LMFDB - Embedded newform 6015.2.a.b.1.3

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:	$1$
Dimension:	$23$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
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)

$f(q)$	$=$	$q-2.22931 q^{2} +1.00000 q^{3} +2.96981 q^{4} +1.00000 q^{5} -2.22931 q^{6} -0.230360 q^{7} -2.16201 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.22931 q^{2} +1.00000 q^{3} +2.96981 q^{4} +1.00000 q^{5} -2.22931 q^{6} -0.230360 q^{7} -2.16201 q^{8} +1.00000 q^{9} -2.22931 q^{10} +2.86243 q^{11} +2.96981 q^{12} +0.193596 q^{13} +0.513544 q^{14} +1.00000 q^{15} -1.11984 q^{16} -6.48565 q^{17} -2.22931 q^{18} -5.05286 q^{19} +2.96981 q^{20} -0.230360 q^{21} -6.38124 q^{22} +0.00109693 q^{23} -2.16201 q^{24} +1.00000 q^{25} -0.431585 q^{26} +1.00000 q^{27} -0.684127 q^{28} -4.00231 q^{29} -2.22931 q^{30} +2.40709 q^{31} +6.82048 q^{32} +2.86243 q^{33} +14.4585 q^{34} -0.230360 q^{35} +2.96981 q^{36} +0.157972 q^{37} +11.2644 q^{38} +0.193596 q^{39} -2.16201 q^{40} +2.23082 q^{41} +0.513544 q^{42} +9.21807 q^{43} +8.50088 q^{44} +1.00000 q^{45} -0.00244540 q^{46} +11.9263 q^{47} -1.11984 q^{48} -6.94693 q^{49} -2.22931 q^{50} -6.48565 q^{51} +0.574944 q^{52} -8.32236 q^{53} -2.22931 q^{54} +2.86243 q^{55} +0.498042 q^{56} -5.05286 q^{57} +8.92237 q^{58} -10.1651 q^{59} +2.96981 q^{60} -3.67229 q^{61} -5.36614 q^{62} -0.230360 q^{63} -12.9653 q^{64} +0.193596 q^{65} -6.38124 q^{66} -7.53639 q^{67} -19.2612 q^{68} +0.00109693 q^{69} +0.513544 q^{70} -8.52198 q^{71} -2.16201 q^{72} +0.460719 q^{73} -0.352169 q^{74} +1.00000 q^{75} -15.0060 q^{76} -0.659390 q^{77} -0.431585 q^{78} -3.30315 q^{79} -1.11984 q^{80} +1.00000 q^{81} -4.97319 q^{82} -1.08158 q^{83} -0.684127 q^{84} -6.48565 q^{85} -20.5499 q^{86} -4.00231 q^{87} -6.18861 q^{88} +3.25258 q^{89} -2.22931 q^{90} -0.0445969 q^{91} +0.00325769 q^{92} +2.40709 q^{93} -26.5874 q^{94} -5.05286 q^{95} +6.82048 q^{96} -3.56991 q^{97} +15.4869 q^{98} +2.86243 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 23 q - 5 q^{2} + 23 q^{3} + 9 q^{4} + 23 q^{5} - 5 q^{6} - 16 q^{7} - 12 q^{8} + 23 q^{9}+O(q^{10}) $ 23 * q - 5 * q^2 + 23 * q^3 + 9 * q^4 + 23 * q^5 - 5 * q^6 - 16 * q^7 - 12 * q^8 + 23 * q^9	\( 23 q - 5 q^{2} + 23 q^{3} + 9 q^{4} + 23 q^{5} - 5 q^{6} - 16 q^{7} - 12 q^{8} + 23 q^{9} - 5 q^{10} - 13 q^{11} + 9 q^{12} - 18 q^{13} - 6 q^{14} + 23 q^{15} - 11 q^{16} - 34 q^{17} - 5 q^{18} - 35 q^{19} + 9 q^{20} - 16 q^{21} - 11 q^{22} - 14 q^{23} - 12 q^{24} + 23 q^{25} - 6 q^{26} + 23 q^{27} - 26 q^{28} - 43 q^{29} - 5 q^{30} - 21 q^{31} - 14 q^{32} - 13 q^{33} - 12 q^{34} - 16 q^{35} + 9 q^{36} - 18 q^{37} + 6 q^{38} - 18 q^{39} - 12 q^{40} - 45 q^{41} - 6 q^{42} - 43 q^{43} - 11 q^{44} + 23 q^{45} - 29 q^{46} - 14 q^{47} - 11 q^{48} - 25 q^{49} - 5 q^{50} - 34 q^{51} - 20 q^{52} - 3 q^{53} - 5 q^{54} - 13 q^{55} + 3 q^{56} - 35 q^{57} + 10 q^{58} - 9 q^{59} + 9 q^{60} - 67 q^{61} - 7 q^{62} - 16 q^{63} - 8 q^{64} - 18 q^{65} - 11 q^{66} - 32 q^{67} - 24 q^{68} - 14 q^{69} - 6 q^{70} - 8 q^{71} - 12 q^{72} - 39 q^{73} - 16 q^{74} + 23 q^{75} - 48 q^{76} - 26 q^{77} - 6 q^{78} - 59 q^{79} - 11 q^{80} + 23 q^{81} - q^{82} - 23 q^{83} - 26 q^{84} - 34 q^{85} - 7 q^{86} - 43 q^{87} + 17 q^{88} - 51 q^{89} - 5 q^{90} - 37 q^{91} + 11 q^{92} - 21 q^{93} + 8 q^{94} - 35 q^{95} - 14 q^{96} - 29 q^{97} + 32 q^{98} - 13 q^{99}+O(q^{100}) \) 23 * q - 5 * q^2 + 23 * q^3 + 9 * q^4 + 23 * q^5 - 5 * q^6 - 16 * q^7 - 12 * q^8 + 23 * q^9 - 5 * q^10 - 13 * q^11 + 9 * q^12 - 18 * q^13 - 6 * q^14 + 23 * q^15 - 11 * q^16 - 34 * q^17 - 5 * q^18 - 35 * q^19 + 9 * q^20 - 16 * q^21 - 11 * q^22 - 14 * q^23 - 12 * q^24 + 23 * q^25 - 6 * q^26 + 23 * q^27 - 26 * q^28 - 43 * q^29 - 5 * q^30 - 21 * q^31 - 14 * q^32 - 13 * q^33 - 12 * q^34 - 16 * q^35 + 9 * q^36 - 18 * q^37 + 6 * q^38 - 18 * q^39 - 12 * q^40 - 45 * q^41 - 6 * q^42 - 43 * q^43 - 11 * q^44 + 23 * q^45 - 29 * q^46 - 14 * q^47 - 11 * q^48 - 25 * q^49 - 5 * q^50 - 34 * q^51 - 20 * q^52 - 3 * q^53 - 5 * q^54 - 13 * q^55 + 3 * q^56 - 35 * q^57 + 10 * q^58 - 9 * q^59 + 9 * q^60 - 67 * q^61 - 7 * q^62 - 16 * q^63 - 8 * q^64 - 18 * q^65 - 11 * q^66 - 32 * q^67 - 24 * q^68 - 14 * q^69 - 6 * q^70 - 8 * q^71 - 12 * q^72 - 39 * q^73 - 16 * q^74 + 23 * q^75 - 48 * q^76 - 26 * q^77 - 6 * q^78 - 59 * q^79 - 11 * q^80 + 23 * q^81 - q^82 - 23 * q^83 - 26 * q^84 - 34 * q^85 - 7 * q^86 - 43 * q^87 + 17 * q^88 - 51 * q^89 - 5 * q^90 - 37 * q^91 + 11 * q^92 - 21 * q^93 + 8 * q^94 - 35 * q^95 - 14 * q^96 - 29 * q^97 + 32 * q^98 - 13 * 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 $

$2$	−2.22931	−1.57636	−0.788179	−	0.615446i	$-0.788976\pi$
$2$	−2.22931	−1.57636	−0.788179	+	0.615446i	$0.788976\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	2.96981	1.48491
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−2.22931	−0.910111
$7$	−0.230360	−0.0870680	−0.0435340	−	0.999052i	$-0.513862\pi$
$7$	−0.230360	−0.0870680	−0.0435340	+	0.999052i	$0.513862\pi$
$8$	−2.16201	−0.764387
$9$	1.00000	0.333333
$10$	−2.22931	−0.704969
$11$	2.86243	0.863055	0.431528	−	0.902100i	$-0.357975\pi$
$11$	2.86243	0.863055	0.431528	+	0.902100i	$0.357975\pi$
$12$	2.96981	0.857311
$13$	0.193596	0.0536939	0.0268470	−	0.999640i	$-0.491453\pi$
$13$	0.193596	0.0536939	0.0268470	+	0.999640i	$0.491453\pi$
$14$	0.513544	0.137250
$15$	1.00000	0.258199
$16$	−1.11984	−0.279959
$17$	−6.48565	−1.57300	−0.786500	−	0.617590i	$-0.788109\pi$
$17$	−6.48565	−1.57300	−0.786500	+	0.617590i	$0.788109\pi$
$18$	−2.22931	−0.525453
$19$	−5.05286	−1.15921	−0.579603	−	0.814899i	$-0.696792\pi$
$19$	−5.05286	−1.15921	−0.579603	+	0.814899i	$0.696792\pi$
$20$	2.96981	0.664070
$21$	−0.230360	−0.0502687
$22$	−6.38124	−1.36048
$23$	0.00109693	0.000228726 0	0.000114363	−	1.00000i	$-0.499964\pi$
$23$	0.00109693	0.000228726 0	0.000114363		1.00000i	$0.499964\pi$
$24$	−2.16201	−0.441319
$25$	1.00000	0.200000
$26$	−0.431585	−0.0846409
$27$	1.00000	0.192450
$28$	−0.684127	−0.129288
$29$	−4.00231	−0.743209	−0.371605	−	0.928391i	$-0.621192\pi$
$29$	−4.00231	−0.743209	−0.371605	+	0.928391i	$0.621192\pi$
$30$	−2.22931	−0.407014
$31$	2.40709	0.432326	0.216163	−	0.976357i	$-0.430646\pi$
$31$	2.40709	0.432326	0.216163	+	0.976357i	$0.430646\pi$
$32$	6.82048	1.20570
$33$	2.86243	0.498285
$34$	14.4585	2.47961
$35$	−0.230360	−0.0389380
$36$	2.96981	0.494969
$37$	0.157972	0.0259705	0.0129852	−	0.999916i	$-0.495867\pi$
$37$	0.157972	0.0259705	0.0129852	+	0.999916i	$0.495867\pi$
$38$	11.2644	1.82732
$39$	0.193596	0.0310002
$40$	−2.16201	−0.341844
$41$	2.23082	0.348396	0.174198	−	0.984711i	$-0.444267\pi$
$41$	2.23082	0.348396	0.174198	+	0.984711i	$0.444267\pi$
$42$	0.513544	0.0792416
$43$	9.21807	1.40574	0.702871	−	0.711317i	$-0.251901\pi$
$43$	9.21807	1.40574	0.702871	+	0.711317i	$0.251901\pi$
$44$	8.50088	1.28156
$45$	1.00000	0.149071
$46$	−0.00244540	−0.000360555 0
$47$	11.9263	1.73963	0.869814	−	0.493380i	$-0.164239\pi$
$47$	11.9263	1.73963	0.869814	+	0.493380i	$0.164239\pi$
$48$	−1.11984	−0.161634
$49$	−6.94693	−0.992419
$50$	−2.22931	−0.315272
$51$	−6.48565	−0.908172
$52$	0.574944	0.0797304
$53$	−8.32236	−1.14316	−0.571582	−	0.820545i	$-0.693670\pi$
$53$	−8.32236	−1.14316	−0.571582	+	0.820545i	$0.693670\pi$
$54$	−2.22931	−0.303370
$55$	2.86243	0.385970
$56$	0.498042	0.0665536
$57$	−5.05286	−0.669267
$58$	8.92237	1.17156
$59$	−10.1651	−1.32338	−0.661690	−	0.749778i	$-0.730160\pi$
$59$	−10.1651	−1.32338	−0.661690	+	0.749778i	$0.730160\pi$
$60$	2.96981	0.383401
$61$	−3.67229	−0.470189	−0.235094	−	0.971973i	$-0.575540\pi$
$61$	−3.67229	−0.470189	−0.235094	+	0.971973i	$0.575540\pi$
$62$	−5.36614	−0.681501
$63$	−0.230360	−0.0290227
$64$	−12.9653	−1.62066
$65$	0.193596	0.0240126
$66$	−6.38124	−0.785476
$67$	−7.53639	−0.920717	−0.460358	−	0.887733i	$-0.652279\pi$
$67$	−7.53639	−0.920717	−0.460358	+	0.887733i	$0.652279\pi$
$68$	−19.2612	−2.33576
$69$	0.00109693	0.000132055 0
$70$	0.513544	0.0613802
$71$	−8.52198	−1.01137	−0.505687	−	0.862717i	$-0.668761\pi$
$71$	−8.52198	−1.01137	−0.505687	+	0.862717i	$0.668761\pi$
$72$	−2.16201	−0.254796
$73$	0.460719	0.0539231	0.0269615	−	0.999636i	$-0.491417\pi$
$73$	0.460719	0.0539231	0.0269615	+	0.999636i	$0.491417\pi$
$74$	−0.352169	−0.0409388
$75$	1.00000	0.115470
$76$	−15.0060	−1.72131
$77$	−0.659390	−0.0751445
$78$	−0.431585	−0.0488674
$79$	−3.30315	−0.371633	−0.185816	−	0.982584i	$-0.559493\pi$
$79$	−3.30315	−0.371633	−0.185816	+	0.982584i	$0.559493\pi$
$80$	−1.11984	−0.125202
$81$	1.00000	0.111111
$82$	−4.97319	−0.549197
$83$	−1.08158	−0.118719	−0.0593593	−	0.998237i	$-0.518906\pi$
$83$	−1.08158	−0.118719	−0.0593593	+	0.998237i	$0.518906\pi$
$84$	−0.684127	−0.0746444
$85$	−6.48565	−0.703467
$86$	−20.5499	−2.21595
$87$	−4.00231	−0.429092
$88$	−6.18861	−0.659708
$89$	3.25258	0.344773	0.172387	−	0.985029i	$-0.444852\pi$
$89$	3.25258	0.344773	0.172387	+	0.985029i	$0.444852\pi$
$90$	−2.22931	−0.234990
$91$	−0.0445969	−0.00467502
$92$	0.00325769	0.000339637 0
$93$	2.40709	0.249603
$94$	−26.5874	−2.74228
$95$	−5.05286	−0.518412
$96$	6.82048	0.696113
$97$	−3.56991	−0.362469	−0.181235	−	0.983440i	$-0.558009\pi$
$97$	−3.56991	−0.362469	−0.181235	+	0.983440i	$0.558009\pi$
$98$	15.4869	1.56441
$99$	2.86243	0.287685
$100$	2.96981	0.296981
$101$	10.7906	1.07371	0.536854	−	0.843675i	$-0.319613\pi$
$101$	10.7906	1.07371	0.536854	+	0.843675i	$0.319613\pi$
$102$	14.4585	1.43161
$103$	−13.1680	−1.29748	−0.648742	−	0.761009i	$-0.724704\pi$
$103$	−13.1680	−1.29748	−0.648742	+	0.761009i	$0.724704\pi$
$104$	−0.418557	−0.0410429
$105$	−0.230360	−0.0224809
$106$	18.5531	1.80204
$107$	4.11693	0.397999	0.199000	−	0.980000i	$-0.436231\pi$
$107$	4.11693	0.397999	0.199000	+	0.980000i	$0.436231\pi$
$108$	2.96981	0.285770
$109$	−8.38716	−0.803345	−0.401672	−	0.915783i	$-0.631571\pi$
$109$	−8.38716	−0.803345	−0.401672	+	0.915783i	$0.631571\pi$
$110$	−6.38124	−0.608427
$111$	0.157972	0.0149941
$112$	0.257966	0.0243755
$113$	19.7279	1.85585	0.927924	−	0.372769i	$-0.121592\pi$
$113$	19.7279	1.85585	0.927924	+	0.372769i	$0.121592\pi$
$114$	11.2644	1.05501
$115$	0.00109693	0.000102290 0
$116$	−11.8861	−1.10360
$117$	0.193596	0.0178980
$118$	22.6611	2.08612
$119$	1.49404	0.136958
$120$	−2.16201	−0.197364
$121$	−2.80649	−0.255135
$122$	8.18667	0.741186
$123$	2.23082	0.201147
$124$	7.14860	0.641963
$125$	1.00000	0.0894427
$126$	0.513544	0.0457501
$127$	−18.9436	−1.68097	−0.840486	−	0.541833i	$-0.817730\pi$
$127$	−18.9436	−1.68097	−0.840486	+	0.541833i	$0.817730\pi$
$128$	15.2626	1.34904
$129$	9.21807	0.811606
$130$	−0.431585	−0.0378525
$131$	−6.28159	−0.548825	−0.274413	−	0.961612i	$-0.588483\pi$
$131$	−6.28159	−0.548825	−0.274413	+	0.961612i	$0.588483\pi$
$132$	8.50088	0.739907
$133$	1.16398	0.100930
$134$	16.8009	1.45138
$135$	1.00000	0.0860663
$136$	14.0220	1.20238
$137$	1.65850	0.141695	0.0708477	−	0.997487i	$-0.477430\pi$
$137$	1.65850	0.141695	0.0708477	+	0.997487i	$0.477430\pi$
$138$	−0.00244540	−0.000208166 0
$139$	−14.3744	−1.21922	−0.609611	−	0.792701i	$-0.708674\pi$
$139$	−14.3744	−1.21922	−0.609611	+	0.792701i	$0.708674\pi$
$140$	−0.684127	−0.0578193
$141$	11.9263	1.00437
$142$	18.9981	1.59429
$143$	0.554156	0.0463408
$144$	−1.11984	−0.0933197
$145$	−4.00231	−0.332373
$146$	−1.02708	−0.0850021
$147$	−6.94693	−0.572973
$148$	0.469148	0.0385637
$149$	4.06985	0.333415	0.166708	−	0.986006i	$-0.446686\pi$
$149$	4.06985	0.333415	0.166708	+	0.986006i	$0.446686\pi$
$150$	−2.22931	−0.182022
$151$	−15.0693	−1.22632	−0.613160	−	0.789959i	$-0.710102\pi$
$151$	−15.0693	−1.22632	−0.613160	+	0.789959i	$0.710102\pi$
$152$	10.9243	0.886081
$153$	−6.48565	−0.524334
$154$	1.46998	0.118455
$155$	2.40709	0.193342
$156$	0.574944	0.0460324
$157$	19.5824	1.56285	0.781424	−	0.624001i	$-0.214494\pi$
$157$	19.5824	1.56285	0.781424	+	0.624001i	$0.214494\pi$
$158$	7.36373	0.585827
$159$	−8.32236	−0.660006
$160$	6.82048	0.539207
$161$	−0.000252690 0	−1.99148e−5 0
$162$	−2.22931	−0.175151
$163$	−24.2116	−1.89640	−0.948200	−	0.317674i	$-0.897098\pi$
$163$	−24.2116	−1.89640	−0.948200	+	0.317674i	$0.897098\pi$
$164$	6.62513	0.517336
$165$	2.86243	0.222840
$166$	2.41117	0.187143
$167$	−9.08101	−0.702710	−0.351355	−	0.936242i	$-0.614279\pi$
$167$	−9.08101	−0.702710	−0.351355	+	0.936242i	$0.614279\pi$
$168$	0.498042	0.0384248
$169$	−12.9625	−0.997117
$170$	14.4585	1.10892
$171$	−5.05286	−0.386402
$172$	27.3759	2.08740
$173$	12.3852	0.941629	0.470815	−	0.882232i	$-0.343960\pi$
$173$	12.3852	0.941629	0.470815	+	0.882232i	$0.343960\pi$
$174$	8.92237	0.676403
$175$	−0.230360	−0.0174136
$176$	−3.20545	−0.241620
$177$	−10.1651	−0.764054
$178$	−7.25101	−0.543486
$179$	−10.8473	−0.810766	−0.405383	−	0.914147i	$-0.632862\pi$
$179$	−10.8473	−0.810766	−0.405383	+	0.914147i	$0.632862\pi$
$180$	2.96981	0.221357
$181$	−12.0739	−0.897448	−0.448724	−	0.893670i	$-0.648121\pi$
$181$	−12.0739	−0.897448	−0.448724	+	0.893670i	$0.648121\pi$
$182$	0.0994202	0.00736951
$183$	−3.67229	−0.271464
$184$	−0.00237158	−0.000174835 0
$185$	0.157972	0.0116143
$186$	−5.36614	−0.393465
$187$	−18.5647	−1.35759
$188$	35.4188	2.58318
$189$	−0.230360	−0.0167562
$190$	11.2644	0.817204
$191$	16.3635	1.18402	0.592011	−	0.805930i	$-0.298334\pi$
$191$	16.3635	1.18402	0.592011	+	0.805930i	$0.298334\pi$
$192$	−12.9653	−0.935689
$193$	−7.95335	−0.572494	−0.286247	−	0.958156i	$-0.592408\pi$
$193$	−7.95335	−0.572494	−0.286247	+	0.958156i	$0.592408\pi$
$194$	7.95842	0.571381
$195$	0.193596	0.0138637
$196$	−20.6311	−1.47365
$197$	14.0696	1.00242	0.501209	−	0.865326i	$-0.332889\pi$
$197$	14.0696	1.00242	0.501209	+	0.865326i	$0.332889\pi$
$198$	−6.38124	−0.453495
$199$	−2.21113	−0.156743	−0.0783715	−	0.996924i	$-0.524972\pi$
$199$	−2.21113	−0.156743	−0.0783715	+	0.996924i	$0.524972\pi$
$200$	−2.16201	−0.152877
$201$	−7.53639	−0.531576
$202$	−24.0556	−1.69255
$203$	0.921972	0.0647098
$204$	−19.2612	−1.34855
$205$	2.23082	0.155807
$206$	29.3556	2.04530
$207$	0.00109693	7.62421e−5 0
$208$	−0.216796	−0.0150321
$209$	−14.4635	−1.00046
$210$	0.513544	0.0354379
$211$	22.8922	1.57596	0.787982	−	0.615698i	$-0.211126\pi$
$211$	22.8922	1.57596	0.787982	+	0.615698i	$0.211126\pi$
$212$	−24.7159	−1.69749
$213$	−8.52198	−0.583917
$214$	−9.17791	−0.627389
$215$	9.21807	0.628667
$216$	−2.16201	−0.147106
$217$	−0.554498	−0.0376418
$218$	18.6976	1.26636
$219$	0.460719	0.0311325
$220$	8.50088	0.573130
$221$	−1.25560	−0.0844606
$222$	−0.352169	−0.0236360
$223$	14.6029	0.977885	0.488943	−	0.872316i	$-0.337383\pi$
$223$	14.6029	0.977885	0.488943	+	0.872316i	$0.337383\pi$
$224$	−1.57117	−0.104978
$225$	1.00000	0.0666667
$226$	−43.9796	−2.92548
$227$	−15.7876	−1.04786	−0.523931	−	0.851761i	$-0.675535\pi$
$227$	−15.7876	−1.04786	−0.523931	+	0.851761i	$0.675535\pi$
$228$	−15.0060	−0.993799
$229$	−15.7394	−1.04009	−0.520045	−	0.854139i	$-0.674085\pi$
$229$	−15.7394	−1.04009	−0.520045	+	0.854139i	$0.674085\pi$
$230$	−0.00244540	−0.000161245 0
$231$	−0.659390	−0.0433847
$232$	8.65303	0.568099
$233$	22.8737	1.49851	0.749254	−	0.662283i	$-0.230412\pi$
$233$	22.8737	1.49851	0.749254	+	0.662283i	$0.230412\pi$
$234$	−0.431585	−0.0282136
$235$	11.9263	0.777985
$236$	−30.1884	−1.96510
$237$	−3.30315	−0.214562
$238$	−3.33067	−0.215895
$239$	−23.9169	−1.54705	−0.773527	−	0.633763i	$-0.781509\pi$
$239$	−23.9169	−1.54705	−0.773527	+	0.633763i	$0.781509\pi$
$240$	−1.11984	−0.0722851
$241$	22.9291	1.47699	0.738495	−	0.674258i	$-0.235537\pi$
$241$	22.9291	1.47699	0.738495	+	0.674258i	$0.235537\pi$
$242$	6.25653	0.402185
$243$	1.00000	0.0641500
$244$	−10.9060	−0.698186
$245$	−6.94693	−0.443823
$246$	−4.97319	−0.317079
$247$	−0.978214	−0.0622423
$248$	−5.20415	−0.330464
$249$	−1.08158	−0.0685422
$250$	−2.22931	−0.140994
$251$	20.0323	1.26443	0.632214	−	0.774794i	$-0.282146\pi$
$251$	20.0323	1.26443	0.632214	+	0.774794i	$0.282146\pi$
$252$	−0.684127	−0.0430960
$253$	0.00313990	0.000197404 0
$254$	42.2311	2.64981
$255$	−6.48565	−0.406147
$256$	−8.09456	−0.505910
$257$	−5.04967	−0.314990	−0.157495	−	0.987520i	$-0.550342\pi$
$257$	−5.04967	−0.314990	−0.157495	+	0.987520i	$0.550342\pi$
$258$	−20.5499	−1.27938
$259$	−0.0363905	−0.00226120
$260$	0.574944	0.0356565
$261$	−4.00231	−0.247736
$262$	14.0036	0.865146
$263$	−31.8580	−1.96445	−0.982226	−	0.187704i	$-0.939895\pi$
$263$	−31.8580	−1.96445	−0.982226	+	0.187704i	$0.939895\pi$
$264$	−6.18861	−0.380883
$265$	−8.32236	−0.511239
$266$	−2.59486	−0.159101
$267$	3.25258	0.199055
$268$	−22.3817	−1.36718
$269$	−14.4306	−0.879847	−0.439923	−	0.898035i	$-0.644994\pi$
$269$	−14.4306	−0.879847	−0.439923	+	0.898035i	$0.644994\pi$
$270$	−2.22931	−0.135671
$271$	−9.72422	−0.590704	−0.295352	−	0.955388i	$-0.595437\pi$
$271$	−9.72422	−0.590704	−0.295352	+	0.955388i	$0.595437\pi$
$272$	7.26286	0.440376
$273$	−0.0445969	−0.00269913
$274$	−3.69731	−0.223363
$275$	2.86243	0.172611
$276$	0.00325769	0.000196090 0
$277$	2.46947	0.148376	0.0741881	−	0.997244i	$-0.476363\pi$
$277$	2.46947	0.148376	0.0741881	+	0.997244i	$0.476363\pi$
$278$	32.0450	1.92193
$279$	2.40709	0.144109
$280$	0.498042	0.0297637
$281$	−6.84424	−0.408293	−0.204147	−	0.978940i	$-0.565442\pi$
$281$	−6.84424	−0.408293	−0.204147	+	0.978940i	$0.565442\pi$
$282$	−26.5874	−1.58325
$283$	−7.21012	−0.428597	−0.214299	−	0.976768i	$-0.568747\pi$
$283$	−7.21012	−0.428597	−0.214299	+	0.976768i	$0.568747\pi$
$284$	−25.3087	−1.50179
$285$	−5.05286	−0.299305
$286$	−1.23538	−0.0730498
$287$	−0.513893	−0.0303342
$288$	6.82048	0.401901
$289$	25.0636	1.47433
$290$	8.92237	0.523940
$291$	−3.56991	−0.209272
$292$	1.36825	0.0800707
$293$	−4.94708	−0.289011	−0.144506	−	0.989504i	$-0.546159\pi$
$293$	−4.94708	−0.289011	−0.144506	+	0.989504i	$0.546159\pi$
$294$	15.4869	0.903212
$295$	−10.1651	−0.591834
$296$	−0.341538	−0.0198515
$297$	2.86243	0.166095
$298$	−9.07295	−0.525582
$299$	0.000212362 0	1.22812e−5 0
$300$	2.96981	0.171462
$301$	−2.12348	−0.122395
$302$	33.5940	1.93312
$303$	10.7906	0.619906
$304$	5.65837	0.324530
$305$	−3.67229	−0.210275
$306$	14.4585	0.826538
$307$	7.22697	0.412465	0.206232	−	0.978503i	$-0.433880\pi$
$307$	7.22697	0.412465	0.206232	+	0.978503i	$0.433880\pi$
$308$	−1.95827	−0.111583
$309$	−13.1680	−0.749102
$310$	−5.36614	−0.304776
$311$	34.2536	1.94234	0.971171	−	0.238385i	$-0.0766181\pi$
$311$	34.2536	1.94234	0.971171	+	0.238385i	$0.0766181\pi$
$312$	−0.418557	−0.0236961
$313$	23.1482	1.30842	0.654208	−	0.756315i	$-0.273002\pi$
$313$	23.1482	1.30842	0.654208	+	0.756315i	$0.273002\pi$
$314$	−43.6552	−2.46361
$315$	−0.230360	−0.0129793
$316$	−9.80972	−0.551840
$317$	−22.1669	−1.24501	−0.622507	−	0.782614i	$-0.713886\pi$
$317$	−22.1669	−1.24501	−0.622507	+	0.782614i	$0.713886\pi$
$318$	18.5531	1.04041
$319$	−11.4563	−0.641431
$320$	−12.9653	−0.724781
$321$	4.11693	0.229785
$322$	0.000563324 0	3.13928e−5 0
$323$	32.7711	1.82343
$324$	2.96981	0.164990
$325$	0.193596	0.0107388
$326$	53.9751	2.98941
$327$	−8.38716	−0.463811
$328$	−4.82307	−0.266309
$329$	−2.74734	−0.151466
$330$	−6.38124	−0.351276
$331$	9.96558	0.547758	0.273879	−	0.961764i	$-0.411693\pi$
$331$	9.96558	0.547758	0.273879	+	0.961764i	$0.411693\pi$
$332$	−3.21209	−0.176286
$333$	0.157972	0.00865682
$334$	20.2444	1.10772
$335$	−7.53639	−0.411757
$336$	0.257966	0.0140732
$337$	−28.1607	−1.53401	−0.767007	−	0.641639i	$-0.778255\pi$
$337$	−28.1607	−1.53401	−0.767007	+	0.641639i	$0.778255\pi$
$338$	28.8974	1.57181
$339$	19.7279	1.07147
$340$	−19.2612	−1.04458
$341$	6.89012	0.373121
$342$	11.2644	0.609108
$343$	3.21282	0.173476
$344$	−19.9296	−1.07453
$345$	0.00109693	5.90569e−5 0
$346$	−27.6104	−1.48435
$347$	3.05301	0.163894	0.0819470	−	0.996637i	$-0.473886\pi$
$347$	3.05301	0.163894	0.0819470	+	0.996637i	$0.473886\pi$
$348$	−11.8861	−0.637162
$349$	−33.8123	−1.80993	−0.904964	−	0.425487i	$-0.860103\pi$
$349$	−33.8123	−1.80993	−0.904964	+	0.425487i	$0.860103\pi$
$350$	0.513544	0.0274501
$351$	0.193596	0.0103334
$352$	19.5232	1.04059
$353$	−21.1486	−1.12563	−0.562813	−	0.826584i	$-0.690281\pi$
$353$	−21.1486	−1.12563	−0.562813	+	0.826584i	$0.690281\pi$
$354$	22.6611	1.20442
$355$	−8.52198	−0.452300
$356$	9.65957	0.511956
$357$	1.49404	0.0790728
$358$	24.1820	1.27806
$359$	−13.3535	−0.704768	−0.352384	−	0.935855i	$-0.614629\pi$
$359$	−13.3535	−0.704768	−0.352384	+	0.935855i	$0.614629\pi$
$360$	−2.16201	−0.113948
$361$	6.53137	0.343756
$362$	26.9165	1.41470
$363$	−2.80649	−0.147303
$364$	−0.132444	−0.00694197
$365$	0.460719	0.0241151
$366$	8.18667	0.427924
$367$	−0.283955	−0.0148223	−0.00741116	−	0.999973i	$-0.502359\pi$
$367$	−0.283955	−0.0148223	−0.00741116	+	0.999973i	$0.502359\pi$
$368$	−0.00122839	−6.40340e−5 0
$369$	2.23082	0.116132
$370$	−0.352169	−0.0183084
$371$	1.91714	0.0995331
$372$	7.14860	0.370638
$373$	28.7228	1.48721	0.743605	−	0.668619i	$-0.233114\pi$
$373$	28.7228	1.48721	0.743605	+	0.668619i	$0.233114\pi$
$374$	41.3865	2.14004
$375$	1.00000	0.0516398
$376$	−25.7848	−1.32975
$377$	−0.774831	−0.0399058
$378$	0.513544	0.0264139
$379$	−3.25672	−0.167286	−0.0836432	−	0.996496i	$-0.526656\pi$
$379$	−3.25672	−0.167286	−0.0836432	+	0.996496i	$0.526656\pi$
$380$	−15.0060	−0.769794
$381$	−18.9436	−0.970510
$382$	−36.4793	−1.86644
$383$	33.1812	1.69548	0.847739	−	0.530413i	$-0.177963\pi$
$383$	33.1812	1.69548	0.847739	+	0.530413i	$0.177963\pi$
$384$	15.2626	0.778868
$385$	−0.659390	−0.0336056
$386$	17.7305	0.902457
$387$	9.21807	0.468581
$388$	−10.6020	−0.538233
$389$	16.5889	0.841091	0.420546	−	0.907271i	$-0.361839\pi$
$389$	16.5889	0.841091	0.420546	+	0.907271i	$0.361839\pi$
$390$	−0.431585	−0.0218542
$391$	−0.00711432	−0.000359787 0
$392$	15.0194	0.758592
$393$	−6.28159	−0.316864
$394$	−31.3655	−1.58017
$395$	−3.30315	−0.166199
$396$	8.50088	0.427186
$397$	−0.795340	−0.0399170	−0.0199585	−	0.999801i	$-0.506353\pi$
$397$	−0.795340	−0.0399170	−0.0199585	+	0.999801i	$0.506353\pi$
$398$	4.92929	0.247083
$399$	1.16398	0.0582718
$400$	−1.11984	−0.0559918
$401$	−1.00000	−0.0499376
$401$	−1.00000	−0.0499376
$402$	16.8009	0.837955
$403$	0.466003	0.0232133
$404$	32.0462	1.59436
$405$	1.00000	0.0496904
$406$	−2.05536	−0.102006
$407$	0.452184	0.0224140
$408$	14.0220	0.694195
$409$	−7.02303	−0.347267	−0.173633	−	0.984810i	$-0.555551\pi$
$409$	−7.02303	−0.347267	−0.173633	+	0.984810i	$0.555551\pi$
$410$	−4.97319	−0.245608
$411$	1.65850	0.0818079
$412$	−39.1066	−1.92664
$413$	2.34163	0.115224
$414$	−0.00244540	−0.000120185 0
$415$	−1.08158	−0.0530926
$416$	1.32042	0.0647389
$417$	−14.3744	−0.703918
$418$	32.2435	1.57708
$419$	12.7471	0.622737	0.311368	−	0.950289i	$-0.399213\pi$
$419$	12.7471	0.622737	0.311368	+	0.950289i	$0.399213\pi$
$420$	−0.684127	−0.0333820
$421$	12.3138	0.600135	0.300068	−	0.953918i	$-0.402991\pi$
$421$	12.3138	0.600135	0.300068	+	0.953918i	$0.402991\pi$
$422$	−51.0338	−2.48428
$423$	11.9263	0.579876
$424$	17.9931	0.873820
$425$	−6.48565	−0.314600
$426$	18.9981	0.920462
$427$	0.845950	0.0409384
$428$	12.2265	0.590991
$429$	0.554156	0.0267549
$430$	−20.5499	−0.991005
$431$	−32.8976	−1.58462	−0.792310	−	0.610118i	$-0.791122\pi$
$431$	−32.8976	−1.58462	−0.792310	+	0.610118i	$0.791122\pi$
$432$	−1.11984	−0.0538782
$433$	−11.5815	−0.556571	−0.278285	−	0.960498i	$-0.589766\pi$
$433$	−11.5815	−0.556571	−0.278285	+	0.960498i	$0.589766\pi$
$434$	1.23615	0.0593369
$435$	−4.00231	−0.191896
$436$	−24.9083	−1.19289
$437$	−0.00554265	−0.000265141 0
$438$	−1.02708	−0.0490760
$439$	−6.88597	−0.328649	−0.164325	−	0.986406i	$-0.552544\pi$
$439$	−6.88597	−0.328649	−0.164325	+	0.986406i	$0.552544\pi$
$440$	−6.18861	−0.295030
$441$	−6.94693	−0.330806
$442$	2.79911	0.133140
$443$	10.6976	0.508258	0.254129	−	0.967170i	$-0.418211\pi$
$443$	10.6976	0.508258	0.254129	+	0.967170i	$0.418211\pi$
$444$	0.469148	0.0222648
$445$	3.25258	0.154187
$446$	−32.5544	−1.54150
$447$	4.06985	0.192497
$448$	2.98669	0.141108
$449$	12.3770	0.584106	0.292053	−	0.956402i	$-0.405662\pi$
$449$	12.3770	0.584106	0.292053	+	0.956402i	$0.405662\pi$
$450$	−2.22931	−0.105091
$451$	6.38558	0.300685
$452$	58.5883	2.75576
$453$	−15.0693	−0.708016
$454$	35.1955	1.65181
$455$	−0.0445969	−0.00209073
$456$	10.9243	0.511579
$457$	−12.7742	−0.597552	−0.298776	−	0.954323i	$-0.596578\pi$
$457$	−12.7742	−0.597552	−0.298776	+	0.954323i	$0.596578\pi$
$458$	35.0880	1.63956
$459$	−6.48565	−0.302724
$460$	0.00325769	0.000151890 0
$461$	−29.0158	−1.35140	−0.675701	−	0.737176i	$-0.736159\pi$
$461$	−29.0158	−1.35140	−0.675701	+	0.737176i	$0.736159\pi$
$462$	1.46998	0.0683899
$463$	−38.2425	−1.77728	−0.888640	−	0.458605i	$-0.848349\pi$
$463$	−38.2425	−1.77728	−0.888640	+	0.458605i	$0.848349\pi$
$464$	4.48193	0.208068
$465$	2.40709	0.111626
$466$	−50.9926	−2.36219
$467$	31.7929	1.47120	0.735599	−	0.677417i	$-0.236901\pi$
$467$	31.7929	1.47120	0.735599	+	0.677417i	$0.236901\pi$
$468$	0.574944	0.0265768
$469$	1.73609	0.0801650
$470$	−26.5874	−1.22638
$471$	19.5824	0.902310
$472$	21.9770	1.01157
$473$	26.3861	1.21323
$474$	7.36373	0.338227
$475$	−5.05286	−0.231841
$476$	4.43701	0.203370
$477$	−8.32236	−0.381055
$478$	53.3181	2.43871
$479$	−7.84812	−0.358590	−0.179295	−	0.983795i	$-0.557382\pi$
$479$	−7.84812	−0.358590	−0.179295	+	0.983795i	$0.557382\pi$
$480$	6.82048	0.311311
$481$	0.0305828	0.00139446
$482$	−51.1159	−2.32827
$483$	−0.000252690 0	−1.14978e−5 0
$484$	−8.33475	−0.378852
$485$	−3.56991	−0.162101
$486$	−2.22931	−0.101123
$487$	−0.538125	−0.0243848	−0.0121924	−	0.999926i	$-0.503881\pi$
$487$	−0.538125	−0.0243848	−0.0121924	+	0.999926i	$0.503881\pi$
$488$	7.93954	0.359406
$489$	−24.2116	−1.09489
$490$	15.4869	0.699625
$491$	10.8460	0.489475	0.244738	−	0.969589i	$-0.421298\pi$
$491$	10.8460	0.489475	0.244738	+	0.969589i	$0.421298\pi$
$492$	6.62513	0.298684
$493$	25.9575	1.16907
$494$	2.18074	0.0981161
$495$	2.86243	0.128657
$496$	−2.69555	−0.121034
$497$	1.96313	0.0880583
$498$	2.41117	0.108047
$499$	36.8075	1.64773	0.823865	−	0.566786i	$-0.191813\pi$
$499$	36.8075	1.64773	0.823865	+	0.566786i	$0.191813\pi$
$500$	2.96981	0.132814
$501$	−9.08101	−0.405710
$502$	−44.6582	−1.99319
$503$	26.8580	1.19754	0.598770	−	0.800921i	$-0.295656\pi$
$503$	26.8580	1.19754	0.598770	+	0.800921i	$0.295656\pi$
$504$	0.498042	0.0221845
$505$	10.7906	0.480177
$506$	−0.00699979	−0.000311179 0
$507$	−12.9625	−0.575686
$508$	−56.2589	−2.49609
$509$	−27.8070	−1.23252	−0.616261	−	0.787542i	$-0.711353\pi$
$509$	−27.8070	−1.23252	−0.616261	+	0.787542i	$0.711353\pi$
$510$	14.4585	0.640233
$511$	−0.106131	−0.00469497
$512$	−12.4800	−0.551544
$513$	−5.05286	−0.223089
$514$	11.2573	0.496536
$515$	−13.1680	−0.580252
$516$	27.3759	1.20516
$517$	34.1382	1.50140
$518$	0.0811257	0.00356446
$519$	12.3852	0.543650
$520$	−0.418557	−0.0183549
$521$	−14.2951	−0.626281	−0.313140	−	0.949707i	$-0.601381\pi$
$521$	−14.2951	−0.626281	−0.313140	+	0.949707i	$0.601381\pi$
$522$	8.92237	0.390522
$523$	−31.0667	−1.35845	−0.679226	−	0.733929i	$-0.737684\pi$
$523$	−31.0667	−1.35845	−0.679226	+	0.733929i	$0.737684\pi$
$524$	−18.6552	−0.814954
$525$	−0.230360	−0.0100537
$526$	71.0214	3.09668
$527$	−15.6115	−0.680049
$528$	−3.20545	−0.139499
$529$	−23.0000	−1.00000
$530$	18.5531	0.805896
$531$	−10.1651	−0.441127
$532$	3.45680	0.149871
$533$	0.431879	0.0187068
$534$	−7.25101	−0.313782
$535$	4.11693	0.177991
$536$	16.2938	0.703784
$537$	−10.8473	−0.468096
$538$	32.1702	1.38695
$539$	−19.8851	−0.856513
$540$	2.96981	0.127800
$541$	−37.8714	−1.62822	−0.814110	−	0.580711i	$-0.802775\pi$
$541$	−37.8714	−1.62822	−0.814110	+	0.580711i	$0.802775\pi$
$542$	21.6783	0.931162
$543$	−12.0739	−0.518142
$544$	−44.2353	−1.89657
$545$	−8.38716	−0.359267
$546$	0.0994202	0.00425479
$547$	−19.0241	−0.813411	−0.406705	−	0.913559i	$-0.633322\pi$
$547$	−19.0241	−0.813411	−0.406705	+	0.913559i	$0.633322\pi$
$548$	4.92544	0.210404
$549$	−3.67229	−0.156730
$550$	−6.38124	−0.272097
$551$	20.2231	0.861532
$552$	−0.00237158	−0.000100941 0
$553$	0.760914	0.0323573
$554$	−5.50522	−0.233894
$555$	0.157972	0.00670555
$556$	−42.6893	−1.81043
$557$	25.0728	1.06237	0.531185	−	0.847256i	$-0.321747\pi$
$557$	25.0728	1.06237	0.531185	+	0.847256i	$0.321747\pi$
$558$	−5.36614	−0.227167
$559$	1.78458	0.0754798
$560$	0.257966	0.0109010
$561$	−18.5647	−0.783803
$562$	15.2579	0.643616
$563$	22.3952	0.943844	0.471922	−	0.881640i	$-0.343560\pi$
$563$	22.3952	0.943844	0.471922	+	0.881640i	$0.343560\pi$
$564$	35.4188	1.49140
$565$	19.7279	0.829961
$566$	16.0736	0.675623
$567$	−0.230360	−0.00967422
$568$	18.4246	0.773080
$569$	−36.9188	−1.54772	−0.773858	−	0.633359i	$-0.781676\pi$
$569$	−36.9188	−1.54772	−0.773858	+	0.633359i	$0.781676\pi$
$570$	11.2644	0.471813
$571$	−37.7306	−1.57898	−0.789488	−	0.613767i	$-0.789654\pi$
$571$	−37.7306	−1.57898	−0.789488	+	0.613767i	$0.789654\pi$
$572$	1.64574	0.0688118
$573$	16.3635	0.683595
$574$	1.14563	0.0478175
$575$	0.00109693	4.57453e−5 0
$576$	−12.9653	−0.540220
$577$	23.0794	0.960809	0.480404	−	0.877047i	$-0.340490\pi$
$577$	23.0794	0.960809	0.480404	+	0.877047i	$0.340490\pi$
$578$	−55.8745	−2.32407
$579$	−7.95335	−0.330530
$580$	−11.8861	−0.493543
$581$	0.249153	0.0103366
$582$	7.95842	0.329887
$583$	−23.8222	−0.986614
$584$	−0.996079	−0.0412181
$585$	0.193596	0.00800422
$586$	11.0286	0.455586
$587$	−21.1530	−0.873078	−0.436539	−	0.899685i	$-0.643796\pi$
$587$	−21.1530	−0.873078	−0.436539	+	0.899685i	$0.643796\pi$
$588$	−20.6311	−0.850812
$589$	−12.1627	−0.501154
$590$	22.6611	0.932942
$591$	14.0696	0.578747
$592$	−0.176903	−0.00727067
$593$	−11.9838	−0.492114	−0.246057	−	0.969255i	$-0.579135\pi$
$593$	−11.9838	−0.492114	−0.246057	+	0.969255i	$0.579135\pi$
$594$	−6.38124	−0.261825
$595$	1.49404	0.0612495
$596$	12.0867	0.495091
$597$	−2.21113	−0.0904956
$598$	−0.000473420 0	−1.93596e−5 0
$599$	−13.8241	−0.564838	−0.282419	−	0.959291i	$-0.591137\pi$
$599$	−13.8241	−0.564838	−0.282419	+	0.959291i	$0.591137\pi$
$600$	−2.16201	−0.0882638
$601$	−19.0784	−0.778226	−0.389113	−	0.921190i	$-0.627218\pi$
$601$	−19.0784	−0.778226	−0.389113	+	0.921190i	$0.627218\pi$
$602$	4.73389	0.192939
$603$	−7.53639	−0.306906
$604$	−44.7529	−1.82097
$605$	−2.80649	−0.114100
$606$	−24.0556	−0.977194
$607$	46.8016	1.89962	0.949809	−	0.312831i	$-0.101277\pi$
$607$	46.8016	1.89962	0.949809	+	0.312831i	$0.101277\pi$
$608$	−34.4629	−1.39766
$609$	0.921972	0.0373602
$610$	8.18667	0.331469
$611$	2.30888	0.0934074
$612$	−19.2612	−0.778586
$613$	6.26676	0.253112	0.126556	−	0.991959i	$-0.459608\pi$
$613$	6.26676	0.253112	0.126556	+	0.991959i	$0.459608\pi$
$614$	−16.1111	−0.650193
$615$	2.23082	0.0899555
$616$	1.42561	0.0574395
$617$	17.8650	0.719219	0.359610	−	0.933103i	$-0.382910\pi$
$617$	17.8650	0.719219	0.359610	+	0.933103i	$0.382910\pi$
$618$	29.3556	1.18085
$619$	16.0037	0.643245	0.321622	−	0.946868i	$-0.395772\pi$
$619$	16.0037	0.643245	0.321622	+	0.946868i	$0.395772\pi$
$620$	7.14860	0.287095
$621$	0.00109693	4.40184e−5 0
$622$	−76.3617	−3.06183
$623$	−0.749266	−0.0300187
$624$	−0.216796	−0.00867879
$625$	1.00000	0.0400000
$626$	−51.6045	−2.06253
$627$	−14.4635	−0.577615
$628$	58.1561	2.32068
$629$	−1.02455	−0.0408516
$630$	0.513544	0.0204601
$631$	46.5309	1.85237	0.926183	−	0.377075i	$-0.123070\pi$
$631$	46.5309	1.85237	0.926183	+	0.377075i	$0.123070\pi$
$632$	7.14144	0.284071
$633$	22.8922	0.909883
$634$	49.4168	1.96259
$635$	−18.9436	−0.751754
$636$	−24.7159	−0.980048
$637$	−1.34490	−0.0532869
$638$	25.5397	1.01113
$639$	−8.52198	−0.337124
$640$	15.2626	0.603309
$641$	−44.4432	−1.75540	−0.877701	−	0.479208i	$-0.840924\pi$
$641$	−44.4432	−1.75540	−0.877701	+	0.479208i	$0.840924\pi$
$642$	−9.17791	−0.362223
$643$	−32.7904	−1.29313	−0.646564	−	0.762859i	$-0.723795\pi$
$643$	−32.7904	−1.29313	−0.646564	+	0.762859i	$0.723795\pi$
$644$	−0.000750442 0	−2.95715e−5 0
$645$	9.21807	0.362961
$646$	−73.0568	−2.87438
$647$	−3.17229	−0.124716	−0.0623578	−	0.998054i	$-0.519862\pi$
$647$	−3.17229	−0.124716	−0.0623578	+	0.998054i	$0.519862\pi$
$648$	−2.16201	−0.0849318
$649$	−29.0968	−1.14215
$650$	−0.431585	−0.0169282
$651$	−0.554498	−0.0217325
$652$	−71.9040	−2.81598
$653$	14.2469	0.557524	0.278762	−	0.960360i	$-0.410076\pi$
$653$	14.2469	0.557524	0.278762	+	0.960360i	$0.410076\pi$
$654$	18.6976	0.731133
$655$	−6.28159	−0.245442
$656$	−2.49816	−0.0975367
$657$	0.460719	0.0179744
$658$	6.12467	0.238765
$659$	−36.3013	−1.41410	−0.707048	−	0.707165i	$-0.749974\pi$
$659$	−36.3013	−1.41410	−0.707048	+	0.707165i	$0.749974\pi$
$660$	8.50088	0.330896
$661$	42.2030	1.64151	0.820754	−	0.571282i	$-0.193554\pi$
$661$	42.2030	1.64151	0.820754	+	0.571282i	$0.193554\pi$
$662$	−22.2164	−0.863463
$663$	−1.25560	−0.0487633
$664$	2.33839	0.0907469
$665$	1.16398	0.0451371
$666$	−0.352169	−0.0136463
$667$	−0.00439026	−0.000169992 0
$668$	−26.9689	−1.04346
$669$	14.6029	0.564582
$670$	16.8009	0.649077
$671$	−10.5117	−0.405799
$672$	−1.57117	−0.0606091
$673$	13.6346	0.525577	0.262788	−	0.964854i	$-0.415358\pi$
$673$	13.6346	0.525577	0.262788	+	0.964854i	$0.415358\pi$
$674$	62.7790	2.41816
$675$	1.00000	0.0384900
$676$	−38.4963	−1.48063
$677$	0.00354542	0.000136262 0	6.81308e−5	−	1.00000i	$-0.499978\pi$
$677$	0.00354542	0.000136262 0	6.81308e−5		1.00000i	$0.499978\pi$
$678$	−43.9796	−1.68903
$679$	0.822365	0.0315595
$680$	14.0220	0.537721
$681$	−15.7876	−0.604983
$682$	−15.3602	−0.588173
$683$	24.7622	0.947499	0.473750	−	0.880660i	$-0.342900\pi$
$683$	24.7622	0.947499	0.473750	+	0.880660i	$0.342900\pi$
$684$	−15.0060	−0.573770
$685$	1.65850	0.0633681
$686$	−7.16236	−0.273460
$687$	−15.7394	−0.600496
$688$	−10.3227	−0.393550
$689$	−1.61118	−0.0613810
$690$	−0.00244540	−9.30949e−5 0
$691$	2.10273	0.0799914	0.0399957	−	0.999200i	$-0.487266\pi$
$691$	2.10273	0.0799914	0.0399957	+	0.999200i	$0.487266\pi$
$692$	36.7817	1.39823
$693$	−0.659390	−0.0250482
$694$	−6.80610	−0.258356
$695$	−14.3744	−0.545253
$696$	8.65303	0.327992
$697$	−14.4683	−0.548027
$698$	75.3779	2.85310
$699$	22.8737	0.865164
$700$	−0.684127	−0.0258576
$701$	−51.8360	−1.95782	−0.978909	−	0.204297i	$-0.934509\pi$
$701$	−51.8360	−1.95782	−0.978909	+	0.204297i	$0.934509\pi$
$702$	−0.431585	−0.0162891
$703$	−0.798211	−0.0301051
$704$	−37.1122	−1.39872
$705$	11.9263	0.449170
$706$	47.1467	1.77439
$707$	−2.48573	−0.0934856
$708$	−30.1884	−1.13455
$709$	39.8083	1.49503	0.747516	−	0.664244i	$-0.231246\pi$
$709$	39.8083	1.49503	0.747516	+	0.664244i	$0.231246\pi$
$710$	18.9981	0.712987
$711$	−3.30315	−0.123878
$712$	−7.03213	−0.263540
$713$	0.00264042	9.88843e−5 0
$714$	−3.33067	−0.124647
$715$	0.554156	0.0207242
$716$	−32.2145	−1.20391
$717$	−23.9169	−0.893192
$718$	29.7690	1.11097
$719$	25.3847	0.946690	0.473345	−	0.880877i	$-0.343046\pi$
$719$	25.3847	0.946690	0.473345	+	0.880877i	$0.343046\pi$
$720$	−1.11984	−0.0417338
$721$	3.03339	0.112969
$722$	−14.5604	−0.541883
$723$	22.9291	0.852741
$724$	−35.8573	−1.33263
$725$	−4.00231	−0.148642
$726$	6.25653	0.232202
$727$	−2.31751	−0.0859516	−0.0429758	−	0.999076i	$-0.513684\pi$
$727$	−2.31751	−0.0859516	−0.0429758	+	0.999076i	$0.513684\pi$
$728$	0.0964190	0.00357352
$729$	1.00000	0.0370370
$730$	−1.02708	−0.0380141
$731$	−59.7852	−2.21123
$732$	−10.9060	−0.403098
$733$	−34.9988	−1.29271	−0.646356	−	0.763036i	$-0.723708\pi$
$733$	−34.9988	−1.29271	−0.646356	+	0.763036i	$0.723708\pi$
$734$	0.633023	0.0233653
$735$	−6.94693	−0.256242
$736$	0.00748162	0.000275776 0
$737$	−21.5724	−0.794630
$738$	−4.97319	−0.183066
$739$	42.9925	1.58151	0.790753	−	0.612136i	$-0.209689\pi$
$739$	42.9925	1.58151	0.790753	+	0.612136i	$0.209689\pi$
$740$	0.469148	0.0172462
$741$	−0.978214	−0.0359356
$742$	−4.27390	−0.156900
$743$	10.9876	0.403096	0.201548	−	0.979479i	$-0.435403\pi$
$743$	10.9876	0.403096	0.201548	+	0.979479i	$0.435403\pi$
$744$	−5.20415	−0.190794
$745$	4.06985	0.149108
$746$	−64.0320	−2.34438
$747$	−1.08158	−0.0395729
$748$	−55.1337	−2.01589
$749$	−0.948378	−0.0346530
$750$	−2.22931	−0.0814028
$751$	−46.2671	−1.68831	−0.844155	−	0.536098i	$-0.819898\pi$
$751$	−46.2671	−1.68831	−0.844155	+	0.536098i	$0.819898\pi$
$752$	−13.3555	−0.487025
$753$	20.0323	0.730018
$754$	1.72734	0.0629059
$755$	−15.0693	−0.548427
$756$	−0.684127	−0.0248815
$757$	11.9951	0.435968	0.217984	−	0.975952i	$-0.430052\pi$
$757$	11.9951	0.435968	0.217984	+	0.975952i	$0.430052\pi$
$758$	7.26023	0.263703
$759$	0.00313990	0.000113971 0
$760$	10.9243	0.396267
$761$	−24.3282	−0.881896	−0.440948	−	0.897533i	$-0.645358\pi$
$761$	−24.3282	−0.881896	−0.440948	+	0.897533i	$0.645358\pi$
$762$	42.2311	1.52987
$763$	1.93207	0.0699456
$764$	48.5966	1.75816
$765$	−6.48565	−0.234489
$766$	−73.9710	−2.67268
$767$	−1.96792	−0.0710575
$768$	−8.09456	−0.292087
$769$	9.20045	0.331777	0.165888	−	0.986145i	$-0.446951\pi$
$769$	9.20045	0.331777	0.165888	+	0.986145i	$0.446951\pi$
$770$	1.46998	0.0529746
$771$	−5.04967	−0.181859
$772$	−23.6200	−0.850101
$773$	29.4201	1.05817	0.529085	−	0.848569i	$-0.322535\pi$
$773$	29.4201	1.05817	0.529085	+	0.848569i	$0.322535\pi$
$774$	−20.5499	−0.738652
$775$	2.40709	0.0864652
$776$	7.71818	0.277067
$777$	−0.0363905	−0.00130550
$778$	−36.9818	−1.32586
$779$	−11.2720	−0.403863
$780$	0.574944	0.0205863
$781$	−24.3936	−0.872871
$782$	0.0158600	0.000567153 0
$783$	−4.00231	−0.143031
$784$	7.77943	0.277837
$785$	19.5824	0.698927
$786$	14.0036	0.499492
$787$	−16.4702	−0.587098	−0.293549	−	0.955944i	$-0.594836\pi$
$787$	−16.4702	−0.587098	−0.293549	+	0.955944i	$0.594836\pi$
$788$	41.7841	1.48850
$789$	−31.8580	−1.13418
$790$	7.36373	0.261990
$791$	−4.54453	−0.161585
$792$	−6.18861	−0.219903
$793$	−0.710942	−0.0252463
$794$	1.77306	0.0629235
$795$	−8.32236	−0.295164
$796$	−6.56665	−0.232749
$797$	−6.84037	−0.242298	−0.121149	−	0.992634i	$-0.538658\pi$
$797$	−6.84037	−0.242298	−0.121149	+	0.992634i	$0.538658\pi$
$798$	−2.59486	−0.0918572
$799$	−77.3497	−2.73644
$800$	6.82048	0.241141
$801$	3.25258	0.114924
$802$	2.22931	0.0787196
$803$	1.31878	0.0465386
$804$	−22.3817	−0.789341
$805$	−0.000252690 0	−8.90615e−6 0
$806$	−1.03886	−0.0365924
$807$	−14.4306	−0.507980
$808$	−23.3295	−0.820728
$809$	−29.7889	−1.04732	−0.523660	−	0.851927i	$-0.675434\pi$
$809$	−29.7889	−1.04732	−0.523660	+	0.851927i	$0.675434\pi$
$810$	−2.22931	−0.0783299
$811$	−38.8726	−1.36500	−0.682501	−	0.730885i	$-0.739108\pi$
$811$	−38.8726	−1.36500	−0.682501	+	0.730885i	$0.739108\pi$
$812$	2.73809	0.0960880
$813$	−9.72422	−0.341043
$814$	−1.00806	−0.0353324
$815$	−24.2116	−0.848096
$816$	7.26286	0.254251
$817$	−46.5776	−1.62954
$818$	15.6565	0.547417
$819$	−0.0445969	−0.00155834
$820$	6.62513	0.231360
$821$	−17.3747	−0.606380	−0.303190	−	0.952930i	$-0.598052\pi$
$821$	−17.3747	−0.606380	−0.303190	+	0.952930i	$0.598052\pi$
$822$	−3.69731	−0.128959
$823$	−26.1708	−0.912255	−0.456128	−	0.889914i	$-0.650764\pi$
$823$	−26.1708	−0.912255	−0.456128	+	0.889914i	$0.650764\pi$
$824$	28.4694	0.991779
$825$	2.86243	0.0996570
$826$	−5.22021	−0.181634
$827$	17.2651	0.600368	0.300184	−	0.953881i	$-0.402952\pi$
$827$	17.2651	0.600368	0.300184	+	0.953881i	$0.402952\pi$
$828$	0.00325769	0.000113212 0
$829$	−41.4491	−1.43959	−0.719793	−	0.694188i	$-0.755763\pi$
$829$	−41.4491	−1.43959	−0.719793	+	0.694188i	$0.755763\pi$
$830$	2.41117	0.0836930
$831$	2.46947	0.0856651
$832$	−2.51003	−0.0870196
$833$	45.0554	1.56108
$834$	32.0450	1.10963
$835$	−9.08101	−0.314261
$836$	−42.9538	−1.48559
$837$	2.40709	0.0832012
$838$	−28.4172	−0.981656
$839$	51.3536	1.77292	0.886462	−	0.462802i	$-0.153156\pi$
$839$	51.3536	1.77292	0.886462	+	0.462802i	$0.153156\pi$
$840$	0.498042	0.0171841
$841$	−12.9816	−0.447640
$842$	−27.4511	−0.946029
$843$	−6.84424	−0.235728
$844$	67.9855	2.34016
$845$	−12.9625	−0.445924
$846$	−26.5874	−0.914093
$847$	0.646504	0.0222141
$848$	9.31969	0.320039
$849$	−7.21012	−0.247451
$850$	14.4585	0.495923
$851$	0.000173285 0	5.94013e−6 0
$852$	−25.3087	−0.867062
$853$	29.9490	1.02543	0.512717	−	0.858558i	$-0.328639\pi$
$853$	29.9490	1.02543	0.512717	+	0.858558i	$0.328639\pi$
$854$	−1.88588	−0.0645336
$855$	−5.05286	−0.172804
$856$	−8.90086	−0.304225
$857$	−17.8631	−0.610193	−0.305097	−	0.952321i	$-0.598689\pi$
$857$	−17.8631	−0.610193	−0.305097	+	0.952321i	$0.598689\pi$
$858$	−1.23538	−0.0421753
$859$	36.3819	1.24133	0.620667	−	0.784075i	$-0.286862\pi$
$859$	36.3819	1.24133	0.620667	+	0.784075i	$0.286862\pi$
$860$	27.3759	0.933512
$861$	−0.513893	−0.0175134
$862$	73.3388	2.49793
$863$	−12.1517	−0.413648	−0.206824	−	0.978378i	$-0.566313\pi$
$863$	−12.1517	−0.413648	−0.206824	+	0.978378i	$0.566313\pi$
$864$	6.82048	0.232038
$865$	12.3852	0.421109
$866$	25.8187	0.877355
$867$	25.0636	0.851206
$868$	−1.64675	−0.0558945
$869$	−9.45502	−0.320740
$870$	8.92237	0.302497
$871$	−1.45902	−0.0494369
$872$	18.1331	0.614066
$873$	−3.56991	−0.120823
$874$	0.0123563	0.000417957 0
$875$	−0.230360	−0.00778760
$876$	1.36825	0.0462288
$877$	−0.458917	−0.0154965	−0.00774827	−	0.999970i	$-0.502466\pi$
$877$	−0.458917	−0.0154965	−0.00774827	+	0.999970i	$0.502466\pi$
$878$	15.3509	0.518069
$879$	−4.94708	−0.166861
$880$	−3.20545	−0.108056
$881$	−32.4876	−1.09454	−0.547268	−	0.836957i	$-0.684332\pi$
$881$	−32.4876	−1.09454	−0.547268	+	0.836957i	$0.684332\pi$
$882$	15.4869	0.521470
$883$	−46.8638	−1.57709	−0.788546	−	0.614976i	$-0.789166\pi$
$883$	−46.8638	−1.57709	−0.788546	+	0.614976i	$0.789166\pi$
$884$	−3.72889	−0.125416
$885$	−10.1651	−0.341695
$886$	−23.8482	−0.801196
$887$	−40.2519	−1.35153	−0.675764	−	0.737118i	$-0.736186\pi$
$887$	−40.2519	−1.35153	−0.675764	+	0.737118i	$0.736186\pi$
$888$	−0.341538	−0.0114613
$889$	4.36385	0.146359
$890$	−7.25101	−0.243054
$891$	2.86243	0.0958950
$892$	43.3680	1.45207
$893$	−60.2618	−2.01659
$894$	−9.07295	−0.303445
$895$	−10.8473	−0.362586
$896$	−3.51591	−0.117458
$897$	0.000212362 0	7.09056e−6 0
$898$	−27.5921	−0.920761
$899$	−9.63390	−0.321309
$900$	2.96981	0.0989938
$901$	53.9759	1.79820
$902$	−14.2354	−0.473988
$903$	−2.12348	−0.0706649
$904$	−42.6520	−1.41859
$905$	−12.0739	−0.401351
$906$	33.5940	1.11609
$907$	17.1253	0.568635	0.284318	−	0.958730i	$-0.408233\pi$
$907$	17.1253	0.568635	0.284318	+	0.958730i	$0.408233\pi$
$908$	−46.8863	−1.55598
$909$	10.7906	0.357903
$910$	0.0994202	0.00329575
$911$	49.0459	1.62496	0.812482	−	0.582986i	$-0.198116\pi$
$911$	49.0459	1.62496	0.812482	+	0.582986i	$0.198116\pi$
$912$	5.65837	0.187367
$913$	−3.09594	−0.102461
$914$	28.4776	0.941956
$915$	−3.67229	−0.121402
$916$	−46.7431	−1.54444
$917$	1.44703	0.0477851
$918$	14.4585	0.477202
$919$	31.5486	1.04069	0.520346	−	0.853955i	$-0.325803\pi$
$919$	31.5486	1.04069	0.520346	+	0.853955i	$0.325803\pi$
$920$	−0.00237158	−7.81888e−5 0
$921$	7.22697	0.238137
$922$	64.6852	2.13029
$923$	−1.64982	−0.0543046
$924$	−1.95827	−0.0644222
$925$	0.157972	0.00519409
$926$	85.2543	2.80163
$927$	−13.1680	−0.432494
$928$	−27.2977	−0.896090
$929$	34.5542	1.13369	0.566844	−	0.823825i	$-0.308164\pi$
$929$	34.5542	1.13369	0.566844	+	0.823825i	$0.308164\pi$
$930$	−5.36614	−0.175963
$931$	35.1019	1.15042
$932$	67.9307	2.22514
$933$	34.2536	1.12141
$934$	−70.8761	−2.31914
$935$	−18.5647	−0.607131
$936$	−0.418557	−0.0136810
$937$	0.599342	0.0195797	0.00978983	−	0.999952i	$-0.496884\pi$
$937$	0.599342	0.0195797	0.00978983	+	0.999952i	$0.496884\pi$
$938$	−3.87027	−0.126369
$939$	23.1482	0.755414
$940$	35.4188	1.15524
$941$	−2.16310	−0.0705149	−0.0352575	−	0.999378i	$-0.511225\pi$
$941$	−2.16310	−0.0705149	−0.0352575	+	0.999378i	$0.511225\pi$
$942$	−43.6552	−1.42236
$943$	0.00244707	7.96874e−5 0
$944$	11.3832	0.370492
$945$	−0.230360	−0.00749362
$946$	−58.8227	−1.91249
$947$	44.4594	1.44474	0.722369	−	0.691508i	$-0.243053\pi$
$947$	44.4594	1.44474	0.722369	+	0.691508i	$0.243053\pi$
$948$	−9.80972	−0.318605
$949$	0.0891934	0.00289534
$950$	11.2644	0.365465
$951$	−22.1669	−0.718810
$952$	−3.23012	−0.104689
$953$	8.91843	0.288896	0.144448	−	0.989512i	$-0.453859\pi$
$953$	8.91843	0.288896	0.144448	+	0.989512i	$0.453859\pi$
$954$	18.5531	0.600679
$955$	16.3635	0.529511
$956$	−71.0287	−2.29723
$957$	−11.4563	−0.370330
$958$	17.4959	0.565266
$959$	−0.382053	−0.0123371
$960$	−12.9653	−0.418453
$961$	−25.2059	−0.813094
$962$	−0.0681785	−0.00219816
$963$	4.11693	0.132666
$964$	68.0950	2.19319
$965$	−7.95335	−0.256027
$966$	0.000563324 0	1.81246e−5 0
$967$	−38.8687	−1.24993	−0.624966	−	0.780652i	$-0.714887\pi$
$967$	−38.8687	−1.24993	−0.624966	+	0.780652i	$0.714887\pi$
$968$	6.06766	0.195022
$969$	32.7711	1.05276
$970$	7.95842	0.255529
$971$	18.9080	0.606787	0.303394	−	0.952865i	$-0.401880\pi$
$971$	18.9080	0.606787	0.303394	+	0.952865i	$0.401880\pi$
$972$	2.96981	0.0952568
$973$	3.31130	0.106155
$974$	1.19965	0.0384391
$975$	0.193596	0.00620004
$976$	4.11237	0.131634
$977$	−15.7422	−0.503638	−0.251819	−	0.967774i	$-0.581029\pi$
$977$	−15.7422	−0.503638	−0.251819	+	0.967774i	$0.581029\pi$
$978$	53.9751	1.72593
$979$	9.31030	0.297558
$980$	−20.6311	−0.659036
$981$	−8.38716	−0.267782
$982$	−24.1792	−0.771589
$983$	26.1407	0.833759	0.416880	−	0.908962i	$-0.363124\pi$
$983$	26.1407	0.833759	0.416880	+	0.908962i	$0.363124\pi$
$984$	−4.82307	−0.153754
$985$	14.0696	0.448295
$986$	−57.8674	−1.84287
$987$	−2.74734	−0.0874489
$988$	−2.90511	−0.0924239
$989$	0.0101116	0.000321530 0
$990$	−6.38124	−0.202809
$991$	9.34129	0.296736	0.148368	−	0.988932i	$-0.452598\pi$
$991$	9.34129	0.296736	0.148368	+	0.988932i	$0.452598\pi$
$992$	16.4175	0.521256
$993$	9.96558	0.316248
$994$	−4.37641	−0.138811
$995$	−2.21113	−0.0700976
$996$	−3.21209	−0.101779
$997$	20.2560	0.641513	0.320757	−	0.947162i	$-0.396063\pi$
$997$	20.2560	0.641513	0.320757	+	0.947162i	$0.396063\pi$
$998$	−82.0553	−2.59741
$999$	0.157972	0.00499802

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6015.2.a.b.1.3	✓	23

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6015.2.a.b.1.3	✓	23	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)

\(f(q)\)	\(=\)	\(q-2.22931 q^{2} +1.00000 q^{3} +2.96981 q^{4} +1.00000 q^{5} -2.22931 q^{6} -0.230360 q^{7} -2.16201 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.22931 q^{2} +1.00000 q^{3} +2.96981 q^{4} +1.00000 q^{5} -2.22931 q^{6} -0.230360 q^{7} -2.16201 q^{8} +1.00000 q^{9} -2.22931 q^{10} +2.86243 q^{11} +2.96981 q^{12} +0.193596 q^{13} +0.513544 q^{14} +1.00000 q^{15} -1.11984 q^{16} -6.48565 q^{17} -2.22931 q^{18} -5.05286 q^{19} +2.96981 q^{20} -0.230360 q^{21} -6.38124 q^{22} +0.00109693 q^{23} -2.16201 q^{24} +1.00000 q^{25} -0.431585 q^{26} +1.00000 q^{27} -0.684127 q^{28} -4.00231 q^{29} -2.22931 q^{30} +2.40709 q^{31} +6.82048 q^{32} +2.86243 q^{33} +14.4585 q^{34} -0.230360 q^{35} +2.96981 q^{36} +0.157972 q^{37} +11.2644 q^{38} +0.193596 q^{39} -2.16201 q^{40} +2.23082 q^{41} +0.513544 q^{42} +9.21807 q^{43} +8.50088 q^{44} +1.00000 q^{45} -0.00244540 q^{46} +11.9263 q^{47} -1.11984 q^{48} -6.94693 q^{49} -2.22931 q^{50} -6.48565 q^{51} +0.574944 q^{52} -8.32236 q^{53} -2.22931 q^{54} +2.86243 q^{55} +0.498042 q^{56} -5.05286 q^{57} +8.92237 q^{58} -10.1651 q^{59} +2.96981 q^{60} -3.67229 q^{61} -5.36614 q^{62} -0.230360 q^{63} -12.9653 q^{64} +0.193596 q^{65} -6.38124 q^{66} -7.53639 q^{67} -19.2612 q^{68} +0.00109693 q^{69} +0.513544 q^{70} -8.52198 q^{71} -2.16201 q^{72} +0.460719 q^{73} -0.352169 q^{74} +1.00000 q^{75} -15.0060 q^{76} -0.659390 q^{77} -0.431585 q^{78} -3.30315 q^{79} -1.11984 q^{80} +1.00000 q^{81} -4.97319 q^{82} -1.08158 q^{83} -0.684127 q^{84} -6.48565 q^{85} -20.5499 q^{86} -4.00231 q^{87} -6.18861 q^{88} +3.25258 q^{89} -2.22931 q^{90} -0.0445969 q^{91} +0.00325769 q^{92} +2.40709 q^{93} -26.5874 q^{94} -5.05286 q^{95} +6.82048 q^{96} -3.56991 q^{97} +15.4869 q^{98} +2.86243 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 23 q - 5 q^{2} + 23 q^{3} + 9 q^{4} + 23 q^{5} - 5 q^{6} - 16 q^{7} - 12 q^{8} + 23 q^{9}+O(q^{10}) \) 23 * q - 5 * q^2 + 23 * q^3 + 9 * q^4 + 23 * q^5 - 5 * q^6 - 16 * q^7 - 12 * q^8 + 23 * q^9	\( 23 q - 5 q^{2} + 23 q^{3} + 9 q^{4} + 23 q^{5} - 5 q^{6} - 16 q^{7} - 12 q^{8} + 23 q^{9} - 5 q^{10} - 13 q^{11} + 9 q^{12} - 18 q^{13} - 6 q^{14} + 23 q^{15} - 11 q^{16} - 34 q^{17} - 5 q^{18} - 35 q^{19} + 9 q^{20} - 16 q^{21} - 11 q^{22} - 14 q^{23} - 12 q^{24} + 23 q^{25} - 6 q^{26} + 23 q^{27} - 26 q^{28} - 43 q^{29} - 5 q^{30} - 21 q^{31} - 14 q^{32} - 13 q^{33} - 12 q^{34} - 16 q^{35} + 9 q^{36} - 18 q^{37} + 6 q^{38} - 18 q^{39} - 12 q^{40} - 45 q^{41} - 6 q^{42} - 43 q^{43} - 11 q^{44} + 23 q^{45} - 29 q^{46} - 14 q^{47} - 11 q^{48} - 25 q^{49} - 5 q^{50} - 34 q^{51} - 20 q^{52} - 3 q^{53} - 5 q^{54} - 13 q^{55} + 3 q^{56} - 35 q^{57} + 10 q^{58} - 9 q^{59} + 9 q^{60} - 67 q^{61} - 7 q^{62} - 16 q^{63} - 8 q^{64} - 18 q^{65} - 11 q^{66} - 32 q^{67} - 24 q^{68} - 14 q^{69} - 6 q^{70} - 8 q^{71} - 12 q^{72} - 39 q^{73} - 16 q^{74} + 23 q^{75} - 48 q^{76} - 26 q^{77} - 6 q^{78} - 59 q^{79} - 11 q^{80} + 23 q^{81} - q^{82} - 23 q^{83} - 26 q^{84} - 34 q^{85} - 7 q^{86} - 43 q^{87} + 17 q^{88} - 51 q^{89} - 5 q^{90} - 37 q^{91} + 11 q^{92} - 21 q^{93} + 8 q^{94} - 35 q^{95} - 14 q^{96} - 29 q^{97} + 32 q^{98} - 13 q^{99}+O(q^{100}) \) 23 * q - 5 * q^2 + 23 * q^3 + 9 * q^4 + 23 * q^5 - 5 * q^6 - 16 * q^7 - 12 * q^8 + 23 * q^9 - 5 * q^10 - 13 * q^11 + 9 * q^12 - 18 * q^13 - 6 * q^14 + 23 * q^15 - 11 * q^16 - 34 * q^17 - 5 * q^18 - 35 * q^19 + 9 * q^20 - 16 * q^21 - 11 * q^22 - 14 * q^23 - 12 * q^24 + 23 * q^25 - 6 * q^26 + 23 * q^27 - 26 * q^28 - 43 * q^29 - 5 * q^30 - 21 * q^31 - 14 * q^32 - 13 * q^33 - 12 * q^34 - 16 * q^35 + 9 * q^36 - 18 * q^37 + 6 * q^38 - 18 * q^39 - 12 * q^40 - 45 * q^41 - 6 * q^42 - 43 * q^43 - 11 * q^44 + 23 * q^45 - 29 * q^46 - 14 * q^47 - 11 * q^48 - 25 * q^49 - 5 * q^50 - 34 * q^51 - 20 * q^52 - 3 * q^53 - 5 * q^54 - 13 * q^55 + 3 * q^56 - 35 * q^57 + 10 * q^58 - 9 * q^59 + 9 * q^60 - 67 * q^61 - 7 * q^62 - 16 * q^63 - 8 * q^64 - 18 * q^65 - 11 * q^66 - 32 * q^67 - 24 * q^68 - 14 * q^69 - 6 * q^70 - 8 * q^71 - 12 * q^72 - 39 * q^73 - 16 * q^74 + 23 * q^75 - 48 * q^76 - 26 * q^77 - 6 * q^78 - 59 * q^79 - 11 * q^80 + 23 * q^81 - q^82 - 23 * q^83 - 26 * q^84 - 34 * q^85 - 7 * q^86 - 43 * q^87 + 17 * q^88 - 51 * q^89 - 5 * q^90 - 37 * q^91 + 11 * q^92 - 21 * q^93 + 8 * q^94 - 35 * q^95 - 14 * q^96 - 29 * q^97 + 32 * q^98 - 13 * q^99

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