08562	0.262609
$949$	−10.0444	−0.326054
$950$	−3.24278	−0.105210
$951$	26.0808	0.845727
$952$	1.30777	0.0423851
$953$	54.0991	1.75244	0.876222	−	0.481908i	$-0.160056\pi$
$953$	54.0991	1.75244	0.876222	+	0.481908i	$0.160056\pi$
$954$	−4.16154	−0.134735
$955$	−1.46961	−0.0475554
$956$	−2.85483	−0.0923319
$957$	−4.97417	−0.160792
$958$	27.4332	0.886327
$959$	−5.16772	−0.166874
$960$	1.90136	0.0613662
$961$	10.7528	0.346865
$962$	−46.4153	−1.49649
$963$	5.95403	0.191866
$964$	14.5844	0.469733
$965$	−3.04517	−0.0980274
$966$	3.10760	0.0999854
$967$	16.0995	0.517724	0.258862	−	0.965914i	$-0.416653\pi$
$967$	16.0995	0.517724	0.258862	+	0.965914i	$0.416653\pi$
$968$	2.43195	0.0781657
$969$	−11.9200	−0.382925
$970$	0.225504	0.00724051
$971$	−9.76754	−0.313455	−0.156728	−	0.987642i	$-0.550095\pi$
$971$	−9.76754	−0.313455	−0.156728	+	0.987642i	$0.550095\pi$
$972$	−6.29850	−0.202024
$973$	9.05815	0.290391
$974$	14.2221	0.455706
$975$	−7.95055	−0.254621
$976$	10.8459	0.347168
$977$	−15.5385	−0.497119	−0.248560	−	0.968617i	$-0.579957\pi$
$977$	−15.5385	−0.497119	−0.248560	+	0.968617i	$0.579957\pi$
$978$	−36.3727	−1.16307
$979$	−24.3613	−0.778592
$980$	−6.54241	−0.208990
$981$	−4.69233	−0.149815
$982$	−5.55428	−0.177244
$983$	55.0941	1.75723	0.878614	−	0.477533i	$-0.158469\pi$
$983$	55.0941	1.75723	0.878614	+	0.477533i	$0.158469\pi$
$984$	−2.40003	−0.0765102
$985$	26.7931	0.853698
$986$	−1.38000	−0.0439483
$987$	7.32646	0.233204
$988$	13.5597	0.431391
$989$	−27.9209	−0.887833
$990$	2.25460	0.0716560
$991$	−31.3337	−0.995347	−0.497673	−	0.867364i	$-0.665812\pi$
$991$	−31.3337	−0.995347	−0.497673	+	0.867364i	$0.665812\pi$
$992$	−6.46164	−0.205157
$993$	36.2257	1.14959
$994$	−9.24473	−0.293225
$995$	−16.1059	−0.510592
$996$	1.90136	0.0602470
$997$	−19.4580	−0.616241	−0.308120	−	0.951347i	$-0.599700\pi$
$997$	−19.4580	−0.616241	−0.308120	+	0.951347i	$0.599700\pi$
$998$	28.5067	0.902365
$999$	−50.3326	−1.59245

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	830.2.a.k.1.4	✓	5
3.2	odd	2		7470.2.a.bv.1.3		5
4.3	odd	2		6640.2.a.z.1.2		5
5.4	even	2		4150.2.a.bd.1.2		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
830.2.a.k.1.4	✓	5	1.1	even	1	trivial
4150.2.a.bd.1.2		5	5.4	even	2
6640.2.a.z.1.2		5	4.3	odd	2
7470.2.a.bv.1.3		5	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 830 = 2 \cdot 5 \cdot 83 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	830.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.90136 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.90136 q^{6} +0.676454 q^{7} +1.00000 q^{8} +0.615178 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.90136 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.90136 q^{6} +0.676454 q^{7} +1.00000 q^{8} +0.615178 q^{9} +1.00000 q^{10} +3.66496 q^{11} +1.90136 q^{12} -4.18150 q^{13} +0.676454 q^{14} +1.90136 q^{15} +1.00000 q^{16} +1.93328 q^{17} +0.615178 q^{18} -3.24278 q^{19} +1.00000 q^{20} +1.28618 q^{21} +3.66496 q^{22} +2.41614 q^{23} +1.90136 q^{24} +1.00000 q^{25} -4.18150 q^{26} -4.53441 q^{27} +0.676454 q^{28} -0.713816 q^{29} +1.90136 q^{30} -6.46164 q^{31} +1.00000 q^{32} +6.96842 q^{33} +1.93328 q^{34} +0.676454 q^{35} +0.615178 q^{36} +11.1001 q^{37} -3.24278 q^{38} -7.95055 q^{39} +1.00000 q^{40} -1.26227 q^{41} +1.28618 q^{42} -11.5560 q^{43} +3.66496 q^{44} +0.615178 q^{45} +2.41614 q^{46} +5.69628 q^{47} +1.90136 q^{48} -6.54241 q^{49} +1.00000 q^{50} +3.67586 q^{51} -4.18150 q^{52} -6.76477 q^{53} -4.53441 q^{54} +3.66496 q^{55} +0.676454 q^{56} -6.16570 q^{57} -0.713816 q^{58} +12.3803 q^{59} +1.90136 q^{60} +10.8459 q^{61} -6.46164 q^{62} +0.416140 q^{63} +1.00000 q^{64} -4.18150 q^{65} +6.96842 q^{66} -13.1206 q^{67} +1.93328 q^{68} +4.59396 q^{69} +0.676454 q^{70} -13.6665 q^{71} +0.615178 q^{72} +2.40210 q^{73} +11.1001 q^{74} +1.90136 q^{75} -3.24278 q^{76} +2.47918 q^{77} -7.95055 q^{78} +4.25254 q^{79} +1.00000 q^{80} -10.4671 q^{81} -1.26227 q^{82} +1.00000 q^{83} +1.28618 q^{84} +1.93328 q^{85} -11.5560 q^{86} -1.35722 q^{87} +3.66496 q^{88} -6.64709 q^{89} +0.615178 q^{90} -2.82859 q^{91} +2.41614 q^{92} -12.2859 q^{93} +5.69628 q^{94} -3.24278 q^{95} +1.90136 q^{96} +0.225504 q^{97} -6.54241 q^{98} +2.25460 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 5 q^{2} + 2 q^{3} + 5 q^{4} + 5 q^{5} + 2 q^{6} + 5 q^{7} + 5 q^{8} + 3 q^{9}+O(q^{10}) \) 5 * q + 5 * q^2 + 2 * q^3 + 5 * q^4 + 5 * q^5 + 2 * q^6 + 5 * q^7 + 5 * q^8 + 3 * q^9	\( 5 q + 5 q^{2} + 2 q^{3} + 5 q^{4} + 5 q^{5} + 2 q^{6} + 5 q^{7} + 5 q^{8} + 3 q^{9} + 5 q^{10} + q^{11} + 2 q^{12} + 4 q^{13} + 5 q^{14} + 2 q^{15} + 5 q^{16} - q^{17} + 3 q^{18} + 7 q^{19} + 5 q^{20} - q^{21} + q^{22} + 8 q^{23} + 2 q^{24} + 5 q^{25} + 4 q^{26} - q^{27} + 5 q^{28} - 11 q^{29} + 2 q^{30} + 10 q^{31} + 5 q^{32} - 5 q^{33} - q^{34} + 5 q^{35} + 3 q^{36} + 8 q^{37} + 7 q^{38} - 14 q^{39} + 5 q^{40} - 3 q^{41} - q^{42} - 2 q^{43} + q^{44} + 3 q^{45} + 8 q^{46} + 7 q^{47} + 2 q^{48} - 12 q^{49} + 5 q^{50} + 19 q^{51} + 4 q^{52} - 12 q^{53} - q^{54} + q^{55} + 5 q^{56} - 6 q^{57} - 11 q^{58} - 3 q^{59} + 2 q^{60} + 11 q^{61} + 10 q^{62} - 2 q^{63} + 5 q^{64} + 4 q^{65} - 5 q^{66} + 4 q^{67} - q^{68} - 26 q^{69} + 5 q^{70} + 4 q^{71} + 3 q^{72} - 3 q^{73} + 8 q^{74} + 2 q^{75} + 7 q^{76} - q^{77} - 14 q^{78} - 12 q^{79} + 5 q^{80} - 19 q^{81} - 3 q^{82} + 5 q^{83} - q^{84} - q^{85} - 2 q^{86} + 9 q^{87} + q^{88} - 30 q^{89} + 3 q^{90} + 14 q^{91} + 8 q^{92} - 10 q^{93} + 7 q^{94} + 7 q^{95} + 2 q^{96} - 7 q^{97} - 12 q^{98} - 36 q^{99}+O(q^{100}) \) 5 * q + 5 * q^2 + 2 * q^3 + 5 * q^4 + 5 * q^5 + 2 * q^6 + 5 * q^7 + 5 * q^8 + 3 * q^9 + 5 * q^10 + q^11 + 2 * q^12 + 4 * q^13 + 5 * q^14 + 2 * q^15 + 5 * q^16 - q^17 + 3 * q^18 + 7 * q^19 + 5 * q^20 - q^21 + q^22 + 8 * q^23 + 2 * q^24 + 5 * q^25 + 4 * q^26 - q^27 + 5 * q^28 - 11 * q^29 + 2 * q^30 + 10 * q^31 + 5 * q^32 - 5 * q^33 - q^34 + 5 * q^35 + 3 * q^36 + 8 * q^37 + 7 * q^38 - 14 * q^39 + 5 * q^40 - 3 * q^41 - q^42 - 2 * q^43 + q^44 + 3 * q^45 + 8 * q^46 + 7 * q^47 + 2 * q^48 - 12 * q^49 + 5 * q^50 + 19 * q^51 + 4 * q^52 - 12 * q^53 - q^54 + q^55 + 5 * q^56 - 6 * q^57 - 11 * q^58 - 3 * q^59 + 2 * q^60 + 11 * q^61 + 10 * q^62 - 2 * q^63 + 5 * q^64 + 4 * q^65 - 5 * q^66 + 4 * q^67 - q^68 - 26 * q^69 + 5 * q^70 + 4 * q^71 + 3 * q^72 - 3 * q^73 + 8 * q^74 + 2 * q^75 + 7 * q^76 - q^77 - 14 * q^78 - 12 * q^79 + 5 * q^80 - 19 * q^81 - 3 * q^82 + 5 * q^83 - q^84 - q^85 - 2 * q^86 + 9 * q^87 + q^88 - 30 * q^89 + 3 * q^90 + 14 * q^91 + 8 * q^92 - 10 * q^93 + 7 * q^94 + 7 * q^95 + 2 * q^96 - 7 * q^97 - 12 * q^98 - 36 * q^99

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