LMFDB - Embedded newform 8007.2.a.j.1.61

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8007, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8007 = 3 \cdot 17 \cdot 157 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8007.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$63.9362168984$
Analytic rank:	$0$
Dimension:	$64$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.61
Character	$\chi$	$=$	8007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.72724 q^{2} -1.00000 q^{3} +5.43783 q^{4} -4.05273 q^{5} -2.72724 q^{6} +4.43401 q^{7} +9.37579 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.72724 q^{2} -1.00000 q^{3} +5.43783 q^{4} -4.05273 q^{5} -2.72724 q^{6} +4.43401 q^{7} +9.37579 q^{8} +1.00000 q^{9} -11.0528 q^{10} +4.80253 q^{11} -5.43783 q^{12} +2.74491 q^{13} +12.0926 q^{14} +4.05273 q^{15} +14.6944 q^{16} +1.00000 q^{17} +2.72724 q^{18} +3.84305 q^{19} -22.0381 q^{20} -4.43401 q^{21} +13.0976 q^{22} +1.06493 q^{23} -9.37579 q^{24} +11.4246 q^{25} +7.48603 q^{26} -1.00000 q^{27} +24.1114 q^{28} -4.00615 q^{29} +11.0528 q^{30} -0.868946 q^{31} +21.3234 q^{32} -4.80253 q^{33} +2.72724 q^{34} -17.9699 q^{35} +5.43783 q^{36} -9.12900 q^{37} +10.4809 q^{38} -2.74491 q^{39} -37.9976 q^{40} -8.14259 q^{41} -12.0926 q^{42} -9.98491 q^{43} +26.1153 q^{44} -4.05273 q^{45} +2.90433 q^{46} +7.50306 q^{47} -14.6944 q^{48} +12.6604 q^{49} +31.1577 q^{50} -1.00000 q^{51} +14.9264 q^{52} +5.35375 q^{53} -2.72724 q^{54} -19.4634 q^{55} +41.5723 q^{56} -3.84305 q^{57} -10.9257 q^{58} -12.7675 q^{59} +22.0381 q^{60} +7.29092 q^{61} -2.36982 q^{62} +4.43401 q^{63} +28.7654 q^{64} -11.1244 q^{65} -13.0976 q^{66} +3.00074 q^{67} +5.43783 q^{68} -1.06493 q^{69} -49.0081 q^{70} -7.42927 q^{71} +9.37579 q^{72} +0.424850 q^{73} -24.8970 q^{74} -11.4246 q^{75} +20.8979 q^{76} +21.2945 q^{77} -7.48603 q^{78} +6.32805 q^{79} -59.5523 q^{80} +1.00000 q^{81} -22.2068 q^{82} -10.1966 q^{83} -24.1114 q^{84} -4.05273 q^{85} -27.2312 q^{86} +4.00615 q^{87} +45.0275 q^{88} +12.3120 q^{89} -11.0528 q^{90} +12.1710 q^{91} +5.79093 q^{92} +0.868946 q^{93} +20.4626 q^{94} -15.5749 q^{95} -21.3234 q^{96} -10.4488 q^{97} +34.5281 q^{98} +4.80253 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9}+O(q^{10}) $ 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9	\( 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9} + 12 q^{10} - 7 q^{11} - 77 q^{12} + 24 q^{13} - 14 q^{14} + 3 q^{15} + 103 q^{16} + 64 q^{17} + 5 q^{18} + 26 q^{19} - 24 q^{20} - 5 q^{21} + 25 q^{22} + 20 q^{23} - 18 q^{24} + 141 q^{25} + 9 q^{26} - 64 q^{27} + 14 q^{28} + 5 q^{29} - 12 q^{30} + 11 q^{31} + 31 q^{32} + 7 q^{33} + 5 q^{34} - 3 q^{35} + 77 q^{36} + 50 q^{37} + 8 q^{38} - 24 q^{39} + 28 q^{40} - 9 q^{41} + 14 q^{42} + 59 q^{43} - 6 q^{44} - 3 q^{45} + 11 q^{47} - 103 q^{48} + 163 q^{49} + 20 q^{50} - 64 q^{51} + 65 q^{52} + 39 q^{53} - 5 q^{54} + 35 q^{55} - 34 q^{56} - 26 q^{57} - 27 q^{58} - 65 q^{59} + 24 q^{60} + 15 q^{61} + 18 q^{62} + 5 q^{63} + 152 q^{64} + 49 q^{65} - 25 q^{66} + 56 q^{67} + 77 q^{68} - 20 q^{69} + 28 q^{70} - 18 q^{71} + 18 q^{72} + 37 q^{73} - 76 q^{74} - 141 q^{75} + 30 q^{76} + 80 q^{77} - 9 q^{78} + 20 q^{79} - 144 q^{80} + 64 q^{81} + 27 q^{82} + 3 q^{83} - 14 q^{84} - 3 q^{85} + 12 q^{86} - 5 q^{87} + 108 q^{88} + 42 q^{89} + 12 q^{90} + 25 q^{91} + 18 q^{92} - 11 q^{93} + 60 q^{94} + 42 q^{95} - 31 q^{96} + 72 q^{97} + 18 q^{98} - 7 q^{99}+O(q^{100}) \) 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9 + 12 * q^10 - 7 * q^11 - 77 * q^12 + 24 * q^13 - 14 * q^14 + 3 * q^15 + 103 * q^16 + 64 * q^17 + 5 * q^18 + 26 * q^19 - 24 * q^20 - 5 * q^21 + 25 * q^22 + 20 * q^23 - 18 * q^24 + 141 * q^25 + 9 * q^26 - 64 * q^27 + 14 * q^28 + 5 * q^29 - 12 * q^30 + 11 * q^31 + 31 * q^32 + 7 * q^33 + 5 * q^34 - 3 * q^35 + 77 * q^36 + 50 * q^37 + 8 * q^38 - 24 * q^39 + 28 * q^40 - 9 * q^41 + 14 * q^42 + 59 * q^43 - 6 * q^44 - 3 * q^45 + 11 * q^47 - 103 * q^48 + 163 * q^49 + 20 * q^50 - 64 * q^51 + 65 * q^52 + 39 * q^53 - 5 * q^54 + 35 * q^55 - 34 * q^56 - 26 * q^57 - 27 * q^58 - 65 * q^59 + 24 * q^60 + 15 * q^61 + 18 * q^62 + 5 * q^63 + 152 * q^64 + 49 * q^65 - 25 * q^66 + 56 * q^67 + 77 * q^68 - 20 * q^69 + 28 * q^70 - 18 * q^71 + 18 * q^72 + 37 * q^73 - 76 * q^74 - 141 * q^75 + 30 * q^76 + 80 * q^77 - 9 * q^78 + 20 * q^79 - 144 * q^80 + 64 * q^81 + 27 * q^82 + 3 * q^83 - 14 * q^84 - 3 * q^85 + 12 * q^86 - 5 * q^87 + 108 * q^88 + 42 * q^89 + 12 * q^90 + 25 * q^91 + 18 * q^92 - 11 * q^93 + 60 * q^94 + 42 * q^95 - 31 * q^96 + 72 * q^97 + 18 * q^98 - 7 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	2.72724	1.92845	0.964225	−	0.265087i	$-0.0854006\pi$
$2$	2.72724	1.92845	0.964225	+	0.265087i	$0.0854006\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	5.43783	2.71892
$5$	−4.05273	−1.81244	−0.906219	−	0.422810i	$-0.861044\pi$
$5$	−4.05273	−1.81244	−0.906219	+	0.422810i	$0.861044\pi$
$6$	−2.72724	−1.11339
$7$	4.43401	1.67590	0.837949	−	0.545748i	$-0.183755\pi$
$7$	4.43401	1.67590	0.837949	+	0.545748i	$0.183755\pi$
$8$	9.37579	3.31484
$9$	1.00000	0.333333
$10$	−11.0528	−3.49519
$11$	4.80253	1.44802	0.724008	−	0.689791i	$-0.242298\pi$
$11$	4.80253	1.44802	0.724008	+	0.689791i	$0.242298\pi$
$12$	−5.43783	−1.56977
$13$	2.74491	0.761302	0.380651	−	0.924719i	$-0.375700\pi$
$13$	2.74491	0.761302	0.380651	+	0.924719i	$0.375700\pi$
$14$	12.0926	3.23188
$15$	4.05273	1.04641
$16$	14.6944	3.67359
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	2.72724	0.642816
$19$	3.84305	0.881656	0.440828	−	0.897591i	$-0.354685\pi$
$19$	3.84305	0.881656	0.440828	+	0.897591i	$0.354685\pi$
$20$	−22.0381	−4.92786
$21$	−4.43401	−0.967580
$22$	13.0976	2.79243
$23$	1.06493	0.222054	0.111027	−	0.993817i	$-0.464586\pi$
$23$	1.06493	0.222054	0.111027	+	0.993817i	$0.464586\pi$
$24$	−9.37579	−1.91383
$25$	11.4246	2.28493
$26$	7.48603	1.46813
$27$	−1.00000	−0.192450
$28$	24.1114	4.55663
$29$	−4.00615	−0.743924	−0.371962	−	0.928248i	$-0.621315\pi$
$29$	−4.00615	−0.743924	−0.371962	+	0.928248i	$0.621315\pi$
$30$	11.0528	2.01795
$31$	−0.868946	−0.156067	−0.0780337	−	0.996951i	$-0.524864\pi$
$31$	−0.868946	−0.156067	−0.0780337	+	0.996951i	$0.524864\pi$
$32$	21.3234	3.76949
$33$	−4.80253	−0.836013
$34$	2.72724	0.467718
$35$	−17.9699	−3.03746
$36$	5.43783	0.906305
$37$	−9.12900	−1.50080	−0.750399	−	0.660985i	$-0.770139\pi$
$37$	−9.12900	−1.50080	−0.750399	+	0.660985i	$0.770139\pi$
$38$	10.4809	1.70023
$39$	−2.74491	−0.439538
$40$	−37.9976	−6.00794
$41$	−8.14259	−1.27166	−0.635830	−	0.771829i	$-0.719342\pi$
$41$	−8.14259	−1.27166	−0.635830	+	0.771829i	$0.719342\pi$
$42$	−12.0926	−1.86593
$43$	−9.98491	−1.52268	−0.761342	−	0.648350i	$-0.775459\pi$
$43$	−9.98491	−1.52268	−0.761342	+	0.648350i	$0.775459\pi$
$44$	26.1153	3.93704
$45$	−4.05273	−0.604146
$46$	2.90433	0.428220
$47$	7.50306	1.09443	0.547217	−	0.836991i	$-0.315687\pi$
$47$	7.50306	1.09443	0.547217	+	0.836991i	$0.315687\pi$
$48$	−14.6944	−2.12095
$49$	12.6604	1.80863
$50$	31.1577	4.40637
$51$	−1.00000	−0.140028
$52$	14.9264	2.06992
$53$	5.35375	0.735395	0.367697	−	0.929946i	$-0.380146\pi$
$53$	5.35375	0.735395	0.367697	+	0.929946i	$0.380146\pi$
$54$	−2.72724	−0.371130
$55$	−19.4634	−2.62444
$56$	41.5723	5.55534
$57$	−3.84305	−0.509025
$58$	−10.9257	−1.43462
$59$	−12.7675	−1.66219	−0.831093	−	0.556133i	$-0.812285\pi$
$59$	−12.7675	−1.66219	−0.831093	+	0.556133i	$0.812285\pi$
$60$	22.0381	2.84510
$61$	7.29092	0.933506	0.466753	−	0.884388i	$-0.345424\pi$
$61$	7.29092	0.933506	0.466753	+	0.884388i	$0.345424\pi$
$62$	−2.36982	−0.300968
$63$	4.43401	0.558633
$64$	28.7654	3.59568
$65$	−11.1244	−1.37981
$66$	−13.0976	−1.61221
$67$	3.00074	0.366598	0.183299	−	0.983057i	$-0.441322\pi$
$67$	3.00074	0.366598	0.183299	+	0.983057i	$0.441322\pi$
$68$	5.43783	0.659434
$69$	−1.06493	−0.128203
$70$	−49.0081	−5.85759
$71$	−7.42927	−0.881692	−0.440846	−	0.897583i	$-0.645322\pi$
$71$	−7.42927	−0.881692	−0.440846	+	0.897583i	$0.645322\pi$
$72$	9.37579	1.10495
$73$	0.424850	0.0497250	0.0248625	−	0.999691i	$-0.492085\pi$
$73$	0.424850	0.0497250	0.0248625	+	0.999691i	$0.492085\pi$
$74$	−24.8970	−2.89421
$75$	−11.4246	−1.31920
$76$	20.8979	2.39715
$77$	21.2945	2.42673
$78$	−7.48603	−0.847626
$79$	6.32805	0.711962	0.355981	−	0.934493i	$-0.384147\pi$
$79$	6.32805	0.711962	0.355981	+	0.934493i	$0.384147\pi$
$80$	−59.5523	−6.65815
$81$	1.00000	0.111111
$82$	−22.2068	−2.45233
$83$	−10.1966	−1.11922	−0.559610	−	0.828756i	$-0.689049\pi$
$83$	−10.1966	−1.11922	−0.559610	+	0.828756i	$0.689049\pi$
$84$	−24.1114	−2.63077
$85$	−4.05273	−0.439581
$86$	−27.2312	−2.93642
$87$	4.00615	0.429504
$88$	45.0275	4.79995
$89$	12.3120	1.30507	0.652534	−	0.757759i	$-0.273706\pi$
$89$	12.3120	1.30507	0.652534	+	0.757759i	$0.273706\pi$
$90$	−11.0528	−1.16506
$91$	12.1710	1.27586
$92$	5.79093	0.603747
$93$	0.868946	0.0901055
$94$	20.4626	2.11056
$95$	−15.5749	−1.59795
$96$	−21.3234	−2.17631
$97$	−10.4488	−1.06092	−0.530459	−	0.847711i	$-0.677980\pi$
$97$	−10.4488	−1.06092	−0.530459	+	0.847711i	$0.677980\pi$
$98$	34.5281	3.48786
$99$	4.80253	0.482672
$100$	62.1253	6.21253
$101$	−1.67215	−0.166385	−0.0831924	−	0.996534i	$-0.526512\pi$
$101$	−1.67215	−0.166385	−0.0831924	+	0.996534i	$0.526512\pi$
$102$	−2.72724	−0.270037
$103$	−1.70083	−0.167588	−0.0837938	−	0.996483i	$-0.526704\pi$
$103$	−1.70083	−0.167588	−0.0837938	+	0.996483i	$0.526704\pi$
$104$	25.7357	2.52360
$105$	17.9699	1.75368
$106$	14.6010	1.41817
$107$	13.5660	1.31148	0.655738	−	0.754988i	$-0.272357\pi$
$107$	13.5660	1.31148	0.655738	+	0.754988i	$0.272357\pi$
$108$	−5.43783	−0.523256
$109$	15.1191	1.44814	0.724072	−	0.689725i	$-0.242268\pi$
$109$	15.1191	1.44814	0.724072	+	0.689725i	$0.242268\pi$
$110$	−53.0812	−5.06110
$111$	9.12900	0.866486
$112$	65.1549	6.15656
$113$	3.29528	0.309994	0.154997	−	0.987915i	$-0.450463\pi$
$113$	3.29528	0.309994	0.154997	+	0.987915i	$0.450463\pi$
$114$	−10.4809	−0.981628
$115$	−4.31589	−0.402459
$116$	−21.7848	−2.02267
$117$	2.74491	0.253767
$118$	−34.8200	−3.20544
$119$	4.43401	0.406465
$120$	37.9976	3.46869
$121$	12.0643	1.09675
$122$	19.8841	1.80022
$123$	8.14259	0.734193
$124$	−4.72518	−0.424334
$125$	−26.0374	−2.32885
$126$	12.0926	1.07729
$127$	21.0847	1.87097	0.935483	−	0.353372i	$-0.114965\pi$
$127$	21.0847	1.87097	0.935483	+	0.353372i	$0.114965\pi$
$128$	35.8032	3.16459
$129$	9.98491	0.879122
$130$	−30.3389	−2.66090
$131$	−8.79889	−0.768763	−0.384381	−	0.923174i	$-0.625585\pi$
$131$	−8.79889	−0.768763	−0.384381	+	0.923174i	$0.625585\pi$
$132$	−26.1153	−2.27305
$133$	17.0401	1.47757
$134$	8.18373	0.706966
$135$	4.05273	0.348804
$136$	9.37579	0.803967
$137$	−13.1132	−1.12033	−0.560167	−	0.828380i	$-0.689263\pi$
$137$	−13.1132	−1.12033	−0.560167	+	0.828380i	$0.689263\pi$
$138$	−2.90433	−0.247233
$139$	−14.3324	−1.21566	−0.607831	−	0.794067i	$-0.707960\pi$
$139$	−14.3324	−1.21566	−0.607831	+	0.794067i	$0.707960\pi$
$140$	−97.7171	−8.25860
$141$	−7.50306	−0.631871
$142$	−20.2614	−1.70030
$143$	13.1825	1.10238
$144$	14.6944	1.22453
$145$	16.2359	1.34831
$146$	1.15867	0.0958921
$147$	−12.6604	−1.04422
$148$	−49.6420	−4.08054
$149$	−12.4218	−1.01764	−0.508818	−	0.860874i	$-0.669918\pi$
$149$	−12.4218	−1.01764	−0.508818	+	0.860874i	$0.669918\pi$
$150$	−31.1577	−2.54402
$151$	6.31340	0.513777	0.256889	−	0.966441i	$-0.417303\pi$
$151$	6.31340	0.513777	0.256889	+	0.966441i	$0.417303\pi$
$152$	36.0316	2.92255
$153$	1.00000	0.0808452
$154$	58.0751	4.67982
$155$	3.52161	0.282862
$156$	−14.9264	−1.19507
$157$	−1.00000	−0.0798087
$157$	−1.00000	−0.0798087
$158$	17.2581	1.37298
$159$	−5.35375	−0.424580
$160$	−86.4182	−6.83196
$161$	4.72193	0.372140
$162$	2.72724	0.214272
$163$	24.5657	1.92414	0.962068	−	0.272810i	$-0.0879531\pi$
$163$	24.5657	1.92414	0.962068	+	0.272810i	$0.0879531\pi$
$164$	−44.2781	−3.45754
$165$	19.4634	1.51522
$166$	−27.8085	−2.15836
$167$	−9.72992	−0.752924	−0.376462	−	0.926432i	$-0.622859\pi$
$167$	−9.72992	−0.752924	−0.376462	+	0.926432i	$0.622859\pi$
$168$	−41.5723	−3.20738
$169$	−5.46545	−0.420420
$170$	−11.0528	−0.847709
$171$	3.84305	0.293885
$172$	−54.2962	−4.14005
$173$	−14.6780	−1.11595	−0.557974	−	0.829858i	$-0.688421\pi$
$173$	−14.6780	−1.11595	−0.557974	+	0.829858i	$0.688421\pi$
$174$	10.9257	0.828277
$175$	50.6570	3.82931
$176$	70.5700	5.31942
$177$	12.7675	0.959664
$178$	33.5777	2.51676
$179$	−5.34753	−0.399693	−0.199847	−	0.979827i	$-0.564044\pi$
$179$	−5.34753	−0.399693	−0.199847	+	0.979827i	$0.564044\pi$
$180$	−22.0381	−1.64262
$181$	−3.01992	−0.224469	−0.112234	−	0.993682i	$-0.535801\pi$
$181$	−3.01992	−0.224469	−0.112234	+	0.993682i	$0.535801\pi$
$182$	33.1931	2.46044
$183$	−7.29092	−0.538960
$184$	9.98460	0.736074
$185$	36.9974	2.72010
$186$	2.36982	0.173764
$187$	4.80253	0.351196
$188$	40.8004	2.97567
$189$	−4.43401	−0.322527
$190$	−42.4764	−3.08156
$191$	25.2167	1.82462	0.912309	−	0.409503i	$-0.134298\pi$
$191$	25.2167	1.82462	0.912309	+	0.409503i	$0.134298\pi$
$192$	−28.7654	−2.07596
$193$	−19.7106	−1.41880	−0.709401	−	0.704805i	$-0.751034\pi$
$193$	−19.7106	−1.41880	−0.709401	+	0.704805i	$0.751034\pi$
$194$	−28.4965	−2.04593
$195$	11.1244	0.796635
$196$	68.8454	4.91753
$197$	5.92252	0.421962	0.210981	−	0.977490i	$-0.432334\pi$
$197$	5.92252	0.421962	0.210981	+	0.977490i	$0.432334\pi$
$198$	13.0976	0.930809
$199$	11.5677	0.820010	0.410005	−	0.912083i	$-0.365527\pi$
$199$	11.5677	0.820010	0.410005	+	0.912083i	$0.365527\pi$
$200$	107.115	7.57418
$201$	−3.00074	−0.211656
$202$	−4.56034	−0.320865
$203$	−17.7633	−1.24674
$204$	−5.43783	−0.380724
$205$	32.9998	2.30480
$206$	−4.63857	−0.323184
$207$	1.06493	0.0740180
$208$	40.3347	2.79671
$209$	18.4564	1.27665
$210$	49.0081	3.38188
$211$	15.0663	1.03721	0.518604	−	0.855015i	$-0.326452\pi$
$211$	15.0663	1.03721	0.518604	+	0.855015i	$0.326452\pi$
$212$	29.1128	1.99948
$213$	7.42927	0.509045
$214$	36.9978	2.52912
$215$	40.4662	2.75977
$216$	−9.37579	−0.637942
$217$	−3.85292	−0.261553
$218$	41.2333	2.79267
$219$	−0.424850	−0.0287087
$220$	−105.838	−7.13563
$221$	2.74491	0.184643
$222$	24.8970	1.67097
$223$	−11.2079	−0.750535	−0.375267	−	0.926917i	$-0.622449\pi$
$223$	−11.2079	−0.750535	−0.375267	+	0.926917i	$0.622449\pi$
$224$	94.5483	6.31728
$225$	11.4246	0.761643
$226$	8.98702	0.597808
$227$	−4.79565	−0.318298	−0.159149	−	0.987255i	$-0.550875\pi$
$227$	−4.79565	−0.318298	−0.159149	+	0.987255i	$0.550875\pi$
$228$	−20.8979	−1.38400
$229$	−29.0395	−1.91899	−0.959494	−	0.281731i	$-0.909092\pi$
$229$	−29.0395	−1.91899	−0.959494	+	0.281731i	$0.909092\pi$
$230$	−11.7705	−0.776122
$231$	−21.2945	−1.40107
$232$	−37.5608	−2.46599
$233$	−6.92864	−0.453910	−0.226955	−	0.973905i	$-0.572877\pi$
$233$	−6.92864	−0.453910	−0.226955	+	0.973905i	$0.572877\pi$
$234$	7.48603	0.489377
$235$	−30.4079	−1.98359
$236$	−69.4275	−4.51935
$237$	−6.32805	−0.411051
$238$	12.0926	0.783847
$239$	21.3332	1.37993	0.689964	−	0.723844i	$-0.257626\pi$
$239$	21.3332	1.37993	0.689964	+	0.723844i	$0.257626\pi$
$240$	59.5523	3.84408
$241$	−4.12655	−0.265814	−0.132907	−	0.991129i	$-0.542431\pi$
$241$	−4.12655	−0.265814	−0.132907	+	0.991129i	$0.542431\pi$
$242$	32.9021	2.11503
$243$	−1.00000	−0.0641500
$244$	39.6468	2.53813
$245$	−51.3094	−3.27804
$246$	22.2068	1.41585
$247$	10.5488	0.671207
$248$	−8.14706	−0.517339
$249$	10.1966	0.646183
$250$	−71.0101	−4.49107
$251$	−27.6146	−1.74302	−0.871508	−	0.490381i	$-0.836858\pi$
$251$	−27.6146	−1.74302	−0.871508	+	0.490381i	$0.836858\pi$
$252$	24.1114	1.51888
$253$	5.11438	0.321538
$254$	57.5030	3.60806
$255$	4.05273	0.253792
$256$	40.1132	2.50708
$257$	20.6479	1.28798	0.643990	−	0.765034i	$-0.277278\pi$
$257$	20.6479	1.28798	0.643990	+	0.765034i	$0.277278\pi$
$258$	27.2312	1.69534
$259$	−40.4781	−2.51519
$260$	−60.4926	−3.75159
$261$	−4.00615	−0.247975
$262$	−23.9967	−1.48252
$263$	4.25735	0.262520	0.131260	−	0.991348i	$-0.458098\pi$
$263$	4.25735	0.262520	0.131260	+	0.991348i	$0.458098\pi$
$264$	−45.0275	−2.77125
$265$	−21.6973	−1.33286
$266$	46.4725	2.84941
$267$	−12.3120	−0.753482
$268$	16.3175	0.996750
$269$	−0.680025	−0.0414619	−0.0207309	−	0.999785i	$-0.506599\pi$
$269$	−0.680025	−0.0414619	−0.0207309	+	0.999785i	$0.506599\pi$
$270$	11.0528	0.672650
$271$	13.9457	0.847140	0.423570	−	0.905863i	$-0.360777\pi$
$271$	13.9457	0.847140	0.423570	+	0.905863i	$0.360777\pi$
$272$	14.6944	0.890976
$273$	−12.1710	−0.736621
$274$	−35.7627	−2.16051
$275$	54.8672	3.30861
$276$	−5.79093	−0.348573
$277$	5.60217	0.336602	0.168301	−	0.985736i	$-0.446172\pi$
$277$	5.60217	0.336602	0.168301	+	0.985736i	$0.446172\pi$
$278$	−39.0880	−2.34434
$279$	−0.868946	−0.0520225
$280$	−168.482	−10.0687
$281$	6.98478	0.416677	0.208339	−	0.978057i	$-0.433194\pi$
$281$	6.98478	0.416677	0.208339	+	0.978057i	$0.433194\pi$
$282$	−20.4626	−1.21853
$283$	−16.1455	−0.959753	−0.479876	−	0.877336i	$-0.659318\pi$
$283$	−16.1455	−0.959753	−0.479876	+	0.877336i	$0.659318\pi$
$284$	−40.3991	−2.39725
$285$	15.5749	0.922575
$286$	35.9519	2.12588
$287$	−36.1043	−2.13117
$288$	21.3234	1.25650
$289$	1.00000	0.0588235
$290$	44.2791	2.60016
$291$	10.4488	0.612521
$292$	2.31027	0.135198
$293$	22.6900	1.32556	0.662781	−	0.748813i	$-0.269376\pi$
$293$	22.6900	1.32556	0.662781	+	0.748813i	$0.269376\pi$
$294$	−34.5281	−2.01372
$295$	51.7433	3.01261
$296$	−85.5916	−4.97491
$297$	−4.80253	−0.278671
$298$	−33.8773	−1.96246
$299$	2.92315	0.169050
$300$	−62.1253	−3.58680
$301$	−44.2732	−2.55186
$302$	17.2181	0.990793
$303$	1.67215	0.0960623
$304$	56.4712	3.23884
$305$	−29.5481	−1.69192
$306$	2.72724	0.155906
$307$	14.7697	0.842953	0.421476	−	0.906839i	$-0.361512\pi$
$307$	14.7697	0.842953	0.421476	+	0.906839i	$0.361512\pi$
$308$	115.796	6.59807
$309$	1.70083	0.0967567
$310$	9.60426	0.545486
$311$	16.1833	0.917672	0.458836	−	0.888521i	$-0.348267\pi$
$311$	16.1833	0.917672	0.458836	+	0.888521i	$0.348267\pi$
$312$	−25.7357	−1.45700
$313$	7.68400	0.434326	0.217163	−	0.976135i	$-0.430320\pi$
$313$	7.68400	0.434326	0.217163	+	0.976135i	$0.430320\pi$
$314$	−2.72724	−0.153907
$315$	−17.9699	−1.01249
$316$	34.4109	1.93576
$317$	−27.5037	−1.54476	−0.772380	−	0.635161i	$-0.780934\pi$
$317$	−27.5037	−1.54476	−0.772380	+	0.635161i	$0.780934\pi$
$318$	−14.6010	−0.818782
$319$	−19.2396	−1.07721
$320$	−116.578	−6.51694
$321$	−13.5660	−0.757181
$322$	12.8778	0.717653
$323$	3.84305	0.213833
$324$	5.43783	0.302102
$325$	31.3596	1.73952
$326$	66.9966	3.71060
$327$	−15.1191	−0.836086
$328$	−76.3433	−4.21535
$329$	33.2686	1.83416
$330$	53.0812	2.92203
$331$	24.9825	1.37316	0.686581	−	0.727053i	$-0.259111\pi$
$331$	24.9825	1.37316	0.686581	+	0.727053i	$0.259111\pi$
$332$	−55.4473	−3.04307
$333$	−9.12900	−0.500266
$334$	−26.5358	−1.45198
$335$	−12.1612	−0.664437
$336$	−65.1549	−3.55449
$337$	−5.58023	−0.303974	−0.151987	−	0.988382i	$-0.548567\pi$
$337$	−5.58023	−0.303974	−0.151987	+	0.988382i	$0.548567\pi$
$338$	−14.9056	−0.810758
$339$	−3.29528	−0.178975
$340$	−22.0381	−1.19518
$341$	−4.17314	−0.225988
$342$	10.4809	0.566743
$343$	25.0985	1.35519
$344$	−93.6164	−5.04746
$345$	4.31589	0.232360
$346$	−40.0304	−2.15205
$347$	1.31394	0.0705362	0.0352681	−	0.999378i	$-0.488771\pi$
$347$	1.31394	0.0705362	0.0352681	+	0.999378i	$0.488771\pi$
$348$	21.7848	1.16779
$349$	−16.8745	−0.903271	−0.451635	−	0.892203i	$-0.649159\pi$
$349$	−16.8745	−0.903271	−0.451635	+	0.892203i	$0.649159\pi$
$350$	138.154	7.38462
$351$	−2.74491	−0.146513
$352$	102.406	5.45828
$353$	−17.3016	−0.920873	−0.460436	−	0.887693i	$-0.652307\pi$
$353$	−17.3016	−0.920873	−0.460436	+	0.887693i	$0.652307\pi$
$354$	34.8200	1.85066
$355$	30.1088	1.59801
$356$	66.9505	3.54837
$357$	−4.43401	−0.234673
$358$	−14.5840	−0.770788
$359$	−24.6300	−1.29992	−0.649960	−	0.759968i	$-0.725214\pi$
$359$	−24.6300	−1.29992	−0.649960	+	0.759968i	$0.725214\pi$
$360$	−37.9976	−2.00265
$361$	−4.23096	−0.222682
$362$	−8.23604	−0.432876
$363$	−12.0643	−0.633210
$364$	66.1837	3.46897
$365$	−1.72180	−0.0901234
$366$	−19.8841	−1.03936
$367$	24.5071	1.27926	0.639631	−	0.768682i	$-0.279087\pi$
$367$	24.5071	1.27926	0.639631	+	0.768682i	$0.279087\pi$
$368$	15.6485	0.815736
$369$	−8.14259	−0.423887
$370$	100.901	5.24558
$371$	23.7386	1.23245
$372$	4.72518	0.244989
$373$	−32.3772	−1.67643	−0.838213	−	0.545343i	$-0.816399\pi$
$373$	−32.3772	−1.67643	−0.838213	+	0.545343i	$0.816399\pi$
$374$	13.0976	0.677263
$375$	26.0374	1.34456
$376$	70.3471	3.62787
$377$	−10.9965	−0.566350
$378$	−12.0926	−0.621976
$379$	−22.9965	−1.18125	−0.590625	−	0.806947i	$-0.701119\pi$
$379$	−22.9965	−1.18125	−0.590625	+	0.806947i	$0.701119\pi$
$380$	−84.6935	−4.34468
$381$	−21.0847	−1.08020
$382$	68.7720	3.51868
$383$	−20.7055	−1.05800	−0.529000	−	0.848622i	$-0.677433\pi$
$383$	−20.7055	−1.05800	−0.529000	+	0.848622i	$0.677433\pi$
$384$	−35.8032	−1.82708
$385$	−86.3007	−4.39829
$386$	−53.7556	−2.73609
$387$	−9.98491	−0.507561
$388$	−56.8190	−2.88455
$389$	17.7157	0.898221	0.449110	−	0.893476i	$-0.351741\pi$
$389$	17.7157	0.898221	0.449110	+	0.893476i	$0.351741\pi$
$390$	30.3389	1.53627
$391$	1.06493	0.0538560
$392$	118.702	5.99534
$393$	8.79889	0.443845
$394$	16.1521	0.813732
$395$	−25.6459	−1.29039
$396$	26.1153	1.31235
$397$	10.0560	0.504696	0.252348	−	0.967637i	$-0.418797\pi$
$397$	10.0560	0.504696	0.252348	+	0.967637i	$0.418797\pi$
$398$	31.5478	1.58135
$399$	−17.0401	−0.853073
$400$	167.878	8.39389
$401$	−28.2073	−1.40860	−0.704302	−	0.709901i	$-0.748740\pi$
$401$	−28.2073	−1.40860	−0.704302	+	0.709901i	$0.748740\pi$
$402$	−8.18373	−0.408167
$403$	−2.38518	−0.118814
$404$	−9.09285	−0.452386
$405$	−4.05273	−0.201382
$406$	−48.4448	−2.40427
$407$	−43.8423	−2.17318
$408$	−9.37579	−0.464171
$409$	17.1685	0.848928	0.424464	−	0.905445i	$-0.360463\pi$
$409$	17.1685	0.848928	0.424464	+	0.905445i	$0.360463\pi$
$410$	89.9982	4.44470
$411$	13.1132	0.646825
$412$	−9.24882	−0.455657
$413$	−56.6112	−2.78566
$414$	2.90433	0.142740
$415$	41.3240	2.02852
$416$	58.5310	2.86972
$417$	14.3324	0.701862
$418$	50.3349	2.46196
$419$	−29.5393	−1.44309	−0.721544	−	0.692368i	$-0.756567\pi$
$419$	−29.5393	−1.44309	−0.721544	+	0.692368i	$0.756567\pi$
$420$	97.7171	4.76810
$421$	−34.2459	−1.66904	−0.834522	−	0.550975i	$-0.814256\pi$
$421$	−34.2459	−1.66904	−0.834522	+	0.550975i	$0.814256\pi$
$422$	41.0894	2.00020
$423$	7.50306	0.364811
$424$	50.1957	2.43772
$425$	11.4246	0.554177
$426$	20.2614	0.981668
$427$	32.3280	1.56446
$428$	73.7697	3.56579
$429$	−13.1825	−0.636458
$430$	110.361	5.32207
$431$	−21.0069	−1.01186	−0.505932	−	0.862573i	$-0.668851\pi$
$431$	−21.0069	−1.01186	−0.505932	+	0.862573i	$0.668851\pi$
$432$	−14.6944	−0.706983
$433$	15.7972	0.759166	0.379583	−	0.925158i	$-0.376067\pi$
$433$	15.7972	0.759166	0.379583	+	0.925158i	$0.376067\pi$
$434$	−10.5078	−0.504392
$435$	−16.2359	−0.778450
$436$	82.2149	3.93738
$437$	4.09260	0.195775
$438$	−1.15867	−0.0553633
$439$	39.9510	1.90676	0.953379	−	0.301776i	$-0.0975795\pi$
$439$	39.9510	1.90676	0.953379	+	0.301776i	$0.0975795\pi$
$440$	−182.484	−8.69960
$441$	12.6604	0.602878
$442$	7.48603	0.356074
$443$	22.6687	1.07702	0.538511	−	0.842619i	$-0.318987\pi$
$443$	22.6687	1.07702	0.538511	+	0.842619i	$0.318987\pi$
$444$	49.6420	2.35590
$445$	−49.8972	−2.36535
$446$	−30.5665	−1.44737
$447$	12.4218	0.587533
$448$	127.546	6.02599
$449$	−38.7565	−1.82903	−0.914516	−	0.404550i	$-0.867428\pi$
$449$	−38.7565	−1.82903	−0.914516	+	0.404550i	$0.867428\pi$
$450$	31.1577	1.46879
$451$	−39.1050	−1.84138
$452$	17.9192	0.842848
$453$	−6.31340	−0.296629
$454$	−13.0789	−0.613822
$455$	−49.3257	−2.31242
$456$	−36.0316	−1.68734
$457$	9.25744	0.433045	0.216522	−	0.976278i	$-0.430529\pi$
$457$	9.25744	0.433045	0.216522	+	0.976278i	$0.430529\pi$
$458$	−79.1978	−3.70067
$459$	−1.00000	−0.0466760
$460$	−23.4691	−1.09425
$461$	26.9894	1.25702	0.628511	−	0.777801i	$-0.283665\pi$
$461$	26.9894	1.25702	0.628511	+	0.777801i	$0.283665\pi$
$462$	−58.0751	−2.70190
$463$	−24.5625	−1.14152	−0.570758	−	0.821119i	$-0.693350\pi$
$463$	−24.5625	−1.14152	−0.570758	+	0.821119i	$0.693350\pi$
$464$	−58.8678	−2.73287
$465$	−3.52161	−0.163311
$466$	−18.8961	−0.875343
$467$	7.11153	0.329082	0.164541	−	0.986370i	$-0.447386\pi$
$467$	7.11153	0.329082	0.164541	+	0.986370i	$0.447386\pi$
$468$	14.9264	0.689972
$469$	13.3053	0.614382
$470$	−82.9296	−3.82526
$471$	1.00000	0.0460776
$472$	−119.705	−5.50989
$473$	−47.9528	−2.20487
$474$	−17.2581	−0.792691
$475$	43.9055	2.01452
$476$	24.1114	1.10514
$477$	5.35375	0.245132
$478$	58.1806	2.66112
$479$	−7.78534	−0.355721	−0.177861	−	0.984056i	$-0.556918\pi$
$479$	−7.78534	−0.355721	−0.177861	+	0.984056i	$0.556918\pi$
$480$	86.4182	3.94443
$481$	−25.0583	−1.14256
$482$	−11.2541	−0.512609
$483$	−4.72193	−0.214855
$484$	65.6035	2.98198
$485$	42.3463	1.92285
$486$	−2.72724	−0.123710
$487$	−14.1100	−0.639387	−0.319694	−	0.947521i	$-0.603580\pi$
$487$	−14.1100	−0.639387	−0.319694	+	0.947521i	$0.603580\pi$
$488$	68.3581	3.09443
$489$	−24.5657	−1.11090
$490$	−139.933	−6.32153
$491$	32.9346	1.48632	0.743159	−	0.669115i	$-0.233327\pi$
$491$	32.9346	1.48632	0.743159	+	0.669115i	$0.233327\pi$
$492$	44.2781	1.99621
$493$	−4.00615	−0.180428
$494$	28.7692	1.29439
$495$	−19.4634	−0.874813
$496$	−12.7686	−0.573327
$497$	−32.9415	−1.47763
$498$	27.8085	1.24613
$499$	−8.77176	−0.392678	−0.196339	−	0.980536i	$-0.562905\pi$
$499$	−8.77176	−0.392678	−0.196339	+	0.980536i	$0.562905\pi$
$500$	−141.587	−6.33195
$501$	9.72992	0.434701
$502$	−75.3116	−3.36132
$503$	−33.0211	−1.47234	−0.736170	−	0.676797i	$-0.763368\pi$
$503$	−33.0211	−1.47234	−0.736170	+	0.676797i	$0.763368\pi$
$504$	41.5723	1.85178
$505$	6.77676	0.301562
$506$	13.9481	0.620070
$507$	5.46545	0.242729
$508$	114.655	5.08700
$509$	−20.5172	−0.909408	−0.454704	−	0.890643i	$-0.650255\pi$
$509$	−20.5172	−0.909408	−0.454704	+	0.890643i	$0.650255\pi$
$510$	11.0528	0.489425
$511$	1.88379	0.0833340
$512$	37.7918	1.67018
$513$	−3.84305	−0.169675
$514$	56.3118	2.48381
$515$	6.89300	0.303742
$516$	54.2962	2.39026
$517$	36.0336	1.58476
$518$	−110.393	−4.85041
$519$	14.6780	0.644293
$520$	−104.300	−4.57386
$521$	−25.5814	−1.12074	−0.560370	−	0.828242i	$-0.689341\pi$
$521$	−25.5814	−1.12074	−0.560370	+	0.828242i	$0.689341\pi$
$522$	−10.9257	−0.478206
$523$	6.86188	0.300049	0.150025	−	0.988682i	$-0.452065\pi$
$523$	6.86188	0.300049	0.150025	+	0.988682i	$0.452065\pi$
$524$	−47.8469	−2.09020
$525$	−50.6570	−2.21085
$526$	11.6108	0.506256
$527$	−0.868946	−0.0378519
$528$	−70.5700	−3.07117
$529$	−21.8659	−0.950692
$530$	−59.1738	−2.57035
$531$	−12.7675	−0.554062
$532$	92.6614	4.01738
$533$	−22.3507	−0.968117
$534$	−33.5777	−1.45305
$535$	−54.9794	−2.37697
$536$	28.1343	1.21522
$537$	5.34753	0.230763
$538$	−1.85459	−0.0799571
$539$	60.8021	2.61893
$540$	22.0381	0.948368
$541$	1.47957	0.0636118	0.0318059	−	0.999494i	$-0.489874\pi$
$541$	1.47957	0.0636118	0.0318059	+	0.999494i	$0.489874\pi$
$542$	38.0332	1.63367
$543$	3.01992	0.129597
$544$	21.3234	0.914235
$545$	−61.2735	−2.62467
$546$	−33.1931	−1.42054
$547$	25.6308	1.09589	0.547947	−	0.836513i	$-0.315409\pi$
$547$	25.6308	1.09589	0.547947	+	0.836513i	$0.315409\pi$
$548$	−71.3072	−3.04609
$549$	7.29092	0.311169
$550$	149.636	6.38049
$551$	−15.3958	−0.655885
$552$	−9.98460	−0.424973
$553$	28.0586	1.19318
$554$	15.2785	0.649119
$555$	−36.9974	−1.57045
$556$	−77.9374	−3.30528
$557$	26.0090	1.10203	0.551017	−	0.834494i	$-0.314240\pi$
$557$	26.0090	1.10203	0.551017	+	0.834494i	$0.314240\pi$
$558$	−2.36982	−0.100323
$559$	−27.4077	−1.15922
$560$	−264.055	−11.1584
$561$	−4.80253	−0.202763
$562$	19.0492	0.803541
$563$	7.20245	0.303547	0.151774	−	0.988415i	$-0.451502\pi$
$563$	7.20245	0.303547	0.151774	+	0.988415i	$0.451502\pi$
$564$	−40.8004	−1.71801
$565$	−13.3549	−0.561845
$566$	−44.0327	−1.85083
$567$	4.43401	0.186211
$568$	−69.6553	−2.92267
$569$	−9.54056	−0.399961	−0.199981	−	0.979800i	$-0.564088\pi$
$569$	−9.54056	−0.399961	−0.199981	+	0.979800i	$0.564088\pi$
$570$	42.4764	1.77914
$571$	15.6243	0.653856	0.326928	−	0.945049i	$-0.393987\pi$
$571$	15.6243	0.653856	0.326928	+	0.945049i	$0.393987\pi$
$572$	71.6843	2.99727
$573$	−25.2167	−1.05344
$574$	−98.4652	−4.10986
$575$	12.1665	0.507378
$576$	28.7654	1.19856
$577$	19.6792	0.819256	0.409628	−	0.912253i	$-0.365659\pi$
$577$	19.6792	0.819256	0.409628	+	0.912253i	$0.365659\pi$
$578$	2.72724	0.113438
$579$	19.7106	0.819146
$580$	88.2879	3.66595
$581$	−45.2118	−1.87570
$582$	28.4965	1.18122
$583$	25.7116	1.06486
$584$	3.98331	0.164830
$585$	−11.1244	−0.459937
$586$	61.8809	2.55628
$587$	3.97612	0.164112	0.0820559	−	0.996628i	$-0.473851\pi$
$587$	3.97612	0.164112	0.0820559	+	0.996628i	$0.473851\pi$
$588$	−68.8454	−2.83914
$589$	−3.33941	−0.137598
$590$	141.116	5.80966
$591$	−5.92252	−0.243620
$592$	−134.145	−5.51332
$593$	34.7167	1.42564	0.712822	−	0.701345i	$-0.247417\pi$
$593$	34.7167	1.42564	0.712822	+	0.701345i	$0.247417\pi$
$594$	−13.0976	−0.537403
$595$	−17.9699	−0.736692
$596$	−67.5479	−2.76687
$597$	−11.5677	−0.473433
$598$	7.97213	0.326005
$599$	16.1407	0.659491	0.329746	−	0.944070i	$-0.393037\pi$
$599$	16.1407	0.659491	0.329746	+	0.944070i	$0.393037\pi$
$600$	−107.115	−4.37295
$601$	14.7351	0.601057	0.300528	−	0.953773i	$-0.402837\pi$
$601$	14.7351	0.601057	0.300528	+	0.953773i	$0.402837\pi$
$602$	−120.744	−4.92114
$603$	3.00074	0.122199
$604$	34.3312	1.39692
$605$	−48.8933	−1.98779
$606$	4.56034	0.185251
$607$	−25.8771	−1.05032	−0.525159	−	0.851004i	$-0.675994\pi$
$607$	−25.8771	−1.05032	−0.525159	+	0.851004i	$0.675994\pi$
$608$	81.9471	3.32339
$609$	17.7633	0.719806
$610$	−80.5848	−3.26278
$611$	20.5952	0.833194
$612$	5.43783	0.219811
$613$	−34.4907	−1.39307	−0.696533	−	0.717525i	$-0.745275\pi$
$613$	−34.4907	−1.39307	−0.696533	+	0.717525i	$0.745275\pi$
$614$	40.2806	1.62559
$615$	−32.9998	−1.33068
$616$	199.652	8.04422
$617$	−40.4309	−1.62769	−0.813844	−	0.581084i	$-0.802629\pi$
$617$	−40.4309	−1.62769	−0.813844	+	0.581084i	$0.802629\pi$
$618$	4.63857	0.186590
$619$	25.9947	1.04482	0.522408	−	0.852696i	$-0.325034\pi$
$619$	25.9947	1.04482	0.522408	+	0.852696i	$0.325034\pi$
$620$	19.1499	0.769079
$621$	−1.06493	−0.0427343
$622$	44.1358	1.76968
$623$	54.5915	2.18716
$624$	−40.3347	−1.61468
$625$	48.3992	1.93597
$626$	20.9561	0.837575
$627$	−18.4564	−0.737076
$628$	−5.43783	−0.216993
$629$	−9.12900	−0.363997
$630$	−49.0081	−1.95253
$631$	0.965719	0.0384447	0.0192223	−	0.999815i	$-0.493881\pi$
$631$	0.965719	0.0384447	0.0192223	+	0.999815i	$0.493881\pi$
$632$	59.3305	2.36004
$633$	−15.0663	−0.598832
$634$	−75.0091	−2.97899
$635$	−85.4507	−3.39101
$636$	−29.1128	−1.15440
$637$	34.7518	1.37692
$638$	−52.4711	−2.07735
$639$	−7.42927	−0.293897
$640$	−145.101	−5.73562
$641$	17.2125	0.679854	0.339927	−	0.940452i	$-0.389598\pi$
$641$	17.2125	0.679854	0.339927	+	0.940452i	$0.389598\pi$
$642$	−36.9978	−1.46019
$643$	3.84066	0.151461	0.0757305	−	0.997128i	$-0.475871\pi$
$643$	3.84066	0.151461	0.0757305	+	0.997128i	$0.475871\pi$
$644$	25.6771	1.01182
$645$	−40.4662	−1.59335
$646$	10.4809	0.412366
$647$	18.4711	0.726175	0.363087	−	0.931755i	$-0.381723\pi$
$647$	18.4711	0.726175	0.363087	+	0.931755i	$0.381723\pi$
$648$	9.37579	0.368316
$649$	−61.3163	−2.40687
$650$	85.5252	3.35458
$651$	3.85292	0.151008
$652$	133.584	5.23156
$653$	5.57473	0.218156	0.109078	−	0.994033i	$-0.465210\pi$
$653$	5.57473	0.218156	0.109078	+	0.994033i	$0.465210\pi$
$654$	−41.2333	−1.61235
$655$	35.6596	1.39333
$656$	−119.650	−4.67155
$657$	0.424850	0.0165750
$658$	90.7315	3.53708
$659$	−21.6037	−0.841560	−0.420780	−	0.907163i	$-0.638244\pi$
$659$	−21.6037	−0.841560	−0.420780	+	0.907163i	$0.638244\pi$
$660$	105.838	4.11976
$661$	8.20186	0.319015	0.159508	−	0.987197i	$-0.449009\pi$
$661$	8.20186	0.319015	0.159508	+	0.987197i	$0.449009\pi$
$662$	68.1332	2.64807
$663$	−2.74491	−0.106604
$664$	−95.6011	−3.71004
$665$	−69.0591	−2.67800
$666$	−24.8970	−0.964738
$667$	−4.26629	−0.165191
$668$	−52.9097	−2.04714
$669$	11.2079	0.433321
$670$	−33.1665	−1.28133
$671$	35.0148	1.35173
$672$	−94.5483	−3.64728
$673$	−14.9777	−0.577349	−0.288675	−	0.957427i	$-0.593215\pi$
$673$	−14.9777	−0.577349	−0.288675	+	0.957427i	$0.593215\pi$
$674$	−15.2186	−0.586199
$675$	−11.4246	−0.439735
$676$	−29.7202	−1.14309
$677$	34.5038	1.32609	0.663045	−	0.748579i	$-0.269264\pi$
$677$	34.5038	1.32609	0.663045	+	0.748579i	$0.269264\pi$
$678$	−8.98702	−0.345145
$679$	−46.3302	−1.77799
$680$	−37.9976	−1.45714
$681$	4.79565	0.183770
$682$	−11.3811	−0.435807
$683$	−1.79406	−0.0686478	−0.0343239	−	0.999411i	$-0.510928\pi$
$683$	−1.79406	−0.0686478	−0.0343239	+	0.999411i	$0.510928\pi$
$684$	20.8979	0.799050
$685$	53.1441	2.03053
$686$	68.4495	2.61341
$687$	29.0395	1.10793
$688$	−146.722	−5.59372
$689$	14.6956	0.559857
$690$	11.7705	0.448094
$691$	35.4341	1.34798	0.673989	−	0.738742i	$-0.264580\pi$
$691$	35.4341	1.34798	0.673989	+	0.738742i	$0.264580\pi$
$692$	−79.8166	−3.03417
$693$	21.2945	0.808909
$694$	3.58344	0.136025
$695$	58.0855	2.20331
$696$	37.5608	1.42374
$697$	−8.14259	−0.308423
$698$	−46.0208	−1.74191
$699$	6.92864	0.262065
$700$	275.464	10.4116
$701$	13.8461	0.522961	0.261481	−	0.965209i	$-0.415789\pi$
$701$	13.8461	0.522961	0.261481	+	0.965209i	$0.415789\pi$
$702$	−7.48603	−0.282542
$703$	−35.0832	−1.32319
$704$	138.147	5.20660
$705$	30.4079	1.14523
$706$	−47.1857	−1.77586
$707$	−7.41431	−0.278844
$708$	69.4275	2.60925
$709$	0.00928858	0.000348840 0	0.000174420	−	1.00000i	$-0.499944\pi$
$709$	0.00928858	0.000348840 0	0.000174420		1.00000i	$0.499944\pi$
$710$	82.1140	3.08168
$711$	6.32805	0.237321
$712$	115.435	4.32610
$713$	−0.925371	−0.0346554
$714$	−12.0926	−0.452554
$715$	−53.4252	−1.99799
$716$	−29.0790	−1.08673
$717$	−21.3332	−0.796701
$718$	−67.1718	−2.50683
$719$	13.7460	0.512640	0.256320	−	0.966592i	$-0.417490\pi$
$719$	13.7460	0.512640	0.256320	+	0.966592i	$0.417490\pi$
$720$	−59.5523	−2.21938
$721$	−7.54149	−0.280860
$722$	−11.5388	−0.429431
$723$	4.12655	0.153468
$724$	−16.4218	−0.610311
$725$	−45.7688	−1.69981
$726$	−32.9021	−1.22111
$727$	−16.1688	−0.599666	−0.299833	−	0.953992i	$-0.596931\pi$
$727$	−16.1688	−0.599666	−0.299833	+	0.953992i	$0.596931\pi$
$728$	114.112	4.22929
$729$	1.00000	0.0370370
$730$	−4.69577	−0.173798
$731$	−9.98491	−0.369305
$732$	−39.6468	−1.46539
$733$	14.4632	0.534209	0.267105	−	0.963668i	$-0.413933\pi$
$733$	14.4632	0.534209	0.267105	+	0.963668i	$0.413933\pi$
$734$	66.8368	2.46699
$735$	51.3094	1.89258
$736$	22.7081	0.837030
$737$	14.4111	0.530841
$738$	−22.2068	−0.817444
$739$	−0.834957	−0.0307144	−0.0153572	−	0.999882i	$-0.504889\pi$
$739$	−0.834957	−0.0307144	−0.0153572	+	0.999882i	$0.504889\pi$
$740$	201.186	7.39573
$741$	−10.5488	−0.387521
$742$	64.7408	2.37671
$743$	5.93649	0.217789	0.108894	−	0.994053i	$-0.465269\pi$
$743$	5.93649	0.217789	0.108894	+	0.994053i	$0.465269\pi$
$744$	8.14706	0.298686
$745$	50.3424	1.84440
$746$	−88.3002	−3.23290
$747$	−10.1966	−0.373074
$748$	26.1153	0.954871
$749$	60.1519	2.19790
$750$	71.0101	2.59292
$751$	43.5831	1.59037	0.795185	−	0.606367i	$-0.207374\pi$
$751$	43.5831	1.59037	0.795185	+	0.606367i	$0.207374\pi$
$752$	110.253	4.02050
$753$	27.6146	1.00633
$754$	−29.9902	−1.09218
$755$	−25.5865	−0.931189
$756$	−24.1114	−0.876923
$757$	41.3759	1.50383	0.751916	−	0.659258i	$-0.229130\pi$
$757$	41.3759	1.50383	0.751916	+	0.659258i	$0.229130\pi$
$758$	−62.7169	−2.27798
$759$	−5.11438	−0.185640
$760$	−146.027	−5.29694
$761$	−6.17293	−0.223769	−0.111884	−	0.993721i	$-0.535689\pi$
$761$	−6.17293	−0.223769	−0.111884	+	0.993721i	$0.535689\pi$
$762$	−57.5030	−2.08312
$763$	67.0381	2.42694
$764$	137.124	4.96098
$765$	−4.05273	−0.146527
$766$	−56.4688	−2.04030
$767$	−35.0457	−1.26543
$768$	−40.1132	−1.44746
$769$	−4.49657	−0.162150	−0.0810751	−	0.996708i	$-0.525835\pi$
$769$	−4.49657	−0.162150	−0.0810751	+	0.996708i	$0.525835\pi$
$770$	−235.363	−8.48188
$771$	−20.6479	−0.743616
$772$	−107.183	−3.85760
$773$	−27.5980	−0.992631	−0.496315	−	0.868142i	$-0.665314\pi$
$773$	−27.5980	−0.992631	−0.496315	+	0.868142i	$0.665314\pi$
$774$	−27.2312	−0.978806
$775$	−9.92740	−0.356603
$776$	−97.9660	−3.51678
$777$	40.4781	1.45214
$778$	48.3149	1.73217
$779$	−31.2924	−1.12117
$780$	60.4926	2.16598
$781$	−35.6793	−1.27670
$782$	2.90433	0.103859
$783$	4.00615	0.143168
$784$	186.037	6.64418
$785$	4.05273	0.144648
$786$	23.9967	0.855933
$787$	7.51065	0.267726	0.133863	−	0.991000i	$-0.457262\pi$
$787$	7.51065	0.267726	0.133863	+	0.991000i	$0.457262\pi$
$788$	32.2057	1.14728
$789$	−4.25735	−0.151566
$790$	−69.9425	−2.48844
$791$	14.6113	0.519519
$792$	45.0275	1.59998
$793$	20.0129	0.710680
$794$	27.4251	0.973280
$795$	21.6973	0.769525
$796$	62.9031	2.22954
$797$	−38.2913	−1.35635	−0.678173	−	0.734902i	$-0.737228\pi$
$797$	−38.2913	−1.35635	−0.678173	+	0.734902i	$0.737228\pi$
$798$	−46.4725	−1.64511
$799$	7.50306	0.265439
$800$	243.613	8.61301
$801$	12.3120	0.435023
$802$	−76.9279	−2.71642
$803$	2.04036	0.0720026
$804$	−16.3175	−0.575474
$805$	−19.1367	−0.674481
$806$	−6.50496	−0.229127
$807$	0.680025	0.0239380
$808$	−15.6777	−0.551539
$809$	31.0468	1.09155	0.545773	−	0.837933i	$-0.316236\pi$
$809$	31.0468	1.09155	0.545773	+	0.837933i	$0.316236\pi$
$810$	−11.0528	−0.388355
$811$	10.2609	0.360308	0.180154	−	0.983638i	$-0.442340\pi$
$811$	10.2609	0.360308	0.180154	+	0.983638i	$0.442340\pi$
$812$	−96.5939	−3.38978
$813$	−13.9457	−0.489097
$814$	−119.568	−4.19087
$815$	−99.5583	−3.48737
$816$	−14.6944	−0.514405
$817$	−38.3725	−1.34248
$818$	46.8226	1.63711
$819$	12.1710	0.425288
$820$	179.447	6.26657
$821$	−0.892835	−0.0311601	−0.0155801	−	0.999879i	$-0.504959\pi$
$821$	−0.892835	−0.0311601	−0.0155801	+	0.999879i	$0.504959\pi$
$822$	35.7627	1.24737
$823$	22.8359	0.796011	0.398005	−	0.917383i	$-0.369703\pi$
$823$	22.8359	0.796011	0.398005	+	0.917383i	$0.369703\pi$
$824$	−15.9466	−0.555526
$825$	−54.8672	−1.91023
$826$	−154.392	−5.37200
$827$	7.68813	0.267342	0.133671	−	0.991026i	$-0.457323\pi$
$827$	7.68813	0.267342	0.133671	+	0.991026i	$0.457323\pi$
$828$	5.79093	0.201249
$829$	1.17232	0.0407163	0.0203582	−	0.999793i	$-0.493519\pi$
$829$	1.17232	0.0407163	0.0203582	+	0.999793i	$0.493519\pi$
$830$	112.701	3.91189
$831$	−5.60217	−0.194337
$832$	78.9585	2.73739
$833$	12.6604	0.438658
$834$	39.0880	1.35351
$835$	39.4328	1.36463
$836$	100.363	3.47111
$837$	0.868946	0.0300352
$838$	−80.5607	−2.78292
$839$	−13.0114	−0.449202	−0.224601	−	0.974451i	$-0.572108\pi$
$839$	−13.0114	−0.449202	−0.224601	+	0.974451i	$0.572108\pi$
$840$	168.482	5.81317
$841$	−12.9508	−0.446578
$842$	−93.3968	−3.21867
$843$	−6.98478	−0.240569
$844$	81.9281	2.82008
$845$	22.1500	0.761984
$846$	20.4626	0.703520
$847$	53.4931	1.83804
$848$	78.6700	2.70154
$849$	16.1455	0.554113
$850$	31.1577	1.06870
$851$	−9.72178	−0.333258
$852$	40.3991	1.38405
$853$	−43.8608	−1.50176	−0.750882	−	0.660436i	$-0.770371\pi$
$853$	−43.8608	−1.50176	−0.750882	+	0.660436i	$0.770371\pi$
$854$	88.1662	3.01698
$855$	−15.5749	−0.532649
$856$	127.192	4.34734
$857$	42.1785	1.44079	0.720395	−	0.693564i	$-0.243960\pi$
$857$	42.1785	1.44079	0.720395	+	0.693564i	$0.243960\pi$
$858$	−35.9519	−1.22738
$859$	28.2055	0.962358	0.481179	−	0.876622i	$-0.340209\pi$
$859$	28.2055	0.962358	0.481179	+	0.876622i	$0.340209\pi$
$860$	220.048	7.50358
$861$	36.1043	1.23043
$862$	−57.2907	−1.95133
$863$	−30.4612	−1.03691	−0.518455	−	0.855105i	$-0.673493\pi$
$863$	−30.4612	−1.03691	−0.518455	+	0.855105i	$0.673493\pi$
$864$	−21.3234	−0.725438
$865$	59.4861	2.02259
$866$	43.0828	1.46401
$867$	−1.00000	−0.0339618
$868$	−20.9515	−0.711141
$869$	30.3906	1.03093
$870$	−44.2791	−1.50120
$871$	8.23676	0.279092
$872$	141.753	4.80037
$873$	−10.4488	−0.353639
$874$	11.1615	0.377543
$875$	−115.450	−3.90292
$876$	−2.31027	−0.0780566
$877$	−48.2824	−1.63038	−0.815190	−	0.579194i	$-0.803367\pi$
$877$	−48.2824	−1.63038	−0.815190	+	0.579194i	$0.803367\pi$
$878$	108.956	3.67709
$879$	−22.6900	−0.765313
$880$	−286.002	−9.64111
$881$	52.9591	1.78424	0.892119	−	0.451801i	$-0.149218\pi$
$881$	52.9591	1.78424	0.892119	+	0.451801i	$0.149218\pi$
$882$	34.5281	1.16262
$883$	−13.0091	−0.437791	−0.218895	−	0.975748i	$-0.570245\pi$
$883$	−13.0091	−0.437791	−0.218895	+	0.975748i	$0.570245\pi$
$884$	14.9264	0.502028
$885$	−51.7433	−1.73933
$886$	61.8229	2.07698
$887$	−32.2387	−1.08247	−0.541235	−	0.840871i	$-0.682043\pi$
$887$	−32.2387	−1.08247	−0.541235	+	0.840871i	$0.682043\pi$
$888$	85.5916	2.87227
$889$	93.4898	3.13555
$890$	−136.082	−4.56147
$891$	4.80253	0.160891
$892$	−60.9465	−2.04064
$893$	28.8346	0.964914
$894$	33.8773	1.13303
$895$	21.6721	0.724419
$896$	158.752	5.30353
$897$	−2.92315	−0.0976012
$898$	−105.698	−3.52720
$899$	3.48113	0.116102
$900$	62.1253	2.07084
$901$	5.35375	0.178359
$902$	−106.649	−3.55102
$903$	44.2732	1.47332
$904$	30.8959	1.02758
$905$	12.2389	0.406835
$906$	−17.2181	−0.572035
$907$	12.0638	0.400573	0.200286	−	0.979737i	$-0.435813\pi$
$907$	12.0638	0.400573	0.200286	+	0.979737i	$0.435813\pi$
$908$	−26.0779	−0.865427
$909$	−1.67215	−0.0554616
$910$	−134.523	−4.45939
$911$	15.7193	0.520803	0.260402	−	0.965500i	$-0.416145\pi$
$911$	15.7193	0.520803	0.260402	+	0.965500i	$0.416145\pi$
$912$	−56.4712	−1.86995
$913$	−48.9694	−1.62065
$914$	25.2472	0.835105
$915$	29.5481	0.976831
$916$	−157.912	−5.21756
$917$	−39.0144	−1.28837
$918$	−2.72724	−0.0900123
$919$	18.1013	0.597108	0.298554	−	0.954393i	$-0.403496\pi$
$919$	18.1013	0.597108	0.298554	+	0.954393i	$0.403496\pi$
$920$	−40.4649	−1.33409
$921$	−14.7697	−0.486679
$922$	73.6065	2.42410
$923$	−20.3927	−0.671234
$924$	−115.796	−3.80940
$925$	−104.296	−3.42922
$926$	−66.9877	−2.20135
$927$	−1.70083	−0.0558625
$928$	−85.4249	−2.80421
$929$	−59.7965	−1.96186	−0.980929	−	0.194365i	$-0.937735\pi$
$929$	−59.7965	−1.96186	−0.980929	+	0.194365i	$0.937735\pi$
$930$	−9.60426	−0.314936
$931$	48.6547	1.59459
$932$	−37.6768	−1.23414
$933$	−16.1833	−0.529818
$934$	19.3948	0.634619
$935$	−19.4634	−0.636520
$936$	25.7357	0.841199
$937$	36.8898	1.20514	0.602569	−	0.798067i	$-0.294144\pi$
$937$	36.8898	1.20514	0.602569	+	0.798067i	$0.294144\pi$
$938$	36.2867	1.18480
$939$	−7.68400	−0.250758
$940$	−165.353	−5.39322
$941$	47.0434	1.53357	0.766785	−	0.641904i	$-0.221855\pi$
$941$	47.0434	1.53357	0.766785	+	0.641904i	$0.221855\pi$
$942$	2.72724	0.0888582
$943$	−8.67133	−0.282377
$944$	−187.610	−6.10619
$945$	17.9699	0.584559
$946$	−130.779	−4.25198
$947$	12.7295	0.413653	0.206827	−	0.978378i	$-0.433686\pi$
$947$	12.7295	0.413653	0.206827	+	0.978378i	$0.433686\pi$
$948$	−34.4109	−1.11761
$949$	1.16618	0.0378557
$950$	119.741	3.88490
$951$	27.5037	0.891867
$952$	41.5723	1.34737
$953$	−32.4280	−1.05044	−0.525222	−	0.850965i	$-0.676018\pi$
$953$	−32.4280	−1.05044	−0.525222	+	0.850965i	$0.676018\pi$
$954$	14.6010	0.472724
$955$	−102.197	−3.30700
$956$	116.006	3.75191
$957$	19.2396	0.621930
$958$	−21.2325	−0.685990
$959$	−58.1439	−1.87756
$960$	116.578	3.76255
$961$	−30.2449	−0.975643
$962$	−68.3400	−2.20337
$963$	13.5660	0.437159
$964$	−22.4395	−0.722726
$965$	79.8819	2.57149
$966$	−12.8778	−0.414337
$967$	−17.5752	−0.565180	−0.282590	−	0.959241i	$-0.591194\pi$
$967$	−17.5752	−0.565180	−0.282590	+	0.959241i	$0.591194\pi$
$968$	113.112	3.63556
$969$	−3.84305	−0.123457
$970$	115.489	3.70811
$971$	−48.3118	−1.55040	−0.775200	−	0.631716i	$-0.782351\pi$
$971$	−48.3118	−1.55040	−0.775200	+	0.631716i	$0.782351\pi$
$972$	−5.43783	−0.174419
$973$	−63.5502	−2.03732
$974$	−38.4815	−1.23303
$975$	−31.3596	−1.00431
$976$	107.135	3.42932
$977$	−55.7408	−1.78331	−0.891654	−	0.452718i	$-0.850454\pi$
$977$	−55.7408	−1.78331	−0.891654	+	0.452718i	$0.850454\pi$
$978$	−66.9966	−2.14231
$979$	59.1287	1.88976
$980$	−279.012	−8.91271
$981$	15.1191	0.482715
$982$	89.8205	2.86629
$983$	−32.4065	−1.03361	−0.516804	−	0.856104i	$-0.672878\pi$
$983$	−32.4065	−1.03361	−0.516804	+	0.856104i	$0.672878\pi$
$984$	76.3433	2.43373
$985$	−24.0024	−0.764779
$986$	−10.9257	−0.347946
$987$	−33.2686	−1.05895
$988$	57.3628	1.82495
$989$	−10.6333	−0.338118
$990$	−53.0812	−1.68703
$991$	−0.332617	−0.0105659	−0.00528297	−	0.999986i	$-0.501682\pi$
$991$	−0.332617	−0.0105659	−0.00528297	+	0.999986i	$0.501682\pi$
$992$	−18.5289	−0.588294
$993$	−24.9825	−0.792796
$994$	−89.8392	−2.84953
$995$	−46.8807	−1.48622
$996$	55.4473	1.75692
$997$	−10.1691	−0.322058	−0.161029	−	0.986950i	$-0.551481\pi$
$997$	−10.1691	−0.322058	−0.161029	+	0.986950i	$0.551481\pi$
$998$	−23.9227	−0.757259
$999$	9.12900	0.288829

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.j.1.61	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.j.1.61	✓	64	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 8007 = 3 \cdot 17 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8007.a (trivial)

\(f(q)\)	\(=\)	\(q+2.72724 q^{2} -1.00000 q^{3} +5.43783 q^{4} -4.05273 q^{5} -2.72724 q^{6} +4.43401 q^{7} +9.37579 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.72724 q^{2} -1.00000 q^{3} +5.43783 q^{4} -4.05273 q^{5} -2.72724 q^{6} +4.43401 q^{7} +9.37579 q^{8} +1.00000 q^{9} -11.0528 q^{10} +4.80253 q^{11} -5.43783 q^{12} +2.74491 q^{13} +12.0926 q^{14} +4.05273 q^{15} +14.6944 q^{16} +1.00000 q^{17} +2.72724 q^{18} +3.84305 q^{19} -22.0381 q^{20} -4.43401 q^{21} +13.0976 q^{22} +1.06493 q^{23} -9.37579 q^{24} +11.4246 q^{25} +7.48603 q^{26} -1.00000 q^{27} +24.1114 q^{28} -4.00615 q^{29} +11.0528 q^{30} -0.868946 q^{31} +21.3234 q^{32} -4.80253 q^{33} +2.72724 q^{34} -17.9699 q^{35} +5.43783 q^{36} -9.12900 q^{37} +10.4809 q^{38} -2.74491 q^{39} -37.9976 q^{40} -8.14259 q^{41} -12.0926 q^{42} -9.98491 q^{43} +26.1153 q^{44} -4.05273 q^{45} +2.90433 q^{46} +7.50306 q^{47} -14.6944 q^{48} +12.6604 q^{49} +31.1577 q^{50} -1.00000 q^{51} +14.9264 q^{52} +5.35375 q^{53} -2.72724 q^{54} -19.4634 q^{55} +41.5723 q^{56} -3.84305 q^{57} -10.9257 q^{58} -12.7675 q^{59} +22.0381 q^{60} +7.29092 q^{61} -2.36982 q^{62} +4.43401 q^{63} +28.7654 q^{64} -11.1244 q^{65} -13.0976 q^{66} +3.00074 q^{67} +5.43783 q^{68} -1.06493 q^{69} -49.0081 q^{70} -7.42927 q^{71} +9.37579 q^{72} +0.424850 q^{73} -24.8970 q^{74} -11.4246 q^{75} +20.8979 q^{76} +21.2945 q^{77} -7.48603 q^{78} +6.32805 q^{79} -59.5523 q^{80} +1.00000 q^{81} -22.2068 q^{82} -10.1966 q^{83} -24.1114 q^{84} -4.05273 q^{85} -27.2312 q^{86} +4.00615 q^{87} +45.0275 q^{88} +12.3120 q^{89} -11.0528 q^{90} +12.1710 q^{91} +5.79093 q^{92} +0.868946 q^{93} +20.4626 q^{94} -15.5749 q^{95} -21.3234 q^{96} -10.4488 q^{97} +34.5281 q^{98} +4.80253 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9}+O(q^{10}) \) 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9	\( 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9} + 12 q^{10} - 7 q^{11} - 77 q^{12} + 24 q^{13} - 14 q^{14} + 3 q^{15} + 103 q^{16} + 64 q^{17} + 5 q^{18} + 26 q^{19} - 24 q^{20} - 5 q^{21} + 25 q^{22} + 20 q^{23} - 18 q^{24} + 141 q^{25} + 9 q^{26} - 64 q^{27} + 14 q^{28} + 5 q^{29} - 12 q^{30} + 11 q^{31} + 31 q^{32} + 7 q^{33} + 5 q^{34} - 3 q^{35} + 77 q^{36} + 50 q^{37} + 8 q^{38} - 24 q^{39} + 28 q^{40} - 9 q^{41} + 14 q^{42} + 59 q^{43} - 6 q^{44} - 3 q^{45} + 11 q^{47} - 103 q^{48} + 163 q^{49} + 20 q^{50} - 64 q^{51} + 65 q^{52} + 39 q^{53} - 5 q^{54} + 35 q^{55} - 34 q^{56} - 26 q^{57} - 27 q^{58} - 65 q^{59} + 24 q^{60} + 15 q^{61} + 18 q^{62} + 5 q^{63} + 152 q^{64} + 49 q^{65} - 25 q^{66} + 56 q^{67} + 77 q^{68} - 20 q^{69} + 28 q^{70} - 18 q^{71} + 18 q^{72} + 37 q^{73} - 76 q^{74} - 141 q^{75} + 30 q^{76} + 80 q^{77} - 9 q^{78} + 20 q^{79} - 144 q^{80} + 64 q^{81} + 27 q^{82} + 3 q^{83} - 14 q^{84} - 3 q^{85} + 12 q^{86} - 5 q^{87} + 108 q^{88} + 42 q^{89} + 12 q^{90} + 25 q^{91} + 18 q^{92} - 11 q^{93} + 60 q^{94} + 42 q^{95} - 31 q^{96} + 72 q^{97} + 18 q^{98} - 7 q^{99}+O(q^{100}) \) 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9 + 12 * q^10 - 7 * q^11 - 77 * q^12 + 24 * q^13 - 14 * q^14 + 3 * q^15 + 103 * q^16 + 64 * q^17 + 5 * q^18 + 26 * q^19 - 24 * q^20 - 5 * q^21 + 25 * q^22 + 20 * q^23 - 18 * q^24 + 141 * q^25 + 9 * q^26 - 64 * q^27 + 14 * q^28 + 5 * q^29 - 12 * q^30 + 11 * q^31 + 31 * q^32 + 7 * q^33 + 5 * q^34 - 3 * q^35 + 77 * q^36 + 50 * q^37 + 8 * q^38 - 24 * q^39 + 28 * q^40 - 9 * q^41 + 14 * q^42 + 59 * q^43 - 6 * q^44 - 3 * q^45 + 11 * q^47 - 103 * q^48 + 163 * q^49 + 20 * q^50 - 64 * q^51 + 65 * q^52 + 39 * q^53 - 5 * q^54 + 35 * q^55 - 34 * q^56 - 26 * q^57 - 27 * q^58 - 65 * q^59 + 24 * q^60 + 15 * q^61 + 18 * q^62 + 5 * q^63 + 152 * q^64 + 49 * q^65 - 25 * q^66 + 56 * q^67 + 77 * q^68 - 20 * q^69 + 28 * q^70 - 18 * q^71 + 18 * q^72 + 37 * q^73 - 76 * q^74 - 141 * q^75 + 30 * q^76 + 80 * q^77 - 9 * q^78 + 20 * q^79 - 144 * q^80 + 64 * q^81 + 27 * q^82 + 3 * q^83 - 14 * q^84 - 3 * q^85 + 12 * q^86 - 5 * q^87 + 108 * q^88 + 42 * q^89 + 12 * q^90 + 25 * q^91 + 18 * q^92 - 11 * q^93 + 60 * q^94 + 42 * q^95 - 31 * q^96 + 72 * q^97 + 18 * q^98 - 7 * q^99

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