LMFDB - Embedded newform 4031.2.a.d.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4031,2,Mod(1,4031)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4031, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4031.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4031 = 29 \cdot 139 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4031.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:	$32.1876970548$
Analytic rank:	$0$
Dimension:	$98$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	4031.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.99223 q^{2} -2.07417 q^{3} +1.96900 q^{4} +0.414014 q^{5} +4.13224 q^{6} +4.11338 q^{7} +0.0617619 q^{8} +1.30220 q^{9} +O(q^{10})$	\(q-1.99223 q^{2} -2.07417 q^{3} +1.96900 q^{4} +0.414014 q^{5} +4.13224 q^{6} +4.11338 q^{7} +0.0617619 q^{8} +1.30220 q^{9} -0.824814 q^{10} +0.0711767 q^{11} -4.08405 q^{12} +5.35263 q^{13} -8.19483 q^{14} -0.858738 q^{15} -4.06104 q^{16} -1.30394 q^{17} -2.59429 q^{18} +6.21315 q^{19} +0.815194 q^{20} -8.53188 q^{21} -0.141801 q^{22} +3.43957 q^{23} -0.128105 q^{24} -4.82859 q^{25} -10.6637 q^{26} +3.52154 q^{27} +8.09925 q^{28} +1.00000 q^{29} +1.71081 q^{30} +1.93826 q^{31} +7.96702 q^{32} -0.147633 q^{33} +2.59776 q^{34} +1.70300 q^{35} +2.56403 q^{36} +7.44940 q^{37} -12.3781 q^{38} -11.1023 q^{39} +0.0255703 q^{40} +8.46456 q^{41} +16.9975 q^{42} +8.21326 q^{43} +0.140147 q^{44} +0.539129 q^{45} -6.85243 q^{46} +5.71041 q^{47} +8.42331 q^{48} +9.91993 q^{49} +9.61969 q^{50} +2.70460 q^{51} +10.5393 q^{52} +0.794426 q^{53} -7.01573 q^{54} +0.0294682 q^{55} +0.254050 q^{56} -12.8872 q^{57} -1.99223 q^{58} -0.726774 q^{59} -1.69085 q^{60} +7.32394 q^{61} -3.86146 q^{62} +5.35644 q^{63} -7.75010 q^{64} +2.21607 q^{65} +0.294120 q^{66} -8.72825 q^{67} -2.56746 q^{68} -7.13427 q^{69} -3.39278 q^{70} -0.514702 q^{71} +0.0804262 q^{72} +3.73452 q^{73} -14.8410 q^{74} +10.0153 q^{75} +12.2337 q^{76} +0.292777 q^{77} +22.1184 q^{78} +0.115298 q^{79} -1.68133 q^{80} -11.2109 q^{81} -16.8634 q^{82} -0.0662891 q^{83} -16.7993 q^{84} -0.539850 q^{85} -16.3627 q^{86} -2.07417 q^{87} +0.00439601 q^{88} -7.93276 q^{89} -1.07407 q^{90} +22.0174 q^{91} +6.77251 q^{92} -4.02028 q^{93} -11.3765 q^{94} +2.57233 q^{95} -16.5250 q^{96} +12.6805 q^{97} -19.7628 q^{98} +0.0926863 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 98 q + 6 q^{2} + 6 q^{3} + 116 q^{4} + q^{5} + 7 q^{6} + 12 q^{7} + 15 q^{8} + 136 q^{9}+O(q^{10}) $ 98 * q + 6 * q^2 + 6 * q^3 + 116 * q^4 + q^5 + 7 * q^6 + 12 * q^7 + 15 * q^8 + 136 * q^9	\( 98 q + 6 q^{2} + 6 q^{3} + 116 q^{4} + q^{5} + 7 q^{6} + 12 q^{7} + 15 q^{8} + 136 q^{9} + 16 q^{10} + 25 q^{11} + 8 q^{12} + 18 q^{13} + 34 q^{14} + 14 q^{15} + 136 q^{16} + 35 q^{17} + 20 q^{18} + 48 q^{19} - 20 q^{20} + 62 q^{21} + 32 q^{22} + q^{23} + 8 q^{24} + 173 q^{25} + 15 q^{26} + 18 q^{27} + 37 q^{28} + 98 q^{29} - 6 q^{30} + 20 q^{31} + 16 q^{32} + 24 q^{33} - 6 q^{34} + 11 q^{35} + 155 q^{36} + 62 q^{37} - 5 q^{38} + 45 q^{39} + 38 q^{40} + 50 q^{41} + 7 q^{42} + 72 q^{43} + 92 q^{44} - 13 q^{45} + 32 q^{46} - 16 q^{47} - 13 q^{48} + 194 q^{49} + 50 q^{50} + 2 q^{51} + 83 q^{52} - 11 q^{53} + 58 q^{54} + 32 q^{55} + 106 q^{56} + 84 q^{57} + 6 q^{58} + 20 q^{59} + 62 q^{60} + 142 q^{61} - 27 q^{62} + 26 q^{63} + 213 q^{64} + 13 q^{65} - 35 q^{66} + 5 q^{67} + 69 q^{68} + 68 q^{69} - 2 q^{70} - 10 q^{71} - 9 q^{72} + 74 q^{73} + 21 q^{74} + 19 q^{75} + 116 q^{76} + 41 q^{77} - 162 q^{78} + 104 q^{79} - 86 q^{80} + 230 q^{81} + 53 q^{82} - 19 q^{83} + 76 q^{84} + 125 q^{85} + 9 q^{86} + 6 q^{87} + 68 q^{88} + 120 q^{89} + 122 q^{90} + 30 q^{91} + 3 q^{92} - 56 q^{93} + 22 q^{94} + 32 q^{95} - 55 q^{96} + 98 q^{97} - 15 q^{98} + 69 q^{99}+O(q^{100}) \) 98 * q + 6 * q^2 + 6 * q^3 + 116 * q^4 + q^5 + 7 * q^6 + 12 * q^7 + 15 * q^8 + 136 * q^9 + 16 * q^10 + 25 * q^11 + 8 * q^12 + 18 * q^13 + 34 * q^14 + 14 * q^15 + 136 * q^16 + 35 * q^17 + 20 * q^18 + 48 * q^19 - 20 * q^20 + 62 * q^21 + 32 * q^22 + q^23 + 8 * q^24 + 173 * q^25 + 15 * q^26 + 18 * q^27 + 37 * q^28 + 98 * q^29 - 6 * q^30 + 20 * q^31 + 16 * q^32 + 24 * q^33 - 6 * q^34 + 11 * q^35 + 155 * q^36 + 62 * q^37 - 5 * q^38 + 45 * q^39 + 38 * q^40 + 50 * q^41 + 7 * q^42 + 72 * q^43 + 92 * q^44 - 13 * q^45 + 32 * q^46 - 16 * q^47 - 13 * q^48 + 194 * q^49 + 50 * q^50 + 2 * q^51 + 83 * q^52 - 11 * q^53 + 58 * q^54 + 32 * q^55 + 106 * q^56 + 84 * q^57 + 6 * q^58 + 20 * q^59 + 62 * q^60 + 142 * q^61 - 27 * q^62 + 26 * q^63 + 213 * q^64 + 13 * q^65 - 35 * q^66 + 5 * q^67 + 69 * q^68 + 68 * q^69 - 2 * q^70 - 10 * q^71 - 9 * q^72 + 74 * q^73 + 21 * q^74 + 19 * q^75 + 116 * q^76 + 41 * q^77 - 162 * q^78 + 104 * q^79 - 86 * q^80 + 230 * q^81 + 53 * q^82 - 19 * q^83 + 76 * q^84 + 125 * q^85 + 9 * q^86 + 6 * q^87 + 68 * q^88 + 120 * q^89 + 122 * q^90 + 30 * q^91 + 3 * q^92 - 56 * q^93 + 22 * q^94 + 32 * q^95 - 55 * q^96 + 98 * q^97 - 15 * q^98 + 69 * 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 $

$2$	−1.99223	−1.40872	−0.704361	−	0.709842i	$-0.748766\pi$
$2$	−1.99223	−1.40872	−0.704361	+	0.709842i	$0.748766\pi$
$3$	−2.07417	−1.19753	−0.598763	−	0.800927i	$-0.704341\pi$
$3$	−2.07417	−1.19753	−0.598763	+	0.800927i	$0.704341\pi$
$4$	1.96900	0.984499
$5$	0.414014	0.185153	0.0925764	−	0.995706i	$-0.470490\pi$
$5$	0.414014	0.185153	0.0925764	+	0.995706i	$0.470490\pi$
$6$	4.13224	1.68698
$7$	4.11338	1.55471	0.777357	−	0.629060i	$-0.216560\pi$
$7$	4.11338	1.55471	0.777357	+	0.629060i	$0.216560\pi$
$8$	0.0617619	0.0218361
$9$	1.30220	0.434066
$10$	−0.824814	−0.260829
$11$	0.0711767	0.0214606	0.0107303	−	0.999942i	$-0.496584\pi$
$11$	0.0711767	0.0214606	0.0107303	+	0.999942i	$0.496584\pi$
$12$	−4.08405	−1.17896
$13$	5.35263	1.48455	0.742277	−	0.670094i	$-0.233746\pi$
$13$	5.35263	1.48455	0.742277	+	0.670094i	$0.233746\pi$
$14$	−8.19483	−2.19016
$15$	−0.858738	−0.221725
$16$	−4.06104	−1.01526
$17$	−1.30394	−0.316252	−0.158126	−	0.987419i	$-0.550545\pi$
$17$	−1.30394	−0.316252	−0.158126	+	0.987419i	$0.550545\pi$
$18$	−2.59429	−0.611479
$19$	6.21315	1.42539	0.712697	−	0.701472i	$-0.247473\pi$
$19$	6.21315	1.42539	0.712697	+	0.701472i	$0.247473\pi$
$20$	0.815194	0.182283
$21$	−8.53188	−1.86181
$22$	−0.141801	−0.0302320
$23$	3.43957	0.717200	0.358600	−	0.933491i	$-0.383254\pi$
$23$	3.43957	0.717200	0.358600	+	0.933491i	$0.383254\pi$
$24$	−0.128105	−0.0261493
$25$	−4.82859	−0.965718
$26$	−10.6637	−2.09132
$27$	3.52154	0.677720
$28$	8.09925	1.53061
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	1.71081	0.312349
$31$	1.93826	0.348121	0.174061	−	0.984735i	$-0.444311\pi$
$31$	1.93826	0.348121	0.174061	+	0.984735i	$0.444311\pi$
$32$	7.96702	1.40838
$33$	−0.147633	−0.0256996
$34$	2.59776	0.445511
$35$	1.70300	0.287860
$36$	2.56403	0.427338
$37$	7.44940	1.22467	0.612337	−	0.790597i	$-0.290230\pi$
$37$	7.44940	1.22467	0.612337	+	0.790597i	$0.290230\pi$
$38$	−12.3781	−2.00799
$39$	−11.1023	−1.77779
$40$	0.0255703	0.00404302
$41$	8.46456	1.32194	0.660971	−	0.750412i	$-0.270145\pi$
$41$	8.46456	1.32194	0.660971	+	0.750412i	$0.270145\pi$
$42$	16.9975	2.62277
$43$	8.21326	1.25251	0.626255	−	0.779618i	$-0.284587\pi$
$43$	8.21326	1.25251	0.626255	+	0.779618i	$0.284587\pi$
$44$	0.140147	0.0211279
$45$	0.539129	0.0803686
$46$	−6.85243	−1.01034
$47$	5.71041	0.832949	0.416475	−	0.909147i	$-0.363265\pi$
$47$	5.71041	0.832949	0.416475	+	0.909147i	$0.363265\pi$
$48$	8.42331	1.21580
$49$	9.91993	1.41713
$50$	9.61969	1.36043
$51$	2.70460	0.378720
$52$	10.5393	1.46154
$53$	0.794426	0.109123	0.0545614	−	0.998510i	$-0.482624\pi$
$53$	0.794426	0.109123	0.0545614	+	0.998510i	$0.482624\pi$
$54$	−7.01573	−0.954719
$55$	0.0294682	0.00397349
$56$	0.254050	0.0339489
$57$	−12.8872	−1.70695
$58$	−1.99223	−0.261593
$59$	−0.726774	−0.0946180	−0.0473090	−	0.998880i	$-0.515065\pi$
$59$	−0.726774	−0.0946180	−0.0473090	+	0.998880i	$0.515065\pi$
$60$	−1.69085	−0.218288
$61$	7.32394	0.937734	0.468867	−	0.883269i	$-0.344662\pi$
$61$	7.32394	0.937734	0.468867	+	0.883269i	$0.344662\pi$
$62$	−3.86146	−0.490406
$63$	5.35644	0.674848
$64$	−7.75010	−0.968762
$65$	2.21607	0.274869
$66$	0.294120	0.0362036
$67$	−8.72825	−1.06633	−0.533163	−	0.846013i	$-0.678997\pi$
$67$	−8.72825	−1.06633	−0.533163	+	0.846013i	$0.678997\pi$
$68$	−2.56746	−0.311350
$69$	−7.13427	−0.858865
$70$	−3.39278	−0.405514
$71$	−0.514702	−0.0610839	−0.0305419	−	0.999533i	$-0.509723\pi$
$71$	−0.514702	−0.0610839	−0.0305419	+	0.999533i	$0.509723\pi$
$72$	0.0804262	0.00947832
$73$	3.73452	0.437092	0.218546	−	0.975827i	$-0.429869\pi$
$73$	3.73452	0.437092	0.218546	+	0.975827i	$0.429869\pi$
$74$	−14.8410	−1.72523
$75$	10.0153	1.15647
$76$	12.2337	1.40330
$77$	0.292777	0.0333651
$78$	22.1184	2.50441
$79$	0.115298	0.0129721	0.00648605	−	0.999979i	$-0.497935\pi$
$79$	0.115298	0.0129721	0.00648605	+	0.999979i	$0.497935\pi$
$80$	−1.68133	−0.187978
$81$	−11.2109	−1.24565
$82$	−16.8634	−1.86225
$83$	−0.0662891	−0.00727617	−0.00363808	−	0.999993i	$-0.501158\pi$
$83$	−0.0662891	−0.00727617	−0.00363808	+	0.999993i	$0.501158\pi$
$84$	−16.7993	−1.83295
$85$	−0.539850	−0.0585550
$86$	−16.3627	−1.76444
$87$	−2.07417	−0.222375
$88$	0.00439601	0.000468616 0
$89$	−7.93276	−0.840871	−0.420435	−	0.907322i	$-0.638123\pi$
$89$	−7.93276	−0.840871	−0.420435	+	0.907322i	$0.638123\pi$
$90$	−1.07407	−0.113217
$91$	22.0174	2.30805
$92$	6.77251	0.706083
$93$	−4.02028	−0.416884
$94$	−11.3765	−1.17339
$95$	2.57233	0.263916
$96$	−16.5250	−1.68658
$97$	12.6805	1.28751	0.643757	−	0.765230i	$-0.277375\pi$
$97$	12.6805	1.28751	0.643757	+	0.765230i	$0.277375\pi$
$98$	−19.7628	−1.99635
$99$	0.0926863	0.00931532
$100$	−9.50749	−0.950749
$101$	−14.6432	−1.45705	−0.728525	−	0.685020i	$-0.759794\pi$
$101$	−14.6432	−1.45705	−0.728525	+	0.685020i	$0.759794\pi$
$102$	−5.38820	−0.533511
$103$	4.02952	0.397040	0.198520	−	0.980097i	$-0.436386\pi$
$103$	4.02952	0.397040	0.198520	+	0.980097i	$0.436386\pi$
$104$	0.330589	0.0324169
$105$	−3.53232	−0.344719
$106$	−1.58268	−0.153724
$107$	5.17991	0.500761	0.250380	−	0.968148i	$-0.419444\pi$
$107$	5.17991	0.500761	0.250380	+	0.968148i	$0.419444\pi$
$108$	6.93390	0.667215
$109$	8.81963	0.844767	0.422383	−	0.906417i	$-0.361194\pi$
$109$	8.81963	0.844767	0.422383	+	0.906417i	$0.361194\pi$
$110$	−0.0587076	−0.00559755
$111$	−15.4514	−1.46658
$112$	−16.7046	−1.57844
$113$	−14.1613	−1.33218	−0.666090	−	0.745871i	$-0.732034\pi$
$113$	−14.1613	−1.33218	−0.666090	+	0.745871i	$0.732034\pi$
$114$	25.6742	2.40461
$115$	1.42403	0.132792
$116$	1.96900	0.182817
$117$	6.97019	0.644394
$118$	1.44791	0.133290
$119$	−5.36361	−0.491681
$120$	−0.0530373	−0.00484162
$121$	−10.9949	−0.999539
$122$	−14.5910	−1.32101
$123$	−17.5570	−1.58306
$124$	3.81643	0.342725
$125$	−4.06918	−0.363958
$126$	−10.6713	−0.950674
$127$	8.47933	0.752419	0.376209	−	0.926535i	$-0.377227\pi$
$127$	8.47933	0.752419	0.376209	+	0.926535i	$0.377227\pi$
$128$	−0.494036	−0.0436670
$129$	−17.0357	−1.49991
$130$	−4.41493	−0.387215
$131$	19.2326	1.68036	0.840181	−	0.542306i	$-0.182449\pi$
$131$	19.2326	1.68036	0.840181	+	0.542306i	$0.182449\pi$
$132$	−0.290689	−0.0253012
$133$	25.5571	2.21608
$134$	17.3887	1.50216
$135$	1.45797	0.125482
$136$	−0.0805338	−0.00690572
$137$	−20.1089	−1.71802	−0.859012	−	0.511956i	$-0.828921\pi$
$137$	−20.1089	−1.71802	−0.859012	+	0.511956i	$0.828921\pi$
$138$	14.2131	1.20990
$139$	−1.00000	−0.0848189
$139$	−1.00000	−0.0848189
$140$	3.35321	0.283398
$141$	−11.8444	−0.997478
$142$	1.02541	0.0860503
$143$	0.380983	0.0318594
$144$	−5.28828	−0.440690
$145$	0.414014	0.0343820
$146$	−7.44003	−0.615741
$147$	−20.5757	−1.69705
$148$	14.6679	1.20569
$149$	−15.1289	−1.23941	−0.619704	−	0.784836i	$-0.712747\pi$
$149$	−15.1289	−1.23941	−0.619704	+	0.784836i	$0.712747\pi$
$150$	−19.9529	−1.62915
$151$	−17.1398	−1.39482	−0.697408	−	0.716674i	$-0.745663\pi$
$151$	−17.1398	−1.39482	−0.697408	+	0.716674i	$0.745663\pi$
$152$	0.383736	0.0311251
$153$	−1.69799	−0.137274
$154$	−0.583281	−0.0470021
$155$	0.802466	0.0644556
$156$	−21.8604	−1.75023
$157$	20.2899	1.61931	0.809656	−	0.586904i	$-0.199654\pi$
$157$	20.2899	1.61931	0.809656	+	0.586904i	$0.199654\pi$
$158$	−0.229702	−0.0182741
$159$	−1.64778	−0.130677
$160$	3.29846	0.260766
$161$	14.1483	1.11504
$162$	22.3347	1.75478
$163$	−19.6617	−1.54002	−0.770010	−	0.638031i	$-0.779749\pi$
$163$	−19.6617	−1.54002	−0.770010	+	0.638031i	$0.779749\pi$
$164$	16.6667	1.30145
$165$	−0.0611222	−0.00475835
$166$	0.132063	0.0102501
$167$	−4.60847	−0.356614	−0.178307	−	0.983975i	$-0.557062\pi$
$167$	−4.60847	−0.356614	−0.178307	+	0.983975i	$0.557062\pi$
$168$	−0.526944	−0.0406546
$169$	15.6507	1.20390
$170$	1.07551	0.0824877
$171$	8.09076	0.618716
$172$	16.1719	1.23310
$173$	10.7411	0.816631	0.408315	−	0.912841i	$-0.366116\pi$
$173$	10.7411	0.816631	0.408315	+	0.912841i	$0.366116\pi$
$174$	4.13224	0.313264
$175$	−19.8619	−1.50142
$176$	−0.289052	−0.0217881
$177$	1.50746	0.113307
$178$	15.8039	1.18455
$179$	−8.04419	−0.601251	−0.300625	−	0.953742i	$-0.597195\pi$
$179$	−8.04419	−0.601251	−0.300625	+	0.953742i	$0.597195\pi$
$180$	1.06154	0.0791228
$181$	−16.5545	−1.23049	−0.615244	−	0.788337i	$-0.710942\pi$
$181$	−16.5545	−1.23049	−0.615244	+	0.788337i	$0.710942\pi$
$182$	−43.8639	−3.25141
$183$	−15.1911	−1.12296
$184$	0.212434	0.0156609
$185$	3.08416	0.226752
$186$	8.00935	0.587274
$187$	−0.0928102	−0.00678696
$188$	11.2438	0.820038
$189$	14.4854	1.05366
$190$	−5.12469	−0.371784
$191$	−16.0966	−1.16471	−0.582353	−	0.812936i	$-0.697868\pi$
$191$	−16.0966	−1.16471	−0.582353	+	0.812936i	$0.697868\pi$
$192$	16.0751	1.16012
$193$	−8.63742	−0.621735	−0.310867	−	0.950453i	$-0.600620\pi$
$193$	−8.63742	−0.621735	−0.310867	+	0.950453i	$0.600620\pi$
$194$	−25.2626	−1.81375
$195$	−4.59651	−0.329163
$196$	19.5323	1.39517
$197$	−7.59664	−0.541238	−0.270619	−	0.962687i	$-0.587228\pi$
$197$	−7.59664	−0.541238	−0.270619	+	0.962687i	$0.587228\pi$
$198$	−0.184653	−0.0131227
$199$	−6.86256	−0.486474	−0.243237	−	0.969967i	$-0.578209\pi$
$199$	−6.86256	−0.486474	−0.243237	+	0.969967i	$0.578209\pi$
$200$	−0.298223	−0.0210875
$201$	18.1039	1.27695
$202$	29.1726	2.05258
$203$	4.11338	0.288703
$204$	5.32535	0.372849
$205$	3.50445	0.244761
$206$	−8.02775	−0.559320
$207$	4.47900	0.311312
$208$	−21.7373	−1.50721
$209$	0.442232	0.0305898
$210$	7.03721	0.485614
$211$	−7.98380	−0.549627	−0.274814	−	0.961497i	$-0.588616\pi$
$211$	−7.98380	−0.549627	−0.274814	+	0.961497i	$0.588616\pi$
$212$	1.56422	0.107431
$213$	1.06758	0.0731495
$214$	−10.3196	−0.705433
$215$	3.40041	0.231906
$216$	0.217497	0.0147988
$217$	7.97280	0.541229
$218$	−17.5708	−1.19004
$219$	−7.74604	−0.523429
$220$	0.0580228	0.00391190
$221$	−6.97952	−0.469493
$222$	30.7827	2.06600
$223$	−26.2868	−1.76029	−0.880146	−	0.474702i	$-0.842556\pi$
$223$	−26.2868	−1.76029	−0.880146	+	0.474702i	$0.842556\pi$
$224$	32.7714	2.18963
$225$	−6.28779	−0.419186
$226$	28.2126	1.87667
$227$	−5.94390	−0.394511	−0.197255	−	0.980352i	$-0.563203\pi$
$227$	−5.94390	−0.394511	−0.197255	+	0.980352i	$0.563203\pi$
$228$	−25.3748	−1.68049
$229$	24.6457	1.62863	0.814317	−	0.580421i	$-0.197112\pi$
$229$	24.6457	1.62863	0.814317	+	0.580421i	$0.197112\pi$
$230$	−2.83700	−0.187067
$231$	−0.607271	−0.0399555
$232$	0.0617619	0.00405486
$233$	5.75797	0.377217	0.188609	−	0.982052i	$-0.439602\pi$
$233$	5.75797	0.377217	0.188609	+	0.982052i	$0.439602\pi$
$234$	−13.8863	−0.907773
$235$	2.36419	0.154223
$236$	−1.43102	−0.0931513
$237$	−0.239149	−0.0155344
$238$	10.6856	0.692642
$239$	12.3751	0.800477	0.400239	−	0.916411i	$-0.368927\pi$
$239$	12.3751	0.800477	0.400239	+	0.916411i	$0.368927\pi$
$240$	3.48737	0.225109
$241$	29.9698	1.93052	0.965262	−	0.261285i	$-0.0841461\pi$
$241$	29.9698	1.93052	0.965262	+	0.261285i	$0.0841461\pi$
$242$	21.9045	1.40807
$243$	12.6887	0.813980
$244$	14.4208	0.923199
$245$	4.10699	0.262386
$246$	34.9776	2.23009
$247$	33.2567	2.11607
$248$	0.119710	0.00760162
$249$	0.137495	0.00871339
$250$	8.10676	0.512716
$251$	8.21262	0.518376	0.259188	−	0.965827i	$-0.416545\pi$
$251$	8.21262	0.518376	0.259188	+	0.965827i	$0.416545\pi$
$252$	10.5468	0.664388
$253$	0.244817	0.0153915
$254$	−16.8928	−1.05995
$255$	1.11974	0.0701210
$256$	16.4844	1.03028
$257$	−13.3481	−0.832634	−0.416317	−	0.909220i	$-0.636679\pi$
$257$	−13.3481	−0.832634	−0.416317	+	0.909220i	$0.636679\pi$
$258$	33.9392	2.11296
$259$	30.6423	1.90402
$260$	4.36343	0.270609
$261$	1.30220	0.0806041
$262$	−38.3159	−2.36716
$263$	17.8528	1.10085	0.550425	−	0.834885i	$-0.314466\pi$
$263$	17.8528	1.10085	0.550425	+	0.834885i	$0.314466\pi$
$264$	−0.00911809	−0.000561179 0
$265$	0.328904	0.0202044
$266$	−50.9157	−3.12184
$267$	16.4539	1.00696
$268$	−17.1859	−1.04980
$269$	−14.5461	−0.886892	−0.443446	−	0.896301i	$-0.646244\pi$
$269$	−14.5461	−0.886892	−0.443446	+	0.896301i	$0.646244\pi$
$270$	−2.90461	−0.176769
$271$	0.674790	0.0409906	0.0204953	−	0.999790i	$-0.493476\pi$
$271$	0.674790	0.0409906	0.0204953	+	0.999790i	$0.493476\pi$
$272$	5.29536	0.321078
$273$	−45.6680	−2.76395
$274$	40.0617	2.42022
$275$	−0.343683	−0.0207249
$276$	−14.0474	−0.845552
$277$	−27.2743	−1.63875	−0.819377	−	0.573254i	$-0.805681\pi$
$277$	−27.2743	−1.63875	−0.819377	+	0.573254i	$0.805681\pi$
$278$	1.99223	0.119486
$279$	2.52400	0.151108
$280$	0.105180	0.00628573
$281$	30.6194	1.82660	0.913299	−	0.407290i	$-0.133526\pi$
$281$	30.6194	1.82660	0.913299	+	0.407290i	$0.133526\pi$
$282$	23.5968	1.40517
$283$	9.39472	0.558458	0.279229	−	0.960225i	$-0.409921\pi$
$283$	9.39472	0.558458	0.279229	+	0.960225i	$0.409921\pi$
$284$	−1.01345	−0.0601371
$285$	−5.33547	−0.316046
$286$	−0.759008	−0.0448811
$287$	34.8180	2.05524
$288$	10.3746	0.611332
$289$	−15.2997	−0.899985
$290$	−0.824814	−0.0484347
$291$	−26.3017	−1.54183
$292$	7.35326	0.430317
$293$	−19.3385	−1.12977	−0.564883	−	0.825171i	$-0.691079\pi$
$293$	−19.3385	−1.12977	−0.564883	+	0.825171i	$0.691079\pi$
$294$	40.9915	2.39068
$295$	−0.300895	−0.0175188
$296$	0.460089	0.0267421
$297$	0.250651	0.0145443
$298$	30.1403	1.74598
$299$	18.4108	1.06472
$300$	19.7202	1.13855
$301$	33.7843	1.94729
$302$	34.1465	1.96491
$303$	30.3725	1.74485
$304$	−25.2319	−1.44715
$305$	3.03222	0.173624
$306$	3.38279	0.193381
$307$	−4.47444	−0.255370	−0.127685	−	0.991815i	$-0.540755\pi$
$307$	−4.47444	−0.255370	−0.127685	+	0.991815i	$0.540755\pi$
$308$	0.576478	0.0328479
$309$	−8.35792	−0.475466
$310$	−1.59870	−0.0908001
$311$	1.40943	0.0799217	0.0399608	−	0.999201i	$-0.487277\pi$
$311$	1.40943	0.0799217	0.0399608	+	0.999201i	$0.487277\pi$
$312$	−0.685698	−0.0388200
$313$	−3.45916	−0.195524	−0.0977618	−	0.995210i	$-0.531168\pi$
$313$	−3.45916	−0.195524	−0.0977618	+	0.995210i	$0.531168\pi$
$314$	−40.4223	−2.28116
$315$	2.21764	0.124950
$316$	0.227023	0.0127710
$317$	17.3559	0.974804	0.487402	−	0.873178i	$-0.337945\pi$
$317$	17.3559	0.974804	0.487402	+	0.873178i	$0.337945\pi$
$318$	3.28276	0.184088
$319$	0.0711767	0.00398513
$320$	−3.20865	−0.179369
$321$	−10.7440	−0.599674
$322$	−28.1867	−1.57078
$323$	−8.10158	−0.450784
$324$	−22.0742	−1.22634
$325$	−25.8457	−1.43366
$326$	39.1707	2.16946
$327$	−18.2934	−1.01163
$328$	0.522787	0.0288661
$329$	23.4891	1.29500
$330$	0.121770	0.00670320
$331$	−27.1664	−1.49320	−0.746601	−	0.665272i	$-0.768316\pi$
$331$	−27.1664	−1.49320	−0.746601	+	0.665272i	$0.768316\pi$
$332$	−0.130523	−0.00716338
$333$	9.70060	0.531590
$334$	9.18116	0.502371
$335$	−3.61362	−0.197433
$336$	34.6483	1.89022
$337$	−4.51436	−0.245913	−0.122956	−	0.992412i	$-0.539238\pi$
$337$	−4.51436	−0.245913	−0.122956	+	0.992412i	$0.539238\pi$
$338$	−31.1798	−1.69596
$339$	29.3730	1.59532
$340$	−1.06296	−0.0576473
$341$	0.137959	0.00747089
$342$	−16.1187	−0.871599
$343$	12.0108	0.648522
$344$	0.507266	0.0273500
$345$	−2.95369	−0.159021
$346$	−21.3988	−1.15041
$347$	−17.3506	−0.931429	−0.465714	−	0.884935i	$-0.654203\pi$
$347$	−17.3506	−0.931429	−0.465714	+	0.884935i	$0.654203\pi$
$348$	−4.08405	−0.218928
$349$	26.3646	1.41126	0.705632	−	0.708578i	$-0.250663\pi$
$349$	26.3646	1.41126	0.705632	+	0.708578i	$0.250663\pi$
$350$	39.5695	2.11508
$351$	18.8495	1.00611
$352$	0.567067	0.0302248
$353$	−11.7216	−0.623880	−0.311940	−	0.950102i	$-0.600979\pi$
$353$	−11.7216	−0.623880	−0.311940	+	0.950102i	$0.600979\pi$
$354$	−3.00321	−0.159619
$355$	−0.213094	−0.0113099
$356$	−15.6196	−0.827837
$357$	11.1251	0.588801
$358$	16.0259	0.846995
$359$	−27.7827	−1.46632	−0.733158	−	0.680058i	$-0.761955\pi$
$359$	−27.7827	−1.46632	−0.733158	+	0.680058i	$0.761955\pi$
$360$	0.0332976	0.00175494
$361$	19.6033	1.03175
$362$	32.9805	1.73342
$363$	22.8054	1.19697
$364$	43.3523	2.27228
$365$	1.54614	0.0809288
$366$	30.2643	1.58194
$367$	17.0947	0.892334	0.446167	−	0.894950i	$-0.352789\pi$
$367$	17.0947	0.892334	0.446167	+	0.894950i	$0.352789\pi$
$368$	−13.9682	−0.728145
$369$	11.0225	0.573810
$370$	−6.14437	−0.319431
$371$	3.26778	0.169655
$372$	−7.91593	−0.410422
$373$	−2.00354	−0.103739	−0.0518697	−	0.998654i	$-0.516518\pi$
$373$	−2.00354	−0.103739	−0.0518697	+	0.998654i	$0.516518\pi$
$374$	0.184900	0.00956094
$375$	8.44019	0.435849
$376$	0.352686	0.0181884
$377$	5.35263	0.275675
$378$	−28.8584	−1.48431
$379$	−10.2006	−0.523972	−0.261986	−	0.965072i	$-0.584377\pi$
$379$	−10.2006	−0.523972	−0.261986	+	0.965072i	$0.584377\pi$
$380$	5.06492	0.259825
$381$	−17.5876	−0.901040
$382$	32.0681	1.64075
$383$	36.0311	1.84110	0.920552	−	0.390621i	$-0.127740\pi$
$383$	36.0311	1.84110	0.920552	+	0.390621i	$0.127740\pi$
$384$	1.02472	0.0522923
$385$	0.121214	0.00617764
$386$	17.2078	0.875852
$387$	10.6953	0.543672
$388$	24.9680	1.26756
$389$	−2.56908	−0.130258	−0.0651288	−	0.997877i	$-0.520746\pi$
$389$	−2.56908	−0.130258	−0.0651288	+	0.997877i	$0.520746\pi$
$390$	9.15733	0.463699
$391$	−4.48499	−0.226816
$392$	0.612673	0.0309447
$393$	−39.8918	−2.01228
$394$	15.1343	0.762454
$395$	0.0477352	0.00240182
$396$	0.182499	0.00917093
$397$	−36.1908	−1.81637	−0.908183	−	0.418573i	$-0.862530\pi$
$397$	−36.1908	−1.81637	−0.908183	+	0.418573i	$0.862530\pi$
$398$	13.6718	0.685307
$399$	−53.0098	−2.65381
$400$	19.6091	0.980456
$401$	22.7445	1.13581	0.567904	−	0.823095i	$-0.307755\pi$
$401$	22.7445	1.13581	0.567904	+	0.823095i	$0.307755\pi$
$402$	−36.0672	−1.79887
$403$	10.3748	0.516805
$404$	−28.8324	−1.43446
$405$	−4.64146	−0.230636
$406$	−8.19483	−0.406702
$407$	0.530224	0.0262822
$408$	0.167041	0.00826977
$409$	25.2568	1.24887	0.624435	−	0.781077i	$-0.285329\pi$
$409$	25.2568	1.24887	0.624435	+	0.781077i	$0.285329\pi$
$410$	−6.98168	−0.344801
$411$	41.7095	2.05738
$412$	7.93412	0.390886
$413$	−2.98950	−0.147104
$414$	−8.92322	−0.438553
$415$	−0.0274446	−0.00134720
$416$	42.6446	2.09082
$417$	2.07417	0.101573
$418$	−0.881030	−0.0430926
$419$	13.4859	0.658831	0.329415	−	0.944185i	$-0.393148\pi$
$419$	13.4859	0.658831	0.329415	+	0.944185i	$0.393148\pi$
$420$	−6.95513	−0.339376
$421$	30.2409	1.47385	0.736926	−	0.675974i	$-0.236277\pi$
$421$	30.2409	1.47385	0.736926	+	0.675974i	$0.236277\pi$
$422$	15.9056	0.774273
$423$	7.43609	0.361555
$424$	0.0490652	0.00238282
$425$	6.29620	0.305410
$426$	−2.12687	−0.103047
$427$	30.1262	1.45791
$428$	10.1992	0.492999
$429$	−0.790225	−0.0381524
$430$	−6.77441	−0.326691
$431$	2.56108	0.123363	0.0616814	−	0.998096i	$-0.480354\pi$
$431$	2.56108	0.123363	0.0616814	+	0.998096i	$0.480354\pi$
$432$	−14.3011	−0.688062
$433$	−16.9643	−0.815250	−0.407625	−	0.913149i	$-0.633643\pi$
$433$	−16.9643	−0.815250	−0.407625	+	0.913149i	$0.633643\pi$
$434$	−15.8837	−0.762441
$435$	−0.858738	−0.0411733
$436$	17.3658	0.831672
$437$	21.3706	1.02229
$438$	15.4319	0.737366
$439$	4.07646	0.194559	0.0972794	−	0.995257i	$-0.468986\pi$
$439$	4.07646	0.194559	0.0972794	+	0.995257i	$0.468986\pi$
$440$	0.00182001	8.67656e−5 0
$441$	12.9177	0.615129
$442$	13.9048	0.661385
$443$	0.585988	0.0278411	0.0139206	−	0.999903i	$-0.495569\pi$
$443$	0.585988	0.0278411	0.0139206	+	0.999903i	$0.495569\pi$
$444$	−30.4237	−1.44385
$445$	−3.28428	−0.155690
$446$	52.3694	2.47976
$447$	31.3800	1.48422
$448$	−31.8791	−1.50615
$449$	18.8033	0.887382	0.443691	−	0.896180i	$-0.353669\pi$
$449$	18.8033	0.887382	0.443691	+	0.896180i	$0.353669\pi$
$450$	12.5267	0.590516
$451$	0.602480	0.0283697
$452$	−27.8835	−1.31153
$453$	35.5509	1.67033
$454$	11.8417	0.555756
$455$	9.11554	0.427343
$456$	−0.795935	−0.0372731
$457$	24.5060	1.14634	0.573172	−	0.819435i	$-0.305713\pi$
$457$	24.5060	1.14634	0.573172	+	0.819435i	$0.305713\pi$
$458$	−49.1000	−2.29429
$459$	−4.59187	−0.214330
$460$	2.80392	0.130733
$461$	−38.6073	−1.79812	−0.899061	−	0.437824i	$-0.855749\pi$
$461$	−38.6073	−1.79812	−0.899061	+	0.437824i	$0.855749\pi$
$462$	1.20983	0.0562862
$463$	−29.7014	−1.38034	−0.690171	−	0.723646i	$-0.742465\pi$
$463$	−29.7014	−1.38034	−0.690171	+	0.723646i	$0.742465\pi$
$464$	−4.06104	−0.188529
$465$	−1.66445	−0.0771872
$466$	−11.4712	−0.531395
$467$	−34.0721	−1.57667	−0.788334	−	0.615247i	$-0.789056\pi$
$467$	−34.0721	−1.57667	−0.788334	+	0.615247i	$0.789056\pi$
$468$	13.7243	0.634406
$469$	−35.9026	−1.65783
$470$	−4.71003	−0.217257
$471$	−42.0848	−1.93917
$472$	−0.0448869	−0.00206609
$473$	0.584593	0.0268796
$474$	0.476441	0.0218837
$475$	−30.0008	−1.37653
$476$	−10.5609	−0.484060
$477$	1.03450	0.0473665
$478$	−24.6541	−1.12765
$479$	−8.88766	−0.406088	−0.203044	−	0.979170i	$-0.565083\pi$
$479$	−8.88766	−0.406088	−0.203044	+	0.979170i	$0.565083\pi$
$480$	−6.84159	−0.312274
$481$	39.8739	1.81809
$482$	−59.7068	−2.71957
$483$	−29.3460	−1.33529
$484$	−21.6490	−0.984046
$485$	5.24993	0.238387
$486$	−25.2789	−1.14667
$487$	19.9462	0.903848	0.451924	−	0.892056i	$-0.350738\pi$
$487$	19.9462	0.903848	0.451924	+	0.892056i	$0.350738\pi$
$488$	0.452340	0.0204765
$489$	40.7817	1.84421
$490$	−8.18209	−0.369629
$491$	0.308713	0.0139320	0.00696602	−	0.999976i	$-0.497783\pi$
$491$	0.308713	0.0139320	0.00696602	+	0.999976i	$0.497783\pi$
$492$	−34.5696	−1.55852
$493$	−1.30394	−0.0587265
$494$	−66.2552	−2.98096
$495$	0.0383734	0.00172476
$496$	−7.87134	−0.353434
$497$	−2.11717	−0.0949679
$498$	−0.273922	−0.0122748
$499$	26.8930	1.20390	0.601949	−	0.798535i	$-0.294391\pi$
$499$	26.8930	1.20390	0.601949	+	0.798535i	$0.294391\pi$
$500$	−8.01221	−0.358317
$501$	9.55878	0.427055
$502$	−16.3615	−0.730248
$503$	−10.5421	−0.470051	−0.235026	−	0.971989i	$-0.575517\pi$
$503$	−10.5421	−0.470051	−0.235026	+	0.971989i	$0.575517\pi$
$504$	0.330824	0.0147361
$505$	−6.06248	−0.269777
$506$	−0.487734	−0.0216824
$507$	−32.4622	−1.44170
$508$	16.6958	0.740756
$509$	15.4869	0.686444	0.343222	−	0.939254i	$-0.388482\pi$
$509$	15.4869	0.686444	0.343222	+	0.939254i	$0.388482\pi$
$510$	−2.23079	−0.0987811
$511$	15.3615	0.679553
$512$	−31.8528	−1.40771
$513$	21.8798	0.966018
$514$	26.5926	1.17295
$515$	1.66828	0.0735131
$516$	−33.5433	−1.47666
$517$	0.406449	0.0178756
$518$	−61.0466	−2.68223
$519$	−22.2789	−0.977936
$520$	0.136868	0.00600208
$521$	34.5027	1.51159	0.755795	−	0.654808i	$-0.227251\pi$
$521$	34.5027	1.51159	0.755795	+	0.654808i	$0.227251\pi$
$522$	−2.59429	−0.113549
$523$	−19.9660	−0.873051	−0.436526	−	0.899692i	$-0.643791\pi$
$523$	−19.9660	−0.873051	−0.436526	+	0.899692i	$0.643791\pi$
$524$	37.8690	1.65432
$525$	41.1969	1.79798
$526$	−35.5669	−1.55079
$527$	−2.52737	−0.110094
$528$	0.599544	0.0260918
$529$	−11.1694	−0.485624
$530$	−0.655254	−0.0284624
$531$	−0.946405	−0.0410705
$532$	50.3219	2.18173
$533$	45.3077	1.96249
$534$	−32.7801	−1.41853
$535$	2.14456	0.0927173
$536$	−0.539073	−0.0232844
$537$	16.6850	0.720013
$538$	28.9793	1.24938
$539$	0.706068	0.0304125
$540$	2.87073	0.123537
$541$	34.0897	1.46563	0.732815	−	0.680428i	$-0.238206\pi$
$541$	34.0897	1.46563	0.732815	+	0.680428i	$0.238206\pi$
$542$	−1.34434	−0.0577444
$543$	34.3369	1.47354
$544$	−10.3885	−0.445404
$545$	3.65145	0.156411
$546$	90.9814	3.89364
$547$	−27.6530	−1.18236	−0.591179	−	0.806541i	$-0.701337\pi$
$547$	−27.6530	−1.18236	−0.591179	+	0.806541i	$0.701337\pi$
$548$	−39.5945	−1.69139
$549$	9.53722	0.407039
$550$	0.684698	0.0291956
$551$	6.21315	0.264689
$552$	−0.440626	−0.0187543
$553$	0.474267	0.0201679
$554$	54.3368	2.30855
$555$	−6.39709	−0.271541
$556$	−1.96900	−0.0835041
$557$	−38.7636	−1.64247	−0.821233	−	0.570593i	$-0.806713\pi$
$557$	−38.7636	−1.64247	−0.821233	+	0.570593i	$0.806713\pi$
$558$	−5.02839	−0.212869
$559$	43.9626	1.85942
$560$	−6.91595	−0.292252
$561$	0.192505	0.00812755
$562$	−61.0009	−2.57317
$563$	−38.3527	−1.61637	−0.808186	−	0.588927i	$-0.799551\pi$
$563$	−38.3527	−1.61637	−0.808186	+	0.588927i	$0.799551\pi$
$564$	−23.3216	−0.982016
$565$	−5.86297	−0.246657
$566$	−18.7165	−0.786713
$567$	−46.1146	−1.93663
$568$	−0.0317890	−0.00133383
$569$	−36.1893	−1.51713	−0.758566	−	0.651596i	$-0.774100\pi$
$569$	−36.1893	−1.51713	−0.758566	+	0.651596i	$0.774100\pi$
$570$	10.6295	0.445221
$571$	−30.8387	−1.29056	−0.645279	−	0.763947i	$-0.723259\pi$
$571$	−30.8387	−1.29056	−0.645279	+	0.763947i	$0.723259\pi$
$572$	0.750155	0.0313656
$573$	33.3871	1.39476
$574$	−69.3656	−2.89526
$575$	−16.6083	−0.692613
$576$	−10.0922	−0.420507
$577$	40.8407	1.70022	0.850110	−	0.526605i	$-0.176535\pi$
$577$	40.8407	1.70022	0.850110	+	0.526605i	$0.176535\pi$
$578$	30.4807	1.26783
$579$	17.9155	0.744543
$580$	0.815194	0.0338491
$581$	−0.272672	−0.0113124
$582$	52.3991	2.17201
$583$	0.0565447	0.00234184
$584$	0.230651	0.00954439
$585$	2.88576	0.119311
$586$	38.5268	1.59153
$587$	−30.9531	−1.27757	−0.638787	−	0.769384i	$-0.720563\pi$
$587$	−30.9531	−1.27757	−0.638787	+	0.769384i	$0.720563\pi$
$588$	−40.5134	−1.67075
$589$	12.0427	0.496210
$590$	0.599454	0.0246791
$591$	15.7567	0.648146
$592$	−30.2523	−1.24336
$593$	34.4643	1.41528	0.707640	−	0.706573i	$-0.249760\pi$
$593$	34.4643	1.41528	0.707640	+	0.706573i	$0.249760\pi$
$594$	−0.499357	−0.0204888
$595$	−2.22061	−0.0910362
$596$	−29.7888	−1.22020
$597$	14.2341	0.582565
$598$	−36.6785	−1.49990
$599$	16.9729	0.693494	0.346747	−	0.937959i	$-0.387286\pi$
$599$	16.9729	0.693494	0.346747	+	0.937959i	$0.387286\pi$
$600$	0.618566	0.0252529
$601$	−35.1194	−1.43255	−0.716276	−	0.697817i	$-0.754155\pi$
$601$	−35.1194	−1.43255	−0.716276	+	0.697817i	$0.754155\pi$
$602$	−67.3062	−2.74320
$603$	−11.3659	−0.462856
$604$	−33.7482	−1.37320
$605$	−4.55206	−0.185068
$606$	−60.5091	−2.45801
$607$	12.7025	0.515577	0.257789	−	0.966201i	$-0.417006\pi$
$607$	12.7025	0.515577	0.257789	+	0.966201i	$0.417006\pi$
$608$	49.5003	2.00750
$609$	−8.53188	−0.345729
$610$	−6.04089	−0.244588
$611$	30.5657	1.23656
$612$	−3.34334	−0.135146
$613$	7.93014	0.320295	0.160148	−	0.987093i	$-0.448803\pi$
$613$	7.93014	0.320295	0.160148	+	0.987093i	$0.448803\pi$
$614$	8.91413	0.359745
$615$	−7.26884	−0.293108
$616$	0.0180825	0.000728564 0
$617$	−15.9149	−0.640710	−0.320355	−	0.947298i	$-0.603802\pi$
$617$	−15.9149	−0.640710	−0.320355	+	0.947298i	$0.603802\pi$
$618$	16.6509	0.669799
$619$	39.6825	1.59497	0.797487	−	0.603337i	$-0.206162\pi$
$619$	39.6825	1.59497	0.797487	+	0.603337i	$0.206162\pi$
$620$	1.58006	0.0634565
$621$	12.1126	0.486061
$622$	−2.80792	−0.112587
$623$	−32.6305	−1.30731
$624$	45.0869	1.80492
$625$	22.4583	0.898330
$626$	6.89147	0.275438
$627$	−0.917266	−0.0366321
$628$	39.9508	1.59421
$629$	−9.71358	−0.387306
$630$	−4.41807	−0.176020
$631$	−19.6664	−0.782908	−0.391454	−	0.920198i	$-0.628028\pi$
$631$	−19.6664	−0.782908	−0.391454	+	0.920198i	$0.628028\pi$
$632$	0.00712105	0.000283260 0
$633$	16.5598	0.658193
$634$	−34.5770	−1.37323
$635$	3.51056	0.139312
$636$	−3.24447	−0.128652
$637$	53.0977	2.10381
$638$	−0.141801	−0.00561395
$639$	−0.670244	−0.0265145
$640$	−0.204538	−0.00808507
$641$	31.9730	1.26286	0.631430	−	0.775433i	$-0.282468\pi$
$641$	31.9730	1.26286	0.631430	+	0.775433i	$0.282468\pi$
$642$	21.4046	0.844774
$643$	40.2136	1.58587	0.792935	−	0.609306i	$-0.208552\pi$
$643$	40.2136	1.58587	0.792935	+	0.609306i	$0.208552\pi$
$644$	27.8579	1.09776
$645$	−7.05304	−0.277713
$646$	16.1403	0.635030
$647$	−38.2894	−1.50531	−0.752656	−	0.658414i	$-0.771228\pi$
$647$	−38.2894	−1.50531	−0.752656	+	0.658414i	$0.771228\pi$
$648$	−0.692404	−0.0272002
$649$	−0.0517294	−0.00203056
$650$	51.4907	2.01963
$651$	−16.5370	−0.648135
$652$	−38.7138	−1.51615
$653$	10.7015	0.418783	0.209392	−	0.977832i	$-0.432852\pi$
$653$	10.7015	0.418783	0.209392	+	0.977832i	$0.432852\pi$
$654$	36.4448	1.42511
$655$	7.96258	0.311124
$656$	−34.3749	−1.34212
$657$	4.86308	0.189727
$658$	−46.7958	−1.82429
$659$	−28.1213	−1.09545	−0.547726	−	0.836658i	$-0.684506\pi$
$659$	−28.1213	−1.09545	−0.547726	+	0.836658i	$0.684506\pi$
$660$	−0.120349	−0.00468460
$661$	−7.97958	−0.310370	−0.155185	−	0.987885i	$-0.549597\pi$
$661$	−7.97958	−0.310370	−0.155185	+	0.987885i	$0.549597\pi$
$662$	54.1219	2.10351
$663$	14.4767	0.562230
$664$	−0.00409414	−0.000158883 0
$665$	10.5810	0.410314
$666$	−19.3259	−0.748862
$667$	3.43957	0.133181
$668$	−9.07408	−0.351087
$669$	54.5234	2.10799
$670$	7.19918	0.278129
$671$	0.521294	0.0201243
$672$	−67.9737	−2.62214
$673$	−38.3897	−1.47981	−0.739906	−	0.672710i	$-0.765130\pi$
$673$	−38.3897	−1.47981	−0.739906	+	0.672710i	$0.765130\pi$
$674$	8.99366	0.346423
$675$	−17.0041	−0.654487
$676$	30.8162	1.18524
$677$	−27.7033	−1.06472	−0.532362	−	0.846517i	$-0.678695\pi$
$677$	−27.7033	−1.06472	−0.532362	+	0.846517i	$0.678695\pi$
$678$	−58.5178	−2.24736
$679$	52.1600	2.00172
$680$	−0.0333421	−0.00127861
$681$	12.3287	0.472437
$682$	−0.274846	−0.0105244
$683$	−3.76358	−0.144009	−0.0720047	−	0.997404i	$-0.522940\pi$
$683$	−3.76358	−0.144009	−0.0720047	+	0.997404i	$0.522940\pi$
$684$	15.9307	0.609125
$685$	−8.32539	−0.318097
$686$	−23.9283	−0.913587
$687$	−51.1195	−1.95033
$688$	−33.3544	−1.27162
$689$	4.25227	0.161999
$690$	5.88444	0.224017
$691$	28.4999	1.08419	0.542093	−	0.840319i	$-0.317632\pi$
$691$	28.4999	1.08419	0.542093	+	0.840319i	$0.317632\pi$
$692$	21.1492	0.803972
$693$	0.381254	0.0144826
$694$	34.5665	1.31212
$695$	−0.414014	−0.0157045
$696$	−0.128105	−0.00485580
$697$	−11.0373	−0.418067
$698$	−52.5245	−1.98808
$699$	−11.9430	−0.451727
$700$	−39.1080	−1.47814
$701$	40.7013	1.53727	0.768633	−	0.639690i	$-0.220937\pi$
$701$	40.7013	1.53727	0.768633	+	0.639690i	$0.220937\pi$
$702$	−37.5526	−1.41733
$703$	46.2843	1.74564
$704$	−0.551627	−0.0207902
$705$	−4.90375	−0.184686
$706$	23.3523	0.878874
$707$	−60.2330	−2.26529
$708$	2.96818	0.111551
$709$	30.3768	1.14083	0.570413	−	0.821358i	$-0.306783\pi$
$709$	30.3768	1.14083	0.570413	+	0.821358i	$0.306783\pi$
$710$	0.424533	0.0159325
$711$	0.150142	0.00563075
$712$	−0.489942	−0.0183613
$713$	6.66677	0.249673
$714$	−22.1637	−0.829457
$715$	0.157732	0.00589886
$716$	−15.8390	−0.591931
$717$	−25.6681	−0.958592
$718$	55.3497	2.06563
$719$	6.29265	0.234676	0.117338	−	0.993092i	$-0.462564\pi$
$719$	6.29265	0.234676	0.117338	+	0.993092i	$0.462564\pi$
$720$	−2.18943	−0.0815951
$721$	16.5750	0.617284
$722$	−39.0543	−1.45345
$723$	−62.1626	−2.31185
$724$	−32.5958	−1.21141
$725$	−4.82859	−0.179329
$726$	−45.4337	−1.68620
$727$	−14.6523	−0.543426	−0.271713	−	0.962378i	$-0.587590\pi$
$727$	−14.6523	−0.543426	−0.271713	+	0.962378i	$0.587590\pi$
$728$	1.35984	0.0503989
$729$	7.31405	0.270891
$730$	−3.08028	−0.114006
$731$	−10.7096	−0.396109
$732$	−29.9113	−1.10555
$733$	−4.28385	−0.158228	−0.0791138	−	0.996866i	$-0.525209\pi$
$733$	−4.28385	−0.158228	−0.0791138	+	0.996866i	$0.525209\pi$
$734$	−34.0566	−1.25705
$735$	−8.51862	−0.314214
$736$	27.4031	1.01009
$737$	−0.621248	−0.0228840
$738$	−21.9595	−0.808339
$739$	21.0334	0.773726	0.386863	−	0.922137i	$-0.373559\pi$
$739$	21.0334	0.773726	0.386863	+	0.922137i	$0.373559\pi$
$740$	6.07271	0.223237
$741$	−68.9802	−2.53405
$742$	−6.51018	−0.238996
$743$	39.2006	1.43813	0.719064	−	0.694943i	$-0.244571\pi$
$743$	39.2006	1.43813	0.719064	+	0.694943i	$0.244571\pi$
$744$	−0.248300	−0.00910312
$745$	−6.26358	−0.229480
$746$	3.99153	0.146140
$747$	−0.0863215	−0.00315834
$748$	−0.182743	−0.00668176
$749$	21.3070	0.778539
$750$	−16.8148	−0.613991
$751$	−24.1789	−0.882299	−0.441149	−	0.897434i	$-0.645429\pi$
$751$	−24.1789	−0.882299	−0.441149	+	0.897434i	$0.645429\pi$
$752$	−23.1902	−0.845660
$753$	−17.0344	−0.620768
$754$	−10.6637	−0.388349
$755$	−7.09612	−0.258254
$756$	28.5218	1.03733
$757$	−4.50531	−0.163748	−0.0818741	−	0.996643i	$-0.526091\pi$
$757$	−4.50531	−0.163748	−0.0818741	+	0.996643i	$0.526091\pi$
$758$	20.3221	0.738131
$759$	−0.507794	−0.0184318
$760$	0.158872	0.00576290
$761$	−33.1958	−1.20335	−0.601673	−	0.798743i	$-0.705499\pi$
$761$	−33.1958	−1.20335	−0.601673	+	0.798743i	$0.705499\pi$
$762$	35.0386	1.26932
$763$	36.2785	1.31337
$764$	−31.6941	−1.14665
$765$	−0.702992	−0.0254167
$766$	−71.7824	−2.59360
$767$	−3.89016	−0.140465
$768$	−34.1916	−1.23378
$769$	−2.04532	−0.0737560	−0.0368780	−	0.999320i	$-0.511741\pi$
$769$	−2.04532	−0.0737560	−0.0368780	+	0.999320i	$0.511741\pi$
$770$	−0.241487	−0.00870258
$771$	27.6864	0.997100
$772$	−17.0071	−0.612098
$773$	−17.4890	−0.629036	−0.314518	−	0.949252i	$-0.601843\pi$
$773$	−17.4890	−0.629036	−0.314518	+	0.949252i	$0.601843\pi$
$774$	−21.3075	−0.765884
$775$	−9.35905	−0.336187
$776$	0.783174	0.0281143
$777$	−63.5574	−2.28011
$778$	5.11822	0.183497
$779$	52.5916	1.88429
$780$	−9.05052	−0.324061
$781$	−0.0366348	−0.00131090
$782$	8.93516	0.319521
$783$	3.52154	0.125849
$784$	−40.2852	−1.43876
$785$	8.40032	0.299820
$786$	79.4738	2.83474
$787$	−22.8278	−0.813724	−0.406862	−	0.913490i	$-0.633377\pi$
$787$	−22.8278	−0.813724	−0.406862	+	0.913490i	$0.633377\pi$
$788$	−14.9578	−0.532848
$789$	−37.0298	−1.31830
$790$	−0.0950998	−0.00338350
$791$	−58.2508	−2.07116
$792$	0.00572448	0.000203410 0
$793$	39.2024	1.39212
$794$	72.1006	2.55876
$795$	−0.682204	−0.0241953
$796$	−13.5124	−0.478933
$797$	−19.8685	−0.703777	−0.351889	−	0.936042i	$-0.614460\pi$
$797$	−19.8685	−0.703777	−0.351889	+	0.936042i	$0.614460\pi$
$798$	105.608	3.73848
$799$	−7.44604	−0.263422
$800$	−38.4695	−1.36010
$801$	−10.3300	−0.364994
$802$	−45.3124	−1.60004
$803$	0.265811	0.00938025
$804$	35.6466	1.25716
$805$	5.85759	0.206453
$806$	−20.6690	−0.728034
$807$	30.1712	1.06208
$808$	−0.904389	−0.0318163
$809$	38.7615	1.36278	0.681392	−	0.731919i	$-0.261375\pi$
$809$	38.7615	1.36278	0.681392	+	0.731919i	$0.261375\pi$
$810$	9.24688	0.324902
$811$	−28.4569	−0.999257	−0.499629	−	0.866240i	$-0.666530\pi$
$811$	−28.4569	−0.999257	−0.499629	+	0.866240i	$0.666530\pi$
$812$	8.09925	0.284228
$813$	−1.39963	−0.0490873
$814$	−1.05633	−0.0370244
$815$	−8.14021	−0.285139
$816$	−10.9835	−0.384499
$817$	51.0302	1.78532
$818$	−50.3175	−1.75931
$819$	28.6711	1.00185
$820$	6.90025	0.240967
$821$	−10.3817	−0.362325	−0.181162	−	0.983453i	$-0.557986\pi$
$821$	−10.3817	−0.362325	−0.181162	+	0.983453i	$0.557986\pi$
$822$	−83.0950	−2.89827
$823$	14.9763	0.522041	0.261020	−	0.965333i	$-0.415941\pi$
$823$	14.9763	0.522041	0.261020	+	0.965333i	$0.415941\pi$
$824$	0.248871	0.00866982
$825$	0.712859	0.0248186
$826$	5.95579	0.207228
$827$	−32.3299	−1.12422	−0.562111	−	0.827062i	$-0.690010\pi$
$827$	−32.3299	−1.12422	−0.562111	+	0.827062i	$0.690010\pi$
$828$	8.81915	0.306487
$829$	23.1320	0.803409	0.401704	−	0.915769i	$-0.368418\pi$
$829$	23.1320	0.803409	0.401704	+	0.915769i	$0.368418\pi$
$830$	0.0546761	0.00189784
$831$	56.5717	1.96245
$832$	−41.4834	−1.43818
$833$	−12.9350	−0.448171
$834$	−4.13224	−0.143088
$835$	−1.90797	−0.0660282
$836$	0.870754	0.0301157
$837$	6.82564	0.235929
$838$	−26.8671	−0.928110
$839$	12.9244	0.446201	0.223100	−	0.974795i	$-0.428382\pi$
$839$	12.9244	0.446201	0.223100	+	0.974795i	$0.428382\pi$
$840$	−0.218163	−0.00752732
$841$	1.00000	0.0344828
$842$	−60.2470	−2.07625
$843$	−63.5099	−2.18740
$844$	−15.7201	−0.541108
$845$	6.47961	0.222905
$846$	−14.8144	−0.509331
$847$	−45.2264	−1.55400
$848$	−3.22620	−0.110788
$849$	−19.4863	−0.668768
$850$	−12.5435	−0.430239
$851$	25.6227	0.878336
$852$	2.10207	0.0720156
$853$	46.2415	1.58328	0.791639	−	0.610988i	$-0.209228\pi$
$853$	46.2415	1.58328	0.791639	+	0.610988i	$0.209228\pi$
$854$	−60.0184	−2.05379
$855$	3.34969	0.114557
$856$	0.319921	0.0109347
$857$	14.7045	0.502296	0.251148	−	0.967949i	$-0.419192\pi$
$857$	14.7045	0.502296	0.251148	+	0.967949i	$0.419192\pi$
$858$	1.57431	0.0537462
$859$	−7.56594	−0.258146	−0.129073	−	0.991635i	$-0.541200\pi$
$859$	−7.56594	−0.258146	−0.129073	+	0.991635i	$0.541200\pi$
$860$	6.69540	0.228311
$861$	−72.2185	−2.46120
$862$	−5.10227	−0.173784
$863$	25.8978	0.881573	0.440786	−	0.897612i	$-0.354700\pi$
$863$	25.8978	0.881573	0.440786	+	0.897612i	$0.354700\pi$
$864$	28.0562	0.954490
$865$	4.44697	0.151202
$866$	33.7968	1.14846
$867$	31.7343	1.07775
$868$	15.6984	0.532839
$869$	0.00820657	0.000278389 0
$870$	1.71081	0.0580018
$871$	−46.7191	−1.58302
$872$	0.544716	0.0184464
$873$	16.5126	0.558866
$874$	−42.5752	−1.44013
$875$	−16.7381	−0.565851
$876$	−15.2519	−0.515315
$877$	−6.57663	−0.222077	−0.111039	−	0.993816i	$-0.535418\pi$
$877$	−6.57663	−0.222077	−0.111039	+	0.993816i	$0.535418\pi$
$878$	−8.12127	−0.274079
$879$	40.1114	1.35292
$880$	−0.119672	−0.00403413
$881$	42.2411	1.42314	0.711569	−	0.702616i	$-0.247985\pi$
$881$	42.2411	1.42314	0.711569	+	0.702616i	$0.247985\pi$
$882$	−25.7351	−0.866547
$883$	7.47722	0.251628	0.125814	−	0.992054i	$-0.459846\pi$
$883$	7.47722	0.251628	0.125814	+	0.992054i	$0.459846\pi$
$884$	−13.7427	−0.462216
$885$	0.624109	0.0209792
$886$	−1.16743	−0.0392204
$887$	−17.2130	−0.577956	−0.288978	−	0.957336i	$-0.593315\pi$
$887$	−17.2130	−0.577956	−0.288978	+	0.957336i	$0.593315\pi$
$888$	−0.954305	−0.0320244
$889$	34.8787	1.16979
$890$	6.54305	0.219323
$891$	−0.797954	−0.0267325
$892$	−51.7586	−1.73301
$893$	35.4797	1.18728
$894$	−62.5163	−2.09086
$895$	−3.33041	−0.111323
$896$	−2.03216	−0.0678896
$897$	−38.1871	−1.27503
$898$	−37.4606	−1.25008
$899$	1.93826	0.0646445
$900$	−12.3806	−0.412688
$901$	−1.03588	−0.0345103
$902$	−1.20028	−0.0399650
$903$	−70.0745	−2.33193
$904$	−0.874627	−0.0290897
$905$	−6.85381	−0.227828
$906$	−70.8257	−2.35303
$907$	−32.8936	−1.09221	−0.546107	−	0.837715i	$-0.683891\pi$
$907$	−32.8936	−1.09221	−0.546107	+	0.837715i	$0.683891\pi$
$908$	−11.7035	−0.388396
$909$	−19.0683	−0.632456
$910$	−18.1603	−0.602008
$911$	29.2592	0.969402	0.484701	−	0.874680i	$-0.338928\pi$
$911$	29.2592	0.969402	0.484701	+	0.874680i	$0.338928\pi$
$912$	52.3353	1.73299
$913$	−0.00471824	−0.000156151 0
$914$	−48.8217	−1.61488
$915$	−6.28934	−0.207919
$916$	48.5273	1.60339
$917$	79.1112	2.61248
$918$	9.14809	0.301932
$919$	−43.1613	−1.42376	−0.711880	−	0.702301i	$-0.752156\pi$
$919$	−43.1613	−1.42376	−0.711880	+	0.702301i	$0.752156\pi$
$920$	0.0879508	0.00289965
$921$	9.28076	0.305811
$922$	76.9148	2.53305
$923$	−2.75501	−0.0906823
$924$	−1.19572	−0.0393362
$925$	−35.9701	−1.18269
$926$	59.1722	1.94452
$927$	5.24723	0.172342
$928$	7.96702	0.261530
$929$	18.7665	0.615708	0.307854	−	0.951434i	$-0.400389\pi$
$929$	18.7665	0.615708	0.307854	+	0.951434i	$0.400389\pi$
$930$	3.31598	0.108735
$931$	61.6340	2.01997
$932$	11.3374	0.371370
$933$	−2.92341	−0.0957082
$934$	67.8796	2.22109
$935$	−0.0384248	−0.00125662
$936$	0.430492	0.0140711
$937$	13.0380	0.425933	0.212966	−	0.977060i	$-0.431688\pi$
$937$	13.0380	0.425933	0.212966	+	0.977060i	$0.431688\pi$
$938$	71.5265	2.33542
$939$	7.17491	0.234144
$940$	4.65509	0.151832
$941$	29.8314	0.972477	0.486239	−	0.873826i	$-0.338369\pi$
$941$	29.8314	0.972477	0.486239	+	0.873826i	$0.338369\pi$
$942$	83.8429	2.73175
$943$	29.1144	0.948097
$944$	2.95146	0.0960619
$945$	5.99718	0.195088
$946$	−1.16465	−0.0378659
$947$	−27.1959	−0.883749	−0.441874	−	0.897077i	$-0.645686\pi$
$947$	−27.1959	−0.883749	−0.441874	+	0.897077i	$0.645686\pi$
$948$	−0.470884	−0.0152936
$949$	19.9895	0.648886
$950$	59.7686	1.93915
$951$	−35.9991	−1.16735
$952$	−0.331266	−0.0107364
$953$	35.2976	1.14340	0.571701	−	0.820462i	$-0.306284\pi$
$953$	35.2976	1.14340	0.571701	+	0.820462i	$0.306284\pi$
$954$	−2.06097	−0.0667263
$955$	−6.66421	−0.215649
$956$	24.3665	0.788069
$957$	−0.147633	−0.00477230
$958$	17.7063	0.572065
$959$	−82.7158	−2.67103
$960$	6.65530	0.214799
$961$	−27.2432	−0.878812
$962$	−79.4382	−2.56119
$963$	6.74527	0.217363
$964$	59.0105	1.90060
$965$	−3.57601	−0.115116
$966$	58.4641	1.88105
$967$	−36.9562	−1.18843	−0.594215	−	0.804306i	$-0.702537\pi$
$967$	−36.9562	−1.18843	−0.594215	+	0.804306i	$0.702537\pi$
$968$	−0.679068	−0.0218261
$969$	16.8041	0.539825
$970$	−10.4591	−0.335821
$971$	−46.2406	−1.48393	−0.741966	−	0.670437i	$-0.766107\pi$
$971$	−46.2406	−1.48393	−0.741966	+	0.670437i	$0.766107\pi$
$972$	24.9840	0.801363
$973$	−4.11338	−0.131869
$974$	−39.7375	−1.27327
$975$	53.6084	1.71684
$976$	−29.7428	−0.952044
$977$	−11.7666	−0.376446	−0.188223	−	0.982126i	$-0.560273\pi$
$977$	−11.7666	−0.376446	−0.188223	+	0.982126i	$0.560273\pi$
$978$	−81.2468	−2.59799
$979$	−0.564628	−0.0180456
$980$	8.08666	0.258319
$981$	11.4849	0.366685
$982$	−0.615030	−0.0196264
$983$	−49.0031	−1.56296	−0.781479	−	0.623932i	$-0.785534\pi$
$983$	−49.0031	−1.56296	−0.781479	+	0.623932i	$0.785534\pi$
$984$	−1.08435	−0.0345678
$985$	−3.14512	−0.100212
$986$	2.59776	0.0827294
$987$	−48.7205	−1.55079
$988$	65.4825	2.08327
$989$	28.2501	0.898300
$990$	−0.0764489	−0.00242971
$991$	42.8254	1.36039	0.680197	−	0.733029i	$-0.261894\pi$
$991$	42.8254	1.36039	0.680197	+	0.733029i	$0.261894\pi$
$992$	15.4421	0.490288
$993$	56.3479	1.78815
$994$	4.21789	0.133783
$995$	−2.84120	−0.0900720
$996$	0.270728	0.00857833
$997$	44.1955	1.39968	0.699842	−	0.714298i	$-0.253254\pi$
$997$	44.1955	1.39968	0.699842	+	0.714298i	$0.253254\pi$
$998$	−53.5772	−1.69596
$999$	26.2333	0.829986

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4031.2.a.d.1.16	✓	98

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4031.2.a.d.1.16	✓	98	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:	\( N \)	\(=\)	\( 4031 = 29 \cdot 139 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4031.a (trivial)

\(f(q)\)	\(=\)	\(q-1.99223 q^{2} -2.07417 q^{3} +1.96900 q^{4} +0.414014 q^{5} +4.13224 q^{6} +4.11338 q^{7} +0.0617619 q^{8} +1.30220 q^{9} +O(q^{10})\)	\(q-1.99223 q^{2} -2.07417 q^{3} +1.96900 q^{4} +0.414014 q^{5} +4.13224 q^{6} +4.11338 q^{7} +0.0617619 q^{8} +1.30220 q^{9} -0.824814 q^{10} +0.0711767 q^{11} -4.08405 q^{12} +5.35263 q^{13} -8.19483 q^{14} -0.858738 q^{15} -4.06104 q^{16} -1.30394 q^{17} -2.59429 q^{18} +6.21315 q^{19} +0.815194 q^{20} -8.53188 q^{21} -0.141801 q^{22} +3.43957 q^{23} -0.128105 q^{24} -4.82859 q^{25} -10.6637 q^{26} +3.52154 q^{27} +8.09925 q^{28} +1.00000 q^{29} +1.71081 q^{30} +1.93826 q^{31} +7.96702 q^{32} -0.147633 q^{33} +2.59776 q^{34} +1.70300 q^{35} +2.56403 q^{36} +7.44940 q^{37} -12.3781 q^{38} -11.1023 q^{39} +0.0255703 q^{40} +8.46456 q^{41} +16.9975 q^{42} +8.21326 q^{43} +0.140147 q^{44} +0.539129 q^{45} -6.85243 q^{46} +5.71041 q^{47} +8.42331 q^{48} +9.91993 q^{49} +9.61969 q^{50} +2.70460 q^{51} +10.5393 q^{52} +0.794426 q^{53} -7.01573 q^{54} +0.0294682 q^{55} +0.254050 q^{56} -12.8872 q^{57} -1.99223 q^{58} -0.726774 q^{59} -1.69085 q^{60} +7.32394 q^{61} -3.86146 q^{62} +5.35644 q^{63} -7.75010 q^{64} +2.21607 q^{65} +0.294120 q^{66} -8.72825 q^{67} -2.56746 q^{68} -7.13427 q^{69} -3.39278 q^{70} -0.514702 q^{71} +0.0804262 q^{72} +3.73452 q^{73} -14.8410 q^{74} +10.0153 q^{75} +12.2337 q^{76} +0.292777 q^{77} +22.1184 q^{78} +0.115298 q^{79} -1.68133 q^{80} -11.2109 q^{81} -16.8634 q^{82} -0.0662891 q^{83} -16.7993 q^{84} -0.539850 q^{85} -16.3627 q^{86} -2.07417 q^{87} +0.00439601 q^{88} -7.93276 q^{89} -1.07407 q^{90} +22.0174 q^{91} +6.77251 q^{92} -4.02028 q^{93} -11.3765 q^{94} +2.57233 q^{95} -16.5250 q^{96} +12.6805 q^{97} -19.7628 q^{98} +0.0926863 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 98 q + 6 q^{2} + 6 q^{3} + 116 q^{4} + q^{5} + 7 q^{6} + 12 q^{7} + 15 q^{8} + 136 q^{9}+O(q^{10}) \) 98 * q + 6 * q^2 + 6 * q^3 + 116 * q^4 + q^5 + 7 * q^6 + 12 * q^7 + 15 * q^8 + 136 * q^9	\( 98 q + 6 q^{2} + 6 q^{3} + 116 q^{4} + q^{5} + 7 q^{6} + 12 q^{7} + 15 q^{8} + 136 q^{9} + 16 q^{10} + 25 q^{11} + 8 q^{12} + 18 q^{13} + 34 q^{14} + 14 q^{15} + 136 q^{16} + 35 q^{17} + 20 q^{18} + 48 q^{19} - 20 q^{20} + 62 q^{21} + 32 q^{22} + q^{23} + 8 q^{24} + 173 q^{25} + 15 q^{26} + 18 q^{27} + 37 q^{28} + 98 q^{29} - 6 q^{30} + 20 q^{31} + 16 q^{32} + 24 q^{33} - 6 q^{34} + 11 q^{35} + 155 q^{36} + 62 q^{37} - 5 q^{38} + 45 q^{39} + 38 q^{40} + 50 q^{41} + 7 q^{42} + 72 q^{43} + 92 q^{44} - 13 q^{45} + 32 q^{46} - 16 q^{47} - 13 q^{48} + 194 q^{49} + 50 q^{50} + 2 q^{51} + 83 q^{52} - 11 q^{53} + 58 q^{54} + 32 q^{55} + 106 q^{56} + 84 q^{57} + 6 q^{58} + 20 q^{59} + 62 q^{60} + 142 q^{61} - 27 q^{62} + 26 q^{63} + 213 q^{64} + 13 q^{65} - 35 q^{66} + 5 q^{67} + 69 q^{68} + 68 q^{69} - 2 q^{70} - 10 q^{71} - 9 q^{72} + 74 q^{73} + 21 q^{74} + 19 q^{75} + 116 q^{76} + 41 q^{77} - 162 q^{78} + 104 q^{79} - 86 q^{80} + 230 q^{81} + 53 q^{82} - 19 q^{83} + 76 q^{84} + 125 q^{85} + 9 q^{86} + 6 q^{87} + 68 q^{88} + 120 q^{89} + 122 q^{90} + 30 q^{91} + 3 q^{92} - 56 q^{93} + 22 q^{94} + 32 q^{95} - 55 q^{96} + 98 q^{97} - 15 q^{98} + 69 q^{99}+O(q^{100}) \) 98 * q + 6 * q^2 + 6 * q^3 + 116 * q^4 + q^5 + 7 * q^6 + 12 * q^7 + 15 * q^8 + 136 * q^9 + 16 * q^10 + 25 * q^11 + 8 * q^12 + 18 * q^13 + 34 * q^14 + 14 * q^15 + 136 * q^16 + 35 * q^17 + 20 * q^18 + 48 * q^19 - 20 * q^20 + 62 * q^21 + 32 * q^22 + q^23 + 8 * q^24 + 173 * q^25 + 15 * q^26 + 18 * q^27 + 37 * q^28 + 98 * q^29 - 6 * q^30 + 20 * q^31 + 16 * q^32 + 24 * q^33 - 6 * q^34 + 11 * q^35 + 155 * q^36 + 62 * q^37 - 5 * q^38 + 45 * q^39 + 38 * q^40 + 50 * q^41 + 7 * q^42 + 72 * q^43 + 92 * q^44 - 13 * q^45 + 32 * q^46 - 16 * q^47 - 13 * q^48 + 194 * q^49 + 50 * q^50 + 2 * q^51 + 83 * q^52 - 11 * q^53 + 58 * q^54 + 32 * q^55 + 106 * q^56 + 84 * q^57 + 6 * q^58 + 20 * q^59 + 62 * q^60 + 142 * q^61 - 27 * q^62 + 26 * q^63 + 213 * q^64 + 13 * q^65 - 35 * q^66 + 5 * q^67 + 69 * q^68 + 68 * q^69 - 2 * q^70 - 10 * q^71 - 9 * q^72 + 74 * q^73 + 21 * q^74 + 19 * q^75 + 116 * q^76 + 41 * q^77 - 162 * q^78 + 104 * q^79 - 86 * q^80 + 230 * q^81 + 53 * q^82 - 19 * q^83 + 76 * q^84 + 125 * q^85 + 9 * q^86 + 6 * q^87 + 68 * q^88 + 120 * q^89 + 122 * q^90 + 30 * q^91 + 3 * q^92 - 56 * q^93 + 22 * q^94 + 32 * q^95 - 55 * q^96 + 98 * q^97 - 15 * q^98 + 69 * q^99

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