LMFDB - Embedded newform 8017.2.a.a.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8017,2,Mod(1,8017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8017, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8017 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8017.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:	$64.0160673005$
Analytic rank:	$1$
Dimension:	$327$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	8017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.76002 q^{2} -0.752350 q^{3} +5.61769 q^{4} -2.62302 q^{5} +2.07650 q^{6} +4.59409 q^{7} -9.98488 q^{8} -2.43397 q^{9} +O(q^{10})$	\(q-2.76002 q^{2} -0.752350 q^{3} +5.61769 q^{4} -2.62302 q^{5} +2.07650 q^{6} +4.59409 q^{7} -9.98488 q^{8} -2.43397 q^{9} +7.23958 q^{10} +2.12045 q^{11} -4.22647 q^{12} +2.60752 q^{13} -12.6798 q^{14} +1.97343 q^{15} +16.3230 q^{16} -0.262375 q^{17} +6.71780 q^{18} -6.38245 q^{19} -14.7353 q^{20} -3.45636 q^{21} -5.85247 q^{22} +0.941829 q^{23} +7.51212 q^{24} +1.88023 q^{25} -7.19680 q^{26} +4.08825 q^{27} +25.8082 q^{28} +0.982750 q^{29} -5.44669 q^{30} -2.38731 q^{31} -25.0821 q^{32} -1.59532 q^{33} +0.724158 q^{34} -12.0504 q^{35} -13.6733 q^{36} +4.25590 q^{37} +17.6157 q^{38} -1.96177 q^{39} +26.1905 q^{40} -0.146980 q^{41} +9.53962 q^{42} +4.49893 q^{43} +11.9120 q^{44} +6.38435 q^{45} -2.59946 q^{46} +2.03437 q^{47} -12.2806 q^{48} +14.1057 q^{49} -5.18947 q^{50} +0.197397 q^{51} +14.6482 q^{52} -7.92689 q^{53} -11.2836 q^{54} -5.56198 q^{55} -45.8714 q^{56} +4.80184 q^{57} -2.71240 q^{58} +0.667569 q^{59} +11.0861 q^{60} -5.29793 q^{61} +6.58902 q^{62} -11.1819 q^{63} +36.5809 q^{64} -6.83958 q^{65} +4.40311 q^{66} +10.6526 q^{67} -1.47394 q^{68} -0.708585 q^{69} +33.2593 q^{70} -12.5770 q^{71} +24.3029 q^{72} -2.98526 q^{73} -11.7463 q^{74} -1.41459 q^{75} -35.8546 q^{76} +9.74153 q^{77} +5.41451 q^{78} -7.94639 q^{79} -42.8157 q^{80} +4.22612 q^{81} +0.405666 q^{82} -14.3877 q^{83} -19.4168 q^{84} +0.688214 q^{85} -12.4171 q^{86} -0.739371 q^{87} -21.1724 q^{88} +8.46989 q^{89} -17.6209 q^{90} +11.9792 q^{91} +5.29090 q^{92} +1.79609 q^{93} -5.61490 q^{94} +16.7413 q^{95} +18.8705 q^{96} +3.84796 q^{97} -38.9319 q^{98} -5.16111 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 327 q - 23 q^{2} - 48 q^{3} + 315 q^{4} - 55 q^{5} - 38 q^{6} - 87 q^{7} - 69 q^{8} + 303 q^{9}+O(q^{10}) $ 327 * q - 23 * q^2 - 48 * q^3 + 315 * q^4 - 55 * q^5 - 38 * q^6 - 87 * q^7 - 69 * q^8 + 303 * q^9	\( 327 q - 23 q^{2} - 48 q^{3} + 315 q^{4} - 55 q^{5} - 38 q^{6} - 87 q^{7} - 69 q^{8} + 303 q^{9} - 48 q^{10} - 70 q^{11} - 120 q^{12} - 53 q^{13} - 52 q^{14} - 77 q^{15} + 295 q^{16} - 164 q^{17} - 58 q^{18} - 47 q^{19} - 153 q^{20} - 39 q^{21} - 68 q^{22} - 256 q^{23} - 107 q^{24} + 288 q^{25} - 95 q^{26} - 189 q^{27} - 167 q^{28} - 99 q^{29} - 81 q^{30} - 71 q^{31} - 146 q^{32} - 95 q^{33} - 40 q^{34} - 192 q^{35} + 261 q^{36} - 54 q^{37} - 179 q^{38} - 115 q^{39} - 121 q^{40} - 111 q^{41} - 62 q^{42} - 110 q^{43} - 157 q^{44} - 137 q^{45} - 11 q^{46} - 324 q^{47} - 236 q^{48} + 296 q^{49} - 73 q^{50} - 88 q^{51} - 138 q^{52} - 170 q^{53} - 127 q^{54} - 151 q^{55} - 151 q^{56} - 106 q^{57} - 81 q^{58} - 123 q^{59} - 83 q^{60} - 62 q^{61} - 287 q^{62} - 400 q^{63} + 263 q^{64} - 143 q^{65} - 64 q^{66} - 95 q^{67} - 442 q^{68} - 22 q^{69} - 26 q^{70} - 210 q^{71} - 129 q^{72} - 121 q^{73} - 159 q^{74} - 194 q^{75} - 86 q^{76} - 178 q^{77} - 68 q^{78} - 145 q^{79} - 338 q^{80} + 259 q^{81} - 103 q^{82} - 418 q^{83} - 102 q^{84} - 40 q^{85} - 89 q^{86} - 372 q^{87} - 186 q^{88} - 100 q^{89} - 150 q^{90} - 69 q^{91} - 458 q^{92} - 81 q^{93} - 46 q^{94} - 377 q^{95} - 190 q^{96} - 87 q^{97} - 147 q^{98} - 171 q^{99}+O(q^{100}) \) 327 * q - 23 * q^2 - 48 * q^3 + 315 * q^4 - 55 * q^5 - 38 * q^6 - 87 * q^7 - 69 * q^8 + 303 * q^9 - 48 * q^10 - 70 * q^11 - 120 * q^12 - 53 * q^13 - 52 * q^14 - 77 * q^15 + 295 * q^16 - 164 * q^17 - 58 * q^18 - 47 * q^19 - 153 * q^20 - 39 * q^21 - 68 * q^22 - 256 * q^23 - 107 * q^24 + 288 * q^25 - 95 * q^26 - 189 * q^27 - 167 * q^28 - 99 * q^29 - 81 * q^30 - 71 * q^31 - 146 * q^32 - 95 * q^33 - 40 * q^34 - 192 * q^35 + 261 * q^36 - 54 * q^37 - 179 * q^38 - 115 * q^39 - 121 * q^40 - 111 * q^41 - 62 * q^42 - 110 * q^43 - 157 * q^44 - 137 * q^45 - 11 * q^46 - 324 * q^47 - 236 * q^48 + 296 * q^49 - 73 * q^50 - 88 * q^51 - 138 * q^52 - 170 * q^53 - 127 * q^54 - 151 * q^55 - 151 * q^56 - 106 * q^57 - 81 * q^58 - 123 * q^59 - 83 * q^60 - 62 * q^61 - 287 * q^62 - 400 * q^63 + 263 * q^64 - 143 * q^65 - 64 * q^66 - 95 * q^67 - 442 * q^68 - 22 * q^69 - 26 * q^70 - 210 * q^71 - 129 * q^72 - 121 * q^73 - 159 * q^74 - 194 * q^75 - 86 * q^76 - 178 * q^77 - 68 * q^78 - 145 * q^79 - 338 * q^80 + 259 * q^81 - 103 * q^82 - 418 * q^83 - 102 * q^84 - 40 * q^85 - 89 * q^86 - 372 * q^87 - 186 * q^88 - 100 * q^89 - 150 * q^90 - 69 * q^91 - 458 * q^92 - 81 * q^93 - 46 * q^94 - 377 * q^95 - 190 * q^96 - 87 * q^97 - 147 * q^98 - 171 * 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 $

$2$	−2.76002	−1.95163	−0.975813	−	0.218607i	$-0.929849\pi$
$2$	−2.76002	−1.95163	−0.975813	+	0.218607i	$0.929849\pi$
$3$	−0.752350	−0.434369	−0.217185	−	0.976131i	$-0.569687\pi$
$3$	−0.752350	−0.434369	−0.217185	+	0.976131i	$0.569687\pi$
$4$	5.61769	2.80884
$5$	−2.62302	−1.17305	−0.586525	−	0.809931i	$-0.699504\pi$
$5$	−2.62302	−1.17305	−0.586525	+	0.809931i	$0.699504\pi$
$6$	2.07650	0.847726
$7$	4.59409	1.73640	0.868201	−	0.496212i	$-0.165276\pi$
$7$	4.59409	1.73640	0.868201	+	0.496212i	$0.165276\pi$
$8$	−9.98488	−3.53019
$9$	−2.43397	−0.811323
$10$	7.23958	2.28936
$11$	2.12045	0.639339	0.319670	−	0.947529i	$-0.396428\pi$
$11$	2.12045	0.639339	0.319670	+	0.947529i	$0.396428\pi$
$12$	−4.22647	−1.22008
$13$	2.60752	0.723197	0.361598	−	0.932334i	$-0.382231\pi$
$13$	2.60752	0.723197	0.361598	+	0.932334i	$0.382231\pi$
$14$	−12.6798	−3.38881
$15$	1.97343	0.509537
$16$	16.3230	4.08076
$17$	−0.262375	−0.0636352	−0.0318176	−	0.999494i	$-0.510130\pi$
$17$	−0.262375	−0.0636352	−0.0318176	+	0.999494i	$0.510130\pi$
$18$	6.71780	1.58340
$19$	−6.38245	−1.46424	−0.732118	−	0.681178i	$-0.761468\pi$
$19$	−6.38245	−1.46424	−0.732118	+	0.681178i	$0.761468\pi$
$20$	−14.7353	−3.29491
$21$	−3.45636	−0.754240
$22$	−5.85247	−1.24775
$23$	0.941829	0.196385	0.0981925	−	0.995167i	$-0.468694\pi$
$23$	0.941829	0.196385	0.0981925	+	0.995167i	$0.468694\pi$
$24$	7.51212	1.53340
$25$	1.88023	0.376047
$26$	−7.19680	−1.41141
$27$	4.08825	0.786783
$28$	25.8082	4.87729
$29$	0.982750	0.182492	0.0912460	−	0.995828i	$-0.470915\pi$
$29$	0.982750	0.182492	0.0912460	+	0.995828i	$0.470915\pi$
$30$	−5.44669	−0.994426
$31$	−2.38731	−0.428774	−0.214387	−	0.976749i	$-0.568775\pi$
$31$	−2.38731	−0.428774	−0.214387	+	0.976749i	$0.568775\pi$
$32$	−25.0821	−4.43393
$33$	−1.59532	−0.277709
$34$	0.724158	0.124192
$35$	−12.0504	−2.03689
$36$	−13.6733	−2.27888
$37$	4.25590	0.699665	0.349833	−	0.936812i	$-0.386238\pi$
$37$	4.25590	0.699665	0.349833	+	0.936812i	$0.386238\pi$
$38$	17.6157	2.85764
$39$	−1.96177	−0.314134
$40$	26.1905	4.14109
$41$	−0.146980	−0.0229544	−0.0114772	−	0.999934i	$-0.503653\pi$
$41$	−0.146980	−0.0229544	−0.0114772	+	0.999934i	$0.503653\pi$
$42$	9.53962	1.47199
$43$	4.49893	0.686081	0.343040	−	0.939321i	$-0.388543\pi$
$43$	4.49893	0.686081	0.343040	+	0.939321i	$0.388543\pi$
$44$	11.9120	1.79580
$45$	6.38435	0.951723
$46$	−2.59946	−0.383270
$47$	2.03437	0.296744	0.148372	−	0.988932i	$-0.452597\pi$
$47$	2.03437	0.296744	0.148372	+	0.988932i	$0.452597\pi$
$48$	−12.2806	−1.77256
$49$	14.1057	2.01510
$50$	−5.18947	−0.733902
$51$	0.197397	0.0276412
$52$	14.6482	2.03135
$53$	−7.92689	−1.08884	−0.544421	−	0.838812i	$-0.683251\pi$
$53$	−7.92689	−1.08884	−0.544421	+	0.838812i	$0.683251\pi$
$54$	−11.2836	−1.53551
$55$	−5.56198	−0.749977
$56$	−45.8714	−6.12983
$57$	4.80184	0.636019
$58$	−2.71240	−0.356156
$59$	0.667569	0.0869101	0.0434550	−	0.999055i	$-0.486163\pi$
$59$	0.667569	0.0869101	0.0434550	+	0.999055i	$0.486163\pi$
$60$	11.0861	1.43121
$61$	−5.29793	−0.678331	−0.339165	−	0.940727i	$-0.610145\pi$
$61$	−5.29793	−0.678331	−0.339165	+	0.940727i	$0.610145\pi$
$62$	6.58902	0.836806
$63$	−11.1819	−1.40878
$64$	36.5809	4.57262
$65$	−6.83958	−0.848346
$66$	4.40311	0.541985
$67$	10.6526	1.30142	0.650710	−	0.759326i	$-0.274471\pi$
$67$	10.6526	1.30142	0.650710	+	0.759326i	$0.274471\pi$
$68$	−1.47394	−0.178741
$69$	−0.708585	−0.0853036
$70$	33.2593	3.97524
$71$	−12.5770	−1.49261	−0.746306	−	0.665604i	$-0.768174\pi$
$71$	−12.5770	−1.49261	−0.746306	+	0.665604i	$0.768174\pi$
$72$	24.3029	2.86412
$73$	−2.98526	−0.349398	−0.174699	−	0.984622i	$-0.555895\pi$
$73$	−2.98526	−0.349398	−0.174699	+	0.984622i	$0.555895\pi$
$74$	−11.7463	−1.36549
$75$	−1.41459	−0.163343
$76$	−35.8546	−4.11281
$77$	9.74153	1.11015
$78$	5.41451	0.613073
$79$	−7.94639	−0.894038	−0.447019	−	0.894524i	$-0.647514\pi$
$79$	−7.94639	−0.894038	−0.447019	+	0.894524i	$0.647514\pi$
$80$	−42.8157	−4.78694
$81$	4.22612	0.469569
$82$	0.405666	0.0447983
$83$	−14.3877	−1.57926	−0.789629	−	0.613584i	$-0.789727\pi$
$83$	−14.3877	−1.57926	−0.789629	+	0.613584i	$0.789727\pi$
$84$	−19.4168	−2.11854
$85$	0.688214	0.0746473
$86$	−12.4171	−1.33897
$87$	−0.739371	−0.0792689
$88$	−21.1724	−2.25699
$89$	8.46989	0.897806	0.448903	−	0.893580i	$-0.351815\pi$
$89$	8.46989	0.897806	0.448903	+	0.893580i	$0.351815\pi$
$90$	−17.6209	−1.85741
$91$	11.9792	1.25576
$92$	5.29090	0.551615
$93$	1.79609	0.186246
$94$	−5.61490	−0.579133
$95$	16.7413	1.71762
$96$	18.8705	1.92596
$97$	3.84796	0.390701	0.195350	−	0.980734i	$-0.437416\pi$
$97$	3.84796	0.390701	0.195350	+	0.980734i	$0.437416\pi$
$98$	−38.9319	−3.93271
$99$	−5.16111	−0.518711
$100$	10.5626	1.05626
$101$	−0.0400515	−0.00398527	−0.00199264	−	0.999998i	$-0.500634\pi$
$101$	−0.0400515	−0.00398527	−0.00199264	+	0.999998i	$0.500634\pi$
$102$	−0.544820	−0.0539452
$103$	10.7695	1.06115	0.530575	−	0.847638i	$-0.321976\pi$
$103$	10.7695	1.06115	0.530575	+	0.847638i	$0.321976\pi$
$104$	−26.0358	−2.55302
$105$	9.06611	0.884761
$106$	21.8783	2.12501
$107$	−7.59320	−0.734063	−0.367031	−	0.930209i	$-0.619626\pi$
$107$	−7.59320	−0.734063	−0.367031	+	0.930209i	$0.619626\pi$
$108$	22.9665	2.20995
$109$	1.49684	0.143371	0.0716856	−	0.997427i	$-0.477162\pi$
$109$	1.49684	0.143371	0.0716856	+	0.997427i	$0.477162\pi$
$110$	15.3512	1.46367
$111$	−3.20192	−0.303913
$112$	74.9895	7.08585
$113$	−0.276222	−0.0259848	−0.0129924	−	0.999916i	$-0.504136\pi$
$113$	−0.276222	−0.0259848	−0.0129924	+	0.999916i	$0.504136\pi$
$114$	−13.2531	−1.24127
$115$	−2.47044	−0.230369
$116$	5.52078	0.512592
$117$	−6.34663	−0.586746
$118$	−1.84250	−0.169616
$119$	−1.20537	−0.110496
$120$	−19.7044	−1.79876
$121$	−6.50370	−0.591245
$122$	14.6224	1.32385
$123$	0.110580	0.00997067
$124$	−13.4112	−1.20436
$125$	8.18321	0.731929
$126$	30.8622	2.74942
$127$	−8.27008	−0.733851	−0.366926	−	0.930250i	$-0.619590\pi$
$127$	−8.27008	−0.733851	−0.366926	+	0.930250i	$0.619590\pi$
$128$	−50.7997	−4.49010
$129$	−3.38477	−0.298012
$130$	18.8774	1.65565
$131$	−3.45744	−0.302078	−0.151039	−	0.988528i	$-0.548262\pi$
$131$	−3.45744	−0.302078	−0.151039	+	0.988528i	$0.548262\pi$
$132$	−8.96200	−0.780042
$133$	−29.3216	−2.54250
$134$	−29.4013	−2.53989
$135$	−10.7235	−0.922936
$136$	2.61978	0.224644
$137$	7.19265	0.614509	0.307255	−	0.951627i	$-0.400590\pi$
$137$	7.19265	0.614509	0.307255	+	0.951627i	$0.400590\pi$
$138$	1.95571	0.166481
$139$	2.54364	0.215749	0.107874	−	0.994165i	$-0.465596\pi$
$139$	2.54364	0.215749	0.107874	+	0.994165i	$0.465596\pi$
$140$	−67.6953	−5.72130
$141$	−1.53056	−0.128896
$142$	34.7126	2.91302
$143$	5.52912	0.462368
$144$	−39.7298	−3.31082
$145$	−2.57777	−0.214072
$146$	8.23936	0.681894
$147$	−10.6124	−0.875295
$148$	23.9083	1.96525
$149$	8.26731	0.677285	0.338642	−	0.940915i	$-0.390032\pi$
$149$	8.26731	0.677285	0.338642	+	0.940915i	$0.390032\pi$
$150$	3.90430	0.318785
$151$	−11.0179	−0.896626	−0.448313	−	0.893877i	$-0.647975\pi$
$151$	−11.0179	−0.896626	−0.448313	+	0.893877i	$0.647975\pi$
$152$	63.7280	5.16902
$153$	0.638612	0.0516287
$154$	−26.8868	−2.16660
$155$	6.26197	0.502973
$156$	−11.0206	−0.882354
$157$	−21.7764	−1.73794	−0.868972	−	0.494861i	$-0.835219\pi$
$157$	−21.7764	−1.73794	−0.868972	+	0.494861i	$0.835219\pi$
$158$	21.9322	1.74483
$159$	5.96379	0.472960
$160$	65.7909	5.20122
$161$	4.32685	0.341004
$162$	−11.6642	−0.916423
$163$	−11.6850	−0.915240	−0.457620	−	0.889148i	$-0.651298\pi$
$163$	−11.6850	−0.915240	−0.457620	+	0.889148i	$0.651298\pi$
$164$	−0.825685	−0.0644752
$165$	4.18455	0.325767
$166$	39.7104	3.08212
$167$	−8.63686	−0.668341	−0.334170	−	0.942513i	$-0.608456\pi$
$167$	−8.63686	−0.668341	−0.334170	+	0.942513i	$0.608456\pi$
$168$	34.5114	2.66261
$169$	−6.20083	−0.476987
$170$	−1.89948	−0.145684
$171$	15.5347	1.18797
$172$	25.2736	1.92709
$173$	6.83916	0.519972	0.259986	−	0.965612i	$-0.416282\pi$
$173$	6.83916	0.519972	0.259986	+	0.965612i	$0.416282\pi$
$174$	2.04068	0.154703
$175$	8.63796	0.652968
$176$	34.6122	2.60899
$177$	−0.502245	−0.0377511
$178$	−23.3770	−1.75218
$179$	19.9640	1.49218	0.746091	−	0.665844i	$-0.231928\pi$
$179$	19.9640	1.49218	0.746091	+	0.665844i	$0.231928\pi$
$180$	35.8653	2.67324
$181$	−1.94085	−0.144263	−0.0721313	−	0.997395i	$-0.522980\pi$
$181$	−1.94085	−0.144263	−0.0721313	+	0.997395i	$0.522980\pi$
$182$	−33.0628	−2.45078
$183$	3.98590	0.294646
$184$	−9.40405	−0.693276
$185$	−11.1633	−0.820743
$186$	−4.95725	−0.363483
$187$	−0.556352	−0.0406845
$188$	11.4285	0.833507
$189$	18.7818	1.36617
$190$	−46.2063	−3.35215
$191$	13.6544	0.987996	0.493998	−	0.869463i	$-0.335535\pi$
$191$	13.6544	0.987996	0.493998	+	0.869463i	$0.335535\pi$
$192$	−27.5217	−1.98620
$193$	22.5852	1.62571	0.812857	−	0.582463i	$-0.197911\pi$
$193$	22.5852	1.62571	0.812857	+	0.582463i	$0.197911\pi$
$194$	−10.6204	−0.762502
$195$	5.14576	0.368495
$196$	79.2412	5.66009
$197$	−20.7953	−1.48161	−0.740803	−	0.671722i	$-0.765555\pi$
$197$	−20.7953	−1.48161	−0.740803	+	0.671722i	$0.765555\pi$
$198$	14.2447	1.01233
$199$	2.67744	0.189799	0.0948993	−	0.995487i	$-0.469747\pi$
$199$	2.67744	0.189799	0.0948993	+	0.995487i	$0.469747\pi$
$200$	−18.7739	−1.32751
$201$	−8.01447	−0.565297
$202$	0.110543	0.00777776
$203$	4.51484	0.316880
$204$	1.10892	0.0776398
$205$	0.385530	0.0269266
$206$	−29.7240	−2.07097
$207$	−2.29238	−0.159332
$208$	42.5627	2.95119
$209$	−13.5337	−0.936143
$210$	−25.0226	−1.72672
$211$	−22.9617	−1.58075	−0.790373	−	0.612626i	$-0.790113\pi$
$211$	−22.9617	−1.58075	−0.790373	+	0.612626i	$0.790113\pi$
$212$	−44.5308	−3.05839
$213$	9.46227	0.648344
$214$	20.9574	1.43262
$215$	−11.8008	−0.804807
$216$	−40.8206	−2.77749
$217$	−10.9675	−0.744524
$218$	−4.13130	−0.279807
$219$	2.24596	0.151768
$220$	−31.2455	−2.10657
$221$	−0.684148	−0.0460208
$222$	8.83736	0.593125
$223$	−2.14305	−0.143509	−0.0717546	−	0.997422i	$-0.522860\pi$
$223$	−2.14305	−0.143509	−0.0717546	+	0.997422i	$0.522860\pi$
$224$	−115.229	−7.69909
$225$	−4.57643	−0.305095
$226$	0.762377	0.0507126
$227$	−3.46156	−0.229752	−0.114876	−	0.993380i	$-0.536647\pi$
$227$	−3.46156	−0.229752	−0.114876	+	0.993380i	$0.536647\pi$
$228$	26.9752	1.78648
$229$	3.56144	0.235347	0.117673	−	0.993052i	$-0.462456\pi$
$229$	3.56144	0.235347	0.117673	+	0.993052i	$0.462456\pi$
$230$	6.81845	0.449595
$231$	−7.32904	−0.482215
$232$	−9.81263	−0.644231
$233$	−19.2721	−1.26256	−0.631278	−	0.775556i	$-0.717469\pi$
$233$	−19.2721	−1.26256	−0.631278	+	0.775556i	$0.717469\pi$
$234$	17.5168	1.14511
$235$	−5.33620	−0.348095
$236$	3.75019	0.244117
$237$	5.97846	0.388343
$238$	3.32685	0.215648
$239$	−17.7028	−1.14510	−0.572549	−	0.819871i	$-0.694045\pi$
$239$	−17.7028	−1.14510	−0.572549	+	0.819871i	$0.694045\pi$
$240$	32.2124	2.07930
$241$	15.0557	0.969823	0.484911	−	0.874563i	$-0.338852\pi$
$241$	15.0557	0.969823	0.484911	+	0.874563i	$0.338852\pi$
$242$	17.9503	1.15389
$243$	−15.4443	−0.990749
$244$	−29.7621	−1.90533
$245$	−36.9994	−2.36381
$246$	−0.305203	−0.0194590
$247$	−16.6424	−1.05893
$248$	23.8370	1.51365
$249$	10.8246	0.685981
$250$	−22.5858	−1.42845
$251$	19.9495	1.25920	0.629599	−	0.776920i	$-0.283219\pi$
$251$	19.9495	1.25920	0.629599	+	0.776920i	$0.283219\pi$
$252$	−62.8163	−3.95706
$253$	1.99710	0.125557
$254$	22.8256	1.43220
$255$	−0.517778	−0.0324245
$256$	67.0462	4.19039
$257$	−13.0081	−0.811421	−0.405711	−	0.914002i	$-0.632976\pi$
$257$	−13.0081	−0.811421	−0.405711	+	0.914002i	$0.632976\pi$
$258$	9.34202	0.581609
$259$	19.5520	1.21490
$260$	−38.4226	−2.38287
$261$	−2.39198	−0.148060
$262$	9.54258	0.589542
$263$	−9.02791	−0.556685	−0.278342	−	0.960482i	$-0.589785\pi$
$263$	−9.02791	−0.556685	−0.278342	+	0.960482i	$0.589785\pi$
$264$	15.9291	0.980366
$265$	20.7924	1.27727
$266$	80.9280	4.96201
$267$	−6.37232	−0.389980
$268$	59.8429	3.65549
$269$	30.7235	1.87324	0.936622	−	0.350340i	$-0.113934\pi$
$269$	30.7235	1.87324	0.936622	+	0.350340i	$0.113934\pi$
$270$	29.5972	1.80123
$271$	−12.8764	−0.782184	−0.391092	−	0.920351i	$-0.627903\pi$
$271$	−12.8764	−0.782184	−0.391092	+	0.920351i	$0.627903\pi$
$272$	−4.28275	−0.259680
$273$	−9.01254	−0.545464
$274$	−19.8518	−1.19929
$275$	3.98694	0.240421
$276$	−3.98061	−0.239605
$277$	−4.88989	−0.293805	−0.146902	−	0.989151i	$-0.546930\pi$
$277$	−4.88989	−0.293805	−0.146902	+	0.989151i	$0.546930\pi$
$278$	−7.02049	−0.421061
$279$	5.81064	0.347874
$280$	120.322	7.19059
$281$	3.88183	0.231571	0.115785	−	0.993274i	$-0.463062\pi$
$281$	3.88183	0.231571	0.115785	+	0.993274i	$0.463062\pi$
$282$	4.22437	0.251558
$283$	7.12535	0.423558	0.211779	−	0.977318i	$-0.432074\pi$
$283$	7.12535	0.423558	0.211779	+	0.977318i	$0.432074\pi$
$284$	−70.6535	−4.19251
$285$	−12.5953	−0.746082
$286$	−15.2605	−0.902369
$287$	−0.675237	−0.0398580
$288$	61.0491	3.59735
$289$	−16.9312	−0.995951
$290$	7.11469	0.417789
$291$	−2.89501	−0.169708
$292$	−16.7702	−0.981405
$293$	2.34259	0.136856	0.0684279	−	0.997656i	$-0.478202\pi$
$293$	2.34259	0.136856	0.0684279	+	0.997656i	$0.478202\pi$
$294$	29.2904	1.70825
$295$	−1.75105	−0.101950
$296$	−42.4946	−2.46995
$297$	8.66891	0.503021
$298$	−22.8179	−1.32181
$299$	2.45584	0.142025
$300$	−7.94674	−0.458805
$301$	20.6685	1.19131
$302$	30.4096	1.74988
$303$	0.0301327	0.00173108
$304$	−104.181	−5.97519
$305$	13.8966	0.795716
$306$	−1.76258	−0.100760
$307$	20.8486	1.18989	0.594946	−	0.803766i	$-0.297173\pi$
$307$	20.8486	1.18989	0.594946	+	0.803766i	$0.297173\pi$
$308$	54.7249	3.11824
$309$	−8.10242	−0.460931
$310$	−17.2831	−0.981616
$311$	26.9437	1.52784	0.763919	−	0.645312i	$-0.223273\pi$
$311$	26.9437	1.52784	0.763919	+	0.645312i	$0.223273\pi$
$312$	19.5880	1.10895
$313$	−5.57460	−0.315095	−0.157548	−	0.987511i	$-0.550359\pi$
$313$	−5.57460	−0.315095	−0.157548	+	0.987511i	$0.550359\pi$
$314$	60.1031	3.39182
$315$	29.3303	1.65257
$316$	−44.6403	−2.51121
$317$	−10.1237	−0.568603	−0.284301	−	0.958735i	$-0.591762\pi$
$317$	−10.1237	−0.568603	−0.284301	+	0.958735i	$0.591762\pi$
$318$	−16.4602	−0.923040
$319$	2.08387	0.116674
$320$	−95.9525	−5.36391
$321$	5.71274	0.318854
$322$	−11.9422	−0.665511
$323$	1.67459	0.0931769
$324$	23.7410	1.31895
$325$	4.90275	0.271956
$326$	32.2508	1.78621
$327$	−1.12615	−0.0622761
$328$	1.46757	0.0810332
$329$	9.34609	0.515267
$330$	−11.5494	−0.635775
$331$	24.2875	1.33496	0.667482	−	0.744626i	$-0.267372\pi$
$331$	24.2875	1.33496	0.667482	+	0.744626i	$0.267372\pi$
$332$	−80.8258	−4.43589
$333$	−10.3587	−0.567655
$334$	23.8379	1.30435
$335$	−27.9419	−1.52663
$336$	−56.4184	−3.07787
$337$	−30.1263	−1.64108	−0.820541	−	0.571588i	$-0.806328\pi$
$337$	−30.1263	−1.64108	−0.820541	+	0.571588i	$0.806328\pi$
$338$	17.1144	0.930900
$339$	0.207816	0.0112870
$340$	3.86617	0.209673
$341$	−5.06217	−0.274132
$342$	−42.8760	−2.31847
$343$	32.6441	1.76261
$344$	−44.9213	−2.42199
$345$	1.85863	0.100065
$346$	−18.8762	−1.01479
$347$	17.9663	0.964484	0.482242	−	0.876038i	$-0.339823\pi$
$347$	17.9663	0.964484	0.482242	+	0.876038i	$0.339823\pi$
$348$	−4.15356	−0.222654
$349$	24.7167	1.32305	0.661527	−	0.749921i	$-0.269909\pi$
$349$	24.7167	1.32305	0.661527	+	0.749921i	$0.269909\pi$
$350$	−23.8409	−1.27435
$351$	10.6602	0.568999
$352$	−53.1853	−2.83479
$353$	−32.5800	−1.73406	−0.867029	−	0.498257i	$-0.833974\pi$
$353$	−32.5800	−1.73406	−0.867029	+	0.498257i	$0.833974\pi$
$354$	1.38621	0.0736760
$355$	32.9896	1.75091
$356$	47.5812	2.52180
$357$	0.906862	0.0479962
$358$	−55.1011	−2.91218
$359$	12.9035	0.681023	0.340512	−	0.940240i	$-0.389400\pi$
$359$	12.9035	0.681023	0.340512	+	0.940240i	$0.389400\pi$
$360$	−63.7470	−3.35976
$361$	21.7357	1.14399
$362$	5.35679	0.281546
$363$	4.89305	0.256819
$364$	67.2954	3.52724
$365$	7.83039	0.409861
$366$	−11.0011	−0.575039
$367$	−9.37738	−0.489495	−0.244748	−	0.969587i	$-0.578705\pi$
$367$	−9.37738	−0.489495	−0.244748	+	0.969587i	$0.578705\pi$
$368$	15.3735	0.801400
$369$	0.357744	0.0186234
$370$	30.8109	1.60178
$371$	−36.4169	−1.89067
$372$	10.0899	0.523136
$373$	−0.544342	−0.0281850	−0.0140925	−	0.999901i	$-0.504486\pi$
$373$	−0.544342	−0.0281850	−0.0140925	+	0.999901i	$0.504486\pi$
$374$	1.53554	0.0794009
$375$	−6.15664	−0.317927
$376$	−20.3130	−1.04756
$377$	2.56254	0.131978
$378$	−51.8380	−2.66626
$379$	4.93280	0.253381	0.126691	−	0.991942i	$-0.459564\pi$
$379$	4.93280	0.253381	0.126691	+	0.991942i	$0.459564\pi$
$380$	94.0474	4.82453
$381$	6.22199	0.318762
$382$	−37.6863	−1.92820
$383$	13.8384	0.707110	0.353555	−	0.935414i	$-0.384973\pi$
$383$	13.8384	0.707110	0.353555	+	0.935414i	$0.384973\pi$
$384$	38.2192	1.95036
$385$	−25.5522	−1.30226
$386$	−62.3354	−3.17279
$387$	−10.9503	−0.556633
$388$	21.6166	1.09742
$389$	36.2385	1.83737	0.918683	−	0.394996i	$-0.129254\pi$
$389$	36.2385	1.83737	0.918683	+	0.394996i	$0.129254\pi$
$390$	−14.2024	−0.719165
$391$	−0.247112	−0.0124970
$392$	−140.843	−7.11366
$393$	2.60120	0.131213
$394$	57.3955	2.89154
$395$	20.8435	1.04875
$396$	−28.9935	−1.45698
$397$	2.35784	0.118336	0.0591682	−	0.998248i	$-0.481155\pi$
$397$	2.35784	0.118336	0.0591682	+	0.998248i	$0.481155\pi$
$398$	−7.38977	−0.370416
$399$	22.0601	1.10438
$400$	30.6911	1.53456
$401$	−3.04725	−0.152172	−0.0760862	−	0.997101i	$-0.524242\pi$
$401$	−3.04725	−0.152172	−0.0760862	+	0.997101i	$0.524242\pi$
$402$	22.1201	1.10325
$403$	−6.22497	−0.310088
$404$	−0.224997	−0.0111940
$405$	−11.0852	−0.550828
$406$	−12.4610	−0.618431
$407$	9.02442	0.447324
$408$	−1.97099	−0.0975785
$409$	13.7512	0.679953	0.339976	−	0.940434i	$-0.389581\pi$
$409$	13.7512	0.679953	0.339976	+	0.940434i	$0.389581\pi$
$410$	−1.06407	−0.0525507
$411$	−5.41139	−0.266924
$412$	60.4996	2.98060
$413$	3.06687	0.150911
$414$	6.32702	0.310956
$415$	37.7393	1.85255
$416$	−65.4022	−3.20660
$417$	−1.91371	−0.0937147
$418$	37.3531	1.82700
$419$	15.4998	0.757217	0.378608	−	0.925557i	$-0.376403\pi$
$419$	15.4998	0.757217	0.378608	+	0.925557i	$0.376403\pi$
$420$	50.9306	2.48516
$421$	−25.9606	−1.26524	−0.632622	−	0.774461i	$-0.718021\pi$
$421$	−25.9606	−1.26524	−0.632622	+	0.774461i	$0.718021\pi$
$422$	63.3746	3.08503
$423$	−4.95160	−0.240755
$424$	79.1490	3.84382
$425$	−0.493325	−0.0239298
$426$	−26.1160	−1.26533
$427$	−24.3392	−1.17786
$428$	−42.6562	−2.06187
$429$	−4.15983	−0.200838
$430$	32.5704	1.57068
$431$	22.9757	1.10670	0.553349	−	0.832949i	$-0.313349\pi$
$431$	22.9757	1.10670	0.553349	+	0.832949i	$0.313349\pi$
$432$	66.7326	3.21067
$433$	15.9132	0.764738	0.382369	−	0.924010i	$-0.375108\pi$
$433$	15.9132	0.764738	0.382369	+	0.924010i	$0.375108\pi$
$434$	30.2705	1.45303
$435$	1.93939	0.0929864
$436$	8.40878	0.402707
$437$	−6.01118	−0.287554
$438$	−6.19888	−0.296194
$439$	−17.5928	−0.839660	−0.419830	−	0.907603i	$-0.637910\pi$
$439$	−17.5928	−0.839660	−0.419830	+	0.907603i	$0.637910\pi$
$440$	55.5357	2.64756
$441$	−34.3328	−1.63489
$442$	1.88826	0.0898153
$443$	26.5373	1.26083	0.630413	−	0.776260i	$-0.282886\pi$
$443$	26.5373	1.26083	0.630413	+	0.776260i	$0.282886\pi$
$444$	−17.9874	−0.853645
$445$	−22.2167	−1.05317
$446$	5.91485	0.280076
$447$	−6.21991	−0.294192
$448$	168.056	7.93990
$449$	1.73248	0.0817607	0.0408803	−	0.999164i	$-0.486984\pi$
$449$	1.73248	0.0817607	0.0408803	+	0.999164i	$0.486984\pi$
$450$	12.6310	0.595432
$451$	−0.311663	−0.0146756
$452$	−1.55173	−0.0729872
$453$	8.28933	0.389467
$454$	9.55395	0.448389
$455$	−31.4217	−1.47307
$456$	−47.9458	−2.24527
$457$	−1.56351	−0.0731380	−0.0365690	−	0.999331i	$-0.511643\pi$
$457$	−1.56351	−0.0731380	−0.0365690	+	0.999331i	$0.511643\pi$
$458$	−9.82964	−0.459309
$459$	−1.07265	−0.0500671
$460$	−13.8781	−0.647072
$461$	−26.7141	−1.24420	−0.622100	−	0.782938i	$-0.713720\pi$
$461$	−26.7141	−1.24420	−0.622100	+	0.782938i	$0.713720\pi$
$462$	20.2283	0.941104
$463$	0.114887	0.00533925	0.00266962	−	0.999996i	$-0.499150\pi$
$463$	0.114887	0.00533925	0.00266962	+	0.999996i	$0.499150\pi$
$464$	16.0415	0.744706
$465$	−4.71119	−0.218476
$466$	53.1913	2.46404
$467$	−9.56653	−0.442686	−0.221343	−	0.975196i	$-0.571044\pi$
$467$	−9.56653	−0.442686	−0.221343	+	0.975196i	$0.571044\pi$
$468$	−35.6534	−1.64808
$469$	48.9389	2.25979
$470$	14.7280	0.679352
$471$	16.3834	0.754909
$472$	−6.66559	−0.306809
$473$	9.53976	0.438639
$474$	−16.5006	−0.757900
$475$	−12.0005	−0.550621
$476$	−6.77141	−0.310367
$477$	19.2938	0.883403
$478$	48.8599	2.23480
$479$	−0.284301	−0.0129900	−0.00649502	−	0.999979i	$-0.502067\pi$
$479$	−0.284301	−0.0129900	−0.00649502	+	0.999979i	$0.502067\pi$
$480$	−49.4977	−2.25925
$481$	11.0974	0.505996
$482$	−41.5540	−1.89273
$483$	−3.25530	−0.148121
$484$	−36.5357	−1.66072
$485$	−10.0933	−0.458312
$486$	42.6264	1.93357
$487$	−7.21485	−0.326936	−0.163468	−	0.986549i	$-0.552268\pi$
$487$	−7.21485	−0.326936	−0.163468	+	0.986549i	$0.552268\pi$
$488$	52.8992	2.39463
$489$	8.79121	0.397552
$490$	102.119	4.61327
$491$	11.1777	0.504441	0.252220	−	0.967670i	$-0.418839\pi$
$491$	11.1777	0.504441	0.252220	+	0.967670i	$0.418839\pi$
$492$	0.621204	0.0280060
$493$	−0.257849	−0.0116129
$494$	45.9333	2.06664
$495$	13.5377	0.608474
$496$	−38.9682	−1.74972
$497$	−57.7797	−2.59177
$498$	−29.8761	−1.33878
$499$	29.8748	1.33738	0.668690	−	0.743541i	$-0.266855\pi$
$499$	29.8748	1.33738	0.668690	+	0.743541i	$0.266855\pi$
$500$	45.9707	2.05587
$501$	6.49794	0.290307
$502$	−55.0608	−2.45749
$503$	−27.8185	−1.24037	−0.620183	−	0.784457i	$-0.712942\pi$
$503$	−27.8185	−1.24037	−0.620183	+	0.784457i	$0.712942\pi$
$504$	111.650	4.97327
$505$	0.105056	0.00467493
$506$	−5.51203	−0.245040
$507$	4.66519	0.207188
$508$	−46.4587	−2.06127
$509$	−35.7537	−1.58476	−0.792378	−	0.610030i	$-0.791157\pi$
$509$	−35.7537	−1.58476	−0.792378	+	0.610030i	$0.791157\pi$
$510$	1.42907	0.0632805
$511$	−13.7145	−0.606696
$512$	−83.4492	−3.68797
$513$	−26.0930	−1.15204
$514$	35.9025	1.58359
$515$	−28.2486	−1.24478
$516$	−19.0146	−0.837071
$517$	4.31378	0.189720
$518$	−53.9638	−2.37103
$519$	−5.14544	−0.225860
$520$	68.2924	2.99482
$521$	−38.9221	−1.70521	−0.852604	−	0.522558i	$-0.824978\pi$
$521$	−38.9221	−1.70521	−0.852604	+	0.522558i	$0.824978\pi$
$522$	6.60191	0.288958
$523$	40.1104	1.75391	0.876954	−	0.480575i	$-0.159572\pi$
$523$	40.1104	1.75391	0.876954	+	0.480575i	$0.159572\pi$
$524$	−19.4228	−0.848489
$525$	−6.49877	−0.283629
$526$	24.9172	1.08644
$527$	0.626370	0.0272851
$528$	−26.0405	−1.13327
$529$	−22.1130	−0.961433
$530$	−57.3873	−2.49275
$531$	−1.62484	−0.0705122
$532$	−164.719	−7.14149
$533$	−0.383252	−0.0166005
$534$	17.5877	0.761094
$535$	19.9171	0.861092
$536$	−106.365	−4.59426
$537$	−15.0199	−0.648158
$538$	−84.7974	−3.65587
$539$	29.9103	1.28833
$540$	−60.2416	−2.59238
$541$	−42.4857	−1.82660	−0.913301	−	0.407286i	$-0.866475\pi$
$541$	−42.4857	−1.82660	−0.913301	+	0.407286i	$0.866475\pi$
$542$	35.5390	1.52653
$543$	1.46020	0.0626632
$544$	6.58091	0.282154
$545$	−3.92624	−0.168182
$546$	24.8748	1.06454
$547$	−0.254591	−0.0108855	−0.00544276	−	0.999985i	$-0.501732\pi$
$547$	−0.254591	−0.0108855	−0.00544276	+	0.999985i	$0.501732\pi$
$548$	40.4061	1.72606
$549$	12.8950	0.550346
$550$	−11.0040	−0.469213
$551$	−6.27235	−0.267211
$552$	7.07514	0.301138
$553$	−36.5064	−1.55241
$554$	13.4962	0.573397
$555$	8.39871	0.356505
$556$	14.2894	0.606005
$557$	9.30898	0.394434	0.197217	−	0.980360i	$-0.436810\pi$
$557$	9.30898	0.394434	0.197217	+	0.980360i	$0.436810\pi$
$558$	−16.0375	−0.678920
$559$	11.7311	0.496171
$560$	−196.699	−8.31205
$561$	0.418571	0.0176721
$562$	−10.7139	−0.451940
$563$	−45.8188	−1.93103	−0.965516	−	0.260345i	$-0.916164\pi$
$563$	−45.8188	−1.93103	−0.965516	+	0.260345i	$0.916164\pi$
$564$	−8.59821	−0.362050
$565$	0.724536	0.0304814
$566$	−19.6661	−0.826627
$567$	19.4152	0.815361
$568$	125.579	5.26920
$569$	27.0940	1.13584	0.567919	−	0.823084i	$-0.307749\pi$
$569$	27.0940	1.13584	0.567919	+	0.823084i	$0.307749\pi$
$570$	34.7633	1.45607
$571$	−16.5420	−0.692262	−0.346131	−	0.938186i	$-0.612505\pi$
$571$	−16.5420	−0.692262	−0.346131	+	0.938186i	$0.612505\pi$
$572$	31.0609	1.29872
$573$	−10.2729	−0.429155
$574$	1.86367	0.0777879
$575$	1.77086	0.0738499
$576$	−89.0369	−3.70987
$577$	−13.9605	−0.581184	−0.290592	−	0.956847i	$-0.593852\pi$
$577$	−13.9605	−0.581184	−0.290592	+	0.956847i	$0.593852\pi$
$578$	46.7303	1.94372
$579$	−16.9919	−0.706161
$580$	−14.4811	−0.601296
$581$	−66.0985	−2.74223
$582$	7.99027	0.331207
$583$	−16.8086	−0.696140
$584$	29.8074	1.23344
$585$	16.6473	0.688283
$586$	−6.46559	−0.267091
$587$	−41.5072	−1.71319	−0.856593	−	0.515992i	$-0.827423\pi$
$587$	−41.5072	−1.71319	−0.856593	+	0.515992i	$0.827423\pi$
$588$	−59.6171	−2.45857
$589$	15.2369	0.627826
$590$	4.83292	0.198968
$591$	15.6454	0.643564
$592$	69.4692	2.85517
$593$	23.1961	0.952549	0.476275	−	0.879297i	$-0.341987\pi$
$593$	23.1961	0.952549	0.476275	+	0.879297i	$0.341987\pi$
$594$	−23.9263	−0.981710
$595$	3.16172	0.129618
$596$	46.4432	1.90239
$597$	−2.01437	−0.0824427
$598$	−6.77816	−0.277180
$599$	−23.0291	−0.940942	−0.470471	−	0.882415i	$-0.655916\pi$
$599$	−23.0291	−0.940942	−0.470471	+	0.882415i	$0.655916\pi$
$600$	14.1245	0.576632
$601$	−20.6590	−0.842700	−0.421350	−	0.906898i	$-0.638444\pi$
$601$	−20.6590	−0.842700	−0.421350	+	0.906898i	$0.638444\pi$
$602$	−57.0454	−2.32500
$603$	−25.9281	−1.05587
$604$	−61.8952	−2.51848
$605$	17.0593	0.693560
$606$	−0.0831668	−0.00337842
$607$	31.8115	1.29119	0.645595	−	0.763680i	$-0.276609\pi$
$607$	31.8115	1.29119	0.645595	+	0.763680i	$0.276609\pi$
$608$	160.085	6.49232
$609$	−3.39674	−0.137643
$610$	−38.3548	−1.55294
$611$	5.30467	0.214604
$612$	3.58752	0.145017
$613$	27.8632	1.12538	0.562691	−	0.826667i	$-0.309766\pi$
$613$	27.8632	1.12538	0.562691	+	0.826667i	$0.309766\pi$
$614$	−57.5424	−2.32222
$615$	−0.290054	−0.0116961
$616$	−97.2680	−3.91904
$617$	21.1802	0.852682	0.426341	−	0.904563i	$-0.359802\pi$
$617$	21.1802	0.852682	0.426341	+	0.904563i	$0.359802\pi$
$618$	22.3628	0.899564
$619$	8.58454	0.345042	0.172521	−	0.985006i	$-0.444809\pi$
$619$	8.58454	0.345042	0.172521	+	0.985006i	$0.444809\pi$
$620$	35.1778	1.41277
$621$	3.85043	0.154512
$622$	−74.3651	−2.98177
$623$	38.9114	1.55895
$624$	−32.0220	−1.28191
$625$	−30.8659	−1.23464
$626$	15.3860	0.614948
$627$	10.1820	0.406632
$628$	−122.333	−4.88161
$629$	−1.11664	−0.0445234
$630$	−80.9521	−3.22521
$631$	15.2702	0.607897	0.303949	−	0.952688i	$-0.401695\pi$
$631$	15.2702	0.607897	0.303949	+	0.952688i	$0.401695\pi$
$632$	79.3437	3.15612
$633$	17.2752	0.686628
$634$	27.9415	1.10970
$635$	21.6926	0.860844
$636$	33.5027	1.32847
$637$	36.7808	1.45731
$638$	−5.75151	−0.227705
$639$	30.6120	1.21099
$640$	133.249	5.26712
$641$	−16.7664	−0.662233	−0.331117	−	0.943590i	$-0.607425\pi$
$641$	−16.7664	−0.662233	−0.331117	+	0.943590i	$0.607425\pi$
$642$	−15.7673	−0.622284
$643$	−11.8639	−0.467868	−0.233934	−	0.972252i	$-0.575160\pi$
$643$	−11.8639	−0.467868	−0.233934	+	0.972252i	$0.575160\pi$
$644$	24.3069	0.957826
$645$	8.87832	0.349584
$646$	−4.62191	−0.181846
$647$	−29.8393	−1.17310	−0.586552	−	0.809911i	$-0.699515\pi$
$647$	−29.8393	−1.17310	−0.586552	+	0.809911i	$0.699515\pi$
$648$	−42.1973	−1.65767
$649$	1.41555	0.0555650
$650$	−13.5317	−0.530756
$651$	8.25141	0.323398
$652$	−65.6427	−2.57077
$653$	14.1353	0.553156	0.276578	−	0.960991i	$-0.410800\pi$
$653$	14.1353	0.553156	0.276578	+	0.960991i	$0.410800\pi$
$654$	3.10818	0.121540
$655$	9.06892	0.354352
$656$	−2.39915	−0.0936712
$657$	7.26603	0.283475
$658$	−25.7954	−1.00561
$659$	30.8214	1.20063	0.600315	−	0.799764i	$-0.295042\pi$
$659$	30.8214	1.20063	0.600315	+	0.799764i	$0.295042\pi$
$660$	23.5075	0.915029
$661$	−25.4667	−0.990539	−0.495270	−	0.868739i	$-0.664931\pi$
$661$	−25.4667	−0.990539	−0.495270	+	0.868739i	$0.664931\pi$
$662$	−67.0340	−2.60535
$663$	0.514718	0.0199900
$664$	143.660	5.57508
$665$	76.9111	2.98248
$666$	28.5903	1.10785
$667$	0.925583	0.0358387
$668$	−48.5192	−1.87726
$669$	1.61232	0.0623360
$670$	77.1202	2.97941
$671$	−11.2340	−0.433684
$672$	86.6929	3.34425
$673$	−2.50572	−0.0965883	−0.0482941	−	0.998833i	$-0.515378\pi$
$673$	−2.50572	−0.0965883	−0.0482941	+	0.998833i	$0.515378\pi$
$674$	83.1490	3.20278
$675$	7.68685	0.295867
$676$	−34.8343	−1.33978
$677$	−46.3437	−1.78113	−0.890566	−	0.454854i	$-0.849691\pi$
$677$	−46.3437	−1.78113	−0.890566	+	0.454854i	$0.849691\pi$
$678$	−0.573574	−0.0220280
$679$	17.6779	0.678414
$680$	−6.87173	−0.263519
$681$	2.60430	0.0997971
$682$	13.9717	0.535003
$683$	38.9556	1.49059	0.745297	−	0.666733i	$-0.232308\pi$
$683$	38.9556	1.49059	0.745297	+	0.666733i	$0.232308\pi$
$684$	87.2691	3.33682
$685$	−18.8665	−0.720850
$686$	−90.0982	−3.43996
$687$	−2.67945	−0.102227
$688$	73.4363	2.79973
$689$	−20.6695	−0.787447
$690$	−5.12986	−0.195290
$691$	−31.6395	−1.20362	−0.601811	−	0.798638i	$-0.705554\pi$
$691$	−31.6395	−1.20362	−0.601811	+	0.798638i	$0.705554\pi$
$692$	38.4203	1.46052
$693$	−23.7106	−0.900691
$694$	−49.5874	−1.88231
$695$	−6.67202	−0.253084
$696$	7.38253	0.279834
$697$	0.0385637	0.00146070
$698$	−68.2185	−2.58211
$699$	14.4994	0.548416
$700$	48.5254	1.83409
$701$	−14.0154	−0.529355	−0.264677	−	0.964337i	$-0.585265\pi$
$701$	−14.0154	−0.529355	−0.264677	+	0.964337i	$0.585265\pi$
$702$	−29.4223	−1.11047
$703$	−27.1631	−1.02447
$704$	77.5680	2.92345
$705$	4.01469	0.151202
$706$	89.9213	3.38423
$707$	−0.184000	−0.00692004
$708$	−2.82146	−0.106037
$709$	−6.09134	−0.228765	−0.114382	−	0.993437i	$-0.536489\pi$
$709$	−6.09134	−0.228765	−0.114382	+	0.993437i	$0.536489\pi$
$710$	−91.0519	−3.41712
$711$	19.3413	0.725354
$712$	−84.5708	−3.16942
$713$	−2.24844	−0.0842048
$714$	−2.50295	−0.0936707
$715$	−14.5030	−0.542381
$716$	112.152	4.19131
$717$	13.3187	0.497395
$718$	−35.6140	−1.32910
$719$	−50.8798	−1.89750	−0.948749	−	0.316031i	$-0.897650\pi$
$719$	−50.8798	−1.89750	−0.948749	+	0.316031i	$0.897650\pi$
$720$	104.212	3.88375
$721$	49.4760	1.84258
$722$	−59.9909	−2.23263
$723$	−11.3271	−0.421261
$724$	−10.9031	−0.405211
$725$	1.84780	0.0686255
$726$	−13.5049	−0.501214
$727$	−40.0768	−1.48637	−0.743184	−	0.669087i	$-0.766685\pi$
$727$	−40.0768	−1.48637	−0.743184	+	0.669087i	$0.766685\pi$
$728$	−119.611	−4.43307
$729$	−1.05888	−0.0392177
$730$	−21.6120	−0.799896
$731$	−1.18041	−0.0436589
$732$	22.3915	0.827615
$733$	−8.05903	−0.297667	−0.148833	−	0.988862i	$-0.547552\pi$
$733$	−8.05903	−0.297667	−0.148833	+	0.988862i	$0.547552\pi$
$734$	25.8817	0.955312
$735$	27.8365	1.02677
$736$	−23.6231	−0.870758
$737$	22.5883	0.832049
$738$	−0.987379	−0.0363459
$739$	4.26908	0.157041	0.0785203	−	0.996913i	$-0.474980\pi$
$739$	4.26908	0.157041	0.0785203	+	0.996913i	$0.474980\pi$
$740$	−62.7120	−2.30534
$741$	12.5209	0.459967
$742$	100.511	3.68988
$743$	22.7761	0.835573	0.417787	−	0.908545i	$-0.362806\pi$
$743$	22.7761	0.835573	0.417787	+	0.908545i	$0.362806\pi$
$744$	−17.9338	−0.657484
$745$	−21.6853	−0.794489
$746$	1.50239	0.0550065
$747$	35.0193	1.28129
$748$	−3.12541	−0.114276
$749$	−34.8839	−1.27463
$750$	16.9924	0.620475
$751$	50.1581	1.83030	0.915148	−	0.403117i	$-0.132073\pi$
$751$	50.1581	1.83030	0.915148	+	0.403117i	$0.132073\pi$
$752$	33.2072	1.21094
$753$	−15.0090	−0.546957
$754$	−7.07266	−0.257571
$755$	28.9002	1.05179
$756$	105.510	3.83737
$757$	40.2974	1.46463	0.732317	−	0.680964i	$-0.238439\pi$
$757$	40.2974	1.46463	0.732317	+	0.680964i	$0.238439\pi$
$758$	−13.6146	−0.494505
$759$	−1.50252	−0.0545380
$760$	−167.160	−6.06353
$761$	−3.38288	−0.122629	−0.0613147	−	0.998118i	$-0.519529\pi$
$761$	−3.38288	−0.122629	−0.0613147	+	0.998118i	$0.519529\pi$
$762$	−17.1728	−0.622105
$763$	6.87662	0.248950
$764$	76.7060	2.77513
$765$	−1.67509	−0.0605631
$766$	−38.1942	−1.38001
$767$	1.74070	0.0628531
$768$	−50.4422	−1.82018
$769$	−32.5110	−1.17238	−0.586189	−	0.810174i	$-0.699372\pi$
$769$	−32.5110	−1.17238	−0.586189	+	0.810174i	$0.699372\pi$
$770$	70.5246	2.54153
$771$	9.78662	0.352456
$772$	126.876	4.56638
$773$	52.9828	1.90566	0.952829	−	0.303508i	$-0.0981579\pi$
$773$	52.9828	1.90566	0.952829	+	0.303508i	$0.0981579\pi$
$774$	30.2229	1.08634
$775$	−4.48870	−0.161239
$776$	−38.4214	−1.37925
$777$	−14.7099	−0.527716
$778$	−100.019	−3.58585
$779$	0.938090	0.0336106
$780$	28.9073	1.03505
$781$	−26.6688	−0.954285
$782$	0.682034	0.0243895
$783$	4.01772	0.143582
$784$	230.247	8.22312
$785$	57.1199	2.03870
$786$	−7.17935	−0.256079
$787$	−18.6961	−0.666443	−0.333221	−	0.942849i	$-0.608136\pi$
$787$	−18.6961	−0.666443	−0.333221	+	0.942849i	$0.608136\pi$
$788$	−116.822	−4.16160
$789$	6.79214	0.241807
$790$	−57.5285	−2.04677
$791$	−1.26899	−0.0451200
$792$	51.5330	1.83115
$793$	−13.8145	−0.490567
$794$	−6.50767	−0.230949
$795$	−15.6432	−0.554805
$796$	15.0410	0.533115
$797$	30.9729	1.09712	0.548558	−	0.836113i	$-0.315177\pi$
$797$	30.9729	1.09712	0.548558	+	0.836113i	$0.315177\pi$
$798$	−60.8862	−2.15535
$799$	−0.533768	−0.0188834
$800$	−47.1602	−1.66736
$801$	−20.6155	−0.728411
$802$	8.41046	0.296984
$803$	−6.33009	−0.223384
$804$	−45.0228	−1.58783
$805$	−11.3494	−0.400014
$806$	17.1810	0.605175
$807$	−23.1148	−0.813680
$808$	0.399909	0.0140688
$809$	−45.8091	−1.61056	−0.805280	−	0.592894i	$-0.797985\pi$
$809$	−45.8091	−1.61056	−0.805280	+	0.592894i	$0.797985\pi$
$810$	30.5953	1.07501
$811$	−27.8169	−0.976784	−0.488392	−	0.872624i	$-0.662416\pi$
$811$	−27.8169	−0.976784	−0.488392	+	0.872624i	$0.662416\pi$
$812$	25.3630	0.890066
$813$	9.68754	0.339757
$814$	−24.9075	−0.873009
$815$	30.6500	1.07362
$816$	3.22213	0.112797
$817$	−28.7142	−1.00458
$818$	−37.9535	−1.32701
$819$	−29.1570	−1.01883
$820$	2.16579	0.0756326
$821$	10.1746	0.355097	0.177549	−	0.984112i	$-0.443183\pi$
$821$	10.1746	0.355097	0.177549	+	0.984112i	$0.443183\pi$
$822$	14.9355	0.520936
$823$	−18.2799	−0.637199	−0.318599	−	0.947889i	$-0.603212\pi$
$823$	−18.2799	−0.637199	−0.318599	+	0.947889i	$0.603212\pi$
$824$	−107.532	−3.74606
$825$	−2.99957	−0.104432
$826$	−8.46462	−0.294522
$827$	−52.6382	−1.83041	−0.915206	−	0.402987i	$-0.867972\pi$
$827$	−52.6382	−1.83041	−0.915206	+	0.402987i	$0.867972\pi$
$828$	−12.8779	−0.447538
$829$	46.3991	1.61151	0.805754	−	0.592251i	$-0.201761\pi$
$829$	46.3991	1.61151	0.805754	+	0.592251i	$0.201761\pi$
$830$	−104.161	−3.61548
$831$	3.67890	0.127620
$832$	95.3856	3.30690
$833$	−3.70097	−0.128231
$834$	5.28186	0.182896
$835$	22.6547	0.783997
$836$	−76.0279	−2.62948
$837$	−9.75992	−0.337352
$838$	−42.7798	−1.47780
$839$	5.97731	0.206360	0.103180	−	0.994663i	$-0.467098\pi$
$839$	5.97731	0.206360	0.103180	+	0.994663i	$0.467098\pi$
$840$	−90.5240	−3.12337
$841$	−28.0342	−0.966697
$842$	71.6518	2.46928
$843$	−2.92050	−0.100587
$844$	−128.992	−4.44007
$845$	16.2649	0.559529
$846$	13.6665	0.469864
$847$	−29.8786	−1.02664
$848$	−129.391	−4.44331
$849$	−5.36076	−0.183981
$850$	1.36159	0.0467020
$851$	4.00833	0.137404
$852$	53.1561	1.82110
$853$	−37.2941	−1.27693	−0.638463	−	0.769653i	$-0.720429\pi$
$853$	−37.2941	−1.27693	−0.638463	+	0.769653i	$0.720429\pi$
$854$	67.1765	2.29873
$855$	−40.7478	−1.39355
$856$	75.8172	2.59138
$857$	−52.7376	−1.80148	−0.900741	−	0.434357i	$-0.856976\pi$
$857$	−52.7376	−1.80148	−0.900741	+	0.434357i	$0.856976\pi$
$858$	11.4812	0.391962
$859$	17.4253	0.594543	0.297271	−	0.954793i	$-0.403923\pi$
$859$	17.4253	0.594543	0.297271	+	0.954793i	$0.403923\pi$
$860$	−66.2932	−2.26058
$861$	0.508015	0.0173131
$862$	−63.4132	−2.15986
$863$	−40.3461	−1.37340	−0.686698	−	0.726943i	$-0.740941\pi$
$863$	−40.3461	−1.37340	−0.686698	+	0.726943i	$0.740941\pi$
$864$	−102.542	−3.48854
$865$	−17.9393	−0.609953
$866$	−43.9206	−1.49248
$867$	12.7382	0.432610
$868$	−61.6121	−2.09125
$869$	−16.8499	−0.571594
$870$	−5.35274	−0.181475
$871$	27.7769	0.941183
$872$	−14.9458	−0.506127
$873$	−9.36581	−0.316985
$874$	16.5910	0.561198
$875$	37.5944	1.27092
$876$	12.6171	0.426292
$877$	−46.5219	−1.57093	−0.785467	−	0.618904i	$-0.787577\pi$
$877$	−46.5219	−1.57093	−0.785467	+	0.618904i	$0.787577\pi$
$878$	48.5565	1.63870
$879$	−1.76245	−0.0594459
$880$	−90.7884	−3.06048
$881$	−35.5082	−1.19630	−0.598150	−	0.801384i	$-0.704097\pi$
$881$	−35.5082	−1.19630	−0.598150	+	0.801384i	$0.704097\pi$
$882$	94.7590	3.19070
$883$	−39.1448	−1.31733	−0.658663	−	0.752438i	$-0.728878\pi$
$883$	−39.1448	−1.31733	−0.658663	+	0.752438i	$0.728878\pi$
$884$	−3.84333	−0.129265
$885$	1.31740	0.0442839
$886$	−73.2434	−2.46066
$887$	−16.2146	−0.544434	−0.272217	−	0.962236i	$-0.587757\pi$
$887$	−16.2146	−0.544434	−0.272217	+	0.962236i	$0.587757\pi$
$888$	31.9708	1.07287
$889$	−37.9935	−1.27426
$890$	61.3184	2.05540
$891$	8.96127	0.300214
$892$	−12.0390	−0.403095
$893$	−12.9843	−0.434503
$894$	17.1671	0.574152
$895$	−52.3661	−1.75040
$896$	−233.379	−7.79663
$897$	−1.84765	−0.0616913
$898$	−4.78167	−0.159566
$899$	−2.34613	−0.0782478
$900$	−25.7090	−0.856965
$901$	2.07982	0.0692887
$902$	0.860194	0.0286413
$903$	−15.5499	−0.517470
$904$	2.75804	0.0917311
$905$	5.09090	0.169227
$906$	−22.8787	−0.760093
$907$	−23.7103	−0.787288	−0.393644	−	0.919263i	$-0.628786\pi$
$907$	−23.7103	−0.787288	−0.393644	+	0.919263i	$0.628786\pi$
$908$	−19.4460	−0.645337
$909$	0.0974842	0.00323335
$910$	86.7243	2.87488
$911$	−46.9692	−1.55616	−0.778080	−	0.628165i	$-0.783806\pi$
$911$	−46.9692	−1.55616	−0.778080	+	0.628165i	$0.783806\pi$
$912$	78.3806	2.59544
$913$	−30.5084	−1.00968
$914$	4.31532	0.142738
$915$	−10.4551	−0.345635
$916$	20.0071	0.661052
$917$	−15.8838	−0.524528
$918$	2.96054	0.0977123
$919$	15.4589	0.509943	0.254972	−	0.966949i	$-0.417934\pi$
$919$	15.4589	0.509943	0.254972	+	0.966949i	$0.417934\pi$
$920$	24.6670	0.813247
$921$	−15.6854	−0.516852
$922$	73.7314	2.42821
$923$	−32.7947	−1.07945
$924$	−41.1723	−1.35447
$925$	8.00208	0.263107
$926$	−0.317090	−0.0104202
$927$	−26.2126	−0.860935
$928$	−24.6494	−0.809157
$929$	5.35233	0.175604	0.0878022	−	0.996138i	$-0.472016\pi$
$929$	5.35233	0.175604	0.0878022	+	0.996138i	$0.472016\pi$
$930$	13.0030	0.426384
$931$	−90.0288	−2.95057
$932$	−108.265	−3.54633
$933$	−20.2711	−0.663646
$934$	26.4038	0.863958
$935$	1.45932	0.0477249
$936$	63.3703	2.07132
$937$	32.9023	1.07487	0.537436	−	0.843304i	$-0.319393\pi$
$937$	32.9023	1.07487	0.537436	+	0.843304i	$0.319393\pi$
$938$	−135.072	−4.41027
$939$	4.19405	0.136868
$940$	−29.9771	−0.977745
$941$	−21.9325	−0.714979	−0.357490	−	0.933917i	$-0.616367\pi$
$941$	−21.9325	−0.714979	−0.357490	+	0.933917i	$0.616367\pi$
$942$	−45.2186	−1.47330
$943$	−0.138430	−0.00450789
$944$	10.8968	0.354659
$945$	−49.2650	−1.60259
$946$	−26.3299	−0.856058
$947$	−21.8661	−0.710551	−0.355276	−	0.934762i	$-0.615613\pi$
$947$	−21.8661	−0.710551	−0.355276	+	0.934762i	$0.615613\pi$
$948$	33.5851	1.09079
$949$	−7.78413	−0.252683
$950$	33.1216	1.07461
$951$	7.61655	0.246984
$952$	12.0355	0.390073
$953$	39.2271	1.27069	0.635344	−	0.772229i	$-0.280858\pi$
$953$	39.2271	1.27069	0.635344	+	0.772229i	$0.280858\pi$
$954$	−53.2512	−1.72407
$955$	−35.8157	−1.15897
$956$	−99.4486	−3.21640
$957$	−1.56780	−0.0506797
$958$	0.784675	0.0253517
$959$	33.0437	1.06704
$960$	72.1898	2.32992
$961$	−25.3007	−0.816153
$962$	−30.6289	−0.987514
$963$	18.4816	0.595562
$964$	84.5782	2.72408
$965$	−59.2413	−1.90704
$966$	8.98469	0.289078
$967$	−46.5640	−1.49740	−0.748699	−	0.662910i	$-0.769321\pi$
$967$	−46.5640	−1.49740	−0.748699	+	0.662910i	$0.769321\pi$
$968$	64.9386	2.08721
$969$	−1.25988	−0.0404732
$970$	27.8576	0.894453
$971$	−20.7960	−0.667376	−0.333688	−	0.942684i	$-0.608293\pi$
$971$	−20.7960	−0.667376	−0.333688	+	0.942684i	$0.608293\pi$
$972$	−86.7610	−2.78286
$973$	11.6857	0.374627
$974$	19.9131	0.638057
$975$	−3.68858	−0.118129
$976$	−86.4784	−2.76811
$977$	27.5674	0.881958	0.440979	−	0.897517i	$-0.354631\pi$
$977$	27.5674	0.881958	0.440979	+	0.897517i	$0.354631\pi$
$978$	−24.2639	−0.775873
$979$	17.9600	0.574003
$980$	−207.851	−6.63957
$981$	−3.64326	−0.116320
$982$	−30.8505	−0.984480
$983$	27.4251	0.874726	0.437363	−	0.899285i	$-0.355912\pi$
$983$	27.4251	0.874726	0.437363	+	0.899285i	$0.355912\pi$
$984$	−1.10413	−0.0351983
$985$	54.5466	1.73800
$986$	0.711666	0.0226641
$987$	−7.03153	−0.223816
$988$	−93.4918	−2.97437
$989$	4.23723	0.134736
$990$	−37.3642	−1.18751
$991$	6.60771	0.209901	0.104950	−	0.994477i	$-0.466532\pi$
$991$	6.60771	0.209901	0.104950	+	0.994477i	$0.466532\pi$
$992$	59.8788	1.90115
$993$	−18.2727	−0.579867
$994$	159.473	5.05817
$995$	−7.02297	−0.222643
$996$	60.8092	1.92681
$997$	−54.6773	−1.73165	−0.865824	−	0.500348i	$-0.833205\pi$
$997$	−54.6773	−1.73165	−0.865824	+	0.500348i	$0.833205\pi$
$998$	−82.4550	−2.61007
$999$	17.3992	0.550485

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8017.2.a.a.1.5	✓	327

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8017.2.a.a.1.5	✓	327	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:	\( N \)	\(=\)	\( 8017 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8017.a (trivial)

\(f(q)\)	\(=\)	\(q-2.76002 q^{2} -0.752350 q^{3} +5.61769 q^{4} -2.62302 q^{5} +2.07650 q^{6} +4.59409 q^{7} -9.98488 q^{8} -2.43397 q^{9} +O(q^{10})\)	\(q-2.76002 q^{2} -0.752350 q^{3} +5.61769 q^{4} -2.62302 q^{5} +2.07650 q^{6} +4.59409 q^{7} -9.98488 q^{8} -2.43397 q^{9} +7.23958 q^{10} +2.12045 q^{11} -4.22647 q^{12} +2.60752 q^{13} -12.6798 q^{14} +1.97343 q^{15} +16.3230 q^{16} -0.262375 q^{17} +6.71780 q^{18} -6.38245 q^{19} -14.7353 q^{20} -3.45636 q^{21} -5.85247 q^{22} +0.941829 q^{23} +7.51212 q^{24} +1.88023 q^{25} -7.19680 q^{26} +4.08825 q^{27} +25.8082 q^{28} +0.982750 q^{29} -5.44669 q^{30} -2.38731 q^{31} -25.0821 q^{32} -1.59532 q^{33} +0.724158 q^{34} -12.0504 q^{35} -13.6733 q^{36} +4.25590 q^{37} +17.6157 q^{38} -1.96177 q^{39} +26.1905 q^{40} -0.146980 q^{41} +9.53962 q^{42} +4.49893 q^{43} +11.9120 q^{44} +6.38435 q^{45} -2.59946 q^{46} +2.03437 q^{47} -12.2806 q^{48} +14.1057 q^{49} -5.18947 q^{50} +0.197397 q^{51} +14.6482 q^{52} -7.92689 q^{53} -11.2836 q^{54} -5.56198 q^{55} -45.8714 q^{56} +4.80184 q^{57} -2.71240 q^{58} +0.667569 q^{59} +11.0861 q^{60} -5.29793 q^{61} +6.58902 q^{62} -11.1819 q^{63} +36.5809 q^{64} -6.83958 q^{65} +4.40311 q^{66} +10.6526 q^{67} -1.47394 q^{68} -0.708585 q^{69} +33.2593 q^{70} -12.5770 q^{71} +24.3029 q^{72} -2.98526 q^{73} -11.7463 q^{74} -1.41459 q^{75} -35.8546 q^{76} +9.74153 q^{77} +5.41451 q^{78} -7.94639 q^{79} -42.8157 q^{80} +4.22612 q^{81} +0.405666 q^{82} -14.3877 q^{83} -19.4168 q^{84} +0.688214 q^{85} -12.4171 q^{86} -0.739371 q^{87} -21.1724 q^{88} +8.46989 q^{89} -17.6209 q^{90} +11.9792 q^{91} +5.29090 q^{92} +1.79609 q^{93} -5.61490 q^{94} +16.7413 q^{95} +18.8705 q^{96} +3.84796 q^{97} -38.9319 q^{98} -5.16111 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 327 q - 23 q^{2} - 48 q^{3} + 315 q^{4} - 55 q^{5} - 38 q^{6} - 87 q^{7} - 69 q^{8} + 303 q^{9}+O(q^{10}) \) 327 * q - 23 * q^2 - 48 * q^3 + 315 * q^4 - 55 * q^5 - 38 * q^6 - 87 * q^7 - 69 * q^8 + 303 * q^9	\( 327 q - 23 q^{2} - 48 q^{3} + 315 q^{4} - 55 q^{5} - 38 q^{6} - 87 q^{7} - 69 q^{8} + 303 q^{9} - 48 q^{10} - 70 q^{11} - 120 q^{12} - 53 q^{13} - 52 q^{14} - 77 q^{15} + 295 q^{16} - 164 q^{17} - 58 q^{18} - 47 q^{19} - 153 q^{20} - 39 q^{21} - 68 q^{22} - 256 q^{23} - 107 q^{24} + 288 q^{25} - 95 q^{26} - 189 q^{27} - 167 q^{28} - 99 q^{29} - 81 q^{30} - 71 q^{31} - 146 q^{32} - 95 q^{33} - 40 q^{34} - 192 q^{35} + 261 q^{36} - 54 q^{37} - 179 q^{38} - 115 q^{39} - 121 q^{40} - 111 q^{41} - 62 q^{42} - 110 q^{43} - 157 q^{44} - 137 q^{45} - 11 q^{46} - 324 q^{47} - 236 q^{48} + 296 q^{49} - 73 q^{50} - 88 q^{51} - 138 q^{52} - 170 q^{53} - 127 q^{54} - 151 q^{55} - 151 q^{56} - 106 q^{57} - 81 q^{58} - 123 q^{59} - 83 q^{60} - 62 q^{61} - 287 q^{62} - 400 q^{63} + 263 q^{64} - 143 q^{65} - 64 q^{66} - 95 q^{67} - 442 q^{68} - 22 q^{69} - 26 q^{70} - 210 q^{71} - 129 q^{72} - 121 q^{73} - 159 q^{74} - 194 q^{75} - 86 q^{76} - 178 q^{77} - 68 q^{78} - 145 q^{79} - 338 q^{80} + 259 q^{81} - 103 q^{82} - 418 q^{83} - 102 q^{84} - 40 q^{85} - 89 q^{86} - 372 q^{87} - 186 q^{88} - 100 q^{89} - 150 q^{90} - 69 q^{91} - 458 q^{92} - 81 q^{93} - 46 q^{94} - 377 q^{95} - 190 q^{96} - 87 q^{97} - 147 q^{98} - 171 q^{99}+O(q^{100}) \) 327 * q - 23 * q^2 - 48 * q^3 + 315 * q^4 - 55 * q^5 - 38 * q^6 - 87 * q^7 - 69 * q^8 + 303 * q^9 - 48 * q^10 - 70 * q^11 - 120 * q^12 - 53 * q^13 - 52 * q^14 - 77 * q^15 + 295 * q^16 - 164 * q^17 - 58 * q^18 - 47 * q^19 - 153 * q^20 - 39 * q^21 - 68 * q^22 - 256 * q^23 - 107 * q^24 + 288 * q^25 - 95 * q^26 - 189 * q^27 - 167 * q^28 - 99 * q^29 - 81 * q^30 - 71 * q^31 - 146 * q^32 - 95 * q^33 - 40 * q^34 - 192 * q^35 + 261 * q^36 - 54 * q^37 - 179 * q^38 - 115 * q^39 - 121 * q^40 - 111 * q^41 - 62 * q^42 - 110 * q^43 - 157 * q^44 - 137 * q^45 - 11 * q^46 - 324 * q^47 - 236 * q^48 + 296 * q^49 - 73 * q^50 - 88 * q^51 - 138 * q^52 - 170 * q^53 - 127 * q^54 - 151 * q^55 - 151 * q^56 - 106 * q^57 - 81 * q^58 - 123 * q^59 - 83 * q^60 - 62 * q^61 - 287 * q^62 - 400 * q^63 + 263 * q^64 - 143 * q^65 - 64 * q^66 - 95 * q^67 - 442 * q^68 - 22 * q^69 - 26 * q^70 - 210 * q^71 - 129 * q^72 - 121 * q^73 - 159 * q^74 - 194 * q^75 - 86 * q^76 - 178 * q^77 - 68 * q^78 - 145 * q^79 - 338 * q^80 + 259 * q^81 - 103 * q^82 - 418 * q^83 - 102 * q^84 - 40 * q^85 - 89 * q^86 - 372 * q^87 - 186 * q^88 - 100 * q^89 - 150 * q^90 - 69 * q^91 - 458 * q^92 - 81 * q^93 - 46 * q^94 - 377 * q^95 - 190 * q^96 - 87 * q^97 - 147 * q^98 - 171 * q^99

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