LMFDB - Embedded newform 4730.2.a.bc.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4730,2,Mod(1,4730)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4730, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("4730.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4730 = 2 \cdot 5 \cdot 11 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4730.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:	$37.7692401561$
Analytic rank:	$0$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - 24x^{9} - x^{8} + 200x^{7} + 14x^{6} - 653x^{5} - 26x^{4} + 620x^{3} - 177x^{2} - 90x + 32 $ x^11 - 24x^9 - x^8 + 200x^7 + 14x^6 - 653x^5 - 26x^4 + 620x^3 - 177x^2 - 90x + 32
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			$-1.44320$ of defining polynomial
Character	$\chi$	$=$	4730.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.44320 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.44320 q^{6} -0.640387 q^{7} -1.00000 q^{8} -0.917168 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.44320 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.44320 q^{6} -0.640387 q^{7} -1.00000 q^{8} -0.917168 q^{9} +1.00000 q^{10} +1.00000 q^{11} -1.44320 q^{12} +0.757336 q^{13} +0.640387 q^{14} +1.44320 q^{15} +1.00000 q^{16} +7.53708 q^{17} +0.917168 q^{18} +6.81466 q^{19} -1.00000 q^{20} +0.924207 q^{21} -1.00000 q^{22} +2.80832 q^{23} +1.44320 q^{24} +1.00000 q^{25} -0.757336 q^{26} +5.65326 q^{27} -0.640387 q^{28} +3.10812 q^{29} -1.44320 q^{30} -1.80728 q^{31} -1.00000 q^{32} -1.44320 q^{33} -7.53708 q^{34} +0.640387 q^{35} -0.917168 q^{36} -5.83081 q^{37} -6.81466 q^{38} -1.09299 q^{39} +1.00000 q^{40} +3.37580 q^{41} -0.924207 q^{42} -1.00000 q^{43} +1.00000 q^{44} +0.917168 q^{45} -2.80832 q^{46} -12.0482 q^{47} -1.44320 q^{48} -6.58990 q^{49} -1.00000 q^{50} -10.8775 q^{51} +0.757336 q^{52} -11.7280 q^{53} -5.65326 q^{54} -1.00000 q^{55} +0.640387 q^{56} -9.83493 q^{57} -3.10812 q^{58} -1.43484 q^{59} +1.44320 q^{60} -0.646661 q^{61} +1.80728 q^{62} +0.587342 q^{63} +1.00000 q^{64} -0.757336 q^{65} +1.44320 q^{66} +8.17626 q^{67} +7.53708 q^{68} -4.05297 q^{69} -0.640387 q^{70} -11.6054 q^{71} +0.917168 q^{72} +3.72659 q^{73} +5.83081 q^{74} -1.44320 q^{75} +6.81466 q^{76} -0.640387 q^{77} +1.09299 q^{78} +15.2771 q^{79} -1.00000 q^{80} -5.40730 q^{81} -3.37580 q^{82} +0.00506967 q^{83} +0.924207 q^{84} -7.53708 q^{85} +1.00000 q^{86} -4.48564 q^{87} -1.00000 q^{88} +15.7982 q^{89} -0.917168 q^{90} -0.484988 q^{91} +2.80832 q^{92} +2.60827 q^{93} +12.0482 q^{94} -6.81466 q^{95} +1.44320 q^{96} +4.35586 q^{97} +6.58990 q^{98} -0.917168 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q - 11 q^{2} + 11 q^{4} - 11 q^{5} - 11 q^{8} + 15 q^{9}+O(q^{10}) $ 11 * q - 11 * q^2 + 11 * q^4 - 11 * q^5 - 11 * q^8 + 15 * q^9	$ 11 q - 11 q^{2} + 11 q^{4} - 11 q^{5} - 11 q^{8} + 15 q^{9} + 11 q^{10} + 11 q^{11} - q^{13} + 11 q^{16} - 15 q^{17} - 15 q^{18} + 14 q^{19} - 11 q^{20} + 7 q^{21} - 11 q^{22} - 2 q^{23} + 11 q^{25} + q^{26} + 3 q^{27} + 6 q^{29} + 13 q^{31} - 11 q^{32} + 15 q^{34} + 15 q^{36} + 16 q^{37} - 14 q^{38} + 4 q^{39} + 11 q^{40} - 7 q^{41} - 7 q^{42} - 11 q^{43} + 11 q^{44} - 15 q^{45} + 2 q^{46} - 19 q^{47} + 23 q^{49} - 11 q^{50} + 32 q^{51} - q^{52} - 16 q^{53} - 3 q^{54} - 11 q^{55} - 2 q^{57} - 6 q^{58} + 7 q^{59} + 20 q^{61} - 13 q^{62} + 11 q^{64} + q^{65} + 9 q^{67} - 15 q^{68} + 10 q^{69} + 13 q^{71} - 15 q^{72} + 20 q^{73} - 16 q^{74} + 14 q^{76} - 4 q^{78} + 13 q^{79} - 11 q^{80} + 19 q^{81} + 7 q^{82} - 6 q^{83} + 7 q^{84} + 15 q^{85} + 11 q^{86} - 23 q^{87} - 11 q^{88} + 10 q^{89} + 15 q^{90} + 43 q^{91} - 2 q^{92} + 22 q^{93} + 19 q^{94} - 14 q^{95} + 3 q^{97} - 23 q^{98} + 15 q^{99}+O(q^{100}) $ 11 * q - 11 * q^2 + 11 * q^4 - 11 * q^5 - 11 * q^8 + 15 * q^9 + 11 * q^10 + 11 * q^11 - q^13 + 11 * q^16 - 15 * q^17 - 15 * q^18 + 14 * q^19 - 11 * q^20 + 7 * q^21 - 11 * q^22 - 2 * q^23 + 11 * q^25 + q^26 + 3 * q^27 + 6 * q^29 + 13 * q^31 - 11 * q^32 + 15 * q^34 + 15 * q^36 + 16 * q^37 - 14 * q^38 + 4 * q^39 + 11 * q^40 - 7 * q^41 - 7 * q^42 - 11 * q^43 + 11 * q^44 - 15 * q^45 + 2 * q^46 - 19 * q^47 + 23 * q^49 - 11 * q^50 + 32 * q^51 - q^52 - 16 * q^53 - 3 * q^54 - 11 * q^55 - 2 * q^57 - 6 * q^58 + 7 * q^59 + 20 * q^61 - 13 * q^62 + 11 * q^64 + q^65 + 9 * q^67 - 15 * q^68 + 10 * q^69 + 13 * q^71 - 15 * q^72 + 20 * q^73 - 16 * q^74 + 14 * q^76 - 4 * q^78 + 13 * q^79 - 11 * q^80 + 19 * q^81 + 7 * q^82 - 6 * q^83 + 7 * q^84 + 15 * q^85 + 11 * q^86 - 23 * q^87 - 11 * q^88 + 10 * q^89 + 15 * q^90 + 43 * q^91 - 2 * q^92 + 22 * q^93 + 19 * q^94 - 14 * q^95 + 3 * q^97 - 23 * q^98 + 15 * 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
$3$	−1.44320	−0.833233	−0.416617	−	0.909082i	$-0.636784\pi$
$3$	−1.44320	−0.833233	−0.416617	+	0.909082i	$0.636784\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	1.44320	0.589185
$7$	−0.640387	−0.242043	−0.121022	−	0.992650i	$-0.538617\pi$
$7$	−0.640387	−0.242043	−0.121022	+	0.992650i	$0.538617\pi$
$8$	−1.00000	−0.353553
$9$	−0.917168	−0.305723
$10$	1.00000	0.316228
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−1.44320	−0.416617
$13$	0.757336	0.210047	0.105024	−	0.994470i	$-0.466508\pi$
$13$	0.757336	0.210047	0.105024	+	0.994470i	$0.466508\pi$
$14$	0.640387	0.171151
$15$	1.44320	0.372633
$16$	1.00000	0.250000
$17$	7.53708	1.82801	0.914005	−	0.405703i	$-0.132973\pi$
$17$	7.53708	1.82801	0.914005	+	0.405703i	$0.132973\pi$
$18$	0.917168	0.216179
$19$	6.81466	1.56339	0.781695	−	0.623661i	$-0.214356\pi$
$19$	6.81466	1.56339	0.781695	+	0.623661i	$0.214356\pi$
$20$	−1.00000	−0.223607
$21$	0.924207	0.201679
$22$	−1.00000	−0.213201
$23$	2.80832	0.585575	0.292788	−	0.956177i	$-0.405417\pi$
$23$	2.80832	0.585575	0.292788	+	0.956177i	$0.405417\pi$
$24$	1.44320	0.294592
$25$	1.00000	0.200000
$26$	−0.757336	−0.148526
$27$	5.65326	1.08797
$28$	−0.640387	−0.121022
$29$	3.10812	0.577163	0.288581	−	0.957455i	$-0.406816\pi$
$29$	3.10812	0.577163	0.288581	+	0.957455i	$0.406816\pi$
$30$	−1.44320	−0.263491
$31$	−1.80728	−0.324598	−0.162299	−	0.986742i	$-0.551891\pi$
$31$	−1.80728	−0.324598	−0.162299	+	0.986742i	$0.551891\pi$
$32$	−1.00000	−0.176777
$33$	−1.44320	−0.251229
$34$	−7.53708	−1.29260
$35$	0.640387	0.108245
$36$	−0.917168	−0.152861
$37$	−5.83081	−0.958580	−0.479290	−	0.877657i	$-0.659106\pi$
$37$	−5.83081	−0.958580	−0.479290	+	0.877657i	$0.659106\pi$
$38$	−6.81466	−1.10548
$39$	−1.09299	−0.175018
$40$	1.00000	0.158114
$41$	3.37580	0.527211	0.263605	−	0.964631i	$-0.415088\pi$
$41$	3.37580	0.527211	0.263605	+	0.964631i	$0.415088\pi$
$42$	−0.924207	−0.142608
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	1.00000	0.150756
$45$	0.917168	0.136723
$46$	−2.80832	−0.414064
$47$	−12.0482	−1.75741	−0.878703	−	0.477370i	$-0.841590\pi$
$47$	−12.0482	−1.75741	−0.878703	+	0.477370i	$0.841590\pi$
$48$	−1.44320	−0.208308
$49$	−6.58990	−0.941415
$50$	−1.00000	−0.141421
$51$	−10.8775	−1.52316
$52$	0.757336	0.105024
$53$	−11.7280	−1.61097	−0.805485	−	0.592616i	$-0.798095\pi$
$53$	−11.7280	−1.61097	−0.805485	+	0.592616i	$0.798095\pi$
$54$	−5.65326	−0.769312
$55$	−1.00000	−0.134840
$56$	0.640387	0.0855753
$57$	−9.83493	−1.30267
$58$	−3.10812	−0.408116
$59$	−1.43484	−0.186800	−0.0934001	−	0.995629i	$-0.529774\pi$
$59$	−1.43484	−0.186800	−0.0934001	+	0.995629i	$0.529774\pi$
$60$	1.44320	0.186317
$61$	−0.646661	−0.0827964	−0.0413982	−	0.999143i	$-0.513181\pi$
$61$	−0.646661	−0.0827964	−0.0413982	+	0.999143i	$0.513181\pi$
$62$	1.80728	0.229525
$63$	0.587342	0.0739981
$64$	1.00000	0.125000
$65$	−0.757336	−0.0939360
$66$	1.44320	0.177646
$67$	8.17626	0.998889	0.499445	−	0.866346i	$-0.333537\pi$
$67$	8.17626	0.998889	0.499445	+	0.866346i	$0.333537\pi$
$68$	7.53708	0.914005
$69$	−4.05297	−0.487921
$70$	−0.640387	−0.0765408
$71$	−11.6054	−1.37730	−0.688652	−	0.725092i	$-0.741797\pi$
$71$	−11.6054	−1.37730	−0.688652	+	0.725092i	$0.741797\pi$
$72$	0.917168	0.108089
$73$	3.72659	0.436164	0.218082	−	0.975930i	$-0.430020\pi$
$73$	3.72659	0.436164	0.218082	+	0.975930i	$0.430020\pi$
$74$	5.83081	0.677818
$75$	−1.44320	−0.166647
$76$	6.81466	0.781695
$77$	−0.640387	−0.0729788
$78$	1.09299	0.123757
$79$	15.2771	1.71880	0.859402	−	0.511300i	$-0.170836\pi$
$79$	15.2771	1.71880	0.859402	+	0.511300i	$0.170836\pi$
$80$	−1.00000	−0.111803
$81$	−5.40730	−0.600811
$82$	−3.37580	−0.372794
$83$	0.00506967	0.000556468 0	0.000278234	−	1.00000i	$-0.499911\pi$
$83$	0.00506967	0.000556468 0	0.000278234		1.00000i	$0.499911\pi$
$84$	0.924207	0.100839
$85$	−7.53708	−0.817511
$86$	1.00000	0.107833
$87$	−4.48564	−0.480911
$88$	−1.00000	−0.106600
$89$	15.7982	1.67460	0.837301	−	0.546742i	$-0.184132\pi$
$89$	15.7982	1.67460	0.837301	+	0.546742i	$0.184132\pi$
$90$	−0.917168	−0.0966780
$91$	−0.484988	−0.0508405
$92$	2.80832	0.292788
$93$	2.60827	0.270466
$94$	12.0482	1.24267
$95$	−6.81466	−0.699169
$96$	1.44320	0.147296
$97$	4.35586	0.442271	0.221135	−	0.975243i	$-0.429024\pi$
$97$	4.35586	0.442271	0.221135	+	0.975243i	$0.429024\pi$
$98$	6.58990	0.665681
$99$	−0.917168	−0.0921788
$100$	1.00000	0.100000
$101$	8.86033	0.881636	0.440818	−	0.897596i	$-0.354688\pi$
$101$	8.86033	0.881636	0.440818	+	0.897596i	$0.354688\pi$
$102$	10.8775	1.07704
$103$	−14.7671	−1.45505	−0.727524	−	0.686082i	$-0.759329\pi$
$103$	−14.7671	−1.45505	−0.727524	+	0.686082i	$0.759329\pi$
$104$	−0.757336	−0.0742629
$105$	−0.924207	−0.0901934
$106$	11.7280	1.13913
$107$	−17.5871	−1.70021	−0.850105	−	0.526614i	$-0.823461\pi$
$107$	−17.5871	−1.70021	−0.850105	+	0.526614i	$0.823461\pi$
$108$	5.65326	0.543986
$109$	2.85631	0.273585	0.136792	−	0.990600i	$-0.456321\pi$
$109$	2.85631	0.273585	0.136792	+	0.990600i	$0.456321\pi$
$110$	1.00000	0.0953463
$111$	8.41504	0.798721
$112$	−0.640387	−0.0605108
$113$	15.3096	1.44020	0.720101	−	0.693869i	$-0.244095\pi$
$113$	15.3096	1.44020	0.720101	+	0.693869i	$0.244095\pi$
$114$	9.83493	0.921125
$115$	−2.80832	−0.261877
$116$	3.10812	0.288581
$117$	−0.694604	−0.0642162
$118$	1.43484	0.132088
$119$	−4.82665	−0.442458
$120$	−1.44320	−0.131746
$121$	1.00000	0.0909091
$122$	0.646661	0.0585459
$123$	−4.87196	−0.439290
$124$	−1.80728	−0.162299
$125$	−1.00000	−0.0894427
$126$	−0.587342	−0.0523246
$127$	−4.73952	−0.420564	−0.210282	−	0.977641i	$-0.567438\pi$
$127$	−4.73952	−0.420564	−0.210282	+	0.977641i	$0.567438\pi$
$128$	−1.00000	−0.0883883
$129$	1.44320	0.127067
$130$	0.757336	0.0664228
$131$	20.3207	1.77543	0.887715	−	0.460394i	$-0.152292\pi$
$131$	20.3207	1.77543	0.887715	+	0.460394i	$0.152292\pi$
$132$	−1.44320	−0.125615
$133$	−4.36401	−0.378408
$134$	−8.17626	−0.706321
$135$	−5.65326	−0.486556
$136$	−7.53708	−0.646299
$137$	−3.30282	−0.282179	−0.141089	−	0.989997i	$-0.545061\pi$
$137$	−3.30282	−0.282179	−0.141089	+	0.989997i	$0.545061\pi$
$138$	4.05297	0.345012
$139$	6.67522	0.566185	0.283092	−	0.959093i	$-0.408640\pi$
$139$	6.67522	0.566185	0.283092	+	0.959093i	$0.408640\pi$
$140$	0.640387	0.0541225
$141$	17.3879	1.46433
$142$	11.6054	0.973901
$143$	0.757336	0.0633316
$144$	−0.917168	−0.0764306
$145$	−3.10812	−0.258115
$146$	−3.72659	−0.308415
$147$	9.51056	0.784418
$148$	−5.83081	−0.479290
$149$	−10.4860	−0.859046	−0.429523	−	0.903056i	$-0.641318\pi$
$149$	−10.4860	−0.859046	−0.429523	+	0.903056i	$0.641318\pi$
$150$	1.44320	0.117837
$151$	10.2094	0.830827	0.415414	−	0.909633i	$-0.363637\pi$
$151$	10.2094	0.830827	0.415414	+	0.909633i	$0.363637\pi$
$152$	−6.81466	−0.552742
$153$	−6.91277	−0.558864
$154$	0.640387	0.0516038
$155$	1.80728	0.145164
$156$	−1.09299	−0.0875092
$157$	−16.7302	−1.33521	−0.667607	−	0.744514i	$-0.732681\pi$
$157$	−16.7302	−1.33521	−0.667607	+	0.744514i	$0.732681\pi$
$158$	−15.2771	−1.21538
$159$	16.9259	1.34231
$160$	1.00000	0.0790569
$161$	−1.79841	−0.141735
$162$	5.40730	0.424838
$163$	12.3215	0.965093	0.482546	−	0.875870i	$-0.339712\pi$
$163$	12.3215	0.965093	0.482546	+	0.875870i	$0.339712\pi$
$164$	3.37580	0.263605
$165$	1.44320	0.112353
$166$	−0.00506967	−0.000393483 0
$167$	10.3303	0.799382	0.399691	−	0.916650i	$-0.369117\pi$
$167$	10.3303	0.799382	0.399691	+	0.916650i	$0.369117\pi$
$168$	−0.924207	−0.0713041
$169$	−12.4264	−0.955880
$170$	7.53708	0.578068
$171$	−6.25018	−0.477963
$172$	−1.00000	−0.0762493
$173$	13.1316	0.998378	0.499189	−	0.866493i	$-0.333631\pi$
$173$	13.1316	0.998378	0.499189	+	0.866493i	$0.333631\pi$
$174$	4.48564	0.340056
$175$	−0.640387	−0.0484087
$176$	1.00000	0.0753778
$177$	2.07076	0.155648
$178$	−15.7982	−1.18412
$179$	9.38237	0.701272	0.350636	−	0.936512i	$-0.385966\pi$
$179$	9.38237	0.701272	0.350636	+	0.936512i	$0.385966\pi$
$180$	0.917168	0.0683617
$181$	−2.51149	−0.186678	−0.0933389	−	0.995634i	$-0.529754\pi$
$181$	−2.51149	−0.186678	−0.0933389	+	0.995634i	$0.529754\pi$
$182$	0.484988	0.0359497
$183$	0.933262	0.0689887
$184$	−2.80832	−0.207032
$185$	5.83081	0.428690
$186$	−2.60827	−0.191248
$187$	7.53708	0.551166
$188$	−12.0482	−0.878703
$189$	−3.62028	−0.263336
$190$	6.81466	0.494387
$191$	−6.05758	−0.438311	−0.219156	−	0.975690i	$-0.570330\pi$
$191$	−6.05758	−0.438311	−0.219156	+	0.975690i	$0.570330\pi$
$192$	−1.44320	−0.104154
$193$	13.7290	0.988233	0.494117	−	0.869396i	$-0.335492\pi$
$193$	13.7290	0.988233	0.494117	+	0.869396i	$0.335492\pi$
$194$	−4.35586	−0.312733
$195$	1.09299	0.0782706
$196$	−6.58990	−0.470707
$197$	−11.7998	−0.840702	−0.420351	−	0.907362i	$-0.638093\pi$
$197$	−11.7998	−0.840702	−0.420351	+	0.907362i	$0.638093\pi$
$198$	0.917168	0.0651803
$199$	24.8849	1.76404	0.882020	−	0.471211i	$-0.156183\pi$
$199$	24.8849	1.76404	0.882020	+	0.471211i	$0.156183\pi$
$200$	−1.00000	−0.0707107
$201$	−11.8000	−0.832308
$202$	−8.86033	−0.623411
$203$	−1.99040	−0.139698
$204$	−10.8775	−0.761579
$205$	−3.37580	−0.235776
$206$	14.7671	1.02887
$207$	−2.57570	−0.179024
$208$	0.757336	0.0525118
$209$	6.81466	0.471380
$210$	0.924207	0.0637764
$211$	22.6412	1.55868	0.779341	−	0.626600i	$-0.215554\pi$
$211$	22.6412	1.55868	0.779341	+	0.626600i	$0.215554\pi$
$212$	−11.7280	−0.805485
$213$	16.7489	1.14762
$214$	17.5871	1.20223
$215$	1.00000	0.0681994
$216$	−5.65326	−0.384656
$217$	1.15736	0.0785667
$218$	−2.85631	−0.193454
$219$	−5.37822	−0.363427
$220$	−1.00000	−0.0674200
$221$	5.70810	0.383969
$222$	−8.41504	−0.564781
$223$	20.2740	1.35765	0.678824	−	0.734301i	$-0.262490\pi$
$223$	20.2740	1.35765	0.678824	+	0.734301i	$0.262490\pi$
$224$	0.640387	0.0427876
$225$	−0.917168	−0.0611445
$226$	−15.3096	−1.01838
$227$	19.4097	1.28827	0.644133	−	0.764914i	$-0.277218\pi$
$227$	19.4097	1.28827	0.644133	+	0.764914i	$0.277218\pi$
$228$	−9.83493	−0.651334
$229$	−14.8400	−0.980653	−0.490327	−	0.871539i	$-0.663123\pi$
$229$	−14.8400	−0.980653	−0.490327	+	0.871539i	$0.663123\pi$
$230$	2.80832	0.185175
$231$	0.924207	0.0608084
$232$	−3.10812	−0.204058
$233$	−10.6839	−0.699929	−0.349964	−	0.936763i	$-0.613806\pi$
$233$	−10.6839	−0.699929	−0.349964	+	0.936763i	$0.613806\pi$
$234$	0.694604	0.0454077
$235$	12.0482	0.785935
$236$	−1.43484	−0.0934001
$237$	−22.0479	−1.43217
$238$	4.82665	0.312865
$239$	−12.0716	−0.780845	−0.390423	−	0.920636i	$-0.627671\pi$
$239$	−12.0716	−0.780845	−0.390423	+	0.920636i	$0.627671\pi$
$240$	1.44320	0.0931583
$241$	12.6492	0.814809	0.407404	−	0.913248i	$-0.366434\pi$
$241$	12.6492	0.814809	0.407404	+	0.913248i	$0.366434\pi$
$242$	−1.00000	−0.0642824
$243$	−9.15597	−0.587356
$244$	−0.646661	−0.0413982
$245$	6.58990	0.421014
$246$	4.87196	0.310625
$247$	5.16098	0.328386
$248$	1.80728	0.114763
$249$	−0.00731656	−0.000463668 0
$250$	1.00000	0.0632456
$251$	−17.7886	−1.12281	−0.561403	−	0.827542i	$-0.689738\pi$
$251$	−17.7886	−1.12281	−0.561403	+	0.827542i	$0.689738\pi$
$252$	0.587342	0.0369991
$253$	2.80832	0.176558
$254$	4.73952	0.297384
$255$	10.8775	0.681177
$256$	1.00000	0.0625000
$257$	−24.0684	−1.50135	−0.750673	−	0.660673i	$-0.770271\pi$
$257$	−24.0684	−1.50135	−0.750673	+	0.660673i	$0.770271\pi$
$258$	−1.44320	−0.0898498
$259$	3.73398	0.232018
$260$	−0.757336	−0.0469680
$261$	−2.85067	−0.176452
$262$	−20.3207	−1.25542
$263$	−28.3535	−1.74835	−0.874175	−	0.485612i	$-0.838597\pi$
$263$	−28.3535	−1.74835	−0.874175	+	0.485612i	$0.838597\pi$
$264$	1.44320	0.0888229
$265$	11.7280	0.720448
$266$	4.36401	0.267575
$267$	−22.8000	−1.39533
$268$	8.17626	0.499445
$269$	21.5735	1.31536	0.657680	−	0.753298i	$-0.271538\pi$
$269$	21.5735	1.31536	0.657680	+	0.753298i	$0.271538\pi$
$270$	5.65326	0.344047
$271$	3.92309	0.238311	0.119155	−	0.992876i	$-0.461981\pi$
$271$	3.92309	0.238311	0.119155	+	0.992876i	$0.461981\pi$
$272$	7.53708	0.457003
$273$	0.699936	0.0423620
$274$	3.30282	0.199531
$275$	1.00000	0.0603023
$276$	−4.05297	−0.243960
$277$	−24.6418	−1.48058	−0.740290	−	0.672288i	$-0.765312\pi$
$277$	−24.6418	−1.48058	−0.740290	+	0.672288i	$0.765312\pi$
$278$	−6.67522	−0.400353
$279$	1.65758	0.0992368
$280$	−0.640387	−0.0382704
$281$	−0.725679	−0.0432904	−0.0216452	−	0.999766i	$-0.506890\pi$
$281$	−0.725679	−0.0432904	−0.0216452	+	0.999766i	$0.506890\pi$
$282$	−17.3879	−1.03544
$283$	17.8385	1.06039	0.530194	−	0.847876i	$-0.322119\pi$
$283$	17.8385	1.06039	0.530194	+	0.847876i	$0.322119\pi$
$284$	−11.6054	−0.688652
$285$	9.83493	0.582571
$286$	−0.757336	−0.0447822
$287$	−2.16182	−0.127608
$288$	0.917168	0.0540446
$289$	39.8076	2.34162
$290$	3.10812	0.182515
$291$	−6.28639	−0.368515
$292$	3.72659	0.218082
$293$	−5.55780	−0.324690	−0.162345	−	0.986734i	$-0.551906\pi$
$293$	−5.55780	−0.324690	−0.162345	+	0.986734i	$0.551906\pi$
$294$	−9.51056	−0.554667
$295$	1.43484	0.0835396
$296$	5.83081	0.338909
$297$	5.65326	0.328036
$298$	10.4860	0.607437
$299$	2.12684	0.122999
$300$	−1.44320	−0.0833233
$301$	0.640387	0.0369113
$302$	−10.2094	−0.587484
$303$	−12.7873	−0.734608
$304$	6.81466	0.390847
$305$	0.646661	0.0370277
$306$	6.91277	0.395177
$307$	−8.93291	−0.509828	−0.254914	−	0.966964i	$-0.582047\pi$
$307$	−8.93291	−0.509828	−0.254914	+	0.966964i	$0.582047\pi$
$308$	−0.640387	−0.0364894
$309$	21.3120	1.21239
$310$	−1.80728	−0.102647
$311$	−16.9690	−0.962221	−0.481110	−	0.876660i	$-0.659766\pi$
$311$	−16.9690	−0.962221	−0.481110	+	0.876660i	$0.659766\pi$
$312$	1.09299	0.0618783
$313$	24.4856	1.38401	0.692005	−	0.721893i	$-0.256728\pi$
$313$	24.4856	1.38401	0.692005	+	0.721893i	$0.256728\pi$
$314$	16.7302	0.944139
$315$	−0.587342	−0.0330930
$316$	15.2771	0.859402
$317$	−19.5417	−1.09757	−0.548786	−	0.835963i	$-0.684910\pi$
$317$	−19.5417	−1.09757	−0.548786	+	0.835963i	$0.684910\pi$
$318$	−16.9259	−0.949159
$319$	3.10812	0.174021
$320$	−1.00000	−0.0559017
$321$	25.3817	1.41667
$322$	1.79841	0.100222
$323$	51.3626	2.85789
$324$	−5.40730	−0.300406
$325$	0.757336	0.0420094
$326$	−12.3215	−0.682424
$327$	−4.12223	−0.227960
$328$	−3.37580	−0.186397
$329$	7.71548	0.425368
$330$	−1.44320	−0.0794457
$331$	29.6577	1.63013	0.815066	−	0.579368i	$-0.196701\pi$
$331$	29.6577	1.63013	0.815066	+	0.579368i	$0.196701\pi$
$332$	0.00506967	0.000278234 0
$333$	5.34783	0.293060
$334$	−10.3303	−0.565248
$335$	−8.17626	−0.446717
$336$	0.924207	0.0504196
$337$	4.04964	0.220598	0.110299	−	0.993898i	$-0.464819\pi$
$337$	4.04964	0.220598	0.110299	+	0.993898i	$0.464819\pi$
$338$	12.4264	0.675909
$339$	−22.0948	−1.20002
$340$	−7.53708	−0.408756
$341$	−1.80728	−0.0978699
$342$	6.25018	0.337971
$343$	8.70279	0.469907
$344$	1.00000	0.0539164
$345$	4.05297	0.218205
$346$	−13.1316	−0.705960
$347$	22.3133	1.19784	0.598920	−	0.800809i	$-0.295597\pi$
$347$	22.3133	1.19784	0.598920	+	0.800809i	$0.295597\pi$
$348$	−4.48564	−0.240456
$349$	21.9845	1.17680	0.588401	−	0.808569i	$-0.299758\pi$
$349$	21.9845	1.17680	0.588401	+	0.808569i	$0.299758\pi$
$350$	0.640387	0.0342301
$351$	4.28142	0.228525
$352$	−1.00000	−0.0533002
$353$	−15.9880	−0.850958	−0.425479	−	0.904968i	$-0.639894\pi$
$353$	−15.9880	−0.850958	−0.425479	+	0.904968i	$0.639894\pi$
$354$	−2.07076	−0.110060
$355$	11.6054	0.615949
$356$	15.7982	0.837301
$357$	6.96582	0.368671
$358$	−9.38237	−0.495874
$359$	20.8481	1.10032	0.550160	−	0.835059i	$-0.314567\pi$
$359$	20.8481	1.10032	0.550160	+	0.835059i	$0.314567\pi$
$360$	−0.917168	−0.0483390
$361$	27.4395	1.44419
$362$	2.51149	0.132001
$363$	−1.44320	−0.0757485
$364$	−0.484988	−0.0254203
$365$	−3.72659	−0.195059
$366$	−0.933262	−0.0487824
$367$	5.99676	0.313028	0.156514	−	0.987676i	$-0.449974\pi$
$367$	5.99676	0.313028	0.156514	+	0.987676i	$0.449974\pi$
$368$	2.80832	0.146394
$369$	−3.09617	−0.161180
$370$	−5.83081	−0.303130
$371$	7.51048	0.389925
$372$	2.60827	0.135233
$373$	3.78007	0.195725	0.0978623	−	0.995200i	$-0.468800\pi$
$373$	3.78007	0.195725	0.0978623	+	0.995200i	$0.468800\pi$
$374$	−7.53708	−0.389733
$375$	1.44320	0.0745266
$376$	12.0482	0.621337
$377$	2.35389	0.121231
$378$	3.62028	0.186207
$379$	−0.931294	−0.0478374	−0.0239187	−	0.999714i	$-0.507614\pi$
$379$	−0.931294	−0.0478374	−0.0239187	+	0.999714i	$0.507614\pi$
$380$	−6.81466	−0.349584
$381$	6.84008	0.350428
$382$	6.05758	0.309933
$383$	−5.86286	−0.299578	−0.149789	−	0.988718i	$-0.547859\pi$
$383$	−5.86286	−0.299578	−0.149789	+	0.988718i	$0.547859\pi$
$384$	1.44320	0.0736481
$385$	0.640387	0.0326371
$386$	−13.7290	−0.698786
$387$	0.917168	0.0466223
$388$	4.35586	0.221135
$389$	−0.338027	−0.0171386	−0.00856932	−	0.999963i	$-0.502728\pi$
$389$	−0.338027	−0.0171386	−0.00856932	+	0.999963i	$0.502728\pi$
$390$	−1.09299	−0.0553457
$391$	21.1665	1.07044
$392$	6.58990	0.332840
$393$	−29.3269	−1.47935
$394$	11.7998	0.594466
$395$	−15.2771	−0.768673
$396$	−0.917168	−0.0460894
$397$	14.3049	0.717941	0.358971	−	0.933349i	$-0.383128\pi$
$397$	14.3049	0.717941	0.358971	+	0.933349i	$0.383128\pi$
$398$	−24.8849	−1.24737
$399$	6.29815	0.315302
$400$	1.00000	0.0500000
$401$	9.03502	0.451188	0.225594	−	0.974221i	$-0.427568\pi$
$401$	9.03502	0.451188	0.225594	+	0.974221i	$0.427568\pi$
$402$	11.8000	0.588530
$403$	−1.36872	−0.0681808
$404$	8.86033	0.440818
$405$	5.40730	0.268691
$406$	1.99040	0.0987817
$407$	−5.83081	−0.289023
$408$	10.8775	0.538518
$409$	−30.4406	−1.50519	−0.752595	−	0.658483i	$-0.771198\pi$
$409$	−30.4406	−1.50519	−0.752595	+	0.658483i	$0.771198\pi$
$410$	3.37580	0.166719
$411$	4.76663	0.235121
$412$	−14.7671	−0.727524
$413$	0.918852	0.0452138
$414$	2.57570	0.126589
$415$	−0.00506967	−0.000248860 0
$416$	−0.757336	−0.0371315
$417$	−9.63369	−0.471764
$418$	−6.81466	−0.333316
$419$	26.9015	1.31422	0.657112	−	0.753793i	$-0.271778\pi$
$419$	26.9015	1.31422	0.657112	+	0.753793i	$0.271778\pi$
$420$	−0.924207	−0.0450967
$421$	10.2739	0.500719	0.250360	−	0.968153i	$-0.419451\pi$
$421$	10.2739	0.500719	0.250360	+	0.968153i	$0.419451\pi$
$422$	−22.6412	−1.10215
$423$	11.0502	0.537278
$424$	11.7280	0.569564
$425$	7.53708	0.365602
$426$	−16.7489	−0.811487
$427$	0.414113	0.0200403
$428$	−17.5871	−0.850105
$429$	−1.09299	−0.0527700
$430$	−1.00000	−0.0482243
$431$	−10.9691	−0.528365	−0.264183	−	0.964473i	$-0.585102\pi$
$431$	−10.9691	−0.528365	−0.264183	+	0.964473i	$0.585102\pi$
$432$	5.65326	0.271993
$433$	−8.85880	−0.425727	−0.212863	−	0.977082i	$-0.568279\pi$
$433$	−8.85880	−0.425727	−0.212863	+	0.977082i	$0.568279\pi$
$434$	−1.15736	−0.0555551
$435$	4.48564	0.215070
$436$	2.85631	0.136792
$437$	19.1377	0.915482
$438$	5.37822	0.256981
$439$	−1.24109	−0.0592340	−0.0296170	−	0.999561i	$-0.509429\pi$
$439$	−1.24109	−0.0592340	−0.0296170	+	0.999561i	$0.509429\pi$
$440$	1.00000	0.0476731
$441$	6.04405	0.287812
$442$	−5.70810	−0.271507
$443$	−32.3337	−1.53622	−0.768111	−	0.640317i	$-0.778803\pi$
$443$	−32.3337	−1.53622	−0.768111	+	0.640317i	$0.778803\pi$
$444$	8.41504	0.399360
$445$	−15.7982	−0.748905
$446$	−20.2740	−0.960003
$447$	15.1334	0.715785
$448$	−0.640387	−0.0302554
$449$	−31.2931	−1.47681	−0.738406	−	0.674357i	$-0.764421\pi$
$449$	−31.2931	−1.47681	−0.738406	+	0.674357i	$0.764421\pi$
$450$	0.917168	0.0432357
$451$	3.37580	0.158960
$452$	15.3096	0.720101
$453$	−14.7342	−0.692273
$454$	−19.4097	−0.910941
$455$	0.484988	0.0227366
$456$	9.83493	0.460563
$457$	17.9971	0.841871	0.420935	−	0.907091i	$-0.361702\pi$
$457$	17.9971	0.841871	0.420935	+	0.907091i	$0.361702\pi$
$458$	14.8400	0.693427
$459$	42.6091	1.98882
$460$	−2.80832	−0.130939
$461$	−7.84578	−0.365414	−0.182707	−	0.983167i	$-0.558486\pi$
$461$	−7.84578	−0.365414	−0.182707	+	0.983167i	$0.558486\pi$
$462$	−0.924207	−0.0429980
$463$	−7.05415	−0.327834	−0.163917	−	0.986474i	$-0.552413\pi$
$463$	−7.05415	−0.327834	−0.163917	+	0.986474i	$0.552413\pi$
$464$	3.10812	0.144291
$465$	−2.60827	−0.120956
$466$	10.6839	0.494924
$467$	−17.0542	−0.789176	−0.394588	−	0.918858i	$-0.629113\pi$
$467$	−17.0542	−0.789176	−0.394588	+	0.918858i	$0.629113\pi$
$468$	−0.694604	−0.0321081
$469$	−5.23597	−0.241775
$470$	−12.0482	−0.555740
$471$	24.1450	1.11254
$472$	1.43484	0.0660438
$473$	−1.00000	−0.0459800
$474$	22.0479	1.01269
$475$	6.81466	0.312678
$476$	−4.82665	−0.221229
$477$	10.7566	0.492510
$478$	12.0716	0.552141
$479$	31.6526	1.44624	0.723122	−	0.690721i	$-0.242707\pi$
$479$	31.6526	1.44624	0.723122	+	0.690721i	$0.242707\pi$
$480$	−1.44320	−0.0658729
$481$	−4.41589	−0.201347
$482$	−12.6492	−0.576157
$483$	2.59547	0.118098
$484$	1.00000	0.0454545
$485$	−4.35586	−0.197790
$486$	9.15597	0.415323
$487$	22.6360	1.02574	0.512868	−	0.858467i	$-0.328583\pi$
$487$	22.6360	1.02574	0.512868	+	0.858467i	$0.328583\pi$
$488$	0.646661	0.0292730
$489$	−17.7824	−0.804147
$490$	−6.58990	−0.297702
$491$	−21.2169	−0.957506	−0.478753	−	0.877950i	$-0.658911\pi$
$491$	−21.2169	−0.957506	−0.478753	+	0.877950i	$0.658911\pi$
$492$	−4.87196	−0.219645
$493$	23.4261	1.05506
$494$	−5.16098	−0.232204
$495$	0.917168	0.0412236
$496$	−1.80728	−0.0811494
$497$	7.43193	0.333367
$498$	0.00731656	0.000327863 0
$499$	−21.3983	−0.957919	−0.478960	−	0.877837i	$-0.658986\pi$
$499$	−21.3983	−0.957919	−0.478960	+	0.877837i	$0.658986\pi$
$500$	−1.00000	−0.0447214
$501$	−14.9087	−0.666071
$502$	17.7886	0.793944
$503$	24.9458	1.11228	0.556140	−	0.831089i	$-0.312282\pi$
$503$	24.9458	1.11228	0.556140	+	0.831089i	$0.312282\pi$
$504$	−0.587342	−0.0261623
$505$	−8.86033	−0.394280
$506$	−2.80832	−0.124845
$507$	17.9339	0.796471
$508$	−4.73952	−0.210282
$509$	8.53518	0.378315	0.189158	−	0.981947i	$-0.439424\pi$
$509$	8.53518	0.378315	0.189158	+	0.981947i	$0.439424\pi$
$510$	−10.8775	−0.481665
$511$	−2.38646	−0.105571
$512$	−1.00000	−0.0441942
$513$	38.5251	1.70092
$514$	24.0684	1.06161
$515$	14.7671	0.650718
$516$	1.44320	0.0635334
$517$	−12.0482	−0.529878
$518$	−3.73398	−0.164061
$519$	−18.9516	−0.831882
$520$	0.757336	0.0332114
$521$	−1.32716	−0.0581438	−0.0290719	−	0.999577i	$-0.509255\pi$
$521$	−1.32716	−0.0581438	−0.0290719	+	0.999577i	$0.509255\pi$
$522$	2.85067	0.124770
$523$	40.4054	1.76681	0.883403	−	0.468614i	$-0.155246\pi$
$523$	40.4054	1.76681	0.883403	+	0.468614i	$0.155246\pi$
$524$	20.3207	0.887715
$525$	0.924207	0.0403357
$526$	28.3535	1.23627
$527$	−13.6216	−0.593368
$528$	−1.44320	−0.0628073
$529$	−15.1133	−0.657101
$530$	−11.7280	−0.509434
$531$	1.31599	0.0571090
$532$	−4.36401	−0.189204
$533$	2.55661	0.110739
$534$	22.8000	0.986650
$535$	17.5871	0.760357
$536$	−8.17626	−0.353161
$537$	−13.5407	−0.584323
$538$	−21.5735	−0.930099
$539$	−6.58990	−0.283847
$540$	−5.65326	−0.243278
$541$	−23.2088	−0.997824	−0.498912	−	0.866653i	$-0.666267\pi$
$541$	−23.2088	−0.997824	−0.498912	+	0.866653i	$0.666267\pi$
$542$	−3.92309	−0.168511
$543$	3.62459	0.155546
$544$	−7.53708	−0.323150
$545$	−2.85631	−0.122351
$546$	−0.699936	−0.0299545
$547$	−9.22425	−0.394400	−0.197200	−	0.980363i	$-0.563185\pi$
$547$	−9.22425	−0.394400	−0.197200	+	0.980363i	$0.563185\pi$
$548$	−3.30282	−0.141089
$549$	0.593096	0.0253127
$550$	−1.00000	−0.0426401
$551$	21.1808	0.902330
$552$	4.05297	0.172506
$553$	−9.78323	−0.416025
$554$	24.6418	1.04693
$555$	−8.41504	−0.357199
$556$	6.67522	0.283092
$557$	14.3652	0.608672	0.304336	−	0.952565i	$-0.401565\pi$
$557$	14.3652	0.608672	0.304336	+	0.952565i	$0.401565\pi$
$558$	−1.65758	−0.0701710
$559$	−0.757336	−0.0320319
$560$	0.640387	0.0270613
$561$	−10.8775	−0.459250
$562$	0.725679	0.0306109
$563$	6.92950	0.292043	0.146022	−	0.989281i	$-0.453353\pi$
$563$	6.92950	0.292043	0.146022	+	0.989281i	$0.453353\pi$
$564$	17.3879	0.732164
$565$	−15.3096	−0.644078
$566$	−17.8385	−0.749808
$567$	3.46276	0.145422
$568$	11.6054	0.486951
$569$	−36.8541	−1.54500	−0.772501	−	0.635013i	$-0.780995\pi$
$569$	−36.8541	−1.54500	−0.772501	+	0.635013i	$0.780995\pi$
$570$	−9.83493	−0.411940
$571$	46.1749	1.93236	0.966179	−	0.257872i	$-0.0830214\pi$
$571$	46.1749	1.93236	0.966179	+	0.257872i	$0.0830214\pi$
$572$	0.757336	0.0316658
$573$	8.74231	0.365215
$574$	2.16182	0.0902324
$575$	2.80832	0.117115
$576$	−0.917168	−0.0382153
$577$	12.7826	0.532148	0.266074	−	0.963953i	$-0.414273\pi$
$577$	12.7826	0.532148	0.266074	+	0.963953i	$0.414273\pi$
$578$	−39.8076	−1.65578
$579$	−19.8137	−0.823429
$580$	−3.10812	−0.129058
$581$	−0.00324655	−0.000134689 0
$582$	6.28639	0.260579
$583$	−11.7280	−0.485726
$584$	−3.72659	−0.154207
$585$	0.694604	0.0287184
$586$	5.55780	0.229590
$587$	37.5826	1.55120	0.775601	−	0.631224i	$-0.217447\pi$
$587$	37.5826	1.55120	0.775601	+	0.631224i	$0.217447\pi$
$588$	9.51056	0.392209
$589$	−12.3160	−0.507472
$590$	−1.43484	−0.0590714
$591$	17.0295	0.700500
$592$	−5.83081	−0.239645
$593$	35.1718	1.44433	0.722166	−	0.691719i	$-0.243146\pi$
$593$	35.1718	1.44433	0.722166	+	0.691719i	$0.243146\pi$
$594$	−5.65326	−0.231956
$595$	4.82665	0.197873
$596$	−10.4860	−0.429523
$597$	−35.9139	−1.46986
$598$	−2.12684	−0.0869731
$599$	31.2440	1.27660	0.638298	−	0.769789i	$-0.279639\pi$
$599$	31.2440	1.27660	0.638298	+	0.769789i	$0.279639\pi$
$600$	1.44320	0.0589185
$601$	−15.0389	−0.613449	−0.306724	−	0.951798i	$-0.599233\pi$
$601$	−15.0389	−0.613449	−0.306724	+	0.951798i	$0.599233\pi$
$602$	−0.640387	−0.0261002
$603$	−7.49900	−0.305383
$604$	10.2094	0.415414
$605$	−1.00000	−0.0406558
$606$	12.7873	0.519447
$607$	−40.1452	−1.62944	−0.814721	−	0.579853i	$-0.803110\pi$
$607$	−40.1452	−1.62944	−0.814721	+	0.579853i	$0.803110\pi$
$608$	−6.81466	−0.276371
$609$	2.87255	0.116401
$610$	−0.646661	−0.0261825
$611$	−9.12451	−0.369138
$612$	−6.91277	−0.279432
$613$	26.9584	1.08884	0.544419	−	0.838813i	$-0.316750\pi$
$613$	26.9584	1.08884	0.544419	+	0.838813i	$0.316750\pi$
$614$	8.93291	0.360503
$615$	4.87196	0.196456
$616$	0.640387	0.0258019
$617$	27.3827	1.10239	0.551193	−	0.834378i	$-0.314173\pi$
$617$	27.3827	1.10239	0.551193	+	0.834378i	$0.314173\pi$
$618$	−21.3120	−0.857293
$619$	−17.3707	−0.698187	−0.349093	−	0.937088i	$-0.613510\pi$
$619$	−17.3707	−0.698187	−0.349093	+	0.937088i	$0.613510\pi$
$620$	1.80728	0.0725822
$621$	15.8762	0.637089
$622$	16.9690	0.680393
$623$	−10.1169	−0.405327
$624$	−1.09299	−0.0437546
$625$	1.00000	0.0400000
$626$	−24.4856	−0.978643
$627$	−9.83493	−0.392769
$628$	−16.7302	−0.667607
$629$	−43.9473	−1.75229
$630$	0.587342	0.0234003
$631$	21.2857	0.847372	0.423686	−	0.905809i	$-0.360736\pi$
$631$	21.2857	0.847372	0.423686	+	0.905809i	$0.360736\pi$
$632$	−15.2771	−0.607689
$633$	−32.6758	−1.29875
$634$	19.5417	0.776101
$635$	4.73952	0.188082
$636$	16.9259	0.671157
$637$	−4.99077	−0.197742
$638$	−3.10812	−0.123052
$639$	10.6441	0.421073
$640$	1.00000	0.0395285
$641$	19.1677	0.757079	0.378540	−	0.925585i	$-0.376426\pi$
$641$	19.1677	0.757079	0.378540	+	0.925585i	$0.376426\pi$
$642$	−25.3817	−1.00174
$643$	−6.74986	−0.266189	−0.133094	−	0.991103i	$-0.542491\pi$
$643$	−6.74986	−0.266189	−0.133094	+	0.991103i	$0.542491\pi$
$644$	−1.79841	−0.0708673
$645$	−1.44320	−0.0568260
$646$	−51.3626	−2.02083
$647$	−25.2383	−0.992222	−0.496111	−	0.868259i	$-0.665239\pi$
$647$	−25.2383	−0.992222	−0.496111	+	0.868259i	$0.665239\pi$
$648$	5.40730	0.212419
$649$	−1.43484	−0.0563224
$650$	−0.757336	−0.0297052
$651$	−1.67030	−0.0654644
$652$	12.3215	0.482546
$653$	−14.7292	−0.576398	−0.288199	−	0.957570i	$-0.593057\pi$
$653$	−14.7292	−0.576398	−0.288199	+	0.957570i	$0.593057\pi$
$654$	4.12223	0.161192
$655$	−20.3207	−0.793996
$656$	3.37580	0.131803
$657$	−3.41791	−0.133345
$658$	−7.71548	−0.300781
$659$	0.715355	0.0278663	0.0139331	−	0.999903i	$-0.495565\pi$
$659$	0.715355	0.0278663	0.0139331	+	0.999903i	$0.495565\pi$
$660$	1.44320	0.0561766
$661$	−23.3345	−0.907606	−0.453803	−	0.891102i	$-0.649933\pi$
$661$	−23.3345	−0.907606	−0.453803	+	0.891102i	$0.649933\pi$
$662$	−29.6577	−1.15268
$663$	−8.23795	−0.319935
$664$	−0.00506967	−0.000196741 0
$665$	4.36401	0.169229
$666$	−5.34783	−0.207224
$667$	8.72859	0.337972
$668$	10.3303	0.399691
$669$	−29.2595	−1.13124
$670$	8.17626	0.315877
$671$	−0.646661	−0.0249641
$672$	−0.924207	−0.0356521
$673$	2.60359	0.100361	0.0501806	−	0.998740i	$-0.484020\pi$
$673$	2.60359	0.100361	0.0501806	+	0.998740i	$0.484020\pi$
$674$	−4.04964	−0.155986
$675$	5.65326	0.217594
$676$	−12.4264	−0.477940
$677$	−45.1052	−1.73353	−0.866767	−	0.498713i	$-0.833806\pi$
$677$	−45.1052	−1.73353	−0.866767	+	0.498713i	$0.833806\pi$
$678$	22.0948	0.848545
$679$	−2.78944	−0.107049
$680$	7.53708	0.289034
$681$	−28.0121	−1.07343
$682$	1.80728	0.0692045
$683$	6.13504	0.234751	0.117375	−	0.993088i	$-0.462552\pi$
$683$	6.13504	0.234751	0.117375	+	0.993088i	$0.462552\pi$
$684$	−6.25018	−0.238982
$685$	3.30282	0.126194
$686$	−8.70279	−0.332274
$687$	21.4171	0.817113
$688$	−1.00000	−0.0381246
$689$	−8.88207	−0.338380
$690$	−4.05297	−0.154294
$691$	−16.4123	−0.624352	−0.312176	−	0.950024i	$-0.601058\pi$
$691$	−16.4123	−0.624352	−0.312176	+	0.950024i	$0.601058\pi$
$692$	13.1316	0.499189
$693$	0.587342	0.0223113
$694$	−22.3133	−0.847001
$695$	−6.67522	−0.253206
$696$	4.48564	0.170028
$697$	25.4437	0.963747
$698$	−21.9845	−0.832125
$699$	15.4191	0.583204
$700$	−0.640387	−0.0242043
$701$	27.8252	1.05094	0.525472	−	0.850811i	$-0.323889\pi$
$701$	27.8252	1.05094	0.525472	+	0.850811i	$0.323889\pi$
$702$	−4.28142	−0.161592
$703$	−39.7350	−1.49863
$704$	1.00000	0.0376889
$705$	−17.3879	−0.654867
$706$	15.9880	0.601718
$707$	−5.67404	−0.213394
$708$	2.07076	0.0778241
$709$	5.19004	0.194916	0.0974581	−	0.995240i	$-0.468929\pi$
$709$	5.19004	0.194916	0.0974581	+	0.995240i	$0.468929\pi$
$710$	−11.6054	−0.435542
$711$	−14.0116	−0.525478
$712$	−15.7982	−0.592061
$713$	−5.07543	−0.190076
$714$	−6.96582	−0.260689
$715$	−0.757336	−0.0283228
$716$	9.38237	0.350636
$717$	17.4217	0.650626
$718$	−20.8481	−0.778044
$719$	48.5121	1.80920	0.904599	−	0.426264i	$-0.140170\pi$
$719$	48.5121	1.80920	0.904599	+	0.426264i	$0.140170\pi$
$720$	0.917168	0.0341808
$721$	9.45668	0.352185
$722$	−27.4395	−1.02119
$723$	−18.2554	−0.678925
$724$	−2.51149	−0.0933389
$725$	3.10812	0.115433
$726$	1.44320	0.0535623
$727$	−28.3637	−1.05195	−0.525976	−	0.850499i	$-0.676300\pi$
$727$	−28.3637	−1.05195	−0.525976	+	0.850499i	$0.676300\pi$
$728$	0.484988	0.0179748
$729$	29.4358	1.09022
$730$	3.72659	0.137927
$731$	−7.53708	−0.278769
$732$	0.933262	0.0344944
$733$	29.9172	1.10502	0.552508	−	0.833507i	$-0.313671\pi$
$733$	29.9172	1.10502	0.552508	+	0.833507i	$0.313671\pi$
$734$	−5.99676	−0.221344
$735$	−9.51056	−0.350802
$736$	−2.80832	−0.103516
$737$	8.17626	0.301176
$738$	3.09617	0.113972
$739$	36.2449	1.33329	0.666645	−	0.745375i	$-0.267730\pi$
$739$	36.2449	1.33329	0.666645	+	0.745375i	$0.267730\pi$
$740$	5.83081	0.214345
$741$	−7.44834	−0.273622
$742$	−7.51048	−0.275718
$743$	−27.3195	−1.00225	−0.501127	−	0.865374i	$-0.667081\pi$
$743$	−27.3195	−1.00225	−0.501127	+	0.865374i	$0.667081\pi$
$744$	−2.60827	−0.0956240
$745$	10.4860	0.384177
$746$	−3.78007	−0.138398
$747$	−0.00464974	−0.000170125 0
$748$	7.53708	0.275583
$749$	11.2625	0.411524
$750$	−1.44320	−0.0526983
$751$	−6.67301	−0.243501	−0.121751	−	0.992561i	$-0.538851\pi$
$751$	−6.67301	−0.243501	−0.121751	+	0.992561i	$0.538851\pi$
$752$	−12.0482	−0.439351
$753$	25.6725	0.935560
$754$	−2.35389	−0.0857236
$755$	−10.2094	−0.371557
$756$	−3.62028	−0.131668
$757$	25.9636	0.943663	0.471832	−	0.881689i	$-0.343593\pi$
$757$	25.9636	0.943663	0.471832	+	0.881689i	$0.343593\pi$
$758$	0.931294	0.0338261
$759$	−4.05297	−0.147114
$760$	6.81466	0.247194
$761$	−15.6708	−0.568065	−0.284032	−	0.958815i	$-0.591672\pi$
$761$	−15.6708	−0.568065	−0.284032	+	0.958815i	$0.591672\pi$
$762$	−6.84008	−0.247790
$763$	−1.82914	−0.0662194
$764$	−6.05758	−0.219156
$765$	6.91277	0.249932
$766$	5.86286	0.211834
$767$	−1.08666	−0.0392369
$768$	−1.44320	−0.0520771
$769$	1.35503	0.0488635	0.0244317	−	0.999702i	$-0.492222\pi$
$769$	1.35503	0.0488635	0.0244317	+	0.999702i	$0.492222\pi$
$770$	−0.640387	−0.0230779
$771$	34.7356	1.25097
$772$	13.7290	0.494117
$773$	37.3023	1.34167	0.670835	−	0.741607i	$-0.265936\pi$
$773$	37.3023	1.34167	0.670835	+	0.741607i	$0.265936\pi$
$774$	−0.917168	−0.0329669
$775$	−1.80728	−0.0649195
$776$	−4.35586	−0.156366
$777$	−5.38888	−0.193325
$778$	0.338027	0.0121188
$779$	23.0049	0.824236
$780$	1.09299	0.0391353
$781$	−11.6054	−0.415273
$782$	−21.1665	−0.756914
$783$	17.5710	0.627937
$784$	−6.58990	−0.235354
$785$	16.7302	0.597126
$786$	29.3269	1.04606
$787$	19.2250	0.685296	0.342648	−	0.939464i	$-0.388676\pi$
$787$	19.2250	0.685296	0.342648	+	0.939464i	$0.388676\pi$
$788$	−11.7998	−0.420351
$789$	40.9198	1.45678
$790$	15.2771	0.543534
$791$	−9.80404	−0.348592
$792$	0.917168	0.0325901
$793$	−0.489740	−0.0173912
$794$	−14.3049	−0.507661
$795$	−16.9259	−0.600301
$796$	24.8849	0.882020
$797$	−26.6273	−0.943188	−0.471594	−	0.881816i	$-0.656321\pi$
$797$	−26.6273	−0.943188	−0.471594	+	0.881816i	$0.656321\pi$
$798$	−6.29815	−0.222952
$799$	−90.8080	−3.21255
$800$	−1.00000	−0.0353553
$801$	−14.4896	−0.511964
$802$	−9.03502	−0.319038
$803$	3.72659	0.131509
$804$	−11.8000	−0.416154
$805$	1.79841	0.0633857
$806$	1.36872	0.0482111
$807$	−31.1349	−1.09600
$808$	−8.86033	−0.311705
$809$	−5.14845	−0.181010	−0.0905050	−	0.995896i	$-0.528848\pi$
$809$	−5.14845	−0.181010	−0.0905050	+	0.995896i	$0.528848\pi$
$810$	−5.40730	−0.189993
$811$	24.0757	0.845414	0.422707	−	0.906266i	$-0.361080\pi$
$811$	24.0757	0.845414	0.422707	+	0.906266i	$0.361080\pi$
$812$	−1.99040	−0.0698492
$813$	−5.66182	−0.198569
$814$	5.83081	0.204370
$815$	−12.3215	−0.431603
$816$	−10.8775	−0.380790
$817$	−6.81466	−0.238415
$818$	30.4406	1.06433
$819$	0.444815	0.0155431
$820$	−3.37580	−0.117888
$821$	28.9075	1.00888	0.504439	−	0.863448i	$-0.331699\pi$
$821$	28.9075	1.00888	0.504439	+	0.863448i	$0.331699\pi$
$822$	−4.76663	−0.166255
$823$	−19.2687	−0.671664	−0.335832	−	0.941922i	$-0.609017\pi$
$823$	−19.2687	−0.671664	−0.335832	+	0.941922i	$0.609017\pi$
$824$	14.7671	0.514437
$825$	−1.44320	−0.0502458
$826$	−0.918852	−0.0319710
$827$	24.2252	0.842394	0.421197	−	0.906969i	$-0.361610\pi$
$827$	24.2252	0.842394	0.421197	+	0.906969i	$0.361610\pi$
$828$	−2.57570	−0.0895118
$829$	33.3143	1.15705	0.578526	−	0.815664i	$-0.303628\pi$
$829$	33.3143	1.15705	0.578526	+	0.815664i	$0.303628\pi$
$830$	0.00506967	0.000175971 0
$831$	35.5630	1.23367
$832$	0.757336	0.0262559
$833$	−49.6686	−1.72092
$834$	9.63369	0.333587
$835$	−10.3303	−0.357494
$836$	6.81466	0.235690
$837$	−10.2171	−0.353153
$838$	−26.9015	−0.929297
$839$	−40.4120	−1.39518	−0.697589	−	0.716499i	$-0.745744\pi$
$839$	−40.4120	−1.39518	−0.697589	+	0.716499i	$0.745744\pi$
$840$	0.924207	0.0318882
$841$	−19.3396	−0.666883
$842$	−10.2739	−0.354062
$843$	1.04730	0.0360710
$844$	22.6412	0.779341
$845$	12.4264	0.427483
$846$	−11.0502	−0.379913
$847$	−0.640387	−0.0220039
$848$	−11.7280	−0.402743
$849$	−25.7445	−0.883550
$850$	−7.53708	−0.258520
$851$	−16.3748	−0.561321
$852$	16.7489	0.573808
$853$	50.9769	1.74542	0.872708	−	0.488243i	$-0.162362\pi$
$853$	50.9769	1.74542	0.872708	+	0.488243i	$0.162362\pi$
$854$	−0.414113	−0.0141707
$855$	6.25018	0.213752
$856$	17.5871	0.601115
$857$	15.4274	0.526992	0.263496	−	0.964661i	$-0.415125\pi$
$857$	15.4274	0.526992	0.263496	+	0.964661i	$0.415125\pi$
$858$	1.09299	0.0373140
$859$	46.2666	1.57860	0.789298	−	0.614011i	$-0.210445\pi$
$859$	46.2666	1.57860	0.789298	+	0.614011i	$0.210445\pi$
$860$	1.00000	0.0340997
$861$	3.11994	0.106327
$862$	10.9691	0.373611
$863$	13.3520	0.454506	0.227253	−	0.973836i	$-0.427026\pi$
$863$	13.3520	0.454506	0.227253	+	0.973836i	$0.427026\pi$
$864$	−5.65326	−0.192328
$865$	−13.1316	−0.446488
$866$	8.85880	0.301034
$867$	−57.4504	−1.95112
$868$	1.15736	0.0392834
$869$	15.2771	0.518239
$870$	−4.48564	−0.152078
$871$	6.19218	0.209814
$872$	−2.85631	−0.0967269
$873$	−3.99506	−0.135212
$874$	−19.1377	−0.647344
$875$	0.640387	0.0216490
$876$	−5.37822	−0.181713
$877$	16.3890	0.553416	0.276708	−	0.960954i	$-0.410757\pi$
$877$	16.3890	0.553416	0.276708	+	0.960954i	$0.410757\pi$
$878$	1.24109	0.0418848
$879$	8.02102	0.270542
$880$	−1.00000	−0.0337100
$881$	36.8160	1.24036	0.620182	−	0.784458i	$-0.287059\pi$
$881$	36.8160	1.24036	0.620182	+	0.784458i	$0.287059\pi$
$882$	−6.04405	−0.203514
$883$	56.1087	1.88821	0.944104	−	0.329646i	$-0.106930\pi$
$883$	56.1087	1.88821	0.944104	+	0.329646i	$0.106930\pi$
$884$	5.70810	0.191984
$885$	−2.07076	−0.0696080
$886$	32.3337	1.08627
$887$	−18.4081	−0.618085	−0.309042	−	0.951048i	$-0.600008\pi$
$887$	−18.4081	−0.618085	−0.309042	+	0.951048i	$0.600008\pi$
$888$	−8.41504	−0.282390
$889$	3.03512	0.101795
$890$	15.7982	0.529556
$891$	−5.40730	−0.181151
$892$	20.2740	0.678824
$893$	−82.1041	−2.74751
$894$	−15.1334	−0.506137
$895$	−9.38237	−0.313618
$896$	0.640387	0.0213938
$897$	−3.06946	−0.102486
$898$	31.2931	1.04426
$899$	−5.61725	−0.187346
$900$	−0.917168	−0.0305723
$901$	−88.3952	−2.94487
$902$	−3.37580	−0.112402
$903$	−0.924207	−0.0307557
$904$	−15.3096	−0.509189
$905$	2.51149	0.0834849
$906$	14.7342	0.489511
$907$	−10.0977	−0.335290	−0.167645	−	0.985847i	$-0.553616\pi$
$907$	−10.0977	−0.335290	−0.167645	+	0.985847i	$0.553616\pi$
$908$	19.4097	0.644133
$909$	−8.12641	−0.269536
$910$	−0.484988	−0.0160772
$911$	16.4015	0.543406	0.271703	−	0.962381i	$-0.412413\pi$
$911$	16.4015	0.543406	0.271703	+	0.962381i	$0.412413\pi$
$912$	−9.83493	−0.325667
$913$	0.00506967	0.000167782 0
$914$	−17.9971	−0.595292
$915$	−0.933262	−0.0308527
$916$	−14.8400	−0.490327
$917$	−13.0131	−0.429731
$918$	−42.6091	−1.40631
$919$	30.4650	1.00495	0.502474	−	0.864592i	$-0.332423\pi$
$919$	30.4650	1.00495	0.502474	+	0.864592i	$0.332423\pi$
$920$	2.80832	0.0925876
$921$	12.8920	0.424806
$922$	7.84578	0.258387
$923$	−8.78917	−0.289299
$924$	0.924207	0.0304042
$925$	−5.83081	−0.191716
$926$	7.05415	0.231814
$927$	13.5439	0.444841
$928$	−3.10812	−0.102029
$929$	25.8731	0.848868	0.424434	−	0.905459i	$-0.360473\pi$
$929$	25.8731	0.848868	0.424434	+	0.905459i	$0.360473\pi$
$930$	2.60827	0.0855287
$931$	−44.9079	−1.47180
$932$	−10.6839	−0.349964
$933$	24.4896	0.801754
$934$	17.0542	0.558032
$935$	−7.53708	−0.246489
$936$	0.694604	0.0227039
$937$	−28.0446	−0.916177	−0.458088	−	0.888907i	$-0.651466\pi$
$937$	−28.0446	−0.916177	−0.458088	+	0.888907i	$0.651466\pi$
$938$	5.23597	0.170960
$939$	−35.3377	−1.15320
$940$	12.0482	0.392968
$941$	−56.6372	−1.84632	−0.923159	−	0.384418i	$-0.874402\pi$
$941$	−56.6372	−1.84632	−0.923159	+	0.384418i	$0.874402\pi$
$942$	−24.1450	−0.786688
$943$	9.48032	0.308722
$944$	−1.43484	−0.0467000
$945$	3.62028	0.117768
$946$	1.00000	0.0325128
$947$	−57.0428	−1.85364	−0.926821	−	0.375504i	$-0.877470\pi$
$947$	−57.0428	−1.85364	−0.926821	+	0.375504i	$0.877470\pi$
$948$	−22.0479	−0.716083
$949$	2.82228	0.0916151
$950$	−6.81466	−0.221097
$951$	28.2026	0.914533
$952$	4.82665	0.156432
$953$	13.6225	0.441275	0.220638	−	0.975356i	$-0.429186\pi$
$953$	13.6225	0.441275	0.220638	+	0.975356i	$0.429186\pi$
$954$	−10.7566	−0.348257
$955$	6.05758	0.196019
$956$	−12.0716	−0.390423
$957$	−4.48564	−0.145000
$958$	−31.6526	−1.02265
$959$	2.11508	0.0682995
$960$	1.44320	0.0465791
$961$	−27.7337	−0.894636
$962$	4.41589	0.142374
$963$	16.1303	0.519792
$964$	12.6492	0.407404
$965$	−13.7290	−0.441951
$966$	−2.59547	−0.0835079
$967$	50.2247	1.61512	0.807558	−	0.589788i	$-0.200789\pi$
$967$	50.2247	1.61512	0.807558	+	0.589788i	$0.200789\pi$
$968$	−1.00000	−0.0321412
$969$	−74.1266	−2.38129
$970$	4.35586	0.139858
$971$	8.41979	0.270204	0.135102	−	0.990832i	$-0.456864\pi$
$971$	8.41979	0.270204	0.135102	+	0.990832i	$0.456864\pi$
$972$	−9.15597	−0.293678
$973$	−4.27472	−0.137041
$974$	−22.6360	−0.725305
$975$	−1.09299	−0.0350037
$976$	−0.646661	−0.0206991
$977$	−39.7674	−1.27227	−0.636136	−	0.771577i	$-0.719468\pi$
$977$	−39.7674	−1.27227	−0.636136	+	0.771577i	$0.719468\pi$
$978$	17.7824	0.568618
$979$	15.7982	0.504912
$980$	6.58990	0.210507
$981$	−2.61972	−0.0836411
$982$	21.2169	0.677059
$983$	26.2932	0.838621	0.419311	−	0.907843i	$-0.362272\pi$
$983$	26.2932	0.838621	0.419311	+	0.907843i	$0.362272\pi$
$984$	4.87196	0.155312
$985$	11.7998	0.375973
$986$	−23.4261	−0.746040
$987$	−11.1350	−0.354431
$988$	5.16098	0.164193
$989$	−2.80832	−0.0892994
$990$	−0.917168	−0.0291495
$991$	−16.3528	−0.519464	−0.259732	−	0.965681i	$-0.583634\pi$
$991$	−16.3528	−0.519464	−0.259732	+	0.965681i	$0.583634\pi$
$992$	1.80728	0.0573813
$993$	−42.8020	−1.35828
$994$	−7.43193	−0.235726
$995$	−24.8849	−0.788903
$996$	−0.00731656	−0.000231834 0
$997$	−41.3250	−1.30878	−0.654388	−	0.756159i	$-0.727073\pi$
$997$	−41.3250	−1.30878	−0.654388	+	0.756159i	$0.727073\pi$
$998$	21.3983	0.677351
$999$	−32.9631	−1.04291

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4730.2.a.bc.1.4	✓	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4730.2.a.bc.1.4	✓	11	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4730 = 2 \cdot 5 \cdot 11 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4730.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.44320 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.44320 q^{6} -0.640387 q^{7} -1.00000 q^{8} -0.917168 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.44320 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.44320 q^{6} -0.640387 q^{7} -1.00000 q^{8} -0.917168 q^{9} +1.00000 q^{10} +1.00000 q^{11} -1.44320 q^{12} +0.757336 q^{13} +0.640387 q^{14} +1.44320 q^{15} +1.00000 q^{16} +7.53708 q^{17} +0.917168 q^{18} +6.81466 q^{19} -1.00000 q^{20} +0.924207 q^{21} -1.00000 q^{22} +2.80832 q^{23} +1.44320 q^{24} +1.00000 q^{25} -0.757336 q^{26} +5.65326 q^{27} -0.640387 q^{28} +3.10812 q^{29} -1.44320 q^{30} -1.80728 q^{31} -1.00000 q^{32} -1.44320 q^{33} -7.53708 q^{34} +0.640387 q^{35} -0.917168 q^{36} -5.83081 q^{37} -6.81466 q^{38} -1.09299 q^{39} +1.00000 q^{40} +3.37580 q^{41} -0.924207 q^{42} -1.00000 q^{43} +1.00000 q^{44} +0.917168 q^{45} -2.80832 q^{46} -12.0482 q^{47} -1.44320 q^{48} -6.58990 q^{49} -1.00000 q^{50} -10.8775 q^{51} +0.757336 q^{52} -11.7280 q^{53} -5.65326 q^{54} -1.00000 q^{55} +0.640387 q^{56} -9.83493 q^{57} -3.10812 q^{58} -1.43484 q^{59} +1.44320 q^{60} -0.646661 q^{61} +1.80728 q^{62} +0.587342 q^{63} +1.00000 q^{64} -0.757336 q^{65} +1.44320 q^{66} +8.17626 q^{67} +7.53708 q^{68} -4.05297 q^{69} -0.640387 q^{70} -11.6054 q^{71} +0.917168 q^{72} +3.72659 q^{73} +5.83081 q^{74} -1.44320 q^{75} +6.81466 q^{76} -0.640387 q^{77} +1.09299 q^{78} +15.2771 q^{79} -1.00000 q^{80} -5.40730 q^{81} -3.37580 q^{82} +0.00506967 q^{83} +0.924207 q^{84} -7.53708 q^{85} +1.00000 q^{86} -4.48564 q^{87} -1.00000 q^{88} +15.7982 q^{89} -0.917168 q^{90} -0.484988 q^{91} +2.80832 q^{92} +2.60827 q^{93} +12.0482 q^{94} -6.81466 q^{95} +1.44320 q^{96} +4.35586 q^{97} +6.58990 q^{98} -0.917168 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 11 q^{2} + 11 q^{4} - 11 q^{5} - 11 q^{8} + 15 q^{9}+O(q^{10}) \) 11 * q - 11 * q^2 + 11 * q^4 - 11 * q^5 - 11 * q^8 + 15 * q^9	\( 11 q - 11 q^{2} + 11 q^{4} - 11 q^{5} - 11 q^{8} + 15 q^{9} + 11 q^{10} + 11 q^{11} - q^{13} + 11 q^{16} - 15 q^{17} - 15 q^{18} + 14 q^{19} - 11 q^{20} + 7 q^{21} - 11 q^{22} - 2 q^{23} + 11 q^{25} + q^{26} + 3 q^{27} + 6 q^{29} + 13 q^{31} - 11 q^{32} + 15 q^{34} + 15 q^{36} + 16 q^{37} - 14 q^{38} + 4 q^{39} + 11 q^{40} - 7 q^{41} - 7 q^{42} - 11 q^{43} + 11 q^{44} - 15 q^{45} + 2 q^{46} - 19 q^{47} + 23 q^{49} - 11 q^{50} + 32 q^{51} - q^{52} - 16 q^{53} - 3 q^{54} - 11 q^{55} - 2 q^{57} - 6 q^{58} + 7 q^{59} + 20 q^{61} - 13 q^{62} + 11 q^{64} + q^{65} + 9 q^{67} - 15 q^{68} + 10 q^{69} + 13 q^{71} - 15 q^{72} + 20 q^{73} - 16 q^{74} + 14 q^{76} - 4 q^{78} + 13 q^{79} - 11 q^{80} + 19 q^{81} + 7 q^{82} - 6 q^{83} + 7 q^{84} + 15 q^{85} + 11 q^{86} - 23 q^{87} - 11 q^{88} + 10 q^{89} + 15 q^{90} + 43 q^{91} - 2 q^{92} + 22 q^{93} + 19 q^{94} - 14 q^{95} + 3 q^{97} - 23 q^{98} + 15 q^{99}+O(q^{100}) \) 11 * q - 11 * q^2 + 11 * q^4 - 11 * q^5 - 11 * q^8 + 15 * q^9 + 11 * q^10 + 11 * q^11 - q^13 + 11 * q^16 - 15 * q^17 - 15 * q^18 + 14 * q^19 - 11 * q^20 + 7 * q^21 - 11 * q^22 - 2 * q^23 + 11 * q^25 + q^26 + 3 * q^27 + 6 * q^29 + 13 * q^31 - 11 * q^32 + 15 * q^34 + 15 * q^36 + 16 * q^37 - 14 * q^38 + 4 * q^39 + 11 * q^40 - 7 * q^41 - 7 * q^42 - 11 * q^43 + 11 * q^44 - 15 * q^45 + 2 * q^46 - 19 * q^47 + 23 * q^49 - 11 * q^50 + 32 * q^51 - q^52 - 16 * q^53 - 3 * q^54 - 11 * q^55 - 2 * q^57 - 6 * q^58 + 7 * q^59 + 20 * q^61 - 13 * q^62 + 11 * q^64 + q^65 + 9 * q^67 - 15 * q^68 + 10 * q^69 + 13 * q^71 - 15 * q^72 + 20 * q^73 - 16 * q^74 + 14 * q^76 - 4 * q^78 + 13 * q^79 - 11 * q^80 + 19 * q^81 + 7 * q^82 - 6 * q^83 + 7 * q^84 + 15 * q^85 + 11 * q^86 - 23 * q^87 - 11 * q^88 + 10 * q^89 + 15 * q^90 + 43 * q^91 - 2 * q^92 + 22 * q^93 + 19 * q^94 - 14 * q^95 + 3 * q^97 - 23 * q^98 + 15 * q^99

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