LMFDB - Embedded newform 1815.2.a.j.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1815,2,Mod(1,1815)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1815, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1815.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1815 = 3 \cdot 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1815.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:	$14.4928479669$
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			1.1
Root			$-0.618034$ of defining polynomial
Character	$\chi$	$=$	1815.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.618034 q^{2} -1.00000 q^{3} -1.61803 q^{4} -1.00000 q^{5} +0.618034 q^{6} +3.23607 q^{7} +2.23607 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.618034 q^{2} -1.00000 q^{3} -1.61803 q^{4} -1.00000 q^{5} +0.618034 q^{6} +3.23607 q^{7} +2.23607 q^{8} +1.00000 q^{9} +0.618034 q^{10} +1.61803 q^{12} +5.23607 q^{13} -2.00000 q^{14} +1.00000 q^{15} +1.85410 q^{16} -5.47214 q^{17} -0.618034 q^{18} +6.47214 q^{19} +1.61803 q^{20} -3.23607 q^{21} -4.70820 q^{23} -2.23607 q^{24} +1.00000 q^{25} -3.23607 q^{26} -1.00000 q^{27} -5.23607 q^{28} -1.23607 q^{29} -0.618034 q^{30} -6.70820 q^{31} -5.61803 q^{32} +3.38197 q^{34} -3.23607 q^{35} -1.61803 q^{36} +0.763932 q^{37} -4.00000 q^{38} -5.23607 q^{39} -2.23607 q^{40} +3.52786 q^{41} +2.00000 q^{42} -5.23607 q^{43} -1.00000 q^{45} +2.90983 q^{46} +8.70820 q^{47} -1.85410 q^{48} +3.47214 q^{49} -0.618034 q^{50} +5.47214 q^{51} -8.47214 q^{52} +9.94427 q^{53} +0.618034 q^{54} +7.23607 q^{56} -6.47214 q^{57} +0.763932 q^{58} +11.7082 q^{59} -1.61803 q^{60} -1.47214 q^{61} +4.14590 q^{62} +3.23607 q^{63} -0.236068 q^{64} -5.23607 q^{65} +11.2361 q^{67} +8.85410 q^{68} +4.70820 q^{69} +2.00000 q^{70} -14.4721 q^{71} +2.23607 q^{72} -10.4721 q^{73} -0.472136 q^{74} -1.00000 q^{75} -10.4721 q^{76} +3.23607 q^{78} +12.7082 q^{79} -1.85410 q^{80} +1.00000 q^{81} -2.18034 q^{82} -4.00000 q^{83} +5.23607 q^{84} +5.47214 q^{85} +3.23607 q^{86} +1.23607 q^{87} +4.76393 q^{89} +0.618034 q^{90} +16.9443 q^{91} +7.61803 q^{92} +6.70820 q^{93} -5.38197 q^{94} -6.47214 q^{95} +5.61803 q^{96} +12.7639 q^{97} -2.14590 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - 2 q^{3} - q^{4} - 2 q^{5} - q^{6} + 2 q^{7} + 2 q^{9}+O(q^{10}) $ 2 * q + q^2 - 2 * q^3 - q^4 - 2 * q^5 - q^6 + 2 * q^7 + 2 * q^9	$ 2 q + q^{2} - 2 q^{3} - q^{4} - 2 q^{5} - q^{6} + 2 q^{7} + 2 q^{9} - q^{10} + q^{12} + 6 q^{13} - 4 q^{14} + 2 q^{15} - 3 q^{16} - 2 q^{17} + q^{18} + 4 q^{19} + q^{20} - 2 q^{21} + 4 q^{23} + 2 q^{25} - 2 q^{26} - 2 q^{27} - 6 q^{28} + 2 q^{29} + q^{30} - 9 q^{32} + 9 q^{34} - 2 q^{35} - q^{36} + 6 q^{37} - 8 q^{38} - 6 q^{39} + 16 q^{41} + 4 q^{42} - 6 q^{43} - 2 q^{45} + 17 q^{46} + 4 q^{47} + 3 q^{48} - 2 q^{49} + q^{50} + 2 q^{51} - 8 q^{52} + 2 q^{53} - q^{54} + 10 q^{56} - 4 q^{57} + 6 q^{58} + 10 q^{59} - q^{60} + 6 q^{61} + 15 q^{62} + 2 q^{63} + 4 q^{64} - 6 q^{65} + 18 q^{67} + 11 q^{68} - 4 q^{69} + 4 q^{70} - 20 q^{71} - 12 q^{73} + 8 q^{74} - 2 q^{75} - 12 q^{76} + 2 q^{78} + 12 q^{79} + 3 q^{80} + 2 q^{81} + 18 q^{82} - 8 q^{83} + 6 q^{84} + 2 q^{85} + 2 q^{86} - 2 q^{87} + 14 q^{89} - q^{90} + 16 q^{91} + 13 q^{92} - 13 q^{94} - 4 q^{95} + 9 q^{96} + 30 q^{97} - 11 q^{98}+O(q^{100}) $ 2 * q + q^2 - 2 * q^3 - q^4 - 2 * q^5 - q^6 + 2 * q^7 + 2 * q^9 - q^10 + q^12 + 6 * q^13 - 4 * q^14 + 2 * q^15 - 3 * q^16 - 2 * q^17 + q^18 + 4 * q^19 + q^20 - 2 * q^21 + 4 * q^23 + 2 * q^25 - 2 * q^26 - 2 * q^27 - 6 * q^28 + 2 * q^29 + q^30 - 9 * q^32 + 9 * q^34 - 2 * q^35 - q^36 + 6 * q^37 - 8 * q^38 - 6 * q^39 + 16 * q^41 + 4 * q^42 - 6 * q^43 - 2 * q^45 + 17 * q^46 + 4 * q^47 + 3 * q^48 - 2 * q^49 + q^50 + 2 * q^51 - 8 * q^52 + 2 * q^53 - q^54 + 10 * q^56 - 4 * q^57 + 6 * q^58 + 10 * q^59 - q^60 + 6 * q^61 + 15 * q^62 + 2 * q^63 + 4 * q^64 - 6 * q^65 + 18 * q^67 + 11 * q^68 - 4 * q^69 + 4 * q^70 - 20 * q^71 - 12 * q^73 + 8 * q^74 - 2 * q^75 - 12 * q^76 + 2 * q^78 + 12 * q^79 + 3 * q^80 + 2 * q^81 + 18 * q^82 - 8 * q^83 + 6 * q^84 + 2 * q^85 + 2 * q^86 - 2 * q^87 + 14 * q^89 - q^90 + 16 * q^91 + 13 * q^92 - 13 * q^94 - 4 * q^95 + 9 * q^96 + 30 * q^97 - 11 * 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 $

$2$	−0.618034	−0.437016	−0.218508	−	0.975835i	$-0.570119\pi$
$2$	−0.618034	−0.437016	−0.218508	+	0.975835i	$0.570119\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.61803	−0.809017
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0.618034	0.252311
$7$	3.23607	1.22312	0.611559	−	0.791199i	$-0.290543\pi$
$7$	3.23607	1.22312	0.611559	+	0.791199i	$0.290543\pi$
$8$	2.23607	0.790569
$9$	1.00000	0.333333
$10$	0.618034	0.195440
$11$	0	0
$11$	0	0
$12$	1.61803	0.467086
$13$	5.23607	1.45222	0.726112	−	0.687576i	$-0.241325\pi$
$13$	5.23607	1.45222	0.726112	+	0.687576i	$0.241325\pi$
$14$	−2.00000	−0.534522
$15$	1.00000	0.258199
$16$	1.85410	0.463525
$17$	−5.47214	−1.32719	−0.663594	−	0.748093i	$-0.730970\pi$
$17$	−5.47214	−1.32719	−0.663594	+	0.748093i	$0.730970\pi$
$18$	−0.618034	−0.145672
$19$	6.47214	1.48481	0.742405	−	0.669951i	$-0.233685\pi$
$19$	6.47214	1.48481	0.742405	+	0.669951i	$0.233685\pi$
$20$	1.61803	0.361803
$21$	−3.23607	−0.706168
$22$	0	0
$23$	−4.70820	−0.981728	−0.490864	−	0.871236i	$-0.663319\pi$
$23$	−4.70820	−0.981728	−0.490864	+	0.871236i	$0.663319\pi$
$24$	−2.23607	−0.456435
$25$	1.00000	0.200000
$26$	−3.23607	−0.634645
$27$	−1.00000	−0.192450
$28$	−5.23607	−0.989524
$29$	−1.23607	−0.229532	−0.114766	−	0.993393i	$-0.536612\pi$
$29$	−1.23607	−0.229532	−0.114766	+	0.993393i	$0.536612\pi$
$30$	−0.618034	−0.112837
$31$	−6.70820	−1.20483	−0.602414	−	0.798183i	$-0.705795\pi$
$31$	−6.70820	−1.20483	−0.602414	+	0.798183i	$0.705795\pi$
$32$	−5.61803	−0.993137
$33$	0	0
$34$	3.38197	0.580002
$35$	−3.23607	−0.546995
$36$	−1.61803	−0.269672
$37$	0.763932	0.125590	0.0627948	−	0.998026i	$-0.479999\pi$
$37$	0.763932	0.125590	0.0627948	+	0.998026i	$0.479999\pi$
$38$	−4.00000	−0.648886
$39$	−5.23607	−0.838442
$40$	−2.23607	−0.353553
$41$	3.52786	0.550960	0.275480	−	0.961307i	$-0.411163\pi$
$41$	3.52786	0.550960	0.275480	+	0.961307i	$0.411163\pi$
$42$	2.00000	0.308607
$43$	−5.23607	−0.798493	−0.399246	−	0.916844i	$-0.630728\pi$
$43$	−5.23607	−0.798493	−0.399246	+	0.916844i	$0.630728\pi$
$44$	0	0
$45$	−1.00000	−0.149071
$46$	2.90983	0.429031
$47$	8.70820	1.27022	0.635111	−	0.772421i	$-0.280954\pi$
$47$	8.70820	1.27022	0.635111	+	0.772421i	$0.280954\pi$
$48$	−1.85410	−0.267617
$49$	3.47214	0.496019
$50$	−0.618034	−0.0874032
$51$	5.47214	0.766252
$52$	−8.47214	−1.17487
$53$	9.94427	1.36595	0.682975	−	0.730441i	$-0.260686\pi$
$53$	9.94427	1.36595	0.682975	+	0.730441i	$0.260686\pi$
$54$	0.618034	0.0841038
$55$	0	0
$56$	7.23607	0.966960
$57$	−6.47214	−0.857255
$58$	0.763932	0.100309
$59$	11.7082	1.52428	0.762139	−	0.647413i	$-0.224149\pi$
$59$	11.7082	1.52428	0.762139	+	0.647413i	$0.224149\pi$
$60$	−1.61803	−0.208887
$61$	−1.47214	−0.188488	−0.0942438	−	0.995549i	$-0.530043\pi$
$61$	−1.47214	−0.188488	−0.0942438	+	0.995549i	$0.530043\pi$
$62$	4.14590	0.526530
$63$	3.23607	0.407706
$64$	−0.236068	−0.0295085
$65$	−5.23607	−0.649454
$66$	0	0
$67$	11.2361	1.37270	0.686352	−	0.727269i	$-0.259211\pi$
$67$	11.2361	1.37270	0.686352	+	0.727269i	$0.259211\pi$
$68$	8.85410	1.07372
$69$	4.70820	0.566801
$70$	2.00000	0.239046
$71$	−14.4721	−1.71753	−0.858763	−	0.512373i	$-0.828767\pi$
$71$	−14.4721	−1.71753	−0.858763	+	0.512373i	$0.828767\pi$
$72$	2.23607	0.263523
$73$	−10.4721	−1.22567	−0.612835	−	0.790211i	$-0.709971\pi$
$73$	−10.4721	−1.22567	−0.612835	+	0.790211i	$0.709971\pi$
$74$	−0.472136	−0.0548847
$75$	−1.00000	−0.115470
$76$	−10.4721	−1.20124
$77$	0	0
$78$	3.23607	0.366413
$79$	12.7082	1.42978	0.714892	−	0.699235i	$-0.246476\pi$
$79$	12.7082	1.42978	0.714892	+	0.699235i	$0.246476\pi$
$80$	−1.85410	−0.207295
$81$	1.00000	0.111111
$82$	−2.18034	−0.240778
$83$	−4.00000	−0.439057	−0.219529	−	0.975606i	$-0.570452\pi$
$83$	−4.00000	−0.439057	−0.219529	+	0.975606i	$0.570452\pi$
$84$	5.23607	0.571302
$85$	5.47214	0.593536
$86$	3.23607	0.348954
$87$	1.23607	0.132520
$88$	0	0
$89$	4.76393	0.504976	0.252488	−	0.967600i	$-0.418751\pi$
$89$	4.76393	0.504976	0.252488	+	0.967600i	$0.418751\pi$
$90$	0.618034	0.0651465
$91$	16.9443	1.77624
$92$	7.61803	0.794235
$93$	6.70820	0.695608
$94$	−5.38197	−0.555107
$95$	−6.47214	−0.664027
$96$	5.61803	0.573388
$97$	12.7639	1.29598	0.647990	−	0.761648i	$-0.275610\pi$
$97$	12.7639	1.29598	0.647990	+	0.761648i	$0.275610\pi$
$98$	−2.14590	−0.216768
$99$	0	0
$100$	−1.61803	−0.161803
$101$	−5.52786	−0.550043	−0.275022	−	0.961438i	$-0.588685\pi$
$101$	−5.52786	−0.550043	−0.275022	+	0.961438i	$0.588685\pi$
$102$	−3.38197	−0.334865
$103$	−0.944272	−0.0930419	−0.0465209	−	0.998917i	$-0.514813\pi$
$103$	−0.944272	−0.0930419	−0.0465209	+	0.998917i	$0.514813\pi$
$104$	11.7082	1.14808
$105$	3.23607	0.315808
$106$	−6.14590	−0.596942
$107$	14.2361	1.37625	0.688126	−	0.725591i	$-0.258433\pi$
$107$	14.2361	1.37625	0.688126	+	0.725591i	$0.258433\pi$
$108$	1.61803	0.155695
$109$	14.9443	1.43140	0.715701	−	0.698407i	$-0.246107\pi$
$109$	14.9443	1.43140	0.715701	+	0.698407i	$0.246107\pi$
$110$	0	0
$111$	−0.763932	−0.0725092
$112$	6.00000	0.566947
$113$	−12.4164	−1.16804	−0.584019	−	0.811740i	$-0.698521\pi$
$113$	−12.4164	−1.16804	−0.584019	+	0.811740i	$0.698521\pi$
$114$	4.00000	0.374634
$115$	4.70820	0.439042
$116$	2.00000	0.185695
$117$	5.23607	0.484075
$118$	−7.23607	−0.666134
$119$	−17.7082	−1.62331
$120$	2.23607	0.204124
$121$	0	0
$122$	0.909830	0.0823721
$123$	−3.52786	−0.318097
$124$	10.8541	0.974727
$125$	−1.00000	−0.0894427
$126$	−2.00000	−0.178174
$127$	3.70820	0.329050	0.164525	−	0.986373i	$-0.447391\pi$
$127$	3.70820	0.329050	0.164525	+	0.986373i	$0.447391\pi$
$128$	11.3820	1.00603
$129$	5.23607	0.461010
$130$	3.23607	0.283822
$131$	−0.472136	−0.0412507	−0.0206254	−	0.999787i	$-0.506566\pi$
$131$	−0.472136	−0.0412507	−0.0206254	+	0.999787i	$0.506566\pi$
$132$	0	0
$133$	20.9443	1.81610
$134$	−6.94427	−0.599894
$135$	1.00000	0.0860663
$136$	−12.2361	−1.04923
$137$	17.4721	1.49275	0.746373	−	0.665528i	$-0.231794\pi$
$137$	17.4721	1.49275	0.746373	+	0.665528i	$0.231794\pi$
$138$	−2.90983	−0.247701
$139$	−7.29180	−0.618482	−0.309241	−	0.950984i	$-0.600075\pi$
$139$	−7.29180	−0.618482	−0.309241	+	0.950984i	$0.600075\pi$
$140$	5.23607	0.442529
$141$	−8.70820	−0.733363
$142$	8.94427	0.750587
$143$	0	0
$144$	1.85410	0.154508
$145$	1.23607	0.102650
$146$	6.47214	0.535638
$147$	−3.47214	−0.286377
$148$	−1.23607	−0.101604
$149$	−4.29180	−0.351598	−0.175799	−	0.984426i	$-0.556251\pi$
$149$	−4.29180	−0.351598	−0.175799	+	0.984426i	$0.556251\pi$
$150$	0.618034	0.0504623
$151$	7.29180	0.593398	0.296699	−	0.954971i	$-0.404114\pi$
$151$	7.29180	0.593398	0.296699	+	0.954971i	$0.404114\pi$
$152$	14.4721	1.17385
$153$	−5.47214	−0.442396
$154$	0	0
$155$	6.70820	0.538816
$156$	8.47214	0.678314
$157$	2.29180	0.182905	0.0914526	−	0.995809i	$-0.470849\pi$
$157$	2.29180	0.182905	0.0914526	+	0.995809i	$0.470849\pi$
$158$	−7.85410	−0.624839
$159$	−9.94427	−0.788632
$160$	5.61803	0.444145
$161$	−15.2361	−1.20077
$162$	−0.618034	−0.0485573
$163$	6.18034	0.484082	0.242041	−	0.970266i	$-0.422183\pi$
$163$	6.18034	0.484082	0.242041	+	0.970266i	$0.422183\pi$
$164$	−5.70820	−0.445736
$165$	0	0
$166$	2.47214	0.191875
$167$	3.18034	0.246102	0.123051	−	0.992400i	$-0.460732\pi$
$167$	3.18034	0.246102	0.123051	+	0.992400i	$0.460732\pi$
$168$	−7.23607	−0.558275
$169$	14.4164	1.10895
$170$	−3.38197	−0.259385
$171$	6.47214	0.494937
$172$	8.47214	0.645994
$173$	2.94427	0.223849	0.111924	−	0.993717i	$-0.464299\pi$
$173$	2.94427	0.223849	0.111924	+	0.993717i	$0.464299\pi$
$174$	−0.763932	−0.0579135
$175$	3.23607	0.244624
$176$	0	0
$177$	−11.7082	−0.880042
$178$	−2.94427	−0.220683
$179$	−20.1803	−1.50835	−0.754175	−	0.656674i	$-0.771963\pi$
$179$	−20.1803	−1.50835	−0.754175	+	0.656674i	$0.771963\pi$
$180$	1.61803	0.120601
$181$	−21.4164	−1.59187	−0.795935	−	0.605383i	$-0.793020\pi$
$181$	−21.4164	−1.59187	−0.795935	+	0.605383i	$0.793020\pi$
$182$	−10.4721	−0.776246
$183$	1.47214	0.108823
$184$	−10.5279	−0.776124
$185$	−0.763932	−0.0561654
$186$	−4.14590	−0.303992
$187$	0	0
$188$	−14.0902	−1.02763
$189$	−3.23607	−0.235389
$190$	4.00000	0.290191
$191$	27.5967	1.99683	0.998415	−	0.0562752i	$-0.0179224\pi$
$191$	27.5967	1.99683	0.998415	+	0.0562752i	$0.0179224\pi$
$192$	0.236068	0.0170367
$193$	16.1803	1.16469	0.582343	−	0.812943i	$-0.302136\pi$
$193$	16.1803	1.16469	0.582343	+	0.812943i	$0.302136\pi$
$194$	−7.88854	−0.566364
$195$	5.23607	0.374963
$196$	−5.61803	−0.401288
$197$	−1.41641	−0.100915	−0.0504574	−	0.998726i	$-0.516068\pi$
$197$	−1.41641	−0.100915	−0.0504574	+	0.998726i	$0.516068\pi$
$198$	0	0
$199$	16.2361	1.15094	0.575472	−	0.817821i	$-0.304818\pi$
$199$	16.2361	1.15094	0.575472	+	0.817821i	$0.304818\pi$
$200$	2.23607	0.158114
$201$	−11.2361	−0.792531
$202$	3.41641	0.240378
$203$	−4.00000	−0.280745
$204$	−8.85410	−0.619911
$205$	−3.52786	−0.246397
$206$	0.583592	0.0406608
$207$	−4.70820	−0.327243
$208$	9.70820	0.673143
$209$	0	0
$210$	−2.00000	−0.138013
$211$	1.76393	0.121434	0.0607170	−	0.998155i	$-0.480661\pi$
$211$	1.76393	0.121434	0.0607170	+	0.998155i	$0.480661\pi$
$212$	−16.0902	−1.10508
$213$	14.4721	0.991614
$214$	−8.79837	−0.601444
$215$	5.23607	0.357097
$216$	−2.23607	−0.152145
$217$	−21.7082	−1.47365
$218$	−9.23607	−0.625545
$219$	10.4721	0.707641
$220$	0	0
$221$	−28.6525	−1.92737
$222$	0.472136	0.0316877
$223$	9.05573	0.606416	0.303208	−	0.952924i	$-0.401942\pi$
$223$	9.05573	0.606416	0.303208	+	0.952924i	$0.401942\pi$
$224$	−18.1803	−1.21473
$225$	1.00000	0.0666667
$226$	7.67376	0.510451
$227$	16.7082	1.10896	0.554481	−	0.832196i	$-0.312917\pi$
$227$	16.7082	1.10896	0.554481	+	0.832196i	$0.312917\pi$
$228$	10.4721	0.693534
$229$	7.00000	0.462573	0.231287	−	0.972886i	$-0.425707\pi$
$229$	7.00000	0.462573	0.231287	+	0.972886i	$0.425707\pi$
$230$	−2.90983	−0.191869
$231$	0	0
$232$	−2.76393	−0.181461
$233$	10.8885	0.713332	0.356666	−	0.934232i	$-0.383913\pi$
$233$	10.8885	0.713332	0.356666	+	0.934232i	$0.383913\pi$
$234$	−3.23607	−0.211548
$235$	−8.70820	−0.568061
$236$	−18.9443	−1.23317
$237$	−12.7082	−0.825487
$238$	10.9443	0.709412
$239$	−24.6525	−1.59464	−0.797318	−	0.603559i	$-0.793749\pi$
$239$	−24.6525	−1.59464	−0.797318	+	0.603559i	$0.793749\pi$
$240$	1.85410	0.119682
$241$	−17.9443	−1.15589	−0.577946	−	0.816075i	$-0.696146\pi$
$241$	−17.9443	−1.15589	−0.577946	+	0.816075i	$0.696146\pi$
$242$	0	0
$243$	−1.00000	−0.0641500
$244$	2.38197	0.152490
$245$	−3.47214	−0.221827
$246$	2.18034	0.139013
$247$	33.8885	2.15628
$248$	−15.0000	−0.952501
$249$	4.00000	0.253490
$250$	0.618034	0.0390879
$251$	−23.7082	−1.49645	−0.748224	−	0.663446i	$-0.769093\pi$
$251$	−23.7082	−1.49645	−0.748224	+	0.663446i	$0.769093\pi$
$252$	−5.23607	−0.329841
$253$	0	0
$254$	−2.29180	−0.143800
$255$	−5.47214	−0.342678
$256$	−6.56231	−0.410144
$257$	28.8885	1.80202	0.901009	−	0.433801i	$-0.142828\pi$
$257$	28.8885	1.80202	0.901009	+	0.433801i	$0.142828\pi$
$258$	−3.23607	−0.201469
$259$	2.47214	0.153611
$260$	8.47214	0.525420
$261$	−1.23607	−0.0765107
$262$	0.291796	0.0180272
$263$	20.1246	1.24094	0.620468	−	0.784231i	$-0.286943\pi$
$263$	20.1246	1.24094	0.620468	+	0.784231i	$0.286943\pi$
$264$	0	0
$265$	−9.94427	−0.610872
$266$	−12.9443	−0.793664
$267$	−4.76393	−0.291548
$268$	−18.1803	−1.11054
$269$	7.05573	0.430195	0.215098	−	0.976593i	$-0.430993\pi$
$269$	7.05573	0.430195	0.215098	+	0.976593i	$0.430993\pi$
$270$	−0.618034	−0.0376124
$271$	−24.2361	−1.47224	−0.736118	−	0.676853i	$-0.763343\pi$
$271$	−24.2361	−1.47224	−0.736118	+	0.676853i	$0.763343\pi$
$272$	−10.1459	−0.615185
$273$	−16.9443	−1.02551
$274$	−10.7984	−0.652354
$275$	0	0
$276$	−7.61803	−0.458552
$277$	−4.94427	−0.297073	−0.148536	−	0.988907i	$-0.547456\pi$
$277$	−4.94427	−0.297073	−0.148536	+	0.988907i	$0.547456\pi$
$278$	4.50658	0.270287
$279$	−6.70820	−0.401610
$280$	−7.23607	−0.432438
$281$	15.2361	0.908908	0.454454	−	0.890770i	$-0.349834\pi$
$281$	15.2361	0.908908	0.454454	+	0.890770i	$0.349834\pi$
$282$	5.38197	0.320491
$283$	11.8885	0.706701	0.353350	−	0.935491i	$-0.385042\pi$
$283$	11.8885	0.706701	0.353350	+	0.935491i	$0.385042\pi$
$284$	23.4164	1.38951
$285$	6.47214	0.383376
$286$	0	0
$287$	11.4164	0.673889
$288$	−5.61803	−0.331046
$289$	12.9443	0.761428
$290$	−0.763932	−0.0448596
$291$	−12.7639	−0.748235
$292$	16.9443	0.991589
$293$	21.4721	1.25442	0.627208	−	0.778852i	$-0.284198\pi$
$293$	21.4721	1.25442	0.627208	+	0.778852i	$0.284198\pi$
$294$	2.14590	0.125151
$295$	−11.7082	−0.681678
$296$	1.70820	0.0992873
$297$	0	0
$298$	2.65248	0.153654
$299$	−24.6525	−1.42569
$300$	1.61803	0.0934172
$301$	−16.9443	−0.976652
$302$	−4.50658	−0.259324
$303$	5.52786	0.317567
$304$	12.0000	0.688247
$305$	1.47214	0.0842943
$306$	3.38197	0.193334
$307$	−11.8885	−0.678515	−0.339258	−	0.940694i	$-0.610176\pi$
$307$	−11.8885	−0.678515	−0.339258	+	0.940694i	$0.610176\pi$
$308$	0	0
$309$	0.944272	0.0537178
$310$	−4.14590	−0.235471
$311$	−3.23607	−0.183501	−0.0917503	−	0.995782i	$-0.529246\pi$
$311$	−3.23607	−0.183501	−0.0917503	+	0.995782i	$0.529246\pi$
$312$	−11.7082	−0.662847
$313$	22.7639	1.28669	0.643347	−	0.765575i	$-0.277545\pi$
$313$	22.7639	1.28669	0.643347	+	0.765575i	$0.277545\pi$
$314$	−1.41641	−0.0799325
$315$	−3.23607	−0.182332
$316$	−20.5623	−1.15672
$317$	−3.94427	−0.221532	−0.110766	−	0.993846i	$-0.535330\pi$
$317$	−3.94427	−0.221532	−0.110766	+	0.993846i	$0.535330\pi$
$318$	6.14590	0.344645
$319$	0	0
$320$	0.236068	0.0131966
$321$	−14.2361	−0.794580
$322$	9.41641	0.524756
$323$	−35.4164	−1.97062
$324$	−1.61803	−0.0898908
$325$	5.23607	0.290445
$326$	−3.81966	−0.211551
$327$	−14.9443	−0.826420
$328$	7.88854	0.435572
$329$	28.1803	1.55363
$330$	0	0
$331$	−17.1803	−0.944317	−0.472158	−	0.881514i	$-0.656525\pi$
$331$	−17.1803	−0.944317	−0.472158	+	0.881514i	$0.656525\pi$
$332$	6.47214	0.355205
$333$	0.763932	0.0418632
$334$	−1.96556	−0.107551
$335$	−11.2361	−0.613892
$336$	−6.00000	−0.327327
$337$	−7.88854	−0.429716	−0.214858	−	0.976645i	$-0.568929\pi$
$337$	−7.88854	−0.429716	−0.214858	+	0.976645i	$0.568929\pi$
$338$	−8.90983	−0.484631
$339$	12.4164	0.674367
$340$	−8.85410	−0.480181
$341$	0	0
$342$	−4.00000	−0.216295
$343$	−11.4164	−0.616428
$344$	−11.7082	−0.631264
$345$	−4.70820	−0.253481
$346$	−1.81966	−0.0978255
$347$	−14.2361	−0.764232	−0.382116	−	0.924114i	$-0.624805\pi$
$347$	−14.2361	−0.764232	−0.382116	+	0.924114i	$0.624805\pi$
$348$	−2.00000	−0.107211
$349$	−15.0000	−0.802932	−0.401466	−	0.915874i	$-0.631499\pi$
$349$	−15.0000	−0.802932	−0.401466	+	0.915874i	$0.631499\pi$
$350$	−2.00000	−0.106904
$351$	−5.23607	−0.279481
$352$	0	0
$353$	−7.00000	−0.372572	−0.186286	−	0.982496i	$-0.559645\pi$
$353$	−7.00000	−0.372572	−0.186286	+	0.982496i	$0.559645\pi$
$354$	7.23607	0.384593
$355$	14.4721	0.768101
$356$	−7.70820	−0.408534
$357$	17.7082	0.937218
$358$	12.4721	0.659173
$359$	7.41641	0.391423	0.195712	−	0.980662i	$-0.437298\pi$
$359$	7.41641	0.391423	0.195712	+	0.980662i	$0.437298\pi$
$360$	−2.23607	−0.117851
$361$	22.8885	1.20466
$362$	13.2361	0.695672
$363$	0	0
$364$	−27.4164	−1.43701
$365$	10.4721	0.548137
$366$	−0.909830	−0.0475576
$367$	4.76393	0.248675	0.124338	−	0.992240i	$-0.460319\pi$
$367$	4.76393	0.248675	0.124338	+	0.992240i	$0.460319\pi$
$368$	−8.72949	−0.455056
$369$	3.52786	0.183653
$370$	0.472136	0.0245452
$371$	32.1803	1.67072
$372$	−10.8541	−0.562759
$373$	29.8885	1.54757	0.773785	−	0.633448i	$-0.218361\pi$
$373$	29.8885	1.54757	0.773785	+	0.633448i	$0.218361\pi$
$374$	0	0
$375$	1.00000	0.0516398
$376$	19.4721	1.00420
$377$	−6.47214	−0.333332
$378$	2.00000	0.102869
$379$	30.5967	1.57165	0.785825	−	0.618449i	$-0.212239\pi$
$379$	30.5967	1.57165	0.785825	+	0.618449i	$0.212239\pi$
$380$	10.4721	0.537209
$381$	−3.70820	−0.189977
$382$	−17.0557	−0.872647
$383$	16.0000	0.817562	0.408781	−	0.912633i	$-0.365954\pi$
$383$	16.0000	0.817562	0.408781	+	0.912633i	$0.365954\pi$
$384$	−11.3820	−0.580834
$385$	0	0
$386$	−10.0000	−0.508987
$387$	−5.23607	−0.266164
$388$	−20.6525	−1.04847
$389$	−21.5967	−1.09500	−0.547499	−	0.836806i	$-0.684420\pi$
$389$	−21.5967	−1.09500	−0.547499	+	0.836806i	$0.684420\pi$
$390$	−3.23607	−0.163865
$391$	25.7639	1.30294
$392$	7.76393	0.392138
$393$	0.472136	0.0238161
$394$	0.875388	0.0441014
$395$	−12.7082	−0.639419
$396$	0	0
$397$	−17.4164	−0.874104	−0.437052	−	0.899436i	$-0.643978\pi$
$397$	−17.4164	−0.874104	−0.437052	+	0.899436i	$0.643978\pi$
$398$	−10.0344	−0.502981
$399$	−20.9443	−1.04853
$400$	1.85410	0.0927051
$401$	20.9443	1.04591	0.522954	−	0.852361i	$-0.324830\pi$
$401$	20.9443	1.04591	0.522954	+	0.852361i	$0.324830\pi$
$402$	6.94427	0.346349
$403$	−35.1246	−1.74968
$404$	8.94427	0.444994
$405$	−1.00000	−0.0496904
$406$	2.47214	0.122690
$407$	0	0
$408$	12.2361	0.605776
$409$	36.7771	1.81851	0.909255	−	0.416240i	$-0.136652\pi$
$409$	36.7771	1.81851	0.909255	+	0.416240i	$0.136652\pi$
$410$	2.18034	0.107679
$411$	−17.4721	−0.861837
$412$	1.52786	0.0752725
$413$	37.8885	1.86437
$414$	2.90983	0.143010
$415$	4.00000	0.196352
$416$	−29.4164	−1.44226
$417$	7.29180	0.357081
$418$	0	0
$419$	−14.0000	−0.683945	−0.341972	−	0.939710i	$-0.611095\pi$
$419$	−14.0000	−0.683945	−0.341972	+	0.939710i	$0.611095\pi$
$420$	−5.23607	−0.255494
$421$	29.8328	1.45396	0.726981	−	0.686657i	$-0.240923\pi$
$421$	29.8328	1.45396	0.726981	+	0.686657i	$0.240923\pi$
$422$	−1.09017	−0.0530686
$423$	8.70820	0.423407
$424$	22.2361	1.07988
$425$	−5.47214	−0.265438
$426$	−8.94427	−0.433351
$427$	−4.76393	−0.230543
$428$	−23.0344	−1.11341
$429$	0	0
$430$	−3.23607	−0.156057
$431$	−5.81966	−0.280323	−0.140162	−	0.990129i	$-0.544762\pi$
$431$	−5.81966	−0.280323	−0.140162	+	0.990129i	$0.544762\pi$
$432$	−1.85410	−0.0892055
$433$	25.2361	1.21277	0.606384	−	0.795172i	$-0.292619\pi$
$433$	25.2361	1.21277	0.606384	+	0.795172i	$0.292619\pi$
$434$	13.4164	0.644008
$435$	−1.23607	−0.0592649
$436$	−24.1803	−1.15803
$437$	−30.4721	−1.45768
$438$	−6.47214	−0.309251
$439$	−8.12461	−0.387767	−0.193883	−	0.981025i	$-0.562108\pi$
$439$	−8.12461	−0.387767	−0.193883	+	0.981025i	$0.562108\pi$
$440$	0	0
$441$	3.47214	0.165340
$442$	17.7082	0.842293
$443$	7.41641	0.352364	0.176182	−	0.984358i	$-0.443625\pi$
$443$	7.41641	0.352364	0.176182	+	0.984358i	$0.443625\pi$
$444$	1.23607	0.0586612
$445$	−4.76393	−0.225832
$446$	−5.59675	−0.265014
$447$	4.29180	0.202995
$448$	−0.763932	−0.0360924
$449$	−10.0000	−0.471929	−0.235965	−	0.971762i	$-0.575825\pi$
$449$	−10.0000	−0.471929	−0.235965	+	0.971762i	$0.575825\pi$
$450$	−0.618034	−0.0291344
$451$	0	0
$452$	20.0902	0.944962
$453$	−7.29180	−0.342598
$454$	−10.3262	−0.484634
$455$	−16.9443	−0.794360
$456$	−14.4721	−0.677720
$457$	−34.3607	−1.60732	−0.803662	−	0.595085i	$-0.797118\pi$
$457$	−34.3607	−1.60732	−0.803662	+	0.595085i	$0.797118\pi$
$458$	−4.32624	−0.202152
$459$	5.47214	0.255417
$460$	−7.61803	−0.355193
$461$	30.1803	1.40564	0.702819	−	0.711368i	$-0.251924\pi$
$461$	30.1803	1.40564	0.702819	+	0.711368i	$0.251924\pi$
$462$	0	0
$463$	6.00000	0.278844	0.139422	−	0.990233i	$-0.455476\pi$
$463$	6.00000	0.278844	0.139422	+	0.990233i	$0.455476\pi$
$464$	−2.29180	−0.106394
$465$	−6.70820	−0.311086
$466$	−6.72949	−0.311738
$467$	−3.76393	−0.174174	−0.0870870	−	0.996201i	$-0.527756\pi$
$467$	−3.76393	−0.174174	−0.0870870	+	0.996201i	$0.527756\pi$
$468$	−8.47214	−0.391625
$469$	36.3607	1.67898
$470$	5.38197	0.248252
$471$	−2.29180	−0.105600
$472$	26.1803	1.20505
$473$	0	0
$474$	7.85410	0.360751
$475$	6.47214	0.296962
$476$	28.6525	1.31328
$477$	9.94427	0.455317
$478$	15.2361	0.696882
$479$	−0.291796	−0.0133325	−0.00666625	−	0.999978i	$-0.502122\pi$
$479$	−0.291796	−0.0133325	−0.00666625	+	0.999978i	$0.502122\pi$
$480$	−5.61803	−0.256427
$481$	4.00000	0.182384
$482$	11.0902	0.505143
$483$	15.2361	0.693265
$484$	0	0
$485$	−12.7639	−0.579580
$486$	0.618034	0.0280346
$487$	−11.7082	−0.530549	−0.265275	−	0.964173i	$-0.585463\pi$
$487$	−11.7082	−0.530549	−0.265275	+	0.964173i	$0.585463\pi$
$488$	−3.29180	−0.149013
$489$	−6.18034	−0.279485
$490$	2.14590	0.0969418
$491$	−38.4721	−1.73622	−0.868112	−	0.496369i	$-0.834666\pi$
$491$	−38.4721	−1.73622	−0.868112	+	0.496369i	$0.834666\pi$
$492$	5.70820	0.257346
$493$	6.76393	0.304632
$494$	−20.9443	−0.942327
$495$	0	0
$496$	−12.4377	−0.558469
$497$	−46.8328	−2.10074
$498$	−2.47214	−0.110779
$499$	−0.944272	−0.0422714	−0.0211357	−	0.999777i	$-0.506728\pi$
$499$	−0.944272	−0.0422714	−0.0211357	+	0.999777i	$0.506728\pi$
$500$	1.61803	0.0723607
$501$	−3.18034	−0.142087
$502$	14.6525	0.653972
$503$	−23.1803	−1.03356	−0.516780	−	0.856118i	$-0.672870\pi$
$503$	−23.1803	−1.03356	−0.516780	+	0.856118i	$0.672870\pi$
$504$	7.23607	0.322320
$505$	5.52786	0.245987
$506$	0	0
$507$	−14.4164	−0.640255
$508$	−6.00000	−0.266207
$509$	15.5967	0.691314	0.345657	−	0.938361i	$-0.387656\pi$
$509$	15.5967	0.691314	0.345657	+	0.938361i	$0.387656\pi$
$510$	3.38197	0.149756
$511$	−33.8885	−1.49914
$512$	−18.7082	−0.826794
$513$	−6.47214	−0.285752
$514$	−17.8541	−0.787511
$515$	0.944272	0.0416096
$516$	−8.47214	−0.372965
$517$	0	0
$518$	−1.52786	−0.0671305
$519$	−2.94427	−0.129239
$520$	−11.7082	−0.513439
$521$	17.8197	0.780693	0.390347	−	0.920668i	$-0.372355\pi$
$521$	17.8197	0.780693	0.390347	+	0.920668i	$0.372355\pi$
$522$	0.763932	0.0334364
$523$	−24.5410	−1.07310	−0.536552	−	0.843867i	$-0.680273\pi$
$523$	−24.5410	−1.07310	−0.536552	+	0.843867i	$0.680273\pi$
$524$	0.763932	0.0333725
$525$	−3.23607	−0.141234
$526$	−12.4377	−0.542309
$527$	36.7082	1.59903
$528$	0	0
$529$	−0.832816	−0.0362094
$530$	6.14590	0.266961
$531$	11.7082	0.508093
$532$	−33.8885	−1.46925
$533$	18.4721	0.800117
$534$	2.94427	0.127411
$535$	−14.2361	−0.615479
$536$	25.1246	1.08522
$537$	20.1803	0.870846
$538$	−4.36068	−0.188002
$539$	0	0
$540$	−1.61803	−0.0696291
$541$	−43.3050	−1.86183	−0.930913	−	0.365242i	$-0.880986\pi$
$541$	−43.3050	−1.86183	−0.930913	+	0.365242i	$0.880986\pi$
$542$	14.9787	0.643391
$543$	21.4164	0.919066
$544$	30.7426	1.31808
$545$	−14.9443	−0.640142
$546$	10.4721	0.448166
$547$	−9.59675	−0.410327	−0.205164	−	0.978728i	$-0.565773\pi$
$547$	−9.59675	−0.410327	−0.205164	+	0.978728i	$0.565773\pi$
$548$	−28.2705	−1.20766
$549$	−1.47214	−0.0628292
$550$	0	0
$551$	−8.00000	−0.340811
$552$	10.5279	0.448096
$553$	41.1246	1.74880
$554$	3.05573	0.129825
$555$	0.763932	0.0324271
$556$	11.7984	0.500363
$557$	−8.52786	−0.361337	−0.180669	−	0.983544i	$-0.557826\pi$
$557$	−8.52786	−0.361337	−0.180669	+	0.983544i	$0.557826\pi$
$558$	4.14590	0.175510
$559$	−27.4164	−1.15959
$560$	−6.00000	−0.253546
$561$	0	0
$562$	−9.41641	−0.397207
$563$	−0.944272	−0.0397963	−0.0198982	−	0.999802i	$-0.506334\pi$
$563$	−0.944272	−0.0397963	−0.0198982	+	0.999802i	$0.506334\pi$
$564$	14.0902	0.593303
$565$	12.4164	0.522362
$566$	−7.34752	−0.308839
$567$	3.23607	0.135902
$568$	−32.3607	−1.35782
$569$	−19.7082	−0.826211	−0.413105	−	0.910683i	$-0.635556\pi$
$569$	−19.7082	−0.826211	−0.413105	+	0.910683i	$0.635556\pi$
$570$	−4.00000	−0.167542
$571$	0.124612	0.00521484	0.00260742	−	0.999997i	$-0.499170\pi$
$571$	0.124612	0.00521484	0.00260742	+	0.999997i	$0.499170\pi$
$572$	0	0
$573$	−27.5967	−1.15287
$574$	−7.05573	−0.294500
$575$	−4.70820	−0.196346
$576$	−0.236068	−0.00983617
$577$	20.0000	0.832611	0.416305	−	0.909225i	$-0.363325\pi$
$577$	20.0000	0.832611	0.416305	+	0.909225i	$0.363325\pi$
$578$	−8.00000	−0.332756
$579$	−16.1803	−0.672432
$580$	−2.00000	−0.0830455
$581$	−12.9443	−0.537019
$582$	7.88854	0.326991
$583$	0	0
$584$	−23.4164	−0.968978
$585$	−5.23607	−0.216485
$586$	−13.2705	−0.548200
$587$	−11.6525	−0.480949	−0.240475	−	0.970655i	$-0.577303\pi$
$587$	−11.6525	−0.480949	−0.240475	+	0.970655i	$0.577303\pi$
$588$	5.61803	0.231684
$589$	−43.4164	−1.78894
$590$	7.23607	0.297904
$591$	1.41641	0.0582632
$592$	1.41641	0.0582140
$593$	−34.9443	−1.43499	−0.717495	−	0.696564i	$-0.754711\pi$
$593$	−34.9443	−1.43499	−0.717495	+	0.696564i	$0.754711\pi$
$594$	0	0
$595$	17.7082	0.725966
$596$	6.94427	0.284448
$597$	−16.2361	−0.664498
$598$	15.2361	0.623049
$599$	−31.0132	−1.26716	−0.633582	−	0.773676i	$-0.718416\pi$
$599$	−31.0132	−1.26716	−0.633582	+	0.773676i	$0.718416\pi$
$600$	−2.23607	−0.0912871
$601$	28.4721	1.16140	0.580701	−	0.814117i	$-0.302778\pi$
$601$	28.4721	1.16140	0.580701	+	0.814117i	$0.302778\pi$
$602$	10.4721	0.426812
$603$	11.2361	0.457568
$604$	−11.7984	−0.480069
$605$	0	0
$606$	−3.41641	−0.138782
$607$	6.29180	0.255376	0.127688	−	0.991814i	$-0.459244\pi$
$607$	6.29180	0.255376	0.127688	+	0.991814i	$0.459244\pi$
$608$	−36.3607	−1.47462
$609$	4.00000	0.162088
$610$	−0.909830	−0.0368379
$611$	45.5967	1.84465
$612$	8.85410	0.357906
$613$	−14.8328	−0.599092	−0.299546	−	0.954082i	$-0.596835\pi$
$613$	−14.8328	−0.599092	−0.299546	+	0.954082i	$0.596835\pi$
$614$	7.34752	0.296522
$615$	3.52786	0.142257
$616$	0	0
$617$	41.7771	1.68188	0.840941	−	0.541127i	$-0.182002\pi$
$617$	41.7771	1.68188	0.840941	+	0.541127i	$0.182002\pi$
$618$	−0.583592	−0.0234755
$619$	−9.52786	−0.382957	−0.191479	−	0.981497i	$-0.561328\pi$
$619$	−9.52786	−0.382957	−0.191479	+	0.981497i	$0.561328\pi$
$620$	−10.8541	−0.435911
$621$	4.70820	0.188934
$622$	2.00000	0.0801927
$623$	15.4164	0.617645
$624$	−9.70820	−0.388639
$625$	1.00000	0.0400000
$626$	−14.0689	−0.562306
$627$	0	0
$628$	−3.70820	−0.147973
$629$	−4.18034	−0.166681
$630$	2.00000	0.0796819
$631$	9.18034	0.365464	0.182732	−	0.983163i	$-0.441506\pi$
$631$	9.18034	0.365464	0.182732	+	0.983163i	$0.441506\pi$
$632$	28.4164	1.13034
$633$	−1.76393	−0.0701100
$634$	2.43769	0.0968132
$635$	−3.70820	−0.147156
$636$	16.0902	0.638017
$637$	18.1803	0.720331
$638$	0	0
$639$	−14.4721	−0.572509
$640$	−11.3820	−0.449912
$641$	−9.12461	−0.360400	−0.180200	−	0.983630i	$-0.557675\pi$
$641$	−9.12461	−0.360400	−0.180200	+	0.983630i	$0.557675\pi$
$642$	8.79837	0.347244
$643$	−28.8328	−1.13706	−0.568528	−	0.822664i	$-0.692487\pi$
$643$	−28.8328	−1.13706	−0.568528	+	0.822664i	$0.692487\pi$
$644$	24.6525	0.971444
$645$	−5.23607	−0.206170
$646$	21.8885	0.861193
$647$	−16.2361	−0.638306	−0.319153	−	0.947703i	$-0.603398\pi$
$647$	−16.2361	−0.638306	−0.319153	+	0.947703i	$0.603398\pi$
$648$	2.23607	0.0878410
$649$	0	0
$650$	−3.23607	−0.126929
$651$	21.7082	0.850812
$652$	−10.0000	−0.391630
$653$	16.8328	0.658719	0.329359	−	0.944205i	$-0.393167\pi$
$653$	16.8328	0.658719	0.329359	+	0.944205i	$0.393167\pi$
$654$	9.23607	0.361159
$655$	0.472136	0.0184479
$656$	6.54102	0.255384
$657$	−10.4721	−0.408557
$658$	−17.4164	−0.678962
$659$	35.5967	1.38665	0.693326	−	0.720624i	$-0.256145\pi$
$659$	35.5967	1.38665	0.693326	+	0.720624i	$0.256145\pi$
$660$	0	0
$661$	45.7771	1.78052	0.890261	−	0.455450i	$-0.150522\pi$
$661$	45.7771	1.78052	0.890261	+	0.455450i	$0.150522\pi$
$662$	10.6180	0.412682
$663$	28.6525	1.11277
$664$	−8.94427	−0.347105
$665$	−20.9443	−0.812184
$666$	−0.472136	−0.0182949
$667$	5.81966	0.225338
$668$	−5.14590	−0.199101
$669$	−9.05573	−0.350115
$670$	6.94427	0.268281
$671$	0	0
$672$	18.1803	0.701322
$673$	−27.5967	−1.06378	−0.531888	−	0.846815i	$-0.678517\pi$
$673$	−27.5967	−1.06378	−0.531888	+	0.846815i	$0.678517\pi$
$674$	4.87539	0.187793
$675$	−1.00000	−0.0384900
$676$	−23.3262	−0.897163
$677$	5.41641	0.208169	0.104085	−	0.994568i	$-0.466809\pi$
$677$	5.41641	0.208169	0.104085	+	0.994568i	$0.466809\pi$
$678$	−7.67376	−0.294709
$679$	41.3050	1.58514
$680$	12.2361	0.469232
$681$	−16.7082	−0.640260
$682$	0	0
$683$	−24.0000	−0.918334	−0.459167	−	0.888350i	$-0.651852\pi$
$683$	−24.0000	−0.918334	−0.459167	+	0.888350i	$0.651852\pi$
$684$	−10.4721	−0.400412
$685$	−17.4721	−0.667576
$686$	7.05573	0.269389
$687$	−7.00000	−0.267067
$688$	−9.70820	−0.370122
$689$	52.0689	1.98367
$690$	2.90983	0.110775
$691$	−37.5410	−1.42813	−0.714064	−	0.700081i	$-0.753147\pi$
$691$	−37.5410	−1.42813	−0.714064	+	0.700081i	$0.753147\pi$
$692$	−4.76393	−0.181098
$693$	0	0
$694$	8.79837	0.333982
$695$	7.29180	0.276594
$696$	2.76393	0.104767
$697$	−19.3050	−0.731227
$698$	9.27051	0.350894
$699$	−10.8885	−0.411843
$700$	−5.23607	−0.197905
$701$	36.1803	1.36651	0.683256	−	0.730179i	$-0.260563\pi$
$701$	36.1803	1.36651	0.683256	+	0.730179i	$0.260563\pi$
$702$	3.23607	0.122138
$703$	4.94427	0.186477
$704$	0	0
$705$	8.70820	0.327970
$706$	4.32624	0.162820
$707$	−17.8885	−0.672768
$708$	18.9443	0.711969
$709$	−17.9443	−0.673911	−0.336956	−	0.941521i	$-0.609397\pi$
$709$	−17.9443	−0.673911	−0.336956	+	0.941521i	$0.609397\pi$
$710$	−8.94427	−0.335673
$711$	12.7082	0.476595
$712$	10.6525	0.399218
$713$	31.5836	1.18281
$714$	−10.9443	−0.409579
$715$	0	0
$716$	32.6525	1.22028
$717$	24.6525	0.920664
$718$	−4.58359	−0.171058
$719$	26.3607	0.983087	0.491544	−	0.870853i	$-0.336433\pi$
$719$	26.3607	0.983087	0.491544	+	0.870853i	$0.336433\pi$
$720$	−1.85410	−0.0690983
$721$	−3.05573	−0.113801
$722$	−14.1459	−0.526456
$723$	17.9443	0.667355
$724$	34.6525	1.28785
$725$	−1.23607	−0.0459064
$726$	0	0
$727$	44.8328	1.66276	0.831379	−	0.555706i	$-0.187552\pi$
$727$	44.8328	1.66276	0.831379	+	0.555706i	$0.187552\pi$
$728$	37.8885	1.40424
$729$	1.00000	0.0370370
$730$	−6.47214	−0.239544
$731$	28.6525	1.05975
$732$	−2.38197	−0.0880400
$733$	47.8885	1.76880	0.884402	−	0.466726i	$-0.154567\pi$
$733$	47.8885	1.76880	0.884402	+	0.466726i	$0.154567\pi$
$734$	−2.94427	−0.108675
$735$	3.47214	0.128072
$736$	26.4508	0.974991
$737$	0	0
$738$	−2.18034	−0.0802594
$739$	1.65248	0.0607873	0.0303937	−	0.999538i	$-0.490324\pi$
$739$	1.65248	0.0607873	0.0303937	+	0.999538i	$0.490324\pi$
$740$	1.23607	0.0454388
$741$	−33.8885	−1.24493
$742$	−19.8885	−0.730131
$743$	2.23607	0.0820334	0.0410167	−	0.999158i	$-0.486940\pi$
$743$	2.23607	0.0820334	0.0410167	+	0.999158i	$0.486940\pi$
$744$	15.0000	0.549927
$745$	4.29180	0.157239
$746$	−18.4721	−0.676313
$747$	−4.00000	−0.146352
$748$	0	0
$749$	46.0689	1.68332
$750$	−0.618034	−0.0225674
$751$	−34.0132	−1.24116	−0.620579	−	0.784144i	$-0.713102\pi$
$751$	−34.0132	−1.24116	−0.620579	+	0.784144i	$0.713102\pi$
$752$	16.1459	0.588780
$753$	23.7082	0.863975
$754$	4.00000	0.145671
$755$	−7.29180	−0.265376
$756$	5.23607	0.190434
$757$	18.9443	0.688541	0.344271	−	0.938870i	$-0.388126\pi$
$757$	18.9443	0.688541	0.344271	+	0.938870i	$0.388126\pi$
$758$	−18.9098	−0.686836
$759$	0	0
$760$	−14.4721	−0.524960
$761$	−44.6525	−1.61865	−0.809325	−	0.587360i	$-0.800167\pi$
$761$	−44.6525	−1.61865	−0.809325	+	0.587360i	$0.800167\pi$
$762$	2.29180	0.0830230
$763$	48.3607	1.75077
$764$	−44.6525	−1.61547
$765$	5.47214	0.197845
$766$	−9.88854	−0.357288
$767$	61.3050	2.21359
$768$	6.56231	0.236797
$769$	−24.5279	−0.884497	−0.442249	−	0.896892i	$-0.645819\pi$
$769$	−24.5279	−0.884497	−0.442249	+	0.896892i	$0.645819\pi$
$770$	0	0
$771$	−28.8885	−1.04040
$772$	−26.1803	−0.942251
$773$	−7.94427	−0.285736	−0.142868	−	0.989742i	$-0.545632\pi$
$773$	−7.94427	−0.285736	−0.142868	+	0.989742i	$0.545632\pi$
$774$	3.23607	0.116318
$775$	−6.70820	−0.240966
$776$	28.5410	1.02456
$777$	−2.47214	−0.0886874
$778$	13.3475	0.478532
$779$	22.8328	0.818071
$780$	−8.47214	−0.303351
$781$	0	0
$782$	−15.9230	−0.569405
$783$	1.23607	0.0441735
$784$	6.43769	0.229918
$785$	−2.29180	−0.0817977
$786$	−0.291796	−0.0104080
$787$	−27.0557	−0.964433	−0.482216	−	0.876052i	$-0.660168\pi$
$787$	−27.0557	−0.964433	−0.482216	+	0.876052i	$0.660168\pi$
$788$	2.29180	0.0816419
$789$	−20.1246	−0.716455
$790$	7.85410	0.279436
$791$	−40.1803	−1.42865
$792$	0	0
$793$	−7.70820	−0.273726
$794$	10.7639	0.381998
$795$	9.94427	0.352687
$796$	−26.2705	−0.931134
$797$	30.0000	1.06265	0.531327	−	0.847167i	$-0.321693\pi$
$797$	30.0000	1.06265	0.531327	+	0.847167i	$0.321693\pi$
$798$	12.9443	0.458222
$799$	−47.6525	−1.68582
$800$	−5.61803	−0.198627
$801$	4.76393	0.168325
$802$	−12.9443	−0.457078
$803$	0	0
$804$	18.1803	0.641171
$805$	15.2361	0.537001
$806$	21.7082	0.764639
$807$	−7.05573	−0.248373
$808$	−12.3607	−0.434847
$809$	−8.00000	−0.281265	−0.140633	−	0.990062i	$-0.544914\pi$
$809$	−8.00000	−0.281265	−0.140633	+	0.990062i	$0.544914\pi$
$810$	0.618034	0.0217155
$811$	7.87539	0.276542	0.138271	−	0.990394i	$-0.455845\pi$
$811$	7.87539	0.276542	0.138271	+	0.990394i	$0.455845\pi$
$812$	6.47214	0.227127
$813$	24.2361	0.849996
$814$	0	0
$815$	−6.18034	−0.216488
$816$	10.1459	0.355177
$817$	−33.8885	−1.18561
$818$	−22.7295	−0.794718
$819$	16.9443	0.592081
$820$	5.70820	0.199339
$821$	−33.7771	−1.17883	−0.589414	−	0.807831i	$-0.700641\pi$
$821$	−33.7771	−1.17883	−0.589414	+	0.807831i	$0.700641\pi$
$822$	10.7984	0.376637
$823$	38.2492	1.33328	0.666642	−	0.745378i	$-0.267731\pi$
$823$	38.2492	1.33328	0.666642	+	0.745378i	$0.267731\pi$
$824$	−2.11146	−0.0735561
$825$	0	0
$826$	−23.4164	−0.814761
$827$	8.94427	0.311023	0.155511	−	0.987834i	$-0.450297\pi$
$827$	8.94427	0.311023	0.155511	+	0.987834i	$0.450297\pi$
$828$	7.61803	0.264745
$829$	−11.0000	−0.382046	−0.191023	−	0.981586i	$-0.561180\pi$
$829$	−11.0000	−0.382046	−0.191023	+	0.981586i	$0.561180\pi$
$830$	−2.47214	−0.0858091
$831$	4.94427	0.171515
$832$	−1.23607	−0.0428529
$833$	−19.0000	−0.658311
$834$	−4.50658	−0.156050
$835$	−3.18034	−0.110060
$836$	0	0
$837$	6.70820	0.231869
$838$	8.65248	0.298895
$839$	28.3607	0.979119	0.489560	−	0.871970i	$-0.337158\pi$
$839$	28.3607	0.979119	0.489560	+	0.871970i	$0.337158\pi$
$840$	7.23607	0.249668
$841$	−27.4721	−0.947315
$842$	−18.4377	−0.635405
$843$	−15.2361	−0.524758
$844$	−2.85410	−0.0982422
$845$	−14.4164	−0.495940
$846$	−5.38197	−0.185036
$847$	0	0
$848$	18.4377	0.633153
$849$	−11.8885	−0.408014
$850$	3.38197	0.116000
$851$	−3.59675	−0.123295
$852$	−23.4164	−0.802233
$853$	−31.8885	−1.09184	−0.545921	−	0.837836i	$-0.683820\pi$
$853$	−31.8885	−1.09184	−0.545921	+	0.837836i	$0.683820\pi$
$854$	2.94427	0.100751
$855$	−6.47214	−0.221342
$856$	31.8328	1.08802
$857$	1.00000	0.0341593	0.0170797	−	0.999854i	$-0.494563\pi$
$857$	1.00000	0.0341593	0.0170797	+	0.999854i	$0.494563\pi$
$858$	0	0
$859$	−26.8328	−0.915524	−0.457762	−	0.889075i	$-0.651349\pi$
$859$	−26.8328	−0.915524	−0.457762	+	0.889075i	$0.651349\pi$
$860$	−8.47214	−0.288897
$861$	−11.4164	−0.389070
$862$	3.59675	0.122506
$863$	−37.8885	−1.28974	−0.644871	−	0.764292i	$-0.723089\pi$
$863$	−37.8885	−1.28974	−0.644871	+	0.764292i	$0.723089\pi$
$864$	5.61803	0.191129
$865$	−2.94427	−0.100108
$866$	−15.5967	−0.529999
$867$	−12.9443	−0.439611
$868$	35.1246	1.19221
$869$	0	0
$870$	0.763932	0.0258997
$871$	58.8328	1.99347
$872$	33.4164	1.13162
$873$	12.7639	0.431994
$874$	18.8328	0.637029
$875$	−3.23607	−0.109399
$876$	−16.9443	−0.572494
$877$	11.3050	0.381741	0.190871	−	0.981615i	$-0.438869\pi$
$877$	11.3050	0.381741	0.190871	+	0.981615i	$0.438869\pi$
$878$	5.02129	0.169460
$879$	−21.4721	−0.724237
$880$	0	0
$881$	38.8328	1.30831	0.654155	−	0.756360i	$-0.273024\pi$
$881$	38.8328	1.30831	0.654155	+	0.756360i	$0.273024\pi$
$882$	−2.14590	−0.0722561
$883$	10.1803	0.342596	0.171298	−	0.985219i	$-0.445204\pi$
$883$	10.1803	0.342596	0.171298	+	0.985219i	$0.445204\pi$
$884$	46.3607	1.55928
$885$	11.7082	0.393567
$886$	−4.58359	−0.153989
$887$	16.9443	0.568933	0.284466	−	0.958686i	$-0.408184\pi$
$887$	16.9443	0.568933	0.284466	+	0.958686i	$0.408184\pi$
$888$	−1.70820	−0.0573236
$889$	12.0000	0.402467
$890$	2.94427	0.0986922
$891$	0	0
$892$	−14.6525	−0.490601
$893$	56.3607	1.88604
$894$	−2.65248	−0.0887121
$895$	20.1803	0.674554
$896$	36.8328	1.23050
$897$	24.6525	0.823122
$898$	6.18034	0.206241
$899$	8.29180	0.276547
$900$	−1.61803	−0.0539345
$901$	−54.4164	−1.81287
$902$	0	0
$903$	16.9443	0.563870
$904$	−27.7639	−0.923415
$905$	21.4164	0.711905
$906$	4.50658	0.149721
$907$	−42.0000	−1.39459	−0.697294	−	0.716786i	$-0.745613\pi$
$907$	−42.0000	−1.39459	−0.697294	+	0.716786i	$0.745613\pi$
$908$	−27.0344	−0.897169
$909$	−5.52786	−0.183348
$910$	10.4721	0.347148
$911$	47.9574	1.58890	0.794450	−	0.607329i	$-0.207759\pi$
$911$	47.9574	1.58890	0.794450	+	0.607329i	$0.207759\pi$
$912$	−12.0000	−0.397360
$913$	0	0
$914$	21.2361	0.702427
$915$	−1.47214	−0.0486673
$916$	−11.3262	−0.374229
$917$	−1.52786	−0.0504545
$918$	−3.38197	−0.111622
$919$	3.41641	0.112697	0.0563484	−	0.998411i	$-0.482054\pi$
$919$	3.41641	0.112697	0.0563484	+	0.998411i	$0.482054\pi$
$920$	10.5279	0.347093
$921$	11.8885	0.391741
$922$	−18.6525	−0.614287
$923$	−75.7771	−2.49423
$924$	0	0
$925$	0.763932	0.0251179
$926$	−3.70820	−0.121859
$927$	−0.944272	−0.0310140
$928$	6.94427	0.227957
$929$	50.9443	1.67143	0.835714	−	0.549165i	$-0.185054\pi$
$929$	50.9443	1.67143	0.835714	+	0.549165i	$0.185054\pi$
$930$	4.14590	0.135949
$931$	22.4721	0.736495
$932$	−17.6180	−0.577098
$933$	3.23607	0.105944
$934$	2.32624	0.0761168
$935$	0	0
$936$	11.7082	0.382695
$937$	33.1246	1.08213	0.541067	−	0.840980i	$-0.318021\pi$
$937$	33.1246	1.08213	0.541067	+	0.840980i	$0.318021\pi$
$938$	−22.4721	−0.733741
$939$	−22.7639	−0.742873
$940$	14.0902	0.459571
$941$	−45.2361	−1.47465	−0.737327	−	0.675536i	$-0.763912\pi$
$941$	−45.2361	−1.47465	−0.737327	+	0.675536i	$0.763912\pi$
$942$	1.41641	0.0461491
$943$	−16.6099	−0.540893
$944$	21.7082	0.706542
$945$	3.23607	0.105269
$946$	0	0
$947$	−18.2361	−0.592593	−0.296296	−	0.955096i	$-0.595752\pi$
$947$	−18.2361	−0.592593	−0.296296	+	0.955096i	$0.595752\pi$
$948$	20.5623	0.667833
$949$	−54.8328	−1.77995
$950$	−4.00000	−0.129777
$951$	3.94427	0.127902
$952$	−39.5967	−1.28334
$953$	31.8885	1.03297	0.516486	−	0.856296i	$-0.327240\pi$
$953$	31.8885	1.03297	0.516486	+	0.856296i	$0.327240\pi$
$954$	−6.14590	−0.198981
$955$	−27.5967	−0.893010
$956$	39.8885	1.29009
$957$	0	0
$958$	0.180340	0.00582652
$959$	56.5410	1.82580
$960$	−0.236068	−0.00761906
$961$	14.0000	0.451613
$962$	−2.47214	−0.0797049
$963$	14.2361	0.458751
$964$	29.0344	0.935136
$965$	−16.1803	−0.520864
$966$	−9.41641	−0.302968
$967$	−32.0000	−1.02905	−0.514525	−	0.857475i	$-0.672032\pi$
$967$	−32.0000	−1.02905	−0.514525	+	0.857475i	$0.672032\pi$
$968$	0	0
$969$	35.4164	1.13774
$970$	7.88854	0.253286
$971$	29.2361	0.938230	0.469115	−	0.883137i	$-0.344573\pi$
$971$	29.2361	0.938230	0.469115	+	0.883137i	$0.344573\pi$
$972$	1.61803	0.0518985
$973$	−23.5967	−0.756477
$974$	7.23607	0.231859
$975$	−5.23607	−0.167688
$976$	−2.72949	−0.0873689
$977$	−15.9443	−0.510102	−0.255051	−	0.966928i	$-0.582092\pi$
$977$	−15.9443	−0.510102	−0.255051	+	0.966928i	$0.582092\pi$
$978$	3.81966	0.122139
$979$	0	0
$980$	5.61803	0.179462
$981$	14.9443	0.477134
$982$	23.7771	0.758757
$983$	−55.1803	−1.75998	−0.879990	−	0.474993i	$-0.842451\pi$
$983$	−55.1803	−1.75998	−0.879990	+	0.474993i	$0.842451\pi$
$984$	−7.88854	−0.251478
$985$	1.41641	0.0451305
$986$	−4.18034	−0.133129
$987$	−28.1803	−0.896990
$988$	−54.8328	−1.74446
$989$	24.6525	0.783903
$990$	0	0
$991$	6.23607	0.198095	0.0990476	−	0.995083i	$-0.468420\pi$
$991$	6.23607	0.198095	0.0990476	+	0.995083i	$0.468420\pi$
$992$	37.6869	1.19656
$993$	17.1803	0.545202
$994$	28.9443	0.918057
$995$	−16.2361	−0.514718
$996$	−6.47214	−0.205077
$997$	38.7639	1.22767	0.613833	−	0.789436i	$-0.289627\pi$
$997$	38.7639	1.22767	0.613833	+	0.789436i	$0.289627\pi$
$998$	0.583592	0.0184733
$999$	−0.763932	−0.0241697

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1815.2.a.j.1.1	yes	2
3.2	odd	2		5445.2.a.o.1.2		2
5.4	even	2		9075.2.a.bd.1.2		2
11.10	odd	2		1815.2.a.f.1.2	✓	2
33.32	even	2		5445.2.a.x.1.1		2
55.54	odd	2		9075.2.a.bx.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1815.2.a.f.1.2	✓	2	11.10	odd	2
1815.2.a.j.1.1	yes	2	1.1	even	1	trivial
5445.2.a.o.1.2		2	3.2	odd	2
5445.2.a.x.1.1		2	33.32	even	2
9075.2.a.bd.1.2		2	5.4	even	2
9075.2.a.bx.1.1		2	55.54	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:	\( N \)	\(=\)	\( 1815 = 3 \cdot 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1815.a (trivial)

\(f(q)\)	\(=\)	\(q-0.618034 q^{2} -1.00000 q^{3} -1.61803 q^{4} -1.00000 q^{5} +0.618034 q^{6} +3.23607 q^{7} +2.23607 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.618034 q^{2} -1.00000 q^{3} -1.61803 q^{4} -1.00000 q^{5} +0.618034 q^{6} +3.23607 q^{7} +2.23607 q^{8} +1.00000 q^{9} +0.618034 q^{10} +1.61803 q^{12} +5.23607 q^{13} -2.00000 q^{14} +1.00000 q^{15} +1.85410 q^{16} -5.47214 q^{17} -0.618034 q^{18} +6.47214 q^{19} +1.61803 q^{20} -3.23607 q^{21} -4.70820 q^{23} -2.23607 q^{24} +1.00000 q^{25} -3.23607 q^{26} -1.00000 q^{27} -5.23607 q^{28} -1.23607 q^{29} -0.618034 q^{30} -6.70820 q^{31} -5.61803 q^{32} +3.38197 q^{34} -3.23607 q^{35} -1.61803 q^{36} +0.763932 q^{37} -4.00000 q^{38} -5.23607 q^{39} -2.23607 q^{40} +3.52786 q^{41} +2.00000 q^{42} -5.23607 q^{43} -1.00000 q^{45} +2.90983 q^{46} +8.70820 q^{47} -1.85410 q^{48} +3.47214 q^{49} -0.618034 q^{50} +5.47214 q^{51} -8.47214 q^{52} +9.94427 q^{53} +0.618034 q^{54} +7.23607 q^{56} -6.47214 q^{57} +0.763932 q^{58} +11.7082 q^{59} -1.61803 q^{60} -1.47214 q^{61} +4.14590 q^{62} +3.23607 q^{63} -0.236068 q^{64} -5.23607 q^{65} +11.2361 q^{67} +8.85410 q^{68} +4.70820 q^{69} +2.00000 q^{70} -14.4721 q^{71} +2.23607 q^{72} -10.4721 q^{73} -0.472136 q^{74} -1.00000 q^{75} -10.4721 q^{76} +3.23607 q^{78} +12.7082 q^{79} -1.85410 q^{80} +1.00000 q^{81} -2.18034 q^{82} -4.00000 q^{83} +5.23607 q^{84} +5.47214 q^{85} +3.23607 q^{86} +1.23607 q^{87} +4.76393 q^{89} +0.618034 q^{90} +16.9443 q^{91} +7.61803 q^{92} +6.70820 q^{93} -5.38197 q^{94} -6.47214 q^{95} +5.61803 q^{96} +12.7639 q^{97} -2.14590 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - 2 q^{3} - q^{4} - 2 q^{5} - q^{6} + 2 q^{7} + 2 q^{9}+O(q^{10}) \) 2 * q + q^2 - 2 * q^3 - q^4 - 2 * q^5 - q^6 + 2 * q^7 + 2 * q^9	\( 2 q + q^{2} - 2 q^{3} - q^{4} - 2 q^{5} - q^{6} + 2 q^{7} + 2 q^{9} - q^{10} + q^{12} + 6 q^{13} - 4 q^{14} + 2 q^{15} - 3 q^{16} - 2 q^{17} + q^{18} + 4 q^{19} + q^{20} - 2 q^{21} + 4 q^{23} + 2 q^{25} - 2 q^{26} - 2 q^{27} - 6 q^{28} + 2 q^{29} + q^{30} - 9 q^{32} + 9 q^{34} - 2 q^{35} - q^{36} + 6 q^{37} - 8 q^{38} - 6 q^{39} + 16 q^{41} + 4 q^{42} - 6 q^{43} - 2 q^{45} + 17 q^{46} + 4 q^{47} + 3 q^{48} - 2 q^{49} + q^{50} + 2 q^{51} - 8 q^{52} + 2 q^{53} - q^{54} + 10 q^{56} - 4 q^{57} + 6 q^{58} + 10 q^{59} - q^{60} + 6 q^{61} + 15 q^{62} + 2 q^{63} + 4 q^{64} - 6 q^{65} + 18 q^{67} + 11 q^{68} - 4 q^{69} + 4 q^{70} - 20 q^{71} - 12 q^{73} + 8 q^{74} - 2 q^{75} - 12 q^{76} + 2 q^{78} + 12 q^{79} + 3 q^{80} + 2 q^{81} + 18 q^{82} - 8 q^{83} + 6 q^{84} + 2 q^{85} + 2 q^{86} - 2 q^{87} + 14 q^{89} - q^{90} + 16 q^{91} + 13 q^{92} - 13 q^{94} - 4 q^{95} + 9 q^{96} + 30 q^{97} - 11 q^{98}+O(q^{100}) \) 2 * q + q^2 - 2 * q^3 - q^4 - 2 * q^5 - q^6 + 2 * q^7 + 2 * q^9 - q^10 + q^12 + 6 * q^13 - 4 * q^14 + 2 * q^15 - 3 * q^16 - 2 * q^17 + q^18 + 4 * q^19 + q^20 - 2 * q^21 + 4 * q^23 + 2 * q^25 - 2 * q^26 - 2 * q^27 - 6 * q^28 + 2 * q^29 + q^30 - 9 * q^32 + 9 * q^34 - 2 * q^35 - q^36 + 6 * q^37 - 8 * q^38 - 6 * q^39 + 16 * q^41 + 4 * q^42 - 6 * q^43 - 2 * q^45 + 17 * q^46 + 4 * q^47 + 3 * q^48 - 2 * q^49 + q^50 + 2 * q^51 - 8 * q^52 + 2 * q^53 - q^54 + 10 * q^56 - 4 * q^57 + 6 * q^58 + 10 * q^59 - q^60 + 6 * q^61 + 15 * q^62 + 2 * q^63 + 4 * q^64 - 6 * q^65 + 18 * q^67 + 11 * q^68 - 4 * q^69 + 4 * q^70 - 20 * q^71 - 12 * q^73 + 8 * q^74 - 2 * q^75 - 12 * q^76 + 2 * q^78 + 12 * q^79 + 3 * q^80 + 2 * q^81 + 18 * q^82 - 8 * q^83 + 6 * q^84 + 2 * q^85 + 2 * q^86 - 2 * q^87 + 14 * q^89 - q^90 + 16 * q^91 + 13 * q^92 - 13 * q^94 - 4 * q^95 + 9 * q^96 + 30 * q^97 - 11 * q^98

Introduction

L-functions

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Database

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