LMFDB - Embedded newform 8018.2.a.i.1.41

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8018,2,Mod(1,8018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8018, 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("8018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8018 = 2 \cdot 19 \cdot 211 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8018.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:	$64.0240523407$
Analytic rank:	$0$
Dimension:	$43$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.41
Character	$\chi$	$=$	8018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +3.03979 q^{3} +1.00000 q^{4} -1.94518 q^{5} -3.03979 q^{6} -1.79760 q^{7} -1.00000 q^{8} +6.24035 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +3.03979 q^{3} +1.00000 q^{4} -1.94518 q^{5} -3.03979 q^{6} -1.79760 q^{7} -1.00000 q^{8} +6.24035 q^{9} +1.94518 q^{10} +5.47942 q^{11} +3.03979 q^{12} -0.765313 q^{13} +1.79760 q^{14} -5.91295 q^{15} +1.00000 q^{16} -7.27882 q^{17} -6.24035 q^{18} +1.00000 q^{19} -1.94518 q^{20} -5.46432 q^{21} -5.47942 q^{22} +4.90576 q^{23} -3.03979 q^{24} -1.21627 q^{25} +0.765313 q^{26} +9.85000 q^{27} -1.79760 q^{28} +7.47464 q^{29} +5.91295 q^{30} +1.88266 q^{31} -1.00000 q^{32} +16.6563 q^{33} +7.27882 q^{34} +3.49665 q^{35} +6.24035 q^{36} +6.70756 q^{37} -1.00000 q^{38} -2.32639 q^{39} +1.94518 q^{40} -6.02260 q^{41} +5.46432 q^{42} +6.18949 q^{43} +5.47942 q^{44} -12.1386 q^{45} -4.90576 q^{46} +11.4534 q^{47} +3.03979 q^{48} -3.76865 q^{49} +1.21627 q^{50} -22.1261 q^{51} -0.765313 q^{52} -10.1745 q^{53} -9.85000 q^{54} -10.6585 q^{55} +1.79760 q^{56} +3.03979 q^{57} -7.47464 q^{58} -3.73154 q^{59} -5.91295 q^{60} +0.819167 q^{61} -1.88266 q^{62} -11.2176 q^{63} +1.00000 q^{64} +1.48867 q^{65} -16.6563 q^{66} +3.52275 q^{67} -7.27882 q^{68} +14.9125 q^{69} -3.49665 q^{70} +2.61137 q^{71} -6.24035 q^{72} +11.8254 q^{73} -6.70756 q^{74} -3.69720 q^{75} +1.00000 q^{76} -9.84978 q^{77} +2.32639 q^{78} -10.8406 q^{79} -1.94518 q^{80} +11.2209 q^{81} +6.02260 q^{82} -4.97058 q^{83} -5.46432 q^{84} +14.1586 q^{85} -6.18949 q^{86} +22.7214 q^{87} -5.47942 q^{88} -14.2516 q^{89} +12.1386 q^{90} +1.37572 q^{91} +4.90576 q^{92} +5.72290 q^{93} -11.4534 q^{94} -1.94518 q^{95} -3.03979 q^{96} -4.32506 q^{97} +3.76865 q^{98} +34.1935 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 43 q - 43 q^{2} + 43 q^{4} + 19 q^{7} - 43 q^{8} + 53 q^{9}+O(q^{10}) $ 43 * q - 43 * q^2 + 43 * q^4 + 19 * q^7 - 43 * q^8 + 53 * q^9	$ 43 q - 43 q^{2} + 43 q^{4} + 19 q^{7} - 43 q^{8} + 53 q^{9} + 14 q^{11} + 3 q^{13} - 19 q^{14} + q^{15} + 43 q^{16} + 8 q^{17} - 53 q^{18} + 43 q^{19} - 14 q^{22} + 43 q^{23} + 97 q^{25} - 3 q^{26} + 15 q^{27} + 19 q^{28} - 25 q^{29} - q^{30} + 22 q^{31} - 43 q^{32} + 22 q^{33} - 8 q^{34} - 6 q^{35} + 53 q^{36} + 42 q^{37} - 43 q^{38} + 9 q^{39} - 40 q^{41} + 72 q^{43} + 14 q^{44} - q^{45} - 43 q^{46} + 27 q^{47} + 86 q^{49} - 97 q^{50} - 3 q^{51} + 3 q^{52} - 5 q^{53} - 15 q^{54} + 86 q^{55} - 19 q^{56} + 25 q^{58} - 43 q^{59} + q^{60} + 31 q^{61} - 22 q^{62} + 38 q^{63} + 43 q^{64} - 32 q^{65} - 22 q^{66} + 15 q^{67} + 8 q^{68} - 7 q^{69} + 6 q^{70} + 14 q^{71} - 53 q^{72} + 93 q^{73} - 42 q^{74} - 13 q^{75} + 43 q^{76} + 38 q^{77} - 9 q^{78} + 15 q^{79} + 43 q^{81} + 40 q^{82} + 34 q^{83} + 16 q^{85} - 72 q^{86} + 60 q^{87} - 14 q^{88} - 37 q^{89} + q^{90} - 3 q^{91} + 43 q^{92} + 19 q^{93} - 27 q^{94} + 27 q^{97} - 86 q^{98} - 24 q^{99}+O(q^{100}) $ 43 * q - 43 * q^2 + 43 * q^4 + 19 * q^7 - 43 * q^8 + 53 * q^9 + 14 * q^11 + 3 * q^13 - 19 * q^14 + q^15 + 43 * q^16 + 8 * q^17 - 53 * q^18 + 43 * q^19 - 14 * q^22 + 43 * q^23 + 97 * q^25 - 3 * q^26 + 15 * q^27 + 19 * q^28 - 25 * q^29 - q^30 + 22 * q^31 - 43 * q^32 + 22 * q^33 - 8 * q^34 - 6 * q^35 + 53 * q^36 + 42 * q^37 - 43 * q^38 + 9 * q^39 - 40 * q^41 + 72 * q^43 + 14 * q^44 - q^45 - 43 * q^46 + 27 * q^47 + 86 * q^49 - 97 * q^50 - 3 * q^51 + 3 * q^52 - 5 * q^53 - 15 * q^54 + 86 * q^55 - 19 * q^56 + 25 * q^58 - 43 * q^59 + q^60 + 31 * q^61 - 22 * q^62 + 38 * q^63 + 43 * q^64 - 32 * q^65 - 22 * q^66 + 15 * q^67 + 8 * q^68 - 7 * q^69 + 6 * q^70 + 14 * q^71 - 53 * q^72 + 93 * q^73 - 42 * q^74 - 13 * q^75 + 43 * q^76 + 38 * q^77 - 9 * q^78 + 15 * q^79 + 43 * q^81 + 40 * q^82 + 34 * q^83 + 16 * q^85 - 72 * q^86 + 60 * q^87 - 14 * q^88 - 37 * q^89 + q^90 - 3 * q^91 + 43 * q^92 + 19 * q^93 - 27 * q^94 + 27 * q^97 - 86 * q^98 - 24 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	3.03979	1.75503	0.877513	−	0.479553i	$-0.159201\pi$
$3$	3.03979	1.75503	0.877513	+	0.479553i	$0.159201\pi$
$4$	1.00000	0.500000
$5$	−1.94518	−0.869912	−0.434956	−	0.900452i	$-0.643236\pi$
$5$	−1.94518	−0.869912	−0.434956	+	0.900452i	$0.643236\pi$
$6$	−3.03979	−1.24099
$7$	−1.79760	−0.679427	−0.339714	−	0.940529i	$-0.610330\pi$
$7$	−1.79760	−0.679427	−0.339714	+	0.940529i	$0.610330\pi$
$8$	−1.00000	−0.353553
$9$	6.24035	2.08012
$10$	1.94518	0.615121
$11$	5.47942	1.65211	0.826054	−	0.563591i	$-0.190581\pi$
$11$	5.47942	1.65211	0.826054	+	0.563591i	$0.190581\pi$
$12$	3.03979	0.877513
$13$	−0.765313	−0.212260	−0.106130	−	0.994352i	$-0.533846\pi$
$13$	−0.765313	−0.212260	−0.106130	+	0.994352i	$0.533846\pi$
$14$	1.79760	0.480428
$15$	−5.91295	−1.52672
$16$	1.00000	0.250000
$17$	−7.27882	−1.76537	−0.882686	−	0.469962i	$-0.844267\pi$
$17$	−7.27882	−1.76537	−0.882686	+	0.469962i	$0.844267\pi$
$18$	−6.24035	−1.47086
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−1.94518	−0.434956
$21$	−5.46432	−1.19241
$22$	−5.47942	−1.16822
$23$	4.90576	1.02292	0.511461	−	0.859307i	$-0.329105\pi$
$23$	4.90576	1.02292	0.511461	+	0.859307i	$0.329105\pi$
$24$	−3.03979	−0.620495
$25$	−1.21627	−0.243253
$26$	0.765313	0.150090
$27$	9.85000	1.89563
$28$	−1.79760	−0.339714
$29$	7.47464	1.38801	0.694003	−	0.719972i	$-0.255846\pi$
$29$	7.47464	1.38801	0.694003	+	0.719972i	$0.255846\pi$
$30$	5.91295	1.07955
$31$	1.88266	0.338136	0.169068	−	0.985604i	$-0.445924\pi$
$31$	1.88266	0.338136	0.169068	+	0.985604i	$0.445924\pi$
$32$	−1.00000	−0.176777
$33$	16.6563	2.89949
$34$	7.27882	1.24831
$35$	3.49665	0.591042
$36$	6.24035	1.04006
$37$	6.70756	1.10272	0.551358	−	0.834269i	$-0.314110\pi$
$37$	6.70756	1.10272	0.551358	+	0.834269i	$0.314110\pi$
$38$	−1.00000	−0.162221
$39$	−2.32639	−0.372521
$40$	1.94518	0.307560
$41$	−6.02260	−0.940573	−0.470286	−	0.882514i	$-0.655849\pi$
$41$	−6.02260	−0.940573	−0.470286	+	0.882514i	$0.655849\pi$
$42$	5.46432	0.843163
$43$	6.18949	0.943888	0.471944	−	0.881628i	$-0.343552\pi$
$43$	6.18949	0.943888	0.471944	+	0.881628i	$0.343552\pi$
$44$	5.47942	0.826054
$45$	−12.1386	−1.80952
$46$	−4.90576	−0.723315
$47$	11.4534	1.67065	0.835326	−	0.549754i	$-0.185279\pi$
$47$	11.4534	1.67065	0.835326	+	0.549754i	$0.185279\pi$
$48$	3.03979	0.438757
$49$	−3.76865	−0.538379
$50$	1.21627	0.172006
$51$	−22.1261	−3.09828
$52$	−0.765313	−0.106130
$53$	−10.1745	−1.39758	−0.698790	−	0.715326i	$-0.746278\pi$
$53$	−10.1745	−1.39758	−0.698790	+	0.715326i	$0.746278\pi$
$54$	−9.85000	−1.34041
$55$	−10.6585	−1.43719
$56$	1.79760	0.240214
$57$	3.03979	0.402631
$58$	−7.47464	−0.981468
$59$	−3.73154	−0.485805	−0.242903	−	0.970051i	$-0.578100\pi$
$59$	−3.73154	−0.485805	−0.242903	+	0.970051i	$0.578100\pi$
$60$	−5.91295	−0.763359
$61$	0.819167	0.104884	0.0524418	−	0.998624i	$-0.483300\pi$
$61$	0.819167	0.104884	0.0524418	+	0.998624i	$0.483300\pi$
$62$	−1.88266	−0.239098
$63$	−11.2176	−1.41329
$64$	1.00000	0.125000
$65$	1.48867	0.184647
$66$	−16.6563	−2.05025
$67$	3.52275	0.430372	0.215186	−	0.976573i	$-0.430964\pi$
$67$	3.52275	0.430372	0.215186	+	0.976573i	$0.430964\pi$
$68$	−7.27882	−0.882686
$69$	14.9125	1.79525
$70$	−3.49665	−0.417930
$71$	2.61137	0.309913	0.154956	−	0.987921i	$-0.450476\pi$
$71$	2.61137	0.309913	0.154956	+	0.987921i	$0.450476\pi$
$72$	−6.24035	−0.735432
$73$	11.8254	1.38405	0.692027	−	0.721872i	$-0.256718\pi$
$73$	11.8254	1.38405	0.692027	+	0.721872i	$0.256718\pi$
$74$	−6.70756	−0.779738
$75$	−3.69720	−0.426916
$76$	1.00000	0.114708
$77$	−9.84978	−1.12249
$78$	2.32639	0.263412
$79$	−10.8406	−1.21967	−0.609834	−	0.792529i	$-0.708764\pi$
$79$	−10.8406	−1.21967	−0.609834	+	0.792529i	$0.708764\pi$
$80$	−1.94518	−0.217478
$81$	11.2209	1.24677
$82$	6.02260	0.665085
$83$	−4.97058	−0.545592	−0.272796	−	0.962072i	$-0.587948\pi$
$83$	−4.97058	−0.545592	−0.272796	+	0.962072i	$0.587948\pi$
$84$	−5.46432	−0.596206
$85$	14.1586	1.53572
$86$	−6.18949	−0.667430
$87$	22.7214	2.43599
$88$	−5.47942	−0.584108
$89$	−14.2516	−1.51067	−0.755333	−	0.655341i	$-0.772525\pi$
$89$	−14.2516	−1.51067	−0.755333	+	0.655341i	$0.772525\pi$
$90$	12.1386	1.27952
$91$	1.37572	0.144215
$92$	4.90576	0.511461
$93$	5.72290	0.593437
$94$	−11.4534	−1.18133
$95$	−1.94518	−0.199571
$96$	−3.03979	−0.310248
$97$	−4.32506	−0.439143	−0.219572	−	0.975596i	$-0.570466\pi$
$97$	−4.32506	−0.439143	−0.219572	+	0.975596i	$0.570466\pi$
$98$	3.76865	0.380691
$99$	34.1935	3.43658
$100$	−1.21627	−0.121627
$101$	6.47753	0.644538	0.322269	−	0.946648i	$-0.395554\pi$
$101$	6.47753	0.644538	0.322269	+	0.946648i	$0.395554\pi$
$102$	22.1261	2.19081
$103$	0.516069	0.0508498	0.0254249	−	0.999677i	$-0.491906\pi$
$103$	0.516069	0.0508498	0.0254249	+	0.999677i	$0.491906\pi$
$104$	0.765313	0.0750451
$105$	10.6291	1.03729
$106$	10.1745	0.988239
$107$	2.12099	0.205044	0.102522	−	0.994731i	$-0.467309\pi$
$107$	2.12099	0.205044	0.102522	+	0.994731i	$0.467309\pi$
$108$	9.85000	0.947816
$109$	3.75383	0.359551	0.179776	−	0.983708i	$-0.442463\pi$
$109$	3.75383	0.359551	0.179776	+	0.983708i	$0.442463\pi$
$110$	10.6585	1.01625
$111$	20.3896	1.93530
$112$	−1.79760	−0.169857
$113$	13.8860	1.30628	0.653142	−	0.757236i	$-0.273451\pi$
$113$	13.8860	1.30628	0.653142	+	0.757236i	$0.273451\pi$
$114$	−3.03979	−0.284703
$115$	−9.54260	−0.889852
$116$	7.47464	0.694003
$117$	−4.77582	−0.441525
$118$	3.73154	0.343516
$119$	13.0844	1.19944
$120$	5.91295	0.539776
$121$	19.0241	1.72946
$122$	−0.819167	−0.0741639
$123$	−18.3075	−1.65073
$124$	1.88266	0.169068
$125$	12.0918	1.08152
$126$	11.2176	0.999345
$127$	17.6619	1.56724	0.783621	−	0.621240i	$-0.213371\pi$
$127$	17.6619	1.56724	0.783621	+	0.621240i	$0.213371\pi$
$128$	−1.00000	−0.0883883
$129$	18.8148	1.65655
$130$	−1.48867	−0.130565
$131$	14.1610	1.23725	0.618627	−	0.785684i	$-0.287689\pi$
$131$	14.1610	1.23725	0.618627	+	0.785684i	$0.287689\pi$
$132$	16.6563	1.44975
$133$	−1.79760	−0.155871
$134$	−3.52275	−0.304319
$135$	−19.1600	−1.64903
$136$	7.27882	0.624154
$137$	8.06959	0.689432	0.344716	−	0.938707i	$-0.387975\pi$
$137$	8.06959	0.689432	0.344716	+	0.938707i	$0.387975\pi$
$138$	−14.9125	−1.26944
$139$	−15.6214	−1.32499	−0.662494	−	0.749067i	$-0.730502\pi$
$139$	−15.6214	−1.32499	−0.662494	+	0.749067i	$0.730502\pi$
$140$	3.49665	0.295521
$141$	34.8160	2.93204
$142$	−2.61137	−0.219141
$143$	−4.19347	−0.350676
$144$	6.24035	0.520029
$145$	−14.5395	−1.20744
$146$	−11.8254	−0.978674
$147$	−11.4559	−0.944869
$148$	6.70756	0.551358
$149$	−1.79651	−0.147176	−0.0735878	−	0.997289i	$-0.523445\pi$
$149$	−1.79651	−0.147176	−0.0735878	+	0.997289i	$0.523445\pi$
$150$	3.69720	0.301875
$151$	10.8950	0.886624	0.443312	−	0.896367i	$-0.353803\pi$
$151$	10.8950	0.886624	0.443312	+	0.896367i	$0.353803\pi$
$152$	−1.00000	−0.0811107
$153$	−45.4224	−3.67218
$154$	9.84978	0.793718
$155$	−3.66212	−0.294149
$156$	−2.32639	−0.186261
$157$	13.2426	1.05688	0.528438	−	0.848972i	$-0.322778\pi$
$157$	13.2426	1.05688	0.528438	+	0.848972i	$0.322778\pi$
$158$	10.8406	0.862435
$159$	−30.9285	−2.45279
$160$	1.94518	0.153780
$161$	−8.81857	−0.695001
$162$	−11.2209	−0.881598
$163$	−4.76131	−0.372935	−0.186467	−	0.982461i	$-0.559704\pi$
$163$	−4.76131	−0.372935	−0.186467	+	0.982461i	$0.559704\pi$
$164$	−6.02260	−0.470286
$165$	−32.3996	−2.52230
$166$	4.97058	0.385792
$167$	2.55348	0.197594	0.0987972	−	0.995108i	$-0.468500\pi$
$167$	2.55348	0.197594	0.0987972	+	0.995108i	$0.468500\pi$
$168$	5.46432	0.421581
$169$	−12.4143	−0.954946
$170$	−14.1586	−1.08592
$171$	6.24035	0.477211
$172$	6.18949	0.471944
$173$	−7.39929	−0.562558	−0.281279	−	0.959626i	$-0.590759\pi$
$173$	−7.39929	−0.562558	−0.281279	+	0.959626i	$0.590759\pi$
$174$	−22.7214	−1.72250
$175$	2.18636	0.165273
$176$	5.47942	0.413027
$177$	−11.3431	−0.852601
$178$	14.2516	1.06820
$179$	17.3367	1.29581	0.647903	−	0.761723i	$-0.275646\pi$
$179$	17.3367	1.29581	0.647903	+	0.761723i	$0.275646\pi$
$180$	−12.1386	−0.904759
$181$	17.2270	1.28047	0.640235	−	0.768179i	$-0.278837\pi$
$181$	17.2270	1.28047	0.640235	+	0.768179i	$0.278837\pi$
$182$	−1.37572	−0.101975
$183$	2.49010	0.184073
$184$	−4.90576	−0.361657
$185$	−13.0474	−0.959266
$186$	−5.72290	−0.419624
$187$	−39.8837	−2.91659
$188$	11.4534	0.835326
$189$	−17.7063	−1.28794
$190$	1.94518	0.141118
$191$	17.6670	1.27834	0.639171	−	0.769064i	$-0.279277\pi$
$191$	17.6670	1.27834	0.639171	+	0.769064i	$0.279277\pi$
$192$	3.03979	0.219378
$193$	26.9141	1.93732	0.968659	−	0.248395i	$-0.0799029\pi$
$193$	26.9141	1.93732	0.968659	+	0.248395i	$0.0799029\pi$
$194$	4.32506	0.310521
$195$	4.52526	0.324061
$196$	−3.76865	−0.269189
$197$	13.3687	0.952478	0.476239	−	0.879316i	$-0.342000\pi$
$197$	13.3687	0.952478	0.476239	+	0.879316i	$0.342000\pi$
$198$	−34.1935	−2.43003
$199$	−5.26739	−0.373395	−0.186698	−	0.982417i	$-0.559778\pi$
$199$	−5.26739	−0.373395	−0.186698	+	0.982417i	$0.559778\pi$
$200$	1.21627	0.0860030
$201$	10.7084	0.755314
$202$	−6.47753	−0.455757
$203$	−13.4364	−0.943049
$204$	−22.1261	−1.54914
$205$	11.7151	0.818215
$206$	−0.516069	−0.0359563
$207$	30.6137	2.12780
$208$	−0.765313	−0.0530649
$209$	5.47942	0.379020
$210$	−10.6291	−0.733477
$211$	−1.00000	−0.0688428
$211$	−1.00000	−0.0688428
$212$	−10.1745	−0.698790
$213$	7.93803	0.543905
$214$	−2.12099	−0.144988
$215$	−12.0397	−0.821100
$216$	−9.85000	−0.670207
$217$	−3.38426	−0.229739
$218$	−3.75383	−0.254241
$219$	35.9467	2.42905
$220$	−10.6585	−0.718594
$221$	5.57058	0.374717
$222$	−20.3896	−1.36846
$223$	−24.9628	−1.67163	−0.835815	−	0.549011i	$-0.815004\pi$
$223$	−24.9628	−1.67163	−0.835815	+	0.549011i	$0.815004\pi$
$224$	1.79760	0.120107
$225$	−7.58993	−0.505995
$226$	−13.8860	−0.923682
$227$	−0.386638	−0.0256621	−0.0128310	−	0.999918i	$-0.504084\pi$
$227$	−0.386638	−0.0256621	−0.0128310	+	0.999918i	$0.504084\pi$
$228$	3.03979	0.201315
$229$	11.4152	0.754341	0.377170	−	0.926144i	$-0.376897\pi$
$229$	11.4152	0.754341	0.377170	+	0.926144i	$0.376897\pi$
$230$	9.54260	0.629220
$231$	−29.9413	−1.96999
$232$	−7.47464	−0.490734
$233$	9.62473	0.630537	0.315269	−	0.949002i	$-0.397905\pi$
$233$	9.62473	0.630537	0.315269	+	0.949002i	$0.397905\pi$
$234$	4.77582	0.312205
$235$	−22.2790	−1.45332
$236$	−3.73154	−0.242903
$237$	−32.9533	−2.14055
$238$	−13.0844	−0.848134
$239$	−19.8967	−1.28701	−0.643506	−	0.765441i	$-0.722521\pi$
$239$	−19.8967	−1.28701	−0.643506	+	0.765441i	$0.722521\pi$
$240$	−5.91295	−0.381680
$241$	−13.9525	−0.898760	−0.449380	−	0.893341i	$-0.648355\pi$
$241$	−13.9525	−0.898760	−0.449380	+	0.893341i	$0.648355\pi$
$242$	−19.0241	−1.22291
$243$	4.55928	0.292478
$244$	0.819167	0.0524418
$245$	7.33071	0.468342
$246$	18.3075	1.16724
$247$	−0.765313	−0.0486957
$248$	−1.88266	−0.119549
$249$	−15.1095	−0.957528
$250$	−12.0918	−0.764751
$251$	−10.1324	−0.639550	−0.319775	−	0.947493i	$-0.603607\pi$
$251$	−10.1324	−0.639550	−0.319775	+	0.947493i	$0.603607\pi$
$252$	−11.2176	−0.706644
$253$	26.8807	1.68998
$254$	−17.6619	−1.10821
$255$	43.0393	2.69523
$256$	1.00000	0.0625000
$257$	−16.3401	−1.01927	−0.509633	−	0.860392i	$-0.670219\pi$
$257$	−16.3401	−1.01927	−0.509633	+	0.860392i	$0.670219\pi$
$258$	−18.8148	−1.17136
$259$	−12.0575	−0.749216
$260$	1.48867	0.0923236
$261$	46.6444	2.88721
$262$	−14.1610	−0.874871
$263$	24.4908	1.51017	0.755083	−	0.655629i	$-0.227596\pi$
$263$	24.4908	1.51017	0.755083	+	0.655629i	$0.227596\pi$
$264$	−16.6563	−1.02513
$265$	19.7913	1.21577
$266$	1.79760	0.110218
$267$	−43.3219	−2.65126
$268$	3.52275	0.215186
$269$	17.0738	1.04101	0.520504	−	0.853859i	$-0.325744\pi$
$269$	17.0738	1.04101	0.520504	+	0.853859i	$0.325744\pi$
$270$	19.1600	1.16604
$271$	−7.37507	−0.448004	−0.224002	−	0.974589i	$-0.571912\pi$
$271$	−7.37507	−0.448004	−0.224002	+	0.974589i	$0.571912\pi$
$272$	−7.27882	−0.441343
$273$	4.18192	0.253101
$274$	−8.06959	−0.487502
$275$	−6.66444	−0.401881
$276$	14.9125	0.897627
$277$	9.67048	0.581043	0.290521	−	0.956869i	$-0.406171\pi$
$277$	9.67048	0.581043	0.290521	+	0.956869i	$0.406171\pi$
$278$	15.6214	0.936908
$279$	11.7485	0.703362
$280$	−3.49665	−0.208965
$281$	3.02293	0.180333	0.0901663	−	0.995927i	$-0.471260\pi$
$281$	3.02293	0.180333	0.0901663	+	0.995927i	$0.471260\pi$
$282$	−34.8160	−2.07326
$283$	−8.86864	−0.527186	−0.263593	−	0.964634i	$-0.584908\pi$
$283$	−8.86864	−0.527186	−0.263593	+	0.964634i	$0.584908\pi$
$284$	2.61137	0.154956
$285$	−5.91295	−0.350253
$286$	4.19347	0.247965
$287$	10.8262	0.639051
$288$	−6.24035	−0.367716
$289$	35.9812	2.11654
$290$	14.5395	0.853791
$291$	−13.1473	−0.770708
$292$	11.8254	0.692027
$293$	11.2344	0.656322	0.328161	−	0.944622i	$-0.393571\pi$
$293$	11.2344	0.656322	0.328161	+	0.944622i	$0.393571\pi$
$294$	11.4559	0.668123
$295$	7.25853	0.422608
$296$	−6.70756	−0.389869
$297$	53.9723	3.13179
$298$	1.79651	0.104069
$299$	−3.75444	−0.217125
$300$	−3.69720	−0.213458
$301$	−11.1262	−0.641303
$302$	−10.8950	−0.626938
$303$	19.6903	1.13118
$304$	1.00000	0.0573539
$305$	−1.59343	−0.0912395
$306$	45.4224	2.59662
$307$	−0.585514	−0.0334170	−0.0167085	−	0.999860i	$-0.505319\pi$
$307$	−0.585514	−0.0334170	−0.0167085	+	0.999860i	$0.505319\pi$
$308$	−9.84978	−0.561244
$309$	1.56875	0.0892428
$310$	3.66212	0.207994
$311$	25.1146	1.42412	0.712060	−	0.702119i	$-0.247762\pi$
$311$	25.1146	1.42412	0.712060	+	0.702119i	$0.247762\pi$
$312$	2.32639	0.131706
$313$	15.2714	0.863191	0.431595	−	0.902067i	$-0.357951\pi$
$313$	15.2714	0.863191	0.431595	+	0.902067i	$0.357951\pi$
$314$	−13.2426	−0.747324
$315$	21.8203	1.22944
$316$	−10.8406	−0.609834
$317$	−18.9194	−1.06262	−0.531311	−	0.847177i	$-0.678300\pi$
$317$	−18.9194	−1.06262	−0.531311	+	0.847177i	$0.678300\pi$
$318$	30.9285	1.73439
$319$	40.9567	2.29313
$320$	−1.94518	−0.108739
$321$	6.44737	0.359857
$322$	8.81857	0.491440
$323$	−7.27882	−0.405004
$324$	11.2209	0.623384
$325$	0.930825	0.0516329
$326$	4.76131	0.263705
$327$	11.4109	0.631022
$328$	6.02260	0.332543
$329$	−20.5886	−1.13509
$330$	32.3996	1.78354
$331$	31.0251	1.70530	0.852648	−	0.522486i	$-0.174995\pi$
$331$	31.0251	1.70530	0.852648	+	0.522486i	$0.174995\pi$
$332$	−4.97058	−0.272796
$333$	41.8575	2.29378
$334$	−2.55348	−0.139720
$335$	−6.85238	−0.374386
$336$	−5.46432	−0.298103
$337$	−18.6642	−1.01671	−0.508353	−	0.861149i	$-0.669745\pi$
$337$	−18.6642	−1.01671	−0.508353	+	0.861149i	$0.669745\pi$
$338$	12.4143	0.675249
$339$	42.2105	2.29256
$340$	14.1586	0.767859
$341$	10.3159	0.558637
$342$	−6.24035	−0.337439
$343$	19.3577	1.04522
$344$	−6.18949	−0.333715
$345$	−29.0075	−1.56171
$346$	7.39929	0.397788
$347$	−11.8770	−0.637593	−0.318797	−	0.947823i	$-0.603279\pi$
$347$	−11.8770	−0.637593	−0.318797	+	0.947823i	$0.603279\pi$
$348$	22.7214	1.21799
$349$	16.0106	0.857027	0.428513	−	0.903535i	$-0.359037\pi$
$349$	16.0106	0.857027	0.428513	+	0.903535i	$0.359037\pi$
$350$	−2.18636	−0.116866
$351$	−7.53833	−0.402366
$352$	−5.47942	−0.292054
$353$	−1.27552	−0.0678890	−0.0339445	−	0.999424i	$-0.510807\pi$
$353$	−1.27552	−0.0678890	−0.0339445	+	0.999424i	$0.510807\pi$
$354$	11.3431	0.602880
$355$	−5.07959	−0.269597
$356$	−14.2516	−0.755333
$357$	39.7738	2.10505
$358$	−17.3367	−0.916273
$359$	−11.4190	−0.602674	−0.301337	−	0.953518i	$-0.597433\pi$
$359$	−11.4190	−0.602674	−0.301337	+	0.953518i	$0.597433\pi$
$360$	12.1386	0.639761
$361$	1.00000	0.0526316
$362$	−17.2270	−0.905429
$363$	57.8293	3.03525
$364$	1.37572	0.0721075
$365$	−23.0025	−1.20400
$366$	−2.49010	−0.130160
$367$	10.8782	0.567837	0.283918	−	0.958848i	$-0.408366\pi$
$367$	10.8782	0.567837	0.283918	+	0.958848i	$0.408366\pi$
$368$	4.90576	0.255730
$369$	−37.5832	−1.95650
$370$	13.0474	0.678304
$371$	18.2897	0.949555
$372$	5.72290	0.296719
$373$	−10.6766	−0.552816	−0.276408	−	0.961040i	$-0.589144\pi$
$373$	−10.6766	−0.552816	−0.276408	+	0.961040i	$0.589144\pi$
$374$	39.8837	2.06234
$375$	36.7565	1.89810
$376$	−11.4534	−0.590665
$377$	−5.72044	−0.294618
$378$	17.7063	0.910714
$379$	13.7158	0.704533	0.352266	−	0.935900i	$-0.385411\pi$
$379$	13.7158	0.704533	0.352266	+	0.935900i	$0.385411\pi$
$380$	−1.94518	−0.0997857
$381$	53.6886	2.75055
$382$	−17.6670	−0.903925
$383$	−21.5752	−1.10244	−0.551220	−	0.834360i	$-0.685838\pi$
$383$	−21.5752	−1.10244	−0.551220	+	0.834360i	$0.685838\pi$
$384$	−3.03979	−0.155124
$385$	19.1596	0.976465
$386$	−26.9141	−1.36989
$387$	38.6246	1.96340
$388$	−4.32506	−0.219572
$389$	−13.9998	−0.709820	−0.354910	−	0.934901i	$-0.615488\pi$
$389$	−13.9998	−0.709820	−0.354910	+	0.934901i	$0.615488\pi$
$390$	−4.52526	−0.229145
$391$	−35.7081	−1.80584
$392$	3.76865	0.190346
$393$	43.0466	2.17141
$394$	−13.3687	−0.673504
$395$	21.0870	1.06100
$396$	34.1935	1.71829
$397$	10.2632	0.515096	0.257548	−	0.966265i	$-0.417085\pi$
$397$	10.2632	0.515096	0.257548	+	0.966265i	$0.417085\pi$
$398$	5.26739	0.264030
$399$	−5.46432	−0.273558
$400$	−1.21627	−0.0608133
$401$	−11.4190	−0.570239	−0.285119	−	0.958492i	$-0.592033\pi$
$401$	−11.4190	−0.570239	−0.285119	+	0.958492i	$0.592033\pi$
$402$	−10.7084	−0.534088
$403$	−1.44083	−0.0717726
$404$	6.47753	0.322269
$405$	−21.8267	−1.08458
$406$	13.4364	0.666836
$407$	36.7536	1.82181
$408$	22.1261	1.09541
$409$	−36.4212	−1.80091	−0.900455	−	0.434948i	$-0.856767\pi$
$409$	−36.4212	−1.80091	−0.900455	+	0.434948i	$0.856767\pi$
$410$	−11.7151	−0.578566
$411$	24.5299	1.20997
$412$	0.516069	0.0254249
$413$	6.70780	0.330069
$414$	−30.6137	−1.50458
$415$	9.66868	0.474617
$416$	0.765313	0.0375226
$417$	−47.4858	−2.32539
$418$	−5.47942	−0.268007
$419$	11.8364	0.578245	0.289123	−	0.957292i	$-0.406636\pi$
$419$	11.8364	0.578245	0.289123	+	0.957292i	$0.406636\pi$
$420$	10.6291	0.518647
$421$	38.5601	1.87930	0.939652	−	0.342133i	$-0.111149\pi$
$421$	38.5601	1.87930	0.939652	+	0.342133i	$0.111149\pi$
$422$	1.00000	0.0486792
$423$	71.4733	3.47515
$424$	10.1745	0.494119
$425$	8.85298	0.429433
$426$	−7.93803	−0.384599
$427$	−1.47253	−0.0712608
$428$	2.12099	0.102522
$429$	−12.7473	−0.615445
$430$	12.0397	0.580605
$431$	−22.8519	−1.10074	−0.550370	−	0.834921i	$-0.685513\pi$
$431$	−22.8519	−1.10074	−0.550370	+	0.834921i	$0.685513\pi$
$432$	9.85000	0.473908
$433$	26.8056	1.28819	0.644097	−	0.764943i	$-0.277233\pi$
$433$	26.8056	1.28819	0.644097	+	0.764943i	$0.277233\pi$
$434$	3.38426	0.162450
$435$	−44.1972	−2.11909
$436$	3.75383	0.179776
$437$	4.90576	0.234674
$438$	−35.9467	−1.71760
$439$	−25.5103	−1.21754	−0.608769	−	0.793348i	$-0.708336\pi$
$439$	−25.5103	−1.21754	−0.608769	+	0.793348i	$0.708336\pi$
$440$	10.6585	0.508123
$441$	−23.5177	−1.11989
$442$	−5.57058	−0.264965
$443$	10.6587	0.506409	0.253205	−	0.967413i	$-0.418515\pi$
$443$	10.6587	0.506409	0.253205	+	0.967413i	$0.418515\pi$
$444$	20.3896	0.967648
$445$	27.7220	1.31415
$446$	24.9628	1.18202
$447$	−5.46101	−0.258297
$448$	−1.79760	−0.0849284
$449$	−12.3607	−0.583339	−0.291670	−	0.956519i	$-0.594211\pi$
$449$	−12.3607	−0.583339	−0.291670	+	0.956519i	$0.594211\pi$
$450$	7.58993	0.357793
$451$	−33.0004	−1.55393
$452$	13.8860	0.653142
$453$	33.1186	1.55605
$454$	0.386638	0.0181458
$455$	−2.67603	−0.125454
$456$	−3.03979	−0.142351
$457$	−19.3159	−0.903558	−0.451779	−	0.892130i	$-0.649210\pi$
$457$	−19.3159	−0.903558	−0.451779	+	0.892130i	$0.649210\pi$
$458$	−11.4152	−0.533399
$459$	−71.6963	−3.34650
$460$	−9.54260	−0.444926
$461$	−29.5472	−1.37615	−0.688075	−	0.725639i	$-0.741544\pi$
$461$	−29.5472	−1.37615	−0.688075	+	0.725639i	$0.741544\pi$
$462$	29.9413	1.39300
$463$	13.5625	0.630304	0.315152	−	0.949041i	$-0.397944\pi$
$463$	13.5625	0.630304	0.315152	+	0.949041i	$0.397944\pi$
$464$	7.47464	0.347001
$465$	−11.1321	−0.516238
$466$	−9.62473	−0.445857
$467$	16.4298	0.760279	0.380140	−	0.924929i	$-0.375876\pi$
$467$	16.4298	0.760279	0.380140	+	0.924929i	$0.375876\pi$
$468$	−4.77582	−0.220762
$469$	−6.33247	−0.292406
$470$	22.2790	1.02765
$471$	40.2548	1.85484
$472$	3.73154	0.171758
$473$	33.9148	1.55941
$474$	32.9533	1.51360
$475$	−1.21627	−0.0558061
$476$	13.0844	0.599721
$477$	−63.4927	−2.90713
$478$	19.8967	0.910055
$479$	−28.7187	−1.31219	−0.656096	−	0.754678i	$-0.727793\pi$
$479$	−28.7187	−1.31219	−0.656096	+	0.754678i	$0.727793\pi$
$480$	5.91295	0.269888
$481$	−5.13339	−0.234062
$482$	13.9525	0.635519
$483$	−26.8066	−1.21974
$484$	19.0241	0.864730
$485$	8.41303	0.382016
$486$	−4.55928	−0.206813
$487$	33.5915	1.52218	0.761088	−	0.648649i	$-0.224666\pi$
$487$	33.5915	1.52218	0.761088	+	0.648649i	$0.224666\pi$
$488$	−0.819167	−0.0370820
$489$	−14.4734	−0.654510
$490$	−7.33071	−0.331168
$491$	−23.0646	−1.04089	−0.520446	−	0.853894i	$-0.674234\pi$
$491$	−23.0646	−1.04089	−0.520446	+	0.853894i	$0.674234\pi$
$492$	−18.3075	−0.825365
$493$	−54.4065	−2.45035
$494$	0.765313	0.0344331
$495$	−66.5126	−2.98952
$496$	1.88266	0.0845340
$497$	−4.69419	−0.210563
$498$	15.1095	0.677074
$499$	−5.52423	−0.247299	−0.123649	−	0.992326i	$-0.539460\pi$
$499$	−5.52423	−0.247299	−0.123649	+	0.992326i	$0.539460\pi$
$500$	12.0918	0.540760
$501$	7.76206	0.346783
$502$	10.1324	0.452230
$503$	−43.2058	−1.92645	−0.963225	−	0.268695i	$-0.913408\pi$
$503$	−43.2058	−1.92645	−0.963225	+	0.268695i	$0.913408\pi$
$504$	11.2176	0.499673
$505$	−12.6000	−0.560691
$506$	−26.8807	−1.19499
$507$	−37.7369	−1.67595
$508$	17.6619	0.783621
$509$	−31.4982	−1.39613	−0.698066	−	0.716033i	$-0.745956\pi$
$509$	−31.4982	−1.39613	−0.698066	+	0.716033i	$0.745956\pi$
$510$	−43.0393	−1.90581
$511$	−21.2572	−0.940364
$512$	−1.00000	−0.0441942
$513$	9.85000	0.434888
$514$	16.3401	0.720730
$515$	−1.00385	−0.0442349
$516$	18.8148	0.828274
$517$	62.7581	2.76010
$518$	12.0575	0.529775
$519$	−22.4923	−0.987304
$520$	−1.48867	−0.0652826
$521$	−3.69427	−0.161849	−0.0809244	−	0.996720i	$-0.525787\pi$
$521$	−3.69427	−0.161849	−0.0809244	+	0.996720i	$0.525787\pi$
$522$	−46.6444	−2.04157
$523$	37.0433	1.61979	0.809896	−	0.586573i	$-0.199523\pi$
$523$	37.0433	1.61979	0.809896	+	0.586573i	$0.199523\pi$
$524$	14.1610	0.618627
$525$	6.64607	0.290058
$526$	−24.4908	−1.06785
$527$	−13.7036	−0.596936
$528$	16.6563	0.724873
$529$	1.06649	0.0463690
$530$	−19.7913	−0.859681
$531$	−23.2861	−1.01053
$532$	−1.79760	−0.0779356
$533$	4.60918	0.199646
$534$	43.3219	1.87472
$535$	−4.12571	−0.178370
$536$	−3.52275	−0.152159
$537$	52.7000	2.27417
$538$	−17.0738	−0.736104
$539$	−20.6500	−0.889460
$540$	−19.1600	−0.824517
$541$	19.0415	0.818657	0.409329	−	0.912387i	$-0.365763\pi$
$541$	19.0415	0.818657	0.409329	+	0.912387i	$0.365763\pi$
$542$	7.37507	0.316786
$543$	52.3664	2.24726
$544$	7.27882	0.312077
$545$	−7.30187	−0.312778
$546$	−4.18192	−0.178969
$547$	−23.4788	−1.00388	−0.501940	−	0.864902i	$-0.667380\pi$
$547$	−23.4788	−1.00388	−0.501940	+	0.864902i	$0.667380\pi$
$548$	8.06959	0.344716
$549$	5.11189	0.218170
$550$	6.66444	0.284173
$551$	7.47464	0.318430
$552$	−14.9125	−0.634718
$553$	19.4871	0.828675
$554$	−9.67048	−0.410859
$555$	−39.6615	−1.68354
$556$	−15.6214	−0.662494
$557$	34.0947	1.44464	0.722320	−	0.691559i	$-0.243076\pi$
$557$	34.0947	1.44464	0.722320	+	0.691559i	$0.243076\pi$
$558$	−11.7485	−0.497352
$559$	−4.73690	−0.200349
$560$	3.49665	0.147760
$561$	−121.238	−5.11869
$562$	−3.02293	−0.127514
$563$	−43.7988	−1.84590	−0.922950	−	0.384921i	$-0.874229\pi$
$563$	−43.7988	−1.84590	−0.922950	+	0.384921i	$0.874229\pi$
$564$	34.8160	1.46602
$565$	−27.0108	−1.13635
$566$	8.86864	0.372777
$567$	−20.1707	−0.847088
$568$	−2.61137	−0.109571
$569$	−35.7629	−1.49926	−0.749630	−	0.661857i	$-0.769769\pi$
$569$	−35.7629	−1.49926	−0.749630	+	0.661857i	$0.769769\pi$
$570$	5.91295	0.247666
$571$	38.8164	1.62442	0.812209	−	0.583367i	$-0.198265\pi$
$571$	38.8164	1.62442	0.812209	+	0.583367i	$0.198265\pi$
$572$	−4.19347	−0.175338
$573$	53.7042	2.24352
$574$	−10.8262	−0.451877
$575$	−5.96671	−0.248829
$576$	6.24035	0.260015
$577$	21.5198	0.895879	0.447940	−	0.894064i	$-0.352158\pi$
$577$	21.5198	0.895879	0.447940	+	0.894064i	$0.352158\pi$
$578$	−35.9812	−1.49662
$579$	81.8133	3.40004
$580$	−14.5395	−0.603721
$581$	8.93509	0.370690
$582$	13.1473	0.544973
$583$	−55.7506	−2.30895
$584$	−11.8254	−0.489337
$585$	9.28984	0.384088
$586$	−11.2344	−0.464090
$587$	1.72750	0.0713015	0.0356508	−	0.999364i	$-0.488650\pi$
$587$	1.72750	0.0713015	0.0356508	+	0.999364i	$0.488650\pi$
$588$	−11.4559	−0.472434
$589$	1.88266	0.0775737
$590$	−7.25853	−0.298829
$591$	40.6380	1.67162
$592$	6.70756	0.275679
$593$	−9.76541	−0.401017	−0.200509	−	0.979692i	$-0.564260\pi$
$593$	−9.76541	−0.401017	−0.200509	+	0.979692i	$0.564260\pi$
$594$	−53.9723	−2.21451
$595$	−25.4515	−1.04341
$596$	−1.79651	−0.0735878
$597$	−16.0118	−0.655318
$598$	3.75444	0.153531
$599$	9.27140	0.378819	0.189410	−	0.981898i	$-0.439343\pi$
$599$	9.27140	0.378819	0.189410	+	0.981898i	$0.439343\pi$
$600$	3.69720	0.150938
$601$	4.74391	0.193508	0.0967540	−	0.995308i	$-0.469154\pi$
$601$	4.74391	0.193508	0.0967540	+	0.995308i	$0.469154\pi$
$602$	11.1262	0.453470
$603$	21.9832	0.895224
$604$	10.8950	0.443312
$605$	−37.0053	−1.50448
$606$	−19.6903	−0.799866
$607$	26.6408	1.08131	0.540657	−	0.841243i	$-0.318176\pi$
$607$	26.6408	1.08131	0.540657	+	0.841243i	$0.318176\pi$
$608$	−1.00000	−0.0405554
$609$	−40.8438	−1.65507
$610$	1.59343	0.0645161
$611$	−8.76545	−0.354612
$612$	−45.4224	−1.83609
$613$	−29.9777	−1.21079	−0.605394	−	0.795926i	$-0.706985\pi$
$613$	−29.9777	−1.21079	−0.605394	+	0.795926i	$0.706985\pi$
$614$	0.585514	0.0236294
$615$	35.6114	1.43599
$616$	9.84978	0.396859
$617$	−29.2070	−1.17583	−0.587914	−	0.808923i	$-0.700051\pi$
$617$	−29.2070	−1.17583	−0.587914	+	0.808923i	$0.700051\pi$
$618$	−1.56875	−0.0631042
$619$	21.1157	0.848713	0.424356	−	0.905495i	$-0.360500\pi$
$619$	21.1157	0.848713	0.424356	+	0.905495i	$0.360500\pi$
$620$	−3.66212	−0.147074
$621$	48.3217	1.93908
$622$	−25.1146	−1.00701
$623$	25.6186	1.02639
$624$	−2.32639	−0.0931303
$625$	−17.4394	−0.697574
$626$	−15.2714	−0.610368
$627$	16.6563	0.665189
$628$	13.2426	0.528438
$629$	−48.8231	−1.94671
$630$	−21.8203	−0.869342
$631$	−4.61525	−0.183730	−0.0918651	−	0.995771i	$-0.529283\pi$
$631$	−4.61525	−0.183730	−0.0918651	+	0.995771i	$0.529283\pi$
$632$	10.8406	0.431218
$633$	−3.03979	−0.120821
$634$	18.9194	0.751387
$635$	−34.3556	−1.36336
$636$	−30.9285	−1.22640
$637$	2.88420	0.114276
$638$	−40.9567	−1.62149
$639$	16.2959	0.644655
$640$	1.94518	0.0768901
$641$	−35.5088	−1.40251	−0.701257	−	0.712909i	$-0.747377\pi$
$641$	−35.5088	−1.40251	−0.701257	+	0.712909i	$0.747377\pi$
$642$	−6.44737	−0.254457
$643$	−19.2904	−0.760738	−0.380369	−	0.924835i	$-0.624203\pi$
$643$	−19.2904	−0.760738	−0.380369	+	0.924835i	$0.624203\pi$
$644$	−8.81857	−0.347500
$645$	−36.5982	−1.44105
$646$	7.27882	0.286381
$647$	−16.1245	−0.633920	−0.316960	−	0.948439i	$-0.602662\pi$
$647$	−16.1245	−0.633920	−0.316960	+	0.948439i	$0.602662\pi$
$648$	−11.2209	−0.440799
$649$	−20.4467	−0.802603
$650$	−0.930825	−0.0365100
$651$	−10.2875	−0.403198
$652$	−4.76131	−0.186467
$653$	34.2667	1.34096	0.670481	−	0.741927i	$-0.266088\pi$
$653$	34.2667	1.34096	0.670481	+	0.741927i	$0.266088\pi$
$654$	−11.4109	−0.446200
$655$	−27.5458	−1.07630
$656$	−6.02260	−0.235143
$657$	73.7944	2.87899
$658$	20.5886	0.802628
$659$	10.8277	0.421788	0.210894	−	0.977509i	$-0.432363\pi$
$659$	10.8277	0.421788	0.210894	+	0.977509i	$0.432363\pi$
$660$	−32.3996	−1.26115
$661$	−7.33994	−0.285490	−0.142745	−	0.989759i	$-0.545593\pi$
$661$	−7.33994	−0.285490	−0.142745	+	0.989759i	$0.545593\pi$
$662$	−31.0251	−1.20583
$663$	16.9334	0.657639
$664$	4.97058	0.192896
$665$	3.49665	0.135594
$666$	−41.8575	−1.62195
$667$	36.6688	1.41982
$668$	2.55348	0.0987972
$669$	−75.8816	−2.93375
$670$	6.85238	0.264731
$671$	4.48856	0.173279
$672$	5.46432	0.210791
$673$	30.9158	1.19172	0.595858	−	0.803090i	$-0.296812\pi$
$673$	30.9158	1.19172	0.595858	+	0.803090i	$0.296812\pi$
$674$	18.6642	0.718919
$675$	−11.9802	−0.461119
$676$	−12.4143	−0.477473
$677$	26.7995	1.02999	0.514995	−	0.857193i	$-0.327794\pi$
$677$	26.7995	1.02999	0.514995	+	0.857193i	$0.327794\pi$
$678$	−42.2105	−1.62109
$679$	7.77471	0.298366
$680$	−14.1586	−0.542959
$681$	−1.17530	−0.0450376
$682$	−10.3159	−0.395016
$683$	−24.6197	−0.942045	−0.471022	−	0.882121i	$-0.656115\pi$
$683$	−24.6197	−0.942045	−0.471022	+	0.882121i	$0.656115\pi$
$684$	6.24035	0.238606
$685$	−15.6968	−0.599745
$686$	−19.3577	−0.739080
$687$	34.7000	1.32389
$688$	6.18949	0.235972
$689$	7.78671	0.296650
$690$	29.0075	1.10430
$691$	49.1040	1.86800	0.934002	−	0.357269i	$-0.116292\pi$
$691$	49.1040	1.86800	0.934002	+	0.357269i	$0.116292\pi$
$692$	−7.39929	−0.281279
$693$	−61.4661	−2.33490
$694$	11.8770	0.450846
$695$	30.3864	1.15262
$696$	−22.7214	−0.861251
$697$	43.8374	1.66046
$698$	−16.0106	−0.606009
$699$	29.2572	1.10661
$700$	2.18636	0.0826365
$701$	15.8454	0.598474	0.299237	−	0.954179i	$-0.403268\pi$
$701$	15.8454	0.598474	0.299237	+	0.954179i	$0.403268\pi$
$702$	7.53833	0.284516
$703$	6.70756	0.252981
$704$	5.47942	0.206513
$705$	−67.7235	−2.55062
$706$	1.27552	0.0480048
$707$	−11.6440	−0.437917
$708$	−11.3431	−0.426300
$709$	−24.1401	−0.906600	−0.453300	−	0.891358i	$-0.649753\pi$
$709$	−24.1401	−0.906600	−0.453300	+	0.891358i	$0.649753\pi$
$710$	5.07959	0.190634
$711$	−67.6494	−2.53705
$712$	14.2516	0.534101
$713$	9.23589	0.345887
$714$	−39.7738	−1.48850
$715$	8.15707	0.305057
$716$	17.3367	0.647903
$717$	−60.4819	−2.25874
$718$	11.4190	0.426155
$719$	24.2512	0.904418	0.452209	−	0.891912i	$-0.350636\pi$
$719$	24.2512	0.904418	0.452209	+	0.891912i	$0.350636\pi$
$720$	−12.1386	−0.452380
$721$	−0.927684	−0.0345488
$722$	−1.00000	−0.0372161
$723$	−42.4128	−1.57735
$724$	17.2270	0.640235
$725$	−9.09115	−0.337637
$726$	−57.8293	−2.14624
$727$	−47.7552	−1.77114	−0.885571	−	0.464504i	$-0.846233\pi$
$727$	−47.7552	−1.77114	−0.885571	+	0.464504i	$0.846233\pi$
$728$	−1.37572	−0.0509877
$729$	−19.8035	−0.733462
$730$	23.0025	0.851360
$731$	−45.0522	−1.66631
$732$	2.49010	0.0920367
$733$	43.3815	1.60233	0.801165	−	0.598443i	$-0.204214\pi$
$733$	43.3815	1.60233	0.801165	+	0.598443i	$0.204214\pi$
$734$	−10.8782	−0.401521
$735$	22.2839	0.821952
$736$	−4.90576	−0.180829
$737$	19.3026	0.711021
$738$	37.5832	1.38346
$739$	−5.62684	−0.206987	−0.103493	−	0.994630i	$-0.533002\pi$
$739$	−5.62684	−0.206987	−0.103493	+	0.994630i	$0.533002\pi$
$740$	−13.0474	−0.479633
$741$	−2.32639	−0.0854622
$742$	−18.2897	−0.671436
$743$	−37.7922	−1.38646	−0.693230	−	0.720716i	$-0.743813\pi$
$743$	−37.7922	−1.38646	−0.693230	+	0.720716i	$0.743813\pi$
$744$	−5.72290	−0.209812
$745$	3.49453	0.128030
$746$	10.6766	0.390900
$747$	−31.0181	−1.13489
$748$	−39.8837	−1.45829
$749$	−3.81268	−0.139312
$750$	−36.7565	−1.34216
$751$	35.4911	1.29509	0.647545	−	0.762028i	$-0.275796\pi$
$751$	35.4911	1.29509	0.647545	+	0.762028i	$0.275796\pi$
$752$	11.4534	0.417663
$753$	−30.8004	−1.12243
$754$	5.72044	0.208326
$755$	−21.1928	−0.771285
$756$	−17.7063	−0.643972
$757$	5.70919	0.207504	0.103752	−	0.994603i	$-0.466915\pi$
$757$	5.70919	0.207504	0.103752	+	0.994603i	$0.466915\pi$
$758$	−13.7158	−0.498180
$759$	81.7119	2.96595
$760$	1.94518	0.0705592
$761$	−22.1454	−0.802770	−0.401385	−	0.915909i	$-0.631471\pi$
$761$	−22.1454	−0.802770	−0.401385	+	0.915909i	$0.631471\pi$
$762$	−53.6886	−1.94493
$763$	−6.74786	−0.244289
$764$	17.6670	0.639171
$765$	88.3548	3.19447
$766$	21.5752	0.779543
$767$	2.85580	0.103117
$768$	3.03979	0.109689
$769$	14.4565	0.521316	0.260658	−	0.965431i	$-0.416060\pi$
$769$	14.4565	0.521316	0.260658	+	0.965431i	$0.416060\pi$
$770$	−19.1596	−0.690465
$771$	−49.6705	−1.78884
$772$	26.9141	0.968659
$773$	45.0850	1.62159	0.810797	−	0.585328i	$-0.199034\pi$
$773$	45.0850	1.62159	0.810797	+	0.585328i	$0.199034\pi$
$774$	−38.6246	−1.38833
$775$	−2.28982	−0.0822527
$776$	4.32506	0.155261
$777$	−36.6523	−1.31489
$778$	13.9998	0.501918
$779$	−6.02260	−0.215782
$780$	4.52526	0.162030
$781$	14.3088	0.512010
$782$	35.7081	1.27692
$783$	73.6252	2.63115
$784$	−3.76865	−0.134595
$785$	−25.7593	−0.919388
$786$	−43.0466	−1.53542
$787$	−50.3869	−1.79610	−0.898050	−	0.439894i	$-0.855016\pi$
$787$	−50.3869	−1.79610	−0.898050	+	0.439894i	$0.855016\pi$
$788$	13.3687	0.476239
$789$	74.4470	2.65038
$790$	−21.0870	−0.750243
$791$	−24.9614	−0.887524
$792$	−34.1935	−1.21501
$793$	−0.626919	−0.0222626
$794$	−10.2632	−0.364228
$795$	60.1616	2.13371
$796$	−5.26739	−0.186698
$797$	48.8693	1.73104	0.865520	−	0.500875i	$-0.166988\pi$
$797$	48.8693	1.73104	0.865520	+	0.500875i	$0.166988\pi$
$798$	5.46432	0.193435
$799$	−83.3674	−2.94933
$800$	1.21627	0.0430015
$801$	−88.9350	−3.14236
$802$	11.4190	0.403220
$803$	64.7962	2.28661
$804$	10.7084	0.377657
$805$	17.1537	0.604590
$806$	1.44083	0.0507509
$807$	51.9009	1.82700
$808$	−6.47753	−0.227879
$809$	37.2228	1.30868	0.654341	−	0.756199i	$-0.272946\pi$
$809$	37.2228	1.30868	0.654341	+	0.756199i	$0.272946\pi$
$810$	21.8267	0.766913
$811$	27.0878	0.951181	0.475590	−	0.879667i	$-0.342234\pi$
$811$	27.0878	0.951181	0.475590	+	0.879667i	$0.342234\pi$
$812$	−13.4364	−0.471524
$813$	−22.4187	−0.786258
$814$	−36.7536	−1.28821
$815$	9.26162	0.324420
$816$	−22.1261	−0.774569
$817$	6.18949	0.216543
$818$	36.4212	1.27344
$819$	8.58499	0.299984
$820$	11.7151	0.409108
$821$	−31.7886	−1.10943	−0.554715	−	0.832041i	$-0.687173\pi$
$821$	−31.7886	−1.10943	−0.554715	+	0.832041i	$0.687173\pi$
$822$	−24.5299	−0.855578
$823$	−14.0371	−0.489304	−0.244652	−	0.969611i	$-0.578674\pi$
$823$	−14.0371	−0.489304	−0.244652	+	0.969611i	$0.578674\pi$
$824$	−0.516069	−0.0179781
$825$	−20.2585	−0.705311
$826$	−6.70780	−0.233394
$827$	24.3094	0.845322	0.422661	−	0.906288i	$-0.361096\pi$
$827$	24.3094	0.845322	0.422661	+	0.906288i	$0.361096\pi$
$828$	30.6137	1.06390
$829$	23.6828	0.822537	0.411268	−	0.911514i	$-0.365086\pi$
$829$	23.6828	0.822537	0.411268	+	0.911514i	$0.365086\pi$
$830$	−9.66868	−0.335605
$831$	29.3963	1.01975
$832$	−0.765313	−0.0265325
$833$	27.4313	0.950439
$834$	47.4858	1.64430
$835$	−4.96699	−0.171890
$836$	5.47942	0.189510
$837$	18.5442	0.640982
$838$	−11.8364	−0.408881
$839$	−42.5418	−1.46871	−0.734353	−	0.678768i	$-0.762514\pi$
$839$	−42.5418	−1.46871	−0.734353	+	0.678768i	$0.762514\pi$
$840$	−10.6291	−0.366739
$841$	26.8702	0.926559
$842$	−38.5601	−1.32887
$843$	9.18907	0.316488
$844$	−1.00000	−0.0344214
$845$	24.1481	0.830719
$846$	−71.4733	−2.45730
$847$	−34.1976	−1.17504
$848$	−10.1745	−0.349395
$849$	−26.9589	−0.925225
$850$	−8.85298	−0.303655
$851$	32.9057	1.12799
$852$	7.93803	0.271953
$853$	10.1375	0.347102	0.173551	−	0.984825i	$-0.444476\pi$
$853$	10.1375	0.347102	0.173551	+	0.984825i	$0.444476\pi$
$854$	1.47253	0.0503890
$855$	−12.1386	−0.415132
$856$	−2.12099	−0.0724939
$857$	42.0013	1.43474	0.717368	−	0.696694i	$-0.245347\pi$
$857$	42.0013	1.43474	0.717368	+	0.696694i	$0.245347\pi$
$858$	12.7473	0.435186
$859$	−53.5787	−1.82808	−0.914040	−	0.405623i	$-0.867054\pi$
$859$	−53.5787	−1.82808	−0.914040	+	0.405623i	$0.867054\pi$
$860$	−12.0397	−0.410550
$861$	32.9094	1.12155
$862$	22.8519	0.778340
$863$	−4.40887	−0.150080	−0.0750399	−	0.997181i	$-0.523908\pi$
$863$	−4.40887	−0.150080	−0.0750399	+	0.997181i	$0.523908\pi$
$864$	−9.85000	−0.335104
$865$	14.3930	0.489376
$866$	−26.8056	−0.910891
$867$	109.375	3.71459
$868$	−3.38426	−0.114869
$869$	−59.4005	−2.01502
$870$	44.1972	1.49842
$871$	−2.69600	−0.0913506
$872$	−3.75383	−0.127121
$873$	−26.9899	−0.913469
$874$	−4.90576	−0.165940
$875$	−21.7361	−0.734815
$876$	35.9467	1.21453
$877$	9.56862	0.323109	0.161555	−	0.986864i	$-0.448349\pi$
$877$	9.56862	0.323109	0.161555	+	0.986864i	$0.448349\pi$
$878$	25.5103	0.860929
$879$	34.1503	1.15186
$880$	−10.6585	−0.359297
$881$	46.6552	1.57185	0.785927	−	0.618320i	$-0.212186\pi$
$881$	46.6552	1.57185	0.785927	+	0.618320i	$0.212186\pi$
$882$	23.5177	0.791882
$883$	−3.95573	−0.133121	−0.0665605	−	0.997782i	$-0.521203\pi$
$883$	−3.95573	−0.133121	−0.0665605	+	0.997782i	$0.521203\pi$
$884$	5.57058	0.187359
$885$	22.0644	0.741688
$886$	−10.6587	−0.358085
$887$	−40.4422	−1.35792	−0.678959	−	0.734176i	$-0.737569\pi$
$887$	−40.4422	−1.35792	−0.678959	+	0.734176i	$0.737569\pi$
$888$	−20.3896	−0.684231
$889$	−31.7490	−1.06483
$890$	−27.7220	−0.929242
$891$	61.4841	2.05980
$892$	−24.9628	−0.835815
$893$	11.4534	0.383274
$894$	5.46101	0.182644
$895$	−33.7230	−1.12724
$896$	1.79760	0.0600534
$897$	−11.4127	−0.381060
$898$	12.3607	0.412483
$899$	14.0722	0.469335
$900$	−7.58993	−0.252998
$901$	74.0587	2.46725
$902$	33.0004	1.09879
$903$	−33.8214	−1.12550
$904$	−13.8860	−0.461841
$905$	−33.5096	−1.11390
$906$	−33.1186	−1.10029
$907$	25.5551	0.848544	0.424272	−	0.905535i	$-0.360530\pi$
$907$	25.5551	0.848544	0.424272	+	0.905535i	$0.360530\pi$
$908$	−0.386638	−0.0128310
$909$	40.4220	1.34071
$910$	2.67603	0.0887096
$911$	−20.7597	−0.687798	−0.343899	−	0.939007i	$-0.611748\pi$
$911$	−20.7597	−0.687798	−0.343899	+	0.939007i	$0.611748\pi$
$912$	3.03979	0.100658
$913$	−27.2359	−0.901377
$914$	19.3159	0.638912
$915$	−4.84370	−0.160128
$916$	11.4152	0.377170
$917$	−25.4558	−0.840625
$918$	71.6963	2.36633
$919$	−41.4536	−1.36743	−0.683714	−	0.729750i	$-0.739636\pi$
$919$	−41.4536	−1.36743	−0.683714	+	0.729750i	$0.739636\pi$
$920$	9.54260	0.314610
$921$	−1.77984	−0.0586478
$922$	29.5472	0.973085
$923$	−1.99852	−0.0657820
$924$	−29.9413	−0.984997
$925$	−8.15819	−0.268239
$926$	−13.5625	−0.445692
$927$	3.22045	0.105774
$928$	−7.47464	−0.245367
$929$	−19.4151	−0.636987	−0.318494	−	0.947925i	$-0.603177\pi$
$929$	−19.4151	−0.636987	−0.318494	+	0.947925i	$0.603177\pi$
$930$	11.1321	0.365036
$931$	−3.76865	−0.123513
$932$	9.62473	0.315269
$933$	76.3433	2.49937
$934$	−16.4298	−0.537599
$935$	77.5811	2.53717
$936$	4.77582	0.156103
$937$	−37.7610	−1.23360	−0.616799	−	0.787121i	$-0.711571\pi$
$937$	−37.7610	−1.23360	−0.616799	+	0.787121i	$0.711571\pi$
$938$	6.33247	0.206763
$939$	46.4219	1.51492
$940$	−22.2790	−0.726660
$941$	−47.4793	−1.54778	−0.773890	−	0.633320i	$-0.781692\pi$
$941$	−47.4793	−1.54778	−0.773890	+	0.633320i	$0.781692\pi$
$942$	−40.2548	−1.31157
$943$	−29.5455	−0.962132
$944$	−3.73154	−0.121451
$945$	34.4420	1.12040
$946$	−33.9148	−1.10267
$947$	2.43249	0.0790453	0.0395227	−	0.999219i	$-0.487416\pi$
$947$	2.43249	0.0790453	0.0395227	+	0.999219i	$0.487416\pi$
$948$	−32.9533	−1.07027
$949$	−9.05010	−0.293779
$950$	1.21627	0.0394609
$951$	−57.5112	−1.86493
$952$	−13.0844	−0.424067
$953$	−35.3401	−1.14478	−0.572389	−	0.819982i	$-0.693983\pi$
$953$	−35.3401	−1.14478	−0.572389	+	0.819982i	$0.693983\pi$
$954$	63.4927	2.05565
$955$	−34.3656	−1.11205
$956$	−19.8967	−0.643506
$957$	124.500	4.02451
$958$	28.7187	0.927860
$959$	−14.5059	−0.468419
$960$	−5.91295	−0.190840
$961$	−27.4556	−0.885664
$962$	5.13339	0.165507
$963$	13.2357	0.426515
$964$	−13.9525	−0.449380
$965$	−52.3528	−1.68530
$966$	26.8066	0.862490
$967$	7.79886	0.250794	0.125397	−	0.992107i	$-0.459979\pi$
$967$	7.79886	0.250794	0.125397	+	0.992107i	$0.459979\pi$
$968$	−19.0241	−0.611457
$969$	−22.1261	−0.710793
$970$	−8.41303	−0.270126
$971$	51.3455	1.64776	0.823878	−	0.566768i	$-0.191806\pi$
$971$	51.3455	1.64776	0.823878	+	0.566768i	$0.191806\pi$
$972$	4.55928	0.146239
$973$	28.0809	0.900233
$974$	−33.5915	−1.07634
$975$	2.82952	0.0906170
$976$	0.819167	0.0262209
$977$	−2.48780	−0.0795917	−0.0397959	−	0.999208i	$-0.512671\pi$
$977$	−2.48780	−0.0795917	−0.0397959	+	0.999208i	$0.512671\pi$
$978$	14.4734	0.462809
$979$	−78.0906	−2.49578
$980$	7.33071	0.234171
$981$	23.4252	0.747908
$982$	23.0646	0.736022
$983$	−38.8053	−1.23770	−0.618849	−	0.785510i	$-0.712401\pi$
$983$	−38.8053	−1.23770	−0.618849	+	0.785510i	$0.712401\pi$
$984$	18.3075	0.583621
$985$	−26.0045	−0.828572
$986$	54.4065	1.73266
$987$	−62.5851	−1.99211
$988$	−0.765313	−0.0243479
$989$	30.3642	0.965524
$990$	66.5126	2.11391
$991$	−18.1094	−0.575265	−0.287632	−	0.957741i	$-0.592868\pi$
$991$	−18.1094	−0.575265	−0.287632	+	0.957741i	$0.592868\pi$
$992$	−1.88266	−0.0597746
$993$	94.3100	2.99284
$994$	4.69419	0.148891
$995$	10.2460	0.324821
$996$	−15.1095	−0.478764
$997$	16.9616	0.537180	0.268590	−	0.963255i	$-0.413442\pi$
$997$	16.9616	0.537180	0.268590	+	0.963255i	$0.413442\pi$
$998$	5.52423	0.174867
$999$	66.0695	2.09035

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.i.1.41	✓	43

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.i.1.41	✓	43	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:	\( N \)	\(=\)	\( 8018 = 2 \cdot 19 \cdot 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8018.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +3.03979 q^{3} +1.00000 q^{4} -1.94518 q^{5} -3.03979 q^{6} -1.79760 q^{7} -1.00000 q^{8} +6.24035 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +3.03979 q^{3} +1.00000 q^{4} -1.94518 q^{5} -3.03979 q^{6} -1.79760 q^{7} -1.00000 q^{8} +6.24035 q^{9} +1.94518 q^{10} +5.47942 q^{11} +3.03979 q^{12} -0.765313 q^{13} +1.79760 q^{14} -5.91295 q^{15} +1.00000 q^{16} -7.27882 q^{17} -6.24035 q^{18} +1.00000 q^{19} -1.94518 q^{20} -5.46432 q^{21} -5.47942 q^{22} +4.90576 q^{23} -3.03979 q^{24} -1.21627 q^{25} +0.765313 q^{26} +9.85000 q^{27} -1.79760 q^{28} +7.47464 q^{29} +5.91295 q^{30} +1.88266 q^{31} -1.00000 q^{32} +16.6563 q^{33} +7.27882 q^{34} +3.49665 q^{35} +6.24035 q^{36} +6.70756 q^{37} -1.00000 q^{38} -2.32639 q^{39} +1.94518 q^{40} -6.02260 q^{41} +5.46432 q^{42} +6.18949 q^{43} +5.47942 q^{44} -12.1386 q^{45} -4.90576 q^{46} +11.4534 q^{47} +3.03979 q^{48} -3.76865 q^{49} +1.21627 q^{50} -22.1261 q^{51} -0.765313 q^{52} -10.1745 q^{53} -9.85000 q^{54} -10.6585 q^{55} +1.79760 q^{56} +3.03979 q^{57} -7.47464 q^{58} -3.73154 q^{59} -5.91295 q^{60} +0.819167 q^{61} -1.88266 q^{62} -11.2176 q^{63} +1.00000 q^{64} +1.48867 q^{65} -16.6563 q^{66} +3.52275 q^{67} -7.27882 q^{68} +14.9125 q^{69} -3.49665 q^{70} +2.61137 q^{71} -6.24035 q^{72} +11.8254 q^{73} -6.70756 q^{74} -3.69720 q^{75} +1.00000 q^{76} -9.84978 q^{77} +2.32639 q^{78} -10.8406 q^{79} -1.94518 q^{80} +11.2209 q^{81} +6.02260 q^{82} -4.97058 q^{83} -5.46432 q^{84} +14.1586 q^{85} -6.18949 q^{86} +22.7214 q^{87} -5.47942 q^{88} -14.2516 q^{89} +12.1386 q^{90} +1.37572 q^{91} +4.90576 q^{92} +5.72290 q^{93} -11.4534 q^{94} -1.94518 q^{95} -3.03979 q^{96} -4.32506 q^{97} +3.76865 q^{98} +34.1935 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 43 q - 43 q^{2} + 43 q^{4} + 19 q^{7} - 43 q^{8} + 53 q^{9}+O(q^{10}) \) 43 * q - 43 * q^2 + 43 * q^4 + 19 * q^7 - 43 * q^8 + 53 * q^9	\( 43 q - 43 q^{2} + 43 q^{4} + 19 q^{7} - 43 q^{8} + 53 q^{9} + 14 q^{11} + 3 q^{13} - 19 q^{14} + q^{15} + 43 q^{16} + 8 q^{17} - 53 q^{18} + 43 q^{19} - 14 q^{22} + 43 q^{23} + 97 q^{25} - 3 q^{26} + 15 q^{27} + 19 q^{28} - 25 q^{29} - q^{30} + 22 q^{31} - 43 q^{32} + 22 q^{33} - 8 q^{34} - 6 q^{35} + 53 q^{36} + 42 q^{37} - 43 q^{38} + 9 q^{39} - 40 q^{41} + 72 q^{43} + 14 q^{44} - q^{45} - 43 q^{46} + 27 q^{47} + 86 q^{49} - 97 q^{50} - 3 q^{51} + 3 q^{52} - 5 q^{53} - 15 q^{54} + 86 q^{55} - 19 q^{56} + 25 q^{58} - 43 q^{59} + q^{60} + 31 q^{61} - 22 q^{62} + 38 q^{63} + 43 q^{64} - 32 q^{65} - 22 q^{66} + 15 q^{67} + 8 q^{68} - 7 q^{69} + 6 q^{70} + 14 q^{71} - 53 q^{72} + 93 q^{73} - 42 q^{74} - 13 q^{75} + 43 q^{76} + 38 q^{77} - 9 q^{78} + 15 q^{79} + 43 q^{81} + 40 q^{82} + 34 q^{83} + 16 q^{85} - 72 q^{86} + 60 q^{87} - 14 q^{88} - 37 q^{89} + q^{90} - 3 q^{91} + 43 q^{92} + 19 q^{93} - 27 q^{94} + 27 q^{97} - 86 q^{98} - 24 q^{99}+O(q^{100}) \) 43 * q - 43 * q^2 + 43 * q^4 + 19 * q^7 - 43 * q^8 + 53 * q^9 + 14 * q^11 + 3 * q^13 - 19 * q^14 + q^15 + 43 * q^16 + 8 * q^17 - 53 * q^18 + 43 * q^19 - 14 * q^22 + 43 * q^23 + 97 * q^25 - 3 * q^26 + 15 * q^27 + 19 * q^28 - 25 * q^29 - q^30 + 22 * q^31 - 43 * q^32 + 22 * q^33 - 8 * q^34 - 6 * q^35 + 53 * q^36 + 42 * q^37 - 43 * q^38 + 9 * q^39 - 40 * q^41 + 72 * q^43 + 14 * q^44 - q^45 - 43 * q^46 + 27 * q^47 + 86 * q^49 - 97 * q^50 - 3 * q^51 + 3 * q^52 - 5 * q^53 - 15 * q^54 + 86 * q^55 - 19 * q^56 + 25 * q^58 - 43 * q^59 + q^60 + 31 * q^61 - 22 * q^62 + 38 * q^63 + 43 * q^64 - 32 * q^65 - 22 * q^66 + 15 * q^67 + 8 * q^68 - 7 * q^69 + 6 * q^70 + 14 * q^71 - 53 * q^72 + 93 * q^73 - 42 * q^74 - 13 * q^75 + 43 * q^76 + 38 * q^77 - 9 * q^78 + 15 * q^79 + 43 * q^81 + 40 * q^82 + 34 * q^83 + 16 * q^85 - 72 * q^86 + 60 * q^87 - 14 * q^88 - 37 * q^89 + q^90 - 3 * q^91 + 43 * q^92 + 19 * q^93 - 27 * q^94 + 27 * q^97 - 86 * q^98 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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