LMFDB - Embedded newform 8023.2.a.c.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8023,2,Mod(1,8023)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8023, 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("8023.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8023 = 71 \cdot 113 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8023.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:	$64.0639775417$
Analytic rank:	$1$
Dimension:	$158$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	8023.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.74732 q^{2} +2.10960 q^{3} +5.54775 q^{4} +3.39073 q^{5} -5.79574 q^{6} -0.0705501 q^{7} -9.74679 q^{8} +1.45041 q^{9} +O(q^{10})$	\(q-2.74732 q^{2} +2.10960 q^{3} +5.54775 q^{4} +3.39073 q^{5} -5.79574 q^{6} -0.0705501 q^{7} -9.74679 q^{8} +1.45041 q^{9} -9.31541 q^{10} -4.86039 q^{11} +11.7035 q^{12} +2.06905 q^{13} +0.193823 q^{14} +7.15308 q^{15} +15.6820 q^{16} -2.52700 q^{17} -3.98473 q^{18} -5.74187 q^{19} +18.8109 q^{20} -0.148832 q^{21} +13.3530 q^{22} +6.77197 q^{23} -20.5618 q^{24} +6.49705 q^{25} -5.68433 q^{26} -3.26902 q^{27} -0.391394 q^{28} -4.60912 q^{29} -19.6518 q^{30} +5.42280 q^{31} -23.5899 q^{32} -10.2535 q^{33} +6.94248 q^{34} -0.239216 q^{35} +8.04651 q^{36} +10.4954 q^{37} +15.7747 q^{38} +4.36486 q^{39} -33.0487 q^{40} -7.49278 q^{41} +0.408890 q^{42} -5.59125 q^{43} -26.9642 q^{44} +4.91795 q^{45} -18.6047 q^{46} -12.9389 q^{47} +33.0828 q^{48} -6.99502 q^{49} -17.8495 q^{50} -5.33097 q^{51} +11.4786 q^{52} +6.07795 q^{53} +8.98102 q^{54} -16.4803 q^{55} +0.687637 q^{56} -12.1130 q^{57} +12.6627 q^{58} -4.42794 q^{59} +39.6835 q^{60} -7.53661 q^{61} -14.8982 q^{62} -0.102327 q^{63} +33.4449 q^{64} +7.01558 q^{65} +28.1696 q^{66} -13.6186 q^{67} -14.0192 q^{68} +14.2861 q^{69} +0.657203 q^{70} -1.00000 q^{71} -14.1368 q^{72} -13.5795 q^{73} -28.8343 q^{74} +13.7062 q^{75} -31.8545 q^{76} +0.342901 q^{77} -11.9917 q^{78} +9.27609 q^{79} +53.1735 q^{80} -11.2475 q^{81} +20.5850 q^{82} -5.20125 q^{83} -0.825685 q^{84} -8.56839 q^{85} +15.3609 q^{86} -9.72341 q^{87} +47.3732 q^{88} -15.9877 q^{89} -13.5112 q^{90} -0.145972 q^{91} +37.5692 q^{92} +11.4399 q^{93} +35.5471 q^{94} -19.4691 q^{95} -49.7652 q^{96} +15.8297 q^{97} +19.2175 q^{98} -7.04956 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 158 q - 24 q^{2} - 23 q^{3} + 158 q^{4} - 31 q^{5} - 17 q^{6} - 2 q^{7} - 69 q^{8} + 135 q^{9}+O(q^{10}) $ 158 * q - 24 * q^2 - 23 * q^3 + 158 * q^4 - 31 * q^5 - 17 * q^6 - 2 * q^7 - 69 * q^8 + 135 * q^9	\( 158 q - 24 q^{2} - 23 q^{3} + 158 q^{4} - 31 q^{5} - 17 q^{6} - 2 q^{7} - 69 q^{8} + 135 q^{9} - 10 q^{10} - 10 q^{11} - 46 q^{12} - 28 q^{13} - 27 q^{14} - 41 q^{15} + 150 q^{16} - 137 q^{17} - 67 q^{18} - 42 q^{19} - 66 q^{20} - 46 q^{21} - 8 q^{22} - 26 q^{23} - 48 q^{24} + 129 q^{25} - 67 q^{26} - 89 q^{27} - 21 q^{28} - 79 q^{29} - 11 q^{30} + 7 q^{31} - 147 q^{32} - 112 q^{33} - 28 q^{34} - 53 q^{35} + 141 q^{36} - 60 q^{37} - 53 q^{38} - 3 q^{39} - 48 q^{40} - 128 q^{41} + 32 q^{42} - 63 q^{43} - 88 q^{45} - 2 q^{46} - 92 q^{47} - 131 q^{48} + 122 q^{49} - 116 q^{50} - 12 q^{51} - 89 q^{52} - 94 q^{53} - 71 q^{54} - 12 q^{55} - 104 q^{56} - 93 q^{57} - 65 q^{58} - 54 q^{59} - 12 q^{60} + 17 q^{61} - 97 q^{62} - 28 q^{63} + 163 q^{64} - 163 q^{65} - 65 q^{66} - 35 q^{67} - 217 q^{68} - 46 q^{69} - 79 q^{70} - 158 q^{71} - 99 q^{72} - 165 q^{73} - 94 q^{75} - 93 q^{76} - 140 q^{77} + 25 q^{78} - 61 q^{79} - 134 q^{80} + 114 q^{81} + 10 q^{82} - 158 q^{83} - 160 q^{84} + 23 q^{85} - 122 q^{86} - 71 q^{87} - 14 q^{88} - 251 q^{89} - 6 q^{90} - 57 q^{91} - 58 q^{92} - 52 q^{93} - 64 q^{94} - 84 q^{95} - 98 q^{96} - 48 q^{97} - 84 q^{98} + 85 q^{99}+O(q^{100}) \) 158 * q - 24 * q^2 - 23 * q^3 + 158 * q^4 - 31 * q^5 - 17 * q^6 - 2 * q^7 - 69 * q^8 + 135 * q^9 - 10 * q^10 - 10 * q^11 - 46 * q^12 - 28 * q^13 - 27 * q^14 - 41 * q^15 + 150 * q^16 - 137 * q^17 - 67 * q^18 - 42 * q^19 - 66 * q^20 - 46 * q^21 - 8 * q^22 - 26 * q^23 - 48 * q^24 + 129 * q^25 - 67 * q^26 - 89 * q^27 - 21 * q^28 - 79 * q^29 - 11 * q^30 + 7 * q^31 - 147 * q^32 - 112 * q^33 - 28 * q^34 - 53 * q^35 + 141 * q^36 - 60 * q^37 - 53 * q^38 - 3 * q^39 - 48 * q^40 - 128 * q^41 + 32 * q^42 - 63 * q^43 - 88 * q^45 - 2 * q^46 - 92 * q^47 - 131 * q^48 + 122 * q^49 - 116 * q^50 - 12 * q^51 - 89 * q^52 - 94 * q^53 - 71 * q^54 - 12 * q^55 - 104 * q^56 - 93 * q^57 - 65 * q^58 - 54 * q^59 - 12 * q^60 + 17 * q^61 - 97 * q^62 - 28 * q^63 + 163 * q^64 - 163 * q^65 - 65 * q^66 - 35 * q^67 - 217 * q^68 - 46 * q^69 - 79 * q^70 - 158 * q^71 - 99 * q^72 - 165 * q^73 - 94 * q^75 - 93 * q^76 - 140 * q^77 + 25 * q^78 - 61 * q^79 - 134 * q^80 + 114 * q^81 + 10 * q^82 - 158 * q^83 - 160 * q^84 + 23 * q^85 - 122 * q^86 - 71 * q^87 - 14 * q^88 - 251 * q^89 - 6 * q^90 - 57 * q^91 - 58 * q^92 - 52 * q^93 - 64 * q^94 - 84 * q^95 - 98 * q^96 - 48 * q^97 - 84 * q^98 + 85 * 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 $

$2$	−2.74732	−1.94265	−0.971323	−	0.237763i	$-0.923586\pi$
$2$	−2.74732	−1.94265	−0.971323	+	0.237763i	$0.923586\pi$
$3$	2.10960	1.21798	0.608989	−	0.793179i	$-0.291575\pi$
$3$	2.10960	1.21798	0.608989	+	0.793179i	$0.291575\pi$
$4$	5.54775	2.77387
$5$	3.39073	1.51638	0.758190	−	0.652033i	$-0.226084\pi$
$5$	3.39073	1.51638	0.758190	+	0.652033i	$0.226084\pi$
$6$	−5.79574	−2.36610
$7$	−0.0705501	−0.0266654	−0.0133327	−	0.999911i	$-0.504244\pi$
$7$	−0.0705501	−0.0266654	−0.0133327	+	0.999911i	$0.504244\pi$
$8$	−9.74679	−3.44601
$9$	1.45041	0.483470
$10$	−9.31541	−2.94579
$11$	−4.86039	−1.46546	−0.732732	−	0.680518i	$-0.761755\pi$
$11$	−4.86039	−1.46546	−0.732732	+	0.680518i	$0.761755\pi$
$12$	11.7035	3.37852
$13$	2.06905	0.573851	0.286925	−	0.957953i	$-0.407367\pi$
$13$	2.06905	0.573851	0.286925	+	0.957953i	$0.407367\pi$
$14$	0.193823	0.0518015
$15$	7.15308	1.84692
$16$	15.6820	3.92050
$17$	−2.52700	−0.612889	−0.306444	−	0.951889i	$-0.599139\pi$
$17$	−2.52700	−0.612889	−0.306444	+	0.951889i	$0.599139\pi$
$18$	−3.98473	−0.939211
$19$	−5.74187	−1.31728	−0.658638	−	0.752460i	$-0.728867\pi$
$19$	−5.74187	−1.31728	−0.658638	+	0.752460i	$0.728867\pi$
$20$	18.8109	4.20625
$21$	−0.148832	−0.0324779
$22$	13.3530	2.84688
$23$	6.77197	1.41205	0.706026	−	0.708186i	$-0.250486\pi$
$23$	6.77197	1.41205	0.706026	+	0.708186i	$0.250486\pi$
$24$	−20.5618	−4.19716
$25$	6.49705	1.29941
$26$	−5.68433	−1.11479
$27$	−3.26902	−0.629122
$28$	−0.391394	−0.0739666
$29$	−4.60912	−0.855893	−0.427946	−	0.903804i	$-0.640763\pi$
$29$	−4.60912	−0.855893	−0.427946	+	0.903804i	$0.640763\pi$
$30$	−19.6518	−3.58791
$31$	5.42280	0.973964	0.486982	−	0.873412i	$-0.338098\pi$
$31$	5.42280	0.973964	0.486982	+	0.873412i	$0.338098\pi$
$32$	−23.5899	−4.17014
$33$	−10.2535	−1.78490
$34$	6.94248	1.19063
$35$	−0.239216	−0.0404350
$36$	8.04651	1.34108
$37$	10.4954	1.72544	0.862719	−	0.505684i	$-0.168760\pi$
$37$	10.4954	1.72544	0.862719	+	0.505684i	$0.168760\pi$
$38$	15.7747	2.55900
$39$	4.36486	0.698937
$40$	−33.0487	−5.22546
$41$	−7.49278	−1.17018	−0.585088	−	0.810970i	$-0.698940\pi$
$41$	−7.49278	−1.17018	−0.585088	+	0.810970i	$0.698940\pi$
$42$	0.408890	0.0630931
$43$	−5.59125	−0.852657	−0.426328	−	0.904568i	$-0.640193\pi$
$43$	−5.59125	−0.852657	−0.426328	+	0.904568i	$0.640193\pi$
$44$	−26.9642	−4.06501
$45$	4.91795	0.733124
$46$	−18.6047	−2.74312
$47$	−12.9389	−1.88733	−0.943663	−	0.330907i	$-0.892645\pi$
$47$	−12.9389	−1.88733	−0.943663	+	0.330907i	$0.892645\pi$
$48$	33.0828	4.77509
$49$	−6.99502	−0.999289
$50$	−17.8495	−2.52430
$51$	−5.33097	−0.746485
$52$	11.4786	1.59179
$53$	6.07795	0.834871	0.417436	−	0.908707i	$-0.362929\pi$
$53$	6.07795	0.834871	0.417436	+	0.908707i	$0.362929\pi$
$54$	8.98102	1.22216
$55$	−16.4803	−2.22220
$56$	0.687637	0.0918894
$57$	−12.1130	−1.60441
$58$	12.6627	1.66270
$59$	−4.42794	−0.576469	−0.288234	−	0.957560i	$-0.593068\pi$
$59$	−4.42794	−0.576469	−0.288234	+	0.957560i	$0.593068\pi$
$60$	39.6835	5.12312
$61$	−7.53661	−0.964964	−0.482482	−	0.875906i	$-0.660265\pi$
$61$	−7.53661	−0.964964	−0.482482	+	0.875906i	$0.660265\pi$
$62$	−14.8982	−1.89207
$63$	−0.102327	−0.0128919
$64$	33.4449	4.18061
$65$	7.01558	0.870176
$66$	28.1696	3.46743
$67$	−13.6186	−1.66378	−0.831888	−	0.554944i	$-0.812740\pi$
$67$	−13.6186	−1.66378	−0.831888	+	0.554944i	$0.812740\pi$
$68$	−14.0192	−1.70008
$69$	14.2861	1.71985
$70$	0.657203	0.0785508
$71$	−1.00000	−0.118678
$71$	−1.00000	−0.118678
$72$	−14.1368	−1.66604
$73$	−13.5795	−1.58936	−0.794682	−	0.607026i	$-0.792362\pi$
$73$	−13.5795	−1.58936	−0.794682	+	0.607026i	$0.792362\pi$
$74$	−28.8343	−3.35191
$75$	13.7062	1.58265
$76$	−31.8545	−3.65396
$77$	0.342901	0.0390772
$78$	−11.9917	−1.35779
$79$	9.27609	1.04364	0.521821	−	0.853055i	$-0.325253\pi$
$79$	9.27609	1.04364	0.521821	+	0.853055i	$0.325253\pi$
$80$	53.1735	5.94498
$81$	−11.2475	−1.24973
$82$	20.5850	2.27324
$83$	−5.20125	−0.570912	−0.285456	−	0.958392i	$-0.592145\pi$
$83$	−5.20125	−0.570912	−0.285456	+	0.958392i	$0.592145\pi$
$84$	−0.825685	−0.0900896
$85$	−8.56839	−0.929373
$86$	15.3609	1.65641
$87$	−9.72341	−1.04246
$88$	47.3732	5.05000
$89$	−15.9877	−1.69469	−0.847345	−	0.531042i	$-0.821800\pi$
$89$	−15.9877	−1.69469	−0.847345	+	0.531042i	$0.821800\pi$
$90$	−13.5112	−1.42420
$91$	−0.145972	−0.0153020
$92$	37.5692	3.91686
$93$	11.4399	1.18627
$94$	35.5471	3.66641
$95$	−19.4691	−1.99749
$96$	−49.7652	−5.07914
$97$	15.8297	1.60726	0.803632	−	0.595126i	$-0.202898\pi$
$97$	15.8297	1.60726	0.803632	+	0.595126i	$0.202898\pi$
$98$	19.2175	1.94126
$99$	−7.04956	−0.708507
$100$	36.0440	3.60440
$101$	−13.0662	−1.30013	−0.650066	−	0.759878i	$-0.725259\pi$
$101$	−13.0662	−1.30013	−0.650066	+	0.759878i	$0.725259\pi$
$102$	14.6459	1.45016
$103$	0.223196	0.0219921	0.0109961	−	0.999940i	$-0.496500\pi$
$103$	0.223196	0.0219921	0.0109961	+	0.999940i	$0.496500\pi$
$104$	−20.1666	−1.97750
$105$	−0.504651	−0.0492489
$106$	−16.6981	−1.62186
$107$	15.6841	1.51624	0.758120	−	0.652115i	$-0.226118\pi$
$107$	15.6841	1.51624	0.758120	+	0.652115i	$0.226118\pi$
$108$	−18.1357	−1.74511
$109$	3.18412	0.304984	0.152492	−	0.988305i	$-0.451270\pi$
$109$	3.18412	0.304984	0.152492	+	0.988305i	$0.451270\pi$
$110$	45.2766	4.31695
$111$	22.1411	2.10154
$112$	−1.10637	−0.104542
$113$	−1.00000	−0.0940721
$113$	−1.00000	−0.0940721
$114$	33.2784	3.11681
$115$	22.9619	2.14121
$116$	−25.5703	−2.37414
$117$	3.00097	0.277439
$118$	12.1649	1.11987
$119$	0.178280	0.0163429
$120$	−69.7196	−6.36450
$121$	12.6234	1.14758
$122$	20.7055	1.87458
$123$	−15.8068	−1.42525
$124$	30.0844	2.70165
$125$	5.07611	0.454021
$126$	0.281123	0.0250445
$127$	0.560148	0.0497051	0.0248526	−	0.999691i	$-0.492088\pi$
$127$	0.560148	0.0497051	0.0248526	+	0.999691i	$0.492088\pi$
$128$	−44.7039	−3.95130
$129$	−11.7953	−1.03852
$130$	−19.2740	−1.69044
$131$	14.5177	1.26842	0.634209	−	0.773162i	$-0.281326\pi$
$131$	14.5177	1.26842	0.634209	+	0.773162i	$0.281326\pi$
$132$	−56.8837	−4.95109
$133$	0.405090	0.0351257
$134$	37.4146	3.23213
$135$	−11.0844	−0.953989
$136$	24.6302	2.11202
$137$	2.73647	0.233792	0.116896	−	0.993144i	$-0.462706\pi$
$137$	2.73647	0.233792	0.116896	+	0.993144i	$0.462706\pi$
$138$	−39.2485	−3.34106
$139$	−3.26153	−0.276640	−0.138320	−	0.990388i	$-0.544170\pi$
$139$	−3.26153	−0.276640	−0.138320	+	0.990388i	$0.544170\pi$
$140$	−1.32711	−0.112161
$141$	−27.2958	−2.29872
$142$	2.74732	0.230550
$143$	−10.0564	−0.840957
$144$	22.7453	1.89545
$145$	−15.6283	−1.29786
$146$	37.3073	3.08757
$147$	−14.7567	−1.21711
$148$	58.2260	4.78615
$149$	−20.2705	−1.66062	−0.830312	−	0.557299i	$-0.811838\pi$
$149$	−20.2705	−1.66062	−0.830312	+	0.557299i	$0.811838\pi$
$150$	−37.6552	−3.07454
$151$	10.0843	0.820645	0.410323	−	0.911940i	$-0.365416\pi$
$151$	10.0843	0.820645	0.410323	+	0.911940i	$0.365416\pi$
$152$	55.9648	4.53935
$153$	−3.66519	−0.296313
$154$	−0.942058	−0.0759132
$155$	18.3873	1.47690
$156$	24.2152	1.93876
$157$	3.76686	0.300628	0.150314	−	0.988638i	$-0.451972\pi$
$157$	3.76686	0.300628	0.150314	+	0.988638i	$0.451972\pi$
$158$	−25.4844	−2.02743
$159$	12.8220	1.01685
$160$	−79.9870	−6.32353
$161$	−0.477763	−0.0376530
$162$	30.9006	2.42778
$163$	−2.70915	−0.212197	−0.106099	−	0.994356i	$-0.533836\pi$
$163$	−2.70915	−0.212197	−0.106099	+	0.994356i	$0.533836\pi$
$164$	−41.5681	−3.24592
$165$	−34.7668	−2.70659
$166$	14.2895	1.10908
$167$	−7.94152	−0.614533	−0.307267	−	0.951623i	$-0.599414\pi$
$167$	−7.94152	−0.614533	−0.307267	+	0.951623i	$0.599414\pi$
$168$	1.45064	0.111919
$169$	−8.71904	−0.670695
$170$	23.5401	1.80544
$171$	−8.32806	−0.636863
$172$	−31.0188	−2.36516
$173$	14.3204	1.08876	0.544380	−	0.838839i	$-0.316765\pi$
$173$	14.3204	1.08876	0.544380	+	0.838839i	$0.316765\pi$
$174$	26.7133	2.02513
$175$	−0.458368	−0.0346494
$176$	−76.2208	−5.74536
$177$	−9.34118	−0.702126
$178$	43.9232	3.29218
$179$	14.4205	1.07784	0.538920	−	0.842357i	$-0.318832\pi$
$179$	14.4205	1.07784	0.538920	+	0.842357i	$0.318832\pi$
$180$	27.2835	2.03359
$181$	−15.4170	−1.14594	−0.572968	−	0.819578i	$-0.694208\pi$
$181$	−15.4170	−1.14594	−0.572968	+	0.819578i	$0.694208\pi$
$182$	0.401030	0.0297263
$183$	−15.8992	−1.17530
$184$	−66.0049	−4.86595
$185$	35.5872	2.61642
$186$	−31.4291	−2.30450
$187$	12.2822	0.898166
$188$	−71.7815	−5.23521
$189$	0.230629	0.0167758
$190$	53.4879	3.88042
$191$	16.6125	1.20204	0.601020	−	0.799234i	$-0.294761\pi$
$191$	16.6125	1.20204	0.601020	+	0.799234i	$0.294761\pi$
$192$	70.5553	5.09189
$193$	4.20881	0.302957	0.151478	−	0.988461i	$-0.451597\pi$
$193$	4.20881	0.302957	0.151478	+	0.988461i	$0.451597\pi$
$194$	−43.4892	−3.12235
$195$	14.8001	1.05986
$196$	−38.8066	−2.77190
$197$	−10.1778	−0.725139	−0.362569	−	0.931957i	$-0.618100\pi$
$197$	−10.1778	−0.725139	−0.362569	+	0.931957i	$0.618100\pi$
$198$	19.3674	1.37638
$199$	−3.60505	−0.255555	−0.127778	−	0.991803i	$-0.540784\pi$
$199$	−3.60505	−0.255555	−0.127778	+	0.991803i	$0.540784\pi$
$200$	−63.3254	−4.47778
$201$	−28.7298	−2.02644
$202$	35.8969	2.52570
$203$	0.325174	0.0228228
$204$	−29.5749	−2.07066
$205$	−25.4060	−1.77443
$206$	−0.613189	−0.0427229
$207$	9.82212	0.682685
$208$	32.4469	2.24978
$209$	27.9078	1.93042
$210$	1.38644	0.0956731
$211$	2.90904	0.200267	0.100133	−	0.994974i	$-0.468073\pi$
$211$	2.90904	0.200267	0.100133	+	0.994974i	$0.468073\pi$
$212$	33.7190	2.31583
$213$	−2.10960	−0.144547
$214$	−43.0892	−2.94552
$215$	−18.9584	−1.29295
$216$	31.8624	2.16796
$217$	−0.382579	−0.0259712
$218$	−8.74780	−0.592475
$219$	−28.6474	−1.93581
$220$	−91.4285	−6.16411
$221$	−5.22849	−0.351707
$222$	−60.8287	−4.08256
$223$	−5.94964	−0.398418	−0.199209	−	0.979957i	$-0.563837\pi$
$223$	−5.94964	−0.398418	−0.199209	+	0.979957i	$0.563837\pi$
$224$	1.66427	0.111199
$225$	9.42339	0.628226
$226$	2.74732	0.182749
$227$	7.06787	0.469111	0.234556	−	0.972103i	$-0.424637\pi$
$227$	7.06787	0.469111	0.234556	+	0.972103i	$0.424637\pi$
$228$	−67.2002	−4.45044
$229$	−22.0972	−1.46023	−0.730114	−	0.683326i	$-0.760533\pi$
$229$	−22.0972	−1.46023	−0.730114	+	0.683326i	$0.760533\pi$
$230$	−63.0837	−4.15961
$231$	0.723384	0.0475952
$232$	44.9242	2.94942
$233$	−23.2399	−1.52250	−0.761248	−	0.648460i	$-0.775413\pi$
$233$	−23.2399	−1.52250	−0.761248	+	0.648460i	$0.775413\pi$
$234$	−8.24460	−0.538967
$235$	−43.8722	−2.86191
$236$	−24.5651	−1.59905
$237$	19.5688	1.27113
$238$	−0.489793	−0.0317486
$239$	−10.4329	−0.674846	−0.337423	−	0.941353i	$-0.609555\pi$
$239$	−10.4329	−0.674846	−0.337423	+	0.941353i	$0.609555\pi$
$240$	112.175	7.24085
$241$	22.4864	1.44848	0.724238	−	0.689550i	$-0.242192\pi$
$241$	22.4864	1.44848	0.724238	+	0.689550i	$0.242192\pi$
$242$	−34.6805	−2.22935
$243$	−13.9208	−0.893017
$244$	−41.8112	−2.67669
$245$	−23.7182	−1.51530
$246$	43.4262	2.76875
$247$	−11.8802	−0.755920
$248$	−52.8549	−3.35629
$249$	−10.9726	−0.695358
$250$	−13.9457	−0.882002
$251$	6.05768	0.382357	0.191179	−	0.981555i	$-0.438769\pi$
$251$	6.05768	0.382357	0.191179	+	0.981555i	$0.438769\pi$
$252$	−0.567682	−0.0357606
$253$	−32.9144	−2.06931
$254$	−1.53890	−0.0965594
$255$	−18.0759	−1.13196
$256$	55.9259	3.49537
$257$	−15.4251	−0.962194	−0.481097	−	0.876667i	$-0.659762\pi$
$257$	−15.4251	−0.962194	−0.481097	+	0.876667i	$0.659762\pi$
$258$	32.4054	2.01747
$259$	−0.740453	−0.0460095
$260$	38.9207	2.41376
$261$	−6.68512	−0.413798
$262$	−39.8847	−2.46409
$263$	19.3766	1.19481	0.597405	−	0.801940i	$-0.296198\pi$
$263$	19.3766	1.19481	0.597405	+	0.801940i	$0.296198\pi$
$264$	99.9385	6.15079
$265$	20.6087	1.26598
$266$	−1.11291	−0.0682369
$267$	−33.7276	−2.06410
$268$	−75.5525	−4.61510
$269$	−9.60622	−0.585701	−0.292851	−	0.956158i	$-0.594604\pi$
$269$	−9.60622	−0.585701	−0.292851	+	0.956158i	$0.594604\pi$
$270$	30.4522	1.85326
$271$	24.8514	1.50962	0.754808	−	0.655945i	$-0.227730\pi$
$271$	24.8514	1.50962	0.754808	+	0.655945i	$0.227730\pi$
$272$	−39.6285	−2.40283
$273$	−0.307942	−0.0186375
$274$	−7.51794	−0.454176
$275$	−31.5782	−1.90424
$276$	79.2559	4.77064
$277$	9.29688	0.558595	0.279298	−	0.960205i	$-0.409898\pi$
$277$	9.29688	0.558595	0.279298	+	0.960205i	$0.409898\pi$
$278$	8.96046	0.537413
$279$	7.86528	0.470882
$280$	2.33159	0.139339
$281$	7.19069	0.428961	0.214480	−	0.976728i	$-0.431194\pi$
$281$	7.19069	0.428961	0.214480	+	0.976728i	$0.431194\pi$
$282$	74.9902	4.46560
$283$	28.8931	1.71751	0.858757	−	0.512383i	$-0.171237\pi$
$283$	28.8931	1.71751	0.858757	+	0.512383i	$0.171237\pi$
$284$	−5.54775	−0.329198
$285$	−41.0721	−2.43290
$286$	27.6281	1.63368
$287$	0.528616	0.0312032
$288$	−34.2150	−2.01614
$289$	−10.6142	−0.624367
$290$	42.9359	2.52128
$291$	33.3944	1.95761
$292$	−75.3358	−4.40869
$293$	−9.86677	−0.576423	−0.288212	−	0.957567i	$-0.593061\pi$
$293$	−9.86677	−0.576423	−0.288212	+	0.957567i	$0.593061\pi$
$294$	40.5413	2.36442
$295$	−15.0139	−0.874146
$296$	−102.297	−5.94588
$297$	15.8887	0.921956
$298$	55.6895	3.22600
$299$	14.0115	0.810307
$300$	76.0384	4.39008
$301$	0.394463	0.0227365
$302$	−27.7047	−1.59422
$303$	−27.5644	−1.58353
$304$	−90.0441	−5.16439
$305$	−25.5546	−1.46325
$306$	10.0694	0.575632
$307$	−6.05059	−0.345326	−0.172663	−	0.984981i	$-0.555237\pi$
$307$	−6.05059	−0.345326	−0.172663	+	0.984981i	$0.555237\pi$
$308$	1.90233	0.108395
$309$	0.470854	0.0267859
$310$	−50.5156	−2.86910
$311$	−31.6751	−1.79613	−0.898066	−	0.439860i	$-0.855028\pi$
$311$	−31.6751	−1.79613	−0.898066	+	0.439860i	$0.855028\pi$
$312$	−42.5434	−2.40855
$313$	1.83352	0.103637	0.0518183	−	0.998657i	$-0.483498\pi$
$313$	1.83352	0.103637	0.0518183	+	0.998657i	$0.483498\pi$
$314$	−10.3487	−0.584014
$315$	−0.346962	−0.0195491
$316$	51.4614	2.89493
$317$	0.687550	0.0386167	0.0193083	−	0.999814i	$-0.493854\pi$
$317$	0.687550	0.0386167	0.0193083	+	0.999814i	$0.493854\pi$
$318$	−35.2262	−1.97539
$319$	22.4022	1.25428
$320$	113.403	6.33939
$321$	33.0872	1.84675
$322$	1.31257	0.0731465
$323$	14.5097	0.807344
$324$	−62.3985	−3.46659
$325$	13.4427	0.745668
$326$	7.44290	0.412224
$327$	6.71722	0.371463
$328$	73.0305	4.03244
$329$	0.912838	0.0503264
$330$	95.5154	5.25795
$331$	−16.7905	−0.922891	−0.461446	−	0.887168i	$-0.652669\pi$
$331$	−16.7905	−0.922891	−0.461446	+	0.887168i	$0.652669\pi$
$332$	−28.8552	−1.58364
$333$	15.2227	0.834197
$334$	21.8179	1.19382
$335$	−46.1770	−2.52292
$336$	−2.33399	−0.127330
$337$	−0.359970	−0.0196088	−0.00980441	−	0.999952i	$-0.503121\pi$
$337$	−0.359970	−0.0196088	−0.00980441	+	0.999952i	$0.503121\pi$
$338$	23.9540	1.30292
$339$	−2.10960	−0.114578
$340$	−47.5353	−2.57796
$341$	−26.3570	−1.42731
$342$	22.8798	1.23720
$343$	0.987350	0.0533119
$344$	54.4967	2.93826
$345$	48.4404	2.60795
$346$	−39.3427	−2.11508
$347$	28.6773	1.53948	0.769739	−	0.638359i	$-0.220386\pi$
$347$	28.6773	1.53948	0.769739	+	0.638359i	$0.220386\pi$
$348$	−53.9430	−2.89165
$349$	33.5987	1.79850	0.899250	−	0.437435i	$-0.144113\pi$
$349$	33.5987	1.79850	0.899250	+	0.437435i	$0.144113\pi$
$350$	1.25928	0.0673114
$351$	−6.76375	−0.361022
$352$	114.656	6.11119
$353$	35.2677	1.87711	0.938556	−	0.345128i	$-0.112165\pi$
$353$	35.2677	1.87711	0.938556	+	0.345128i	$0.112165\pi$
$354$	25.6632	1.36398
$355$	−3.39073	−0.179961
$356$	−88.6956	−4.70086
$357$	0.376100	0.0199053
$358$	−39.6177	−2.09386
$359$	14.2910	0.754251	0.377126	−	0.926162i	$-0.376912\pi$
$359$	14.2910	0.754251	0.377126	+	0.926162i	$0.376912\pi$
$360$	−47.9342	−2.52635
$361$	13.9691	0.735216
$362$	42.3554	2.22615
$363$	26.6303	1.39773
$364$	−0.809814	−0.0424458
$365$	−46.0445	−2.41008
$366$	43.6802	2.28320
$367$	8.63696	0.450846	0.225423	−	0.974261i	$-0.427624\pi$
$367$	8.63696	0.450846	0.225423	+	0.974261i	$0.427624\pi$
$368$	106.198	5.53596
$369$	−10.8676	−0.565744
$370$	−97.7692	−5.08278
$371$	−0.428800	−0.0222622
$372$	63.4659	3.29056
$373$	−14.4634	−0.748889	−0.374444	−	0.927249i	$-0.622167\pi$
$373$	−14.4634	−0.748889	−0.374444	+	0.927249i	$0.622167\pi$
$374$	−33.7432	−1.74482
$375$	10.7086	0.552987
$376$	126.112	6.50375
$377$	−9.53650	−0.491155
$378$	−0.633612	−0.0325895
$379$	24.0416	1.23494	0.617468	−	0.786596i	$-0.288159\pi$
$379$	24.0416	1.23494	0.617468	+	0.786596i	$0.288159\pi$
$380$	−108.010	−5.54079
$381$	1.18169	0.0605397
$382$	−45.6399	−2.33514
$383$	−24.3095	−1.24216	−0.621079	−	0.783748i	$-0.713305\pi$
$383$	−24.3095	−1.24216	−0.621079	+	0.783748i	$0.713305\pi$
$384$	−94.3072	−4.81260
$385$	1.16269	0.0592559
$386$	−11.5629	−0.588538
$387$	−8.10959	−0.412234
$388$	87.8193	4.45835
$389$	23.7805	1.20572	0.602860	−	0.797847i	$-0.294028\pi$
$389$	23.7805	1.20572	0.602860	+	0.797847i	$0.294028\pi$
$390$	−40.6605	−2.05892
$391$	−17.1128	−0.865431
$392$	68.1790	3.44356
$393$	30.6265	1.54491
$394$	27.9617	1.40869
$395$	31.4527	1.58256
$396$	−39.1092	−1.96531
$397$	−6.58099	−0.330291	−0.165145	−	0.986269i	$-0.552809\pi$
$397$	−6.58099	−0.330291	−0.165145	+	0.986269i	$0.552809\pi$
$398$	9.90422	0.496454
$399$	0.854577	0.0427824
$400$	101.887	5.09435
$401$	−15.2578	−0.761938	−0.380969	−	0.924588i	$-0.624409\pi$
$401$	−15.2578	−0.761938	−0.380969	+	0.924588i	$0.624409\pi$
$402$	78.9298	3.93666
$403$	11.2200	0.558910
$404$	−72.4878	−3.60640
$405$	−38.1374	−1.89506
$406$	−0.893357	−0.0443365
$407$	−51.0119	−2.52857
$408$	51.9598	2.57239
$409$	3.98816	0.197202	0.0986009	−	0.995127i	$-0.468563\pi$
$409$	3.98816	0.197202	0.0986009	+	0.995127i	$0.468563\pi$
$410$	69.7983	3.44709
$411$	5.77285	0.284754
$412$	1.23823	0.0610034
$413$	0.312392	0.0153718
$414$	−26.9845	−1.32621
$415$	−17.6360	−0.865720
$416$	−48.8086	−2.39304
$417$	−6.88053	−0.336941
$418$	−76.6714	−3.75012
$419$	−24.9568	−1.21922	−0.609610	−	0.792701i	$-0.708674\pi$
$419$	−24.9568	−1.21922	−0.609610	+	0.792701i	$0.708674\pi$
$420$	−2.79968	−0.136610
$421$	−25.8614	−1.26041	−0.630205	−	0.776429i	$-0.717029\pi$
$421$	−25.8614	−1.26041	−0.630205	+	0.776429i	$0.717029\pi$
$422$	−7.99206	−0.389047
$423$	−18.7666	−0.912465
$424$	−59.2405	−2.87697
$425$	−16.4181	−0.796394
$426$	5.79574	0.280804
$427$	0.531709	0.0257312
$428$	87.0115	4.20586
$429$	−21.2149	−1.02427
$430$	52.0848	2.51175
$431$	5.08003	0.244697	0.122348	−	0.992487i	$-0.460957\pi$
$431$	5.08003	0.244697	0.122348	+	0.992487i	$0.460957\pi$
$432$	−51.2648	−2.46648
$433$	−6.42184	−0.308614	−0.154307	−	0.988023i	$-0.549314\pi$
$433$	−6.42184	−0.308614	−0.154307	+	0.988023i	$0.549314\pi$
$434$	1.05107	0.0504528
$435$	−32.9694	−1.58076
$436$	17.6647	0.845987
$437$	−38.8838	−1.86006
$438$	78.7034	3.76059
$439$	−10.5406	−0.503078	−0.251539	−	0.967847i	$-0.580937\pi$
$439$	−10.5406	−0.503078	−0.251539	+	0.967847i	$0.580937\pi$
$440$	160.630	7.65773
$441$	−10.1456	−0.483126
$442$	14.3643	0.683242
$443$	−33.0925	−1.57227	−0.786136	−	0.618054i	$-0.787921\pi$
$443$	−33.0925	−1.57227	−0.786136	+	0.618054i	$0.787921\pi$
$444$	122.834	5.82942
$445$	−54.2099	−2.56980
$446$	16.3456	0.773984
$447$	−42.7626	−2.02260
$448$	−2.35954	−0.111478
$449$	33.7618	1.59332	0.796659	−	0.604429i	$-0.206599\pi$
$449$	33.7618	1.59332	0.796659	+	0.604429i	$0.206599\pi$
$450$	−25.8890	−1.22042
$451$	36.4178	1.71485
$452$	−5.54775	−0.260944
$453$	21.2737	0.999528
$454$	−19.4177	−0.911317
$455$	−0.494950	−0.0232036
$456$	118.063	5.52882
$457$	−8.64831	−0.404551	−0.202276	−	0.979329i	$-0.564834\pi$
$457$	−8.64831	−0.404551	−0.202276	+	0.979329i	$0.564834\pi$
$458$	60.7081	2.83670
$459$	8.26082	0.385582
$460$	127.387	5.93945
$461$	−9.86146	−0.459294	−0.229647	−	0.973274i	$-0.573757\pi$
$461$	−9.86146	−0.459294	−0.229647	+	0.973274i	$0.573757\pi$
$462$	−1.98737	−0.0924606
$463$	9.92849	0.461416	0.230708	−	0.973023i	$-0.425896\pi$
$463$	9.92849	0.461416	0.230708	+	0.973023i	$0.425896\pi$
$464$	−72.2804	−3.35553
$465$	38.7898	1.79883
$466$	63.8474	2.95767
$467$	−31.1371	−1.44085	−0.720427	−	0.693530i	$-0.756054\pi$
$467$	−31.1371	−1.44085	−0.720427	+	0.693530i	$0.756054\pi$
$468$	16.6486	0.769582
$469$	0.960793	0.0443653
$470$	120.531	5.55967
$471$	7.94656	0.366158
$472$	43.1582	1.98652
$473$	27.1756	1.24954
$474$	−53.7618	−2.46936
$475$	−37.3053	−1.71168
$476$	0.989055	0.0453333
$477$	8.81552	0.403635
$478$	28.6624	1.31099
$479$	3.21017	0.146676	0.0733382	−	0.997307i	$-0.476635\pi$
$479$	3.21017	0.146676	0.0733382	+	0.997307i	$0.476635\pi$
$480$	−168.740	−7.70191
$481$	21.7155	0.990143
$482$	−61.7772	−2.81388
$483$	−1.00789	−0.0458605
$484$	70.0315	3.18325
$485$	53.6743	2.43722
$486$	38.2447	1.73482
$487$	35.6704	1.61638	0.808189	−	0.588923i	$-0.200448\pi$
$487$	35.6704	1.61638	0.808189	+	0.588923i	$0.200448\pi$
$488$	73.4578	3.32528
$489$	−5.71523	−0.258452
$490$	65.1615	2.94370
$491$	15.2861	0.689854	0.344927	−	0.938629i	$-0.387904\pi$
$491$	15.2861	0.689854	0.344927	+	0.938629i	$0.387904\pi$
$492$	−87.6919	−3.95346
$493$	11.6473	0.524567
$494$	32.6387	1.46848
$495$	−23.9032	−1.07437
$496$	85.0405	3.81843
$497$	0.0705501	0.00316460
$498$	30.1451	1.35083
$499$	27.4267	1.22779	0.613893	−	0.789389i	$-0.289603\pi$
$499$	27.4267	1.22779	0.613893	+	0.789389i	$0.289603\pi$
$500$	28.1610	1.25940
$501$	−16.7534	−0.748488
$502$	−16.6424	−0.742785
$503$	−27.3541	−1.21966	−0.609831	−	0.792532i	$-0.708762\pi$
$503$	−27.3541	−1.21966	−0.609831	+	0.792532i	$0.708762\pi$
$504$	0.997355	0.0444257
$505$	−44.3038	−1.97149
$506$	90.4263	4.01994
$507$	−18.3937	−0.816892
$508$	3.10756	0.137876
$509$	5.98267	0.265177	0.132589	−	0.991171i	$-0.457671\pi$
$509$	5.98267	0.265177	0.132589	+	0.991171i	$0.457671\pi$
$510$	49.6602	2.19899
$511$	0.958037	0.0423811
$512$	−64.2385	−2.83897
$513$	18.7703	0.828728
$514$	42.3778	1.86920
$515$	0.756797	0.0333484
$516$	−65.4373	−2.88072
$517$	62.8879	2.76581
$518$	2.03426	0.0893803
$519$	30.2103	1.32609
$520$	−68.3794	−2.99864
$521$	−23.9557	−1.04952	−0.524758	−	0.851251i	$-0.675844\pi$
$521$	−23.9557	−1.04952	−0.524758	+	0.851251i	$0.675844\pi$
$522$	18.3661	0.803864
$523$	39.7192	1.73680	0.868400	−	0.495864i	$-0.165149\pi$
$523$	39.7192	1.73680	0.868400	+	0.495864i	$0.165149\pi$
$524$	80.5406	3.51843
$525$	−0.966973	−0.0422021
$526$	−53.2336	−2.32109
$527$	−13.7035	−0.596932
$528$	−160.795	−6.99772
$529$	22.8595	0.993893
$530$	−56.6186	−2.45936
$531$	−6.42232	−0.278705
$532$	2.24734	0.0974344
$533$	−15.5029	−0.671506
$534$	92.6604	4.00981
$535$	53.1806	2.29920
$536$	132.738	5.73339
$537$	30.4215	1.31279
$538$	26.3913	1.13781
$539$	33.9986	1.46442
$540$	−61.4932	−2.64625
$541$	−18.6229	−0.800659	−0.400330	−	0.916371i	$-0.631104\pi$
$541$	−18.6229	−0.800659	−0.400330	+	0.916371i	$0.631104\pi$
$542$	−68.2747	−2.93265
$543$	−32.5237	−1.39572
$544$	59.6118	2.55583
$545$	10.7965	0.462471
$546$	0.846013	0.0362060
$547$	−19.5826	−0.837293	−0.418646	−	0.908149i	$-0.637495\pi$
$547$	−19.5826	−0.837293	−0.418646	+	0.908149i	$0.637495\pi$
$548$	15.1812	0.648510
$549$	−10.9312	−0.466531
$550$	86.7554	3.69926
$551$	26.4650	1.12745
$552$	−139.244	−5.92662
$553$	−0.654429	−0.0278292
$554$	−25.5415	−1.08515
$555$	75.0747	3.18674
$556$	−18.0942	−0.767364
$557$	−22.1231	−0.937384	−0.468692	−	0.883362i	$-0.655275\pi$
$557$	−22.1231	−0.937384	−0.468692	+	0.883362i	$0.655275\pi$
$558$	−21.6084	−0.914758
$559$	−11.5686	−0.489298
$560$	−3.75140	−0.158525
$561$	25.9106	1.09395
$562$	−19.7551	−0.833319
$563$	8.51277	0.358770	0.179385	−	0.983779i	$-0.442589\pi$
$563$	8.51277	0.358770	0.179385	+	0.983779i	$0.442589\pi$
$564$	−151.430	−6.37637
$565$	−3.39073	−0.142649
$566$	−79.3784	−3.33652
$567$	0.793515	0.0333245
$568$	9.74679	0.408966
$569$	0.332793	0.0139514	0.00697571	−	0.999976i	$-0.497780\pi$
$569$	0.332793	0.0139514	0.00697571	+	0.999976i	$0.497780\pi$
$570$	112.838	4.72626
$571$	−38.5420	−1.61293	−0.806466	−	0.591280i	$-0.798623\pi$
$571$	−38.5420	−1.61293	−0.806466	+	0.591280i	$0.798623\pi$
$572$	−55.7903	−2.33271
$573$	35.0458	1.46406
$574$	−1.45228	−0.0606168
$575$	43.9978	1.83484
$576$	48.5087	2.02120
$577$	−5.33205	−0.221976	−0.110988	−	0.993822i	$-0.535402\pi$
$577$	−5.33205	−0.221976	−0.110988	+	0.993822i	$0.535402\pi$
$578$	29.1607	1.21292
$579$	8.87890	0.368994
$580$	−86.7019	−3.60010
$581$	0.366949	0.0152236
$582$	−91.7449	−3.80295
$583$	−29.5412	−1.22347
$584$	132.357	5.47696
$585$	10.1755	0.420704
$586$	27.1072	1.11979
$587$	10.8665	0.448508	0.224254	−	0.974531i	$-0.428005\pi$
$587$	10.8665	0.448508	0.224254	+	0.974531i	$0.428005\pi$
$588$	−81.8664	−3.37611
$589$	−31.1370	−1.28298
$590$	41.2481	1.69816
$591$	−21.4711	−0.883203
$592$	164.589	6.76459
$593$	−37.5761	−1.54306	−0.771532	−	0.636191i	$-0.780509\pi$
$593$	−37.5761	−1.54306	−0.771532	+	0.636191i	$0.780509\pi$
$594$	−43.6513	−1.79103
$595$	0.604501	0.0247821
$596$	−112.456	−4.60636
$597$	−7.60522	−0.311261
$598$	−38.4941	−1.57414
$599$	−19.8467	−0.810915	−0.405457	−	0.914114i	$-0.632888\pi$
$599$	−19.8467	−0.810915	−0.405457	+	0.914114i	$0.632888\pi$
$600$	−133.591	−5.45384
$601$	10.5686	0.431102	0.215551	−	0.976493i	$-0.430845\pi$
$601$	10.5686	0.431102	0.215551	+	0.976493i	$0.430845\pi$
$602$	−1.08371	−0.0441689
$603$	−19.7525	−0.804385
$604$	55.9449	2.27637
$605$	42.8026	1.74017
$606$	75.7280	3.07624
$607$	−3.58851	−0.145653	−0.0728266	−	0.997345i	$-0.523202\pi$
$607$	−3.58851	−0.145653	−0.0728266	+	0.997345i	$0.523202\pi$
$608$	135.450	5.49323
$609$	0.685987	0.0277976
$610$	70.2066	2.84258
$611$	−26.7711	−1.08304
$612$	−20.3336	−0.821935
$613$	20.0533	0.809946	0.404973	−	0.914329i	$-0.367281\pi$
$613$	20.0533	0.809946	0.404973	+	0.914329i	$0.367281\pi$
$614$	16.6229	0.670845
$615$	−53.5965	−2.16122
$616$	−3.34219	−0.134661
$617$	−4.62763	−0.186301	−0.0931507	−	0.995652i	$-0.529694\pi$
$617$	−4.62763	−0.186301	−0.0931507	+	0.995652i	$0.529694\pi$
$618$	−1.29358	−0.0520356
$619$	−47.2965	−1.90101	−0.950504	−	0.310712i	$-0.899432\pi$
$619$	−47.2965	−1.90101	−0.950504	+	0.310712i	$0.899432\pi$
$620$	102.008	4.09674
$621$	−22.1377	−0.888354
$622$	87.0216	3.48925
$623$	1.12793	0.0451897
$624$	68.4499	2.74019
$625$	−15.2736	−0.610942
$626$	−5.03725	−0.201329
$627$	58.8742	2.35121
$628$	20.8976	0.833904
$629$	−26.5220	−1.05750
$630$	0.953214	0.0379769
$631$	11.1329	0.443193	0.221596	−	0.975138i	$-0.428873\pi$
$631$	11.1329	0.443193	0.221596	+	0.975138i	$0.428873\pi$
$632$	−90.4121	−3.59640
$633$	6.13691	0.243920
$634$	−1.88892	−0.0750185
$635$	1.89931	0.0753719
$636$	71.1335	2.82063
$637$	−14.4730	−0.573443
$638$	−61.5458	−2.43662
$639$	−1.45041	−0.0573773
$640$	−151.579	−5.99168
$641$	−3.23752	−0.127874	−0.0639371	−	0.997954i	$-0.520366\pi$
$641$	−3.23752	−0.127874	−0.0639371	+	0.997954i	$0.520366\pi$
$642$	−90.9010	−3.58758
$643$	−32.8030	−1.29362	−0.646811	−	0.762650i	$-0.723898\pi$
$643$	−32.8030	−1.29362	−0.646811	+	0.762650i	$0.723898\pi$
$644$	−2.65051	−0.104445
$645$	−39.9946	−1.57479
$646$	−39.8628	−1.56838
$647$	24.5601	0.965557	0.482778	−	0.875743i	$-0.339628\pi$
$647$	24.5601	0.965557	0.482778	+	0.875743i	$0.339628\pi$
$648$	109.627	4.30657
$649$	21.5215	0.844794
$650$	−36.9314	−1.44857
$651$	−0.807089	−0.0316323
$652$	−15.0297	−0.588608
$653$	−13.9745	−0.546864	−0.273432	−	0.961891i	$-0.588159\pi$
$653$	−13.9745	−0.546864	−0.273432	+	0.961891i	$0.588159\pi$
$654$	−18.4543	−0.721622
$655$	49.2256	1.92340
$656$	−117.502	−4.58768
$657$	−19.6959	−0.768409
$658$	−2.50785	−0.0977664
$659$	2.28226	0.0889043	0.0444522	−	0.999012i	$-0.485846\pi$
$659$	2.28226	0.0889043	0.0444522	+	0.999012i	$0.485846\pi$
$660$	−192.877	−7.50774
$661$	−49.1212	−1.91059	−0.955296	−	0.295651i	$-0.904464\pi$
$661$	−49.1212	−1.91059	−0.955296	+	0.295651i	$0.904464\pi$
$662$	46.1289	1.79285
$663$	−11.0300	−0.428371
$664$	50.6955	1.96737
$665$	1.37355	0.0532640
$666$	−41.8215	−1.62055
$667$	−31.2128	−1.20857
$668$	−44.0576	−1.70464
$669$	−12.5514	−0.485264
$670$	126.863	4.90114
$671$	36.6309	1.41412
$672$	3.51094	0.135438
$673$	−4.02890	−0.155303	−0.0776513	−	0.996981i	$-0.524742\pi$
$673$	−4.02890	−0.155303	−0.0776513	+	0.996981i	$0.524742\pi$
$674$	0.988952	0.0380930
$675$	−21.2390	−0.817488
$676$	−48.3710	−1.86042
$677$	−33.5593	−1.28979	−0.644895	−	0.764272i	$-0.723099\pi$
$677$	−33.5593	−1.28979	−0.644895	+	0.764272i	$0.723099\pi$
$678$	5.79574	0.222584
$679$	−1.11679	−0.0428584
$680$	83.5143	3.20263
$681$	14.9104	0.571367
$682$	72.4109	2.77276
$683$	46.5275	1.78033	0.890163	−	0.455643i	$-0.150591\pi$
$683$	46.5275	1.78033	0.890163	+	0.455643i	$0.150591\pi$
$684$	−46.2020	−1.76658
$685$	9.27863	0.354518
$686$	−2.71256	−0.103566
$687$	−46.6163	−1.77852
$688$	−87.6820	−3.34285
$689$	12.5756	0.479091
$690$	−133.081	−5.06632
$691$	−16.8527	−0.641108	−0.320554	−	0.947230i	$-0.603869\pi$
$691$	−16.8527	−0.641108	−0.320554	+	0.947230i	$0.603869\pi$
$692$	79.4460	3.02008
$693$	0.497347	0.0188927
$694$	−78.7856	−2.99066
$695$	−11.0590	−0.419491
$696$	94.7720	3.59232
$697$	18.9343	0.717187
$698$	−92.3064	−3.49385
$699$	−49.0269	−1.85437
$700$	−2.54291	−0.0961130
$701$	−2.05005	−0.0774295	−0.0387147	−	0.999250i	$-0.512326\pi$
$701$	−2.05005	−0.0774295	−0.0387147	+	0.999250i	$0.512326\pi$
$702$	18.5822	0.701339
$703$	−60.2634	−2.27288
$704$	−162.555	−6.12653
$705$	−92.5527	−3.48574
$706$	−96.8916	−3.64656
$707$	0.921819	0.0346686
$708$	−51.8225	−1.94761
$709$	27.2969	1.02516	0.512579	−	0.858640i	$-0.328690\pi$
$709$	27.2969	1.02516	0.512579	+	0.858640i	$0.328690\pi$
$710$	9.31541	0.349601
$711$	13.4541	0.504569
$712$	155.829	5.83992
$713$	36.7231	1.37529
$714$	−1.03327	−0.0386690
$715$	−34.0985	−1.27521
$716$	80.0014	2.98979
$717$	−22.0092	−0.821947
$718$	−39.2620	−1.46524
$719$	25.5237	0.951875	0.475938	−	0.879479i	$-0.342109\pi$
$719$	25.5237	0.951875	0.475938	+	0.879479i	$0.342109\pi$
$720$	77.1233	2.87422
$721$	−0.0157465	−0.000586430 0
$722$	−38.3775	−1.42826
$723$	47.4373	1.76421
$724$	−85.5296	−3.17868
$725$	−29.9457	−1.11216
$726$	−73.1620	−2.71530
$727$	28.2944	1.04938	0.524691	−	0.851293i	$-0.324181\pi$
$727$	28.2944	1.04938	0.524691	+	0.851293i	$0.324181\pi$
$728$	1.42275	0.0527308
$729$	4.37541	0.162052
$730$	126.499	4.68193
$731$	14.1291	0.522584
$732$	−88.2049	−3.26015
$733$	32.2757	1.19213	0.596066	−	0.802936i	$-0.296730\pi$
$733$	32.2757	1.19213	0.596066	+	0.802936i	$0.296730\pi$
$734$	−23.7285	−0.875833
$735$	−50.0360	−1.84560
$736$	−159.750	−5.88846
$737$	66.1917	2.43820
$738$	29.8567	1.09904
$739$	36.0417	1.32581	0.662907	−	0.748701i	$-0.269322\pi$
$739$	36.0417	1.32581	0.662907	+	0.748701i	$0.269322\pi$
$740$	197.429	7.25762
$741$	−25.0625	−0.920693
$742$	1.17805	0.0432476
$743$	25.9553	0.952208	0.476104	−	0.879389i	$-0.342049\pi$
$743$	25.9553	0.952208	0.476104	+	0.879389i	$0.342049\pi$
$744$	−111.503	−4.08789
$745$	−68.7318	−2.51814
$746$	39.7357	1.45483
$747$	−7.54395	−0.276019
$748$	68.1388	2.49140
$749$	−1.10652	−0.0404312
$750$	−29.4198	−1.07426
$751$	25.0095	0.912610	0.456305	−	0.889823i	$-0.349173\pi$
$751$	25.0095	0.912610	0.456305	+	0.889823i	$0.349173\pi$
$752$	−202.907	−7.39927
$753$	12.7793	0.465703
$754$	26.1998	0.954140
$755$	34.1930	1.24441
$756$	1.27947	0.0465340
$757$	−49.1146	−1.78510	−0.892551	−	0.450947i	$-0.851086\pi$
$757$	−49.1146	−1.78510	−0.892551	+	0.450947i	$0.851086\pi$
$758$	−66.0499	−2.39904
$759$	−69.4362	−2.52038
$760$	189.762	6.88338
$761$	−39.9875	−1.44955	−0.724774	−	0.688987i	$-0.758056\pi$
$761$	−39.9875	−1.44955	−0.724774	+	0.688987i	$0.758056\pi$
$762$	−3.24647	−0.117607
$763$	−0.224640	−0.00813252
$764$	92.1621	3.33431
$765$	−12.4277	−0.449324
$766$	66.7859	2.41307
$767$	−9.16162	−0.330807
$768$	117.981	4.25728
$769$	−5.27196	−0.190112	−0.0950558	−	0.995472i	$-0.530303\pi$
$769$	−5.27196	−0.190112	−0.0950558	+	0.995472i	$0.530303\pi$
$770$	−3.19427	−0.115113
$771$	−32.5409	−1.17193
$772$	23.3494	0.840364
$773$	−41.5028	−1.49275	−0.746377	−	0.665524i	$-0.768208\pi$
$773$	−41.5028	−1.49275	−0.746377	+	0.665524i	$0.768208\pi$
$774$	22.2796	0.800824
$775$	35.2322	1.26558
$776$	−154.289	−5.53865
$777$	−1.56206	−0.0560386
$778$	−65.3326	−2.34229
$779$	43.0226	1.54144
$780$	82.1071	2.93991
$781$	4.86039	0.173919
$782$	47.0143	1.68123
$783$	15.0673	0.538461
$784$	−109.696	−3.91772
$785$	12.7724	0.455866
$786$	−84.1408	−3.00120
$787$	−34.8188	−1.24116	−0.620578	−	0.784145i	$-0.713102\pi$
$787$	−34.8188	−1.24116	−0.620578	+	0.784145i	$0.713102\pi$
$788$	−56.4639	−2.01144
$789$	40.8768	1.45525
$790$	−86.4106	−3.07435
$791$	0.0705501	0.00250847
$792$	68.7106	2.44152
$793$	−15.5936	−0.553745
$794$	18.0801	0.641638
$795$	43.4761	1.54194
$796$	−19.9999	−0.708879
$797$	−35.7960	−1.26796	−0.633980	−	0.773349i	$-0.718580\pi$
$797$	−35.7960	−1.26796	−0.633980	+	0.773349i	$0.718580\pi$
$798$	−2.34779	−0.0831110
$799$	32.6966	1.15672
$800$	−153.265	−5.41873
$801$	−23.1887	−0.819331
$802$	41.9180	1.48018
$803$	66.0018	2.32915
$804$	−159.386	−5.62109
$805$	−1.61997	−0.0570963
$806$	−30.8250	−1.08576
$807$	−20.2653	−0.713371
$808$	127.353	4.48027
$809$	−2.93962	−0.103351	−0.0516757	−	0.998664i	$-0.516456\pi$
$809$	−2.93962	−0.103351	−0.0516757	+	0.998664i	$0.516456\pi$
$810$	104.775	3.68143
$811$	−26.0315	−0.914091	−0.457045	−	0.889443i	$-0.651092\pi$
$811$	−26.0315	−0.914091	−0.457045	+	0.889443i	$0.651092\pi$
$812$	1.80398	0.0633075
$813$	52.4265	1.83868
$814$	140.146	4.91211
$815$	−9.18601	−0.321772
$816$	−83.6003	−2.92660
$817$	32.1042	1.12318
$818$	−10.9567	−0.383094
$819$	−0.211718	−0.00739804
$820$	−140.946	−4.92205
$821$	20.9181	0.730048	0.365024	−	0.930998i	$-0.381061\pi$
$821$	20.9181	0.730048	0.365024	+	0.930998i	$0.381061\pi$
$822$	−15.8599	−0.553176
$823$	−29.2742	−1.02043	−0.510217	−	0.860046i	$-0.670435\pi$
$823$	−29.2742	−1.02043	−0.510217	+	0.860046i	$0.670435\pi$
$824$	−2.17544	−0.0757851
$825$	−66.6174	−2.31932
$826$	−0.858239	−0.0298619
$827$	23.2797	0.809516	0.404758	−	0.914424i	$-0.367356\pi$
$827$	23.2797	0.809516	0.404758	+	0.914424i	$0.367356\pi$
$828$	54.4907	1.89368
$829$	35.9960	1.25019	0.625096	−	0.780548i	$-0.285060\pi$
$829$	35.9960	1.25019	0.625096	+	0.780548i	$0.285060\pi$
$830$	48.4518	1.68179
$831$	19.6127	0.680357
$832$	69.1990	2.39905
$833$	17.6765	0.612453
$834$	18.9030	0.654557
$835$	−26.9276	−0.931867
$836$	154.825	5.35474
$837$	−17.7272	−0.612743
$838$	68.5643	2.36851
$839$	21.5665	0.744558	0.372279	−	0.928121i	$-0.378576\pi$
$839$	21.5665	0.744558	0.372279	+	0.928121i	$0.378576\pi$
$840$	4.91872	0.169712
$841$	−7.75597	−0.267447
$842$	71.0496	2.44853
$843$	15.1695	0.522465
$844$	16.1386	0.555515
$845$	−29.5639	−1.01703
$846$	51.5579	1.77260
$847$	−0.890583	−0.0306008
$848$	95.3146	3.27312
$849$	60.9528	2.09189
$850$	45.1057	1.54711
$851$	71.0747	2.43641
$852$	−11.7035	−0.400956
$853$	6.56556	0.224800	0.112400	−	0.993663i	$-0.464146\pi$
$853$	6.56556	0.224800	0.112400	+	0.993663i	$0.464146\pi$
$854$	−1.46077	−0.0499866
$855$	−28.2382	−0.965727
$856$	−152.870	−5.22498
$857$	−25.9975	−0.888057	−0.444029	−	0.896013i	$-0.646451\pi$
$857$	−25.9975	−0.888057	−0.444029	+	0.896013i	$0.646451\pi$
$858$	58.2842	1.98979
$859$	27.9677	0.954246	0.477123	−	0.878837i	$-0.341680\pi$
$859$	27.9677	0.954246	0.477123	+	0.878837i	$0.341680\pi$
$860$	−105.176	−3.58649
$861$	1.11517	0.0380048
$862$	−13.9565	−0.475359
$863$	−19.9730	−0.679889	−0.339944	−	0.940446i	$-0.610408\pi$
$863$	−19.9730	−0.679889	−0.339944	+	0.940446i	$0.610408\pi$
$864$	77.1157	2.62353
$865$	48.5566	1.65097
$866$	17.6428	0.599528
$867$	−22.3918	−0.760466
$868$	−2.12245	−0.0720408
$869$	−45.0855	−1.52942
$870$	90.5775	3.07087
$871$	−28.1775	−0.954759
$872$	−31.0350	−1.05098
$873$	22.9596	0.777064
$874$	106.826	3.61344
$875$	−0.358120	−0.0121067
$876$	−158.928	−5.36969
$877$	6.70562	0.226433	0.113216	−	0.993570i	$-0.463885\pi$
$877$	6.70562	0.226433	0.113216	+	0.993570i	$0.463885\pi$
$878$	28.9585	0.977302
$879$	−20.8149	−0.702070
$880$	−258.444	−8.71215
$881$	−9.70235	−0.326880	−0.163440	−	0.986553i	$-0.552259\pi$
$881$	−9.70235	−0.326880	−0.163440	+	0.986553i	$0.552259\pi$
$882$	27.8733	0.938543
$883$	39.7784	1.33865	0.669325	−	0.742970i	$-0.266583\pi$
$883$	39.7784	1.33865	0.669325	+	0.742970i	$0.266583\pi$
$884$	−29.0064	−0.975590
$885$	−31.6734	−1.06469
$886$	90.9156	3.05437
$887$	2.06359	0.0692885	0.0346442	−	0.999400i	$-0.488970\pi$
$887$	2.06359	0.0692885	0.0346442	+	0.999400i	$0.488970\pi$
$888$	−215.805	−7.24194
$889$	−0.0395185	−0.00132541
$890$	148.932	4.99220
$891$	54.6675	1.83143
$892$	−33.0071	−1.10516
$893$	74.2933	2.48613
$894$	117.482	3.92920
$895$	48.8961	1.63442
$896$	3.15386	0.105363
$897$	29.5587	0.986936
$898$	−92.7543	−3.09525
$899$	−24.9944	−0.833609
$900$	52.2786	1.74262
$901$	−15.3590	−0.511683
$902$	−100.051	−3.33135
$903$	0.832159	0.0276925
$904$	9.74679	0.324173
$905$	−52.2749	−1.73768
$906$	−58.4457	−1.94173
$907$	−17.4025	−0.577841	−0.288921	−	0.957353i	$-0.593296\pi$
$907$	−17.4025	−0.577841	−0.288921	+	0.957353i	$0.593296\pi$
$908$	39.2108	1.30126
$909$	−18.9513	−0.628574
$910$	1.35979	0.0450764
$911$	−30.5724	−1.01291	−0.506455	−	0.862267i	$-0.669044\pi$
$911$	−30.5724	−1.01291	−0.506455	+	0.862267i	$0.669044\pi$
$912$	−189.957	−6.29011
$913$	25.2801	0.836650
$914$	23.7597	0.785900
$915$	−53.9100	−1.78221
$916$	−122.590	−4.05049
$917$	−1.02423	−0.0338229
$918$	−22.6951	−0.749049
$919$	50.4772	1.66509	0.832544	−	0.553958i	$-0.186883\pi$
$919$	50.4772	1.66509	0.832544	+	0.553958i	$0.186883\pi$
$920$	−223.805	−7.37863
$921$	−12.7643	−0.420599
$922$	27.0926	0.892246
$923$	−2.06905	−0.0681035
$924$	4.01315	0.132023
$925$	68.1894	2.24205
$926$	−27.2767	−0.896368
$927$	0.323725	0.0106325
$928$	108.729	3.56920
$929$	−23.5744	−0.773452	−0.386726	−	0.922195i	$-0.626394\pi$
$929$	−23.5744	−0.773452	−0.386726	+	0.922195i	$0.626394\pi$
$930$	−106.568	−3.49449
$931$	40.1645	1.31634
$932$	−128.929	−4.22322
$933$	−66.8218	−2.18765
$934$	85.5436	2.79907
$935$	41.6458	1.36196
$936$	−29.2498	−0.956059
$937$	11.9325	0.389819	0.194909	−	0.980821i	$-0.437559\pi$
$937$	11.9325	0.389819	0.194909	+	0.980821i	$0.437559\pi$
$938$	−2.63960	−0.0861861
$939$	3.86799	0.126227
$940$	−243.392	−7.93857
$941$	7.70366	0.251132	0.125566	−	0.992085i	$-0.459925\pi$
$941$	7.70366	0.251132	0.125566	+	0.992085i	$0.459925\pi$
$942$	−21.8317	−0.711316
$943$	−50.7409	−1.65235
$944$	−69.4390	−2.26005
$945$	0.782002	0.0254385
$946$	−74.6601	−2.42741
$947$	−28.5590	−0.928043	−0.464022	−	0.885824i	$-0.653594\pi$
$947$	−28.5590	−0.928043	−0.464022	+	0.885824i	$0.653594\pi$
$948$	108.563	3.52596
$949$	−28.0967	−0.912057
$950$	102.489	3.32519
$951$	1.45046	0.0470342
$952$	−1.73766	−0.0563180
$953$	−30.7035	−0.994584	−0.497292	−	0.867583i	$-0.665672\pi$
$953$	−30.7035	−0.994584	−0.497292	+	0.867583i	$0.665672\pi$
$954$	−24.2190	−0.784120
$955$	56.3286	1.82275
$956$	−57.8789	−1.87194
$957$	47.2596	1.52768
$958$	−8.81935	−0.284940
$959$	−0.193058	−0.00623417
$960$	239.234	7.72124
$961$	−1.59320	−0.0513935
$962$	−59.6595	−1.92350
$963$	22.7484	0.733056
$964$	124.749	4.01789
$965$	14.2709	0.459398
$966$	2.76899	0.0890908
$967$	−56.8044	−1.82671	−0.913353	−	0.407169i	$-0.866516\pi$
$967$	−56.8044	−1.82671	−0.913353	+	0.407169i	$0.866516\pi$
$968$	−123.038	−3.95458
$969$	30.6097	0.983326
$970$	−147.460	−4.73467
$971$	28.8651	0.926326	0.463163	−	0.886273i	$-0.346714\pi$
$971$	28.8651	0.926326	0.463163	+	0.886273i	$0.346714\pi$
$972$	−77.2289	−2.47712
$973$	0.230102	0.00737672
$974$	−97.9978	−3.14005
$975$	28.3587	0.908207
$976$	−118.189	−3.78315
$977$	−38.7301	−1.23909	−0.619543	−	0.784962i	$-0.712682\pi$
$977$	−38.7301	−1.23909	−0.619543	+	0.784962i	$0.712682\pi$
$978$	15.7015	0.502080
$979$	77.7064	2.48351
$980$	−131.583	−4.20326
$981$	4.61828	0.147450
$982$	−41.9959	−1.34014
$983$	−26.2927	−0.838608	−0.419304	−	0.907846i	$-0.637726\pi$
$983$	−26.2927	−0.838608	−0.419304	+	0.907846i	$0.637726\pi$
$984$	154.065	4.91142
$985$	−34.5102	−1.09959
$986$	−31.9988	−1.01905
$987$	1.92572	0.0612964
$988$	−65.9084	−2.09683
$989$	−37.8637	−1.20400
$990$	65.6695	2.08711
$991$	35.5457	1.12915	0.564573	−	0.825383i	$-0.309041\pi$
$991$	35.5457	1.12915	0.564573	+	0.825383i	$0.309041\pi$
$992$	−127.923	−4.06157
$993$	−35.4213	−1.12406
$994$	−0.193823	−0.00614771
$995$	−12.2238	−0.387519
$996$	−60.8730	−1.92884
$997$	31.8339	1.00819	0.504095	−	0.863648i	$-0.331826\pi$
$997$	31.8339	1.00819	0.504095	+	0.863648i	$0.331826\pi$
$998$	−75.3497	−2.38515
$999$	−34.3097	−1.08551

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8023.2.a.c.1.4	✓	158

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8023.2.a.c.1.4	✓	158	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:	\( N \)	\(=\)	\( 8023 = 71 \cdot 113 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8023.a (trivial)

\(f(q)\)	\(=\)	\(q-2.74732 q^{2} +2.10960 q^{3} +5.54775 q^{4} +3.39073 q^{5} -5.79574 q^{6} -0.0705501 q^{7} -9.74679 q^{8} +1.45041 q^{9} +O(q^{10})\)	\(q-2.74732 q^{2} +2.10960 q^{3} +5.54775 q^{4} +3.39073 q^{5} -5.79574 q^{6} -0.0705501 q^{7} -9.74679 q^{8} +1.45041 q^{9} -9.31541 q^{10} -4.86039 q^{11} +11.7035 q^{12} +2.06905 q^{13} +0.193823 q^{14} +7.15308 q^{15} +15.6820 q^{16} -2.52700 q^{17} -3.98473 q^{18} -5.74187 q^{19} +18.8109 q^{20} -0.148832 q^{21} +13.3530 q^{22} +6.77197 q^{23} -20.5618 q^{24} +6.49705 q^{25} -5.68433 q^{26} -3.26902 q^{27} -0.391394 q^{28} -4.60912 q^{29} -19.6518 q^{30} +5.42280 q^{31} -23.5899 q^{32} -10.2535 q^{33} +6.94248 q^{34} -0.239216 q^{35} +8.04651 q^{36} +10.4954 q^{37} +15.7747 q^{38} +4.36486 q^{39} -33.0487 q^{40} -7.49278 q^{41} +0.408890 q^{42} -5.59125 q^{43} -26.9642 q^{44} +4.91795 q^{45} -18.6047 q^{46} -12.9389 q^{47} +33.0828 q^{48} -6.99502 q^{49} -17.8495 q^{50} -5.33097 q^{51} +11.4786 q^{52} +6.07795 q^{53} +8.98102 q^{54} -16.4803 q^{55} +0.687637 q^{56} -12.1130 q^{57} +12.6627 q^{58} -4.42794 q^{59} +39.6835 q^{60} -7.53661 q^{61} -14.8982 q^{62} -0.102327 q^{63} +33.4449 q^{64} +7.01558 q^{65} +28.1696 q^{66} -13.6186 q^{67} -14.0192 q^{68} +14.2861 q^{69} +0.657203 q^{70} -1.00000 q^{71} -14.1368 q^{72} -13.5795 q^{73} -28.8343 q^{74} +13.7062 q^{75} -31.8545 q^{76} +0.342901 q^{77} -11.9917 q^{78} +9.27609 q^{79} +53.1735 q^{80} -11.2475 q^{81} +20.5850 q^{82} -5.20125 q^{83} -0.825685 q^{84} -8.56839 q^{85} +15.3609 q^{86} -9.72341 q^{87} +47.3732 q^{88} -15.9877 q^{89} -13.5112 q^{90} -0.145972 q^{91} +37.5692 q^{92} +11.4399 q^{93} +35.5471 q^{94} -19.4691 q^{95} -49.7652 q^{96} +15.8297 q^{97} +19.2175 q^{98} -7.04956 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 158 q - 24 q^{2} - 23 q^{3} + 158 q^{4} - 31 q^{5} - 17 q^{6} - 2 q^{7} - 69 q^{8} + 135 q^{9}+O(q^{10}) \) 158 * q - 24 * q^2 - 23 * q^3 + 158 * q^4 - 31 * q^5 - 17 * q^6 - 2 * q^7 - 69 * q^8 + 135 * q^9	\( 158 q - 24 q^{2} - 23 q^{3} + 158 q^{4} - 31 q^{5} - 17 q^{6} - 2 q^{7} - 69 q^{8} + 135 q^{9} - 10 q^{10} - 10 q^{11} - 46 q^{12} - 28 q^{13} - 27 q^{14} - 41 q^{15} + 150 q^{16} - 137 q^{17} - 67 q^{18} - 42 q^{19} - 66 q^{20} - 46 q^{21} - 8 q^{22} - 26 q^{23} - 48 q^{24} + 129 q^{25} - 67 q^{26} - 89 q^{27} - 21 q^{28} - 79 q^{29} - 11 q^{30} + 7 q^{31} - 147 q^{32} - 112 q^{33} - 28 q^{34} - 53 q^{35} + 141 q^{36} - 60 q^{37} - 53 q^{38} - 3 q^{39} - 48 q^{40} - 128 q^{41} + 32 q^{42} - 63 q^{43} - 88 q^{45} - 2 q^{46} - 92 q^{47} - 131 q^{48} + 122 q^{49} - 116 q^{50} - 12 q^{51} - 89 q^{52} - 94 q^{53} - 71 q^{54} - 12 q^{55} - 104 q^{56} - 93 q^{57} - 65 q^{58} - 54 q^{59} - 12 q^{60} + 17 q^{61} - 97 q^{62} - 28 q^{63} + 163 q^{64} - 163 q^{65} - 65 q^{66} - 35 q^{67} - 217 q^{68} - 46 q^{69} - 79 q^{70} - 158 q^{71} - 99 q^{72} - 165 q^{73} - 94 q^{75} - 93 q^{76} - 140 q^{77} + 25 q^{78} - 61 q^{79} - 134 q^{80} + 114 q^{81} + 10 q^{82} - 158 q^{83} - 160 q^{84} + 23 q^{85} - 122 q^{86} - 71 q^{87} - 14 q^{88} - 251 q^{89} - 6 q^{90} - 57 q^{91} - 58 q^{92} - 52 q^{93} - 64 q^{94} - 84 q^{95} - 98 q^{96} - 48 q^{97} - 84 q^{98} + 85 q^{99}+O(q^{100}) \) 158 * q - 24 * q^2 - 23 * q^3 + 158 * q^4 - 31 * q^5 - 17 * q^6 - 2 * q^7 - 69 * q^8 + 135 * q^9 - 10 * q^10 - 10 * q^11 - 46 * q^12 - 28 * q^13 - 27 * q^14 - 41 * q^15 + 150 * q^16 - 137 * q^17 - 67 * q^18 - 42 * q^19 - 66 * q^20 - 46 * q^21 - 8 * q^22 - 26 * q^23 - 48 * q^24 + 129 * q^25 - 67 * q^26 - 89 * q^27 - 21 * q^28 - 79 * q^29 - 11 * q^30 + 7 * q^31 - 147 * q^32 - 112 * q^33 - 28 * q^34 - 53 * q^35 + 141 * q^36 - 60 * q^37 - 53 * q^38 - 3 * q^39 - 48 * q^40 - 128 * q^41 + 32 * q^42 - 63 * q^43 - 88 * q^45 - 2 * q^46 - 92 * q^47 - 131 * q^48 + 122 * q^49 - 116 * q^50 - 12 * q^51 - 89 * q^52 - 94 * q^53 - 71 * q^54 - 12 * q^55 - 104 * q^56 - 93 * q^57 - 65 * q^58 - 54 * q^59 - 12 * q^60 + 17 * q^61 - 97 * q^62 - 28 * q^63 + 163 * q^64 - 163 * q^65 - 65 * q^66 - 35 * q^67 - 217 * q^68 - 46 * q^69 - 79 * q^70 - 158 * q^71 - 99 * q^72 - 165 * q^73 - 94 * q^75 - 93 * q^76 - 140 * q^77 + 25 * q^78 - 61 * q^79 - 134 * q^80 + 114 * q^81 + 10 * q^82 - 158 * q^83 - 160 * q^84 + 23 * q^85 - 122 * q^86 - 71 * q^87 - 14 * q^88 - 251 * q^89 - 6 * q^90 - 57 * q^91 - 58 * q^92 - 52 * q^93 - 64 * q^94 - 84 * q^95 - 98 * q^96 - 48 * q^97 - 84 * q^98 + 85 * q^99

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