LMFDB - Embedded newform 799.2.a.g.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [799,2,Mod(1,799)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(799, 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("799.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 799 = 17 \cdot 47 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	799.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:	$6.38004712150$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 4 x^{19} - 24 x^{18} + 108 x^{17} + 221 x^{16} - 1200 x^{15} - 931 x^{14} + 7128 x^{13} + \cdots + 63 $ x^20 - 4x^19 - 24x^18 + 108x^17 + 221x^16 - 1200x^15 - 931x^14 + 7128x^13 + 1280x^12 - 24559x^11 + 3411x^10 + 49829x^9 - 15132x^8 - 58070x^7 + 20659x^6 + 36738x^5 - 11129x^4 - 11299x^3 + 1589x^2 + 1289*x + 63
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$-0.351266$ of defining polynomial
Character	$\chi$	$=$	799.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.351266 q^{2} -1.36638 q^{3} -1.87661 q^{4} -3.75140 q^{5} +0.479962 q^{6} -1.09877 q^{7} +1.36172 q^{8} -1.13301 q^{9} +O(q^{10})$	\(q-0.351266 q^{2} -1.36638 q^{3} -1.87661 q^{4} -3.75140 q^{5} +0.479962 q^{6} -1.09877 q^{7} +1.36172 q^{8} -1.13301 q^{9} +1.31774 q^{10} -4.08488 q^{11} +2.56416 q^{12} -6.95278 q^{13} +0.385959 q^{14} +5.12583 q^{15} +3.27490 q^{16} -1.00000 q^{17} +0.397989 q^{18} -2.29177 q^{19} +7.03993 q^{20} +1.50133 q^{21} +1.43488 q^{22} +1.76335 q^{23} -1.86063 q^{24} +9.07304 q^{25} +2.44228 q^{26} +5.64726 q^{27} +2.06196 q^{28} -5.76310 q^{29} -1.80053 q^{30} -7.13338 q^{31} -3.87381 q^{32} +5.58149 q^{33} +0.351266 q^{34} +4.12192 q^{35} +2.12623 q^{36} -7.65596 q^{37} +0.805023 q^{38} +9.50013 q^{39} -5.10837 q^{40} +9.69884 q^{41} -0.527366 q^{42} +5.40037 q^{43} +7.66574 q^{44} +4.25039 q^{45} -0.619404 q^{46} +1.00000 q^{47} -4.47474 q^{48} -5.79271 q^{49} -3.18705 q^{50} +1.36638 q^{51} +13.0477 q^{52} -5.62873 q^{53} -1.98369 q^{54} +15.3241 q^{55} -1.49621 q^{56} +3.13143 q^{57} +2.02438 q^{58} +7.29740 q^{59} -9.61920 q^{60} +6.52587 q^{61} +2.50572 q^{62} +1.24492 q^{63} -5.18906 q^{64} +26.0827 q^{65} -1.96059 q^{66} +0.285403 q^{67} +1.87661 q^{68} -2.40940 q^{69} -1.44789 q^{70} -10.6030 q^{71} -1.54285 q^{72} -12.5918 q^{73} +2.68928 q^{74} -12.3972 q^{75} +4.30077 q^{76} +4.48833 q^{77} -3.33707 q^{78} -14.6491 q^{79} -12.2855 q^{80} -4.31724 q^{81} -3.40687 q^{82} -5.61580 q^{83} -2.81741 q^{84} +3.75140 q^{85} -1.89697 q^{86} +7.87457 q^{87} -5.56248 q^{88} +10.7994 q^{89} -1.49302 q^{90} +7.63948 q^{91} -3.30912 q^{92} +9.74690 q^{93} -0.351266 q^{94} +8.59737 q^{95} +5.29308 q^{96} +6.96451 q^{97} +2.03478 q^{98} +4.62823 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 4 q^{2} + 3 q^{3} + 24 q^{4} + 13 q^{5} + 11 q^{6} - 3 q^{7} + 12 q^{8} + 37 q^{9}+O(q^{10}) $ 20 * q + 4 * q^2 + 3 * q^3 + 24 * q^4 + 13 * q^5 + 11 * q^6 - 3 * q^7 + 12 * q^8 + 37 * q^9	\( 20 q + 4 q^{2} + 3 q^{3} + 24 q^{4} + 13 q^{5} + 11 q^{6} - 3 q^{7} + 12 q^{8} + 37 q^{9} - 2 q^{10} + 10 q^{11} + 8 q^{12} + q^{13} + 13 q^{14} + q^{15} + 28 q^{16} - 20 q^{17} + 15 q^{18} + 5 q^{19} + 37 q^{20} + 6 q^{21} - 19 q^{22} + 4 q^{23} + 30 q^{24} + 41 q^{25} - 9 q^{26} + 6 q^{27} - 25 q^{28} + 26 q^{29} - 25 q^{30} + 6 q^{31} + 28 q^{32} + 29 q^{33} - 4 q^{34} + 21 q^{35} - 5 q^{36} - 8 q^{37} - 21 q^{38} - 19 q^{39} - 25 q^{40} + 69 q^{41} + 3 q^{42} - 7 q^{43} + 16 q^{44} + 39 q^{45} - 24 q^{46} + 20 q^{47} + 26 q^{48} + 53 q^{49} + 16 q^{50} - 3 q^{51} + 18 q^{52} + 29 q^{53} + 23 q^{54} + 5 q^{55} - 22 q^{56} - 36 q^{57} - q^{58} + 55 q^{59} - 103 q^{60} - 17 q^{61} - 7 q^{62} - 9 q^{63} + 58 q^{64} + 40 q^{65} + 50 q^{66} - 6 q^{67} - 24 q^{68} + 17 q^{69} - 15 q^{70} + 47 q^{71} + 7 q^{72} - 32 q^{73} - 67 q^{74} - 22 q^{75} - 5 q^{76} + 4 q^{77} - 60 q^{78} - 26 q^{79} + 108 q^{80} + 68 q^{81} + 25 q^{82} + 3 q^{83} + 24 q^{84} - 13 q^{85} + 8 q^{86} - 41 q^{87} - 47 q^{88} + 119 q^{89} - 54 q^{90} - 35 q^{91} - 15 q^{93} + 4 q^{94} - 48 q^{95} - 84 q^{96} - 13 q^{97} + q^{98} - 5 q^{99}+O(q^{100}) \) 20 * q + 4 * q^2 + 3 * q^3 + 24 * q^4 + 13 * q^5 + 11 * q^6 - 3 * q^7 + 12 * q^8 + 37 * q^9 - 2 * q^10 + 10 * q^11 + 8 * q^12 + q^13 + 13 * q^14 + q^15 + 28 * q^16 - 20 * q^17 + 15 * q^18 + 5 * q^19 + 37 * q^20 + 6 * q^21 - 19 * q^22 + 4 * q^23 + 30 * q^24 + 41 * q^25 - 9 * q^26 + 6 * q^27 - 25 * q^28 + 26 * q^29 - 25 * q^30 + 6 * q^31 + 28 * q^32 + 29 * q^33 - 4 * q^34 + 21 * q^35 - 5 * q^36 - 8 * q^37 - 21 * q^38 - 19 * q^39 - 25 * q^40 + 69 * q^41 + 3 * q^42 - 7 * q^43 + 16 * q^44 + 39 * q^45 - 24 * q^46 + 20 * q^47 + 26 * q^48 + 53 * q^49 + 16 * q^50 - 3 * q^51 + 18 * q^52 + 29 * q^53 + 23 * q^54 + 5 * q^55 - 22 * q^56 - 36 * q^57 - q^58 + 55 * q^59 - 103 * q^60 - 17 * q^61 - 7 * q^62 - 9 * q^63 + 58 * q^64 + 40 * q^65 + 50 * q^66 - 6 * q^67 - 24 * q^68 + 17 * q^69 - 15 * q^70 + 47 * q^71 + 7 * q^72 - 32 * q^73 - 67 * q^74 - 22 * q^75 - 5 * q^76 + 4 * q^77 - 60 * q^78 - 26 * q^79 + 108 * q^80 + 68 * q^81 + 25 * q^82 + 3 * q^83 + 24 * q^84 - 13 * q^85 + 8 * q^86 - 41 * q^87 - 47 * q^88 + 119 * q^89 - 54 * q^90 - 35 * q^91 - 15 * q^93 + 4 * q^94 - 48 * q^95 - 84 * q^96 - 13 * q^97 + q^98 - 5 * 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 $

$2$	−0.351266	−0.248383	−0.124191	−	0.992258i	$-0.539634\pi$
$2$	−0.351266	−0.248383	−0.124191	+	0.992258i	$0.539634\pi$
$3$	−1.36638	−0.788878	−0.394439	−	0.918922i	$-0.629061\pi$
$3$	−1.36638	−0.788878	−0.394439	+	0.918922i	$0.629061\pi$
$4$	−1.87661	−0.938306
$5$	−3.75140	−1.67768	−0.838840	−	0.544379i	$-0.816765\pi$
$5$	−3.75140	−1.67768	−0.838840	+	0.544379i	$0.816765\pi$
$6$	0.479962	0.195944
$7$	−1.09877	−0.415295	−0.207647	−	0.978204i	$-0.566581\pi$
$7$	−1.09877	−0.415295	−0.207647	+	0.978204i	$0.566581\pi$
$8$	1.36172	0.481442
$9$	−1.13301	−0.377671
$10$	1.31774	0.416707
$11$	−4.08488	−1.23164	−0.615819	−	0.787887i	$-0.711175\pi$
$11$	−4.08488	−1.23164	−0.615819	+	0.787887i	$0.711175\pi$
$12$	2.56416	0.740209
$13$	−6.95278	−1.92836	−0.964178	−	0.265257i	$-0.914543\pi$
$13$	−6.95278	−1.92836	−0.964178	+	0.265257i	$0.914543\pi$
$14$	0.385959	0.103152
$15$	5.12583	1.32348
$16$	3.27490	0.818724
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	0.397989	0.0938069
$19$	−2.29177	−0.525769	−0.262885	−	0.964827i	$-0.584674\pi$
$19$	−2.29177	−0.525769	−0.262885	+	0.964827i	$0.584674\pi$
$20$	7.03993	1.57418
$21$	1.50133	0.327617
$22$	1.43488	0.305918
$23$	1.76335	0.367683	0.183842	−	0.982956i	$-0.441147\pi$
$23$	1.76335	0.367683	0.183842	+	0.982956i	$0.441147\pi$
$24$	−1.86063	−0.379799
$25$	9.07304	1.81461
$26$	2.44228	0.478970
$27$	5.64726	1.08681
$28$	2.06196	0.389673
$29$	−5.76310	−1.07018	−0.535091	−	0.844795i	$-0.679722\pi$
$29$	−5.76310	−1.07018	−0.535091	+	0.844795i	$0.679722\pi$
$30$	−1.80053	−0.328731
$31$	−7.13338	−1.28119	−0.640597	−	0.767877i	$-0.721313\pi$
$31$	−7.13338	−1.28119	−0.640597	+	0.767877i	$0.721313\pi$
$32$	−3.87381	−0.684799
$33$	5.58149	0.971613
$34$	0.351266	0.0602417
$35$	4.12192	0.696731
$36$	2.12623	0.354371
$37$	−7.65596	−1.25863	−0.629316	−	0.777149i	$-0.716665\pi$
$37$	−7.65596	−1.25863	−0.629316	+	0.777149i	$0.716665\pi$
$38$	0.805023	0.130592
$39$	9.50013	1.52124
$40$	−5.10837	−0.807705
$41$	9.69884	1.51470	0.757352	−	0.653007i	$-0.226493\pi$
$41$	9.69884	1.51470	0.757352	+	0.653007i	$0.226493\pi$
$42$	−0.527366	−0.0813744
$43$	5.40037	0.823549	0.411775	−	0.911286i	$-0.364909\pi$
$43$	5.40037	0.823549	0.411775	+	0.911286i	$0.364909\pi$
$44$	7.66574	1.15565
$45$	4.25039	0.633611
$46$	−0.619404	−0.0913261
$47$	1.00000	0.145865
$47$	1.00000	0.145865
$48$	−4.47474	−0.645874
$49$	−5.79271	−0.827530
$50$	−3.18705	−0.450717
$51$	1.36638	0.191331
$52$	13.0477	1.80939
$53$	−5.62873	−0.773166	−0.386583	−	0.922255i	$-0.626345\pi$
$53$	−5.62873	−0.773166	−0.386583	+	0.922255i	$0.626345\pi$
$54$	−1.98369	−0.269946
$55$	15.3241	2.06630
$56$	−1.49621	−0.199940
$57$	3.13143	0.414768
$58$	2.02438	0.265814
$59$	7.29740	0.950040	0.475020	−	0.879975i	$-0.342441\pi$
$59$	7.29740	0.950040	0.475020	+	0.879975i	$0.342441\pi$
$60$	−9.61920	−1.24183
$61$	6.52587	0.835552	0.417776	−	0.908550i	$-0.362810\pi$
$61$	6.52587	0.835552	0.417776	+	0.908550i	$0.362810\pi$
$62$	2.50572	0.318226
$63$	1.24492	0.156845
$64$	−5.18906	−0.648632
$65$	26.0827	3.23516
$66$	−1.96059	−0.241332
$67$	0.285403	0.0348676	0.0174338	−	0.999848i	$-0.494450\pi$
$67$	0.285403	0.0348676	0.0174338	+	0.999848i	$0.494450\pi$
$68$	1.87661	0.227573
$69$	−2.40940	−0.290057
$70$	−1.44789	−0.173056
$71$	−10.6030	−1.25835	−0.629173	−	0.777265i	$-0.716606\pi$
$71$	−10.6030	−1.25835	−0.629173	+	0.777265i	$0.716606\pi$
$72$	−1.54285	−0.181827
$73$	−12.5918	−1.47376	−0.736880	−	0.676024i	$-0.763702\pi$
$73$	−12.5918	−1.47376	−0.736880	+	0.676024i	$0.763702\pi$
$74$	2.68928	0.312623
$75$	−12.3972	−1.43150
$76$	4.30077	0.493332
$77$	4.48833	0.511493
$78$	−3.33707	−0.377849
$79$	−14.6491	−1.64815	−0.824074	−	0.566482i	$-0.808304\pi$
$79$	−14.6491	−1.64815	−0.824074	+	0.566482i	$0.808304\pi$
$80$	−12.2855	−1.37356
$81$	−4.31724	−0.479694
$82$	−3.40687	−0.376226
$83$	−5.61580	−0.616415	−0.308207	−	0.951319i	$-0.599729\pi$
$83$	−5.61580	−0.616415	−0.308207	+	0.951319i	$0.599729\pi$
$84$	−2.81741	−0.307405
$85$	3.75140	0.406897
$86$	−1.89697	−0.204555
$87$	7.87457	0.844243
$88$	−5.56248	−0.592962
$89$	10.7994	1.14474	0.572369	−	0.819996i	$-0.306025\pi$
$89$	10.7994	1.14474	0.572369	+	0.819996i	$0.306025\pi$
$90$	−1.49302	−0.157378
$91$	7.63948	0.800835
$92$	−3.30912	−0.344999
$93$	9.74690	1.01071
$94$	−0.351266	−0.0362303
$95$	8.59737	0.882072
$96$	5.29308	0.540223
$97$	6.96451	0.707139	0.353569	−	0.935408i	$-0.384968\pi$
$97$	6.96451	0.707139	0.353569	+	0.935408i	$0.384968\pi$
$98$	2.03478	0.205544
$99$	4.62823	0.465154
$100$	−17.0266	−1.70266
$101$	−11.4685	−1.14116	−0.570578	−	0.821243i	$-0.693281\pi$
$101$	−11.4685	−1.14116	−0.570578	+	0.821243i	$0.693281\pi$
$102$	−0.479962	−0.0475233
$103$	−1.68427	−0.165956	−0.0829779	−	0.996551i	$-0.526443\pi$
$103$	−1.68427	−0.165956	−0.0829779	+	0.996551i	$0.526443\pi$
$104$	−9.46776	−0.928391
$105$	−5.63209	−0.549636
$106$	1.97718	0.192041
$107$	−15.5565	−1.50391	−0.751953	−	0.659217i	$-0.770888\pi$
$107$	−15.5565	−1.50391	−0.751953	+	0.659217i	$0.770888\pi$
$108$	−10.5977	−1.01976
$109$	−17.1979	−1.64726	−0.823628	−	0.567130i	$-0.808054\pi$
$109$	−17.1979	−1.64726	−0.823628	+	0.567130i	$0.808054\pi$
$110$	−5.38282	−0.513232
$111$	10.4609	0.992908
$112$	−3.59835	−0.340012
$113$	−3.07170	−0.288962	−0.144481	−	0.989508i	$-0.546151\pi$
$113$	−3.07170	−0.288962	−0.144481	+	0.989508i	$0.546151\pi$
$114$	−1.09997	−0.103021
$115$	−6.61503	−0.616854
$116$	10.8151	1.00416
$117$	7.87759	0.728284
$118$	−2.56333	−0.235974
$119$	1.09877	0.100724
$120$	6.97997	0.637181
$121$	5.68628	0.516935
$122$	−2.29232	−0.207537
$123$	−13.2523	−1.19492
$124$	13.3866	1.20215
$125$	−15.2796	−1.36665
$126$	−0.437297	−0.0389575
$127$	−7.73139	−0.686050	−0.343025	−	0.939326i	$-0.611452\pi$
$127$	−7.73139	−0.686050	−0.343025	+	0.939326i	$0.611452\pi$
$128$	9.57035	0.845908
$129$	−7.37895	−0.649680
$130$	−9.16197	−0.803558
$131$	19.5279	1.70616	0.853080	−	0.521780i	$-0.174732\pi$
$131$	19.5279	1.70616	0.853080	+	0.521780i	$0.174732\pi$
$132$	−10.4743	−0.911671
$133$	2.51812	0.218349
$134$	−0.100253	−0.00866050
$135$	−21.1851	−1.82333
$136$	−1.36172	−0.116767
$137$	2.92308	0.249735	0.124868	−	0.992173i	$-0.460149\pi$
$137$	2.92308	0.249735	0.124868	+	0.992173i	$0.460149\pi$
$138$	0.846340	0.0720452
$139$	−17.5156	−1.48565	−0.742826	−	0.669484i	$-0.766515\pi$
$139$	−17.5156	−1.48565	−0.742826	+	0.669484i	$0.766515\pi$
$140$	−7.73524	−0.653747
$141$	−1.36638	−0.115070
$142$	3.72448	0.312551
$143$	28.4013	2.37504
$144$	−3.71050	−0.309208
$145$	21.6197	1.79542
$146$	4.42308	0.366056
$147$	7.91503	0.652821
$148$	14.3673	1.18098
$149$	−4.98198	−0.408140	−0.204070	−	0.978956i	$-0.565417\pi$
$149$	−4.98198	−0.408140	−0.204070	+	0.978956i	$0.565417\pi$
$150$	4.35472	0.355561
$151$	9.62168	0.783002	0.391501	−	0.920178i	$-0.371956\pi$
$151$	9.62168	0.783002	0.391501	+	0.920178i	$0.371956\pi$
$152$	−3.12076	−0.253127
$153$	1.13301	0.0915987
$154$	−1.57660	−0.127046
$155$	26.7602	2.14943
$156$	−17.8281	−1.42739
$157$	−14.0544	−1.12166	−0.560832	−	0.827930i	$-0.689519\pi$
$157$	−14.0544	−1.12166	−0.560832	+	0.827930i	$0.689519\pi$
$158$	5.14572	0.409371
$159$	7.69097	0.609934
$160$	14.5322	1.14887
$161$	−1.93751	−0.152697
$162$	1.51650	0.119148
$163$	−19.8362	−1.55369	−0.776847	−	0.629690i	$-0.783182\pi$
$163$	−19.8362	−1.55369	−0.776847	+	0.629690i	$0.783182\pi$
$164$	−18.2010	−1.42126
$165$	−20.9384	−1.63006
$166$	1.97264	0.153107
$167$	9.42987	0.729705	0.364853	−	0.931065i	$-0.381119\pi$
$167$	9.42987	0.729705	0.364853	+	0.931065i	$0.381119\pi$
$168$	2.04439	0.157728
$169$	35.3412	2.71855
$170$	−1.31774	−0.101066
$171$	2.59661	0.198568
$172$	−10.1344	−0.772741
$173$	−2.64002	−0.200717	−0.100359	−	0.994951i	$-0.531999\pi$
$173$	−2.64002	−0.200717	−0.100359	+	0.994951i	$0.531999\pi$
$174$	−2.76607	−0.209695
$175$	−9.96915	−0.753597
$176$	−13.3776	−1.00837
$177$	−9.97100	−0.749466
$178$	−3.79348	−0.284333
$179$	−3.54153	−0.264707	−0.132353	−	0.991203i	$-0.542253\pi$
$179$	−3.54153	−0.264707	−0.132353	+	0.991203i	$0.542253\pi$
$180$	−7.97633	−0.594521
$181$	9.49409	0.705690	0.352845	−	0.935682i	$-0.385214\pi$
$181$	9.49409	0.705690	0.352845	+	0.935682i	$0.385214\pi$
$182$	−2.68349	−0.198914
$183$	−8.91680	−0.659149
$184$	2.40119	0.177018
$185$	28.7206	2.11158
$186$	−3.42375	−0.251042
$187$	4.08488	0.298716
$188$	−1.87661	−0.136866
$189$	−6.20501	−0.451348
$190$	−3.01997	−0.219091
$191$	−1.95066	−0.141145	−0.0705725	−	0.997507i	$-0.522483\pi$
$191$	−1.95066	−0.141145	−0.0705725	+	0.997507i	$0.522483\pi$
$192$	7.09021	0.511692
$193$	−13.0344	−0.938233	−0.469117	−	0.883136i	$-0.655428\pi$
$193$	−13.0344	−0.938233	−0.469117	+	0.883136i	$0.655428\pi$
$194$	−2.44640	−0.175641
$195$	−35.6388	−2.55215
$196$	10.8707	0.776477
$197$	9.12034	0.649797	0.324899	−	0.945749i	$-0.394670\pi$
$197$	9.12034	0.649797	0.324899	+	0.945749i	$0.394670\pi$
$198$	−1.62574	−0.115536
$199$	−13.7212	−0.972668	−0.486334	−	0.873773i	$-0.661666\pi$
$199$	−13.7212	−0.972668	−0.486334	+	0.873773i	$0.661666\pi$
$200$	12.3550	0.873628
$201$	−0.389968	−0.0275063
$202$	4.02849	0.283444
$203$	6.33230	0.444440
$204$	−2.56416	−0.179527
$205$	−36.3843	−2.54119
$206$	0.591627	0.0412206
$207$	−1.99789	−0.138863
$208$	−22.7696	−1.57879
$209$	9.36163	0.647558
$210$	1.97836	0.136520
$211$	−13.6456	−0.939399	−0.469699	−	0.882826i	$-0.655638\pi$
$211$	−13.6456	−0.939399	−0.469699	+	0.882826i	$0.655638\pi$
$212$	10.5629	0.725466
$213$	14.4877	0.992682
$214$	5.46448	0.373544
$215$	−20.2590	−1.38165
$216$	7.69000	0.523238
$217$	7.83792	0.532073
$218$	6.04103	0.409150
$219$	17.2052	1.16262
$220$	−28.7573	−1.93882
$221$	6.95278	0.467695
$222$	−3.67457	−0.246621
$223$	16.0221	1.07292	0.536458	−	0.843927i	$-0.319762\pi$
$223$	16.0221	1.07292	0.536458	+	0.843927i	$0.319762\pi$
$224$	4.25641	0.284393
$225$	−10.2799	−0.685325
$226$	1.07899	0.0717731
$227$	−9.77404	−0.648726	−0.324363	−	0.945933i	$-0.605150\pi$
$227$	−9.77404	−0.648726	−0.324363	+	0.945933i	$0.605150\pi$
$228$	−5.87648	−0.389179
$229$	23.1278	1.52833	0.764166	−	0.645020i	$-0.223151\pi$
$229$	23.1278	1.52833	0.764166	+	0.645020i	$0.223151\pi$
$230$	2.32364	0.153216
$231$	−6.13276	−0.403506
$232$	−7.84775	−0.515230
$233$	−26.8210	−1.75710	−0.878552	−	0.477647i	$-0.841490\pi$
$233$	−26.8210	−1.75710	−0.878552	+	0.477647i	$0.841490\pi$
$234$	−2.76713	−0.180893
$235$	−3.75140	−0.244715
$236$	−13.6944	−0.891429
$237$	20.0161	1.30019
$238$	−0.385959	−0.0250180
$239$	5.49895	0.355697	0.177849	−	0.984058i	$-0.443086\pi$
$239$	5.49895	0.355697	0.177849	+	0.984058i	$0.443086\pi$
$240$	16.7866	1.08357
$241$	13.4721	0.867816	0.433908	−	0.900957i	$-0.357134\pi$
$241$	13.4721	0.867816	0.433908	+	0.900957i	$0.357134\pi$
$242$	−1.99740	−0.128398
$243$	−11.0428	−0.708395
$244$	−12.2465	−0.784003
$245$	21.7308	1.38833
$246$	4.65508	0.296797
$247$	15.9342	1.01387
$248$	−9.71369	−0.616820
$249$	7.67331	0.486276
$250$	5.36721	0.339452
$251$	−5.56286	−0.351124	−0.175562	−	0.984468i	$-0.556174\pi$
$251$	−5.56286	−0.351124	−0.175562	+	0.984468i	$0.556174\pi$
$252$	−2.33622	−0.147168
$253$	−7.20307	−0.452853
$254$	2.71578	0.170403
$255$	−5.12583	−0.320992
$256$	7.01637	0.438523
$257$	15.4196	0.961845	0.480923	−	0.876763i	$-0.340302\pi$
$257$	15.4196	0.961845	0.480923	+	0.876763i	$0.340302\pi$
$258$	2.59197	0.161369
$259$	8.41211	0.522703
$260$	−48.9471	−3.03557
$261$	6.52967	0.404176
$262$	−6.85949	−0.423781
$263$	−1.21877	−0.0751523	−0.0375762	−	0.999294i	$-0.511964\pi$
$263$	−1.21877	−0.0751523	−0.0375762	+	0.999294i	$0.511964\pi$
$264$	7.60045	0.467775
$265$	21.1157	1.29712
$266$	−0.884532	−0.0542341
$267$	−14.7561	−0.903059
$268$	−0.535591	−0.0327164
$269$	11.0702	0.674964	0.337482	−	0.941332i	$-0.390425\pi$
$269$	11.0702	0.674964	0.337482	+	0.941332i	$0.390425\pi$
$270$	7.44162	0.452883
$271$	20.0692	1.21911	0.609557	−	0.792742i	$-0.291347\pi$
$271$	20.0692	1.21911	0.609557	+	0.792742i	$0.291347\pi$
$272$	−3.27490	−0.198570
$273$	−10.4384	−0.631762
$274$	−1.02678	−0.0620299
$275$	−37.0623	−2.23494
$276$	4.52150	0.272163
$277$	11.0804	0.665754	0.332877	−	0.942970i	$-0.391981\pi$
$277$	11.0804	0.665754	0.332877	+	0.942970i	$0.391981\pi$
$278$	6.15263	0.369010
$279$	8.08222	0.483870
$280$	5.61291	0.335435
$281$	12.5464	0.748455	0.374227	−	0.927337i	$-0.377908\pi$
$281$	12.5464	0.748455	0.374227	+	0.927337i	$0.377908\pi$
$282$	0.479962	0.0285813
$283$	−22.7425	−1.35190	−0.675950	−	0.736948i	$-0.736266\pi$
$283$	−22.7425	−1.35190	−0.675950	+	0.736948i	$0.736266\pi$
$284$	19.8977	1.18071
$285$	−11.7473	−0.695847
$286$	−9.97642	−0.589918
$287$	−10.6568	−0.629048
$288$	4.38907	0.258629
$289$	1.00000	0.0588235
$290$	−7.59428	−0.445951
$291$	−9.51615	−0.557846
$292$	23.6299	1.38284
$293$	10.6938	0.624741	0.312371	−	0.949960i	$-0.398877\pi$
$293$	10.6938	0.624741	0.312371	+	0.949960i	$0.398877\pi$
$294$	−2.78028	−0.162149
$295$	−27.3755	−1.59386
$296$	−10.4253	−0.605958
$297$	−23.0684	−1.33856
$298$	1.75000	0.101375
$299$	−12.2602	−0.709024
$300$	23.2647	1.34319
$301$	−5.93375	−0.342015
$302$	−3.37977	−0.194484
$303$	15.6703	0.900234
$304$	−7.50533	−0.430460
$305$	−24.4812	−1.40179
$306$	−0.397989	−0.0227515
$307$	4.23456	0.241679	0.120840	−	0.992672i	$-0.461441\pi$
$307$	4.23456	0.241679	0.120840	+	0.992672i	$0.461441\pi$
$308$	−8.42286	−0.479937
$309$	2.30135	0.130919
$310$	−9.39996	−0.533882
$311$	−0.873971	−0.0495583	−0.0247792	−	0.999693i	$-0.507888\pi$
$311$	−0.873971	−0.0495583	−0.0247792	+	0.999693i	$0.507888\pi$
$312$	12.9365	0.732387
$313$	1.18586	0.0670286	0.0335143	−	0.999438i	$-0.489330\pi$
$313$	1.18586	0.0670286	0.0335143	+	0.999438i	$0.489330\pi$
$314$	4.93684	0.278602
$315$	−4.67019	−0.263135
$316$	27.4906	1.54647
$317$	32.7270	1.83813	0.919066	−	0.394104i	$-0.128945\pi$
$317$	32.7270	1.83813	0.919066	+	0.394104i	$0.128945\pi$
$318$	−2.70158	−0.151497
$319$	23.5416	1.31808
$320$	19.4663	1.08820
$321$	21.2561	1.18640
$322$	0.680580	0.0379273
$323$	2.29177	0.127518
$324$	8.10179	0.450099
$325$	−63.0829	−3.49921
$326$	6.96780	0.385911
$327$	23.4988	1.29948
$328$	13.2071	0.729242
$329$	−1.09877	−0.0605769
$330$	7.35497	0.404878
$331$	−25.2707	−1.38900	−0.694500	−	0.719492i	$-0.744375\pi$
$331$	−25.2707	−1.38900	−0.694500	+	0.719492i	$0.744375\pi$
$332$	10.5387	0.578386
$333$	8.67430	0.475349
$334$	−3.31239	−0.181246
$335$	−1.07066	−0.0584966
$336$	4.91670	0.268228
$337$	13.5358	0.737341	0.368670	−	0.929560i	$-0.379813\pi$
$337$	13.5358	0.737341	0.368670	+	0.929560i	$0.379813\pi$
$338$	−12.4142	−0.675242
$339$	4.19711	0.227956
$340$	−7.03993	−0.381794
$341$	29.1391	1.57797
$342$	−0.912101	−0.0493208
$343$	14.0562	0.758963
$344$	7.35381	0.396491
$345$	9.03862	0.486623
$346$	0.927350	0.0498547
$347$	−15.9625	−0.856911	−0.428455	−	0.903563i	$-0.640942\pi$
$347$	−15.9625	−0.856911	−0.428455	+	0.903563i	$0.640942\pi$
$348$	−14.7775	−0.792158
$349$	−13.7260	−0.734734	−0.367367	−	0.930076i	$-0.619741\pi$
$349$	−13.7260	−0.734734	−0.367367	+	0.930076i	$0.619741\pi$
$350$	3.50182	0.187180
$351$	−39.2641	−2.09576
$352$	15.8241	0.843425
$353$	−10.4994	−0.558829	−0.279415	−	0.960171i	$-0.590140\pi$
$353$	−10.4994	−0.558829	−0.279415	+	0.960171i	$0.590140\pi$
$354$	3.50248	0.186154
$355$	39.7762	2.11110
$356$	−20.2664	−1.07411
$357$	−1.50133	−0.0794588
$358$	1.24402	0.0657485
$359$	0.329081	0.0173682	0.00868410	−	0.999962i	$-0.497236\pi$
$359$	0.329081	0.0173682	0.00868410	+	0.999962i	$0.497236\pi$
$360$	5.78785	0.305047
$361$	−13.7478	−0.723567
$362$	−3.33495	−0.175281
$363$	−7.76960	−0.407799
$364$	−14.3363	−0.751429
$365$	47.2370	2.47250
$366$	3.13217	0.163721
$367$	−29.4043	−1.53489	−0.767446	−	0.641114i	$-0.778473\pi$
$367$	−29.4043	−1.53489	−0.767446	+	0.641114i	$0.778473\pi$
$368$	5.77478	0.301031
$369$	−10.9889	−0.572060
$370$	−10.0886	−0.524480
$371$	6.18466	0.321092
$372$	−18.2911	−0.948351
$373$	−17.8180	−0.922580	−0.461290	−	0.887250i	$-0.652613\pi$
$373$	−17.8180	−0.922580	−0.461290	+	0.887250i	$0.652613\pi$
$374$	−1.43488	−0.0741960
$375$	20.8777	1.07812
$376$	1.36172	0.0702255
$377$	40.0696	2.06369
$378$	2.17961	0.112107
$379$	32.9417	1.69210	0.846051	−	0.533101i	$-0.178974\pi$
$379$	32.9417	1.69210	0.846051	+	0.533101i	$0.178974\pi$
$380$	−16.1339	−0.827653
$381$	10.5640	0.541210
$382$	0.685202	0.0350580
$383$	−7.60450	−0.388572	−0.194286	−	0.980945i	$-0.562239\pi$
$383$	−7.60450	−0.388572	−0.194286	+	0.980945i	$0.562239\pi$
$384$	−13.0767	−0.667318
$385$	−16.8376	−0.858121
$386$	4.57853	0.233041
$387$	−6.11869	−0.311031
$388$	−13.0697	−0.663513
$389$	21.6997	1.10022	0.550108	−	0.835094i	$-0.314587\pi$
$389$	21.6997	1.10022	0.550108	+	0.835094i	$0.314587\pi$
$390$	12.5187	0.633910
$391$	−1.76335	−0.0891763
$392$	−7.88807	−0.398408
$393$	−26.6825	−1.34595
$394$	−3.20367	−0.161398
$395$	54.9545	2.76506
$396$	−8.68539	−0.436457
$397$	−9.03447	−0.453427	−0.226713	−	0.973962i	$-0.572798\pi$
$397$	−9.03447	−0.453427	−0.226713	+	0.973962i	$0.572798\pi$
$398$	4.81978	0.241594
$399$	−3.44071	−0.172251
$400$	29.7133	1.48566
$401$	14.7948	0.738817	0.369408	−	0.929267i	$-0.379560\pi$
$401$	14.7948	0.738817	0.369408	+	0.929267i	$0.379560\pi$
$402$	0.136983	0.00683208
$403$	49.5969	2.47060
$404$	21.5219	1.07075
$405$	16.1957	0.804772
$406$	−2.22432	−0.110391
$407$	31.2737	1.55018
$408$	1.86063	0.0921148
$409$	−1.65528	−0.0818482	−0.0409241	−	0.999162i	$-0.513030\pi$
$409$	−1.65528	−0.0818482	−0.0409241	+	0.999162i	$0.513030\pi$
$410$	12.7806	0.631187
$411$	−3.99402	−0.197011
$412$	3.16072	0.155717
$413$	−8.01813	−0.394547
$414$	0.701793	0.0344912
$415$	21.0672	1.03415
$416$	26.9337	1.32054
$417$	23.9329	1.17200
$418$	−3.28843	−0.160842
$419$	12.1170	0.591953	0.295976	−	0.955195i	$-0.404355\pi$
$419$	12.1170	0.591953	0.295976	+	0.955195i	$0.404355\pi$
$420$	10.5693	0.515727
$421$	−27.1258	−1.32203	−0.661016	−	0.750372i	$-0.729874\pi$
$421$	−27.1258	−1.32203	−0.661016	+	0.750372i	$0.729874\pi$
$422$	4.79322	0.233330
$423$	−1.13301	−0.0550890
$424$	−7.66477	−0.372234
$425$	−9.07304	−0.440107
$426$	−5.08905	−0.246565
$427$	−7.17040	−0.347000
$428$	29.1936	1.41112
$429$	−38.8069	−1.87362
$430$	7.11630	0.343178
$431$	−15.8647	−0.764176	−0.382088	−	0.924126i	$-0.624795\pi$
$431$	−15.8647	−0.764176	−0.382088	+	0.924126i	$0.624795\pi$
$432$	18.4942	0.889802
$433$	−32.5279	−1.56319	−0.781596	−	0.623785i	$-0.785594\pi$
$433$	−32.5279	−1.56319	−0.781596	+	0.623785i	$0.785594\pi$
$434$	−2.75320	−0.132158
$435$	−29.5407	−1.41637
$436$	32.2737	1.54563
$437$	−4.04119	−0.193316
$438$	−6.04359	−0.288774
$439$	−33.5664	−1.60203	−0.801017	−	0.598641i	$-0.795708\pi$
$439$	−33.5664	−1.60203	−0.801017	+	0.598641i	$0.795708\pi$
$440$	20.8671	0.994801
$441$	6.56322	0.312534
$442$	−2.44228	−0.116167
$443$	6.64648	0.315784	0.157892	−	0.987456i	$-0.449530\pi$
$443$	6.64648	0.315784	0.157892	+	0.987456i	$0.449530\pi$
$444$	−19.6311	−0.931651
$445$	−40.5131	−1.92050
$446$	−5.62801	−0.266494
$447$	6.80726	0.321973
$448$	5.70156	0.269373
$449$	8.87649	0.418907	0.209454	−	0.977819i	$-0.432831\pi$
$449$	8.87649	0.418907	0.209454	+	0.977819i	$0.432831\pi$
$450$	3.61097	0.170223
$451$	−39.6186	−1.86557
$452$	5.76440	0.271134
$453$	−13.1469	−0.617693
$454$	3.43329	0.161132
$455$	−28.6588	−1.34355
$456$	4.26414	0.199687
$457$	22.3105	1.04364	0.521821	−	0.853055i	$-0.325253\pi$
$457$	22.3105	1.04364	0.521821	+	0.853055i	$0.325253\pi$
$458$	−8.12403	−0.379611
$459$	−5.64726	−0.263591
$460$	12.4138	0.578798
$461$	39.6968	1.84887	0.924433	−	0.381344i	$-0.124539\pi$
$461$	39.6968	1.84887	0.924433	+	0.381344i	$0.124539\pi$
$462$	2.15423	0.100224
$463$	−2.43059	−0.112959	−0.0564794	−	0.998404i	$-0.517988\pi$
$463$	−2.43059	−0.112959	−0.0564794	+	0.998404i	$0.517988\pi$
$464$	−18.8736	−0.876183
$465$	−36.5645	−1.69564
$466$	9.42132	0.436434
$467$	−22.3520	−1.03433	−0.517163	−	0.855887i	$-0.673012\pi$
$467$	−22.3520	−1.03433	−0.517163	+	0.855887i	$0.673012\pi$
$468$	−14.7832	−0.683353
$469$	−0.313591	−0.0144803
$470$	1.31774	0.0607829
$471$	19.2036	0.884857
$472$	9.93703	0.457389
$473$	−22.0599	−1.01432
$474$	−7.03099	−0.322944
$475$	−20.7934	−0.954065
$476$	−2.06196	−0.0945097
$477$	6.37743	0.292002
$478$	−1.93159	−0.0883491
$479$	−11.8879	−0.543174	−0.271587	−	0.962414i	$-0.587549\pi$
$479$	−11.8879	−0.543174	−0.271587	+	0.962414i	$0.587549\pi$
$480$	−19.8565	−0.906321
$481$	53.2303	2.42709
$482$	−4.73231	−0.215551
$483$	2.64736	0.120459
$484$	−10.6709	−0.485043
$485$	−26.1267	−1.18635
$486$	3.87896	0.175953
$487$	16.7609	0.759508	0.379754	−	0.925088i	$-0.376009\pi$
$487$	16.7609	0.759508	0.379754	+	0.925088i	$0.376009\pi$
$488$	8.88642	0.402269
$489$	27.1038	1.22568
$490$	−7.63330	−0.344837
$491$	−25.3995	−1.14626	−0.573131	−	0.819464i	$-0.694271\pi$
$491$	−25.3995	−1.14626	−0.573131	+	0.819464i	$0.694271\pi$
$492$	24.8694	1.12120
$493$	5.76310	0.259557
$494$	−5.59715	−0.251828
$495$	−17.3624	−0.780380
$496$	−23.3611	−1.04894
$497$	11.6502	0.522584
$498$	−2.69537	−0.120783
$499$	−12.0035	−0.537349	−0.268675	−	0.963231i	$-0.586586\pi$
$499$	−12.0035	−0.537349	−0.268675	+	0.963231i	$0.586586\pi$
$500$	28.6739	1.28234
$501$	−12.8848	−0.575649
$502$	1.95404	0.0872132
$503$	−25.8535	−1.15275	−0.576375	−	0.817185i	$-0.695533\pi$
$503$	−25.8535	−1.15275	−0.576375	+	0.817185i	$0.695533\pi$
$504$	1.69523	0.0755116
$505$	43.0229	1.91449
$506$	2.53019	0.112481
$507$	−48.2894	−2.14461
$508$	14.5088	0.643725
$509$	26.5733	1.17784	0.588920	−	0.808191i	$-0.299553\pi$
$509$	26.5733	1.17784	0.588920	+	0.808191i	$0.299553\pi$
$510$	1.80053	0.0797289
$511$	13.8355	0.612044
$512$	−21.6053	−0.954829
$513$	−12.9422	−0.571414
$514$	−5.41637	−0.238906
$515$	6.31837	0.278421
$516$	13.8474	0.609599
$517$	−4.08488	−0.179653
$518$	−2.95489	−0.129830
$519$	3.60726	0.158341
$520$	35.5174	1.55754
$521$	38.3997	1.68232	0.841160	−	0.540786i	$-0.181873\pi$
$521$	38.3997	1.68232	0.841160	+	0.540786i	$0.181873\pi$
$522$	−2.29365	−0.100390
$523$	10.3410	0.452179	0.226090	−	0.974107i	$-0.427406\pi$
$523$	10.3410	0.452179	0.226090	+	0.974107i	$0.427406\pi$
$524$	−36.6463	−1.60090
$525$	13.6216	0.594496
$526$	0.428111	0.0186665
$527$	7.13338	0.310735
$528$	18.2788	0.795483
$529$	−19.8906	−0.864809
$530$	−7.41722	−0.322183
$531$	−8.26805	−0.358803
$532$	−4.72554	−0.204878
$533$	−67.4339	−2.92089
$534$	5.18332	0.224304
$535$	58.3588	2.52307
$536$	0.388640	0.0167867
$537$	4.83907	0.208821
$538$	−3.88860	−0.167649
$539$	23.6626	1.01922
$540$	39.7563	1.71084
$541$	30.1292	1.29536	0.647678	−	0.761914i	$-0.275740\pi$
$541$	30.1292	1.29536	0.647678	+	0.761914i	$0.275740\pi$
$542$	−7.04962	−0.302807
$543$	−12.9725	−0.556703
$544$	3.87381	0.166088
$545$	64.5161	2.76357
$546$	3.66666	0.156919
$547$	1.14280	0.0488627	0.0244314	−	0.999702i	$-0.492222\pi$
$547$	1.14280	0.0488627	0.0244314	+	0.999702i	$0.492222\pi$
$548$	−5.48548	−0.234328
$549$	−7.39389	−0.315564
$550$	13.0187	0.555121
$551$	13.2077	0.562668
$552$	−3.28093	−0.139646
$553$	16.0959	0.684467
$554$	−3.89216	−0.165362
$555$	−39.2432	−1.66578
$556$	32.8700	1.39400
$557$	−23.7522	−1.00641	−0.503207	−	0.864166i	$-0.667847\pi$
$557$	−23.7522	−1.00641	−0.503207	+	0.864166i	$0.667847\pi$
$558$	−2.83901	−0.120185
$559$	−37.5476	−1.58810
$560$	13.4989	0.570431
$561$	−5.58149	−0.235651
$562$	−4.40712	−0.185903
$563$	−14.2362	−0.599984	−0.299992	−	0.953942i	$-0.596984\pi$
$563$	−14.2362	−0.599984	−0.299992	+	0.953942i	$0.596984\pi$
$564$	2.56416	0.107971
$565$	11.5232	0.484785
$566$	7.98866	0.335789
$567$	4.74364	0.199214
$568$	−14.4384	−0.605820
$569$	17.2353	0.722540	0.361270	−	0.932461i	$-0.382343\pi$
$569$	17.2353	0.722540	0.361270	+	0.932461i	$0.382343\pi$
$570$	4.12641	0.172836
$571$	20.0375	0.838543	0.419272	−	0.907861i	$-0.362285\pi$
$571$	20.0375	0.838543	0.419272	+	0.907861i	$0.362285\pi$
$572$	−53.2983	−2.22851
$573$	2.66534	0.111346
$574$	3.74336	0.156245
$575$	15.9989	0.667201
$576$	5.87927	0.244970
$577$	−20.3903	−0.848859	−0.424430	−	0.905461i	$-0.639525\pi$
$577$	−20.3903	−0.848859	−0.424430	+	0.905461i	$0.639525\pi$
$578$	−0.351266	−0.0146107
$579$	17.8098	0.740152
$580$	−40.5718	−1.68465
$581$	6.17046	0.255994
$582$	3.34270	0.138559
$583$	22.9927	0.952261
$584$	−17.1466	−0.709530
$585$	−29.5520	−1.22183
$586$	−3.75639	−0.155175
$587$	39.7623	1.64116	0.820582	−	0.571528i	$-0.193649\pi$
$587$	39.7623	1.64116	0.820582	+	0.571528i	$0.193649\pi$
$588$	−14.8534	−0.612546
$589$	16.3481	0.673612
$590$	9.61609	0.395888
$591$	−12.4618	−0.512611
$592$	−25.0725	−1.03047
$593$	−17.9893	−0.738733	−0.369366	−	0.929284i	$-0.620425\pi$
$593$	−17.9893	−0.738733	−0.369366	+	0.929284i	$0.620425\pi$
$594$	8.10314	0.332476
$595$	−4.12192	−0.168982
$596$	9.34924	0.382960
$597$	18.7483	0.767317
$598$	4.30658	0.176109
$599$	−42.9815	−1.75618	−0.878089	−	0.478498i	$-0.841181\pi$
$599$	−42.9815	−1.75618	−0.878089	+	0.478498i	$0.841181\pi$
$600$	−16.8815	−0.689186
$601$	−23.5828	−0.961963	−0.480981	−	0.876731i	$-0.659720\pi$
$601$	−23.5828	−0.961963	−0.480981	+	0.876731i	$0.659720\pi$
$602$	2.08432	0.0849507
$603$	−0.323366	−0.0131685
$604$	−18.0562	−0.734695
$605$	−21.3315	−0.867250
$606$	−5.50444	−0.223602
$607$	−39.9404	−1.62113	−0.810565	−	0.585648i	$-0.800840\pi$
$607$	−39.9404	−1.62113	−0.810565	+	0.585648i	$0.800840\pi$
$608$	8.87789	0.360046
$609$	−8.65231	−0.350609
$610$	8.59941	0.348180
$611$	−6.95278	−0.281280
$612$	−2.12623	−0.0859476
$613$	−31.4717	−1.27113	−0.635565	−	0.772047i	$-0.719233\pi$
$613$	−31.4717	−1.27113	−0.635565	+	0.772047i	$0.719233\pi$
$614$	−1.48746	−0.0600289
$615$	49.7146	2.00469
$616$	6.11187	0.246254
$617$	−39.5114	−1.59067	−0.795335	−	0.606170i	$-0.792705\pi$
$617$	−39.5114	−1.59067	−0.795335	+	0.606170i	$0.792705\pi$
$618$	−0.808385	−0.0325180
$619$	2.85254	0.114653	0.0573266	−	0.998355i	$-0.481742\pi$
$619$	2.85254	0.114653	0.0573266	+	0.998355i	$0.481742\pi$
$620$	−50.2185	−2.01683
$621$	9.95807	0.399604
$622$	0.306996	0.0123094
$623$	−11.8661	−0.475403
$624$	31.1119	1.24547
$625$	11.9548	0.478193
$626$	−0.416552	−0.0166488
$627$	−12.7915	−0.510844
$628$	26.3747	1.05246
$629$	7.65596	0.305263
$630$	1.64048	0.0653582
$631$	2.98954	0.119012	0.0595059	−	0.998228i	$-0.481047\pi$
$631$	2.98954	0.119012	0.0595059	+	0.998228i	$0.481047\pi$
$632$	−19.9480	−0.793487
$633$	18.6450	0.741071
$634$	−11.4959	−0.456560
$635$	29.0036	1.15097
$636$	−14.4330	−0.572304
$637$	40.2755	1.59577
$638$	−8.26937	−0.327387
$639$	12.0134	0.475241
$640$	−35.9023	−1.41916
$641$	42.6779	1.68568	0.842838	−	0.538167i	$-0.180883\pi$
$641$	42.6779	1.68568	0.842838	+	0.538167i	$0.180883\pi$
$642$	−7.46654	−0.294681
$643$	−7.16323	−0.282490	−0.141245	−	0.989975i	$-0.545111\pi$
$643$	−7.16323	−0.282490	−0.141245	+	0.989975i	$0.545111\pi$
$644$	3.63595	0.143276
$645$	27.6814	1.08995
$646$	−0.805023	−0.0316732
$647$	−9.21704	−0.362359	−0.181180	−	0.983450i	$-0.557992\pi$
$647$	−9.21704	−0.362359	−0.181180	+	0.983450i	$0.557992\pi$
$648$	−5.87889	−0.230945
$649$	−29.8090	−1.17011
$650$	22.1589	0.869143
$651$	−10.7096	−0.419741
$652$	37.2249	1.45784
$653$	10.0396	0.392882	0.196441	−	0.980516i	$-0.437062\pi$
$653$	10.0396	0.392882	0.196441	+	0.980516i	$0.437062\pi$
$654$	−8.25432	−0.322769
$655$	−73.2571	−2.86239
$656$	31.7627	1.24012
$657$	14.2667	0.556596
$658$	0.385959	0.0150463
$659$	15.4382	0.601386	0.300693	−	0.953721i	$-0.402782\pi$
$659$	15.4382	0.601386	0.300693	+	0.953721i	$0.402782\pi$
$660$	39.2933	1.52949
$661$	−7.99260	−0.310876	−0.155438	−	0.987846i	$-0.549679\pi$
$661$	−7.99260	−0.310876	−0.155438	+	0.987846i	$0.549679\pi$
$662$	8.87673	0.345004
$663$	−9.50013	−0.368954
$664$	−7.64717	−0.296768
$665$	−9.44650	−0.366320
$666$	−3.04699	−0.118068
$667$	−10.1623	−0.393488
$668$	−17.6962	−0.684687
$669$	−21.8922	−0.846401
$670$	0.376088	0.0145295
$671$	−26.6574	−1.02910
$672$	−5.81586	−0.224352
$673$	−4.75007	−0.183102	−0.0915509	−	0.995800i	$-0.529182\pi$
$673$	−4.75007	−0.183102	−0.0915509	+	0.995800i	$0.529182\pi$
$674$	−4.75466	−0.183143
$675$	51.2378	1.97214
$676$	−66.3217	−2.55084
$677$	−21.3407	−0.820189	−0.410095	−	0.912043i	$-0.634504\pi$
$677$	−21.3407	−0.820189	−0.410095	+	0.912043i	$0.634504\pi$
$678$	−1.47430	−0.0566202
$679$	−7.65237	−0.293671
$680$	5.10837	0.195897
$681$	13.3550	0.511766
$682$	−10.2356	−0.391940
$683$	−17.8269	−0.682127	−0.341064	−	0.940040i	$-0.610787\pi$
$683$	−17.8269	−0.682127	−0.341064	+	0.940040i	$0.610787\pi$
$684$	−4.87283	−0.186317
$685$	−10.9656	−0.418976
$686$	−4.93747	−0.188513
$687$	−31.6014	−1.20567
$688$	17.6857	0.674260
$689$	39.1354	1.49094
$690$	−3.17496	−0.120869
$691$	20.8472	0.793066	0.396533	−	0.918020i	$-0.370213\pi$
$691$	20.8472	0.793066	0.396533	+	0.918020i	$0.370213\pi$
$692$	4.95430	0.188334
$693$	−5.08534	−0.193176
$694$	5.60708	0.212842
$695$	65.7081	2.49245
$696$	10.7230	0.406454
$697$	−9.69884	−0.367370
$698$	4.82147	0.182495
$699$	36.6476	1.38614
$700$	18.7082	0.707104
$701$	22.9609	0.867221	0.433611	−	0.901100i	$-0.357239\pi$
$701$	22.9609	0.867221	0.433611	+	0.901100i	$0.357239\pi$
$702$	13.7922	0.520552
$703$	17.5457	0.661750
$704$	21.1967	0.798881
$705$	5.12583	0.193050
$706$	3.68810	0.138804
$707$	12.6012	0.473916
$708$	18.7117	0.703229
$709$	0.797162	0.0299380	0.0149690	−	0.999888i	$-0.495235\pi$
$709$	0.797162	0.0299380	0.0149690	+	0.999888i	$0.495235\pi$
$710$	−13.9720	−0.524361
$711$	16.5976	0.622458
$712$	14.7058	0.551125
$713$	−12.5786	−0.471073
$714$	0.527366	0.0197362
$715$	−106.545	−3.98455
$716$	6.64608	0.248376
$717$	−7.51364	−0.280602
$718$	−0.115595	−0.00431396
$719$	10.1503	0.378543	0.189271	−	0.981925i	$-0.439387\pi$
$719$	10.1503	0.378543	0.189271	+	0.981925i	$0.439387\pi$
$720$	13.9196	0.518752
$721$	1.85062	0.0689206
$722$	4.82913	0.179721
$723$	−18.4080	−0.684602
$724$	−17.8167	−0.662153
$725$	−52.2888	−1.94196
$726$	2.72920	0.101290
$727$	−36.6661	−1.35987	−0.679935	−	0.733273i	$-0.737992\pi$
$727$	−36.6661	−1.35987	−0.679935	+	0.733273i	$0.737992\pi$
$728$	10.4029	0.385556
$729$	28.0403	1.03853
$730$	−16.5928	−0.614125
$731$	−5.40037	−0.199740
$732$	16.7334	0.618483
$733$	4.73185	0.174775	0.0873875	−	0.996174i	$-0.472148\pi$
$733$	4.73185	0.174775	0.0873875	+	0.996174i	$0.472148\pi$
$734$	10.3287	0.381241
$735$	−29.6925	−1.09522
$736$	−6.83086	−0.251789
$737$	−1.16584	−0.0429442
$738$	3.86003	0.142090
$739$	13.7391	0.505400	0.252700	−	0.967545i	$-0.418681\pi$
$739$	13.7391	0.505400	0.252700	+	0.967545i	$0.418681\pi$
$740$	−53.8975	−1.98131
$741$	−21.7721	−0.799820
$742$	−2.17246	−0.0797536
$743$	−32.7627	−1.20195	−0.600974	−	0.799269i	$-0.705220\pi$
$743$	−32.7627	−1.20195	−0.600974	+	0.799269i	$0.705220\pi$
$744$	13.2726	0.486596
$745$	18.6894	0.684727
$746$	6.25885	0.229153
$747$	6.36278	0.232802
$748$	−7.66574	−0.280287
$749$	17.0930	0.624564
$750$	−7.33364	−0.267787
$751$	25.9225	0.945926	0.472963	−	0.881082i	$-0.343184\pi$
$751$	25.9225	0.945926	0.472963	+	0.881082i	$0.343184\pi$
$752$	3.27490	0.119423
$753$	7.60096	0.276994
$754$	−14.0751	−0.512585
$755$	−36.0948	−1.31363
$756$	11.6444	0.423503
$757$	−2.69491	−0.0979481	−0.0489740	−	0.998800i	$-0.515595\pi$
$757$	−2.69491	−0.0979481	−0.0489740	+	0.998800i	$0.515595\pi$
$758$	−11.5713	−0.420289
$759$	9.84211	0.357246
$760$	11.7072	0.424666
$761$	−15.1422	−0.548903	−0.274452	−	0.961601i	$-0.588496\pi$
$761$	−15.1422	−0.548903	−0.274452	+	0.961601i	$0.588496\pi$
$762$	−3.71078	−0.134427
$763$	18.8964	0.684096
$764$	3.66064	0.132437
$765$	−4.25039	−0.153673
$766$	2.67121	0.0965146
$767$	−50.7372	−1.83202
$768$	−9.58701	−0.345941
$769$	1.64052	0.0591586	0.0295793	−	0.999562i	$-0.490583\pi$
$769$	1.64052	0.0591586	0.0295793	+	0.999562i	$0.490583\pi$
$770$	5.91446	0.213142
$771$	−21.0689	−0.758779
$772$	24.4604	0.880350
$773$	−17.0250	−0.612345	−0.306173	−	0.951976i	$-0.599048\pi$
$773$	−17.0250	−0.612345	−0.306173	+	0.951976i	$0.599048\pi$
$774$	2.14929	0.0772546
$775$	−64.7215	−2.32486
$776$	9.48373	0.340446
$777$	−11.4941	−0.412349
$778$	−7.62235	−0.273275
$779$	−22.2275	−0.796385
$780$	66.8802	2.39470
$781$	43.3121	1.54983
$782$	0.619404	0.0221498
$783$	−32.5457	−1.16309
$784$	−18.9705	−0.677519
$785$	52.7238	1.88179
$786$	9.37265	0.334312
$787$	−45.8670	−1.63498	−0.817491	−	0.575941i	$-0.804636\pi$
$787$	−45.8670	−1.63498	−0.817491	+	0.575941i	$0.804636\pi$
$788$	−17.1153	−0.609709
$789$	1.66529	0.0592861
$790$	−19.3037	−0.686794
$791$	3.37508	0.120004
$792$	6.30236	0.223945
$793$	−45.3729	−1.61124
$794$	3.17350	0.112623
$795$	−28.8519	−1.02327
$796$	25.7493	0.912660
$797$	−17.1032	−0.605828	−0.302914	−	0.953018i	$-0.597960\pi$
$797$	−17.1032	−0.605828	−0.302914	+	0.953018i	$0.597960\pi$
$798$	1.20860	0.0427841
$799$	−1.00000	−0.0353775
$800$	−35.1472	−1.24264
$801$	−12.2359	−0.432334
$802$	−5.19691	−0.183509
$803$	51.4361	1.81514
$804$	0.731820	0.0258093
$805$	7.26837	0.256176
$806$	−17.4217	−0.613653
$807$	−15.1261	−0.532465
$808$	−15.6169	−0.549400
$809$	−23.2884	−0.818776	−0.409388	−	0.912360i	$-0.634258\pi$
$809$	−23.2884	−0.818776	−0.409388	+	0.912360i	$0.634258\pi$
$810$	−5.68901	−0.199891
$811$	35.9939	1.26392	0.631958	−	0.775002i	$-0.282251\pi$
$811$	35.9939	1.26392	0.631958	+	0.775002i	$0.282251\pi$
$812$	−11.8833	−0.417021
$813$	−27.4221	−0.961733
$814$	−10.9854	−0.385038
$815$	74.4137	2.60660
$816$	4.47474	0.156647
$817$	−12.3764	−0.432997
$818$	0.581443	0.0203297
$819$	−8.65563	−0.302452
$820$	68.2792	2.38441
$821$	−36.1459	−1.26150	−0.630750	−	0.775986i	$-0.717253\pi$
$821$	−36.1459	−1.26150	−0.630750	+	0.775986i	$0.717253\pi$
$822$	1.40297	0.0489341
$823$	−16.2421	−0.566162	−0.283081	−	0.959096i	$-0.591357\pi$
$823$	−16.2421	−0.566162	−0.283081	+	0.959096i	$0.591357\pi$
$824$	−2.29351	−0.0798981
$825$	50.6411	1.76310
$826$	2.81650	0.0979986
$827$	−14.7275	−0.512124	−0.256062	−	0.966660i	$-0.582425\pi$
$827$	−14.7275	−0.512124	−0.256062	+	0.966660i	$0.582425\pi$
$828$	3.74927	0.130296
$829$	8.36071	0.290379	0.145190	−	0.989404i	$-0.453621\pi$
$829$	8.36071	0.290379	0.145190	+	0.989404i	$0.453621\pi$
$830$	−7.40018	−0.256864
$831$	−15.1400	−0.525199
$832$	36.0784	1.25079
$833$	5.79271	0.200706
$834$	−8.40682	−0.291104
$835$	−35.3753	−1.22421
$836$	−17.5682	−0.607607
$837$	−40.2840	−1.39242
$838$	−4.25628	−0.147031
$839$	−42.7849	−1.47710	−0.738549	−	0.674200i	$-0.764489\pi$
$839$	−42.7849	−1.47710	−0.738549	+	0.674200i	$0.764489\pi$
$840$	−7.66935	−0.264618
$841$	4.21333	0.145287
$842$	9.52838	0.328370
$843$	−17.1431	−0.590440
$844$	25.6074	0.881443
$845$	−132.579	−4.56086
$846$	0.397989	0.0136831
$847$	−6.24789	−0.214680
$848$	−18.4335	−0.633010
$849$	31.0748	1.06648
$850$	3.18705	0.109315
$851$	−13.5001	−0.462778
$852$	−27.1878	−0.931440
$853$	1.89159	0.0647669	0.0323835	−	0.999476i	$-0.489690\pi$
$853$	1.89159	0.0647669	0.0323835	+	0.999476i	$0.489690\pi$
$854$	2.51872	0.0861888
$855$	−9.74094	−0.333133
$856$	−21.1837	−0.724043
$857$	−28.6632	−0.979116	−0.489558	−	0.871971i	$-0.662842\pi$
$857$	−28.6632	−0.979116	−0.489558	+	0.871971i	$0.662842\pi$
$858$	13.6316	0.465374
$859$	−22.8812	−0.780697	−0.390348	−	0.920667i	$-0.627645\pi$
$859$	−22.8812	−0.780697	−0.390348	+	0.920667i	$0.627645\pi$
$860$	38.0183	1.29641
$861$	14.5611	0.496243
$862$	5.57274	0.189808
$863$	16.2485	0.553104	0.276552	−	0.960999i	$-0.410808\pi$
$863$	16.2485	0.553104	0.276552	+	0.960999i	$0.410808\pi$
$864$	−21.8764	−0.744249
$865$	9.90379	0.336739
$866$	11.4260	0.388270
$867$	−1.36638	−0.0464046
$868$	−14.7087	−0.499247
$869$	59.8397	2.02992
$870$	10.3767	0.351801
$871$	−1.98435	−0.0672370
$872$	−23.4187	−0.793058
$873$	−7.89088	−0.267066
$874$	1.41953	0.0480165
$875$	16.7887	0.567563
$876$	−32.2874	−1.09089
$877$	−4.69255	−0.158456	−0.0792281	−	0.996857i	$-0.525246\pi$
$877$	−4.69255	−0.158456	−0.0792281	+	0.996857i	$0.525246\pi$
$878$	11.7907	0.397918
$879$	−14.6118	−0.492845
$880$	50.1847	1.69173
$881$	37.1621	1.25202	0.626011	−	0.779814i	$-0.284686\pi$
$881$	37.1621	1.25202	0.626011	+	0.779814i	$0.284686\pi$
$882$	−2.30544	−0.0776281
$883$	−26.0233	−0.875755	−0.437877	−	0.899035i	$-0.644270\pi$
$883$	−26.0233	−0.875755	−0.437877	+	0.899035i	$0.644270\pi$
$884$	−13.0477	−0.438841
$885$	37.4053	1.25736
$886$	−2.33468	−0.0784352
$887$	−6.79034	−0.227997	−0.113999	−	0.993481i	$-0.536366\pi$
$887$	−6.79034	−0.227997	−0.113999	+	0.993481i	$0.536366\pi$
$888$	14.2449	0.478027
$889$	8.49499	0.284913
$890$	14.2309	0.477020
$891$	17.6354	0.590809
$892$	−30.0672	−1.00672
$893$	−2.29177	−0.0766913
$894$	−2.39116	−0.0799724
$895$	13.2857	0.444093
$896$	−10.5156	−0.351301
$897$	16.7520	0.559333
$898$	−3.11801	−0.104049
$899$	41.1104	1.37111
$900$	19.2913	0.643044
$901$	5.62873	0.187520
$902$	13.9167	0.463375
$903$	8.10774	0.269809
$904$	−4.18281	−0.139118
$905$	−35.6162	−1.18392
$906$	4.61804	0.153424
$907$	3.85001	0.127838	0.0639188	−	0.997955i	$-0.479640\pi$
$907$	3.85001	0.127838	0.0639188	+	0.997955i	$0.479640\pi$
$908$	18.3421	0.608703
$909$	12.9939	0.430982
$910$	10.0669	0.333713
$911$	−34.2800	−1.13575	−0.567873	−	0.823116i	$-0.692234\pi$
$911$	−34.2800	−1.13575	−0.567873	+	0.823116i	$0.692234\pi$
$912$	10.2551	0.339580
$913$	22.9399	0.759200
$914$	−7.83692	−0.259222
$915$	33.4505	1.10584
$916$	−43.4020	−1.43404
$917$	−21.4566	−0.708559
$918$	1.98369	0.0654715
$919$	−19.7590	−0.651789	−0.325895	−	0.945406i	$-0.605665\pi$
$919$	−19.7590	−0.651789	−0.325895	+	0.945406i	$0.605665\pi$
$920$	−9.00783	−0.296979
$921$	−5.78601	−0.190655
$922$	−13.9442	−0.459226
$923$	73.7205	2.42654
$924$	11.5088	0.378612
$925$	−69.4628	−2.28392
$926$	0.853782	0.0280570
$927$	1.90830	0.0626767
$928$	22.3251	0.732859
$929$	26.4647	0.868279	0.434140	−	0.900846i	$-0.357052\pi$
$929$	26.4647	0.868279	0.434140	+	0.900846i	$0.357052\pi$
$930$	12.8439	0.421168
$931$	13.2756	0.435090
$932$	50.3327	1.64870
$933$	1.19417	0.0390955
$934$	7.85149	0.256909
$935$	−15.3241	−0.501150
$936$	10.7271	0.350626
$937$	48.5212	1.58512	0.792560	−	0.609794i	$-0.208748\pi$
$937$	48.5212	1.58512	0.792560	+	0.609794i	$0.208748\pi$
$938$	0.110154	0.00359666
$939$	−1.62033	−0.0528774
$940$	7.03993	0.229617
$941$	−4.38267	−0.142871	−0.0714355	−	0.997445i	$-0.522758\pi$
$941$	−4.38267	−0.142871	−0.0714355	+	0.997445i	$0.522758\pi$
$942$	−6.74559	−0.219783
$943$	17.1024	0.556931
$944$	23.8982	0.777821
$945$	23.2775	0.757218
$946$	7.74890	0.251938
$947$	−32.2914	−1.04933	−0.524664	−	0.851309i	$-0.675809\pi$
$947$	−32.2914	−1.04933	−0.524664	+	0.851309i	$0.675809\pi$
$948$	−37.5625	−1.21997
$949$	87.5481	2.84193
$950$	7.30400	0.236973
$951$	−44.7174	−1.45006
$952$	1.49621	0.0484926
$953$	−27.7403	−0.898596	−0.449298	−	0.893382i	$-0.648326\pi$
$953$	−27.7403	−0.898596	−0.449298	+	0.893382i	$0.648326\pi$
$954$	−2.24017	−0.0725283
$955$	7.31772	0.236796
$956$	−10.3194	−0.333753
$957$	−32.1667	−1.03980
$958$	4.17583	0.134915
$959$	−3.21178	−0.103714
$960$	−26.5982	−0.858455
$961$	19.8852	0.641457
$962$	−18.6980	−0.602847
$963$	17.6257	0.567982
$964$	−25.2820	−0.814277
$965$	48.8971	1.57405
$966$	−0.929929	−0.0299200
$967$	45.6867	1.46919	0.734593	−	0.678508i	$-0.237373\pi$
$967$	45.6867	1.46919	0.734593	+	0.678508i	$0.237373\pi$
$968$	7.74314	0.248874
$969$	−3.13143	−0.100596
$970$	9.17743	0.294669
$971$	−39.6291	−1.27176	−0.635879	−	0.771789i	$-0.719362\pi$
$971$	−39.6291	−1.27176	−0.635879	+	0.771789i	$0.719362\pi$
$972$	20.7230	0.664691
$973$	19.2455	0.616984
$974$	−5.88753	−0.188649
$975$	86.1950	2.76045
$976$	21.3715	0.684086
$977$	−20.6859	−0.661800	−0.330900	−	0.943666i	$-0.607352\pi$
$977$	−20.6859	−0.661800	−0.330900	+	0.943666i	$0.607352\pi$
$978$	−9.52064	−0.304437
$979$	−44.1144	−1.40990
$980$	−40.7803	−1.30268
$981$	19.4854	0.622121
$982$	8.92197	0.284712
$983$	−2.22311	−0.0709063	−0.0354532	−	0.999371i	$-0.511287\pi$
$983$	−2.22311	−0.0709063	−0.0354532	+	0.999371i	$0.511287\pi$
$984$	−18.0459	−0.575283
$985$	−34.2141	−1.09015
$986$	−2.02438	−0.0644695
$987$	1.50133	0.0477878
$988$	−29.9023	−0.951320
$989$	9.52273	0.302805
$990$	6.09881	0.193833
$991$	−6.32147	−0.200808	−0.100404	−	0.994947i	$-0.532014\pi$
$991$	−6.32147	−0.200808	−0.100404	+	0.994947i	$0.532014\pi$
$992$	27.6333	0.877360
$993$	34.5293	1.09575
$994$	−4.09233	−0.129801
$995$	51.4737	1.63182
$996$	−14.3998	−0.456276
$997$	26.7128	0.846001	0.423001	−	0.906129i	$-0.360977\pi$
$997$	26.7128	0.846001	0.423001	+	0.906129i	$0.360977\pi$
$998$	4.21641	0.133468
$999$	−43.2352	−1.36790

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	799.2.a.g.1.9	✓	20
3.2	odd	2		7191.2.a.bb.1.12		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
799.2.a.g.1.9	✓	20	1.1	even	1	trivial
7191.2.a.bb.1.12		20	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:	\( N \)	\(=\)	\( 799 = 17 \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	799.a (trivial)

\(f(q)\)	\(=\)	\(q-0.351266 q^{2} -1.36638 q^{3} -1.87661 q^{4} -3.75140 q^{5} +0.479962 q^{6} -1.09877 q^{7} +1.36172 q^{8} -1.13301 q^{9} +O(q^{10})\)	\(q-0.351266 q^{2} -1.36638 q^{3} -1.87661 q^{4} -3.75140 q^{5} +0.479962 q^{6} -1.09877 q^{7} +1.36172 q^{8} -1.13301 q^{9} +1.31774 q^{10} -4.08488 q^{11} +2.56416 q^{12} -6.95278 q^{13} +0.385959 q^{14} +5.12583 q^{15} +3.27490 q^{16} -1.00000 q^{17} +0.397989 q^{18} -2.29177 q^{19} +7.03993 q^{20} +1.50133 q^{21} +1.43488 q^{22} +1.76335 q^{23} -1.86063 q^{24} +9.07304 q^{25} +2.44228 q^{26} +5.64726 q^{27} +2.06196 q^{28} -5.76310 q^{29} -1.80053 q^{30} -7.13338 q^{31} -3.87381 q^{32} +5.58149 q^{33} +0.351266 q^{34} +4.12192 q^{35} +2.12623 q^{36} -7.65596 q^{37} +0.805023 q^{38} +9.50013 q^{39} -5.10837 q^{40} +9.69884 q^{41} -0.527366 q^{42} +5.40037 q^{43} +7.66574 q^{44} +4.25039 q^{45} -0.619404 q^{46} +1.00000 q^{47} -4.47474 q^{48} -5.79271 q^{49} -3.18705 q^{50} +1.36638 q^{51} +13.0477 q^{52} -5.62873 q^{53} -1.98369 q^{54} +15.3241 q^{55} -1.49621 q^{56} +3.13143 q^{57} +2.02438 q^{58} +7.29740 q^{59} -9.61920 q^{60} +6.52587 q^{61} +2.50572 q^{62} +1.24492 q^{63} -5.18906 q^{64} +26.0827 q^{65} -1.96059 q^{66} +0.285403 q^{67} +1.87661 q^{68} -2.40940 q^{69} -1.44789 q^{70} -10.6030 q^{71} -1.54285 q^{72} -12.5918 q^{73} +2.68928 q^{74} -12.3972 q^{75} +4.30077 q^{76} +4.48833 q^{77} -3.33707 q^{78} -14.6491 q^{79} -12.2855 q^{80} -4.31724 q^{81} -3.40687 q^{82} -5.61580 q^{83} -2.81741 q^{84} +3.75140 q^{85} -1.89697 q^{86} +7.87457 q^{87} -5.56248 q^{88} +10.7994 q^{89} -1.49302 q^{90} +7.63948 q^{91} -3.30912 q^{92} +9.74690 q^{93} -0.351266 q^{94} +8.59737 q^{95} +5.29308 q^{96} +6.96451 q^{97} +2.03478 q^{98} +4.62823 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{2} + 3 q^{3} + 24 q^{4} + 13 q^{5} + 11 q^{6} - 3 q^{7} + 12 q^{8} + 37 q^{9}+O(q^{10}) \) 20 * q + 4 * q^2 + 3 * q^3 + 24 * q^4 + 13 * q^5 + 11 * q^6 - 3 * q^7 + 12 * q^8 + 37 * q^9	\( 20 q + 4 q^{2} + 3 q^{3} + 24 q^{4} + 13 q^{5} + 11 q^{6} - 3 q^{7} + 12 q^{8} + 37 q^{9} - 2 q^{10} + 10 q^{11} + 8 q^{12} + q^{13} + 13 q^{14} + q^{15} + 28 q^{16} - 20 q^{17} + 15 q^{18} + 5 q^{19} + 37 q^{20} + 6 q^{21} - 19 q^{22} + 4 q^{23} + 30 q^{24} + 41 q^{25} - 9 q^{26} + 6 q^{27} - 25 q^{28} + 26 q^{29} - 25 q^{30} + 6 q^{31} + 28 q^{32} + 29 q^{33} - 4 q^{34} + 21 q^{35} - 5 q^{36} - 8 q^{37} - 21 q^{38} - 19 q^{39} - 25 q^{40} + 69 q^{41} + 3 q^{42} - 7 q^{43} + 16 q^{44} + 39 q^{45} - 24 q^{46} + 20 q^{47} + 26 q^{48} + 53 q^{49} + 16 q^{50} - 3 q^{51} + 18 q^{52} + 29 q^{53} + 23 q^{54} + 5 q^{55} - 22 q^{56} - 36 q^{57} - q^{58} + 55 q^{59} - 103 q^{60} - 17 q^{61} - 7 q^{62} - 9 q^{63} + 58 q^{64} + 40 q^{65} + 50 q^{66} - 6 q^{67} - 24 q^{68} + 17 q^{69} - 15 q^{70} + 47 q^{71} + 7 q^{72} - 32 q^{73} - 67 q^{74} - 22 q^{75} - 5 q^{76} + 4 q^{77} - 60 q^{78} - 26 q^{79} + 108 q^{80} + 68 q^{81} + 25 q^{82} + 3 q^{83} + 24 q^{84} - 13 q^{85} + 8 q^{86} - 41 q^{87} - 47 q^{88} + 119 q^{89} - 54 q^{90} - 35 q^{91} - 15 q^{93} + 4 q^{94} - 48 q^{95} - 84 q^{96} - 13 q^{97} + q^{98} - 5 q^{99}+O(q^{100}) \) 20 * q + 4 * q^2 + 3 * q^3 + 24 * q^4 + 13 * q^5 + 11 * q^6 - 3 * q^7 + 12 * q^8 + 37 * q^9 - 2 * q^10 + 10 * q^11 + 8 * q^12 + q^13 + 13 * q^14 + q^15 + 28 * q^16 - 20 * q^17 + 15 * q^18 + 5 * q^19 + 37 * q^20 + 6 * q^21 - 19 * q^22 + 4 * q^23 + 30 * q^24 + 41 * q^25 - 9 * q^26 + 6 * q^27 - 25 * q^28 + 26 * q^29 - 25 * q^30 + 6 * q^31 + 28 * q^32 + 29 * q^33 - 4 * q^34 + 21 * q^35 - 5 * q^36 - 8 * q^37 - 21 * q^38 - 19 * q^39 - 25 * q^40 + 69 * q^41 + 3 * q^42 - 7 * q^43 + 16 * q^44 + 39 * q^45 - 24 * q^46 + 20 * q^47 + 26 * q^48 + 53 * q^49 + 16 * q^50 - 3 * q^51 + 18 * q^52 + 29 * q^53 + 23 * q^54 + 5 * q^55 - 22 * q^56 - 36 * q^57 - q^58 + 55 * q^59 - 103 * q^60 - 17 * q^61 - 7 * q^62 - 9 * q^63 + 58 * q^64 + 40 * q^65 + 50 * q^66 - 6 * q^67 - 24 * q^68 + 17 * q^69 - 15 * q^70 + 47 * q^71 + 7 * q^72 - 32 * q^73 - 67 * q^74 - 22 * q^75 - 5 * q^76 + 4 * q^77 - 60 * q^78 - 26 * q^79 + 108 * q^80 + 68 * q^81 + 25 * q^82 + 3 * q^83 + 24 * q^84 - 13 * q^85 + 8 * q^86 - 41 * q^87 - 47 * q^88 + 119 * q^89 - 54 * q^90 - 35 * q^91 - 15 * q^93 + 4 * q^94 - 48 * q^95 - 84 * q^96 - 13 * q^97 + q^98 - 5 * q^99

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