LMFDB - Embedded newform 5290.2.a.bl.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5290,2,Mod(1,5290)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5290, 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("5290.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5290 = 2 \cdot 5 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5290.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:	$42.2408626693$
Analytic rank:	$0$
Dimension:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - 5 x^{14} - 24 x^{13} + 142 x^{12} + 184 x^{11} - 1488 x^{10} - 426 x^{9} + 7165 x^{8} + \cdots - 32 $ x^15 - 5x^14 - 24x^13 + 142x^12 + 184x^11 - 1488x^10 - 426x^9 + 7165x^8 - 206x^7 - 16453x^6 + 637x^5 + 16290x^4 + 1068x^3 - 4992x^2 - 848x - 32
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 230)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Root			$3.36041$ of defining polynomial
Character	$\chi$	$=$	5290.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +3.36041 q^{3} +1.00000 q^{4} +1.00000 q^{5} +3.36041 q^{6} -2.28078 q^{7} +1.00000 q^{8} +8.29236 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +3.36041 q^{3} +1.00000 q^{4} +1.00000 q^{5} +3.36041 q^{6} -2.28078 q^{7} +1.00000 q^{8} +8.29236 q^{9} +1.00000 q^{10} +2.85022 q^{11} +3.36041 q^{12} -2.53026 q^{13} -2.28078 q^{14} +3.36041 q^{15} +1.00000 q^{16} -5.36731 q^{17} +8.29236 q^{18} +3.81026 q^{19} +1.00000 q^{20} -7.66437 q^{21} +2.85022 q^{22} +3.36041 q^{24} +1.00000 q^{25} -2.53026 q^{26} +17.7845 q^{27} -2.28078 q^{28} +2.25138 q^{29} +3.36041 q^{30} +8.13074 q^{31} +1.00000 q^{32} +9.57791 q^{33} -5.36731 q^{34} -2.28078 q^{35} +8.29236 q^{36} -0.287882 q^{37} +3.81026 q^{38} -8.50271 q^{39} +1.00000 q^{40} -6.34402 q^{41} -7.66437 q^{42} -6.66094 q^{43} +2.85022 q^{44} +8.29236 q^{45} +10.6363 q^{47} +3.36041 q^{48} -1.79803 q^{49} +1.00000 q^{50} -18.0364 q^{51} -2.53026 q^{52} +11.3038 q^{53} +17.7845 q^{54} +2.85022 q^{55} -2.28078 q^{56} +12.8041 q^{57} +2.25138 q^{58} -3.21219 q^{59} +3.36041 q^{60} -0.432976 q^{61} +8.13074 q^{62} -18.9131 q^{63} +1.00000 q^{64} -2.53026 q^{65} +9.57791 q^{66} +3.21516 q^{67} -5.36731 q^{68} -2.28078 q^{70} +1.82598 q^{71} +8.29236 q^{72} -12.2217 q^{73} -0.287882 q^{74} +3.36041 q^{75} +3.81026 q^{76} -6.50073 q^{77} -8.50271 q^{78} +5.77393 q^{79} +1.00000 q^{80} +34.8862 q^{81} -6.34402 q^{82} +9.21547 q^{83} -7.66437 q^{84} -5.36731 q^{85} -6.66094 q^{86} +7.56555 q^{87} +2.85022 q^{88} -17.5926 q^{89} +8.29236 q^{90} +5.77097 q^{91} +27.3226 q^{93} +10.6363 q^{94} +3.81026 q^{95} +3.36041 q^{96} +5.13654 q^{97} -1.79803 q^{98} +23.6351 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q + 15 q^{2} + 5 q^{3} + 15 q^{4} + 15 q^{5} + 5 q^{6} - 4 q^{7} + 15 q^{8} + 28 q^{9}+O(q^{10}) $ 15 * q + 15 * q^2 + 5 * q^3 + 15 * q^4 + 15 * q^5 + 5 * q^6 - 4 * q^7 + 15 * q^8 + 28 * q^9	\( 15 q + 15 q^{2} + 5 q^{3} + 15 q^{4} + 15 q^{5} + 5 q^{6} - 4 q^{7} + 15 q^{8} + 28 q^{9} + 15 q^{10} + 7 q^{11} + 5 q^{12} + 17 q^{13} - 4 q^{14} + 5 q^{15} + 15 q^{16} + 2 q^{17} + 28 q^{18} + 18 q^{19} + 15 q^{20} + 7 q^{22} + 5 q^{24} + 15 q^{25} + 17 q^{26} + 29 q^{27} - 4 q^{28} + 35 q^{29} + 5 q^{30} + 19 q^{31} + 15 q^{32} - 21 q^{33} + 2 q^{34} - 4 q^{35} + 28 q^{36} - 12 q^{37} + 18 q^{38} + 26 q^{39} + 15 q^{40} + 27 q^{41} + 12 q^{43} + 7 q^{44} + 28 q^{45} + 40 q^{47} + 5 q^{48} + 29 q^{49} + 15 q^{50} - 27 q^{51} + 17 q^{52} - 20 q^{53} + 29 q^{54} + 7 q^{55} - 4 q^{56} - 11 q^{57} + 35 q^{58} + 15 q^{59} + 5 q^{60} + 28 q^{61} + 19 q^{62} - 51 q^{63} + 15 q^{64} + 17 q^{65} - 21 q^{66} + 4 q^{67} + 2 q^{68} - 4 q^{70} + 22 q^{71} + 28 q^{72} + 48 q^{73} - 12 q^{74} + 5 q^{75} + 18 q^{76} + 45 q^{77} + 26 q^{78} - 2 q^{79} + 15 q^{80} + 79 q^{81} + 27 q^{82} - 29 q^{83} + 2 q^{85} + 12 q^{86} - 7 q^{87} + 7 q^{88} + 20 q^{89} + 28 q^{90} + 6 q^{91} + 63 q^{93} + 40 q^{94} + 18 q^{95} + 5 q^{96} - 22 q^{97} + 29 q^{98} + 23 q^{99}+O(q^{100}) \) 15 * q + 15 * q^2 + 5 * q^3 + 15 * q^4 + 15 * q^5 + 5 * q^6 - 4 * q^7 + 15 * q^8 + 28 * q^9 + 15 * q^10 + 7 * q^11 + 5 * q^12 + 17 * q^13 - 4 * q^14 + 5 * q^15 + 15 * q^16 + 2 * q^17 + 28 * q^18 + 18 * q^19 + 15 * q^20 + 7 * q^22 + 5 * q^24 + 15 * q^25 + 17 * q^26 + 29 * q^27 - 4 * q^28 + 35 * q^29 + 5 * q^30 + 19 * q^31 + 15 * q^32 - 21 * q^33 + 2 * q^34 - 4 * q^35 + 28 * q^36 - 12 * q^37 + 18 * q^38 + 26 * q^39 + 15 * q^40 + 27 * q^41 + 12 * q^43 + 7 * q^44 + 28 * q^45 + 40 * q^47 + 5 * q^48 + 29 * q^49 + 15 * q^50 - 27 * q^51 + 17 * q^52 - 20 * q^53 + 29 * q^54 + 7 * q^55 - 4 * q^56 - 11 * q^57 + 35 * q^58 + 15 * q^59 + 5 * q^60 + 28 * q^61 + 19 * q^62 - 51 * q^63 + 15 * q^64 + 17 * q^65 - 21 * q^66 + 4 * q^67 + 2 * q^68 - 4 * q^70 + 22 * q^71 + 28 * q^72 + 48 * q^73 - 12 * q^74 + 5 * q^75 + 18 * q^76 + 45 * q^77 + 26 * q^78 - 2 * q^79 + 15 * q^80 + 79 * q^81 + 27 * q^82 - 29 * q^83 + 2 * q^85 + 12 * q^86 - 7 * q^87 + 7 * q^88 + 20 * q^89 + 28 * q^90 + 6 * q^91 + 63 * q^93 + 40 * q^94 + 18 * q^95 + 5 * q^96 - 22 * q^97 + 29 * q^98 + 23 * 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
$3$	3.36041	1.94013	0.970067	−	0.242837i	$-0.0780780\pi$
$3$	3.36041	1.94013	0.970067	+	0.242837i	$0.0780780\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	3.36041	1.37188
$7$	−2.28078	−0.862055	−0.431027	−	0.902339i	$-0.641849\pi$
$7$	−2.28078	−0.862055	−0.431027	+	0.902339i	$0.641849\pi$
$8$	1.00000	0.353553
$9$	8.29236	2.76412
$10$	1.00000	0.316228
$11$	2.85022	0.859374	0.429687	−	0.902978i	$-0.358624\pi$
$11$	2.85022	0.859374	0.429687	+	0.902978i	$0.358624\pi$
$12$	3.36041	0.970067
$13$	−2.53026	−0.701767	−0.350884	−	0.936419i	$-0.614119\pi$
$13$	−2.53026	−0.701767	−0.350884	+	0.936419i	$0.614119\pi$
$14$	−2.28078	−0.609565
$15$	3.36041	0.867654
$16$	1.00000	0.250000
$17$	−5.36731	−1.30176	−0.650882	−	0.759179i	$-0.725601\pi$
$17$	−5.36731	−1.30176	−0.650882	+	0.759179i	$0.725601\pi$
$18$	8.29236	1.95453
$19$	3.81026	0.874134	0.437067	−	0.899429i	$-0.356017\pi$
$19$	3.81026	0.874134	0.437067	+	0.899429i	$0.356017\pi$
$20$	1.00000	0.223607
$21$	−7.66437	−1.67250
$22$	2.85022	0.607669
$23$	0	0
$23$	0	0
$24$	3.36041	0.685941
$25$	1.00000	0.200000
$26$	−2.53026	−0.496224
$27$	17.7845	3.42263
$28$	−2.28078	−0.431027
$29$	2.25138	0.418070	0.209035	−	0.977908i	$-0.432968\pi$
$29$	2.25138	0.418070	0.209035	+	0.977908i	$0.432968\pi$
$30$	3.36041	0.613524
$31$	8.13074	1.46032	0.730162	−	0.683274i	$-0.239445\pi$
$31$	8.13074	1.46032	0.730162	+	0.683274i	$0.239445\pi$
$32$	1.00000	0.176777
$33$	9.57791	1.66730
$34$	−5.36731	−0.920486
$35$	−2.28078	−0.385523
$36$	8.29236	1.38206
$37$	−0.287882	−0.0473275	−0.0236637	−	0.999720i	$-0.507533\pi$
$37$	−0.287882	−0.0473275	−0.0236637	+	0.999720i	$0.507533\pi$
$38$	3.81026	0.618106
$39$	−8.50271	−1.36152
$40$	1.00000	0.158114
$41$	−6.34402	−0.990770	−0.495385	−	0.868674i	$-0.664973\pi$
$41$	−6.34402	−0.990770	−0.495385	+	0.868674i	$0.664973\pi$
$42$	−7.66437	−1.18264
$43$	−6.66094	−1.01578	−0.507892	−	0.861421i	$-0.669575\pi$
$43$	−6.66094	−1.01578	−0.507892	+	0.861421i	$0.669575\pi$
$44$	2.85022	0.429687
$45$	8.29236	1.23615
$46$	0	0
$47$	10.6363	1.55146	0.775730	−	0.631064i	$-0.217382\pi$
$47$	10.6363	1.55146	0.775730	+	0.631064i	$0.217382\pi$
$48$	3.36041	0.485034
$49$	−1.79803	−0.256862
$50$	1.00000	0.141421
$51$	−18.0364	−2.52560
$52$	−2.53026	−0.350884
$53$	11.3038	1.55270	0.776350	−	0.630302i	$-0.217069\pi$
$53$	11.3038	1.55270	0.776350	+	0.630302i	$0.217069\pi$
$54$	17.7845	2.42017
$55$	2.85022	0.384324
$56$	−2.28078	−0.304782
$57$	12.8041	1.69594
$58$	2.25138	0.295620
$59$	−3.21219	−0.418191	−0.209096	−	0.977895i	$-0.567052\pi$
$59$	−3.21219	−0.418191	−0.209096	+	0.977895i	$0.567052\pi$
$60$	3.36041	0.433827
$61$	−0.432976	−0.0554369	−0.0277184	−	0.999616i	$-0.508824\pi$
$61$	−0.432976	−0.0554369	−0.0277184	+	0.999616i	$0.508824\pi$
$62$	8.13074	1.03260
$63$	−18.9131	−2.38282
$64$	1.00000	0.125000
$65$	−2.53026	−0.313840
$66$	9.57791	1.17896
$67$	3.21516	0.392794	0.196397	−	0.980524i	$-0.437076\pi$
$67$	3.21516	0.392794	0.196397	+	0.980524i	$0.437076\pi$
$68$	−5.36731	−0.650882
$69$	0	0
$70$	−2.28078	−0.272606
$71$	1.82598	0.216704	0.108352	−	0.994113i	$-0.465443\pi$
$71$	1.82598	0.216704	0.108352	+	0.994113i	$0.465443\pi$
$72$	8.29236	0.977264
$73$	−12.2217	−1.43044	−0.715222	−	0.698898i	$-0.753674\pi$
$73$	−12.2217	−1.43044	−0.715222	+	0.698898i	$0.753674\pi$
$74$	−0.287882	−0.0334656
$75$	3.36041	0.388027
$76$	3.81026	0.437067
$77$	−6.50073	−0.740827
$78$	−8.50271	−0.962742
$79$	5.77393	0.649618	0.324809	−	0.945780i	$-0.394700\pi$
$79$	5.77393	0.649618	0.324809	+	0.945780i	$0.394700\pi$
$80$	1.00000	0.111803
$81$	34.8862	3.87624
$82$	−6.34402	−0.700580
$83$	9.21547	1.01153	0.505765	−	0.862671i	$-0.331210\pi$
$83$	9.21547	1.01153	0.505765	+	0.862671i	$0.331210\pi$
$84$	−7.66437	−0.836251
$85$	−5.36731	−0.582166
$86$	−6.66094	−0.718268
$87$	7.56555	0.811112
$88$	2.85022	0.303834
$89$	−17.5926	−1.86481	−0.932407	−	0.361410i	$-0.882295\pi$
$89$	−17.5926	−1.86481	−0.932407	+	0.361410i	$0.882295\pi$
$90$	8.29236	0.874092
$91$	5.77097	0.604962
$92$	0	0
$93$	27.3226	2.83322
$94$	10.6363	1.09705
$95$	3.81026	0.390925
$96$	3.36041	0.342971
$97$	5.13654	0.521537	0.260768	−	0.965401i	$-0.416024\pi$
$97$	5.13654	0.521537	0.260768	+	0.965401i	$0.416024\pi$
$98$	−1.79803	−0.181629
$99$	23.6351	2.37541
$100$	1.00000	0.100000
$101$	−4.59006	−0.456728	−0.228364	−	0.973576i	$-0.573338\pi$
$101$	−4.59006	−0.456728	−0.228364	+	0.973576i	$0.573338\pi$
$102$	−18.0364	−1.78587
$103$	−8.68867	−0.856120	−0.428060	−	0.903750i	$-0.640803\pi$
$103$	−8.68867	−0.856120	−0.428060	+	0.903750i	$0.640803\pi$
$104$	−2.53026	−0.248112
$105$	−7.66437	−0.747966
$106$	11.3038	1.09792
$107$	−1.18201	−0.114270	−0.0571348	−	0.998366i	$-0.518196\pi$
$107$	−1.18201	−0.114270	−0.0571348	+	0.998366i	$0.518196\pi$
$108$	17.7845	1.71132
$109$	2.90403	0.278156	0.139078	−	0.990281i	$-0.455586\pi$
$109$	2.90403	0.278156	0.139078	+	0.990281i	$0.455586\pi$
$110$	2.85022	0.271758
$111$	−0.967401	−0.0918216
$112$	−2.28078	−0.215514
$113$	−20.2781	−1.90760	−0.953801	−	0.300439i	$-0.902867\pi$
$113$	−20.2781	−1.90760	−0.953801	+	0.300439i	$0.902867\pi$
$114$	12.8041	1.19921
$115$	0	0
$116$	2.25138	0.209035
$117$	−20.9818	−1.93977
$118$	−3.21219	−0.295706
$119$	12.2417	1.12219
$120$	3.36041	0.306762
$121$	−2.87625	−0.261477
$122$	−0.432976	−0.0391998
$123$	−21.3185	−1.92223
$124$	8.13074	0.730162
$125$	1.00000	0.0894427
$126$	−18.9131	−1.68491
$127$	15.0035	1.33135	0.665674	−	0.746242i	$-0.268144\pi$
$127$	15.0035	1.33135	0.665674	+	0.746242i	$0.268144\pi$
$128$	1.00000	0.0883883
$129$	−22.3835	−1.97076
$130$	−2.53026	−0.221918
$131$	4.42611	0.386711	0.193356	−	0.981129i	$-0.438063\pi$
$131$	4.42611	0.386711	0.193356	+	0.981129i	$0.438063\pi$
$132$	9.57791	0.833650
$133$	−8.69038	−0.753552
$134$	3.21516	0.277747
$135$	17.7845	1.53065
$136$	−5.36731	−0.460243
$137$	9.35873	0.799570	0.399785	−	0.916609i	$-0.369085\pi$
$137$	9.35873	0.799570	0.399785	+	0.916609i	$0.369085\pi$
$138$	0	0
$139$	−6.15826	−0.522337	−0.261169	−	0.965293i	$-0.584108\pi$
$139$	−6.15826	−0.522337	−0.261169	+	0.965293i	$0.584108\pi$
$140$	−2.28078	−0.192761
$141$	35.7423	3.01004
$142$	1.82598	0.153233
$143$	−7.21179	−0.603080
$144$	8.29236	0.691030
$145$	2.25138	0.186967
$146$	−12.2217	−1.01148
$147$	−6.04213	−0.498346
$148$	−0.287882	−0.0236637
$149$	−15.0093	−1.22961	−0.614804	−	0.788680i	$-0.710765\pi$
$149$	−15.0093	−1.22961	−0.614804	+	0.788680i	$0.710765\pi$
$150$	3.36041	0.274376
$151$	−6.42011	−0.522461	−0.261231	−	0.965276i	$-0.584128\pi$
$151$	−6.42011	−0.522461	−0.261231	+	0.965276i	$0.584128\pi$
$152$	3.81026	0.309053
$153$	−44.5077	−3.59823
$154$	−6.50073	−0.523844
$155$	8.13074	0.653077
$156$	−8.50271	−0.680761
$157$	−4.25236	−0.339375	−0.169688	−	0.985498i	$-0.554276\pi$
$157$	−4.25236	−0.339375	−0.169688	+	0.985498i	$0.554276\pi$
$158$	5.77393	0.459349
$159$	37.9855	3.01245
$160$	1.00000	0.0790569
$161$	0	0
$162$	34.8862	2.74092
$163$	−4.15333	−0.325314	−0.162657	−	0.986683i	$-0.552006\pi$
$163$	−4.15333	−0.325314	−0.162657	+	0.986683i	$0.552006\pi$
$164$	−6.34402	−0.495385
$165$	9.57791	0.745639
$166$	9.21547	0.715259
$167$	−20.3207	−1.57246	−0.786232	−	0.617931i	$-0.787971\pi$
$167$	−20.3207	−1.57246	−0.786232	+	0.617931i	$0.787971\pi$
$168$	−7.66437	−0.591319
$169$	−6.59780	−0.507523
$170$	−5.36731	−0.411654
$171$	31.5961	2.41621
$172$	−6.66094	−0.507892
$173$	−1.71238	−0.130190	−0.0650948	−	0.997879i	$-0.520735\pi$
$173$	−1.71238	−0.130190	−0.0650948	+	0.997879i	$0.520735\pi$
$174$	7.56555	0.573543
$175$	−2.28078	−0.172411
$176$	2.85022	0.214843
$177$	−10.7943	−0.811348
$178$	−17.5926	−1.31862
$179$	−8.49218	−0.634736	−0.317368	−	0.948303i	$-0.602799\pi$
$179$	−8.49218	−0.634736	−0.317368	+	0.948303i	$0.602799\pi$
$180$	8.29236	0.618076
$181$	−2.19346	−0.163039	−0.0815194	−	0.996672i	$-0.525977\pi$
$181$	−2.19346	−0.163039	−0.0815194	+	0.996672i	$0.525977\pi$
$182$	5.77097	0.427772
$183$	−1.45498	−0.107555
$184$	0	0
$185$	−0.287882	−0.0211655
$186$	27.3226	2.00339
$187$	−15.2980	−1.11870
$188$	10.6363	0.775730
$189$	−40.5626	−2.95050
$190$	3.81026	0.276426
$191$	5.19440	0.375853	0.187927	−	0.982183i	$-0.439823\pi$
$191$	5.19440	0.375853	0.187927	+	0.982183i	$0.439823\pi$
$192$	3.36041	0.242517
$193$	−25.3700	−1.82617	−0.913086	−	0.407767i	$-0.866308\pi$
$193$	−25.3700	−1.82617	−0.913086	+	0.407767i	$0.866308\pi$
$194$	5.13654	0.368782
$195$	−8.50271	−0.608891
$196$	−1.79803	−0.128431
$197$	−24.8721	−1.77206	−0.886032	−	0.463625i	$-0.846549\pi$
$197$	−24.8721	−1.77206	−0.886032	+	0.463625i	$0.846549\pi$
$198$	23.6351	1.67967
$199$	9.17006	0.650049	0.325024	−	0.945706i	$-0.394628\pi$
$199$	9.17006	0.650049	0.325024	+	0.945706i	$0.394628\pi$
$200$	1.00000	0.0707107
$201$	10.8042	0.762073
$202$	−4.59006	−0.322955
$203$	−5.13490	−0.360399
$204$	−18.0364	−1.26280
$205$	−6.34402	−0.443086
$206$	−8.68867	−0.605369
$207$	0	0
$208$	−2.53026	−0.175442
$209$	10.8601	0.751208
$210$	−7.66437	−0.528891
$211$	−9.96457	−0.685990	−0.342995	−	0.939337i	$-0.611441\pi$
$211$	−9.96457	−0.685990	−0.342995	+	0.939337i	$0.611441\pi$
$212$	11.3038	0.776350
$213$	6.13605	0.420435
$214$	−1.18201	−0.0808008
$215$	−6.66094	−0.454272
$216$	17.7845	1.21008
$217$	−18.5444	−1.25888
$218$	2.90403	0.196686
$219$	−41.0700	−2.77525
$220$	2.85022	0.192162
$221$	13.5807	0.913535
$222$	−0.967401	−0.0649277
$223$	−17.6887	−1.18452	−0.592262	−	0.805745i	$-0.701765\pi$
$223$	−17.6887	−1.18452	−0.592262	+	0.805745i	$0.701765\pi$
$224$	−2.28078	−0.152391
$225$	8.29236	0.552824
$226$	−20.2781	−1.34888
$227$	17.9461	1.19112	0.595561	−	0.803310i	$-0.296930\pi$
$227$	17.9461	1.19112	0.595561	+	0.803310i	$0.296930\pi$
$228$	12.8041	0.847969
$229$	17.0199	1.12471	0.562354	−	0.826897i	$-0.309896\pi$
$229$	17.0199	1.12471	0.562354	+	0.826897i	$0.309896\pi$
$230$	0	0
$231$	−21.8451	−1.43730
$232$	2.25138	0.147810
$233$	6.23742	0.408627	0.204313	−	0.978906i	$-0.434504\pi$
$233$	6.23742	0.408627	0.204313	+	0.978906i	$0.434504\pi$
$234$	−20.9818	−1.37162
$235$	10.6363	0.693834
$236$	−3.21219	−0.209096
$237$	19.4028	1.26035
$238$	12.2417	0.793509
$239$	10.8435	0.701409	0.350704	−	0.936486i	$-0.385942\pi$
$239$	10.8435	0.701409	0.350704	+	0.936486i	$0.385942\pi$
$240$	3.36041	0.216914
$241$	13.4385	0.865652	0.432826	−	0.901477i	$-0.357516\pi$
$241$	13.4385	0.865652	0.432826	+	0.901477i	$0.357516\pi$
$242$	−2.87625	−0.184892
$243$	63.8784	4.09780
$244$	−0.432976	−0.0277184
$245$	−1.79803	−0.114872
$246$	−21.3185	−1.35922
$247$	−9.64095	−0.613439
$248$	8.13074	0.516302
$249$	30.9678	1.96250
$250$	1.00000	0.0632456
$251$	1.25526	0.0792314	0.0396157	−	0.999215i	$-0.487387\pi$
$251$	1.25526	0.0792314	0.0396157	+	0.999215i	$0.487387\pi$
$252$	−18.9131	−1.19141
$253$	0	0
$254$	15.0035	0.941406
$255$	−18.0364	−1.12948
$256$	1.00000	0.0625000
$257$	−17.1950	−1.07260	−0.536298	−	0.844029i	$-0.680178\pi$
$257$	−17.1950	−1.07260	−0.536298	+	0.844029i	$0.680178\pi$
$258$	−22.3835	−1.39354
$259$	0.656595	0.0407989
$260$	−2.53026	−0.156920
$261$	18.6692	1.15560
$262$	4.42611	0.273446
$263$	8.43147	0.519907	0.259953	−	0.965621i	$-0.416293\pi$
$263$	8.43147	0.519907	0.259953	+	0.965621i	$0.416293\pi$
$264$	9.57791	0.589480
$265$	11.3038	0.694388
$266$	−8.69038	−0.532841
$267$	−59.1184	−3.61799
$268$	3.21516	0.196397
$269$	−4.00209	−0.244012	−0.122006	−	0.992529i	$-0.538933\pi$
$269$	−4.00209	−0.244012	−0.122006	+	0.992529i	$0.538933\pi$
$270$	17.7845	1.08233
$271$	10.8739	0.660542	0.330271	−	0.943886i	$-0.392860\pi$
$271$	10.8739	0.660542	0.330271	+	0.943886i	$0.392860\pi$
$272$	−5.36731	−0.325441
$273$	19.3928	1.17371
$274$	9.35873	0.565381
$275$	2.85022	0.171875
$276$	0	0
$277$	16.7413	1.00589	0.502944	−	0.864319i	$-0.332250\pi$
$277$	16.7413	1.00589	0.502944	+	0.864319i	$0.332250\pi$
$278$	−6.15826	−0.369348
$279$	67.4230	4.03651
$280$	−2.28078	−0.136303
$281$	11.4212	0.681333	0.340666	−	0.940184i	$-0.389347\pi$
$281$	11.4212	0.681333	0.340666	+	0.940184i	$0.389347\pi$
$282$	35.7423	2.12842
$283$	−23.1309	−1.37499	−0.687494	−	0.726191i	$-0.741289\pi$
$283$	−23.1309	−1.37499	−0.687494	+	0.726191i	$0.741289\pi$
$284$	1.82598	0.108352
$285$	12.8041	0.758447
$286$	−7.21179	−0.426442
$287$	14.4693	0.854098
$288$	8.29236	0.488632
$289$	11.8080	0.694587
$290$	2.25138	0.132205
$291$	17.2609	1.01185
$292$	−12.2217	−0.715222
$293$	−8.50515	−0.496876	−0.248438	−	0.968648i	$-0.579917\pi$
$293$	−8.50515	−0.496876	−0.248438	+	0.968648i	$0.579917\pi$
$294$	−6.04213	−0.352384
$295$	−3.21219	−0.187021
$296$	−0.287882	−0.0167328
$297$	50.6898	2.94132
$298$	−15.0093	−0.869463
$299$	0	0
$300$	3.36041	0.194013
$301$	15.1922	0.875661
$302$	−6.42011	−0.369436
$303$	−15.4245	−0.886113
$304$	3.81026	0.218534
$305$	−0.432976	−0.0247921
$306$	−44.5077	−2.54433
$307$	14.3619	0.819675	0.409837	−	0.912159i	$-0.365585\pi$
$307$	14.3619	0.819675	0.409837	+	0.912159i	$0.365585\pi$
$308$	−6.50073	−0.370414
$309$	−29.1975	−1.66099
$310$	8.13074	0.461795
$311$	9.84225	0.558103	0.279051	−	0.960276i	$-0.409980\pi$
$311$	9.84225	0.558103	0.279051	+	0.960276i	$0.409980\pi$
$312$	−8.50271	−0.481371
$313$	−17.9182	−1.01279	−0.506397	−	0.862301i	$-0.669023\pi$
$313$	−17.9182	−1.01279	−0.506397	+	0.862301i	$0.669023\pi$
$314$	−4.25236	−0.239975
$315$	−18.9131	−1.06563
$316$	5.77393	0.324809
$317$	27.7037	1.55599	0.777997	−	0.628268i	$-0.216236\pi$
$317$	27.7037	1.55599	0.777997	+	0.628268i	$0.216236\pi$
$318$	37.9855	2.13012
$319$	6.41691	0.359278
$320$	1.00000	0.0559017
$321$	−3.97205	−0.221698
$322$	0	0
$323$	−20.4509	−1.13792
$324$	34.8862	1.93812
$325$	−2.53026	−0.140353
$326$	−4.15333	−0.230031
$327$	9.75874	0.539660
$328$	−6.34402	−0.350290
$329$	−24.2590	−1.33744
$330$	9.57791	0.527247
$331$	6.04553	0.332293	0.166146	−	0.986101i	$-0.446868\pi$
$331$	6.04553	0.332293	0.166146	+	0.986101i	$0.446868\pi$
$332$	9.21547	0.505765
$333$	−2.38722	−0.130819
$334$	−20.3207	−1.11190
$335$	3.21516	0.175663
$336$	−7.66437	−0.418125
$337$	6.41981	0.349709	0.174855	−	0.984594i	$-0.444054\pi$
$337$	6.41981	0.349709	0.174855	+	0.984594i	$0.444054\pi$
$338$	−6.59780	−0.358873
$339$	−68.1427	−3.70100
$340$	−5.36731	−0.291083
$341$	23.1744	1.25496
$342$	31.5961	1.70852
$343$	20.0664	1.08348
$344$	−6.66094	−0.359134
$345$	0	0
$346$	−1.71238	−0.0920580
$347$	−27.5602	−1.47951	−0.739755	−	0.672876i	$-0.765059\pi$
$347$	−27.5602	−1.47951	−0.739755	+	0.672876i	$0.765059\pi$
$348$	7.56555	0.405556
$349$	−1.03754	−0.0555382	−0.0277691	−	0.999614i	$-0.508840\pi$
$349$	−1.03754	−0.0555382	−0.0277691	+	0.999614i	$0.508840\pi$
$350$	−2.28078	−0.121913
$351$	−44.9994	−2.40189
$352$	2.85022	0.151917
$353$	−12.3822	−0.659035	−0.329518	−	0.944149i	$-0.606886\pi$
$353$	−12.3822	−0.659035	−0.329518	+	0.944149i	$0.606886\pi$
$354$	−10.7943	−0.573709
$355$	1.82598	0.0969130
$356$	−17.5926	−0.932407
$357$	41.1370	2.17720
$358$	−8.49218	−0.448826
$359$	−20.3944	−1.07637	−0.538187	−	0.842825i	$-0.680891\pi$
$359$	−20.3944	−1.07637	−0.538187	+	0.842825i	$0.680891\pi$
$360$	8.29236	0.437046
$361$	−4.48189	−0.235889
$362$	−2.19346	−0.115286
$363$	−9.66537	−0.507300
$364$	5.77097	0.302481
$365$	−12.2217	−0.639714
$366$	−1.45498	−0.0760528
$367$	−11.4610	−0.598258	−0.299129	−	0.954213i	$-0.596696\pi$
$367$	−11.4610	−0.598258	−0.299129	+	0.954213i	$0.596696\pi$
$368$	0	0
$369$	−52.6069	−2.73861
$370$	−0.287882	−0.0149663
$371$	−25.7816	−1.33851
$372$	27.3226	1.41661
$373$	10.7172	0.554914	0.277457	−	0.960738i	$-0.410508\pi$
$373$	10.7172	0.554914	0.277457	+	0.960738i	$0.410508\pi$
$374$	−15.2980	−0.791041
$375$	3.36041	0.173531
$376$	10.6363	0.548524
$377$	−5.69656	−0.293388
$378$	−40.5626	−2.08632
$379$	−2.33545	−0.119964	−0.0599819	−	0.998199i	$-0.519104\pi$
$379$	−2.33545	−0.119964	−0.0599819	+	0.998199i	$0.519104\pi$
$380$	3.81026	0.195462
$381$	50.4181	2.58300
$382$	5.19440	0.265768
$383$	−15.8767	−0.811264	−0.405632	−	0.914037i	$-0.632948\pi$
$383$	−15.8767	−0.811264	−0.405632	+	0.914037i	$0.632948\pi$
$384$	3.36041	0.171485
$385$	−6.50073	−0.331308
$386$	−25.3700	−1.29130
$387$	−55.2349	−2.80775
$388$	5.13654	0.260768
$389$	−19.7966	−1.00373	−0.501864	−	0.864947i	$-0.667352\pi$
$389$	−19.7966	−1.00373	−0.501864	+	0.864947i	$0.667352\pi$
$390$	−8.50271	−0.430551
$391$	0	0
$392$	−1.79803	−0.0908144
$393$	14.8736	0.750272
$394$	−24.8721	−1.25304
$395$	5.77393	0.290518
$396$	23.6351	1.18771
$397$	−6.82962	−0.342769	−0.171384	−	0.985204i	$-0.554824\pi$
$397$	−6.82962	−0.342769	−0.171384	+	0.985204i	$0.554824\pi$
$398$	9.17006	0.459654
$399$	−29.2033	−1.46199
$400$	1.00000	0.0500000
$401$	16.0428	0.801141	0.400570	−	0.916266i	$-0.368812\pi$
$401$	16.0428	0.801141	0.400570	+	0.916266i	$0.368812\pi$
$402$	10.8042	0.538867
$403$	−20.5729	−1.02481
$404$	−4.59006	−0.228364
$405$	34.8862	1.73351
$406$	−5.13490	−0.254841
$407$	−0.820526	−0.0406720
$408$	−18.0364	−0.892933
$409$	−21.9889	−1.08728	−0.543640	−	0.839319i	$-0.682954\pi$
$409$	−21.9889	−1.08728	−0.543640	+	0.839319i	$0.682954\pi$
$410$	−6.34402	−0.313309
$411$	31.4492	1.55127
$412$	−8.68867	−0.428060
$413$	7.32630	0.360504
$414$	0	0
$415$	9.21547	0.452370
$416$	−2.53026	−0.124056
$417$	−20.6943	−1.01340
$418$	10.8601	0.531184
$419$	16.0146	0.782365	0.391183	−	0.920313i	$-0.372066\pi$
$419$	16.0146	0.782365	0.391183	+	0.920313i	$0.372066\pi$
$420$	−7.66437	−0.373983
$421$	27.6179	1.34601	0.673007	−	0.739636i	$-0.265002\pi$
$421$	27.6179	1.34601	0.673007	+	0.739636i	$0.265002\pi$
$422$	−9.96457	−0.485068
$423$	88.1999	4.28843
$424$	11.3038	0.548962
$425$	−5.36731	−0.260353
$426$	6.13605	0.297292
$427$	0.987523	0.0477896
$428$	−1.18201	−0.0571348
$429$	−24.2346	−1.17006
$430$	−6.66094	−0.321219
$431$	−7.93971	−0.382442	−0.191221	−	0.981547i	$-0.561245\pi$
$431$	−7.93971	−0.382442	−0.191221	+	0.981547i	$0.561245\pi$
$432$	17.7845	0.855658
$433$	25.4879	1.22487	0.612435	−	0.790521i	$-0.290190\pi$
$433$	25.4879	1.22487	0.612435	+	0.790521i	$0.290190\pi$
$434$	−18.5444	−0.890162
$435$	7.56555	0.362740
$436$	2.90403	0.139078
$437$	0	0
$438$	−41.0700	−1.96240
$439$	31.2523	1.49159	0.745796	−	0.666175i	$-0.232070\pi$
$439$	31.2523	1.49159	0.745796	+	0.666175i	$0.232070\pi$
$440$	2.85022	0.135879
$441$	−14.9099	−0.709997
$442$	13.5807	0.645967
$443$	−21.3332	−1.01357	−0.506786	−	0.862072i	$-0.669167\pi$
$443$	−21.3332	−1.01357	−0.506786	+	0.862072i	$0.669167\pi$
$444$	−0.967401	−0.0459108
$445$	−17.5926	−0.833970
$446$	−17.6887	−0.837585
$447$	−50.4373	−2.38560
$448$	−2.28078	−0.107757
$449$	18.7895	0.886733	0.443366	−	0.896341i	$-0.353784\pi$
$449$	18.7895	0.886733	0.443366	+	0.896341i	$0.353784\pi$
$450$	8.29236	0.390906
$451$	−18.0819	−0.851442
$452$	−20.2781	−0.953801
$453$	−21.5742	−1.01365
$454$	17.9461	0.842251
$455$	5.77097	0.270547
$456$	12.8041	0.599605
$457$	−7.81719	−0.365673	−0.182836	−	0.983143i	$-0.558528\pi$
$457$	−7.81719	−0.365673	−0.182836	+	0.983143i	$0.558528\pi$
$458$	17.0199	0.795288
$459$	−95.4550	−4.45546
$460$	0	0
$461$	12.9203	0.601759	0.300879	−	0.953662i	$-0.402720\pi$
$461$	12.9203	0.601759	0.300879	+	0.953662i	$0.402720\pi$
$462$	−21.8451	−1.01633
$463$	−30.7375	−1.42849	−0.714246	−	0.699895i	$-0.753230\pi$
$463$	−30.7375	−1.42849	−0.714246	+	0.699895i	$0.753230\pi$
$464$	2.25138	0.104517
$465$	27.3226	1.26706
$466$	6.23742	0.288943
$467$	−37.9469	−1.75597	−0.877987	−	0.478684i	$-0.841114\pi$
$467$	−37.9469	−1.75597	−0.877987	+	0.478684i	$0.841114\pi$
$468$	−20.9818	−0.969885
$469$	−7.33307	−0.338610
$470$	10.6363	0.490615
$471$	−14.2897	−0.658434
$472$	−3.21219	−0.147853
$473$	−18.9851	−0.872938
$474$	19.4028	0.891199
$475$	3.81026	0.174827
$476$	12.2417	0.561096
$477$	93.7354	4.29185
$478$	10.8435	0.495971
$479$	−5.95372	−0.272032	−0.136016	−	0.990707i	$-0.543430\pi$
$479$	−5.95372	−0.272032	−0.136016	+	0.990707i	$0.543430\pi$
$480$	3.36041	0.153381
$481$	0.728415	0.0332129
$482$	13.4385	0.612108
$483$	0	0
$484$	−2.87625	−0.130738
$485$	5.13654	0.233238
$486$	63.8784	2.89758
$487$	5.99757	0.271776	0.135888	−	0.990724i	$-0.456611\pi$
$487$	5.99757	0.271776	0.135888	+	0.990724i	$0.456611\pi$
$488$	−0.432976	−0.0195999
$489$	−13.9569	−0.631152
$490$	−1.79803	−0.0812268
$491$	31.1270	1.40474	0.702371	−	0.711811i	$-0.252125\pi$
$491$	31.1270	1.40474	0.702371	+	0.711811i	$0.252125\pi$
$492$	−21.3185	−0.961113
$493$	−12.0838	−0.544228
$494$	−9.64095	−0.433767
$495$	23.6351	1.06232
$496$	8.13074	0.365081
$497$	−4.16467	−0.186811
$498$	30.9678	1.38770
$499$	33.5490	1.50186	0.750930	−	0.660381i	$-0.229605\pi$
$499$	33.5490	1.50186	0.750930	+	0.660381i	$0.229605\pi$
$500$	1.00000	0.0447214
$501$	−68.2859	−3.05079
$502$	1.25526	0.0560251
$503$	−36.8967	−1.64514	−0.822572	−	0.568661i	$-0.807461\pi$
$503$	−36.8967	−1.64514	−0.822572	+	0.568661i	$0.807461\pi$
$504$	−18.9131	−0.842455
$505$	−4.59006	−0.204255
$506$	0	0
$507$	−22.1713	−0.984662
$508$	15.0035	0.665674
$509$	12.3996	0.549603	0.274801	−	0.961501i	$-0.411388\pi$
$509$	12.3996	0.549603	0.274801	+	0.961501i	$0.411388\pi$
$510$	−18.0364	−0.798663
$511$	27.8751	1.23312
$512$	1.00000	0.0441942
$513$	67.7637	2.99184
$514$	−17.1950	−0.758440
$515$	−8.68867	−0.382869
$516$	−22.3835	−0.985378
$517$	30.3157	1.33328
$518$	0.656595	0.0288491
$519$	−5.75429	−0.252585
$520$	−2.53026	−0.110959
$521$	−11.3060	−0.495324	−0.247662	−	0.968846i	$-0.579662\pi$
$521$	−11.3060	−0.495324	−0.247662	+	0.968846i	$0.579662\pi$
$522$	18.6692	0.817130
$523$	20.3456	0.889652	0.444826	−	0.895617i	$-0.353265\pi$
$523$	20.3456	0.889652	0.444826	+	0.895617i	$0.353265\pi$
$524$	4.42611	0.193356
$525$	−7.66437	−0.334500
$526$	8.43147	0.367629
$527$	−43.6402	−1.90100
$528$	9.57791	0.416825
$529$	0	0
$530$	11.3038	0.491007
$531$	−26.6366	−1.15593
$532$	−8.69038	−0.376776
$533$	16.0520	0.695290
$534$	−59.1184	−2.55830
$535$	−1.18201	−0.0511029
$536$	3.21516	0.138874
$537$	−28.5372	−1.23147
$538$	−4.00209	−0.172543
$539$	−5.12479	−0.220740
$540$	17.7845	0.765324
$541$	−4.44851	−0.191256	−0.0956282	−	0.995417i	$-0.530486\pi$
$541$	−4.44851	−0.191256	−0.0956282	+	0.995417i	$0.530486\pi$
$542$	10.8739	0.467074
$543$	−7.37093	−0.316317
$544$	−5.36731	−0.230121
$545$	2.90403	0.124395
$546$	19.3928	0.829936
$547$	−17.2602	−0.737993	−0.368996	−	0.929431i	$-0.620299\pi$
$547$	−17.2602	−0.737993	−0.368996	+	0.929431i	$0.620299\pi$
$548$	9.35873	0.399785
$549$	−3.59039	−0.153234
$550$	2.85022	0.121534
$551$	8.57833	0.365449
$552$	0	0
$553$	−13.1691	−0.560006
$554$	16.7413	0.711270
$555$	−0.967401	−0.0410639
$556$	−6.15826	−0.261169
$557$	16.3183	0.691426	0.345713	−	0.938340i	$-0.387637\pi$
$557$	16.3183	0.691426	0.345713	+	0.938340i	$0.387637\pi$
$558$	67.4230	2.85424
$559$	16.8539	0.712844
$560$	−2.28078	−0.0963806
$561$	−51.4076	−2.17043
$562$	11.4212	0.481775
$563$	32.2816	1.36051	0.680253	−	0.732977i	$-0.261870\pi$
$563$	32.2816	1.36051	0.680253	+	0.732977i	$0.261870\pi$
$564$	35.7423	1.50502
$565$	−20.2781	−0.853106
$566$	−23.1309	−0.972263
$567$	−79.5678	−3.34153
$568$	1.82598	0.0766165
$569$	−42.4295	−1.77874	−0.889369	−	0.457190i	$-0.848856\pi$
$569$	−42.4295	−1.77874	−0.889369	+	0.457190i	$0.848856\pi$
$570$	12.8041	0.536303
$571$	30.8798	1.29228	0.646139	−	0.763220i	$-0.276383\pi$
$571$	30.8798	1.29228	0.646139	+	0.763220i	$0.276383\pi$
$572$	−7.21179	−0.301540
$573$	17.4553	0.729206
$574$	14.4693	0.603938
$575$	0	0
$576$	8.29236	0.345515
$577$	36.5932	1.52339	0.761697	−	0.647933i	$-0.224366\pi$
$577$	36.5932	1.52339	0.761697	+	0.647933i	$0.224366\pi$
$578$	11.8080	0.491148
$579$	−85.2536	−3.54302
$580$	2.25138	0.0934833
$581$	−21.0185	−0.871994
$582$	17.2609	0.715487
$583$	32.2184	1.33435
$584$	−12.2217	−0.505738
$585$	−20.9818	−0.867491
$586$	−8.50515	−0.351344
$587$	0.534685	0.0220688	0.0110344	−	0.999939i	$-0.496488\pi$
$587$	0.534685	0.0220688	0.0110344	+	0.999939i	$0.496488\pi$
$588$	−6.04213	−0.249173
$589$	30.9803	1.27652
$590$	−3.21219	−0.132244
$591$	−83.5804	−3.43804
$592$	−0.287882	−0.0118319
$593$	−1.67387	−0.0687376	−0.0343688	−	0.999409i	$-0.510942\pi$
$593$	−1.67387	−0.0687376	−0.0343688	+	0.999409i	$0.510942\pi$
$594$	50.6898	2.07983
$595$	12.2417	0.501859
$596$	−15.0093	−0.614804
$597$	30.8152	1.26118
$598$	0	0
$599$	8.68552	0.354881	0.177440	−	0.984132i	$-0.443218\pi$
$599$	8.68552	0.354881	0.177440	+	0.984132i	$0.443218\pi$
$600$	3.36041	0.137188
$601$	−5.79457	−0.236366	−0.118183	−	0.992992i	$-0.537707\pi$
$601$	−5.79457	−0.236366	−0.118183	+	0.992992i	$0.537707\pi$
$602$	15.1922	0.619186
$603$	26.6612	1.08573
$604$	−6.42011	−0.261231
$605$	−2.87625	−0.116936
$606$	−15.4245	−0.626576
$607$	−31.6272	−1.28371	−0.641854	−	0.766827i	$-0.721835\pi$
$607$	−31.6272	−1.28371	−0.641854	+	0.766827i	$0.721835\pi$
$608$	3.81026	0.154527
$609$	−17.2554	−0.699223
$610$	−0.432976	−0.0175307
$611$	−26.9125	−1.08876
$612$	−44.5077	−1.79912
$613$	−21.0154	−0.848803	−0.424402	−	0.905474i	$-0.639516\pi$
$613$	−21.0154	−0.848803	−0.424402	+	0.905474i	$0.639516\pi$
$614$	14.3619	0.579597
$615$	−21.3185	−0.859646
$616$	−6.50073	−0.261922
$617$	9.22401	0.371345	0.185672	−	0.982612i	$-0.440554\pi$
$617$	9.22401	0.371345	0.185672	+	0.982612i	$0.440554\pi$
$618$	−29.1975	−1.17450
$619$	−26.7089	−1.07352	−0.536760	−	0.843735i	$-0.680352\pi$
$619$	−26.7089	−1.07352	−0.536760	+	0.843735i	$0.680352\pi$
$620$	8.13074	0.326538
$621$	0	0
$622$	9.84225	0.394638
$623$	40.1249	1.60757
$624$	−8.50271	−0.340381
$625$	1.00000	0.0400000
$626$	−17.9182	−0.716153
$627$	36.4944	1.45744
$628$	−4.25236	−0.169688
$629$	1.54515	0.0616091
$630$	−18.9131	−0.753515
$631$	−21.9214	−0.872676	−0.436338	−	0.899783i	$-0.643725\pi$
$631$	−21.9214	−0.872676	−0.436338	+	0.899783i	$0.643725\pi$
$632$	5.77393	0.229675
$633$	−33.4851	−1.33091
$634$	27.7037	1.10025
$635$	15.0035	0.595397
$636$	37.9855	1.50622
$637$	4.54949	0.180257
$638$	6.41691	0.254048
$639$	15.1417	0.598996
$640$	1.00000	0.0395285
$641$	−8.81167	−0.348040	−0.174020	−	0.984742i	$-0.555676\pi$
$641$	−8.81167	−0.348040	−0.174020	+	0.984742i	$0.555676\pi$
$642$	−3.97205	−0.156764
$643$	15.4190	0.608065	0.304033	−	0.952662i	$-0.401667\pi$
$643$	15.4190	0.608065	0.304033	+	0.952662i	$0.401667\pi$
$644$	0	0
$645$	−22.3835	−0.881349
$646$	−20.4509	−0.804628
$647$	−2.66380	−0.104725	−0.0523623	−	0.998628i	$-0.516675\pi$
$647$	−2.66380	−0.104725	−0.0523623	+	0.998628i	$0.516675\pi$
$648$	34.8862	1.37046
$649$	−9.15545	−0.359383
$650$	−2.53026	−0.0992449
$651$	−62.3170	−2.44239
$652$	−4.15333	−0.162657
$653$	5.56658	0.217837	0.108919	−	0.994051i	$-0.465261\pi$
$653$	5.56658	0.217837	0.108919	+	0.994051i	$0.465261\pi$
$654$	9.75874	0.381597
$655$	4.42611	0.172943
$656$	−6.34402	−0.247693
$657$	−101.347	−3.95392
$658$	−24.2590	−0.945716
$659$	35.7936	1.39432	0.697161	−	0.716914i	$-0.254446\pi$
$659$	35.7936	1.39432	0.697161	+	0.716914i	$0.254446\pi$
$660$	9.57791	0.372820
$661$	−5.17573	−0.201313	−0.100656	−	0.994921i	$-0.532094\pi$
$661$	−5.17573	−0.201313	−0.100656	+	0.994921i	$0.532094\pi$
$662$	6.04553	0.234966
$663$	45.6366	1.77238
$664$	9.21547	0.357630
$665$	−8.69038	−0.336999
$666$	−2.38722	−0.0925029
$667$	0	0
$668$	−20.3207	−0.786232
$669$	−59.4414	−2.29814
$670$	3.21516	0.124212
$671$	−1.23408	−0.0476410
$672$	−7.66437	−0.295659
$673$	11.2678	0.434344	0.217172	−	0.976133i	$-0.430317\pi$
$673$	11.2678	0.434344	0.217172	+	0.976133i	$0.430317\pi$
$674$	6.41981	0.247282
$675$	17.7845	0.684526
$676$	−6.59780	−0.253761
$677$	6.38872	0.245538	0.122769	−	0.992435i	$-0.460823\pi$
$677$	6.38872	0.245538	0.122769	+	0.992435i	$0.460823\pi$
$678$	−68.1427	−2.61701
$679$	−11.7153	−0.449593
$680$	−5.36731	−0.205827
$681$	60.3062	2.31094
$682$	23.1744	0.887393
$683$	−14.7968	−0.566184	−0.283092	−	0.959093i	$-0.591360\pi$
$683$	−14.7968	−0.566184	−0.283092	+	0.959093i	$0.591360\pi$
$684$	31.5961	1.20811
$685$	9.35873	0.357579
$686$	20.0664	0.766139
$687$	57.1939	2.18208
$688$	−6.66094	−0.253946
$689$	−28.6016	−1.08963
$690$	0	0
$691$	8.28147	0.315042	0.157521	−	0.987516i	$-0.449650\pi$
$691$	8.28147	0.315042	0.157521	+	0.987516i	$0.449650\pi$
$692$	−1.71238	−0.0650948
$693$	−53.9064	−2.04774
$694$	−27.5602	−1.04617
$695$	−6.15826	−0.233596
$696$	7.56555	0.286771
$697$	34.0503	1.28975
$698$	−1.03754	−0.0392714
$699$	20.9603	0.792791
$700$	−2.28078	−0.0862055
$701$	−27.9501	−1.05566	−0.527831	−	0.849349i	$-0.676995\pi$
$701$	−27.9501	−1.05566	−0.527831	+	0.849349i	$0.676995\pi$
$702$	−44.9994	−1.69839
$703$	−1.09691	−0.0413706
$704$	2.85022	0.107422
$705$	35.7423	1.34613
$706$	−12.3822	−0.466008
$707$	10.4689	0.393724
$708$	−10.7943	−0.405674
$709$	−43.5319	−1.63487	−0.817437	−	0.576018i	$-0.804606\pi$
$709$	−43.5319	−1.63487	−0.817437	+	0.576018i	$0.804606\pi$
$710$	1.82598	0.0685279
$711$	47.8795	1.79562
$712$	−17.5926	−0.659311
$713$	0	0
$714$	41.1370	1.53951
$715$	−7.21179	−0.269706
$716$	−8.49218	−0.317368
$717$	36.4387	1.36083
$718$	−20.3944	−0.761111
$719$	37.3220	1.39187	0.695937	−	0.718102i	$-0.254989\pi$
$719$	37.3220	1.39187	0.695937	+	0.718102i	$0.254989\pi$
$720$	8.29236	0.309038
$721$	19.8170	0.738023
$722$	−4.48189	−0.166799
$723$	45.1590	1.67948
$724$	−2.19346	−0.0815194
$725$	2.25138	0.0836140
$726$	−9.66537	−0.358715
$727$	36.7138	1.36164	0.680820	−	0.732451i	$-0.261624\pi$
$727$	36.7138	1.36164	0.680820	+	0.732451i	$0.261624\pi$
$728$	5.77097	0.213886
$729$	109.999	4.07404
$730$	−12.2217	−0.452346
$731$	35.7513	1.32231
$732$	−1.45498	−0.0537775
$733$	35.3307	1.30497	0.652484	−	0.757802i	$-0.273727\pi$
$733$	35.3307	1.30497	0.652484	+	0.757802i	$0.273727\pi$
$734$	−11.4610	−0.423032
$735$	−6.04213	−0.222867
$736$	0	0
$737$	9.16390	0.337557
$738$	−52.6069	−1.93649
$739$	3.57286	0.131430	0.0657149	−	0.997838i	$-0.479067\pi$
$739$	3.57286	0.131430	0.0657149	+	0.997838i	$0.479067\pi$
$740$	−0.287882	−0.0105827
$741$	−32.3975	−1.19015
$742$	−25.7816	−0.946471
$743$	10.9990	0.403516	0.201758	−	0.979435i	$-0.435335\pi$
$743$	10.9990	0.403516	0.201758	+	0.979435i	$0.435335\pi$
$744$	27.3226	1.00170
$745$	−15.0093	−0.549897
$746$	10.7172	0.392383
$747$	76.4180	2.79599
$748$	−15.2980	−0.559351
$749$	2.69592	0.0985066
$750$	3.36041	0.122705
$751$	43.3226	1.58086	0.790432	−	0.612550i	$-0.209856\pi$
$751$	43.3226	1.58086	0.790432	+	0.612550i	$0.209856\pi$
$752$	10.6363	0.387865
$753$	4.21819	0.153720
$754$	−5.69656	−0.207456
$755$	−6.42011	−0.233652
$756$	−40.5626	−1.47525
$757$	41.8273	1.52024	0.760119	−	0.649784i	$-0.225141\pi$
$757$	41.8273	1.52024	0.760119	+	0.649784i	$0.225141\pi$
$758$	−2.33545	−0.0848272
$759$	0	0
$760$	3.81026	0.138213
$761$	−35.8075	−1.29802	−0.649011	−	0.760779i	$-0.724817\pi$
$761$	−35.8075	−1.29802	−0.649011	+	0.760779i	$0.724817\pi$
$762$	50.4181	1.82645
$763$	−6.62346	−0.239786
$764$	5.19440	0.187927
$765$	−44.5077	−1.60918
$766$	−15.8767	−0.573650
$767$	8.12767	0.293473
$768$	3.36041	0.121258
$769$	2.66369	0.0960552	0.0480276	−	0.998846i	$-0.484706\pi$
$769$	2.66369	0.0960552	0.0480276	+	0.998846i	$0.484706\pi$
$770$	−6.50073	−0.234270
$771$	−57.7824	−2.08098
$772$	−25.3700	−0.913086
$773$	−20.4636	−0.736025	−0.368013	−	0.929821i	$-0.619962\pi$
$773$	−20.4636	−0.736025	−0.368013	+	0.929821i	$0.619962\pi$
$774$	−55.2349	−1.98538
$775$	8.13074	0.292065
$776$	5.13654	0.184391
$777$	2.20643	0.0791553
$778$	−19.7966	−0.709742
$779$	−24.1724	−0.866066
$780$	−8.50271	−0.304446
$781$	5.20445	0.186230
$782$	0	0
$783$	40.0396	1.43090
$784$	−1.79803	−0.0642154
$785$	−4.25236	−0.151773
$786$	14.8736	0.530522
$787$	0.868120	0.0309451	0.0154726	−	0.999880i	$-0.495075\pi$
$787$	0.868120	0.0309451	0.0154726	+	0.999880i	$0.495075\pi$
$788$	−24.8721	−0.886032
$789$	28.3332	1.00869
$790$	5.77393	0.205427
$791$	46.2499	1.64446
$792$	23.6351	0.839835
$793$	1.09554	0.0389038
$794$	−6.82962	−0.242374
$795$	37.9855	1.34721
$796$	9.17006	0.325024
$797$	−10.6031	−0.375581	−0.187790	−	0.982209i	$-0.560133\pi$
$797$	−10.6031	−0.375581	−0.187790	+	0.982209i	$0.560133\pi$
$798$	−29.2033	−1.03378
$799$	−57.0882	−2.01963
$800$	1.00000	0.0353553
$801$	−145.884	−5.15457
$802$	16.0428	0.566492
$803$	−34.8346	−1.22929
$804$	10.8042	0.381036
$805$	0	0
$806$	−20.5729	−0.724648
$807$	−13.4487	−0.473416
$808$	−4.59006	−0.161478
$809$	41.5541	1.46096	0.730482	−	0.682932i	$-0.239296\pi$
$809$	41.5541	1.46096	0.730482	+	0.682932i	$0.239296\pi$
$810$	34.8862	1.22578
$811$	−10.0211	−0.351890	−0.175945	−	0.984400i	$-0.556298\pi$
$811$	−10.0211	−0.351890	−0.175945	+	0.984400i	$0.556298\pi$
$812$	−5.13490	−0.180200
$813$	36.5408	1.28154
$814$	−0.820526	−0.0287594
$815$	−4.15333	−0.145485
$816$	−18.0364	−0.631399
$817$	−25.3799	−0.887932
$818$	−21.9889	−0.768823
$819$	47.8549	1.67219
$820$	−6.34402	−0.221543
$821$	38.7780	1.35336	0.676681	−	0.736277i	$-0.263418\pi$
$821$	38.7780	1.35336	0.676681	+	0.736277i	$0.263418\pi$
$822$	31.4492	1.09692
$823$	46.9517	1.63663	0.818317	−	0.574768i	$-0.194908\pi$
$823$	46.9517	1.63663	0.818317	+	0.574768i	$0.194908\pi$
$824$	−8.68867	−0.302684
$825$	9.57791	0.333460
$826$	7.32630	0.254915
$827$	36.7382	1.27751	0.638756	−	0.769409i	$-0.279449\pi$
$827$	36.7382	1.27751	0.638756	+	0.769409i	$0.279449\pi$
$828$	0	0
$829$	−2.22627	−0.0773216	−0.0386608	−	0.999252i	$-0.512309\pi$
$829$	−2.22627	−0.0773216	−0.0386608	+	0.999252i	$0.512309\pi$
$830$	9.21547	0.319874
$831$	56.2577	1.95156
$832$	−2.53026	−0.0877209
$833$	9.65059	0.334373
$834$	−20.6943	−0.716585
$835$	−20.3207	−0.703227
$836$	10.8601	0.375604
$837$	144.601	4.99815
$838$	16.0146	0.553216
$839$	−4.79210	−0.165442	−0.0827208	−	0.996573i	$-0.526361\pi$
$839$	−4.79210	−0.165442	−0.0827208	+	0.996573i	$0.526361\pi$
$840$	−7.66437	−0.264446
$841$	−23.9313	−0.825218
$842$	27.6179	0.951776
$843$	38.3800	1.32188
$844$	−9.96457	−0.342995
$845$	−6.59780	−0.226971
$846$	88.1999	3.03237
$847$	6.56009	0.225407
$848$	11.3038	0.388175
$849$	−77.7292	−2.66766
$850$	−5.36731	−0.184097
$851$	0	0
$852$	6.13605	0.210218
$853$	−0.821422	−0.0281250	−0.0140625	−	0.999901i	$-0.504476\pi$
$853$	−0.821422	−0.0281250	−0.0140625	+	0.999901i	$0.504476\pi$
$854$	0.987523	0.0337924
$855$	31.5961	1.08056
$856$	−1.18201	−0.0404004
$857$	−2.06571	−0.0705631	−0.0352816	−	0.999377i	$-0.511233\pi$
$857$	−2.06571	−0.0705631	−0.0352816	+	0.999377i	$0.511233\pi$
$858$	−24.2346	−0.827355
$859$	0.844903	0.0288277	0.0144139	−	0.999896i	$-0.495412\pi$
$859$	0.844903	0.0288277	0.0144139	+	0.999896i	$0.495412\pi$
$860$	−6.66094	−0.227136
$861$	48.6229	1.65706
$862$	−7.93971	−0.270428
$863$	−5.42892	−0.184803	−0.0924013	−	0.995722i	$-0.529454\pi$
$863$	−5.42892	−0.184803	−0.0924013	+	0.995722i	$0.529454\pi$
$864$	17.7845	0.605041
$865$	−1.71238	−0.0582226
$866$	25.4879	0.866114
$867$	39.6797	1.34759
$868$	−18.5444	−0.629439
$869$	16.4570	0.558265
$870$	7.56555	0.256496
$871$	−8.13517	−0.275650
$872$	2.90403	0.0983429
$873$	42.5941	1.44159
$874$	0	0
$875$	−2.28078	−0.0771045
$876$	−41.0700	−1.38763
$877$	−1.97259	−0.0666097	−0.0333048	−	0.999445i	$-0.510603\pi$
$877$	−1.97259	−0.0666097	−0.0333048	+	0.999445i	$0.510603\pi$
$878$	31.2523	1.05471
$879$	−28.5808	−0.964006
$880$	2.85022	0.0960809
$881$	12.9925	0.437727	0.218864	−	0.975755i	$-0.429765\pi$
$881$	12.9925	0.437727	0.218864	+	0.975755i	$0.429765\pi$
$882$	−14.9099	−0.502044
$883$	−46.3818	−1.56087	−0.780435	−	0.625237i	$-0.785003\pi$
$883$	−46.3818	−1.56087	−0.780435	+	0.625237i	$0.785003\pi$
$884$	13.5807	0.456767
$885$	−10.7943	−0.362846
$886$	−21.3332	−0.716704
$887$	32.8113	1.10170	0.550848	−	0.834605i	$-0.314304\pi$
$887$	32.8113	1.10170	0.550848	+	0.834605i	$0.314304\pi$
$888$	−0.967401	−0.0324638
$889$	−34.2198	−1.14770
$890$	−17.5926	−0.589706
$891$	99.4333	3.33114
$892$	−17.6887	−0.592262
$893$	40.5270	1.35619
$894$	−50.4373	−1.68688
$895$	−8.49218	−0.283862
$896$	−2.28078	−0.0761956
$897$	0	0
$898$	18.7895	0.627015
$899$	18.3053	0.610517
$900$	8.29236	0.276412
$901$	−60.6711	−2.02125
$902$	−18.0819	−0.602060
$903$	51.0519	1.69890
$904$	−20.2781	−0.674439
$905$	−2.19346	−0.0729131
$906$	−21.5742	−0.716755
$907$	−15.2650	−0.506865	−0.253432	−	0.967353i	$-0.581560\pi$
$907$	−15.2650	−0.506865	−0.253432	+	0.967353i	$0.581560\pi$
$908$	17.9461	0.595561
$909$	−38.0624	−1.26245
$910$	5.77097	0.191306
$911$	−26.7893	−0.887568	−0.443784	−	0.896134i	$-0.646364\pi$
$911$	−26.7893	−0.887568	−0.443784	+	0.896134i	$0.646364\pi$
$912$	12.8041	0.423985
$913$	26.2661	0.869282
$914$	−7.81719	−0.258570
$915$	−1.45498	−0.0481000
$916$	17.0199	0.562354
$917$	−10.0950	−0.333366
$918$	−95.4550	−3.15048
$919$	51.0831	1.68508	0.842538	−	0.538637i	$-0.181060\pi$
$919$	51.0831	1.68508	0.842538	+	0.538637i	$0.181060\pi$
$920$	0	0
$921$	48.2617	1.59028
$922$	12.9203	0.425508
$923$	−4.62020	−0.152076
$924$	−21.8451	−0.718652
$925$	−0.287882	−0.00946549
$926$	−30.7375	−1.01010
$927$	−72.0496	−2.36642
$928$	2.25138	0.0739050
$929$	16.7182	0.548507	0.274254	−	0.961657i	$-0.411569\pi$
$929$	16.7182	0.548507	0.274254	+	0.961657i	$0.411569\pi$
$930$	27.3226	0.895944
$931$	−6.85098	−0.224532
$932$	6.23742	0.204313
$933$	33.0740	1.08279
$934$	−37.9469	−1.24166
$935$	−15.2980	−0.500298
$936$	−20.9818	−0.685812
$937$	−51.6104	−1.68604	−0.843019	−	0.537883i	$-0.819224\pi$
$937$	−51.6104	−1.68604	−0.843019	+	0.537883i	$0.819224\pi$
$938$	−7.33307	−0.239433
$939$	−60.2124	−1.96496
$940$	10.6363	0.346917
$941$	1.29941	0.0423594	0.0211797	−	0.999776i	$-0.493258\pi$
$941$	1.29941	0.0423594	0.0211797	+	0.999776i	$0.493258\pi$
$942$	−14.2897	−0.465583
$943$	0	0
$944$	−3.21219	−0.104548
$945$	−40.5626	−1.31950
$946$	−18.9851	−0.617260
$947$	−9.24667	−0.300476	−0.150238	−	0.988650i	$-0.548004\pi$
$947$	−9.24667	−0.300476	−0.150238	+	0.988650i	$0.548004\pi$
$948$	19.4028	0.630173
$949$	30.9241	1.00384
$950$	3.81026	0.123621
$951$	93.0957	3.01884
$952$	12.2417	0.396754
$953$	46.5118	1.50666	0.753332	−	0.657641i	$-0.228445\pi$
$953$	46.5118	1.50666	0.753332	+	0.657641i	$0.228445\pi$
$954$	93.7354	3.03480
$955$	5.19440	0.168087
$956$	10.8435	0.350704
$957$	21.5635	0.697048
$958$	−5.95372	−0.192356
$959$	−21.3452	−0.689273
$960$	3.36041	0.108457
$961$	35.1089	1.13255
$962$	0.728415	0.0234850
$963$	−9.80169	−0.315855
$964$	13.4385	0.432826
$965$	−25.3700	−0.816689
$966$	0	0
$967$	−15.3631	−0.494045	−0.247022	−	0.969010i	$-0.579452\pi$
$967$	−15.3631	−0.494045	−0.247022	+	0.969010i	$0.579452\pi$
$968$	−2.87625	−0.0924460
$969$	−68.7233	−2.20771
$970$	5.13654	0.164924
$971$	53.3756	1.71290	0.856452	−	0.516227i	$-0.172664\pi$
$971$	53.3756	1.71290	0.856452	+	0.516227i	$0.172664\pi$
$972$	63.8784	2.04890
$973$	14.0457	0.450283
$974$	5.99757	0.192174
$975$	−8.50271	−0.272305
$976$	−0.432976	−0.0138592
$977$	−47.0119	−1.50405	−0.752023	−	0.659137i	$-0.770922\pi$
$977$	−47.0119	−1.50405	−0.752023	+	0.659137i	$0.770922\pi$
$978$	−13.9569	−0.446292
$979$	−50.1428	−1.60257
$980$	−1.79803	−0.0574360
$981$	24.0813	0.768856
$982$	31.1270	0.993302
$983$	−2.02732	−0.0646615	−0.0323308	−	0.999477i	$-0.510293\pi$
$983$	−2.02732	−0.0646615	−0.0323308	+	0.999477i	$0.510293\pi$
$984$	−21.3185	−0.679610
$985$	−24.8721	−0.792491
$986$	−12.0838	−0.384827
$987$	−81.5203	−2.59482
$988$	−9.64095	−0.306719
$989$	0	0
$990$	23.6351	0.751171
$991$	28.3418	0.900306	0.450153	−	0.892951i	$-0.351369\pi$
$991$	28.3418	0.900306	0.450153	+	0.892951i	$0.351369\pi$
$992$	8.13074	0.258151
$993$	20.3155	0.644692
$994$	−4.16467	−0.132095
$995$	9.17006	0.290711
$996$	30.9678	0.981251
$997$	−11.7605	−0.372460	−0.186230	−	0.982506i	$-0.559627\pi$
$997$	−11.7605	−0.372460	−0.186230	+	0.982506i	$0.559627\pi$
$998$	33.5490	1.06198
$999$	−5.11984	−0.161984

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5290.2.a.bl.1.15		15
23.11	odd	22		230.2.g.d.121.1	✓	30
23.21	odd	22		230.2.g.d.211.1	yes	30
23.22	odd	2		5290.2.a.bk.1.15		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.g.d.121.1	✓	30	23.11	odd	22
230.2.g.d.211.1	yes	30	23.21	odd	22
5290.2.a.bk.1.15		15	23.22	odd	2
5290.2.a.bl.1.15		15	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:	\( N \)	\(=\)	\( 5290 = 2 \cdot 5 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5290.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +3.36041 q^{3} +1.00000 q^{4} +1.00000 q^{5} +3.36041 q^{6} -2.28078 q^{7} +1.00000 q^{8} +8.29236 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +3.36041 q^{3} +1.00000 q^{4} +1.00000 q^{5} +3.36041 q^{6} -2.28078 q^{7} +1.00000 q^{8} +8.29236 q^{9} +1.00000 q^{10} +2.85022 q^{11} +3.36041 q^{12} -2.53026 q^{13} -2.28078 q^{14} +3.36041 q^{15} +1.00000 q^{16} -5.36731 q^{17} +8.29236 q^{18} +3.81026 q^{19} +1.00000 q^{20} -7.66437 q^{21} +2.85022 q^{22} +3.36041 q^{24} +1.00000 q^{25} -2.53026 q^{26} +17.7845 q^{27} -2.28078 q^{28} +2.25138 q^{29} +3.36041 q^{30} +8.13074 q^{31} +1.00000 q^{32} +9.57791 q^{33} -5.36731 q^{34} -2.28078 q^{35} +8.29236 q^{36} -0.287882 q^{37} +3.81026 q^{38} -8.50271 q^{39} +1.00000 q^{40} -6.34402 q^{41} -7.66437 q^{42} -6.66094 q^{43} +2.85022 q^{44} +8.29236 q^{45} +10.6363 q^{47} +3.36041 q^{48} -1.79803 q^{49} +1.00000 q^{50} -18.0364 q^{51} -2.53026 q^{52} +11.3038 q^{53} +17.7845 q^{54} +2.85022 q^{55} -2.28078 q^{56} +12.8041 q^{57} +2.25138 q^{58} -3.21219 q^{59} +3.36041 q^{60} -0.432976 q^{61} +8.13074 q^{62} -18.9131 q^{63} +1.00000 q^{64} -2.53026 q^{65} +9.57791 q^{66} +3.21516 q^{67} -5.36731 q^{68} -2.28078 q^{70} +1.82598 q^{71} +8.29236 q^{72} -12.2217 q^{73} -0.287882 q^{74} +3.36041 q^{75} +3.81026 q^{76} -6.50073 q^{77} -8.50271 q^{78} +5.77393 q^{79} +1.00000 q^{80} +34.8862 q^{81} -6.34402 q^{82} +9.21547 q^{83} -7.66437 q^{84} -5.36731 q^{85} -6.66094 q^{86} +7.56555 q^{87} +2.85022 q^{88} -17.5926 q^{89} +8.29236 q^{90} +5.77097 q^{91} +27.3226 q^{93} +10.6363 q^{94} +3.81026 q^{95} +3.36041 q^{96} +5.13654 q^{97} -1.79803 q^{98} +23.6351 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q + 15 q^{2} + 5 q^{3} + 15 q^{4} + 15 q^{5} + 5 q^{6} - 4 q^{7} + 15 q^{8} + 28 q^{9}+O(q^{10}) \) 15 * q + 15 * q^2 + 5 * q^3 + 15 * q^4 + 15 * q^5 + 5 * q^6 - 4 * q^7 + 15 * q^8 + 28 * q^9	\( 15 q + 15 q^{2} + 5 q^{3} + 15 q^{4} + 15 q^{5} + 5 q^{6} - 4 q^{7} + 15 q^{8} + 28 q^{9} + 15 q^{10} + 7 q^{11} + 5 q^{12} + 17 q^{13} - 4 q^{14} + 5 q^{15} + 15 q^{16} + 2 q^{17} + 28 q^{18} + 18 q^{19} + 15 q^{20} + 7 q^{22} + 5 q^{24} + 15 q^{25} + 17 q^{26} + 29 q^{27} - 4 q^{28} + 35 q^{29} + 5 q^{30} + 19 q^{31} + 15 q^{32} - 21 q^{33} + 2 q^{34} - 4 q^{35} + 28 q^{36} - 12 q^{37} + 18 q^{38} + 26 q^{39} + 15 q^{40} + 27 q^{41} + 12 q^{43} + 7 q^{44} + 28 q^{45} + 40 q^{47} + 5 q^{48} + 29 q^{49} + 15 q^{50} - 27 q^{51} + 17 q^{52} - 20 q^{53} + 29 q^{54} + 7 q^{55} - 4 q^{56} - 11 q^{57} + 35 q^{58} + 15 q^{59} + 5 q^{60} + 28 q^{61} + 19 q^{62} - 51 q^{63} + 15 q^{64} + 17 q^{65} - 21 q^{66} + 4 q^{67} + 2 q^{68} - 4 q^{70} + 22 q^{71} + 28 q^{72} + 48 q^{73} - 12 q^{74} + 5 q^{75} + 18 q^{76} + 45 q^{77} + 26 q^{78} - 2 q^{79} + 15 q^{80} + 79 q^{81} + 27 q^{82} - 29 q^{83} + 2 q^{85} + 12 q^{86} - 7 q^{87} + 7 q^{88} + 20 q^{89} + 28 q^{90} + 6 q^{91} + 63 q^{93} + 40 q^{94} + 18 q^{95} + 5 q^{96} - 22 q^{97} + 29 q^{98} + 23 q^{99}+O(q^{100}) \) 15 * q + 15 * q^2 + 5 * q^3 + 15 * q^4 + 15 * q^5 + 5 * q^6 - 4 * q^7 + 15 * q^8 + 28 * q^9 + 15 * q^10 + 7 * q^11 + 5 * q^12 + 17 * q^13 - 4 * q^14 + 5 * q^15 + 15 * q^16 + 2 * q^17 + 28 * q^18 + 18 * q^19 + 15 * q^20 + 7 * q^22 + 5 * q^24 + 15 * q^25 + 17 * q^26 + 29 * q^27 - 4 * q^28 + 35 * q^29 + 5 * q^30 + 19 * q^31 + 15 * q^32 - 21 * q^33 + 2 * q^34 - 4 * q^35 + 28 * q^36 - 12 * q^37 + 18 * q^38 + 26 * q^39 + 15 * q^40 + 27 * q^41 + 12 * q^43 + 7 * q^44 + 28 * q^45 + 40 * q^47 + 5 * q^48 + 29 * q^49 + 15 * q^50 - 27 * q^51 + 17 * q^52 - 20 * q^53 + 29 * q^54 + 7 * q^55 - 4 * q^56 - 11 * q^57 + 35 * q^58 + 15 * q^59 + 5 * q^60 + 28 * q^61 + 19 * q^62 - 51 * q^63 + 15 * q^64 + 17 * q^65 - 21 * q^66 + 4 * q^67 + 2 * q^68 - 4 * q^70 + 22 * q^71 + 28 * q^72 + 48 * q^73 - 12 * q^74 + 5 * q^75 + 18 * q^76 + 45 * q^77 + 26 * q^78 - 2 * q^79 + 15 * q^80 + 79 * q^81 + 27 * q^82 - 29 * q^83 + 2 * q^85 + 12 * q^86 - 7 * q^87 + 7 * q^88 + 20 * q^89 + 28 * q^90 + 6 * q^91 + 63 * q^93 + 40 * q^94 + 18 * q^95 + 5 * q^96 - 22 * q^97 + 29 * q^98 + 23 * q^99

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