LMFDB - Embedded newform 5054.2.a.d.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5054,2,Mod(1,5054)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5054, 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("5054.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5054 = 2 \cdot 7 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5054.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:	$40.3563931816$
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			1.2
Root			$-0.618034$ of defining polynomial
Character	$\chi$	$=$	5054.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +0.618034 q^{3} +1.00000 q^{4} +2.85410 q^{5} -0.618034 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.61803 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +0.618034 q^{3} +1.00000 q^{4} +2.85410 q^{5} -0.618034 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.61803 q^{9} -2.85410 q^{10} -0.618034 q^{11} +0.618034 q^{12} -2.00000 q^{13} +1.00000 q^{14} +1.76393 q^{15} +1.00000 q^{16} +1.23607 q^{17} +2.61803 q^{18} +2.85410 q^{20} -0.618034 q^{21} +0.618034 q^{22} -0.618034 q^{24} +3.14590 q^{25} +2.00000 q^{26} -3.47214 q^{27} -1.00000 q^{28} -10.0902 q^{29} -1.76393 q^{30} +0.472136 q^{31} -1.00000 q^{32} -0.381966 q^{33} -1.23607 q^{34} -2.85410 q^{35} -2.61803 q^{36} +2.09017 q^{37} -1.23607 q^{39} -2.85410 q^{40} +8.85410 q^{41} +0.618034 q^{42} +3.61803 q^{43} -0.618034 q^{44} -7.47214 q^{45} +10.6180 q^{47} +0.618034 q^{48} +1.00000 q^{49} -3.14590 q^{50} +0.763932 q^{51} -2.00000 q^{52} -2.32624 q^{53} +3.47214 q^{54} -1.76393 q^{55} +1.00000 q^{56} +10.0902 q^{58} -11.6180 q^{59} +1.76393 q^{60} -7.56231 q^{61} -0.472136 q^{62} +2.61803 q^{63} +1.00000 q^{64} -5.70820 q^{65} +0.381966 q^{66} -7.23607 q^{67} +1.23607 q^{68} +2.85410 q^{70} -7.56231 q^{71} +2.61803 q^{72} -4.94427 q^{73} -2.09017 q^{74} +1.94427 q^{75} +0.618034 q^{77} +1.23607 q^{78} +0.0901699 q^{79} +2.85410 q^{80} +5.70820 q^{81} -8.85410 q^{82} +0.291796 q^{83} -0.618034 q^{84} +3.52786 q^{85} -3.61803 q^{86} -6.23607 q^{87} +0.618034 q^{88} +4.32624 q^{89} +7.47214 q^{90} +2.00000 q^{91} +0.291796 q^{93} -10.6180 q^{94} -0.618034 q^{96} -3.38197 q^{97} -1.00000 q^{98} +1.61803 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} + q^{11} - q^{12} - 4 q^{13} + 2 q^{14} + 8 q^{15} + 2 q^{16} - 2 q^{17} + 3 q^{18} - q^{20} + q^{21} - q^{22} + q^{24} + 13 q^{25} + 4 q^{26} + 2 q^{27} - 2 q^{28} - 9 q^{29} - 8 q^{30} - 8 q^{31} - 2 q^{32} - 3 q^{33} + 2 q^{34} + q^{35} - 3 q^{36} - 7 q^{37} + 2 q^{39} + q^{40} + 11 q^{41} - q^{42} + 5 q^{43} + q^{44} - 6 q^{45} + 19 q^{47} - q^{48} + 2 q^{49} - 13 q^{50} + 6 q^{51} - 4 q^{52} + 11 q^{53} - 2 q^{54} - 8 q^{55} + 2 q^{56} + 9 q^{58} - 21 q^{59} + 8 q^{60} + 5 q^{61} + 8 q^{62} + 3 q^{63} + 2 q^{64} + 2 q^{65} + 3 q^{66} - 10 q^{67} - 2 q^{68} - q^{70} + 5 q^{71} + 3 q^{72} + 8 q^{73} + 7 q^{74} - 14 q^{75} - q^{77} - 2 q^{78} - 11 q^{79} - q^{80} - 2 q^{81} - 11 q^{82} + 14 q^{83} + q^{84} + 16 q^{85} - 5 q^{86} - 8 q^{87} - q^{88} - 7 q^{89} + 6 q^{90} + 4 q^{91} + 14 q^{93} - 19 q^{94} + q^{96} - 9 q^{97} - 2 q^{98} + 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 + q^11 - q^12 - 4 * q^13 + 2 * q^14 + 8 * q^15 + 2 * q^16 - 2 * q^17 + 3 * q^18 - q^20 + q^21 - q^22 + q^24 + 13 * q^25 + 4 * q^26 + 2 * q^27 - 2 * q^28 - 9 * q^29 - 8 * q^30 - 8 * q^31 - 2 * q^32 - 3 * q^33 + 2 * q^34 + q^35 - 3 * q^36 - 7 * q^37 + 2 * q^39 + q^40 + 11 * q^41 - q^42 + 5 * q^43 + q^44 - 6 * q^45 + 19 * q^47 - q^48 + 2 * q^49 - 13 * q^50 + 6 * q^51 - 4 * q^52 + 11 * q^53 - 2 * q^54 - 8 * q^55 + 2 * q^56 + 9 * q^58 - 21 * q^59 + 8 * q^60 + 5 * q^61 + 8 * q^62 + 3 * q^63 + 2 * q^64 + 2 * q^65 + 3 * q^66 - 10 * q^67 - 2 * q^68 - q^70 + 5 * q^71 + 3 * q^72 + 8 * q^73 + 7 * q^74 - 14 * q^75 - q^77 - 2 * q^78 - 11 * q^79 - q^80 - 2 * q^81 - 11 * q^82 + 14 * q^83 + q^84 + 16 * q^85 - 5 * q^86 - 8 * q^87 - q^88 - 7 * q^89 + 6 * q^90 + 4 * q^91 + 14 * q^93 - 19 * q^94 + q^96 - 9 * q^97 - 2 * q^98 + 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
$3$	0.618034	0.356822	0.178411	−	0.983956i	$-0.442904\pi$
$3$	0.618034	0.356822	0.178411	+	0.983956i	$0.442904\pi$
$4$	1.00000	0.500000
$5$	2.85410	1.27639	0.638197	−	0.769873i	$-0.279681\pi$
$5$	2.85410	1.27639	0.638197	+	0.769873i	$0.279681\pi$
$6$	−0.618034	−0.252311
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.00000	−0.353553
$9$	−2.61803	−0.872678
$10$	−2.85410	−0.902546
$11$	−0.618034	−0.186344	−0.0931721	−	0.995650i	$-0.529701\pi$
$11$	−0.618034	−0.186344	−0.0931721	+	0.995650i	$0.529701\pi$
$12$	0.618034	0.178411
$13$	−2.00000	−0.554700	−0.277350	−	0.960769i	$-0.589456\pi$
$13$	−2.00000	−0.554700	−0.277350	+	0.960769i	$0.589456\pi$
$14$	1.00000	0.267261
$15$	1.76393	0.455445
$16$	1.00000	0.250000
$17$	1.23607	0.299791	0.149895	−	0.988702i	$-0.452106\pi$
$17$	1.23607	0.299791	0.149895	+	0.988702i	$0.452106\pi$
$18$	2.61803	0.617077
$19$	0	0
$19$	0	0
$20$	2.85410	0.638197
$21$	−0.618034	−0.134866
$22$	0.618034	0.131765
$23$	0	0		−	1.00000i	$-0.5\pi$
$23$	0	0			1.00000i	$0.5\pi$
$24$	−0.618034	−0.126156
$25$	3.14590	0.629180
$26$	2.00000	0.392232
$27$	−3.47214	−0.668213
$28$	−1.00000	−0.188982
$29$	−10.0902	−1.87370	−0.936849	−	0.349735i	$-0.886272\pi$
$29$	−10.0902	−1.87370	−0.936849	+	0.349735i	$0.886272\pi$
$30$	−1.76393	−0.322048
$31$	0.472136	0.0847981	0.0423991	−	0.999101i	$-0.486500\pi$
$31$	0.472136	0.0847981	0.0423991	+	0.999101i	$0.486500\pi$
$32$	−1.00000	−0.176777
$33$	−0.381966	−0.0664917
$34$	−1.23607	−0.211984
$35$	−2.85410	−0.482431
$36$	−2.61803	−0.436339
$37$	2.09017	0.343622	0.171811	−	0.985130i	$-0.445038\pi$
$37$	2.09017	0.343622	0.171811	+	0.985130i	$0.445038\pi$
$38$	0	0
$39$	−1.23607	−0.197929
$40$	−2.85410	−0.451273
$41$	8.85410	1.38278	0.691389	−	0.722483i	$-0.256999\pi$
$41$	8.85410	1.38278	0.691389	+	0.722483i	$0.256999\pi$
$42$	0.618034	0.0953647
$43$	3.61803	0.551745	0.275873	−	0.961194i	$-0.411033\pi$
$43$	3.61803	0.551745	0.275873	+	0.961194i	$0.411033\pi$
$44$	−0.618034	−0.0931721
$45$	−7.47214	−1.11388
$46$	0	0
$47$	10.6180	1.54880	0.774400	−	0.632697i	$-0.218052\pi$
$47$	10.6180	1.54880	0.774400	+	0.632697i	$0.218052\pi$
$48$	0.618034	0.0892055
$49$	1.00000	0.142857
$50$	−3.14590	−0.444897
$51$	0.763932	0.106972
$52$	−2.00000	−0.277350
$53$	−2.32624	−0.319533	−0.159767	−	0.987155i	$-0.551074\pi$
$53$	−2.32624	−0.319533	−0.159767	+	0.987155i	$0.551074\pi$
$54$	3.47214	0.472498
$55$	−1.76393	−0.237849
$56$	1.00000	0.133631
$57$	0	0
$58$	10.0902	1.32490
$59$	−11.6180	−1.51254	−0.756270	−	0.654260i	$-0.772980\pi$
$59$	−11.6180	−1.51254	−0.756270	+	0.654260i	$0.772980\pi$
$60$	1.76393	0.227723
$61$	−7.56231	−0.968254	−0.484127	−	0.874998i	$-0.660863\pi$
$61$	−7.56231	−0.968254	−0.484127	+	0.874998i	$0.660863\pi$
$62$	−0.472136	−0.0599613
$63$	2.61803	0.329841
$64$	1.00000	0.125000
$65$	−5.70820	−0.708016
$66$	0.381966	0.0470168
$67$	−7.23607	−0.884026	−0.442013	−	0.897009i	$-0.645736\pi$
$67$	−7.23607	−0.884026	−0.442013	+	0.897009i	$0.645736\pi$
$68$	1.23607	0.149895
$69$	0	0
$70$	2.85410	0.341130
$71$	−7.56231	−0.897481	−0.448740	−	0.893662i	$-0.648127\pi$
$71$	−7.56231	−0.897481	−0.448740	+	0.893662i	$0.648127\pi$
$72$	2.61803	0.308538
$73$	−4.94427	−0.578683	−0.289342	−	0.957226i	$-0.593436\pi$
$73$	−4.94427	−0.578683	−0.289342	+	0.957226i	$0.593436\pi$
$74$	−2.09017	−0.242977
$75$	1.94427	0.224505
$76$	0	0
$77$	0.618034	0.0704315
$78$	1.23607	0.139957
$79$	0.0901699	0.0101449	0.00507246	−	0.999987i	$-0.498385\pi$
$79$	0.0901699	0.0101449	0.00507246	+	0.999987i	$0.498385\pi$
$80$	2.85410	0.319098
$81$	5.70820	0.634245
$82$	−8.85410	−0.977772
$83$	0.291796	0.0320288	0.0160144	−	0.999872i	$-0.494902\pi$
$83$	0.291796	0.0320288	0.0160144	+	0.999872i	$0.494902\pi$
$84$	−0.618034	−0.0674330
$85$	3.52786	0.382651
$86$	−3.61803	−0.390143
$87$	−6.23607	−0.668577
$88$	0.618034	0.0658826
$89$	4.32624	0.458580	0.229290	−	0.973358i	$-0.426360\pi$
$89$	4.32624	0.458580	0.229290	+	0.973358i	$0.426360\pi$
$90$	7.47214	0.787632
$91$	2.00000	0.209657
$92$	0	0
$93$	0.291796	0.0302578
$94$	−10.6180	−1.09517
$95$	0	0
$96$	−0.618034	−0.0630778
$97$	−3.38197	−0.343387	−0.171693	−	0.985150i	$-0.554924\pi$
$97$	−3.38197	−0.343387	−0.171693	+	0.985150i	$0.554924\pi$
$98$	−1.00000	−0.101015
$99$	1.61803	0.162619
$100$	3.14590	0.314590
$101$	10.0000	0.995037	0.497519	−	0.867453i	$-0.334245\pi$
$101$	10.0000	0.995037	0.497519	+	0.867453i	$0.334245\pi$
$102$	−0.763932	−0.0756405
$103$	−10.4721	−1.03185	−0.515925	−	0.856634i	$-0.672552\pi$
$103$	−10.4721	−1.03185	−0.515925	+	0.856634i	$0.672552\pi$
$104$	2.00000	0.196116
$105$	−1.76393	−0.172142
$106$	2.32624	0.225944
$107$	−13.7082	−1.32522	−0.662611	−	0.748964i	$-0.730552\pi$
$107$	−13.7082	−1.32522	−0.662611	+	0.748964i	$0.730552\pi$
$108$	−3.47214	−0.334106
$109$	10.6180	1.01702	0.508512	−	0.861055i	$-0.330196\pi$
$109$	10.6180	1.01702	0.508512	+	0.861055i	$0.330196\pi$
$110$	1.76393	0.168184
$111$	1.29180	0.122612
$112$	−1.00000	−0.0944911
$113$	−19.8885	−1.87096	−0.935478	−	0.353384i	$-0.885031\pi$
$113$	−19.8885	−1.87096	−0.935478	+	0.353384i	$0.885031\pi$
$114$	0	0
$115$	0	0
$116$	−10.0902	−0.936849
$117$	5.23607	0.484075
$118$	11.6180	1.06953
$119$	−1.23607	−0.113310
$120$	−1.76393	−0.161024
$121$	−10.6180	−0.965276
$122$	7.56231	0.684659
$123$	5.47214	0.493406
$124$	0.472136	0.0423991
$125$	−5.29180	−0.473313
$126$	−2.61803	−0.233233
$127$	−14.0344	−1.24536	−0.622678	−	0.782478i	$-0.713955\pi$
$127$	−14.0344	−1.24536	−0.622678	+	0.782478i	$0.713955\pi$
$128$	−1.00000	−0.0883883
$129$	2.23607	0.196875
$130$	5.70820	0.500643
$131$	−11.5279	−1.00719	−0.503597	−	0.863939i	$-0.667990\pi$
$131$	−11.5279	−1.00719	−0.503597	+	0.863939i	$0.667990\pi$
$132$	−0.381966	−0.0332459
$133$	0	0
$134$	7.23607	0.625101
$135$	−9.90983	−0.852902
$136$	−1.23607	−0.105992
$137$	−20.2705	−1.73183	−0.865913	−	0.500194i	$-0.833262\pi$
$137$	−20.2705	−1.73183	−0.865913	+	0.500194i	$0.833262\pi$
$138$	0	0
$139$	14.9443	1.26756	0.633778	−	0.773515i	$-0.281503\pi$
$139$	14.9443	1.26756	0.633778	+	0.773515i	$0.281503\pi$
$140$	−2.85410	−0.241216
$141$	6.56231	0.552646
$142$	7.56231	0.634615
$143$	1.23607	0.103365
$144$	−2.61803	−0.218169
$145$	−28.7984	−2.39157
$146$	4.94427	0.409191
$147$	0.618034	0.0509746
$148$	2.09017	0.171811
$149$	−0.763932	−0.0625837	−0.0312919	−	0.999510i	$-0.509962\pi$
$149$	−0.763932	−0.0625837	−0.0312919	+	0.999510i	$0.509962\pi$
$150$	−1.94427	−0.158749
$151$	−20.9443	−1.70442	−0.852210	−	0.523199i	$-0.824738\pi$
$151$	−20.9443	−1.70442	−0.852210	+	0.523199i	$0.824738\pi$
$152$	0	0
$153$	−3.23607	−0.261621
$154$	−0.618034	−0.0498026
$155$	1.34752	0.108236
$156$	−1.23607	−0.0989646
$157$	−13.0902	−1.04471	−0.522355	−	0.852728i	$-0.674946\pi$
$157$	−13.0902	−1.04471	−0.522355	+	0.852728i	$0.674946\pi$
$158$	−0.0901699	−0.00717354
$159$	−1.43769	−0.114017
$160$	−2.85410	−0.225637
$161$	0	0
$162$	−5.70820	−0.448479
$163$	0.909830	0.0712634	0.0356317	−	0.999365i	$-0.488656\pi$
$163$	0.909830	0.0712634	0.0356317	+	0.999365i	$0.488656\pi$
$164$	8.85410	0.691389
$165$	−1.09017	−0.0848696
$166$	−0.291796	−0.0226478
$167$	−3.52786	−0.272994	−0.136497	−	0.990640i	$-0.543584\pi$
$167$	−3.52786	−0.272994	−0.136497	+	0.990640i	$0.543584\pi$
$168$	0.618034	0.0476824
$169$	−9.00000	−0.692308
$170$	−3.52786	−0.270575
$171$	0	0
$172$	3.61803	0.275873
$173$	−10.9443	−0.832078	−0.416039	−	0.909347i	$-0.636582\pi$
$173$	−10.9443	−0.832078	−0.416039	+	0.909347i	$0.636582\pi$
$174$	6.23607	0.472755
$175$	−3.14590	−0.237808
$176$	−0.618034	−0.0465861
$177$	−7.18034	−0.539707
$178$	−4.32624	−0.324265
$179$	18.1803	1.35886	0.679431	−	0.733739i	$-0.262227\pi$
$179$	18.1803	1.35886	0.679431	+	0.733739i	$0.262227\pi$
$180$	−7.47214	−0.556940
$181$	9.88854	0.735010	0.367505	−	0.930022i	$-0.380212\pi$
$181$	9.88854	0.735010	0.367505	+	0.930022i	$0.380212\pi$
$182$	−2.00000	−0.148250
$183$	−4.67376	−0.345494
$184$	0	0
$185$	5.96556	0.438597
$186$	−0.291796	−0.0213955
$187$	−0.763932	−0.0558642
$188$	10.6180	0.774400
$189$	3.47214	0.252561
$190$	0	0
$191$	−9.41641	−0.681347	−0.340674	−	0.940182i	$-0.610655\pi$
$191$	−9.41641	−0.681347	−0.340674	+	0.940182i	$0.610655\pi$
$192$	0.618034	0.0446028
$193$	9.52786	0.685831	0.342915	−	0.939366i	$-0.388586\pi$
$193$	9.52786	0.685831	0.342915	+	0.939366i	$0.388586\pi$
$194$	3.38197	0.242811
$195$	−3.52786	−0.252636
$196$	1.00000	0.0714286
$197$	−21.1246	−1.50507	−0.752533	−	0.658554i	$-0.771168\pi$
$197$	−21.1246	−1.50507	−0.752533	+	0.658554i	$0.771168\pi$
$198$	−1.61803	−0.114989
$199$	1.61803	0.114699	0.0573497	−	0.998354i	$-0.481735\pi$
$199$	1.61803	0.114699	0.0573497	+	0.998354i	$0.481735\pi$
$200$	−3.14590	−0.222449
$201$	−4.47214	−0.315440
$202$	−10.0000	−0.703598
$203$	10.0902	0.708191
$204$	0.763932	0.0534859
$205$	25.2705	1.76497
$206$	10.4721	0.729628
$207$	0	0
$208$	−2.00000	−0.138675
$209$	0	0
$210$	1.76393	0.121723
$211$	17.1246	1.17891	0.589453	−	0.807802i	$-0.299343\pi$
$211$	17.1246	1.17891	0.589453	+	0.807802i	$0.299343\pi$
$212$	−2.32624	−0.159767
$213$	−4.67376	−0.320241
$214$	13.7082	0.937074
$215$	10.3262	0.704244
$216$	3.47214	0.236249
$217$	−0.472136	−0.0320507
$218$	−10.6180	−0.719144
$219$	−3.05573	−0.206487
$220$	−1.76393	−0.118924
$221$	−2.47214	−0.166294
$222$	−1.29180	−0.0866997
$223$	22.6525	1.51692	0.758461	−	0.651718i	$-0.225952\pi$
$223$	22.6525	1.51692	0.758461	+	0.651718i	$0.225952\pi$
$224$	1.00000	0.0668153
$225$	−8.23607	−0.549071
$226$	19.8885	1.32297
$227$	−20.3607	−1.35139	−0.675693	−	0.737183i	$-0.736155\pi$
$227$	−20.3607	−1.35139	−0.675693	+	0.737183i	$0.736155\pi$
$228$	0	0
$229$	22.2705	1.47168	0.735838	−	0.677157i	$-0.236788\pi$
$229$	22.2705	1.47168	0.735838	+	0.677157i	$0.236788\pi$
$230$	0	0
$231$	0.381966	0.0251315
$232$	10.0902	0.662452
$233$	18.7984	1.23152	0.615761	−	0.787933i	$-0.288849\pi$
$233$	18.7984	1.23152	0.615761	+	0.787933i	$0.288849\pi$
$234$	−5.23607	−0.342292
$235$	30.3050	1.97688
$236$	−11.6180	−0.756270
$237$	0.0557281	0.00361993
$238$	1.23607	0.0801224
$239$	−0.180340	−0.0116652	−0.00583261	−	0.999983i	$-0.501857\pi$
$239$	−0.180340	−0.0116652	−0.00583261	+	0.999983i	$0.501857\pi$
$240$	1.76393	0.113861
$241$	−24.8541	−1.60099	−0.800497	−	0.599337i	$-0.795431\pi$
$241$	−24.8541	−1.60099	−0.800497	+	0.599337i	$0.795431\pi$
$242$	10.6180	0.682553
$243$	13.9443	0.894525
$244$	−7.56231	−0.484127
$245$	2.85410	0.182342
$246$	−5.47214	−0.348891
$247$	0	0
$248$	−0.472136	−0.0299807
$249$	0.180340	0.0114286
$250$	5.29180	0.334683
$251$	22.3607	1.41139	0.705697	−	0.708514i	$-0.250634\pi$
$251$	22.3607	1.41139	0.705697	+	0.708514i	$0.250634\pi$
$252$	2.61803	0.164921
$253$	0	0
$254$	14.0344	0.880599
$255$	2.18034	0.136538
$256$	1.00000	0.0625000
$257$	21.2148	1.32334	0.661671	−	0.749794i	$-0.269848\pi$
$257$	21.2148	1.32334	0.661671	+	0.749794i	$0.269848\pi$
$258$	−2.23607	−0.139212
$259$	−2.09017	−0.129877
$260$	−5.70820	−0.354008
$261$	26.4164	1.63513
$262$	11.5279	0.712194
$263$	22.6525	1.39681	0.698406	−	0.715702i	$-0.253893\pi$
$263$	22.6525	1.39681	0.698406	+	0.715702i	$0.253893\pi$
$264$	0.381966	0.0235084
$265$	−6.63932	−0.407850
$266$	0	0
$267$	2.67376	0.163632
$268$	−7.23607	−0.442013
$269$	−4.00000	−0.243884	−0.121942	−	0.992537i	$-0.538912\pi$
$269$	−4.00000	−0.243884	−0.121942	+	0.992537i	$0.538912\pi$
$270$	9.90983	0.603093
$271$	−18.5623	−1.12758	−0.563790	−	0.825918i	$-0.690657\pi$
$271$	−18.5623	−1.12758	−0.563790	+	0.825918i	$0.690657\pi$
$272$	1.23607	0.0749476
$273$	1.23607	0.0748102
$274$	20.2705	1.22459
$275$	−1.94427	−0.117244
$276$	0	0
$277$	−4.47214	−0.268705	−0.134352	−	0.990934i	$-0.542895\pi$
$277$	−4.47214	−0.268705	−0.134352	+	0.990934i	$0.542895\pi$
$278$	−14.9443	−0.896298
$279$	−1.23607	−0.0740015
$280$	2.85410	0.170565
$281$	−6.47214	−0.386095	−0.193048	−	0.981189i	$-0.561837\pi$
$281$	−6.47214	−0.386095	−0.193048	+	0.981189i	$0.561837\pi$
$282$	−6.56231	−0.390780
$283$	−0.583592	−0.0346910	−0.0173455	−	0.999850i	$-0.505522\pi$
$283$	−0.583592	−0.0346910	−0.0173455	+	0.999850i	$0.505522\pi$
$284$	−7.56231	−0.448740
$285$	0	0
$286$	−1.23607	−0.0730902
$287$	−8.85410	−0.522641
$288$	2.61803	0.154269
$289$	−15.4721	−0.910126
$290$	28.7984	1.69110
$291$	−2.09017	−0.122528
$292$	−4.94427	−0.289342
$293$	−10.4721	−0.611789	−0.305894	−	0.952065i	$-0.598955\pi$
$293$	−10.4721	−0.611789	−0.305894	+	0.952065i	$0.598955\pi$
$294$	−0.618034	−0.0360445
$295$	−33.1591	−1.93059
$296$	−2.09017	−0.121489
$297$	2.14590	0.124518
$298$	0.763932	0.0442534
$299$	0	0
$300$	1.94427	0.112253
$301$	−3.61803	−0.208540
$302$	20.9443	1.20521
$303$	6.18034	0.355051
$304$	0	0
$305$	−21.5836	−1.23587
$306$	3.23607	0.184994
$307$	26.0902	1.48904	0.744522	−	0.667598i	$-0.232677\pi$
$307$	26.0902	1.48904	0.744522	+	0.667598i	$0.232677\pi$
$308$	0.618034	0.0352158
$309$	−6.47214	−0.368187
$310$	−1.34752	−0.0765342
$311$	17.0902	0.969095	0.484547	−	0.874765i	$-0.338984\pi$
$311$	17.0902	0.969095	0.484547	+	0.874765i	$0.338984\pi$
$312$	1.23607	0.0699786
$313$	0.472136	0.0266867	0.0133434	−	0.999911i	$-0.495753\pi$
$313$	0.472136	0.0266867	0.0133434	+	0.999911i	$0.495753\pi$
$314$	13.0902	0.738721
$315$	7.47214	0.421007
$316$	0.0901699	0.00507246
$317$	7.27051	0.408353	0.204176	−	0.978934i	$-0.434548\pi$
$317$	7.27051	0.408353	0.204176	+	0.978934i	$0.434548\pi$
$318$	1.43769	0.0806219
$319$	6.23607	0.349153
$320$	2.85410	0.159549
$321$	−8.47214	−0.472869
$322$	0	0
$323$	0	0
$324$	5.70820	0.317122
$325$	−6.29180	−0.349006
$326$	−0.909830	−0.0503908
$327$	6.56231	0.362896
$328$	−8.85410	−0.488886
$329$	−10.6180	−0.585391
$330$	1.09017	0.0600119
$331$	8.76393	0.481709	0.240855	−	0.970561i	$-0.422572\pi$
$331$	8.76393	0.481709	0.240855	+	0.970561i	$0.422572\pi$
$332$	0.291796	0.0160144
$333$	−5.47214	−0.299871
$334$	3.52786	0.193036
$335$	−20.6525	−1.12837
$336$	−0.618034	−0.0337165
$337$	−25.2361	−1.37470	−0.687348	−	0.726328i	$-0.741225\pi$
$337$	−25.2361	−1.37470	−0.687348	+	0.726328i	$0.741225\pi$
$338$	9.00000	0.489535
$339$	−12.2918	−0.667599
$340$	3.52786	0.191325
$341$	−0.291796	−0.0158016
$342$	0	0
$343$	−1.00000	−0.0539949
$344$	−3.61803	−0.195071
$345$	0	0
$346$	10.9443	0.588368
$347$	−21.8885	−1.17504	−0.587519	−	0.809210i	$-0.699895\pi$
$347$	−21.8885	−1.17504	−0.587519	+	0.809210i	$0.699895\pi$
$348$	−6.23607	−0.334288
$349$	0.111456	0.00596611	0.00298306	−	0.999996i	$-0.499050\pi$
$349$	0.111456	0.00596611	0.00298306	+	0.999996i	$0.499050\pi$
$350$	3.14590	0.168155
$351$	6.94427	0.370658
$352$	0.618034	0.0329413
$353$	26.3607	1.40304	0.701519	−	0.712651i	$-0.252506\pi$
$353$	26.3607	1.40304	0.701519	+	0.712651i	$0.252506\pi$
$354$	7.18034	0.381631
$355$	−21.5836	−1.14554
$356$	4.32624	0.229290
$357$	−0.763932	−0.0404316
$358$	−18.1803	−0.960861
$359$	−36.6525	−1.93444	−0.967222	−	0.253933i	$-0.918276\pi$
$359$	−36.6525	−1.93444	−0.967222	+	0.253933i	$0.918276\pi$
$360$	7.47214	0.393816
$361$	0	0
$362$	−9.88854	−0.519730
$363$	−6.56231	−0.344432
$364$	2.00000	0.104828
$365$	−14.1115	−0.738627
$366$	4.67376	0.244301
$367$	10.0344	0.523794	0.261897	−	0.965096i	$-0.415652\pi$
$367$	10.0344	0.523794	0.261897	+	0.965096i	$0.415652\pi$
$368$	0	0
$369$	−23.1803	−1.20672
$370$	−5.96556	−0.310135
$371$	2.32624	0.120772
$372$	0.291796	0.0151289
$373$	21.3262	1.10423	0.552115	−	0.833768i	$-0.313821\pi$
$373$	21.3262	1.10423	0.552115	+	0.833768i	$0.313821\pi$
$374$	0.763932	0.0395020
$375$	−3.27051	−0.168888
$376$	−10.6180	−0.547583
$377$	20.1803	1.03934
$378$	−3.47214	−0.178587
$379$	−23.1246	−1.18783	−0.593916	−	0.804527i	$-0.702419\pi$
$379$	−23.1246	−1.18783	−0.593916	+	0.804527i	$0.702419\pi$
$380$	0	0
$381$	−8.67376	−0.444370
$382$	9.41641	0.481785
$383$	32.6525	1.66846	0.834232	−	0.551414i	$-0.185911\pi$
$383$	32.6525	1.66846	0.834232	+	0.551414i	$0.185911\pi$
$384$	−0.618034	−0.0315389
$385$	1.76393	0.0898983
$386$	−9.52786	−0.484956
$387$	−9.47214	−0.481496
$388$	−3.38197	−0.171693
$389$	7.05573	0.357740	0.178870	−	0.983873i	$-0.442756\pi$
$389$	7.05573	0.357740	0.178870	+	0.983873i	$0.442756\pi$
$390$	3.52786	0.178640
$391$	0	0
$392$	−1.00000	−0.0505076
$393$	−7.12461	−0.359389
$394$	21.1246	1.06424
$395$	0.257354	0.0129489
$396$	1.61803	0.0813093
$397$	4.43769	0.222721	0.111361	−	0.993780i	$-0.464479\pi$
$397$	4.43769	0.222721	0.111361	+	0.993780i	$0.464479\pi$
$398$	−1.61803	−0.0811047
$399$	0	0
$400$	3.14590	0.157295
$401$	−29.4164	−1.46899	−0.734493	−	0.678617i	$-0.762580\pi$
$401$	−29.4164	−1.46899	−0.734493	+	0.678617i	$0.762580\pi$
$402$	4.47214	0.223050
$403$	−0.944272	−0.0470375
$404$	10.0000	0.497519
$405$	16.2918	0.809546
$406$	−10.0902	−0.500767
$407$	−1.29180	−0.0640320
$408$	−0.763932	−0.0378203
$409$	−25.2705	−1.24955	−0.624773	−	0.780806i	$-0.714809\pi$
$409$	−25.2705	−1.24955	−0.624773	+	0.780806i	$0.714809\pi$
$410$	−25.2705	−1.24802
$411$	−12.5279	−0.617954
$412$	−10.4721	−0.515925
$413$	11.6180	0.571686
$414$	0	0
$415$	0.832816	0.0408813
$416$	2.00000	0.0980581
$417$	9.23607	0.452292
$418$	0	0
$419$	−34.6525	−1.69288	−0.846442	−	0.532481i	$-0.821260\pi$
$419$	−34.6525	−1.69288	−0.846442	+	0.532481i	$0.821260\pi$
$420$	−1.76393	−0.0860711
$421$	7.52786	0.366886	0.183443	−	0.983030i	$-0.441276\pi$
$421$	7.52786	0.366886	0.183443	+	0.983030i	$0.441276\pi$
$422$	−17.1246	−0.833613
$423$	−27.7984	−1.35160
$424$	2.32624	0.112972
$425$	3.88854	0.188622
$426$	4.67376	0.226445
$427$	7.56231	0.365966
$428$	−13.7082	−0.662611
$429$	0.763932	0.0368830
$430$	−10.3262	−0.497975
$431$	20.1459	0.970394	0.485197	−	0.874405i	$-0.338748\pi$
$431$	20.1459	0.970394	0.485197	+	0.874405i	$0.338748\pi$
$432$	−3.47214	−0.167053
$433$	−0.854102	−0.0410455	−0.0205228	−	0.999789i	$-0.506533\pi$
$433$	−0.854102	−0.0410455	−0.0205228	+	0.999789i	$0.506533\pi$
$434$	0.472136	0.0226633
$435$	−17.7984	−0.853367
$436$	10.6180	0.508512
$437$	0	0
$438$	3.05573	0.146008
$439$	18.2918	0.873020	0.436510	−	0.899699i	$-0.356214\pi$
$439$	18.2918	0.873020	0.436510	+	0.899699i	$0.356214\pi$
$440$	1.76393	0.0840922
$441$	−2.61803	−0.124668
$442$	2.47214	0.117588
$443$	−6.67376	−0.317080	−0.158540	−	0.987353i	$-0.550679\pi$
$443$	−6.67376	−0.317080	−0.158540	+	0.987353i	$0.550679\pi$
$444$	1.29180	0.0613059
$445$	12.3475	0.585329
$446$	−22.6525	−1.07263
$447$	−0.472136	−0.0223313
$448$	−1.00000	−0.0472456
$449$	−5.34752	−0.252365	−0.126183	−	0.992007i	$-0.540273\pi$
$449$	−5.34752	−0.252365	−0.126183	+	0.992007i	$0.540273\pi$
$450$	8.23607	0.388252
$451$	−5.47214	−0.257673
$452$	−19.8885	−0.935478
$453$	−12.9443	−0.608175
$454$	20.3607	0.955574
$455$	5.70820	0.267605
$456$	0	0
$457$	−7.09017	−0.331664	−0.165832	−	0.986154i	$-0.553031\pi$
$457$	−7.09017	−0.331664	−0.165832	+	0.986154i	$0.553031\pi$
$458$	−22.2705	−1.04063
$459$	−4.29180	−0.200324
$460$	0	0
$461$	−14.6180	−0.680830	−0.340415	−	0.940275i	$-0.610568\pi$
$461$	−14.6180	−0.680830	−0.340415	+	0.940275i	$0.610568\pi$
$462$	−0.381966	−0.0177707
$463$	4.36068	0.202658	0.101329	−	0.994853i	$-0.467691\pi$
$463$	4.36068	0.202658	0.101329	+	0.994853i	$0.467691\pi$
$464$	−10.0902	−0.468424
$465$	0.832816	0.0386209
$466$	−18.7984	−0.870818
$467$	28.0000	1.29569	0.647843	−	0.761774i	$-0.275671\pi$
$467$	28.0000	1.29569	0.647843	+	0.761774i	$0.275671\pi$
$468$	5.23607	0.242037
$469$	7.23607	0.334131
$470$	−30.3050	−1.39786
$471$	−8.09017	−0.372775
$472$	11.6180	0.534763
$473$	−2.23607	−0.102815
$474$	−0.0557281	−0.00255968
$475$	0	0
$476$	−1.23607	−0.0566551
$477$	6.09017	0.278850
$478$	0.180340	0.00824855
$479$	26.3820	1.20542	0.602711	−	0.797959i	$-0.294087\pi$
$479$	26.3820	1.20542	0.602711	+	0.797959i	$0.294087\pi$
$480$	−1.76393	−0.0805121
$481$	−4.18034	−0.190607
$482$	24.8541	1.13207
$483$	0	0
$484$	−10.6180	−0.482638
$485$	−9.65248	−0.438296
$486$	−13.9443	−0.632525
$487$	19.5066	0.883927	0.441964	−	0.897033i	$-0.354282\pi$
$487$	19.5066	0.883927	0.441964	+	0.897033i	$0.354282\pi$
$488$	7.56231	0.342330
$489$	0.562306	0.0254284
$490$	−2.85410	−0.128935
$491$	31.4164	1.41780	0.708901	−	0.705308i	$-0.249191\pi$
$491$	31.4164	1.41780	0.708901	+	0.705308i	$0.249191\pi$
$492$	5.47214	0.246703
$493$	−12.4721	−0.561717
$494$	0	0
$495$	4.61803	0.207565
$496$	0.472136	0.0211995
$497$	7.56231	0.339216
$498$	−0.180340	−0.00808122
$499$	−35.6180	−1.59448	−0.797241	−	0.603661i	$-0.793708\pi$
$499$	−35.6180	−1.59448	−0.797241	+	0.603661i	$0.793708\pi$
$500$	−5.29180	−0.236656
$501$	−2.18034	−0.0974104
$502$	−22.3607	−0.998006
$503$	20.2705	0.903817	0.451909	−	0.892064i	$-0.350743\pi$
$503$	20.2705	0.903817	0.451909	+	0.892064i	$0.350743\pi$
$504$	−2.61803	−0.116617
$505$	28.5410	1.27006
$506$	0	0
$507$	−5.56231	−0.247031
$508$	−14.0344	−0.622678
$509$	−27.5967	−1.22320	−0.611602	−	0.791165i	$-0.709475\pi$
$509$	−27.5967	−1.22320	−0.611602	+	0.791165i	$0.709475\pi$
$510$	−2.18034	−0.0965471
$511$	4.94427	0.218722
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	−21.2148	−0.935744
$515$	−29.8885	−1.31705
$516$	2.23607	0.0984374
$517$	−6.56231	−0.288610
$518$	2.09017	0.0918368
$519$	−6.76393	−0.296904
$520$	5.70820	0.250321
$521$	7.52786	0.329802	0.164901	−	0.986310i	$-0.447270\pi$
$521$	7.52786	0.329802	0.164901	+	0.986310i	$0.447270\pi$
$522$	−26.4164	−1.15621
$523$	16.0000	0.699631	0.349816	−	0.936819i	$-0.386244\pi$
$523$	16.0000	0.699631	0.349816	+	0.936819i	$0.386244\pi$
$524$	−11.5279	−0.503597
$525$	−1.94427	−0.0848550
$526$	−22.6525	−0.987695
$527$	0.583592	0.0254217
$528$	−0.381966	−0.0166229
$529$	−23.0000	−1.00000
$530$	6.63932	0.288394
$531$	30.4164	1.31996
$532$	0	0
$533$	−17.7082	−0.767027
$534$	−2.67376	−0.115705
$535$	−39.1246	−1.69150
$536$	7.23607	0.312551
$537$	11.2361	0.484872
$538$	4.00000	0.172452
$539$	−0.618034	−0.0266206
$540$	−9.90983	−0.426451
$541$	−42.0689	−1.80868	−0.904341	−	0.426810i	$-0.859637\pi$
$541$	−42.0689	−1.80868	−0.904341	+	0.426810i	$0.859637\pi$
$542$	18.5623	0.797319
$543$	6.11146	0.262268
$544$	−1.23607	−0.0529960
$545$	30.3050	1.29812
$546$	−1.23607	−0.0528988
$547$	−20.1803	−0.862849	−0.431425	−	0.902149i	$-0.641989\pi$
$547$	−20.1803	−0.862849	−0.431425	+	0.902149i	$0.641989\pi$
$548$	−20.2705	−0.865913
$549$	19.7984	0.844974
$550$	1.94427	0.0829040
$551$	0	0
$552$	0	0
$553$	−0.0901699	−0.00383442
$554$	4.47214	0.190003
$555$	3.68692	0.156501
$556$	14.9443	0.633778
$557$	2.65248	0.112389	0.0561945	−	0.998420i	$-0.482103\pi$
$557$	2.65248	0.112389	0.0561945	+	0.998420i	$0.482103\pi$
$558$	1.23607	0.0523269
$559$	−7.23607	−0.306053
$560$	−2.85410	−0.120608
$561$	−0.472136	−0.0199336
$562$	6.47214	0.273011
$563$	33.2705	1.40218	0.701092	−	0.713070i	$-0.252696\pi$
$563$	33.2705	1.40218	0.701092	+	0.713070i	$0.252696\pi$
$564$	6.56231	0.276323
$565$	−56.7639	−2.38808
$566$	0.583592	0.0245302
$567$	−5.70820	−0.239722
$568$	7.56231	0.317307
$569$	4.65248	0.195042	0.0975210	−	0.995233i	$-0.468909\pi$
$569$	4.65248	0.195042	0.0975210	+	0.995233i	$0.468909\pi$
$570$	0	0
$571$	14.5066	0.607081	0.303541	−	0.952818i	$-0.401831\pi$
$571$	14.5066	0.607081	0.303541	+	0.952818i	$0.401831\pi$
$572$	1.23607	0.0516826
$573$	−5.81966	−0.243120
$574$	8.85410	0.369563
$575$	0	0
$576$	−2.61803	−0.109085
$577$	0.652476	0.0271629	0.0135815	−	0.999908i	$-0.495677\pi$
$577$	0.652476	0.0271629	0.0135815	+	0.999908i	$0.495677\pi$
$578$	15.4721	0.643556
$579$	5.88854	0.244720
$580$	−28.7984	−1.19579
$581$	−0.291796	−0.0121057
$582$	2.09017	0.0866403
$583$	1.43769	0.0595432
$584$	4.94427	0.204595
$585$	14.9443	0.617870
$586$	10.4721	0.432600
$587$	16.4721	0.679878	0.339939	−	0.940448i	$-0.389594\pi$
$587$	16.4721	0.679878	0.339939	+	0.940448i	$0.389594\pi$
$588$	0.618034	0.0254873
$589$	0	0
$590$	33.1591	1.36514
$591$	−13.0557	−0.537041
$592$	2.09017	0.0859055
$593$	−45.4164	−1.86503	−0.932514	−	0.361133i	$-0.882390\pi$
$593$	−45.4164	−1.86503	−0.932514	+	0.361133i	$0.882390\pi$
$594$	−2.14590	−0.0880473
$595$	−3.52786	−0.144628
$596$	−0.763932	−0.0312919
$597$	1.00000	0.0409273
$598$	0	0
$599$	−8.14590	−0.332832	−0.166416	−	0.986056i	$-0.553220\pi$
$599$	−8.14590	−0.332832	−0.166416	+	0.986056i	$0.553220\pi$
$600$	−1.94427	−0.0793746
$601$	−10.5836	−0.431714	−0.215857	−	0.976425i	$-0.569254\pi$
$601$	−10.5836	−0.431714	−0.215857	+	0.976425i	$0.569254\pi$
$602$	3.61803	0.147460
$603$	18.9443	0.771470
$604$	−20.9443	−0.852210
$605$	−30.3050	−1.23207
$606$	−6.18034	−0.251059
$607$	0.944272	0.0383268	0.0191634	−	0.999816i	$-0.493900\pi$
$607$	0.944272	0.0383268	0.0191634	+	0.999816i	$0.493900\pi$
$608$	0	0
$609$	6.23607	0.252698
$610$	21.5836	0.873894
$611$	−21.2361	−0.859119
$612$	−3.23607	−0.130810
$613$	−31.5967	−1.27618	−0.638090	−	0.769962i	$-0.720275\pi$
$613$	−31.5967	−1.27618	−0.638090	+	0.769962i	$0.720275\pi$
$614$	−26.0902	−1.05291
$615$	15.6180	0.629780
$616$	−0.618034	−0.0249013
$617$	27.6869	1.11463	0.557317	−	0.830300i	$-0.311831\pi$
$617$	27.6869	1.11463	0.557317	+	0.830300i	$0.311831\pi$
$618$	6.47214	0.260347
$619$	−4.00000	−0.160774	−0.0803868	−	0.996764i	$-0.525616\pi$
$619$	−4.00000	−0.160774	−0.0803868	+	0.996764i	$0.525616\pi$
$620$	1.34752	0.0541179
$621$	0	0
$622$	−17.0902	−0.685253
$623$	−4.32624	−0.173327
$624$	−1.23607	−0.0494823
$625$	−30.8328	−1.23331
$626$	−0.472136	−0.0188703
$627$	0	0
$628$	−13.0902	−0.522355
$629$	2.58359	0.103015
$630$	−7.47214	−0.297697
$631$	−34.4721	−1.37231	−0.686157	−	0.727453i	$-0.740704\pi$
$631$	−34.4721	−1.37231	−0.686157	+	0.727453i	$0.740704\pi$
$632$	−0.0901699	−0.00358677
$633$	10.5836	0.420660
$634$	−7.27051	−0.288749
$635$	−40.0557	−1.58956
$636$	−1.43769	−0.0570083
$637$	−2.00000	−0.0792429
$638$	−6.23607	−0.246888
$639$	19.7984	0.783212
$640$	−2.85410	−0.112818
$641$	35.4164	1.39886	0.699432	−	0.714699i	$-0.253436\pi$
$641$	35.4164	1.39886	0.699432	+	0.714699i	$0.253436\pi$
$642$	8.47214	0.334369
$643$	48.8328	1.92578	0.962889	−	0.269897i	$-0.0869897\pi$
$643$	48.8328	1.92578	0.962889	+	0.269897i	$0.0869897\pi$
$644$	0	0
$645$	6.38197	0.251290
$646$	0	0
$647$	14.5623	0.572503	0.286252	−	0.958154i	$-0.407591\pi$
$647$	14.5623	0.572503	0.286252	+	0.958154i	$0.407591\pi$
$648$	−5.70820	−0.224239
$649$	7.18034	0.281853
$650$	6.29180	0.246785
$651$	−0.291796	−0.0114364
$652$	0.909830	0.0356317
$653$	−32.3607	−1.26637	−0.633186	−	0.774000i	$-0.718253\pi$
$653$	−32.3607	−1.26637	−0.633186	+	0.774000i	$0.718253\pi$
$654$	−6.56231	−0.256606
$655$	−32.9017	−1.28558
$656$	8.85410	0.345695
$657$	12.9443	0.505004
$658$	10.6180	0.413934
$659$	−12.7639	−0.497212	−0.248606	−	0.968605i	$-0.579972\pi$
$659$	−12.7639	−0.497212	−0.248606	+	0.968605i	$0.579972\pi$
$660$	−1.09017	−0.0424348
$661$	−5.52786	−0.215009	−0.107504	−	0.994205i	$-0.534286\pi$
$661$	−5.52786	−0.215009	−0.107504	+	0.994205i	$0.534286\pi$
$662$	−8.76393	−0.340620
$663$	−1.52786	−0.0593373
$664$	−0.291796	−0.0113239
$665$	0	0
$666$	5.47214	0.212041
$667$	0	0
$668$	−3.52786	−0.136497
$669$	14.0000	0.541271
$670$	20.6525	0.797875
$671$	4.67376	0.180429
$672$	0.618034	0.0238412
$673$	−12.0000	−0.462566	−0.231283	−	0.972887i	$-0.574292\pi$
$673$	−12.0000	−0.462566	−0.231283	+	0.972887i	$0.574292\pi$
$674$	25.2361	0.972057
$675$	−10.9230	−0.420426
$676$	−9.00000	−0.346154
$677$	−30.7639	−1.18235	−0.591177	−	0.806542i	$-0.701337\pi$
$677$	−30.7639	−1.18235	−0.591177	+	0.806542i	$0.701337\pi$
$678$	12.2918	0.472064
$679$	3.38197	0.129788
$680$	−3.52786	−0.135287
$681$	−12.5836	−0.482204
$682$	0.291796	0.0111734
$683$	15.3475	0.587257	0.293628	−	0.955920i	$-0.405137\pi$
$683$	15.3475	0.587257	0.293628	+	0.955920i	$0.405137\pi$
$684$	0	0
$685$	−57.8541	−2.21049
$686$	1.00000	0.0381802
$687$	13.7639	0.525127
$688$	3.61803	0.137936
$689$	4.65248	0.177245
$690$	0	0
$691$	−14.1803	−0.539446	−0.269723	−	0.962938i	$-0.586932\pi$
$691$	−14.1803	−0.539446	−0.269723	+	0.962938i	$0.586932\pi$
$692$	−10.9443	−0.416039
$693$	−1.61803	−0.0614640
$694$	21.8885	0.830878
$695$	42.6525	1.61790
$696$	6.23607	0.236378
$697$	10.9443	0.414544
$698$	−0.111456	−0.00421868
$699$	11.6180	0.439434
$700$	−3.14590	−0.118904
$701$	28.5410	1.07798	0.538990	−	0.842312i	$-0.318806\pi$
$701$	28.5410	1.07798	0.538990	+	0.842312i	$0.318806\pi$
$702$	−6.94427	−0.262095
$703$	0	0
$704$	−0.618034	−0.0232930
$705$	18.7295	0.705393
$706$	−26.3607	−0.992097
$707$	−10.0000	−0.376089
$708$	−7.18034	−0.269854
$709$	−14.1803	−0.532554	−0.266277	−	0.963897i	$-0.585794\pi$
$709$	−14.1803	−0.532554	−0.266277	+	0.963897i	$0.585794\pi$
$710$	21.5836	0.810018
$711$	−0.236068	−0.00885324
$712$	−4.32624	−0.162133
$713$	0	0
$714$	0.763932	0.0285894
$715$	3.52786	0.131935
$716$	18.1803	0.679431
$717$	−0.111456	−0.00416241
$718$	36.6525	1.36786
$719$	8.58359	0.320114	0.160057	−	0.987108i	$-0.448832\pi$
$719$	8.58359	0.320114	0.160057	+	0.987108i	$0.448832\pi$
$720$	−7.47214	−0.278470
$721$	10.4721	0.390003
$722$	0	0
$723$	−15.3607	−0.571270
$724$	9.88854	0.367505
$725$	−31.7426	−1.17889
$726$	6.56231	0.243550
$727$	10.9787	0.407178	0.203589	−	0.979056i	$-0.434739\pi$
$727$	10.9787	0.407178	0.203589	+	0.979056i	$0.434739\pi$
$728$	−2.00000	−0.0741249
$729$	−8.50658	−0.315058
$730$	14.1115	0.522288
$731$	4.47214	0.165408
$732$	−4.67376	−0.172747
$733$	−36.9230	−1.36378	−0.681891	−	0.731454i	$-0.738842\pi$
$733$	−36.9230	−1.36378	−0.681891	+	0.731454i	$0.738842\pi$
$734$	−10.0344	−0.370378
$735$	1.76393	0.0650636
$736$	0	0
$737$	4.47214	0.164733
$738$	23.1803	0.853280
$739$	8.20163	0.301702	0.150851	−	0.988557i	$-0.451799\pi$
$739$	8.20163	0.301702	0.150851	+	0.988557i	$0.451799\pi$
$740$	5.96556	0.219298
$741$	0	0
$742$	−2.32624	−0.0853989
$743$	30.3820	1.11461	0.557303	−	0.830309i	$-0.311836\pi$
$743$	30.3820	1.11461	0.557303	+	0.830309i	$0.311836\pi$
$744$	−0.291796	−0.0106978
$745$	−2.18034	−0.0798815
$746$	−21.3262	−0.780809
$747$	−0.763932	−0.0279508
$748$	−0.763932	−0.0279321
$749$	13.7082	0.500887
$750$	3.27051	0.119422
$751$	6.74265	0.246043	0.123021	−	0.992404i	$-0.460742\pi$
$751$	6.74265	0.246043	0.123021	+	0.992404i	$0.460742\pi$
$752$	10.6180	0.387200
$753$	13.8197	0.503616
$754$	−20.1803	−0.734925
$755$	−59.7771	−2.17551
$756$	3.47214	0.126280
$757$	−31.4164	−1.14185	−0.570924	−	0.821003i	$-0.693415\pi$
$757$	−31.4164	−1.14185	−0.570924	+	0.821003i	$0.693415\pi$
$758$	23.1246	0.839924
$759$	0	0
$760$	0	0
$761$	14.3607	0.520574	0.260287	−	0.965531i	$-0.416183\pi$
$761$	14.3607	0.520574	0.260287	+	0.965531i	$0.416183\pi$
$762$	8.67376	0.314217
$763$	−10.6180	−0.384399
$764$	−9.41641	−0.340674
$765$	−9.23607	−0.333931
$766$	−32.6525	−1.17978
$767$	23.2361	0.839006
$768$	0.618034	0.0223014
$769$	21.7082	0.782818	0.391409	−	0.920217i	$-0.371988\pi$
$769$	21.7082	0.782818	0.391409	+	0.920217i	$0.371988\pi$
$770$	−1.76393	−0.0635677
$771$	13.1115	0.472198
$772$	9.52786	0.342915
$773$	37.2361	1.33929	0.669644	−	0.742682i	$-0.266447\pi$
$773$	37.2361	1.33929	0.669644	+	0.742682i	$0.266447\pi$
$774$	9.47214	0.340469
$775$	1.48529	0.0533532
$776$	3.38197	0.121406
$777$	−1.29180	−0.0463429
$778$	−7.05573	−0.252960
$779$	0	0
$780$	−3.52786	−0.126318
$781$	4.67376	0.167240
$782$	0	0
$783$	35.0344	1.25203
$784$	1.00000	0.0357143
$785$	−37.3607	−1.33346
$786$	7.12461	0.254126
$787$	27.6180	0.984477	0.492238	−	0.870460i	$-0.336179\pi$
$787$	27.6180	0.984477	0.492238	+	0.870460i	$0.336179\pi$
$788$	−21.1246	−0.752533
$789$	14.0000	0.498413
$790$	−0.257354	−0.00915625
$791$	19.8885	0.707155
$792$	−1.61803	−0.0574943
$793$	15.1246	0.537091
$794$	−4.43769	−0.157488
$795$	−4.10333	−0.145530
$796$	1.61803	0.0573497
$797$	33.0557	1.17089	0.585447	−	0.810711i	$-0.300919\pi$
$797$	33.0557	1.17089	0.585447	+	0.810711i	$0.300919\pi$
$798$	0	0
$799$	13.1246	0.464315
$800$	−3.14590	−0.111224
$801$	−11.3262	−0.400193
$802$	29.4164	1.03873
$803$	3.05573	0.107834
$804$	−4.47214	−0.157720
$805$	0	0
$806$	0.944272	0.0332606
$807$	−2.47214	−0.0870233
$808$	−10.0000	−0.351799
$809$	−25.7984	−0.907023	−0.453511	−	0.891251i	$-0.649829\pi$
$809$	−25.7984	−0.907023	−0.453511	+	0.891251i	$0.649829\pi$
$810$	−16.2918	−0.572435
$811$	−20.0344	−0.703504	−0.351752	−	0.936093i	$-0.614414\pi$
$811$	−20.0344	−0.703504	−0.351752	+	0.936093i	$0.614414\pi$
$812$	10.0902	0.354096
$813$	−11.4721	−0.402345
$814$	1.29180	0.0452774
$815$	2.59675	0.0909601
$816$	0.763932	0.0267430
$817$	0	0
$818$	25.2705	0.883563
$819$	−5.23607	−0.182963
$820$	25.2705	0.882484
$821$	3.70820	0.129417	0.0647086	−	0.997904i	$-0.479388\pi$
$821$	3.70820	0.129417	0.0647086	+	0.997904i	$0.479388\pi$
$822$	12.5279	0.436959
$823$	25.2361	0.879674	0.439837	−	0.898078i	$-0.355036\pi$
$823$	25.2361	0.879674	0.439837	+	0.898078i	$0.355036\pi$
$824$	10.4721	0.364814
$825$	−1.20163	−0.0418353
$826$	−11.6180	−0.404243
$827$	40.6525	1.41363	0.706813	−	0.707401i	$-0.250132\pi$
$827$	40.6525	1.41363	0.706813	+	0.707401i	$0.250132\pi$
$828$	0	0
$829$	16.7639	0.582235	0.291118	−	0.956687i	$-0.405973\pi$
$829$	16.7639	0.582235	0.291118	+	0.956687i	$0.405973\pi$
$830$	−0.832816	−0.0289075
$831$	−2.76393	−0.0958797
$832$	−2.00000	−0.0693375
$833$	1.23607	0.0428272
$834$	−9.23607	−0.319819
$835$	−10.0689	−0.348448
$836$	0	0
$837$	−1.63932	−0.0566632
$838$	34.6525	1.19705
$839$	−25.4164	−0.877472	−0.438736	−	0.898616i	$-0.644574\pi$
$839$	−25.4164	−0.877472	−0.438736	+	0.898616i	$0.644574\pi$
$840$	1.76393	0.0608614
$841$	72.8115	2.51074
$842$	−7.52786	−0.259427
$843$	−4.00000	−0.137767
$844$	17.1246	0.589453
$845$	−25.6869	−0.883657
$846$	27.7984	0.955728
$847$	10.6180	0.364840
$848$	−2.32624	−0.0798833
$849$	−0.360680	−0.0123785
$850$	−3.88854	−0.133376
$851$	0	0
$852$	−4.67376	−0.160120
$853$	−12.7426	−0.436300	−0.218150	−	0.975915i	$-0.570002\pi$
$853$	−12.7426	−0.436300	−0.218150	+	0.975915i	$0.570002\pi$
$854$	−7.56231	−0.258777
$855$	0	0
$856$	13.7082	0.468537
$857$	9.41641	0.321658	0.160829	−	0.986982i	$-0.448583\pi$
$857$	9.41641	0.321658	0.160829	+	0.986982i	$0.448583\pi$
$858$	−0.763932	−0.0260802
$859$	−3.88854	−0.132675	−0.0663377	−	0.997797i	$-0.521131\pi$
$859$	−3.88854	−0.132675	−0.0663377	+	0.997797i	$0.521131\pi$
$860$	10.3262	0.352122
$861$	−5.47214	−0.186490
$862$	−20.1459	−0.686172
$863$	27.3262	0.930196	0.465098	−	0.885259i	$-0.346019\pi$
$863$	27.3262	0.930196	0.465098	+	0.885259i	$0.346019\pi$
$864$	3.47214	0.118124
$865$	−31.2361	−1.06206
$866$	0.854102	0.0290236
$867$	−9.56231	−0.324753
$868$	−0.472136	−0.0160253
$869$	−0.0557281	−0.00189045
$870$	17.7984	0.603421
$871$	14.4721	0.490370
$872$	−10.6180	−0.359572
$873$	8.85410	0.299666
$874$	0	0
$875$	5.29180	0.178895
$876$	−3.05573	−0.103243
$877$	−18.9098	−0.638540	−0.319270	−	0.947664i	$-0.603438\pi$
$877$	−18.9098	−0.638540	−0.319270	+	0.947664i	$0.603438\pi$
$878$	−18.2918	−0.617318
$879$	−6.47214	−0.218300
$880$	−1.76393	−0.0594621
$881$	25.7082	0.866131	0.433066	−	0.901362i	$-0.357432\pi$
$881$	25.7082	0.866131	0.433066	+	0.901362i	$0.357432\pi$
$882$	2.61803	0.0881538
$883$	−28.3951	−0.955572	−0.477786	−	0.878476i	$-0.658561\pi$
$883$	−28.3951	−0.955572	−0.477786	+	0.878476i	$0.658561\pi$
$884$	−2.47214	−0.0831469
$885$	−20.4934	−0.688879
$886$	6.67376	0.224209
$887$	−48.3607	−1.62379	−0.811896	−	0.583802i	$-0.801565\pi$
$887$	−48.3607	−1.62379	−0.811896	+	0.583802i	$0.801565\pi$
$888$	−1.29180	−0.0433498
$889$	14.0344	0.470700
$890$	−12.3475	−0.413890
$891$	−3.52786	−0.118188
$892$	22.6525	0.758461
$893$	0	0
$894$	0.472136	0.0157906
$895$	51.8885	1.73444
$896$	1.00000	0.0334077
$897$	0	0
$898$	5.34752	0.178449
$899$	−4.76393	−0.158886
$900$	−8.23607	−0.274536
$901$	−2.87539	−0.0957931
$902$	5.47214	0.182202
$903$	−2.23607	−0.0744117
$904$	19.8885	0.661483
$905$	28.2229	0.938161
$906$	12.9443	0.430045
$907$	8.94427	0.296990	0.148495	−	0.988913i	$-0.452557\pi$
$907$	8.94427	0.296990	0.148495	+	0.988913i	$0.452557\pi$
$908$	−20.3607	−0.675693
$909$	−26.1803	−0.868347
$910$	−5.70820	−0.189225
$911$	26.3820	0.874074	0.437037	−	0.899444i	$-0.356028\pi$
$911$	26.3820	0.874074	0.437037	+	0.899444i	$0.356028\pi$
$912$	0	0
$913$	−0.180340	−0.00596838
$914$	7.09017	0.234522
$915$	−13.3394	−0.440987
$916$	22.2705	0.735838
$917$	11.5279	0.380684
$918$	4.29180	0.141650
$919$	−51.9574	−1.71392	−0.856959	−	0.515385i	$-0.827649\pi$
$919$	−51.9574	−1.71392	−0.856959	+	0.515385i	$0.827649\pi$
$920$	0	0
$921$	16.1246	0.531324
$922$	14.6180	0.481419
$923$	15.1246	0.497833
$924$	0.381966	0.0125658
$925$	6.57546	0.216200
$926$	−4.36068	−0.143301
$927$	27.4164	0.900473
$928$	10.0902	0.331226
$929$	3.23607	0.106172	0.0530860	−	0.998590i	$-0.483094\pi$
$929$	3.23607	0.106172	0.0530860	+	0.998590i	$0.483094\pi$
$930$	−0.832816	−0.0273091
$931$	0	0
$932$	18.7984	0.615761
$933$	10.5623	0.345794
$934$	−28.0000	−0.916188
$935$	−2.18034	−0.0713047
$936$	−5.23607	−0.171146
$937$	21.8197	0.712817	0.356409	−	0.934330i	$-0.384001\pi$
$937$	21.8197	0.712817	0.356409	+	0.934330i	$0.384001\pi$
$938$	−7.23607	−0.236266
$939$	0.291796	0.00952240
$940$	30.3050	0.988439
$941$	45.0132	1.46739	0.733693	−	0.679481i	$-0.237795\pi$
$941$	45.0132	1.46739	0.733693	+	0.679481i	$0.237795\pi$
$942$	8.09017	0.263592
$943$	0	0
$944$	−11.6180	−0.378135
$945$	9.90983	0.322367
$946$	2.23607	0.0727008
$947$	3.67376	0.119381	0.0596906	−	0.998217i	$-0.480989\pi$
$947$	3.67376	0.119381	0.0596906	+	0.998217i	$0.480989\pi$
$948$	0.0557281	0.00180996
$949$	9.88854	0.320996
$950$	0	0
$951$	4.49342	0.145709
$952$	1.23607	0.0400612
$953$	−11.7082	−0.379266	−0.189633	−	0.981855i	$-0.560730\pi$
$953$	−11.7082	−0.379266	−0.189633	+	0.981855i	$0.560730\pi$
$954$	−6.09017	−0.197177
$955$	−26.8754	−0.869667
$956$	−0.180340	−0.00583261
$957$	3.85410	0.124585
$958$	−26.3820	−0.852363
$959$	20.2705	0.654569
$960$	1.76393	0.0569307
$961$	−30.7771	−0.992809
$962$	4.18034	0.134780
$963$	35.8885	1.15649
$964$	−24.8541	−0.800497
$965$	27.1935	0.875390
$966$	0	0
$967$	−48.7214	−1.56677	−0.783387	−	0.621535i	$-0.786509\pi$
$967$	−48.7214	−1.56677	−0.783387	+	0.621535i	$0.786509\pi$
$968$	10.6180	0.341277
$969$	0	0
$970$	9.65248	0.309922
$971$	54.5066	1.74920	0.874600	−	0.484846i	$-0.161124\pi$
$971$	54.5066	1.74920	0.874600	+	0.484846i	$0.161124\pi$
$972$	13.9443	0.447263
$973$	−14.9443	−0.479091
$974$	−19.5066	−0.625031
$975$	−3.88854	−0.124533
$976$	−7.56231	−0.242064
$977$	30.6525	0.980660	0.490330	−	0.871537i	$-0.336876\pi$
$977$	30.6525	0.980660	0.490330	+	0.871537i	$0.336876\pi$
$978$	−0.562306	−0.0179806
$979$	−2.67376	−0.0854538
$980$	2.85410	0.0911709
$981$	−27.7984	−0.887534
$982$	−31.4164	−1.00254
$983$	27.0132	0.861586	0.430793	−	0.902451i	$-0.358234\pi$
$983$	27.0132	0.861586	0.430793	+	0.902451i	$0.358234\pi$
$984$	−5.47214	−0.174445
$985$	−60.2918	−1.92106
$986$	12.4721	0.397194
$987$	−6.56231	−0.208880
$988$	0	0
$989$	0	0
$990$	−4.61803	−0.146771
$991$	−45.6738	−1.45087	−0.725437	−	0.688288i	$-0.758362\pi$
$991$	−45.6738	−1.45087	−0.725437	+	0.688288i	$0.758362\pi$
$992$	−0.472136	−0.0149903
$993$	5.41641	0.171885
$994$	−7.56231	−0.239862
$995$	4.61803	0.146402
$996$	0.180340	0.00571429
$997$	−11.4377	−0.362235	−0.181118	−	0.983461i	$-0.557971\pi$
$997$	−11.4377	−0.362235	−0.181118	+	0.983461i	$0.557971\pi$
$998$	35.6180	1.12747
$999$	−7.25735	−0.229613

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5054.2.a.d.1.2	✓	2
19.18	odd	2		5054.2.a.o.1.1	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5054.2.a.d.1.2	✓	2	1.1	even	1	trivial
5054.2.a.o.1.1	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:	\( N \)	\(=\)	\( 5054 = 2 \cdot 7 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5054.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +0.618034 q^{3} +1.00000 q^{4} +2.85410 q^{5} -0.618034 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.61803 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +0.618034 q^{3} +1.00000 q^{4} +2.85410 q^{5} -0.618034 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.61803 q^{9} -2.85410 q^{10} -0.618034 q^{11} +0.618034 q^{12} -2.00000 q^{13} +1.00000 q^{14} +1.76393 q^{15} +1.00000 q^{16} +1.23607 q^{17} +2.61803 q^{18} +2.85410 q^{20} -0.618034 q^{21} +0.618034 q^{22} -0.618034 q^{24} +3.14590 q^{25} +2.00000 q^{26} -3.47214 q^{27} -1.00000 q^{28} -10.0902 q^{29} -1.76393 q^{30} +0.472136 q^{31} -1.00000 q^{32} -0.381966 q^{33} -1.23607 q^{34} -2.85410 q^{35} -2.61803 q^{36} +2.09017 q^{37} -1.23607 q^{39} -2.85410 q^{40} +8.85410 q^{41} +0.618034 q^{42} +3.61803 q^{43} -0.618034 q^{44} -7.47214 q^{45} +10.6180 q^{47} +0.618034 q^{48} +1.00000 q^{49} -3.14590 q^{50} +0.763932 q^{51} -2.00000 q^{52} -2.32624 q^{53} +3.47214 q^{54} -1.76393 q^{55} +1.00000 q^{56} +10.0902 q^{58} -11.6180 q^{59} +1.76393 q^{60} -7.56231 q^{61} -0.472136 q^{62} +2.61803 q^{63} +1.00000 q^{64} -5.70820 q^{65} +0.381966 q^{66} -7.23607 q^{67} +1.23607 q^{68} +2.85410 q^{70} -7.56231 q^{71} +2.61803 q^{72} -4.94427 q^{73} -2.09017 q^{74} +1.94427 q^{75} +0.618034 q^{77} +1.23607 q^{78} +0.0901699 q^{79} +2.85410 q^{80} +5.70820 q^{81} -8.85410 q^{82} +0.291796 q^{83} -0.618034 q^{84} +3.52786 q^{85} -3.61803 q^{86} -6.23607 q^{87} +0.618034 q^{88} +4.32624 q^{89} +7.47214 q^{90} +2.00000 q^{91} +0.291796 q^{93} -10.6180 q^{94} -0.618034 q^{96} -3.38197 q^{97} -1.00000 q^{98} +1.61803 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - q^{3} + 2 q^{4} - q^{5} + q^{6} - 2 q^{7} - 2 q^{8} - 3 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 - q^3 + 2 * q^4 - q^5 + q^6 - 2 * q^7 - 2 * q^8 - 3 * q^9	\( 2 q - 2 q^{2} - q^{3} + 2 q^{4} - q^{5} + q^{6} - 2 q^{7} - 2 q^{8} - 3 q^{9} + q^{10} + q^{11} - q^{12} - 4 q^{13} + 2 q^{14} + 8 q^{15} + 2 q^{16} - 2 q^{17} + 3 q^{18} - q^{20} + q^{21} - q^{22} + q^{24} + 13 q^{25} + 4 q^{26} + 2 q^{27} - 2 q^{28} - 9 q^{29} - 8 q^{30} - 8 q^{31} - 2 q^{32} - 3 q^{33} + 2 q^{34} + q^{35} - 3 q^{36} - 7 q^{37} + 2 q^{39} + q^{40} + 11 q^{41} - q^{42} + 5 q^{43} + q^{44} - 6 q^{45} + 19 q^{47} - q^{48} + 2 q^{49} - 13 q^{50} + 6 q^{51} - 4 q^{52} + 11 q^{53} - 2 q^{54} - 8 q^{55} + 2 q^{56} + 9 q^{58} - 21 q^{59} + 8 q^{60} + 5 q^{61} + 8 q^{62} + 3 q^{63} + 2 q^{64} + 2 q^{65} + 3 q^{66} - 10 q^{67} - 2 q^{68} - q^{70} + 5 q^{71} + 3 q^{72} + 8 q^{73} + 7 q^{74} - 14 q^{75} - q^{77} - 2 q^{78} - 11 q^{79} - q^{80} - 2 q^{81} - 11 q^{82} + 14 q^{83} + q^{84} + 16 q^{85} - 5 q^{86} - 8 q^{87} - q^{88} - 7 q^{89} + 6 q^{90} + 4 q^{91} + 14 q^{93} - 19 q^{94} + q^{96} - 9 q^{97} - 2 q^{98} + q^{99}+O(q^{100}) \) 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 + q^11 - q^12 - 4 * q^13 + 2 * q^14 + 8 * q^15 + 2 * q^16 - 2 * q^17 + 3 * q^18 - q^20 + q^21 - q^22 + q^24 + 13 * q^25 + 4 * q^26 + 2 * q^27 - 2 * q^28 - 9 * q^29 - 8 * q^30 - 8 * q^31 - 2 * q^32 - 3 * q^33 + 2 * q^34 + q^35 - 3 * q^36 - 7 * q^37 + 2 * q^39 + q^40 + 11 * q^41 - q^42 + 5 * q^43 + q^44 - 6 * q^45 + 19 * q^47 - q^48 + 2 * q^49 - 13 * q^50 + 6 * q^51 - 4 * q^52 + 11 * q^53 - 2 * q^54 - 8 * q^55 + 2 * q^56 + 9 * q^58 - 21 * q^59 + 8 * q^60 + 5 * q^61 + 8 * q^62 + 3 * q^63 + 2 * q^64 + 2 * q^65 + 3 * q^66 - 10 * q^67 - 2 * q^68 - q^70 + 5 * q^71 + 3 * q^72 + 8 * q^73 + 7 * q^74 - 14 * q^75 - q^77 - 2 * q^78 - 11 * q^79 - q^80 - 2 * q^81 - 11 * q^82 + 14 * q^83 + q^84 + 16 * q^85 - 5 * q^86 - 8 * q^87 - q^88 - 7 * q^89 + 6 * q^90 + 4 * q^91 + 14 * q^93 - 19 * q^94 + q^96 - 9 * q^97 - 2 * q^98 + q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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