LMFDB - Embedded newform 8018.2.a.i.1.9

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			1.9
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)

$f(q)$	$=$	$q-1.00000 q^{2} -2.12309 q^{3} +1.00000 q^{4} +0.333090 q^{5} +2.12309 q^{6} -1.76432 q^{7} -1.00000 q^{8} +1.50753 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.12309 q^{3} +1.00000 q^{4} +0.333090 q^{5} +2.12309 q^{6} -1.76432 q^{7} -1.00000 q^{8} +1.50753 q^{9} -0.333090 q^{10} +2.78319 q^{11} -2.12309 q^{12} -2.44141 q^{13} +1.76432 q^{14} -0.707182 q^{15} +1.00000 q^{16} +1.58660 q^{17} -1.50753 q^{18} +1.00000 q^{19} +0.333090 q^{20} +3.74581 q^{21} -2.78319 q^{22} -6.35811 q^{23} +2.12309 q^{24} -4.88905 q^{25} +2.44141 q^{26} +3.16866 q^{27} -1.76432 q^{28} -2.79372 q^{29} +0.707182 q^{30} -7.86377 q^{31} -1.00000 q^{32} -5.90896 q^{33} -1.58660 q^{34} -0.587677 q^{35} +1.50753 q^{36} +7.62477 q^{37} -1.00000 q^{38} +5.18335 q^{39} -0.333090 q^{40} -7.49828 q^{41} -3.74581 q^{42} +2.34034 q^{43} +2.78319 q^{44} +0.502142 q^{45} +6.35811 q^{46} +12.3993 q^{47} -2.12309 q^{48} -3.88719 q^{49} +4.88905 q^{50} -3.36850 q^{51} -2.44141 q^{52} +3.76219 q^{53} -3.16866 q^{54} +0.927052 q^{55} +1.76432 q^{56} -2.12309 q^{57} +2.79372 q^{58} -5.11125 q^{59} -0.707182 q^{60} +10.7768 q^{61} +7.86377 q^{62} -2.65975 q^{63} +1.00000 q^{64} -0.813211 q^{65} +5.90896 q^{66} -3.95764 q^{67} +1.58660 q^{68} +13.4989 q^{69} +0.587677 q^{70} -14.0866 q^{71} -1.50753 q^{72} -0.427081 q^{73} -7.62477 q^{74} +10.3799 q^{75} +1.00000 q^{76} -4.91042 q^{77} -5.18335 q^{78} +6.23091 q^{79} +0.333090 q^{80} -11.2499 q^{81} +7.49828 q^{82} +8.20249 q^{83} +3.74581 q^{84} +0.528482 q^{85} -2.34034 q^{86} +5.93133 q^{87} -2.78319 q^{88} -12.3229 q^{89} -0.502142 q^{90} +4.30743 q^{91} -6.35811 q^{92} +16.6955 q^{93} -12.3993 q^{94} +0.333090 q^{95} +2.12309 q^{96} -16.9777 q^{97} +3.88719 q^{98} +4.19572 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−2.12309	−1.22577	−0.612884	−	0.790173i	$-0.709991\pi$
$3$	−2.12309	−1.22577	−0.612884	+	0.790173i	$0.709991\pi$
$4$	1.00000	0.500000
$5$	0.333090	0.148963	0.0744813	−	0.997222i	$-0.476270\pi$
$5$	0.333090	0.148963	0.0744813	+	0.997222i	$0.476270\pi$
$6$	2.12309	0.866749
$7$	−1.76432	−0.666849	−0.333425	−	0.942777i	$-0.608204\pi$
$7$	−1.76432	−0.666849	−0.333425	+	0.942777i	$0.608204\pi$
$8$	−1.00000	−0.353553
$9$	1.50753	0.502508
$10$	−0.333090	−0.105332
$11$	2.78319	0.839162	0.419581	−	0.907718i	$-0.362177\pi$
$11$	2.78319	0.839162	0.419581	+	0.907718i	$0.362177\pi$
$12$	−2.12309	−0.612884
$13$	−2.44141	−0.677126	−0.338563	−	0.940944i	$-0.609941\pi$
$13$	−2.44141	−0.677126	−0.338563	+	0.940944i	$0.609941\pi$
$14$	1.76432	0.471534
$15$	−0.707182	−0.182594
$16$	1.00000	0.250000
$17$	1.58660	0.384807	0.192404	−	0.981316i	$-0.438372\pi$
$17$	1.58660	0.384807	0.192404	+	0.981316i	$0.438372\pi$
$18$	−1.50753	−0.355327
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	0.333090	0.0744813
$21$	3.74581	0.817403
$22$	−2.78319	−0.593377
$23$	−6.35811	−1.32576	−0.662879	−	0.748727i	$-0.730666\pi$
$23$	−6.35811	−1.32576	−0.662879	+	0.748727i	$0.730666\pi$
$24$	2.12309	0.433375
$25$	−4.88905	−0.977810
$26$	2.44141	0.478801
$27$	3.16866	0.609810
$28$	−1.76432	−0.333425
$29$	−2.79372	−0.518781	−0.259391	−	0.965772i	$-0.583522\pi$
$29$	−2.79372	−0.518781	−0.259391	+	0.965772i	$0.583522\pi$
$30$	0.707182	0.129113
$31$	−7.86377	−1.41238	−0.706188	−	0.708025i	$-0.749587\pi$
$31$	−7.86377	−1.41238	−0.706188	+	0.708025i	$0.749587\pi$
$32$	−1.00000	−0.176777
$33$	−5.90896	−1.02862
$34$	−1.58660	−0.272100
$35$	−0.587677	−0.0993355
$36$	1.50753	0.251254
$37$	7.62477	1.25350	0.626752	−	0.779219i	$-0.284384\pi$
$37$	7.62477	1.25350	0.626752	+	0.779219i	$0.284384\pi$
$38$	−1.00000	−0.162221
$39$	5.18335	0.830000
$40$	−0.333090	−0.0526662
$41$	−7.49828	−1.17103	−0.585517	−	0.810660i	$-0.699109\pi$
$41$	−7.49828	−1.17103	−0.585517	+	0.810660i	$0.699109\pi$
$42$	−3.74581	−0.577991
$43$	2.34034	0.356899	0.178449	−	0.983949i	$-0.442892\pi$
$43$	2.34034	0.356899	0.178449	+	0.983949i	$0.442892\pi$
$44$	2.78319	0.419581
$45$	0.502142	0.0748549
$46$	6.35811	0.937452
$47$	12.3993	1.80862	0.904312	−	0.426871i	$-0.140384\pi$
$47$	12.3993	1.80862	0.904312	+	0.426871i	$0.140384\pi$
$48$	−2.12309	−0.306442
$49$	−3.88719	−0.555312
$50$	4.88905	0.691416
$51$	−3.36850	−0.471685
$52$	−2.44141	−0.338563
$53$	3.76219	0.516777	0.258388	−	0.966041i	$-0.416809\pi$
$53$	3.76219	0.516777	0.258388	+	0.966041i	$0.416809\pi$
$54$	−3.16866	−0.431200
$55$	0.927052	0.125004
$56$	1.76432	0.235767
$57$	−2.12309	−0.281211
$58$	2.79372	0.366834
$59$	−5.11125	−0.665428	−0.332714	−	0.943028i	$-0.607964\pi$
$59$	−5.11125	−0.665428	−0.332714	+	0.943028i	$0.607964\pi$
$60$	−0.707182	−0.0912968
$61$	10.7768	1.37983	0.689915	−	0.723891i	$-0.257648\pi$
$61$	10.7768	1.37983	0.689915	+	0.723891i	$0.257648\pi$
$62$	7.86377	0.998700
$63$	−2.65975	−0.335097
$64$	1.00000	0.125000
$65$	−0.813211	−0.100866
$66$	5.90896	0.727343
$67$	−3.95764	−0.483503	−0.241751	−	0.970338i	$-0.577722\pi$
$67$	−3.95764	−0.483503	−0.241751	+	0.970338i	$0.577722\pi$
$68$	1.58660	0.192404
$69$	13.4989	1.62507
$70$	0.587677	0.0702408
$71$	−14.0866	−1.67177	−0.835887	−	0.548901i	$-0.815046\pi$
$71$	−14.0866	−1.67177	−0.835887	+	0.548901i	$0.815046\pi$
$72$	−1.50753	−0.177664
$73$	−0.427081	−0.0499861	−0.0249930	−	0.999688i	$-0.507956\pi$
$73$	−0.427081	−0.0499861	−0.0249930	+	0.999688i	$0.507956\pi$
$74$	−7.62477	−0.886361
$75$	10.3799	1.19857
$76$	1.00000	0.114708
$77$	−4.91042	−0.559595
$78$	−5.18335	−0.586899
$79$	6.23091	0.701032	0.350516	−	0.936557i	$-0.386006\pi$
$79$	6.23091	0.701032	0.350516	+	0.936557i	$0.386006\pi$
$80$	0.333090	0.0372406
$81$	−11.2499	−1.24999
$82$	7.49828	0.828046
$83$	8.20249	0.900340	0.450170	−	0.892943i	$-0.351363\pi$
$83$	8.20249	0.900340	0.450170	+	0.892943i	$0.351363\pi$
$84$	3.74581	0.408701
$85$	0.528482	0.0573219
$86$	−2.34034	−0.252366
$87$	5.93133	0.635906
$88$	−2.78319	−0.296689
$89$	−12.3229	−1.30622	−0.653110	−	0.757263i	$-0.726536\pi$
$89$	−12.3229	−1.30622	−0.653110	+	0.757263i	$0.726536\pi$
$90$	−0.502142	−0.0529304
$91$	4.30743	0.451541
$92$	−6.35811	−0.662879
$93$	16.6955	1.73125
$94$	−12.3993	−1.27889
$95$	0.333090	0.0341744
$96$	2.12309	0.216687
$97$	−16.9777	−1.72383	−0.861914	−	0.507055i	$-0.830734\pi$
$97$	−16.9777	−1.72383	−0.861914	+	0.507055i	$0.830734\pi$
$98$	3.88719	0.392665
$99$	4.19572	0.421686
$100$	−4.88905	−0.488905
$101$	5.03181	0.500683	0.250342	−	0.968158i	$-0.419457\pi$
$101$	5.03181	0.500683	0.250342	+	0.968158i	$0.419457\pi$
$102$	3.36850	0.333531
$103$	−5.43732	−0.535755	−0.267877	−	0.963453i	$-0.586322\pi$
$103$	−5.43732	−0.535755	−0.267877	+	0.963453i	$0.586322\pi$
$104$	2.44141	0.239400
$105$	1.24769	0.121762
$106$	−3.76219	−0.365416
$107$	4.22048	0.408009	0.204005	−	0.978970i	$-0.434604\pi$
$107$	4.22048	0.408009	0.204005	+	0.978970i	$0.434604\pi$
$108$	3.16866	0.304905
$109$	7.00297	0.670763	0.335381	−	0.942082i	$-0.391135\pi$
$109$	7.00297	0.670763	0.335381	+	0.942082i	$0.391135\pi$
$110$	−0.927052	−0.0883910
$111$	−16.1881	−1.53651
$112$	−1.76432	−0.166712
$113$	13.4182	1.26228	0.631139	−	0.775669i	$-0.282588\pi$
$113$	13.4182	1.26228	0.631139	+	0.775669i	$0.282588\pi$
$114$	2.12309	0.198846
$115$	−2.11783	−0.197488
$116$	−2.79372	−0.259391
$117$	−3.68049	−0.340262
$118$	5.11125	0.470529
$119$	−2.79927	−0.256608
$120$	0.707182	0.0645566
$121$	−3.25388	−0.295807
$122$	−10.7768	−0.975687
$123$	15.9195	1.43542
$124$	−7.86377	−0.706188
$125$	−3.29395	−0.294620
$126$	2.65975	0.236950
$127$	−7.73245	−0.686144	−0.343072	−	0.939309i	$-0.611467\pi$
$127$	−7.73245	−0.686144	−0.343072	+	0.939309i	$0.611467\pi$
$128$	−1.00000	−0.0883883
$129$	−4.96877	−0.437475
$130$	0.813211	0.0713234
$131$	16.5846	1.44900	0.724501	−	0.689274i	$-0.242070\pi$
$131$	16.5846	1.44900	0.724501	+	0.689274i	$0.242070\pi$
$132$	−5.90896	−0.514309
$133$	−1.76432	−0.152986
$134$	3.95764	0.341888
$135$	1.05545	0.0908388
$136$	−1.58660	−0.136050
$137$	−5.51333	−0.471035	−0.235518	−	0.971870i	$-0.575679\pi$
$137$	−5.51333	−0.471035	−0.235518	+	0.971870i	$0.575679\pi$
$138$	−13.4989	−1.14910
$139$	−12.4713	−1.05780	−0.528902	−	0.848683i	$-0.677396\pi$
$139$	−12.4713	−1.05780	−0.528902	+	0.848683i	$0.677396\pi$
$140$	−0.587677	−0.0496678
$141$	−26.3249	−2.21696
$142$	14.0866	1.18212
$143$	−6.79491	−0.568219
$144$	1.50753	0.125627
$145$	−0.930562	−0.0772790
$146$	0.427081	0.0353455
$147$	8.25286	0.680684
$148$	7.62477	0.626752
$149$	−12.6048	−1.03263	−0.516313	−	0.856400i	$-0.672696\pi$
$149$	−12.6048	−1.03263	−0.516313	+	0.856400i	$0.672696\pi$
$150$	−10.3799	−0.847516
$151$	8.67276	0.705779	0.352890	−	0.935665i	$-0.385199\pi$
$151$	8.67276	0.705779	0.352890	+	0.935665i	$0.385199\pi$
$152$	−1.00000	−0.0811107
$153$	2.39184	0.193369
$154$	4.91042	0.395693
$155$	−2.61935	−0.210391
$156$	5.18335	0.415000
$157$	11.0305	0.880330	0.440165	−	0.897917i	$-0.354920\pi$
$157$	11.0305	0.880330	0.440165	+	0.897917i	$0.354920\pi$
$158$	−6.23091	−0.495705
$159$	−7.98749	−0.633449
$160$	−0.333090	−0.0263331
$161$	11.2177	0.884080
$162$	11.2499	0.883879
$163$	−17.5287	−1.37295	−0.686477	−	0.727151i	$-0.740844\pi$
$163$	−17.5287	−1.37295	−0.686477	+	0.727151i	$0.740844\pi$
$164$	−7.49828	−0.585517
$165$	−1.96822	−0.153226
$166$	−8.20249	−0.636637
$167$	−3.70106	−0.286397	−0.143198	−	0.989694i	$-0.545739\pi$
$167$	−3.70106	−0.286397	−0.143198	+	0.989694i	$0.545739\pi$
$168$	−3.74581	−0.288995
$169$	−7.03950	−0.541500
$170$	−0.528482	−0.0405327
$171$	1.50753	0.115283
$172$	2.34034	0.178449
$173$	−7.62424	−0.579660	−0.289830	−	0.957078i	$-0.593599\pi$
$173$	−7.62424	−0.579660	−0.289830	+	0.957078i	$0.593599\pi$
$174$	−5.93133	−0.449653
$175$	8.62583	0.652052
$176$	2.78319	0.209791
$177$	10.8517	0.815660
$178$	12.3229	0.923637
$179$	23.3385	1.74440	0.872201	−	0.489148i	$-0.162692\pi$
$179$	23.3385	1.74440	0.872201	+	0.489148i	$0.162692\pi$
$180$	0.502142	0.0374275
$181$	−13.3513	−0.992398	−0.496199	−	0.868209i	$-0.665271\pi$
$181$	−13.3513	−0.992398	−0.496199	+	0.868209i	$0.665271\pi$
$182$	−4.30743	−0.319288
$183$	−22.8802	−1.69135
$184$	6.35811	0.468726
$185$	2.53974	0.186725
$186$	−16.6955	−1.22418
$187$	4.41581	0.322916
$188$	12.3993	0.904312
$189$	−5.59053	−0.406651
$190$	−0.333090	−0.0241649
$191$	10.3451	0.748543	0.374271	−	0.927319i	$-0.377893\pi$
$191$	10.3451	0.748543	0.374271	+	0.927319i	$0.377893\pi$
$192$	−2.12309	−0.153221
$193$	−11.5897	−0.834243	−0.417122	−	0.908851i	$-0.636961\pi$
$193$	−11.5897	−0.834243	−0.417122	+	0.908851i	$0.636961\pi$
$194$	16.9777	1.21893
$195$	1.72652	0.123639
$196$	−3.88719	−0.277656
$197$	−5.40531	−0.385113	−0.192556	−	0.981286i	$-0.561678\pi$
$197$	−5.40531	−0.385113	−0.192556	+	0.981286i	$0.561678\pi$
$198$	−4.19572	−0.298177
$199$	−5.96485	−0.422837	−0.211418	−	0.977396i	$-0.567808\pi$
$199$	−5.96485	−0.422837	−0.211418	+	0.977396i	$0.567808\pi$
$200$	4.88905	0.345708
$201$	8.40244	0.592662
$202$	−5.03181	−0.354037
$203$	4.92901	0.345949
$204$	−3.36850	−0.235842
$205$	−2.49760	−0.174440
$206$	5.43732	0.378836
$207$	−9.58501	−0.666204
$208$	−2.44141	−0.169282
$209$	2.78319	0.192517
$210$	−1.24769	−0.0860990
$211$	−1.00000	−0.0688428
$211$	−1.00000	−0.0688428
$212$	3.76219	0.258388
$213$	29.9072	2.04921
$214$	−4.22048	−0.288506
$215$	0.779546	0.0531646
$216$	−3.16866	−0.215600
$217$	13.8742	0.941841
$218$	−7.00297	−0.474301
$219$	0.906733	0.0612714
$220$	0.927052	0.0625019
$221$	−3.87355	−0.260563
$222$	16.1881	1.08647
$223$	16.4981	1.10480	0.552398	−	0.833580i	$-0.313713\pi$
$223$	16.4981	1.10480	0.552398	+	0.833580i	$0.313713\pi$
$224$	1.76432	0.117883
$225$	−7.37037	−0.491358
$226$	−13.4182	−0.892566
$227$	6.14178	0.407645	0.203822	−	0.979008i	$-0.434664\pi$
$227$	6.14178	0.407645	0.203822	+	0.979008i	$0.434664\pi$
$228$	−2.12309	−0.140605
$229$	−11.1590	−0.737410	−0.368705	−	0.929546i	$-0.620199\pi$
$229$	−11.1590	−0.737410	−0.368705	+	0.929546i	$0.620199\pi$
$230$	2.11783	0.139645
$231$	10.4253	0.685933
$232$	2.79372	0.183417
$233$	16.1404	1.05740	0.528698	−	0.848810i	$-0.322680\pi$
$233$	16.1404	1.05740	0.528698	+	0.848810i	$0.322680\pi$
$234$	3.68049	0.240601
$235$	4.13009	0.269417
$236$	−5.11125	−0.332714
$237$	−13.2288	−0.859303
$238$	2.79927	0.181450
$239$	−13.4560	−0.870393	−0.435197	−	0.900335i	$-0.643321\pi$
$239$	−13.4560	−0.870393	−0.435197	+	0.900335i	$0.643321\pi$
$240$	−0.707182	−0.0456484
$241$	18.9494	1.22064	0.610318	−	0.792157i	$-0.291042\pi$
$241$	18.9494	1.22064	0.610318	+	0.792157i	$0.291042\pi$
$242$	3.25388	0.209167
$243$	14.3787	0.922393
$244$	10.7768	0.689915
$245$	−1.29478	−0.0827207
$246$	−15.9195	−1.01499
$247$	−2.44141	−0.155343
$248$	7.86377	0.499350
$249$	−17.4147	−1.10361
$250$	3.29395	0.208328
$251$	15.9531	1.00695	0.503475	−	0.864010i	$-0.332054\pi$
$251$	15.9531	1.00695	0.503475	+	0.864010i	$0.332054\pi$
$252$	−2.65975	−0.167549
$253$	−17.6958	−1.11253
$254$	7.73245	0.485177
$255$	−1.12202	−0.0702634
$256$	1.00000	0.0625000
$257$	11.6029	0.723769	0.361885	−	0.932223i	$-0.382133\pi$
$257$	11.6029	0.723769	0.361885	+	0.932223i	$0.382133\pi$
$258$	4.96877	0.309342
$259$	−13.4525	−0.835898
$260$	−0.813211	−0.0504332
$261$	−4.21161	−0.260692
$262$	−16.5846	−1.02460
$263$	−23.1791	−1.42928	−0.714642	−	0.699490i	$-0.753410\pi$
$263$	−23.1791	−1.42928	−0.714642	+	0.699490i	$0.753410\pi$
$264$	5.90896	0.363672
$265$	1.25315	0.0769804
$266$	1.76432	0.108177
$267$	26.1626	1.60112
$268$	−3.95764	−0.241751
$269$	0.689711	0.0420524	0.0210262	−	0.999779i	$-0.493307\pi$
$269$	0.689711	0.0420524	0.0210262	+	0.999779i	$0.493307\pi$
$270$	−1.05545	−0.0642327
$271$	−13.6617	−0.829889	−0.414945	−	0.909847i	$-0.636199\pi$
$271$	−13.6617	−0.829889	−0.414945	+	0.909847i	$0.636199\pi$
$272$	1.58660	0.0962018
$273$	−9.14507	−0.553485
$274$	5.51333	0.333072
$275$	−13.6071	−0.820541
$276$	13.4989	0.812536
$277$	17.7689	1.06763	0.533813	−	0.845602i	$-0.320758\pi$
$277$	17.7689	1.06763	0.533813	+	0.845602i	$0.320758\pi$
$278$	12.4713	0.747980
$279$	−11.8548	−0.709731
$280$	0.587677	0.0351204
$281$	9.52455	0.568187	0.284093	−	0.958797i	$-0.408307\pi$
$281$	9.52455	0.568187	0.284093	+	0.958797i	$0.408307\pi$
$282$	26.3249	1.56762
$283$	6.29969	0.374478	0.187239	−	0.982314i	$-0.440046\pi$
$283$	6.29969	0.374478	0.187239	+	0.982314i	$0.440046\pi$
$284$	−14.0866	−0.835887
$285$	−0.707182	−0.0418898
$286$	6.79491	0.401791
$287$	13.2293	0.780903
$288$	−1.50753	−0.0888318
$289$	−14.4827	−0.851923
$290$	0.930562	0.0546445
$291$	36.0453	2.11301
$292$	−0.427081	−0.0249930
$293$	−23.0461	−1.34637	−0.673184	−	0.739475i	$-0.735074\pi$
$293$	−23.0461	−1.34637	−0.673184	+	0.739475i	$0.735074\pi$
$294$	−8.25286	−0.481316
$295$	−1.70251	−0.0991238
$296$	−7.62477	−0.443181
$297$	8.81898	0.511729
$298$	12.6048	0.730177
$299$	15.5228	0.897705
$300$	10.3799	0.599284
$301$	−4.12911	−0.237998
$302$	−8.67276	−0.499061
$303$	−10.6830	−0.613722
$304$	1.00000	0.0573539
$305$	3.58965	0.205543
$306$	−2.39184	−0.136732
$307$	14.5614	0.831065	0.415533	−	0.909578i	$-0.363595\pi$
$307$	14.5614	0.831065	0.415533	+	0.909578i	$0.363595\pi$
$308$	−4.91042	−0.279797
$309$	11.5439	0.656711
$310$	2.61935	0.148769
$311$	−17.6685	−1.00189	−0.500944	−	0.865480i	$-0.667014\pi$
$311$	−17.6685	−1.00189	−0.500944	+	0.865480i	$0.667014\pi$
$312$	−5.18335	−0.293449
$313$	−30.2725	−1.71110	−0.855551	−	0.517718i	$-0.826782\pi$
$313$	−30.2725	−1.71110	−0.855551	+	0.517718i	$0.826782\pi$
$314$	−11.0305	−0.622488
$315$	−0.885938	−0.0499169
$316$	6.23091	0.350516
$317$	7.13010	0.400466	0.200233	−	0.979748i	$-0.435830\pi$
$317$	7.13010	0.400466	0.200233	+	0.979748i	$0.435830\pi$
$318$	7.98749	0.447916
$319$	−7.77545	−0.435342
$320$	0.333090	0.0186203
$321$	−8.96047	−0.500125
$322$	−11.2177	−0.625139
$323$	1.58660	0.0882809
$324$	−11.2499	−0.624997
$325$	11.9362	0.662101
$326$	17.5287	0.970826
$327$	−14.8680	−0.822200
$328$	7.49828	0.414023
$329$	−21.8763	−1.20608
$330$	1.96822	0.108347
$331$	−5.61509	−0.308633	−0.154317	−	0.988021i	$-0.549318\pi$
$331$	−5.61509	−0.308633	−0.154317	+	0.988021i	$0.549318\pi$
$332$	8.20249	0.450170
$333$	11.4945	0.629896
$334$	3.70106	0.202513
$335$	−1.31825	−0.0720238
$336$	3.74581	0.204351
$337$	17.9540	0.978015	0.489007	−	0.872280i	$-0.337359\pi$
$337$	17.9540	0.978015	0.489007	+	0.872280i	$0.337359\pi$
$338$	7.03950	0.382898
$339$	−28.4881	−1.54726
$340$	0.528482	0.0286609
$341$	−21.8863	−1.18521
$342$	−1.50753	−0.0815176
$343$	19.2084	1.03716
$344$	−2.34034	−0.126183
$345$	4.49634	0.242075
$346$	7.62424	0.409882
$347$	28.7405	1.54287	0.771436	−	0.636307i	$-0.219539\pi$
$347$	28.7405	1.54287	0.771436	+	0.636307i	$0.219539\pi$
$348$	5.93133	0.317953
$349$	12.1864	0.652325	0.326162	−	0.945314i	$-0.394244\pi$
$349$	12.1864	0.652325	0.326162	+	0.945314i	$0.394244\pi$
$350$	−8.62583	−0.461070
$351$	−7.73602	−0.412918
$352$	−2.78319	−0.148344
$353$	−21.5319	−1.14603	−0.573014	−	0.819545i	$-0.694226\pi$
$353$	−21.5319	−1.14603	−0.573014	+	0.819545i	$0.694226\pi$
$354$	−10.8517	−0.576759
$355$	−4.69212	−0.249032
$356$	−12.3229	−0.653110
$357$	5.94311	0.314543
$358$	−23.3385	−1.23348
$359$	13.4604	0.710412	0.355206	−	0.934788i	$-0.384411\pi$
$359$	13.4604	0.710412	0.355206	+	0.934788i	$0.384411\pi$
$360$	−0.502142	−0.0264652
$361$	1.00000	0.0526316
$362$	13.3513	0.701731
$363$	6.90828	0.362591
$364$	4.30743	0.225771
$365$	−0.142257	−0.00744605
$366$	22.8802	1.19597
$367$	25.2439	1.31772	0.658861	−	0.752265i	$-0.271039\pi$
$367$	25.2439	1.31772	0.658861	+	0.752265i	$0.271039\pi$
$368$	−6.35811	−0.331439
$369$	−11.3038	−0.588455
$370$	−2.53974	−0.132035
$371$	−6.63770	−0.344612
$372$	16.6955	0.865623
$373$	15.3892	0.796824	0.398412	−	0.917207i	$-0.369561\pi$
$373$	15.3892	0.796824	0.398412	+	0.917207i	$0.369561\pi$
$374$	−4.41581	−0.228336
$375$	6.99336	0.361135
$376$	−12.3993	−0.639445
$377$	6.82063	0.351280
$378$	5.59053	0.287546
$379$	10.3505	0.531668	0.265834	−	0.964019i	$-0.414353\pi$
$379$	10.3505	0.531668	0.265834	+	0.964019i	$0.414353\pi$
$380$	0.333090	0.0170872
$381$	16.4167	0.841053
$382$	−10.3451	−0.529300
$383$	−20.8028	−1.06297	−0.531486	−	0.847067i	$-0.678366\pi$
$383$	−20.8028	−1.06297	−0.531486	+	0.847067i	$0.678366\pi$
$384$	2.12309	0.108344
$385$	−1.63561	−0.0833586
$386$	11.5897	0.589899
$387$	3.52813	0.179345
$388$	−16.9777	−0.861914
$389$	−9.20756	−0.466842	−0.233421	−	0.972376i	$-0.574992\pi$
$389$	−9.20756	−0.466842	−0.233421	+	0.972376i	$0.574992\pi$
$390$	−1.72652	−0.0874259
$391$	−10.0878	−0.510161
$392$	3.88719	0.196333
$393$	−35.2106	−1.77614
$394$	5.40531	0.272316
$395$	2.07546	0.104428
$396$	4.19572	0.210843
$397$	−0.898344	−0.0450866	−0.0225433	−	0.999746i	$-0.507176\pi$
$397$	−0.898344	−0.0450866	−0.0225433	+	0.999746i	$0.507176\pi$
$398$	5.96485	0.298991
$399$	3.74581	0.187525
$400$	−4.88905	−0.244453
$401$	−15.7267	−0.785352	−0.392676	−	0.919677i	$-0.628451\pi$
$401$	−15.7267	−0.785352	−0.392676	+	0.919677i	$0.628451\pi$
$402$	−8.40244	−0.419076
$403$	19.1987	0.956357
$404$	5.03181	0.250342
$405$	−3.74725	−0.186202
$406$	−4.92901	−0.244623
$407$	21.2211	1.05189
$408$	3.36850	0.166766
$409$	−3.91117	−0.193395	−0.0966974	−	0.995314i	$-0.530828\pi$
$409$	−3.91117	−0.193395	−0.0966974	+	0.995314i	$0.530828\pi$
$410$	2.49760	0.123348
$411$	11.7053	0.577380
$412$	−5.43732	−0.267877
$413$	9.01786	0.443740
$414$	9.58501	0.471078
$415$	2.73217	0.134117
$416$	2.44141	0.119700
$417$	26.4778	1.29662
$418$	−2.78319	−0.136130
$419$	−8.82156	−0.430961	−0.215481	−	0.976508i	$-0.569132\pi$
$419$	−8.82156	−0.430961	−0.215481	+	0.976508i	$0.569132\pi$
$420$	1.24769	0.0608812
$421$	−28.5922	−1.39350	−0.696749	−	0.717315i	$-0.745371\pi$
$421$	−28.5922	−1.39350	−0.696749	+	0.717315i	$0.745371\pi$
$422$	1.00000	0.0486792
$423$	18.6923	0.908849
$424$	−3.76219	−0.182708
$425$	−7.75698	−0.376269
$426$	−29.9072	−1.44901
$427$	−19.0137	−0.920138
$428$	4.22048	0.204005
$429$	14.4262	0.696505
$430$	−0.779546	−0.0375930
$431$	−30.1698	−1.45323	−0.726615	−	0.687045i	$-0.758908\pi$
$431$	−30.1698	−1.45323	−0.726615	+	0.687045i	$0.758908\pi$
$432$	3.16866	0.152452
$433$	−3.46093	−0.166322	−0.0831608	−	0.996536i	$-0.526502\pi$
$433$	−3.46093	−0.166322	−0.0831608	+	0.996536i	$0.526502\pi$
$434$	−13.8742	−0.665982
$435$	1.97567	0.0947261
$436$	7.00297	0.335381
$437$	−6.35811	−0.304150
$438$	−0.906733	−0.0433254
$439$	20.4362	0.975366	0.487683	−	0.873021i	$-0.337842\pi$
$439$	20.4362	0.975366	0.487683	+	0.873021i	$0.337842\pi$
$440$	−0.927052	−0.0441955
$441$	−5.86003	−0.279049
$442$	3.87355	0.184246
$443$	14.9907	0.712227	0.356114	−	0.934443i	$-0.384102\pi$
$443$	14.9907	0.712227	0.356114	+	0.934443i	$0.384102\pi$
$444$	−16.1881	−0.768253
$445$	−4.10462	−0.194578
$446$	−16.4981	−0.781209
$447$	26.7612	1.26576
$448$	−1.76432	−0.0833561
$449$	−28.8233	−1.36026	−0.680128	−	0.733094i	$-0.738076\pi$
$449$	−28.8233	−1.36026	−0.680128	+	0.733094i	$0.738076\pi$
$450$	7.37037	0.347442
$451$	−20.8691	−0.982688
$452$	13.4182	0.631139
$453$	−18.4131	−0.865122
$454$	−6.14178	−0.288248
$455$	1.43476	0.0672627
$456$	2.12309	0.0994230
$457$	19.8584	0.928936	0.464468	−	0.885590i	$-0.346246\pi$
$457$	19.8584	0.928936	0.464468	+	0.885590i	$0.346246\pi$
$458$	11.1590	0.521428
$459$	5.02741	0.234659
$460$	−2.11783	−0.0987441
$461$	22.5011	1.04798	0.523991	−	0.851724i	$-0.324443\pi$
$461$	22.5011	1.04798	0.523991	+	0.851724i	$0.324443\pi$
$462$	−10.4253	−0.485028
$463$	15.4279	0.716997	0.358498	−	0.933530i	$-0.383289\pi$
$463$	15.4279	0.716997	0.358498	+	0.933530i	$0.383289\pi$
$464$	−2.79372	−0.129695
$465$	5.56112	0.257891
$466$	−16.1404	−0.747692
$467$	36.5132	1.68963	0.844815	−	0.535058i	$-0.179710\pi$
$467$	36.5132	1.68963	0.844815	+	0.535058i	$0.179710\pi$
$468$	−3.68049	−0.170131
$469$	6.98253	0.322423
$470$	−4.13009	−0.190507
$471$	−23.4188	−1.07908
$472$	5.11125	0.235264
$473$	6.51361	0.299496
$474$	13.2288	0.607619
$475$	−4.88905	−0.224325
$476$	−2.79927	−0.128304
$477$	5.67160	0.259685
$478$	13.4560	0.615461
$479$	2.98748	0.136502	0.0682508	−	0.997668i	$-0.478258\pi$
$479$	2.98748	0.136502	0.0682508	+	0.997668i	$0.478258\pi$
$480$	0.707182	0.0322783
$481$	−18.6152	−0.848780
$482$	−18.9494	−0.863120
$483$	−23.8163	−1.08368
$484$	−3.25388	−0.147903
$485$	−5.65512	−0.256786
$486$	−14.3787	−0.652231
$487$	19.0261	0.862156	0.431078	−	0.902315i	$-0.358133\pi$
$487$	19.0261	0.862156	0.431078	+	0.902315i	$0.358133\pi$
$488$	−10.7768	−0.487843
$489$	37.2151	1.68292
$490$	1.29478	0.0584924
$491$	11.1132	0.501533	0.250766	−	0.968048i	$-0.419317\pi$
$491$	11.1132	0.501533	0.250766	+	0.968048i	$0.419317\pi$
$492$	15.9195	0.717709
$493$	−4.43252	−0.199631
$494$	2.44141	0.109844
$495$	1.39755	0.0628154
$496$	−7.86377	−0.353094
$497$	24.8533	1.11482
$498$	17.4147	0.780369
$499$	26.3232	1.17839	0.589193	−	0.807992i	$-0.299446\pi$
$499$	26.3232	1.17839	0.589193	+	0.807992i	$0.299446\pi$
$500$	−3.29395	−0.147310
$501$	7.85770	0.351056
$502$	−15.9531	−0.712022
$503$	16.0132	0.713994	0.356997	−	0.934106i	$-0.383801\pi$
$503$	16.0132	0.713994	0.356997	+	0.934106i	$0.383801\pi$
$504$	2.65975	0.118475
$505$	1.67605	0.0745831
$506$	17.6958	0.786675
$507$	14.9455	0.663754
$508$	−7.73245	−0.343072
$509$	−22.5343	−0.998814	−0.499407	−	0.866367i	$-0.666449\pi$
$509$	−22.5343	−0.998814	−0.499407	+	0.866367i	$0.666449\pi$
$510$	1.12202	0.0496837
$511$	0.753507	0.0333332
$512$	−1.00000	−0.0441942
$513$	3.16866	0.139900
$514$	−11.6029	−0.511782
$515$	−1.81112	−0.0798074
$516$	−4.96877	−0.218738
$517$	34.5096	1.51773
$518$	13.4525	0.591069
$519$	16.1870	0.710529
$520$	0.813211	0.0356617
$521$	17.1749	0.752445	0.376222	−	0.926529i	$-0.377223\pi$
$521$	17.1749	0.752445	0.376222	+	0.926529i	$0.377223\pi$
$522$	4.21161	0.184337
$523$	10.4627	0.457500	0.228750	−	0.973485i	$-0.426536\pi$
$523$	10.4627	0.457500	0.228750	+	0.973485i	$0.426536\pi$
$524$	16.5846	0.724501
$525$	−18.3135	−0.799265
$526$	23.1791	1.01066
$527$	−12.4767	−0.543493
$528$	−5.90896	−0.257155
$529$	17.4256	0.757634
$530$	−1.25315	−0.0544334
$531$	−7.70534	−0.334383
$532$	−1.76432	−0.0764928
$533$	18.3064	0.792938
$534$	−26.1626	−1.13217
$535$	1.40580	0.0607781
$536$	3.95764	0.170944
$537$	−49.5498	−2.13823
$538$	−0.689711	−0.0297356
$539$	−10.8188	−0.465997
$540$	1.05545	0.0454194
$541$	27.9550	1.20188	0.600939	−	0.799295i	$-0.294793\pi$
$541$	27.9550	1.20188	0.600939	+	0.799295i	$0.294793\pi$
$542$	13.6617	0.586820
$543$	28.3462	1.21645
$544$	−1.58660	−0.0680250
$545$	2.33262	0.0999185
$546$	9.14507	0.391373
$547$	37.3777	1.59815	0.799077	−	0.601228i	$-0.205322\pi$
$547$	37.3777	1.59815	0.799077	+	0.601228i	$0.205322\pi$
$548$	−5.51333	−0.235518
$549$	16.2463	0.693376
$550$	13.6071	0.580210
$551$	−2.79372	−0.119017
$552$	−13.4989	−0.574550
$553$	−10.9933	−0.467483
$554$	−17.7689	−0.754926
$555$	−5.39210	−0.228882
$556$	−12.4713	−0.528902
$557$	−17.0254	−0.721388	−0.360694	−	0.932684i	$-0.617460\pi$
$557$	−17.0254	−0.721388	−0.360694	+	0.932684i	$0.617460\pi$
$558$	11.8548	0.501855
$559$	−5.71374	−0.241666
$560$	−0.587677	−0.0248339
$561$	−9.37517	−0.395820
$562$	−9.52455	−0.401769
$563$	−31.2610	−1.31749	−0.658746	−	0.752365i	$-0.728913\pi$
$563$	−31.2610	−1.31749	−0.658746	+	0.752365i	$0.728913\pi$
$564$	−26.3249	−1.10848
$565$	4.46948	0.188032
$566$	−6.29969	−0.264796
$567$	19.8485	0.833557
$568$	14.0866	0.591062
$569$	4.55332	0.190885	0.0954426	−	0.995435i	$-0.469573\pi$
$569$	4.55332	0.190885	0.0954426	+	0.995435i	$0.469573\pi$
$570$	0.707182	0.0296206
$571$	7.96717	0.333416	0.166708	−	0.986006i	$-0.446686\pi$
$571$	7.96717	0.333416	0.166708	+	0.986006i	$0.446686\pi$
$572$	−6.79491	−0.284109
$573$	−21.9635	−0.917540
$574$	−13.2293	−0.552182
$575$	31.0851	1.29634
$576$	1.50753	0.0628135
$577$	39.2853	1.63547	0.817734	−	0.575597i	$-0.195230\pi$
$577$	39.2853	1.63547	0.817734	+	0.575597i	$0.195230\pi$
$578$	14.4827	0.602401
$579$	24.6060	1.02259
$580$	−0.930562	−0.0386395
$581$	−14.4718	−0.600391
$582$	−36.0453	−1.49413
$583$	10.4709	0.433660
$584$	0.427081	0.0176727
$585$	−1.22594	−0.0506862
$586$	23.0461	0.952026
$587$	27.9512	1.15367	0.576835	−	0.816861i	$-0.304288\pi$
$587$	27.9512	1.15367	0.576835	+	0.816861i	$0.304288\pi$
$588$	8.25286	0.340342
$589$	−7.86377	−0.324021
$590$	1.70251	0.0700911
$591$	11.4760	0.472059
$592$	7.62477	0.313376
$593$	20.5002	0.841842	0.420921	−	0.907097i	$-0.361707\pi$
$593$	20.5002	0.841842	0.420921	+	0.907097i	$0.361707\pi$
$594$	−8.81898	−0.361847
$595$	−0.932409	−0.0382250
$596$	−12.6048	−0.516313
$597$	12.6639	0.518300
$598$	−15.5228	−0.634774
$599$	26.7305	1.09218	0.546089	−	0.837727i	$-0.316116\pi$
$599$	26.7305	1.09218	0.546089	+	0.837727i	$0.316116\pi$
$600$	−10.3799	−0.423758
$601$	9.55928	0.389931	0.194966	−	0.980810i	$-0.437540\pi$
$601$	9.55928	0.389931	0.194966	+	0.980810i	$0.437540\pi$
$602$	4.12911	0.168290
$603$	−5.96624	−0.242964
$604$	8.67276	0.352890
$605$	−1.08383	−0.0440642
$606$	10.6830	0.433967
$607$	38.5502	1.56470	0.782352	−	0.622837i	$-0.214020\pi$
$607$	38.5502	1.56470	0.782352	+	0.622837i	$0.214020\pi$
$608$	−1.00000	−0.0405554
$609$	−10.4648	−0.424053
$610$	−3.58965	−0.145341
$611$	−30.2718	−1.22467
$612$	2.39184	0.0966845
$613$	41.2605	1.66650	0.833248	−	0.552900i	$-0.186479\pi$
$613$	41.2605	1.66650	0.833248	+	0.552900i	$0.186479\pi$
$614$	−14.5614	−0.587652
$615$	5.30265	0.213823
$616$	4.91042	0.197847
$617$	−33.4199	−1.34544	−0.672718	−	0.739899i	$-0.734873\pi$
$617$	−33.4199	−1.34544	−0.672718	+	0.739899i	$0.734873\pi$
$618$	−11.5439	−0.464365
$619$	−27.8728	−1.12030	−0.560152	−	0.828390i	$-0.689257\pi$
$619$	−27.8728	−1.12030	−0.560152	+	0.828390i	$0.689257\pi$
$620$	−2.61935	−0.105196
$621$	−20.1467	−0.808460
$622$	17.6685	0.708442
$623$	21.7414	0.871052
$624$	5.18335	0.207500
$625$	23.3481	0.933923
$626$	30.2725	1.20993
$627$	−5.90896	−0.235981
$628$	11.0305	0.440165
$629$	12.0975	0.482358
$630$	0.885938	0.0352966
$631$	7.75430	0.308694	0.154347	−	0.988017i	$-0.450673\pi$
$631$	7.75430	0.308694	0.154347	+	0.988017i	$0.450673\pi$
$632$	−6.23091	−0.247852
$633$	2.12309	0.0843854
$634$	−7.13010	−0.283173
$635$	−2.57560	−0.102210
$636$	−7.98749	−0.316724
$637$	9.49023	0.376017
$638$	7.77545	0.307833
$639$	−21.2359	−0.840081
$640$	−0.333090	−0.0131666
$641$	23.9271	0.945063	0.472531	−	0.881314i	$-0.343340\pi$
$641$	23.9271	0.945063	0.472531	+	0.881314i	$0.343340\pi$
$642$	8.96047	0.353642
$643$	32.0383	1.26347	0.631733	−	0.775186i	$-0.282344\pi$
$643$	32.0383	1.26347	0.631733	+	0.775186i	$0.282344\pi$
$644$	11.2177	0.442040
$645$	−1.65505	−0.0651675
$646$	−1.58660	−0.0624240
$647$	42.7902	1.68226	0.841128	−	0.540836i	$-0.181892\pi$
$647$	42.7902	1.68226	0.841128	+	0.540836i	$0.181892\pi$
$648$	11.2499	0.441940
$649$	−14.2256	−0.558402
$650$	−11.9362	−0.468176
$651$	−29.4562	−1.15448
$652$	−17.5287	−0.686477
$653$	−8.63560	−0.337937	−0.168969	−	0.985621i	$-0.554044\pi$
$653$	−8.63560	−0.337937	−0.168969	+	0.985621i	$0.554044\pi$
$654$	14.8680	0.581383
$655$	5.52417	0.215847
$656$	−7.49828	−0.292759
$657$	−0.643836	−0.0251184
$658$	21.8763	0.852827
$659$	−26.0853	−1.01614	−0.508069	−	0.861316i	$-0.669641\pi$
$659$	−26.0853	−1.01614	−0.508069	+	0.861316i	$0.669641\pi$
$660$	−1.96822	−0.0766128
$661$	16.0323	0.623584	0.311792	−	0.950150i	$-0.399071\pi$
$661$	16.0323	0.623584	0.311792	+	0.950150i	$0.399071\pi$
$662$	5.61509	0.218237
$663$	8.22391	0.319390
$664$	−8.20249	−0.318318
$665$	−0.587677	−0.0227891
$666$	−11.4945	−0.445404
$667$	17.7628	0.687778
$668$	−3.70106	−0.143198
$669$	−35.0271	−1.35422
$670$	1.31825	0.0509285
$671$	29.9939	1.15790
$672$	−3.74581	−0.144498
$673$	12.0770	0.465535	0.232768	−	0.972532i	$-0.425222\pi$
$673$	12.0770	0.465535	0.232768	+	0.972532i	$0.425222\pi$
$674$	−17.9540	−0.691561
$675$	−15.4918	−0.596278
$676$	−7.03950	−0.270750
$677$	−18.8675	−0.725137	−0.362569	−	0.931957i	$-0.618100\pi$
$677$	−18.8675	−0.725137	−0.362569	+	0.931957i	$0.618100\pi$
$678$	28.4881	1.09408
$679$	29.9541	1.14953
$680$	−0.528482	−0.0202663
$681$	−13.0396	−0.499678
$682$	21.8863	0.838072
$683$	−9.87593	−0.377892	−0.188946	−	0.981987i	$-0.560507\pi$
$683$	−9.87593	−0.377892	−0.188946	+	0.981987i	$0.560507\pi$
$684$	1.50753	0.0576417
$685$	−1.83644	−0.0701666
$686$	−19.2084	−0.733382
$687$	23.6917	0.903894
$688$	2.34034	0.0892247
$689$	−9.18507	−0.349923
$690$	−4.49634	−0.171173
$691$	35.5992	1.35426	0.677129	−	0.735865i	$-0.263224\pi$
$691$	35.5992	1.35426	0.677129	+	0.735865i	$0.263224\pi$
$692$	−7.62424	−0.289830
$693$	−7.40258	−0.281201
$694$	−28.7405	−1.09098
$695$	−4.15408	−0.157573
$696$	−5.93133	−0.224827
$697$	−11.8968	−0.450623
$698$	−12.1864	−0.461263
$699$	−34.2677	−1.29612
$700$	8.62583	0.326026
$701$	3.59072	0.135620	0.0678098	−	0.997698i	$-0.478399\pi$
$701$	3.59072	0.135620	0.0678098	+	0.997698i	$0.478399\pi$
$702$	7.73602	0.291977
$703$	7.62477	0.287574
$704$	2.78319	0.104895
$705$	−8.76857	−0.330243
$706$	21.5319	0.810364
$707$	−8.87770	−0.333880
$708$	10.8517	0.407830
$709$	1.70550	0.0640515	0.0320258	−	0.999487i	$-0.489804\pi$
$709$	1.70550	0.0640515	0.0320258	+	0.999487i	$0.489804\pi$
$710$	4.69212	0.176092
$711$	9.39326	0.352275
$712$	12.3229	0.461818
$713$	49.9988	1.87247
$714$	−5.94311	−0.222415
$715$	−2.26332	−0.0846433
$716$	23.3385	0.872201
$717$	28.5682	1.06690
$718$	−13.4604	−0.502337
$719$	11.4388	0.426595	0.213297	−	0.976987i	$-0.431580\pi$
$719$	11.4388	0.426595	0.213297	+	0.976987i	$0.431580\pi$
$720$	0.502142	0.0187137
$721$	9.59315	0.357268
$722$	−1.00000	−0.0372161
$723$	−40.2313	−1.49622
$724$	−13.3513	−0.496199
$725$	13.6587	0.507270
$726$	−6.90828	−0.256390
$727$	−37.8561	−1.40400	−0.702002	−	0.712175i	$-0.747710\pi$
$727$	−37.8561	−1.40400	−0.702002	+	0.712175i	$0.747710\pi$
$728$	−4.30743	−0.159644
$729$	3.22253	0.119353
$730$	0.142257	0.00526515
$731$	3.71319	0.137337
$732$	−22.8802	−0.845676
$733$	52.8110	1.95062	0.975309	−	0.220845i	$-0.0708815\pi$
$733$	52.8110	1.95062	0.975309	+	0.220845i	$0.0708815\pi$
$734$	−25.2439	−0.931770
$735$	2.74895	0.101396
$736$	6.35811	0.234363
$737$	−11.0149	−0.405737
$738$	11.3038	0.416100
$739$	−7.89581	−0.290452	−0.145226	−	0.989399i	$-0.546391\pi$
$739$	−7.89581	−0.290452	−0.145226	+	0.989399i	$0.546391\pi$
$740$	2.53974	0.0933626
$741$	5.18335	0.190415
$742$	6.63770	0.243678
$743$	23.1531	0.849405	0.424703	−	0.905333i	$-0.360379\pi$
$743$	23.1531	0.849405	0.424703	+	0.905333i	$0.360379\pi$
$744$	−16.6955	−0.612088
$745$	−4.19854	−0.153823
$746$	−15.3892	−0.563439
$747$	12.3655	0.452429
$748$	4.41581	0.161458
$749$	−7.44626	−0.272081
$750$	−6.99336	−0.255361
$751$	34.0778	1.24352	0.621758	−	0.783209i	$-0.286419\pi$
$751$	34.0778	1.24352	0.621758	+	0.783209i	$0.286419\pi$
$752$	12.3993	0.452156
$753$	−33.8699	−1.23429
$754$	−6.82063	−0.248393
$755$	2.88881	0.105135
$756$	−5.59053	−0.203325
$757$	45.6526	1.65927	0.829636	−	0.558305i	$-0.188548\pi$
$757$	45.6526	1.65927	0.829636	+	0.558305i	$0.188548\pi$
$758$	−10.3505	−0.375946
$759$	37.5698	1.36370
$760$	−0.333090	−0.0120825
$761$	−42.5321	−1.54179	−0.770894	−	0.636964i	$-0.780190\pi$
$761$	−42.5321	−1.54179	−0.770894	+	0.636964i	$0.780190\pi$
$762$	−16.4167	−0.594714
$763$	−12.3555	−0.447298
$764$	10.3451	0.374271
$765$	0.796699	0.0288047
$766$	20.8028	0.751635
$767$	12.4787	0.450579
$768$	−2.12309	−0.0766105
$769$	−2.94334	−0.106139	−0.0530697	−	0.998591i	$-0.516901\pi$
$769$	−2.94334	−0.106139	−0.0530697	+	0.998591i	$0.516901\pi$
$770$	1.63561	0.0589434
$771$	−24.6340	−0.887173
$772$	−11.5897	−0.417122
$773$	−4.65732	−0.167512	−0.0837561	−	0.996486i	$-0.526692\pi$
$773$	−4.65732	−0.167512	−0.0837561	+	0.996486i	$0.526692\pi$
$774$	−3.52813	−0.126816
$775$	38.4464	1.38104
$776$	16.9777	0.609465
$777$	28.5609	1.02462
$778$	9.20756	0.330107
$779$	−7.49828	−0.268654
$780$	1.72652	0.0618195
$781$	−39.2057	−1.40289
$782$	10.0878	0.360739
$783$	−8.85237	−0.316358
$784$	−3.88719	−0.138828
$785$	3.67416	0.131136
$786$	35.2106	1.25592
$787$	2.92751	0.104355	0.0521773	−	0.998638i	$-0.483384\pi$
$787$	2.92751	0.104355	0.0521773	+	0.998638i	$0.483384\pi$
$788$	−5.40531	−0.192556
$789$	49.2114	1.75197
$790$	−2.07546	−0.0738414
$791$	−23.6740	−0.841750
$792$	−4.19572	−0.149089
$793$	−26.3107	−0.934319
$794$	0.898344	0.0318810
$795$	−2.66055	−0.0943601
$796$	−5.96485	−0.211418
$797$	−45.1887	−1.60067	−0.800333	−	0.599556i	$-0.795344\pi$
$797$	−45.1887	−1.60067	−0.800333	+	0.599556i	$0.795344\pi$
$798$	−3.74581	−0.132600
$799$	19.6728	0.695972
$800$	4.88905	0.172854
$801$	−18.5770	−0.656386
$802$	15.7267	0.555328
$803$	−1.18865	−0.0419464
$804$	8.40244	0.296331
$805$	3.73652	0.131695
$806$	−19.1987	−0.676246
$807$	−1.46432	−0.0515465
$808$	−5.03181	−0.177018
$809$	17.9098	0.629674	0.314837	−	0.949146i	$-0.398050\pi$
$809$	17.9098	0.629674	0.314837	+	0.949146i	$0.398050\pi$
$810$	3.74725	0.131665
$811$	−13.8269	−0.485528	−0.242764	−	0.970085i	$-0.578054\pi$
$811$	−13.8269	−0.485528	−0.242764	+	0.970085i	$0.578054\pi$
$812$	4.92901	0.172974
$813$	29.0051	1.01725
$814$	−21.2211	−0.743801
$815$	−5.83865	−0.204519
$816$	−3.36850	−0.117921
$817$	2.34034	0.0818782
$818$	3.91117	0.136751
$819$	6.49355	0.226903
$820$	−2.49760	−0.0872201
$821$	34.4812	1.20340	0.601701	−	0.798722i	$-0.294490\pi$
$821$	34.4812	1.20340	0.601701	+	0.798722i	$0.294490\pi$
$822$	−11.7053	−0.408270
$823$	−3.43427	−0.119711	−0.0598556	−	0.998207i	$-0.519064\pi$
$823$	−3.43427	−0.119711	−0.0598556	+	0.998207i	$0.519064\pi$
$824$	5.43732	0.189418
$825$	28.8892	1.00579
$826$	−9.01786	−0.313772
$827$	−3.75620	−0.130616	−0.0653080	−	0.997865i	$-0.520803\pi$
$827$	−3.75620	−0.130616	−0.0653080	+	0.997865i	$0.520803\pi$
$828$	−9.58501	−0.333102
$829$	23.2036	0.805896	0.402948	−	0.915223i	$-0.367986\pi$
$829$	23.2036	0.805896	0.402948	+	0.915223i	$0.367986\pi$
$830$	−2.73217	−0.0948350
$831$	−37.7249	−1.30866
$832$	−2.44141	−0.0846408
$833$	−6.16742	−0.213688
$834$	−26.4778	−0.916851
$835$	−1.23279	−0.0426624
$836$	2.78319	0.0962585
$837$	−24.9177	−0.861280
$838$	8.82156	0.304736
$839$	22.9638	0.792800	0.396400	−	0.918078i	$-0.370259\pi$
$839$	22.9638	0.792800	0.396400	+	0.918078i	$0.370259\pi$
$840$	−1.24769	−0.0430495
$841$	−21.1951	−0.730866
$842$	28.5922	0.985352
$843$	−20.2215	−0.696465
$844$	−1.00000	−0.0344214
$845$	−2.34479	−0.0806632
$846$	−18.6923	−0.642653
$847$	5.74087	0.197259
$848$	3.76219	0.129194
$849$	−13.3748	−0.459023
$850$	7.75698	0.266062
$851$	−48.4791	−1.66184
$852$	29.9072	1.02460
$853$	−14.8217	−0.507484	−0.253742	−	0.967272i	$-0.581661\pi$
$853$	−14.8217	−0.507484	−0.253742	+	0.967272i	$0.581661\pi$
$854$	19.0137	0.650636
$855$	0.502142	0.0171729
$856$	−4.22048	−0.144253
$857$	−19.6442	−0.671033	−0.335517	−	0.942034i	$-0.608911\pi$
$857$	−19.6442	−0.671033	−0.335517	+	0.942034i	$0.608911\pi$
$858$	−14.4262	−0.492503
$859$	−28.8560	−0.984555	−0.492278	−	0.870438i	$-0.663836\pi$
$859$	−28.8560	−0.984555	−0.492278	+	0.870438i	$0.663836\pi$
$860$	0.779546	0.0265823
$861$	−28.0871	−0.957207
$862$	30.1698	1.02759
$863$	31.0054	1.05544	0.527719	−	0.849419i	$-0.323048\pi$
$863$	31.0054	1.05544	0.527719	+	0.849419i	$0.323048\pi$
$864$	−3.16866	−0.107800
$865$	−2.53956	−0.0863476
$866$	3.46093	0.117607
$867$	30.7481	1.04426
$868$	13.8742	0.470921
$869$	17.3418	0.588280
$870$	−1.97567	−0.0669815
$871$	9.66224	0.327392
$872$	−7.00297	−0.237150
$873$	−25.5944	−0.866238
$874$	6.35811	0.215066
$875$	5.81157	0.196467
$876$	0.906733	0.0306357
$877$	−24.8562	−0.839335	−0.419667	−	0.907678i	$-0.637853\pi$
$877$	−24.8562	−0.839335	−0.419667	+	0.907678i	$0.637853\pi$
$878$	−20.4362	−0.689688
$879$	48.9290	1.65034
$880$	0.927052	0.0312509
$881$	44.5322	1.50033	0.750164	−	0.661252i	$-0.229974\pi$
$881$	44.5322	1.50033	0.750164	+	0.661252i	$0.229974\pi$
$882$	5.86003	0.197318
$883$	4.46316	0.150197	0.0750986	−	0.997176i	$-0.476073\pi$
$883$	4.46316	0.150197	0.0750986	+	0.997176i	$0.476073\pi$
$884$	−3.87355	−0.130282
$885$	3.61458	0.121503
$886$	−14.9907	−0.503621
$887$	4.27791	0.143638	0.0718191	−	0.997418i	$-0.477120\pi$
$887$	4.27791	0.143638	0.0718191	+	0.997418i	$0.477120\pi$
$888$	16.1881	0.543237
$889$	13.6425	0.457554
$890$	4.10462	0.137587
$891$	−31.3107	−1.04895
$892$	16.4981	0.552398
$893$	12.3993	0.414927
$894$	−26.7612	−0.895028
$895$	7.77383	0.259851
$896$	1.76432	0.0589417
$897$	−32.9563	−1.10038
$898$	28.8233	0.961846
$899$	21.9692	0.732714
$900$	−7.37037	−0.245679
$901$	5.96910	0.198860
$902$	20.8691	0.694865
$903$	8.76648	0.291730
$904$	−13.4182	−0.446283
$905$	−4.44721	−0.147830
$906$	18.4131	0.611734
$907$	10.6367	0.353186	0.176593	−	0.984284i	$-0.443492\pi$
$907$	10.6367	0.353186	0.176593	+	0.984284i	$0.443492\pi$
$908$	6.14178	0.203822
$909$	7.58558	0.251598
$910$	−1.43476	−0.0475619
$911$	−28.4917	−0.943971	−0.471986	−	0.881606i	$-0.656463\pi$
$911$	−28.4917	−0.943971	−0.471986	+	0.881606i	$0.656463\pi$
$912$	−2.12309	−0.0703026
$913$	22.8291	0.755532
$914$	−19.8584	−0.656857
$915$	−7.62117	−0.251948
$916$	−11.1590	−0.368705
$917$	−29.2605	−0.966265
$918$	−5.02741	−0.165929
$919$	54.4982	1.79773	0.898866	−	0.438224i	$-0.144392\pi$
$919$	54.4982	1.79773	0.898866	+	0.438224i	$0.144392\pi$
$920$	2.11783	0.0698226
$921$	−30.9153	−1.01869
$922$	−22.5011	−0.741035
$923$	34.3913	1.13200
$924$	10.4253	0.342967
$925$	−37.2779	−1.22569
$926$	−15.4279	−0.506993
$927$	−8.19689	−0.269221
$928$	2.79372	0.0917084
$929$	21.8487	0.716833	0.358417	−	0.933562i	$-0.383317\pi$
$929$	21.8487	0.716833	0.358417	+	0.933562i	$0.383317\pi$
$930$	−5.56112	−0.182356
$931$	−3.88719	−0.127397
$932$	16.1404	0.528698
$933$	37.5119	1.22808
$934$	−36.5132	−1.19475
$935$	1.47086	0.0481024
$936$	3.68049	0.120301
$937$	36.1045	1.17948	0.589741	−	0.807592i	$-0.299230\pi$
$937$	36.1045	1.17948	0.589741	+	0.807592i	$0.299230\pi$
$938$	−6.98253	−0.227988
$939$	64.2713	2.09742
$940$	4.13009	0.134709
$941$	−30.3452	−0.989225	−0.494612	−	0.869114i	$-0.664690\pi$
$941$	−30.3452	−0.989225	−0.494612	+	0.869114i	$0.664690\pi$
$942$	23.4188	0.763026
$943$	47.6749	1.55251
$944$	−5.11125	−0.166357
$945$	−1.86215	−0.0605758
$946$	−6.51361	−0.211776
$947$	10.8576	0.352824	0.176412	−	0.984316i	$-0.443551\pi$
$947$	10.8576	0.352824	0.176412	+	0.984316i	$0.443551\pi$
$948$	−13.2288	−0.429652
$949$	1.04268	0.0338469
$950$	4.88905	0.158622
$951$	−15.1379	−0.490879
$952$	2.79927	0.0907248
$953$	−10.7636	−0.348669	−0.174334	−	0.984687i	$-0.555777\pi$
$953$	−10.7636	−0.348669	−0.174334	+	0.984687i	$0.555777\pi$
$954$	−5.67160	−0.183625
$955$	3.44584	0.111505
$956$	−13.4560	−0.435197
$957$	16.5080	0.533628
$958$	−2.98748	−0.0965212
$959$	9.72726	0.314109
$960$	−0.707182	−0.0228242
$961$	30.8389	0.994805
$962$	18.6152	0.600178
$963$	6.36248	0.205028
$964$	18.9494	0.610318
$965$	−3.86041	−0.124271
$966$	23.8163	0.766276
$967$	−19.9088	−0.640224	−0.320112	−	0.947380i	$-0.603721\pi$
$967$	−19.9088	−0.640224	−0.320112	+	0.947380i	$0.603721\pi$
$968$	3.25388	0.104584
$969$	−3.36850	−0.108212
$970$	5.65512	0.181575
$971$	−3.46901	−0.111326	−0.0556628	−	0.998450i	$-0.517727\pi$
$971$	−3.46901	−0.111326	−0.0556628	+	0.998450i	$0.517727\pi$
$972$	14.3787	0.461197
$973$	22.0034	0.705396
$974$	−19.0261	−0.609636
$975$	−25.3417	−0.811582
$976$	10.7768	0.344957
$977$	8.52903	0.272868	0.136434	−	0.990649i	$-0.456436\pi$
$977$	8.52903	0.272868	0.136434	+	0.990649i	$0.456436\pi$
$978$	−37.2151	−1.19001
$979$	−34.2968	−1.09613
$980$	−1.29478	−0.0413604
$981$	10.5572	0.337064
$982$	−11.1132	−0.354637
$983$	−35.4777	−1.13156	−0.565782	−	0.824555i	$-0.691426\pi$
$983$	−35.4777	−1.13156	−0.565782	+	0.824555i	$0.691426\pi$
$984$	−15.9195	−0.507497
$985$	−1.80046	−0.0573674
$986$	4.43252	0.141160
$987$	46.4454	1.47837
$988$	−2.44141	−0.0776717
$989$	−14.8802	−0.473162
$990$	−1.39755	−0.0444172
$991$	−21.8378	−0.693700	−0.346850	−	0.937921i	$-0.612749\pi$
$991$	−21.8378	−0.693700	−0.346850	+	0.937921i	$0.612749\pi$
$992$	7.86377	0.249675
$993$	11.9214	0.378313
$994$	−24.8533	−0.788298
$995$	−1.98683	−0.0629868
$996$	−17.4147	−0.551804
$997$	−23.6683	−0.749581	−0.374791	−	0.927109i	$-0.622285\pi$
$997$	−23.6683	−0.749581	−0.374791	+	0.927109i	$0.622285\pi$
$998$	−26.3232	−0.833245
$999$	24.1603	0.764399

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.i.1.9	✓	43

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.i.1.9	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.12309 q^{3} +1.00000 q^{4} +0.333090 q^{5} +2.12309 q^{6} -1.76432 q^{7} -1.00000 q^{8} +1.50753 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.12309 q^{3} +1.00000 q^{4} +0.333090 q^{5} +2.12309 q^{6} -1.76432 q^{7} -1.00000 q^{8} +1.50753 q^{9} -0.333090 q^{10} +2.78319 q^{11} -2.12309 q^{12} -2.44141 q^{13} +1.76432 q^{14} -0.707182 q^{15} +1.00000 q^{16} +1.58660 q^{17} -1.50753 q^{18} +1.00000 q^{19} +0.333090 q^{20} +3.74581 q^{21} -2.78319 q^{22} -6.35811 q^{23} +2.12309 q^{24} -4.88905 q^{25} +2.44141 q^{26} +3.16866 q^{27} -1.76432 q^{28} -2.79372 q^{29} +0.707182 q^{30} -7.86377 q^{31} -1.00000 q^{32} -5.90896 q^{33} -1.58660 q^{34} -0.587677 q^{35} +1.50753 q^{36} +7.62477 q^{37} -1.00000 q^{38} +5.18335 q^{39} -0.333090 q^{40} -7.49828 q^{41} -3.74581 q^{42} +2.34034 q^{43} +2.78319 q^{44} +0.502142 q^{45} +6.35811 q^{46} +12.3993 q^{47} -2.12309 q^{48} -3.88719 q^{49} +4.88905 q^{50} -3.36850 q^{51} -2.44141 q^{52} +3.76219 q^{53} -3.16866 q^{54} +0.927052 q^{55} +1.76432 q^{56} -2.12309 q^{57} +2.79372 q^{58} -5.11125 q^{59} -0.707182 q^{60} +10.7768 q^{61} +7.86377 q^{62} -2.65975 q^{63} +1.00000 q^{64} -0.813211 q^{65} +5.90896 q^{66} -3.95764 q^{67} +1.58660 q^{68} +13.4989 q^{69} +0.587677 q^{70} -14.0866 q^{71} -1.50753 q^{72} -0.427081 q^{73} -7.62477 q^{74} +10.3799 q^{75} +1.00000 q^{76} -4.91042 q^{77} -5.18335 q^{78} +6.23091 q^{79} +0.333090 q^{80} -11.2499 q^{81} +7.49828 q^{82} +8.20249 q^{83} +3.74581 q^{84} +0.528482 q^{85} -2.34034 q^{86} +5.93133 q^{87} -2.78319 q^{88} -12.3229 q^{89} -0.502142 q^{90} +4.30743 q^{91} -6.35811 q^{92} +16.6955 q^{93} -12.3993 q^{94} +0.333090 q^{95} +2.12309 q^{96} -16.9777 q^{97} +3.88719 q^{98} +4.19572 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 43 q - 43 q^{2} + 43 q^{4} + 19 q^{7} - 43 q^{8} + 53 q^{9}+O(q^{10}) \) 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

Related objects

Downloads

Learn more