LMFDB - Embedded newform 6026.2.a.e.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6026,2,Mod(1,6026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6026, 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("6026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6026 = 2 \cdot 23 \cdot 131 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6026.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:	$48.1178522580$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{12})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 3 $ x^2 - 3
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.73205$ of defining polynomial
Character	$\chi$	$=$	6026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +2.73205 q^{3} +1.00000 q^{4} +1.73205 q^{5} +2.73205 q^{6} +2.00000 q^{7} +1.00000 q^{8} +4.46410 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +2.73205 q^{3} +1.00000 q^{4} +1.73205 q^{5} +2.73205 q^{6} +2.00000 q^{7} +1.00000 q^{8} +4.46410 q^{9} +1.73205 q^{10} +1.73205 q^{11} +2.73205 q^{12} -2.73205 q^{13} +2.00000 q^{14} +4.73205 q^{15} +1.00000 q^{16} -1.73205 q^{17} +4.46410 q^{18} +3.26795 q^{19} +1.73205 q^{20} +5.46410 q^{21} +1.73205 q^{22} -1.00000 q^{23} +2.73205 q^{24} -2.00000 q^{25} -2.73205 q^{26} +4.00000 q^{27} +2.00000 q^{28} -2.53590 q^{29} +4.73205 q^{30} +8.00000 q^{31} +1.00000 q^{32} +4.73205 q^{33} -1.73205 q^{34} +3.46410 q^{35} +4.46410 q^{36} -7.46410 q^{37} +3.26795 q^{38} -7.46410 q^{39} +1.73205 q^{40} +6.46410 q^{41} +5.46410 q^{42} +1.19615 q^{43} +1.73205 q^{44} +7.73205 q^{45} -1.00000 q^{46} -5.66025 q^{47} +2.73205 q^{48} -3.00000 q^{49} -2.00000 q^{50} -4.73205 q^{51} -2.73205 q^{52} +3.46410 q^{53} +4.00000 q^{54} +3.00000 q^{55} +2.00000 q^{56} +8.92820 q^{57} -2.53590 q^{58} +10.7321 q^{59} +4.73205 q^{60} +7.19615 q^{61} +8.00000 q^{62} +8.92820 q^{63} +1.00000 q^{64} -4.73205 q^{65} +4.73205 q^{66} -13.1244 q^{67} -1.73205 q^{68} -2.73205 q^{69} +3.46410 q^{70} +10.7321 q^{71} +4.46410 q^{72} -6.19615 q^{73} -7.46410 q^{74} -5.46410 q^{75} +3.26795 q^{76} +3.46410 q^{77} -7.46410 q^{78} -13.4641 q^{79} +1.73205 q^{80} -2.46410 q^{81} +6.46410 q^{82} +8.19615 q^{83} +5.46410 q^{84} -3.00000 q^{85} +1.19615 q^{86} -6.92820 q^{87} +1.73205 q^{88} +2.53590 q^{89} +7.73205 q^{90} -5.46410 q^{91} -1.00000 q^{92} +21.8564 q^{93} -5.66025 q^{94} +5.66025 q^{95} +2.73205 q^{96} -7.46410 q^{97} -3.00000 q^{98} +7.73205 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + 2 q^{6} + 4 q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + 2 * q^6 + 4 * q^7 + 2 * q^8 + 2 * q^9	$ 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + 2 q^{6} + 4 q^{7} + 2 q^{8} + 2 q^{9} + 2 q^{12} - 2 q^{13} + 4 q^{14} + 6 q^{15} + 2 q^{16} + 2 q^{18} + 10 q^{19} + 4 q^{21} - 2 q^{23} + 2 q^{24} - 4 q^{25} - 2 q^{26} + 8 q^{27} + 4 q^{28} - 12 q^{29} + 6 q^{30} + 16 q^{31} + 2 q^{32} + 6 q^{33} + 2 q^{36} - 8 q^{37} + 10 q^{38} - 8 q^{39} + 6 q^{41} + 4 q^{42} - 8 q^{43} + 12 q^{45} - 2 q^{46} + 6 q^{47} + 2 q^{48} - 6 q^{49} - 4 q^{50} - 6 q^{51} - 2 q^{52} + 8 q^{54} + 6 q^{55} + 4 q^{56} + 4 q^{57} - 12 q^{58} + 18 q^{59} + 6 q^{60} + 4 q^{61} + 16 q^{62} + 4 q^{63} + 2 q^{64} - 6 q^{65} + 6 q^{66} - 2 q^{67} - 2 q^{69} + 18 q^{71} + 2 q^{72} - 2 q^{73} - 8 q^{74} - 4 q^{75} + 10 q^{76} - 8 q^{78} - 20 q^{79} + 2 q^{81} + 6 q^{82} + 6 q^{83} + 4 q^{84} - 6 q^{85} - 8 q^{86} + 12 q^{89} + 12 q^{90} - 4 q^{91} - 2 q^{92} + 16 q^{93} + 6 q^{94} - 6 q^{95} + 2 q^{96} - 8 q^{97} - 6 q^{98} + 12 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + 2 * q^6 + 4 * q^7 + 2 * q^8 + 2 * q^9 + 2 * q^12 - 2 * q^13 + 4 * q^14 + 6 * q^15 + 2 * q^16 + 2 * q^18 + 10 * q^19 + 4 * q^21 - 2 * q^23 + 2 * q^24 - 4 * q^25 - 2 * q^26 + 8 * q^27 + 4 * q^28 - 12 * q^29 + 6 * q^30 + 16 * q^31 + 2 * q^32 + 6 * q^33 + 2 * q^36 - 8 * q^37 + 10 * q^38 - 8 * q^39 + 6 * q^41 + 4 * q^42 - 8 * q^43 + 12 * q^45 - 2 * q^46 + 6 * q^47 + 2 * q^48 - 6 * q^49 - 4 * q^50 - 6 * q^51 - 2 * q^52 + 8 * q^54 + 6 * q^55 + 4 * q^56 + 4 * q^57 - 12 * q^58 + 18 * q^59 + 6 * q^60 + 4 * q^61 + 16 * q^62 + 4 * q^63 + 2 * q^64 - 6 * q^65 + 6 * q^66 - 2 * q^67 - 2 * q^69 + 18 * q^71 + 2 * q^72 - 2 * q^73 - 8 * q^74 - 4 * q^75 + 10 * q^76 - 8 * q^78 - 20 * q^79 + 2 * q^81 + 6 * q^82 + 6 * q^83 + 4 * q^84 - 6 * q^85 - 8 * q^86 + 12 * q^89 + 12 * q^90 - 4 * q^91 - 2 * q^92 + 16 * q^93 + 6 * q^94 - 6 * q^95 + 2 * q^96 - 8 * q^97 - 6 * q^98 + 12 * 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
$3$	2.73205	1.57735	0.788675	−	0.614810i	$-0.210767\pi$
$3$	2.73205	1.57735	0.788675	+	0.614810i	$0.210767\pi$
$4$	1.00000	0.500000
$5$	1.73205	0.774597	0.387298	−	0.921954i	$-0.373408\pi$
$5$	1.73205	0.774597	0.387298	+	0.921954i	$0.373408\pi$
$6$	2.73205	1.11536
$7$	2.00000	0.755929	0.377964	−	0.925820i	$-0.376624\pi$
$7$	2.00000	0.755929	0.377964	+	0.925820i	$0.376624\pi$
$8$	1.00000	0.353553
$9$	4.46410	1.48803
$10$	1.73205	0.547723
$11$	1.73205	0.522233	0.261116	−	0.965307i	$-0.415909\pi$
$11$	1.73205	0.522233	0.261116	+	0.965307i	$0.415909\pi$
$12$	2.73205	0.788675
$13$	−2.73205	−0.757735	−0.378867	−	0.925451i	$-0.623686\pi$
$13$	−2.73205	−0.757735	−0.378867	+	0.925451i	$0.623686\pi$
$14$	2.00000	0.534522
$15$	4.73205	1.22181
$16$	1.00000	0.250000
$17$	−1.73205	−0.420084	−0.210042	−	0.977692i	$-0.567360\pi$
$17$	−1.73205	−0.420084	−0.210042	+	0.977692i	$0.567360\pi$
$18$	4.46410	1.05220
$19$	3.26795	0.749719	0.374859	−	0.927082i	$-0.377691\pi$
$19$	3.26795	0.749719	0.374859	+	0.927082i	$0.377691\pi$
$20$	1.73205	0.387298
$21$	5.46410	1.19236
$22$	1.73205	0.369274
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	2.73205	0.557678
$25$	−2.00000	−0.400000
$26$	−2.73205	−0.535799
$27$	4.00000	0.769800
$28$	2.00000	0.377964
$29$	−2.53590	−0.470905	−0.235452	−	0.971886i	$-0.575657\pi$
$29$	−2.53590	−0.470905	−0.235452	+	0.971886i	$0.575657\pi$
$30$	4.73205	0.863950
$31$	8.00000	1.43684	0.718421	−	0.695608i	$-0.244865\pi$
$31$	8.00000	1.43684	0.718421	+	0.695608i	$0.244865\pi$
$32$	1.00000	0.176777
$33$	4.73205	0.823744
$34$	−1.73205	−0.297044
$35$	3.46410	0.585540
$36$	4.46410	0.744017
$37$	−7.46410	−1.22709	−0.613545	−	0.789659i	$-0.710257\pi$
$37$	−7.46410	−1.22709	−0.613545	+	0.789659i	$0.710257\pi$
$38$	3.26795	0.530131
$39$	−7.46410	−1.19521
$40$	1.73205	0.273861
$41$	6.46410	1.00952	0.504762	−	0.863259i	$-0.331580\pi$
$41$	6.46410	1.00952	0.504762	+	0.863259i	$0.331580\pi$
$42$	5.46410	0.843129
$43$	1.19615	0.182412	0.0912058	−	0.995832i	$-0.470928\pi$
$43$	1.19615	0.182412	0.0912058	+	0.995832i	$0.470928\pi$
$44$	1.73205	0.261116
$45$	7.73205	1.15263
$46$	−1.00000	−0.147442
$47$	−5.66025	−0.825633	−0.412816	−	0.910814i	$-0.635455\pi$
$47$	−5.66025	−0.825633	−0.412816	+	0.910814i	$0.635455\pi$
$48$	2.73205	0.394338
$49$	−3.00000	−0.428571
$50$	−2.00000	−0.282843
$51$	−4.73205	−0.662620
$52$	−2.73205	−0.378867
$53$	3.46410	0.475831	0.237915	−	0.971286i	$-0.423536\pi$
$53$	3.46410	0.475831	0.237915	+	0.971286i	$0.423536\pi$
$54$	4.00000	0.544331
$55$	3.00000	0.404520
$56$	2.00000	0.267261
$57$	8.92820	1.18257
$58$	−2.53590	−0.332980
$59$	10.7321	1.39719	0.698597	−	0.715515i	$-0.253808\pi$
$59$	10.7321	1.39719	0.698597	+	0.715515i	$0.253808\pi$
$60$	4.73205	0.610905
$61$	7.19615	0.921373	0.460686	−	0.887563i	$-0.347603\pi$
$61$	7.19615	0.921373	0.460686	+	0.887563i	$0.347603\pi$
$62$	8.00000	1.01600
$63$	8.92820	1.12485
$64$	1.00000	0.125000
$65$	−4.73205	−0.586939
$66$	4.73205	0.582475
$67$	−13.1244	−1.60340	−0.801698	−	0.597730i	$-0.796070\pi$
$67$	−13.1244	−1.60340	−0.801698	+	0.597730i	$0.796070\pi$
$68$	−1.73205	−0.210042
$69$	−2.73205	−0.328900
$70$	3.46410	0.414039
$71$	10.7321	1.27366	0.636830	−	0.771004i	$-0.280245\pi$
$71$	10.7321	1.27366	0.636830	+	0.771004i	$0.280245\pi$
$72$	4.46410	0.526099
$73$	−6.19615	−0.725205	−0.362602	−	0.931944i	$-0.618112\pi$
$73$	−6.19615	−0.725205	−0.362602	+	0.931944i	$0.618112\pi$
$74$	−7.46410	−0.867684
$75$	−5.46410	−0.630940
$76$	3.26795	0.374859
$77$	3.46410	0.394771
$78$	−7.46410	−0.845143
$79$	−13.4641	−1.51483	−0.757415	−	0.652934i	$-0.773538\pi$
$79$	−13.4641	−1.51483	−0.757415	+	0.652934i	$0.773538\pi$
$80$	1.73205	0.193649
$81$	−2.46410	−0.273789
$82$	6.46410	0.713841
$83$	8.19615	0.899645	0.449822	−	0.893118i	$-0.351487\pi$
$83$	8.19615	0.899645	0.449822	+	0.893118i	$0.351487\pi$
$84$	5.46410	0.596182
$85$	−3.00000	−0.325396
$86$	1.19615	0.128984
$87$	−6.92820	−0.742781
$88$	1.73205	0.184637
$89$	2.53590	0.268805	0.134402	−	0.990927i	$-0.457089\pi$
$89$	2.53590	0.268805	0.134402	+	0.990927i	$0.457089\pi$
$90$	7.73205	0.815030
$91$	−5.46410	−0.572793
$92$	−1.00000	−0.104257
$93$	21.8564	2.26640
$94$	−5.66025	−0.583811
$95$	5.66025	0.580730
$96$	2.73205	0.278839
$97$	−7.46410	−0.757865	−0.378932	−	0.925424i	$-0.623709\pi$
$97$	−7.46410	−0.757865	−0.378932	+	0.925424i	$0.623709\pi$
$98$	−3.00000	−0.303046
$99$	7.73205	0.777100
$100$	−2.00000	−0.200000
$101$	−2.53590	−0.252331	−0.126166	−	0.992009i	$-0.540267\pi$
$101$	−2.53590	−0.252331	−0.126166	+	0.992009i	$0.540267\pi$
$102$	−4.73205	−0.468543
$103$	9.73205	0.958927	0.479464	−	0.877562i	$-0.340831\pi$
$103$	9.73205	0.958927	0.479464	+	0.877562i	$0.340831\pi$
$104$	−2.73205	−0.267900
$105$	9.46410	0.923602
$106$	3.46410	0.336463
$107$	4.26795	0.412598	0.206299	−	0.978489i	$-0.433858\pi$
$107$	4.26795	0.412598	0.206299	+	0.978489i	$0.433858\pi$
$108$	4.00000	0.384900
$109$	−9.19615	−0.880832	−0.440416	−	0.897794i	$-0.645169\pi$
$109$	−9.19615	−0.880832	−0.440416	+	0.897794i	$0.645169\pi$
$110$	3.00000	0.286039
$111$	−20.3923	−1.93555
$112$	2.00000	0.188982
$113$	−8.19615	−0.771029	−0.385515	−	0.922702i	$-0.625976\pi$
$113$	−8.19615	−0.771029	−0.385515	+	0.922702i	$0.625976\pi$
$114$	8.92820	0.836203
$115$	−1.73205	−0.161515
$116$	−2.53590	−0.235452
$117$	−12.1962	−1.12753
$118$	10.7321	0.987965
$119$	−3.46410	−0.317554
$120$	4.73205	0.431975
$121$	−8.00000	−0.727273
$122$	7.19615	0.651509
$123$	17.6603	1.59237
$124$	8.00000	0.718421
$125$	−12.1244	−1.08444
$126$	8.92820	0.795388
$127$	5.80385	0.515008	0.257504	−	0.966277i	$-0.417100\pi$
$127$	5.80385	0.515008	0.257504	+	0.966277i	$0.417100\pi$
$128$	1.00000	0.0883883
$129$	3.26795	0.287727
$130$	−4.73205	−0.415028
$131$	−1.00000	−0.0873704
$131$	−1.00000	−0.0873704
$132$	4.73205	0.411872
$133$	6.53590	0.566734
$134$	−13.1244	−1.13377
$135$	6.92820	0.596285
$136$	−1.73205	−0.148522
$137$	−18.1244	−1.54847	−0.774234	−	0.632899i	$-0.781865\pi$
$137$	−18.1244	−1.54847	−0.774234	+	0.632899i	$0.781865\pi$
$138$	−2.73205	−0.232568
$139$	17.0000	1.44192	0.720961	−	0.692976i	$-0.243701\pi$
$139$	17.0000	1.44192	0.720961	+	0.692976i	$0.243701\pi$
$140$	3.46410	0.292770
$141$	−15.4641	−1.30231
$142$	10.7321	0.900614
$143$	−4.73205	−0.395714
$144$	4.46410	0.372008
$145$	−4.39230	−0.364761
$146$	−6.19615	−0.512797
$147$	−8.19615	−0.676007
$148$	−7.46410	−0.613545
$149$	14.1962	1.16299	0.581497	−	0.813549i	$-0.302467\pi$
$149$	14.1962	1.16299	0.581497	+	0.813549i	$0.302467\pi$
$150$	−5.46410	−0.446142
$151$	2.46410	0.200526	0.100263	−	0.994961i	$-0.468032\pi$
$151$	2.46410	0.200526	0.100263	+	0.994961i	$0.468032\pi$
$152$	3.26795	0.265066
$153$	−7.73205	−0.625099
$154$	3.46410	0.279145
$155$	13.8564	1.11297
$156$	−7.46410	−0.597606
$157$	14.0000	1.11732	0.558661	−	0.829396i	$-0.311315\pi$
$157$	14.0000	1.11732	0.558661	+	0.829396i	$0.311315\pi$
$158$	−13.4641	−1.07115
$159$	9.46410	0.750552
$160$	1.73205	0.136931
$161$	−2.00000	−0.157622
$162$	−2.46410	−0.193598
$163$	14.4641	1.13292	0.566458	−	0.824091i	$-0.308313\pi$
$163$	14.4641	1.13292	0.566458	+	0.824091i	$0.308313\pi$
$164$	6.46410	0.504762
$165$	8.19615	0.638070
$166$	8.19615	0.636145
$167$	−16.8564	−1.30439	−0.652194	−	0.758052i	$-0.726151\pi$
$167$	−16.8564	−1.30439	−0.652194	+	0.758052i	$0.726151\pi$
$168$	5.46410	0.421565
$169$	−5.53590	−0.425838
$170$	−3.00000	−0.230089
$171$	14.5885	1.11561
$172$	1.19615	0.0912058
$173$	−19.3923	−1.47437	−0.737185	−	0.675691i	$-0.763845\pi$
$173$	−19.3923	−1.47437	−0.737185	+	0.675691i	$0.763845\pi$
$174$	−6.92820	−0.525226
$175$	−4.00000	−0.302372
$176$	1.73205	0.130558
$177$	29.3205	2.20386
$178$	2.53590	0.190074
$179$	−6.92820	−0.517838	−0.258919	−	0.965899i	$-0.583366\pi$
$179$	−6.92820	−0.517838	−0.258919	+	0.965899i	$0.583366\pi$
$180$	7.73205	0.576313
$181$	17.4641	1.29810	0.649048	−	0.760747i	$-0.275167\pi$
$181$	17.4641	1.29810	0.649048	+	0.760747i	$0.275167\pi$
$182$	−5.46410	−0.405026
$183$	19.6603	1.45333
$184$	−1.00000	−0.0737210
$185$	−12.9282	−0.950500
$186$	21.8564	1.60259
$187$	−3.00000	−0.219382
$188$	−5.66025	−0.412816
$189$	8.00000	0.581914
$190$	5.66025	0.410638
$191$	−25.5167	−1.84632	−0.923160	−	0.384415i	$-0.874403\pi$
$191$	−25.5167	−1.84632	−0.923160	+	0.384415i	$0.874403\pi$
$192$	2.73205	0.197169
$193$	−24.3205	−1.75063	−0.875314	−	0.483555i	$-0.839345\pi$
$193$	−24.3205	−1.75063	−0.875314	+	0.483555i	$0.839345\pi$
$194$	−7.46410	−0.535891
$195$	−12.9282	−0.925808
$196$	−3.00000	−0.214286
$197$	−21.0000	−1.49619	−0.748094	−	0.663593i	$-0.769031\pi$
$197$	−21.0000	−1.49619	−0.748094	+	0.663593i	$0.769031\pi$
$198$	7.73205	0.549493
$199$	21.7321	1.54054	0.770272	−	0.637715i	$-0.220120\pi$
$199$	21.7321	1.54054	0.770272	+	0.637715i	$0.220120\pi$
$200$	−2.00000	−0.141421
$201$	−35.8564	−2.52912
$202$	−2.53590	−0.178425
$203$	−5.07180	−0.355970
$204$	−4.73205	−0.331310
$205$	11.1962	0.781973
$206$	9.73205	0.678064
$207$	−4.46410	−0.310277
$208$	−2.73205	−0.189434
$209$	5.66025	0.391528
$210$	9.46410	0.653085
$211$	−26.0526	−1.79353	−0.896766	−	0.442505i	$-0.854090\pi$
$211$	−26.0526	−1.79353	−0.896766	+	0.442505i	$0.854090\pi$
$212$	3.46410	0.237915
$213$	29.3205	2.00901
$214$	4.26795	0.291751
$215$	2.07180	0.141295
$216$	4.00000	0.272166
$217$	16.0000	1.08615
$218$	−9.19615	−0.622842
$219$	−16.9282	−1.14390
$220$	3.00000	0.202260
$221$	4.73205	0.318312
$222$	−20.3923	−1.36864
$223$	26.0000	1.74109	0.870544	−	0.492090i	$-0.163767\pi$
$223$	26.0000	1.74109	0.870544	+	0.492090i	$0.163767\pi$
$224$	2.00000	0.133631
$225$	−8.92820	−0.595214
$226$	−8.19615	−0.545200
$227$	−6.00000	−0.398234	−0.199117	−	0.979976i	$-0.563807\pi$
$227$	−6.00000	−0.398234	−0.199117	+	0.979976i	$0.563807\pi$
$228$	8.92820	0.591285
$229$	−12.7846	−0.844831	−0.422415	−	0.906402i	$-0.638818\pi$
$229$	−12.7846	−0.844831	−0.422415	+	0.906402i	$0.638818\pi$
$230$	−1.73205	−0.114208
$231$	9.46410	0.622692
$232$	−2.53590	−0.166490
$233$	−7.39230	−0.484286	−0.242143	−	0.970241i	$-0.577850\pi$
$233$	−7.39230	−0.484286	−0.242143	+	0.970241i	$0.577850\pi$
$234$	−12.1962	−0.797287
$235$	−9.80385	−0.639532
$236$	10.7321	0.698597
$237$	−36.7846	−2.38942
$238$	−3.46410	−0.224544
$239$	10.3923	0.672222	0.336111	−	0.941822i	$-0.390888\pi$
$239$	10.3923	0.672222	0.336111	+	0.941822i	$0.390888\pi$
$240$	4.73205	0.305453
$241$	−5.73205	−0.369234	−0.184617	−	0.982811i	$-0.559104\pi$
$241$	−5.73205	−0.369234	−0.184617	+	0.982811i	$0.559104\pi$
$242$	−8.00000	−0.514259
$243$	−18.7321	−1.20166
$244$	7.19615	0.460686
$245$	−5.19615	−0.331970
$246$	17.6603	1.12598
$247$	−8.92820	−0.568088
$248$	8.00000	0.508001
$249$	22.3923	1.41905
$250$	−12.1244	−0.766812
$251$	31.5167	1.98931	0.994657	−	0.103235i	$-0.0329194\pi$
$251$	31.5167	1.98931	0.994657	+	0.103235i	$0.0329194\pi$
$252$	8.92820	0.562424
$253$	−1.73205	−0.108893
$254$	5.80385	0.364166
$255$	−8.19615	−0.513263
$256$	1.00000	0.0625000
$257$	11.3205	0.706154	0.353077	−	0.935594i	$-0.385135\pi$
$257$	11.3205	0.706154	0.353077	+	0.935594i	$0.385135\pi$
$258$	3.26795	0.203454
$259$	−14.9282	−0.927593
$260$	−4.73205	−0.293469
$261$	−11.3205	−0.700722
$262$	−1.00000	−0.0617802
$263$	−2.87564	−0.177320	−0.0886599	−	0.996062i	$-0.528258\pi$
$263$	−2.87564	−0.177320	−0.0886599	+	0.996062i	$0.528258\pi$
$264$	4.73205	0.291238
$265$	6.00000	0.368577
$266$	6.53590	0.400742
$267$	6.92820	0.423999
$268$	−13.1244	−0.801698
$269$	−20.1962	−1.23138	−0.615691	−	0.787988i	$-0.711123\pi$
$269$	−20.1962	−1.23138	−0.615691	+	0.787988i	$0.711123\pi$
$270$	6.92820	0.421637
$271$	26.4641	1.60758	0.803790	−	0.594913i	$-0.202814\pi$
$271$	26.4641	1.60758	0.803790	+	0.594913i	$0.202814\pi$
$272$	−1.73205	−0.105021
$273$	−14.9282	−0.903496
$274$	−18.1244	−1.09493
$275$	−3.46410	−0.208893
$276$	−2.73205	−0.164450
$277$	−14.3923	−0.864750	−0.432375	−	0.901694i	$-0.642324\pi$
$277$	−14.3923	−0.864750	−0.432375	+	0.901694i	$0.642324\pi$
$278$	17.0000	1.01959
$279$	35.7128	2.13807
$280$	3.46410	0.207020
$281$	21.5885	1.28786	0.643930	−	0.765085i	$-0.277303\pi$
$281$	21.5885	1.28786	0.643930	+	0.765085i	$0.277303\pi$
$282$	−15.4641	−0.920874
$283$	−2.39230	−0.142208	−0.0711039	−	0.997469i	$-0.522652\pi$
$283$	−2.39230	−0.142208	−0.0711039	+	0.997469i	$0.522652\pi$
$284$	10.7321	0.636830
$285$	15.4641	0.916014
$286$	−4.73205	−0.279812
$287$	12.9282	0.763128
$288$	4.46410	0.263050
$289$	−14.0000	−0.823529
$290$	−4.39230	−0.257925
$291$	−20.3923	−1.19542
$292$	−6.19615	−0.362602
$293$	−0.339746	−0.0198482	−0.00992409	−	0.999951i	$-0.503159\pi$
$293$	−0.339746	−0.0198482	−0.00992409	+	0.999951i	$0.503159\pi$
$294$	−8.19615	−0.478009
$295$	18.5885	1.08226
$296$	−7.46410	−0.433842
$297$	6.92820	0.402015
$298$	14.1962	0.822361
$299$	2.73205	0.157999
$300$	−5.46410	−0.315470
$301$	2.39230	0.137890
$302$	2.46410	0.141793
$303$	−6.92820	−0.398015
$304$	3.26795	0.187430
$305$	12.4641	0.713692
$306$	−7.73205	−0.442012
$307$	−12.1962	−0.696071	−0.348036	−	0.937481i	$-0.613151\pi$
$307$	−12.1962	−0.696071	−0.348036	+	0.937481i	$0.613151\pi$
$308$	3.46410	0.197386
$309$	26.5885	1.51256
$310$	13.8564	0.786991
$311$	9.00000	0.510343	0.255172	−	0.966896i	$-0.417868\pi$
$311$	9.00000	0.510343	0.255172	+	0.966896i	$0.417868\pi$
$312$	−7.46410	−0.422572
$313$	−4.92820	−0.278559	−0.139279	−	0.990253i	$-0.544479\pi$
$313$	−4.92820	−0.278559	−0.139279	+	0.990253i	$0.544479\pi$
$314$	14.0000	0.790066
$315$	15.4641	0.871303
$316$	−13.4641	−0.757415
$317$	−14.1962	−0.797335	−0.398668	−	0.917095i	$-0.630527\pi$
$317$	−14.1962	−0.797335	−0.398668	+	0.917095i	$0.630527\pi$
$318$	9.46410	0.530720
$319$	−4.39230	−0.245922
$320$	1.73205	0.0968246
$321$	11.6603	0.650812
$322$	−2.00000	−0.111456
$323$	−5.66025	−0.314945
$324$	−2.46410	−0.136895
$325$	5.46410	0.303094
$326$	14.4641	0.801092
$327$	−25.1244	−1.38938
$328$	6.46410	0.356920
$329$	−11.3205	−0.624120
$330$	8.19615	0.451183
$331$	6.39230	0.351353	0.175676	−	0.984448i	$-0.443789\pi$
$331$	6.39230	0.351353	0.175676	+	0.984448i	$0.443789\pi$
$332$	8.19615	0.449822
$333$	−33.3205	−1.82595
$334$	−16.8564	−0.922342
$335$	−22.7321	−1.24198
$336$	5.46410	0.298091
$337$	−0.196152	−0.0106851	−0.00534255	−	0.999986i	$-0.501701\pi$
$337$	−0.196152	−0.0106851	−0.00534255	+	0.999986i	$0.501701\pi$
$338$	−5.53590	−0.301113
$339$	−22.3923	−1.21618
$340$	−3.00000	−0.162698
$341$	13.8564	0.750366
$342$	14.5885	0.788853
$343$	−20.0000	−1.07990
$344$	1.19615	0.0644922
$345$	−4.73205	−0.254765
$346$	−19.3923	−1.04254
$347$	−10.8564	−0.582802	−0.291401	−	0.956601i	$-0.594121\pi$
$347$	−10.8564	−0.582802	−0.291401	+	0.956601i	$0.594121\pi$
$348$	−6.92820	−0.371391
$349$	33.8564	1.81229	0.906146	−	0.422965i	$-0.139011\pi$
$349$	33.8564	1.81229	0.906146	+	0.422965i	$0.139011\pi$
$350$	−4.00000	−0.213809
$351$	−10.9282	−0.583304
$352$	1.73205	0.0923186
$353$	26.3205	1.40090	0.700450	−	0.713702i	$-0.252983\pi$
$353$	26.3205	1.40090	0.700450	+	0.713702i	$0.252983\pi$
$354$	29.3205	1.55837
$355$	18.5885	0.986573
$356$	2.53590	0.134402
$357$	−9.46410	−0.500893
$358$	−6.92820	−0.366167
$359$	27.5885	1.45606	0.728032	−	0.685544i	$-0.240435\pi$
$359$	27.5885	1.45606	0.728032	+	0.685544i	$0.240435\pi$
$360$	7.73205	0.407515
$361$	−8.32051	−0.437921
$362$	17.4641	0.917893
$363$	−21.8564	−1.14716
$364$	−5.46410	−0.286397
$365$	−10.7321	−0.561741
$366$	19.6603	1.02766
$367$	−34.5885	−1.80550	−0.902751	−	0.430163i	$-0.858456\pi$
$367$	−34.5885	−1.80550	−0.902751	+	0.430163i	$0.858456\pi$
$368$	−1.00000	−0.0521286
$369$	28.8564	1.50220
$370$	−12.9282	−0.672105
$371$	6.92820	0.359694
$372$	21.8564	1.13320
$373$	18.0526	0.934726	0.467363	−	0.884065i	$-0.345204\pi$
$373$	18.0526	0.934726	0.467363	+	0.884065i	$0.345204\pi$
$374$	−3.00000	−0.155126
$375$	−33.1244	−1.71053
$376$	−5.66025	−0.291905
$377$	6.92820	0.356821
$378$	8.00000	0.411476
$379$	8.12436	0.417320	0.208660	−	0.977988i	$-0.433090\pi$
$379$	8.12436	0.417320	0.208660	+	0.977988i	$0.433090\pi$
$380$	5.66025	0.290365
$381$	15.8564	0.812348
$382$	−25.5167	−1.30555
$383$	−1.60770	−0.0821494	−0.0410747	−	0.999156i	$-0.513078\pi$
$383$	−1.60770	−0.0821494	−0.0410747	+	0.999156i	$0.513078\pi$
$384$	2.73205	0.139419
$385$	6.00000	0.305788
$386$	−24.3205	−1.23788
$387$	5.33975	0.271435
$388$	−7.46410	−0.378932
$389$	−13.2679	−0.672712	−0.336356	−	0.941735i	$-0.609194\pi$
$389$	−13.2679	−0.672712	−0.336356	+	0.941735i	$0.609194\pi$
$390$	−12.9282	−0.654645
$391$	1.73205	0.0875936
$392$	−3.00000	−0.151523
$393$	−2.73205	−0.137814
$394$	−21.0000	−1.05796
$395$	−23.3205	−1.17338
$396$	7.73205	0.388550
$397$	10.1962	0.511730	0.255865	−	0.966712i	$-0.417640\pi$
$397$	10.1962	0.511730	0.255865	+	0.966712i	$0.417640\pi$
$398$	21.7321	1.08933
$399$	17.8564	0.893938
$400$	−2.00000	−0.100000
$401$	−39.7128	−1.98316	−0.991582	−	0.129483i	$-0.958668\pi$
$401$	−39.7128	−1.98316	−0.991582	+	0.129483i	$0.958668\pi$
$402$	−35.8564	−1.78836
$403$	−21.8564	−1.08875
$404$	−2.53590	−0.126166
$405$	−4.26795	−0.212076
$406$	−5.07180	−0.251709
$407$	−12.9282	−0.640827
$408$	−4.73205	−0.234271
$409$	−13.2487	−0.655107	−0.327553	−	0.944833i	$-0.606224\pi$
$409$	−13.2487	−0.655107	−0.327553	+	0.944833i	$0.606224\pi$
$410$	11.1962	0.552939
$411$	−49.5167	−2.44248
$412$	9.73205	0.479464
$413$	21.4641	1.05618
$414$	−4.46410	−0.219399
$415$	14.1962	0.696862
$416$	−2.73205	−0.133950
$417$	46.4449	2.27441
$418$	5.66025	0.276852
$419$	5.66025	0.276522	0.138261	−	0.990396i	$-0.455849\pi$
$419$	5.66025	0.276522	0.138261	+	0.990396i	$0.455849\pi$
$420$	9.46410	0.461801
$421$	−2.14359	−0.104472	−0.0522362	−	0.998635i	$-0.516635\pi$
$421$	−2.14359	−0.104472	−0.0522362	+	0.998635i	$0.516635\pi$
$422$	−26.0526	−1.26822
$423$	−25.2679	−1.22857
$424$	3.46410	0.168232
$425$	3.46410	0.168034
$426$	29.3205	1.42058
$427$	14.3923	0.696492
$428$	4.26795	0.206299
$429$	−12.9282	−0.624180
$430$	2.07180	0.0999109
$431$	−28.9808	−1.39595	−0.697977	−	0.716120i	$-0.745916\pi$
$431$	−28.9808	−1.39595	−0.697977	+	0.716120i	$0.745916\pi$
$432$	4.00000	0.192450
$433$	−25.5885	−1.22970	−0.614851	−	0.788643i	$-0.710784\pi$
$433$	−25.5885	−1.22970	−0.614851	+	0.788643i	$0.710784\pi$
$434$	16.0000	0.768025
$435$	−12.0000	−0.575356
$436$	−9.19615	−0.440416
$437$	−3.26795	−0.156327
$438$	−16.9282	−0.808861
$439$	31.7846	1.51700	0.758498	−	0.651675i	$-0.225933\pi$
$439$	31.7846	1.51700	0.758498	+	0.651675i	$0.225933\pi$
$440$	3.00000	0.143019
$441$	−13.3923	−0.637729
$442$	4.73205	0.225081
$443$	20.5359	0.975690	0.487845	−	0.872930i	$-0.337783\pi$
$443$	20.5359	0.975690	0.487845	+	0.872930i	$0.337783\pi$
$444$	−20.3923	−0.967776
$445$	4.39230	0.208215
$446$	26.0000	1.23114
$447$	38.7846	1.83445
$448$	2.00000	0.0944911
$449$	−8.53590	−0.402834	−0.201417	−	0.979506i	$-0.564555\pi$
$449$	−8.53590	−0.402834	−0.201417	+	0.979506i	$0.564555\pi$
$450$	−8.92820	−0.420880
$451$	11.1962	0.527206
$452$	−8.19615	−0.385515
$453$	6.73205	0.316299
$454$	−6.00000	−0.281594
$455$	−9.46410	−0.443684
$456$	8.92820	0.418101
$457$	28.7846	1.34649	0.673244	−	0.739421i	$-0.264901\pi$
$457$	28.7846	1.34649	0.673244	+	0.739421i	$0.264901\pi$
$458$	−12.7846	−0.597386
$459$	−6.92820	−0.323381
$460$	−1.73205	−0.0807573
$461$	12.4641	0.580511	0.290256	−	0.956949i	$-0.406260\pi$
$461$	12.4641	0.580511	0.290256	+	0.956949i	$0.406260\pi$
$462$	9.46410	0.440310
$463$	−27.3205	−1.26969	−0.634846	−	0.772639i	$-0.718936\pi$
$463$	−27.3205	−1.26969	−0.634846	+	0.772639i	$0.718936\pi$
$464$	−2.53590	−0.117726
$465$	37.8564	1.75555
$466$	−7.39230	−0.342442
$467$	36.1244	1.67164	0.835818	−	0.549007i	$-0.184994\pi$
$467$	36.1244	1.67164	0.835818	+	0.549007i	$0.184994\pi$
$468$	−12.1962	−0.563767
$469$	−26.2487	−1.21205
$470$	−9.80385	−0.452218
$471$	38.2487	1.76241
$472$	10.7321	0.493983
$473$	2.07180	0.0952613
$474$	−36.7846	−1.68957
$475$	−6.53590	−0.299888
$476$	−3.46410	−0.158777
$477$	15.4641	0.708053
$478$	10.3923	0.475333
$479$	22.5167	1.02881	0.514406	−	0.857547i	$-0.328012\pi$
$479$	22.5167	1.02881	0.514406	+	0.857547i	$0.328012\pi$
$480$	4.73205	0.215988
$481$	20.3923	0.929809
$482$	−5.73205	−0.261088
$483$	−5.46410	−0.248625
$484$	−8.00000	−0.363636
$485$	−12.9282	−0.587039
$486$	−18.7321	−0.849703
$487$	−3.78461	−0.171497	−0.0857485	−	0.996317i	$-0.527328\pi$
$487$	−3.78461	−0.171497	−0.0857485	+	0.996317i	$0.527328\pi$
$488$	7.19615	0.325755
$489$	39.5167	1.78701
$490$	−5.19615	−0.234738
$491$	21.0000	0.947717	0.473858	−	0.880601i	$-0.342861\pi$
$491$	21.0000	0.947717	0.473858	+	0.880601i	$0.342861\pi$
$492$	17.6603	0.796186
$493$	4.39230	0.197819
$494$	−8.92820	−0.401699
$495$	13.3923	0.601939
$496$	8.00000	0.359211
$497$	21.4641	0.962797
$498$	22.3923	1.00342
$499$	36.1769	1.61950	0.809751	−	0.586774i	$-0.199602\pi$
$499$	36.1769	1.61950	0.809751	+	0.586774i	$0.199602\pi$
$500$	−12.1244	−0.542218
$501$	−46.0526	−2.05748
$502$	31.5167	1.40666
$503$	24.1244	1.07565	0.537826	−	0.843056i	$-0.319246\pi$
$503$	24.1244	1.07565	0.537826	+	0.843056i	$0.319246\pi$
$504$	8.92820	0.397694
$505$	−4.39230	−0.195455
$506$	−1.73205	−0.0769991
$507$	−15.1244	−0.671696
$508$	5.80385	0.257504
$509$	−15.9282	−0.706005	−0.353003	−	0.935622i	$-0.614839\pi$
$509$	−15.9282	−0.706005	−0.353003	+	0.935622i	$0.614839\pi$
$510$	−8.19615	−0.362932
$511$	−12.3923	−0.548203
$512$	1.00000	0.0441942
$513$	13.0718	0.577134
$514$	11.3205	0.499326
$515$	16.8564	0.742782
$516$	3.26795	0.143863
$517$	−9.80385	−0.431173
$518$	−14.9282	−0.655908
$519$	−52.9808	−2.32560
$520$	−4.73205	−0.207514
$521$	27.5885	1.20867	0.604336	−	0.796729i	$-0.293438\pi$
$521$	27.5885	1.20867	0.604336	+	0.796729i	$0.293438\pi$
$522$	−11.3205	−0.495485
$523$	15.2679	0.667621	0.333810	−	0.942640i	$-0.391665\pi$
$523$	15.2679	0.667621	0.333810	+	0.942640i	$0.391665\pi$
$524$	−1.00000	−0.0436852
$525$	−10.9282	−0.476946
$526$	−2.87564	−0.125384
$527$	−13.8564	−0.603595
$528$	4.73205	0.205936
$529$	1.00000	0.0434783
$530$	6.00000	0.260623
$531$	47.9090	2.07907
$532$	6.53590	0.283367
$533$	−17.6603	−0.764951
$534$	6.92820	0.299813
$535$	7.39230	0.319597
$536$	−13.1244	−0.566886
$537$	−18.9282	−0.816812
$538$	−20.1962	−0.870718
$539$	−5.19615	−0.223814
$540$	6.92820	0.298142
$541$	12.8564	0.552740	0.276370	−	0.961051i	$-0.410868\pi$
$541$	12.8564	0.552740	0.276370	+	0.961051i	$0.410868\pi$
$542$	26.4641	1.13673
$543$	47.7128	2.04755
$544$	−1.73205	−0.0742611
$545$	−15.9282	−0.682289
$546$	−14.9282	−0.638868
$547$	5.92820	0.253472	0.126736	−	0.991937i	$-0.459550\pi$
$547$	5.92820	0.253472	0.126736	+	0.991937i	$0.459550\pi$
$548$	−18.1244	−0.774234
$549$	32.1244	1.37103
$550$	−3.46410	−0.147710
$551$	−8.28719	−0.353046
$552$	−2.73205	−0.116284
$553$	−26.9282	−1.14510
$554$	−14.3923	−0.611470
$555$	−35.3205	−1.49927
$556$	17.0000	0.720961
$557$	−13.9808	−0.592384	−0.296192	−	0.955128i	$-0.595717\pi$
$557$	−13.9808	−0.592384	−0.296192	+	0.955128i	$0.595717\pi$
$558$	35.7128	1.51184
$559$	−3.26795	−0.138220
$560$	3.46410	0.146385
$561$	−8.19615	−0.346042
$562$	21.5885	0.910654
$563$	−3.46410	−0.145994	−0.0729972	−	0.997332i	$-0.523256\pi$
$563$	−3.46410	−0.145994	−0.0729972	+	0.997332i	$0.523256\pi$
$564$	−15.4641	−0.651156
$565$	−14.1962	−0.597237
$566$	−2.39230	−0.100556
$567$	−4.92820	−0.206965
$568$	10.7321	0.450307
$569$	−11.3205	−0.474580	−0.237290	−	0.971439i	$-0.576259\pi$
$569$	−11.3205	−0.474580	−0.237290	+	0.971439i	$0.576259\pi$
$570$	15.4641	0.647720
$571$	−11.6077	−0.485767	−0.242883	−	0.970055i	$-0.578093\pi$
$571$	−11.6077	−0.485767	−0.242883	+	0.970055i	$0.578093\pi$
$572$	−4.73205	−0.197857
$573$	−69.7128	−2.91229
$574$	12.9282	0.539613
$575$	2.00000	0.0834058
$576$	4.46410	0.186004
$577$	−15.7846	−0.657122	−0.328561	−	0.944483i	$-0.606564\pi$
$577$	−15.7846	−0.657122	−0.328561	+	0.944483i	$0.606564\pi$
$578$	−14.0000	−0.582323
$579$	−66.4449	−2.76135
$580$	−4.39230	−0.182381
$581$	16.3923	0.680067
$582$	−20.3923	−0.845288
$583$	6.00000	0.248495
$584$	−6.19615	−0.256399
$585$	−21.1244	−0.873385
$586$	−0.339746	−0.0140348
$587$	−28.6410	−1.18214	−0.591071	−	0.806620i	$-0.701295\pi$
$587$	−28.6410	−1.18214	−0.591071	+	0.806620i	$0.701295\pi$
$588$	−8.19615	−0.338004
$589$	26.1436	1.07723
$590$	18.5885	0.765275
$591$	−57.3731	−2.36001
$592$	−7.46410	−0.306773
$593$	−22.9808	−0.943707	−0.471853	−	0.881677i	$-0.656415\pi$
$593$	−22.9808	−0.943707	−0.471853	+	0.881677i	$0.656415\pi$
$594$	6.92820	0.284268
$595$	−6.00000	−0.245976
$596$	14.1962	0.581497
$597$	59.3731	2.42998
$598$	2.73205	0.111722
$599$	25.3923	1.03750	0.518751	−	0.854926i	$-0.326397\pi$
$599$	25.3923	1.03750	0.518751	+	0.854926i	$0.326397\pi$
$600$	−5.46410	−0.223071
$601$	−32.1769	−1.31252	−0.656262	−	0.754533i	$-0.727863\pi$
$601$	−32.1769	−1.31252	−0.656262	+	0.754533i	$0.727863\pi$
$602$	2.39230	0.0975031
$603$	−58.5885	−2.38591
$604$	2.46410	0.100263
$605$	−13.8564	−0.563343
$606$	−6.92820	−0.281439
$607$	−28.5885	−1.16037	−0.580185	−	0.814485i	$-0.697020\pi$
$607$	−28.5885	−1.16037	−0.580185	+	0.814485i	$0.697020\pi$
$608$	3.26795	0.132533
$609$	−13.8564	−0.561490
$610$	12.4641	0.504657
$611$	15.4641	0.625611
$612$	−7.73205	−0.312550
$613$	27.9808	1.13013	0.565066	−	0.825046i	$-0.308851\pi$
$613$	27.9808	1.13013	0.565066	+	0.825046i	$0.308851\pi$
$614$	−12.1962	−0.492197
$615$	30.5885	1.23345
$616$	3.46410	0.139573
$617$	32.6603	1.31485	0.657426	−	0.753519i	$-0.271645\pi$
$617$	32.6603	1.31485	0.657426	+	0.753519i	$0.271645\pi$
$618$	26.5885	1.06954
$619$	−31.3731	−1.26099	−0.630495	−	0.776193i	$-0.717148\pi$
$619$	−31.3731	−1.26099	−0.630495	+	0.776193i	$0.717148\pi$
$620$	13.8564	0.556487
$621$	−4.00000	−0.160514
$622$	9.00000	0.360867
$623$	5.07180	0.203197
$624$	−7.46410	−0.298803
$625$	−11.0000	−0.440000
$626$	−4.92820	−0.196971
$627$	15.4641	0.617577
$628$	14.0000	0.558661
$629$	12.9282	0.515481
$630$	15.4641	0.616105
$631$	−32.6410	−1.29942	−0.649709	−	0.760183i	$-0.725109\pi$
$631$	−32.6410	−1.29942	−0.649709	+	0.760183i	$0.725109\pi$
$632$	−13.4641	−0.535573
$633$	−71.1769	−2.82903
$634$	−14.1962	−0.563801
$635$	10.0526	0.398924
$636$	9.46410	0.375276
$637$	8.19615	0.324743
$638$	−4.39230	−0.173893
$639$	47.9090	1.89525
$640$	1.73205	0.0684653
$641$	26.4449	1.04451	0.522255	−	0.852790i	$-0.325091\pi$
$641$	26.4449	1.04451	0.522255	+	0.852790i	$0.325091\pi$
$642$	11.6603	0.460194
$643$	−44.3923	−1.75066	−0.875331	−	0.483525i	$-0.839356\pi$
$643$	−44.3923	−1.75066	−0.875331	+	0.483525i	$0.839356\pi$
$644$	−2.00000	−0.0788110
$645$	5.66025	0.222872
$646$	−5.66025	−0.222700
$647$	22.8564	0.898578	0.449289	−	0.893386i	$-0.351677\pi$
$647$	22.8564	0.898578	0.449289	+	0.893386i	$0.351677\pi$
$648$	−2.46410	−0.0967991
$649$	18.5885	0.729661
$650$	5.46410	0.214320
$651$	43.7128	1.71324
$652$	14.4641	0.566458
$653$	−17.0718	−0.668071	−0.334036	−	0.942560i	$-0.608411\pi$
$653$	−17.0718	−0.668071	−0.334036	+	0.942560i	$0.608411\pi$
$654$	−25.1244	−0.982440
$655$	−1.73205	−0.0676768
$656$	6.46410	0.252381
$657$	−27.6603	−1.07913
$658$	−11.3205	−0.441319
$659$	−14.6603	−0.571082	−0.285541	−	0.958366i	$-0.592173\pi$
$659$	−14.6603	−0.571082	−0.285541	+	0.958366i	$0.592173\pi$
$660$	8.19615	0.319035
$661$	40.1962	1.56345	0.781725	−	0.623624i	$-0.214340\pi$
$661$	40.1962	1.56345	0.781725	+	0.623624i	$0.214340\pi$
$662$	6.39230	0.248444
$663$	12.9282	0.502090
$664$	8.19615	0.318072
$665$	11.3205	0.438990
$666$	−33.3205	−1.29114
$667$	2.53590	0.0981904
$668$	−16.8564	−0.652194
$669$	71.0333	2.74631
$670$	−22.7321	−0.878216
$671$	12.4641	0.481171
$672$	5.46410	0.210782
$673$	−33.6603	−1.29751	−0.648754	−	0.760998i	$-0.724709\pi$
$673$	−33.6603	−1.29751	−0.648754	+	0.760998i	$0.724709\pi$
$674$	−0.196152	−0.00755551
$675$	−8.00000	−0.307920
$676$	−5.53590	−0.212919
$677$	5.41154	0.207982	0.103991	−	0.994578i	$-0.466839\pi$
$677$	5.41154	0.207982	0.103991	+	0.994578i	$0.466839\pi$
$678$	−22.3923	−0.859971
$679$	−14.9282	−0.572892
$680$	−3.00000	−0.115045
$681$	−16.3923	−0.628154
$682$	13.8564	0.530589
$683$	−39.8038	−1.52305	−0.761526	−	0.648134i	$-0.775549\pi$
$683$	−39.8038	−1.52305	−0.761526	+	0.648134i	$0.775549\pi$
$684$	14.5885	0.557804
$685$	−31.3923	−1.19944
$686$	−20.0000	−0.763604
$687$	−34.9282	−1.33259
$688$	1.19615	0.0456029
$689$	−9.46410	−0.360554
$690$	−4.73205	−0.180146
$691$	20.0000	0.760836	0.380418	−	0.924815i	$-0.375780\pi$
$691$	20.0000	0.760836	0.380418	+	0.924815i	$0.375780\pi$
$692$	−19.3923	−0.737185
$693$	15.4641	0.587433
$694$	−10.8564	−0.412104
$695$	29.4449	1.11691
$696$	−6.92820	−0.262613
$697$	−11.1962	−0.424085
$698$	33.8564	1.28148
$699$	−20.1962	−0.763889
$700$	−4.00000	−0.151186
$701$	34.3923	1.29898	0.649490	−	0.760370i	$-0.274983\pi$
$701$	34.3923	1.29898	0.649490	+	0.760370i	$0.274983\pi$
$702$	−10.9282	−0.412458
$703$	−24.3923	−0.919973
$704$	1.73205	0.0652791
$705$	−26.7846	−1.00877
$706$	26.3205	0.990585
$707$	−5.07180	−0.190745
$708$	29.3205	1.10193
$709$	−28.9282	−1.08642	−0.543211	−	0.839596i	$-0.682792\pi$
$709$	−28.9282	−1.08642	−0.543211	+	0.839596i	$0.682792\pi$
$710$	18.5885	0.697612
$711$	−60.1051	−2.25412
$712$	2.53590	0.0950368
$713$	−8.00000	−0.299602
$714$	−9.46410	−0.354185
$715$	−8.19615	−0.306519
$716$	−6.92820	−0.258919
$717$	28.3923	1.06033
$718$	27.5885	1.02959
$719$	9.24871	0.344919	0.172459	−	0.985017i	$-0.444829\pi$
$719$	9.24871	0.344919	0.172459	+	0.985017i	$0.444829\pi$
$720$	7.73205	0.288157
$721$	19.4641	0.724881
$722$	−8.32051	−0.309657
$723$	−15.6603	−0.582411
$724$	17.4641	0.649048
$725$	5.07180	0.188362
$726$	−21.8564	−0.811167
$727$	10.4115	0.386143	0.193071	−	0.981185i	$-0.438155\pi$
$727$	10.4115	0.386143	0.193071	+	0.981185i	$0.438155\pi$
$728$	−5.46410	−0.202513
$729$	−43.7846	−1.62165
$730$	−10.7321	−0.397211
$731$	−2.07180	−0.0766282
$732$	19.6603	0.726664
$733$	28.7846	1.06318	0.531592	−	0.847001i	$-0.321594\pi$
$733$	28.7846	1.06318	0.531592	+	0.847001i	$0.321594\pi$
$734$	−34.5885	−1.27668
$735$	−14.1962	−0.523633
$736$	−1.00000	−0.0368605
$737$	−22.7321	−0.837346
$738$	28.8564	1.06222
$739$	12.9808	0.477505	0.238753	−	0.971080i	$-0.423262\pi$
$739$	12.9808	0.477505	0.238753	+	0.971080i	$0.423262\pi$
$740$	−12.9282	−0.475250
$741$	−24.3923	−0.896074
$742$	6.92820	0.254342
$743$	−11.1962	−0.410747	−0.205373	−	0.978684i	$-0.565841\pi$
$743$	−11.1962	−0.410747	−0.205373	+	0.978684i	$0.565841\pi$
$744$	21.8564	0.801295
$745$	24.5885	0.900851
$746$	18.0526	0.660951
$747$	36.5885	1.33870
$748$	−3.00000	−0.109691
$749$	8.53590	0.311895
$750$	−33.1244	−1.20953
$751$	35.5885	1.29864	0.649321	−	0.760515i	$-0.275053\pi$
$751$	35.5885	1.29864	0.649321	+	0.760515i	$0.275053\pi$
$752$	−5.66025	−0.206408
$753$	86.1051	3.13784
$754$	6.92820	0.252310
$755$	4.26795	0.155327
$756$	8.00000	0.290957
$757$	50.3731	1.83084	0.915420	−	0.402500i	$-0.131859\pi$
$757$	50.3731	1.83084	0.915420	+	0.402500i	$0.131859\pi$
$758$	8.12436	0.295090
$759$	−4.73205	−0.171763
$760$	5.66025	0.205319
$761$	−18.6795	−0.677131	−0.338566	−	0.940943i	$-0.609942\pi$
$761$	−18.6795	−0.677131	−0.338566	+	0.940943i	$0.609942\pi$
$762$	15.8564	0.574417
$763$	−18.3923	−0.665846
$764$	−25.5167	−0.923160
$765$	−13.3923	−0.484200
$766$	−1.60770	−0.0580884
$767$	−29.3205	−1.05870
$768$	2.73205	0.0985844
$769$	21.1769	0.763659	0.381830	−	0.924233i	$-0.375294\pi$
$769$	21.1769	0.763659	0.381830	+	0.924233i	$0.375294\pi$
$770$	6.00000	0.216225
$771$	30.9282	1.11385
$772$	−24.3205	−0.875314
$773$	−36.9282	−1.32822	−0.664108	−	0.747637i	$-0.731188\pi$
$773$	−36.9282	−1.32822	−0.664108	+	0.747637i	$0.731188\pi$
$774$	5.33975	0.191933
$775$	−16.0000	−0.574737
$776$	−7.46410	−0.267946
$777$	−40.7846	−1.46314
$778$	−13.2679	−0.475679
$779$	21.1244	0.756859
$780$	−12.9282	−0.462904
$781$	18.5885	0.665147
$782$	1.73205	0.0619380
$783$	−10.1436	−0.362502
$784$	−3.00000	−0.107143
$785$	24.2487	0.865474
$786$	−2.73205	−0.0974490
$787$	55.1962	1.96753	0.983765	−	0.179461i	$-0.0574352\pi$
$787$	55.1962	1.96753	0.983765	+	0.179461i	$0.0574352\pi$
$788$	−21.0000	−0.748094
$789$	−7.85641	−0.279695
$790$	−23.3205	−0.829706
$791$	−16.3923	−0.582843
$792$	7.73205	0.274746
$793$	−19.6603	−0.698156
$794$	10.1962	0.361848
$795$	16.3923	0.581375
$796$	21.7321	0.770272
$797$	−47.1962	−1.67177	−0.835887	−	0.548902i	$-0.815046\pi$
$797$	−47.1962	−1.67177	−0.835887	+	0.548902i	$0.815046\pi$
$798$	17.8564	0.632110
$799$	9.80385	0.346835
$800$	−2.00000	−0.0707107
$801$	11.3205	0.399990
$802$	−39.7128	−1.40231
$803$	−10.7321	−0.378726
$804$	−35.8564	−1.26456
$805$	−3.46410	−0.122094
$806$	−21.8564	−0.769859
$807$	−55.1769	−1.94232
$808$	−2.53590	−0.0892126
$809$	−21.8038	−0.766582	−0.383291	−	0.923628i	$-0.625209\pi$
$809$	−21.8038	−0.766582	−0.383291	+	0.923628i	$0.625209\pi$
$810$	−4.26795	−0.149960
$811$	22.7846	0.800076	0.400038	−	0.916499i	$-0.368997\pi$
$811$	22.7846	0.800076	0.400038	+	0.916499i	$0.368997\pi$
$812$	−5.07180	−0.177985
$813$	72.3013	2.53572
$814$	−12.9282	−0.453133
$815$	25.0526	0.877553
$816$	−4.73205	−0.165655
$817$	3.90897	0.136757
$818$	−13.2487	−0.463230
$819$	−24.3923	−0.852336
$820$	11.1962	0.390987
$821$	0.588457	0.0205373	0.0102687	−	0.999947i	$-0.496731\pi$
$821$	0.588457	0.0205373	0.0102687	+	0.999947i	$0.496731\pi$
$822$	−49.5167	−1.72709
$823$	−25.8038	−0.899466	−0.449733	−	0.893163i	$-0.648481\pi$
$823$	−25.8038	−0.899466	−0.449733	+	0.893163i	$0.648481\pi$
$824$	9.73205	0.339032
$825$	−9.46410	−0.329498
$826$	21.4641	0.746832
$827$	20.7846	0.722752	0.361376	−	0.932420i	$-0.382307\pi$
$827$	20.7846	0.722752	0.361376	+	0.932420i	$0.382307\pi$
$828$	−4.46410	−0.155138
$829$	−26.0526	−0.904843	−0.452421	−	0.891804i	$-0.649440\pi$
$829$	−26.0526	−0.904843	−0.452421	+	0.891804i	$0.649440\pi$
$830$	14.1962	0.492756
$831$	−39.3205	−1.36401
$832$	−2.73205	−0.0947168
$833$	5.19615	0.180036
$834$	46.4449	1.60825
$835$	−29.1962	−1.01037
$836$	5.66025	0.195764
$837$	32.0000	1.10608
$838$	5.66025	0.195530
$839$	31.8564	1.09981	0.549903	−	0.835229i	$-0.314665\pi$
$839$	31.8564	1.09981	0.549903	+	0.835229i	$0.314665\pi$
$840$	9.46410	0.326543
$841$	−22.5692	−0.778249
$842$	−2.14359	−0.0738731
$843$	58.9808	2.03141
$844$	−26.0526	−0.896766
$845$	−9.58846	−0.329853
$846$	−25.2679	−0.868730
$847$	−16.0000	−0.549767
$848$	3.46410	0.118958
$849$	−6.53590	−0.224311
$850$	3.46410	0.118818
$851$	7.46410	0.255866
$852$	29.3205	1.00450
$853$	−6.53590	−0.223785	−0.111892	−	0.993720i	$-0.535691\pi$
$853$	−6.53590	−0.223785	−0.111892	+	0.993720i	$0.535691\pi$
$854$	14.3923	0.492495
$855$	25.2679	0.864146
$856$	4.26795	0.145876
$857$	44.1051	1.50660	0.753301	−	0.657676i	$-0.228460\pi$
$857$	44.1051	1.50660	0.753301	+	0.657676i	$0.228460\pi$
$858$	−12.9282	−0.441362
$859$	−40.0000	−1.36478	−0.682391	−	0.730987i	$-0.739060\pi$
$859$	−40.0000	−1.36478	−0.682391	+	0.730987i	$0.739060\pi$
$860$	2.07180	0.0706477
$861$	35.3205	1.20372
$862$	−28.9808	−0.987089
$863$	36.9282	1.25705	0.628525	−	0.777789i	$-0.283659\pi$
$863$	36.9282	1.25705	0.628525	+	0.777789i	$0.283659\pi$
$864$	4.00000	0.136083
$865$	−33.5885	−1.14204
$866$	−25.5885	−0.869531
$867$	−38.2487	−1.29899
$868$	16.0000	0.543075
$869$	−23.3205	−0.791094
$870$	−12.0000	−0.406838
$871$	35.8564	1.21495
$872$	−9.19615	−0.311421
$873$	−33.3205	−1.12773
$874$	−3.26795	−0.110540
$875$	−24.2487	−0.819756
$876$	−16.9282	−0.571951
$877$	−34.2487	−1.15650	−0.578248	−	0.815861i	$-0.696264\pi$
$877$	−34.2487	−1.15650	−0.578248	+	0.815861i	$0.696264\pi$
$878$	31.7846	1.07268
$879$	−0.928203	−0.0313075
$880$	3.00000	0.101130
$881$	−18.0000	−0.606435	−0.303218	−	0.952921i	$-0.598061\pi$
$881$	−18.0000	−0.606435	−0.303218	+	0.952921i	$0.598061\pi$
$882$	−13.3923	−0.450942
$883$	30.8564	1.03840	0.519200	−	0.854653i	$-0.326230\pi$
$883$	30.8564	1.03840	0.519200	+	0.854653i	$0.326230\pi$
$884$	4.73205	0.159156
$885$	50.7846	1.70711
$886$	20.5359	0.689917
$887$	−46.1769	−1.55047	−0.775235	−	0.631674i	$-0.782368\pi$
$887$	−46.1769	−1.55047	−0.775235	+	0.631674i	$0.782368\pi$
$888$	−20.3923	−0.684321
$889$	11.6077	0.389310
$890$	4.39230	0.147230
$891$	−4.26795	−0.142982
$892$	26.0000	0.870544
$893$	−18.4974	−0.618993
$894$	38.7846	1.29715
$895$	−12.0000	−0.401116
$896$	2.00000	0.0668153
$897$	7.46410	0.249219
$898$	−8.53590	−0.284847
$899$	−20.2872	−0.676616
$900$	−8.92820	−0.297607
$901$	−6.00000	−0.199889
$902$	11.1962	0.372791
$903$	6.53590	0.217501
$904$	−8.19615	−0.272600
$905$	30.2487	1.00550
$906$	6.73205	0.223657
$907$	16.9090	0.561453	0.280726	−	0.959788i	$-0.409425\pi$
$907$	16.9090	0.561453	0.280726	+	0.959788i	$0.409425\pi$
$908$	−6.00000	−0.199117
$909$	−11.3205	−0.375478
$910$	−9.46410	−0.313732
$911$	57.9615	1.92035	0.960175	−	0.279398i	$-0.0901348\pi$
$911$	57.9615	1.92035	0.960175	+	0.279398i	$0.0901348\pi$
$912$	8.92820	0.295642
$913$	14.1962	0.469824
$914$	28.7846	0.952110
$915$	34.0526	1.12574
$916$	−12.7846	−0.422415
$917$	−2.00000	−0.0660458
$918$	−6.92820	−0.228665
$919$	39.9808	1.31884	0.659422	−	0.751773i	$-0.270801\pi$
$919$	39.9808	1.31884	0.659422	+	0.751773i	$0.270801\pi$
$920$	−1.73205	−0.0571040
$921$	−33.3205	−1.09795
$922$	12.4641	0.410483
$923$	−29.3205	−0.965096
$924$	9.46410	0.311346
$925$	14.9282	0.490836
$926$	−27.3205	−0.897808
$927$	43.4449	1.42692
$928$	−2.53590	−0.0832449
$929$	−40.8564	−1.34046	−0.670228	−	0.742156i	$-0.733804\pi$
$929$	−40.8564	−1.34046	−0.670228	+	0.742156i	$0.733804\pi$
$930$	37.8564	1.24136
$931$	−9.80385	−0.321308
$932$	−7.39230	−0.242143
$933$	24.5885	0.804990
$934$	36.1244	1.18203
$935$	−5.19615	−0.169932
$936$	−12.1962	−0.398644
$937$	−23.8564	−0.779355	−0.389677	−	0.920951i	$-0.627413\pi$
$937$	−23.8564	−0.779355	−0.389677	+	0.920951i	$0.627413\pi$
$938$	−26.2487	−0.857051
$939$	−13.4641	−0.439384
$940$	−9.80385	−0.319766
$941$	−28.7321	−0.936638	−0.468319	−	0.883559i	$-0.655140\pi$
$941$	−28.7321	−0.936638	−0.468319	+	0.883559i	$0.655140\pi$
$942$	38.2487	1.24621
$943$	−6.46410	−0.210500
$944$	10.7321	0.349299
$945$	13.8564	0.450749
$946$	2.07180	0.0673599
$947$	20.7846	0.675409	0.337705	−	0.941252i	$-0.390350\pi$
$947$	20.7846	0.675409	0.337705	+	0.941252i	$0.390350\pi$
$948$	−36.7846	−1.19471
$949$	16.9282	0.549513
$950$	−6.53590	−0.212053
$951$	−38.7846	−1.25768
$952$	−3.46410	−0.112272
$953$	59.3205	1.92158	0.960790	−	0.277278i	$-0.0894321\pi$
$953$	59.3205	1.92158	0.960790	+	0.277278i	$0.0894321\pi$
$954$	15.4641	0.500669
$955$	−44.1962	−1.43015
$956$	10.3923	0.336111
$957$	−12.0000	−0.387905
$958$	22.5167	0.727480
$959$	−36.2487	−1.17053
$960$	4.73205	0.152726
$961$	33.0000	1.06452
$962$	20.3923	0.657474
$963$	19.0526	0.613960
$964$	−5.73205	−0.184617
$965$	−42.1244	−1.35603
$966$	−5.46410	−0.175805
$967$	−20.3923	−0.655772	−0.327886	−	0.944717i	$-0.606336\pi$
$967$	−20.3923	−0.655772	−0.327886	+	0.944717i	$0.606336\pi$
$968$	−8.00000	−0.257130
$969$	−15.4641	−0.496779
$970$	−12.9282	−0.415100
$971$	7.60770	0.244143	0.122071	−	0.992521i	$-0.461046\pi$
$971$	7.60770	0.244143	0.122071	+	0.992521i	$0.461046\pi$
$972$	−18.7321	−0.600831
$973$	34.0000	1.08999
$974$	−3.78461	−0.121267
$975$	14.9282	0.478085
$976$	7.19615	0.230343
$977$	−16.0526	−0.513567	−0.256783	−	0.966469i	$-0.582663\pi$
$977$	−16.0526	−0.513567	−0.256783	+	0.966469i	$0.582663\pi$
$978$	39.5167	1.26360
$979$	4.39230	0.140379
$980$	−5.19615	−0.165985
$981$	−41.0526	−1.31071
$982$	21.0000	0.670137
$983$	12.2487	0.390673	0.195337	−	0.980736i	$-0.437420\pi$
$983$	12.2487	0.390673	0.195337	+	0.980736i	$0.437420\pi$
$984$	17.6603	0.562988
$985$	−36.3731	−1.15894
$986$	4.39230	0.139879
$987$	−30.9282	−0.984456
$988$	−8.92820	−0.284044
$989$	−1.19615	−0.0380354
$990$	13.3923	0.425635
$991$	51.1769	1.62569	0.812844	−	0.582481i	$-0.197918\pi$
$991$	51.1769	1.62569	0.812844	+	0.582481i	$0.197918\pi$
$992$	8.00000	0.254000
$993$	17.4641	0.554207
$994$	21.4641	0.680800
$995$	37.6410	1.19330
$996$	22.3923	0.709527
$997$	8.58846	0.271999	0.136000	−	0.990709i	$-0.456575\pi$
$997$	8.58846	0.271999	0.136000	+	0.990709i	$0.456575\pi$
$998$	36.1769	1.14516
$999$	−29.8564	−0.944615

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.e.1.2	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.e.1.2	✓	2	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:	\( N \)	\(=\)	\( 6026 = 2 \cdot 23 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6026.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.73205 q^{3} +1.00000 q^{4} +1.73205 q^{5} +2.73205 q^{6} +2.00000 q^{7} +1.00000 q^{8} +4.46410 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +2.73205 q^{3} +1.00000 q^{4} +1.73205 q^{5} +2.73205 q^{6} +2.00000 q^{7} +1.00000 q^{8} +4.46410 q^{9} +1.73205 q^{10} +1.73205 q^{11} +2.73205 q^{12} -2.73205 q^{13} +2.00000 q^{14} +4.73205 q^{15} +1.00000 q^{16} -1.73205 q^{17} +4.46410 q^{18} +3.26795 q^{19} +1.73205 q^{20} +5.46410 q^{21} +1.73205 q^{22} -1.00000 q^{23} +2.73205 q^{24} -2.00000 q^{25} -2.73205 q^{26} +4.00000 q^{27} +2.00000 q^{28} -2.53590 q^{29} +4.73205 q^{30} +8.00000 q^{31} +1.00000 q^{32} +4.73205 q^{33} -1.73205 q^{34} +3.46410 q^{35} +4.46410 q^{36} -7.46410 q^{37} +3.26795 q^{38} -7.46410 q^{39} +1.73205 q^{40} +6.46410 q^{41} +5.46410 q^{42} +1.19615 q^{43} +1.73205 q^{44} +7.73205 q^{45} -1.00000 q^{46} -5.66025 q^{47} +2.73205 q^{48} -3.00000 q^{49} -2.00000 q^{50} -4.73205 q^{51} -2.73205 q^{52} +3.46410 q^{53} +4.00000 q^{54} +3.00000 q^{55} +2.00000 q^{56} +8.92820 q^{57} -2.53590 q^{58} +10.7321 q^{59} +4.73205 q^{60} +7.19615 q^{61} +8.00000 q^{62} +8.92820 q^{63} +1.00000 q^{64} -4.73205 q^{65} +4.73205 q^{66} -13.1244 q^{67} -1.73205 q^{68} -2.73205 q^{69} +3.46410 q^{70} +10.7321 q^{71} +4.46410 q^{72} -6.19615 q^{73} -7.46410 q^{74} -5.46410 q^{75} +3.26795 q^{76} +3.46410 q^{77} -7.46410 q^{78} -13.4641 q^{79} +1.73205 q^{80} -2.46410 q^{81} +6.46410 q^{82} +8.19615 q^{83} +5.46410 q^{84} -3.00000 q^{85} +1.19615 q^{86} -6.92820 q^{87} +1.73205 q^{88} +2.53590 q^{89} +7.73205 q^{90} -5.46410 q^{91} -1.00000 q^{92} +21.8564 q^{93} -5.66025 q^{94} +5.66025 q^{95} +2.73205 q^{96} -7.46410 q^{97} -3.00000 q^{98} +7.73205 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + 2 q^{6} + 4 q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + 2 * q^6 + 4 * q^7 + 2 * q^8 + 2 * q^9	\( 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + 2 q^{6} + 4 q^{7} + 2 q^{8} + 2 q^{9} + 2 q^{12} - 2 q^{13} + 4 q^{14} + 6 q^{15} + 2 q^{16} + 2 q^{18} + 10 q^{19} + 4 q^{21} - 2 q^{23} + 2 q^{24} - 4 q^{25} - 2 q^{26} + 8 q^{27} + 4 q^{28} - 12 q^{29} + 6 q^{30} + 16 q^{31} + 2 q^{32} + 6 q^{33} + 2 q^{36} - 8 q^{37} + 10 q^{38} - 8 q^{39} + 6 q^{41} + 4 q^{42} - 8 q^{43} + 12 q^{45} - 2 q^{46} + 6 q^{47} + 2 q^{48} - 6 q^{49} - 4 q^{50} - 6 q^{51} - 2 q^{52} + 8 q^{54} + 6 q^{55} + 4 q^{56} + 4 q^{57} - 12 q^{58} + 18 q^{59} + 6 q^{60} + 4 q^{61} + 16 q^{62} + 4 q^{63} + 2 q^{64} - 6 q^{65} + 6 q^{66} - 2 q^{67} - 2 q^{69} + 18 q^{71} + 2 q^{72} - 2 q^{73} - 8 q^{74} - 4 q^{75} + 10 q^{76} - 8 q^{78} - 20 q^{79} + 2 q^{81} + 6 q^{82} + 6 q^{83} + 4 q^{84} - 6 q^{85} - 8 q^{86} + 12 q^{89} + 12 q^{90} - 4 q^{91} - 2 q^{92} + 16 q^{93} + 6 q^{94} - 6 q^{95} + 2 q^{96} - 8 q^{97} - 6 q^{98} + 12 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + 2 * q^6 + 4 * q^7 + 2 * q^8 + 2 * q^9 + 2 * q^12 - 2 * q^13 + 4 * q^14 + 6 * q^15 + 2 * q^16 + 2 * q^18 + 10 * q^19 + 4 * q^21 - 2 * q^23 + 2 * q^24 - 4 * q^25 - 2 * q^26 + 8 * q^27 + 4 * q^28 - 12 * q^29 + 6 * q^30 + 16 * q^31 + 2 * q^32 + 6 * q^33 + 2 * q^36 - 8 * q^37 + 10 * q^38 - 8 * q^39 + 6 * q^41 + 4 * q^42 - 8 * q^43 + 12 * q^45 - 2 * q^46 + 6 * q^47 + 2 * q^48 - 6 * q^49 - 4 * q^50 - 6 * q^51 - 2 * q^52 + 8 * q^54 + 6 * q^55 + 4 * q^56 + 4 * q^57 - 12 * q^58 + 18 * q^59 + 6 * q^60 + 4 * q^61 + 16 * q^62 + 4 * q^63 + 2 * q^64 - 6 * q^65 + 6 * q^66 - 2 * q^67 - 2 * q^69 + 18 * q^71 + 2 * q^72 - 2 * q^73 - 8 * q^74 - 4 * q^75 + 10 * q^76 - 8 * q^78 - 20 * q^79 + 2 * q^81 + 6 * q^82 + 6 * q^83 + 4 * q^84 - 6 * q^85 - 8 * q^86 + 12 * q^89 + 12 * q^90 - 4 * q^91 - 2 * q^92 + 16 * q^93 + 6 * q^94 - 6 * q^95 + 2 * q^96 - 8 * q^97 - 6 * q^98 + 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more