LMFDB - Embedded newform 8002.2.a.g.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8002,2,Mod(1,8002)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8002, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8002.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8002 = 2 \cdot 4001 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8002.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:	$63.8962916974$
Analytic rank:	$0$
Dimension:	$95$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	8002.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.66813 q^{3} +1.00000 q^{4} +2.32067 q^{5} -2.66813 q^{6} -4.26871 q^{7} +1.00000 q^{8} +4.11889 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.66813 q^{3} +1.00000 q^{4} +2.32067 q^{5} -2.66813 q^{6} -4.26871 q^{7} +1.00000 q^{8} +4.11889 q^{9} +2.32067 q^{10} -4.23356 q^{11} -2.66813 q^{12} -3.78776 q^{13} -4.26871 q^{14} -6.19183 q^{15} +1.00000 q^{16} -1.70928 q^{17} +4.11889 q^{18} -7.24866 q^{19} +2.32067 q^{20} +11.3894 q^{21} -4.23356 q^{22} -8.51781 q^{23} -2.66813 q^{24} +0.385493 q^{25} -3.78776 q^{26} -2.98535 q^{27} -4.26871 q^{28} +3.81988 q^{29} -6.19183 q^{30} -3.73365 q^{31} +1.00000 q^{32} +11.2957 q^{33} -1.70928 q^{34} -9.90624 q^{35} +4.11889 q^{36} -4.14485 q^{37} -7.24866 q^{38} +10.1062 q^{39} +2.32067 q^{40} -0.257938 q^{41} +11.3894 q^{42} -6.76383 q^{43} -4.23356 q^{44} +9.55858 q^{45} -8.51781 q^{46} +9.25392 q^{47} -2.66813 q^{48} +11.2218 q^{49} +0.385493 q^{50} +4.56058 q^{51} -3.78776 q^{52} +2.17450 q^{53} -2.98535 q^{54} -9.82467 q^{55} -4.26871 q^{56} +19.3403 q^{57} +3.81988 q^{58} -0.323192 q^{59} -6.19183 q^{60} -4.27538 q^{61} -3.73365 q^{62} -17.5823 q^{63} +1.00000 q^{64} -8.79013 q^{65} +11.2957 q^{66} +16.0833 q^{67} -1.70928 q^{68} +22.7266 q^{69} -9.90624 q^{70} -12.0703 q^{71} +4.11889 q^{72} -2.30411 q^{73} -4.14485 q^{74} -1.02854 q^{75} -7.24866 q^{76} +18.0718 q^{77} +10.1062 q^{78} +14.8037 q^{79} +2.32067 q^{80} -4.39140 q^{81} -0.257938 q^{82} +8.40005 q^{83} +11.3894 q^{84} -3.96667 q^{85} -6.76383 q^{86} -10.1919 q^{87} -4.23356 q^{88} +8.03637 q^{89} +9.55858 q^{90} +16.1688 q^{91} -8.51781 q^{92} +9.96184 q^{93} +9.25392 q^{94} -16.8217 q^{95} -2.66813 q^{96} +4.54719 q^{97} +11.2218 q^{98} -17.4376 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 95 q + 95 q^{2} + 24 q^{3} + 95 q^{4} + 36 q^{5} + 24 q^{6} + 21 q^{7} + 95 q^{8} + 121 q^{9}+O(q^{10}) $ 95 * q + 95 * q^2 + 24 * q^3 + 95 * q^4 + 36 * q^5 + 24 * q^6 + 21 * q^7 + 95 * q^8 + 121 * q^9	\( 95 q + 95 q^{2} + 24 q^{3} + 95 q^{4} + 36 q^{5} + 24 q^{6} + 21 q^{7} + 95 q^{8} + 121 q^{9} + 36 q^{10} + 40 q^{11} + 24 q^{12} + 52 q^{13} + 21 q^{14} + 15 q^{15} + 95 q^{16} + 84 q^{17} + 121 q^{18} + 37 q^{19} + 36 q^{20} + 36 q^{21} + 40 q^{22} + 37 q^{23} + 24 q^{24} + 133 q^{25} + 52 q^{26} + 93 q^{27} + 21 q^{28} + 66 q^{29} + 15 q^{30} + 10 q^{31} + 95 q^{32} + 63 q^{33} + 84 q^{34} + 55 q^{35} + 121 q^{36} + 49 q^{37} + 37 q^{38} + 14 q^{39} + 36 q^{40} + 98 q^{41} + 36 q^{42} + 37 q^{43} + 40 q^{44} + 97 q^{45} + 37 q^{46} + 91 q^{47} + 24 q^{48} + 170 q^{49} + 133 q^{50} + 22 q^{51} + 52 q^{52} + 70 q^{53} + 93 q^{54} - q^{55} + 21 q^{56} + 50 q^{57} + 66 q^{58} + 72 q^{59} + 15 q^{60} + 97 q^{61} + 10 q^{62} + 75 q^{63} + 95 q^{64} + 75 q^{65} + 63 q^{66} + 39 q^{67} + 84 q^{68} + 65 q^{69} + 55 q^{70} + 28 q^{71} + 121 q^{72} + 117 q^{73} + 49 q^{74} + 62 q^{75} + 37 q^{76} + 92 q^{77} + 14 q^{78} + q^{79} + 36 q^{80} + 155 q^{81} + 98 q^{82} + 117 q^{83} + 36 q^{84} + 81 q^{85} + 37 q^{86} + 46 q^{87} + 40 q^{88} + 90 q^{89} + 97 q^{90} + 65 q^{91} + 37 q^{92} + 36 q^{93} + 91 q^{94} + 38 q^{95} + 24 q^{96} + 111 q^{97} + 170 q^{98} + 97 q^{99}+O(q^{100}) \) 95 * q + 95 * q^2 + 24 * q^3 + 95 * q^4 + 36 * q^5 + 24 * q^6 + 21 * q^7 + 95 * q^8 + 121 * q^9 + 36 * q^10 + 40 * q^11 + 24 * q^12 + 52 * q^13 + 21 * q^14 + 15 * q^15 + 95 * q^16 + 84 * q^17 + 121 * q^18 + 37 * q^19 + 36 * q^20 + 36 * q^21 + 40 * q^22 + 37 * q^23 + 24 * q^24 + 133 * q^25 + 52 * q^26 + 93 * q^27 + 21 * q^28 + 66 * q^29 + 15 * q^30 + 10 * q^31 + 95 * q^32 + 63 * q^33 + 84 * q^34 + 55 * q^35 + 121 * q^36 + 49 * q^37 + 37 * q^38 + 14 * q^39 + 36 * q^40 + 98 * q^41 + 36 * q^42 + 37 * q^43 + 40 * q^44 + 97 * q^45 + 37 * q^46 + 91 * q^47 + 24 * q^48 + 170 * q^49 + 133 * q^50 + 22 * q^51 + 52 * q^52 + 70 * q^53 + 93 * q^54 - q^55 + 21 * q^56 + 50 * q^57 + 66 * q^58 + 72 * q^59 + 15 * q^60 + 97 * q^61 + 10 * q^62 + 75 * q^63 + 95 * q^64 + 75 * q^65 + 63 * q^66 + 39 * q^67 + 84 * q^68 + 65 * q^69 + 55 * q^70 + 28 * q^71 + 121 * q^72 + 117 * q^73 + 49 * q^74 + 62 * q^75 + 37 * q^76 + 92 * q^77 + 14 * q^78 + q^79 + 36 * q^80 + 155 * q^81 + 98 * q^82 + 117 * q^83 + 36 * q^84 + 81 * q^85 + 37 * q^86 + 46 * q^87 + 40 * q^88 + 90 * q^89 + 97 * q^90 + 65 * q^91 + 37 * q^92 + 36 * q^93 + 91 * q^94 + 38 * q^95 + 24 * q^96 + 111 * q^97 + 170 * q^98 + 97 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−2.66813	−1.54044	−0.770221	−	0.637777i	$-0.779854\pi$
$3$	−2.66813	−1.54044	−0.770221	+	0.637777i	$0.779854\pi$
$4$	1.00000	0.500000
$5$	2.32067	1.03783	0.518917	−	0.854825i	$-0.326335\pi$
$5$	2.32067	1.03783	0.518917	+	0.854825i	$0.326335\pi$
$6$	−2.66813	−1.08926
$7$	−4.26871	−1.61342	−0.806709	−	0.590948i	$-0.798754\pi$
$7$	−4.26871	−1.61342	−0.806709	+	0.590948i	$0.798754\pi$
$8$	1.00000	0.353553
$9$	4.11889	1.37296
$10$	2.32067	0.733859
$11$	−4.23356	−1.27647	−0.638233	−	0.769844i	$-0.720334\pi$
$11$	−4.23356	−1.27647	−0.638233	+	0.769844i	$0.720334\pi$
$12$	−2.66813	−0.770221
$13$	−3.78776	−1.05054	−0.525268	−	0.850937i	$-0.676035\pi$
$13$	−3.78776	−1.05054	−0.525268	+	0.850937i	$0.676035\pi$
$14$	−4.26871	−1.14086
$15$	−6.19183	−1.59872
$16$	1.00000	0.250000
$17$	−1.70928	−0.414561	−0.207281	−	0.978282i	$-0.566461\pi$
$17$	−1.70928	−0.414561	−0.207281	+	0.978282i	$0.566461\pi$
$18$	4.11889	0.970832
$19$	−7.24866	−1.66296	−0.831478	−	0.555558i	$-0.812505\pi$
$19$	−7.24866	−1.66296	−0.831478	+	0.555558i	$0.812505\pi$
$20$	2.32067	0.518917
$21$	11.3894	2.48538
$22$	−4.23356	−0.902597
$23$	−8.51781	−1.77609	−0.888043	−	0.459761i	$-0.847935\pi$
$23$	−8.51781	−1.77609	−0.888043	+	0.459761i	$0.847935\pi$
$24$	−2.66813	−0.544629
$25$	0.385493	0.0770985
$26$	−3.78776	−0.742841
$27$	−2.98535	−0.574531
$28$	−4.26871	−0.806709
$29$	3.81988	0.709335	0.354667	−	0.934993i	$-0.384594\pi$
$29$	3.81988	0.709335	0.354667	+	0.934993i	$0.384594\pi$
$30$	−6.19183	−1.13047
$31$	−3.73365	−0.670583	−0.335292	−	0.942114i	$-0.608835\pi$
$31$	−3.73365	−0.670583	−0.335292	+	0.942114i	$0.608835\pi$
$32$	1.00000	0.176777
$33$	11.2957	1.96632
$34$	−1.70928	−0.293139
$35$	−9.90624	−1.67446
$36$	4.11889	0.686482
$37$	−4.14485	−0.681409	−0.340704	−	0.940171i	$-0.610666\pi$
$37$	−4.14485	−0.681409	−0.340704	+	0.940171i	$0.610666\pi$
$38$	−7.24866	−1.17589
$39$	10.1062	1.61829
$40$	2.32067	0.366930
$41$	−0.257938	−0.0402832	−0.0201416	−	0.999797i	$-0.506412\pi$
$41$	−0.257938	−0.0402832	−0.0201416	+	0.999797i	$0.506412\pi$
$42$	11.3894	1.75743
$43$	−6.76383	−1.03147	−0.515737	−	0.856747i	$-0.672482\pi$
$43$	−6.76383	−1.03147	−0.515737	+	0.856747i	$0.672482\pi$
$44$	−4.23356	−0.638233
$45$	9.55858	1.42491
$46$	−8.51781	−1.25588
$47$	9.25392	1.34982	0.674911	−	0.737899i	$-0.264182\pi$
$47$	9.25392	1.34982	0.674911	+	0.737899i	$0.264182\pi$
$48$	−2.66813	−0.385111
$49$	11.2218	1.60312
$50$	0.385493	0.0545169
$51$	4.56058	0.638608
$52$	−3.78776	−0.525268
$53$	2.17450	0.298691	0.149346	−	0.988785i	$-0.452283\pi$
$53$	2.17450	0.298691	0.149346	+	0.988785i	$0.452283\pi$
$54$	−2.98535	−0.406254
$55$	−9.82467	−1.32476
$56$	−4.26871	−0.570430
$57$	19.3403	2.56169
$58$	3.81988	0.501575
$59$	−0.323192	−0.0420760	−0.0210380	−	0.999779i	$-0.506697\pi$
$59$	−0.323192	−0.0420760	−0.0210380	+	0.999779i	$0.506697\pi$
$60$	−6.19183	−0.799362
$61$	−4.27538	−0.547406	−0.273703	−	0.961814i	$-0.588249\pi$
$61$	−4.27538	−0.547406	−0.273703	+	0.961814i	$0.588249\pi$
$62$	−3.73365	−0.474174
$63$	−17.5823	−2.21517
$64$	1.00000	0.125000
$65$	−8.79013	−1.09028
$66$	11.2957	1.39040
$67$	16.0833	1.96489	0.982445	−	0.186553i	$-0.0597316\pi$
$67$	16.0833	1.96489	0.982445	+	0.186553i	$0.0597316\pi$
$68$	−1.70928	−0.207281
$69$	22.7266	2.73596
$70$	−9.90624	−1.18402
$71$	−12.0703	−1.43248	−0.716242	−	0.697852i	$-0.754139\pi$
$71$	−12.0703	−1.43248	−0.716242	+	0.697852i	$0.754139\pi$
$72$	4.11889	0.485416
$73$	−2.30411	−0.269675	−0.134838	−	0.990868i	$-0.543051\pi$
$73$	−2.30411	−0.269675	−0.134838	+	0.990868i	$0.543051\pi$
$74$	−4.14485	−0.481829
$75$	−1.02854	−0.118766
$76$	−7.24866	−0.831478
$77$	18.0718	2.05947
$78$	10.1062	1.14430
$79$	14.8037	1.66555	0.832774	−	0.553614i	$-0.186752\pi$
$79$	14.8037	1.66555	0.832774	+	0.553614i	$0.186752\pi$
$80$	2.32067	0.259458
$81$	−4.39140	−0.487933
$82$	−0.257938	−0.0284845
$83$	8.40005	0.922026	0.461013	−	0.887393i	$-0.347486\pi$
$83$	8.40005	0.922026	0.461013	+	0.887393i	$0.347486\pi$
$84$	11.3894	1.24269
$85$	−3.96667	−0.430246
$86$	−6.76383	−0.729362
$87$	−10.1919	−1.09269
$88$	−4.23356	−0.451299
$89$	8.03637	0.851853	0.425927	−	0.904758i	$-0.359948\pi$
$89$	8.03637	0.851853	0.425927	+	0.904758i	$0.359948\pi$
$90$	9.55858	1.00756
$91$	16.1688	1.69495
$92$	−8.51781	−0.888043
$93$	9.96184	1.03300
$94$	9.25392	0.954469
$95$	−16.8217	−1.72587
$96$	−2.66813	−0.272314
$97$	4.54719	0.461697	0.230849	−	0.972990i	$-0.425850\pi$
$97$	4.54719	0.461697	0.230849	+	0.972990i	$0.425850\pi$
$98$	11.2218	1.13358
$99$	−17.4376	−1.75254
$100$	0.385493	0.0385493
$101$	−11.7873	−1.17288	−0.586442	−	0.809991i	$-0.699472\pi$
$101$	−11.7873	−1.17288	−0.586442	+	0.809991i	$0.699472\pi$
$102$	4.56058	0.451564
$103$	−10.7863	−1.06280	−0.531401	−	0.847121i	$-0.678334\pi$
$103$	−10.7863	−1.06280	−0.531401	+	0.847121i	$0.678334\pi$
$104$	−3.78776	−0.371420
$105$	26.4311	2.57941
$106$	2.17450	0.211207
$107$	12.3014	1.18922	0.594609	−	0.804015i	$-0.297307\pi$
$107$	12.3014	1.18922	0.594609	+	0.804015i	$0.297307\pi$
$108$	−2.98535	−0.287265
$109$	−2.97436	−0.284892	−0.142446	−	0.989803i	$-0.545497\pi$
$109$	−2.97436	−0.284892	−0.142446	+	0.989803i	$0.545497\pi$
$110$	−9.82467	−0.936746
$111$	11.0590	1.04967
$112$	−4.26871	−0.403355
$113$	7.61571	0.716425	0.358213	−	0.933640i	$-0.383386\pi$
$113$	7.61571	0.716425	0.358213	+	0.933640i	$0.383386\pi$
$114$	19.3403	1.81139
$115$	−19.7670	−1.84328
$116$	3.81988	0.354667
$117$	−15.6014	−1.44235
$118$	−0.323192	−0.0297522
$119$	7.29642	0.668861
$120$	−6.19183	−0.565234
$121$	6.92299	0.629363
$122$	−4.27538	−0.387075
$123$	0.688211	0.0620539
$124$	−3.73365	−0.335292
$125$	−10.7087	−0.957818
$126$	−17.5823	−1.56636
$127$	13.9927	1.24165	0.620825	−	0.783949i	$-0.286798\pi$
$127$	13.9927	1.24165	0.620825	+	0.783949i	$0.286798\pi$
$128$	1.00000	0.0883883
$129$	18.0467	1.58893
$130$	−8.79013	−0.770945
$131$	0.321253	0.0280680	0.0140340	−	0.999902i	$-0.495533\pi$
$131$	0.321253	0.0280680	0.0140340	+	0.999902i	$0.495533\pi$
$132$	11.2957	0.983161
$133$	30.9424	2.68304
$134$	16.0833	1.38939
$135$	−6.92800	−0.596267
$136$	−1.70928	−0.146570
$137$	5.62000	0.480149	0.240074	−	0.970755i	$-0.422828\pi$
$137$	5.62000	0.480149	0.240074	+	0.970755i	$0.422828\pi$
$138$	22.7266	1.93461
$139$	10.9956	0.932638	0.466319	−	0.884617i	$-0.345580\pi$
$139$	10.9956	0.932638	0.466319	+	0.884617i	$0.345580\pi$
$140$	−9.90624	−0.837230
$141$	−24.6906	−2.07933
$142$	−12.0703	−1.01292
$143$	16.0357	1.34097
$144$	4.11889	0.343241
$145$	8.86468	0.736171
$146$	−2.30411	−0.190689
$147$	−29.9413	−2.46952
$148$	−4.14485	−0.340704
$149$	−11.2735	−0.923559	−0.461780	−	0.886995i	$-0.652789\pi$
$149$	−11.2735	−0.923559	−0.461780	+	0.886995i	$0.652789\pi$
$150$	−1.02854	−0.0839802
$151$	−23.5178	−1.91385	−0.956925	−	0.290336i	$-0.906233\pi$
$151$	−23.5178	−1.91385	−0.956925	+	0.290336i	$0.906233\pi$
$152$	−7.24866	−0.587944
$153$	−7.04034	−0.569178
$154$	18.0718	1.45627
$155$	−8.66455	−0.695954
$156$	10.1062	0.809145
$157$	17.9976	1.43636	0.718180	−	0.695857i	$-0.244975\pi$
$157$	17.9976	1.43636	0.718180	+	0.695857i	$0.244975\pi$
$158$	14.8037	1.17772
$159$	−5.80185	−0.460117
$160$	2.32067	0.183465
$161$	36.3600	2.86557
$162$	−4.39140	−0.345021
$163$	−20.1149	−1.57552	−0.787760	−	0.615982i	$-0.788759\pi$
$163$	−20.1149	−1.57552	−0.787760	+	0.615982i	$0.788759\pi$
$164$	−0.257938	−0.0201416
$165$	26.2135	2.04071
$166$	8.40005	0.651971
$167$	10.8656	0.840807	0.420403	−	0.907337i	$-0.361889\pi$
$167$	10.8656	0.840807	0.420403	+	0.907337i	$0.361889\pi$
$168$	11.3894	0.878714
$169$	1.34712	0.103625
$170$	−3.96667	−0.304230
$171$	−29.8564	−2.28318
$172$	−6.76383	−0.515737
$173$	−20.0569	−1.52490	−0.762448	−	0.647049i	$-0.776003\pi$
$173$	−20.0569	−1.52490	−0.762448	+	0.647049i	$0.776003\pi$
$174$	−10.1919	−0.772648
$175$	−1.64555	−0.124392
$176$	−4.23356	−0.319116
$177$	0.862316	0.0648157
$178$	8.03637	0.602351
$179$	−14.5750	−1.08939	−0.544693	−	0.838635i	$-0.683354\pi$
$179$	−14.5750	−1.08939	−0.544693	+	0.838635i	$0.683354\pi$
$180$	9.55858	0.712454
$181$	11.9697	0.889700	0.444850	−	0.895605i	$-0.353257\pi$
$181$	11.9697	0.889700	0.444850	+	0.895605i	$0.353257\pi$
$182$	16.1688	1.19851
$183$	11.4073	0.843248
$184$	−8.51781	−0.627941
$185$	−9.61881	−0.707189
$186$	9.96184	0.730438
$187$	7.23633	0.529173
$188$	9.25392	0.674911
$189$	12.7436	0.926958
$190$	−16.8217	−1.22038
$191$	−21.2049	−1.53433	−0.767165	−	0.641449i	$-0.778333\pi$
$191$	−21.2049	−1.53433	−0.767165	+	0.641449i	$0.778333\pi$
$192$	−2.66813	−0.192555
$193$	−0.633796	−0.0456216	−0.0228108	−	0.999740i	$-0.507262\pi$
$193$	−0.633796	−0.0456216	−0.0228108	+	0.999740i	$0.507262\pi$
$194$	4.54719	0.326469
$195$	23.4532	1.67952
$196$	11.2218	0.801560
$197$	−0.596415	−0.0424928	−0.0212464	−	0.999774i	$-0.506763\pi$
$197$	−0.596415	−0.0424928	−0.0212464	+	0.999774i	$0.506763\pi$
$198$	−17.4376	−1.23923
$199$	−11.3984	−0.808014	−0.404007	−	0.914756i	$-0.632383\pi$
$199$	−11.3984	−0.808014	−0.404007	+	0.914756i	$0.632383\pi$
$200$	0.385493	0.0272585
$201$	−42.9123	−3.02680
$202$	−11.7873	−0.829354
$203$	−16.3060	−1.14445
$204$	4.56058	0.319304
$205$	−0.598588	−0.0418072
$206$	−10.7863	−0.751514
$207$	−35.0839	−2.43850
$208$	−3.78776	−0.262634
$209$	30.6876	2.12270
$210$	26.4311	1.82392
$211$	4.31203	0.296852	0.148426	−	0.988924i	$-0.452579\pi$
$211$	4.31203	0.296852	0.148426	+	0.988924i	$0.452579\pi$
$212$	2.17450	0.149346
$213$	32.2051	2.20666
$214$	12.3014	0.840904
$215$	−15.6966	−1.07050
$216$	−2.98535	−0.203127
$217$	15.9378	1.08193
$218$	−2.97436	−0.201449
$219$	6.14765	0.415420
$220$	−9.82467	−0.662379
$221$	6.47434	0.435511
$222$	11.0590	0.742230
$223$	−8.82879	−0.591220	−0.295610	−	0.955309i	$-0.595523\pi$
$223$	−8.82879	−0.591220	−0.295610	+	0.955309i	$0.595523\pi$
$224$	−4.26871	−0.285215
$225$	1.58780	0.105854
$226$	7.61571	0.506589
$227$	18.7481	1.24435	0.622177	−	0.782876i	$-0.286248\pi$
$227$	18.7481	1.24435	0.622177	+	0.782876i	$0.286248\pi$
$228$	19.3403	1.28084
$229$	−21.9064	−1.44762	−0.723809	−	0.690000i	$-0.757611\pi$
$229$	−21.9064	−1.44762	−0.723809	+	0.690000i	$0.757611\pi$
$230$	−19.7670	−1.30340
$231$	−48.2178	−3.17250
$232$	3.81988	0.250788
$233$	14.7410	0.965712	0.482856	−	0.875700i	$-0.339599\pi$
$233$	14.7410	0.965712	0.482856	+	0.875700i	$0.339599\pi$
$234$	−15.6014	−1.01989
$235$	21.4753	1.40089
$236$	−0.323192	−0.0210380
$237$	−39.4981	−2.56568
$238$	7.29642	0.472956
$239$	−17.1795	−1.11125	−0.555624	−	0.831434i	$-0.687521\pi$
$239$	−17.1795	−1.11125	−0.555624	+	0.831434i	$0.687521\pi$
$240$	−6.19183	−0.399681
$241$	26.9380	1.73523	0.867614	−	0.497238i	$-0.165653\pi$
$241$	26.9380	1.73523	0.867614	+	0.497238i	$0.165653\pi$
$242$	6.92299	0.445027
$243$	20.6728	1.32616
$244$	−4.27538	−0.273703
$245$	26.0422	1.66377
$246$	0.688211	0.0438787
$247$	27.4562	1.74699
$248$	−3.73365	−0.237087
$249$	−22.4124	−1.42033
$250$	−10.7087	−0.677280
$251$	4.23571	0.267356	0.133678	−	0.991025i	$-0.457321\pi$
$251$	4.23571	0.267356	0.133678	+	0.991025i	$0.457321\pi$
$252$	−17.5823	−1.10758
$253$	36.0606	2.26711
$254$	13.9927	0.877979
$255$	10.5836	0.662769
$256$	1.00000	0.0625000
$257$	−7.18865	−0.448416	−0.224208	−	0.974541i	$-0.571979\pi$
$257$	−7.18865	−0.448416	−0.224208	+	0.974541i	$0.571979\pi$
$258$	18.0467	1.12354
$259$	17.6931	1.09940
$260$	−8.79013	−0.545140
$261$	15.7337	0.973891
$262$	0.321253	0.0198471
$263$	4.05419	0.249992	0.124996	−	0.992157i	$-0.460108\pi$
$263$	4.05419	0.249992	0.124996	+	0.992157i	$0.460108\pi$
$264$	11.2957	0.695200
$265$	5.04630	0.309992
$266$	30.9424	1.89720
$267$	−21.4420	−1.31223
$268$	16.0833	0.982445
$269$	0.226251	0.0137948	0.00689738	−	0.999976i	$-0.497804\pi$
$269$	0.226251	0.0137948	0.00689738	+	0.999976i	$0.497804\pi$
$270$	−6.92800	−0.421624
$271$	−19.3851	−1.17756	−0.588781	−	0.808292i	$-0.700392\pi$
$271$	−19.3851	−1.17756	−0.588781	+	0.808292i	$0.700392\pi$
$272$	−1.70928	−0.103640
$273$	−43.1405	−2.61098
$274$	5.62000	0.339516
$275$	−1.63200	−0.0984136
$276$	22.7266	1.36798
$277$	−2.57006	−0.154420	−0.0772101	−	0.997015i	$-0.524601\pi$
$277$	−2.57006	−0.154420	−0.0772101	+	0.997015i	$0.524601\pi$
$278$	10.9956	0.659474
$279$	−15.3785	−0.920687
$280$	−9.90624	−0.592011
$281$	−23.9792	−1.43048	−0.715238	−	0.698881i	$-0.753682\pi$
$281$	−23.9792	−1.43048	−0.715238	+	0.698881i	$0.753682\pi$
$282$	−24.6906	−1.47030
$283$	16.7112	0.993380	0.496690	−	0.867928i	$-0.334549\pi$
$283$	16.7112	0.993380	0.496690	+	0.867928i	$0.334549\pi$
$284$	−12.0703	−0.716242
$285$	44.8824	2.65861
$286$	16.0357	0.948210
$287$	1.10106	0.0649936
$288$	4.11889	0.242708
$289$	−14.0784	−0.828139
$290$	8.86468	0.520552
$291$	−12.1325	−0.711218
$292$	−2.30411	−0.134838
$293$	3.54579	0.207147	0.103574	−	0.994622i	$-0.466972\pi$
$293$	3.54579	0.207147	0.103574	+	0.994622i	$0.466972\pi$
$294$	−29.9413	−1.74621
$295$	−0.750020	−0.0436679
$296$	−4.14485	−0.240914
$297$	12.6386	0.733368
$298$	−11.2735	−0.653055
$299$	32.2634	1.86584
$300$	−1.02854	−0.0593830
$301$	28.8728	1.66420
$302$	−23.5178	−1.35330
$303$	31.4501	1.80676
$304$	−7.24866	−0.415739
$305$	−9.92173	−0.568117
$306$	−7.04034	−0.402470
$307$	−10.9244	−0.623486	−0.311743	−	0.950166i	$-0.600913\pi$
$307$	−10.9244	−0.623486	−0.311743	+	0.950166i	$0.600913\pi$
$308$	18.0718	1.02974
$309$	28.7791	1.63719
$310$	−8.66455	−0.492114
$311$	7.38088	0.418531	0.209266	−	0.977859i	$-0.432893\pi$
$311$	7.38088	0.418531	0.209266	+	0.977859i	$0.432893\pi$
$312$	10.1062	0.572152
$313$	−1.94665	−0.110031	−0.0550157	−	0.998485i	$-0.517521\pi$
$313$	−1.94665	−0.110031	−0.0550157	+	0.998485i	$0.517521\pi$
$314$	17.9976	1.01566
$315$	−40.8028	−2.29897
$316$	14.8037	0.832774
$317$	19.9170	1.11865	0.559325	−	0.828948i	$-0.311060\pi$
$317$	19.9170	1.11865	0.559325	+	0.828948i	$0.311060\pi$
$318$	−5.80185	−0.325352
$319$	−16.1717	−0.905441
$320$	2.32067	0.129729
$321$	−32.8216	−1.83192
$322$	36.3600	2.02626
$323$	12.3900	0.689397
$324$	−4.39140	−0.243967
$325$	−1.46015	−0.0809947
$326$	−20.1149	−1.11406
$327$	7.93598	0.438861
$328$	−0.257938	−0.0142422
$329$	−39.5023	−2.17783
$330$	26.2135	1.44300
$331$	24.8770	1.36736	0.683681	−	0.729781i	$-0.260378\pi$
$331$	24.8770	1.36736	0.683681	+	0.729781i	$0.260378\pi$
$332$	8.40005	0.461013
$333$	−17.0722	−0.935550
$334$	10.8656	0.594540
$335$	37.3240	2.03923
$336$	11.3894	0.621345
$337$	22.7276	1.23805	0.619025	−	0.785371i	$-0.287528\pi$
$337$	22.7276	1.23805	0.619025	+	0.785371i	$0.287528\pi$
$338$	1.34712	0.0732736
$339$	−20.3197	−1.10361
$340$	−3.96667	−0.215123
$341$	15.8066	0.855976
$342$	−29.8564	−1.61445
$343$	−18.0218	−0.973087
$344$	−6.76383	−0.364681
$345$	52.7408	2.83947
$346$	−20.0569	−1.07826
$347$	−3.27914	−0.176033	−0.0880167	−	0.996119i	$-0.528053\pi$
$347$	−3.27914	−0.176033	−0.0880167	+	0.996119i	$0.528053\pi$
$348$	−10.1919	−0.546345
$349$	−32.4242	−1.73563	−0.867814	−	0.496888i	$-0.834476\pi$
$349$	−32.4242	−1.73563	−0.867814	+	0.496888i	$0.834476\pi$
$350$	−1.64555	−0.0879586
$351$	11.3078	0.603565
$352$	−4.23356	−0.225649
$353$	−27.5233	−1.46492	−0.732459	−	0.680812i	$-0.761627\pi$
$353$	−27.5233	−1.46492	−0.732459	+	0.680812i	$0.761627\pi$
$354$	0.862316	0.0458316
$355$	−28.0112	−1.48668
$356$	8.03637	0.425927
$357$	−19.4678	−1.03034
$358$	−14.5750	−0.770313
$359$	0.586624	0.0309609	0.0154804	−	0.999880i	$-0.495072\pi$
$359$	0.586624	0.0309609	0.0154804	+	0.999880i	$0.495072\pi$
$360$	9.55858	0.503781
$361$	33.5430	1.76542
$362$	11.9697	0.629113
$363$	−18.4714	−0.969498
$364$	16.1688	0.847477
$365$	−5.34707	−0.279878
$366$	11.4073	0.596267
$367$	−16.4693	−0.859689	−0.429844	−	0.902903i	$-0.641432\pi$
$367$	−16.4693	−0.859689	−0.429844	+	0.902903i	$0.641432\pi$
$368$	−8.51781	−0.444021
$369$	−1.06242	−0.0553073
$370$	−9.61881	−0.500058
$371$	−9.28232	−0.481914
$372$	9.96184	0.516498
$373$	−21.6184	−1.11936	−0.559679	−	0.828709i	$-0.689076\pi$
$373$	−21.6184	−1.11936	−0.559679	+	0.828709i	$0.689076\pi$
$374$	7.23633	0.374182
$375$	28.5722	1.47546
$376$	9.25392	0.477234
$377$	−14.4688	−0.745181
$378$	12.7436	0.655459
$379$	−0.261596	−0.0134373	−0.00671863	−	0.999977i	$-0.502139\pi$
$379$	−0.261596	−0.0134373	−0.00671863	+	0.999977i	$0.502139\pi$
$380$	−16.8217	−0.862936
$381$	−37.3342	−1.91269
$382$	−21.2049	−1.08494
$383$	4.00618	0.204706	0.102353	−	0.994748i	$-0.467363\pi$
$383$	4.00618	0.204706	0.102353	+	0.994748i	$0.467363\pi$
$384$	−2.66813	−0.136157
$385$	41.9386	2.13739
$386$	−0.633796	−0.0322594
$387$	−27.8595	−1.41618
$388$	4.54719	0.230849
$389$	17.2120	0.872685	0.436342	−	0.899781i	$-0.356274\pi$
$389$	17.2120	0.872685	0.436342	+	0.899781i	$0.356274\pi$
$390$	23.4532	1.18760
$391$	14.5593	0.736296
$392$	11.2218	0.566789
$393$	−0.857143	−0.0432372
$394$	−0.596415	−0.0300469
$395$	34.3545	1.72856
$396$	−17.4376	−0.876271
$397$	21.9820	1.10325	0.551623	−	0.834094i	$-0.314009\pi$
$397$	21.9820	1.10325	0.551623	+	0.834094i	$0.314009\pi$
$398$	−11.3984	−0.571352
$399$	−82.5581	−4.13308
$400$	0.385493	0.0192746
$401$	1.61413	0.0806057	0.0403028	−	0.999188i	$-0.487168\pi$
$401$	1.61413	0.0806057	0.0403028	+	0.999188i	$0.487168\pi$
$402$	−42.9123	−2.14027
$403$	14.1422	0.704471
$404$	−11.7873	−0.586442
$405$	−10.1910	−0.506393
$406$	−16.3060	−0.809251
$407$	17.5474	0.869794
$408$	4.56058	0.225782
$409$	−10.9940	−0.543618	−0.271809	−	0.962351i	$-0.587622\pi$
$409$	−10.9940	−0.543618	−0.271809	+	0.962351i	$0.587622\pi$
$410$	−0.598588	−0.0295622
$411$	−14.9949	−0.739642
$412$	−10.7863	−0.531401
$413$	1.37961	0.0678862
$414$	−35.0839	−1.72428
$415$	19.4937	0.956909
$416$	−3.78776	−0.185710
$417$	−29.3377	−1.43667
$418$	30.6876	1.50098
$419$	−20.8156	−1.01691	−0.508454	−	0.861089i	$-0.669783\pi$
$419$	−20.8156	−1.01691	−0.508454	+	0.861089i	$0.669783\pi$
$420$	26.4311	1.28971
$421$	−14.8466	−0.723578	−0.361789	−	0.932260i	$-0.617834\pi$
$421$	−14.8466	−0.723578	−0.361789	+	0.932260i	$0.617834\pi$
$422$	4.31203	0.209906
$423$	38.1159	1.85326
$424$	2.17450	0.105603
$425$	−0.658915	−0.0319621
$426$	32.2051	1.56034
$427$	18.2503	0.883196
$428$	12.3014	0.594609
$429$	−42.7852	−2.06569
$430$	−15.6966	−0.756957
$431$	−27.5981	−1.32935	−0.664676	−	0.747131i	$-0.731431\pi$
$431$	−27.5981	−1.32935	−0.664676	+	0.747131i	$0.731431\pi$
$432$	−2.98535	−0.143633
$433$	−4.60831	−0.221461	−0.110731	−	0.993850i	$-0.535319\pi$
$433$	−4.60831	−0.221461	−0.110731	+	0.993850i	$0.535319\pi$
$434$	15.9378	0.765041
$435$	−23.6521	−1.13403
$436$	−2.97436	−0.142446
$437$	61.7426	2.95355
$438$	6.14765	0.293746
$439$	20.6770	0.986858	0.493429	−	0.869786i	$-0.335743\pi$
$439$	20.6770	0.986858	0.493429	+	0.869786i	$0.335743\pi$
$440$	−9.82467	−0.468373
$441$	46.2216	2.20103
$442$	6.47434	0.307953
$443$	−36.4992	−1.73413	−0.867066	−	0.498194i	$-0.833997\pi$
$443$	−36.4992	−1.73413	−0.867066	+	0.498194i	$0.833997\pi$
$444$	11.0590	0.524836
$445$	18.6497	0.884082
$446$	−8.82879	−0.418055
$447$	30.0791	1.42269
$448$	−4.26871	−0.201677
$449$	−13.7345	−0.648171	−0.324086	−	0.946028i	$-0.605057\pi$
$449$	−13.7345	−0.648171	−0.324086	+	0.946028i	$0.605057\pi$
$450$	1.58780	0.0748498
$451$	1.09200	0.0514200
$452$	7.61571	0.358213
$453$	62.7484	2.94818
$454$	18.7481	0.879892
$455$	37.5225	1.75908
$456$	19.3403	0.905694
$457$	10.0633	0.470742	0.235371	−	0.971906i	$-0.424370\pi$
$457$	10.0633	0.470742	0.235371	+	0.971906i	$0.424370\pi$
$458$	−21.9064	−1.02362
$459$	5.10280	0.238178
$460$	−19.7670	−0.921640
$461$	11.2167	0.522414	0.261207	−	0.965283i	$-0.415879\pi$
$461$	11.2167	0.522414	0.261207	+	0.965283i	$0.415879\pi$
$462$	−48.2178	−2.24330
$463$	36.3661	1.69008	0.845038	−	0.534706i	$-0.179578\pi$
$463$	36.3661	1.69008	0.845038	+	0.534706i	$0.179578\pi$
$464$	3.81988	0.177334
$465$	23.1181	1.07208
$466$	14.7410	0.682862
$467$	−27.2699	−1.26190	−0.630951	−	0.775823i	$-0.717335\pi$
$467$	−27.2699	−1.26190	−0.630951	+	0.775823i	$0.717335\pi$
$468$	−15.6014	−0.721174
$469$	−68.6549	−3.17019
$470$	21.4753	0.990580
$471$	−48.0197	−2.21263
$472$	−0.323192	−0.0148761
$473$	28.6350	1.31664
$474$	−39.4981	−1.81421
$475$	−2.79430	−0.128211
$476$	7.29642	0.334431
$477$	8.95655	0.410092
$478$	−17.1795	−0.785771
$479$	33.9691	1.55209	0.776044	−	0.630679i	$-0.217224\pi$
$479$	33.9691	1.55209	0.776044	+	0.630679i	$0.217224\pi$
$480$	−6.19183	−0.282617
$481$	15.6997	0.715844
$482$	26.9380	1.22699
$483$	−97.0131	−4.41425
$484$	6.92299	0.314682
$485$	10.5525	0.479165
$486$	20.6728	0.937739
$487$	32.9812	1.49452	0.747259	−	0.664533i	$-0.231369\pi$
$487$	32.9812	1.49452	0.747259	+	0.664533i	$0.231369\pi$
$488$	−4.27538	−0.193537
$489$	53.6691	2.42700
$490$	26.0422	1.17646
$491$	32.8051	1.48047	0.740237	−	0.672347i	$-0.234713\pi$
$491$	32.8051	1.48047	0.740237	+	0.672347i	$0.234713\pi$
$492$	0.688211	0.0310270
$493$	−6.52926	−0.294063
$494$	27.4562	1.23531
$495$	−40.4668	−1.81885
$496$	−3.73365	−0.167646
$497$	51.5246	2.31120
$498$	−22.4124	−1.00432
$499$	34.5672	1.54744	0.773719	−	0.633528i	$-0.218394\pi$
$499$	34.5672	1.54744	0.773719	+	0.633528i	$0.218394\pi$
$500$	−10.7087	−0.478909
$501$	−28.9908	−1.29521
$502$	4.23571	0.189049
$503$	−14.6741	−0.654285	−0.327142	−	0.944975i	$-0.606086\pi$
$503$	−14.6741	−0.654285	−0.327142	+	0.944975i	$0.606086\pi$
$504$	−17.5823	−0.783180
$505$	−27.3545	−1.21726
$506$	36.0606	1.60309
$507$	−3.59428	−0.159628
$508$	13.9927	0.620825
$509$	4.62883	0.205169	0.102585	−	0.994724i	$-0.467289\pi$
$509$	4.62883	0.205169	0.102585	+	0.994724i	$0.467289\pi$
$510$	10.5836	0.468649
$511$	9.83556	0.435100
$512$	1.00000	0.0441942
$513$	21.6398	0.955419
$514$	−7.18865	−0.317078
$515$	−25.0313	−1.10301
$516$	18.0467	0.794463
$517$	−39.1770	−1.72300
$518$	17.6931	0.777392
$519$	53.5143	2.34902
$520$	−8.79013	−0.385472
$521$	28.0758	1.23002	0.615010	−	0.788519i	$-0.289152\pi$
$521$	28.0758	1.23002	0.615010	+	0.788519i	$0.289152\pi$
$522$	15.7337	0.688645
$523$	−14.2276	−0.622130	−0.311065	−	0.950389i	$-0.600686\pi$
$523$	−14.2276	−0.622130	−0.311065	+	0.950389i	$0.600686\pi$
$524$	0.321253	0.0140340
$525$	4.39055	0.191619
$526$	4.05419	0.176771
$527$	6.38185	0.277998
$528$	11.2957	0.491580
$529$	49.5530	2.15448
$530$	5.04630	0.219197
$531$	−1.33119	−0.0577688
$532$	30.9424	1.34152
$533$	0.977007	0.0423189
$534$	−21.4420	−0.927888
$535$	28.5474	1.23421
$536$	16.0833	0.694693
$537$	38.8879	1.67814
$538$	0.226251	0.00975437
$539$	−47.5083	−2.04633
$540$	−6.92800	−0.298134
$541$	−37.5799	−1.61568	−0.807842	−	0.589399i	$-0.799365\pi$
$541$	−37.5799	−1.61568	−0.807842	+	0.589399i	$0.799365\pi$
$542$	−19.3851	−0.832663
$543$	−31.9366	−1.37053
$544$	−1.70928	−0.0732848
$545$	−6.90251	−0.295671
$546$	−43.1405	−1.84624
$547$	44.8734	1.91865	0.959325	−	0.282304i	$-0.0910986\pi$
$547$	44.8734	1.91865	0.959325	+	0.282304i	$0.0910986\pi$
$548$	5.62000	0.240074
$549$	−17.6098	−0.751570
$550$	−1.63200	−0.0695889
$551$	−27.6890	−1.17959
$552$	22.7266	0.967307
$553$	−63.1927	−2.68723
$554$	−2.57006	−0.109192
$555$	25.6642	1.08938
$556$	10.9956	0.466319
$557$	5.24508	0.222241	0.111121	−	0.993807i	$-0.464556\pi$
$557$	5.24508	0.222241	0.111121	+	0.993807i	$0.464556\pi$
$558$	−15.3785	−0.651024
$559$	25.6197	1.08360
$560$	−9.90624	−0.418615
$561$	−19.3074	−0.815161
$562$	−23.9792	−1.01150
$563$	42.6054	1.79561	0.897803	−	0.440398i	$-0.145163\pi$
$563$	42.6054	1.79561	0.897803	+	0.440398i	$0.145163\pi$
$564$	−24.6906	−1.03966
$565$	17.6735	0.743530
$566$	16.7112	0.702425
$567$	18.7456	0.787240
$568$	−12.0703	−0.506459
$569$	−11.3178	−0.474465	−0.237233	−	0.971453i	$-0.576240\pi$
$569$	−11.3178	−0.474465	−0.237233	+	0.971453i	$0.576240\pi$
$570$	44.8824	1.87992
$571$	24.0416	1.00611	0.503054	−	0.864255i	$-0.332210\pi$
$571$	24.0416	1.00611	0.503054	+	0.864255i	$0.332210\pi$
$572$	16.0357	0.670486
$573$	56.5773	2.36355
$574$	1.10106	0.0459574
$575$	−3.28355	−0.136934
$576$	4.11889	0.171621
$577$	21.8068	0.907828	0.453914	−	0.891045i	$-0.350027\pi$
$577$	21.8068	0.907828	0.453914	+	0.891045i	$0.350027\pi$
$578$	−14.0784	−0.585583
$579$	1.69105	0.0702775
$580$	8.86468	0.368086
$581$	−35.8574	−1.48761
$582$	−12.1325	−0.502907
$583$	−9.20588	−0.381269
$584$	−2.30411	−0.0953447
$585$	−36.2056	−1.49692
$586$	3.54579	0.146475
$587$	−31.5861	−1.30370	−0.651848	−	0.758350i	$-0.726006\pi$
$587$	−31.5861	−1.30370	−0.651848	+	0.758350i	$0.726006\pi$
$588$	−29.9413	−1.23476
$589$	27.0639	1.11515
$590$	−0.750020	−0.0308779
$591$	1.59131	0.0654577
$592$	−4.14485	−0.170352
$593$	15.3957	0.632227	0.316113	−	0.948721i	$-0.397622\pi$
$593$	15.3957	0.632227	0.316113	+	0.948721i	$0.397622\pi$
$594$	12.6386	0.518570
$595$	16.9325	0.694167
$596$	−11.2735	−0.461780
$597$	30.4125	1.24470
$598$	32.2634	1.31935
$599$	6.38808	0.261010	0.130505	−	0.991448i	$-0.458340\pi$
$599$	6.38808	0.261010	0.130505	+	0.991448i	$0.458340\pi$
$600$	−1.02854	−0.0419901
$601$	−10.8284	−0.441699	−0.220850	−	0.975308i	$-0.570883\pi$
$601$	−10.8284	−0.441699	−0.220850	+	0.975308i	$0.570883\pi$
$602$	28.8728	1.17677
$603$	66.2455	2.69772
$604$	−23.5178	−0.956925
$605$	16.0660	0.653174
$606$	31.4501	1.27757
$607$	8.03885	0.326287	0.163143	−	0.986602i	$-0.447837\pi$
$607$	8.03885	0.326287	0.163143	+	0.986602i	$0.447837\pi$
$608$	−7.24866	−0.293972
$609$	43.5064	1.76297
$610$	−9.92173	−0.401719
$611$	−35.0516	−1.41804
$612$	−7.04034	−0.284589
$613$	2.95772	0.119461	0.0597306	−	0.998215i	$-0.480976\pi$
$613$	2.95772	0.119461	0.0597306	+	0.998215i	$0.480976\pi$
$614$	−10.9244	−0.440871
$615$	1.59711	0.0644016
$616$	18.0718	0.728134
$617$	−39.2506	−1.58017	−0.790085	−	0.612998i	$-0.789964\pi$
$617$	−39.2506	−1.58017	−0.790085	+	0.612998i	$0.789964\pi$
$618$	28.7791	1.15766
$619$	−7.76158	−0.311964	−0.155982	−	0.987760i	$-0.549854\pi$
$619$	−7.76158	−0.311964	−0.155982	+	0.987760i	$0.549854\pi$
$620$	−8.66455	−0.347977
$621$	25.4286	1.02042
$622$	7.38088	0.295946
$623$	−34.3049	−1.37440
$624$	10.1062	0.404572
$625$	−26.7789	−1.07115
$626$	−1.94665	−0.0778040
$627$	−81.8783	−3.26991
$628$	17.9976	0.718180
$629$	7.08471	0.282486
$630$	−40.8028	−1.62562
$631$	−31.5683	−1.25671	−0.628356	−	0.777926i	$-0.716272\pi$
$631$	−31.5683	−1.25671	−0.628356	+	0.777926i	$0.716272\pi$
$632$	14.8037	0.588860
$633$	−11.5050	−0.457284
$634$	19.9170	0.791006
$635$	32.4723	1.28863
$636$	−5.80185	−0.230058
$637$	−42.5056	−1.68414
$638$	−16.1717	−0.640244
$639$	−49.7163	−1.96675
$640$	2.32067	0.0917324
$641$	4.63907	0.183232	0.0916161	−	0.995794i	$-0.470797\pi$
$641$	4.63907	0.183232	0.0916161	+	0.995794i	$0.470797\pi$
$642$	−32.8216	−1.29536
$643$	50.5318	1.99278	0.996390	−	0.0848920i	$-0.0270545\pi$
$643$	50.5318	1.99278	0.996390	+	0.0848920i	$0.0270545\pi$
$644$	36.3600	1.43278
$645$	41.8805	1.64904
$646$	12.3900	0.487478
$647$	30.9532	1.21690	0.608448	−	0.793593i	$-0.291792\pi$
$647$	30.9532	1.21690	0.608448	+	0.793593i	$0.291792\pi$
$648$	−4.39140	−0.172510
$649$	1.36825	0.0537085
$650$	−1.46015	−0.0572719
$651$	−42.5242	−1.66665
$652$	−20.1149	−0.787760
$653$	−29.2708	−1.14545	−0.572727	−	0.819746i	$-0.694115\pi$
$653$	−29.2708	−1.14545	−0.572727	+	0.819746i	$0.694115\pi$
$654$	7.93598	0.310321
$655$	0.745521	0.0291299
$656$	−0.257938	−0.0100708
$657$	−9.49038	−0.370255
$658$	−39.5023	−1.53996
$659$	−36.6534	−1.42781	−0.713907	−	0.700240i	$-0.753076\pi$
$659$	−36.6534	−1.42781	−0.713907	+	0.700240i	$0.753076\pi$
$660$	26.2135	1.02036
$661$	22.6006	0.879063	0.439532	−	0.898227i	$-0.355144\pi$
$661$	22.6006	0.879063	0.439532	+	0.898227i	$0.355144\pi$
$662$	24.8770	0.966871
$663$	−17.2744	−0.670881
$664$	8.40005	0.325985
$665$	71.8069	2.78455
$666$	−17.0722	−0.661534
$667$	−32.5370	−1.25984
$668$	10.8656	0.420403
$669$	23.5563	0.910740
$670$	37.3240	1.44195
$671$	18.1001	0.698745
$672$	11.3894	0.439357
$673$	−10.4100	−0.401277	−0.200638	−	0.979665i	$-0.564302\pi$
$673$	−10.4100	−0.401277	−0.200638	+	0.979665i	$0.564302\pi$
$674$	22.7276	0.875433
$675$	−1.15083	−0.0442955
$676$	1.34712	0.0518123
$677$	20.0428	0.770306	0.385153	−	0.922853i	$-0.374149\pi$
$677$	20.0428	0.770306	0.385153	+	0.922853i	$0.374149\pi$
$678$	−20.3197	−0.780372
$679$	−19.4106	−0.744911
$680$	−3.96667	−0.152115
$681$	−50.0223	−1.91686
$682$	15.8066	0.605266
$683$	−29.7049	−1.13662	−0.568312	−	0.822813i	$-0.692403\pi$
$683$	−29.7049	−1.13662	−0.568312	+	0.822813i	$0.692403\pi$
$684$	−29.8564	−1.14159
$685$	13.0421	0.498314
$686$	−18.0218	−0.688076
$687$	58.4492	2.22997
$688$	−6.76383	−0.257868
$689$	−8.23650	−0.313786
$690$	52.7408	2.00781
$691$	16.6726	0.634256	0.317128	−	0.948383i	$-0.397282\pi$
$691$	16.6726	0.634256	0.317128	+	0.948383i	$0.397282\pi$
$692$	−20.0569	−0.762448
$693$	74.4358	2.82758
$694$	−3.27914	−0.124474
$695$	25.5172	0.967923
$696$	−10.1919	−0.386324
$697$	0.440889	0.0166998
$698$	−32.4242	−1.22727
$699$	−39.3307	−1.48762
$700$	−1.64555	−0.0621961
$701$	1.05122	0.0397039	0.0198520	−	0.999803i	$-0.493681\pi$
$701$	1.05122	0.0397039	0.0198520	+	0.999803i	$0.493681\pi$
$702$	11.3078	0.426785
$703$	30.0446	1.13315
$704$	−4.23356	−0.159558
$705$	−57.2987	−2.15799
$706$	−27.5233	−1.03585
$707$	50.3167	1.89235
$708$	0.862316	0.0324078
$709$	−24.6175	−0.924529	−0.462264	−	0.886742i	$-0.652963\pi$
$709$	−24.6175	−0.924529	−0.462264	+	0.886742i	$0.652963\pi$
$710$	−28.0112	−1.05124
$711$	60.9749	2.28674
$712$	8.03637	0.301176
$713$	31.8025	1.19101
$714$	−19.4678	−0.728562
$715$	37.2135	1.39171
$716$	−14.5750	−0.544693
$717$	45.8370	1.71181
$718$	0.586624	0.0218926
$719$	25.3431	0.945137	0.472569	−	0.881294i	$-0.343327\pi$
$719$	25.3431	0.945137	0.472569	+	0.881294i	$0.343327\pi$
$720$	9.55858	0.356227
$721$	46.0434	1.71474
$722$	33.5430	1.24834
$723$	−71.8739	−2.67302
$724$	11.9697	0.444850
$725$	1.47254	0.0546887
$726$	−18.4714	−0.685539
$727$	−22.6503	−0.840055	−0.420027	−	0.907511i	$-0.637980\pi$
$727$	−22.6503	−0.840055	−0.420027	+	0.907511i	$0.637980\pi$
$728$	16.1688	0.599257
$729$	−41.9835	−1.55495
$730$	−5.34707	−0.197904
$731$	11.5613	0.427609
$732$	11.4073	0.421624
$733$	−20.9527	−0.773906	−0.386953	−	0.922099i	$-0.626472\pi$
$733$	−20.9527	−0.773906	−0.386953	+	0.922099i	$0.626472\pi$
$734$	−16.4693	−0.607892
$735$	−69.4838	−2.56295
$736$	−8.51781	−0.313970
$737$	−68.0896	−2.50811
$738$	−1.06242	−0.0391082
$739$	35.0162	1.28809	0.644046	−	0.764986i	$-0.277254\pi$
$739$	35.0162	1.28809	0.644046	+	0.764986i	$0.277254\pi$
$740$	−9.61881	−0.353594
$741$	−73.2565	−2.69114
$742$	−9.28232	−0.340765
$743$	14.2423	0.522498	0.261249	−	0.965271i	$-0.415866\pi$
$743$	14.2423	0.522498	0.261249	+	0.965271i	$0.415866\pi$
$744$	9.96184	0.365219
$745$	−26.1620	−0.958501
$746$	−21.6184	−0.791506
$747$	34.5989	1.26591
$748$	7.23633	0.264587
$749$	−52.5109	−1.91871
$750$	28.5722	1.04331
$751$	18.6287	0.679773	0.339886	−	0.940467i	$-0.389611\pi$
$751$	18.6287	0.679773	0.339886	+	0.940467i	$0.389611\pi$
$752$	9.25392	0.337456
$753$	−11.3014	−0.411846
$754$	−14.4688	−0.526923
$755$	−54.5769	−1.98626
$756$	12.7436	0.463479
$757$	−4.88432	−0.177524	−0.0887619	−	0.996053i	$-0.528291\pi$
$757$	−4.88432	−0.177524	−0.0887619	+	0.996053i	$0.528291\pi$
$758$	−0.261596	−0.00950158
$759$	−96.2142	−3.49235
$760$	−16.8217	−0.610188
$761$	31.0122	1.12419	0.562095	−	0.827073i	$-0.309996\pi$
$761$	31.0122	1.12419	0.562095	+	0.827073i	$0.309996\pi$
$762$	−37.3342	−1.35248
$763$	12.6967	0.459651
$764$	−21.2049	−0.767165
$765$	−16.3383	−0.590712
$766$	4.00618	0.144749
$767$	1.22417	0.0442023
$768$	−2.66813	−0.0962777
$769$	−12.0260	−0.433669	−0.216834	−	0.976208i	$-0.569573\pi$
$769$	−12.0260	−0.433669	−0.216834	+	0.976208i	$0.569573\pi$
$770$	41.9386	1.51136
$771$	19.1802	0.690759
$772$	−0.633796	−0.0228108
$773$	−13.2293	−0.475824	−0.237912	−	0.971287i	$-0.576463\pi$
$773$	−13.2293	−0.475824	−0.237912	+	0.971287i	$0.576463\pi$
$774$	−27.8595	−1.00139
$775$	−1.43929	−0.0517010
$776$	4.54719	0.163235
$777$	−47.2075	−1.69356
$778$	17.2120	0.617081
$779$	1.86970	0.0669891
$780$	23.4532	0.839758
$781$	51.1004	1.82851
$782$	14.5593	0.520640
$783$	−11.4037	−0.407534
$784$	11.2218	0.400780
$785$	41.7663	1.49070
$786$	−0.857143	−0.0305733
$787$	17.1397	0.610964	0.305482	−	0.952198i	$-0.401182\pi$
$787$	17.1397	0.610964	0.305482	+	0.952198i	$0.401182\pi$
$788$	−0.596415	−0.0212464
$789$	−10.8171	−0.385098
$790$	34.3545	1.22228
$791$	−32.5092	−1.15589
$792$	−17.4376	−0.619617
$793$	16.1941	0.575070
$794$	21.9820	0.780112
$795$	−13.4642	−0.477525
$796$	−11.3984	−0.404007
$797$	−8.28525	−0.293478	−0.146739	−	0.989175i	$-0.546878\pi$
$797$	−8.28525	−0.293478	−0.146739	+	0.989175i	$0.546878\pi$
$798$	−82.5581	−2.92253
$799$	−15.8175	−0.559585
$800$	0.385493	0.0136292
$801$	33.1009	1.16956
$802$	1.61413	0.0569968
$803$	9.75457	0.344231
$804$	−42.9123	−1.51340
$805$	84.3794	2.97398
$806$	14.1422	0.498136
$807$	−0.603666	−0.0212500
$808$	−11.7873	−0.414677
$809$	−35.1417	−1.23552	−0.617758	−	0.786368i	$-0.711959\pi$
$809$	−35.1417	−1.23552	−0.617758	+	0.786368i	$0.711959\pi$
$810$	−10.1910	−0.358074
$811$	12.8445	0.451031	0.225516	−	0.974240i	$-0.427593\pi$
$811$	12.8445	0.451031	0.225516	+	0.974240i	$0.427593\pi$
$812$	−16.3060	−0.572227
$813$	51.7220	1.81397
$814$	17.5474	0.615037
$815$	−46.6800	−1.63513
$816$	4.56058	0.159652
$817$	49.0287	1.71530
$818$	−10.9940	−0.384396
$819$	66.5977	2.32711
$820$	−0.598588	−0.0209036
$821$	1.05373	0.0367755	0.0183878	−	0.999831i	$-0.494147\pi$
$821$	1.05373	0.0367755	0.0183878	+	0.999831i	$0.494147\pi$
$822$	−14.9949	−0.523006
$823$	12.6277	0.440172	0.220086	−	0.975480i	$-0.429366\pi$
$823$	12.6277	0.440172	0.220086	+	0.975480i	$0.429366\pi$
$824$	−10.7863	−0.375757
$825$	4.35439	0.151601
$826$	1.37961	0.0480028
$827$	32.8680	1.14293	0.571466	−	0.820626i	$-0.306375\pi$
$827$	32.8680	1.14293	0.571466	+	0.820626i	$0.306375\pi$
$828$	−35.0839	−1.21925
$829$	7.16068	0.248701	0.124350	−	0.992238i	$-0.460315\pi$
$829$	7.16068	0.248701	0.124350	+	0.992238i	$0.460315\pi$
$830$	19.4937	0.676637
$831$	6.85726	0.237876
$832$	−3.78776	−0.131317
$833$	−19.1813	−0.664592
$834$	−29.3377	−1.01588
$835$	25.2155	0.872617
$836$	30.6876	1.06135
$837$	11.1462	0.385270
$838$	−20.8156	−0.719063
$839$	−26.2409	−0.905937	−0.452968	−	0.891527i	$-0.649635\pi$
$839$	−26.2409	−0.905937	−0.452968	+	0.891527i	$0.649635\pi$
$840$	26.4311	0.911959
$841$	−14.4085	−0.496844
$842$	−14.8466	−0.511647
$843$	63.9794	2.20357
$844$	4.31203	0.148426
$845$	3.12621	0.107545
$846$	38.1159	1.31045
$847$	−29.5522	−1.01543
$848$	2.17450	0.0746728
$849$	−44.5877	−1.53024
$850$	−0.658915	−0.0226006
$851$	35.3050	1.21024
$852$	32.2051	1.10333
$853$	−16.2353	−0.555885	−0.277943	−	0.960598i	$-0.589653\pi$
$853$	−16.2353	−0.555885	−0.277943	+	0.960598i	$0.589653\pi$
$854$	18.2503	0.624514
$855$	−69.2868	−2.36956
$856$	12.3014	0.420452
$857$	9.07480	0.309989	0.154995	−	0.987915i	$-0.450464\pi$
$857$	9.07480	0.309989	0.154995	+	0.987915i	$0.450464\pi$
$858$	−42.7852	−1.46066
$859$	−20.9673	−0.715396	−0.357698	−	0.933837i	$-0.616438\pi$
$859$	−20.9673	−0.715396	−0.357698	+	0.933837i	$0.616438\pi$
$860$	−15.6966	−0.535249
$861$	−2.93777	−0.100119
$862$	−27.5981	−0.939994
$863$	−14.9197	−0.507872	−0.253936	−	0.967221i	$-0.581725\pi$
$863$	−14.9197	−0.507872	−0.253936	+	0.967221i	$0.581725\pi$
$864$	−2.98535	−0.101564
$865$	−46.5453	−1.58259
$866$	−4.60831	−0.156597
$867$	37.5628	1.27570
$868$	15.9378	0.540966
$869$	−62.6723	−2.12601
$870$	−23.6521	−0.801880
$871$	−60.9197	−2.06419
$872$	−2.97436	−0.100725
$873$	18.7294	0.633894
$874$	61.7426	2.08848
$875$	45.7124	1.54536
$876$	6.14765	0.207710
$877$	24.4394	0.825260	0.412630	−	0.910899i	$-0.364610\pi$
$877$	24.4394	0.825260	0.412630	+	0.910899i	$0.364610\pi$
$878$	20.6770	0.697814
$879$	−9.46060	−0.319098
$880$	−9.82467	−0.331190
$881$	−22.9999	−0.774887	−0.387443	−	0.921893i	$-0.626642\pi$
$881$	−22.9999	−0.774887	−0.387443	+	0.921893i	$0.626642\pi$
$882$	46.2216	1.55636
$883$	−53.9924	−1.81699	−0.908495	−	0.417897i	$-0.862767\pi$
$883$	−53.9924	−1.81699	−0.908495	+	0.417897i	$0.862767\pi$
$884$	6.47434	0.217756
$885$	2.00115	0.0672679
$886$	−36.4992	−1.22622
$887$	8.00911	0.268920	0.134460	−	0.990919i	$-0.457070\pi$
$887$	8.00911	0.268920	0.134460	+	0.990919i	$0.457070\pi$
$888$	11.0590	0.371115
$889$	−59.7306	−2.00330
$890$	18.6497	0.625140
$891$	18.5912	0.622829
$892$	−8.82879	−0.295610
$893$	−67.0785	−2.24470
$894$	30.0791	1.00599
$895$	−33.8237	−1.13060
$896$	−4.26871	−0.142607
$897$	−86.0828	−2.87422
$898$	−13.7345	−0.458326
$899$	−14.2621	−0.475668
$900$	1.58780	0.0529268
$901$	−3.71684	−0.123826
$902$	1.09200	0.0363595
$903$	−77.0362	−2.56360
$904$	7.61571	0.253295
$905$	27.7776	0.923360
$906$	62.7484	2.08468
$907$	−38.0015	−1.26182	−0.630910	−	0.775856i	$-0.717318\pi$
$907$	−38.0015	−1.26182	−0.630910	+	0.775856i	$0.717318\pi$
$908$	18.7481	0.622177
$909$	−48.5508	−1.61033
$910$	37.5225	1.24386
$911$	−41.8459	−1.38642	−0.693209	−	0.720737i	$-0.743804\pi$
$911$	−41.8459	−1.38642	−0.693209	+	0.720737i	$0.743804\pi$
$912$	19.3403	0.640422
$913$	−35.5621	−1.17693
$914$	10.0633	0.332865
$915$	26.4724	0.875151
$916$	−21.9064	−0.723809
$917$	−1.37133	−0.0452855
$918$	5.10280	0.168417
$919$	55.5569	1.83265	0.916327	−	0.400431i	$-0.131140\pi$
$919$	55.5569	1.83265	0.916327	+	0.400431i	$0.131140\pi$
$920$	−19.7670	−0.651698
$921$	29.1476	0.960445
$922$	11.2167	0.369403
$923$	45.7195	1.50487
$924$	−48.2178	−1.58625
$925$	−1.59781	−0.0525356
$926$	36.3661	1.19506
$927$	−44.4274	−1.45919
$928$	3.81988	0.125394
$929$	−14.4330	−0.473532	−0.236766	−	0.971567i	$-0.576087\pi$
$929$	−14.4330	−0.473532	−0.236766	+	0.971567i	$0.576087\pi$
$930$	23.1181	0.758073
$931$	−81.3433	−2.66592
$932$	14.7410	0.482856
$933$	−19.6931	−0.644724
$934$	−27.2699	−0.892300
$935$	16.7931	0.549194
$936$	−15.6014	−0.509947
$937$	−19.3420	−0.631877	−0.315938	−	0.948780i	$-0.602319\pi$
$937$	−19.3420	−0.631877	−0.315938	+	0.948780i	$0.602319\pi$
$938$	−68.6549	−2.24166
$939$	5.19392	0.169497
$940$	21.4753	0.700446
$941$	46.7740	1.52479	0.762395	−	0.647112i	$-0.224024\pi$
$941$	46.7740	1.52479	0.762395	+	0.647112i	$0.224024\pi$
$942$	−48.0197	−1.56457
$943$	2.19707	0.0715463
$944$	−0.323192	−0.0105190
$945$	29.5736	0.962029
$946$	28.6350	0.931005
$947$	−15.9285	−0.517606	−0.258803	−	0.965930i	$-0.583328\pi$
$947$	−15.9285	−0.517606	−0.258803	+	0.965930i	$0.583328\pi$
$948$	−39.4981	−1.28284
$949$	8.72741	0.283304
$950$	−2.79430	−0.0906592
$951$	−53.1411	−1.72322
$952$	7.29642	0.236478
$953$	−18.7886	−0.608624	−0.304312	−	0.952572i	$-0.598427\pi$
$953$	−18.7886	−0.608624	−0.304312	+	0.952572i	$0.598427\pi$
$954$	8.95655	0.289979
$955$	−49.2094	−1.59238
$956$	−17.1795	−0.555624
$957$	43.1481	1.39478
$958$	33.9691	1.09749
$959$	−23.9901	−0.774681
$960$	−6.19183	−0.199840
$961$	−17.0599	−0.550318
$962$	15.6997	0.506178
$963$	50.6680	1.63275
$964$	26.9380	0.867614
$965$	−1.47083	−0.0473476
$966$	−97.0131	−3.12134
$967$	−34.8570	−1.12092	−0.560462	−	0.828180i	$-0.689376\pi$
$967$	−34.8570	−1.12092	−0.560462	+	0.828180i	$0.689376\pi$
$968$	6.92299	0.222513
$969$	−33.0580	−1.06198
$970$	10.5525	0.338821
$971$	−19.4826	−0.625227	−0.312613	−	0.949880i	$-0.601204\pi$
$971$	−19.4826	−0.625227	−0.312613	+	0.949880i	$0.601204\pi$
$972$	20.6728	0.663082
$973$	−46.9371	−1.50474
$974$	32.9812	1.05678
$975$	3.89587	0.124768
$976$	−4.27538	−0.136852
$977$	0.273921	0.00876351	0.00438175	−	0.999990i	$-0.498605\pi$
$977$	0.273921	0.00876351	0.00438175	+	0.999990i	$0.498605\pi$
$978$	53.6691	1.71615
$979$	−34.0224	−1.08736
$980$	26.0422	0.831886
$981$	−12.2511	−0.391147
$982$	32.8051	1.04685
$983$	35.6464	1.13694	0.568472	−	0.822703i	$-0.307535\pi$
$983$	35.6464	1.13694	0.568472	+	0.822703i	$0.307535\pi$
$984$	0.688211	0.0219394
$985$	−1.38408	−0.0441004
$986$	−6.52926	−0.207934
$987$	105.397	3.35482
$988$	27.4562	0.873497
$989$	57.6130	1.83199
$990$	−40.4668	−1.28612
$991$	−44.4527	−1.41209	−0.706043	−	0.708169i	$-0.749521\pi$
$991$	−44.4527	−1.41209	−0.706043	+	0.708169i	$0.749521\pi$
$992$	−3.73365	−0.118543
$993$	−66.3749	−2.10634
$994$	51.5246	1.63426
$995$	−26.4520	−0.838584
$996$	−22.4124	−0.710164
$997$	50.3797	1.59554	0.797771	−	0.602961i	$-0.206012\pi$
$997$	50.3797	1.59554	0.797771	+	0.602961i	$0.206012\pi$
$998$	34.5672	1.09420
$999$	12.3738	0.391490

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8002.2.a.g.1.12	✓	95

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8002.2.a.g.1.12	✓	95	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:	\( N \)	\(=\)	\( 8002 = 2 \cdot 4001 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8002.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.66813 q^{3} +1.00000 q^{4} +2.32067 q^{5} -2.66813 q^{6} -4.26871 q^{7} +1.00000 q^{8} +4.11889 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.66813 q^{3} +1.00000 q^{4} +2.32067 q^{5} -2.66813 q^{6} -4.26871 q^{7} +1.00000 q^{8} +4.11889 q^{9} +2.32067 q^{10} -4.23356 q^{11} -2.66813 q^{12} -3.78776 q^{13} -4.26871 q^{14} -6.19183 q^{15} +1.00000 q^{16} -1.70928 q^{17} +4.11889 q^{18} -7.24866 q^{19} +2.32067 q^{20} +11.3894 q^{21} -4.23356 q^{22} -8.51781 q^{23} -2.66813 q^{24} +0.385493 q^{25} -3.78776 q^{26} -2.98535 q^{27} -4.26871 q^{28} +3.81988 q^{29} -6.19183 q^{30} -3.73365 q^{31} +1.00000 q^{32} +11.2957 q^{33} -1.70928 q^{34} -9.90624 q^{35} +4.11889 q^{36} -4.14485 q^{37} -7.24866 q^{38} +10.1062 q^{39} +2.32067 q^{40} -0.257938 q^{41} +11.3894 q^{42} -6.76383 q^{43} -4.23356 q^{44} +9.55858 q^{45} -8.51781 q^{46} +9.25392 q^{47} -2.66813 q^{48} +11.2218 q^{49} +0.385493 q^{50} +4.56058 q^{51} -3.78776 q^{52} +2.17450 q^{53} -2.98535 q^{54} -9.82467 q^{55} -4.26871 q^{56} +19.3403 q^{57} +3.81988 q^{58} -0.323192 q^{59} -6.19183 q^{60} -4.27538 q^{61} -3.73365 q^{62} -17.5823 q^{63} +1.00000 q^{64} -8.79013 q^{65} +11.2957 q^{66} +16.0833 q^{67} -1.70928 q^{68} +22.7266 q^{69} -9.90624 q^{70} -12.0703 q^{71} +4.11889 q^{72} -2.30411 q^{73} -4.14485 q^{74} -1.02854 q^{75} -7.24866 q^{76} +18.0718 q^{77} +10.1062 q^{78} +14.8037 q^{79} +2.32067 q^{80} -4.39140 q^{81} -0.257938 q^{82} +8.40005 q^{83} +11.3894 q^{84} -3.96667 q^{85} -6.76383 q^{86} -10.1919 q^{87} -4.23356 q^{88} +8.03637 q^{89} +9.55858 q^{90} +16.1688 q^{91} -8.51781 q^{92} +9.96184 q^{93} +9.25392 q^{94} -16.8217 q^{95} -2.66813 q^{96} +4.54719 q^{97} +11.2218 q^{98} -17.4376 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 95 q + 95 q^{2} + 24 q^{3} + 95 q^{4} + 36 q^{5} + 24 q^{6} + 21 q^{7} + 95 q^{8} + 121 q^{9}+O(q^{10}) \) 95 * q + 95 * q^2 + 24 * q^3 + 95 * q^4 + 36 * q^5 + 24 * q^6 + 21 * q^7 + 95 * q^8 + 121 * q^9	\( 95 q + 95 q^{2} + 24 q^{3} + 95 q^{4} + 36 q^{5} + 24 q^{6} + 21 q^{7} + 95 q^{8} + 121 q^{9} + 36 q^{10} + 40 q^{11} + 24 q^{12} + 52 q^{13} + 21 q^{14} + 15 q^{15} + 95 q^{16} + 84 q^{17} + 121 q^{18} + 37 q^{19} + 36 q^{20} + 36 q^{21} + 40 q^{22} + 37 q^{23} + 24 q^{24} + 133 q^{25} + 52 q^{26} + 93 q^{27} + 21 q^{28} + 66 q^{29} + 15 q^{30} + 10 q^{31} + 95 q^{32} + 63 q^{33} + 84 q^{34} + 55 q^{35} + 121 q^{36} + 49 q^{37} + 37 q^{38} + 14 q^{39} + 36 q^{40} + 98 q^{41} + 36 q^{42} + 37 q^{43} + 40 q^{44} + 97 q^{45} + 37 q^{46} + 91 q^{47} + 24 q^{48} + 170 q^{49} + 133 q^{50} + 22 q^{51} + 52 q^{52} + 70 q^{53} + 93 q^{54} - q^{55} + 21 q^{56} + 50 q^{57} + 66 q^{58} + 72 q^{59} + 15 q^{60} + 97 q^{61} + 10 q^{62} + 75 q^{63} + 95 q^{64} + 75 q^{65} + 63 q^{66} + 39 q^{67} + 84 q^{68} + 65 q^{69} + 55 q^{70} + 28 q^{71} + 121 q^{72} + 117 q^{73} + 49 q^{74} + 62 q^{75} + 37 q^{76} + 92 q^{77} + 14 q^{78} + q^{79} + 36 q^{80} + 155 q^{81} + 98 q^{82} + 117 q^{83} + 36 q^{84} + 81 q^{85} + 37 q^{86} + 46 q^{87} + 40 q^{88} + 90 q^{89} + 97 q^{90} + 65 q^{91} + 37 q^{92} + 36 q^{93} + 91 q^{94} + 38 q^{95} + 24 q^{96} + 111 q^{97} + 170 q^{98} + 97 q^{99}+O(q^{100}) \) 95 * q + 95 * q^2 + 24 * q^3 + 95 * q^4 + 36 * q^5 + 24 * q^6 + 21 * q^7 + 95 * q^8 + 121 * q^9 + 36 * q^10 + 40 * q^11 + 24 * q^12 + 52 * q^13 + 21 * q^14 + 15 * q^15 + 95 * q^16 + 84 * q^17 + 121 * q^18 + 37 * q^19 + 36 * q^20 + 36 * q^21 + 40 * q^22 + 37 * q^23 + 24 * q^24 + 133 * q^25 + 52 * q^26 + 93 * q^27 + 21 * q^28 + 66 * q^29 + 15 * q^30 + 10 * q^31 + 95 * q^32 + 63 * q^33 + 84 * q^34 + 55 * q^35 + 121 * q^36 + 49 * q^37 + 37 * q^38 + 14 * q^39 + 36 * q^40 + 98 * q^41 + 36 * q^42 + 37 * q^43 + 40 * q^44 + 97 * q^45 + 37 * q^46 + 91 * q^47 + 24 * q^48 + 170 * q^49 + 133 * q^50 + 22 * q^51 + 52 * q^52 + 70 * q^53 + 93 * q^54 - q^55 + 21 * q^56 + 50 * q^57 + 66 * q^58 + 72 * q^59 + 15 * q^60 + 97 * q^61 + 10 * q^62 + 75 * q^63 + 95 * q^64 + 75 * q^65 + 63 * q^66 + 39 * q^67 + 84 * q^68 + 65 * q^69 + 55 * q^70 + 28 * q^71 + 121 * q^72 + 117 * q^73 + 49 * q^74 + 62 * q^75 + 37 * q^76 + 92 * q^77 + 14 * q^78 + q^79 + 36 * q^80 + 155 * q^81 + 98 * q^82 + 117 * q^83 + 36 * q^84 + 81 * q^85 + 37 * q^86 + 46 * q^87 + 40 * q^88 + 90 * q^89 + 97 * q^90 + 65 * q^91 + 37 * q^92 + 36 * q^93 + 91 * q^94 + 38 * q^95 + 24 * q^96 + 111 * q^97 + 170 * q^98 + 97 * q^99

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