LMFDB - Embedded newform 8007.2.a.c.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("8007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$63.9362168984$
Analytic rank:	$1$
Dimension:	$39$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
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)

$f(q)$	$=$	$q-1.11359 q^{2} -1.00000 q^{3} -0.759925 q^{4} +3.93850 q^{5} +1.11359 q^{6} -0.664710 q^{7} +3.07342 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.11359 q^{2} -1.00000 q^{3} -0.759925 q^{4} +3.93850 q^{5} +1.11359 q^{6} -0.664710 q^{7} +3.07342 q^{8} +1.00000 q^{9} -4.38586 q^{10} -0.0151446 q^{11} +0.759925 q^{12} -6.55713 q^{13} +0.740212 q^{14} -3.93850 q^{15} -1.90266 q^{16} +1.00000 q^{17} -1.11359 q^{18} -4.92435 q^{19} -2.99296 q^{20} +0.664710 q^{21} +0.0168648 q^{22} -3.50617 q^{23} -3.07342 q^{24} +10.5118 q^{25} +7.30193 q^{26} -1.00000 q^{27} +0.505129 q^{28} +1.35514 q^{29} +4.38586 q^{30} +2.28531 q^{31} -4.02805 q^{32} +0.0151446 q^{33} -1.11359 q^{34} -2.61796 q^{35} -0.759925 q^{36} +7.08441 q^{37} +5.48369 q^{38} +6.55713 q^{39} +12.1046 q^{40} +4.03352 q^{41} -0.740212 q^{42} +5.32242 q^{43} +0.0115088 q^{44} +3.93850 q^{45} +3.90443 q^{46} +7.02539 q^{47} +1.90266 q^{48} -6.55816 q^{49} -11.7058 q^{50} -1.00000 q^{51} +4.98293 q^{52} -4.34647 q^{53} +1.11359 q^{54} -0.0596470 q^{55} -2.04293 q^{56} +4.92435 q^{57} -1.50907 q^{58} +3.23899 q^{59} +2.99296 q^{60} -1.92272 q^{61} -2.54489 q^{62} -0.664710 q^{63} +8.29091 q^{64} -25.8252 q^{65} -0.0168648 q^{66} +4.40690 q^{67} -0.759925 q^{68} +3.50617 q^{69} +2.91532 q^{70} -9.05453 q^{71} +3.07342 q^{72} -0.978746 q^{73} -7.88910 q^{74} -10.5118 q^{75} +3.74213 q^{76} +0.0100668 q^{77} -7.30193 q^{78} +11.6224 q^{79} -7.49364 q^{80} +1.00000 q^{81} -4.49167 q^{82} -1.32842 q^{83} -0.505129 q^{84} +3.93850 q^{85} -5.92698 q^{86} -1.35514 q^{87} -0.0465457 q^{88} -12.7814 q^{89} -4.38586 q^{90} +4.35859 q^{91} +2.66443 q^{92} -2.28531 q^{93} -7.82339 q^{94} -19.3945 q^{95} +4.02805 q^{96} -8.64352 q^{97} +7.30308 q^{98} -0.0151446 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 39 q - 4 q^{2} - 39 q^{3} + 30 q^{4} - 3 q^{5} + 4 q^{6} - 5 q^{7} - 3 q^{8} + 39 q^{9}+O(q^{10}) $ 39 * q - 4 * q^2 - 39 * q^3 + 30 * q^4 - 3 * q^5 + 4 * q^6 - 5 * q^7 - 3 * q^8 + 39 * q^9	\( 39 q - 4 q^{2} - 39 q^{3} + 30 q^{4} - 3 q^{5} + 4 q^{6} - 5 q^{7} - 3 q^{8} + 39 q^{9} + 4 q^{10} + q^{11} - 30 q^{12} - 26 q^{13} - 4 q^{14} + 3 q^{15} + 8 q^{16} + 39 q^{17} - 4 q^{18} - 14 q^{19} - 14 q^{20} + 5 q^{21} - 17 q^{22} + 2 q^{23} + 3 q^{24} - 6 q^{25} - 17 q^{26} - 39 q^{27} - 14 q^{28} - 7 q^{29} - 4 q^{30} - q^{31} - 30 q^{32} - q^{33} - 4 q^{34} + q^{35} + 30 q^{36} - 24 q^{37} - 20 q^{38} + 26 q^{39} + 12 q^{40} + q^{41} + 4 q^{42} - 41 q^{43} - 2 q^{44} - 3 q^{45} - 6 q^{46} - 9 q^{47} - 8 q^{48} - 10 q^{49} - 9 q^{50} - 39 q^{51} - 37 q^{52} - 47 q^{53} + 4 q^{54} - 39 q^{55} + 8 q^{56} + 14 q^{57} - 27 q^{58} + 41 q^{59} + 14 q^{60} - 41 q^{61} + 36 q^{62} - 5 q^{63} - 47 q^{64} - 39 q^{65} + 17 q^{66} - 36 q^{67} + 30 q^{68} - 2 q^{69} - 52 q^{70} - 2 q^{71} - 3 q^{72} - 63 q^{73} - 6 q^{74} + 6 q^{75} - 34 q^{76} - 64 q^{77} + 17 q^{78} + 20 q^{79} - 28 q^{80} + 39 q^{81} - 37 q^{82} + 45 q^{83} + 14 q^{84} - 3 q^{85} + 32 q^{86} + 7 q^{87} + 6 q^{88} - 32 q^{89} + 4 q^{90} - 11 q^{91} + 28 q^{92} + q^{93} - 44 q^{94} + 22 q^{95} + 30 q^{96} - 20 q^{97} + 63 q^{98} + q^{99}+O(q^{100}) \) 39 * q - 4 * q^2 - 39 * q^3 + 30 * q^4 - 3 * q^5 + 4 * q^6 - 5 * q^7 - 3 * q^8 + 39 * q^9 + 4 * q^10 + q^11 - 30 * q^12 - 26 * q^13 - 4 * q^14 + 3 * q^15 + 8 * q^16 + 39 * q^17 - 4 * q^18 - 14 * q^19 - 14 * q^20 + 5 * q^21 - 17 * q^22 + 2 * q^23 + 3 * q^24 - 6 * q^25 - 17 * q^26 - 39 * q^27 - 14 * q^28 - 7 * q^29 - 4 * q^30 - q^31 - 30 * q^32 - q^33 - 4 * q^34 + q^35 + 30 * q^36 - 24 * q^37 - 20 * q^38 + 26 * q^39 + 12 * q^40 + q^41 + 4 * q^42 - 41 * q^43 - 2 * q^44 - 3 * q^45 - 6 * q^46 - 9 * q^47 - 8 * q^48 - 10 * q^49 - 9 * q^50 - 39 * q^51 - 37 * q^52 - 47 * q^53 + 4 * q^54 - 39 * q^55 + 8 * q^56 + 14 * q^57 - 27 * q^58 + 41 * q^59 + 14 * q^60 - 41 * q^61 + 36 * q^62 - 5 * q^63 - 47 * q^64 - 39 * q^65 + 17 * q^66 - 36 * q^67 + 30 * q^68 - 2 * q^69 - 52 * q^70 - 2 * q^71 - 3 * q^72 - 63 * q^73 - 6 * q^74 + 6 * q^75 - 34 * q^76 - 64 * q^77 + 17 * q^78 + 20 * q^79 - 28 * q^80 + 39 * q^81 - 37 * q^82 + 45 * q^83 + 14 * q^84 - 3 * q^85 + 32 * q^86 + 7 * q^87 + 6 * q^88 - 32 * q^89 + 4 * q^90 - 11 * q^91 + 28 * q^92 + q^93 - 44 * q^94 + 22 * q^95 + 30 * q^96 - 20 * q^97 + 63 * q^98 + q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.11359	−0.787425	−0.393712	−	0.919234i	$-0.628809\pi$
$2$	−1.11359	−0.787425	−0.393712	+	0.919234i	$0.628809\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−0.759925	−0.379962
$5$	3.93850	1.76135	0.880675	−	0.473721i	$-0.157090\pi$
$5$	3.93850	1.76135	0.880675	+	0.473721i	$0.157090\pi$
$6$	1.11359	0.454620
$7$	−0.664710	−0.251237	−0.125618	−	0.992079i	$-0.540091\pi$
$7$	−0.664710	−0.251237	−0.125618	+	0.992079i	$0.540091\pi$
$8$	3.07342	1.08662
$9$	1.00000	0.333333
$10$	−4.38586	−1.38693
$11$	−0.0151446	−0.00456627	−0.00228314	−	0.999997i	$-0.500727\pi$
$11$	−0.0151446	−0.00456627	−0.00228314	+	0.999997i	$0.500727\pi$
$12$	0.759925	0.219371
$13$	−6.55713	−1.81862	−0.909310	−	0.416118i	$-0.863390\pi$
$13$	−6.55713	−1.81862	−0.909310	+	0.416118i	$0.863390\pi$
$14$	0.740212	0.197830
$15$	−3.93850	−1.01692
$16$	−1.90266	−0.475666
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−1.11359	−0.262475
$19$	−4.92435	−1.12972	−0.564862	−	0.825186i	$-0.691070\pi$
$19$	−4.92435	−1.12972	−0.564862	+	0.825186i	$0.691070\pi$
$20$	−2.99296	−0.669247
$21$	0.664710	0.145052
$22$	0.0168648	0.00359559
$23$	−3.50617	−0.731088	−0.365544	−	0.930794i	$-0.619117\pi$
$23$	−3.50617	−0.731088	−0.365544	+	0.930794i	$0.619117\pi$
$24$	−3.07342	−0.627358
$25$	10.5118	2.10235
$26$	7.30193	1.43203
$27$	−1.00000	−0.192450
$28$	0.505129	0.0954605
$29$	1.35514	0.251644	0.125822	−	0.992053i	$-0.459843\pi$
$29$	1.35514	0.251644	0.125822	+	0.992053i	$0.459843\pi$
$30$	4.38586	0.800745
$31$	2.28531	0.410454	0.205227	−	0.978714i	$-0.434207\pi$
$31$	2.28531	0.410454	0.205227	+	0.978714i	$0.434207\pi$
$32$	−4.02805	−0.712065
$33$	0.0151446	0.00263634
$34$	−1.11359	−0.190979
$35$	−2.61796	−0.442516
$36$	−0.759925	−0.126654
$37$	7.08441	1.16467	0.582335	−	0.812949i	$-0.302139\pi$
$37$	7.08441	1.16467	0.582335	+	0.812949i	$0.302139\pi$
$38$	5.48369	0.889572
$39$	6.55713	1.04998
$40$	12.1046	1.91391
$41$	4.03352	0.629930	0.314965	−	0.949103i	$-0.398007\pi$
$41$	4.03352	0.629930	0.314965	+	0.949103i	$0.398007\pi$
$42$	−0.740212	−0.114217
$43$	5.32242	0.811662	0.405831	−	0.913948i	$-0.366982\pi$
$43$	5.32242	0.811662	0.405831	+	0.913948i	$0.366982\pi$
$44$	0.0115088	0.00173501
$45$	3.93850	0.587117
$46$	3.90443	0.575676
$47$	7.02539	1.02476	0.512380	−	0.858759i	$-0.328764\pi$
$47$	7.02539	1.02476	0.512380	+	0.858759i	$0.328764\pi$
$48$	1.90266	0.274626
$49$	−6.55816	−0.936880
$50$	−11.7058	−1.65544
$51$	−1.00000	−0.140028
$52$	4.98293	0.691008
$53$	−4.34647	−0.597033	−0.298517	−	0.954404i	$-0.596492\pi$
$53$	−4.34647	−0.597033	−0.298517	+	0.954404i	$0.596492\pi$
$54$	1.11359	0.151540
$55$	−0.0596470	−0.00804280
$56$	−2.04293	−0.272998
$57$	4.92435	0.652246
$58$	−1.50907	−0.198151
$59$	3.23899	0.421681	0.210840	−	0.977521i	$-0.432380\pi$
$59$	3.23899	0.421681	0.210840	+	0.977521i	$0.432380\pi$
$60$	2.99296	0.386390
$61$	−1.92272	−0.246179	−0.123090	−	0.992396i	$-0.539280\pi$
$61$	−1.92272	−0.246179	−0.123090	+	0.992396i	$0.539280\pi$
$62$	−2.54489	−0.323202
$63$	−0.664710	−0.0837456
$64$	8.29091	1.03636
$65$	−25.8252	−3.20323
$66$	−0.0168648	−0.00207592
$67$	4.40690	0.538388	0.269194	−	0.963086i	$-0.413243\pi$
$67$	4.40690	0.538388	0.269194	+	0.963086i	$0.413243\pi$
$68$	−0.759925	−0.0921544
$69$	3.50617	0.422094
$70$	2.91532	0.348448
$71$	−9.05453	−1.07458	−0.537288	−	0.843399i	$-0.680551\pi$
$71$	−9.05453	−1.07458	−0.537288	+	0.843399i	$0.680551\pi$
$72$	3.07342	0.362205
$73$	−0.978746	−0.114554	−0.0572768	−	0.998358i	$-0.518242\pi$
$73$	−0.978746	−0.114554	−0.0572768	+	0.998358i	$0.518242\pi$
$74$	−7.88910	−0.917090
$75$	−10.5118	−1.21379
$76$	3.74213	0.429252
$77$	0.0100668	0.00114721
$78$	−7.30193	−0.826781
$79$	11.6224	1.30763	0.653813	−	0.756656i	$-0.273168\pi$
$79$	11.6224	1.30763	0.653813	+	0.756656i	$0.273168\pi$
$80$	−7.49364	−0.837814
$81$	1.00000	0.111111
$82$	−4.49167	−0.496022
$83$	−1.32842	−0.145813	−0.0729065	−	0.997339i	$-0.523227\pi$
$83$	−1.32842	−0.145813	−0.0729065	+	0.997339i	$0.523227\pi$
$84$	−0.505129	−0.0551141
$85$	3.93850	0.427190
$86$	−5.92698	−0.639123
$87$	−1.35514	−0.145287
$88$	−0.0465457	−0.00496179
$89$	−12.7814	−1.35482	−0.677412	−	0.735604i	$-0.736899\pi$
$89$	−12.7814	−1.35482	−0.677412	+	0.735604i	$0.736899\pi$
$90$	−4.38586	−0.462310
$91$	4.35859	0.456904
$92$	2.66443	0.277786
$93$	−2.28531	−0.236976
$94$	−7.82339	−0.806921
$95$	−19.3945	−1.98984
$96$	4.02805	0.411111
$97$	−8.64352	−0.877616	−0.438808	−	0.898581i	$-0.644599\pi$
$97$	−8.64352	−0.877616	−0.438808	+	0.898581i	$0.644599\pi$
$98$	7.30308	0.737723
$99$	−0.0151446	−0.00152209
$100$	−7.98815	−0.798815
$101$	−12.5700	−1.25076	−0.625378	−	0.780322i	$-0.715055\pi$
$101$	−12.5700	−1.25076	−0.625378	+	0.780322i	$0.715055\pi$
$102$	1.11359	0.110262
$103$	7.23706	0.713088	0.356544	−	0.934278i	$-0.383955\pi$
$103$	7.23706	0.713088	0.356544	+	0.934278i	$0.383955\pi$
$104$	−20.1528	−1.97614
$105$	2.61796	0.255487
$106$	4.84017	0.470119
$107$	12.2336	1.18267	0.591335	−	0.806426i	$-0.298601\pi$
$107$	12.2336	1.18267	0.591335	+	0.806426i	$0.298601\pi$
$108$	0.759925	0.0731238
$109$	−6.26634	−0.600206	−0.300103	−	0.953907i	$-0.597021\pi$
$109$	−6.26634	−0.600206	−0.300103	+	0.953907i	$0.597021\pi$
$110$	0.0664221	0.00633310
$111$	−7.08441	−0.672422
$112$	1.26472	0.119505
$113$	−10.8110	−1.01701	−0.508506	−	0.861058i	$-0.669802\pi$
$113$	−10.8110	−1.01701	−0.508506	+	0.861058i	$0.669802\pi$
$114$	−5.48369	−0.513595
$115$	−13.8091	−1.28770
$116$	−1.02981	−0.0956153
$117$	−6.55713	−0.606207
$118$	−3.60690	−0.332042
$119$	−0.664710	−0.0609338
$120$	−12.1046	−1.10500
$121$	−10.9998	−0.999979
$122$	2.14112	0.193847
$123$	−4.03352	−0.363690
$124$	−1.73666	−0.155957
$125$	21.7081	1.94163
$126$	0.740212	0.0659433
$127$	−2.07988	−0.184560	−0.0922798	−	0.995733i	$-0.529415\pi$
$127$	−2.07988	−0.184560	−0.0922798	+	0.995733i	$0.529415\pi$
$128$	−1.17655	−0.103993
$129$	−5.32242	−0.468613
$130$	28.7586	2.52230
$131$	0.232449	0.0203092	0.0101546	−	0.999948i	$-0.496768\pi$
$131$	0.232449	0.0203092	0.0101546	+	0.999948i	$0.496768\pi$
$132$	−0.0115088	−0.00100171
$133$	3.27326	0.283828
$134$	−4.90746	−0.423940
$135$	−3.93850	−0.338972
$136$	3.07342	0.263543
$137$	−13.9666	−1.19325	−0.596625	−	0.802520i	$-0.703492\pi$
$137$	−13.9666	−1.19325	−0.596625	+	0.802520i	$0.703492\pi$
$138$	−3.90443	−0.332367
$139$	18.9680	1.60884	0.804420	−	0.594061i	$-0.202476\pi$
$139$	18.9680	1.60884	0.804420	+	0.594061i	$0.202476\pi$
$140$	1.98945	0.168139
$141$	−7.02539	−0.591645
$142$	10.0830	0.846147
$143$	0.0993052	0.00830432
$144$	−1.90266	−0.158555
$145$	5.33723	0.443233
$146$	1.08992	0.0902023
$147$	6.55816	0.540908
$148$	−5.38362	−0.442531
$149$	2.38031	0.195002	0.0975012	−	0.995235i	$-0.468915\pi$
$149$	2.38031	0.195002	0.0975012	+	0.995235i	$0.468915\pi$
$150$	11.7058	0.955771
$151$	3.47724	0.282973	0.141487	−	0.989940i	$-0.454812\pi$
$151$	3.47724	0.282973	0.141487	+	0.989940i	$0.454812\pi$
$152$	−15.1346	−1.22758
$153$	1.00000	0.0808452
$154$	−0.0112102	−0.000903345 0
$155$	9.00069	0.722953
$156$	−4.98293	−0.398953
$157$	1.00000	0.0798087
$157$	1.00000	0.0798087
$158$	−12.9426	−1.02966
$159$	4.34647	0.344697
$160$	−15.8645	−1.25420
$161$	2.33059	0.183676
$162$	−1.11359	−0.0874916
$163$	−16.2912	−1.27602	−0.638012	−	0.770026i	$-0.720243\pi$
$163$	−16.2912	−1.27602	−0.638012	+	0.770026i	$0.720243\pi$
$164$	−3.06517	−0.239350
$165$	0.0596470	0.00464351
$166$	1.47931	0.114817
$167$	13.8795	1.07403	0.537014	−	0.843573i	$-0.319552\pi$
$167$	13.8795	1.07403	0.537014	+	0.843573i	$0.319552\pi$
$168$	2.04293	0.157615
$169$	29.9960	2.30738
$170$	−4.38586	−0.336380
$171$	−4.92435	−0.376574
$172$	−4.04464	−0.308401
$173$	−9.58200	−0.728506	−0.364253	−	0.931300i	$-0.618676\pi$
$173$	−9.58200	−0.728506	−0.364253	+	0.931300i	$0.618676\pi$
$174$	1.50907	0.114402
$175$	−6.98727	−0.528188
$176$	0.0288151	0.00217202
$177$	−3.23899	−0.243457
$178$	14.2332	1.06682
$179$	−9.80673	−0.732990	−0.366495	−	0.930420i	$-0.619442\pi$
$179$	−9.80673	−0.732990	−0.366495	+	0.930420i	$0.619442\pi$
$180$	−2.99296	−0.223082
$181$	−26.0286	−1.93469	−0.967346	−	0.253458i	$-0.918432\pi$
$181$	−26.0286	−1.93469	−0.967346	+	0.253458i	$0.918432\pi$
$182$	−4.85367	−0.359778
$183$	1.92272	0.142132
$184$	−10.7759	−0.794412
$185$	27.9019	2.05139
$186$	2.54489	0.186600
$187$	−0.0151446	−0.00110748
$188$	−5.33877	−0.389370
$189$	0.664710	0.0483505
$190$	21.5975	1.56685
$191$	1.36601	0.0988409	0.0494205	−	0.998778i	$-0.484263\pi$
$191$	1.36601	0.0988409	0.0494205	+	0.998778i	$0.484263\pi$
$192$	−8.29091	−0.598345
$193$	−10.7373	−0.772891	−0.386446	−	0.922312i	$-0.626297\pi$
$193$	−10.7373	−0.772891	−0.386446	+	0.922312i	$0.626297\pi$
$194$	9.62530	0.691057
$195$	25.8252	1.84938
$196$	4.98371	0.355979
$197$	−2.86772	−0.204317	−0.102158	−	0.994768i	$-0.532575\pi$
$197$	−2.86772	−0.204317	−0.102158	+	0.994768i	$0.532575\pi$
$198$	0.0168648	0.00119853
$199$	10.5008	0.744379	0.372190	−	0.928157i	$-0.378607\pi$
$199$	10.5008	0.744379	0.372190	+	0.928157i	$0.378607\pi$
$200$	32.3070	2.28445
$201$	−4.40690	−0.310839
$202$	13.9977	0.984877
$203$	−0.900778	−0.0632222
$204$	0.759925	0.0532054
$205$	15.8860	1.10953
$206$	−8.05909	−0.561503
$207$	−3.50617	−0.243696
$208$	12.4760	0.865056
$209$	0.0745773	0.00515862
$210$	−2.91532	−0.201176
$211$	−25.7438	−1.77227	−0.886137	−	0.463423i	$-0.846621\pi$
$211$	−25.7438	−1.77227	−0.886137	+	0.463423i	$0.846621\pi$
$212$	3.30299	0.226850
$213$	9.05453	0.620406
$214$	−13.6232	−0.931264
$215$	20.9624	1.42962
$216$	−3.07342	−0.209119
$217$	−1.51907	−0.103121
$218$	6.97811	0.472617
$219$	0.978746	0.0661375
$220$	0.0453272	0.00305596
$221$	−6.55713	−0.441080
$222$	7.88910	0.529482
$223$	−3.99789	−0.267719	−0.133859	−	0.991000i	$-0.542737\pi$
$223$	−3.99789	−0.267719	−0.133859	+	0.991000i	$0.542737\pi$
$224$	2.67748	0.178897
$225$	10.5118	0.700784
$226$	12.0390	0.800821
$227$	0.220792	0.0146545	0.00732724	−	0.999973i	$-0.497668\pi$
$227$	0.220792	0.0146545	0.00732724	+	0.999973i	$0.497668\pi$
$228$	−3.74213	−0.247829
$229$	−12.5886	−0.831878	−0.415939	−	0.909392i	$-0.636547\pi$
$229$	−12.5886	−0.831878	−0.415939	+	0.909392i	$0.636547\pi$
$230$	15.3776	1.01397
$231$	−0.0100668	−0.000662345 0
$232$	4.16492	0.273441
$233$	12.4088	0.812925	0.406463	−	0.913667i	$-0.366762\pi$
$233$	12.4088	0.812925	0.406463	+	0.913667i	$0.366762\pi$
$234$	7.30193	0.477342
$235$	27.6695	1.80496
$236$	−2.46139	−0.160223
$237$	−11.6224	−0.754958
$238$	0.740212	0.0479808
$239$	22.5900	1.46123	0.730614	−	0.682791i	$-0.239234\pi$
$239$	22.5900	1.46123	0.730614	+	0.682791i	$0.239234\pi$
$240$	7.49364	0.483712
$241$	27.9041	1.79746	0.898730	−	0.438503i	$-0.144491\pi$
$241$	27.9041	1.79746	0.898730	+	0.438503i	$0.144491\pi$
$242$	12.2492	0.787408
$243$	−1.00000	−0.0641500
$244$	1.46112	0.0935388
$245$	−25.8293	−1.65017
$246$	4.49167	0.286379
$247$	32.2896	2.05454
$248$	7.02371	0.446006
$249$	1.32842	0.0841852
$250$	−24.1738	−1.52889
$251$	−0.225146	−0.0142111	−0.00710553	−	0.999975i	$-0.502262\pi$
$251$	−0.225146	−0.0142111	−0.00710553	+	0.999975i	$0.502262\pi$
$252$	0.505129	0.0318202
$253$	0.0530996	0.00333834
$254$	2.31613	0.145327
$255$	−3.93850	−0.246638
$256$	−15.2716	−0.954477
$257$	−19.5245	−1.21791	−0.608953	−	0.793206i	$-0.708410\pi$
$257$	−19.5245	−1.21791	−0.608953	+	0.793206i	$0.708410\pi$
$258$	5.92698	0.368998
$259$	−4.70908	−0.292608
$260$	19.6252	1.21711
$261$	1.35514	0.0838814
$262$	−0.258852	−0.0159919
$263$	−22.8667	−1.41002	−0.705010	−	0.709197i	$-0.749058\pi$
$263$	−22.8667	−1.41002	−0.705010	+	0.709197i	$0.749058\pi$
$264$	0.0465457	0.00286469
$265$	−17.1186	−1.05158
$266$	−3.64506	−0.223493
$267$	12.7814	0.782208
$268$	−3.34891	−0.204567
$269$	10.7794	0.657230	0.328615	−	0.944464i	$-0.393418\pi$
$269$	10.7794	0.657230	0.328615	+	0.944464i	$0.393418\pi$
$270$	4.38586	0.266915
$271$	−1.20599	−0.0732586	−0.0366293	−	0.999329i	$-0.511662\pi$
$271$	−1.20599	−0.0732586	−0.0366293	+	0.999329i	$0.511662\pi$
$272$	−1.90266	−0.115366
$273$	−4.35859	−0.263794
$274$	15.5531	0.939595
$275$	−0.159197	−0.00959991
$276$	−2.66443	−0.160380
$277$	−27.7740	−1.66878	−0.834389	−	0.551175i	$-0.814180\pi$
$277$	−27.7740	−1.66878	−0.834389	+	0.551175i	$0.814180\pi$
$278$	−21.1225	−1.26684
$279$	2.28531	0.136818
$280$	−8.04607	−0.480845
$281$	−3.62902	−0.216489	−0.108245	−	0.994124i	$-0.534523\pi$
$281$	−3.62902	−0.216489	−0.108245	+	0.994124i	$0.534523\pi$
$282$	7.82339	0.465876
$283$	−18.8576	−1.12097	−0.560483	−	0.828166i	$-0.689385\pi$
$283$	−18.8576	−1.12097	−0.560483	+	0.828166i	$0.689385\pi$
$284$	6.88076	0.408298
$285$	19.3945	1.14883
$286$	−0.110585	−0.00653902
$287$	−2.68112	−0.158262
$288$	−4.02805	−0.237355
$289$	1.00000	0.0588235
$290$	−5.94347	−0.349013
$291$	8.64352	0.506692
$292$	0.743773	0.0435260
$293$	−21.7810	−1.27246	−0.636230	−	0.771499i	$-0.719507\pi$
$293$	−21.7810	−1.27246	−0.636230	+	0.771499i	$0.719507\pi$
$294$	−7.30308	−0.425924
$295$	12.7568	0.742727
$296$	21.7733	1.26555
$297$	0.0151446	0.000878779 0
$298$	−2.65068	−0.153550
$299$	22.9904	1.32957
$300$	7.98815	0.461196
$301$	−3.53787	−0.203919
$302$	−3.87220	−0.222820
$303$	12.5700	0.722125
$304$	9.36938	0.537371
$305$	−7.57263	−0.433607
$306$	−1.11359	−0.0636595
$307$	13.6863	0.781121	0.390561	−	0.920577i	$-0.372281\pi$
$307$	13.6863	0.781121	0.390561	+	0.920577i	$0.372281\pi$
$308$	−0.00764999	−0.000435899 0
$309$	−7.23706	−0.411702
$310$	−10.0230	−0.569271
$311$	−17.5550	−0.995453	−0.497726	−	0.867334i	$-0.665832\pi$
$311$	−17.5550	−0.995453	−0.497726	+	0.867334i	$0.665832\pi$
$312$	20.1528	1.14093
$313$	9.29290	0.525266	0.262633	−	0.964896i	$-0.415409\pi$
$313$	9.29290	0.525266	0.262633	+	0.964896i	$0.415409\pi$
$314$	−1.11359	−0.0628433
$315$	−2.61796	−0.147505
$316$	−8.83217	−0.496848
$317$	−1.29130	−0.0725266	−0.0362633	−	0.999342i	$-0.511546\pi$
$317$	−1.29130	−0.0725266	−0.0362633	+	0.999342i	$0.511546\pi$
$318$	−4.84017	−0.271423
$319$	−0.0205231	−0.00114908
$320$	32.6537	1.82540
$321$	−12.2336	−0.682815
$322$	−2.59531	−0.144631
$323$	−4.92435	−0.273998
$324$	−0.759925	−0.0422180
$325$	−68.9270	−3.82338
$326$	18.1417	1.00477
$327$	6.26634	0.346529
$328$	12.3967	0.684492
$329$	−4.66985	−0.257457
$330$	−0.0664221	−0.00365642
$331$	30.8688	1.69670	0.848351	−	0.529434i	$-0.177596\pi$
$331$	30.8688	1.69670	0.848351	+	0.529434i	$0.177596\pi$
$332$	1.00950	0.0554035
$333$	7.08441	0.388223
$334$	−15.4560	−0.845716
$335$	17.3566	0.948290
$336$	−1.26472	−0.0689961
$337$	9.25954	0.504399	0.252200	−	0.967675i	$-0.418846\pi$
$337$	9.25954	0.504399	0.252200	+	0.967675i	$0.418846\pi$
$338$	−33.4031	−1.81689
$339$	10.8110	0.587172
$340$	−2.99296	−0.162316
$341$	−0.0346101	−0.00187424
$342$	5.48369	0.296524
$343$	9.01224	0.486615
$344$	16.3580	0.881965
$345$	13.8091	0.743455
$346$	10.6704	0.573643
$347$	−20.0062	−1.07399	−0.536995	−	0.843586i	$-0.680440\pi$
$347$	−20.0062	−1.07399	−0.536995	+	0.843586i	$0.680440\pi$
$348$	1.02981	0.0552035
$349$	−8.25066	−0.441648	−0.220824	−	0.975314i	$-0.570875\pi$
$349$	−8.25066	−0.441648	−0.220824	+	0.975314i	$0.570875\pi$
$350$	7.78093	0.415908
$351$	6.55713	0.349994
$352$	0.0610032	0.00325148
$353$	−25.4092	−1.35240	−0.676198	−	0.736720i	$-0.736374\pi$
$353$	−25.4092	−1.35240	−0.676198	+	0.736720i	$0.736374\pi$
$354$	3.60690	0.191704
$355$	−35.6613	−1.89270
$356$	9.71289	0.514782
$357$	0.664710	0.0351802
$358$	10.9206	0.577174
$359$	−29.2973	−1.54625	−0.773125	−	0.634254i	$-0.781307\pi$
$359$	−29.2973	−1.54625	−0.773125	+	0.634254i	$0.781307\pi$
$360$	12.1046	0.637971
$361$	5.24921	0.276274
$362$	28.9851	1.52342
$363$	10.9998	0.577338
$364$	−3.31220	−0.173606
$365$	−3.85479	−0.201769
$366$	−2.14112	−0.111918
$367$	−22.1441	−1.15591	−0.577956	−	0.816068i	$-0.696150\pi$
$367$	−22.1441	−1.15591	−0.577956	+	0.816068i	$0.696150\pi$
$368$	6.67107	0.347754
$369$	4.03352	0.209977
$370$	−31.0712	−1.61532
$371$	2.88914	0.149997
$372$	1.73666	0.0900418
$373$	31.3667	1.62411	0.812053	−	0.583583i	$-0.198350\pi$
$373$	31.3667	1.62411	0.812053	+	0.583583i	$0.198350\pi$
$374$	0.0168648	0.000872060 0
$375$	−21.7081	−1.12100
$376$	21.5920	1.11352
$377$	−8.88586	−0.457645
$378$	−0.740212	−0.0380724
$379$	35.4501	1.82095	0.910474	−	0.413566i	$-0.135717\pi$
$379$	35.4501	1.82095	0.910474	+	0.413566i	$0.135717\pi$
$380$	14.7384	0.756063
$381$	2.07988	0.106556
$382$	−1.52117	−0.0778298
$383$	−5.54890	−0.283535	−0.141768	−	0.989900i	$-0.545279\pi$
$383$	−5.54890	−0.283535	−0.141768	+	0.989900i	$0.545279\pi$
$384$	1.17655	0.0600406
$385$	0.0396479	0.00202065
$386$	11.9570	0.608594
$387$	5.32242	0.270554
$388$	6.56842	0.333461
$389$	29.4950	1.49545	0.747727	−	0.664007i	$-0.231145\pi$
$389$	29.4950	1.49545	0.747727	+	0.664007i	$0.231145\pi$
$390$	−28.7586	−1.45625
$391$	−3.50617	−0.177315
$392$	−20.1560	−1.01803
$393$	−0.232449	−0.0117255
$394$	3.19346	0.160884
$395$	45.7749	2.30319
$396$	0.0115088	0.000578337 0
$397$	−30.7013	−1.54085	−0.770427	−	0.637529i	$-0.779957\pi$
$397$	−30.7013	−1.54085	−0.770427	+	0.637529i	$0.779957\pi$
$398$	−11.6935	−0.586142
$399$	−3.27326	−0.163868
$400$	−20.0004	−1.00002
$401$	−32.6316	−1.62954	−0.814772	−	0.579782i	$-0.803138\pi$
$401$	−32.6316	−1.62954	−0.814772	+	0.579782i	$0.803138\pi$
$402$	4.90746	0.244762
$403$	−14.9851	−0.746460
$404$	9.55222	0.475241
$405$	3.93850	0.195706
$406$	1.00309	0.0497827
$407$	−0.107291	−0.00531820
$408$	−3.07342	−0.152157
$409$	−16.2914	−0.805559	−0.402779	−	0.915297i	$-0.631956\pi$
$409$	−16.2914	−0.805559	−0.402779	+	0.915297i	$0.631956\pi$
$410$	−17.6904	−0.873669
$411$	13.9666	0.688923
$412$	−5.49962	−0.270947
$413$	−2.15299	−0.105942
$414$	3.90443	0.191892
$415$	−5.23198	−0.256828
$416$	26.4124	1.29498
$417$	−18.9680	−0.928865
$418$	−0.0830483	−0.00406203
$419$	−0.751310	−0.0367039	−0.0183519	−	0.999832i	$-0.505842\pi$
$419$	−0.751310	−0.0367039	−0.0183519	+	0.999832i	$0.505842\pi$
$420$	−1.98945	−0.0970753
$421$	−4.74793	−0.231400	−0.115700	−	0.993284i	$-0.536911\pi$
$421$	−4.74793	−0.231400	−0.115700	+	0.993284i	$0.536911\pi$
$422$	28.6679	1.39553
$423$	7.02539	0.341586
$424$	−13.3585	−0.648746
$425$	10.5118	0.509895
$426$	−10.0830	−0.488523
$427$	1.27805	0.0618492
$428$	−9.29665	−0.449370
$429$	−0.0993052	−0.00479450
$430$	−23.3434	−1.12572
$431$	−18.9753	−0.914010	−0.457005	−	0.889464i	$-0.651078\pi$
$431$	−18.9753	−0.914010	−0.457005	+	0.889464i	$0.651078\pi$
$432$	1.90266	0.0915420
$433$	−25.5898	−1.22977	−0.614885	−	0.788617i	$-0.710797\pi$
$433$	−25.5898	−1.22977	−0.614885	+	0.788617i	$0.710797\pi$
$434$	1.69161	0.0812001
$435$	−5.33723	−0.255901
$436$	4.76195	0.228056
$437$	17.2656	0.825927
$438$	−1.08992	−0.0520783
$439$	−20.4446	−0.975769	−0.487884	−	0.872908i	$-0.662231\pi$
$439$	−20.4446	−0.975769	−0.487884	+	0.872908i	$0.662231\pi$
$440$	−0.183320	−0.00873944
$441$	−6.55816	−0.312293
$442$	7.30193	0.347318
$443$	23.3161	1.10778	0.553892	−	0.832589i	$-0.313142\pi$
$443$	23.3161	1.10778	0.553892	+	0.832589i	$0.313142\pi$
$444$	5.38362	0.255495
$445$	−50.3395	−2.38632
$446$	4.45200	0.210808
$447$	−2.38031	−0.112585
$448$	−5.51105	−0.260373
$449$	23.2036	1.09505	0.547523	−	0.836791i	$-0.315571\pi$
$449$	23.2036	1.09505	0.547523	+	0.836791i	$0.315571\pi$
$450$	−11.7058	−0.551815
$451$	−0.0610861	−0.00287643
$452$	8.21554	0.386426
$453$	−3.47724	−0.163375
$454$	−0.245871	−0.0115393
$455$	17.1663	0.804768
$456$	15.1346	0.708741
$457$	−1.52731	−0.0714444	−0.0357222	−	0.999362i	$-0.511373\pi$
$457$	−1.52731	−0.0714444	−0.0357222	+	0.999362i	$0.511373\pi$
$458$	14.0185	0.655041
$459$	−1.00000	−0.0466760
$460$	10.4938	0.489278
$461$	−25.8424	−1.20360	−0.601801	−	0.798646i	$-0.705550\pi$
$461$	−25.8424	−1.20360	−0.601801	+	0.798646i	$0.705550\pi$
$462$	0.0112102	0.000521547 0
$463$	9.49382	0.441215	0.220608	−	0.975363i	$-0.429196\pi$
$463$	9.49382	0.441215	0.220608	+	0.975363i	$0.429196\pi$
$464$	−2.57839	−0.119699
$465$	−9.00069	−0.417397
$466$	−13.8182	−0.640117
$467$	27.6421	1.27912	0.639561	−	0.768740i	$-0.279116\pi$
$467$	27.6421	1.27912	0.639561	+	0.768740i	$0.279116\pi$
$468$	4.98293	0.230336
$469$	−2.92931	−0.135263
$470$	−30.8124	−1.42127
$471$	−1.00000	−0.0460776
$472$	9.95476	0.458205
$473$	−0.0806060	−0.00370627
$474$	12.9426	0.594472
$475$	−51.7636	−2.37508
$476$	0.505129	0.0231526
$477$	−4.34647	−0.199011
$478$	−25.1560	−1.15061
$479$	−12.5582	−0.573798	−0.286899	−	0.957961i	$-0.592624\pi$
$479$	−12.5582	−0.573798	−0.286899	+	0.957961i	$0.592624\pi$
$480$	15.8645	0.724110
$481$	−46.4534	−2.11809
$482$	−31.0736	−1.41536
$483$	−2.33059	−0.106045
$484$	8.35900	0.379954
$485$	−34.0425	−1.54579
$486$	1.11359	0.0505133
$487$	−11.0650	−0.501402	−0.250701	−	0.968065i	$-0.580661\pi$
$487$	−11.0650	−0.501402	−0.250701	+	0.968065i	$0.580661\pi$
$488$	−5.90932	−0.267502
$489$	16.2912	0.736713
$490$	28.7632	1.29939
$491$	40.7709	1.83997	0.919984	−	0.391957i	$-0.128202\pi$
$491$	40.7709	1.83997	0.919984	+	0.391957i	$0.128202\pi$
$492$	3.06517	0.138189
$493$	1.35514	0.0610327
$494$	−35.9573	−1.61779
$495$	−0.0596470	−0.00268093
$496$	−4.34818	−0.195239
$497$	6.01864	0.269973
$498$	−1.47931	−0.0662895
$499$	−36.1389	−1.61780	−0.808900	−	0.587946i	$-0.799937\pi$
$499$	−36.1389	−1.61780	−0.808900	+	0.587946i	$0.799937\pi$
$500$	−16.4965	−0.737746
$501$	−13.8795	−0.620090
$502$	0.250719	0.0111901
$503$	10.1957	0.454605	0.227302	−	0.973824i	$-0.427009\pi$
$503$	10.1957	0.454605	0.227302	+	0.973824i	$0.427009\pi$
$504$	−2.04293	−0.0909993
$505$	−49.5067	−2.20302
$506$	−0.0591310	−0.00262870
$507$	−29.9960	−1.33217
$508$	1.58055	0.0701257
$509$	42.4059	1.87961	0.939804	−	0.341713i	$-0.111007\pi$
$509$	42.4059	1.87961	0.939804	+	0.341713i	$0.111007\pi$
$510$	4.38586	0.194209
$511$	0.650582	0.0287801
$512$	19.3594	0.855572
$513$	4.92435	0.217415
$514$	21.7423	0.959010
$515$	28.5031	1.25600
$516$	4.04464	0.178055
$517$	−0.106397	−0.00467933
$518$	5.24396	0.230407
$519$	9.58200	0.420603
$520$	−79.3717	−3.48068
$521$	23.7044	1.03851	0.519254	−	0.854620i	$-0.326210\pi$
$521$	23.7044	1.03851	0.519254	+	0.854620i	$0.326210\pi$
$522$	−1.50907	−0.0660502
$523$	9.60297	0.419909	0.209954	−	0.977711i	$-0.432668\pi$
$523$	9.60297	0.419909	0.209954	+	0.977711i	$0.432668\pi$
$524$	−0.176644	−0.00771671
$525$	6.98727	0.304950
$526$	25.4640	1.11028
$527$	2.28531	0.0995497
$528$	−0.0288151	−0.00125402
$529$	−10.7067	−0.465511
$530$	19.0630	0.828043
$531$	3.23899	0.140560
$532$	−2.48743	−0.107844
$533$	−26.4483	−1.14560
$534$	−14.2332	−0.615930
$535$	48.1822	2.08310
$536$	13.5442	0.585021
$537$	9.80673	0.423192
$538$	−12.0038	−0.517519
$539$	0.0993208	0.00427805
$540$	2.99296	0.128797
$541$	4.36780	0.187786	0.0938931	−	0.995582i	$-0.470069\pi$
$541$	4.36780	0.187786	0.0938931	+	0.995582i	$0.470069\pi$
$542$	1.34297	0.0576856
$543$	26.0286	1.11700
$544$	−4.02805	−0.172701
$545$	−24.6800	−1.05717
$546$	4.85367	0.207718
$547$	−37.6063	−1.60793	−0.803964	−	0.594678i	$-0.797280\pi$
$547$	−37.6063	−1.60793	−0.803964	+	0.594678i	$0.797280\pi$
$548$	10.6136	0.453390
$549$	−1.92272	−0.0820597
$550$	0.177279	0.00755921
$551$	−6.67321	−0.284288
$552$	10.7759	0.458654
$553$	−7.72554	−0.328523
$554$	30.9288	1.31404
$555$	−27.9019	−1.18437
$556$	−14.4142	−0.611299
$557$	−38.3173	−1.62355	−0.811777	−	0.583967i	$-0.801500\pi$
$557$	−38.3173	−1.62355	−0.811777	+	0.583967i	$0.801500\pi$
$558$	−2.54489	−0.107734
$559$	−34.8998	−1.47611
$560$	4.98110	0.210490
$561$	0.0151446	0.000639406 0
$562$	4.04123	0.170469
$563$	−45.8768	−1.93348	−0.966738	−	0.255769i	$-0.917671\pi$
$563$	−45.8768	−1.93348	−0.966738	+	0.255769i	$0.917671\pi$
$564$	5.33877	0.224803
$565$	−42.5791	−1.79131
$566$	20.9996	0.882677
$567$	−0.664710	−0.0279152
$568$	−27.8283	−1.16765
$569$	9.88892	0.414565	0.207283	−	0.978281i	$-0.433538\pi$
$569$	9.88892	0.414565	0.207283	+	0.978281i	$0.433538\pi$
$570$	−21.5975	−0.904620
$571$	−8.14297	−0.340773	−0.170386	−	0.985377i	$-0.554502\pi$
$571$	−8.14297	−0.340773	−0.170386	+	0.985377i	$0.554502\pi$
$572$	−0.0754645	−0.00315533
$573$	−1.36601	−0.0570658
$574$	2.98566	0.124619
$575$	−36.8561	−1.53700
$576$	8.29091	0.345455
$577$	−38.1297	−1.58736	−0.793680	−	0.608335i	$-0.791838\pi$
$577$	−38.1297	−1.58736	−0.793680	+	0.608335i	$0.791838\pi$
$578$	−1.11359	−0.0463191
$579$	10.7373	0.446229
$580$	−4.05590	−0.168412
$581$	0.883014	0.0366336
$582$	−9.62530	−0.398982
$583$	0.0658256	0.00272622
$584$	−3.00809	−0.124476
$585$	−25.8252	−1.06774
$586$	24.2550	1.00197
$587$	−10.1282	−0.418035	−0.209017	−	0.977912i	$-0.567027\pi$
$587$	−10.1282	−0.418035	−0.209017	+	0.977912i	$0.567027\pi$
$588$	−4.98371	−0.205525
$589$	−11.2537	−0.463699
$590$	−14.2058	−0.584842
$591$	2.86772	0.117962
$592$	−13.4793	−0.553994
$593$	26.3363	1.08150	0.540752	−	0.841182i	$-0.318140\pi$
$593$	26.3363	1.08150	0.540752	+	0.841182i	$0.318140\pi$
$594$	−0.0168648	−0.000691973 0
$595$	−2.61796	−0.107326
$596$	−1.80885	−0.0740936
$597$	−10.5008	−0.429767
$598$	−25.6018	−1.04694
$599$	−16.4916	−0.673829	−0.336915	−	0.941535i	$-0.609383\pi$
$599$	−16.4916	−0.673829	−0.336915	+	0.941535i	$0.609383\pi$
$600$	−32.3070	−1.31893
$601$	21.4464	0.874816	0.437408	−	0.899263i	$-0.355897\pi$
$601$	21.4464	0.874816	0.437408	+	0.899263i	$0.355897\pi$
$602$	3.93972	0.160571
$603$	4.40690	0.179463
$604$	−2.64244	−0.107519
$605$	−43.3226	−1.76131
$606$	−13.9977	−0.568619
$607$	36.0688	1.46399	0.731994	−	0.681311i	$-0.238590\pi$
$607$	36.0688	1.46399	0.731994	+	0.681311i	$0.238590\pi$
$608$	19.8355	0.804436
$609$	0.900778	0.0365014
$610$	8.43278	0.341433
$611$	−46.0664	−1.86365
$612$	−0.759925	−0.0307181
$613$	−18.7169	−0.755968	−0.377984	−	0.925812i	$-0.623383\pi$
$613$	−18.7169	−0.755968	−0.377984	+	0.925812i	$0.623383\pi$
$614$	−15.2409	−0.615074
$615$	−15.8860	−0.640586
$616$	0.0309394	0.00124658
$617$	−35.5557	−1.43142	−0.715710	−	0.698398i	$-0.753897\pi$
$617$	−35.5557	−1.43142	−0.715710	+	0.698398i	$0.753897\pi$
$618$	8.05909	0.324184
$619$	22.2461	0.894144	0.447072	−	0.894498i	$-0.352467\pi$
$619$	22.2461	0.894144	0.447072	+	0.894498i	$0.352467\pi$
$620$	−6.83985	−0.274695
$621$	3.50617	0.140698
$622$	19.5490	0.783844
$623$	8.49591	0.340382
$624$	−12.4760	−0.499441
$625$	32.9384	1.31753
$626$	−10.3485	−0.413607
$627$	−0.0745773	−0.00297833
$628$	−0.759925	−0.0303243
$629$	7.08441	0.282474
$630$	2.91532	0.116149
$631$	−33.5509	−1.33564	−0.667820	−	0.744323i	$-0.732772\pi$
$631$	−33.5509	−1.33564	−0.667820	+	0.744323i	$0.732772\pi$
$632$	35.7205	1.42089
$633$	25.7438	1.02322
$634$	1.43797	0.0571093
$635$	−8.19161	−0.325074
$636$	−3.30299	−0.130972
$637$	43.0027	1.70383
$638$	0.0228543	0.000904810 0
$639$	−9.05453	−0.358192
$640$	−4.63384	−0.183169
$641$	−28.7304	−1.13478	−0.567391	−	0.823449i	$-0.692047\pi$
$641$	−28.7304	−1.13478	−0.567391	+	0.823449i	$0.692047\pi$
$642$	13.6232	0.537666
$643$	−13.4185	−0.529174	−0.264587	−	0.964362i	$-0.585236\pi$
$643$	−13.4185	−0.529174	−0.264587	+	0.964362i	$0.585236\pi$
$644$	−1.77107	−0.0697900
$645$	−20.9624	−0.825392
$646$	5.48369	0.215753
$647$	10.3249	0.405912	0.202956	−	0.979188i	$-0.434945\pi$
$647$	10.3249	0.405912	0.202956	+	0.979188i	$0.434945\pi$
$648$	3.07342	0.120735
$649$	−0.0490532	−0.00192551
$650$	76.7562	3.01063
$651$	1.51907	0.0595370
$652$	12.3801	0.484841
$653$	22.2499	0.870707	0.435354	−	0.900260i	$-0.356623\pi$
$653$	22.2499	0.870707	0.435354	+	0.900260i	$0.356623\pi$
$654$	−6.97811	−0.272866
$655$	0.915499	0.0357715
$656$	−7.67444	−0.299636
$657$	−0.978746	−0.0381845
$658$	5.20028	0.202728
$659$	10.2906	0.400863	0.200431	−	0.979708i	$-0.435766\pi$
$659$	10.2906	0.400863	0.200431	+	0.979708i	$0.435766\pi$
$660$	−0.0453272	−0.00176436
$661$	22.5099	0.875535	0.437767	−	0.899088i	$-0.355769\pi$
$661$	22.5099	0.875535	0.437767	+	0.899088i	$0.355769\pi$
$662$	−34.3751	−1.33603
$663$	6.55713	0.254658
$664$	−4.08279	−0.158443
$665$	12.8917	0.499920
$666$	−7.88910	−0.305697
$667$	−4.75137	−0.183974
$668$	−10.5474	−0.408090
$669$	3.99789	0.154568
$670$	−19.3280	−0.746707
$671$	0.0291188	0.00112412
$672$	−2.67748	−0.103286
$673$	−3.48694	−0.134412	−0.0672058	−	0.997739i	$-0.521408\pi$
$673$	−3.48694	−0.134412	−0.0672058	+	0.997739i	$0.521408\pi$
$674$	−10.3113	−0.397176
$675$	−10.5118	−0.404598
$676$	−22.7947	−0.876718
$677$	−2.33938	−0.0899097	−0.0449549	−	0.998989i	$-0.514314\pi$
$677$	−2.33938	−0.0899097	−0.0449549	+	0.998989i	$0.514314\pi$
$678$	−12.0390	−0.462354
$679$	5.74543	0.220489
$680$	12.1046	0.464192
$681$	−0.220792	−0.00846077
$682$	0.0385414	0.00147583
$683$	−4.56267	−0.174586	−0.0872929	−	0.996183i	$-0.527822\pi$
$683$	−4.56267	−0.174586	−0.0872929	+	0.996183i	$0.527822\pi$
$684$	3.74213	0.143084
$685$	−55.0076	−2.10173
$686$	−10.0359	−0.383173
$687$	12.5886	0.480285
$688$	−10.1268	−0.386080
$689$	28.5004	1.08578
$690$	−15.3776	−0.585414
$691$	−22.7211	−0.864352	−0.432176	−	0.901789i	$-0.642254\pi$
$691$	−22.7211	−0.864352	−0.432176	+	0.901789i	$0.642254\pi$
$692$	7.28160	0.276805
$693$	0.0100668	0.000382405 0
$694$	22.2786	0.845686
$695$	74.7052	2.83373
$696$	−4.16492	−0.157871
$697$	4.03352	0.152780
$698$	9.18782	0.347764
$699$	−12.4088	−0.469343
$700$	5.30980	0.200692
$701$	−0.376777	−0.0142307	−0.00711534	−	0.999975i	$-0.502265\pi$
$701$	−0.376777	−0.0142307	−0.00711534	+	0.999975i	$0.502265\pi$
$702$	−7.30193	−0.275594
$703$	−34.8861	−1.31575
$704$	−0.125563	−0.00473232
$705$	−27.6695	−1.04209
$706$	28.2954	1.06491
$707$	8.35537	0.314236
$708$	2.46139	0.0925047
$709$	0.759236	0.0285137	0.0142569	−	0.999898i	$-0.495462\pi$
$709$	0.759236	0.0285137	0.0142569	+	0.999898i	$0.495462\pi$
$710$	39.7119	1.49036
$711$	11.6224	0.435875
$712$	−39.2825	−1.47217
$713$	−8.01269	−0.300078
$714$	−0.740212	−0.0277017
$715$	0.391113	0.0146268
$716$	7.45238	0.278509
$717$	−22.5900	−0.843640
$718$	32.6250	1.21756
$719$	−7.56058	−0.281962	−0.140981	−	0.990012i	$-0.545026\pi$
$719$	−7.56058	−0.281962	−0.140981	+	0.990012i	$0.545026\pi$
$720$	−7.49364	−0.279271
$721$	−4.81054	−0.179154
$722$	−5.84545	−0.217545
$723$	−27.9041	−1.03776
$724$	19.7798	0.735111
$725$	14.2450	0.529045
$726$	−12.2492	−0.454610
$727$	−7.62625	−0.282842	−0.141421	−	0.989950i	$-0.545167\pi$
$727$	−7.62625	−0.282842	−0.141421	+	0.989950i	$0.545167\pi$
$728$	13.3958	0.496480
$729$	1.00000	0.0370370
$730$	4.29264	0.158878
$731$	5.32242	0.196857
$732$	−1.46112	−0.0540046
$733$	19.8527	0.733277	0.366638	−	0.930364i	$-0.380509\pi$
$733$	19.8527	0.733277	0.366638	+	0.930364i	$0.380509\pi$
$734$	24.6594	0.910194
$735$	25.8293	0.952728
$736$	14.1230	0.520582
$737$	−0.0667407	−0.00245843
$738$	−4.49167	−0.165341
$739$	3.40987	0.125434	0.0627171	−	0.998031i	$-0.480023\pi$
$739$	3.40987	0.125434	0.0627171	+	0.998031i	$0.480023\pi$
$740$	−21.2034	−0.779451
$741$	−32.2896	−1.18619
$742$	−3.21731	−0.118111
$743$	−33.5979	−1.23259	−0.616293	−	0.787517i	$-0.711366\pi$
$743$	−33.5979	−1.23259	−0.616293	+	0.787517i	$0.711366\pi$
$744$	−7.02371	−0.257502
$745$	9.37483	0.343467
$746$	−34.9296	−1.27886
$747$	−1.32842	−0.0486044
$748$	0.0115088	0.000420802 0
$749$	−8.13182	−0.297130
$750$	24.1738	0.882703
$751$	0.610032	0.0222604	0.0111302	−	0.999938i	$-0.496457\pi$
$751$	0.610032	0.0222604	0.0111302	+	0.999938i	$0.496457\pi$
$752$	−13.3670	−0.487443
$753$	0.225146	0.00820476
$754$	9.89518	0.360361
$755$	13.6951	0.498415
$756$	−0.505129	−0.0183714
$757$	1.27772	0.0464397	0.0232198	−	0.999730i	$-0.492608\pi$
$757$	1.27772	0.0464397	0.0232198	+	0.999730i	$0.492608\pi$
$758$	−39.4767	−1.43386
$759$	−0.0530996	−0.00192739
$760$	−59.6075	−2.16219
$761$	43.5102	1.57724	0.788621	−	0.614880i	$-0.210795\pi$
$761$	43.5102	1.57724	0.788621	+	0.614880i	$0.210795\pi$
$762$	−2.31613	−0.0839045
$763$	4.16530	0.150794
$764$	−1.03806	−0.0375558
$765$	3.93850	0.142397
$766$	6.17918	0.223263
$767$	−21.2385	−0.766877
$768$	15.2716	0.551068
$769$	19.6201	0.707519	0.353760	−	0.935336i	$-0.384903\pi$
$769$	19.6201	0.707519	0.353760	+	0.935336i	$0.384903\pi$
$770$	−0.0441514	−0.00159111
$771$	19.5245	0.703159
$772$	8.15958	0.293670
$773$	32.7614	1.17835	0.589173	−	0.808007i	$-0.299454\pi$
$773$	32.7614	1.17835	0.589173	+	0.808007i	$0.299454\pi$
$774$	−5.92698	−0.213041
$775$	24.0226	0.862919
$776$	−26.5651	−0.953632
$777$	4.70908	0.168937
$778$	−32.8452	−1.17756
$779$	−19.8625	−0.711646
$780$	−19.6252	−0.702696
$781$	0.137127	0.00490680
$782$	3.90443	0.139622
$783$	−1.35514	−0.0484289
$784$	12.4780	0.445642
$785$	3.93850	0.140571
$786$	0.258852	0.00923294
$787$	30.2991	1.08004	0.540022	−	0.841651i	$-0.318416\pi$
$787$	30.2991	1.08004	0.540022	+	0.841651i	$0.318416\pi$
$788$	2.17925	0.0776327
$789$	22.8667	0.814075
$790$	−50.9743	−1.81358
$791$	7.18617	0.255511
$792$	−0.0465457	−0.00165393
$793$	12.6075	0.447706
$794$	34.1885	1.21331
$795$	17.1186	0.607132
$796$	−7.97979	−0.282836
$797$	1.57065	0.0556353	0.0278176	−	0.999613i	$-0.491144\pi$
$797$	1.57065	0.0556353	0.0278176	+	0.999613i	$0.491144\pi$
$798$	3.64506	0.129034
$799$	7.02539	0.248541
$800$	−42.3419	−1.49701
$801$	−12.7814	−0.451608
$802$	36.3381	1.28314
$803$	0.0148227	0.000523083 0
$804$	3.34891	0.118107
$805$	9.17901	0.323518
$806$	16.6872	0.587781
$807$	−10.7794	−0.379452
$808$	−38.6327	−1.35909
$809$	−22.1480	−0.778684	−0.389342	−	0.921093i	$-0.627298\pi$
$809$	−22.1480	−0.778684	−0.389342	+	0.921093i	$0.627298\pi$
$810$	−4.38586	−0.154103
$811$	−6.45117	−0.226531	−0.113266	−	0.993565i	$-0.536131\pi$
$811$	−6.45117	−0.226531	−0.113266	+	0.993565i	$0.536131\pi$
$812$	0.684523	0.0240221
$813$	1.20599	0.0422959
$814$	0.119477	0.00418768
$815$	−64.1628	−2.24753
$816$	1.90266	0.0666066
$817$	−26.2095	−0.916953
$818$	18.1419	0.634317
$819$	4.35859	0.152301
$820$	−12.0722	−0.421579
$821$	10.9347	0.381623	0.190811	−	0.981627i	$-0.438888\pi$
$821$	10.9347	0.381623	0.190811	+	0.981627i	$0.438888\pi$
$822$	−15.5531	−0.542475
$823$	7.93657	0.276652	0.138326	−	0.990387i	$-0.455828\pi$
$823$	7.93657	0.276652	0.138326	+	0.990387i	$0.455828\pi$
$824$	22.2425	0.774853
$825$	0.159197	0.00554251
$826$	2.39754	0.0834211
$827$	−33.8913	−1.17852	−0.589258	−	0.807945i	$-0.700580\pi$
$827$	−33.8913	−1.17852	−0.589258	+	0.807945i	$0.700580\pi$
$828$	2.66443	0.0925953
$829$	0.0697440	0.00242231	0.00121115	−	0.999999i	$-0.499614\pi$
$829$	0.0697440	0.00242231	0.00121115	+	0.999999i	$0.499614\pi$
$830$	5.82626	0.202233
$831$	27.7740	0.963470
$832$	−54.3646	−1.88475
$833$	−6.55816	−0.227227
$834$	21.1225	0.731411
$835$	54.6644	1.89174
$836$	−0.0566732	−0.00196008
$837$	−2.28531	−0.0789919
$838$	0.836649	0.0289015
$839$	2.62829	0.0907387	0.0453693	−	0.998970i	$-0.485554\pi$
$839$	2.62829	0.0907387	0.0453693	+	0.998970i	$0.485554\pi$
$840$	8.04607	0.277616
$841$	−27.1636	−0.936675
$842$	5.28724	0.182210
$843$	3.62902	0.124990
$844$	19.5633	0.673398
$845$	118.139	4.06411
$846$	−7.82339	−0.268974
$847$	7.31165	0.251231
$848$	8.26987	0.283989
$849$	18.8576	0.647191
$850$	−11.7058	−0.401504
$851$	−24.8392	−0.851476
$852$	−6.88076	−0.235731
$853$	−23.3262	−0.798673	−0.399336	−	0.916805i	$-0.630759\pi$
$853$	−23.3262	−0.798673	−0.399336	+	0.916805i	$0.630759\pi$
$854$	−1.42322	−0.0487016
$855$	−19.3945	−0.663279
$856$	37.5991	1.28511
$857$	17.7569	0.606566	0.303283	−	0.952901i	$-0.401917\pi$
$857$	17.7569	0.606566	0.303283	+	0.952901i	$0.401917\pi$
$858$	0.110585	0.00377531
$859$	−52.4706	−1.79027	−0.895136	−	0.445793i	$-0.852922\pi$
$859$	−52.4706	−1.79027	−0.895136	+	0.445793i	$0.852922\pi$
$860$	−15.9298	−0.543202
$861$	2.68112	0.0913723
$862$	21.1307	0.719714
$863$	−0.204116	−0.00694821	−0.00347410	−	0.999994i	$-0.501106\pi$
$863$	−0.204116	−0.00694821	−0.00347410	+	0.999994i	$0.501106\pi$
$864$	4.02805	0.137037
$865$	−37.7387	−1.28315
$866$	28.4965	0.968350
$867$	−1.00000	−0.0339618
$868$	1.15438	0.0391821
$869$	−0.176017	−0.00597097
$870$	5.94347	0.201503
$871$	−28.8966	−0.979124
$872$	−19.2591	−0.652194
$873$	−8.64352	−0.292539
$874$	−19.2268	−0.650355
$875$	−14.4296	−0.487808
$876$	−0.743773	−0.0251298
$877$	−23.8795	−0.806355	−0.403177	−	0.915122i	$-0.632094\pi$
$877$	−23.8795	−0.806355	−0.403177	+	0.915122i	$0.632094\pi$
$878$	22.7669	0.768344
$879$	21.7810	0.734655
$880$	0.113488	0.00382569
$881$	24.7023	0.832240	0.416120	−	0.909310i	$-0.363390\pi$
$881$	24.7023	0.832240	0.416120	+	0.909310i	$0.363390\pi$
$882$	7.30308	0.245908
$883$	−36.9163	−1.24233	−0.621167	−	0.783679i	$-0.713341\pi$
$883$	−36.9163	−1.24233	−0.621167	+	0.783679i	$0.713341\pi$
$884$	4.98293	0.167594
$885$	−12.7568	−0.428814
$886$	−25.9645	−0.872296
$887$	43.2671	1.45277	0.726384	−	0.687289i	$-0.241199\pi$
$887$	43.2671	1.45277	0.726384	+	0.687289i	$0.241199\pi$
$888$	−21.7733	−0.730665
$889$	1.38252	0.0463682
$890$	56.0574	1.87905
$891$	−0.0151446	−0.000507364 0
$892$	3.03810	0.101723
$893$	−34.5955	−1.15769
$894$	2.65068	0.0886519
$895$	−38.6238	−1.29105
$896$	0.782064	0.0261269
$897$	−22.9904	−0.767628
$898$	−25.8392	−0.862266
$899$	3.09693	0.103288
$900$	−7.98815	−0.266272
$901$	−4.34647	−0.144802
$902$	0.0680246	0.00226497
$903$	3.53787	0.117733
$904$	−33.2267	−1.10510
$905$	−102.514	−3.40767
$906$	3.87220	0.128645
$907$	6.45801	0.214435	0.107217	−	0.994236i	$-0.465806\pi$
$907$	6.45801	0.214435	0.107217	+	0.994236i	$0.465806\pi$
$908$	−0.167785	−0.00556815
$909$	−12.5700	−0.416919
$910$	−19.1162	−0.633694
$911$	−36.2803	−1.20202	−0.601009	−	0.799242i	$-0.705235\pi$
$911$	−36.2803	−1.20202	−0.601009	+	0.799242i	$0.705235\pi$
$912$	−9.36938	−0.310251
$913$	0.0201184	0.000665822 0
$914$	1.70079	0.0562571
$915$	7.57263	0.250343
$916$	9.56639	0.316082
$917$	−0.154511	−0.00510240
$918$	1.11359	0.0367538
$919$	8.31689	0.274349	0.137174	−	0.990547i	$-0.456198\pi$
$919$	8.31689	0.274349	0.137174	+	0.990547i	$0.456198\pi$
$920$	−42.4410	−1.39924
$921$	−13.6863	−0.450980
$922$	28.7778	0.947746
$923$	59.3718	1.95424
$924$	0.00764999	0.000251666 0
$925$	74.4696	2.44855
$926$	−10.5722	−0.347424
$927$	7.23706	0.237696
$928$	−5.45859	−0.179187
$929$	−46.4731	−1.52473	−0.762366	−	0.647146i	$-0.775962\pi$
$929$	−46.4731	−1.52473	−0.762366	+	0.647146i	$0.775962\pi$
$930$	10.0230	0.328669
$931$	32.2947	1.05842
$932$	−9.42973	−0.308881
$933$	17.5550	0.574725
$934$	−30.7819	−1.00721
$935$	−0.0596470	−0.00195067
$936$	−20.1528	−0.658714
$937$	12.8746	0.420595	0.210297	−	0.977637i	$-0.432557\pi$
$937$	12.8746	0.420595	0.210297	+	0.977637i	$0.432557\pi$
$938$	3.26204	0.106509
$939$	−9.29290	−0.303262
$940$	−21.0267	−0.685817
$941$	−8.67994	−0.282958	−0.141479	−	0.989941i	$-0.545186\pi$
$941$	−8.67994	−0.282958	−0.141479	+	0.989941i	$0.545186\pi$
$942$	1.11359	0.0362826
$943$	−14.1422	−0.460534
$944$	−6.16271	−0.200579
$945$	2.61796	0.0851622
$946$	0.0897618	0.00291841
$947$	−31.5129	−1.02403	−0.512016	−	0.858976i	$-0.671101\pi$
$947$	−31.5129	−1.02403	−0.512016	+	0.858976i	$0.671101\pi$
$948$	8.83217	0.286856
$949$	6.41777	0.208330
$950$	57.6432	1.87019
$951$	1.29130	0.0418733
$952$	−2.04293	−0.0662117
$953$	−32.9176	−1.06631	−0.533153	−	0.846019i	$-0.678993\pi$
$953$	−32.9176	−1.06631	−0.533153	+	0.846019i	$0.678993\pi$
$954$	4.84017	0.156706
$955$	5.38002	0.174093
$956$	−17.1667	−0.555211
$957$	0.0205231	0.000663419 0
$958$	13.9846	0.451823
$959$	9.28376	0.299788
$960$	−32.6537	−1.05389
$961$	−25.7774	−0.831528
$962$	51.7299	1.66784
$963$	12.2336	0.394224
$964$	−21.2050	−0.682967
$965$	−42.2890	−1.36133
$966$	2.59531	0.0835028
$967$	9.44389	0.303695	0.151847	−	0.988404i	$-0.451478\pi$
$967$	9.44389	0.303695	0.151847	+	0.988404i	$0.451478\pi$
$968$	−33.8069	−1.08659
$969$	4.92435	0.158193
$970$	37.9092	1.21719
$971$	5.16195	0.165655	0.0828274	−	0.996564i	$-0.473605\pi$
$971$	5.16195	0.165655	0.0828274	+	0.996564i	$0.473605\pi$
$972$	0.759925	0.0243746
$973$	−12.6082	−0.404200
$974$	12.3218	0.394816
$975$	68.9270	2.20743
$976$	3.65829	0.117099
$977$	11.9041	0.380847	0.190423	−	0.981702i	$-0.439014\pi$
$977$	11.9041	0.380847	0.190423	+	0.981702i	$0.439014\pi$
$978$	−18.1417	−0.580106
$979$	0.193569	0.00618650
$980$	19.6283	0.627004
$981$	−6.26634	−0.200069
$982$	−45.4020	−1.44884
$983$	−32.7585	−1.04483	−0.522416	−	0.852691i	$-0.674969\pi$
$983$	−32.7585	−1.04483	−0.522416	+	0.852691i	$0.674969\pi$
$984$	−12.3967	−0.395192
$985$	−11.2945	−0.359874
$986$	−1.50907	−0.0480586
$987$	4.66985	0.148643
$988$	−24.5377	−0.780647
$989$	−18.6613	−0.593396
$990$	0.0664221	0.00211103
$991$	11.1383	0.353821	0.176911	−	0.984227i	$-0.443390\pi$
$991$	11.1383	0.353821	0.176911	+	0.984227i	$0.443390\pi$
$992$	−9.20534	−0.292270
$993$	−30.8688	−0.979591
$994$	−6.70227	−0.212583
$995$	41.3572	1.31111
$996$	−1.00950	−0.0319872
$997$	47.7077	1.51092	0.755459	−	0.655196i	$-0.227414\pi$
$997$	47.7077	1.51092	0.755459	+	0.655196i	$0.227414\pi$
$998$	40.2438	1.27390
$999$	−7.08441	−0.224141

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.c.1.13	✓	39

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.c.1.13	✓	39	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.11359 q^{2} -1.00000 q^{3} -0.759925 q^{4} +3.93850 q^{5} +1.11359 q^{6} -0.664710 q^{7} +3.07342 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.11359 q^{2} -1.00000 q^{3} -0.759925 q^{4} +3.93850 q^{5} +1.11359 q^{6} -0.664710 q^{7} +3.07342 q^{8} +1.00000 q^{9} -4.38586 q^{10} -0.0151446 q^{11} +0.759925 q^{12} -6.55713 q^{13} +0.740212 q^{14} -3.93850 q^{15} -1.90266 q^{16} +1.00000 q^{17} -1.11359 q^{18} -4.92435 q^{19} -2.99296 q^{20} +0.664710 q^{21} +0.0168648 q^{22} -3.50617 q^{23} -3.07342 q^{24} +10.5118 q^{25} +7.30193 q^{26} -1.00000 q^{27} +0.505129 q^{28} +1.35514 q^{29} +4.38586 q^{30} +2.28531 q^{31} -4.02805 q^{32} +0.0151446 q^{33} -1.11359 q^{34} -2.61796 q^{35} -0.759925 q^{36} +7.08441 q^{37} +5.48369 q^{38} +6.55713 q^{39} +12.1046 q^{40} +4.03352 q^{41} -0.740212 q^{42} +5.32242 q^{43} +0.0115088 q^{44} +3.93850 q^{45} +3.90443 q^{46} +7.02539 q^{47} +1.90266 q^{48} -6.55816 q^{49} -11.7058 q^{50} -1.00000 q^{51} +4.98293 q^{52} -4.34647 q^{53} +1.11359 q^{54} -0.0596470 q^{55} -2.04293 q^{56} +4.92435 q^{57} -1.50907 q^{58} +3.23899 q^{59} +2.99296 q^{60} -1.92272 q^{61} -2.54489 q^{62} -0.664710 q^{63} +8.29091 q^{64} -25.8252 q^{65} -0.0168648 q^{66} +4.40690 q^{67} -0.759925 q^{68} +3.50617 q^{69} +2.91532 q^{70} -9.05453 q^{71} +3.07342 q^{72} -0.978746 q^{73} -7.88910 q^{74} -10.5118 q^{75} +3.74213 q^{76} +0.0100668 q^{77} -7.30193 q^{78} +11.6224 q^{79} -7.49364 q^{80} +1.00000 q^{81} -4.49167 q^{82} -1.32842 q^{83} -0.505129 q^{84} +3.93850 q^{85} -5.92698 q^{86} -1.35514 q^{87} -0.0465457 q^{88} -12.7814 q^{89} -4.38586 q^{90} +4.35859 q^{91} +2.66443 q^{92} -2.28531 q^{93} -7.82339 q^{94} -19.3945 q^{95} +4.02805 q^{96} -8.64352 q^{97} +7.30308 q^{98} -0.0151446 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q - 4 q^{2} - 39 q^{3} + 30 q^{4} - 3 q^{5} + 4 q^{6} - 5 q^{7} - 3 q^{8} + 39 q^{9}+O(q^{10}) \) 39 * q - 4 * q^2 - 39 * q^3 + 30 * q^4 - 3 * q^5 + 4 * q^6 - 5 * q^7 - 3 * q^8 + 39 * q^9	\( 39 q - 4 q^{2} - 39 q^{3} + 30 q^{4} - 3 q^{5} + 4 q^{6} - 5 q^{7} - 3 q^{8} + 39 q^{9} + 4 q^{10} + q^{11} - 30 q^{12} - 26 q^{13} - 4 q^{14} + 3 q^{15} + 8 q^{16} + 39 q^{17} - 4 q^{18} - 14 q^{19} - 14 q^{20} + 5 q^{21} - 17 q^{22} + 2 q^{23} + 3 q^{24} - 6 q^{25} - 17 q^{26} - 39 q^{27} - 14 q^{28} - 7 q^{29} - 4 q^{30} - q^{31} - 30 q^{32} - q^{33} - 4 q^{34} + q^{35} + 30 q^{36} - 24 q^{37} - 20 q^{38} + 26 q^{39} + 12 q^{40} + q^{41} + 4 q^{42} - 41 q^{43} - 2 q^{44} - 3 q^{45} - 6 q^{46} - 9 q^{47} - 8 q^{48} - 10 q^{49} - 9 q^{50} - 39 q^{51} - 37 q^{52} - 47 q^{53} + 4 q^{54} - 39 q^{55} + 8 q^{56} + 14 q^{57} - 27 q^{58} + 41 q^{59} + 14 q^{60} - 41 q^{61} + 36 q^{62} - 5 q^{63} - 47 q^{64} - 39 q^{65} + 17 q^{66} - 36 q^{67} + 30 q^{68} - 2 q^{69} - 52 q^{70} - 2 q^{71} - 3 q^{72} - 63 q^{73} - 6 q^{74} + 6 q^{75} - 34 q^{76} - 64 q^{77} + 17 q^{78} + 20 q^{79} - 28 q^{80} + 39 q^{81} - 37 q^{82} + 45 q^{83} + 14 q^{84} - 3 q^{85} + 32 q^{86} + 7 q^{87} + 6 q^{88} - 32 q^{89} + 4 q^{90} - 11 q^{91} + 28 q^{92} + q^{93} - 44 q^{94} + 22 q^{95} + 30 q^{96} - 20 q^{97} + 63 q^{98} + q^{99}+O(q^{100}) \) 39 * q - 4 * q^2 - 39 * q^3 + 30 * q^4 - 3 * q^5 + 4 * q^6 - 5 * q^7 - 3 * q^8 + 39 * q^9 + 4 * q^10 + q^11 - 30 * q^12 - 26 * q^13 - 4 * q^14 + 3 * q^15 + 8 * q^16 + 39 * q^17 - 4 * q^18 - 14 * q^19 - 14 * q^20 + 5 * q^21 - 17 * q^22 + 2 * q^23 + 3 * q^24 - 6 * q^25 - 17 * q^26 - 39 * q^27 - 14 * q^28 - 7 * q^29 - 4 * q^30 - q^31 - 30 * q^32 - q^33 - 4 * q^34 + q^35 + 30 * q^36 - 24 * q^37 - 20 * q^38 + 26 * q^39 + 12 * q^40 + q^41 + 4 * q^42 - 41 * q^43 - 2 * q^44 - 3 * q^45 - 6 * q^46 - 9 * q^47 - 8 * q^48 - 10 * q^49 - 9 * q^50 - 39 * q^51 - 37 * q^52 - 47 * q^53 + 4 * q^54 - 39 * q^55 + 8 * q^56 + 14 * q^57 - 27 * q^58 + 41 * q^59 + 14 * q^60 - 41 * q^61 + 36 * q^62 - 5 * q^63 - 47 * q^64 - 39 * q^65 + 17 * q^66 - 36 * q^67 + 30 * q^68 - 2 * q^69 - 52 * q^70 - 2 * q^71 - 3 * q^72 - 63 * q^73 - 6 * q^74 + 6 * q^75 - 34 * q^76 - 64 * q^77 + 17 * q^78 + 20 * q^79 - 28 * q^80 + 39 * q^81 - 37 * q^82 + 45 * q^83 + 14 * q^84 - 3 * q^85 + 32 * q^86 + 7 * q^87 + 6 * q^88 - 32 * q^89 + 4 * q^90 - 11 * q^91 + 28 * q^92 + q^93 - 44 * q^94 + 22 * q^95 + 30 * q^96 - 20 * q^97 + 63 * q^98 + q^99

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