LMFDB - Embedded newform 7942.2.a.u.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7942,2,Mod(1,7942)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7942, 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("7942.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7942 = 2 \cdot 11 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7942.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:	$63.4171892853$
Analytic rank:	$1$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$1.61803$ of defining polynomial
Character	$\chi$	$=$	7942.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.61803 q^{3} +1.00000 q^{4} -2.85410 q^{5} +1.61803 q^{6} +3.23607 q^{7} -1.00000 q^{8} -0.381966 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.61803 q^{3} +1.00000 q^{4} -2.85410 q^{5} +1.61803 q^{6} +3.23607 q^{7} -1.00000 q^{8} -0.381966 q^{9} +2.85410 q^{10} +1.00000 q^{11} -1.61803 q^{12} -5.23607 q^{13} -3.23607 q^{14} +4.61803 q^{15} +1.00000 q^{16} +6.47214 q^{17} +0.381966 q^{18} -2.85410 q^{20} -5.23607 q^{21} -1.00000 q^{22} -2.85410 q^{23} +1.61803 q^{24} +3.14590 q^{25} +5.23607 q^{26} +5.47214 q^{27} +3.23607 q^{28} -10.4721 q^{29} -4.61803 q^{30} +6.09017 q^{31} -1.00000 q^{32} -1.61803 q^{33} -6.47214 q^{34} -9.23607 q^{35} -0.381966 q^{36} -5.38197 q^{37} +8.47214 q^{39} +2.85410 q^{40} +10.9443 q^{41} +5.23607 q^{42} -3.23607 q^{43} +1.00000 q^{44} +1.09017 q^{45} +2.85410 q^{46} +3.09017 q^{47} -1.61803 q^{48} +3.47214 q^{49} -3.14590 q^{50} -10.4721 q^{51} -5.23607 q^{52} +1.14590 q^{53} -5.47214 q^{54} -2.85410 q^{55} -3.23607 q^{56} +10.4721 q^{58} -7.85410 q^{59} +4.61803 q^{60} +6.94427 q^{61} -6.09017 q^{62} -1.23607 q^{63} +1.00000 q^{64} +14.9443 q^{65} +1.61803 q^{66} +4.14590 q^{67} +6.47214 q^{68} +4.61803 q^{69} +9.23607 q^{70} -1.52786 q^{71} +0.381966 q^{72} -5.70820 q^{73} +5.38197 q^{74} -5.09017 q^{75} +3.23607 q^{77} -8.47214 q^{78} -16.4721 q^{79} -2.85410 q^{80} -7.70820 q^{81} -10.9443 q^{82} +6.00000 q^{83} -5.23607 q^{84} -18.4721 q^{85} +3.23607 q^{86} +16.9443 q^{87} -1.00000 q^{88} +1.85410 q^{89} -1.09017 q^{90} -16.9443 q^{91} -2.85410 q^{92} -9.85410 q^{93} -3.09017 q^{94} +1.61803 q^{96} +16.4721 q^{97} -3.47214 q^{98} -0.381966 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - q^{3} + 2 q^{4} + q^{5} + q^{6} + 2 q^{7} - 2 q^{8} - 3 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 - q^3 + 2 * q^4 + q^5 + q^6 + 2 * q^7 - 2 * q^8 - 3 * q^9	$ 2 q - 2 q^{2} - q^{3} + 2 q^{4} + q^{5} + q^{6} + 2 q^{7} - 2 q^{8} - 3 q^{9} - q^{10} + 2 q^{11} - q^{12} - 6 q^{13} - 2 q^{14} + 7 q^{15} + 2 q^{16} + 4 q^{17} + 3 q^{18} + q^{20} - 6 q^{21} - 2 q^{22} + q^{23} + q^{24} + 13 q^{25} + 6 q^{26} + 2 q^{27} + 2 q^{28} - 12 q^{29} - 7 q^{30} + q^{31} - 2 q^{32} - q^{33} - 4 q^{34} - 14 q^{35} - 3 q^{36} - 13 q^{37} + 8 q^{39} - q^{40} + 4 q^{41} + 6 q^{42} - 2 q^{43} + 2 q^{44} - 9 q^{45} - q^{46} - 5 q^{47} - q^{48} - 2 q^{49} - 13 q^{50} - 12 q^{51} - 6 q^{52} + 9 q^{53} - 2 q^{54} + q^{55} - 2 q^{56} + 12 q^{58} - 9 q^{59} + 7 q^{60} - 4 q^{61} - q^{62} + 2 q^{63} + 2 q^{64} + 12 q^{65} + q^{66} + 15 q^{67} + 4 q^{68} + 7 q^{69} + 14 q^{70} - 12 q^{71} + 3 q^{72} + 2 q^{73} + 13 q^{74} + q^{75} + 2 q^{77} - 8 q^{78} - 24 q^{79} + q^{80} - 2 q^{81} - 4 q^{82} + 12 q^{83} - 6 q^{84} - 28 q^{85} + 2 q^{86} + 16 q^{87} - 2 q^{88} - 3 q^{89} + 9 q^{90} - 16 q^{91} + q^{92} - 13 q^{93} + 5 q^{94} + q^{96} + 24 q^{97} + 2 q^{98} - 3 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 - q^3 + 2 * q^4 + q^5 + q^6 + 2 * q^7 - 2 * q^8 - 3 * q^9 - q^10 + 2 * q^11 - q^12 - 6 * q^13 - 2 * q^14 + 7 * q^15 + 2 * q^16 + 4 * q^17 + 3 * q^18 + q^20 - 6 * q^21 - 2 * q^22 + q^23 + q^24 + 13 * q^25 + 6 * q^26 + 2 * q^27 + 2 * q^28 - 12 * q^29 - 7 * q^30 + q^31 - 2 * q^32 - q^33 - 4 * q^34 - 14 * q^35 - 3 * q^36 - 13 * q^37 + 8 * q^39 - q^40 + 4 * q^41 + 6 * q^42 - 2 * q^43 + 2 * q^44 - 9 * q^45 - q^46 - 5 * q^47 - q^48 - 2 * q^49 - 13 * q^50 - 12 * q^51 - 6 * q^52 + 9 * q^53 - 2 * q^54 + q^55 - 2 * q^56 + 12 * q^58 - 9 * q^59 + 7 * q^60 - 4 * q^61 - q^62 + 2 * q^63 + 2 * q^64 + 12 * q^65 + q^66 + 15 * q^67 + 4 * q^68 + 7 * q^69 + 14 * q^70 - 12 * q^71 + 3 * q^72 + 2 * q^73 + 13 * q^74 + q^75 + 2 * q^77 - 8 * q^78 - 24 * q^79 + q^80 - 2 * q^81 - 4 * q^82 + 12 * q^83 - 6 * q^84 - 28 * q^85 + 2 * q^86 + 16 * q^87 - 2 * q^88 - 3 * q^89 + 9 * q^90 - 16 * q^91 + q^92 - 13 * q^93 + 5 * q^94 + q^96 + 24 * q^97 + 2 * q^98 - 3 * 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
$3$	−1.61803	−0.934172	−0.467086	−	0.884212i	$-0.654696\pi$
$3$	−1.61803	−0.934172	−0.467086	+	0.884212i	$0.654696\pi$
$4$	1.00000	0.500000
$5$	−2.85410	−1.27639	−0.638197	−	0.769873i	$-0.720319\pi$
$5$	−2.85410	−1.27639	−0.638197	+	0.769873i	$0.720319\pi$
$6$	1.61803	0.660560
$7$	3.23607	1.22312	0.611559	−	0.791199i	$-0.290543\pi$
$7$	3.23607	1.22312	0.611559	+	0.791199i	$0.290543\pi$
$8$	−1.00000	−0.353553
$9$	−0.381966	−0.127322
$10$	2.85410	0.902546
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−1.61803	−0.467086
$13$	−5.23607	−1.45222	−0.726112	−	0.687576i	$-0.758675\pi$
$13$	−5.23607	−1.45222	−0.726112	+	0.687576i	$0.758675\pi$
$14$	−3.23607	−0.864876
$15$	4.61803	1.19237
$16$	1.00000	0.250000
$17$	6.47214	1.56972	0.784862	−	0.619671i	$-0.212734\pi$
$17$	6.47214	1.56972	0.784862	+	0.619671i	$0.212734\pi$
$18$	0.381966	0.0900303
$19$	0	0
$19$	0	0
$20$	−2.85410	−0.638197
$21$	−5.23607	−1.14260
$22$	−1.00000	−0.213201
$23$	−2.85410	−0.595121	−0.297561	−	0.954703i	$-0.596173\pi$
$23$	−2.85410	−0.595121	−0.297561	+	0.954703i	$0.596173\pi$
$24$	1.61803	0.330280
$25$	3.14590	0.629180
$26$	5.23607	1.02688
$27$	5.47214	1.05311
$28$	3.23607	0.611559
$29$	−10.4721	−1.94463	−0.972313	−	0.233681i	$-0.924923\pi$
$29$	−10.4721	−1.94463	−0.972313	+	0.233681i	$0.924923\pi$
$30$	−4.61803	−0.843134
$31$	6.09017	1.09383	0.546913	−	0.837189i	$-0.315803\pi$
$31$	6.09017	1.09383	0.546913	+	0.837189i	$0.315803\pi$
$32$	−1.00000	−0.176777
$33$	−1.61803	−0.281664
$34$	−6.47214	−1.10996
$35$	−9.23607	−1.56118
$36$	−0.381966	−0.0636610
$37$	−5.38197	−0.884790	−0.442395	−	0.896820i	$-0.645871\pi$
$37$	−5.38197	−0.884790	−0.442395	+	0.896820i	$0.645871\pi$
$38$	0	0
$39$	8.47214	1.35663
$40$	2.85410	0.451273
$41$	10.9443	1.70921	0.854604	−	0.519280i	$-0.173800\pi$
$41$	10.9443	1.70921	0.854604	+	0.519280i	$0.173800\pi$
$42$	5.23607	0.807943
$43$	−3.23607	−0.493496	−0.246748	−	0.969080i	$-0.579362\pi$
$43$	−3.23607	−0.493496	−0.246748	+	0.969080i	$0.579362\pi$
$44$	1.00000	0.150756
$45$	1.09017	0.162513
$46$	2.85410	0.420814
$47$	3.09017	0.450748	0.225374	−	0.974272i	$-0.427640\pi$
$47$	3.09017	0.450748	0.225374	+	0.974272i	$0.427640\pi$
$48$	−1.61803	−0.233543
$49$	3.47214	0.496019
$50$	−3.14590	−0.444897
$51$	−10.4721	−1.46639
$52$	−5.23607	−0.726112
$53$	1.14590	0.157401	0.0787006	−	0.996898i	$-0.474923\pi$
$53$	1.14590	0.157401	0.0787006	+	0.996898i	$0.474923\pi$
$54$	−5.47214	−0.744663
$55$	−2.85410	−0.384847
$56$	−3.23607	−0.432438
$57$	0	0
$58$	10.4721	1.37506
$59$	−7.85410	−1.02252	−0.511258	−	0.859427i	$-0.670821\pi$
$59$	−7.85410	−1.02252	−0.511258	+	0.859427i	$0.670821\pi$
$60$	4.61803	0.596186
$61$	6.94427	0.889123	0.444561	−	0.895748i	$-0.353360\pi$
$61$	6.94427	0.889123	0.444561	+	0.895748i	$0.353360\pi$
$62$	−6.09017	−0.773452
$63$	−1.23607	−0.155730
$64$	1.00000	0.125000
$65$	14.9443	1.85361
$66$	1.61803	0.199166
$67$	4.14590	0.506502	0.253251	−	0.967401i	$-0.418500\pi$
$67$	4.14590	0.506502	0.253251	+	0.967401i	$0.418500\pi$
$68$	6.47214	0.784862
$69$	4.61803	0.555946
$70$	9.23607	1.10392
$71$	−1.52786	−0.181324	−0.0906621	−	0.995882i	$-0.528898\pi$
$71$	−1.52786	−0.181324	−0.0906621	+	0.995882i	$0.528898\pi$
$72$	0.381966	0.0450151
$73$	−5.70820	−0.668095	−0.334047	−	0.942556i	$-0.608415\pi$
$73$	−5.70820	−0.668095	−0.334047	+	0.942556i	$0.608415\pi$
$74$	5.38197	0.625641
$75$	−5.09017	−0.587762
$76$	0	0
$77$	3.23607	0.368784
$78$	−8.47214	−0.959280
$79$	−16.4721	−1.85326	−0.926630	−	0.375974i	$-0.877308\pi$
$79$	−16.4721	−1.85326	−0.926630	+	0.375974i	$0.877308\pi$
$80$	−2.85410	−0.319098
$81$	−7.70820	−0.856467
$82$	−10.9443	−1.20859
$83$	6.00000	0.658586	0.329293	−	0.944228i	$-0.393190\pi$
$83$	6.00000	0.658586	0.329293	+	0.944228i	$0.393190\pi$
$84$	−5.23607	−0.571302
$85$	−18.4721	−2.00358
$86$	3.23607	0.348954
$87$	16.9443	1.81662
$88$	−1.00000	−0.106600
$89$	1.85410	0.196534	0.0982672	−	0.995160i	$-0.468670\pi$
$89$	1.85410	0.196534	0.0982672	+	0.995160i	$0.468670\pi$
$90$	−1.09017	−0.114914
$91$	−16.9443	−1.77624
$92$	−2.85410	−0.297561
$93$	−9.85410	−1.02182
$94$	−3.09017	−0.318727
$95$	0	0
$96$	1.61803	0.165140
$97$	16.4721	1.67249	0.836246	−	0.548354i	$-0.184746\pi$
$97$	16.4721	1.67249	0.836246	+	0.548354i	$0.184746\pi$
$98$	−3.47214	−0.350739
$99$	−0.381966	−0.0383890
$100$	3.14590	0.314590
$101$	10.7639	1.07105	0.535526	−	0.844519i	$-0.320114\pi$
$101$	10.7639	1.07105	0.535526	+	0.844519i	$0.320114\pi$
$102$	10.4721	1.03690
$103$	0.944272	0.0930419	0.0465209	−	0.998917i	$-0.485187\pi$
$103$	0.944272	0.0930419	0.0465209	+	0.998917i	$0.485187\pi$
$104$	5.23607	0.513439
$105$	14.9443	1.45841
$106$	−1.14590	−0.111299
$107$	−6.00000	−0.580042	−0.290021	−	0.957020i	$-0.593662\pi$
$107$	−6.00000	−0.580042	−0.290021	+	0.957020i	$0.593662\pi$
$108$	5.47214	0.526557
$109$	10.1803	0.975100	0.487550	−	0.873095i	$-0.337891\pi$
$109$	10.1803	0.975100	0.487550	+	0.873095i	$0.337891\pi$
$110$	2.85410	0.272128
$111$	8.70820	0.826546
$112$	3.23607	0.305780
$113$	−14.7984	−1.39211	−0.696057	−	0.717987i	$-0.745064\pi$
$113$	−14.7984	−1.39211	−0.696057	+	0.717987i	$0.745064\pi$
$114$	0	0
$115$	8.14590	0.759609
$116$	−10.4721	−0.972313
$117$	2.00000	0.184900
$118$	7.85410	0.723029
$119$	20.9443	1.91996
$120$	−4.61803	−0.421567
$121$	1.00000	0.0909091
$122$	−6.94427	−0.628705
$123$	−17.7082	−1.59669
$124$	6.09017	0.546913
$125$	5.29180	0.473313
$126$	1.23607	0.110118
$127$	9.41641	0.835571	0.417786	−	0.908546i	$-0.362806\pi$
$127$	9.41641	0.835571	0.417786	+	0.908546i	$0.362806\pi$
$128$	−1.00000	−0.0883883
$129$	5.23607	0.461010
$130$	−14.9443	−1.31070
$131$	−17.4164	−1.52168	−0.760839	−	0.648940i	$-0.775212\pi$
$131$	−17.4164	−1.52168	−0.760839	+	0.648940i	$0.775212\pi$
$132$	−1.61803	−0.140832
$133$	0	0
$134$	−4.14590	−0.358151
$135$	−15.6180	−1.34419
$136$	−6.47214	−0.554981
$137$	13.8541	1.18364	0.591818	−	0.806072i	$-0.298410\pi$
$137$	13.8541	1.18364	0.591818	+	0.806072i	$0.298410\pi$
$138$	−4.61803	−0.393113
$139$	13.4164	1.13796	0.568982	−	0.822350i	$-0.307337\pi$
$139$	13.4164	1.13796	0.568982	+	0.822350i	$0.307337\pi$
$140$	−9.23607	−0.780590
$141$	−5.00000	−0.421076
$142$	1.52786	0.128216
$143$	−5.23607	−0.437862
$144$	−0.381966	−0.0318305
$145$	29.8885	2.48211
$146$	5.70820	0.472414
$147$	−5.61803	−0.463368
$148$	−5.38197	−0.442395
$149$	−18.7639	−1.53720	−0.768601	−	0.639729i	$-0.779047\pi$
$149$	−18.7639	−1.53720	−0.768601	+	0.639729i	$0.779047\pi$
$150$	5.09017	0.415611
$151$	16.4721	1.34048	0.670242	−	0.742143i	$-0.266190\pi$
$151$	16.4721	1.34048	0.670242	+	0.742143i	$0.266190\pi$
$152$	0	0
$153$	−2.47214	−0.199860
$154$	−3.23607	−0.260770
$155$	−17.3820	−1.39615
$156$	8.47214	0.678314
$157$	15.5623	1.24201	0.621004	−	0.783808i	$-0.286725\pi$
$157$	15.5623	1.24201	0.621004	+	0.783808i	$0.286725\pi$
$158$	16.4721	1.31045
$159$	−1.85410	−0.147040
$160$	2.85410	0.225637
$161$	−9.23607	−0.727904
$162$	7.70820	0.605614
$163$	3.14590	0.246406	0.123203	−	0.992382i	$-0.460683\pi$
$163$	3.14590	0.246406	0.123203	+	0.992382i	$0.460683\pi$
$164$	10.9443	0.854604
$165$	4.61803	0.359513
$166$	−6.00000	−0.465690
$167$	−25.2361	−1.95283	−0.976413	−	0.215912i	$-0.930728\pi$
$167$	−25.2361	−1.95283	−0.976413	+	0.215912i	$0.930728\pi$
$168$	5.23607	0.403971
$169$	14.4164	1.10895
$170$	18.4721	1.41675
$171$	0	0
$172$	−3.23607	−0.246748
$173$	−15.2361	−1.15838	−0.579188	−	0.815194i	$-0.696630\pi$
$173$	−15.2361	−1.15838	−0.579188	+	0.815194i	$0.696630\pi$
$174$	−16.9443	−1.28454
$175$	10.1803	0.769561
$176$	1.00000	0.0753778
$177$	12.7082	0.955207
$178$	−1.85410	−0.138971
$179$	12.0902	0.903662	0.451831	−	0.892104i	$-0.350771\pi$
$179$	12.0902	0.903662	0.451831	+	0.892104i	$0.350771\pi$
$180$	1.09017	0.0812565
$181$	1.67376	0.124410	0.0622049	−	0.998063i	$-0.480187\pi$
$181$	1.67376	0.124410	0.0622049	+	0.998063i	$0.480187\pi$
$182$	16.9443	1.25599
$183$	−11.2361	−0.830594
$184$	2.85410	0.210407
$185$	15.3607	1.12934
$186$	9.85410	0.722538
$187$	6.47214	0.473289
$188$	3.09017	0.225374
$189$	17.7082	1.28808
$190$	0	0
$191$	−3.38197	−0.244710	−0.122355	−	0.992486i	$-0.539045\pi$
$191$	−3.38197	−0.244710	−0.122355	+	0.992486i	$0.539045\pi$
$192$	−1.61803	−0.116772
$193$	23.8885	1.71954	0.859768	−	0.510686i	$-0.170608\pi$
$193$	23.8885	1.71954	0.859768	+	0.510686i	$0.170608\pi$
$194$	−16.4721	−1.18263
$195$	−24.1803	−1.73159
$196$	3.47214	0.248010
$197$	−13.5279	−0.963820	−0.481910	−	0.876221i	$-0.660057\pi$
$197$	−13.5279	−0.963820	−0.481910	+	0.876221i	$0.660057\pi$
$198$	0.381966	0.0271451
$199$	6.67376	0.473090	0.236545	−	0.971620i	$-0.423985\pi$
$199$	6.67376	0.473090	0.236545	+	0.971620i	$0.423985\pi$
$200$	−3.14590	−0.222449
$201$	−6.70820	−0.473160
$202$	−10.7639	−0.757348
$203$	−33.8885	−2.37851
$204$	−10.4721	−0.733196
$205$	−31.2361	−2.18162
$206$	−0.944272	−0.0657905
$207$	1.09017	0.0757720
$208$	−5.23607	−0.363056
$209$	0	0
$210$	−14.9443	−1.03125
$211$	6.94427	0.478063	0.239032	−	0.971012i	$-0.423170\pi$
$211$	6.94427	0.478063	0.239032	+	0.971012i	$0.423170\pi$
$212$	1.14590	0.0787006
$213$	2.47214	0.169388
$214$	6.00000	0.410152
$215$	9.23607	0.629895
$216$	−5.47214	−0.372332
$217$	19.7082	1.33788
$218$	−10.1803	−0.689500
$219$	9.23607	0.624116
$220$	−2.85410	−0.192424
$221$	−33.8885	−2.27959
$222$	−8.70820	−0.584456
$223$	−9.56231	−0.640339	−0.320170	−	0.947360i	$-0.603740\pi$
$223$	−9.56231	−0.640339	−0.320170	+	0.947360i	$0.603740\pi$
$224$	−3.23607	−0.216219
$225$	−1.20163	−0.0801084
$226$	14.7984	0.984373
$227$	−22.3607	−1.48413	−0.742065	−	0.670328i	$-0.766154\pi$
$227$	−22.3607	−1.48413	−0.742065	+	0.670328i	$0.766154\pi$
$228$	0	0
$229$	−3.61803	−0.239086	−0.119543	−	0.992829i	$-0.538143\pi$
$229$	−3.61803	−0.239086	−0.119543	+	0.992829i	$0.538143\pi$
$230$	−8.14590	−0.537125
$231$	−5.23607	−0.344508
$232$	10.4721	0.687529
$233$	1.52786	0.100094	0.0500469	−	0.998747i	$-0.484063\pi$
$233$	1.52786	0.100094	0.0500469	+	0.998747i	$0.484063\pi$
$234$	−2.00000	−0.130744
$235$	−8.81966	−0.575331
$236$	−7.85410	−0.511258
$237$	26.6525	1.73126
$238$	−20.9443	−1.35762
$239$	19.7082	1.27482	0.637409	−	0.770526i	$-0.280006\pi$
$239$	19.7082	1.27482	0.637409	+	0.770526i	$0.280006\pi$
$240$	4.61803	0.298093
$241$	10.0000	0.644157	0.322078	−	0.946713i	$-0.395619\pi$
$241$	10.0000	0.644157	0.322078	+	0.946713i	$0.395619\pi$
$242$	−1.00000	−0.0642824
$243$	−3.94427	−0.253025
$244$	6.94427	0.444561
$245$	−9.90983	−0.633116
$246$	17.7082	1.12903
$247$	0	0
$248$	−6.09017	−0.386726
$249$	−9.70820	−0.615232
$250$	−5.29180	−0.334683
$251$	4.14590	0.261687	0.130843	−	0.991403i	$-0.458231\pi$
$251$	4.14590	0.261687	0.130843	+	0.991403i	$0.458231\pi$
$252$	−1.23607	−0.0778650
$253$	−2.85410	−0.179436
$254$	−9.41641	−0.590838
$255$	29.8885	1.87169
$256$	1.00000	0.0625000
$257$	−26.9443	−1.68074	−0.840369	−	0.542015i	$-0.817662\pi$
$257$	−26.9443	−1.68074	−0.840369	+	0.542015i	$0.817662\pi$
$258$	−5.23607	−0.325983
$259$	−17.4164	−1.08220
$260$	14.9443	0.926804
$261$	4.00000	0.247594
$262$	17.4164	1.07599
$263$	29.2361	1.80277	0.901387	−	0.433015i	$-0.142550\pi$
$263$	29.2361	1.80277	0.901387	+	0.433015i	$0.142550\pi$
$264$	1.61803	0.0995831
$265$	−3.27051	−0.200906
$266$	0	0
$267$	−3.00000	−0.183597
$268$	4.14590	0.253251
$269$	19.5623	1.19273	0.596367	−	0.802712i	$-0.296610\pi$
$269$	19.5623	1.19273	0.596367	+	0.802712i	$0.296610\pi$
$270$	15.6180	0.950483
$271$	−20.7639	−1.26132	−0.630660	−	0.776060i	$-0.717216\pi$
$271$	−20.7639	−1.26132	−0.630660	+	0.776060i	$0.717216\pi$
$272$	6.47214	0.392431
$273$	27.4164	1.65932
$274$	−13.8541	−0.836957
$275$	3.14590	0.189705
$276$	4.61803	0.277973
$277$	13.7082	0.823646	0.411823	−	0.911264i	$-0.364892\pi$
$277$	13.7082	0.823646	0.411823	+	0.911264i	$0.364892\pi$
$278$	−13.4164	−0.804663
$279$	−2.32624	−0.139268
$280$	9.23607	0.551961
$281$	−11.2361	−0.670288	−0.335144	−	0.942167i	$-0.608785\pi$
$281$	−11.2361	−0.670288	−0.335144	+	0.942167i	$0.608785\pi$
$282$	5.00000	0.297746
$283$	16.9443	1.00723	0.503616	−	0.863927i	$-0.332003\pi$
$283$	16.9443	1.00723	0.503616	+	0.863927i	$0.332003\pi$
$284$	−1.52786	−0.0906621
$285$	0	0
$286$	5.23607	0.309615
$287$	35.4164	2.09056
$288$	0.381966	0.0225076
$289$	24.8885	1.46403
$290$	−29.8885	−1.75512
$291$	−26.6525	−1.56240
$292$	−5.70820	−0.334047
$293$	23.4164	1.36800	0.684001	−	0.729481i	$-0.260239\pi$
$293$	23.4164	1.36800	0.684001	+	0.729481i	$0.260239\pi$
$294$	5.61803	0.327650
$295$	22.4164	1.30513
$296$	5.38197	0.312820
$297$	5.47214	0.317526
$298$	18.7639	1.08697
$299$	14.9443	0.864250
$300$	−5.09017	−0.293881
$301$	−10.4721	−0.603604
$302$	−16.4721	−0.947865
$303$	−17.4164	−1.00055
$304$	0	0
$305$	−19.8197	−1.13487
$306$	2.47214	0.141323
$307$	−2.58359	−0.147453	−0.0737267	−	0.997278i	$-0.523489\pi$
$307$	−2.58359	−0.147453	−0.0737267	+	0.997278i	$0.523489\pi$
$308$	3.23607	0.184392
$309$	−1.52786	−0.0869171
$310$	17.3820	0.987229
$311$	−30.5066	−1.72987	−0.864935	−	0.501884i	$-0.832640\pi$
$311$	−30.5066	−1.72987	−0.864935	+	0.501884i	$0.832640\pi$
$312$	−8.47214	−0.479640
$313$	3.52786	0.199407	0.0997033	−	0.995017i	$-0.468211\pi$
$313$	3.52786	0.199407	0.0997033	+	0.995017i	$0.468211\pi$
$314$	−15.5623	−0.878232
$315$	3.52786	0.198773
$316$	−16.4721	−0.926630
$317$	−9.41641	−0.528878	−0.264439	−	0.964402i	$-0.585187\pi$
$317$	−9.41641	−0.528878	−0.264439	+	0.964402i	$0.585187\pi$
$318$	1.85410	0.103973
$319$	−10.4721	−0.586327
$320$	−2.85410	−0.159549
$321$	9.70820	0.541859
$322$	9.23607	0.514706
$323$	0	0
$324$	−7.70820	−0.428234
$325$	−16.4721	−0.913710
$326$	−3.14590	−0.174235
$327$	−16.4721	−0.910911
$328$	−10.9443	−0.604296
$329$	10.0000	0.551318
$330$	−4.61803	−0.254214
$331$	7.14590	0.392774	0.196387	−	0.980526i	$-0.437079\pi$
$331$	7.14590	0.392774	0.196387	+	0.980526i	$0.437079\pi$
$332$	6.00000	0.329293
$333$	2.05573	0.112653
$334$	25.2361	1.38086
$335$	−11.8328	−0.646496
$336$	−5.23607	−0.285651
$337$	3.88854	0.211822	0.105911	−	0.994376i	$-0.466224\pi$
$337$	3.88854	0.211822	0.105911	+	0.994376i	$0.466224\pi$
$338$	−14.4164	−0.784149
$339$	23.9443	1.30047
$340$	−18.4721	−1.00179
$341$	6.09017	0.329801
$342$	0	0
$343$	−11.4164	−0.616428
$344$	3.23607	0.174477
$345$	−13.1803	−0.709606
$346$	15.2361	0.819096
$347$	−12.9443	−0.694885	−0.347442	−	0.937701i	$-0.612950\pi$
$347$	−12.9443	−0.694885	−0.347442	+	0.937701i	$0.612950\pi$
$348$	16.9443	0.908308
$349$	17.8885	0.957552	0.478776	−	0.877937i	$-0.341081\pi$
$349$	17.8885	0.957552	0.478776	+	0.877937i	$0.341081\pi$
$350$	−10.1803	−0.544162
$351$	−28.6525	−1.52936
$352$	−1.00000	−0.0533002
$353$	−21.8541	−1.16318	−0.581588	−	0.813483i	$-0.697568\pi$
$353$	−21.8541	−1.16318	−0.581588	+	0.813483i	$0.697568\pi$
$354$	−12.7082	−0.675433
$355$	4.36068	0.231441
$356$	1.85410	0.0982672
$357$	−33.8885	−1.79357
$358$	−12.0902	−0.638985
$359$	−18.0000	−0.950004	−0.475002	−	0.879985i	$-0.657553\pi$
$359$	−18.0000	−0.950004	−0.475002	+	0.879985i	$0.657553\pi$
$360$	−1.09017	−0.0574570
$361$	0	0
$362$	−1.67376	−0.0879710
$363$	−1.61803	−0.0849248
$364$	−16.9443	−0.888121
$365$	16.2918	0.852752
$366$	11.2361	0.587319
$367$	−9.20163	−0.480321	−0.240160	−	0.970733i	$-0.577200\pi$
$367$	−9.20163	−0.480321	−0.240160	+	0.970733i	$0.577200\pi$
$368$	−2.85410	−0.148780
$369$	−4.18034	−0.217620
$370$	−15.3607	−0.798564
$371$	3.70820	0.192520
$372$	−9.85410	−0.510911
$373$	−1.34752	−0.0697722	−0.0348861	−	0.999391i	$-0.511107\pi$
$373$	−1.34752	−0.0697722	−0.0348861	+	0.999391i	$0.511107\pi$
$374$	−6.47214	−0.334666
$375$	−8.56231	−0.442156
$376$	−3.09017	−0.159363
$377$	54.8328	2.82403
$378$	−17.7082	−0.910812
$379$	−30.8328	−1.58378	−0.791888	−	0.610667i	$-0.790901\pi$
$379$	−30.8328	−1.58378	−0.791888	+	0.610667i	$0.790901\pi$
$380$	0	0
$381$	−15.2361	−0.780567
$382$	3.38197	0.173036
$383$	−6.85410	−0.350228	−0.175114	−	0.984548i	$-0.556029\pi$
$383$	−6.85410	−0.350228	−0.175114	+	0.984548i	$0.556029\pi$
$384$	1.61803	0.0825700
$385$	−9.23607	−0.470714
$386$	−23.8885	−1.21589
$387$	1.23607	0.0628329
$388$	16.4721	0.836246
$389$	−3.79837	−0.192585	−0.0962926	−	0.995353i	$-0.530698\pi$
$389$	−3.79837	−0.192585	−0.0962926	+	0.995353i	$0.530698\pi$
$390$	24.1803	1.22442
$391$	−18.4721	−0.934176
$392$	−3.47214	−0.175369
$393$	28.1803	1.42151
$394$	13.5279	0.681524
$395$	47.0132	2.36549
$396$	−0.381966	−0.0191945
$397$	−16.3820	−0.822187	−0.411094	−	0.911593i	$-0.634853\pi$
$397$	−16.3820	−0.822187	−0.411094	+	0.911593i	$0.634853\pi$
$398$	−6.67376	−0.334525
$399$	0	0
$400$	3.14590	0.157295
$401$	−13.9787	−0.698064	−0.349032	−	0.937111i	$-0.613489\pi$
$401$	−13.9787	−0.698064	−0.349032	+	0.937111i	$0.613489\pi$
$402$	6.70820	0.334575
$403$	−31.8885	−1.58848
$404$	10.7639	0.535526
$405$	22.0000	1.09319
$406$	33.8885	1.68186
$407$	−5.38197	−0.266774
$408$	10.4721	0.518448
$409$	15.7082	0.776721	0.388360	−	0.921508i	$-0.373042\pi$
$409$	15.7082	0.776721	0.388360	+	0.921508i	$0.373042\pi$
$410$	31.2361	1.54264
$411$	−22.4164	−1.10572
$412$	0.944272	0.0465209
$413$	−25.4164	−1.25066
$414$	−1.09017	−0.0535789
$415$	−17.1246	−0.840614
$416$	5.23607	0.256719
$417$	−21.7082	−1.06306
$418$	0	0
$419$	−0.673762	−0.0329154	−0.0164577	−	0.999865i	$-0.505239\pi$
$419$	−0.673762	−0.0329154	−0.0164577	+	0.999865i	$0.505239\pi$
$420$	14.9443	0.729206
$421$	−33.4508	−1.63029	−0.815147	−	0.579254i	$-0.803344\pi$
$421$	−33.4508	−1.63029	−0.815147	+	0.579254i	$0.803344\pi$
$422$	−6.94427	−0.338042
$423$	−1.18034	−0.0573901
$424$	−1.14590	−0.0556497
$425$	20.3607	0.987638
$426$	−2.47214	−0.119775
$427$	22.4721	1.08750
$428$	−6.00000	−0.290021
$429$	8.47214	0.409039
$430$	−9.23607	−0.445403
$431$	14.7639	0.711154	0.355577	−	0.934647i	$-0.384284\pi$
$431$	14.7639	0.711154	0.355577	+	0.934647i	$0.384284\pi$
$432$	5.47214	0.263278
$433$	9.79837	0.470880	0.235440	−	0.971889i	$-0.424347\pi$
$433$	9.79837	0.470880	0.235440	+	0.971889i	$0.424347\pi$
$434$	−19.7082	−0.946024
$435$	−48.3607	−2.31872
$436$	10.1803	0.487550
$437$	0	0
$438$	−9.23607	−0.441316
$439$	−7.34752	−0.350678	−0.175339	−	0.984508i	$-0.556102\pi$
$439$	−7.34752	−0.350678	−0.175339	+	0.984508i	$0.556102\pi$
$440$	2.85410	0.136064
$441$	−1.32624	−0.0631542
$442$	33.8885	1.61191
$443$	15.2705	0.725524	0.362762	−	0.931882i	$-0.381834\pi$
$443$	15.2705	0.725524	0.362762	+	0.931882i	$0.381834\pi$
$444$	8.70820	0.413273
$445$	−5.29180	−0.250855
$446$	9.56231	0.452788
$447$	30.3607	1.43601
$448$	3.23607	0.152890
$449$	−5.56231	−0.262501	−0.131251	−	0.991349i	$-0.541899\pi$
$449$	−5.56231	−0.262501	−0.131251	+	0.991349i	$0.541899\pi$
$450$	1.20163	0.0566452
$451$	10.9443	0.515346
$452$	−14.7984	−0.696057
$453$	−26.6525	−1.25224
$454$	22.3607	1.04944
$455$	48.3607	2.26718
$456$	0	0
$457$	−4.76393	−0.222847	−0.111424	−	0.993773i	$-0.535541\pi$
$457$	−4.76393	−0.222847	−0.111424	+	0.993773i	$0.535541\pi$
$458$	3.61803	0.169060
$459$	35.4164	1.65310
$460$	8.14590	0.379804
$461$	−20.6525	−0.961882	−0.480941	−	0.876753i	$-0.659705\pi$
$461$	−20.6525	−0.961882	−0.480941	+	0.876753i	$0.659705\pi$
$462$	5.23607	0.243604
$463$	−39.1591	−1.81988	−0.909938	−	0.414745i	$-0.863871\pi$
$463$	−39.1591	−1.81988	−0.909938	+	0.414745i	$0.863871\pi$
$464$	−10.4721	−0.486157
$465$	28.1246	1.30425
$466$	−1.52786	−0.0707769
$467$	1.61803	0.0748737	0.0374368	−	0.999299i	$-0.488081\pi$
$467$	1.61803	0.0748737	0.0374368	+	0.999299i	$0.488081\pi$
$468$	2.00000	0.0924500
$469$	13.4164	0.619512
$470$	8.81966	0.406821
$471$	−25.1803	−1.16025
$472$	7.85410	0.361514
$473$	−3.23607	−0.148795
$474$	−26.6525	−1.22419
$475$	0	0
$476$	20.9443	0.959979
$477$	−0.437694	−0.0200406
$478$	−19.7082	−0.901432
$479$	−17.1246	−0.782443	−0.391222	−	0.920296i	$-0.627947\pi$
$479$	−17.1246	−0.782443	−0.391222	+	0.920296i	$0.627947\pi$
$480$	−4.61803	−0.210783
$481$	28.1803	1.28491
$482$	−10.0000	−0.455488
$483$	14.9443	0.679988
$484$	1.00000	0.0454545
$485$	−47.0132	−2.13476
$486$	3.94427	0.178916
$487$	10.8541	0.491846	0.245923	−	0.969289i	$-0.420909\pi$
$487$	10.8541	0.491846	0.245923	+	0.969289i	$0.420909\pi$
$488$	−6.94427	−0.314352
$489$	−5.09017	−0.230185
$490$	9.90983	0.447680
$491$	22.9443	1.03546	0.517730	−	0.855544i	$-0.326777\pi$
$491$	22.9443	1.03546	0.517730	+	0.855544i	$0.326777\pi$
$492$	−17.7082	−0.798347
$493$	−67.7771	−3.05253
$494$	0	0
$495$	1.09017	0.0489995
$496$	6.09017	0.273457
$497$	−4.94427	−0.221781
$498$	9.70820	0.435035
$499$	−2.03444	−0.0910741	−0.0455371	−	0.998963i	$-0.514500\pi$
$499$	−2.03444	−0.0910741	−0.0455371	+	0.998963i	$0.514500\pi$
$500$	5.29180	0.236656
$501$	40.8328	1.82428
$502$	−4.14590	−0.185040
$503$	4.76393	0.212413	0.106207	−	0.994344i	$-0.466130\pi$
$503$	4.76393	0.212413	0.106207	+	0.994344i	$0.466130\pi$
$504$	1.23607	0.0550588
$505$	−30.7214	−1.36708
$506$	2.85410	0.126880
$507$	−23.3262	−1.03595
$508$	9.41641	0.417786
$509$	−16.4721	−0.730115	−0.365057	−	0.930985i	$-0.618951\pi$
$509$	−16.4721	−0.730115	−0.365057	+	0.930985i	$0.618951\pi$
$510$	−29.8885	−1.32349
$511$	−18.4721	−0.817159
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	26.9443	1.18846
$515$	−2.69505	−0.118758
$516$	5.23607	0.230505
$517$	3.09017	0.135906
$518$	17.4164	0.765233
$519$	24.6525	1.08212
$520$	−14.9443	−0.655350
$521$	−26.0000	−1.13908	−0.569540	−	0.821963i	$-0.692879\pi$
$521$	−26.0000	−1.13908	−0.569540	+	0.821963i	$0.692879\pi$
$522$	−4.00000	−0.175075
$523$	1.23607	0.0540495	0.0270247	−	0.999635i	$-0.491397\pi$
$523$	1.23607	0.0540495	0.0270247	+	0.999635i	$0.491397\pi$
$524$	−17.4164	−0.760839
$525$	−16.4721	−0.718903
$526$	−29.2361	−1.27475
$527$	39.4164	1.71701
$528$	−1.61803	−0.0704159
$529$	−14.8541	−0.645831
$530$	3.27051	0.142062
$531$	3.00000	0.130189
$532$	0	0
$533$	−57.3050	−2.48215
$534$	3.00000	0.129823
$535$	17.1246	0.740362
$536$	−4.14590	−0.179076
$537$	−19.5623	−0.844176
$538$	−19.5623	−0.843391
$539$	3.47214	0.149555
$540$	−15.6180	−0.672093
$541$	−8.83282	−0.379752	−0.189876	−	0.981808i	$-0.560809\pi$
$541$	−8.83282	−0.379752	−0.189876	+	0.981808i	$0.560809\pi$
$542$	20.7639	0.891887
$543$	−2.70820	−0.116220
$544$	−6.47214	−0.277491
$545$	−29.0557	−1.24461
$546$	−27.4164	−1.17331
$547$	14.7639	0.631260	0.315630	−	0.948882i	$-0.397784\pi$
$547$	14.7639	0.631260	0.315630	+	0.948882i	$0.397784\pi$
$548$	13.8541	0.591818
$549$	−2.65248	−0.113205
$550$	−3.14590	−0.134142
$551$	0	0
$552$	−4.61803	−0.196557
$553$	−53.3050	−2.26676
$554$	−13.7082	−0.582406
$555$	−24.8541	−1.05500
$556$	13.4164	0.568982
$557$	−46.1803	−1.95672	−0.978362	−	0.206901i	$-0.933662\pi$
$557$	−46.1803	−1.95672	−0.978362	+	0.206901i	$0.933662\pi$
$558$	2.32624	0.0984775
$559$	16.9443	0.716666
$560$	−9.23607	−0.390295
$561$	−10.4721	−0.442134
$562$	11.2361	0.473965
$563$	−4.36068	−0.183781	−0.0918904	−	0.995769i	$-0.529291\pi$
$563$	−4.36068	−0.183781	−0.0918904	+	0.995769i	$0.529291\pi$
$564$	−5.00000	−0.210538
$565$	42.2361	1.77688
$566$	−16.9443	−0.712221
$567$	−24.9443	−1.04756
$568$	1.52786	0.0641078
$569$	7.05573	0.295792	0.147896	−	0.989003i	$-0.452750\pi$
$569$	7.05573	0.295792	0.147896	+	0.989003i	$0.452750\pi$
$570$	0	0
$571$	−14.8328	−0.620734	−0.310367	−	0.950617i	$-0.600452\pi$
$571$	−14.8328	−0.620734	−0.310367	+	0.950617i	$0.600452\pi$
$572$	−5.23607	−0.218931
$573$	5.47214	0.228602
$574$	−35.4164	−1.47825
$575$	−8.97871	−0.374438
$576$	−0.381966	−0.0159153
$577$	−19.6869	−0.819577	−0.409789	−	0.912181i	$-0.634398\pi$
$577$	−19.6869	−0.819577	−0.409789	+	0.912181i	$0.634398\pi$
$578$	−24.8885	−1.03523
$579$	−38.6525	−1.60634
$580$	29.8885	1.24105
$581$	19.4164	0.805528
$582$	26.6525	1.10478
$583$	1.14590	0.0474582
$584$	5.70820	0.236207
$585$	−5.70820	−0.236005
$586$	−23.4164	−0.967323
$587$	−45.4508	−1.87596	−0.937979	−	0.346693i	$-0.887305\pi$
$587$	−45.4508	−1.87596	−0.937979	+	0.346693i	$0.887305\pi$
$588$	−5.61803	−0.231684
$589$	0	0
$590$	−22.4164	−0.922869
$591$	21.8885	0.900374
$592$	−5.38197	−0.221197
$593$	5.59675	0.229831	0.114915	−	0.993375i	$-0.463340\pi$
$593$	5.59675	0.229831	0.114915	+	0.993375i	$0.463340\pi$
$594$	−5.47214	−0.224524
$595$	−59.7771	−2.45062
$596$	−18.7639	−0.768601
$597$	−10.7984	−0.441948
$598$	−14.9443	−0.611117
$599$	−8.03444	−0.328278	−0.164139	−	0.986437i	$-0.552485\pi$
$599$	−8.03444	−0.328278	−0.164139	+	0.986437i	$0.552485\pi$
$600$	5.09017	0.207805
$601$	10.0000	0.407909	0.203954	−	0.978980i	$-0.434621\pi$
$601$	10.0000	0.407909	0.203954	+	0.978980i	$0.434621\pi$
$602$	10.4721	0.426812
$603$	−1.58359	−0.0644889
$604$	16.4721	0.670242
$605$	−2.85410	−0.116036
$606$	17.4164	0.707493
$607$	−41.7771	−1.69568	−0.847840	−	0.530252i	$-0.822097\pi$
$607$	−41.7771	−1.69568	−0.847840	+	0.530252i	$0.822097\pi$
$608$	0	0
$609$	54.8328	2.22194
$610$	19.8197	0.802475
$611$	−16.1803	−0.654586
$612$	−2.47214	−0.0999302
$613$	−39.2361	−1.58473	−0.792365	−	0.610047i	$-0.791150\pi$
$613$	−39.2361	−1.58473	−0.792365	+	0.610047i	$0.791150\pi$
$614$	2.58359	0.104265
$615$	50.5410	2.03801
$616$	−3.23607	−0.130385
$617$	−14.9656	−0.602491	−0.301245	−	0.953547i	$-0.597402\pi$
$617$	−14.9656	−0.602491	−0.301245	+	0.953547i	$0.597402\pi$
$618$	1.52786	0.0614597
$619$	−17.9656	−0.722097	−0.361048	−	0.932547i	$-0.617581\pi$
$619$	−17.9656	−0.722097	−0.361048	+	0.932547i	$0.617581\pi$
$620$	−17.3820	−0.698077
$621$	−15.6180	−0.626730
$622$	30.5066	1.22320
$623$	6.00000	0.240385
$624$	8.47214	0.339157
$625$	−30.8328	−1.23331
$626$	−3.52786	−0.141002
$627$	0	0
$628$	15.5623	0.621004
$629$	−34.8328	−1.38888
$630$	−3.52786	−0.140553
$631$	23.9787	0.954578	0.477289	−	0.878747i	$-0.341620\pi$
$631$	23.9787	0.954578	0.477289	+	0.878747i	$0.341620\pi$
$632$	16.4721	0.655226
$633$	−11.2361	−0.446594
$634$	9.41641	0.373973
$635$	−26.8754	−1.06652
$636$	−1.85410	−0.0735199
$637$	−18.1803	−0.720331
$638$	10.4721	0.414596
$639$	0.583592	0.0230865
$640$	2.85410	0.112818
$641$	5.97871	0.236145	0.118072	−	0.993005i	$-0.462328\pi$
$641$	5.97871	0.236145	0.118072	+	0.993005i	$0.462328\pi$
$642$	−9.70820	−0.383152
$643$	−28.1459	−1.10997	−0.554983	−	0.831862i	$-0.687275\pi$
$643$	−28.1459	−1.10997	−0.554983	+	0.831862i	$0.687275\pi$
$644$	−9.23607	−0.363952
$645$	−14.9443	−0.588430
$646$	0	0
$647$	11.7426	0.461651	0.230826	−	0.972995i	$-0.425857\pi$
$647$	11.7426	0.461651	0.230826	+	0.972995i	$0.425857\pi$
$648$	7.70820	0.302807
$649$	−7.85410	−0.308300
$650$	16.4721	0.646090
$651$	−31.8885	−1.24981
$652$	3.14590	0.123203
$653$	−46.6180	−1.82430	−0.912152	−	0.409851i	$-0.865581\pi$
$653$	−46.6180	−1.82430	−0.912152	+	0.409851i	$0.865581\pi$
$654$	16.4721	0.644111
$655$	49.7082	1.94226
$656$	10.9443	0.427302
$657$	2.18034	0.0850632
$658$	−10.0000	−0.389841
$659$	−9.88854	−0.385203	−0.192601	−	0.981277i	$-0.561692\pi$
$659$	−9.88854	−0.385203	−0.192601	+	0.981277i	$0.561692\pi$
$660$	4.61803	0.179757
$661$	19.7984	0.770067	0.385034	−	0.922902i	$-0.374190\pi$
$661$	19.7984	0.770067	0.385034	+	0.922902i	$0.374190\pi$
$662$	−7.14590	−0.277733
$663$	54.8328	2.12953
$664$	−6.00000	−0.232845
$665$	0	0
$666$	−2.05573	−0.0796578
$667$	29.8885	1.15729
$668$	−25.2361	−0.976413
$669$	15.4721	0.598187
$670$	11.8328	0.457142
$671$	6.94427	0.268081
$672$	5.23607	0.201986
$673$	29.8885	1.15212	0.576059	−	0.817408i	$-0.304590\pi$
$673$	29.8885	1.15212	0.576059	+	0.817408i	$0.304590\pi$
$674$	−3.88854	−0.149781
$675$	17.2148	0.662597
$676$	14.4164	0.554477
$677$	24.8328	0.954403	0.477201	−	0.878794i	$-0.341651\pi$
$677$	24.8328	0.954403	0.477201	+	0.878794i	$0.341651\pi$
$678$	−23.9443	−0.919574
$679$	53.3050	2.04566
$680$	18.4721	0.708374
$681$	36.1803	1.38643
$682$	−6.09017	−0.233205
$683$	−38.9230	−1.48935	−0.744673	−	0.667429i	$-0.767395\pi$
$683$	−38.9230	−1.48935	−0.744673	+	0.667429i	$0.767395\pi$
$684$	0	0
$685$	−39.5410	−1.51078
$686$	11.4164	0.435880
$687$	5.85410	0.223348
$688$	−3.23607	−0.123374
$689$	−6.00000	−0.228582
$690$	13.1803	0.501767
$691$	26.3820	1.00362	0.501809	−	0.864979i	$-0.332668\pi$
$691$	26.3820	1.00362	0.501809	+	0.864979i	$0.332668\pi$
$692$	−15.2361	−0.579188
$693$	−1.23607	−0.0469543
$694$	12.9443	0.491358
$695$	−38.2918	−1.45249
$696$	−16.9443	−0.642271
$697$	70.8328	2.68298
$698$	−17.8885	−0.677091
$699$	−2.47214	−0.0935048
$700$	10.1803	0.384781
$701$	36.6525	1.38434	0.692172	−	0.721732i	$-0.256654\pi$
$701$	36.6525	1.38434	0.692172	+	0.721732i	$0.256654\pi$
$702$	28.6525	1.08142
$703$	0	0
$704$	1.00000	0.0376889
$705$	14.2705	0.537458
$706$	21.8541	0.822490
$707$	34.8328	1.31002
$708$	12.7082	0.477604
$709$	−16.8328	−0.632170	−0.316085	−	0.948731i	$-0.602368\pi$
$709$	−16.8328	−0.632170	−0.316085	+	0.948731i	$0.602368\pi$
$710$	−4.36068	−0.163653
$711$	6.29180	0.235961
$712$	−1.85410	−0.0694854
$713$	−17.3820	−0.650960
$714$	33.8885	1.26825
$715$	14.9443	0.558884
$716$	12.0902	0.451831
$717$	−31.8885	−1.19090
$718$	18.0000	0.671754
$719$	−20.9787	−0.782374	−0.391187	−	0.920311i	$-0.627935\pi$
$719$	−20.9787	−0.782374	−0.391187	+	0.920311i	$0.627935\pi$
$720$	1.09017	0.0406282
$721$	3.05573	0.113801
$722$	0	0
$723$	−16.1803	−0.601753
$724$	1.67376	0.0622049
$725$	−32.9443	−1.22352
$726$	1.61803	0.0600509
$727$	−19.1591	−0.710570	−0.355285	−	0.934758i	$-0.615616\pi$
$727$	−19.1591	−0.710570	−0.355285	+	0.934758i	$0.615616\pi$
$728$	16.9443	0.627996
$729$	29.5066	1.09284
$730$	−16.2918	−0.602986
$731$	−20.9443	−0.774652
$732$	−11.2361	−0.415297
$733$	18.0689	0.667389	0.333695	−	0.942681i	$-0.391705\pi$
$733$	18.0689	0.667389	0.333695	+	0.942681i	$0.391705\pi$
$734$	9.20163	0.339638
$735$	16.0344	0.591439
$736$	2.85410	0.105204
$737$	4.14590	0.152716
$738$	4.18034	0.153880
$739$	15.8197	0.581936	0.290968	−	0.956733i	$-0.406023\pi$
$739$	15.8197	0.581936	0.290968	+	0.956733i	$0.406023\pi$
$740$	15.3607	0.564670
$741$	0	0
$742$	−3.70820	−0.136132
$743$	−24.1803	−0.887091	−0.443545	−	0.896252i	$-0.646279\pi$
$743$	−24.1803	−0.887091	−0.443545	+	0.896252i	$0.646279\pi$
$744$	9.85410	0.361269
$745$	53.5542	1.96207
$746$	1.34752	0.0493364
$747$	−2.29180	−0.0838524
$748$	6.47214	0.236645
$749$	−19.4164	−0.709460
$750$	8.56231	0.312651
$751$	29.3262	1.07013	0.535065	−	0.844811i	$-0.320287\pi$
$751$	29.3262	1.07013	0.535065	+	0.844811i	$0.320287\pi$
$752$	3.09017	0.112687
$753$	−6.70820	−0.244461
$754$	−54.8328	−1.99689
$755$	−47.0132	−1.71098
$756$	17.7082	0.644041
$757$	−33.0557	−1.20143	−0.600715	−	0.799463i	$-0.705118\pi$
$757$	−33.0557	−1.20143	−0.600715	+	0.799463i	$0.705118\pi$
$758$	30.8328	1.11990
$759$	4.61803	0.167624
$760$	0	0
$761$	−28.9443	−1.04923	−0.524615	−	0.851340i	$-0.675791\pi$
$761$	−28.9443	−1.04923	−0.524615	+	0.851340i	$0.675791\pi$
$762$	15.2361	0.551945
$763$	32.9443	1.19266
$764$	−3.38197	−0.122355
$765$	7.05573	0.255100
$766$	6.85410	0.247649
$767$	41.1246	1.48492
$768$	−1.61803	−0.0583858
$769$	−44.3607	−1.59969	−0.799844	−	0.600209i	$-0.795084\pi$
$769$	−44.3607	−1.59969	−0.799844	+	0.600209i	$0.795084\pi$
$770$	9.23607	0.332845
$771$	43.5967	1.57010
$772$	23.8885	0.859768
$773$	−46.3262	−1.66624	−0.833119	−	0.553093i	$-0.813447\pi$
$773$	−46.3262	−1.66624	−0.833119	+	0.553093i	$0.813447\pi$
$774$	−1.23607	−0.0444295
$775$	19.1591	0.688214
$776$	−16.4721	−0.591315
$777$	28.1803	1.01096
$778$	3.79837	0.136178
$779$	0	0
$780$	−24.1803	−0.865795
$781$	−1.52786	−0.0546713
$782$	18.4721	0.660562
$783$	−57.3050	−2.04791
$784$	3.47214	0.124005
$785$	−44.4164	−1.58529
$786$	−28.1803	−1.00516
$787$	−15.5967	−0.555964	−0.277982	−	0.960586i	$-0.589666\pi$
$787$	−15.5967	−0.555964	−0.277982	+	0.960586i	$0.589666\pi$
$788$	−13.5279	−0.481910
$789$	−47.3050	−1.68410
$790$	−47.0132	−1.67265
$791$	−47.8885	−1.70272
$792$	0.381966	0.0135726
$793$	−36.3607	−1.29121
$794$	16.3820	0.581374
$795$	5.29180	0.187681
$796$	6.67376	0.236545
$797$	9.90983	0.351024	0.175512	−	0.984477i	$-0.443842\pi$
$797$	9.90983	0.351024	0.175512	+	0.984477i	$0.443842\pi$
$798$	0	0
$799$	20.0000	0.707549
$800$	−3.14590	−0.111224
$801$	−0.708204	−0.0250232
$802$	13.9787	0.493606
$803$	−5.70820	−0.201438
$804$	−6.70820	−0.236580
$805$	26.3607	0.929092
$806$	31.8885	1.12323
$807$	−31.6525	−1.11422
$808$	−10.7639	−0.378674
$809$	−23.0557	−0.810596	−0.405298	−	0.914185i	$-0.632832\pi$
$809$	−23.0557	−0.810596	−0.405298	+	0.914185i	$0.632832\pi$
$810$	−22.0000	−0.773001
$811$	−17.8885	−0.628152	−0.314076	−	0.949398i	$-0.601695\pi$
$811$	−17.8885	−0.628152	−0.314076	+	0.949398i	$0.601695\pi$
$812$	−33.8885	−1.18925
$813$	33.5967	1.17829
$814$	5.38197	0.188638
$815$	−8.97871	−0.314511
$816$	−10.4721	−0.366598
$817$	0	0
$818$	−15.7082	−0.549224
$819$	6.47214	0.226155
$820$	−31.2361	−1.09081
$821$	−5.23607	−0.182740	−0.0913700	−	0.995817i	$-0.529125\pi$
$821$	−5.23607	−0.182740	−0.0913700	+	0.995817i	$0.529125\pi$
$822$	22.4164	0.781862
$823$	−21.1459	−0.737100	−0.368550	−	0.929608i	$-0.620146\pi$
$823$	−21.1459	−0.737100	−0.368550	+	0.929608i	$0.620146\pi$
$824$	−0.944272	−0.0328953
$825$	−5.09017	−0.177217
$826$	25.4164	0.884350
$827$	52.6525	1.83091	0.915453	−	0.402425i	$-0.131833\pi$
$827$	52.6525	1.83091	0.915453	+	0.402425i	$0.131833\pi$
$828$	1.09017	0.0378860
$829$	23.3050	0.809414	0.404707	−	0.914446i	$-0.367373\pi$
$829$	23.3050	0.809414	0.404707	+	0.914446i	$0.367373\pi$
$830$	17.1246	0.594404
$831$	−22.1803	−0.769427
$832$	−5.23607	−0.181528
$833$	22.4721	0.778613
$834$	21.7082	0.751694
$835$	72.0263	2.49257
$836$	0	0
$837$	33.3262	1.15192
$838$	0.673762	0.0232747
$839$	−22.4508	−0.775089	−0.387545	−	0.921851i	$-0.626677\pi$
$839$	−22.4508	−0.775089	−0.387545	+	0.921851i	$0.626677\pi$
$840$	−14.9443	−0.515626
$841$	80.6656	2.78157
$842$	33.4508	1.15279
$843$	18.1803	0.626164
$844$	6.94427	0.239032
$845$	−41.1459	−1.41546
$846$	1.18034	0.0405809
$847$	3.23607	0.111193
$848$	1.14590	0.0393503
$849$	−27.4164	−0.940929
$850$	−20.3607	−0.698366
$851$	15.3607	0.526557
$852$	2.47214	0.0846940
$853$	−36.8328	−1.26113	−0.630566	−	0.776136i	$-0.717177\pi$
$853$	−36.8328	−1.26113	−0.630566	+	0.776136i	$0.717177\pi$
$854$	−22.4721	−0.768981
$855$	0	0
$856$	6.00000	0.205076
$857$	54.5410	1.86309	0.931543	−	0.363632i	$-0.118463\pi$
$857$	54.5410	1.86309	0.931543	+	0.363632i	$0.118463\pi$
$858$	−8.47214	−0.289234
$859$	13.0344	0.444729	0.222365	−	0.974964i	$-0.428622\pi$
$859$	13.0344	0.444729	0.222365	+	0.974964i	$0.428622\pi$
$860$	9.23607	0.314947
$861$	−57.3050	−1.95295
$862$	−14.7639	−0.502862
$863$	−10.4934	−0.357200	−0.178600	−	0.983922i	$-0.557157\pi$
$863$	−10.4934	−0.357200	−0.178600	+	0.983922i	$0.557157\pi$
$864$	−5.47214	−0.186166
$865$	43.4853	1.47854
$866$	−9.79837	−0.332962
$867$	−40.2705	−1.36766
$868$	19.7082	0.668940
$869$	−16.4721	−0.558779
$870$	48.3607	1.63958
$871$	−21.7082	−0.735554
$872$	−10.1803	−0.344750
$873$	−6.29180	−0.212945
$874$	0	0
$875$	17.1246	0.578918
$876$	9.23607	0.312058
$877$	−13.3050	−0.449276	−0.224638	−	0.974442i	$-0.572120\pi$
$877$	−13.3050	−0.449276	−0.224638	+	0.974442i	$0.572120\pi$
$878$	7.34752	0.247967
$879$	−37.8885	−1.27795
$880$	−2.85410	−0.0962118
$881$	−18.0000	−0.606435	−0.303218	−	0.952921i	$-0.598061\pi$
$881$	−18.0000	−0.606435	−0.303218	+	0.952921i	$0.598061\pi$
$882$	1.32624	0.0446568
$883$	33.6180	1.13134	0.565668	−	0.824633i	$-0.308618\pi$
$883$	33.6180	1.13134	0.565668	+	0.824633i	$0.308618\pi$
$884$	−33.8885	−1.13980
$885$	−36.2705	−1.21922
$886$	−15.2705	−0.513023
$887$	1.70820	0.0573559	0.0286779	−	0.999589i	$-0.490870\pi$
$887$	1.70820	0.0573559	0.0286779	+	0.999589i	$0.490870\pi$
$888$	−8.70820	−0.292228
$889$	30.4721	1.02200
$890$	5.29180	0.177381
$891$	−7.70820	−0.258235
$892$	−9.56231	−0.320170
$893$	0	0
$894$	−30.3607	−1.01541
$895$	−34.5066	−1.15343
$896$	−3.23607	−0.108109
$897$	−24.1803	−0.807358
$898$	5.56231	0.185617
$899$	−63.7771	−2.12708
$900$	−1.20163	−0.0400542
$901$	7.41641	0.247076
$902$	−10.9443	−0.364404
$903$	16.9443	0.563870
$904$	14.7984	0.492187
$905$	−4.77709	−0.158796
$906$	26.6525	0.885469
$907$	−13.4377	−0.446191	−0.223096	−	0.974797i	$-0.571616\pi$
$907$	−13.4377	−0.446191	−0.223096	+	0.974797i	$0.571616\pi$
$908$	−22.3607	−0.742065
$909$	−4.11146	−0.136368
$910$	−48.3607	−1.60314
$911$	−16.3820	−0.542759	−0.271379	−	0.962472i	$-0.587480\pi$
$911$	−16.3820	−0.542759	−0.271379	+	0.962472i	$0.587480\pi$
$912$	0	0
$913$	6.00000	0.198571
$914$	4.76393	0.157577
$915$	32.0689	1.06016
$916$	−3.61803	−0.119543
$917$	−56.3607	−1.86119
$918$	−35.4164	−1.16892
$919$	−49.0132	−1.61679	−0.808397	−	0.588637i	$-0.799665\pi$
$919$	−49.0132	−1.61679	−0.808397	+	0.588637i	$0.799665\pi$
$920$	−8.14590	−0.268562
$921$	4.18034	0.137747
$922$	20.6525	0.680153
$923$	8.00000	0.263323
$924$	−5.23607	−0.172254
$925$	−16.9311	−0.556692
$926$	39.1591	1.28685
$927$	−0.360680	−0.0118463
$928$	10.4721	0.343765
$929$	42.3394	1.38911	0.694555	−	0.719439i	$-0.255601\pi$
$929$	42.3394	1.38911	0.694555	+	0.719439i	$0.255601\pi$
$930$	−28.1246	−0.922242
$931$	0	0
$932$	1.52786	0.0500469
$933$	49.3607	1.61600
$934$	−1.61803	−0.0529437
$935$	−18.4721	−0.604103
$936$	−2.00000	−0.0653720
$937$	10.1803	0.332577	0.166289	−	0.986077i	$-0.446822\pi$
$937$	10.1803	0.332577	0.166289	+	0.986077i	$0.446822\pi$
$938$	−13.4164	−0.438061
$939$	−5.70820	−0.186280
$940$	−8.81966	−0.287666
$941$	6.58359	0.214619	0.107309	−	0.994226i	$-0.465776\pi$
$941$	6.58359	0.214619	0.107309	+	0.994226i	$0.465776\pi$
$942$	25.1803	0.820420
$943$	−31.2361	−1.01719
$944$	−7.85410	−0.255629
$945$	−50.5410	−1.64410
$946$	3.23607	0.105214
$947$	−54.8328	−1.78183	−0.890914	−	0.454173i	$-0.849935\pi$
$947$	−54.8328	−1.78183	−0.890914	+	0.454173i	$0.849935\pi$
$948$	26.6525	0.865632
$949$	29.8885	0.970223
$950$	0	0
$951$	15.2361	0.494063
$952$	−20.9443	−0.678808
$953$	−0.583592	−0.0189044	−0.00945220	−	0.999955i	$-0.503009\pi$
$953$	−0.583592	−0.0189044	−0.00945220	+	0.999955i	$0.503009\pi$
$954$	0.437694	0.0141709
$955$	9.65248	0.312347
$956$	19.7082	0.637409
$957$	16.9443	0.547731
$958$	17.1246	0.553271
$959$	44.8328	1.44773
$960$	4.61803	0.149046
$961$	6.09017	0.196457
$962$	−28.1803	−0.908571
$963$	2.29180	0.0738521
$964$	10.0000	0.322078
$965$	−68.1803	−2.19480
$966$	−14.9443	−0.480824
$967$	−55.9574	−1.79947	−0.899735	−	0.436437i	$-0.856240\pi$
$967$	−55.9574	−1.79947	−0.899735	+	0.436437i	$0.856240\pi$
$968$	−1.00000	−0.0321412
$969$	0	0
$970$	47.0132	1.50950
$971$	31.2705	1.00352	0.501759	−	0.865007i	$-0.332686\pi$
$971$	31.2705	1.00352	0.501759	+	0.865007i	$0.332686\pi$
$972$	−3.94427	−0.126513
$973$	43.4164	1.39187
$974$	−10.8541	−0.347788
$975$	26.6525	0.853562
$976$	6.94427	0.222281
$977$	2.14590	0.0686534	0.0343267	−	0.999411i	$-0.489071\pi$
$977$	2.14590	0.0686534	0.0343267	+	0.999411i	$0.489071\pi$
$978$	5.09017	0.162766
$979$	1.85410	0.0592574
$980$	−9.90983	−0.316558
$981$	−3.88854	−0.124152
$982$	−22.9443	−0.732181
$983$	61.6312	1.96573	0.982865	−	0.184328i	$-0.0590108\pi$
$983$	61.6312	1.96573	0.982865	+	0.184328i	$0.0590108\pi$
$984$	17.7082	0.564517
$985$	38.6099	1.23021
$986$	67.7771	2.15846
$987$	−16.1803	−0.515026
$988$	0	0
$989$	9.23607	0.293690
$990$	−1.09017	−0.0346479
$991$	18.6738	0.593192	0.296596	−	0.955003i	$-0.404149\pi$
$991$	18.6738	0.593192	0.296596	+	0.955003i	$0.404149\pi$
$992$	−6.09017	−0.193363
$993$	−11.5623	−0.366919
$994$	4.94427	0.156823
$995$	−19.0476	−0.603849
$996$	−9.70820	−0.307616
$997$	−26.0689	−0.825610	−0.412805	−	0.910819i	$-0.635451\pi$
$997$	−26.0689	−0.825610	−0.412805	+	0.910819i	$0.635451\pi$
$998$	2.03444	0.0643991
$999$	−29.4508	−0.931784

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7942.2.a.u.1.1	✓	2
19.18	odd	2		7942.2.a.z.1.2	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7942.2.a.u.1.1	✓	2	1.1	even	1	trivial
7942.2.a.z.1.2	yes	2	19.18	odd	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:	\( N \)	\(=\)	\( 7942 = 2 \cdot 11 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7942.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.61803 q^{3} +1.00000 q^{4} -2.85410 q^{5} +1.61803 q^{6} +3.23607 q^{7} -1.00000 q^{8} -0.381966 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.61803 q^{3} +1.00000 q^{4} -2.85410 q^{5} +1.61803 q^{6} +3.23607 q^{7} -1.00000 q^{8} -0.381966 q^{9} +2.85410 q^{10} +1.00000 q^{11} -1.61803 q^{12} -5.23607 q^{13} -3.23607 q^{14} +4.61803 q^{15} +1.00000 q^{16} +6.47214 q^{17} +0.381966 q^{18} -2.85410 q^{20} -5.23607 q^{21} -1.00000 q^{22} -2.85410 q^{23} +1.61803 q^{24} +3.14590 q^{25} +5.23607 q^{26} +5.47214 q^{27} +3.23607 q^{28} -10.4721 q^{29} -4.61803 q^{30} +6.09017 q^{31} -1.00000 q^{32} -1.61803 q^{33} -6.47214 q^{34} -9.23607 q^{35} -0.381966 q^{36} -5.38197 q^{37} +8.47214 q^{39} +2.85410 q^{40} +10.9443 q^{41} +5.23607 q^{42} -3.23607 q^{43} +1.00000 q^{44} +1.09017 q^{45} +2.85410 q^{46} +3.09017 q^{47} -1.61803 q^{48} +3.47214 q^{49} -3.14590 q^{50} -10.4721 q^{51} -5.23607 q^{52} +1.14590 q^{53} -5.47214 q^{54} -2.85410 q^{55} -3.23607 q^{56} +10.4721 q^{58} -7.85410 q^{59} +4.61803 q^{60} +6.94427 q^{61} -6.09017 q^{62} -1.23607 q^{63} +1.00000 q^{64} +14.9443 q^{65} +1.61803 q^{66} +4.14590 q^{67} +6.47214 q^{68} +4.61803 q^{69} +9.23607 q^{70} -1.52786 q^{71} +0.381966 q^{72} -5.70820 q^{73} +5.38197 q^{74} -5.09017 q^{75} +3.23607 q^{77} -8.47214 q^{78} -16.4721 q^{79} -2.85410 q^{80} -7.70820 q^{81} -10.9443 q^{82} +6.00000 q^{83} -5.23607 q^{84} -18.4721 q^{85} +3.23607 q^{86} +16.9443 q^{87} -1.00000 q^{88} +1.85410 q^{89} -1.09017 q^{90} -16.9443 q^{91} -2.85410 q^{92} -9.85410 q^{93} -3.09017 q^{94} +1.61803 q^{96} +16.4721 q^{97} -3.47214 q^{98} -0.381966 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - q^{3} + 2 q^{4} + q^{5} + q^{6} + 2 q^{7} - 2 q^{8} - 3 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 - q^3 + 2 * q^4 + q^5 + q^6 + 2 * q^7 - 2 * q^8 - 3 * q^9	\( 2 q - 2 q^{2} - q^{3} + 2 q^{4} + q^{5} + q^{6} + 2 q^{7} - 2 q^{8} - 3 q^{9} - q^{10} + 2 q^{11} - q^{12} - 6 q^{13} - 2 q^{14} + 7 q^{15} + 2 q^{16} + 4 q^{17} + 3 q^{18} + q^{20} - 6 q^{21} - 2 q^{22} + q^{23} + q^{24} + 13 q^{25} + 6 q^{26} + 2 q^{27} + 2 q^{28} - 12 q^{29} - 7 q^{30} + q^{31} - 2 q^{32} - q^{33} - 4 q^{34} - 14 q^{35} - 3 q^{36} - 13 q^{37} + 8 q^{39} - q^{40} + 4 q^{41} + 6 q^{42} - 2 q^{43} + 2 q^{44} - 9 q^{45} - q^{46} - 5 q^{47} - q^{48} - 2 q^{49} - 13 q^{50} - 12 q^{51} - 6 q^{52} + 9 q^{53} - 2 q^{54} + q^{55} - 2 q^{56} + 12 q^{58} - 9 q^{59} + 7 q^{60} - 4 q^{61} - q^{62} + 2 q^{63} + 2 q^{64} + 12 q^{65} + q^{66} + 15 q^{67} + 4 q^{68} + 7 q^{69} + 14 q^{70} - 12 q^{71} + 3 q^{72} + 2 q^{73} + 13 q^{74} + q^{75} + 2 q^{77} - 8 q^{78} - 24 q^{79} + q^{80} - 2 q^{81} - 4 q^{82} + 12 q^{83} - 6 q^{84} - 28 q^{85} + 2 q^{86} + 16 q^{87} - 2 q^{88} - 3 q^{89} + 9 q^{90} - 16 q^{91} + q^{92} - 13 q^{93} + 5 q^{94} + q^{96} + 24 q^{97} + 2 q^{98} - 3 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 - q^3 + 2 * q^4 + q^5 + q^6 + 2 * q^7 - 2 * q^8 - 3 * q^9 - q^10 + 2 * q^11 - q^12 - 6 * q^13 - 2 * q^14 + 7 * q^15 + 2 * q^16 + 4 * q^17 + 3 * q^18 + q^20 - 6 * q^21 - 2 * q^22 + q^23 + q^24 + 13 * q^25 + 6 * q^26 + 2 * q^27 + 2 * q^28 - 12 * q^29 - 7 * q^30 + q^31 - 2 * q^32 - q^33 - 4 * q^34 - 14 * q^35 - 3 * q^36 - 13 * q^37 + 8 * q^39 - q^40 + 4 * q^41 + 6 * q^42 - 2 * q^43 + 2 * q^44 - 9 * q^45 - q^46 - 5 * q^47 - q^48 - 2 * q^49 - 13 * q^50 - 12 * q^51 - 6 * q^52 + 9 * q^53 - 2 * q^54 + q^55 - 2 * q^56 + 12 * q^58 - 9 * q^59 + 7 * q^60 - 4 * q^61 - q^62 + 2 * q^63 + 2 * q^64 + 12 * q^65 + q^66 + 15 * q^67 + 4 * q^68 + 7 * q^69 + 14 * q^70 - 12 * q^71 + 3 * q^72 + 2 * q^73 + 13 * q^74 + q^75 + 2 * q^77 - 8 * q^78 - 24 * q^79 + q^80 - 2 * q^81 - 4 * q^82 + 12 * q^83 - 6 * q^84 - 28 * q^85 + 2 * q^86 + 16 * q^87 - 2 * q^88 - 3 * q^89 + 9 * q^90 - 16 * q^91 + q^92 - 13 * q^93 + 5 * q^94 + q^96 + 24 * q^97 + 2 * q^98 - 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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