LMFDB - Embedded newform 8015.2.a.l.1.36

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8015,2,Mod(1,8015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8015, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("8015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8015 = 5 \cdot 7 \cdot 229 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8015.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:	$64.0000972201$
Analytic rank:	$0$
Dimension:	$62$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.36
Character	$\chi$	$=$	8015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.335014 q^{2} -2.24041 q^{3} -1.88777 q^{4} -1.00000 q^{5} -0.750569 q^{6} -1.00000 q^{7} -1.30246 q^{8} +2.01944 q^{9} +O(q^{10})$	\(q+0.335014 q^{2} -2.24041 q^{3} -1.88777 q^{4} -1.00000 q^{5} -0.750569 q^{6} -1.00000 q^{7} -1.30246 q^{8} +2.01944 q^{9} -0.335014 q^{10} +3.08966 q^{11} +4.22937 q^{12} -2.34431 q^{13} -0.335014 q^{14} +2.24041 q^{15} +3.33919 q^{16} +0.387513 q^{17} +0.676540 q^{18} +2.68213 q^{19} +1.88777 q^{20} +2.24041 q^{21} +1.03508 q^{22} +7.98383 q^{23} +2.91804 q^{24} +1.00000 q^{25} -0.785378 q^{26} +2.19687 q^{27} +1.88777 q^{28} -9.13609 q^{29} +0.750569 q^{30} -5.31346 q^{31} +3.72359 q^{32} -6.92211 q^{33} +0.129822 q^{34} +1.00000 q^{35} -3.81222 q^{36} -0.994796 q^{37} +0.898552 q^{38} +5.25222 q^{39} +1.30246 q^{40} +4.24736 q^{41} +0.750569 q^{42} +4.40582 q^{43} -5.83256 q^{44} -2.01944 q^{45} +2.67470 q^{46} +4.86496 q^{47} -7.48115 q^{48} +1.00000 q^{49} +0.335014 q^{50} -0.868188 q^{51} +4.42551 q^{52} -13.1706 q^{53} +0.735982 q^{54} -3.08966 q^{55} +1.30246 q^{56} -6.00907 q^{57} -3.06072 q^{58} +10.2348 q^{59} -4.22937 q^{60} -4.84523 q^{61} -1.78009 q^{62} -2.01944 q^{63} -5.43092 q^{64} +2.34431 q^{65} -2.31901 q^{66} -15.4928 q^{67} -0.731533 q^{68} -17.8871 q^{69} +0.335014 q^{70} -6.13446 q^{71} -2.63023 q^{72} -6.33820 q^{73} -0.333271 q^{74} -2.24041 q^{75} -5.06323 q^{76} -3.08966 q^{77} +1.75957 q^{78} -7.92124 q^{79} -3.33919 q^{80} -10.9802 q^{81} +1.42293 q^{82} -9.73242 q^{83} -4.22937 q^{84} -0.387513 q^{85} +1.47601 q^{86} +20.4686 q^{87} -4.02416 q^{88} +11.9796 q^{89} -0.676540 q^{90} +2.34431 q^{91} -15.0716 q^{92} +11.9043 q^{93} +1.62983 q^{94} -2.68213 q^{95} -8.34237 q^{96} +8.91853 q^{97} +0.335014 q^{98} +6.23938 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9}+O(q^{10}) $ 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9} - 2 q^{10} - 13 q^{11} + 37 q^{12} + 31 q^{13} - 2 q^{14} - 11 q^{15} + 64 q^{16} + 30 q^{17} + 18 q^{18} + 20 q^{19} - 64 q^{20} - 11 q^{21} + 7 q^{22} + 29 q^{24} + 62 q^{25} + 59 q^{27} - 64 q^{28} - 29 q^{29} - 3 q^{30} + 20 q^{31} + 22 q^{32} + 72 q^{33} + 13 q^{34} + 62 q^{35} + 53 q^{36} + 35 q^{37} + 34 q^{38} - 6 q^{39} - 15 q^{40} + 13 q^{41} - 3 q^{42} - 4 q^{43} - 44 q^{44} - 69 q^{45} - 19 q^{46} + 58 q^{47} + 64 q^{48} + 62 q^{49} + 2 q^{50} - 30 q^{51} + 82 q^{52} + 18 q^{53} + 22 q^{54} + 13 q^{55} - 15 q^{56} + 21 q^{57} + 18 q^{58} - 11 q^{59} - 37 q^{60} + 24 q^{61} + 48 q^{62} - 69 q^{63} + 65 q^{64} - 31 q^{65} + 25 q^{66} - 6 q^{67} + 65 q^{68} + 27 q^{69} + 2 q^{70} - 35 q^{71} + 53 q^{72} + 116 q^{73} - 69 q^{74} + 11 q^{75} + 65 q^{76} + 13 q^{77} + 102 q^{78} - 83 q^{79} - 64 q^{80} + 126 q^{81} + 71 q^{82} + 84 q^{83} - 37 q^{84} - 30 q^{85} + 24 q^{86} + 49 q^{87} + 20 q^{88} - 16 q^{89} - 18 q^{90} - 31 q^{91} + 19 q^{92} + 65 q^{93} + 54 q^{94} - 20 q^{95} + 17 q^{96} + 155 q^{97} + 2 q^{98} + 6 q^{99}+O(q^{100}) \) 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9 - 2 * q^10 - 13 * q^11 + 37 * q^12 + 31 * q^13 - 2 * q^14 - 11 * q^15 + 64 * q^16 + 30 * q^17 + 18 * q^18 + 20 * q^19 - 64 * q^20 - 11 * q^21 + 7 * q^22 + 29 * q^24 + 62 * q^25 + 59 * q^27 - 64 * q^28 - 29 * q^29 - 3 * q^30 + 20 * q^31 + 22 * q^32 + 72 * q^33 + 13 * q^34 + 62 * q^35 + 53 * q^36 + 35 * q^37 + 34 * q^38 - 6 * q^39 - 15 * q^40 + 13 * q^41 - 3 * q^42 - 4 * q^43 - 44 * q^44 - 69 * q^45 - 19 * q^46 + 58 * q^47 + 64 * q^48 + 62 * q^49 + 2 * q^50 - 30 * q^51 + 82 * q^52 + 18 * q^53 + 22 * q^54 + 13 * q^55 - 15 * q^56 + 21 * q^57 + 18 * q^58 - 11 * q^59 - 37 * q^60 + 24 * q^61 + 48 * q^62 - 69 * q^63 + 65 * q^64 - 31 * q^65 + 25 * q^66 - 6 * q^67 + 65 * q^68 + 27 * q^69 + 2 * q^70 - 35 * q^71 + 53 * q^72 + 116 * q^73 - 69 * q^74 + 11 * q^75 + 65 * q^76 + 13 * q^77 + 102 * q^78 - 83 * q^79 - 64 * q^80 + 126 * q^81 + 71 * q^82 + 84 * q^83 - 37 * q^84 - 30 * q^85 + 24 * q^86 + 49 * q^87 + 20 * q^88 - 16 * q^89 - 18 * q^90 - 31 * q^91 + 19 * q^92 + 65 * q^93 + 54 * q^94 - 20 * q^95 + 17 * q^96 + 155 * q^97 + 2 * q^98 + 6 * 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 $

$2$	0.335014	0.236891	0.118445	−	0.992961i	$-0.462209\pi$
$2$	0.335014	0.236891	0.118445	+	0.992961i	$0.462209\pi$
$3$	−2.24041	−1.29350	−0.646751	−	0.762702i	$-0.723873\pi$
$3$	−2.24041	−1.29350	−0.646751	+	0.762702i	$0.723873\pi$
$4$	−1.88777	−0.943883
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−0.750569	−0.306419
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.30246	−0.460488
$9$	2.01944	0.673145
$10$	−0.335014	−0.105941
$11$	3.08966	0.931569	0.465784	−	0.884898i	$-0.345772\pi$
$11$	3.08966	0.931569	0.465784	+	0.884898i	$0.345772\pi$
$12$	4.22937	1.22091
$13$	−2.34431	−0.650195	−0.325098	−	0.945680i	$-0.605397\pi$
$13$	−2.34431	−0.650195	−0.325098	+	0.945680i	$0.605397\pi$
$14$	−0.335014	−0.0895364
$15$	2.24041	0.578471
$16$	3.33919	0.834797
$17$	0.387513	0.0939857	0.0469928	−	0.998895i	$-0.485036\pi$
$17$	0.387513	0.0939857	0.0469928	+	0.998895i	$0.485036\pi$
$18$	0.676540	0.159462
$19$	2.68213	0.615323	0.307661	−	0.951496i	$-0.400454\pi$
$19$	2.68213	0.615323	0.307661	+	0.951496i	$0.400454\pi$
$20$	1.88777	0.422117
$21$	2.24041	0.488897
$22$	1.03508	0.220680
$23$	7.98383	1.66474	0.832372	−	0.554217i	$-0.186982\pi$
$23$	7.98383	1.66474	0.832372	+	0.554217i	$0.186982\pi$
$24$	2.91804	0.595642
$25$	1.00000	0.200000
$26$	−0.785378	−0.154025
$27$	2.19687	0.422787
$28$	1.88777	0.356754
$29$	−9.13609	−1.69653	−0.848265	−	0.529572i	$-0.822353\pi$
$29$	−9.13609	−1.69653	−0.848265	+	0.529572i	$0.822353\pi$
$30$	0.750569	0.137035
$31$	−5.31346	−0.954326	−0.477163	−	0.878815i	$-0.658335\pi$
$31$	−5.31346	−0.954326	−0.477163	+	0.878815i	$0.658335\pi$
$32$	3.72359	0.658244
$33$	−6.92211	−1.20499
$34$	0.129822	0.0222644
$35$	1.00000	0.169031
$36$	−3.81222	−0.635370
$37$	−0.994796	−0.163543	−0.0817717	−	0.996651i	$-0.526058\pi$
$37$	−0.994796	−0.163543	−0.0817717	+	0.996651i	$0.526058\pi$
$38$	0.898552	0.145764
$39$	5.25222	0.841028
$40$	1.30246	0.205937
$41$	4.24736	0.663326	0.331663	−	0.943398i	$-0.392390\pi$
$41$	4.24736	0.663326	0.331663	+	0.943398i	$0.392390\pi$
$42$	0.750569	0.115815
$43$	4.40582	0.671881	0.335941	−	0.941883i	$-0.390946\pi$
$43$	4.40582	0.671881	0.335941	+	0.941883i	$0.390946\pi$
$44$	−5.83256	−0.879292
$45$	−2.01944	−0.301040
$46$	2.67470	0.394363
$47$	4.86496	0.709627	0.354814	−	0.934937i	$-0.384544\pi$
$47$	4.86496	0.709627	0.354814	+	0.934937i	$0.384544\pi$
$48$	−7.48115	−1.07981
$49$	1.00000	0.142857
$50$	0.335014	0.0473782
$51$	−0.868188	−0.121571
$52$	4.42551	0.613708
$53$	−13.1706	−1.80913	−0.904564	−	0.426338i	$-0.859803\pi$
$53$	−13.1706	−1.80913	−0.904564	+	0.426338i	$0.859803\pi$
$54$	0.735982	0.100154
$55$	−3.08966	−0.416610
$56$	1.30246	0.174048
$57$	−6.00907	−0.795921
$58$	−3.06072	−0.401893
$59$	10.2348	1.33245	0.666226	−	0.745750i	$-0.267909\pi$
$59$	10.2348	1.33245	0.666226	+	0.745750i	$0.267909\pi$
$60$	−4.22937	−0.546009
$61$	−4.84523	−0.620368	−0.310184	−	0.950676i	$-0.600391\pi$
$61$	−4.84523	−0.620368	−0.310184	+	0.950676i	$0.600391\pi$
$62$	−1.78009	−0.226071
$63$	−2.01944	−0.254425
$64$	−5.43092	−0.678865
$65$	2.34431	0.290776
$66$	−2.31901	−0.285450
$67$	−15.4928	−1.89275	−0.946376	−	0.323067i	$-0.895286\pi$
$67$	−15.4928	−1.89275	−0.946376	+	0.323067i	$0.895286\pi$
$68$	−0.731533	−0.0887115
$69$	−17.8871	−2.15335
$70$	0.335014	0.0400419
$71$	−6.13446	−0.728027	−0.364013	−	0.931394i	$-0.618594\pi$
$71$	−6.13446	−0.728027	−0.364013	+	0.931394i	$0.618594\pi$
$72$	−2.63023	−0.309975
$73$	−6.33820	−0.741830	−0.370915	−	0.928667i	$-0.620956\pi$
$73$	−6.33820	−0.741830	−0.370915	+	0.928667i	$0.620956\pi$
$74$	−0.333271	−0.0387420
$75$	−2.24041	−0.258700
$76$	−5.06323	−0.580793
$77$	−3.08966	−0.352100
$78$	1.75957	0.199232
$79$	−7.92124	−0.891209	−0.445604	−	0.895230i	$-0.647011\pi$
$79$	−7.92124	−0.891209	−0.445604	+	0.895230i	$0.647011\pi$
$80$	−3.33919	−0.373333
$81$	−10.9802	−1.22002
$82$	1.42293	0.157136
$83$	−9.73242	−1.06827	−0.534136	−	0.845399i	$-0.679363\pi$
$83$	−9.73242	−1.06827	−0.534136	+	0.845399i	$0.679363\pi$
$84$	−4.22937	−0.461462
$85$	−0.387513	−0.0420317
$86$	1.47601	0.159163
$87$	20.4686	2.19446
$88$	−4.02416	−0.428976
$89$	11.9796	1.26984	0.634919	−	0.772579i	$-0.281033\pi$
$89$	11.9796	1.26984	0.634919	+	0.772579i	$0.281033\pi$
$90$	−0.676540	−0.0713136
$91$	2.34431	0.245751
$92$	−15.0716	−1.57132
$93$	11.9043	1.23442
$94$	1.62983	0.168104
$95$	−2.68213	−0.275181
$96$	−8.34237	−0.851439
$97$	8.91853	0.905539	0.452770	−	0.891628i	$-0.350436\pi$
$97$	8.91853	0.905539	0.452770	+	0.891628i	$0.350436\pi$
$98$	0.335014	0.0338416
$99$	6.23938	0.627081
$100$	−1.88777	−0.188777
$101$	−1.24600	−0.123982	−0.0619908	−	0.998077i	$-0.519745\pi$
$101$	−1.24600	−0.123982	−0.0619908	+	0.998077i	$0.519745\pi$
$102$	−0.290855	−0.0287990
$103$	8.02045	0.790278	0.395139	−	0.918621i	$-0.370696\pi$
$103$	8.02045	0.790278	0.395139	+	0.918621i	$0.370696\pi$
$104$	3.05337	0.299407
$105$	−2.24041	−0.218642
$106$	−4.41236	−0.428566
$107$	13.4191	1.29727	0.648636	−	0.761099i	$-0.275340\pi$
$107$	13.4191	1.29727	0.648636	+	0.761099i	$0.275340\pi$
$108$	−4.14717	−0.399061
$109$	−5.11814	−0.490229	−0.245114	−	0.969494i	$-0.578825\pi$
$109$	−5.11814	−0.490229	−0.245114	+	0.969494i	$0.578825\pi$
$110$	−1.03508	−0.0986912
$111$	2.22875	0.211544
$112$	−3.33919	−0.315524
$113$	9.16426	0.862101	0.431050	−	0.902328i	$-0.358143\pi$
$113$	9.16426	0.862101	0.431050	+	0.902328i	$0.358143\pi$
$114$	−2.01312	−0.188546
$115$	−7.98383	−0.744496
$116$	17.2468	1.60133
$117$	−4.73419	−0.437676
$118$	3.42879	0.315646
$119$	−0.387513	−0.0355232
$120$	−2.91804	−0.266379
$121$	−1.45398	−0.132180
$122$	−1.62322	−0.146960
$123$	−9.51583	−0.858014
$124$	10.0306	0.900772
$125$	−1.00000	−0.0894427
$126$	−0.676540	−0.0602710
$127$	16.3534	1.45113	0.725563	−	0.688156i	$-0.241580\pi$
$127$	16.3534	1.45113	0.725563	+	0.688156i	$0.241580\pi$
$128$	−9.26662	−0.819061
$129$	−9.87084	−0.869079
$130$	0.785378	0.0688822
$131$	−8.49544	−0.742250	−0.371125	−	0.928583i	$-0.621028\pi$
$131$	−8.49544	−0.742250	−0.371125	+	0.928583i	$0.621028\pi$
$132$	13.0673	1.13736
$133$	−2.68213	−0.232570
$134$	−5.19033	−0.448376
$135$	−2.19687	−0.189076
$136$	−0.504719	−0.0432793
$137$	−6.22459	−0.531803	−0.265901	−	0.964000i	$-0.585670\pi$
$137$	−6.22459	−0.531803	−0.265901	+	0.964000i	$0.585670\pi$
$138$	−5.99242	−0.510109
$139$	−16.1363	−1.36866	−0.684330	−	0.729172i	$-0.739905\pi$
$139$	−16.1363	−1.36866	−0.684330	+	0.729172i	$0.739905\pi$
$140$	−1.88777	−0.159545
$141$	−10.8995	−0.917903
$142$	−2.05513	−0.172463
$143$	−7.24314	−0.605702
$144$	6.74328	0.561940
$145$	9.13609	0.758711
$146$	−2.12339	−0.175733
$147$	−2.24041	−0.184786
$148$	1.87794	0.154366
$149$	−4.91856	−0.402944	−0.201472	−	0.979494i	$-0.564573\pi$
$149$	−4.91856	−0.402944	−0.201472	+	0.979494i	$0.564573\pi$
$150$	−0.750569	−0.0612837
$151$	11.6046	0.944371	0.472186	−	0.881499i	$-0.343465\pi$
$151$	11.6046	0.944371	0.472186	+	0.881499i	$0.343465\pi$
$152$	−3.49336	−0.283349
$153$	0.782557	0.0632660
$154$	−1.03508	−0.0834093
$155$	5.31346	0.426788
$156$	−9.91496	−0.793832
$157$	13.3293	1.06380	0.531899	−	0.846808i	$-0.321479\pi$
$157$	13.3293	1.06380	0.531899	+	0.846808i	$0.321479\pi$
$158$	−2.65373	−0.211119
$159$	29.5076	2.34011
$160$	−3.72359	−0.294376
$161$	−7.98383	−0.629214
$162$	−3.67852	−0.289012
$163$	−14.1670	−1.10965	−0.554824	−	0.831968i	$-0.687215\pi$
$163$	−14.1670	−1.10965	−0.554824	+	0.831968i	$0.687215\pi$
$164$	−8.01802	−0.626102
$165$	6.92211	0.538886
$166$	−3.26050	−0.253064
$167$	5.01242	0.387873	0.193936	−	0.981014i	$-0.437874\pi$
$167$	5.01242	0.387873	0.193936	+	0.981014i	$0.437874\pi$
$168$	−2.91804	−0.225131
$169$	−7.50420	−0.577246
$170$	−0.129822	−0.00995692
$171$	5.41639	0.414202
$172$	−8.31715	−0.634177
$173$	1.96609	0.149479	0.0747394	−	0.997203i	$-0.476188\pi$
$173$	1.96609	0.149479	0.0747394	+	0.997203i	$0.476188\pi$
$174$	6.85727	0.519848
$175$	−1.00000	−0.0755929
$176$	10.3170	0.777671
$177$	−22.9300	−1.72353
$178$	4.01335	0.300813
$179$	−6.13097	−0.458250	−0.229125	−	0.973397i	$-0.573586\pi$
$179$	−6.13097	−0.458250	−0.229125	+	0.973397i	$0.573586\pi$
$180$	3.81222	0.284146
$181$	−22.1672	−1.64768	−0.823839	−	0.566824i	$-0.808172\pi$
$181$	−22.1672	−1.64768	−0.823839	+	0.566824i	$0.808172\pi$
$182$	0.785378	0.0582161
$183$	10.8553	0.802447
$184$	−10.3986	−0.766595
$185$	0.994796	0.0731388
$186$	3.98812	0.292423
$187$	1.19728	0.0875541
$188$	−9.18390	−0.669805
$189$	−2.19687	−0.159799
$190$	−0.898552	−0.0651878
$191$	3.66299	0.265045	0.132522	−	0.991180i	$-0.457692\pi$
$191$	3.66299	0.265045	0.132522	+	0.991180i	$0.457692\pi$
$192$	12.1675	0.878113
$193$	−5.69038	−0.409602	−0.204801	−	0.978804i	$-0.565655\pi$
$193$	−5.69038	−0.409602	−0.204801	+	0.978804i	$0.565655\pi$
$194$	2.98784	0.214514
$195$	−5.25222	−0.376119
$196$	−1.88777	−0.134840
$197$	−11.3511	−0.808732	−0.404366	−	0.914597i	$-0.632508\pi$
$197$	−11.3511	−0.808732	−0.404366	+	0.914597i	$0.632508\pi$
$198$	2.09028	0.148550
$199$	6.02661	0.427215	0.213608	−	0.976920i	$-0.431479\pi$
$199$	6.02661	0.427215	0.213608	+	0.976920i	$0.431479\pi$
$200$	−1.30246	−0.0920976
$201$	34.7103	2.44828
$202$	−0.417428	−0.0293701
$203$	9.13609	0.641228
$204$	1.63893	0.114748
$205$	−4.24736	−0.296649
$206$	2.68697	0.187210
$207$	16.1228	1.12061
$208$	−7.82810	−0.542781
$209$	8.28688	0.573216
$210$	−0.750569	−0.0517942
$211$	−12.1781	−0.838376	−0.419188	−	0.907900i	$-0.637685\pi$
$211$	−12.1781	−0.838376	−0.419188	+	0.907900i	$0.637685\pi$
$212$	24.8631	1.70760
$213$	13.7437	0.941704
$214$	4.49558	0.307312
$215$	−4.40582	−0.300474
$216$	−2.86132	−0.194688
$217$	5.31346	0.360701
$218$	−1.71465	−0.116131
$219$	14.2002	0.959558
$220$	5.83256	0.393231
$221$	−0.908451	−0.0611090
$222$	0.746663	0.0501128
$223$	12.2152	0.817992	0.408996	−	0.912536i	$-0.365879\pi$
$223$	12.2152	0.817992	0.408996	+	0.912536i	$0.365879\pi$
$224$	−3.72359	−0.248793
$225$	2.01944	0.134629
$226$	3.07016	0.204224
$227$	26.7572	1.77594	0.887969	−	0.459904i	$-0.152116\pi$
$227$	26.7572	1.77594	0.887969	+	0.459904i	$0.152116\pi$
$228$	11.3437	0.751256
$229$	1.00000	0.0660819
$229$	1.00000	0.0660819
$230$	−2.67470	−0.176364
$231$	6.92211	0.455442
$232$	11.8994	0.781232
$233$	−27.2797	−1.78715	−0.893577	−	0.448911i	$-0.851812\pi$
$233$	−27.2797	−1.78715	−0.893577	+	0.448911i	$0.851812\pi$
$234$	−1.58602	−0.103681
$235$	−4.86496	−0.317355
$236$	−19.3208	−1.25768
$237$	17.7468	1.15278
$238$	−0.129822	−0.00841514
$239$	−9.68197	−0.626274	−0.313137	−	0.949708i	$-0.601380\pi$
$239$	−9.68197	−0.626274	−0.313137	+	0.949708i	$0.601380\pi$
$240$	7.48115	0.482906
$241$	14.2686	0.919122	0.459561	−	0.888146i	$-0.348007\pi$
$241$	14.2686	0.919122	0.459561	+	0.888146i	$0.348007\pi$
$242$	−0.487103	−0.0313121
$243$	18.0095	1.15531
$244$	9.14666	0.585555
$245$	−1.00000	−0.0638877
$246$	−3.18794	−0.203256
$247$	−6.28775	−0.400080
$248$	6.92056	0.439456
$249$	21.8046	1.38181
$250$	−0.335014	−0.0211882
$251$	22.6824	1.43170	0.715849	−	0.698255i	$-0.246040\pi$
$251$	22.6824	1.43170	0.715849	+	0.698255i	$0.246040\pi$
$252$	3.81222	0.240147
$253$	24.6674	1.55082
$254$	5.47861	0.343758
$255$	0.868188	0.0543680
$256$	7.75739	0.484837
$257$	17.2507	1.07607	0.538036	−	0.842922i	$-0.319167\pi$
$257$	17.2507	1.07607	0.538036	+	0.842922i	$0.319167\pi$
$258$	−3.30687	−0.205877
$259$	0.994796	0.0618136
$260$	−4.42551	−0.274459
$261$	−18.4497	−1.14201
$262$	−2.84609	−0.175832
$263$	17.8368	1.09987	0.549933	−	0.835209i	$-0.314653\pi$
$263$	17.8368	1.09987	0.549933	+	0.835209i	$0.314653\pi$
$264$	9.01576	0.554881
$265$	13.1706	0.809067
$266$	−0.898552	−0.0550938
$267$	−26.8393	−1.64254
$268$	29.2469	1.78654
$269$	21.8253	1.33071	0.665356	−	0.746526i	$-0.268280\pi$
$269$	21.8253	1.33071	0.665356	+	0.746526i	$0.268280\pi$
$270$	−0.735982	−0.0447904
$271$	11.1052	0.674593	0.337297	−	0.941398i	$-0.390488\pi$
$271$	11.1052	0.674593	0.337297	+	0.941398i	$0.390488\pi$
$272$	1.29398	0.0784590
$273$	−5.25222	−0.317879
$274$	−2.08533	−0.125979
$275$	3.08966	0.186314
$276$	33.7666	2.03251
$277$	21.2309	1.27564	0.637820	−	0.770185i	$-0.279836\pi$
$277$	21.2309	1.27564	0.637820	+	0.770185i	$0.279836\pi$
$278$	−5.40588	−0.324223
$279$	−10.7302	−0.642400
$280$	−1.30246	−0.0778367
$281$	−10.6590	−0.635863	−0.317932	−	0.948114i	$-0.602988\pi$
$281$	−10.6590	−0.635863	−0.317932	+	0.948114i	$0.602988\pi$
$282$	−3.65149	−0.217443
$283$	−16.4149	−0.975767	−0.487884	−	0.872909i	$-0.662231\pi$
$283$	−16.4149	−0.975767	−0.487884	+	0.872909i	$0.662231\pi$
$284$	11.5804	0.687172
$285$	6.00907	0.355947
$286$	−2.42656	−0.143485
$287$	−4.24736	−0.250714
$288$	7.51955	0.443094
$289$	−16.8498	−0.991167
$290$	3.06072	0.179732
$291$	−19.9812	−1.17132
$292$	11.9650	0.700200
$293$	−11.0893	−0.647846	−0.323923	−	0.946084i	$-0.605002\pi$
$293$	−11.0893	−0.647846	−0.323923	+	0.946084i	$0.605002\pi$
$294$	−0.750569	−0.0437741
$295$	−10.2348	−0.595890
$296$	1.29568	0.0753098
$297$	6.78758	0.393855
$298$	−1.64779	−0.0954539
$299$	−18.7166	−1.08241
$300$	4.22937	0.244183
$301$	−4.40582	−0.253947
$302$	3.88772	0.223713
$303$	2.79155	0.160370
$304$	8.95614	0.513670
$305$	4.84523	0.277437
$306$	0.262168	0.0149871
$307$	−2.20307	−0.125736	−0.0628680	−	0.998022i	$-0.520025\pi$
$307$	−2.20307	−0.125736	−0.0628680	+	0.998022i	$0.520025\pi$
$308$	5.83256	0.332341
$309$	−17.9691	−1.02223
$310$	1.78009	0.101102
$311$	−6.04539	−0.342802	−0.171401	−	0.985201i	$-0.554829\pi$
$311$	−6.04539	−0.342802	−0.171401	+	0.985201i	$0.554829\pi$
$312$	−6.84079	−0.387284
$313$	−2.93484	−0.165887	−0.0829436	−	0.996554i	$-0.526432\pi$
$313$	−2.93484	−0.165887	−0.0829436	+	0.996554i	$0.526432\pi$
$314$	4.46552	0.252004
$315$	2.01944	0.113782
$316$	14.9534	0.841197
$317$	10.9997	0.617807	0.308903	−	0.951093i	$-0.400038\pi$
$317$	10.9997	0.617807	0.308903	+	0.951093i	$0.400038\pi$
$318$	9.88549	0.554351
$319$	−28.2275	−1.58043
$320$	5.43092	0.303598
$321$	−30.0642	−1.67802
$322$	−2.67470	−0.149055
$323$	1.03936	0.0578315
$324$	20.7280	1.15156
$325$	−2.34431	−0.130039
$326$	−4.74616	−0.262866
$327$	11.4667	0.634111
$328$	−5.53201	−0.305454
$329$	−4.86496	−0.268214
$330$	2.31901	0.127657
$331$	27.7886	1.52740	0.763700	−	0.645571i	$-0.223381\pi$
$331$	27.7886	1.52740	0.763700	+	0.645571i	$0.223381\pi$
$332$	18.3725	1.00832
$333$	−2.00893	−0.110088
$334$	1.67923	0.0918835
$335$	15.4928	0.846465
$336$	7.48115	0.408130
$337$	3.48215	0.189685	0.0948424	−	0.995492i	$-0.469765\pi$
$337$	3.48215	0.189685	0.0948424	+	0.995492i	$0.469765\pi$
$338$	−2.51401	−0.136744
$339$	−20.5317	−1.11513
$340$	0.731533	0.0396730
$341$	−16.4168	−0.889020
$342$	1.81457	0.0981206
$343$	−1.00000	−0.0539949
$344$	−5.73839	−0.309393
$345$	17.8871	0.963007
$346$	0.658667	0.0354102
$347$	28.6632	1.53872	0.769360	−	0.638815i	$-0.220575\pi$
$347$	28.6632	1.53872	0.769360	+	0.638815i	$0.220575\pi$
$348$	−38.6399	−2.07132
$349$	6.12059	0.327628	0.163814	−	0.986491i	$-0.447620\pi$
$349$	6.12059	0.327628	0.163814	+	0.986491i	$0.447620\pi$
$350$	−0.335014	−0.0179073
$351$	−5.15014	−0.274894
$352$	11.5046	0.613200
$353$	−1.64350	−0.0874748	−0.0437374	−	0.999043i	$-0.513926\pi$
$353$	−1.64350	−0.0874748	−0.0437374	+	0.999043i	$0.513926\pi$
$354$	−7.68189	−0.408288
$355$	6.13446	0.325584
$356$	−22.6147	−1.19858
$357$	0.868188	0.0459494
$358$	−2.05396	−0.108555
$359$	−9.75230	−0.514707	−0.257353	−	0.966317i	$-0.582850\pi$
$359$	−9.75230	−0.514707	−0.257353	+	0.966317i	$0.582850\pi$
$360$	2.63023	0.138625
$361$	−11.8062	−0.621378
$362$	−7.42634	−0.390320
$363$	3.25750	0.170974
$364$	−4.42551	−0.231960
$365$	6.33820	0.331756
$366$	3.63668	0.190092
$367$	16.8750	0.880868	0.440434	−	0.897785i	$-0.354825\pi$
$367$	16.8750	0.880868	0.440434	+	0.897785i	$0.354825\pi$
$368$	26.6595	1.38972
$369$	8.57727	0.446515
$370$	0.333271	0.0173259
$371$	13.1706	0.683786
$372$	−22.4726	−1.16515
$373$	−15.4879	−0.801932	−0.400966	−	0.916093i	$-0.631325\pi$
$373$	−15.4879	−0.801932	−0.400966	+	0.916093i	$0.631325\pi$
$374$	0.401108	0.0207408
$375$	2.24041	0.115694
$376$	−6.33640	−0.326775
$377$	21.4179	1.10308
$378$	−0.735982	−0.0378548
$379$	−13.4710	−0.691958	−0.345979	−	0.938242i	$-0.612453\pi$
$379$	−13.4710	−0.691958	−0.345979	+	0.938242i	$0.612453\pi$
$380$	5.06323	0.259738
$381$	−36.6382	−1.87703
$382$	1.22715	0.0627867
$383$	−4.84972	−0.247809	−0.123905	−	0.992294i	$-0.539542\pi$
$383$	−4.84972	−0.247809	−0.123905	+	0.992294i	$0.539542\pi$
$384$	20.7610	1.05946
$385$	3.08966	0.157464
$386$	−1.90636	−0.0970311
$387$	8.89727	0.452274
$388$	−16.8361	−0.854723
$389$	1.80404	0.0914684	0.0457342	−	0.998954i	$-0.485437\pi$
$389$	1.80404	0.0914684	0.0457342	+	0.998954i	$0.485437\pi$
$390$	−1.75957	−0.0890992
$391$	3.09384	0.156462
$392$	−1.30246	−0.0657840
$393$	19.0333	0.960101
$394$	−3.80278	−0.191581
$395$	7.92124	0.398561
$396$	−11.7785	−0.591891
$397$	9.67307	0.485477	0.242739	−	0.970092i	$-0.421954\pi$
$397$	9.67307	0.485477	0.242739	+	0.970092i	$0.421954\pi$
$398$	2.01900	0.101203
$399$	6.00907	0.300830
$400$	3.33919	0.166959
$401$	4.92980	0.246183	0.123091	−	0.992395i	$-0.460719\pi$
$401$	4.92980	0.246183	0.123091	+	0.992395i	$0.460719\pi$
$402$	11.6285	0.579975
$403$	12.4564	0.620498
$404$	2.35216	0.117024
$405$	10.9802	0.545610
$406$	3.06072	0.151901
$407$	−3.07359	−0.152352
$408$	1.13078	0.0559818
$409$	−5.43787	−0.268885	−0.134443	−	0.990921i	$-0.542924\pi$
$409$	−5.43787	−0.268885	−0.134443	+	0.990921i	$0.542924\pi$
$410$	−1.42293	−0.0702734
$411$	13.9456	0.687887
$412$	−15.1407	−0.745930
$413$	−10.2348	−0.503619
$414$	5.40138	0.265463
$415$	9.73242	0.477745
$416$	−8.72926	−0.427987
$417$	36.1519	1.77036
$418$	2.77622	0.135790
$419$	3.19118	0.155899	0.0779497	−	0.996957i	$-0.475163\pi$
$419$	3.19118	0.155899	0.0779497	+	0.996957i	$0.475163\pi$
$420$	4.22937	0.206372
$421$	−4.22398	−0.205864	−0.102932	−	0.994688i	$-0.532822\pi$
$421$	−4.22398	−0.205864	−0.102932	+	0.994688i	$0.532822\pi$
$422$	−4.07984	−0.198604
$423$	9.82447	0.477682
$424$	17.1542	0.833082
$425$	0.387513	0.0187971
$426$	4.60434	0.223081
$427$	4.84523	0.234477
$428$	−25.3321	−1.22447
$429$	16.2276	0.783476
$430$	−1.47601	−0.0711797
$431$	30.8051	1.48383	0.741916	−	0.670493i	$-0.233917\pi$
$431$	30.8051	1.48383	0.741916	+	0.670493i	$0.233917\pi$
$432$	7.33575	0.352942
$433$	13.3957	0.643754	0.321877	−	0.946781i	$-0.395686\pi$
$433$	13.3957	0.643754	0.321877	+	0.946781i	$0.395686\pi$
$434$	1.78009	0.0854469
$435$	−20.4686	−0.981394
$436$	9.66184	0.462718
$437$	21.4137	1.02436
$438$	4.75726	0.227311
$439$	−19.5760	−0.934310	−0.467155	−	0.884175i	$-0.654721\pi$
$439$	−19.5760	−0.934310	−0.467155	+	0.884175i	$0.654721\pi$
$440$	4.02416	0.191844
$441$	2.01944	0.0961636
$442$	−0.304344	−0.0144762
$443$	41.3997	1.96696	0.983480	−	0.181016i	$-0.0579385\pi$
$443$	41.3997	1.96696	0.983480	+	0.181016i	$0.0579385\pi$
$444$	−4.20736	−0.199672
$445$	−11.9796	−0.567889
$446$	4.09228	0.193775
$447$	11.0196	0.521209
$448$	5.43092	0.256587
$449$	−12.3489	−0.582781	−0.291390	−	0.956604i	$-0.594118\pi$
$449$	−12.3489	−0.582781	−0.291390	+	0.956604i	$0.594118\pi$
$450$	0.676540	0.0318924
$451$	13.1229	0.617934
$452$	−17.3000	−0.813722
$453$	−25.9991	−1.22155
$454$	8.96405	0.420703
$455$	−2.34431	−0.109903
$456$	7.82656	0.366512
$457$	14.2761	0.667807	0.333904	−	0.942607i	$-0.391634\pi$
$457$	14.2761	0.667807	0.333904	+	0.942607i	$0.391634\pi$
$458$	0.335014	0.0156542
$459$	0.851314	0.0397359
$460$	15.0716	0.702717
$461$	−16.3596	−0.761944	−0.380972	−	0.924587i	$-0.624411\pi$
$461$	−16.3596	−0.761944	−0.380972	+	0.924587i	$0.624411\pi$
$462$	2.31901	0.107890
$463$	−31.5238	−1.46504	−0.732518	−	0.680747i	$-0.761655\pi$
$463$	−31.5238	−1.46504	−0.732518	+	0.680747i	$0.761655\pi$
$464$	−30.5071	−1.41626
$465$	−11.9043	−0.552050
$466$	−9.13909	−0.423360
$467$	−12.2226	−0.565593	−0.282797	−	0.959180i	$-0.591262\pi$
$467$	−12.2226	−0.565593	−0.282797	+	0.959180i	$0.591262\pi$
$468$	8.93704	0.413115
$469$	15.4928	0.715393
$470$	−1.62983	−0.0751785
$471$	−29.8632	−1.37602
$472$	−13.3303	−0.613578
$473$	13.6125	0.625904
$474$	5.94544	0.273083
$475$	2.68213	0.123065
$476$	0.731533	0.0335298
$477$	−26.5973	−1.21781
$478$	−3.24360	−0.148359
$479$	−4.92589	−0.225070	−0.112535	−	0.993648i	$-0.535897\pi$
$479$	−4.92589	−0.225070	−0.112535	+	0.993648i	$0.535897\pi$
$480$	8.34237	0.380775
$481$	2.33211	0.106335
$482$	4.78019	0.217732
$483$	17.8871	0.813889
$484$	2.74476	0.124762
$485$	−8.91853	−0.404970
$486$	6.03345	0.273683
$487$	40.3102	1.82663	0.913315	−	0.407253i	$-0.133513\pi$
$487$	40.3102	1.82663	0.913315	+	0.407253i	$0.133513\pi$
$488$	6.31071	0.285672
$489$	31.7400	1.43533
$490$	−0.335014	−0.0151344
$491$	20.1638	0.909981	0.454990	−	0.890496i	$-0.349643\pi$
$491$	20.1638	0.909981	0.454990	+	0.890496i	$0.349643\pi$
$492$	17.9637	0.809864
$493$	−3.54035	−0.159450
$494$	−2.10649	−0.0947753
$495$	−6.23938	−0.280439
$496$	−17.7427	−0.796669
$497$	6.13446	0.275168
$498$	7.30485	0.327338
$499$	−8.30873	−0.371950	−0.185975	−	0.982555i	$-0.559544\pi$
$499$	−8.30873	−0.371950	−0.185975	+	0.982555i	$0.559544\pi$
$500$	1.88777	0.0844234
$501$	−11.2299	−0.501714
$502$	7.59892	0.339156
$503$	4.33965	0.193496	0.0967478	−	0.995309i	$-0.469156\pi$
$503$	4.33965	0.193496	0.0967478	+	0.995309i	$0.469156\pi$
$504$	2.63023	0.117160
$505$	1.24600	0.0554463
$506$	8.26392	0.367376
$507$	16.8125	0.746668
$508$	−30.8713	−1.36969
$509$	−6.28405	−0.278536	−0.139268	−	0.990255i	$-0.544475\pi$
$509$	−6.28405	−0.278536	−0.139268	+	0.990255i	$0.544475\pi$
$510$	0.290855	0.0128793
$511$	6.33820	0.280385
$512$	21.1321	0.933915
$513$	5.89228	0.260151
$514$	5.77925	0.254912
$515$	−8.02045	−0.353423
$516$	18.6338	0.820309
$517$	15.0311	0.661066
$518$	0.333271	0.0146431
$519$	−4.40484	−0.193351
$520$	−3.05337	−0.133899
$521$	25.1102	1.10010	0.550049	−	0.835133i	$-0.314609\pi$
$521$	25.1102	1.10010	0.550049	+	0.835133i	$0.314609\pi$
$522$	−6.18093	−0.270532
$523$	−13.7141	−0.599675	−0.299837	−	0.953990i	$-0.596932\pi$
$523$	−13.7141	−0.599675	−0.299837	+	0.953990i	$0.596932\pi$
$524$	16.0374	0.700597
$525$	2.24041	0.0977795
$526$	5.97559	0.260548
$527$	−2.05903	−0.0896930
$528$	−23.1142	−1.00592
$529$	40.7416	1.77137
$530$	4.41236	0.191661
$531$	20.6684	0.896933
$532$	5.06323	0.219519
$533$	−9.95714	−0.431292
$534$	−8.99154	−0.389102
$535$	−13.4191	−0.580157
$536$	20.1788	0.871590
$537$	13.7359	0.592747
$538$	7.31179	0.315234
$539$	3.08966	0.133081
$540$	4.14717	0.178466
$541$	6.28269	0.270114	0.135057	−	0.990838i	$-0.456878\pi$
$541$	6.28269	0.270114	0.135057	+	0.990838i	$0.456878\pi$
$542$	3.72040	0.159805
$543$	49.6637	2.13127
$544$	1.44294	0.0618655
$545$	5.11814	0.219237
$546$	−1.75957	−0.0753026
$547$	−24.6002	−1.05183	−0.525915	−	0.850537i	$-0.676277\pi$
$547$	−24.6002	−1.05183	−0.525915	+	0.850537i	$0.676277\pi$
$548$	11.7506	0.501959
$549$	−9.78463	−0.417598
$550$	1.03508	0.0441360
$551$	−24.5042	−1.04391
$552$	23.2971	0.991592
$553$	7.92124	0.336845
$554$	7.11265	0.302188
$555$	−2.22875	−0.0946052
$556$	30.4615	1.29186
$557$	24.3518	1.03182	0.515910	−	0.856643i	$-0.327454\pi$
$557$	24.3518	1.03182	0.515910	+	0.856643i	$0.327454\pi$
$558$	−3.59477	−0.152179
$559$	−10.3286	−0.436854
$560$	3.33919	0.141106
$561$	−2.68241	−0.113251
$562$	−3.57092	−0.150630
$563$	−40.9017	−1.72380	−0.861900	−	0.507078i	$-0.830726\pi$
$563$	−40.9017	−1.72380	−0.861900	+	0.507078i	$0.830726\pi$
$564$	20.5757	0.866393
$565$	−9.16426	−0.385543
$566$	−5.49924	−0.231150
$567$	10.9802	0.461125
$568$	7.98988	0.335248
$569$	30.8329	1.29258	0.646291	−	0.763091i	$-0.276319\pi$
$569$	30.8329	1.29258	0.646291	+	0.763091i	$0.276319\pi$
$570$	2.01312	0.0843205
$571$	−12.1919	−0.510214	−0.255107	−	0.966913i	$-0.582111\pi$
$571$	−12.1919	−0.510214	−0.255107	+	0.966913i	$0.582111\pi$
$572$	13.6733	0.571711
$573$	−8.20660	−0.342836
$574$	−1.42293	−0.0593918
$575$	7.98383	0.332949
$576$	−10.9674	−0.456975
$577$	−35.5602	−1.48039	−0.740196	−	0.672391i	$-0.765267\pi$
$577$	−35.5602	−1.48039	−0.740196	+	0.672391i	$0.765267\pi$
$578$	−5.64494	−0.234798
$579$	12.7488	0.529821
$580$	−17.2468	−0.716134
$581$	9.73242	0.403769
$582$	−6.69397	−0.277474
$583$	−40.6929	−1.68533
$584$	8.25523	0.341604
$585$	4.73419	0.195735
$586$	−3.71509	−0.153469
$587$	3.31738	0.136923	0.0684616	−	0.997654i	$-0.478191\pi$
$587$	3.31738	0.136923	0.0684616	+	0.997654i	$0.478191\pi$
$588$	4.22937	0.174416
$589$	−14.2514	−0.587219
$590$	−3.42879	−0.141161
$591$	25.4311	1.04610
$592$	−3.32181	−0.136526
$593$	16.6255	0.682727	0.341364	−	0.939931i	$-0.389111\pi$
$593$	16.6255	0.682727	0.341364	+	0.939931i	$0.389111\pi$
$594$	2.27394	0.0933007
$595$	0.387513	0.0158865
$596$	9.28509	0.380332
$597$	−13.5021	−0.552604
$598$	−6.27033	−0.256413
$599$	−1.47184	−0.0601378	−0.0300689	−	0.999548i	$-0.509573\pi$
$599$	−1.47184	−0.0601378	−0.0300689	+	0.999548i	$0.509573\pi$
$600$	2.91804	0.119128
$601$	24.4064	0.995558	0.497779	−	0.867304i	$-0.334149\pi$
$601$	24.4064	0.995558	0.497779	+	0.867304i	$0.334149\pi$
$602$	−1.47601	−0.0601578
$603$	−31.2868	−1.27410
$604$	−21.9068	−0.891376
$605$	1.45398	0.0591125
$606$	0.935209	0.0379903
$607$	−30.4277	−1.23502	−0.617511	−	0.786563i	$-0.711859\pi$
$607$	−30.4277	−1.23502	−0.617511	+	0.786563i	$0.711859\pi$
$608$	9.98716	0.405033
$609$	−20.4686	−0.829429
$610$	1.62322	0.0657224
$611$	−11.4050	−0.461396
$612$	−1.47728	−0.0597157
$613$	−6.16136	−0.248855	−0.124427	−	0.992229i	$-0.539709\pi$
$613$	−6.16136	−0.248855	−0.124427	+	0.992229i	$0.539709\pi$
$614$	−0.738061	−0.0297857
$615$	9.51583	0.383715
$616$	4.02416	0.162138
$617$	42.1317	1.69616	0.848078	−	0.529871i	$-0.177760\pi$
$617$	42.1317	1.69616	0.848078	+	0.529871i	$0.177760\pi$
$618$	−6.01990	−0.242156
$619$	12.5510	0.504468	0.252234	−	0.967666i	$-0.418835\pi$
$619$	12.5510	0.504468	0.252234	+	0.967666i	$0.418835\pi$
$620$	−10.0306	−0.402837
$621$	17.5394	0.703833
$622$	−2.02529	−0.0812068
$623$	−11.9796	−0.479954
$624$	17.5382	0.702088
$625$	1.00000	0.0400000
$626$	−0.983215	−0.0392972
$627$	−18.5660	−0.741455
$628$	−25.1627	−1.00410
$629$	−0.385496	−0.0153707
$630$	0.676540	0.0269540
$631$	20.4775	0.815198	0.407599	−	0.913161i	$-0.366366\pi$
$631$	20.4775	0.815198	0.407599	+	0.913161i	$0.366366\pi$
$632$	10.3171	0.410391
$633$	27.2840	1.08444
$634$	3.68507	0.146353
$635$	−16.3534	−0.648963
$636$	−55.7035	−2.20879
$637$	−2.34431	−0.0928850
$638$	−9.45660	−0.374391
$639$	−12.3882	−0.490068
$640$	9.26662	0.366295
$641$	−9.31252	−0.367822	−0.183911	−	0.982943i	$-0.558876\pi$
$641$	−9.31252	−0.367822	−0.183911	+	0.982943i	$0.558876\pi$
$642$	−10.0719	−0.397508
$643$	29.5314	1.16461	0.582303	−	0.812972i	$-0.302152\pi$
$643$	29.5314	1.16461	0.582303	+	0.812972i	$0.302152\pi$
$644$	15.0716	0.593904
$645$	9.87084	0.388664
$646$	0.348201	0.0136998
$647$	−26.9368	−1.05899	−0.529496	−	0.848312i	$-0.677619\pi$
$647$	−26.9368	−1.05899	−0.529496	+	0.848312i	$0.677619\pi$
$648$	14.3012	0.561805
$649$	31.6220	1.24127
$650$	−0.785378	−0.0308051
$651$	−11.9043	−0.466568
$652$	26.7441	1.04738
$653$	5.23289	0.204779	0.102389	−	0.994744i	$-0.467351\pi$
$653$	5.23289	0.204779	0.102389	+	0.994744i	$0.467351\pi$
$654$	3.84152	0.150215
$655$	8.49544	0.331944
$656$	14.1827	0.553743
$657$	−12.7996	−0.499359
$658$	−1.62983	−0.0635374
$659$	8.18222	0.318734	0.159367	−	0.987219i	$-0.449055\pi$
$659$	8.18222	0.318734	0.159367	+	0.987219i	$0.449055\pi$
$660$	−13.0673	−0.508645
$661$	36.5815	1.42286	0.711429	−	0.702758i	$-0.248049\pi$
$661$	36.5815	1.42286	0.711429	+	0.702758i	$0.248049\pi$
$662$	9.30958	0.361827
$663$	2.03530	0.0790446
$664$	12.6761	0.491926
$665$	2.68213	0.104009
$666$	−0.673019	−0.0260790
$667$	−72.9410	−2.82429
$668$	−9.46227	−0.366106
$669$	−27.3671	−1.05807
$670$	5.19033	0.200520
$671$	−14.9701	−0.577916
$672$	8.34237	0.321814
$673$	30.5860	1.17900	0.589502	−	0.807767i	$-0.299324\pi$
$673$	30.5860	1.17900	0.589502	+	0.807767i	$0.299324\pi$
$674$	1.16657	0.0449346
$675$	2.19687	0.0845574
$676$	14.1662	0.544853
$677$	24.9903	0.960455	0.480228	−	0.877144i	$-0.340554\pi$
$677$	24.9903	0.960455	0.480228	+	0.877144i	$0.340554\pi$
$678$	−6.87841	−0.264164
$679$	−8.91853	−0.342262
$680$	0.504719	0.0193551
$681$	−59.9471	−2.29718
$682$	−5.49987	−0.210601
$683$	39.1779	1.49910	0.749550	−	0.661948i	$-0.230270\pi$
$683$	39.1779	1.49910	0.749550	+	0.661948i	$0.230270\pi$
$684$	−10.2249	−0.390958
$685$	6.22459	0.237829
$686$	−0.335014	−0.0127909
$687$	−2.24041	−0.0854770
$688$	14.7119	0.560885
$689$	30.8761	1.17629
$690$	5.99242	0.228128
$691$	−18.6598	−0.709852	−0.354926	−	0.934894i	$-0.615494\pi$
$691$	−18.6598	−0.709852	−0.354926	+	0.934894i	$0.615494\pi$
$692$	−3.71151	−0.141090
$693$	−6.23938	−0.237014
$694$	9.60258	0.364509
$695$	16.1363	0.612084
$696$	−26.6595	−1.01052
$697$	1.64591	0.0623432
$698$	2.05048	0.0776120
$699$	61.1177	2.31168
$700$	1.88777	0.0713508
$701$	−0.375612	−0.0141867	−0.00709334	−	0.999975i	$-0.502258\pi$
$701$	−0.375612	−0.0141867	−0.00709334	+	0.999975i	$0.502258\pi$
$702$	−1.72537	−0.0651199
$703$	−2.66817	−0.100632
$704$	−16.7797	−0.632410
$705$	10.8995	0.410499
$706$	−0.550597	−0.0207220
$707$	1.24600	0.0468607
$708$	43.2865	1.62681
$709$	−7.74436	−0.290845	−0.145423	−	0.989370i	$-0.546454\pi$
$709$	−7.74436	−0.290845	−0.145423	+	0.989370i	$0.546454\pi$
$710$	2.05513	0.0771278
$711$	−15.9964	−0.599913
$712$	−15.6030	−0.584745
$713$	−42.4218	−1.58871
$714$	0.290855	0.0108850
$715$	7.24314	0.270878
$716$	11.5738	0.432534
$717$	21.6916	0.810087
$718$	−3.26716	−0.121929
$719$	−37.2087	−1.38765	−0.693824	−	0.720144i	$-0.744076\pi$
$719$	−37.2087	−1.38765	−0.693824	+	0.720144i	$0.744076\pi$
$720$	−6.74328	−0.251307
$721$	−8.02045	−0.298697
$722$	−3.95524	−0.147199
$723$	−31.9675	−1.18889
$724$	41.8466	1.55521
$725$	−9.13609	−0.339306
$726$	1.09131	0.0405023
$727$	−9.80771	−0.363748	−0.181874	−	0.983322i	$-0.558216\pi$
$727$	−9.80771	−0.363748	−0.181874	+	0.983322i	$0.558216\pi$
$728$	−3.05337	−0.113165
$729$	−7.40813	−0.274375
$730$	2.12339	0.0785901
$731$	1.70731	0.0631472
$732$	−20.4923	−0.757416
$733$	16.8853	0.623673	0.311836	−	0.950136i	$-0.399056\pi$
$733$	16.8853	0.623673	0.311836	+	0.950136i	$0.399056\pi$
$734$	5.65337	0.208670
$735$	2.24041	0.0826388
$736$	29.7285	1.09581
$737$	−47.8677	−1.76323
$738$	2.87351	0.105775
$739$	−3.52987	−0.129849	−0.0649243	−	0.997890i	$-0.520681\pi$
$739$	−3.52987	−0.129849	−0.0649243	+	0.997890i	$0.520681\pi$
$740$	−1.87794	−0.0690345
$741$	14.0871	0.517504
$742$	4.41236	0.161983
$743$	−34.9510	−1.28223	−0.641114	−	0.767445i	$-0.721528\pi$
$743$	−34.9510	−1.28223	−0.641114	+	0.767445i	$0.721528\pi$
$744$	−15.5049	−0.568437
$745$	4.91856	0.180202
$746$	−5.18866	−0.189970
$747$	−19.6540	−0.719102
$748$	−2.26019	−0.0826408
$749$	−13.4191	−0.490322
$750$	0.750569	0.0274069
$751$	−41.7657	−1.52405	−0.762025	−	0.647547i	$-0.775795\pi$
$751$	−41.7657	−1.52405	−0.762025	+	0.647547i	$0.775795\pi$
$752$	16.2450	0.592395
$753$	−50.8178	−1.85190
$754$	7.17529	0.261309
$755$	−11.6046	−0.422336
$756$	4.14717	0.150831
$757$	−9.56815	−0.347760	−0.173880	−	0.984767i	$-0.555631\pi$
$757$	−9.56815	−0.347760	−0.173880	+	0.984767i	$0.555631\pi$
$758$	−4.51297	−0.163919
$759$	−55.2650	−2.00599
$760$	3.49336	0.126717
$761$	24.5402	0.889581	0.444790	−	0.895635i	$-0.353278\pi$
$761$	24.5402	0.889581	0.444790	+	0.895635i	$0.353278\pi$
$762$	−12.2743	−0.444652
$763$	5.11814	0.185289
$764$	−6.91487	−0.250171
$765$	−0.782557	−0.0282934
$766$	−1.62473	−0.0587037
$767$	−23.9935	−0.866354
$768$	−17.3797	−0.627137
$769$	1.72991	0.0623821	0.0311910	−	0.999513i	$-0.490070\pi$
$769$	1.72991	0.0623821	0.0311910	+	0.999513i	$0.490070\pi$
$770$	1.03508	0.0373018
$771$	−38.6487	−1.39190
$772$	10.7421	0.386617
$773$	37.3269	1.34256	0.671278	−	0.741206i	$-0.265746\pi$
$773$	37.3269	1.34256	0.671278	+	0.741206i	$0.265746\pi$
$774$	2.98071	0.107140
$775$	−5.31346	−0.190865
$776$	−11.6160	−0.416990
$777$	−2.22875	−0.0799560
$778$	0.604379	0.0216680
$779$	11.3920	0.408160
$780$	9.91496	0.355013
$781$	−18.9534	−0.678207
$782$	1.03648	0.0370645
$783$	−20.0708	−0.717271
$784$	3.33919	0.119257
$785$	−13.3293	−0.475745
$786$	6.37641	0.227439
$787$	0.999973	0.0356452	0.0178226	−	0.999841i	$-0.494327\pi$
$787$	0.999973	0.0356452	0.0178226	+	0.999841i	$0.494327\pi$
$788$	21.4282	0.763348
$789$	−39.9618	−1.42268
$790$	2.65373	0.0944154
$791$	−9.16426	−0.325843
$792$	−8.12652	−0.288763
$793$	11.3587	0.403361
$794$	3.24062	0.115005
$795$	−29.5076	−1.04653
$796$	−11.3768	−0.403241
$797$	−5.95192	−0.210828	−0.105414	−	0.994428i	$-0.533617\pi$
$797$	−5.95192	−0.210828	−0.105414	+	0.994428i	$0.533617\pi$
$798$	2.01312	0.0712639
$799$	1.88523	0.0666948
$800$	3.72359	0.131649
$801$	24.1921	0.854785
$802$	1.65155	0.0583184
$803$	−19.5829	−0.691066
$804$	−65.5249	−2.31089
$805$	7.98383	0.281393
$806$	4.17308	0.146990
$807$	−48.8976	−1.72128
$808$	1.62286	0.0570921
$809$	5.05286	0.177649	0.0888245	−	0.996047i	$-0.471689\pi$
$809$	5.05286	0.177649	0.0888245	+	0.996047i	$0.471689\pi$
$810$	3.67852	0.129250
$811$	28.0490	0.984935	0.492467	−	0.870331i	$-0.336095\pi$
$811$	28.0490	0.984935	0.492467	+	0.870331i	$0.336095\pi$
$812$	−17.2468	−0.605244
$813$	−24.8802	−0.872587
$814$	−1.02970	−0.0360908
$815$	14.1670	0.496250
$816$	−2.89904	−0.101487
$817$	11.8170	0.413424
$818$	−1.82176	−0.0636965
$819$	4.73419	0.165426
$820$	8.01802	0.280001
$821$	−7.31960	−0.255456	−0.127728	−	0.991809i	$-0.540768\pi$
$821$	−7.31960	−0.255456	−0.127728	+	0.991809i	$0.540768\pi$
$822$	4.67199	0.162954
$823$	−17.9358	−0.625202	−0.312601	−	0.949884i	$-0.601200\pi$
$823$	−17.9358	−0.625202	−0.312601	+	0.949884i	$0.601200\pi$
$824$	−10.4463	−0.363914
$825$	−6.92211	−0.240997
$826$	−3.42879	−0.119303
$827$	−4.40875	−0.153307	−0.0766537	−	0.997058i	$-0.524424\pi$
$827$	−4.40875	−0.153307	−0.0766537	+	0.997058i	$0.524424\pi$
$828$	−30.4361	−1.05773
$829$	1.28356	0.0445800	0.0222900	−	0.999752i	$-0.492904\pi$
$829$	1.28356	0.0445800	0.0222900	+	0.999752i	$0.492904\pi$
$830$	3.26050	0.113174
$831$	−47.5659	−1.65004
$832$	12.7318	0.441395
$833$	0.387513	0.0134265
$834$	12.1114	0.419383
$835$	−5.01242	−0.173462
$836$	−15.6437	−0.541048
$837$	−11.6730	−0.403477
$838$	1.06909	0.0369311
$839$	−35.5928	−1.22880	−0.614401	−	0.788994i	$-0.710602\pi$
$839$	−35.5928	−1.22880	−0.614401	+	0.788994i	$0.710602\pi$
$840$	2.91804	0.100682
$841$	54.4682	1.87821
$842$	−1.41509	−0.0487674
$843$	23.8805	0.822490
$844$	22.9894	0.791328
$845$	7.50420	0.258152
$846$	3.29134	0.113159
$847$	1.45398	0.0499592
$848$	−43.9793	−1.51025
$849$	36.7762	1.26216
$850$	0.129822	0.00445287
$851$	−7.94228	−0.272258
$852$	−25.9449	−0.888858
$853$	−11.0497	−0.378334	−0.189167	−	0.981945i	$-0.560579\pi$
$853$	−11.0497	−0.378334	−0.189167	+	0.981945i	$0.560579\pi$
$854$	1.62322	0.0555455
$855$	−5.41639	−0.185237
$856$	−17.4778	−0.597378
$857$	−18.5622	−0.634072	−0.317036	−	0.948413i	$-0.602688\pi$
$857$	−18.5622	−0.634072	−0.317036	+	0.948413i	$0.602688\pi$
$858$	5.43648	0.185598
$859$	48.5446	1.65632	0.828160	−	0.560491i	$-0.189388\pi$
$859$	48.5446	1.65632	0.828160	+	0.560491i	$0.189388\pi$
$860$	8.31715	0.283613
$861$	9.51583	0.324299
$862$	10.3202	0.351506
$863$	18.5868	0.632701	0.316350	−	0.948642i	$-0.397542\pi$
$863$	18.5868	0.632701	0.316350	+	0.948642i	$0.397542\pi$
$864$	8.18023	0.278297
$865$	−1.96609	−0.0668489
$866$	4.48774	0.152500
$867$	37.7505	1.28208
$868$	−10.0306	−0.340460
$869$	−24.4740	−0.830222
$870$	−6.85727	−0.232483
$871$	36.3201	1.23066
$872$	6.66615	0.225744
$873$	18.0104	0.609559
$874$	7.17389	0.242660
$875$	1.00000	0.0338062
$876$	−26.8066	−0.905710
$877$	−3.11892	−0.105318	−0.0526592	−	0.998613i	$-0.516770\pi$
$877$	−3.11892	−0.105318	−0.0526592	+	0.998613i	$0.516770\pi$
$878$	−6.55823	−0.221330
$879$	24.8446	0.837989
$880$	−10.3170	−0.347785
$881$	−3.25242	−0.109577	−0.0547885	−	0.998498i	$-0.517448\pi$
$881$	−3.25242	−0.109577	−0.0547885	+	0.998498i	$0.517448\pi$
$882$	0.676540	0.0227803
$883$	2.80699	0.0944627	0.0472314	−	0.998884i	$-0.484960\pi$
$883$	2.80699	0.0944627	0.0472314	+	0.998884i	$0.484960\pi$
$884$	1.71494	0.0576798
$885$	22.9300	0.770785
$886$	13.8695	0.465955
$887$	−20.4029	−0.685063	−0.342532	−	0.939506i	$-0.611284\pi$
$887$	−20.4029	−0.685063	−0.342532	+	0.939506i	$0.611284\pi$
$888$	−2.90285	−0.0974133
$889$	−16.3534	−0.548474
$890$	−4.01335	−0.134528
$891$	−33.9251	−1.13653
$892$	−23.0595	−0.772089
$893$	13.0485	0.436650
$894$	3.69172	0.123470
$895$	6.13097	0.204936
$896$	9.26662	0.309576
$897$	41.9329	1.40010
$898$	−4.13706	−0.138055
$899$	48.5443	1.61904
$900$	−3.81222	−0.127074
$901$	−5.10380	−0.170032
$902$	4.39637	0.146383
$903$	9.87084	0.328481
$904$	−11.9360	−0.396987
$905$	22.1672	0.736864
$906$	−8.71008	−0.289373
$907$	−45.1193	−1.49816	−0.749081	−	0.662479i	$-0.769505\pi$
$907$	−45.1193	−1.49816	−0.749081	+	0.662479i	$0.769505\pi$
$908$	−50.5113	−1.67628
$909$	−2.51622	−0.0834576
$910$	−0.785378	−0.0260350
$911$	−29.4454	−0.975571	−0.487785	−	0.872964i	$-0.662195\pi$
$911$	−29.4454	−0.975571	−0.487785	+	0.872964i	$0.662195\pi$
$912$	−20.0654	−0.664433
$913$	−30.0699	−0.995168
$914$	4.78269	0.158197
$915$	−10.8553	−0.358865
$916$	−1.88777	−0.0623735
$917$	8.49544	0.280544
$918$	0.285202	0.00941308
$919$	34.4829	1.13749	0.568743	−	0.822515i	$-0.307430\pi$
$919$	34.4829	1.13749	0.568743	+	0.822515i	$0.307430\pi$
$920$	10.3986	0.342832
$921$	4.93579	0.162640
$922$	−5.48071	−0.180498
$923$	14.3811	0.473360
$924$	−13.0673	−0.429883
$925$	−0.994796	−0.0327087
$926$	−10.5609	−0.347054
$927$	16.1968	0.531972
$928$	−34.0191	−1.11673
$929$	−25.4432	−0.834764	−0.417382	−	0.908731i	$-0.637052\pi$
$929$	−25.4432	−0.834764	−0.417382	+	0.908731i	$0.637052\pi$
$930$	−3.98812	−0.130776
$931$	2.68213	0.0879033
$932$	51.4977	1.68686
$933$	13.5441	0.443415
$934$	−4.09474	−0.133984
$935$	−1.19728	−0.0391554
$936$	6.16608	0.201545
$937$	47.2850	1.54473	0.772367	−	0.635177i	$-0.219073\pi$
$937$	47.2850	1.54473	0.772367	+	0.635177i	$0.219073\pi$
$938$	5.19033	0.169470
$939$	6.57525	0.214575
$940$	9.18390	0.299546
$941$	−32.3707	−1.05525	−0.527627	−	0.849476i	$-0.676918\pi$
$941$	−32.3707	−1.05525	−0.527627	+	0.849476i	$0.676918\pi$
$942$	−10.0046	−0.325967
$943$	33.9102	1.10427
$944$	34.1758	1.11233
$945$	2.19687	0.0714641
$946$	4.56038	0.148271
$947$	55.2679	1.79597	0.897983	−	0.440030i	$-0.145032\pi$
$947$	55.2679	1.79597	0.897983	+	0.440030i	$0.145032\pi$
$948$	−33.5018	−1.08809
$949$	14.8587	0.482334
$950$	0.898552	0.0291529
$951$	−24.6439	−0.799134
$952$	0.504719	0.0163580
$953$	−40.2474	−1.30374	−0.651870	−	0.758331i	$-0.726015\pi$
$953$	−40.2474	−1.30374	−0.651870	+	0.758331i	$0.726015\pi$
$954$	−8.91047	−0.288487
$955$	−3.66299	−0.118532
$956$	18.2773	0.591130
$957$	63.2411	2.04429
$958$	−1.65024	−0.0533170
$959$	6.22459	0.201002
$960$	−12.1675	−0.392704
$961$	−2.76713	−0.0892621
$962$	0.781291	0.0251898
$963$	27.0990	0.873252
$964$	−26.9358	−0.867544
$965$	5.69038	0.183180
$966$	5.99242	0.192803
$967$	0.139045	0.00447140	0.00223570	−	0.999998i	$-0.499288\pi$
$967$	0.139045	0.00447140	0.00223570	+	0.999998i	$0.499288\pi$
$968$	1.89374	0.0608671
$969$	−2.32859	−0.0748052
$970$	−2.98784	−0.0959336
$971$	30.2278	0.970057	0.485028	−	0.874498i	$-0.338809\pi$
$971$	30.2278	0.970057	0.485028	+	0.874498i	$0.338809\pi$
$972$	−33.9977	−1.09048
$973$	16.1363	0.517305
$974$	13.5045	0.432712
$975$	5.25222	0.168206
$976$	−16.1791	−0.517882
$977$	40.6852	1.30164	0.650818	−	0.759234i	$-0.274426\pi$
$977$	40.6852	1.30164	0.650818	+	0.759234i	$0.274426\pi$
$978$	10.6333	0.340017
$979$	37.0130	1.18294
$980$	1.88777	0.0603025
$981$	−10.3357	−0.329995
$982$	6.75517	0.215566
$983$	32.1677	1.02599	0.512996	−	0.858391i	$-0.328536\pi$
$983$	32.1677	1.02599	0.512996	+	0.858391i	$0.328536\pi$
$984$	12.3940	0.395105
$985$	11.3511	0.361676
$986$	−1.18607	−0.0377721
$987$	10.8995	0.346935
$988$	11.8698	0.377629
$989$	35.1753	1.11851
$990$	−2.09028	−0.0664335
$991$	14.8819	0.472739	0.236369	−	0.971663i	$-0.424042\pi$
$991$	14.8819	0.472739	0.236369	+	0.971663i	$0.424042\pi$
$992$	−19.7852	−0.628179
$993$	−62.2579	−1.97569
$994$	2.05513	0.0651849
$995$	−6.02661	−0.191057
$996$	−41.1620	−1.30427
$997$	54.4571	1.72467	0.862337	−	0.506335i	$-0.169000\pi$
$997$	54.4571	1.72467	0.862337	+	0.506335i	$0.169000\pi$
$998$	−2.78354	−0.0881115
$999$	−2.18543	−0.0691441

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.l.1.36	✓	62

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.l.1.36	✓	62	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:	\( N \)	\(=\)	\( 8015 = 5 \cdot 7 \cdot 229 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8015.a (trivial)

\(f(q)\)	\(=\)	\(q+0.335014 q^{2} -2.24041 q^{3} -1.88777 q^{4} -1.00000 q^{5} -0.750569 q^{6} -1.00000 q^{7} -1.30246 q^{8} +2.01944 q^{9} +O(q^{10})\)	\(q+0.335014 q^{2} -2.24041 q^{3} -1.88777 q^{4} -1.00000 q^{5} -0.750569 q^{6} -1.00000 q^{7} -1.30246 q^{8} +2.01944 q^{9} -0.335014 q^{10} +3.08966 q^{11} +4.22937 q^{12} -2.34431 q^{13} -0.335014 q^{14} +2.24041 q^{15} +3.33919 q^{16} +0.387513 q^{17} +0.676540 q^{18} +2.68213 q^{19} +1.88777 q^{20} +2.24041 q^{21} +1.03508 q^{22} +7.98383 q^{23} +2.91804 q^{24} +1.00000 q^{25} -0.785378 q^{26} +2.19687 q^{27} +1.88777 q^{28} -9.13609 q^{29} +0.750569 q^{30} -5.31346 q^{31} +3.72359 q^{32} -6.92211 q^{33} +0.129822 q^{34} +1.00000 q^{35} -3.81222 q^{36} -0.994796 q^{37} +0.898552 q^{38} +5.25222 q^{39} +1.30246 q^{40} +4.24736 q^{41} +0.750569 q^{42} +4.40582 q^{43} -5.83256 q^{44} -2.01944 q^{45} +2.67470 q^{46} +4.86496 q^{47} -7.48115 q^{48} +1.00000 q^{49} +0.335014 q^{50} -0.868188 q^{51} +4.42551 q^{52} -13.1706 q^{53} +0.735982 q^{54} -3.08966 q^{55} +1.30246 q^{56} -6.00907 q^{57} -3.06072 q^{58} +10.2348 q^{59} -4.22937 q^{60} -4.84523 q^{61} -1.78009 q^{62} -2.01944 q^{63} -5.43092 q^{64} +2.34431 q^{65} -2.31901 q^{66} -15.4928 q^{67} -0.731533 q^{68} -17.8871 q^{69} +0.335014 q^{70} -6.13446 q^{71} -2.63023 q^{72} -6.33820 q^{73} -0.333271 q^{74} -2.24041 q^{75} -5.06323 q^{76} -3.08966 q^{77} +1.75957 q^{78} -7.92124 q^{79} -3.33919 q^{80} -10.9802 q^{81} +1.42293 q^{82} -9.73242 q^{83} -4.22937 q^{84} -0.387513 q^{85} +1.47601 q^{86} +20.4686 q^{87} -4.02416 q^{88} +11.9796 q^{89} -0.676540 q^{90} +2.34431 q^{91} -15.0716 q^{92} +11.9043 q^{93} +1.62983 q^{94} -2.68213 q^{95} -8.34237 q^{96} +8.91853 q^{97} +0.335014 q^{98} +6.23938 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9}+O(q^{10}) \) 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9} - 2 q^{10} - 13 q^{11} + 37 q^{12} + 31 q^{13} - 2 q^{14} - 11 q^{15} + 64 q^{16} + 30 q^{17} + 18 q^{18} + 20 q^{19} - 64 q^{20} - 11 q^{21} + 7 q^{22} + 29 q^{24} + 62 q^{25} + 59 q^{27} - 64 q^{28} - 29 q^{29} - 3 q^{30} + 20 q^{31} + 22 q^{32} + 72 q^{33} + 13 q^{34} + 62 q^{35} + 53 q^{36} + 35 q^{37} + 34 q^{38} - 6 q^{39} - 15 q^{40} + 13 q^{41} - 3 q^{42} - 4 q^{43} - 44 q^{44} - 69 q^{45} - 19 q^{46} + 58 q^{47} + 64 q^{48} + 62 q^{49} + 2 q^{50} - 30 q^{51} + 82 q^{52} + 18 q^{53} + 22 q^{54} + 13 q^{55} - 15 q^{56} + 21 q^{57} + 18 q^{58} - 11 q^{59} - 37 q^{60} + 24 q^{61} + 48 q^{62} - 69 q^{63} + 65 q^{64} - 31 q^{65} + 25 q^{66} - 6 q^{67} + 65 q^{68} + 27 q^{69} + 2 q^{70} - 35 q^{71} + 53 q^{72} + 116 q^{73} - 69 q^{74} + 11 q^{75} + 65 q^{76} + 13 q^{77} + 102 q^{78} - 83 q^{79} - 64 q^{80} + 126 q^{81} + 71 q^{82} + 84 q^{83} - 37 q^{84} - 30 q^{85} + 24 q^{86} + 49 q^{87} + 20 q^{88} - 16 q^{89} - 18 q^{90} - 31 q^{91} + 19 q^{92} + 65 q^{93} + 54 q^{94} - 20 q^{95} + 17 q^{96} + 155 q^{97} + 2 q^{98} + 6 q^{99}+O(q^{100}) \) 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9 - 2 * q^10 - 13 * q^11 + 37 * q^12 + 31 * q^13 - 2 * q^14 - 11 * q^15 + 64 * q^16 + 30 * q^17 + 18 * q^18 + 20 * q^19 - 64 * q^20 - 11 * q^21 + 7 * q^22 + 29 * q^24 + 62 * q^25 + 59 * q^27 - 64 * q^28 - 29 * q^29 - 3 * q^30 + 20 * q^31 + 22 * q^32 + 72 * q^33 + 13 * q^34 + 62 * q^35 + 53 * q^36 + 35 * q^37 + 34 * q^38 - 6 * q^39 - 15 * q^40 + 13 * q^41 - 3 * q^42 - 4 * q^43 - 44 * q^44 - 69 * q^45 - 19 * q^46 + 58 * q^47 + 64 * q^48 + 62 * q^49 + 2 * q^50 - 30 * q^51 + 82 * q^52 + 18 * q^53 + 22 * q^54 + 13 * q^55 - 15 * q^56 + 21 * q^57 + 18 * q^58 - 11 * q^59 - 37 * q^60 + 24 * q^61 + 48 * q^62 - 69 * q^63 + 65 * q^64 - 31 * q^65 + 25 * q^66 - 6 * q^67 + 65 * q^68 + 27 * q^69 + 2 * q^70 - 35 * q^71 + 53 * q^72 + 116 * q^73 - 69 * q^74 + 11 * q^75 + 65 * q^76 + 13 * q^77 + 102 * q^78 - 83 * q^79 - 64 * q^80 + 126 * q^81 + 71 * q^82 + 84 * q^83 - 37 * q^84 - 30 * q^85 + 24 * q^86 + 49 * q^87 + 20 * q^88 - 16 * q^89 - 18 * q^90 - 31 * q^91 + 19 * q^92 + 65 * q^93 + 54 * q^94 - 20 * q^95 + 17 * q^96 + 155 * q^97 + 2 * q^98 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more