LMFDB - Embedded newform 8027.2.a.e.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8027,2,Mod(1,8027)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8027, 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("8027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8027 = 23 \cdot 349 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8027.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:	$64.0959177025$
Analytic rank:	$0$
Dimension:	$169$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	8027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.47925 q^{2} -2.94109 q^{3} +4.14669 q^{4} -0.477027 q^{5} +7.29170 q^{6} -3.55930 q^{7} -5.32218 q^{8} +5.65002 q^{9} +O(q^{10})$	\(q-2.47925 q^{2} -2.94109 q^{3} +4.14669 q^{4} -0.477027 q^{5} +7.29170 q^{6} -3.55930 q^{7} -5.32218 q^{8} +5.65002 q^{9} +1.18267 q^{10} +3.53933 q^{11} -12.1958 q^{12} +6.06714 q^{13} +8.82439 q^{14} +1.40298 q^{15} +4.90164 q^{16} +8.03988 q^{17} -14.0078 q^{18} -8.27975 q^{19} -1.97808 q^{20} +10.4682 q^{21} -8.77489 q^{22} -1.00000 q^{23} +15.6530 q^{24} -4.77244 q^{25} -15.0420 q^{26} -7.79394 q^{27} -14.7593 q^{28} +1.54154 q^{29} -3.47834 q^{30} -4.69777 q^{31} -1.50805 q^{32} -10.4095 q^{33} -19.9329 q^{34} +1.69788 q^{35} +23.4289 q^{36} +5.20369 q^{37} +20.5276 q^{38} -17.8440 q^{39} +2.53882 q^{40} +6.55205 q^{41} -25.9533 q^{42} +6.18799 q^{43} +14.6765 q^{44} -2.69521 q^{45} +2.47925 q^{46} +8.68594 q^{47} -14.4162 q^{48} +5.66859 q^{49} +11.8321 q^{50} -23.6460 q^{51} +25.1585 q^{52} +5.14559 q^{53} +19.3231 q^{54} -1.68836 q^{55} +18.9432 q^{56} +24.3515 q^{57} -3.82188 q^{58} -4.91297 q^{59} +5.81772 q^{60} +13.3684 q^{61} +11.6469 q^{62} -20.1101 q^{63} -6.06445 q^{64} -2.89419 q^{65} +25.8078 q^{66} +10.4636 q^{67} +33.3389 q^{68} +2.94109 q^{69} -4.20947 q^{70} +7.82798 q^{71} -30.0704 q^{72} +11.1675 q^{73} -12.9013 q^{74} +14.0362 q^{75} -34.3335 q^{76} -12.5975 q^{77} +44.2398 q^{78} +15.5270 q^{79} -2.33822 q^{80} +5.97264 q^{81} -16.2442 q^{82} +2.57784 q^{83} +43.4084 q^{84} -3.83524 q^{85} -15.3416 q^{86} -4.53382 q^{87} -18.8370 q^{88} +7.11826 q^{89} +6.68211 q^{90} -21.5948 q^{91} -4.14669 q^{92} +13.8166 q^{93} -21.5346 q^{94} +3.94967 q^{95} +4.43531 q^{96} -5.86205 q^{97} -14.0538 q^{98} +19.9973 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 169 q + 6 q^{2} + 2 q^{3} + 186 q^{4} + 28 q^{5} + 5 q^{6} + 38 q^{7} + 18 q^{8} + 185 q^{9}+O(q^{10}) $ 169 * q + 6 * q^2 + 2 * q^3 + 186 * q^4 + 28 * q^5 + 5 * q^6 + 38 * q^7 + 18 * q^8 + 185 * q^9	\( 169 q + 6 q^{2} + 2 q^{3} + 186 q^{4} + 28 q^{5} + 5 q^{6} + 38 q^{7} + 18 q^{8} + 185 q^{9} + 28 q^{10} + 17 q^{11} + 10 q^{12} + 91 q^{13} + 20 q^{14} + 29 q^{15} + 200 q^{16} + 16 q^{17} + 31 q^{18} + 30 q^{19} + 45 q^{20} + 49 q^{21} + 76 q^{22} - 169 q^{23} + 3 q^{24} + 241 q^{25} - 15 q^{26} + 14 q^{27} + 118 q^{28} + 23 q^{29} + 52 q^{30} + 45 q^{31} + 42 q^{32} + 62 q^{33} + 65 q^{34} - 16 q^{35} + 199 q^{36} + 226 q^{37} + 49 q^{38} + 17 q^{39} + 95 q^{40} + 19 q^{41} + 32 q^{42} + 71 q^{43} + 46 q^{44} + 127 q^{45} - 6 q^{46} + 27 q^{47} + 5 q^{48} + 239 q^{49} + 24 q^{50} + 39 q^{51} + 154 q^{52} + 111 q^{53} + 22 q^{54} + 47 q^{55} + 39 q^{56} + 122 q^{57} + 146 q^{58} - 73 q^{59} + 109 q^{60} + 125 q^{61} + 14 q^{62} + 109 q^{63} + 260 q^{64} + 73 q^{65} + 26 q^{66} + 152 q^{67} + 40 q^{68} - 2 q^{69} + 76 q^{70} - 79 q^{71} + 126 q^{72} + 106 q^{73} + 23 q^{74} + 12 q^{75} + 122 q^{76} + 63 q^{77} + 101 q^{78} + 82 q^{79} + 134 q^{80} + 225 q^{81} + 125 q^{82} + 28 q^{83} + 73 q^{84} + 197 q^{85} + 97 q^{86} + 18 q^{87} + 183 q^{88} + 54 q^{89} + 52 q^{90} + 106 q^{91} - 186 q^{92} + 194 q^{93} + q^{94} + 18 q^{95} - 39 q^{96} + 239 q^{97} + 5 q^{98} + 85 q^{99}+O(q^{100}) \) 169 * q + 6 * q^2 + 2 * q^3 + 186 * q^4 + 28 * q^5 + 5 * q^6 + 38 * q^7 + 18 * q^8 + 185 * q^9 + 28 * q^10 + 17 * q^11 + 10 * q^12 + 91 * q^13 + 20 * q^14 + 29 * q^15 + 200 * q^16 + 16 * q^17 + 31 * q^18 + 30 * q^19 + 45 * q^20 + 49 * q^21 + 76 * q^22 - 169 * q^23 + 3 * q^24 + 241 * q^25 - 15 * q^26 + 14 * q^27 + 118 * q^28 + 23 * q^29 + 52 * q^30 + 45 * q^31 + 42 * q^32 + 62 * q^33 + 65 * q^34 - 16 * q^35 + 199 * q^36 + 226 * q^37 + 49 * q^38 + 17 * q^39 + 95 * q^40 + 19 * q^41 + 32 * q^42 + 71 * q^43 + 46 * q^44 + 127 * q^45 - 6 * q^46 + 27 * q^47 + 5 * q^48 + 239 * q^49 + 24 * q^50 + 39 * q^51 + 154 * q^52 + 111 * q^53 + 22 * q^54 + 47 * q^55 + 39 * q^56 + 122 * q^57 + 146 * q^58 - 73 * q^59 + 109 * q^60 + 125 * q^61 + 14 * q^62 + 109 * q^63 + 260 * q^64 + 73 * q^65 + 26 * q^66 + 152 * q^67 + 40 * q^68 - 2 * q^69 + 76 * q^70 - 79 * q^71 + 126 * q^72 + 106 * q^73 + 23 * q^74 + 12 * q^75 + 122 * q^76 + 63 * q^77 + 101 * q^78 + 82 * q^79 + 134 * q^80 + 225 * q^81 + 125 * q^82 + 28 * q^83 + 73 * q^84 + 197 * q^85 + 97 * q^86 + 18 * q^87 + 183 * q^88 + 54 * q^89 + 52 * q^90 + 106 * q^91 - 186 * q^92 + 194 * q^93 + q^94 + 18 * q^95 - 39 * q^96 + 239 * q^97 + 5 * q^98 + 85 * 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 $

$2$	−2.47925	−1.75310	−0.876548	−	0.481315i	$-0.840159\pi$
$2$	−2.47925	−1.75310	−0.876548	+	0.481315i	$0.840159\pi$
$3$	−2.94109	−1.69804	−0.849020	−	0.528361i	$-0.822807\pi$
$3$	−2.94109	−1.69804	−0.849020	+	0.528361i	$0.822807\pi$
$4$	4.14669	2.07334
$5$	−0.477027	−0.213333	−0.106667	−	0.994295i	$-0.534018\pi$
$5$	−0.477027	−0.213333	−0.106667	+	0.994295i	$0.534018\pi$
$6$	7.29170	2.97683
$7$	−3.55930	−1.34529	−0.672644	−	0.739967i	$-0.734841\pi$
$7$	−3.55930	−1.34529	−0.672644	+	0.739967i	$0.734841\pi$
$8$	−5.32218	−1.88167
$9$	5.65002	1.88334
$10$	1.18267	0.373993
$11$	3.53933	1.06715	0.533574	−	0.845753i	$-0.320848\pi$
$11$	3.53933	1.06715	0.533574	+	0.845753i	$0.320848\pi$
$12$	−12.1958	−3.52062
$13$	6.06714	1.68272	0.841361	−	0.540473i	$-0.181755\pi$
$13$	6.06714	1.68272	0.841361	+	0.540473i	$0.181755\pi$
$14$	8.82439	2.35842
$15$	1.40298	0.362248
$16$	4.90164	1.22541
$17$	8.03988	1.94996	0.974979	−	0.222299i	$-0.0713561\pi$
$17$	8.03988	1.94996	0.974979	+	0.222299i	$0.0713561\pi$
$18$	−14.0078	−3.30167
$19$	−8.27975	−1.89951	−0.949753	−	0.313002i	$-0.898665\pi$
$19$	−8.27975	−1.89951	−0.949753	+	0.313002i	$0.898665\pi$
$20$	−1.97808	−0.442313
$21$	10.4682	2.28435
$22$	−8.77489	−1.87081
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	15.6530	3.19516
$25$	−4.77244	−0.954489
$26$	−15.0420	−2.94997
$27$	−7.79394	−1.49994
$28$	−14.7593	−2.78924
$29$	1.54154	0.286258	0.143129	−	0.989704i	$-0.454284\pi$
$29$	1.54154	0.286258	0.143129	+	0.989704i	$0.454284\pi$
$30$	−3.47834	−0.635055
$31$	−4.69777	−0.843744	−0.421872	−	0.906655i	$-0.638627\pi$
$31$	−4.69777	−0.843744	−0.421872	+	0.906655i	$0.638627\pi$
$32$	−1.50805	−0.266588
$33$	−10.4095	−1.81206
$34$	−19.9329	−3.41846
$35$	1.69788	0.286994
$36$	23.4289	3.90481
$37$	5.20369	0.855481	0.427741	−	0.903902i	$-0.359310\pi$
$37$	5.20369	0.855481	0.427741	+	0.903902i	$0.359310\pi$
$38$	20.5276	3.33001
$39$	−17.8440	−2.85733
$40$	2.53882	0.401423
$41$	6.55205	1.02326	0.511629	−	0.859206i	$-0.329042\pi$
$41$	6.55205	1.02326	0.511629	+	0.859206i	$0.329042\pi$
$42$	−25.9533	−4.00469
$43$	6.18799	0.943660	0.471830	−	0.881690i	$-0.343594\pi$
$43$	6.18799	0.943660	0.471830	+	0.881690i	$0.343594\pi$
$44$	14.6765	2.21257
$45$	−2.69521	−0.401779
$46$	2.47925	0.365546
$47$	8.68594	1.26697	0.633487	−	0.773753i	$-0.281623\pi$
$47$	8.68594	1.26697	0.633487	+	0.773753i	$0.281623\pi$
$48$	−14.4162	−2.08080
$49$	5.66859	0.809798
$50$	11.8321	1.67331
$51$	−23.6460	−3.31110
$52$	25.1585	3.48886
$53$	5.14559	0.706801	0.353400	−	0.935472i	$-0.385025\pi$
$53$	5.14559	0.706801	0.353400	+	0.935472i	$0.385025\pi$
$54$	19.3231	2.62955
$55$	−1.68836	−0.227658
$56$	18.9432	2.53139
$57$	24.3515	3.22544
$58$	−3.82188	−0.501837
$59$	−4.91297	−0.639614	−0.319807	−	0.947483i	$-0.603618\pi$
$59$	−4.91297	−0.639614	−0.319807	+	0.947483i	$0.603618\pi$
$60$	5.81772	0.751065
$61$	13.3684	1.71165	0.855827	−	0.517262i	$-0.173049\pi$
$61$	13.3684	1.71165	0.855827	+	0.517262i	$0.173049\pi$
$62$	11.6469	1.47916
$63$	−20.1101	−2.53363
$64$	−6.06445	−0.758057
$65$	−2.89419	−0.358980
$66$	25.8078	3.17672
$67$	10.4636	1.27834	0.639168	−	0.769067i	$-0.279279\pi$
$67$	10.4636	1.27834	0.639168	+	0.769067i	$0.279279\pi$
$68$	33.3389	4.04293
$69$	2.94109	0.354066
$70$	−4.20947	−0.503128
$71$	7.82798	0.929010	0.464505	−	0.885571i	$-0.346232\pi$
$71$	7.82798	0.929010	0.464505	+	0.885571i	$0.346232\pi$
$72$	−30.0704	−3.54383
$73$	11.1675	1.30706	0.653531	−	0.756900i	$-0.273287\pi$
$73$	11.1675	1.30706	0.653531	+	0.756900i	$0.273287\pi$
$74$	−12.9013	−1.49974
$75$	14.0362	1.62076
$76$	−34.3335	−3.93833
$77$	−12.5975	−1.43562
$78$	44.2398	5.00917
$79$	15.5270	1.74693	0.873464	−	0.486889i	$-0.161868\pi$
$79$	15.5270	1.74693	0.873464	+	0.486889i	$0.161868\pi$
$80$	−2.33822	−0.261421
$81$	5.97264	0.663626
$82$	−16.2442	−1.79387
$83$	2.57784	0.282955	0.141478	−	0.989941i	$-0.454815\pi$
$83$	2.57784	0.282955	0.141478	+	0.989941i	$0.454815\pi$
$84$	43.4084	4.73625
$85$	−3.83524	−0.415990
$86$	−15.3416	−1.65433
$87$	−4.53382	−0.486077
$88$	−18.8370	−2.00803
$89$	7.11826	0.754534	0.377267	−	0.926104i	$-0.376864\pi$
$89$	7.11826	0.754534	0.377267	+	0.926104i	$0.376864\pi$
$90$	6.68211	0.704356
$91$	−21.5948	−2.26375
$92$	−4.14669	−0.432322
$93$	13.8166	1.43271
$94$	−21.5346	−2.22113
$95$	3.94967	0.405227
$96$	4.43531	0.452677
$97$	−5.86205	−0.595201	−0.297601	−	0.954690i	$-0.596186\pi$
$97$	−5.86205	−0.595201	−0.297601	+	0.954690i	$0.596186\pi$
$98$	−14.0538	−1.41965
$99$	19.9973	2.00980
$100$	−19.7898	−1.97898
$101$	5.12163	0.509621	0.254811	−	0.966991i	$-0.417987\pi$
$101$	5.12163	0.509621	0.254811	+	0.966991i	$0.417987\pi$
$102$	58.6244	5.80468
$103$	−9.70492	−0.956254	−0.478127	−	0.878291i	$-0.658684\pi$
$103$	−9.70492	−0.956254	−0.478127	+	0.878291i	$0.658684\pi$
$104$	−32.2904	−3.16634
$105$	−4.99362	−0.487328
$106$	−12.7572	−1.23909
$107$	−0.253567	−0.0245133	−0.0122566	−	0.999925i	$-0.503902\pi$
$107$	−0.253567	−0.0245133	−0.0122566	+	0.999925i	$0.503902\pi$
$108$	−32.3190	−3.10990
$109$	2.52210	0.241573	0.120786	−	0.992679i	$-0.461458\pi$
$109$	2.52210	0.241573	0.120786	+	0.992679i	$0.461458\pi$
$110$	4.18586	0.399107
$111$	−15.3045	−1.45264
$112$	−17.4464	−1.64853
$113$	−3.02536	−0.284602	−0.142301	−	0.989823i	$-0.545450\pi$
$113$	−3.02536	−0.284602	−0.142301	+	0.989823i	$0.545450\pi$
$114$	−60.3735	−5.65450
$115$	0.477027	0.0444830
$116$	6.39231	0.593511
$117$	34.2795	3.16914
$118$	12.1805	1.12130
$119$	−28.6163	−2.62325
$120$	−7.46691	−0.681633
$121$	1.52687	0.138807
$122$	−33.1437	−3.00069
$123$	−19.2702	−1.73753
$124$	−19.4802	−1.74937
$125$	4.66172	0.416957
$126$	49.8579	4.44170
$127$	14.8865	1.32096	0.660481	−	0.750843i	$-0.270352\pi$
$127$	14.8865	1.32096	0.660481	+	0.750843i	$0.270352\pi$
$128$	18.0514	1.59553
$129$	−18.1994	−1.60237
$130$	7.17543	0.629327
$131$	−3.14364	−0.274661	−0.137330	−	0.990525i	$-0.543852\pi$
$131$	−3.14364	−0.274661	−0.137330	+	0.990525i	$0.543852\pi$
$132$	−43.1649	−3.75703
$133$	29.4701	2.55538
$134$	−25.9420	−2.24104
$135$	3.71792	0.319988
$136$	−42.7897	−3.66918
$137$	17.0233	1.45440	0.727200	−	0.686425i	$-0.240821\pi$
$137$	17.0233	1.45440	0.727200	+	0.686425i	$0.240821\pi$
$138$	−7.29170	−0.620711
$139$	−8.21535	−0.696817	−0.348408	−	0.937343i	$-0.613278\pi$
$139$	−8.21535	−0.696817	−0.348408	+	0.937343i	$0.613278\pi$
$140$	7.04058	0.595038
$141$	−25.5461	−2.15137
$142$	−19.4075	−1.62864
$143$	21.4736	1.79572
$144$	27.6944	2.30786
$145$	−0.735359	−0.0610682
$146$	−27.6871	−2.29140
$147$	−16.6718	−1.37507
$148$	21.5781	1.77371
$149$	−17.8143	−1.45940	−0.729702	−	0.683765i	$-0.760341\pi$
$149$	−17.8143	−1.45940	−0.729702	+	0.683765i	$0.760341\pi$
$150$	−34.7993	−2.84135
$151$	6.89497	0.561105	0.280552	−	0.959839i	$-0.409482\pi$
$151$	6.89497	0.561105	0.280552	+	0.959839i	$0.409482\pi$
$152$	44.0663	3.57425
$153$	45.4255	3.67243
$154$	31.2324	2.51678
$155$	2.24096	0.179998
$156$	−73.9936	−5.92423
$157$	10.0994	0.806020	0.403010	−	0.915196i	$-0.367964\pi$
$157$	10.0994	0.806020	0.403010	+	0.915196i	$0.367964\pi$
$158$	−38.4954	−3.06253
$159$	−15.1336	−1.20018
$160$	0.719381	0.0568721
$161$	3.55930	0.280512
$162$	−14.8077	−1.16340
$163$	21.0155	1.64606	0.823029	−	0.567999i	$-0.192282\pi$
$163$	21.0155	1.64606	0.823029	+	0.567999i	$0.192282\pi$
$164$	27.1693	2.12157
$165$	4.96562	0.386573
$166$	−6.39112	−0.496047
$167$	−12.7385	−0.985736	−0.492868	−	0.870104i	$-0.664052\pi$
$167$	−12.7385	−0.985736	−0.492868	+	0.870104i	$0.664052\pi$
$168$	−55.7137	−4.29841
$169$	23.8102	1.83156
$170$	9.50853	0.729271
$171$	−46.7807	−3.57741
$172$	25.6597	1.95653
$173$	−11.7928	−0.896591	−0.448295	−	0.893886i	$-0.647969\pi$
$173$	−11.7928	−0.896591	−0.448295	+	0.893886i	$0.647969\pi$
$174$	11.2405	0.852139
$175$	16.9865	1.28406
$176$	17.3485	1.30770
$177$	14.4495	1.08609
$178$	−17.6480	−1.32277
$179$	−23.1716	−1.73193	−0.865964	−	0.500106i	$-0.833294\pi$
$179$	−23.1716	−1.73193	−0.865964	+	0.500106i	$0.833294\pi$
$180$	−11.1762	−0.833025
$181$	5.69130	0.423031	0.211516	−	0.977375i	$-0.432160\pi$
$181$	5.69130	0.423031	0.211516	+	0.977375i	$0.432160\pi$
$182$	53.5388	3.96856
$183$	−39.3178	−2.90646
$184$	5.32218	0.392356
$185$	−2.48230	−0.182502
$186$	−34.2547	−2.51168
$187$	28.4558	2.08089
$188$	36.0179	2.62687
$189$	27.7409	2.01786
$190$	−9.79222	−0.710402
$191$	−17.7571	−1.28486	−0.642430	−	0.766344i	$-0.722074\pi$
$191$	−17.7571	−1.28486	−0.642430	+	0.766344i	$0.722074\pi$
$192$	17.8361	1.28721
$193$	12.1845	0.877058	0.438529	−	0.898717i	$-0.355500\pi$
$193$	12.1845	0.877058	0.438529	+	0.898717i	$0.355500\pi$
$194$	14.5335	1.04344
$195$	8.51209	0.609563
$196$	23.5059	1.67899
$197$	−10.3695	−0.738793	−0.369397	−	0.929272i	$-0.620436\pi$
$197$	−10.3695	−0.738793	−0.369397	+	0.929272i	$0.620436\pi$
$198$	−49.5783	−3.52338
$199$	−6.48853	−0.459959	−0.229980	−	0.973195i	$-0.573866\pi$
$199$	−6.48853	−0.459959	−0.229980	+	0.973195i	$0.573866\pi$
$200$	25.3998	1.79604
$201$	−30.7745	−2.17066
$202$	−12.6978	−0.893415
$203$	−5.48681	−0.385099
$204$	−98.0526	−6.86506
$205$	−3.12551	−0.218295
$206$	24.0609	1.67640
$207$	−5.65002	−0.392703
$208$	29.7390	2.06203
$209$	−29.3048	−2.02705
$210$	12.3804	0.854332
$211$	5.36822	0.369564	0.184782	−	0.982780i	$-0.440842\pi$
$211$	5.36822	0.369564	0.184782	+	0.982780i	$0.440842\pi$
$212$	21.3371	1.46544
$213$	−23.0228	−1.57750
$214$	0.628657	0.0429741
$215$	−2.95184	−0.201314
$216$	41.4807	2.82241
$217$	16.7207	1.13508
$218$	−6.25291	−0.423500
$219$	−32.8447	−2.21944
$220$	−7.00109	−0.472014
$221$	48.7791	3.28124
$222$	37.9438	2.54662
$223$	4.11810	0.275768	0.137884	−	0.990448i	$-0.455970\pi$
$223$	4.11810	0.275768	0.137884	+	0.990448i	$0.455970\pi$
$224$	5.36760	0.358638
$225$	−26.9644	−1.79763
$226$	7.50063	0.498935
$227$	18.0400	1.19735	0.598677	−	0.800991i	$-0.295693\pi$
$227$	18.0400	1.19735	0.598677	+	0.800991i	$0.295693\pi$
$228$	100.978	6.68744
$229$	3.11246	0.205677	0.102838	−	0.994698i	$-0.467208\pi$
$229$	3.11246	0.205677	0.102838	+	0.994698i	$0.467208\pi$
$230$	−1.18267	−0.0779830
$231$	37.0505	2.43774
$232$	−8.20438	−0.538644
$233$	−24.6464	−1.61464	−0.807319	−	0.590115i	$-0.799082\pi$
$233$	−24.6464	−1.61464	−0.807319	+	0.590115i	$0.799082\pi$
$234$	−84.9874	−5.55580
$235$	−4.14343	−0.270288
$236$	−20.3725	−1.32614
$237$	−45.6664	−2.96635
$238$	70.9470	4.59881
$239$	5.23716	0.338764	0.169382	−	0.985551i	$-0.445823\pi$
$239$	5.23716	0.338764	0.169382	+	0.985551i	$0.445823\pi$
$240$	6.87691	0.443903
$241$	−25.2800	−1.62843	−0.814214	−	0.580565i	$-0.802832\pi$
$241$	−25.2800	−1.62843	−0.814214	+	0.580565i	$0.802832\pi$
$242$	−3.78550	−0.243341
$243$	5.81575	0.373081
$244$	55.4348	3.54885
$245$	−2.70407	−0.172757
$246$	47.7756	3.04606
$247$	−50.2344	−3.19634
$248$	25.0024	1.58765
$249$	−7.58167	−0.480469
$250$	−11.5576	−0.730966
$251$	4.59095	0.289778	0.144889	−	0.989448i	$-0.453717\pi$
$251$	4.59095	0.289778	0.144889	+	0.989448i	$0.453717\pi$
$252$	−83.3902	−5.25309
$253$	−3.53933	−0.222516
$254$	−36.9073	−2.31577
$255$	11.2798	0.706368
$256$	−32.6251	−2.03907
$257$	15.4217	0.961977	0.480989	−	0.876727i	$-0.340278\pi$
$257$	15.4217	0.961977	0.480989	+	0.876727i	$0.340278\pi$
$258$	45.1210	2.80911
$259$	−18.5215	−1.15087
$260$	−12.0013	−0.744290
$261$	8.70975	0.539120
$262$	7.79386	0.481506
$263$	12.8198	0.790504	0.395252	−	0.918573i	$-0.370657\pi$
$263$	12.8198	0.790504	0.395252	+	0.918573i	$0.370657\pi$
$264$	55.4012	3.40971
$265$	−2.45459	−0.150784
$266$	−73.0637	−4.47983
$267$	−20.9355	−1.28123
$268$	43.3894	2.65043
$269$	0.545295	0.0332472	0.0166236	−	0.999862i	$-0.494708\pi$
$269$	0.545295	0.0332472	0.0166236	+	0.999862i	$0.494708\pi$
$270$	−9.21766	−0.560969
$271$	24.0407	1.46037	0.730185	−	0.683250i	$-0.239434\pi$
$271$	24.0407	1.46037	0.730185	+	0.683250i	$0.239434\pi$
$272$	39.4086	2.38950
$273$	63.5121	3.84393
$274$	−42.2051	−2.54970
$275$	−16.8913	−1.01858
$276$	12.1958	0.734100
$277$	−14.3193	−0.860361	−0.430180	−	0.902743i	$-0.641550\pi$
$277$	−14.3193	−0.860361	−0.430180	+	0.902743i	$0.641550\pi$
$278$	20.3679	1.22159
$279$	−26.5425	−1.58906
$280$	−9.03643	−0.540030
$281$	4.87304	0.290701	0.145351	−	0.989380i	$-0.453569\pi$
$281$	4.87304	0.290701	0.145351	+	0.989380i	$0.453569\pi$
$282$	63.3353	3.77156
$283$	19.1370	1.13757	0.568787	−	0.822485i	$-0.307413\pi$
$283$	19.1370	1.13757	0.568787	+	0.822485i	$0.307413\pi$
$284$	32.4602	1.92616
$285$	−11.6163	−0.688092
$286$	−53.2385	−3.14806
$287$	−23.3207	−1.37658
$288$	−8.52051	−0.502076
$289$	47.6397	2.80233
$290$	1.82314	0.107058
$291$	17.2408	1.01068
$292$	46.3083	2.70999
$293$	−6.11526	−0.357257	−0.178629	−	0.983917i	$-0.557166\pi$
$293$	−6.11526	−0.357257	−0.178629	+	0.983917i	$0.557166\pi$
$294$	41.3337	2.41063
$295$	2.34362	0.136451
$296$	−27.6950	−1.60974
$297$	−27.5853	−1.60066
$298$	44.1661	2.55848
$299$	−6.06714	−0.350872
$300$	58.2037	3.36039
$301$	−22.0249	−1.26949
$302$	−17.0944	−0.983670
$303$	−15.0632	−0.865357
$304$	−40.5844	−2.32767
$305$	−6.37711	−0.365152
$306$	−112.621	−6.43812
$307$	9.10632	0.519725	0.259863	−	0.965646i	$-0.416323\pi$
$307$	9.10632	0.519725	0.259863	+	0.965646i	$0.416323\pi$
$308$	−52.2380	−2.97654
$309$	28.5430	1.62376
$310$	−5.55591	−0.315555
$311$	13.9669	0.791989	0.395995	−	0.918253i	$-0.370400\pi$
$311$	13.9669	0.791989	0.395995	+	0.918253i	$0.370400\pi$
$312$	94.9691	5.37656
$313$	−34.5742	−1.95425	−0.977124	−	0.212670i	$-0.931784\pi$
$313$	−34.5742	−1.95425	−0.977124	+	0.212670i	$0.931784\pi$
$314$	−25.0390	−1.41303
$315$	9.59306	0.540508
$316$	64.3857	3.62198
$317$	−19.7182	−1.10748	−0.553742	−	0.832689i	$-0.686800\pi$
$317$	−19.7182	−1.10748	−0.553742	+	0.832689i	$0.686800\pi$
$318$	37.5201	2.10402
$319$	5.45604	0.305480
$320$	2.89291	0.161719
$321$	0.745765	0.0416245
$322$	−8.82439	−0.491764
$323$	−66.5682	−3.70395
$324$	24.7667	1.37593
$325$	−28.9551	−1.60614
$326$	−52.1026	−2.88570
$327$	−7.41771	−0.410200
$328$	−34.8712	−1.92544
$329$	−30.9158	−1.70444
$330$	−12.3110	−0.677699
$331$	−21.2841	−1.16988	−0.584941	−	0.811076i	$-0.698882\pi$
$331$	−21.2841	−1.16988	−0.584941	+	0.811076i	$0.698882\pi$
$332$	10.6895	0.586663
$333$	29.4009	1.61116
$334$	31.5820	1.72809
$335$	−4.99144	−0.272711
$336$	51.3114	2.79927
$337$	−19.3575	−1.05447	−0.527235	−	0.849719i	$-0.676771\pi$
$337$	−19.3575	−1.05447	−0.527235	+	0.849719i	$0.676771\pi$
$338$	−59.0315	−3.21089
$339$	8.89787	0.483266
$340$	−15.9036	−0.862491
$341$	−16.6270	−0.900400
$342$	115.981	6.27154
$343$	4.73890	0.255876
$344$	−32.9336	−1.77566
$345$	−1.40298	−0.0755339
$346$	29.2373	1.57181
$347$	28.0287	1.50466	0.752329	−	0.658787i	$-0.228930\pi$
$347$	28.0287	1.50466	0.752329	+	0.658787i	$0.228930\pi$
$348$	−18.8004	−1.00780
$349$	1.00000	0.0535288
$349$	1.00000	0.0535288
$350$	−42.1139	−2.25108
$351$	−47.2870	−2.52399
$352$	−5.33749	−0.284489
$353$	−19.8332	−1.05561	−0.527807	−	0.849364i	$-0.676986\pi$
$353$	−19.8332	−1.05561	−0.527807	+	0.849364i	$0.676986\pi$
$354$	−35.8239	−1.90402
$355$	−3.73416	−0.198189
$356$	29.5172	1.56441
$357$	84.1632	4.45439
$358$	57.4483	3.03624
$359$	5.45182	0.287736	0.143868	−	0.989597i	$-0.454046\pi$
$359$	5.45182	0.287736	0.143868	+	0.989597i	$0.454046\pi$
$360$	14.3444	0.756016
$361$	49.5543	2.60812
$362$	−14.1102	−0.741614
$363$	−4.49067	−0.235699
$364$	−89.5467	−4.69352
$365$	−5.32722	−0.278839
$366$	97.4787	5.09530
$367$	−29.6261	−1.54647	−0.773234	−	0.634121i	$-0.781362\pi$
$367$	−29.6261	−1.54647	−0.773234	+	0.634121i	$0.781362\pi$
$368$	−4.90164	−0.255516
$369$	37.0192	1.92714
$370$	6.15425	0.319944
$371$	−18.3147	−0.950850
$372$	57.2930	2.97050
$373$	14.9212	0.772591	0.386295	−	0.922375i	$-0.373755\pi$
$373$	14.9212	0.772591	0.386295	+	0.922375i	$0.373755\pi$
$374$	−70.5491	−3.64801
$375$	−13.7106	−0.708010
$376$	−46.2281	−2.38403
$377$	9.35277	0.481692
$378$	−68.7768	−3.53749
$379$	−30.3472	−1.55883	−0.779417	−	0.626506i	$-0.784484\pi$
$379$	−30.3472	−1.55883	−0.779417	+	0.626506i	$0.784484\pi$
$380$	16.3780	0.840176
$381$	−43.7825	−2.24305
$382$	44.0244	2.25248
$383$	−2.57892	−0.131776	−0.0658882	−	0.997827i	$-0.520988\pi$
$383$	−2.57892	−0.131776	−0.0658882	+	0.997827i	$0.520988\pi$
$384$	−53.0908	−2.70928
$385$	6.00937	0.306266
$386$	−30.2084	−1.53757
$387$	34.9622	1.77723
$388$	−24.3081	−1.23406
$389$	−22.3933	−1.13539	−0.567693	−	0.823241i	$-0.692164\pi$
$389$	−22.3933	−1.13539	−0.567693	+	0.823241i	$0.692164\pi$
$390$	−21.1036	−1.06862
$391$	−8.03988	−0.406594
$392$	−30.1692	−1.52378
$393$	9.24572	0.466385
$394$	25.7085	1.29517
$395$	−7.40682	−0.372677
$396$	82.9225	4.16701
$397$	−37.3786	−1.87598	−0.937989	−	0.346665i	$-0.887314\pi$
$397$	−37.3786	−1.87598	−0.937989	+	0.346665i	$0.887314\pi$
$398$	16.0867	0.806353
$399$	−86.6742	−4.33914
$400$	−23.3928	−1.16964
$401$	19.0729	0.952457	0.476229	−	0.879321i	$-0.342003\pi$
$401$	19.0729	0.952457	0.476229	+	0.879321i	$0.342003\pi$
$402$	76.2977	3.80538
$403$	−28.5020	−1.41979
$404$	21.2378	1.05662
$405$	−2.84911	−0.141573
$406$	13.6032	0.675115
$407$	18.4176	0.912926
$408$	125.848	6.23042
$409$	22.0828	1.09193	0.545963	−	0.837809i	$-0.316164\pi$
$409$	22.0828	1.09193	0.545963	+	0.837809i	$0.316164\pi$
$410$	7.74892	0.382692
$411$	−50.0671	−2.46963
$412$	−40.2433	−1.98264
$413$	17.4867	0.860464
$414$	14.0078	0.688446
$415$	−1.22970	−0.0603637
$416$	−9.14956	−0.448594
$417$	24.1621	1.18322
$418$	72.6539	3.55362
$419$	18.1174	0.885095	0.442547	−	0.896745i	$-0.354075\pi$
$419$	18.1174	0.885095	0.442547	+	0.896745i	$0.354075\pi$
$420$	−20.7070	−1.01040
$421$	14.1901	0.691582	0.345791	−	0.938312i	$-0.387611\pi$
$421$	14.1901	0.691582	0.345791	+	0.938312i	$0.387611\pi$
$422$	−13.3092	−0.647881
$423$	49.0757	2.38614
$424$	−27.3857	−1.32997
$425$	−38.3699	−1.86121
$426$	57.0793	2.76550
$427$	−47.5822	−2.30267
$428$	−1.05146	−0.0508245
$429$	−63.1559	−3.04920
$430$	7.31835	0.352922
$431$	18.1177	0.872700	0.436350	−	0.899777i	$-0.356271\pi$
$431$	18.1177	0.872700	0.436350	+	0.899777i	$0.356271\pi$
$432$	−38.2031	−1.83805
$433$	−20.8224	−1.00066	−0.500329	−	0.865835i	$-0.666788\pi$
$433$	−20.8224	−1.00066	−0.500329	+	0.865835i	$0.666788\pi$
$434$	−41.4549	−1.98990
$435$	2.16276	0.103696
$436$	10.4583	0.500864
$437$	8.27975	0.396074
$438$	81.4304	3.89089
$439$	−12.6756	−0.604974	−0.302487	−	0.953153i	$-0.597817\pi$
$439$	−12.6756	−0.604974	−0.302487	+	0.953153i	$0.597817\pi$
$440$	8.98574	0.428379
$441$	32.0276	1.52512
$442$	−120.936	−5.75232
$443$	−22.6592	−1.07657	−0.538286	−	0.842762i	$-0.680928\pi$
$443$	−22.6592	−1.07657	−0.538286	+	0.842762i	$0.680928\pi$
$444$	−63.4631	−3.01182
$445$	−3.39561	−0.160967
$446$	−10.2098	−0.483448
$447$	52.3935	2.47813
$448$	21.5852	1.01980
$449$	−4.92667	−0.232504	−0.116252	−	0.993220i	$-0.537088\pi$
$449$	−4.92667	−0.232504	−0.116252	+	0.993220i	$0.537088\pi$
$450$	66.8515	3.15141
$451$	23.1899	1.09197
$452$	−12.5452	−0.590078
$453$	−20.2787	−0.952778
$454$	−44.7256	−2.09908
$455$	10.3013	0.482932
$456$	−129.603	−6.06922
$457$	−1.68211	−0.0786858	−0.0393429	−	0.999226i	$-0.512526\pi$
$457$	−1.68211	−0.0786858	−0.0393429	+	0.999226i	$0.512526\pi$
$458$	−7.71656	−0.360571
$459$	−62.6623	−2.92483
$460$	1.97808	0.0922286
$461$	42.0420	1.95809	0.979046	−	0.203640i	$-0.0652771\pi$
$461$	42.0420	1.95809	0.979046	+	0.203640i	$0.0652771\pi$
$462$	−91.8575	−4.27360
$463$	2.76598	0.128546	0.0642730	−	0.997932i	$-0.479527\pi$
$463$	2.76598	0.128546	0.0642730	+	0.997932i	$0.479527\pi$
$464$	7.55610	0.350783
$465$	−6.59088	−0.305645
$466$	61.1046	2.83061
$467$	9.00774	0.416828	0.208414	−	0.978041i	$-0.433170\pi$
$467$	9.00774	0.416828	0.208414	+	0.978041i	$0.433170\pi$
$468$	142.146	6.57071
$469$	−37.2431	−1.71973
$470$	10.2726	0.473840
$471$	−29.7033	−1.36865
$472$	26.1477	1.20354
$473$	21.9014	1.00703
$474$	113.219	5.20030
$475$	39.5147	1.81306
$476$	−118.663	−5.43890
$477$	29.0726	1.33115
$478$	−12.9842	−0.593885
$479$	−9.50414	−0.434255	−0.217128	−	0.976143i	$-0.569669\pi$
$479$	−9.50414	−0.434255	−0.217128	+	0.976143i	$0.569669\pi$
$480$	−2.11577	−0.0965710
$481$	31.5715	1.43954
$482$	62.6755	2.85479
$483$	−10.4682	−0.476320
$484$	6.33147	0.287794
$485$	2.79636	0.126976
$486$	−14.4187	−0.654046
$487$	11.6581	0.528277	0.264138	−	0.964485i	$-0.414912\pi$
$487$	11.6581	0.528277	0.264138	+	0.964485i	$0.414912\pi$
$488$	−71.1492	−3.22078
$489$	−61.8084	−2.79507
$490$	6.70407	0.302859
$491$	−24.7657	−1.11766	−0.558831	−	0.829282i	$-0.688750\pi$
$491$	−24.7657	−1.11766	−0.558831	+	0.829282i	$0.688750\pi$
$492$	−79.9074	−3.60250
$493$	12.3938	0.558190
$494$	124.544	5.60349
$495$	−9.53925	−0.428757
$496$	−23.0268	−1.03393
$497$	−27.8621	−1.24978
$498$	18.7969	0.842308
$499$	−11.5640	−0.517676	−0.258838	−	0.965921i	$-0.583340\pi$
$499$	−11.5640	−0.517676	−0.258838	+	0.965921i	$0.583340\pi$
$500$	19.3307	0.864496
$501$	37.4652	1.67382
$502$	−11.3821	−0.508009
$503$	−27.6288	−1.23191	−0.615953	−	0.787783i	$-0.711229\pi$
$503$	−27.6288	−1.23191	−0.615953	+	0.787783i	$0.711229\pi$
$504$	107.029	4.76747
$505$	−2.44316	−0.108719
$506$	8.77489	0.390092
$507$	−70.0281	−3.11006
$508$	61.7296	2.73881
$509$	−32.7530	−1.45175	−0.725875	−	0.687827i	$-0.758565\pi$
$509$	−32.7530	−1.45175	−0.725875	+	0.687827i	$0.758565\pi$
$510$	−27.9655	−1.23833
$511$	−39.7486	−1.75837
$512$	44.7829	1.97914
$513$	64.5319	2.84915
$514$	−38.2342	−1.68644
$515$	4.62951	0.204001
$516$	−75.4674	−3.32227
$517$	30.7424	1.35205
$518$	45.9194	2.01758
$519$	34.6837	1.52245
$520$	15.4034	0.675484
$521$	−2.58479	−0.113242	−0.0566208	−	0.998396i	$-0.518033\pi$
$521$	−2.58479	−0.113242	−0.0566208	+	0.998396i	$0.518033\pi$
$522$	−21.5937	−0.945129
$523$	−8.52419	−0.372737	−0.186368	−	0.982480i	$-0.559672\pi$
$523$	−8.52419	−0.372737	−0.186368	+	0.982480i	$0.559672\pi$
$524$	−13.0357	−0.569466
$525$	−49.9590	−2.18039
$526$	−31.7836	−1.38583
$527$	−37.7695	−1.64526
$528$	−51.0237	−2.22052
$529$	1.00000	0.0434783
$530$	6.08553	0.264339
$531$	−27.7583	−1.20461
$532$	122.203	5.29818
$533$	39.7522	1.72186
$534$	51.9043	2.24612
$535$	0.120959	0.00522949
$536$	−55.6893	−2.40541
$537$	68.1499	2.94088
$538$	−1.35192	−0.0582855
$539$	20.0630	0.864175
$540$	15.4171	0.663445
$541$	−6.05750	−0.260432	−0.130216	−	0.991486i	$-0.541567\pi$
$541$	−6.05750	−0.260432	−0.130216	+	0.991486i	$0.541567\pi$
$542$	−59.6030	−2.56017
$543$	−16.7386	−0.718324
$544$	−12.1245	−0.519835
$545$	−1.20311	−0.0515355
$546$	−157.463	−6.73878
$547$	34.6363	1.48094	0.740471	−	0.672088i	$-0.234602\pi$
$547$	34.6363	1.48094	0.740471	+	0.672088i	$0.234602\pi$
$548$	70.5904	3.01547
$549$	75.5319	3.22362
$550$	41.8777	1.78567
$551$	−12.7636	−0.543748
$552$	−15.6530	−0.666236
$553$	−55.2653	−2.35012
$554$	35.5010	1.50829
$555$	7.30067	0.309896
$556$	−34.0665	−1.44474
$557$	−13.3741	−0.566679	−0.283339	−	0.959020i	$-0.591442\pi$
$557$	−13.3741	−0.566679	−0.283339	+	0.959020i	$0.591442\pi$
$558$	65.8054	2.78577
$559$	37.5434	1.58792
$560$	8.32241	0.351686
$561$	−83.6911	−3.53344
$562$	−12.0815	−0.509627
$563$	−1.93510	−0.0815548	−0.0407774	−	0.999168i	$-0.512983\pi$
$563$	−1.93510	−0.0815548	−0.0407774	+	0.999168i	$0.512983\pi$
$564$	−105.932	−4.46054
$565$	1.44318	0.0607151
$566$	−47.4454	−1.99428
$567$	−21.2584	−0.892768
$568$	−41.6619	−1.74809
$569$	−6.38617	−0.267722	−0.133861	−	0.991000i	$-0.542738\pi$
$569$	−6.38617	−0.267722	−0.133861	+	0.991000i	$0.542738\pi$
$570$	28.7998	1.20629
$571$	5.00175	0.209317	0.104658	−	0.994508i	$-0.466625\pi$
$571$	5.00175	0.209317	0.104658	+	0.994508i	$0.466625\pi$
$572$	89.0445	3.72314
$573$	52.2253	2.18174
$574$	57.8178	2.41327
$575$	4.77244	0.199025
$576$	−34.2643	−1.42768
$577$	3.74541	0.155923	0.0779617	−	0.996956i	$-0.475159\pi$
$577$	3.74541	0.155923	0.0779617	+	0.996956i	$0.475159\pi$
$578$	−118.111	−4.91276
$579$	−35.8357	−1.48928
$580$	−3.04930	−0.126615
$581$	−9.17531	−0.380656
$582$	−42.7444	−1.77181
$583$	18.2119	0.754261
$584$	−59.4356	−2.45946
$585$	−16.3522	−0.676082
$586$	15.1613	0.626306
$587$	14.9459	0.616885	0.308442	−	0.951243i	$-0.400192\pi$
$587$	14.9459	0.616885	0.308442	+	0.951243i	$0.400192\pi$
$588$	−69.1329	−2.85099
$589$	38.8963	1.60270
$590$	−5.81042	−0.239211
$591$	30.4975	1.25450
$592$	25.5066	1.04832
$593$	−0.593906	−0.0243888	−0.0121944	−	0.999926i	$-0.503882\pi$
$593$	−0.593906	−0.0243888	−0.0121944	+	0.999926i	$0.503882\pi$
$594$	68.3910	2.80612
$595$	13.6508	0.559627
$596$	−73.8704	−3.02585
$597$	19.0833	0.781029
$598$	15.0420	0.615112
$599$	40.3924	1.65039	0.825194	−	0.564850i	$-0.191066\pi$
$599$	40.3924	1.65039	0.825194	+	0.564850i	$0.191066\pi$
$600$	−74.7031	−3.04974
$601$	6.96429	0.284079	0.142040	−	0.989861i	$-0.454634\pi$
$601$	6.96429	0.284079	0.142040	+	0.989861i	$0.454634\pi$
$602$	54.6052	2.22554
$603$	59.1197	2.40754
$604$	28.5913	1.16336
$605$	−0.728360	−0.0296120
$606$	37.3454	1.51705
$607$	9.38815	0.381053	0.190527	−	0.981682i	$-0.438980\pi$
$607$	9.38815	0.381053	0.190527	+	0.981682i	$0.438980\pi$
$608$	12.4863	0.506385
$609$	16.1372	0.653913
$610$	15.8105	0.640147
$611$	52.6988	2.13197
$612$	188.365	7.61421
$613$	14.9497	0.603814	0.301907	−	0.953337i	$-0.402377\pi$
$613$	14.9497	0.603814	0.301907	+	0.953337i	$0.402377\pi$
$614$	−22.5769	−0.911128
$615$	9.19240	0.370673
$616$	67.0463	2.70137
$617$	25.6607	1.03306	0.516531	−	0.856268i	$-0.327223\pi$
$617$	25.6607	1.03306	0.516531	+	0.856268i	$0.327223\pi$
$618$	−70.7654	−2.84660
$619$	14.4287	0.579937	0.289969	−	0.957036i	$-0.406355\pi$
$619$	14.4287	0.579937	0.289969	+	0.957036i	$0.406355\pi$
$620$	9.29257	0.373199
$621$	7.79394	0.312760
$622$	−34.6274	−1.38843
$623$	−25.3360	−1.01507
$624$	−87.4650	−3.50140
$625$	21.6385	0.865538
$626$	85.7181	3.42598
$627$	86.1881	3.44202
$628$	41.8791	1.67116
$629$	41.8370	1.66815
$630$	−23.7836	−0.947561
$631$	−33.4834	−1.33295	−0.666476	−	0.745526i	$-0.732198\pi$
$631$	−33.4834	−1.33295	−0.666476	+	0.745526i	$0.732198\pi$
$632$	−82.6376	−3.28715
$633$	−15.7884	−0.627534
$634$	48.8863	1.94152
$635$	−7.10126	−0.281805
$636$	−62.7545	−2.48838
$637$	34.3921	1.36267
$638$	−13.5269	−0.535535
$639$	44.2282	1.74964
$640$	−8.61101	−0.340380
$641$	22.6533	0.894751	0.447375	−	0.894346i	$-0.352359\pi$
$641$	22.6533	0.894751	0.447375	+	0.894346i	$0.352359\pi$
$642$	−1.84894	−0.0729718
$643$	−16.9823	−0.669716	−0.334858	−	0.942269i	$-0.608688\pi$
$643$	−16.9823	−0.669716	−0.334858	+	0.942269i	$0.608688\pi$
$644$	14.7593	0.581597
$645$	8.68163	0.341839
$646$	165.039	6.49338
$647$	−12.1582	−0.477988	−0.238994	−	0.971021i	$-0.576818\pi$
$647$	−12.1582	−0.477988	−0.238994	+	0.971021i	$0.576818\pi$
$648$	−31.7874	−1.24873
$649$	−17.3886	−0.682563
$650$	71.7870	2.81572
$651$	−49.1772	−1.92741
$652$	87.1446	3.41285
$653$	−19.1090	−0.747794	−0.373897	−	0.927470i	$-0.621979\pi$
$653$	−19.1090	−0.747794	−0.373897	+	0.927470i	$0.621979\pi$
$654$	18.3904	0.719120
$655$	1.49960	0.0585942
$656$	32.1158	1.25391
$657$	63.0968	2.46164
$658$	76.6481	2.98805
$659$	37.0601	1.44366	0.721829	−	0.692072i	$-0.243302\pi$
$659$	37.0601	1.44366	0.721829	+	0.692072i	$0.243302\pi$
$660$	20.5909	0.801498
$661$	−0.674417	−0.0262318	−0.0131159	−	0.999914i	$-0.504175\pi$
$661$	−0.674417	−0.0262318	−0.0131159	+	0.999914i	$0.504175\pi$
$662$	52.7688	2.05092
$663$	−143.464	−5.57167
$664$	−13.7197	−0.532429
$665$	−14.0580	−0.545147
$666$	−72.8923	−2.82452
$667$	−1.54154	−0.0596889
$668$	−52.8227	−2.04377
$669$	−12.1117	−0.468265
$670$	12.3750	0.478089
$671$	47.3154	1.82659
$672$	−15.7866	−0.608981
$673$	−10.4603	−0.403216	−0.201608	−	0.979466i	$-0.564617\pi$
$673$	−10.4603	−0.403216	−0.201608	+	0.979466i	$0.564617\pi$
$674$	47.9921	1.84859
$675$	37.1961	1.43168
$676$	98.7336	3.79745
$677$	−45.9891	−1.76750	−0.883752	−	0.467956i	$-0.844991\pi$
$677$	−45.9891	−1.76750	−0.883752	+	0.467956i	$0.844991\pi$
$678$	−22.0600	−0.847211
$679$	20.8648	0.800717
$680$	20.4118	0.782758
$681$	−53.0571	−2.03315
$682$	41.2224	1.57849
$683$	13.7063	0.524458	0.262229	−	0.965006i	$-0.415542\pi$
$683$	13.7063	0.524458	0.262229	+	0.965006i	$0.415542\pi$
$684$	−193.985	−7.41720
$685$	−8.12059	−0.310272
$686$	−11.7489	−0.448576
$687$	−9.15402	−0.349248
$688$	30.3313	1.15637
$689$	31.2190	1.18935
$690$	3.47834	0.132418
$691$	−19.4544	−0.740081	−0.370040	−	0.929016i	$-0.620656\pi$
$691$	−19.4544	−0.740081	−0.370040	+	0.929016i	$0.620656\pi$
$692$	−48.9011	−1.85894
$693$	−71.1763	−2.70376
$694$	−69.4901	−2.63781
$695$	3.91894	0.148654
$696$	24.1298	0.914639
$697$	52.6777	1.99531
$698$	−2.47925	−0.0938411
$699$	72.4873	2.74172
$700$	70.4379	2.66230
$701$	−34.5170	−1.30369	−0.651844	−	0.758353i	$-0.726004\pi$
$701$	−34.5170	−1.30369	−0.651844	+	0.758353i	$0.726004\pi$
$702$	117.236	4.42480
$703$	−43.0852	−1.62499
$704$	−21.4641	−0.808959
$705$	12.1862	0.458959
$706$	49.1715	1.85059
$707$	−18.2294	−0.685587
$708$	59.9175	2.25184
$709$	−0.939591	−0.0352871	−0.0176435	−	0.999844i	$-0.505616\pi$
$709$	−0.939591	−0.0352871	−0.0176435	+	0.999844i	$0.505616\pi$
$710$	9.25792	0.347443
$711$	87.7280	3.29006
$712$	−37.8847	−1.41979
$713$	4.69777	0.175933
$714$	−208.662	−7.80897
$715$	−10.2435	−0.383086
$716$	−96.0855	−3.59088
$717$	−15.4030	−0.575234
$718$	−13.5164	−0.504429
$719$	−14.7840	−0.551348	−0.275674	−	0.961251i	$-0.588901\pi$
$719$	−14.7840	−0.551348	−0.275674	+	0.961251i	$0.588901\pi$
$720$	−13.2110	−0.492344
$721$	34.5427	1.28644
$722$	−122.858	−4.57228
$723$	74.3508	2.76514
$724$	23.6000	0.877089
$725$	−7.35694	−0.273230
$726$	11.1335	0.413203
$727$	0.806509	0.0299118	0.0149559	−	0.999888i	$-0.495239\pi$
$727$	0.806509	0.0299118	0.0149559	+	0.999888i	$0.495239\pi$
$728$	114.931	4.25963
$729$	−35.0226	−1.29713
$730$	13.2075	0.488832
$731$	49.7507	1.84010
$732$	−163.039	−6.02608
$733$	−23.3243	−0.861503	−0.430751	−	0.902471i	$-0.641751\pi$
$733$	−23.3243	−0.861503	−0.430751	+	0.902471i	$0.641751\pi$
$734$	73.4505	2.71111
$735$	7.95292	0.293348
$736$	1.50805	0.0555875
$737$	37.0343	1.36417
$738$	−91.7799	−3.37846
$739$	4.76720	0.175364	0.0876822	−	0.996148i	$-0.472054\pi$
$739$	4.76720	0.175364	0.0876822	+	0.996148i	$0.472054\pi$
$740$	−10.2933	−0.378390
$741$	147.744	5.42751
$742$	45.4067	1.66693
$743$	38.6657	1.41851	0.709253	−	0.704954i	$-0.249032\pi$
$743$	38.6657	1.41851	0.709253	+	0.704954i	$0.249032\pi$
$744$	−73.5342	−2.69589
$745$	8.49791	0.311339
$746$	−36.9934	−1.35443
$747$	14.5649	0.532900
$748$	117.997	4.31441
$749$	0.902521	0.0329774
$750$	33.9919	1.24121
$751$	−37.1402	−1.35527	−0.677633	−	0.735400i	$-0.736994\pi$
$751$	−37.1402	−1.35527	−0.677633	+	0.735400i	$0.736994\pi$
$752$	42.5754	1.55256
$753$	−13.5024	−0.492055
$754$	−23.1879	−0.844453
$755$	−3.28909	−0.119702
$756$	115.033	4.18371
$757$	−18.4415	−0.670269	−0.335134	−	0.942170i	$-0.608782\pi$
$757$	−18.4415	−0.670269	−0.335134	+	0.942170i	$0.608782\pi$
$758$	75.2385	2.73278
$759$	10.4095	0.377841
$760$	−21.0208	−0.762506
$761$	−28.7645	−1.04271	−0.521356	−	0.853339i	$-0.674574\pi$
$761$	−28.7645	−1.04271	−0.521356	+	0.853339i	$0.674574\pi$
$762$	108.548	3.93227
$763$	−8.97688	−0.324985
$764$	−73.6332	−2.66396
$765$	−21.6692	−0.783451
$766$	6.39378	0.231017
$767$	−29.8077	−1.07629
$768$	95.9533	3.46242
$769$	−18.4440	−0.665108	−0.332554	−	0.943084i	$-0.607910\pi$
$769$	−18.4440	−0.665108	−0.332554	+	0.943084i	$0.607910\pi$
$770$	−14.8987	−0.536913
$771$	−45.3565	−1.63348
$772$	50.5253	1.81844
$773$	−46.3711	−1.66785	−0.833926	−	0.551877i	$-0.813912\pi$
$773$	−46.3711	−1.66785	−0.833926	+	0.551877i	$0.813912\pi$
$774$	−86.6802	−3.11566
$775$	22.4198	0.805344
$776$	31.1989	1.11997
$777$	54.4733	1.95422
$778$	55.5186	1.99044
$779$	−54.2493	−1.94368
$780$	35.2970	1.26383
$781$	27.7058	0.991392
$782$	19.9329	0.712798
$783$	−12.0147	−0.429371
$784$	27.7854	0.992335
$785$	−4.81769	−0.171951
$786$	−22.9225	−0.817617
$787$	53.8307	1.91886	0.959429	−	0.281949i	$-0.0909809\pi$
$787$	53.8307	1.91886	0.959429	+	0.281949i	$0.0909809\pi$
$788$	−42.9989	−1.53177
$789$	−37.7043	−1.34231
$790$	18.3634	0.653339
$791$	10.7682	0.382872
$792$	−106.429	−3.78179
$793$	81.1083	2.88024
$794$	92.6709	3.28877
$795$	7.21916	0.256037
$796$	−26.9059	−0.953654
$797$	14.8275	0.525218	0.262609	−	0.964902i	$-0.415417\pi$
$797$	14.8275	0.525218	0.262609	+	0.964902i	$0.415417\pi$
$798$	214.887	7.60692
$799$	69.8339	2.47055
$800$	7.19709	0.254455
$801$	40.2183	1.42104
$802$	−47.2866	−1.66975
$803$	39.5256	1.39483
$804$	−127.612	−4.50053
$805$	−1.69788	−0.0598425
$806$	70.6637	2.48902
$807$	−1.60376	−0.0564551
$808$	−27.2582	−0.958942
$809$	−38.2990	−1.34652	−0.673261	−	0.739405i	$-0.735107\pi$
$809$	−38.2990	−1.34652	−0.673261	+	0.739405i	$0.735107\pi$
$810$	7.06366	0.248192
$811$	24.3856	0.856295	0.428148	−	0.903709i	$-0.359166\pi$
$811$	24.3856	0.856295	0.428148	+	0.903709i	$0.359166\pi$
$812$	−22.7521	−0.798442
$813$	−70.7059	−2.47977
$814$	−45.6618	−1.60045
$815$	−10.0250	−0.351159
$816$	−115.904	−4.05746
$817$	−51.2350	−1.79249
$818$	−54.7489	−1.91425
$819$	−122.011	−4.26340
$820$	−12.9605	−0.452600
$821$	9.75859	0.340577	0.170289	−	0.985394i	$-0.445530\pi$
$821$	9.75859	0.340577	0.170289	+	0.985394i	$0.445530\pi$
$822$	124.129	4.32950
$823$	12.8789	0.448931	0.224466	−	0.974482i	$-0.427936\pi$
$823$	12.8789	0.448931	0.224466	+	0.974482i	$0.427936\pi$
$824$	51.6513	1.79936
$825$	49.6788	1.72959
$826$	−43.3539	−1.50848
$827$	−50.6033	−1.75965	−0.879824	−	0.475300i	$-0.842340\pi$
$827$	−50.6033	−1.75965	−0.879824	+	0.475300i	$0.842340\pi$
$828$	−23.4289	−0.814209
$829$	−27.4451	−0.953208	−0.476604	−	0.879118i	$-0.658133\pi$
$829$	−27.4451	−0.953208	−0.476604	+	0.879118i	$0.658133\pi$
$830$	3.04874	0.105823
$831$	42.1142	1.46093
$832$	−36.7939	−1.27560
$833$	45.5747	1.57907
$834$	−59.9039	−2.07430
$835$	6.07662	0.210290
$836$	−121.518	−4.20278
$837$	36.6141	1.26557
$838$	−44.9177	−1.55166
$839$	23.6843	0.817672	0.408836	−	0.912608i	$-0.365935\pi$
$839$	23.6843	0.817672	0.408836	+	0.912608i	$0.365935\pi$
$840$	26.5770	0.916992
$841$	−26.6236	−0.918057
$842$	−35.1807	−1.21241
$843$	−14.3320	−0.493622
$844$	22.2603	0.766233
$845$	−11.3581	−0.390732
$846$	−121.671	−4.18314
$847$	−5.43459	−0.186735
$848$	25.2218	0.866121
$849$	−56.2836	−1.93165
$850$	95.1286	3.26288
$851$	−5.20369	−0.178380
$852$	−95.4683	−3.27069
$853$	6.35888	0.217724	0.108862	−	0.994057i	$-0.465279\pi$
$853$	6.35888	0.217724	0.108862	+	0.994057i	$0.465279\pi$
$854$	117.968	4.03679
$855$	22.3157	0.763180
$856$	1.34953	0.0461260
$857$	53.1464	1.81545	0.907723	−	0.419570i	$-0.137819\pi$
$857$	53.1464	1.81545	0.907723	+	0.419570i	$0.137819\pi$
$858$	156.579	5.34553
$859$	38.3119	1.30719	0.653593	−	0.756846i	$-0.273261\pi$
$859$	38.3119	1.30719	0.653593	+	0.756846i	$0.273261\pi$
$860$	−12.2404	−0.417393
$861$	68.5882	2.33748
$862$	−44.9184	−1.52993
$863$	−34.5754	−1.17696	−0.588481	−	0.808511i	$-0.700274\pi$
$863$	−34.5754	−1.17696	−0.588481	+	0.808511i	$0.700274\pi$
$864$	11.7537	0.399867
$865$	5.62549	0.191272
$866$	51.6239	1.75425
$867$	−140.113	−4.75847
$868$	69.3357	2.35341
$869$	54.9553	1.86423
$870$	−5.36202	−0.181790
$871$	63.4843	2.15108
$872$	−13.4230	−0.454562
$873$	−33.1207	−1.12097
$874$	−20.5276	−0.694356
$875$	−16.5925	−0.560927
$876$	−136.197	−4.60167
$877$	28.4237	0.959800	0.479900	−	0.877323i	$-0.340673\pi$
$877$	28.4237	0.959800	0.479900	+	0.877323i	$0.340673\pi$
$878$	31.4260	1.06058
$879$	17.9855	0.606637
$880$	−8.27573	−0.278975
$881$	−28.3845	−0.956298	−0.478149	−	0.878279i	$-0.658692\pi$
$881$	−28.3845	−0.956298	−0.478149	+	0.878279i	$0.658692\pi$
$882$	−79.4045	−2.67369
$883$	37.1335	1.24964	0.624821	−	0.780768i	$-0.285172\pi$
$883$	37.1335	1.24964	0.624821	+	0.780768i	$0.285172\pi$
$884$	202.272	6.80313
$885$	−6.89280	−0.231699
$886$	56.1779	1.88733
$887$	13.1966	0.443098	0.221549	−	0.975149i	$-0.428889\pi$
$887$	13.1966	0.443098	0.221549	+	0.975149i	$0.428889\pi$
$888$	81.4534	2.73340
$889$	−52.9854	−1.77707
$890$	8.41856	0.282191
$891$	21.1391	0.708188
$892$	17.0765	0.571762
$893$	−71.9174	−2.40662
$894$	−129.897	−4.34439
$895$	11.0535	0.369478
$896$	−64.2503	−2.14645
$897$	17.8440	0.595795
$898$	12.2144	0.407601
$899$	−7.24182	−0.241528
$900$	−111.813	−3.72710
$901$	41.3699	1.37823
$902$	−57.4935	−1.91433
$903$	64.7772	2.15565
$904$	16.1015	0.535529
$905$	−2.71491	−0.0902465
$906$	50.2761	1.67031
$907$	−59.1850	−1.96520	−0.982602	−	0.185722i	$-0.940538\pi$
$907$	−59.1850	−1.96520	−0.982602	+	0.185722i	$0.940538\pi$
$908$	74.8061	2.48253
$909$	28.9373	0.959790
$910$	−25.5395	−0.846626
$911$	−31.2630	−1.03579	−0.517895	−	0.855444i	$-0.673284\pi$
$911$	−31.2630	−1.03579	−0.517895	+	0.855444i	$0.673284\pi$
$912$	119.362	3.95248
$913$	9.12385	0.301955
$914$	4.17038	0.137944
$915$	18.7557	0.620043
$916$	12.9064	0.426439
$917$	11.1891	0.369498
$918$	155.356	5.12750
$919$	7.23410	0.238631	0.119315	−	0.992856i	$-0.461930\pi$
$919$	7.23410	0.238631	0.119315	+	0.992856i	$0.461930\pi$
$920$	−2.53882	−0.0837026
$921$	−26.7825	−0.882514
$922$	−104.233	−3.43272
$923$	47.4934	1.56327
$924$	153.637	5.05428
$925$	−24.8343	−0.816547
$926$	−6.85756	−0.225353
$927$	−54.8329	−1.80095
$928$	−2.32473	−0.0763129
$929$	34.6930	1.13824	0.569120	−	0.822254i	$-0.307284\pi$
$929$	34.6930	1.13824	0.569120	+	0.822254i	$0.307284\pi$
$930$	16.3404	0.535824
$931$	−46.9345	−1.53822
$932$	−102.201	−3.34770
$933$	−41.0779	−1.34483
$934$	−22.3324	−0.730740
$935$	−13.5742	−0.443924
$936$	−182.441	−5.96328
$937$	−16.0430	−0.524104	−0.262052	−	0.965054i	$-0.584399\pi$
$937$	−16.0430	−0.524104	−0.262052	+	0.965054i	$0.584399\pi$
$938$	92.3351	3.01485
$939$	101.686	3.31839
$940$	−17.1815	−0.560399
$941$	12.8208	0.417947	0.208974	−	0.977921i	$-0.432988\pi$
$941$	12.8208	0.417947	0.208974	+	0.977921i	$0.432988\pi$
$942$	73.6419	2.39938
$943$	−6.55205	−0.213364
$944$	−24.0816	−0.783789
$945$	−13.2332	−0.430476
$946$	−54.2990	−1.76541
$947$	47.4348	1.54143	0.770713	−	0.637183i	$-0.219900\pi$
$947$	47.4348	1.54143	0.770713	+	0.637183i	$0.219900\pi$
$948$	−189.364	−6.15027
$949$	67.7550	2.19942
$950$	−97.9668	−3.17846
$951$	57.9930	1.88055
$952$	152.301	4.93611
$953$	−28.7601	−0.931631	−0.465816	−	0.884882i	$-0.654239\pi$
$953$	−28.7601	−0.931631	−0.465816	+	0.884882i	$0.654239\pi$
$954$	−72.0784	−2.33362
$955$	8.47063	0.274103
$956$	21.7169	0.702373
$957$	−16.0467	−0.518716
$958$	23.5632	0.761291
$959$	−60.5910	−1.95659
$960$	−8.50831	−0.274605
$961$	−8.93099	−0.288096
$962$	−78.2737	−2.52365
$963$	−1.43266	−0.0461668
$964$	−104.828	−3.37629
$965$	−5.81233	−0.187106
$966$	25.9533	0.835035
$967$	5.64236	0.181446	0.0907230	−	0.995876i	$-0.471082\pi$
$967$	5.64236	0.181446	0.0907230	+	0.995876i	$0.471082\pi$
$968$	−8.12629	−0.261189
$969$	195.783	6.28946
$970$	−6.93288	−0.222601
$971$	42.9631	1.37875	0.689375	−	0.724404i	$-0.257885\pi$
$971$	42.9631	1.37875	0.689375	+	0.724404i	$0.257885\pi$
$972$	24.1161	0.773524
$973$	29.2408	0.937419
$974$	−28.9032	−0.926119
$975$	85.1596	2.72729
$976$	65.5274	2.09748
$977$	47.8280	1.53015	0.765076	−	0.643940i	$-0.222701\pi$
$977$	47.8280	1.53015	0.765076	+	0.643940i	$0.222701\pi$
$978$	153.239	4.90003
$979$	25.1939	0.805200
$980$	−11.2129	−0.358184
$981$	14.2499	0.454964
$982$	61.4004	1.95937
$983$	45.8601	1.46271	0.731355	−	0.681997i	$-0.238888\pi$
$983$	45.8601	1.46271	0.731355	+	0.681997i	$0.238888\pi$
$984$	102.559	3.26947
$985$	4.94651	0.157609
$986$	−30.7274	−0.978561
$987$	90.9263	2.89421
$988$	−208.307	−6.62711
$989$	−6.18799	−0.196767
$990$	23.6502	0.751653
$991$	−14.4070	−0.457652	−0.228826	−	0.973467i	$-0.573489\pi$
$991$	−14.4070	−0.457652	−0.228826	+	0.973467i	$0.573489\pi$
$992$	7.08447	0.224932
$993$	62.5986	1.98651
$994$	69.0771	2.19099
$995$	3.09520	0.0981246
$996$	−31.4388	−0.996177
$997$	34.2781	1.08560	0.542800	−	0.839862i	$-0.317364\pi$
$997$	34.2781	1.08560	0.542800	+	0.839862i	$0.317364\pi$
$998$	28.6701	0.907536
$999$	−40.5572	−1.28317

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8027.2.a.e.1.14	✓	169

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8027.2.a.e.1.14	✓	169	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:	\( N \)	\(=\)	\( 8027 = 23 \cdot 349 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8027.a (trivial)

\(f(q)\)	\(=\)	\(q-2.47925 q^{2} -2.94109 q^{3} +4.14669 q^{4} -0.477027 q^{5} +7.29170 q^{6} -3.55930 q^{7} -5.32218 q^{8} +5.65002 q^{9} +O(q^{10})\)	\(q-2.47925 q^{2} -2.94109 q^{3} +4.14669 q^{4} -0.477027 q^{5} +7.29170 q^{6} -3.55930 q^{7} -5.32218 q^{8} +5.65002 q^{9} +1.18267 q^{10} +3.53933 q^{11} -12.1958 q^{12} +6.06714 q^{13} +8.82439 q^{14} +1.40298 q^{15} +4.90164 q^{16} +8.03988 q^{17} -14.0078 q^{18} -8.27975 q^{19} -1.97808 q^{20} +10.4682 q^{21} -8.77489 q^{22} -1.00000 q^{23} +15.6530 q^{24} -4.77244 q^{25} -15.0420 q^{26} -7.79394 q^{27} -14.7593 q^{28} +1.54154 q^{29} -3.47834 q^{30} -4.69777 q^{31} -1.50805 q^{32} -10.4095 q^{33} -19.9329 q^{34} +1.69788 q^{35} +23.4289 q^{36} +5.20369 q^{37} +20.5276 q^{38} -17.8440 q^{39} +2.53882 q^{40} +6.55205 q^{41} -25.9533 q^{42} +6.18799 q^{43} +14.6765 q^{44} -2.69521 q^{45} +2.47925 q^{46} +8.68594 q^{47} -14.4162 q^{48} +5.66859 q^{49} +11.8321 q^{50} -23.6460 q^{51} +25.1585 q^{52} +5.14559 q^{53} +19.3231 q^{54} -1.68836 q^{55} +18.9432 q^{56} +24.3515 q^{57} -3.82188 q^{58} -4.91297 q^{59} +5.81772 q^{60} +13.3684 q^{61} +11.6469 q^{62} -20.1101 q^{63} -6.06445 q^{64} -2.89419 q^{65} +25.8078 q^{66} +10.4636 q^{67} +33.3389 q^{68} +2.94109 q^{69} -4.20947 q^{70} +7.82798 q^{71} -30.0704 q^{72} +11.1675 q^{73} -12.9013 q^{74} +14.0362 q^{75} -34.3335 q^{76} -12.5975 q^{77} +44.2398 q^{78} +15.5270 q^{79} -2.33822 q^{80} +5.97264 q^{81} -16.2442 q^{82} +2.57784 q^{83} +43.4084 q^{84} -3.83524 q^{85} -15.3416 q^{86} -4.53382 q^{87} -18.8370 q^{88} +7.11826 q^{89} +6.68211 q^{90} -21.5948 q^{91} -4.14669 q^{92} +13.8166 q^{93} -21.5346 q^{94} +3.94967 q^{95} +4.43531 q^{96} -5.86205 q^{97} -14.0538 q^{98} +19.9973 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 169 q + 6 q^{2} + 2 q^{3} + 186 q^{4} + 28 q^{5} + 5 q^{6} + 38 q^{7} + 18 q^{8} + 185 q^{9}+O(q^{10}) \) 169 * q + 6 * q^2 + 2 * q^3 + 186 * q^4 + 28 * q^5 + 5 * q^6 + 38 * q^7 + 18 * q^8 + 185 * q^9	\( 169 q + 6 q^{2} + 2 q^{3} + 186 q^{4} + 28 q^{5} + 5 q^{6} + 38 q^{7} + 18 q^{8} + 185 q^{9} + 28 q^{10} + 17 q^{11} + 10 q^{12} + 91 q^{13} + 20 q^{14} + 29 q^{15} + 200 q^{16} + 16 q^{17} + 31 q^{18} + 30 q^{19} + 45 q^{20} + 49 q^{21} + 76 q^{22} - 169 q^{23} + 3 q^{24} + 241 q^{25} - 15 q^{26} + 14 q^{27} + 118 q^{28} + 23 q^{29} + 52 q^{30} + 45 q^{31} + 42 q^{32} + 62 q^{33} + 65 q^{34} - 16 q^{35} + 199 q^{36} + 226 q^{37} + 49 q^{38} + 17 q^{39} + 95 q^{40} + 19 q^{41} + 32 q^{42} + 71 q^{43} + 46 q^{44} + 127 q^{45} - 6 q^{46} + 27 q^{47} + 5 q^{48} + 239 q^{49} + 24 q^{50} + 39 q^{51} + 154 q^{52} + 111 q^{53} + 22 q^{54} + 47 q^{55} + 39 q^{56} + 122 q^{57} + 146 q^{58} - 73 q^{59} + 109 q^{60} + 125 q^{61} + 14 q^{62} + 109 q^{63} + 260 q^{64} + 73 q^{65} + 26 q^{66} + 152 q^{67} + 40 q^{68} - 2 q^{69} + 76 q^{70} - 79 q^{71} + 126 q^{72} + 106 q^{73} + 23 q^{74} + 12 q^{75} + 122 q^{76} + 63 q^{77} + 101 q^{78} + 82 q^{79} + 134 q^{80} + 225 q^{81} + 125 q^{82} + 28 q^{83} + 73 q^{84} + 197 q^{85} + 97 q^{86} + 18 q^{87} + 183 q^{88} + 54 q^{89} + 52 q^{90} + 106 q^{91} - 186 q^{92} + 194 q^{93} + q^{94} + 18 q^{95} - 39 q^{96} + 239 q^{97} + 5 q^{98} + 85 q^{99}+O(q^{100}) \) 169 * q + 6 * q^2 + 2 * q^3 + 186 * q^4 + 28 * q^5 + 5 * q^6 + 38 * q^7 + 18 * q^8 + 185 * q^9 + 28 * q^10 + 17 * q^11 + 10 * q^12 + 91 * q^13 + 20 * q^14 + 29 * q^15 + 200 * q^16 + 16 * q^17 + 31 * q^18 + 30 * q^19 + 45 * q^20 + 49 * q^21 + 76 * q^22 - 169 * q^23 + 3 * q^24 + 241 * q^25 - 15 * q^26 + 14 * q^27 + 118 * q^28 + 23 * q^29 + 52 * q^30 + 45 * q^31 + 42 * q^32 + 62 * q^33 + 65 * q^34 - 16 * q^35 + 199 * q^36 + 226 * q^37 + 49 * q^38 + 17 * q^39 + 95 * q^40 + 19 * q^41 + 32 * q^42 + 71 * q^43 + 46 * q^44 + 127 * q^45 - 6 * q^46 + 27 * q^47 + 5 * q^48 + 239 * q^49 + 24 * q^50 + 39 * q^51 + 154 * q^52 + 111 * q^53 + 22 * q^54 + 47 * q^55 + 39 * q^56 + 122 * q^57 + 146 * q^58 - 73 * q^59 + 109 * q^60 + 125 * q^61 + 14 * q^62 + 109 * q^63 + 260 * q^64 + 73 * q^65 + 26 * q^66 + 152 * q^67 + 40 * q^68 - 2 * q^69 + 76 * q^70 - 79 * q^71 + 126 * q^72 + 106 * q^73 + 23 * q^74 + 12 * q^75 + 122 * q^76 + 63 * q^77 + 101 * q^78 + 82 * q^79 + 134 * q^80 + 225 * q^81 + 125 * q^82 + 28 * q^83 + 73 * q^84 + 197 * q^85 + 97 * q^86 + 18 * q^87 + 183 * q^88 + 54 * q^89 + 52 * q^90 + 106 * q^91 - 186 * q^92 + 194 * q^93 + q^94 + 18 * q^95 - 39 * q^96 + 239 * q^97 + 5 * q^98 + 85 * q^99

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