LMFDB - Embedded newform 4730.2.a.ba.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} - x^{9} - 21x^{8} + 22x^{7} + 138x^{6} - 154x^{5} - 291x^{4} + 327x^{3} + 97x^{2} - 124x + 16 $ x^10 - x^9 - 21x^8 + 22x^7 + 138x^6 - 154x^5 - 291x^4 + 327x^3 + 97x^2 - 124x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$-0.721995$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +0.721995 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.721995 q^{6} +3.23576 q^{7} +1.00000 q^{8} -2.47872 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +0.721995 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.721995 q^{6} +3.23576 q^{7} +1.00000 q^{8} -2.47872 q^{9} -1.00000 q^{10} -1.00000 q^{11} +0.721995 q^{12} +5.17412 q^{13} +3.23576 q^{14} -0.721995 q^{15} +1.00000 q^{16} -5.34707 q^{17} -2.47872 q^{18} +7.22526 q^{19} -1.00000 q^{20} +2.33620 q^{21} -1.00000 q^{22} -6.21978 q^{23} +0.721995 q^{24} +1.00000 q^{25} +5.17412 q^{26} -3.95561 q^{27} +3.23576 q^{28} +5.06803 q^{29} -0.721995 q^{30} +5.23357 q^{31} +1.00000 q^{32} -0.721995 q^{33} -5.34707 q^{34} -3.23576 q^{35} -2.47872 q^{36} +1.13656 q^{37} +7.22526 q^{38} +3.73569 q^{39} -1.00000 q^{40} +4.10121 q^{41} +2.33620 q^{42} -1.00000 q^{43} -1.00000 q^{44} +2.47872 q^{45} -6.21978 q^{46} +8.41915 q^{47} +0.721995 q^{48} +3.47014 q^{49} +1.00000 q^{50} -3.86055 q^{51} +5.17412 q^{52} +3.19137 q^{53} -3.95561 q^{54} +1.00000 q^{55} +3.23576 q^{56} +5.21660 q^{57} +5.06803 q^{58} +5.31879 q^{59} -0.721995 q^{60} +4.46302 q^{61} +5.23357 q^{62} -8.02056 q^{63} +1.00000 q^{64} -5.17412 q^{65} -0.721995 q^{66} +4.26675 q^{67} -5.34707 q^{68} -4.49065 q^{69} -3.23576 q^{70} +3.58281 q^{71} -2.47872 q^{72} -3.49316 q^{73} +1.13656 q^{74} +0.721995 q^{75} +7.22526 q^{76} -3.23576 q^{77} +3.73569 q^{78} -17.1625 q^{79} -1.00000 q^{80} +4.58024 q^{81} +4.10121 q^{82} +15.4940 q^{83} +2.33620 q^{84} +5.34707 q^{85} -1.00000 q^{86} +3.65909 q^{87} -1.00000 q^{88} +6.47226 q^{89} +2.47872 q^{90} +16.7422 q^{91} -6.21978 q^{92} +3.77861 q^{93} +8.41915 q^{94} -7.22526 q^{95} +0.721995 q^{96} -16.7442 q^{97} +3.47014 q^{98} +2.47872 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 10 q^{2} - q^{3} + 10 q^{4} - 10 q^{5} - q^{6} + 3 q^{7} + 10 q^{8} + 13 q^{9}+O(q^{10}) $ 10 * q + 10 * q^2 - q^3 + 10 * q^4 - 10 * q^5 - q^6 + 3 * q^7 + 10 * q^8 + 13 * q^9	\( 10 q + 10 q^{2} - q^{3} + 10 q^{4} - 10 q^{5} - q^{6} + 3 q^{7} + 10 q^{8} + 13 q^{9} - 10 q^{10} - 10 q^{11} - q^{12} + 6 q^{13} + 3 q^{14} + q^{15} + 10 q^{16} + 3 q^{17} + 13 q^{18} + 3 q^{19} - 10 q^{20} + 11 q^{21} - 10 q^{22} - 6 q^{23} - q^{24} + 10 q^{25} + 6 q^{26} + 8 q^{27} + 3 q^{28} + 14 q^{29} + q^{30} + 6 q^{31} + 10 q^{32} + q^{33} + 3 q^{34} - 3 q^{35} + 13 q^{36} + 10 q^{37} + 3 q^{38} + 24 q^{39} - 10 q^{40} + 26 q^{41} + 11 q^{42} - 10 q^{43} - 10 q^{44} - 13 q^{45} - 6 q^{46} + 3 q^{47} - q^{48} + 33 q^{49} + 10 q^{50} + 18 q^{51} + 6 q^{52} - 9 q^{53} + 8 q^{54} + 10 q^{55} + 3 q^{56} + 18 q^{57} + 14 q^{58} - 9 q^{59} + q^{60} + 22 q^{61} + 6 q^{62} - q^{63} + 10 q^{64} - 6 q^{65} + q^{66} + 18 q^{67} + 3 q^{68} + 6 q^{69} - 3 q^{70} + 27 q^{71} + 13 q^{72} + 28 q^{73} + 10 q^{74} - q^{75} + 3 q^{76} - 3 q^{77} + 24 q^{78} + 3 q^{79} - 10 q^{80} + 30 q^{81} + 26 q^{82} - 11 q^{83} + 11 q^{84} - 3 q^{85} - 10 q^{86} + 30 q^{87} - 10 q^{88} + 16 q^{89} - 13 q^{90} + 32 q^{91} - 6 q^{92} + 52 q^{93} + 3 q^{94} - 3 q^{95} - q^{96} + 22 q^{97} + 33 q^{98} - 13 q^{99}+O(q^{100}) \) 10 * q + 10 * q^2 - q^3 + 10 * q^4 - 10 * q^5 - q^6 + 3 * q^7 + 10 * q^8 + 13 * q^9 - 10 * q^10 - 10 * q^11 - q^12 + 6 * q^13 + 3 * q^14 + q^15 + 10 * q^16 + 3 * q^17 + 13 * q^18 + 3 * q^19 - 10 * q^20 + 11 * q^21 - 10 * q^22 - 6 * q^23 - q^24 + 10 * q^25 + 6 * q^26 + 8 * q^27 + 3 * q^28 + 14 * q^29 + q^30 + 6 * q^31 + 10 * q^32 + q^33 + 3 * q^34 - 3 * q^35 + 13 * q^36 + 10 * q^37 + 3 * q^38 + 24 * q^39 - 10 * q^40 + 26 * q^41 + 11 * q^42 - 10 * q^43 - 10 * q^44 - 13 * q^45 - 6 * q^46 + 3 * q^47 - q^48 + 33 * q^49 + 10 * q^50 + 18 * q^51 + 6 * q^52 - 9 * q^53 + 8 * q^54 + 10 * q^55 + 3 * q^56 + 18 * q^57 + 14 * q^58 - 9 * q^59 + q^60 + 22 * q^61 + 6 * q^62 - q^63 + 10 * q^64 - 6 * q^65 + q^66 + 18 * q^67 + 3 * q^68 + 6 * q^69 - 3 * q^70 + 27 * q^71 + 13 * q^72 + 28 * q^73 + 10 * q^74 - q^75 + 3 * q^76 - 3 * q^77 + 24 * q^78 + 3 * q^79 - 10 * q^80 + 30 * q^81 + 26 * q^82 - 11 * q^83 + 11 * q^84 - 3 * q^85 - 10 * q^86 + 30 * q^87 - 10 * q^88 + 16 * q^89 - 13 * q^90 + 32 * q^91 - 6 * q^92 + 52 * q^93 + 3 * q^94 - 3 * q^95 - q^96 + 22 * q^97 + 33 * q^98 - 13 * 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
$3$	0.721995	0.416844	0.208422	−	0.978039i	$-0.433167\pi$
$3$	0.721995	0.416844	0.208422	+	0.978039i	$0.433167\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0.721995	0.294753
$7$	3.23576	1.22300	0.611501	−	0.791244i	$-0.290566\pi$
$7$	3.23576	1.22300	0.611501	+	0.791244i	$0.290566\pi$
$8$	1.00000	0.353553
$9$	−2.47872	−0.826241
$10$	−1.00000	−0.316228
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	0.721995	0.208422
$13$	5.17412	1.43504	0.717522	−	0.696536i	$-0.245276\pi$
$13$	5.17412	1.43504	0.717522	+	0.696536i	$0.245276\pi$
$14$	3.23576	0.864793
$15$	−0.721995	−0.186418
$16$	1.00000	0.250000
$17$	−5.34707	−1.29685	−0.648427	−	0.761277i	$-0.724573\pi$
$17$	−5.34707	−1.29685	−0.648427	+	0.761277i	$0.724573\pi$
$18$	−2.47872	−0.584241
$19$	7.22526	1.65759	0.828794	−	0.559553i	$-0.189027\pi$
$19$	7.22526	1.65759	0.828794	+	0.559553i	$0.189027\pi$
$20$	−1.00000	−0.223607
$21$	2.33620	0.509801
$22$	−1.00000	−0.213201
$23$	−6.21978	−1.29691	−0.648457	−	0.761251i	$-0.724586\pi$
$23$	−6.21978	−1.29691	−0.648457	+	0.761251i	$0.724586\pi$
$24$	0.721995	0.147377
$25$	1.00000	0.200000
$26$	5.17412	1.01473
$27$	−3.95561	−0.761257
$28$	3.23576	0.611501
$29$	5.06803	0.941110	0.470555	−	0.882371i	$-0.344054\pi$
$29$	5.06803	0.941110	0.470555	+	0.882371i	$0.344054\pi$
$30$	−0.721995	−0.131818
$31$	5.23357	0.939978	0.469989	−	0.882672i	$-0.344258\pi$
$31$	5.23357	0.939978	0.469989	+	0.882672i	$0.344258\pi$
$32$	1.00000	0.176777
$33$	−0.721995	−0.125683
$34$	−5.34707	−0.917015
$35$	−3.23576	−0.546943
$36$	−2.47872	−0.413121
$37$	1.13656	0.186849	0.0934243	−	0.995626i	$-0.470219\pi$
$37$	1.13656	0.186849	0.0934243	+	0.995626i	$0.470219\pi$
$38$	7.22526	1.17209
$39$	3.73569	0.598189
$40$	−1.00000	−0.158114
$41$	4.10121	0.640502	0.320251	−	0.947333i	$-0.396233\pi$
$41$	4.10121	0.640502	0.320251	+	0.947333i	$0.396233\pi$
$42$	2.33620	0.360484
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	−1.00000	−0.150756
$45$	2.47872	0.369506
$46$	−6.21978	−0.917057
$47$	8.41915	1.22806	0.614029	−	0.789283i	$-0.289548\pi$
$47$	8.41915	1.22806	0.614029	+	0.789283i	$0.289548\pi$
$48$	0.721995	0.104211
$49$	3.47014	0.495735
$50$	1.00000	0.141421
$51$	−3.86055	−0.540586
$52$	5.17412	0.717522
$53$	3.19137	0.438369	0.219184	−	0.975683i	$-0.429660\pi$
$53$	3.19137	0.438369	0.219184	+	0.975683i	$0.429660\pi$
$54$	−3.95561	−0.538290
$55$	1.00000	0.134840
$56$	3.23576	0.432397
$57$	5.21660	0.690955
$58$	5.06803	0.665465
$59$	5.31879	0.692448	0.346224	−	0.938152i	$-0.387464\pi$
$59$	5.31879	0.692448	0.346224	+	0.938152i	$0.387464\pi$
$60$	−0.721995	−0.0932091
$61$	4.46302	0.571432	0.285716	−	0.958314i	$-0.407769\pi$
$61$	4.46302	0.571432	0.285716	+	0.958314i	$0.407769\pi$
$62$	5.23357	0.664665
$63$	−8.02056	−1.01050
$64$	1.00000	0.125000
$65$	−5.17412	−0.641771
$66$	−0.721995	−0.0888714
$67$	4.26675	0.521267	0.260633	−	0.965438i	$-0.416069\pi$
$67$	4.26675	0.521267	0.260633	+	0.965438i	$0.416069\pi$
$68$	−5.34707	−0.648427
$69$	−4.49065	−0.540611
$70$	−3.23576	−0.386747
$71$	3.58281	0.425202	0.212601	−	0.977139i	$-0.431807\pi$
$71$	3.58281	0.425202	0.212601	+	0.977139i	$0.431807\pi$
$72$	−2.47872	−0.292120
$73$	−3.49316	−0.408843	−0.204421	−	0.978883i	$-0.565531\pi$
$73$	−3.49316	−0.408843	−0.204421	+	0.978883i	$0.565531\pi$
$74$	1.13656	0.132122
$75$	0.721995	0.0833688
$76$	7.22526	0.828794
$77$	−3.23576	−0.368749
$78$	3.73569	0.422983
$79$	−17.1625	−1.93094	−0.965468	−	0.260522i	$-0.916105\pi$
$79$	−17.1625	−1.93094	−0.965468	+	0.260522i	$0.916105\pi$
$80$	−1.00000	−0.111803
$81$	4.58024	0.508916
$82$	4.10121	0.452903
$83$	15.4940	1.70069	0.850344	−	0.526228i	$-0.176394\pi$
$83$	15.4940	1.70069	0.850344	+	0.526228i	$0.176394\pi$
$84$	2.33620	0.254900
$85$	5.34707	0.579971
$86$	−1.00000	−0.107833
$87$	3.65909	0.392296
$88$	−1.00000	−0.106600
$89$	6.47226	0.686058	0.343029	−	0.939325i	$-0.388547\pi$
$89$	6.47226	0.686058	0.343029	+	0.939325i	$0.388547\pi$
$90$	2.47872	0.261280
$91$	16.7422	1.75506
$92$	−6.21978	−0.648457
$93$	3.77861	0.391824
$94$	8.41915	0.868369
$95$	−7.22526	−0.741296
$96$	0.721995	0.0736883
$97$	−16.7442	−1.70011	−0.850057	−	0.526690i	$-0.823433\pi$
$97$	−16.7442	−1.70011	−0.850057	+	0.526690i	$0.823433\pi$
$98$	3.47014	0.350537
$99$	2.47872	0.249121
$100$	1.00000	0.100000
$101$	−5.96190	−0.593232	−0.296616	−	0.954997i	$-0.595858\pi$
$101$	−5.96190	−0.593232	−0.296616	+	0.954997i	$0.595858\pi$
$102$	−3.86055	−0.382252
$103$	−0.842082	−0.0829728	−0.0414864	−	0.999139i	$-0.513209\pi$
$103$	−0.842082	−0.0829728	−0.0414864	+	0.999139i	$0.513209\pi$
$104$	5.17412	0.507365
$105$	−2.33620	−0.227990
$106$	3.19137	0.309974
$107$	−1.82207	−0.176146	−0.0880729	−	0.996114i	$-0.528071\pi$
$107$	−1.82207	−0.176146	−0.0880729	+	0.996114i	$0.528071\pi$
$108$	−3.95561	−0.380629
$109$	10.7133	1.02615	0.513075	−	0.858344i	$-0.328506\pi$
$109$	10.7133	1.02615	0.513075	+	0.858344i	$0.328506\pi$
$110$	1.00000	0.0953463
$111$	0.820587	0.0778867
$112$	3.23576	0.305751
$113$	−20.3182	−1.91137	−0.955686	−	0.294389i	$-0.904884\pi$
$113$	−20.3182	−1.91137	−0.955686	+	0.294389i	$0.904884\pi$
$114$	5.21660	0.488579
$115$	6.21978	0.579998
$116$	5.06803	0.470555
$117$	−12.8252	−1.18569
$118$	5.31879	0.489634
$119$	−17.3018	−1.58606
$120$	−0.721995	−0.0659088
$121$	1.00000	0.0909091
$122$	4.46302	0.404063
$123$	2.96105	0.266989
$124$	5.23357	0.469989
$125$	−1.00000	−0.0894427
$126$	−8.02056	−0.714528
$127$	−4.60580	−0.408699	−0.204349	−	0.978898i	$-0.565508\pi$
$127$	−4.60580	−0.408699	−0.204349	+	0.978898i	$0.565508\pi$
$128$	1.00000	0.0883883
$129$	−0.721995	−0.0635681
$130$	−5.17412	−0.453801
$131$	−2.08259	−0.181957	−0.0909783	−	0.995853i	$-0.528999\pi$
$131$	−2.08259	−0.181957	−0.0909783	+	0.995853i	$0.528999\pi$
$132$	−0.721995	−0.0628416
$133$	23.3792	2.02723
$134$	4.26675	0.368591
$135$	3.95561	0.340445
$136$	−5.34707	−0.458507
$137$	20.6761	1.76647	0.883237	−	0.468926i	$-0.155359\pi$
$137$	20.6761	1.76647	0.883237	+	0.468926i	$0.155359\pi$
$138$	−4.49065	−0.382270
$139$	14.6138	1.23953	0.619765	−	0.784788i	$-0.287228\pi$
$139$	14.6138	1.23953	0.619765	+	0.784788i	$0.287228\pi$
$140$	−3.23576	−0.273472
$141$	6.07858	0.511909
$142$	3.58281	0.300663
$143$	−5.17412	−0.432682
$144$	−2.47872	−0.206560
$145$	−5.06803	−0.420877
$146$	−3.49316	−0.289096
$147$	2.50542	0.206644
$148$	1.13656	0.0934243
$149$	−15.7820	−1.29291	−0.646456	−	0.762951i	$-0.723750\pi$
$149$	−15.7820	−1.29291	−0.646456	+	0.762951i	$0.723750\pi$
$150$	0.721995	0.0589506
$151$	23.8672	1.94229	0.971143	−	0.238498i	$-0.0766549\pi$
$151$	23.8672	1.94229	0.971143	+	0.238498i	$0.0766549\pi$
$152$	7.22526	0.586046
$153$	13.2539	1.07151
$154$	−3.23576	−0.260745
$155$	−5.23357	−0.420371
$156$	3.73569	0.299094
$157$	20.3268	1.62226	0.811128	−	0.584869i	$-0.198854\pi$
$157$	20.3268	1.62226	0.811128	+	0.584869i	$0.198854\pi$
$158$	−17.1625	−1.36538
$159$	2.30415	0.182731
$160$	−1.00000	−0.0790569
$161$	−20.1257	−1.58613
$162$	4.58024	0.359858
$163$	16.9881	1.33061	0.665307	−	0.746570i	$-0.268301\pi$
$163$	16.9881	1.33061	0.665307	+	0.746570i	$0.268301\pi$
$164$	4.10121	0.320251
$165$	0.721995	0.0562072
$166$	15.4940	1.20257
$167$	−22.1409	−1.71331	−0.856656	−	0.515889i	$-0.827462\pi$
$167$	−22.1409	−1.71331	−0.856656	+	0.515889i	$0.827462\pi$
$168$	2.33620	0.180242
$169$	13.7716	1.05935
$170$	5.34707	0.410101
$171$	−17.9094	−1.36957
$172$	−1.00000	−0.0762493
$173$	10.7964	0.820839	0.410419	−	0.911897i	$-0.365382\pi$
$173$	10.7964	0.820839	0.410419	+	0.911897i	$0.365382\pi$
$174$	3.65909	0.277395
$175$	3.23576	0.244600
$176$	−1.00000	−0.0753778
$177$	3.84014	0.288642
$178$	6.47226	0.485116
$179$	1.96348	0.146757	0.0733787	−	0.997304i	$-0.476622\pi$
$179$	1.96348	0.146757	0.0733787	+	0.997304i	$0.476622\pi$
$180$	2.47872	0.184753
$181$	−24.9045	−1.85114	−0.925568	−	0.378580i	$-0.876412\pi$
$181$	−24.9045	−1.85114	−0.925568	+	0.378580i	$0.876412\pi$
$182$	16.7422	1.24102
$183$	3.22228	0.238198
$184$	−6.21978	−0.458529
$185$	−1.13656	−0.0835612
$186$	3.77861	0.277061
$187$	5.34707	0.391016
$188$	8.41915	0.614029
$189$	−12.7994	−0.931019
$190$	−7.22526	−0.524176
$191$	−23.5529	−1.70423	−0.852113	−	0.523357i	$-0.824679\pi$
$191$	−23.5529	−1.70423	−0.852113	+	0.523357i	$0.824679\pi$
$192$	0.721995	0.0521055
$193$	1.11713	0.0804124	0.0402062	−	0.999191i	$-0.487199\pi$
$193$	1.11713	0.0804124	0.0402062	+	0.999191i	$0.487199\pi$
$194$	−16.7442	−1.20216
$195$	−3.73569	−0.267518
$196$	3.47014	0.247867
$197$	−20.6100	−1.46840	−0.734200	−	0.678933i	$-0.762443\pi$
$197$	−20.6100	−1.46840	−0.734200	+	0.678933i	$0.762443\pi$
$198$	2.47872	0.176155
$199$	15.3103	1.08532	0.542659	−	0.839953i	$-0.317418\pi$
$199$	15.3103	1.08532	0.542659	+	0.839953i	$0.317418\pi$
$200$	1.00000	0.0707107
$201$	3.08057	0.217287
$202$	−5.96190	−0.419478
$203$	16.3989	1.15098
$204$	−3.86055	−0.270293
$205$	−4.10121	−0.286441
$206$	−0.842082	−0.0586707
$207$	15.4171	1.07156
$208$	5.17412	0.358761
$209$	−7.22526	−0.499782
$210$	−2.33620	−0.161213
$211$	−11.6079	−0.799123	−0.399561	−	0.916706i	$-0.630838\pi$
$211$	−11.6079	−0.799123	−0.399561	+	0.916706i	$0.630838\pi$
$212$	3.19137	0.219184
$213$	2.58677	0.177243
$214$	−1.82207	−0.124554
$215$	1.00000	0.0681994
$216$	−3.95561	−0.269145
$217$	16.9346	1.14959
$218$	10.7133	0.725597
$219$	−2.52204	−0.170424
$220$	1.00000	0.0674200
$221$	−27.6664	−1.86104
$222$	0.820587	0.0550742
$223$	−4.02563	−0.269576	−0.134788	−	0.990874i	$-0.543035\pi$
$223$	−4.02563	−0.269576	−0.134788	+	0.990874i	$0.543035\pi$
$224$	3.23576	0.216198
$225$	−2.47872	−0.165248
$226$	−20.3182	−1.35154
$227$	25.8928	1.71857	0.859283	−	0.511501i	$-0.170910\pi$
$227$	25.8928	1.71857	0.859283	+	0.511501i	$0.170910\pi$
$228$	5.21660	0.345478
$229$	24.6583	1.62946	0.814732	−	0.579838i	$-0.196884\pi$
$229$	24.6583	1.62946	0.814732	+	0.579838i	$0.196884\pi$
$230$	6.21978	0.410120
$231$	−2.33620	−0.153711
$232$	5.06803	0.332733
$233$	−7.76365	−0.508614	−0.254307	−	0.967124i	$-0.581847\pi$
$233$	−7.76365	−0.508614	−0.254307	+	0.967124i	$0.581847\pi$
$234$	−12.8252	−0.838411
$235$	−8.41915	−0.549205
$236$	5.31879	0.346224
$237$	−12.3913	−0.804898
$238$	−17.3018	−1.12151
$239$	10.7005	0.692157	0.346078	−	0.938206i	$-0.387513\pi$
$239$	10.7005	0.692157	0.346078	+	0.938206i	$0.387513\pi$
$240$	−0.721995	−0.0466045
$241$	−26.2308	−1.68968	−0.844838	−	0.535023i	$-0.820303\pi$
$241$	−26.2308	−1.68968	−0.844838	+	0.535023i	$0.820303\pi$
$242$	1.00000	0.0642824
$243$	15.1737	0.973396
$244$	4.46302	0.285716
$245$	−3.47014	−0.221699
$246$	2.96105	0.188790
$247$	37.3844	2.37871
$248$	5.23357	0.332332
$249$	11.1866	0.708921
$250$	−1.00000	−0.0632456
$251$	27.2991	1.72310	0.861551	−	0.507671i	$-0.169494\pi$
$251$	27.2991	1.72310	0.861551	+	0.507671i	$0.169494\pi$
$252$	−8.02056	−0.505248
$253$	6.21978	0.391035
$254$	−4.60580	−0.288994
$255$	3.86055	0.241757
$256$	1.00000	0.0625000
$257$	11.3198	0.706108	0.353054	−	0.935603i	$-0.385143\pi$
$257$	11.3198	0.706108	0.353054	+	0.935603i	$0.385143\pi$
$258$	−0.721995	−0.0449494
$259$	3.67762	0.228516
$260$	−5.17412	−0.320886
$261$	−12.5622	−0.777584
$262$	−2.08259	−0.128663
$263$	−15.8128	−0.975061	−0.487530	−	0.873106i	$-0.662102\pi$
$263$	−15.8128	−0.975061	−0.487530	+	0.873106i	$0.662102\pi$
$264$	−0.721995	−0.0444357
$265$	−3.19137	−0.196045
$266$	23.3792	1.43347
$267$	4.67293	0.285979
$268$	4.26675	0.260633
$269$	−6.08952	−0.371284	−0.185642	−	0.982617i	$-0.559437\pi$
$269$	−6.08952	−0.371284	−0.185642	+	0.982617i	$0.559437\pi$
$270$	3.95561	0.240731
$271$	13.0105	0.790329	0.395165	−	0.918610i	$-0.370688\pi$
$271$	13.0105	0.790329	0.395165	+	0.918610i	$0.370688\pi$
$272$	−5.34707	−0.324214
$273$	12.0878	0.731587
$274$	20.6761	1.24909
$275$	−1.00000	−0.0603023
$276$	−4.49065	−0.270305
$277$	−12.7898	−0.768466	−0.384233	−	0.923236i	$-0.625534\pi$
$277$	−12.7898	−0.768466	−0.384233	+	0.923236i	$0.625534\pi$
$278$	14.6138	0.876480
$279$	−12.9726	−0.776648
$280$	−3.23576	−0.193374
$281$	−30.6606	−1.82906	−0.914530	−	0.404519i	$-0.867439\pi$
$281$	−30.6606	−1.82906	−0.914530	+	0.404519i	$0.867439\pi$
$282$	6.07858	0.361974
$283$	15.2901	0.908903	0.454452	−	0.890771i	$-0.349835\pi$
$283$	15.2901	0.908903	0.454452	+	0.890771i	$0.349835\pi$
$284$	3.58281	0.212601
$285$	−5.21660	−0.309005
$286$	−5.17412	−0.305952
$287$	13.2705	0.783335
$288$	−2.47872	−0.146060
$289$	11.5911	0.681832
$290$	−5.06803	−0.297605
$291$	−12.0892	−0.708682
$292$	−3.49316	−0.204421
$293$	−1.19140	−0.0696023	−0.0348011	−	0.999394i	$-0.511080\pi$
$293$	−1.19140	−0.0696023	−0.0348011	+	0.999394i	$0.511080\pi$
$294$	2.50542	0.146119
$295$	−5.31879	−0.309672
$296$	1.13656	0.0660610
$297$	3.95561	0.229528
$298$	−15.7820	−0.914227
$299$	−32.1819	−1.86113
$300$	0.721995	0.0416844
$301$	−3.23576	−0.186506
$302$	23.8672	1.37340
$303$	−4.30446	−0.247285
$304$	7.22526	0.414397
$305$	−4.46302	−0.255552
$306$	13.2539	0.757675
$307$	−8.76111	−0.500023	−0.250012	−	0.968243i	$-0.580434\pi$
$307$	−8.76111	−0.500023	−0.250012	+	0.968243i	$0.580434\pi$
$308$	−3.23576	−0.184375
$309$	−0.607979	−0.0345867
$310$	−5.23357	−0.297247
$311$	−9.04178	−0.512712	−0.256356	−	0.966582i	$-0.582522\pi$
$311$	−9.04178	−0.512712	−0.256356	+	0.966582i	$0.582522\pi$
$312$	3.73569	0.211492
$313$	11.6421	0.658051	0.329026	−	0.944321i	$-0.393280\pi$
$313$	11.6421	0.658051	0.329026	+	0.944321i	$0.393280\pi$
$314$	20.3268	1.14711
$315$	8.02056	0.451907
$316$	−17.1625	−0.965468
$317$	−27.0838	−1.52118	−0.760588	−	0.649234i	$-0.775089\pi$
$317$	−27.0838	−1.52118	−0.760588	+	0.649234i	$0.775089\pi$
$318$	2.30415	0.129211
$319$	−5.06803	−0.283755
$320$	−1.00000	−0.0559017
$321$	−1.31552	−0.0734252
$322$	−20.1257	−1.12156
$323$	−38.6340	−2.14965
$324$	4.58024	0.254458
$325$	5.17412	0.287009
$326$	16.9881	0.940886
$327$	7.73496	0.427744
$328$	4.10121	0.226452
$329$	27.2423	1.50192
$330$	0.721995	0.0397445
$331$	−15.3242	−0.842295	−0.421148	−	0.906992i	$-0.638373\pi$
$331$	−15.3242	−0.842295	−0.421148	+	0.906992i	$0.638373\pi$
$332$	15.4940	0.850344
$333$	−2.81721	−0.154382
$334$	−22.1409	−1.21149
$335$	−4.26675	−0.233118
$336$	2.33620	0.127450
$337$	−2.53544	−0.138114	−0.0690570	−	0.997613i	$-0.521999\pi$
$337$	−2.53544	−0.138114	−0.0690570	+	0.997613i	$0.521999\pi$
$338$	13.7716	0.749074
$339$	−14.6696	−0.796743
$340$	5.34707	0.289986
$341$	−5.23357	−0.283414
$342$	−17.9094	−0.968431
$343$	−11.4218	−0.616718
$344$	−1.00000	−0.0539164
$345$	4.49065	0.241769
$346$	10.7964	0.580421
$347$	−11.9244	−0.640136	−0.320068	−	0.947395i	$-0.603706\pi$
$347$	−11.9244	−0.640136	−0.320068	+	0.947395i	$0.603706\pi$
$348$	3.65909	0.196148
$349$	−15.6610	−0.838313	−0.419156	−	0.907914i	$-0.637674\pi$
$349$	−15.6610	−0.838313	−0.419156	+	0.907914i	$0.637674\pi$
$350$	3.23576	0.172959
$351$	−20.4668	−1.09244
$352$	−1.00000	−0.0533002
$353$	6.12581	0.326044	0.163022	−	0.986622i	$-0.447876\pi$
$353$	6.12581	0.326044	0.163022	+	0.986622i	$0.447876\pi$
$354$	3.84014	0.204101
$355$	−3.58281	−0.190156
$356$	6.47226	0.343029
$357$	−12.4918	−0.661138
$358$	1.96348	0.103773
$359$	−22.5151	−1.18830	−0.594152	−	0.804353i	$-0.702512\pi$
$359$	−22.5151	−1.18830	−0.594152	+	0.804353i	$0.702512\pi$
$360$	2.47872	0.130640
$361$	33.2044	1.74760
$362$	−24.9045	−1.30895
$363$	0.721995	0.0378949
$364$	16.7422	0.877531
$365$	3.49316	0.182840
$366$	3.22228	0.168431
$367$	−15.3463	−0.801068	−0.400534	−	0.916282i	$-0.631175\pi$
$367$	−15.3463	−0.801068	−0.400534	+	0.916282i	$0.631175\pi$
$368$	−6.21978	−0.324229
$369$	−10.1658	−0.529209
$370$	−1.13656	−0.0590867
$371$	10.3265	0.536126
$372$	3.77861	0.195912
$373$	11.6444	0.602924	0.301462	−	0.953478i	$-0.402525\pi$
$373$	11.6444	0.602924	0.301462	+	0.953478i	$0.402525\pi$
$374$	5.34707	0.276490
$375$	−0.721995	−0.0372836
$376$	8.41915	0.434184
$377$	26.2226	1.35053
$378$	−12.7994	−0.658330
$379$	−10.5387	−0.541338	−0.270669	−	0.962672i	$-0.587245\pi$
$379$	−10.5387	−0.541338	−0.270669	+	0.962672i	$0.587245\pi$
$380$	−7.22526	−0.370648
$381$	−3.32536	−0.170363
$382$	−23.5529	−1.20507
$383$	10.5227	0.537686	0.268843	−	0.963184i	$-0.413359\pi$
$383$	10.5227	0.537686	0.268843	+	0.963184i	$0.413359\pi$
$384$	0.721995	0.0368441
$385$	3.23576	0.164910
$386$	1.11713	0.0568602
$387$	2.47872	0.126001
$388$	−16.7442	−0.850057
$389$	20.8771	1.05851	0.529256	−	0.848462i	$-0.322471\pi$
$389$	20.8771	1.05851	0.529256	+	0.848462i	$0.322471\pi$
$390$	−3.73569	−0.189164
$391$	33.2576	1.68191
$392$	3.47014	0.175269
$393$	−1.50362	−0.0758475
$394$	−20.6100	−1.03832
$395$	17.1625	0.863541
$396$	2.47872	0.124561
$397$	−5.08413	−0.255165	−0.127583	−	0.991828i	$-0.540722\pi$
$397$	−5.08413	−0.255165	−0.127583	+	0.991828i	$0.540722\pi$
$398$	15.3103	0.767435
$399$	16.8797	0.845040
$400$	1.00000	0.0500000
$401$	−32.9359	−1.64474	−0.822369	−	0.568954i	$-0.807348\pi$
$401$	−32.9359	−1.64474	−0.822369	+	0.568954i	$0.807348\pi$
$402$	3.08057	0.153645
$403$	27.0792	1.34891
$404$	−5.96190	−0.296616
$405$	−4.58024	−0.227594
$406$	16.3989	0.813865
$407$	−1.13656	−0.0563370
$408$	−3.86055	−0.191126
$409$	6.49270	0.321044	0.160522	−	0.987032i	$-0.448682\pi$
$409$	6.49270	0.321044	0.160522	+	0.987032i	$0.448682\pi$
$410$	−4.10121	−0.202544
$411$	14.9280	0.736344
$412$	−0.842082	−0.0414864
$413$	17.2103	0.846865
$414$	15.4171	0.757711
$415$	−15.4940	−0.760570
$416$	5.17412	0.253682
$417$	10.5511	0.516690
$418$	−7.22526	−0.353399
$419$	2.08487	0.101852	0.0509262	−	0.998702i	$-0.483783\pi$
$419$	2.08487	0.101852	0.0509262	+	0.998702i	$0.483783\pi$
$420$	−2.33620	−0.113995
$421$	12.4190	0.605265	0.302632	−	0.953107i	$-0.402135\pi$
$421$	12.4190	0.605265	0.302632	+	0.953107i	$0.402135\pi$
$422$	−11.6079	−0.565065
$423$	−20.8687	−1.01467
$424$	3.19137	0.154987
$425$	−5.34707	−0.259371
$426$	2.58677	0.125329
$427$	14.4413	0.698862
$428$	−1.82207	−0.0880729
$429$	−3.73569	−0.180361
$430$	1.00000	0.0482243
$431$	−19.8165	−0.954526	−0.477263	−	0.878761i	$-0.658371\pi$
$431$	−19.8165	−0.954526	−0.477263	+	0.878761i	$0.658371\pi$
$432$	−3.95561	−0.190314
$433$	−26.5358	−1.27523	−0.637615	−	0.770356i	$-0.720079\pi$
$433$	−26.5358	−1.27523	−0.637615	+	0.770356i	$0.720079\pi$
$434$	16.9346	0.812886
$435$	−3.65909	−0.175440
$436$	10.7133	0.513075
$437$	−44.9396	−2.14975
$438$	−2.52204	−0.120508
$439$	31.0539	1.48212	0.741060	−	0.671439i	$-0.234323\pi$
$439$	31.0539	1.48212	0.741060	+	0.671439i	$0.234323\pi$
$440$	1.00000	0.0476731
$441$	−8.60153	−0.409596
$442$	−27.6664	−1.31596
$443$	33.0372	1.56965	0.784823	−	0.619720i	$-0.212754\pi$
$443$	33.0372	1.56965	0.784823	+	0.619720i	$0.212754\pi$
$444$	0.820587	0.0389433
$445$	−6.47226	−0.306814
$446$	−4.02563	−0.190619
$447$	−11.3945	−0.538942
$448$	3.23576	0.152875
$449$	16.9027	0.797688	0.398844	−	0.917019i	$-0.369411\pi$
$449$	16.9027	0.797688	0.398844	+	0.917019i	$0.369411\pi$
$450$	−2.47872	−0.116848
$451$	−4.10121	−0.193119
$452$	−20.3182	−0.955686
$453$	17.2320	0.809630
$454$	25.8928	1.21521
$455$	−16.7422	−0.784887
$456$	5.21660	0.244290
$457$	−9.04068	−0.422905	−0.211453	−	0.977388i	$-0.567819\pi$
$457$	−9.04068	−0.422905	−0.211453	+	0.977388i	$0.567819\pi$
$458$	24.6583	1.15220
$459$	21.1509	0.987240
$460$	6.21978	0.289999
$461$	−8.04529	−0.374707	−0.187353	−	0.982293i	$-0.559991\pi$
$461$	−8.04529	−0.374707	−0.187353	+	0.982293i	$0.559991\pi$
$462$	−2.33620	−0.108690
$463$	−17.2778	−0.802969	−0.401484	−	0.915866i	$-0.631506\pi$
$463$	−17.2778	−0.802969	−0.401484	+	0.915866i	$0.631506\pi$
$464$	5.06803	0.235277
$465$	−3.77861	−0.175229
$466$	−7.76365	−0.359644
$467$	16.4213	0.759889	0.379944	−	0.925009i	$-0.375943\pi$
$467$	16.4213	0.759889	0.379944	+	0.925009i	$0.375943\pi$
$468$	−12.8252	−0.592846
$469$	13.8062	0.637511
$470$	−8.41915	−0.388346
$471$	14.6758	0.676227
$472$	5.31879	0.244817
$473$	1.00000	0.0459800
$474$	−12.3913	−0.569149
$475$	7.22526	0.331518
$476$	−17.3018	−0.793028
$477$	−7.91053	−0.362198
$478$	10.7005	0.489429
$479$	−15.1831	−0.693733	−0.346866	−	0.937915i	$-0.612754\pi$
$479$	−15.1831	−0.693733	−0.346866	+	0.937915i	$0.612754\pi$
$480$	−0.721995	−0.0329544
$481$	5.88068	0.268136
$482$	−26.2308	−1.19478
$483$	−14.5307	−0.661168
$484$	1.00000	0.0454545
$485$	16.7442	0.760314
$486$	15.1737	0.688295
$487$	−27.4736	−1.24495	−0.622474	−	0.782640i	$-0.713873\pi$
$487$	−27.4736	−1.24495	−0.622474	+	0.782640i	$0.713873\pi$
$488$	4.46302	0.202032
$489$	12.2653	0.554658
$490$	−3.47014	−0.156765
$491$	4.94674	0.223243	0.111622	−	0.993751i	$-0.464396\pi$
$491$	4.94674	0.223243	0.111622	+	0.993751i	$0.464396\pi$
$492$	2.96105	0.133495
$493$	−27.0991	−1.22048
$494$	37.3844	1.68200
$495$	−2.47872	−0.111410
$496$	5.23357	0.234994
$497$	11.5931	0.520022
$498$	11.1866	0.501283
$499$	−28.8624	−1.29206	−0.646030	−	0.763312i	$-0.723572\pi$
$499$	−28.8624	−1.29206	−0.646030	+	0.763312i	$0.723572\pi$
$500$	−1.00000	−0.0447214
$501$	−15.9856	−0.714183
$502$	27.2991	1.21842
$503$	20.0573	0.894312	0.447156	−	0.894456i	$-0.352437\pi$
$503$	20.0573	0.894312	0.447156	+	0.894456i	$0.352437\pi$
$504$	−8.02056	−0.357264
$505$	5.96190	0.265301
$506$	6.21978	0.276503
$507$	9.94299	0.441584
$508$	−4.60580	−0.204349
$509$	26.4079	1.17051	0.585254	−	0.810850i	$-0.300995\pi$
$509$	26.4079	1.17051	0.585254	+	0.810850i	$0.300995\pi$
$510$	3.86055	0.170948
$511$	−11.3030	−0.500016
$512$	1.00000	0.0441942
$513$	−28.5803	−1.26185
$514$	11.3198	0.499294
$515$	0.842082	0.0371066
$516$	−0.721995	−0.0317840
$517$	−8.41915	−0.370274
$518$	3.67762	0.161585
$519$	7.79498	0.342162
$520$	−5.17412	−0.226900
$521$	−39.6341	−1.73640	−0.868200	−	0.496214i	$-0.834723\pi$
$521$	−39.6341	−1.73640	−0.868200	+	0.496214i	$0.834723\pi$
$522$	−12.5622	−0.549835
$523$	0.260570	0.0113939	0.00569697	−	0.999984i	$-0.498187\pi$
$523$	0.260570	0.0113939	0.00569697	+	0.999984i	$0.498187\pi$
$524$	−2.08259	−0.0909783
$525$	2.33620	0.101960
$526$	−15.8128	−0.689472
$527$	−27.9843	−1.21901
$528$	−0.721995	−0.0314208
$529$	15.6857	0.681988
$530$	−3.19137	−0.138624
$531$	−13.1838	−0.572129
$532$	23.3792	1.01362
$533$	21.2202	0.919148
$534$	4.67293	0.202218
$535$	1.82207	0.0787748
$536$	4.26675	0.184296
$537$	1.41762	0.0611749
$538$	−6.08952	−0.262538
$539$	−3.47014	−0.149470
$540$	3.95561	0.170222
$541$	23.4788	1.00943	0.504716	−	0.863286i	$-0.331597\pi$
$541$	23.4788	1.00943	0.504716	+	0.863286i	$0.331597\pi$
$542$	13.0105	0.558847
$543$	−17.9809	−0.771635
$544$	−5.34707	−0.229254
$545$	−10.7133	−0.458908
$546$	12.0878	0.517310
$547$	12.6280	0.539933	0.269966	−	0.962870i	$-0.412987\pi$
$547$	12.6280	0.539933	0.269966	+	0.962870i	$0.412987\pi$
$548$	20.6761	0.883237
$549$	−11.0626	−0.472140
$550$	−1.00000	−0.0426401
$551$	36.6178	1.55997
$552$	−4.49065	−0.191135
$553$	−55.5338	−2.36154
$554$	−12.7898	−0.543387
$555$	−0.820587	−0.0348320
$556$	14.6138	0.619765
$557$	−2.64031	−0.111873	−0.0559367	−	0.998434i	$-0.517814\pi$
$557$	−2.64031	−0.111873	−0.0559367	+	0.998434i	$0.517814\pi$
$558$	−12.9726	−0.549173
$559$	−5.17412	−0.218842
$560$	−3.23576	−0.136736
$561$	3.86055	0.162993
$562$	−30.6606	−1.29334
$563$	−26.4205	−1.11349	−0.556746	−	0.830683i	$-0.687950\pi$
$563$	−26.4205	−1.11349	−0.556746	+	0.830683i	$0.687950\pi$
$564$	6.07858	0.255954
$565$	20.3182	0.854791
$566$	15.2901	0.642692
$567$	14.8206	0.622405
$568$	3.58281	0.150331
$569$	24.7110	1.03594	0.517970	−	0.855399i	$-0.326688\pi$
$569$	24.7110	1.03594	0.517970	+	0.855399i	$0.326688\pi$
$570$	−5.21660	−0.218499
$571$	−32.7751	−1.37159	−0.685797	−	0.727793i	$-0.740546\pi$
$571$	−32.7751	−1.37159	−0.685797	+	0.727793i	$0.740546\pi$
$572$	−5.17412	−0.216341
$573$	−17.0051	−0.710396
$574$	13.2705	0.553901
$575$	−6.21978	−0.259383
$576$	−2.47872	−0.103280
$577$	−17.4607	−0.726897	−0.363448	−	0.931614i	$-0.618401\pi$
$577$	−17.4607	−0.726897	−0.363448	+	0.931614i	$0.618401\pi$
$578$	11.5911	0.482128
$579$	0.806558	0.0335194
$580$	−5.06803	−0.210439
$581$	50.1349	2.07994
$582$	−12.0892	−0.501114
$583$	−3.19137	−0.132173
$584$	−3.49316	−0.144548
$585$	12.8252	0.530258
$586$	−1.19140	−0.0492162
$587$	25.1420	1.03772	0.518862	−	0.854858i	$-0.326356\pi$
$587$	25.1420	1.03772	0.518862	+	0.854858i	$0.326356\pi$
$588$	2.50542	0.103322
$589$	37.8139	1.55810
$590$	−5.31879	−0.218971
$591$	−14.8803	−0.612094
$592$	1.13656	0.0467121
$593$	6.75564	0.277421	0.138710	−	0.990333i	$-0.455704\pi$
$593$	6.75564	0.277421	0.138710	+	0.990333i	$0.455704\pi$
$594$	3.95561	0.162301
$595$	17.3018	0.709306
$596$	−15.7820	−0.646456
$597$	11.0539	0.452408
$598$	−32.1819	−1.31602
$599$	3.54543	0.144862	0.0724311	−	0.997373i	$-0.476924\pi$
$599$	3.54543	0.144862	0.0724311	+	0.997373i	$0.476924\pi$
$600$	0.721995	0.0294753
$601$	−9.28556	−0.378766	−0.189383	−	0.981903i	$-0.560649\pi$
$601$	−9.28556	−0.378766	−0.189383	+	0.981903i	$0.560649\pi$
$602$	−3.23576	−0.131880
$603$	−10.5761	−0.430692
$604$	23.8672	0.971143
$605$	−1.00000	−0.0406558
$606$	−4.30446	−0.174857
$607$	−11.1741	−0.453544	−0.226772	−	0.973948i	$-0.572817\pi$
$607$	−11.1741	−0.453544	−0.226772	+	0.973948i	$0.572817\pi$
$608$	7.22526	0.293023
$609$	11.8399	0.479779
$610$	−4.46302	−0.180703
$611$	43.5617	1.76232
$612$	13.2539	0.535757
$613$	−30.6649	−1.23854	−0.619271	−	0.785177i	$-0.712572\pi$
$613$	−30.6649	−1.23854	−0.619271	+	0.785177i	$0.712572\pi$
$614$	−8.76111	−0.353570
$615$	−2.96105	−0.119401
$616$	−3.23576	−0.130372
$617$	−5.87884	−0.236673	−0.118337	−	0.992974i	$-0.537756\pi$
$617$	−5.87884	−0.236673	−0.118337	+	0.992974i	$0.537756\pi$
$618$	−0.607979	−0.0244565
$619$	−27.2338	−1.09462	−0.547310	−	0.836930i	$-0.684348\pi$
$619$	−27.2338	−1.09462	−0.547310	+	0.836930i	$0.684348\pi$
$620$	−5.23357	−0.210185
$621$	24.6030	0.987286
$622$	−9.04178	−0.362542
$623$	20.9427	0.839050
$624$	3.73569	0.149547
$625$	1.00000	0.0400000
$626$	11.6421	0.465312
$627$	−5.21660	−0.208331
$628$	20.3268	0.811128
$629$	−6.07724	−0.242315
$630$	8.02056	0.319547
$631$	−14.5753	−0.580233	−0.290116	−	0.956991i	$-0.593694\pi$
$631$	−14.5753	−0.580233	−0.290116	+	0.956991i	$0.593694\pi$
$632$	−17.1625	−0.682689
$633$	−8.38086	−0.333109
$634$	−27.0838	−1.07563
$635$	4.60580	0.182776
$636$	2.30415	0.0913657
$637$	17.9549	0.711401
$638$	−5.06803	−0.200645
$639$	−8.88080	−0.351319
$640$	−1.00000	−0.0395285
$641$	−3.63281	−0.143487	−0.0717437	−	0.997423i	$-0.522856\pi$
$641$	−3.63281	−0.143487	−0.0717437	+	0.997423i	$0.522856\pi$
$642$	−1.31552	−0.0519195
$643$	2.97657	0.117385	0.0586923	−	0.998276i	$-0.481307\pi$
$643$	2.97657	0.117385	0.0586923	+	0.998276i	$0.481307\pi$
$644$	−20.1257	−0.793065
$645$	0.721995	0.0284285
$646$	−38.6340	−1.52003
$647$	−21.6378	−0.850669	−0.425335	−	0.905036i	$-0.639844\pi$
$647$	−21.6378	−0.850669	−0.425335	+	0.905036i	$0.639844\pi$
$648$	4.58024	0.179929
$649$	−5.31879	−0.208781
$650$	5.17412	0.202946
$651$	12.2267	0.479201
$652$	16.9881	0.665307
$653$	−45.5639	−1.78305	−0.891526	−	0.452970i	$-0.850365\pi$
$653$	−45.5639	−1.78305	−0.891526	+	0.452970i	$0.850365\pi$
$654$	7.73496	0.302461
$655$	2.08259	0.0813735
$656$	4.10121	0.160125
$657$	8.65857	0.337803
$658$	27.2423	1.06202
$659$	7.71605	0.300575	0.150287	−	0.988642i	$-0.451980\pi$
$659$	7.71605	0.300575	0.150287	+	0.988642i	$0.451980\pi$
$660$	0.721995	0.0281036
$661$	−44.4032	−1.72709	−0.863543	−	0.504276i	$-0.831759\pi$
$661$	−44.4032	−1.72709	−0.863543	+	0.504276i	$0.831759\pi$
$662$	−15.3242	−0.595593
$663$	−19.9750	−0.775764
$664$	15.4940	0.601284
$665$	−23.3792	−0.906607
$666$	−2.81721	−0.109165
$667$	−31.5221	−1.22054
$668$	−22.1409	−0.856656
$669$	−2.90648	−0.112371
$670$	−4.26675	−0.164839
$671$	−4.46302	−0.172293
$672$	2.33620	0.0901209
$673$	2.80375	0.108077	0.0540383	−	0.998539i	$-0.482791\pi$
$673$	2.80375	0.108077	0.0540383	+	0.998539i	$0.482791\pi$
$674$	−2.53544	−0.0976614
$675$	−3.95561	−0.152251
$676$	13.7716	0.529675
$677$	−40.1552	−1.54329	−0.771644	−	0.636055i	$-0.780565\pi$
$677$	−40.1552	−1.54329	−0.771644	+	0.636055i	$0.780565\pi$
$678$	−14.6696	−0.563382
$679$	−54.1802	−2.07924
$680$	5.34707	0.205051
$681$	18.6945	0.716373
$682$	−5.23357	−0.200404
$683$	−46.8235	−1.79165	−0.895826	−	0.444406i	$-0.853415\pi$
$683$	−46.8235	−1.79165	−0.895826	+	0.444406i	$0.853415\pi$
$684$	−17.9094	−0.684784
$685$	−20.6761	−0.789992
$686$	−11.4218	−0.436085
$687$	17.8031	0.679232
$688$	−1.00000	−0.0381246
$689$	16.5126	0.629079
$690$	4.49065	0.170956
$691$	26.2257	0.997671	0.498836	−	0.866697i	$-0.333761\pi$
$691$	26.2257	0.997671	0.498836	+	0.866697i	$0.333761\pi$
$692$	10.7964	0.410419
$693$	8.02056	0.304676
$694$	−11.9244	−0.452645
$695$	−14.6138	−0.554335
$696$	3.65909	0.138697
$697$	−21.9295	−0.830637
$698$	−15.6610	−0.592777
$699$	−5.60532	−0.212013
$700$	3.23576	0.122300
$701$	−2.39686	−0.0905280	−0.0452640	−	0.998975i	$-0.514413\pi$
$701$	−2.39686	−0.0905280	−0.0452640	+	0.998975i	$0.514413\pi$
$702$	−20.4668	−0.772470
$703$	8.21191	0.309718
$704$	−1.00000	−0.0376889
$705$	−6.07858	−0.228933
$706$	6.12581	0.230548
$707$	−19.2913	−0.725524
$708$	3.84014	0.144321
$709$	26.3395	0.989201	0.494601	−	0.869120i	$-0.335314\pi$
$709$	26.3395	0.989201	0.494601	+	0.869120i	$0.335314\pi$
$710$	−3.58281	−0.134461
$711$	42.5412	1.59542
$712$	6.47226	0.242558
$713$	−32.5517	−1.21907
$714$	−12.4918	−0.467495
$715$	5.17412	0.193501
$716$	1.96348	0.0733787
$717$	7.72569	0.288521
$718$	−22.5151	−0.840258
$719$	38.4255	1.43303	0.716515	−	0.697572i	$-0.245736\pi$
$719$	38.4255	1.43303	0.716515	+	0.697572i	$0.245736\pi$
$720$	2.47872	0.0923766
$721$	−2.72478	−0.101476
$722$	33.2044	1.23574
$723$	−18.9385	−0.704331
$724$	−24.9045	−0.925568
$725$	5.06803	0.188222
$726$	0.721995	0.0267957
$727$	−52.1468	−1.93402	−0.967008	−	0.254745i	$-0.918008\pi$
$727$	−52.1468	−1.93402	−0.967008	+	0.254745i	$0.918008\pi$
$728$	16.7422	0.620508
$729$	−2.78537	−0.103162
$730$	3.49316	0.129287
$731$	5.34707	0.197768
$732$	3.22228	0.119099
$733$	−45.2985	−1.67314	−0.836568	−	0.547862i	$-0.815442\pi$
$733$	−45.2985	−1.67314	−0.836568	+	0.547862i	$0.815442\pi$
$734$	−15.3463	−0.566441
$735$	−2.50542	−0.0924140
$736$	−6.21978	−0.229264
$737$	−4.26675	−0.157168
$738$	−10.1658	−0.374207
$739$	2.54813	0.0937345	0.0468673	−	0.998901i	$-0.485076\pi$
$739$	2.54813	0.0937345	0.0468673	+	0.998901i	$0.485076\pi$
$740$	−1.13656	−0.0417806
$741$	26.9913	0.991551
$742$	10.3265	0.379098
$743$	−29.7936	−1.09302	−0.546511	−	0.837452i	$-0.684044\pi$
$743$	−29.7936	−1.09302	−0.546511	+	0.837452i	$0.684044\pi$
$744$	3.77861	0.138531
$745$	15.7820	0.578208
$746$	11.6444	0.426331
$747$	−38.4053	−1.40518
$748$	5.34707	0.195508
$749$	−5.89577	−0.215427
$750$	−0.721995	−0.0263635
$751$	12.5247	0.457032	0.228516	−	0.973540i	$-0.426613\pi$
$751$	12.5247	0.457032	0.228516	+	0.973540i	$0.426613\pi$
$752$	8.41915	0.307015
$753$	19.7098	0.718264
$754$	26.2226	0.954971
$755$	−23.8672	−0.868617
$756$	−12.7994	−0.465510
$757$	10.9023	0.396251	0.198125	−	0.980177i	$-0.436515\pi$
$757$	10.9023	0.396251	0.198125	+	0.980177i	$0.436515\pi$
$758$	−10.5387	−0.382784
$759$	4.49065	0.163000
$760$	−7.22526	−0.262088
$761$	−13.0149	−0.471791	−0.235895	−	0.971778i	$-0.575802\pi$
$761$	−13.0149	−0.471791	−0.235895	+	0.971778i	$0.575802\pi$
$762$	−3.32536	−0.120465
$763$	34.6657	1.25498
$764$	−23.5529	−0.852113
$765$	−13.2539	−0.479196
$766$	10.5227	0.380201
$767$	27.5201	0.993692
$768$	0.721995	0.0260527
$769$	15.1102	0.544889	0.272445	−	0.962171i	$-0.412168\pi$
$769$	15.1102	0.544889	0.272445	+	0.962171i	$0.412168\pi$
$770$	3.23576	0.116609
$771$	8.17282	0.294337
$772$	1.11713	0.0402062
$773$	32.0126	1.15141	0.575706	−	0.817656i	$-0.304727\pi$
$773$	32.0126	1.15141	0.575706	+	0.817656i	$0.304727\pi$
$774$	2.47872	0.0890959
$775$	5.23357	0.187996
$776$	−16.7442	−0.601081
$777$	2.65522	0.0952556
$778$	20.8771	0.748481
$779$	29.6323	1.06169
$780$	−3.73569	−0.133759
$781$	−3.58281	−0.128203
$782$	33.2576	1.18929
$783$	−20.0471	−0.716427
$784$	3.47014	0.123934
$785$	−20.3268	−0.725495
$786$	−1.50362	−0.0536323
$787$	17.8095	0.634842	0.317421	−	0.948285i	$-0.397183\pi$
$787$	17.8095	0.634842	0.317421	+	0.948285i	$0.397183\pi$
$788$	−20.6100	−0.734200
$789$	−11.4168	−0.406448
$790$	17.1625	0.610615
$791$	−65.7447	−2.33761
$792$	2.47872	0.0880776
$793$	23.0922	0.820029
$794$	−5.08413	−0.180429
$795$	−2.30415	−0.0817199
$796$	15.3103	0.542659
$797$	8.47941	0.300356	0.150178	−	0.988659i	$-0.452015\pi$
$797$	8.47941	0.300356	0.150178	+	0.988659i	$0.452015\pi$
$798$	16.8797	0.597534
$799$	−45.0178	−1.59261
$800$	1.00000	0.0353553
$801$	−16.0429	−0.566849
$802$	−32.9359	−1.16301
$803$	3.49316	0.123271
$804$	3.08057	0.108643
$805$	20.1257	0.709339
$806$	27.0792	0.953823
$807$	−4.39660	−0.154768
$808$	−5.96190	−0.209739
$809$	−24.3661	−0.856666	−0.428333	−	0.903621i	$-0.640899\pi$
$809$	−24.3661	−0.856666	−0.428333	+	0.903621i	$0.640899\pi$
$810$	−4.58024	−0.160933
$811$	−48.8829	−1.71651	−0.858255	−	0.513224i	$-0.828451\pi$
$811$	−48.8829	−1.71651	−0.858255	+	0.513224i	$0.828451\pi$
$812$	16.3989	0.575490
$813$	9.39348	0.329444
$814$	−1.13656	−0.0398363
$815$	−16.9881	−0.595069
$816$	−3.86055	−0.135146
$817$	−7.22526	−0.252780
$818$	6.49270	0.227012
$819$	−41.4993	−1.45010
$820$	−4.10121	−0.143221
$821$	35.9585	1.25496	0.627479	−	0.778633i	$-0.284087\pi$
$821$	35.9585	1.25496	0.627479	+	0.778633i	$0.284087\pi$
$822$	14.9280	0.520674
$823$	39.9834	1.39373	0.696866	−	0.717201i	$-0.254577\pi$
$823$	39.9834	1.39373	0.696866	+	0.717201i	$0.254577\pi$
$824$	−0.842082	−0.0293353
$825$	−0.721995	−0.0251366
$826$	17.2103	0.598824
$827$	30.9912	1.07767	0.538834	−	0.842412i	$-0.318865\pi$
$827$	30.9912	1.07767	0.538834	+	0.842412i	$0.318865\pi$
$828$	15.4171	0.535782
$829$	13.1275	0.455936	0.227968	−	0.973669i	$-0.426792\pi$
$829$	13.1275	0.455936	0.227968	+	0.973669i	$0.426792\pi$
$830$	−15.4940	−0.537804
$831$	−9.23418	−0.320330
$832$	5.17412	0.179380
$833$	−18.5551	−0.642896
$834$	10.5511	0.365355
$835$	22.1409	0.766216
$836$	−7.22526	−0.249891
$837$	−20.7020	−0.715565
$838$	2.08487	0.0720205
$839$	−17.2768	−0.596461	−0.298231	−	0.954494i	$-0.596396\pi$
$839$	−17.2768	−0.596461	−0.298231	+	0.954494i	$0.596396\pi$
$840$	−2.33620	−0.0806066
$841$	−3.31506	−0.114312
$842$	12.4190	0.427987
$843$	−22.1368	−0.762432
$844$	−11.6079	−0.399561
$845$	−13.7716	−0.473756
$846$	−20.8687	−0.717482
$847$	3.23576	0.111182
$848$	3.19137	0.109592
$849$	11.0394	0.378871
$850$	−5.34707	−0.183403
$851$	−7.06913	−0.242327
$852$	2.58677	0.0886213
$853$	41.9212	1.43535	0.717677	−	0.696376i	$-0.245206\pi$
$853$	41.9212	1.43535	0.717677	+	0.696376i	$0.245206\pi$
$854$	14.4413	0.494170
$855$	17.9094	0.612489
$856$	−1.82207	−0.0622769
$857$	19.0367	0.650281	0.325141	−	0.945666i	$-0.394588\pi$
$857$	19.0367	0.650281	0.325141	+	0.945666i	$0.394588\pi$
$858$	−3.73569	−0.127534
$859$	−18.6802	−0.637360	−0.318680	−	0.947862i	$-0.603239\pi$
$859$	−18.6802	−0.637360	−0.318680	+	0.947862i	$0.603239\pi$
$860$	1.00000	0.0340997
$861$	9.58125	0.326528
$862$	−19.8165	−0.674952
$863$	−46.0247	−1.56670	−0.783349	−	0.621582i	$-0.786490\pi$
$863$	−46.0247	−1.56670	−0.783349	+	0.621582i	$0.786490\pi$
$864$	−3.95561	−0.134573
$865$	−10.7964	−0.367090
$866$	−26.5358	−0.901723
$867$	8.36874	0.284217
$868$	16.9346	0.574797
$869$	17.1625	0.582199
$870$	−3.65909	−0.124055
$871$	22.0767	0.748041
$872$	10.7133	0.362799
$873$	41.5042	1.40470
$874$	−44.9396	−1.52010
$875$	−3.23576	−0.109389
$876$	−2.52204	−0.0852118
$877$	−2.82708	−0.0954638	−0.0477319	−	0.998860i	$-0.515199\pi$
$877$	−2.82708	−0.0954638	−0.0477319	+	0.998860i	$0.515199\pi$
$878$	31.0539	1.04802
$879$	−0.860183	−0.0290133
$880$	1.00000	0.0337100
$881$	13.6420	0.459612	0.229806	−	0.973236i	$-0.426191\pi$
$881$	13.6420	0.459612	0.229806	+	0.973236i	$0.426191\pi$
$882$	−8.60153	−0.289628
$883$	39.2276	1.32011	0.660057	−	0.751215i	$-0.270532\pi$
$883$	39.2276	1.32011	0.660057	+	0.751215i	$0.270532\pi$
$884$	−27.6664	−0.930522
$885$	−3.84014	−0.129085
$886$	33.0372	1.10991
$887$	−59.2358	−1.98894	−0.994472	−	0.104998i	$-0.966516\pi$
$887$	−59.2358	−1.98894	−0.994472	+	0.104998i	$0.966516\pi$
$888$	0.820587	0.0275371
$889$	−14.9033	−0.499839
$890$	−6.47226	−0.216951
$891$	−4.58024	−0.153444
$892$	−4.02563	−0.134788
$893$	60.8305	2.03562
$894$	−11.3945	−0.381090
$895$	−1.96348	−0.0656319
$896$	3.23576	0.108099
$897$	−23.2352	−0.775800
$898$	16.9027	0.564051
$899$	26.5239	0.884622
$900$	−2.47872	−0.0826241
$901$	−17.0645	−0.568501
$902$	−4.10121	−0.136555
$903$	−2.33620	−0.0777439
$904$	−20.3182	−0.675772
$905$	24.9045	0.827854
$906$	17.2320	0.572495
$907$	−17.9768	−0.596909	−0.298454	−	0.954424i	$-0.596471\pi$
$907$	−17.9768	−0.596909	−0.298454	+	0.954424i	$0.596471\pi$
$908$	25.8928	0.859283
$909$	14.7779	0.490153
$910$	−16.7422	−0.554999
$911$	−39.0413	−1.29349	−0.646747	−	0.762704i	$-0.723871\pi$
$911$	−39.0413	−1.29349	−0.646747	+	0.762704i	$0.723871\pi$
$912$	5.21660	0.172739
$913$	−15.4940	−0.512776
$914$	−9.04068	−0.299039
$915$	−3.22228	−0.106525
$916$	24.6583	0.814732
$917$	−6.73876	−0.222533
$918$	21.1509	0.698084
$919$	32.6588	1.07731	0.538657	−	0.842525i	$-0.318932\pi$
$919$	32.6588	1.07731	0.538657	+	0.842525i	$0.318932\pi$
$920$	6.21978	0.205060
$921$	−6.32548	−0.208432
$922$	−8.04529	−0.264958
$923$	18.5379	0.610183
$924$	−2.33620	−0.0768554
$925$	1.13656	0.0373697
$926$	−17.2778	−0.567785
$927$	2.08729	0.0685556
$928$	5.06803	0.166366
$929$	−24.0410	−0.788760	−0.394380	−	0.918947i	$-0.629041\pi$
$929$	−24.0410	−0.788760	−0.394380	+	0.918947i	$0.629041\pi$
$930$	−3.77861	−0.123906
$931$	25.0727	0.821724
$932$	−7.76365	−0.254307
$933$	−6.52812	−0.213721
$934$	16.4213	0.537322
$935$	−5.34707	−0.174868
$936$	−12.8252	−0.419206
$937$	−40.8380	−1.33412	−0.667060	−	0.745004i	$-0.732448\pi$
$937$	−40.8380	−1.33412	−0.667060	+	0.745004i	$0.732448\pi$
$938$	13.8062	0.450788
$939$	8.40554	0.274304
$940$	−8.41915	−0.274602
$941$	37.9670	1.23769	0.618844	−	0.785514i	$-0.287601\pi$
$941$	37.9670	1.23769	0.618844	+	0.785514i	$0.287601\pi$
$942$	14.6758	0.478165
$943$	−25.5087	−0.830676
$944$	5.31879	0.173112
$945$	12.7994	0.416365
$946$	1.00000	0.0325128
$947$	−35.0348	−1.13848	−0.569239	−	0.822172i	$-0.692762\pi$
$947$	−35.0348	−1.13848	−0.569239	+	0.822172i	$0.692762\pi$
$948$	−12.3913	−0.402449
$949$	−18.0740	−0.586708
$950$	7.22526	0.234418
$951$	−19.5543	−0.634093
$952$	−17.3018	−0.560756
$953$	−23.3750	−0.757192	−0.378596	−	0.925562i	$-0.623593\pi$
$953$	−23.3750	−0.757192	−0.378596	+	0.925562i	$0.623593\pi$
$954$	−7.91053	−0.256113
$955$	23.5529	0.762153
$956$	10.7005	0.346078
$957$	−3.65909	−0.118282
$958$	−15.1831	−0.490543
$959$	66.9028	2.16040
$960$	−0.721995	−0.0233023
$961$	−3.60971	−0.116442
$962$	5.88068	0.189601
$963$	4.51640	0.145539
$964$	−26.2308	−0.844838
$965$	−1.11713	−0.0359615
$966$	−14.5307	−0.467517
$967$	48.5035	1.55977	0.779884	−	0.625924i	$-0.215278\pi$
$967$	48.5035	1.55977	0.779884	+	0.625924i	$0.215278\pi$
$968$	1.00000	0.0321412
$969$	−27.8935	−0.896069
$970$	16.7442	0.537623
$971$	16.3599	0.525013	0.262506	−	0.964930i	$-0.415451\pi$
$971$	16.3599	0.525013	0.262506	+	0.964930i	$0.415451\pi$
$972$	15.1737	0.486698
$973$	47.2869	1.51595
$974$	−27.4736	−0.880312
$975$	3.73569	0.119638
$976$	4.46302	0.142858
$977$	−9.75988	−0.312246	−0.156123	−	0.987738i	$-0.549900\pi$
$977$	−9.75988	−0.312246	−0.156123	+	0.987738i	$0.549900\pi$
$978$	12.2653	0.392203
$979$	−6.47226	−0.206854
$980$	−3.47014	−0.110850
$981$	−26.5554	−0.847847
$982$	4.94674	0.157857
$983$	−21.3676	−0.681520	−0.340760	−	0.940150i	$-0.610684\pi$
$983$	−21.3676	−0.681520	−0.340760	+	0.940150i	$0.610684\pi$
$984$	2.96105	0.0943949
$985$	20.6100	0.656689
$986$	−27.0991	−0.863011
$987$	19.6688	0.626065
$988$	37.3844	1.18936
$989$	6.21978	0.197778
$990$	−2.47872	−0.0787790
$991$	29.8398	0.947892	0.473946	−	0.880554i	$-0.342829\pi$
$991$	29.8398	0.947892	0.473946	+	0.880554i	$0.342829\pi$
$992$	5.23357	0.166166
$993$	−11.0640	−0.351106
$994$	11.5931	0.367711
$995$	−15.3103	−0.485369
$996$	11.1866	0.354460
$997$	27.8197	0.881058	0.440529	−	0.897738i	$-0.354791\pi$
$997$	27.8197	0.881058	0.440529	+	0.897738i	$0.354791\pi$
$998$	−28.8624	−0.913624
$999$	−4.49577	−0.142240

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4730.2.a.ba.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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.721995 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.721995 q^{6} +3.23576 q^{7} +1.00000 q^{8} -2.47872 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +0.721995 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.721995 q^{6} +3.23576 q^{7} +1.00000 q^{8} -2.47872 q^{9} -1.00000 q^{10} -1.00000 q^{11} +0.721995 q^{12} +5.17412 q^{13} +3.23576 q^{14} -0.721995 q^{15} +1.00000 q^{16} -5.34707 q^{17} -2.47872 q^{18} +7.22526 q^{19} -1.00000 q^{20} +2.33620 q^{21} -1.00000 q^{22} -6.21978 q^{23} +0.721995 q^{24} +1.00000 q^{25} +5.17412 q^{26} -3.95561 q^{27} +3.23576 q^{28} +5.06803 q^{29} -0.721995 q^{30} +5.23357 q^{31} +1.00000 q^{32} -0.721995 q^{33} -5.34707 q^{34} -3.23576 q^{35} -2.47872 q^{36} +1.13656 q^{37} +7.22526 q^{38} +3.73569 q^{39} -1.00000 q^{40} +4.10121 q^{41} +2.33620 q^{42} -1.00000 q^{43} -1.00000 q^{44} +2.47872 q^{45} -6.21978 q^{46} +8.41915 q^{47} +0.721995 q^{48} +3.47014 q^{49} +1.00000 q^{50} -3.86055 q^{51} +5.17412 q^{52} +3.19137 q^{53} -3.95561 q^{54} +1.00000 q^{55} +3.23576 q^{56} +5.21660 q^{57} +5.06803 q^{58} +5.31879 q^{59} -0.721995 q^{60} +4.46302 q^{61} +5.23357 q^{62} -8.02056 q^{63} +1.00000 q^{64} -5.17412 q^{65} -0.721995 q^{66} +4.26675 q^{67} -5.34707 q^{68} -4.49065 q^{69} -3.23576 q^{70} +3.58281 q^{71} -2.47872 q^{72} -3.49316 q^{73} +1.13656 q^{74} +0.721995 q^{75} +7.22526 q^{76} -3.23576 q^{77} +3.73569 q^{78} -17.1625 q^{79} -1.00000 q^{80} +4.58024 q^{81} +4.10121 q^{82} +15.4940 q^{83} +2.33620 q^{84} +5.34707 q^{85} -1.00000 q^{86} +3.65909 q^{87} -1.00000 q^{88} +6.47226 q^{89} +2.47872 q^{90} +16.7422 q^{91} -6.21978 q^{92} +3.77861 q^{93} +8.41915 q^{94} -7.22526 q^{95} +0.721995 q^{96} -16.7442 q^{97} +3.47014 q^{98} +2.47872 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 10 q^{2} - q^{3} + 10 q^{4} - 10 q^{5} - q^{6} + 3 q^{7} + 10 q^{8} + 13 q^{9}+O(q^{10}) \) 10 * q + 10 * q^2 - q^3 + 10 * q^4 - 10 * q^5 - q^6 + 3 * q^7 + 10 * q^8 + 13 * q^9	\( 10 q + 10 q^{2} - q^{3} + 10 q^{4} - 10 q^{5} - q^{6} + 3 q^{7} + 10 q^{8} + 13 q^{9} - 10 q^{10} - 10 q^{11} - q^{12} + 6 q^{13} + 3 q^{14} + q^{15} + 10 q^{16} + 3 q^{17} + 13 q^{18} + 3 q^{19} - 10 q^{20} + 11 q^{21} - 10 q^{22} - 6 q^{23} - q^{24} + 10 q^{25} + 6 q^{26} + 8 q^{27} + 3 q^{28} + 14 q^{29} + q^{30} + 6 q^{31} + 10 q^{32} + q^{33} + 3 q^{34} - 3 q^{35} + 13 q^{36} + 10 q^{37} + 3 q^{38} + 24 q^{39} - 10 q^{40} + 26 q^{41} + 11 q^{42} - 10 q^{43} - 10 q^{44} - 13 q^{45} - 6 q^{46} + 3 q^{47} - q^{48} + 33 q^{49} + 10 q^{50} + 18 q^{51} + 6 q^{52} - 9 q^{53} + 8 q^{54} + 10 q^{55} + 3 q^{56} + 18 q^{57} + 14 q^{58} - 9 q^{59} + q^{60} + 22 q^{61} + 6 q^{62} - q^{63} + 10 q^{64} - 6 q^{65} + q^{66} + 18 q^{67} + 3 q^{68} + 6 q^{69} - 3 q^{70} + 27 q^{71} + 13 q^{72} + 28 q^{73} + 10 q^{74} - q^{75} + 3 q^{76} - 3 q^{77} + 24 q^{78} + 3 q^{79} - 10 q^{80} + 30 q^{81} + 26 q^{82} - 11 q^{83} + 11 q^{84} - 3 q^{85} - 10 q^{86} + 30 q^{87} - 10 q^{88} + 16 q^{89} - 13 q^{90} + 32 q^{91} - 6 q^{92} + 52 q^{93} + 3 q^{94} - 3 q^{95} - q^{96} + 22 q^{97} + 33 q^{98} - 13 q^{99}+O(q^{100}) \) 10 * q + 10 * q^2 - q^3 + 10 * q^4 - 10 * q^5 - q^6 + 3 * q^7 + 10 * q^8 + 13 * q^9 - 10 * q^10 - 10 * q^11 - q^12 + 6 * q^13 + 3 * q^14 + q^15 + 10 * q^16 + 3 * q^17 + 13 * q^18 + 3 * q^19 - 10 * q^20 + 11 * q^21 - 10 * q^22 - 6 * q^23 - q^24 + 10 * q^25 + 6 * q^26 + 8 * q^27 + 3 * q^28 + 14 * q^29 + q^30 + 6 * q^31 + 10 * q^32 + q^33 + 3 * q^34 - 3 * q^35 + 13 * q^36 + 10 * q^37 + 3 * q^38 + 24 * q^39 - 10 * q^40 + 26 * q^41 + 11 * q^42 - 10 * q^43 - 10 * q^44 - 13 * q^45 - 6 * q^46 + 3 * q^47 - q^48 + 33 * q^49 + 10 * q^50 + 18 * q^51 + 6 * q^52 - 9 * q^53 + 8 * q^54 + 10 * q^55 + 3 * q^56 + 18 * q^57 + 14 * q^58 - 9 * q^59 + q^60 + 22 * q^61 + 6 * q^62 - q^63 + 10 * q^64 - 6 * q^65 + q^66 + 18 * q^67 + 3 * q^68 + 6 * q^69 - 3 * q^70 + 27 * q^71 + 13 * q^72 + 28 * q^73 + 10 * q^74 - q^75 + 3 * q^76 - 3 * q^77 + 24 * q^78 + 3 * q^79 - 10 * q^80 + 30 * q^81 + 26 * q^82 - 11 * q^83 + 11 * q^84 - 3 * q^85 - 10 * q^86 + 30 * q^87 - 10 * q^88 + 16 * q^89 - 13 * q^90 + 32 * q^91 - 6 * q^92 + 52 * q^93 + 3 * q^94 - 3 * q^95 - q^96 + 22 * q^97 + 33 * q^98 - 13 * q^99

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