LMFDB - Embedded newform 6015.2.a.e.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6015,2,Mod(1,6015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6015, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6015 = 3 \cdot 5 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6015.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:	$48.0300168158$
Analytic rank:	$0$
Dimension:	$31$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	6015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.707695 q^{2} -1.00000 q^{3} -1.49917 q^{4} -1.00000 q^{5} +0.707695 q^{6} -2.27723 q^{7} +2.47634 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.707695 q^{2} -1.00000 q^{3} -1.49917 q^{4} -1.00000 q^{5} +0.707695 q^{6} -2.27723 q^{7} +2.47634 q^{8} +1.00000 q^{9} +0.707695 q^{10} -3.58796 q^{11} +1.49917 q^{12} +0.368946 q^{13} +1.61159 q^{14} +1.00000 q^{15} +1.24584 q^{16} -4.49330 q^{17} -0.707695 q^{18} -2.53795 q^{19} +1.49917 q^{20} +2.27723 q^{21} +2.53919 q^{22} +2.88768 q^{23} -2.47634 q^{24} +1.00000 q^{25} -0.261102 q^{26} -1.00000 q^{27} +3.41395 q^{28} +1.71085 q^{29} -0.707695 q^{30} -5.68840 q^{31} -5.83436 q^{32} +3.58796 q^{33} +3.17989 q^{34} +2.27723 q^{35} -1.49917 q^{36} -6.15856 q^{37} +1.79610 q^{38} -0.368946 q^{39} -2.47634 q^{40} -5.96838 q^{41} -1.61159 q^{42} -2.76891 q^{43} +5.37896 q^{44} -1.00000 q^{45} -2.04360 q^{46} -4.68032 q^{47} -1.24584 q^{48} -1.81421 q^{49} -0.707695 q^{50} +4.49330 q^{51} -0.553112 q^{52} +6.59110 q^{53} +0.707695 q^{54} +3.58796 q^{55} -5.63921 q^{56} +2.53795 q^{57} -1.21076 q^{58} -3.59670 q^{59} -1.49917 q^{60} +12.5730 q^{61} +4.02566 q^{62} -2.27723 q^{63} +1.63728 q^{64} -0.368946 q^{65} -2.53919 q^{66} -10.6408 q^{67} +6.73620 q^{68} -2.88768 q^{69} -1.61159 q^{70} -14.4754 q^{71} +2.47634 q^{72} -6.33314 q^{73} +4.35839 q^{74} -1.00000 q^{75} +3.80482 q^{76} +8.17063 q^{77} +0.261102 q^{78} -6.73010 q^{79} -1.24584 q^{80} +1.00000 q^{81} +4.22380 q^{82} -3.07183 q^{83} -3.41395 q^{84} +4.49330 q^{85} +1.95954 q^{86} -1.71085 q^{87} -8.88504 q^{88} -7.67031 q^{89} +0.707695 q^{90} -0.840177 q^{91} -4.32911 q^{92} +5.68840 q^{93} +3.31224 q^{94} +2.53795 q^{95} +5.83436 q^{96} -14.6155 q^{97} +1.28391 q^{98} -3.58796 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 31 q + 6 q^{2} - 31 q^{3} + 24 q^{4} - 31 q^{5} - 6 q^{6} - 4 q^{7} + 15 q^{8} + 31 q^{9}+O(q^{10}) $ 31 * q + 6 * q^2 - 31 * q^3 + 24 * q^4 - 31 * q^5 - 6 * q^6 - 4 * q^7 + 15 * q^8 + 31 * q^9	\( 31 q + 6 q^{2} - 31 q^{3} + 24 q^{4} - 31 q^{5} - 6 q^{6} - 4 q^{7} + 15 q^{8} + 31 q^{9} - 6 q^{10} - q^{11} - 24 q^{12} + 8 q^{13} + 8 q^{14} + 31 q^{15} + 10 q^{16} + 42 q^{17} + 6 q^{18} - 19 q^{19} - 24 q^{20} + 4 q^{21} + 17 q^{22} + 26 q^{23} - 15 q^{24} + 31 q^{25} + 4 q^{26} - 31 q^{27} - 16 q^{28} - 11 q^{29} + 6 q^{30} - 3 q^{31} + 41 q^{32} + q^{33} + 6 q^{34} + 4 q^{35} + 24 q^{36} + 10 q^{37} + 12 q^{38} - 8 q^{39} - 15 q^{40} + 27 q^{41} - 8 q^{42} - 37 q^{43} - 9 q^{44} - 31 q^{45} - 23 q^{46} + 48 q^{47} - 10 q^{48} + 31 q^{49} + 6 q^{50} - 42 q^{51} + 18 q^{52} + 35 q^{53} - 6 q^{54} + q^{55} + 7 q^{56} + 19 q^{57} - 26 q^{58} - 3 q^{59} + 24 q^{60} + 11 q^{61} + 49 q^{62} - 4 q^{63} - 27 q^{64} - 8 q^{65} - 17 q^{66} - 44 q^{67} + 72 q^{68} - 26 q^{69} - 8 q^{70} + 6 q^{71} + 15 q^{72} + 49 q^{73} - 6 q^{74} - 31 q^{75} - 36 q^{76} + 66 q^{77} - 4 q^{78} - 41 q^{79} - 10 q^{80} + 31 q^{81} + 9 q^{82} + 53 q^{83} + 16 q^{84} - 42 q^{85} + 3 q^{86} + 11 q^{87} + 21 q^{88} + 31 q^{89} - 6 q^{90} - 45 q^{91} + 45 q^{92} + 3 q^{93} - 4 q^{94} + 19 q^{95} - 41 q^{96} + 37 q^{97} + 41 q^{98} - q^{99}+O(q^{100}) \) 31 * q + 6 * q^2 - 31 * q^3 + 24 * q^4 - 31 * q^5 - 6 * q^6 - 4 * q^7 + 15 * q^8 + 31 * q^9 - 6 * q^10 - q^11 - 24 * q^12 + 8 * q^13 + 8 * q^14 + 31 * q^15 + 10 * q^16 + 42 * q^17 + 6 * q^18 - 19 * q^19 - 24 * q^20 + 4 * q^21 + 17 * q^22 + 26 * q^23 - 15 * q^24 + 31 * q^25 + 4 * q^26 - 31 * q^27 - 16 * q^28 - 11 * q^29 + 6 * q^30 - 3 * q^31 + 41 * q^32 + q^33 + 6 * q^34 + 4 * q^35 + 24 * q^36 + 10 * q^37 + 12 * q^38 - 8 * q^39 - 15 * q^40 + 27 * q^41 - 8 * q^42 - 37 * q^43 - 9 * q^44 - 31 * q^45 - 23 * q^46 + 48 * q^47 - 10 * q^48 + 31 * q^49 + 6 * q^50 - 42 * q^51 + 18 * q^52 + 35 * q^53 - 6 * q^54 + q^55 + 7 * q^56 + 19 * q^57 - 26 * q^58 - 3 * q^59 + 24 * q^60 + 11 * q^61 + 49 * q^62 - 4 * q^63 - 27 * q^64 - 8 * q^65 - 17 * q^66 - 44 * q^67 + 72 * q^68 - 26 * q^69 - 8 * q^70 + 6 * q^71 + 15 * q^72 + 49 * q^73 - 6 * q^74 - 31 * q^75 - 36 * q^76 + 66 * q^77 - 4 * q^78 - 41 * q^79 - 10 * q^80 + 31 * q^81 + 9 * q^82 + 53 * q^83 + 16 * q^84 - 42 * q^85 + 3 * q^86 + 11 * q^87 + 21 * q^88 + 31 * q^89 - 6 * q^90 - 45 * q^91 + 45 * q^92 + 3 * q^93 - 4 * q^94 + 19 * q^95 - 41 * q^96 + 37 * q^97 + 41 * q^98 - q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−0.707695	−0.500416	−0.250208	−	0.968192i	$-0.580499\pi$
$2$	−0.707695	−0.500416	−0.250208	+	0.968192i	$0.580499\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.49917	−0.749584
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0.707695	0.288915
$7$	−2.27723	−0.860713	−0.430357	−	0.902659i	$-0.641612\pi$
$7$	−2.27723	−0.860713	−0.430357	+	0.902659i	$0.641612\pi$
$8$	2.47634	0.875520
$9$	1.00000	0.333333
$10$	0.707695	0.223793
$11$	−3.58796	−1.08181	−0.540906	−	0.841083i	$-0.681919\pi$
$11$	−3.58796	−1.08181	−0.540906	+	0.841083i	$0.681919\pi$
$12$	1.49917	0.432772
$13$	0.368946	0.102327	0.0511636	−	0.998690i	$-0.483707\pi$
$13$	0.368946	0.102327	0.0511636	+	0.998690i	$0.483707\pi$
$14$	1.61159	0.430715
$15$	1.00000	0.258199
$16$	1.24584	0.311459
$17$	−4.49330	−1.08978	−0.544892	−	0.838506i	$-0.683429\pi$
$17$	−4.49330	−1.08978	−0.544892	+	0.838506i	$0.683429\pi$
$18$	−0.707695	−0.166805
$19$	−2.53795	−0.582246	−0.291123	−	0.956686i	$-0.594029\pi$
$19$	−2.53795	−0.582246	−0.291123	+	0.956686i	$0.594029\pi$
$20$	1.49917	0.335224
$21$	2.27723	0.496933
$22$	2.53919	0.541356
$23$	2.88768	0.602122	0.301061	−	0.953605i	$-0.402659\pi$
$23$	2.88768	0.602122	0.301061	+	0.953605i	$0.402659\pi$
$24$	−2.47634	−0.505482
$25$	1.00000	0.200000
$26$	−0.261102	−0.0512062
$27$	−1.00000	−0.192450
$28$	3.41395	0.645176
$29$	1.71085	0.317697	0.158848	−	0.987303i	$-0.449222\pi$
$29$	1.71085	0.317697	0.158848	+	0.987303i	$0.449222\pi$
$30$	−0.707695	−0.129207
$31$	−5.68840	−1.02167	−0.510833	−	0.859680i	$-0.670663\pi$
$31$	−5.68840	−1.02167	−0.510833	+	0.859680i	$0.670663\pi$
$32$	−5.83436	−1.03138
$33$	3.58796	0.624584
$34$	3.17989	0.545346
$35$	2.27723	0.384923
$36$	−1.49917	−0.249861
$37$	−6.15856	−1.01246	−0.506231	−	0.862398i	$-0.668962\pi$
$37$	−6.15856	−1.01246	−0.506231	+	0.862398i	$0.668962\pi$
$38$	1.79610	0.291366
$39$	−0.368946	−0.0590787
$40$	−2.47634	−0.391544
$41$	−5.96838	−0.932105	−0.466052	−	0.884757i	$-0.654324\pi$
$41$	−5.96838	−0.932105	−0.466052	+	0.884757i	$0.654324\pi$
$42$	−1.61159	−0.248673
$43$	−2.76891	−0.422254	−0.211127	−	0.977459i	$-0.567713\pi$
$43$	−2.76891	−0.422254	−0.211127	+	0.977459i	$0.567713\pi$
$44$	5.37896	0.810908
$45$	−1.00000	−0.149071
$46$	−2.04360	−0.301312
$47$	−4.68032	−0.682695	−0.341348	−	0.939937i	$-0.610883\pi$
$47$	−4.68032	−0.682695	−0.341348	+	0.939937i	$0.610883\pi$
$48$	−1.24584	−0.179821
$49$	−1.81421	−0.259173
$50$	−0.707695	−0.100083
$51$	4.49330	0.629187
$52$	−0.553112	−0.0767029
$53$	6.59110	0.905357	0.452679	−	0.891674i	$-0.350468\pi$
$53$	6.59110	0.905357	0.452679	+	0.891674i	$0.350468\pi$
$54$	0.707695	0.0963052
$55$	3.58796	0.483801
$56$	−5.63921	−0.753572
$57$	2.53795	0.336160
$58$	−1.21076	−0.158981
$59$	−3.59670	−0.468250	−0.234125	−	0.972207i	$-0.575222\pi$
$59$	−3.59670	−0.468250	−0.234125	+	0.972207i	$0.575222\pi$
$60$	−1.49917	−0.193542
$61$	12.5730	1.60981	0.804905	−	0.593404i	$-0.202216\pi$
$61$	12.5730	1.60981	0.804905	+	0.593404i	$0.202216\pi$
$62$	4.02566	0.511259
$63$	−2.27723	−0.286904
$64$	1.63728	0.204660
$65$	−0.368946	−0.0457622
$66$	−2.53919	−0.312552
$67$	−10.6408	−1.29997	−0.649987	−	0.759945i	$-0.725226\pi$
$67$	−10.6408	−1.29997	−0.649987	+	0.759945i	$0.725226\pi$
$68$	6.73620	0.816885
$69$	−2.88768	−0.347635
$70$	−1.61159	−0.192622
$71$	−14.4754	−1.71791	−0.858955	−	0.512051i	$-0.828886\pi$
$71$	−14.4754	−1.71791	−0.858955	+	0.512051i	$0.828886\pi$
$72$	2.47634	0.291840
$73$	−6.33314	−0.741238	−0.370619	−	0.928785i	$-0.620854\pi$
$73$	−6.33314	−0.741238	−0.370619	+	0.928785i	$0.620854\pi$
$74$	4.35839	0.506652
$75$	−1.00000	−0.115470
$76$	3.80482	0.436442
$77$	8.17063	0.931130
$78$	0.261102	0.0295639
$79$	−6.73010	−0.757196	−0.378598	−	0.925561i	$-0.623594\pi$
$79$	−6.73010	−0.757196	−0.378598	+	0.925561i	$0.623594\pi$
$80$	−1.24584	−0.139289
$81$	1.00000	0.111111
$82$	4.22380	0.466440
$83$	−3.07183	−0.337178	−0.168589	−	0.985686i	$-0.553921\pi$
$83$	−3.07183	−0.337178	−0.168589	+	0.985686i	$0.553921\pi$
$84$	−3.41395	−0.372493
$85$	4.49330	0.487367
$86$	1.95954	0.211303
$87$	−1.71085	−0.183422
$88$	−8.88504	−0.947148
$89$	−7.67031	−0.813051	−0.406525	−	0.913639i	$-0.633260\pi$
$89$	−7.67031	−0.813051	−0.406525	+	0.913639i	$0.633260\pi$
$90$	0.707695	0.0745977
$91$	−0.840177	−0.0880744
$92$	−4.32911	−0.451341
$93$	5.68840	0.589860
$94$	3.31224	0.341632
$95$	2.53795	0.260389
$96$	5.83436	0.595467
$97$	−14.6155	−1.48398	−0.741991	−	0.670410i	$-0.766118\pi$
$97$	−14.6155	−1.48398	−0.741991	+	0.670410i	$0.766118\pi$
$98$	1.28391	0.129694
$99$	−3.58796	−0.360604
$100$	−1.49917	−0.149917
$101$	−11.8597	−1.18008	−0.590042	−	0.807372i	$-0.700889\pi$
$101$	−11.8597	−1.18008	−0.590042	+	0.807372i	$0.700889\pi$
$102$	−3.17989	−0.314856
$103$	−7.57627	−0.746512	−0.373256	−	0.927728i	$-0.621759\pi$
$103$	−7.57627	−0.746512	−0.373256	+	0.927728i	$0.621759\pi$
$104$	0.913638	0.0895896
$105$	−2.27723	−0.222235
$106$	−4.66449	−0.453056
$107$	2.51174	0.242819	0.121409	−	0.992603i	$-0.461259\pi$
$107$	2.51174	0.242819	0.121409	+	0.992603i	$0.461259\pi$
$108$	1.49917	0.144257
$109$	11.3022	1.08255	0.541275	−	0.840845i	$-0.317942\pi$
$109$	11.3022	1.08255	0.541275	+	0.840845i	$0.317942\pi$
$110$	−2.53919	−0.242102
$111$	6.15856	0.584545
$112$	−2.83706	−0.268077
$113$	−2.55392	−0.240252	−0.120126	−	0.992759i	$-0.538330\pi$
$113$	−2.55392	−0.240252	−0.120126	+	0.992759i	$0.538330\pi$
$114$	−1.79610	−0.168220
$115$	−2.88768	−0.269277
$116$	−2.56485	−0.238140
$117$	0.368946	0.0341091
$118$	2.54537	0.234320
$119$	10.2323	0.937992
$120$	2.47634	0.226058
$121$	1.87349	0.170317
$122$	−8.89786	−0.805575
$123$	5.96838	0.538151
$124$	8.52786	0.765825
$125$	−1.00000	−0.0894427
$126$	1.61159	0.143572
$127$	2.75365	0.244347	0.122173	−	0.992509i	$-0.461014\pi$
$127$	2.75365	0.244347	0.122173	+	0.992509i	$0.461014\pi$
$128$	10.5100	0.928964
$129$	2.76891	0.243789
$130$	0.261102	0.0229001
$131$	−0.801495	−0.0700270	−0.0350135	−	0.999387i	$-0.511147\pi$
$131$	−0.801495	−0.0700270	−0.0350135	+	0.999387i	$0.511147\pi$
$132$	−5.37896	−0.468178
$133$	5.77951	0.501147
$134$	7.53041	0.650528
$135$	1.00000	0.0860663
$136$	−11.1270	−0.954128
$137$	7.21948	0.616802	0.308401	−	0.951256i	$-0.400206\pi$
$137$	7.21948	0.616802	0.308401	+	0.951256i	$0.400206\pi$
$138$	2.04360	0.173962
$139$	1.67421	0.142005	0.0710025	−	0.997476i	$-0.477380\pi$
$139$	1.67421	0.142005	0.0710025	+	0.997476i	$0.477380\pi$
$140$	−3.41395	−0.288532
$141$	4.68032	0.394154
$142$	10.2442	0.859670
$143$	−1.32377	−0.110699
$144$	1.24584	0.103820
$145$	−1.71085	−0.142078
$146$	4.48193	0.370927
$147$	1.81421	0.149634
$148$	9.23272	0.758925
$149$	−1.88371	−0.154320	−0.0771600	−	0.997019i	$-0.524585\pi$
$149$	−1.88371	−0.154320	−0.0771600	+	0.997019i	$0.524585\pi$
$150$	0.707695	0.0577831
$151$	−5.28474	−0.430066	−0.215033	−	0.976607i	$-0.568986\pi$
$151$	−5.28474	−0.430066	−0.215033	+	0.976607i	$0.568986\pi$
$152$	−6.28485	−0.509768
$153$	−4.49330	−0.363262
$154$	−5.78232	−0.465952
$155$	5.68840	0.456903
$156$	0.553112	0.0442844
$157$	21.3730	1.70575	0.852874	−	0.522117i	$-0.174857\pi$
$157$	21.3730	1.70575	0.852874	+	0.522117i	$0.174857\pi$
$158$	4.76286	0.378913
$159$	−6.59110	−0.522708
$160$	5.83436	0.461247
$161$	−6.57591	−0.518254
$162$	−0.707695	−0.0556018
$163$	−15.2758	−1.19649	−0.598247	−	0.801312i	$-0.704136\pi$
$163$	−15.2758	−1.19649	−0.598247	+	0.801312i	$0.704136\pi$
$164$	8.94760	0.698690
$165$	−3.58796	−0.279323
$166$	2.17392	0.168729
$167$	18.4594	1.42843	0.714215	−	0.699926i	$-0.246784\pi$
$167$	18.4594	1.42843	0.714215	+	0.699926i	$0.246784\pi$
$168$	5.63921	0.435075
$169$	−12.8639	−0.989529
$170$	−3.17989	−0.243886
$171$	−2.53795	−0.194082
$172$	4.15105	0.316515
$173$	−6.22220	−0.473065	−0.236533	−	0.971624i	$-0.576011\pi$
$173$	−6.22220	−0.473065	−0.236533	+	0.971624i	$0.576011\pi$
$174$	1.21076	0.0917875
$175$	−2.27723	−0.172143
$176$	−4.47002	−0.336940
$177$	3.59670	0.270344
$178$	5.42824	0.406864
$179$	−12.3595	−0.923789	−0.461895	−	0.886935i	$-0.652830\pi$
$179$	−12.3595	−0.923789	−0.461895	+	0.886935i	$0.652830\pi$
$180$	1.49917	0.111741
$181$	−9.29315	−0.690754	−0.345377	−	0.938464i	$-0.612249\pi$
$181$	−9.29315	−0.690754	−0.345377	+	0.938464i	$0.612249\pi$
$182$	0.594589	0.0440739
$183$	−12.5730	−0.929424
$184$	7.15088	0.527170
$185$	6.15856	0.452787
$186$	−4.02566	−0.295175
$187$	16.1218	1.17894
$188$	7.01659	0.511737
$189$	2.27723	0.165644
$190$	−1.79610	−0.130303
$191$	0.941720	0.0681405	0.0340702	−	0.999419i	$-0.489153\pi$
$191$	0.941720	0.0681405	0.0340702	+	0.999419i	$0.489153\pi$
$192$	−1.63728	−0.118160
$193$	−3.09094	−0.222490	−0.111245	−	0.993793i	$-0.535484\pi$
$193$	−3.09094	−0.222490	−0.111245	+	0.993793i	$0.535484\pi$
$194$	10.3433	0.742609
$195$	0.368946	0.0264208
$196$	2.71980	0.194272
$197$	−19.8837	−1.41665	−0.708326	−	0.705885i	$-0.750549\pi$
$197$	−19.8837	−1.41665	−0.708326	+	0.705885i	$0.750549\pi$
$198$	2.53919	0.180452
$199$	−25.5831	−1.81354	−0.906770	−	0.421625i	$-0.861460\pi$
$199$	−25.5831	−1.81354	−0.906770	+	0.421625i	$0.861460\pi$
$200$	2.47634	0.175104
$201$	10.6408	0.750541
$202$	8.39306	0.590533
$203$	−3.89600	−0.273446
$204$	−6.73620	−0.471629
$205$	5.96838	0.416850
$206$	5.36169	0.373567
$207$	2.88768	0.200707
$208$	0.459647	0.0318708
$209$	9.10609	0.629881
$210$	1.61159	0.111210
$211$	−7.52249	−0.517869	−0.258935	−	0.965895i	$-0.583371\pi$
$211$	−7.52249	−0.517869	−0.258935	+	0.965895i	$0.583371\pi$
$212$	−9.88116	−0.678641
$213$	14.4754	0.991836
$214$	−1.77755	−0.121511
$215$	2.76891	0.188838
$216$	−2.47634	−0.168494
$217$	12.9538	0.879362
$218$	−7.99849	−0.541726
$219$	6.33314	0.427954
$220$	−5.37896	−0.362649
$221$	−1.65779	−0.111515
$222$	−4.35839	−0.292516
$223$	11.0691	0.741240	0.370620	−	0.928785i	$-0.379145\pi$
$223$	11.0691	0.741240	0.370620	+	0.928785i	$0.379145\pi$
$224$	13.2862	0.887722
$225$	1.00000	0.0666667
$226$	1.80739	0.120226
$227$	−6.96612	−0.462358	−0.231179	−	0.972911i	$-0.574258\pi$
$227$	−6.96612	−0.462358	−0.231179	+	0.972911i	$0.574258\pi$
$228$	−3.80482	−0.251980
$229$	11.1345	0.735789	0.367895	−	0.929867i	$-0.380079\pi$
$229$	11.1345	0.735789	0.367895	+	0.929867i	$0.380079\pi$
$230$	2.04360	0.134751
$231$	−8.17063	−0.537588
$232$	4.23665	0.278150
$233$	−8.15835	−0.534471	−0.267236	−	0.963631i	$-0.586110\pi$
$233$	−8.15835	−0.534471	−0.267236	+	0.963631i	$0.586110\pi$
$234$	−0.261102	−0.0170687
$235$	4.68032	0.305311
$236$	5.39205	0.350992
$237$	6.73010	0.437167
$238$	−7.24134	−0.469386
$239$	26.3161	1.70225	0.851123	−	0.524967i	$-0.175922\pi$
$239$	26.3161	1.70225	0.851123	+	0.524967i	$0.175922\pi$
$240$	1.24584	0.0804184
$241$	−4.85826	−0.312948	−0.156474	−	0.987682i	$-0.550013\pi$
$241$	−4.85826	−0.312948	−0.156474	+	0.987682i	$0.550013\pi$
$242$	−1.32586	−0.0852294
$243$	−1.00000	−0.0641500
$244$	−18.8490	−1.20669
$245$	1.81421	0.115906
$246$	−4.22380	−0.269299
$247$	−0.936369	−0.0595797
$248$	−14.0864	−0.894490
$249$	3.07183	0.194670
$250$	0.707695	0.0447586
$251$	2.94725	0.186028	0.0930142	−	0.995665i	$-0.470350\pi$
$251$	2.94725	0.186028	0.0930142	+	0.995665i	$0.470350\pi$
$252$	3.41395	0.215059
$253$	−10.3609	−0.651383
$254$	−1.94874	−0.122275
$255$	−4.49330	−0.281381
$256$	−10.7125	−0.669529
$257$	19.6998	1.22884	0.614419	−	0.788980i	$-0.289391\pi$
$257$	19.6998	1.22884	0.614419	+	0.788980i	$0.289391\pi$
$258$	−1.95954	−0.121996
$259$	14.0245	0.871439
$260$	0.553112	0.0343026
$261$	1.71085	0.105899
$262$	0.567214	0.0350426
$263$	−15.6007	−0.961978	−0.480989	−	0.876727i	$-0.659722\pi$
$263$	−15.6007	−0.961978	−0.480989	+	0.876727i	$0.659722\pi$
$264$	8.88504	0.546836
$265$	−6.59110	−0.404888
$266$	−4.09013	−0.250782
$267$	7.67031	0.469415
$268$	15.9523	0.974440
$269$	20.2237	1.23306	0.616530	−	0.787332i	$-0.288538\pi$
$269$	20.2237	1.23306	0.616530	+	0.787332i	$0.288538\pi$
$270$	−0.707695	−0.0430690
$271$	18.1779	1.10423	0.552113	−	0.833769i	$-0.313822\pi$
$271$	18.1779	1.10423	0.552113	+	0.833769i	$0.313822\pi$
$272$	−5.59791	−0.339423
$273$	0.840177	0.0508498
$274$	−5.10919	−0.308658
$275$	−3.58796	−0.216362
$276$	4.32911	0.260582
$277$	4.16629	0.250328	0.125164	−	0.992136i	$-0.460054\pi$
$277$	4.16629	0.250328	0.125164	+	0.992136i	$0.460054\pi$
$278$	−1.18483	−0.0710616
$279$	−5.68840	−0.340556
$280$	5.63921	0.337007
$281$	−31.3568	−1.87059	−0.935295	−	0.353869i	$-0.884866\pi$
$281$	−31.3568	−1.87059	−0.935295	+	0.353869i	$0.884866\pi$
$282$	−3.31224	−0.197241
$283$	4.82608	0.286880	0.143440	−	0.989659i	$-0.454184\pi$
$283$	4.82608	0.286880	0.143440	+	0.989659i	$0.454184\pi$
$284$	21.7010	1.28772
$285$	−2.53795	−0.150335
$286$	0.936823	0.0553955
$287$	13.5914	0.802275
$288$	−5.83436	−0.343793
$289$	3.18972	0.187631
$290$	1.21076	0.0710983
$291$	14.6155	0.856777
$292$	9.49443	0.555620
$293$	10.7601	0.628612	0.314306	−	0.949322i	$-0.398228\pi$
$293$	10.7601	0.628612	0.314306	+	0.949322i	$0.398228\pi$
$294$	−1.28391	−0.0748790
$295$	3.59670	0.209408
$296$	−15.2507	−0.886430
$297$	3.58796	0.208195
$298$	1.33310	0.0772242
$299$	1.06540	0.0616135
$300$	1.49917	0.0865545
$301$	6.30545	0.363440
$302$	3.73999	0.215212
$303$	11.8597	0.681322
$304$	−3.16187	−0.181346
$305$	−12.5730	−0.719928
$306$	3.17989	0.181782
$307$	−17.0981	−0.975841	−0.487920	−	0.872888i	$-0.662244\pi$
$307$	−17.0981	−0.975841	−0.487920	+	0.872888i	$0.662244\pi$
$308$	−12.2491	−0.697960
$309$	7.57627	0.430999
$310$	−4.02566	−0.228642
$311$	21.2863	1.20703	0.603517	−	0.797350i	$-0.293766\pi$
$311$	21.2863	1.20703	0.603517	+	0.797350i	$0.293766\pi$
$312$	−0.913638	−0.0517246
$313$	29.3814	1.66074	0.830368	−	0.557215i	$-0.188130\pi$
$313$	29.3814	1.66074	0.830368	+	0.557215i	$0.188130\pi$
$314$	−15.1255	−0.853584
$315$	2.27723	0.128308
$316$	10.0896	0.567582
$317$	34.8882	1.95951	0.979757	−	0.200189i	$-0.0641555\pi$
$317$	34.8882	1.95951	0.979757	+	0.200189i	$0.0641555\pi$
$318$	4.66449	0.261572
$319$	−6.13846	−0.343688
$320$	−1.63728	−0.0915267
$321$	−2.51174	−0.140192
$322$	4.65374	0.259343
$323$	11.4038	0.634523
$324$	−1.49917	−0.0832871
$325$	0.368946	0.0204655
$326$	10.8106	0.598745
$327$	−11.3022	−0.625011
$328$	−14.7798	−0.816076
$329$	10.6582	0.587605
$330$	2.53919	0.139778
$331$	−1.87931	−0.103296	−0.0516481	−	0.998665i	$-0.516447\pi$
$331$	−1.87931	−0.103296	−0.0516481	+	0.998665i	$0.516447\pi$
$332$	4.60519	0.252743
$333$	−6.15856	−0.337487
$334$	−13.0636	−0.714810
$335$	10.6408	0.581366
$336$	2.83706	0.154774
$337$	−4.61329	−0.251302	−0.125651	−	0.992074i	$-0.540102\pi$
$337$	−4.61329	−0.251302	−0.125651	+	0.992074i	$0.540102\pi$
$338$	9.10371	0.495176
$339$	2.55392	0.138710
$340$	−6.73620	−0.365322
$341$	20.4098	1.10525
$342$	1.79610	0.0971219
$343$	20.0720	1.08379
$344$	−6.85677	−0.369692
$345$	2.88768	0.155467
$346$	4.40342	0.236730
$347$	−5.90028	−0.316744	−0.158372	−	0.987380i	$-0.550624\pi$
$347$	−5.90028	−0.316744	−0.158372	+	0.987380i	$0.550624\pi$
$348$	2.56485	0.137490
$349$	−2.48111	−0.132811	−0.0664054	−	0.997793i	$-0.521153\pi$
$349$	−2.48111	−0.132811	−0.0664054	+	0.997793i	$0.521153\pi$
$350$	1.61159	0.0861430
$351$	−0.368946	−0.0196929
$352$	20.9335	1.11576
$353$	37.0807	1.97361	0.986804	−	0.161922i	$-0.0517692\pi$
$353$	37.0807	1.97361	0.986804	+	0.161922i	$0.0517692\pi$
$354$	−2.54537	−0.135285
$355$	14.4754	0.768273
$356$	11.4991	0.609450
$357$	−10.2323	−0.541550
$358$	8.74673	0.462279
$359$	−5.25824	−0.277519	−0.138760	−	0.990326i	$-0.544312\pi$
$359$	−5.25824	−0.277519	−0.138760	+	0.990326i	$0.544312\pi$
$360$	−2.47634	−0.130515
$361$	−12.5588	−0.660989
$362$	6.57672	0.345665
$363$	−1.87349	−0.0983326
$364$	1.25957	0.0660192
$365$	6.33314	0.331492
$366$	8.89786	0.465099
$367$	2.32120	0.121166	0.0605828	−	0.998163i	$-0.480704\pi$
$367$	2.32120	0.121166	0.0605828	+	0.998163i	$0.480704\pi$
$368$	3.59757	0.187536
$369$	−5.96838	−0.310702
$370$	−4.35839	−0.226582
$371$	−15.0095	−0.779253
$372$	−8.52786	−0.442149
$373$	21.0695	1.09094	0.545469	−	0.838131i	$-0.316352\pi$
$373$	21.0695	1.09094	0.545469	+	0.838131i	$0.316352\pi$
$374$	−11.4093	−0.589962
$375$	1.00000	0.0516398
$376$	−11.5901	−0.597713
$377$	0.631211	0.0325090
$378$	−1.61159	−0.0828911
$379$	30.5328	1.56836	0.784182	−	0.620531i	$-0.213083\pi$
$379$	30.5328	1.56836	0.784182	+	0.620531i	$0.213083\pi$
$380$	−3.80482	−0.195183
$381$	−2.75365	−0.141074
$382$	−0.666451	−0.0340986
$383$	25.1040	1.28276	0.641378	−	0.767225i	$-0.278363\pi$
$383$	25.1040	1.28276	0.641378	+	0.767225i	$0.278363\pi$
$384$	−10.5100	−0.536338
$385$	−8.17063	−0.416414
$386$	2.18744	0.111338
$387$	−2.76891	−0.140751
$388$	21.9111	1.11237
$389$	−19.2956	−0.978327	−0.489164	−	0.872192i	$-0.662698\pi$
$389$	−19.2956	−0.978327	−0.489164	+	0.872192i	$0.662698\pi$
$390$	−0.261102	−0.0132214
$391$	−12.9752	−0.656183
$392$	−4.49261	−0.226911
$393$	0.801495	0.0404301
$394$	14.0716	0.708916
$395$	6.73010	0.338628
$396$	5.37896	0.270303
$397$	1.00457	0.0504179	0.0252090	−	0.999682i	$-0.491975\pi$
$397$	1.00457	0.0504179	0.0252090	+	0.999682i	$0.491975\pi$
$398$	18.1051	0.907525
$399$	−5.77951	−0.289337
$400$	1.24584	0.0622918
$401$	1.00000	0.0499376
$401$	1.00000	0.0499376
$402$	−7.53041	−0.375583
$403$	−2.09871	−0.104544
$404$	17.7797	0.884572
$405$	−1.00000	−0.0496904
$406$	2.75718	0.136837
$407$	22.0967	1.09529
$408$	11.1270	0.550866
$409$	−12.0879	−0.597709	−0.298855	−	0.954299i	$-0.596605\pi$
$409$	−12.0879	−0.597709	−0.298855	+	0.954299i	$0.596605\pi$
$410$	−4.22380	−0.208598
$411$	−7.21948	−0.356111
$412$	11.3581	0.559573
$413$	8.19051	0.403029
$414$	−2.04360	−0.100437
$415$	3.07183	0.150790
$416$	−2.15257	−0.105538
$417$	−1.67421	−0.0819866
$418$	−6.44434	−0.315203
$419$	11.0145	0.538096	0.269048	−	0.963127i	$-0.413291\pi$
$419$	11.0145	0.538096	0.269048	+	0.963127i	$0.413291\pi$
$420$	3.41395	0.166584
$421$	−34.9234	−1.70206	−0.851030	−	0.525117i	$-0.824022\pi$
$421$	−34.9234	−1.70206	−0.851030	+	0.525117i	$0.824022\pi$
$422$	5.32363	0.259150
$423$	−4.68032	−0.227565
$424$	16.3218	0.792659
$425$	−4.49330	−0.217957
$426$	−10.2442	−0.496331
$427$	−28.6317	−1.38558
$428$	−3.76552	−0.182013
$429$	1.32377	0.0639120
$430$	−1.95954	−0.0944976
$431$	−16.2034	−0.780488	−0.390244	−	0.920711i	$-0.627609\pi$
$431$	−16.2034	−0.780488	−0.390244	+	0.920711i	$0.627609\pi$
$432$	−1.24584	−0.0599403
$433$	−27.2914	−1.31154	−0.655771	−	0.754960i	$-0.727656\pi$
$433$	−27.2914	−1.31154	−0.655771	+	0.754960i	$0.727656\pi$
$434$	−9.16736	−0.440047
$435$	1.71085	0.0820289
$436$	−16.9438	−0.811462
$437$	−7.32879	−0.350583
$438$	−4.48193	−0.214155
$439$	−11.1834	−0.533753	−0.266876	−	0.963731i	$-0.585992\pi$
$439$	−11.1834	−0.533753	−0.266876	+	0.963731i	$0.585992\pi$
$440$	8.88504	0.423577
$441$	−1.81421	−0.0863909
$442$	1.17321	0.0558038
$443$	26.3134	1.25019	0.625093	−	0.780550i	$-0.285061\pi$
$443$	26.3134	1.25019	0.625093	+	0.780550i	$0.285061\pi$
$444$	−9.23272	−0.438165
$445$	7.67031	0.363607
$446$	−7.83353	−0.370929
$447$	1.88371	0.0890966
$448$	−3.72847	−0.176153
$449$	36.7401	1.73387	0.866936	−	0.498420i	$-0.166086\pi$
$449$	36.7401	1.73387	0.866936	+	0.498420i	$0.166086\pi$
$450$	−0.707695	−0.0333611
$451$	21.4143	1.00836
$452$	3.82875	0.180089
$453$	5.28474	0.248299
$454$	4.92989	0.231371
$455$	0.840177	0.0393881
$456$	6.28485	0.294315
$457$	−0.399681	−0.0186963	−0.00934816	−	0.999956i	$-0.502976\pi$
$457$	−0.399681	−0.0186963	−0.00934816	+	0.999956i	$0.502976\pi$
$458$	−7.87984	−0.368201
$459$	4.49330	0.209729
$460$	4.32911	0.201846
$461$	2.50030	0.116450	0.0582252	−	0.998303i	$-0.481456\pi$
$461$	2.50030	0.116450	0.0582252	+	0.998303i	$0.481456\pi$
$462$	5.78232	0.269018
$463$	−31.2279	−1.45129	−0.725643	−	0.688072i	$-0.758457\pi$
$463$	−31.2279	−1.45129	−0.725643	+	0.688072i	$0.758457\pi$
$464$	2.13144	0.0989495
$465$	−5.68840	−0.263793
$466$	5.77363	0.267458
$467$	−2.19768	−0.101696	−0.0508482	−	0.998706i	$-0.516192\pi$
$467$	−2.19768	−0.101696	−0.0508482	+	0.998706i	$0.516192\pi$
$468$	−0.553112	−0.0255676
$469$	24.2315	1.11891
$470$	−3.31224	−0.152782
$471$	−21.3730	−0.984814
$472$	−8.90666	−0.409962
$473$	9.93474	0.456800
$474$	−4.76286	−0.218766
$475$	−2.53795	−0.116449
$476$	−15.3399	−0.703103
$477$	6.59110	0.301786
$478$	−18.6238	−0.851831
$479$	−8.43296	−0.385312	−0.192656	−	0.981266i	$-0.561710\pi$
$479$	−8.43296	−0.385312	−0.192656	+	0.981266i	$0.561710\pi$
$480$	−5.83436	−0.266301
$481$	−2.27218	−0.103602
$482$	3.43817	0.156604
$483$	6.57591	0.299214
$484$	−2.80867	−0.127667
$485$	14.6155	0.663657
$486$	0.707695	0.0321017
$487$	12.4917	0.566054	0.283027	−	0.959112i	$-0.408661\pi$
$487$	12.4917	0.566054	0.283027	+	0.959112i	$0.408661\pi$
$488$	31.1351	1.40942
$489$	15.2758	0.690796
$490$	−1.28391	−0.0580011
$491$	−0.386298	−0.0174334	−0.00871670	−	0.999962i	$-0.502775\pi$
$491$	−0.386298	−0.0174334	−0.00871670	+	0.999962i	$0.502775\pi$
$492$	−8.94760	−0.403389
$493$	−7.68735	−0.346221
$494$	0.662664	0.0298147
$495$	3.58796	0.161267
$496$	−7.08682	−0.318207
$497$	32.9638	1.47863
$498$	−2.17392	−0.0974158
$499$	−10.3918	−0.465201	−0.232600	−	0.972572i	$-0.574723\pi$
$499$	−10.3918	−0.465201	−0.232600	+	0.972572i	$0.574723\pi$
$500$	1.49917	0.0670448
$501$	−18.4594	−0.824705
$502$	−2.08575	−0.0930917
$503$	19.4968	0.869318	0.434659	−	0.900595i	$-0.356869\pi$
$503$	19.4968	0.869318	0.434659	+	0.900595i	$0.356869\pi$
$504$	−5.63921	−0.251191
$505$	11.8597	0.527750
$506$	7.33235	0.325963
$507$	12.8639	0.571305
$508$	−4.12818	−0.183158
$509$	2.28007	0.101062	0.0505311	−	0.998722i	$-0.483909\pi$
$509$	2.28007	0.101062	0.0505311	+	0.998722i	$0.483909\pi$
$510$	3.17989	0.140808
$511$	14.4220	0.637993
$512$	−13.4389	−0.593921
$513$	2.53795	0.112053
$514$	−13.9414	−0.614930
$515$	7.57627	0.333850
$516$	−4.15105	−0.182740
$517$	16.7928	0.738548
$518$	−9.92506	−0.436082
$519$	6.22220	0.273124
$520$	−0.913638	−0.0400657
$521$	29.3539	1.28602	0.643009	−	0.765859i	$-0.277686\pi$
$521$	29.3539	1.28602	0.643009	+	0.765859i	$0.277686\pi$
$522$	−1.21076	−0.0529935
$523$	−39.0922	−1.70938	−0.854692	−	0.519136i	$-0.826254\pi$
$523$	−39.0922	−1.70938	−0.854692	+	0.519136i	$0.826254\pi$
$524$	1.20158	0.0524911
$525$	2.27723	0.0993866
$526$	11.0405	0.481389
$527$	25.5597	1.11340
$528$	4.47002	0.194532
$529$	−14.6613	−0.637449
$530$	4.66449	0.202613
$531$	−3.59670	−0.156083
$532$	−8.66445	−0.375652
$533$	−2.20201	−0.0953797
$534$	−5.42824	−0.234903
$535$	−2.51174	−0.108592
$536$	−26.3502	−1.13815
$537$	12.3595	0.533350
$538$	−14.3122	−0.617043
$539$	6.50932	0.280376
$540$	−1.49917	−0.0645139
$541$	4.16084	0.178888	0.0894441	−	0.995992i	$-0.471491\pi$
$541$	4.16084	0.178888	0.0894441	+	0.995992i	$0.471491\pi$
$542$	−12.8644	−0.552573
$543$	9.29315	0.398807
$544$	26.2155	1.12398
$545$	−11.3022	−0.484131
$546$	−0.594589	−0.0254461
$547$	16.2847	0.696283	0.348142	−	0.937442i	$-0.386813\pi$
$547$	16.2847	0.696283	0.348142	+	0.937442i	$0.386813\pi$
$548$	−10.8232	−0.462344
$549$	12.5730	0.536603
$550$	2.53919	0.108271
$551$	−4.34205	−0.184978
$552$	−7.15088	−0.304362
$553$	15.3260	0.651728
$554$	−2.94846	−0.125268
$555$	−6.15856	−0.261416
$556$	−2.50993	−0.106445
$557$	−12.7445	−0.540001	−0.270001	−	0.962860i	$-0.587024\pi$
$557$	−12.7445	−0.540001	−0.270001	+	0.962860i	$0.587024\pi$
$558$	4.02566	0.170420
$559$	−1.02158	−0.0432081
$560$	2.83706	0.119888
$561$	−16.1218	−0.680663
$562$	22.1911	0.936073
$563$	−2.71922	−0.114601	−0.0573007	−	0.998357i	$-0.518249\pi$
$563$	−2.71922	−0.114601	−0.0573007	+	0.998357i	$0.518249\pi$
$564$	−7.01659	−0.295452
$565$	2.55392	0.107444
$566$	−3.41539	−0.143560
$567$	−2.27723	−0.0956348
$568$	−35.8460	−1.50406
$569$	25.2748	1.05957	0.529787	−	0.848131i	$-0.322272\pi$
$569$	25.2748	1.05957	0.529787	+	0.848131i	$0.322272\pi$
$570$	1.79610	0.0752303
$571$	14.7248	0.616215	0.308107	−	0.951352i	$-0.400304\pi$
$571$	14.7248	0.616215	0.308107	+	0.951352i	$0.400304\pi$
$572$	1.98455	0.0829781
$573$	−0.941720	−0.0393409
$574$	−9.61857	−0.401471
$575$	2.88768	0.120424
$576$	1.63728	0.0682200
$577$	18.5383	0.771760	0.385880	−	0.922549i	$-0.373898\pi$
$577$	18.5383	0.771760	0.385880	+	0.922549i	$0.373898\pi$
$578$	−2.25735	−0.0938934
$579$	3.09094	0.128455
$580$	2.56485	0.106500
$581$	6.99528	0.290213
$582$	−10.3433	−0.428745
$583$	−23.6486	−0.979426
$584$	−15.6830	−0.648969
$585$	−0.368946	−0.0152541
$586$	−7.61487	−0.314568
$587$	21.5723	0.890383	0.445191	−	0.895435i	$-0.353136\pi$
$587$	21.5723	0.890383	0.445191	+	0.895435i	$0.353136\pi$
$588$	−2.71980	−0.112163
$589$	14.4369	0.594862
$590$	−2.54537	−0.104791
$591$	19.8837	0.817905
$592$	−7.67256	−0.315340
$593$	−9.59012	−0.393819	−0.196909	−	0.980422i	$-0.563090\pi$
$593$	−9.59012	−0.393819	−0.196909	+	0.980422i	$0.563090\pi$
$594$	−2.53919	−0.104184
$595$	−10.2323	−0.419483
$596$	2.82400	0.115676
$597$	25.5831	1.04705
$598$	−0.753977	−0.0308324
$599$	−2.96291	−0.121061	−0.0605306	−	0.998166i	$-0.519279\pi$
$599$	−2.96291	−0.121061	−0.0605306	+	0.998166i	$0.519279\pi$
$600$	−2.47634	−0.101096
$601$	−10.4117	−0.424701	−0.212350	−	0.977194i	$-0.568112\pi$
$601$	−10.4117	−0.424701	−0.212350	+	0.977194i	$0.568112\pi$
$602$	−4.46234	−0.181871
$603$	−10.6408	−0.433325
$604$	7.92272	0.322371
$605$	−1.87349	−0.0761681
$606$	−8.39306	−0.340945
$607$	−13.5294	−0.549142	−0.274571	−	0.961567i	$-0.588536\pi$
$607$	−13.5294	−0.549142	−0.274571	+	0.961567i	$0.588536\pi$
$608$	14.8073	0.600517
$609$	3.89600	0.157874
$610$	8.89786	0.360264
$611$	−1.72679	−0.0698583
$612$	6.73620	0.272295
$613$	−27.4689	−1.10946	−0.554728	−	0.832031i	$-0.687178\pi$
$613$	−27.4689	−1.10946	−0.554728	+	0.832031i	$0.687178\pi$
$614$	12.1003	0.488327
$615$	−5.96838	−0.240668
$616$	20.2333	0.815223
$617$	−10.0925	−0.406309	−0.203155	−	0.979147i	$-0.565119\pi$
$617$	−10.0925	−0.406309	−0.203155	+	0.979147i	$0.565119\pi$
$618$	−5.36169	−0.215679
$619$	11.5297	0.463418	0.231709	−	0.972785i	$-0.425568\pi$
$619$	11.5297	0.463418	0.231709	+	0.972785i	$0.425568\pi$
$620$	−8.52786	−0.342487
$621$	−2.88768	−0.115878
$622$	−15.0642	−0.604019
$623$	17.4671	0.699804
$624$	−0.459647	−0.0184006
$625$	1.00000	0.0400000
$626$	−20.7931	−0.831060
$627$	−9.10609	−0.363662
$628$	−32.0416	−1.27860
$629$	27.6723	1.10337
$630$	−1.61159	−0.0642072
$631$	−17.6004	−0.700661	−0.350330	−	0.936626i	$-0.613931\pi$
$631$	−17.6004	−0.700661	−0.350330	+	0.936626i	$0.613931\pi$
$632$	−16.6661	−0.662940
$633$	7.52249	0.298992
$634$	−24.6902	−0.980573
$635$	−2.75365	−0.109275
$636$	9.88116	0.391814
$637$	−0.669346	−0.0265205
$638$	4.34416	0.171987
$639$	−14.4754	−0.572637
$640$	−10.5100	−0.415445
$641$	−8.28728	−0.327328	−0.163664	−	0.986516i	$-0.552331\pi$
$641$	−8.28728	−0.327328	−0.163664	+	0.986516i	$0.552331\pi$
$642$	1.77755	0.0701541
$643$	−39.4926	−1.55744	−0.778719	−	0.627373i	$-0.784130\pi$
$643$	−39.4926	−1.55744	−0.778719	+	0.627373i	$0.784130\pi$
$644$	9.85839	0.388475
$645$	−2.76891	−0.109026
$646$	−8.07040	−0.317526
$647$	10.2446	0.402757	0.201378	−	0.979514i	$-0.435458\pi$
$647$	10.2446	0.402757	0.201378	+	0.979514i	$0.435458\pi$
$648$	2.47634	0.0972800
$649$	12.9048	0.506558
$650$	−0.261102	−0.0102412
$651$	−12.9538	−0.507700
$652$	22.9010	0.896872
$653$	46.5806	1.82284	0.911420	−	0.411476i	$-0.134987\pi$
$653$	46.5806	1.82284	0.911420	+	0.411476i	$0.134987\pi$
$654$	7.99849	0.312766
$655$	0.801495	0.0313170
$656$	−7.43563	−0.290312
$657$	−6.33314	−0.247079
$658$	−7.54275	−0.294047
$659$	−22.5683	−0.879136	−0.439568	−	0.898209i	$-0.644868\pi$
$659$	−22.5683	−0.879136	−0.439568	+	0.898209i	$0.644868\pi$
$660$	5.37896	0.209376
$661$	−26.4821	−1.03004	−0.515018	−	0.857179i	$-0.672215\pi$
$661$	−26.4821	−1.03004	−0.515018	+	0.857179i	$0.672215\pi$
$662$	1.32998	0.0516911
$663$	1.65779	0.0643830
$664$	−7.60692	−0.295206
$665$	−5.77951	−0.224120
$666$	4.35839	0.168884
$667$	4.94038	0.191292
$668$	−27.6737	−1.07073
$669$	−11.0691	−0.427955
$670$	−7.53041	−0.290925
$671$	−45.1115	−1.74151
$672$	−13.2862	−0.512526
$673$	34.9611	1.34765	0.673827	−	0.738890i	$-0.264649\pi$
$673$	34.9611	1.34765	0.673827	+	0.738890i	$0.264649\pi$
$674$	3.26481	0.125756
$675$	−1.00000	−0.0384900
$676$	19.2851	0.741735
$677$	43.9518	1.68920	0.844602	−	0.535395i	$-0.179837\pi$
$677$	43.9518	1.68920	0.844602	+	0.535395i	$0.179837\pi$
$678$	−1.80739	−0.0694126
$679$	33.2830	1.27728
$680$	11.1270	0.426699
$681$	6.96612	0.266942
$682$	−14.4439	−0.553086
$683$	19.9856	0.764728	0.382364	−	0.924012i	$-0.375110\pi$
$683$	19.9856	0.764728	0.382364	+	0.924012i	$0.375110\pi$
$684$	3.80482	0.145481
$685$	−7.21948	−0.275842
$686$	−14.2049	−0.542344
$687$	−11.1345	−0.424808
$688$	−3.44961	−0.131515
$689$	2.43176	0.0926428
$690$	−2.04360	−0.0777983
$691$	−34.2077	−1.30132	−0.650662	−	0.759368i	$-0.725508\pi$
$691$	−34.2077	−1.30132	−0.650662	+	0.759368i	$0.725508\pi$
$692$	9.32812	0.354602
$693$	8.17063	0.310377
$694$	4.17560	0.158504
$695$	−1.67421	−0.0635066
$696$	−4.23665	−0.160590
$697$	26.8177	1.01579
$698$	1.75587	0.0664606
$699$	8.15835	0.308577
$700$	3.41395	0.129035
$701$	−12.4360	−0.469703	−0.234851	−	0.972031i	$-0.575460\pi$
$701$	−12.4360	−0.469703	−0.234851	+	0.972031i	$0.575460\pi$
$702$	0.261102	0.00985465
$703$	15.6301	0.589502
$704$	−5.87450	−0.221403
$705$	−4.68032	−0.176271
$706$	−26.2419	−0.987625
$707$	27.0073	1.01571
$708$	−5.39205	−0.202646
$709$	−38.0308	−1.42828	−0.714139	−	0.700004i	$-0.753182\pi$
$709$	−38.0308	−1.42828	−0.714139	+	0.700004i	$0.753182\pi$
$710$	−10.2442	−0.384456
$711$	−6.73010	−0.252399
$712$	−18.9943	−0.711842
$713$	−16.4263	−0.615168
$714$	7.24134	0.271000
$715$	1.32377	0.0495060
$716$	18.5289	0.692457
$717$	−26.3161	−0.982792
$718$	3.72123	0.138875
$719$	36.0616	1.34487	0.672436	−	0.740155i	$-0.265248\pi$
$719$	36.0616	1.34487	0.672436	+	0.740155i	$0.265248\pi$
$720$	−1.24584	−0.0464296
$721$	17.2529	0.642533
$722$	8.88780	0.330770
$723$	4.85826	0.180681
$724$	13.9320	0.517778
$725$	1.71085	0.0635393
$726$	1.32586	0.0492072
$727$	−12.1223	−0.449589	−0.224795	−	0.974406i	$-0.572171\pi$
$727$	−12.1223	−0.449589	−0.224795	+	0.974406i	$0.572171\pi$
$728$	−2.08057	−0.0771109
$729$	1.00000	0.0370370
$730$	−4.48193	−0.165884
$731$	12.4415	0.460166
$732$	18.8490	0.696681
$733$	30.0224	1.10890	0.554451	−	0.832216i	$-0.312928\pi$
$733$	30.0224	1.10890	0.554451	+	0.832216i	$0.312928\pi$
$734$	−1.64270	−0.0606333
$735$	−1.81421	−0.0669181
$736$	−16.8477	−0.621016
$737$	38.1786	1.40633
$738$	4.22380	0.155480
$739$	−50.5340	−1.85892	−0.929461	−	0.368920i	$-0.879728\pi$
$739$	−50.5340	−1.85892	−0.929461	+	0.368920i	$0.879728\pi$
$740$	−9.23272	−0.339401
$741$	0.936369	0.0343984
$742$	10.6221	0.389951
$743$	−19.5728	−0.718056	−0.359028	−	0.933327i	$-0.616892\pi$
$743$	−19.5728	−0.718056	−0.359028	+	0.933327i	$0.616892\pi$
$744$	14.0864	0.516434
$745$	1.88371	0.0690140
$746$	−14.9108	−0.545923
$747$	−3.07183	−0.112393
$748$	−24.1693	−0.883716
$749$	−5.71981	−0.208997
$750$	−0.707695	−0.0258414
$751$	12.6142	0.460298	0.230149	−	0.973155i	$-0.426079\pi$
$751$	12.6142	0.460298	0.230149	+	0.973155i	$0.426079\pi$
$752$	−5.83092	−0.212632
$753$	−2.94725	−0.107404
$754$	−0.446705	−0.0162680
$755$	5.28474	0.192332
$756$	−3.41395	−0.124164
$757$	40.7356	1.48056	0.740280	−	0.672299i	$-0.234693\pi$
$757$	40.7356	1.48056	0.740280	+	0.672299i	$0.234693\pi$
$758$	−21.6079	−0.784835
$759$	10.3609	0.376076
$760$	6.28485	0.227975
$761$	−4.06394	−0.147318	−0.0736588	−	0.997283i	$-0.523468\pi$
$761$	−4.06394	−0.147318	−0.0736588	+	0.997283i	$0.523468\pi$
$762$	1.94874	0.0705955
$763$	−25.7377	−0.931766
$764$	−1.41180	−0.0510770
$765$	4.49330	0.162456
$766$	−17.7660	−0.641912
$767$	−1.32699	−0.0479147
$768$	10.7125	0.386553
$769$	18.7223	0.675142	0.337571	−	0.941300i	$-0.390395\pi$
$769$	18.7223	0.675142	0.337571	+	0.941300i	$0.390395\pi$
$770$	5.78232	0.208380
$771$	−19.6998	−0.709469
$772$	4.63383	0.166775
$773$	2.29065	0.0823891	0.0411946	−	0.999151i	$-0.486884\pi$
$773$	2.29065	0.0823891	0.0411946	+	0.999151i	$0.486884\pi$
$774$	1.95954	0.0704343
$775$	−5.68840	−0.204333
$776$	−36.1931	−1.29926
$777$	−14.0245	−0.503126
$778$	13.6554	0.489571
$779$	15.1475	0.542715
$780$	−0.553112	−0.0198046
$781$	51.9371	1.85846
$782$	9.18248	0.328365
$783$	−1.71085	−0.0611407
$784$	−2.26021	−0.0807217
$785$	−21.3730	−0.762834
$786$	−0.567214	−0.0202319
$787$	−3.65255	−0.130199	−0.0650996	−	0.997879i	$-0.520737\pi$
$787$	−3.65255	−0.130199	−0.0650996	+	0.997879i	$0.520737\pi$
$788$	29.8089	1.06190
$789$	15.6007	0.555398
$790$	−4.76286	−0.169455
$791$	5.81586	0.206788
$792$	−8.88504	−0.315716
$793$	4.63877	0.164727
$794$	−0.710929	−0.0252299
$795$	6.59110	0.233762
$796$	38.3534	1.35940
$797$	−10.0246	−0.355088	−0.177544	−	0.984113i	$-0.556815\pi$
$797$	−10.0246	−0.355088	−0.177544	+	0.984113i	$0.556815\pi$
$798$	4.09013	0.144789
$799$	21.0301	0.743991
$800$	−5.83436	−0.206276
$801$	−7.67031	−0.271017
$802$	−0.707695	−0.0249896
$803$	22.7231	0.801880
$804$	−15.9523	−0.562593
$805$	6.57591	0.231770
$806$	1.48525	0.0523157
$807$	−20.2237	−0.711907
$808$	−29.3687	−1.03319
$809$	4.88345	0.171693	0.0858466	−	0.996308i	$-0.472641\pi$
$809$	4.88345	0.171693	0.0858466	+	0.996308i	$0.472641\pi$
$810$	0.707695	0.0248659
$811$	−35.6362	−1.25136	−0.625678	−	0.780082i	$-0.715178\pi$
$811$	−35.6362	−1.25136	−0.625678	+	0.780082i	$0.715178\pi$
$812$	5.84076	0.204970
$813$	−18.1779	−0.637525
$814$	−15.6377	−0.548102
$815$	15.2758	0.535088
$816$	5.59791	0.195966
$817$	7.02736	0.245856
$818$	8.55457	0.299104
$819$	−0.840177	−0.0293581
$820$	−8.94760	−0.312464
$821$	−17.3805	−0.606583	−0.303292	−	0.952898i	$-0.598086\pi$
$821$	−17.3805	−0.606583	−0.303292	+	0.952898i	$0.598086\pi$
$822$	5.10919	0.178204
$823$	−4.26581	−0.148697	−0.0743484	−	0.997232i	$-0.523688\pi$
$823$	−4.26581	−0.148697	−0.0743484	+	0.997232i	$0.523688\pi$
$824$	−18.7615	−0.653587
$825$	3.58796	0.124917
$826$	−5.79639	−0.201682
$827$	−29.0387	−1.00977	−0.504887	−	0.863186i	$-0.668466\pi$
$827$	−29.0387	−1.00977	−0.504887	+	0.863186i	$0.668466\pi$
$828$	−4.32911	−0.150447
$829$	2.69997	0.0937740	0.0468870	−	0.998900i	$-0.485070\pi$
$829$	2.69997	0.0937740	0.0468870	+	0.998900i	$0.485070\pi$
$830$	−2.17392	−0.0754580
$831$	−4.16629	−0.144527
$832$	0.604068	0.0209423
$833$	8.15178	0.282443
$834$	1.18483	0.0410274
$835$	−18.4594	−0.638813
$836$	−13.6515	−0.472149
$837$	5.68840	0.196620
$838$	−7.79495	−0.269272
$839$	−27.1790	−0.938323	−0.469161	−	0.883113i	$-0.655444\pi$
$839$	−27.1790	−0.938323	−0.469161	+	0.883113i	$0.655444\pi$
$840$	−5.63921	−0.194571
$841$	−26.0730	−0.899069
$842$	24.7151	0.851739
$843$	31.3568	1.07999
$844$	11.2775	0.388186
$845$	12.8639	0.442531
$846$	3.31224	0.113877
$847$	−4.26637	−0.146594
$848$	8.21143	0.281982
$849$	−4.82608	−0.165630
$850$	3.17989	0.109069
$851$	−17.7839	−0.609625
$852$	−21.7010	−0.743464
$853$	−55.8528	−1.91236	−0.956181	−	0.292776i	$-0.905421\pi$
$853$	−55.8528	−1.91236	−0.956181	+	0.292776i	$0.905421\pi$
$854$	20.2625	0.693369
$855$	2.53795	0.0867962
$856$	6.21993	0.212593
$857$	42.2385	1.44284	0.721421	−	0.692497i	$-0.243489\pi$
$857$	42.2385	1.44284	0.721421	+	0.692497i	$0.243489\pi$
$858$	−0.936823	−0.0319826
$859$	−29.8723	−1.01923	−0.509615	−	0.860403i	$-0.670212\pi$
$859$	−29.8723	−1.01923	−0.509615	+	0.860403i	$0.670212\pi$
$860$	−4.15105	−0.141550
$861$	−13.5914	−0.463194
$862$	11.4670	0.390569
$863$	17.6899	0.602171	0.301086	−	0.953597i	$-0.402651\pi$
$863$	17.6899	0.602171	0.301086	+	0.953597i	$0.402651\pi$
$864$	5.83436	0.198489
$865$	6.22220	0.211561
$866$	19.3140	0.656317
$867$	−3.18972	−0.108329
$868$	−19.4199	−0.659155
$869$	24.1474	0.819143
$870$	−1.21076	−0.0410486
$871$	−3.92587	−0.133023
$872$	27.9880	0.947795
$873$	−14.6155	−0.494661
$874$	5.18655	0.175438
$875$	2.27723	0.0769845
$876$	−9.49443	−0.320787
$877$	26.4704	0.893843	0.446922	−	0.894573i	$-0.352520\pi$
$877$	26.4704	0.893843	0.446922	+	0.894573i	$0.352520\pi$
$878$	7.91441	0.267099
$879$	−10.7601	−0.362929
$880$	4.47002	0.150684
$881$	16.4566	0.554436	0.277218	−	0.960807i	$-0.410588\pi$
$881$	16.4566	0.554436	0.277218	+	0.960807i	$0.410588\pi$
$882$	1.28391	0.0432314
$883$	−45.3322	−1.52555	−0.762775	−	0.646663i	$-0.776164\pi$
$883$	−45.3322	−1.52555	−0.762775	+	0.646663i	$0.776164\pi$
$884$	2.48530	0.0835896
$885$	−3.59670	−0.120902
$886$	−18.6219	−0.625614
$887$	37.8443	1.27069	0.635343	−	0.772230i	$-0.280859\pi$
$887$	37.8443	1.27069	0.635343	+	0.772230i	$0.280859\pi$
$888$	15.2507	0.511781
$889$	−6.27070	−0.210312
$890$	−5.42824	−0.181955
$891$	−3.58796	−0.120201
$892$	−16.5944	−0.555621
$893$	11.8784	0.397497
$894$	−1.33310	−0.0445854
$895$	12.3595	0.413131
$896$	−23.9338	−0.799572
$897$	−1.06540	−0.0355726
$898$	−26.0008	−0.867658
$899$	−9.73199	−0.324580
$900$	−1.49917	−0.0499722
$901$	−29.6158	−0.986645
$902$	−15.1548	−0.504601
$903$	−6.30545	−0.209832
$904$	−6.32438	−0.210346
$905$	9.29315	0.308915
$906$	−3.73999	−0.124253
$907$	35.7912	1.18843	0.594214	−	0.804307i	$-0.297463\pi$
$907$	35.7912	1.18843	0.594214	+	0.804307i	$0.297463\pi$
$908$	10.4434	0.346576
$909$	−11.8597	−0.393361
$910$	−0.594589	−0.0197104
$911$	9.05495	0.300004	0.150002	−	0.988686i	$-0.452072\pi$
$911$	9.05495	0.300004	0.150002	+	0.988686i	$0.452072\pi$
$912$	3.16187	0.104700
$913$	11.0216	0.364763
$914$	0.282853	0.00935594
$915$	12.5730	0.415651
$916$	−16.6925	−0.551536
$917$	1.82519	0.0602731
$918$	−3.17989	−0.104952
$919$	−38.7871	−1.27947	−0.639734	−	0.768596i	$-0.720955\pi$
$919$	−38.7871	−1.27947	−0.639734	+	0.768596i	$0.720955\pi$
$920$	−7.15088	−0.235758
$921$	17.0981	0.563402
$922$	−1.76945	−0.0582737
$923$	−5.34063	−0.175789
$924$	12.2491	0.402967
$925$	−6.15856	−0.202492
$926$	22.0999	0.726247
$927$	−7.57627	−0.248837
$928$	−9.98171	−0.327666
$929$	−24.5115	−0.804195	−0.402098	−	0.915597i	$-0.631719\pi$
$929$	−24.5115	−0.804195	−0.402098	+	0.915597i	$0.631719\pi$
$930$	4.02566	0.132006
$931$	4.60438	0.150902
$932$	12.2307	0.400631
$933$	−21.2863	−0.696881
$934$	1.55529	0.0508906
$935$	−16.1218	−0.527239
$936$	0.913638	0.0298632
$937$	55.6384	1.81763	0.908813	−	0.417203i	$-0.136990\pi$
$937$	55.6384	1.81763	0.908813	+	0.417203i	$0.136990\pi$
$938$	−17.1485	−0.559918
$939$	−29.3814	−0.958827
$940$	−7.01659	−0.228856
$941$	−21.2343	−0.692218	−0.346109	−	0.938194i	$-0.612497\pi$
$941$	−21.2343	−0.692218	−0.346109	+	0.938194i	$0.612497\pi$
$942$	15.1255	0.492817
$943$	−17.2348	−0.561241
$944$	−4.48089	−0.145841
$945$	−2.27723	−0.0740784
$946$	−7.03077	−0.228590
$947$	−47.0116	−1.52767	−0.763837	−	0.645410i	$-0.776687\pi$
$947$	−47.0116	−1.52767	−0.763837	+	0.645410i	$0.776687\pi$
$948$	−10.0896	−0.327693
$949$	−2.33659	−0.0758489
$950$	1.79610	0.0582731
$951$	−34.8882	−1.13133
$952$	25.3387	0.821231
$953$	−40.7510	−1.32006	−0.660028	−	0.751241i	$-0.729455\pi$
$953$	−40.7510	−1.32006	−0.660028	+	0.751241i	$0.729455\pi$
$954$	−4.66449	−0.151019
$955$	−0.941720	−0.0304733
$956$	−39.4522	−1.27598
$957$	6.13846	0.198428
$958$	5.96797	0.192816
$959$	−16.4404	−0.530889
$960$	1.63728	0.0528429
$961$	1.35791	0.0438034
$962$	1.60801	0.0518443
$963$	2.51174	0.0809396
$964$	7.28334	0.234581
$965$	3.09094	0.0995008
$966$	−4.65374	−0.149732
$967$	−34.7892	−1.11874	−0.559372	−	0.828917i	$-0.688958\pi$
$967$	−34.7892	−1.11874	−0.559372	+	0.828917i	$0.688958\pi$
$968$	4.63940	0.149116
$969$	−11.4038	−0.366342
$970$	−10.3433	−0.332105
$971$	−13.9978	−0.449212	−0.224606	−	0.974450i	$-0.572109\pi$
$971$	−13.9978	−0.449212	−0.224606	+	0.974450i	$0.572109\pi$
$972$	1.49917	0.0480858
$973$	−3.81258	−0.122226
$974$	−8.84034	−0.283263
$975$	−0.368946	−0.0118157
$976$	15.6639	0.501390
$977$	−13.7759	−0.440732	−0.220366	−	0.975417i	$-0.570725\pi$
$977$	−13.7759	−0.440732	−0.220366	+	0.975417i	$0.570725\pi$
$978$	−10.8106	−0.345685
$979$	27.5208	0.879568
$980$	−2.71980	−0.0868809
$981$	11.3022	0.360850
$982$	0.273382	0.00872396
$983$	17.6113	0.561712	0.280856	−	0.959750i	$-0.409382\pi$
$983$	17.6113	0.561712	0.280856	+	0.959750i	$0.409382\pi$
$984$	14.7798	0.471162
$985$	19.8837	0.633546
$986$	5.44030	0.173255
$987$	−10.6582	−0.339254
$988$	1.40377	0.0446600
$989$	−7.99571	−0.254249
$990$	−2.53919	−0.0807006
$991$	−26.0904	−0.828790	−0.414395	−	0.910097i	$-0.636007\pi$
$991$	−26.0904	−0.828790	−0.414395	+	0.910097i	$0.636007\pi$
$992$	33.1882	1.05373
$993$	1.87931	0.0596381
$994$	−23.3283	−0.739929
$995$	25.5831	0.811040
$996$	−4.60519	−0.145921
$997$	−34.3868	−1.08904	−0.544521	−	0.838748i	$-0.683288\pi$
$997$	−34.3868	−1.08904	−0.544521	+	0.838748i	$0.683288\pi$
$998$	7.35423	0.232794
$999$	6.15856	0.194848

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6015.2.a.e.1.11	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6015.2.a.e.1.11	✓	31	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:	\( N \)	\(=\)	\( 6015 = 3 \cdot 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6015.a (trivial)

\(f(q)\)	\(=\)	\(q-0.707695 q^{2} -1.00000 q^{3} -1.49917 q^{4} -1.00000 q^{5} +0.707695 q^{6} -2.27723 q^{7} +2.47634 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.707695 q^{2} -1.00000 q^{3} -1.49917 q^{4} -1.00000 q^{5} +0.707695 q^{6} -2.27723 q^{7} +2.47634 q^{8} +1.00000 q^{9} +0.707695 q^{10} -3.58796 q^{11} +1.49917 q^{12} +0.368946 q^{13} +1.61159 q^{14} +1.00000 q^{15} +1.24584 q^{16} -4.49330 q^{17} -0.707695 q^{18} -2.53795 q^{19} +1.49917 q^{20} +2.27723 q^{21} +2.53919 q^{22} +2.88768 q^{23} -2.47634 q^{24} +1.00000 q^{25} -0.261102 q^{26} -1.00000 q^{27} +3.41395 q^{28} +1.71085 q^{29} -0.707695 q^{30} -5.68840 q^{31} -5.83436 q^{32} +3.58796 q^{33} +3.17989 q^{34} +2.27723 q^{35} -1.49917 q^{36} -6.15856 q^{37} +1.79610 q^{38} -0.368946 q^{39} -2.47634 q^{40} -5.96838 q^{41} -1.61159 q^{42} -2.76891 q^{43} +5.37896 q^{44} -1.00000 q^{45} -2.04360 q^{46} -4.68032 q^{47} -1.24584 q^{48} -1.81421 q^{49} -0.707695 q^{50} +4.49330 q^{51} -0.553112 q^{52} +6.59110 q^{53} +0.707695 q^{54} +3.58796 q^{55} -5.63921 q^{56} +2.53795 q^{57} -1.21076 q^{58} -3.59670 q^{59} -1.49917 q^{60} +12.5730 q^{61} +4.02566 q^{62} -2.27723 q^{63} +1.63728 q^{64} -0.368946 q^{65} -2.53919 q^{66} -10.6408 q^{67} +6.73620 q^{68} -2.88768 q^{69} -1.61159 q^{70} -14.4754 q^{71} +2.47634 q^{72} -6.33314 q^{73} +4.35839 q^{74} -1.00000 q^{75} +3.80482 q^{76} +8.17063 q^{77} +0.261102 q^{78} -6.73010 q^{79} -1.24584 q^{80} +1.00000 q^{81} +4.22380 q^{82} -3.07183 q^{83} -3.41395 q^{84} +4.49330 q^{85} +1.95954 q^{86} -1.71085 q^{87} -8.88504 q^{88} -7.67031 q^{89} +0.707695 q^{90} -0.840177 q^{91} -4.32911 q^{92} +5.68840 q^{93} +3.31224 q^{94} +2.53795 q^{95} +5.83436 q^{96} -14.6155 q^{97} +1.28391 q^{98} -3.58796 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q + 6 q^{2} - 31 q^{3} + 24 q^{4} - 31 q^{5} - 6 q^{6} - 4 q^{7} + 15 q^{8} + 31 q^{9}+O(q^{10}) \) 31 * q + 6 * q^2 - 31 * q^3 + 24 * q^4 - 31 * q^5 - 6 * q^6 - 4 * q^7 + 15 * q^8 + 31 * q^9	\( 31 q + 6 q^{2} - 31 q^{3} + 24 q^{4} - 31 q^{5} - 6 q^{6} - 4 q^{7} + 15 q^{8} + 31 q^{9} - 6 q^{10} - q^{11} - 24 q^{12} + 8 q^{13} + 8 q^{14} + 31 q^{15} + 10 q^{16} + 42 q^{17} + 6 q^{18} - 19 q^{19} - 24 q^{20} + 4 q^{21} + 17 q^{22} + 26 q^{23} - 15 q^{24} + 31 q^{25} + 4 q^{26} - 31 q^{27} - 16 q^{28} - 11 q^{29} + 6 q^{30} - 3 q^{31} + 41 q^{32} + q^{33} + 6 q^{34} + 4 q^{35} + 24 q^{36} + 10 q^{37} + 12 q^{38} - 8 q^{39} - 15 q^{40} + 27 q^{41} - 8 q^{42} - 37 q^{43} - 9 q^{44} - 31 q^{45} - 23 q^{46} + 48 q^{47} - 10 q^{48} + 31 q^{49} + 6 q^{50} - 42 q^{51} + 18 q^{52} + 35 q^{53} - 6 q^{54} + q^{55} + 7 q^{56} + 19 q^{57} - 26 q^{58} - 3 q^{59} + 24 q^{60} + 11 q^{61} + 49 q^{62} - 4 q^{63} - 27 q^{64} - 8 q^{65} - 17 q^{66} - 44 q^{67} + 72 q^{68} - 26 q^{69} - 8 q^{70} + 6 q^{71} + 15 q^{72} + 49 q^{73} - 6 q^{74} - 31 q^{75} - 36 q^{76} + 66 q^{77} - 4 q^{78} - 41 q^{79} - 10 q^{80} + 31 q^{81} + 9 q^{82} + 53 q^{83} + 16 q^{84} - 42 q^{85} + 3 q^{86} + 11 q^{87} + 21 q^{88} + 31 q^{89} - 6 q^{90} - 45 q^{91} + 45 q^{92} + 3 q^{93} - 4 q^{94} + 19 q^{95} - 41 q^{96} + 37 q^{97} + 41 q^{98} - q^{99}+O(q^{100}) \) 31 * q + 6 * q^2 - 31 * q^3 + 24 * q^4 - 31 * q^5 - 6 * q^6 - 4 * q^7 + 15 * q^8 + 31 * q^9 - 6 * q^10 - q^11 - 24 * q^12 + 8 * q^13 + 8 * q^14 + 31 * q^15 + 10 * q^16 + 42 * q^17 + 6 * q^18 - 19 * q^19 - 24 * q^20 + 4 * q^21 + 17 * q^22 + 26 * q^23 - 15 * q^24 + 31 * q^25 + 4 * q^26 - 31 * q^27 - 16 * q^28 - 11 * q^29 + 6 * q^30 - 3 * q^31 + 41 * q^32 + q^33 + 6 * q^34 + 4 * q^35 + 24 * q^36 + 10 * q^37 + 12 * q^38 - 8 * q^39 - 15 * q^40 + 27 * q^41 - 8 * q^42 - 37 * q^43 - 9 * q^44 - 31 * q^45 - 23 * q^46 + 48 * q^47 - 10 * q^48 + 31 * q^49 + 6 * q^50 - 42 * q^51 + 18 * q^52 + 35 * q^53 - 6 * q^54 + q^55 + 7 * q^56 + 19 * q^57 - 26 * q^58 - 3 * q^59 + 24 * q^60 + 11 * q^61 + 49 * q^62 - 4 * q^63 - 27 * q^64 - 8 * q^65 - 17 * q^66 - 44 * q^67 + 72 * q^68 - 26 * q^69 - 8 * q^70 + 6 * q^71 + 15 * q^72 + 49 * q^73 - 6 * q^74 - 31 * q^75 - 36 * q^76 + 66 * q^77 - 4 * q^78 - 41 * q^79 - 10 * q^80 + 31 * q^81 + 9 * q^82 + 53 * q^83 + 16 * q^84 - 42 * q^85 + 3 * q^86 + 11 * q^87 + 21 * q^88 + 31 * q^89 - 6 * q^90 - 45 * q^91 + 45 * q^92 + 3 * q^93 - 4 * q^94 + 19 * q^95 - 41 * q^96 + 37 * q^97 + 41 * q^98 - q^99

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