LMFDB - Embedded newform 8007.2.a.c.1.6

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:	$39$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
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)

$f(q)$	$=$	$q-2.11675 q^{2} -1.00000 q^{3} +2.48063 q^{4} +2.70234 q^{5} +2.11675 q^{6} +2.58592 q^{7} -1.01738 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.11675 q^{2} -1.00000 q^{3} +2.48063 q^{4} +2.70234 q^{5} +2.11675 q^{6} +2.58592 q^{7} -1.01738 q^{8} +1.00000 q^{9} -5.72017 q^{10} -4.73579 q^{11} -2.48063 q^{12} +0.962559 q^{13} -5.47374 q^{14} -2.70234 q^{15} -2.80772 q^{16} +1.00000 q^{17} -2.11675 q^{18} -1.82912 q^{19} +6.70351 q^{20} -2.58592 q^{21} +10.0245 q^{22} -1.57778 q^{23} +1.01738 q^{24} +2.30263 q^{25} -2.03750 q^{26} -1.00000 q^{27} +6.41471 q^{28} -3.37414 q^{29} +5.72017 q^{30} -7.71797 q^{31} +7.97802 q^{32} +4.73579 q^{33} -2.11675 q^{34} +6.98802 q^{35} +2.48063 q^{36} -4.06578 q^{37} +3.87179 q^{38} -0.962559 q^{39} -2.74931 q^{40} +2.50977 q^{41} +5.47374 q^{42} +5.29573 q^{43} -11.7478 q^{44} +2.70234 q^{45} +3.33977 q^{46} +9.84991 q^{47} +2.80772 q^{48} -0.313039 q^{49} -4.87409 q^{50} -1.00000 q^{51} +2.38776 q^{52} -2.01369 q^{53} +2.11675 q^{54} -12.7977 q^{55} -2.63086 q^{56} +1.82912 q^{57} +7.14222 q^{58} +13.9608 q^{59} -6.70351 q^{60} -10.0261 q^{61} +16.3370 q^{62} +2.58592 q^{63} -11.2720 q^{64} +2.60116 q^{65} -10.0245 q^{66} +13.4909 q^{67} +2.48063 q^{68} +1.57778 q^{69} -14.7919 q^{70} +1.38426 q^{71} -1.01738 q^{72} +6.22902 q^{73} +8.60623 q^{74} -2.30263 q^{75} -4.53738 q^{76} -12.2463 q^{77} +2.03750 q^{78} -10.5383 q^{79} -7.58742 q^{80} +1.00000 q^{81} -5.31255 q^{82} -0.517354 q^{83} -6.41471 q^{84} +2.70234 q^{85} -11.2097 q^{86} +3.37414 q^{87} +4.81810 q^{88} -1.13656 q^{89} -5.72017 q^{90} +2.48910 q^{91} -3.91389 q^{92} +7.71797 q^{93} -20.8498 q^{94} -4.94290 q^{95} -7.97802 q^{96} -5.39211 q^{97} +0.662626 q^{98} -4.73579 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 39 q - 4 q^{2} - 39 q^{3} + 30 q^{4} - 3 q^{5} + 4 q^{6} - 5 q^{7} - 3 q^{8} + 39 q^{9}+O(q^{10}) $ 39 * q - 4 * q^2 - 39 * q^3 + 30 * q^4 - 3 * q^5 + 4 * q^6 - 5 * q^7 - 3 * q^8 + 39 * q^9	\( 39 q - 4 q^{2} - 39 q^{3} + 30 q^{4} - 3 q^{5} + 4 q^{6} - 5 q^{7} - 3 q^{8} + 39 q^{9} + 4 q^{10} + q^{11} - 30 q^{12} - 26 q^{13} - 4 q^{14} + 3 q^{15} + 8 q^{16} + 39 q^{17} - 4 q^{18} - 14 q^{19} - 14 q^{20} + 5 q^{21} - 17 q^{22} + 2 q^{23} + 3 q^{24} - 6 q^{25} - 17 q^{26} - 39 q^{27} - 14 q^{28} - 7 q^{29} - 4 q^{30} - q^{31} - 30 q^{32} - q^{33} - 4 q^{34} + q^{35} + 30 q^{36} - 24 q^{37} - 20 q^{38} + 26 q^{39} + 12 q^{40} + q^{41} + 4 q^{42} - 41 q^{43} - 2 q^{44} - 3 q^{45} - 6 q^{46} - 9 q^{47} - 8 q^{48} - 10 q^{49} - 9 q^{50} - 39 q^{51} - 37 q^{52} - 47 q^{53} + 4 q^{54} - 39 q^{55} + 8 q^{56} + 14 q^{57} - 27 q^{58} + 41 q^{59} + 14 q^{60} - 41 q^{61} + 36 q^{62} - 5 q^{63} - 47 q^{64} - 39 q^{65} + 17 q^{66} - 36 q^{67} + 30 q^{68} - 2 q^{69} - 52 q^{70} - 2 q^{71} - 3 q^{72} - 63 q^{73} - 6 q^{74} + 6 q^{75} - 34 q^{76} - 64 q^{77} + 17 q^{78} + 20 q^{79} - 28 q^{80} + 39 q^{81} - 37 q^{82} + 45 q^{83} + 14 q^{84} - 3 q^{85} + 32 q^{86} + 7 q^{87} + 6 q^{88} - 32 q^{89} + 4 q^{90} - 11 q^{91} + 28 q^{92} + q^{93} - 44 q^{94} + 22 q^{95} + 30 q^{96} - 20 q^{97} + 63 q^{98} + q^{99}+O(q^{100}) \) 39 * q - 4 * q^2 - 39 * q^3 + 30 * q^4 - 3 * q^5 + 4 * q^6 - 5 * q^7 - 3 * q^8 + 39 * q^9 + 4 * q^10 + q^11 - 30 * q^12 - 26 * q^13 - 4 * q^14 + 3 * q^15 + 8 * q^16 + 39 * q^17 - 4 * q^18 - 14 * q^19 - 14 * q^20 + 5 * q^21 - 17 * q^22 + 2 * q^23 + 3 * q^24 - 6 * q^25 - 17 * q^26 - 39 * q^27 - 14 * q^28 - 7 * q^29 - 4 * q^30 - q^31 - 30 * q^32 - q^33 - 4 * q^34 + q^35 + 30 * q^36 - 24 * q^37 - 20 * q^38 + 26 * q^39 + 12 * q^40 + q^41 + 4 * q^42 - 41 * q^43 - 2 * q^44 - 3 * q^45 - 6 * q^46 - 9 * q^47 - 8 * q^48 - 10 * q^49 - 9 * q^50 - 39 * q^51 - 37 * q^52 - 47 * q^53 + 4 * q^54 - 39 * q^55 + 8 * q^56 + 14 * q^57 - 27 * q^58 + 41 * q^59 + 14 * q^60 - 41 * q^61 + 36 * q^62 - 5 * q^63 - 47 * q^64 - 39 * q^65 + 17 * q^66 - 36 * q^67 + 30 * q^68 - 2 * q^69 - 52 * q^70 - 2 * q^71 - 3 * q^72 - 63 * q^73 - 6 * q^74 + 6 * q^75 - 34 * q^76 - 64 * q^77 + 17 * q^78 + 20 * q^79 - 28 * q^80 + 39 * q^81 - 37 * q^82 + 45 * q^83 + 14 * q^84 - 3 * q^85 + 32 * q^86 + 7 * q^87 + 6 * q^88 - 32 * q^89 + 4 * q^90 - 11 * q^91 + 28 * q^92 + q^93 - 44 * q^94 + 22 * q^95 + 30 * q^96 - 20 * q^97 + 63 * q^98 + 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 $

$2$	−2.11675	−1.49677	−0.748384	−	0.663265i	$-0.769170\pi$
$2$	−2.11675	−1.49677	−0.748384	+	0.663265i	$0.769170\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	2.48063	1.24032
$5$	2.70234	1.20852	0.604261	−	0.796786i	$-0.293468\pi$
$5$	2.70234	1.20852	0.604261	+	0.796786i	$0.293468\pi$
$6$	2.11675	0.864160
$7$	2.58592	0.977384	0.488692	−	0.872456i	$-0.337474\pi$
$7$	2.58592	0.977384	0.488692	+	0.872456i	$0.337474\pi$
$8$	−1.01738	−0.359699
$9$	1.00000	0.333333
$10$	−5.72017	−1.80888
$11$	−4.73579	−1.42789	−0.713947	−	0.700200i	$-0.753094\pi$
$11$	−4.73579	−1.42789	−0.713947	+	0.700200i	$0.753094\pi$
$12$	−2.48063	−0.716097
$13$	0.962559	0.266966	0.133483	−	0.991051i	$-0.457384\pi$
$13$	0.962559	0.266966	0.133483	+	0.991051i	$0.457384\pi$
$14$	−5.47374	−1.46292
$15$	−2.70234	−0.697741
$16$	−2.80772	−0.701931
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−2.11675	−0.498923
$19$	−1.82912	−0.419629	−0.209814	−	0.977741i	$-0.567286\pi$
$19$	−1.82912	−0.419629	−0.209814	+	0.977741i	$0.567286\pi$
$20$	6.70351	1.49895
$21$	−2.58592	−0.564293
$22$	10.0245	2.13723
$23$	−1.57778	−0.328990	−0.164495	−	0.986378i	$-0.552599\pi$
$23$	−1.57778	−0.328990	−0.164495	+	0.986378i	$0.552599\pi$
$24$	1.01738	0.207672
$25$	2.30263	0.460526
$26$	−2.03750	−0.399586
$27$	−1.00000	−0.192450
$28$	6.41471	1.21227
$29$	−3.37414	−0.626563	−0.313281	−	0.949660i	$-0.601428\pi$
$29$	−3.37414	−0.626563	−0.313281	+	0.949660i	$0.601428\pi$
$30$	5.72017	1.04436
$31$	−7.71797	−1.38619	−0.693094	−	0.720847i	$-0.743753\pi$
$31$	−7.71797	−1.38619	−0.693094	+	0.720847i	$0.743753\pi$
$32$	7.97802	1.41033
$33$	4.73579	0.824395
$34$	−2.11675	−0.363020
$35$	6.98802	1.18119
$36$	2.48063	0.413439
$37$	−4.06578	−0.668410	−0.334205	−	0.942500i	$-0.608468\pi$
$37$	−4.06578	−0.668410	−0.334205	+	0.942500i	$0.608468\pi$
$38$	3.87179	0.628087
$39$	−0.962559	−0.154133
$40$	−2.74931	−0.434704
$41$	2.50977	0.391960	0.195980	−	0.980608i	$-0.437211\pi$
$41$	2.50977	0.391960	0.195980	+	0.980608i	$0.437211\pi$
$42$	5.47374	0.844616
$43$	5.29573	0.807592	0.403796	−	0.914849i	$-0.367691\pi$
$43$	5.29573	0.807592	0.403796	+	0.914849i	$0.367691\pi$
$44$	−11.7478	−1.77104
$45$	2.70234	0.402841
$46$	3.33977	0.492422
$47$	9.84991	1.43676	0.718378	−	0.695653i	$-0.244885\pi$
$47$	9.84991	1.43676	0.718378	+	0.695653i	$0.244885\pi$
$48$	2.80772	0.405260
$49$	−0.313039	−0.0447199
$50$	−4.87409	−0.689300
$51$	−1.00000	−0.140028
$52$	2.38776	0.331122
$53$	−2.01369	−0.276602	−0.138301	−	0.990390i	$-0.544164\pi$
$53$	−2.01369	−0.276602	−0.138301	+	0.990390i	$0.544164\pi$
$54$	2.11675	0.288053
$55$	−12.7977	−1.72564
$56$	−2.63086	−0.351564
$57$	1.82912	0.242273
$58$	7.14222	0.937820
$59$	13.9608	1.81755	0.908773	−	0.417290i	$-0.137020\pi$
$59$	13.9608	1.81755	0.908773	+	0.417290i	$0.137020\pi$
$60$	−6.70351	−0.865419
$61$	−10.0261	−1.28371	−0.641855	−	0.766826i	$-0.721835\pi$
$61$	−10.0261	−1.28371	−0.641855	+	0.766826i	$0.721835\pi$
$62$	16.3370	2.07480
$63$	2.58592	0.325795
$64$	−11.2720	−1.40900
$65$	2.60116	0.322634
$66$	−10.0245	−1.23393
$67$	13.4909	1.64817	0.824086	−	0.566464i	$-0.191689\pi$
$67$	13.4909	1.64817	0.824086	+	0.566464i	$0.191689\pi$
$68$	2.48063	0.300821
$69$	1.57778	0.189942
$70$	−14.7919	−1.76797
$71$	1.38426	0.164281	0.0821404	−	0.996621i	$-0.473824\pi$
$71$	1.38426	0.164281	0.0821404	+	0.996621i	$0.473824\pi$
$72$	−1.01738	−0.119900
$73$	6.22902	0.729051	0.364526	−	0.931193i	$-0.381231\pi$
$73$	6.22902	0.729051	0.364526	+	0.931193i	$0.381231\pi$
$74$	8.60623	1.00045
$75$	−2.30263	−0.265885
$76$	−4.53738	−0.520473
$77$	−12.2463	−1.39560
$78$	2.03750	0.230701
$79$	−10.5383	−1.18565	−0.592825	−	0.805331i	$-0.701987\pi$
$79$	−10.5383	−1.18565	−0.592825	+	0.805331i	$0.701987\pi$
$80$	−7.58742	−0.848299
$81$	1.00000	0.111111
$82$	−5.31255	−0.586673
$83$	−0.517354	−0.0567870	−0.0283935	−	0.999597i	$-0.509039\pi$
$83$	−0.517354	−0.0567870	−0.0283935	+	0.999597i	$0.509039\pi$
$84$	−6.41471	−0.699902
$85$	2.70234	0.293110
$86$	−11.2097	−1.20878
$87$	3.37414	0.361746
$88$	4.81810	0.513611
$89$	−1.13656	−0.120475	−0.0602377	−	0.998184i	$-0.519186\pi$
$89$	−1.13656	−0.120475	−0.0602377	+	0.998184i	$0.519186\pi$
$90$	−5.72017	−0.602959
$91$	2.48910	0.260928
$92$	−3.91389	−0.408052
$93$	7.71797	0.800316
$94$	−20.8498	−2.15049
$95$	−4.94290	−0.507131
$96$	−7.97802	−0.814253
$97$	−5.39211	−0.547486	−0.273743	−	0.961803i	$-0.588262\pi$
$97$	−5.39211	−0.547486	−0.273743	+	0.961803i	$0.588262\pi$
$98$	0.662626	0.0669354
$99$	−4.73579	−0.475965
$100$	5.71197	0.571197
$101$	−4.59760	−0.457478	−0.228739	−	0.973488i	$-0.573460\pi$
$101$	−4.59760	−0.457478	−0.228739	+	0.973488i	$0.573460\pi$
$102$	2.11675	0.209590
$103$	−18.4069	−1.81368	−0.906841	−	0.421472i	$-0.861513\pi$
$103$	−18.4069	−1.81368	−0.906841	+	0.421472i	$0.861513\pi$
$104$	−0.979289	−0.0960272
$105$	−6.98802	−0.681961
$106$	4.26248	0.414009
$107$	14.7173	1.42277	0.711386	−	0.702801i	$-0.248068\pi$
$107$	14.7173	1.42277	0.711386	+	0.702801i	$0.248068\pi$
$108$	−2.48063	−0.238699
$109$	5.39265	0.516522	0.258261	−	0.966075i	$-0.416851\pi$
$109$	5.39265	0.516522	0.258261	+	0.966075i	$0.416851\pi$
$110$	27.0895	2.58289
$111$	4.06578	0.385906
$112$	−7.26054	−0.686057
$113$	7.56798	0.711936	0.355968	−	0.934498i	$-0.384151\pi$
$113$	7.56798	0.711936	0.355968	+	0.934498i	$0.384151\pi$
$114$	−3.87179	−0.362626
$115$	−4.26369	−0.397592
$116$	−8.37002	−0.777136
$117$	0.962559	0.0889886
$118$	−29.5516	−2.72045
$119$	2.58592	0.237051
$120$	2.74931	0.250976
$121$	11.4277	1.03888
$122$	21.2227	1.92142
$123$	−2.50977	−0.226298
$124$	−19.1454	−1.71931
$125$	−7.28921	−0.651967
$126$	−5.47374	−0.487639
$127$	9.61815	0.853473	0.426736	−	0.904376i	$-0.359663\pi$
$127$	9.61815	0.853473	0.426736	+	0.904376i	$0.359663\pi$
$128$	7.90402	0.698624
$129$	−5.29573	−0.466263
$130$	−5.50600	−0.482909
$131$	−14.2784	−1.24751	−0.623754	−	0.781621i	$-0.714393\pi$
$131$	−14.2784	−1.24751	−0.623754	+	0.781621i	$0.714393\pi$
$132$	11.7478	1.02251
$133$	−4.72995	−0.410139
$134$	−28.5568	−2.46693
$135$	−2.70234	−0.232580
$136$	−1.01738	−0.0872397
$137$	−21.0716	−1.80027	−0.900136	−	0.435608i	$-0.856533\pi$
$137$	−21.0716	−1.80027	−0.900136	+	0.435608i	$0.856533\pi$
$138$	−3.33977	−0.284300
$139$	−9.13623	−0.774925	−0.387463	−	0.921885i	$-0.626648\pi$
$139$	−9.13623	−0.774925	−0.387463	+	0.921885i	$0.626648\pi$
$140$	17.3347	1.46505
$141$	−9.84991	−0.829512
$142$	−2.93012	−0.245890
$143$	−4.55847	−0.381199
$144$	−2.80772	−0.233977
$145$	−9.11808	−0.757215
$146$	−13.1853	−1.09122
$147$	0.313039	0.0258191
$148$	−10.0857	−0.829039
$149$	−13.8524	−1.13483	−0.567415	−	0.823432i	$-0.692057\pi$
$149$	−13.8524	−1.13483	−0.567415	+	0.823432i	$0.692057\pi$
$150$	4.87409	0.397968
$151$	−9.48517	−0.771892	−0.385946	−	0.922521i	$-0.626125\pi$
$151$	−9.48517	−0.771892	−0.385946	+	0.922521i	$0.626125\pi$
$152$	1.86091	0.150940
$153$	1.00000	0.0808452
$154$	25.9225	2.08889
$155$	−20.8565	−1.67524
$156$	−2.38776	−0.191173
$157$	1.00000	0.0798087
$157$	1.00000	0.0798087
$158$	22.3069	1.77464
$159$	2.01369	0.159696
$160$	21.5593	1.70441
$161$	−4.08001	−0.321550
$162$	−2.11675	−0.166308
$163$	16.2724	1.27455	0.637277	−	0.770635i	$-0.280061\pi$
$163$	16.2724	1.27455	0.637277	+	0.770635i	$0.280061\pi$
$164$	6.22581	0.486154
$165$	12.7977	0.996299
$166$	1.09511	0.0849970
$167$	19.0849	1.47683	0.738416	−	0.674346i	$-0.235574\pi$
$167$	19.0849	1.47683	0.738416	+	0.674346i	$0.235574\pi$
$168$	2.63086	0.202975
$169$	−12.0735	−0.928729
$170$	−5.72017	−0.438717
$171$	−1.82912	−0.139876
$172$	13.1368	1.00167
$173$	−18.0601	−1.37308	−0.686542	−	0.727090i	$-0.740872\pi$
$173$	−18.0601	−1.37308	−0.686542	+	0.727090i	$0.740872\pi$
$174$	−7.14222	−0.541450
$175$	5.95440	0.450110
$176$	13.2968	1.00228
$177$	−13.9608	−1.04936
$178$	2.40582	0.180324
$179$	−13.7942	−1.03103	−0.515513	−	0.856881i	$-0.672399\pi$
$179$	−13.7942	−1.03103	−0.515513	+	0.856881i	$0.672399\pi$
$180$	6.70351	0.499650
$181$	17.7835	1.32184	0.660918	−	0.750458i	$-0.270167\pi$
$181$	17.7835	1.32184	0.660918	+	0.750458i	$0.270167\pi$
$182$	−5.26880	−0.390549
$183$	10.0261	0.741150
$184$	1.60520	0.118337
$185$	−10.9871	−0.807788
$186$	−16.3370	−1.19789
$187$	−4.73579	−0.346315
$188$	24.4340	1.78203
$189$	−2.58592	−0.188098
$190$	10.4629	0.759058
$191$	−10.4251	−0.754332	−0.377166	−	0.926146i	$-0.623101\pi$
$191$	−10.4251	−0.754332	−0.377166	+	0.926146i	$0.623101\pi$
$192$	11.2720	0.813488
$193$	−24.4513	−1.76004	−0.880021	−	0.474934i	$-0.842472\pi$
$193$	−24.4513	−1.76004	−0.880021	+	0.474934i	$0.842472\pi$
$194$	11.4138	0.819460
$195$	−2.60116	−0.186273
$196$	−0.776536	−0.0554669
$197$	−8.87083	−0.632020	−0.316010	−	0.948756i	$-0.602343\pi$
$197$	−8.87083	−0.632020	−0.316010	+	0.948756i	$0.602343\pi$
$198$	10.0245	0.712409
$199$	−4.15033	−0.294209	−0.147104	−	0.989121i	$-0.546995\pi$
$199$	−4.15033	−0.294209	−0.147104	+	0.989121i	$0.546995\pi$
$200$	−2.34265	−0.165650
$201$	−13.4909	−0.951573
$202$	9.73198	0.684739
$203$	−8.72525	−0.612393
$204$	−2.48063	−0.173679
$205$	6.78224	0.473692
$206$	38.9627	2.71466
$207$	−1.57778	−0.109663
$208$	−2.70260	−0.187392
$209$	8.66233	0.599186
$210$	14.7919	1.02074
$211$	−16.5808	−1.14147	−0.570734	−	0.821135i	$-0.693341\pi$
$211$	−16.5808	−1.14147	−0.570734	+	0.821135i	$0.693341\pi$
$212$	−4.99523	−0.343074
$213$	−1.38426	−0.0948476
$214$	−31.1528	−2.12956
$215$	14.3109	0.975993
$216$	1.01738	0.0692240
$217$	−19.9580	−1.35484
$218$	−11.4149	−0.773114
$219$	−6.22902	−0.420918
$220$	−31.7464	−2.14034
$221$	0.962559	0.0647487
$222$	−8.60623	−0.577613
$223$	−15.0648	−1.00881	−0.504406	−	0.863467i	$-0.668288\pi$
$223$	−15.0648	−1.00881	−0.504406	+	0.863467i	$0.668288\pi$
$224$	20.6305	1.37843
$225$	2.30263	0.153509
$226$	−16.0195	−1.06560
$227$	7.22697	0.479671	0.239836	−	0.970814i	$-0.422906\pi$
$227$	7.22697	0.479671	0.239836	+	0.970814i	$0.422906\pi$
$228$	4.53738	0.300495
$229$	−17.6306	−1.16506	−0.582532	−	0.812808i	$-0.697938\pi$
$229$	−17.6306	−1.16506	−0.582532	+	0.812808i	$0.697938\pi$
$230$	9.02518	0.595103
$231$	12.2463	0.805751
$232$	3.43279	0.225374
$233$	17.9972	1.17903	0.589517	−	0.807756i	$-0.299318\pi$
$233$	17.9972	1.17903	0.589517	+	0.807756i	$0.299318\pi$
$234$	−2.03750	−0.133195
$235$	26.6178	1.73635
$236$	34.6317	2.25433
$237$	10.5383	0.684535
$238$	−5.47374	−0.354810
$239$	4.00954	0.259355	0.129678	−	0.991556i	$-0.458606\pi$
$239$	4.00954	0.259355	0.129678	+	0.991556i	$0.458606\pi$
$240$	7.58742	0.489766
$241$	3.89784	0.251082	0.125541	−	0.992088i	$-0.459933\pi$
$241$	3.89784	0.251082	0.125541	+	0.992088i	$0.459933\pi$
$242$	−24.1896	−1.55496
$243$	−1.00000	−0.0641500
$244$	−24.8711	−1.59221
$245$	−0.845938	−0.0540450
$246$	5.31255	0.338716
$247$	−1.76064	−0.112027
$248$	7.85211	0.498610
$249$	0.517354	0.0327860
$250$	15.4294	0.975844
$251$	9.68168	0.611102	0.305551	−	0.952176i	$-0.401159\pi$
$251$	9.68168	0.611102	0.305551	+	0.952176i	$0.401159\pi$
$252$	6.41471	0.404089
$253$	7.47203	0.469763
$254$	−20.3592	−1.27745
$255$	−2.70234	−0.169227
$256$	5.81319	0.363324
$257$	6.35685	0.396530	0.198265	−	0.980149i	$-0.436469\pi$
$257$	6.35685	0.396530	0.198265	+	0.980149i	$0.436469\pi$
$258$	11.2097	0.697888
$259$	−10.5138	−0.653293
$260$	6.45252	0.400168
$261$	−3.37414	−0.208854
$262$	30.2238	1.86723
$263$	22.2354	1.37109	0.685546	−	0.728029i	$-0.259563\pi$
$263$	22.2354	1.37109	0.685546	+	0.728029i	$0.259563\pi$
$264$	−4.81810	−0.296534
$265$	−5.44167	−0.334279
$266$	10.0121	0.613883
$267$	1.13656	0.0695565
$268$	33.4659	2.04426
$269$	8.40774	0.512629	0.256314	−	0.966593i	$-0.417492\pi$
$269$	8.40774	0.512629	0.256314	+	0.966593i	$0.417492\pi$
$270$	5.72017	0.348119
$271$	−1.46369	−0.0889127	−0.0444563	−	0.999011i	$-0.514156\pi$
$271$	−1.46369	−0.0889127	−0.0444563	+	0.999011i	$0.514156\pi$
$272$	−2.80772	−0.170243
$273$	−2.48910	−0.150647
$274$	44.6034	2.69459
$275$	−10.9048	−0.657582
$276$	3.91389	0.235589
$277$	5.57153	0.334761	0.167380	−	0.985892i	$-0.446469\pi$
$277$	5.57153	0.334761	0.167380	+	0.985892i	$0.446469\pi$
$278$	19.3391	1.15988
$279$	−7.71797	−0.462063
$280$	−7.10948	−0.424872
$281$	−18.5574	−1.10704	−0.553521	−	0.832835i	$-0.686716\pi$
$281$	−18.5574	−1.10704	−0.553521	+	0.832835i	$0.686716\pi$
$282$	20.8498	1.24159
$283$	−8.26891	−0.491536	−0.245768	−	0.969329i	$-0.579040\pi$
$283$	−8.26891	−0.491536	−0.245768	+	0.969329i	$0.579040\pi$
$284$	3.43383	0.203760
$285$	4.94290	0.292792
$286$	9.64915	0.570566
$287$	6.49005	0.383095
$288$	7.97802	0.470109
$289$	1.00000	0.0588235
$290$	19.3007	1.13338
$291$	5.39211	0.316091
$292$	15.4519	0.904254
$293$	3.05652	0.178564	0.0892819	−	0.996006i	$-0.471543\pi$
$293$	3.05652	0.178564	0.0892819	+	0.996006i	$0.471543\pi$
$294$	−0.662626	−0.0386452
$295$	37.7269	2.19655
$296$	4.13644	0.240426
$297$	4.73579	0.274798
$298$	29.3220	1.69858
$299$	−1.51871	−0.0878290
$300$	−5.71197	−0.329781
$301$	13.6943	0.789328
$302$	20.0777	1.15534
$303$	4.59760	0.264125
$304$	5.13567	0.294551
$305$	−27.0939	−1.55139
$306$	−2.11675	−0.121007
$307$	−16.5987	−0.947338	−0.473669	−	0.880703i	$-0.657071\pi$
$307$	−16.5987	−0.947338	−0.473669	+	0.880703i	$0.657071\pi$
$308$	−30.3787	−1.73099
$309$	18.4069	1.04713
$310$	44.1481	2.50744
$311$	29.0221	1.64569	0.822847	−	0.568263i	$-0.192384\pi$
$311$	29.0221	1.64569	0.822847	+	0.568263i	$0.192384\pi$
$312$	0.979289	0.0554413
$313$	8.83823	0.499566	0.249783	−	0.968302i	$-0.419641\pi$
$313$	8.83823	0.499566	0.249783	+	0.968302i	$0.419641\pi$
$314$	−2.11675	−0.119455
$315$	6.98802	0.393730
$316$	−26.1416	−1.47058
$317$	−9.38551	−0.527143	−0.263571	−	0.964640i	$-0.584900\pi$
$317$	−9.38551	−0.527143	−0.263571	+	0.964640i	$0.584900\pi$
$318$	−4.26248	−0.239028
$319$	15.9792	0.894665
$320$	−30.4608	−1.70281
$321$	−14.7173	−0.821438
$322$	8.63636	0.481285
$323$	−1.82912	−0.101775
$324$	2.48063	0.137813
$325$	2.21641	0.122945
$326$	−34.4447	−1.90771
$327$	−5.39265	−0.298214
$328$	−2.55339	−0.140987
$329$	25.4710	1.40426
$330$	−27.0895	−1.49123
$331$	−16.7044	−0.918157	−0.459079	−	0.888396i	$-0.651820\pi$
$331$	−16.7044	−0.918157	−0.459079	+	0.888396i	$0.651820\pi$
$332$	−1.28337	−0.0704339
$333$	−4.06578	−0.222803
$334$	−40.3979	−2.21047
$335$	36.4569	1.99185
$336$	7.26054	0.396095
$337$	−20.3820	−1.11028	−0.555140	−	0.831757i	$-0.687335\pi$
$337$	−20.3820	−1.11028	−0.555140	+	0.831757i	$0.687335\pi$
$338$	25.5565	1.39009
$339$	−7.56798	−0.411036
$340$	6.70351	0.363549
$341$	36.5507	1.97933
$342$	3.87179	0.209362
$343$	−18.9109	−1.02109
$344$	−5.38778	−0.290490
$345$	4.26369	0.229550
$346$	38.2287	2.05519
$347$	15.0554	0.808214	0.404107	−	0.914712i	$-0.367582\pi$
$347$	15.0554	0.808214	0.404107	+	0.914712i	$0.367582\pi$
$348$	8.37002	0.448680
$349$	1.61600	0.0865023	0.0432511	−	0.999064i	$-0.486228\pi$
$349$	1.61600	0.0865023	0.0432511	+	0.999064i	$0.486228\pi$
$350$	−12.6040	−0.673711
$351$	−0.962559	−0.0513776
$352$	−37.7822	−2.01380
$353$	−14.1446	−0.752839	−0.376420	−	0.926449i	$-0.622845\pi$
$353$	−14.1446	−0.752839	−0.376420	+	0.926449i	$0.622845\pi$
$354$	29.5516	1.57065
$355$	3.74072	0.198537
$356$	−2.81939	−0.149428
$357$	−2.58592	−0.136861
$358$	29.1989	1.54321
$359$	23.6975	1.25071	0.625354	−	0.780341i	$-0.284954\pi$
$359$	23.6975	1.25071	0.625354	+	0.780341i	$0.284954\pi$
$360$	−2.74931	−0.144901
$361$	−15.6543	−0.823912
$362$	−37.6432	−1.97848
$363$	−11.4277	−0.599798
$364$	6.17454	0.323634
$365$	16.8329	0.881074
$366$	−21.2227	−1.10933
$367$	25.2828	1.31975	0.659874	−	0.751376i	$-0.270609\pi$
$367$	25.2828	1.31975	0.659874	+	0.751376i	$0.270609\pi$
$368$	4.42997	0.230928
$369$	2.50977	0.130653
$370$	23.2570	1.20907
$371$	−5.20724	−0.270346
$372$	19.1454	0.992645
$373$	−23.8156	−1.23312	−0.616562	−	0.787306i	$-0.711475\pi$
$373$	−23.8156	−1.23312	−0.616562	+	0.787306i	$0.711475\pi$
$374$	10.0245	0.518354
$375$	7.28921	0.376413
$376$	−10.0211	−0.516799
$377$	−3.24781	−0.167271
$378$	5.47374	0.281539
$379$	−18.5115	−0.950870	−0.475435	−	0.879751i	$-0.657709\pi$
$379$	−18.5115	−0.950870	−0.475435	+	0.879751i	$0.657709\pi$
$380$	−12.2615	−0.629003
$381$	−9.61815	−0.492753
$382$	22.0673	1.12906
$383$	−19.4435	−0.993517	−0.496758	−	0.867889i	$-0.665477\pi$
$383$	−19.4435	−0.993517	−0.496758	+	0.867889i	$0.665477\pi$
$384$	−7.90402	−0.403351
$385$	−33.0938	−1.68661
$386$	51.7573	2.63438
$387$	5.29573	0.269197
$388$	−13.3759	−0.679056
$389$	−23.9230	−1.21295	−0.606473	−	0.795104i	$-0.707416\pi$
$389$	−23.9230	−1.21295	−0.606473	+	0.795104i	$0.707416\pi$
$390$	5.50600	0.278807
$391$	−1.57778	−0.0797918
$392$	0.318480	0.0160857
$393$	14.2784	0.720249
$394$	18.7773	0.945988
$395$	−28.4780	−1.43288
$396$	−11.7478	−0.590347
$397$	18.2352	0.915200	0.457600	−	0.889158i	$-0.348709\pi$
$397$	18.2352	0.915200	0.457600	+	0.889158i	$0.348709\pi$
$398$	8.78521	0.440363
$399$	4.72995	0.236794
$400$	−6.46514	−0.323257
$401$	−29.3963	−1.46798	−0.733991	−	0.679159i	$-0.762345\pi$
$401$	−29.3963	−1.46798	−0.733991	+	0.679159i	$0.762345\pi$
$402$	28.5568	1.42428
$403$	−7.42900	−0.370065
$404$	−11.4050	−0.567418
$405$	2.70234	0.134280
$406$	18.4692	0.916610
$407$	19.2547	0.954418
$408$	1.01738	0.0503679
$409$	−20.4179	−1.00960	−0.504801	−	0.863236i	$-0.668434\pi$
$409$	−20.4179	−1.00960	−0.504801	+	0.863236i	$0.668434\pi$
$410$	−14.3563	−0.709008
$411$	21.0716	1.03939
$412$	−45.6607	−2.24954
$413$	36.1016	1.77644
$414$	3.33977	0.164141
$415$	−1.39807	−0.0686283
$416$	7.67931	0.376509
$417$	9.13623	0.447403
$418$	−18.3360	−0.896842
$419$	28.5930	1.39686	0.698429	−	0.715679i	$-0.253883\pi$
$419$	28.5930	1.39686	0.698429	+	0.715679i	$0.253883\pi$
$420$	−17.3347	−0.845847
$421$	−6.56225	−0.319824	−0.159912	−	0.987131i	$-0.551121\pi$
$421$	−6.56225	−0.319824	−0.159912	+	0.987131i	$0.551121\pi$
$422$	35.0974	1.70851
$423$	9.84991	0.478919
$424$	2.04869	0.0994932
$425$	2.30263	0.111694
$426$	2.93012	0.141965
$427$	−25.9266	−1.25468
$428$	36.5082	1.76469
$429$	4.55847	0.220085
$430$	−30.2925	−1.46084
$431$	18.3022	0.881587	0.440793	−	0.897609i	$-0.354697\pi$
$431$	18.3022	0.881587	0.440793	+	0.897609i	$0.354697\pi$
$432$	2.80772	0.135087
$433$	−9.43675	−0.453501	−0.226751	−	0.973953i	$-0.572810\pi$
$433$	−9.43675	−0.453501	−0.226751	+	0.973953i	$0.572810\pi$
$434$	42.2461	2.02788
$435$	9.11808	0.437178
$436$	13.3772	0.640651
$437$	2.88595	0.138054
$438$	13.1853	0.630017
$439$	7.93283	0.378613	0.189307	−	0.981918i	$-0.439376\pi$
$439$	7.93283	0.378613	0.189307	+	0.981918i	$0.439376\pi$
$440$	13.0201	0.620711
$441$	−0.313039	−0.0149066
$442$	−2.03750	−0.0969139
$443$	1.24012	0.0589200	0.0294600	−	0.999566i	$-0.490621\pi$
$443$	1.24012	0.0589200	0.0294600	+	0.999566i	$0.490621\pi$
$444$	10.0857	0.478646
$445$	−3.07138	−0.145597
$446$	31.8884	1.50996
$447$	13.8524	0.655195
$448$	−29.1485	−1.37714
$449$	−0.851037	−0.0401629	−0.0200815	−	0.999798i	$-0.506393\pi$
$449$	−0.851037	−0.0401629	−0.0200815	+	0.999798i	$0.506393\pi$
$450$	−4.87409	−0.229767
$451$	−11.8857	−0.559677
$452$	18.7734	0.883026
$453$	9.48517	0.445652
$454$	−15.2977	−0.717957
$455$	6.72638	0.315337
$456$	−1.86091	−0.0871452
$457$	6.54640	0.306228	0.153114	−	0.988209i	$-0.451070\pi$
$457$	6.54640	0.306228	0.153114	+	0.988209i	$0.451070\pi$
$458$	37.3196	1.74383
$459$	−1.00000	−0.0466760
$460$	−10.5767	−0.493139
$461$	−7.59851	−0.353898	−0.176949	−	0.984220i	$-0.556623\pi$
$461$	−7.59851	−0.353898	−0.176949	+	0.984220i	$0.556623\pi$
$462$	−25.9225	−1.20602
$463$	−31.0129	−1.44129	−0.720645	−	0.693304i	$-0.756154\pi$
$463$	−31.0129	−1.44129	−0.720645	+	0.693304i	$0.756154\pi$
$464$	9.47367	0.439804
$465$	20.8565	0.967199
$466$	−38.0955	−1.76474
$467$	1.65725	0.0766883	0.0383442	−	0.999265i	$-0.487792\pi$
$467$	1.65725	0.0766883	0.0383442	+	0.999265i	$0.487792\pi$
$468$	2.38776	0.110374
$469$	34.8863	1.61090
$470$	−56.3432	−2.59892
$471$	−1.00000	−0.0460776
$472$	−14.2035	−0.653769
$473$	−25.0795	−1.15316
$474$	−22.3069	−1.02459
$475$	−4.21178	−0.193250
$476$	6.41471	0.294018
$477$	−2.01369	−0.0922006
$478$	−8.48719	−0.388195
$479$	9.41291	0.430087	0.215043	−	0.976604i	$-0.431011\pi$
$479$	9.41291	0.430087	0.215043	+	0.976604i	$0.431011\pi$
$480$	−21.5593	−0.984042
$481$	−3.91355	−0.178442
$482$	−8.25074	−0.375811
$483$	4.08001	0.185647
$484$	28.3479	1.28854
$485$	−14.5713	−0.661649
$486$	2.11675	0.0960178
$487$	17.2921	0.783580	0.391790	−	0.920055i	$-0.371856\pi$
$487$	17.2921	0.783580	0.391790	+	0.920055i	$0.371856\pi$
$488$	10.2004	0.461749
$489$	−16.2724	−0.735864
$490$	1.79064	0.0808929
$491$	−15.5523	−0.701866	−0.350933	−	0.936400i	$-0.614136\pi$
$491$	−15.5523	−0.701866	−0.350933	+	0.936400i	$0.614136\pi$
$492$	−6.22581	−0.280681
$493$	−3.37414	−0.151964
$494$	3.72683	0.167678
$495$	−12.7977	−0.575214
$496$	21.6699	0.973008
$497$	3.57957	0.160566
$498$	−1.09511	−0.0490730
$499$	11.2547	0.503829	0.251914	−	0.967750i	$-0.418940\pi$
$499$	11.2547	0.503829	0.251914	+	0.967750i	$0.418940\pi$
$500$	−18.0819	−0.808645
$501$	−19.0849	−0.852649
$502$	−20.4937	−0.914679
$503$	−30.8395	−1.37506	−0.687532	−	0.726154i	$-0.741306\pi$
$503$	−30.8395	−1.37506	−0.687532	+	0.726154i	$0.741306\pi$
$504$	−2.63086	−0.117188
$505$	−12.4243	−0.552873
$506$	−15.8164	−0.703126
$507$	12.0735	0.536202
$508$	23.8591	1.05858
$509$	−35.7734	−1.58563	−0.792815	−	0.609462i	$-0.791385\pi$
$509$	−35.7734	−1.58563	−0.792815	+	0.609462i	$0.791385\pi$
$510$	5.72017	0.253294
$511$	16.1077	0.712563
$512$	−28.1131	−1.24244
$513$	1.82912	0.0807576
$514$	−13.4559	−0.593513
$515$	−49.7416	−2.19188
$516$	−13.1368	−0.578314
$517$	−46.6471	−2.05154
$518$	22.2550	0.977829
$519$	18.0601	0.792751
$520$	−2.64637	−0.116051
$521$	32.9437	1.44329	0.721646	−	0.692263i	$-0.243386\pi$
$521$	32.9437	1.44329	0.721646	+	0.692263i	$0.243386\pi$
$522$	7.14222	0.312607
$523$	−5.14906	−0.225153	−0.112576	−	0.993643i	$-0.535910\pi$
$523$	−5.14906	−0.225153	−0.112576	+	0.993643i	$0.535910\pi$
$524$	−35.4194	−1.54731
$525$	−5.95440	−0.259871
$526$	−47.0668	−2.05221
$527$	−7.71797	−0.336200
$528$	−13.2968	−0.578668
$529$	−20.5106	−0.891766
$530$	11.5187	0.500339
$531$	13.9608	0.605849
$532$	−11.7333	−0.508702
$533$	2.41580	0.104640
$534$	−2.40582	−0.104110
$535$	39.7710	1.71945
$536$	−13.7254	−0.592845
$537$	13.7942	0.595264
$538$	−17.7971	−0.767287
$539$	1.48249	0.0638553
$540$	−6.70351	−0.288473
$541$	−26.0456	−1.11979	−0.559895	−	0.828564i	$-0.689158\pi$
$541$	−26.0456	−1.11979	−0.559895	+	0.828564i	$0.689158\pi$
$542$	3.09826	0.133082
$543$	−17.7835	−0.763162
$544$	7.97802	0.342055
$545$	14.5728	0.624228
$546$	5.26880	0.225484
$547$	−2.50962	−0.107304	−0.0536518	−	0.998560i	$-0.517086\pi$
$547$	−2.50962	−0.107304	−0.0536518	+	0.998560i	$0.517086\pi$
$548$	−52.2710	−2.23291
$549$	−10.0261	−0.427903
$550$	23.0826	0.984247
$551$	6.17172	0.262924
$552$	−1.60520	−0.0683220
$553$	−27.2511	−1.15884
$554$	−11.7935	−0.501059
$555$	10.9871	0.466376
$556$	−22.6636	−0.961153
$557$	−14.9683	−0.634228	−0.317114	−	0.948387i	$-0.602714\pi$
$557$	−14.9683	−0.634228	−0.317114	+	0.948387i	$0.602714\pi$
$558$	16.3370	0.691601
$559$	5.09746	0.215599
$560$	−19.6204	−0.829114
$561$	4.73579	0.199945
$562$	39.2814	1.65699
$563$	29.0491	1.22427	0.612137	−	0.790751i	$-0.290310\pi$
$563$	29.0491	1.22427	0.612137	+	0.790751i	$0.290310\pi$
$564$	−24.4340	−1.02886
$565$	20.4512	0.860390
$566$	17.5032	0.735716
$567$	2.58592	0.108598
$568$	−1.40832	−0.0590916
$569$	−5.76387	−0.241634	−0.120817	−	0.992675i	$-0.538551\pi$
$569$	−5.76387	−0.241634	−0.120817	+	0.992675i	$0.538551\pi$
$570$	−10.4629	−0.438242
$571$	−3.29105	−0.137726	−0.0688631	−	0.997626i	$-0.521937\pi$
$571$	−3.29105	−0.137726	−0.0688631	+	0.997626i	$0.521937\pi$
$572$	−11.3079	−0.472807
$573$	10.4251	0.435514
$574$	−13.7378	−0.573405
$575$	−3.63304	−0.151508
$576$	−11.2720	−0.469667
$577$	−34.5350	−1.43771	−0.718856	−	0.695159i	$-0.755334\pi$
$577$	−34.5350	−1.43771	−0.718856	+	0.695159i	$0.755334\pi$
$578$	−2.11675	−0.0880452
$579$	24.4513	1.01616
$580$	−22.6186	−0.939186
$581$	−1.33783	−0.0555027
$582$	−11.4138	−0.473115
$583$	9.53641	0.394958
$584$	−6.33728	−0.262239
$585$	2.60116	0.107545
$586$	−6.46989	−0.267269
$587$	21.2075	0.875328	0.437664	−	0.899139i	$-0.355806\pi$
$587$	21.2075	0.875328	0.437664	+	0.899139i	$0.355806\pi$
$588$	0.776536	0.0320238
$589$	14.1171	0.581684
$590$	−79.8584	−3.28772
$591$	8.87083	0.364897
$592$	11.4156	0.469177
$593$	−33.7769	−1.38705	−0.693526	−	0.720432i	$-0.743944\pi$
$593$	−33.7769	−1.38705	−0.693526	+	0.720432i	$0.743944\pi$
$594$	−10.0245	−0.411309
$595$	6.98802	0.286481
$596$	−34.3626	−1.40755
$597$	4.15033	0.169862
$598$	3.21472	0.131460
$599$	−5.72526	−0.233928	−0.116964	−	0.993136i	$-0.537316\pi$
$599$	−5.72526	−0.233928	−0.116964	+	0.993136i	$0.537316\pi$
$600$	2.34265	0.0956383
$601$	−34.5496	−1.40931	−0.704654	−	0.709551i	$-0.748898\pi$
$601$	−34.5496	−1.40931	−0.704654	+	0.709551i	$0.748898\pi$
$602$	−28.9875	−1.18144
$603$	13.4909	0.549391
$604$	−23.5292	−0.957391
$605$	30.8815	1.25551
$606$	−9.73198	−0.395335
$607$	7.20401	0.292402	0.146201	−	0.989255i	$-0.453295\pi$
$607$	7.20401	0.292402	0.146201	+	0.989255i	$0.453295\pi$
$608$	−14.5927	−0.591814
$609$	8.72525	0.353565
$610$	57.3510	2.32208
$611$	9.48112	0.383565
$612$	2.48063	0.100274
$613$	22.6179	0.913526	0.456763	−	0.889588i	$-0.349009\pi$
$613$	22.6179	0.913526	0.456763	+	0.889588i	$0.349009\pi$
$614$	35.1353	1.41795
$615$	−6.78224	−0.273486
$616$	12.4592	0.501996
$617$	−0.859429	−0.0345993	−0.0172997	−	0.999850i	$-0.505507\pi$
$617$	−0.859429	−0.0345993	−0.0172997	+	0.999850i	$0.505507\pi$
$618$	−38.9627	−1.56731
$619$	−37.2049	−1.49539	−0.747696	−	0.664041i	$-0.768840\pi$
$619$	−37.2049	−1.49539	−0.747696	+	0.664041i	$0.768840\pi$
$620$	−51.7375	−2.07783
$621$	1.57778	0.0633141
$622$	−61.4326	−2.46322
$623$	−2.93906	−0.117751
$624$	2.70260	0.108191
$625$	−31.2110	−1.24844
$626$	−18.7083	−0.747735
$627$	−8.66233	−0.345940
$628$	2.48063	0.0989880
$629$	−4.06578	−0.162113
$630$	−14.7919	−0.589323
$631$	−31.9578	−1.27222	−0.636110	−	0.771598i	$-0.719458\pi$
$631$	−31.9578	−1.27222	−0.636110	+	0.771598i	$0.719458\pi$
$632$	10.7215	0.426477
$633$	16.5808	0.659027
$634$	19.8668	0.789011
$635$	25.9915	1.03144
$636$	4.99523	0.198074
$637$	−0.301319	−0.0119387
$638$	−33.8241	−1.33911
$639$	1.38426	0.0547603
$640$	21.3593	0.844302
$641$	33.3319	1.31653	0.658266	−	0.752785i	$-0.271290\pi$
$641$	33.3319	1.31653	0.658266	+	0.752785i	$0.271290\pi$
$642$	31.1528	1.22950
$643$	−35.9168	−1.41642	−0.708210	−	0.706002i	$-0.750497\pi$
$643$	−35.9168	−1.41642	−0.708210	+	0.706002i	$0.750497\pi$
$644$	−10.1210	−0.398823
$645$	−14.3109	−0.563490
$646$	3.87179	0.152334
$647$	21.4121	0.841798	0.420899	−	0.907107i	$-0.361715\pi$
$647$	21.4121	0.841798	0.420899	+	0.907107i	$0.361715\pi$
$648$	−1.01738	−0.0399665
$649$	−66.1156	−2.59526
$650$	−4.69160	−0.184020
$651$	19.9580	0.782216
$652$	40.3659	1.58085
$653$	−32.9303	−1.28866	−0.644331	−	0.764747i	$-0.722864\pi$
$653$	−32.9303	−1.28866	−0.644331	+	0.764747i	$0.722864\pi$
$654$	11.4149	0.446358
$655$	−38.5850	−1.50764
$656$	−7.04674	−0.275129
$657$	6.22902	0.243017
$658$	−53.9158	−2.10186
$659$	−39.7646	−1.54901	−0.774504	−	0.632569i	$-0.782000\pi$
$659$	−39.7646	−1.54901	−0.774504	+	0.632569i	$0.782000\pi$
$660$	31.7464	1.23573
$661$	41.4788	1.61334	0.806669	−	0.591004i	$-0.201268\pi$
$661$	41.4788	1.61334	0.806669	+	0.591004i	$0.201268\pi$
$662$	35.3591	1.37427
$663$	−0.962559	−0.0373827
$664$	0.526346	0.0204262
$665$	−12.7819	−0.495662
$666$	8.60623	0.333485
$667$	5.32366	0.206133
$668$	47.3426	1.83174
$669$	15.0648	0.582438
$670$	−77.1701	−2.98134
$671$	47.4815	1.83300
$672$	−20.6305	−0.795838
$673$	7.35066	0.283347	0.141674	−	0.989913i	$-0.454752\pi$
$673$	7.35066	0.283347	0.141674	+	0.989913i	$0.454752\pi$
$674$	43.1437	1.66183
$675$	−2.30263	−0.0886282
$676$	−29.9499	−1.15192
$677$	−8.12386	−0.312225	−0.156113	−	0.987739i	$-0.549896\pi$
$677$	−8.12386	−0.312225	−0.156113	+	0.987739i	$0.549896\pi$
$678$	16.0195	0.615226
$679$	−13.9435	−0.535104
$680$	−2.74931	−0.105431
$681$	−7.22697	−0.276938
$682$	−77.3686	−2.96260
$683$	23.2449	0.889440	0.444720	−	0.895670i	$-0.353303\pi$
$683$	23.2449	0.889440	0.444720	+	0.895670i	$0.353303\pi$
$684$	−4.53738	−0.173491
$685$	−56.9427	−2.17567
$686$	40.0297	1.52834
$687$	17.6306	0.672650
$688$	−14.8690	−0.566874
$689$	−1.93830	−0.0738432
$690$	−9.02518	−0.343583
$691$	36.5450	1.39024	0.695119	−	0.718894i	$-0.255351\pi$
$691$	36.5450	1.39024	0.695119	+	0.718894i	$0.255351\pi$
$692$	−44.8005	−1.70306
$693$	−12.2463	−0.465200
$694$	−31.8684	−1.20971
$695$	−24.6892	−0.936514
$696$	−3.43279	−0.130120
$697$	2.50977	0.0950642
$698$	−3.42066	−0.129474
$699$	−17.9972	−0.680715
$700$	14.7707	0.558279
$701$	−40.7214	−1.53803	−0.769013	−	0.639233i	$-0.779252\pi$
$701$	−40.7214	−1.53803	−0.769013	+	0.639233i	$0.779252\pi$
$702$	2.03750	0.0769004
$703$	7.43679	0.280484
$704$	53.3819	2.01191
$705$	−26.6178	−1.00248
$706$	29.9405	1.12683
$707$	−11.8890	−0.447132
$708$	−34.6317	−1.30154
$709$	50.9596	1.91383	0.956913	−	0.290374i	$-0.0937796\pi$
$709$	50.9596	1.91383	0.956913	+	0.290374i	$0.0937796\pi$
$710$	−7.91818	−0.297164
$711$	−10.5383	−0.395217
$712$	1.15632	0.0433348
$713$	12.1773	0.456042
$714$	5.47374	0.204850
$715$	−12.3185	−0.460687
$716$	−34.2184	−1.27880
$717$	−4.00954	−0.149739
$718$	−50.1618	−1.87202
$719$	−5.40396	−0.201534	−0.100767	−	0.994910i	$-0.532130\pi$
$719$	−5.40396	−0.201534	−0.100767	+	0.994910i	$0.532130\pi$
$720$	−7.58742	−0.282766
$721$	−47.5986	−1.77266
$722$	33.1363	1.23321
$723$	−3.89784	−0.144962
$724$	44.1143	1.63950
$725$	−7.76940	−0.288548
$726$	24.1896	0.897759
$727$	−52.6766	−1.95367	−0.976834	−	0.213998i	$-0.931351\pi$
$727$	−52.6766	−1.95367	−0.976834	+	0.213998i	$0.931351\pi$
$728$	−2.53236	−0.0938555
$729$	1.00000	0.0370370
$730$	−35.6311	−1.31876
$731$	5.29573	0.195870
$732$	24.8711	0.919261
$733$	−19.4634	−0.718898	−0.359449	−	0.933165i	$-0.617035\pi$
$733$	−19.4634	−0.718898	−0.359449	+	0.933165i	$0.617035\pi$
$734$	−53.5173	−1.97536
$735$	0.845938	0.0312029
$736$	−12.5876	−0.463983
$737$	−63.8899	−2.35342
$738$	−5.31255	−0.195558
$739$	−9.30742	−0.342379	−0.171189	−	0.985238i	$-0.554761\pi$
$739$	−9.30742	−0.342379	−0.171189	+	0.985238i	$0.554761\pi$
$740$	−27.2550	−1.00191
$741$	1.76064	0.0646786
$742$	11.0224	0.404646
$743$	−24.1453	−0.885804	−0.442902	−	0.896570i	$-0.646051\pi$
$743$	−24.1453	−0.885804	−0.442902	+	0.896570i	$0.646051\pi$
$744$	−7.85211	−0.287872
$745$	−37.4338	−1.37147
$746$	50.4116	1.84570
$747$	−0.517354	−0.0189290
$748$	−11.7478	−0.429540
$749$	38.0576	1.39060
$750$	−15.4294	−0.563404
$751$	32.1838	1.17440	0.587201	−	0.809441i	$-0.300230\pi$
$751$	32.1838	1.17440	0.587201	+	0.809441i	$0.300230\pi$
$752$	−27.6558	−1.00850
$753$	−9.68168	−0.352820
$754$	6.87481	0.250366
$755$	−25.6321	−0.932849
$756$	−6.41471	−0.233301
$757$	13.8079	0.501857	0.250929	−	0.968006i	$-0.419264\pi$
$757$	13.8079	0.501857	0.250929	+	0.968006i	$0.419264\pi$
$758$	39.1841	1.42323
$759$	−7.47203	−0.271218
$760$	5.02881	0.182414
$761$	−18.3060	−0.663591	−0.331796	−	0.943351i	$-0.607654\pi$
$761$	−18.3060	−0.663591	−0.331796	+	0.943351i	$0.607654\pi$
$762$	20.3592	0.737537
$763$	13.9449	0.504841
$764$	−25.8608	−0.935610
$765$	2.70234	0.0977032
$766$	41.1571	1.48707
$767$	13.4381	0.485223
$768$	−5.81319	−0.209765
$769$	44.1198	1.59100	0.795500	−	0.605953i	$-0.207208\pi$
$769$	44.1198	1.59100	0.795500	+	0.605953i	$0.207208\pi$
$770$	70.0513	2.52447
$771$	−6.35685	−0.228936
$772$	−60.6547	−2.18301
$773$	−1.50139	−0.0540013	−0.0270007	−	0.999635i	$-0.508596\pi$
$773$	−1.50139	−0.0540013	−0.0270007	+	0.999635i	$0.508596\pi$
$774$	−11.2097	−0.402926
$775$	−17.7716	−0.638375
$776$	5.48583	0.196930
$777$	10.5138	0.377179
$778$	50.6391	1.81550
$779$	−4.59067	−0.164478
$780$	−6.45252	−0.231037
$781$	−6.55554	−0.234576
$782$	3.33977	0.119430
$783$	3.37414	0.120582
$784$	0.878929	0.0313903
$785$	2.70234	0.0964506
$786$	−30.2238	−1.07805
$787$	0.592086	0.0211056	0.0105528	−	0.999944i	$-0.496641\pi$
$787$	0.592086	0.0211056	0.0105528	+	0.999944i	$0.496641\pi$
$788$	−22.0053	−0.783905
$789$	−22.2354	−0.791601
$790$	60.2808	2.14470
$791$	19.5702	0.695835
$792$	4.81810	0.171204
$793$	−9.65071	−0.342707
$794$	−38.5995	−1.36984
$795$	5.44167	0.192996
$796$	−10.2954	−0.364912
$797$	39.9050	1.41351	0.706754	−	0.707460i	$-0.250159\pi$
$797$	39.9050	1.41351	0.706754	+	0.707460i	$0.250159\pi$
$798$	−10.0121	−0.354425
$799$	9.84991	0.348465
$800$	18.3704	0.649492
$801$	−1.13656	−0.0401585
$802$	62.2247	2.19723
$803$	−29.4993	−1.04101
$804$	−33.4659	−1.18025
$805$	−11.0256	−0.388600
$806$	15.7253	0.553901
$807$	−8.40774	−0.295966
$808$	4.67751	0.164554
$809$	13.5794	0.477426	0.238713	−	0.971090i	$-0.423275\pi$
$809$	13.5794	0.477426	0.238713	+	0.971090i	$0.423275\pi$
$810$	−5.72017	−0.200986
$811$	27.2952	0.958464	0.479232	−	0.877688i	$-0.340915\pi$
$811$	27.2952	0.958464	0.479232	+	0.877688i	$0.340915\pi$
$812$	−21.6442	−0.759561
$813$	1.46369	0.0513338
$814$	−40.7573	−1.42854
$815$	43.9736	1.54033
$816$	2.80772	0.0982900
$817$	−9.68653	−0.338889
$818$	43.2197	1.51114
$819$	2.48910	0.0869761
$820$	16.8242	0.587528
$821$	24.3438	0.849605	0.424802	−	0.905286i	$-0.360344\pi$
$821$	24.3438	0.849605	0.424802	+	0.905286i	$0.360344\pi$
$822$	−44.6034	−1.55572
$823$	25.5260	0.889779	0.444890	−	0.895585i	$-0.353243\pi$
$823$	25.5260	0.889779	0.444890	+	0.895585i	$0.353243\pi$
$824$	18.7268	0.652379
$825$	10.9048	0.379655
$826$	−76.4180	−2.65892
$827$	24.1257	0.838933	0.419467	−	0.907771i	$-0.362217\pi$
$827$	24.1257	0.838933	0.419467	+	0.907771i	$0.362217\pi$
$828$	−3.91389	−0.136017
$829$	33.4584	1.16206	0.581030	−	0.813882i	$-0.302650\pi$
$829$	33.4584	1.16206	0.581030	+	0.813882i	$0.302650\pi$
$830$	2.95936	0.102721
$831$	−5.57153	−0.193274
$832$	−10.8500	−0.376155
$833$	−0.313039	−0.0108462
$834$	−19.3391	−0.669659
$835$	51.5737	1.78478
$836$	21.4881	0.743180
$837$	7.71797	0.266772
$838$	−60.5242	−2.09077
$839$	−35.7714	−1.23496	−0.617482	−	0.786585i	$-0.711847\pi$
$839$	−35.7714	−1.23496	−0.617482	+	0.786585i	$0.711847\pi$
$840$	7.10948	0.245300
$841$	−17.6151	−0.607419
$842$	13.8906	0.478703
$843$	18.5574	0.639151
$844$	−41.1309	−1.41578
$845$	−32.6266	−1.12239
$846$	−20.8498	−0.716831
$847$	29.5510	1.01539
$848$	5.65389	0.194155
$849$	8.26891	0.283788
$850$	−4.87409	−0.167180
$851$	6.41490	0.219900
$852$	−3.43383	−0.117641
$853$	−33.1808	−1.13609	−0.568045	−	0.822998i	$-0.692300\pi$
$853$	−33.1808	−1.13609	−0.568045	+	0.822998i	$0.692300\pi$
$854$	54.8802	1.87796
$855$	−4.94290	−0.169044
$856$	−14.9731	−0.511769
$857$	−0.0367367	−0.00125490	−0.000627450	−	1.00000i	$-0.500200\pi$
$857$	−0.0367367	−0.00125490	−0.000627450		1.00000i	$0.500200\pi$
$858$	−9.64915	−0.329417
$859$	−0.839921	−0.0286577	−0.0143289	−	0.999897i	$-0.504561\pi$
$859$	−0.839921	−0.0286577	−0.0143289	+	0.999897i	$0.504561\pi$
$860$	35.5000	1.21054
$861$	−6.49005	−0.221180
$862$	−38.7412	−1.31953
$863$	25.6723	0.873897	0.436948	−	0.899487i	$-0.356059\pi$
$863$	25.6723	0.873897	0.436948	+	0.899487i	$0.356059\pi$
$864$	−7.97802	−0.271418
$865$	−48.8045	−1.65940
$866$	19.9753	0.678787
$867$	−1.00000	−0.0339618
$868$	−49.5085	−1.68043
$869$	49.9071	1.69298
$870$	−19.3007	−0.654355
$871$	12.9858	0.440006
$872$	−5.48638	−0.185792
$873$	−5.39211	−0.182495
$874$	−6.10883	−0.206634
$875$	−18.8493	−0.637222
$876$	−15.4519	−0.522072
$877$	−0.310842	−0.0104964	−0.00524819	−	0.999986i	$-0.501671\pi$
$877$	−0.310842	−0.0104964	−0.00524819	+	0.999986i	$0.501671\pi$
$878$	−16.7918	−0.566697
$879$	−3.05652	−0.103094
$880$	35.9324	1.21128
$881$	−5.38906	−0.181562	−0.0907809	−	0.995871i	$-0.528936\pi$
$881$	−5.38906	−0.181562	−0.0907809	+	0.995871i	$0.528936\pi$
$882$	0.662626	0.0223118
$883$	−5.96807	−0.200842	−0.100421	−	0.994945i	$-0.532019\pi$
$883$	−5.96807	−0.200842	−0.100421	+	0.994945i	$0.532019\pi$
$884$	2.38776	0.0803089
$885$	−37.7269	−1.26818
$886$	−2.62503	−0.0881896
$887$	−52.1104	−1.74970	−0.874848	−	0.484397i	$-0.839039\pi$
$887$	−52.1104	−1.74970	−0.874848	+	0.484397i	$0.839039\pi$
$888$	−4.13644	−0.138810
$889$	24.8717	0.834171
$890$	6.50134	0.217925
$891$	−4.73579	−0.158655
$892$	−37.3702	−1.25125
$893$	−18.0167	−0.602905
$894$	−29.3220	−0.980675
$895$	−37.2766	−1.24602
$896$	20.4391	0.682824
$897$	1.51871	0.0507081
$898$	1.80143	0.0601146
$899$	26.0415	0.868534
$900$	5.71197	0.190399
$901$	−2.01369	−0.0670858
$902$	25.1591	0.837707
$903$	−13.6943	−0.455719
$904$	−7.69952	−0.256082
$905$	48.0570	1.59747
$906$	−20.0777	−0.667038
$907$	12.5979	0.418305	0.209152	−	0.977883i	$-0.432929\pi$
$907$	12.5979	0.418305	0.209152	+	0.977883i	$0.432929\pi$
$908$	17.9275	0.594944
$909$	−4.59760	−0.152493
$910$	−14.2381	−0.471987
$911$	−23.5107	−0.778943	−0.389471	−	0.921039i	$-0.627342\pi$
$911$	−23.5107	−0.778943	−0.389471	+	0.921039i	$0.627342\pi$
$912$	−5.13567	−0.170059
$913$	2.45008	0.0810858
$914$	−13.8571	−0.458352
$915$	27.0939	0.895697
$916$	−43.7351	−1.44505
$917$	−36.9227	−1.21930
$918$	2.11675	0.0698632
$919$	31.5304	1.04009	0.520046	−	0.854138i	$-0.325915\pi$
$919$	31.5304	1.04009	0.520046	+	0.854138i	$0.325915\pi$
$920$	4.33780	0.143013
$921$	16.5987	0.546946
$922$	16.0842	0.529704
$923$	1.33243	0.0438574
$924$	30.3787	0.999386
$925$	−9.36197	−0.307820
$926$	65.6465	2.15728
$927$	−18.4069	−0.604561
$928$	−26.9190	−0.883659
$929$	−53.4910	−1.75498	−0.877491	−	0.479593i	$-0.840784\pi$
$929$	−53.4910	−1.75498	−0.877491	+	0.479593i	$0.840784\pi$
$930$	−44.1481	−1.44767
$931$	0.572587	0.0187658
$932$	44.6444	1.46237
$933$	−29.0221	−0.950142
$934$	−3.50798	−0.114785
$935$	−12.7977	−0.418529
$936$	−0.979289	−0.0320091
$937$	−6.10729	−0.199517	−0.0997583	−	0.995012i	$-0.531807\pi$
$937$	−6.10729	−0.199517	−0.0997583	+	0.995012i	$0.531807\pi$
$938$	−73.8455	−2.41114
$939$	−8.83823	−0.288425
$940$	66.0289	2.15363
$941$	36.3841	1.18609	0.593043	−	0.805171i	$-0.297926\pi$
$941$	36.3841	1.18609	0.593043	+	0.805171i	$0.297926\pi$
$942$	2.11675	0.0689675
$943$	−3.95986	−0.128951
$944$	−39.1982	−1.27579
$945$	−6.98802	−0.227320
$946$	53.0870	1.72601
$947$	24.7180	0.803227	0.401613	−	0.915809i	$-0.368450\pi$
$947$	24.7180	0.803227	0.401613	+	0.915809i	$0.368450\pi$
$948$	26.1416	0.849041
$949$	5.99579	0.194632
$950$	8.91529	0.289250
$951$	9.38551	0.304346
$952$	−2.63086	−0.0852667
$953$	13.5788	0.439860	0.219930	−	0.975516i	$-0.429417\pi$
$953$	13.5788	0.439860	0.219930	+	0.975516i	$0.429417\pi$
$954$	4.26248	0.138003
$955$	−28.1721	−0.911627
$956$	9.94619	0.321683
$957$	−15.9792	−0.516535
$958$	−19.9248	−0.643741
$959$	−54.4895	−1.75956
$960$	30.4608	0.983118
$961$	28.5670	0.921516
$962$	8.28401	0.267087
$963$	14.7173	0.474257
$964$	9.66910	0.311421
$965$	−66.0756	−2.12705
$966$	−8.63636	−0.277870
$967$	7.96388	0.256101	0.128050	−	0.991768i	$-0.459128\pi$
$967$	7.96388	0.256101	0.128050	+	0.991768i	$0.459128\pi$
$968$	−11.6263	−0.373684
$969$	1.82912	0.0587598
$970$	30.8438	0.990335
$971$	7.30300	0.234365	0.117182	−	0.993110i	$-0.462614\pi$
$971$	7.30300	0.234365	0.117182	+	0.993110i	$0.462614\pi$
$972$	−2.48063	−0.0795664
$973$	−23.6255	−0.757400
$974$	−36.6031	−1.17284
$975$	−2.21641	−0.0709821
$976$	28.1505	0.901076
$977$	50.2548	1.60779	0.803897	−	0.594769i	$-0.202756\pi$
$977$	50.2548	1.60779	0.803897	+	0.594769i	$0.202756\pi$
$978$	34.4447	1.10142
$979$	5.38252	0.172026
$980$	−2.09846	−0.0670329
$981$	5.39265	0.172174
$982$	32.9204	1.05053
$983$	−6.27920	−0.200275	−0.100138	−	0.994974i	$-0.531928\pi$
$983$	−6.27920	−0.200275	−0.100138	+	0.994974i	$0.531928\pi$
$984$	2.55339	0.0813991
$985$	−23.9720	−0.763811
$986$	7.14222	0.227455
$987$	−25.4710	−0.810752
$988$	−4.36749	−0.138948
$989$	−8.35550	−0.265690
$990$	27.0895	0.860962
$991$	3.99064	0.126767	0.0633834	−	0.997989i	$-0.479811\pi$
$991$	3.99064	0.126767	0.0633834	+	0.997989i	$0.479811\pi$
$992$	−61.5741	−1.95498
$993$	16.7044	0.530098
$994$	−7.57705	−0.240329
$995$	−11.2156	−0.355558
$996$	1.28337	0.0406650
$997$	−19.2038	−0.608190	−0.304095	−	0.952642i	$-0.598354\pi$
$997$	−19.2038	−0.608190	−0.304095	+	0.952642i	$0.598354\pi$
$998$	−23.8234	−0.754115
$999$	4.06578	0.128635

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.c.1.6	✓	39

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.c.1.6	✓	39	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)

\(f(q)\)	\(=\)	\(q-2.11675 q^{2} -1.00000 q^{3} +2.48063 q^{4} +2.70234 q^{5} +2.11675 q^{6} +2.58592 q^{7} -1.01738 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.11675 q^{2} -1.00000 q^{3} +2.48063 q^{4} +2.70234 q^{5} +2.11675 q^{6} +2.58592 q^{7} -1.01738 q^{8} +1.00000 q^{9} -5.72017 q^{10} -4.73579 q^{11} -2.48063 q^{12} +0.962559 q^{13} -5.47374 q^{14} -2.70234 q^{15} -2.80772 q^{16} +1.00000 q^{17} -2.11675 q^{18} -1.82912 q^{19} +6.70351 q^{20} -2.58592 q^{21} +10.0245 q^{22} -1.57778 q^{23} +1.01738 q^{24} +2.30263 q^{25} -2.03750 q^{26} -1.00000 q^{27} +6.41471 q^{28} -3.37414 q^{29} +5.72017 q^{30} -7.71797 q^{31} +7.97802 q^{32} +4.73579 q^{33} -2.11675 q^{34} +6.98802 q^{35} +2.48063 q^{36} -4.06578 q^{37} +3.87179 q^{38} -0.962559 q^{39} -2.74931 q^{40} +2.50977 q^{41} +5.47374 q^{42} +5.29573 q^{43} -11.7478 q^{44} +2.70234 q^{45} +3.33977 q^{46} +9.84991 q^{47} +2.80772 q^{48} -0.313039 q^{49} -4.87409 q^{50} -1.00000 q^{51} +2.38776 q^{52} -2.01369 q^{53} +2.11675 q^{54} -12.7977 q^{55} -2.63086 q^{56} +1.82912 q^{57} +7.14222 q^{58} +13.9608 q^{59} -6.70351 q^{60} -10.0261 q^{61} +16.3370 q^{62} +2.58592 q^{63} -11.2720 q^{64} +2.60116 q^{65} -10.0245 q^{66} +13.4909 q^{67} +2.48063 q^{68} +1.57778 q^{69} -14.7919 q^{70} +1.38426 q^{71} -1.01738 q^{72} +6.22902 q^{73} +8.60623 q^{74} -2.30263 q^{75} -4.53738 q^{76} -12.2463 q^{77} +2.03750 q^{78} -10.5383 q^{79} -7.58742 q^{80} +1.00000 q^{81} -5.31255 q^{82} -0.517354 q^{83} -6.41471 q^{84} +2.70234 q^{85} -11.2097 q^{86} +3.37414 q^{87} +4.81810 q^{88} -1.13656 q^{89} -5.72017 q^{90} +2.48910 q^{91} -3.91389 q^{92} +7.71797 q^{93} -20.8498 q^{94} -4.94290 q^{95} -7.97802 q^{96} -5.39211 q^{97} +0.662626 q^{98} -4.73579 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q - 4 q^{2} - 39 q^{3} + 30 q^{4} - 3 q^{5} + 4 q^{6} - 5 q^{7} - 3 q^{8} + 39 q^{9}+O(q^{10}) \) 39 * q - 4 * q^2 - 39 * q^3 + 30 * q^4 - 3 * q^5 + 4 * q^6 - 5 * q^7 - 3 * q^8 + 39 * q^9	\( 39 q - 4 q^{2} - 39 q^{3} + 30 q^{4} - 3 q^{5} + 4 q^{6} - 5 q^{7} - 3 q^{8} + 39 q^{9} + 4 q^{10} + q^{11} - 30 q^{12} - 26 q^{13} - 4 q^{14} + 3 q^{15} + 8 q^{16} + 39 q^{17} - 4 q^{18} - 14 q^{19} - 14 q^{20} + 5 q^{21} - 17 q^{22} + 2 q^{23} + 3 q^{24} - 6 q^{25} - 17 q^{26} - 39 q^{27} - 14 q^{28} - 7 q^{29} - 4 q^{30} - q^{31} - 30 q^{32} - q^{33} - 4 q^{34} + q^{35} + 30 q^{36} - 24 q^{37} - 20 q^{38} + 26 q^{39} + 12 q^{40} + q^{41} + 4 q^{42} - 41 q^{43} - 2 q^{44} - 3 q^{45} - 6 q^{46} - 9 q^{47} - 8 q^{48} - 10 q^{49} - 9 q^{50} - 39 q^{51} - 37 q^{52} - 47 q^{53} + 4 q^{54} - 39 q^{55} + 8 q^{56} + 14 q^{57} - 27 q^{58} + 41 q^{59} + 14 q^{60} - 41 q^{61} + 36 q^{62} - 5 q^{63} - 47 q^{64} - 39 q^{65} + 17 q^{66} - 36 q^{67} + 30 q^{68} - 2 q^{69} - 52 q^{70} - 2 q^{71} - 3 q^{72} - 63 q^{73} - 6 q^{74} + 6 q^{75} - 34 q^{76} - 64 q^{77} + 17 q^{78} + 20 q^{79} - 28 q^{80} + 39 q^{81} - 37 q^{82} + 45 q^{83} + 14 q^{84} - 3 q^{85} + 32 q^{86} + 7 q^{87} + 6 q^{88} - 32 q^{89} + 4 q^{90} - 11 q^{91} + 28 q^{92} + q^{93} - 44 q^{94} + 22 q^{95} + 30 q^{96} - 20 q^{97} + 63 q^{98} + q^{99}+O(q^{100}) \) 39 * q - 4 * q^2 - 39 * q^3 + 30 * q^4 - 3 * q^5 + 4 * q^6 - 5 * q^7 - 3 * q^8 + 39 * q^9 + 4 * q^10 + q^11 - 30 * q^12 - 26 * q^13 - 4 * q^14 + 3 * q^15 + 8 * q^16 + 39 * q^17 - 4 * q^18 - 14 * q^19 - 14 * q^20 + 5 * q^21 - 17 * q^22 + 2 * q^23 + 3 * q^24 - 6 * q^25 - 17 * q^26 - 39 * q^27 - 14 * q^28 - 7 * q^29 - 4 * q^30 - q^31 - 30 * q^32 - q^33 - 4 * q^34 + q^35 + 30 * q^36 - 24 * q^37 - 20 * q^38 + 26 * q^39 + 12 * q^40 + q^41 + 4 * q^42 - 41 * q^43 - 2 * q^44 - 3 * q^45 - 6 * q^46 - 9 * q^47 - 8 * q^48 - 10 * q^49 - 9 * q^50 - 39 * q^51 - 37 * q^52 - 47 * q^53 + 4 * q^54 - 39 * q^55 + 8 * q^56 + 14 * q^57 - 27 * q^58 + 41 * q^59 + 14 * q^60 - 41 * q^61 + 36 * q^62 - 5 * q^63 - 47 * q^64 - 39 * q^65 + 17 * q^66 - 36 * q^67 + 30 * q^68 - 2 * q^69 - 52 * q^70 - 2 * q^71 - 3 * q^72 - 63 * q^73 - 6 * q^74 + 6 * q^75 - 34 * q^76 - 64 * q^77 + 17 * q^78 + 20 * q^79 - 28 * q^80 + 39 * q^81 - 37 * q^82 + 45 * q^83 + 14 * q^84 - 3 * q^85 + 32 * q^86 + 7 * q^87 + 6 * q^88 - 32 * q^89 + 4 * q^90 - 11 * q^91 + 28 * q^92 + q^93 - 44 * q^94 + 22 * q^95 + 30 * q^96 - 20 * q^97 + 63 * q^98 + q^99

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