LMFDB - Embedded newform 8007.2.a.j.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8007,2,Mod(1,8007)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8007, 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("8007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8007 = 3 \cdot 17 \cdot 157 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8007.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:	$63.9362168984$
Analytic rank:	$0$
Dimension:	$64$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	8007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.54273 q^{2} -1.00000 q^{3} +4.46545 q^{4} -2.67798 q^{5} +2.54273 q^{6} +2.94599 q^{7} -6.26898 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.54273 q^{2} -1.00000 q^{3} +4.46545 q^{4} -2.67798 q^{5} +2.54273 q^{6} +2.94599 q^{7} -6.26898 q^{8} +1.00000 q^{9} +6.80937 q^{10} +1.14862 q^{11} -4.46545 q^{12} +5.66604 q^{13} -7.49086 q^{14} +2.67798 q^{15} +7.00938 q^{16} +1.00000 q^{17} -2.54273 q^{18} +6.65907 q^{19} -11.9584 q^{20} -2.94599 q^{21} -2.92063 q^{22} -4.86607 q^{23} +6.26898 q^{24} +2.17158 q^{25} -14.4072 q^{26} -1.00000 q^{27} +13.1552 q^{28} +7.98328 q^{29} -6.80937 q^{30} +8.48950 q^{31} -5.28497 q^{32} -1.14862 q^{33} -2.54273 q^{34} -7.88932 q^{35} +4.46545 q^{36} +1.03093 q^{37} -16.9322 q^{38} -5.66604 q^{39} +16.7882 q^{40} -9.73755 q^{41} +7.49086 q^{42} +3.63622 q^{43} +5.12913 q^{44} -2.67798 q^{45} +12.3731 q^{46} +9.61783 q^{47} -7.00938 q^{48} +1.67889 q^{49} -5.52174 q^{50} -1.00000 q^{51} +25.3014 q^{52} +13.7771 q^{53} +2.54273 q^{54} -3.07599 q^{55} -18.4684 q^{56} -6.65907 q^{57} -20.2993 q^{58} +14.9266 q^{59} +11.9584 q^{60} -5.54929 q^{61} -21.5865 q^{62} +2.94599 q^{63} -0.580516 q^{64} -15.1735 q^{65} +2.92063 q^{66} +10.3001 q^{67} +4.46545 q^{68} +4.86607 q^{69} +20.0604 q^{70} +10.3559 q^{71} -6.26898 q^{72} +1.44898 q^{73} -2.62138 q^{74} -2.17158 q^{75} +29.7358 q^{76} +3.38384 q^{77} +14.4072 q^{78} -1.75552 q^{79} -18.7710 q^{80} +1.00000 q^{81} +24.7599 q^{82} +14.2150 q^{83} -13.1552 q^{84} -2.67798 q^{85} -9.24590 q^{86} -7.98328 q^{87} -7.20069 q^{88} -4.33431 q^{89} +6.80937 q^{90} +16.6921 q^{91} -21.7292 q^{92} -8.48950 q^{93} -24.4555 q^{94} -17.8329 q^{95} +5.28497 q^{96} -6.00271 q^{97} -4.26895 q^{98} +1.14862 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9}+O(q^{10}) $ 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9	\( 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9} + 12 q^{10} - 7 q^{11} - 77 q^{12} + 24 q^{13} - 14 q^{14} + 3 q^{15} + 103 q^{16} + 64 q^{17} + 5 q^{18} + 26 q^{19} - 24 q^{20} - 5 q^{21} + 25 q^{22} + 20 q^{23} - 18 q^{24} + 141 q^{25} + 9 q^{26} - 64 q^{27} + 14 q^{28} + 5 q^{29} - 12 q^{30} + 11 q^{31} + 31 q^{32} + 7 q^{33} + 5 q^{34} - 3 q^{35} + 77 q^{36} + 50 q^{37} + 8 q^{38} - 24 q^{39} + 28 q^{40} - 9 q^{41} + 14 q^{42} + 59 q^{43} - 6 q^{44} - 3 q^{45} + 11 q^{47} - 103 q^{48} + 163 q^{49} + 20 q^{50} - 64 q^{51} + 65 q^{52} + 39 q^{53} - 5 q^{54} + 35 q^{55} - 34 q^{56} - 26 q^{57} - 27 q^{58} - 65 q^{59} + 24 q^{60} + 15 q^{61} + 18 q^{62} + 5 q^{63} + 152 q^{64} + 49 q^{65} - 25 q^{66} + 56 q^{67} + 77 q^{68} - 20 q^{69} + 28 q^{70} - 18 q^{71} + 18 q^{72} + 37 q^{73} - 76 q^{74} - 141 q^{75} + 30 q^{76} + 80 q^{77} - 9 q^{78} + 20 q^{79} - 144 q^{80} + 64 q^{81} + 27 q^{82} + 3 q^{83} - 14 q^{84} - 3 q^{85} + 12 q^{86} - 5 q^{87} + 108 q^{88} + 42 q^{89} + 12 q^{90} + 25 q^{91} + 18 q^{92} - 11 q^{93} + 60 q^{94} + 42 q^{95} - 31 q^{96} + 72 q^{97} + 18 q^{98} - 7 q^{99}+O(q^{100}) \) 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9 + 12 * q^10 - 7 * q^11 - 77 * q^12 + 24 * q^13 - 14 * q^14 + 3 * q^15 + 103 * q^16 + 64 * q^17 + 5 * q^18 + 26 * q^19 - 24 * q^20 - 5 * q^21 + 25 * q^22 + 20 * q^23 - 18 * q^24 + 141 * q^25 + 9 * q^26 - 64 * q^27 + 14 * q^28 + 5 * q^29 - 12 * q^30 + 11 * q^31 + 31 * q^32 + 7 * q^33 + 5 * q^34 - 3 * q^35 + 77 * q^36 + 50 * q^37 + 8 * q^38 - 24 * q^39 + 28 * q^40 - 9 * q^41 + 14 * q^42 + 59 * q^43 - 6 * q^44 - 3 * q^45 + 11 * q^47 - 103 * q^48 + 163 * q^49 + 20 * q^50 - 64 * q^51 + 65 * q^52 + 39 * q^53 - 5 * q^54 + 35 * q^55 - 34 * q^56 - 26 * q^57 - 27 * q^58 - 65 * q^59 + 24 * q^60 + 15 * q^61 + 18 * q^62 + 5 * q^63 + 152 * q^64 + 49 * q^65 - 25 * q^66 + 56 * q^67 + 77 * q^68 - 20 * q^69 + 28 * q^70 - 18 * q^71 + 18 * q^72 + 37 * q^73 - 76 * q^74 - 141 * q^75 + 30 * q^76 + 80 * q^77 - 9 * q^78 + 20 * q^79 - 144 * q^80 + 64 * q^81 + 27 * q^82 + 3 * q^83 - 14 * q^84 - 3 * q^85 + 12 * q^86 - 5 * q^87 + 108 * q^88 + 42 * q^89 + 12 * q^90 + 25 * q^91 + 18 * q^92 - 11 * q^93 + 60 * q^94 + 42 * q^95 - 31 * q^96 + 72 * q^97 + 18 * q^98 - 7 * 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 $

$2$	−2.54273	−1.79798	−0.898989	−	0.437970i	$-0.855697\pi$
$2$	−2.54273	−1.79798	−0.898989	+	0.437970i	$0.855697\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	4.46545	2.23273
$5$	−2.67798	−1.19763	−0.598815	−	0.800888i	$-0.704361\pi$
$5$	−2.67798	−1.19763	−0.598815	+	0.800888i	$0.704361\pi$
$6$	2.54273	1.03806
$7$	2.94599	1.11348	0.556741	−	0.830686i	$-0.312052\pi$
$7$	2.94599	1.11348	0.556741	+	0.830686i	$0.312052\pi$
$8$	−6.26898	−2.21642
$9$	1.00000	0.333333
$10$	6.80937	2.15331
$11$	1.14862	0.346323	0.173161	−	0.984893i	$-0.444602\pi$
$11$	1.14862	0.346323	0.173161	+	0.984893i	$0.444602\pi$
$12$	−4.46545	−1.28907
$13$	5.66604	1.57148	0.785738	−	0.618559i	$-0.212283\pi$
$13$	5.66604	1.57148	0.785738	+	0.618559i	$0.212283\pi$
$14$	−7.49086	−2.00202
$15$	2.67798	0.691452
$16$	7.00938	1.75234
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−2.54273	−0.599326
$19$	6.65907	1.52769	0.763847	−	0.645397i	$-0.223308\pi$
$19$	6.65907	1.52769	0.763847	+	0.645397i	$0.223308\pi$
$20$	−11.9584	−2.67398
$21$	−2.94599	−0.642869
$22$	−2.92063	−0.622681
$23$	−4.86607	−1.01465	−0.507323	−	0.861756i	$-0.669365\pi$
$23$	−4.86607	−1.01465	−0.507323	+	0.861756i	$0.669365\pi$
$24$	6.26898	1.27965
$25$	2.17158	0.434316
$26$	−14.4072	−2.82548
$27$	−1.00000	−0.192450
$28$	13.1552	2.48610
$29$	7.98328	1.48246	0.741229	−	0.671252i	$-0.234243\pi$
$29$	7.98328	1.48246	0.741229	+	0.671252i	$0.234243\pi$
$30$	−6.80937	−1.24322
$31$	8.48950	1.52476	0.762380	−	0.647130i	$-0.224031\pi$
$31$	8.48950	1.52476	0.762380	+	0.647130i	$0.224031\pi$
$32$	−5.28497	−0.934260
$33$	−1.14862	−0.199950
$34$	−2.54273	−0.436074
$35$	−7.88932	−1.33354
$36$	4.46545	0.744242
$37$	1.03093	0.169485	0.0847423	−	0.996403i	$-0.472993\pi$
$37$	1.03093	0.169485	0.0847423	+	0.996403i	$0.472993\pi$
$38$	−16.9322	−2.74676
$39$	−5.66604	−0.907292
$40$	16.7882	2.65445
$41$	−9.73755	−1.52075	−0.760375	−	0.649484i	$-0.774985\pi$
$41$	−9.73755	−1.52075	−0.760375	+	0.649484i	$0.774985\pi$
$42$	7.49086	1.15586
$43$	3.63622	0.554518	0.277259	−	0.960795i	$-0.410574\pi$
$43$	3.63622	0.554518	0.277259	+	0.960795i	$0.410574\pi$
$44$	5.12913	0.773245
$45$	−2.67798	−0.399210
$46$	12.3731	1.82431
$47$	9.61783	1.40290	0.701452	−	0.712717i	$-0.252535\pi$
$47$	9.61783	1.40290	0.701452	+	0.712717i	$0.252535\pi$
$48$	−7.00938	−1.01172
$49$	1.67889	0.239841
$50$	−5.52174	−0.780891
$51$	−1.00000	−0.140028
$52$	25.3014	3.50868
$53$	13.7771	1.89242	0.946212	−	0.323546i	$-0.104875\pi$
$53$	13.7771	1.89242	0.946212	+	0.323546i	$0.104875\pi$
$54$	2.54273	0.346021
$55$	−3.07599	−0.414767
$56$	−18.4684	−2.46794
$57$	−6.65907	−0.882015
$58$	−20.2993	−2.66543
$59$	14.9266	1.94328	0.971638	−	0.236472i	$-0.0759911\pi$
$59$	14.9266	1.94328	0.971638	+	0.236472i	$0.0759911\pi$
$60$	11.9584	1.54382
$61$	−5.54929	−0.710514	−0.355257	−	0.934769i	$-0.615607\pi$
$61$	−5.54929	−0.710514	−0.355257	+	0.934769i	$0.615607\pi$
$62$	−21.5865	−2.74148
$63$	2.94599	0.371160
$64$	−0.580516	−0.0725645
$65$	−15.1735	−1.88205
$66$	2.92063	0.359505
$67$	10.3001	1.25836	0.629178	−	0.777261i	$-0.283392\pi$
$67$	10.3001	1.25836	0.629178	+	0.777261i	$0.283392\pi$
$68$	4.46545	0.541516
$69$	4.86607	0.585806
$70$	20.0604	2.39767
$71$	10.3559	1.22902	0.614510	−	0.788909i	$-0.289354\pi$
$71$	10.3559	1.22902	0.614510	+	0.788909i	$0.289354\pi$
$72$	−6.26898	−0.738806
$73$	1.44898	0.169590	0.0847949	−	0.996398i	$-0.472976\pi$
$73$	1.44898	0.169590	0.0847949	+	0.996398i	$0.472976\pi$
$74$	−2.62138	−0.304730
$75$	−2.17158	−0.250753
$76$	29.7358	3.41093
$77$	3.38384	0.385624
$78$	14.4072	1.63129
$79$	−1.75552	−0.197512	−0.0987559	−	0.995112i	$-0.531486\pi$
$79$	−1.75552	−0.197512	−0.0987559	+	0.995112i	$0.531486\pi$
$80$	−18.7710	−2.09866
$81$	1.00000	0.111111
$82$	24.7599	2.73428
$83$	14.2150	1.56030	0.780149	−	0.625593i	$-0.215143\pi$
$83$	14.2150	1.56030	0.780149	+	0.625593i	$0.215143\pi$
$84$	−13.1552	−1.43535
$85$	−2.67798	−0.290468
$86$	−9.24590	−0.997011
$87$	−7.98328	−0.855898
$88$	−7.20069	−0.767596
$89$	−4.33431	−0.459436	−0.229718	−	0.973257i	$-0.573780\pi$
$89$	−4.33431	−0.459436	−0.229718	+	0.973257i	$0.573780\pi$
$90$	6.80937	0.717771
$91$	16.6921	1.74981
$92$	−21.7292	−2.26543
$93$	−8.48950	−0.880320
$94$	−24.4555	−2.52239
$95$	−17.8329	−1.82961
$96$	5.28497	0.539395
$97$	−6.00271	−0.609483	−0.304742	−	0.952435i	$-0.598570\pi$
$97$	−6.00271	−0.609483	−0.304742	+	0.952435i	$0.598570\pi$
$98$	−4.26895	−0.431229
$99$	1.14862	0.115441
$100$	9.69710	0.969710
$101$	−3.33028	−0.331375	−0.165687	−	0.986178i	$-0.552984\pi$
$101$	−3.33028	−0.331375	−0.165687	+	0.986178i	$0.552984\pi$
$102$	2.54273	0.251767
$103$	−0.902439	−0.0889199	−0.0444600	−	0.999011i	$-0.514157\pi$
$103$	−0.902439	−0.0889199	−0.0444600	+	0.999011i	$0.514157\pi$
$104$	−35.5203	−3.48305
$105$	7.88932	0.769919
$106$	−35.0313	−3.40254
$107$	10.9399	1.05760	0.528801	−	0.848746i	$-0.322642\pi$
$107$	10.9399	1.05760	0.528801	+	0.848746i	$0.322642\pi$
$108$	−4.46545	−0.429689
$109$	14.5605	1.39464	0.697321	−	0.716759i	$-0.254375\pi$
$109$	14.5605	1.39464	0.697321	+	0.716759i	$0.254375\pi$
$110$	7.82140	0.745741
$111$	−1.03093	−0.0978520
$112$	20.6496	1.95120
$113$	6.44854	0.606628	0.303314	−	0.952891i	$-0.401907\pi$
$113$	6.44854	0.606628	0.303314	+	0.952891i	$0.401907\pi$
$114$	16.9322	1.58584
$115$	13.0312	1.21517
$116$	35.6490	3.30992
$117$	5.66604	0.523826
$118$	−37.9542	−3.49397
$119$	2.94599	0.270059
$120$	−16.7882	−1.53255
$121$	−9.68066	−0.880060
$122$	14.1103	1.27749
$123$	9.73755	0.878006
$124$	37.9095	3.40437
$125$	7.57445	0.677480
$126$	−7.49086	−0.667339
$127$	−8.02012	−0.711671	−0.355835	−	0.934549i	$-0.615804\pi$
$127$	−8.02012	−0.711671	−0.355835	+	0.934549i	$0.615804\pi$
$128$	12.0460	1.06473
$129$	−3.63622	−0.320151
$130$	38.5822	3.38388
$131$	11.2240	0.980648	0.490324	−	0.871540i	$-0.336878\pi$
$131$	11.2240	0.980648	0.490324	+	0.871540i	$0.336878\pi$
$132$	−5.12913	−0.446433
$133$	19.6176	1.70106
$134$	−26.1903	−2.26250
$135$	2.67798	0.230484
$136$	−6.26898	−0.537560
$137$	13.1733	1.12547	0.562734	−	0.826638i	$-0.309749\pi$
$137$	13.1733	1.12547	0.562734	+	0.826638i	$0.309749\pi$
$138$	−12.3731	−1.05327
$139$	−20.3308	−1.72444	−0.862218	−	0.506537i	$-0.830925\pi$
$139$	−20.3308	−1.72444	−0.862218	+	0.506537i	$0.830925\pi$
$140$	−35.2294	−2.97743
$141$	−9.61783	−0.809967
$142$	−26.3322	−2.20975
$143$	6.50814	0.544238
$144$	7.00938	0.584115
$145$	−21.3791	−1.77544
$146$	−3.68435	−0.304919
$147$	−1.67889	−0.138472
$148$	4.60359	0.378413
$149$	−4.27599	−0.350303	−0.175151	−	0.984542i	$-0.556041\pi$
$149$	−4.27599	−0.350303	−0.175151	+	0.984542i	$0.556041\pi$
$150$	5.52174	0.450848
$151$	−18.5641	−1.51072	−0.755361	−	0.655309i	$-0.772538\pi$
$151$	−18.5641	−1.51072	−0.755361	+	0.655309i	$0.772538\pi$
$152$	−41.7455	−3.38601
$153$	1.00000	0.0808452
$154$	−8.60417	−0.693344
$155$	−22.7347	−1.82610
$156$	−25.3014	−2.02574
$157$	−1.00000	−0.0798087
$157$	−1.00000	−0.0798087
$158$	4.46381	0.355122
$159$	−13.7771	−1.09259
$160$	14.1531	1.11890
$161$	−14.3354	−1.12979
$162$	−2.54273	−0.199775
$163$	−11.5849	−0.907397	−0.453699	−	0.891155i	$-0.649896\pi$
$163$	−11.5849	−0.907397	−0.453699	+	0.891155i	$0.649896\pi$
$164$	−43.4826	−3.39542
$165$	3.07599	0.239466
$166$	−36.1448	−2.80538
$167$	−3.97649	−0.307710	−0.153855	−	0.988093i	$-0.549169\pi$
$167$	−3.97649	−0.307710	−0.153855	+	0.988093i	$0.549169\pi$
$168$	18.4684	1.42487
$169$	19.1040	1.46954
$170$	6.80937	0.522255
$171$	6.65907	0.509232
$172$	16.2374	1.23809
$173$	9.89085	0.751987	0.375994	−	0.926622i	$-0.377301\pi$
$173$	9.89085	0.751987	0.375994	+	0.926622i	$0.377301\pi$
$174$	20.2993	1.53889
$175$	6.39747	0.483603
$176$	8.05113	0.606877
$177$	−14.9266	−1.12195
$178$	11.0210	0.826056
$179$	3.11527	0.232846	0.116423	−	0.993200i	$-0.462857\pi$
$179$	3.11527	0.232846	0.116423	+	0.993200i	$0.462857\pi$
$180$	−11.9584	−0.891327
$181$	−13.3295	−0.990775	−0.495387	−	0.868672i	$-0.664974\pi$
$181$	−13.3295	−0.990775	−0.495387	+	0.868672i	$0.664974\pi$
$182$	−42.4435	−3.14612
$183$	5.54929	0.410215
$184$	30.5053	2.24888
$185$	−2.76082	−0.202980
$186$	21.5865	1.58280
$187$	1.14862	0.0839957
$188$	42.9480	3.13230
$189$	−2.94599	−0.214290
$190$	45.3441	3.28960
$191$	−8.78858	−0.635919	−0.317959	−	0.948104i	$-0.602998\pi$
$191$	−8.78858	−0.635919	−0.317959	+	0.948104i	$0.602998\pi$
$192$	0.580516	0.0418952
$193$	20.7784	1.49566	0.747831	−	0.663889i	$-0.231095\pi$
$193$	20.7784	1.49566	0.747831	+	0.663889i	$0.231095\pi$
$194$	15.2633	1.09584
$195$	15.1735	1.08660
$196$	7.49699	0.535499
$197$	−23.7695	−1.69351	−0.846753	−	0.531986i	$-0.821446\pi$
$197$	−23.7695	−1.69351	−0.846753	+	0.531986i	$0.821446\pi$
$198$	−2.92063	−0.207560
$199$	15.2002	1.07751	0.538756	−	0.842462i	$-0.318894\pi$
$199$	15.2002	1.07751	0.538756	+	0.842462i	$0.318894\pi$
$200$	−13.6136	−0.962626
$201$	−10.3001	−0.726512
$202$	8.46798	0.595805
$203$	23.5187	1.65069
$204$	−4.46545	−0.312644
$205$	26.0770	1.82130
$206$	2.29465	0.159876
$207$	−4.86607	−0.338215
$208$	39.7154	2.75377
$209$	7.64876	0.529076
$210$	−20.0604	−1.38430
$211$	15.7713	1.08574	0.542869	−	0.839817i	$-0.317338\pi$
$211$	15.7713	1.08574	0.542869	+	0.839817i	$0.317338\pi$
$212$	61.5208	4.22527
$213$	−10.3559	−0.709575
$214$	−27.8172	−1.90154
$215$	−9.73772	−0.664107
$216$	6.26898	0.426550
$217$	25.0100	1.69779
$218$	−37.0233	−2.50754
$219$	−1.44898	−0.0979127
$220$	−13.7357	−0.926061
$221$	5.66604	0.381139
$222$	2.62138	0.175936
$223$	9.15149	0.612829	0.306415	−	0.951898i	$-0.400871\pi$
$223$	9.15149	0.612829	0.306415	+	0.951898i	$0.400871\pi$
$224$	−15.5695	−1.04028
$225$	2.17158	0.144772
$226$	−16.3969	−1.09070
$227$	−20.5423	−1.36344	−0.681720	−	0.731613i	$-0.738768\pi$
$227$	−20.5423	−1.36344	−0.681720	+	0.731613i	$0.738768\pi$
$228$	−29.7358	−1.96930
$229$	−14.8520	−0.981448	−0.490724	−	0.871315i	$-0.663268\pi$
$229$	−14.8520	−0.981448	−0.490724	+	0.871315i	$0.663268\pi$
$230$	−33.1349	−2.18485
$231$	−3.38384	−0.222640
$232$	−50.0470	−3.28575
$233$	−6.18493	−0.405188	−0.202594	−	0.979263i	$-0.564937\pi$
$233$	−6.18493	−0.405188	−0.202594	+	0.979263i	$0.564937\pi$
$234$	−14.4072	−0.941827
$235$	−25.7564	−1.68016
$236$	66.6540	4.33881
$237$	1.75552	0.114033
$238$	−7.49086	−0.485560
$239$	−8.90165	−0.575800	−0.287900	−	0.957660i	$-0.592957\pi$
$239$	−8.90165	−0.575800	−0.287900	+	0.957660i	$0.592957\pi$
$240$	18.7710	1.21166
$241$	−9.59092	−0.617805	−0.308903	−	0.951094i	$-0.599962\pi$
$241$	−9.59092	−0.617805	−0.308903	+	0.951094i	$0.599962\pi$
$242$	24.6153	1.58233
$243$	−1.00000	−0.0641500
$244$	−24.7801	−1.58638
$245$	−4.49602	−0.287240
$246$	−24.7599	−1.57864
$247$	37.7305	2.40074
$248$	−53.2205	−3.37950
$249$	−14.2150	−0.900839
$250$	−19.2598	−1.21809
$251$	−12.8153	−0.808898	−0.404449	−	0.914561i	$-0.632537\pi$
$251$	−12.8153	−0.808898	−0.404449	+	0.914561i	$0.632537\pi$
$252$	13.1552	0.828700
$253$	−5.58928	−0.351395
$254$	20.3930	1.27957
$255$	2.67798	0.167702
$256$	−29.4687	−1.84180
$257$	−18.2418	−1.13789	−0.568945	−	0.822375i	$-0.692648\pi$
$257$	−18.2418	−1.13789	−0.568945	+	0.822375i	$0.692648\pi$
$258$	9.24590	0.575625
$259$	3.03713	0.188718
$260$	−67.7568	−4.20210
$261$	7.98328	0.494153
$262$	−28.5396	−1.76318
$263$	12.8203	0.790531	0.395266	−	0.918567i	$-0.370653\pi$
$263$	12.8203	0.790531	0.395266	+	0.918567i	$0.370653\pi$
$264$	7.20069	0.443172
$265$	−36.8947	−2.26642
$266$	−49.8821	−3.05847
$267$	4.33431	0.265256
$268$	45.9946	2.80957
$269$	14.0139	0.854440	0.427220	−	0.904148i	$-0.359493\pi$
$269$	14.0139	0.854440	0.427220	+	0.904148i	$0.359493\pi$
$270$	−6.80937	−0.414405
$271$	1.72927	0.105046	0.0525230	−	0.998620i	$-0.483274\pi$
$271$	1.72927	0.105046	0.0525230	+	0.998620i	$0.483274\pi$
$272$	7.00938	0.425006
$273$	−16.6921	−1.01025
$274$	−33.4960	−2.02357
$275$	2.49433	0.150414
$276$	21.7292	1.30794
$277$	−20.2522	−1.21684	−0.608419	−	0.793616i	$-0.708196\pi$
$277$	−20.2522	−1.21684	−0.608419	+	0.793616i	$0.708196\pi$
$278$	51.6957	3.10050
$279$	8.48950	0.508253
$280$	49.4579	2.95568
$281$	5.78300	0.344985	0.172492	−	0.985011i	$-0.444818\pi$
$281$	5.78300	0.344985	0.172492	+	0.985011i	$0.444818\pi$
$282$	24.4555	1.45630
$283$	−11.5004	−0.683630	−0.341815	−	0.939767i	$-0.611042\pi$
$283$	−11.5004	−0.683630	−0.341815	+	0.939767i	$0.611042\pi$
$284$	46.2438	2.74407
$285$	17.8329	1.05633
$286$	−16.5484	−0.978529
$287$	−28.6868	−1.69333
$288$	−5.28497	−0.311420
$289$	1.00000	0.0588235
$290$	54.3611	3.19219
$291$	6.00271	0.351885
$292$	6.47034	0.378648
$293$	5.66538	0.330975	0.165488	−	0.986212i	$-0.447080\pi$
$293$	5.66538	0.330975	0.165488	+	0.986212i	$0.447080\pi$
$294$	4.26895	0.248970
$295$	−39.9731	−2.32733
$296$	−6.46290	−0.375649
$297$	−1.14862	−0.0666499
$298$	10.8727	0.629837
$299$	−27.5713	−1.59449
$300$	−9.69710	−0.559862
$301$	10.7123	0.617445
$302$	47.2033	2.71625
$303$	3.33028	0.191319
$304$	46.6759	2.67705
$305$	14.8609	0.850932
$306$	−2.54273	−0.145358
$307$	24.2299	1.38288	0.691438	−	0.722436i	$-0.256978\pi$
$307$	24.2299	1.38288	0.691438	+	0.722436i	$0.256978\pi$
$308$	15.1104	0.860994
$309$	0.902439	0.0513379
$310$	57.8082	3.28328
$311$	−1.55255	−0.0880371	−0.0440185	−	0.999031i	$-0.514016\pi$
$311$	−1.55255	−0.0880371	−0.0440185	+	0.999031i	$0.514016\pi$
$312$	35.5203	2.01094
$313$	−22.4840	−1.27087	−0.635436	−	0.772153i	$-0.719180\pi$
$313$	−22.4840	−1.27087	−0.635436	+	0.772153i	$0.719180\pi$
$314$	2.54273	0.143494
$315$	−7.88932	−0.444513
$316$	−7.83921	−0.440990
$317$	−24.6033	−1.38186	−0.690929	−	0.722922i	$-0.742798\pi$
$317$	−24.6033	−1.38186	−0.690929	+	0.722922i	$0.742798\pi$
$318$	35.0313	1.96446
$319$	9.16978	0.513409
$320$	1.55461	0.0869054
$321$	−10.9399	−0.610606
$322$	36.4510	2.03134
$323$	6.65907	0.370520
$324$	4.46545	0.248081
$325$	12.3043	0.682518
$326$	29.4572	1.63148
$327$	−14.5605	−0.805197
$328$	61.0445	3.37062
$329$	28.3341	1.56211
$330$	−7.82140	−0.430554
$331$	−9.42272	−0.517920	−0.258960	−	0.965888i	$-0.583380\pi$
$331$	−9.42272	−0.517920	−0.258960	+	0.965888i	$0.583380\pi$
$332$	63.4764	3.48372
$333$	1.03093	0.0564949
$334$	10.1111	0.553256
$335$	−27.5834	−1.50704
$336$	−20.6496	−1.12653
$337$	−9.58223	−0.521977	−0.260989	−	0.965342i	$-0.584048\pi$
$337$	−9.58223	−0.521977	−0.260989	+	0.965342i	$0.584048\pi$
$338$	−48.5762	−2.64220
$339$	−6.44854	−0.350237
$340$	−11.9584	−0.648535
$341$	9.75124	0.528059
$342$	−16.9322	−0.915588
$343$	−15.6760	−0.846423
$344$	−22.7954	−1.22904
$345$	−13.0312	−0.701578
$346$	−25.1497	−1.35206
$347$	−27.3762	−1.46963	−0.734816	−	0.678267i	$-0.762731\pi$
$347$	−27.3762	−1.46963	−0.734816	+	0.678267i	$0.762731\pi$
$348$	−35.6490	−1.91099
$349$	17.9630	0.961540	0.480770	−	0.876847i	$-0.340357\pi$
$349$	17.9630	0.961540	0.480770	+	0.876847i	$0.340357\pi$
$350$	−16.2670	−0.869508
$351$	−5.66604	−0.302431
$352$	−6.07044	−0.323556
$353$	−27.5292	−1.46523	−0.732615	−	0.680644i	$-0.761700\pi$
$353$	−27.5292	−1.46523	−0.732615	+	0.680644i	$0.761700\pi$
$354$	37.9542	2.01724
$355$	−27.7329	−1.47191
$356$	−19.3547	−1.02580
$357$	−2.94599	−0.155919
$358$	−7.92127	−0.418652
$359$	11.4062	0.601995	0.300998	−	0.953625i	$-0.402680\pi$
$359$	11.4062	0.601995	0.300998	+	0.953625i	$0.402680\pi$
$360$	16.7882	0.884816
$361$	25.3432	1.33385
$362$	33.8933	1.78139
$363$	9.68066	0.508103
$364$	74.5379	3.90685
$365$	−3.88033	−0.203106
$366$	−14.1103	−0.737559
$367$	18.3147	0.956021	0.478010	−	0.878354i	$-0.341358\pi$
$367$	18.3147	0.956021	0.478010	+	0.878354i	$0.341358\pi$
$368$	−34.1081	−1.77801
$369$	−9.73755	−0.506917
$370$	7.02001	0.364953
$371$	40.5872	2.10718
$372$	−37.9095	−1.96551
$373$	20.9121	1.08279	0.541394	−	0.840769i	$-0.317897\pi$
$373$	20.9121	1.08279	0.541394	+	0.840769i	$0.317897\pi$
$374$	−2.92063	−0.151022
$375$	−7.57445	−0.391143
$376$	−60.2939	−3.10942
$377$	45.2336	2.32965
$378$	7.49086	0.385288
$379$	2.98218	0.153184	0.0765922	−	0.997063i	$-0.475596\pi$
$379$	2.98218	0.153184	0.0765922	+	0.997063i	$0.475596\pi$
$380$	−79.6318	−4.08503
$381$	8.02012	0.410883
$382$	22.3469	1.14337
$383$	32.8908	1.68064	0.840322	−	0.542088i	$-0.182366\pi$
$383$	32.8908	1.68064	0.840322	+	0.542088i	$0.182366\pi$
$384$	−12.0460	−0.614722
$385$	−9.06185	−0.461835
$386$	−52.8338	−2.68917
$387$	3.63622	0.184839
$388$	−26.8048	−1.36081
$389$	−32.0896	−1.62701	−0.813505	−	0.581558i	$-0.802443\pi$
$389$	−32.0896	−1.62701	−0.813505	+	0.581558i	$0.802443\pi$
$390$	−38.5822	−1.95368
$391$	−4.86607	−0.246088
$392$	−10.5249	−0.531587
$393$	−11.2240	−0.566177
$394$	60.4393	3.04489
$395$	4.70126	0.236546
$396$	5.12913	0.257748
$397$	−23.8666	−1.19783	−0.598914	−	0.800813i	$-0.704401\pi$
$397$	−23.8666	−1.19783	−0.598914	+	0.800813i	$0.704401\pi$
$398$	−38.6499	−1.93734
$399$	−19.6176	−0.982107
$400$	15.2214	0.761072
$401$	−27.9994	−1.39822	−0.699112	−	0.715012i	$-0.746421\pi$
$401$	−27.9994	−1.39822	−0.699112	+	0.715012i	$0.746421\pi$
$402$	26.1903	1.30625
$403$	48.1018	2.39612
$404$	−14.8712	−0.739870
$405$	−2.67798	−0.133070
$406$	−59.8016	−2.96790
$407$	1.18416	0.0586964
$408$	6.26898	0.310361
$409$	−9.86637	−0.487861	−0.243930	−	0.969793i	$-0.578437\pi$
$409$	−9.86637	−0.487861	−0.243930	+	0.969793i	$0.578437\pi$
$410$	−66.3066	−3.27465
$411$	−13.1733	−0.649790
$412$	−4.02980	−0.198534
$413$	43.9737	2.16380
$414$	12.3731	0.608104
$415$	−38.0675	−1.86866
$416$	−29.9449	−1.46817
$417$	20.3308	0.995604
$418$	−19.4487	−0.951267
$419$	10.3559	0.505919	0.252959	−	0.967477i	$-0.418596\pi$
$419$	10.3559	0.505919	0.252959	+	0.967477i	$0.418596\pi$
$420$	35.2294	1.71902
$421$	17.7266	0.863940	0.431970	−	0.901888i	$-0.357819\pi$
$421$	17.7266	0.863940	0.431970	+	0.901888i	$0.357819\pi$
$422$	−40.1020	−1.95213
$423$	9.61783	0.467635
$424$	−86.3681	−4.19440
$425$	2.17158	0.105337
$426$	26.3322	1.27580
$427$	−16.3482	−0.791144
$428$	48.8517	2.36133
$429$	−6.50814	−0.314216
$430$	24.7603	1.19405
$431$	5.07575	0.244490	0.122245	−	0.992500i	$-0.460991\pi$
$431$	5.07575	0.244490	0.122245	+	0.992500i	$0.460991\pi$
$432$	−7.00938	−0.337239
$433$	−1.50363	−0.0722599	−0.0361300	−	0.999347i	$-0.511503\pi$
$433$	−1.50363	−0.0722599	−0.0361300	+	0.999347i	$0.511503\pi$
$434$	−63.5936	−3.05259
$435$	21.3791	1.02505
$436$	65.0192	3.11386
$437$	−32.4035	−1.55007
$438$	3.68435	0.176045
$439$	−14.2046	−0.677949	−0.338975	−	0.940796i	$-0.610080\pi$
$439$	−14.2046	−0.677949	−0.338975	+	0.940796i	$0.610080\pi$
$440$	19.2833	0.919296
$441$	1.67889	0.0799469
$442$	−14.4072	−0.685280
$443$	−36.1147	−1.71586	−0.857932	−	0.513764i	$-0.828251\pi$
$443$	−36.1147	−1.71586	−0.857932	+	0.513764i	$0.828251\pi$
$444$	−4.60359	−0.218477
$445$	11.6072	0.550234
$446$	−23.2697	−1.10185
$447$	4.27599	0.202247
$448$	−1.71020	−0.0807993
$449$	−9.30746	−0.439246	−0.219623	−	0.975585i	$-0.570483\pi$
$449$	−9.30746	−0.439246	−0.219623	+	0.975585i	$0.570483\pi$
$450$	−5.52174	−0.260297
$451$	−11.1848	−0.526671
$452$	28.7957	1.35444
$453$	18.5641	0.872216
$454$	52.2334	2.45144
$455$	−44.7012	−2.09562
$456$	41.7455	1.95491
$457$	22.4678	1.05100	0.525499	−	0.850794i	$-0.323879\pi$
$457$	22.4678	1.05100	0.525499	+	0.850794i	$0.323879\pi$
$458$	37.7646	1.76462
$459$	−1.00000	−0.0466760
$460$	58.1904	2.71314
$461$	11.1532	0.519457	0.259729	−	0.965682i	$-0.416367\pi$
$461$	11.1532	0.519457	0.259729	+	0.965682i	$0.416367\pi$
$462$	8.60417	0.400302
$463$	−6.37371	−0.296211	−0.148106	−	0.988972i	$-0.547318\pi$
$463$	−6.37371	−0.296211	−0.148106	+	0.988972i	$0.547318\pi$
$464$	55.9578	2.59778
$465$	22.7347	1.05430
$466$	15.7266	0.728520
$467$	−4.10325	−0.189876	−0.0949379	−	0.995483i	$-0.530265\pi$
$467$	−4.10325	−0.189876	−0.0949379	+	0.995483i	$0.530265\pi$
$468$	25.3014	1.16956
$469$	30.3440	1.40116
$470$	65.4914	3.02089
$471$	1.00000	0.0460776
$472$	−93.5744	−4.30711
$473$	4.17664	0.192042
$474$	−4.46381	−0.205030
$475$	14.4607	0.663503
$476$	13.1552	0.602968
$477$	13.7771	0.630808
$478$	22.6345	1.03528
$479$	−25.2367	−1.15309	−0.576547	−	0.817064i	$-0.695600\pi$
$479$	−25.2367	−1.15309	−0.576547	+	0.817064i	$0.695600\pi$
$480$	−14.1531	−0.645996
$481$	5.84131	0.266341
$482$	24.3871	1.11080
$483$	14.3354	0.652284
$484$	−43.2286	−1.96494
$485$	16.0751	0.729935
$486$	2.54273	0.115340
$487$	−38.9121	−1.76328	−0.881638	−	0.471926i	$-0.843559\pi$
$487$	−38.9121	−1.76328	−0.881638	+	0.471926i	$0.843559\pi$
$488$	34.7884	1.57480
$489$	11.5849	0.523886
$490$	11.4322	0.516452
$491$	−29.8868	−1.34877	−0.674387	−	0.738378i	$-0.735592\pi$
$491$	−29.8868	−1.34877	−0.674387	+	0.738378i	$0.735592\pi$
$492$	43.4826	1.96035
$493$	7.98328	0.359549
$494$	−95.9384	−4.31647
$495$	−3.07599	−0.138256
$496$	59.5061	2.67190
$497$	30.5085	1.36849
$498$	36.1448	1.61969
$499$	−33.6178	−1.50494	−0.752469	−	0.658628i	$-0.771137\pi$
$499$	−33.6178	−1.50494	−0.752469	+	0.658628i	$0.771137\pi$
$500$	33.8234	1.51263
$501$	3.97649	0.177657
$502$	32.5859	1.45438
$503$	−21.6655	−0.966018	−0.483009	−	0.875616i	$-0.660456\pi$
$503$	−21.6655	−0.966018	−0.483009	+	0.875616i	$0.660456\pi$
$504$	−18.4684	−0.822647
$505$	8.91842	0.396864
$506$	14.2120	0.631801
$507$	−19.1040	−0.848438
$508$	−35.8135	−1.58897
$509$	−30.7088	−1.36114	−0.680571	−	0.732682i	$-0.738268\pi$
$509$	−30.7088	−1.36114	−0.680571	+	0.732682i	$0.738268\pi$
$510$	−6.80937	−0.301524
$511$	4.26868	0.188835
$512$	50.8389	2.24678
$513$	−6.65907	−0.294005
$514$	46.3838	2.04590
$515$	2.41671	0.106493
$516$	−16.2374	−0.714810
$517$	11.0473	0.485858
$518$	−7.72258	−0.339311
$519$	−9.89085	−0.434160
$520$	95.1226	4.17140
$521$	−21.0919	−0.924052	−0.462026	−	0.886866i	$-0.652877\pi$
$521$	−21.0919	−0.924052	−0.462026	+	0.886866i	$0.652877\pi$
$522$	−20.2993	−0.888476
$523$	28.9815	1.26727	0.633637	−	0.773631i	$-0.281561\pi$
$523$	28.9815	1.26727	0.633637	+	0.773631i	$0.281561\pi$
$524$	50.1204	2.18952
$525$	−6.39747	−0.279208
$526$	−32.5984	−1.42136
$527$	8.48950	0.369808
$528$	−8.05113	−0.350381
$529$	0.678634	0.0295058
$530$	93.8131	4.07498
$531$	14.9266	0.647759
$532$	87.6014	3.79800
$533$	−55.1734	−2.38982
$534$	−11.0210	−0.476924
$535$	−29.2969	−1.26661
$536$	−64.5710	−2.78904
$537$	−3.11527	−0.134434
$538$	−35.6334	−1.53626
$539$	1.92841	0.0830624
$540$	11.9584	0.514608
$541$	−39.1386	−1.68270	−0.841351	−	0.540490i	$-0.818239\pi$
$541$	−39.1386	−1.68270	−0.841351	+	0.540490i	$0.818239\pi$
$542$	−4.39707	−0.188870
$543$	13.3295	0.572024
$544$	−5.28497	−0.226591
$545$	−38.9927	−1.67026
$546$	42.4435	1.81641
$547$	13.0844	0.559450	0.279725	−	0.960080i	$-0.409757\pi$
$547$	13.0844	0.559450	0.279725	+	0.960080i	$0.409757\pi$
$548$	58.8247	2.51286
$549$	−5.54929	−0.236838
$550$	−6.34239	−0.270441
$551$	53.1612	2.26474
$552$	−30.5053	−1.29839
$553$	−5.17176	−0.219926
$554$	51.4958	2.18785
$555$	2.76082	0.117190
$556$	−90.7863	−3.85020
$557$	1.86466	0.0790082	0.0395041	−	0.999219i	$-0.487422\pi$
$557$	1.86466	0.0790082	0.0395041	+	0.999219i	$0.487422\pi$
$558$	−21.5865	−0.913828
$559$	20.6029	0.871412
$560$	−55.2992	−2.33682
$561$	−1.14862	−0.0484949
$562$	−14.7046	−0.620275
$563$	−37.2297	−1.56905	−0.784523	−	0.620099i	$-0.787092\pi$
$563$	−37.2297	−1.56905	−0.784523	+	0.620099i	$0.787092\pi$
$564$	−42.9480	−1.80844
$565$	−17.2691	−0.726516
$566$	29.2425	1.22915
$567$	2.94599	0.123720
$568$	−64.9209	−2.72402
$569$	−13.1522	−0.551367	−0.275683	−	0.961248i	$-0.588904\pi$
$569$	−13.1522	−0.551367	−0.275683	+	0.961248i	$0.588904\pi$
$570$	−45.3441	−1.89925
$571$	6.97925	0.292073	0.146036	−	0.989279i	$-0.453348\pi$
$571$	6.97925	0.292073	0.146036	+	0.989279i	$0.453348\pi$
$572$	29.0618	1.21514
$573$	8.78858	0.367148
$574$	72.9426	3.04457
$575$	−10.5671	−0.440677
$576$	−0.580516	−0.0241882
$577$	31.6789	1.31881	0.659405	−	0.751788i	$-0.270808\pi$
$577$	31.6789	1.31881	0.659405	+	0.751788i	$0.270808\pi$
$578$	−2.54273	−0.105763
$579$	−20.7784	−0.863521
$580$	−95.4673	−3.96406
$581$	41.8773	1.73736
$582$	−15.2633	−0.632682
$583$	15.8247	0.655390
$584$	−9.08359	−0.375882
$585$	−15.1735	−0.627349
$586$	−14.4055	−0.595086
$587$	4.00509	0.165308	0.0826538	−	0.996578i	$-0.473660\pi$
$587$	4.00509	0.165308	0.0826538	+	0.996578i	$0.473660\pi$
$588$	−7.49699	−0.309171
$589$	56.5322	2.32937
$590$	101.641	4.18448
$591$	23.7695	0.977746
$592$	7.22621	0.296995
$593$	−0.572225	−0.0234985	−0.0117492	−	0.999931i	$-0.503740\pi$
$593$	−0.572225	−0.0234985	−0.0117492	+	0.999931i	$0.503740\pi$
$594$	2.92063	0.119835
$595$	−7.88932	−0.323430
$596$	−19.0942	−0.782131
$597$	−15.2002	−0.622102
$598$	70.1064	2.86686
$599$	6.26893	0.256141	0.128071	−	0.991765i	$-0.459122\pi$
$599$	6.26893	0.256141	0.128071	+	0.991765i	$0.459122\pi$
$600$	13.6136	0.555772
$601$	3.24638	0.132422	0.0662112	−	0.997806i	$-0.478909\pi$
$601$	3.24638	0.132422	0.0662112	+	0.997806i	$0.478909\pi$
$602$	−27.2384	−1.11015
$603$	10.3001	0.419452
$604$	−82.8970	−3.37303
$605$	25.9246	1.05399
$606$	−8.46798	−0.343988
$607$	15.5336	0.630489	0.315245	−	0.949010i	$-0.397913\pi$
$607$	15.5336	0.630489	0.315245	+	0.949010i	$0.397913\pi$
$608$	−35.1930	−1.42726
$609$	−23.5187	−0.953026
$610$	−37.7872	−1.52996
$611$	54.4950	2.20463
$612$	4.46545	0.180505
$613$	−8.94320	−0.361212	−0.180606	−	0.983556i	$-0.557806\pi$
$613$	−8.94320	−0.361212	−0.180606	+	0.983556i	$0.557806\pi$
$614$	−61.6101	−2.48638
$615$	−26.0770	−1.05153
$616$	−21.2132	−0.854704
$617$	42.5049	1.71118	0.855592	−	0.517651i	$-0.173193\pi$
$617$	42.5049	1.71118	0.855592	+	0.517651i	$0.173193\pi$
$618$	−2.29465	−0.0923045
$619$	29.8724	1.20067	0.600337	−	0.799747i	$-0.295033\pi$
$619$	29.8724	1.20067	0.600337	+	0.799747i	$0.295033\pi$
$620$	−101.521	−4.07718
$621$	4.86607	0.195269
$622$	3.94771	0.158289
$623$	−12.7689	−0.511573
$624$	−39.7154	−1.58989
$625$	−31.1421	−1.24569
$626$	57.1707	2.28500
$627$	−7.64876	−0.305462
$628$	−4.46545	−0.178191
$629$	1.03093	0.0411060
$630$	20.0604	0.799224
$631$	37.2974	1.48479	0.742394	−	0.669964i	$-0.233690\pi$
$631$	37.2974	1.48479	0.742394	+	0.669964i	$0.233690\pi$
$632$	11.0053	0.437768
$633$	−15.7713	−0.626851
$634$	62.5594	2.48455
$635$	21.4777	0.852318
$636$	−61.5208	−2.43946
$637$	9.51263	0.376904
$638$	−23.3162	−0.923099
$639$	10.3559	0.409673
$640$	−32.2591	−1.27515
$641$	−45.8235	−1.80992	−0.904959	−	0.425498i	$-0.860099\pi$
$641$	−45.8235	−1.80992	−0.904959	+	0.425498i	$0.860099\pi$
$642$	27.8172	1.09786
$643$	−40.5538	−1.59928	−0.799642	−	0.600477i	$-0.794977\pi$
$643$	−40.5538	−1.59928	−0.799642	+	0.600477i	$0.794977\pi$
$644$	−64.0142	−2.52251
$645$	9.73772	0.383422
$646$	−16.9322	−0.666188
$647$	40.4860	1.59167	0.795834	−	0.605514i	$-0.207033\pi$
$647$	40.4860	1.59167	0.795834	+	0.605514i	$0.207033\pi$
$648$	−6.26898	−0.246269
$649$	17.1450	0.673001
$650$	−31.2864	−1.22715
$651$	−25.0100	−0.980220
$652$	−51.7317	−2.02597
$653$	−14.6748	−0.574270	−0.287135	−	0.957890i	$-0.592703\pi$
$653$	−14.6748	−0.574270	−0.287135	+	0.957890i	$0.592703\pi$
$654$	37.0233	1.44773
$655$	−30.0577	−1.17445
$656$	−68.2542	−2.66488
$657$	1.44898	0.0565299
$658$	−72.0458	−2.80864
$659$	−33.7038	−1.31291	−0.656457	−	0.754363i	$-0.727946\pi$
$659$	−33.7038	−1.31291	−0.656457	+	0.754363i	$0.727946\pi$
$660$	13.7357	0.534661
$661$	−13.3403	−0.518876	−0.259438	−	0.965760i	$-0.583537\pi$
$661$	−13.3403	−0.518876	−0.259438	+	0.965760i	$0.583537\pi$
$662$	23.9594	0.931209
$663$	−5.66604	−0.220051
$664$	−89.1135	−3.45827
$665$	−52.5355	−2.03724
$666$	−2.62138	−0.101577
$667$	−38.8472	−1.50417
$668$	−17.7568	−0.687033
$669$	−9.15149	−0.353817
$670$	70.1371	2.70963
$671$	−6.37405	−0.246067
$672$	15.5695	0.600607
$673$	15.8351	0.610397	0.305198	−	0.952289i	$-0.401277\pi$
$673$	15.8351	0.610397	0.305198	+	0.952289i	$0.401277\pi$
$674$	24.3650	0.938504
$675$	−2.17158	−0.0835842
$676$	85.3080	3.28108
$677$	48.2236	1.85338	0.926692	−	0.375821i	$-0.122639\pi$
$677$	48.2236	1.85338	0.926692	+	0.375821i	$0.122639\pi$
$678$	16.3969	0.629718
$679$	−17.6840	−0.678648
$680$	16.7882	0.643798
$681$	20.5423	0.787183
$682$	−24.7947	−0.949439
$683$	46.9093	1.79493	0.897467	−	0.441082i	$-0.145405\pi$
$683$	46.9093	1.79493	0.897467	+	0.441082i	$0.145405\pi$
$684$	29.7358	1.13698
$685$	−35.2778	−1.34789
$686$	39.8597	1.52185
$687$	14.8520	0.566639
$688$	25.4876	0.971706
$689$	78.0614	2.97390
$690$	33.1349	1.26142
$691$	40.8271	1.55314	0.776569	−	0.630033i	$-0.216959\pi$
$691$	40.8271	1.55314	0.776569	+	0.630033i	$0.216959\pi$
$692$	44.1671	1.67898
$693$	3.38384	0.128541
$694$	69.6102	2.64237
$695$	54.4455	2.06524
$696$	50.0470	1.89703
$697$	−9.73755	−0.368836
$698$	−45.6751	−1.72883
$699$	6.18493	0.233936
$700$	28.5676	1.07975
$701$	−32.2668	−1.21870	−0.609351	−	0.792901i	$-0.708570\pi$
$701$	−32.2668	−1.21870	−0.609351	+	0.792901i	$0.708570\pi$
$702$	14.4072	0.543764
$703$	6.86506	0.258921
$704$	−0.666794	−0.0251308
$705$	25.7564	0.970041
$706$	69.9991	2.63445
$707$	−9.81098	−0.368980
$708$	−66.6540	−2.50501
$709$	−10.9244	−0.410276	−0.205138	−	0.978733i	$-0.565764\pi$
$709$	−10.9244	−0.410276	−0.205138	+	0.978733i	$0.565764\pi$
$710$	70.5172	2.64646
$711$	−1.75552	−0.0658372
$712$	27.1717	1.01830
$713$	−41.3105	−1.54709
$714$	7.49086	0.280338
$715$	−17.4287	−0.651796
$716$	13.9111	0.519882
$717$	8.90165	0.332438
$718$	−29.0028	−1.08237
$719$	2.81368	0.104933	0.0524663	−	0.998623i	$-0.483292\pi$
$719$	2.81368	0.104933	0.0524663	+	0.998623i	$0.483292\pi$
$720$	−18.7710	−0.699553
$721$	−2.65858	−0.0990107
$722$	−64.4407	−2.39824
$723$	9.59092	0.356690
$724$	−59.5223	−2.21213
$725$	17.3363	0.643856
$726$	−24.6153	−0.913559
$727$	−11.0598	−0.410185	−0.205092	−	0.978743i	$-0.565749\pi$
$727$	−11.0598	−0.410185	−0.205092	+	0.978743i	$0.565749\pi$
$728$	−104.643	−3.87831
$729$	1.00000	0.0370370
$730$	9.86661	0.365180
$731$	3.63622	0.134490
$732$	24.7801	0.915899
$733$	21.0413	0.777178	0.388589	−	0.921411i	$-0.372963\pi$
$733$	21.0413	0.777178	0.388589	+	0.921411i	$0.372963\pi$
$734$	−46.5693	−1.71890
$735$	4.49602	0.165838
$736$	25.7170	0.947943
$737$	11.8309	0.435797
$738$	24.7599	0.911426
$739$	−3.50290	−0.128856	−0.0644281	−	0.997922i	$-0.520522\pi$
$739$	−3.50290	−0.128856	−0.0644281	+	0.997922i	$0.520522\pi$
$740$	−12.3283	−0.453198
$741$	−37.7305	−1.38607
$742$	−103.202	−3.78866
$743$	17.3606	0.636899	0.318450	−	0.947940i	$-0.396838\pi$
$743$	17.3606	0.636899	0.318450	+	0.947940i	$0.396838\pi$
$744$	53.2205	1.95116
$745$	11.4510	0.419533
$746$	−53.1738	−1.94683
$747$	14.2150	0.520100
$748$	5.12913	0.187539
$749$	32.2289	1.17762
$750$	19.2598	0.703267
$751$	−3.73919	−0.136445	−0.0682225	−	0.997670i	$-0.521733\pi$
$751$	−3.73919	−0.136445	−0.0682225	+	0.997670i	$0.521733\pi$
$752$	67.4150	2.45837
$753$	12.8153	0.467017
$754$	−115.017	−4.18866
$755$	49.7142	1.80928
$756$	−13.1552	−0.478450
$757$	−1.88287	−0.0684341	−0.0342170	−	0.999414i	$-0.510894\pi$
$757$	−1.88287	−0.0684341	−0.0342170	+	0.999414i	$0.510894\pi$
$758$	−7.58287	−0.275422
$759$	5.58928	0.202878
$760$	111.794	4.05518
$761$	47.0097	1.70410	0.852050	−	0.523460i	$-0.175359\pi$
$761$	47.0097	1.70410	0.852050	+	0.523460i	$0.175359\pi$
$762$	−20.3930	−0.738760
$763$	42.8951	1.55291
$764$	−39.2450	−1.41983
$765$	−2.67798	−0.0968226
$766$	−83.6324	−3.02176
$767$	84.5747	3.05381
$768$	29.4687	1.06336
$769$	3.99993	0.144241	0.0721205	−	0.997396i	$-0.477023\pi$
$769$	3.99993	0.144241	0.0721205	+	0.997396i	$0.477023\pi$
$770$	23.0418	0.830369
$771$	18.2418	0.656961
$772$	92.7850	3.33941
$773$	45.8037	1.64745	0.823723	−	0.566992i	$-0.191893\pi$
$773$	45.8037	1.64745	0.823723	+	0.566992i	$0.191893\pi$
$774$	−9.24590	−0.332337
$775$	18.4356	0.662228
$776$	37.6309	1.35087
$777$	−3.03713	−0.108956
$778$	81.5952	2.92533
$779$	−64.8430	−2.32324
$780$	67.7568	2.42608
$781$	11.8950	0.425638
$782$	12.3731	0.442460
$783$	−7.98328	−0.285299
$784$	11.7679	0.420284
$785$	2.67798	0.0955812
$786$	28.5396	1.01797
$787$	−37.0113	−1.31931	−0.659655	−	0.751568i	$-0.729298\pi$
$787$	−37.0113	−1.31931	−0.659655	+	0.751568i	$0.729298\pi$
$788$	−106.142	−3.78114
$789$	−12.8203	−0.456413
$790$	−11.9540	−0.425304
$791$	18.9974	0.675469
$792$	−7.20069	−0.255865
$793$	−31.4425	−1.11656
$794$	60.6862	2.15367
$795$	36.8947	1.30852
$796$	67.8757	2.40579
$797$	−31.2415	−1.10663	−0.553315	−	0.832972i	$-0.686637\pi$
$797$	−31.2415	−1.10663	−0.553315	+	0.832972i	$0.686637\pi$
$798$	49.8821	1.76581
$799$	9.61783	0.340254
$800$	−11.4767	−0.405764
$801$	−4.33431	−0.153145
$802$	71.1948	2.51398
$803$	1.66433	0.0587328
$804$	−45.9946	−1.62210
$805$	38.3900	1.35307
$806$	−122.310	−4.30818
$807$	−14.0139	−0.493311
$808$	20.8774	0.734465
$809$	−9.29265	−0.326712	−0.163356	−	0.986567i	$-0.552232\pi$
$809$	−9.29265	−0.326712	−0.163356	+	0.986567i	$0.552232\pi$
$810$	6.80937	0.239257
$811$	−21.9752	−0.771654	−0.385827	−	0.922571i	$-0.626084\pi$
$811$	−21.9752	−0.771654	−0.385827	+	0.922571i	$0.626084\pi$
$812$	105.022	3.68554
$813$	−1.72927	−0.0606483
$814$	−3.01098	−0.105535
$815$	31.0241	1.08673
$816$	−7.00938	−0.245377
$817$	24.2138	0.847134
$818$	25.0875	0.877163
$819$	16.6921	0.583270
$820$	116.446	4.06646
$821$	1.19974	0.0418710	0.0209355	−	0.999781i	$-0.493336\pi$
$821$	1.19974	0.0418710	0.0209355	+	0.999781i	$0.493336\pi$
$822$	33.4960	1.16831
$823$	41.0775	1.43187	0.715936	−	0.698166i	$-0.246000\pi$
$823$	41.0775	1.43187	0.715936	+	0.698166i	$0.246000\pi$
$824$	5.65737	0.197084
$825$	−2.49433	−0.0868414
$826$	−111.813	−3.89047
$827$	7.45083	0.259091	0.129545	−	0.991573i	$-0.458648\pi$
$827$	7.45083	0.259091	0.129545	+	0.991573i	$0.458648\pi$
$828$	−21.7292	−0.755142
$829$	7.04979	0.244849	0.122425	−	0.992478i	$-0.460933\pi$
$829$	7.04979	0.244849	0.122425	+	0.992478i	$0.460933\pi$
$830$	96.7952	3.35981
$831$	20.2522	0.702542
$832$	−3.28923	−0.114033
$833$	1.67889	0.0581699
$834$	−51.6957	−1.79007
$835$	10.6490	0.368523
$836$	34.1552	1.18128
$837$	−8.48950	−0.293440
$838$	−26.3322	−0.909631
$839$	15.2193	0.525428	0.262714	−	0.964874i	$-0.415382\pi$
$839$	15.2193	0.525428	0.262714	+	0.964874i	$0.415382\pi$
$840$	−49.4579	−1.70646
$841$	34.7328	1.19768
$842$	−45.0738	−1.55335
$843$	−5.78300	−0.199177
$844$	70.4259	2.42416
$845$	−51.1601	−1.75996
$846$	−24.4555	−0.840797
$847$	−28.5192	−0.979931
$848$	96.5686	3.31618
$849$	11.5004	0.394694
$850$	−5.52174	−0.189394
$851$	−5.01660	−0.171967
$852$	−46.2438	−1.58429
$853$	44.8014	1.53397	0.766985	−	0.641665i	$-0.221756\pi$
$853$	44.8014	1.53397	0.766985	+	0.641665i	$0.221756\pi$
$854$	41.5690	1.42246
$855$	−17.8329	−0.609871
$856$	−68.5820	−2.34409
$857$	8.04126	0.274684	0.137342	−	0.990524i	$-0.456144\pi$
$857$	8.04126	0.274684	0.137342	+	0.990524i	$0.456144\pi$
$858$	16.5484	0.564954
$859$	18.6670	0.636910	0.318455	−	0.947938i	$-0.396836\pi$
$859$	18.6670	0.636910	0.318455	+	0.947938i	$0.396836\pi$
$860$	−43.4833	−1.48277
$861$	28.6868	0.977643
$862$	−12.9062	−0.439588
$863$	−23.4954	−0.799794	−0.399897	−	0.916560i	$-0.630954\pi$
$863$	−23.4954	−0.799794	−0.399897	+	0.916560i	$0.630954\pi$
$864$	5.28497	0.179798
$865$	−26.4875	−0.900602
$866$	3.82332	0.129922
$867$	−1.00000	−0.0339618
$868$	111.681	3.79070
$869$	−2.01643	−0.0684028
$870$	−54.3611	−1.84301
$871$	58.3607	1.97748
$872$	−91.2794	−3.09111
$873$	−6.00271	−0.203161
$874$	82.3932	2.78699
$875$	22.3143	0.754361
$876$	−6.47034	−0.218612
$877$	2.98976	0.100957	0.0504786	−	0.998725i	$-0.483925\pi$
$877$	2.98976	0.100957	0.0504786	+	0.998725i	$0.483925\pi$
$878$	36.1184	1.21894
$879$	−5.66538	−0.191089
$880$	−21.5608	−0.726814
$881$	−44.9227	−1.51348	−0.756742	−	0.653714i	$-0.773210\pi$
$881$	−44.9227	−1.51348	−0.756742	+	0.653714i	$0.773210\pi$
$882$	−4.26895	−0.143743
$883$	6.73305	0.226585	0.113293	−	0.993562i	$-0.463860\pi$
$883$	6.73305	0.226585	0.113293	+	0.993562i	$0.463860\pi$
$884$	25.3014	0.850980
$885$	39.9731	1.34368
$886$	91.8299	3.08509
$887$	8.95244	0.300594	0.150297	−	0.988641i	$-0.451977\pi$
$887$	8.95244	0.300594	0.150297	+	0.988641i	$0.451977\pi$
$888$	6.46290	0.216881
$889$	−23.6272	−0.792432
$890$	−29.5139	−0.989309
$891$	1.14862	0.0384803
$892$	40.8656	1.36828
$893$	64.0458	2.14321
$894$	−10.8727	−0.363637
$895$	−8.34263	−0.278863
$896$	35.4876	1.18556
$897$	27.5713	0.920580
$898$	23.6663	0.789755
$899$	67.7741	2.26039
$900$	9.69710	0.323237
$901$	13.7771	0.458980
$902$	28.4398	0.946943
$903$	−10.7123	−0.356482
$904$	−40.4258	−1.34454
$905$	35.6962	1.18658
$906$	−47.2033	−1.56822
$907$	7.36387	0.244513	0.122257	−	0.992499i	$-0.460987\pi$
$907$	7.36387	0.244513	0.122257	+	0.992499i	$0.460987\pi$
$908$	−91.7307	−3.04419
$909$	−3.33028	−0.110458
$910$	113.663	3.76789
$911$	3.85375	0.127680	0.0638402	−	0.997960i	$-0.479665\pi$
$911$	3.85375	0.127680	0.0638402	+	0.997960i	$0.479665\pi$
$912$	−46.6759	−1.54559
$913$	16.3277	0.540367
$914$	−57.1294	−1.88967
$915$	−14.8609	−0.491286
$916$	−66.3210	−2.19131
$917$	33.0659	1.09193
$918$	2.54273	0.0839225
$919$	15.5684	0.513553	0.256777	−	0.966471i	$-0.417340\pi$
$919$	15.5684	0.513553	0.256777	+	0.966471i	$0.417340\pi$
$920$	−81.6925	−2.69332
$921$	−24.2299	−0.798403
$922$	−28.3596	−0.933973
$923$	58.6770	1.93138
$924$	−15.1104	−0.497095
$925$	2.23876	0.0736099
$926$	16.2066	0.532582
$927$	−0.902439	−0.0296400
$928$	−42.1914	−1.38500
$929$	−19.5795	−0.642382	−0.321191	−	0.947014i	$-0.604083\pi$
$929$	−19.5795	−0.642382	−0.321191	+	0.947014i	$0.604083\pi$
$930$	−57.8082	−1.89560
$931$	11.1798	0.366404
$932$	−27.6185	−0.904675
$933$	1.55255	0.0508282
$934$	10.4334	0.341392
$935$	−3.07599	−0.100596
$936$	−35.5203	−1.16102
$937$	−46.2258	−1.51013	−0.755066	−	0.655649i	$-0.772395\pi$
$937$	−46.2258	−1.51013	−0.755066	+	0.655649i	$0.772395\pi$
$938$	−77.1565	−2.51925
$939$	22.4840	0.733739
$940$	−115.014	−3.75134
$941$	15.7648	0.513917	0.256958	−	0.966422i	$-0.417280\pi$
$941$	15.7648	0.513917	0.256958	+	0.966422i	$0.417280\pi$
$942$	−2.54273	−0.0828465
$943$	47.3836	1.54302
$944$	104.626	3.40529
$945$	7.88932	0.256640
$946$	−10.6201	−0.345288
$947$	37.4702	1.21762	0.608809	−	0.793317i	$-0.291648\pi$
$947$	37.4702	1.21762	0.608809	+	0.793317i	$0.291648\pi$
$948$	7.83921	0.254606
$949$	8.20995	0.266506
$950$	−36.7696	−1.19296
$951$	24.6033	0.797816
$952$	−18.4684	−0.598563
$953$	−13.1411	−0.425683	−0.212842	−	0.977087i	$-0.568272\pi$
$953$	−13.1411	−0.425683	−0.212842	+	0.977087i	$0.568272\pi$
$954$	−35.0313	−1.13418
$955$	23.5356	0.761595
$956$	−39.7499	−1.28560
$957$	−9.16978	−0.296417
$958$	64.1700	2.07324
$959$	38.8084	1.25319
$960$	−1.55461	−0.0501749
$961$	41.0716	1.32489
$962$	−14.8529	−0.478875
$963$	10.9399	0.352534
$964$	−42.8278	−1.37939
$965$	−55.6442	−1.79125
$966$	−36.4510	−1.17279
$967$	38.3319	1.23267	0.616335	−	0.787484i	$-0.288617\pi$
$967$	38.3319	1.23267	0.616335	+	0.787484i	$0.288617\pi$
$968$	60.6879	1.95058
$969$	−6.65907	−0.213920
$970$	−40.8747	−1.31241
$971$	−36.8988	−1.18414	−0.592070	−	0.805886i	$-0.701689\pi$
$971$	−36.8988	−1.18414	−0.592070	+	0.805886i	$0.701689\pi$
$972$	−4.46545	−0.143230
$973$	−59.8944	−1.92013
$974$	98.9429	3.17033
$975$	−12.3043	−0.394052
$976$	−38.8971	−1.24507
$977$	−25.1925	−0.805981	−0.402990	−	0.915204i	$-0.632029\pi$
$977$	−25.1925	−0.805981	−0.402990	+	0.915204i	$0.632029\pi$
$978$	−29.4572	−0.941936
$979$	−4.97849	−0.159113
$980$	−20.0768	−0.641330
$981$	14.5605	0.464881
$982$	75.9941	2.42507
$983$	37.1597	1.18521	0.592606	−	0.805493i	$-0.298099\pi$
$983$	37.1597	1.18521	0.592606	+	0.805493i	$0.298099\pi$
$984$	−61.0445	−1.94603
$985$	63.6542	2.02819
$986$	−20.2993	−0.646461
$987$	−28.3341	−0.901883
$988$	168.484	5.36019
$989$	−17.6941	−0.562639
$990$	7.82140	0.248580
$991$	−41.6746	−1.32384	−0.661919	−	0.749576i	$-0.730258\pi$
$991$	−41.6746	−1.32384	−0.661919	+	0.749576i	$0.730258\pi$
$992$	−44.8668	−1.42452
$993$	9.42272	0.299021
$994$	−77.5746	−2.46052
$995$	−40.7058	−1.29046
$996$	−63.4764	−2.01133
$997$	−21.4095	−0.678045	−0.339022	−	0.940778i	$-0.610096\pi$
$997$	−21.4095	−0.678045	−0.339022	+	0.940778i	$0.610096\pi$
$998$	85.4807	2.70585
$999$	−1.03093	−0.0326173

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.j.1.4	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.j.1.4	✓	64	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:	\( N \)	\(=\)	\( 8007 = 3 \cdot 17 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8007.a (trivial)

\(f(q)\)	\(=\)	\(q-2.54273 q^{2} -1.00000 q^{3} +4.46545 q^{4} -2.67798 q^{5} +2.54273 q^{6} +2.94599 q^{7} -6.26898 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.54273 q^{2} -1.00000 q^{3} +4.46545 q^{4} -2.67798 q^{5} +2.54273 q^{6} +2.94599 q^{7} -6.26898 q^{8} +1.00000 q^{9} +6.80937 q^{10} +1.14862 q^{11} -4.46545 q^{12} +5.66604 q^{13} -7.49086 q^{14} +2.67798 q^{15} +7.00938 q^{16} +1.00000 q^{17} -2.54273 q^{18} +6.65907 q^{19} -11.9584 q^{20} -2.94599 q^{21} -2.92063 q^{22} -4.86607 q^{23} +6.26898 q^{24} +2.17158 q^{25} -14.4072 q^{26} -1.00000 q^{27} +13.1552 q^{28} +7.98328 q^{29} -6.80937 q^{30} +8.48950 q^{31} -5.28497 q^{32} -1.14862 q^{33} -2.54273 q^{34} -7.88932 q^{35} +4.46545 q^{36} +1.03093 q^{37} -16.9322 q^{38} -5.66604 q^{39} +16.7882 q^{40} -9.73755 q^{41} +7.49086 q^{42} +3.63622 q^{43} +5.12913 q^{44} -2.67798 q^{45} +12.3731 q^{46} +9.61783 q^{47} -7.00938 q^{48} +1.67889 q^{49} -5.52174 q^{50} -1.00000 q^{51} +25.3014 q^{52} +13.7771 q^{53} +2.54273 q^{54} -3.07599 q^{55} -18.4684 q^{56} -6.65907 q^{57} -20.2993 q^{58} +14.9266 q^{59} +11.9584 q^{60} -5.54929 q^{61} -21.5865 q^{62} +2.94599 q^{63} -0.580516 q^{64} -15.1735 q^{65} +2.92063 q^{66} +10.3001 q^{67} +4.46545 q^{68} +4.86607 q^{69} +20.0604 q^{70} +10.3559 q^{71} -6.26898 q^{72} +1.44898 q^{73} -2.62138 q^{74} -2.17158 q^{75} +29.7358 q^{76} +3.38384 q^{77} +14.4072 q^{78} -1.75552 q^{79} -18.7710 q^{80} +1.00000 q^{81} +24.7599 q^{82} +14.2150 q^{83} -13.1552 q^{84} -2.67798 q^{85} -9.24590 q^{86} -7.98328 q^{87} -7.20069 q^{88} -4.33431 q^{89} +6.80937 q^{90} +16.6921 q^{91} -21.7292 q^{92} -8.48950 q^{93} -24.4555 q^{94} -17.8329 q^{95} +5.28497 q^{96} -6.00271 q^{97} -4.26895 q^{98} +1.14862 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9}+O(q^{10}) \) 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9	\( 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9} + 12 q^{10} - 7 q^{11} - 77 q^{12} + 24 q^{13} - 14 q^{14} + 3 q^{15} + 103 q^{16} + 64 q^{17} + 5 q^{18} + 26 q^{19} - 24 q^{20} - 5 q^{21} + 25 q^{22} + 20 q^{23} - 18 q^{24} + 141 q^{25} + 9 q^{26} - 64 q^{27} + 14 q^{28} + 5 q^{29} - 12 q^{30} + 11 q^{31} + 31 q^{32} + 7 q^{33} + 5 q^{34} - 3 q^{35} + 77 q^{36} + 50 q^{37} + 8 q^{38} - 24 q^{39} + 28 q^{40} - 9 q^{41} + 14 q^{42} + 59 q^{43} - 6 q^{44} - 3 q^{45} + 11 q^{47} - 103 q^{48} + 163 q^{49} + 20 q^{50} - 64 q^{51} + 65 q^{52} + 39 q^{53} - 5 q^{54} + 35 q^{55} - 34 q^{56} - 26 q^{57} - 27 q^{58} - 65 q^{59} + 24 q^{60} + 15 q^{61} + 18 q^{62} + 5 q^{63} + 152 q^{64} + 49 q^{65} - 25 q^{66} + 56 q^{67} + 77 q^{68} - 20 q^{69} + 28 q^{70} - 18 q^{71} + 18 q^{72} + 37 q^{73} - 76 q^{74} - 141 q^{75} + 30 q^{76} + 80 q^{77} - 9 q^{78} + 20 q^{79} - 144 q^{80} + 64 q^{81} + 27 q^{82} + 3 q^{83} - 14 q^{84} - 3 q^{85} + 12 q^{86} - 5 q^{87} + 108 q^{88} + 42 q^{89} + 12 q^{90} + 25 q^{91} + 18 q^{92} - 11 q^{93} + 60 q^{94} + 42 q^{95} - 31 q^{96} + 72 q^{97} + 18 q^{98} - 7 q^{99}+O(q^{100}) \) 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9 + 12 * q^10 - 7 * q^11 - 77 * q^12 + 24 * q^13 - 14 * q^14 + 3 * q^15 + 103 * q^16 + 64 * q^17 + 5 * q^18 + 26 * q^19 - 24 * q^20 - 5 * q^21 + 25 * q^22 + 20 * q^23 - 18 * q^24 + 141 * q^25 + 9 * q^26 - 64 * q^27 + 14 * q^28 + 5 * q^29 - 12 * q^30 + 11 * q^31 + 31 * q^32 + 7 * q^33 + 5 * q^34 - 3 * q^35 + 77 * q^36 + 50 * q^37 + 8 * q^38 - 24 * q^39 + 28 * q^40 - 9 * q^41 + 14 * q^42 + 59 * q^43 - 6 * q^44 - 3 * q^45 + 11 * q^47 - 103 * q^48 + 163 * q^49 + 20 * q^50 - 64 * q^51 + 65 * q^52 + 39 * q^53 - 5 * q^54 + 35 * q^55 - 34 * q^56 - 26 * q^57 - 27 * q^58 - 65 * q^59 + 24 * q^60 + 15 * q^61 + 18 * q^62 + 5 * q^63 + 152 * q^64 + 49 * q^65 - 25 * q^66 + 56 * q^67 + 77 * q^68 - 20 * q^69 + 28 * q^70 - 18 * q^71 + 18 * q^72 + 37 * q^73 - 76 * q^74 - 141 * q^75 + 30 * q^76 + 80 * q^77 - 9 * q^78 + 20 * q^79 - 144 * q^80 + 64 * q^81 + 27 * q^82 + 3 * q^83 - 14 * q^84 - 3 * q^85 + 12 * q^86 - 5 * q^87 + 108 * q^88 + 42 * q^89 + 12 * q^90 + 25 * q^91 + 18 * q^92 - 11 * q^93 + 60 * q^94 + 42 * q^95 - 31 * q^96 + 72 * q^97 + 18 * q^98 - 7 * q^99

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