LMFDB - Embedded newform 8023.2.a.c.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8023, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8023.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8023 = 71 \cdot 113 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8023.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$64.0639775417$
Analytic rank:	$1$
Dimension:	$158$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
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)

$f(q)$	$=$	$q-2.51950 q^{2} -2.51323 q^{3} +4.34790 q^{4} +1.49157 q^{5} +6.33210 q^{6} -1.81281 q^{7} -5.91556 q^{8} +3.31634 q^{9} +O(q^{10})$	\(q-2.51950 q^{2} -2.51323 q^{3} +4.34790 q^{4} +1.49157 q^{5} +6.33210 q^{6} -1.81281 q^{7} -5.91556 q^{8} +3.31634 q^{9} -3.75802 q^{10} +0.112037 q^{11} -10.9273 q^{12} -2.05744 q^{13} +4.56738 q^{14} -3.74866 q^{15} +6.20847 q^{16} -0.998471 q^{17} -8.35554 q^{18} +2.42110 q^{19} +6.48521 q^{20} +4.55601 q^{21} -0.282278 q^{22} -4.58166 q^{23} +14.8672 q^{24} -2.77522 q^{25} +5.18373 q^{26} -0.795043 q^{27} -7.88192 q^{28} -1.78517 q^{29} +9.44478 q^{30} -1.50305 q^{31} -3.81115 q^{32} -0.281575 q^{33} +2.51565 q^{34} -2.70393 q^{35} +14.4191 q^{36} +1.83538 q^{37} -6.09997 q^{38} +5.17083 q^{39} -8.82347 q^{40} +3.52083 q^{41} -11.4789 q^{42} +1.61704 q^{43} +0.487126 q^{44} +4.94656 q^{45} +11.5435 q^{46} +3.42421 q^{47} -15.6033 q^{48} -3.71372 q^{49} +6.99217 q^{50} +2.50939 q^{51} -8.94556 q^{52} -7.80459 q^{53} +2.00311 q^{54} +0.167111 q^{55} +10.7238 q^{56} -6.08478 q^{57} +4.49775 q^{58} +9.72052 q^{59} -16.2988 q^{60} +6.10379 q^{61} +3.78695 q^{62} -6.01189 q^{63} -2.81473 q^{64} -3.06882 q^{65} +0.709429 q^{66} -4.61058 q^{67} -4.34126 q^{68} +11.5148 q^{69} +6.81257 q^{70} -1.00000 q^{71} -19.6180 q^{72} +15.7775 q^{73} -4.62425 q^{74} +6.97477 q^{75} +10.5267 q^{76} -0.203101 q^{77} -13.0279 q^{78} +12.0908 q^{79} +9.26037 q^{80} -7.95090 q^{81} -8.87074 q^{82} +11.6775 q^{83} +19.8091 q^{84} -1.48929 q^{85} -4.07413 q^{86} +4.48655 q^{87} -0.662761 q^{88} +9.20666 q^{89} -12.4629 q^{90} +3.72975 q^{91} -19.9206 q^{92} +3.77753 q^{93} -8.62733 q^{94} +3.61124 q^{95} +9.57831 q^{96} -1.36224 q^{97} +9.35675 q^{98} +0.371553 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 158 q - 24 q^{2} - 23 q^{3} + 158 q^{4} - 31 q^{5} - 17 q^{6} - 2 q^{7} - 69 q^{8} + 135 q^{9}+O(q^{10}) $ 158 * q - 24 * q^2 - 23 * q^3 + 158 * q^4 - 31 * q^5 - 17 * q^6 - 2 * q^7 - 69 * q^8 + 135 * q^9	\( 158 q - 24 q^{2} - 23 q^{3} + 158 q^{4} - 31 q^{5} - 17 q^{6} - 2 q^{7} - 69 q^{8} + 135 q^{9} - 10 q^{10} - 10 q^{11} - 46 q^{12} - 28 q^{13} - 27 q^{14} - 41 q^{15} + 150 q^{16} - 137 q^{17} - 67 q^{18} - 42 q^{19} - 66 q^{20} - 46 q^{21} - 8 q^{22} - 26 q^{23} - 48 q^{24} + 129 q^{25} - 67 q^{26} - 89 q^{27} - 21 q^{28} - 79 q^{29} - 11 q^{30} + 7 q^{31} - 147 q^{32} - 112 q^{33} - 28 q^{34} - 53 q^{35} + 141 q^{36} - 60 q^{37} - 53 q^{38} - 3 q^{39} - 48 q^{40} - 128 q^{41} + 32 q^{42} - 63 q^{43} - 88 q^{45} - 2 q^{46} - 92 q^{47} - 131 q^{48} + 122 q^{49} - 116 q^{50} - 12 q^{51} - 89 q^{52} - 94 q^{53} - 71 q^{54} - 12 q^{55} - 104 q^{56} - 93 q^{57} - 65 q^{58} - 54 q^{59} - 12 q^{60} + 17 q^{61} - 97 q^{62} - 28 q^{63} + 163 q^{64} - 163 q^{65} - 65 q^{66} - 35 q^{67} - 217 q^{68} - 46 q^{69} - 79 q^{70} - 158 q^{71} - 99 q^{72} - 165 q^{73} - 94 q^{75} - 93 q^{76} - 140 q^{77} + 25 q^{78} - 61 q^{79} - 134 q^{80} + 114 q^{81} + 10 q^{82} - 158 q^{83} - 160 q^{84} + 23 q^{85} - 122 q^{86} - 71 q^{87} - 14 q^{88} - 251 q^{89} - 6 q^{90} - 57 q^{91} - 58 q^{92} - 52 q^{93} - 64 q^{94} - 84 q^{95} - 98 q^{96} - 48 q^{97} - 84 q^{98} + 85 q^{99}+O(q^{100}) \) 158 * q - 24 * q^2 - 23 * q^3 + 158 * q^4 - 31 * q^5 - 17 * q^6 - 2 * q^7 - 69 * q^8 + 135 * q^9 - 10 * q^10 - 10 * q^11 - 46 * q^12 - 28 * q^13 - 27 * q^14 - 41 * q^15 + 150 * q^16 - 137 * q^17 - 67 * q^18 - 42 * q^19 - 66 * q^20 - 46 * q^21 - 8 * q^22 - 26 * q^23 - 48 * q^24 + 129 * q^25 - 67 * q^26 - 89 * q^27 - 21 * q^28 - 79 * q^29 - 11 * q^30 + 7 * q^31 - 147 * q^32 - 112 * q^33 - 28 * q^34 - 53 * q^35 + 141 * q^36 - 60 * q^37 - 53 * q^38 - 3 * q^39 - 48 * q^40 - 128 * q^41 + 32 * q^42 - 63 * q^43 - 88 * q^45 - 2 * q^46 - 92 * q^47 - 131 * q^48 + 122 * q^49 - 116 * q^50 - 12 * q^51 - 89 * q^52 - 94 * q^53 - 71 * q^54 - 12 * q^55 - 104 * q^56 - 93 * q^57 - 65 * q^58 - 54 * q^59 - 12 * q^60 + 17 * q^61 - 97 * q^62 - 28 * q^63 + 163 * q^64 - 163 * q^65 - 65 * q^66 - 35 * q^67 - 217 * q^68 - 46 * q^69 - 79 * q^70 - 158 * q^71 - 99 * q^72 - 165 * q^73 - 94 * q^75 - 93 * q^76 - 140 * q^77 + 25 * q^78 - 61 * q^79 - 134 * q^80 + 114 * q^81 + 10 * q^82 - 158 * q^83 - 160 * q^84 + 23 * q^85 - 122 * q^86 - 71 * q^87 - 14 * q^88 - 251 * q^89 - 6 * q^90 - 57 * q^91 - 58 * q^92 - 52 * q^93 - 64 * q^94 - 84 * q^95 - 98 * q^96 - 48 * q^97 - 84 * q^98 + 85 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.51950	−1.78156	−0.890780	−	0.454436i	$-0.849841\pi$
$2$	−2.51950	−1.78156	−0.890780	+	0.454436i	$0.849841\pi$
$3$	−2.51323	−1.45102	−0.725508	−	0.688214i	$-0.758395\pi$
$3$	−2.51323	−1.45102	−0.725508	+	0.688214i	$0.758395\pi$
$4$	4.34790	2.17395
$5$	1.49157	0.667051	0.333525	−	0.942741i	$-0.391762\pi$
$5$	1.49157	0.667051	0.333525	+	0.942741i	$0.391762\pi$
$6$	6.33210	2.58507
$7$	−1.81281	−0.685177	−0.342589	−	0.939486i	$-0.611304\pi$
$7$	−1.81281	−0.685177	−0.342589	+	0.939486i	$0.611304\pi$
$8$	−5.91556	−2.09147
$9$	3.31634	1.10545
$10$	−3.75802	−1.18839
$11$	0.112037	0.0337804	0.0168902	−	0.999857i	$-0.494623\pi$
$11$	0.112037	0.0337804	0.0168902	+	0.999857i	$0.494623\pi$
$12$	−10.9273	−3.15444
$13$	−2.05744	−0.570631	−0.285316	−	0.958434i	$-0.592098\pi$
$13$	−2.05744	−0.570631	−0.285316	+	0.958434i	$0.592098\pi$
$14$	4.56738	1.22068
$15$	−3.74866	−0.967901
$16$	6.20847	1.55212
$17$	−0.998471	−0.242165	−0.121082	−	0.992642i	$-0.538637\pi$
$17$	−0.998471	−0.242165	−0.121082	+	0.992642i	$0.538637\pi$
$18$	−8.35554	−1.96942
$19$	2.42110	0.555438	0.277719	−	0.960662i	$-0.410422\pi$
$19$	2.42110	0.555438	0.277719	+	0.960662i	$0.410422\pi$
$20$	6.48521	1.45014
$21$	4.55601	0.994203
$22$	−0.282278	−0.0601818
$23$	−4.58166	−0.955343	−0.477672	−	0.878539i	$-0.658519\pi$
$23$	−4.58166	−0.955343	−0.477672	+	0.878539i	$0.658519\pi$
$24$	14.8672	3.03475
$25$	−2.77522	−0.555044
$26$	5.18373	1.01661
$27$	−0.795043	−0.153006
$28$	−7.88192	−1.48954
$29$	−1.78517	−0.331498	−0.165749	−	0.986168i	$-0.553004\pi$
$29$	−1.78517	−0.331498	−0.165749	+	0.986168i	$0.553004\pi$
$30$	9.44478	1.72437
$31$	−1.50305	−0.269957	−0.134978	−	0.990849i	$-0.543096\pi$
$31$	−1.50305	−0.269957	−0.134978	+	0.990849i	$0.543096\pi$
$32$	−3.81115	−0.673722
$33$	−0.281575	−0.0490159
$34$	2.51565	0.431431
$35$	−2.70393	−0.457048
$36$	14.4191	2.40319
$37$	1.83538	0.301735	0.150867	−	0.988554i	$-0.451793\pi$
$37$	1.83538	0.301735	0.150867	+	0.988554i	$0.451793\pi$
$38$	−6.09997	−0.989545
$39$	5.17083	0.827995
$40$	−8.82347	−1.39511
$41$	3.52083	0.549861	0.274930	−	0.961464i	$-0.411345\pi$
$41$	3.52083	0.549861	0.274930	+	0.961464i	$0.411345\pi$
$42$	−11.4789	−1.77123
$43$	1.61704	0.246596	0.123298	−	0.992370i	$-0.460653\pi$
$43$	1.61704	0.246596	0.123298	+	0.992370i	$0.460653\pi$
$44$	0.487126	0.0734370
$45$	4.94656	0.737389
$46$	11.5435	1.70200
$47$	3.42421	0.499473	0.249737	−	0.968314i	$-0.419656\pi$
$47$	3.42421	0.499473	0.249737	+	0.968314i	$0.419656\pi$
$48$	−15.6033	−2.25215
$49$	−3.71372	−0.530532
$50$	6.99217	0.988843
$51$	2.50939	0.351385
$52$	−8.94556	−1.24053
$53$	−7.80459	−1.07204	−0.536022	−	0.844204i	$-0.680073\pi$
$53$	−7.80459	−1.07204	−0.536022	+	0.844204i	$0.680073\pi$
$54$	2.00311	0.272589
$55$	0.167111	0.0225332
$56$	10.7238	1.43302
$57$	−6.08478	−0.805949
$58$	4.49775	0.590583
$59$	9.72052	1.26550	0.632752	−	0.774354i	$-0.281925\pi$
$59$	9.72052	1.26550	0.632752	+	0.774354i	$0.281925\pi$
$60$	−16.2988	−2.10417
$61$	6.10379	0.781511	0.390755	−	0.920495i	$-0.372214\pi$
$61$	6.10379	0.781511	0.390755	+	0.920495i	$0.372214\pi$
$62$	3.78695	0.480944
$63$	−6.01189	−0.757428
$64$	−2.81473	−0.351841
$65$	−3.06882	−0.380640
$66$	0.709429	0.0873247
$67$	−4.61058	−0.563272	−0.281636	−	0.959521i	$-0.590877\pi$
$67$	−4.61058	−0.563272	−0.281636	+	0.959521i	$0.590877\pi$
$68$	−4.34126	−0.526455
$69$	11.5148	1.38622
$70$	6.81257	0.814258
$71$	−1.00000	−0.118678
$71$	−1.00000	−0.118678
$72$	−19.6180	−2.31201
$73$	15.7775	1.84661	0.923306	−	0.384066i	$-0.125476\pi$
$73$	15.7775	1.84661	0.923306	+	0.384066i	$0.125476\pi$
$74$	−4.62425	−0.537559
$75$	6.97477	0.805377
$76$	10.5267	1.20750
$77$	−0.203101	−0.0231456
$78$	−13.0279	−1.47512
$79$	12.0908	1.36033	0.680163	−	0.733061i	$-0.261909\pi$
$79$	12.0908	1.36033	0.680163	+	0.733061i	$0.261909\pi$
$80$	9.26037	1.03534
$81$	−7.95090	−0.883433
$82$	−8.87074	−0.979609
$83$	11.6775	1.28178	0.640888	−	0.767634i	$-0.278566\pi$
$83$	11.6775	1.28178	0.640888	+	0.767634i	$0.278566\pi$
$84$	19.8091	2.16135
$85$	−1.48929	−0.161536
$86$	−4.07413	−0.439325
$87$	4.48655	0.481009
$88$	−0.662761	−0.0706505
$89$	9.20666	0.975904	0.487952	−	0.872871i	$-0.337744\pi$
$89$	9.20666	0.975904	0.487952	+	0.872871i	$0.337744\pi$
$90$	−12.4629	−1.31370
$91$	3.72975	0.390984
$92$	−19.9206	−2.07687
$93$	3.77753	0.391711
$94$	−8.62733	−0.889841
$95$	3.61124	0.370505
$96$	9.57831	0.977582
$97$	−1.36224	−0.138315	−0.0691574	−	0.997606i	$-0.522031\pi$
$97$	−1.36224	−0.138315	−0.0691574	+	0.997606i	$0.522031\pi$
$98$	9.35675	0.945174
$99$	0.371553	0.0373425
$100$	−12.0664	−1.20664
$101$	−6.66565	−0.663257	−0.331629	−	0.943410i	$-0.607598\pi$
$101$	−6.66565	−0.663257	−0.331629	+	0.943410i	$0.607598\pi$
$102$	−6.32242	−0.626013
$103$	−12.4447	−1.22621	−0.613104	−	0.790002i	$-0.710079\pi$
$103$	−12.4447	−1.22621	−0.613104	+	0.790002i	$0.710079\pi$
$104$	12.1709	1.19346
$105$	6.79561	0.663184
$106$	19.6637	1.90991
$107$	−4.02551	−0.389160	−0.194580	−	0.980887i	$-0.562334\pi$
$107$	−4.02551	−0.389160	−0.194580	+	0.980887i	$0.562334\pi$
$108$	−3.45677	−0.332628
$109$	0.903714	0.0865601	0.0432801	−	0.999063i	$-0.486219\pi$
$109$	0.903714	0.0865601	0.0432801	+	0.999063i	$0.486219\pi$
$110$	−0.421037	−0.0401443
$111$	−4.61274	−0.437822
$112$	−11.2548	−1.06348
$113$	−1.00000	−0.0940721
$113$	−1.00000	−0.0940721
$114$	15.3306	1.43585
$115$	−6.83387	−0.637262
$116$	−7.76176	−0.720661
$117$	−6.82318	−0.630803
$118$	−24.4909	−2.25457
$119$	1.81004	0.165926
$120$	22.1754	2.02433
$121$	−10.9874	−0.998859
$122$	−15.3785	−1.39231
$123$	−8.84866	−0.797856
$124$	−6.53514	−0.586873
$125$	−11.5973	−1.03729
$126$	15.1470	1.34940
$127$	−12.1269	−1.07609	−0.538045	−	0.842916i	$-0.680837\pi$
$127$	−12.1269	−1.07609	−0.538045	+	0.842916i	$0.680837\pi$
$128$	14.7140	1.30055
$129$	−4.06399	−0.357815
$130$	7.73190	0.678133
$131$	3.93681	0.343961	0.171980	−	0.985100i	$-0.444983\pi$
$131$	3.93681	0.343961	0.171980	+	0.985100i	$0.444983\pi$
$132$	−1.22426	−0.106558
$133$	−4.38899	−0.380573
$134$	11.6164	1.00350
$135$	−1.18586	−0.102063
$136$	5.90651	0.506479
$137$	−3.95166	−0.337613	−0.168807	−	0.985649i	$-0.553991\pi$
$137$	−3.95166	−0.337613	−0.168807	+	0.985649i	$0.553991\pi$
$138$	−29.0116	−2.46963
$139$	6.91616	0.586621	0.293310	−	0.956017i	$-0.405243\pi$
$139$	6.91616	0.586621	0.293310	+	0.956017i	$0.405243\pi$
$140$	−11.7564	−0.993601
$141$	−8.60585	−0.724743
$142$	2.51950	0.211432
$143$	−0.230509	−0.0192762
$144$	20.5894	1.71578
$145$	−2.66271	−0.221126
$146$	−39.7514	−3.28985
$147$	9.33346	0.769810
$148$	7.98007	0.655957
$149$	−21.6485	−1.77351	−0.886757	−	0.462236i	$-0.847047\pi$
$149$	−21.6485	−1.77351	−0.886757	+	0.462236i	$0.847047\pi$
$150$	−17.5730	−1.43483
$151$	12.1857	0.991655	0.495828	−	0.868421i	$-0.334865\pi$
$151$	12.1857	0.991655	0.495828	+	0.868421i	$0.334865\pi$
$152$	−14.3221	−1.16168
$153$	−3.31127	−0.267700
$154$	0.511715	0.0412352
$155$	−2.24191	−0.180075
$156$	22.4823	1.80002
$157$	23.1601	1.84838	0.924188	−	0.381938i	$-0.124743\pi$
$157$	23.1601	1.84838	0.924188	+	0.381938i	$0.124743\pi$
$158$	−30.4630	−2.42350
$159$	19.6148	1.55555
$160$	−5.68460	−0.449407
$161$	8.30568	0.654579
$162$	20.0323	1.57389
$163$	−13.8010	−1.08098	−0.540488	−	0.841351i	$-0.681761\pi$
$163$	−13.8010	−1.08098	−0.540488	+	0.841351i	$0.681761\pi$
$164$	15.3082	1.19537
$165$	−0.419989	−0.0326961
$166$	−29.4216	−2.28356
$167$	1.67578	0.129676	0.0648378	−	0.997896i	$-0.479347\pi$
$167$	1.67578	0.129676	0.0648378	+	0.997896i	$0.479347\pi$
$168$	−26.9514	−2.07934
$169$	−8.76694	−0.674380
$170$	3.75227	0.287786
$171$	8.02919	0.614007
$172$	7.03073	0.536088
$173$	−15.0424	−1.14365	−0.571827	−	0.820374i	$-0.693765\pi$
$173$	−15.0424	−1.14365	−0.571827	+	0.820374i	$0.693765\pi$
$174$	−11.3039	−0.856946
$175$	5.03094	0.380303
$176$	0.695577	0.0524311
$177$	−24.4299	−1.83627
$178$	−23.1962	−1.73863
$179$	−2.71136	−0.202656	−0.101328	−	0.994853i	$-0.532309\pi$
$179$	−2.71136	−0.202656	−0.101328	+	0.994853i	$0.532309\pi$
$180$	21.5072	1.60305
$181$	21.7466	1.61641	0.808205	−	0.588902i	$-0.200440\pi$
$181$	21.7466	1.61641	0.808205	+	0.588902i	$0.200440\pi$
$182$	−9.39711	−0.696560
$183$	−15.3403	−1.13398
$184$	27.1031	1.99807
$185$	2.73760	0.201272
$186$	−9.51750	−0.697857
$187$	−0.111866	−0.00818042
$188$	14.8882	1.08583
$189$	1.44126	0.104836
$190$	−9.09853	−0.660077
$191$	12.3654	0.894732	0.447366	−	0.894351i	$-0.352362\pi$
$191$	12.3654	0.894732	0.447366	+	0.894351i	$0.352362\pi$
$192$	7.07407	0.510527
$193$	−1.94654	−0.140115	−0.0700575	−	0.997543i	$-0.522318\pi$
$193$	−1.94654	−0.140115	−0.0700575	+	0.997543i	$0.522318\pi$
$194$	3.43218	0.246416
$195$	7.71266	0.552315
$196$	−16.1469	−1.15335
$197$	−27.7265	−1.97543	−0.987714	−	0.156269i	$-0.950053\pi$
$197$	−27.7265	−1.97543	−0.987714	+	0.156269i	$0.950053\pi$
$198$	−0.936129	−0.0665278
$199$	27.2259	1.92999	0.964995	−	0.262269i	$-0.0844709\pi$
$199$	27.2259	1.92999	0.964995	+	0.262269i	$0.0844709\pi$
$200$	16.4170	1.16085
$201$	11.5875	0.817317
$202$	16.7941	1.18163
$203$	3.23618	0.227135
$204$	10.9106	0.763894
$205$	5.25156	0.366785
$206$	31.3544	2.18456
$207$	−15.1944	−1.05608
$208$	−12.7736	−0.885687
$209$	0.271252	0.0187629
$210$	−17.1216	−1.18150
$211$	1.46873	0.101112	0.0505559	−	0.998721i	$-0.483901\pi$
$211$	1.46873	0.101112	0.0505559	+	0.998721i	$0.483901\pi$
$212$	−33.9336	−2.33057
$213$	2.51323	0.172204
$214$	10.1423	0.693312
$215$	2.41193	0.164492
$216$	4.70312	0.320007
$217$	2.72475	0.184968
$218$	−2.27691	−0.154212
$219$	−39.6524	−2.67946
$220$	0.726582	0.0489862
$221$	2.05429	0.138187
$222$	11.6218	0.780006
$223$	−11.5952	−0.776473	−0.388237	−	0.921560i	$-0.626916\pi$
$223$	−11.5952	−0.776473	−0.388237	+	0.921560i	$0.626916\pi$
$224$	6.90888	0.461619
$225$	−9.20357	−0.613571
$226$	2.51950	0.167595
$227$	−12.1596	−0.807058	−0.403529	−	0.914967i	$-0.632217\pi$
$227$	−12.1596	−0.807058	−0.403529	+	0.914967i	$0.632217\pi$
$228$	−26.4561	−1.75210
$229$	10.0846	0.666406	0.333203	−	0.942855i	$-0.391871\pi$
$229$	10.0846	0.666406	0.333203	+	0.942855i	$0.391871\pi$
$230$	17.2180	1.13532
$231$	0.510441	0.0335846
$232$	10.5603	0.693317
$233$	−2.11264	−0.138404	−0.0692020	−	0.997603i	$-0.522045\pi$
$233$	−2.11264	−0.138404	−0.0692020	+	0.997603i	$0.522045\pi$
$234$	17.1910	1.12381
$235$	5.10746	0.333174
$236$	42.2639	2.75115
$237$	−30.3871	−1.97386
$238$	−4.56040	−0.295607
$239$	15.2071	0.983667	0.491834	−	0.870689i	$-0.336327\pi$
$239$	15.2071	0.983667	0.491834	+	0.870689i	$0.336327\pi$
$240$	−23.2735	−1.50230
$241$	25.4306	1.63813	0.819066	−	0.573700i	$-0.194492\pi$
$241$	25.4306	1.63813	0.819066	+	0.573700i	$0.194492\pi$
$242$	27.6829	1.77953
$243$	22.3676	1.43488
$244$	26.5387	1.69897
$245$	−5.53928	−0.353892
$246$	22.2942	1.42143
$247$	−4.98126	−0.316950
$248$	8.89141	0.564605
$249$	−29.3484	−1.85988
$250$	29.2194	1.84800
$251$	0.115702	0.00730302	0.00365151	−	0.999993i	$-0.498838\pi$
$251$	0.115702	0.00730302	0.00365151	+	0.999993i	$0.498838\pi$
$252$	−26.1391	−1.64661
$253$	−0.513315	−0.0322719
$254$	30.5538	1.91712
$255$	3.74293	0.234392
$256$	−31.4426	−1.96516
$257$	16.3672	1.02096	0.510478	−	0.859891i	$-0.329468\pi$
$257$	16.3672	1.02096	0.510478	+	0.859891i	$0.329468\pi$
$258$	10.2393	0.637468
$259$	−3.32720	−0.206742
$260$	−13.3429	−0.827493
$261$	−5.92024	−0.366454
$262$	−9.91881	−0.612786
$263$	12.3090	0.759008	0.379504	−	0.925190i	$-0.376095\pi$
$263$	12.3090	0.759008	0.379504	+	0.925190i	$0.376095\pi$
$264$	1.66567	0.102515
$265$	−11.6411	−0.715107
$266$	11.0581	0.678014
$267$	−23.1385	−1.41605
$268$	−20.0464	−1.22453
$269$	−17.8838	−1.09039	−0.545197	−	0.838308i	$-0.683545\pi$
$269$	−17.8838	−1.09039	−0.545197	+	0.838308i	$0.683545\pi$
$270$	2.98779	0.181831
$271$	5.26761	0.319985	0.159992	−	0.987118i	$-0.448853\pi$
$271$	5.26761	0.319985	0.159992	+	0.987118i	$0.448853\pi$
$272$	−6.19897	−0.375868
$273$	−9.37372	−0.567324
$274$	9.95624	0.601478
$275$	−0.310927	−0.0187496
$276$	50.0652	3.01357
$277$	−11.4057	−0.685299	−0.342650	−	0.939463i	$-0.611324\pi$
$277$	−11.4057	−0.685299	−0.342650	+	0.939463i	$0.611324\pi$
$278$	−17.4253	−1.04510
$279$	−4.98464	−0.298423
$280$	15.9953	0.955900
$281$	7.81009	0.465911	0.232955	−	0.972487i	$-0.425160\pi$
$281$	7.81009	0.465911	0.232955	+	0.972487i	$0.425160\pi$
$282$	21.6825	1.29117
$283$	25.4615	1.51353	0.756764	−	0.653689i	$-0.226779\pi$
$283$	25.4615	1.51353	0.756764	+	0.653689i	$0.226779\pi$
$284$	−4.34790	−0.258001
$285$	−9.07588	−0.537609
$286$	0.580769	0.0343416
$287$	−6.38258	−0.376752
$288$	−12.6391	−0.744765
$289$	−16.0031	−0.941356
$290$	6.70871	0.393949
$291$	3.42364	0.200697
$292$	68.5989	4.01445
$293$	−10.2983	−0.601630	−0.300815	−	0.953682i	$-0.597259\pi$
$293$	−10.2983	−0.601630	−0.300815	+	0.953682i	$0.597259\pi$
$294$	−23.5157	−1.37146
$295$	14.4988	0.844156
$296$	−10.8573	−0.631068
$297$	−0.0890741	−0.00516860
$298$	54.5435	3.15962
$299$	9.42650	0.545149
$300$	30.3256	1.75085
$301$	−2.93138	−0.168962
$302$	−30.7018	−1.76669
$303$	16.7523	0.962397
$304$	15.0313	0.862104
$305$	9.10424	0.521307
$306$	8.34277	0.476924
$307$	2.93345	0.167421	0.0837104	−	0.996490i	$-0.473323\pi$
$307$	2.93345	0.167421	0.0837104	+	0.996490i	$0.473323\pi$
$308$	−0.883066	−0.0503173
$309$	31.2763	1.77925
$310$	5.64851	0.320814
$311$	−3.54731	−0.201149	−0.100575	−	0.994930i	$-0.532068\pi$
$311$	−3.54731	−0.201149	−0.100575	+	0.994930i	$0.532068\pi$
$312$	−30.5883	−1.73172
$313$	15.5425	0.878517	0.439258	−	0.898361i	$-0.355241\pi$
$313$	15.5425	0.878517	0.439258	+	0.898361i	$0.355241\pi$
$314$	−58.3520	−3.29299
$315$	−8.96716	−0.505243
$316$	52.5699	2.95729
$317$	5.89069	0.330854	0.165427	−	0.986222i	$-0.447100\pi$
$317$	5.89069	0.330854	0.165427	+	0.986222i	$0.447100\pi$
$318$	−49.4195	−2.77131
$319$	−0.200005	−0.0111981
$320$	−4.19836	−0.234696
$321$	10.1170	0.564678
$322$	−20.9262	−1.16617
$323$	−2.41740	−0.134507
$324$	−34.5698	−1.92054
$325$	5.70985	0.316725
$326$	34.7717	1.92582
$327$	−2.27124	−0.125600
$328$	−20.8276	−1.15001
$329$	−6.20745	−0.342228
$330$	1.05816	0.0582500
$331$	−19.4021	−1.06644	−0.533219	−	0.845977i	$-0.679018\pi$
$331$	−19.4021	−1.06644	−0.533219	+	0.845977i	$0.679018\pi$
$332$	50.7728	2.78652
$333$	6.08675	0.333552
$334$	−4.22213	−0.231025
$335$	−6.87701	−0.375731
$336$	28.2859	1.54312
$337$	−32.4584	−1.76812	−0.884060	−	0.467374i	$-0.845200\pi$
$337$	−32.4584	−1.76812	−0.884060	+	0.467374i	$0.845200\pi$
$338$	22.0883	1.20145
$339$	2.51323	0.136500
$340$	−6.47529	−0.351172
$341$	−0.168398	−0.00911924
$342$	−20.2296	−1.09389
$343$	19.4219	1.04869
$344$	−9.56568	−0.515747
$345$	17.1751	0.924678
$346$	37.8994	2.03749
$347$	−0.653619	−0.0350881	−0.0175440	−	0.999846i	$-0.505585\pi$
$347$	−0.653619	−0.0350881	−0.0175440	+	0.999846i	$0.505585\pi$
$348$	19.5071	1.04569
$349$	13.8769	0.742815	0.371408	−	0.928470i	$-0.378875\pi$
$349$	13.8769	0.742815	0.371408	+	0.928470i	$0.378875\pi$
$350$	−12.6755	−0.677533
$351$	1.63575	0.0873100
$352$	−0.426989	−0.0227586
$353$	3.33171	0.177329	0.0886646	−	0.996062i	$-0.471740\pi$
$353$	3.33171	0.177329	0.0886646	+	0.996062i	$0.471740\pi$
$354$	61.5514	3.27142
$355$	−1.49157	−0.0791643
$356$	40.0297	2.12157
$357$	−4.54905	−0.240761
$358$	6.83128	0.361044
$359$	21.6449	1.14238	0.571188	−	0.820819i	$-0.306483\pi$
$359$	21.6449	1.14238	0.571188	+	0.820819i	$0.306483\pi$
$360$	−29.2617	−1.54222
$361$	−13.1383	−0.691489
$362$	−54.7906	−2.87973
$363$	27.6140	1.44936
$364$	16.2166	0.849980
$365$	23.5332	1.23178
$366$	38.6499	2.02026
$367$	−8.23227	−0.429721	−0.214860	−	0.976645i	$-0.568930\pi$
$367$	−8.23227	−0.429721	−0.214860	+	0.976645i	$0.568930\pi$
$368$	−28.4451	−1.48280
$369$	11.6763	0.607842
$370$	−6.89740	−0.358579
$371$	14.1482	0.734540
$372$	16.4243	0.851562
$373$	11.7365	0.607695	0.303847	−	0.952721i	$-0.401729\pi$
$373$	11.7365	0.607695	0.303847	+	0.952721i	$0.401729\pi$
$374$	0.281846	0.0145739
$375$	29.1467	1.50513
$376$	−20.2561	−1.04463
$377$	3.67288	0.189163
$378$	−3.63126	−0.186772
$379$	14.5218	0.745932	0.372966	−	0.927845i	$-0.378341\pi$
$379$	14.5218	0.745932	0.372966	+	0.927845i	$0.378341\pi$
$380$	15.7013	0.805460
$381$	30.4778	1.56142
$382$	−31.1548	−1.59402
$383$	16.5023	0.843228	0.421614	−	0.906775i	$-0.361464\pi$
$383$	16.5023	0.843228	0.421614	+	0.906775i	$0.361464\pi$
$384$	−36.9798	−1.88712
$385$	−0.302940	−0.0154393
$386$	4.90432	0.249623
$387$	5.36265	0.272599
$388$	−5.92291	−0.300690
$389$	−3.38791	−0.171774	−0.0858869	−	0.996305i	$-0.527372\pi$
$389$	−3.38791	−0.171774	−0.0858869	+	0.996305i	$0.527372\pi$
$390$	−19.4321	−0.983981
$391$	4.57466	0.231350
$392$	21.9688	1.10959
$393$	−9.89412	−0.499092
$394$	69.8570	3.51934
$395$	18.0344	0.907407
$396$	1.61548	0.0811807
$397$	4.63107	0.232427	0.116213	−	0.993224i	$-0.462924\pi$
$397$	4.63107	0.232427	0.116213	+	0.993224i	$0.462924\pi$
$398$	−68.5957	−3.43839
$399$	11.0305	0.552218
$400$	−17.2298	−0.861492
$401$	23.4815	1.17261	0.586304	−	0.810091i	$-0.300582\pi$
$401$	23.4815	1.17261	0.586304	+	0.810091i	$0.300582\pi$
$402$	−29.1947	−1.45610
$403$	3.09245	0.154046
$404$	−28.9816	−1.44189
$405$	−11.8593	−0.589295
$406$	−8.15356	−0.404654
$407$	0.205630	0.0101927
$408$	−14.8444	−0.734910
$409$	6.82493	0.337471	0.168736	−	0.985661i	$-0.446032\pi$
$409$	6.82493	0.337471	0.168736	+	0.985661i	$0.446032\pi$
$410$	−13.2313	−0.653449
$411$	9.93145	0.489883
$412$	−54.1082	−2.66572
$413$	−17.6215	−0.867095
$414$	38.2823	1.88147
$415$	17.4179	0.855010
$416$	7.84121	0.384447
$417$	−17.3819	−0.851196
$418$	−0.683421	−0.0334272
$419$	−18.4506	−0.901370	−0.450685	−	0.892683i	$-0.648820\pi$
$419$	−18.4506	−0.901370	−0.450685	+	0.892683i	$0.648820\pi$
$420$	29.5467	1.44173
$421$	22.5985	1.10138	0.550691	−	0.834709i	$-0.314364\pi$
$421$	22.5985	1.10138	0.550691	+	0.834709i	$0.314364\pi$
$422$	−3.70048	−0.180137
$423$	11.3559	0.552141
$424$	46.1685	2.24214
$425$	2.77097	0.134412
$426$	−6.33210	−0.306791
$427$	−11.0650	−0.535473
$428$	−17.5025	−0.846016
$429$	0.579324	0.0279700
$430$	−6.07686	−0.293052
$431$	−21.0244	−1.01271	−0.506354	−	0.862326i	$-0.669007\pi$
$431$	−21.0244	−1.01271	−0.506354	+	0.862326i	$0.669007\pi$
$432$	−4.93600	−0.237483
$433$	−23.0217	−1.10635	−0.553176	−	0.833064i	$-0.686584\pi$
$433$	−23.0217	−1.10635	−0.553176	+	0.833064i	$0.686584\pi$
$434$	−6.86502	−0.329532
$435$	6.69201	0.320857
$436$	3.92926	0.188178
$437$	−11.0927	−0.530634
$438$	99.9045	4.77362
$439$	−25.5662	−1.22021	−0.610104	−	0.792322i	$-0.708872\pi$
$439$	−25.5662	−1.22021	−0.610104	+	0.792322i	$0.708872\pi$
$440$	−0.988554	−0.0471275
$441$	−12.3160	−0.586475
$442$	−5.17581	−0.246188
$443$	23.6798	1.12506	0.562532	−	0.826776i	$-0.309827\pi$
$443$	23.6798	1.12506	0.562532	+	0.826776i	$0.309827\pi$
$444$	−20.0558	−0.951805
$445$	13.7324	0.650977
$446$	29.2142	1.38333
$447$	54.4077	2.57340
$448$	5.10256	0.241073
$449$	10.4198	0.491741	0.245870	−	0.969303i	$-0.420926\pi$
$449$	10.4198	0.491741	0.245870	+	0.969303i	$0.420926\pi$
$450$	23.1884	1.09311
$451$	0.394462	0.0185745
$452$	−4.34790	−0.204508
$453$	−30.6254	−1.43891
$454$	30.6361	1.43782
$455$	5.56318	0.260806
$456$	35.9949	1.68561
$457$	14.6985	0.687569	0.343784	−	0.939049i	$-0.388291\pi$
$457$	14.6985	0.687569	0.343784	+	0.939049i	$0.388291\pi$
$458$	−25.4081	−1.18724
$459$	0.793827	0.0370527
$460$	−29.7130	−1.38538
$461$	12.4736	0.580951	0.290476	−	0.956882i	$-0.406186\pi$
$461$	12.4736	0.580951	0.290476	+	0.956882i	$0.406186\pi$
$462$	−1.28606	−0.0598329
$463$	9.88583	0.459433	0.229717	−	0.973258i	$-0.426220\pi$
$463$	9.88583	0.459433	0.229717	+	0.973258i	$0.426220\pi$
$464$	−11.0832	−0.514524
$465$	5.63445	0.261291
$466$	5.32282	0.246575
$467$	−4.48560	−0.207569	−0.103784	−	0.994600i	$-0.533095\pi$
$467$	−4.48560	−0.207569	−0.103784	+	0.994600i	$0.533095\pi$
$468$	−29.6665	−1.37134
$469$	8.35810	0.385941
$470$	−12.8683	−0.593569
$471$	−58.2067	−2.68202
$472$	−57.5023	−2.64676
$473$	0.181168	0.00833011
$474$	76.5605	3.51654
$475$	−6.71907	−0.308292
$476$	7.86987	0.360715
$477$	−25.8827	−1.18509
$478$	−38.3144	−1.75246
$479$	19.2893	0.881348	0.440674	−	0.897667i	$-0.354739\pi$
$479$	19.2893	0.881348	0.440674	+	0.897667i	$0.354739\pi$
$480$	14.2867	0.652097
$481$	−3.77619	−0.172179
$482$	−64.0726	−2.91843
$483$	−20.8741	−0.949805
$484$	−47.7724	−2.17147
$485$	−2.03188	−0.0922630
$486$	−56.3553	−2.55633
$487$	19.1242	0.866602	0.433301	−	0.901249i	$-0.357349\pi$
$487$	19.1242	0.866602	0.433301	+	0.901249i	$0.357349\pi$
$488$	−36.1073	−1.63450
$489$	34.6851	1.56851
$490$	13.9562	0.630479
$491$	−4.04055	−0.182347	−0.0911736	−	0.995835i	$-0.529062\pi$
$491$	−4.04055	−0.182347	−0.0911736	+	0.995835i	$0.529062\pi$
$492$	−38.4731	−1.73450
$493$	1.78244	0.0802772
$494$	12.5503	0.564665
$495$	0.554197	0.0249093
$496$	−9.33167	−0.419004
$497$	1.81281	0.0813156
$498$	73.9434	3.31348
$499$	−21.2637	−0.951896	−0.475948	−	0.879473i	$-0.657895\pi$
$499$	−21.2637	−0.951896	−0.475948	+	0.879473i	$0.657895\pi$
$500$	−50.4239	−2.25503
$501$	−4.21162	−0.188161
$502$	−0.291511	−0.0130108
$503$	9.17310	0.409008	0.204504	−	0.978866i	$-0.434442\pi$
$503$	9.17310	0.409008	0.204504	+	0.978866i	$0.434442\pi$
$504$	35.5637	1.58413
$505$	−9.94229	−0.442426
$506$	1.29330	0.0574942
$507$	22.0334	0.978536
$508$	−52.7267	−2.33937
$509$	−30.5656	−1.35480	−0.677398	−	0.735617i	$-0.736892\pi$
$509$	−30.5656	−1.35480	−0.677398	+	0.735617i	$0.736892\pi$
$510$	−9.43034	−0.417582
$511$	−28.6015	−1.26526
$512$	49.7917	2.20050
$513$	−1.92488	−0.0849853
$514$	−41.2372	−1.81889
$515$	−18.5621	−0.817943
$516$	−17.6699	−0.777872
$517$	0.383638	0.0168724
$518$	8.38289	0.368323
$519$	37.8051	1.65946
$520$	18.1538	0.796095
$521$	−3.48867	−0.152842	−0.0764208	−	0.997076i	$-0.524349\pi$
$521$	−3.48867	−0.152842	−0.0764208	+	0.997076i	$0.524349\pi$
$522$	14.9161	0.652859
$523$	38.8187	1.69742	0.848711	−	0.528857i	$-0.177379\pi$
$523$	38.8187	1.69742	0.848711	+	0.528857i	$0.177379\pi$
$524$	17.1169	0.747754
$525$	−12.6439	−0.551826
$526$	−31.0127	−1.35222
$527$	1.50076	0.0653740
$528$	−1.74815	−0.0760784
$529$	−2.00835	−0.0873197
$530$	29.3298	1.27401
$531$	32.2366	1.39895
$532$	−19.0829	−0.827348
$533$	−7.24389	−0.313768
$534$	58.2975	2.52278
$535$	−6.00432	−0.259590
$536$	27.2742	1.17806
$537$	6.81427	0.294058
$538$	45.0583	1.94260
$539$	−0.416074	−0.0179216
$540$	−5.15602	−0.221880
$541$	13.4545	0.578455	0.289228	−	0.957260i	$-0.406602\pi$
$541$	13.4545	0.578455	0.289228	+	0.957260i	$0.406602\pi$
$542$	−13.2718	−0.570071
$543$	−54.6542	−2.34544
$544$	3.80532	0.163152
$545$	1.34795	0.0577400
$546$	23.6171	1.01072
$547$	−19.2032	−0.821070	−0.410535	−	0.911845i	$-0.634658\pi$
$547$	−19.2032	−0.821070	−0.410535	+	0.911845i	$0.634658\pi$
$548$	−17.1815	−0.733956
$549$	20.2423	0.863919
$550$	0.783381	0.0334035
$551$	−4.32207	−0.184127
$552$	−68.1164	−2.89923
$553$	−21.9184	−0.932065
$554$	28.7366	1.22090
$555$	−6.88023	−0.292050
$556$	30.0708	1.27529
$557$	−43.0376	−1.82356	−0.911780	−	0.410679i	$-0.865292\pi$
$557$	−43.0376	−1.82356	−0.911780	+	0.410679i	$0.865292\pi$
$558$	12.5588	0.531658
$559$	−3.32696	−0.140715
$560$	−16.7873	−0.709392
$561$	0.281144	0.0118699
$562$	−19.6776	−0.830047
$563$	−17.6181	−0.742512	−0.371256	−	0.928530i	$-0.621073\pi$
$563$	−17.6181	−0.742512	−0.371256	+	0.928530i	$0.621073\pi$
$564$	−37.4174	−1.57556
$565$	−1.49157	−0.0627508
$566$	−64.1503	−2.69644
$567$	14.4135	0.605308
$568$	5.91556	0.248211
$569$	−36.7055	−1.53877	−0.769386	−	0.638784i	$-0.779438\pi$
$569$	−36.7055	−1.53877	−0.769386	+	0.638784i	$0.779438\pi$
$570$	22.8667	0.957782
$571$	−10.2738	−0.429945	−0.214972	−	0.976620i	$-0.568966\pi$
$571$	−10.2738	−0.429945	−0.214972	+	0.976620i	$0.568966\pi$
$572$	−1.00223	−0.0419054
$573$	−31.0772	−1.29827
$574$	16.0809	0.671206
$575$	12.7151	0.530257
$576$	−9.33460	−0.388942
$577$	13.8926	0.578357	0.289179	−	0.957275i	$-0.406618\pi$
$577$	13.8926	0.578357	0.289179	+	0.957275i	$0.406618\pi$
$578$	40.3198	1.67708
$579$	4.89211	0.203309
$580$	−11.5772	−0.480717
$581$	−21.1691	−0.878244
$582$	−8.62587	−0.357554
$583$	−0.874402	−0.0362140
$584$	−93.3325	−3.86212
$585$	−10.1773	−0.420778
$586$	25.9465	1.07184
$587$	8.37627	0.345726	0.172863	−	0.984946i	$-0.444698\pi$
$587$	8.37627	0.345726	0.172863	+	0.984946i	$0.444698\pi$
$588$	40.5810	1.67353
$589$	−3.63904	−0.149944
$590$	−36.5299	−1.50391
$591$	69.6831	2.86638
$592$	11.3949	0.468328
$593$	−36.2203	−1.48739	−0.743695	−	0.668519i	$-0.766929\pi$
$593$	−36.2203	−1.48739	−0.743695	+	0.668519i	$0.766929\pi$
$594$	0.224423	0.00920817
$595$	2.69980	0.110681
$596$	−94.1256	−3.85553
$597$	−68.4249	−2.80045
$598$	−23.7501	−0.971215
$599$	−4.93393	−0.201595	−0.100797	−	0.994907i	$-0.532139\pi$
$599$	−4.93393	−0.201595	−0.100797	+	0.994907i	$0.532139\pi$
$600$	−41.2597	−1.68442
$601$	−39.1390	−1.59651	−0.798257	−	0.602317i	$-0.794244\pi$
$601$	−39.1390	−1.59651	−0.798257	+	0.602317i	$0.794244\pi$
$602$	7.38563	0.301016
$603$	−15.2903	−0.622668
$604$	52.9821	2.15581
$605$	−16.3886	−0.666289
$606$	−42.2076	−1.71457
$607$	−27.4186	−1.11289	−0.556444	−	0.830885i	$-0.687835\pi$
$607$	−27.4186	−1.11289	−0.556444	+	0.830885i	$0.687835\pi$
$608$	−9.22716	−0.374211
$609$	−8.13326	−0.329576
$610$	−22.9382	−0.928740
$611$	−7.04512	−0.285015
$612$	−14.3971	−0.581968
$613$	31.0735	1.25505	0.627523	−	0.778598i	$-0.284069\pi$
$613$	31.0735	1.25505	0.627523	+	0.778598i	$0.284069\pi$
$614$	−7.39084	−0.298270
$615$	−13.1984	−0.532211
$616$	1.20146	0.0484081
$617$	29.6654	1.19428	0.597142	−	0.802135i	$-0.296303\pi$
$617$	29.6654	1.19428	0.597142	+	0.802135i	$0.296303\pi$
$618$	−78.8009	−3.16984
$619$	41.5777	1.67115	0.835574	−	0.549378i	$-0.185135\pi$
$619$	41.5777	1.67115	0.835574	+	0.549378i	$0.185135\pi$
$620$	−9.74762	−0.391474
$621$	3.64262	0.146173
$622$	8.93746	0.358360
$623$	−16.6899	−0.668667
$624$	32.1029	1.28515
$625$	−3.42208	−0.136883
$626$	−39.1595	−1.56513
$627$	−0.681720	−0.0272253
$628$	100.698	4.01828
$629$	−1.83258	−0.0730696
$630$	22.5928	0.900119
$631$	47.3417	1.88464	0.942322	−	0.334708i	$-0.108638\pi$
$631$	47.3417	1.88464	0.942322	+	0.334708i	$0.108638\pi$
$632$	−71.5241	−2.84508
$633$	−3.69127	−0.146715
$634$	−14.8416	−0.589436
$635$	−18.0882	−0.717806
$636$	85.2831	3.38170
$637$	7.64077	0.302738
$638$	0.503914	0.0199501
$639$	−3.31634	−0.131192
$640$	21.9470	0.867531
$641$	−38.9648	−1.53902	−0.769509	−	0.638636i	$-0.779499\pi$
$641$	−38.9648	−1.53902	−0.769509	+	0.638636i	$0.779499\pi$
$642$	−25.4899	−1.00601
$643$	−21.9566	−0.865883	−0.432942	−	0.901422i	$-0.642524\pi$
$643$	−21.9566	−0.865883	−0.432942	+	0.901422i	$0.642524\pi$
$644$	36.1123	1.42302
$645$	−6.06173	−0.238680
$646$	6.09064	0.239633
$647$	3.81388	0.149939	0.0749696	−	0.997186i	$-0.476114\pi$
$647$	3.81388	0.149939	0.0749696	+	0.997186i	$0.476114\pi$
$648$	47.0340	1.84767
$649$	1.08906	0.0427492
$650$	−14.3860	−0.564265
$651$	−6.84793	−0.268392
$652$	−60.0054	−2.34999
$653$	−30.2758	−1.18479	−0.592393	−	0.805649i	$-0.701817\pi$
$653$	−30.2758	−1.18479	−0.592393	+	0.805649i	$0.701817\pi$
$654$	5.72241	0.223764
$655$	5.87203	0.229439
$656$	21.8589	0.853448
$657$	52.3235	2.04133
$658$	15.6397	0.609699
$659$	−14.0433	−0.547048	−0.273524	−	0.961865i	$-0.588189\pi$
$659$	−14.0433	−0.547048	−0.273524	+	0.961865i	$0.588189\pi$
$660$	−1.82607	−0.0710797
$661$	−1.43467	−0.0558021	−0.0279010	−	0.999611i	$-0.508882\pi$
$661$	−1.43467	−0.0558021	−0.0279010	+	0.999611i	$0.508882\pi$
$662$	48.8838	1.89992
$663$	−5.16292	−0.200511
$664$	−69.0791	−2.68079
$665$	−6.54648	−0.253862
$666$	−15.3356	−0.594243
$667$	8.17906	0.316694
$668$	7.28613	0.281909
$669$	29.1415	1.12668
$670$	17.3267	0.669387
$671$	0.683850	0.0263997
$672$	−17.3636	−0.669817
$673$	−11.2622	−0.434126	−0.217063	−	0.976158i	$-0.569648\pi$
$673$	−11.2622	−0.434126	−0.217063	+	0.976158i	$0.569648\pi$
$674$	81.7790	3.15001
$675$	2.20642	0.0849250
$676$	−38.1178	−1.46607
$677$	−39.0254	−1.49987	−0.749933	−	0.661514i	$-0.769914\pi$
$677$	−39.0254	−1.49987	−0.749933	+	0.661514i	$0.769914\pi$
$678$	−6.33210	−0.243183
$679$	2.46949	0.0947702
$680$	8.80998	0.337847
$681$	30.5598	1.17105
$682$	0.424279	0.0162465
$683$	−46.5823	−1.78242	−0.891211	−	0.453588i	$-0.850144\pi$
$683$	−46.5823	−1.78242	−0.891211	+	0.453588i	$0.850144\pi$
$684$	34.9101	1.33482
$685$	−5.89419	−0.225205
$686$	−48.9337	−1.86830
$687$	−25.3448	−0.966966
$688$	10.0393	0.382746
$689$	16.0575	0.611742
$690$	−43.2728	−1.64737
$691$	−6.48614	−0.246744	−0.123372	−	0.992360i	$-0.539371\pi$
$691$	−6.48614	−0.246744	−0.123372	+	0.992360i	$0.539371\pi$
$692$	−65.4030	−2.48625
$693$	−0.673554	−0.0255862
$694$	1.64680	0.0625115
$695$	10.3159	0.391306
$696$	−26.5405	−1.00601
$697$	−3.51544	−0.133157
$698$	−34.9630	−1.32337
$699$	5.30957	0.200826
$700$	21.8740	0.826761
$701$	−20.5170	−0.774917	−0.387459	−	0.921887i	$-0.626647\pi$
$701$	−20.5170	−0.774917	−0.387459	+	0.921887i	$0.626647\pi$
$702$	−4.12129	−0.155548
$703$	4.44364	0.167595
$704$	−0.315353	−0.0118853
$705$	−12.8362	−0.483441
$706$	−8.39427	−0.315922
$707$	12.0836	0.454449
$708$	−106.219	−3.99196
$709$	39.6901	1.49059	0.745297	−	0.666733i	$-0.232308\pi$
$709$	39.6901	1.49059	0.745297	+	0.666733i	$0.232308\pi$
$710$	3.75802	0.141036
$711$	40.0974	1.50377
$712$	−54.4625	−2.04107
$713$	6.88649	0.257901
$714$	11.4613	0.428930
$715$	−0.343821	−0.0128582
$716$	−11.7887	−0.440565
$717$	−38.2191	−1.42732
$718$	−54.5345	−2.03521
$719$	−36.4367	−1.35886	−0.679430	−	0.733740i	$-0.737773\pi$
$719$	−36.4367	−1.35886	−0.679430	+	0.733740i	$0.737773\pi$
$720$	30.7105	1.14451
$721$	22.5598	0.840170
$722$	33.1020	1.23193
$723$	−63.9131	−2.37695
$724$	94.5520	3.51400
$725$	4.95424	0.183996
$726$	−69.5737	−2.58212
$727$	7.37854	0.273655	0.136827	−	0.990595i	$-0.456309\pi$
$727$	7.37854	0.273655	0.136827	+	0.990595i	$0.456309\pi$
$728$	−22.0635	−0.817729
$729$	−32.3623	−1.19860
$730$	−59.2920	−2.19449
$731$	−1.61457	−0.0597168
$732$	−66.6980	−2.46523
$733$	26.1846	0.967151	0.483576	−	0.875303i	$-0.339338\pi$
$733$	26.1846	0.967151	0.483576	+	0.875303i	$0.339338\pi$
$734$	20.7412	0.765573
$735$	13.9215	0.513503
$736$	17.4614	0.643636
$737$	−0.516555	−0.0190276
$738$	−29.4184	−1.08291
$739$	−21.0245	−0.773398	−0.386699	−	0.922206i	$-0.626385\pi$
$739$	−21.0245	−0.773398	−0.386699	+	0.922206i	$0.626385\pi$
$740$	11.9028	0.437557
$741$	12.5191	0.459900
$742$	−35.6466	−1.30863
$743$	−2.21400	−0.0812238	−0.0406119	−	0.999175i	$-0.512931\pi$
$743$	−2.21400	−0.0812238	−0.0406119	+	0.999175i	$0.512931\pi$
$744$	−22.3462	−0.819251
$745$	−32.2903	−1.18302
$746$	−29.5703	−1.08264
$747$	38.7267	1.41694
$748$	−0.486381	−0.0177838
$749$	7.29747	0.266644
$750$	−73.4352	−2.68147
$751$	28.6994	1.04726	0.523628	−	0.851947i	$-0.324578\pi$
$751$	28.6994	1.04726	0.523628	+	0.851947i	$0.324578\pi$
$752$	21.2591	0.775241
$753$	−0.290785	−0.0105968
$754$	−9.25385	−0.337005
$755$	18.1758	0.661484
$756$	6.26646	0.227909
$757$	−4.92786	−0.179106	−0.0895530	−	0.995982i	$-0.528544\pi$
$757$	−4.92786	−0.179106	−0.0895530	+	0.995982i	$0.528544\pi$
$758$	−36.5876	−1.32892
$759$	1.29008	0.0468270
$760$	−21.3625	−0.774899
$761$	−8.61243	−0.312200	−0.156100	−	0.987741i	$-0.549892\pi$
$761$	−8.61243	−0.312200	−0.156100	+	0.987741i	$0.549892\pi$
$762$	−76.7889	−2.78177
$763$	−1.63826	−0.0593090
$764$	53.7637	1.94510
$765$	−4.93900	−0.178570
$766$	−41.5776	−1.50226
$767$	−19.9994	−0.722137
$768$	79.0226	2.85148
$769$	−9.99362	−0.360379	−0.180190	−	0.983632i	$-0.557671\pi$
$769$	−9.99362	−0.360379	−0.180190	+	0.983632i	$0.557671\pi$
$770$	0.763259	0.0275060
$771$	−41.1345	−1.48142
$772$	−8.46337	−0.304603
$773$	23.6651	0.851176	0.425588	−	0.904917i	$-0.360067\pi$
$773$	23.6651	0.851176	0.425588	+	0.904917i	$0.360067\pi$
$774$	−13.5112	−0.485651
$775$	4.17130	0.149838
$776$	8.05843	0.289281
$777$	8.36202	0.299986
$778$	8.53585	0.306025
$779$	8.52426	0.305413
$780$	33.5339	1.20071
$781$	−0.112037	−0.00400900
$782$	−11.5259	−0.412164
$783$	1.41929	0.0507212
$784$	−23.0565	−0.823448
$785$	34.5449	1.23296
$786$	24.9283	0.889162
$787$	14.2056	0.506375	0.253188	−	0.967417i	$-0.418521\pi$
$787$	14.2056	0.506375	0.253188	+	0.967417i	$0.418521\pi$
$788$	−120.552	−4.29449
$789$	−30.9355	−1.10133
$790$	−45.4376	−1.61660
$791$	1.81281	0.0644561
$792$	−2.19794	−0.0781005
$793$	−12.5582	−0.445955
$794$	−11.6680	−0.414082
$795$	29.2568	1.03763
$796$	118.375	4.19571
$797$	−32.7404	−1.15972	−0.579862	−	0.814714i	$-0.696894\pi$
$797$	−32.7404	−1.15972	−0.579862	+	0.814714i	$0.696894\pi$
$798$	−27.7915	−0.983809
$799$	−3.41898	−0.120955
$800$	10.5768	0.373945
$801$	30.5324	1.07881
$802$	−59.1617	−2.08907
$803$	1.76766	0.0623793
$804$	50.3812	1.77681
$805$	12.3885	0.436638
$806$	−7.79143	−0.274441
$807$	44.9462	1.58218
$808$	39.4311	1.38718
$809$	−32.6130	−1.14661	−0.573306	−	0.819341i	$-0.694339\pi$
$809$	−32.6130	−1.14661	−0.573306	+	0.819341i	$0.694339\pi$
$810$	29.8796	1.04986
$811$	14.4438	0.507189	0.253594	−	0.967311i	$-0.418387\pi$
$811$	14.4438	0.507189	0.253594	+	0.967311i	$0.418387\pi$
$812$	14.0706	0.493781
$813$	−13.2387	−0.464303
$814$	−0.518087	−0.0181589
$815$	−20.5851	−0.721066
$816$	15.5795	0.545391
$817$	3.91501	0.136969
$818$	−17.1955	−0.601225
$819$	12.3691	0.432212
$820$	22.8333	0.797373
$821$	−49.4511	−1.72585	−0.862927	−	0.505328i	$-0.831372\pi$
$821$	−49.4511	−1.72585	−0.862927	+	0.505328i	$0.831372\pi$
$822$	−25.0223	−0.872755
$823$	3.53562	0.123244	0.0616219	−	0.998100i	$-0.480373\pi$
$823$	3.53562	0.123244	0.0616219	+	0.998100i	$0.480373\pi$
$824$	73.6171	2.56457
$825$	0.781432	0.0272060
$826$	44.3973	1.54478
$827$	15.8575	0.551419	0.275710	−	0.961241i	$-0.411087\pi$
$827$	15.8575	0.551419	0.275710	+	0.961241i	$0.411087\pi$
$828$	−66.0637	−2.29587
$829$	−6.37825	−0.221526	−0.110763	−	0.993847i	$-0.535329\pi$
$829$	−6.37825	−0.221526	−0.110763	+	0.993847i	$0.535329\pi$
$830$	−43.8844	−1.52325
$831$	28.6651	0.994380
$832$	5.79113	0.200771
$833$	3.70805	0.128476
$834$	43.7938	1.51646
$835$	2.49954	0.0865002
$836$	1.17938	0.0407897
$837$	1.19499	0.0413050
$838$	46.4863	1.60584
$839$	−33.3714	−1.15211	−0.576054	−	0.817411i	$-0.695408\pi$
$839$	−33.3714	−1.15211	−0.576054	+	0.817411i	$0.695408\pi$
$840$	−40.1998	−1.38703
$841$	−25.8132	−0.890109
$842$	−56.9369	−1.96218
$843$	−19.6286	−0.676044
$844$	6.38591	0.219812
$845$	−13.0765	−0.449845
$846$	−28.6112	−0.983672
$847$	19.9181	0.684395
$848$	−48.4546	−1.66394
$849$	−63.9906	−2.19615
$850$	−6.98148	−0.239463
$851$	−8.40910	−0.288260
$852$	10.9273	0.374363
$853$	6.75493	0.231284	0.115642	−	0.993291i	$-0.463107\pi$
$853$	6.75493	0.231284	0.115642	+	0.993291i	$0.463107\pi$
$854$	27.8784	0.953978
$855$	11.9761	0.409574
$856$	23.8131	0.813915
$857$	−15.3282	−0.523600	−0.261800	−	0.965122i	$-0.584316\pi$
$857$	−15.3282	−0.523600	−0.261800	+	0.965122i	$0.584316\pi$
$858$	−1.45961	−0.0498302
$859$	2.68990	0.0917781	0.0458891	−	0.998947i	$-0.485388\pi$
$859$	2.68990	0.0917781	0.0458891	+	0.998947i	$0.485388\pi$
$860$	10.4868	0.357598
$861$	16.0409	0.546673
$862$	52.9710	1.80420
$863$	−9.56976	−0.325758	−0.162879	−	0.986646i	$-0.552078\pi$
$863$	−9.56976	−0.325758	−0.162879	+	0.986646i	$0.552078\pi$
$864$	3.03003	0.103084
$865$	−22.4368	−0.762875
$866$	58.0033	1.97103
$867$	40.2194	1.36592
$868$	11.8470	0.402112
$869$	1.35462	0.0459524
$870$	−16.8606	−0.571626
$871$	9.48600	0.321421
$872$	−5.34597	−0.181037
$873$	−4.51767	−0.152900
$874$	27.9480	0.945355
$875$	21.0237	0.710729
$876$	−172.405	−5.82503
$877$	9.91033	0.334648	0.167324	−	0.985902i	$-0.446487\pi$
$877$	9.91033	0.334648	0.167324	+	0.985902i	$0.446487\pi$
$878$	64.4141	2.17387
$879$	25.8819	0.872975
$880$	1.03750	0.0349742
$881$	4.73194	0.159423	0.0797116	−	0.996818i	$-0.474600\pi$
$881$	4.73194	0.159423	0.0797116	+	0.996818i	$0.474600\pi$
$882$	31.0302	1.04484
$883$	16.7152	0.562510	0.281255	−	0.959633i	$-0.409249\pi$
$883$	16.7152	0.562510	0.281255	+	0.959633i	$0.409249\pi$
$884$	8.93188	0.300412
$885$	−36.4390	−1.22488
$886$	−59.6615	−2.00437
$887$	20.6408	0.693050	0.346525	−	0.938041i	$-0.387362\pi$
$887$	20.6408	0.693050	0.346525	+	0.938041i	$0.387362\pi$
$888$	27.2869	0.915690
$889$	21.9838	0.737312
$890$	−34.5988	−1.15975
$891$	−0.890794	−0.0298427
$892$	−50.4149	−1.68802
$893$	8.29036	0.277426
$894$	−137.081	−4.58466
$895$	−4.04418	−0.135182
$896$	−26.6737	−0.891106
$897$	−23.6910	−0.791019
$898$	−26.2527	−0.876065
$899$	2.68321	0.0894901
$900$	−40.0163	−1.33388
$901$	7.79266	0.259611
$902$	−0.993850	−0.0330916
$903$	7.36724	0.245166
$904$	5.91556	0.196749
$905$	32.4365	1.07823
$906$	77.1609	2.56350
$907$	−12.4698	−0.414053	−0.207026	−	0.978335i	$-0.566379\pi$
$907$	−12.4698	−0.414053	−0.207026	+	0.978335i	$0.566379\pi$
$908$	−52.8686	−1.75451
$909$	−22.1056	−0.733196
$910$	−14.0165	−0.464641
$911$	35.2855	1.16906	0.584530	−	0.811372i	$-0.301279\pi$
$911$	35.2855	1.16906	0.584530	+	0.811372i	$0.301279\pi$
$912$	−37.7772	−1.25093
$913$	1.30831	0.0432989
$914$	−37.0331	−1.22494
$915$	−22.8811	−0.756425
$916$	43.8467	1.44874
$917$	−7.13668	−0.235674
$918$	−2.00005	−0.0660115
$919$	−41.4040	−1.36579	−0.682896	−	0.730516i	$-0.739280\pi$
$919$	−41.4040	−1.36579	−0.682896	+	0.730516i	$0.739280\pi$
$920$	40.4262	1.33281
$921$	−7.37244	−0.242930
$922$	−31.4272	−1.03500
$923$	2.05744	0.0677215
$924$	2.21935	0.0730113
$925$	−5.09358	−0.167476
$926$	−24.9074	−0.818508
$927$	−41.2707	−1.35551
$928$	6.80356	0.223338
$929$	−26.4568	−0.868018	−0.434009	−	0.900909i	$-0.642901\pi$
$929$	−26.4568	−0.868018	−0.434009	+	0.900909i	$0.642901\pi$
$930$	−14.1960	−0.465506
$931$	−8.99129	−0.294678
$932$	−9.18558	−0.300884
$933$	8.91521	0.291871
$934$	11.3015	0.369796
$935$	−0.166855	−0.00545676
$936$	40.3629	1.31930
$937$	−19.7293	−0.644527	−0.322264	−	0.946650i	$-0.604444\pi$
$937$	−19.7293	−0.644527	−0.322264	+	0.946650i	$0.604444\pi$
$938$	−21.0583	−0.687577
$939$	−39.0620	−1.27474
$940$	22.2067	0.724304
$941$	−17.4689	−0.569470	−0.284735	−	0.958606i	$-0.591906\pi$
$941$	−17.4689	−0.569470	−0.284735	+	0.958606i	$0.591906\pi$
$942$	146.652	4.77818
$943$	−16.1312	−0.525305
$944$	60.3496	1.96421
$945$	2.14974	0.0699311
$946$	−0.456453	−0.0148406
$947$	−19.5799	−0.636261	−0.318130	−	0.948047i	$-0.603055\pi$
$947$	−19.5799	−0.636261	−0.318130	+	0.948047i	$0.603055\pi$
$948$	−132.120	−4.29107
$949$	−32.4612	−1.05373
$950$	16.9287	0.549241
$951$	−14.8047	−0.480075
$952$	−10.7074	−0.347028
$953$	−33.5019	−1.08523	−0.542616	−	0.839981i	$-0.682566\pi$
$953$	−33.5019	−1.08523	−0.542616	+	0.839981i	$0.682566\pi$
$954$	65.2116	2.11130
$955$	18.4439	0.596831
$956$	66.1191	2.13845
$957$	0.502660	0.0162487
$958$	−48.5994	−1.57017
$959$	7.16361	0.231325
$960$	10.5515	0.340547
$961$	−28.7408	−0.927123
$962$	9.51413	0.306748
$963$	−13.3500	−0.430196
$964$	110.570	3.56122
$965$	−2.90340	−0.0934638
$966$	52.5924	1.69213
$967$	22.0935	0.710479	0.355239	−	0.934775i	$-0.384399\pi$
$967$	22.0935	0.710479	0.355239	+	0.934775i	$0.384399\pi$
$968$	64.9969	2.08908
$969$	6.07548	0.195172
$970$	5.11934	0.164372
$971$	−32.2311	−1.03435	−0.517173	−	0.855881i	$-0.673016\pi$
$971$	−32.2311	−1.03435	−0.517173	+	0.855881i	$0.673016\pi$
$972$	97.2522	3.11937
$973$	−12.5377	−0.401939
$974$	−48.1836	−1.54390
$975$	−14.3502	−0.459573
$976$	37.8952	1.21300
$977$	44.6411	1.42820	0.714098	−	0.700046i	$-0.246837\pi$
$977$	44.6411	1.42820	0.714098	+	0.700046i	$0.246837\pi$
$978$	−87.3893	−2.79440
$979$	1.03149	0.0329664
$980$	−24.0843	−0.769344
$981$	2.99703	0.0956877
$982$	10.1802	0.324862
$983$	−33.1297	−1.05667	−0.528337	−	0.849035i	$-0.677184\pi$
$983$	−33.1297	−1.05667	−0.528337	+	0.849035i	$0.677184\pi$
$984$	52.3447	1.66869
$985$	−41.3560	−1.31771
$986$	−4.49087	−0.143018
$987$	15.6008	0.496578
$988$	−21.6581	−0.689035
$989$	−7.40872	−0.235584
$990$	−1.39630	−0.0443774
$991$	−17.3320	−0.550569	−0.275284	−	0.961363i	$-0.588772\pi$
$991$	−17.3320	−0.550569	−0.275284	+	0.961363i	$0.588772\pi$
$992$	5.72836	0.181876
$993$	48.7621	1.54742
$994$	−4.56738	−0.144869
$995$	40.6093	1.28740
$996$	−127.604	−4.04329
$997$	−15.2928	−0.484329	−0.242165	−	0.970235i	$-0.577857\pi$
$997$	−15.2928	−0.484329	−0.242165	+	0.970235i	$0.577857\pi$
$998$	53.5741	1.69586
$999$	−1.45921	−0.0461673

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8023.2.a.c.1.14	✓	158

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8023.2.a.c.1.14	✓	158	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 8023 = 71 \cdot 113 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8023.a (trivial)

\(f(q)\)	\(=\)	\(q-2.51950 q^{2} -2.51323 q^{3} +4.34790 q^{4} +1.49157 q^{5} +6.33210 q^{6} -1.81281 q^{7} -5.91556 q^{8} +3.31634 q^{9} +O(q^{10})\)	\(q-2.51950 q^{2} -2.51323 q^{3} +4.34790 q^{4} +1.49157 q^{5} +6.33210 q^{6} -1.81281 q^{7} -5.91556 q^{8} +3.31634 q^{9} -3.75802 q^{10} +0.112037 q^{11} -10.9273 q^{12} -2.05744 q^{13} +4.56738 q^{14} -3.74866 q^{15} +6.20847 q^{16} -0.998471 q^{17} -8.35554 q^{18} +2.42110 q^{19} +6.48521 q^{20} +4.55601 q^{21} -0.282278 q^{22} -4.58166 q^{23} +14.8672 q^{24} -2.77522 q^{25} +5.18373 q^{26} -0.795043 q^{27} -7.88192 q^{28} -1.78517 q^{29} +9.44478 q^{30} -1.50305 q^{31} -3.81115 q^{32} -0.281575 q^{33} +2.51565 q^{34} -2.70393 q^{35} +14.4191 q^{36} +1.83538 q^{37} -6.09997 q^{38} +5.17083 q^{39} -8.82347 q^{40} +3.52083 q^{41} -11.4789 q^{42} +1.61704 q^{43} +0.487126 q^{44} +4.94656 q^{45} +11.5435 q^{46} +3.42421 q^{47} -15.6033 q^{48} -3.71372 q^{49} +6.99217 q^{50} +2.50939 q^{51} -8.94556 q^{52} -7.80459 q^{53} +2.00311 q^{54} +0.167111 q^{55} +10.7238 q^{56} -6.08478 q^{57} +4.49775 q^{58} +9.72052 q^{59} -16.2988 q^{60} +6.10379 q^{61} +3.78695 q^{62} -6.01189 q^{63} -2.81473 q^{64} -3.06882 q^{65} +0.709429 q^{66} -4.61058 q^{67} -4.34126 q^{68} +11.5148 q^{69} +6.81257 q^{70} -1.00000 q^{71} -19.6180 q^{72} +15.7775 q^{73} -4.62425 q^{74} +6.97477 q^{75} +10.5267 q^{76} -0.203101 q^{77} -13.0279 q^{78} +12.0908 q^{79} +9.26037 q^{80} -7.95090 q^{81} -8.87074 q^{82} +11.6775 q^{83} +19.8091 q^{84} -1.48929 q^{85} -4.07413 q^{86} +4.48655 q^{87} -0.662761 q^{88} +9.20666 q^{89} -12.4629 q^{90} +3.72975 q^{91} -19.9206 q^{92} +3.77753 q^{93} -8.62733 q^{94} +3.61124 q^{95} +9.57831 q^{96} -1.36224 q^{97} +9.35675 q^{98} +0.371553 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 158 q - 24 q^{2} - 23 q^{3} + 158 q^{4} - 31 q^{5} - 17 q^{6} - 2 q^{7} - 69 q^{8} + 135 q^{9}+O(q^{10}) \) 158 * q - 24 * q^2 - 23 * q^3 + 158 * q^4 - 31 * q^5 - 17 * q^6 - 2 * q^7 - 69 * q^8 + 135 * q^9	\( 158 q - 24 q^{2} - 23 q^{3} + 158 q^{4} - 31 q^{5} - 17 q^{6} - 2 q^{7} - 69 q^{8} + 135 q^{9} - 10 q^{10} - 10 q^{11} - 46 q^{12} - 28 q^{13} - 27 q^{14} - 41 q^{15} + 150 q^{16} - 137 q^{17} - 67 q^{18} - 42 q^{19} - 66 q^{20} - 46 q^{21} - 8 q^{22} - 26 q^{23} - 48 q^{24} + 129 q^{25} - 67 q^{26} - 89 q^{27} - 21 q^{28} - 79 q^{29} - 11 q^{30} + 7 q^{31} - 147 q^{32} - 112 q^{33} - 28 q^{34} - 53 q^{35} + 141 q^{36} - 60 q^{37} - 53 q^{38} - 3 q^{39} - 48 q^{40} - 128 q^{41} + 32 q^{42} - 63 q^{43} - 88 q^{45} - 2 q^{46} - 92 q^{47} - 131 q^{48} + 122 q^{49} - 116 q^{50} - 12 q^{51} - 89 q^{52} - 94 q^{53} - 71 q^{54} - 12 q^{55} - 104 q^{56} - 93 q^{57} - 65 q^{58} - 54 q^{59} - 12 q^{60} + 17 q^{61} - 97 q^{62} - 28 q^{63} + 163 q^{64} - 163 q^{65} - 65 q^{66} - 35 q^{67} - 217 q^{68} - 46 q^{69} - 79 q^{70} - 158 q^{71} - 99 q^{72} - 165 q^{73} - 94 q^{75} - 93 q^{76} - 140 q^{77} + 25 q^{78} - 61 q^{79} - 134 q^{80} + 114 q^{81} + 10 q^{82} - 158 q^{83} - 160 q^{84} + 23 q^{85} - 122 q^{86} - 71 q^{87} - 14 q^{88} - 251 q^{89} - 6 q^{90} - 57 q^{91} - 58 q^{92} - 52 q^{93} - 64 q^{94} - 84 q^{95} - 98 q^{96} - 48 q^{97} - 84 q^{98} + 85 q^{99}+O(q^{100}) \) 158 * q - 24 * q^2 - 23 * q^3 + 158 * q^4 - 31 * q^5 - 17 * q^6 - 2 * q^7 - 69 * q^8 + 135 * q^9 - 10 * q^10 - 10 * q^11 - 46 * q^12 - 28 * q^13 - 27 * q^14 - 41 * q^15 + 150 * q^16 - 137 * q^17 - 67 * q^18 - 42 * q^19 - 66 * q^20 - 46 * q^21 - 8 * q^22 - 26 * q^23 - 48 * q^24 + 129 * q^25 - 67 * q^26 - 89 * q^27 - 21 * q^28 - 79 * q^29 - 11 * q^30 + 7 * q^31 - 147 * q^32 - 112 * q^33 - 28 * q^34 - 53 * q^35 + 141 * q^36 - 60 * q^37 - 53 * q^38 - 3 * q^39 - 48 * q^40 - 128 * q^41 + 32 * q^42 - 63 * q^43 - 88 * q^45 - 2 * q^46 - 92 * q^47 - 131 * q^48 + 122 * q^49 - 116 * q^50 - 12 * q^51 - 89 * q^52 - 94 * q^53 - 71 * q^54 - 12 * q^55 - 104 * q^56 - 93 * q^57 - 65 * q^58 - 54 * q^59 - 12 * q^60 + 17 * q^61 - 97 * q^62 - 28 * q^63 + 163 * q^64 - 163 * q^65 - 65 * q^66 - 35 * q^67 - 217 * q^68 - 46 * q^69 - 79 * q^70 - 158 * q^71 - 99 * q^72 - 165 * q^73 - 94 * q^75 - 93 * q^76 - 140 * q^77 + 25 * q^78 - 61 * q^79 - 134 * q^80 + 114 * q^81 + 10 * q^82 - 158 * q^83 - 160 * q^84 + 23 * q^85 - 122 * q^86 - 71 * q^87 - 14 * q^88 - 251 * q^89 - 6 * q^90 - 57 * q^91 - 58 * q^92 - 52 * q^93 - 64 * q^94 - 84 * q^95 - 98 * q^96 - 48 * q^97 - 84 * q^98 + 85 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more