LMFDB - Embedded newform 1334.2.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1334,2,Mod(1,1334)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1334, 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("1334.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1334 = 2 \cdot 23 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1334.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:	$10.6520436296$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	4.4.37108.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 7x^{2} + 5x + 8 $ x^4 - x^3 - 7x^2 + 5x + 8
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.48604$ of defining polynomial
Character	$\chi$	$=$	1334.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.18039 q^{3} +1.00000 q^{4} +2.18039 q^{5} +2.18039 q^{6} +4.66643 q^{7} -1.00000 q^{8} +1.75411 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.18039 q^{3} +1.00000 q^{4} +2.18039 q^{5} +2.18039 q^{6} +4.66643 q^{7} -1.00000 q^{8} +1.75411 q^{9} -2.18039 q^{10} -2.48604 q^{11} -2.18039 q^{12} -4.48604 q^{13} -4.66643 q^{14} -4.75411 q^{15} +1.00000 q^{16} -2.62885 q^{17} -1.75411 q^{18} -2.93450 q^{19} +2.18039 q^{20} -10.1746 q^{21} +2.48604 q^{22} -1.00000 q^{23} +2.18039 q^{24} -0.245891 q^{25} +4.48604 q^{26} +2.71653 q^{27} +4.66643 q^{28} -1.00000 q^{29} +4.75411 q^{30} -10.4860 q^{31} -1.00000 q^{32} +5.42054 q^{33} +2.62885 q^{34} +10.1746 q^{35} +1.75411 q^{36} -7.27773 q^{37} +2.93450 q^{38} +9.78132 q^{39} -2.18039 q^{40} +7.63851 q^{41} +10.1746 q^{42} -8.35504 q^{43} -2.48604 q^{44} +3.82464 q^{45} +1.00000 q^{46} +12.7158 q^{47} -2.18039 q^{48} +14.7756 q^{49} +0.245891 q^{50} +5.73193 q^{51} -4.48604 q^{52} -13.6328 q^{53} -2.71653 q^{54} -5.42054 q^{55} -4.66643 q^{56} +6.39836 q^{57} +1.00000 q^{58} +4.97208 q^{59} -4.75411 q^{60} -1.33357 q^{61} +10.4860 q^{62} +8.18543 q^{63} +1.00000 q^{64} -9.78132 q^{65} -5.42054 q^{66} +0.628853 q^{67} -2.62885 q^{68} +2.18039 q^{69} -10.1746 q^{70} +1.50822 q^{71} -1.75411 q^{72} +3.63851 q^{73} +7.27773 q^{74} +0.536139 q^{75} -2.93450 q^{76} -11.6009 q^{77} -9.78132 q^{78} -9.68861 q^{79} +2.18039 q^{80} -11.1854 q^{81} -7.63851 q^{82} +7.86900 q^{83} -10.1746 q^{84} -5.73193 q^{85} +8.35504 q^{86} +2.18039 q^{87} +2.48604 q^{88} -12.4979 q^{89} -3.82464 q^{90} -20.9338 q^{91} -1.00000 q^{92} +22.8637 q^{93} -12.7158 q^{94} -6.39836 q^{95} +2.18039 q^{96} -8.72157 q^{97} -14.7756 q^{98} -4.36078 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} + q^{3} + 4 q^{4} - q^{5} - q^{6} - 4 q^{8} + 7 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 + q^3 + 4 * q^4 - q^5 - q^6 - 4 * q^8 + 7 * q^9	$ 4 q - 4 q^{2} + q^{3} + 4 q^{4} - q^{5} - q^{6} - 4 q^{8} + 7 q^{9} + q^{10} - q^{11} + q^{12} - 9 q^{13} - 19 q^{15} + 4 q^{16} - 7 q^{18} - 2 q^{19} - q^{20} - 22 q^{21} + q^{22} - 4 q^{23} - q^{24} - q^{25} + 9 q^{26} + 19 q^{27} - 4 q^{29} + 19 q^{30} - 33 q^{31} - 4 q^{32} + 3 q^{33} + 22 q^{35} + 7 q^{36} - 12 q^{37} + 2 q^{38} + q^{39} + q^{40} - 6 q^{41} + 22 q^{42} - 5 q^{43} - q^{44} - 22 q^{45} + 4 q^{46} + 3 q^{47} + q^{48} + 12 q^{49} + q^{50} + 14 q^{51} - 9 q^{52} - 9 q^{53} - 19 q^{54} - 3 q^{55} - 2 q^{57} + 4 q^{58} + 2 q^{59} - 19 q^{60} - 24 q^{61} + 33 q^{62} - 24 q^{63} + 4 q^{64} - q^{65} - 3 q^{66} - 8 q^{67} - q^{69} - 22 q^{70} + 6 q^{71} - 7 q^{72} - 22 q^{73} + 12 q^{74} + 20 q^{75} - 2 q^{76} - 18 q^{77} - q^{78} - 29 q^{79} - q^{80} + 12 q^{81} + 6 q^{82} + 12 q^{83} - 22 q^{84} - 14 q^{85} + 5 q^{86} - q^{87} + q^{88} - 20 q^{89} + 22 q^{90} - 18 q^{91} - 4 q^{92} - 5 q^{93} - 3 q^{94} + 2 q^{95} - q^{96} + 4 q^{97} - 12 q^{98} + 2 q^{99}+O(q^{100}) $ 4 * q - 4 * q^2 + q^3 + 4 * q^4 - q^5 - q^6 - 4 * q^8 + 7 * q^9 + q^10 - q^11 + q^12 - 9 * q^13 - 19 * q^15 + 4 * q^16 - 7 * q^18 - 2 * q^19 - q^20 - 22 * q^21 + q^22 - 4 * q^23 - q^24 - q^25 + 9 * q^26 + 19 * q^27 - 4 * q^29 + 19 * q^30 - 33 * q^31 - 4 * q^32 + 3 * q^33 + 22 * q^35 + 7 * q^36 - 12 * q^37 + 2 * q^38 + q^39 + q^40 - 6 * q^41 + 22 * q^42 - 5 * q^43 - q^44 - 22 * q^45 + 4 * q^46 + 3 * q^47 + q^48 + 12 * q^49 + q^50 + 14 * q^51 - 9 * q^52 - 9 * q^53 - 19 * q^54 - 3 * q^55 - 2 * q^57 + 4 * q^58 + 2 * q^59 - 19 * q^60 - 24 * q^61 + 33 * q^62 - 24 * q^63 + 4 * q^64 - q^65 - 3 * q^66 - 8 * q^67 - q^69 - 22 * q^70 + 6 * q^71 - 7 * q^72 - 22 * q^73 + 12 * q^74 + 20 * q^75 - 2 * q^76 - 18 * q^77 - q^78 - 29 * q^79 - q^80 + 12 * q^81 + 6 * q^82 + 12 * q^83 - 22 * q^84 - 14 * q^85 + 5 * q^86 - q^87 + q^88 - 20 * q^89 + 22 * q^90 - 18 * q^91 - 4 * q^92 - 5 * q^93 - 3 * q^94 + 2 * q^95 - q^96 + 4 * q^97 - 12 * q^98 + 2 * 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
$3$	−2.18039	−1.25885	−0.629425	−	0.777061i	$-0.716709\pi$
$3$	−2.18039	−1.25885	−0.629425	+	0.777061i	$0.716709\pi$
$4$	1.00000	0.500000
$5$	2.18039	0.975101	0.487550	−	0.873095i	$-0.337891\pi$
$5$	2.18039	0.975101	0.487550	+	0.873095i	$0.337891\pi$
$6$	2.18039	0.890141
$7$	4.66643	1.76375	0.881873	−	0.471488i	$-0.156283\pi$
$7$	4.66643	1.76375	0.881873	+	0.471488i	$0.156283\pi$
$8$	−1.00000	−0.353553
$9$	1.75411	0.584703
$10$	−2.18039	−0.689500
$11$	−2.48604	−0.749569	−0.374785	−	0.927112i	$-0.622283\pi$
$11$	−2.48604	−0.749569	−0.374785	+	0.927112i	$0.622283\pi$
$12$	−2.18039	−0.629425
$13$	−4.48604	−1.24420	−0.622102	−	0.782936i	$-0.713721\pi$
$13$	−4.48604	−1.24420	−0.622102	+	0.782936i	$0.713721\pi$
$14$	−4.66643	−1.24716
$15$	−4.75411	−1.22751
$16$	1.00000	0.250000
$17$	−2.62885	−0.637591	−0.318795	−	0.947824i	$-0.603278\pi$
$17$	−2.62885	−0.637591	−0.318795	+	0.947824i	$0.603278\pi$
$18$	−1.75411	−0.413447
$19$	−2.93450	−0.673221	−0.336610	−	0.941644i	$-0.609281\pi$
$19$	−2.93450	−0.673221	−0.336610	+	0.941644i	$0.609281\pi$
$20$	2.18039	0.487550
$21$	−10.1746	−2.22029
$22$	2.48604	0.530025
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	2.18039	0.445071
$25$	−0.245891	−0.0491782
$26$	4.48604	0.879785
$27$	2.71653	0.522797
$28$	4.66643	0.881873
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	4.75411	0.867978
$31$	−10.4860	−1.88335	−0.941674	−	0.336526i	$-0.890748\pi$
$31$	−10.4860	−1.88335	−0.941674	+	0.336526i	$0.890748\pi$
$32$	−1.00000	−0.176777
$33$	5.42054	0.943595
$34$	2.62885	0.450845
$35$	10.1746	1.71983
$36$	1.75411	0.292351
$37$	−7.27773	−1.19645	−0.598225	−	0.801328i	$-0.704127\pi$
$37$	−7.27773	−1.19645	−0.598225	+	0.801328i	$0.704127\pi$
$38$	2.93450	0.476039
$39$	9.78132	1.56627
$40$	−2.18039	−0.344750
$41$	7.63851	1.19293	0.596467	−	0.802637i	$-0.296570\pi$
$41$	7.63851	1.19293	0.596467	+	0.802637i	$0.296570\pi$
$42$	10.1746	1.56998
$43$	−8.35504	−1.27413	−0.637066	−	0.770809i	$-0.719852\pi$
$43$	−8.35504	−1.27413	−0.637066	+	0.770809i	$0.719852\pi$
$44$	−2.48604	−0.374785
$45$	3.82464	0.570144
$46$	1.00000	0.147442
$47$	12.7158	1.85479	0.927397	−	0.374079i	$-0.122041\pi$
$47$	12.7158	1.85479	0.927397	+	0.374079i	$0.122041\pi$
$48$	−2.18039	−0.314712
$49$	14.7756	2.11080
$50$	0.245891	0.0347743
$51$	5.73193	0.802631
$52$	−4.48604	−0.622102
$53$	−13.6328	−1.87260	−0.936302	−	0.351195i	$-0.885775\pi$
$53$	−13.6328	−1.87260	−0.936302	+	0.351195i	$0.885775\pi$
$54$	−2.71653	−0.369673
$55$	−5.42054	−0.730905
$56$	−4.66643	−0.623578
$57$	6.39836	0.847484
$58$	1.00000	0.131306
$59$	4.97208	0.647310	0.323655	−	0.946175i	$-0.395088\pi$
$59$	4.97208	0.647310	0.323655	+	0.946175i	$0.395088\pi$
$60$	−4.75411	−0.613753
$61$	−1.33357	−0.170746	−0.0853730	−	0.996349i	$-0.527208\pi$
$61$	−1.33357	−0.170746	−0.0853730	+	0.996349i	$0.527208\pi$
$62$	10.4860	1.33173
$63$	8.18543	1.03127
$64$	1.00000	0.125000
$65$	−9.78132	−1.21322
$66$	−5.42054	−0.667222
$67$	0.628853	0.0768267	0.0384133	−	0.999262i	$-0.487770\pi$
$67$	0.628853	0.0768267	0.0384133	+	0.999262i	$0.487770\pi$
$68$	−2.62885	−0.318795
$69$	2.18039	0.262488
$70$	−10.1746	−1.21610
$71$	1.50822	0.178993	0.0894963	−	0.995987i	$-0.471474\pi$
$71$	1.50822	0.178993	0.0894963	+	0.995987i	$0.471474\pi$
$72$	−1.75411	−0.206724
$73$	3.63851	0.425855	0.212928	−	0.977068i	$-0.431700\pi$
$73$	3.63851	0.425855	0.212928	+	0.977068i	$0.431700\pi$
$74$	7.27773	0.846018
$75$	0.536139	0.0619080
$76$	−2.93450	−0.336610
$77$	−11.6009	−1.32205
$78$	−9.78132	−1.10752
$79$	−9.68861	−1.09005	−0.545027	−	0.838419i	$-0.683481\pi$
$79$	−9.68861	−1.09005	−0.545027	+	0.838419i	$0.683481\pi$
$80$	2.18039	0.243775
$81$	−11.1854	−1.24283
$82$	−7.63851	−0.843532
$83$	7.86900	0.863735	0.431868	−	0.901937i	$-0.357855\pi$
$83$	7.86900	0.863735	0.431868	+	0.901937i	$0.357855\pi$
$84$	−10.1746	−1.11015
$85$	−5.73193	−0.621715
$86$	8.35504	0.900947
$87$	2.18039	0.233763
$88$	2.48604	0.265013
$89$	−12.4979	−1.32477	−0.662385	−	0.749164i	$-0.730456\pi$
$89$	−12.4979	−1.32477	−0.662385	+	0.749164i	$0.730456\pi$
$90$	−3.82464	−0.403153
$91$	−20.9338	−2.19446
$92$	−1.00000	−0.104257
$93$	22.8637	2.37085
$94$	−12.7158	−1.31154
$95$	−6.39836	−0.656458
$96$	2.18039	0.222535
$97$	−8.72157	−0.885541	−0.442771	−	0.896635i	$-0.646004\pi$
$97$	−8.72157	−0.885541	−0.442771	+	0.896635i	$0.646004\pi$
$98$	−14.7756	−1.49256
$99$	−4.36078	−0.438275
$100$	−0.245891	−0.0245891
$101$	−8.37834	−0.833676	−0.416838	−	0.908981i	$-0.636862\pi$
$101$	−8.37834	−0.833676	−0.416838	+	0.908981i	$0.636862\pi$
$102$	−5.73193	−0.567546
$103$	−17.4080	−1.71526	−0.857632	−	0.514265i	$-0.828065\pi$
$103$	−17.4080	−1.71526	−0.857632	+	0.514265i	$0.828065\pi$
$104$	4.48604	0.439892
$105$	−22.1847	−2.16501
$106$	13.6328	1.32413
$107$	11.8690	1.14742	0.573710	−	0.819059i	$-0.305504\pi$
$107$	11.8690	1.14742	0.573710	+	0.819059i	$0.305504\pi$
$108$	2.71653	0.261398
$109$	−11.9675	−1.14627	−0.573137	−	0.819459i	$-0.694274\pi$
$109$	−11.9675	−1.14627	−0.573137	+	0.819459i	$0.694274\pi$
$110$	5.42054	0.516828
$111$	15.8683	1.50615
$112$	4.66643	0.440936
$113$	8.97208	0.844022	0.422011	−	0.906591i	$-0.361324\pi$
$113$	8.97208	0.844022	0.422011	+	0.906591i	$0.361324\pi$
$114$	−6.39836	−0.599261
$115$	−2.18039	−0.203323
$116$	−1.00000	−0.0928477
$117$	−7.86900	−0.727489
$118$	−4.97208	−0.457717
$119$	−12.2674	−1.12455
$120$	4.75411	0.433989
$121$	−4.81961	−0.438146
$122$	1.33357	0.120736
$123$	−16.6549	−1.50173
$124$	−10.4860	−0.941674
$125$	−11.4381	−1.02305
$126$	−8.18543	−0.729216
$127$	21.0357	1.86662	0.933310	−	0.359070i	$-0.116906\pi$
$127$	21.0357	1.86662	0.933310	+	0.359070i	$0.116906\pi$
$128$	−1.00000	−0.0883883
$129$	18.2173	1.60394
$130$	9.78132	0.857879
$131$	−2.57372	−0.224867	−0.112433	−	0.993659i	$-0.535864\pi$
$131$	−2.57372	−0.224867	−0.112433	+	0.993659i	$0.535864\pi$
$132$	5.42054	0.471797
$133$	−13.6936	−1.18739
$134$	−0.628853	−0.0543247
$135$	5.92310	0.509779
$136$	2.62885	0.225422
$137$	4.74837	0.405680	0.202840	−	0.979212i	$-0.434983\pi$
$137$	4.74837	0.405680	0.202840	+	0.979212i	$0.434983\pi$
$138$	−2.18039	−0.185607
$139$	15.8683	1.34593	0.672966	−	0.739674i	$-0.265020\pi$
$139$	15.8683	1.34593	0.672966	+	0.739674i	$0.265020\pi$
$140$	10.1746	0.859915
$141$	−27.7255	−2.33491
$142$	−1.50822	−0.126567
$143$	11.1525	0.932616
$144$	1.75411	0.146176
$145$	−2.18039	−0.181072
$146$	−3.63851	−0.301125
$147$	−32.2166	−2.65718
$148$	−7.27773	−0.598225
$149$	−0.311390	−0.0255101	−0.0127550	−	0.999919i	$-0.504060\pi$
$149$	−0.311390	−0.0255101	−0.0127550	+	0.999919i	$0.504060\pi$
$150$	−0.536139	−0.0437756
$151$	−11.7380	−0.955225	−0.477613	−	0.878571i	$-0.658498\pi$
$151$	−11.7380	−0.955225	−0.477613	+	0.878571i	$0.658498\pi$
$152$	2.93450	0.238019
$153$	−4.61129	−0.372801
$154$	11.6009	0.934830
$155$	−22.8637	−1.83645
$156$	9.78132	0.783133
$157$	−14.9521	−1.19330	−0.596652	−	0.802500i	$-0.703503\pi$
$157$	−14.9521	−1.19330	−0.596652	+	0.802500i	$0.703503\pi$
$158$	9.68861	0.770784
$159$	29.7248	2.35733
$160$	−2.18039	−0.172375
$161$	−4.66643	−0.367766
$162$	11.1854	0.878810
$163$	20.8461	1.63279	0.816397	−	0.577491i	$-0.195968\pi$
$163$	20.8461	1.63279	0.816397	+	0.577491i	$0.195968\pi$
$164$	7.63851	0.596467
$165$	11.8189	0.920100
$166$	−7.86900	−0.610753
$167$	8.00000	0.619059	0.309529	−	0.950890i	$-0.399829\pi$
$167$	8.00000	0.619059	0.309529	+	0.950890i	$0.399829\pi$
$168$	10.1746	0.784991
$169$	7.12455	0.548042
$170$	5.73193	0.439619
$171$	−5.14743	−0.393634
$172$	−8.35504	−0.637066
$173$	−16.6657	−1.26707	−0.633536	−	0.773713i	$-0.718397\pi$
$173$	−16.6657	−1.26707	−0.633536	+	0.773713i	$0.718397\pi$
$174$	−2.18039	−0.165295
$175$	−1.14743	−0.0867379
$176$	−2.48604	−0.187392
$177$	−10.8411	−0.814866
$178$	12.4979	0.936754
$179$	3.08306	0.230439	0.115219	−	0.993340i	$-0.463243\pi$
$179$	3.08306	0.230439	0.115219	+	0.993340i	$0.463243\pi$
$180$	3.82464	0.285072
$181$	7.52003	0.558960	0.279480	−	0.960152i	$-0.409838\pi$
$181$	7.52003	0.558960	0.279480	+	0.960152i	$0.409838\pi$
$182$	20.9338	1.55172
$183$	2.90770	0.214944
$184$	1.00000	0.0737210
$185$	−15.8683	−1.16666
$186$	−22.8637	−1.67645
$187$	6.53543	0.477918
$188$	12.7158	0.927397
$189$	12.6765	0.922080
$190$	6.39836	0.464186
$191$	−2.97208	−0.215052	−0.107526	−	0.994202i	$-0.534293\pi$
$191$	−2.97208	−0.215052	−0.107526	+	0.994202i	$0.534293\pi$
$192$	−2.18039	−0.157356
$193$	22.7101	1.63471	0.817354	−	0.576136i	$-0.195440\pi$
$193$	22.7101	1.63471	0.817354	+	0.576136i	$0.195440\pi$
$194$	8.72157	0.626172
$195$	21.3271	1.52727
$196$	14.7756	1.05540
$197$	−6.72157	−0.478892	−0.239446	−	0.970910i	$-0.576966\pi$
$197$	−6.72157	−0.478892	−0.239446	+	0.970910i	$0.576966\pi$
$198$	4.36078	0.309907
$199$	12.9721	0.919566	0.459783	−	0.888031i	$-0.347927\pi$
$199$	12.9721	0.919566	0.459783	+	0.888031i	$0.347927\pi$
$200$	0.245891	0.0173871
$201$	−1.37115	−0.0967132
$202$	8.37834	0.589498
$203$	−4.66643	−0.327519
$204$	5.73193	0.401315
$205$	16.6549	1.16323
$206$	17.4080	1.21287
$207$	−1.75411	−0.121919
$208$	−4.48604	−0.311051
$209$	7.29528	0.504625
$210$	22.1847	1.53089
$211$	−11.0773	−0.762594	−0.381297	−	0.924453i	$-0.624522\pi$
$211$	−11.0773	−0.762594	−0.381297	+	0.924453i	$0.624522\pi$
$212$	−13.6328	−0.936302
$213$	−3.28851	−0.225325
$214$	−11.8690	−0.811348
$215$	−18.2173	−1.24241
$216$	−2.71653	−0.184837
$217$	−48.9324	−3.32175
$218$	11.9675	0.810539
$219$	−7.93338	−0.536088
$220$	−5.42054	−0.365453
$221$	11.7931	0.793292
$222$	−15.8683	−1.06501
$223$	16.7216	1.11976	0.559879	−	0.828574i	$-0.310847\pi$
$223$	16.7216	1.11976	0.559879	+	0.828574i	$0.310847\pi$
$224$	−4.66643	−0.311789
$225$	−0.431320	−0.0287547
$226$	−8.97208	−0.596814
$227$	−21.1285	−1.40235	−0.701173	−	0.712991i	$-0.747340\pi$
$227$	−21.1285	−1.40235	−0.701173	+	0.712991i	$0.747340\pi$
$228$	6.39836	0.423742
$229$	7.31284	0.483246	0.241623	−	0.970370i	$-0.422320\pi$
$229$	7.31284	0.483246	0.241623	+	0.970370i	$0.422320\pi$
$230$	2.18039	0.143771
$231$	25.2946	1.66426
$232$	1.00000	0.0656532
$233$	4.38408	0.287211	0.143605	−	0.989635i	$-0.454130\pi$
$233$	4.38408	0.287211	0.143605	+	0.989635i	$0.454130\pi$
$234$	7.86900	0.514413
$235$	27.7255	1.80861
$236$	4.97208	0.323655
$237$	21.1250	1.37221
$238$	12.2674	0.795175
$239$	2.55370	0.165185	0.0825925	−	0.996583i	$-0.473680\pi$
$239$	2.55370	0.165185	0.0825925	+	0.996583i	$0.473680\pi$
$240$	−4.75411	−0.306876
$241$	−30.4538	−1.96170	−0.980852	−	0.194756i	$-0.937609\pi$
$241$	−30.4538	−1.96170	−0.980852	+	0.194756i	$0.937609\pi$
$242$	4.81961	0.309816
$243$	16.2390	1.04173
$244$	−1.33357	−0.0853730
$245$	32.2166	2.05824
$246$	16.6549	1.06188
$247$	13.1643	0.837623
$248$	10.4860	0.665864
$249$	−17.1575	−1.08731
$250$	11.4381	0.723409
$251$	−10.5497	−0.665892	−0.332946	−	0.942946i	$-0.608043\pi$
$251$	−10.5497	−0.665892	−0.332946	+	0.942946i	$0.608043\pi$
$252$	8.18543	0.515634
$253$	2.48604	0.156296
$254$	−21.0357	−1.31990
$255$	12.4979	0.782646
$256$	1.00000	0.0625000
$257$	20.3192	1.26748	0.633739	−	0.773547i	$-0.281519\pi$
$257$	20.3192	1.26748	0.633739	+	0.773547i	$0.281519\pi$
$258$	−18.2173	−1.13416
$259$	−33.9610	−2.11023
$260$	−9.78132	−0.606612
$261$	−1.75411	−0.108577
$262$	2.57372	0.159005
$263$	−10.6958	−0.659532	−0.329766	−	0.944063i	$-0.606970\pi$
$263$	−10.6958	−0.659532	−0.329766	+	0.944063i	$0.606970\pi$
$264$	−5.42054	−0.333611
$265$	−29.7248	−1.82598
$266$	13.6936	0.839611
$267$	27.2502	1.66769
$268$	0.628853	0.0384133
$269$	−18.8472	−1.14913	−0.574566	−	0.818459i	$-0.694829\pi$
$269$	−18.8472	−1.14913	−0.574566	+	0.818459i	$0.694829\pi$
$270$	−5.92310	−0.360469
$271$	−23.3064	−1.41576	−0.707881	−	0.706331i	$-0.750349\pi$
$271$	−23.3064	−1.41576	−0.707881	+	0.706331i	$0.750349\pi$
$272$	−2.62885	−0.159398
$273$	45.6439	2.76249
$274$	−4.74837	−0.286859
$275$	0.611295	0.0368625
$276$	2.18039	0.131244
$277$	30.9889	1.86194	0.930972	−	0.365090i	$-0.118962\pi$
$277$	30.9889	1.86194	0.930972	+	0.365090i	$0.118962\pi$
$278$	−15.8683	−0.951717
$279$	−18.3937	−1.10120
$280$	−10.1746	−0.608052
$281$	−9.81890	−0.585747	−0.292873	−	0.956151i	$-0.594611\pi$
$281$	−9.81890	−0.585747	−0.292873	+	0.956151i	$0.594611\pi$
$282$	27.7255	1.65103
$283$	−24.6160	−1.46327	−0.731633	−	0.681698i	$-0.761242\pi$
$283$	−24.6160	−1.46327	−0.731633	+	0.681698i	$0.761242\pi$
$284$	1.50822	0.0894963
$285$	13.9509	0.826382
$286$	−11.1525	−0.659459
$287$	35.6446	2.10403
$288$	−1.75411	−0.103362
$289$	−10.0891	−0.593478
$290$	2.18039	0.128037
$291$	19.0164	1.11476
$292$	3.63851	0.212928
$293$	2.95206	0.172461	0.0862306	−	0.996275i	$-0.472518\pi$
$293$	2.95206	0.172461	0.0862306	+	0.996275i	$0.472518\pi$
$294$	32.2166	1.87891
$295$	10.8411	0.631192
$296$	7.27773	0.423009
$297$	−6.75340	−0.391872
$298$	0.311390	0.0180384
$299$	4.48604	0.259434
$300$	0.536139	0.0309540
$301$	−38.9882	−2.24724
$302$	11.7380	0.675446
$303$	18.2681	1.04947
$304$	−2.93450	−0.168305
$305$	−2.90770	−0.166495
$306$	4.61129	0.263610
$307$	24.0129	1.37049	0.685243	−	0.728314i	$-0.259696\pi$
$307$	24.0129	1.37049	0.685243	+	0.728314i	$0.259696\pi$
$308$	−11.6009	−0.661024
$309$	37.9563	2.15926
$310$	22.8637	1.29857
$311$	9.59486	0.544075	0.272037	−	0.962287i	$-0.412303\pi$
$311$	9.59486	0.544075	0.272037	+	0.962287i	$0.412303\pi$
$312$	−9.78132	−0.553758
$313$	−33.0093	−1.86579	−0.932897	−	0.360142i	$-0.882728\pi$
$313$	−33.0093	−1.86579	−0.932897	+	0.360142i	$0.882728\pi$
$314$	14.9521	0.843794
$315$	17.8474	1.00559
$316$	−9.68861	−0.545027
$317$	−2.47422	−0.138966	−0.0694831	−	0.997583i	$-0.522135\pi$
$317$	−2.47422	−0.138966	−0.0694831	+	0.997583i	$0.522135\pi$
$318$	−29.7248	−1.66688
$319$	2.48604	0.139191
$320$	2.18039	0.121888
$321$	−25.8791	−1.44443
$322$	4.66643	0.260050
$323$	7.71437	0.429239
$324$	−11.1854	−0.621413
$325$	1.10308	0.0611877
$326$	−20.8461	−1.15456
$327$	26.0938	1.44299
$328$	−7.63851	−0.421766
$329$	59.3375	3.27138
$330$	−11.8189	−0.650609
$331$	−7.24589	−0.398270	−0.199135	−	0.979972i	$-0.563813\pi$
$331$	−7.24589	−0.398270	−0.199135	+	0.979972i	$0.563813\pi$
$332$	7.86900	0.431868
$333$	−12.7659	−0.699568
$334$	−8.00000	−0.437741
$335$	1.37115	0.0749137
$336$	−10.1746	−0.555073
$337$	−9.58337	−0.522040	−0.261020	−	0.965333i	$-0.584059\pi$
$337$	−9.58337	−0.522040	−0.261020	+	0.965333i	$0.584059\pi$
$338$	−7.12455	−0.387524
$339$	−19.5626	−1.06250
$340$	−5.73193	−0.310858
$341$	26.0687	1.41170
$342$	5.14743	0.278341
$343$	36.2842	1.95916
$344$	8.35504	0.450474
$345$	4.75411	0.255953
$346$	16.6657	0.895955
$347$	3.20186	0.171885	0.0859425	−	0.996300i	$-0.472610\pi$
$347$	3.20186	0.171885	0.0859425	+	0.996300i	$0.472610\pi$
$348$	2.18039	0.116881
$349$	−10.1865	−0.545269	−0.272634	−	0.962118i	$-0.587895\pi$
$349$	−10.1865	−0.545269	−0.272634	+	0.962118i	$0.587895\pi$
$350$	1.14743	0.0613329
$351$	−12.1865	−0.650465
$352$	2.48604	0.132506
$353$	17.9817	0.957071	0.478536	−	0.878068i	$-0.341168\pi$
$353$	17.9817	0.957071	0.478536	+	0.878068i	$0.341168\pi$
$354$	10.8411	0.576197
$355$	3.28851	0.174536
$356$	−12.4979	−0.662385
$357$	26.7477	1.41564
$358$	−3.08306	−0.162945
$359$	4.19724	0.221522	0.110761	−	0.993847i	$-0.464671\pi$
$359$	4.19724	0.221522	0.110761	+	0.993847i	$0.464671\pi$
$360$	−3.82464	−0.201576
$361$	−10.3887	−0.546774
$362$	−7.52003	−0.395244
$363$	10.5086	0.551560
$364$	−20.9338	−1.09723
$365$	7.93338	0.415252
$366$	−2.90770	−0.151988
$367$	3.95094	0.206237	0.103119	−	0.994669i	$-0.467118\pi$
$367$	3.95094	0.206237	0.103119	+	0.994669i	$0.467118\pi$
$368$	−1.00000	−0.0521286
$369$	13.3988	0.697513
$370$	15.8683	0.824953
$371$	−63.6164	−3.30280
$372$	22.8637	1.18543
$373$	−6.18039	−0.320009	−0.160004	−	0.987116i	$-0.551151\pi$
$373$	−6.18039	−0.320009	−0.160004	+	0.987116i	$0.551151\pi$
$374$	−6.53543	−0.337939
$375$	24.9395	1.28787
$376$	−12.7158	−0.655769
$377$	4.48604	0.231043
$378$	−12.6765	−0.652009
$379$	−4.37227	−0.224588	−0.112294	−	0.993675i	$-0.535820\pi$
$379$	−4.37227	−0.224588	−0.112294	+	0.993675i	$0.535820\pi$
$380$	−6.39836	−0.328229
$381$	−45.8662	−2.34980
$382$	2.97208	0.152065
$383$	0.317133	0.0162047	0.00810237	−	0.999967i	$-0.497421\pi$
$383$	0.317133	0.0162047	0.00810237	+	0.999967i	$0.497421\pi$
$384$	2.18039	0.111268
$385$	−25.2946	−1.28913
$386$	−22.7101	−1.15591
$387$	−14.6557	−0.744989
$388$	−8.72157	−0.442771
$389$	−30.1625	−1.52930	−0.764649	−	0.644447i	$-0.777087\pi$
$389$	−30.1625	−1.52930	−0.764649	+	0.644447i	$0.777087\pi$
$390$	−21.3271	−1.07994
$391$	2.62885	0.132947
$392$	−14.7756	−0.746280
$393$	5.61171	0.283073
$394$	6.72157	0.338628
$395$	−21.1250	−1.06291
$396$	−4.36078	−0.219138
$397$	−16.2187	−0.813992	−0.406996	−	0.913430i	$-0.633424\pi$
$397$	−16.2187	−0.813992	−0.406996	+	0.913430i	$0.633424\pi$
$398$	−12.9721	−0.650232
$399$	29.8575	1.49475
$400$	−0.245891	−0.0122946
$401$	28.4678	1.42161	0.710806	−	0.703388i	$-0.248330\pi$
$401$	28.4678	1.42161	0.710806	+	0.703388i	$0.248330\pi$
$402$	1.37115	0.0683866
$403$	47.0408	2.34327
$404$	−8.37834	−0.416838
$405$	−24.3886	−1.21188
$406$	4.66643	0.231591
$407$	18.0927	0.896823
$408$	−5.73193	−0.283773
$409$	−6.48100	−0.320465	−0.160232	−	0.987079i	$-0.551224\pi$
$409$	−6.48100	−0.320465	−0.160232	+	0.987079i	$0.551224\pi$
$410$	−16.6549	−0.822529
$411$	−10.3533	−0.510691
$412$	−17.4080	−0.857632
$413$	23.2019	1.14169
$414$	1.75411	0.0862097
$415$	17.1575	0.842229
$416$	4.48604	0.219946
$417$	−34.5991	−1.69433
$418$	−7.29528	−0.356824
$419$	−16.7913	−0.820309	−0.410155	−	0.912016i	$-0.634525\pi$
$419$	−16.7913	−0.820309	−0.410155	+	0.912016i	$0.634525\pi$
$420$	−22.1847	−1.08250
$421$	9.95996	0.485419	0.242709	−	0.970099i	$-0.421964\pi$
$421$	9.95996	0.485419	0.242709	+	0.970099i	$0.421964\pi$
$422$	11.0773	0.539235
$423$	22.3049	1.08450
$424$	13.6328	0.662066
$425$	0.646412	0.0313556
$426$	3.28851	0.159329
$427$	−6.22301	−0.301152
$428$	11.8690	0.573710
$429$	−24.3168	−1.17402
$430$	18.2173	0.878514
$431$	23.2770	1.12121	0.560607	−	0.828082i	$-0.310568\pi$
$431$	23.2770	1.12121	0.560607	+	0.828082i	$0.310568\pi$
$432$	2.71653	0.130699
$433$	26.8665	1.29112	0.645560	−	0.763710i	$-0.276624\pi$
$433$	26.8665	1.29112	0.645560	+	0.763710i	$0.276624\pi$
$434$	48.9324	2.34883
$435$	4.75411	0.227942
$436$	−11.9675	−0.573137
$437$	2.93450	0.140376
$438$	7.93338	0.379071
$439$	0.759852	0.0362657	0.0181329	−	0.999836i	$-0.494228\pi$
$439$	0.759852	0.0362657	0.0181329	+	0.999836i	$0.494228\pi$
$440$	5.42054	0.258414
$441$	25.9180	1.23419
$442$	−11.7931	−0.560942
$443$	11.6324	0.552674	0.276337	−	0.961061i	$-0.410879\pi$
$443$	11.6324	0.552674	0.276337	+	0.961061i	$0.410879\pi$
$444$	15.8683	0.753076
$445$	−27.2502	−1.29178
$446$	−16.7216	−0.791789
$447$	0.678953	0.0321134
$448$	4.66643	0.220468
$449$	10.3293	0.487469	0.243734	−	0.969842i	$-0.421627\pi$
$449$	10.3293	0.487469	0.243734	+	0.969842i	$0.421627\pi$
$450$	0.431320	0.0203326
$451$	−18.9896	−0.894187
$452$	8.97208	0.422011
$453$	25.5934	1.20249
$454$	21.1285	0.991608
$455$	−45.6439	−2.13982
$456$	−6.39836	−0.299631
$457$	33.6844	1.57569	0.787845	−	0.615874i	$-0.211197\pi$
$457$	33.6844	1.57569	0.787845	+	0.615874i	$0.211197\pi$
$458$	−7.31284	−0.341707
$459$	−7.14136	−0.333330
$460$	−2.18039	−0.101661
$461$	9.27526	0.431992	0.215996	−	0.976394i	$-0.430700\pi$
$461$	9.27526	0.431992	0.215996	+	0.976394i	$0.430700\pi$
$462$	−25.2946	−1.17681
$463$	−20.6464	−0.959520	−0.479760	−	0.877400i	$-0.659276\pi$
$463$	−20.6464	−0.959520	−0.479760	+	0.877400i	$0.659276\pi$
$464$	−1.00000	−0.0464238
$465$	49.8518	2.31182
$466$	−4.38408	−0.203089
$467$	25.1700	1.16473	0.582365	−	0.812927i	$-0.302127\pi$
$467$	25.1700	1.16473	0.582365	+	0.812927i	$0.302127\pi$
$468$	−7.86900	−0.363745
$469$	2.93450	0.135503
$470$	−27.7255	−1.27888
$471$	32.6013	1.50219
$472$	−4.97208	−0.228858
$473$	20.7710	0.955050
$474$	−21.1250	−0.970302
$475$	0.721568	0.0331078
$476$	−12.2674	−0.562274
$477$	−23.9134	−1.09492
$478$	−2.55370	−0.116803
$479$	−28.1553	−1.28645	−0.643225	−	0.765677i	$-0.722404\pi$
$479$	−28.1553	−1.28645	−0.643225	+	0.765677i	$0.722404\pi$
$480$	4.75411	0.216994
$481$	32.6482	1.48863
$482$	30.4538	1.38713
$483$	10.1746	0.462963
$484$	−4.81961	−0.219073
$485$	−19.0164	−0.863492
$486$	−16.2390	−0.736617
$487$	−11.3855	−0.515928	−0.257964	−	0.966155i	$-0.583052\pi$
$487$	−11.3855	−0.515928	−0.257964	+	0.966155i	$0.583052\pi$
$488$	1.33357	0.0603678
$489$	−45.4527	−2.05544
$490$	−32.2166	−1.45540
$491$	−31.9728	−1.44291	−0.721457	−	0.692460i	$-0.756527\pi$
$491$	−31.9728	−1.44291	−0.721457	+	0.692460i	$0.756527\pi$
$492$	−16.6549	−0.750863
$493$	2.62885	0.118398
$494$	−13.1643	−0.592289
$495$	−9.50822	−0.427363
$496$	−10.4860	−0.470837
$497$	7.03799	0.315697
$498$	17.1575	0.768846
$499$	23.9248	1.07102	0.535512	−	0.844528i	$-0.320119\pi$
$499$	23.9248	1.07102	0.535512	+	0.844528i	$0.320119\pi$
$500$	−11.4381	−0.511527
$501$	−17.4431	−0.779302
$502$	10.5497	0.470857
$503$	17.3096	0.771795	0.385898	−	0.922542i	$-0.373892\pi$
$503$	17.3096	0.771795	0.385898	+	0.922542i	$0.373892\pi$
$504$	−8.18543	−0.364608
$505$	−18.2681	−0.812918
$506$	−2.48604	−0.110518
$507$	−15.5343	−0.689903
$508$	21.0357	0.933310
$509$	5.48175	0.242974	0.121487	−	0.992593i	$-0.461234\pi$
$509$	5.48175	0.242974	0.121487	+	0.992593i	$0.461234\pi$
$510$	−12.4979	−0.553414
$511$	16.9789	0.751100
$512$	−1.00000	−0.0441942
$513$	−7.97166	−0.351957
$514$	−20.3192	−0.896242
$515$	−37.9563	−1.67255
$516$	18.2173	0.801970
$517$	−31.6120	−1.39030
$518$	33.9610	1.49216
$519$	36.3378	1.59505
$520$	9.78132	0.428939
$521$	12.2126	0.535042	0.267521	−	0.963552i	$-0.413796\pi$
$521$	12.2126	0.535042	0.267521	+	0.963552i	$0.413796\pi$
$522$	1.75411	0.0767753
$523$	−39.8276	−1.74154	−0.870769	−	0.491693i	$-0.836378\pi$
$523$	−39.8276	−1.74154	−0.870769	+	0.491693i	$0.836378\pi$
$524$	−2.57372	−0.112433
$525$	2.50186	0.109190
$526$	10.6958	0.466359
$527$	27.5663	1.20081
$528$	5.42054	0.235899
$529$	1.00000	0.0434783
$530$	29.7248	1.29116
$531$	8.72157	0.378484
$532$	−13.6936	−0.593695
$533$	−34.2667	−1.48425
$534$	−27.2502	−1.17923
$535$	25.8791	1.11885
$536$	−0.628853	−0.0271623
$537$	−6.72227	−0.290088
$538$	18.8472	0.812558
$539$	−36.7327	−1.58219
$540$	5.92310	0.254890
$541$	9.78777	0.420809	0.210405	−	0.977614i	$-0.432522\pi$
$541$	9.78777	0.420809	0.210405	+	0.977614i	$0.432522\pi$
$542$	23.3064	1.00110
$543$	−16.3966	−0.703646
$544$	2.62885	0.112711
$545$	−26.0938	−1.11773
$546$	−45.6439	−1.95338
$547$	9.19108	0.392982	0.196491	−	0.980506i	$-0.437045\pi$
$547$	9.19108	0.392982	0.196491	+	0.980506i	$0.437045\pi$
$548$	4.74837	0.202840
$549$	−2.33922	−0.0998357
$550$	−0.611295	−0.0260657
$551$	2.93450	0.125014
$552$	−2.18039	−0.0928036
$553$	−45.2112	−1.92258
$554$	−30.9889	−1.31659
$555$	34.5991	1.46865
$556$	15.8683	0.672966
$557$	−3.81994	−0.161856	−0.0809280	−	0.996720i	$-0.525788\pi$
$557$	−3.81994	−0.161856	−0.0809280	+	0.996720i	$0.525788\pi$
$558$	18.3937	0.778666
$559$	37.4810	1.58528
$560$	10.1746	0.429957
$561$	−14.2498	−0.601627
$562$	9.81890	0.414185
$563$	38.6586	1.62926	0.814632	−	0.579978i	$-0.196939\pi$
$563$	38.6586	1.62926	0.814632	+	0.579978i	$0.196939\pi$
$564$	−27.7255	−1.16745
$565$	19.5626	0.823007
$566$	24.6160	1.03469
$567$	−52.1960	−2.19203
$568$	−1.50822	−0.0632834
$569$	6.26490	0.262638	0.131319	−	0.991340i	$-0.458079\pi$
$569$	6.26490	0.262638	0.131319	+	0.991340i	$0.458079\pi$
$570$	−13.9509	−0.584340
$571$	−11.2341	−0.470131	−0.235066	−	0.971979i	$-0.575531\pi$
$571$	−11.2341	−0.470131	−0.235066	+	0.971979i	$0.575531\pi$
$572$	11.1525	0.466308
$573$	6.48030	0.270718
$574$	−35.6446	−1.48778
$575$	0.245891	0.0102544
$576$	1.75411	0.0730879
$577$	−6.11881	−0.254729	−0.127365	−	0.991856i	$-0.540652\pi$
$577$	−6.11881	−0.254729	−0.127365	+	0.991856i	$0.540652\pi$
$578$	10.0891	0.419652
$579$	−49.5169	−2.05785
$580$	−2.18039	−0.0905358
$581$	36.7202	1.52341
$582$	−19.0164	−0.788257
$583$	33.8916	1.40365
$584$	−3.63851	−0.150563
$585$	−17.1575	−0.709376
$586$	−2.95206	−0.121948
$587$	22.4166	0.925233	0.462617	−	0.886558i	$-0.346911\pi$
$587$	22.4166	0.925233	0.462617	+	0.886558i	$0.346911\pi$
$588$	−32.2166	−1.32859
$589$	30.7713	1.26791
$590$	−10.8411	−0.446320
$591$	14.6557	0.602853
$592$	−7.27773	−0.299113
$593$	−13.0408	−0.535521	−0.267760	−	0.963486i	$-0.586284\pi$
$593$	−13.0408	−0.535521	−0.267760	+	0.963486i	$0.586284\pi$
$594$	6.75340	0.277095
$595$	−26.7477	−1.09655
$596$	−0.311390	−0.0127550
$597$	−28.2842	−1.15760
$598$	−4.48604	−0.183448
$599$	38.3329	1.56624	0.783120	−	0.621871i	$-0.213627\pi$
$599$	38.3329	1.56624	0.783120	+	0.621871i	$0.213627\pi$
$600$	−0.536139	−0.0218878
$601$	38.2261	1.55928	0.779638	−	0.626230i	$-0.215403\pi$
$601$	38.2261	1.55928	0.779638	+	0.626230i	$0.215403\pi$
$602$	38.9882	1.58904
$603$	1.10308	0.0449208
$604$	−11.7380	−0.477613
$605$	−10.5086	−0.427237
$606$	−18.2681	−0.742090
$607$	−36.8729	−1.49663	−0.748313	−	0.663346i	$-0.769136\pi$
$607$	−36.8729	−1.49663	−0.748313	+	0.663346i	$0.769136\pi$
$608$	2.93450	0.119010
$609$	10.1746	0.412298
$610$	2.90770	0.117729
$611$	−57.0437	−2.30774
$612$	−4.61129	−0.186401
$613$	39.3798	1.59053	0.795267	−	0.606259i	$-0.207330\pi$
$613$	39.3798	1.59053	0.795267	+	0.606259i	$0.207330\pi$
$614$	−24.0129	−0.969080
$615$	−36.3143	−1.46433
$616$	11.6009	0.467415
$617$	−19.8132	−0.797648	−0.398824	−	0.917028i	$-0.630582\pi$
$617$	−19.8132	−0.797648	−0.398824	+	0.917028i	$0.630582\pi$
$618$	−37.9563	−1.52683
$619$	0.820731	0.0329880	0.0164940	−	0.999864i	$-0.494750\pi$
$619$	0.820731	0.0329880	0.0164940	+	0.999864i	$0.494750\pi$
$620$	−22.8637	−0.918227
$621$	−2.71653	−0.109011
$622$	−9.59486	−0.384719
$623$	−58.3204	−2.33656
$624$	9.78132	0.391566
$625$	−23.7101	−0.948403
$626$	33.0093	1.31932
$627$	−15.9066	−0.635248
$628$	−14.9521	−0.596652
$629$	19.1321	0.762846
$630$	−17.8474	−0.711059
$631$	2.92772	0.116551	0.0582754	−	0.998301i	$-0.481440\pi$
$631$	2.92772	0.116551	0.0582754	+	0.998301i	$0.481440\pi$
$632$	9.68861	0.385392
$633$	24.1529	0.959991
$634$	2.47422	0.0982640
$635$	45.8662	1.82014
$636$	29.7248	1.17866
$637$	−66.2838	−2.62626
$638$	−2.48604	−0.0984232
$639$	2.64558	0.104657
$640$	−2.18039	−0.0861876
$641$	0.0765681	0.00302426	0.00151213	−	0.999999i	$-0.499519\pi$
$641$	0.0765681	0.00302426	0.00151213	+	0.999999i	$0.499519\pi$
$642$	25.8791	1.02137
$643$	0.144239	0.00568824	0.00284412	−	0.999996i	$-0.499095\pi$
$643$	0.144239	0.00568824	0.00284412	+	0.999996i	$0.499095\pi$
$644$	−4.66643	−0.183883
$645$	39.7208	1.56400
$646$	−7.71437	−0.303518
$647$	12.3110	0.483996	0.241998	−	0.970277i	$-0.422197\pi$
$647$	12.3110	0.483996	0.241998	+	0.970277i	$0.422197\pi$
$648$	11.1854	0.439405
$649$	−12.3608	−0.485203
$650$	−1.10308	−0.0432662
$651$	106.692	4.18158
$652$	20.8461	0.816397
$653$	23.7573	0.929696	0.464848	−	0.885391i	$-0.346109\pi$
$653$	23.7573	0.929696	0.464848	+	0.885391i	$0.346109\pi$
$654$	−26.0938	−1.02035
$655$	−5.61171	−0.219268
$656$	7.63851	0.298234
$657$	6.38234	0.248999
$658$	−59.3375	−2.31322
$659$	19.7140	0.767948	0.383974	−	0.923344i	$-0.374555\pi$
$659$	19.7140	0.767948	0.383974	+	0.923344i	$0.374555\pi$
$660$	11.8189	0.460050
$661$	35.9105	1.39676	0.698379	−	0.715728i	$-0.253905\pi$
$661$	35.9105	1.39676	0.698379	+	0.715728i	$0.253905\pi$
$662$	7.24589	0.281620
$663$	−25.7137	−0.998636
$664$	−7.86900	−0.305376
$665$	−29.8575	−1.15782
$666$	12.7659	0.494670
$667$	1.00000	0.0387202
$668$	8.00000	0.309529
$669$	−36.4596	−1.40961
$670$	−1.37115	−0.0529720
$671$	3.31530	0.127986
$672$	10.1746	0.392496
$673$	30.7777	1.18639	0.593197	−	0.805057i	$-0.297865\pi$
$673$	30.7777	1.18639	0.593197	+	0.805057i	$0.297865\pi$
$674$	9.58337	0.369138
$675$	−0.667971	−0.0257102
$676$	7.12455	0.274021
$677$	32.1732	1.23652	0.618259	−	0.785974i	$-0.287838\pi$
$677$	32.1732	1.23652	0.618259	+	0.785974i	$0.287838\pi$
$678$	19.5626	0.751299
$679$	−40.6986	−1.56187
$680$	5.73193	0.219810
$681$	46.0683	1.76534
$682$	−26.0687	−0.998222
$683$	−2.50327	−0.0957849	−0.0478924	−	0.998852i	$-0.515250\pi$
$683$	−2.50327	−0.0957849	−0.0478924	+	0.998852i	$0.515250\pi$
$684$	−5.14743	−0.196817
$685$	10.3533	0.395579
$686$	−36.2842	−1.38534
$687$	−15.9449	−0.608334
$688$	−8.35504	−0.318533
$689$	61.1571	2.32990
$690$	−4.75411	−0.180986
$691$	−5.35288	−0.203633	−0.101817	−	0.994803i	$-0.532465\pi$
$691$	−5.35288	−0.203633	−0.101817	+	0.994803i	$0.532465\pi$
$692$	−16.6657	−0.633536
$693$	−20.3493	−0.773006
$694$	−3.20186	−0.121541
$695$	34.5991	1.31242
$696$	−2.18039	−0.0826475
$697$	−20.0805	−0.760604
$698$	10.1865	0.385563
$699$	−9.55902	−0.361555
$700$	−1.14743	−0.0433689
$701$	4.08265	0.154200	0.0770999	−	0.997023i	$-0.475434\pi$
$701$	4.08265	0.154200	0.0770999	+	0.997023i	$0.475434\pi$
$702$	12.1865	0.459948
$703$	21.3565	0.805475
$704$	−2.48604	−0.0936961
$705$	−60.4524	−2.27677
$706$	−17.9817	−0.676752
$707$	−39.0970	−1.47039
$708$	−10.8411	−0.407433
$709$	−6.03359	−0.226596	−0.113298	−	0.993561i	$-0.536142\pi$
$709$	−6.03359	−0.226596	−0.113298	+	0.993561i	$0.536142\pi$
$710$	−3.28851	−0.123415
$711$	−16.9949	−0.637358
$712$	12.4979	0.468377
$713$	10.4860	0.392705
$714$	−26.7477	−1.00101
$715$	24.3168	0.909395
$716$	3.08306	0.115219
$717$	−5.56806	−0.207943
$718$	−4.19724	−0.156640
$719$	−38.9865	−1.45395	−0.726975	−	0.686664i	$-0.759074\pi$
$719$	−38.9865	−1.45395	−0.726975	+	0.686664i	$0.759074\pi$
$720$	3.82464	0.142536
$721$	−81.2333	−3.02529
$722$	10.3887	0.386628
$723$	66.4013	2.46949
$724$	7.52003	0.279480
$725$	0.245891	0.00913217
$726$	−10.5086	−0.390012
$727$	−34.3776	−1.27500	−0.637498	−	0.770452i	$-0.720031\pi$
$727$	−34.3776	−1.27500	−0.637498	+	0.770452i	$0.720031\pi$
$728$	20.9338	0.775858
$729$	−1.85115	−0.0685613
$730$	−7.93338	−0.293627
$731$	21.9642	0.812374
$732$	2.90770	0.107472
$733$	24.1096	0.890507	0.445254	−	0.895405i	$-0.353114\pi$
$733$	24.1096	0.890507	0.445254	+	0.895405i	$0.353114\pi$
$734$	−3.95094	−0.145832
$735$	−70.2447	−2.59102
$736$	1.00000	0.0368605
$737$	−1.56335	−0.0575869
$738$	−13.3988	−0.493216
$739$	−18.5344	−0.681799	−0.340899	−	0.940100i	$-0.610732\pi$
$739$	−18.5344	−0.681799	−0.340899	+	0.940100i	$0.610732\pi$
$740$	−15.8683	−0.583330
$741$	−28.7033	−1.05444
$742$	63.6164	2.33543
$743$	−11.0776	−0.406399	−0.203200	−	0.979137i	$-0.565134\pi$
$743$	−11.0776	−0.406399	−0.203200	+	0.979137i	$0.565134\pi$
$744$	−22.8637	−0.838223
$745$	−0.678953	−0.0248749
$746$	6.18039	0.226280
$747$	13.8031	0.505028
$748$	6.53543	0.238959
$749$	55.3859	2.02376
$750$	−24.9395	−0.910663
$751$	27.9556	1.02012	0.510058	−	0.860140i	$-0.329624\pi$
$751$	27.9556	1.02012	0.510058	+	0.860140i	$0.329624\pi$
$752$	12.7158	0.463698
$753$	23.0025	0.838258
$754$	−4.48604	−0.163372
$755$	−25.5934	−0.931441
$756$	12.6765	0.461040
$757$	45.9356	1.66956	0.834778	−	0.550586i	$-0.185596\pi$
$757$	45.9356	1.66956	0.834778	+	0.550586i	$0.185596\pi$
$758$	4.37227	0.158808
$759$	−5.42054	−0.196753
$760$	6.39836	0.232093
$761$	15.5766	0.564651	0.282326	−	0.959319i	$-0.408894\pi$
$761$	15.5766	0.564651	0.282326	+	0.959319i	$0.408894\pi$
$762$	45.8662	1.66156
$763$	−55.8453	−2.02174
$764$	−2.97208	−0.107526
$765$	−10.0544	−0.363519
$766$	−0.317133	−0.0114585
$767$	−22.3049	−0.805385
$768$	−2.18039	−0.0786781
$769$	−20.0115	−0.721633	−0.360816	−	0.932637i	$-0.617502\pi$
$769$	−20.0115	−0.721633	−0.360816	+	0.932637i	$0.617502\pi$
$770$	25.2946	0.911553
$771$	−44.3039	−1.59556
$772$	22.7101	0.817354
$773$	−20.1280	−0.723956	−0.361978	−	0.932187i	$-0.617898\pi$
$773$	−20.1280	−0.723956	−0.361978	+	0.932187i	$0.617898\pi$
$774$	14.6557	0.526787
$775$	2.57842	0.0926197
$776$	8.72157	0.313086
$777$	74.0483	2.65647
$778$	30.1625	1.08138
$779$	−22.4152	−0.803108
$780$	21.3271	0.763633
$781$	−3.74949	−0.134167
$782$	−2.62885	−0.0940076
$783$	−2.71653	−0.0970809
$784$	14.7756	0.527699
$785$	−32.6013	−1.16359
$786$	−5.61171	−0.200163
$787$	−34.3211	−1.22341	−0.611707	−	0.791084i	$-0.709517\pi$
$787$	−34.3211	−1.22341	−0.611707	+	0.791084i	$0.709517\pi$
$788$	−6.72157	−0.239446
$789$	23.3210	0.830251
$790$	21.1250	0.751593
$791$	41.8676	1.48864
$792$	4.36078	0.154954
$793$	5.98244	0.212443
$794$	16.2187	0.575579
$795$	64.8117	2.29863
$796$	12.9721	0.459783
$797$	−44.2935	−1.56895	−0.784477	−	0.620157i	$-0.787069\pi$
$797$	−44.2935	−1.56895	−0.784477	+	0.620157i	$0.787069\pi$
$798$	−29.8575	−1.05694
$799$	−33.4280	−1.18260
$800$	0.245891	0.00869356
$801$	−21.9226	−0.774597
$802$	−28.4678	−1.00523
$803$	−9.04548	−0.319208
$804$	−1.37115	−0.0483566
$805$	−10.1746	−0.358609
$806$	−47.0408	−1.65694
$807$	41.0942	1.44658
$808$	8.37834	0.294749
$809$	−53.9069	−1.89527	−0.947633	−	0.319361i	$-0.896532\pi$
$809$	−53.9069	−1.89527	−0.947633	+	0.319361i	$0.896532\pi$
$810$	24.3886	0.856929
$811$	−26.4667	−0.929373	−0.464686	−	0.885475i	$-0.653833\pi$
$811$	−26.4667	−0.929373	−0.464686	+	0.885475i	$0.653833\pi$
$812$	−4.66643	−0.163760
$813$	50.8171	1.78223
$814$	−18.0927	−0.634149
$815$	45.4527	1.59214
$816$	5.73193	0.200658
$817$	24.5179	0.857772
$818$	6.48100	0.226603
$819$	−36.7202	−1.28311
$820$	16.6549	0.581616
$821$	50.6812	1.76878	0.884392	−	0.466745i	$-0.154573\pi$
$821$	50.6812	1.76878	0.884392	+	0.466745i	$0.154573\pi$
$822$	10.3533	0.361113
$823$	−1.60023	−0.0557804	−0.0278902	−	0.999611i	$-0.508879\pi$
$823$	−1.60023	−0.0557804	−0.0278902	+	0.999611i	$0.508879\pi$
$824$	17.4080	0.606437
$825$	−1.33286	−0.0464043
$826$	−23.2019	−0.807296
$827$	−32.8078	−1.14084	−0.570420	−	0.821353i	$-0.693220\pi$
$827$	−32.8078	−1.14084	−0.570420	+	0.821353i	$0.693220\pi$
$828$	−1.75411	−0.0609595
$829$	−2.07516	−0.0720731	−0.0360366	−	0.999350i	$-0.511473\pi$
$829$	−2.07516	−0.0720731	−0.0360366	+	0.999350i	$0.511473\pi$
$830$	−17.1575	−0.595546
$831$	−67.5680	−2.34391
$832$	−4.48604	−0.155525
$833$	−38.8428	−1.34582
$834$	34.5991	1.19807
$835$	17.4431	0.603645
$836$	7.29528	0.252313
$837$	−28.4856	−0.984608
$838$	16.7913	0.580046
$839$	−14.7724	−0.509999	−0.254999	−	0.966941i	$-0.582075\pi$
$839$	−14.7724	−0.509999	−0.254999	+	0.966941i	$0.582075\pi$
$840$	22.1847	0.765446
$841$	1.00000	0.0344828
$842$	−9.95996	−0.343243
$843$	21.4091	0.737367
$844$	−11.0773	−0.381297
$845$	15.5343	0.534397
$846$	−22.3049	−0.766860
$847$	−22.4904	−0.772778
$848$	−13.6328	−0.468151
$849$	53.6724	1.84203
$850$	−0.646412	−0.0221717
$851$	7.27773	0.249477
$852$	−3.28851	−0.112662
$853$	24.9148	0.853067	0.426534	−	0.904472i	$-0.359735\pi$
$853$	24.9148	0.853067	0.426534	+	0.904472i	$0.359735\pi$
$854$	6.22301	0.212947
$855$	−11.2234	−0.383833
$856$	−11.8690	−0.405674
$857$	30.4671	1.04074	0.520368	−	0.853942i	$-0.325795\pi$
$857$	30.4671	1.04074	0.520368	+	0.853942i	$0.325795\pi$
$858$	24.3168	0.830160
$859$	16.9632	0.578776	0.289388	−	0.957212i	$-0.406548\pi$
$859$	16.9632	0.578776	0.289388	+	0.957212i	$0.406548\pi$
$860$	−18.2173	−0.621204
$861$	−77.7192	−2.64866
$862$	−23.2770	−0.792818
$863$	34.6640	1.17998	0.589988	−	0.807412i	$-0.299133\pi$
$863$	34.6640	1.17998	0.589988	+	0.807412i	$0.299133\pi$
$864$	−2.71653	−0.0924183
$865$	−36.3378	−1.23552
$866$	−26.8665	−0.912960
$867$	21.9983	0.747100
$868$	−48.9324	−1.66087
$869$	24.0863	0.817071
$870$	−4.75411	−0.161179
$871$	−2.82106	−0.0955880
$872$	11.9675	0.405269
$873$	−15.2986	−0.517778
$874$	−2.93450	−0.0992610
$875$	−53.3751	−1.80441
$876$	−7.93338	−0.268044
$877$	−45.7889	−1.54618	−0.773091	−	0.634295i	$-0.781291\pi$
$877$	−45.7889	−1.54618	−0.773091	+	0.634295i	$0.781291\pi$
$878$	−0.759852	−0.0256438
$879$	−6.43665	−0.217103
$880$	−5.42054	−0.182726
$881$	14.3769	0.484371	0.242186	−	0.970230i	$-0.422136\pi$
$881$	14.3769	0.484371	0.242186	+	0.970230i	$0.422136\pi$
$882$	−25.9180	−0.872704
$883$	−20.2025	−0.679868	−0.339934	−	0.940449i	$-0.610405\pi$
$883$	−20.2025	−0.679868	−0.339934	+	0.940449i	$0.610405\pi$
$884$	11.7931	0.396646
$885$	−23.6378	−0.794576
$886$	−11.6324	−0.390799
$887$	−28.8614	−0.969072	−0.484536	−	0.874771i	$-0.661012\pi$
$887$	−28.8614	−0.969072	−0.484536	+	0.874771i	$0.661012\pi$
$888$	−15.8683	−0.532505
$889$	98.1619	3.29224
$890$	27.2502	0.913430
$891$	27.8074	0.931584
$892$	16.7216	0.559879
$893$	−37.3146	−1.24869
$894$	−0.678953	−0.0227076
$895$	6.72227	0.224701
$896$	−4.66643	−0.155895
$897$	−9.78132	−0.326589
$898$	−10.3293	−0.344692
$899$	10.4860	0.349729
$900$	−0.431320	−0.0143773
$901$	35.8385	1.19396
$902$	18.9896	0.632286
$903$	85.0096	2.82894
$904$	−8.97208	−0.298407
$905$	16.3966	0.545042
$906$	−25.5934	−0.850285
$907$	16.3844	0.544036	0.272018	−	0.962292i	$-0.412309\pi$
$907$	16.3844	0.544036	0.272018	+	0.962292i	$0.412309\pi$
$908$	−21.1285	−0.701173
$909$	−14.6965	−0.487453
$910$	45.6439	1.51308
$911$	−55.0018	−1.82229	−0.911145	−	0.412085i	$-0.864801\pi$
$911$	−55.0018	−1.82229	−0.911145	+	0.412085i	$0.864801\pi$
$912$	6.39836	0.211871
$913$	−19.5626	−0.647429
$914$	−33.6844	−1.11418
$915$	6.33993	0.209592
$916$	7.31284	0.241623
$917$	−12.0101	−0.396608
$918$	7.14136	0.235700
$919$	−30.3952	−1.00264	−0.501322	−	0.865261i	$-0.667153\pi$
$919$	−30.3952	−1.00264	−0.501322	+	0.865261i	$0.667153\pi$
$920$	2.18039	0.0718854
$921$	−52.3575	−1.72524
$922$	−9.27526	−0.305465
$923$	−6.76592	−0.222703
$924$	25.2946	0.832131
$925$	1.78953	0.0588393
$926$	20.6464	0.678483
$927$	−30.5356	−1.00292
$928$	1.00000	0.0328266
$929$	47.6288	1.56265	0.781325	−	0.624125i	$-0.214544\pi$
$929$	47.6288	1.56265	0.781325	+	0.624125i	$0.214544\pi$
$930$	−49.8518	−1.63470
$931$	−43.3590	−1.42103
$932$	4.38408	0.143605
$933$	−20.9206	−0.684908
$934$	−25.1700	−0.823589
$935$	14.2498	0.466018
$936$	7.86900	0.257206
$937$	−24.0945	−0.787132	−0.393566	−	0.919296i	$-0.628759\pi$
$937$	−24.0945	−0.787132	−0.393566	+	0.919296i	$0.628759\pi$
$938$	−2.93450	−0.0958148
$939$	71.9732	2.34876
$940$	27.7255	0.904306
$941$	−24.4284	−0.796344	−0.398172	−	0.917311i	$-0.630355\pi$
$941$	−24.4284	−0.796344	−0.398172	+	0.917311i	$0.630355\pi$
$942$	−32.6013	−1.06221
$943$	−7.63851	−0.248744
$944$	4.97208	0.161827
$945$	27.6397	0.899121
$946$	−20.7710	−0.675322
$947$	7.12413	0.231503	0.115752	−	0.993278i	$-0.463072\pi$
$947$	7.12413	0.231503	0.115752	+	0.993278i	$0.463072\pi$
$948$	21.1250	0.686107
$949$	−16.3225	−0.529851
$950$	−0.721568	−0.0234107
$951$	5.39478	0.174938
$952$	12.2674	0.397588
$953$	−49.1013	−1.59055	−0.795273	−	0.606251i	$-0.792673\pi$
$953$	−49.1013	−1.59055	−0.795273	+	0.606251i	$0.792673\pi$
$954$	23.9134	0.774224
$955$	−6.48030	−0.209697
$956$	2.55370	0.0825925
$957$	−5.42054	−0.175221
$958$	28.1553	0.909658
$959$	22.1579	0.715517
$960$	−4.75411	−0.153438
$961$	78.9570	2.54700
$962$	−32.6482	−1.05262
$963$	20.8195	0.670900
$964$	−30.4538	−0.980852
$965$	49.5169	1.59400
$966$	−10.1746	−0.327364
$967$	8.94807	0.287751	0.143875	−	0.989596i	$-0.454044\pi$
$967$	8.94807	0.287751	0.143875	+	0.989596i	$0.454044\pi$
$968$	4.81961	0.154908
$969$	−16.8204	−0.540348
$970$	19.0164	0.610581
$971$	−16.9606	−0.544291	−0.272146	−	0.962256i	$-0.587733\pi$
$971$	−16.9606	−0.544291	−0.272146	+	0.962256i	$0.587733\pi$
$972$	16.2390	0.520867
$973$	74.0483	2.37388
$974$	11.3855	0.364816
$975$	−2.40514	−0.0770261
$976$	−1.33357	−0.0426865
$977$	−3.42666	−0.109629	−0.0548143	−	0.998497i	$-0.517457\pi$
$977$	−3.42666	−0.109629	−0.0548143	+	0.998497i	$0.517457\pi$
$978$	45.4527	1.45342
$979$	31.0702	0.993007
$980$	32.2166	1.02912
$981$	−20.9922	−0.670230
$982$	31.9728	1.02029
$983$	−14.9517	−0.476885	−0.238442	−	0.971157i	$-0.576637\pi$
$983$	−14.9517	−0.476885	−0.238442	+	0.971157i	$0.576637\pi$
$984$	16.6549	0.530940
$985$	−14.6557	−0.466968
$986$	−2.62885	−0.0837197
$987$	−129.379	−4.11818
$988$	13.1643	0.418812
$989$	8.35504	0.265675
$990$	9.50822	0.302191
$991$	−4.21223	−0.133806	−0.0669029	−	0.997759i	$-0.521312\pi$
$991$	−4.21223	−0.133806	−0.0669029	+	0.997759i	$0.521312\pi$
$992$	10.4860	0.332932
$993$	15.7989	0.501362
$994$	−7.03799	−0.223232
$995$	28.2842	0.896670
$996$	−17.1575	−0.543656
$997$	−6.43418	−0.203773	−0.101886	−	0.994796i	$-0.532488\pi$
$997$	−6.43418	−0.203773	−0.101886	+	0.994796i	$0.532488\pi$
$998$	−23.9248	−0.757328
$999$	−19.7702	−0.625500

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1334.2.a.d.1.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1334.2.a.d.1.1	✓	4	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:	\( N \)	\(=\)	\( 1334 = 2 \cdot 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1334.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.18039 q^{3} +1.00000 q^{4} +2.18039 q^{5} +2.18039 q^{6} +4.66643 q^{7} -1.00000 q^{8} +1.75411 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.18039 q^{3} +1.00000 q^{4} +2.18039 q^{5} +2.18039 q^{6} +4.66643 q^{7} -1.00000 q^{8} +1.75411 q^{9} -2.18039 q^{10} -2.48604 q^{11} -2.18039 q^{12} -4.48604 q^{13} -4.66643 q^{14} -4.75411 q^{15} +1.00000 q^{16} -2.62885 q^{17} -1.75411 q^{18} -2.93450 q^{19} +2.18039 q^{20} -10.1746 q^{21} +2.48604 q^{22} -1.00000 q^{23} +2.18039 q^{24} -0.245891 q^{25} +4.48604 q^{26} +2.71653 q^{27} +4.66643 q^{28} -1.00000 q^{29} +4.75411 q^{30} -10.4860 q^{31} -1.00000 q^{32} +5.42054 q^{33} +2.62885 q^{34} +10.1746 q^{35} +1.75411 q^{36} -7.27773 q^{37} +2.93450 q^{38} +9.78132 q^{39} -2.18039 q^{40} +7.63851 q^{41} +10.1746 q^{42} -8.35504 q^{43} -2.48604 q^{44} +3.82464 q^{45} +1.00000 q^{46} +12.7158 q^{47} -2.18039 q^{48} +14.7756 q^{49} +0.245891 q^{50} +5.73193 q^{51} -4.48604 q^{52} -13.6328 q^{53} -2.71653 q^{54} -5.42054 q^{55} -4.66643 q^{56} +6.39836 q^{57} +1.00000 q^{58} +4.97208 q^{59} -4.75411 q^{60} -1.33357 q^{61} +10.4860 q^{62} +8.18543 q^{63} +1.00000 q^{64} -9.78132 q^{65} -5.42054 q^{66} +0.628853 q^{67} -2.62885 q^{68} +2.18039 q^{69} -10.1746 q^{70} +1.50822 q^{71} -1.75411 q^{72} +3.63851 q^{73} +7.27773 q^{74} +0.536139 q^{75} -2.93450 q^{76} -11.6009 q^{77} -9.78132 q^{78} -9.68861 q^{79} +2.18039 q^{80} -11.1854 q^{81} -7.63851 q^{82} +7.86900 q^{83} -10.1746 q^{84} -5.73193 q^{85} +8.35504 q^{86} +2.18039 q^{87} +2.48604 q^{88} -12.4979 q^{89} -3.82464 q^{90} -20.9338 q^{91} -1.00000 q^{92} +22.8637 q^{93} -12.7158 q^{94} -6.39836 q^{95} +2.18039 q^{96} -8.72157 q^{97} -14.7756 q^{98} -4.36078 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} + q^{3} + 4 q^{4} - q^{5} - q^{6} - 4 q^{8} + 7 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 + q^3 + 4 * q^4 - q^5 - q^6 - 4 * q^8 + 7 * q^9	\( 4 q - 4 q^{2} + q^{3} + 4 q^{4} - q^{5} - q^{6} - 4 q^{8} + 7 q^{9} + q^{10} - q^{11} + q^{12} - 9 q^{13} - 19 q^{15} + 4 q^{16} - 7 q^{18} - 2 q^{19} - q^{20} - 22 q^{21} + q^{22} - 4 q^{23} - q^{24} - q^{25} + 9 q^{26} + 19 q^{27} - 4 q^{29} + 19 q^{30} - 33 q^{31} - 4 q^{32} + 3 q^{33} + 22 q^{35} + 7 q^{36} - 12 q^{37} + 2 q^{38} + q^{39} + q^{40} - 6 q^{41} + 22 q^{42} - 5 q^{43} - q^{44} - 22 q^{45} + 4 q^{46} + 3 q^{47} + q^{48} + 12 q^{49} + q^{50} + 14 q^{51} - 9 q^{52} - 9 q^{53} - 19 q^{54} - 3 q^{55} - 2 q^{57} + 4 q^{58} + 2 q^{59} - 19 q^{60} - 24 q^{61} + 33 q^{62} - 24 q^{63} + 4 q^{64} - q^{65} - 3 q^{66} - 8 q^{67} - q^{69} - 22 q^{70} + 6 q^{71} - 7 q^{72} - 22 q^{73} + 12 q^{74} + 20 q^{75} - 2 q^{76} - 18 q^{77} - q^{78} - 29 q^{79} - q^{80} + 12 q^{81} + 6 q^{82} + 12 q^{83} - 22 q^{84} - 14 q^{85} + 5 q^{86} - q^{87} + q^{88} - 20 q^{89} + 22 q^{90} - 18 q^{91} - 4 q^{92} - 5 q^{93} - 3 q^{94} + 2 q^{95} - q^{96} + 4 q^{97} - 12 q^{98} + 2 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 + q^3 + 4 * q^4 - q^5 - q^6 - 4 * q^8 + 7 * q^9 + q^10 - q^11 + q^12 - 9 * q^13 - 19 * q^15 + 4 * q^16 - 7 * q^18 - 2 * q^19 - q^20 - 22 * q^21 + q^22 - 4 * q^23 - q^24 - q^25 + 9 * q^26 + 19 * q^27 - 4 * q^29 + 19 * q^30 - 33 * q^31 - 4 * q^32 + 3 * q^33 + 22 * q^35 + 7 * q^36 - 12 * q^37 + 2 * q^38 + q^39 + q^40 - 6 * q^41 + 22 * q^42 - 5 * q^43 - q^44 - 22 * q^45 + 4 * q^46 + 3 * q^47 + q^48 + 12 * q^49 + q^50 + 14 * q^51 - 9 * q^52 - 9 * q^53 - 19 * q^54 - 3 * q^55 - 2 * q^57 + 4 * q^58 + 2 * q^59 - 19 * q^60 - 24 * q^61 + 33 * q^62 - 24 * q^63 + 4 * q^64 - q^65 - 3 * q^66 - 8 * q^67 - q^69 - 22 * q^70 + 6 * q^71 - 7 * q^72 - 22 * q^73 + 12 * q^74 + 20 * q^75 - 2 * q^76 - 18 * q^77 - q^78 - 29 * q^79 - q^80 + 12 * q^81 + 6 * q^82 + 12 * q^83 - 22 * q^84 - 14 * q^85 + 5 * q^86 - q^87 + q^88 - 20 * q^89 + 22 * q^90 - 18 * q^91 - 4 * q^92 - 5 * q^93 - 3 * q^94 + 2 * q^95 - q^96 + 4 * q^97 - 12 * q^98 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more