LMFDB - Embedded newform 5054.2.a.l.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)

$f(q)$	$=$	$q+1.00000 q^{2} +0.618034 q^{3} +1.00000 q^{4} -0.381966 q^{5} +0.618034 q^{6} +1.00000 q^{7} +1.00000 q^{8} -2.61803 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +0.618034 q^{3} +1.00000 q^{4} -0.381966 q^{5} +0.618034 q^{6} +1.00000 q^{7} +1.00000 q^{8} -2.61803 q^{9} -0.381966 q^{10} +1.85410 q^{11} +0.618034 q^{12} -4.47214 q^{13} +1.00000 q^{14} -0.236068 q^{15} +1.00000 q^{16} +5.23607 q^{17} -2.61803 q^{18} -0.381966 q^{20} +0.618034 q^{21} +1.85410 q^{22} -8.94427 q^{23} +0.618034 q^{24} -4.85410 q^{25} -4.47214 q^{26} -3.47214 q^{27} +1.00000 q^{28} -6.85410 q^{29} -0.236068 q^{30} -6.00000 q^{31} +1.00000 q^{32} +1.14590 q^{33} +5.23607 q^{34} -0.381966 q^{35} -2.61803 q^{36} -1.14590 q^{37} -2.76393 q^{39} -0.381966 q^{40} -10.5623 q^{41} +0.618034 q^{42} -2.85410 q^{43} +1.85410 q^{44} +1.00000 q^{45} -8.94427 q^{46} -4.14590 q^{47} +0.618034 q^{48} +1.00000 q^{49} -4.85410 q^{50} +3.23607 q^{51} -4.47214 q^{52} +11.8541 q^{53} -3.47214 q^{54} -0.708204 q^{55} +1.00000 q^{56} -6.85410 q^{58} -8.56231 q^{59} -0.236068 q^{60} +11.5623 q^{61} -6.00000 q^{62} -2.61803 q^{63} +1.00000 q^{64} +1.70820 q^{65} +1.14590 q^{66} -0.763932 q^{67} +5.23607 q^{68} -5.52786 q^{69} -0.381966 q^{70} +11.5623 q^{71} -2.61803 q^{72} -1.14590 q^{74} -3.00000 q^{75} +1.85410 q^{77} -2.76393 q^{78} +15.3262 q^{79} -0.381966 q^{80} +5.70820 q^{81} -10.5623 q^{82} +6.76393 q^{83} +0.618034 q^{84} -2.00000 q^{85} -2.85410 q^{86} -4.23607 q^{87} +1.85410 q^{88} +9.85410 q^{89} +1.00000 q^{90} -4.47214 q^{91} -8.94427 q^{92} -3.70820 q^{93} -4.14590 q^{94} +0.618034 q^{96} -13.8541 q^{97} +1.00000 q^{98} -4.85410 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - q^{3} + 2 q^{4} - 3 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 - 3 * q^5 - q^6 + 2 * q^7 + 2 * q^8 - 3 * q^9	$ 2 q + 2 q^{2} - q^{3} + 2 q^{4} - 3 q^{5} - q^{6} + 2 q^{7} + 2 q^{8} - 3 q^{9} - 3 q^{10} - 3 q^{11} - q^{12} + 2 q^{14} + 4 q^{15} + 2 q^{16} + 6 q^{17} - 3 q^{18} - 3 q^{20} - q^{21} - 3 q^{22} - q^{24} - 3 q^{25} + 2 q^{27} + 2 q^{28} - 7 q^{29} + 4 q^{30} - 12 q^{31} + 2 q^{32} + 9 q^{33} + 6 q^{34} - 3 q^{35} - 3 q^{36} - 9 q^{37} - 10 q^{39} - 3 q^{40} - q^{41} - q^{42} + q^{43} - 3 q^{44} + 2 q^{45} - 15 q^{47} - q^{48} + 2 q^{49} - 3 q^{50} + 2 q^{51} + 17 q^{53} + 2 q^{54} + 12 q^{55} + 2 q^{56} - 7 q^{58} + 3 q^{59} + 4 q^{60} + 3 q^{61} - 12 q^{62} - 3 q^{63} + 2 q^{64} - 10 q^{65} + 9 q^{66} - 6 q^{67} + 6 q^{68} - 20 q^{69} - 3 q^{70} + 3 q^{71} - 3 q^{72} - 9 q^{74} - 6 q^{75} - 3 q^{77} - 10 q^{78} + 15 q^{79} - 3 q^{80} - 2 q^{81} - q^{82} + 18 q^{83} - q^{84} - 4 q^{85} + q^{86} - 4 q^{87} - 3 q^{88} + 13 q^{89} + 2 q^{90} + 6 q^{93} - 15 q^{94} - q^{96} - 21 q^{97} + 2 q^{98} - 3 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 - q^3 + 2 * q^4 - 3 * q^5 - q^6 + 2 * q^7 + 2 * q^8 - 3 * q^9 - 3 * q^10 - 3 * q^11 - q^12 + 2 * q^14 + 4 * q^15 + 2 * q^16 + 6 * q^17 - 3 * q^18 - 3 * q^20 - q^21 - 3 * q^22 - q^24 - 3 * q^25 + 2 * q^27 + 2 * q^28 - 7 * q^29 + 4 * q^30 - 12 * q^31 + 2 * q^32 + 9 * q^33 + 6 * q^34 - 3 * q^35 - 3 * q^36 - 9 * q^37 - 10 * q^39 - 3 * q^40 - q^41 - q^42 + q^43 - 3 * q^44 + 2 * q^45 - 15 * q^47 - q^48 + 2 * q^49 - 3 * q^50 + 2 * q^51 + 17 * q^53 + 2 * q^54 + 12 * q^55 + 2 * q^56 - 7 * q^58 + 3 * q^59 + 4 * q^60 + 3 * q^61 - 12 * q^62 - 3 * q^63 + 2 * q^64 - 10 * q^65 + 9 * q^66 - 6 * q^67 + 6 * q^68 - 20 * q^69 - 3 * q^70 + 3 * q^71 - 3 * q^72 - 9 * q^74 - 6 * q^75 - 3 * q^77 - 10 * q^78 + 15 * q^79 - 3 * q^80 - 2 * q^81 - q^82 + 18 * q^83 - q^84 - 4 * q^85 + q^86 - 4 * q^87 - 3 * q^88 + 13 * q^89 + 2 * q^90 + 6 * q^93 - 15 * q^94 - q^96 - 21 * q^97 + 2 * q^98 - 3 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	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
$5$	−0.381966	−0.170820	−0.0854102	−	0.996346i	$-0.527220\pi$
$5$	−0.381966	−0.170820	−0.0854102	+	0.996346i	$0.527220\pi$
$6$	0.618034	0.252311
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	−2.61803	−0.872678
$10$	−0.381966	−0.120788
$11$	1.85410	0.559033	0.279516	−	0.960141i	$-0.409826\pi$
$11$	1.85410	0.559033	0.279516	+	0.960141i	$0.409826\pi$
$12$	0.618034	0.178411
$13$	−4.47214	−1.24035	−0.620174	−	0.784465i	$-0.712938\pi$
$13$	−4.47214	−1.24035	−0.620174	+	0.784465i	$0.712938\pi$
$14$	1.00000	0.267261
$15$	−0.236068	−0.0609525
$16$	1.00000	0.250000
$17$	5.23607	1.26993	0.634967	−	0.772540i	$-0.281014\pi$
$17$	5.23607	1.26993	0.634967	+	0.772540i	$0.281014\pi$
$18$	−2.61803	−0.617077
$19$	0	0
$19$	0	0
$20$	−0.381966	−0.0854102
$21$	0.618034	0.134866
$22$	1.85410	0.395296
$23$	−8.94427	−1.86501	−0.932505	−	0.361158i	$-0.882382\pi$
$23$	−8.94427	−1.86501	−0.932505	+	0.361158i	$0.882382\pi$
$24$	0.618034	0.126156
$25$	−4.85410	−0.970820
$26$	−4.47214	−0.877058
$27$	−3.47214	−0.668213
$28$	1.00000	0.188982
$29$	−6.85410	−1.27277	−0.636387	−	0.771370i	$-0.719572\pi$
$29$	−6.85410	−1.27277	−0.636387	+	0.771370i	$0.719572\pi$
$30$	−0.236068	−0.0430999
$31$	−6.00000	−1.07763	−0.538816	−	0.842424i	$-0.681128\pi$
$31$	−6.00000	−1.07763	−0.538816	+	0.842424i	$0.681128\pi$
$32$	1.00000	0.176777
$33$	1.14590	0.199475
$34$	5.23607	0.897978
$35$	−0.381966	−0.0645640
$36$	−2.61803	−0.436339
$37$	−1.14590	−0.188384	−0.0941922	−	0.995554i	$-0.530027\pi$
$37$	−1.14590	−0.188384	−0.0941922	+	0.995554i	$0.530027\pi$
$38$	0	0
$39$	−2.76393	−0.442583
$40$	−0.381966	−0.0603941
$41$	−10.5623	−1.64956	−0.824778	−	0.565457i	$-0.808700\pi$
$41$	−10.5623	−1.64956	−0.824778	+	0.565457i	$0.808700\pi$
$42$	0.618034	0.0953647
$43$	−2.85410	−0.435246	−0.217623	−	0.976033i	$-0.569830\pi$
$43$	−2.85410	−0.435246	−0.217623	+	0.976033i	$0.569830\pi$
$44$	1.85410	0.279516
$45$	1.00000	0.149071
$46$	−8.94427	−1.31876
$47$	−4.14590	−0.604741	−0.302371	−	0.953190i	$-0.597778\pi$
$47$	−4.14590	−0.604741	−0.302371	+	0.953190i	$0.597778\pi$
$48$	0.618034	0.0892055
$49$	1.00000	0.142857
$50$	−4.85410	−0.686474
$51$	3.23607	0.453140
$52$	−4.47214	−0.620174
$53$	11.8541	1.62829	0.814143	−	0.580664i	$-0.197207\pi$
$53$	11.8541	1.62829	0.814143	+	0.580664i	$0.197207\pi$
$54$	−3.47214	−0.472498
$55$	−0.708204	−0.0954942
$56$	1.00000	0.133631
$57$	0	0
$58$	−6.85410	−0.899988
$59$	−8.56231	−1.11472	−0.557359	−	0.830272i	$-0.688185\pi$
$59$	−8.56231	−1.11472	−0.557359	+	0.830272i	$0.688185\pi$
$60$	−0.236068	−0.0304762
$61$	11.5623	1.48040	0.740201	−	0.672386i	$-0.234730\pi$
$61$	11.5623	1.48040	0.740201	+	0.672386i	$0.234730\pi$
$62$	−6.00000	−0.762001
$63$	−2.61803	−0.329841
$64$	1.00000	0.125000
$65$	1.70820	0.211877
$66$	1.14590	0.141050
$67$	−0.763932	−0.0933292	−0.0466646	−	0.998911i	$-0.514859\pi$
$67$	−0.763932	−0.0933292	−0.0466646	+	0.998911i	$0.514859\pi$
$68$	5.23607	0.634967
$69$	−5.52786	−0.665477
$70$	−0.381966	−0.0456537
$71$	11.5623	1.37219	0.686097	−	0.727510i	$-0.259323\pi$
$71$	11.5623	1.37219	0.686097	+	0.727510i	$0.259323\pi$
$72$	−2.61803	−0.308538
$73$	0	0		−	1.00000i	$-0.5\pi$
$73$	0	0			1.00000i	$0.5\pi$
$74$	−1.14590	−0.133208
$75$	−3.00000	−0.346410
$76$	0	0
$77$	1.85410	0.211295
$78$	−2.76393	−0.312954
$79$	15.3262	1.72434	0.862168	−	0.506622i	$-0.169106\pi$
$79$	15.3262	1.72434	0.862168	+	0.506622i	$0.169106\pi$
$80$	−0.381966	−0.0427051
$81$	5.70820	0.634245
$82$	−10.5623	−1.16641
$83$	6.76393	0.742438	0.371219	−	0.928545i	$-0.378940\pi$
$83$	6.76393	0.742438	0.371219	+	0.928545i	$0.378940\pi$
$84$	0.618034	0.0674330
$85$	−2.00000	−0.216930
$86$	−2.85410	−0.307766
$87$	−4.23607	−0.454154
$88$	1.85410	0.197648
$89$	9.85410	1.04453	0.522266	−	0.852782i	$-0.325087\pi$
$89$	9.85410	1.04453	0.522266	+	0.852782i	$0.325087\pi$
$90$	1.00000	0.105409
$91$	−4.47214	−0.468807
$92$	−8.94427	−0.932505
$93$	−3.70820	−0.384523
$94$	−4.14590	−0.427617
$95$	0	0
$96$	0.618034	0.0630778
$97$	−13.8541	−1.40667	−0.703335	−	0.710858i	$-0.748307\pi$
$97$	−13.8541	−1.40667	−0.703335	+	0.710858i	$0.748307\pi$
$98$	1.00000	0.101015
$99$	−4.85410	−0.487856
$100$	−4.85410	−0.485410
$101$	−14.9443	−1.48701	−0.743505	−	0.668730i	$-0.766838\pi$
$101$	−14.9443	−1.48701	−0.743505	+	0.668730i	$0.766838\pi$
$102$	3.23607	0.320418
$103$	8.94427	0.881305	0.440653	−	0.897678i	$-0.354747\pi$
$103$	8.94427	0.881305	0.440653	+	0.897678i	$0.354747\pi$
$104$	−4.47214	−0.438529
$105$	−0.236068	−0.0230379
$106$	11.8541	1.15137
$107$	−6.29180	−0.608251	−0.304125	−	0.952632i	$-0.598364\pi$
$107$	−6.29180	−0.608251	−0.304125	+	0.952632i	$0.598364\pi$
$108$	−3.47214	−0.334106
$109$	−4.14590	−0.397105	−0.198553	−	0.980090i	$-0.563624\pi$
$109$	−4.14590	−0.397105	−0.198553	+	0.980090i	$0.563624\pi$
$110$	−0.708204	−0.0675246
$111$	−0.708204	−0.0672197
$112$	1.00000	0.0944911
$113$	−10.0000	−0.940721	−0.470360	−	0.882474i	$-0.655876\pi$
$113$	−10.0000	−0.940721	−0.470360	+	0.882474i	$0.655876\pi$
$114$	0	0
$115$	3.41641	0.318582
$116$	−6.85410	−0.636387
$117$	11.7082	1.08242
$118$	−8.56231	−0.788224
$119$	5.23607	0.479990
$120$	−0.236068	−0.0215500
$121$	−7.56231	−0.687482
$122$	11.5623	1.04680
$123$	−6.52786	−0.588598
$124$	−6.00000	−0.538816
$125$	3.76393	0.336656
$126$	−2.61803	−0.233233
$127$	−10.9098	−0.968091	−0.484045	−	0.875043i	$-0.660833\pi$
$127$	−10.9098	−0.968091	−0.484045	+	0.875043i	$0.660833\pi$
$128$	1.00000	0.0883883
$129$	−1.76393	−0.155306
$130$	1.70820	0.149819
$131$	4.47214	0.390732	0.195366	−	0.980730i	$-0.437410\pi$
$131$	4.47214	0.390732	0.195366	+	0.980730i	$0.437410\pi$
$132$	1.14590	0.0997376
$133$	0	0
$134$	−0.763932	−0.0659937
$135$	1.32624	0.114144
$136$	5.23607	0.448989
$137$	5.61803	0.479981	0.239991	−	0.970775i	$-0.422856\pi$
$137$	5.61803	0.479981	0.239991	+	0.970775i	$0.422856\pi$
$138$	−5.52786	−0.470563
$139$	6.00000	0.508913	0.254457	−	0.967084i	$-0.418103\pi$
$139$	6.00000	0.508913	0.254457	+	0.967084i	$0.418103\pi$
$140$	−0.381966	−0.0322820
$141$	−2.56231	−0.215785
$142$	11.5623	0.970287
$143$	−8.29180	−0.693395
$144$	−2.61803	−0.218169
$145$	2.61803	0.217416
$146$	0	0
$147$	0.618034	0.0509746
$148$	−1.14590	−0.0941922
$149$	−12.7639	−1.04566	−0.522831	−	0.852436i	$-0.675124\pi$
$149$	−12.7639	−1.04566	−0.522831	+	0.852436i	$0.675124\pi$
$150$	−3.00000	−0.244949
$151$	−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
$153$	−13.7082	−1.10824
$154$	1.85410	0.149408
$155$	2.29180	0.184081
$156$	−2.76393	−0.221292
$157$	−3.85410	−0.307591	−0.153795	−	0.988103i	$-0.549150\pi$
$157$	−3.85410	−0.307591	−0.153795	+	0.988103i	$0.549150\pi$
$158$	15.3262	1.21929
$159$	7.32624	0.581008
$160$	−0.381966	−0.0301971
$161$	−8.94427	−0.704907
$162$	5.70820	0.448479
$163$	13.2705	1.03943	0.519713	−	0.854341i	$-0.326039\pi$
$163$	13.2705	1.03943	0.519713	+	0.854341i	$0.326039\pi$
$164$	−10.5623	−0.824778
$165$	−0.437694	−0.0340744
$166$	6.76393	0.524983
$167$	10.0000	0.773823	0.386912	−	0.922117i	$-0.373542\pi$
$167$	10.0000	0.773823	0.386912	+	0.922117i	$0.373542\pi$
$168$	0.618034	0.0476824
$169$	7.00000	0.538462
$170$	−2.00000	−0.153393
$171$	0	0
$172$	−2.85410	−0.217623
$173$	−18.0000	−1.36851	−0.684257	−	0.729241i	$-0.739873\pi$
$173$	−18.0000	−1.36851	−0.684257	+	0.729241i	$0.739873\pi$
$174$	−4.23607	−0.321135
$175$	−4.85410	−0.366936
$176$	1.85410	0.139758
$177$	−5.29180	−0.397756
$178$	9.85410	0.738596
$179$	−4.29180	−0.320784	−0.160392	−	0.987053i	$-0.551276\pi$
$179$	−4.29180	−0.320784	−0.160392	+	0.987053i	$0.551276\pi$
$180$	1.00000	0.0745356
$181$	−19.4164	−1.44321	−0.721605	−	0.692305i	$-0.756595\pi$
$181$	−19.4164	−1.44321	−0.721605	+	0.692305i	$0.756595\pi$
$182$	−4.47214	−0.331497
$183$	7.14590	0.528240
$184$	−8.94427	−0.659380
$185$	0.437694	0.0321799
$186$	−3.70820	−0.271899
$187$	9.70820	0.709934
$188$	−4.14590	−0.302371
$189$	−3.47214	−0.252561
$190$	0	0
$191$	−2.94427	−0.213040	−0.106520	−	0.994311i	$-0.533971\pi$
$191$	−2.94427	−0.213040	−0.106520	+	0.994311i	$0.533971\pi$
$192$	0.618034	0.0446028
$193$	3.05573	0.219956	0.109978	−	0.993934i	$-0.464922\pi$
$193$	3.05573	0.219956	0.109978	+	0.993934i	$0.464922\pi$
$194$	−13.8541	−0.994667
$195$	1.05573	0.0756023
$196$	1.00000	0.0714286
$197$	−0.763932	−0.0544279	−0.0272140	−	0.999630i	$-0.508664\pi$
$197$	−0.763932	−0.0544279	−0.0272140	+	0.999630i	$0.508664\pi$
$198$	−4.85410	−0.344966
$199$	−18.5623	−1.31585	−0.657923	−	0.753085i	$-0.728565\pi$
$199$	−18.5623	−1.31585	−0.657923	+	0.753085i	$0.728565\pi$
$200$	−4.85410	−0.343237
$201$	−0.472136	−0.0333019
$202$	−14.9443	−1.05148
$203$	−6.85410	−0.481064
$204$	3.23607	0.226570
$205$	4.03444	0.281778
$206$	8.94427	0.623177
$207$	23.4164	1.62755
$208$	−4.47214	−0.310087
$209$	0	0
$210$	−0.236068	−0.0162902
$211$	−12.7639	−0.878705	−0.439353	−	0.898315i	$-0.644792\pi$
$211$	−12.7639	−0.878705	−0.439353	+	0.898315i	$0.644792\pi$
$212$	11.8541	0.814143
$213$	7.14590	0.489629
$214$	−6.29180	−0.430098
$215$	1.09017	0.0743490
$216$	−3.47214	−0.236249
$217$	−6.00000	−0.407307
$218$	−4.14590	−0.280796
$219$	0	0
$220$	−0.708204	−0.0477471
$221$	−23.4164	−1.57516
$222$	−0.708204	−0.0475315
$223$	0.763932	0.0511567	0.0255783	−	0.999673i	$-0.491857\pi$
$223$	0.763932	0.0511567	0.0255783	+	0.999673i	$0.491857\pi$
$224$	1.00000	0.0668153
$225$	12.7082	0.847214
$226$	−10.0000	−0.665190
$227$	7.41641	0.492244	0.246122	−	0.969239i	$-0.420844\pi$
$227$	7.41641	0.492244	0.246122	+	0.969239i	$0.420844\pi$
$228$	0	0
$229$	17.1459	1.13303	0.566516	−	0.824050i	$-0.308291\pi$
$229$	17.1459	1.13303	0.566516	+	0.824050i	$0.308291\pi$
$230$	3.41641	0.225271
$231$	1.14590	0.0753946
$232$	−6.85410	−0.449994
$233$	−7.09017	−0.464492	−0.232246	−	0.972657i	$-0.574608\pi$
$233$	−7.09017	−0.464492	−0.232246	+	0.972657i	$0.574608\pi$
$234$	11.7082	0.765389
$235$	1.58359	0.103302
$236$	−8.56231	−0.557359
$237$	9.47214	0.615281
$238$	5.23607	0.339404
$239$	−8.18034	−0.529142	−0.264571	−	0.964366i	$-0.585230\pi$
$239$	−8.18034	−0.529142	−0.264571	+	0.964366i	$0.585230\pi$
$240$	−0.236068	−0.0152381
$241$	2.56231	0.165053	0.0825263	−	0.996589i	$-0.473701\pi$
$241$	2.56231	0.165053	0.0825263	+	0.996589i	$0.473701\pi$
$242$	−7.56231	−0.486123
$243$	13.9443	0.894525
$244$	11.5623	0.740201
$245$	−0.381966	−0.0244029
$246$	−6.52786	−0.416201
$247$	0	0
$248$	−6.00000	−0.381000
$249$	4.18034	0.264918
$250$	3.76393	0.238052
$251$	26.9443	1.70071	0.850354	−	0.526212i	$-0.176388\pi$
$251$	26.9443	1.70071	0.850354	+	0.526212i	$0.176388\pi$
$252$	−2.61803	−0.164921
$253$	−16.5836	−1.04260
$254$	−10.9098	−0.684544
$255$	−1.23607	−0.0774056
$256$	1.00000	0.0625000
$257$	−3.14590	−0.196236	−0.0981179	−	0.995175i	$-0.531282\pi$
$257$	−3.14590	−0.196236	−0.0981179	+	0.995175i	$0.531282\pi$
$258$	−1.76393	−0.109818
$259$	−1.14590	−0.0712026
$260$	1.70820	0.105938
$261$	17.9443	1.11072
$262$	4.47214	0.276289
$263$	−18.6525	−1.15016	−0.575080	−	0.818097i	$-0.695029\pi$
$263$	−18.6525	−1.15016	−0.575080	+	0.818097i	$0.695029\pi$
$264$	1.14590	0.0705251
$265$	−4.52786	−0.278144
$266$	0	0
$267$	6.09017	0.372712
$268$	−0.763932	−0.0466646
$269$	31.4164	1.91549	0.957746	−	0.287615i	$-0.0928624\pi$
$269$	31.4164	1.91549	0.957746	+	0.287615i	$0.0928624\pi$
$270$	1.32624	0.0807123
$271$	22.5623	1.37056	0.685281	−	0.728279i	$-0.259679\pi$
$271$	22.5623	1.37056	0.685281	+	0.728279i	$0.259679\pi$
$272$	5.23607	0.317483
$273$	−2.76393	−0.167281
$274$	5.61803	0.339398
$275$	−9.00000	−0.542720
$276$	−5.52786	−0.332738
$277$	1.41641	0.0851037	0.0425519	−	0.999094i	$-0.486451\pi$
$277$	1.41641	0.0851037	0.0425519	+	0.999094i	$0.486451\pi$
$278$	6.00000	0.359856
$279$	15.7082	0.940426
$280$	−0.381966	−0.0228268
$281$	−3.41641	−0.203806	−0.101903	−	0.994794i	$-0.532493\pi$
$281$	−3.41641	−0.203806	−0.101903	+	0.994794i	$0.532493\pi$
$282$	−2.56231	−0.152583
$283$	8.00000	0.475551	0.237775	−	0.971320i	$-0.423582\pi$
$283$	8.00000	0.475551	0.237775	+	0.971320i	$0.423582\pi$
$284$	11.5623	0.686097
$285$	0	0
$286$	−8.29180	−0.490304
$287$	−10.5623	−0.623473
$288$	−2.61803	−0.154269
$289$	10.4164	0.612730
$290$	2.61803	0.153736
$291$	−8.56231	−0.501931
$292$	0	0
$293$	−4.58359	−0.267776	−0.133888	−	0.990996i	$-0.542746\pi$
$293$	−4.58359	−0.267776	−0.133888	+	0.990996i	$0.542746\pi$
$294$	0.618034	0.0360445
$295$	3.27051	0.190416
$296$	−1.14590	−0.0666040
$297$	−6.43769	−0.373553
$298$	−12.7639	−0.739395
$299$	40.0000	2.31326
$300$	−3.00000	−0.173205
$301$	−2.85410	−0.164508
$302$	−20.9443	−1.20521
$303$	−9.23607	−0.530598
$304$	0	0
$305$	−4.41641	−0.252883
$306$	−13.7082	−0.783646
$307$	27.9787	1.59683	0.798415	−	0.602108i	$-0.205672\pi$
$307$	27.9787	1.59683	0.798415	+	0.602108i	$0.205672\pi$
$308$	1.85410	0.105647
$309$	5.52786	0.314469
$310$	2.29180	0.130165
$311$	−5.67376	−0.321730	−0.160865	−	0.986976i	$-0.551428\pi$
$311$	−5.67376	−0.321730	−0.160865	+	0.986976i	$0.551428\pi$
$312$	−2.76393	−0.156477
$313$	10.0000	0.565233	0.282617	−	0.959233i	$-0.408798\pi$
$313$	10.0000	0.565233	0.282617	+	0.959233i	$0.408798\pi$
$314$	−3.85410	−0.217500
$315$	1.00000	0.0563436
$316$	15.3262	0.862168
$317$	−34.6869	−1.94821	−0.974106	−	0.226093i	$-0.927405\pi$
$317$	−34.6869	−1.94821	−0.974106	+	0.226093i	$0.927405\pi$
$318$	7.32624	0.410835
$319$	−12.7082	−0.711523
$320$	−0.381966	−0.0213525
$321$	−3.88854	−0.217037
$322$	−8.94427	−0.498445
$323$	0	0
$324$	5.70820	0.317122
$325$	21.7082	1.20415
$326$	13.2705	0.734986
$327$	−2.56231	−0.141696
$328$	−10.5623	−0.583206
$329$	−4.14590	−0.228571
$330$	−0.437694	−0.0240943
$331$	−9.70820	−0.533611	−0.266806	−	0.963750i	$-0.585968\pi$
$331$	−9.70820	−0.533611	−0.266806	+	0.963750i	$0.585968\pi$
$332$	6.76393	0.371219
$333$	3.00000	0.164399
$334$	10.0000	0.547176
$335$	0.291796	0.0159425
$336$	0.618034	0.0337165
$337$	3.70820	0.201999	0.100999	−	0.994886i	$-0.467796\pi$
$337$	3.70820	0.201999	0.100999	+	0.994886i	$0.467796\pi$
$338$	7.00000	0.380750
$339$	−6.18034	−0.335670
$340$	−2.00000	−0.108465
$341$	−11.1246	−0.602432
$342$	0	0
$343$	1.00000	0.0539949
$344$	−2.85410	−0.153883
$345$	2.11146	0.113677
$346$	−18.0000	−0.967686
$347$	−8.94427	−0.480154	−0.240077	−	0.970754i	$-0.577173\pi$
$347$	−8.94427	−0.480154	−0.240077	+	0.970754i	$0.577173\pi$
$348$	−4.23607	−0.227077
$349$	36.8328	1.97162	0.985808	−	0.167878i	$-0.0536916\pi$
$349$	36.8328	1.97162	0.985808	+	0.167878i	$0.0536916\pi$
$350$	−4.85410	−0.259463
$351$	15.5279	0.828816
$352$	1.85410	0.0988240
$353$	−13.4164	−0.714083	−0.357042	−	0.934088i	$-0.616215\pi$
$353$	−13.4164	−0.714083	−0.357042	+	0.934088i	$0.616215\pi$
$354$	−5.29180	−0.281256
$355$	−4.41641	−0.234399
$356$	9.85410	0.522266
$357$	3.23607	0.171271
$358$	−4.29180	−0.226828
$359$	15.7082	0.829047	0.414524	−	0.910039i	$-0.363948\pi$
$359$	15.7082	0.829047	0.414524	+	0.910039i	$0.363948\pi$
$360$	1.00000	0.0527046
$361$	0	0
$362$	−19.4164	−1.02050
$363$	−4.67376	−0.245309
$364$	−4.47214	−0.234404
$365$	0	0
$366$	7.14590	0.373522
$367$	27.2705	1.42351	0.711755	−	0.702428i	$-0.247901\pi$
$367$	27.2705	1.42351	0.711755	+	0.702428i	$0.247901\pi$
$368$	−8.94427	−0.466252
$369$	27.6525	1.43953
$370$	0.437694	0.0227546
$371$	11.8541	0.615434
$372$	−3.70820	−0.192261
$373$	−12.3820	−0.641114	−0.320557	−	0.947229i	$-0.603870\pi$
$373$	−12.3820	−0.641114	−0.320557	+	0.947229i	$0.603870\pi$
$374$	9.70820	0.501999
$375$	2.32624	0.120126
$376$	−4.14590	−0.213808
$377$	30.6525	1.57868
$378$	−3.47214	−0.178587
$379$	−9.81966	−0.504402	−0.252201	−	0.967675i	$-0.581154\pi$
$379$	−9.81966	−0.504402	−0.252201	+	0.967675i	$0.581154\pi$
$380$	0	0
$381$	−6.74265	−0.345436
$382$	−2.94427	−0.150642
$383$	−27.1246	−1.38600	−0.693001	−	0.720936i	$-0.743712\pi$
$383$	−27.1246	−1.38600	−0.693001	+	0.720936i	$0.743712\pi$
$384$	0.618034	0.0315389
$385$	−0.708204	−0.0360934
$386$	3.05573	0.155532
$387$	7.47214	0.379830
$388$	−13.8541	−0.703335
$389$	25.3050	1.28301	0.641506	−	0.767118i	$-0.278310\pi$
$389$	25.3050	1.28301	0.641506	+	0.767118i	$0.278310\pi$
$390$	1.05573	0.0534589
$391$	−46.8328	−2.36844
$392$	1.00000	0.0505076
$393$	2.76393	0.139422
$394$	−0.763932	−0.0384863
$395$	−5.85410	−0.294552
$396$	−4.85410	−0.243928
$397$	−8.43769	−0.423476	−0.211738	−	0.977326i	$-0.567912\pi$
$397$	−8.43769	−0.423476	−0.211738	+	0.977326i	$0.567912\pi$
$398$	−18.5623	−0.930444
$399$	0	0
$400$	−4.85410	−0.242705
$401$	−1.41641	−0.0707320	−0.0353660	−	0.999374i	$-0.511260\pi$
$401$	−1.41641	−0.0707320	−0.0353660	+	0.999374i	$0.511260\pi$
$402$	−0.472136	−0.0235480
$403$	26.8328	1.33664
$404$	−14.9443	−0.743505
$405$	−2.18034	−0.108342
$406$	−6.85410	−0.340163
$407$	−2.12461	−0.105313
$408$	3.23607	0.160209
$409$	−22.7984	−1.12731	−0.563654	−	0.826011i	$-0.690605\pi$
$409$	−22.7984	−1.12731	−0.563654	+	0.826011i	$0.690605\pi$
$410$	4.03444	0.199247
$411$	3.47214	0.171268
$412$	8.94427	0.440653
$413$	−8.56231	−0.421324
$414$	23.4164	1.15085
$415$	−2.58359	−0.126824
$416$	−4.47214	−0.219265
$417$	3.70820	0.181592
$418$	0	0
$419$	18.6525	0.911233	0.455617	−	0.890176i	$-0.349419\pi$
$419$	18.6525	0.911233	0.455617	+	0.890176i	$0.349419\pi$
$420$	−0.236068	−0.0115189
$421$	−28.4721	−1.38765	−0.693823	−	0.720145i	$-0.744075\pi$
$421$	−28.4721	−1.38765	−0.693823	+	0.720145i	$0.744075\pi$
$422$	−12.7639	−0.621338
$423$	10.8541	0.527744
$424$	11.8541	0.575686
$425$	−25.4164	−1.23288
$426$	7.14590	0.346220
$427$	11.5623	0.559539
$428$	−6.29180	−0.304125
$429$	−5.12461	−0.247419
$430$	1.09017	0.0525727
$431$	−16.1459	−0.777721	−0.388860	−	0.921297i	$-0.627131\pi$
$431$	−16.1459	−0.777721	−0.388860	+	0.921297i	$0.627131\pi$
$432$	−3.47214	−0.167053
$433$	5.61803	0.269985	0.134993	−	0.990847i	$-0.456899\pi$
$433$	5.61803	0.269985	0.134993	+	0.990847i	$0.456899\pi$
$434$	−6.00000	−0.288009
$435$	1.61803	0.0775788
$436$	−4.14590	−0.198553
$437$	0	0
$438$	0	0
$439$	−20.1803	−0.963155	−0.481578	−	0.876403i	$-0.659936\pi$
$439$	−20.1803	−0.963155	−0.481578	+	0.876403i	$0.659936\pi$
$440$	−0.708204	−0.0337623
$441$	−2.61803	−0.124668
$442$	−23.4164	−1.11380
$443$	−10.0902	−0.479398	−0.239699	−	0.970847i	$-0.577049\pi$
$443$	−10.0902	−0.479398	−0.239699	+	0.970847i	$0.577049\pi$
$444$	−0.708204	−0.0336099
$445$	−3.76393	−0.178427
$446$	0.763932	0.0361732
$447$	−7.88854	−0.373115
$448$	1.00000	0.0472456
$449$	13.7082	0.646930	0.323465	−	0.946240i	$-0.395152\pi$
$449$	13.7082	0.646930	0.323465	+	0.946240i	$0.395152\pi$
$450$	12.7082	0.599070
$451$	−19.5836	−0.922155
$452$	−10.0000	−0.470360
$453$	−12.9443	−0.608175
$454$	7.41641	0.348069
$455$	1.70820	0.0800818
$456$	0	0
$457$	37.8541	1.77074	0.885370	−	0.464887i	$-0.153905\pi$
$457$	37.8541	1.77074	0.885370	+	0.464887i	$0.153905\pi$
$458$	17.1459	0.801175
$459$	−18.1803	−0.848586
$460$	3.41641	0.159291
$461$	−3.49342	−0.162705	−0.0813524	−	0.996685i	$-0.525924\pi$
$461$	−3.49342	−0.162705	−0.0813524	+	0.996685i	$0.525924\pi$
$462$	1.14590	0.0533120
$463$	−12.0000	−0.557687	−0.278844	−	0.960337i	$-0.589951\pi$
$463$	−12.0000	−0.557687	−0.278844	+	0.960337i	$0.589951\pi$
$464$	−6.85410	−0.318194
$465$	1.41641	0.0656843
$466$	−7.09017	−0.328446
$467$	4.36068	0.201788	0.100894	−	0.994897i	$-0.467830\pi$
$467$	4.36068	0.201788	0.100894	+	0.994897i	$0.467830\pi$
$468$	11.7082	0.541212
$469$	−0.763932	−0.0352751
$470$	1.58359	0.0730457
$471$	−2.38197	−0.109755
$472$	−8.56231	−0.394112
$473$	−5.29180	−0.243317
$474$	9.47214	0.435070
$475$	0	0
$476$	5.23607	0.239995
$477$	−31.0344	−1.42097
$478$	−8.18034	−0.374160
$479$	20.6738	0.944608	0.472304	−	0.881436i	$-0.343422\pi$
$479$	20.6738	0.944608	0.472304	+	0.881436i	$0.343422\pi$
$480$	−0.236068	−0.0107750
$481$	5.12461	0.233662
$482$	2.56231	0.116710
$483$	−5.52786	−0.251527
$484$	−7.56231	−0.343741
$485$	5.29180	0.240288
$486$	13.9443	0.632525
$487$	−28.0902	−1.27289	−0.636444	−	0.771323i	$-0.719595\pi$
$487$	−28.0902	−1.27289	−0.636444	+	0.771323i	$0.719595\pi$
$488$	11.5623	0.523401
$489$	8.20163	0.370890
$490$	−0.381966	−0.0172555
$491$	4.36068	0.196795	0.0983974	−	0.995147i	$-0.468628\pi$
$491$	4.36068	0.196795	0.0983974	+	0.995147i	$0.468628\pi$
$492$	−6.52786	−0.294299
$493$	−35.8885	−1.61634
$494$	0	0
$495$	1.85410	0.0833357
$496$	−6.00000	−0.269408
$497$	11.5623	0.518640
$498$	4.18034	0.187326
$499$	41.6869	1.86616	0.933081	−	0.359665i	$-0.117109\pi$
$499$	41.6869	1.86616	0.933081	+	0.359665i	$0.117109\pi$
$500$	3.76393	0.168328
$501$	6.18034	0.276117
$502$	26.9443	1.20258
$503$	−21.2148	−0.945920	−0.472960	−	0.881084i	$-0.656815\pi$
$503$	−21.2148	−0.945920	−0.472960	+	0.881084i	$0.656815\pi$
$504$	−2.61803	−0.116617
$505$	5.70820	0.254012
$506$	−16.5836	−0.737231
$507$	4.32624	0.192135
$508$	−10.9098	−0.484045
$509$	−5.12461	−0.227144	−0.113572	−	0.993530i	$-0.536229\pi$
$509$	−5.12461	−0.227144	−0.113572	+	0.993530i	$0.536229\pi$
$510$	−1.23607	−0.0547340
$511$	0	0
$512$	1.00000	0.0441942
$513$	0	0
$514$	−3.14590	−0.138760
$515$	−3.41641	−0.150545
$516$	−1.76393	−0.0776528
$517$	−7.68692	−0.338070
$518$	−1.14590	−0.0503479
$519$	−11.1246	−0.488316
$520$	1.70820	0.0749097
$521$	−5.41641	−0.237297	−0.118649	−	0.992936i	$-0.537856\pi$
$521$	−5.41641	−0.237297	−0.118649	+	0.992936i	$0.537856\pi$
$522$	17.9443	0.785399
$523$	−24.0000	−1.04945	−0.524723	−	0.851273i	$-0.675831\pi$
$523$	−24.0000	−1.04945	−0.524723	+	0.851273i	$0.675831\pi$
$524$	4.47214	0.195366
$525$	−3.00000	−0.130931
$526$	−18.6525	−0.813287
$527$	−31.4164	−1.36852
$528$	1.14590	0.0498688
$529$	57.0000	2.47826
$530$	−4.52786	−0.196678
$531$	22.4164	0.972789
$532$	0	0
$533$	47.2361	2.04602
$534$	6.09017	0.263547
$535$	2.40325	0.103902
$536$	−0.763932	−0.0329968
$537$	−2.65248	−0.114463
$538$	31.4164	1.35446
$539$	1.85410	0.0798618
$540$	1.32624	0.0570722
$541$	−21.1246	−0.908218	−0.454109	−	0.890946i	$-0.650042\pi$
$541$	−21.1246	−0.908218	−0.454109	+	0.890946i	$0.650042\pi$
$542$	22.5623	0.969134
$543$	−12.0000	−0.514969
$544$	5.23607	0.224495
$545$	1.58359	0.0678336
$546$	−2.76393	−0.118285
$547$	18.6525	0.797522	0.398761	−	0.917055i	$-0.369440\pi$
$547$	18.6525	0.797522	0.398761	+	0.917055i	$0.369440\pi$
$548$	5.61803	0.239991
$549$	−30.2705	−1.29191
$550$	−9.00000	−0.383761
$551$	0	0
$552$	−5.52786	−0.235282
$553$	15.3262	0.651738
$554$	1.41641	0.0601774
$555$	0.270510	0.0114825
$556$	6.00000	0.254457
$557$	26.0689	1.10457	0.552287	−	0.833654i	$-0.313755\pi$
$557$	26.0689	1.10457	0.552287	+	0.833654i	$0.313755\pi$
$558$	15.7082	0.664981
$559$	12.7639	0.539857
$560$	−0.381966	−0.0161410
$561$	6.00000	0.253320
$562$	−3.41641	−0.144112
$563$	−13.5623	−0.571583	−0.285792	−	0.958292i	$-0.592256\pi$
$563$	−13.5623	−0.571583	−0.285792	+	0.958292i	$0.592256\pi$
$564$	−2.56231	−0.107893
$565$	3.81966	0.160694
$566$	8.00000	0.336265
$567$	5.70820	0.239722
$568$	11.5623	0.485144
$569$	12.2918	0.515299	0.257649	−	0.966238i	$-0.417052\pi$
$569$	12.2918	0.515299	0.257649	+	0.966238i	$0.417052\pi$
$570$	0	0
$571$	−44.6869	−1.87009	−0.935045	−	0.354530i	$-0.884641\pi$
$571$	−44.6869	−1.87009	−0.935045	+	0.354530i	$0.884641\pi$
$572$	−8.29180	−0.346697
$573$	−1.81966	−0.0760174
$574$	−10.5623	−0.440862
$575$	43.4164	1.81059
$576$	−2.61803	−0.109085
$577$	27.1246	1.12921	0.564606	−	0.825360i	$-0.309028\pi$
$577$	27.1246	1.12921	0.564606	+	0.825360i	$0.309028\pi$
$578$	10.4164	0.433265
$579$	1.88854	0.0784852
$580$	2.61803	0.108708
$581$	6.76393	0.280615
$582$	−8.56231	−0.354919
$583$	21.9787	0.910265
$584$	0	0
$585$	−4.47214	−0.184900
$586$	−4.58359	−0.189346
$587$	28.4721	1.17517	0.587585	−	0.809162i	$-0.300079\pi$
$587$	28.4721	1.17517	0.587585	+	0.809162i	$0.300079\pi$
$588$	0.618034	0.0254873
$589$	0	0
$590$	3.27051	0.134645
$591$	−0.472136	−0.0194211
$592$	−1.14590	−0.0470961
$593$	7.52786	0.309132	0.154566	−	0.987982i	$-0.450602\pi$
$593$	7.52786	0.309132	0.154566	+	0.987982i	$0.450602\pi$
$594$	−6.43769	−0.264142
$595$	−2.00000	−0.0819920
$596$	−12.7639	−0.522831
$597$	−11.4721	−0.469523
$598$	40.0000	1.63572
$599$	34.9787	1.42919	0.714596	−	0.699538i	$-0.246611\pi$
$599$	34.9787	1.42919	0.714596	+	0.699538i	$0.246611\pi$
$600$	−3.00000	−0.122474
$601$	34.3607	1.40160	0.700801	−	0.713357i	$-0.252826\pi$
$601$	34.3607	1.40160	0.700801	+	0.713357i	$0.252826\pi$
$602$	−2.85410	−0.116325
$603$	2.00000	0.0814463
$604$	−20.9443	−0.852210
$605$	2.88854	0.117436
$606$	−9.23607	−0.375190
$607$	28.3607	1.15112	0.575562	−	0.817758i	$-0.304783\pi$
$607$	28.3607	1.15112	0.575562	+	0.817758i	$0.304783\pi$
$608$	0	0
$609$	−4.23607	−0.171654
$610$	−4.41641	−0.178815
$611$	18.5410	0.750089
$612$	−13.7082	−0.554121
$613$	25.7082	1.03834	0.519172	−	0.854670i	$-0.326240\pi$
$613$	25.7082	1.03834	0.519172	+	0.854670i	$0.326240\pi$
$614$	27.9787	1.12913
$615$	2.49342	0.100544
$616$	1.85410	0.0747039
$617$	−30.9230	−1.24491	−0.622456	−	0.782655i	$-0.713865\pi$
$617$	−30.9230	−1.24491	−0.622456	+	0.782655i	$0.713865\pi$
$618$	5.52786	0.222363
$619$	−8.58359	−0.345004	−0.172502	−	0.985009i	$-0.555185\pi$
$619$	−8.58359	−0.345004	−0.172502	+	0.985009i	$0.555185\pi$
$620$	2.29180	0.0920407
$621$	31.0557	1.24622
$622$	−5.67376	−0.227497
$623$	9.85410	0.394796
$624$	−2.76393	−0.110646
$625$	22.8328	0.913313
$626$	10.0000	0.399680
$627$	0	0
$628$	−3.85410	−0.153795
$629$	−6.00000	−0.239236
$630$	1.00000	0.0398410
$631$	−30.8328	−1.22744	−0.613718	−	0.789526i	$-0.710327\pi$
$631$	−30.8328	−1.22744	−0.613718	+	0.789526i	$0.710327\pi$
$632$	15.3262	0.609645
$633$	−7.88854	−0.313541
$634$	−34.6869	−1.37759
$635$	4.16718	0.165370
$636$	7.32624	0.290504
$637$	−4.47214	−0.177192
$638$	−12.7082	−0.503123
$639$	−30.2705	−1.19748
$640$	−0.381966	−0.0150985
$641$	−19.4164	−0.766902	−0.383451	−	0.923561i	$-0.625265\pi$
$641$	−19.4164	−0.766902	−0.383451	+	0.923561i	$0.625265\pi$
$642$	−3.88854	−0.153469
$643$	−5.41641	−0.213602	−0.106801	−	0.994280i	$-0.534061\pi$
$643$	−5.41641	−0.213602	−0.106801	+	0.994280i	$0.534061\pi$
$644$	−8.94427	−0.352454
$645$	0.673762	0.0265294
$646$	0	0
$647$	15.3262	0.602537	0.301268	−	0.953539i	$-0.402590\pi$
$647$	15.3262	0.602537	0.301268	+	0.953539i	$0.402590\pi$
$648$	5.70820	0.224239
$649$	−15.8754	−0.623163
$650$	21.7082	0.851466
$651$	−3.70820	−0.145336
$652$	13.2705	0.519713
$653$	−22.4721	−0.879403	−0.439701	−	0.898144i	$-0.644916\pi$
$653$	−22.4721	−0.879403	−0.439701	+	0.898144i	$0.644916\pi$
$654$	−2.56231	−0.100194
$655$	−1.70820	−0.0667451
$656$	−10.5623	−0.412389
$657$	0	0
$658$	−4.14590	−0.161624
$659$	41.1246	1.60199	0.800994	−	0.598673i	$-0.204305\pi$
$659$	41.1246	1.60199	0.800994	+	0.598673i	$0.204305\pi$
$660$	−0.437694	−0.0170372
$661$	−26.8328	−1.04368	−0.521838	−	0.853045i	$-0.674753\pi$
$661$	−26.8328	−1.04368	−0.521838	+	0.853045i	$0.674753\pi$
$662$	−9.70820	−0.377320
$663$	−14.4721	−0.562051
$664$	6.76393	0.262491
$665$	0	0
$666$	3.00000	0.116248
$667$	61.3050	2.37374
$668$	10.0000	0.386912
$669$	0.472136	0.0182538
$670$	0.291796	0.0112731
$671$	21.4377	0.827593
$672$	0.618034	0.0238412
$673$	20.9443	0.807342	0.403671	−	0.914904i	$-0.367734\pi$
$673$	20.9443	0.807342	0.403671	+	0.914904i	$0.367734\pi$
$674$	3.70820	0.142835
$675$	16.8541	0.648715
$676$	7.00000	0.269231
$677$	28.2918	1.08734	0.543671	−	0.839298i	$-0.317034\pi$
$677$	28.2918	1.08734	0.543671	+	0.839298i	$0.317034\pi$
$678$	−6.18034	−0.237355
$679$	−13.8541	−0.531672
$680$	−2.00000	−0.0766965
$681$	4.58359	0.175644
$682$	−11.1246	−0.425983
$683$	15.7082	0.601058	0.300529	−	0.953773i	$-0.402837\pi$
$683$	15.7082	0.601058	0.300529	+	0.953773i	$0.402837\pi$
$684$	0	0
$685$	−2.14590	−0.0819905
$686$	1.00000	0.0381802
$687$	10.5967	0.404291
$688$	−2.85410	−0.108812
$689$	−53.0132	−2.01964
$690$	2.11146	0.0803818
$691$	−46.5410	−1.77050	−0.885252	−	0.465112i	$-0.846014\pi$
$691$	−46.5410	−1.77050	−0.885252	+	0.465112i	$0.846014\pi$
$692$	−18.0000	−0.684257
$693$	−4.85410	−0.184392
$694$	−8.94427	−0.339520
$695$	−2.29180	−0.0869328
$696$	−4.23607	−0.160568
$697$	−55.3050	−2.09482
$698$	36.8328	1.39414
$699$	−4.38197	−0.165741
$700$	−4.85410	−0.183468
$701$	−0.763932	−0.0288533	−0.0144267	−	0.999896i	$-0.504592\pi$
$701$	−0.763932	−0.0288533	−0.0144267	+	0.999896i	$0.504592\pi$
$702$	15.5279	0.586061
$703$	0	0
$704$	1.85410	0.0698791
$705$	0.978714	0.0368605
$706$	−13.4164	−0.504933
$707$	−14.9443	−0.562037
$708$	−5.29180	−0.198878
$709$	−31.1246	−1.16891	−0.584455	−	0.811426i	$-0.698692\pi$
$709$	−31.1246	−1.16891	−0.584455	+	0.811426i	$0.698692\pi$
$710$	−4.41641	−0.165745
$711$	−40.1246	−1.50479
$712$	9.85410	0.369298
$713$	53.6656	2.00979
$714$	3.23607	0.121107
$715$	3.16718	0.118446
$716$	−4.29180	−0.160392
$717$	−5.05573	−0.188810
$718$	15.7082	0.586225
$719$	−28.3607	−1.05767	−0.528837	−	0.848723i	$-0.677372\pi$
$719$	−28.3607	−1.05767	−0.528837	+	0.848723i	$0.677372\pi$
$720$	1.00000	0.0372678
$721$	8.94427	0.333102
$722$	0	0
$723$	1.58359	0.0588944
$724$	−19.4164	−0.721605
$725$	33.2705	1.23564
$726$	−4.67376	−0.173460
$727$	8.43769	0.312937	0.156468	−	0.987683i	$-0.449989\pi$
$727$	8.43769	0.312937	0.156468	+	0.987683i	$0.449989\pi$
$728$	−4.47214	−0.165748
$729$	−8.50658	−0.315058
$730$	0	0
$731$	−14.9443	−0.552734
$732$	7.14590	0.264120
$733$	0.562306	0.0207692	0.0103846	−	0.999946i	$-0.496694\pi$
$733$	0.562306	0.0207692	0.0103846	+	0.999946i	$0.496694\pi$
$734$	27.2705	1.00657
$735$	−0.236068	−0.00870750
$736$	−8.94427	−0.329690
$737$	−1.41641	−0.0521741
$738$	27.6525	1.01790
$739$	1.72949	0.0636203	0.0318102	−	0.999494i	$-0.489873\pi$
$739$	1.72949	0.0636203	0.0318102	+	0.999494i	$0.489873\pi$
$740$	0.437694	0.0160900
$741$	0	0
$742$	11.8541	0.435178
$743$	21.9787	0.806321	0.403160	−	0.915129i	$-0.367912\pi$
$743$	21.9787	0.806321	0.403160	+	0.915129i	$0.367912\pi$
$744$	−3.70820	−0.135949
$745$	4.87539	0.178620
$746$	−12.3820	−0.453336
$747$	−17.7082	−0.647909
$748$	9.70820	0.354967
$749$	−6.29180	−0.229897
$750$	2.32624	0.0849422
$751$	−15.3262	−0.559262	−0.279631	−	0.960107i	$-0.590212\pi$
$751$	−15.3262	−0.559262	−0.279631	+	0.960107i	$0.590212\pi$
$752$	−4.14590	−0.151185
$753$	16.6525	0.606850
$754$	30.6525	1.11630
$755$	8.00000	0.291150
$756$	−3.47214	−0.126280
$757$	−34.2492	−1.24481	−0.622405	−	0.782696i	$-0.713844\pi$
$757$	−34.2492	−1.24481	−0.622405	+	0.782696i	$0.713844\pi$
$758$	−9.81966	−0.356666
$759$	−10.2492	−0.372023
$760$	0	0
$761$	53.7771	1.94942	0.974709	−	0.223478i	$-0.0717411\pi$
$761$	53.7771	1.94942	0.974709	+	0.223478i	$0.0717411\pi$
$762$	−6.74265	−0.244260
$763$	−4.14590	−0.150092
$764$	−2.94427	−0.106520
$765$	5.23607	0.189310
$766$	−27.1246	−0.980052
$767$	38.2918	1.38264
$768$	0.618034	0.0223014
$769$	25.7082	0.927062	0.463531	−	0.886081i	$-0.346582\pi$
$769$	25.7082	0.927062	0.463531	+	0.886081i	$0.346582\pi$
$770$	−0.708204	−0.0255219
$771$	−1.94427	−0.0700212
$772$	3.05573	0.109978
$773$	11.7082	0.421115	0.210557	−	0.977581i	$-0.432472\pi$
$773$	11.7082	0.421115	0.210557	+	0.977581i	$0.432472\pi$
$774$	7.47214	0.268580
$775$	29.1246	1.04619
$776$	−13.8541	−0.497333
$777$	−0.708204	−0.0254067
$778$	25.3050	0.907226
$779$	0	0
$780$	1.05573	0.0378011
$781$	21.4377	0.767101
$782$	−46.8328	−1.67474
$783$	23.7984	0.850484
$784$	1.00000	0.0357143
$785$	1.47214	0.0525428
$786$	2.76393	0.0985862
$787$	−6.27051	−0.223520	−0.111760	−	0.993735i	$-0.535649\pi$
$787$	−6.27051	−0.223520	−0.111760	+	0.993735i	$0.535649\pi$
$788$	−0.763932	−0.0272140
$789$	−11.5279	−0.410403
$790$	−5.85410	−0.208280
$791$	−10.0000	−0.355559
$792$	−4.85410	−0.172483
$793$	−51.7082	−1.83621
$794$	−8.43769	−0.299443
$795$	−2.79837	−0.0992481
$796$	−18.5623	−0.657923
$797$	−8.83282	−0.312874	−0.156437	−	0.987688i	$-0.550001\pi$
$797$	−8.83282	−0.312874	−0.156437	+	0.987688i	$0.550001\pi$
$798$	0	0
$799$	−21.7082	−0.767981
$800$	−4.85410	−0.171618
$801$	−25.7984	−0.911541
$802$	−1.41641	−0.0500151
$803$	0	0
$804$	−0.472136	−0.0166510
$805$	3.41641	0.120413
$806$	26.8328	0.945146
$807$	19.4164	0.683490
$808$	−14.9443	−0.525738
$809$	13.0344	0.458267	0.229133	−	0.973395i	$-0.426411\pi$
$809$	13.0344	0.458267	0.229133	+	0.973395i	$0.426411\pi$
$810$	−2.18034	−0.0766093
$811$	−48.9787	−1.71988	−0.859938	−	0.510399i	$-0.829498\pi$
$811$	−48.9787	−1.71988	−0.859938	+	0.510399i	$0.829498\pi$
$812$	−6.85410	−0.240532
$813$	13.9443	0.489047
$814$	−2.12461	−0.0744676
$815$	−5.06888	−0.177555
$816$	3.23607	0.113285
$817$	0	0
$818$	−22.7984	−0.797126
$819$	11.7082	0.409118
$820$	4.03444	0.140889
$821$	47.1246	1.64466	0.822330	−	0.569011i	$-0.192674\pi$
$821$	47.1246	1.64466	0.822330	+	0.569011i	$0.192674\pi$
$822$	3.47214	0.121105
$823$	−15.7082	−0.547554	−0.273777	−	0.961793i	$-0.588273\pi$
$823$	−15.7082	−0.547554	−0.273777	+	0.961793i	$0.588273\pi$
$824$	8.94427	0.311588
$825$	−5.56231	−0.193655
$826$	−8.56231	−0.297921
$827$	−49.9574	−1.73719	−0.868595	−	0.495523i	$-0.834977\pi$
$827$	−49.9574	−1.73719	−0.868595	+	0.495523i	$0.834977\pi$
$828$	23.4164	0.813776
$829$	−5.12461	−0.177985	−0.0889926	−	0.996032i	$-0.528365\pi$
$829$	−5.12461	−0.177985	−0.0889926	+	0.996032i	$0.528365\pi$
$830$	−2.58359	−0.0896778
$831$	0.875388	0.0303669
$832$	−4.47214	−0.155043
$833$	5.23607	0.181419
$834$	3.70820	0.128405
$835$	−3.81966	−0.132185
$836$	0	0
$837$	20.8328	0.720087
$838$	18.6525	0.644339
$839$	−48.8328	−1.68590	−0.842948	−	0.537995i	$-0.819182\pi$
$839$	−48.8328	−1.68590	−0.842948	+	0.537995i	$0.819182\pi$
$840$	−0.236068	−0.00814512
$841$	17.9787	0.619956
$842$	−28.4721	−0.981215
$843$	−2.11146	−0.0727224
$844$	−12.7639	−0.439353
$845$	−2.67376	−0.0919802
$846$	10.8541	0.373172
$847$	−7.56231	−0.259844
$848$	11.8541	0.407072
$849$	4.94427	0.169687
$850$	−25.4164	−0.871776
$851$	10.2492	0.351339
$852$	7.14590	0.244814
$853$	10.2705	0.351656	0.175828	−	0.984421i	$-0.443740\pi$
$853$	10.2705	0.351656	0.175828	+	0.984421i	$0.443740\pi$
$854$	11.5623	0.395654
$855$	0	0
$856$	−6.29180	−0.215049
$857$	48.2492	1.64816	0.824081	−	0.566472i	$-0.191692\pi$
$857$	48.2492	1.64816	0.824081	+	0.566472i	$0.191692\pi$
$858$	−5.12461	−0.174951
$859$	−34.0000	−1.16007	−0.580033	−	0.814593i	$-0.696960\pi$
$859$	−34.0000	−1.16007	−0.580033	+	0.814593i	$0.696960\pi$
$860$	1.09017	0.0371745
$861$	−6.52786	−0.222469
$862$	−16.1459	−0.549931
$863$	−2.02129	−0.0688054	−0.0344027	−	0.999408i	$-0.510953\pi$
$863$	−2.02129	−0.0688054	−0.0344027	+	0.999408i	$0.510953\pi$
$864$	−3.47214	−0.118124
$865$	6.87539	0.233770
$866$	5.61803	0.190909
$867$	6.43769	0.218636
$868$	−6.00000	−0.203653
$869$	28.4164	0.963961
$870$	1.61803	0.0548565
$871$	3.41641	0.115761
$872$	−4.14590	−0.140398
$873$	36.2705	1.22757
$874$	0	0
$875$	3.76393	0.127244
$876$	0	0
$877$	−26.3951	−0.891300	−0.445650	−	0.895207i	$-0.647027\pi$
$877$	−26.3951	−0.891300	−0.445650	+	0.895207i	$0.647027\pi$
$878$	−20.1803	−0.681053
$879$	−2.83282	−0.0955485
$880$	−0.708204	−0.0238735
$881$	32.1803	1.08418	0.542092	−	0.840319i	$-0.317633\pi$
$881$	32.1803	1.08418	0.542092	+	0.840319i	$0.317633\pi$
$882$	−2.61803	−0.0881538
$883$	32.6869	1.10000	0.550001	−	0.835164i	$-0.314627\pi$
$883$	32.6869	1.10000	0.550001	+	0.835164i	$0.314627\pi$
$884$	−23.4164	−0.787579
$885$	2.02129	0.0679448
$886$	−10.0902	−0.338986
$887$	50.8328	1.70680	0.853399	−	0.521257i	$-0.174537\pi$
$887$	50.8328	1.70680	0.853399	+	0.521257i	$0.174537\pi$
$888$	−0.708204	−0.0237658
$889$	−10.9098	−0.365904
$890$	−3.76393	−0.126167
$891$	10.5836	0.354564
$892$	0.763932	0.0255783
$893$	0	0
$894$	−7.88854	−0.263832
$895$	1.63932	0.0547964
$896$	1.00000	0.0334077
$897$	24.7214	0.825422
$898$	13.7082	0.457449
$899$	41.1246	1.37158
$900$	12.7082	0.423607
$901$	62.0689	2.06781
$902$	−19.5836	−0.652062
$903$	−1.76393	−0.0587000
$904$	−10.0000	−0.332595
$905$	7.41641	0.246530
$906$	−12.9443	−0.430045
$907$	−48.0000	−1.59381	−0.796907	−	0.604102i	$-0.793532\pi$
$907$	−48.0000	−1.59381	−0.796907	+	0.604102i	$0.793532\pi$
$908$	7.41641	0.246122
$909$	39.1246	1.29768
$910$	1.70820	0.0566264
$911$	43.1459	1.42949	0.714744	−	0.699386i	$-0.246543\pi$
$911$	43.1459	1.42949	0.714744	+	0.699386i	$0.246543\pi$
$912$	0	0
$913$	12.5410	0.415047
$914$	37.8541	1.25210
$915$	−2.72949	−0.0902342
$916$	17.1459	0.566516
$917$	4.47214	0.147683
$918$	−18.1803	−0.600041
$919$	−25.7082	−0.848035	−0.424018	−	0.905654i	$-0.639381\pi$
$919$	−25.7082	−0.848035	−0.424018	+	0.905654i	$0.639381\pi$
$920$	3.41641	0.112636
$921$	17.2918	0.569784
$922$	−3.49342	−0.115050
$923$	−51.7082	−1.70200
$924$	1.14590	0.0376973
$925$	5.56231	0.182887
$926$	−12.0000	−0.394344
$927$	−23.4164	−0.769096
$928$	−6.85410	−0.224997
$929$	47.2361	1.54977	0.774883	−	0.632105i	$-0.217809\pi$
$929$	47.2361	1.54977	0.774883	+	0.632105i	$0.217809\pi$
$930$	1.41641	0.0464458
$931$	0	0
$932$	−7.09017	−0.232246
$933$	−3.50658	−0.114800
$934$	4.36068	0.142686
$935$	−3.70820	−0.121271
$936$	11.7082	0.382695
$937$	0.291796	0.00953256	0.00476628	−	0.999989i	$-0.498483\pi$
$937$	0.291796	0.00953256	0.00476628	+	0.999989i	$0.498483\pi$
$938$	−0.763932	−0.0249433
$939$	6.18034	0.201688
$940$	1.58359	0.0516511
$941$	20.2918	0.661494	0.330747	−	0.943720i	$-0.392699\pi$
$941$	20.2918	0.661494	0.330747	+	0.943720i	$0.392699\pi$
$942$	−2.38197	−0.0776086
$943$	94.4721	3.07644
$944$	−8.56231	−0.278679
$945$	1.32624	0.0431425
$946$	−5.29180	−0.172051
$947$	−49.8541	−1.62004	−0.810020	−	0.586402i	$-0.800544\pi$
$947$	−49.8541	−1.62004	−0.810020	+	0.586402i	$0.800544\pi$
$948$	9.47214	0.307641
$949$	0	0
$950$	0	0
$951$	−21.4377	−0.695165
$952$	5.23607	0.169702
$953$	−15.7082	−0.508839	−0.254419	−	0.967094i	$-0.581884\pi$
$953$	−15.7082	−0.508839	−0.254419	+	0.967094i	$0.581884\pi$
$954$	−31.0344	−1.00478
$955$	1.12461	0.0363916
$956$	−8.18034	−0.264571
$957$	−7.85410	−0.253887
$958$	20.6738	0.667939
$959$	5.61803	0.181416
$960$	−0.236068	−0.00761906
$961$	5.00000	0.161290
$962$	5.12461	0.165224
$963$	16.4721	0.530807
$964$	2.56231	0.0825263
$965$	−1.16718	−0.0375730
$966$	−5.52786	−0.177856
$967$	−26.2492	−0.844118	−0.422059	−	0.906568i	$-0.638693\pi$
$967$	−26.2492	−0.844118	−0.422059	+	0.906568i	$0.638693\pi$
$968$	−7.56231	−0.243062
$969$	0	0
$970$	5.29180	0.169909
$971$	−45.2705	−1.45280	−0.726400	−	0.687272i	$-0.758808\pi$
$971$	−45.2705	−1.45280	−0.726400	+	0.687272i	$0.758808\pi$
$972$	13.9443	0.447263
$973$	6.00000	0.192351
$974$	−28.0902	−0.900067
$975$	13.4164	0.429669
$976$	11.5623	0.370100
$977$	−22.2918	−0.713178	−0.356589	−	0.934261i	$-0.616060\pi$
$977$	−22.2918	−0.713178	−0.356589	+	0.934261i	$0.616060\pi$
$978$	8.20163	0.262259
$979$	18.2705	0.583928
$980$	−0.381966	−0.0122015
$981$	10.8541	0.346545
$982$	4.36068	0.139155
$983$	21.1246	0.673770	0.336885	−	0.941546i	$-0.390627\pi$
$983$	21.1246	0.673770	0.336885	+	0.941546i	$0.390627\pi$
$984$	−6.52786	−0.208101
$985$	0.291796	0.00929740
$986$	−35.8885	−1.14292
$987$	−2.56231	−0.0815591
$988$	0	0
$989$	25.5279	0.811739
$990$	1.85410	0.0589272
$991$	26.3951	0.838469	0.419234	−	0.907878i	$-0.362299\pi$
$991$	26.3951	0.838469	0.419234	+	0.907878i	$0.362299\pi$
$992$	−6.00000	−0.190500
$993$	−6.00000	−0.190404
$994$	11.5623	0.366734
$995$	7.09017	0.224773
$996$	4.18034	0.132459
$997$	−45.1459	−1.42978	−0.714892	−	0.699234i	$-0.753524\pi$
$997$	−45.1459	−1.42978	−0.714892	+	0.699234i	$0.753524\pi$
$998$	41.6869	1.31958
$999$	3.97871	0.125881

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5054.2.a.g.1.1	✓	2	19.18	odd	2
5054.2.a.l.1.2	yes	2	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 5054 = 2 \cdot 7 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5054.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.618034 q^{3} +1.00000 q^{4} -0.381966 q^{5} +0.618034 q^{6} +1.00000 q^{7} +1.00000 q^{8} -2.61803 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +0.618034 q^{3} +1.00000 q^{4} -0.381966 q^{5} +0.618034 q^{6} +1.00000 q^{7} +1.00000 q^{8} -2.61803 q^{9} -0.381966 q^{10} +1.85410 q^{11} +0.618034 q^{12} -4.47214 q^{13} +1.00000 q^{14} -0.236068 q^{15} +1.00000 q^{16} +5.23607 q^{17} -2.61803 q^{18} -0.381966 q^{20} +0.618034 q^{21} +1.85410 q^{22} -8.94427 q^{23} +0.618034 q^{24} -4.85410 q^{25} -4.47214 q^{26} -3.47214 q^{27} +1.00000 q^{28} -6.85410 q^{29} -0.236068 q^{30} -6.00000 q^{31} +1.00000 q^{32} +1.14590 q^{33} +5.23607 q^{34} -0.381966 q^{35} -2.61803 q^{36} -1.14590 q^{37} -2.76393 q^{39} -0.381966 q^{40} -10.5623 q^{41} +0.618034 q^{42} -2.85410 q^{43} +1.85410 q^{44} +1.00000 q^{45} -8.94427 q^{46} -4.14590 q^{47} +0.618034 q^{48} +1.00000 q^{49} -4.85410 q^{50} +3.23607 q^{51} -4.47214 q^{52} +11.8541 q^{53} -3.47214 q^{54} -0.708204 q^{55} +1.00000 q^{56} -6.85410 q^{58} -8.56231 q^{59} -0.236068 q^{60} +11.5623 q^{61} -6.00000 q^{62} -2.61803 q^{63} +1.00000 q^{64} +1.70820 q^{65} +1.14590 q^{66} -0.763932 q^{67} +5.23607 q^{68} -5.52786 q^{69} -0.381966 q^{70} +11.5623 q^{71} -2.61803 q^{72} -1.14590 q^{74} -3.00000 q^{75} +1.85410 q^{77} -2.76393 q^{78} +15.3262 q^{79} -0.381966 q^{80} +5.70820 q^{81} -10.5623 q^{82} +6.76393 q^{83} +0.618034 q^{84} -2.00000 q^{85} -2.85410 q^{86} -4.23607 q^{87} +1.85410 q^{88} +9.85410 q^{89} +1.00000 q^{90} -4.47214 q^{91} -8.94427 q^{92} -3.70820 q^{93} -4.14590 q^{94} +0.618034 q^{96} -13.8541 q^{97} +1.00000 q^{98} -4.85410 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - q^{3} + 2 q^{4} - 3 q^{5} - q^{6} + 2 q^{7} + 2 q^{8} - 3 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 - q^3 + 2 * q^4 - 3 * q^5 - q^6 + 2 * q^7 + 2 * q^8 - 3 * q^9	\( 2 q + 2 q^{2} - q^{3} + 2 q^{4} - 3 q^{5} - q^{6} + 2 q^{7} + 2 q^{8} - 3 q^{9} - 3 q^{10} - 3 q^{11} - q^{12} + 2 q^{14} + 4 q^{15} + 2 q^{16} + 6 q^{17} - 3 q^{18} - 3 q^{20} - q^{21} - 3 q^{22} - q^{24} - 3 q^{25} + 2 q^{27} + 2 q^{28} - 7 q^{29} + 4 q^{30} - 12 q^{31} + 2 q^{32} + 9 q^{33} + 6 q^{34} - 3 q^{35} - 3 q^{36} - 9 q^{37} - 10 q^{39} - 3 q^{40} - q^{41} - q^{42} + q^{43} - 3 q^{44} + 2 q^{45} - 15 q^{47} - q^{48} + 2 q^{49} - 3 q^{50} + 2 q^{51} + 17 q^{53} + 2 q^{54} + 12 q^{55} + 2 q^{56} - 7 q^{58} + 3 q^{59} + 4 q^{60} + 3 q^{61} - 12 q^{62} - 3 q^{63} + 2 q^{64} - 10 q^{65} + 9 q^{66} - 6 q^{67} + 6 q^{68} - 20 q^{69} - 3 q^{70} + 3 q^{71} - 3 q^{72} - 9 q^{74} - 6 q^{75} - 3 q^{77} - 10 q^{78} + 15 q^{79} - 3 q^{80} - 2 q^{81} - q^{82} + 18 q^{83} - q^{84} - 4 q^{85} + q^{86} - 4 q^{87} - 3 q^{88} + 13 q^{89} + 2 q^{90} + 6 q^{93} - 15 q^{94} - q^{96} - 21 q^{97} + 2 q^{98} - 3 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - q^3 + 2 * q^4 - 3 * q^5 - q^6 + 2 * q^7 + 2 * q^8 - 3 * q^9 - 3 * q^10 - 3 * q^11 - q^12 + 2 * q^14 + 4 * q^15 + 2 * q^16 + 6 * q^17 - 3 * q^18 - 3 * q^20 - q^21 - 3 * q^22 - q^24 - 3 * q^25 + 2 * q^27 + 2 * q^28 - 7 * q^29 + 4 * q^30 - 12 * q^31 + 2 * q^32 + 9 * q^33 + 6 * q^34 - 3 * q^35 - 3 * q^36 - 9 * q^37 - 10 * q^39 - 3 * q^40 - q^41 - q^42 + q^43 - 3 * q^44 + 2 * q^45 - 15 * q^47 - q^48 + 2 * q^49 - 3 * q^50 + 2 * q^51 + 17 * q^53 + 2 * q^54 + 12 * q^55 + 2 * q^56 - 7 * q^58 + 3 * q^59 + 4 * q^60 + 3 * q^61 - 12 * q^62 - 3 * q^63 + 2 * q^64 - 10 * q^65 + 9 * q^66 - 6 * q^67 + 6 * q^68 - 20 * q^69 - 3 * q^70 + 3 * q^71 - 3 * q^72 - 9 * q^74 - 6 * q^75 - 3 * q^77 - 10 * q^78 + 15 * q^79 - 3 * q^80 - 2 * q^81 - q^82 + 18 * q^83 - q^84 - 4 * q^85 + q^86 - 4 * q^87 - 3 * q^88 + 13 * q^89 + 2 * q^90 + 6 * q^93 - 15 * q^94 - q^96 - 21 * q^97 + 2 * q^98 - 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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