LMFDB - Embedded newform 8035.2.a.e.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8035,2,Mod(1,8035)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8035, 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("8035.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8035 = 5 \cdot 1607 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8035.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:	$64.1597980241$
Analytic rank:	$0$
Dimension:	$153$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	8035.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.31112 q^{2} +3.30909 q^{3} +3.34126 q^{4} +1.00000 q^{5} -7.64768 q^{6} +0.225615 q^{7} -3.09980 q^{8} +7.95005 q^{9} +O(q^{10})$	\(q-2.31112 q^{2} +3.30909 q^{3} +3.34126 q^{4} +1.00000 q^{5} -7.64768 q^{6} +0.225615 q^{7} -3.09980 q^{8} +7.95005 q^{9} -2.31112 q^{10} +0.662342 q^{11} +11.0565 q^{12} +2.92402 q^{13} -0.521423 q^{14} +3.30909 q^{15} +0.481483 q^{16} -5.12902 q^{17} -18.3735 q^{18} +3.17639 q^{19} +3.34126 q^{20} +0.746580 q^{21} -1.53075 q^{22} -4.47644 q^{23} -10.2575 q^{24} +1.00000 q^{25} -6.75775 q^{26} +16.3801 q^{27} +0.753838 q^{28} +7.05047 q^{29} -7.64768 q^{30} +6.45822 q^{31} +5.08684 q^{32} +2.19175 q^{33} +11.8538 q^{34} +0.225615 q^{35} +26.5632 q^{36} -8.74995 q^{37} -7.34099 q^{38} +9.67584 q^{39} -3.09980 q^{40} +7.33300 q^{41} -1.72543 q^{42} -3.51990 q^{43} +2.21305 q^{44} +7.95005 q^{45} +10.3456 q^{46} -1.72056 q^{47} +1.59327 q^{48} -6.94910 q^{49} -2.31112 q^{50} -16.9724 q^{51} +9.76991 q^{52} +1.12992 q^{53} -37.8564 q^{54} +0.662342 q^{55} -0.699362 q^{56} +10.5109 q^{57} -16.2945 q^{58} +4.26722 q^{59} +11.0565 q^{60} +2.82564 q^{61} -14.9257 q^{62} +1.79365 q^{63} -12.7192 q^{64} +2.92402 q^{65} -5.06538 q^{66} +9.95420 q^{67} -17.1374 q^{68} -14.8129 q^{69} -0.521423 q^{70} +12.4929 q^{71} -24.6436 q^{72} -14.9405 q^{73} +20.2221 q^{74} +3.30909 q^{75} +10.6131 q^{76} +0.149434 q^{77} -22.3620 q^{78} -9.47426 q^{79} +0.481483 q^{80} +30.3531 q^{81} -16.9474 q^{82} +10.2318 q^{83} +2.49452 q^{84} -5.12902 q^{85} +8.13489 q^{86} +23.3306 q^{87} -2.05313 q^{88} +4.22567 q^{89} -18.3735 q^{90} +0.659704 q^{91} -14.9569 q^{92} +21.3708 q^{93} +3.97642 q^{94} +3.17639 q^{95} +16.8328 q^{96} -5.40434 q^{97} +16.0602 q^{98} +5.26565 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 153 q + 18 q^{2} + 7 q^{3} + 176 q^{4} + 153 q^{5} + 19 q^{6} + 5 q^{7} + 57 q^{8} + 206 q^{9}+O(q^{10}) $ 153 * q + 18 * q^2 + 7 * q^3 + 176 * q^4 + 153 * q^5 + 19 * q^6 + 5 * q^7 + 57 * q^8 + 206 * q^9	\( 153 q + 18 q^{2} + 7 q^{3} + 176 q^{4} + 153 q^{5} + 19 q^{6} + 5 q^{7} + 57 q^{8} + 206 q^{9} + 18 q^{10} + 38 q^{11} + 14 q^{12} + 28 q^{13} + 53 q^{14} + 7 q^{15} + 214 q^{16} + 50 q^{17} + 47 q^{18} + 65 q^{19} + 176 q^{20} + 109 q^{21} + 13 q^{22} + 52 q^{23} + 66 q^{24} + 153 q^{25} + 36 q^{26} + 19 q^{27} + 26 q^{28} + 172 q^{29} + 19 q^{30} + 60 q^{31} + 107 q^{32} + 4 q^{33} + 40 q^{34} + 5 q^{35} + 241 q^{36} + 65 q^{37} + 29 q^{38} + 56 q^{39} + 57 q^{40} + 152 q^{41} - 19 q^{42} + 22 q^{43} + 97 q^{44} + 206 q^{45} + 86 q^{46} + 37 q^{47} - 4 q^{48} + 260 q^{49} + 18 q^{50} + 102 q^{51} - 6 q^{52} + 169 q^{53} + 64 q^{54} + 38 q^{55} + 146 q^{56} + 40 q^{57} - 9 q^{58} + 64 q^{59} + 14 q^{60} + 164 q^{61} + 12 q^{62} + 19 q^{63} + 259 q^{64} + 28 q^{65} + 6 q^{66} + 5 q^{67} + 112 q^{68} + 119 q^{69} + 53 q^{70} + 100 q^{71} + 77 q^{72} + 10 q^{73} + 98 q^{74} + 7 q^{75} + 126 q^{76} + 80 q^{77} - 4 q^{78} + 110 q^{79} + 214 q^{80} + 305 q^{81} - 27 q^{82} + 36 q^{83} + 172 q^{84} + 50 q^{85} + 44 q^{86} + 23 q^{87} + 47 q^{88} + 143 q^{89} + 47 q^{90} + 82 q^{91} + 130 q^{92} + 31 q^{93} + 77 q^{94} + 65 q^{95} + 57 q^{96} + 11 q^{97} + 29 q^{98} + 99 q^{99}+O(q^{100}) \) 153 * q + 18 * q^2 + 7 * q^3 + 176 * q^4 + 153 * q^5 + 19 * q^6 + 5 * q^7 + 57 * q^8 + 206 * q^9 + 18 * q^10 + 38 * q^11 + 14 * q^12 + 28 * q^13 + 53 * q^14 + 7 * q^15 + 214 * q^16 + 50 * q^17 + 47 * q^18 + 65 * q^19 + 176 * q^20 + 109 * q^21 + 13 * q^22 + 52 * q^23 + 66 * q^24 + 153 * q^25 + 36 * q^26 + 19 * q^27 + 26 * q^28 + 172 * q^29 + 19 * q^30 + 60 * q^31 + 107 * q^32 + 4 * q^33 + 40 * q^34 + 5 * q^35 + 241 * q^36 + 65 * q^37 + 29 * q^38 + 56 * q^39 + 57 * q^40 + 152 * q^41 - 19 * q^42 + 22 * q^43 + 97 * q^44 + 206 * q^45 + 86 * q^46 + 37 * q^47 - 4 * q^48 + 260 * q^49 + 18 * q^50 + 102 * q^51 - 6 * q^52 + 169 * q^53 + 64 * q^54 + 38 * q^55 + 146 * q^56 + 40 * q^57 - 9 * q^58 + 64 * q^59 + 14 * q^60 + 164 * q^61 + 12 * q^62 + 19 * q^63 + 259 * q^64 + 28 * q^65 + 6 * q^66 + 5 * q^67 + 112 * q^68 + 119 * q^69 + 53 * q^70 + 100 * q^71 + 77 * q^72 + 10 * q^73 + 98 * q^74 + 7 * q^75 + 126 * q^76 + 80 * q^77 - 4 * q^78 + 110 * q^79 + 214 * q^80 + 305 * q^81 - 27 * q^82 + 36 * q^83 + 172 * q^84 + 50 * q^85 + 44 * q^86 + 23 * q^87 + 47 * q^88 + 143 * q^89 + 47 * q^90 + 82 * q^91 + 130 * q^92 + 31 * q^93 + 77 * q^94 + 65 * q^95 + 57 * q^96 + 11 * q^97 + 29 * q^98 + 99 * 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 $

$2$	−2.31112	−1.63421	−0.817103	−	0.576492i	$-0.804421\pi$
$2$	−2.31112	−1.63421	−0.817103	+	0.576492i	$0.804421\pi$
$3$	3.30909	1.91050	0.955251	−	0.295797i	$-0.0955852\pi$
$3$	3.30909	1.91050	0.955251	+	0.295797i	$0.0955852\pi$
$4$	3.34126	1.67063
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−7.64768	−3.12215
$7$	0.225615	0.0852745	0.0426373	−	0.999091i	$-0.486424\pi$
$7$	0.225615	0.0852745	0.0426373	+	0.999091i	$0.486424\pi$
$8$	−3.09980	−1.09594
$9$	7.95005	2.65002
$10$	−2.31112	−0.730839
$11$	0.662342	0.199703	0.0998517	−	0.995002i	$-0.468163\pi$
$11$	0.662342	0.199703	0.0998517	+	0.995002i	$0.468163\pi$
$12$	11.0565	3.19174
$13$	2.92402	0.810978	0.405489	−	0.914100i	$-0.367101\pi$
$13$	2.92402	0.810978	0.405489	+	0.914100i	$0.367101\pi$
$14$	−0.521423	−0.139356
$15$	3.30909	0.854402
$16$	0.481483	0.120371
$17$	−5.12902	−1.24397	−0.621985	−	0.783029i	$-0.713674\pi$
$17$	−5.12902	−1.24397	−0.621985	+	0.783029i	$0.713674\pi$
$18$	−18.3735	−4.33067
$19$	3.17639	0.728713	0.364356	−	0.931260i	$-0.381289\pi$
$19$	3.17639	0.728713	0.364356	+	0.931260i	$0.381289\pi$
$20$	3.34126	0.747128
$21$	0.746580	0.162917
$22$	−1.53075	−0.326357
$23$	−4.47644	−0.933403	−0.466701	−	0.884415i	$-0.654558\pi$
$23$	−4.47644	−0.933403	−0.466701	+	0.884415i	$0.654558\pi$
$24$	−10.2575	−2.09380
$25$	1.00000	0.200000
$26$	−6.75775	−1.32530
$27$	16.3801	3.15236
$28$	0.753838	0.142462
$29$	7.05047	1.30924	0.654620	−	0.755958i	$-0.272829\pi$
$29$	7.05047	1.30924	0.654620	+	0.755958i	$0.272829\pi$
$30$	−7.64768	−1.39627
$31$	6.45822	1.15993	0.579965	−	0.814641i	$-0.303066\pi$
$31$	6.45822	1.15993	0.579965	+	0.814641i	$0.303066\pi$
$32$	5.08684	0.899234
$33$	2.19175	0.381534
$34$	11.8538	2.03290
$35$	0.225615	0.0381359
$36$	26.5632	4.42719
$37$	−8.74995	−1.43848	−0.719241	−	0.694761i	$-0.755510\pi$
$37$	−8.74995	−1.43848	−0.719241	+	0.694761i	$0.755510\pi$
$38$	−7.34099	−1.19087
$39$	9.67584	1.54937
$40$	−3.09980	−0.490121
$41$	7.33300	1.14522	0.572611	−	0.819827i	$-0.305930\pi$
$41$	7.33300	1.14522	0.572611	+	0.819827i	$0.305930\pi$
$42$	−1.72543	−0.266240
$43$	−3.51990	−0.536779	−0.268390	−	0.963310i	$-0.586491\pi$
$43$	−3.51990	−0.536779	−0.268390	+	0.963310i	$0.586491\pi$
$44$	2.21305	0.333630
$45$	7.95005	1.18512
$46$	10.3456	1.52537
$47$	−1.72056	−0.250970	−0.125485	−	0.992096i	$-0.540049\pi$
$47$	−1.72056	−0.250970	−0.125485	+	0.992096i	$0.540049\pi$
$48$	1.59327	0.229968
$49$	−6.94910	−0.992728
$50$	−2.31112	−0.326841
$51$	−16.9724	−2.37661
$52$	9.76991	1.35484
$53$	1.12992	0.155207	0.0776036	−	0.996984i	$-0.475273\pi$
$53$	1.12992	0.155207	0.0776036	+	0.996984i	$0.475273\pi$
$54$	−37.8564	−5.15160
$55$	0.662342	0.0893101
$56$	−0.699362	−0.0934562
$57$	10.5109	1.39221
$58$	−16.2945	−2.13957
$59$	4.26722	0.555545	0.277772	−	0.960647i	$-0.410404\pi$
$59$	4.26722	0.555545	0.277772	+	0.960647i	$0.410404\pi$
$60$	11.0565	1.42739
$61$	2.82564	0.361786	0.180893	−	0.983503i	$-0.442101\pi$
$61$	2.82564	0.361786	0.180893	+	0.983503i	$0.442101\pi$
$62$	−14.9257	−1.89556
$63$	1.79365	0.225979
$64$	−12.7192	−1.58990
$65$	2.92402	0.362680
$66$	−5.06538	−0.623505
$67$	9.95420	1.21610	0.608050	−	0.793899i	$-0.291952\pi$
$67$	9.95420	1.21610	0.608050	+	0.793899i	$0.291952\pi$
$68$	−17.1374	−2.07821
$69$	−14.8129	−1.78327
$70$	−0.521423	−0.0623220
$71$	12.4929	1.48264	0.741320	−	0.671152i	$-0.234200\pi$
$71$	12.4929	1.48264	0.741320	+	0.671152i	$0.234200\pi$
$72$	−24.6436	−2.90427
$73$	−14.9405	−1.74865	−0.874327	−	0.485337i	$-0.838697\pi$
$73$	−14.9405	−1.74865	−0.874327	+	0.485337i	$0.838697\pi$
$74$	20.2221	2.35078
$75$	3.30909	0.382100
$76$	10.6131	1.21741
$77$	0.149434	0.0170296
$78$	−22.3620	−2.53200
$79$	−9.47426	−1.06594	−0.532969	−	0.846135i	$-0.678924\pi$
$79$	−9.47426	−1.06594	−0.532969	+	0.846135i	$0.678924\pi$
$80$	0.481483	0.0538314
$81$	30.3531	3.37257
$82$	−16.9474	−1.87153
$83$	10.2318	1.12309	0.561545	−	0.827447i	$-0.310207\pi$
$83$	10.2318	1.12309	0.561545	+	0.827447i	$0.310207\pi$
$84$	2.49452	0.272174
$85$	−5.12902	−0.556320
$86$	8.13489	0.877208
$87$	23.3306	2.50130
$88$	−2.05313	−0.218864
$89$	4.22567	0.447920	0.223960	−	0.974598i	$-0.428102\pi$
$89$	4.22567	0.447920	0.223960	+	0.974598i	$0.428102\pi$
$90$	−18.3735	−1.93674
$91$	0.659704	0.0691558
$92$	−14.9569	−1.55937
$93$	21.3708	2.21605
$94$	3.97642	0.410136
$95$	3.17639	0.325890
$96$	16.8328	1.71799
$97$	−5.40434	−0.548728	−0.274364	−	0.961626i	$-0.588467\pi$
$97$	−5.40434	−0.548728	−0.274364	+	0.961626i	$0.588467\pi$
$98$	16.0602	1.62232
$99$	5.26565	0.529218
$100$	3.34126	0.334126
$101$	3.35238	0.333575	0.166787	−	0.985993i	$-0.446661\pi$
$101$	3.35238	0.333575	0.166787	+	0.985993i	$0.446661\pi$
$102$	39.2251	3.88386
$103$	4.92484	0.485259	0.242630	−	0.970119i	$-0.421990\pi$
$103$	4.92484	0.485259	0.242630	+	0.970119i	$0.421990\pi$
$104$	−9.06388	−0.888787
$105$	0.746580	0.0728588
$106$	−2.61139	−0.253640
$107$	14.6250	1.41385	0.706926	−	0.707288i	$-0.250082\pi$
$107$	14.6250	1.41385	0.706926	+	0.707288i	$0.250082\pi$
$108$	54.7302	5.26642
$109$	12.6180	1.20858	0.604292	−	0.796763i	$-0.293456\pi$
$109$	12.6180	1.20858	0.604292	+	0.796763i	$0.293456\pi$
$110$	−1.53075	−0.145951
$111$	−28.9543	−2.74822
$112$	0.108630	0.0102646
$113$	−14.5656	−1.37021	−0.685107	−	0.728442i	$-0.740245\pi$
$113$	−14.5656	−1.37021	−0.685107	+	0.728442i	$0.740245\pi$
$114$	−24.2920	−2.27515
$115$	−4.47644	−0.417430
$116$	23.5574	2.18725
$117$	23.2461	2.14910
$118$	−9.86204	−0.907875
$119$	−1.15719	−0.106079
$120$	−10.2575	−0.936378
$121$	−10.5613	−0.960119
$122$	−6.53037	−0.591232
$123$	24.2655	2.18795
$124$	21.5786	1.93781
$125$	1.00000	0.0894427
$126$	−4.14534	−0.369296
$127$	−2.27723	−0.202072	−0.101036	−	0.994883i	$-0.532216\pi$
$127$	−2.27723	−0.202072	−0.101036	+	0.994883i	$0.532216\pi$
$128$	19.2220	1.69900
$129$	−11.6476	−1.02552
$130$	−6.75775	−0.592694
$131$	14.1540	1.23664	0.618318	−	0.785928i	$-0.287814\pi$
$131$	14.1540	1.23664	0.618318	+	0.785928i	$0.287814\pi$
$132$	7.32318	0.637401
$133$	0.716641	0.0621406
$134$	−23.0053	−1.98736
$135$	16.3801	1.40978
$136$	15.8989	1.36332
$137$	13.2361	1.13084	0.565419	−	0.824804i	$-0.308715\pi$
$137$	13.2361	1.13084	0.565419	+	0.824804i	$0.308715\pi$
$138$	34.2344	2.91423
$139$	−10.1535	−0.861210	−0.430605	−	0.902541i	$-0.641700\pi$
$139$	−10.1535	−0.861210	−0.430605	+	0.902541i	$0.641700\pi$
$140$	0.753838	0.0637110
$141$	−5.69349	−0.479478
$142$	−28.8726	−2.42294
$143$	1.93670	0.161955
$144$	3.82781	0.318984
$145$	7.05047	0.585510
$146$	34.5292	2.85766
$147$	−22.9952	−1.89661
$148$	−29.2358	−2.40317
$149$	−6.37237	−0.522045	−0.261022	−	0.965333i	$-0.584060\pi$
$149$	−6.37237	−0.522045	−0.261022	+	0.965333i	$0.584060\pi$
$150$	−7.64768	−0.624431
$151$	1.73913	0.141529	0.0707643	−	0.997493i	$-0.477456\pi$
$151$	1.73913	0.141529	0.0707643	+	0.997493i	$0.477456\pi$
$152$	−9.84616	−0.798629
$153$	−40.7760	−3.29654
$154$	−0.345360	−0.0278299
$155$	6.45822	0.518737
$156$	32.3295	2.58843
$157$	5.73893	0.458016	0.229008	−	0.973425i	$-0.426452\pi$
$157$	5.73893	0.458016	0.229008	+	0.973425i	$0.426452\pi$
$158$	21.8961	1.74196
$159$	3.73902	0.296523
$160$	5.08684	0.402150
$161$	−1.00995	−0.0795955
$162$	−70.1496	−5.51147
$163$	−19.2470	−1.50754	−0.753770	−	0.657138i	$-0.771767\pi$
$163$	−19.2470	−1.50754	−0.753770	+	0.657138i	$0.771767\pi$
$164$	24.5014	1.91324
$165$	2.19175	0.170627
$166$	−23.6469	−1.83536
$167$	7.23110	0.559559	0.279780	−	0.960064i	$-0.409739\pi$
$167$	7.23110	0.559559	0.279780	+	0.960064i	$0.409739\pi$
$168$	−2.31425	−0.178548
$169$	−4.45009	−0.342315
$170$	11.8538	0.909142
$171$	25.2524	1.93110
$172$	−11.7609	−0.896759
$173$	−20.4893	−1.55778	−0.778888	−	0.627163i	$-0.784216\pi$
$173$	−20.4893	−1.55778	−0.778888	+	0.627163i	$0.784216\pi$
$174$	−53.9197	−4.08764
$175$	0.225615	0.0170549
$176$	0.318906	0.0240384
$177$	14.1206	1.06137
$178$	−9.76601	−0.731993
$179$	−24.4419	−1.82687	−0.913435	−	0.406984i	$-0.866580\pi$
$179$	−24.4419	−1.82687	−0.913435	+	0.406984i	$0.866580\pi$
$180$	26.5632	1.97990
$181$	3.86698	0.287430	0.143715	−	0.989619i	$-0.454095\pi$
$181$	3.86698	0.287430	0.143715	+	0.989619i	$0.454095\pi$
$182$	−1.52465	−0.113015
$183$	9.35027	0.691192
$184$	13.8761	1.02296
$185$	−8.74995	−0.643309
$186$	−49.3904	−3.62148
$187$	−3.39716	−0.248425
$188$	−5.74884	−0.419277
$189$	3.69561	0.268816
$190$	−7.34099	−0.532572
$191$	10.6811	0.772860	0.386430	−	0.922319i	$-0.373708\pi$
$191$	10.6811	0.772860	0.386430	+	0.922319i	$0.373708\pi$
$192$	−42.0890	−3.03751
$193$	12.3256	0.887216	0.443608	−	0.896221i	$-0.353698\pi$
$193$	12.3256	0.887216	0.443608	+	0.896221i	$0.353698\pi$
$194$	12.4901	0.896734
$195$	9.67584	0.692901
$196$	−23.2187	−1.65848
$197$	−1.42548	−0.101561	−0.0507807	−	0.998710i	$-0.516171\pi$
$197$	−1.42548	−0.101561	−0.0507807	+	0.998710i	$0.516171\pi$
$198$	−12.1695	−0.864850
$199$	21.4388	1.51975	0.759877	−	0.650067i	$-0.225259\pi$
$199$	21.4388	1.51975	0.759877	+	0.650067i	$0.225259\pi$
$200$	−3.09980	−0.219189
$201$	32.9393	2.32336
$202$	−7.74775	−0.545130
$203$	1.59069	0.111645
$204$	−56.7090	−3.97043
$205$	7.33300	0.512159
$206$	−11.3819	−0.793014
$207$	−35.5879	−2.47353
$208$	1.40787	0.0976180
$209$	2.10385	0.145526
$210$	−1.72543	−0.119066
$211$	21.4673	1.47787	0.738936	−	0.673776i	$-0.235329\pi$
$211$	21.4673	1.47787	0.738936	+	0.673776i	$0.235329\pi$
$212$	3.77537	0.259293
$213$	41.3402	2.83258
$214$	−33.8000	−2.31052
$215$	−3.51990	−0.240055
$216$	−50.7751	−3.45481
$217$	1.45707	0.0989125
$218$	−29.1616	−1.97507
$219$	−49.4394	−3.34081
$220$	2.21305	0.149204
$221$	−14.9974	−1.00883
$222$	66.9168	4.49116
$223$	5.27802	0.353442	0.176721	−	0.984261i	$-0.443451\pi$
$223$	5.27802	0.353442	0.176721	+	0.984261i	$0.443451\pi$
$224$	1.14767	0.0766818
$225$	7.95005	0.530003
$226$	33.6628	2.23921
$227$	23.3398	1.54912	0.774560	−	0.632501i	$-0.217972\pi$
$227$	23.3398	1.54912	0.774560	+	0.632501i	$0.217972\pi$
$228$	35.1197	2.32586
$229$	−10.1097	−0.668070	−0.334035	−	0.942561i	$-0.608410\pi$
$229$	−10.1097	−0.668070	−0.334035	+	0.942561i	$0.608410\pi$
$230$	10.3456	0.682167
$231$	0.494491	0.0325351
$232$	−21.8550	−1.43485
$233$	20.8152	1.36365	0.681826	−	0.731515i	$-0.261186\pi$
$233$	20.8152	1.36365	0.681826	+	0.731515i	$0.261186\pi$
$234$	−53.7245	−3.51208
$235$	−1.72056	−0.112237
$236$	14.2579	0.928109
$237$	−31.3512	−2.03648
$238$	2.67439	0.173355
$239$	−25.2186	−1.63125	−0.815627	−	0.578578i	$-0.803608\pi$
$239$	−25.2186	−1.63125	−0.815627	+	0.578578i	$0.803608\pi$
$240$	1.59327	0.102845
$241$	−6.81361	−0.438903	−0.219451	−	0.975623i	$-0.570427\pi$
$241$	−6.81361	−0.438903	−0.219451	+	0.975623i	$0.570427\pi$
$242$	24.4084	1.56903
$243$	51.3007	3.29094
$244$	9.44118	0.604409
$245$	−6.94910	−0.443962
$246$	−56.0805	−3.57556
$247$	9.28782	0.590970
$248$	−20.0192	−1.27122
$249$	33.8580	2.14566
$250$	−2.31112	−0.146168
$251$	9.58678	0.605112	0.302556	−	0.953132i	$-0.402160\pi$
$251$	9.58678	0.605112	0.302556	+	0.953132i	$0.402160\pi$
$252$	5.99305	0.377527
$253$	−2.96493	−0.186404
$254$	5.26295	0.330227
$255$	−16.9724	−1.06285
$256$	−18.9857	−1.18661
$257$	−3.40766	−0.212564	−0.106282	−	0.994336i	$-0.533895\pi$
$257$	−3.40766	−0.212564	−0.106282	+	0.994336i	$0.533895\pi$
$258$	26.9191	1.67591
$259$	−1.97412	−0.122666
$260$	9.76991	0.605904
$261$	56.0516	3.46951
$262$	−32.7114	−2.02092
$263$	2.32345	0.143270	0.0716351	−	0.997431i	$-0.477178\pi$
$263$	2.32345	0.143270	0.0716351	+	0.997431i	$0.477178\pi$
$264$	−6.79397	−0.418140
$265$	1.12992	0.0694107
$266$	−1.65624	−0.101551
$267$	13.9831	0.855752
$268$	33.2595	2.03165
$269$	−5.66317	−0.345289	−0.172645	−	0.984984i	$-0.555231\pi$
$269$	−5.66317	−0.345289	−0.172645	+	0.984984i	$0.555231\pi$
$270$	−37.8564	−2.30387
$271$	10.5749	0.642380	0.321190	−	0.947015i	$-0.395917\pi$
$271$	10.5749	0.642380	0.321190	+	0.947015i	$0.395917\pi$
$272$	−2.46953	−0.149738
$273$	2.18302	0.132122
$274$	−30.5902	−1.84802
$275$	0.662342	0.0399407
$276$	−49.4938	−2.97918
$277$	32.6854	1.96387	0.981937	−	0.189208i	$-0.0605921\pi$
$277$	32.6854	1.96387	0.981937	+	0.189208i	$0.0605921\pi$
$278$	23.4659	1.40739
$279$	51.3431	3.07383
$280$	−0.699362	−0.0417949
$281$	−4.04722	−0.241437	−0.120718	−	0.992687i	$-0.538520\pi$
$281$	−4.04722	−0.241437	−0.120718	+	0.992687i	$0.538520\pi$
$282$	13.1583	0.783566
$283$	9.52245	0.566051	0.283025	−	0.959112i	$-0.408662\pi$
$283$	9.52245	0.566051	0.283025	+	0.959112i	$0.408662\pi$
$284$	41.7421	2.47694
$285$	10.5109	0.622614
$286$	−4.47594	−0.264668
$287$	1.65444	0.0976584
$288$	40.4406	2.38299
$289$	9.30684	0.547461
$290$	−16.2945	−0.956843
$291$	−17.8834	−1.04835
$292$	−49.9201	−2.92135
$293$	−14.7634	−0.862486	−0.431243	−	0.902236i	$-0.641925\pi$
$293$	−14.7634	−0.862486	−0.431243	+	0.902236i	$0.641925\pi$
$294$	53.1445	3.09945
$295$	4.26722	0.248447
$296$	27.1231	1.57650
$297$	10.8492	0.629537
$298$	14.7273	0.853129
$299$	−13.0892	−0.756969
$300$	11.0565	0.638348
$301$	−0.794143	−0.0457736
$302$	−4.01934	−0.231287
$303$	11.0933	0.637295
$304$	1.52937	0.0877157
$305$	2.82564	0.161795
$306$	94.2380	5.38723
$307$	−21.9498	−1.25274	−0.626370	−	0.779526i	$-0.715460\pi$
$307$	−21.9498	−1.25274	−0.626370	+	0.779526i	$0.715460\pi$
$308$	0.499299	0.0284502
$309$	16.2967	0.927089
$310$	−14.9257	−0.847722
$311$	−29.6950	−1.68385	−0.841923	−	0.539597i	$-0.818577\pi$
$311$	−29.6950	−1.68385	−0.841923	+	0.539597i	$0.818577\pi$
$312$	−29.9932	−1.69803
$313$	−11.2115	−0.633712	−0.316856	−	0.948474i	$-0.602627\pi$
$313$	−11.2115	−0.633712	−0.316856	+	0.948474i	$0.602627\pi$
$314$	−13.2633	−0.748493
$315$	1.79365	0.101061
$316$	−31.6559	−1.78079
$317$	−19.4230	−1.09090	−0.545452	−	0.838142i	$-0.683642\pi$
$317$	−19.4230	−1.09090	−0.545452	+	0.838142i	$0.683642\pi$
$318$	−8.64131	−0.484580
$319$	4.66982	0.261460
$320$	−12.7192	−0.711027
$321$	48.3954	2.70117
$322$	2.33412	0.130075
$323$	−16.2917	−0.906497
$324$	101.418	5.63431
$325$	2.92402	0.162196
$326$	44.4820	2.46363
$327$	41.7540	2.30900
$328$	−22.7308	−1.25510
$329$	−0.388185	−0.0214013
$330$	−5.06538	−0.278840
$331$	9.31017	0.511733	0.255867	−	0.966712i	$-0.417639\pi$
$331$	9.31017	0.511733	0.255867	+	0.966712i	$0.417639\pi$
$332$	34.1872	1.87626
$333$	−69.5625	−3.81200
$334$	−16.7119	−0.914435
$335$	9.95420	0.543856
$336$	0.359466	0.0196105
$337$	22.4068	1.22058	0.610289	−	0.792179i	$-0.291053\pi$
$337$	22.4068	1.22058	0.610289	+	0.792179i	$0.291053\pi$
$338$	10.2847	0.559413
$339$	−48.1988	−2.61780
$340$	−17.1374	−0.929404
$341$	4.27755	0.231642
$342$	−58.3613	−3.15582
$343$	−3.14713	−0.169929
$344$	10.9110	0.588281
$345$	−14.8129	−0.797502
$346$	47.3532	2.54573
$347$	19.2454	1.03315	0.516574	−	0.856243i	$-0.327207\pi$
$347$	19.2454	1.03315	0.516574	+	0.856243i	$0.327207\pi$
$348$	77.9535	4.17875
$349$	−3.73826	−0.200104	−0.100052	−	0.994982i	$-0.531901\pi$
$349$	−3.73826	−0.200104	−0.100052	+	0.994982i	$0.531901\pi$
$350$	−0.521423	−0.0278712
$351$	47.8959	2.55649
$352$	3.36922	0.179580
$353$	−26.1822	−1.39354	−0.696770	−	0.717295i	$-0.745380\pi$
$353$	−26.1822	−1.39354	−0.696770	+	0.717295i	$0.745380\pi$
$354$	−32.6343	−1.73450
$355$	12.4929	0.663056
$356$	14.1190	0.748308
$357$	−3.82922	−0.202664
$358$	56.4880	2.98548
$359$	8.67859	0.458038	0.229019	−	0.973422i	$-0.426448\pi$
$359$	8.67859	0.458038	0.229019	+	0.973422i	$0.426448\pi$
$360$	−24.6436	−1.29883
$361$	−8.91058	−0.468978
$362$	−8.93704	−0.469720
$363$	−34.9483	−1.83431
$364$	2.20424	0.115534
$365$	−14.9405	−0.782022
$366$	−21.6096	−1.12955
$367$	10.0849	0.526427	0.263214	−	0.964738i	$-0.415218\pi$
$367$	10.0849	0.526427	0.263214	+	0.964738i	$0.415218\pi$
$368$	−2.15533	−0.112354
$369$	58.2977	3.03486
$370$	20.2221	1.05130
$371$	0.254928	0.0132352
$372$	71.4053	3.70219
$373$	−8.60598	−0.445601	−0.222800	−	0.974864i	$-0.571520\pi$
$373$	−8.60598	−0.445601	−0.222800	+	0.974864i	$0.571520\pi$
$374$	7.85124	0.405978
$375$	3.30909	0.170880
$376$	5.33340	0.275049
$377$	20.6157	1.06176
$378$	−8.54098	−0.439301
$379$	−7.84429	−0.402934	−0.201467	−	0.979495i	$-0.564571\pi$
$379$	−7.84429	−0.402934	−0.201467	+	0.979495i	$0.564571\pi$
$380$	10.6131	0.544441
$381$	−7.53555	−0.386058
$382$	−24.6853	−1.26301
$383$	−26.5585	−1.35708	−0.678539	−	0.734565i	$-0.737386\pi$
$383$	−26.5585	−1.35708	−0.678539	+	0.734565i	$0.737386\pi$
$384$	63.6071	3.24594
$385$	0.149434	0.00761588
$386$	−28.4859	−1.44989
$387$	−27.9834	−1.42247
$388$	−18.0573	−0.916720
$389$	25.0323	1.26919	0.634595	−	0.772845i	$-0.281167\pi$
$389$	25.0323	1.26919	0.634595	+	0.772845i	$0.281167\pi$
$390$	−22.3620	−1.13234
$391$	22.9598	1.16113
$392$	21.5408	1.08798
$393$	46.8366	2.36260
$394$	3.29445	0.165972
$395$	−9.47426	−0.476702
$396$	17.5939	0.884126
$397$	−37.3083	−1.87245	−0.936224	−	0.351403i	$-0.885705\pi$
$397$	−37.3083	−1.87245	−0.936224	+	0.351403i	$0.885705\pi$
$398$	−49.5475	−2.48359
$399$	2.37143	0.118720
$400$	0.481483	0.0240741
$401$	5.91908	0.295585	0.147792	−	0.989018i	$-0.452783\pi$
$401$	5.91908	0.295585	0.147792	+	0.989018i	$0.452783\pi$
$402$	−76.1266	−3.79685
$403$	18.8840	0.940678
$404$	11.2012	0.557279
$405$	30.3531	1.50826
$406$	−3.67628	−0.182451
$407$	−5.79545	−0.287270
$408$	52.6109	2.60463
$409$	−27.3500	−1.35237	−0.676186	−	0.736731i	$-0.736369\pi$
$409$	−27.3500	−1.35237	−0.676186	+	0.736731i	$0.736369\pi$
$410$	−16.9474	−0.836974
$411$	43.7994	2.16047
$412$	16.4552	0.810688
$413$	0.962750	0.0473738
$414$	82.2479	4.04226
$415$	10.2318	0.502261
$416$	14.8740	0.729259
$417$	−33.5988	−1.64534
$418$	−4.86225	−0.237820
$419$	24.8756	1.21525	0.607625	−	0.794224i	$-0.292122\pi$
$419$	24.8756	1.21525	0.607625	+	0.794224i	$0.292122\pi$
$420$	2.49452	0.121720
$421$	3.94585	0.192309	0.0961544	−	0.995366i	$-0.469346\pi$
$421$	3.94585	0.192309	0.0961544	+	0.995366i	$0.469346\pi$
$422$	−49.6135	−2.41515
$423$	−13.6786	−0.665074
$424$	−3.50254	−0.170098
$425$	−5.12902	−0.248794
$426$	−95.5420	−4.62903
$427$	0.637507	0.0308511
$428$	48.8658	2.36202
$429$	6.40871	0.309416
$430$	8.13489	0.392299
$431$	−7.80234	−0.375825	−0.187913	−	0.982186i	$-0.560172\pi$
$431$	−7.80234	−0.375825	−0.187913	+	0.982186i	$0.560172\pi$
$432$	7.88675	0.379452
$433$	6.55691	0.315105	0.157553	−	0.987511i	$-0.449640\pi$
$433$	6.55691	0.315105	0.157553	+	0.987511i	$0.449640\pi$
$434$	−3.36746	−0.161643
$435$	23.3306	1.11862
$436$	42.1599	2.01909
$437$	−14.2189	−0.680183
$438$	114.260	5.45957
$439$	−15.1347	−0.722342	−0.361171	−	0.932500i	$-0.617623\pi$
$439$	−15.1347	−0.722342	−0.361171	+	0.932500i	$0.617623\pi$
$440$	−2.05313	−0.0978789
$441$	−55.2457	−2.63075
$442$	34.6607	1.64864
$443$	29.7347	1.41274	0.706370	−	0.707843i	$-0.250332\pi$
$443$	29.7347	1.41274	0.706370	+	0.707843i	$0.250332\pi$
$444$	−96.7438	−4.59126
$445$	4.22567	0.200316
$446$	−12.1981	−0.577598
$447$	−21.0867	−0.997367
$448$	−2.86965	−0.135578
$449$	37.3183	1.76116	0.880580	−	0.473898i	$-0.157153\pi$
$449$	37.3183	1.76116	0.880580	+	0.473898i	$0.157153\pi$
$450$	−18.3735	−0.866134
$451$	4.85695	0.228705
$452$	−48.6674	−2.28912
$453$	5.75494	0.270391
$454$	−53.9411	−2.53158
$455$	0.659704	0.0309274
$456$	−32.5818	−1.52578
$457$	−10.3689	−0.485035	−0.242517	−	0.970147i	$-0.577973\pi$
$457$	−10.3689	−0.485035	−0.242517	+	0.970147i	$0.577973\pi$
$458$	23.3648	1.09176
$459$	−84.0141	−3.92144
$460$	−14.9569	−0.697371
$461$	9.35487	0.435700	0.217850	−	0.975982i	$-0.430096\pi$
$461$	9.35487	0.435700	0.217850	+	0.975982i	$0.430096\pi$
$462$	−1.14283	−0.0531691
$463$	−25.1692	−1.16971	−0.584856	−	0.811137i	$-0.698849\pi$
$463$	−25.1692	−1.16971	−0.584856	+	0.811137i	$0.698849\pi$
$464$	3.39468	0.157594
$465$	21.3708	0.991047
$466$	−48.1064	−2.22849
$467$	−11.2776	−0.521863	−0.260931	−	0.965357i	$-0.584030\pi$
$467$	−11.2776	−0.521863	−0.260931	+	0.965357i	$0.584030\pi$
$468$	77.6713	3.59036
$469$	2.24582	0.103702
$470$	3.97642	0.183419
$471$	18.9906	0.875041
$472$	−13.2275	−0.608846
$473$	−2.33137	−0.107197
$474$	72.4561	3.32802
$475$	3.17639	0.145743
$476$	−3.86645	−0.177219
$477$	8.98296	0.411301
$478$	58.2831	2.66581
$479$	37.6092	1.71841	0.859204	−	0.511634i	$-0.170959\pi$
$479$	37.6092	1.71841	0.859204	+	0.511634i	$0.170959\pi$
$480$	16.8328	0.768308
$481$	−25.5850	−1.16658
$482$	15.7470	0.717258
$483$	−3.34202	−0.152067
$484$	−35.2880	−1.60400
$485$	−5.40434	−0.245399
$486$	−118.562	−5.37808
$487$	−14.3116	−0.648520	−0.324260	−	0.945968i	$-0.605115\pi$
$487$	−14.3116	−0.648520	−0.324260	+	0.945968i	$0.605115\pi$
$488$	−8.75891	−0.396497
$489$	−63.6899	−2.88016
$490$	16.0602	0.725525
$491$	−7.95400	−0.358959	−0.179480	−	0.983762i	$-0.557441\pi$
$491$	−7.95400	−0.358959	−0.179480	+	0.983762i	$0.557441\pi$
$492$	81.0774	3.65525
$493$	−36.1620	−1.62865
$494$	−21.4652	−0.965766
$495$	5.26565	0.236673
$496$	3.10952	0.139622
$497$	2.81860	0.126431
$498$	−78.2498	−3.50646
$499$	−27.9701	−1.25211	−0.626057	−	0.779777i	$-0.715332\pi$
$499$	−27.9701	−1.25211	−0.626057	+	0.779777i	$0.715332\pi$
$500$	3.34126	0.149426
$501$	23.9283	1.06904
$502$	−22.1562	−0.988878
$503$	−9.69723	−0.432378	−0.216189	−	0.976352i	$-0.569363\pi$
$503$	−9.69723	−0.432378	−0.216189	+	0.976352i	$0.569363\pi$
$504$	−5.55996	−0.247660
$505$	3.35238	0.149179
$506$	6.85231	0.304622
$507$	−14.7257	−0.653993
$508$	−7.60882	−0.337587
$509$	−24.5393	−1.08768	−0.543842	−	0.839188i	$-0.683031\pi$
$509$	−24.5393	−1.08768	−0.543842	+	0.839188i	$0.683031\pi$
$510$	39.2251	1.73692
$511$	−3.37081	−0.149116
$512$	5.43422	0.240161
$513$	52.0296	2.29716
$514$	7.87549	0.347373
$515$	4.92484	0.217015
$516$	−38.9178	−1.71326
$517$	−1.13960	−0.0501195
$518$	4.56242	0.200461
$519$	−67.8010	−2.97613
$520$	−9.06388	−0.397478
$521$	11.4183	0.500243	0.250122	−	0.968214i	$-0.419529\pi$
$521$	11.4183	0.500243	0.250122	+	0.968214i	$0.419529\pi$
$522$	−129.542	−5.66989
$523$	9.98169	0.436469	0.218235	−	0.975896i	$-0.429970\pi$
$523$	9.98169	0.436469	0.218235	+	0.975896i	$0.429970\pi$
$524$	47.2920	2.06596
$525$	0.746580	0.0325834
$526$	−5.36977	−0.234133
$527$	−33.1243	−1.44292
$528$	1.05529	0.0459255
$529$	−2.96146	−0.128759
$530$	−2.61139	−0.113431
$531$	33.9246	1.47220
$532$	2.39448	0.103814
$533$	21.4419	0.928750
$534$	−32.3166	−1.39847
$535$	14.6250	0.632294
$536$	−30.8560	−1.33278
$537$	−80.8802	−3.49024
$538$	13.0882	0.564274
$539$	−4.60268	−0.198251
$540$	54.7302	2.35521
$541$	−6.19835	−0.266488	−0.133244	−	0.991083i	$-0.542539\pi$
$541$	−6.19835	−0.266488	−0.133244	+	0.991083i	$0.542539\pi$
$542$	−24.4399	−1.04978
$543$	12.7962	0.549136
$544$	−26.0905	−1.11862
$545$	12.6180	0.540495
$546$	−5.04521	−0.215915
$547$	32.6315	1.39522	0.697610	−	0.716477i	$-0.254247\pi$
$547$	32.6315	1.39522	0.697610	+	0.716477i	$0.254247\pi$
$548$	44.2252	1.88921
$549$	22.4640	0.958738
$550$	−1.53075	−0.0652713
$551$	22.3950	0.954059
$552$	45.9171	1.95436
$553$	−2.13754	−0.0908974
$554$	−75.5397	−3.20937
$555$	−28.9543	−1.22904
$556$	−33.9255	−1.43876
$557$	2.34294	0.0992736	0.0496368	−	0.998767i	$-0.484194\pi$
$557$	2.34294	0.0992736	0.0496368	+	0.998767i	$0.484194\pi$
$558$	−118.660	−5.02328
$559$	−10.2923	−0.435316
$560$	0.108630	0.00459045
$561$	−11.2415	−0.474617
$562$	9.35360	0.394558
$563$	−9.26229	−0.390359	−0.195180	−	0.980768i	$-0.562529\pi$
$563$	−9.26229	−0.390359	−0.195180	+	0.980768i	$0.562529\pi$
$564$	−19.0234	−0.801030
$565$	−14.5656	−0.612779
$566$	−22.0075	−0.925043
$567$	6.84813	0.287594
$568$	−38.7256	−1.62489
$569$	0.671669	0.0281578	0.0140789	−	0.999901i	$-0.495518\pi$
$569$	0.671669	0.0281578	0.0140789	+	0.999901i	$0.495518\pi$
$570$	−24.2920	−1.01748
$571$	−5.61658	−0.235047	−0.117523	−	0.993070i	$-0.537495\pi$
$571$	−5.61658	−0.235047	−0.117523	+	0.993070i	$0.537495\pi$
$572$	6.47102	0.270567
$573$	35.3448	1.47655
$574$	−3.82360	−0.159594
$575$	−4.47644	−0.186681
$576$	−101.119	−4.21327
$577$	−41.5967	−1.73169	−0.865846	−	0.500311i	$-0.833219\pi$
$577$	−41.5967	−1.73169	−0.865846	+	0.500311i	$0.833219\pi$
$578$	−21.5092	−0.894665
$579$	40.7865	1.69503
$580$	23.5574	0.978169
$581$	2.30846	0.0957709
$582$	41.3307	1.71321
$583$	0.748396	0.0309954
$584$	46.3126	1.91643
$585$	23.2461	0.961109
$586$	34.1199	1.40948
$587$	21.4839	0.886737	0.443368	−	0.896340i	$-0.353783\pi$
$587$	21.4839	0.886737	0.443368	+	0.896340i	$0.353783\pi$
$588$	−76.8327	−3.16853
$589$	20.5138	0.845256
$590$	−9.86204	−0.406014
$591$	−4.71704	−0.194033
$592$	−4.21295	−0.173151
$593$	20.6112	0.846401	0.423200	−	0.906036i	$-0.360907\pi$
$593$	20.6112	0.846401	0.423200	+	0.906036i	$0.360907\pi$
$594$	−25.0739	−1.02879
$595$	−1.15719	−0.0474400
$596$	−21.2917	−0.872143
$597$	70.9428	2.90349
$598$	30.2507	1.23704
$599$	−5.66772	−0.231577	−0.115788	−	0.993274i	$-0.536939\pi$
$599$	−5.66772	−0.231577	−0.115788	+	0.993274i	$0.536939\pi$
$600$	−10.2575	−0.418761
$601$	−30.6898	−1.25186	−0.625931	−	0.779878i	$-0.715281\pi$
$601$	−30.6898	−1.25186	−0.625931	+	0.779878i	$0.715281\pi$
$602$	1.83536	0.0748035
$603$	79.1364	3.22268
$604$	5.81089	0.236442
$605$	−10.5613	−0.429378
$606$	−25.6380	−1.04147
$607$	2.82351	0.114603	0.0573015	−	0.998357i	$-0.481750\pi$
$607$	2.82351	0.114603	0.0573015	+	0.998357i	$0.481750\pi$
$608$	16.1578	0.655283
$609$	5.26374	0.213298
$610$	−6.53037	−0.264407
$611$	−5.03096	−0.203531
$612$	−136.243	−5.50729
$613$	−11.7612	−0.475031	−0.237516	−	0.971384i	$-0.576333\pi$
$613$	−11.7612	−0.475031	−0.237516	+	0.971384i	$0.576333\pi$
$614$	50.7285	2.04724
$615$	24.2655	0.978481
$616$	−0.463217	−0.0186635
$617$	−12.9423	−0.521037	−0.260518	−	0.965469i	$-0.583893\pi$
$617$	−12.9423	−0.521037	−0.260518	+	0.965469i	$0.583893\pi$
$618$	−37.6636	−1.51505
$619$	−30.6994	−1.23391	−0.616956	−	0.786997i	$-0.711634\pi$
$619$	−30.6994	−1.23391	−0.616956	+	0.786997i	$0.711634\pi$
$620$	21.5786	0.866616
$621$	−73.3248	−2.94242
$622$	68.6285	2.75175
$623$	0.953375	0.0381962
$624$	4.65875	0.186499
$625$	1.00000	0.0400000
$626$	25.9111	1.03562
$627$	6.96183	0.278029
$628$	19.1752	0.765175
$629$	44.8786	1.78943
$630$	−4.14534	−0.165154
$631$	30.5620	1.21665	0.608326	−	0.793687i	$-0.291841\pi$
$631$	30.5620	1.21665	0.608326	+	0.793687i	$0.291841\pi$
$632$	29.3683	1.16821
$633$	71.0372	2.82348
$634$	44.8888	1.78276
$635$	−2.27723	−0.0903692
$636$	12.4930	0.495380
$637$	−20.3193	−0.805081
$638$	−10.7925	−0.427279
$639$	99.3195	3.92902
$640$	19.2220	0.759814
$641$	−36.3265	−1.43481	−0.717404	−	0.696657i	$-0.754670\pi$
$641$	−36.3265	−1.43481	−0.717404	+	0.696657i	$0.754670\pi$
$642$	−111.847	−4.41426
$643$	−45.5057	−1.79457	−0.897285	−	0.441451i	$-0.854464\pi$
$643$	−45.5057	−1.79457	−0.897285	+	0.441451i	$0.854464\pi$
$644$	−3.37451	−0.132975
$645$	−11.6476	−0.458626
$646$	37.6521	1.48140
$647$	2.30197	0.0904997	0.0452498	−	0.998976i	$-0.485592\pi$
$647$	2.30197	0.0904997	0.0452498	+	0.998976i	$0.485592\pi$
$648$	−94.0886	−3.69615
$649$	2.82636	0.110944
$650$	−6.75775	−0.265061
$651$	4.82158	0.188973
$652$	−64.3091	−2.51854
$653$	8.56360	0.335119	0.167560	−	0.985862i	$-0.446411\pi$
$653$	8.56360	0.335119	0.167560	+	0.985862i	$0.446411\pi$
$654$	−96.4983	−3.77338
$655$	14.1540	0.553041
$656$	3.53072	0.137851
$657$	−118.778	−4.63396
$658$	0.897141	0.0349742
$659$	−40.9908	−1.59677	−0.798387	−	0.602144i	$-0.794313\pi$
$659$	−40.9908	−1.59677	−0.798387	+	0.602144i	$0.794313\pi$
$660$	7.32318	0.285054
$661$	0.871646	0.0339031	0.0169516	−	0.999856i	$-0.494604\pi$
$661$	0.871646	0.0339031	0.0169516	+	0.999856i	$0.494604\pi$
$662$	−21.5169	−0.836278
$663$	−49.6276	−1.92738
$664$	−31.7166	−1.23084
$665$	0.716641	0.0277901
$666$	160.767	6.22959
$667$	−31.5610	−1.22205
$668$	24.1609	0.934815
$669$	17.4654	0.675252
$670$	−23.0053	−0.888773
$671$	1.87154	0.0722499
$672$	3.79773	0.146501
$673$	22.7876	0.878397	0.439198	−	0.898390i	$-0.355263\pi$
$673$	22.7876	0.878397	0.439198	+	0.898390i	$0.355263\pi$
$674$	−51.7848	−1.99468
$675$	16.3801	0.630472
$676$	−14.8689	−0.571881
$677$	−24.1464	−0.928022	−0.464011	−	0.885829i	$-0.653590\pi$
$677$	−24.1464	−0.928022	−0.464011	+	0.885829i	$0.653590\pi$
$678$	111.393	4.27802
$679$	−1.21930	−0.0467925
$680$	15.8989	0.609696
$681$	77.2335	2.95959
$682$	−9.88590	−0.378551
$683$	−46.0159	−1.76075	−0.880375	−	0.474278i	$-0.842709\pi$
$683$	−46.0159	−1.76075	−0.880375	+	0.474278i	$0.842709\pi$
$684$	84.3748	3.22615
$685$	13.2361	0.505726
$686$	7.27338	0.277699
$687$	−33.4540	−1.27635
$688$	−1.69477	−0.0646125
$689$	3.30393	0.125870
$690$	34.2344	1.30328
$691$	−24.0957	−0.916645	−0.458323	−	0.888786i	$-0.651550\pi$
$691$	−24.0957	−0.916645	−0.458323	+	0.888786i	$0.651550\pi$
$692$	−68.4601	−2.60246
$693$	1.18801	0.0451288
$694$	−44.4784	−1.68838
$695$	−10.1535	−0.385145
$696$	−72.3202	−2.74129
$697$	−37.6111	−1.42462
$698$	8.63954	0.327011
$699$	68.8794	2.60526
$700$	0.753838	0.0284924
$701$	38.1729	1.44177	0.720884	−	0.693055i	$-0.243736\pi$
$701$	38.1729	1.44177	0.720884	+	0.693055i	$0.243736\pi$
$702$	−110.693	−4.17784
$703$	−27.7932	−1.04824
$704$	−8.42448	−0.317509
$705$	−5.69349	−0.214429
$706$	60.5101	2.27733
$707$	0.756349	0.0284454
$708$	47.1806	1.77315
$709$	6.44294	0.241970	0.120985	−	0.992654i	$-0.461395\pi$
$709$	6.44294	0.241970	0.120985	+	0.992654i	$0.461395\pi$
$710$	−28.8726	−1.08357
$711$	−75.3209	−2.82475
$712$	−13.0987	−0.490896
$713$	−28.9098	−1.08268
$714$	8.84978	0.331195
$715$	1.93670	0.0724285
$716$	−81.6665	−3.05202
$717$	−83.4505	−3.11651
$718$	−20.0572	−0.748529
$719$	36.3833	1.35687	0.678435	−	0.734661i	$-0.262659\pi$
$719$	36.3833	1.35687	0.678435	+	0.734661i	$0.262659\pi$
$720$	3.82781	0.142654
$721$	1.11112	0.0413803
$722$	20.5934	0.766406
$723$	−22.5468	−0.838525
$724$	12.9206	0.480189
$725$	7.05047	0.261848
$726$	80.7695	2.99764
$727$	13.1092	0.486193	0.243096	−	0.970002i	$-0.421837\pi$
$727$	13.1092	0.486193	0.243096	+	0.970002i	$0.421837\pi$
$728$	−2.04495	−0.0757909
$729$	78.6991	2.91478
$730$	34.5292	1.27798
$731$	18.0536	0.667738
$732$	31.2417	1.15473
$733$	−2.82047	−0.104176	−0.0520881	−	0.998642i	$-0.516588\pi$
$733$	−2.82047	−0.104176	−0.0520881	+	0.998642i	$0.516588\pi$
$734$	−23.3074	−0.860291
$735$	−22.9952	−0.848189
$736$	−22.7709	−0.839348
$737$	6.59308	0.242859
$738$	−134.733	−4.95958
$739$	20.9038	0.768960	0.384480	−	0.923133i	$-0.374381\pi$
$739$	20.9038	0.768960	0.384480	+	0.923133i	$0.374381\pi$
$740$	−29.2358	−1.07473
$741$	30.7342	1.12905
$742$	−0.589169	−0.0216291
$743$	−22.3935	−0.821539	−0.410770	−	0.911739i	$-0.634740\pi$
$743$	−22.3935	−0.821539	−0.410770	+	0.911739i	$0.634740\pi$
$744$	−66.2452	−2.42867
$745$	−6.37237	−0.233466
$746$	19.8894	0.728203
$747$	81.3435	2.97620
$748$	−11.3508	−0.415026
$749$	3.29962	0.120566
$750$	−7.64768	−0.279254
$751$	−23.0525	−0.841198	−0.420599	−	0.907247i	$-0.638180\pi$
$751$	−23.0525	−0.841198	−0.420599	+	0.907247i	$0.638180\pi$
$752$	−0.828421	−0.0302094
$753$	31.7235	1.15607
$754$	−47.6453	−1.73514
$755$	1.73913	0.0632935
$756$	12.3480	0.449092
$757$	48.5058	1.76297	0.881487	−	0.472208i	$-0.156543\pi$
$757$	48.5058	1.76297	0.881487	+	0.472208i	$0.156543\pi$
$758$	18.1291	0.658477
$759$	−9.81122	−0.356125
$760$	−9.84616	−0.357158
$761$	−15.5658	−0.564260	−0.282130	−	0.959376i	$-0.591041\pi$
$761$	−15.5658	−0.564260	−0.282130	+	0.959376i	$0.591041\pi$
$762$	17.4155	0.630898
$763$	2.84681	0.103061
$764$	35.6884	1.29116
$765$	−40.7760	−1.47426
$766$	61.3798	2.21774
$767$	12.4775	0.450535
$768$	−62.8253	−2.26701
$769$	8.82432	0.318213	0.159106	−	0.987261i	$-0.449139\pi$
$769$	8.82432	0.318213	0.159106	+	0.987261i	$0.449139\pi$
$770$	−0.345360	−0.0124459
$771$	−11.2762	−0.406103
$772$	41.1830	1.48221
$773$	15.4901	0.557139	0.278569	−	0.960416i	$-0.410140\pi$
$773$	15.4901	0.557139	0.278569	+	0.960416i	$0.410140\pi$
$774$	64.6728	2.32462
$775$	6.45822	0.231986
$776$	16.7524	0.601375
$777$	−6.53254	−0.234353
$778$	−57.8526	−2.07412
$779$	23.2924	0.834538
$780$	32.3295	1.15758
$781$	8.27459	0.296088
$782$	−53.0627	−1.89752
$783$	115.488	4.12719
$784$	−3.34587	−0.119495
$785$	5.73893	0.204831
$786$	−108.245	−3.86097
$787$	−44.3325	−1.58028	−0.790142	−	0.612924i	$-0.789993\pi$
$787$	−44.3325	−1.58028	−0.790142	+	0.612924i	$0.789993\pi$
$788$	−4.76290	−0.169671
$789$	7.68851	0.273718
$790$	21.8961	0.779029
$791$	−3.28622	−0.116844
$792$	−16.3225	−0.579993
$793$	8.26223	0.293400
$794$	86.2237	3.05997
$795$	3.73902	0.132609
$796$	71.6325	2.53895
$797$	48.0054	1.70044	0.850220	−	0.526428i	$-0.176469\pi$
$797$	48.0054	1.70044	0.850220	+	0.526428i	$0.176469\pi$
$798$	−5.48064	−0.194013
$799$	8.82480	0.312199
$800$	5.08684	0.179847
$801$	33.5943	1.18700
$802$	−13.6797	−0.483047
$803$	−9.89572	−0.349212
$804$	110.059	3.88147
$805$	−1.00995	−0.0355962
$806$	−43.6431	−1.53726
$807$	−18.7399	−0.659676
$808$	−10.3917	−0.365579
$809$	29.3435	1.03166	0.515831	−	0.856690i	$-0.327483\pi$
$809$	29.3435	1.03166	0.515831	+	0.856690i	$0.327483\pi$
$810$	−70.1496	−2.46481
$811$	−55.4109	−1.94574	−0.972870	−	0.231353i	$-0.925685\pi$
$811$	−55.4109	−1.94574	−0.972870	+	0.231353i	$0.925685\pi$
$812$	5.31491	0.186517
$813$	34.9933	1.22727
$814$	13.3940	0.469458
$815$	−19.2470	−0.674192
$816$	−8.17190	−0.286074
$817$	−11.1806	−0.391158
$818$	63.2091	2.21006
$819$	5.24468	0.183264
$820$	24.5014	0.855628
$821$	−42.5043	−1.48341	−0.741705	−	0.670726i	$-0.765983\pi$
$821$	−42.5043	−1.48341	−0.741705	+	0.670726i	$0.765983\pi$
$822$	−101.226	−3.53065
$823$	−50.0174	−1.74350	−0.871748	−	0.489954i	$-0.837014\pi$
$823$	−50.0174	−1.74350	−0.871748	+	0.489954i	$0.837014\pi$
$824$	−15.2660	−0.531817
$825$	2.19175	0.0763068
$826$	−2.22503	−0.0774186
$827$	−43.5673	−1.51498	−0.757492	−	0.652844i	$-0.773576\pi$
$827$	−43.5673	−1.51498	−0.757492	+	0.652844i	$0.773576\pi$
$828$	−118.908	−4.13235
$829$	15.8103	0.549113	0.274557	−	0.961571i	$-0.411469\pi$
$829$	15.8103	0.549113	0.274557	+	0.961571i	$0.411469\pi$
$830$	−23.6469	−0.820797
$831$	108.159	3.75198
$832$	−37.1913	−1.28938
$833$	35.6421	1.23492
$834$	77.6508	2.68883
$835$	7.23110	0.250242
$836$	7.02951	0.243121
$837$	105.786	3.65652
$838$	−57.4903	−1.98597
$839$	−40.8609	−1.41068	−0.705338	−	0.708871i	$-0.749205\pi$
$839$	−40.8609	−1.41068	−0.705338	+	0.708871i	$0.749205\pi$
$840$	−2.31425	−0.0798492
$841$	20.7091	0.714107
$842$	−9.11931	−0.314272
$843$	−13.3926	−0.461266
$844$	71.7278	2.46897
$845$	−4.45009	−0.153088
$846$	31.6127	1.08687
$847$	−2.38279	−0.0818737
$848$	0.544039	0.0186824
$849$	31.5106	1.08144
$850$	11.8538	0.406581
$851$	39.1686	1.34268
$852$	138.128	4.73220
$853$	47.3049	1.61969	0.809845	−	0.586644i	$-0.199551\pi$
$853$	47.3049	1.61969	0.809845	+	0.586644i	$0.199551\pi$
$854$	−1.47335	−0.0504171
$855$	25.2524	0.863614
$856$	−45.3345	−1.54950
$857$	−9.44951	−0.322789	−0.161395	−	0.986890i	$-0.551599\pi$
$857$	−9.44951	−0.322789	−0.161395	+	0.986890i	$0.551599\pi$
$858$	−14.8113	−0.505649
$859$	−53.6953	−1.83206	−0.916029	−	0.401111i	$-0.868624\pi$
$859$	−53.6953	−1.83206	−0.916029	+	0.401111i	$0.868624\pi$
$860$	−11.7609	−0.401043
$861$	5.47468	0.186576
$862$	18.0321	0.614176
$863$	2.69643	0.0917876	0.0458938	−	0.998946i	$-0.485386\pi$
$863$	2.69643	0.0917876	0.0458938	+	0.998946i	$0.485386\pi$
$864$	83.3231	2.83471
$865$	−20.4893	−0.696658
$866$	−15.1538	−0.514946
$867$	30.7971	1.04593
$868$	4.86845	0.165246
$869$	−6.27520	−0.212872
$870$	−53.9197	−1.82805
$871$	29.1063	0.986230
$872$	−39.1132	−1.32454
$873$	−42.9648	−1.45414
$874$	32.8615	1.11156
$875$	0.225615	0.00762719
$876$	−165.190	−5.58125
$877$	39.5679	1.33611	0.668057	−	0.744110i	$-0.267126\pi$
$877$	39.5679	1.33611	0.668057	+	0.744110i	$0.267126\pi$
$878$	34.9781	1.18045
$879$	−48.8533	−1.64778
$880$	0.318906	0.0107503
$881$	36.2384	1.22090	0.610452	−	0.792054i	$-0.290988\pi$
$881$	36.2384	1.22090	0.610452	+	0.792054i	$0.290988\pi$
$882$	127.679	4.29918
$883$	−20.8483	−0.701601	−0.350801	−	0.936450i	$-0.614090\pi$
$883$	−20.8483	−0.701601	−0.350801	+	0.936450i	$0.614090\pi$
$884$	−50.1101	−1.68538
$885$	14.1206	0.474659
$886$	−68.7204	−2.30871
$887$	46.2253	1.55209	0.776047	−	0.630675i	$-0.217222\pi$
$887$	46.2253	1.55209	0.776047	+	0.630675i	$0.217222\pi$
$888$	89.7526	3.01190
$889$	−0.513778	−0.0172316
$890$	−9.76601	−0.327357
$891$	20.1041	0.673514
$892$	17.6352	0.590471
$893$	−5.46517	−0.182885
$894$	48.7338	1.62990
$895$	−24.4419	−0.817001
$896$	4.33677	0.144881
$897$	−43.3134	−1.44619
$898$	−86.2469	−2.87810
$899$	45.5335	1.51863
$900$	26.5632	0.885438
$901$	−5.79541	−0.193073
$902$	−11.2250	−0.373751
$903$	−2.62789	−0.0874506
$904$	45.1504	1.50168
$905$	3.86698	0.128543
$906$	−13.3003	−0.441874
$907$	20.9887	0.696920	0.348460	−	0.937324i	$-0.386705\pi$
$907$	20.9887	0.696920	0.348460	+	0.937324i	$0.386705\pi$
$908$	77.9844	2.58800
$909$	26.6516	0.883978
$910$	−1.52465	−0.0505417
$911$	15.3498	0.508561	0.254280	−	0.967131i	$-0.418161\pi$
$911$	15.3498	0.508561	0.254280	+	0.967131i	$0.418161\pi$
$912$	5.06083	0.167581
$913$	6.77696	0.224285
$914$	23.9636	0.792647
$915$	9.35027	0.309111
$916$	−33.7792	−1.11610
$917$	3.19335	0.105454
$918$	194.166	6.40844
$919$	−23.3000	−0.768595	−0.384298	−	0.923209i	$-0.625556\pi$
$919$	−23.3000	−0.768595	−0.384298	+	0.923209i	$0.625556\pi$
$920$	13.8761	0.457481
$921$	−72.6337	−2.39336
$922$	−21.6202	−0.712023
$923$	36.5296	1.20239
$924$	1.65222	0.0543541
$925$	−8.74995	−0.287696
$926$	58.1689	1.91155
$927$	39.1528	1.28595
$928$	35.8646	1.17731
$929$	34.8454	1.14324	0.571621	−	0.820518i	$-0.306315\pi$
$929$	34.8454	1.14324	0.571621	+	0.820518i	$0.306315\pi$
$930$	−49.3904	−1.61957
$931$	−22.0730	−0.723414
$932$	69.5490	2.27815
$933$	−98.2632	−3.21699
$934$	26.0637	0.852831
$935$	−3.39716	−0.111099
$936$	−72.0583	−2.35530
$937$	18.5328	0.605441	0.302720	−	0.953079i	$-0.402105\pi$
$937$	18.5328	0.605441	0.302720	+	0.953079i	$0.402105\pi$
$938$	−5.19035	−0.169471
$939$	−37.0999	−1.21071
$940$	−5.74884	−0.187506
$941$	42.2418	1.37704	0.688521	−	0.725216i	$-0.258260\pi$
$941$	42.2418	1.37704	0.688521	+	0.725216i	$0.258260\pi$
$942$	−43.8895	−1.43000
$943$	−32.8258	−1.06895
$944$	2.05459	0.0668713
$945$	3.69561	0.120218
$946$	5.38808	0.175181
$947$	2.17240	0.0705936	0.0352968	−	0.999377i	$-0.488762\pi$
$947$	2.17240	0.0705936	0.0352968	+	0.999377i	$0.488762\pi$
$948$	−104.752	−3.40219
$949$	−43.6864	−1.41812
$950$	−7.34099	−0.238173
$951$	−64.2723	−2.08417
$952$	3.58704	0.116257
$953$	−29.4304	−0.953343	−0.476672	−	0.879081i	$-0.658157\pi$
$953$	−29.4304	−0.953343	−0.476672	+	0.879081i	$0.658157\pi$
$954$	−20.7607	−0.672151
$955$	10.6811	0.345633
$956$	−84.2618	−2.72522
$957$	15.4528	0.499519
$958$	−86.9192	−2.80823
$959$	2.98627	0.0964316
$960$	−42.0890	−1.35842
$961$	10.7086	0.345438
$962$	59.1300	1.90643
$963$	116.269	3.74673
$964$	−22.7660	−0.733244
$965$	12.3256	0.396775
$966$	7.72380	0.248509
$967$	59.8725	1.92537	0.962685	−	0.270624i	$-0.0872299\pi$
$967$	59.8725	1.92537	0.962685	+	0.270624i	$0.0872299\pi$
$968$	32.7379	1.05224
$969$	−53.9108	−1.73186
$970$	12.4901	0.401032
$971$	−23.6822	−0.759999	−0.379999	−	0.924987i	$-0.624076\pi$
$971$	−23.6822	−0.759999	−0.379999	+	0.924987i	$0.624076\pi$
$972$	171.409	5.49794
$973$	−2.29079	−0.0734393
$974$	33.0757	1.05981
$975$	9.67584	0.309875
$976$	1.36050	0.0435484
$977$	−28.5080	−0.912051	−0.456026	−	0.889967i	$-0.650727\pi$
$977$	−28.5080	−0.912051	−0.456026	+	0.889967i	$0.650727\pi$
$978$	147.195	4.70677
$979$	2.79884	0.0894512
$980$	−23.2187	−0.741695
$981$	100.314	3.20277
$982$	18.3826	0.586613
$983$	2.79693	0.0892083	0.0446041	−	0.999005i	$-0.485797\pi$
$983$	2.79693	0.0892083	0.0446041	+	0.999005i	$0.485797\pi$
$984$	−75.2183	−2.39787
$985$	−1.42548	−0.0454196
$986$	83.5746	2.66156
$987$	−1.28454	−0.0408873
$988$	31.0330	0.987291
$989$	15.7566	0.501031
$990$	−12.1695	−0.386773
$991$	−30.1293	−0.957087	−0.478544	−	0.878064i	$-0.658835\pi$
$991$	−30.1293	−0.957087	−0.478544	+	0.878064i	$0.658835\pi$
$992$	32.8519	1.04305
$993$	30.8082	0.977667
$994$	−6.51411	−0.206615
$995$	21.4388	0.679655
$996$	113.128	3.58461
$997$	43.4325	1.37552	0.687761	−	0.725937i	$-0.258594\pi$
$997$	43.4325	1.37552	0.687761	+	0.725937i	$0.258594\pi$
$998$	64.6422	2.04621
$999$	−143.325	−4.53461

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8035.2.a.e.1.17	✓	153

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8035.2.a.e.1.17	✓	153	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:	\( N \)	\(=\)	\( 8035 = 5 \cdot 1607 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8035.a (trivial)

\(f(q)\)	\(=\)	\(q-2.31112 q^{2} +3.30909 q^{3} +3.34126 q^{4} +1.00000 q^{5} -7.64768 q^{6} +0.225615 q^{7} -3.09980 q^{8} +7.95005 q^{9} +O(q^{10})\)	\(q-2.31112 q^{2} +3.30909 q^{3} +3.34126 q^{4} +1.00000 q^{5} -7.64768 q^{6} +0.225615 q^{7} -3.09980 q^{8} +7.95005 q^{9} -2.31112 q^{10} +0.662342 q^{11} +11.0565 q^{12} +2.92402 q^{13} -0.521423 q^{14} +3.30909 q^{15} +0.481483 q^{16} -5.12902 q^{17} -18.3735 q^{18} +3.17639 q^{19} +3.34126 q^{20} +0.746580 q^{21} -1.53075 q^{22} -4.47644 q^{23} -10.2575 q^{24} +1.00000 q^{25} -6.75775 q^{26} +16.3801 q^{27} +0.753838 q^{28} +7.05047 q^{29} -7.64768 q^{30} +6.45822 q^{31} +5.08684 q^{32} +2.19175 q^{33} +11.8538 q^{34} +0.225615 q^{35} +26.5632 q^{36} -8.74995 q^{37} -7.34099 q^{38} +9.67584 q^{39} -3.09980 q^{40} +7.33300 q^{41} -1.72543 q^{42} -3.51990 q^{43} +2.21305 q^{44} +7.95005 q^{45} +10.3456 q^{46} -1.72056 q^{47} +1.59327 q^{48} -6.94910 q^{49} -2.31112 q^{50} -16.9724 q^{51} +9.76991 q^{52} +1.12992 q^{53} -37.8564 q^{54} +0.662342 q^{55} -0.699362 q^{56} +10.5109 q^{57} -16.2945 q^{58} +4.26722 q^{59} +11.0565 q^{60} +2.82564 q^{61} -14.9257 q^{62} +1.79365 q^{63} -12.7192 q^{64} +2.92402 q^{65} -5.06538 q^{66} +9.95420 q^{67} -17.1374 q^{68} -14.8129 q^{69} -0.521423 q^{70} +12.4929 q^{71} -24.6436 q^{72} -14.9405 q^{73} +20.2221 q^{74} +3.30909 q^{75} +10.6131 q^{76} +0.149434 q^{77} -22.3620 q^{78} -9.47426 q^{79} +0.481483 q^{80} +30.3531 q^{81} -16.9474 q^{82} +10.2318 q^{83} +2.49452 q^{84} -5.12902 q^{85} +8.13489 q^{86} +23.3306 q^{87} -2.05313 q^{88} +4.22567 q^{89} -18.3735 q^{90} +0.659704 q^{91} -14.9569 q^{92} +21.3708 q^{93} +3.97642 q^{94} +3.17639 q^{95} +16.8328 q^{96} -5.40434 q^{97} +16.0602 q^{98} +5.26565 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 153 q + 18 q^{2} + 7 q^{3} + 176 q^{4} + 153 q^{5} + 19 q^{6} + 5 q^{7} + 57 q^{8} + 206 q^{9}+O(q^{10}) \) 153 * q + 18 * q^2 + 7 * q^3 + 176 * q^4 + 153 * q^5 + 19 * q^6 + 5 * q^7 + 57 * q^8 + 206 * q^9	\( 153 q + 18 q^{2} + 7 q^{3} + 176 q^{4} + 153 q^{5} + 19 q^{6} + 5 q^{7} + 57 q^{8} + 206 q^{9} + 18 q^{10} + 38 q^{11} + 14 q^{12} + 28 q^{13} + 53 q^{14} + 7 q^{15} + 214 q^{16} + 50 q^{17} + 47 q^{18} + 65 q^{19} + 176 q^{20} + 109 q^{21} + 13 q^{22} + 52 q^{23} + 66 q^{24} + 153 q^{25} + 36 q^{26} + 19 q^{27} + 26 q^{28} + 172 q^{29} + 19 q^{30} + 60 q^{31} + 107 q^{32} + 4 q^{33} + 40 q^{34} + 5 q^{35} + 241 q^{36} + 65 q^{37} + 29 q^{38} + 56 q^{39} + 57 q^{40} + 152 q^{41} - 19 q^{42} + 22 q^{43} + 97 q^{44} + 206 q^{45} + 86 q^{46} + 37 q^{47} - 4 q^{48} + 260 q^{49} + 18 q^{50} + 102 q^{51} - 6 q^{52} + 169 q^{53} + 64 q^{54} + 38 q^{55} + 146 q^{56} + 40 q^{57} - 9 q^{58} + 64 q^{59} + 14 q^{60} + 164 q^{61} + 12 q^{62} + 19 q^{63} + 259 q^{64} + 28 q^{65} + 6 q^{66} + 5 q^{67} + 112 q^{68} + 119 q^{69} + 53 q^{70} + 100 q^{71} + 77 q^{72} + 10 q^{73} + 98 q^{74} + 7 q^{75} + 126 q^{76} + 80 q^{77} - 4 q^{78} + 110 q^{79} + 214 q^{80} + 305 q^{81} - 27 q^{82} + 36 q^{83} + 172 q^{84} + 50 q^{85} + 44 q^{86} + 23 q^{87} + 47 q^{88} + 143 q^{89} + 47 q^{90} + 82 q^{91} + 130 q^{92} + 31 q^{93} + 77 q^{94} + 65 q^{95} + 57 q^{96} + 11 q^{97} + 29 q^{98} + 99 q^{99}+O(q^{100}) \) 153 * q + 18 * q^2 + 7 * q^3 + 176 * q^4 + 153 * q^5 + 19 * q^6 + 5 * q^7 + 57 * q^8 + 206 * q^9 + 18 * q^10 + 38 * q^11 + 14 * q^12 + 28 * q^13 + 53 * q^14 + 7 * q^15 + 214 * q^16 + 50 * q^17 + 47 * q^18 + 65 * q^19 + 176 * q^20 + 109 * q^21 + 13 * q^22 + 52 * q^23 + 66 * q^24 + 153 * q^25 + 36 * q^26 + 19 * q^27 + 26 * q^28 + 172 * q^29 + 19 * q^30 + 60 * q^31 + 107 * q^32 + 4 * q^33 + 40 * q^34 + 5 * q^35 + 241 * q^36 + 65 * q^37 + 29 * q^38 + 56 * q^39 + 57 * q^40 + 152 * q^41 - 19 * q^42 + 22 * q^43 + 97 * q^44 + 206 * q^45 + 86 * q^46 + 37 * q^47 - 4 * q^48 + 260 * q^49 + 18 * q^50 + 102 * q^51 - 6 * q^52 + 169 * q^53 + 64 * q^54 + 38 * q^55 + 146 * q^56 + 40 * q^57 - 9 * q^58 + 64 * q^59 + 14 * q^60 + 164 * q^61 + 12 * q^62 + 19 * q^63 + 259 * q^64 + 28 * q^65 + 6 * q^66 + 5 * q^67 + 112 * q^68 + 119 * q^69 + 53 * q^70 + 100 * q^71 + 77 * q^72 + 10 * q^73 + 98 * q^74 + 7 * q^75 + 126 * q^76 + 80 * q^77 - 4 * q^78 + 110 * q^79 + 214 * q^80 + 305 * q^81 - 27 * q^82 + 36 * q^83 + 172 * q^84 + 50 * q^85 + 44 * q^86 + 23 * q^87 + 47 * q^88 + 143 * q^89 + 47 * q^90 + 82 * q^91 + 130 * q^92 + 31 * q^93 + 77 * q^94 + 65 * q^95 + 57 * q^96 + 11 * q^97 + 29 * q^98 + 99 * q^99

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