LMFDB - Embedded newform 847.2.a.h.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [847,2,Mod(1,847)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(847, 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("847.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 847 = 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	847.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:	$6.76332905120$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.61803$ of defining polynomial
Character	$\chi$	$=$	847.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.61803 q^{2} +0.618034 q^{3} +4.85410 q^{4} +1.00000 q^{5} +1.61803 q^{6} -1.00000 q^{7} +7.47214 q^{8} -2.61803 q^{9} +O(q^{10})$	\(q+2.61803 q^{2} +0.618034 q^{3} +4.85410 q^{4} +1.00000 q^{5} +1.61803 q^{6} -1.00000 q^{7} +7.47214 q^{8} -2.61803 q^{9} +2.61803 q^{10} +3.00000 q^{12} -3.23607 q^{13} -2.61803 q^{14} +0.618034 q^{15} +9.85410 q^{16} +8.09017 q^{17} -6.85410 q^{18} +6.23607 q^{19} +4.85410 q^{20} -0.618034 q^{21} -6.09017 q^{23} +4.61803 q^{24} -4.00000 q^{25} -8.47214 q^{26} -3.47214 q^{27} -4.85410 q^{28} +2.38197 q^{29} +1.61803 q^{30} +0.236068 q^{31} +10.8541 q^{32} +21.1803 q^{34} -1.00000 q^{35} -12.7082 q^{36} -2.47214 q^{37} +16.3262 q^{38} -2.00000 q^{39} +7.47214 q^{40} -11.1803 q^{41} -1.61803 q^{42} -7.56231 q^{43} -2.61803 q^{45} -15.9443 q^{46} -4.38197 q^{47} +6.09017 q^{48} +1.00000 q^{49} -10.4721 q^{50} +5.00000 q^{51} -15.7082 q^{52} -4.61803 q^{53} -9.09017 q^{54} -7.47214 q^{56} +3.85410 q^{57} +6.23607 q^{58} -0.0901699 q^{59} +3.00000 q^{60} +5.38197 q^{61} +0.618034 q^{62} +2.61803 q^{63} +8.70820 q^{64} -3.23607 q^{65} +7.32624 q^{67} +39.2705 q^{68} -3.76393 q^{69} -2.61803 q^{70} -4.90983 q^{71} -19.5623 q^{72} +9.76393 q^{73} -6.47214 q^{74} -2.47214 q^{75} +30.2705 q^{76} -5.23607 q^{78} -8.61803 q^{79} +9.85410 q^{80} +5.70820 q^{81} -29.2705 q^{82} +10.7082 q^{83} -3.00000 q^{84} +8.09017 q^{85} -19.7984 q^{86} +1.47214 q^{87} +0.145898 q^{89} -6.85410 q^{90} +3.23607 q^{91} -29.5623 q^{92} +0.145898 q^{93} -11.4721 q^{94} +6.23607 q^{95} +6.70820 q^{96} +7.00000 q^{97} +2.61803 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 3 q^{2} - q^{3} + 3 q^{4} + 2 q^{5} + q^{6} - 2 q^{7} + 6 q^{8} - 3 q^{9}+O(q^{10}) $ 2 * q + 3 * q^2 - q^3 + 3 * q^4 + 2 * q^5 + q^6 - 2 * q^7 + 6 * q^8 - 3 * q^9	$ 2 q + 3 q^{2} - q^{3} + 3 q^{4} + 2 q^{5} + q^{6} - 2 q^{7} + 6 q^{8} - 3 q^{9} + 3 q^{10} + 6 q^{12} - 2 q^{13} - 3 q^{14} - q^{15} + 13 q^{16} + 5 q^{17} - 7 q^{18} + 8 q^{19} + 3 q^{20} + q^{21} - q^{23} + 7 q^{24} - 8 q^{25} - 8 q^{26} + 2 q^{27} - 3 q^{28} + 7 q^{29} + q^{30} - 4 q^{31} + 15 q^{32} + 20 q^{34} - 2 q^{35} - 12 q^{36} + 4 q^{37} + 17 q^{38} - 4 q^{39} + 6 q^{40} - q^{42} + 5 q^{43} - 3 q^{45} - 14 q^{46} - 11 q^{47} + q^{48} + 2 q^{49} - 12 q^{50} + 10 q^{51} - 18 q^{52} - 7 q^{53} - 7 q^{54} - 6 q^{56} + q^{57} + 8 q^{58} + 11 q^{59} + 6 q^{60} + 13 q^{61} - q^{62} + 3 q^{63} + 4 q^{64} - 2 q^{65} - q^{67} + 45 q^{68} - 12 q^{69} - 3 q^{70} - 21 q^{71} - 19 q^{72} + 24 q^{73} - 4 q^{74} + 4 q^{75} + 27 q^{76} - 6 q^{78} - 15 q^{79} + 13 q^{80} - 2 q^{81} - 25 q^{82} + 8 q^{83} - 6 q^{84} + 5 q^{85} - 15 q^{86} - 6 q^{87} + 7 q^{89} - 7 q^{90} + 2 q^{91} - 39 q^{92} + 7 q^{93} - 14 q^{94} + 8 q^{95} + 14 q^{97} + 3 q^{98}+O(q^{100}) $ 2 * q + 3 * q^2 - q^3 + 3 * q^4 + 2 * q^5 + q^6 - 2 * q^7 + 6 * q^8 - 3 * q^9 + 3 * q^10 + 6 * q^12 - 2 * q^13 - 3 * q^14 - q^15 + 13 * q^16 + 5 * q^17 - 7 * q^18 + 8 * q^19 + 3 * q^20 + q^21 - q^23 + 7 * q^24 - 8 * q^25 - 8 * q^26 + 2 * q^27 - 3 * q^28 + 7 * q^29 + q^30 - 4 * q^31 + 15 * q^32 + 20 * q^34 - 2 * q^35 - 12 * q^36 + 4 * q^37 + 17 * q^38 - 4 * q^39 + 6 * q^40 - q^42 + 5 * q^43 - 3 * q^45 - 14 * q^46 - 11 * q^47 + q^48 + 2 * q^49 - 12 * q^50 + 10 * q^51 - 18 * q^52 - 7 * q^53 - 7 * q^54 - 6 * q^56 + q^57 + 8 * q^58 + 11 * q^59 + 6 * q^60 + 13 * q^61 - q^62 + 3 * q^63 + 4 * q^64 - 2 * q^65 - q^67 + 45 * q^68 - 12 * q^69 - 3 * q^70 - 21 * q^71 - 19 * q^72 + 24 * q^73 - 4 * q^74 + 4 * q^75 + 27 * q^76 - 6 * q^78 - 15 * q^79 + 13 * q^80 - 2 * q^81 - 25 * q^82 + 8 * q^83 - 6 * q^84 + 5 * q^85 - 15 * q^86 - 6 * q^87 + 7 * q^89 - 7 * q^90 + 2 * q^91 - 39 * q^92 + 7 * q^93 - 14 * q^94 + 8 * q^95 + 14 * q^97 + 3 * q^98

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 $

$2$	2.61803	1.85123	0.925615	−	0.378467i	$-0.123549\pi$
$2$	2.61803	1.85123	0.925615	+	0.378467i	$0.123549\pi$
$3$	0.618034	0.356822	0.178411	−	0.983956i	$-0.442904\pi$
$3$	0.618034	0.356822	0.178411	+	0.983956i	$0.442904\pi$
$4$	4.85410	2.42705
$5$	1.00000	0.447214	0.223607	−	0.974679i	$-0.428217\pi$
$5$	1.00000	0.447214	0.223607	+	0.974679i	$0.428217\pi$
$6$	1.61803	0.660560
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	7.47214	2.64180
$9$	−2.61803	−0.872678
$10$	2.61803	0.827895
$11$	0	0
$11$	0	0
$12$	3.00000	0.866025
$13$	−3.23607	−0.897524	−0.448762	−	0.893651i	$-0.648135\pi$
$13$	−3.23607	−0.897524	−0.448762	+	0.893651i	$0.648135\pi$
$14$	−2.61803	−0.699699
$15$	0.618034	0.159576
$16$	9.85410	2.46353
$17$	8.09017	1.96215	0.981077	−	0.193617i	$-0.0620219\pi$
$17$	8.09017	1.96215	0.981077	+	0.193617i	$0.0620219\pi$
$18$	−6.85410	−1.61553
$19$	6.23607	1.43065	0.715326	−	0.698791i	$-0.246278\pi$
$19$	6.23607	1.43065	0.715326	+	0.698791i	$0.246278\pi$
$20$	4.85410	1.08541
$21$	−0.618034	−0.134866
$22$	0	0
$23$	−6.09017	−1.26989	−0.634944	−	0.772558i	$-0.718977\pi$
$23$	−6.09017	−1.26989	−0.634944	+	0.772558i	$0.718977\pi$
$24$	4.61803	0.942652
$25$	−4.00000	−0.800000
$26$	−8.47214	−1.66152
$27$	−3.47214	−0.668213
$28$	−4.85410	−0.917339
$29$	2.38197	0.442320	0.221160	−	0.975238i	$-0.429016\pi$
$29$	2.38197	0.442320	0.221160	+	0.975238i	$0.429016\pi$
$30$	1.61803	0.295411
$31$	0.236068	0.0423991	0.0211995	−	0.999775i	$-0.493251\pi$
$31$	0.236068	0.0423991	0.0211995	+	0.999775i	$0.493251\pi$
$32$	10.8541	1.91875
$33$	0	0
$34$	21.1803	3.63240
$35$	−1.00000	−0.169031
$36$	−12.7082	−2.11803
$37$	−2.47214	−0.406417	−0.203208	−	0.979136i	$-0.565137\pi$
$37$	−2.47214	−0.406417	−0.203208	+	0.979136i	$0.565137\pi$
$38$	16.3262	2.64847
$39$	−2.00000	−0.320256
$40$	7.47214	1.18145
$41$	−11.1803	−1.74608	−0.873038	−	0.487652i	$-0.837853\pi$
$41$	−11.1803	−1.74608	−0.873038	+	0.487652i	$0.837853\pi$
$42$	−1.61803	−0.249668
$43$	−7.56231	−1.15324	−0.576620	−	0.817012i	$-0.695629\pi$
$43$	−7.56231	−1.15324	−0.576620	+	0.817012i	$0.695629\pi$
$44$	0	0
$45$	−2.61803	−0.390273
$46$	−15.9443	−2.35085
$47$	−4.38197	−0.639175	−0.319588	−	0.947557i	$-0.603544\pi$
$47$	−4.38197	−0.639175	−0.319588	+	0.947557i	$0.603544\pi$
$48$	6.09017	0.879040
$49$	1.00000	0.142857
$50$	−10.4721	−1.48098
$51$	5.00000	0.700140
$52$	−15.7082	−2.17834
$53$	−4.61803	−0.634336	−0.317168	−	0.948369i	$-0.602732\pi$
$53$	−4.61803	−0.634336	−0.317168	+	0.948369i	$0.602732\pi$
$54$	−9.09017	−1.23702
$55$	0	0
$56$	−7.47214	−0.998506
$57$	3.85410	0.510488
$58$	6.23607	0.818836
$59$	−0.0901699	−0.0117391	−0.00586956	−	0.999983i	$-0.501868\pi$
$59$	−0.0901699	−0.0117391	−0.00586956	+	0.999983i	$0.501868\pi$
$60$	3.00000	0.387298
$61$	5.38197	0.689090	0.344545	−	0.938770i	$-0.388033\pi$
$61$	5.38197	0.689090	0.344545	+	0.938770i	$0.388033\pi$
$62$	0.618034	0.0784904
$63$	2.61803	0.329841
$64$	8.70820	1.08853
$65$	−3.23607	−0.401385
$66$	0	0
$67$	7.32624	0.895042	0.447521	−	0.894273i	$-0.352307\pi$
$67$	7.32624	0.895042	0.447521	+	0.894273i	$0.352307\pi$
$68$	39.2705	4.76225
$69$	−3.76393	−0.453124
$70$	−2.61803	−0.312915
$71$	−4.90983	−0.582690	−0.291345	−	0.956618i	$-0.594103\pi$
$71$	−4.90983	−0.582690	−0.291345	+	0.956618i	$0.594103\pi$
$72$	−19.5623	−2.30544
$73$	9.76393	1.14278	0.571391	−	0.820678i	$-0.306404\pi$
$73$	9.76393	1.14278	0.571391	+	0.820678i	$0.306404\pi$
$74$	−6.47214	−0.752371
$75$	−2.47214	−0.285458
$76$	30.2705	3.47227
$77$	0	0
$78$	−5.23607	−0.592868
$79$	−8.61803	−0.969605	−0.484802	−	0.874624i	$-0.661108\pi$
$79$	−8.61803	−0.969605	−0.484802	+	0.874624i	$0.661108\pi$
$80$	9.85410	1.10172
$81$	5.70820	0.634245
$82$	−29.2705	−3.23239
$83$	10.7082	1.17538	0.587689	−	0.809087i	$-0.300038\pi$
$83$	10.7082	1.17538	0.587689	+	0.809087i	$0.300038\pi$
$84$	−3.00000	−0.327327
$85$	8.09017	0.877502
$86$	−19.7984	−2.13491
$87$	1.47214	0.157830
$88$	0	0
$89$	0.145898	0.0154652	0.00773258	−	0.999970i	$-0.497539\pi$
$89$	0.145898	0.0154652	0.00773258	+	0.999970i	$0.497539\pi$
$90$	−6.85410	−0.722486
$91$	3.23607	0.339232
$92$	−29.5623	−3.08208
$93$	0.145898	0.0151289
$94$	−11.4721	−1.18326
$95$	6.23607	0.639807
$96$	6.70820	0.684653
$97$	7.00000	0.710742	0.355371	−	0.934725i	$-0.384354\pi$
$97$	7.00000	0.710742	0.355371	+	0.934725i	$0.384354\pi$
$98$	2.61803	0.264461
$99$	0	0
$100$	−19.4164	−1.94164
$101$	−9.79837	−0.974975	−0.487487	−	0.873130i	$-0.662086\pi$
$101$	−9.79837	−0.974975	−0.487487	+	0.873130i	$0.662086\pi$
$102$	13.0902	1.29612
$103$	2.14590	0.211442	0.105721	−	0.994396i	$-0.466285\pi$
$103$	2.14590	0.211442	0.105721	+	0.994396i	$0.466285\pi$
$104$	−24.1803	−2.37108
$105$	−0.618034	−0.0603139
$106$	−12.0902	−1.17430
$107$	10.7082	1.03520	0.517601	−	0.855622i	$-0.326825\pi$
$107$	10.7082	1.03520	0.517601	+	0.855622i	$0.326825\pi$
$108$	−16.8541	−1.62179
$109$	10.4721	1.00305	0.501524	−	0.865144i	$-0.332773\pi$
$109$	10.4721	1.00305	0.501524	+	0.865144i	$0.332773\pi$
$110$	0	0
$111$	−1.52786	−0.145018
$112$	−9.85410	−0.931125
$113$	6.85410	0.644780	0.322390	−	0.946607i	$-0.395514\pi$
$113$	6.85410	0.644780	0.322390	+	0.946607i	$0.395514\pi$
$114$	10.0902	0.945031
$115$	−6.09017	−0.567911
$116$	11.5623	1.07353
$117$	8.47214	0.783249
$118$	−0.236068	−0.0217318
$119$	−8.09017	−0.741625
$120$	4.61803	0.421567
$121$	0	0
$122$	14.0902	1.27566
$123$	−6.90983	−0.623038
$124$	1.14590	0.102905
$125$	−9.00000	−0.804984
$126$	6.85410	0.610612
$127$	14.9443	1.32609	0.663045	−	0.748580i	$-0.269264\pi$
$127$	14.9443	1.32609	0.663045	+	0.748580i	$0.269264\pi$
$128$	1.09017	0.0963583
$129$	−4.67376	−0.411502
$130$	−8.47214	−0.743055
$131$	−1.05573	−0.0922394	−0.0461197	−	0.998936i	$-0.514686\pi$
$131$	−1.05573	−0.0922394	−0.0461197	+	0.998936i	$0.514686\pi$
$132$	0	0
$133$	−6.23607	−0.540736
$134$	19.1803	1.65693
$135$	−3.47214	−0.298834
$136$	60.4508	5.18362
$137$	0.326238	0.0278724	0.0139362	−	0.999903i	$-0.495564\pi$
$137$	0.326238	0.0278724	0.0139362	+	0.999903i	$0.495564\pi$
$138$	−9.85410	−0.838837
$139$	5.94427	0.504187	0.252093	−	0.967703i	$-0.418881\pi$
$139$	5.94427	0.504187	0.252093	+	0.967703i	$0.418881\pi$
$140$	−4.85410	−0.410246
$141$	−2.70820	−0.228072
$142$	−12.8541	−1.07869
$143$	0	0
$144$	−25.7984	−2.14986
$145$	2.38197	0.197812
$146$	25.5623	2.11555
$147$	0.618034	0.0509746
$148$	−12.0000	−0.986394
$149$	2.14590	0.175799	0.0878994	−	0.996129i	$-0.471985\pi$
$149$	2.14590	0.175799	0.0878994	+	0.996129i	$0.471985\pi$
$150$	−6.47214	−0.528448
$151$	−17.9443	−1.46028	−0.730142	−	0.683295i	$-0.760546\pi$
$151$	−17.9443	−1.46028	−0.730142	+	0.683295i	$0.760546\pi$
$152$	46.5967	3.77950
$153$	−21.1803	−1.71233
$154$	0	0
$155$	0.236068	0.0189614
$156$	−9.70820	−0.777278
$157$	−15.8885	−1.26804	−0.634022	−	0.773315i	$-0.718597\pi$
$157$	−15.8885	−1.26804	−0.634022	+	0.773315i	$0.718597\pi$
$158$	−22.5623	−1.79496
$159$	−2.85410	−0.226345
$160$	10.8541	0.858092
$161$	6.09017	0.479973
$162$	14.9443	1.17413
$163$	4.70820	0.368775	0.184387	−	0.982854i	$-0.440970\pi$
$163$	4.70820	0.368775	0.184387	+	0.982854i	$0.440970\pi$
$164$	−54.2705	−4.23781
$165$	0	0
$166$	28.0344	2.17589
$167$	2.47214	0.191300	0.0956498	−	0.995415i	$-0.469507\pi$
$167$	2.47214	0.191300	0.0956498	+	0.995415i	$0.469507\pi$
$168$	−4.61803	−0.356289
$169$	−2.52786	−0.194451
$170$	21.1803	1.62446
$171$	−16.3262	−1.24850
$172$	−36.7082	−2.79897
$173$	17.6180	1.33947	0.669737	−	0.742598i	$-0.266407\pi$
$173$	17.6180	1.33947	0.669737	+	0.742598i	$0.266407\pi$
$174$	3.85410	0.292179
$175$	4.00000	0.302372
$176$	0	0
$177$	−0.0557281	−0.00418878
$178$	0.381966	0.0286296
$179$	−8.23607	−0.615593	−0.307796	−	0.951452i	$-0.599592\pi$
$179$	−8.23607	−0.615593	−0.307796	+	0.951452i	$0.599592\pi$
$180$	−12.7082	−0.947214
$181$	19.4164	1.44321	0.721605	−	0.692305i	$-0.243405\pi$
$181$	19.4164	1.44321	0.721605	+	0.692305i	$0.243405\pi$
$182$	8.47214	0.627996
$183$	3.32624	0.245883
$184$	−45.5066	−3.35479
$185$	−2.47214	−0.181755
$186$	0.381966	0.0280071
$187$	0	0
$188$	−21.2705	−1.55131
$189$	3.47214	0.252561
$190$	16.3262	1.18443
$191$	20.2361	1.46423	0.732115	−	0.681181i	$-0.238533\pi$
$191$	20.2361	1.46423	0.732115	+	0.681181i	$0.238533\pi$
$192$	5.38197	0.388410
$193$	−0.326238	−0.0234831	−0.0117416	−	0.999931i	$-0.503738\pi$
$193$	−0.326238	−0.0234831	−0.0117416	+	0.999931i	$0.503738\pi$
$194$	18.3262	1.31575
$195$	−2.00000	−0.143223
$196$	4.85410	0.346722
$197$	17.7082	1.26166	0.630829	−	0.775922i	$-0.282715\pi$
$197$	17.7082	1.26166	0.630829	+	0.775922i	$0.282715\pi$
$198$	0	0
$199$	−3.76393	−0.266818	−0.133409	−	0.991061i	$-0.542592\pi$
$199$	−3.76393	−0.266818	−0.133409	+	0.991061i	$0.542592\pi$
$200$	−29.8885	−2.11344
$201$	4.52786	0.319371
$202$	−25.6525	−1.80490
$203$	−2.38197	−0.167181
$204$	24.2705	1.69928
$205$	−11.1803	−0.780869
$206$	5.61803	0.391427
$207$	15.9443	1.10820
$208$	−31.8885	−2.21107
$209$	0	0
$210$	−1.61803	−0.111655
$211$	−13.3820	−0.921253	−0.460626	−	0.887594i	$-0.652375\pi$
$211$	−13.3820	−0.921253	−0.460626	+	0.887594i	$0.652375\pi$
$212$	−22.4164	−1.53957
$213$	−3.03444	−0.207917
$214$	28.0344	1.91639
$215$	−7.56231	−0.515745
$216$	−25.9443	−1.76528
$217$	−0.236068	−0.0160253
$218$	27.4164	1.85687
$219$	6.03444	0.407770
$220$	0	0
$221$	−26.1803	−1.76108
$222$	−4.00000	−0.268462
$223$	−27.0344	−1.81036	−0.905180	−	0.425028i	$-0.860264\pi$
$223$	−27.0344	−1.81036	−0.905180	+	0.425028i	$0.860264\pi$
$224$	−10.8541	−0.725220
$225$	10.4721	0.698142
$226$	17.9443	1.19364
$227$	−13.0344	−0.865126	−0.432563	−	0.901604i	$-0.642391\pi$
$227$	−13.0344	−0.865126	−0.432563	+	0.901604i	$0.642391\pi$
$228$	18.7082	1.23898
$229$	11.2361	0.742500	0.371250	−	0.928533i	$-0.378929\pi$
$229$	11.2361	0.742500	0.371250	+	0.928533i	$0.378929\pi$
$230$	−15.9443	−1.05133
$231$	0	0
$232$	17.7984	1.16852
$233$	2.58359	0.169257	0.0846284	−	0.996413i	$-0.473030\pi$
$233$	2.58359	0.169257	0.0846284	+	0.996413i	$0.473030\pi$
$234$	22.1803	1.44997
$235$	−4.38197	−0.285848
$236$	−0.437694	−0.0284915
$237$	−5.32624	−0.345976
$238$	−21.1803	−1.37292
$239$	5.90983	0.382275	0.191138	−	0.981563i	$-0.438782\pi$
$239$	5.90983	0.382275	0.191138	+	0.981563i	$0.438782\pi$
$240$	6.09017	0.393119
$241$	17.2705	1.11249	0.556246	−	0.831018i	$-0.312241\pi$
$241$	17.2705	1.11249	0.556246	+	0.831018i	$0.312241\pi$
$242$	0	0
$243$	13.9443	0.894525
$244$	26.1246	1.67246
$245$	1.00000	0.0638877
$246$	−18.0902	−1.15339
$247$	−20.1803	−1.28404
$248$	1.76393	0.112010
$249$	6.61803	0.419401
$250$	−23.5623	−1.49021
$251$	23.0000	1.45175	0.725874	−	0.687828i	$-0.241436\pi$
$251$	23.0000	1.45175	0.725874	+	0.687828i	$0.241436\pi$
$252$	12.7082	0.800542
$253$	0	0
$254$	39.1246	2.45490
$255$	5.00000	0.313112
$256$	−14.5623	−0.910144
$257$	11.5623	0.721237	0.360618	−	0.932713i	$-0.382566\pi$
$257$	11.5623	0.721237	0.360618	+	0.932713i	$0.382566\pi$
$258$	−12.2361	−0.761784
$259$	2.47214	0.153611
$260$	−15.7082	−0.974181
$261$	−6.23607	−0.386003
$262$	−2.76393	−0.170756
$263$	−23.1246	−1.42592	−0.712962	−	0.701202i	$-0.752647\pi$
$263$	−23.1246	−1.42592	−0.712962	+	0.701202i	$0.752647\pi$
$264$	0	0
$265$	−4.61803	−0.283684
$266$	−16.3262	−1.00103
$267$	0.0901699	0.00551831
$268$	35.5623	2.17231
$269$	10.1459	0.618606	0.309303	−	0.950963i	$-0.399904\pi$
$269$	10.1459	0.618606	0.309303	+	0.950963i	$0.399904\pi$
$270$	−9.09017	−0.553210
$271$	−19.7984	−1.20267	−0.601333	−	0.798999i	$-0.705363\pi$
$271$	−19.7984	−1.20267	−0.601333	+	0.798999i	$0.705363\pi$
$272$	79.7214	4.83382
$273$	2.00000	0.121046
$274$	0.854102	0.0515982
$275$	0	0
$276$	−18.2705	−1.09976
$277$	6.03444	0.362574	0.181287	−	0.983430i	$-0.441974\pi$
$277$	6.03444	0.362574	0.181287	+	0.983430i	$0.441974\pi$
$278$	15.5623	0.933365
$279$	−0.618034	−0.0370007
$280$	−7.47214	−0.446546
$281$	2.81966	0.168207	0.0841034	−	0.996457i	$-0.473197\pi$
$281$	2.81966	0.168207	0.0841034	+	0.996457i	$0.473197\pi$
$282$	−7.09017	−0.422213
$283$	5.94427	0.353350	0.176675	−	0.984269i	$-0.443466\pi$
$283$	5.94427	0.353350	0.176675	+	0.984269i	$0.443466\pi$
$284$	−23.8328	−1.41422
$285$	3.85410	0.228297
$286$	0	0
$287$	11.1803	0.659955
$288$	−28.4164	−1.67445
$289$	48.4508	2.85005
$290$	6.23607	0.366195
$291$	4.32624	0.253609
$292$	47.3951	2.77359
$293$	11.0000	0.642627	0.321313	−	0.946973i	$-0.395876\pi$
$293$	11.0000	0.642627	0.321313	+	0.946973i	$0.395876\pi$
$294$	1.61803	0.0943657
$295$	−0.0901699	−0.00524990
$296$	−18.4721	−1.07367
$297$	0	0
$298$	5.61803	0.325444
$299$	19.7082	1.13975
$300$	−12.0000	−0.692820
$301$	7.56231	0.435884
$302$	−46.9787	−2.70332
$303$	−6.05573	−0.347892
$304$	61.4508	3.52445
$305$	5.38197	0.308170
$306$	−55.4508	−3.16991
$307$	0.819660	0.0467805	0.0233902	−	0.999726i	$-0.492554\pi$
$307$	0.819660	0.0467805	0.0233902	+	0.999726i	$0.492554\pi$
$308$	0	0
$309$	1.32624	0.0754470
$310$	0.618034	0.0351020
$311$	9.00000	0.510343	0.255172	−	0.966896i	$-0.417868\pi$
$311$	9.00000	0.510343	0.255172	+	0.966896i	$0.417868\pi$
$312$	−14.9443	−0.846053
$313$	2.67376	0.151130	0.0755650	−	0.997141i	$-0.475924\pi$
$313$	2.67376	0.151130	0.0755650	+	0.997141i	$0.475924\pi$
$314$	−41.5967	−2.34744
$315$	2.61803	0.147510
$316$	−41.8328	−2.35328
$317$	−24.5623	−1.37956	−0.689778	−	0.724021i	$-0.742292\pi$
$317$	−24.5623	−1.37956	−0.689778	+	0.724021i	$0.742292\pi$
$318$	−7.47214	−0.419017
$319$	0	0
$320$	8.70820	0.486803
$321$	6.61803	0.369383
$322$	15.9443	0.888540
$323$	50.4508	2.80716
$324$	27.7082	1.53934
$325$	12.9443	0.718019
$326$	12.3262	0.682687
$327$	6.47214	0.357910
$328$	−83.5410	−4.61278
$329$	4.38197	0.241586
$330$	0	0
$331$	−16.1803	−0.889352	−0.444676	−	0.895692i	$-0.646681\pi$
$331$	−16.1803	−0.889352	−0.444676	+	0.895692i	$0.646681\pi$
$332$	51.9787	2.85270
$333$	6.47214	0.354671
$334$	6.47214	0.354140
$335$	7.32624	0.400275
$336$	−6.09017	−0.332246
$337$	−8.05573	−0.438823	−0.219412	−	0.975632i	$-0.570414\pi$
$337$	−8.05573	−0.438823	−0.219412	+	0.975632i	$0.570414\pi$
$338$	−6.61803	−0.359974
$339$	4.23607	0.230072
$340$	39.2705	2.12974
$341$	0	0
$342$	−42.7426	−2.31126
$343$	−1.00000	−0.0539949
$344$	−56.5066	−3.04663
$345$	−3.76393	−0.202643
$346$	46.1246	2.47967
$347$	−33.6525	−1.80656	−0.903280	−	0.429052i	$-0.858848\pi$
$347$	−33.6525	−1.80656	−0.903280	+	0.429052i	$0.858848\pi$
$348$	7.14590	0.383060
$349$	−8.20163	−0.439023	−0.219511	−	0.975610i	$-0.570446\pi$
$349$	−8.20163	−0.439023	−0.219511	+	0.975610i	$0.570446\pi$
$350$	10.4721	0.559759
$351$	11.2361	0.599737
$352$	0	0
$353$	12.9098	0.687121	0.343560	−	0.939131i	$-0.388367\pi$
$353$	12.9098	0.687121	0.343560	+	0.939131i	$0.388367\pi$
$354$	−0.145898	−0.00775439
$355$	−4.90983	−0.260587
$356$	0.708204	0.0375347
$357$	−5.00000	−0.264628
$358$	−21.5623	−1.13960
$359$	13.3820	0.706273	0.353137	−	0.935572i	$-0.385115\pi$
$359$	13.3820	0.706273	0.353137	+	0.935572i	$0.385115\pi$
$360$	−19.5623	−1.03102
$361$	19.8885	1.04677
$362$	50.8328	2.67171
$363$	0	0
$364$	15.7082	0.823334
$365$	9.76393	0.511068
$366$	8.70820	0.455185
$367$	−20.8328	−1.08746	−0.543732	−	0.839259i	$-0.682989\pi$
$367$	−20.8328	−1.08746	−0.543732	+	0.839259i	$0.682989\pi$
$368$	−60.0132	−3.12840
$369$	29.2705	1.52376
$370$	−6.47214	−0.336470
$371$	4.61803	0.239756
$372$	0.708204	0.0367187
$373$	35.5623	1.84135	0.920673	−	0.390334i	$-0.127641\pi$
$373$	35.5623	1.84135	0.920673	+	0.390334i	$0.127641\pi$
$374$	0	0
$375$	−5.56231	−0.287236
$376$	−32.7426	−1.68857
$377$	−7.70820	−0.396993
$378$	9.09017	0.467548
$379$	−26.0689	−1.33907	−0.669534	−	0.742781i	$-0.733506\pi$
$379$	−26.0689	−1.33907	−0.669534	+	0.742781i	$0.733506\pi$
$380$	30.2705	1.55284
$381$	9.23607	0.473178
$382$	52.9787	2.71063
$383$	14.5967	0.745859	0.372929	−	0.927860i	$-0.378353\pi$
$383$	14.5967	0.745859	0.372929	+	0.927860i	$0.378353\pi$
$384$	0.673762	0.0343828
$385$	0	0
$386$	−0.854102	−0.0434726
$387$	19.7984	1.00641
$388$	33.9787	1.72501
$389$	−11.8197	−0.599281	−0.299640	−	0.954052i	$-0.596867\pi$
$389$	−11.8197	−0.599281	−0.299640	+	0.954052i	$0.596867\pi$
$390$	−5.23607	−0.265139
$391$	−49.2705	−2.49172
$392$	7.47214	0.377400
$393$	−0.652476	−0.0329131
$394$	46.3607	2.33562
$395$	−8.61803	−0.433620
$396$	0	0
$397$	−23.1803	−1.16339	−0.581694	−	0.813408i	$-0.697610\pi$
$397$	−23.1803	−1.16339	−0.581694	+	0.813408i	$0.697610\pi$
$398$	−9.85410	−0.493941
$399$	−3.85410	−0.192946
$400$	−39.4164	−1.97082
$401$	−26.4721	−1.32196	−0.660978	−	0.750406i	$-0.729858\pi$
$401$	−26.4721	−1.32196	−0.660978	+	0.750406i	$0.729858\pi$
$402$	11.8541	0.591229
$403$	−0.763932	−0.0380542
$404$	−47.5623	−2.36631
$405$	5.70820	0.283643
$406$	−6.23607	−0.309491
$407$	0	0
$408$	37.3607	1.84963
$409$	4.29180	0.212216	0.106108	−	0.994355i	$-0.466161\pi$
$409$	4.29180	0.212216	0.106108	+	0.994355i	$0.466161\pi$
$410$	−29.2705	−1.44557
$411$	0.201626	0.00994548
$412$	10.4164	0.513180
$413$	0.0901699	0.00443697
$414$	41.7426	2.05154
$415$	10.7082	0.525645
$416$	−35.1246	−1.72213
$417$	3.67376	0.179905
$418$	0	0
$419$	−5.88854	−0.287674	−0.143837	−	0.989601i	$-0.545944\pi$
$419$	−5.88854	−0.287674	−0.143837	+	0.989601i	$0.545944\pi$
$420$	−3.00000	−0.146385
$421$	5.23607	0.255190	0.127595	−	0.991826i	$-0.459274\pi$
$421$	5.23607	0.255190	0.127595	+	0.991826i	$0.459274\pi$
$422$	−35.0344	−1.70545
$423$	11.4721	0.557794
$424$	−34.5066	−1.67579
$425$	−32.3607	−1.56972
$426$	−7.94427	−0.384901
$427$	−5.38197	−0.260452
$428$	51.9787	2.51249
$429$	0	0
$430$	−19.7984	−0.954762
$431$	7.14590	0.344206	0.172103	−	0.985079i	$-0.444944\pi$
$431$	7.14590	0.344206	0.172103	+	0.985079i	$0.444944\pi$
$432$	−34.2148	−1.64616
$433$	−38.0344	−1.82782	−0.913909	−	0.405918i	$-0.866952\pi$
$433$	−38.0344	−1.82782	−0.913909	+	0.405918i	$0.866952\pi$
$434$	−0.618034	−0.0296666
$435$	1.47214	0.0705835
$436$	50.8328	2.43445
$437$	−37.9787	−1.81677
$438$	15.7984	0.754876
$439$	−5.61803	−0.268134	−0.134067	−	0.990972i	$-0.542804\pi$
$439$	−5.61803	−0.268134	−0.134067	+	0.990972i	$0.542804\pi$
$440$	0	0
$441$	−2.61803	−0.124668
$442$	−68.5410	−3.26016
$443$	−8.09017	−0.384376	−0.192188	−	0.981358i	$-0.561558\pi$
$443$	−8.09017	−0.384376	−0.192188	+	0.981358i	$0.561558\pi$
$444$	−7.41641	−0.351967
$445$	0.145898	0.00691623
$446$	−70.7771	−3.35139
$447$	1.32624	0.0627289
$448$	−8.70820	−0.411424
$449$	−3.32624	−0.156975	−0.0784874	−	0.996915i	$-0.525009\pi$
$449$	−3.32624	−0.156975	−0.0784874	+	0.996915i	$0.525009\pi$
$450$	27.4164	1.29242
$451$	0	0
$452$	33.2705	1.56491
$453$	−11.0902	−0.521062
$454$	−34.1246	−1.60155
$455$	3.23607	0.151709
$456$	28.7984	1.34861
$457$	6.85410	0.320621	0.160311	−	0.987067i	$-0.448750\pi$
$457$	6.85410	0.320621	0.160311	+	0.987067i	$0.448750\pi$
$458$	29.4164	1.37454
$459$	−28.0902	−1.31114
$460$	−29.5623	−1.37835
$461$	−19.5066	−0.908512	−0.454256	−	0.890871i	$-0.650095\pi$
$461$	−19.5066	−0.908512	−0.454256	+	0.890871i	$0.650095\pi$
$462$	0	0
$463$	17.7639	0.825560	0.412780	−	0.910831i	$-0.364558\pi$
$463$	17.7639	0.825560	0.412780	+	0.910831i	$0.364558\pi$
$464$	23.4721	1.08967
$465$	0.145898	0.00676586
$466$	6.76393	0.313333
$467$	33.5066	1.55050	0.775250	−	0.631655i	$-0.217624\pi$
$467$	33.5066	1.55050	0.775250	+	0.631655i	$0.217624\pi$
$468$	41.1246	1.90099
$469$	−7.32624	−0.338294
$470$	−11.4721	−0.529170
$471$	−9.81966	−0.452466
$472$	−0.673762	−0.0310124
$473$	0	0
$474$	−13.9443	−0.640482
$475$	−24.9443	−1.14452
$476$	−39.2705	−1.79996
$477$	12.0902	0.553571
$478$	15.4721	0.707679
$479$	−26.2361	−1.19876	−0.599378	−	0.800466i	$-0.704585\pi$
$479$	−26.2361	−1.19876	−0.599378	+	0.800466i	$0.704585\pi$
$480$	6.70820	0.306186
$481$	8.00000	0.364769
$482$	45.2148	2.05948
$483$	3.76393	0.171265
$484$	0	0
$485$	7.00000	0.317854
$486$	36.5066	1.65597
$487$	16.5967	0.752070	0.376035	−	0.926605i	$-0.377287\pi$
$487$	16.5967	0.752070	0.376035	+	0.926605i	$0.377287\pi$
$488$	40.2148	1.82044
$489$	2.90983	0.131587
$490$	2.61803	0.118271
$491$	−28.8541	−1.30217	−0.651084	−	0.759006i	$-0.725685\pi$
$491$	−28.8541	−1.30217	−0.651084	+	0.759006i	$0.725685\pi$
$492$	−33.5410	−1.51215
$493$	19.2705	0.867900
$494$	−52.8328	−2.37706
$495$	0	0
$496$	2.32624	0.104451
$497$	4.90983	0.220236
$498$	17.3262	0.776407
$499$	1.09017	0.0488027	0.0244014	−	0.999702i	$-0.492232\pi$
$499$	1.09017	0.0488027	0.0244014	+	0.999702i	$0.492232\pi$
$500$	−43.6869	−1.95374
$501$	1.52786	0.0682599
$502$	60.2148	2.68752
$503$	−18.8328	−0.839714	−0.419857	−	0.907590i	$-0.637920\pi$
$503$	−18.8328	−0.839714	−0.419857	+	0.907590i	$0.637920\pi$
$504$	19.5623	0.871374
$505$	−9.79837	−0.436022
$506$	0	0
$507$	−1.56231	−0.0693844
$508$	72.5410	3.21849
$509$	31.7426	1.40697	0.703484	−	0.710711i	$-0.251627\pi$
$509$	31.7426	1.40697	0.703484	+	0.710711i	$0.251627\pi$
$510$	13.0902	0.579642
$511$	−9.76393	−0.431931
$512$	−40.3050	−1.78124
$513$	−21.6525	−0.955980
$514$	30.2705	1.33517
$515$	2.14590	0.0945596
$516$	−22.6869	−0.998736
$517$	0	0
$518$	6.47214	0.284369
$519$	10.8885	0.477954
$520$	−24.1803	−1.06038
$521$	−7.76393	−0.340144	−0.170072	−	0.985432i	$-0.554400\pi$
$521$	−7.76393	−0.340144	−0.170072	+	0.985432i	$0.554400\pi$
$522$	−16.3262	−0.714580
$523$	3.56231	0.155769	0.0778844	−	0.996962i	$-0.475183\pi$
$523$	3.56231	0.155769	0.0778844	+	0.996962i	$0.475183\pi$
$524$	−5.12461	−0.223870
$525$	2.47214	0.107893
$526$	−60.5410	−2.63971
$527$	1.90983	0.0831935
$528$	0	0
$529$	14.0902	0.612616
$530$	−12.0902	−0.525163
$531$	0.236068	0.0102445
$532$	−30.2705	−1.31239
$533$	36.1803	1.56714
$534$	0.236068	0.0102157
$535$	10.7082	0.462956
$536$	54.7426	2.36452
$537$	−5.09017	−0.219657
$538$	26.5623	1.14518
$539$	0	0
$540$	−16.8541	−0.725285
$541$	12.7082	0.546368	0.273184	−	0.961962i	$-0.411923\pi$
$541$	12.7082	0.546368	0.273184	+	0.961962i	$0.411923\pi$
$542$	−51.8328	−2.22641
$543$	12.0000	0.514969
$544$	87.8115	3.76489
$545$	10.4721	0.448577
$546$	5.23607	0.224083
$547$	35.2705	1.50806	0.754029	−	0.656841i	$-0.228108\pi$
$547$	35.2705	1.50806	0.754029	+	0.656841i	$0.228108\pi$
$548$	1.58359	0.0676477
$549$	−14.0902	−0.601354
$550$	0	0
$551$	14.8541	0.632806
$552$	−28.1246	−1.19706
$553$	8.61803	0.366476
$554$	15.7984	0.671209
$555$	−1.52786	−0.0648542
$556$	28.8541	1.22369
$557$	14.2361	0.603202	0.301601	−	0.953434i	$-0.402479\pi$
$557$	14.2361	0.603202	0.301601	+	0.953434i	$0.402479\pi$
$558$	−1.61803	−0.0684968
$559$	24.4721	1.03506
$560$	−9.85410	−0.416412
$561$	0	0
$562$	7.38197	0.311389
$563$	−14.9787	−0.631278	−0.315639	−	0.948879i	$-0.602219\pi$
$563$	−14.9787	−0.631278	−0.315639	+	0.948879i	$0.602219\pi$
$564$	−13.1459	−0.553542
$565$	6.85410	0.288354
$566$	15.5623	0.654133
$567$	−5.70820	−0.239722
$568$	−36.6869	−1.53935
$569$	25.3050	1.06084	0.530419	−	0.847735i	$-0.322034\pi$
$569$	25.3050	1.06084	0.530419	+	0.847735i	$0.322034\pi$
$570$	10.0902	0.422631
$571$	28.3050	1.18453	0.592263	−	0.805745i	$-0.298235\pi$
$571$	28.3050	1.18453	0.592263	+	0.805745i	$0.298235\pi$
$572$	0	0
$573$	12.5066	0.522470
$574$	29.2705	1.22173
$575$	24.3607	1.01591
$576$	−22.7984	−0.949932
$577$	−21.6525	−0.901404	−0.450702	−	0.892674i	$-0.648826\pi$
$577$	−21.6525	−0.901404	−0.450702	+	0.892674i	$0.648826\pi$
$578$	126.846	5.27610
$579$	−0.201626	−0.00837930
$580$	11.5623	0.480099
$581$	−10.7082	−0.444251
$582$	11.3262	0.469488
$583$	0	0
$584$	72.9574	3.01900
$585$	8.47214	0.350280
$586$	28.7984	1.18965
$587$	1.00000	0.0412744	0.0206372	−	0.999787i	$-0.493431\pi$
$587$	1.00000	0.0412744	0.0206372	+	0.999787i	$0.493431\pi$
$588$	3.00000	0.123718
$589$	1.47214	0.0606583
$590$	−0.236068	−0.00971876
$591$	10.9443	0.450187
$592$	−24.3607	−1.00122
$593$	29.1246	1.19600	0.598002	−	0.801494i	$-0.295961\pi$
$593$	29.1246	1.19600	0.598002	+	0.801494i	$0.295961\pi$
$594$	0	0
$595$	−8.09017	−0.331665
$596$	10.4164	0.426673
$597$	−2.32624	−0.0952066
$598$	51.5967	2.10995
$599$	−16.0000	−0.653742	−0.326871	−	0.945069i	$-0.605994\pi$
$599$	−16.0000	−0.653742	−0.326871	+	0.945069i	$0.605994\pi$
$600$	−18.4721	−0.754122
$601$	−0.291796	−0.0119026	−0.00595130	−	0.999982i	$-0.501894\pi$
$601$	−0.291796	−0.0119026	−0.00595130	+	0.999982i	$0.501894\pi$
$602$	19.7984	0.806921
$603$	−19.1803	−0.781084
$604$	−87.1033	−3.54418
$605$	0	0
$606$	−15.8541	−0.644029
$607$	−44.7984	−1.81831	−0.909155	−	0.416458i	$-0.863271\pi$
$607$	−44.7984	−1.81831	−0.909155	+	0.416458i	$0.863271\pi$
$608$	67.6869	2.74507
$609$	−1.47214	−0.0596540
$610$	14.0902	0.570494
$611$	14.1803	0.573675
$612$	−102.812	−4.15591
$613$	−34.8885	−1.40914	−0.704568	−	0.709637i	$-0.748859\pi$
$613$	−34.8885	−1.40914	−0.704568	+	0.709637i	$0.748859\pi$
$614$	2.14590	0.0866014
$615$	−6.90983	−0.278631
$616$	0	0
$617$	−17.4164	−0.701158	−0.350579	−	0.936533i	$-0.614015\pi$
$617$	−17.4164	−0.701158	−0.350579	+	0.936533i	$0.614015\pi$
$618$	3.47214	0.139670
$619$	−26.2918	−1.05676	−0.528378	−	0.849009i	$-0.677200\pi$
$619$	−26.2918	−1.05676	−0.528378	+	0.849009i	$0.677200\pi$
$620$	1.14590	0.0460204
$621$	21.1459	0.848556
$622$	23.5623	0.944762
$623$	−0.145898	−0.00584528
$624$	−19.7082	−0.788960
$625$	11.0000	0.440000
$626$	7.00000	0.279776
$627$	0	0
$628$	−77.1246	−3.07761
$629$	−20.0000	−0.797452
$630$	6.85410	0.273074
$631$	−35.8328	−1.42648	−0.713241	−	0.700919i	$-0.752773\pi$
$631$	−35.8328	−1.42648	−0.713241	+	0.700919i	$0.752773\pi$
$632$	−64.3951	−2.56150
$633$	−8.27051	−0.328723
$634$	−64.3050	−2.55388
$635$	14.9443	0.593045
$636$	−13.8541	−0.549351
$637$	−3.23607	−0.128218
$638$	0	0
$639$	12.8541	0.508500
$640$	1.09017	0.0430928
$641$	0.347524	0.0137264	0.00686319	−	0.999976i	$-0.497815\pi$
$641$	0.347524	0.0137264	0.00686319	+	0.999976i	$0.497815\pi$
$642$	17.3262	0.683812
$643$	28.4164	1.12063	0.560317	−	0.828278i	$-0.310679\pi$
$643$	28.4164	1.12063	0.560317	+	0.828278i	$0.310679\pi$
$644$	29.5623	1.16492
$645$	−4.67376	−0.184029
$646$	132.082	5.19670
$647$	−16.1803	−0.636115	−0.318057	−	0.948071i	$-0.603030\pi$
$647$	−16.1803	−0.636115	−0.318057	+	0.948071i	$0.603030\pi$
$648$	42.6525	1.67555
$649$	0	0
$650$	33.8885	1.32922
$651$	−0.145898	−0.00571819
$652$	22.8541	0.895036
$653$	13.7639	0.538624	0.269312	−	0.963053i	$-0.413204\pi$
$653$	13.7639	0.538624	0.269312	+	0.963053i	$0.413204\pi$
$654$	16.9443	0.662573
$655$	−1.05573	−0.0412507
$656$	−110.172	−4.30150
$657$	−25.5623	−0.997281
$658$	11.4721	0.447230
$659$	−22.5279	−0.877561	−0.438780	−	0.898594i	$-0.644589\pi$
$659$	−22.5279	−0.877561	−0.438780	+	0.898594i	$0.644589\pi$
$660$	0	0
$661$	−14.4377	−0.561561	−0.280781	−	0.959772i	$-0.590593\pi$
$661$	−14.4377	−0.561561	−0.280781	+	0.959772i	$0.590593\pi$
$662$	−42.3607	−1.64639
$663$	−16.1803	−0.628392
$664$	80.0132	3.10511
$665$	−6.23607	−0.241824
$666$	16.9443	0.656577
$667$	−14.5066	−0.561697
$668$	12.0000	0.464294
$669$	−16.7082	−0.645976
$670$	19.1803	0.741001
$671$	0	0
$672$	−6.70820	−0.258775
$673$	33.4164	1.28811	0.644054	−	0.764980i	$-0.277251\pi$
$673$	33.4164	1.28811	0.644054	+	0.764980i	$0.277251\pi$
$674$	−21.0902	−0.812363
$675$	13.8885	0.534570
$676$	−12.2705	−0.471943
$677$	2.72949	0.104903	0.0524514	−	0.998623i	$-0.483297\pi$
$677$	2.72949	0.104903	0.0524514	+	0.998623i	$0.483297\pi$
$678$	11.0902	0.425915
$679$	−7.00000	−0.268635
$680$	60.4508	2.31818
$681$	−8.05573	−0.308696
$682$	0	0
$683$	38.5066	1.47341	0.736707	−	0.676213i	$-0.236380\pi$
$683$	38.5066	1.47341	0.736707	+	0.676213i	$0.236380\pi$
$684$	−79.2492	−3.03017
$685$	0.326238	0.0124649
$686$	−2.61803	−0.0999570
$687$	6.94427	0.264940
$688$	−74.5197	−2.84104
$689$	14.9443	0.569331
$690$	−9.85410	−0.375139
$691$	−48.5410	−1.84659	−0.923294	−	0.384095i	$-0.874514\pi$
$691$	−48.5410	−1.84659	−0.923294	+	0.384095i	$0.874514\pi$
$692$	85.5197	3.25097
$693$	0	0
$694$	−88.1033	−3.34436
$695$	5.94427	0.225479
$696$	11.0000	0.416954
$697$	−90.4508	−3.42607
$698$	−21.4721	−0.812732
$699$	1.59675	0.0603945
$700$	19.4164	0.733871
$701$	19.5066	0.736753	0.368377	−	0.929677i	$-0.379914\pi$
$701$	19.5066	0.736753	0.368377	+	0.929677i	$0.379914\pi$
$702$	29.4164	1.11025
$703$	−15.4164	−0.581441
$704$	0	0
$705$	−2.70820	−0.101997
$706$	33.7984	1.27202
$707$	9.79837	0.368506
$708$	−0.270510	−0.0101664
$709$	22.0344	0.827521	0.413760	−	0.910386i	$-0.364215\pi$
$709$	22.0344	0.827521	0.413760	+	0.910386i	$0.364215\pi$
$710$	−12.8541	−0.482406
$711$	22.5623	0.846153
$712$	1.09017	0.0408558
$713$	−1.43769	−0.0538421
$714$	−13.0902	−0.489887
$715$	0	0
$716$	−39.9787	−1.49407
$717$	3.65248	0.136404
$718$	35.0344	1.30747
$719$	32.8885	1.22654	0.613268	−	0.789875i	$-0.289855\pi$
$719$	32.8885	1.22654	0.613268	+	0.789875i	$0.289855\pi$
$720$	−25.7984	−0.961449
$721$	−2.14590	−0.0799174
$722$	52.0689	1.93780
$723$	10.6738	0.396961
$724$	94.2492	3.50274
$725$	−9.52786	−0.353856
$726$	0	0
$727$	43.4508	1.61150	0.805751	−	0.592254i	$-0.201762\pi$
$727$	43.4508	1.61150	0.805751	+	0.592254i	$0.201762\pi$
$728$	24.1803	0.896183
$729$	−8.50658	−0.315058
$730$	25.5623	0.946103
$731$	−61.1803	−2.26284
$732$	16.1459	0.596770
$733$	−35.0557	−1.29481	−0.647406	−	0.762145i	$-0.724146\pi$
$733$	−35.0557	−1.29481	−0.647406	+	0.762145i	$0.724146\pi$
$734$	−54.5410	−2.01315
$735$	0.618034	0.0227965
$736$	−66.1033	−2.43660
$737$	0	0
$738$	76.6312	2.82083
$739$	13.6180	0.500947	0.250474	−	0.968123i	$-0.419414\pi$
$739$	13.6180	0.500947	0.250474	+	0.968123i	$0.419414\pi$
$740$	−12.0000	−0.441129
$741$	−12.4721	−0.458175
$742$	12.0902	0.443844
$743$	26.0902	0.957156	0.478578	−	0.878045i	$-0.341152\pi$
$743$	26.0902	0.957156	0.478578	+	0.878045i	$0.341152\pi$
$744$	1.09017	0.0399676
$745$	2.14590	0.0786196
$746$	93.1033	3.40875
$747$	−28.0344	−1.02573
$748$	0	0
$749$	−10.7082	−0.391269
$750$	−14.5623	−0.531740
$751$	−21.3050	−0.777429	−0.388714	−	0.921358i	$-0.627081\pi$
$751$	−21.3050	−0.777429	−0.388714	+	0.921358i	$0.627081\pi$
$752$	−43.1803	−1.57462
$753$	14.2148	0.518015
$754$	−20.1803	−0.734925
$755$	−17.9443	−0.653059
$756$	16.8541	0.612978
$757$	−19.2361	−0.699147	−0.349573	−	0.936909i	$-0.613673\pi$
$757$	−19.2361	−0.699147	−0.349573	+	0.936909i	$0.613673\pi$
$758$	−68.2492	−2.47892
$759$	0	0
$760$	46.5967	1.69024
$761$	47.3050	1.71480	0.857402	−	0.514648i	$-0.172077\pi$
$761$	47.3050	1.71480	0.857402	+	0.514648i	$0.172077\pi$
$762$	24.1803	0.875961
$763$	−10.4721	−0.379117
$764$	98.2279	3.55376
$765$	−21.1803	−0.765777
$766$	38.2148	1.38076
$767$	0.291796	0.0105361
$768$	−9.00000	−0.324760
$769$	−28.4377	−1.02549	−0.512745	−	0.858541i	$-0.671371\pi$
$769$	−28.4377	−1.02549	−0.512745	+	0.858541i	$0.671371\pi$
$770$	0	0
$771$	7.14590	0.257353
$772$	−1.58359	−0.0569947
$773$	35.7639	1.28634	0.643170	−	0.765724i	$-0.277619\pi$
$773$	35.7639	1.28634	0.643170	+	0.765724i	$0.277619\pi$
$774$	51.8328	1.86309
$775$	−0.944272	−0.0339192
$776$	52.3050	1.87764
$777$	1.52786	0.0548118
$778$	−30.9443	−1.10941
$779$	−69.7214	−2.49803
$780$	−9.70820	−0.347609
$781$	0	0
$782$	−128.992	−4.61274
$783$	−8.27051	−0.295564
$784$	9.85410	0.351932
$785$	−15.8885	−0.567086
$786$	−1.70820	−0.0609296
$787$	−0.437694	−0.0156021	−0.00780105	−	0.999970i	$-0.502483\pi$
$787$	−0.437694	−0.0156021	−0.00780105	+	0.999970i	$0.502483\pi$
$788$	85.9574	3.06211
$789$	−14.2918	−0.508801
$790$	−22.5623	−0.802731
$791$	−6.85410	−0.243704
$792$	0	0
$793$	−17.4164	−0.618475
$794$	−60.6869	−2.15370
$795$	−2.85410	−0.101225
$796$	−18.2705	−0.647581
$797$	27.7639	0.983449	0.491724	−	0.870751i	$-0.336367\pi$
$797$	27.7639	0.983449	0.491724	+	0.870751i	$0.336367\pi$
$798$	−10.0902	−0.357188
$799$	−35.4508	−1.25416
$800$	−43.4164	−1.53500
$801$	−0.381966	−0.0134961
$802$	−69.3050	−2.44724
$803$	0	0
$804$	21.9787	0.775129
$805$	6.09017	0.214650
$806$	−2.00000	−0.0704470
$807$	6.27051	0.220732
$808$	−73.2148	−2.57569
$809$	5.50658	0.193601	0.0968005	−	0.995304i	$-0.469139\pi$
$809$	5.50658	0.193601	0.0968005	+	0.995304i	$0.469139\pi$
$810$	14.9443	0.525088
$811$	−54.8328	−1.92544	−0.962720	−	0.270499i	$-0.912811\pi$
$811$	−54.8328	−1.92544	−0.962720	+	0.270499i	$0.912811\pi$
$812$	−11.5623	−0.405757
$813$	−12.2361	−0.429138
$814$	0	0
$815$	4.70820	0.164921
$816$	49.2705	1.72481
$817$	−47.1591	−1.64989
$818$	11.2361	0.392860
$819$	−8.47214	−0.296040
$820$	−54.2705	−1.89521
$821$	50.6656	1.76824	0.884121	−	0.467257i	$-0.154758\pi$
$821$	50.6656	1.76824	0.884121	+	0.467257i	$0.154758\pi$
$822$	0.527864	0.0184114
$823$	3.88854	0.135546	0.0677731	−	0.997701i	$-0.478411\pi$
$823$	3.88854	0.135546	0.0677731	+	0.997701i	$0.478411\pi$
$824$	16.0344	0.558586
$825$	0	0
$826$	0.236068	0.00821386
$827$	−29.5967	−1.02918	−0.514590	−	0.857436i	$-0.672056\pi$
$827$	−29.5967	−1.02918	−0.514590	+	0.857436i	$0.672056\pi$
$828$	77.3951	2.68967
$829$	−1.02129	−0.0354707	−0.0177354	−	0.999843i	$-0.505646\pi$
$829$	−1.02129	−0.0354707	−0.0177354	+	0.999843i	$0.505646\pi$
$830$	28.0344	0.973090
$831$	3.72949	0.129375
$832$	−28.1803	−0.976978
$833$	8.09017	0.280308
$834$	9.61803	0.333045
$835$	2.47214	0.0855518
$836$	0	0
$837$	−0.819660	−0.0283316
$838$	−15.4164	−0.532551
$839$	−18.5967	−0.642031	−0.321016	−	0.947074i	$-0.604024\pi$
$839$	−18.5967	−0.642031	−0.321016	+	0.947074i	$0.604024\pi$
$840$	−4.61803	−0.159337
$841$	−23.3262	−0.804353
$842$	13.7082	0.472416
$843$	1.74265	0.0600199
$844$	−64.9574	−2.23593
$845$	−2.52786	−0.0869612
$846$	30.0344	1.03261
$847$	0	0
$848$	−45.5066	−1.56270
$849$	3.67376	0.126083
$850$	−84.7214	−2.90592
$851$	15.0557	0.516104
$852$	−14.7295	−0.504624
$853$	46.0902	1.57810	0.789049	−	0.614331i	$-0.210574\pi$
$853$	46.0902	1.57810	0.789049	+	0.614331i	$0.210574\pi$
$854$	−14.0902	−0.482156
$855$	−16.3262	−0.558346
$856$	80.0132	2.73479
$857$	3.90983	0.133557	0.0667786	−	0.997768i	$-0.478728\pi$
$857$	3.90983	0.133557	0.0667786	+	0.997768i	$0.478728\pi$
$858$	0	0
$859$	1.43769	0.0490535	0.0245267	−	0.999699i	$-0.492192\pi$
$859$	1.43769	0.0490535	0.0245267	+	0.999699i	$0.492192\pi$
$860$	−36.7082	−1.25174
$861$	6.90983	0.235486
$862$	18.7082	0.637204
$863$	−30.0557	−1.02311	−0.511554	−	0.859251i	$-0.670930\pi$
$863$	−30.0557	−1.02311	−0.511554	+	0.859251i	$0.670930\pi$
$864$	−37.6869	−1.28213
$865$	17.6180	0.599031
$866$	−99.5755	−3.38371
$867$	29.9443	1.01696
$868$	−1.14590	−0.0388943
$869$	0	0
$870$	3.85410	0.130666
$871$	−23.7082	−0.803322
$872$	78.2492	2.64985
$873$	−18.3262	−0.620249
$874$	−99.4296	−3.36326
$875$	9.00000	0.304256
$876$	29.2918	0.989678
$877$	−13.0000	−0.438979	−0.219489	−	0.975615i	$-0.570439\pi$
$877$	−13.0000	−0.438979	−0.219489	+	0.975615i	$0.570439\pi$
$878$	−14.7082	−0.496378
$879$	6.79837	0.229303
$880$	0	0
$881$	20.8541	0.702593	0.351296	−	0.936264i	$-0.385741\pi$
$881$	20.8541	0.702593	0.351296	+	0.936264i	$0.385741\pi$
$882$	−6.85410	−0.230790
$883$	−46.6312	−1.56926	−0.784632	−	0.619961i	$-0.787148\pi$
$883$	−46.6312	−1.56926	−0.784632	+	0.619961i	$0.787148\pi$
$884$	−127.082	−4.27423
$885$	−0.0557281	−0.00187328
$886$	−21.1803	−0.711567
$887$	−5.78522	−0.194249	−0.0971243	−	0.995272i	$-0.530964\pi$
$887$	−5.78522	−0.194249	−0.0971243	+	0.995272i	$0.530964\pi$
$888$	−11.4164	−0.383110
$889$	−14.9443	−0.501215
$890$	0.381966	0.0128035
$891$	0	0
$892$	−131.228	−4.39384
$893$	−27.3262	−0.914438
$894$	3.47214	0.116126
$895$	−8.23607	−0.275301
$896$	−1.09017	−0.0364200
$897$	12.1803	0.406690
$898$	−8.70820	−0.290597
$899$	0.562306	0.0187540
$900$	50.8328	1.69443
$901$	−37.3607	−1.24466
$902$	0	0
$903$	4.67376	0.155533
$904$	51.2148	1.70338
$905$	19.4164	0.645423
$906$	−29.0344	−0.964605
$907$	−20.2361	−0.671928	−0.335964	−	0.941875i	$-0.609062\pi$
$907$	−20.2361	−0.671928	−0.335964	+	0.941875i	$0.609062\pi$
$908$	−63.2705	−2.09971
$909$	25.6525	0.850839
$910$	8.47214	0.280849
$911$	−22.8197	−0.756049	−0.378025	−	0.925796i	$-0.623397\pi$
$911$	−22.8197	−0.756049	−0.378025	+	0.925796i	$0.623397\pi$
$912$	37.9787	1.25760
$913$	0	0
$914$	17.9443	0.593544
$915$	3.32624	0.109962
$916$	54.5410	1.80209
$917$	1.05573	0.0348632
$918$	−73.5410	−2.42722
$919$	−20.8885	−0.689049	−0.344525	−	0.938777i	$-0.611960\pi$
$919$	−20.8885	−0.689049	−0.344525	+	0.938777i	$0.611960\pi$
$920$	−45.5066	−1.50031
$921$	0.506578	0.0166923
$922$	−51.0689	−1.68186
$923$	15.8885	0.522978
$924$	0	0
$925$	9.88854	0.325133
$926$	46.5066	1.52830
$927$	−5.61803	−0.184520
$928$	25.8541	0.848702
$929$	24.0000	0.787414	0.393707	−	0.919236i	$-0.371192\pi$
$929$	24.0000	0.787414	0.393707	+	0.919236i	$0.371192\pi$
$930$	0.381966	0.0125252
$931$	6.23607	0.204379
$932$	12.5410	0.410795
$933$	5.56231	0.182102
$934$	87.7214	2.87033
$935$	0	0
$936$	63.3050	2.06919
$937$	−37.7214	−1.23230	−0.616152	−	0.787628i	$-0.711309\pi$
$937$	−37.7214	−1.23230	−0.616152	+	0.787628i	$0.711309\pi$
$938$	−19.1803	−0.626260
$939$	1.65248	0.0539265
$940$	−21.2705	−0.693768
$941$	31.0689	1.01282	0.506408	−	0.862294i	$-0.330973\pi$
$941$	31.0689	1.01282	0.506408	+	0.862294i	$0.330973\pi$
$942$	−25.7082	−0.837619
$943$	68.0902	2.21732
$944$	−0.888544	−0.0289196
$945$	3.47214	0.112949
$946$	0	0
$947$	19.7082	0.640431	0.320215	−	0.947345i	$-0.396245\pi$
$947$	19.7082	0.640431	0.320215	+	0.947345i	$0.396245\pi$
$948$	−25.8541	−0.839702
$949$	−31.5967	−1.02567
$950$	−65.3050	−2.11877
$951$	−15.1803	−0.492256
$952$	−60.4508	−1.95922
$953$	1.76393	0.0571394	0.0285697	−	0.999592i	$-0.490905\pi$
$953$	1.76393	0.0571394	0.0285697	+	0.999592i	$0.490905\pi$
$954$	31.6525	1.02479
$955$	20.2361	0.654824
$956$	28.6869	0.927801
$957$	0	0
$958$	−68.6869	−2.21917
$959$	−0.326238	−0.0105348
$960$	5.38197	0.173702
$961$	−30.9443	−0.998202
$962$	20.9443	0.675270
$963$	−28.0344	−0.903397
$964$	83.8328	2.70007
$965$	−0.326238	−0.0105020
$966$	9.85410	0.317051
$967$	28.4508	0.914918	0.457459	−	0.889231i	$-0.348760\pi$
$967$	28.4508	0.914918	0.457459	+	0.889231i	$0.348760\pi$
$968$	0	0
$969$	31.1803	1.00166
$970$	18.3262	0.588420
$971$	52.2492	1.67676	0.838379	−	0.545088i	$-0.183504\pi$
$971$	52.2492	1.67676	0.838379	+	0.545088i	$0.183504\pi$
$972$	67.6869	2.17106
$973$	−5.94427	−0.190565
$974$	43.4508	1.39226
$975$	8.00000	0.256205
$976$	53.0344	1.69759
$977$	−33.1803	−1.06153	−0.530767	−	0.847518i	$-0.678096\pi$
$977$	−33.1803	−1.06153	−0.530767	+	0.847518i	$0.678096\pi$
$978$	7.61803	0.243598
$979$	0	0
$980$	4.85410	0.155059
$981$	−27.4164	−0.875339
$982$	−75.5410	−2.41061
$983$	−14.6180	−0.466243	−0.233121	−	0.972448i	$-0.574894\pi$
$983$	−14.6180	−0.466243	−0.233121	+	0.972448i	$0.574894\pi$
$984$	−51.6312	−1.64594
$985$	17.7082	0.564230
$986$	50.4508	1.60668
$987$	2.70820	0.0862031
$988$	−97.9574	−3.11644
$989$	46.0557	1.46449
$990$	0	0
$991$	−34.2705	−1.08864	−0.544319	−	0.838878i	$-0.683212\pi$
$991$	−34.2705	−1.08864	−0.544319	+	0.838878i	$0.683212\pi$
$992$	2.56231	0.0813533
$993$	−10.0000	−0.317340
$994$	12.8541	0.407707
$995$	−3.76393	−0.119325
$996$	32.1246	1.01791
$997$	−26.8673	−0.850895	−0.425447	−	0.904983i	$-0.639883\pi$
$997$	−26.8673	−0.850895	−0.425447	+	0.904983i	$0.639883\pi$
$998$	2.85410	0.0903450
$999$	8.58359	0.271573

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.2.a.h.1.2	yes	2
3.2	odd	2		7623.2.a.t.1.1		2
7.6	odd	2		5929.2.a.s.1.2		2
11.2	odd	10		847.2.f.l.323.1		4
11.3	even	5		847.2.f.j.372.1		4
11.4	even	5		847.2.f.j.148.1		4
11.5	even	5		847.2.f.c.729.1		4
11.6	odd	10		847.2.f.l.729.1		4
11.7	odd	10		847.2.f.d.148.1		4
11.8	odd	10		847.2.f.d.372.1		4
11.9	even	5		847.2.f.c.323.1		4
11.10	odd	2		847.2.a.d.1.1	✓	2
33.32	even	2		7623.2.a.bx.1.2		2
77.76	even	2		5929.2.a.i.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
847.2.a.d.1.1	✓	2	11.10	odd	2
847.2.a.h.1.2	yes	2	1.1	even	1	trivial
847.2.f.c.323.1		4	11.9	even	5
847.2.f.c.729.1		4	11.5	even	5
847.2.f.d.148.1		4	11.7	odd	10
847.2.f.d.372.1		4	11.8	odd	10
847.2.f.j.148.1		4	11.4	even	5
847.2.f.j.372.1		4	11.3	even	5
847.2.f.l.323.1		4	11.2	odd	10
847.2.f.l.729.1		4	11.6	odd	10
5929.2.a.i.1.1		2	77.76	even	2
5929.2.a.s.1.2		2	7.6	odd	2
7623.2.a.t.1.1		2	3.2	odd	2
7623.2.a.bx.1.2		2	33.32	even	2

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:	\( N \)	\(=\)	\( 847 = 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	847.a (trivial)

\(f(q)\)	\(=\)	\(q+2.61803 q^{2} +0.618034 q^{3} +4.85410 q^{4} +1.00000 q^{5} +1.61803 q^{6} -1.00000 q^{7} +7.47214 q^{8} -2.61803 q^{9} +O(q^{10})\)	\(q+2.61803 q^{2} +0.618034 q^{3} +4.85410 q^{4} +1.00000 q^{5} +1.61803 q^{6} -1.00000 q^{7} +7.47214 q^{8} -2.61803 q^{9} +2.61803 q^{10} +3.00000 q^{12} -3.23607 q^{13} -2.61803 q^{14} +0.618034 q^{15} +9.85410 q^{16} +8.09017 q^{17} -6.85410 q^{18} +6.23607 q^{19} +4.85410 q^{20} -0.618034 q^{21} -6.09017 q^{23} +4.61803 q^{24} -4.00000 q^{25} -8.47214 q^{26} -3.47214 q^{27} -4.85410 q^{28} +2.38197 q^{29} +1.61803 q^{30} +0.236068 q^{31} +10.8541 q^{32} +21.1803 q^{34} -1.00000 q^{35} -12.7082 q^{36} -2.47214 q^{37} +16.3262 q^{38} -2.00000 q^{39} +7.47214 q^{40} -11.1803 q^{41} -1.61803 q^{42} -7.56231 q^{43} -2.61803 q^{45} -15.9443 q^{46} -4.38197 q^{47} +6.09017 q^{48} +1.00000 q^{49} -10.4721 q^{50} +5.00000 q^{51} -15.7082 q^{52} -4.61803 q^{53} -9.09017 q^{54} -7.47214 q^{56} +3.85410 q^{57} +6.23607 q^{58} -0.0901699 q^{59} +3.00000 q^{60} +5.38197 q^{61} +0.618034 q^{62} +2.61803 q^{63} +8.70820 q^{64} -3.23607 q^{65} +7.32624 q^{67} +39.2705 q^{68} -3.76393 q^{69} -2.61803 q^{70} -4.90983 q^{71} -19.5623 q^{72} +9.76393 q^{73} -6.47214 q^{74} -2.47214 q^{75} +30.2705 q^{76} -5.23607 q^{78} -8.61803 q^{79} +9.85410 q^{80} +5.70820 q^{81} -29.2705 q^{82} +10.7082 q^{83} -3.00000 q^{84} +8.09017 q^{85} -19.7984 q^{86} +1.47214 q^{87} +0.145898 q^{89} -6.85410 q^{90} +3.23607 q^{91} -29.5623 q^{92} +0.145898 q^{93} -11.4721 q^{94} +6.23607 q^{95} +6.70820 q^{96} +7.00000 q^{97} +2.61803 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 3 q^{2} - q^{3} + 3 q^{4} + 2 q^{5} + q^{6} - 2 q^{7} + 6 q^{8} - 3 q^{9}+O(q^{10}) \) 2 * q + 3 * q^2 - q^3 + 3 * q^4 + 2 * q^5 + q^6 - 2 * q^7 + 6 * q^8 - 3 * q^9	\( 2 q + 3 q^{2} - q^{3} + 3 q^{4} + 2 q^{5} + q^{6} - 2 q^{7} + 6 q^{8} - 3 q^{9} + 3 q^{10} + 6 q^{12} - 2 q^{13} - 3 q^{14} - q^{15} + 13 q^{16} + 5 q^{17} - 7 q^{18} + 8 q^{19} + 3 q^{20} + q^{21} - q^{23} + 7 q^{24} - 8 q^{25} - 8 q^{26} + 2 q^{27} - 3 q^{28} + 7 q^{29} + q^{30} - 4 q^{31} + 15 q^{32} + 20 q^{34} - 2 q^{35} - 12 q^{36} + 4 q^{37} + 17 q^{38} - 4 q^{39} + 6 q^{40} - q^{42} + 5 q^{43} - 3 q^{45} - 14 q^{46} - 11 q^{47} + q^{48} + 2 q^{49} - 12 q^{50} + 10 q^{51} - 18 q^{52} - 7 q^{53} - 7 q^{54} - 6 q^{56} + q^{57} + 8 q^{58} + 11 q^{59} + 6 q^{60} + 13 q^{61} - q^{62} + 3 q^{63} + 4 q^{64} - 2 q^{65} - q^{67} + 45 q^{68} - 12 q^{69} - 3 q^{70} - 21 q^{71} - 19 q^{72} + 24 q^{73} - 4 q^{74} + 4 q^{75} + 27 q^{76} - 6 q^{78} - 15 q^{79} + 13 q^{80} - 2 q^{81} - 25 q^{82} + 8 q^{83} - 6 q^{84} + 5 q^{85} - 15 q^{86} - 6 q^{87} + 7 q^{89} - 7 q^{90} + 2 q^{91} - 39 q^{92} + 7 q^{93} - 14 q^{94} + 8 q^{95} + 14 q^{97} + 3 q^{98}+O(q^{100}) \) 2 * q + 3 * q^2 - q^3 + 3 * q^4 + 2 * q^5 + q^6 - 2 * q^7 + 6 * q^8 - 3 * q^9 + 3 * q^10 + 6 * q^12 - 2 * q^13 - 3 * q^14 - q^15 + 13 * q^16 + 5 * q^17 - 7 * q^18 + 8 * q^19 + 3 * q^20 + q^21 - q^23 + 7 * q^24 - 8 * q^25 - 8 * q^26 + 2 * q^27 - 3 * q^28 + 7 * q^29 + q^30 - 4 * q^31 + 15 * q^32 + 20 * q^34 - 2 * q^35 - 12 * q^36 + 4 * q^37 + 17 * q^38 - 4 * q^39 + 6 * q^40 - q^42 + 5 * q^43 - 3 * q^45 - 14 * q^46 - 11 * q^47 + q^48 + 2 * q^49 - 12 * q^50 + 10 * q^51 - 18 * q^52 - 7 * q^53 - 7 * q^54 - 6 * q^56 + q^57 + 8 * q^58 + 11 * q^59 + 6 * q^60 + 13 * q^61 - q^62 + 3 * q^63 + 4 * q^64 - 2 * q^65 - q^67 + 45 * q^68 - 12 * q^69 - 3 * q^70 - 21 * q^71 - 19 * q^72 + 24 * q^73 - 4 * q^74 + 4 * q^75 + 27 * q^76 - 6 * q^78 - 15 * q^79 + 13 * q^80 - 2 * q^81 - 25 * q^82 + 8 * q^83 - 6 * q^84 + 5 * q^85 - 15 * q^86 - 6 * q^87 + 7 * q^89 - 7 * q^90 + 2 * q^91 - 39 * q^92 + 7 * q^93 - 14 * q^94 + 8 * q^95 + 14 * q^97 + 3 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more