LMFDB - Embedded newform 8018.2.a.f.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8018,2,Mod(1,8018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8018, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("8018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8018 = 2 \cdot 19 \cdot 211 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8018.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:	$64.0240523407$
Analytic rank:	$1$
Dimension:	$34$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	8018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.46365 q^{3} +1.00000 q^{4} -0.0638040 q^{5} +2.46365 q^{6} +3.24244 q^{7} -1.00000 q^{8} +3.06956 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.46365 q^{3} +1.00000 q^{4} -0.0638040 q^{5} +2.46365 q^{6} +3.24244 q^{7} -1.00000 q^{8} +3.06956 q^{9} +0.0638040 q^{10} +1.81445 q^{11} -2.46365 q^{12} -6.18473 q^{13} -3.24244 q^{14} +0.157191 q^{15} +1.00000 q^{16} +2.99383 q^{17} -3.06956 q^{18} -1.00000 q^{19} -0.0638040 q^{20} -7.98822 q^{21} -1.81445 q^{22} -0.142289 q^{23} +2.46365 q^{24} -4.99593 q^{25} +6.18473 q^{26} -0.171366 q^{27} +3.24244 q^{28} +1.88437 q^{29} -0.157191 q^{30} +8.38673 q^{31} -1.00000 q^{32} -4.47016 q^{33} -2.99383 q^{34} -0.206880 q^{35} +3.06956 q^{36} -0.447694 q^{37} +1.00000 q^{38} +15.2370 q^{39} +0.0638040 q^{40} -10.3628 q^{41} +7.98822 q^{42} +9.43065 q^{43} +1.81445 q^{44} -0.195850 q^{45} +0.142289 q^{46} -4.96054 q^{47} -2.46365 q^{48} +3.51340 q^{49} +4.99593 q^{50} -7.37575 q^{51} -6.18473 q^{52} +3.48668 q^{53} +0.171366 q^{54} -0.115769 q^{55} -3.24244 q^{56} +2.46365 q^{57} -1.88437 q^{58} +2.98972 q^{59} +0.157191 q^{60} +4.57273 q^{61} -8.38673 q^{62} +9.95285 q^{63} +1.00000 q^{64} +0.394610 q^{65} +4.47016 q^{66} -6.70410 q^{67} +2.99383 q^{68} +0.350551 q^{69} +0.206880 q^{70} -13.2336 q^{71} -3.06956 q^{72} -11.2113 q^{73} +0.447694 q^{74} +12.3082 q^{75} -1.00000 q^{76} +5.88323 q^{77} -15.2370 q^{78} -3.92645 q^{79} -0.0638040 q^{80} -8.78649 q^{81} +10.3628 q^{82} +4.00145 q^{83} -7.98822 q^{84} -0.191018 q^{85} -9.43065 q^{86} -4.64242 q^{87} -1.81445 q^{88} -8.86710 q^{89} +0.195850 q^{90} -20.0536 q^{91} -0.142289 q^{92} -20.6619 q^{93} +4.96054 q^{94} +0.0638040 q^{95} +2.46365 q^{96} +2.20408 q^{97} -3.51340 q^{98} +5.56955 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q - 34 q^{2} - 10 q^{3} + 34 q^{4} + 7 q^{5} + 10 q^{6} - 6 q^{7} - 34 q^{8} + 38 q^{9}+O(q^{10}) $ 34 * q - 34 * q^2 - 10 * q^3 + 34 * q^4 + 7 * q^5 + 10 * q^6 - 6 * q^7 - 34 * q^8 + 38 * q^9	\( 34 q - 34 q^{2} - 10 q^{3} + 34 q^{4} + 7 q^{5} + 10 q^{6} - 6 q^{7} - 34 q^{8} + 38 q^{9} - 7 q^{10} + 4 q^{11} - 10 q^{12} - 5 q^{13} + 6 q^{14} - 17 q^{15} + 34 q^{16} + 8 q^{17} - 38 q^{18} - 34 q^{19} + 7 q^{20} - 4 q^{22} - 24 q^{23} + 10 q^{24} + 5 q^{25} + 5 q^{26} - 31 q^{27} - 6 q^{28} + 24 q^{29} + 17 q^{30} - 28 q^{31} - 34 q^{32} - 16 q^{33} - 8 q^{34} + 2 q^{35} + 38 q^{36} - 36 q^{37} + 34 q^{38} - 9 q^{39} - 7 q^{40} + 9 q^{41} - 24 q^{43} + 4 q^{44} + 22 q^{45} + 24 q^{46} - 29 q^{47} - 10 q^{48} + 22 q^{49} - 5 q^{50} - 21 q^{51} - 5 q^{52} - 9 q^{53} + 31 q^{54} - 28 q^{55} + 6 q^{56} + 10 q^{57} - 24 q^{58} - 28 q^{59} - 17 q^{60} + 23 q^{61} + 28 q^{62} - 27 q^{63} + 34 q^{64} - 6 q^{65} + 16 q^{66} - 51 q^{67} + 8 q^{68} - 17 q^{69} - 2 q^{70} - 31 q^{71} - 38 q^{72} - 26 q^{73} + 36 q^{74} - 109 q^{75} - 34 q^{76} - 28 q^{77} + 9 q^{78} - 36 q^{79} + 7 q^{80} + 6 q^{81} - 9 q^{82} - 10 q^{83} - 32 q^{85} + 24 q^{86} - 8 q^{87} - 4 q^{88} - 34 q^{89} - 22 q^{90} - 41 q^{91} - 24 q^{92} - 33 q^{93} + 29 q^{94} - 7 q^{95} + 10 q^{96} - 56 q^{97} - 22 q^{98} - 28 q^{99}+O(q^{100}) \) 34 * q - 34 * q^2 - 10 * q^3 + 34 * q^4 + 7 * q^5 + 10 * q^6 - 6 * q^7 - 34 * q^8 + 38 * q^9 - 7 * q^10 + 4 * q^11 - 10 * q^12 - 5 * q^13 + 6 * q^14 - 17 * q^15 + 34 * q^16 + 8 * q^17 - 38 * q^18 - 34 * q^19 + 7 * q^20 - 4 * q^22 - 24 * q^23 + 10 * q^24 + 5 * q^25 + 5 * q^26 - 31 * q^27 - 6 * q^28 + 24 * q^29 + 17 * q^30 - 28 * q^31 - 34 * q^32 - 16 * q^33 - 8 * q^34 + 2 * q^35 + 38 * q^36 - 36 * q^37 + 34 * q^38 - 9 * q^39 - 7 * q^40 + 9 * q^41 - 24 * q^43 + 4 * q^44 + 22 * q^45 + 24 * q^46 - 29 * q^47 - 10 * q^48 + 22 * q^49 - 5 * q^50 - 21 * q^51 - 5 * q^52 - 9 * q^53 + 31 * q^54 - 28 * q^55 + 6 * q^56 + 10 * q^57 - 24 * q^58 - 28 * q^59 - 17 * q^60 + 23 * q^61 + 28 * q^62 - 27 * q^63 + 34 * q^64 - 6 * q^65 + 16 * q^66 - 51 * q^67 + 8 * q^68 - 17 * q^69 - 2 * q^70 - 31 * q^71 - 38 * q^72 - 26 * q^73 + 36 * q^74 - 109 * q^75 - 34 * q^76 - 28 * q^77 + 9 * q^78 - 36 * q^79 + 7 * q^80 + 6 * q^81 - 9 * q^82 - 10 * q^83 - 32 * q^85 + 24 * q^86 - 8 * q^87 - 4 * q^88 - 34 * q^89 - 22 * q^90 - 41 * q^91 - 24 * q^92 - 33 * q^93 + 29 * q^94 - 7 * q^95 + 10 * q^96 - 56 * q^97 - 22 * q^98 - 28 * 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
$3$	−2.46365	−1.42239	−0.711194	−	0.702996i	$-0.751845\pi$
$3$	−2.46365	−1.42239	−0.711194	+	0.702996i	$0.751845\pi$
$4$	1.00000	0.500000
$5$	−0.0638040	−0.0285340	−0.0142670	−	0.999898i	$-0.504541\pi$
$5$	−0.0638040	−0.0285340	−0.0142670	+	0.999898i	$0.504541\pi$
$6$	2.46365	1.00578
$7$	3.24244	1.22553	0.612763	−	0.790267i	$-0.290058\pi$
$7$	3.24244	1.22553	0.612763	+	0.790267i	$0.290058\pi$
$8$	−1.00000	−0.353553
$9$	3.06956	1.02319
$10$	0.0638040	0.0201766
$11$	1.81445	0.547076	0.273538	−	0.961861i	$-0.411806\pi$
$11$	1.81445	0.547076	0.273538	+	0.961861i	$0.411806\pi$
$12$	−2.46365	−0.711194
$13$	−6.18473	−1.71533	−0.857667	−	0.514205i	$-0.828087\pi$
$13$	−6.18473	−1.71533	−0.857667	+	0.514205i	$0.828087\pi$
$14$	−3.24244	−0.866578
$15$	0.157191	0.0405864
$16$	1.00000	0.250000
$17$	2.99383	0.726111	0.363055	−	0.931768i	$-0.381734\pi$
$17$	2.99383	0.726111	0.363055	+	0.931768i	$0.381734\pi$
$18$	−3.06956	−0.723502
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	−0.0638040	−0.0142670
$21$	−7.98822	−1.74317
$22$	−1.81445	−0.386841
$23$	−0.142289	−0.0296694	−0.0148347	−	0.999890i	$-0.504722\pi$
$23$	−0.142289	−0.0296694	−0.0148347	+	0.999890i	$0.504722\pi$
$24$	2.46365	0.502890
$25$	−4.99593	−0.999186
$26$	6.18473	1.21292
$27$	−0.171366	−0.0329794
$28$	3.24244	0.612763
$29$	1.88437	0.349918	0.174959	−	0.984576i	$-0.444021\pi$
$29$	1.88437	0.349918	0.174959	+	0.984576i	$0.444021\pi$
$30$	−0.157191	−0.0286989
$31$	8.38673	1.50630	0.753150	−	0.657849i	$-0.228533\pi$
$31$	8.38673	1.50630	0.753150	+	0.657849i	$0.228533\pi$
$32$	−1.00000	−0.176777
$33$	−4.47016	−0.778154
$34$	−2.99383	−0.513438
$35$	−0.206880	−0.0349692
$36$	3.06956	0.511593
$37$	−0.447694	−0.0736005	−0.0368003	−	0.999323i	$-0.511717\pi$
$37$	−0.447694	−0.0736005	−0.0368003	+	0.999323i	$0.511717\pi$
$38$	1.00000	0.162221
$39$	15.2370	2.43987
$40$	0.0638040	0.0100883
$41$	−10.3628	−1.61840	−0.809198	−	0.587536i	$-0.800098\pi$
$41$	−10.3628	−1.61840	−0.809198	+	0.587536i	$0.800098\pi$
$42$	7.98822	1.23261
$43$	9.43065	1.43816	0.719080	−	0.694927i	$-0.244563\pi$
$43$	9.43065	1.43816	0.719080	+	0.694927i	$0.244563\pi$
$44$	1.81445	0.273538
$45$	−0.195850	−0.0291956
$46$	0.142289	0.0209794
$47$	−4.96054	−0.723569	−0.361785	−	0.932262i	$-0.617832\pi$
$47$	−4.96054	−0.723569	−0.361785	+	0.932262i	$0.617832\pi$
$48$	−2.46365	−0.355597
$49$	3.51340	0.501915
$50$	4.99593	0.706531
$51$	−7.37575	−1.03281
$52$	−6.18473	−0.857667
$53$	3.48668	0.478933	0.239466	−	0.970905i	$-0.423028\pi$
$53$	3.48668	0.478933	0.239466	+	0.970905i	$0.423028\pi$
$54$	0.171366	0.0233199
$55$	−0.115769	−0.0156103
$56$	−3.24244	−0.433289
$57$	2.46365	0.326318
$58$	−1.88437	−0.247430
$59$	2.98972	0.389228	0.194614	−	0.980880i	$-0.437655\pi$
$59$	2.98972	0.389228	0.194614	+	0.980880i	$0.437655\pi$
$60$	0.157191	0.0202932
$61$	4.57273	0.585478	0.292739	−	0.956192i	$-0.405433\pi$
$61$	4.57273	0.585478	0.292739	+	0.956192i	$0.405433\pi$
$62$	−8.38673	−1.06512
$63$	9.95285	1.25394
$64$	1.00000	0.125000
$65$	0.394610	0.0489454
$66$	4.47016	0.550238
$67$	−6.70410	−0.819036	−0.409518	−	0.912302i	$-0.634303\pi$
$67$	−6.70410	−0.819036	−0.409518	+	0.912302i	$0.634303\pi$
$68$	2.99383	0.363055
$69$	0.350551	0.0422014
$70$	0.206880	0.0247269
$71$	−13.2336	−1.57054	−0.785272	−	0.619151i	$-0.787477\pi$
$71$	−13.2336	−1.57054	−0.785272	+	0.619151i	$0.787477\pi$
$72$	−3.06956	−0.361751
$73$	−11.2113	−1.31219	−0.656094	−	0.754679i	$-0.727792\pi$
$73$	−11.2113	−1.31219	−0.656094	+	0.754679i	$0.727792\pi$
$74$	0.447694	0.0520434
$75$	12.3082	1.42123
$76$	−1.00000	−0.114708
$77$	5.88323	0.670456
$78$	−15.2370	−1.72525
$79$	−3.92645	−0.441761	−0.220880	−	0.975301i	$-0.570893\pi$
$79$	−3.92645	−0.441761	−0.220880	+	0.975301i	$0.570893\pi$
$80$	−0.0638040	−0.00713350
$81$	−8.78649	−0.976276
$82$	10.3628	1.14438
$83$	4.00145	0.439216	0.219608	−	0.975588i	$-0.429522\pi$
$83$	4.00145	0.439216	0.219608	+	0.975588i	$0.429522\pi$
$84$	−7.98822	−0.871587
$85$	−0.191018	−0.0207189
$86$	−9.43065	−1.01693
$87$	−4.64242	−0.497719
$88$	−1.81445	−0.193421
$89$	−8.86710	−0.939911	−0.469955	−	0.882690i	$-0.655730\pi$
$89$	−8.86710	−0.939911	−0.469955	+	0.882690i	$0.655730\pi$
$90$	0.195850	0.0206444
$91$	−20.0536	−2.10219
$92$	−0.142289	−0.0148347
$93$	−20.6619	−2.14254
$94$	4.96054	0.511641
$95$	0.0638040	0.00654615
$96$	2.46365	0.251445
$97$	2.20408	0.223791	0.111895	−	0.993720i	$-0.464308\pi$
$97$	2.20408	0.223791	0.111895	+	0.993720i	$0.464308\pi$
$98$	−3.51340	−0.354907
$99$	5.56955	0.559761
$100$	−4.99593	−0.499593
$101$	7.66406	0.762603	0.381301	−	0.924451i	$-0.375476\pi$
$101$	7.66406	0.762603	0.381301	+	0.924451i	$0.375476\pi$
$102$	7.37575	0.730308
$103$	12.0826	1.19053	0.595265	−	0.803530i	$-0.297047\pi$
$103$	12.0826	1.19053	0.595265	+	0.803530i	$0.297047\pi$
$104$	6.18473	0.606462
$105$	0.509681	0.0497397
$106$	−3.48668	−0.338657
$107$	−1.02906	−0.0994830	−0.0497415	−	0.998762i	$-0.515840\pi$
$107$	−1.02906	−0.0994830	−0.0497415	+	0.998762i	$0.515840\pi$
$108$	−0.171366	−0.0164897
$109$	−7.65541	−0.733256	−0.366628	−	0.930368i	$-0.619488\pi$
$109$	−7.65541	−0.733256	−0.366628	+	0.930368i	$0.619488\pi$
$110$	0.115769	0.0110381
$111$	1.10296	0.104688
$112$	3.24244	0.306382
$113$	−7.16054	−0.673607	−0.336804	−	0.941575i	$-0.609346\pi$
$113$	−7.16054	−0.673607	−0.336804	+	0.941575i	$0.609346\pi$
$114$	−2.46365	−0.230742
$115$	0.00907864	0.000846587 0
$116$	1.88437	0.174959
$117$	−18.9844	−1.75511
$118$	−2.98972	−0.275226
$119$	9.70731	0.889868
$120$	−0.157191	−0.0143495
$121$	−7.70778	−0.700708
$122$	−4.57273	−0.413996
$123$	25.5303	2.30199
$124$	8.38673	0.753150
$125$	0.637780	0.0570448
$126$	−9.95285	−0.886670
$127$	−10.2450	−0.909095	−0.454548	−	0.890722i	$-0.650199\pi$
$127$	−10.2450	−0.909095	−0.454548	+	0.890722i	$0.650199\pi$
$128$	−1.00000	−0.0883883
$129$	−23.2338	−2.04562
$130$	−0.394610	−0.0346096
$131$	10.3789	0.906806	0.453403	−	0.891306i	$-0.350210\pi$
$131$	10.3789	0.906806	0.453403	+	0.891306i	$0.350210\pi$
$132$	−4.47016	−0.389077
$133$	−3.24244	−0.281155
$134$	6.70410	0.579146
$135$	0.0109338	0.000941034 0
$136$	−2.99383	−0.256719
$137$	17.5839	1.50230	0.751148	−	0.660134i	$-0.229501\pi$
$137$	17.5839	1.50230	0.751148	+	0.660134i	$0.229501\pi$
$138$	−0.350551	−0.0298409
$139$	−12.0072	−1.01844	−0.509218	−	0.860638i	$-0.670065\pi$
$139$	−12.0072	−1.01844	−0.509218	+	0.860638i	$0.670065\pi$
$140$	−0.206880	−0.0174846
$141$	12.2210	1.02920
$142$	13.2336	1.11054
$143$	−11.2219	−0.938419
$144$	3.06956	0.255796
$145$	−0.120230	−0.00998458
$146$	11.2113	0.927857
$147$	−8.65578	−0.713917
$148$	−0.447694	−0.0368003
$149$	16.8503	1.38043	0.690216	−	0.723604i	$-0.257516\pi$
$149$	16.8503	1.38043	0.690216	+	0.723604i	$0.257516\pi$
$150$	−12.3082	−1.00496
$151$	14.3539	1.16811	0.584053	−	0.811715i	$-0.301466\pi$
$151$	14.3539	1.16811	0.584053	+	0.811715i	$0.301466\pi$
$152$	1.00000	0.0811107
$153$	9.18974	0.742946
$154$	−5.88323	−0.474084
$155$	−0.535107	−0.0429808
$156$	15.2370	1.21994
$157$	−17.1541	−1.36905	−0.684523	−	0.728992i	$-0.739989\pi$
$157$	−17.1541	−1.36905	−0.684523	+	0.728992i	$0.739989\pi$
$158$	3.92645	0.312372
$159$	−8.58996	−0.681228
$160$	0.0638040	0.00504415
$161$	−0.461365	−0.0363606
$162$	8.78649	0.690332
$163$	−15.4266	−1.20831	−0.604154	−	0.796868i	$-0.706489\pi$
$163$	−15.4266	−1.20831	−0.604154	+	0.796868i	$0.706489\pi$
$164$	−10.3628	−0.809198
$165$	0.285214	0.0222039
$166$	−4.00145	−0.310573
$167$	−0.0738214	−0.00571247	−0.00285624	−	0.999996i	$-0.500909\pi$
$167$	−0.0738214	−0.00571247	−0.00285624	+	0.999996i	$0.500909\pi$
$168$	7.98822	0.616305
$169$	25.2509	1.94237
$170$	0.191018	0.0146504
$171$	−3.06956	−0.234735
$172$	9.43065	0.719080
$173$	9.65770	0.734261	0.367131	−	0.930169i	$-0.380340\pi$
$173$	9.65770	0.734261	0.367131	+	0.930169i	$0.380340\pi$
$174$	4.64242	0.351941
$175$	−16.1990	−1.22453
$176$	1.81445	0.136769
$177$	−7.36561	−0.553633
$178$	8.86710	0.664617
$179$	12.5121	0.935196	0.467598	−	0.883941i	$-0.345119\pi$
$179$	12.5121	0.935196	0.467598	+	0.883941i	$0.345119\pi$
$180$	−0.195850	−0.0145978
$181$	12.3961	0.921396	0.460698	−	0.887557i	$-0.347599\pi$
$181$	12.3961	0.921396	0.460698	+	0.887557i	$0.347599\pi$
$182$	20.0536	1.48647
$183$	−11.2656	−0.832777
$184$	0.142289	0.0104897
$185$	0.0285647	0.00210012
$186$	20.6619	1.51501
$187$	5.43215	0.397238
$188$	−4.96054	−0.361785
$189$	−0.555643	−0.0404171
$190$	−0.0638040	−0.00462883
$191$	−14.0475	−1.01644	−0.508220	−	0.861227i	$-0.669696\pi$
$191$	−14.0475	−1.01644	−0.508220	+	0.861227i	$0.669696\pi$
$192$	−2.46365	−0.177798
$193$	−5.38469	−0.387598	−0.193799	−	0.981041i	$-0.562081\pi$
$193$	−5.38469	−0.387598	−0.193799	+	0.981041i	$0.562081\pi$
$194$	−2.20408	−0.158244
$195$	−0.972181	−0.0696193
$196$	3.51340	0.250957
$197$	−12.8316	−0.914213	−0.457107	−	0.889412i	$-0.651114\pi$
$197$	−12.8316	−0.914213	−0.457107	+	0.889412i	$0.651114\pi$
$198$	−5.56955	−0.395811
$199$	21.8427	1.54838	0.774192	−	0.632950i	$-0.218156\pi$
$199$	21.8427	1.54838	0.774192	+	0.632950i	$0.218156\pi$
$200$	4.99593	0.353266
$201$	16.5165	1.16499
$202$	−7.66406	−0.539241
$203$	6.10995	0.428834
$204$	−7.37575	−0.516405
$205$	0.661188	0.0461794
$206$	−12.0826	−0.841831
$207$	−0.436766	−0.0303573
$208$	−6.18473	−0.428834
$209$	−1.81445	−0.125508
$210$	−0.509681	−0.0351713
$211$	−1.00000	−0.0688428
$211$	−1.00000	−0.0688428
$212$	3.48668	0.239466
$213$	32.6030	2.23392
$214$	1.02906	0.0703451
$215$	−0.601713	−0.0410365
$216$	0.171366	0.0116600
$217$	27.1934	1.84601
$218$	7.65541	0.518490
$219$	27.6208	1.86644
$220$	−0.115769	−0.00780514
$221$	−18.5160	−1.24552
$222$	−1.10296	−0.0740259
$223$	−1.42620	−0.0955052	−0.0477526	−	0.998859i	$-0.515206\pi$
$223$	−1.42620	−0.0955052	−0.0477526	+	0.998859i	$0.515206\pi$
$224$	−3.24244	−0.216644
$225$	−15.3353	−1.02235
$226$	7.16054	0.476312
$227$	−18.0578	−1.19854	−0.599269	−	0.800548i	$-0.704542\pi$
$227$	−18.0578	−1.19854	−0.599269	+	0.800548i	$0.704542\pi$
$228$	2.46365	0.163159
$229$	13.0825	0.864515	0.432257	−	0.901750i	$-0.357717\pi$
$229$	13.0825	0.864515	0.432257	+	0.901750i	$0.357717\pi$
$230$	−0.00907864	−0.000598627 0
$231$	−14.4942	−0.953649
$232$	−1.88437	−0.123715
$233$	−23.6783	−1.55122	−0.775609	−	0.631214i	$-0.782557\pi$
$233$	−23.6783	−1.55122	−0.775609	+	0.631214i	$0.782557\pi$
$234$	18.9844	1.24105
$235$	0.316502	0.0206463
$236$	2.98972	0.194614
$237$	9.67340	0.628355
$238$	−9.70731	−0.629232
$239$	22.0557	1.42666	0.713332	−	0.700827i	$-0.247185\pi$
$239$	22.0557	1.42666	0.713332	+	0.700827i	$0.247185\pi$
$240$	0.157191	0.0101466
$241$	−11.3034	−0.728115	−0.364057	−	0.931376i	$-0.618609\pi$
$241$	−11.3034	−0.728115	−0.364057	+	0.931376i	$0.618609\pi$
$242$	7.70778	0.495475
$243$	22.1609	1.42162
$244$	4.57273	0.292739
$245$	−0.224169	−0.0143216
$246$	−25.5303	−1.62775
$247$	6.18473	0.393525
$248$	−8.38673	−0.532558
$249$	−9.85817	−0.624736
$250$	−0.637780	−0.0403368
$251$	−14.5250	−0.916808	−0.458404	−	0.888744i	$-0.651579\pi$
$251$	−14.5250	−0.916808	−0.458404	+	0.888744i	$0.651579\pi$
$252$	9.95285	0.626971
$253$	−0.258177	−0.0162314
$254$	10.2450	0.642827
$255$	0.470602	0.0294702
$256$	1.00000	0.0625000
$257$	−13.9317	−0.869036	−0.434518	−	0.900663i	$-0.643081\pi$
$257$	−13.9317	−0.869036	−0.434518	+	0.900663i	$0.643081\pi$
$258$	23.2338	1.44647
$259$	−1.45162	−0.0901994
$260$	0.394610	0.0244727
$261$	5.78418	0.358032
$262$	−10.3789	−0.641209
$263$	25.6929	1.58429	0.792145	−	0.610333i	$-0.208965\pi$
$263$	25.6929	1.58429	0.792145	+	0.610333i	$0.208965\pi$
$264$	4.47016	0.275119
$265$	−0.222464	−0.0136659
$266$	3.24244	0.198807
$267$	21.8454	1.33692
$268$	−6.70410	−0.409518
$269$	24.9095	1.51876	0.759379	−	0.650649i	$-0.225503\pi$
$269$	24.9095	1.51876	0.759379	+	0.650649i	$0.225503\pi$
$270$	−0.0109338	−0.000665412 0
$271$	5.15392	0.313078	0.156539	−	0.987672i	$-0.449966\pi$
$271$	5.15392	0.313078	0.156539	+	0.987672i	$0.449966\pi$
$272$	2.99383	0.181528
$273$	49.4050	2.99013
$274$	−17.5839	−1.06228
$275$	−9.06485	−0.546631
$276$	0.350551	0.0211007
$277$	9.12431	0.548227	0.274113	−	0.961697i	$-0.411616\pi$
$277$	9.12431	0.548227	0.274113	+	0.961697i	$0.411616\pi$
$278$	12.0072	0.720143
$279$	25.7435	1.54123
$280$	0.206880	0.0123635
$281$	9.08087	0.541719	0.270860	−	0.962619i	$-0.412692\pi$
$281$	9.08087	0.541719	0.270860	+	0.962619i	$0.412692\pi$
$282$	−12.2210	−0.727751
$283$	8.03240	0.477477	0.238738	−	0.971084i	$-0.423266\pi$
$283$	8.03240	0.477477	0.238738	+	0.971084i	$0.423266\pi$
$284$	−13.2336	−0.785272
$285$	−0.157191	−0.00931116
$286$	11.2219	0.663562
$287$	−33.6007	−1.98339
$288$	−3.06956	−0.180875
$289$	−8.03697	−0.472763
$290$	0.120230	0.00706016
$291$	−5.43008	−0.318317
$292$	−11.2113	−0.656094
$293$	−4.55557	−0.266139	−0.133070	−	0.991107i	$-0.542483\pi$
$293$	−4.55557	−0.266139	−0.133070	+	0.991107i	$0.542483\pi$
$294$	8.65578	0.504816
$295$	−0.190756	−0.0111062
$296$	0.447694	0.0260217
$297$	−0.310934	−0.0180422
$298$	−16.8503	−0.976112
$299$	0.880021	0.0508930
$300$	12.3082	0.710615
$301$	30.5783	1.76250
$302$	−14.3539	−0.825976
$303$	−18.8815	−1.08472
$304$	−1.00000	−0.0573539
$305$	−0.291758	−0.0167060
$306$	−9.18974	−0.525342
$307$	−7.55740	−0.431324	−0.215662	−	0.976468i	$-0.569191\pi$
$307$	−7.55740	−0.431324	−0.215662	+	0.976468i	$0.569191\pi$
$308$	5.88323	0.335228
$309$	−29.7672	−1.69339
$310$	0.535107	0.0303920
$311$	27.8873	1.58134	0.790672	−	0.612240i	$-0.209731\pi$
$311$	27.8873	1.58134	0.790672	+	0.612240i	$0.209731\pi$
$312$	−15.2370	−0.862625
$313$	−18.8074	−1.06306	−0.531528	−	0.847041i	$-0.678382\pi$
$313$	−18.8074	−1.06306	−0.531528	+	0.847041i	$0.678382\pi$
$314$	17.1541	0.968061
$315$	−0.635032	−0.0357800
$316$	−3.92645	−0.220880
$317$	−32.9643	−1.85146	−0.925731	−	0.378183i	$-0.876549\pi$
$317$	−32.9643	−1.85146	−0.925731	+	0.378183i	$0.876549\pi$
$318$	8.58996	0.481701
$319$	3.41909	0.191432
$320$	−0.0638040	−0.00356675
$321$	2.53524	0.141503
$322$	0.461365	0.0257108
$323$	−2.99383	−0.166581
$324$	−8.78649	−0.488138
$325$	30.8985	1.71394
$326$	15.4266	0.854403
$327$	18.8602	1.04297
$328$	10.3628	0.572190
$329$	−16.0842	−0.886753
$330$	−0.285214	−0.0157005
$331$	3.39601	0.186662	0.0933308	−	0.995635i	$-0.470249\pi$
$331$	3.39601	0.186662	0.0933308	+	0.995635i	$0.470249\pi$
$332$	4.00145	0.219608
$333$	−1.37422	−0.0753070
$334$	0.0738214	0.00403933
$335$	0.427748	0.0233704
$336$	−7.98822	−0.435793
$337$	10.6295	0.579028	0.289514	−	0.957174i	$-0.406506\pi$
$337$	10.6295	0.579028	0.289514	+	0.957174i	$0.406506\pi$
$338$	−25.2509	−1.37347
$339$	17.6410	0.958130
$340$	−0.191018	−0.0103594
$341$	15.2173	0.824061
$342$	3.06956	0.165983
$343$	−11.3051	−0.610417
$344$	−9.43065	−0.508467
$345$	−0.0223666	−0.00120417
$346$	−9.65770	−0.519201
$347$	−18.6487	−1.00112	−0.500559	−	0.865703i	$-0.666872\pi$
$347$	−18.6487	−1.00112	−0.500559	+	0.865703i	$0.666872\pi$
$348$	−4.64242	−0.248860
$349$	27.0351	1.44716	0.723578	−	0.690242i	$-0.242496\pi$
$349$	27.0351	1.44716	0.723578	+	0.690242i	$0.242496\pi$
$350$	16.1990	0.865872
$351$	1.05985	0.0565707
$352$	−1.81445	−0.0967103
$353$	−14.6637	−0.780472	−0.390236	−	0.920715i	$-0.627606\pi$
$353$	−14.6637	−0.780472	−0.390236	+	0.920715i	$0.627606\pi$
$354$	7.36561	0.391478
$355$	0.844359	0.0448139
$356$	−8.86710	−0.469955
$357$	−23.9154	−1.26574
$358$	−12.5121	−0.661284
$359$	−25.2586	−1.33310	−0.666550	−	0.745461i	$-0.732230\pi$
$359$	−25.2586	−1.33310	−0.666550	+	0.745461i	$0.732230\pi$
$360$	0.195850	0.0103222
$361$	1.00000	0.0526316
$362$	−12.3961	−0.651525
$363$	18.9893	0.996678
$364$	−20.0536	−1.05109
$365$	0.715328	0.0374420
$366$	11.2656	0.588862
$367$	−30.8463	−1.61017	−0.805083	−	0.593163i	$-0.797879\pi$
$367$	−30.8463	−1.61017	−0.805083	+	0.593163i	$0.797879\pi$
$368$	−0.142289	−0.00741735
$369$	−31.8092	−1.65592
$370$	−0.0285647	−0.00148501
$371$	11.3054	0.586945
$372$	−20.6619	−1.07127
$373$	−16.2752	−0.842696	−0.421348	−	0.906899i	$-0.638443\pi$
$373$	−16.2752	−0.842696	−0.421348	+	0.906899i	$0.638443\pi$
$374$	−5.43215	−0.280890
$375$	−1.57127	−0.0811398
$376$	4.96054	0.255820
$377$	−11.6543	−0.600227
$378$	0.555643	0.0285792
$379$	−30.2278	−1.55270	−0.776349	−	0.630304i	$-0.782930\pi$
$379$	−30.2278	−1.55270	−0.776349	+	0.630304i	$0.782930\pi$
$380$	0.0638040	0.00327308
$381$	25.2400	1.29309
$382$	14.0475	0.718732
$383$	26.1709	1.33727	0.668634	−	0.743592i	$-0.266879\pi$
$383$	26.1709	1.33727	0.668634	+	0.743592i	$0.266879\pi$
$384$	2.46365	0.125722
$385$	−0.375374	−0.0191308
$386$	5.38469	0.274073
$387$	28.9479	1.47151
$388$	2.20408	0.111895
$389$	23.2243	1.17752	0.588759	−	0.808308i	$-0.299617\pi$
$389$	23.2243	1.17752	0.588759	+	0.808308i	$0.299617\pi$
$390$	0.972181	0.0492283
$391$	−0.425991	−0.0215433
$392$	−3.51340	−0.177454
$393$	−25.5699	−1.28983
$394$	12.8316	0.646446
$395$	0.250523	0.0126052
$396$	5.56955	0.279880
$397$	−16.8631	−0.846337	−0.423168	−	0.906051i	$-0.639082\pi$
$397$	−16.8631	−0.846337	−0.423168	+	0.906051i	$0.639082\pi$
$398$	−21.8427	−1.09487
$399$	7.98822	0.399911
$400$	−4.99593	−0.249796
$401$	−15.8367	−0.790845	−0.395422	−	0.918499i	$-0.629402\pi$
$401$	−15.8367	−0.790845	−0.395422	+	0.918499i	$0.629402\pi$
$402$	−16.5165	−0.823770
$403$	−51.8696	−2.58381
$404$	7.66406	0.381301
$405$	0.560613	0.0278571
$406$	−6.10995	−0.303232
$407$	−0.812318	−0.0402651
$408$	7.37575	0.365154
$409$	−8.83200	−0.436714	−0.218357	−	0.975869i	$-0.570070\pi$
$409$	−8.83200	−0.436714	−0.218357	+	0.975869i	$0.570070\pi$
$410$	−0.661188	−0.0326537
$411$	−43.3206	−2.13685
$412$	12.0826	0.595265
$413$	9.69397	0.477009
$414$	0.436766	0.0214659
$415$	−0.255309	−0.0125326
$416$	6.18473	0.303231
$417$	29.5815	1.44861
$418$	1.81445	0.0887475
$419$	9.05400	0.442317	0.221159	−	0.975238i	$-0.429016\pi$
$419$	9.05400	0.442317	0.221159	+	0.975238i	$0.429016\pi$
$420$	0.509681	0.0248699
$421$	12.1882	0.594018	0.297009	−	0.954875i	$-0.404011\pi$
$421$	12.1882	0.594018	0.297009	+	0.954875i	$0.404011\pi$
$422$	1.00000	0.0486792
$423$	−15.2267	−0.740346
$424$	−3.48668	−0.169328
$425$	−14.9570	−0.725520
$426$	−32.6030	−1.57962
$427$	14.8268	0.717519
$428$	−1.02906	−0.0497415
$429$	27.6467	1.33480
$430$	0.601713	0.0290172
$431$	−32.3186	−1.55673	−0.778365	−	0.627812i	$-0.783951\pi$
$431$	−32.3186	−1.55673	−0.778365	+	0.627812i	$0.783951\pi$
$432$	−0.171366	−0.00824485
$433$	19.3512	0.929961	0.464980	−	0.885321i	$-0.346061\pi$
$433$	19.3512	0.929961	0.464980	+	0.885321i	$0.346061\pi$
$434$	−27.1934	−1.30533
$435$	0.296205	0.0142019
$436$	−7.65541	−0.366628
$437$	0.142289	0.00680663
$438$	−27.6208	−1.31977
$439$	−35.6457	−1.70128	−0.850638	−	0.525752i	$-0.823784\pi$
$439$	−35.6457	−1.70128	−0.850638	+	0.525752i	$0.823784\pi$
$440$	0.115769	0.00551907
$441$	10.7846	0.513552
$442$	18.5160	0.880718
$443$	13.3557	0.634551	0.317275	−	0.948333i	$-0.397232\pi$
$443$	13.3557	0.634551	0.317275	+	0.948333i	$0.397232\pi$
$444$	1.10296	0.0523442
$445$	0.565756	0.0268194
$446$	1.42620	0.0675324
$447$	−41.5132	−1.96351
$448$	3.24244	0.153191
$449$	16.6425	0.785408	0.392704	−	0.919665i	$-0.371540\pi$
$449$	16.6425	0.785408	0.392704	+	0.919665i	$0.371540\pi$
$450$	15.3353	0.722913
$451$	−18.8027	−0.885386
$452$	−7.16054	−0.336804
$453$	−35.3630	−1.66150
$454$	18.0578	0.847494
$455$	1.27950	0.0599839
$456$	−2.46365	−0.115371
$457$	17.7077	0.828332	0.414166	−	0.910201i	$-0.364073\pi$
$457$	17.7077	0.828332	0.414166	+	0.910201i	$0.364073\pi$
$458$	−13.0825	−0.611304
$459$	−0.513041	−0.0239467
$460$	0.00907864	0.000423294 0
$461$	33.5594	1.56302	0.781509	−	0.623893i	$-0.214450\pi$
$461$	33.5594	1.56302	0.781509	+	0.623893i	$0.214450\pi$
$462$	14.4942	0.674331
$463$	−41.6369	−1.93503	−0.967514	−	0.252816i	$-0.918643\pi$
$463$	−41.6369	−1.93503	−0.967514	+	0.252816i	$0.918643\pi$
$464$	1.88437	0.0874796
$465$	1.31831	0.0611354
$466$	23.6783	1.09688
$467$	24.9248	1.15338	0.576692	−	0.816962i	$-0.304343\pi$
$467$	24.9248	1.15338	0.576692	+	0.816962i	$0.304343\pi$
$468$	−18.9844	−0.877553
$469$	−21.7376	−1.00375
$470$	−0.316502	−0.0145992
$471$	42.2616	1.94731
$472$	−2.98972	−0.137613
$473$	17.1114	0.786783
$474$	−9.67340	−0.444314
$475$	4.99593	0.229229
$476$	9.70731	0.444934
$477$	10.7026	0.490037
$478$	−22.0557	−1.00880
$479$	22.1305	1.01117	0.505583	−	0.862778i	$-0.331277\pi$
$479$	22.1305	1.01117	0.505583	+	0.862778i	$0.331277\pi$
$480$	−0.157191	−0.00717473
$481$	2.76887	0.126250
$482$	11.3034	0.514855
$483$	1.13664	0.0517189
$484$	−7.70778	−0.350354
$485$	−0.140629	−0.00638565
$486$	−22.1609	−1.00524
$487$	3.16629	0.143478	0.0717391	−	0.997423i	$-0.477145\pi$
$487$	3.16629	0.143478	0.0717391	+	0.997423i	$0.477145\pi$
$488$	−4.57273	−0.206998
$489$	38.0058	1.71868
$490$	0.224169	0.0101269
$491$	−21.5232	−0.971327	−0.485664	−	0.874146i	$-0.661422\pi$
$491$	−21.5232	−0.971327	−0.485664	+	0.874146i	$0.661422\pi$
$492$	25.5303	1.15099
$493$	5.64148	0.254080
$494$	−6.18473	−0.278264
$495$	−0.355359	−0.0159722
$496$	8.38673	0.376575
$497$	−42.9092	−1.92474
$498$	9.85817	0.441755
$499$	24.0079	1.07474	0.537370	−	0.843347i	$-0.319418\pi$
$499$	24.0079	1.07474	0.537370	+	0.843347i	$0.319418\pi$
$500$	0.637780	0.0285224
$501$	0.181870	0.00812535
$502$	14.5250	0.648281
$503$	−18.2537	−0.813893	−0.406947	−	0.913452i	$-0.633407\pi$
$503$	−18.2537	−0.813893	−0.406947	+	0.913452i	$0.633407\pi$
$504$	−9.95285	−0.443335
$505$	−0.488998	−0.0217601
$506$	0.258177	0.0114773
$507$	−62.2092	−2.76281
$508$	−10.2450	−0.454548
$509$	−17.4821	−0.774880	−0.387440	−	0.921895i	$-0.626641\pi$
$509$	−17.4821	−0.774880	−0.387440	+	0.921895i	$0.626641\pi$
$510$	−0.470602	−0.0208386
$511$	−36.3521	−1.60812
$512$	−1.00000	−0.0441942
$513$	0.171366	0.00756599
$514$	13.9317	0.614501
$515$	−0.770915	−0.0339706
$516$	−23.2338	−1.02281
$517$	−9.00064	−0.395848
$518$	1.45162	0.0637806
$519$	−23.7932	−1.04440
$520$	−0.394610	−0.0173048
$521$	30.2143	1.32371	0.661857	−	0.749630i	$-0.269769\pi$
$521$	30.2143	1.32371	0.661857	+	0.749630i	$0.269769\pi$
$522$	−5.78418	−0.253167
$523$	−36.8934	−1.61324	−0.806618	−	0.591073i	$-0.798705\pi$
$523$	−36.8934	−1.61324	−0.806618	+	0.591073i	$0.798705\pi$
$524$	10.3789	0.453403
$525$	39.9086	1.74175
$526$	−25.6929	−1.12026
$527$	25.1084	1.09374
$528$	−4.47016	−0.194539
$529$	−22.9798	−0.999120
$530$	0.222464	0.00966323
$531$	9.17711	0.398253
$532$	−3.24244	−0.140578
$533$	64.0911	2.77609
$534$	−21.8454	−0.945343
$535$	0.0656582	0.00283865
$536$	6.70410	0.289573
$537$	−30.8253	−1.33021
$538$	−24.9095	−1.07392
$539$	6.37488	0.274586
$540$	0.0109338	0.000470517 0
$541$	−30.0123	−1.29033	−0.645164	−	0.764044i	$-0.723211\pi$
$541$	−30.0123	−1.29033	−0.645164	+	0.764044i	$0.723211\pi$
$542$	−5.15392	−0.221380
$543$	−30.5397	−1.31058
$544$	−2.99383	−0.128359
$545$	0.488446	0.0209227
$546$	−49.4050	−2.11434
$547$	−25.8116	−1.10362	−0.551812	−	0.833969i	$-0.686063\pi$
$547$	−25.8116	−1.10362	−0.551812	+	0.833969i	$0.686063\pi$
$548$	17.5839	0.751148
$549$	14.0363	0.599053
$550$	9.06485	0.386526
$551$	−1.88437	−0.0802768
$552$	−0.350551	−0.0149204
$553$	−12.7313	−0.541389
$554$	−9.12431	−0.387655
$555$	−0.0703733	−0.00298718
$556$	−12.0072	−0.509218
$557$	−13.7354	−0.581986	−0.290993	−	0.956725i	$-0.593986\pi$
$557$	−13.7354	−0.581986	−0.290993	+	0.956725i	$0.593986\pi$
$558$	−25.7435	−1.08981
$559$	−58.3260	−2.46693
$560$	−0.206880	−0.00874230
$561$	−13.3829	−0.565026
$562$	−9.08087	−0.383053
$563$	22.2159	0.936287	0.468144	−	0.883652i	$-0.344923\pi$
$563$	22.2159	0.936287	0.468144	+	0.883652i	$0.344923\pi$
$564$	12.2210	0.514598
$565$	0.456871	0.0192207
$566$	−8.03240	−0.337627
$567$	−28.4896	−1.19645
$568$	13.2336	0.555271
$569$	−28.6945	−1.20294	−0.601469	−	0.798896i	$-0.705418\pi$
$569$	−28.6945	−1.20294	−0.601469	+	0.798896i	$0.705418\pi$
$570$	0.157191	0.00658399
$571$	−35.7563	−1.49636	−0.748178	−	0.663498i	$-0.769071\pi$
$571$	−35.7563	−1.49636	−0.748178	+	0.663498i	$0.769071\pi$
$572$	−11.2219	−0.469209
$573$	34.6081	1.44577
$574$	33.6007	1.40247
$575$	0.710868	0.0296452
$576$	3.06956	0.127898
$577$	−13.5398	−0.563670	−0.281835	−	0.959463i	$-0.590943\pi$
$577$	−13.5398	−0.563670	−0.281835	+	0.959463i	$0.590943\pi$
$578$	8.03697	0.334294
$579$	13.2660	0.551315
$580$	−0.120230	−0.00499229
$581$	12.9745	0.538271
$582$	5.43008	0.225084
$583$	6.32640	0.262013
$584$	11.2113	0.463928
$585$	1.21128	0.0500802
$586$	4.55557	0.188189
$587$	−37.7131	−1.55658	−0.778292	−	0.627902i	$-0.783914\pi$
$587$	−37.7131	−1.55658	−0.778292	+	0.627902i	$0.783914\pi$
$588$	−8.65578	−0.356959
$589$	−8.38673	−0.345569
$590$	0.190756	0.00785329
$591$	31.6125	1.30037
$592$	−0.447694	−0.0184001
$593$	21.9626	0.901896	0.450948	−	0.892550i	$-0.351086\pi$
$593$	21.9626	0.901896	0.450948	+	0.892550i	$0.351086\pi$
$594$	0.310934	0.0127578
$595$	−0.619365	−0.0253915
$596$	16.8503	0.690216
$597$	−53.8126	−2.20240
$598$	−0.880021	−0.0359868
$599$	−26.4084	−1.07902	−0.539510	−	0.841979i	$-0.681390\pi$
$599$	−26.4084	−1.07902	−0.539510	+	0.841979i	$0.681390\pi$
$600$	−12.3082	−0.502480
$601$	−18.2337	−0.743770	−0.371885	−	0.928279i	$-0.621288\pi$
$601$	−18.2337	−0.743770	−0.371885	+	0.928279i	$0.621288\pi$
$602$	−30.5783	−1.24628
$603$	−20.5786	−0.838026
$604$	14.3539	0.584053
$605$	0.491787	0.0199940
$606$	18.8815	0.767010
$607$	−45.3963	−1.84258	−0.921289	−	0.388879i	$-0.872862\pi$
$607$	−45.3963	−1.84258	−0.921289	+	0.388879i	$0.872862\pi$
$608$	1.00000	0.0405554
$609$	−15.0528	−0.609968
$610$	0.291758	0.0118130
$611$	30.6796	1.24116
$612$	9.18974	0.371473
$613$	37.2161	1.50314	0.751571	−	0.659652i	$-0.229296\pi$
$613$	37.2161	1.50314	0.751571	+	0.659652i	$0.229296\pi$
$614$	7.55740	0.304992
$615$	−1.62893	−0.0656849
$616$	−5.88323	−0.237042
$617$	9.05290	0.364456	0.182228	−	0.983256i	$-0.441669\pi$
$617$	9.05290	0.364456	0.182228	+	0.983256i	$0.441669\pi$
$618$	29.7672	1.19741
$619$	9.99067	0.401559	0.200779	−	0.979636i	$-0.435653\pi$
$619$	9.99067	0.401559	0.200779	+	0.979636i	$0.435653\pi$
$620$	−0.535107	−0.0214904
$621$	0.0243836	0.000978479 0
$622$	−27.8873	−1.11818
$623$	−28.7510	−1.15189
$624$	15.2370	0.609968
$625$	24.9390	0.997558
$626$	18.8074	0.751694
$627$	4.47016	0.178521
$628$	−17.1541	−0.684523
$629$	−1.34032	−0.0534421
$630$	0.635032	0.0253003
$631$	−42.0381	−1.67351	−0.836755	−	0.547577i	$-0.815550\pi$
$631$	−42.0381	−1.67351	−0.836755	+	0.547577i	$0.815550\pi$
$632$	3.92645	0.156186
$633$	2.46365	0.0979212
$634$	32.9643	1.30918
$635$	0.653671	0.0259401
$636$	−8.58996	−0.340614
$637$	−21.7294	−0.860952
$638$	−3.41909	−0.135363
$639$	−40.6214	−1.60696
$640$	0.0638040	0.00252207
$641$	4.12200	0.162809	0.0814046	−	0.996681i	$-0.474059\pi$
$641$	4.12200	0.162809	0.0814046	+	0.996681i	$0.474059\pi$
$642$	−2.53524	−0.100058
$643$	6.22845	0.245626	0.122813	−	0.992430i	$-0.460808\pi$
$643$	6.22845	0.245626	0.122813	+	0.992430i	$0.460808\pi$
$644$	−0.461365	−0.0181803
$645$	1.48241	0.0583698
$646$	2.99383	0.117791
$647$	−34.7613	−1.36661	−0.683304	−	0.730134i	$-0.739458\pi$
$647$	−34.7613	−1.36661	−0.683304	+	0.730134i	$0.739458\pi$
$648$	8.78649	0.345166
$649$	5.42468	0.212937
$650$	−30.8985	−1.21194
$651$	−66.9950	−2.62574
$652$	−15.4266	−0.604154
$653$	−24.6032	−0.962796	−0.481398	−	0.876502i	$-0.659871\pi$
$653$	−24.6032	−0.962796	−0.481398	+	0.876502i	$0.659871\pi$
$654$	−18.8602	−0.737494
$655$	−0.662213	−0.0258748
$656$	−10.3628	−0.404599
$657$	−34.4138	−1.34261
$658$	16.0842	0.627029
$659$	−10.2206	−0.398137	−0.199069	−	0.979986i	$-0.563792\pi$
$659$	−10.2206	−0.398137	−0.199069	+	0.979986i	$0.563792\pi$
$660$	0.285214	0.0111019
$661$	2.64938	0.103049	0.0515244	−	0.998672i	$-0.483592\pi$
$661$	2.64938	0.103049	0.0515244	+	0.998672i	$0.483592\pi$
$662$	−3.39601	−0.131990
$663$	45.6170	1.77162
$664$	−4.00145	−0.155286
$665$	0.206880	0.00802248
$666$	1.37422	0.0532501
$667$	−0.268126	−0.0103819
$668$	−0.0738214	−0.00285624
$669$	3.51365	0.135845
$670$	−0.427748	−0.0165254
$671$	8.29697	0.320301
$672$	7.98822	0.308152
$673$	−11.0373	−0.425456	−0.212728	−	0.977111i	$-0.568235\pi$
$673$	−11.0373	−0.425456	−0.212728	+	0.977111i	$0.568235\pi$
$674$	−10.6295	−0.409435
$675$	0.856132	0.0329525
$676$	25.2509	0.971187
$677$	38.1764	1.46724	0.733620	−	0.679560i	$-0.237829\pi$
$677$	38.1764	1.46724	0.733620	+	0.679560i	$0.237829\pi$
$678$	−17.6410	−0.677500
$679$	7.14660	0.274261
$680$	0.191018	0.00732522
$681$	44.4880	1.70478
$682$	−15.2173	−0.582699
$683$	−9.12638	−0.349211	−0.174606	−	0.984638i	$-0.555865\pi$
$683$	−9.12638	−0.349211	−0.174606	+	0.984638i	$0.555865\pi$
$684$	−3.06956	−0.117367
$685$	−1.12192	−0.0428665
$686$	11.3051	0.431630
$687$	−32.2306	−1.22967
$688$	9.43065	0.359540
$689$	−21.5642	−0.821530
$690$	0.0223666	0.000851480 0
$691$	−49.9686	−1.90089	−0.950447	−	0.310887i	$-0.899374\pi$
$691$	−49.9686	−1.90089	−0.950447	+	0.310887i	$0.899374\pi$
$692$	9.65770	0.367131
$693$	18.0589	0.686001
$694$	18.6487	0.707897
$695$	0.766106	0.0290601
$696$	4.64242	0.175970
$697$	−31.0245	−1.17514
$698$	−27.0351	−1.02329
$699$	58.3350	2.20643
$700$	−16.1990	−0.612264
$701$	43.9046	1.65825	0.829127	−	0.559060i	$-0.188838\pi$
$701$	43.9046	1.65825	0.829127	+	0.559060i	$0.188838\pi$
$702$	−1.05985	−0.0400015
$703$	0.447694	0.0168851
$704$	1.81445	0.0683845
$705$	−0.779750	−0.0293671
$706$	14.6637	0.551877
$707$	24.8502	0.934589
$708$	−7.36561	−0.276816
$709$	−21.6353	−0.812532	−0.406266	−	0.913755i	$-0.633169\pi$
$709$	−21.6353	−0.812532	−0.406266	+	0.913755i	$0.633169\pi$
$710$	−0.844359	−0.0316882
$711$	−12.0525	−0.452003
$712$	8.86710	0.332309
$713$	−1.19334	−0.0446910
$714$	23.9154	0.895011
$715$	0.715999	0.0267769
$716$	12.5121	0.467598
$717$	−54.3374	−2.02927
$718$	25.2586	0.942643
$719$	−9.59982	−0.358013	−0.179006	−	0.983848i	$-0.557288\pi$
$719$	−9.59982	−0.358013	−0.179006	+	0.983848i	$0.557288\pi$
$720$	−0.195850	−0.00729890
$721$	39.1769	1.45903
$722$	−1.00000	−0.0372161
$723$	27.8476	1.03566
$724$	12.3961	0.460698
$725$	−9.41417	−0.349633
$726$	−18.9893	−0.704758
$727$	−36.2426	−1.34417	−0.672083	−	0.740476i	$-0.734600\pi$
$727$	−36.2426	−1.34417	−0.672083	+	0.740476i	$0.734600\pi$
$728$	20.0536	0.743236
$729$	−28.2372	−1.04582
$730$	−0.715328	−0.0264755
$731$	28.2338	1.04426
$732$	−11.2656	−0.416388
$733$	44.5708	1.64626	0.823129	−	0.567854i	$-0.192226\pi$
$733$	44.5708	1.64626	0.823129	+	0.567854i	$0.192226\pi$
$734$	30.8463	1.13856
$735$	0.552274	0.0203709
$736$	0.142289	0.00524486
$737$	−12.1642	−0.448075
$738$	31.8092	1.17091
$739$	27.0437	0.994818	0.497409	−	0.867516i	$-0.334285\pi$
$739$	27.0437	0.994818	0.497409	+	0.867516i	$0.334285\pi$
$740$	0.0285647	0.00105006
$741$	−15.2370	−0.559745
$742$	−11.3054	−0.415033
$743$	−41.3944	−1.51861	−0.759307	−	0.650732i	$-0.774462\pi$
$743$	−41.3944	−1.51861	−0.759307	+	0.650732i	$0.774462\pi$
$744$	20.6619	0.757503
$745$	−1.07512	−0.0393893
$746$	16.2752	0.595876
$747$	12.2827	0.449400
$748$	5.43215	0.198619
$749$	−3.33666	−0.121919
$750$	1.57127	0.0573745
$751$	54.2407	1.97927	0.989635	−	0.143605i	$-0.0458696\pi$
$751$	54.2407	1.97927	0.989635	+	0.143605i	$0.0458696\pi$
$752$	−4.96054	−0.180892
$753$	35.7844	1.30406
$754$	11.6543	0.424425
$755$	−0.915838	−0.0333308
$756$	−0.555643	−0.0202086
$757$	−50.0049	−1.81746	−0.908730	−	0.417385i	$-0.862947\pi$
$757$	−50.0049	−1.81746	−0.908730	+	0.417385i	$0.862947\pi$
$758$	30.2278	1.09792
$759$	0.636056	0.0230874
$760$	−0.0638040	−0.00231441
$761$	−3.29367	−0.119395	−0.0596977	−	0.998217i	$-0.519014\pi$
$761$	−3.29367	−0.119395	−0.0596977	+	0.998217i	$0.519014\pi$
$762$	−25.2400	−0.914350
$763$	−24.8222	−0.898624
$764$	−14.0475	−0.508220
$765$	−0.586342	−0.0211992
$766$	−26.1709	−0.945591
$767$	−18.4906	−0.667656
$768$	−2.46365	−0.0888992
$769$	−37.2546	−1.34343	−0.671717	−	0.740808i	$-0.734443\pi$
$769$	−37.2546	−1.34343	−0.671717	+	0.740808i	$0.734443\pi$
$770$	0.375374	0.0135275
$771$	34.3228	1.23611
$772$	−5.38469	−0.193799
$773$	9.87091	0.355032	0.177516	−	0.984118i	$-0.443194\pi$
$773$	9.87091	0.355032	0.177516	+	0.984118i	$0.443194\pi$
$774$	−28.9479	−1.04051
$775$	−41.8995	−1.50507
$776$	−2.20408	−0.0791220
$777$	3.57628	0.128298
$778$	−23.2243	−0.832632
$779$	10.3628	0.371286
$780$	−0.972181	−0.0348097
$781$	−24.0117	−0.859207
$782$	0.425991	0.0152334
$783$	−0.322916	−0.0115401
$784$	3.51340	0.125479
$785$	1.09450	0.0390644
$786$	25.5699	0.912047
$787$	−19.8196	−0.706491	−0.353246	−	0.935531i	$-0.614922\pi$
$787$	−19.8196	−0.706491	−0.353246	+	0.935531i	$0.614922\pi$
$788$	−12.8316	−0.457107
$789$	−63.2981	−2.25347
$790$	−0.250523	−0.00891322
$791$	−23.2176	−0.825523
$792$	−5.56955	−0.197905
$793$	−28.2811	−1.00429
$794$	16.8631	0.598451
$795$	0.548074	0.0194382
$796$	21.8427	0.774192
$797$	−18.8434	−0.667469	−0.333734	−	0.942667i	$-0.608309\pi$
$797$	−18.8434	−0.667469	−0.333734	+	0.942667i	$0.608309\pi$
$798$	−7.98822	−0.282780
$799$	−14.8510	−0.525391
$800$	4.99593	0.176633
$801$	−27.2181	−0.961703
$802$	15.8367	0.559212
$803$	−20.3424	−0.717867
$804$	16.5165	0.582493
$805$	0.0294369	0.00103751
$806$	51.8696	1.82703
$807$	−61.3682	−2.16026
$808$	−7.66406	−0.269621
$809$	11.7855	0.414355	0.207178	−	0.978303i	$-0.433572\pi$
$809$	11.7855	0.414355	0.207178	+	0.978303i	$0.433572\pi$
$810$	−0.560613	−0.0196979
$811$	1.58032	0.0554927	0.0277463	−	0.999615i	$-0.491167\pi$
$811$	1.58032	0.0554927	0.0277463	+	0.999615i	$0.491167\pi$
$812$	6.10995	0.214417
$813$	−12.6974	−0.445318
$814$	0.812318	0.0284717
$815$	0.984282	0.0344779
$816$	−7.37575	−0.258203
$817$	−9.43065	−0.329937
$818$	8.83200	0.308804
$819$	−61.5557	−2.15093
$820$	0.661188	0.0230897
$821$	−16.6072	−0.579596	−0.289798	−	0.957088i	$-0.593588\pi$
$821$	−16.6072	−0.579596	−0.289798	+	0.957088i	$0.593588\pi$
$822$	43.3206	1.51098
$823$	37.3627	1.30238	0.651191	−	0.758913i	$-0.274269\pi$
$823$	37.3627	1.30238	0.651191	+	0.758913i	$0.274269\pi$
$824$	−12.0826	−0.420916
$825$	22.3326	0.777521
$826$	−9.69397	−0.337296
$827$	47.4718	1.65076	0.825378	−	0.564581i	$-0.190962\pi$
$827$	47.4718	1.65076	0.825378	+	0.564581i	$0.190962\pi$
$828$	−0.436766	−0.0151787
$829$	−34.9343	−1.21332	−0.606659	−	0.794962i	$-0.707491\pi$
$829$	−34.9343	−1.21332	−0.606659	+	0.794962i	$0.707491\pi$
$830$	0.255309	0.00886189
$831$	−22.4791	−0.779791
$832$	−6.18473	−0.214417
$833$	10.5185	0.364446
$834$	−29.5815	−1.02432
$835$	0.00471010	0.000163000 0
$836$	−1.81445	−0.0627539
$837$	−1.43720	−0.0496769
$838$	−9.05400	−0.312765
$839$	22.9026	0.790685	0.395342	−	0.918534i	$-0.370626\pi$
$839$	22.9026	0.790685	0.395342	+	0.918534i	$0.370626\pi$
$840$	−0.509681	−0.0175857
$841$	−25.4492	−0.877557
$842$	−12.1882	−0.420034
$843$	−22.3721	−0.770534
$844$	−1.00000	−0.0344214
$845$	−1.61111	−0.0554237
$846$	15.2267	0.523504
$847$	−24.9920	−0.858736
$848$	3.48668	0.119733
$849$	−19.7890	−0.679157
$850$	14.9570	0.513020
$851$	0.0637022	0.00218368
$852$	32.6030	1.11696
$853$	16.3848	0.561006	0.280503	−	0.959853i	$-0.409499\pi$
$853$	16.3848	0.561006	0.280503	+	0.959853i	$0.409499\pi$
$854$	−14.8268	−0.507362
$855$	0.195850	0.00669793
$856$	1.02906	0.0351726
$857$	−37.8599	−1.29327	−0.646635	−	0.762800i	$-0.723824\pi$
$857$	−37.8599	−1.29327	−0.646635	+	0.762800i	$0.723824\pi$
$858$	−27.6467	−0.943843
$859$	45.8994	1.56607	0.783034	−	0.621979i	$-0.213671\pi$
$859$	45.8994	1.56607	0.783034	+	0.621979i	$0.213671\pi$
$860$	−0.601713	−0.0205182
$861$	82.7803	2.82115
$862$	32.3186	1.10077
$863$	56.8778	1.93614	0.968071	−	0.250677i	$-0.0806532\pi$
$863$	56.8778	1.93614	0.968071	+	0.250677i	$0.0806532\pi$
$864$	0.171366	0.00582999
$865$	−0.616200	−0.0209514
$866$	−19.3512	−0.657582
$867$	19.8003	0.672452
$868$	27.1934	0.923005
$869$	−7.12434	−0.241677
$870$	−0.296205	−0.0100423
$871$	41.4630	1.40492
$872$	7.65541	0.259245
$873$	6.76556	0.228979
$874$	−0.142289	−0.00481301
$875$	2.06796	0.0699099
$876$	27.6208	0.933220
$877$	−47.1899	−1.59349	−0.796746	−	0.604315i	$-0.793447\pi$
$877$	−47.1899	−1.59349	−0.796746	+	0.604315i	$0.793447\pi$
$878$	35.6457	1.20298
$879$	11.2233	0.378553
$880$	−0.115769	−0.00390257
$881$	18.5342	0.624431	0.312216	−	0.950011i	$-0.398929\pi$
$881$	18.5342	0.624431	0.312216	+	0.950011i	$0.398929\pi$
$882$	−10.7846	−0.363136
$883$	25.4821	0.857542	0.428771	−	0.903413i	$-0.358947\pi$
$883$	25.4821	0.857542	0.428771	+	0.903413i	$0.358947\pi$
$884$	−18.5160	−0.622762
$885$	0.469955	0.0157974
$886$	−13.3557	−0.448695
$887$	−10.0908	−0.338817	−0.169409	−	0.985546i	$-0.554186\pi$
$887$	−10.0908	−0.338817	−0.169409	+	0.985546i	$0.554186\pi$
$888$	−1.10296	−0.0370130
$889$	−33.2187	−1.11412
$890$	−0.565756	−0.0189642
$891$	−15.9426	−0.534098
$892$	−1.42620	−0.0477526
$893$	4.96054	0.165998
$894$	41.5132	1.38841
$895$	−0.798320	−0.0266849
$896$	−3.24244	−0.108322
$897$	−2.16806	−0.0723895
$898$	−16.6425	−0.555367
$899$	15.8037	0.527082
$900$	−15.3353	−0.511176
$901$	10.4385	0.347758
$902$	18.8027	0.626063
$903$	−75.3341	−2.50696
$904$	7.16054	0.238156
$905$	−0.790922	−0.0262911
$906$	35.3630	1.17486
$907$	17.2445	0.572593	0.286296	−	0.958141i	$-0.407576\pi$
$907$	17.2445	0.572593	0.286296	+	0.958141i	$0.407576\pi$
$908$	−18.0578	−0.599269
$909$	23.5253	0.780284
$910$	−1.27950	−0.0424150
$911$	−32.0433	−1.06164	−0.530821	−	0.847484i	$-0.678116\pi$
$911$	−32.0433	−1.06164	−0.530821	+	0.847484i	$0.678116\pi$
$912$	2.46365	0.0815795
$913$	7.26042	0.240285
$914$	−17.7077	−0.585719
$915$	0.718790	0.0237625
$916$	13.0825	0.432257
$917$	33.6528	1.11131
$918$	0.513041	0.0169329
$919$	−23.3239	−0.769384	−0.384692	−	0.923045i	$-0.625692\pi$
$919$	−23.3239	−0.769384	−0.384692	+	0.923045i	$0.625692\pi$
$920$	−0.00907864	−0.000299314 0
$921$	18.6188	0.613509
$922$	−33.5594	−1.10522
$923$	81.8464	2.69401
$924$	−14.4942	−0.476824
$925$	2.23665	0.0735406
$926$	41.6369	1.36827
$927$	37.0881	1.21813
$928$	−1.88437	−0.0618574
$929$	−29.3269	−0.962185	−0.481093	−	0.876670i	$-0.659760\pi$
$929$	−29.3269	−0.962185	−0.481093	+	0.876670i	$0.659760\pi$
$930$	−1.31831	−0.0432292
$931$	−3.51340	−0.115147
$932$	−23.6783	−0.775609
$933$	−68.7045	−2.24928
$934$	−24.9248	−0.815565
$935$	−0.346593	−0.0113348
$936$	18.9844	0.620524
$937$	−35.8742	−1.17196	−0.585979	−	0.810326i	$-0.699290\pi$
$937$	−35.8742	−1.17196	−0.585979	+	0.810326i	$0.699290\pi$
$938$	21.7376	0.709758
$939$	46.3348	1.51208
$940$	0.316502	0.0103232
$941$	25.4859	0.830816	0.415408	−	0.909635i	$-0.363639\pi$
$941$	25.4859	0.830816	0.415408	+	0.909635i	$0.363639\pi$
$942$	−42.2616	−1.37696
$943$	1.47452	0.0480169
$944$	2.98972	0.0973070
$945$	0.0354523	0.00115326
$946$	−17.1114	−0.556340
$947$	18.5929	0.604188	0.302094	−	0.953278i	$-0.402314\pi$
$947$	18.5929	0.604188	0.302094	+	0.953278i	$0.402314\pi$
$948$	9.67340	0.314177
$949$	69.3391	2.25084
$950$	−4.99593	−0.162089
$951$	81.2125	2.63350
$952$	−9.70731	−0.314616
$953$	−35.4636	−1.14878	−0.574389	−	0.818582i	$-0.694760\pi$
$953$	−35.4636	−1.14878	−0.574389	+	0.818582i	$0.694760\pi$
$954$	−10.7026	−0.346509
$955$	0.896286	0.0290031
$956$	22.0557	0.713332
$957$	−8.42342	−0.272291
$958$	−22.1305	−0.715003
$959$	57.0148	1.84110
$960$	0.157191	0.00507330
$961$	39.3372	1.26894
$962$	−2.76887	−0.0892719
$963$	−3.15876	−0.101790
$964$	−11.3034	−0.364057
$965$	0.343565	0.0110597
$966$	−1.13664	−0.0365708
$967$	−16.4220	−0.528097	−0.264048	−	0.964509i	$-0.585058\pi$
$967$	−16.4220	−0.528097	−0.264048	+	0.964509i	$0.585058\pi$
$968$	7.70778	0.247738
$969$	7.37575	0.236943
$970$	0.140629	0.00451533
$971$	−18.9869	−0.609317	−0.304659	−	0.952462i	$-0.598542\pi$
$971$	−18.9869	−0.609317	−0.304659	+	0.952462i	$0.598542\pi$
$972$	22.1609	0.710811
$973$	−38.9325	−1.24812
$974$	−3.16629	−0.101454
$975$	−76.1229	−2.43788
$976$	4.57273	0.146370
$977$	−19.6897	−0.629929	−0.314964	−	0.949104i	$-0.601993\pi$
$977$	−19.6897	−0.629929	−0.314964	+	0.949104i	$0.601993\pi$
$978$	−38.0058	−1.21529
$979$	−16.0889	−0.514203
$980$	−0.224169	−0.00716082
$981$	−23.4987	−0.750257
$982$	21.5232	0.686832
$983$	38.7750	1.23673	0.618366	−	0.785891i	$-0.287795\pi$
$983$	38.7750	1.23673	0.618366	+	0.785891i	$0.287795\pi$
$984$	−25.5303	−0.813875
$985$	0.818707	0.0260862
$986$	−5.64148	−0.179661
$987$	39.6259	1.26131
$988$	6.18473	0.196762
$989$	−1.34188	−0.0426694
$990$	0.355359	0.0112941
$991$	−31.1071	−0.988150	−0.494075	−	0.869419i	$-0.664493\pi$
$991$	−31.1071	−0.988150	−0.494075	+	0.869419i	$0.664493\pi$
$992$	−8.38673	−0.266279
$993$	−8.36657	−0.265505
$994$	42.9092	1.36100
$995$	−1.39365	−0.0441816
$996$	−9.85817	−0.312368
$997$	−60.2155	−1.90704	−0.953522	−	0.301322i	$-0.902572\pi$
$997$	−60.2155	−1.90704	−0.953522	+	0.301322i	$0.902572\pi$
$998$	−24.0079	−0.759956
$999$	0.0767196	0.00242730

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.f.1.7	✓	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.f.1.7	✓	34	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:	\( N \)	\(=\)	\( 8018 = 2 \cdot 19 \cdot 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8018.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.46365 q^{3} +1.00000 q^{4} -0.0638040 q^{5} +2.46365 q^{6} +3.24244 q^{7} -1.00000 q^{8} +3.06956 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.46365 q^{3} +1.00000 q^{4} -0.0638040 q^{5} +2.46365 q^{6} +3.24244 q^{7} -1.00000 q^{8} +3.06956 q^{9} +0.0638040 q^{10} +1.81445 q^{11} -2.46365 q^{12} -6.18473 q^{13} -3.24244 q^{14} +0.157191 q^{15} +1.00000 q^{16} +2.99383 q^{17} -3.06956 q^{18} -1.00000 q^{19} -0.0638040 q^{20} -7.98822 q^{21} -1.81445 q^{22} -0.142289 q^{23} +2.46365 q^{24} -4.99593 q^{25} +6.18473 q^{26} -0.171366 q^{27} +3.24244 q^{28} +1.88437 q^{29} -0.157191 q^{30} +8.38673 q^{31} -1.00000 q^{32} -4.47016 q^{33} -2.99383 q^{34} -0.206880 q^{35} +3.06956 q^{36} -0.447694 q^{37} +1.00000 q^{38} +15.2370 q^{39} +0.0638040 q^{40} -10.3628 q^{41} +7.98822 q^{42} +9.43065 q^{43} +1.81445 q^{44} -0.195850 q^{45} +0.142289 q^{46} -4.96054 q^{47} -2.46365 q^{48} +3.51340 q^{49} +4.99593 q^{50} -7.37575 q^{51} -6.18473 q^{52} +3.48668 q^{53} +0.171366 q^{54} -0.115769 q^{55} -3.24244 q^{56} +2.46365 q^{57} -1.88437 q^{58} +2.98972 q^{59} +0.157191 q^{60} +4.57273 q^{61} -8.38673 q^{62} +9.95285 q^{63} +1.00000 q^{64} +0.394610 q^{65} +4.47016 q^{66} -6.70410 q^{67} +2.99383 q^{68} +0.350551 q^{69} +0.206880 q^{70} -13.2336 q^{71} -3.06956 q^{72} -11.2113 q^{73} +0.447694 q^{74} +12.3082 q^{75} -1.00000 q^{76} +5.88323 q^{77} -15.2370 q^{78} -3.92645 q^{79} -0.0638040 q^{80} -8.78649 q^{81} +10.3628 q^{82} +4.00145 q^{83} -7.98822 q^{84} -0.191018 q^{85} -9.43065 q^{86} -4.64242 q^{87} -1.81445 q^{88} -8.86710 q^{89} +0.195850 q^{90} -20.0536 q^{91} -0.142289 q^{92} -20.6619 q^{93} +4.96054 q^{94} +0.0638040 q^{95} +2.46365 q^{96} +2.20408 q^{97} -3.51340 q^{98} +5.56955 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 34 q^{2} - 10 q^{3} + 34 q^{4} + 7 q^{5} + 10 q^{6} - 6 q^{7} - 34 q^{8} + 38 q^{9}+O(q^{10}) \) 34 * q - 34 * q^2 - 10 * q^3 + 34 * q^4 + 7 * q^5 + 10 * q^6 - 6 * q^7 - 34 * q^8 + 38 * q^9	\( 34 q - 34 q^{2} - 10 q^{3} + 34 q^{4} + 7 q^{5} + 10 q^{6} - 6 q^{7} - 34 q^{8} + 38 q^{9} - 7 q^{10} + 4 q^{11} - 10 q^{12} - 5 q^{13} + 6 q^{14} - 17 q^{15} + 34 q^{16} + 8 q^{17} - 38 q^{18} - 34 q^{19} + 7 q^{20} - 4 q^{22} - 24 q^{23} + 10 q^{24} + 5 q^{25} + 5 q^{26} - 31 q^{27} - 6 q^{28} + 24 q^{29} + 17 q^{30} - 28 q^{31} - 34 q^{32} - 16 q^{33} - 8 q^{34} + 2 q^{35} + 38 q^{36} - 36 q^{37} + 34 q^{38} - 9 q^{39} - 7 q^{40} + 9 q^{41} - 24 q^{43} + 4 q^{44} + 22 q^{45} + 24 q^{46} - 29 q^{47} - 10 q^{48} + 22 q^{49} - 5 q^{50} - 21 q^{51} - 5 q^{52} - 9 q^{53} + 31 q^{54} - 28 q^{55} + 6 q^{56} + 10 q^{57} - 24 q^{58} - 28 q^{59} - 17 q^{60} + 23 q^{61} + 28 q^{62} - 27 q^{63} + 34 q^{64} - 6 q^{65} + 16 q^{66} - 51 q^{67} + 8 q^{68} - 17 q^{69} - 2 q^{70} - 31 q^{71} - 38 q^{72} - 26 q^{73} + 36 q^{74} - 109 q^{75} - 34 q^{76} - 28 q^{77} + 9 q^{78} - 36 q^{79} + 7 q^{80} + 6 q^{81} - 9 q^{82} - 10 q^{83} - 32 q^{85} + 24 q^{86} - 8 q^{87} - 4 q^{88} - 34 q^{89} - 22 q^{90} - 41 q^{91} - 24 q^{92} - 33 q^{93} + 29 q^{94} - 7 q^{95} + 10 q^{96} - 56 q^{97} - 22 q^{98} - 28 q^{99}+O(q^{100}) \) 34 * q - 34 * q^2 - 10 * q^3 + 34 * q^4 + 7 * q^5 + 10 * q^6 - 6 * q^7 - 34 * q^8 + 38 * q^9 - 7 * q^10 + 4 * q^11 - 10 * q^12 - 5 * q^13 + 6 * q^14 - 17 * q^15 + 34 * q^16 + 8 * q^17 - 38 * q^18 - 34 * q^19 + 7 * q^20 - 4 * q^22 - 24 * q^23 + 10 * q^24 + 5 * q^25 + 5 * q^26 - 31 * q^27 - 6 * q^28 + 24 * q^29 + 17 * q^30 - 28 * q^31 - 34 * q^32 - 16 * q^33 - 8 * q^34 + 2 * q^35 + 38 * q^36 - 36 * q^37 + 34 * q^38 - 9 * q^39 - 7 * q^40 + 9 * q^41 - 24 * q^43 + 4 * q^44 + 22 * q^45 + 24 * q^46 - 29 * q^47 - 10 * q^48 + 22 * q^49 - 5 * q^50 - 21 * q^51 - 5 * q^52 - 9 * q^53 + 31 * q^54 - 28 * q^55 + 6 * q^56 + 10 * q^57 - 24 * q^58 - 28 * q^59 - 17 * q^60 + 23 * q^61 + 28 * q^62 - 27 * q^63 + 34 * q^64 - 6 * q^65 + 16 * q^66 - 51 * q^67 + 8 * q^68 - 17 * q^69 - 2 * q^70 - 31 * q^71 - 38 * q^72 - 26 * q^73 + 36 * q^74 - 109 * q^75 - 34 * q^76 - 28 * q^77 + 9 * q^78 - 36 * q^79 + 7 * q^80 + 6 * q^81 - 9 * q^82 - 10 * q^83 - 32 * q^85 + 24 * q^86 - 8 * q^87 - 4 * q^88 - 34 * q^89 - 22 * q^90 - 41 * q^91 - 24 * q^92 - 33 * q^93 + 29 * q^94 - 7 * q^95 + 10 * q^96 - 56 * q^97 - 22 * q^98 - 28 * q^99

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