LMFDB - Embedded newform 4730.2.a.bc.1.2

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			1.2
Root			$-2.74176$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -2.74176 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.74176 q^{6} +3.45531 q^{7} -1.00000 q^{8} +4.51722 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.74176 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.74176 q^{6} +3.45531 q^{7} -1.00000 q^{8} +4.51722 q^{9} +1.00000 q^{10} +1.00000 q^{11} -2.74176 q^{12} +2.23890 q^{13} -3.45531 q^{14} +2.74176 q^{15} +1.00000 q^{16} -3.54650 q^{17} -4.51722 q^{18} +2.53201 q^{19} -1.00000 q^{20} -9.47360 q^{21} -1.00000 q^{22} -5.12108 q^{23} +2.74176 q^{24} +1.00000 q^{25} -2.23890 q^{26} -4.15985 q^{27} +3.45531 q^{28} +7.42077 q^{29} -2.74176 q^{30} +10.0816 q^{31} -1.00000 q^{32} -2.74176 q^{33} +3.54650 q^{34} -3.45531 q^{35} +4.51722 q^{36} +7.76357 q^{37} -2.53201 q^{38} -6.13852 q^{39} +1.00000 q^{40} +2.24595 q^{41} +9.47360 q^{42} -1.00000 q^{43} +1.00000 q^{44} -4.51722 q^{45} +5.12108 q^{46} +5.73889 q^{47} -2.74176 q^{48} +4.93914 q^{49} -1.00000 q^{50} +9.72364 q^{51} +2.23890 q^{52} +6.42870 q^{53} +4.15985 q^{54} -1.00000 q^{55} -3.45531 q^{56} -6.94215 q^{57} -7.42077 q^{58} +1.14981 q^{59} +2.74176 q^{60} -11.4749 q^{61} -10.0816 q^{62} +15.6084 q^{63} +1.00000 q^{64} -2.23890 q^{65} +2.74176 q^{66} -0.434762 q^{67} -3.54650 q^{68} +14.0408 q^{69} +3.45531 q^{70} +1.77353 q^{71} -4.51722 q^{72} +6.98587 q^{73} -7.76357 q^{74} -2.74176 q^{75} +2.53201 q^{76} +3.45531 q^{77} +6.13852 q^{78} +2.60283 q^{79} -1.00000 q^{80} -2.14637 q^{81} -2.24595 q^{82} -13.4238 q^{83} -9.47360 q^{84} +3.54650 q^{85} +1.00000 q^{86} -20.3459 q^{87} -1.00000 q^{88} -4.60130 q^{89} +4.51722 q^{90} +7.73609 q^{91} -5.12108 q^{92} -27.6412 q^{93} -5.73889 q^{94} -2.53201 q^{95} +2.74176 q^{96} +14.6645 q^{97} -4.93914 q^{98} +4.51722 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−2.74176	−1.58295	−0.791477	−	0.611199i	$-0.790687\pi$
$3$	−2.74176	−1.58295	−0.791477	+	0.611199i	$0.790687\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	2.74176	1.11932
$7$	3.45531	1.30598	0.652991	−	0.757365i	$-0.273514\pi$
$7$	3.45531	1.30598	0.652991	+	0.757365i	$0.273514\pi$
$8$	−1.00000	−0.353553
$9$	4.51722	1.50574
$10$	1.00000	0.316228
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−2.74176	−0.791477
$13$	2.23890	0.620960	0.310480	−	0.950580i	$-0.399510\pi$
$13$	2.23890	0.620960	0.310480	+	0.950580i	$0.399510\pi$
$14$	−3.45531	−0.923469
$15$	2.74176	0.707918
$16$	1.00000	0.250000
$17$	−3.54650	−0.860153	−0.430076	−	0.902793i	$-0.641513\pi$
$17$	−3.54650	−0.860153	−0.430076	+	0.902793i	$0.641513\pi$
$18$	−4.51722	−1.06472
$19$	2.53201	0.580883	0.290441	−	0.956893i	$-0.406198\pi$
$19$	2.53201	0.580883	0.290441	+	0.956893i	$0.406198\pi$
$20$	−1.00000	−0.223607
$21$	−9.47360	−2.06731
$22$	−1.00000	−0.213201
$23$	−5.12108	−1.06782	−0.533910	−	0.845542i	$-0.679278\pi$
$23$	−5.12108	−1.06782	−0.533910	+	0.845542i	$0.679278\pi$
$24$	2.74176	0.559658
$25$	1.00000	0.200000
$26$	−2.23890	−0.439085
$27$	−4.15985	−0.800564
$28$	3.45531	0.652991
$29$	7.42077	1.37800	0.689001	−	0.724760i	$-0.258050\pi$
$29$	7.42077	1.37800	0.689001	+	0.724760i	$0.258050\pi$
$30$	−2.74176	−0.500574
$31$	10.0816	1.81071	0.905353	−	0.424660i	$-0.139606\pi$
$31$	10.0816	1.81071	0.905353	+	0.424660i	$0.139606\pi$
$32$	−1.00000	−0.176777
$33$	−2.74176	−0.477278
$34$	3.54650	0.608220
$35$	−3.45531	−0.584053
$36$	4.51722	0.752870
$37$	7.76357	1.27632	0.638162	−	0.769902i	$-0.279695\pi$
$37$	7.76357	1.27632	0.638162	+	0.769902i	$0.279695\pi$
$38$	−2.53201	−0.410746
$39$	−6.13852	−0.982950
$40$	1.00000	0.158114
$41$	2.24595	0.350758	0.175379	−	0.984501i	$-0.443885\pi$
$41$	2.24595	0.350758	0.175379	+	0.984501i	$0.443885\pi$
$42$	9.47360	1.46181
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	1.00000	0.150756
$45$	−4.51722	−0.673388
$46$	5.12108	0.755062
$47$	5.73889	0.837103	0.418551	−	0.908193i	$-0.362538\pi$
$47$	5.73889	0.837103	0.418551	+	0.908193i	$0.362538\pi$
$48$	−2.74176	−0.395738
$49$	4.93914	0.705591
$50$	−1.00000	−0.141421
$51$	9.72364	1.36158
$52$	2.23890	0.310480
$53$	6.42870	0.883050	0.441525	−	0.897249i	$-0.354438\pi$
$53$	6.42870	0.883050	0.441525	+	0.897249i	$0.354438\pi$
$54$	4.15985	0.566084
$55$	−1.00000	−0.134840
$56$	−3.45531	−0.461735
$57$	−6.94215	−0.919510
$58$	−7.42077	−0.974395
$59$	1.14981	0.149693	0.0748465	−	0.997195i	$-0.476153\pi$
$59$	1.14981	0.149693	0.0748465	+	0.997195i	$0.476153\pi$
$60$	2.74176	0.353959
$61$	−11.4749	−1.46921	−0.734603	−	0.678497i	$-0.762632\pi$
$61$	−11.4749	−1.46921	−0.734603	+	0.678497i	$0.762632\pi$
$62$	−10.0816	−1.28036
$63$	15.6084	1.96647
$64$	1.00000	0.125000
$65$	−2.23890	−0.277702
$66$	2.74176	0.337487
$67$	−0.434762	−0.0531146	−0.0265573	−	0.999647i	$-0.508454\pi$
$67$	−0.434762	−0.0531146	−0.0265573	+	0.999647i	$0.508454\pi$
$68$	−3.54650	−0.430076
$69$	14.0408	1.69031
$70$	3.45531	0.412988
$71$	1.77353	0.210479	0.105239	−	0.994447i	$-0.466439\pi$
$71$	1.77353	0.210479	0.105239	+	0.994447i	$0.466439\pi$
$72$	−4.51722	−0.532360
$73$	6.98587	0.817634	0.408817	−	0.912616i	$-0.365941\pi$
$73$	6.98587	0.817634	0.408817	+	0.912616i	$0.365941\pi$
$74$	−7.76357	−0.902497
$75$	−2.74176	−0.316591
$76$	2.53201	0.290441
$77$	3.45531	0.393769
$78$	6.13852	0.695051
$79$	2.60283	0.292842	0.146421	−	0.989222i	$-0.453225\pi$
$79$	2.60283	0.292842	0.146421	+	0.989222i	$0.453225\pi$
$80$	−1.00000	−0.111803
$81$	−2.14637	−0.238485
$82$	−2.24595	−0.248023
$83$	−13.4238	−1.47345	−0.736727	−	0.676190i	$-0.763630\pi$
$83$	−13.4238	−1.47345	−0.736727	+	0.676190i	$0.763630\pi$
$84$	−9.47360	−1.03365
$85$	3.54650	0.384672
$86$	1.00000	0.107833
$87$	−20.3459	−2.18131
$88$	−1.00000	−0.106600
$89$	−4.60130	−0.487737	−0.243868	−	0.969808i	$-0.578416\pi$
$89$	−4.60130	−0.487737	−0.243868	+	0.969808i	$0.578416\pi$
$90$	4.51722	0.476157
$91$	7.73609	0.810963
$92$	−5.12108	−0.533910
$93$	−27.6412	−2.86626
$94$	−5.73889	−0.591921
$95$	−2.53201	−0.259779
$96$	2.74176	0.279829
$97$	14.6645	1.48895	0.744476	−	0.667650i	$-0.232700\pi$
$97$	14.6645	1.48895	0.744476	+	0.667650i	$0.232700\pi$
$98$	−4.93914	−0.498928
$99$	4.51722	0.453998
$100$	1.00000	0.100000
$101$	−6.38856	−0.635685	−0.317843	−	0.948144i	$-0.602958\pi$
$101$	−6.38856	−0.635685	−0.317843	+	0.948144i	$0.602958\pi$
$102$	−9.72364	−0.962783
$103$	−13.5053	−1.33071	−0.665357	−	0.746526i	$-0.731721\pi$
$103$	−13.5053	−1.33071	−0.665357	+	0.746526i	$0.731721\pi$
$104$	−2.23890	−0.219542
$105$	9.47360	0.924529
$106$	−6.42870	−0.624411
$107$	0.0113717	0.00109934	0.000549670	−	1.00000i	$-0.499825\pi$
$107$	0.0113717	0.00109934	0.000549670		1.00000i	$0.499825\pi$
$108$	−4.15985	−0.400282
$109$	9.57009	0.916648	0.458324	−	0.888785i	$-0.348450\pi$
$109$	9.57009	0.916648	0.458324	+	0.888785i	$0.348450\pi$
$110$	1.00000	0.0953463
$111$	−21.2858	−2.02036
$112$	3.45531	0.326496
$113$	−19.6574	−1.84921	−0.924605	−	0.380928i	$-0.875605\pi$
$113$	−19.6574	−1.84921	−0.924605	+	0.380928i	$0.875605\pi$
$114$	6.94215	0.650192
$115$	5.12108	0.477543
$116$	7.42077	0.689001
$117$	10.1136	0.935005
$118$	−1.14981	−0.105849
$119$	−12.2542	−1.12334
$120$	−2.74176	−0.250287
$121$	1.00000	0.0909091
$122$	11.4749	1.03889
$123$	−6.15784	−0.555234
$124$	10.0816	0.905353
$125$	−1.00000	−0.0894427
$126$	−15.6084	−1.39051
$127$	−13.5793	−1.20497	−0.602483	−	0.798131i	$-0.705822\pi$
$127$	−13.5793	−1.20497	−0.602483	+	0.798131i	$0.705822\pi$
$128$	−1.00000	−0.0883883
$129$	2.74176	0.241398
$130$	2.23890	0.196365
$131$	7.20257	0.629291	0.314646	−	0.949209i	$-0.398114\pi$
$131$	7.20257	0.629291	0.314646	+	0.949209i	$0.398114\pi$
$132$	−2.74176	−0.238639
$133$	8.74887	0.758623
$134$	0.434762	0.0375577
$135$	4.15985	0.358023
$136$	3.54650	0.304110
$137$	−11.8070	−1.00874	−0.504372	−	0.863487i	$-0.668276\pi$
$137$	−11.8070	−1.00874	−0.504372	+	0.863487i	$0.668276\pi$
$138$	−14.0408	−1.19523
$139$	−0.653289	−0.0554112	−0.0277056	−	0.999616i	$-0.508820\pi$
$139$	−0.653289	−0.0554112	−0.0277056	+	0.999616i	$0.508820\pi$
$140$	−3.45531	−0.292027
$141$	−15.7346	−1.32509
$142$	−1.77353	−0.148831
$143$	2.23890	0.187226
$144$	4.51722	0.376435
$145$	−7.42077	−0.616261
$146$	−6.98587	−0.578155
$147$	−13.5419	−1.11692
$148$	7.76357	0.638162
$149$	6.78814	0.556106	0.278053	−	0.960566i	$-0.410311\pi$
$149$	6.78814	0.556106	0.278053	+	0.960566i	$0.410311\pi$
$150$	2.74176	0.223863
$151$	12.1221	0.986482	0.493241	−	0.869893i	$-0.335812\pi$
$151$	12.1221	0.986482	0.493241	+	0.869893i	$0.335812\pi$
$152$	−2.53201	−0.205373
$153$	−16.0203	−1.29517
$154$	−3.45531	−0.278436
$155$	−10.0816	−0.809772
$156$	−6.13852	−0.491475
$157$	−18.0897	−1.44372	−0.721860	−	0.692040i	$-0.756712\pi$
$157$	−18.0897	−1.44372	−0.721860	+	0.692040i	$0.756712\pi$
$158$	−2.60283	−0.207070
$159$	−17.6259	−1.39783
$160$	1.00000	0.0790569
$161$	−17.6949	−1.39455
$162$	2.14637	0.168635
$163$	−1.61084	−0.126171	−0.0630855	−	0.998008i	$-0.520094\pi$
$163$	−1.61084	−0.126171	−0.0630855	+	0.998008i	$0.520094\pi$
$164$	2.24595	0.175379
$165$	2.74176	0.213445
$166$	13.4238	1.04189
$167$	2.22160	0.171913	0.0859564	−	0.996299i	$-0.472605\pi$
$167$	2.22160	0.171913	0.0859564	+	0.996299i	$0.472605\pi$
$168$	9.47360	0.730904
$169$	−7.98731	−0.614409
$170$	−3.54650	−0.272004
$171$	11.4376	0.874659
$172$	−1.00000	−0.0762493
$173$	20.4663	1.55603	0.778014	−	0.628247i	$-0.216227\pi$
$173$	20.4663	1.55603	0.778014	+	0.628247i	$0.216227\pi$
$174$	20.3459	1.54242
$175$	3.45531	0.261197
$176$	1.00000	0.0753778
$177$	−3.15251	−0.236957
$178$	4.60130	0.344882
$179$	21.0934	1.57660	0.788299	−	0.615292i	$-0.210962\pi$
$179$	21.0934	1.57660	0.788299	+	0.615292i	$0.210962\pi$
$180$	−4.51722	−0.336694
$181$	−7.19455	−0.534767	−0.267383	−	0.963590i	$-0.586159\pi$
$181$	−7.19455	−0.534767	−0.267383	+	0.963590i	$0.586159\pi$
$182$	−7.73609	−0.573437
$183$	31.4613	2.32569
$184$	5.12108	0.377531
$185$	−7.76357	−0.570789
$186$	27.6412	2.02675
$187$	−3.54650	−0.259346
$188$	5.73889	0.418551
$189$	−14.3736	−1.04552
$190$	2.53201	0.183691
$191$	12.3708	0.895119	0.447559	−	0.894254i	$-0.352293\pi$
$191$	12.3708	0.895119	0.447559	+	0.894254i	$0.352293\pi$
$192$	−2.74176	−0.197869
$193$	0.110090	0.00792443	0.00396222	−	0.999992i	$-0.498739\pi$
$193$	0.110090	0.00792443	0.00396222	+	0.999992i	$0.498739\pi$
$194$	−14.6645	−1.05285
$195$	6.13852	0.439589
$196$	4.93914	0.352795
$197$	−7.74261	−0.551638	−0.275819	−	0.961210i	$-0.588949\pi$
$197$	−7.74261	−0.551638	−0.275819	+	0.961210i	$0.588949\pi$
$198$	−4.51722	−0.321025
$199$	24.3707	1.72760	0.863798	−	0.503838i	$-0.168079\pi$
$199$	24.3707	1.72760	0.863798	+	0.503838i	$0.168079\pi$
$200$	−1.00000	−0.0707107
$201$	1.19201	0.0840779
$202$	6.38856	0.449497
$203$	25.6410	1.79965
$204$	9.72364	0.680791
$205$	−2.24595	−0.156864
$206$	13.5053	0.940957
$207$	−23.1331	−1.60786
$208$	2.23890	0.155240
$209$	2.53201	0.175143
$210$	−9.47360	−0.653741
$211$	9.89216	0.681004	0.340502	−	0.940244i	$-0.389403\pi$
$211$	9.89216	0.681004	0.340502	+	0.940244i	$0.389403\pi$
$212$	6.42870	0.441525
$213$	−4.86257	−0.333178
$214$	−0.0113717	−0.000777350 0
$215$	1.00000	0.0681994
$216$	4.15985	0.283042
$217$	34.8350	2.36475
$218$	−9.57009	−0.648168
$219$	−19.1536	−1.29428
$220$	−1.00000	−0.0674200
$221$	−7.94027	−0.534120
$222$	21.2858	1.42861
$223$	2.25558	0.151044	0.0755222	−	0.997144i	$-0.475938\pi$
$223$	2.25558	0.151044	0.0755222	+	0.997144i	$0.475938\pi$
$224$	−3.45531	−0.230867
$225$	4.51722	0.301148
$226$	19.6574	1.30759
$227$	−5.66634	−0.376088	−0.188044	−	0.982161i	$-0.560215\pi$
$227$	−5.66634	−0.376088	−0.188044	+	0.982161i	$0.560215\pi$
$228$	−6.94215	−0.459755
$229$	23.7130	1.56700	0.783500	−	0.621392i	$-0.213433\pi$
$229$	23.7130	1.56700	0.783500	+	0.621392i	$0.213433\pi$
$230$	−5.12108	−0.337674
$231$	−9.47360	−0.623317
$232$	−7.42077	−0.487197
$233$	0.949658	0.0622141	0.0311071	−	0.999516i	$-0.490097\pi$
$233$	0.949658	0.0622141	0.0311071	+	0.999516i	$0.490097\pi$
$234$	−10.1136	−0.661148
$235$	−5.73889	−0.374364
$236$	1.14981	0.0748465
$237$	−7.13634	−0.463555
$238$	12.2542	0.794324
$239$	−2.35813	−0.152535	−0.0762673	−	0.997087i	$-0.524300\pi$
$239$	−2.35813	−0.152535	−0.0762673	+	0.997087i	$0.524300\pi$
$240$	2.74176	0.176980
$241$	−17.1899	−1.10730	−0.553648	−	0.832751i	$-0.686765\pi$
$241$	−17.1899	−1.10730	−0.553648	+	0.832751i	$0.686765\pi$
$242$	−1.00000	−0.0642824
$243$	18.3644	1.17808
$244$	−11.4749	−0.734603
$245$	−4.93914	−0.315550
$246$	6.15784	0.392609
$247$	5.66892	0.360705
$248$	−10.0816	−0.640181
$249$	36.8048	2.33241
$250$	1.00000	0.0632456
$251$	−23.7071	−1.49638	−0.748191	−	0.663483i	$-0.769077\pi$
$251$	−23.7071	−1.49638	−0.748191	+	0.663483i	$0.769077\pi$
$252$	15.6084	0.983236
$253$	−5.12108	−0.321960
$254$	13.5793	0.852040
$255$	−9.72364	−0.608918
$256$	1.00000	0.0625000
$257$	−11.7930	−0.735628	−0.367814	−	0.929899i	$-0.619894\pi$
$257$	−11.7930	−0.735628	−0.367814	+	0.929899i	$0.619894\pi$
$258$	−2.74176	−0.170694
$259$	26.8255	1.66686
$260$	−2.23890	−0.138851
$261$	33.5213	2.07491
$262$	−7.20257	−0.444976
$263$	5.55774	0.342705	0.171352	−	0.985210i	$-0.445186\pi$
$263$	5.55774	0.342705	0.171352	+	0.985210i	$0.445186\pi$
$264$	2.74176	0.168743
$265$	−6.42870	−0.394912
$266$	−8.74887	−0.536427
$267$	12.6156	0.772065
$268$	−0.434762	−0.0265573
$269$	8.49381	0.517877	0.258938	−	0.965894i	$-0.416627\pi$
$269$	8.49381	0.517877	0.258938	+	0.965894i	$0.416627\pi$
$270$	−4.15985	−0.253161
$271$	16.8433	1.02316	0.511580	−	0.859236i	$-0.329060\pi$
$271$	16.8433	1.02316	0.511580	+	0.859236i	$0.329060\pi$
$272$	−3.54650	−0.215038
$273$	−21.2105	−1.28372
$274$	11.8070	0.713289
$275$	1.00000	0.0603023
$276$	14.0408	0.845154
$277$	28.6402	1.72082	0.860412	−	0.509599i	$-0.170206\pi$
$277$	28.6402	1.72082	0.860412	+	0.509599i	$0.170206\pi$
$278$	0.653289	0.0391816
$279$	45.5408	2.72645
$280$	3.45531	0.206494
$281$	−27.7837	−1.65744	−0.828719	−	0.559665i	$-0.810930\pi$
$281$	−27.7837	−1.65744	−0.828719	+	0.559665i	$0.810930\pi$
$282$	15.7346	0.936983
$283$	5.08910	0.302516	0.151258	−	0.988494i	$-0.451668\pi$
$283$	5.08910	0.302516	0.151258	+	0.988494i	$0.451668\pi$
$284$	1.77353	0.105239
$285$	6.94215	0.411217
$286$	−2.23890	−0.132389
$287$	7.76043	0.458084
$288$	−4.51722	−0.266180
$289$	−4.42234	−0.260138
$290$	7.42077	0.435763
$291$	−40.2064	−2.35694
$292$	6.98587	0.408817
$293$	5.23763	0.305986	0.152993	−	0.988227i	$-0.451109\pi$
$293$	5.23763	0.305986	0.152993	+	0.988227i	$0.451109\pi$
$294$	13.5419	0.789780
$295$	−1.14981	−0.0669447
$296$	−7.76357	−0.451249
$297$	−4.15985	−0.241379
$298$	−6.78814	−0.393226
$299$	−11.4656	−0.663073
$300$	−2.74176	−0.158295
$301$	−3.45531	−0.199160
$302$	−12.1221	−0.697548
$303$	17.5159	1.00626
$304$	2.53201	0.145221
$305$	11.4749	0.657049
$306$	16.0203	0.915821
$307$	−17.5342	−1.00073	−0.500364	−	0.865815i	$-0.666801\pi$
$307$	−17.5342	−1.00073	−0.500364	+	0.865815i	$0.666801\pi$
$308$	3.45531	0.196884
$309$	37.0281	2.10646
$310$	10.0816	0.572596
$311$	4.31937	0.244929	0.122464	−	0.992473i	$-0.460920\pi$
$311$	4.31937	0.244929	0.122464	+	0.992473i	$0.460920\pi$
$312$	6.13852	0.347525
$313$	−17.2084	−0.972675	−0.486337	−	0.873771i	$-0.661667\pi$
$313$	−17.2084	−0.972675	−0.486337	+	0.873771i	$0.661667\pi$
$314$	18.0897	1.02086
$315$	−15.6084	−0.879433
$316$	2.60283	0.146421
$317$	19.3527	1.08696	0.543478	−	0.839424i	$-0.317107\pi$
$317$	19.3527	1.08696	0.543478	+	0.839424i	$0.317107\pi$
$318$	17.6259	0.988413
$319$	7.42077	0.415483
$320$	−1.00000	−0.0559017
$321$	−0.0311783	−0.00174020
$322$	17.6949	0.986098
$323$	−8.97977	−0.499648
$324$	−2.14637	−0.119243
$325$	2.23890	0.124192
$326$	1.61084	0.0892164
$327$	−26.2388	−1.45101
$328$	−2.24595	−0.124012
$329$	19.8296	1.09324
$330$	−2.74176	−0.150929
$331$	−1.95449	−0.107428	−0.0537141	−	0.998556i	$-0.517106\pi$
$331$	−1.95449	−0.107428	−0.0537141	+	0.998556i	$0.517106\pi$
$332$	−13.4238	−0.736727
$333$	35.0698	1.92181
$334$	−2.22160	−0.121561
$335$	0.434762	0.0237536
$336$	−9.47360	−0.516827
$337$	−35.1913	−1.91699	−0.958496	−	0.285106i	$-0.907971\pi$
$337$	−35.1913	−1.91699	−0.958496	+	0.285106i	$0.907971\pi$
$338$	7.98731	0.434453
$339$	53.8957	2.92721
$340$	3.54650	0.192336
$341$	10.0816	0.545948
$342$	−11.4376	−0.618477
$343$	−7.12091	−0.384493
$344$	1.00000	0.0539164
$345$	−14.0408	−0.755929
$346$	−20.4663	−1.10028
$347$	25.7403	1.38181	0.690905	−	0.722946i	$-0.257212\pi$
$347$	25.7403	1.38181	0.690905	+	0.722946i	$0.257212\pi$
$348$	−20.3459	−1.09066
$349$	1.90620	0.102036	0.0510182	−	0.998698i	$-0.483753\pi$
$349$	1.90620	0.102036	0.0510182	+	0.998698i	$0.483753\pi$
$350$	−3.45531	−0.184694
$351$	−9.31351	−0.497118
$352$	−1.00000	−0.0533002
$353$	−2.70773	−0.144118	−0.0720589	−	0.997400i	$-0.522957\pi$
$353$	−2.70773	−0.144118	−0.0720589	+	0.997400i	$0.522957\pi$
$354$	3.15251	0.167554
$355$	−1.77353	−0.0941289
$356$	−4.60130	−0.243868
$357$	33.5981	1.77820
$358$	−21.0934	−1.11482
$359$	2.20172	0.116202	0.0581012	−	0.998311i	$-0.481495\pi$
$359$	2.20172	0.116202	0.0581012	+	0.998311i	$0.481495\pi$
$360$	4.51722	0.238079
$361$	−12.5889	−0.662575
$362$	7.19455	0.378137
$363$	−2.74176	−0.143905
$364$	7.73609	0.405481
$365$	−6.98587	−0.365657
$366$	−31.4613	−1.64451
$367$	−3.00727	−0.156978	−0.0784892	−	0.996915i	$-0.525010\pi$
$367$	−3.00727	−0.156978	−0.0784892	+	0.996915i	$0.525010\pi$
$368$	−5.12108	−0.266955
$369$	10.1454	0.528151
$370$	7.76357	0.403609
$371$	22.2131	1.15325
$372$	−27.6412	−1.43313
$373$	30.0497	1.55591	0.777957	−	0.628318i	$-0.216256\pi$
$373$	30.0497	1.55591	0.777957	+	0.628318i	$0.216256\pi$
$374$	3.54650	0.183385
$375$	2.74176	0.141584
$376$	−5.73889	−0.295961
$377$	16.6144	0.855684
$378$	14.3736	0.739296
$379$	24.4596	1.25640	0.628201	−	0.778051i	$-0.283791\pi$
$379$	24.4596	1.25640	0.628201	+	0.778051i	$0.283791\pi$
$380$	−2.53201	−0.129889
$381$	37.2311	1.90741
$382$	−12.3708	−0.632944
$383$	−16.1757	−0.826538	−0.413269	−	0.910609i	$-0.635613\pi$
$383$	−16.1757	−0.826538	−0.413269	+	0.910609i	$0.635613\pi$
$384$	2.74176	0.139915
$385$	−3.45531	−0.176099
$386$	−0.110090	−0.00560342
$387$	−4.51722	−0.229623
$388$	14.6645	0.744476
$389$	−14.2268	−0.721328	−0.360664	−	0.932696i	$-0.617450\pi$
$389$	−14.2268	−0.721328	−0.360664	+	0.932696i	$0.617450\pi$
$390$	−6.13852	−0.310836
$391$	18.1619	0.918487
$392$	−4.93914	−0.249464
$393$	−19.7477	−0.996139
$394$	7.74261	0.390067
$395$	−2.60283	−0.130963
$396$	4.51722	0.226999
$397$	−21.3375	−1.07090	−0.535450	−	0.844567i	$-0.679858\pi$
$397$	−21.3375	−1.07090	−0.535450	+	0.844567i	$0.679858\pi$
$398$	−24.3707	−1.22160
$399$	−23.9872	−1.20086
$400$	1.00000	0.0500000
$401$	28.9779	1.44709	0.723544	−	0.690278i	$-0.242512\pi$
$401$	28.9779	1.44709	0.723544	+	0.690278i	$0.242512\pi$
$402$	−1.19201	−0.0594521
$403$	22.5717	1.12438
$404$	−6.38856	−0.317843
$405$	2.14637	0.106654
$406$	−25.6410	−1.27254
$407$	7.76357	0.384826
$408$	−9.72364	−0.481392
$409$	−15.5171	−0.767271	−0.383636	−	0.923485i	$-0.625328\pi$
$409$	−15.5171	−0.767271	−0.383636	+	0.923485i	$0.625328\pi$
$410$	2.24595	0.110919
$411$	32.3720	1.59679
$412$	−13.5053	−0.665357
$413$	3.97296	0.195496
$414$	23.1331	1.13693
$415$	13.4238	0.658949
$416$	−2.23890	−0.109771
$417$	1.79116	0.0877134
$418$	−2.53201	−0.123845
$419$	38.5208	1.88187	0.940933	−	0.338593i	$-0.109951\pi$
$419$	38.5208	1.88187	0.940933	+	0.338593i	$0.109951\pi$
$420$	9.47360	0.462264
$421$	−20.1004	−0.979632	−0.489816	−	0.871826i	$-0.662936\pi$
$421$	−20.1004	−0.979632	−0.489816	+	0.871826i	$0.662936\pi$
$422$	−9.89216	−0.481543
$423$	25.9238	1.26046
$424$	−6.42870	−0.312205
$425$	−3.54650	−0.172031
$426$	4.86257	0.235592
$427$	−39.6492	−1.91876
$428$	0.0113717	0.000549670 0
$429$	−6.13852	−0.296371
$430$	−1.00000	−0.0482243
$431$	0.765435	0.0368697	0.0184348	−	0.999830i	$-0.494132\pi$
$431$	0.765435	0.0368697	0.0184348	+	0.999830i	$0.494132\pi$
$432$	−4.15985	−0.200141
$433$	−33.8037	−1.62450	−0.812252	−	0.583307i	$-0.801759\pi$
$433$	−33.8037	−1.62450	−0.812252	+	0.583307i	$0.801759\pi$
$434$	−34.8350	−1.67213
$435$	20.3459	0.975513
$436$	9.57009	0.458324
$437$	−12.9666	−0.620278
$438$	19.1536	0.915192
$439$	17.7766	0.848432	0.424216	−	0.905561i	$-0.360550\pi$
$439$	17.7766	0.848432	0.424216	+	0.905561i	$0.360550\pi$
$440$	1.00000	0.0476731
$441$	22.3112	1.06244
$442$	7.94027	0.377680
$443$	14.9588	0.710713	0.355357	−	0.934731i	$-0.384359\pi$
$443$	14.9588	0.710713	0.355357	+	0.934731i	$0.384359\pi$
$444$	−21.2858	−1.01018
$445$	4.60130	0.218123
$446$	−2.25558	−0.106805
$447$	−18.6114	−0.880290
$448$	3.45531	0.163248
$449$	30.0723	1.41920	0.709599	−	0.704606i	$-0.248876\pi$
$449$	30.0723	1.41920	0.709599	+	0.704606i	$0.248876\pi$
$450$	−4.51722	−0.212944
$451$	2.24595	0.105758
$452$	−19.6574	−0.924605
$453$	−33.2358	−1.56155
$454$	5.66634	0.265935
$455$	−7.73609	−0.362674
$456$	6.94215	0.325096
$457$	20.6688	0.966844	0.483422	−	0.875387i	$-0.339394\pi$
$457$	20.6688	0.966844	0.483422	+	0.875387i	$0.339394\pi$
$458$	−23.7130	−1.10804
$459$	14.7529	0.688607
$460$	5.12108	0.238772
$461$	13.0042	0.605666	0.302833	−	0.953044i	$-0.402068\pi$
$461$	13.0042	0.605666	0.302833	+	0.953044i	$0.402068\pi$
$462$	9.47360	0.440752
$463$	30.7753	1.43025	0.715124	−	0.698997i	$-0.246370\pi$
$463$	30.7753	1.43025	0.715124	+	0.698997i	$0.246370\pi$
$464$	7.42077	0.344501
$465$	27.6412	1.28183
$466$	−0.949658	−0.0439920
$467$	23.1635	1.07188	0.535939	−	0.844256i	$-0.319958\pi$
$467$	23.1635	1.07188	0.535939	+	0.844256i	$0.319958\pi$
$468$	10.1136	0.467502
$469$	−1.50224	−0.0693668
$470$	5.73889	0.264715
$471$	49.5977	2.28534
$472$	−1.14981	−0.0529245
$473$	−1.00000	−0.0459800
$474$	7.13634	0.327783
$475$	2.53201	0.116177
$476$	−12.2542	−0.561672
$477$	29.0399	1.32964
$478$	2.35813	0.107858
$479$	−40.1677	−1.83531	−0.917654	−	0.397379i	$-0.869920\pi$
$479$	−40.1677	−1.83531	−0.917654	+	0.397379i	$0.869920\pi$
$480$	−2.74176	−0.125143
$481$	17.3819	0.792546
$482$	17.1899	0.782977
$483$	48.5151	2.20751
$484$	1.00000	0.0454545
$485$	−14.6645	−0.665879
$486$	−18.3644	−0.833025
$487$	14.2939	0.647717	0.323859	−	0.946105i	$-0.395020\pi$
$487$	14.2939	0.647717	0.323859	+	0.946105i	$0.395020\pi$
$488$	11.4749	0.519443
$489$	4.41654	0.199723
$490$	4.93914	0.223127
$491$	36.1171	1.62994	0.814972	−	0.579500i	$-0.196752\pi$
$491$	36.1171	1.62994	0.814972	+	0.579500i	$0.196752\pi$
$492$	−6.15784	−0.277617
$493$	−26.3178	−1.18529
$494$	−5.66892	−0.255057
$495$	−4.51722	−0.203034
$496$	10.0816	0.452677
$497$	6.12807	0.274882
$498$	−36.8048	−1.64926
$499$	28.4087	1.27175	0.635875	−	0.771792i	$-0.280639\pi$
$499$	28.4087	1.27175	0.635875	+	0.771792i	$0.280639\pi$
$500$	−1.00000	−0.0447214
$501$	−6.09109	−0.272130
$502$	23.7071	1.05810
$503$	29.2718	1.30516	0.652582	−	0.757718i	$-0.273686\pi$
$503$	29.2718	1.30516	0.652582	+	0.757718i	$0.273686\pi$
$504$	−15.6084	−0.695253
$505$	6.38856	0.284287
$506$	5.12108	0.227660
$507$	21.8993	0.972580
$508$	−13.5793	−0.602483
$509$	1.62530	0.0720401	0.0360200	−	0.999351i	$-0.488532\pi$
$509$	1.62530	0.0720401	0.0360200	+	0.999351i	$0.488532\pi$
$510$	9.72364	0.430570
$511$	24.1383	1.06782
$512$	−1.00000	−0.0441942
$513$	−10.5328	−0.465034
$514$	11.7930	0.520168
$515$	13.5053	0.595113
$516$	2.74176	0.120699
$517$	5.73889	0.252396
$518$	−26.8255	−1.17865
$519$	−56.1137	−2.46312
$520$	2.23890	0.0981824
$521$	15.3578	0.672836	0.336418	−	0.941713i	$-0.390785\pi$
$521$	15.3578	0.672836	0.336418	+	0.941713i	$0.390785\pi$
$522$	−33.5213	−1.46719
$523$	5.66539	0.247730	0.123865	−	0.992299i	$-0.460471\pi$
$523$	5.66539	0.247730	0.123865	+	0.992299i	$0.460471\pi$
$524$	7.20257	0.314646
$525$	−9.47360	−0.413462
$526$	−5.55774	−0.242329
$527$	−35.7543	−1.55748
$528$	−2.74176	−0.119320
$529$	3.22547	0.140238
$530$	6.42870	0.279245
$531$	5.19396	0.225399
$532$	8.74887	0.379311
$533$	5.02846	0.217807
$534$	−12.6156	−0.545932
$535$	−0.0113717	−0.000491639 0
$536$	0.434762	0.0187789
$537$	−57.8331	−2.49568
$538$	−8.49381	−0.366194
$539$	4.93914	0.212744
$540$	4.15985	0.179012
$541$	−42.6566	−1.83395	−0.916976	−	0.398943i	$-0.869377\pi$
$541$	−42.6566	−1.83395	−0.916976	+	0.398943i	$0.869377\pi$
$542$	−16.8433	−0.723483
$543$	19.7257	0.846511
$544$	3.54650	0.152055
$545$	−9.57009	−0.409938
$546$	21.2105	0.907724
$547$	6.71244	0.287003	0.143502	−	0.989650i	$-0.454164\pi$
$547$	6.71244	0.287003	0.143502	+	0.989650i	$0.454164\pi$
$548$	−11.8070	−0.504372
$549$	−51.8346	−2.21224
$550$	−1.00000	−0.0426401
$551$	18.7895	0.800458
$552$	−14.0408	−0.597614
$553$	8.99359	0.382446
$554$	−28.6402	−1.21681
$555$	21.2858	0.903533
$556$	−0.653289	−0.0277056
$557$	36.7844	1.55860	0.779302	−	0.626648i	$-0.215574\pi$
$557$	36.7844	1.55860	0.779302	+	0.626648i	$0.215574\pi$
$558$	−45.5408	−1.92789
$559$	−2.23890	−0.0946955
$560$	−3.45531	−0.146013
$561$	9.72364	0.410532
$562$	27.7837	1.17199
$563$	−6.32174	−0.266430	−0.133215	−	0.991087i	$-0.542530\pi$
$563$	−6.32174	−0.266430	−0.133215	+	0.991087i	$0.542530\pi$
$564$	−15.7346	−0.662547
$565$	19.6574	0.826992
$566$	−5.08910	−0.213911
$567$	−7.41636	−0.311458
$568$	−1.77353	−0.0744155
$569$	7.16732	0.300470	0.150235	−	0.988650i	$-0.451997\pi$
$569$	7.16732	0.300470	0.150235	+	0.988650i	$0.451997\pi$
$570$	−6.94215	−0.290775
$571$	−9.09027	−0.380416	−0.190208	−	0.981744i	$-0.560916\pi$
$571$	−9.09027	−0.380416	−0.190208	+	0.981744i	$0.560916\pi$
$572$	2.23890	0.0936132
$573$	−33.9177	−1.41693
$574$	−7.76043	−0.323914
$575$	−5.12108	−0.213564
$576$	4.51722	0.188218
$577$	−35.1409	−1.46293	−0.731467	−	0.681877i	$-0.761164\pi$
$577$	−35.1409	−1.46293	−0.731467	+	0.681877i	$0.761164\pi$
$578$	4.42234	0.183945
$579$	−0.301839	−0.0125440
$580$	−7.42077	−0.308131
$581$	−46.3834	−1.92431
$582$	40.2064	1.66661
$583$	6.42870	0.266250
$584$	−6.98587	−0.289077
$585$	−10.1136	−0.418147
$586$	−5.23763	−0.216365
$587$	−27.8653	−1.15013	−0.575063	−	0.818109i	$-0.695022\pi$
$587$	−27.8653	−1.15013	−0.575063	+	0.818109i	$0.695022\pi$
$588$	−13.5419	−0.558459
$589$	25.5267	1.05181
$590$	1.14981	0.0473371
$591$	21.2283	0.873217
$592$	7.76357	0.319081
$593$	28.2814	1.16138	0.580688	−	0.814126i	$-0.302784\pi$
$593$	28.2814	1.16138	0.580688	+	0.814126i	$0.302784\pi$
$594$	4.15985	0.170681
$595$	12.2542	0.502375
$596$	6.78814	0.278053
$597$	−66.8186	−2.73470
$598$	11.4656	0.468863
$599$	−33.1238	−1.35340	−0.676701	−	0.736258i	$-0.736591\pi$
$599$	−33.1238	−1.35340	−0.676701	+	0.736258i	$0.736591\pi$
$600$	2.74176	0.111932
$601$	17.2472	0.703530	0.351765	−	0.936088i	$-0.385582\pi$
$601$	17.2472	0.703530	0.351765	+	0.936088i	$0.385582\pi$
$602$	3.45531	0.140828
$603$	−1.96392	−0.0799768
$604$	12.1221	0.493241
$605$	−1.00000	−0.0406558
$606$	−17.5159	−0.711533
$607$	37.5019	1.52216	0.761078	−	0.648661i	$-0.224671\pi$
$607$	37.5019	1.52216	0.761078	+	0.648661i	$0.224671\pi$
$608$	−2.53201	−0.102687
$609$	−70.3014	−2.84876
$610$	−11.4749	−0.464604
$611$	12.8488	0.519807
$612$	−16.0203	−0.647583
$613$	12.2591	0.495139	0.247569	−	0.968870i	$-0.420368\pi$
$613$	12.2591	0.495139	0.247569	+	0.968870i	$0.420368\pi$
$614$	17.5342	0.707622
$615$	6.15784	0.248308
$616$	−3.45531	−0.139218
$617$	−22.8017	−0.917960	−0.458980	−	0.888447i	$-0.651785\pi$
$617$	−22.8017	−0.917960	−0.458980	+	0.888447i	$0.651785\pi$
$618$	−37.0281	−1.48949
$619$	−14.5480	−0.584733	−0.292366	−	0.956306i	$-0.594443\pi$
$619$	−14.5480	−0.584733	−0.292366	+	0.956306i	$0.594443\pi$
$620$	−10.0816	−0.404886
$621$	21.3029	0.854858
$622$	−4.31937	−0.173191
$623$	−15.8989	−0.636976
$624$	−6.13852	−0.245738
$625$	1.00000	0.0400000
$626$	17.2084	0.687785
$627$	−6.94215	−0.277243
$628$	−18.0897	−0.721860
$629$	−27.5335	−1.09783
$630$	15.6084	0.621853
$631$	18.2502	0.726528	0.363264	−	0.931686i	$-0.381662\pi$
$631$	18.2502	0.726528	0.363264	+	0.931686i	$0.381662\pi$
$632$	−2.60283	−0.103535
$633$	−27.1219	−1.07800
$634$	−19.3527	−0.768594
$635$	13.5793	0.538878
$636$	−17.6259	−0.698913
$637$	11.0582	0.438144
$638$	−7.42077	−0.293791
$639$	8.01141	0.316926
$640$	1.00000	0.0395285
$641$	−1.77475	−0.0700984	−0.0350492	−	0.999386i	$-0.511159\pi$
$641$	−1.77475	−0.0700984	−0.0350492	+	0.999386i	$0.511159\pi$
$642$	0.0311783	0.00123051
$643$	−39.7770	−1.56865	−0.784326	−	0.620348i	$-0.786991\pi$
$643$	−39.7770	−1.56865	−0.784326	+	0.620348i	$0.786991\pi$
$644$	−17.6949	−0.697277
$645$	−2.74176	−0.107957
$646$	8.97977	0.353304
$647$	20.3991	0.801972	0.400986	−	0.916084i	$-0.368668\pi$
$647$	20.3991	0.801972	0.400986	+	0.916084i	$0.368668\pi$
$648$	2.14637	0.0843173
$649$	1.14981	0.0451341
$650$	−2.23890	−0.0878170
$651$	−95.5089	−3.74329
$652$	−1.61084	−0.0630855
$653$	36.0085	1.40912	0.704561	−	0.709643i	$-0.251144\pi$
$653$	36.0085	1.40912	0.704561	+	0.709643i	$0.251144\pi$
$654$	26.2388	1.02602
$655$	−7.20257	−0.281428
$656$	2.24595	0.0876895
$657$	31.5567	1.23115
$658$	−19.8296	−0.773039
$659$	22.6724	0.883192	0.441596	−	0.897214i	$-0.354412\pi$
$659$	22.6724	0.883192	0.441596	+	0.897214i	$0.354412\pi$
$660$	2.74176	0.106723
$661$	30.1085	1.17109	0.585543	−	0.810641i	$-0.300881\pi$
$661$	30.1085	1.17109	0.585543	+	0.810641i	$0.300881\pi$
$662$	1.95449	0.0759632
$663$	21.7703	0.845487
$664$	13.4238	0.520945
$665$	−8.74887	−0.339266
$666$	−35.0698	−1.35893
$667$	−38.0024	−1.47146
$668$	2.22160	0.0859564
$669$	−6.18424	−0.239096
$670$	−0.434762	−0.0167963
$671$	−11.4749	−0.442983
$672$	9.47360	0.365452
$673$	11.5463	0.445079	0.222539	−	0.974924i	$-0.428565\pi$
$673$	11.5463	0.445079	0.222539	+	0.974924i	$0.428565\pi$
$674$	35.1913	1.35552
$675$	−4.15985	−0.160113
$676$	−7.98731	−0.307204
$677$	0.0524858	0.00201719	0.00100860	−	0.999999i	$-0.499679\pi$
$677$	0.0524858	0.00201719	0.00100860	+	0.999999i	$0.499679\pi$
$678$	−53.8957	−2.06985
$679$	50.6702	1.94454
$680$	−3.54650	−0.136002
$681$	15.5357	0.595330
$682$	−10.0816	−0.386044
$683$	−1.64947	−0.0631152	−0.0315576	−	0.999502i	$-0.510047\pi$
$683$	−1.64947	−0.0631152	−0.0315576	+	0.999502i	$0.510047\pi$
$684$	11.4376	0.437329
$685$	11.8070	0.451124
$686$	7.12091	0.271878
$687$	−65.0152	−2.48049
$688$	−1.00000	−0.0381246
$689$	14.3932	0.548339
$690$	14.0408	0.534522
$691$	2.31492	0.0880636	0.0440318	−	0.999030i	$-0.485980\pi$
$691$	2.31492	0.0880636	0.0440318	+	0.999030i	$0.485980\pi$
$692$	20.4663	0.778014
$693$	15.6084	0.592913
$694$	−25.7403	−0.977087
$695$	0.653289	0.0247806
$696$	20.3459	0.771211
$697$	−7.96525	−0.301705
$698$	−1.90620	−0.0721506
$699$	−2.60373	−0.0984821
$700$	3.45531	0.130598
$701$	−29.1695	−1.10172	−0.550859	−	0.834598i	$-0.685700\pi$
$701$	−29.1695	−1.10172	−0.550859	+	0.834598i	$0.685700\pi$
$702$	9.31351	0.351516
$703$	19.6574	0.741394
$704$	1.00000	0.0376889
$705$	15.7346	0.592600
$706$	2.70773	0.101907
$707$	−22.0744	−0.830194
$708$	−3.15251	−0.118478
$709$	−4.76369	−0.178904	−0.0894521	−	0.995991i	$-0.528512\pi$
$709$	−4.76369	−0.178904	−0.0894521	+	0.995991i	$0.528512\pi$
$710$	1.77353	0.0665592
$711$	11.7576	0.440944
$712$	4.60130	0.172441
$713$	−51.6286	−1.93351
$714$	−33.5981	−1.25738
$715$	−2.23890	−0.0837302
$716$	21.0934	0.788299
$717$	6.46541	0.241455
$718$	−2.20172	−0.0821675
$719$	−33.9199	−1.26500	−0.632499	−	0.774561i	$-0.717971\pi$
$719$	−33.9199	−1.26500	−0.632499	+	0.774561i	$0.717971\pi$
$720$	−4.51722	−0.168347
$721$	−46.6648	−1.73789
$722$	12.5889	0.468511
$723$	47.1304	1.75280
$724$	−7.19455	−0.267383
$725$	7.42077	0.275600
$726$	2.74176	0.101756
$727$	36.6901	1.36076	0.680381	−	0.732859i	$-0.261814\pi$
$727$	36.6901	1.36076	0.680381	+	0.732859i	$0.261814\pi$
$728$	−7.73609	−0.286719
$729$	−43.9115	−1.62635
$730$	6.98587	0.258559
$731$	3.54650	0.131172
$732$	31.4613	1.16284
$733$	28.1274	1.03891	0.519455	−	0.854498i	$-0.326135\pi$
$733$	28.1274	1.03891	0.519455	+	0.854498i	$0.326135\pi$
$734$	3.00727	0.111000
$735$	13.5419	0.499501
$736$	5.12108	0.188766
$737$	−0.434762	−0.0160147
$738$	−10.1454	−0.373459
$739$	22.8267	0.839693	0.419847	−	0.907595i	$-0.362084\pi$
$739$	22.8267	0.839693	0.419847	+	0.907595i	$0.362084\pi$
$740$	−7.76357	−0.285395
$741$	−15.5428	−0.570979
$742$	−22.2131	−0.815469
$743$	23.0660	0.846209	0.423105	−	0.906081i	$-0.360940\pi$
$743$	23.0660	0.846209	0.423105	+	0.906081i	$0.360940\pi$
$744$	27.6412	1.01338
$745$	−6.78814	−0.248698
$746$	−30.0497	−1.10020
$747$	−60.6383	−2.21864
$748$	−3.54650	−0.129673
$749$	0.0392925	0.00143572
$750$	−2.74176	−0.100115
$751$	14.6874	0.535951	0.267975	−	0.963426i	$-0.413645\pi$
$751$	14.6874	0.535951	0.267975	+	0.963426i	$0.413645\pi$
$752$	5.73889	0.209276
$753$	64.9992	2.36870
$754$	−16.6144	−0.605060
$755$	−12.1221	−0.441168
$756$	−14.3736	−0.522761
$757$	20.0616	0.729153	0.364576	−	0.931173i	$-0.381214\pi$
$757$	20.0616	0.729153	0.364576	+	0.931173i	$0.381214\pi$
$758$	−24.4596	−0.888411
$759$	14.0408	0.509647
$760$	2.53201	0.0918456
$761$	−23.3513	−0.846485	−0.423242	−	0.906016i	$-0.639108\pi$
$761$	−23.3513	−0.846485	−0.423242	+	0.906016i	$0.639108\pi$
$762$	−37.2311	−1.34874
$763$	33.0676	1.19713
$764$	12.3708	0.447559
$765$	16.0203	0.579216
$766$	16.1757	0.584451
$767$	2.57432	0.0929533
$768$	−2.74176	−0.0989346
$769$	6.52564	0.235321	0.117660	−	0.993054i	$-0.462461\pi$
$769$	6.52564	0.235321	0.117660	+	0.993054i	$0.462461\pi$
$770$	3.45531	0.124521
$771$	32.3336	1.16446
$772$	0.110090	0.00396222
$773$	−28.4322	−1.02263	−0.511317	−	0.859392i	$-0.670842\pi$
$773$	−28.4322	−1.02263	−0.511317	+	0.859392i	$0.670842\pi$
$774$	4.51722	0.162368
$775$	10.0816	0.362141
$776$	−14.6645	−0.526424
$777$	−73.5490	−2.63856
$778$	14.2268	0.510056
$779$	5.68676	0.203749
$780$	6.13852	0.219794
$781$	1.77353	0.0634617
$782$	−18.1619	−0.649469
$783$	−30.8693	−1.10318
$784$	4.93914	0.176398
$785$	18.0897	0.645651
$786$	19.7477	0.704376
$787$	−21.3785	−0.762062	−0.381031	−	0.924562i	$-0.624431\pi$
$787$	−21.3785	−0.762062	−0.381031	+	0.924562i	$0.624431\pi$
$788$	−7.74261	−0.275819
$789$	−15.2380	−0.542485
$790$	2.60283	0.0926047
$791$	−67.9222	−2.41504
$792$	−4.51722	−0.160513
$793$	−25.6911	−0.912318
$794$	21.3375	0.757240
$795$	17.6259	0.625127
$796$	24.3707	0.863798
$797$	−22.5555	−0.798958	−0.399479	−	0.916742i	$-0.630809\pi$
$797$	−22.5555	−0.798958	−0.399479	+	0.916742i	$0.630809\pi$
$798$	23.9872	0.849139
$799$	−20.3530	−0.720036
$800$	−1.00000	−0.0353553
$801$	−20.7851	−0.734405
$802$	−28.9779	−1.02325
$803$	6.98587	0.246526
$804$	1.19201	0.0420390
$805$	17.6949	0.623663
$806$	−22.5717	−0.795054
$807$	−23.2880	−0.819775
$808$	6.38856	0.224749
$809$	14.7023	0.516904	0.258452	−	0.966024i	$-0.416788\pi$
$809$	14.7023	0.516904	0.258452	+	0.966024i	$0.416788\pi$
$810$	−2.14637	−0.0754157
$811$	30.1323	1.05809	0.529043	−	0.848595i	$-0.322551\pi$
$811$	30.1323	1.05809	0.529043	+	0.848595i	$0.322551\pi$
$812$	25.6410	0.899824
$813$	−46.1803	−1.61961
$814$	−7.76357	−0.272113
$815$	1.61084	0.0564254
$816$	9.72364	0.340395
$817$	−2.53201	−0.0885838
$818$	15.5171	0.542543
$819$	34.9457	1.22110
$820$	−2.24595	−0.0784319
$821$	−17.1437	−0.598320	−0.299160	−	0.954203i	$-0.596706\pi$
$821$	−17.1437	−0.598320	−0.299160	+	0.954203i	$0.596706\pi$
$822$	−32.3720	−1.12910
$823$	29.2224	1.01863	0.509314	−	0.860581i	$-0.329899\pi$
$823$	29.2224	1.01863	0.509314	+	0.860581i	$0.329899\pi$
$824$	13.5053	0.470478
$825$	−2.74176	−0.0954557
$826$	−3.97296	−0.138237
$827$	−11.2461	−0.391064	−0.195532	−	0.980697i	$-0.562643\pi$
$827$	−11.2461	−0.391064	−0.195532	+	0.980697i	$0.562643\pi$
$828$	−23.1331	−0.803929
$829$	−27.5247	−0.955971	−0.477985	−	0.878368i	$-0.658633\pi$
$829$	−27.5247	−0.955971	−0.477985	+	0.878368i	$0.658633\pi$
$830$	−13.4238	−0.465947
$831$	−78.5245	−2.72398
$832$	2.23890	0.0776200
$833$	−17.5166	−0.606916
$834$	−1.79116	−0.0620227
$835$	−2.22160	−0.0768818
$836$	2.53201	0.0875714
$837$	−41.9379	−1.44959
$838$	−38.5208	−1.33068
$839$	−45.2967	−1.56382	−0.781909	−	0.623393i	$-0.785754\pi$
$839$	−45.2967	−1.56382	−0.781909	+	0.623393i	$0.785754\pi$
$840$	−9.47360	−0.326870
$841$	26.0678	0.898890
$842$	20.1004	0.692704
$843$	76.1762	2.62365
$844$	9.89216	0.340502
$845$	7.98731	0.274772
$846$	−25.9238	−0.891280
$847$	3.45531	0.118726
$848$	6.42870	0.220762
$849$	−13.9531	−0.478868
$850$	3.54650	0.121644
$851$	−39.7579	−1.36288
$852$	−4.86257	−0.166589
$853$	55.2085	1.89030	0.945151	−	0.326635i	$-0.105915\pi$
$853$	55.2085	1.89030	0.945151	+	0.326635i	$0.105915\pi$
$854$	39.6492	1.35677
$855$	−11.4376	−0.391159
$856$	−0.0113717	−0.000388675 0
$857$	−27.7366	−0.947463	−0.473731	−	0.880669i	$-0.657093\pi$
$857$	−27.7366	−0.947463	−0.473731	+	0.880669i	$0.657093\pi$
$858$	6.13852	0.209566
$859$	37.8867	1.29268	0.646339	−	0.763050i	$-0.276299\pi$
$859$	37.8867	1.29268	0.646339	+	0.763050i	$0.276299\pi$
$860$	1.00000	0.0340997
$861$	−21.2772	−0.725125
$862$	−0.765435	−0.0260708
$863$	53.6964	1.82785	0.913923	−	0.405888i	$-0.133038\pi$
$863$	53.6964	1.82785	0.913923	+	0.405888i	$0.133038\pi$
$864$	4.15985	0.141521
$865$	−20.4663	−0.695877
$866$	33.8037	1.14870
$867$	12.1250	0.411786
$868$	34.8350	1.18238
$869$	2.60283	0.0882951
$870$	−20.3459	−0.689792
$871$	−0.973389	−0.0329820
$872$	−9.57009	−0.324084
$873$	66.2427	2.24198
$874$	12.9666	0.438603
$875$	−3.45531	−0.116811
$876$	−19.1536	−0.647139
$877$	0.740357	0.0250001	0.0125000	−	0.999922i	$-0.496021\pi$
$877$	0.740357	0.0250001	0.0125000	+	0.999922i	$0.496021\pi$
$878$	−17.7766	−0.599932
$879$	−14.3603	−0.484361
$880$	−1.00000	−0.0337100
$881$	17.3173	0.583435	0.291717	−	0.956505i	$-0.405773\pi$
$881$	17.3173	0.583435	0.291717	+	0.956505i	$0.405773\pi$
$882$	−22.3112	−0.751256
$883$	−4.51520	−0.151948	−0.0759742	−	0.997110i	$-0.524207\pi$
$883$	−4.51520	−0.151948	−0.0759742	+	0.997110i	$0.524207\pi$
$884$	−7.94027	−0.267060
$885$	3.15251	0.105970
$886$	−14.9588	−0.502550
$887$	1.78714	0.0600062	0.0300031	−	0.999550i	$-0.490448\pi$
$887$	1.78714	0.0600062	0.0300031	+	0.999550i	$0.490448\pi$
$888$	21.2858	0.714305
$889$	−46.9206	−1.57367
$890$	−4.60130	−0.154236
$891$	−2.14637	−0.0719061
$892$	2.25558	0.0755222
$893$	14.5309	0.486259
$894$	18.6114	0.622459
$895$	−21.0934	−0.705076
$896$	−3.45531	−0.115434
$897$	31.4359	1.04961
$898$	−30.0723	−1.00352
$899$	74.8131	2.49516
$900$	4.51722	0.150574
$901$	−22.7994	−0.759558
$902$	−2.24595	−0.0747819
$903$	9.47360	0.315262
$904$	19.6574	0.653794
$905$	7.19455	0.239155
$906$	33.2358	1.10419
$907$	−16.1438	−0.536045	−0.268023	−	0.963413i	$-0.586370\pi$
$907$	−16.1438	−0.536045	−0.268023	+	0.963413i	$0.586370\pi$
$908$	−5.66634	−0.188044
$909$	−28.8585	−0.957177
$910$	7.73609	0.256449
$911$	15.9204	0.527466	0.263733	−	0.964596i	$-0.415046\pi$
$911$	15.9204	0.527466	0.263733	+	0.964596i	$0.415046\pi$
$912$	−6.94215	−0.229878
$913$	−13.4238	−0.444263
$914$	−20.6688	−0.683662
$915$	−31.4613	−1.04008
$916$	23.7130	0.783500
$917$	24.8871	0.821843
$918$	−14.7529	−0.486919
$919$	−7.46941	−0.246393	−0.123197	−	0.992382i	$-0.539315\pi$
$919$	−7.46941	−0.246393	−0.123197	+	0.992382i	$0.539315\pi$
$920$	−5.12108	−0.168837
$921$	48.0744	1.58411
$922$	−13.0042	−0.428271
$923$	3.97075	0.130699
$924$	−9.47360	−0.311659
$925$	7.76357	0.255265
$926$	−30.7753	−1.01134
$927$	−61.0063	−2.00371
$928$	−7.42077	−0.243599
$929$	−37.8656	−1.24233	−0.621165	−	0.783680i	$-0.713340\pi$
$929$	−37.8656	−1.24233	−0.621165	+	0.783680i	$0.713340\pi$
$930$	−27.6412	−0.906392
$931$	12.5059	0.409866
$932$	0.949658	0.0311071
$933$	−11.8426	−0.387711
$934$	−23.1635	−0.757933
$935$	3.54650	0.115983
$936$	−10.1136	−0.330574
$937$	50.1377	1.63793	0.818964	−	0.573845i	$-0.194549\pi$
$937$	50.1377	1.63793	0.818964	+	0.573845i	$0.194549\pi$
$938$	1.50224	0.0490497
$939$	47.1811	1.53970
$940$	−5.73889	−0.187182
$941$	14.5911	0.475655	0.237828	−	0.971307i	$-0.423565\pi$
$941$	14.5911	0.475655	0.237828	+	0.971307i	$0.423565\pi$
$942$	−49.5977	−1.61598
$943$	−11.5017	−0.374546
$944$	1.14981	0.0374232
$945$	14.3736	0.467572
$946$	1.00000	0.0325128
$947$	40.8093	1.32612	0.663062	−	0.748564i	$-0.269257\pi$
$947$	40.8093	1.32612	0.663062	+	0.748564i	$0.269257\pi$
$948$	−7.13634	−0.231777
$949$	15.6407	0.507718
$950$	−2.53201	−0.0821492
$951$	−53.0604	−1.72060
$952$	12.2542	0.397162
$953$	−0.00995018	−0.000322318 0	−0.000161159	−	1.00000i	$-0.500051\pi$
$953$	−0.00995018	−0.000322318 0	−0.000161159		1.00000i	$0.500051\pi$
$954$	−29.0399	−0.940201
$955$	−12.3708	−0.400309
$956$	−2.35813	−0.0762673
$957$	−20.3459	−0.657691
$958$	40.1677	1.29776
$959$	−40.7969	−1.31740
$960$	2.74176	0.0884898
$961$	70.6384	2.27866
$962$	−17.3819	−0.560415
$963$	0.0513683	0.00165532
$964$	−17.1899	−0.553648
$965$	−0.110090	−0.00354391
$966$	−48.5151	−1.56095
$967$	25.0605	0.805891	0.402945	−	0.915224i	$-0.367986\pi$
$967$	25.0605	0.805891	0.402945	+	0.915224i	$0.367986\pi$
$968$	−1.00000	−0.0321412
$969$	24.6203	0.790919
$970$	14.6645	0.470848
$971$	−11.5222	−0.369765	−0.184883	−	0.982761i	$-0.559191\pi$
$971$	−11.5222	−0.369765	−0.184883	+	0.982761i	$0.559191\pi$
$972$	18.3644	0.589038
$973$	−2.25731	−0.0723661
$974$	−14.2939	−0.458005
$975$	−6.13852	−0.196590
$976$	−11.4749	−0.367302
$977$	−36.5125	−1.16814	−0.584070	−	0.811704i	$-0.698541\pi$
$977$	−36.5125	−1.16814	−0.584070	+	0.811704i	$0.698541\pi$
$978$	−4.41654	−0.141225
$979$	−4.60130	−0.147058
$980$	−4.93914	−0.157775
$981$	43.2302	1.38024
$982$	−36.1171	−1.15254
$983$	14.7876	0.471652	0.235826	−	0.971795i	$-0.424220\pi$
$983$	14.7876	0.471652	0.235826	+	0.971795i	$0.424220\pi$
$984$	6.15784	0.196305
$985$	7.74261	0.246700
$986$	26.3178	0.838128
$987$	−54.3679	−1.73055
$988$	5.66892	0.180352
$989$	5.12108	0.162841
$990$	4.51722	0.143567
$991$	−22.6870	−0.720676	−0.360338	−	0.932822i	$-0.617339\pi$
$991$	−22.6870	−0.720676	−0.360338	+	0.932822i	$0.617339\pi$
$992$	−10.0816	−0.320091
$993$	5.35872	0.170054
$994$	−6.12807	−0.194371
$995$	−24.3707	−0.772605
$996$	36.8048	1.16621
$997$	29.0401	0.919708	0.459854	−	0.887995i	$-0.347902\pi$
$997$	29.0401	0.919708	0.459854	+	0.887995i	$0.347902\pi$
$998$	−28.4087	−0.899263
$999$	−32.2953	−1.02178

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4730.2.a.bc.1.2	✓	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4730.2.a.bc.1.2	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.74176 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.74176 q^{6} +3.45531 q^{7} -1.00000 q^{8} +4.51722 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.74176 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.74176 q^{6} +3.45531 q^{7} -1.00000 q^{8} +4.51722 q^{9} +1.00000 q^{10} +1.00000 q^{11} -2.74176 q^{12} +2.23890 q^{13} -3.45531 q^{14} +2.74176 q^{15} +1.00000 q^{16} -3.54650 q^{17} -4.51722 q^{18} +2.53201 q^{19} -1.00000 q^{20} -9.47360 q^{21} -1.00000 q^{22} -5.12108 q^{23} +2.74176 q^{24} +1.00000 q^{25} -2.23890 q^{26} -4.15985 q^{27} +3.45531 q^{28} +7.42077 q^{29} -2.74176 q^{30} +10.0816 q^{31} -1.00000 q^{32} -2.74176 q^{33} +3.54650 q^{34} -3.45531 q^{35} +4.51722 q^{36} +7.76357 q^{37} -2.53201 q^{38} -6.13852 q^{39} +1.00000 q^{40} +2.24595 q^{41} +9.47360 q^{42} -1.00000 q^{43} +1.00000 q^{44} -4.51722 q^{45} +5.12108 q^{46} +5.73889 q^{47} -2.74176 q^{48} +4.93914 q^{49} -1.00000 q^{50} +9.72364 q^{51} +2.23890 q^{52} +6.42870 q^{53} +4.15985 q^{54} -1.00000 q^{55} -3.45531 q^{56} -6.94215 q^{57} -7.42077 q^{58} +1.14981 q^{59} +2.74176 q^{60} -11.4749 q^{61} -10.0816 q^{62} +15.6084 q^{63} +1.00000 q^{64} -2.23890 q^{65} +2.74176 q^{66} -0.434762 q^{67} -3.54650 q^{68} +14.0408 q^{69} +3.45531 q^{70} +1.77353 q^{71} -4.51722 q^{72} +6.98587 q^{73} -7.76357 q^{74} -2.74176 q^{75} +2.53201 q^{76} +3.45531 q^{77} +6.13852 q^{78} +2.60283 q^{79} -1.00000 q^{80} -2.14637 q^{81} -2.24595 q^{82} -13.4238 q^{83} -9.47360 q^{84} +3.54650 q^{85} +1.00000 q^{86} -20.3459 q^{87} -1.00000 q^{88} -4.60130 q^{89} +4.51722 q^{90} +7.73609 q^{91} -5.12108 q^{92} -27.6412 q^{93} -5.73889 q^{94} -2.53201 q^{95} +2.74176 q^{96} +14.6645 q^{97} -4.93914 q^{98} +4.51722 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 11 q^{2} + 11 q^{4} - 11 q^{5} - 11 q^{8} + 15 q^{9}+O(q^{10}) \) 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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