LMFDB - Embedded newform 8002.2.a.g.1.5

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			1.5
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)

$f(q)$	$=$	$q+1.00000 q^{2} -2.82799 q^{3} +1.00000 q^{4} +4.14459 q^{5} -2.82799 q^{6} +4.30276 q^{7} +1.00000 q^{8} +4.99754 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.82799 q^{3} +1.00000 q^{4} +4.14459 q^{5} -2.82799 q^{6} +4.30276 q^{7} +1.00000 q^{8} +4.99754 q^{9} +4.14459 q^{10} +5.25831 q^{11} -2.82799 q^{12} -0.947866 q^{13} +4.30276 q^{14} -11.7209 q^{15} +1.00000 q^{16} +6.98796 q^{17} +4.99754 q^{18} -4.41705 q^{19} +4.14459 q^{20} -12.1682 q^{21} +5.25831 q^{22} -5.69976 q^{23} -2.82799 q^{24} +12.1777 q^{25} -0.947866 q^{26} -5.64903 q^{27} +4.30276 q^{28} -4.52215 q^{29} -11.7209 q^{30} -3.08736 q^{31} +1.00000 q^{32} -14.8705 q^{33} +6.98796 q^{34} +17.8332 q^{35} +4.99754 q^{36} +2.58495 q^{37} -4.41705 q^{38} +2.68056 q^{39} +4.14459 q^{40} +6.60693 q^{41} -12.1682 q^{42} +7.81694 q^{43} +5.25831 q^{44} +20.7128 q^{45} -5.69976 q^{46} -2.76960 q^{47} -2.82799 q^{48} +11.5137 q^{49} +12.1777 q^{50} -19.7619 q^{51} -0.947866 q^{52} -0.526427 q^{53} -5.64903 q^{54} +21.7936 q^{55} +4.30276 q^{56} +12.4914 q^{57} -4.52215 q^{58} -0.834258 q^{59} -11.7209 q^{60} -1.45129 q^{61} -3.08736 q^{62} +21.5032 q^{63} +1.00000 q^{64} -3.92852 q^{65} -14.8705 q^{66} +7.98655 q^{67} +6.98796 q^{68} +16.1189 q^{69} +17.8332 q^{70} +3.49804 q^{71} +4.99754 q^{72} -1.38616 q^{73} +2.58495 q^{74} -34.4384 q^{75} -4.41705 q^{76} +22.6252 q^{77} +2.68056 q^{78} -14.2703 q^{79} +4.14459 q^{80} +0.982793 q^{81} +6.60693 q^{82} -3.49807 q^{83} -12.1682 q^{84} +28.9622 q^{85} +7.81694 q^{86} +12.7886 q^{87} +5.25831 q^{88} +5.12769 q^{89} +20.7128 q^{90} -4.07844 q^{91} -5.69976 q^{92} +8.73102 q^{93} -2.76960 q^{94} -18.3069 q^{95} -2.82799 q^{96} -9.35906 q^{97} +11.5137 q^{98} +26.2786 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−2.82799	−1.63274	−0.816371	−	0.577528i	$-0.804018\pi$
$3$	−2.82799	−1.63274	−0.816371	+	0.577528i	$0.804018\pi$
$4$	1.00000	0.500000
$5$	4.14459	1.85352	0.926760	−	0.375655i	$-0.122582\pi$
$5$	4.14459	1.85352	0.926760	+	0.375655i	$0.122582\pi$
$6$	−2.82799	−1.15452
$7$	4.30276	1.62629	0.813145	−	0.582061i	$-0.197754\pi$
$7$	4.30276	1.62629	0.813145	+	0.582061i	$0.197754\pi$
$8$	1.00000	0.353553
$9$	4.99754	1.66585
$10$	4.14459	1.31064
$11$	5.25831	1.58544	0.792720	−	0.609586i	$-0.208664\pi$
$11$	5.25831	1.58544	0.792720	+	0.609586i	$0.208664\pi$
$12$	−2.82799	−0.816371
$13$	−0.947866	−0.262891	−0.131445	−	0.991323i	$-0.541962\pi$
$13$	−0.947866	−0.262891	−0.131445	+	0.991323i	$0.541962\pi$
$14$	4.30276	1.14996
$15$	−11.7209	−3.02632
$16$	1.00000	0.250000
$17$	6.98796	1.69483	0.847414	−	0.530932i	$-0.178158\pi$
$17$	6.98796	1.69483	0.847414	+	0.530932i	$0.178158\pi$
$18$	4.99754	1.17793
$19$	−4.41705	−1.01334	−0.506671	−	0.862140i	$-0.669124\pi$
$19$	−4.41705	−1.01334	−0.506671	+	0.862140i	$0.669124\pi$
$20$	4.14459	0.926760
$21$	−12.1682	−2.65531
$22$	5.25831	1.12108
$23$	−5.69976	−1.18848	−0.594242	−	0.804287i	$-0.702548\pi$
$23$	−5.69976	−1.18848	−0.594242	+	0.804287i	$0.702548\pi$
$24$	−2.82799	−0.577262
$25$	12.1777	2.43553
$26$	−0.947866	−0.185892
$27$	−5.64903	−1.08716
$28$	4.30276	0.813145
$29$	−4.52215	−0.839742	−0.419871	−	0.907584i	$-0.637925\pi$
$29$	−4.52215	−0.839742	−0.419871	+	0.907584i	$0.637925\pi$
$30$	−11.7209	−2.13993
$31$	−3.08736	−0.554506	−0.277253	−	0.960797i	$-0.589424\pi$
$31$	−3.08736	−0.554506	−0.277253	+	0.960797i	$0.589424\pi$
$32$	1.00000	0.176777
$33$	−14.8705	−2.58862
$34$	6.98796	1.19842
$35$	17.8332	3.01436
$36$	4.99754	0.832924
$37$	2.58495	0.424963	0.212482	−	0.977165i	$-0.431845\pi$
$37$	2.58495	0.424963	0.212482	+	0.977165i	$0.431845\pi$
$38$	−4.41705	−0.716540
$39$	2.68056	0.429233
$40$	4.14459	0.655318
$41$	6.60693	1.03183	0.515915	−	0.856640i	$-0.327452\pi$
$41$	6.60693	1.03183	0.515915	+	0.856640i	$0.327452\pi$
$42$	−12.1682	−1.87759
$43$	7.81694	1.19207	0.596036	−	0.802958i	$-0.296742\pi$
$43$	7.81694	1.19207	0.596036	+	0.802958i	$0.296742\pi$
$44$	5.25831	0.792720
$45$	20.7128	3.08768
$46$	−5.69976	−0.840384
$47$	−2.76960	−0.403987	−0.201994	−	0.979387i	$-0.564742\pi$
$47$	−2.76960	−0.403987	−0.201994	+	0.979387i	$0.564742\pi$
$48$	−2.82799	−0.408186
$49$	11.5137	1.64482
$50$	12.1777	1.72218
$51$	−19.7619	−2.76722
$52$	−0.947866	−0.131445
$53$	−0.526427	−0.0723103	−0.0361551	−	0.999346i	$-0.511511\pi$
$53$	−0.526427	−0.0723103	−0.0361551	+	0.999346i	$0.511511\pi$
$54$	−5.64903	−0.768736
$55$	21.7936	2.93864
$56$	4.30276	0.574980
$57$	12.4914	1.65452
$58$	−4.52215	−0.593788
$59$	−0.834258	−0.108611	−0.0543056	−	0.998524i	$-0.517295\pi$
$59$	−0.834258	−0.108611	−0.0543056	+	0.998524i	$0.517295\pi$
$60$	−11.7209	−1.51316
$61$	−1.45129	−0.185819	−0.0929096	−	0.995675i	$-0.529617\pi$
$61$	−1.45129	−0.185819	−0.0929096	+	0.995675i	$0.529617\pi$
$62$	−3.08736	−0.392095
$63$	21.5032	2.70915
$64$	1.00000	0.125000
$65$	−3.92852	−0.487273
$66$	−14.8705	−1.83043
$67$	7.98655	0.975713	0.487856	−	0.872924i	$-0.337779\pi$
$67$	7.98655	0.975713	0.487856	+	0.872924i	$0.337779\pi$
$68$	6.98796	0.847414
$69$	16.1189	1.94049
$70$	17.8332	2.13147
$71$	3.49804	0.415141	0.207570	−	0.978220i	$-0.433444\pi$
$71$	3.49804	0.415141	0.207570	+	0.978220i	$0.433444\pi$
$72$	4.99754	0.588966
$73$	−1.38616	−0.162238	−0.0811188	−	0.996704i	$-0.525849\pi$
$73$	−1.38616	−0.162238	−0.0811188	+	0.996704i	$0.525849\pi$
$74$	2.58495	0.300494
$75$	−34.4384	−3.97660
$76$	−4.41705	−0.506671
$77$	22.6252	2.57839
$78$	2.68056	0.303513
$79$	−14.2703	−1.60553	−0.802767	−	0.596293i	$-0.796640\pi$
$79$	−14.2703	−1.60553	−0.802767	+	0.596293i	$0.796640\pi$
$80$	4.14459	0.463380
$81$	0.982793	0.109199
$82$	6.60693	0.729613
$83$	−3.49807	−0.383963	−0.191981	−	0.981399i	$-0.561491\pi$
$83$	−3.49807	−0.383963	−0.191981	+	0.981399i	$0.561491\pi$
$84$	−12.1682	−1.32766
$85$	28.9622	3.14140
$86$	7.81694	0.842922
$87$	12.7886	1.37108
$88$	5.25831	0.560538
$89$	5.12769	0.543534	0.271767	−	0.962363i	$-0.412392\pi$
$89$	5.12769	0.543534	0.271767	+	0.962363i	$0.412392\pi$
$90$	20.7128	2.18332
$91$	−4.07844	−0.427536
$92$	−5.69976	−0.594242
$93$	8.73102	0.905365
$94$	−2.76960	−0.285662
$95$	−18.3069	−1.87825
$96$	−2.82799	−0.288631
$97$	−9.35906	−0.950269	−0.475134	−	0.879913i	$-0.657601\pi$
$97$	−9.35906	−0.950269	−0.475134	+	0.879913i	$0.657601\pi$
$98$	11.5137	1.16306
$99$	26.2786	2.64110
$100$	12.1777	1.21777
$101$	−6.41224	−0.638041	−0.319021	−	0.947748i	$-0.603354\pi$
$101$	−6.41224	−0.638041	−0.319021	+	0.947748i	$0.603354\pi$
$102$	−19.7619	−1.95672
$103$	−17.9129	−1.76501	−0.882503	−	0.470307i	$-0.844143\pi$
$103$	−17.9129	−1.76501	−0.882503	+	0.470307i	$0.844143\pi$
$104$	−0.947866	−0.0929459
$105$	−50.4321	−4.92167
$106$	−0.526427	−0.0511311
$107$	−15.0480	−1.45474	−0.727372	−	0.686244i	$-0.759258\pi$
$107$	−15.0480	−1.45474	−0.727372	+	0.686244i	$0.759258\pi$
$108$	−5.64903	−0.543578
$109$	4.10469	0.393158	0.196579	−	0.980488i	$-0.437017\pi$
$109$	4.10469	0.393158	0.196579	+	0.980488i	$0.437017\pi$
$110$	21.7936	2.07794
$111$	−7.31022	−0.693855
$112$	4.30276	0.406572
$113$	−7.80299	−0.734044	−0.367022	−	0.930212i	$-0.619623\pi$
$113$	−7.80299	−0.734044	−0.367022	+	0.930212i	$0.619623\pi$
$114$	12.4914	1.16993
$115$	−23.6232	−2.20288
$116$	−4.52215	−0.419871
$117$	−4.73700	−0.437936
$118$	−0.834258	−0.0767997
$119$	30.0675	2.75628
$120$	−11.7209	−1.06997
$121$	16.6498	1.51362
$122$	−1.45129	−0.131394
$123$	−18.6843	−1.68471
$124$	−3.08736	−0.277253
$125$	29.7485	2.66079
$126$	21.5032	1.91566
$127$	3.33199	0.295667	0.147833	−	0.989012i	$-0.452770\pi$
$127$	3.33199	0.295667	0.147833	+	0.989012i	$0.452770\pi$
$128$	1.00000	0.0883883
$129$	−22.1062	−1.94635
$130$	−3.92852	−0.344554
$131$	13.6149	1.18954	0.594769	−	0.803897i	$-0.297244\pi$
$131$	13.6149	1.18954	0.594769	+	0.803897i	$0.297244\pi$
$132$	−14.8705	−1.29431
$133$	−19.0055	−1.64799
$134$	7.98655	0.689933
$135$	−23.4129	−2.01507
$136$	6.98796	0.599212
$137$	2.70357	0.230981	0.115491	−	0.993309i	$-0.463156\pi$
$137$	2.70357	0.230981	0.115491	+	0.993309i	$0.463156\pi$
$138$	16.1189	1.37213
$139$	11.6214	0.985717	0.492858	−	0.870110i	$-0.335952\pi$
$139$	11.6214	0.985717	0.492858	+	0.870110i	$0.335952\pi$
$140$	17.8332	1.50718
$141$	7.83240	0.659607
$142$	3.49804	0.293549
$143$	−4.98417	−0.416798
$144$	4.99754	0.416462
$145$	−18.7425	−1.55648
$146$	−1.38616	−0.114719
$147$	−32.5607	−2.68556
$148$	2.58495	0.212482
$149$	9.69217	0.794013	0.397007	−	0.917816i	$-0.370049\pi$
$149$	9.69217	0.794013	0.397007	+	0.917816i	$0.370049\pi$
$150$	−34.4384	−2.81188
$151$	−10.8803	−0.885427	−0.442713	−	0.896663i	$-0.645984\pi$
$151$	−10.8803	−0.885427	−0.442713	+	0.896663i	$0.645984\pi$
$152$	−4.41705	−0.358270
$153$	34.9226	2.82332
$154$	22.6252	1.82319
$155$	−12.7958	−1.02779
$156$	2.68056	0.214616
$157$	−18.3100	−1.46129	−0.730647	−	0.682755i	$-0.760782\pi$
$157$	−18.3100	−1.46129	−0.730647	+	0.682755i	$0.760782\pi$
$158$	−14.2703	−1.13528
$159$	1.48873	0.118064
$160$	4.14459	0.327659
$161$	−24.5247	−1.93282
$162$	0.982793	0.0772155
$163$	−25.1337	−1.96863	−0.984314	−	0.176428i	$-0.943546\pi$
$163$	−25.1337	−1.96863	−0.984314	+	0.176428i	$0.943546\pi$
$164$	6.60693	0.515915
$165$	−61.6320	−4.79805
$166$	−3.49807	−0.271503
$167$	20.2456	1.56665	0.783326	−	0.621611i	$-0.213522\pi$
$167$	20.2456	1.56665	0.783326	+	0.621611i	$0.213522\pi$
$168$	−12.1682	−0.938794
$169$	−12.1016	−0.930888
$170$	28.9622	2.22130
$171$	−22.0744	−1.68807
$172$	7.81694	0.596036
$173$	7.52307	0.571968	0.285984	−	0.958234i	$-0.407680\pi$
$173$	7.52307	0.571968	0.285984	+	0.958234i	$0.407680\pi$
$174$	12.7886	0.969502
$175$	52.3976	3.96088
$176$	5.25831	0.396360
$177$	2.35928	0.177334
$178$	5.12769	0.384337
$179$	−21.7219	−1.62357	−0.811784	−	0.583958i	$-0.801503\pi$
$179$	−21.7219	−1.62357	−0.811784	+	0.583958i	$0.801503\pi$
$180$	20.7128	1.54384
$181$	−15.7490	−1.17062	−0.585308	−	0.810811i	$-0.699026\pi$
$181$	−15.7490	−1.17062	−0.585308	+	0.810811i	$0.699026\pi$
$182$	−4.07844	−0.302314
$183$	4.10425	0.303395
$184$	−5.69976	−0.420192
$185$	10.7136	0.787677
$186$	8.73102	0.640190
$187$	36.7448	2.68705
$188$	−2.76960	−0.201994
$189$	−24.3064	−1.76803
$190$	−18.3069	−1.32812
$191$	−11.4586	−0.829115	−0.414558	−	0.910023i	$-0.636064\pi$
$191$	−11.4586	−0.829115	−0.414558	+	0.910023i	$0.636064\pi$
$192$	−2.82799	−0.204093
$193$	−6.35968	−0.457780	−0.228890	−	0.973452i	$-0.573510\pi$
$193$	−6.35968	−0.457780	−0.228890	+	0.973452i	$0.573510\pi$
$194$	−9.35906	−0.671941
$195$	11.1098	0.795591
$196$	11.5137	0.822409
$197$	−15.8358	−1.12825	−0.564127	−	0.825688i	$-0.690787\pi$
$197$	−15.8358	−1.12825	−0.564127	+	0.825688i	$0.690787\pi$
$198$	26.2786	1.86754
$199$	11.0988	0.786775	0.393388	−	0.919373i	$-0.371303\pi$
$199$	11.0988	0.786775	0.393388	+	0.919373i	$0.371303\pi$
$200$	12.1777	0.861091
$201$	−22.5859	−1.59309
$202$	−6.41224	−0.451163
$203$	−19.4577	−1.36566
$204$	−19.7619	−1.38361
$205$	27.3830	1.91251
$206$	−17.9129	−1.24805
$207$	−28.4848	−1.97983
$208$	−0.947866	−0.0657227
$209$	−23.2262	−1.60659
$210$	−50.4321	−3.48015
$211$	−12.5821	−0.866188	−0.433094	−	0.901349i	$-0.642578\pi$
$211$	−12.5821	−0.866188	−0.433094	+	0.901349i	$0.642578\pi$
$212$	−0.526427	−0.0361551
$213$	−9.89243	−0.677818
$214$	−15.0480	−1.02866
$215$	32.3980	2.20953
$216$	−5.64903	−0.384368
$217$	−13.2842	−0.901787
$218$	4.10469	0.278005
$219$	3.92005	0.264892
$220$	21.7936	1.46932
$221$	−6.62365	−0.445555
$222$	−7.31022	−0.490630
$223$	−3.19285	−0.213809	−0.106904	−	0.994269i	$-0.534094\pi$
$223$	−3.19285	−0.213809	−0.106904	+	0.994269i	$0.534094\pi$
$224$	4.30276	0.287490
$225$	60.8584	4.05723
$226$	−7.80299	−0.519047
$227$	19.3606	1.28501	0.642503	−	0.766283i	$-0.277896\pi$
$227$	19.3606	1.28501	0.642503	+	0.766283i	$0.277896\pi$
$228$	12.4914	0.827262
$229$	28.3848	1.87572	0.937859	−	0.347016i	$-0.112805\pi$
$229$	28.3848	1.87572	0.937859	+	0.347016i	$0.112805\pi$
$230$	−23.6232	−1.55767
$231$	−63.9840	−4.20984
$232$	−4.52215	−0.296894
$233$	−10.8599	−0.711458	−0.355729	−	0.934589i	$-0.615767\pi$
$233$	−10.8599	−0.711458	−0.355729	+	0.934589i	$0.615767\pi$
$234$	−4.73700	−0.309667
$235$	−11.4789	−0.748799
$236$	−0.834258	−0.0543056
$237$	40.3563	2.62142
$238$	30.0675	1.94899
$239$	−20.8468	−1.34847	−0.674234	−	0.738518i	$-0.735526\pi$
$239$	−20.8468	−1.34847	−0.674234	+	0.738518i	$0.735526\pi$
$240$	−11.7209	−0.756580
$241$	21.6663	1.39565	0.697825	−	0.716268i	$-0.254151\pi$
$241$	21.6663	1.39565	0.697825	+	0.716268i	$0.254151\pi$
$242$	16.6498	1.07029
$243$	14.1678	0.908862
$244$	−1.45129	−0.0929096
$245$	47.7197	3.04870
$246$	−18.6843	−1.19127
$247$	4.18677	0.266398
$248$	−3.08736	−0.196047
$249$	9.89251	0.626912
$250$	29.7485	1.88146
$251$	3.60170	0.227337	0.113669	−	0.993519i	$-0.463740\pi$
$251$	3.60170	0.227337	0.113669	+	0.993519i	$0.463740\pi$
$252$	21.5032	1.35457
$253$	−29.9711	−1.88427
$254$	3.33199	0.209068
$255$	−81.9050	−5.12909
$256$	1.00000	0.0625000
$257$	−31.1181	−1.94110	−0.970548	−	0.240908i	$-0.922555\pi$
$257$	−31.1181	−1.94110	−0.970548	+	0.240908i	$0.922555\pi$
$258$	−22.1062	−1.37627
$259$	11.1224	0.691113
$260$	−3.92852	−0.243636
$261$	−22.5996	−1.39888
$262$	13.6149	0.841130
$263$	−1.30077	−0.0802087	−0.0401043	−	0.999195i	$-0.512769\pi$
$263$	−1.30077	−0.0802087	−0.0401043	+	0.999195i	$0.512769\pi$
$264$	−14.8705	−0.915214
$265$	−2.18183	−0.134028
$266$	−19.0055	−1.16530
$267$	−14.5011	−0.887451
$268$	7.98655	0.487856
$269$	−6.56854	−0.400491	−0.200245	−	0.979746i	$-0.564174\pi$
$269$	−6.56854	−0.400491	−0.200245	+	0.979746i	$0.564174\pi$
$270$	−23.4129	−1.42487
$271$	3.60241	0.218831	0.109416	−	0.993996i	$-0.465102\pi$
$271$	3.60241	0.218831	0.109416	+	0.993996i	$0.465102\pi$
$272$	6.98796	0.423707
$273$	11.5338	0.698057
$274$	2.70357	0.163328
$275$	64.0340	3.86139
$276$	16.1189	0.970243
$277$	6.09176	0.366018	0.183009	−	0.983111i	$-0.441416\pi$
$277$	6.09176	0.366018	0.183009	+	0.983111i	$0.441416\pi$
$278$	11.6214	0.697007
$279$	−15.4292	−0.923722
$280$	17.8332	1.06574
$281$	3.84420	0.229325	0.114663	−	0.993404i	$-0.463421\pi$
$281$	3.84420	0.229325	0.114663	+	0.993404i	$0.463421\pi$
$282$	7.83240	0.466413
$283$	12.5802	0.747812	0.373906	−	0.927467i	$-0.378018\pi$
$283$	12.5802	0.747812	0.373906	+	0.927467i	$0.378018\pi$
$284$	3.49804	0.207570
$285$	51.7717	3.06669
$286$	−4.98417	−0.294720
$287$	28.4280	1.67805
$288$	4.99754	0.294483
$289$	31.8315	1.87244
$290$	−18.7425	−1.10060
$291$	26.4674	1.55154
$292$	−1.38616	−0.0811188
$293$	−7.18297	−0.419634	−0.209817	−	0.977741i	$-0.567287\pi$
$293$	−7.18297	−0.419634	−0.209817	+	0.977741i	$0.567287\pi$
$294$	−32.5607	−1.89898
$295$	−3.45766	−0.201313
$296$	2.58495	0.150247
$297$	−29.7044	−1.72362
$298$	9.69217	0.561452
$299$	5.40261	0.312441
$300$	−34.4384	−1.98830
$301$	33.6344	1.93865
$302$	−10.8803	−0.626091
$303$	18.1338	1.04176
$304$	−4.41705	−0.253335
$305$	−6.01503	−0.344419
$306$	34.9226	1.99639
$307$	−5.01023	−0.285949	−0.142974	−	0.989726i	$-0.545667\pi$
$307$	−5.01023	−0.285949	−0.142974	+	0.989726i	$0.545667\pi$
$308$	22.6252	1.28919
$309$	50.6574	2.88180
$310$	−12.7958	−0.726755
$311$	−31.5503	−1.78905	−0.894526	−	0.447015i	$-0.852487\pi$
$311$	−31.5503	−1.78905	−0.894526	+	0.447015i	$0.852487\pi$
$312$	2.68056	0.151757
$313$	3.59654	0.203289	0.101644	−	0.994821i	$-0.467590\pi$
$313$	3.59654	0.203289	0.101644	+	0.994821i	$0.467590\pi$
$314$	−18.3100	−1.03329
$315$	89.1221	5.02146
$316$	−14.2703	−0.802767
$317$	8.76732	0.492422	0.246211	−	0.969216i	$-0.420814\pi$
$317$	8.76732	0.492422	0.246211	+	0.969216i	$0.420814\pi$
$318$	1.48873	0.0834839
$319$	−23.7789	−1.33136
$320$	4.14459	0.231690
$321$	42.5556	2.37522
$322$	−24.5247	−1.36671
$323$	−30.8662	−1.71744
$324$	0.982793	0.0545996
$325$	−11.5428	−0.640279
$326$	−25.1337	−1.39203
$327$	−11.6080	−0.641926
$328$	6.60693	0.364807
$329$	−11.9169	−0.657001
$330$	−61.6320	−3.39273
$331$	26.0635	1.43258	0.716291	−	0.697802i	$-0.245838\pi$
$331$	26.0635	1.43258	0.716291	+	0.697802i	$0.245838\pi$
$332$	−3.49807	−0.191981
$333$	12.9184	0.707924
$334$	20.2456	1.10779
$335$	33.1010	1.80850
$336$	−12.1682	−0.663828
$337$	−5.52587	−0.301013	−0.150507	−	0.988609i	$-0.548091\pi$
$337$	−5.52587	−0.301013	−0.150507	+	0.988609i	$0.548091\pi$
$338$	−12.1016	−0.658238
$339$	22.0668	1.19850
$340$	28.9622	1.57070
$341$	−16.2343	−0.879136
$342$	−22.0744	−1.19365
$343$	19.4215	1.04866
$344$	7.81694	0.421461
$345$	66.8063	3.59673
$346$	7.52307	0.404443
$347$	−30.4336	−1.63376	−0.816881	−	0.576806i	$-0.804299\pi$
$347$	−30.4336	−1.63376	−0.816881	+	0.576806i	$0.804299\pi$
$348$	12.7886	0.685541
$349$	−21.1016	−1.12955	−0.564773	−	0.825247i	$-0.691036\pi$
$349$	−21.1016	−1.12955	−0.564773	+	0.825247i	$0.691036\pi$
$350$	52.3976	2.80077
$351$	5.35452	0.285803
$352$	5.25831	0.280269
$353$	−16.8358	−0.896078	−0.448039	−	0.894014i	$-0.647877\pi$
$353$	−16.8358	−0.896078	−0.448039	+	0.894014i	$0.647877\pi$
$354$	2.35928	0.125394
$355$	14.4980	0.769472
$356$	5.12769	0.271767
$357$	−85.0306	−4.50030
$358$	−21.7219	−1.14804
$359$	−9.57722	−0.505466	−0.252733	−	0.967536i	$-0.581329\pi$
$359$	−9.57722	−0.505466	−0.252733	+	0.967536i	$0.581329\pi$
$360$	20.7128	1.09166
$361$	0.510341	0.0268600
$362$	−15.7490	−0.827750
$363$	−47.0856	−2.47135
$364$	−4.07844	−0.213768
$365$	−5.74507	−0.300711
$366$	4.10425	0.214533
$367$	−3.03076	−0.158204	−0.0791022	−	0.996867i	$-0.525205\pi$
$367$	−3.03076	−0.158204	−0.0791022	+	0.996867i	$0.525205\pi$
$368$	−5.69976	−0.297121
$369$	33.0184	1.71887
$370$	10.7136	0.556972
$371$	−2.26509	−0.117597
$372$	8.73102	0.452683
$373$	17.9815	0.931046	0.465523	−	0.885036i	$-0.345866\pi$
$373$	17.9815	0.931046	0.465523	+	0.885036i	$0.345866\pi$
$374$	36.7448	1.90003
$375$	−84.1286	−4.34438
$376$	−2.76960	−0.142831
$377$	4.28639	0.220760
$378$	−24.3064	−1.25019
$379$	5.18428	0.266298	0.133149	−	0.991096i	$-0.457491\pi$
$379$	5.18428	0.266298	0.133149	+	0.991096i	$0.457491\pi$
$380$	−18.3069	−0.939124
$381$	−9.42286	−0.482748
$382$	−11.4586	−0.586273
$383$	−11.6643	−0.596018	−0.298009	−	0.954563i	$-0.596323\pi$
$383$	−11.6643	−0.596018	−0.298009	+	0.954563i	$0.596323\pi$
$384$	−2.82799	−0.144315
$385$	93.7725	4.77909
$386$	−6.35968	−0.323699
$387$	39.0655	1.98581
$388$	−9.35906	−0.475134
$389$	26.4612	1.34164	0.670818	−	0.741622i	$-0.265943\pi$
$389$	26.4612	1.34164	0.670818	+	0.741622i	$0.265943\pi$
$390$	11.1098	0.562568
$391$	−39.8297	−2.01427
$392$	11.5137	0.581531
$393$	−38.5028	−1.94221
$394$	−15.8358	−0.797796
$395$	−59.1446	−2.97589
$396$	26.2786	1.32055
$397$	27.6257	1.38649	0.693247	−	0.720700i	$-0.256179\pi$
$397$	27.6257	1.38649	0.693247	+	0.720700i	$0.256179\pi$
$398$	11.0988	0.556334
$399$	53.7474	2.69074
$400$	12.1777	0.608883
$401$	−3.04532	−0.152076	−0.0760381	−	0.997105i	$-0.524227\pi$
$401$	−3.04532	−0.152076	−0.0760381	+	0.997105i	$0.524227\pi$
$402$	−22.5859	−1.12648
$403$	2.92640	0.145774
$404$	−6.41224	−0.319021
$405$	4.07328	0.202403
$406$	−19.4577	−0.965671
$407$	13.5925	0.673754
$408$	−19.7619	−0.978359
$409$	−27.5849	−1.36398	−0.681992	−	0.731360i	$-0.738886\pi$
$409$	−27.5849	−1.36398	−0.681992	+	0.731360i	$0.738886\pi$
$410$	27.3830	1.35235
$411$	−7.64567	−0.377133
$412$	−17.9129	−0.882503
$413$	−3.58961	−0.176633
$414$	−28.4848	−1.39995
$415$	−14.4981	−0.711682
$416$	−0.947866	−0.0464729
$417$	−32.8653	−1.60942
$418$	−23.2262	−1.13603
$419$	−6.17946	−0.301886	−0.150943	−	0.988542i	$-0.548231\pi$
$419$	−6.17946	−0.301886	−0.150943	+	0.988542i	$0.548231\pi$
$420$	−50.4321	−2.46084
$421$	12.2635	0.597689	0.298844	−	0.954302i	$-0.403399\pi$
$421$	12.2635	0.597689	0.298844	+	0.954302i	$0.403399\pi$
$422$	−12.5821	−0.612487
$423$	−13.8412	−0.672981
$424$	−0.526427	−0.0255655
$425$	85.0970	4.12781
$426$	−9.89243	−0.479290
$427$	−6.24457	−0.302196
$428$	−15.0480	−0.727372
$429$	14.0952	0.680523
$430$	32.3980	1.56237
$431$	−11.5482	−0.556256	−0.278128	−	0.960544i	$-0.589714\pi$
$431$	−11.5482	−0.556256	−0.278128	+	0.960544i	$0.589714\pi$
$432$	−5.64903	−0.271789
$433$	28.6315	1.37594	0.687970	−	0.725739i	$-0.258502\pi$
$433$	28.6315	1.37594	0.687970	+	0.725739i	$0.258502\pi$
$434$	−13.2842	−0.637660
$435$	53.0036	2.54133
$436$	4.10469	0.196579
$437$	25.1762	1.20434
$438$	3.92005	0.187307
$439$	−32.6896	−1.56019	−0.780095	−	0.625661i	$-0.784829\pi$
$439$	−32.6896	−1.56019	−0.780095	+	0.625661i	$0.784829\pi$
$440$	21.7936	1.03897
$441$	57.5403	2.74002
$442$	−6.62365	−0.315055
$443$	−13.8910	−0.659982	−0.329991	−	0.943984i	$-0.607046\pi$
$443$	−13.8910	−0.659982	−0.329991	+	0.943984i	$0.607046\pi$
$444$	−7.31022	−0.346928
$445$	21.2522	1.00745
$446$	−3.19285	−0.151186
$447$	−27.4094	−1.29642
$448$	4.30276	0.203286
$449$	29.8121	1.40692	0.703460	−	0.710735i	$-0.251637\pi$
$449$	29.8121	1.40692	0.703460	+	0.710735i	$0.251637\pi$
$450$	60.8584	2.86889
$451$	34.7413	1.63590
$452$	−7.80299	−0.367022
$453$	30.7694	1.44567
$454$	19.3606	0.908637
$455$	−16.9035	−0.792447
$456$	12.4914	0.584963
$457$	33.3895	1.56189	0.780947	−	0.624597i	$-0.214737\pi$
$457$	33.3895	1.56189	0.780947	+	0.624597i	$0.214737\pi$
$458$	28.3848	1.32633
$459$	−39.4752	−1.84254
$460$	−23.6232	−1.10144
$461$	−17.1334	−0.797982	−0.398991	−	0.916955i	$-0.630640\pi$
$461$	−17.1334	−0.797982	−0.398991	+	0.916955i	$0.630640\pi$
$462$	−63.9840	−2.97681
$463$	27.5520	1.28045	0.640225	−	0.768187i	$-0.278841\pi$
$463$	27.5520	1.28045	0.640225	+	0.768187i	$0.278841\pi$
$464$	−4.52215	−0.209936
$465$	36.1866	1.67811
$466$	−10.8599	−0.503077
$467$	−20.9913	−0.971359	−0.485680	−	0.874137i	$-0.661428\pi$
$467$	−20.9913	−0.971359	−0.485680	+	0.874137i	$0.661428\pi$
$468$	−4.73700	−0.218968
$469$	34.3642	1.58679
$470$	−11.4789	−0.529481
$471$	51.7805	2.38592
$472$	−0.834258	−0.0383999
$473$	41.1039	1.88996
$474$	40.3563	1.85363
$475$	−53.7894	−2.46803
$476$	30.0675	1.37814
$477$	−2.63084	−0.120458
$478$	−20.8468	−0.953511
$479$	33.3418	1.52342	0.761712	−	0.647916i	$-0.224359\pi$
$479$	33.3418	1.52342	0.761712	+	0.647916i	$0.224359\pi$
$480$	−11.7209	−0.534983
$481$	−2.45019	−0.111719
$482$	21.6663	0.986873
$483$	69.3557	3.15579
$484$	16.6498	0.756811
$485$	−38.7895	−1.76134
$486$	14.1678	0.642663
$487$	21.3992	0.969691	0.484845	−	0.874600i	$-0.338876\pi$
$487$	21.3992	0.969691	0.484845	+	0.874600i	$0.338876\pi$
$488$	−1.45129	−0.0656970
$489$	71.0781	3.21426
$490$	47.7197	2.15576
$491$	11.4405	0.516301	0.258150	−	0.966105i	$-0.416887\pi$
$491$	11.4405	0.516301	0.258150	+	0.966105i	$0.416887\pi$
$492$	−18.6843	−0.842355
$493$	−31.6006	−1.42322
$494$	4.18677	0.188372
$495$	108.914	4.89533
$496$	−3.08736	−0.138626
$497$	15.0512	0.675140
$498$	9.89251	0.443294
$499$	−12.5232	−0.560615	−0.280308	−	0.959910i	$-0.590436\pi$
$499$	−12.5232	−0.560615	−0.280308	+	0.959910i	$0.590436\pi$
$500$	29.7485	1.33039
$501$	−57.2544	−2.55794
$502$	3.60170	0.160752
$503$	−36.7560	−1.63887	−0.819436	−	0.573171i	$-0.805713\pi$
$503$	−36.7560	−1.63887	−0.819436	+	0.573171i	$0.805713\pi$
$504$	21.5032	0.957829
$505$	−26.5761	−1.18262
$506$	−29.9711	−1.33238
$507$	34.2231	1.51990
$508$	3.33199	0.147833
$509$	33.7205	1.49464	0.747318	−	0.664467i	$-0.231341\pi$
$509$	33.7205	1.49464	0.747318	+	0.664467i	$0.231341\pi$
$510$	−81.9050	−3.62682
$511$	−5.96431	−0.263845
$512$	1.00000	0.0441942
$513$	24.9521	1.10166
$514$	−31.1181	−1.37256
$515$	−74.2415	−3.27147
$516$	−22.1062	−0.973173
$517$	−14.5634	−0.640498
$518$	11.1224	0.488691
$519$	−21.2752	−0.933876
$520$	−3.92852	−0.172277
$521$	27.9711	1.22543	0.612717	−	0.790302i	$-0.290076\pi$
$521$	27.9711	1.22543	0.612717	+	0.790302i	$0.290076\pi$
$522$	−22.5996	−0.989159
$523$	27.1640	1.18780	0.593898	−	0.804540i	$-0.297588\pi$
$523$	27.1640	1.18780	0.593898	+	0.804540i	$0.297588\pi$
$524$	13.6149	0.594769
$525$	−148.180	−6.46710
$526$	−1.30077	−0.0567161
$527$	−21.5743	−0.939792
$528$	−14.8705	−0.647154
$529$	9.48732	0.412492
$530$	−2.18183	−0.0947724
$531$	−4.16924	−0.180930
$532$	−19.0055	−0.823993
$533$	−6.26248	−0.271258
$534$	−14.5011	−0.627523
$535$	−62.3678	−2.69639
$536$	7.98655	0.344967
$537$	61.4293	2.65087
$538$	−6.56854	−0.283190
$539$	60.5428	2.60776
$540$	−23.4129	−1.00753
$541$	45.3319	1.94897	0.974486	−	0.224449i	$-0.0720584\pi$
$541$	45.3319	1.94897	0.974486	+	0.224449i	$0.0720584\pi$
$542$	3.60241	0.154737
$543$	44.5381	1.91131
$544$	6.98796	0.299606
$545$	17.0123	0.728726
$546$	11.5338	0.493601
$547$	42.3597	1.81117	0.905585	−	0.424164i	$-0.139432\pi$
$547$	42.3597	1.81117	0.905585	+	0.424164i	$0.139432\pi$
$548$	2.70357	0.115491
$549$	−7.25290	−0.309546
$550$	64.0340	2.73042
$551$	19.9746	0.850945
$552$	16.1189	0.686066
$553$	−61.4016	−2.61106
$554$	6.09176	0.258814
$555$	−30.2979	−1.28607
$556$	11.6214	0.492858
$557$	−31.9884	−1.35539	−0.677697	−	0.735341i	$-0.737022\pi$
$557$	−31.9884	−1.35539	−0.677697	+	0.735341i	$0.737022\pi$
$558$	−15.4292	−0.653170
$559$	−7.40941	−0.313385
$560$	17.8332	0.753590
$561$	−103.914	−4.38726
$562$	3.84420	0.162158
$563$	17.7707	0.748945	0.374473	−	0.927238i	$-0.377824\pi$
$563$	17.7707	0.748945	0.374473	+	0.927238i	$0.377824\pi$
$564$	7.83240	0.329804
$565$	−32.3402	−1.36056
$566$	12.5802	0.528783
$567$	4.22872	0.177590
$568$	3.49804	0.146775
$569$	−38.5751	−1.61715	−0.808575	−	0.588392i	$-0.799761\pi$
$569$	−38.5751	−1.61715	−0.808575	+	0.588392i	$0.799761\pi$
$570$	51.7717	2.16848
$571$	−38.2341	−1.60005	−0.800024	−	0.599968i	$-0.795180\pi$
$571$	−38.2341	−1.60005	−0.800024	+	0.599968i	$0.795180\pi$
$572$	−4.98417	−0.208399
$573$	32.4048	1.35373
$574$	28.4280	1.18656
$575$	−69.4098	−2.89459
$576$	4.99754	0.208231
$577$	−7.81830	−0.325480	−0.162740	−	0.986669i	$-0.552033\pi$
$577$	−7.81830	−0.325480	−0.162740	+	0.986669i	$0.552033\pi$
$578$	31.8315	1.32402
$579$	17.9851	0.747436
$580$	−18.7425	−0.778239
$581$	−15.0513	−0.624435
$582$	26.4674	1.09711
$583$	−2.76812	−0.114644
$584$	−1.38616	−0.0573597
$585$	−19.6329	−0.811722
$586$	−7.18297	−0.296726
$587$	42.2109	1.74223	0.871115	−	0.491079i	$-0.163397\pi$
$587$	42.2109	1.74223	0.871115	+	0.491079i	$0.163397\pi$
$588$	−32.5607	−1.34278
$589$	13.6370	0.561903
$590$	−3.45766	−0.142350
$591$	44.7835	1.84215
$592$	2.58495	0.106241
$593$	−32.6904	−1.34243	−0.671216	−	0.741262i	$-0.734228\pi$
$593$	−32.6904	−1.34243	−0.671216	+	0.741262i	$0.734228\pi$
$594$	−29.7044	−1.21878
$595$	124.618	5.10882
$596$	9.69217	0.397007
$597$	−31.3874	−1.28460
$598$	5.40261	0.220929
$599$	3.84582	0.157136	0.0785680	−	0.996909i	$-0.474965\pi$
$599$	3.84582	0.157136	0.0785680	+	0.996909i	$0.474965\pi$
$600$	−34.4384	−1.40594
$601$	25.3533	1.03418	0.517090	−	0.855931i	$-0.327015\pi$
$601$	25.3533	1.03418	0.517090	+	0.855931i	$0.327015\pi$
$602$	33.6344	1.37084
$603$	39.9131	1.62539
$604$	−10.8803	−0.442713
$605$	69.0068	2.80553
$606$	18.1338	0.736633
$607$	−25.9899	−1.05490	−0.527448	−	0.849587i	$-0.676851\pi$
$607$	−25.9899	−1.05490	−0.527448	+	0.849587i	$0.676851\pi$
$608$	−4.41705	−0.179135
$609$	55.0263	2.22978
$610$	−6.01503	−0.243541
$611$	2.62521	0.106205
$612$	34.9226	1.41166
$613$	−2.18774	−0.0883620	−0.0441810	−	0.999024i	$-0.514068\pi$
$613$	−2.18774	−0.0883620	−0.0441810	+	0.999024i	$0.514068\pi$
$614$	−5.01023	−0.202196
$615$	−77.4390	−3.12264
$616$	22.6252	0.911597
$617$	37.5255	1.51072	0.755360	−	0.655310i	$-0.227462\pi$
$617$	37.5255	1.51072	0.755360	+	0.655310i	$0.227462\pi$
$618$	50.6574	2.03774
$619$	−29.8409	−1.19941	−0.599703	−	0.800223i	$-0.704715\pi$
$619$	−29.8409	−1.19941	−0.599703	+	0.800223i	$0.704715\pi$
$620$	−12.7958	−0.513894
$621$	32.1981	1.29207
$622$	−31.5503	−1.26505
$623$	22.0632	0.883944
$624$	2.68056	0.107308
$625$	62.4072	2.49629
$626$	3.59654	0.143747
$627$	65.6836	2.62315
$628$	−18.3100	−0.730647
$629$	18.0635	0.720240
$630$	89.1221	3.55071
$631$	−28.5890	−1.13811	−0.569055	−	0.822299i	$-0.692691\pi$
$631$	−28.5890	−1.13811	−0.569055	+	0.822299i	$0.692691\pi$
$632$	−14.2703	−0.567642
$633$	35.5821	1.41426
$634$	8.76732	0.348195
$635$	13.8098	0.548024
$636$	1.48873	0.0590320
$637$	−10.9135	−0.432407
$638$	−23.7789	−0.941415
$639$	17.4816	0.691561
$640$	4.14459	0.163829
$641$	33.4639	1.32175	0.660873	−	0.750498i	$-0.270186\pi$
$641$	33.4639	1.32175	0.660873	+	0.750498i	$0.270186\pi$
$642$	42.5556	1.67953
$643$	40.7661	1.60766	0.803829	−	0.594860i	$-0.202792\pi$
$643$	40.7661	1.60766	0.803829	+	0.594860i	$0.202792\pi$
$644$	−24.5247	−0.966409
$645$	−91.6214	−3.60759
$646$	−30.8662	−1.21441
$647$	−2.06157	−0.0810487	−0.0405244	−	0.999179i	$-0.512903\pi$
$647$	−2.06157	−0.0810487	−0.0405244	+	0.999179i	$0.512903\pi$
$648$	0.982793	0.0386078
$649$	−4.38679	−0.172197
$650$	−11.5428	−0.452746
$651$	37.5675	1.47239
$652$	−25.1337	−0.984314
$653$	32.2787	1.26316	0.631582	−	0.775309i	$-0.282406\pi$
$653$	32.2787	1.26316	0.631582	+	0.775309i	$0.282406\pi$
$654$	−11.6080	−0.453910
$655$	56.4282	2.20483
$656$	6.60693	0.257957
$657$	−6.92739	−0.270263
$658$	−11.9169	−0.464570
$659$	−2.14713	−0.0836405	−0.0418202	−	0.999125i	$-0.513316\pi$
$659$	−2.14713	−0.0836405	−0.0418202	+	0.999125i	$0.513316\pi$
$660$	−61.6320	−2.39902
$661$	−29.6799	−1.15442	−0.577208	−	0.816597i	$-0.695858\pi$
$661$	−29.6799	−1.15442	−0.577208	+	0.816597i	$0.695858\pi$
$662$	26.0635	1.01299
$663$	18.7316	0.727476
$664$	−3.49807	−0.135751
$665$	−78.7701	−3.05457
$666$	12.9184	0.500578
$667$	25.7752	0.998020
$668$	20.2456	0.783326
$669$	9.02935	0.349095
$670$	33.1010	1.27880
$671$	−7.63136	−0.294605
$672$	−12.1682	−0.469397
$673$	−2.60182	−0.100293	−0.0501463	−	0.998742i	$-0.515969\pi$
$673$	−2.60182	−0.100293	−0.0501463	+	0.998742i	$0.515969\pi$
$674$	−5.52587	−0.212849
$675$	−68.7920	−2.64781
$676$	−12.1016	−0.465444
$677$	−47.8574	−1.83931	−0.919655	−	0.392727i	$-0.871532\pi$
$677$	−47.8574	−1.83931	−0.919655	+	0.392727i	$0.871532\pi$
$678$	22.0668	0.847470
$679$	−40.2698	−1.54541
$680$	28.9622	1.11065
$681$	−54.7516	−2.09808
$682$	−16.2343	−0.621643
$683$	−33.3375	−1.27562	−0.637812	−	0.770192i	$-0.720160\pi$
$683$	−33.3375	−1.27562	−0.637812	+	0.770192i	$0.720160\pi$
$684$	−22.0744	−0.844036
$685$	11.2052	0.428128
$686$	19.4215	0.741515
$687$	−80.2719	−3.06256
$688$	7.81694	0.298018
$689$	0.498982	0.0190097
$690$	66.8063	2.54327
$691$	−23.0223	−0.875811	−0.437906	−	0.899021i	$-0.644280\pi$
$691$	−23.0223	−0.875811	−0.437906	+	0.899021i	$0.644280\pi$
$692$	7.52307	0.285984
$693$	113.071	4.29520
$694$	−30.4336	−1.15524
$695$	48.1661	1.82704
$696$	12.7886	0.484751
$697$	46.1689	1.74877
$698$	−21.1016	−0.798709
$699$	30.7118	1.16163
$700$	52.3976	1.98044
$701$	−28.9454	−1.09325	−0.546627	−	0.837376i	$-0.684088\pi$
$701$	−28.9454	−1.09325	−0.546627	+	0.837376i	$0.684088\pi$
$702$	5.35452	0.202093
$703$	−11.4179	−0.430633
$704$	5.25831	0.198180
$705$	32.4621	1.22259
$706$	−16.8358	−0.633623
$707$	−27.5903	−1.03764
$708$	2.35928	0.0886670
$709$	16.4463	0.617654	0.308827	−	0.951118i	$-0.400064\pi$
$709$	16.4463	0.617654	0.308827	+	0.951118i	$0.400064\pi$
$710$	14.4980	0.544099
$711$	−71.3164	−2.67457
$712$	5.12769	0.192168
$713$	17.5972	0.659021
$714$	−85.0306	−3.18219
$715$	−20.6574	−0.772542
$716$	−21.7219	−0.811784
$717$	58.9546	2.20170
$718$	−9.57722	−0.357419
$719$	−10.3089	−0.384457	−0.192228	−	0.981350i	$-0.561571\pi$
$719$	−10.3089	−0.384457	−0.192228	+	0.981350i	$0.561571\pi$
$720$	20.7128	0.771920
$721$	−77.0747	−2.87041
$722$	0.510341	0.0189929
$723$	−61.2722	−2.27874
$724$	−15.7490	−0.585308
$725$	−55.0693	−2.04522
$726$	−47.0856	−1.74751
$727$	−42.4539	−1.57453	−0.787264	−	0.616616i	$-0.788503\pi$
$727$	−42.4539	−1.57453	−0.787264	+	0.616616i	$0.788503\pi$
$728$	−4.07844	−0.151157
$729$	−43.0147	−1.59314
$730$	−5.74507	−0.212635
$731$	54.6244	2.02036
$732$	4.10425	0.151697
$733$	21.3756	0.789528	0.394764	−	0.918783i	$-0.370826\pi$
$733$	21.3756	0.789528	0.394764	+	0.918783i	$0.370826\pi$
$734$	−3.03076	−0.111867
$735$	−134.951	−4.97774
$736$	−5.69976	−0.210096
$737$	41.9958	1.54693
$738$	33.0184	1.21542
$739$	0.563534	0.0207299	0.0103650	−	0.999946i	$-0.496701\pi$
$739$	0.563534	0.0207299	0.0103650	+	0.999946i	$0.496701\pi$
$740$	10.7136	0.393839
$741$	−11.8402	−0.434959
$742$	−2.26509	−0.0831540
$743$	−31.3395	−1.14973	−0.574867	−	0.818247i	$-0.694946\pi$
$743$	−31.3395	−1.14973	−0.574867	+	0.818247i	$0.694946\pi$
$744$	8.73102	0.320095
$745$	40.1701	1.47172
$746$	17.9815	0.658349
$747$	−17.4817	−0.639623
$748$	36.7448	1.34352
$749$	−64.7478	−2.36583
$750$	−84.1286	−3.07194
$751$	−4.39433	−0.160351	−0.0801756	−	0.996781i	$-0.525548\pi$
$751$	−4.39433	−0.160351	−0.0801756	+	0.996781i	$0.525548\pi$
$752$	−2.76960	−0.100997
$753$	−10.1856	−0.371183
$754$	4.28639	0.156101
$755$	−45.0945	−1.64116
$756$	−24.3064	−0.884016
$757$	45.5909	1.65703	0.828515	−	0.559967i	$-0.189186\pi$
$757$	45.5909	1.65703	0.828515	+	0.559967i	$0.189186\pi$
$758$	5.18428	0.188301
$759$	84.7581	3.07653
$760$	−18.3069	−0.664061
$761$	21.9343	0.795119	0.397559	−	0.917576i	$-0.369857\pi$
$761$	21.9343	0.795119	0.397559	+	0.917576i	$0.369857\pi$
$762$	−9.42286	−0.341354
$763$	17.6615	0.639389
$764$	−11.4586	−0.414558
$765$	144.740	5.23309
$766$	−11.6643	−0.421448
$767$	0.790765	0.0285529
$768$	−2.82799	−0.102046
$769$	21.3103	0.768468	0.384234	−	0.923236i	$-0.374466\pi$
$769$	21.3103	0.768468	0.384234	+	0.923236i	$0.374466\pi$
$770$	93.7725	3.37932
$771$	88.0019	3.16931
$772$	−6.35968	−0.228890
$773$	8.16928	0.293828	0.146914	−	0.989149i	$-0.453066\pi$
$773$	8.16928	0.293828	0.146914	+	0.989149i	$0.453066\pi$
$774$	39.0655	1.40418
$775$	−37.5968	−1.35052
$776$	−9.35906	−0.335971
$777$	−31.4541	−1.12841
$778$	26.4612	0.948680
$779$	−29.1831	−1.04559
$780$	11.1098	0.397796
$781$	18.3938	0.658181
$782$	−39.8297	−1.42431
$783$	25.5458	0.912931
$784$	11.5137	0.411205
$785$	−75.8874	−2.70854
$786$	−38.5028	−1.37335
$787$	49.1481	1.75194	0.875971	−	0.482363i	$-0.160222\pi$
$787$	49.1481	1.75194	0.875971	+	0.482363i	$0.160222\pi$
$788$	−15.8358	−0.564127
$789$	3.67856	0.130960
$790$	−59.1446	−2.10427
$791$	−33.5744	−1.19377
$792$	26.2786	0.933770
$793$	1.37563	0.0488501
$794$	27.6257	0.980400
$795$	6.17019	0.218834
$796$	11.0988	0.393388
$797$	49.7217	1.76123	0.880617	−	0.473828i	$-0.157128\pi$
$797$	49.7217	1.76123	0.880617	+	0.473828i	$0.157128\pi$
$798$	53.7474	1.90264
$799$	−19.3538	−0.684689
$800$	12.1777	0.430546
$801$	25.6259	0.905445
$802$	−3.04532	−0.107534
$803$	−7.28886	−0.257218
$804$	−22.5859	−0.796544
$805$	−101.645	−3.58251
$806$	2.92640	0.103078
$807$	18.5758	0.653898
$808$	−6.41224	−0.225582
$809$	−47.6933	−1.67681	−0.838404	−	0.545049i	$-0.816511\pi$
$809$	−47.6933	−1.67681	−0.838404	+	0.545049i	$0.816511\pi$
$810$	4.07328	0.143120
$811$	−12.8900	−0.452628	−0.226314	−	0.974054i	$-0.572667\pi$
$811$	−12.8900	−0.452628	−0.226314	+	0.974054i	$0.572667\pi$
$812$	−19.4577	−0.682832
$813$	−10.1876	−0.357295
$814$	13.5925	0.476416
$815$	−104.169	−3.64889
$816$	−19.7619	−0.691804
$817$	−34.5278	−1.20798
$818$	−27.5849	−0.964482
$819$	−20.3822	−0.712210
$820$	27.3830	0.956257
$821$	−42.5928	−1.48650	−0.743249	−	0.669015i	$-0.766716\pi$
$821$	−42.5928	−1.48650	−0.743249	+	0.669015i	$0.766716\pi$
$822$	−7.64567	−0.266673
$823$	−33.4492	−1.16597	−0.582983	−	0.812485i	$-0.698114\pi$
$823$	−33.4492	−1.16597	−0.582983	+	0.812485i	$0.698114\pi$
$824$	−17.9129	−0.624024
$825$	−181.088	−6.30466
$826$	−3.58961	−0.124899
$827$	−3.05558	−0.106253	−0.0531264	−	0.998588i	$-0.516919\pi$
$827$	−3.05558	−0.106253	−0.0531264	+	0.998588i	$0.516919\pi$
$828$	−28.4848	−0.989916
$829$	27.2964	0.948043	0.474021	−	0.880513i	$-0.342802\pi$
$829$	27.2964	0.948043	0.474021	+	0.880513i	$0.342802\pi$
$830$	−14.4981	−0.503235
$831$	−17.2274	−0.597613
$832$	−0.947866	−0.0328613
$833$	80.4574	2.78768
$834$	−32.8653	−1.13803
$835$	83.9098	2.90382
$836$	−23.2262	−0.803296
$837$	17.4406	0.602835
$838$	−6.17946	−0.213466
$839$	−3.94524	−0.136205	−0.0681025	−	0.997678i	$-0.521694\pi$
$839$	−3.94524	−0.136205	−0.0681025	+	0.997678i	$0.521694\pi$
$840$	−50.4321	−1.74007
$841$	−8.55015	−0.294833
$842$	12.2635	0.422630
$843$	−10.8714	−0.374429
$844$	−12.5821	−0.433094
$845$	−50.1560	−1.72542
$846$	−13.8412	−0.475870
$847$	71.6402	2.46159
$848$	−0.526427	−0.0180776
$849$	−35.5766	−1.22098
$850$	85.0970	2.91880
$851$	−14.7336	−0.505062
$852$	−9.89243	−0.338909
$853$	24.0330	0.822874	0.411437	−	0.911438i	$-0.365027\pi$
$853$	24.0330	0.822874	0.411437	+	0.911438i	$0.365027\pi$
$854$	−6.24457	−0.213685
$855$	−91.4894	−3.12887
$856$	−15.0480	−0.514329
$857$	27.8066	0.949854	0.474927	−	0.880025i	$-0.342474\pi$
$857$	27.8066	0.949854	0.474927	+	0.880025i	$0.342474\pi$
$858$	14.0952	0.481202
$859$	27.3910	0.934569	0.467284	−	0.884107i	$-0.345232\pi$
$859$	27.3910	0.934569	0.467284	+	0.884107i	$0.345232\pi$
$860$	32.3980	1.10476
$861$	−80.3942	−2.73983
$862$	−11.5482	−0.393332
$863$	45.9950	1.56569	0.782843	−	0.622219i	$-0.213769\pi$
$863$	45.9950	1.56569	0.782843	+	0.622219i	$0.213769\pi$
$864$	−5.64903	−0.192184
$865$	31.1801	1.06015
$866$	28.6315	0.972937
$867$	−90.0193	−3.05722
$868$	−13.2842	−0.450894
$869$	−75.0377	−2.54548
$870$	53.0036	1.79699
$871$	−7.57018	−0.256506
$872$	4.10469	0.139002
$873$	−46.7723	−1.58300
$874$	25.1762	0.851596
$875$	128.001	4.32721
$876$	3.92005	0.132446
$877$	−22.7829	−0.769323	−0.384662	−	0.923058i	$-0.625682\pi$
$877$	−22.7829	−0.769323	−0.384662	+	0.923058i	$0.625682\pi$
$878$	−32.6896	−1.10322
$879$	20.3134	0.685154
$880$	21.7936	0.734661
$881$	46.9093	1.58041	0.790206	−	0.612841i	$-0.209973\pi$
$881$	46.9093	1.58041	0.790206	+	0.612841i	$0.209973\pi$
$882$	57.5403	1.93748
$883$	32.9657	1.10938	0.554692	−	0.832055i	$-0.312836\pi$
$883$	32.9657	1.10938	0.554692	+	0.832055i	$0.312836\pi$
$884$	−6.62365	−0.222777
$885$	9.77825	0.328692
$886$	−13.8910	−0.466677
$887$	−10.9758	−0.368530	−0.184265	−	0.982877i	$-0.558990\pi$
$887$	−10.9758	−0.368530	−0.184265	+	0.982877i	$0.558990\pi$
$888$	−7.31022	−0.245315
$889$	14.3368	0.480840
$890$	21.2522	0.712376
$891$	5.16783	0.173129
$892$	−3.19285	−0.106904
$893$	12.2335	0.409377
$894$	−27.4094	−0.916707
$895$	−90.0283	−3.00932
$896$	4.30276	0.143745
$897$	−15.2785	−0.510136
$898$	29.8121	0.994843
$899$	13.9615	0.465642
$900$	60.8584	2.02861
$901$	−3.67865	−0.122554
$902$	34.7413	1.15676
$903$	−95.1178	−3.16532
$904$	−7.80299	−0.259524
$905$	−65.2733	−2.16976
$906$	30.7694	1.02225
$907$	25.7861	0.856213	0.428107	−	0.903728i	$-0.359181\pi$
$907$	25.7861	0.856213	0.428107	+	0.903728i	$0.359181\pi$
$908$	19.3606	0.642503
$909$	−32.0454	−1.06288
$910$	−16.9035	−0.560345
$911$	0.315041	0.0104378	0.00521890	−	0.999986i	$-0.498339\pi$
$911$	0.315041	0.0104378	0.00521890	+	0.999986i	$0.498339\pi$
$912$	12.4914	0.413631
$913$	−18.3939	−0.608750
$914$	33.3895	1.10443
$915$	17.0105	0.562348
$916$	28.3848	0.937859
$917$	58.5816	1.93453
$918$	−39.4752	−1.30288
$919$	7.73415	0.255126	0.127563	−	0.991830i	$-0.459284\pi$
$919$	7.73415	0.255126	0.127563	+	0.991830i	$0.459284\pi$
$920$	−23.6232	−0.778834
$921$	14.1689	0.466880
$922$	−17.1334	−0.564259
$923$	−3.31567	−0.109137
$924$	−63.9840	−2.10492
$925$	31.4787	1.03501
$926$	27.5520	0.905415
$927$	−89.5202	−2.94023
$928$	−4.52215	−0.148447
$929$	−5.33488	−0.175032	−0.0875158	−	0.996163i	$-0.527893\pi$
$929$	−5.33488	−0.175032	−0.0875158	+	0.996163i	$0.527893\pi$
$930$	36.1866	1.18660
$931$	−50.8567	−1.66676
$932$	−10.8599	−0.355729
$933$	89.2240	2.92106
$934$	−20.9913	−0.686855
$935$	152.293	4.98050
$936$	−4.73700	−0.154834
$937$	42.1559	1.37717	0.688586	−	0.725154i	$-0.258232\pi$
$937$	42.1559	1.37717	0.688586	+	0.725154i	$0.258232\pi$
$938$	34.3642	1.12203
$939$	−10.1710	−0.331918
$940$	−11.4789	−0.374399
$941$	−9.64374	−0.314377	−0.157188	−	0.987569i	$-0.550243\pi$
$941$	−9.64374	−0.314377	−0.157188	+	0.987569i	$0.550243\pi$
$942$	51.7805	1.68710
$943$	−37.6579	−1.22631
$944$	−0.834258	−0.0271528
$945$	−100.740	−3.27708
$946$	41.1039	1.33640
$947$	18.6698	0.606686	0.303343	−	0.952881i	$-0.401897\pi$
$947$	18.6698	0.606686	0.303343	+	0.952881i	$0.401897\pi$
$948$	40.3563	1.31071
$949$	1.31389	0.0426508
$950$	−53.7894	−1.74516
$951$	−24.7939	−0.803997
$952$	30.0675	0.974493
$953$	40.1027	1.29905	0.649527	−	0.760338i	$-0.274967\pi$
$953$	40.1027	1.29905	0.649527	+	0.760338i	$0.274967\pi$
$954$	−2.63084	−0.0851766
$955$	−47.4913	−1.53678
$956$	−20.8468	−0.674234
$957$	67.2465	2.17377
$958$	33.3418	1.07722
$959$	11.6328	0.375643
$960$	−11.7209	−0.378290
$961$	−21.4682	−0.692523
$962$	−2.45019	−0.0789972
$963$	−75.2029	−2.42338
$964$	21.6663	0.697825
$965$	−26.3583	−0.848503
$966$	69.3557	2.23148
$967$	41.2749	1.32731	0.663655	−	0.748039i	$-0.269004\pi$
$967$	41.2749	1.32731	0.663655	+	0.748039i	$0.269004\pi$
$968$	16.6498	0.535146
$969$	87.2893	2.80414
$970$	−38.7895	−1.24546
$971$	8.01603	0.257247	0.128623	−	0.991694i	$-0.458944\pi$
$971$	8.01603	0.257247	0.128623	+	0.991694i	$0.458944\pi$
$972$	14.1678	0.454431
$973$	50.0042	1.60306
$974$	21.3992	0.685675
$975$	32.6429	1.04541
$976$	−1.45129	−0.0464548
$977$	−28.7847	−0.920903	−0.460452	−	0.887685i	$-0.652312\pi$
$977$	−28.7847	−0.920903	−0.460452	+	0.887685i	$0.652312\pi$
$978$	71.0781	2.27283
$979$	26.9630	0.861741
$980$	47.7197	1.52435
$981$	20.5134	0.654941
$982$	11.4405	0.365080
$983$	33.1272	1.05660	0.528298	−	0.849059i	$-0.322831\pi$
$983$	33.1272	1.05660	0.528298	+	0.849059i	$0.322831\pi$
$984$	−18.6843	−0.595635
$985$	−65.6330	−2.09124
$986$	−31.6006	−1.00637
$987$	33.7009	1.07271
$988$	4.18677	0.133199
$989$	−44.5547	−1.41676
$990$	108.914	3.46152
$991$	−15.6009	−0.495580	−0.247790	−	0.968814i	$-0.579704\pi$
$991$	−15.6009	−0.495580	−0.247790	+	0.968814i	$0.579704\pi$
$992$	−3.08736	−0.0980237
$993$	−73.7075	−2.33904
$994$	15.0512	0.477396
$995$	46.0002	1.45830
$996$	9.89251	0.313456
$997$	−29.4346	−0.932204	−0.466102	−	0.884731i	$-0.654342\pi$
$997$	−29.4346	−0.932204	−0.466102	+	0.884731i	$0.654342\pi$
$998$	−12.5232	−0.396415
$999$	−14.6025	−0.462002

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8002.2.a.g.1.5	✓	95

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8002.2.a.g.1.5	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.82799 q^{3} +1.00000 q^{4} +4.14459 q^{5} -2.82799 q^{6} +4.30276 q^{7} +1.00000 q^{8} +4.99754 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.82799 q^{3} +1.00000 q^{4} +4.14459 q^{5} -2.82799 q^{6} +4.30276 q^{7} +1.00000 q^{8} +4.99754 q^{9} +4.14459 q^{10} +5.25831 q^{11} -2.82799 q^{12} -0.947866 q^{13} +4.30276 q^{14} -11.7209 q^{15} +1.00000 q^{16} +6.98796 q^{17} +4.99754 q^{18} -4.41705 q^{19} +4.14459 q^{20} -12.1682 q^{21} +5.25831 q^{22} -5.69976 q^{23} -2.82799 q^{24} +12.1777 q^{25} -0.947866 q^{26} -5.64903 q^{27} +4.30276 q^{28} -4.52215 q^{29} -11.7209 q^{30} -3.08736 q^{31} +1.00000 q^{32} -14.8705 q^{33} +6.98796 q^{34} +17.8332 q^{35} +4.99754 q^{36} +2.58495 q^{37} -4.41705 q^{38} +2.68056 q^{39} +4.14459 q^{40} +6.60693 q^{41} -12.1682 q^{42} +7.81694 q^{43} +5.25831 q^{44} +20.7128 q^{45} -5.69976 q^{46} -2.76960 q^{47} -2.82799 q^{48} +11.5137 q^{49} +12.1777 q^{50} -19.7619 q^{51} -0.947866 q^{52} -0.526427 q^{53} -5.64903 q^{54} +21.7936 q^{55} +4.30276 q^{56} +12.4914 q^{57} -4.52215 q^{58} -0.834258 q^{59} -11.7209 q^{60} -1.45129 q^{61} -3.08736 q^{62} +21.5032 q^{63} +1.00000 q^{64} -3.92852 q^{65} -14.8705 q^{66} +7.98655 q^{67} +6.98796 q^{68} +16.1189 q^{69} +17.8332 q^{70} +3.49804 q^{71} +4.99754 q^{72} -1.38616 q^{73} +2.58495 q^{74} -34.4384 q^{75} -4.41705 q^{76} +22.6252 q^{77} +2.68056 q^{78} -14.2703 q^{79} +4.14459 q^{80} +0.982793 q^{81} +6.60693 q^{82} -3.49807 q^{83} -12.1682 q^{84} +28.9622 q^{85} +7.81694 q^{86} +12.7886 q^{87} +5.25831 q^{88} +5.12769 q^{89} +20.7128 q^{90} -4.07844 q^{91} -5.69976 q^{92} +8.73102 q^{93} -2.76960 q^{94} -18.3069 q^{95} -2.82799 q^{96} -9.35906 q^{97} +11.5137 q^{98} +26.2786 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 95 q + 95 q^{2} + 24 q^{3} + 95 q^{4} + 36 q^{5} + 24 q^{6} + 21 q^{7} + 95 q^{8} + 121 q^{9}+O(q^{10}) \) 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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