LMFDB - Embedded newform 8023.2.a.d.1.19

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:	$0$
Dimension:	$165$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
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)

$f(q)$	$=$	$q-2.16974 q^{2} -2.66568 q^{3} +2.70776 q^{4} -3.38518 q^{5} +5.78382 q^{6} -1.43929 q^{7} -1.53565 q^{8} +4.10584 q^{9} +O(q^{10})$	\(q-2.16974 q^{2} -2.66568 q^{3} +2.70776 q^{4} -3.38518 q^{5} +5.78382 q^{6} -1.43929 q^{7} -1.53565 q^{8} +4.10584 q^{9} +7.34496 q^{10} -6.09542 q^{11} -7.21801 q^{12} -6.06658 q^{13} +3.12287 q^{14} +9.02381 q^{15} -2.08356 q^{16} +6.20226 q^{17} -8.90859 q^{18} +7.51145 q^{19} -9.16626 q^{20} +3.83668 q^{21} +13.2255 q^{22} +5.02657 q^{23} +4.09355 q^{24} +6.45947 q^{25} +13.1629 q^{26} -2.94780 q^{27} -3.89724 q^{28} +3.40051 q^{29} -19.5793 q^{30} +6.09346 q^{31} +7.59208 q^{32} +16.2484 q^{33} -13.4573 q^{34} +4.87225 q^{35} +11.1176 q^{36} -4.88603 q^{37} -16.2979 q^{38} +16.1716 q^{39} +5.19845 q^{40} -1.64434 q^{41} -8.32458 q^{42} +11.5109 q^{43} -16.5049 q^{44} -13.8990 q^{45} -10.9063 q^{46} +6.12986 q^{47} +5.55410 q^{48} -4.92845 q^{49} -14.0154 q^{50} -16.5332 q^{51} -16.4268 q^{52} +3.86833 q^{53} +6.39596 q^{54} +20.6341 q^{55} +2.21024 q^{56} -20.0231 q^{57} -7.37822 q^{58} +3.36473 q^{59} +24.4343 q^{60} +3.97155 q^{61} -13.2212 q^{62} -5.90948 q^{63} -12.3057 q^{64} +20.5365 q^{65} -35.2548 q^{66} -2.82936 q^{67} +16.7942 q^{68} -13.3992 q^{69} -10.5715 q^{70} +1.00000 q^{71} -6.30512 q^{72} -1.67810 q^{73} +10.6014 q^{74} -17.2189 q^{75} +20.3392 q^{76} +8.77306 q^{77} -35.0880 q^{78} +0.243743 q^{79} +7.05324 q^{80} -4.45961 q^{81} +3.56779 q^{82} +12.5735 q^{83} +10.3888 q^{84} -20.9958 q^{85} -24.9756 q^{86} -9.06467 q^{87} +9.36043 q^{88} +15.2432 q^{89} +30.1572 q^{90} +8.73156 q^{91} +13.6107 q^{92} -16.2432 q^{93} -13.3002 q^{94} -25.4276 q^{95} -20.2380 q^{96} +10.0938 q^{97} +10.6934 q^{98} -25.0268 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 165 q + 22 q^{2} + 18 q^{3} + 166 q^{4} + 28 q^{5} + 16 q^{6} + 24 q^{7} + 66 q^{8} + 177 q^{9}+O(q^{10}) $ 165 * q + 22 * q^2 + 18 * q^3 + 166 * q^4 + 28 * q^5 + 16 * q^6 + 24 * q^7 + 66 * q^8 + 177 * q^9	\( 165 q + 22 q^{2} + 18 q^{3} + 166 q^{4} + 28 q^{5} + 16 q^{6} + 24 q^{7} + 66 q^{8} + 177 q^{9} + 14 q^{10} + 18 q^{11} + 54 q^{12} + 44 q^{13} + 26 q^{14} + 24 q^{15} + 168 q^{16} + 143 q^{17} + 57 q^{18} + 20 q^{19} + 49 q^{20} + 39 q^{21} + 25 q^{22} + 52 q^{23} + 27 q^{24} + 175 q^{25} + 48 q^{26} + 69 q^{27} + 28 q^{28} + 58 q^{29} - 11 q^{30} + 28 q^{31} + 114 q^{32} + 110 q^{33} + 55 q^{34} + 67 q^{35} + 202 q^{36} + 44 q^{37} + 35 q^{38} + 27 q^{39} + 53 q^{40} + 141 q^{41} + 40 q^{42} + 29 q^{43} + 52 q^{44} + 54 q^{45} + 29 q^{46} + 87 q^{47} + 53 q^{48} + 143 q^{49} + 16 q^{50} + 37 q^{51} + 105 q^{52} + 101 q^{53} - 36 q^{54} + 72 q^{55} + 57 q^{56} + 82 q^{57} + 4 q^{58} + 103 q^{59} + 53 q^{60} + 16 q^{61} + 54 q^{62} + 126 q^{63} + 136 q^{64} + 159 q^{65} + 53 q^{66} + 60 q^{67} + 220 q^{68} + 81 q^{69} + 16 q^{70} + 165 q^{71} + 176 q^{72} + 124 q^{73} + 29 q^{74} + 44 q^{75} + 18 q^{76} + 127 q^{77} - 91 q^{78} + 14 q^{79} + 158 q^{80} + 213 q^{81} + 20 q^{82} + 116 q^{83} + 67 q^{84} + 59 q^{85} + 30 q^{86} + 28 q^{87} + 79 q^{88} + 195 q^{89} + 16 q^{90} - 26 q^{91} + 173 q^{92} + 116 q^{93} + 53 q^{94} + 26 q^{95} - 36 q^{96} + 88 q^{97} + 150 q^{98} + 12 q^{99}+O(q^{100}) \) 165 * q + 22 * q^2 + 18 * q^3 + 166 * q^4 + 28 * q^5 + 16 * q^6 + 24 * q^7 + 66 * q^8 + 177 * q^9 + 14 * q^10 + 18 * q^11 + 54 * q^12 + 44 * q^13 + 26 * q^14 + 24 * q^15 + 168 * q^16 + 143 * q^17 + 57 * q^18 + 20 * q^19 + 49 * q^20 + 39 * q^21 + 25 * q^22 + 52 * q^23 + 27 * q^24 + 175 * q^25 + 48 * q^26 + 69 * q^27 + 28 * q^28 + 58 * q^29 - 11 * q^30 + 28 * q^31 + 114 * q^32 + 110 * q^33 + 55 * q^34 + 67 * q^35 + 202 * q^36 + 44 * q^37 + 35 * q^38 + 27 * q^39 + 53 * q^40 + 141 * q^41 + 40 * q^42 + 29 * q^43 + 52 * q^44 + 54 * q^45 + 29 * q^46 + 87 * q^47 + 53 * q^48 + 143 * q^49 + 16 * q^50 + 37 * q^51 + 105 * q^52 + 101 * q^53 - 36 * q^54 + 72 * q^55 + 57 * q^56 + 82 * q^57 + 4 * q^58 + 103 * q^59 + 53 * q^60 + 16 * q^61 + 54 * q^62 + 126 * q^63 + 136 * q^64 + 159 * q^65 + 53 * q^66 + 60 * q^67 + 220 * q^68 + 81 * q^69 + 16 * q^70 + 165 * q^71 + 176 * q^72 + 124 * q^73 + 29 * q^74 + 44 * q^75 + 18 * q^76 + 127 * q^77 - 91 * q^78 + 14 * q^79 + 158 * q^80 + 213 * q^81 + 20 * q^82 + 116 * q^83 + 67 * q^84 + 59 * q^85 + 30 * q^86 + 28 * q^87 + 79 * q^88 + 195 * q^89 + 16 * q^90 - 26 * q^91 + 173 * q^92 + 116 * q^93 + 53 * q^94 + 26 * q^95 - 36 * q^96 + 88 * q^97 + 150 * q^98 + 12 * 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 $

$2$	−2.16974	−1.53424	−0.767118	−	0.641506i	$-0.778310\pi$
$2$	−2.16974	−1.53424	−0.767118	+	0.641506i	$0.778310\pi$
$3$	−2.66568	−1.53903	−0.769515	−	0.638629i	$-0.779502\pi$
$3$	−2.66568	−1.53903	−0.769515	+	0.638629i	$0.779502\pi$
$4$	2.70776	1.35388
$5$	−3.38518	−1.51390	−0.756950	−	0.653473i	$-0.773311\pi$
$5$	−3.38518	−1.51390	−0.756950	+	0.653473i	$0.773311\pi$
$6$	5.78382	2.36123
$7$	−1.43929	−0.543999	−0.272000	−	0.962297i	$-0.587685\pi$
$7$	−1.43929	−0.543999	−0.272000	+	0.962297i	$0.587685\pi$
$8$	−1.53565	−0.542934
$9$	4.10584	1.36861
$10$	7.34496	2.32268
$11$	−6.09542	−1.83784	−0.918919	−	0.394446i	$-0.870937\pi$
$11$	−6.09542	−1.83784	−0.918919	+	0.394446i	$0.870937\pi$
$12$	−7.21801	−2.08366
$13$	−6.06658	−1.68257	−0.841284	−	0.540593i	$-0.818200\pi$
$13$	−6.06658	−1.68257	−0.841284	+	0.540593i	$0.818200\pi$
$14$	3.12287	0.834623
$15$	9.02381	2.32994
$16$	−2.08356	−0.520891
$17$	6.20226	1.50427	0.752134	−	0.659010i	$-0.229024\pi$
$17$	6.20226	1.50427	0.752134	+	0.659010i	$0.229024\pi$
$18$	−8.90859	−2.09977
$19$	7.51145	1.72324	0.861622	−	0.507551i	$-0.169449\pi$
$19$	7.51145	1.72324	0.861622	+	0.507551i	$0.169449\pi$
$20$	−9.16626	−2.04964
$21$	3.83668	0.837231
$22$	13.2255	2.81968
$23$	5.02657	1.04811	0.524056	−	0.851684i	$-0.324418\pi$
$23$	5.02657	1.04811	0.524056	+	0.851684i	$0.324418\pi$
$24$	4.09355	0.835591
$25$	6.45947	1.29189
$26$	13.1629	2.58146
$27$	−2.94780	−0.567305
$28$	−3.89724	−0.736509
$29$	3.40051	0.631459	0.315730	−	0.948849i	$-0.397751\pi$
$29$	3.40051	0.631459	0.315730	+	0.948849i	$0.397751\pi$
$30$	−19.5793	−3.57467
$31$	6.09346	1.09442	0.547209	−	0.836996i	$-0.315690\pi$
$31$	6.09346	1.09442	0.547209	+	0.836996i	$0.315690\pi$
$32$	7.59208	1.34210
$33$	16.2484	2.82849
$34$	−13.4573	−2.30790
$35$	4.87225	0.823561
$36$	11.1176	1.85294
$37$	−4.88603	−0.803258	−0.401629	−	0.915802i	$-0.631556\pi$
$37$	−4.88603	−0.803258	−0.401629	+	0.915802i	$0.631556\pi$
$38$	−16.2979	−2.64386
$39$	16.1716	2.58952
$40$	5.19845	0.821948
$41$	−1.64434	−0.256803	−0.128402	−	0.991722i	$-0.540985\pi$
$41$	−1.64434	−0.256803	−0.128402	+	0.991722i	$0.540985\pi$
$42$	−8.32458	−1.28451
$43$	11.5109	1.75539	0.877697	−	0.479216i	$-0.159079\pi$
$43$	11.5109	1.75539	0.877697	+	0.479216i	$0.159079\pi$
$44$	−16.5049	−2.48821
$45$	−13.8990	−2.07194
$46$	−10.9063	−1.60805
$47$	6.12986	0.894132	0.447066	−	0.894501i	$-0.352469\pi$
$47$	6.12986	0.894132	0.447066	+	0.894501i	$0.352469\pi$
$48$	5.55410	0.801666
$49$	−4.92845	−0.704065
$50$	−14.0154	−1.98207
$51$	−16.5332	−2.31511
$52$	−16.4268	−2.27799
$53$	3.86833	0.531356	0.265678	−	0.964062i	$-0.414404\pi$
$53$	3.86833	0.531356	0.265678	+	0.964062i	$0.414404\pi$
$54$	6.39596	0.870380
$55$	20.6341	2.78230
$56$	2.21024	0.295356
$57$	−20.0231	−2.65212
$58$	−7.37822	−0.968807
$59$	3.36473	0.438050	0.219025	−	0.975719i	$-0.429712\pi$
$59$	3.36473	0.438050	0.219025	+	0.975719i	$0.429712\pi$
$60$	24.4343	3.15445
$61$	3.97155	0.508505	0.254253	−	0.967138i	$-0.418170\pi$
$61$	3.97155	0.508505	0.254253	+	0.967138i	$0.418170\pi$
$62$	−13.2212	−1.67910
$63$	−5.90948	−0.744524
$64$	−12.3057	−1.53821
$65$	20.5365	2.54724
$66$	−35.2548	−4.33957
$67$	−2.82936	−0.345661	−0.172831	−	0.984952i	$-0.555291\pi$
$67$	−2.82936	−0.345661	−0.172831	+	0.984952i	$0.555291\pi$
$68$	16.7942	2.03660
$69$	−13.3992	−1.61308
$70$	−10.5715	−1.26354
$71$	1.00000	0.118678
$71$	1.00000	0.118678
$72$	−6.30512	−0.743066
$73$	−1.67810	−0.196407	−0.0982034	−	0.995166i	$-0.531310\pi$
$73$	−1.67810	−0.196407	−0.0982034	+	0.995166i	$0.531310\pi$
$74$	10.6014	1.23239
$75$	−17.2189	−1.98826
$76$	20.3392	2.33306
$77$	8.77306	0.999783
$78$	−35.0880	−3.97294
$79$	0.243743	0.0274232	0.0137116	−	0.999906i	$-0.495635\pi$
$79$	0.243743	0.0274232	0.0137116	+	0.999906i	$0.495635\pi$
$80$	7.05324	0.788576
$81$	−4.45961	−0.495513
$82$	3.56779	0.393997
$83$	12.5735	1.38012	0.690058	−	0.723754i	$-0.257585\pi$
$83$	12.5735	1.38012	0.690058	+	0.723754i	$0.257585\pi$
$84$	10.3888	1.13351
$85$	−20.9958	−2.27731
$86$	−24.9756	−2.69319
$87$	−9.06467	−0.971834
$88$	9.36043	0.997825
$89$	15.2432	1.61578	0.807890	−	0.589334i	$-0.200610\pi$
$89$	15.2432	1.61578	0.807890	+	0.589334i	$0.200610\pi$
$90$	30.1572	3.17885
$91$	8.73156	0.915316
$92$	13.6107	1.41902
$93$	−16.2432	−1.68434
$94$	−13.3002	−1.37181
$95$	−25.4276	−2.60882
$96$	−20.2380	−2.06554
$97$	10.0938	1.02487	0.512437	−	0.858725i	$-0.328743\pi$
$97$	10.0938	1.02487	0.512437	+	0.858725i	$0.328743\pi$
$98$	10.6934	1.08020
$99$	−25.0268	−2.51529
$100$	17.4907	1.74907
$101$	−1.86433	−0.185508	−0.0927539	−	0.995689i	$-0.529567\pi$
$101$	−1.86433	−0.185508	−0.0927539	+	0.995689i	$0.529567\pi$
$102$	35.8727	3.55193
$103$	−17.7684	−1.75078	−0.875389	−	0.483420i	$-0.839394\pi$
$103$	−17.7684	−1.75078	−0.875389	+	0.483420i	$0.839394\pi$
$104$	9.31615	0.913523
$105$	−12.9879	−1.26748
$106$	−8.39326	−0.815226
$107$	17.9130	1.73171	0.865856	−	0.500294i	$-0.166775\pi$
$107$	17.9130	1.73171	0.865856	+	0.500294i	$0.166775\pi$
$108$	−7.98194	−0.768063
$109$	−11.5189	−1.10331	−0.551656	−	0.834072i	$-0.686004\pi$
$109$	−11.5189	−1.10331	−0.551656	+	0.834072i	$0.686004\pi$
$110$	−44.7706	−4.26871
$111$	13.0246	1.23624
$112$	2.99884	0.283364
$113$	−1.00000	−0.0940721
$113$	−1.00000	−0.0940721
$114$	43.4448	4.06898
$115$	−17.0159	−1.58674
$116$	9.20776	0.854919
$117$	−24.9084	−2.30278
$118$	−7.30057	−0.672072
$119$	−8.92683	−0.818321
$120$	−13.8574	−1.26500
$121$	26.1541	2.37765
$122$	−8.61723	−0.780167
$123$	4.38329	0.395228
$124$	16.4996	1.48171
$125$	−4.94058	−0.441899
$126$	12.8220	1.14228
$127$	13.8447	1.22852	0.614259	−	0.789104i	$-0.289455\pi$
$127$	13.8447	1.22852	0.614259	+	0.789104i	$0.289455\pi$
$128$	11.5160	1.01788
$129$	−30.6843	−2.70160
$130$	−44.5588	−3.90807
$131$	−10.8171	−0.945092	−0.472546	−	0.881306i	$-0.656665\pi$
$131$	−10.8171	−0.945092	−0.472546	+	0.881306i	$0.656665\pi$
$132$	43.9968	3.82943
$133$	−10.8111	−0.937444
$134$	6.13896	0.530325
$135$	9.97886	0.858844
$136$	−9.52449	−0.816719
$137$	19.2342	1.64329	0.821643	−	0.570002i	$-0.193058\pi$
$137$	19.2342	1.64329	0.821643	+	0.570002i	$0.193058\pi$
$138$	29.0728	2.47484
$139$	0.376145	0.0319042	0.0159521	−	0.999873i	$-0.494922\pi$
$139$	0.376145	0.0319042	0.0159521	+	0.999873i	$0.494922\pi$
$140$	13.1929	1.11500
$141$	−16.3402	−1.37610
$142$	−2.16974	−0.182080
$143$	36.9784	3.09229
$144$	−8.55477	−0.712897
$145$	−11.5114	−0.955966
$146$	3.64103	0.301334
$147$	13.1377	1.08358
$148$	−13.2302	−1.08751
$149$	3.77837	0.309536	0.154768	−	0.987951i	$-0.450537\pi$
$149$	3.77837	0.309536	0.154768	+	0.987951i	$0.450537\pi$
$150$	37.3604	3.05047
$151$	17.7618	1.44544	0.722718	−	0.691143i	$-0.242893\pi$
$151$	17.7618	1.44544	0.722718	+	0.691143i	$0.242893\pi$
$152$	−11.5349	−0.935608
$153$	25.4655	2.05876
$154$	−19.0352	−1.53390
$155$	−20.6275	−1.65684
$156$	43.7887	3.50590
$157$	7.59039	0.605779	0.302890	−	0.953026i	$-0.402049\pi$
$157$	7.59039	0.605779	0.302890	+	0.953026i	$0.402049\pi$
$158$	−0.528858	−0.0420737
$159$	−10.3117	−0.817773
$160$	−25.7006	−2.03181
$161$	−7.23468	−0.570172
$162$	9.67619	0.760233
$163$	13.0871	1.02506	0.512531	−	0.858669i	$-0.328708\pi$
$163$	13.0871	1.02506	0.512531	+	0.858669i	$0.328708\pi$
$164$	−4.45248	−0.347680
$165$	−55.0039	−4.28205
$166$	−27.2811	−2.11742
$167$	11.3954	0.881804	0.440902	−	0.897555i	$-0.354659\pi$
$167$	11.3954	0.881804	0.440902	+	0.897555i	$0.354659\pi$
$168$	−5.89179	−0.454561
$169$	23.8035	1.83103
$170$	45.5553	3.49394
$171$	30.8408	2.35845
$172$	31.1687	2.37659
$173$	−13.8884	−1.05591	−0.527956	−	0.849272i	$-0.677041\pi$
$173$	−13.8884	−1.05591	−0.527956	+	0.849272i	$0.677041\pi$
$174$	19.6679	1.49102
$175$	−9.29703	−0.702790
$176$	12.7002	0.957313
$177$	−8.96927	−0.674172
$178$	−33.0738	−2.47899
$179$	8.12828	0.607536	0.303768	−	0.952746i	$-0.401755\pi$
$179$	8.12828	0.607536	0.303768	+	0.952746i	$0.401755\pi$
$180$	−37.6352	−2.80516
$181$	−8.48740	−0.630863	−0.315432	−	0.948948i	$-0.602149\pi$
$181$	−8.48740	−0.630863	−0.315432	+	0.948948i	$0.602149\pi$
$182$	−18.9452	−1.40431
$183$	−10.5869	−0.782605
$184$	−7.71905	−0.569056
$185$	16.5401	1.21605
$186$	35.2435	2.58418
$187$	−37.8054	−2.76460
$188$	16.5982	1.21055
$189$	4.24274	0.308614
$190$	55.1713	4.00254
$191$	−8.17066	−0.591208	−0.295604	−	0.955311i	$-0.595521\pi$
$191$	−8.17066	−0.591208	−0.295604	+	0.955311i	$0.595521\pi$
$192$	32.8030	2.36735
$193$	9.44403	0.679796	0.339898	−	0.940462i	$-0.389607\pi$
$193$	9.44403	0.679796	0.339898	+	0.940462i	$0.389607\pi$
$194$	−21.9010	−1.57240
$195$	−54.7437	−3.92028
$196$	−13.3451	−0.953218
$197$	−3.58113	−0.255145	−0.127572	−	0.991829i	$-0.540718\pi$
$197$	−3.58113	−0.255145	−0.127572	+	0.991829i	$0.540718\pi$
$198$	54.3016	3.85904
$199$	−25.1924	−1.78584	−0.892919	−	0.450217i	$-0.851347\pi$
$199$	−25.1924	−1.78584	−0.892919	+	0.450217i	$0.851347\pi$
$200$	−9.91948	−0.701413
$201$	7.54215	0.531983
$202$	4.04511	0.284613
$203$	−4.89431	−0.343513
$204$	−44.7680	−3.13438
$205$	5.56640	0.388774
$206$	38.5529	2.68610
$207$	20.6383	1.43446
$208$	12.6401	0.876434
$209$	−45.7854	−3.16704
$210$	28.1802	1.94462
$211$	−26.2615	−1.80791	−0.903957	−	0.427623i	$-0.859351\pi$
$211$	−26.2615	−1.80791	−0.903957	+	0.427623i	$0.859351\pi$
$212$	10.4745	0.719392
$213$	−2.66568	−0.182649
$214$	−38.8664	−2.65685
$215$	−38.9665	−2.65749
$216$	4.52679	0.308009
$217$	−8.77024	−0.595363
$218$	24.9930	1.69274
$219$	4.47327	0.302276
$220$	55.8722	3.76690
$221$	−37.6265	−2.53103
$222$	−28.2599	−1.89668
$223$	−22.1606	−1.48399	−0.741993	−	0.670408i	$-0.766119\pi$
$223$	−22.1606	−1.48399	−0.741993	+	0.670408i	$0.766119\pi$
$224$	−10.9272	−0.730103
$225$	26.5215	1.76810
$226$	2.16974	0.144329
$227$	0.0583340	0.00387176	0.00193588	−	0.999998i	$-0.499384\pi$
$227$	0.0583340	0.00387176	0.00193588	+	0.999998i	$0.499384\pi$
$228$	−54.2177	−3.59065
$229$	−22.3431	−1.47648	−0.738238	−	0.674540i	$-0.764342\pi$
$229$	−22.3431	−1.47648	−0.738238	+	0.674540i	$0.764342\pi$
$230$	36.9200	2.43443
$231$	−23.3861	−1.53870
$232$	−5.22199	−0.342841
$233$	1.21677	0.0797131	0.0398566	−	0.999205i	$-0.487310\pi$
$233$	1.21677	0.0797131	0.0398566	+	0.999205i	$0.487310\pi$
$234$	54.0447	3.53301
$235$	−20.7507	−1.35363
$236$	9.11086	0.593067
$237$	−0.649741	−0.0422052
$238$	19.3689	1.25550
$239$	8.39317	0.542909	0.271455	−	0.962451i	$-0.412495\pi$
$239$	8.39317	0.542909	0.271455	+	0.962451i	$0.412495\pi$
$240$	−18.8017	−1.21364
$241$	10.8050	0.696013	0.348007	−	0.937492i	$-0.386859\pi$
$241$	10.8050	0.696013	0.348007	+	0.937492i	$0.386859\pi$
$242$	−56.7476	−3.64788
$243$	20.7313	1.32991
$244$	10.7540	0.688455
$245$	16.6837	1.06588
$246$	−9.51058	−0.606372
$247$	−45.5688	−2.89947
$248$	−9.35742	−0.594197
$249$	−33.5168	−2.12404
$250$	10.7198	0.677977
$251$	23.6337	1.49175	0.745873	−	0.666088i	$-0.232033\pi$
$251$	23.6337	1.49175	0.745873	+	0.666088i	$0.232033\pi$
$252$	−16.0014	−1.00800
$253$	−30.6391	−1.92626
$254$	−30.0393	−1.88484
$255$	55.9680	3.50485
$256$	−0.375205	−0.0234503
$257$	17.7736	1.10869	0.554344	−	0.832288i	$-0.312969\pi$
$257$	17.7736	1.10869	0.554344	+	0.832288i	$0.312969\pi$
$258$	66.5769	4.14490
$259$	7.03239	0.436972
$260$	55.6079	3.44866
$261$	13.9619	0.864223
$262$	23.4702	1.44999
$263$	−17.7452	−1.09422	−0.547109	−	0.837061i	$-0.684272\pi$
$263$	−17.7452	−1.09422	−0.547109	+	0.837061i	$0.684272\pi$
$264$	−24.9519	−1.53568
$265$	−13.0950	−0.804420
$266$	23.4573	1.43826
$267$	−40.6335	−2.48673
$268$	−7.66122	−0.467983
$269$	−5.67653	−0.346104	−0.173052	−	0.984913i	$-0.555363\pi$
$269$	−5.67653	−0.346104	−0.173052	+	0.984913i	$0.555363\pi$
$270$	−21.6515	−1.31767
$271$	−2.80030	−0.170106	−0.0850531	−	0.996376i	$-0.527106\pi$
$271$	−2.80030	−0.170106	−0.0850531	+	0.996376i	$0.527106\pi$
$272$	−12.9228	−0.783559
$273$	−23.2755	−1.40870
$274$	−41.7331	−2.52119
$275$	−39.3732	−2.37429
$276$	−36.2818	−2.18391
$277$	17.1000	1.02744	0.513721	−	0.857957i	$-0.328267\pi$
$277$	17.1000	1.02744	0.513721	+	0.857957i	$0.328267\pi$
$278$	−0.816135	−0.0489485
$279$	25.0188	1.49783
$280$	−7.48207	−0.447139
$281$	12.7227	0.758975	0.379487	−	0.925197i	$-0.376100\pi$
$281$	12.7227	0.758975	0.379487	+	0.925197i	$0.376100\pi$
$282$	35.4540	2.11126
$283$	−9.28975	−0.552218	−0.276109	−	0.961126i	$-0.589045\pi$
$283$	−9.28975	−0.552218	−0.276109	+	0.961126i	$0.589045\pi$
$284$	2.70776	0.160676
$285$	67.7819	4.01505
$286$	−80.2334	−4.74430
$287$	2.36668	0.139701
$288$	31.1718	1.83682
$289$	21.4680	1.26282
$290$	24.9766	1.46668
$291$	−26.9069	−1.57731
$292$	−4.54389	−0.265911
$293$	14.3710	0.839563	0.419781	−	0.907625i	$-0.362107\pi$
$293$	14.3710	0.839563	0.419781	+	0.907625i	$0.362107\pi$
$294$	−28.5053	−1.66246
$295$	−11.3902	−0.663164
$296$	7.50322	0.436116
$297$	17.9681	1.04262
$298$	−8.19807	−0.474901
$299$	−30.4941	−1.76352
$300$	−46.6245	−2.69187
$301$	−16.5675	−0.954933
$302$	−38.5385	−2.21764
$303$	4.96970	0.285502
$304$	−15.6506	−0.897621
$305$	−13.4444	−0.769827
$306$	−55.2534	−3.15862
$307$	17.4221	0.994331	0.497166	−	0.867656i	$-0.334374\pi$
$307$	17.4221	0.994331	0.497166	+	0.867656i	$0.334374\pi$
$308$	23.7553	1.35359
$309$	47.3649	2.69450
$310$	44.7562	2.54198
$311$	3.25690	0.184682	0.0923408	−	0.995727i	$-0.470565\pi$
$311$	3.25690	0.184682	0.0923408	+	0.995727i	$0.470565\pi$
$312$	−24.8338	−1.40594
$313$	11.3482	0.641441	0.320720	−	0.947174i	$-0.396075\pi$
$313$	11.3482	0.641441	0.320720	+	0.947174i	$0.396075\pi$
$314$	−16.4692	−0.929408
$315$	20.0047	1.12714
$316$	0.659997	0.0371278
$317$	−10.0378	−0.563777	−0.281888	−	0.959447i	$-0.590961\pi$
$317$	−10.0378	−0.563777	−0.281888	+	0.959447i	$0.590961\pi$
$318$	22.3737	1.25466
$319$	−20.7276	−1.16052
$320$	41.6570	2.32870
$321$	−47.7502	−2.66516
$322$	15.6973	0.874779
$323$	46.5879	2.59222
$324$	−12.0756	−0.670864
$325$	−39.1869	−2.17370
$326$	−28.3956	−1.57269
$327$	30.7057	1.69803
$328$	2.52513	0.139427
$329$	−8.82263	−0.486407
$330$	119.344	6.56967
$331$	8.37999	0.460606	0.230303	−	0.973119i	$-0.426028\pi$
$331$	8.37999	0.460606	0.230303	+	0.973119i	$0.426028\pi$
$332$	34.0459	1.86851
$333$	−20.0612	−1.09935
$334$	−24.7251	−1.35289
$335$	9.57790	0.523296
$336$	−7.99395	−0.436106
$337$	0.837863	0.0456413	0.0228206	−	0.999740i	$-0.492735\pi$
$337$	0.837863	0.0456413	0.0228206	+	0.999740i	$0.492735\pi$
$338$	−51.6472	−2.80924
$339$	2.66568	0.144780
$340$	−56.8515	−3.08321
$341$	−37.1422	−2.01136
$342$	−66.9164	−3.61842
$343$	17.1685	0.927010
$344$	−17.6767	−0.953063
$345$	45.3588	2.44204
$346$	30.1341	1.62002
$347$	−16.7842	−0.901024	−0.450512	−	0.892770i	$-0.648758\pi$
$347$	−16.7842	−0.901024	−0.450512	+	0.892770i	$0.648758\pi$
$348$	−24.5449	−1.31575
$349$	−2.13976	−0.114539	−0.0572694	−	0.998359i	$-0.518239\pi$
$349$	−2.13976	−0.114539	−0.0572694	+	0.998359i	$0.518239\pi$
$350$	20.1721	1.07825
$351$	17.8831	0.954530
$352$	−46.2769	−2.46657
$353$	20.2187	1.07613	0.538066	−	0.842902i	$-0.319155\pi$
$353$	20.2187	1.07613	0.538066	+	0.842902i	$0.319155\pi$
$354$	19.4610	1.03434
$355$	−3.38518	−0.179667
$356$	41.2750	2.18757
$357$	23.7961	1.25942
$358$	−17.6362	−0.932104
$359$	−33.6452	−1.77573	−0.887864	−	0.460106i	$-0.847812\pi$
$359$	−33.6452	−1.77573	−0.887864	+	0.460106i	$0.847812\pi$
$360$	21.3440	1.12493
$361$	37.4218	1.96957
$362$	18.4154	0.967893
$363$	−69.7185	−3.65927
$364$	23.6429	1.23923
$365$	5.68068	0.297340
$366$	22.9708	1.20070
$367$	−14.4410	−0.753813	−0.376907	−	0.926251i	$-0.623012\pi$
$367$	−14.4410	−0.753813	−0.376907	+	0.926251i	$0.623012\pi$
$368$	−10.4732	−0.545952
$369$	−6.75140	−0.351464
$370$	−35.8877	−1.86571
$371$	−5.56764	−0.289057
$372$	−43.9827	−2.28040
$373$	−6.15825	−0.318862	−0.159431	−	0.987209i	$-0.550966\pi$
$373$	−6.15825	−0.318862	−0.159431	+	0.987209i	$0.550966\pi$
$374$	82.0277	4.24155
$375$	13.1700	0.680096
$376$	−9.41332	−0.485455
$377$	−20.6295	−1.06247
$378$	−9.20562	−0.473486
$379$	−1.15824	−0.0594949	−0.0297475	−	0.999557i	$-0.509470\pi$
$379$	−1.15824	−0.0594949	−0.0297475	+	0.999557i	$0.509470\pi$
$380$	−68.8519	−3.53203
$381$	−36.9055	−1.89073
$382$	17.7282	0.907053
$383$	−6.99218	−0.357284	−0.178642	−	0.983914i	$-0.557170\pi$
$383$	−6.99218	−0.357284	−0.178642	+	0.983914i	$0.557170\pi$
$384$	−30.6978	−1.56654
$385$	−29.6984	−1.51357
$386$	−20.4911	−1.04297
$387$	47.2618	2.40245
$388$	27.3317	1.38756
$389$	−0.949779	−0.0481557	−0.0240779	−	0.999710i	$-0.507665\pi$
$389$	−0.949779	−0.0481557	−0.0240779	+	0.999710i	$0.507665\pi$
$390$	118.779	6.01463
$391$	31.1761	1.57664
$392$	7.56837	0.382261
$393$	28.8348	1.45452
$394$	7.77010	0.391452
$395$	−0.825115	−0.0415161
$396$	−67.7665	−3.40540
$397$	34.2018	1.71654	0.858271	−	0.513197i	$-0.171539\pi$
$397$	34.2018	1.71654	0.858271	+	0.513197i	$0.171539\pi$
$398$	54.6608	2.73990
$399$	28.8190	1.44275
$400$	−13.4587	−0.672935
$401$	24.5029	1.22362	0.611809	−	0.791006i	$-0.290442\pi$
$401$	24.5029	1.22362	0.611809	+	0.791006i	$0.290442\pi$
$402$	−16.3645	−0.816187
$403$	−36.9665	−1.84143
$404$	−5.04815	−0.251155
$405$	15.0966	0.750157
$406$	10.6194	0.527031
$407$	29.7824	1.47626
$408$	25.3892	1.25695
$409$	30.3998	1.50318	0.751588	−	0.659633i	$-0.229288\pi$
$409$	30.3998	1.50318	0.751588	+	0.659633i	$0.229288\pi$
$410$	−12.0776	−0.596472
$411$	−51.2721	−2.52907
$412$	−48.1127	−2.37034
$413$	−4.84281	−0.238299
$414$	−44.7796	−2.20080
$415$	−42.5635	−2.08936
$416$	−46.0580	−2.25818
$417$	−1.00268	−0.0491015
$418$	99.3423	4.85899
$419$	5.75080	0.280945	0.140472	−	0.990085i	$-0.455138\pi$
$419$	5.75080	0.280945	0.140472	+	0.990085i	$0.455138\pi$
$420$	−35.1680	−1.71602
$421$	−0.875456	−0.0426671	−0.0213336	−	0.999772i	$-0.506791\pi$
$421$	−0.875456	−0.0426671	−0.0213336	+	0.999772i	$0.506791\pi$
$422$	56.9805	2.77377
$423$	25.1682	1.22372
$424$	−5.94040	−0.288491
$425$	40.0633	1.94336
$426$	5.78382	0.280227
$427$	−5.71621	−0.276627
$428$	48.5040	2.34453
$429$	−98.5724	−4.75912
$430$	84.5470	4.07722
$431$	19.2155	0.925579	0.462789	−	0.886468i	$-0.346849\pi$
$431$	19.2155	0.925579	0.462789	+	0.886468i	$0.346849\pi$
$432$	6.14193	0.295504
$433$	−33.9276	−1.63045	−0.815227	−	0.579141i	$-0.803388\pi$
$433$	−33.9276	−1.63045	−0.815227	+	0.579141i	$0.803388\pi$
$434$	19.0291	0.913427
$435$	30.6856	1.47126
$436$	−31.1905	−1.49375
$437$	37.7568	1.80615
$438$	−9.70582	−0.463762
$439$	18.9270	0.903336	0.451668	−	0.892186i	$-0.350829\pi$
$439$	18.9270	0.903336	0.451668	+	0.892186i	$0.350829\pi$
$440$	−31.6868	−1.51061
$441$	−20.2354	−0.963592
$442$	81.6397	3.88320
$443$	18.9951	0.902484	0.451242	−	0.892402i	$-0.350981\pi$
$443$	18.9951	0.902484	0.451242	+	0.892402i	$0.350981\pi$
$444$	35.2674	1.67372
$445$	−51.6012	−2.44613
$446$	48.0827	2.27678
$447$	−10.0719	−0.476385
$448$	17.7114	0.836786
$449$	13.9843	0.659960	0.329980	−	0.943988i	$-0.392958\pi$
$449$	13.9843	0.659960	0.329980	+	0.943988i	$0.392958\pi$
$450$	−57.5448	−2.71269
$451$	10.0230	0.471963
$452$	−2.70776	−0.127362
$453$	−47.3473	−2.22457
$454$	−0.126569	−0.00594019
$455$	−29.5579	−1.38570
$456$	30.7484	1.43993
$457$	31.7660	1.48595	0.742976	−	0.669318i	$-0.233414\pi$
$457$	31.7660	1.48595	0.742976	+	0.669318i	$0.233414\pi$
$458$	48.4787	2.26526
$459$	−18.2831	−0.853380
$460$	−46.0748	−2.14825
$461$	1.56138	0.0727208	0.0363604	−	0.999339i	$-0.488424\pi$
$461$	1.56138	0.0727208	0.0363604	+	0.999339i	$0.488424\pi$
$462$	50.7418	2.36072
$463$	−0.974676	−0.0452970	−0.0226485	−	0.999743i	$-0.507210\pi$
$463$	−0.974676	−0.0452970	−0.0226485	+	0.999743i	$0.507210\pi$
$464$	−7.08518	−0.328921
$465$	54.9863	2.54993
$466$	−2.64007	−0.122299
$467$	32.9859	1.52640	0.763202	−	0.646159i	$-0.223626\pi$
$467$	32.9859	1.52640	0.763202	+	0.646159i	$0.223626\pi$
$468$	−67.4459	−3.11769
$469$	4.07226	0.188039
$470$	45.0236	2.07678
$471$	−20.2335	−0.932312
$472$	−5.16704	−0.237832
$473$	−70.1637	−3.22613
$474$	1.40977	0.0647527
$475$	48.5200	2.22625
$476$	−24.1717	−1.10791
$477$	15.8827	0.727221
$478$	−18.2110	−0.832951
$479$	−17.3930	−0.794705	−0.397353	−	0.917666i	$-0.630071\pi$
$479$	−17.3930	−0.794705	−0.397353	+	0.917666i	$0.630071\pi$
$480$	68.5095	3.12702
$481$	29.6415	1.35154
$482$	−23.4441	−1.06785
$483$	19.2853	0.877512
$484$	70.8191	3.21905
$485$	−34.1695	−1.55156
$486$	−44.9815	−2.04040
$487$	−13.0618	−0.591885	−0.295943	−	0.955206i	$-0.595634\pi$
$487$	−13.0618	−0.591885	−0.295943	+	0.955206i	$0.595634\pi$
$488$	−6.09891	−0.276085
$489$	−34.8861	−1.57760
$490$	−36.1993	−1.63532
$491$	−42.1321	−1.90140	−0.950698	−	0.310120i	$-0.899631\pi$
$491$	−42.1321	−1.90140	−0.950698	+	0.310120i	$0.899631\pi$
$492$	11.8689	0.535091
$493$	21.0909	0.949884
$494$	98.8724	4.44848
$495$	84.7203	3.80790
$496$	−12.6961	−0.570072
$497$	−1.43929	−0.0645608
$498$	72.7226	3.25878
$499$	−33.4988	−1.49961	−0.749806	−	0.661658i	$-0.769853\pi$
$499$	−33.4988	−1.49961	−0.749806	+	0.661658i	$0.769853\pi$
$500$	−13.3779	−0.598278
$501$	−30.3765	−1.35712
$502$	−51.2789	−2.28869
$503$	−13.0498	−0.581863	−0.290932	−	0.956744i	$-0.593965\pi$
$503$	−13.0498	−0.581863	−0.290932	+	0.956744i	$0.593965\pi$
$504$	9.07488	0.404227
$505$	6.31110	0.280840
$506$	66.4787	2.95534
$507$	−63.4523	−2.81802
$508$	37.4881	1.66326
$509$	6.44225	0.285548	0.142774	−	0.989755i	$-0.454398\pi$
$509$	6.44225	0.285548	0.142774	+	0.989755i	$0.454398\pi$
$510$	−121.436	−5.37727
$511$	2.41527	0.106845
$512$	−22.2178	−0.981898
$513$	−22.1423	−0.977605
$514$	−38.5641	−1.70099
$515$	60.1495	2.65050
$516$	−83.0857	−3.65764
$517$	−37.3641	−1.64327
$518$	−15.2584	−0.670418
$519$	37.0219	1.62508
$520$	−31.5369	−1.38298
$521$	−3.19730	−0.140076	−0.0700382	−	0.997544i	$-0.522312\pi$
$521$	−3.19730	−0.140076	−0.0700382	+	0.997544i	$0.522312\pi$
$522$	−30.2938	−1.32592
$523$	−24.8635	−1.08720	−0.543602	−	0.839343i	$-0.682940\pi$
$523$	−24.8635	−1.08720	−0.543602	+	0.839343i	$0.682940\pi$
$524$	−29.2900	−1.27954
$525$	24.7829	1.08161
$526$	38.5025	1.67879
$527$	37.7932	1.64630
$528$	−33.8546	−1.47333
$529$	2.26641	0.0985394
$530$	28.4127	1.23417
$531$	13.8150	0.599521
$532$	−29.2739	−1.26919
$533$	9.97554	0.432089
$534$	88.1641	3.81523
$535$	−60.6387	−2.62164
$536$	4.34490	0.187671
$537$	−21.6674	−0.935016
$538$	12.3166	0.531005
$539$	30.0410	1.29396
$540$	27.0203	1.16277
$541$	42.7304	1.83712	0.918562	−	0.395277i	$-0.129351\pi$
$541$	42.7304	1.83712	0.918562	+	0.395277i	$0.129351\pi$
$542$	6.07592	0.260983
$543$	22.6247	0.970918
$544$	47.0880	2.01888
$545$	38.9937	1.67031
$546$	50.5017	2.16128
$547$	7.13512	0.305076	0.152538	−	0.988298i	$-0.451255\pi$
$547$	7.13512	0.305076	0.152538	+	0.988298i	$0.451255\pi$
$548$	52.0815	2.22481
$549$	16.3066	0.695947
$550$	85.4295	3.64272
$551$	25.5428	1.08816
$552$	20.5765	0.875794
$553$	−0.350816	−0.0149182
$554$	−37.1026	−1.57634
$555$	−44.0906	−1.87154
$556$	1.01851	0.0431944
$557$	7.44816	0.315589	0.157794	−	0.987472i	$-0.449562\pi$
$557$	7.44816	0.315589	0.157794	+	0.987472i	$0.449562\pi$
$558$	−54.2841	−2.29803
$559$	−69.8318	−2.95357
$560$	−10.1516	−0.428985
$561$	100.777	4.25481
$562$	−27.6050	−1.16445
$563$	3.70005	0.155939	0.0779694	−	0.996956i	$-0.475156\pi$
$563$	3.70005	0.155939	0.0779694	+	0.996956i	$0.475156\pi$
$564$	−44.2454	−1.86307
$565$	3.38518	0.142416
$566$	20.1563	0.847233
$567$	6.41866	0.269559
$568$	−1.53565	−0.0644344
$569$	26.9781	1.13098	0.565491	−	0.824755i	$-0.308687\pi$
$569$	26.9781	1.13098	0.565491	+	0.824755i	$0.308687\pi$
$570$	−147.069	−6.16003
$571$	12.5529	0.525324	0.262662	−	0.964888i	$-0.415400\pi$
$571$	12.5529	0.525324	0.262662	+	0.964888i	$0.415400\pi$
$572$	100.129	4.18658
$573$	21.7804	0.909887
$574$	−5.13508	−0.214334
$575$	32.4690	1.35405
$576$	−50.5252	−2.10522
$577$	32.5917	1.35681	0.678404	−	0.734689i	$-0.262672\pi$
$577$	32.5917	1.35681	0.678404	+	0.734689i	$0.262672\pi$
$578$	−46.5800	−1.93747
$579$	−25.1747	−1.04623
$580$	−31.1700	−1.29426
$581$	−18.0968	−0.750782
$582$	58.3809	2.41997
$583$	−23.5791	−0.976547
$584$	2.57697	0.106636
$585$	84.3195	3.48618
$586$	−31.1813	−1.28809
$587$	3.31705	0.136909	0.0684547	−	0.997654i	$-0.478193\pi$
$587$	3.31705	0.136909	0.0684547	+	0.997654i	$0.478193\pi$
$588$	35.5736	1.46703
$589$	45.7707	1.88595
$590$	24.7138	1.01745
$591$	9.54613	0.392675
$592$	10.1803	0.418409
$593$	9.41567	0.386655	0.193328	−	0.981134i	$-0.438072\pi$
$593$	9.41567	0.386655	0.193328	+	0.981134i	$0.438072\pi$
$594$	−38.9861	−1.59962
$595$	30.2190	1.23886
$596$	10.2309	0.419074
$597$	67.1547	2.74846
$598$	66.1642	2.70566
$599$	4.72676	0.193130	0.0965650	−	0.995327i	$-0.469214\pi$
$599$	4.72676	0.193130	0.0965650	+	0.995327i	$0.469214\pi$
$600$	26.4421	1.07950
$601$	−46.9474	−1.91502	−0.957512	−	0.288393i	$-0.906879\pi$
$601$	−46.9474	−1.91502	−0.957512	+	0.288393i	$0.906879\pi$
$602$	35.9470	1.46509
$603$	−11.6169	−0.473076
$604$	48.0947	1.95694
$605$	−88.5366	−3.59953
$606$	−10.7829	−0.438027
$607$	19.4563	0.789709	0.394854	−	0.918744i	$-0.370795\pi$
$607$	19.4563	0.789709	0.394854	+	0.918744i	$0.370795\pi$
$608$	57.0275	2.31277
$609$	13.0467	0.528677
$610$	29.1709	1.18110
$611$	−37.1873	−1.50444
$612$	68.9543	2.78731
$613$	−28.3219	−1.14391	−0.571956	−	0.820285i	$-0.693815\pi$
$613$	−28.3219	−1.14391	−0.571956	+	0.820285i	$0.693815\pi$
$614$	−37.8014	−1.52554
$615$	−14.8382	−0.598335
$616$	−13.4723	−0.542816
$617$	8.29970	0.334133	0.167067	−	0.985946i	$-0.446570\pi$
$617$	8.29970	0.334133	0.167067	+	0.985946i	$0.446570\pi$
$618$	−102.769	−4.13399
$619$	−7.73179	−0.310767	−0.155383	−	0.987854i	$-0.549661\pi$
$619$	−7.73179	−0.310767	−0.155383	+	0.987854i	$0.549661\pi$
$620$	−55.8543	−2.24316
$621$	−14.8173	−0.594600
$622$	−7.06661	−0.283345
$623$	−21.9394	−0.878983
$624$	−33.6944	−1.34886
$625$	−15.5726	−0.622903
$626$	−24.6227	−0.984121
$627$	122.049	4.87417
$628$	20.5529	0.820152
$629$	−30.3044	−1.20832
$630$	−43.4049	−1.72929
$631$	16.7670	0.667482	0.333741	−	0.942665i	$-0.391689\pi$
$631$	16.7670	0.667482	0.333741	+	0.942665i	$0.391689\pi$
$632$	−0.374304	−0.0148890
$633$	70.0046	2.78243
$634$	21.7793	0.864966
$635$	−46.8668	−1.85985
$636$	−27.9217	−1.10717
$637$	29.8989	1.18464
$638$	44.9733	1.78051
$639$	4.10584	0.162424
$640$	−38.9836	−1.54096
$641$	−7.35734	−0.290597	−0.145299	−	0.989388i	$-0.546414\pi$
$641$	−7.35734	−0.290597	−0.145299	+	0.989388i	$0.546414\pi$
$642$	103.605	4.08898
$643$	−9.93369	−0.391746	−0.195873	−	0.980629i	$-0.562754\pi$
$643$	−9.93369	−0.391746	−0.195873	+	0.980629i	$0.562754\pi$
$644$	−19.5898	−0.771945
$645$	103.872	4.08996
$646$	−101.084	−3.97708
$647$	12.5429	0.493111	0.246555	−	0.969129i	$-0.420701\pi$
$647$	12.5429	0.493111	0.246555	+	0.969129i	$0.420701\pi$
$648$	6.84840	0.269031
$649$	−20.5094	−0.805065
$650$	85.0253	3.33497
$651$	23.3786	0.916281
$652$	35.4368	1.38781
$653$	22.5135	0.881019	0.440510	−	0.897748i	$-0.354798\pi$
$653$	22.5135	0.881019	0.440510	+	0.897748i	$0.354798\pi$
$654$	−66.6234	−2.60518
$655$	36.6178	1.43078
$656$	3.42609	0.133766
$657$	−6.89000	−0.268805
$658$	19.1428	0.746264
$659$	−19.2796	−0.751028	−0.375514	−	0.926817i	$-0.622534\pi$
$659$	−19.2796	−0.751028	−0.375514	+	0.926817i	$0.622534\pi$
$660$	−148.937	−5.79738
$661$	37.9334	1.47544	0.737719	−	0.675108i	$-0.235903\pi$
$661$	37.9334	1.47544	0.737719	+	0.675108i	$0.235903\pi$
$662$	−18.1824	−0.706678
$663$	100.300	3.89534
$664$	−19.3084	−0.749312
$665$	36.5977	1.41920
$666$	43.5276	1.68666
$667$	17.0929	0.661840
$668$	30.8560	1.19386
$669$	59.0731	2.28390
$670$	−20.7815	−0.802860
$671$	−24.2083	−0.934551
$672$	29.1283	1.12365
$673$	6.86402	0.264589	0.132294	−	0.991210i	$-0.457766\pi$
$673$	6.86402	0.264589	0.132294	+	0.991210i	$0.457766\pi$
$674$	−1.81794	−0.0700245
$675$	−19.0413	−0.732899
$676$	64.4540	2.47900
$677$	10.2353	0.393376	0.196688	−	0.980466i	$-0.436981\pi$
$677$	10.2353	0.393376	0.196688	+	0.980466i	$0.436981\pi$
$678$	−5.78382	−0.222126
$679$	−14.5279	−0.557531
$680$	32.2422	1.23643
$681$	−0.155500	−0.00595876
$682$	80.5889	3.08591
$683$	−5.25691	−0.201150	−0.100575	−	0.994929i	$-0.532068\pi$
$683$	−5.25691	−0.201150	−0.100575	+	0.994929i	$0.532068\pi$
$684$	83.5094	3.19306
$685$	−65.1112	−2.48777
$686$	−37.2511	−1.42225
$687$	59.5596	2.27234
$688$	−23.9836	−0.914368
$689$	−23.4676	−0.894043
$690$	−98.4167	−3.74666
$691$	−24.9652	−0.949721	−0.474861	−	0.880061i	$-0.657502\pi$
$691$	−24.9652	−0.949721	−0.474861	+	0.880061i	$0.657502\pi$
$692$	−37.6063	−1.42958
$693$	36.0208	1.36832
$694$	36.4173	1.38238
$695$	−1.27332	−0.0482998
$696$	13.9201	0.527642
$697$	−10.1986	−0.386301
$698$	4.64272	0.175730
$699$	−3.24351	−0.122681
$700$	−25.1741	−0.951492
$701$	−49.4819	−1.86891	−0.934453	−	0.356086i	$-0.884111\pi$
$701$	−49.4819	−1.86891	−0.934453	+	0.356086i	$0.884111\pi$
$702$	−38.8016	−1.46447
$703$	−36.7011	−1.38421
$704$	75.0084	2.82698
$705$	55.3147	2.08327
$706$	−43.8693	−1.65104
$707$	2.68331	0.100916
$708$	−24.2866	−0.912747
$709$	45.2110	1.69793	0.848967	−	0.528447i	$-0.177225\pi$
$709$	45.2110	1.69793	0.848967	+	0.528447i	$0.177225\pi$
$710$	7.34496	0.275651
$711$	1.00077	0.0375318
$712$	−23.4083	−0.877262
$713$	30.6292	1.14707
$714$	−51.6312	−1.93225
$715$	−125.179	−4.68142
$716$	22.0094	0.822531
$717$	−22.3735	−0.835553
$718$	73.0013	2.72439
$719$	−18.9214	−0.705649	−0.352825	−	0.935690i	$-0.614779\pi$
$719$	−18.9214	−0.705649	−0.352825	+	0.935690i	$0.614779\pi$
$720$	28.9595	1.07926
$721$	25.5739	0.952422
$722$	−81.1955	−3.02178
$723$	−28.8027	−1.07119
$724$	−22.9818	−0.854113
$725$	21.9655	0.815779
$726$	151.271	5.61419
$727$	2.90078	0.107584	0.0537921	−	0.998552i	$-0.482869\pi$
$727$	2.90078	0.107584	0.0537921	+	0.998552i	$0.482869\pi$
$728$	−13.4086	−0.496956
$729$	−41.8841	−1.55126
$730$	−12.3256	−0.456190
$731$	71.3935	2.64058
$732$	−28.6667	−1.05955
$733$	6.77507	0.250243	0.125121	−	0.992141i	$-0.460068\pi$
$733$	6.77507	0.250243	0.125121	+	0.992141i	$0.460068\pi$
$734$	31.3331	1.15653
$735$	−44.4734	−1.64043
$736$	38.1621	1.40667
$737$	17.2461	0.635269
$738$	14.6488	0.539229
$739$	−18.1070	−0.666076	−0.333038	−	0.942913i	$-0.608074\pi$
$739$	−18.1070	−0.666076	−0.333038	+	0.942913i	$0.608074\pi$
$740$	44.7866	1.64639
$741$	121.472	4.46238
$742$	12.0803	0.443482
$743$	18.7634	0.688364	0.344182	−	0.938903i	$-0.388156\pi$
$743$	18.7634	0.688364	0.344182	+	0.938903i	$0.388156\pi$
$744$	24.9439	0.914487
$745$	−12.7905	−0.468607
$746$	13.3618	0.489210
$747$	51.6246	1.88884
$748$	−102.368	−3.74294
$749$	−25.7819	−0.942050
$750$	−28.5754	−1.04343
$751$	19.8694	0.725045	0.362523	−	0.931975i	$-0.381916\pi$
$751$	19.8694	0.725045	0.362523	+	0.931975i	$0.381916\pi$
$752$	−12.7719	−0.465745
$753$	−62.9998	−2.29584
$754$	44.7606	1.63008
$755$	−60.1270	−2.18825
$756$	11.4883	0.417826
$757$	0.865815	0.0314686	0.0157343	−	0.999876i	$-0.494991\pi$
$757$	0.865815	0.0314686	0.0157343	+	0.999876i	$0.494991\pi$
$758$	2.51308	0.0912792
$759$	81.6738	2.96457
$760$	39.0479	1.41642
$761$	26.3352	0.954652	0.477326	−	0.878726i	$-0.341606\pi$
$761$	26.3352	0.954652	0.477326	+	0.878726i	$0.341606\pi$
$762$	80.0752	2.90082
$763$	16.5790	0.600201
$764$	−22.1242	−0.800425
$765$	−86.2053	−3.11676
$766$	15.1712	0.548157
$767$	−20.4124	−0.737049
$768$	1.00018	0.0360907
$769$	−54.9268	−1.98071	−0.990355	−	0.138554i	$-0.955755\pi$
$769$	−54.9268	−1.98071	−0.990355	+	0.138554i	$0.955755\pi$
$770$	64.4378	2.32218
$771$	−47.3787	−1.70630
$772$	25.5721	0.920362
$773$	19.6448	0.706575	0.353288	−	0.935515i	$-0.385064\pi$
$773$	19.6448	0.706575	0.353288	+	0.935515i	$0.385064\pi$
$774$	−102.546	−3.68593
$775$	39.3606	1.41387
$776$	−15.5006	−0.556439
$777$	−18.7461	−0.672512
$778$	2.06077	0.0738822
$779$	−12.3514	−0.442535
$780$	−148.233	−5.30758
$781$	−6.09542	−0.218111
$782$	−67.6439	−2.41894
$783$	−10.0240	−0.358230
$784$	10.2687	0.366741
$785$	−25.6949	−0.917089
$786$	−62.5640	−2.23158
$787$	−24.2082	−0.862930	−0.431465	−	0.902130i	$-0.642003\pi$
$787$	−24.2082	−0.862930	−0.431465	+	0.902130i	$0.642003\pi$
$788$	−9.69682	−0.345435
$789$	47.3031	1.68403
$790$	1.79028	0.0636954
$791$	1.43929	0.0511752
$792$	38.4324	1.36564
$793$	−24.0938	−0.855595
$794$	−74.2090	−2.63358
$795$	34.9071	1.23803
$796$	−68.2148	−2.41781
$797$	−9.03128	−0.319904	−0.159952	−	0.987125i	$-0.551134\pi$
$797$	−9.03128	−0.319904	−0.159952	+	0.987125i	$0.551134\pi$
$798$	−62.5296	−2.21352
$799$	38.0190	1.34502
$800$	49.0408	1.73385
$801$	62.5862	2.21138
$802$	−53.1649	−1.87732
$803$	10.2287	0.360964
$804$	20.4223	0.720240
$805$	24.4907	0.863184
$806$	80.2076	2.82519
$807$	15.1318	0.532665
$808$	2.86296	0.100718
$809$	25.3969	0.892908	0.446454	−	0.894807i	$-0.352687\pi$
$809$	25.3969	0.892908	0.446454	+	0.894807i	$0.352687\pi$
$810$	−32.7557	−1.15092
$811$	−23.3669	−0.820521	−0.410261	−	0.911968i	$-0.634562\pi$
$811$	−23.3669	−0.820521	−0.410261	+	0.911968i	$0.634562\pi$
$812$	−13.2526	−0.465076
$813$	7.46470	0.261799
$814$	−64.6199	−2.26493
$815$	−44.3023	−1.55184
$816$	34.4480	1.20592
$817$	86.4634	3.02497
$818$	−65.9596	−2.30622
$819$	35.8503	1.25271
$820$	15.0725	0.526354
$821$	23.1734	0.808757	0.404378	−	0.914592i	$-0.367488\pi$
$821$	23.1734	0.808757	0.404378	+	0.914592i	$0.367488\pi$
$822$	111.247	3.88019
$823$	−56.8566	−1.98190	−0.990948	−	0.134249i	$-0.957138\pi$
$823$	−56.8566	−1.98190	−0.990948	+	0.134249i	$0.957138\pi$
$824$	27.2861	0.950556
$825$	104.956	3.65411
$826$	10.5076	0.365607
$827$	−18.6498	−0.648518	−0.324259	−	0.945968i	$-0.605115\pi$
$827$	−18.6498	−0.648518	−0.324259	+	0.945968i	$0.605115\pi$
$828$	55.8835	1.94208
$829$	11.5920	0.402608	0.201304	−	0.979529i	$-0.435482\pi$
$829$	11.5920	0.402608	0.201304	+	0.979529i	$0.435482\pi$
$830$	92.3515	3.20557
$831$	−45.5832	−1.58126
$832$	74.6535	2.58815
$833$	−30.5675	−1.05910
$834$	2.17555	0.0753333
$835$	−38.5756	−1.33496
$836$	−123.976	−4.28779
$837$	−17.9623	−0.620869
$838$	−12.4777	−0.431036
$839$	26.1422	0.902530	0.451265	−	0.892390i	$-0.350973\pi$
$839$	26.1422	0.902530	0.451265	+	0.892390i	$0.350973\pi$
$840$	19.9448	0.688160
$841$	−17.4365	−0.601259
$842$	1.89951	0.0654614
$843$	−33.9147	−1.16808
$844$	−71.1097	−2.44770
$845$	−80.5791	−2.77200
$846$	−54.6084	−1.87748
$847$	−37.6433	−1.29344
$848$	−8.05991	−0.276778
$849$	24.7635	0.849880
$850$	−86.9269	−2.98157
$851$	−24.5600	−0.841904
$852$	−7.21801	−0.247285
$853$	10.7118	0.366765	0.183383	−	0.983042i	$-0.441295\pi$
$853$	10.7118	0.366765	0.183383	+	0.983042i	$0.441295\pi$
$854$	12.4027	0.424410
$855$	−104.402	−3.57046
$856$	−27.5080	−0.940205
$857$	16.4061	0.560422	0.280211	−	0.959938i	$-0.409596\pi$
$857$	16.4061	0.560422	0.280211	+	0.959938i	$0.409596\pi$
$858$	213.876	7.30162
$859$	12.2268	0.417171	0.208586	−	0.978004i	$-0.433114\pi$
$859$	12.2268	0.417171	0.208586	+	0.978004i	$0.433114\pi$
$860$	−105.512	−3.59792
$861$	−6.30881	−0.215004
$862$	−41.6926	−1.42006
$863$	19.2168	0.654149	0.327074	−	0.944999i	$-0.393937\pi$
$863$	19.2168	0.654149	0.327074	+	0.944999i	$0.393937\pi$
$864$	−22.3800	−0.761382
$865$	47.0146	1.59855
$866$	73.6139	2.50150
$867$	−57.2268	−1.94352
$868$	−23.7477	−0.806049
$869$	−1.48572	−0.0503995
$870$	−66.5796	−2.25726
$871$	17.1645	0.581598
$872$	17.6890	0.599026
$873$	41.4437	1.40266
$874$	−81.9223	−2.77106
$875$	7.11091	0.240393
$876$	12.1125	0.409245
$877$	−9.18300	−0.310088	−0.155044	−	0.987908i	$-0.549552\pi$
$877$	−9.18300	−0.310088	−0.155044	+	0.987908i	$0.549552\pi$
$878$	−41.0666	−1.38593
$879$	−38.3085	−1.29211
$880$	−42.9925	−1.44928
$881$	29.9817	1.01011	0.505054	−	0.863088i	$-0.331473\pi$
$881$	29.9817	1.01011	0.505054	+	0.863088i	$0.331473\pi$
$882$	43.9055	1.47838
$883$	−45.9984	−1.54797	−0.773985	−	0.633204i	$-0.781740\pi$
$883$	−45.9984	−1.54797	−0.773985	+	0.633204i	$0.781740\pi$
$884$	−101.884	−3.42671
$885$	30.3626	1.02063
$886$	−41.2143	−1.38462
$887$	9.38333	0.315061	0.157531	−	0.987514i	$-0.449647\pi$
$887$	9.38333	0.315061	0.157531	+	0.987514i	$0.449647\pi$
$888$	−20.0012	−0.671195
$889$	−19.9265	−0.668313
$890$	111.961	3.75294
$891$	27.1832	0.910672
$892$	−60.0056	−2.00914
$893$	46.0441	1.54081
$894$	21.8534	0.730887
$895$	−27.5157	−0.919749
$896$	−16.5748	−0.553724
$897$	81.2875	2.71411
$898$	−30.3423	−1.01253
$899$	20.7209	0.691081
$900$	71.8139	2.39380
$901$	23.9924	0.799303
$902$	−21.7472	−0.724102
$903$	44.1635	1.46967
$904$	1.53565	0.0510749
$905$	28.7314	0.955064
$906$	102.731	3.41301
$907$	14.1961	0.471375	0.235688	−	0.971829i	$-0.424266\pi$
$907$	14.1961	0.471375	0.235688	+	0.971829i	$0.424266\pi$
$908$	0.157954	0.00524190
$909$	−7.65463	−0.253888
$910$	64.1329	2.12599
$911$	28.7540	0.952662	0.476331	−	0.879266i	$-0.341966\pi$
$911$	28.7540	0.952662	0.476331	+	0.879266i	$0.341966\pi$
$912$	41.7194	1.38147
$913$	−76.6405	−2.53643
$914$	−68.9239	−2.27980
$915$	35.8386	1.18479
$916$	−60.4998	−1.99897
$917$	15.5689	0.514130
$918$	39.6694	1.30929
$919$	29.9655	0.988470	0.494235	−	0.869328i	$-0.335448\pi$
$919$	29.9655	0.988470	0.494235	+	0.869328i	$0.335448\pi$
$920$	26.1304	0.861494
$921$	−46.4417	−1.53031
$922$	−3.38779	−0.111571
$923$	−6.06658	−0.199684
$924$	−63.3240	−2.08321
$925$	−31.5612	−1.03772
$926$	2.11479	0.0694963
$927$	−72.9543	−2.39614
$928$	25.8170	0.847483
$929$	−41.6375	−1.36608	−0.683041	−	0.730380i	$-0.739343\pi$
$929$	−41.6375	−1.36608	−0.683041	+	0.730380i	$0.739343\pi$
$930$	−119.306	−3.91219
$931$	−37.0198	−1.21328
$932$	3.29471	0.107922
$933$	−8.68184	−0.284231
$934$	−71.5707	−2.34186
$935$	127.978	4.18533
$936$	38.2506	1.25026
$937$	24.3356	0.795009	0.397505	−	0.917600i	$-0.369876\pi$
$937$	24.3356	0.795009	0.397505	+	0.917600i	$0.369876\pi$
$938$	−8.83573	−0.288497
$939$	−30.2508	−0.987196
$940$	−56.1879	−1.83265
$941$	44.1740	1.44003	0.720015	−	0.693958i	$-0.244135\pi$
$941$	44.1740	1.44003	0.720015	+	0.693958i	$0.244135\pi$
$942$	43.9015	1.43039
$943$	−8.26540	−0.269159
$944$	−7.01062	−0.228176
$945$	−14.3624	−0.467210
$946$	152.237	4.94964
$947$	37.5641	1.22067	0.610334	−	0.792144i	$-0.291035\pi$
$947$	37.5641	1.22067	0.610334	+	0.792144i	$0.291035\pi$
$948$	−1.75934	−0.0571407
$949$	10.1803	0.330468
$950$	−105.276	−3.41559
$951$	26.7574	0.867669
$952$	13.7085	0.444294
$953$	14.6093	0.473243	0.236621	−	0.971602i	$-0.423960\pi$
$953$	14.6093	0.473243	0.236621	+	0.971602i	$0.423960\pi$
$954$	−34.4614	−1.11573
$955$	27.6592	0.895031
$956$	22.7267	0.735033
$957$	55.2530	1.78607
$958$	37.7382	1.21926
$959$	−27.6835	−0.893947
$960$	−111.044	−3.58394
$961$	6.13030	0.197752
$962$	−64.3142	−2.07357
$963$	73.5477	2.37004
$964$	29.2574	0.942318
$965$	−31.9698	−1.02914
$966$	−41.8441	−1.34631
$967$	22.2169	0.714447	0.357224	−	0.934019i	$-0.383723\pi$
$967$	22.2169	0.714447	0.357224	+	0.934019i	$0.383723\pi$
$968$	−40.1636	−1.29091
$969$	−124.188	−3.98951
$970$	74.1388	2.38045
$971$	58.0033	1.86142	0.930708	−	0.365763i	$-0.119192\pi$
$971$	58.0033	1.86142	0.930708	+	0.365763i	$0.119192\pi$
$972$	56.1354	1.80054
$973$	−0.541380	−0.0173559
$974$	28.3406	0.908092
$975$	104.460	3.34539
$976$	−8.27498	−0.264876
$977$	11.7627	0.376323	0.188161	−	0.982138i	$-0.439747\pi$
$977$	11.7627	0.376323	0.188161	+	0.982138i	$0.439747\pi$
$978$	75.6936	2.42041
$979$	−92.9139	−2.96954
$980$	45.1755	1.44308
$981$	−47.2948	−1.51001
$982$	91.4156	2.91719
$983$	−7.81308	−0.249199	−0.124599	−	0.992207i	$-0.539765\pi$
$983$	−7.81308	−0.249199	−0.124599	+	0.992207i	$0.539765\pi$
$984$	−6.73119	−0.214583
$985$	12.1228	0.386264
$986$	−45.7616	−1.45735
$987$	23.5183	0.748595
$988$	−123.389	−3.92554
$989$	57.8603	1.83985
$990$	−183.821	−5.84221
$991$	−54.4711	−1.73033	−0.865165	−	0.501487i	$-0.832787\pi$
$991$	−54.4711	−1.73033	−0.865165	+	0.501487i	$0.832787\pi$
$992$	46.2621	1.46882
$993$	−22.3384	−0.708886
$994$	3.12287	0.0990516
$995$	85.2808	2.70358
$996$	−90.7554	−2.87569
$997$	16.2884	0.515858	0.257929	−	0.966164i	$-0.416960\pi$
$997$	16.2884	0.515858	0.257929	+	0.966164i	$0.416960\pi$
$998$	72.6836	2.30076
$999$	14.4031	0.455692

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8023.2.a.d.1.19	✓	165

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8023.2.a.d.1.19	✓	165	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)

\(f(q)\)	\(=\)	\(q-2.16974 q^{2} -2.66568 q^{3} +2.70776 q^{4} -3.38518 q^{5} +5.78382 q^{6} -1.43929 q^{7} -1.53565 q^{8} +4.10584 q^{9} +O(q^{10})\)	\(q-2.16974 q^{2} -2.66568 q^{3} +2.70776 q^{4} -3.38518 q^{5} +5.78382 q^{6} -1.43929 q^{7} -1.53565 q^{8} +4.10584 q^{9} +7.34496 q^{10} -6.09542 q^{11} -7.21801 q^{12} -6.06658 q^{13} +3.12287 q^{14} +9.02381 q^{15} -2.08356 q^{16} +6.20226 q^{17} -8.90859 q^{18} +7.51145 q^{19} -9.16626 q^{20} +3.83668 q^{21} +13.2255 q^{22} +5.02657 q^{23} +4.09355 q^{24} +6.45947 q^{25} +13.1629 q^{26} -2.94780 q^{27} -3.89724 q^{28} +3.40051 q^{29} -19.5793 q^{30} +6.09346 q^{31} +7.59208 q^{32} +16.2484 q^{33} -13.4573 q^{34} +4.87225 q^{35} +11.1176 q^{36} -4.88603 q^{37} -16.2979 q^{38} +16.1716 q^{39} +5.19845 q^{40} -1.64434 q^{41} -8.32458 q^{42} +11.5109 q^{43} -16.5049 q^{44} -13.8990 q^{45} -10.9063 q^{46} +6.12986 q^{47} +5.55410 q^{48} -4.92845 q^{49} -14.0154 q^{50} -16.5332 q^{51} -16.4268 q^{52} +3.86833 q^{53} +6.39596 q^{54} +20.6341 q^{55} +2.21024 q^{56} -20.0231 q^{57} -7.37822 q^{58} +3.36473 q^{59} +24.4343 q^{60} +3.97155 q^{61} -13.2212 q^{62} -5.90948 q^{63} -12.3057 q^{64} +20.5365 q^{65} -35.2548 q^{66} -2.82936 q^{67} +16.7942 q^{68} -13.3992 q^{69} -10.5715 q^{70} +1.00000 q^{71} -6.30512 q^{72} -1.67810 q^{73} +10.6014 q^{74} -17.2189 q^{75} +20.3392 q^{76} +8.77306 q^{77} -35.0880 q^{78} +0.243743 q^{79} +7.05324 q^{80} -4.45961 q^{81} +3.56779 q^{82} +12.5735 q^{83} +10.3888 q^{84} -20.9958 q^{85} -24.9756 q^{86} -9.06467 q^{87} +9.36043 q^{88} +15.2432 q^{89} +30.1572 q^{90} +8.73156 q^{91} +13.6107 q^{92} -16.2432 q^{93} -13.3002 q^{94} -25.4276 q^{95} -20.2380 q^{96} +10.0938 q^{97} +10.6934 q^{98} -25.0268 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 165 q + 22 q^{2} + 18 q^{3} + 166 q^{4} + 28 q^{5} + 16 q^{6} + 24 q^{7} + 66 q^{8} + 177 q^{9}+O(q^{10}) \) 165 * q + 22 * q^2 + 18 * q^3 + 166 * q^4 + 28 * q^5 + 16 * q^6 + 24 * q^7 + 66 * q^8 + 177 * q^9	\( 165 q + 22 q^{2} + 18 q^{3} + 166 q^{4} + 28 q^{5} + 16 q^{6} + 24 q^{7} + 66 q^{8} + 177 q^{9} + 14 q^{10} + 18 q^{11} + 54 q^{12} + 44 q^{13} + 26 q^{14} + 24 q^{15} + 168 q^{16} + 143 q^{17} + 57 q^{18} + 20 q^{19} + 49 q^{20} + 39 q^{21} + 25 q^{22} + 52 q^{23} + 27 q^{24} + 175 q^{25} + 48 q^{26} + 69 q^{27} + 28 q^{28} + 58 q^{29} - 11 q^{30} + 28 q^{31} + 114 q^{32} + 110 q^{33} + 55 q^{34} + 67 q^{35} + 202 q^{36} + 44 q^{37} + 35 q^{38} + 27 q^{39} + 53 q^{40} + 141 q^{41} + 40 q^{42} + 29 q^{43} + 52 q^{44} + 54 q^{45} + 29 q^{46} + 87 q^{47} + 53 q^{48} + 143 q^{49} + 16 q^{50} + 37 q^{51} + 105 q^{52} + 101 q^{53} - 36 q^{54} + 72 q^{55} + 57 q^{56} + 82 q^{57} + 4 q^{58} + 103 q^{59} + 53 q^{60} + 16 q^{61} + 54 q^{62} + 126 q^{63} + 136 q^{64} + 159 q^{65} + 53 q^{66} + 60 q^{67} + 220 q^{68} + 81 q^{69} + 16 q^{70} + 165 q^{71} + 176 q^{72} + 124 q^{73} + 29 q^{74} + 44 q^{75} + 18 q^{76} + 127 q^{77} - 91 q^{78} + 14 q^{79} + 158 q^{80} + 213 q^{81} + 20 q^{82} + 116 q^{83} + 67 q^{84} + 59 q^{85} + 30 q^{86} + 28 q^{87} + 79 q^{88} + 195 q^{89} + 16 q^{90} - 26 q^{91} + 173 q^{92} + 116 q^{93} + 53 q^{94} + 26 q^{95} - 36 q^{96} + 88 q^{97} + 150 q^{98} + 12 q^{99}+O(q^{100}) \) 165 * q + 22 * q^2 + 18 * q^3 + 166 * q^4 + 28 * q^5 + 16 * q^6 + 24 * q^7 + 66 * q^8 + 177 * q^9 + 14 * q^10 + 18 * q^11 + 54 * q^12 + 44 * q^13 + 26 * q^14 + 24 * q^15 + 168 * q^16 + 143 * q^17 + 57 * q^18 + 20 * q^19 + 49 * q^20 + 39 * q^21 + 25 * q^22 + 52 * q^23 + 27 * q^24 + 175 * q^25 + 48 * q^26 + 69 * q^27 + 28 * q^28 + 58 * q^29 - 11 * q^30 + 28 * q^31 + 114 * q^32 + 110 * q^33 + 55 * q^34 + 67 * q^35 + 202 * q^36 + 44 * q^37 + 35 * q^38 + 27 * q^39 + 53 * q^40 + 141 * q^41 + 40 * q^42 + 29 * q^43 + 52 * q^44 + 54 * q^45 + 29 * q^46 + 87 * q^47 + 53 * q^48 + 143 * q^49 + 16 * q^50 + 37 * q^51 + 105 * q^52 + 101 * q^53 - 36 * q^54 + 72 * q^55 + 57 * q^56 + 82 * q^57 + 4 * q^58 + 103 * q^59 + 53 * q^60 + 16 * q^61 + 54 * q^62 + 126 * q^63 + 136 * q^64 + 159 * q^65 + 53 * q^66 + 60 * q^67 + 220 * q^68 + 81 * q^69 + 16 * q^70 + 165 * q^71 + 176 * q^72 + 124 * q^73 + 29 * q^74 + 44 * q^75 + 18 * q^76 + 127 * q^77 - 91 * q^78 + 14 * q^79 + 158 * q^80 + 213 * q^81 + 20 * q^82 + 116 * q^83 + 67 * q^84 + 59 * q^85 + 30 * q^86 + 28 * q^87 + 79 * q^88 + 195 * q^89 + 16 * q^90 - 26 * q^91 + 173 * q^92 + 116 * q^93 + 53 * q^94 + 26 * q^95 - 36 * q^96 + 88 * q^97 + 150 * q^98 + 12 * q^99

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