LMFDB - Embedded newform 4015.2.a.g.1.1

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			1.1
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)

$f(q)$	$=$	$q-2.80101 q^{2} +2.07520 q^{3} +5.84563 q^{4} -1.00000 q^{5} -5.81265 q^{6} +2.07490 q^{7} -10.7716 q^{8} +1.30645 q^{9} +O(q^{10})$	\(q-2.80101 q^{2} +2.07520 q^{3} +5.84563 q^{4} -1.00000 q^{5} -5.81265 q^{6} +2.07490 q^{7} -10.7716 q^{8} +1.30645 q^{9} +2.80101 q^{10} -1.00000 q^{11} +12.1308 q^{12} +1.98267 q^{13} -5.81181 q^{14} -2.07520 q^{15} +18.4801 q^{16} +3.61126 q^{17} -3.65938 q^{18} +2.78330 q^{19} -5.84563 q^{20} +4.30583 q^{21} +2.80101 q^{22} -7.33612 q^{23} -22.3533 q^{24} +1.00000 q^{25} -5.55347 q^{26} -3.51445 q^{27} +12.1291 q^{28} -6.72797 q^{29} +5.81265 q^{30} -5.57037 q^{31} -30.2197 q^{32} -2.07520 q^{33} -10.1152 q^{34} -2.07490 q^{35} +7.63705 q^{36} -10.3090 q^{37} -7.79603 q^{38} +4.11444 q^{39} +10.7716 q^{40} +1.87474 q^{41} -12.0607 q^{42} -5.39574 q^{43} -5.84563 q^{44} -1.30645 q^{45} +20.5485 q^{46} -4.68119 q^{47} +38.3499 q^{48} -2.69479 q^{49} -2.80101 q^{50} +7.49409 q^{51} +11.5900 q^{52} +6.09265 q^{53} +9.84398 q^{54} +1.00000 q^{55} -22.3501 q^{56} +5.77590 q^{57} +18.8451 q^{58} -10.2241 q^{59} -12.1308 q^{60} -8.88569 q^{61} +15.6026 q^{62} +2.71076 q^{63} +47.6852 q^{64} -1.98267 q^{65} +5.81265 q^{66} -7.41154 q^{67} +21.1101 q^{68} -15.2239 q^{69} +5.81181 q^{70} +4.59630 q^{71} -14.0726 q^{72} -1.00000 q^{73} +28.8755 q^{74} +2.07520 q^{75} +16.2701 q^{76} -2.07490 q^{77} -11.5246 q^{78} +12.2712 q^{79} -18.4801 q^{80} -11.2125 q^{81} -5.25115 q^{82} -3.41707 q^{83} +25.1703 q^{84} -3.61126 q^{85} +15.1135 q^{86} -13.9619 q^{87} +10.7716 q^{88} -0.0234421 q^{89} +3.65938 q^{90} +4.11385 q^{91} -42.8842 q^{92} -11.5596 q^{93} +13.1120 q^{94} -2.78330 q^{95} -62.7118 q^{96} +5.51740 q^{97} +7.54812 q^{98} -1.30645 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.80101	−1.98061	−0.990305	−	0.138911i	$-0.955640\pi$
$2$	−2.80101	−1.98061	−0.990305	+	0.138911i	$0.955640\pi$
$3$	2.07520	1.19812	0.599059	−	0.800705i	$-0.295542\pi$
$3$	2.07520	1.19812	0.599059	+	0.800705i	$0.295542\pi$
$4$	5.84563	2.92281
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−5.81265	−2.37300
$7$	2.07490	0.784239	0.392119	−	0.919914i	$-0.371742\pi$
$7$	2.07490	0.784239	0.392119	+	0.919914i	$0.371742\pi$
$8$	−10.7716	−3.80835
$9$	1.30645	0.435485
$10$	2.80101	0.885756
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	12.1308	3.50187
$13$	1.98267	0.549894	0.274947	−	0.961459i	$-0.411340\pi$
$13$	1.98267	0.549894	0.274947	+	0.961459i	$0.411340\pi$
$14$	−5.81181	−1.55327
$15$	−2.07520	−0.535814
$16$	18.4801	4.62003
$17$	3.61126	0.875860	0.437930	−	0.899009i	$-0.355712\pi$
$17$	3.61126	0.875860	0.437930	+	0.899009i	$0.355712\pi$
$18$	−3.65938	−0.862525
$19$	2.78330	0.638532	0.319266	−	0.947665i	$-0.396564\pi$
$19$	2.78330	0.638532	0.319266	+	0.947665i	$0.396564\pi$
$20$	−5.84563	−1.30712
$21$	4.30583	0.939610
$22$	2.80101	0.597176
$23$	−7.33612	−1.52969	−0.764843	−	0.644217i	$-0.777183\pi$
$23$	−7.33612	−1.52969	−0.764843	+	0.644217i	$0.777183\pi$
$24$	−22.3533	−4.56284
$25$	1.00000	0.200000
$26$	−5.55347	−1.08913
$27$	−3.51445	−0.676355
$28$	12.1291	2.29218
$29$	−6.72797	−1.24935	−0.624676	−	0.780884i	$-0.714769\pi$
$29$	−6.72797	−1.24935	−0.624676	+	0.780884i	$0.714769\pi$
$30$	5.81265	1.06124
$31$	−5.57037	−1.00047	−0.500234	−	0.865890i	$-0.666753\pi$
$31$	−5.57037	−1.00047	−0.500234	+	0.865890i	$0.666753\pi$
$32$	−30.2197	−5.34213
$33$	−2.07520	−0.361246
$34$	−10.1152	−1.73474
$35$	−2.07490	−0.350722
$36$	7.63705	1.27284
$37$	−10.3090	−1.69479	−0.847393	−	0.530966i	$-0.821829\pi$
$37$	−10.3090	−1.69479	−0.847393	+	0.530966i	$0.821829\pi$
$38$	−7.79603	−1.26468
$39$	4.11444	0.658838
$40$	10.7716	1.70314
$41$	1.87474	0.292785	0.146392	−	0.989227i	$-0.453234\pi$
$41$	1.87474	0.292785	0.146392	+	0.989227i	$0.453234\pi$
$42$	−12.0607	−1.86100
$43$	−5.39574	−0.822842	−0.411421	−	0.911445i	$-0.634967\pi$
$43$	−5.39574	−0.822842	−0.411421	+	0.911445i	$0.634967\pi$
$44$	−5.84563	−0.881262
$45$	−1.30645	−0.194755
$46$	20.5485	3.02971
$47$	−4.68119	−0.682821	−0.341411	−	0.939914i	$-0.610905\pi$
$47$	−4.68119	−0.682821	−0.341411	+	0.939914i	$0.610905\pi$
$48$	38.3499	5.53534
$49$	−2.69479	−0.384970
$50$	−2.80101	−0.396122
$51$	7.49409	1.04938
$52$	11.5900	1.60724
$53$	6.09265	0.836890	0.418445	−	0.908242i	$-0.362575\pi$
$53$	6.09265	0.836890	0.418445	+	0.908242i	$0.362575\pi$
$54$	9.84398	1.33960
$55$	1.00000	0.134840
$56$	−22.3501	−2.98665
$57$	5.77590	0.765036
$58$	18.8451	2.47448
$59$	−10.2241	−1.33106	−0.665532	−	0.746369i	$-0.731795\pi$
$59$	−10.2241	−1.33106	−0.665532	+	0.746369i	$0.731795\pi$
$60$	−12.1308	−1.56609
$61$	−8.88569	−1.13770	−0.568848	−	0.822442i	$-0.692611\pi$
$61$	−8.88569	−1.13770	−0.568848	+	0.822442i	$0.692611\pi$
$62$	15.6026	1.98154
$63$	2.71076	0.341524
$64$	47.6852	5.96065
$65$	−1.98267	−0.245920
$66$	5.81265	0.715487
$67$	−7.41154	−0.905463	−0.452732	−	0.891647i	$-0.649550\pi$
$67$	−7.41154	−0.905463	−0.452732	+	0.891647i	$0.649550\pi$
$68$	21.1101	2.55998
$69$	−15.2239	−1.83274
$70$	5.81181	0.694644
$71$	4.59630	0.545480	0.272740	−	0.962088i	$-0.412070\pi$
$71$	4.59630	0.545480	0.272740	+	0.962088i	$0.412070\pi$
$72$	−14.0726	−1.65848
$73$	−1.00000	−0.117041
$73$	−1.00000	−0.117041
$74$	28.8755	3.35671
$75$	2.07520	0.239623
$76$	16.2701	1.86631
$77$	−2.07490	−0.236457
$78$	−11.5246	−1.30490
$79$	12.2712	1.38062	0.690309	−	0.723515i	$-0.257475\pi$
$79$	12.2712	1.38062	0.690309	+	0.723515i	$0.257475\pi$
$80$	−18.4801	−2.06614
$81$	−11.2125	−1.24584
$82$	−5.25115	−0.579892
$83$	−3.41707	−0.375072	−0.187536	−	0.982258i	$-0.560050\pi$
$83$	−3.41707	−0.375072	−0.187536	+	0.982258i	$0.560050\pi$
$84$	25.1703	2.74631
$85$	−3.61126	−0.391696
$86$	15.1135	1.62973
$87$	−13.9619	−1.49687
$88$	10.7716	1.14826
$89$	−0.0234421	−0.00248485	−0.00124243	−	0.999999i	$-0.500395\pi$
$89$	−0.0234421	−0.00248485	−0.00124243	+	0.999999i	$0.500395\pi$
$90$	3.65938	0.385733
$91$	4.11385	0.431248
$92$	−42.8842	−4.47099
$93$	−11.5596	−1.19868
$94$	13.1120	1.35240
$95$	−2.78330	−0.285560
$96$	−62.7118	−6.40050
$97$	5.51740	0.560207	0.280104	−	0.959970i	$-0.409631\pi$
$97$	5.51740	0.560207	0.280104	+	0.959970i	$0.409631\pi$
$98$	7.54812	0.762475
$99$	−1.30645	−0.131304
$100$	5.84563	0.584563
$101$	4.00632	0.398643	0.199322	−	0.979934i	$-0.436126\pi$
$101$	4.00632	0.398643	0.199322	+	0.979934i	$0.436126\pi$
$102$	−20.9910	−2.07842
$103$	4.21681	0.415495	0.207747	−	0.978183i	$-0.433387\pi$
$103$	4.21681	0.415495	0.207747	+	0.978183i	$0.433387\pi$
$104$	−21.3566	−2.09419
$105$	−4.30583	−0.420206
$106$	−17.0655	−1.65755
$107$	−0.668394	−0.0646161	−0.0323081	−	0.999478i	$-0.510286\pi$
$107$	−0.668394	−0.0646161	−0.0323081	+	0.999478i	$0.510286\pi$
$108$	−20.5441	−1.97686
$109$	3.30981	0.317023	0.158511	−	0.987357i	$-0.449331\pi$
$109$	3.30981	0.317023	0.158511	+	0.987357i	$0.449331\pi$
$110$	−2.80101	−0.267065
$111$	−21.3932	−2.03055
$112$	38.3444	3.62321
$113$	−5.92966	−0.557815	−0.278908	−	0.960318i	$-0.589972\pi$
$113$	−5.92966	−0.557815	−0.278908	+	0.960318i	$0.589972\pi$
$114$	−16.1783	−1.51524
$115$	7.33612	0.684096
$116$	−39.3292	−3.65163
$117$	2.59027	0.239471
$118$	28.6378	2.63632
$119$	7.49301	0.686883
$120$	22.3533	2.04057
$121$	1.00000	0.0909091
$122$	24.8889	2.25333
$123$	3.89045	0.350790
$124$	−32.5623	−2.92418
$125$	−1.00000	−0.0894427
$126$	−7.59286	−0.676426
$127$	15.7607	1.39854	0.699269	−	0.714859i	$-0.253509\pi$
$127$	15.7607	1.39854	0.699269	+	0.714859i	$0.253509\pi$
$128$	−73.1271	−6.46358
$129$	−11.1972	−0.985862
$130$	5.55347	0.487072
$131$	0.0431697	0.00377176	0.00188588	−	0.999998i	$-0.499400\pi$
$131$	0.0431697	0.00377176	0.00188588	+	0.999998i	$0.499400\pi$
$132$	−12.1308	−1.05585
$133$	5.77506	0.500762
$134$	20.7597	1.79337
$135$	3.51445	0.302475
$136$	−38.8992	−3.33558
$137$	−18.1506	−1.55071	−0.775357	−	0.631524i	$-0.782430\pi$
$137$	−18.1506	−1.55071	−0.775357	+	0.631524i	$0.782430\pi$
$138$	42.6422	3.62995
$139$	10.9468	0.928493	0.464246	−	0.885706i	$-0.346325\pi$
$139$	10.9468	0.928493	0.464246	+	0.885706i	$0.346325\pi$
$140$	−12.1291	−1.02510
$141$	−9.71440	−0.818100
$142$	−12.8742	−1.08038
$143$	−1.98267	−0.165799
$144$	24.1434	2.01195
$145$	6.72797	0.558728
$146$	2.80101	0.231813
$147$	−5.59222	−0.461239
$148$	−60.2625	−4.95354
$149$	7.35267	0.602354	0.301177	−	0.953568i	$-0.402620\pi$
$149$	7.35267	0.602354	0.301177	+	0.953568i	$0.402620\pi$
$150$	−5.81265	−0.474600
$151$	−12.1490	−0.988670	−0.494335	−	0.869271i	$-0.664588\pi$
$151$	−12.1490	−0.988670	−0.494335	+	0.869271i	$0.664588\pi$
$152$	−29.9806	−2.43175
$153$	4.71795	0.381423
$154$	5.81181	0.468329
$155$	5.57037	0.447423
$156$	24.0515	1.92566
$157$	−12.0311	−0.960185	−0.480092	−	0.877218i	$-0.659397\pi$
$157$	−12.0311	−0.960185	−0.480092	+	0.877218i	$0.659397\pi$
$158$	−34.3717	−2.73446
$159$	12.6435	1.00269
$160$	30.2197	2.38907
$161$	−15.2217	−1.19964
$162$	31.4064	2.46752
$163$	−11.5012	−0.900847	−0.450423	−	0.892815i	$-0.648727\pi$
$163$	−11.5012	−0.900847	−0.450423	+	0.892815i	$0.648727\pi$
$164$	10.9590	0.855756
$165$	2.07520	0.161554
$166$	9.57124	0.742872
$167$	−10.7908	−0.835015	−0.417507	−	0.908674i	$-0.637096\pi$
$167$	−10.7908	−0.835015	−0.417507	+	0.908674i	$0.637096\pi$
$168$	−46.3808	−3.57836
$169$	−9.06901	−0.697616
$170$	10.1152	0.775797
$171$	3.63625	0.278071
$172$	−31.5415	−2.40502
$173$	4.27727	0.325195	0.162597	−	0.986692i	$-0.448013\pi$
$173$	4.27727	0.325195	0.162597	+	0.986692i	$0.448013\pi$
$174$	39.1073	2.96472
$175$	2.07490	0.156848
$176$	−18.4801	−1.39299
$177$	−21.2171	−1.59477
$178$	0.0656613	0.00492153
$179$	21.5202	1.60849	0.804246	−	0.594297i	$-0.202569\pi$
$179$	21.5202	1.60849	0.804246	+	0.594297i	$0.202569\pi$
$180$	−7.63705	−0.569232
$181$	13.0327	0.968715	0.484358	−	0.874870i	$-0.339053\pi$
$181$	13.0327	0.968715	0.484358	+	0.874870i	$0.339053\pi$
$182$	−11.5229	−0.854134
$183$	−18.4396	−1.36309
$184$	79.0219	5.82557
$185$	10.3090	0.757931
$186$	32.3786	2.37411
$187$	−3.61126	−0.264082
$188$	−27.3645	−1.99576
$189$	−7.29213	−0.530424
$190$	7.79603	0.565583
$191$	21.2892	1.54044	0.770218	−	0.637781i	$-0.220148\pi$
$191$	21.2892	1.54044	0.770218	+	0.637781i	$0.220148\pi$
$192$	98.9563	7.14155
$193$	−17.5538	−1.26355	−0.631774	−	0.775152i	$-0.717673\pi$
$193$	−17.5538	−1.26355	−0.631774	+	0.775152i	$0.717673\pi$
$194$	−15.4543	−1.10955
$195$	−4.11444	−0.294641
$196$	−15.7527	−1.12520
$197$	9.49385	0.676409	0.338204	−	0.941073i	$-0.390180\pi$
$197$	9.49385	0.676409	0.338204	+	0.941073i	$0.390180\pi$
$198$	3.65938	0.260061
$199$	−3.35247	−0.237650	−0.118825	−	0.992915i	$-0.537913\pi$
$199$	−3.35247	−0.237650	−0.118825	+	0.992915i	$0.537913\pi$
$200$	−10.7716	−0.761669
$201$	−15.3804	−1.08485
$202$	−11.2217	−0.789557
$203$	−13.9599	−0.979791
$204$	43.8077	3.06715
$205$	−1.87474	−0.130937
$206$	−11.8113	−0.822932
$207$	−9.58430	−0.666155
$208$	36.6400	2.54053
$209$	−2.78330	−0.192525
$210$	12.0607	0.832265
$211$	−16.1788	−1.11379	−0.556897	−	0.830582i	$-0.688008\pi$
$211$	−16.1788	−1.11379	−0.556897	+	0.830582i	$0.688008\pi$
$212$	35.6154	2.44607
$213$	9.53823	0.653549
$214$	1.87218	0.127979
$215$	5.39574	0.367986
$216$	37.8563	2.57579
$217$	−11.5580	−0.784606
$218$	−9.27081	−0.627898
$219$	−2.07520	−0.140229
$220$	5.84563	0.394112
$221$	7.15995	0.481630
$222$	59.9224	4.02173
$223$	4.10030	0.274577	0.137288	−	0.990531i	$-0.456161\pi$
$223$	4.10030	0.274577	0.137288	+	0.990531i	$0.456161\pi$
$224$	−62.7028	−4.18951
$225$	1.30645	0.0870969
$226$	16.6090	1.10481
$227$	−19.1401	−1.27037	−0.635186	−	0.772359i	$-0.719077\pi$
$227$	−19.1401	−1.27037	−0.635186	+	0.772359i	$0.719077\pi$
$228$	33.7638	2.23606
$229$	23.6834	1.56504	0.782522	−	0.622623i	$-0.213933\pi$
$229$	23.6834	1.56504	0.782522	+	0.622623i	$0.213933\pi$
$230$	−20.5485	−1.35493
$231$	−4.30583	−0.283303
$232$	72.4712	4.75797
$233$	−8.80474	−0.576818	−0.288409	−	0.957507i	$-0.593126\pi$
$233$	−8.80474	−0.576818	−0.288409	+	0.957507i	$0.593126\pi$
$234$	−7.25536	−0.474298
$235$	4.68119	0.305367
$236$	−59.7663	−3.89045
$237$	25.4652	1.65414
$238$	−20.9880	−1.36045
$239$	18.6365	1.20549	0.602746	−	0.797933i	$-0.294073\pi$
$239$	18.6365	1.20549	0.602746	+	0.797933i	$0.294073\pi$
$240$	−38.3499	−2.47548
$241$	−14.3625	−0.925167	−0.462584	−	0.886576i	$-0.653078\pi$
$241$	−14.3625	−0.925167	−0.462584	+	0.886576i	$0.653078\pi$
$242$	−2.80101	−0.180055
$243$	−12.7249	−0.816304
$244$	−51.9425	−3.32528
$245$	2.69479	0.172164
$246$	−10.8972	−0.694779
$247$	5.51836	0.351125
$248$	60.0020	3.81013
$249$	−7.09111	−0.449381
$250$	2.80101	0.177151
$251$	28.7455	1.81440	0.907201	−	0.420698i	$-0.138215\pi$
$251$	28.7455	1.81440	0.907201	+	0.420698i	$0.138215\pi$
$252$	15.8461	0.998211
$253$	7.33612	0.461218
$254$	−44.1459	−2.76996
$255$	−7.49409	−0.469298
$256$	109.459	6.84119
$257$	−9.76511	−0.609131	−0.304565	−	0.952491i	$-0.598511\pi$
$257$	−9.76511	−0.609131	−0.304565	+	0.952491i	$0.598511\pi$
$258$	31.3635	1.95261
$259$	−21.3901	−1.32912
$260$	−11.5900	−0.718779
$261$	−8.78979	−0.544074
$262$	−0.120919	−0.00747038
$263$	−12.3297	−0.760284	−0.380142	−	0.924928i	$-0.624125\pi$
$263$	−12.3297	−0.760284	−0.380142	+	0.924928i	$0.624125\pi$
$264$	22.3533	1.37575
$265$	−6.09265	−0.374268
$266$	−16.1760	−0.991813
$267$	−0.0486470	−0.00297715
$268$	−43.3251	−2.64650
$269$	−9.45175	−0.576283	−0.288142	−	0.957588i	$-0.593037\pi$
$269$	−9.45175	−0.576283	−0.288142	+	0.957588i	$0.593037\pi$
$270$	−9.84398	−0.599086
$271$	15.1999	0.923326	0.461663	−	0.887055i	$-0.347253\pi$
$271$	15.1999	0.923326	0.461663	+	0.887055i	$0.347253\pi$
$272$	66.7365	4.04650
$273$	8.53705	0.516686
$274$	50.8400	3.07136
$275$	−1.00000	−0.0603023
$276$	−88.9933	−5.35677
$277$	−3.04248	−0.182805	−0.0914025	−	0.995814i	$-0.529135\pi$
$277$	−3.04248	−0.182805	−0.0914025	+	0.995814i	$0.529135\pi$
$278$	−30.6620	−1.83898
$279$	−7.27743	−0.435689
$280$	22.3501	1.33567
$281$	16.9505	1.01118	0.505590	−	0.862774i	$-0.331275\pi$
$281$	16.9505	1.01118	0.505590	+	0.862774i	$0.331275\pi$
$282$	27.2101	1.62034
$283$	−13.0502	−0.775756	−0.387878	−	0.921711i	$-0.626792\pi$
$283$	−13.0502	−0.775756	−0.387878	+	0.921711i	$0.626792\pi$
$284$	26.8682	1.59434
$285$	−5.77590	−0.342135
$286$	5.55347	0.328384
$287$	3.88989	0.229613
$288$	−39.4806	−2.32642
$289$	−3.95879	−0.232870
$290$	−18.8451	−1.10662
$291$	11.4497	0.671194
$292$	−5.84563	−0.342090
$293$	24.8364	1.45096	0.725478	−	0.688245i	$-0.241619\pi$
$293$	24.8364	1.45096	0.725478	+	0.688245i	$0.241619\pi$
$294$	15.6638	0.913534
$295$	10.2241	0.595270
$296$	111.044	6.45433
$297$	3.51445	0.203929
$298$	−20.5949	−1.19303
$299$	−14.5451	−0.841165
$300$	12.1308	0.700375
$301$	−11.1956	−0.645305
$302$	34.0294	1.95817
$303$	8.31391	0.477621
$304$	51.4357	2.95004
$305$	8.88569	0.508793
$306$	−13.2150	−0.755451
$307$	6.86736	0.391941	0.195970	−	0.980610i	$-0.437214\pi$
$307$	6.86736	0.391941	0.195970	+	0.980610i	$0.437214\pi$
$308$	−12.1291	−0.691120
$309$	8.75072	0.497811
$310$	−15.6026	−0.886170
$311$	−16.5491	−0.938416	−0.469208	−	0.883088i	$-0.655461\pi$
$311$	−16.5491	−0.938416	−0.469208	+	0.883088i	$0.655461\pi$
$312$	−44.3192	−2.50908
$313$	−23.1318	−1.30749	−0.653745	−	0.756715i	$-0.726803\pi$
$313$	−23.1318	−1.30749	−0.653745	+	0.756715i	$0.726803\pi$
$314$	33.6991	1.90175
$315$	−2.71076	−0.152734
$316$	71.7329	4.03529
$317$	23.7367	1.33319	0.666593	−	0.745422i	$-0.267752\pi$
$317$	23.7367	1.33319	0.666593	+	0.745422i	$0.267752\pi$
$318$	−35.4144	−1.98594
$319$	6.72797	0.376694
$320$	−47.6852	−2.66568
$321$	−1.38705	−0.0774177
$322$	42.6361	2.37602
$323$	10.0512	0.559265
$324$	−65.5444	−3.64135
$325$	1.98267	0.109979
$326$	32.2150	1.78423
$327$	6.86853	0.379830
$328$	−20.1940	−1.11503
$329$	−9.71300	−0.535495
$330$	−5.81265	−0.319976
$331$	−25.0858	−1.37884	−0.689419	−	0.724362i	$-0.742134\pi$
$331$	−25.0858	−1.37884	−0.689419	+	0.724362i	$0.742134\pi$
$332$	−19.9749	−1.09627
$333$	−13.4682	−0.738053
$334$	30.2250	1.65384
$335$	7.41154	0.404935
$336$	79.5723	4.34103
$337$	−23.5974	−1.28543	−0.642715	−	0.766105i	$-0.722192\pi$
$337$	−23.5974	−1.28543	−0.642715	+	0.766105i	$0.722192\pi$
$338$	25.4024	1.38171
$339$	−12.3052	−0.668328
$340$	−21.1101	−1.14486
$341$	5.57037	0.301653
$342$	−10.1852	−0.550750
$343$	−20.1157	−1.08615
$344$	58.1209	3.13367
$345$	15.2239	0.819628
$346$	−11.9807	−0.644084
$347$	33.7259	1.81050	0.905250	−	0.424880i	$-0.139684\pi$
$347$	33.7259	1.81050	0.905250	+	0.424880i	$0.139684\pi$
$348$	−81.6160	−4.37508
$349$	8.26546	0.442440	0.221220	−	0.975224i	$-0.428996\pi$
$349$	8.26546	0.442440	0.221220	+	0.975224i	$0.428996\pi$
$350$	−5.81181	−0.310654
$351$	−6.96799	−0.371924
$352$	30.2197	1.61071
$353$	4.65859	0.247952	0.123976	−	0.992285i	$-0.460435\pi$
$353$	4.65859	0.247952	0.123976	+	0.992285i	$0.460435\pi$
$354$	59.4291	3.15862
$355$	−4.59630	−0.243946
$356$	−0.137034	−0.00726277
$357$	15.5495	0.822966
$358$	−60.2781	−3.18579
$359$	0.775040	0.0409051	0.0204525	−	0.999791i	$-0.493489\pi$
$359$	0.775040	0.0409051	0.0204525	+	0.999791i	$0.493489\pi$
$360$	14.0726	0.741693
$361$	−11.2533	−0.592277
$362$	−36.5048	−1.91865
$363$	2.07520	0.108920
$364$	24.0480	1.26046
$365$	1.00000	0.0523424
$366$	51.6494	2.69976
$367$	26.7609	1.39691	0.698453	−	0.715656i	$-0.253872\pi$
$367$	26.7609	1.39691	0.698453	+	0.715656i	$0.253872\pi$
$368$	−135.572	−7.06720
$369$	2.44926	0.127503
$370$	−28.8755	−1.50117
$371$	12.6416	0.656321
$372$	−67.5733	−3.50351
$373$	−19.2335	−0.995871	−0.497936	−	0.867214i	$-0.665908\pi$
$373$	−19.2335	−0.995871	−0.497936	+	0.867214i	$0.665908\pi$
$374$	10.1152	0.523043
$375$	−2.07520	−0.107163
$376$	50.4240	2.60042
$377$	−13.3394	−0.687012
$378$	20.4253	1.05056
$379$	23.5187	1.20807	0.604037	−	0.796956i	$-0.293558\pi$
$379$	23.5187	1.20807	0.604037	+	0.796956i	$0.293558\pi$
$380$	−16.2701	−0.834640
$381$	32.7066	1.67561
$382$	−59.6313	−3.05100
$383$	−37.3859	−1.91033	−0.955164	−	0.296077i	$-0.904321\pi$
$383$	−37.3859	−1.91033	−0.955164	+	0.296077i	$0.904321\pi$
$384$	−151.753	−7.74413
$385$	2.07490	0.105747
$386$	49.1682	2.50260
$387$	−7.04929	−0.358335
$388$	32.2527	1.63738
$389$	−21.4278	−1.08643	−0.543217	−	0.839592i	$-0.682794\pi$
$389$	−21.4278	−1.08643	−0.543217	+	0.839592i	$0.682794\pi$
$390$	11.5246	0.583569
$391$	−26.4926	−1.33979
$392$	29.0273	1.46610
$393$	0.0895858	0.00451901
$394$	−26.5923	−1.33970
$395$	−12.2712	−0.617431
$396$	−7.63705	−0.383776
$397$	−26.1371	−1.31178	−0.655891	−	0.754855i	$-0.727707\pi$
$397$	−26.1371	−1.31178	−0.655891	+	0.754855i	$0.727707\pi$
$398$	9.39029	0.470693
$399$	11.9844	0.599971
$400$	18.4801	0.924006
$401$	−8.37353	−0.418154	−0.209077	−	0.977899i	$-0.567046\pi$
$401$	−8.37353	−0.418154	−0.209077	+	0.977899i	$0.567046\pi$
$402$	43.0806	2.14867
$403$	−11.0442	−0.550152
$404$	23.4194	1.16516
$405$	11.2125	0.557156
$406$	39.1017	1.94058
$407$	10.3090	0.510997
$408$	−80.7235	−3.99641
$409$	20.3668	1.00707	0.503536	−	0.863974i	$-0.332032\pi$
$409$	20.3668	1.00707	0.503536	+	0.863974i	$0.332032\pi$
$410$	5.25115	0.259336
$411$	−37.6662	−1.85794
$412$	24.6499	1.21441
$413$	−21.2140	−1.04387
$414$	26.8457	1.31939
$415$	3.41707	0.167737
$416$	−59.9157	−2.93761
$417$	22.7167	1.11244
$418$	7.79603	0.381316
$419$	−17.5709	−0.858393	−0.429197	−	0.903211i	$-0.641203\pi$
$419$	−17.5709	−0.858393	−0.429197	+	0.903211i	$0.641203\pi$
$420$	−25.1703	−1.22819
$421$	29.7132	1.44813	0.724066	−	0.689731i	$-0.242271\pi$
$421$	29.7132	1.44813	0.724066	+	0.689731i	$0.242271\pi$
$422$	45.3168	2.20599
$423$	−6.11576	−0.297358
$424$	−65.6277	−3.18716
$425$	3.61126	0.175172
$426$	−26.7166	−1.29443
$427$	−18.4369	−0.892226
$428$	−3.90719	−0.188861
$429$	−4.11444	−0.198647
$430$	−15.1135	−0.728837
$431$	−39.6533	−1.91003	−0.955015	−	0.296557i	$-0.904161\pi$
$431$	−39.6533	−1.91003	−0.955015	+	0.296557i	$0.904161\pi$
$432$	−64.9474	−3.12478
$433$	−3.83081	−0.184097	−0.0920485	−	0.995755i	$-0.529341\pi$
$433$	−3.83081	−0.184097	−0.0920485	+	0.995755i	$0.529341\pi$
$434$	32.3739	1.55400
$435$	13.9619	0.669421
$436$	19.3479	0.926599
$437$	−20.4186	−0.976754
$438$	5.81265	0.277739
$439$	22.0584	1.05279	0.526394	−	0.850241i	$-0.323544\pi$
$439$	22.0584	1.05279	0.526394	+	0.850241i	$0.323544\pi$
$440$	−10.7716	−0.513517
$441$	−3.52062	−0.167648
$442$	−20.0550	−0.953921
$443$	26.7281	1.26989	0.634944	−	0.772558i	$-0.281023\pi$
$443$	26.7281	1.26989	0.634944	+	0.772558i	$0.281023\pi$
$444$	−125.057	−5.93493
$445$	0.0234421	0.00111126
$446$	−11.4850	−0.543829
$447$	15.2583	0.721691
$448$	98.9420	4.67457
$449$	−38.1460	−1.80022	−0.900110	−	0.435662i	$-0.856514\pi$
$449$	−38.1460	−1.80022	−0.900110	+	0.435662i	$0.856514\pi$
$450$	−3.65938	−0.172505
$451$	−1.87474	−0.0882779
$452$	−34.6626	−1.63039
$453$	−25.2116	−1.18454
$454$	53.6115	2.51611
$455$	−4.11385	−0.192860
$456$	−62.2158	−2.91352
$457$	−33.1458	−1.55049	−0.775247	−	0.631658i	$-0.782375\pi$
$457$	−33.1458	−1.55049	−0.775247	+	0.631658i	$0.782375\pi$
$458$	−66.3373	−3.09974
$459$	−12.6916	−0.592392
$460$	42.8842	1.99949
$461$	25.1071	1.16935	0.584677	−	0.811266i	$-0.301221\pi$
$461$	25.1071	1.16935	0.584677	+	0.811266i	$0.301221\pi$
$462$	12.0607	0.561113
$463$	−8.17775	−0.380052	−0.190026	−	0.981779i	$-0.560857\pi$
$463$	−8.17775	−0.380052	−0.190026	+	0.981779i	$0.560857\pi$
$464$	−124.334	−5.77205
$465$	11.5596	0.536065
$466$	24.6621	1.14245
$467$	15.6482	0.724113	0.362056	−	0.932156i	$-0.382075\pi$
$467$	15.6482	0.724113	0.362056	+	0.932156i	$0.382075\pi$
$468$	15.1418	0.699928
$469$	−15.3782	−0.710099
$470$	−13.1120	−0.604813
$471$	−24.9669	−1.15041
$472$	110.130	5.06915
$473$	5.39574	0.248096
$474$	−71.3281	−3.27621
$475$	2.78330	0.127706
$476$	43.8013	2.00763
$477$	7.95977	0.364453
$478$	−52.2008	−2.38761
$479$	0.227192	0.0103807	0.00519033	−	0.999987i	$-0.498348\pi$
$479$	0.227192	0.0103807	0.00519033	+	0.999987i	$0.498348\pi$
$480$	62.7118	2.86239
$481$	−20.4393	−0.931953
$482$	40.2293	1.83240
$483$	−31.5881	−1.43731
$484$	5.84563	0.265710
$485$	−5.51740	−0.250532
$486$	35.6426	1.61678
$487$	−30.7054	−1.39139	−0.695697	−	0.718335i	$-0.744904\pi$
$487$	−30.7054	−1.39139	−0.695697	+	0.718335i	$0.744904\pi$
$488$	95.7134	4.33274
$489$	−23.8674	−1.07932
$490$	−7.54812	−0.340989
$491$	−32.0887	−1.44814	−0.724070	−	0.689726i	$-0.757731\pi$
$491$	−32.0887	−1.44814	−0.724070	+	0.689726i	$0.757731\pi$
$492$	22.7422	1.02530
$493$	−24.2965	−1.09426
$494$	−15.4570	−0.695442
$495$	1.30645	0.0587207
$496$	−102.941	−4.62219
$497$	9.53686	0.427786
$498$	19.8622	0.890048
$499$	−10.2656	−0.459551	−0.229776	−	0.973244i	$-0.573799\pi$
$499$	−10.2656	−0.459551	−0.229776	+	0.973244i	$0.573799\pi$
$500$	−5.84563	−0.261424
$501$	−22.3930	−1.00045
$502$	−80.5164	−3.59362
$503$	−20.4417	−0.911450	−0.455725	−	0.890121i	$-0.650620\pi$
$503$	−20.4417	−0.911450	−0.455725	+	0.890121i	$0.650620\pi$
$504$	−29.1993	−1.30064
$505$	−4.00632	−0.178279
$506$	−20.5485	−0.913492
$507$	−18.8200	−0.835826
$508$	92.1313	4.08767
$509$	34.7550	1.54049	0.770243	−	0.637750i	$-0.220135\pi$
$509$	34.7550	1.54049	0.770243	+	0.637750i	$0.220135\pi$
$510$	20.9910	0.929496
$511$	−2.07490	−0.0917882
$512$	−160.341	−7.08614
$513$	−9.78175	−0.431875
$514$	27.3521	1.20645
$515$	−4.21681	−0.185815
$516$	−65.4549	−2.88149
$517$	4.68119	0.205878
$518$	59.9138	2.63246
$519$	8.87619	0.389622
$520$	21.3566	0.936549
$521$	−0.205319	−0.00899519	−0.00449760	−	0.999990i	$-0.501432\pi$
$521$	−0.205319	−0.00899519	−0.00449760	+	0.999990i	$0.501432\pi$
$522$	24.6202	1.07760
$523$	27.5471	1.20455	0.602275	−	0.798289i	$-0.294261\pi$
$523$	27.5471	1.20455	0.602275	+	0.798289i	$0.294261\pi$
$524$	0.252354	0.0110241
$525$	4.30583	0.187922
$526$	34.5357	1.50583
$527$	−20.1161	−0.876270
$528$	−38.3499	−1.66897
$529$	30.8186	1.33994
$530$	17.0655	0.741280
$531$	−13.3573	−0.579658
$532$	33.7589	1.46363
$533$	3.71699	0.161001
$534$	0.136260	0.00589656
$535$	0.668394	0.0288972
$536$	79.8343	3.44832
$537$	44.6586	1.92716
$538$	26.4744	1.14139
$539$	2.69479	0.116073
$540$	20.5441	0.884079
$541$	−31.5516	−1.35651	−0.678255	−	0.734827i	$-0.737263\pi$
$541$	−31.5516	−1.35651	−0.678255	+	0.734827i	$0.737263\pi$
$542$	−42.5749	−1.82875
$543$	27.0455	1.16063
$544$	−109.131	−4.67896
$545$	−3.30981	−0.141777
$546$	−23.9123	−1.02335
$547$	19.9659	0.853679	0.426839	−	0.904327i	$-0.359627\pi$
$547$	19.9659	0.853679	0.426839	+	0.904327i	$0.359627\pi$
$548$	−106.102	−4.53245
$549$	−11.6088	−0.495449
$550$	2.80101	0.119435
$551$	−18.7259	−0.797752
$552$	163.986	6.97972
$553$	25.4615	1.08273
$554$	8.52200	0.362065
$555$	21.3932	0.908090
$556$	63.9908	2.71381
$557$	28.1636	1.19333	0.596666	−	0.802490i	$-0.296492\pi$
$557$	28.1636	1.19333	0.596666	+	0.802490i	$0.296492\pi$
$558$	20.3841	0.862929
$559$	−10.6980	−0.452476
$560$	−38.3444	−1.62035
$561$	−7.49409	−0.316401
$562$	−47.4783	−2.00275
$563$	8.84111	0.372608	0.186304	−	0.982492i	$-0.440349\pi$
$563$	8.84111	0.372608	0.186304	+	0.982492i	$0.440349\pi$
$564$	−56.7868	−2.39115
$565$	5.92966	0.249463
$566$	36.5538	1.53647
$567$	−23.2649	−0.977034
$568$	−49.5096	−2.07738
$569$	24.8526	1.04187	0.520937	−	0.853595i	$-0.325583\pi$
$569$	24.8526	1.04187	0.520937	+	0.853595i	$0.325583\pi$
$570$	16.1783	0.677635
$571$	27.8274	1.16454	0.582270	−	0.812996i	$-0.302165\pi$
$571$	27.8274	1.16454	0.582270	+	0.812996i	$0.302165\pi$
$572$	−11.5900	−0.484601
$573$	44.1794	1.84562
$574$	−10.8956	−0.454774
$575$	−7.33612	−0.305937
$576$	62.2985	2.59577
$577$	39.2939	1.63582	0.817912	−	0.575343i	$-0.195131\pi$
$577$	39.2939	1.63582	0.817912	+	0.575343i	$0.195131\pi$
$578$	11.0886	0.461225
$579$	−36.4276	−1.51388
$580$	39.3292	1.63306
$581$	−7.09009	−0.294146
$582$	−32.0707	−1.32937
$583$	−6.09265	−0.252332
$584$	10.7716	0.445733
$585$	−2.59027	−0.107094
$586$	−69.5668	−2.87378
$587$	−46.6855	−1.92692	−0.963458	−	0.267858i	$-0.913684\pi$
$587$	−46.6855	−1.92692	−0.963458	+	0.267858i	$0.913684\pi$
$588$	−32.6901	−1.34812
$589$	−15.5040	−0.638831
$590$	−28.6378	−1.17900
$591$	19.7016	0.810417
$592$	−190.511	−7.82996
$593$	−28.8231	−1.18362	−0.591812	−	0.806076i	$-0.701587\pi$
$593$	−28.8231	−1.18362	−0.591812	+	0.806076i	$0.701587\pi$
$594$	−9.84398	−0.403903
$595$	−7.49301	−0.307183
$596$	42.9810	1.76057
$597$	−6.95705	−0.284733
$598$	40.7409	1.66602
$599$	−17.4748	−0.714002	−0.357001	−	0.934104i	$-0.616201\pi$
$599$	−17.4748	−0.714002	−0.357001	+	0.934104i	$0.616201\pi$
$600$	−22.3533	−0.912569
$601$	−9.03330	−0.368476	−0.184238	−	0.982882i	$-0.558982\pi$
$601$	−9.03330	−0.368476	−0.184238	+	0.982882i	$0.558982\pi$
$602$	31.3590	1.27810
$603$	−9.68283	−0.394315
$604$	−71.0185	−2.88970
$605$	−1.00000	−0.0406558
$606$	−23.2873	−0.945982
$607$	−5.41199	−0.219666	−0.109833	−	0.993950i	$-0.535032\pi$
$607$	−5.41199	−0.219666	−0.109833	+	0.993950i	$0.535032\pi$
$608$	−84.1103	−3.41112
$609$	−28.9695	−1.17390
$610$	−24.8889	−1.00772
$611$	−9.28126	−0.375480
$612$	27.5794	1.11483
$613$	−10.6660	−0.430794	−0.215397	−	0.976527i	$-0.569105\pi$
$613$	−10.6660	−0.430794	−0.215397	+	0.976527i	$0.569105\pi$
$614$	−19.2355	−0.776282
$615$	−3.89045	−0.156878
$616$	22.3501	0.900509
$617$	33.8591	1.36312	0.681558	−	0.731764i	$-0.261303\pi$
$617$	33.8591	1.36312	0.681558	+	0.731764i	$0.261303\pi$
$618$	−24.5108	−0.985970
$619$	2.05703	0.0826790	0.0413395	−	0.999145i	$-0.486837\pi$
$619$	2.05703	0.0826790	0.0413395	+	0.999145i	$0.486837\pi$
$620$	32.5623	1.30773
$621$	25.7824	1.03461
$622$	46.3542	1.85864
$623$	−0.0486399	−0.00194872
$624$	76.0353	3.04385
$625$	1.00000	0.0400000
$626$	64.7924	2.58963
$627$	−5.77590	−0.230667
$628$	−70.3292	−2.80644
$629$	−37.2284	−1.48439
$630$	7.59286	0.302507
$631$	14.8761	0.592209	0.296105	−	0.955155i	$-0.404312\pi$
$631$	14.8761	0.592209	0.296105	+	0.955155i	$0.404312\pi$
$632$	−132.181	−5.25787
$633$	−33.5742	−1.33445
$634$	−66.4866	−2.64052
$635$	−15.7607	−0.625445
$636$	73.9090	2.93068
$637$	−5.34288	−0.211693
$638$	−18.8451	−0.746084
$639$	6.00485	0.237548
$640$	73.1271	2.89060
$641$	12.8625	0.508037	0.254019	−	0.967199i	$-0.418248\pi$
$641$	12.8625	0.508037	0.254019	+	0.967199i	$0.418248\pi$
$642$	3.88514	0.153334
$643$	37.1308	1.46430	0.732148	−	0.681146i	$-0.238518\pi$
$643$	37.1308	1.46430	0.732148	+	0.681146i	$0.238518\pi$
$644$	−88.9805	−3.50632
$645$	11.1972	0.440891
$646$	−28.1535	−1.10768
$647$	−17.1867	−0.675679	−0.337840	−	0.941204i	$-0.609696\pi$
$647$	−17.1867	−0.675679	−0.337840	+	0.941204i	$0.609696\pi$
$648$	120.777	4.74458
$649$	10.2241	0.401331
$650$	−5.55347	−0.217825
$651$	−23.9851	−0.940050
$652$	−67.2320	−2.63301
$653$	3.26703	0.127849	0.0639244	−	0.997955i	$-0.479638\pi$
$653$	3.26703	0.127849	0.0639244	+	0.997955i	$0.479638\pi$
$654$	−19.2388	−0.752296
$655$	−0.0431697	−0.00168678
$656$	34.6454	1.35267
$657$	−1.30645	−0.0509696
$658$	27.2062	1.06061
$659$	−18.1638	−0.707563	−0.353781	−	0.935328i	$-0.615104\pi$
$659$	−18.1638	−0.707563	−0.353781	+	0.935328i	$0.615104\pi$
$660$	12.1308	0.472193
$661$	−39.5002	−1.53638	−0.768191	−	0.640221i	$-0.778843\pi$
$661$	−39.5002	−1.53638	−0.768191	+	0.640221i	$0.778843\pi$
$662$	70.2654	2.73094
$663$	14.8583	0.577049
$664$	36.8074	1.42841
$665$	−5.77506	−0.223947
$666$	37.7245	1.46180
$667$	49.3572	1.91112
$668$	−63.0788	−2.44059
$669$	8.50895	0.328975
$670$	−20.7597	−0.802019
$671$	8.88569	0.343028
$672$	−130.121	−5.01952
$673$	37.3246	1.43876	0.719379	−	0.694618i	$-0.244427\pi$
$673$	37.3246	1.43876	0.719379	+	0.694618i	$0.244427\pi$
$674$	66.0963	2.54594
$675$	−3.51445	−0.135271
$676$	−53.0141	−2.03900
$677$	−9.18255	−0.352914	−0.176457	−	0.984308i	$-0.556464\pi$
$677$	−9.18255	−0.352914	−0.176457	+	0.984308i	$0.556464\pi$
$678$	34.4670	1.32370
$679$	11.4481	0.439336
$680$	38.8992	1.49171
$681$	−39.7195	−1.52205
$682$	−15.6026	−0.597456
$683$	−34.1060	−1.30503	−0.652515	−	0.757776i	$-0.726286\pi$
$683$	−34.1060	−1.30503	−0.652515	+	0.757776i	$0.726286\pi$
$684$	21.2562	0.812750
$685$	18.1506	0.693500
$686$	56.3442	2.15123
$687$	49.1478	1.87511
$688$	−99.7139	−3.80156
$689$	12.0797	0.460201
$690$	−42.6422	−1.62336
$691$	−26.2119	−0.997148	−0.498574	−	0.866847i	$-0.666143\pi$
$691$	−26.2119	−0.997148	−0.498574	+	0.866847i	$0.666143\pi$
$692$	25.0033	0.950485
$693$	−2.71076	−0.102973
$694$	−94.4663	−3.58589
$695$	−10.9468	−0.415235
$696$	150.392	5.70060
$697$	6.77017	0.256438
$698$	−23.1516	−0.876301
$699$	−18.2716	−0.691095
$700$	12.1291	0.458437
$701$	3.79997	0.143523	0.0717614	−	0.997422i	$-0.477138\pi$
$701$	3.79997	0.143523	0.0717614	+	0.997422i	$0.477138\pi$
$702$	19.5174	0.736636
$703$	−28.6930	−1.08218
$704$	−47.6852	−1.79720
$705$	9.71440	0.365865
$706$	−13.0487	−0.491096
$707$	8.31271	0.312632
$708$	−124.027	−4.66122
$709$	25.1676	0.945189	0.472595	−	0.881280i	$-0.343317\pi$
$709$	25.1676	0.945189	0.472595	+	0.881280i	$0.343317\pi$
$710$	12.8742	0.483162
$711$	16.0318	0.601238
$712$	0.252509	0.00946318
$713$	40.8649	1.53040
$714$	−43.5542	−1.62997
$715$	1.98267	0.0741477
$716$	125.799	4.70132
$717$	38.6744	1.44432
$718$	−2.17089	−0.0810170
$719$	−34.8800	−1.30080	−0.650402	−	0.759591i	$-0.725399\pi$
$719$	−34.8800	−1.30080	−0.650402	+	0.759591i	$0.725399\pi$
$720$	−24.1434	−0.899773
$721$	8.74946	0.325847
$722$	31.5204	1.17307
$723$	−29.8050	−1.10846
$724$	76.1845	2.83138
$725$	−6.72797	−0.249871
$726$	−5.81265	−0.215727
$727$	28.1438	1.04380	0.521898	−	0.853008i	$-0.325224\pi$
$727$	28.1438	1.04380	0.521898	+	0.853008i	$0.325224\pi$
$728$	−44.3128	−1.64234
$729$	7.23086	0.267810
$730$	−2.80101	−0.103670
$731$	−19.4854	−0.720694
$732$	−107.791	−3.98407
$733$	−1.23998	−0.0457997	−0.0228999	−	0.999738i	$-0.507290\pi$
$733$	−1.23998	−0.0457997	−0.0228999	+	0.999738i	$0.507290\pi$
$734$	−74.9573	−2.76672
$735$	5.59222	0.206272
$736$	221.695	8.17178
$737$	7.41154	0.273007
$738$	−6.86039	−0.252534
$739$	32.3808	1.19115	0.595574	−	0.803300i	$-0.296925\pi$
$739$	32.3808	1.19115	0.595574	+	0.803300i	$0.296925\pi$
$740$	60.2625	2.21529
$741$	11.4517	0.420689
$742$	−35.4093	−1.29992
$743$	27.1383	0.995608	0.497804	−	0.867289i	$-0.334140\pi$
$743$	27.1383	0.995608	0.497804	+	0.867289i	$0.334140\pi$
$744$	124.516	4.56498
$745$	−7.35267	−0.269381
$746$	53.8730	1.97243
$747$	−4.46425	−0.163338
$748$	−21.1101	−0.771862
$749$	−1.38685	−0.0506745
$750$	5.81265	0.212248
$751$	−19.8639	−0.724844	−0.362422	−	0.932014i	$-0.618050\pi$
$751$	−19.8639	−0.724844	−0.362422	+	0.932014i	$0.618050\pi$
$752$	−86.5089	−3.15466
$753$	59.6527	2.17387
$754$	37.3636	1.36070
$755$	12.1490	0.442147
$756$	−42.6271	−1.55033
$757$	9.24196	0.335905	0.167952	−	0.985795i	$-0.446285\pi$
$757$	9.24196	0.335905	0.167952	+	0.985795i	$0.446285\pi$
$758$	−65.8760	−2.39272
$759$	15.2239	0.552593
$760$	29.9806	1.08751
$761$	6.53588	0.236925	0.118463	−	0.992959i	$-0.462203\pi$
$761$	6.53588	0.236925	0.118463	+	0.992959i	$0.462203\pi$
$762$	−91.6115	−3.31873
$763$	6.86754	0.248621
$764$	124.449	4.50241
$765$	−4.71795	−0.170578
$766$	104.718	3.78361
$767$	−20.2710	−0.731945
$768$	227.149	8.19655
$769$	12.2892	0.443159	0.221580	−	0.975142i	$-0.428879\pi$
$769$	12.2892	0.443159	0.221580	+	0.975142i	$0.428879\pi$
$770$	−5.81181	−0.209443
$771$	−20.2645	−0.729810
$772$	−102.613	−3.69312
$773$	1.37327	0.0493932	0.0246966	−	0.999695i	$-0.492138\pi$
$773$	1.37327	0.0493932	0.0246966	+	0.999695i	$0.492138\pi$
$774$	19.7451	0.709722
$775$	−5.57037	−0.200094
$776$	−59.4314	−2.13346
$777$	−44.3887	−1.59244
$778$	60.0194	2.15180
$779$	5.21795	0.186953
$780$	−24.0515	−0.861181
$781$	−4.59630	−0.164468
$782$	74.2060	2.65360
$783$	23.6451	0.845007
$784$	−49.8000	−1.77857
$785$	12.0311	0.429408
$786$	−0.250930	−0.00895039
$787$	−34.7371	−1.23824	−0.619121	−	0.785295i	$-0.712511\pi$
$787$	−34.7371	−1.23824	−0.619121	+	0.785295i	$0.712511\pi$
$788$	55.4975	1.97702
$789$	−25.5867	−0.910910
$790$	34.3717	1.22289
$791$	−12.3034	−0.437460
$792$	14.0726	0.500049
$793$	−17.6174	−0.625613
$794$	73.2101	2.59813
$795$	−12.6435	−0.448417
$796$	−19.5973	−0.694608
$797$	20.3607	0.721213	0.360607	−	0.932718i	$-0.382570\pi$
$797$	20.3607	0.721213	0.360607	+	0.932718i	$0.382570\pi$
$798$	−33.5684	−1.18831
$799$	−16.9050	−0.598056
$800$	−30.2197	−1.06843
$801$	−0.0306260	−0.00108212
$802$	23.4543	0.828200
$803$	1.00000	0.0352892
$804$	−89.9082	−3.17082
$805$	15.2217	0.536495
$806$	30.9349	1.08964
$807$	−19.6143	−0.690455
$808$	−43.1545	−1.51817
$809$	31.0641	1.09216	0.546079	−	0.837734i	$-0.316120\pi$
$809$	31.0641	1.09216	0.546079	+	0.837734i	$0.316120\pi$
$810$	−31.4064	−1.10351
$811$	−3.23534	−0.113608	−0.0568041	−	0.998385i	$-0.518091\pi$
$811$	−3.23534	−0.113608	−0.0568041	+	0.998385i	$0.518091\pi$
$812$	−81.6042	−2.86375
$813$	31.5428	1.10625
$814$	−28.8755	−1.01209
$815$	11.5012	0.402871
$816$	138.492	4.84818
$817$	−15.0179	−0.525411
$818$	−57.0475	−1.99462
$819$	5.37455	0.187802
$820$	−10.9590	−0.382706
$821$	−29.4399	−1.02746	−0.513729	−	0.857953i	$-0.671736\pi$
$821$	−29.4399	−1.02746	−0.513729	+	0.857953i	$0.671736\pi$
$822$	105.503	3.67985
$823$	33.1270	1.15474	0.577368	−	0.816484i	$-0.304080\pi$
$823$	33.1270	1.15474	0.577368	+	0.816484i	$0.304080\pi$
$824$	−45.4219	−1.58235
$825$	−2.07520	−0.0722492
$826$	59.4205	2.06750
$827$	−23.3112	−0.810608	−0.405304	−	0.914182i	$-0.632834\pi$
$827$	−23.3112	−0.810608	−0.405304	+	0.914182i	$0.632834\pi$
$828$	−56.0263	−1.94705
$829$	−18.0287	−0.626163	−0.313081	−	0.949726i	$-0.601361\pi$
$829$	−18.0287	−0.626163	−0.313081	+	0.949726i	$0.601361\pi$
$830$	−9.57124	−0.332222
$831$	−6.31375	−0.219022
$832$	94.5441	3.27773
$833$	−9.73158	−0.337179
$834$	−63.6297	−2.20332
$835$	10.7908	0.373430
$836$	−16.2701	−0.562714
$837$	19.5768	0.676672
$838$	49.2161	1.70014
$839$	34.1516	1.17904	0.589522	−	0.807752i	$-0.299316\pi$
$839$	34.1516	1.17904	0.589522	+	0.807752i	$0.299316\pi$
$840$	46.3808	1.60029
$841$	16.2656	0.560882
$842$	−83.2268	−2.86818
$843$	35.1756	1.21151
$844$	−94.5752	−3.25541
$845$	9.06901	0.311984
$846$	17.1303	0.588951
$847$	2.07490	0.0712944
$848$	112.593	3.86646
$849$	−27.0818	−0.929447
$850$	−10.1152	−0.346947
$851$	75.6279	2.59249
$852$	55.7570	1.91020
$853$	−50.8487	−1.74103	−0.870514	−	0.492144i	$-0.836213\pi$
$853$	−50.8487	−1.74103	−0.870514	+	0.492144i	$0.836213\pi$
$854$	51.6419	1.76715
$855$	−3.63625	−0.124357
$856$	7.19969	0.246081
$857$	44.2076	1.51010	0.755051	−	0.655666i	$-0.227612\pi$
$857$	44.2076	1.51010	0.755051	+	0.655666i	$0.227612\pi$
$858$	11.5246	0.393442
$859$	−16.6623	−0.568509	−0.284255	−	0.958749i	$-0.591746\pi$
$859$	−16.6623	−0.568509	−0.284255	+	0.958749i	$0.591746\pi$
$860$	31.5415	1.07556
$861$	8.07231	0.275103
$862$	111.069	3.78302
$863$	14.4716	0.492621	0.246310	−	0.969191i	$-0.420782\pi$
$863$	14.4716	0.492621	0.246310	+	0.969191i	$0.420782\pi$
$864$	106.205	3.61318
$865$	−4.27727	−0.145432
$866$	10.7301	0.364624
$867$	−8.21528	−0.279006
$868$	−67.5636	−2.29326
$869$	−12.2712	−0.416272
$870$	−39.1073	−1.32586
$871$	−14.6946	−0.497909
$872$	−35.6521	−1.20733
$873$	7.20823	0.243962
$874$	57.1926	1.93457
$875$	−2.07490	−0.0701444
$876$	−12.1308	−0.409863
$877$	−2.90482	−0.0980887	−0.0490444	−	0.998797i	$-0.515618\pi$
$877$	−2.90482	−0.0980887	−0.0490444	+	0.998797i	$0.515618\pi$
$878$	−61.7856	−2.08516
$879$	51.5404	1.73842
$880$	18.4801	0.622965
$881$	−5.90941	−0.199093	−0.0995465	−	0.995033i	$-0.531739\pi$
$881$	−5.90941	−0.199093	−0.0995465	+	0.995033i	$0.531739\pi$
$882$	9.86127	0.332046
$883$	−20.5783	−0.692515	−0.346257	−	0.938140i	$-0.612548\pi$
$883$	−20.5783	−0.692515	−0.346257	+	0.938140i	$0.612548\pi$
$884$	41.8544	1.40772
$885$	21.2171	0.713203
$886$	−74.8655	−2.51515
$887$	45.8831	1.54060	0.770302	−	0.637679i	$-0.220105\pi$
$887$	45.8831	1.54060	0.770302	+	0.637679i	$0.220105\pi$
$888$	230.439	7.73304
$889$	32.7019	1.09679
$890$	−0.0656613	−0.00220097
$891$	11.2125	0.375634
$892$	23.9689	0.802537
$893$	−13.0291	−0.436003
$894$	−42.7385	−1.42939
$895$	−21.5202	−0.719339
$896$	−151.731	−5.06899
$897$	−30.1840	−1.00781
$898$	106.847	3.56553
$899$	37.4773	1.24994
$900$	7.63705	0.254568
$901$	22.0021	0.732998
$902$	5.25115	0.174844
$903$	−23.2332	−0.773151
$904$	63.8721	2.12435
$905$	−13.0327	−0.433223
$906$	70.6177	2.34612
$907$	−9.54976	−0.317095	−0.158547	−	0.987351i	$-0.550681\pi$
$907$	−9.54976	−0.317095	−0.158547	+	0.987351i	$0.550681\pi$
$908$	−111.886	−3.71306
$909$	5.23407	0.173603
$910$	11.5229	0.381981
$911$	25.9535	0.859879	0.429940	−	0.902858i	$-0.358535\pi$
$911$	25.9535	0.859879	0.429940	+	0.902858i	$0.358535\pi$
$912$	106.739	3.53449
$913$	3.41707	0.113089
$914$	92.8415	3.07092
$915$	18.4396	0.609594
$916$	138.444	4.57433
$917$	0.0895729	0.00295796
$918$	35.5492	1.17330
$919$	46.1683	1.52295	0.761475	−	0.648194i	$-0.224475\pi$
$919$	46.1683	1.52295	0.761475	+	0.648194i	$0.224475\pi$
$920$	−79.0219	−2.60527
$921$	14.2511	0.469591
$922$	−70.3251	−2.31603
$923$	9.11295	0.299956
$924$	−25.1703	−0.828042
$925$	−10.3090	−0.338957
$926$	22.9059	0.752735
$927$	5.50907	0.180942
$928$	203.317	6.67421
$929$	2.63183	0.0863474	0.0431737	−	0.999068i	$-0.486253\pi$
$929$	2.63183	0.0863474	0.0431737	+	0.999068i	$0.486253\pi$
$930$	−32.3786	−1.06174
$931$	−7.50040	−0.245816
$932$	−51.4692	−1.68593
$933$	−34.3428	−1.12433
$934$	−43.8307	−1.43418
$935$	3.61126	0.118101
$936$	−27.9014	−0.911986
$937$	32.7625	1.07030	0.535151	−	0.844756i	$-0.320255\pi$
$937$	32.7625	1.07030	0.535151	+	0.844756i	$0.320255\pi$
$938$	43.0744	1.40643
$939$	−48.0032	−1.56653
$940$	27.3645	0.892531
$941$	−17.5689	−0.572731	−0.286365	−	0.958121i	$-0.592447\pi$
$941$	−17.5689	−0.572731	−0.286365	+	0.958121i	$0.592447\pi$
$942$	69.9324	2.27852
$943$	−13.7533	−0.447869
$944$	−188.943	−6.14956
$945$	7.29213	0.237213
$946$	−15.1135	−0.491382
$947$	11.8536	0.385189	0.192595	−	0.981278i	$-0.438310\pi$
$947$	11.8536	0.385189	0.192595	+	0.981278i	$0.438310\pi$
$948$	148.860	4.83475
$949$	−1.98267	−0.0643602
$950$	−7.79603	−0.252937
$951$	49.2584	1.59731
$952$	−80.7119	−2.61589
$953$	9.39412	0.304305	0.152153	−	0.988357i	$-0.451379\pi$
$953$	9.39412	0.304305	0.152153	+	0.988357i	$0.451379\pi$
$954$	−22.2953	−0.721838
$955$	−21.2892	−0.688903
$956$	108.942	3.52343
$957$	13.9619	0.451324
$958$	−0.636365	−0.0205600
$959$	−37.6608	−1.21613
$960$	−98.9563	−3.19380
$961$	0.0290350	0.000936612 0
$962$	57.2506	1.84583
$963$	−0.873227	−0.0281393
$964$	−83.9576	−2.70409
$965$	17.5538	0.565076
$966$	88.4784	2.84675
$967$	1.53476	0.0493547	0.0246773	−	0.999695i	$-0.492144\pi$
$967$	1.53476	0.0493547	0.0246773	+	0.999695i	$0.492144\pi$
$968$	−10.7716	−0.346213
$969$	20.8583	0.670064
$970$	15.4543	0.496207
$971$	−24.8293	−0.796809	−0.398405	−	0.917210i	$-0.630436\pi$
$971$	−24.8293	−0.796809	−0.398405	+	0.917210i	$0.630436\pi$
$972$	−74.3852	−2.38591
$973$	22.7135	0.728160
$974$	86.0060	2.75581
$975$	4.11444	0.131768
$976$	−164.209	−5.25619
$977$	−42.2733	−1.35244	−0.676221	−	0.736699i	$-0.736383\pi$
$977$	−42.2733	−1.35244	−0.676221	+	0.736699i	$0.736383\pi$
$978$	66.8526	2.13771
$979$	0.0234421	0.000749212 0
$980$	15.7527	0.503203
$981$	4.32412	0.138059
$982$	89.8805	2.86820
$983$	−40.1534	−1.28069	−0.640347	−	0.768086i	$-0.721209\pi$
$983$	−40.1534	−1.28069	−0.640347	+	0.768086i	$0.721209\pi$
$984$	−41.9065	−1.33593
$985$	−9.49385	−0.302499
$986$	68.0545	2.16730
$987$	−20.1564	−0.641586
$988$	32.2583	1.02627
$989$	39.5838	1.25869
$990$	−3.65938	−0.116303
$991$	−48.4625	−1.53946	−0.769731	−	0.638368i	$-0.779610\pi$
$991$	−48.4625	−1.53946	−0.769731	+	0.638368i	$0.779610\pi$
$992$	168.335	5.34463
$993$	−52.0580	−1.65201
$994$	−26.7128	−0.847278
$995$	3.35247	0.106280
$996$	−41.4520	−1.31346
$997$	60.8088	1.92583	0.962917	−	0.269799i	$-0.0869573\pi$
$997$	60.8088	1.92583	0.962917	+	0.269799i	$0.0869573\pi$
$998$	28.7540	0.910191
$999$	36.2303	1.14628

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4015.2.a.g.1.1	✓	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)

\(f(q)\)	\(=\)	\(q-2.80101 q^{2} +2.07520 q^{3} +5.84563 q^{4} -1.00000 q^{5} -5.81265 q^{6} +2.07490 q^{7} -10.7716 q^{8} +1.30645 q^{9} +O(q^{10})\)	\(q-2.80101 q^{2} +2.07520 q^{3} +5.84563 q^{4} -1.00000 q^{5} -5.81265 q^{6} +2.07490 q^{7} -10.7716 q^{8} +1.30645 q^{9} +2.80101 q^{10} -1.00000 q^{11} +12.1308 q^{12} +1.98267 q^{13} -5.81181 q^{14} -2.07520 q^{15} +18.4801 q^{16} +3.61126 q^{17} -3.65938 q^{18} +2.78330 q^{19} -5.84563 q^{20} +4.30583 q^{21} +2.80101 q^{22} -7.33612 q^{23} -22.3533 q^{24} +1.00000 q^{25} -5.55347 q^{26} -3.51445 q^{27} +12.1291 q^{28} -6.72797 q^{29} +5.81265 q^{30} -5.57037 q^{31} -30.2197 q^{32} -2.07520 q^{33} -10.1152 q^{34} -2.07490 q^{35} +7.63705 q^{36} -10.3090 q^{37} -7.79603 q^{38} +4.11444 q^{39} +10.7716 q^{40} +1.87474 q^{41} -12.0607 q^{42} -5.39574 q^{43} -5.84563 q^{44} -1.30645 q^{45} +20.5485 q^{46} -4.68119 q^{47} +38.3499 q^{48} -2.69479 q^{49} -2.80101 q^{50} +7.49409 q^{51} +11.5900 q^{52} +6.09265 q^{53} +9.84398 q^{54} +1.00000 q^{55} -22.3501 q^{56} +5.77590 q^{57} +18.8451 q^{58} -10.2241 q^{59} -12.1308 q^{60} -8.88569 q^{61} +15.6026 q^{62} +2.71076 q^{63} +47.6852 q^{64} -1.98267 q^{65} +5.81265 q^{66} -7.41154 q^{67} +21.1101 q^{68} -15.2239 q^{69} +5.81181 q^{70} +4.59630 q^{71} -14.0726 q^{72} -1.00000 q^{73} +28.8755 q^{74} +2.07520 q^{75} +16.2701 q^{76} -2.07490 q^{77} -11.5246 q^{78} +12.2712 q^{79} -18.4801 q^{80} -11.2125 q^{81} -5.25115 q^{82} -3.41707 q^{83} +25.1703 q^{84} -3.61126 q^{85} +15.1135 q^{86} -13.9619 q^{87} +10.7716 q^{88} -0.0234421 q^{89} +3.65938 q^{90} +4.11385 q^{91} -42.8842 q^{92} -11.5596 q^{93} +13.1120 q^{94} -2.78330 q^{95} -62.7118 q^{96} +5.51740 q^{97} +7.54812 q^{98} -1.30645 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 5 q^{2} - 7 q^{3} + 37 q^{4} - 32 q^{5} - 3 q^{6} - 18 q^{8} + 29 q^{9}+O(q^{10}) \) 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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