LMFDB - Embedded newform 8007.2.a.e.1.2

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:	$1$
Dimension:	$46$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
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)

$f(q)$	$=$	$q-2.76060 q^{2} +1.00000 q^{3} +5.62090 q^{4} -0.677149 q^{5} -2.76060 q^{6} +3.14387 q^{7} -9.99585 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.76060 q^{2} +1.00000 q^{3} +5.62090 q^{4} -0.677149 q^{5} -2.76060 q^{6} +3.14387 q^{7} -9.99585 q^{8} +1.00000 q^{9} +1.86934 q^{10} -2.07367 q^{11} +5.62090 q^{12} +5.11851 q^{13} -8.67895 q^{14} -0.677149 q^{15} +16.3527 q^{16} -1.00000 q^{17} -2.76060 q^{18} +1.32055 q^{19} -3.80619 q^{20} +3.14387 q^{21} +5.72457 q^{22} +1.26188 q^{23} -9.99585 q^{24} -4.54147 q^{25} -14.1301 q^{26} +1.00000 q^{27} +17.6714 q^{28} +2.79382 q^{29} +1.86934 q^{30} -1.04665 q^{31} -25.1516 q^{32} -2.07367 q^{33} +2.76060 q^{34} -2.12887 q^{35} +5.62090 q^{36} +1.14118 q^{37} -3.64550 q^{38} +5.11851 q^{39} +6.76869 q^{40} -8.84359 q^{41} -8.67895 q^{42} -12.3593 q^{43} -11.6559 q^{44} -0.677149 q^{45} -3.48354 q^{46} +2.89101 q^{47} +16.3527 q^{48} +2.88389 q^{49} +12.5372 q^{50} -1.00000 q^{51} +28.7706 q^{52} -6.36246 q^{53} -2.76060 q^{54} +1.40418 q^{55} -31.4256 q^{56} +1.32055 q^{57} -7.71262 q^{58} -4.43671 q^{59} -3.80619 q^{60} -14.2855 q^{61} +2.88937 q^{62} +3.14387 q^{63} +36.7280 q^{64} -3.46599 q^{65} +5.72457 q^{66} -6.45138 q^{67} -5.62090 q^{68} +1.26188 q^{69} +5.87694 q^{70} -13.7214 q^{71} -9.99585 q^{72} -0.815601 q^{73} -3.15033 q^{74} -4.54147 q^{75} +7.42268 q^{76} -6.51934 q^{77} -14.1301 q^{78} -5.63591 q^{79} -11.0732 q^{80} +1.00000 q^{81} +24.4136 q^{82} +3.91819 q^{83} +17.6714 q^{84} +0.677149 q^{85} +34.1190 q^{86} +2.79382 q^{87} +20.7281 q^{88} +6.79853 q^{89} +1.86934 q^{90} +16.0919 q^{91} +7.09289 q^{92} -1.04665 q^{93} -7.98092 q^{94} -0.894209 q^{95} -25.1516 q^{96} -10.8745 q^{97} -7.96125 q^{98} -2.07367 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 46 q - 5 q^{2} + 46 q^{3} + 43 q^{4} - 19 q^{5} - 5 q^{6} + q^{7} - 18 q^{8} + 46 q^{9}+O(q^{10}) $ 46 * q - 5 * q^2 + 46 * q^3 + 43 * q^4 - 19 * q^5 - 5 * q^6 + q^7 - 18 * q^8 + 46 * q^9	\( 46 q - 5 q^{2} + 46 q^{3} + 43 q^{4} - 19 q^{5} - 5 q^{6} + q^{7} - 18 q^{8} + 46 q^{9} - 10 q^{10} - 25 q^{11} + 43 q^{12} - 8 q^{13} - 28 q^{14} - 19 q^{15} + 33 q^{16} - 46 q^{17} - 5 q^{18} - 2 q^{19} - 56 q^{20} + q^{21} - 19 q^{22} - 64 q^{23} - 18 q^{24} + 11 q^{25} - 13 q^{26} + 46 q^{27} - 38 q^{28} - 51 q^{29} - 10 q^{30} - 19 q^{31} - 61 q^{32} - 25 q^{33} + 5 q^{34} - 39 q^{35} + 43 q^{36} - 46 q^{37} - 48 q^{38} - 8 q^{39} - 10 q^{40} - 53 q^{41} - 28 q^{42} - 33 q^{43} - 62 q^{44} - 19 q^{45} + 2 q^{46} - 45 q^{47} + 33 q^{48} + 21 q^{49} - 60 q^{50} - 46 q^{51} - 63 q^{52} - 47 q^{53} - 5 q^{54} + 5 q^{55} - 82 q^{56} - 2 q^{57} - 21 q^{58} - 65 q^{59} - 56 q^{60} - 37 q^{61} - 46 q^{62} + q^{63} + 74 q^{64} - 85 q^{65} - 19 q^{66} - 52 q^{67} - 43 q^{68} - 64 q^{69} - 20 q^{70} - 48 q^{71} - 18 q^{72} - 39 q^{73} - 16 q^{74} + 11 q^{75} + 42 q^{76} - 78 q^{77} - 13 q^{78} - 26 q^{79} - 78 q^{80} + 46 q^{81} + 3 q^{82} - 47 q^{83} - 38 q^{84} + 19 q^{85} - 6 q^{86} - 51 q^{87} - 58 q^{88} - 58 q^{89} - 10 q^{90} - 43 q^{91} - 68 q^{92} - 19 q^{93} - 78 q^{95} - 61 q^{96} - 44 q^{97} - 4 q^{98} - 25 q^{99}+O(q^{100}) \) 46 * q - 5 * q^2 + 46 * q^3 + 43 * q^4 - 19 * q^5 - 5 * q^6 + q^7 - 18 * q^8 + 46 * q^9 - 10 * q^10 - 25 * q^11 + 43 * q^12 - 8 * q^13 - 28 * q^14 - 19 * q^15 + 33 * q^16 - 46 * q^17 - 5 * q^18 - 2 * q^19 - 56 * q^20 + q^21 - 19 * q^22 - 64 * q^23 - 18 * q^24 + 11 * q^25 - 13 * q^26 + 46 * q^27 - 38 * q^28 - 51 * q^29 - 10 * q^30 - 19 * q^31 - 61 * q^32 - 25 * q^33 + 5 * q^34 - 39 * q^35 + 43 * q^36 - 46 * q^37 - 48 * q^38 - 8 * q^39 - 10 * q^40 - 53 * q^41 - 28 * q^42 - 33 * q^43 - 62 * q^44 - 19 * q^45 + 2 * q^46 - 45 * q^47 + 33 * q^48 + 21 * q^49 - 60 * q^50 - 46 * q^51 - 63 * q^52 - 47 * q^53 - 5 * q^54 + 5 * q^55 - 82 * q^56 - 2 * q^57 - 21 * q^58 - 65 * q^59 - 56 * q^60 - 37 * q^61 - 46 * q^62 + q^63 + 74 * q^64 - 85 * q^65 - 19 * q^66 - 52 * q^67 - 43 * q^68 - 64 * q^69 - 20 * q^70 - 48 * q^71 - 18 * q^72 - 39 * q^73 - 16 * q^74 + 11 * q^75 + 42 * q^76 - 78 * q^77 - 13 * q^78 - 26 * q^79 - 78 * q^80 + 46 * q^81 + 3 * q^82 - 47 * q^83 - 38 * q^84 + 19 * q^85 - 6 * q^86 - 51 * q^87 - 58 * q^88 - 58 * q^89 - 10 * q^90 - 43 * q^91 - 68 * q^92 - 19 * q^93 - 78 * q^95 - 61 * q^96 - 44 * q^97 - 4 * q^98 - 25 * 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 $

$2$	−2.76060	−1.95204	−0.976019	−	0.217686i	$-0.930149\pi$
$2$	−2.76060	−1.95204	−0.976019	+	0.217686i	$0.930149\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	5.62090	2.81045
$5$	−0.677149	−0.302830	−0.151415	−	0.988470i	$-0.548383\pi$
$5$	−0.677149	−0.302830	−0.151415	+	0.988470i	$0.548383\pi$
$6$	−2.76060	−1.12701
$7$	3.14387	1.18827	0.594135	−	0.804366i	$-0.297495\pi$
$7$	3.14387	1.18827	0.594135	+	0.804366i	$0.297495\pi$
$8$	−9.99585	−3.53407
$9$	1.00000	0.333333
$10$	1.86934	0.591136
$11$	−2.07367	−0.625235	−0.312617	−	0.949879i	$-0.601206\pi$
$11$	−2.07367	−0.625235	−0.312617	+	0.949879i	$0.601206\pi$
$12$	5.62090	1.62261
$13$	5.11851	1.41962	0.709809	−	0.704394i	$-0.248781\pi$
$13$	5.11851	1.41962	0.709809	+	0.704394i	$0.248781\pi$
$14$	−8.67895	−2.31955
$15$	−0.677149	−0.174839
$16$	16.3527	4.08818
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−2.76060	−0.650679
$19$	1.32055	0.302955	0.151477	−	0.988461i	$-0.451597\pi$
$19$	1.32055	0.302955	0.151477	+	0.988461i	$0.451597\pi$
$20$	−3.80619	−0.851090
$21$	3.14387	0.686048
$22$	5.72457	1.22048
$23$	1.26188	0.263120	0.131560	−	0.991308i	$-0.458001\pi$
$23$	1.26188	0.263120	0.131560	+	0.991308i	$0.458001\pi$
$24$	−9.99585	−2.04040
$25$	−4.54147	−0.908294
$26$	−14.1301	−2.77115
$27$	1.00000	0.192450
$28$	17.6714	3.33957
$29$	2.79382	0.518800	0.259400	−	0.965770i	$-0.416475\pi$
$29$	2.79382	0.518800	0.259400	+	0.965770i	$0.416475\pi$
$30$	1.86934	0.341293
$31$	−1.04665	−0.187983	−0.0939916	−	0.995573i	$-0.529963\pi$
$31$	−1.04665	−0.187983	−0.0939916	+	0.995573i	$0.529963\pi$
$32$	−25.1516	−4.44622
$33$	−2.07367	−0.360979
$34$	2.76060	0.473439
$35$	−2.12887	−0.359844
$36$	5.62090	0.936817
$37$	1.14118	0.187608	0.0938042	−	0.995591i	$-0.470097\pi$
$37$	1.14118	0.187608	0.0938042	+	0.995591i	$0.470097\pi$
$38$	−3.64550	−0.591379
$39$	5.11851	0.819617
$40$	6.76869	1.07022
$41$	−8.84359	−1.38114	−0.690569	−	0.723267i	$-0.742640\pi$
$41$	−8.84359	−1.38114	−0.690569	+	0.723267i	$0.742640\pi$
$42$	−8.67895	−1.33919
$43$	−12.3593	−1.88477	−0.942385	−	0.334529i	$-0.891423\pi$
$43$	−12.3593	−1.88477	−0.942385	+	0.334529i	$0.891423\pi$
$44$	−11.6559	−1.75719
$45$	−0.677149	−0.100943
$46$	−3.48354	−0.513620
$47$	2.89101	0.421698	0.210849	−	0.977519i	$-0.432377\pi$
$47$	2.89101	0.421698	0.210849	+	0.977519i	$0.432377\pi$
$48$	16.3527	2.36031
$49$	2.88389	0.411984
$50$	12.5372	1.77302
$51$	−1.00000	−0.140028
$52$	28.7706	3.98977
$53$	−6.36246	−0.873952	−0.436976	−	0.899473i	$-0.643950\pi$
$53$	−6.36246	−0.873952	−0.436976	+	0.899473i	$0.643950\pi$
$54$	−2.76060	−0.375670
$55$	1.40418	0.189340
$56$	−31.4256	−4.19942
$57$	1.32055	0.174911
$58$	−7.71262	−1.01272
$59$	−4.43671	−0.577610	−0.288805	−	0.957388i	$-0.593258\pi$
$59$	−4.43671	−0.577610	−0.288805	+	0.957388i	$0.593258\pi$
$60$	−3.80619	−0.491377
$61$	−14.2855	−1.82908	−0.914538	−	0.404499i	$-0.867446\pi$
$61$	−14.2855	−1.82908	−0.914538	+	0.404499i	$0.867446\pi$
$62$	2.88937	0.366950
$63$	3.14387	0.396090
$64$	36.7280	4.59100
$65$	−3.46599	−0.429904
$66$	5.72457	0.704645
$67$	−6.45138	−0.788161	−0.394081	−	0.919076i	$-0.628937\pi$
$67$	−6.45138	−0.788161	−0.394081	+	0.919076i	$0.628937\pi$
$68$	−5.62090	−0.681634
$69$	1.26188	0.151912
$70$	5.87694	0.702429
$71$	−13.7214	−1.62843	−0.814217	−	0.580561i	$-0.802833\pi$
$71$	−13.7214	−1.62843	−0.814217	+	0.580561i	$0.802833\pi$
$72$	−9.99585	−1.17802
$73$	−0.815601	−0.0954589	−0.0477294	−	0.998860i	$-0.515199\pi$
$73$	−0.815601	−0.0954589	−0.0477294	+	0.998860i	$0.515199\pi$
$74$	−3.15033	−0.366219
$75$	−4.54147	−0.524404
$76$	7.42268	0.851439
$77$	−6.51934	−0.742947
$78$	−14.1301	−1.59992
$79$	−5.63591	−0.634090	−0.317045	−	0.948411i	$-0.602691\pi$
$79$	−5.63591	−0.634090	−0.317045	+	0.948411i	$0.602691\pi$
$80$	−11.0732	−1.23803
$81$	1.00000	0.111111
$82$	24.4136	2.69603
$83$	3.91819	0.430078	0.215039	−	0.976605i	$-0.431012\pi$
$83$	3.91819	0.430078	0.215039	+	0.976605i	$0.431012\pi$
$84$	17.6714	1.92810
$85$	0.677149	0.0734471
$86$	34.1190	3.67914
$87$	2.79382	0.299529
$88$	20.7281	2.20962
$89$	6.79853	0.720643	0.360322	−	0.932828i	$-0.382667\pi$
$89$	6.79853	0.720643	0.360322	+	0.932828i	$0.382667\pi$
$90$	1.86934	0.197045
$91$	16.0919	1.68689
$92$	7.09289	0.739485
$93$	−1.04665	−0.108532
$94$	−7.98092	−0.823169
$95$	−0.894209	−0.0917439
$96$	−25.1516	−2.56703
$97$	−10.8745	−1.10414	−0.552070	−	0.833797i	$-0.686162\pi$
$97$	−10.8745	−1.10414	−0.552070	+	0.833797i	$0.686162\pi$
$98$	−7.96125	−0.804208
$99$	−2.07367	−0.208412
$100$	−25.5272	−2.55272
$101$	−0.683072	−0.0679682	−0.0339841	−	0.999422i	$-0.510820\pi$
$101$	−0.683072	−0.0679682	−0.0339841	+	0.999422i	$0.510820\pi$
$102$	2.76060	0.273340
$103$	−10.4174	−1.02646	−0.513229	−	0.858252i	$-0.671551\pi$
$103$	−10.4174	−1.02646	−0.513229	+	0.858252i	$0.671551\pi$
$104$	−51.1639	−5.01703
$105$	−2.12887	−0.207756
$106$	17.5642	1.70599
$107$	−4.74721	−0.458930	−0.229465	−	0.973317i	$-0.573698\pi$
$107$	−4.74721	−0.458930	−0.229465	+	0.973317i	$0.573698\pi$
$108$	5.62090	0.540872
$109$	−5.05330	−0.484018	−0.242009	−	0.970274i	$-0.577806\pi$
$109$	−5.05330	−0.484018	−0.242009	+	0.970274i	$0.577806\pi$
$110$	−3.87639	−0.369599
$111$	1.14118	0.108316
$112$	51.4108	4.85786
$113$	1.01792	0.0957581	0.0478790	−	0.998853i	$-0.484754\pi$
$113$	1.01792	0.0957581	0.0478790	+	0.998853i	$0.484754\pi$
$114$	−3.64550	−0.341433
$115$	−0.854480	−0.0796806
$116$	15.7038	1.45806
$117$	5.11851	0.473206
$118$	12.2480	1.12752
$119$	−3.14387	−0.288198
$120$	6.76869	0.617894
$121$	−6.69990	−0.609081
$122$	39.4367	3.57043
$123$	−8.84359	−0.797400
$124$	−5.88310	−0.528318
$125$	6.46100	0.577889
$126$	−8.67895	−0.773182
$127$	3.11216	0.276160	0.138080	−	0.990421i	$-0.455907\pi$
$127$	3.11216	0.276160	0.138080	+	0.990421i	$0.455907\pi$
$128$	−51.0881	−4.51559
$129$	−12.3593	−1.08817
$130$	9.56822	0.839188
$131$	4.19643	0.366644	0.183322	−	0.983053i	$-0.441315\pi$
$131$	4.19643	0.366644	0.183322	+	0.983053i	$0.441315\pi$
$132$	−11.6559	−1.01452
$133$	4.15163	0.359992
$134$	17.8097	1.53852
$135$	−0.677149	−0.0582797
$136$	9.99585	0.857137
$137$	13.4645	1.15035	0.575174	−	0.818031i	$-0.304934\pi$
$137$	13.4645	1.15035	0.575174	+	0.818031i	$0.304934\pi$
$138$	−3.48354	−0.296538
$139$	−4.51887	−0.383285	−0.191643	−	0.981465i	$-0.561381\pi$
$139$	−4.51887	−0.383285	−0.191643	+	0.981465i	$0.561381\pi$
$140$	−11.9661	−1.01132
$141$	2.89101	0.243467
$142$	37.8793	3.17876
$143$	−10.6141	−0.887595
$144$	16.3527	1.36273
$145$	−1.89183	−0.157108
$146$	2.25155	0.186339
$147$	2.88389	0.237859
$148$	6.41444	0.527264
$149$	−6.44984	−0.528391	−0.264196	−	0.964469i	$-0.585106\pi$
$149$	−6.44984	−0.528391	−0.264196	+	0.964469i	$0.585106\pi$
$150$	12.5372	1.02366
$151$	18.8081	1.53058	0.765291	−	0.643684i	$-0.222595\pi$
$151$	18.8081	1.53058	0.765291	+	0.643684i	$0.222595\pi$
$152$	−13.2000	−1.07066
$153$	−1.00000	−0.0808452
$154$	17.9973	1.45026
$155$	0.708736	0.0569270
$156$	28.7706	2.30349
$157$	1.00000	0.0798087
$157$	1.00000	0.0798087
$158$	15.5585	1.23777
$159$	−6.36246	−0.504576
$160$	17.0314	1.34645
$161$	3.96717	0.312657
$162$	−2.76060	−0.216893
$163$	−24.8104	−1.94330	−0.971651	−	0.236418i	$-0.924026\pi$
$163$	−24.8104	−1.94330	−0.971651	+	0.236418i	$0.924026\pi$
$164$	−49.7090	−3.88162
$165$	1.40418	0.109316
$166$	−10.8166	−0.839528
$167$	7.58853	0.587218	0.293609	−	0.955926i	$-0.405144\pi$
$167$	7.58853	0.587218	0.293609	+	0.955926i	$0.405144\pi$
$168$	−31.4256	−2.42454
$169$	13.1991	1.01532
$170$	−1.86934	−0.143372
$171$	1.32055	0.100985
$172$	−69.4702	−5.29706
$173$	−0.321536	−0.0244459	−0.0122230	−	0.999925i	$-0.503891\pi$
$173$	−0.321536	−0.0244459	−0.0122230	+	0.999925i	$0.503891\pi$
$174$	−7.71262	−0.584692
$175$	−14.2778	−1.07930
$176$	−33.9102	−2.55607
$177$	−4.43671	−0.333483
$178$	−18.7680	−1.40672
$179$	19.2910	1.44188	0.720940	−	0.692998i	$-0.243710\pi$
$179$	19.2910	1.44188	0.720940	+	0.692998i	$0.243710\pi$
$180$	−3.80619	−0.283697
$181$	−10.4593	−0.777436	−0.388718	−	0.921357i	$-0.627082\pi$
$181$	−10.4593	−0.777436	−0.388718	+	0.921357i	$0.627082\pi$
$182$	−44.4233	−3.29287
$183$	−14.2855	−1.05602
$184$	−12.6135	−0.929883
$185$	−0.772747	−0.0568135
$186$	2.88937	0.211859
$187$	2.07367	0.151642
$188$	16.2501	1.18516
$189$	3.14387	0.228683
$190$	2.46855	0.179087
$191$	−17.6034	−1.27374	−0.636869	−	0.770972i	$-0.719771\pi$
$191$	−17.6034	−1.27374	−0.636869	+	0.770972i	$0.719771\pi$
$192$	36.7280	2.65062
$193$	1.13470	0.0816773	0.0408386	−	0.999166i	$-0.486997\pi$
$193$	1.13470	0.0816773	0.0408386	+	0.999166i	$0.486997\pi$
$194$	30.0202	2.15532
$195$	−3.46599	−0.248205
$196$	16.2100	1.15786
$197$	−15.6748	−1.11678	−0.558392	−	0.829577i	$-0.688581\pi$
$197$	−15.6748	−1.11678	−0.558392	+	0.829577i	$0.688581\pi$
$198$	5.72457	0.406827
$199$	−2.91334	−0.206521	−0.103261	−	0.994654i	$-0.532928\pi$
$199$	−2.91334	−0.206521	−0.103261	+	0.994654i	$0.532928\pi$
$200$	45.3959	3.20997
$201$	−6.45138	−0.455045
$202$	1.88569	0.132676
$203$	8.78340	0.616474
$204$	−5.62090	−0.393542
$205$	5.98843	0.418250
$206$	28.7583	2.00368
$207$	1.26188	0.0877066
$208$	83.7016	5.80366
$209$	−2.73838	−0.189418
$210$	5.87694	0.405548
$211$	1.99437	0.137298	0.0686490	−	0.997641i	$-0.478131\pi$
$211$	1.99437	0.137298	0.0686490	+	0.997641i	$0.478131\pi$
$212$	−35.7628	−2.45620
$213$	−13.7214	−0.940176
$214$	13.1051	0.895849
$215$	8.36907	0.570766
$216$	−9.99585	−0.680132
$217$	−3.29051	−0.223375
$218$	13.9501	0.944822
$219$	−0.815601	−0.0551132
$220$	7.89278	0.532131
$221$	−5.11851	−0.344308
$222$	−3.15033	−0.211436
$223$	−2.95748	−0.198047	−0.0990237	−	0.995085i	$-0.531572\pi$
$223$	−2.95748	−0.198047	−0.0990237	+	0.995085i	$0.531572\pi$
$224$	−79.0733	−5.28331
$225$	−4.54147	−0.302765
$226$	−2.81007	−0.186923
$227$	−12.6127	−0.837132	−0.418566	−	0.908186i	$-0.637467\pi$
$227$	−12.6127	−0.837132	−0.418566	+	0.908186i	$0.637467\pi$
$228$	7.42268	0.491579
$229$	8.41701	0.556212	0.278106	−	0.960550i	$-0.410293\pi$
$229$	8.41701	0.556212	0.278106	+	0.960550i	$0.410293\pi$
$230$	2.35887	0.155540
$231$	−6.51934	−0.428941
$232$	−27.9266	−1.83347
$233$	6.72680	0.440688	0.220344	−	0.975422i	$-0.429282\pi$
$233$	6.72680	0.440688	0.220344	+	0.975422i	$0.429282\pi$
$234$	−14.1301	−0.923716
$235$	−1.95765	−0.127703
$236$	−24.9383	−1.62334
$237$	−5.63591	−0.366092
$238$	8.67895	0.562573
$239$	13.6784	0.884782	0.442391	−	0.896822i	$-0.354130\pi$
$239$	13.6784	0.884782	0.442391	+	0.896822i	$0.354130\pi$
$240$	−11.0732	−0.714775
$241$	−8.88981	−0.572643	−0.286322	−	0.958134i	$-0.592433\pi$
$241$	−8.88981	−0.572643	−0.286322	+	0.958134i	$0.592433\pi$
$242$	18.4957	1.18895
$243$	1.00000	0.0641500
$244$	−80.2977	−5.14053
$245$	−1.95282	−0.124761
$246$	24.4136	1.55655
$247$	6.75924	0.430080
$248$	10.4621	0.664346
$249$	3.91819	0.248305
$250$	−17.8362	−1.12806
$251$	2.89315	0.182614	0.0913070	−	0.995823i	$-0.470896\pi$
$251$	2.89315	0.182614	0.0913070	+	0.995823i	$0.470896\pi$
$252$	17.6714	1.11319
$253$	−2.61672	−0.164512
$254$	−8.59144	−0.539075
$255$	0.677149	0.0424047
$256$	67.5777	4.22361
$257$	5.42647	0.338494	0.169247	−	0.985574i	$-0.445866\pi$
$257$	5.42647	0.338494	0.169247	+	0.985574i	$0.445866\pi$
$258$	34.1190	2.12415
$259$	3.58771	0.222929
$260$	−19.4820	−1.20822
$261$	2.79382	0.172933
$262$	−11.5847	−0.715702
$263$	−19.4244	−1.19776	−0.598881	−	0.800838i	$-0.704388\pi$
$263$	−19.4244	−1.19776	−0.598881	+	0.800838i	$0.704388\pi$
$264$	20.7281	1.27573
$265$	4.30834	0.264659
$266$	−11.4610	−0.702717
$267$	6.79853	0.416063
$268$	−36.2626	−2.21509
$269$	−13.0613	−0.796359	−0.398179	−	0.917308i	$-0.630358\pi$
$269$	−13.0613	−0.796359	−0.398179	+	0.917308i	$0.630358\pi$
$270$	1.86934	0.113764
$271$	−22.4597	−1.36433	−0.682164	−	0.731199i	$-0.738961\pi$
$271$	−22.4597	−1.36433	−0.682164	+	0.731199i	$0.738961\pi$
$272$	−16.3527	−0.991530
$273$	16.0919	0.973926
$274$	−37.1700	−2.24552
$275$	9.41750	0.567897
$276$	7.09289	0.426942
$277$	18.1823	1.09247	0.546233	−	0.837633i	$-0.316061\pi$
$277$	18.1823	1.09247	0.546233	+	0.837633i	$0.316061\pi$
$278$	12.4748	0.748187
$279$	−1.04665	−0.0626611
$280$	21.2798	1.27171
$281$	−12.2995	−0.733726	−0.366863	−	0.930275i	$-0.619568\pi$
$281$	−12.2995	−0.733726	−0.366863	+	0.930275i	$0.619568\pi$
$282$	−7.98092	−0.475257
$283$	13.4204	0.797758	0.398879	−	0.917004i	$-0.369399\pi$
$283$	13.4204	0.797758	0.398879	+	0.917004i	$0.369399\pi$
$284$	−77.1268	−4.57663
$285$	−0.894209	−0.0529683
$286$	29.3012	1.73262
$287$	−27.8031	−1.64116
$288$	−25.1516	−1.48207
$289$	1.00000	0.0588235
$290$	5.22260	0.306681
$291$	−10.8745	−0.637476
$292$	−4.58441	−0.268283
$293$	21.0032	1.22702	0.613509	−	0.789688i	$-0.289757\pi$
$293$	21.0032	1.22702	0.613509	+	0.789688i	$0.289757\pi$
$294$	−7.96125	−0.464310
$295$	3.00431	0.174918
$296$	−11.4070	−0.663021
$297$	−2.07367	−0.120326
$298$	17.8054	1.03144
$299$	6.45893	0.373530
$300$	−25.5272	−1.47381
$301$	−38.8559	−2.23962
$302$	−51.9216	−2.98775
$303$	−0.683072	−0.0392414
$304$	21.5946	1.23853
$305$	9.67345	0.553900
$306$	2.76060	0.157813
$307$	−2.31157	−0.131928	−0.0659642	−	0.997822i	$-0.521012\pi$
$307$	−2.31157	−0.131928	−0.0659642	+	0.997822i	$0.521012\pi$
$308$	−36.6445	−2.08802
$309$	−10.4174	−0.592626
$310$	−1.95653	−0.111124
$311$	2.29825	0.130322	0.0651609	−	0.997875i	$-0.479244\pi$
$311$	2.29825	0.130322	0.0651609	+	0.997875i	$0.479244\pi$
$312$	−51.1639	−2.89658
$313$	7.60296	0.429745	0.214872	−	0.976642i	$-0.431066\pi$
$313$	7.60296	0.429745	0.214872	+	0.976642i	$0.431066\pi$
$314$	−2.76060	−0.155790
$315$	−2.12887	−0.119948
$316$	−31.6789	−1.78208
$317$	−0.421117	−0.0236523	−0.0118262	−	0.999930i	$-0.503764\pi$
$317$	−0.421117	−0.0236523	−0.0118262	+	0.999930i	$0.503764\pi$
$318$	17.5642	0.984952
$319$	−5.79346	−0.324372
$320$	−24.8704	−1.39030
$321$	−4.74721	−0.264963
$322$	−10.9518	−0.610318
$323$	−1.32055	−0.0734773
$324$	5.62090	0.312272
$325$	−23.2455	−1.28943
$326$	68.4916	3.79340
$327$	−5.05330	−0.279448
$328$	88.3993	4.88103
$329$	9.08895	0.501090
$330$	−3.87639	−0.213388
$331$	−6.39080	−0.351270	−0.175635	−	0.984455i	$-0.556198\pi$
$331$	−6.39080	−0.351270	−0.175635	+	0.984455i	$0.556198\pi$
$332$	22.0238	1.20871
$333$	1.14118	0.0625361
$334$	−20.9489	−1.14627
$335$	4.36854	0.238679
$336$	51.4108	2.80469
$337$	−22.7087	−1.23702	−0.618510	−	0.785777i	$-0.712263\pi$
$337$	−22.7087	−1.23702	−0.618510	+	0.785777i	$0.712263\pi$
$338$	−36.4375	−1.98194
$339$	1.01792	0.0552859
$340$	3.80619	0.206420
$341$	2.17040	0.117534
$342$	−3.64550	−0.197126
$343$	−12.9405	−0.698721
$344$	123.541	6.66091
$345$	−0.854480	−0.0460036
$346$	0.887631	0.0477194
$347$	21.7522	1.16772	0.583861	−	0.811854i	$-0.301541\pi$
$347$	21.7522	1.16772	0.583861	+	0.811854i	$0.301541\pi$
$348$	15.7038	0.841812
$349$	12.0038	0.642551	0.321275	−	0.946986i	$-0.395888\pi$
$349$	12.0038	0.642551	0.321275	+	0.946986i	$0.395888\pi$
$350$	39.4152	2.10683
$351$	5.11851	0.273206
$352$	52.1561	2.77993
$353$	−1.00882	−0.0536939	−0.0268470	−	0.999640i	$-0.508547\pi$
$353$	−1.00882	−0.0536939	−0.0268470	+	0.999640i	$0.508547\pi$
$354$	12.2480	0.650972
$355$	9.29145	0.493139
$356$	38.2139	2.02533
$357$	−3.14387	−0.166391
$358$	−53.2548	−2.81460
$359$	26.7983	1.41436	0.707180	−	0.707033i	$-0.249967\pi$
$359$	26.7983	1.41436	0.707180	+	0.707033i	$0.249967\pi$
$360$	6.76869	0.356741
$361$	−17.2562	−0.908218
$362$	28.8740	1.51758
$363$	−6.69990	−0.351653
$364$	90.4510	4.74092
$365$	0.552284	0.0289078
$366$	39.4367	2.06139
$367$	26.8416	1.40112	0.700560	−	0.713594i	$-0.252934\pi$
$367$	26.8416	1.40112	0.700560	+	0.713594i	$0.252934\pi$
$368$	20.6352	1.07568
$369$	−8.84359	−0.460379
$370$	2.13324	0.110902
$371$	−20.0027	−1.03849
$372$	−5.88310	−0.305024
$373$	−0.452858	−0.0234481	−0.0117241	−	0.999931i	$-0.503732\pi$
$373$	−0.452858	−0.0234481	−0.0117241	+	0.999931i	$0.503732\pi$
$374$	−5.72457	−0.296010
$375$	6.46100	0.333645
$376$	−28.8981	−1.49031
$377$	14.3002	0.736498
$378$	−8.67895	−0.446397
$379$	25.2634	1.29770	0.648848	−	0.760918i	$-0.275251\pi$
$379$	25.2634	1.29770	0.648848	+	0.760918i	$0.275251\pi$
$380$	−5.02626	−0.257842
$381$	3.11216	0.159441
$382$	48.5959	2.48638
$383$	21.4661	1.09687	0.548434	−	0.836194i	$-0.315224\pi$
$383$	21.4661	1.09687	0.548434	+	0.836194i	$0.315224\pi$
$384$	−51.0881	−2.60708
$385$	4.41456	0.224987
$386$	−3.13244	−0.159437
$387$	−12.3593	−0.628257
$388$	−61.1246	−3.10313
$389$	2.06444	0.104671	0.0523356	−	0.998630i	$-0.483333\pi$
$389$	2.06444	0.104671	0.0523356	+	0.998630i	$0.483333\pi$
$390$	9.56822	0.484505
$391$	−1.26188	−0.0638159
$392$	−28.8269	−1.45598
$393$	4.19643	0.211682
$394$	43.2718	2.18000
$395$	3.81636	0.192022
$396$	−11.6559	−0.585731
$397$	−12.0212	−0.603326	−0.301663	−	0.953415i	$-0.597542\pi$
$397$	−12.0212	−0.603326	−0.301663	+	0.953415i	$0.597542\pi$
$398$	8.04257	0.403138
$399$	4.15163	0.207841
$400$	−74.2654	−3.71327
$401$	−32.9380	−1.64484	−0.822422	−	0.568878i	$-0.807378\pi$
$401$	−32.9380	−1.64484	−0.822422	+	0.568878i	$0.807378\pi$
$402$	17.8097	0.888265
$403$	−5.35727	−0.266865
$404$	−3.83948	−0.191021
$405$	−0.677149	−0.0336478
$406$	−24.2474	−1.20338
$407$	−2.36642	−0.117299
$408$	9.99585	0.494869
$409$	17.8596	0.883100	0.441550	−	0.897237i	$-0.354429\pi$
$409$	17.8596	0.883100	0.441550	+	0.897237i	$0.354429\pi$
$410$	−16.5317	−0.816440
$411$	13.4645	0.664154
$412$	−58.5552	−2.88481
$413$	−13.9484	−0.686356
$414$	−3.48354	−0.171207
$415$	−2.65320	−0.130241
$416$	−128.739	−6.31194
$417$	−4.51887	−0.221290
$418$	7.55957	0.369751
$419$	−8.79922	−0.429870	−0.214935	−	0.976628i	$-0.568954\pi$
$419$	−8.79922	−0.429870	−0.214935	+	0.976628i	$0.568954\pi$
$420$	−11.9661	−0.583888
$421$	36.8792	1.79738	0.898691	−	0.438583i	$-0.144519\pi$
$421$	36.8792	1.79738	0.898691	+	0.438583i	$0.144519\pi$
$422$	−5.50565	−0.268011
$423$	2.89101	0.140566
$424$	63.5983	3.08860
$425$	4.54147	0.220294
$426$	37.8793	1.83526
$427$	−44.9118	−2.17344
$428$	−26.6836	−1.28980
$429$	−10.6141	−0.512453
$430$	−23.1036	−1.11416
$431$	−10.5544	−0.508388	−0.254194	−	0.967153i	$-0.581810\pi$
$431$	−10.5544	−0.508388	−0.254194	+	0.967153i	$0.581810\pi$
$432$	16.3527	0.786771
$433$	12.1603	0.584385	0.292193	−	0.956359i	$-0.405615\pi$
$433$	12.1603	0.584385	0.292193	+	0.956359i	$0.405615\pi$
$434$	9.08379	0.436036
$435$	−1.89183	−0.0907065
$436$	−28.4041	−1.36031
$437$	1.66637	0.0797133
$438$	2.25155	0.107583
$439$	39.3094	1.87614	0.938068	−	0.346453i	$-0.112614\pi$
$439$	39.3094	1.87614	0.938068	+	0.346453i	$0.112614\pi$
$440$	−14.0360	−0.669141
$441$	2.88389	0.137328
$442$	14.1301	0.672102
$443$	7.46622	0.354731	0.177365	−	0.984145i	$-0.443243\pi$
$443$	7.46622	0.354731	0.177365	+	0.984145i	$0.443243\pi$
$444$	6.41444	0.304416
$445$	−4.60362	−0.218233
$446$	8.16441	0.386596
$447$	−6.44984	−0.305067
$448$	115.468	5.45535
$449$	36.1899	1.70791	0.853954	−	0.520348i	$-0.174198\pi$
$449$	36.1899	1.70791	0.853954	+	0.520348i	$0.174198\pi$
$450$	12.5372	0.591008
$451$	18.3387	0.863535
$452$	5.72164	0.269123
$453$	18.8081	0.883682
$454$	34.8185	1.63411
$455$	−10.8966	−0.510841
$456$	−13.2000	−0.618147
$457$	4.00965	0.187563	0.0937817	−	0.995593i	$-0.470104\pi$
$457$	4.00965	0.187563	0.0937817	+	0.995593i	$0.470104\pi$
$458$	−23.2360	−1.08575
$459$	−1.00000	−0.0466760
$460$	−4.80295	−0.223938
$461$	−14.0063	−0.652340	−0.326170	−	0.945311i	$-0.605758\pi$
$461$	−14.0063	−0.652340	−0.326170	+	0.945311i	$0.605758\pi$
$462$	17.9973	0.837309
$463$	−40.8451	−1.89823	−0.949117	−	0.314924i	$-0.898021\pi$
$463$	−40.8451	−1.89823	−0.949117	+	0.314924i	$0.898021\pi$
$464$	45.6866	2.12095
$465$	0.708736	0.0328668
$466$	−18.5700	−0.860239
$467$	19.8667	0.919322	0.459661	−	0.888095i	$-0.347971\pi$
$467$	19.8667	0.919322	0.459661	+	0.888095i	$0.347971\pi$
$468$	28.7706	1.32992
$469$	−20.2823	−0.936548
$470$	5.40428	0.249281
$471$	1.00000	0.0460776
$472$	44.3487	2.04131
$473$	25.6290	1.17842
$474$	15.5585	0.714625
$475$	−5.99723	−0.275172
$476$	−17.6714	−0.809965
$477$	−6.36246	−0.291317
$478$	−37.7606	−1.72713
$479$	−20.1498	−0.920669	−0.460334	−	0.887746i	$-0.652270\pi$
$479$	−20.1498	−0.920669	−0.460334	+	0.887746i	$0.652270\pi$
$480$	17.0314	0.777373
$481$	5.84112	0.266332
$482$	24.5412	1.11782
$483$	3.96717	0.180513
$484$	−37.6595	−1.71179
$485$	7.36368	0.334367
$486$	−2.76060	−0.125223
$487$	17.5488	0.795211	0.397606	−	0.917556i	$-0.369841\pi$
$487$	17.5488	0.795211	0.397606	+	0.917556i	$0.369841\pi$
$488$	142.796	6.46408
$489$	−24.8104	−1.12197
$490$	5.39096	0.243539
$491$	18.4100	0.830833	0.415416	−	0.909631i	$-0.363636\pi$
$491$	18.4100	0.830833	0.415416	+	0.909631i	$0.363636\pi$
$492$	−49.7090	−2.24105
$493$	−2.79382	−0.125827
$494$	−18.6595	−0.839533
$495$	1.40418	0.0631134
$496$	−17.1155	−0.768510
$497$	−43.1383	−1.93502
$498$	−10.8166	−0.484702
$499$	37.7091	1.68809	0.844045	−	0.536273i	$-0.180168\pi$
$499$	37.7091	1.68809	0.844045	+	0.536273i	$0.180168\pi$
$500$	36.3166	1.62413
$501$	7.58853	0.339030
$502$	−7.98682	−0.356469
$503$	−22.1498	−0.987613	−0.493806	−	0.869572i	$-0.664395\pi$
$503$	−22.1498	−0.987613	−0.493806	+	0.869572i	$0.664395\pi$
$504$	−31.4256	−1.39981
$505$	0.462541	0.0205828
$506$	7.22370	0.321133
$507$	13.1991	0.586194
$508$	17.4932	0.776134
$509$	27.7313	1.22917	0.614585	−	0.788851i	$-0.289323\pi$
$509$	27.7313	1.22917	0.614585	+	0.788851i	$0.289323\pi$
$510$	−1.86934	−0.0827756
$511$	−2.56414	−0.113431
$512$	−84.3786	−3.72904
$513$	1.32055	0.0583037
$514$	−14.9803	−0.660753
$515$	7.05414	0.310842
$516$	−69.4702	−3.05826
$517$	−5.99500	−0.263660
$518$	−9.90421	−0.435166
$519$	−0.321536	−0.0141139
$520$	34.6456	1.51931
$521$	21.2034	0.928938	0.464469	−	0.885589i	$-0.346245\pi$
$521$	21.2034	0.928938	0.464469	+	0.885589i	$0.346245\pi$
$522$	−7.71262	−0.337572
$523$	−27.4540	−1.20048	−0.600240	−	0.799820i	$-0.704928\pi$
$523$	−27.4540	−1.20048	−0.600240	+	0.799820i	$0.704928\pi$
$524$	23.5877	1.03043
$525$	−14.2778	−0.623133
$526$	53.6231	2.33808
$527$	1.04665	0.0455926
$528$	−33.9102	−1.47575
$529$	−21.4077	−0.930768
$530$	−11.8936	−0.516624
$531$	−4.43671	−0.192537
$532$	23.3359	1.01174
$533$	−45.2660	−1.96069
$534$	−18.7680	−0.812172
$535$	3.21457	0.138978
$536$	64.4870	2.78541
$537$	19.2910	0.832470
$538$	36.0569	1.55452
$539$	−5.98023	−0.257587
$540$	−3.80619	−0.163792
$541$	18.8676	0.811182	0.405591	−	0.914055i	$-0.367066\pi$
$541$	18.8676	0.811182	0.405591	+	0.914055i	$0.367066\pi$
$542$	62.0021	2.66322
$543$	−10.4593	−0.448853
$544$	25.1516	1.07837
$545$	3.42184	0.146575
$546$	−44.4233	−1.90114
$547$	24.8923	1.06432	0.532159	−	0.846645i	$-0.321381\pi$
$547$	24.8923	1.06432	0.532159	+	0.846645i	$0.321381\pi$
$548$	75.6825	3.23300
$549$	−14.2855	−0.609692
$550$	−25.9979	−1.10856
$551$	3.68938	0.157173
$552$	−12.6135	−0.536868
$553$	−17.7186	−0.753470
$554$	−50.1939	−2.13254
$555$	−0.772747	−0.0328013
$556$	−25.4001	−1.07720
$557$	−24.7797	−1.04995	−0.524974	−	0.851118i	$-0.675925\pi$
$557$	−24.7797	−1.04995	−0.524974	+	0.851118i	$0.675925\pi$
$558$	2.88937	0.122317
$559$	−63.2610	−2.67566
$560$	−34.8128	−1.47111
$561$	2.07367	0.0875504
$562$	33.9539	1.43226
$563$	−42.4418	−1.78871	−0.894354	−	0.447360i	$-0.852364\pi$
$563$	−42.4418	−1.78871	−0.894354	+	0.447360i	$0.852364\pi$
$564$	16.2501	0.684253
$565$	−0.689285	−0.0289984
$566$	−37.0482	−1.55725
$567$	3.14387	0.132030
$568$	137.157	5.75499
$569$	−18.6400	−0.781431	−0.390715	−	0.920512i	$-0.627772\pi$
$569$	−18.6400	−0.781431	−0.390715	+	0.920512i	$0.627772\pi$
$570$	2.46855	0.103396
$571$	20.0120	0.837474	0.418737	−	0.908108i	$-0.362473\pi$
$571$	20.0120	0.837474	0.418737	+	0.908108i	$0.362473\pi$
$572$	−59.6608	−2.49454
$573$	−17.6034	−0.735393
$574$	76.7531	3.20361
$575$	−5.73078	−0.238990
$576$	36.7280	1.53033
$577$	−16.1352	−0.671718	−0.335859	−	0.941912i	$-0.609027\pi$
$577$	−16.1352	−0.671718	−0.335859	+	0.941912i	$0.609027\pi$
$578$	−2.76060	−0.114826
$579$	1.13470	0.0471564
$580$	−10.6338	−0.441545
$581$	12.3183	0.511048
$582$	30.0202	1.24438
$583$	13.1936	0.546425
$584$	8.15263	0.337358
$585$	−3.46599	−0.143301
$586$	−57.9813	−2.39519
$587$	23.8858	0.985871	0.492935	−	0.870066i	$-0.335924\pi$
$587$	23.8858	0.985871	0.492935	+	0.870066i	$0.335924\pi$
$588$	16.2100	0.668491
$589$	−1.38215	−0.0569504
$590$	−8.29370	−0.341446
$591$	−15.6748	−0.644776
$592$	18.6614	0.766977
$593$	−9.10968	−0.374090	−0.187045	−	0.982351i	$-0.559891\pi$
$593$	−9.10968	−0.374090	−0.187045	+	0.982351i	$0.559891\pi$
$594$	5.72457	0.234882
$595$	2.12887	0.0872750
$596$	−36.2539	−1.48502
$597$	−2.91334	−0.119235
$598$	−17.8305	−0.729144
$599$	−19.0805	−0.779606	−0.389803	−	0.920898i	$-0.627457\pi$
$599$	−19.0805	−0.779606	−0.389803	+	0.920898i	$0.627457\pi$
$600$	45.3959	1.85328
$601$	3.40864	0.139041	0.0695207	−	0.997581i	$-0.477853\pi$
$601$	3.40864	0.139041	0.0695207	+	0.997581i	$0.477853\pi$
$602$	107.265	4.37181
$603$	−6.45138	−0.262720
$604$	105.719	4.30163
$605$	4.53683	0.184448
$606$	1.88569	0.0766008
$607$	8.80303	0.357304	0.178652	−	0.983912i	$-0.442826\pi$
$607$	8.80303	0.357304	0.178652	+	0.983912i	$0.442826\pi$
$608$	−33.2139	−1.34700
$609$	8.78340	0.355921
$610$	−26.7045	−1.08123
$611$	14.7977	0.598650
$612$	−5.62090	−0.227211
$613$	23.2586	0.939405	0.469703	−	0.882825i	$-0.344361\pi$
$613$	23.2586	0.939405	0.469703	+	0.882825i	$0.344361\pi$
$614$	6.38132	0.257529
$615$	5.98843	0.241477
$616$	65.1663	2.62563
$617$	2.03154	0.0817866	0.0408933	−	0.999164i	$-0.486980\pi$
$617$	2.03154	0.0817866	0.0408933	+	0.999164i	$0.486980\pi$
$618$	28.7583	1.15683
$619$	31.1951	1.25384	0.626919	−	0.779084i	$-0.284316\pi$
$619$	31.1951	1.25384	0.626919	+	0.779084i	$0.284316\pi$
$620$	3.98373	0.159991
$621$	1.26188	0.0506374
$622$	−6.34455	−0.254393
$623$	21.3737	0.856318
$624$	83.7016	3.35075
$625$	18.3323	0.733291
$626$	−20.9887	−0.838878
$627$	−2.73838	−0.109360
$628$	5.62090	0.224298
$629$	−1.14118	−0.0455017
$630$	5.87694	0.234143
$631$	20.2642	0.806705	0.403352	−	0.915045i	$-0.367845\pi$
$631$	20.2642	0.806705	0.403352	+	0.915045i	$0.367845\pi$
$632$	56.3358	2.24092
$633$	1.99437	0.0792691
$634$	1.16254	0.0461702
$635$	−2.10740	−0.0836296
$636$	−35.7628	−1.41809
$637$	14.7612	0.584860
$638$	15.9934	0.633186
$639$	−13.7214	−0.542811
$640$	34.5943	1.36746
$641$	47.7941	1.88775	0.943876	−	0.330299i	$-0.107150\pi$
$641$	47.7941	1.88775	0.943876	+	0.330299i	$0.107150\pi$
$642$	13.1051	0.517219
$643$	−29.9901	−1.18269	−0.591346	−	0.806418i	$-0.701403\pi$
$643$	−29.9901	−1.18269	−0.591346	+	0.806418i	$0.701403\pi$
$644$	22.2991	0.878707
$645$	8.36907	0.329532
$646$	3.64550	0.143430
$647$	−41.6952	−1.63921	−0.819604	−	0.572930i	$-0.805807\pi$
$647$	−41.6952	−1.63921	−0.819604	+	0.572930i	$0.805807\pi$
$648$	−9.99585	−0.392674
$649$	9.20026	0.361142
$650$	64.1716	2.51702
$651$	−3.29051	−0.128965
$652$	−139.457	−5.46156
$653$	19.4940	0.762858	0.381429	−	0.924398i	$-0.375432\pi$
$653$	19.4940	0.762858	0.381429	+	0.924398i	$0.375432\pi$
$654$	13.9501	0.545493
$655$	−2.84161	−0.111031
$656$	−144.617	−5.64634
$657$	−0.815601	−0.0318196
$658$	−25.0909	−0.978147
$659$	13.5672	0.528504	0.264252	−	0.964454i	$-0.414875\pi$
$659$	13.5672	0.528504	0.264252	+	0.964454i	$0.414875\pi$
$660$	7.89278	0.307226
$661$	5.59687	0.217693	0.108847	−	0.994059i	$-0.465284\pi$
$661$	5.59687	0.217693	0.108847	+	0.994059i	$0.465284\pi$
$662$	17.6424	0.685692
$663$	−5.11851	−0.198786
$664$	−39.1657	−1.51992
$665$	−2.81127	−0.109016
$666$	−3.15033	−0.122073
$667$	3.52546	0.136506
$668$	42.6544	1.65035
$669$	−2.95748	−0.114343
$670$	−12.0598	−0.465911
$671$	29.6235	1.14360
$672$	−79.0733	−3.05032
$673$	19.1066	0.736504	0.368252	−	0.929726i	$-0.379956\pi$
$673$	19.1066	0.736504	0.368252	+	0.929726i	$0.379956\pi$
$674$	62.6895	2.41471
$675$	−4.54147	−0.174801
$676$	74.1910	2.85350
$677$	−45.8575	−1.76245	−0.881223	−	0.472701i	$-0.843279\pi$
$677$	−45.8575	−1.76245	−0.881223	+	0.472701i	$0.843279\pi$
$678$	−2.81007	−0.107920
$679$	−34.1880	−1.31202
$680$	−6.76869	−0.259567
$681$	−12.6127	−0.483318
$682$	−5.99160	−0.229430
$683$	−19.8726	−0.760402	−0.380201	−	0.924904i	$-0.624145\pi$
$683$	−19.8726	−0.760402	−0.380201	+	0.924904i	$0.624145\pi$
$684$	7.42268	0.283813
$685$	−9.11746	−0.348360
$686$	35.7235	1.36393
$687$	8.41701	0.321129
$688$	−202.108	−7.70529
$689$	−32.5663	−1.24068
$690$	2.35887	0.0898008
$691$	21.1493	0.804557	0.402278	−	0.915517i	$-0.368218\pi$
$691$	21.1493	0.804557	0.402278	+	0.915517i	$0.368218\pi$
$692$	−1.80732	−0.0687041
$693$	−6.51934	−0.247649
$694$	−60.0492	−2.27944
$695$	3.05995	0.116070
$696$	−27.9266	−1.05856
$697$	8.84359	0.334975
$698$	−33.1378	−1.25428
$699$	6.72680	0.254431
$700$	−80.2539	−3.03331
$701$	−43.5604	−1.64525	−0.822626	−	0.568583i	$-0.807492\pi$
$701$	−43.5604	−1.64525	−0.822626	+	0.568583i	$0.807492\pi$
$702$	−14.1301	−0.533308
$703$	1.50698	0.0568368
$704$	−76.1618	−2.87046
$705$	−1.95765	−0.0737292
$706$	2.78494	0.104813
$707$	−2.14748	−0.0807645
$708$	−24.9383	−0.937238
$709$	−16.9167	−0.635322	−0.317661	−	0.948204i	$-0.602897\pi$
$709$	−16.9167	−0.635322	−0.317661	+	0.948204i	$0.602897\pi$
$710$	−25.6500	−0.962626
$711$	−5.63591	−0.211363
$712$	−67.9572	−2.54680
$713$	−1.32074	−0.0494621
$714$	8.67895	0.324801
$715$	7.18732	0.268791
$716$	108.433	4.05233
$717$	13.6784	0.510829
$718$	−73.9794	−2.76089
$719$	−28.2602	−1.05393	−0.526964	−	0.849888i	$-0.676670\pi$
$719$	−28.2602	−1.05393	−0.526964	+	0.849888i	$0.676670\pi$
$720$	−11.0732	−0.412675
$721$	−32.7509	−1.21971
$722$	47.6373	1.77288
$723$	−8.88981	−0.330616
$724$	−58.7909	−2.18495
$725$	−12.6881	−0.471223
$726$	18.4957	0.686441
$727$	36.1396	1.34034	0.670171	−	0.742206i	$-0.266221\pi$
$727$	36.1396	1.34034	0.670171	+	0.742206i	$0.266221\pi$
$728$	−160.852	−5.96158
$729$	1.00000	0.0370370
$730$	−1.52463	−0.0564292
$731$	12.3593	0.457124
$732$	−80.2977	−2.96789
$733$	−5.29296	−0.195500	−0.0977500	−	0.995211i	$-0.531165\pi$
$733$	−5.29296	−0.195500	−0.0977500	+	0.995211i	$0.531165\pi$
$734$	−74.0988	−2.73504
$735$	−1.95282	−0.0720309
$736$	−31.7383	−1.16989
$737$	13.3780	0.492786
$738$	24.4136	0.898677
$739$	13.0956	0.481730	0.240865	−	0.970559i	$-0.422569\pi$
$739$	13.0956	0.481730	0.240865	+	0.970559i	$0.422569\pi$
$740$	−4.34354	−0.159672
$741$	6.75924	0.248307
$742$	55.2195	2.02717
$743$	5.27872	0.193658	0.0968288	−	0.995301i	$-0.469130\pi$
$743$	5.27872	0.193658	0.0968288	+	0.995301i	$0.469130\pi$
$744$	10.4621	0.383560
$745$	4.36750	0.160013
$746$	1.25016	0.0457716
$747$	3.91819	0.143359
$748$	11.6559	0.426182
$749$	−14.9246	−0.545333
$750$	−17.8362	−0.651287
$751$	8.96559	0.327159	0.163579	−	0.986530i	$-0.447696\pi$
$751$	8.96559	0.327159	0.163579	+	0.986530i	$0.447696\pi$
$752$	47.2760	1.72398
$753$	2.89315	0.105432
$754$	−39.4771	−1.43767
$755$	−12.7359	−0.463507
$756$	17.6714	0.642701
$757$	−10.0218	−0.364249	−0.182125	−	0.983275i	$-0.558297\pi$
$757$	−10.0218	−0.364249	−0.182125	+	0.983275i	$0.558297\pi$
$758$	−69.7422	−2.53315
$759$	−2.61672	−0.0949808
$760$	8.93838	0.324229
$761$	52.6570	1.90881	0.954407	−	0.298510i	$-0.0964895\pi$
$761$	52.6570	1.90881	0.954407	+	0.298510i	$0.0964895\pi$
$762$	−8.59144	−0.311235
$763$	−15.8869	−0.575144
$764$	−98.9470	−3.57978
$765$	0.677149	0.0244824
$766$	−59.2594	−2.14113
$767$	−22.7093	−0.819986
$768$	67.5777	2.43850
$769$	46.5962	1.68030	0.840150	−	0.542353i	$-0.182467\pi$
$769$	46.5962	1.68030	0.840150	+	0.542353i	$0.182467\pi$
$770$	−12.1868	−0.439183
$771$	5.42647	0.195430
$772$	6.37802	0.229550
$773$	−20.4378	−0.735097	−0.367548	−	0.930004i	$-0.619803\pi$
$773$	−20.4378	−0.735097	−0.367548	+	0.930004i	$0.619803\pi$
$774$	34.1190	1.22638
$775$	4.75331	0.170744
$776$	108.700	3.90211
$777$	3.58771	0.128708
$778$	−5.69909	−0.204322
$779$	−11.6784	−0.418422
$780$	−19.4820	−0.697568
$781$	28.4537	1.01815
$782$	3.48354	0.124571
$783$	2.79382	0.0998431
$784$	47.1594	1.68427
$785$	−0.677149	−0.0241685
$786$	−11.5847	−0.413211
$787$	42.8208	1.52640	0.763199	−	0.646163i	$-0.223628\pi$
$787$	42.8208	1.52640	0.763199	+	0.646163i	$0.223628\pi$
$788$	−88.1066	−3.13867
$789$	−19.4244	−0.691528
$790$	−10.5354	−0.374834
$791$	3.20021	0.113786
$792$	20.7281	0.736541
$793$	−73.1207	−2.59659
$794$	33.1856	1.17771
$795$	4.30834	0.152801
$796$	−16.3756	−0.580418
$797$	11.1258	0.394095	0.197048	−	0.980394i	$-0.436865\pi$
$797$	11.1258	0.394095	0.197048	+	0.980394i	$0.436865\pi$
$798$	−11.4610	−0.405714
$799$	−2.89101	−0.102277
$800$	114.225	4.03847
$801$	6.79853	0.240214
$802$	90.9285	3.21080
$803$	1.69129	0.0596842
$804$	−36.2626	−1.27888
$805$	−2.68637	−0.0946820
$806$	14.7893	0.520930
$807$	−13.0613	−0.459778
$808$	6.82788	0.240204
$809$	−18.4187	−0.647566	−0.323783	−	0.946131i	$-0.604955\pi$
$809$	−18.4187	−0.647566	−0.323783	+	0.946131i	$0.604955\pi$
$810$	1.86934	0.0656818
$811$	28.6276	1.00525	0.502626	−	0.864504i	$-0.332367\pi$
$811$	28.6276	1.00525	0.502626	+	0.864504i	$0.332367\pi$
$812$	49.3706	1.73257
$813$	−22.4597	−0.787695
$814$	6.53274	0.228973
$815$	16.8004	0.588491
$816$	−16.3527	−0.572460
$817$	−16.3210	−0.571000
$818$	−49.3031	−1.72384
$819$	16.0919	0.562296
$820$	33.6604	1.17547
$821$	48.7037	1.69977	0.849885	−	0.526968i	$-0.176671\pi$
$821$	48.7037	1.69977	0.849885	+	0.526968i	$0.176671\pi$
$822$	−37.1700	−1.29645
$823$	−50.6702	−1.76625	−0.883126	−	0.469136i	$-0.844565\pi$
$823$	−50.6702	−1.76625	−0.883126	+	0.469136i	$0.844565\pi$
$824$	104.131	3.62757
$825$	9.41750	0.327875
$826$	38.5059	1.33979
$827$	−20.2177	−0.703038	−0.351519	−	0.936181i	$-0.614335\pi$
$827$	−20.2177	−0.703038	−0.351519	+	0.936181i	$0.614335\pi$
$828$	7.09289	0.246495
$829$	−1.11565	−0.0387481	−0.0193740	−	0.999812i	$-0.506167\pi$
$829$	−1.11565	−0.0387481	−0.0193740	+	0.999812i	$0.506167\pi$
$830$	7.32443	0.254235
$831$	18.1823	0.630736
$832$	187.993	6.51748
$833$	−2.88389	−0.0999208
$834$	12.4748	0.431966
$835$	−5.13857	−0.177827
$836$	−15.3922	−0.532349
$837$	−1.04665	−0.0361774
$838$	24.2911	0.839122
$839$	−46.7403	−1.61366	−0.806828	−	0.590787i	$-0.798817\pi$
$839$	−46.7403	−1.61366	−0.806828	+	0.590787i	$0.798817\pi$
$840$	21.2798	0.734224
$841$	−21.1946	−0.730847
$842$	−101.809	−3.50856
$843$	−12.2995	−0.423617
$844$	11.2102	0.385869
$845$	−8.93778	−0.307469
$846$	−7.98092	−0.274390
$847$	−21.0636	−0.723753
$848$	−104.044	−3.57287
$849$	13.4204	0.460586
$850$	−12.5372	−0.430021
$851$	1.44003	0.0493634
$852$	−77.1268	−2.64232
$853$	−33.0862	−1.13285	−0.566424	−	0.824114i	$-0.691674\pi$
$853$	−33.0862	−1.13285	−0.566424	+	0.824114i	$0.691674\pi$
$854$	123.984	4.24263
$855$	−0.894209	−0.0305813
$856$	47.4524	1.62189
$857$	37.8379	1.29252	0.646259	−	0.763118i	$-0.276333\pi$
$857$	37.8379	1.29252	0.646259	+	0.763118i	$0.276333\pi$
$858$	29.3012	1.00033
$859$	−39.3519	−1.34267	−0.671335	−	0.741154i	$-0.734279\pi$
$859$	−39.3519	−1.34267	−0.671335	+	0.741154i	$0.734279\pi$
$860$	47.0417	1.60411
$861$	−27.8031	−0.947526
$862$	29.1365	0.992393
$863$	28.8886	0.983379	0.491690	−	0.870771i	$-0.336379\pi$
$863$	28.8886	0.983379	0.491690	+	0.870771i	$0.336379\pi$
$864$	−25.1516	−0.855675
$865$	0.217728	0.00740297
$866$	−33.5696	−1.14074
$867$	1.00000	0.0339618
$868$	−18.4957	−0.627784
$869$	11.6870	0.396455
$870$	5.22260	0.177063
$871$	−33.0214	−1.11889
$872$	50.5121	1.71055
$873$	−10.8745	−0.368047
$874$	−4.60018	−0.155603
$875$	20.3125	0.686688
$876$	−4.58441	−0.154893
$877$	−24.2504	−0.818876	−0.409438	−	0.912338i	$-0.634275\pi$
$877$	−24.2504	−0.818876	−0.409438	+	0.912338i	$0.634275\pi$
$878$	−108.517	−3.66229
$879$	21.0032	0.708419
$880$	22.9622	0.774057
$881$	−33.3623	−1.12400	−0.562002	−	0.827136i	$-0.689969\pi$
$881$	−33.3623	−1.12400	−0.562002	+	0.827136i	$0.689969\pi$
$882$	−7.96125	−0.268069
$883$	25.2569	0.849962	0.424981	−	0.905202i	$-0.360281\pi$
$883$	25.2569	0.849962	0.424981	+	0.905202i	$0.360281\pi$
$884$	−28.7706	−0.967661
$885$	3.00431	0.100989
$886$	−20.6112	−0.692448
$887$	−12.6760	−0.425619	−0.212809	−	0.977094i	$-0.568261\pi$
$887$	−12.6760	−0.425619	−0.212809	+	0.977094i	$0.568261\pi$
$888$	−11.4070	−0.382795
$889$	9.78423	0.328152
$890$	12.7087	0.425998
$891$	−2.07367	−0.0694705
$892$	−16.6237	−0.556602
$893$	3.81772	0.127755
$894$	17.8054	0.595502
$895$	−13.0629	−0.436645
$896$	−160.614	−5.36574
$897$	6.45893	0.215657
$898$	−99.9059	−3.33390
$899$	−2.92414	−0.0975257
$900$	−25.5272	−0.850905
$901$	6.36246	0.211964
$902$	−50.6257	−1.68565
$903$	−38.8559	−1.29304
$904$	−10.1750	−0.338416
$905$	7.08253	0.235431
$906$	−51.9216	−1.72498
$907$	−44.8810	−1.49025	−0.745124	−	0.666925i	$-0.767610\pi$
$907$	−44.8810	−1.49025	−0.745124	+	0.666925i	$0.767610\pi$
$908$	−70.8946	−2.35272
$909$	−0.683072	−0.0226561
$910$	30.0812	0.997181
$911$	−47.8158	−1.58421	−0.792104	−	0.610386i	$-0.791014\pi$
$911$	−47.8158	−1.58421	−0.792104	+	0.610386i	$0.791014\pi$
$912$	21.5946	0.715068
$913$	−8.12504	−0.268900
$914$	−11.0690	−0.366131
$915$	9.67345	0.319794
$916$	47.3112	1.56321
$917$	13.1930	0.435671
$918$	2.76060	0.0911133
$919$	−16.5303	−0.545285	−0.272642	−	0.962115i	$-0.587898\pi$
$919$	−16.5303	−0.545285	−0.272642	+	0.962115i	$0.587898\pi$
$920$	8.54125	0.281597
$921$	−2.31157	−0.0761689
$922$	38.6659	1.27339
$923$	−70.2332	−2.31175
$924$	−36.6445	−1.20552
$925$	−5.18262	−0.170403
$926$	112.757	3.70542
$927$	−10.4174	−0.342152
$928$	−70.2692	−2.30670
$929$	−34.1173	−1.11935	−0.559676	−	0.828712i	$-0.689074\pi$
$929$	−34.1173	−1.11935	−0.559676	+	0.828712i	$0.689074\pi$
$930$	−1.95653	−0.0641573
$931$	3.80831	0.124812
$932$	37.8107	1.23853
$933$	2.29825	0.0752414
$934$	−54.8440	−1.79455
$935$	−1.40418	−0.0459217
$936$	−51.1639	−1.67234
$937$	−38.1875	−1.24753	−0.623766	−	0.781611i	$-0.714398\pi$
$937$	−38.1875	−1.24753	−0.623766	+	0.781611i	$0.714398\pi$
$938$	55.9912	1.82818
$939$	7.60296	0.248113
$940$	−11.0037	−0.358902
$941$	−3.24152	−0.105671	−0.0528353	−	0.998603i	$-0.516826\pi$
$941$	−3.24152	−0.105671	−0.0528353	+	0.998603i	$0.516826\pi$
$942$	−2.76060	−0.0899451
$943$	−11.1595	−0.363404
$944$	−72.5523	−2.36138
$945$	−2.12887	−0.0692520
$946$	−70.7515	−2.30033
$947$	−19.4148	−0.630898	−0.315449	−	0.948943i	$-0.602155\pi$
$947$	−19.4148	−0.630898	−0.315449	+	0.948943i	$0.602155\pi$
$948$	−31.6789	−1.02888
$949$	−4.17466	−0.135515
$950$	16.5559	0.537146
$951$	−0.421117	−0.0136557
$952$	31.4256	1.01851
$953$	22.8141	0.739023	0.369511	−	0.929226i	$-0.379525\pi$
$953$	22.8141	0.739023	0.369511	+	0.929226i	$0.379525\pi$
$954$	17.5642	0.568662
$955$	11.9201	0.385726
$956$	76.8850	2.48664
$957$	−5.79346	−0.187276
$958$	55.6256	1.79718
$959$	42.3305	1.36692
$960$	−24.8704	−0.802687
$961$	−29.9045	−0.964662
$962$	−16.1250	−0.519891
$963$	−4.74721	−0.152977
$964$	−49.9688	−1.60939
$965$	−0.768359	−0.0247344
$966$	−10.9518	−0.352367
$967$	2.41482	0.0776553	0.0388277	−	0.999246i	$-0.487638\pi$
$967$	2.41482	0.0776553	0.0388277	+	0.999246i	$0.487638\pi$
$968$	66.9712	2.15254
$969$	−1.32055	−0.0424221
$970$	−20.3282	−0.652698
$971$	−36.1202	−1.15915	−0.579576	−	0.814918i	$-0.696782\pi$
$971$	−36.1202	−1.15915	−0.579576	+	0.814918i	$0.696782\pi$
$972$	5.62090	0.180291
$973$	−14.2067	−0.455446
$974$	−48.4451	−1.55228
$975$	−23.2455	−0.744453
$976$	−233.608	−7.47760
$977$	−23.1685	−0.741226	−0.370613	−	0.928787i	$-0.620852\pi$
$977$	−23.1685	−0.741226	−0.370613	+	0.928787i	$0.620852\pi$
$978$	68.4916	2.19012
$979$	−14.0979	−0.450571
$980$	−10.9766	−0.350635
$981$	−5.05330	−0.161339
$982$	−50.8227	−1.62182
$983$	−37.6772	−1.20171	−0.600857	−	0.799356i	$-0.705174\pi$
$983$	−37.6772	−1.20171	−0.600857	+	0.799356i	$0.705174\pi$
$984$	88.3993	2.81807
$985$	10.6142	0.338196
$986$	7.71262	0.245620
$987$	9.08895	0.289305
$988$	37.9930	1.20872
$989$	−15.5959	−0.495920
$990$	−3.87639	−0.123200
$991$	−13.8694	−0.440575	−0.220287	−	0.975435i	$-0.570700\pi$
$991$	−13.8694	−0.440575	−0.220287	+	0.975435i	$0.570700\pi$
$992$	26.3248	0.835815
$993$	−6.39080	−0.202806
$994$	119.087	3.77723
$995$	1.97277	0.0625409
$996$	22.0238	0.697850
$997$	4.02316	0.127415	0.0637074	−	0.997969i	$-0.479708\pi$
$997$	4.02316	0.127415	0.0637074	+	0.997969i	$0.479708\pi$
$998$	−104.100	−3.29521
$999$	1.14118	0.0361052

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.e.1.2	✓	46

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.e.1.2	✓	46	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)

\(f(q)\)	\(=\)	\(q-2.76060 q^{2} +1.00000 q^{3} +5.62090 q^{4} -0.677149 q^{5} -2.76060 q^{6} +3.14387 q^{7} -9.99585 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.76060 q^{2} +1.00000 q^{3} +5.62090 q^{4} -0.677149 q^{5} -2.76060 q^{6} +3.14387 q^{7} -9.99585 q^{8} +1.00000 q^{9} +1.86934 q^{10} -2.07367 q^{11} +5.62090 q^{12} +5.11851 q^{13} -8.67895 q^{14} -0.677149 q^{15} +16.3527 q^{16} -1.00000 q^{17} -2.76060 q^{18} +1.32055 q^{19} -3.80619 q^{20} +3.14387 q^{21} +5.72457 q^{22} +1.26188 q^{23} -9.99585 q^{24} -4.54147 q^{25} -14.1301 q^{26} +1.00000 q^{27} +17.6714 q^{28} +2.79382 q^{29} +1.86934 q^{30} -1.04665 q^{31} -25.1516 q^{32} -2.07367 q^{33} +2.76060 q^{34} -2.12887 q^{35} +5.62090 q^{36} +1.14118 q^{37} -3.64550 q^{38} +5.11851 q^{39} +6.76869 q^{40} -8.84359 q^{41} -8.67895 q^{42} -12.3593 q^{43} -11.6559 q^{44} -0.677149 q^{45} -3.48354 q^{46} +2.89101 q^{47} +16.3527 q^{48} +2.88389 q^{49} +12.5372 q^{50} -1.00000 q^{51} +28.7706 q^{52} -6.36246 q^{53} -2.76060 q^{54} +1.40418 q^{55} -31.4256 q^{56} +1.32055 q^{57} -7.71262 q^{58} -4.43671 q^{59} -3.80619 q^{60} -14.2855 q^{61} +2.88937 q^{62} +3.14387 q^{63} +36.7280 q^{64} -3.46599 q^{65} +5.72457 q^{66} -6.45138 q^{67} -5.62090 q^{68} +1.26188 q^{69} +5.87694 q^{70} -13.7214 q^{71} -9.99585 q^{72} -0.815601 q^{73} -3.15033 q^{74} -4.54147 q^{75} +7.42268 q^{76} -6.51934 q^{77} -14.1301 q^{78} -5.63591 q^{79} -11.0732 q^{80} +1.00000 q^{81} +24.4136 q^{82} +3.91819 q^{83} +17.6714 q^{84} +0.677149 q^{85} +34.1190 q^{86} +2.79382 q^{87} +20.7281 q^{88} +6.79853 q^{89} +1.86934 q^{90} +16.0919 q^{91} +7.09289 q^{92} -1.04665 q^{93} -7.98092 q^{94} -0.894209 q^{95} -25.1516 q^{96} -10.8745 q^{97} -7.96125 q^{98} -2.07367 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 46 q - 5 q^{2} + 46 q^{3} + 43 q^{4} - 19 q^{5} - 5 q^{6} + q^{7} - 18 q^{8} + 46 q^{9}+O(q^{10}) \) 46 * q - 5 * q^2 + 46 * q^3 + 43 * q^4 - 19 * q^5 - 5 * q^6 + q^7 - 18 * q^8 + 46 * q^9	\( 46 q - 5 q^{2} + 46 q^{3} + 43 q^{4} - 19 q^{5} - 5 q^{6} + q^{7} - 18 q^{8} + 46 q^{9} - 10 q^{10} - 25 q^{11} + 43 q^{12} - 8 q^{13} - 28 q^{14} - 19 q^{15} + 33 q^{16} - 46 q^{17} - 5 q^{18} - 2 q^{19} - 56 q^{20} + q^{21} - 19 q^{22} - 64 q^{23} - 18 q^{24} + 11 q^{25} - 13 q^{26} + 46 q^{27} - 38 q^{28} - 51 q^{29} - 10 q^{30} - 19 q^{31} - 61 q^{32} - 25 q^{33} + 5 q^{34} - 39 q^{35} + 43 q^{36} - 46 q^{37} - 48 q^{38} - 8 q^{39} - 10 q^{40} - 53 q^{41} - 28 q^{42} - 33 q^{43} - 62 q^{44} - 19 q^{45} + 2 q^{46} - 45 q^{47} + 33 q^{48} + 21 q^{49} - 60 q^{50} - 46 q^{51} - 63 q^{52} - 47 q^{53} - 5 q^{54} + 5 q^{55} - 82 q^{56} - 2 q^{57} - 21 q^{58} - 65 q^{59} - 56 q^{60} - 37 q^{61} - 46 q^{62} + q^{63} + 74 q^{64} - 85 q^{65} - 19 q^{66} - 52 q^{67} - 43 q^{68} - 64 q^{69} - 20 q^{70} - 48 q^{71} - 18 q^{72} - 39 q^{73} - 16 q^{74} + 11 q^{75} + 42 q^{76} - 78 q^{77} - 13 q^{78} - 26 q^{79} - 78 q^{80} + 46 q^{81} + 3 q^{82} - 47 q^{83} - 38 q^{84} + 19 q^{85} - 6 q^{86} - 51 q^{87} - 58 q^{88} - 58 q^{89} - 10 q^{90} - 43 q^{91} - 68 q^{92} - 19 q^{93} - 78 q^{95} - 61 q^{96} - 44 q^{97} - 4 q^{98} - 25 q^{99}+O(q^{100}) \) 46 * q - 5 * q^2 + 46 * q^3 + 43 * q^4 - 19 * q^5 - 5 * q^6 + q^7 - 18 * q^8 + 46 * q^9 - 10 * q^10 - 25 * q^11 + 43 * q^12 - 8 * q^13 - 28 * q^14 - 19 * q^15 + 33 * q^16 - 46 * q^17 - 5 * q^18 - 2 * q^19 - 56 * q^20 + q^21 - 19 * q^22 - 64 * q^23 - 18 * q^24 + 11 * q^25 - 13 * q^26 + 46 * q^27 - 38 * q^28 - 51 * q^29 - 10 * q^30 - 19 * q^31 - 61 * q^32 - 25 * q^33 + 5 * q^34 - 39 * q^35 + 43 * q^36 - 46 * q^37 - 48 * q^38 - 8 * q^39 - 10 * q^40 - 53 * q^41 - 28 * q^42 - 33 * q^43 - 62 * q^44 - 19 * q^45 + 2 * q^46 - 45 * q^47 + 33 * q^48 + 21 * q^49 - 60 * q^50 - 46 * q^51 - 63 * q^52 - 47 * q^53 - 5 * q^54 + 5 * q^55 - 82 * q^56 - 2 * q^57 - 21 * q^58 - 65 * q^59 - 56 * q^60 - 37 * q^61 - 46 * q^62 + q^63 + 74 * q^64 - 85 * q^65 - 19 * q^66 - 52 * q^67 - 43 * q^68 - 64 * q^69 - 20 * q^70 - 48 * q^71 - 18 * q^72 - 39 * q^73 - 16 * q^74 + 11 * q^75 + 42 * q^76 - 78 * q^77 - 13 * q^78 - 26 * q^79 - 78 * q^80 + 46 * q^81 + 3 * q^82 - 47 * q^83 - 38 * q^84 + 19 * q^85 - 6 * q^86 - 51 * q^87 - 58 * q^88 - 58 * q^89 - 10 * q^90 - 43 * q^91 - 68 * q^92 - 19 * q^93 - 78 * q^95 - 61 * q^96 - 44 * q^97 - 4 * q^98 - 25 * q^99

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