LMFDB - Embedded newform 4015.2.a.g.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4015,2,Mod(1,4015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4015, 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("4015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4015 = 5 \cdot 11 \cdot 73 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4015.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:	$32.0599364115$
Analytic rank:	$1$
Dimension:	$32$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	4015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.960547 q^{2} -2.83486 q^{3} -1.07735 q^{4} -1.00000 q^{5} +2.72301 q^{6} +4.60653 q^{7} +2.95594 q^{8} +5.03641 q^{9} +O(q^{10})$	\(q-0.960547 q^{2} -2.83486 q^{3} -1.07735 q^{4} -1.00000 q^{5} +2.72301 q^{6} +4.60653 q^{7} +2.95594 q^{8} +5.03641 q^{9} +0.960547 q^{10} -1.00000 q^{11} +3.05413 q^{12} +5.21688 q^{13} -4.42479 q^{14} +2.83486 q^{15} -0.684620 q^{16} -2.22036 q^{17} -4.83771 q^{18} -0.638361 q^{19} +1.07735 q^{20} -13.0588 q^{21} +0.960547 q^{22} -3.47932 q^{23} -8.37966 q^{24} +1.00000 q^{25} -5.01106 q^{26} -5.77292 q^{27} -4.96284 q^{28} -1.49916 q^{29} -2.72301 q^{30} -9.63747 q^{31} -5.25427 q^{32} +2.83486 q^{33} +2.13276 q^{34} -4.60653 q^{35} -5.42597 q^{36} -5.21880 q^{37} +0.613176 q^{38} -14.7891 q^{39} -2.95594 q^{40} +0.623729 q^{41} +12.5436 q^{42} +10.8450 q^{43} +1.07735 q^{44} -5.03641 q^{45} +3.34205 q^{46} +2.97153 q^{47} +1.94080 q^{48} +14.2201 q^{49} -0.960547 q^{50} +6.29441 q^{51} -5.62040 q^{52} -11.6022 q^{53} +5.54516 q^{54} +1.00000 q^{55} +13.6166 q^{56} +1.80966 q^{57} +1.44002 q^{58} -2.15135 q^{59} -3.05413 q^{60} +5.74304 q^{61} +9.25725 q^{62} +23.2003 q^{63} +6.41621 q^{64} -5.21688 q^{65} -2.72301 q^{66} +1.16670 q^{67} +2.39211 q^{68} +9.86338 q^{69} +4.42479 q^{70} -3.90696 q^{71} +14.8873 q^{72} -1.00000 q^{73} +5.01290 q^{74} -2.83486 q^{75} +0.687738 q^{76} -4.60653 q^{77} +14.2056 q^{78} +8.46255 q^{79} +0.684620 q^{80} +1.25617 q^{81} -0.599121 q^{82} +14.3491 q^{83} +14.0689 q^{84} +2.22036 q^{85} -10.4171 q^{86} +4.24991 q^{87} -2.95594 q^{88} -8.22493 q^{89} +4.83771 q^{90} +24.0317 q^{91} +3.74845 q^{92} +27.3208 q^{93} -2.85430 q^{94} +0.638361 q^{95} +14.8951 q^{96} -16.8183 q^{97} -13.6591 q^{98} -5.03641 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 5 q^{2} - 7 q^{3} + 37 q^{4} - 32 q^{5} - 3 q^{6} - 18 q^{8} + 29 q^{9}+O(q^{10}) $ 32 * q - 5 * q^2 - 7 * q^3 + 37 * q^4 - 32 * q^5 - 3 * q^6 - 18 * q^8 + 29 * q^9	\( 32 q - 5 q^{2} - 7 q^{3} + 37 q^{4} - 32 q^{5} - 3 q^{6} - 18 q^{8} + 29 q^{9} + 5 q^{10} - 32 q^{11} - 24 q^{12} - q^{13} - 5 q^{14} + 7 q^{15} + 47 q^{16} - 30 q^{17} - 11 q^{18} + 16 q^{19} - 37 q^{20} + q^{21} + 5 q^{22} - 26 q^{23} - 21 q^{24} + 32 q^{25} - q^{26} - 31 q^{27} - 24 q^{28} - 10 q^{29} + 3 q^{30} - 2 q^{31} - 31 q^{32} + 7 q^{33} - 14 q^{34} + 38 q^{36} - 28 q^{37} - 63 q^{38} - 2 q^{39} + 18 q^{40} - 62 q^{41} - 9 q^{42} + 8 q^{43} - 37 q^{44} - 29 q^{45} + 19 q^{46} - 21 q^{47} - 79 q^{48} + 34 q^{49} - 5 q^{50} + 17 q^{51} + 15 q^{52} - 32 q^{53} + 5 q^{54} + 32 q^{55} - 52 q^{56} - 57 q^{57} + 4 q^{58} - 37 q^{59} + 24 q^{60} + 15 q^{61} - 22 q^{62} + 5 q^{63} + 70 q^{64} + q^{65} + 3 q^{66} - 42 q^{67} - 81 q^{68} - 8 q^{69} + 5 q^{70} - 40 q^{71} - 27 q^{72} - 32 q^{73} - 17 q^{74} - 7 q^{75} + 21 q^{76} - 105 q^{78} + 18 q^{79} - 47 q^{80} + 12 q^{81} - 70 q^{82} - 26 q^{83} + 22 q^{84} + 30 q^{85} - 45 q^{86} - 18 q^{87} + 18 q^{88} - 83 q^{89} + 11 q^{90} - 18 q^{91} - 73 q^{92} - 68 q^{93} + 56 q^{94} - 16 q^{95} - 35 q^{96} - 99 q^{97} - 61 q^{98} - 29 q^{99}+O(q^{100}) \) 32 * q - 5 * q^2 - 7 * q^3 + 37 * q^4 - 32 * q^5 - 3 * q^6 - 18 * q^8 + 29 * q^9 + 5 * q^10 - 32 * q^11 - 24 * q^12 - q^13 - 5 * q^14 + 7 * q^15 + 47 * q^16 - 30 * q^17 - 11 * q^18 + 16 * q^19 - 37 * q^20 + q^21 + 5 * q^22 - 26 * q^23 - 21 * q^24 + 32 * q^25 - q^26 - 31 * q^27 - 24 * q^28 - 10 * q^29 + 3 * q^30 - 2 * q^31 - 31 * q^32 + 7 * q^33 - 14 * q^34 + 38 * q^36 - 28 * q^37 - 63 * q^38 - 2 * q^39 + 18 * q^40 - 62 * q^41 - 9 * q^42 + 8 * q^43 - 37 * q^44 - 29 * q^45 + 19 * q^46 - 21 * q^47 - 79 * q^48 + 34 * q^49 - 5 * q^50 + 17 * q^51 + 15 * q^52 - 32 * q^53 + 5 * q^54 + 32 * q^55 - 52 * q^56 - 57 * q^57 + 4 * q^58 - 37 * q^59 + 24 * q^60 + 15 * q^61 - 22 * q^62 + 5 * q^63 + 70 * q^64 + q^65 + 3 * q^66 - 42 * q^67 - 81 * q^68 - 8 * q^69 + 5 * q^70 - 40 * q^71 - 27 * q^72 - 32 * q^73 - 17 * q^74 - 7 * q^75 + 21 * q^76 - 105 * q^78 + 18 * q^79 - 47 * q^80 + 12 * q^81 - 70 * q^82 - 26 * q^83 + 22 * q^84 + 30 * q^85 - 45 * q^86 - 18 * q^87 + 18 * q^88 - 83 * q^89 + 11 * q^90 - 18 * q^91 - 73 * q^92 - 68 * q^93 + 56 * q^94 - 16 * q^95 - 35 * q^96 - 99 * q^97 - 61 * q^98 - 29 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−0.960547	−0.679209	−0.339605	−	0.940568i	$-0.610293\pi$
$2$	−0.960547	−0.679209	−0.339605	+	0.940568i	$0.610293\pi$
$3$	−2.83486	−1.63670	−0.818352	−	0.574717i	$-0.805112\pi$
$3$	−2.83486	−1.63670	−0.818352	+	0.574717i	$0.805112\pi$
$4$	−1.07735	−0.538675
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	2.72301	1.11167
$7$	4.60653	1.74110	0.870552	−	0.492076i	$-0.163762\pi$
$7$	4.60653	1.74110	0.870552	+	0.492076i	$0.163762\pi$
$8$	2.95594	1.04508
$9$	5.03641	1.67880
$10$	0.960547	0.303752
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	3.05413	0.881651
$13$	5.21688	1.44690	0.723451	−	0.690376i	$-0.242555\pi$
$13$	5.21688	1.44690	0.723451	+	0.690376i	$0.242555\pi$
$14$	−4.42479	−1.18257
$15$	2.83486	0.731957
$16$	−0.684620	−0.171155
$17$	−2.22036	−0.538517	−0.269259	−	0.963068i	$-0.586779\pi$
$17$	−2.22036	−0.538517	−0.269259	+	0.963068i	$0.586779\pi$
$18$	−4.83771	−1.14026
$19$	−0.638361	−0.146450	−0.0732251	−	0.997315i	$-0.523329\pi$
$19$	−0.638361	−0.146450	−0.0732251	+	0.997315i	$0.523329\pi$
$20$	1.07735	0.240903
$21$	−13.0588	−2.84967
$22$	0.960547	0.204789
$23$	−3.47932	−0.725489	−0.362744	−	0.931889i	$-0.618160\pi$
$23$	−3.47932	−0.725489	−0.362744	+	0.931889i	$0.618160\pi$
$24$	−8.37966	−1.71049
$25$	1.00000	0.200000
$26$	−5.01106	−0.982749
$27$	−5.77292	−1.11100
$28$	−4.96284	−0.937889
$29$	−1.49916	−0.278387	−0.139194	−	0.990265i	$-0.544451\pi$
$29$	−1.49916	−0.278387	−0.139194	+	0.990265i	$0.544451\pi$
$30$	−2.72301	−0.497152
$31$	−9.63747	−1.73094	−0.865471	−	0.500960i	$-0.832980\pi$
$31$	−9.63747	−1.73094	−0.865471	+	0.500960i	$0.832980\pi$
$32$	−5.25427	−0.928832
$33$	2.83486	0.493485
$34$	2.13276	0.365766
$35$	−4.60653	−0.778645
$36$	−5.42597	−0.904328
$37$	−5.21880	−0.857965	−0.428983	−	0.903313i	$-0.641128\pi$
$37$	−5.21880	−0.857965	−0.428983	+	0.903313i	$0.641128\pi$
$38$	0.613176	0.0994703
$39$	−14.7891	−2.36815
$40$	−2.95594	−0.467375
$41$	0.623729	0.0974102	0.0487051	−	0.998813i	$-0.484491\pi$
$41$	0.623729	0.0974102	0.0487051	+	0.998813i	$0.484491\pi$
$42$	12.5436	1.93552
$43$	10.8450	1.65385	0.826924	−	0.562313i	$-0.190088\pi$
$43$	10.8450	1.65385	0.826924	+	0.562313i	$0.190088\pi$
$44$	1.07735	0.162417
$45$	−5.03641	−0.750783
$46$	3.34205	0.492759
$47$	2.97153	0.433443	0.216721	−	0.976233i	$-0.430464\pi$
$47$	2.97153	0.433443	0.216721	+	0.976233i	$0.430464\pi$
$48$	1.94080	0.280130
$49$	14.2201	2.03144
$50$	−0.960547	−0.135842
$51$	6.29441	0.881394
$52$	−5.62040	−0.779409
$53$	−11.6022	−1.59369	−0.796844	−	0.604186i	$-0.793499\pi$
$53$	−11.6022	−1.59369	−0.796844	+	0.604186i	$0.793499\pi$
$54$	5.54516	0.754601
$55$	1.00000	0.134840
$56$	13.6166	1.81960
$57$	1.80966	0.239696
$58$	1.44002	0.189083
$59$	−2.15135	−0.280082	−0.140041	−	0.990146i	$-0.544723\pi$
$59$	−2.15135	−0.280082	−0.140041	+	0.990146i	$0.544723\pi$
$60$	−3.05413	−0.394286
$61$	5.74304	0.735321	0.367661	−	0.929960i	$-0.380159\pi$
$61$	5.74304	0.735321	0.367661	+	0.929960i	$0.380159\pi$
$62$	9.25725	1.17567
$63$	23.2003	2.92297
$64$	6.41621	0.802026
$65$	−5.21688	−0.647074
$66$	−2.72301	−0.335180
$67$	1.16670	0.142535	0.0712676	−	0.997457i	$-0.477296\pi$
$67$	1.16670	0.142535	0.0712676	+	0.997457i	$0.477296\pi$
$68$	2.39211	0.290086
$69$	9.86338	1.18741
$70$	4.42479	0.528863
$71$	−3.90696	−0.463671	−0.231835	−	0.972755i	$-0.574473\pi$
$71$	−3.90696	−0.463671	−0.231835	+	0.972755i	$0.574473\pi$
$72$	14.8873	1.75449
$73$	−1.00000	−0.117041
$73$	−1.00000	−0.117041
$74$	5.01290	0.582738
$75$	−2.83486	−0.327341
$76$	0.687738	0.0788890
$77$	−4.60653	−0.524963
$78$	14.2056	1.60847
$79$	8.46255	0.952111	0.476056	−	0.879415i	$-0.342066\pi$
$79$	8.46255	0.952111	0.476056	+	0.879415i	$0.342066\pi$
$80$	0.684620	0.0765428
$81$	1.25617	0.139574
$82$	−0.599121	−0.0661619
$83$	14.3491	1.57502	0.787508	−	0.616304i	$-0.211371\pi$
$83$	14.3491	1.57502	0.787508	+	0.616304i	$0.211371\pi$
$84$	14.0689	1.53505
$85$	2.22036	0.240832
$86$	−10.4171	−1.12331
$87$	4.24991	0.455638
$88$	−2.95594	−0.315104
$89$	−8.22493	−0.871841	−0.435921	−	0.899985i	$-0.643577\pi$
$89$	−8.22493	−0.871841	−0.435921	+	0.899985i	$0.643577\pi$
$90$	4.83771	0.509939
$91$	24.0317	2.51921
$92$	3.74845	0.390803
$93$	27.3208	2.83304
$94$	−2.85430	−0.294398
$95$	0.638361	0.0654945
$96$	14.8951	1.52022
$97$	−16.8183	−1.70764	−0.853821	−	0.520567i	$-0.825720\pi$
$97$	−16.8183	−1.70764	−0.853821	+	0.520567i	$0.825720\pi$
$98$	−13.6591	−1.37978
$99$	−5.03641	−0.506178
$100$	−1.07735	−0.107735
$101$	−5.06325	−0.503812	−0.251906	−	0.967752i	$-0.581057\pi$
$101$	−5.06325	−0.503812	−0.251906	+	0.967752i	$0.581057\pi$
$102$	−6.04608	−0.598651
$103$	−11.1651	−1.10013	−0.550063	−	0.835123i	$-0.685396\pi$
$103$	−11.1651	−1.10013	−0.550063	+	0.835123i	$0.685396\pi$
$104$	15.4208	1.51213
$105$	13.0588	1.27441
$106$	11.1445	1.08245
$107$	−10.3861	−1.00406	−0.502030	−	0.864850i	$-0.667413\pi$
$107$	−10.3861	−1.00406	−0.502030	+	0.864850i	$0.667413\pi$
$108$	6.21945	0.598467
$109$	−8.64330	−0.827878	−0.413939	−	0.910305i	$-0.635847\pi$
$109$	−8.64330	−0.827878	−0.413939	+	0.910305i	$0.635847\pi$
$110$	−0.960547	−0.0915846
$111$	14.7945	1.40424
$112$	−3.15372	−0.297999
$113$	−6.23598	−0.586632	−0.293316	−	0.956016i	$-0.594759\pi$
$113$	−6.23598	−0.586632	−0.293316	+	0.956016i	$0.594759\pi$
$114$	−1.73827	−0.162803
$115$	3.47932	0.324449
$116$	1.61512	0.149960
$117$	26.2743	2.42906
$118$	2.06647	0.190234
$119$	−10.2282	−0.937615
$120$	8.37966	0.764955
$121$	1.00000	0.0909091
$122$	−5.51646	−0.499437
$123$	−1.76818	−0.159432
$124$	10.3829	0.932414
$125$	−1.00000	−0.0894427
$126$	−22.2850	−1.98531
$127$	−11.4137	−1.01280	−0.506402	−	0.862298i	$-0.669025\pi$
$127$	−11.4137	−1.01280	−0.506402	+	0.862298i	$0.669025\pi$
$128$	4.34546	0.384088
$129$	−30.7440	−2.70686
$130$	5.01106	0.439499
$131$	0.817932	0.0714631	0.0357315	−	0.999361i	$-0.488624\pi$
$131$	0.817932	0.0714631	0.0357315	+	0.999361i	$0.488624\pi$
$132$	−3.05413	−0.265828
$133$	−2.94063	−0.254985
$134$	−1.12067	−0.0968112
$135$	5.77292	0.496854
$136$	−6.56326	−0.562795
$137$	11.4157	0.975307	0.487653	−	0.873037i	$-0.337853\pi$
$137$	11.4157	0.975307	0.487653	+	0.873037i	$0.337853\pi$
$138$	−9.47424	−0.806501
$139$	−14.9857	−1.27107	−0.635534	−	0.772073i	$-0.719220\pi$
$139$	−14.9857	−1.27107	−0.635534	+	0.772073i	$0.719220\pi$
$140$	4.96284	0.419437
$141$	−8.42387	−0.709418
$142$	3.75282	0.314930
$143$	−5.21688	−0.436257
$144$	−3.44802	−0.287335
$145$	1.49916	0.124499
$146$	0.960547	0.0794954
$147$	−40.3119	−3.32487
$148$	5.62247	0.462164
$149$	8.15012	0.667684	0.333842	−	0.942629i	$-0.391655\pi$
$149$	8.15012	0.667684	0.333842	+	0.942629i	$0.391655\pi$
$150$	2.72301	0.222333
$151$	20.3215	1.65374	0.826872	−	0.562390i	$-0.190118\pi$
$151$	20.3215	1.65374	0.826872	+	0.562390i	$0.190118\pi$
$152$	−1.88696	−0.153052
$153$	−11.1827	−0.904064
$154$	4.42479	0.356560
$155$	9.63747	0.774100
$156$	15.9330	1.27566
$157$	6.23717	0.497781	0.248890	−	0.968532i	$-0.419934\pi$
$157$	6.23717	0.497781	0.248890	+	0.968532i	$0.419934\pi$
$158$	−8.12868	−0.646683
$159$	32.8906	2.60840
$160$	5.25427	0.415386
$161$	−16.0276	−1.26315
$162$	−1.20661	−0.0948002
$163$	3.59619	0.281675	0.140838	−	0.990033i	$-0.455020\pi$
$163$	3.59619	0.281675	0.140838	+	0.990033i	$0.455020\pi$
$164$	−0.671974	−0.0524724
$165$	−2.83486	−0.220693
$166$	−13.7830	−1.06977
$167$	−21.8011	−1.68702	−0.843509	−	0.537116i	$-0.819514\pi$
$167$	−21.8011	−1.68702	−0.843509	+	0.537116i	$0.819514\pi$
$168$	−38.6011	−2.97814
$169$	14.2158	1.09352
$170$	−2.13276	−0.163576
$171$	−3.21505	−0.245861
$172$	−11.6839	−0.890886
$173$	−3.64033	−0.276769	−0.138385	−	0.990379i	$-0.544191\pi$
$173$	−3.64033	−0.276769	−0.138385	+	0.990379i	$0.544191\pi$
$174$	−4.08224	−0.309474
$175$	4.60653	0.348221
$176$	0.684620	0.0516052
$177$	6.09876	0.458411
$178$	7.90044	0.592163
$179$	−5.90976	−0.441716	−0.220858	−	0.975306i	$-0.570886\pi$
$179$	−5.90976	−0.441716	−0.220858	+	0.975306i	$0.570886\pi$
$180$	5.42597	0.404428
$181$	15.6762	1.16520	0.582602	−	0.812758i	$-0.302035\pi$
$181$	15.6762	1.16520	0.582602	+	0.812758i	$0.302035\pi$
$182$	−23.0836	−1.71107
$183$	−16.2807	−1.20350
$184$	−10.2847	−0.758196
$185$	5.21880	0.383694
$186$	−26.2430	−1.92423
$187$	2.22036	0.162369
$188$	−3.20138	−0.233485
$189$	−26.5931	−1.93436
$190$	−0.613176	−0.0444845
$191$	24.7838	1.79329	0.896646	−	0.442748i	$-0.145996\pi$
$191$	24.7838	1.79329	0.896646	+	0.442748i	$0.145996\pi$
$192$	−18.1890	−1.31268
$193$	6.45602	0.464714	0.232357	−	0.972631i	$-0.425356\pi$
$193$	6.45602	0.464714	0.232357	+	0.972631i	$0.425356\pi$
$194$	16.1548	1.15985
$195$	14.7891	1.05907
$196$	−15.3200	−1.09429
$197$	−25.2634	−1.79994	−0.899972	−	0.435948i	$-0.856413\pi$
$197$	−25.2634	−1.79994	−0.899972	+	0.435948i	$0.856413\pi$
$198$	4.83771	0.343801
$199$	−1.48435	−0.105223	−0.0526115	−	0.998615i	$-0.516755\pi$
$199$	−1.48435	−0.105223	−0.0526115	+	0.998615i	$0.516755\pi$
$200$	2.95594	0.209016
$201$	−3.30743	−0.233288
$202$	4.86349	0.342194
$203$	−6.90593	−0.484701
$204$	−6.78128	−0.474784
$205$	−0.623729	−0.0435632
$206$	10.7246	0.747216
$207$	−17.5233	−1.21795
$208$	−3.57158	−0.247644
$209$	0.638361	0.0441564
$210$	−12.5436	−0.865593
$211$	16.5953	1.14247	0.571233	−	0.820788i	$-0.306465\pi$
$211$	16.5953	1.14247	0.571233	+	0.820788i	$0.306465\pi$
$212$	12.4996	0.858479
$213$	11.0757	0.758892
$214$	9.97631	0.681967
$215$	−10.8450	−0.739624
$216$	−17.0644	−1.16108
$217$	−44.3953	−3.01375
$218$	8.30230	0.562302
$219$	2.83486	0.191562
$220$	−1.07735	−0.0726349
$221$	−11.5834	−0.779182
$222$	−14.2109	−0.953770
$223$	−10.9175	−0.731091	−0.365545	−	0.930793i	$-0.619118\pi$
$223$	−10.9175	−0.731091	−0.365545	+	0.930793i	$0.619118\pi$
$224$	−24.2039	−1.61719
$225$	5.03641	0.335760
$226$	5.98995	0.398446
$227$	15.8376	1.05118	0.525590	−	0.850738i	$-0.323845\pi$
$227$	15.8376	1.05118	0.525590	+	0.850738i	$0.323845\pi$
$228$	−1.94964	−0.129118
$229$	29.6260	1.95774	0.978870	−	0.204484i	$-0.0655518\pi$
$229$	29.6260	1.95774	0.978870	+	0.204484i	$0.0655518\pi$
$230$	−3.34205	−0.220368
$231$	13.0588	0.859209
$232$	−4.43143	−0.290938
$233$	14.4102	0.944046	0.472023	−	0.881586i	$-0.343524\pi$
$233$	14.4102	0.944046	0.472023	+	0.881586i	$0.343524\pi$
$234$	−25.2377	−1.64984
$235$	−2.97153	−0.193842
$236$	2.31775	0.150873
$237$	−23.9901	−1.55833
$238$	9.82464	0.636837
$239$	−13.4821	−0.872086	−0.436043	−	0.899926i	$-0.643620\pi$
$239$	−13.4821	−0.872086	−0.436043	+	0.899926i	$0.643620\pi$
$240$	−1.94080	−0.125278
$241$	−9.18534	−0.591680	−0.295840	−	0.955237i	$-0.595600\pi$
$241$	−9.18534	−0.591680	−0.295840	+	0.955237i	$0.595600\pi$
$242$	−0.960547	−0.0617463
$243$	13.7577	0.882557
$244$	−6.18726	−0.396099
$245$	−14.2201	−0.908489
$246$	1.69842	0.108287
$247$	−3.33025	−0.211899
$248$	−28.4878	−1.80898
$249$	−40.6776	−2.57784
$250$	0.960547	0.0607503
$251$	29.0501	1.83363	0.916814	−	0.399314i	$-0.130752\pi$
$251$	29.0501	1.83363	0.916814	+	0.399314i	$0.130752\pi$
$252$	−24.9949	−1.57453
$253$	3.47932	0.218743
$254$	10.9634	0.687905
$255$	−6.29441	−0.394171
$256$	−17.0064	−1.06290
$257$	−30.4656	−1.90039	−0.950196	−	0.311652i	$-0.899118\pi$
$257$	−30.4656	−1.90039	−0.950196	+	0.311652i	$0.899118\pi$
$258$	29.5311	1.83853
$259$	−24.0405	−1.49381
$260$	5.62040	0.348562
$261$	−7.55039	−0.467357
$262$	−0.785662	−0.0485384
$263$	−5.25290	−0.323908	−0.161954	−	0.986798i	$-0.551780\pi$
$263$	−5.25290	−0.323908	−0.161954	+	0.986798i	$0.551780\pi$
$264$	8.37966	0.515732
$265$	11.6022	0.712719
$266$	2.82461	0.173188
$267$	23.3165	1.42695
$268$	−1.25694	−0.0767801
$269$	0.675126	0.0411632	0.0205816	−	0.999788i	$-0.493448\pi$
$269$	0.675126	0.0411632	0.0205816	+	0.999788i	$0.493448\pi$
$270$	−5.54516	−0.337468
$271$	−4.64816	−0.282356	−0.141178	−	0.989984i	$-0.545089\pi$
$271$	−4.64816	−0.282356	−0.141178	+	0.989984i	$0.545089\pi$
$272$	1.52011	0.0921699
$273$	−68.1264	−4.12320
$274$	−10.9653	−0.662437
$275$	−1.00000	−0.0603023
$276$	−10.6263	−0.639628
$277$	12.8977	0.774946	0.387473	−	0.921881i	$-0.373348\pi$
$277$	12.8977	0.774946	0.387473	+	0.921881i	$0.373348\pi$
$278$	14.3944	0.863321
$279$	−48.5382	−2.90591
$280$	−13.6166	−0.813748
$281$	−13.3983	−0.799273	−0.399636	−	0.916674i	$-0.630864\pi$
$281$	−13.3983	−0.799273	−0.399636	+	0.916674i	$0.630864\pi$
$282$	8.09153	0.481843
$283$	−9.20149	−0.546972	−0.273486	−	0.961876i	$-0.588177\pi$
$283$	−9.20149	−0.546972	−0.273486	+	0.961876i	$0.588177\pi$
$284$	4.20916	0.249768
$285$	−1.80966	−0.107195
$286$	5.01106	0.296310
$287$	2.87323	0.169601
$288$	−26.4626	−1.55933
$289$	−12.0700	−0.709999
$290$	−1.44002	−0.0845606
$291$	47.6775	2.79490
$292$	1.07735	0.0630471
$293$	−9.50958	−0.555556	−0.277778	−	0.960645i	$-0.589598\pi$
$293$	−9.50958	−0.555556	−0.277778	+	0.960645i	$0.589598\pi$
$294$	38.7215	2.25828
$295$	2.15135	0.125256
$296$	−15.4264	−0.896644
$297$	5.77292	0.334979
$298$	−7.82858	−0.453497
$299$	−18.1512	−1.04971
$300$	3.05413	0.176330
$301$	49.9578	2.87952
$302$	−19.5198	−1.12324
$303$	14.3536	0.824591
$304$	0.437035	0.0250657
$305$	−5.74304	−0.328846
$306$	10.7415	0.614049
$307$	12.6652	0.722841	0.361421	−	0.932403i	$-0.382292\pi$
$307$	12.6652	0.722841	0.361421	+	0.932403i	$0.382292\pi$
$308$	4.96284	0.282784
$309$	31.6513	1.80058
$310$	−9.25725	−0.525776
$311$	−7.36538	−0.417652	−0.208826	−	0.977953i	$-0.566964\pi$
$311$	−7.36538	−0.417652	−0.208826	+	0.977953i	$0.566964\pi$
$312$	−43.7157	−2.47491
$313$	13.6080	0.769170	0.384585	−	0.923090i	$-0.374345\pi$
$313$	13.6080	0.769170	0.384585	+	0.923090i	$0.374345\pi$
$314$	−5.99110	−0.338097
$315$	−23.2003	−1.30719
$316$	−9.11712	−0.512878
$317$	−21.6450	−1.21570	−0.607852	−	0.794050i	$-0.707969\pi$
$317$	−21.6450	−1.21570	−0.607852	+	0.794050i	$0.707969\pi$
$318$	−31.5930	−1.77165
$319$	1.49916	0.0839369
$320$	−6.41621	−0.358677
$321$	29.4430	1.64335
$322$	15.3953	0.857945
$323$	1.41739	0.0788659
$324$	−1.35333	−0.0751852
$325$	5.21688	0.289380
$326$	−3.45431	−0.191316
$327$	24.5025	1.35499
$328$	1.84371	0.101802
$329$	13.6885	0.754669
$330$	2.72301	0.149897
$331$	−17.2623	−0.948819	−0.474410	−	0.880304i	$-0.657338\pi$
$331$	−17.2623	−0.948819	−0.474410	+	0.880304i	$0.657338\pi$
$332$	−15.4590	−0.848421
$333$	−26.2840	−1.44035
$334$	20.9409	1.14584
$335$	−1.16670	−0.0637437
$336$	8.94034	0.487736
$337$	−27.2578	−1.48483	−0.742413	−	0.669943i	$-0.766319\pi$
$337$	−27.2578	−1.48483	−0.742413	+	0.669943i	$0.766319\pi$
$338$	−13.6550	−0.742732
$339$	17.6781	0.960143
$340$	−2.39211	−0.129730
$341$	9.63747	0.521898
$342$	3.08820	0.166991
$343$	33.2596	1.79585
$344$	32.0572	1.72841
$345$	−9.86338	−0.531026
$346$	3.49671	0.187984
$347$	−27.1975	−1.46004	−0.730018	−	0.683428i	$-0.760488\pi$
$347$	−27.1975	−1.46004	−0.730018	+	0.683428i	$0.760488\pi$
$348$	−4.57863	−0.245441
$349$	1.32330	0.0708344	0.0354172	−	0.999373i	$-0.488724\pi$
$349$	1.32330	0.0708344	0.0354172	+	0.999373i	$0.488724\pi$
$350$	−4.42479	−0.236515
$351$	−30.1166	−1.60751
$352$	5.25427	0.280053
$353$	−10.7778	−0.573642	−0.286821	−	0.957984i	$-0.592599\pi$
$353$	−10.7778	−0.573642	−0.286821	+	0.957984i	$0.592599\pi$
$354$	−5.85815	−0.311357
$355$	3.90696	0.207360
$356$	8.86113	0.469639
$357$	28.9954	1.53460
$358$	5.67660	0.300018
$359$	−5.41551	−0.285820	−0.142910	−	0.989736i	$-0.545646\pi$
$359$	−5.41551	−0.285820	−0.142910	+	0.989736i	$0.545646\pi$
$360$	−14.8873	−0.784630
$361$	−18.5925	−0.978552
$362$	−15.0577	−0.791418
$363$	−2.83486	−0.148791
$364$	−25.8905	−1.35703
$365$	1.00000	0.0523424
$366$	15.6384	0.817431
$367$	−22.6122	−1.18035	−0.590174	−	0.807276i	$-0.700941\pi$
$367$	−22.6122	−1.18035	−0.590174	+	0.807276i	$0.700941\pi$
$368$	2.38201	0.124171
$369$	3.14135	0.163532
$370$	−5.01290	−0.260608
$371$	−53.4459	−2.77478
$372$	−29.4341	−1.52609
$373$	1.53220	0.0793341	0.0396671	−	0.999213i	$-0.487370\pi$
$373$	1.53220	0.0793341	0.0396671	+	0.999213i	$0.487370\pi$
$374$	−2.13276	−0.110283
$375$	2.83486	0.146391
$376$	8.78367	0.452983
$377$	−7.82094	−0.402799
$378$	25.5439	1.31384
$379$	−27.7448	−1.42516	−0.712578	−	0.701592i	$-0.752473\pi$
$379$	−27.7448	−1.42516	−0.712578	+	0.701592i	$0.752473\pi$
$380$	−0.687738	−0.0352802
$381$	32.3562	1.65766
$382$	−23.8060	−1.21802
$383$	23.9375	1.22315	0.611576	−	0.791186i	$-0.290536\pi$
$383$	23.9375	1.22315	0.611576	+	0.791186i	$0.290536\pi$
$384$	−12.3188	−0.628639
$385$	4.60653	0.234770
$386$	−6.20131	−0.315638
$387$	54.6199	2.77648
$388$	18.1192	0.919863
$389$	26.2213	1.32947	0.664736	−	0.747078i	$-0.268544\pi$
$389$	26.2213	1.32947	0.664736	+	0.747078i	$0.268544\pi$
$390$	−14.2056	−0.719330
$391$	7.72536	0.390688
$392$	42.0338	2.12303
$393$	−2.31872	−0.116964
$394$	24.2667	1.22254
$395$	−8.46255	−0.425797
$396$	5.42597	0.272665
$397$	9.22800	0.463140	0.231570	−	0.972818i	$-0.425614\pi$
$397$	9.22800	0.463140	0.231570	+	0.972818i	$0.425614\pi$
$398$	1.42579	0.0714685
$399$	8.33626	0.417335
$400$	−0.684620	−0.0342310
$401$	9.01085	0.449981	0.224990	−	0.974361i	$-0.427765\pi$
$401$	9.01085	0.449981	0.224990	+	0.974361i	$0.427765\pi$
$402$	3.17694	0.158451
$403$	−50.2775	−2.50450
$404$	5.45488	0.271391
$405$	−1.25617	−0.0624195
$406$	6.63347	0.329214
$407$	5.21880	0.258686
$408$	18.6059	0.921129
$409$	−33.0850	−1.63595	−0.817975	−	0.575254i	$-0.804903\pi$
$409$	−33.0850	−1.63595	−0.817975	+	0.575254i	$0.804903\pi$
$410$	0.599121	0.0295885
$411$	−32.3618	−1.59629
$412$	12.0287	0.592610
$413$	−9.91024	−0.487651
$414$	16.8319	0.827245
$415$	−14.3491	−0.704369
$416$	−27.4109	−1.34393
$417$	42.4822	2.08036
$418$	−0.613176	−0.0299914
$419$	12.4072	0.606129	0.303065	−	0.952970i	$-0.401990\pi$
$419$	12.4072	0.606129	0.303065	+	0.952970i	$0.401990\pi$
$420$	−14.0689	−0.686494
$421$	21.1762	1.03206	0.516032	−	0.856569i	$-0.327409\pi$
$421$	21.1762	1.03206	0.516032	+	0.856569i	$0.327409\pi$
$422$	−15.9405	−0.775973
$423$	14.9659	0.727665
$424$	−34.2954	−1.66553
$425$	−2.22036	−0.107703
$426$	−10.6387	−0.515447
$427$	26.4555	1.28027
$428$	11.1894	0.540861
$429$	14.7891	0.714024
$430$	10.4171	0.502359
$431$	−29.5549	−1.42361	−0.711805	−	0.702377i	$-0.752122\pi$
$431$	−29.5549	−1.42361	−0.711805	+	0.702377i	$0.752122\pi$
$432$	3.95225	0.190153
$433$	−34.1865	−1.64290	−0.821449	−	0.570282i	$-0.806834\pi$
$433$	−34.1865	−1.64290	−0.821449	+	0.570282i	$0.806834\pi$
$434$	42.6438	2.04697
$435$	−4.24991	−0.203767
$436$	9.31185	0.445957
$437$	2.22106	0.106248
$438$	−2.72301	−0.130111
$439$	−2.70033	−0.128880	−0.0644399	−	0.997922i	$-0.520526\pi$
$439$	−2.70033	−0.128880	−0.0644399	+	0.997922i	$0.520526\pi$
$440$	2.95594	0.140919
$441$	71.6182	3.41039
$442$	11.1264	0.529227
$443$	−2.07904	−0.0987782	−0.0493891	−	0.998780i	$-0.515727\pi$
$443$	−2.07904	−0.0987782	−0.0493891	+	0.998780i	$0.515727\pi$
$444$	−15.9389	−0.756426
$445$	8.22493	0.389899
$446$	10.4868	0.496564
$447$	−23.1044	−1.09280
$448$	29.5565	1.39641
$449$	25.9195	1.22322	0.611608	−	0.791161i	$-0.290523\pi$
$449$	25.9195	1.22322	0.611608	+	0.791161i	$0.290523\pi$
$450$	−4.83771	−0.228052
$451$	−0.623729	−0.0293703
$452$	6.71833	0.316004
$453$	−57.6086	−2.70669
$454$	−15.2128	−0.713971
$455$	−24.0317	−1.12662
$456$	5.34925	0.250502
$457$	−21.5206	−1.00669	−0.503346	−	0.864085i	$-0.667898\pi$
$457$	−21.5206	−1.00669	−0.503346	+	0.864085i	$0.667898\pi$
$458$	−28.4571	−1.32972
$459$	12.8180	0.598292
$460$	−3.74845	−0.174772
$461$	3.84026	0.178859	0.0894294	−	0.995993i	$-0.471496\pi$
$461$	3.84026	0.178859	0.0894294	+	0.995993i	$0.471496\pi$
$462$	−12.5436	−0.583583
$463$	15.5748	0.723822	0.361911	−	0.932213i	$-0.382124\pi$
$463$	15.5748	0.723822	0.361911	+	0.932213i	$0.382124\pi$
$464$	1.02636	0.0476474
$465$	−27.3208	−1.26697
$466$	−13.8417	−0.641205
$467$	−17.7258	−0.820251	−0.410126	−	0.912029i	$-0.634515\pi$
$467$	−17.7258	−0.820251	−0.410126	+	0.912029i	$0.634515\pi$
$468$	−28.3066	−1.30847
$469$	5.37444	0.248169
$470$	2.85430	0.131659
$471$	−17.6815	−0.814720
$472$	−6.35925	−0.292708
$473$	−10.8450	−0.498654
$474$	23.0436	1.05843
$475$	−0.638361	−0.0292900
$476$	11.0193	0.505069
$477$	−58.4335	−2.67549
$478$	12.9502	0.592329
$479$	0.409728	0.0187210	0.00936048	−	0.999956i	$-0.497020\pi$
$479$	0.409728	0.0187210	0.00936048	+	0.999956i	$0.497020\pi$
$480$	−14.8951	−0.679865
$481$	−27.2258	−1.24139
$482$	8.82296	0.401875
$483$	45.4359	2.06741
$484$	−1.07735	−0.0489704
$485$	16.8183	0.763680
$486$	−13.2149	−0.599441
$487$	26.7967	1.21427	0.607136	−	0.794598i	$-0.292318\pi$
$487$	26.7967	1.21427	0.607136	+	0.794598i	$0.292318\pi$
$488$	16.9761	0.768471
$489$	−10.1947	−0.461019
$490$	13.6591	0.617054
$491$	23.6874	1.06900	0.534498	−	0.845170i	$-0.320501\pi$
$491$	23.6874	1.06900	0.534498	+	0.845170i	$0.320501\pi$
$492$	1.90495	0.0858818
$493$	3.32868	0.149916
$494$	3.19886	0.143924
$495$	5.03641	0.226370
$496$	6.59801	0.296259
$497$	−17.9975	−0.807299
$498$	39.0727	1.75089
$499$	−38.5644	−1.72638	−0.863190	−	0.504879i	$-0.831537\pi$
$499$	−38.5644	−1.72638	−0.863190	+	0.504879i	$0.831537\pi$
$500$	1.07735	0.0481805
$501$	61.8029	2.76115
$502$	−27.9040	−1.24542
$503$	36.7363	1.63799	0.818996	−	0.573799i	$-0.194531\pi$
$503$	36.7363	1.63799	0.818996	+	0.573799i	$0.194531\pi$
$504$	68.5788	3.05474
$505$	5.06325	0.225311
$506$	−3.34205	−0.148572
$507$	−40.2998	−1.78978
$508$	12.2966	0.545571
$509$	−23.4889	−1.04113	−0.520563	−	0.853823i	$-0.674278\pi$
$509$	−23.4889	−1.04113	−0.520563	+	0.853823i	$0.674278\pi$
$510$	6.04608	0.267725
$511$	−4.60653	−0.203781
$512$	7.64457	0.337845
$513$	3.68521	0.162706
$514$	29.2637	1.29076
$515$	11.1651	0.491991
$516$	33.1221	1.45812
$517$	−2.97153	−0.130688
$518$	23.0921	1.01461
$519$	10.3198	0.452990
$520$	−15.4208	−0.676246
$521$	18.4256	0.807240	0.403620	−	0.914927i	$-0.367752\pi$
$521$	18.4256	0.807240	0.403620	+	0.914927i	$0.367752\pi$
$522$	7.25250	0.317433
$523$	31.2335	1.36575	0.682874	−	0.730536i	$-0.260730\pi$
$523$	31.2335	1.36575	0.682874	+	0.730536i	$0.260730\pi$
$524$	−0.881198	−0.0384953
$525$	−13.0588	−0.569935
$526$	5.04565	0.220001
$527$	21.3987	0.932142
$528$	−1.94080	−0.0844624
$529$	−10.8943	−0.473666
$530$	−11.1445	−0.484085
$531$	−10.8351	−0.470202
$532$	3.16808	0.137354
$533$	3.25392	0.140943
$534$	−22.3966	−0.969196
$535$	10.3861	0.449029
$536$	3.44870	0.148961
$537$	16.7533	0.722959
$538$	−0.648491	−0.0279584
$539$	−14.2201	−0.612503
$540$	−6.21945	−0.267642
$541$	−32.6881	−1.40537	−0.702686	−	0.711500i	$-0.748016\pi$
$541$	−32.6881	−1.40537	−0.702686	+	0.711500i	$0.748016\pi$
$542$	4.46478	0.191779
$543$	−44.4398	−1.90709
$544$	11.6664	0.500192
$545$	8.64330	0.370238
$546$	65.4386	2.80051
$547$	14.4174	0.616443	0.308221	−	0.951315i	$-0.400266\pi$
$547$	14.4174	0.616443	0.308221	+	0.951315i	$0.400266\pi$
$548$	−12.2987	−0.525373
$549$	28.9243	1.23446
$550$	0.960547	0.0409579
$551$	0.957007	0.0407699
$552$	29.1555	1.24094
$553$	38.9830	1.65773
$554$	−12.3888	−0.526351
$555$	−14.7945	−0.627993
$556$	16.1448	0.684692
$557$	−5.14918	−0.218178	−0.109089	−	0.994032i	$-0.534793\pi$
$557$	−5.14918	−0.218178	−0.109089	+	0.994032i	$0.534793\pi$
$558$	46.6233	1.97372
$559$	56.5771	2.39296
$560$	3.15372	0.133269
$561$	−6.29441	−0.265750
$562$	12.8697	0.542874
$563$	20.7904	0.876210	0.438105	−	0.898924i	$-0.355650\pi$
$563$	20.7904	0.876210	0.438105	+	0.898924i	$0.355650\pi$
$564$	9.07545	0.382145
$565$	6.23598	0.262350
$566$	8.83847	0.371508
$567$	5.78658	0.243013
$568$	−11.5487	−0.484574
$569$	25.1584	1.05470	0.527348	−	0.849649i	$-0.323186\pi$
$569$	25.1584	1.05470	0.527348	+	0.849649i	$0.323186\pi$
$570$	1.73827	0.0728079
$571$	11.9479	0.500002	0.250001	−	0.968246i	$-0.419569\pi$
$571$	11.9479	0.500002	0.250001	+	0.968246i	$0.419569\pi$
$572$	5.62040	0.235001
$573$	−70.2585	−2.93509
$574$	−2.75987	−0.115195
$575$	−3.47932	−0.145098
$576$	32.3146	1.34644
$577$	10.6673	0.444085	0.222042	−	0.975037i	$-0.428728\pi$
$577$	10.6673	0.444085	0.222042	+	0.975037i	$0.428728\pi$
$578$	11.5938	0.482238
$579$	−18.3019	−0.760600
$580$	−1.61512	−0.0670642
$581$	66.0995	2.74227
$582$	−45.7965	−1.89833
$583$	11.6022	0.480515
$584$	−2.95594	−0.122318
$585$	−26.2743	−1.08631
$586$	9.13440	0.377339
$587$	−45.3661	−1.87246	−0.936230	−	0.351389i	$-0.885710\pi$
$587$	−45.3661	−1.87246	−0.936230	+	0.351389i	$0.885710\pi$
$588$	43.4300	1.79102
$589$	6.15219	0.253497
$590$	−2.06647	−0.0850752
$591$	71.6181	2.94598
$592$	3.57289	0.146845
$593$	−37.6922	−1.54783	−0.773917	−	0.633288i	$-0.781705\pi$
$593$	−37.6922	−1.54783	−0.773917	+	0.633288i	$0.781705\pi$
$594$	−5.54516	−0.227521
$595$	10.2282	0.419314
$596$	−8.78053	−0.359664
$597$	4.20793	0.172219
$598$	17.4351	0.712974
$599$	29.2105	1.19351	0.596754	−	0.802425i	$-0.296457\pi$
$599$	29.2105	1.19351	0.596754	+	0.802425i	$0.296457\pi$
$600$	−8.37966	−0.342098
$601$	2.09327	0.0853864	0.0426932	−	0.999088i	$-0.486406\pi$
$601$	2.09327	0.0853864	0.0426932	+	0.999088i	$0.486406\pi$
$602$	−47.9869	−1.95580
$603$	5.87598	0.239288
$604$	−21.8934	−0.890830
$605$	−1.00000	−0.0406558
$606$	−13.7873	−0.560070
$607$	−33.9910	−1.37965	−0.689827	−	0.723975i	$-0.742313\pi$
$607$	−33.9910	−1.37965	−0.689827	+	0.723975i	$0.742313\pi$
$608$	3.35412	0.136028
$609$	19.5773	0.793313
$610$	5.51646	0.223355
$611$	15.5021	0.627149
$612$	12.0476	0.486996
$613$	−42.2968	−1.70835	−0.854175	−	0.519986i	$-0.825937\pi$
$613$	−42.2968	−1.70835	−0.854175	+	0.519986i	$0.825937\pi$
$614$	−12.1655	−0.490960
$615$	1.76818	0.0713000
$616$	−13.6166	−0.548629
$617$	−16.9104	−0.680787	−0.340394	−	0.940283i	$-0.610560\pi$
$617$	−16.9104	−0.680787	−0.340394	+	0.940283i	$0.610560\pi$
$618$	−30.4026	−1.22297
$619$	−10.8139	−0.434646	−0.217323	−	0.976100i	$-0.569732\pi$
$619$	−10.8139	−0.434646	−0.217323	+	0.976100i	$0.569732\pi$
$620$	−10.3829	−0.416988
$621$	20.0858	0.806017
$622$	7.07479	0.283673
$623$	−37.8884	−1.51797
$624$	10.1249	0.405321
$625$	1.00000	0.0400000
$626$	−13.0711	−0.522427
$627$	−1.80966	−0.0722709
$628$	−6.71961	−0.268142
$629$	11.5876	0.462029
$630$	22.2850	0.887857
$631$	6.50153	0.258822	0.129411	−	0.991591i	$-0.458691\pi$
$631$	6.50153	0.258822	0.129411	+	0.991591i	$0.458691\pi$
$632$	25.0148	0.995035
$633$	−47.0452	−1.86988
$634$	20.7910	0.825718
$635$	11.4137	0.452939
$636$	−35.4347	−1.40508
$637$	74.1845	2.93930
$638$	−1.44002	−0.0570108
$639$	−19.6770	−0.778412
$640$	−4.34546	−0.171769
$641$	−6.40531	−0.252995	−0.126497	−	0.991967i	$-0.540373\pi$
$641$	−6.40531	−0.252995	−0.126497	+	0.991967i	$0.540373\pi$
$642$	−28.2814	−1.11618
$643$	−2.29157	−0.0903706	−0.0451853	−	0.998979i	$-0.514388\pi$
$643$	−2.29157	−0.0903706	−0.0451853	+	0.998979i	$0.514388\pi$
$644$	17.2673	0.680428
$645$	30.7440	1.21055
$646$	−1.36147	−0.0535665
$647$	−33.7687	−1.32759	−0.663793	−	0.747916i	$-0.731055\pi$
$647$	−33.7687	−1.32759	−0.663793	+	0.747916i	$0.731055\pi$
$648$	3.71316	0.145867
$649$	2.15135	0.0844478
$650$	−5.01106	−0.196550
$651$	125.854	4.93262
$652$	−3.87435	−0.151731
$653$	16.6041	0.649768	0.324884	−	0.945754i	$-0.394675\pi$
$653$	16.6041	0.649768	0.324884	+	0.945754i	$0.394675\pi$
$654$	−23.5358	−0.920323
$655$	−0.817932	−0.0319592
$656$	−0.427018	−0.0166722
$657$	−5.03641	−0.196489
$658$	−13.1484	−0.512578
$659$	−13.5443	−0.527611	−0.263805	−	0.964576i	$-0.584978\pi$
$659$	−13.5443	−0.527611	−0.263805	+	0.964576i	$0.584978\pi$
$660$	3.05413	0.118882
$661$	−30.6525	−1.19224	−0.596122	−	0.802894i	$-0.703292\pi$
$661$	−30.6525	−1.19224	−0.596122	+	0.802894i	$0.703292\pi$
$662$	16.5812	0.644447
$663$	32.8372	1.27529
$664$	42.4150	1.64602
$665$	2.94063	0.114033
$666$	25.2470	0.978302
$667$	5.21607	0.201967
$668$	23.4874	0.908753
$669$	30.9496	1.19658
$670$	1.12067	0.0432953
$671$	−5.74304	−0.221708
$672$	68.6147	2.64687
$673$	−7.70194	−0.296888	−0.148444	−	0.988921i	$-0.547426\pi$
$673$	−7.70194	−0.296888	−0.148444	+	0.988921i	$0.547426\pi$
$674$	26.1824	1.00851
$675$	−5.77292	−0.222200
$676$	−15.3154	−0.589054
$677$	−9.92817	−0.381570	−0.190785	−	0.981632i	$-0.561103\pi$
$677$	−9.92817	−0.381570	−0.190785	+	0.981632i	$0.561103\pi$
$678$	−16.9807	−0.652138
$679$	−77.4740	−2.97318
$680$	6.56326	0.251689
$681$	−44.8974	−1.72047
$682$	−9.25725	−0.354478
$683$	1.25861	0.0481592	0.0240796	−	0.999710i	$-0.492334\pi$
$683$	1.25861	0.0481592	0.0240796	+	0.999710i	$0.492334\pi$
$684$	3.46373	0.132439
$685$	−11.4157	−0.436170
$686$	−31.9474	−1.21976
$687$	−83.9854	−3.20424
$688$	−7.42471	−0.283064
$689$	−60.5274	−2.30591
$690$	9.47424	0.360678
$691$	−7.37598	−0.280596	−0.140298	−	0.990109i	$-0.544806\pi$
$691$	−7.37598	−0.280596	−0.140298	+	0.990109i	$0.544806\pi$
$692$	3.92191	0.149089
$693$	−23.2003	−0.881308
$694$	26.1244	0.991670
$695$	14.9857	0.568439
$696$	12.5625	0.476179
$697$	−1.38491	−0.0524571
$698$	−1.27109	−0.0481114
$699$	−40.8509	−1.54512
$700$	−4.96284	−0.187578
$701$	25.2489	0.953639	0.476819	−	0.879001i	$-0.341790\pi$
$701$	25.2489	0.953639	0.476819	+	0.879001i	$0.341790\pi$
$702$	28.9284	1.09183
$703$	3.33148	0.125649
$704$	−6.41621	−0.241820
$705$	8.42387	0.317261
$706$	10.3525	0.389623
$707$	−23.3240	−0.877189
$708$	−6.57049	−0.246934
$709$	13.8253	0.519221	0.259610	−	0.965713i	$-0.416406\pi$
$709$	13.8253	0.519221	0.259610	+	0.965713i	$0.416406\pi$
$710$	−3.75282	−0.140841
$711$	42.6208	1.59841
$712$	−24.3124	−0.911146
$713$	33.5319	1.25578
$714$	−27.8514	−1.04231
$715$	5.21688	0.195100
$716$	6.36687	0.237941
$717$	38.2199	1.42735
$718$	5.20185	0.194131
$719$	−12.4104	−0.462829	−0.231414	−	0.972855i	$-0.574335\pi$
$719$	−12.4104	−0.462829	−0.231414	+	0.972855i	$0.574335\pi$
$720$	3.44802	0.128500
$721$	−51.4322	−1.91543
$722$	17.8590	0.664642
$723$	26.0391	0.968405
$724$	−16.8888	−0.627666
$725$	−1.49916	−0.0556775
$726$	2.72301	0.101060
$727$	44.7524	1.65977	0.829887	−	0.557931i	$-0.188405\pi$
$727$	44.7524	1.65977	0.829887	+	0.557931i	$0.188405\pi$
$728$	71.0362	2.63278
$729$	−42.7696	−1.58406
$730$	−0.960547	−0.0355514
$731$	−24.0799	−0.890626
$732$	17.5400	0.648297
$733$	−42.5346	−1.57105	−0.785526	−	0.618829i	$-0.787608\pi$
$733$	−42.5346	−1.57105	−0.785526	+	0.618829i	$0.787608\pi$
$734$	21.7201	0.801703
$735$	40.3119	1.48693
$736$	18.2813	0.673858
$737$	−1.16670	−0.0429760
$738$	−3.01742	−0.111073
$739$	42.2293	1.55343	0.776715	−	0.629852i	$-0.216885\pi$
$739$	42.2293	1.55343	0.776715	+	0.629852i	$0.216885\pi$
$740$	−5.62247	−0.206686
$741$	9.44079	0.346816
$742$	51.3373	1.88465
$743$	49.6134	1.82014	0.910069	−	0.414457i	$-0.136029\pi$
$743$	49.6134	1.82014	0.910069	+	0.414457i	$0.136029\pi$
$744$	80.7587	2.96076
$745$	−8.15012	−0.298597
$746$	−1.47175	−0.0538845
$747$	72.2678	2.64414
$748$	−2.39211	−0.0874641
$749$	−47.8437	−1.74817
$750$	−2.72301	−0.0994303
$751$	−40.4750	−1.47695	−0.738476	−	0.674280i	$-0.764454\pi$
$751$	−40.4750	−1.47695	−0.738476	+	0.674280i	$0.764454\pi$
$752$	−2.03437	−0.0741859
$753$	−82.3530	−3.00111
$754$	7.51239	0.273585
$755$	−20.3215	−0.739577
$756$	28.6501	1.04199
$757$	38.6994	1.40655	0.703277	−	0.710916i	$-0.251719\pi$
$757$	38.6994	1.40655	0.703277	+	0.710916i	$0.251719\pi$
$758$	26.6502	0.967980
$759$	−9.86338	−0.358018
$760$	1.88696	0.0684471
$761$	14.8753	0.539231	0.269615	−	0.962968i	$-0.413103\pi$
$761$	14.8753	0.539231	0.269615	+	0.962968i	$0.413103\pi$
$762$	−31.0797	−1.12590
$763$	−39.8156	−1.44142
$764$	−26.7008	−0.966001
$765$	11.1827	0.404310
$766$	−22.9931	−0.830776
$767$	−11.2233	−0.405250
$768$	48.2108	1.73966
$769$	−37.9069	−1.36696	−0.683479	−	0.729971i	$-0.739534\pi$
$769$	−37.9069	−1.36696	−0.683479	+	0.729971i	$0.739534\pi$
$770$	−4.42479	−0.159458
$771$	86.3656	3.11038
$772$	−6.95538	−0.250330
$773$	−8.04823	−0.289475	−0.144737	−	0.989470i	$-0.546234\pi$
$773$	−8.04823	−0.289475	−0.144737	+	0.989470i	$0.546234\pi$
$774$	−52.4650	−1.88581
$775$	−9.63747	−0.346188
$776$	−49.7139	−1.78463
$777$	68.1515	2.44492
$778$	−25.1868	−0.902990
$779$	−0.398165	−0.0142657
$780$	−15.9330	−0.570494
$781$	3.90696	0.139802
$782$	−7.42057	−0.265359
$783$	8.65454	0.309288
$784$	−9.73536	−0.347692
$785$	−6.23717	−0.222614
$786$	2.22724	0.0794430
$787$	7.55946	0.269466	0.134733	−	0.990882i	$-0.456982\pi$
$787$	7.55946	0.269466	0.134733	+	0.990882i	$0.456982\pi$
$788$	27.2175	0.969584
$789$	14.8912	0.530141
$790$	8.12868	0.289205
$791$	−28.7262	−1.02139
$792$	−14.8873	−0.528997
$793$	29.9608	1.06394
$794$	−8.86393	−0.314569
$795$	−32.8906	−1.16651
$796$	1.59917	0.0566810
$797$	−4.40338	−0.155976	−0.0779879	−	0.996954i	$-0.524850\pi$
$797$	−4.40338	−0.155976	−0.0779879	+	0.996954i	$0.524850\pi$
$798$	−8.00737	−0.283458
$799$	−6.59789	−0.233416
$800$	−5.25427	−0.185766
$801$	−41.4241	−1.46365
$802$	−8.65535	−0.305631
$803$	1.00000	0.0352892
$804$	3.56325	0.125666
$805$	16.0276	0.564899
$806$	48.2939	1.70108
$807$	−1.91389	−0.0673720
$808$	−14.9666	−0.526525
$809$	−29.7635	−1.04643	−0.523214	−	0.852201i	$-0.675267\pi$
$809$	−29.7635	−1.04643	−0.523214	+	0.852201i	$0.675267\pi$
$810$	1.20661	0.0423959
$811$	−22.4770	−0.789274	−0.394637	−	0.918837i	$-0.629130\pi$
$811$	−22.4770	−0.789274	−0.394637	+	0.918837i	$0.629130\pi$
$812$	7.44010	0.261096
$813$	13.1769	0.462133
$814$	−5.01290	−0.175702
$815$	−3.59619	−0.125969
$816$	−4.30928	−0.150855
$817$	−6.92303	−0.242206
$818$	31.7797	1.11115
$819$	121.033	4.22925
$820$	0.671974	0.0234664
$821$	−50.3715	−1.75798	−0.878989	−	0.476841i	$-0.841782\pi$
$821$	−50.3715	−1.75798	−0.878989	+	0.476841i	$0.841782\pi$
$822$	31.0850	1.08421
$823$	−20.7565	−0.723527	−0.361764	−	0.932270i	$-0.617825\pi$
$823$	−20.7565	−0.723527	−0.361764	+	0.932270i	$0.617825\pi$
$824$	−33.0032	−1.14972
$825$	2.83486	0.0986970
$826$	9.51925	0.331217
$827$	3.40215	0.118304	0.0591522	−	0.998249i	$-0.481160\pi$
$827$	3.40215	0.118304	0.0591522	+	0.998249i	$0.481160\pi$
$828$	18.8787	0.656080
$829$	26.1890	0.909582	0.454791	−	0.890598i	$-0.349714\pi$
$829$	26.1890	0.909582	0.454791	+	0.890598i	$0.349714\pi$
$830$	13.7830	0.478414
$831$	−36.5631	−1.26836
$832$	33.4726	1.16045
$833$	−31.5738	−1.09397
$834$	−40.8061	−1.41300
$835$	21.8011	0.754457
$836$	−0.687738	−0.0237859
$837$	55.6363	1.92307
$838$	−11.9177	−0.411689
$839$	−3.06110	−0.105681	−0.0528405	−	0.998603i	$-0.516828\pi$
$839$	−3.06110	−0.105681	−0.0528405	+	0.998603i	$0.516828\pi$
$840$	38.6011	1.33187
$841$	−26.7525	−0.922500
$842$	−20.3407	−0.700988
$843$	37.9821	1.30817
$844$	−17.8789	−0.615417
$845$	−14.2158	−0.489039
$846$	−14.3754	−0.494237
$847$	4.60653	0.158282
$848$	7.94311	0.272767
$849$	26.0849	0.895231
$850$	2.13276	0.0731532
$851$	18.1579	0.622444
$852$	−11.9324	−0.408796
$853$	−0.959489	−0.0328523	−0.0164261	−	0.999865i	$-0.505229\pi$
$853$	−0.959489	−0.0328523	−0.0164261	+	0.999865i	$0.505229\pi$
$854$	−25.4117	−0.869572
$855$	3.21505	0.109952
$856$	−30.7006	−1.04932
$857$	−6.13315	−0.209505	−0.104752	−	0.994498i	$-0.533405\pi$
$857$	−6.13315	−0.209505	−0.104752	+	0.994498i	$0.533405\pi$
$858$	−14.2056	−0.484972
$859$	−25.3885	−0.866244	−0.433122	−	0.901335i	$-0.642588\pi$
$859$	−25.3885	−0.866244	−0.433122	+	0.901335i	$0.642588\pi$
$860$	11.6839	0.398416
$861$	−8.14518	−0.277587
$862$	28.3889	0.966929
$863$	−6.05422	−0.206088	−0.103044	−	0.994677i	$-0.532858\pi$
$863$	−6.05422	−0.206088	−0.103044	+	0.994677i	$0.532858\pi$
$864$	30.3325	1.03193
$865$	3.64033	0.123775
$866$	32.8377	1.11587
$867$	34.2167	1.16206
$868$	47.8292	1.62343
$869$	−8.46255	−0.287072
$870$	4.08224	0.138401
$871$	6.08653	0.206234
$872$	−25.5491	−0.865200
$873$	−84.7039	−2.86679
$874$	−2.13344	−0.0721646
$875$	−4.60653	−0.155729
$876$	−3.05413	−0.103189
$877$	−38.3280	−1.29425	−0.647123	−	0.762386i	$-0.724028\pi$
$877$	−38.3280	−1.29425	−0.647123	+	0.762386i	$0.724028\pi$
$878$	2.59380	0.0875364
$879$	26.9583	0.909281
$880$	−0.684620	−0.0230785
$881$	7.42507	0.250157	0.125078	−	0.992147i	$-0.460082\pi$
$881$	7.42507	0.250157	0.125078	+	0.992147i	$0.460082\pi$
$882$	−68.7927	−2.31637
$883$	12.3111	0.414301	0.207151	−	0.978309i	$-0.433581\pi$
$883$	12.3111	0.414301	0.207151	+	0.978309i	$0.433581\pi$
$884$	12.4793	0.419725
$885$	−6.09876	−0.205008
$886$	1.99702	0.0670911
$887$	−41.9694	−1.40919	−0.704597	−	0.709608i	$-0.748872\pi$
$887$	−41.9694	−1.40919	−0.704597	+	0.709608i	$0.748872\pi$
$888$	43.7318	1.46754
$889$	−52.5776	−1.76340
$890$	−7.90044	−0.264823
$891$	−1.25617	−0.0420832
$892$	11.7620	0.393820
$893$	−1.89691	−0.0634778
$894$	22.1929	0.742241
$895$	5.90976	0.197541
$896$	20.0175	0.668738
$897$	51.4560	1.71807
$898$	−24.8969	−0.830820
$899$	14.4481	0.481872
$900$	−5.42597	−0.180866
$901$	25.7611	0.858228
$902$	0.599121	0.0199486
$903$	−141.623	−4.71293
$904$	−18.4332	−0.613079
$905$	−15.6762	−0.521095
$906$	55.3358	1.83841
$907$	45.2536	1.50262	0.751311	−	0.659948i	$-0.229422\pi$
$907$	45.2536	1.50262	0.751311	+	0.659948i	$0.229422\pi$
$908$	−17.0626	−0.566244
$909$	−25.5006	−0.845800
$910$	23.0836	0.765213
$911$	−3.49391	−0.115758	−0.0578792	−	0.998324i	$-0.518434\pi$
$911$	−3.49391	−0.115758	−0.0578792	+	0.998324i	$0.518434\pi$
$912$	−1.23893	−0.0410251
$913$	−14.3491	−0.474885
$914$	20.6716	0.683755
$915$	16.2807	0.538223
$916$	−31.9175	−1.05458
$917$	3.76783	0.124425
$918$	−12.3123	−0.406365
$919$	−17.2575	−0.569271	−0.284636	−	0.958636i	$-0.591873\pi$
$919$	−17.2575	−0.569271	−0.284636	+	0.958636i	$0.591873\pi$
$920$	10.2847	0.339075
$921$	−35.9040	−1.18308
$922$	−3.68875	−0.121483
$923$	−20.3821	−0.670886
$924$	−14.0689	−0.462834
$925$	−5.21880	−0.171593
$926$	−14.9603	−0.491627
$927$	−56.2318	−1.84689
$928$	7.87700	0.258575
$929$	−20.7923	−0.682172	−0.341086	−	0.940032i	$-0.610795\pi$
$929$	−20.7923	−0.682172	−0.341086	+	0.940032i	$0.610795\pi$
$930$	26.2430	0.860540
$931$	−9.07756	−0.297505
$932$	−15.5249	−0.508533
$933$	20.8798	0.683573
$934$	17.0264	0.557122
$935$	−2.22036	−0.0726137
$936$	77.6653	2.53857
$937$	36.0427	1.17746	0.588732	−	0.808328i	$-0.299627\pi$
$937$	36.0427	1.17746	0.588732	+	0.808328i	$0.299627\pi$
$938$	−5.16240	−0.168558
$939$	−38.5767	−1.25890
$940$	3.20138	0.104418
$941$	−53.2891	−1.73718	−0.868588	−	0.495535i	$-0.834972\pi$
$941$	−53.2891	−1.73718	−0.868588	+	0.495535i	$0.834972\pi$
$942$	16.9839	0.553365
$943$	−2.17016	−0.0706700
$944$	1.47286	0.0479374
$945$	26.5931	0.865074
$946$	10.4171	0.338691
$947$	53.1126	1.72593	0.862963	−	0.505267i	$-0.168606\pi$
$947$	53.1126	1.72593	0.862963	+	0.505267i	$0.168606\pi$
$948$	25.8457	0.839430
$949$	−5.21688	−0.169347
$950$	0.613176	0.0198941
$951$	61.3605	1.98975
$952$	−30.2338	−0.979884
$953$	−49.0272	−1.58815	−0.794073	−	0.607823i	$-0.792043\pi$
$953$	−49.0272	−1.58815	−0.794073	+	0.607823i	$0.792043\pi$
$954$	56.1281	1.81721
$955$	−24.7838	−0.801985
$956$	14.5250	0.469771
$957$	−4.24991	−0.137380
$958$	−0.393563	−0.0127155
$959$	52.5866	1.69811
$960$	18.1890	0.587049
$961$	61.8809	1.99616
$962$	26.1517	0.843164
$963$	−52.3085	−1.68562
$964$	9.89582	0.318723
$965$	−6.45602	−0.207827
$966$	−43.6433	−1.40420
$967$	−48.7044	−1.56623	−0.783115	−	0.621877i	$-0.786370\pi$
$967$	−48.7044	−1.56623	−0.783115	+	0.621877i	$0.786370\pi$
$968$	2.95594	0.0950075
$969$	−4.01811	−0.129080
$970$	−16.1548	−0.518699
$971$	13.3535	0.428533	0.214267	−	0.976775i	$-0.431264\pi$
$971$	13.3535	0.428533	0.214267	+	0.976775i	$0.431264\pi$
$972$	−14.8218	−0.475411
$973$	−69.0319	−2.21306
$974$	−25.7394	−0.824745
$975$	−14.7891	−0.473630
$976$	−3.93180	−0.125854
$977$	−2.63089	−0.0841695	−0.0420848	−	0.999114i	$-0.513400\pi$
$977$	−2.63089	−0.0841695	−0.0420848	+	0.999114i	$0.513400\pi$
$978$	9.79246	0.313128
$979$	8.22493	0.262870
$980$	15.3200	0.489380
$981$	−43.5312	−1.38984
$982$	−22.7528	−0.726072
$983$	−13.8236	−0.440904	−0.220452	−	0.975398i	$-0.570753\pi$
$983$	−13.8236	−0.440904	−0.220452	+	0.975398i	$0.570753\pi$
$984$	−5.22664	−0.166619
$985$	25.2634	0.804959
$986$	−3.19736	−0.101825
$987$	−38.8048	−1.23517
$988$	3.58785	0.114145
$989$	−37.7333	−1.19985
$990$	−4.83771	−0.153752
$991$	−14.8076	−0.470381	−0.235190	−	0.971949i	$-0.575571\pi$
$991$	−14.8076	−0.470381	−0.235190	+	0.971949i	$0.575571\pi$
$992$	50.6379	1.60775
$993$	48.9360	1.55294
$994$	17.2875	0.548325
$995$	1.48435	0.0470572
$996$	43.8240	1.38862
$997$	20.4057	0.646254	0.323127	−	0.946356i	$-0.395266\pi$
$997$	20.4057	0.646254	0.323127	+	0.946356i	$0.395266\pi$
$998$	37.0429	1.17257
$999$	30.1277	0.953198

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4015.2.a.g.1.13	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4015.2.a.g.1.13	✓	32	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:	\( N \)	\(=\)	\( 4015 = 5 \cdot 11 \cdot 73 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4015.a (trivial)

\(f(q)\)	\(=\)	\(q-0.960547 q^{2} -2.83486 q^{3} -1.07735 q^{4} -1.00000 q^{5} +2.72301 q^{6} +4.60653 q^{7} +2.95594 q^{8} +5.03641 q^{9} +O(q^{10})\)	\(q-0.960547 q^{2} -2.83486 q^{3} -1.07735 q^{4} -1.00000 q^{5} +2.72301 q^{6} +4.60653 q^{7} +2.95594 q^{8} +5.03641 q^{9} +0.960547 q^{10} -1.00000 q^{11} +3.05413 q^{12} +5.21688 q^{13} -4.42479 q^{14} +2.83486 q^{15} -0.684620 q^{16} -2.22036 q^{17} -4.83771 q^{18} -0.638361 q^{19} +1.07735 q^{20} -13.0588 q^{21} +0.960547 q^{22} -3.47932 q^{23} -8.37966 q^{24} +1.00000 q^{25} -5.01106 q^{26} -5.77292 q^{27} -4.96284 q^{28} -1.49916 q^{29} -2.72301 q^{30} -9.63747 q^{31} -5.25427 q^{32} +2.83486 q^{33} +2.13276 q^{34} -4.60653 q^{35} -5.42597 q^{36} -5.21880 q^{37} +0.613176 q^{38} -14.7891 q^{39} -2.95594 q^{40} +0.623729 q^{41} +12.5436 q^{42} +10.8450 q^{43} +1.07735 q^{44} -5.03641 q^{45} +3.34205 q^{46} +2.97153 q^{47} +1.94080 q^{48} +14.2201 q^{49} -0.960547 q^{50} +6.29441 q^{51} -5.62040 q^{52} -11.6022 q^{53} +5.54516 q^{54} +1.00000 q^{55} +13.6166 q^{56} +1.80966 q^{57} +1.44002 q^{58} -2.15135 q^{59} -3.05413 q^{60} +5.74304 q^{61} +9.25725 q^{62} +23.2003 q^{63} +6.41621 q^{64} -5.21688 q^{65} -2.72301 q^{66} +1.16670 q^{67} +2.39211 q^{68} +9.86338 q^{69} +4.42479 q^{70} -3.90696 q^{71} +14.8873 q^{72} -1.00000 q^{73} +5.01290 q^{74} -2.83486 q^{75} +0.687738 q^{76} -4.60653 q^{77} +14.2056 q^{78} +8.46255 q^{79} +0.684620 q^{80} +1.25617 q^{81} -0.599121 q^{82} +14.3491 q^{83} +14.0689 q^{84} +2.22036 q^{85} -10.4171 q^{86} +4.24991 q^{87} -2.95594 q^{88} -8.22493 q^{89} +4.83771 q^{90} +24.0317 q^{91} +3.74845 q^{92} +27.3208 q^{93} -2.85430 q^{94} +0.638361 q^{95} +14.8951 q^{96} -16.8183 q^{97} -13.6591 q^{98} -5.03641 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 5 q^{2} - 7 q^{3} + 37 q^{4} - 32 q^{5} - 3 q^{6} - 18 q^{8} + 29 q^{9}+O(q^{10}) \) 32 * q - 5 * q^2 - 7 * q^3 + 37 * q^4 - 32 * q^5 - 3 * q^6 - 18 * q^8 + 29 * q^9	\( 32 q - 5 q^{2} - 7 q^{3} + 37 q^{4} - 32 q^{5} - 3 q^{6} - 18 q^{8} + 29 q^{9} + 5 q^{10} - 32 q^{11} - 24 q^{12} - q^{13} - 5 q^{14} + 7 q^{15} + 47 q^{16} - 30 q^{17} - 11 q^{18} + 16 q^{19} - 37 q^{20} + q^{21} + 5 q^{22} - 26 q^{23} - 21 q^{24} + 32 q^{25} - q^{26} - 31 q^{27} - 24 q^{28} - 10 q^{29} + 3 q^{30} - 2 q^{31} - 31 q^{32} + 7 q^{33} - 14 q^{34} + 38 q^{36} - 28 q^{37} - 63 q^{38} - 2 q^{39} + 18 q^{40} - 62 q^{41} - 9 q^{42} + 8 q^{43} - 37 q^{44} - 29 q^{45} + 19 q^{46} - 21 q^{47} - 79 q^{48} + 34 q^{49} - 5 q^{50} + 17 q^{51} + 15 q^{52} - 32 q^{53} + 5 q^{54} + 32 q^{55} - 52 q^{56} - 57 q^{57} + 4 q^{58} - 37 q^{59} + 24 q^{60} + 15 q^{61} - 22 q^{62} + 5 q^{63} + 70 q^{64} + q^{65} + 3 q^{66} - 42 q^{67} - 81 q^{68} - 8 q^{69} + 5 q^{70} - 40 q^{71} - 27 q^{72} - 32 q^{73} - 17 q^{74} - 7 q^{75} + 21 q^{76} - 105 q^{78} + 18 q^{79} - 47 q^{80} + 12 q^{81} - 70 q^{82} - 26 q^{83} + 22 q^{84} + 30 q^{85} - 45 q^{86} - 18 q^{87} + 18 q^{88} - 83 q^{89} + 11 q^{90} - 18 q^{91} - 73 q^{92} - 68 q^{93} + 56 q^{94} - 16 q^{95} - 35 q^{96} - 99 q^{97} - 61 q^{98} - 29 q^{99}+O(q^{100}) \) 32 * q - 5 * q^2 - 7 * q^3 + 37 * q^4 - 32 * q^5 - 3 * q^6 - 18 * q^8 + 29 * q^9 + 5 * q^10 - 32 * q^11 - 24 * q^12 - q^13 - 5 * q^14 + 7 * q^15 + 47 * q^16 - 30 * q^17 - 11 * q^18 + 16 * q^19 - 37 * q^20 + q^21 + 5 * q^22 - 26 * q^23 - 21 * q^24 + 32 * q^25 - q^26 - 31 * q^27 - 24 * q^28 - 10 * q^29 + 3 * q^30 - 2 * q^31 - 31 * q^32 + 7 * q^33 - 14 * q^34 + 38 * q^36 - 28 * q^37 - 63 * q^38 - 2 * q^39 + 18 * q^40 - 62 * q^41 - 9 * q^42 + 8 * q^43 - 37 * q^44 - 29 * q^45 + 19 * q^46 - 21 * q^47 - 79 * q^48 + 34 * q^49 - 5 * q^50 + 17 * q^51 + 15 * q^52 - 32 * q^53 + 5 * q^54 + 32 * q^55 - 52 * q^56 - 57 * q^57 + 4 * q^58 - 37 * q^59 + 24 * q^60 + 15 * q^61 - 22 * q^62 + 5 * q^63 + 70 * q^64 + q^65 + 3 * q^66 - 42 * q^67 - 81 * q^68 - 8 * q^69 + 5 * q^70 - 40 * q^71 - 27 * q^72 - 32 * q^73 - 17 * q^74 - 7 * q^75 + 21 * q^76 - 105 * q^78 + 18 * q^79 - 47 * q^80 + 12 * q^81 - 70 * q^82 - 26 * q^83 + 22 * q^84 + 30 * q^85 - 45 * q^86 - 18 * q^87 + 18 * q^88 - 83 * q^89 + 11 * q^90 - 18 * q^91 - 73 * q^92 - 68 * q^93 + 56 * q^94 - 16 * q^95 - 35 * q^96 - 99 * q^97 - 61 * q^98 - 29 * q^99

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