LMFDB - Embedded newform 8007.2.a.j.1.21

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			1.21
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)

$f(q)$	$=$	$q-1.13907 q^{2} -1.00000 q^{3} -0.702517 q^{4} +4.37521 q^{5} +1.13907 q^{6} +2.87869 q^{7} +3.07836 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.13907 q^{2} -1.00000 q^{3} -0.702517 q^{4} +4.37521 q^{5} +1.13907 q^{6} +2.87869 q^{7} +3.07836 q^{8} +1.00000 q^{9} -4.98367 q^{10} -4.98597 q^{11} +0.702517 q^{12} +0.467696 q^{13} -3.27903 q^{14} -4.37521 q^{15} -2.10144 q^{16} +1.00000 q^{17} -1.13907 q^{18} +8.07630 q^{19} -3.07366 q^{20} -2.87869 q^{21} +5.67938 q^{22} -9.12460 q^{23} -3.07836 q^{24} +14.1424 q^{25} -0.532739 q^{26} -1.00000 q^{27} -2.02233 q^{28} -3.46636 q^{29} +4.98367 q^{30} +1.58824 q^{31} -3.76303 q^{32} +4.98597 q^{33} -1.13907 q^{34} +12.5949 q^{35} -0.702517 q^{36} +2.71372 q^{37} -9.19948 q^{38} -0.467696 q^{39} +13.4685 q^{40} -12.3960 q^{41} +3.27903 q^{42} -5.71658 q^{43} +3.50273 q^{44} +4.37521 q^{45} +10.3936 q^{46} -5.46273 q^{47} +2.10144 q^{48} +1.28684 q^{49} -16.1092 q^{50} -1.00000 q^{51} -0.328564 q^{52} +11.2449 q^{53} +1.13907 q^{54} -21.8147 q^{55} +8.86164 q^{56} -8.07630 q^{57} +3.94844 q^{58} -6.45176 q^{59} +3.07366 q^{60} +4.32360 q^{61} -1.80911 q^{62} +2.87869 q^{63} +8.48923 q^{64} +2.04627 q^{65} -5.67938 q^{66} +9.87470 q^{67} -0.702517 q^{68} +9.12460 q^{69} -14.3464 q^{70} -1.10160 q^{71} +3.07836 q^{72} +1.32225 q^{73} -3.09112 q^{74} -14.1424 q^{75} -5.67374 q^{76} -14.3531 q^{77} +0.532739 q^{78} +11.7407 q^{79} -9.19422 q^{80} +1.00000 q^{81} +14.1200 q^{82} +11.3391 q^{83} +2.02233 q^{84} +4.37521 q^{85} +6.51159 q^{86} +3.46636 q^{87} -15.3486 q^{88} +12.0589 q^{89} -4.98367 q^{90} +1.34635 q^{91} +6.41019 q^{92} -1.58824 q^{93} +6.22244 q^{94} +35.3355 q^{95} +3.76303 q^{96} +5.38336 q^{97} -1.46581 q^{98} -4.98597 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.13907	−0.805445	−0.402722	−	0.915322i	$-0.631936\pi$
$2$	−1.13907	−0.805445	−0.402722	+	0.915322i	$0.631936\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−0.702517	−0.351259
$5$	4.37521	1.95665	0.978326	−	0.207070i	$-0.0663928\pi$
$5$	4.37521	1.95665	0.978326	+	0.207070i	$0.0663928\pi$
$6$	1.13907	0.465024
$7$	2.87869	1.08804	0.544021	−	0.839072i	$-0.316901\pi$
$7$	2.87869	1.08804	0.544021	+	0.839072i	$0.316901\pi$
$8$	3.07836	1.08836
$9$	1.00000	0.333333
$10$	−4.98367	−1.57598
$11$	−4.98597	−1.50333	−0.751663	−	0.659547i	$-0.770748\pi$
$11$	−4.98597	−1.50333	−0.751663	+	0.659547i	$0.770748\pi$
$12$	0.702517	0.202799
$13$	0.467696	0.129716	0.0648578	−	0.997895i	$-0.479341\pi$
$13$	0.467696	0.129716	0.0648578	+	0.997895i	$0.479341\pi$
$14$	−3.27903	−0.876358
$15$	−4.37521	−1.12967
$16$	−2.10144	−0.525359
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−1.13907	−0.268482
$19$	8.07630	1.85283	0.926415	−	0.376504i	$-0.122874\pi$
$19$	8.07630	1.85283	0.926415	+	0.376504i	$0.122874\pi$
$20$	−3.07366	−0.687291
$21$	−2.87869	−0.628181
$22$	5.67938	1.21085
$23$	−9.12460	−1.90261	−0.951305	−	0.308251i	$-0.900256\pi$
$23$	−9.12460	−1.90261	−0.951305	+	0.308251i	$0.900256\pi$
$24$	−3.07836	−0.628367
$25$	14.1424	2.82849
$26$	−0.532739	−0.104479
$27$	−1.00000	−0.192450
$28$	−2.02233	−0.382184
$29$	−3.46636	−0.643688	−0.321844	−	0.946793i	$-0.604303\pi$
$29$	−3.46636	−0.643688	−0.321844	+	0.946793i	$0.604303\pi$
$30$	4.98367	0.909890
$31$	1.58824	0.285256	0.142628	−	0.989776i	$-0.454445\pi$
$31$	1.58824	0.285256	0.142628	+	0.989776i	$0.454445\pi$
$32$	−3.76303	−0.665217
$33$	4.98597	0.867946
$34$	−1.13907	−0.195349
$35$	12.5949	2.12892
$36$	−0.702517	−0.117086
$37$	2.71372	0.446132	0.223066	−	0.974803i	$-0.428393\pi$
$37$	2.71372	0.446132	0.223066	+	0.974803i	$0.428393\pi$
$38$	−9.19948	−1.49235
$39$	−0.467696	−0.0748913
$40$	13.4685	2.12955
$41$	−12.3960	−1.93593	−0.967967	−	0.251077i	$-0.919215\pi$
$41$	−12.3960	−1.93593	−0.967967	+	0.251077i	$0.919215\pi$
$42$	3.27903	0.505965
$43$	−5.71658	−0.871770	−0.435885	−	0.900002i	$-0.643565\pi$
$43$	−5.71658	−0.871770	−0.435885	+	0.900002i	$0.643565\pi$
$44$	3.50273	0.528056
$45$	4.37521	0.652217
$46$	10.3936	1.53245
$47$	−5.46273	−0.796821	−0.398410	−	0.917207i	$-0.630438\pi$
$47$	−5.46273	−0.796821	−0.398410	+	0.917207i	$0.630438\pi$
$48$	2.10144	0.303316
$49$	1.28684	0.183835
$50$	−16.1092	−2.27819
$51$	−1.00000	−0.140028
$52$	−0.328564	−0.0455637
$53$	11.2449	1.54460	0.772301	−	0.635257i	$-0.219106\pi$
$53$	11.2449	1.54460	0.772301	+	0.635257i	$0.219106\pi$
$54$	1.13907	0.155008
$55$	−21.8147	−2.94149
$56$	8.86164	1.18419
$57$	−8.07630	−1.06973
$58$	3.94844	0.518455
$59$	−6.45176	−0.839948	−0.419974	−	0.907536i	$-0.637961\pi$
$59$	−6.45176	−0.839948	−0.419974	+	0.907536i	$0.637961\pi$
$60$	3.07366	0.396808
$61$	4.32360	0.553580	0.276790	−	0.960930i	$-0.410729\pi$
$61$	4.32360	0.553580	0.276790	+	0.960930i	$0.410729\pi$
$62$	−1.80911	−0.229758
$63$	2.87869	0.362681
$64$	8.48923	1.06115
$65$	2.04627	0.253808
$66$	−5.67938	−0.699083
$67$	9.87470	1.20639	0.603194	−	0.797595i	$-0.293895\pi$
$67$	9.87470	1.20639	0.603194	+	0.797595i	$0.293895\pi$
$68$	−0.702517	−0.0851927
$69$	9.12460	1.09847
$70$	−14.3464	−1.71473
$71$	−1.10160	−0.130736	−0.0653682	−	0.997861i	$-0.520822\pi$
$71$	−1.10160	−0.130736	−0.0653682	+	0.997861i	$0.520822\pi$
$72$	3.07836	0.362788
$73$	1.32225	0.154758	0.0773789	−	0.997002i	$-0.475345\pi$
$73$	1.32225	0.154758	0.0773789	+	0.997002i	$0.475345\pi$
$74$	−3.09112	−0.359335
$75$	−14.1424	−1.63303
$76$	−5.67374	−0.650822
$77$	−14.3531	−1.63568
$78$	0.532739	0.0603208
$79$	11.7407	1.32093	0.660464	−	0.750858i	$-0.270360\pi$
$79$	11.7407	1.32093	0.660464	+	0.750858i	$0.270360\pi$
$80$	−9.19422	−1.02794
$81$	1.00000	0.111111
$82$	14.1200	1.55929
$83$	11.3391	1.24463	0.622313	−	0.782768i	$-0.286193\pi$
$83$	11.3391	1.24463	0.622313	+	0.782768i	$0.286193\pi$
$84$	2.02233	0.220654
$85$	4.37521	0.474558
$86$	6.51159	0.702163
$87$	3.46636	0.371633
$88$	−15.3486	−1.63617
$89$	12.0589	1.27824	0.639120	−	0.769107i	$-0.279299\pi$
$89$	12.0589	1.27824	0.639120	+	0.769107i	$0.279299\pi$
$90$	−4.98367	−0.525325
$91$	1.34635	0.141136
$92$	6.41019	0.668308
$93$	−1.58824	−0.164692
$94$	6.22244	0.641795
$95$	35.3355	3.62534
$96$	3.76303	0.384063
$97$	5.38336	0.546597	0.273299	−	0.961929i	$-0.411885\pi$
$97$	5.38336	0.546597	0.273299	+	0.961929i	$0.411885\pi$
$98$	−1.46581	−0.148069
$99$	−4.98597	−0.501109
$100$	−9.93531	−0.993531
$101$	6.20613	0.617533	0.308766	−	0.951138i	$-0.400084\pi$
$101$	6.20613	0.617533	0.308766	+	0.951138i	$0.400084\pi$
$102$	1.13907	0.112785
$103$	1.87409	0.184660	0.0923298	−	0.995728i	$-0.470569\pi$
$103$	1.87409	0.184660	0.0923298	+	0.995728i	$0.470569\pi$
$104$	1.43974	0.141178
$105$	−12.5949	−1.22913
$106$	−12.8087	−1.24409
$107$	−17.3708	−1.67930	−0.839648	−	0.543132i	$-0.817238\pi$
$107$	−17.3708	−1.67930	−0.839648	+	0.543132i	$0.817238\pi$
$108$	0.702517	0.0675997
$109$	16.3213	1.56330	0.781648	−	0.623720i	$-0.214380\pi$
$109$	16.3213	1.56330	0.781648	+	0.623720i	$0.214380\pi$
$110$	24.8484	2.36921
$111$	−2.71372	−0.257575
$112$	−6.04938	−0.571612
$113$	15.3088	1.44013	0.720065	−	0.693907i	$-0.244112\pi$
$113$	15.3088	1.44013	0.720065	+	0.693907i	$0.244112\pi$
$114$	9.19948	0.861610
$115$	−39.9220	−3.72275
$116$	2.43518	0.226101
$117$	0.467696	0.0432385
$118$	7.34902	0.676532
$119$	2.87869	0.263889
$120$	−13.4685	−1.22950
$121$	13.8599	1.25999
$122$	−4.92488	−0.445878
$123$	12.3960	1.11771
$124$	−1.11576	−0.100198
$125$	40.0001	3.57771
$126$	−3.27903	−0.292119
$127$	8.13495	0.721860	0.360930	−	0.932593i	$-0.382459\pi$
$127$	8.13495	0.721860	0.360930	+	0.932593i	$0.382459\pi$
$128$	−2.14377	−0.189485
$129$	5.71658	0.503317
$130$	−2.33084	−0.204428
$131$	−11.9081	−1.04041	−0.520206	−	0.854041i	$-0.674145\pi$
$131$	−11.9081	−1.04041	−0.520206	+	0.854041i	$0.674145\pi$
$132$	−3.50273	−0.304874
$133$	23.2491	2.01596
$134$	−11.2480	−0.971678
$135$	−4.37521	−0.376558
$136$	3.07836	0.263967
$137$	16.6112	1.41919	0.709595	−	0.704610i	$-0.248878\pi$
$137$	16.6112	1.41919	0.709595	+	0.704610i	$0.248878\pi$
$138$	−10.3936	−0.884759
$139$	−1.93971	−0.164524	−0.0822618	−	0.996611i	$-0.526214\pi$
$139$	−1.93971	−0.164524	−0.0822618	+	0.996611i	$0.526214\pi$
$140$	−8.84810	−0.747801
$141$	5.46273	0.460045
$142$	1.25481	0.105301
$143$	−2.33192	−0.195005
$144$	−2.10144	−0.175120
$145$	−15.1661	−1.25947
$146$	−1.50614	−0.124649
$147$	−1.28684	−0.106137
$148$	−1.90643	−0.156708
$149$	10.1268	0.829619	0.414810	−	0.909908i	$-0.363848\pi$
$149$	10.1268	0.829619	0.414810	+	0.909908i	$0.363848\pi$
$150$	16.1092	1.31531
$151$	0.379225	0.0308609	0.0154304	−	0.999881i	$-0.495088\pi$
$151$	0.379225	0.0308609	0.0154304	+	0.999881i	$0.495088\pi$
$152$	24.8618	2.01655
$153$	1.00000	0.0808452
$154$	16.3492	1.31745
$155$	6.94886	0.558146
$156$	0.328564	0.0263062
$157$	−1.00000	−0.0798087
$157$	−1.00000	−0.0798087
$158$	−13.3734	−1.06393
$159$	−11.2449	−0.891776
$160$	−16.4641	−1.30160
$161$	−26.2669	−2.07012
$162$	−1.13907	−0.0894939
$163$	10.2563	0.803336	0.401668	−	0.915785i	$-0.368431\pi$
$163$	10.2563	0.803336	0.401668	+	0.915785i	$0.368431\pi$
$164$	8.70842	0.680013
$165$	21.8147	1.69827
$166$	−12.9160	−1.00248
$167$	4.94994	0.383038	0.191519	−	0.981489i	$-0.438659\pi$
$167$	4.94994	0.383038	0.191519	+	0.981489i	$0.438659\pi$
$168$	−8.86164	−0.683690
$169$	−12.7813	−0.983174
$170$	−4.98367	−0.382230
$171$	8.07630	0.617610
$172$	4.01600	0.306217
$173$	−7.29981	−0.554994	−0.277497	−	0.960726i	$-0.589505\pi$
$173$	−7.29981	−0.554994	−0.277497	+	0.960726i	$0.589505\pi$
$174$	−3.94844	−0.299330
$175$	40.7117	3.07751
$176$	10.4777	0.789786
$177$	6.45176	0.484944
$178$	−13.7359	−1.02955
$179$	11.7509	0.878302	0.439151	−	0.898413i	$-0.355279\pi$
$179$	11.7509	0.878302	0.439151	+	0.898413i	$0.355279\pi$
$180$	−3.07366	−0.229097
$181$	−2.31626	−0.172166	−0.0860832	−	0.996288i	$-0.527435\pi$
$181$	−2.31626	−0.172166	−0.0860832	+	0.996288i	$0.527435\pi$
$182$	−1.53359	−0.113677
$183$	−4.32360	−0.319609
$184$	−28.0888	−2.07073
$185$	11.8731	0.872926
$186$	1.80911	0.132651
$187$	−4.98597	−0.364610
$188$	3.83766	0.279890
$189$	−2.87869	−0.209394
$190$	−40.2496	−2.92002
$191$	−4.82010	−0.348770	−0.174385	−	0.984678i	$-0.555794\pi$
$191$	−4.82010	−0.348770	−0.174385	+	0.984678i	$0.555794\pi$
$192$	−8.48923	−0.612658
$193$	−12.7773	−0.919727	−0.459864	−	0.887990i	$-0.652102\pi$
$193$	−12.7773	−0.919727	−0.459864	+	0.887990i	$0.652102\pi$
$194$	−6.13203	−0.440254
$195$	−2.04627	−0.146536
$196$	−0.904030	−0.0645736
$197$	23.4244	1.66892	0.834459	−	0.551070i	$-0.185780\pi$
$197$	23.4244	1.66892	0.834459	+	0.551070i	$0.185780\pi$
$198$	5.67938	0.403616
$199$	11.7173	0.830615	0.415308	−	0.909681i	$-0.363674\pi$
$199$	11.7173	0.830615	0.415308	+	0.909681i	$0.363674\pi$
$200$	43.5355	3.07843
$201$	−9.87470	−0.696508
$202$	−7.06922	−0.497389
$203$	−9.97858	−0.700359
$204$	0.702517	0.0491860
$205$	−54.2352	−3.78795
$206$	−2.13472	−0.148733
$207$	−9.12460	−0.634203
$208$	−0.982833	−0.0681472
$209$	−40.2682	−2.78541
$210$	14.3464	0.989998
$211$	−5.37984	−0.370363	−0.185182	−	0.982704i	$-0.559287\pi$
$211$	−5.37984	−0.370363	−0.185182	+	0.982704i	$0.559287\pi$
$212$	−7.89971	−0.542554
$213$	1.10160	0.0754807
$214$	19.7865	1.35258
$215$	−25.0112	−1.70575
$216$	−3.07836	−0.209456
$217$	4.57204	0.310370
$218$	−18.5911	−1.25915
$219$	−1.32225	−0.0893495
$220$	15.3252	1.03322
$221$	0.467696	0.0314606
$222$	3.09112	0.207462
$223$	25.0870	1.67995	0.839974	−	0.542626i	$-0.182570\pi$
$223$	25.0870	1.67995	0.839974	+	0.542626i	$0.182570\pi$
$224$	−10.8326	−0.723784
$225$	14.1424	0.942829
$226$	−17.4378	−1.15994
$227$	−19.8659	−1.31855	−0.659274	−	0.751903i	$-0.729136\pi$
$227$	−19.8659	−1.31855	−0.659274	+	0.751903i	$0.729136\pi$
$228$	5.67374	0.375753
$229$	12.6389	0.835201	0.417600	−	0.908631i	$-0.362871\pi$
$229$	12.6389	0.835201	0.417600	+	0.908631i	$0.362871\pi$
$230$	45.4740	2.99847
$231$	14.3531	0.944362
$232$	−10.6707	−0.700567
$233$	−21.8249	−1.42980	−0.714898	−	0.699228i	$-0.753527\pi$
$233$	−21.8249	−1.42980	−0.714898	+	0.699228i	$0.753527\pi$
$234$	−0.532739	−0.0348262
$235$	−23.9006	−1.55910
$236$	4.53247	0.295039
$237$	−11.7407	−0.762638
$238$	−3.27903	−0.212548
$239$	22.9048	1.48159	0.740793	−	0.671734i	$-0.234450\pi$
$239$	22.9048	1.48159	0.740793	+	0.671734i	$0.234450\pi$
$240$	9.19422	0.593484
$241$	−21.3224	−1.37350	−0.686748	−	0.726896i	$-0.740962\pi$
$241$	−21.3224	−1.37350	−0.686748	+	0.726896i	$0.740962\pi$
$242$	−15.7874	−1.01485
$243$	−1.00000	−0.0641500
$244$	−3.03740	−0.194450
$245$	5.63021	0.359701
$246$	−14.1200	−0.900255
$247$	3.77725	0.240341
$248$	4.88916	0.310462
$249$	−11.3391	−0.718586
$250$	−45.5629	−2.88165
$251$	7.94727	0.501627	0.250813	−	0.968035i	$-0.419302\pi$
$251$	7.94727	0.501627	0.250813	+	0.968035i	$0.419302\pi$
$252$	−2.02233	−0.127395
$253$	45.4950	2.86025
$254$	−9.26629	−0.581419
$255$	−4.37521	−0.273986
$256$	−14.5366	−0.908535
$257$	4.80365	0.299644	0.149822	−	0.988713i	$-0.452130\pi$
$257$	4.80365	0.299644	0.149822	+	0.988713i	$0.452130\pi$
$258$	−6.51159	−0.405394
$259$	7.81195	0.485411
$260$	−1.43754	−0.0891523
$261$	−3.46636	−0.214563
$262$	13.5641	0.837994
$263$	24.4003	1.50459	0.752293	−	0.658829i	$-0.228948\pi$
$263$	24.4003	1.50459	0.752293	+	0.658829i	$0.228948\pi$
$264$	15.3486	0.944642
$265$	49.1986	3.02225
$266$	−26.4824	−1.62374
$267$	−12.0589	−0.737993
$268$	−6.93715	−0.423754
$269$	−5.17399	−0.315463	−0.157732	−	0.987482i	$-0.550418\pi$
$269$	−5.17399	−0.315463	−0.157732	+	0.987482i	$0.550418\pi$
$270$	4.98367	0.303297
$271$	14.3079	0.869141	0.434571	−	0.900638i	$-0.356900\pi$
$271$	14.3079	0.869141	0.434571	+	0.900638i	$0.356900\pi$
$272$	−2.10144	−0.127418
$273$	−1.34635	−0.0814848
$274$	−18.9213	−1.14308
$275$	−70.5138	−4.25214
$276$	−6.41019	−0.385848
$277$	−4.88785	−0.293682	−0.146841	−	0.989160i	$-0.546911\pi$
$277$	−4.88785	−0.293682	−0.146841	+	0.989160i	$0.546911\pi$
$278$	2.20946	0.132515
$279$	1.58824	0.0950852
$280$	38.7715	2.31704
$281$	17.6270	1.05154	0.525770	−	0.850627i	$-0.323777\pi$
$281$	17.6270	1.05154	0.525770	+	0.850627i	$0.323777\pi$
$282$	−6.22244	−0.370541
$283$	−9.10645	−0.541322	−0.270661	−	0.962675i	$-0.587242\pi$
$283$	−9.10645	−0.541322	−0.270661	+	0.962675i	$0.587242\pi$
$284$	0.773896	0.0459223
$285$	−35.3355	−2.09309
$286$	2.65622	0.157066
$287$	−35.6843	−2.10638
$288$	−3.76303	−0.221739
$289$	1.00000	0.0588235
$290$	17.2752	1.01444
$291$	−5.38336	−0.315578
$292$	−0.928904	−0.0543600
$293$	14.6984	0.858690	0.429345	−	0.903141i	$-0.358745\pi$
$293$	14.6984	0.858690	0.429345	+	0.903141i	$0.358745\pi$
$294$	1.46581	0.0854876
$295$	−28.2278	−1.64349
$296$	8.35380	0.485555
$297$	4.98597	0.289315
$298$	−11.5351	−0.668212
$299$	−4.26754	−0.246798
$300$	9.93531	0.573615
$301$	−16.4563	−0.948523
$302$	−0.431964	−0.0248567
$303$	−6.20613	−0.356533
$304$	−16.9718	−0.973401
$305$	18.9166	1.08316
$306$	−1.13907	−0.0651164
$307$	−23.4361	−1.33757	−0.668784	−	0.743456i	$-0.733185\pi$
$307$	−23.4361	−1.33757	−0.668784	+	0.743456i	$0.733185\pi$
$308$	10.0833	0.574547
$309$	−1.87409	−0.106613
$310$	−7.91525	−0.449556
$311$	−8.85828	−0.502307	−0.251154	−	0.967947i	$-0.580810\pi$
$311$	−8.85828	−0.502307	−0.251154	+	0.967947i	$0.580810\pi$
$312$	−1.43974	−0.0815090
$313$	−31.2974	−1.76903	−0.884516	−	0.466511i	$-0.845511\pi$
$313$	−31.2974	−1.76903	−0.884516	+	0.466511i	$0.845511\pi$
$314$	1.13907	0.0642815
$315$	12.5949	0.709640
$316$	−8.24801	−0.463987
$317$	−12.9463	−0.727139	−0.363569	−	0.931567i	$-0.618442\pi$
$317$	−12.9463	−0.727139	−0.363569	+	0.931567i	$0.618442\pi$
$318$	12.8087	0.718276
$319$	17.2832	0.967673
$320$	37.1422	2.07631
$321$	17.3708	0.969541
$322$	29.9198	1.66737
$323$	8.07630	0.449377
$324$	−0.702517	−0.0390287
$325$	6.61436	0.366899
$326$	−11.6827	−0.647043
$327$	−16.3213	−0.902569
$328$	−38.1594	−2.10700
$329$	−15.7255	−0.866975
$330$	−24.8484	−1.36786
$331$	19.5585	1.07503	0.537517	−	0.843253i	$-0.319362\pi$
$331$	19.5585	1.07503	0.537517	+	0.843253i	$0.319362\pi$
$332$	−7.96590	−0.437186
$333$	2.71372	0.148711
$334$	−5.63834	−0.308516
$335$	43.2039	2.36048
$336$	6.04938	0.330021
$337$	3.47921	0.189525	0.0947625	−	0.995500i	$-0.469791\pi$
$337$	3.47921	0.189525	0.0947625	+	0.995500i	$0.469791\pi$
$338$	14.5588	0.791892
$339$	−15.3088	−0.831459
$340$	−3.07366	−0.166693
$341$	−7.91890	−0.428833
$342$	−9.19948	−0.497451
$343$	−16.4464	−0.888022
$344$	−17.5977	−0.948804
$345$	39.9220	2.14933
$346$	8.31500	0.447017
$347$	7.35053	0.394597	0.197298	−	0.980343i	$-0.436783\pi$
$347$	7.35053	0.394597	0.197298	+	0.980343i	$0.436783\pi$
$348$	−2.43518	−0.130539
$349$	−3.38775	−0.181342	−0.0906711	−	0.995881i	$-0.528901\pi$
$349$	−3.38775	−0.181342	−0.0906711	+	0.995881i	$0.528901\pi$
$350$	−46.3735	−2.47877
$351$	−0.467696	−0.0249638
$352$	18.7624	1.00004
$353$	−17.9533	−0.955556	−0.477778	−	0.878481i	$-0.658558\pi$
$353$	−17.9533	−0.955556	−0.477778	+	0.878481i	$0.658558\pi$
$354$	−7.34902	−0.390596
$355$	−4.81975	−0.255806
$356$	−8.47158	−0.448993
$357$	−2.87869	−0.152356
$358$	−13.3851	−0.707424
$359$	−10.4105	−0.549445	−0.274722	−	0.961524i	$-0.588586\pi$
$359$	−10.4105	−0.549445	−0.274722	+	0.961524i	$0.588586\pi$
$360$	13.4685	0.709850
$361$	46.2266	2.43298
$362$	2.63839	0.138671
$363$	−13.8599	−0.727457
$364$	−0.945834	−0.0495752
$365$	5.78513	0.302807
$366$	4.92488	0.257428
$367$	8.71066	0.454693	0.227346	−	0.973814i	$-0.426995\pi$
$367$	8.71066	0.454693	0.227346	+	0.973814i	$0.426995\pi$
$368$	19.1748	0.999553
$369$	−12.3960	−0.645311
$370$	−13.5243	−0.703094
$371$	32.3705	1.68059
$372$	1.11576	0.0578496
$373$	16.0788	0.832528	0.416264	−	0.909244i	$-0.363339\pi$
$373$	16.0788	0.832528	0.416264	+	0.909244i	$0.363339\pi$
$374$	5.67938	0.293674
$375$	−40.0001	−2.06559
$376$	−16.8162	−0.867232
$377$	−1.62120	−0.0834963
$378$	3.27903	0.168655
$379$	19.8313	1.01866	0.509332	−	0.860570i	$-0.329893\pi$
$379$	19.8313	1.01866	0.509332	+	0.860570i	$0.329893\pi$
$380$	−24.8238	−1.27343
$381$	−8.13495	−0.416766
$382$	5.49044	0.280915
$383$	−24.2060	−1.23687	−0.618436	−	0.785835i	$-0.712233\pi$
$383$	−24.2060	−1.23687	−0.618436	+	0.785835i	$0.712233\pi$
$384$	2.14377	0.109399
$385$	−62.7976	−3.20046
$386$	14.5542	0.740790
$387$	−5.71658	−0.290590
$388$	−3.78190	−0.191997
$389$	30.1449	1.52841	0.764203	−	0.644976i	$-0.223133\pi$
$389$	30.1449	1.52841	0.764203	+	0.644976i	$0.223133\pi$
$390$	2.33084	0.118027
$391$	−9.12460	−0.461451
$392$	3.96137	0.200079
$393$	11.9081	0.600682
$394$	−26.6820	−1.34422
$395$	51.3678	2.58460
$396$	3.50273	0.176019
$397$	7.55264	0.379056	0.189528	−	0.981875i	$-0.439304\pi$
$397$	7.55264	0.379056	0.189528	+	0.981875i	$0.439304\pi$
$398$	−13.3468	−0.669015
$399$	−23.2491	−1.16391
$400$	−29.7194	−1.48597
$401$	−11.2941	−0.564002	−0.282001	−	0.959414i	$-0.590998\pi$
$401$	−11.2941	−0.564002	−0.282001	+	0.959414i	$0.590998\pi$
$402$	11.2480	0.560999
$403$	0.742812	0.0370021
$404$	−4.35991	−0.216914
$405$	4.37521	0.217406
$406$	11.3663	0.564101
$407$	−13.5305	−0.670683
$408$	−3.07836	−0.152401
$409$	−2.15216	−0.106417	−0.0532087	−	0.998583i	$-0.516945\pi$
$409$	−2.15216	−0.106417	−0.0532087	+	0.998583i	$0.516945\pi$
$410$	61.7777	3.05098
$411$	−16.6112	−0.819370
$412$	−1.31658	−0.0648632
$413$	−18.5726	−0.913899
$414$	10.3936	0.510816
$415$	49.6109	2.43530
$416$	−1.75996	−0.0862889
$417$	1.93971	0.0949878
$418$	45.8683	2.24349
$419$	−31.5902	−1.54328	−0.771641	−	0.636058i	$-0.780564\pi$
$419$	−31.5902	−1.54328	−0.771641	+	0.636058i	$0.780564\pi$
$420$	8.84810	0.431743
$421$	−8.34801	−0.406857	−0.203429	−	0.979090i	$-0.565208\pi$
$421$	−8.34801	−0.406857	−0.203429	+	0.979090i	$0.565208\pi$
$422$	6.12802	0.298307
$423$	−5.46273	−0.265607
$424$	34.6157	1.68109
$425$	14.1424	0.686009
$426$	−1.25481	−0.0607955
$427$	12.4463	0.602318
$428$	12.2033	0.589867
$429$	2.33192	0.112586
$430$	28.4896	1.37389
$431$	22.4228	1.08007	0.540034	−	0.841643i	$-0.318412\pi$
$431$	22.4228	1.08007	0.540034	+	0.841643i	$0.318412\pi$
$432$	2.10144	0.101105
$433$	−17.8406	−0.857362	−0.428681	−	0.903456i	$-0.641022\pi$
$433$	−17.8406	−0.857362	−0.428681	+	0.903456i	$0.641022\pi$
$434$	−5.20788	−0.249986
$435$	15.1661	0.727157
$436$	−11.4660	−0.549121
$437$	−73.6930	−3.52521
$438$	1.50614	0.0719661
$439$	−19.3994	−0.925884	−0.462942	−	0.886389i	$-0.653206\pi$
$439$	−19.3994	−0.925884	−0.462942	+	0.886389i	$0.653206\pi$
$440$	−67.1534	−3.20141
$441$	1.28684	0.0612783
$442$	−0.532739	−0.0253398
$443$	10.5460	0.501055	0.250527	−	0.968110i	$-0.419396\pi$
$443$	10.5460	0.501055	0.250527	+	0.968110i	$0.419396\pi$
$444$	1.90643	0.0904753
$445$	52.7602	2.50107
$446$	−28.5759	−1.35311
$447$	−10.1268	−0.478981
$448$	24.4379	1.15458
$449$	29.8242	1.40749	0.703746	−	0.710451i	$-0.251509\pi$
$449$	29.8242	1.40749	0.703746	+	0.710451i	$0.251509\pi$
$450$	−16.1092	−0.759397
$451$	61.8062	2.91034
$452$	−10.7547	−0.505858
$453$	−0.379225	−0.0178175
$454$	22.6287	1.06202
$455$	5.89056	0.276154
$456$	−24.8618	−1.16426
$457$	−29.2237	−1.36703	−0.683513	−	0.729938i	$-0.739549\pi$
$457$	−29.2237	−1.36703	−0.683513	+	0.729938i	$0.739549\pi$
$458$	−14.3966	−0.672708
$459$	−1.00000	−0.0466760
$460$	28.0459	1.30765
$461$	−14.1191	−0.657594	−0.328797	−	0.944401i	$-0.606643\pi$
$461$	−14.1191	−0.657594	−0.328797	+	0.944401i	$0.606643\pi$
$462$	−16.3492	−0.760631
$463$	−6.13852	−0.285281	−0.142641	−	0.989775i	$-0.545559\pi$
$463$	−6.13852	−0.285281	−0.142641	+	0.989775i	$0.545559\pi$
$464$	7.28434	0.338167
$465$	−6.94886	−0.322246
$466$	24.8601	1.15162
$467$	−29.5051	−1.36533	−0.682667	−	0.730730i	$-0.739180\pi$
$467$	−29.5051	−1.36533	−0.682667	+	0.730730i	$0.739180\pi$
$468$	−0.328564	−0.0151879
$469$	28.4262	1.31260
$470$	27.2245	1.25577
$471$	1.00000	0.0460776
$472$	−19.8608	−0.914169
$473$	28.5027	1.31056
$474$	13.3734	0.614263
$475$	114.219	5.24071
$476$	−2.02233	−0.0926932
$477$	11.2449	0.514867
$478$	−26.0901	−1.19334
$479$	−10.1179	−0.462299	−0.231149	−	0.972918i	$-0.574249\pi$
$479$	−10.1179	−0.462299	−0.231149	+	0.972918i	$0.574249\pi$
$480$	16.4641	0.751478
$481$	1.26919	0.0578703
$482$	24.2877	1.10628
$483$	26.2669	1.19518
$484$	−9.73682	−0.442583
$485$	23.5533	1.06950
$486$	1.13907	0.0516693
$487$	−33.3921	−1.51314	−0.756570	−	0.653913i	$-0.773126\pi$
$487$	−33.3921	−1.51314	−0.756570	+	0.653913i	$0.773126\pi$
$488$	13.3096	0.602496
$489$	−10.2563	−0.463807
$490$	−6.41321	−0.289719
$491$	−17.0623	−0.770013	−0.385006	−	0.922914i	$-0.625801\pi$
$491$	−17.0623	−0.770013	−0.385006	+	0.922914i	$0.625801\pi$
$492$	−8.70842	−0.392606
$493$	−3.46636	−0.156117
$494$	−4.30256	−0.193581
$495$	−21.8147	−0.980496
$496$	−3.33758	−0.149862
$497$	−3.17118	−0.142247
$498$	12.9160	0.578781
$499$	14.0334	0.628221	0.314111	−	0.949386i	$-0.398294\pi$
$499$	14.0334	0.628221	0.314111	+	0.949386i	$0.398294\pi$
$500$	−28.1007	−1.25670
$501$	−4.94994	−0.221147
$502$	−9.05250	−0.404033
$503$	5.14721	0.229503	0.114751	−	0.993394i	$-0.463393\pi$
$503$	5.14721	0.229503	0.114751	+	0.993394i	$0.463393\pi$
$504$	8.86164	0.394729
$505$	27.1531	1.20830
$506$	−51.8220	−2.30377
$507$	12.7813	0.567636
$508$	−5.71494	−0.253560
$509$	−13.5361	−0.599979	−0.299989	−	0.953943i	$-0.596983\pi$
$509$	−13.5361	−0.599979	−0.299989	+	0.953943i	$0.596983\pi$
$510$	4.98367	0.220681
$511$	3.80635	0.168383
$512$	20.8457	0.921259
$513$	−8.07630	−0.356577
$514$	−5.47170	−0.241346
$515$	8.19953	0.361314
$516$	−4.01600	−0.176794
$517$	27.2370	1.19788
$518$	−8.89836	−0.390972
$519$	7.29981	0.320426
$520$	6.29914	0.276236
$521$	10.8607	0.475814	0.237907	−	0.971288i	$-0.423539\pi$
$521$	10.8607	0.475814	0.237907	+	0.971288i	$0.423539\pi$
$522$	3.94844	0.172818
$523$	27.7013	1.21129	0.605646	−	0.795734i	$-0.292915\pi$
$523$	27.7013	1.21129	0.605646	+	0.795734i	$0.292915\pi$
$524$	8.36561	0.365453
$525$	−40.7117	−1.77680
$526$	−27.7937	−1.21186
$527$	1.58824	0.0691847
$528$	−10.4777	−0.455983
$529$	60.2583	2.61993
$530$	−56.0407	−2.43425
$531$	−6.45176	−0.279983
$532$	−16.3329	−0.708122
$533$	−5.79757	−0.251121
$534$	13.7359	0.594412
$535$	−76.0007	−3.28580
$536$	30.3979	1.31299
$537$	−11.7509	−0.507088
$538$	5.89354	0.254088
$539$	−6.41617	−0.276364
$540$	3.07366	0.132269
$541$	19.0778	0.820217	0.410108	−	0.912037i	$-0.365491\pi$
$541$	19.0778	0.820217	0.410108	+	0.912037i	$0.365491\pi$
$542$	−16.2977	−0.700045
$543$	2.31626	0.0994004
$544$	−3.76303	−0.161339
$545$	71.4090	3.05882
$546$	1.53359	0.0656316
$547$	37.9554	1.62286	0.811428	−	0.584452i	$-0.198691\pi$
$547$	37.9554	1.62286	0.811428	+	0.584452i	$0.198691\pi$
$548$	−11.6696	−0.498503
$549$	4.32360	0.184527
$550$	80.3202	3.42487
$551$	−27.9954	−1.19264
$552$	28.0888	1.19554
$553$	33.7977	1.43722
$554$	5.56760	0.236545
$555$	−11.8731	−0.503984
$556$	1.36268	0.0577904
$557$	−8.02480	−0.340022	−0.170011	−	0.985442i	$-0.554380\pi$
$557$	−8.02480	−0.340022	−0.170011	+	0.985442i	$0.554380\pi$
$558$	−1.80911	−0.0765859
$559$	−2.67362	−0.113082
$560$	−26.4673	−1.11845
$561$	4.98597	0.210508
$562$	−20.0784	−0.846958
$563$	7.03696	0.296572	0.148286	−	0.988944i	$-0.452624\pi$
$563$	7.03696	0.296572	0.148286	+	0.988944i	$0.452624\pi$
$564$	−3.83766	−0.161595
$565$	66.9791	2.81783
$566$	10.3729	0.436005
$567$	2.87869	0.120894
$568$	−3.39113	−0.142289
$569$	44.9231	1.88327	0.941637	−	0.336630i	$-0.109287\pi$
$569$	44.9231	1.88327	0.941637	+	0.336630i	$0.109287\pi$
$570$	40.2496	1.68587
$571$	2.58815	0.108311	0.0541553	−	0.998533i	$-0.482753\pi$
$571$	2.58815	0.108311	0.0541553	+	0.998533i	$0.482753\pi$
$572$	1.63821	0.0684971
$573$	4.82010	0.201363
$574$	40.6469	1.69657
$575$	−129.044	−5.38151
$576$	8.48923	0.353718
$577$	−0.206071	−0.00857886	−0.00428943	−	0.999991i	$-0.501365\pi$
$577$	−0.206071	−0.00857886	−0.00428943	+	0.999991i	$0.501365\pi$
$578$	−1.13907	−0.0473791
$579$	12.7773	0.531005
$580$	10.6544	0.442401
$581$	32.6417	1.35421
$582$	6.13203	0.254181
$583$	−56.0666	−2.32204
$584$	4.07037	0.168433
$585$	2.04627	0.0846027
$586$	−16.7425	−0.691627
$587$	17.3846	0.717539	0.358770	−	0.933426i	$-0.383196\pi$
$587$	17.3846	0.717539	0.358770	+	0.933426i	$0.383196\pi$
$588$	0.904030	0.0372816
$589$	12.8271	0.528530
$590$	32.1535	1.32374
$591$	−23.4244	−0.963550
$592$	−5.70270	−0.234380
$593$	−31.2747	−1.28430	−0.642148	−	0.766581i	$-0.721957\pi$
$593$	−31.2747	−1.28430	−0.642148	+	0.766581i	$0.721957\pi$
$594$	−5.67938	−0.233028
$595$	12.5949	0.516339
$596$	−7.11424	−0.291411
$597$	−11.7173	−0.479556
$598$	4.86103	0.198782
$599$	−21.4045	−0.874563	−0.437282	−	0.899325i	$-0.644059\pi$
$599$	−21.4045	−0.874563	−0.437282	+	0.899325i	$0.644059\pi$
$600$	−43.5355	−1.77733
$601$	−16.2622	−0.663348	−0.331674	−	0.943394i	$-0.607613\pi$
$601$	−16.2622	−0.663348	−0.331674	+	0.943394i	$0.607613\pi$
$602$	18.7448	0.763983
$603$	9.87470	0.402129
$604$	−0.266412	−0.0108401
$605$	60.6400	2.46537
$606$	7.06922	0.287167
$607$	−6.40529	−0.259983	−0.129991	−	0.991515i	$-0.541495\pi$
$607$	−6.40529	−0.259983	−0.129991	+	0.991515i	$0.541495\pi$
$608$	−30.3914	−1.23253
$609$	9.97858	0.404353
$610$	−21.5474	−0.872428
$611$	−2.55490	−0.103360
$612$	−0.702517	−0.0283976
$613$	19.5257	0.788634	0.394317	−	0.918974i	$-0.370981\pi$
$613$	19.5257	0.788634	0.394317	+	0.918974i	$0.370981\pi$
$614$	26.6954	1.07734
$615$	54.2352	2.18697
$616$	−44.1839	−1.78022
$617$	−8.26402	−0.332697	−0.166349	−	0.986067i	$-0.553198\pi$
$617$	−8.26402	−0.332697	−0.166349	+	0.986067i	$0.553198\pi$
$618$	2.13472	0.0858711
$619$	30.2144	1.21442	0.607210	−	0.794541i	$-0.292289\pi$
$619$	30.2144	1.21442	0.607210	+	0.794541i	$0.292289\pi$
$620$	−4.88170	−0.196054
$621$	9.12460	0.366158
$622$	10.0902	0.404581
$623$	34.7138	1.39078
$624$	0.982833	0.0393448
$625$	104.296	4.17186
$626$	35.6499	1.42486
$627$	40.2682	1.60816
$628$	0.702517	0.0280335
$629$	2.71372	0.108203
$630$	−14.3464	−0.571576
$631$	22.6645	0.902260	0.451130	−	0.892458i	$-0.351021\pi$
$631$	22.6645	0.902260	0.451130	+	0.892458i	$0.351021\pi$
$632$	36.1420	1.43765
$633$	5.37984	0.213829
$634$	14.7468	0.585670
$635$	35.5921	1.41243
$636$	7.89971	0.313244
$637$	0.601852	0.0238462
$638$	−19.6868	−0.779407
$639$	−1.10160	−0.0435788
$640$	−9.37945	−0.370756
$641$	12.4550	0.491943	0.245971	−	0.969277i	$-0.420893\pi$
$641$	12.4550	0.491943	0.245971	+	0.969277i	$0.420893\pi$
$642$	−19.7865	−0.780912
$643$	6.77735	0.267272	0.133636	−	0.991030i	$-0.457335\pi$
$643$	6.77735	0.267272	0.133636	+	0.991030i	$0.457335\pi$
$644$	18.4529	0.727147
$645$	25.0112	0.984816
$646$	−9.19948	−0.361949
$647$	4.58103	0.180099	0.0900495	−	0.995937i	$-0.471297\pi$
$647$	4.58103	0.180099	0.0900495	+	0.995937i	$0.471297\pi$
$648$	3.07836	0.120929
$649$	32.1683	1.26272
$650$	−7.53423	−0.295517
$651$	−4.57204	−0.179192
$652$	−7.20524	−0.282179
$653$	38.1118	1.49143	0.745715	−	0.666265i	$-0.232108\pi$
$653$	38.1118	1.49143	0.745715	+	0.666265i	$0.232108\pi$
$654$	18.5911	0.726969
$655$	−52.1002	−2.03572
$656$	26.0495	1.01706
$657$	1.32225	0.0515860
$658$	17.9125	0.698300
$659$	32.5535	1.26811	0.634053	−	0.773290i	$-0.281390\pi$
$659$	32.5535	1.26811	0.634053	+	0.773290i	$0.281390\pi$
$660$	−15.3252	−0.596531
$661$	5.59121	0.217473	0.108736	−	0.994071i	$-0.465320\pi$
$661$	5.59121	0.217473	0.108736	+	0.994071i	$0.465320\pi$
$662$	−22.2786	−0.865881
$663$	−0.467696	−0.0181638
$664$	34.9058	1.35461
$665$	101.720	3.94453
$666$	−3.09112	−0.119778
$667$	31.6292	1.22469
$668$	−3.47742	−0.134545
$669$	−25.0870	−0.969919
$670$	−49.2123	−1.90124
$671$	−21.5573	−0.832211
$672$	10.8326	0.417877
$673$	−10.8811	−0.419437	−0.209718	−	0.977762i	$-0.567255\pi$
$673$	−10.8811	−0.419437	−0.209718	+	0.977762i	$0.567255\pi$
$674$	−3.96307	−0.152652
$675$	−14.1424	−0.544343
$676$	8.97905	0.345348
$677$	0.199946	0.00768454	0.00384227	−	0.999993i	$-0.498777\pi$
$677$	0.199946	0.00768454	0.00384227	+	0.999993i	$0.498777\pi$
$678$	17.4378	0.669694
$679$	15.4970	0.594721
$680$	13.4685	0.516492
$681$	19.8659	0.761264
$682$	9.02019	0.345401
$683$	−17.0356	−0.651849	−0.325924	−	0.945396i	$-0.605675\pi$
$683$	−17.0356	−0.651849	−0.325924	+	0.945396i	$0.605675\pi$
$684$	−5.67374	−0.216941
$685$	72.6774	2.77686
$686$	18.7336	0.715253
$687$	−12.6389	−0.482203
$688$	12.0130	0.457992
$689$	5.25918	0.200359
$690$	−45.4740	−1.73117
$691$	−25.1389	−0.956329	−0.478165	−	0.878270i	$-0.658698\pi$
$691$	−25.1389	−0.956329	−0.478165	+	0.878270i	$0.658698\pi$
$692$	5.12824	0.194946
$693$	−14.3531	−0.545228
$694$	−8.37277	−0.317826
$695$	−8.48661	−0.321916
$696$	10.6707	0.404472
$697$	−12.3960	−0.469533
$698$	3.85889	0.146061
$699$	21.8249	0.825493
$700$	−28.6006	−1.08100
$701$	18.2053	0.687606	0.343803	−	0.939042i	$-0.388285\pi$
$701$	18.2053	0.687606	0.343803	+	0.939042i	$0.388285\pi$
$702$	0.532739	0.0201069
$703$	21.9168	0.826608
$704$	−42.3271	−1.59526
$705$	23.9006	0.900148
$706$	20.4500	0.769648
$707$	17.8655	0.671901
$708$	−4.53247	−0.170341
$709$	33.2470	1.24862	0.624308	−	0.781178i	$-0.285381\pi$
$709$	33.2470	1.24862	0.624308	+	0.781178i	$0.285381\pi$
$710$	5.49003	0.206037
$711$	11.7407	0.440309
$712$	37.1216	1.39119
$713$	−14.4920	−0.542730
$714$	3.27903	0.122715
$715$	−10.2026	−0.381557
$716$	−8.25519	−0.308511
$717$	−22.9048	−0.855394
$718$	11.8583	0.442547
$719$	−11.3965	−0.425019	−0.212510	−	0.977159i	$-0.568164\pi$
$719$	−11.3965	−0.425019	−0.212510	+	0.977159i	$0.568164\pi$
$720$	−9.19422	−0.342648
$721$	5.39492	0.200917
$722$	−52.6554	−1.95963
$723$	21.3224	0.792988
$724$	1.62721	0.0604749
$725$	−49.0228	−1.82066
$726$	15.7874	0.585926
$727$	−13.4770	−0.499834	−0.249917	−	0.968267i	$-0.580403\pi$
$727$	−13.4770	−0.499834	−0.249917	+	0.968267i	$0.580403\pi$
$728$	4.14455	0.153607
$729$	1.00000	0.0370370
$730$	−6.58967	−0.243895
$731$	−5.71658	−0.211435
$732$	3.03740	0.112266
$733$	−25.0273	−0.924404	−0.462202	−	0.886775i	$-0.652940\pi$
$733$	−25.0273	−0.924404	−0.462202	+	0.886775i	$0.652940\pi$
$734$	−9.92206	−0.366230
$735$	−5.63021	−0.207674
$736$	34.3362	1.26565
$737$	−49.2350	−1.81359
$738$	14.1200	0.519763
$739$	−50.3160	−1.85091	−0.925453	−	0.378864i	$-0.876315\pi$
$739$	−50.3160	−1.85091	−0.925453	+	0.378864i	$0.876315\pi$
$740$	−8.34104	−0.306623
$741$	−3.77725	−0.138761
$742$	−36.8723	−1.35362
$743$	42.2671	1.55063	0.775315	−	0.631575i	$-0.217591\pi$
$743$	42.2671	1.55063	0.775315	+	0.631575i	$0.217591\pi$
$744$	−4.88916	−0.179245
$745$	44.3068	1.62328
$746$	−18.3149	−0.670556
$747$	11.3391	0.414876
$748$	3.50273	0.128072
$749$	−50.0050	−1.82714
$750$	45.5629	1.66372
$751$	−16.8109	−0.613437	−0.306719	−	0.951800i	$-0.599231\pi$
$751$	−16.8109	−0.613437	−0.306719	+	0.951800i	$0.599231\pi$
$752$	11.4796	0.418617
$753$	−7.94727	−0.289614
$754$	1.84667	0.0672516
$755$	1.65919	0.0603840
$756$	2.02233	0.0735513
$757$	−17.0726	−0.620516	−0.310258	−	0.950652i	$-0.600415\pi$
$757$	−17.0726	−0.620516	−0.310258	+	0.950652i	$0.600415\pi$
$758$	−22.5892	−0.820477
$759$	−45.4950	−1.65136
$760$	108.775	3.94570
$761$	−19.7650	−0.716481	−0.358241	−	0.933629i	$-0.616623\pi$
$761$	−19.7650	−0.716481	−0.358241	+	0.933629i	$0.616623\pi$
$762$	9.26629	0.335682
$763$	46.9839	1.70093
$764$	3.38620	0.122509
$765$	4.37521	0.158186
$766$	27.5724	0.996232
$767$	−3.01746	−0.108954
$768$	14.5366	0.524543
$769$	19.5270	0.704163	0.352082	−	0.935969i	$-0.385474\pi$
$769$	19.5270	0.704163	0.352082	+	0.935969i	$0.385474\pi$
$770$	71.5309	2.57780
$771$	−4.80365	−0.172999
$772$	8.97624	0.323062
$773$	26.9377	0.968882	0.484441	−	0.874824i	$-0.339023\pi$
$773$	26.9377	0.968882	0.484441	+	0.874824i	$0.339023\pi$
$774$	6.51159	0.234054
$775$	22.4615	0.806842
$776$	16.5719	0.594897
$777$	−7.81195	−0.280252
$778$	−34.3371	−1.23105
$779$	−100.114	−3.58696
$780$	1.43754	0.0514721
$781$	5.49257	0.196540
$782$	10.3936	0.371673
$783$	3.46636	0.123878
$784$	−2.70422	−0.0965793
$785$	−4.37521	−0.156158
$786$	−13.5641	−0.483816
$787$	−8.29940	−0.295842	−0.147921	−	0.988999i	$-0.547258\pi$
$787$	−8.29940	−0.295842	−0.147921	+	0.988999i	$0.547258\pi$
$788$	−16.4560	−0.586222
$789$	−24.4003	−0.868673
$790$	−58.5116	−2.08175
$791$	44.0692	1.56692
$792$	−15.3486	−0.545389
$793$	2.02213	0.0718079
$794$	−8.60299	−0.305309
$795$	−49.1986	−1.74490
$796$	−8.23158	−0.291761
$797$	−26.3607	−0.933745	−0.466873	−	0.884325i	$-0.654619\pi$
$797$	−26.3607	−0.933745	−0.466873	+	0.884325i	$0.654619\pi$
$798$	26.4824	0.937468
$799$	−5.46273	−0.193257
$800$	−53.2185	−1.88156
$801$	12.0589	0.426080
$802$	12.8648	0.454273
$803$	−6.59271	−0.232652
$804$	6.93715	0.244654
$805$	−114.923	−4.05050
$806$	−0.846115	−0.0298031
$807$	5.17399	0.182133
$808$	19.1047	0.672101
$809$	−17.5473	−0.616931	−0.308466	−	0.951236i	$-0.599815\pi$
$809$	−17.5473	−0.616931	−0.308466	+	0.951236i	$0.599815\pi$
$810$	−4.98367	−0.175108
$811$	0.790148	0.0277459	0.0138729	−	0.999904i	$-0.495584\pi$
$811$	0.790148	0.0277459	0.0138729	+	0.999904i	$0.495584\pi$
$812$	7.01012	0.246007
$813$	−14.3079	−0.501799
$814$	15.4122	0.540198
$815$	44.8735	1.57185
$816$	2.10144	0.0735650
$817$	−46.1688	−1.61524
$818$	2.45146	0.0857133
$819$	1.34635	0.0470453
$820$	38.1011	1.33055
$821$	44.6607	1.55867	0.779334	−	0.626609i	$-0.215558\pi$
$821$	44.6607	1.55867	0.779334	+	0.626609i	$0.215558\pi$
$822$	18.9213	0.659957
$823$	−29.8717	−1.04126	−0.520631	−	0.853782i	$-0.674303\pi$
$823$	−29.8717	−1.04126	−0.520631	+	0.853782i	$0.674303\pi$
$824$	5.76912	0.200977
$825$	70.5138	2.45498
$826$	21.1555	0.736095
$827$	−50.7730	−1.76555	−0.882775	−	0.469796i	$-0.844328\pi$
$827$	−50.7730	−1.76555	−0.882775	+	0.469796i	$0.844328\pi$
$828$	6.41019	0.222769
$829$	−1.80004	−0.0625181	−0.0312590	−	0.999511i	$-0.509952\pi$
$829$	−1.80004	−0.0625181	−0.0312590	+	0.999511i	$0.509952\pi$
$830$	−56.5103	−1.96150
$831$	4.88785	0.169557
$832$	3.97038	0.137648
$833$	1.28684	0.0445865
$834$	−2.20946	−0.0765074
$835$	21.6570	0.749472
$836$	28.2891	0.978399
$837$	−1.58824	−0.0548975
$838$	35.9835	1.24303
$839$	37.5400	1.29603	0.648013	−	0.761629i	$-0.275600\pi$
$839$	37.5400	1.29603	0.648013	+	0.761629i	$0.275600\pi$
$840$	−38.7715	−1.33774
$841$	−16.9843	−0.585666
$842$	9.50898	0.327701
$843$	−17.6270	−0.607107
$844$	3.77943	0.130093
$845$	−55.9207	−1.92373
$846$	6.22244	0.213932
$847$	39.8984	1.37092
$848$	−23.6304	−0.811470
$849$	9.10645	0.312533
$850$	−16.1092	−0.552543
$851$	−24.7616	−0.848816
$852$	−0.773896	−0.0265132
$853$	18.1192	0.620391	0.310195	−	0.950673i	$-0.399606\pi$
$853$	18.1192	0.620391	0.310195	+	0.950673i	$0.399606\pi$
$854$	−14.1772	−0.485134
$855$	35.3355	1.20845
$856$	−53.4734	−1.82768
$857$	−11.8333	−0.404219	−0.202109	−	0.979363i	$-0.564780\pi$
$857$	−11.8333	−0.404219	−0.202109	+	0.979363i	$0.564780\pi$
$858$	−2.65622	−0.0906819
$859$	44.7281	1.52610	0.763051	−	0.646338i	$-0.223700\pi$
$859$	44.7281	1.52610	0.763051	+	0.646338i	$0.223700\pi$
$860$	17.5708	0.599160
$861$	35.6843	1.21612
$862$	−25.5411	−0.869935
$863$	48.0892	1.63698	0.818488	−	0.574524i	$-0.194813\pi$
$863$	48.0892	1.63698	0.818488	+	0.574524i	$0.194813\pi$
$864$	3.76303	0.128021
$865$	−31.9382	−1.08593
$866$	20.3217	0.690558
$867$	−1.00000	−0.0339618
$868$	−3.21193	−0.109020
$869$	−58.5386	−1.98579
$870$	−17.2752	−0.585685
$871$	4.61836	0.156487
$872$	50.2428	1.70143
$873$	5.38336	0.182199
$874$	83.9416	2.83937
$875$	115.148	3.89270
$876$	0.928904	0.0313848
$877$	−3.73764	−0.126211	−0.0631056	−	0.998007i	$-0.520101\pi$
$877$	−3.73764	−0.126211	−0.0631056	+	0.998007i	$0.520101\pi$
$878$	22.0973	0.745748
$879$	−14.6984	−0.495765
$880$	45.8421	1.54534
$881$	9.72584	0.327672	0.163836	−	0.986488i	$-0.447613\pi$
$881$	9.72584	0.327672	0.163836	+	0.986488i	$0.447613\pi$
$882$	−1.46581	−0.0493563
$883$	−55.1799	−1.85695	−0.928476	−	0.371392i	$-0.878881\pi$
$883$	−55.1799	−1.85695	−0.928476	+	0.371392i	$0.878881\pi$
$884$	−0.328564	−0.0110508
$885$	28.2278	0.948867
$886$	−12.0126	−0.403572
$887$	−6.99571	−0.234893	−0.117446	−	0.993079i	$-0.537471\pi$
$887$	−6.99571	−0.234893	−0.117446	+	0.993079i	$0.537471\pi$
$888$	−8.35380	−0.280335
$889$	23.4180	0.785414
$890$	−60.0976	−2.01448
$891$	−4.98597	−0.167036
$892$	−17.6240	−0.590096
$893$	−44.1186	−1.47637
$894$	11.5351	0.385793
$895$	51.4125	1.71853
$896$	−6.17126	−0.206167
$897$	4.26754	0.142489
$898$	−33.9719	−1.13366
$899$	−5.50541	−0.183616
$900$	−9.93531	−0.331177
$901$	11.2449	0.374621
$902$	−70.4017	−2.34412
$903$	16.4563	0.547630
$904$	47.1259	1.56739
$905$	−10.1341	−0.336870
$906$	0.431964	0.0143510
$907$	18.7946	0.624064	0.312032	−	0.950072i	$-0.398990\pi$
$907$	18.7946	0.624064	0.312032	+	0.950072i	$0.398990\pi$
$908$	13.9562	0.463151
$909$	6.20613	0.205844
$910$	−6.70977	−0.222427
$911$	−20.3712	−0.674928	−0.337464	−	0.941338i	$-0.609569\pi$
$911$	−20.3712	−0.674928	−0.337464	+	0.941338i	$0.609569\pi$
$912$	16.9718	0.561993
$913$	−56.5364	−1.87108
$914$	33.2879	1.10106
$915$	−18.9166	−0.625364
$916$	−8.87903	−0.293371
$917$	−34.2796	−1.13201
$918$	1.13907	0.0375949
$919$	−51.9071	−1.71226	−0.856128	−	0.516764i	$-0.827137\pi$
$919$	−51.9071	−1.71226	−0.856128	+	0.516764i	$0.827137\pi$
$920$	−122.894	−4.05170
$921$	23.4361	0.772246
$922$	16.0827	0.529656
$923$	−0.515216	−0.0169585
$924$	−10.0833	−0.331715
$925$	38.3786	1.26188
$926$	6.99221	0.229778
$927$	1.87409	0.0615532
$928$	13.0440	0.428192
$929$	−27.3628	−0.897743	−0.448872	−	0.893596i	$-0.648174\pi$
$929$	−27.3628	−0.897743	−0.448872	+	0.893596i	$0.648174\pi$
$930$	7.91525	0.259551
$931$	10.3929	0.340615
$932$	15.3324	0.502228
$933$	8.85828	0.290007
$934$	33.6084	1.09970
$935$	−21.8147	−0.713416
$936$	1.43974	0.0470592
$937$	12.8536	0.419910	0.209955	−	0.977711i	$-0.432668\pi$
$937$	12.8536	0.419910	0.209955	+	0.977711i	$0.432668\pi$
$938$	−32.3795	−1.05723
$939$	31.2974	1.02135
$940$	16.7906	0.547648
$941$	28.4152	0.926309	0.463154	−	0.886278i	$-0.346718\pi$
$941$	28.4152	0.926309	0.463154	+	0.886278i	$0.346718\pi$
$942$	−1.13907	−0.0371129
$943$	113.109	3.68333
$944$	13.5580	0.441274
$945$	−12.5949	−0.409711
$946$	−32.4666	−1.05558
$947$	41.1265	1.33643	0.668216	−	0.743968i	$-0.267058\pi$
$947$	41.1265	1.33643	0.668216	+	0.743968i	$0.267058\pi$
$948$	8.24801	0.267883
$949$	0.618412	0.0200745
$950$	−130.103	−4.22110
$951$	12.9463	0.419814
$952$	8.86164	0.287207
$953$	37.3979	1.21144	0.605719	−	0.795679i	$-0.292886\pi$
$953$	37.3979	1.21144	0.605719	+	0.795679i	$0.292886\pi$
$954$	−12.8087	−0.414697
$955$	−21.0889	−0.682422
$956$	−16.0910	−0.520419
$957$	−17.2832	−0.558686
$958$	11.5250	0.372356
$959$	47.8184	1.54414
$960$	−37.1422	−1.19876
$961$	−28.4775	−0.918629
$962$	−1.44570	−0.0466113
$963$	−17.3708	−0.559765
$964$	14.9793	0.482452
$965$	−55.9032	−1.79959
$966$	−29.9198	−0.962655
$967$	1.94856	0.0626613	0.0313307	−	0.999509i	$-0.490026\pi$
$967$	1.94856	0.0626613	0.0313307	+	0.999509i	$0.490026\pi$
$968$	42.6658	1.37133
$969$	−8.07630	−0.259448
$970$	−26.8289	−0.861424
$971$	−25.9701	−0.833420	−0.416710	−	0.909040i	$-0.636817\pi$
$971$	−25.9701	−0.833420	−0.416710	+	0.909040i	$0.636817\pi$
$972$	0.702517	0.0225332
$973$	−5.58381	−0.179009
$974$	38.0360	1.21875
$975$	−6.61436	−0.211829
$976$	−9.08576	−0.290828
$977$	34.3682	1.09954	0.549768	−	0.835317i	$-0.314716\pi$
$977$	34.3682	1.09954	0.549768	+	0.835317i	$0.314716\pi$
$978$	11.6827	0.373571
$979$	−60.1253	−1.92161
$980$	−3.95532	−0.126348
$981$	16.3213	0.521098
$982$	19.4352	0.620203
$983$	−2.39891	−0.0765134	−0.0382567	−	0.999268i	$-0.512180\pi$
$983$	−2.39891	−0.0765134	−0.0382567	+	0.999268i	$0.512180\pi$
$984$	38.1594	1.21648
$985$	102.486	3.26549
$986$	3.94844	0.125744
$987$	15.7255	0.500548
$988$	−2.65358	−0.0844218
$989$	52.1615	1.65864
$990$	24.8484	0.789735
$991$	−51.5716	−1.63823	−0.819113	−	0.573633i	$-0.805534\pi$
$991$	−51.5716	−1.63823	−0.819113	+	0.573633i	$0.805534\pi$
$992$	−5.97659	−0.189757
$993$	−19.5585	−0.620671
$994$	3.61219	0.114572
$995$	51.2655	1.62523
$996$	7.96590	0.252409
$997$	−1.30413	−0.0413021	−0.0206511	−	0.999787i	$-0.506574\pi$
$997$	−1.30413	−0.0413021	−0.0206511	+	0.999787i	$0.506574\pi$
$998$	−15.9850	−0.505997
$999$	−2.71372	−0.0858582

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.j.1.21	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.j.1.21	✓	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)

\(f(q)\)	\(=\)	\(q-1.13907 q^{2} -1.00000 q^{3} -0.702517 q^{4} +4.37521 q^{5} +1.13907 q^{6} +2.87869 q^{7} +3.07836 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.13907 q^{2} -1.00000 q^{3} -0.702517 q^{4} +4.37521 q^{5} +1.13907 q^{6} +2.87869 q^{7} +3.07836 q^{8} +1.00000 q^{9} -4.98367 q^{10} -4.98597 q^{11} +0.702517 q^{12} +0.467696 q^{13} -3.27903 q^{14} -4.37521 q^{15} -2.10144 q^{16} +1.00000 q^{17} -1.13907 q^{18} +8.07630 q^{19} -3.07366 q^{20} -2.87869 q^{21} +5.67938 q^{22} -9.12460 q^{23} -3.07836 q^{24} +14.1424 q^{25} -0.532739 q^{26} -1.00000 q^{27} -2.02233 q^{28} -3.46636 q^{29} +4.98367 q^{30} +1.58824 q^{31} -3.76303 q^{32} +4.98597 q^{33} -1.13907 q^{34} +12.5949 q^{35} -0.702517 q^{36} +2.71372 q^{37} -9.19948 q^{38} -0.467696 q^{39} +13.4685 q^{40} -12.3960 q^{41} +3.27903 q^{42} -5.71658 q^{43} +3.50273 q^{44} +4.37521 q^{45} +10.3936 q^{46} -5.46273 q^{47} +2.10144 q^{48} +1.28684 q^{49} -16.1092 q^{50} -1.00000 q^{51} -0.328564 q^{52} +11.2449 q^{53} +1.13907 q^{54} -21.8147 q^{55} +8.86164 q^{56} -8.07630 q^{57} +3.94844 q^{58} -6.45176 q^{59} +3.07366 q^{60} +4.32360 q^{61} -1.80911 q^{62} +2.87869 q^{63} +8.48923 q^{64} +2.04627 q^{65} -5.67938 q^{66} +9.87470 q^{67} -0.702517 q^{68} +9.12460 q^{69} -14.3464 q^{70} -1.10160 q^{71} +3.07836 q^{72} +1.32225 q^{73} -3.09112 q^{74} -14.1424 q^{75} -5.67374 q^{76} -14.3531 q^{77} +0.532739 q^{78} +11.7407 q^{79} -9.19422 q^{80} +1.00000 q^{81} +14.1200 q^{82} +11.3391 q^{83} +2.02233 q^{84} +4.37521 q^{85} +6.51159 q^{86} +3.46636 q^{87} -15.3486 q^{88} +12.0589 q^{89} -4.98367 q^{90} +1.34635 q^{91} +6.41019 q^{92} -1.58824 q^{93} +6.22244 q^{94} +35.3355 q^{95} +3.76303 q^{96} +5.38336 q^{97} -1.46581 q^{98} -4.98597 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9}+O(q^{10}) \) 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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