LMFDB - Embedded newform 8007.2.a.j.1.22

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("8007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			1.22
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)

$f(q)$	$=$	$q-0.936365 q^{2} -1.00000 q^{3} -1.12322 q^{4} +2.07077 q^{5} +0.936365 q^{6} +1.85147 q^{7} +2.92447 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.936365 q^{2} -1.00000 q^{3} -1.12322 q^{4} +2.07077 q^{5} +0.936365 q^{6} +1.85147 q^{7} +2.92447 q^{8} +1.00000 q^{9} -1.93899 q^{10} +3.66211 q^{11} +1.12322 q^{12} -3.32575 q^{13} -1.73365 q^{14} -2.07077 q^{15} -0.491931 q^{16} +1.00000 q^{17} -0.936365 q^{18} +3.13358 q^{19} -2.32593 q^{20} -1.85147 q^{21} -3.42907 q^{22} +5.19678 q^{23} -2.92447 q^{24} -0.711930 q^{25} +3.11412 q^{26} -1.00000 q^{27} -2.07961 q^{28} -10.2739 q^{29} +1.93899 q^{30} +10.7583 q^{31} -5.38832 q^{32} -3.66211 q^{33} -0.936365 q^{34} +3.83397 q^{35} -1.12322 q^{36} -3.38446 q^{37} -2.93418 q^{38} +3.32575 q^{39} +6.05590 q^{40} +0.532038 q^{41} +1.73365 q^{42} -4.49036 q^{43} -4.11336 q^{44} +2.07077 q^{45} -4.86608 q^{46} +8.56469 q^{47} +0.491931 q^{48} -3.57205 q^{49} +0.666626 q^{50} -1.00000 q^{51} +3.73556 q^{52} +8.35657 q^{53} +0.936365 q^{54} +7.58336 q^{55} +5.41458 q^{56} -3.13358 q^{57} +9.62010 q^{58} +10.6078 q^{59} +2.32593 q^{60} +9.33469 q^{61} -10.0737 q^{62} +1.85147 q^{63} +6.02930 q^{64} -6.88685 q^{65} +3.42907 q^{66} +8.50407 q^{67} -1.12322 q^{68} -5.19678 q^{69} -3.58999 q^{70} -4.51161 q^{71} +2.92447 q^{72} +4.89334 q^{73} +3.16909 q^{74} +0.711930 q^{75} -3.51971 q^{76} +6.78029 q^{77} -3.11412 q^{78} -12.0245 q^{79} -1.01867 q^{80} +1.00000 q^{81} -0.498182 q^{82} +15.0488 q^{83} +2.07961 q^{84} +2.07077 q^{85} +4.20462 q^{86} +10.2739 q^{87} +10.7097 q^{88} +5.50646 q^{89} -1.93899 q^{90} -6.15754 q^{91} -5.83714 q^{92} -10.7583 q^{93} -8.01967 q^{94} +6.48892 q^{95} +5.38832 q^{96} -14.6948 q^{97} +3.34474 q^{98} +3.66211 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9}+O(q^{10}) $ 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9	\( 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9} + 12 q^{10} - 7 q^{11} - 77 q^{12} + 24 q^{13} - 14 q^{14} + 3 q^{15} + 103 q^{16} + 64 q^{17} + 5 q^{18} + 26 q^{19} - 24 q^{20} - 5 q^{21} + 25 q^{22} + 20 q^{23} - 18 q^{24} + 141 q^{25} + 9 q^{26} - 64 q^{27} + 14 q^{28} + 5 q^{29} - 12 q^{30} + 11 q^{31} + 31 q^{32} + 7 q^{33} + 5 q^{34} - 3 q^{35} + 77 q^{36} + 50 q^{37} + 8 q^{38} - 24 q^{39} + 28 q^{40} - 9 q^{41} + 14 q^{42} + 59 q^{43} - 6 q^{44} - 3 q^{45} + 11 q^{47} - 103 q^{48} + 163 q^{49} + 20 q^{50} - 64 q^{51} + 65 q^{52} + 39 q^{53} - 5 q^{54} + 35 q^{55} - 34 q^{56} - 26 q^{57} - 27 q^{58} - 65 q^{59} + 24 q^{60} + 15 q^{61} + 18 q^{62} + 5 q^{63} + 152 q^{64} + 49 q^{65} - 25 q^{66} + 56 q^{67} + 77 q^{68} - 20 q^{69} + 28 q^{70} - 18 q^{71} + 18 q^{72} + 37 q^{73} - 76 q^{74} - 141 q^{75} + 30 q^{76} + 80 q^{77} - 9 q^{78} + 20 q^{79} - 144 q^{80} + 64 q^{81} + 27 q^{82} + 3 q^{83} - 14 q^{84} - 3 q^{85} + 12 q^{86} - 5 q^{87} + 108 q^{88} + 42 q^{89} + 12 q^{90} + 25 q^{91} + 18 q^{92} - 11 q^{93} + 60 q^{94} + 42 q^{95} - 31 q^{96} + 72 q^{97} + 18 q^{98} - 7 q^{99}+O(q^{100}) \) 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9 + 12 * q^10 - 7 * q^11 - 77 * q^12 + 24 * q^13 - 14 * q^14 + 3 * q^15 + 103 * q^16 + 64 * q^17 + 5 * q^18 + 26 * q^19 - 24 * q^20 - 5 * q^21 + 25 * q^22 + 20 * q^23 - 18 * q^24 + 141 * q^25 + 9 * q^26 - 64 * q^27 + 14 * q^28 + 5 * q^29 - 12 * q^30 + 11 * q^31 + 31 * q^32 + 7 * q^33 + 5 * q^34 - 3 * q^35 + 77 * q^36 + 50 * q^37 + 8 * q^38 - 24 * q^39 + 28 * q^40 - 9 * q^41 + 14 * q^42 + 59 * q^43 - 6 * q^44 - 3 * q^45 + 11 * q^47 - 103 * q^48 + 163 * q^49 + 20 * q^50 - 64 * q^51 + 65 * q^52 + 39 * q^53 - 5 * q^54 + 35 * q^55 - 34 * q^56 - 26 * q^57 - 27 * q^58 - 65 * q^59 + 24 * q^60 + 15 * q^61 + 18 * q^62 + 5 * q^63 + 152 * q^64 + 49 * q^65 - 25 * q^66 + 56 * q^67 + 77 * q^68 - 20 * q^69 + 28 * q^70 - 18 * q^71 + 18 * q^72 + 37 * q^73 - 76 * q^74 - 141 * q^75 + 30 * q^76 + 80 * q^77 - 9 * q^78 + 20 * q^79 - 144 * q^80 + 64 * q^81 + 27 * q^82 + 3 * q^83 - 14 * q^84 - 3 * q^85 + 12 * q^86 - 5 * q^87 + 108 * q^88 + 42 * q^89 + 12 * q^90 + 25 * q^91 + 18 * q^92 - 11 * q^93 + 60 * q^94 + 42 * q^95 - 31 * q^96 + 72 * q^97 + 18 * q^98 - 7 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−0.936365	−0.662110	−0.331055	−	0.943612i	$-0.607405\pi$
$2$	−0.936365	−0.662110	−0.331055	+	0.943612i	$0.607405\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.12322	−0.561611
$5$	2.07077	0.926075	0.463037	−	0.886339i	$-0.346760\pi$
$5$	2.07077	0.926075	0.463037	+	0.886339i	$0.346760\pi$
$6$	0.936365	0.382269
$7$	1.85147	0.699791	0.349895	−	0.936789i	$-0.386217\pi$
$7$	1.85147	0.699791	0.349895	+	0.936789i	$0.386217\pi$
$8$	2.92447	1.03396
$9$	1.00000	0.333333
$10$	−1.93899	−0.613163
$11$	3.66211	1.10417	0.552083	−	0.833789i	$-0.313833\pi$
$11$	3.66211	1.10417	0.552083	+	0.833789i	$0.313833\pi$
$12$	1.12322	0.324246
$13$	−3.32575	−0.922398	−0.461199	−	0.887297i	$-0.652581\pi$
$13$	−3.32575	−0.922398	−0.461199	+	0.887297i	$0.652581\pi$
$14$	−1.73365	−0.463338
$15$	−2.07077	−0.534669
$16$	−0.491931	−0.122983
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−0.936365	−0.220703
$19$	3.13358	0.718894	0.359447	−	0.933166i	$-0.382965\pi$
$19$	3.13358	0.718894	0.359447	+	0.933166i	$0.382965\pi$
$20$	−2.32593	−0.520093
$21$	−1.85147	−0.404024
$22$	−3.42907	−0.731079
$23$	5.19678	1.08360	0.541802	−	0.840506i	$-0.317742\pi$
$23$	5.19678	1.08360	0.541802	+	0.840506i	$0.317742\pi$
$24$	−2.92447	−0.596956
$25$	−0.711930	−0.142386
$26$	3.11412	0.610729
$27$	−1.00000	−0.192450
$28$	−2.07961	−0.393010
$29$	−10.2739	−1.90781	−0.953906	−	0.300106i	$-0.902978\pi$
$29$	−10.2739	−1.90781	−0.953906	+	0.300106i	$0.902978\pi$
$30$	1.93899	0.354010
$31$	10.7583	1.93225	0.966127	−	0.258065i	$-0.0830850\pi$
$31$	10.7583	1.93225	0.966127	+	0.258065i	$0.0830850\pi$
$32$	−5.38832	−0.952530
$33$	−3.66211	−0.637491
$34$	−0.936365	−0.160585
$35$	3.83397	0.648059
$36$	−1.12322	−0.187204
$37$	−3.38446	−0.556402	−0.278201	−	0.960523i	$-0.589738\pi$
$37$	−3.38446	−0.556402	−0.278201	+	0.960523i	$0.589738\pi$
$38$	−2.93418	−0.475987
$39$	3.32575	0.532547
$40$	6.05590	0.957522
$41$	0.532038	0.0830904	0.0415452	−	0.999137i	$-0.486772\pi$
$41$	0.532038	0.0830904	0.0415452	+	0.999137i	$0.486772\pi$
$42$	1.73365	0.267509
$43$	−4.49036	−0.684774	−0.342387	−	0.939559i	$-0.611235\pi$
$43$	−4.49036	−0.684774	−0.342387	+	0.939559i	$0.611235\pi$
$44$	−4.11336	−0.620112
$45$	2.07077	0.308692
$46$	−4.86608	−0.717465
$47$	8.56469	1.24929	0.624644	−	0.780909i	$-0.285244\pi$
$47$	8.56469	1.24929	0.624644	+	0.780909i	$0.285244\pi$
$48$	0.491931	0.0710041
$49$	−3.57205	−0.510293
$50$	0.666626	0.0942752
$51$	−1.00000	−0.140028
$52$	3.73556	0.518028
$53$	8.35657	1.14786	0.573932	−	0.818903i	$-0.305417\pi$
$53$	8.35657	1.14786	0.573932	+	0.818903i	$0.305417\pi$
$54$	0.936365	0.127423
$55$	7.58336	1.02254
$56$	5.41458	0.723554
$57$	−3.13358	−0.415053
$58$	9.62010	1.26318
$59$	10.6078	1.38102	0.690511	−	0.723322i	$-0.257386\pi$
$59$	10.6078	1.38102	0.690511	+	0.723322i	$0.257386\pi$
$60$	2.32593	0.300276
$61$	9.33469	1.19518	0.597592	−	0.801800i	$-0.296124\pi$
$61$	9.33469	1.19518	0.597592	+	0.801800i	$0.296124\pi$
$62$	−10.0737	−1.27936
$63$	1.85147	0.233264
$64$	6.02930	0.753662
$65$	−6.88685	−0.854209
$66$	3.42907	0.422089
$67$	8.50407	1.03894	0.519469	−	0.854489i	$-0.326130\pi$
$67$	8.50407	1.03894	0.519469	+	0.854489i	$0.326130\pi$
$68$	−1.12322	−0.136211
$69$	−5.19678	−0.625619
$70$	−3.58999	−0.429086
$71$	−4.51161	−0.535429	−0.267715	−	0.963498i	$-0.586268\pi$
$71$	−4.51161	−0.535429	−0.267715	+	0.963498i	$0.586268\pi$
$72$	2.92447	0.344653
$73$	4.89334	0.572722	0.286361	−	0.958122i	$-0.407554\pi$
$73$	4.89334	0.572722	0.286361	+	0.958122i	$0.407554\pi$
$74$	3.16909	0.368399
$75$	0.711930	0.0822066
$76$	−3.51971	−0.403738
$77$	6.78029	0.772686
$78$	−3.11412	−0.352604
$79$	−12.0245	−1.35286	−0.676428	−	0.736508i	$-0.736473\pi$
$79$	−12.0245	−1.35286	−0.676428	+	0.736508i	$0.736473\pi$
$80$	−1.01867	−0.113891
$81$	1.00000	0.111111
$82$	−0.498182	−0.0550149
$83$	15.0488	1.65182	0.825912	−	0.563800i	$-0.190661\pi$
$83$	15.0488	1.65182	0.825912	+	0.563800i	$0.190661\pi$
$84$	2.07961	0.226904
$85$	2.07077	0.224606
$86$	4.20462	0.453396
$87$	10.2739	1.10148
$88$	10.7097	1.14166
$89$	5.50646	0.583684	0.291842	−	0.956467i	$-0.405732\pi$
$89$	5.50646	0.583684	0.291842	+	0.956467i	$0.405732\pi$
$90$	−1.93899	−0.204388
$91$	−6.15754	−0.645486
$92$	−5.83714	−0.608563
$93$	−10.7583	−1.11559
$94$	−8.01967	−0.827166
$95$	6.48892	0.665749
$96$	5.38832	0.549943
$97$	−14.6948	−1.49203	−0.746015	−	0.665929i	$-0.768035\pi$
$97$	−14.6948	−1.49203	−0.746015	+	0.665929i	$0.768035\pi$
$98$	3.34474	0.337870
$99$	3.66211	0.368055
$100$	0.799655	0.0799655
$101$	18.4924	1.84007	0.920033	−	0.391841i	$-0.128162\pi$
$101$	18.4924	1.84007	0.920033	+	0.391841i	$0.128162\pi$
$102$	0.936365	0.0927139
$103$	−18.3029	−1.80343	−0.901717	−	0.432326i	$-0.857693\pi$
$103$	−18.3029	−1.80343	−0.901717	+	0.432326i	$0.857693\pi$
$104$	−9.72608	−0.953720
$105$	−3.83397	−0.374157
$106$	−7.82480	−0.760012
$107$	13.8389	1.33786	0.668928	−	0.743328i	$-0.266754\pi$
$107$	13.8389	1.33786	0.668928	+	0.743328i	$0.266754\pi$
$108$	1.12322	0.108082
$109$	−15.3085	−1.46628	−0.733142	−	0.680076i	$-0.761947\pi$
$109$	−15.3085	−1.46628	−0.733142	+	0.680076i	$0.761947\pi$
$110$	−7.10079	−0.677034
$111$	3.38446	0.321239
$112$	−0.910797	−0.0860622
$113$	−6.46896	−0.608549	−0.304274	−	0.952584i	$-0.598414\pi$
$113$	−6.46896	−0.608549	−0.304274	+	0.952584i	$0.598414\pi$
$114$	2.93418	0.274811
$115$	10.7613	1.00350
$116$	11.5398	1.07145
$117$	−3.32575	−0.307466
$118$	−9.93279	−0.914388
$119$	1.85147	0.169724
$120$	−6.05590	−0.552825
$121$	2.41102	0.219183
$122$	−8.74067	−0.791343
$123$	−0.532038	−0.0479722
$124$	−12.0840	−1.08517
$125$	−11.8281	−1.05793
$126$	−1.73365	−0.154446
$127$	−12.9342	−1.14773	−0.573864	−	0.818951i	$-0.694556\pi$
$127$	−12.9342	−1.14773	−0.573864	+	0.818951i	$0.694556\pi$
$128$	5.13102	0.453523
$129$	4.49036	0.395354
$130$	6.44861	0.565580
$131$	8.57754	0.749424	0.374712	−	0.927141i	$-0.377742\pi$
$131$	8.57754	0.749424	0.374712	+	0.927141i	$0.377742\pi$
$132$	4.11336	0.358022
$133$	5.80175	0.503075
$134$	−7.96291	−0.687891
$135$	−2.07077	−0.178223
$136$	2.92447	0.250772
$137$	12.6878	1.08399	0.541995	−	0.840381i	$-0.317669\pi$
$137$	12.6878	1.08399	0.541995	+	0.840381i	$0.317669\pi$
$138$	4.86608	0.414228
$139$	5.26404	0.446490	0.223245	−	0.974762i	$-0.428335\pi$
$139$	5.26404	0.446490	0.223245	+	0.974762i	$0.428335\pi$
$140$	−4.30639	−0.363957
$141$	−8.56469	−0.721277
$142$	4.22451	0.354513
$143$	−12.1793	−1.01848
$144$	−0.491931	−0.0409943
$145$	−21.2748	−1.76678
$146$	−4.58195	−0.379205
$147$	3.57205	0.294618
$148$	3.80150	0.312481
$149$	−20.0306	−1.64097	−0.820487	−	0.571666i	$-0.806297\pi$
$149$	−20.0306	−1.64097	−0.820487	+	0.571666i	$0.806297\pi$
$150$	−0.666626	−0.0544298
$151$	9.63136	0.783789	0.391894	−	0.920010i	$-0.371820\pi$
$151$	9.63136	0.783789	0.391894	+	0.920010i	$0.371820\pi$
$152$	9.16409	0.743306
$153$	1.00000	0.0808452
$154$	−6.34882	−0.511603
$155$	22.2780	1.78941
$156$	−3.73556	−0.299084
$157$	−1.00000	−0.0798087
$157$	−1.00000	−0.0798087
$158$	11.2593	0.895740
$159$	−8.35657	−0.662719
$160$	−11.1579	−0.882113
$161$	9.62170	0.758296
$162$	−0.936365	−0.0735678
$163$	16.8821	1.32231	0.661153	−	0.750251i	$-0.270067\pi$
$163$	16.8821	1.32231	0.661153	+	0.750251i	$0.270067\pi$
$164$	−0.597596	−0.0466644
$165$	−7.58336	−0.590364
$166$	−14.0912	−1.09369
$167$	−19.3263	−1.49551	−0.747756	−	0.663973i	$-0.768869\pi$
$167$	−19.3263	−1.49551	−0.747756	+	0.663973i	$0.768869\pi$
$168$	−5.41458	−0.417744
$169$	−1.93937	−0.149182
$170$	−1.93899	−0.148714
$171$	3.13358	0.239631
$172$	5.04367	0.384576
$173$	5.86156	0.445646	0.222823	−	0.974859i	$-0.428473\pi$
$173$	5.86156	0.445646	0.222823	+	0.974859i	$0.428473\pi$
$174$	−9.62010	−0.729298
$175$	−1.31812	−0.0996404
$176$	−1.80150	−0.135793
$177$	−10.6078	−0.797333
$178$	−5.15606	−0.386463
$179$	13.6426	1.01969	0.509846	−	0.860266i	$-0.329702\pi$
$179$	13.6426	1.01969	0.509846	+	0.860266i	$0.329702\pi$
$180$	−2.32593	−0.173364
$181$	3.94421	0.293171	0.146585	−	0.989198i	$-0.453172\pi$
$181$	3.94421	0.293171	0.146585	+	0.989198i	$0.453172\pi$
$182$	5.76570	0.427382
$183$	−9.33469	−0.690040
$184$	15.1979	1.12040
$185$	−7.00843	−0.515270
$186$	10.0737	0.738642
$187$	3.66211	0.267800
$188$	−9.62004	−0.701614
$189$	−1.85147	−0.134675
$190$	−6.07599	−0.440799
$191$	−2.03469	−0.147225	−0.0736126	−	0.997287i	$-0.523453\pi$
$191$	−2.03469	−0.147225	−0.0736126	+	0.997287i	$0.523453\pi$
$192$	−6.02930	−0.435127
$193$	10.1380	0.729750	0.364875	−	0.931057i	$-0.381112\pi$
$193$	10.1380	0.729750	0.364875	+	0.931057i	$0.381112\pi$
$194$	13.7597	0.987887
$195$	6.88685	0.493178
$196$	4.01220	0.286586
$197$	−25.6698	−1.82890	−0.914450	−	0.404698i	$-0.867377\pi$
$197$	−25.6698	−1.82890	−0.914450	+	0.404698i	$0.867377\pi$
$198$	−3.42907	−0.243693
$199$	20.7651	1.47200	0.735998	−	0.676984i	$-0.236713\pi$
$199$	20.7651	1.47200	0.735998	+	0.676984i	$0.236713\pi$
$200$	−2.08202	−0.147221
$201$	−8.50407	−0.599831
$202$	−17.3157	−1.21833
$203$	−19.0218	−1.33507
$204$	1.12322	0.0786412
$205$	1.10173	0.0769479
$206$	17.1382	1.19407
$207$	5.19678	0.361201
$208$	1.63604	0.113439
$209$	11.4755	0.793778
$210$	3.58999	0.247733
$211$	0.205929	0.0141768	0.00708838	−	0.999975i	$-0.497744\pi$
$211$	0.205929	0.0141768	0.00708838	+	0.999975i	$0.497744\pi$
$212$	−9.38628	−0.644653
$213$	4.51161	0.309130
$214$	−12.9582	−0.885807
$215$	−9.29849	−0.634152
$216$	−2.92447	−0.198985
$217$	19.9188	1.35217
$218$	14.3343	0.970841
$219$	−4.89334	−0.330661
$220$	−8.51779	−0.574270
$221$	−3.32575	−0.223714
$222$	−3.16909	−0.212695
$223$	20.6175	1.38065	0.690325	−	0.723499i	$-0.257467\pi$
$223$	20.6175	1.38065	0.690325	+	0.723499i	$0.257467\pi$
$224$	−9.97633	−0.666572
$225$	−0.711930	−0.0474620
$226$	6.05731	0.402926
$227$	−7.80051	−0.517738	−0.258869	−	0.965912i	$-0.583350\pi$
$227$	−7.80051	−0.517738	−0.258869	+	0.965912i	$0.583350\pi$
$228$	3.51971	0.233098
$229$	−0.501319	−0.0331281	−0.0165641	−	0.999863i	$-0.505273\pi$
$229$	−0.501319	−0.0331281	−0.0165641	+	0.999863i	$0.505273\pi$
$230$	−10.0765	−0.664426
$231$	−6.78029	−0.446110
$232$	−30.0457	−1.97260
$233$	13.0479	0.854793	0.427397	−	0.904064i	$-0.359431\pi$
$233$	13.0479	0.854793	0.427397	+	0.904064i	$0.359431\pi$
$234$	3.11412	0.203576
$235$	17.7355	1.15693
$236$	−11.9149	−0.775596
$237$	12.0245	0.781072
$238$	−1.73365	−0.112376
$239$	−9.80425	−0.634184	−0.317092	−	0.948395i	$-0.602706\pi$
$239$	−9.80425	−0.634184	−0.317092	+	0.948395i	$0.602706\pi$
$240$	1.01867	0.0657551
$241$	−0.624003	−0.0401956	−0.0200978	−	0.999798i	$-0.506398\pi$
$241$	−0.624003	−0.0401956	−0.0200978	+	0.999798i	$0.506398\pi$
$242$	−2.25759	−0.145123
$243$	−1.00000	−0.0641500
$244$	−10.4849	−0.671228
$245$	−7.39688	−0.472569
$246$	0.498182	0.0317629
$247$	−10.4215	−0.663106
$248$	31.4625	1.99787
$249$	−15.0488	−0.953680
$250$	11.0754	0.700469
$251$	−15.4957	−0.978079	−0.489039	−	0.872262i	$-0.662653\pi$
$251$	−15.4957	−0.978079	−0.489039	+	0.872262i	$0.662653\pi$
$252$	−2.07961	−0.131003
$253$	19.0312	1.19648
$254$	12.1112	0.759922
$255$	−2.07077	−0.129676
$256$	−16.8631	−1.05394
$257$	21.4364	1.33717	0.668584	−	0.743637i	$-0.266901\pi$
$257$	21.4364	1.33717	0.668584	+	0.743637i	$0.266901\pi$
$258$	−4.20462	−0.261768
$259$	−6.26624	−0.389365
$260$	7.73546	0.479733
$261$	−10.2739	−0.635937
$262$	−8.03171	−0.496201
$263$	−20.7466	−1.27929	−0.639644	−	0.768671i	$-0.720918\pi$
$263$	−20.7466	−1.27929	−0.639644	+	0.768671i	$0.720918\pi$
$264$	−10.7097	−0.659138
$265$	17.3045	1.06301
$266$	−5.43255	−0.333091
$267$	−5.50646	−0.336990
$268$	−9.55195	−0.583478
$269$	−15.2317	−0.928694	−0.464347	−	0.885653i	$-0.653711\pi$
$269$	−15.2317	−0.928694	−0.464347	+	0.885653i	$0.653711\pi$
$270$	1.93899	0.118003
$271$	4.29386	0.260834	0.130417	−	0.991459i	$-0.458368\pi$
$271$	4.29386	0.260834	0.130417	+	0.991459i	$0.458368\pi$
$272$	−0.491931	−0.0298277
$273$	6.15754	0.372671
$274$	−11.8804	−0.717721
$275$	−2.60716	−0.157218
$276$	5.83714	0.351354
$277$	14.0514	0.844266	0.422133	−	0.906534i	$-0.361281\pi$
$277$	14.0514	0.844266	0.422133	+	0.906534i	$0.361281\pi$
$278$	−4.92906	−0.295625
$279$	10.7583	0.644085
$280$	11.2123	0.670065
$281$	−21.3647	−1.27451	−0.637255	−	0.770653i	$-0.719930\pi$
$281$	−21.3647	−1.27451	−0.637255	+	0.770653i	$0.719930\pi$
$282$	8.01967	0.477565
$283$	20.3152	1.20761	0.603805	−	0.797132i	$-0.293650\pi$
$283$	20.3152	1.20761	0.603805	+	0.797132i	$0.293650\pi$
$284$	5.06753	0.300703
$285$	−6.48892	−0.384370
$286$	11.4042	0.674346
$287$	0.985054	0.0581459
$288$	−5.38832	−0.317510
$289$	1.00000	0.0588235
$290$	19.9210	1.16980
$291$	14.6948	0.861424
$292$	−5.49631	−0.321647
$293$	5.82936	0.340555	0.170277	−	0.985396i	$-0.445534\pi$
$293$	5.82936	0.340555	0.170277	+	0.985396i	$0.445534\pi$
$294$	−3.34474	−0.195069
$295$	21.9663	1.27893
$296$	−9.89777	−0.575296
$297$	−3.66211	−0.212497
$298$	18.7560	1.08650
$299$	−17.2832	−0.999514
$300$	−0.799655	−0.0461681
$301$	−8.31379	−0.479199
$302$	−9.01846	−0.518954
$303$	−18.4924	−1.06236
$304$	−1.54151	−0.0884116
$305$	19.3300	1.10683
$306$	−0.936365	−0.0535284
$307$	−1.54038	−0.0879141	−0.0439571	−	0.999033i	$-0.513996\pi$
$307$	−1.54038	−0.0879141	−0.0439571	+	0.999033i	$0.513996\pi$
$308$	−7.61576	−0.433948
$309$	18.3029	1.04121
$310$	−20.8603	−1.18479
$311$	−26.5199	−1.50381	−0.751904	−	0.659273i	$-0.770864\pi$
$311$	−26.5199	−1.50381	−0.751904	+	0.659273i	$0.770864\pi$
$312$	9.72608	0.550631
$313$	−14.3573	−0.811525	−0.405762	−	0.913979i	$-0.632994\pi$
$313$	−14.3573	−0.811525	−0.405762	+	0.913979i	$0.632994\pi$
$314$	0.936365	0.0528421
$315$	3.83397	0.216020
$316$	13.5061	0.759779
$317$	−23.5911	−1.32501	−0.662504	−	0.749059i	$-0.730506\pi$
$317$	−23.5911	−1.32501	−0.662504	+	0.749059i	$0.730506\pi$
$318$	7.82480	0.438793
$319$	−37.6240	−2.10654
$320$	12.4853	0.697947
$321$	−13.8389	−0.772411
$322$	−9.00942	−0.502075
$323$	3.13358	0.174357
$324$	−1.12322	−0.0624012
$325$	2.36770	0.131337
$326$	−15.8078	−0.875512
$327$	15.3085	0.846559
$328$	1.55593	0.0859119
$329$	15.8573	0.874241
$330$	7.10079	0.390886
$331$	19.5793	1.07618	0.538088	−	0.842889i	$-0.319147\pi$
$331$	19.5793	1.07618	0.538088	+	0.842889i	$0.319147\pi$
$332$	−16.9032	−0.927681
$333$	−3.38446	−0.185467
$334$	18.0964	0.990194
$335$	17.6099	0.962134
$336$	0.910797	0.0496881
$337$	−24.3871	−1.32845	−0.664226	−	0.747532i	$-0.731239\pi$
$337$	−24.3871	−1.32845	−0.664226	+	0.747532i	$0.731239\pi$
$338$	1.81596	0.0987751
$339$	6.46896	0.351346
$340$	−2.32593	−0.126141
$341$	39.3982	2.13353
$342$	−2.93418	−0.158662
$343$	−19.5739	−1.05689
$344$	−13.1320	−0.708027
$345$	−10.7613	−0.579370
$346$	−5.48855	−0.295066
$347$	11.1136	0.596610	0.298305	−	0.954471i	$-0.403579\pi$
$347$	11.1136	0.596610	0.298305	+	0.954471i	$0.403579\pi$
$348$	−11.5398	−0.618600
$349$	−27.6257	−1.47877	−0.739385	−	0.673283i	$-0.764884\pi$
$349$	−27.6257	−1.47877	−0.739385	+	0.673283i	$0.764884\pi$
$350$	1.23424	0.0659729
$351$	3.32575	0.177516
$352$	−19.7326	−1.05175
$353$	−27.6293	−1.47056	−0.735279	−	0.677765i	$-0.762949\pi$
$353$	−27.6293	−1.47056	−0.735279	+	0.677765i	$0.762949\pi$
$354$	9.93279	0.527922
$355$	−9.34248	−0.495848
$356$	−6.18498	−0.327803
$357$	−1.85147	−0.0979903
$358$	−12.7744	−0.675148
$359$	6.31972	0.333542	0.166771	−	0.985996i	$-0.446666\pi$
$359$	6.31972	0.333542	0.166771	+	0.985996i	$0.446666\pi$
$360$	6.05590	0.319174
$361$	−9.18065	−0.483192
$362$	−3.69322	−0.194111
$363$	−2.41102	−0.126546
$364$	6.91628	0.362512
$365$	10.1330	0.530384
$366$	8.74067	0.456882
$367$	29.9695	1.56439	0.782197	−	0.623032i	$-0.214099\pi$
$367$	29.9695	1.56439	0.782197	+	0.623032i	$0.214099\pi$
$368$	−2.55646	−0.133265
$369$	0.532038	0.0276968
$370$	6.56244	0.341165
$371$	15.4720	0.803265
$372$	12.0840	0.626526
$373$	−21.7386	−1.12558	−0.562790	−	0.826600i	$-0.690272\pi$
$373$	−21.7386	−1.12558	−0.562790	+	0.826600i	$0.690272\pi$
$374$	−3.42907	−0.177313
$375$	11.8281	0.610799
$376$	25.0472	1.29171
$377$	34.1684	1.75976
$378$	1.73365	0.0891695
$379$	5.67180	0.291341	0.145670	−	0.989333i	$-0.453466\pi$
$379$	5.67180	0.291341	0.145670	+	0.989333i	$0.453466\pi$
$380$	−7.28849	−0.373892
$381$	12.9342	0.662641
$382$	1.90522	0.0974793
$383$	36.9400	1.88754	0.943772	−	0.330596i	$-0.107250\pi$
$383$	36.9400	1.88754	0.943772	+	0.330596i	$0.107250\pi$
$384$	−5.13102	−0.261841
$385$	14.0404	0.715564
$386$	−9.49287	−0.483174
$387$	−4.49036	−0.228258
$388$	16.5055	0.837940
$389$	−12.3406	−0.625693	−0.312847	−	0.949804i	$-0.601283\pi$
$389$	−12.3406	−0.625693	−0.312847	+	0.949804i	$0.601283\pi$
$390$	−6.44861	−0.326538
$391$	5.19678	0.262813
$392$	−10.4464	−0.527621
$393$	−8.57754	−0.432680
$394$	24.0363	1.21093
$395$	−24.8998	−1.25285
$396$	−4.11336	−0.206704
$397$	29.7691	1.49407	0.747034	−	0.664786i	$-0.231477\pi$
$397$	29.7691	1.49407	0.747034	+	0.664786i	$0.231477\pi$
$398$	−19.4437	−0.974623
$399$	−5.80175	−0.290451
$400$	0.350221	0.0175110
$401$	10.1192	0.505327	0.252663	−	0.967554i	$-0.418693\pi$
$401$	10.1192	0.505327	0.252663	+	0.967554i	$0.418693\pi$
$402$	7.96291	0.397154
$403$	−35.7796	−1.78231
$404$	−20.7711	−1.03340
$405$	2.07077	0.102897
$406$	17.8113	0.883962
$407$	−12.3943	−0.614361
$408$	−2.92447	−0.144783
$409$	14.5139	0.717668	0.358834	−	0.933401i	$-0.383174\pi$
$409$	14.5139	0.717668	0.358834	+	0.933401i	$0.383174\pi$
$410$	−1.03162	−0.0509479
$411$	−12.6878	−0.625842
$412$	20.5582	1.01283
$413$	19.6401	0.966426
$414$	−4.86608	−0.239155
$415$	31.1626	1.52971
$416$	17.9202	0.878611
$417$	−5.26404	−0.257781
$418$	−10.7453	−0.525568
$419$	−2.74164	−0.133938	−0.0669689	−	0.997755i	$-0.521333\pi$
$419$	−2.74164	−0.133938	−0.0669689	+	0.997755i	$0.521333\pi$
$420$	4.30639	0.210130
$421$	−27.1628	−1.32384	−0.661918	−	0.749576i	$-0.730257\pi$
$421$	−27.1628	−1.32384	−0.661918	+	0.749576i	$0.730257\pi$
$422$	−0.192825	−0.00938658
$423$	8.56469	0.416430
$424$	24.4386	1.18684
$425$	−0.711930	−0.0345337
$426$	−4.22451	−0.204678
$427$	17.2829	0.836379
$428$	−15.5441	−0.751354
$429$	12.1793	0.588020
$430$	8.70678	0.419878
$431$	9.54809	0.459915	0.229958	−	0.973201i	$-0.426141\pi$
$431$	9.54809	0.459915	0.229958	+	0.973201i	$0.426141\pi$
$432$	0.491931	0.0236680
$433$	20.2074	0.971104	0.485552	−	0.874208i	$-0.338619\pi$
$433$	20.2074	0.971104	0.485552	+	0.874208i	$0.338619\pi$
$434$	−18.6512	−0.895288
$435$	21.2748	1.02005
$436$	17.1948	0.823481
$437$	16.2846	0.778996
$438$	4.58195	0.218934
$439$	16.6909	0.796614	0.398307	−	0.917252i	$-0.369598\pi$
$439$	16.6909	0.796614	0.398307	+	0.917252i	$0.369598\pi$
$440$	22.1773	1.05726
$441$	−3.57205	−0.170098
$442$	3.11412	0.148123
$443$	38.4884	1.82864	0.914320	−	0.404992i	$-0.132726\pi$
$443$	38.4884	1.82864	0.914320	+	0.404992i	$0.132726\pi$
$444$	−3.80150	−0.180411
$445$	11.4026	0.540535
$446$	−19.3055	−0.914143
$447$	20.0306	0.947416
$448$	11.1631	0.527406
$449$	−10.8849	−0.513691	−0.256846	−	0.966452i	$-0.582683\pi$
$449$	−10.8849	−0.513691	−0.256846	+	0.966452i	$0.582683\pi$
$450$	0.666626	0.0314251
$451$	1.94838	0.0917456
$452$	7.26608	0.341767
$453$	−9.63136	−0.452521
$454$	7.30412	0.342799
$455$	−12.7508	−0.597768
$456$	−9.16409	−0.429148
$457$	−2.11925	−0.0991345	−0.0495672	−	0.998771i	$-0.515784\pi$
$457$	−2.11925	−0.0991345	−0.0495672	+	0.998771i	$0.515784\pi$
$458$	0.469418	0.0219344
$459$	−1.00000	−0.0466760
$460$	−12.0873	−0.563575
$461$	22.0563	1.02727	0.513633	−	0.858010i	$-0.328299\pi$
$461$	22.0563	1.02727	0.513633	+	0.858010i	$0.328299\pi$
$462$	6.34882	0.295374
$463$	−0.910672	−0.0423225	−0.0211612	−	0.999776i	$-0.506736\pi$
$463$	−0.910672	−0.0423225	−0.0211612	+	0.999776i	$0.506736\pi$
$464$	5.05404	0.234628
$465$	−22.2780	−1.03312
$466$	−12.2175	−0.565967
$467$	−32.1824	−1.48923	−0.744613	−	0.667496i	$-0.767366\pi$
$467$	−32.1824	−1.48923	−0.744613	+	0.667496i	$0.767366\pi$
$468$	3.73556	0.172676
$469$	15.7451	0.727039
$470$	−16.6069	−0.766018
$471$	1.00000	0.0460776
$472$	31.0223	1.42792
$473$	−16.4442	−0.756104
$474$	−11.2593	−0.517156
$475$	−2.23089	−0.102360
$476$	−2.07961	−0.0953189
$477$	8.35657	0.382621
$478$	9.18035	0.419900
$479$	30.5362	1.39524	0.697618	−	0.716470i	$-0.254243\pi$
$479$	30.5362	1.39524	0.697618	+	0.716470i	$0.254243\pi$
$480$	11.1579	0.509288
$481$	11.2559	0.513224
$482$	0.584294	0.0266139
$483$	−9.62170	−0.437802
$484$	−2.70811	−0.123096
$485$	−30.4295	−1.38173
$486$	0.936365	0.0424744
$487$	16.5785	0.751245	0.375622	−	0.926773i	$-0.377429\pi$
$487$	16.5785	0.751245	0.375622	+	0.926773i	$0.377429\pi$
$488$	27.2991	1.23577
$489$	−16.8821	−0.763434
$490$	6.92617	0.312893
$491$	18.0914	0.816455	0.408227	−	0.912880i	$-0.366147\pi$
$491$	18.0914	0.816455	0.408227	+	0.912880i	$0.366147\pi$
$492$	0.597596	0.0269417
$493$	−10.2739	−0.462712
$494$	9.75835	0.439049
$495$	7.58336	0.340847
$496$	−5.29236	−0.237634
$497$	−8.35312	−0.374689
$498$	14.0912	0.631441
$499$	−18.8041	−0.841786	−0.420893	−	0.907110i	$-0.638283\pi$
$499$	−18.8041	−0.841786	−0.420893	+	0.907110i	$0.638283\pi$
$500$	13.2855	0.594147
$501$	19.3263	0.863435
$502$	14.5096	0.647595
$503$	28.9591	1.29122	0.645611	−	0.763666i	$-0.276603\pi$
$503$	28.9591	1.29122	0.645611	+	0.763666i	$0.276603\pi$
$504$	5.41458	0.241185
$505$	38.2935	1.70404
$506$	−17.8201	−0.792200
$507$	1.93937	0.0861305
$508$	14.5280	0.644576
$509$	6.26667	0.277765	0.138883	−	0.990309i	$-0.455649\pi$
$509$	6.26667	0.277765	0.138883	+	0.990309i	$0.455649\pi$
$510$	1.93899	0.0858600
$511$	9.05989	0.400786
$512$	5.52796	0.244304
$513$	−3.13358	−0.138351
$514$	−20.0723	−0.885352
$515$	−37.9009	−1.67011
$516$	−5.04367	−0.222035
$517$	31.3648	1.37942
$518$	5.86749	0.257803
$519$	−5.86156	−0.257294
$520$	−20.1404	−0.883216
$521$	−4.86173	−0.212996	−0.106498	−	0.994313i	$-0.533964\pi$
$521$	−4.86173	−0.212996	−0.106498	+	0.994313i	$0.533964\pi$
$522$	9.62010	0.421060
$523$	−2.76663	−0.120976	−0.0604882	−	0.998169i	$-0.519266\pi$
$523$	−2.76663	−0.120976	−0.0604882	+	0.998169i	$0.519266\pi$
$524$	−9.63448	−0.420884
$525$	1.31812	0.0575274
$526$	19.4263	0.847029
$527$	10.7583	0.468641
$528$	1.80150	0.0784004
$529$	4.00653	0.174197
$530$	−16.2033	−0.703828
$531$	10.6078	0.460340
$532$	−6.51665	−0.282532
$533$	−1.76943	−0.0766424
$534$	5.15606	0.223124
$535$	28.6571	1.23895
$536$	24.8699	1.07422
$537$	−13.6426	−0.588719
$538$	14.2624	0.614897
$539$	−13.0812	−0.563448
$540$	2.32593	0.100092
$541$	10.8328	0.465737	0.232868	−	0.972508i	$-0.425189\pi$
$541$	10.8328	0.465737	0.232868	+	0.972508i	$0.425189\pi$
$542$	−4.02062	−0.172700
$543$	−3.94421	−0.169262
$544$	−5.38832	−0.231022
$545$	−31.7002	−1.35789
$546$	−5.76570	−0.246749
$547$	17.3207	0.740579	0.370290	−	0.928916i	$-0.379258\pi$
$547$	17.3207	0.740579	0.370290	+	0.928916i	$0.379258\pi$
$548$	−14.2512	−0.608781
$549$	9.33469	0.398395
$550$	2.44125	0.104095
$551$	−32.1941	−1.37151
$552$	−15.1979	−0.646863
$553$	−22.2630	−0.946717
$554$	−13.1572	−0.558997
$555$	7.00843	0.297491
$556$	−5.91268	−0.250753
$557$	−15.7325	−0.666608	−0.333304	−	0.942819i	$-0.608164\pi$
$557$	−15.7325	−0.666608	−0.333304	+	0.942819i	$0.608164\pi$
$558$	−10.0737	−0.426455
$559$	14.9338	0.631634
$560$	−1.88605	−0.0797001
$561$	−3.66211	−0.154614
$562$	20.0051	0.843866
$563$	−8.07075	−0.340141	−0.170071	−	0.985432i	$-0.554400\pi$
$563$	−8.07075	−0.340141	−0.170071	+	0.985432i	$0.554400\pi$
$564$	9.62004	0.405077
$565$	−13.3957	−0.563561
$566$	−19.0224	−0.799571
$567$	1.85147	0.0777545
$568$	−13.1941	−0.553611
$569$	−26.0045	−1.09017	−0.545083	−	0.838382i	$-0.683502\pi$
$569$	−26.0045	−1.09017	−0.545083	+	0.838382i	$0.683502\pi$
$570$	6.07599	0.254495
$571$	−27.4835	−1.15015	−0.575075	−	0.818101i	$-0.695027\pi$
$571$	−27.4835	−1.15015	−0.575075	+	0.818101i	$0.695027\pi$
$572$	13.6800	0.571990
$573$	2.03469	0.0850005
$574$	−0.922369	−0.0384990
$575$	−3.69974	−0.154290
$576$	6.02930	0.251221
$577$	32.9566	1.37200	0.686001	−	0.727601i	$-0.259365\pi$
$577$	32.9566	1.37200	0.686001	+	0.727601i	$0.259365\pi$
$578$	−0.936365	−0.0389476
$579$	−10.1380	−0.421321
$580$	23.8963	0.992240
$581$	27.8625	1.15593
$582$	−13.7597	−0.570357
$583$	30.6027	1.26743
$584$	14.3105	0.592171
$585$	−6.88685	−0.284736
$586$	−5.45840	−0.225485
$587$	12.9868	0.536025	0.268012	−	0.963416i	$-0.413633\pi$
$587$	12.9868	0.536025	0.268012	+	0.963416i	$0.413633\pi$
$588$	−4.01220	−0.165460
$589$	33.7122	1.38909
$590$	−20.5685	−0.846791
$591$	25.6698	1.05592
$592$	1.66492	0.0684279
$593$	37.1817	1.52687	0.763435	−	0.645885i	$-0.223512\pi$
$593$	37.1817	1.52687	0.763435	+	0.645885i	$0.223512\pi$
$594$	3.42907	0.140696
$595$	3.83397	0.157177
$596$	22.4988	0.921588
$597$	−20.7651	−0.849857
$598$	16.1834	0.661788
$599$	−6.80177	−0.277913	−0.138956	−	0.990299i	$-0.544375\pi$
$599$	−6.80177	−0.277913	−0.138956	+	0.990299i	$0.544375\pi$
$600$	2.08202	0.0849981
$601$	37.6543	1.53595	0.767975	−	0.640480i	$-0.221265\pi$
$601$	37.6543	1.53595	0.767975	+	0.640480i	$0.221265\pi$
$602$	7.78473	0.317282
$603$	8.50407	0.346313
$604$	−10.8181	−0.440184
$605$	4.99265	0.202980
$606$	17.3157	0.703401
$607$	13.9395	0.565788	0.282894	−	0.959151i	$-0.408705\pi$
$607$	13.9395	0.565788	0.282894	+	0.959151i	$0.408705\pi$
$608$	−16.8848	−0.684767
$609$	19.0218	0.770803
$610$	−18.0999	−0.732843
$611$	−28.4840	−1.15234
$612$	−1.12322	−0.0454035
$613$	21.7216	0.877326	0.438663	−	0.898652i	$-0.355452\pi$
$613$	21.7216	0.877326	0.438663	+	0.898652i	$0.355452\pi$
$614$	1.44236	0.0582088
$615$	−1.10173	−0.0444259
$616$	19.8288	0.798924
$617$	13.9048	0.559787	0.279894	−	0.960031i	$-0.409701\pi$
$617$	13.9048	0.559787	0.279894	+	0.960031i	$0.409701\pi$
$618$	−17.1382	−0.689398
$619$	11.1006	0.446172	0.223086	−	0.974799i	$-0.428387\pi$
$619$	11.1006	0.446172	0.223086	+	0.974799i	$0.428387\pi$
$620$	−25.0231	−1.00495
$621$	−5.19678	−0.208540
$622$	24.8323	0.995686
$623$	10.1951	0.408457
$624$	−1.63604	−0.0654941
$625$	−20.9335	−0.837340
$626$	13.4437	0.537319
$627$	−11.4755	−0.458288
$628$	1.12322	0.0448214
$629$	−3.38446	−0.134947
$630$	−3.58999	−0.143029
$631$	−23.2698	−0.926356	−0.463178	−	0.886265i	$-0.653291\pi$
$631$	−23.2698	−0.926356	−0.463178	+	0.886265i	$0.653291\pi$
$632$	−35.1652	−1.39880
$633$	−0.205929	−0.00818496
$634$	22.0899	0.877300
$635$	−26.7838	−1.06288
$636$	9.38628	0.372190
$637$	11.8797	0.470693
$638$	35.2298	1.39476
$639$	−4.51161	−0.178476
$640$	10.6251	0.419996
$641$	24.8599	0.981908	0.490954	−	0.871186i	$-0.336648\pi$
$641$	24.8599	0.981908	0.490954	+	0.871186i	$0.336648\pi$
$642$	12.9582	0.511421
$643$	19.6377	0.774436	0.387218	−	0.921988i	$-0.373436\pi$
$643$	19.6377	0.774436	0.387218	+	0.921988i	$0.373436\pi$
$644$	−10.8073	−0.425867
$645$	9.29849	0.366128
$646$	−2.93418	−0.115444
$647$	−22.5545	−0.886709	−0.443355	−	0.896346i	$-0.646212\pi$
$647$	−22.5545	−0.886709	−0.443355	+	0.896346i	$0.646212\pi$
$648$	2.92447	0.114884
$649$	38.8470	1.52488
$650$	−2.21703	−0.0869592
$651$	−19.9188	−0.780678
$652$	−18.9623	−0.742621
$653$	15.6858	0.613832	0.306916	−	0.951737i	$-0.400703\pi$
$653$	15.6858	0.613832	0.306916	+	0.951737i	$0.400703\pi$
$654$	−14.3343	−0.560515
$655$	17.7621	0.694022
$656$	−0.261726	−0.0102187
$657$	4.89334	0.190907
$658$	−14.8482	−0.578843
$659$	−4.41161	−0.171852	−0.0859259	−	0.996302i	$-0.527385\pi$
$659$	−4.41161	−0.171852	−0.0859259	+	0.996302i	$0.527385\pi$
$660$	8.51779	0.331555
$661$	22.1091	0.859943	0.429971	−	0.902842i	$-0.358524\pi$
$661$	22.1091	0.859943	0.429971	+	0.902842i	$0.358524\pi$
$662$	−18.3334	−0.712546
$663$	3.32575	0.129162
$664$	44.0099	1.70792
$665$	12.0141	0.465885
$666$	3.16909	0.122800
$667$	−53.3911	−2.06731
$668$	21.7077	0.839896
$669$	−20.6175	−0.797119
$670$	−16.4893	−0.637038
$671$	34.1846	1.31968
$672$	9.97633	0.384845
$673$	8.55723	0.329857	0.164928	−	0.986306i	$-0.447261\pi$
$673$	8.55723	0.329857	0.164928	+	0.986306i	$0.447261\pi$
$674$	22.8352	0.879580
$675$	0.711930	0.0274022
$676$	2.17834	0.0837824
$677$	−23.6012	−0.907067	−0.453533	−	0.891239i	$-0.649837\pi$
$677$	−23.6012	−0.907067	−0.453533	+	0.891239i	$0.649837\pi$
$678$	−6.05731	−0.232629
$679$	−27.2070	−1.04411
$680$	6.05590	0.232233
$681$	7.80051	0.298916
$682$	−36.8911	−1.41263
$683$	46.8664	1.79329	0.896647	−	0.442746i	$-0.145996\pi$
$683$	46.8664	1.79329	0.896647	+	0.442746i	$0.145996\pi$
$684$	−3.51971	−0.134579
$685$	26.2734	1.00386
$686$	18.3283	0.699777
$687$	0.501319	0.0191265
$688$	2.20895	0.0842154
$689$	−27.7919	−1.05879
$690$	10.0765	0.383606
$691$	−14.6490	−0.557274	−0.278637	−	0.960397i	$-0.589883\pi$
$691$	−14.6490	−0.557274	−0.278637	+	0.960397i	$0.589883\pi$
$692$	−6.58382	−0.250279
$693$	6.78029	0.257562
$694$	−10.4064	−0.395021
$695$	10.9006	0.413483
$696$	30.0457	1.13888
$697$	0.532038	0.0201524
$698$	25.8677	0.979108
$699$	−13.0479	−0.493515
$700$	1.48054	0.0559591
$701$	8.73964	0.330092	0.165046	−	0.986286i	$-0.447223\pi$
$701$	8.73964	0.330092	0.165046	+	0.986286i	$0.447223\pi$
$702$	−3.11412	−0.117535
$703$	−10.6055	−0.399994
$704$	22.0799	0.832168
$705$	−17.7355	−0.667956
$706$	25.8711	0.973671
$707$	34.2382	1.28766
$708$	11.9149	0.447791
$709$	27.3431	1.02689	0.513445	−	0.858122i	$-0.328369\pi$
$709$	27.3431	1.02689	0.513445	+	0.858122i	$0.328369\pi$
$710$	8.74797	0.328305
$711$	−12.0245	−0.450952
$712$	16.1035	0.603504
$713$	55.9087	2.09380
$714$	1.73365	0.0648804
$715$	−25.2204	−0.943189
$716$	−15.3236	−0.572670
$717$	9.80425	0.366146
$718$	−5.91756	−0.220842
$719$	27.0818	1.00998	0.504991	−	0.863125i	$-0.331496\pi$
$719$	27.0818	1.00998	0.504991	+	0.863125i	$0.331496\pi$
$720$	−1.01867	−0.0379637
$721$	−33.8872	−1.26203
$722$	8.59643	0.319926
$723$	0.624003	0.0232069
$724$	−4.43022	−0.164648
$725$	7.31428	0.271646
$726$	2.25759	0.0837871
$727$	10.8010	0.400587	0.200293	−	0.979736i	$-0.435810\pi$
$727$	10.8010	0.400587	0.200293	+	0.979736i	$0.435810\pi$
$728$	−18.0076	−0.667405
$729$	1.00000	0.0370370
$730$	−9.48815	−0.351172
$731$	−4.49036	−0.166082
$732$	10.4849	0.387534
$733$	25.2743	0.933529	0.466764	−	0.884382i	$-0.345420\pi$
$733$	25.2743	0.933529	0.466764	+	0.884382i	$0.345420\pi$
$734$	−28.0623	−1.03580
$735$	7.39688	0.272838
$736$	−28.0019	−1.03216
$737$	31.1428	1.14716
$738$	−0.498182	−0.0183383
$739$	8.53325	0.313901	0.156950	−	0.987607i	$-0.449834\pi$
$739$	8.53325	0.313901	0.156950	+	0.987607i	$0.449834\pi$
$740$	7.87202	0.289381
$741$	10.4215	0.382844
$742$	−14.4874	−0.531849
$743$	−5.68032	−0.208391	−0.104195	−	0.994557i	$-0.533227\pi$
$743$	−5.68032	−0.208391	−0.104195	+	0.994557i	$0.533227\pi$
$744$	−31.4625	−1.15347
$745$	−41.4787	−1.51966
$746$	20.3552	0.745258
$747$	15.0488	0.550608
$748$	−4.11336	−0.150399
$749$	25.6223	0.936219
$750$	−11.0754	−0.404416
$751$	6.79689	0.248022	0.124011	−	0.992281i	$-0.460424\pi$
$751$	6.79689	0.248022	0.124011	+	0.992281i	$0.460424\pi$
$752$	−4.21324	−0.153641
$753$	15.4957	0.564694
$754$	−31.9941	−1.16515
$755$	19.9443	0.725847
$756$	2.07961	0.0756348
$757$	0.977730	0.0355362	0.0177681	−	0.999842i	$-0.494344\pi$
$757$	0.977730	0.0355362	0.0177681	+	0.999842i	$0.494344\pi$
$758$	−5.31087	−0.192900
$759$	−19.0312	−0.690787
$760$	18.9767	0.688356
$761$	40.2223	1.45806	0.729029	−	0.684483i	$-0.239972\pi$
$761$	40.2223	1.45806	0.729029	+	0.684483i	$0.239972\pi$
$762$	−12.1112	−0.438741
$763$	−28.3432	−1.02609
$764$	2.28541	0.0826833
$765$	2.07077	0.0748687
$766$	−34.5893	−1.24976
$767$	−35.2790	−1.27385
$768$	16.8631	0.608495
$769$	23.2995	0.840202	0.420101	−	0.907477i	$-0.361995\pi$
$769$	23.2995	0.840202	0.420101	+	0.907477i	$0.361995\pi$
$770$	−13.1469	−0.473782
$771$	−21.4364	−0.772014
$772$	−11.3872	−0.409835
$773$	−33.6451	−1.21013	−0.605066	−	0.796175i	$-0.706853\pi$
$773$	−33.6451	−1.21013	−0.605066	+	0.796175i	$0.706853\pi$
$774$	4.20462	0.151132
$775$	−7.65918	−0.275126
$776$	−42.9745	−1.54270
$777$	6.26624	0.224800
$778$	11.5553	0.414278
$779$	1.66719	0.0597331
$780$	−7.73546	−0.276974
$781$	−16.5220	−0.591203
$782$	−4.86608	−0.174011
$783$	10.2739	0.367158
$784$	1.75720	0.0627572
$785$	−2.07077	−0.0739088
$786$	8.03171	0.286482
$787$	−18.5113	−0.659856	−0.329928	−	0.944006i	$-0.607025\pi$
$787$	−18.5113	−0.659856	−0.329928	+	0.944006i	$0.607025\pi$
$788$	28.8329	1.02713
$789$	20.7466	0.738597
$790$	23.3153	0.829522
$791$	−11.9771	−0.425857
$792$	10.7097	0.380554
$793$	−31.0449	−1.10244
$794$	−27.8747	−0.989237
$795$	−17.3045	−0.613728
$796$	−23.3238	−0.826689
$797$	4.51163	0.159810	0.0799051	−	0.996802i	$-0.474538\pi$
$797$	4.51163	0.159810	0.0799051	+	0.996802i	$0.474538\pi$
$798$	5.43255	0.192310
$799$	8.56469	0.302997
$800$	3.83611	0.135627
$801$	5.50646	0.194561
$802$	−9.47523	−0.334582
$803$	17.9199	0.632381
$804$	9.55195	0.336871
$805$	19.9243	0.702239
$806$	33.5027	1.18008
$807$	15.2317	0.536182
$808$	54.0806	1.90255
$809$	−29.4740	−1.03625	−0.518125	−	0.855305i	$-0.673370\pi$
$809$	−29.4740	−1.03625	−0.518125	+	0.855305i	$0.673370\pi$
$810$	−1.93899	−0.0681292
$811$	−4.49179	−0.157728	−0.0788640	−	0.996885i	$-0.525129\pi$
$811$	−4.49179	−0.157728	−0.0788640	+	0.996885i	$0.525129\pi$
$812$	21.3657	0.749789
$813$	−4.29386	−0.150592
$814$	11.6055	0.406774
$815$	34.9588	1.22455
$816$	0.491931	0.0172210
$817$	−14.0709	−0.492280
$818$	−13.5903	−0.475175
$819$	−6.15754	−0.215162
$820$	−1.23748	−0.0432147
$821$	−42.0536	−1.46768	−0.733840	−	0.679322i	$-0.762274\pi$
$821$	−42.0536	−1.46768	−0.733840	+	0.679322i	$0.762274\pi$
$822$	11.8804	0.414376
$823$	0.919371	0.0320473	0.0160236	−	0.999872i	$-0.494899\pi$
$823$	0.919371	0.0320473	0.0160236	+	0.999872i	$0.494899\pi$
$824$	−53.5262	−1.86467
$825$	2.60716	0.0907698
$826$	−18.3903	−0.639880
$827$	−49.1984	−1.71080	−0.855399	−	0.517970i	$-0.826688\pi$
$827$	−49.1984	−1.71080	−0.855399	+	0.517970i	$0.826688\pi$
$828$	−5.83714	−0.202854
$829$	47.6865	1.65622	0.828110	−	0.560565i	$-0.189416\pi$
$829$	47.6865	1.65622	0.828110	+	0.560565i	$0.189416\pi$
$830$	−29.1795	−1.01284
$831$	−14.0514	−0.487437
$832$	−20.0519	−0.695176
$833$	−3.57205	−0.123764
$834$	4.92906	0.170679
$835$	−40.0202	−1.38496
$836$	−12.8895	−0.445794
$837$	−10.7583	−0.371863
$838$	2.56717	0.0886815
$839$	6.08453	0.210061	0.105031	−	0.994469i	$-0.466506\pi$
$839$	6.08453	0.210061	0.105031	+	0.994469i	$0.466506\pi$
$840$	−11.2123	−0.386862
$841$	76.5526	2.63974
$842$	25.4343	0.876525
$843$	21.3647	0.735839
$844$	−0.231304	−0.00796182
$845$	−4.01598	−0.138154
$846$	−8.01967	−0.275722
$847$	4.46393	0.153383
$848$	−4.11086	−0.141168
$849$	−20.3152	−0.697215
$850$	0.666626	0.0228651
$851$	−17.5883	−0.602920
$852$	−5.06753	−0.173611
$853$	−49.1627	−1.68330	−0.841649	−	0.540024i	$-0.818415\pi$
$853$	−49.1627	−1.68330	−0.841649	+	0.540024i	$0.818415\pi$
$854$	−16.1831	−0.553775
$855$	6.48892	0.221916
$856$	40.4714	1.38329
$857$	35.0541	1.19742	0.598712	−	0.800964i	$-0.295679\pi$
$857$	35.0541	1.19742	0.598712	+	0.800964i	$0.295679\pi$
$858$	−11.4042	−0.389334
$859$	−2.07065	−0.0706497	−0.0353248	−	0.999376i	$-0.511247\pi$
$859$	−2.07065	−0.0706497	−0.0353248	+	0.999376i	$0.511247\pi$
$860$	10.4443	0.356146
$861$	−0.985054	−0.0335705
$862$	−8.94049	−0.304514
$863$	−26.5111	−0.902447	−0.451224	−	0.892411i	$-0.649012\pi$
$863$	−26.5111	−0.902447	−0.451224	+	0.892411i	$0.649012\pi$
$864$	5.38832	0.183314
$865$	12.1379	0.412701
$866$	−18.9215	−0.642978
$867$	−1.00000	−0.0339618
$868$	−22.3732	−0.759396
$869$	−44.0348	−1.49378
$870$	−19.9210	−0.675384
$871$	−28.2824	−0.958314
$872$	−44.7692	−1.51608
$873$	−14.6948	−0.497343
$874$	−15.2483	−0.515781
$875$	−21.8993	−0.740333
$876$	5.49631	0.185703
$877$	24.5523	0.829073	0.414537	−	0.910033i	$-0.363944\pi$
$877$	24.5523	0.829073	0.414537	+	0.910033i	$0.363944\pi$
$878$	−15.6288	−0.527446
$879$	−5.82936	−0.196619
$880$	−3.73049	−0.125755
$881$	34.8034	1.17256	0.586279	−	0.810110i	$-0.300592\pi$
$881$	34.8034	1.17256	0.586279	+	0.810110i	$0.300592\pi$
$882$	3.34474	0.112623
$883$	32.9482	1.10879	0.554397	−	0.832252i	$-0.312949\pi$
$883$	32.9482	1.10879	0.554397	+	0.832252i	$0.312949\pi$
$884$	3.73556	0.125640
$885$	−21.9663	−0.738390
$886$	−36.0392	−1.21076
$887$	30.0297	1.00830	0.504150	−	0.863616i	$-0.331806\pi$
$887$	30.0297	1.00830	0.504150	+	0.863616i	$0.331806\pi$
$888$	9.89777	0.332148
$889$	−23.9474	−0.803169
$890$	−10.6770	−0.357893
$891$	3.66211	0.122685
$892$	−23.1580	−0.775388
$893$	26.8382	0.898106
$894$	−18.7560	−0.627294
$895$	28.2505	0.944311
$896$	9.49995	0.317371
$897$	17.2832	0.577069
$898$	10.1923	0.340120
$899$	−110.530	−3.68638
$900$	0.799655	0.0266552
$901$	8.35657	0.278398
$902$	−1.82439	−0.0607457
$903$	8.31379	0.276665
$904$	−18.9183	−0.629214
$905$	8.16753	0.271498
$906$	9.01846	0.299618
$907$	−43.1115	−1.43149	−0.715747	−	0.698360i	$-0.753914\pi$
$907$	−43.1115	−1.43149	−0.715747	+	0.698360i	$0.753914\pi$
$908$	8.76169	0.290767
$909$	18.4924	0.613355
$910$	11.9394	0.395788
$911$	−34.4480	−1.14131	−0.570657	−	0.821188i	$-0.693311\pi$
$911$	−34.4480	−1.14131	−0.570657	+	0.821188i	$0.693311\pi$
$912$	1.54151	0.0510444
$913$	55.1104	1.82389
$914$	1.98439	0.0656379
$915$	−19.3300	−0.639029
$916$	0.563093	0.0186051
$917$	15.8811	0.524440
$918$	0.936365	0.0309046
$919$	−29.7133	−0.980151	−0.490076	−	0.871680i	$-0.663031\pi$
$919$	−29.7133	−0.980151	−0.490076	+	0.871680i	$0.663031\pi$
$920$	31.4712	1.03757
$921$	1.54038	0.0507572
$922$	−20.6528	−0.680162
$923$	15.0045	0.493879
$924$	7.61576	0.250540
$925$	2.40950	0.0792239
$926$	0.852721	0.0280221
$927$	−18.3029	−0.601145
$928$	55.3590	1.81725
$929$	3.41545	0.112057	0.0560286	−	0.998429i	$-0.482156\pi$
$929$	3.41545	0.112057	0.0560286	+	0.998429i	$0.482156\pi$
$930$	20.8603	0.684037
$931$	−11.1933	−0.366846
$932$	−14.6556	−0.480061
$933$	26.5199	0.868224
$934$	30.1345	0.986031
$935$	7.58336	0.248002
$936$	−9.72608	−0.317907
$937$	13.1062	0.428162	0.214081	−	0.976816i	$-0.431324\pi$
$937$	13.1062	0.428162	0.214081	+	0.976816i	$0.431324\pi$
$938$	−14.7431	−0.481380
$939$	14.3573	0.468534
$940$	−19.9209	−0.649747
$941$	−5.54810	−0.180863	−0.0904315	−	0.995903i	$-0.528825\pi$
$941$	−5.54810	−0.180863	−0.0904315	+	0.995903i	$0.528825\pi$
$942$	−0.936365	−0.0305084
$943$	2.76488	0.0900370
$944$	−5.21832	−0.169842
$945$	−3.83397	−0.124719
$946$	15.3978	0.500624
$947$	−7.61818	−0.247558	−0.123779	−	0.992310i	$-0.539501\pi$
$947$	−7.61818	−0.247558	−0.123779	+	0.992310i	$0.539501\pi$
$948$	−13.5061	−0.438659
$949$	−16.2740	−0.528278
$950$	2.08893	0.0677738
$951$	23.5911	0.764993
$952$	5.41458	0.175488
$953$	−2.06863	−0.0670096	−0.0335048	−	0.999439i	$-0.510667\pi$
$953$	−2.06863	−0.0670096	−0.0335048	+	0.999439i	$0.510667\pi$
$954$	−7.82480	−0.253337
$955$	−4.21337	−0.136342
$956$	11.0123	0.356165
$957$	37.6240	1.21621
$958$	−28.5930	−0.923799
$959$	23.4911	0.758567
$960$	−12.4853	−0.402960
$961$	84.7419	2.73361
$962$	−10.5396	−0.339811
$963$	13.8389	0.445952
$964$	0.700893	0.0225743
$965$	20.9934	0.675803
$966$	9.00942	0.289873
$967$	0.299341	0.00962617	0.00481308	−	0.999988i	$-0.498468\pi$
$967$	0.299341	0.00962617	0.00481308	+	0.999988i	$0.498468\pi$
$968$	7.05096	0.226626
$969$	−3.13358	−0.100665
$970$	28.4931	0.914857
$971$	−28.5440	−0.916022	−0.458011	−	0.888947i	$-0.651438\pi$
$971$	−28.5440	−0.916022	−0.458011	+	0.888947i	$0.651438\pi$
$972$	1.12322	0.0360273
$973$	9.74622	0.312450
$974$	−15.5235	−0.497407
$975$	−2.36770	−0.0758272
$976$	−4.59203	−0.146987
$977$	−17.3349	−0.554593	−0.277296	−	0.960784i	$-0.589438\pi$
$977$	−17.3349	−0.554593	−0.277296	+	0.960784i	$0.589438\pi$
$978$	15.8078	0.505477
$979$	20.1652	0.644484
$980$	8.30833	0.265400
$981$	−15.3085	−0.488761
$982$	−16.9402	−0.540583
$983$	−11.4650	−0.365677	−0.182839	−	0.983143i	$-0.558529\pi$
$983$	−11.4650	−0.365677	−0.182839	+	0.983143i	$0.558529\pi$
$984$	−1.55593	−0.0496013
$985$	−53.1562	−1.69370
$986$	9.62010	0.306366
$987$	−15.8573	−0.504743
$988$	11.7057	0.372407
$989$	−23.3354	−0.742024
$990$	−7.10079	−0.225678
$991$	42.9192	1.36337	0.681687	−	0.731644i	$-0.261247\pi$
$991$	42.9192	1.36337	0.681687	+	0.731644i	$0.261247\pi$
$992$	−57.9694	−1.84053
$993$	−19.5793	−0.621330
$994$	7.82157	0.248085
$995$	42.9996	1.36318
$996$	16.9032	0.535597
$997$	−47.3475	−1.49951	−0.749755	−	0.661716i	$-0.769829\pi$
$997$	−47.3475	−1.49951	−0.749755	+	0.661716i	$0.769829\pi$
$998$	17.6075	0.557355
$999$	3.38446	0.107080

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.j.1.22	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.j.1.22	✓	64	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-0.936365 q^{2} -1.00000 q^{3} -1.12322 q^{4} +2.07077 q^{5} +0.936365 q^{6} +1.85147 q^{7} +2.92447 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.936365 q^{2} -1.00000 q^{3} -1.12322 q^{4} +2.07077 q^{5} +0.936365 q^{6} +1.85147 q^{7} +2.92447 q^{8} +1.00000 q^{9} -1.93899 q^{10} +3.66211 q^{11} +1.12322 q^{12} -3.32575 q^{13} -1.73365 q^{14} -2.07077 q^{15} -0.491931 q^{16} +1.00000 q^{17} -0.936365 q^{18} +3.13358 q^{19} -2.32593 q^{20} -1.85147 q^{21} -3.42907 q^{22} +5.19678 q^{23} -2.92447 q^{24} -0.711930 q^{25} +3.11412 q^{26} -1.00000 q^{27} -2.07961 q^{28} -10.2739 q^{29} +1.93899 q^{30} +10.7583 q^{31} -5.38832 q^{32} -3.66211 q^{33} -0.936365 q^{34} +3.83397 q^{35} -1.12322 q^{36} -3.38446 q^{37} -2.93418 q^{38} +3.32575 q^{39} +6.05590 q^{40} +0.532038 q^{41} +1.73365 q^{42} -4.49036 q^{43} -4.11336 q^{44} +2.07077 q^{45} -4.86608 q^{46} +8.56469 q^{47} +0.491931 q^{48} -3.57205 q^{49} +0.666626 q^{50} -1.00000 q^{51} +3.73556 q^{52} +8.35657 q^{53} +0.936365 q^{54} +7.58336 q^{55} +5.41458 q^{56} -3.13358 q^{57} +9.62010 q^{58} +10.6078 q^{59} +2.32593 q^{60} +9.33469 q^{61} -10.0737 q^{62} +1.85147 q^{63} +6.02930 q^{64} -6.88685 q^{65} +3.42907 q^{66} +8.50407 q^{67} -1.12322 q^{68} -5.19678 q^{69} -3.58999 q^{70} -4.51161 q^{71} +2.92447 q^{72} +4.89334 q^{73} +3.16909 q^{74} +0.711930 q^{75} -3.51971 q^{76} +6.78029 q^{77} -3.11412 q^{78} -12.0245 q^{79} -1.01867 q^{80} +1.00000 q^{81} -0.498182 q^{82} +15.0488 q^{83} +2.07961 q^{84} +2.07077 q^{85} +4.20462 q^{86} +10.2739 q^{87} +10.7097 q^{88} +5.50646 q^{89} -1.93899 q^{90} -6.15754 q^{91} -5.83714 q^{92} -10.7583 q^{93} -8.01967 q^{94} +6.48892 q^{95} +5.38832 q^{96} -14.6948 q^{97} +3.34474 q^{98} +3.66211 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9}+O(q^{10}) \) 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9	\( 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9} + 12 q^{10} - 7 q^{11} - 77 q^{12} + 24 q^{13} - 14 q^{14} + 3 q^{15} + 103 q^{16} + 64 q^{17} + 5 q^{18} + 26 q^{19} - 24 q^{20} - 5 q^{21} + 25 q^{22} + 20 q^{23} - 18 q^{24} + 141 q^{25} + 9 q^{26} - 64 q^{27} + 14 q^{28} + 5 q^{29} - 12 q^{30} + 11 q^{31} + 31 q^{32} + 7 q^{33} + 5 q^{34} - 3 q^{35} + 77 q^{36} + 50 q^{37} + 8 q^{38} - 24 q^{39} + 28 q^{40} - 9 q^{41} + 14 q^{42} + 59 q^{43} - 6 q^{44} - 3 q^{45} + 11 q^{47} - 103 q^{48} + 163 q^{49} + 20 q^{50} - 64 q^{51} + 65 q^{52} + 39 q^{53} - 5 q^{54} + 35 q^{55} - 34 q^{56} - 26 q^{57} - 27 q^{58} - 65 q^{59} + 24 q^{60} + 15 q^{61} + 18 q^{62} + 5 q^{63} + 152 q^{64} + 49 q^{65} - 25 q^{66} + 56 q^{67} + 77 q^{68} - 20 q^{69} + 28 q^{70} - 18 q^{71} + 18 q^{72} + 37 q^{73} - 76 q^{74} - 141 q^{75} + 30 q^{76} + 80 q^{77} - 9 q^{78} + 20 q^{79} - 144 q^{80} + 64 q^{81} + 27 q^{82} + 3 q^{83} - 14 q^{84} - 3 q^{85} + 12 q^{86} - 5 q^{87} + 108 q^{88} + 42 q^{89} + 12 q^{90} + 25 q^{91} + 18 q^{92} - 11 q^{93} + 60 q^{94} + 42 q^{95} - 31 q^{96} + 72 q^{97} + 18 q^{98} - 7 q^{99}+O(q^{100}) \) 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9 + 12 * q^10 - 7 * q^11 - 77 * q^12 + 24 * q^13 - 14 * q^14 + 3 * q^15 + 103 * q^16 + 64 * q^17 + 5 * q^18 + 26 * q^19 - 24 * q^20 - 5 * q^21 + 25 * q^22 + 20 * q^23 - 18 * q^24 + 141 * q^25 + 9 * q^26 - 64 * q^27 + 14 * q^28 + 5 * q^29 - 12 * q^30 + 11 * q^31 + 31 * q^32 + 7 * q^33 + 5 * q^34 - 3 * q^35 + 77 * q^36 + 50 * q^37 + 8 * q^38 - 24 * q^39 + 28 * q^40 - 9 * q^41 + 14 * q^42 + 59 * q^43 - 6 * q^44 - 3 * q^45 + 11 * q^47 - 103 * q^48 + 163 * q^49 + 20 * q^50 - 64 * q^51 + 65 * q^52 + 39 * q^53 - 5 * q^54 + 35 * q^55 - 34 * q^56 - 26 * q^57 - 27 * q^58 - 65 * q^59 + 24 * q^60 + 15 * q^61 + 18 * q^62 + 5 * q^63 + 152 * q^64 + 49 * q^65 - 25 * q^66 + 56 * q^67 + 77 * q^68 - 20 * q^69 + 28 * q^70 - 18 * q^71 + 18 * q^72 + 37 * q^73 - 76 * q^74 - 141 * q^75 + 30 * q^76 + 80 * q^77 - 9 * q^78 + 20 * q^79 - 144 * q^80 + 64 * q^81 + 27 * q^82 + 3 * q^83 - 14 * q^84 - 3 * q^85 + 12 * q^86 - 5 * q^87 + 108 * q^88 + 42 * q^89 + 12 * q^90 + 25 * q^91 + 18 * q^92 - 11 * q^93 + 60 * q^94 + 42 * q^95 - 31 * q^96 + 72 * q^97 + 18 * q^98 - 7 * q^99

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