LMFDB - Embedded newform 6034.2.a.k.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6034,2,Mod(1,6034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6034, 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("6034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6034 = 2 \cdot 7 \cdot 431 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6034.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:	$48.1817325796$
Analytic rank:	$1$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 3 x^{19} - 32 x^{18} + 106 x^{17} + 382 x^{16} - 1495 x^{15} - 1963 x^{14} + 10784 x^{13} + \cdots - 44 $ x^20 - 3x^19 - 32x^18 + 106x^17 + 382x^16 - 1495x^15 - 1963x^14 + 10784x^13 + 2170x^12 - 42069x^11 + 19553x^10 + 84697x^9 - 82713x^8 - 68589x^7 + 118845x^6 - 10051x^5 - 53572x^4 + 25598x^3 - 557x^2 - 1040*x - 44
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Root			$1.26295$ of defining polynomial
Character	$\chi$	$=$	6034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.26295 q^{3} +1.00000 q^{4} -3.04196 q^{5} -1.26295 q^{6} +1.00000 q^{7} -1.00000 q^{8} -1.40496 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.26295 q^{3} +1.00000 q^{4} -3.04196 q^{5} -1.26295 q^{6} +1.00000 q^{7} -1.00000 q^{8} -1.40496 q^{9} +3.04196 q^{10} +3.80970 q^{11} +1.26295 q^{12} +5.43358 q^{13} -1.00000 q^{14} -3.84184 q^{15} +1.00000 q^{16} -4.12883 q^{17} +1.40496 q^{18} -7.58964 q^{19} -3.04196 q^{20} +1.26295 q^{21} -3.80970 q^{22} +2.48712 q^{23} -1.26295 q^{24} +4.25350 q^{25} -5.43358 q^{26} -5.56324 q^{27} +1.00000 q^{28} -9.97299 q^{29} +3.84184 q^{30} +9.59602 q^{31} -1.00000 q^{32} +4.81145 q^{33} +4.12883 q^{34} -3.04196 q^{35} -1.40496 q^{36} +5.29027 q^{37} +7.58964 q^{38} +6.86233 q^{39} +3.04196 q^{40} +2.50267 q^{41} -1.26295 q^{42} -3.18614 q^{43} +3.80970 q^{44} +4.27383 q^{45} -2.48712 q^{46} +10.0340 q^{47} +1.26295 q^{48} +1.00000 q^{49} -4.25350 q^{50} -5.21450 q^{51} +5.43358 q^{52} -2.66684 q^{53} +5.56324 q^{54} -11.5889 q^{55} -1.00000 q^{56} -9.58533 q^{57} +9.97299 q^{58} +3.57925 q^{59} -3.84184 q^{60} -11.2712 q^{61} -9.59602 q^{62} -1.40496 q^{63} +1.00000 q^{64} -16.5287 q^{65} -4.81145 q^{66} +3.98143 q^{67} -4.12883 q^{68} +3.14110 q^{69} +3.04196 q^{70} -11.0600 q^{71} +1.40496 q^{72} -10.2486 q^{73} -5.29027 q^{74} +5.37196 q^{75} -7.58964 q^{76} +3.80970 q^{77} -6.86233 q^{78} +1.78536 q^{79} -3.04196 q^{80} -2.81121 q^{81} -2.50267 q^{82} -4.37140 q^{83} +1.26295 q^{84} +12.5597 q^{85} +3.18614 q^{86} -12.5954 q^{87} -3.80970 q^{88} -11.8145 q^{89} -4.27383 q^{90} +5.43358 q^{91} +2.48712 q^{92} +12.1193 q^{93} -10.0340 q^{94} +23.0874 q^{95} -1.26295 q^{96} +10.1182 q^{97} -1.00000 q^{98} -5.35247 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 20 q^{2} + 3 q^{3} + 20 q^{4} - 3 q^{5} - 3 q^{6} + 20 q^{7} - 20 q^{8} + 13 q^{9}+O(q^{10}) $ 20 * q - 20 * q^2 + 3 * q^3 + 20 * q^4 - 3 * q^5 - 3 * q^6 + 20 * q^7 - 20 * q^8 + 13 * q^9	\( 20 q - 20 q^{2} + 3 q^{3} + 20 q^{4} - 3 q^{5} - 3 q^{6} + 20 q^{7} - 20 q^{8} + 13 q^{9} + 3 q^{10} - 8 q^{11} + 3 q^{12} - 4 q^{13} - 20 q^{14} - 25 q^{15} + 20 q^{16} + 9 q^{17} - 13 q^{18} - 14 q^{19} - 3 q^{20} + 3 q^{21} + 8 q^{22} - 23 q^{23} - 3 q^{24} + 31 q^{25} + 4 q^{26} - 21 q^{27} + 20 q^{28} - 48 q^{29} + 25 q^{30} - q^{31} - 20 q^{32} - 29 q^{33} - 9 q^{34} - 3 q^{35} + 13 q^{36} - q^{37} + 14 q^{38} - q^{39} + 3 q^{40} - 27 q^{41} - 3 q^{42} - 3 q^{43} - 8 q^{44} - 12 q^{45} + 23 q^{46} - 26 q^{47} + 3 q^{48} + 20 q^{49} - 31 q^{50} - 17 q^{51} - 4 q^{52} - 43 q^{53} + 21 q^{54} - 16 q^{55} - 20 q^{56} - 25 q^{57} + 48 q^{58} - 19 q^{59} - 25 q^{60} + 9 q^{61} + q^{62} + 13 q^{63} + 20 q^{64} - 87 q^{65} + 29 q^{66} + 32 q^{67} + 9 q^{68} - 23 q^{69} + 3 q^{70} - 63 q^{71} - 13 q^{72} + 2 q^{73} + q^{74} - 8 q^{75} - 14 q^{76} - 8 q^{77} + q^{78} - 51 q^{79} - 3 q^{80} + 4 q^{81} + 27 q^{82} - 24 q^{83} + 3 q^{84} + 31 q^{85} + 3 q^{86} - 33 q^{87} + 8 q^{88} - 35 q^{89} + 12 q^{90} - 4 q^{91} - 23 q^{92} + 17 q^{93} + 26 q^{94} - 30 q^{95} - 3 q^{96} + 5 q^{97} - 20 q^{98} - 31 q^{99}+O(q^{100}) \) 20 * q - 20 * q^2 + 3 * q^3 + 20 * q^4 - 3 * q^5 - 3 * q^6 + 20 * q^7 - 20 * q^8 + 13 * q^9 + 3 * q^10 - 8 * q^11 + 3 * q^12 - 4 * q^13 - 20 * q^14 - 25 * q^15 + 20 * q^16 + 9 * q^17 - 13 * q^18 - 14 * q^19 - 3 * q^20 + 3 * q^21 + 8 * q^22 - 23 * q^23 - 3 * q^24 + 31 * q^25 + 4 * q^26 - 21 * q^27 + 20 * q^28 - 48 * q^29 + 25 * q^30 - q^31 - 20 * q^32 - 29 * q^33 - 9 * q^34 - 3 * q^35 + 13 * q^36 - q^37 + 14 * q^38 - q^39 + 3 * q^40 - 27 * q^41 - 3 * q^42 - 3 * q^43 - 8 * q^44 - 12 * q^45 + 23 * q^46 - 26 * q^47 + 3 * q^48 + 20 * q^49 - 31 * q^50 - 17 * q^51 - 4 * q^52 - 43 * q^53 + 21 * q^54 - 16 * q^55 - 20 * q^56 - 25 * q^57 + 48 * q^58 - 19 * q^59 - 25 * q^60 + 9 * q^61 + q^62 + 13 * q^63 + 20 * q^64 - 87 * q^65 + 29 * q^66 + 32 * q^67 + 9 * q^68 - 23 * q^69 + 3 * q^70 - 63 * q^71 - 13 * q^72 + 2 * q^73 + q^74 - 8 * q^75 - 14 * q^76 - 8 * q^77 + q^78 - 51 * q^79 - 3 * q^80 + 4 * q^81 + 27 * q^82 - 24 * q^83 + 3 * q^84 + 31 * q^85 + 3 * q^86 - 33 * q^87 + 8 * q^88 - 35 * q^89 + 12 * q^90 - 4 * q^91 - 23 * q^92 + 17 * q^93 + 26 * q^94 - 30 * q^95 - 3 * q^96 + 5 * q^97 - 20 * q^98 - 31 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.26295	0.729164	0.364582	−	0.931171i	$-0.381212\pi$
$3$	1.26295	0.729164	0.364582	+	0.931171i	$0.381212\pi$
$4$	1.00000	0.500000
$5$	−3.04196	−1.36040	−0.680202	−	0.733024i	$-0.738108\pi$
$5$	−3.04196	−1.36040	−0.680202	+	0.733024i	$0.738108\pi$
$6$	−1.26295	−0.515597
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.00000	−0.353553
$9$	−1.40496	−0.468320
$10$	3.04196	0.961951
$11$	3.80970	1.14867	0.574333	−	0.818622i	$-0.305261\pi$
$11$	3.80970	1.14867	0.574333	+	0.818622i	$0.305261\pi$
$12$	1.26295	0.364582
$13$	5.43358	1.50700	0.753502	−	0.657446i	$-0.228363\pi$
$13$	5.43358	1.50700	0.753502	+	0.657446i	$0.228363\pi$
$14$	−1.00000	−0.267261
$15$	−3.84184	−0.991958
$16$	1.00000	0.250000
$17$	−4.12883	−1.00139	−0.500694	−	0.865624i	$-0.666922\pi$
$17$	−4.12883	−1.00139	−0.500694	+	0.865624i	$0.666922\pi$
$18$	1.40496	0.331152
$19$	−7.58964	−1.74118	−0.870591	−	0.492007i	$-0.836263\pi$
$19$	−7.58964	−1.74118	−0.870591	+	0.492007i	$0.836263\pi$
$20$	−3.04196	−0.680202
$21$	1.26295	0.275598
$22$	−3.80970	−0.812230
$23$	2.48712	0.518600	0.259300	−	0.965797i	$-0.416508\pi$
$23$	2.48712	0.518600	0.259300	+	0.965797i	$0.416508\pi$
$24$	−1.26295	−0.257798
$25$	4.25350	0.850701
$26$	−5.43358	−1.06561
$27$	−5.56324	−1.07065
$28$	1.00000	0.188982
$29$	−9.97299	−1.85194	−0.925969	−	0.377600i	$-0.876750\pi$
$29$	−9.97299	−1.85194	−0.925969	+	0.377600i	$0.876750\pi$
$30$	3.84184	0.701420
$31$	9.59602	1.72350	0.861748	−	0.507336i	$-0.169370\pi$
$31$	9.59602	1.72350	0.861748	+	0.507336i	$0.169370\pi$
$32$	−1.00000	−0.176777
$33$	4.81145	0.837566
$34$	4.12883	0.708088
$35$	−3.04196	−0.514185
$36$	−1.40496	−0.234160
$37$	5.29027	0.869716	0.434858	−	0.900499i	$-0.356799\pi$
$37$	5.29027	0.869716	0.434858	+	0.900499i	$0.356799\pi$
$38$	7.58964	1.23120
$39$	6.86233	1.09885
$40$	3.04196	0.480976
$41$	2.50267	0.390851	0.195425	−	0.980719i	$-0.437391\pi$
$41$	2.50267	0.390851	0.195425	+	0.980719i	$0.437391\pi$
$42$	−1.26295	−0.194877
$43$	−3.18614	−0.485882	−0.242941	−	0.970041i	$-0.578112\pi$
$43$	−3.18614	−0.485882	−0.242941	+	0.970041i	$0.578112\pi$
$44$	3.80970	0.574333
$45$	4.27383	0.637104
$46$	−2.48712	−0.366705
$47$	10.0340	1.46361	0.731804	−	0.681515i	$-0.238679\pi$
$47$	10.0340	1.46361	0.731804	+	0.681515i	$0.238679\pi$
$48$	1.26295	0.182291
$49$	1.00000	0.142857
$50$	−4.25350	−0.601536
$51$	−5.21450	−0.730176
$52$	5.43358	0.753502
$53$	−2.66684	−0.366319	−0.183159	−	0.983083i	$-0.558632\pi$
$53$	−2.66684	−0.366319	−0.183159	+	0.983083i	$0.558632\pi$
$54$	5.56324	0.757061
$55$	−11.5889	−1.56265
$56$	−1.00000	−0.133631
$57$	−9.58533	−1.26961
$58$	9.97299	1.30952
$59$	3.57925	0.465979	0.232989	−	0.972479i	$-0.425149\pi$
$59$	3.57925	0.465979	0.232989	+	0.972479i	$0.425149\pi$
$60$	−3.84184	−0.495979
$61$	−11.2712	−1.44312	−0.721562	−	0.692350i	$-0.756575\pi$
$61$	−11.2712	−1.44312	−0.721562	+	0.692350i	$0.756575\pi$
$62$	−9.59602	−1.21870
$63$	−1.40496	−0.177008
$64$	1.00000	0.125000
$65$	−16.5287	−2.05013
$66$	−4.81145	−0.592249
$67$	3.98143	0.486409	0.243205	−	0.969975i	$-0.421801\pi$
$67$	3.98143	0.486409	0.243205	+	0.969975i	$0.421801\pi$
$68$	−4.12883	−0.500694
$69$	3.14110	0.378144
$70$	3.04196	0.363583
$71$	−11.0600	−1.31258	−0.656292	−	0.754507i	$-0.727876\pi$
$71$	−11.0600	−1.31258	−0.656292	+	0.754507i	$0.727876\pi$
$72$	1.40496	0.165576
$73$	−10.2486	−1.19951	−0.599754	−	0.800185i	$-0.704735\pi$
$73$	−10.2486	−1.19951	−0.599754	+	0.800185i	$0.704735\pi$
$74$	−5.29027	−0.614982
$75$	5.37196	0.620300
$76$	−7.58964	−0.870591
$77$	3.80970	0.434155
$78$	−6.86233	−0.777006
$79$	1.78536	0.200869	0.100434	−	0.994944i	$-0.467977\pi$
$79$	1.78536	0.200869	0.100434	+	0.994944i	$0.467977\pi$
$80$	−3.04196	−0.340101
$81$	−2.81121	−0.312357
$82$	−2.50267	−0.276373
$83$	−4.37140	−0.479823	−0.239912	−	0.970795i	$-0.577118\pi$
$83$	−4.37140	−0.479823	−0.239912	+	0.970795i	$0.577118\pi$
$84$	1.26295	0.137799
$85$	12.5597	1.36229
$86$	3.18614	0.343571
$87$	−12.5954	−1.35037
$88$	−3.80970	−0.406115
$89$	−11.8145	−1.25234	−0.626170	−	0.779687i	$-0.715378\pi$
$89$	−11.8145	−1.25234	−0.626170	+	0.779687i	$0.715378\pi$
$90$	−4.27383	−0.450501
$91$	5.43358	0.569594
$92$	2.48712	0.259300
$93$	12.1193	1.25671
$94$	−10.0340	−1.03493
$95$	23.0874	2.36871
$96$	−1.26295	−0.128899
$97$	10.1182	1.02735	0.513675	−	0.857985i	$-0.328284\pi$
$97$	10.1182	1.02735	0.513675	+	0.857985i	$0.328284\pi$
$98$	−1.00000	−0.101015
$99$	−5.35247	−0.537943
$100$	4.25350	0.425350
$101$	2.28419	0.227286	0.113643	−	0.993522i	$-0.463748\pi$
$101$	2.28419	0.227286	0.113643	+	0.993522i	$0.463748\pi$
$102$	5.21450	0.516313
$103$	−12.3081	−1.21275	−0.606375	−	0.795179i	$-0.707377\pi$
$103$	−12.3081	−1.21275	−0.606375	+	0.795179i	$0.707377\pi$
$104$	−5.43358	−0.532806
$105$	−3.84184	−0.374925
$106$	2.66684	0.259026
$107$	−2.15363	−0.208199	−0.104100	−	0.994567i	$-0.533196\pi$
$107$	−2.15363	−0.208199	−0.104100	+	0.994567i	$0.533196\pi$
$108$	−5.56324	−0.535323
$109$	16.1460	1.54650	0.773251	−	0.634100i	$-0.218629\pi$
$109$	16.1460	1.54650	0.773251	+	0.634100i	$0.218629\pi$
$110$	11.5889	1.10496
$111$	6.68135	0.634165
$112$	1.00000	0.0944911
$113$	−14.1262	−1.32888	−0.664440	−	0.747342i	$-0.731330\pi$
$113$	−14.1262	−1.32888	−0.664440	+	0.747342i	$0.731330\pi$
$114$	9.58533	0.897748
$115$	−7.56570	−0.705506
$116$	−9.97299	−0.925969
$117$	−7.63396	−0.705760
$118$	−3.57925	−0.329497
$119$	−4.12883	−0.378489
$120$	3.84184	0.350710
$121$	3.51378	0.319434
$122$	11.2712	1.02044
$123$	3.16074	0.284994
$124$	9.59602	0.861748
$125$	2.27081	0.203108
$126$	1.40496	0.125164
$127$	−6.83624	−0.606618	−0.303309	−	0.952892i	$-0.598091\pi$
$127$	−6.83624	−0.606618	−0.303309	+	0.952892i	$0.598091\pi$
$128$	−1.00000	−0.0883883
$129$	−4.02394	−0.354288
$130$	16.5287	1.44966
$131$	15.5834	1.36153	0.680764	−	0.732503i	$-0.261648\pi$
$131$	15.5834	1.36153	0.680764	+	0.732503i	$0.261648\pi$
$132$	4.81145	0.418783
$133$	−7.58964	−0.658105
$134$	−3.98143	−0.343943
$135$	16.9231	1.45651
$136$	4.12883	0.354044
$137$	−20.0257	−1.71091	−0.855454	−	0.517878i	$-0.826722\pi$
$137$	−20.0257	−1.71091	−0.855454	+	0.517878i	$0.826722\pi$
$138$	−3.14110	−0.267388
$139$	−6.52378	−0.553340	−0.276670	−	0.960965i	$-0.589231\pi$
$139$	−6.52378	−0.553340	−0.276670	+	0.960965i	$0.589231\pi$
$140$	−3.04196	−0.257092
$141$	12.6724	1.06721
$142$	11.0600	0.928137
$143$	20.7003	1.73104
$144$	−1.40496	−0.117080
$145$	30.3374	2.51938
$146$	10.2486	0.848180
$147$	1.26295	0.104166
$148$	5.29027	0.434858
$149$	11.1293	0.911749	0.455874	−	0.890044i	$-0.349327\pi$
$149$	11.1293	0.911749	0.455874	+	0.890044i	$0.349327\pi$
$150$	−5.37196	−0.438619
$151$	13.7617	1.11991	0.559954	−	0.828524i	$-0.310819\pi$
$151$	13.7617	1.11991	0.559954	+	0.828524i	$0.310819\pi$
$152$	7.58964	0.615601
$153$	5.80084	0.468970
$154$	−3.80970	−0.306994
$155$	−29.1907	−2.34465
$156$	6.86233	0.549426
$157$	−1.27596	−0.101833	−0.0509164	−	0.998703i	$-0.516214\pi$
$157$	−1.27596	−0.101833	−0.0509164	+	0.998703i	$0.516214\pi$
$158$	−1.78536	−0.142036
$159$	−3.36808	−0.267106
$160$	3.04196	0.240488
$161$	2.48712	0.196012
$162$	2.81121	0.220869
$163$	2.07460	0.162495	0.0812477	−	0.996694i	$-0.474110\pi$
$163$	2.07460	0.162495	0.0812477	+	0.996694i	$0.474110\pi$
$164$	2.50267	0.195425
$165$	−14.6362	−1.13943
$166$	4.37140	0.339286
$167$	−13.6063	−1.05289	−0.526445	−	0.850209i	$-0.676475\pi$
$167$	−13.6063	−1.05289	−0.526445	+	0.850209i	$0.676475\pi$
$168$	−1.26295	−0.0974386
$169$	16.5238	1.27106
$170$	−12.5597	−0.963287
$171$	10.6631	0.815430
$172$	−3.18614	−0.242941
$173$	−4.91704	−0.373836	−0.186918	−	0.982376i	$-0.559850\pi$
$173$	−4.91704	−0.373836	−0.186918	+	0.982376i	$0.559850\pi$
$174$	12.5954	0.954853
$175$	4.25350	0.321535
$176$	3.80970	0.287167
$177$	4.52041	0.339775
$178$	11.8145	0.885538
$179$	−19.9075	−1.48796	−0.743979	−	0.668203i	$-0.767064\pi$
$179$	−19.9075	−1.48796	−0.743979	+	0.668203i	$0.767064\pi$
$180$	4.27383	0.318552
$181$	19.8493	1.47539	0.737695	−	0.675134i	$-0.235914\pi$
$181$	19.8493	1.47539	0.737695	+	0.675134i	$0.235914\pi$
$182$	−5.43358	−0.402764
$183$	−14.2349	−1.05227
$184$	−2.48712	−0.183353
$185$	−16.0928	−1.18317
$186$	−12.1193	−0.888629
$187$	−15.7296	−1.15026
$188$	10.0340	0.731804
$189$	−5.56324	−0.404666
$190$	−23.0874	−1.67493
$191$	−11.2377	−0.813129	−0.406565	−	0.913622i	$-0.633273\pi$
$191$	−11.2377	−0.813129	−0.406565	+	0.913622i	$0.633273\pi$
$192$	1.26295	0.0911455
$193$	−18.9377	−1.36316	−0.681582	−	0.731742i	$-0.738708\pi$
$193$	−18.9377	−1.36316	−0.681582	+	0.731742i	$0.738708\pi$
$194$	−10.1182	−0.726447
$195$	−20.8749	−1.49488
$196$	1.00000	0.0714286
$197$	−11.4499	−0.815769	−0.407885	−	0.913033i	$-0.633733\pi$
$197$	−11.4499	−0.815769	−0.407885	+	0.913033i	$0.633733\pi$
$198$	5.35247	0.380383
$199$	10.6348	0.753881	0.376940	−	0.926238i	$-0.376976\pi$
$199$	10.6348	0.753881	0.376940	+	0.926238i	$0.376976\pi$
$200$	−4.25350	−0.300768
$201$	5.02834	0.354672
$202$	−2.28419	−0.160715
$203$	−9.97299	−0.699967
$204$	−5.21450	−0.365088
$205$	−7.61300	−0.531715
$206$	12.3081	0.857544
$207$	−3.49430	−0.242871
$208$	5.43358	0.376751
$209$	−28.9142	−2.00004
$210$	3.84184	0.265112
$211$	2.77190	0.190826	0.0954129	−	0.995438i	$-0.469583\pi$
$211$	2.77190	0.190826	0.0954129	+	0.995438i	$0.469583\pi$
$212$	−2.66684	−0.183159
$213$	−13.9683	−0.957089
$214$	2.15363	0.147219
$215$	9.69211	0.660997
$216$	5.56324	0.378531
$217$	9.59602	0.651420
$218$	−16.1460	−1.09354
$219$	−12.9435	−0.874638
$220$	−11.5889	−0.781325
$221$	−22.4343	−1.50910
$222$	−6.68135	−0.448423
$223$	−4.54541	−0.304383	−0.152191	−	0.988351i	$-0.548633\pi$
$223$	−4.54541	−0.304383	−0.152191	+	0.988351i	$0.548633\pi$
$224$	−1.00000	−0.0668153
$225$	−5.97600	−0.398400
$226$	14.1262	0.939659
$227$	5.43564	0.360776	0.180388	−	0.983595i	$-0.442265\pi$
$227$	5.43564	0.360776	0.180388	+	0.983595i	$0.442265\pi$
$228$	−9.58533	−0.634804
$229$	−17.7686	−1.17418	−0.587091	−	0.809521i	$-0.699727\pi$
$229$	−17.7686	−1.17418	−0.587091	+	0.809521i	$0.699727\pi$
$230$	7.56570	0.498868
$231$	4.81145	0.316570
$232$	9.97299	0.654759
$233$	7.15570	0.468785	0.234393	−	0.972142i	$-0.424690\pi$
$233$	7.15570	0.468785	0.234393	+	0.972142i	$0.424690\pi$
$234$	7.63396	0.499047
$235$	−30.5230	−1.99110
$236$	3.57925	0.232989
$237$	2.25482	0.146466
$238$	4.12883	0.267632
$239$	22.9104	1.48195	0.740974	−	0.671534i	$-0.234364\pi$
$239$	22.9104	1.48195	0.740974	+	0.671534i	$0.234364\pi$
$240$	−3.84184	−0.247990
$241$	−18.9456	−1.22039	−0.610196	−	0.792250i	$-0.708909\pi$
$241$	−18.9456	−1.22039	−0.610196	+	0.792250i	$0.708909\pi$
$242$	−3.51378	−0.225874
$243$	13.1393	0.842887
$244$	−11.2712	−0.721562
$245$	−3.04196	−0.194344
$246$	−3.16074	−0.201521
$247$	−41.2389	−2.62397
$248$	−9.59602	−0.609348
$249$	−5.52085	−0.349870
$250$	−2.27081	−0.143619
$251$	2.40721	0.151942	0.0759709	−	0.997110i	$-0.475794\pi$
$251$	2.40721	0.151942	0.0759709	+	0.997110i	$0.475794\pi$
$252$	−1.40496	−0.0885041
$253$	9.47516	0.595698
$254$	6.83624	0.428944
$255$	15.8623	0.993335
$256$	1.00000	0.0625000
$257$	0.765111	0.0477263	0.0238631	−	0.999715i	$-0.492403\pi$
$257$	0.765111	0.0477263	0.0238631	+	0.999715i	$0.492403\pi$
$258$	4.02394	0.250519
$259$	5.29027	0.328722
$260$	−16.5287	−1.02507
$261$	14.0116	0.867299
$262$	−15.5834	−0.962745
$263$	−14.7000	−0.906443	−0.453221	−	0.891398i	$-0.649725\pi$
$263$	−14.7000	−0.906443	−0.453221	+	0.891398i	$0.649725\pi$
$264$	−4.81145	−0.296124
$265$	8.11242	0.498342
$266$	7.58964	0.465351
$267$	−14.9212	−0.913161
$268$	3.98143	0.243205
$269$	−28.5972	−1.74360	−0.871800	−	0.489861i	$-0.837047\pi$
$269$	−28.5972	−1.74360	−0.871800	+	0.489861i	$0.837047\pi$
$270$	−16.9231	−1.02991
$271$	22.2550	1.35190	0.675949	−	0.736949i	$-0.263734\pi$
$271$	22.2550	1.35190	0.675949	+	0.736949i	$0.263734\pi$
$272$	−4.12883	−0.250347
$273$	6.86233	0.415327
$274$	20.0257	1.20980
$275$	16.2046	0.977171
$276$	3.14110	0.189072
$277$	−16.1637	−0.971182	−0.485591	−	0.874186i	$-0.661396\pi$
$277$	−16.1637	−0.971182	−0.485591	+	0.874186i	$0.661396\pi$
$278$	6.52378	0.391270
$279$	−13.4820	−0.807148
$280$	3.04196	0.181792
$281$	−24.1876	−1.44291	−0.721455	−	0.692461i	$-0.756526\pi$
$281$	−24.1876	−1.44291	−0.721455	+	0.692461i	$0.756526\pi$
$282$	−12.6724	−0.754632
$283$	20.2793	1.20548	0.602740	−	0.797938i	$-0.294076\pi$
$283$	20.2793	1.20548	0.602740	+	0.797938i	$0.294076\pi$
$284$	−11.0600	−0.656292
$285$	29.1581	1.72718
$286$	−20.7003	−1.22403
$287$	2.50267	0.147728
$288$	1.40496	0.0827880
$289$	0.0472313	0.00277831
$290$	−30.3374	−1.78147
$291$	12.7788	0.749107
$292$	−10.2486	−0.599754
$293$	−7.09376	−0.414422	−0.207211	−	0.978296i	$-0.566439\pi$
$293$	−7.09376	−0.414422	−0.207211	+	0.978296i	$0.566439\pi$
$294$	−1.26295	−0.0736567
$295$	−10.8879	−0.633919
$296$	−5.29027	−0.307491
$297$	−21.1942	−1.22981
$298$	−11.1293	−0.644704
$299$	13.5139	0.781532
$300$	5.37196	0.310150
$301$	−3.18614	−0.183646
$302$	−13.7617	−0.791894
$303$	2.88482	0.165729
$304$	−7.58964	−0.435296
$305$	34.2864	1.96323
$306$	−5.80084	−0.331612
$307$	25.3700	1.44794	0.723972	−	0.689829i	$-0.242314\pi$
$307$	25.3700	1.44794	0.723972	+	0.689829i	$0.242314\pi$
$308$	3.80970	0.217078
$309$	−15.5445	−0.884294
$310$	29.1907	1.65792
$311$	−10.4454	−0.592303	−0.296152	−	0.955141i	$-0.595703\pi$
$311$	−10.4454	−0.592303	−0.296152	+	0.955141i	$0.595703\pi$
$312$	−6.86233	−0.388503
$313$	−21.9222	−1.23912	−0.619558	−	0.784951i	$-0.712688\pi$
$313$	−21.9222	−1.23912	−0.619558	+	0.784951i	$0.712688\pi$
$314$	1.27596	0.0720066
$315$	4.27383	0.240803
$316$	1.78536	0.100434
$317$	−32.6589	−1.83431	−0.917153	−	0.398535i	$-0.869519\pi$
$317$	−32.6589	−1.83431	−0.917153	+	0.398535i	$0.869519\pi$
$318$	3.36808	0.188873
$319$	−37.9941	−2.12726
$320$	−3.04196	−0.170051
$321$	−2.71992	−0.151811
$322$	−2.48712	−0.138602
$323$	31.3363	1.74360
$324$	−2.81121	−0.156178
$325$	23.1117	1.28201
$326$	−2.07460	−0.114902
$327$	20.3915	1.12765
$328$	−2.50267	−0.138187
$329$	10.0340	0.553192
$330$	14.6362	0.805698
$331$	−19.4545	−1.06932	−0.534659	−	0.845068i	$-0.679560\pi$
$331$	−19.4545	−1.06932	−0.534659	+	0.845068i	$0.679560\pi$
$332$	−4.37140	−0.239912
$333$	−7.43262	−0.407305
$334$	13.6063	0.744505
$335$	−12.1113	−0.661713
$336$	1.26295	0.0688995
$337$	−6.80243	−0.370552	−0.185276	−	0.982687i	$-0.559318\pi$
$337$	−6.80243	−0.370552	−0.185276	+	0.982687i	$0.559318\pi$
$338$	−16.5238	−0.898774
$339$	−17.8406	−0.968971
$340$	12.5597	0.681147
$341$	36.5579	1.97972
$342$	−10.6631	−0.576596
$343$	1.00000	0.0539949
$344$	3.18614	0.171785
$345$	−9.55510	−0.514429
$346$	4.91704	0.264342
$347$	22.6624	1.21658	0.608291	−	0.793714i	$-0.291855\pi$
$347$	22.6624	1.21658	0.608291	+	0.793714i	$0.291855\pi$
$348$	−12.5954	−0.675183
$349$	−30.4738	−1.63122	−0.815612	−	0.578600i	$-0.803599\pi$
$349$	−30.4738	−1.63122	−0.815612	+	0.578600i	$0.803599\pi$
$350$	−4.25350	−0.227359
$351$	−30.2283	−1.61347
$352$	−3.80970	−0.203057
$353$	7.35722	0.391585	0.195793	−	0.980645i	$-0.437272\pi$
$353$	7.35722	0.391585	0.195793	+	0.980645i	$0.437272\pi$
$354$	−4.52041	−0.240257
$355$	33.6442	1.78565
$356$	−11.8145	−0.626170
$357$	−5.21450	−0.275981
$358$	19.9075	1.05215
$359$	1.08855	0.0574516	0.0287258	−	0.999587i	$-0.490855\pi$
$359$	1.08855	0.0574516	0.0287258	+	0.999587i	$0.490855\pi$
$360$	−4.27383	−0.225250
$361$	38.6026	2.03172
$362$	−19.8493	−1.04326
$363$	4.43772	0.232920
$364$	5.43358	0.284797
$365$	31.1758	1.63182
$366$	14.2349	0.744070
$367$	−36.3962	−1.89987	−0.949934	−	0.312451i	$-0.898850\pi$
$367$	−36.3962	−1.89987	−0.949934	+	0.312451i	$0.898850\pi$
$368$	2.48712	0.129650
$369$	−3.51615	−0.183043
$370$	16.0928	0.836624
$371$	−2.66684	−0.138455
$372$	12.1193	0.628356
$373$	−2.70844	−0.140238	−0.0701189	−	0.997539i	$-0.522338\pi$
$373$	−2.70844	−0.140238	−0.0701189	+	0.997539i	$0.522338\pi$
$374$	15.7296	0.813357
$375$	2.86792	0.148099
$376$	−10.0340	−0.517464
$377$	−54.1890	−2.79088
$378$	5.56324	0.286142
$379$	−11.3801	−0.584555	−0.292277	−	0.956334i	$-0.594413\pi$
$379$	−11.3801	−0.584555	−0.292277	+	0.956334i	$0.594413\pi$
$380$	23.0874	1.18436
$381$	−8.63382	−0.442324
$382$	11.2377	0.574969
$383$	16.9351	0.865341	0.432671	−	0.901552i	$-0.357571\pi$
$383$	16.9351	0.865341	0.432671	+	0.901552i	$0.357571\pi$
$384$	−1.26295	−0.0644496
$385$	−11.5889	−0.590627
$386$	18.9377	0.963903
$387$	4.47640	0.227548
$388$	10.1182	0.513675
$389$	−20.6249	−1.04572	−0.522862	−	0.852417i	$-0.675136\pi$
$389$	−20.6249	−1.04572	−0.522862	+	0.852417i	$0.675136\pi$
$390$	20.8749	1.05704
$391$	−10.2689	−0.519320
$392$	−1.00000	−0.0505076
$393$	19.6810	0.992777
$394$	11.4499	0.576836
$395$	−5.43099	−0.273263
$396$	−5.35247	−0.268972
$397$	−22.4832	−1.12840	−0.564200	−	0.825638i	$-0.690815\pi$
$397$	−22.4832	−1.12840	−0.564200	+	0.825638i	$0.690815\pi$
$398$	−10.6348	−0.533074
$399$	−9.58533	−0.479866
$400$	4.25350	0.212675
$401$	−8.62467	−0.430696	−0.215348	−	0.976537i	$-0.569089\pi$
$401$	−8.62467	−0.430696	−0.215348	+	0.976537i	$0.569089\pi$
$402$	−5.02834	−0.250791
$403$	52.1407	2.59731
$404$	2.28419	0.113643
$405$	8.55158	0.424931
$406$	9.97299	0.494951
$407$	20.1543	0.999013
$408$	5.21450	0.258156
$409$	9.47022	0.468272	0.234136	−	0.972204i	$-0.424774\pi$
$409$	9.47022	0.468272	0.234136	+	0.972204i	$0.424774\pi$
$410$	7.61300	0.375979
$411$	−25.2914	−1.24753
$412$	−12.3081	−0.606375
$413$	3.57925	0.176123
$414$	3.49430	0.171735
$415$	13.2976	0.652754
$416$	−5.43358	−0.266403
$417$	−8.23920	−0.403475
$418$	28.9142	1.41424
$419$	−10.8467	−0.529897	−0.264948	−	0.964263i	$-0.585355\pi$
$419$	−10.8467	−0.529897	−0.264948	+	0.964263i	$0.585355\pi$
$420$	−3.84184	−0.187462
$421$	−38.2563	−1.86450	−0.932250	−	0.361815i	$-0.882157\pi$
$421$	−38.2563	−1.86450	−0.932250	+	0.361815i	$0.882157\pi$
$422$	−2.77190	−0.134934
$423$	−14.0974	−0.685437
$424$	2.66684	0.129513
$425$	−17.5620	−0.851882
$426$	13.9683	0.676764
$427$	−11.2712	−0.545449
$428$	−2.15363	−0.104100
$429$	26.1434	1.26221
$430$	−9.69211	−0.467395
$431$	1.00000	0.0481683
$431$	1.00000	0.0481683
$432$	−5.56324	−0.267661
$433$	−15.4754	−0.743701	−0.371851	−	0.928293i	$-0.621277\pi$
$433$	−15.4754	−0.743701	−0.371851	+	0.928293i	$0.621277\pi$
$434$	−9.59602	−0.460624
$435$	38.3146	1.83704
$436$	16.1460	0.773251
$437$	−18.8763	−0.902977
$438$	12.9435	0.618462
$439$	5.71605	0.272812	0.136406	−	0.990653i	$-0.456445\pi$
$439$	5.71605	0.272812	0.136406	+	0.990653i	$0.456445\pi$
$440$	11.5889	0.552481
$441$	−1.40496	−0.0669028
$442$	22.4343	1.06709
$443$	−28.1201	−1.33603	−0.668014	−	0.744149i	$-0.732855\pi$
$443$	−28.1201	−1.33603	−0.668014	+	0.744149i	$0.732855\pi$
$444$	6.68135	0.317083
$445$	35.9393	1.70369
$446$	4.54541	0.215231
$447$	14.0558	0.664814
$448$	1.00000	0.0472456
$449$	−4.77287	−0.225246	−0.112623	−	0.993638i	$-0.535925\pi$
$449$	−4.77287	−0.225246	−0.112623	+	0.993638i	$0.535925\pi$
$450$	5.97600	0.281711
$451$	9.53440	0.448957
$452$	−14.1262	−0.664440
$453$	17.3803	0.816596
$454$	−5.43564	−0.255107
$455$	−16.5287	−0.774878
$456$	9.58533	0.448874
$457$	−3.36520	−0.157418	−0.0787088	−	0.996898i	$-0.525080\pi$
$457$	−3.36520	−0.157418	−0.0787088	+	0.996898i	$0.525080\pi$
$458$	17.7686	0.830271
$459$	22.9697	1.07213
$460$	−7.56570	−0.352753
$461$	−3.77669	−0.175898	−0.0879489	−	0.996125i	$-0.528031\pi$
$461$	−3.77669	−0.175898	−0.0879489	+	0.996125i	$0.528031\pi$
$462$	−4.81145	−0.223849
$463$	−9.73703	−0.452518	−0.226259	−	0.974067i	$-0.572650\pi$
$463$	−9.73703	−0.452518	−0.226259	+	0.974067i	$0.572650\pi$
$464$	−9.97299	−0.462984
$465$	−36.8663	−1.70964
$466$	−7.15570	−0.331481
$467$	−0.176598	−0.00817197	−0.00408599	−	0.999992i	$-0.501301\pi$
$467$	−0.176598	−0.00817197	−0.00408599	+	0.999992i	$0.501301\pi$
$468$	−7.63396	−0.352880
$469$	3.98143	0.183845
$470$	30.5230	1.40792
$471$	−1.61147	−0.0742528
$472$	−3.57925	−0.164748
$473$	−12.1382	−0.558117
$474$	−2.25482	−0.103567
$475$	−32.2825	−1.48122
$476$	−4.12883	−0.189245
$477$	3.74680	0.171554
$478$	−22.9104	−1.04790
$479$	15.7454	0.719424	0.359712	−	0.933063i	$-0.382875\pi$
$479$	15.7454	0.719424	0.359712	+	0.933063i	$0.382875\pi$
$480$	3.84184	0.175355
$481$	28.7451	1.31066
$482$	18.9456	0.862948
$483$	3.14110	0.142925
$484$	3.51378	0.159717
$485$	−30.7792	−1.39761
$486$	−13.1393	−0.596011
$487$	4.84175	0.219401	0.109700	−	0.993965i	$-0.465011\pi$
$487$	4.84175	0.219401	0.109700	+	0.993965i	$0.465011\pi$
$488$	11.2712	0.510221
$489$	2.62012	0.118486
$490$	3.04196	0.137422
$491$	−25.0860	−1.13212	−0.566059	−	0.824365i	$-0.691532\pi$
$491$	−25.0860	−1.13212	−0.566059	+	0.824365i	$0.691532\pi$
$492$	3.16074	0.142497
$493$	41.1768	1.85451
$494$	41.2389	1.85542
$495$	16.2820	0.731820
$496$	9.59602	0.430874
$497$	−11.0600	−0.496110
$498$	5.52085	0.247395
$499$	15.5055	0.694120	0.347060	−	0.937843i	$-0.387180\pi$
$499$	15.5055	0.694120	0.347060	+	0.937843i	$0.387180\pi$
$500$	2.27081	0.101554
$501$	−17.1841	−0.767729
$502$	−2.40721	−0.107439
$503$	3.72946	0.166288	0.0831442	−	0.996538i	$-0.473504\pi$
$503$	3.72946	0.166288	0.0831442	+	0.996538i	$0.473504\pi$
$504$	1.40496	0.0625819
$505$	−6.94842	−0.309201
$506$	−9.47516	−0.421222
$507$	20.8687	0.926810
$508$	−6.83624	−0.303309
$509$	−17.8044	−0.789166	−0.394583	−	0.918860i	$-0.629111\pi$
$509$	−17.8044	−0.789166	−0.394583	+	0.918860i	$0.629111\pi$
$510$	−15.8623	−0.702394
$511$	−10.2486	−0.453371
$512$	−1.00000	−0.0441942
$513$	42.2230	1.86419
$514$	−0.765111	−0.0337476
$515$	37.4406	1.64983
$516$	−4.02394	−0.177144
$517$	38.2265	1.68120
$518$	−5.29027	−0.232441
$519$	−6.20997	−0.272587
$520$	16.5287	0.724832
$521$	−11.0456	−0.483915	−0.241957	−	0.970287i	$-0.577789\pi$
$521$	−11.0456	−0.483915	−0.241957	+	0.970287i	$0.577789\pi$
$522$	−14.0116	−0.613273
$523$	0.835149	0.0365185	0.0182592	−	0.999833i	$-0.494188\pi$
$523$	0.835149	0.0365185	0.0182592	+	0.999833i	$0.494188\pi$
$524$	15.5834	0.680764
$525$	5.37196	0.234451
$526$	14.7000	0.640952
$527$	−39.6203	−1.72589
$528$	4.81145	0.209392
$529$	−16.8142	−0.731054
$530$	−8.11242	−0.352381
$531$	−5.02870	−0.218227
$532$	−7.58964	−0.329053
$533$	13.5984	0.589013
$534$	14.9212	0.645702
$535$	6.55124	0.283235
$536$	−3.98143	−0.171972
$537$	−25.1422	−1.08497
$538$	28.5972	1.23291
$539$	3.80970	0.164095
$540$	16.9231	0.728256
$541$	2.96964	0.127675	0.0638375	−	0.997960i	$-0.479666\pi$
$541$	2.96964	0.127675	0.0638375	+	0.997960i	$0.479666\pi$
$542$	−22.2550	−0.955936
$543$	25.0687	1.07580
$544$	4.12883	0.177022
$545$	−49.1153	−2.10387
$546$	−6.86233	−0.293681
$547$	5.82665	0.249130	0.124565	−	0.992211i	$-0.460247\pi$
$547$	5.82665	0.249130	0.124565	+	0.992211i	$0.460247\pi$
$548$	−20.0257	−0.855454
$549$	15.8355	0.675843
$550$	−16.2046	−0.690964
$551$	75.6914	3.22456
$552$	−3.14110	−0.133694
$553$	1.78536	0.0759212
$554$	16.1637	0.686729
$555$	−20.3244	−0.862722
$556$	−6.52378	−0.276670
$557$	32.0089	1.35626	0.678131	−	0.734941i	$-0.262790\pi$
$557$	32.0089	1.35626	0.678131	+	0.734941i	$0.262790\pi$
$558$	13.4820	0.570739
$559$	−17.3122	−0.732226
$560$	−3.04196	−0.128546
$561$	−19.8657	−0.838729
$562$	24.1876	1.02029
$563$	32.3237	1.36228	0.681141	−	0.732152i	$-0.261484\pi$
$563$	32.3237	1.36228	0.681141	+	0.732152i	$0.261484\pi$
$564$	12.6724	0.533605
$565$	42.9712	1.80781
$566$	−20.2793	−0.852403
$567$	−2.81121	−0.118060
$568$	11.0600	0.464069
$569$	−24.3676	−1.02154	−0.510771	−	0.859717i	$-0.670640\pi$
$569$	−24.3676	−1.02154	−0.510771	+	0.859717i	$0.670640\pi$
$570$	−29.1581	−1.22130
$571$	29.0000	1.21361	0.606807	−	0.794849i	$-0.292450\pi$
$571$	29.0000	1.21361	0.606807	+	0.794849i	$0.292450\pi$
$572$	20.7003	0.865522
$573$	−14.1926	−0.592905
$574$	−2.50267	−0.104459
$575$	10.5790	0.441173
$576$	−1.40496	−0.0585400
$577$	5.07225	0.211160	0.105580	−	0.994411i	$-0.466330\pi$
$577$	5.07225	0.211160	0.105580	+	0.994411i	$0.466330\pi$
$578$	−0.0472313	−0.00196456
$579$	−23.9173	−0.993970
$580$	30.3374	1.25969
$581$	−4.37140	−0.181356
$582$	−12.7788	−0.529699
$583$	−10.1599	−0.420778
$584$	10.2486	0.424090
$585$	23.2222	0.960118
$586$	7.09376	0.293040
$587$	−14.9144	−0.615583	−0.307791	−	0.951454i	$-0.599590\pi$
$587$	−14.9144	−0.615583	−0.307791	+	0.951454i	$0.599590\pi$
$588$	1.26295	0.0520831
$589$	−72.8303	−3.00092
$590$	10.8879	0.448249
$591$	−14.4606	−0.594830
$592$	5.29027	0.217429
$593$	31.7476	1.30372	0.651860	−	0.758340i	$-0.273989\pi$
$593$	31.7476	1.30372	0.651860	+	0.758340i	$0.273989\pi$
$594$	21.1942	0.869611
$595$	12.5597	0.514898
$596$	11.1293	0.455874
$597$	13.4312	0.549703
$598$	−13.5139	−0.552626
$599$	−23.7489	−0.970353	−0.485177	−	0.874416i	$-0.661245\pi$
$599$	−23.7489	−0.970353	−0.485177	+	0.874416i	$0.661245\pi$
$600$	−5.37196	−0.219309
$601$	−40.1227	−1.63664	−0.818320	−	0.574763i	$-0.805094\pi$
$601$	−40.1227	−1.63664	−0.818320	+	0.574763i	$0.805094\pi$
$602$	3.18614	0.129858
$603$	−5.59375	−0.227795
$604$	13.7617	0.559954
$605$	−10.6888	−0.434560
$606$	−2.88482	−0.117188
$607$	21.8142	0.885410	0.442705	−	0.896667i	$-0.354019\pi$
$607$	21.8142	0.885410	0.442705	+	0.896667i	$0.354019\pi$
$608$	7.58964	0.307800
$609$	−12.5954	−0.510391
$610$	−34.2864	−1.38821
$611$	54.5205	2.20566
$612$	5.80084	0.234485
$613$	−29.7895	−1.20319	−0.601593	−	0.798802i	$-0.705467\pi$
$613$	−29.7895	−1.20319	−0.601593	+	0.798802i	$0.705467\pi$
$614$	−25.3700	−1.02385
$615$	−9.61484	−0.387708
$616$	−3.80970	−0.153497
$617$	−45.3358	−1.82515	−0.912575	−	0.408909i	$-0.865909\pi$
$617$	−45.3358	−1.82515	−0.912575	+	0.408909i	$0.865909\pi$
$618$	15.5445	0.625290
$619$	7.12318	0.286305	0.143152	−	0.989701i	$-0.454276\pi$
$619$	7.12318	0.286305	0.143152	+	0.989701i	$0.454276\pi$
$620$	−29.1907	−1.17233
$621$	−13.8364	−0.555237
$622$	10.4454	0.418822
$623$	−11.8145	−0.473340
$624$	6.86233	0.274713
$625$	−28.1752	−1.12701
$626$	21.9222	0.876187
$627$	−36.5172	−1.45836
$628$	−1.27596	−0.0509164
$629$	−21.8426	−0.870923
$630$	−4.27383	−0.170273
$631$	37.7778	1.50391	0.751955	−	0.659215i	$-0.229111\pi$
$631$	37.7778	1.50391	0.751955	+	0.659215i	$0.229111\pi$
$632$	−1.78536	−0.0710178
$633$	3.50077	0.139143
$634$	32.6589	1.29705
$635$	20.7956	0.825246
$636$	−3.36808	−0.133553
$637$	5.43358	0.215286
$638$	37.9941	1.50420
$639$	15.5389	0.614709
$640$	3.04196	0.120244
$641$	−27.7983	−1.09797	−0.548984	−	0.835833i	$-0.684985\pi$
$641$	−27.7983	−1.09797	−0.548984	+	0.835833i	$0.684985\pi$
$642$	2.71992	0.107347
$643$	33.7770	1.33203	0.666017	−	0.745937i	$-0.267998\pi$
$643$	33.7770	1.33203	0.666017	+	0.745937i	$0.267998\pi$
$644$	2.48712	0.0980062
$645$	12.2406	0.481975
$646$	−31.3363	−1.23291
$647$	−16.9946	−0.668128	−0.334064	−	0.942550i	$-0.608420\pi$
$647$	−16.9946	−0.668128	−0.334064	+	0.942550i	$0.608420\pi$
$648$	2.81121	0.110435
$649$	13.6358	0.535254
$650$	−23.1117	−0.906517
$651$	12.1193	0.474992
$652$	2.07460	0.0812477
$653$	11.2271	0.439351	0.219676	−	0.975573i	$-0.429500\pi$
$653$	11.2271	0.439351	0.219676	+	0.975573i	$0.429500\pi$
$654$	−20.3915	−0.797372
$655$	−47.4040	−1.85223
$656$	2.50267	0.0977127
$657$	14.3989	0.561753
$658$	−10.0340	−0.391166
$659$	−22.1513	−0.862893	−0.431446	−	0.902139i	$-0.641997\pi$
$659$	−22.1513	−0.862893	−0.431446	+	0.902139i	$0.641997\pi$
$660$	−14.6362	−0.569714
$661$	43.0388	1.67401	0.837007	−	0.547193i	$-0.184303\pi$
$661$	43.0388	1.67401	0.837007	+	0.547193i	$0.184303\pi$
$662$	19.4545	0.756122
$663$	−28.3334	−1.10038
$664$	4.37140	0.169643
$665$	23.0874	0.895289
$666$	7.43262	0.288008
$667$	−24.8040	−0.960415
$668$	−13.6063	−0.526445
$669$	−5.74062	−0.221945
$670$	12.1113	0.467902
$671$	−42.9397	−1.65767
$672$	−1.26295	−0.0487193
$673$	8.08318	0.311584	0.155792	−	0.987790i	$-0.450207\pi$
$673$	8.08318	0.311584	0.155792	+	0.987790i	$0.450207\pi$
$674$	6.80243	0.262020
$675$	−23.6633	−0.910799
$676$	16.5238	0.635529
$677$	−10.5898	−0.406999	−0.203499	−	0.979075i	$-0.565231\pi$
$677$	−10.5898	−0.406999	−0.203499	+	0.979075i	$0.565231\pi$
$678$	17.8406	0.685166
$679$	10.1182	0.388302
$680$	−12.5597	−0.481643
$681$	6.86494	0.263065
$682$	−36.5579	−1.39987
$683$	41.6805	1.59486	0.797430	−	0.603411i	$-0.206192\pi$
$683$	41.6805	1.59486	0.797430	+	0.603411i	$0.206192\pi$
$684$	10.6631	0.407715
$685$	60.9172	2.32753
$686$	−1.00000	−0.0381802
$687$	−22.4408	−0.856171
$688$	−3.18614	−0.121471
$689$	−14.4905	−0.552044
$690$	9.55510	0.363756
$691$	26.2713	0.999408	0.499704	−	0.866196i	$-0.333442\pi$
$691$	26.2713	0.999408	0.499704	+	0.866196i	$0.333442\pi$
$692$	−4.91704	−0.186918
$693$	−5.35247	−0.203323
$694$	−22.6624	−0.860254
$695$	19.8451	0.752766
$696$	12.5954	0.477427
$697$	−10.3331	−0.391393
$698$	30.4738	1.15345
$699$	9.03728	0.341821
$700$	4.25350	0.160767
$701$	34.2676	1.29427	0.647134	−	0.762376i	$-0.275968\pi$
$701$	34.2676	1.29427	0.647134	+	0.762376i	$0.275968\pi$
$702$	30.2283	1.14089
$703$	−40.1513	−1.51433
$704$	3.80970	0.143583
$705$	−38.5490	−1.45184
$706$	−7.35722	−0.276893
$707$	2.28419	0.0859060
$708$	4.52041	0.169887
$709$	36.5555	1.37287	0.686436	−	0.727190i	$-0.259174\pi$
$709$	36.5555	1.37287	0.686436	+	0.727190i	$0.259174\pi$
$710$	−33.6442	−1.26264
$711$	−2.50836	−0.0940708
$712$	11.8145	0.442769
$713$	23.8664	0.893805
$714$	5.21450	0.195148
$715$	−62.9693	−2.35492
$716$	−19.9075	−0.743979
$717$	28.9346	1.08058
$718$	−1.08855	−0.0406244
$719$	−30.8606	−1.15091	−0.575453	−	0.817835i	$-0.695174\pi$
$719$	−30.8606	−1.15091	−0.575453	+	0.817835i	$0.695174\pi$
$720$	4.27383	0.159276
$721$	−12.3081	−0.458377
$722$	−38.6026	−1.43664
$723$	−23.9273	−0.889866
$724$	19.8493	0.737695
$725$	−42.4201	−1.57544
$726$	−4.43772	−0.164699
$727$	2.97890	0.110481	0.0552406	−	0.998473i	$-0.482407\pi$
$727$	2.97890	0.110481	0.0552406	+	0.998473i	$0.482407\pi$
$728$	−5.43358	−0.201382
$729$	25.0279	0.926959
$730$	−31.1758	−1.15387
$731$	13.1550	0.486557
$732$	−14.2349	−0.526137
$733$	−27.4356	−1.01336	−0.506679	−	0.862135i	$-0.669127\pi$
$733$	−27.4356	−1.01336	−0.506679	+	0.862135i	$0.669127\pi$
$734$	36.3962	1.34341
$735$	−3.84184	−0.141708
$736$	−2.48712	−0.0916764
$737$	15.1680	0.558722
$738$	3.51615	0.129431
$739$	−11.2236	−0.412868	−0.206434	−	0.978461i	$-0.566186\pi$
$739$	−11.2236	−0.412868	−0.206434	+	0.978461i	$0.566186\pi$
$740$	−16.0928	−0.591583
$741$	−52.0826	−1.91330
$742$	2.66684	0.0979028
$743$	32.8070	1.20357	0.601786	−	0.798658i	$-0.294456\pi$
$743$	32.8070	1.20357	0.601786	+	0.798658i	$0.294456\pi$
$744$	−12.1193	−0.444315
$745$	−33.8549	−1.24035
$746$	2.70844	0.0991631
$747$	6.14164	0.224711
$748$	−15.7296	−0.575130
$749$	−2.15363	−0.0786919
$750$	−2.86792	−0.104722
$751$	−11.0331	−0.402602	−0.201301	−	0.979529i	$-0.564517\pi$
$751$	−11.0331	−0.402602	−0.201301	+	0.979529i	$0.564517\pi$
$752$	10.0340	0.365902
$753$	3.04019	0.110791
$754$	54.1890	1.97345
$755$	−41.8624	−1.52353
$756$	−5.56324	−0.202333
$757$	−42.3334	−1.53864	−0.769318	−	0.638867i	$-0.779404\pi$
$757$	−42.3334	−1.53864	−0.769318	+	0.638867i	$0.779404\pi$
$758$	11.3801	0.413342
$759$	11.9666	0.434362
$760$	−23.0874	−0.837466
$761$	4.41841	0.160167	0.0800836	−	0.996788i	$-0.474481\pi$
$761$	4.41841	0.160167	0.0800836	+	0.996788i	$0.474481\pi$
$762$	8.63382	0.312770
$763$	16.1460	0.584523
$764$	−11.2377	−0.406565
$765$	−17.6459	−0.637989
$766$	−16.9351	−0.611889
$767$	19.4481	0.702231
$768$	1.26295	0.0455727
$769$	54.1375	1.95225	0.976123	−	0.217218i	$-0.0696981\pi$
$769$	54.1375	1.95225	0.976123	+	0.217218i	$0.0696981\pi$
$770$	11.5889	0.417636
$771$	0.966296	0.0348003
$772$	−18.9377	−0.681582
$773$	39.0253	1.40364	0.701822	−	0.712352i	$-0.252370\pi$
$773$	39.0253	1.40364	0.701822	+	0.712352i	$0.252370\pi$
$774$	−4.47640	−0.160901
$775$	40.8167	1.46618
$776$	−10.1182	−0.363223
$777$	6.68135	0.239692
$778$	20.6249	0.739439
$779$	−18.9943	−0.680543
$780$	−20.8749	−0.747442
$781$	−42.1354	−1.50772
$782$	10.2689	0.367215
$783$	55.4821	1.98277
$784$	1.00000	0.0357143
$785$	3.88142	0.138534
$786$	−19.6810	−0.701999
$787$	−43.0696	−1.53527	−0.767633	−	0.640890i	$-0.778565\pi$
$787$	−43.0696	−1.53527	−0.767633	+	0.640890i	$0.778565\pi$
$788$	−11.4499	−0.407885
$789$	−18.5654	−0.660945
$790$	5.43099	0.193226
$791$	−14.1262	−0.502269
$792$	5.35247	0.190192
$793$	−61.2427	−2.17479
$794$	22.4832	0.797899
$795$	10.2456	0.363373
$796$	10.6348	0.376940
$797$	−17.8826	−0.633433	−0.316716	−	0.948520i	$-0.602580\pi$
$797$	−17.8826	−0.633433	−0.316716	+	0.948520i	$0.602580\pi$
$798$	9.58533	0.339317
$799$	−41.4286	−1.46564
$800$	−4.25350	−0.150384
$801$	16.5990	0.586495
$802$	8.62467	0.304548
$803$	−39.0440	−1.37783
$804$	5.02834	0.177336
$805$	−7.56570	−0.266656
$806$	−52.1407	−1.83658
$807$	−36.1168	−1.27137
$808$	−2.28419	−0.0803577
$809$	45.5136	1.60017	0.800086	−	0.599885i	$-0.204787\pi$
$809$	45.5136	1.60017	0.800086	+	0.599885i	$0.204787\pi$
$810$	−8.55158	−0.300472
$811$	−30.8660	−1.08385	−0.541925	−	0.840427i	$-0.682304\pi$
$811$	−30.8660	−1.08385	−0.541925	+	0.840427i	$0.682304\pi$
$812$	−9.97299	−0.349983
$813$	28.1070	0.985755
$814$	−20.1543	−0.706409
$815$	−6.31085	−0.221060
$816$	−5.21450	−0.182544
$817$	24.1817	0.846010
$818$	−9.47022	−0.331118
$819$	−7.63396	−0.266752
$820$	−7.61300	−0.265858
$821$	−12.4507	−0.434531	−0.217266	−	0.976113i	$-0.569714\pi$
$821$	−12.4507	−0.434531	−0.217266	+	0.976113i	$0.569714\pi$
$822$	25.2914	0.882139
$823$	−28.4418	−0.991418	−0.495709	−	0.868489i	$-0.665092\pi$
$823$	−28.4418	−0.991418	−0.495709	+	0.868489i	$0.665092\pi$
$824$	12.3081	0.428772
$825$	20.4655	0.712518
$826$	−3.57925	−0.124538
$827$	−1.66580	−0.0579254	−0.0289627	−	0.999580i	$-0.509220\pi$
$827$	−1.66580	−0.0579254	−0.0289627	+	0.999580i	$0.509220\pi$
$828$	−3.49430	−0.121435
$829$	0.992208	0.0344608	0.0172304	−	0.999852i	$-0.494515\pi$
$829$	0.992208	0.0344608	0.0172304	+	0.999852i	$0.494515\pi$
$830$	−13.2976	−0.461567
$831$	−20.4139	−0.708151
$832$	5.43358	0.188375
$833$	−4.12883	−0.143055
$834$	8.23920	0.285300
$835$	41.3899	1.43236
$836$	−28.9142	−1.00002
$837$	−53.3850	−1.84525
$838$	10.8467	0.374694
$839$	−45.8859	−1.58416	−0.792078	−	0.610419i	$-0.791001\pi$
$839$	−45.8859	−1.58416	−0.792078	+	0.610419i	$0.791001\pi$
$840$	3.84184	0.132556
$841$	70.4605	2.42967
$842$	38.2563	1.31840
$843$	−30.5477	−1.05212
$844$	2.77190	0.0954129
$845$	−50.2646	−1.72915
$846$	14.0974	0.484677
$847$	3.51378	0.120735
$848$	−2.66684	−0.0915797
$849$	25.6117	0.878993
$850$	17.5620	0.602371
$851$	13.1575	0.451034
$852$	−13.9683	−0.478545
$853$	10.7861	0.369308	0.184654	−	0.982804i	$-0.440884\pi$
$853$	10.7861	0.369308	0.184654	+	0.982804i	$0.440884\pi$
$854$	11.2712	0.385691
$855$	−32.4368	−1.10932
$856$	2.15363	0.0736095
$857$	8.72017	0.297875	0.148938	−	0.988847i	$-0.452415\pi$
$857$	8.72017	0.297875	0.148938	+	0.988847i	$0.452415\pi$
$858$	−26.1434	−0.892521
$859$	56.3578	1.92290	0.961451	−	0.274975i	$-0.0886697\pi$
$859$	56.3578	1.92290	0.961451	+	0.274975i	$0.0886697\pi$
$860$	9.69211	0.330498
$861$	3.16074	0.107718
$862$	−1.00000	−0.0340601
$863$	8.86437	0.301747	0.150873	−	0.988553i	$-0.451791\pi$
$863$	8.86437	0.301747	0.150873	+	0.988553i	$0.451791\pi$
$864$	5.56324	0.189265
$865$	14.9574	0.508568
$866$	15.4754	0.525876
$867$	0.0596507	0.00202584
$868$	9.59602	0.325710
$869$	6.80168	0.230731
$870$	−38.3146	−1.29899
$871$	21.6334	0.733020
$872$	−16.1460	−0.546771
$873$	−14.2157	−0.481129
$874$	18.8763	0.638501
$875$	2.27081	0.0767674
$876$	−12.9435	−0.437319
$877$	8.50069	0.287048	0.143524	−	0.989647i	$-0.454157\pi$
$877$	8.50069	0.287048	0.143524	+	0.989647i	$0.454157\pi$
$878$	−5.71605	−0.192907
$879$	−8.95905	−0.302181
$880$	−11.5889	−0.390663
$881$	−52.8027	−1.77897	−0.889484	−	0.456966i	$-0.848936\pi$
$881$	−52.8027	−1.77897	−0.889484	+	0.456966i	$0.848936\pi$
$882$	1.40496	0.0473075
$883$	32.7160	1.10098	0.550491	−	0.834841i	$-0.314441\pi$
$883$	32.7160	1.10098	0.550491	+	0.834841i	$0.314441\pi$
$884$	−22.4343	−0.754548
$885$	−13.7509	−0.462231
$886$	28.1201	0.944714
$887$	55.9335	1.87806	0.939031	−	0.343832i	$-0.111725\pi$
$887$	55.9335	1.87806	0.939031	+	0.343832i	$0.111725\pi$
$888$	−6.68135	−0.224211
$889$	−6.83624	−0.229280
$890$	−35.9393	−1.20469
$891$	−10.7099	−0.358794
$892$	−4.54541	−0.152191
$893$	−76.1544	−2.54841
$894$	−14.0558	−0.470095
$895$	60.5579	2.02423
$896$	−1.00000	−0.0334077
$897$	17.0674	0.569865
$898$	4.77287	0.159273
$899$	−95.7010	−3.19181
$900$	−5.97600	−0.199200
$901$	11.0109	0.366827
$902$	−9.53440	−0.317461
$903$	−4.02394	−0.133908
$904$	14.1262	0.469830
$905$	−60.3809	−2.00713
$906$	−17.3803	−0.577421
$907$	−9.21960	−0.306132	−0.153066	−	0.988216i	$-0.548915\pi$
$907$	−9.21960	−0.306132	−0.153066	+	0.988216i	$0.548915\pi$
$908$	5.43564	0.180388
$909$	−3.20920	−0.106442
$910$	16.5287	0.547921
$911$	5.79449	0.191980	0.0959901	−	0.995382i	$-0.469398\pi$
$911$	5.79449	0.191980	0.0959901	+	0.995382i	$0.469398\pi$
$912$	−9.58533	−0.317402
$913$	−16.6537	−0.551157
$914$	3.36520	0.111311
$915$	43.3019	1.43152
$916$	−17.7686	−0.587091
$917$	15.5834	0.514609
$918$	−22.9697	−0.758112
$919$	−50.9853	−1.68185	−0.840924	−	0.541153i	$-0.817988\pi$
$919$	−50.9853	−1.68185	−0.840924	+	0.541153i	$0.817988\pi$
$920$	7.56570	0.249434
$921$	32.0411	1.05579
$922$	3.77669	0.124379
$923$	−60.0956	−1.97807
$924$	4.81145	0.158285
$925$	22.5022	0.739868
$926$	9.73703	0.319979
$927$	17.2924	0.567955
$928$	9.97299	0.327379
$929$	19.6826	0.645765	0.322883	−	0.946439i	$-0.395348\pi$
$929$	19.6826	0.645765	0.322883	+	0.946439i	$0.395348\pi$
$930$	36.8663	1.20890
$931$	−7.58964	−0.248740
$932$	7.15570	0.234393
$933$	−13.1920	−0.431886
$934$	0.176598	0.00577846
$935$	47.8487	1.56482
$936$	7.63396	0.249524
$937$	9.05071	0.295674	0.147837	−	0.989012i	$-0.452769\pi$
$937$	9.05071	0.295674	0.147837	+	0.989012i	$0.452769\pi$
$938$	−3.98143	−0.129998
$939$	−27.6866	−0.903519
$940$	−30.5230	−0.995550
$941$	3.96009	0.129095	0.0645476	−	0.997915i	$-0.479440\pi$
$941$	3.96009	0.129095	0.0645476	+	0.997915i	$0.479440\pi$
$942$	1.61147	0.0525046
$943$	6.22443	0.202695
$944$	3.57925	0.116495
$945$	16.9231	0.550510
$946$	12.1382	0.394648
$947$	−16.4558	−0.534740	−0.267370	−	0.963594i	$-0.586155\pi$
$947$	−16.4558	−0.534740	−0.267370	+	0.963594i	$0.586155\pi$
$948$	2.25482	0.0732331
$949$	−55.6866	−1.80766
$950$	32.2825	1.04738
$951$	−41.2465	−1.33751
$952$	4.12883	0.133816
$953$	15.6638	0.507401	0.253701	−	0.967283i	$-0.418352\pi$
$953$	15.6638	0.507401	0.253701	+	0.967283i	$0.418352\pi$
$954$	−3.74680	−0.121307
$955$	34.1845	1.10618
$956$	22.9104	0.740974
$957$	−47.9846	−1.55112
$958$	−15.7454	−0.508709
$959$	−20.0257	−0.646663
$960$	−3.84184	−0.123995
$961$	61.0836	1.97044
$962$	−28.7451	−0.926780
$963$	3.02576	0.0975038
$964$	−18.9456	−0.610196
$965$	57.6076	1.85446
$966$	−3.14110	−0.101063
$967$	11.3338	0.364469	0.182235	−	0.983255i	$-0.441667\pi$
$967$	11.3338	0.364469	0.182235	+	0.983255i	$0.441667\pi$
$968$	−3.51378	−0.112937
$969$	39.5762	1.27137
$970$	30.7792	0.988261
$971$	34.0668	1.09325	0.546627	−	0.837376i	$-0.315912\pi$
$971$	34.0668	1.09325	0.546627	+	0.837376i	$0.315912\pi$
$972$	13.1393	0.421443
$973$	−6.52378	−0.209143
$974$	−4.84175	−0.155140
$975$	29.1889	0.934794
$976$	−11.2712	−0.360781
$977$	53.5751	1.71402	0.857009	−	0.515301i	$-0.172320\pi$
$977$	53.5751	1.71402	0.857009	+	0.515301i	$0.172320\pi$
$978$	−2.62012	−0.0837821
$979$	−45.0098	−1.43852
$980$	−3.04196	−0.0971718
$981$	−22.6844	−0.724258
$982$	25.0860	0.800528
$983$	26.4884	0.844849	0.422424	−	0.906398i	$-0.361179\pi$
$983$	26.4884	0.844849	0.422424	+	0.906398i	$0.361179\pi$
$984$	−3.16074	−0.100761
$985$	34.8300	1.10978
$986$	−41.1768	−1.31134
$987$	12.6724	0.403368
$988$	−41.2389	−1.31198
$989$	−7.92431	−0.251978
$990$	−16.2820	−0.517475
$991$	26.1145	0.829555	0.414777	−	0.909923i	$-0.363859\pi$
$991$	26.1145	0.829555	0.414777	+	0.909923i	$0.363859\pi$
$992$	−9.59602	−0.304674
$993$	−24.5701	−0.779709
$994$	11.0600	0.350803
$995$	−32.3506	−1.02558
$996$	−5.52085	−0.174935
$997$	15.1656	0.480298	0.240149	−	0.970736i	$-0.422804\pi$
$997$	15.1656	0.480298	0.240149	+	0.970736i	$0.422804\pi$
$998$	−15.5055	−0.490817
$999$	−29.4311	−0.931158

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.k.1.14	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.k.1.14	✓	20	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:	\( N \)	\(=\)	\( 6034 = 2 \cdot 7 \cdot 431 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6034.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.26295 q^{3} +1.00000 q^{4} -3.04196 q^{5} -1.26295 q^{6} +1.00000 q^{7} -1.00000 q^{8} -1.40496 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.26295 q^{3} +1.00000 q^{4} -3.04196 q^{5} -1.26295 q^{6} +1.00000 q^{7} -1.00000 q^{8} -1.40496 q^{9} +3.04196 q^{10} +3.80970 q^{11} +1.26295 q^{12} +5.43358 q^{13} -1.00000 q^{14} -3.84184 q^{15} +1.00000 q^{16} -4.12883 q^{17} +1.40496 q^{18} -7.58964 q^{19} -3.04196 q^{20} +1.26295 q^{21} -3.80970 q^{22} +2.48712 q^{23} -1.26295 q^{24} +4.25350 q^{25} -5.43358 q^{26} -5.56324 q^{27} +1.00000 q^{28} -9.97299 q^{29} +3.84184 q^{30} +9.59602 q^{31} -1.00000 q^{32} +4.81145 q^{33} +4.12883 q^{34} -3.04196 q^{35} -1.40496 q^{36} +5.29027 q^{37} +7.58964 q^{38} +6.86233 q^{39} +3.04196 q^{40} +2.50267 q^{41} -1.26295 q^{42} -3.18614 q^{43} +3.80970 q^{44} +4.27383 q^{45} -2.48712 q^{46} +10.0340 q^{47} +1.26295 q^{48} +1.00000 q^{49} -4.25350 q^{50} -5.21450 q^{51} +5.43358 q^{52} -2.66684 q^{53} +5.56324 q^{54} -11.5889 q^{55} -1.00000 q^{56} -9.58533 q^{57} +9.97299 q^{58} +3.57925 q^{59} -3.84184 q^{60} -11.2712 q^{61} -9.59602 q^{62} -1.40496 q^{63} +1.00000 q^{64} -16.5287 q^{65} -4.81145 q^{66} +3.98143 q^{67} -4.12883 q^{68} +3.14110 q^{69} +3.04196 q^{70} -11.0600 q^{71} +1.40496 q^{72} -10.2486 q^{73} -5.29027 q^{74} +5.37196 q^{75} -7.58964 q^{76} +3.80970 q^{77} -6.86233 q^{78} +1.78536 q^{79} -3.04196 q^{80} -2.81121 q^{81} -2.50267 q^{82} -4.37140 q^{83} +1.26295 q^{84} +12.5597 q^{85} +3.18614 q^{86} -12.5954 q^{87} -3.80970 q^{88} -11.8145 q^{89} -4.27383 q^{90} +5.43358 q^{91} +2.48712 q^{92} +12.1193 q^{93} -10.0340 q^{94} +23.0874 q^{95} -1.26295 q^{96} +10.1182 q^{97} -1.00000 q^{98} -5.35247 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 20 q^{2} + 3 q^{3} + 20 q^{4} - 3 q^{5} - 3 q^{6} + 20 q^{7} - 20 q^{8} + 13 q^{9}+O(q^{10}) \) 20 * q - 20 * q^2 + 3 * q^3 + 20 * q^4 - 3 * q^5 - 3 * q^6 + 20 * q^7 - 20 * q^8 + 13 * q^9	\( 20 q - 20 q^{2} + 3 q^{3} + 20 q^{4} - 3 q^{5} - 3 q^{6} + 20 q^{7} - 20 q^{8} + 13 q^{9} + 3 q^{10} - 8 q^{11} + 3 q^{12} - 4 q^{13} - 20 q^{14} - 25 q^{15} + 20 q^{16} + 9 q^{17} - 13 q^{18} - 14 q^{19} - 3 q^{20} + 3 q^{21} + 8 q^{22} - 23 q^{23} - 3 q^{24} + 31 q^{25} + 4 q^{26} - 21 q^{27} + 20 q^{28} - 48 q^{29} + 25 q^{30} - q^{31} - 20 q^{32} - 29 q^{33} - 9 q^{34} - 3 q^{35} + 13 q^{36} - q^{37} + 14 q^{38} - q^{39} + 3 q^{40} - 27 q^{41} - 3 q^{42} - 3 q^{43} - 8 q^{44} - 12 q^{45} + 23 q^{46} - 26 q^{47} + 3 q^{48} + 20 q^{49} - 31 q^{50} - 17 q^{51} - 4 q^{52} - 43 q^{53} + 21 q^{54} - 16 q^{55} - 20 q^{56} - 25 q^{57} + 48 q^{58} - 19 q^{59} - 25 q^{60} + 9 q^{61} + q^{62} + 13 q^{63} + 20 q^{64} - 87 q^{65} + 29 q^{66} + 32 q^{67} + 9 q^{68} - 23 q^{69} + 3 q^{70} - 63 q^{71} - 13 q^{72} + 2 q^{73} + q^{74} - 8 q^{75} - 14 q^{76} - 8 q^{77} + q^{78} - 51 q^{79} - 3 q^{80} + 4 q^{81} + 27 q^{82} - 24 q^{83} + 3 q^{84} + 31 q^{85} + 3 q^{86} - 33 q^{87} + 8 q^{88} - 35 q^{89} + 12 q^{90} - 4 q^{91} - 23 q^{92} + 17 q^{93} + 26 q^{94} - 30 q^{95} - 3 q^{96} + 5 q^{97} - 20 q^{98} - 31 q^{99}+O(q^{100}) \) 20 * q - 20 * q^2 + 3 * q^3 + 20 * q^4 - 3 * q^5 - 3 * q^6 + 20 * q^7 - 20 * q^8 + 13 * q^9 + 3 * q^10 - 8 * q^11 + 3 * q^12 - 4 * q^13 - 20 * q^14 - 25 * q^15 + 20 * q^16 + 9 * q^17 - 13 * q^18 - 14 * q^19 - 3 * q^20 + 3 * q^21 + 8 * q^22 - 23 * q^23 - 3 * q^24 + 31 * q^25 + 4 * q^26 - 21 * q^27 + 20 * q^28 - 48 * q^29 + 25 * q^30 - q^31 - 20 * q^32 - 29 * q^33 - 9 * q^34 - 3 * q^35 + 13 * q^36 - q^37 + 14 * q^38 - q^39 + 3 * q^40 - 27 * q^41 - 3 * q^42 - 3 * q^43 - 8 * q^44 - 12 * q^45 + 23 * q^46 - 26 * q^47 + 3 * q^48 + 20 * q^49 - 31 * q^50 - 17 * q^51 - 4 * q^52 - 43 * q^53 + 21 * q^54 - 16 * q^55 - 20 * q^56 - 25 * q^57 + 48 * q^58 - 19 * q^59 - 25 * q^60 + 9 * q^61 + q^62 + 13 * q^63 + 20 * q^64 - 87 * q^65 + 29 * q^66 + 32 * q^67 + 9 * q^68 - 23 * q^69 + 3 * q^70 - 63 * q^71 - 13 * q^72 + 2 * q^73 + q^74 - 8 * q^75 - 14 * q^76 - 8 * q^77 + q^78 - 51 * q^79 - 3 * q^80 + 4 * q^81 + 27 * q^82 - 24 * q^83 + 3 * q^84 + 31 * q^85 + 3 * q^86 - 33 * q^87 + 8 * q^88 - 35 * q^89 + 12 * q^90 - 4 * q^91 - 23 * q^92 + 17 * q^93 + 26 * q^94 - 30 * q^95 - 3 * q^96 + 5 * q^97 - 20 * q^98 - 31 * q^99

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