LMFDB - Embedded newform 4730.2.a.z.1.7

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:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} - 17x^{8} + 21x^{7} + 107x^{6} - 45x^{5} - 262x^{4} - 47x^{3} + 120x^{2} - 2x - 6 $ x^10 - 2x^9 - 17x^8 + 21x^7 + 107x^6 - 45x^5 - 262x^4 - 47x^3 + 120x^2 - 2*x - 6
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			1.7
Root			$-1.41316$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +2.41316 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.41316 q^{6} -5.00890 q^{7} -1.00000 q^{8} +2.82333 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +2.41316 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.41316 q^{6} -5.00890 q^{7} -1.00000 q^{8} +2.82333 q^{9} -1.00000 q^{10} +1.00000 q^{11} +2.41316 q^{12} +7.13007 q^{13} +5.00890 q^{14} +2.41316 q^{15} +1.00000 q^{16} -2.68227 q^{17} -2.82333 q^{18} -3.51382 q^{19} +1.00000 q^{20} -12.0873 q^{21} -1.00000 q^{22} +6.05399 q^{23} -2.41316 q^{24} +1.00000 q^{25} -7.13007 q^{26} -0.426321 q^{27} -5.00890 q^{28} -7.74615 q^{29} -2.41316 q^{30} +7.62662 q^{31} -1.00000 q^{32} +2.41316 q^{33} +2.68227 q^{34} -5.00890 q^{35} +2.82333 q^{36} +3.83869 q^{37} +3.51382 q^{38} +17.2060 q^{39} -1.00000 q^{40} +3.90400 q^{41} +12.0873 q^{42} +1.00000 q^{43} +1.00000 q^{44} +2.82333 q^{45} -6.05399 q^{46} -0.876784 q^{47} +2.41316 q^{48} +18.0890 q^{49} -1.00000 q^{50} -6.47274 q^{51} +7.13007 q^{52} -1.81678 q^{53} +0.426321 q^{54} +1.00000 q^{55} +5.00890 q^{56} -8.47940 q^{57} +7.74615 q^{58} +1.02302 q^{59} +2.41316 q^{60} +1.82530 q^{61} -7.62662 q^{62} -14.1418 q^{63} +1.00000 q^{64} +7.13007 q^{65} -2.41316 q^{66} +8.02353 q^{67} -2.68227 q^{68} +14.6092 q^{69} +5.00890 q^{70} +8.89481 q^{71} -2.82333 q^{72} -1.68829 q^{73} -3.83869 q^{74} +2.41316 q^{75} -3.51382 q^{76} -5.00890 q^{77} -17.2060 q^{78} +10.0241 q^{79} +1.00000 q^{80} -9.49878 q^{81} -3.90400 q^{82} +7.73554 q^{83} -12.0873 q^{84} -2.68227 q^{85} -1.00000 q^{86} -18.6927 q^{87} -1.00000 q^{88} -9.35787 q^{89} -2.82333 q^{90} -35.7138 q^{91} +6.05399 q^{92} +18.4042 q^{93} +0.876784 q^{94} -3.51382 q^{95} -2.41316 q^{96} -11.8989 q^{97} -18.0890 q^{98} +2.82333 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 10 q^{2} + 8 q^{3} + 10 q^{4} + 10 q^{5} - 8 q^{6} + 3 q^{7} - 10 q^{8} + 14 q^{9}+O(q^{10}) $ 10 * q - 10 * q^2 + 8 * q^3 + 10 * q^4 + 10 * q^5 - 8 * q^6 + 3 * q^7 - 10 * q^8 + 14 * q^9	\( 10 q - 10 q^{2} + 8 q^{3} + 10 q^{4} + 10 q^{5} - 8 q^{6} + 3 q^{7} - 10 q^{8} + 14 q^{9} - 10 q^{10} + 10 q^{11} + 8 q^{12} + 7 q^{13} - 3 q^{14} + 8 q^{15} + 10 q^{16} + 2 q^{17} - 14 q^{18} - 7 q^{19} + 10 q^{20} - 2 q^{21} - 10 q^{22} + 12 q^{23} - 8 q^{24} + 10 q^{25} - 7 q^{26} + 23 q^{27} + 3 q^{28} - 12 q^{29} - 8 q^{30} + 16 q^{31} - 10 q^{32} + 8 q^{33} - 2 q^{34} + 3 q^{35} + 14 q^{36} + 19 q^{37} + 7 q^{38} + 6 q^{39} - 10 q^{40} + 9 q^{41} + 2 q^{42} + 10 q^{43} + 10 q^{44} + 14 q^{45} - 12 q^{46} + 29 q^{47} + 8 q^{48} + 23 q^{49} - 10 q^{50} - 7 q^{51} + 7 q^{52} + 6 q^{53} - 23 q^{54} + 10 q^{55} - 3 q^{56} + 23 q^{57} + 12 q^{58} + 29 q^{59} + 8 q^{60} - 4 q^{61} - 16 q^{62} + 10 q^{64} + 7 q^{65} - 8 q^{66} + 45 q^{67} + 2 q^{68} + 24 q^{69} - 3 q^{70} - 18 q^{71} - 14 q^{72} + 3 q^{73} - 19 q^{74} + 8 q^{75} - 7 q^{76} + 3 q^{77} - 6 q^{78} - 14 q^{79} + 10 q^{80} + 6 q^{81} - 9 q^{82} + 23 q^{83} - 2 q^{84} + 2 q^{85} - 10 q^{86} + 25 q^{87} - 10 q^{88} + q^{89} - 14 q^{90} + q^{91} + 12 q^{92} + 35 q^{93} - 29 q^{94} - 7 q^{95} - 8 q^{96} + 30 q^{97} - 23 q^{98} + 14 q^{99}+O(q^{100}) \) 10 * q - 10 * q^2 + 8 * q^3 + 10 * q^4 + 10 * q^5 - 8 * q^6 + 3 * q^7 - 10 * q^8 + 14 * q^9 - 10 * q^10 + 10 * q^11 + 8 * q^12 + 7 * q^13 - 3 * q^14 + 8 * q^15 + 10 * q^16 + 2 * q^17 - 14 * q^18 - 7 * q^19 + 10 * q^20 - 2 * q^21 - 10 * q^22 + 12 * q^23 - 8 * q^24 + 10 * q^25 - 7 * q^26 + 23 * q^27 + 3 * q^28 - 12 * q^29 - 8 * q^30 + 16 * q^31 - 10 * q^32 + 8 * q^33 - 2 * q^34 + 3 * q^35 + 14 * q^36 + 19 * q^37 + 7 * q^38 + 6 * q^39 - 10 * q^40 + 9 * q^41 + 2 * q^42 + 10 * q^43 + 10 * q^44 + 14 * q^45 - 12 * q^46 + 29 * q^47 + 8 * q^48 + 23 * q^49 - 10 * q^50 - 7 * q^51 + 7 * q^52 + 6 * q^53 - 23 * q^54 + 10 * q^55 - 3 * q^56 + 23 * q^57 + 12 * q^58 + 29 * q^59 + 8 * q^60 - 4 * q^61 - 16 * q^62 + 10 * q^64 + 7 * q^65 - 8 * q^66 + 45 * q^67 + 2 * q^68 + 24 * q^69 - 3 * q^70 - 18 * q^71 - 14 * q^72 + 3 * q^73 - 19 * q^74 + 8 * q^75 - 7 * q^76 + 3 * q^77 - 6 * q^78 - 14 * q^79 + 10 * q^80 + 6 * q^81 - 9 * q^82 + 23 * q^83 - 2 * q^84 + 2 * q^85 - 10 * q^86 + 25 * q^87 - 10 * q^88 + q^89 - 14 * q^90 + q^91 + 12 * q^92 + 35 * q^93 - 29 * q^94 - 7 * q^95 - 8 * q^96 + 30 * q^97 - 23 * q^98 + 14 * 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
$3$	2.41316	1.39324	0.696619	−	0.717441i	$-0.254687\pi$
$3$	2.41316	1.39324	0.696619	+	0.717441i	$0.254687\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−2.41316	−0.985168
$7$	−5.00890	−1.89319	−0.946593	−	0.322432i	$-0.895500\pi$
$7$	−5.00890	−1.89319	−0.946593	+	0.322432i	$0.895500\pi$
$8$	−1.00000	−0.353553
$9$	2.82333	0.941112
$10$	−1.00000	−0.316228
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	2.41316	0.696619
$13$	7.13007	1.97752	0.988762	−	0.149495i	$-0.0477648\pi$
$13$	7.13007	1.97752	0.988762	+	0.149495i	$0.0477648\pi$
$14$	5.00890	1.33868
$15$	2.41316	0.623075
$16$	1.00000	0.250000
$17$	−2.68227	−0.650546	−0.325273	−	0.945620i	$-0.605456\pi$
$17$	−2.68227	−0.650546	−0.325273	+	0.945620i	$0.605456\pi$
$18$	−2.82333	−0.665466
$19$	−3.51382	−0.806125	−0.403063	−	0.915172i	$-0.632054\pi$
$19$	−3.51382	−0.806125	−0.403063	+	0.915172i	$0.632054\pi$
$20$	1.00000	0.223607
$21$	−12.0873	−2.63766
$22$	−1.00000	−0.213201
$23$	6.05399	1.26234	0.631172	−	0.775643i	$-0.282574\pi$
$23$	6.05399	1.26234	0.631172	+	0.775643i	$0.282574\pi$
$24$	−2.41316	−0.492584
$25$	1.00000	0.200000
$26$	−7.13007	−1.39832
$27$	−0.426321	−0.0820455
$28$	−5.00890	−0.946593
$29$	−7.74615	−1.43842	−0.719212	−	0.694790i	$-0.755497\pi$
$29$	−7.74615	−1.43842	−0.719212	+	0.694790i	$0.755497\pi$
$30$	−2.41316	−0.440580
$31$	7.62662	1.36978	0.684891	−	0.728646i	$-0.259850\pi$
$31$	7.62662	1.36978	0.684891	+	0.728646i	$0.259850\pi$
$32$	−1.00000	−0.176777
$33$	2.41316	0.420077
$34$	2.68227	0.460005
$35$	−5.00890	−0.846658
$36$	2.82333	0.470556
$37$	3.83869	0.631076	0.315538	−	0.948913i	$-0.397815\pi$
$37$	3.83869	0.631076	0.315538	+	0.948913i	$0.397815\pi$
$38$	3.51382	0.570017
$39$	17.2060	2.75516
$40$	−1.00000	−0.158114
$41$	3.90400	0.609703	0.304851	−	0.952400i	$-0.401393\pi$
$41$	3.90400	0.609703	0.304851	+	0.952400i	$0.401393\pi$
$42$	12.0873	1.86511
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	1.00000	0.150756
$45$	2.82333	0.420878
$46$	−6.05399	−0.892612
$47$	−0.876784	−0.127892	−0.0639461	−	0.997953i	$-0.520369\pi$
$47$	−0.876784	−0.127892	−0.0639461	+	0.997953i	$0.520369\pi$
$48$	2.41316	0.348309
$49$	18.0890	2.58415
$50$	−1.00000	−0.141421
$51$	−6.47274	−0.906365
$52$	7.13007	0.988762
$53$	−1.81678	−0.249553	−0.124777	−	0.992185i	$-0.539821\pi$
$53$	−1.81678	−0.249553	−0.124777	+	0.992185i	$0.539821\pi$
$54$	0.426321	0.0580149
$55$	1.00000	0.134840
$56$	5.00890	0.669342
$57$	−8.47940	−1.12312
$58$	7.74615	1.01712
$59$	1.02302	0.133186	0.0665932	−	0.997780i	$-0.478787\pi$
$59$	1.02302	0.133186	0.0665932	+	0.997780i	$0.478787\pi$
$60$	2.41316	0.311537
$61$	1.82530	0.233706	0.116853	−	0.993149i	$-0.462719\pi$
$61$	1.82530	0.233706	0.116853	+	0.993149i	$0.462719\pi$
$62$	−7.62662	−0.968582
$63$	−14.1418	−1.78170
$64$	1.00000	0.125000
$65$	7.13007	0.884376
$66$	−2.41316	−0.297039
$67$	8.02353	0.980231	0.490115	−	0.871658i	$-0.336955\pi$
$67$	8.02353	0.980231	0.490115	+	0.871658i	$0.336955\pi$
$68$	−2.68227	−0.325273
$69$	14.6092	1.75875
$70$	5.00890	0.598678
$71$	8.89481	1.05562	0.527810	−	0.849363i	$-0.323013\pi$
$71$	8.89481	1.05562	0.527810	+	0.849363i	$0.323013\pi$
$72$	−2.82333	−0.332733
$73$	−1.68829	−0.197600	−0.0988000	−	0.995107i	$-0.531500\pi$
$73$	−1.68829	−0.197600	−0.0988000	+	0.995107i	$0.531500\pi$
$74$	−3.83869	−0.446238
$75$	2.41316	0.278648
$76$	−3.51382	−0.403063
$77$	−5.00890	−0.570817
$78$	−17.2060	−1.94819
$79$	10.0241	1.12780	0.563902	−	0.825842i	$-0.309300\pi$
$79$	10.0241	1.12780	0.563902	+	0.825842i	$0.309300\pi$
$80$	1.00000	0.111803
$81$	−9.49878	−1.05542
$82$	−3.90400	−0.431125
$83$	7.73554	0.849086	0.424543	−	0.905408i	$-0.360435\pi$
$83$	7.73554	0.849086	0.424543	+	0.905408i	$0.360435\pi$
$84$	−12.0873	−1.31883
$85$	−2.68227	−0.290933
$86$	−1.00000	−0.107833
$87$	−18.6927	−2.00407
$88$	−1.00000	−0.106600
$89$	−9.35787	−0.991932	−0.495966	−	0.868342i	$-0.665186\pi$
$89$	−9.35787	−0.991932	−0.495966	+	0.868342i	$0.665186\pi$
$90$	−2.82333	−0.297606
$91$	−35.7138	−3.74382
$92$	6.05399	0.631172
$93$	18.4042	1.90843
$94$	0.876784	0.0904334
$95$	−3.51382	−0.360510
$96$	−2.41316	−0.246292
$97$	−11.8989	−1.20815	−0.604076	−	0.796926i	$-0.706458\pi$
$97$	−11.8989	−1.20815	−0.604076	+	0.796926i	$0.706458\pi$
$98$	−18.0890	−1.82727
$99$	2.82333	0.283756
$100$	1.00000	0.100000
$101$	11.1320	1.10767	0.553836	−	0.832626i	$-0.313164\pi$
$101$	11.1320	1.10767	0.553836	+	0.832626i	$0.313164\pi$
$102$	6.47274	0.640897
$103$	−8.64427	−0.851745	−0.425872	−	0.904783i	$-0.640033\pi$
$103$	−8.64427	−0.851745	−0.425872	+	0.904783i	$0.640033\pi$
$104$	−7.13007	−0.699161
$105$	−12.0873	−1.17960
$106$	1.81678	0.176461
$107$	15.4780	1.49631	0.748155	−	0.663523i	$-0.230940\pi$
$107$	15.4780	1.49631	0.748155	+	0.663523i	$0.230940\pi$
$108$	−0.426321	−0.0410228
$109$	5.43714	0.520784	0.260392	−	0.965503i	$-0.416148\pi$
$109$	5.43714	0.520784	0.260392	+	0.965503i	$0.416148\pi$
$110$	−1.00000	−0.0953463
$111$	9.26336	0.879239
$112$	−5.00890	−0.473296
$113$	6.86930	0.646210	0.323105	−	0.946363i	$-0.395273\pi$
$113$	6.86930	0.646210	0.323105	+	0.946363i	$0.395273\pi$
$114$	8.47940	0.794169
$115$	6.05399	0.564537
$116$	−7.74615	−0.719212
$117$	20.1306	1.86107
$118$	−1.02302	−0.0941770
$119$	13.4352	1.23160
$120$	−2.41316	−0.220290
$121$	1.00000	0.0909091
$122$	−1.82530	−0.165255
$123$	9.42097	0.849461
$124$	7.62662	0.684891
$125$	1.00000	0.0894427
$126$	14.1418	1.25985
$127$	1.54738	0.137308	0.0686540	−	0.997641i	$-0.478130\pi$
$127$	1.54738	0.137308	0.0686540	+	0.997641i	$0.478130\pi$
$128$	−1.00000	−0.0883883
$129$	2.41316	0.212467
$130$	−7.13007	−0.625348
$131$	−14.1171	−1.23341	−0.616706	−	0.787193i	$-0.711533\pi$
$131$	−14.1171	−1.23341	−0.616706	+	0.787193i	$0.711533\pi$
$132$	2.41316	0.210039
$133$	17.6004	1.52614
$134$	−8.02353	−0.693128
$135$	−0.426321	−0.0366919
$136$	2.68227	0.230003
$137$	3.23436	0.276330	0.138165	−	0.990409i	$-0.455880\pi$
$137$	3.23436	0.276330	0.138165	+	0.990409i	$0.455880\pi$
$138$	−14.6092	−1.24362
$139$	−4.86705	−0.412818	−0.206409	−	0.978466i	$-0.566178\pi$
$139$	−4.86705	−0.412818	−0.206409	+	0.978466i	$0.566178\pi$
$140$	−5.00890	−0.423329
$141$	−2.11582	−0.178184
$142$	−8.89481	−0.746436
$143$	7.13007	0.596246
$144$	2.82333	0.235278
$145$	−7.74615	−0.643283
$146$	1.68829	0.139724
$147$	43.6517	3.60034
$148$	3.83869	0.315538
$149$	8.90513	0.729537	0.364768	−	0.931098i	$-0.381148\pi$
$149$	8.90513	0.729537	0.364768	+	0.931098i	$0.381148\pi$
$150$	−2.41316	−0.197034
$151$	−13.8455	−1.12673	−0.563364	−	0.826209i	$-0.690493\pi$
$151$	−13.8455	−1.12673	−0.563364	+	0.826209i	$0.690493\pi$
$152$	3.51382	0.285008
$153$	−7.57294	−0.612236
$154$	5.00890	0.403628
$155$	7.62662	0.612585
$156$	17.2060	1.37758
$157$	−1.35382	−0.108047	−0.0540234	−	0.998540i	$-0.517205\pi$
$157$	−1.35382	−0.108047	−0.0540234	+	0.998540i	$0.517205\pi$
$158$	−10.0241	−0.797477
$159$	−4.38417	−0.347687
$160$	−1.00000	−0.0790569
$161$	−30.3238	−2.38985
$162$	9.49878	0.746295
$163$	14.2012	1.11232	0.556161	−	0.831074i	$-0.312274\pi$
$163$	14.2012	1.11232	0.556161	+	0.831074i	$0.312274\pi$
$164$	3.90400	0.304851
$165$	2.41316	0.187864
$166$	−7.73554	−0.600395
$167$	17.1331	1.32580	0.662898	−	0.748709i	$-0.269326\pi$
$167$	17.1331	1.32580	0.662898	+	0.748709i	$0.269326\pi$
$168$	12.0873	0.932553
$169$	37.8379	2.91061
$170$	2.68227	0.205721
$171$	−9.92068	−0.758654
$172$	1.00000	0.0762493
$173$	−7.33843	−0.557930	−0.278965	−	0.960301i	$-0.589991\pi$
$173$	−7.33843	−0.557930	−0.278965	+	0.960301i	$0.589991\pi$
$174$	18.6927	1.41709
$175$	−5.00890	−0.378637
$176$	1.00000	0.0753778
$177$	2.46872	0.185560
$178$	9.35787	0.701402
$179$	20.5062	1.53271	0.766353	−	0.642420i	$-0.222070\pi$
$179$	20.5062	1.53271	0.766353	+	0.642420i	$0.222070\pi$
$180$	2.82333	0.210439
$181$	−10.2191	−0.759579	−0.379790	−	0.925073i	$-0.624004\pi$
$181$	−10.2191	−0.759579	−0.379790	+	0.925073i	$0.624004\pi$
$182$	35.7138	2.64728
$183$	4.40474	0.325608
$184$	−6.05399	−0.446306
$185$	3.83869	0.282226
$186$	−18.4042	−1.34946
$187$	−2.68227	−0.196147
$188$	−0.876784	−0.0639461
$189$	2.13540	0.155327
$190$	3.51382	0.254919
$191$	8.94039	0.646904	0.323452	−	0.946245i	$-0.395157\pi$
$191$	8.94039	0.646904	0.323452	+	0.946245i	$0.395157\pi$
$192$	2.41316	0.174155
$193$	23.5154	1.69268	0.846339	−	0.532644i	$-0.178802\pi$
$193$	23.5154	1.69268	0.846339	+	0.532644i	$0.178802\pi$
$194$	11.8989	0.854293
$195$	17.2060	1.23215
$196$	18.0890	1.29207
$197$	−0.533015	−0.0379757	−0.0189879	−	0.999820i	$-0.506044\pi$
$197$	−0.533015	−0.0379757	−0.0189879	+	0.999820i	$0.506044\pi$
$198$	−2.82333	−0.200646
$199$	−8.70787	−0.617284	−0.308642	−	0.951178i	$-0.599875\pi$
$199$	−8.70787	−0.617284	−0.308642	+	0.951178i	$0.599875\pi$
$200$	−1.00000	−0.0707107
$201$	19.3621	1.36569
$202$	−11.1320	−0.783242
$203$	38.7997	2.72320
$204$	−6.47274	−0.453182
$205$	3.90400	0.272667
$206$	8.64427	0.602275
$207$	17.0924	1.18801
$208$	7.13007	0.494381
$209$	−3.51382	−0.243056
$210$	12.0873	0.834100
$211$	21.4706	1.47810	0.739050	−	0.673651i	$-0.235275\pi$
$211$	21.4706	1.47810	0.739050	+	0.673651i	$0.235275\pi$
$212$	−1.81678	−0.124777
$213$	21.4646	1.47073
$214$	−15.4780	−1.05805
$215$	1.00000	0.0681994
$216$	0.426321	0.0290075
$217$	−38.2010	−2.59325
$218$	−5.43714	−0.368250
$219$	−4.07412	−0.275304
$220$	1.00000	0.0674200
$221$	−19.1248	−1.28647
$222$	−9.26336	−0.621716
$223$	25.6498	1.71764	0.858819	−	0.512279i	$-0.171199\pi$
$223$	25.6498	1.71764	0.858819	+	0.512279i	$0.171199\pi$
$224$	5.00890	0.334671
$225$	2.82333	0.188222
$226$	−6.86930	−0.456939
$227$	18.1130	1.20220	0.601100	−	0.799174i	$-0.294729\pi$
$227$	18.1130	1.20220	0.601100	+	0.799174i	$0.294729\pi$
$228$	−8.47940	−0.561562
$229$	−27.1746	−1.79575	−0.897873	−	0.440255i	$-0.854888\pi$
$229$	−27.1746	−1.79575	−0.897873	+	0.440255i	$0.854888\pi$
$230$	−6.05399	−0.399188
$231$	−12.0873	−0.795284
$232$	7.74615	0.508560
$233$	0.871375	0.0570857	0.0285428	−	0.999593i	$-0.490913\pi$
$233$	0.871375	0.0570857	0.0285428	+	0.999593i	$0.490913\pi$
$234$	−20.1306	−1.31598
$235$	−0.876784	−0.0571951
$236$	1.02302	0.0665932
$237$	24.1898	1.57130
$238$	−13.4352	−0.870875
$239$	−9.08899	−0.587918	−0.293959	−	0.955818i	$-0.594973\pi$
$239$	−9.08899	−0.587918	−0.293959	+	0.955818i	$0.594973\pi$
$240$	2.41316	0.155769
$241$	−14.6619	−0.944453	−0.472227	−	0.881477i	$-0.656550\pi$
$241$	−14.6619	−0.944453	−0.472227	+	0.881477i	$0.656550\pi$
$242$	−1.00000	−0.0642824
$243$	−21.6431	−1.38841
$244$	1.82530	0.116853
$245$	18.0890	1.15567
$246$	−9.42097	−0.600659
$247$	−25.0538	−1.59413
$248$	−7.62662	−0.484291
$249$	18.6671	1.18298
$250$	−1.00000	−0.0632456
$251$	−1.80652	−0.114026	−0.0570132	−	0.998373i	$-0.518158\pi$
$251$	−1.80652	−0.114026	−0.0570132	+	0.998373i	$0.518158\pi$
$252$	−14.1418	−0.890849
$253$	6.05399	0.380611
$254$	−1.54738	−0.0970915
$255$	−6.47274	−0.405339
$256$	1.00000	0.0625000
$257$	−11.5395	−0.719817	−0.359908	−	0.932988i	$-0.617192\pi$
$257$	−11.5395	−0.719817	−0.359908	+	0.932988i	$0.617192\pi$
$258$	−2.41316	−0.150237
$259$	−19.2276	−1.19474
$260$	7.13007	0.442188
$261$	−21.8700	−1.35372
$262$	14.1171	0.872154
$263$	14.8920	0.918279	0.459139	−	0.888364i	$-0.348158\pi$
$263$	14.8920	0.918279	0.459139	+	0.888364i	$0.348158\pi$
$264$	−2.41316	−0.148520
$265$	−1.81678	−0.111604
$266$	−17.6004	−1.07915
$267$	−22.5820	−1.38200
$268$	8.02353	0.490115
$269$	−11.9970	−0.731470	−0.365735	−	0.930719i	$-0.619182\pi$
$269$	−11.9970	−0.731470	−0.365735	+	0.930719i	$0.619182\pi$
$270$	0.426321	0.0259451
$271$	−8.55250	−0.519528	−0.259764	−	0.965672i	$-0.583645\pi$
$271$	−8.55250	−0.519528	−0.259764	+	0.965672i	$0.583645\pi$
$272$	−2.68227	−0.162636
$273$	−86.1830	−5.21603
$274$	−3.23436	−0.195395
$275$	1.00000	0.0603023
$276$	14.6092	0.879373
$277$	−2.61654	−0.157213	−0.0786064	−	0.996906i	$-0.525047\pi$
$277$	−2.61654	−0.157213	−0.0786064	+	0.996906i	$0.525047\pi$
$278$	4.86705	0.291906
$279$	21.5325	1.28912
$280$	5.00890	0.299339
$281$	−11.3870	−0.679293	−0.339646	−	0.940553i	$-0.610307\pi$
$281$	−11.3870	−0.679293	−0.339646	+	0.940553i	$0.610307\pi$
$282$	2.11582	0.125995
$283$	23.6527	1.40600	0.703002	−	0.711188i	$-0.251842\pi$
$283$	23.6527	1.40600	0.703002	+	0.711188i	$0.251842\pi$
$284$	8.89481	0.527810
$285$	−8.47940	−0.502276
$286$	−7.13007	−0.421610
$287$	−19.5547	−1.15428
$288$	−2.82333	−0.166367
$289$	−9.80543	−0.576790
$290$	7.74615	0.454870
$291$	−28.7140	−1.68324
$292$	−1.68829	−0.0988000
$293$	−9.36175	−0.546920	−0.273460	−	0.961883i	$-0.588168\pi$
$293$	−9.36175	−0.546920	−0.273460	+	0.961883i	$0.588168\pi$
$294$	−43.6517	−2.54582
$295$	1.02302	0.0595627
$296$	−3.83869	−0.223119
$297$	−0.426321	−0.0247377
$298$	−8.90513	−0.515860
$299$	43.1653	2.49632
$300$	2.41316	0.139324
$301$	−5.00890	−0.288708
$302$	13.8455	0.796716
$303$	26.8632	1.54325
$304$	−3.51382	−0.201531
$305$	1.82530	0.104516
$306$	7.57294	0.432916
$307$	30.2823	1.72830	0.864152	−	0.503231i	$-0.167855\pi$
$307$	30.2823	1.72830	0.864152	+	0.503231i	$0.167855\pi$
$308$	−5.00890	−0.285408
$309$	−20.8600	−1.18668
$310$	−7.62662	−0.433163
$311$	−25.0684	−1.42150	−0.710750	−	0.703445i	$-0.751644\pi$
$311$	−25.0684	−1.42150	−0.710750	+	0.703445i	$0.751644\pi$
$312$	−17.2060	−0.974097
$313$	−23.4292	−1.32430	−0.662149	−	0.749372i	$-0.730355\pi$
$313$	−23.4292	−1.32430	−0.662149	+	0.749372i	$0.730355\pi$
$314$	1.35382	0.0764007
$315$	−14.1418	−0.796800
$316$	10.0241	0.563902
$317$	−10.6997	−0.600952	−0.300476	−	0.953789i	$-0.597146\pi$
$317$	−10.6997	−0.600952	−0.300476	+	0.953789i	$0.597146\pi$
$318$	4.38417	0.245852
$319$	−7.74615	−0.433701
$320$	1.00000	0.0559017
$321$	37.3508	2.08472
$322$	30.3238	1.68988
$323$	9.42500	0.524421
$324$	−9.49878	−0.527710
$325$	7.13007	0.395505
$326$	−14.2012	−0.786531
$327$	13.1207	0.725576
$328$	−3.90400	−0.215562
$329$	4.39172	0.242124
$330$	−2.41316	−0.132840
$331$	20.3200	1.11689	0.558445	−	0.829541i	$-0.311398\pi$
$331$	20.3200	1.11689	0.558445	+	0.829541i	$0.311398\pi$
$332$	7.73554	0.424543
$333$	10.8379	0.593913
$334$	−17.1331	−0.937480
$335$	8.02353	0.438372
$336$	−12.0873	−0.659414
$337$	9.75296	0.531278	0.265639	−	0.964073i	$-0.414417\pi$
$337$	9.75296	0.531278	0.265639	+	0.964073i	$0.414417\pi$
$338$	−37.8379	−2.05811
$339$	16.5767	0.900324
$340$	−2.68227	−0.145466
$341$	7.62662	0.413005
$342$	9.92068	0.536449
$343$	−55.5439	−2.99909
$344$	−1.00000	−0.0539164
$345$	14.6092	0.786535
$346$	7.33843	0.394516
$347$	−27.3345	−1.46739	−0.733696	−	0.679478i	$-0.762206\pi$
$347$	−27.3345	−1.46739	−0.733696	+	0.679478i	$0.762206\pi$
$348$	−18.6927	−1.00203
$349$	−16.3076	−0.872925	−0.436462	−	0.899723i	$-0.643769\pi$
$349$	−16.3076	−0.872925	−0.436462	+	0.899723i	$0.643769\pi$
$350$	5.00890	0.267737
$351$	−3.03970	−0.162247
$352$	−1.00000	−0.0533002
$353$	0.703139	0.0374243	0.0187122	−	0.999825i	$-0.494043\pi$
$353$	0.703139	0.0374243	0.0187122	+	0.999825i	$0.494043\pi$
$354$	−2.46872	−0.131211
$355$	8.89481	0.472088
$356$	−9.35787	−0.495966
$357$	32.4213	1.71592
$358$	−20.5062	−1.08379
$359$	−12.3095	−0.649669	−0.324834	−	0.945771i	$-0.605309\pi$
$359$	−12.3095	−0.649669	−0.324834	+	0.945771i	$0.605309\pi$
$360$	−2.82333	−0.148803
$361$	−6.65308	−0.350162
$362$	10.2191	0.537104
$363$	2.41316	0.126658
$364$	−35.7138	−1.87191
$365$	−1.68829	−0.0883694
$366$	−4.40474	−0.230239
$367$	−17.8166	−0.930020	−0.465010	−	0.885305i	$-0.653949\pi$
$367$	−17.8166	−0.930020	−0.465010	+	0.885305i	$0.653949\pi$
$368$	6.05399	0.315586
$369$	11.0223	0.573798
$370$	−3.83869	−0.199564
$371$	9.10004	0.472451
$372$	18.4042	0.954216
$373$	−17.9785	−0.930894	−0.465447	−	0.885076i	$-0.654106\pi$
$373$	−17.9785	−0.930894	−0.465447	+	0.885076i	$0.654106\pi$
$374$	2.68227	0.138697
$375$	2.41316	0.124615
$376$	0.876784	0.0452167
$377$	−55.2306	−2.84452
$378$	−2.13540	−0.109833
$379$	37.0463	1.90294	0.951472	−	0.307737i	$-0.0995716\pi$
$379$	37.0463	1.90294	0.951472	+	0.307737i	$0.0995716\pi$
$380$	−3.51382	−0.180255
$381$	3.73408	0.191303
$382$	−8.94039	−0.457430
$383$	−10.1265	−0.517441	−0.258720	−	0.965952i	$-0.583301\pi$
$383$	−10.1265	−0.517441	−0.258720	+	0.965952i	$0.583301\pi$
$384$	−2.41316	−0.123146
$385$	−5.00890	−0.255277
$386$	−23.5154	−1.19690
$387$	2.82333	0.143518
$388$	−11.8989	−0.604076
$389$	−29.9366	−1.51785	−0.758923	−	0.651181i	$-0.774274\pi$
$389$	−29.9366	−1.51785	−0.758923	+	0.651181i	$0.774274\pi$
$390$	−17.2060	−0.871259
$391$	−16.2384	−0.821212
$392$	−18.0890	−0.913635
$393$	−34.0667	−1.71844
$394$	0.533015	0.0268529
$395$	10.0241	0.504369
$396$	2.82333	0.141878
$397$	30.8013	1.54587	0.772937	−	0.634483i	$-0.218787\pi$
$397$	30.8013	1.54587	0.772937	+	0.634483i	$0.218787\pi$
$398$	8.70787	0.436486
$399$	42.4724	2.12628
$400$	1.00000	0.0500000
$401$	22.3222	1.11472	0.557358	−	0.830272i	$-0.311815\pi$
$401$	22.3222	1.11472	0.557358	+	0.830272i	$0.311815\pi$
$402$	−19.3621	−0.965692
$403$	54.3783	2.70878
$404$	11.1320	0.553836
$405$	−9.49878	−0.471998
$406$	−38.7997	−1.92560
$407$	3.83869	0.190277
$408$	6.47274	0.320448
$409$	32.8009	1.62190	0.810951	−	0.585114i	$-0.198950\pi$
$409$	32.8009	1.62190	0.810951	+	0.585114i	$0.198950\pi$
$410$	−3.90400	−0.192805
$411$	7.80503	0.384994
$412$	−8.64427	−0.425872
$413$	−5.12422	−0.252146
$414$	−17.0924	−0.840047
$415$	7.73554	0.379723
$416$	−7.13007	−0.349580
$417$	−11.7450	−0.575153
$418$	3.51382	0.171866
$419$	−28.5131	−1.39296	−0.696479	−	0.717578i	$-0.745251\pi$
$419$	−28.5131	−1.39296	−0.696479	+	0.717578i	$0.745251\pi$
$420$	−12.0873	−0.589798
$421$	28.9496	1.41092	0.705458	−	0.708752i	$-0.250742\pi$
$421$	28.9496	1.41092	0.705458	+	0.708752i	$0.250742\pi$
$422$	−21.4706	−1.04517
$423$	−2.47546	−0.120361
$424$	1.81678	0.0882304
$425$	−2.68227	−0.130109
$426$	−21.4646	−1.03996
$427$	−9.14274	−0.442448
$428$	15.4780	0.748155
$429$	17.2060	0.830713
$430$	−1.00000	−0.0482243
$431$	−20.9481	−1.00903	−0.504516	−	0.863402i	$-0.668329\pi$
$431$	−20.9481	−1.00903	−0.504516	+	0.863402i	$0.668329\pi$
$432$	−0.426321	−0.0205114
$433$	−2.69386	−0.129458	−0.0647292	−	0.997903i	$-0.520618\pi$
$433$	−2.69386	−0.129458	−0.0647292	+	0.997903i	$0.520618\pi$
$434$	38.2010	1.83370
$435$	−18.6927	−0.896246
$436$	5.43714	0.260392
$437$	−21.2726	−1.01761
$438$	4.07412	0.194669
$439$	39.6125	1.89060	0.945302	−	0.326198i	$-0.105768\pi$
$439$	39.6125	1.89060	0.945302	+	0.326198i	$0.105768\pi$
$440$	−1.00000	−0.0476731
$441$	51.0714	2.43197
$442$	19.1248	0.909672
$443$	9.40525	0.446857	0.223428	−	0.974720i	$-0.428275\pi$
$443$	9.40525	0.446857	0.223428	+	0.974720i	$0.428275\pi$
$444$	9.26336	0.439619
$445$	−9.35787	−0.443605
$446$	−25.6498	−1.21455
$447$	21.4895	1.01642
$448$	−5.00890	−0.236648
$449$	−38.2727	−1.80620	−0.903101	−	0.429429i	$-0.858715\pi$
$449$	−38.2727	−1.80620	−0.903101	+	0.429429i	$0.858715\pi$
$450$	−2.82333	−0.133093
$451$	3.90400	0.183832
$452$	6.86930	0.323105
$453$	−33.4113	−1.56980
$454$	−18.1130	−0.850084
$455$	−35.7138	−1.67429
$456$	8.47940	0.397084
$457$	13.7202	0.641802	0.320901	−	0.947113i	$-0.396014\pi$
$457$	13.7202	0.641802	0.320901	+	0.947113i	$0.396014\pi$
$458$	27.1746	1.26978
$459$	1.14351	0.0533744
$460$	6.05399	0.282269
$461$	−15.7395	−0.733063	−0.366532	−	0.930406i	$-0.619455\pi$
$461$	−15.7395	−0.733063	−0.366532	+	0.930406i	$0.619455\pi$
$462$	12.0873	0.562350
$463$	10.4522	0.485754	0.242877	−	0.970057i	$-0.421909\pi$
$463$	10.4522	0.485754	0.242877	+	0.970057i	$0.421909\pi$
$464$	−7.74615	−0.359606
$465$	18.4042	0.853476
$466$	−0.871375	−0.0403657
$467$	32.0595	1.48354	0.741768	−	0.670657i	$-0.233988\pi$
$467$	32.0595	1.48354	0.741768	+	0.670657i	$0.233988\pi$
$468$	20.1306	0.930536
$469$	−40.1890	−1.85576
$470$	0.876784	0.0404431
$471$	−3.26699	−0.150535
$472$	−1.02302	−0.0470885
$473$	1.00000	0.0459800
$474$	−24.1898	−1.11108
$475$	−3.51382	−0.161225
$476$	13.4352	0.615802
$477$	−5.12937	−0.234857
$478$	9.08899	0.415721
$479$	−0.619319	−0.0282974	−0.0141487	−	0.999900i	$-0.504504\pi$
$479$	−0.619319	−0.0282974	−0.0141487	+	0.999900i	$0.504504\pi$
$480$	−2.41316	−0.110145
$481$	27.3701	1.24797
$482$	14.6619	0.667829
$483$	−73.1762	−3.32963
$484$	1.00000	0.0454545
$485$	−11.8989	−0.540302
$486$	21.6431	0.981752
$487$	24.5740	1.11356	0.556778	−	0.830662i	$-0.312038\pi$
$487$	24.5740	1.11356	0.556778	+	0.830662i	$0.312038\pi$
$488$	−1.82530	−0.0826275
$489$	34.2697	1.54973
$490$	−18.0890	−0.817180
$491$	−3.57682	−0.161420	−0.0807099	−	0.996738i	$-0.525719\pi$
$491$	−3.57682	−0.161420	−0.0807099	+	0.996738i	$0.525719\pi$
$492$	9.42097	0.424730
$493$	20.7773	0.935761
$494$	25.0538	1.12722
$495$	2.82333	0.126899
$496$	7.62662	0.342445
$497$	−44.5532	−1.99848
$498$	−18.6671	−0.836492
$499$	9.76592	0.437182	0.218591	−	0.975817i	$-0.429854\pi$
$499$	9.76592	0.437182	0.218591	+	0.975817i	$0.429854\pi$
$500$	1.00000	0.0447214
$501$	41.3448	1.84715
$502$	1.80652	0.0806288
$503$	−6.21085	−0.276928	−0.138464	−	0.990367i	$-0.544217\pi$
$503$	−6.21085	−0.276928	−0.138464	+	0.990367i	$0.544217\pi$
$504$	14.1418	0.629926
$505$	11.1320	0.495366
$506$	−6.05399	−0.269133
$507$	91.3088	4.05517
$508$	1.54738	0.0686540
$509$	−21.4408	−0.950348	−0.475174	−	0.879892i	$-0.657615\pi$
$509$	−21.4408	−0.950348	−0.475174	+	0.879892i	$0.657615\pi$
$510$	6.47274	0.286618
$511$	8.45649	0.374093
$512$	−1.00000	−0.0441942
$513$	1.49801	0.0661389
$514$	11.5395	0.508987
$515$	−8.64427	−0.380912
$516$	2.41316	0.106233
$517$	−0.876784	−0.0385609
$518$	19.2276	0.844811
$519$	−17.7088	−0.777330
$520$	−7.13007	−0.312674
$521$	19.7143	0.863701	0.431851	−	0.901945i	$-0.357861\pi$
$521$	19.7143	0.863701	0.431851	+	0.901945i	$0.357861\pi$
$522$	21.8700	0.957223
$523$	−35.0075	−1.53077	−0.765385	−	0.643572i	$-0.777452\pi$
$523$	−35.0075	−1.53077	−0.765385	+	0.643572i	$0.777452\pi$
$524$	−14.1171	−0.616706
$525$	−12.0873	−0.527531
$526$	−14.8920	−0.649321
$527$	−20.4566	−0.891106
$528$	2.41316	0.105019
$529$	13.6508	0.593512
$530$	1.81678	0.0789157
$531$	2.88834	0.125343
$532$	17.6004	0.763072
$533$	27.8358	1.20570
$534$	22.5820	0.977220
$535$	15.4780	0.669171
$536$	−8.02353	−0.346564
$537$	49.4847	2.13542
$538$	11.9970	0.517228
$539$	18.0890	0.779150
$540$	−0.426321	−0.0183459
$541$	8.26716	0.355433	0.177717	−	0.984082i	$-0.443129\pi$
$541$	8.26716	0.355433	0.177717	+	0.984082i	$0.443129\pi$
$542$	8.55250	0.367361
$543$	−24.6603	−1.05827
$544$	2.68227	0.115001
$545$	5.43714	0.232902
$546$	86.1830	3.68829
$547$	−32.2978	−1.38096	−0.690478	−	0.723353i	$-0.742600\pi$
$547$	−32.2978	−1.38096	−0.690478	+	0.723353i	$0.742600\pi$
$548$	3.23436	0.138165
$549$	5.15343	0.219943
$550$	−1.00000	−0.0426401
$551$	27.2186	1.15955
$552$	−14.6092	−0.621810
$553$	−50.2098	−2.13514
$554$	2.61654	0.111166
$555$	9.26336	0.393208
$556$	−4.86705	−0.206409
$557$	−1.38006	−0.0584749	−0.0292374	−	0.999572i	$-0.509308\pi$
$557$	−1.38006	−0.0584749	−0.0292374	+	0.999572i	$0.509308\pi$
$558$	−21.5325	−0.911544
$559$	7.13007	0.301570
$560$	−5.00890	−0.211665
$561$	−6.47274	−0.273279
$562$	11.3870	0.480332
$563$	−44.9494	−1.89439	−0.947195	−	0.320657i	$-0.896096\pi$
$563$	−44.9494	−1.89439	−0.947195	+	0.320657i	$0.896096\pi$
$564$	−2.11582	−0.0890921
$565$	6.86930	0.288994
$566$	−23.6527	−0.994195
$567$	47.5784	1.99811
$568$	−8.89481	−0.373218
$569$	−3.97796	−0.166765	−0.0833823	−	0.996518i	$-0.526572\pi$
$569$	−3.97796	−0.166765	−0.0833823	+	0.996518i	$0.526572\pi$
$570$	8.47940	0.355163
$571$	18.1519	0.759631	0.379816	−	0.925062i	$-0.375987\pi$
$571$	18.1519	0.759631	0.379816	+	0.925062i	$0.375987\pi$
$572$	7.13007	0.298123
$573$	21.5746	0.901292
$574$	19.5547	0.816199
$575$	6.05399	0.252469
$576$	2.82333	0.117639
$577$	19.7959	0.824116	0.412058	−	0.911158i	$-0.364810\pi$
$577$	19.7959	0.824116	0.412058	+	0.911158i	$0.364810\pi$
$578$	9.80543	0.407852
$579$	56.7465	2.35830
$580$	−7.74615	−0.321641
$581$	−38.7465	−1.60748
$582$	28.7140	1.19023
$583$	−1.81678	−0.0752431
$584$	1.68829	0.0698621
$585$	20.1306	0.832297
$586$	9.36175	0.386731
$587$	12.0348	0.496727	0.248364	−	0.968667i	$-0.420107\pi$
$587$	12.0348	0.496727	0.248364	+	0.968667i	$0.420107\pi$
$588$	43.6517	1.80017
$589$	−26.7986	−1.10422
$590$	−1.02302	−0.0421172
$591$	−1.28625	−0.0529092
$592$	3.83869	0.157769
$593$	9.27281	0.380789	0.190394	−	0.981708i	$-0.439023\pi$
$593$	9.27281	0.380789	0.190394	+	0.981708i	$0.439023\pi$
$594$	0.426321	0.0174922
$595$	13.4352	0.550790
$596$	8.90513	0.364768
$597$	−21.0135	−0.860024
$598$	−43.1653	−1.76516
$599$	−21.8347	−0.892140	−0.446070	−	0.894998i	$-0.647177\pi$
$599$	−21.8347	−0.892140	−0.446070	+	0.894998i	$0.647177\pi$
$600$	−2.41316	−0.0985168
$601$	−37.4782	−1.52877	−0.764383	−	0.644762i	$-0.776956\pi$
$601$	−37.4782	−1.52877	−0.764383	+	0.644762i	$0.776956\pi$
$602$	5.00890	0.204147
$603$	22.6531	0.922506
$604$	−13.8455	−0.563364
$605$	1.00000	0.0406558
$606$	−26.8632	−1.09124
$607$	−17.2676	−0.700869	−0.350435	−	0.936587i	$-0.613966\pi$
$607$	−17.2676	−0.700869	−0.350435	+	0.936587i	$0.613966\pi$
$608$	3.51382	0.142504
$609$	93.6298	3.79407
$610$	−1.82530	−0.0739043
$611$	−6.25153	−0.252910
$612$	−7.57294	−0.306118
$613$	−34.8338	−1.40692	−0.703461	−	0.710734i	$-0.748363\pi$
$613$	−34.8338	−1.40692	−0.703461	+	0.710734i	$0.748363\pi$
$614$	−30.2823	−1.22210
$615$	9.42097	0.379890
$616$	5.00890	0.201814
$617$	−2.11051	−0.0849657	−0.0424829	−	0.999097i	$-0.513527\pi$
$617$	−2.11051	−0.0849657	−0.0424829	+	0.999097i	$0.513527\pi$
$618$	20.8600	0.839112
$619$	−38.1171	−1.53206	−0.766028	−	0.642807i	$-0.777770\pi$
$619$	−38.1171	−1.53206	−0.766028	+	0.642807i	$0.777770\pi$
$620$	7.62662	0.306292
$621$	−2.58094	−0.103570
$622$	25.0684	1.00515
$623$	46.8726	1.87791
$624$	17.2060	0.688791
$625$	1.00000	0.0400000
$626$	23.4292	0.936420
$627$	−8.47940	−0.338635
$628$	−1.35382	−0.0540234
$629$	−10.2964	−0.410544
$630$	14.1418	0.563423
$631$	1.36200	0.0542205	0.0271102	−	0.999632i	$-0.491369\pi$
$631$	1.36200	0.0542205	0.0271102	+	0.999632i	$0.491369\pi$
$632$	−10.0241	−0.398739
$633$	51.8120	2.05934
$634$	10.6997	0.424937
$635$	1.54738	0.0614060
$636$	−4.38417	−0.173844
$637$	128.976	5.11022
$638$	7.74615	0.306673
$639$	25.1130	0.993456
$640$	−1.00000	−0.0395285
$641$	43.8228	1.73090	0.865449	−	0.500997i	$-0.167033\pi$
$641$	43.8228	1.73090	0.865449	+	0.500997i	$0.167033\pi$
$642$	−37.3508	−1.47412
$643$	8.56830	0.337901	0.168950	−	0.985625i	$-0.445962\pi$
$643$	8.56830	0.337901	0.168950	+	0.985625i	$0.445962\pi$
$644$	−30.3238	−1.19493
$645$	2.41316	0.0950180
$646$	−9.42500	−0.370822
$647$	−1.02232	−0.0401915	−0.0200958	−	0.999798i	$-0.506397\pi$
$647$	−1.02232	−0.0401915	−0.0200958	+	0.999798i	$0.506397\pi$
$648$	9.49878	0.373148
$649$	1.02302	0.0401572
$650$	−7.13007	−0.279664
$651$	−92.1850	−3.61301
$652$	14.2012	0.556161
$653$	36.1755	1.41566	0.707829	−	0.706384i	$-0.249675\pi$
$653$	36.1755	1.41566	0.707829	+	0.706384i	$0.249675\pi$
$654$	−13.1207	−0.513060
$655$	−14.1171	−0.551599
$656$	3.90400	0.152426
$657$	−4.76662	−0.185964
$658$	−4.39172	−0.171207
$659$	−11.2549	−0.438430	−0.219215	−	0.975677i	$-0.570350\pi$
$659$	−11.2549	−0.438430	−0.219215	+	0.975677i	$0.570350\pi$
$660$	2.41316	0.0939321
$661$	−20.9086	−0.813251	−0.406625	−	0.913595i	$-0.633295\pi$
$661$	−20.9086	−0.813251	−0.406625	+	0.913595i	$0.633295\pi$
$662$	−20.3200	−0.789761
$663$	−46.1511	−1.79236
$664$	−7.73554	−0.300197
$665$	17.6004	0.682512
$666$	−10.8379	−0.419960
$667$	−46.8951	−1.81579
$668$	17.1331	0.662898
$669$	61.8970	2.39308
$670$	−8.02353	−0.309976
$671$	1.82530	0.0704649
$672$	12.0873	0.466276
$673$	5.90228	0.227516	0.113758	−	0.993508i	$-0.463711\pi$
$673$	5.90228	0.227516	0.113758	+	0.993508i	$0.463711\pi$
$674$	−9.75296	−0.375670
$675$	−0.426321	−0.0164091
$676$	37.8379	1.45530
$677$	−33.8782	−1.30205	−0.651023	−	0.759058i	$-0.725660\pi$
$677$	−33.8782	−1.30205	−0.651023	+	0.759058i	$0.725660\pi$
$678$	−16.5767	−0.636625
$679$	59.6005	2.28726
$680$	2.68227	0.102860
$681$	43.7095	1.67495
$682$	−7.62662	−0.292038
$683$	1.47337	0.0563769	0.0281885	−	0.999603i	$-0.491026\pi$
$683$	1.47337	0.0563769	0.0281885	+	0.999603i	$0.491026\pi$
$684$	−9.92068	−0.379327
$685$	3.23436	0.123579
$686$	55.5439	2.12068
$687$	−65.5765	−2.50190
$688$	1.00000	0.0381246
$689$	−12.9537	−0.493498
$690$	−14.6092	−0.556164
$691$	−9.84859	−0.374658	−0.187329	−	0.982297i	$-0.559983\pi$
$691$	−9.84859	−0.374658	−0.187329	+	0.982297i	$0.559983\pi$
$692$	−7.33843	−0.278965
$693$	−14.1418	−0.537202
$694$	27.3345	1.03760
$695$	−4.86705	−0.184618
$696$	18.6927	0.708545
$697$	−10.4716	−0.396639
$698$	16.3076	0.617251
$699$	2.10277	0.0795339
$700$	−5.00890	−0.189319
$701$	10.5295	0.397695	0.198848	−	0.980030i	$-0.436280\pi$
$701$	10.5295	0.397695	0.198848	+	0.980030i	$0.436280\pi$
$702$	3.03970	0.114726
$703$	−13.4884	−0.508726
$704$	1.00000	0.0376889
$705$	−2.11582	−0.0796864
$706$	−0.703139	−0.0264630
$707$	−55.7588	−2.09703
$708$	2.46872	0.0927801
$709$	3.05531	0.114745	0.0573723	−	0.998353i	$-0.481728\pi$
$709$	3.05531	0.114745	0.0573723	+	0.998353i	$0.481728\pi$
$710$	−8.89481	−0.333816
$711$	28.3015	1.06139
$712$	9.35787	0.350701
$713$	46.1715	1.72914
$714$	−32.4213	−1.21334
$715$	7.13007	0.266649
$716$	20.5062	0.766353
$717$	−21.9332	−0.819109
$718$	12.3095	0.459385
$719$	−19.4827	−0.726583	−0.363292	−	0.931676i	$-0.618347\pi$
$719$	−19.4827	−0.726583	−0.363292	+	0.931676i	$0.618347\pi$
$720$	2.82333	0.105219
$721$	43.2982	1.61251
$722$	6.65308	0.247602
$723$	−35.3814	−1.31585
$724$	−10.2191	−0.379790
$725$	−7.74615	−0.287685
$726$	−2.41316	−0.0895607
$727$	18.5835	0.689226	0.344613	−	0.938745i	$-0.388010\pi$
$727$	18.5835	0.689226	0.344613	+	0.938745i	$0.388010\pi$
$728$	35.7138	1.32364
$729$	−23.7319	−0.878960
$730$	1.68829	0.0624866
$731$	−2.68227	−0.0992073
$732$	4.40474	0.162804
$733$	−25.6473	−0.947304	−0.473652	−	0.880712i	$-0.657065\pi$
$733$	−25.6473	−0.947304	−0.473652	+	0.880712i	$0.657065\pi$
$734$	17.8166	0.657623
$735$	43.6517	1.61012
$736$	−6.05399	−0.223153
$737$	8.02353	0.295551
$738$	−11.0223	−0.405737
$739$	−43.2282	−1.59017	−0.795087	−	0.606495i	$-0.792575\pi$
$739$	−43.2282	−1.59017	−0.795087	+	0.606495i	$0.792575\pi$
$740$	3.83869	0.141113
$741$	−60.4587	−2.22101
$742$	−9.10004	−0.334073
$743$	−1.53966	−0.0564847	−0.0282423	−	0.999601i	$-0.508991\pi$
$743$	−1.53966	−0.0564847	−0.0282423	+	0.999601i	$0.508991\pi$
$744$	−18.4042	−0.674732
$745$	8.90513	0.326259
$746$	17.9785	0.658241
$747$	21.8400	0.799085
$748$	−2.68227	−0.0980735
$749$	−77.5275	−2.83279
$750$	−2.41316	−0.0881161
$751$	−35.2472	−1.28619	−0.643094	−	0.765787i	$-0.722349\pi$
$751$	−35.2472	−1.28619	−0.643094	+	0.765787i	$0.722349\pi$
$752$	−0.876784	−0.0319730
$753$	−4.35941	−0.158866
$754$	55.2306	2.01138
$755$	−13.8455	−0.503888
$756$	2.13540	0.0776637
$757$	28.8163	1.04735	0.523673	−	0.851919i	$-0.324561\pi$
$757$	28.8163	1.04735	0.523673	+	0.851919i	$0.324561\pi$
$758$	−37.0463	−1.34558
$759$	14.6092	0.530282
$760$	3.51382	0.127460
$761$	−38.3711	−1.39095	−0.695476	−	0.718549i	$-0.744806\pi$
$761$	−38.3711	−1.39095	−0.695476	+	0.718549i	$0.744806\pi$
$762$	−3.73408	−0.135272
$763$	−27.2341	−0.985940
$764$	8.94039	0.323452
$765$	−7.57294	−0.273800
$766$	10.1265	0.365886
$767$	7.29423	0.263379
$768$	2.41316	0.0870774
$769$	22.5187	0.812044	0.406022	−	0.913863i	$-0.366916\pi$
$769$	22.5187	0.812044	0.406022	+	0.913863i	$0.366916\pi$
$770$	5.00890	0.180508
$771$	−27.8467	−1.00288
$772$	23.5154	0.846339
$773$	−33.3659	−1.20009	−0.600044	−	0.799967i	$-0.704850\pi$
$773$	−33.3659	−1.20009	−0.600044	+	0.799967i	$0.704850\pi$
$774$	−2.82333	−0.101483
$775$	7.62662	0.273956
$776$	11.8989	0.427147
$777$	−46.3992	−1.66456
$778$	29.9366	1.07328
$779$	−13.7179	−0.491497
$780$	17.2060	0.616073
$781$	8.89481	0.318281
$782$	16.2384	0.580685
$783$	3.30235	0.118016
$784$	18.0890	0.646037
$785$	−1.35382	−0.0483200
$786$	34.0667	1.21512
$787$	−38.9605	−1.38879	−0.694396	−	0.719593i	$-0.744328\pi$
$787$	−38.9605	−1.38879	−0.694396	+	0.719593i	$0.744328\pi$
$788$	−0.533015	−0.0189879
$789$	35.9367	1.27938
$790$	−10.0241	−0.356643
$791$	−34.4076	−1.22339
$792$	−2.82333	−0.100323
$793$	13.0145	0.462159
$794$	−30.8013	−1.09310
$795$	−4.38417	−0.155490
$796$	−8.70787	−0.308642
$797$	−20.8370	−0.738084	−0.369042	−	0.929413i	$-0.620314\pi$
$797$	−20.8370	−0.738084	−0.369042	+	0.929413i	$0.620314\pi$
$798$	−42.4724	−1.50351
$799$	2.35177	0.0831997
$800$	−1.00000	−0.0353553
$801$	−26.4204	−0.933519
$802$	−22.3222	−0.788223
$803$	−1.68829	−0.0595786
$804$	19.3621	0.682847
$805$	−30.3238	−1.06877
$806$	−54.3783	−1.91539
$807$	−28.9507	−1.01911
$808$	−11.1320	−0.391621
$809$	15.6011	0.548506	0.274253	−	0.961658i	$-0.411569\pi$
$809$	15.6011	0.548506	0.274253	+	0.961658i	$0.411569\pi$
$810$	9.49878	0.333753
$811$	−36.8109	−1.29260	−0.646302	−	0.763081i	$-0.723686\pi$
$811$	−36.8109	−1.29260	−0.646302	+	0.763081i	$0.723686\pi$
$812$	38.7997	1.36160
$813$	−20.6385	−0.723825
$814$	−3.83869	−0.134546
$815$	14.2012	0.497446
$816$	−6.47274	−0.226591
$817$	−3.51382	−0.122933
$818$	−32.8009	−1.14686
$819$	−100.832	−3.52335
$820$	3.90400	0.136334
$821$	−3.04007	−0.106099	−0.0530495	−	0.998592i	$-0.516894\pi$
$821$	−3.04007	−0.106099	−0.0530495	+	0.998592i	$0.516894\pi$
$822$	−7.80503	−0.272232
$823$	−36.5627	−1.27450	−0.637248	−	0.770659i	$-0.719927\pi$
$823$	−36.5627	−1.27450	−0.637248	+	0.770659i	$0.719927\pi$
$824$	8.64427	0.301137
$825$	2.41316	0.0840154
$826$	5.12422	0.178294
$827$	8.76539	0.304802	0.152401	−	0.988319i	$-0.451299\pi$
$827$	8.76539	0.304802	0.152401	+	0.988319i	$0.451299\pi$
$828$	17.0924	0.594003
$829$	−35.6384	−1.23777	−0.618887	−	0.785480i	$-0.712416\pi$
$829$	−35.6384	−1.23777	−0.618887	+	0.785480i	$0.712416\pi$
$830$	−7.73554	−0.268505
$831$	−6.31413	−0.219035
$832$	7.13007	0.247191
$833$	−48.5197	−1.68111
$834$	11.7450	0.406695
$835$	17.1331	0.592914
$836$	−3.51382	−0.121528
$837$	−3.25139	−0.112384
$838$	28.5131	0.984970
$839$	25.0754	0.865698	0.432849	−	0.901467i	$-0.357508\pi$
$839$	25.0754	0.865698	0.432849	+	0.901467i	$0.357508\pi$
$840$	12.0873	0.417050
$841$	31.0029	1.06906
$842$	−28.9496	−0.997668
$843$	−27.4787	−0.946416
$844$	21.4706	0.739050
$845$	37.8379	1.30166
$846$	2.47546	0.0851079
$847$	−5.00890	−0.172108
$848$	−1.81678	−0.0623883
$849$	57.0776	1.95890
$850$	2.68227	0.0920011
$851$	23.2394	0.796635
$852$	21.4646	0.735365
$853$	12.7351	0.436041	0.218020	−	0.975944i	$-0.430040\pi$
$853$	12.7351	0.436041	0.218020	+	0.975944i	$0.430040\pi$
$854$	9.14274	0.312858
$855$	−9.92068	−0.339280
$856$	−15.4780	−0.529026
$857$	−2.74444	−0.0937484	−0.0468742	−	0.998901i	$-0.514926\pi$
$857$	−2.74444	−0.0937484	−0.0468742	+	0.998901i	$0.514926\pi$
$858$	−17.2060	−0.587403
$859$	−10.8500	−0.370196	−0.185098	−	0.982720i	$-0.559260\pi$
$859$	−10.8500	−0.370196	−0.185098	+	0.982720i	$0.559260\pi$
$860$	1.00000	0.0340997
$861$	−47.1887	−1.60819
$862$	20.9481	0.713494
$863$	42.9042	1.46048	0.730238	−	0.683193i	$-0.239409\pi$
$863$	42.9042	1.46048	0.730238	+	0.683193i	$0.239409\pi$
$864$	0.426321	0.0145037
$865$	−7.33843	−0.249514
$866$	2.69386	0.0915410
$867$	−23.6621	−0.803606
$868$	−38.2010	−1.29662
$869$	10.0241	0.340045
$870$	18.6927	0.633742
$871$	57.2083	1.93843
$872$	−5.43714	−0.184125
$873$	−33.5946	−1.13701
$874$	21.2726	0.719557
$875$	−5.00890	−0.169332
$876$	−4.07412	−0.137652
$877$	34.6807	1.17109	0.585543	−	0.810642i	$-0.300881\pi$
$877$	34.6807	1.17109	0.585543	+	0.810642i	$0.300881\pi$
$878$	−39.6125	−1.33686
$879$	−22.5914	−0.761989
$880$	1.00000	0.0337100
$881$	8.45493	0.284854	0.142427	−	0.989805i	$-0.454509\pi$
$881$	8.45493	0.284854	0.142427	+	0.989805i	$0.454509\pi$
$882$	−51.0714	−1.71966
$883$	30.2302	1.01733	0.508664	−	0.860965i	$-0.330139\pi$
$883$	30.2302	1.01733	0.508664	+	0.860965i	$0.330139\pi$
$884$	−19.1248	−0.643235
$885$	2.46872	0.0829851
$886$	−9.40525	−0.315976
$887$	49.6709	1.66779	0.833893	−	0.551926i	$-0.186107\pi$
$887$	49.6709	1.66779	0.833893	+	0.551926i	$0.186107\pi$
$888$	−9.26336	−0.310858
$889$	−7.75068	−0.259950
$890$	9.35787	0.313676
$891$	−9.49878	−0.318221
$892$	25.6498	0.858819
$893$	3.08086	0.103097
$894$	−21.4895	−0.718716
$895$	20.5062	0.685447
$896$	5.00890	0.167335
$897$	104.165	3.47796
$898$	38.2727	1.27718
$899$	−59.0770	−1.97033
$900$	2.82333	0.0941112
$901$	4.87308	0.162346
$902$	−3.90400	−0.129989
$903$	−12.0873	−0.402239
$904$	−6.86930	−0.228470
$905$	−10.2191	−0.339694
$906$	33.4113	1.11002
$907$	8.18916	0.271917	0.135958	−	0.990715i	$-0.456589\pi$
$907$	8.18916	0.271917	0.135958	+	0.990715i	$0.456589\pi$
$908$	18.1130	0.601100
$909$	31.4293	1.04244
$910$	35.7138	1.18390
$911$	−24.0013	−0.795199	−0.397600	−	0.917559i	$-0.630157\pi$
$911$	−24.0013	−0.795199	−0.397600	+	0.917559i	$0.630157\pi$
$912$	−8.47940	−0.280781
$913$	7.73554	0.256009
$914$	−13.7202	−0.453823
$915$	4.40474	0.145616
$916$	−27.1746	−0.897873
$917$	70.7109	2.33508
$918$	−1.14351	−0.0377414
$919$	−36.7718	−1.21299	−0.606496	−	0.795087i	$-0.707425\pi$
$919$	−36.7718	−1.21299	−0.606496	+	0.795087i	$0.707425\pi$
$920$	−6.05399	−0.199594
$921$	73.0761	2.40794
$922$	15.7395	0.518354
$923$	63.4206	2.08751
$924$	−12.0873	−0.397642
$925$	3.83869	0.126215
$926$	−10.4522	−0.343480
$927$	−24.4057	−0.801587
$928$	7.74615	0.254280
$929$	−30.6815	−1.00663	−0.503314	−	0.864104i	$-0.667886\pi$
$929$	−30.6815	−1.00663	−0.503314	+	0.864104i	$0.667886\pi$
$930$	−18.4042	−0.603499
$931$	−63.5616	−2.08315
$932$	0.871375	0.0285428
$933$	−60.4941	−1.98049
$934$	−32.0595	−1.04902
$935$	−2.68227	−0.0877196
$936$	−20.1306	−0.657988
$937$	53.5103	1.74810	0.874052	−	0.485832i	$-0.161483\pi$
$937$	53.5103	1.74810	0.874052	+	0.485832i	$0.161483\pi$
$938$	40.1890	1.31222
$939$	−56.5384	−1.84506
$940$	−0.876784	−0.0285976
$941$	−47.9431	−1.56290	−0.781450	−	0.623968i	$-0.785519\pi$
$941$	−47.9431	−1.56290	−0.781450	+	0.623968i	$0.785519\pi$
$942$	3.26699	0.106444
$943$	23.6348	0.769654
$944$	1.02302	0.0332966
$945$	2.13540	0.0694645
$946$	−1.00000	−0.0325128
$947$	7.10057	0.230738	0.115369	−	0.993323i	$-0.463195\pi$
$947$	7.10057	0.230738	0.115369	+	0.993323i	$0.463195\pi$
$948$	24.1898	0.785649
$949$	−12.0377	−0.390759
$950$	3.51382	0.114003
$951$	−25.8200	−0.837270
$952$	−13.4352	−0.435438
$953$	−31.9647	−1.03544	−0.517719	−	0.855550i	$-0.673219\pi$
$953$	−31.9647	−1.03544	−0.517719	+	0.855550i	$0.673219\pi$
$954$	5.12937	0.166069
$955$	8.94039	0.289304
$956$	−9.08899	−0.293959
$957$	−18.6927	−0.604249
$958$	0.619319	0.0200093
$959$	−16.2006	−0.523144
$960$	2.41316	0.0778844
$961$	27.1653	0.876301
$962$	−27.3701	−0.882447
$963$	43.6995	1.40820
$964$	−14.6619	−0.472227
$965$	23.5154	0.756989
$966$	73.1762	2.35440
$967$	−19.1061	−0.614411	−0.307206	−	0.951643i	$-0.599394\pi$
$967$	−19.1061	−0.614411	−0.307206	+	0.951643i	$0.599394\pi$
$968$	−1.00000	−0.0321412
$969$	22.7440	0.730644
$970$	11.8989	0.382051
$971$	−38.7112	−1.24230	−0.621150	−	0.783692i	$-0.713334\pi$
$971$	−38.7112	−1.24230	−0.621150	+	0.783692i	$0.713334\pi$
$972$	−21.6431	−0.694203
$973$	24.3785	0.781540
$974$	−24.5740	−0.787402
$975$	17.2060	0.551033
$976$	1.82530	0.0584264
$977$	−2.58123	−0.0825807	−0.0412904	−	0.999147i	$-0.513147\pi$
$977$	−2.58123	−0.0825807	−0.0412904	+	0.999147i	$0.513147\pi$
$978$	−34.2697	−1.09582
$979$	−9.35787	−0.299079
$980$	18.0890	0.577833
$981$	15.3509	0.490116
$982$	3.57682	0.114141
$983$	−35.2738	−1.12506	−0.562530	−	0.826777i	$-0.690172\pi$
$983$	−35.2738	−1.12506	−0.562530	+	0.826777i	$0.690172\pi$
$984$	−9.42097	−0.300330
$985$	−0.533015	−0.0169833
$986$	−20.7773	−0.661683
$987$	10.5979	0.337336
$988$	−25.0538	−0.797066
$989$	6.05399	0.192506
$990$	−2.82333	−0.0897315
$991$	−51.7141	−1.64275	−0.821376	−	0.570387i	$-0.806793\pi$
$991$	−51.7141	−1.64275	−0.821376	+	0.570387i	$0.806793\pi$
$992$	−7.62662	−0.242145
$993$	49.0355	1.55609
$994$	44.5532	1.41314
$995$	−8.70787	−0.276058
$996$	18.6671	0.591489
$997$	6.87510	0.217736	0.108868	−	0.994056i	$-0.465277\pi$
$997$	6.87510	0.217736	0.108868	+	0.994056i	$0.465277\pi$
$998$	−9.76592	−0.309135
$999$	−1.63651	−0.0517770

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4730.2.a.z.1.7	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4730.2.a.z.1.7	✓	10	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.41316 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.41316 q^{6} -5.00890 q^{7} -1.00000 q^{8} +2.82333 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +2.41316 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.41316 q^{6} -5.00890 q^{7} -1.00000 q^{8} +2.82333 q^{9} -1.00000 q^{10} +1.00000 q^{11} +2.41316 q^{12} +7.13007 q^{13} +5.00890 q^{14} +2.41316 q^{15} +1.00000 q^{16} -2.68227 q^{17} -2.82333 q^{18} -3.51382 q^{19} +1.00000 q^{20} -12.0873 q^{21} -1.00000 q^{22} +6.05399 q^{23} -2.41316 q^{24} +1.00000 q^{25} -7.13007 q^{26} -0.426321 q^{27} -5.00890 q^{28} -7.74615 q^{29} -2.41316 q^{30} +7.62662 q^{31} -1.00000 q^{32} +2.41316 q^{33} +2.68227 q^{34} -5.00890 q^{35} +2.82333 q^{36} +3.83869 q^{37} +3.51382 q^{38} +17.2060 q^{39} -1.00000 q^{40} +3.90400 q^{41} +12.0873 q^{42} +1.00000 q^{43} +1.00000 q^{44} +2.82333 q^{45} -6.05399 q^{46} -0.876784 q^{47} +2.41316 q^{48} +18.0890 q^{49} -1.00000 q^{50} -6.47274 q^{51} +7.13007 q^{52} -1.81678 q^{53} +0.426321 q^{54} +1.00000 q^{55} +5.00890 q^{56} -8.47940 q^{57} +7.74615 q^{58} +1.02302 q^{59} +2.41316 q^{60} +1.82530 q^{61} -7.62662 q^{62} -14.1418 q^{63} +1.00000 q^{64} +7.13007 q^{65} -2.41316 q^{66} +8.02353 q^{67} -2.68227 q^{68} +14.6092 q^{69} +5.00890 q^{70} +8.89481 q^{71} -2.82333 q^{72} -1.68829 q^{73} -3.83869 q^{74} +2.41316 q^{75} -3.51382 q^{76} -5.00890 q^{77} -17.2060 q^{78} +10.0241 q^{79} +1.00000 q^{80} -9.49878 q^{81} -3.90400 q^{82} +7.73554 q^{83} -12.0873 q^{84} -2.68227 q^{85} -1.00000 q^{86} -18.6927 q^{87} -1.00000 q^{88} -9.35787 q^{89} -2.82333 q^{90} -35.7138 q^{91} +6.05399 q^{92} +18.4042 q^{93} +0.876784 q^{94} -3.51382 q^{95} -2.41316 q^{96} -11.8989 q^{97} -18.0890 q^{98} +2.82333 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 10 q^{2} + 8 q^{3} + 10 q^{4} + 10 q^{5} - 8 q^{6} + 3 q^{7} - 10 q^{8} + 14 q^{9}+O(q^{10}) \) 10 * q - 10 * q^2 + 8 * q^3 + 10 * q^4 + 10 * q^5 - 8 * q^6 + 3 * q^7 - 10 * q^8 + 14 * q^9	\( 10 q - 10 q^{2} + 8 q^{3} + 10 q^{4} + 10 q^{5} - 8 q^{6} + 3 q^{7} - 10 q^{8} + 14 q^{9} - 10 q^{10} + 10 q^{11} + 8 q^{12} + 7 q^{13} - 3 q^{14} + 8 q^{15} + 10 q^{16} + 2 q^{17} - 14 q^{18} - 7 q^{19} + 10 q^{20} - 2 q^{21} - 10 q^{22} + 12 q^{23} - 8 q^{24} + 10 q^{25} - 7 q^{26} + 23 q^{27} + 3 q^{28} - 12 q^{29} - 8 q^{30} + 16 q^{31} - 10 q^{32} + 8 q^{33} - 2 q^{34} + 3 q^{35} + 14 q^{36} + 19 q^{37} + 7 q^{38} + 6 q^{39} - 10 q^{40} + 9 q^{41} + 2 q^{42} + 10 q^{43} + 10 q^{44} + 14 q^{45} - 12 q^{46} + 29 q^{47} + 8 q^{48} + 23 q^{49} - 10 q^{50} - 7 q^{51} + 7 q^{52} + 6 q^{53} - 23 q^{54} + 10 q^{55} - 3 q^{56} + 23 q^{57} + 12 q^{58} + 29 q^{59} + 8 q^{60} - 4 q^{61} - 16 q^{62} + 10 q^{64} + 7 q^{65} - 8 q^{66} + 45 q^{67} + 2 q^{68} + 24 q^{69} - 3 q^{70} - 18 q^{71} - 14 q^{72} + 3 q^{73} - 19 q^{74} + 8 q^{75} - 7 q^{76} + 3 q^{77} - 6 q^{78} - 14 q^{79} + 10 q^{80} + 6 q^{81} - 9 q^{82} + 23 q^{83} - 2 q^{84} + 2 q^{85} - 10 q^{86} + 25 q^{87} - 10 q^{88} + q^{89} - 14 q^{90} + q^{91} + 12 q^{92} + 35 q^{93} - 29 q^{94} - 7 q^{95} - 8 q^{96} + 30 q^{97} - 23 q^{98} + 14 q^{99}+O(q^{100}) \) 10 * q - 10 * q^2 + 8 * q^3 + 10 * q^4 + 10 * q^5 - 8 * q^6 + 3 * q^7 - 10 * q^8 + 14 * q^9 - 10 * q^10 + 10 * q^11 + 8 * q^12 + 7 * q^13 - 3 * q^14 + 8 * q^15 + 10 * q^16 + 2 * q^17 - 14 * q^18 - 7 * q^19 + 10 * q^20 - 2 * q^21 - 10 * q^22 + 12 * q^23 - 8 * q^24 + 10 * q^25 - 7 * q^26 + 23 * q^27 + 3 * q^28 - 12 * q^29 - 8 * q^30 + 16 * q^31 - 10 * q^32 + 8 * q^33 - 2 * q^34 + 3 * q^35 + 14 * q^36 + 19 * q^37 + 7 * q^38 + 6 * q^39 - 10 * q^40 + 9 * q^41 + 2 * q^42 + 10 * q^43 + 10 * q^44 + 14 * q^45 - 12 * q^46 + 29 * q^47 + 8 * q^48 + 23 * q^49 - 10 * q^50 - 7 * q^51 + 7 * q^52 + 6 * q^53 - 23 * q^54 + 10 * q^55 - 3 * q^56 + 23 * q^57 + 12 * q^58 + 29 * q^59 + 8 * q^60 - 4 * q^61 - 16 * q^62 + 10 * q^64 + 7 * q^65 - 8 * q^66 + 45 * q^67 + 2 * q^68 + 24 * q^69 - 3 * q^70 - 18 * q^71 - 14 * q^72 + 3 * q^73 - 19 * q^74 + 8 * q^75 - 7 * q^76 + 3 * q^77 - 6 * q^78 - 14 * q^79 + 10 * q^80 + 6 * q^81 - 9 * q^82 + 23 * q^83 - 2 * q^84 + 2 * q^85 - 10 * q^86 + 25 * q^87 - 10 * q^88 + q^89 - 14 * q^90 + q^91 + 12 * q^92 + 35 * q^93 - 29 * q^94 - 7 * q^95 - 8 * q^96 + 30 * q^97 - 23 * q^98 + 14 * q^99

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