LMFDB - Embedded newform 547.4.a.a.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [547,4,Mod(1,547)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(547, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("547.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 547 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	547.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:	$32.2740447731$
Analytic rank:	$1$
Dimension:	$65$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	547.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.39733 q^{2} -7.45622 q^{3} +11.3366 q^{4} -12.8080 q^{5} +32.7875 q^{6} -33.9402 q^{7} -14.6719 q^{8} +28.5953 q^{9} +O(q^{10})$	\(q-4.39733 q^{2} -7.45622 q^{3} +11.3366 q^{4} -12.8080 q^{5} +32.7875 q^{6} -33.9402 q^{7} -14.6719 q^{8} +28.5953 q^{9} +56.3210 q^{10} -9.00407 q^{11} -84.5279 q^{12} -87.9841 q^{13} +149.246 q^{14} +95.4993 q^{15} -26.1750 q^{16} +60.2896 q^{17} -125.743 q^{18} +55.0633 q^{19} -145.199 q^{20} +253.066 q^{21} +39.5939 q^{22} -189.249 q^{23} +109.397 q^{24} +39.0448 q^{25} +386.896 q^{26} -11.8947 q^{27} -384.765 q^{28} +92.1574 q^{29} -419.942 q^{30} +30.3394 q^{31} +232.476 q^{32} +67.1364 q^{33} -265.113 q^{34} +434.706 q^{35} +324.172 q^{36} +40.9651 q^{37} -242.132 q^{38} +656.029 q^{39} +187.918 q^{40} +77.7511 q^{41} -1112.81 q^{42} +474.686 q^{43} -102.075 q^{44} -366.248 q^{45} +832.190 q^{46} +215.891 q^{47} +195.167 q^{48} +808.938 q^{49} -171.693 q^{50} -449.532 q^{51} -997.436 q^{52} -759.297 q^{53} +52.3051 q^{54} +115.324 q^{55} +497.969 q^{56} -410.564 q^{57} -405.247 q^{58} -31.2936 q^{59} +1082.63 q^{60} +671.515 q^{61} -133.412 q^{62} -970.530 q^{63} -812.874 q^{64} +1126.90 q^{65} -295.221 q^{66} +922.352 q^{67} +683.476 q^{68} +1411.08 q^{69} -1911.55 q^{70} -277.592 q^{71} -419.548 q^{72} -1175.82 q^{73} -180.137 q^{74} -291.127 q^{75} +624.228 q^{76} +305.600 q^{77} -2884.78 q^{78} +767.428 q^{79} +335.249 q^{80} -683.383 q^{81} -341.897 q^{82} -235.269 q^{83} +2868.89 q^{84} -772.188 q^{85} -2087.35 q^{86} -687.146 q^{87} +132.107 q^{88} -974.698 q^{89} +1610.52 q^{90} +2986.20 q^{91} -2145.43 q^{92} -226.217 q^{93} -949.344 q^{94} -705.250 q^{95} -1733.39 q^{96} +887.219 q^{97} -3557.17 q^{98} -257.474 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 65 q - 12 q^{2} - 35 q^{3} + 234 q^{4} - 151 q^{5} - 60 q^{6} - 74 q^{7} - 144 q^{8} + 468 q^{9}+O(q^{10}) $ 65 * q - 12 * q^2 - 35 * q^3 + 234 * q^4 - 151 * q^5 - 60 * q^6 - 74 * q^7 - 144 * q^8 + 468 * q^9	\( 65 q - 12 q^{2} - 35 q^{3} + 234 q^{4} - 151 q^{5} - 60 q^{6} - 74 q^{7} - 144 q^{8} + 468 q^{9} - 60 q^{10} - 191 q^{11} - 483 q^{12} - 333 q^{13} - 377 q^{14} - 166 q^{15} + 818 q^{16} - 858 q^{17} - 279 q^{18} - 185 q^{19} - 1188 q^{20} - 406 q^{21} - 356 q^{22} - 836 q^{23} - 505 q^{24} + 1156 q^{25} - 696 q^{26} - 1094 q^{27} - 1096 q^{28} - 1209 q^{29} - 1054 q^{30} - 286 q^{31} - 1484 q^{32} - 1296 q^{33} - 763 q^{34} - 1374 q^{35} + 296 q^{36} - 1705 q^{37} - 2535 q^{38} - 622 q^{39} - 888 q^{40} - 1348 q^{41} - 1716 q^{42} - 973 q^{43} - 2568 q^{44} - 4529 q^{45} - 322 q^{46} - 2498 q^{47} - 5358 q^{48} + 2081 q^{49} - 2002 q^{50} - 1108 q^{51} - 3290 q^{52} - 5947 q^{53} - 2783 q^{54} - 1344 q^{55} - 5111 q^{56} - 3134 q^{57} - 1676 q^{58} - 1625 q^{59} - 2902 q^{60} - 3103 q^{61} - 5242 q^{62} - 3106 q^{63} + 1722 q^{64} - 3160 q^{65} - 3672 q^{66} - 2395 q^{67} - 8447 q^{68} - 4944 q^{69} - 597 q^{70} - 2654 q^{71} - 3929 q^{72} - 2116 q^{73} - 3969 q^{74} - 3759 q^{75} - 1844 q^{76} - 9938 q^{77} - 3935 q^{78} - 1206 q^{79} - 11619 q^{80} + 1889 q^{81} - 7674 q^{82} - 4337 q^{83} - 1873 q^{84} - 2624 q^{85} - 3543 q^{86} - 3066 q^{87} - 3689 q^{88} - 5774 q^{89} - 3149 q^{90} - 3148 q^{91} - 8942 q^{92} - 7118 q^{93} - 5137 q^{94} - 2742 q^{95} - 6558 q^{96} - 6378 q^{97} - 7250 q^{98} - 3941 q^{99}+O(q^{100}) \) 65 * q - 12 * q^2 - 35 * q^3 + 234 * q^4 - 151 * q^5 - 60 * q^6 - 74 * q^7 - 144 * q^8 + 468 * q^9 - 60 * q^10 - 191 * q^11 - 483 * q^12 - 333 * q^13 - 377 * q^14 - 166 * q^15 + 818 * q^16 - 858 * q^17 - 279 * q^18 - 185 * q^19 - 1188 * q^20 - 406 * q^21 - 356 * q^22 - 836 * q^23 - 505 * q^24 + 1156 * q^25 - 696 * q^26 - 1094 * q^27 - 1096 * q^28 - 1209 * q^29 - 1054 * q^30 - 286 * q^31 - 1484 * q^32 - 1296 * q^33 - 763 * q^34 - 1374 * q^35 + 296 * q^36 - 1705 * q^37 - 2535 * q^38 - 622 * q^39 - 888 * q^40 - 1348 * q^41 - 1716 * q^42 - 973 * q^43 - 2568 * q^44 - 4529 * q^45 - 322 * q^46 - 2498 * q^47 - 5358 * q^48 + 2081 * q^49 - 2002 * q^50 - 1108 * q^51 - 3290 * q^52 - 5947 * q^53 - 2783 * q^54 - 1344 * q^55 - 5111 * q^56 - 3134 * q^57 - 1676 * q^58 - 1625 * q^59 - 2902 * q^60 - 3103 * q^61 - 5242 * q^62 - 3106 * q^63 + 1722 * q^64 - 3160 * q^65 - 3672 * q^66 - 2395 * q^67 - 8447 * q^68 - 4944 * q^69 - 597 * q^70 - 2654 * q^71 - 3929 * q^72 - 2116 * q^73 - 3969 * q^74 - 3759 * q^75 - 1844 * q^76 - 9938 * q^77 - 3935 * q^78 - 1206 * q^79 - 11619 * q^80 + 1889 * q^81 - 7674 * q^82 - 4337 * q^83 - 1873 * q^84 - 2624 * q^85 - 3543 * q^86 - 3066 * q^87 - 3689 * q^88 - 5774 * q^89 - 3149 * q^90 - 3148 * q^91 - 8942 * q^92 - 7118 * q^93 - 5137 * q^94 - 2742 * q^95 - 6558 * q^96 - 6378 * q^97 - 7250 * q^98 - 3941 * 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 $

$2$	−4.39733	−1.55469	−0.777346	−	0.629073i	$-0.783435\pi$
$2$	−4.39733	−1.55469	−0.777346	+	0.629073i	$0.783435\pi$
$3$	−7.45622	−1.43495	−0.717475	−	0.696584i	$-0.754702\pi$
$3$	−7.45622	−1.43495	−0.717475	+	0.696584i	$0.754702\pi$
$4$	11.3366	1.41707
$5$	−12.8080	−1.14558	−0.572791	−	0.819701i	$-0.694139\pi$
$5$	−12.8080	−1.14558	−0.572791	+	0.819701i	$0.694139\pi$
$6$	32.7875	2.23091
$7$	−33.9402	−1.83260	−0.916299	−	0.400494i	$-0.868839\pi$
$7$	−33.9402	−1.83260	−0.916299	+	0.400494i	$0.868839\pi$
$8$	−14.6719	−0.648414
$9$	28.5953	1.05908
$10$	56.3210	1.78103
$11$	−9.00407	−0.246803	−0.123401	−	0.992357i	$-0.539380\pi$
$11$	−9.00407	−0.246803	−0.123401	+	0.992357i	$0.539380\pi$
$12$	−84.5279	−2.03342
$13$	−87.9841	−1.87711	−0.938554	−	0.345133i	$-0.887834\pi$
$13$	−87.9841	−1.87711	−0.938554	+	0.345133i	$0.887834\pi$
$14$	149.246	2.84913
$15$	95.4993	1.64385
$16$	−26.1750	−0.408984
$17$	60.2896	0.860139	0.430070	−	0.902796i	$-0.358489\pi$
$17$	60.2896	0.860139	0.430070	+	0.902796i	$0.358489\pi$
$18$	−125.743	−1.64655
$19$	55.0633	0.664862	0.332431	−	0.943128i	$-0.392131\pi$
$19$	55.0633	0.664862	0.332431	+	0.943128i	$0.392131\pi$
$20$	−145.199	−1.62337
$21$	253.066	2.62969
$22$	39.5939	0.383702
$23$	−189.249	−1.71570	−0.857850	−	0.513900i	$-0.828200\pi$
$23$	−189.249	−1.71570	−0.857850	+	0.513900i	$0.828200\pi$
$24$	109.397	0.930442
$25$	39.0448	0.312358
$26$	386.896	2.91833
$27$	−11.8947	−0.0847830
$28$	−384.765	−2.59692
$29$	92.1574	0.590110	0.295055	−	0.955480i	$-0.404662\pi$
$29$	92.1574	0.590110	0.295055	+	0.955480i	$0.404662\pi$
$30$	−419.942	−2.55569
$31$	30.3394	0.175778	0.0878888	−	0.996130i	$-0.471988\pi$
$31$	30.3394	0.175778	0.0878888	+	0.996130i	$0.471988\pi$
$32$	232.476	1.28426
$33$	67.1364	0.354150
$34$	−265.113	−1.33725
$35$	434.706	2.09939
$36$	324.172	1.50080
$37$	40.9651	0.182017	0.0910083	−	0.995850i	$-0.470991\pi$
$37$	40.9651	0.182017	0.0910083	+	0.995850i	$0.470991\pi$
$38$	−242.132	−1.03366
$39$	656.029	2.69356
$40$	187.918	0.742812
$41$	77.7511	0.296163	0.148081	−	0.988975i	$-0.452690\pi$
$41$	77.7511	0.296163	0.148081	+	0.988975i	$0.452690\pi$
$42$	−1112.81	−4.08836
$43$	474.686	1.68346	0.841731	−	0.539897i	$-0.181537\pi$
$43$	474.686	1.68346	0.841731	+	0.539897i	$0.181537\pi$
$44$	−102.075	−0.349737
$45$	−366.248	−1.21327
$46$	832.190	2.66739
$47$	215.891	0.670020	0.335010	−	0.942215i	$-0.391260\pi$
$47$	215.891	0.670020	0.335010	+	0.942215i	$0.391260\pi$
$48$	195.167	0.586873
$49$	808.938	2.35842
$50$	−171.693	−0.485621
$51$	−449.532	−1.23426
$52$	−997.436	−2.65999
$53$	−759.297	−1.96788	−0.983938	−	0.178511i	$-0.942872\pi$
$53$	−759.297	−1.96788	−0.983938	+	0.178511i	$0.942872\pi$
$54$	52.3051	0.131812
$55$	115.324	0.282733
$56$	497.969	1.18828
$57$	−410.564	−0.954045
$58$	−405.247	−0.917440
$59$	−31.2936	−0.0690522	−0.0345261	−	0.999404i	$-0.510992\pi$
$59$	−31.2936	−0.0690522	−0.0345261	+	0.999404i	$0.510992\pi$
$60$	1082.63	2.32945
$61$	671.515	1.40949	0.704743	−	0.709463i	$-0.251062\pi$
$61$	671.515	1.40949	0.704743	+	0.709463i	$0.251062\pi$
$62$	−133.412	−0.273280
$63$	−970.530	−1.94088
$64$	−812.874	−1.58764
$65$	1126.90	2.15038
$66$	−295.221	−0.550594
$67$	922.352	1.68184	0.840920	−	0.541160i	$-0.182015\pi$
$67$	922.352	1.68184	0.840920	+	0.541160i	$0.182015\pi$
$68$	683.476	1.21888
$69$	1411.08	2.46194
$70$	−1911.55	−3.26391
$71$	−277.592	−0.464001	−0.232001	−	0.972716i	$-0.574527\pi$
$71$	−277.592	−0.464001	−0.232001	+	0.972716i	$0.574527\pi$
$72$	−419.548	−0.686725
$73$	−1175.82	−1.88519	−0.942597	−	0.333933i	$-0.891624\pi$
$73$	−1175.82	−1.88519	−0.942597	+	0.333933i	$0.891624\pi$
$74$	−180.137	−0.282980
$75$	−291.127	−0.448219
$76$	624.228	0.942156
$77$	305.600	0.452291
$78$	−2884.78	−4.18765
$79$	767.428	1.09294	0.546471	−	0.837478i	$-0.315971\pi$
$79$	767.428	1.09294	0.546471	+	0.837478i	$0.315971\pi$
$80$	335.249	0.468525
$81$	−683.383	−0.937425
$82$	−341.897	−0.460442
$83$	−235.269	−0.311134	−0.155567	−	0.987825i	$-0.549720\pi$
$83$	−235.269	−0.311134	−0.155567	+	0.987825i	$0.549720\pi$
$84$	2868.89	3.72645
$85$	−772.188	−0.985360
$86$	−2087.35	−2.61727
$87$	−687.146	−0.846779
$88$	132.107	0.160030
$89$	−974.698	−1.16087	−0.580437	−	0.814305i	$-0.697118\pi$
$89$	−974.698	−1.16087	−0.580437	+	0.814305i	$0.697118\pi$
$90$	1610.52	1.88626
$91$	2986.20	3.43999
$92$	−2145.43	−2.43126
$93$	−226.217	−0.252232
$94$	−949.344	−1.04167
$95$	−705.250	−0.761654
$96$	−1733.39	−1.84285
$97$	887.219	0.928695	0.464347	−	0.885653i	$-0.346289\pi$
$97$	887.219	0.928695	0.464347	+	0.885653i	$0.346289\pi$
$98$	−3557.17	−3.66662
$99$	−257.474	−0.261385
$100$	442.633	0.442633
$101$	−1119.41	−1.10282	−0.551411	−	0.834234i	$-0.685910\pi$
$101$	−1119.41	−1.10282	−0.551411	+	0.834234i	$0.685910\pi$
$102$	1976.74	1.91889
$103$	−1023.21	−0.978837	−0.489418	−	0.872049i	$-0.662791\pi$
$103$	−1023.21	−0.978837	−0.489418	+	0.872049i	$0.662791\pi$
$104$	1290.90	1.21714
$105$	−3241.27	−3.01253
$106$	3338.88	3.05944
$107$	−517.880	−0.467901	−0.233950	−	0.972249i	$-0.575165\pi$
$107$	−517.880	−0.467901	−0.233950	+	0.972249i	$0.575165\pi$
$108$	−134.845	−0.120143
$109$	−1382.04	−1.21445	−0.607227	−	0.794529i	$-0.707718\pi$
$109$	−1382.04	−1.21445	−0.607227	+	0.794529i	$0.707718\pi$
$110$	−507.119	−0.439563
$111$	−305.445	−0.261185
$112$	888.385	0.749504
$113$	1533.38	1.27653	0.638265	−	0.769817i	$-0.279653\pi$
$113$	1533.38	1.27653	0.638265	+	0.769817i	$0.279653\pi$
$114$	1805.39	1.48325
$115$	2423.90	1.96547
$116$	1044.75	0.836227
$117$	−2515.93	−1.98802
$118$	137.608	0.107355
$119$	−2046.24	−1.57629
$120$	−1401.16	−1.06590
$121$	−1249.93	−0.939088
$122$	−2952.87	−2.19132
$123$	−579.729	−0.424979
$124$	343.944	0.249089
$125$	1100.91	0.787750
$126$	4267.74	3.01747
$127$	−489.017	−0.341679	−0.170839	−	0.985299i	$-0.554648\pi$
$127$	−489.017	−0.341679	−0.170839	+	0.985299i	$0.554648\pi$
$128$	1714.67	1.18404
$129$	−3539.36	−2.41569
$130$	−4955.36	−3.34318
$131$	−2346.00	−1.56467	−0.782333	−	0.622860i	$-0.785971\pi$
$131$	−2346.00	−1.56467	−0.782333	+	0.622860i	$0.785971\pi$
$132$	761.095	0.501855
$133$	−1868.86	−1.21843
$134$	−4055.89	−2.61474
$135$	152.348	0.0971259
$136$	−884.565	−0.557726
$137$	1653.91	1.03141	0.515704	−	0.856767i	$-0.327530\pi$
$137$	1653.91	1.03141	0.515704	+	0.856767i	$0.327530\pi$
$138$	−6205.00	−3.82757
$139$	−327.315	−0.199730	−0.0998652	−	0.995001i	$-0.531841\pi$
$139$	−327.315	−0.199730	−0.0998652	+	0.995001i	$0.531841\pi$
$140$	4928.07	2.97498
$141$	−1609.73	−0.961445
$142$	1220.66	0.721379
$143$	792.215	0.463275
$144$	−748.481	−0.433149
$145$	−1180.35	−0.676020
$146$	5170.47	2.93090
$147$	−6031.62	−3.38422
$148$	464.403	0.257930
$149$	−255.696	−0.140587	−0.0702934	−	0.997526i	$-0.522394\pi$
$149$	−255.696	−0.140587	−0.0702934	+	0.997526i	$0.522394\pi$
$150$	1280.18	0.696842
$151$	3177.16	1.71228	0.856138	−	0.516747i	$-0.172857\pi$
$151$	3177.16	1.71228	0.856138	+	0.516747i	$0.172857\pi$
$152$	−807.885	−0.431106
$153$	1724.00	0.910960
$154$	−1343.83	−0.703173
$155$	−388.586	−0.201368
$156$	7437.11	3.81696
$157$	1171.14	0.595330	0.297665	−	0.954670i	$-0.403792\pi$
$157$	1171.14	0.595330	0.297665	+	0.954670i	$0.403792\pi$
$158$	−3374.64	−1.69919
$159$	5661.49	2.82381
$160$	−2977.55	−1.47122
$161$	6423.14	3.14419
$162$	3005.06	1.45741
$163$	823.134	0.395539	0.197769	−	0.980249i	$-0.436630\pi$
$163$	823.134	0.395539	0.197769	+	0.980249i	$0.436630\pi$
$164$	881.429	0.419683
$165$	−859.883	−0.405708
$166$	1034.56	0.483717
$167$	−393.455	−0.182314	−0.0911571	−	0.995837i	$-0.529057\pi$
$167$	−393.455	−0.182314	−0.0911571	+	0.995837i	$0.529057\pi$
$168$	−3712.97	−1.70513
$169$	5544.20	2.52353
$170$	3395.57	1.53193
$171$	1574.55	0.704145
$172$	5381.30	2.38558
$173$	−111.380	−0.0489483	−0.0244741	−	0.999700i	$-0.507791\pi$
$173$	−111.380	−0.0489483	−0.0244741	+	0.999700i	$0.507791\pi$
$174$	3021.61	1.31648
$175$	−1325.19	−0.572427
$176$	235.682	0.100938
$177$	233.332	0.0990865
$178$	4286.07	1.80480
$179$	1958.51	0.817799	0.408899	−	0.912580i	$-0.365913\pi$
$179$	1958.51	0.817799	0.408899	+	0.912580i	$0.365913\pi$
$180$	−4151.99	−1.71928
$181$	95.9725	0.0394120	0.0197060	−	0.999806i	$-0.493727\pi$
$181$	95.9725	0.0394120	0.0197060	+	0.999806i	$0.493727\pi$
$182$	−13131.3	−5.34812
$183$	−5006.96	−2.02254
$184$	2776.65	1.11248
$185$	−524.681	−0.208515
$186$	994.752	0.392144
$187$	−542.852	−0.212285
$188$	2447.46	0.949464
$189$	403.710	0.155373
$190$	3101.22	1.18414
$191$	1765.96	0.669008	0.334504	−	0.942394i	$-0.391431\pi$
$191$	1765.96	0.669008	0.334504	+	0.942394i	$0.391431\pi$
$192$	6060.97	2.27819
$193$	2243.38	0.836696	0.418348	−	0.908287i	$-0.362609\pi$
$193$	2243.38	0.836696	0.418348	+	0.908287i	$0.362609\pi$
$194$	−3901.40	−1.44383
$195$	−8402.42	−3.08569
$196$	9170.56	3.34204
$197$	336.983	0.121873	0.0609367	−	0.998142i	$-0.480591\pi$
$197$	336.983	0.121873	0.0609367	+	0.998142i	$0.480591\pi$
$198$	1132.20	0.406373
$199$	2459.77	0.876222	0.438111	−	0.898921i	$-0.355648\pi$
$199$	2459.77	0.876222	0.438111	+	0.898921i	$0.355648\pi$
$200$	−572.862	−0.202537
$201$	−6877.27	−2.41336
$202$	4922.40	1.71455
$203$	−3127.84	−1.08144
$204$	−5096.15	−1.74903
$205$	−995.835	−0.339279
$206$	4499.41	1.52179
$207$	−5411.62	−1.81707
$208$	2302.98	0.767708
$209$	−495.794	−0.164090
$210$	14252.9	4.68355
$211$	−3946.98	−1.28778	−0.643889	−	0.765119i	$-0.722680\pi$
$211$	−3946.98	−1.28778	−0.643889	+	0.765119i	$0.722680\pi$
$212$	−8607.81	−2.78862
$213$	2069.79	0.665819
$214$	2277.29	0.727442
$215$	−6079.77	−1.92854
$216$	174.519	0.0549745
$217$	−1029.72	−0.322130
$218$	6077.29	1.88810
$219$	8767.17	2.70516
$220$	1307.38	0.400652
$221$	−5304.52	−1.61457
$222$	1343.14	0.406062
$223$	3455.63	1.03770	0.518848	−	0.854866i	$-0.326361\pi$
$223$	3455.63	1.03770	0.518848	+	0.854866i	$0.326361\pi$
$224$	−7890.27	−2.35353
$225$	1116.50	0.330814
$226$	−6742.76	−1.98461
$227$	−5747.07	−1.68038	−0.840190	−	0.542291i	$-0.817557\pi$
$227$	−5747.07	−1.68038	−0.840190	+	0.542291i	$0.817557\pi$
$228$	−4654.38	−1.35195
$229$	3340.97	0.964094	0.482047	−	0.876145i	$-0.339894\pi$
$229$	3340.97	0.964094	0.482047	+	0.876145i	$0.339894\pi$
$230$	−10658.7	−3.05571
$231$	−2278.62	−0.649015
$232$	−1352.13	−0.382636
$233$	−3032.79	−0.852724	−0.426362	−	0.904553i	$-0.640205\pi$
$233$	−3032.79	−0.852724	−0.426362	+	0.904553i	$0.640205\pi$
$234$	11063.4	3.09075
$235$	−2765.13	−0.767562
$236$	−354.761	−0.0978517
$237$	−5722.12	−1.56832
$238$	8998.00	2.45065
$239$	3120.70	0.844607	0.422304	−	0.906454i	$-0.361222\pi$
$239$	3120.70	0.844607	0.422304	+	0.906454i	$0.361222\pi$
$240$	−2499.69	−0.672311
$241$	−114.629	−0.0306385	−0.0153192	−	0.999883i	$-0.504876\pi$
$241$	−114.629	−0.0306385	−0.0153192	+	0.999883i	$0.504876\pi$
$242$	5496.35	1.45999
$243$	5416.61	1.42994
$244$	7612.66	1.99734
$245$	−10360.9	−2.70176
$246$	2549.26	0.660712
$247$	−4844.69	−1.24802
$248$	−445.137	−0.113977
$249$	1754.22	0.446462
$250$	−4841.09	−1.22471
$251$	6225.71	1.56559	0.782796	−	0.622278i	$-0.213793\pi$
$251$	6225.71	1.56559	0.782796	+	0.622278i	$0.213793\pi$
$252$	−11002.5	−2.75036
$253$	1704.01	0.423439
$254$	2150.37	0.531205
$255$	5757.61	1.41394
$256$	−1036.99	−0.253173
$257$	−2251.72	−0.546530	−0.273265	−	0.961939i	$-0.588104\pi$
$257$	−2251.72	−0.546530	−0.273265	+	0.961939i	$0.588104\pi$
$258$	15563.8	3.75565
$259$	−1390.36	−0.333564
$260$	12775.2	3.04724
$261$	2635.27	0.624977
$262$	10316.2	2.43258
$263$	5823.43	1.36535	0.682677	−	0.730720i	$-0.260816\pi$
$263$	5823.43	1.36535	0.682677	+	0.730720i	$0.260816\pi$
$264$	−985.021	−0.229636
$265$	9725.07	2.25436
$266$	8218.00	1.89428
$267$	7267.57	1.66580
$268$	10456.3	2.38328
$269$	−3195.31	−0.724244	−0.362122	−	0.932131i	$-0.617948\pi$
$269$	−3195.31	−0.724244	−0.362122	+	0.932131i	$0.617948\pi$
$270$	−669.924	−0.151001
$271$	1096.56	0.245797	0.122899	−	0.992419i	$-0.460781\pi$
$271$	1096.56	0.245797	0.122899	+	0.992419i	$0.460781\pi$
$272$	−1578.08	−0.351784
$273$	−22265.8	−4.93621
$274$	−7272.79	−1.60352
$275$	−351.562	−0.0770909
$276$	15996.8	3.48875
$277$	−7382.95	−1.60144	−0.800719	−	0.599040i	$-0.795549\pi$
$277$	−7382.95	−1.60144	−0.800719	+	0.599040i	$0.795549\pi$
$278$	1439.32	0.310519
$279$	867.562	0.186163
$280$	−6377.98	−1.36128
$281$	5196.51	1.10319	0.551597	−	0.834111i	$-0.314019\pi$
$281$	5196.51	1.10319	0.551597	+	0.834111i	$0.314019\pi$
$282$	7078.52	1.49475
$283$	1516.18	0.318471	0.159236	−	0.987241i	$-0.449097\pi$
$283$	1516.18	0.318471	0.159236	+	0.987241i	$0.449097\pi$
$284$	−3146.93	−0.657522
$285$	5258.50	1.09294
$286$	−3483.64	−0.720251
$287$	−2638.89	−0.542748
$288$	6647.71	1.36014
$289$	−1278.17	−0.260161
$290$	5190.40	1.05100
$291$	−6615.30	−1.33263
$292$	−13329.7	−2.67145
$293$	−3488.31	−0.695527	−0.347764	−	0.937582i	$-0.613059\pi$
$293$	−3488.31	−0.695527	−0.347764	+	0.937582i	$0.613059\pi$
$294$	26523.1	5.26142
$295$	400.808	0.0791049
$296$	−601.037	−0.118022
$297$	107.101	0.0209247
$298$	1124.38	0.218569
$299$	16650.9	3.22055
$300$	−3300.37	−0.635157
$301$	−16110.9	−3.08511
$302$	−13971.0	−2.66206
$303$	8346.54	1.58250
$304$	−1441.28	−0.271918
$305$	−8600.76	−1.61468
$306$	−7580.99	−1.41626
$307$	5374.86	0.999217	0.499609	−	0.866251i	$-0.333477\pi$
$307$	5374.86	0.999217	0.499609	+	0.866251i	$0.333477\pi$
$308$	3464.45	0.640927
$309$	7629.31	1.40458
$310$	1708.74	0.313065
$311$	2813.86	0.513052	0.256526	−	0.966537i	$-0.417422\pi$
$311$	2813.86	0.513052	0.256526	+	0.966537i	$0.417422\pi$
$312$	−9625.22	−1.74654
$313$	3032.52	0.547630	0.273815	−	0.961782i	$-0.411714\pi$
$313$	3032.52	0.547630	0.273815	+	0.961782i	$0.411714\pi$
$314$	−5149.88	−0.925555
$315$	12430.5	2.22343
$316$	8699.99	1.54877
$317$	−4279.52	−0.758239	−0.379119	−	0.925348i	$-0.623773\pi$
$317$	−4279.52	−0.758239	−0.379119	+	0.925348i	$0.623773\pi$
$318$	−24895.4	−4.39015
$319$	−829.792	−0.145641
$320$	10411.3	1.81878
$321$	3861.43	0.671415
$322$	−28244.7	−4.88825
$323$	3319.74	0.571874
$324$	−7747.20	−1.32840
$325$	−3435.32	−0.586330
$326$	−3619.59	−0.614941
$327$	10304.8	1.74268
$328$	−1140.76	−0.192036
$329$	−7327.38	−1.22788
$330$	3781.19	0.630751
$331$	−3533.71	−0.586798	−0.293399	−	0.955990i	$-0.594787\pi$
$331$	−3533.71	−0.586798	−0.293399	+	0.955990i	$0.594787\pi$
$332$	−2667.14	−0.440898
$333$	1171.41	0.192771
$334$	1730.15	0.283443
$335$	−11813.5	−1.92669
$336$	−6624.00	−1.07550
$337$	1515.63	0.244990	0.122495	−	0.992469i	$-0.460911\pi$
$337$	1515.63	0.244990	0.122495	+	0.992469i	$0.460911\pi$
$338$	−24379.7	−3.92332
$339$	−11433.2	−1.83176
$340$	−8753.95	−1.39632
$341$	−273.178	−0.0433824
$342$	−6923.82	−1.09473
$343$	−15814.0	−2.48944
$344$	−6964.56	−1.09158
$345$	−18073.1	−2.82036
$346$	489.774	0.0760995
$347$	7514.41	1.16252	0.581260	−	0.813718i	$-0.302560\pi$
$347$	7514.41	1.16252	0.581260	+	0.813718i	$0.302560\pi$
$348$	−7789.87	−1.19994
$349$	−10882.9	−1.66919	−0.834593	−	0.550867i	$-0.814297\pi$
$349$	−10882.9	−1.66919	−0.834593	+	0.550867i	$0.814297\pi$
$350$	5827.29	0.889948
$351$	1046.55	0.159147
$352$	−2093.23	−0.316959
$353$	1477.03	0.222704	0.111352	−	0.993781i	$-0.464482\pi$
$353$	1477.03	0.222704	0.111352	+	0.993781i	$0.464482\pi$
$354$	−1026.04	−0.154049
$355$	3555.39	0.531551
$356$	−11049.7	−1.64504
$357$	15257.2	2.26190
$358$	−8612.23	−1.27143
$359$	−125.526	−0.0184540	−0.00922700	−	0.999957i	$-0.502937\pi$
$359$	−125.526	−0.0184540	−0.00922700	+	0.999957i	$0.502937\pi$
$360$	5373.57	0.786700
$361$	−3827.04	−0.557958
$362$	−422.023	−0.0612736
$363$	9319.73	1.34755
$364$	33853.2	4.87470
$365$	15059.9	2.15964
$366$	22017.3	3.14443
$367$	7709.82	1.09659	0.548296	−	0.836284i	$-0.315277\pi$
$367$	7709.82	1.09659	0.548296	+	0.836284i	$0.315277\pi$
$368$	4953.59	0.701694
$369$	2223.31	0.313661
$370$	2307.20	0.324177
$371$	25770.7	3.60633
$372$	−2564.52	−0.357431
$373$	−644.817	−0.0895103	−0.0447551	−	0.998998i	$-0.514251\pi$
$373$	−644.817	−0.0895103	−0.0447551	+	0.998998i	$0.514251\pi$
$374$	2387.10	0.330037
$375$	−8208.66	−1.13038
$376$	−3167.54	−0.434450
$377$	−8108.39	−1.10770
$378$	−1775.25	−0.241558
$379$	−2789.84	−0.378112	−0.189056	−	0.981966i	$-0.560543\pi$
$379$	−2789.84	−0.378112	−0.189056	+	0.981966i	$0.560543\pi$
$380$	−7995.11	−1.07932
$381$	3646.22	0.490292
$382$	−7765.53	−1.04010
$383$	−1104.71	−0.147383	−0.0736916	−	0.997281i	$-0.523478\pi$
$383$	−1104.71	−0.147383	−0.0736916	+	0.997281i	$0.523478\pi$
$384$	−12785.0	−1.69904
$385$	−3914.13	−0.518136
$386$	−9864.91	−1.30081
$387$	13573.8	1.78293
$388$	10058.0	1.31602
$389$	7270.26	0.947601	0.473801	−	0.880632i	$-0.342882\pi$
$389$	7270.26	0.947601	0.473801	+	0.880632i	$0.342882\pi$
$390$	36948.2	4.79730
$391$	−11409.7	−1.47574
$392$	−11868.7	−1.52923
$393$	17492.3	2.24522
$394$	−1481.83	−0.189476
$395$	−9829.22	−1.25205
$396$	−2918.87	−0.370400
$397$	−1697.98	−0.214658	−0.107329	−	0.994224i	$-0.534230\pi$
$397$	−1697.98	−0.214658	−0.107329	+	0.994224i	$0.534230\pi$
$398$	−10816.4	−1.36226
$399$	13934.6	1.74838
$400$	−1022.00	−0.127750
$401$	−7317.64	−0.911285	−0.455643	−	0.890163i	$-0.650590\pi$
$401$	−7317.64	−0.911285	−0.455643	+	0.890163i	$0.650590\pi$
$402$	30241.6	3.75203
$403$	−2669.38	−0.329954
$404$	−12690.2	−1.56277
$405$	8752.76	1.07390
$406$	13754.2	1.68130
$407$	−368.853	−0.0449222
$408$	6595.51	0.800310
$409$	−5686.94	−0.687533	−0.343767	−	0.939055i	$-0.611703\pi$
$409$	−5686.94	−0.687533	−0.343767	+	0.939055i	$0.611703\pi$
$410$	4379.02	0.527474
$411$	−12331.9	−1.48002
$412$	−11599.7	−1.38708
$413$	1062.11	0.126545
$414$	23796.7	2.82499
$415$	3013.32	0.356429
$416$	−20454.2	−2.41069
$417$	2440.54	0.286603
$418$	2180.17	0.255109
$419$	−9807.12	−1.14346	−0.571729	−	0.820442i	$-0.693727\pi$
$419$	−9807.12	−1.14346	−0.571729	+	0.820442i	$0.693727\pi$
$420$	−36744.8	−4.26896
$421$	−7474.15	−0.865244	−0.432622	−	0.901575i	$-0.642411\pi$
$421$	−7474.15	−0.865244	−0.432622	+	0.901575i	$0.642411\pi$
$422$	17356.2	2.00210
$423$	6173.46	0.709607
$424$	11140.4	1.27600
$425$	2353.99	0.268671
$426$	−9101.54	−1.03514
$427$	−22791.3	−2.58302
$428$	−5870.98	−0.663048
$429$	−5906.93	−0.664777
$430$	26734.8	2.99829
$431$	8600.57	0.961195	0.480597	−	0.876941i	$-0.340420\pi$
$431$	8600.57	0.961195	0.480597	+	0.876941i	$0.340420\pi$
$432$	311.345	0.0346749
$433$	4342.94	0.482005	0.241003	−	0.970524i	$-0.422524\pi$
$433$	4342.94	0.482005	0.241003	+	0.970524i	$0.422524\pi$
$434$	4528.04	0.500813
$435$	8800.97	0.970055
$436$	−15667.6	−1.72096
$437$	−10420.7	−1.14070
$438$	−38552.2	−4.20569
$439$	1146.74	0.124671	0.0623356	−	0.998055i	$-0.480145\pi$
$439$	1146.74	0.124671	0.0623356	+	0.998055i	$0.480145\pi$
$440$	−1692.03	−0.183328
$441$	23131.8	2.49776
$442$	23325.8	2.51017
$443$	−11413.4	−1.22408	−0.612039	−	0.790827i	$-0.709651\pi$
$443$	−11413.4	−1.22408	−0.612039	+	0.790827i	$0.709651\pi$
$444$	−3462.69	−0.370117
$445$	12483.9	1.32988
$446$	−15195.6	−1.61330
$447$	1906.53	0.201735
$448$	27589.1	2.90951
$449$	9937.90	1.04454	0.522270	−	0.852780i	$-0.325085\pi$
$449$	9937.90	1.04454	0.522270	+	0.852780i	$0.325085\pi$
$450$	−4909.61	−0.514313
$451$	−700.076	−0.0730938
$452$	17383.2	1.80893
$453$	−23689.6	−2.45703
$454$	25271.8	2.61248
$455$	−38247.2	−3.94079
$456$	6023.77	0.618616
$457$	14150.5	1.44843	0.724213	−	0.689576i	$-0.242203\pi$
$457$	14150.5	1.44843	0.724213	+	0.689576i	$0.242203\pi$
$458$	−14691.4	−1.49887
$459$	−717.128	−0.0729252
$460$	27478.6	2.78521
$461$	14036.4	1.41809	0.709047	−	0.705161i	$-0.249125\pi$
$461$	14036.4	1.41809	0.709047	+	0.705161i	$0.249125\pi$
$462$	10019.9	1.00902
$463$	−656.817	−0.0659284	−0.0329642	−	0.999457i	$-0.510495\pi$
$463$	−656.817	−0.0659284	−0.0329642	+	0.999457i	$0.510495\pi$
$464$	−2412.22	−0.241346
$465$	2897.39	0.288953
$466$	13336.2	1.32572
$467$	7201.13	0.713551	0.356776	−	0.934190i	$-0.383876\pi$
$467$	7201.13	0.713551	0.356776	+	0.934190i	$0.383876\pi$
$468$	−28522.0	−2.81715
$469$	−31304.8	−3.08214
$470$	12159.2	1.19332
$471$	−8732.25	−0.854270
$472$	459.137	0.0447744
$473$	−4274.10	−0.415483
$474$	25162.1	2.43825
$475$	2149.93	0.207675
$476$	−23197.3	−2.23371
$477$	−21712.3	−2.08415
$478$	−13722.7	−1.31310
$479$	−5353.68	−0.510681	−0.255340	−	0.966851i	$-0.582187\pi$
$479$	−5353.68	−0.510681	−0.255340	+	0.966851i	$0.582187\pi$
$480$	22201.3	2.11113
$481$	−3604.28	−0.341665
$482$	504.060	0.0476334
$483$	−47892.4	−4.51176
$484$	−14169.9	−1.33075
$485$	−11363.5	−1.06390
$486$	−23818.7	−2.22312
$487$	18952.9	1.76353	0.881766	−	0.471687i	$-0.156355\pi$
$487$	18952.9	1.76353	0.881766	+	0.471687i	$0.156355\pi$
$488$	−9852.42	−0.913930
$489$	−6137.47	−0.567579
$490$	45560.2	4.20041
$491$	604.643	0.0555747	0.0277873	−	0.999614i	$-0.491154\pi$
$491$	604.643	0.0555747	0.0277873	+	0.999614i	$0.491154\pi$
$492$	−6572.13	−0.602225
$493$	5556.13	0.507577
$494$	21303.7	1.94028
$495$	3297.73	0.299438
$496$	−794.133	−0.0718903
$497$	9421.52	0.850328
$498$	−7713.88	−0.694111
$499$	1014.84	0.0910431	0.0455216	−	0.998963i	$-0.485505\pi$
$499$	1014.84	0.0910431	0.0455216	+	0.998963i	$0.485505\pi$
$500$	12480.6	1.11630
$501$	2933.69	0.261612
$502$	−27376.5	−2.43401
$503$	−12544.2	−1.11196	−0.555982	−	0.831194i	$-0.687658\pi$
$503$	−12544.2	−1.11196	−0.555982	+	0.831194i	$0.687658\pi$
$504$	14239.5	1.25849
$505$	14337.3	1.26337
$506$	−7493.10	−0.658318
$507$	−41338.8	−3.62115
$508$	−5543.76	−0.484182
$509$	−7068.48	−0.615530	−0.307765	−	0.951462i	$-0.599581\pi$
$509$	−7068.48	−0.615530	−0.307765	+	0.951462i	$0.599581\pi$
$510$	−25318.1	−2.19825
$511$	39907.5	3.45480
$512$	−9157.36	−0.790433
$513$	−654.963	−0.0563690
$514$	9901.55	0.849686
$515$	13105.3	1.12134
$516$	−40124.2	−3.42319
$517$	−1943.90	−0.165363
$518$	6113.89	0.518589
$519$	830.473	0.0702384
$520$	−16533.8	−1.39434
$521$	−5529.29	−0.464957	−0.232478	−	0.972602i	$-0.574683\pi$
$521$	−5529.29	−0.464957	−0.232478	+	0.972602i	$0.574683\pi$
$522$	−11588.1	−0.971647
$523$	6900.90	0.576970	0.288485	−	0.957484i	$-0.406848\pi$
$523$	6900.90	0.576970	0.288485	+	0.957484i	$0.406848\pi$
$524$	−26595.6	−2.21724
$525$	9880.90	0.821405
$526$	−25607.6	−2.12271
$527$	1829.15	0.151193
$528$	−1757.30	−0.144842
$529$	23648.1	1.94363
$530$	−42764.4	−3.50484
$531$	−894.849	−0.0731321
$532$	−21186.4	−1.72659
$533$	−6840.86	−0.555930
$534$	−31957.9	−2.58980
$535$	6633.01	0.536019
$536$	−13532.7	−1.09053
$537$	−14603.1	−1.17350
$538$	14050.9	1.12598
$539$	−7283.74	−0.582064
$540$	1727.10	0.137634
$541$	9338.79	0.742156	0.371078	−	0.928602i	$-0.378988\pi$
$541$	9338.79	0.742156	0.371078	+	0.928602i	$0.378988\pi$
$542$	−4821.93	−0.382139
$543$	−715.593	−0.0565544
$544$	14015.9	1.10464
$545$	17701.2	1.39126
$546$	97910.0	7.67429
$547$	547.000	0.0427569
$547$	547.000	0.0427569
$548$	18749.6	1.46158
$549$	19202.1	1.49276
$550$	1545.94	0.119853
$551$	5074.49	0.392342
$552$	−20703.3	−1.59636
$553$	−26046.7	−2.00292
$554$	32465.3	2.48974
$555$	3912.14	0.299209
$556$	−3710.63	−0.283032
$557$	−528.273	−0.0401861	−0.0200930	−	0.999798i	$-0.506396\pi$
$557$	−528.273	−0.0401861	−0.0200930	+	0.999798i	$0.506396\pi$
$558$	−3814.96	−0.289427
$559$	−41764.8	−3.16004
$560$	−11378.4	−0.858619
$561$	4047.62	0.304618
$562$	−22850.8	−1.71513
$563$	9550.06	0.714897	0.357448	−	0.933933i	$-0.383647\pi$
$563$	9550.06	0.714897	0.357448	+	0.933933i	$0.383647\pi$
$564$	−18248.8	−1.36243
$565$	−19639.5	−1.46237
$566$	−6667.13	−0.495125
$567$	23194.1	1.71792
$568$	4072.81	0.300865
$569$	24814.5	1.82826	0.914128	−	0.405427i	$-0.132877\pi$
$569$	24814.5	1.82826	0.914128	+	0.405427i	$0.132877\pi$
$570$	−23123.4	−1.69918
$571$	−5921.19	−0.433965	−0.216983	−	0.976175i	$-0.569621\pi$
$571$	−5921.19	−0.433965	−0.216983	+	0.976175i	$0.569621\pi$
$572$	8980.99	0.656493
$573$	−13167.4	−0.959994
$574$	11604.1	0.843806
$575$	−7389.17	−0.535913
$576$	−23244.3	−1.68145
$577$	18477.5	1.33315	0.666575	−	0.745438i	$-0.267760\pi$
$577$	18477.5	1.33315	0.666575	+	0.745438i	$0.267760\pi$
$578$	5620.54	0.404470
$579$	−16727.2	−1.20062
$580$	−13381.1	−0.957967
$581$	7985.07	0.570184
$582$	29089.7	2.07183
$583$	6836.76	0.485677
$584$	17251.5	1.22239
$585$	32224.0	2.27743
$586$	15339.3	1.08133
$587$	−11182.4	−0.786283	−0.393141	−	0.919478i	$-0.628612\pi$
$587$	−11182.4	−0.786283	−0.393141	+	0.919478i	$0.628612\pi$
$588$	−68377.8	−4.79567
$589$	1670.58	0.116868
$590$	−1762.49	−0.122984
$591$	−2512.62	−0.174882
$592$	−1072.26	−0.0744420
$593$	−8474.82	−0.586879	−0.293440	−	0.955978i	$-0.594800\pi$
$593$	−8474.82	−0.586879	−0.293440	+	0.955978i	$0.594800\pi$
$594$	−470.959	−0.0325315
$595$	26208.2	1.80577
$596$	−2898.71	−0.199221
$597$	−18340.6	−1.25734
$598$	−73219.5	−5.00697
$599$	−3473.11	−0.236907	−0.118454	−	0.992960i	$-0.537794\pi$
$599$	−3473.11	−0.236907	−0.118454	+	0.992960i	$0.537794\pi$
$600$	4271.39	0.290631
$601$	−1138.91	−0.0773000	−0.0386500	−	0.999253i	$-0.512306\pi$
$601$	−1138.91	−0.0773000	−0.0386500	+	0.999253i	$0.512306\pi$
$602$	70845.1	4.79640
$603$	26374.9	1.78121
$604$	36018.1	2.42641
$605$	16009.1	1.07580
$606$	−36702.5	−2.46029
$607$	−858.029	−0.0573745	−0.0286872	−	0.999588i	$-0.509133\pi$
$607$	−858.029	−0.0573745	−0.0286872	+	0.999588i	$0.509133\pi$
$608$	12800.9	0.853855
$609$	23321.9	1.55181
$610$	37820.4	2.51033
$611$	−18995.0	−1.25770
$612$	19544.2	1.29089
$613$	24183.1	1.59338	0.796692	−	0.604386i	$-0.206581\pi$
$613$	24183.1	1.59338	0.796692	+	0.604386i	$0.206581\pi$
$614$	−23635.1	−1.55348
$615$	7425.17	0.486849
$616$	−4483.75	−0.293272
$617$	4381.84	0.285909	0.142955	−	0.989729i	$-0.454340\pi$
$617$	4381.84	0.285909	0.142955	+	0.989729i	$0.454340\pi$
$618$	−33548.6	−2.18369
$619$	14949.3	0.970700	0.485350	−	0.874320i	$-0.338692\pi$
$619$	14949.3	0.970700	0.485350	+	0.874320i	$0.338692\pi$
$620$	−4405.23	−0.285352
$621$	2251.06	0.145462
$622$	−12373.5	−0.797638
$623$	33081.5	2.12742
$624$	−17171.6	−1.10162
$625$	−18981.1	−1.21479
$626$	−13335.0	−0.851396
$627$	3696.75	0.235461
$628$	13276.6	0.843624
$629$	2469.77	0.156560
$630$	−54661.2	−3.45676
$631$	−13846.1	−0.873539	−0.436770	−	0.899573i	$-0.643878\pi$
$631$	−13846.1	−0.873539	−0.436770	+	0.899573i	$0.643878\pi$
$632$	−11259.7	−0.708679
$633$	29429.5	1.84790
$634$	18818.5	1.17883
$635$	6263.32	0.391421
$636$	64181.7	4.00153
$637$	−71173.7	−4.42701
$638$	3648.87	0.226427
$639$	−7937.81	−0.491416
$640$	−21961.5	−1.35641
$641$	1552.79	0.0956808	0.0478404	−	0.998855i	$-0.484766\pi$
$641$	1552.79	0.0956808	0.0478404	+	0.998855i	$0.484766\pi$
$642$	−16980.0	−1.04384
$643$	9024.97	0.553515	0.276758	−	0.960940i	$-0.410740\pi$
$643$	9024.97	0.553515	0.276758	+	0.960940i	$0.410740\pi$
$644$	72816.3	4.45553
$645$	45332.1	2.76737
$646$	−14598.0	−0.889088
$647$	−25867.0	−1.57177	−0.785887	−	0.618370i	$-0.787793\pi$
$647$	−25867.0	−1.57177	−0.785887	+	0.618370i	$0.787793\pi$
$648$	10026.5	0.607839
$649$	281.770	0.0170423
$650$	15106.2	0.911563
$651$	7677.85	0.462241
$652$	9331.50	0.560506
$653$	−31090.4	−1.86319	−0.931594	−	0.363500i	$-0.881582\pi$
$653$	−31090.4	−1.86319	−0.931594	+	0.363500i	$0.881582\pi$
$654$	−45313.7	−2.70933
$655$	30047.6	1.79245
$656$	−2035.13	−0.121126
$657$	−33622.9	−1.99658
$658$	32220.9	1.90897
$659$	−10952.1	−0.647392	−0.323696	−	0.946161i	$-0.604926\pi$
$659$	−10952.1	−0.647392	−0.323696	+	0.946161i	$0.604926\pi$
$660$	−9748.10	−0.574916
$661$	12611.6	0.742108	0.371054	−	0.928611i	$-0.378996\pi$
$661$	12611.6	0.742108	0.371054	+	0.928611i	$0.378996\pi$
$662$	15538.9	0.912291
$663$	39551.7	2.31683
$664$	3451.85	0.201744
$665$	23936.3	1.39581
$666$	−5151.07	−0.299700
$667$	−17440.7	−1.01245
$668$	−4460.43	−0.258352
$669$	−25766.0	−1.48904
$670$	51947.8	2.99540
$671$	−6046.37	−0.347865
$672$	58831.7	3.37720
$673$	555.314	0.0318065	0.0159033	−	0.999874i	$-0.494938\pi$
$673$	555.314	0.0318065	0.0159033	+	0.999874i	$0.494938\pi$
$674$	−6664.72	−0.380883
$675$	−464.427	−0.0264827
$676$	62852.1	3.57602
$677$	−16976.8	−0.963769	−0.481884	−	0.876235i	$-0.660047\pi$
$677$	−16976.8	−0.963769	−0.481884	+	0.876235i	$0.660047\pi$
$678$	50275.6	2.84782
$679$	−30112.4	−1.70193
$680$	11329.5	0.638921
$681$	42851.4	2.41126
$682$	1201.25	0.0674463
$683$	11282.2	0.632066	0.316033	−	0.948748i	$-0.397649\pi$
$683$	11282.2	0.632066	0.316033	+	0.948748i	$0.397649\pi$
$684$	17850.0	0.997822
$685$	−21183.3	−1.18156
$686$	69539.6	3.87031
$687$	−24911.0	−1.38343
$688$	−12424.9	−0.688510
$689$	66806.0	3.69391
$690$	79473.6	4.38479
$691$	23212.9	1.27794	0.638971	−	0.769230i	$-0.279360\pi$
$691$	23212.9	1.27794	0.638971	+	0.769230i	$0.279360\pi$
$692$	−1262.66	−0.0693631
$693$	8738.72	0.479014
$694$	−33043.4	−1.80736
$695$	4192.26	0.228808
$696$	10081.8	0.549064
$697$	4687.58	0.254741
$698$	47855.6	2.59507
$699$	22613.2	1.22362
$700$	−15023.1	−0.811169
$701$	−27705.7	−1.49277	−0.746383	−	0.665517i	$-0.768211\pi$
$701$	−27705.7	−1.49277	−0.746383	+	0.665517i	$0.768211\pi$
$702$	−4602.02	−0.247424
$703$	2255.67	0.121016
$704$	7319.17	0.391835
$705$	20617.4	1.10141
$706$	−6495.02	−0.346237
$707$	37992.9	2.02103
$708$	2645.18	0.140412
$709$	−10756.2	−0.569759	−0.284879	−	0.958563i	$-0.591954\pi$
$709$	−10756.2	−0.569759	−0.284879	+	0.958563i	$0.591954\pi$
$710$	−15634.3	−0.826399
$711$	21944.8	1.15752
$712$	14300.7	0.752727
$713$	−5741.68	−0.301582
$714$	−67091.1	−3.51656
$715$	−10146.7	−0.530720
$716$	22202.8	1.15888
$717$	−23268.6	−1.21197
$718$	551.978	0.0286903
$719$	6377.98	0.330818	0.165409	−	0.986225i	$-0.447106\pi$
$719$	6377.98	0.330818	0.165409	+	0.986225i	$0.447106\pi$
$720$	9586.55	0.496208
$721$	34728.1	1.79382
$722$	16828.8	0.867454
$723$	854.696	0.0439647
$724$	1088.00	0.0558496
$725$	3598.27	0.184326
$726$	−40982.0	−2.09502
$727$	19468.8	0.993202	0.496601	−	0.867979i	$-0.334581\pi$
$727$	19468.8	0.993202	0.496601	+	0.867979i	$0.334581\pi$
$728$	−43813.3	−2.23053
$729$	−21936.1	−1.11447
$730$	−66223.3	−3.35758
$731$	28618.6	1.44801
$732$	−56761.7	−2.86608
$733$	−17433.2	−0.878459	−0.439229	−	0.898375i	$-0.644748\pi$
$733$	−17433.2	−0.878459	−0.439229	+	0.898375i	$0.644748\pi$
$734$	−33902.7	−1.70486
$735$	77253.0	3.87690
$736$	−43995.7	−2.20340
$737$	−8304.93	−0.415083
$738$	−9776.65	−0.487647
$739$	16933.8	0.842923	0.421462	−	0.906846i	$-0.361517\pi$
$739$	16933.8	0.842923	0.421462	+	0.906846i	$0.361517\pi$
$740$	−5948.07	−0.295480
$741$	36123.1	1.79084
$742$	−113322.	−5.60673
$743$	21465.1	1.05986	0.529931	−	0.848041i	$-0.322218\pi$
$743$	21465.1	1.05986	0.529931	+	0.848041i	$0.322218\pi$
$744$	3319.04	0.163551
$745$	3274.95	0.161054
$746$	2835.47	0.139161
$747$	−6727.58	−0.329517
$748$	−6154.07	−0.300822
$749$	17577.0	0.857475
$750$	36096.2	1.75740
$751$	−20936.7	−1.01730	−0.508648	−	0.860974i	$-0.669855\pi$
$751$	−20936.7	−1.01730	−0.508648	+	0.860974i	$0.669855\pi$
$752$	−5650.94	−0.274028
$753$	−46420.3	−2.24655
$754$	35655.3	1.72213
$755$	−40693.1	−1.96155
$756$	4576.68	0.220175
$757$	5146.41	0.247093	0.123546	−	0.992339i	$-0.460573\pi$
$757$	5146.41	0.247093	0.123546	+	0.992339i	$0.460573\pi$
$758$	12267.9	0.587848
$759$	−12705.5	−0.607615
$760$	10347.4	0.493867
$761$	−8719.51	−0.415351	−0.207675	−	0.978198i	$-0.566590\pi$
$761$	−8719.51	−0.415351	−0.207675	+	0.978198i	$0.566590\pi$
$762$	−16033.6	−0.762254
$763$	46906.7	2.22561
$764$	20019.9	0.948030
$765$	−22080.9	−1.04358
$766$	4857.76	0.229136
$767$	2753.34	0.129618
$768$	7732.07	0.363290
$769$	15168.4	0.711295	0.355647	−	0.934620i	$-0.384260\pi$
$769$	15168.4	0.711295	0.355647	+	0.934620i	$0.384260\pi$
$770$	17211.7	0.805542
$771$	16789.3	0.784243
$772$	25432.2	1.18566
$773$	−38851.8	−1.80777	−0.903883	−	0.427780i	$-0.859296\pi$
$773$	−38851.8	−1.80777	−0.903883	+	0.427780i	$0.859296\pi$
$774$	−59688.4	−2.77191
$775$	1184.59	0.0549056
$776$	−13017.2	−0.602179
$777$	10366.9	0.478647
$778$	−31969.8	−1.47323
$779$	4281.23	0.196908
$780$	−95254.5	−4.37264
$781$	2499.46	0.114517
$782$	50172.4	2.29432
$783$	−1096.19	−0.0500314
$784$	−21173.9	−0.964557
$785$	−14999.9	−0.682000
$786$	−76919.6	−3.49063
$787$	25657.9	1.16214	0.581071	−	0.813853i	$-0.302634\pi$
$787$	25657.9	1.16214	0.581071	+	0.813853i	$0.302634\pi$
$788$	3820.23	0.172703
$789$	−43420.8	−1.95922
$790$	43222.4	1.94656
$791$	−52043.1	−2.33937
$792$	3777.64	0.169486
$793$	−59082.6	−2.64576
$794$	7466.61	0.333728
$795$	−72512.3	−3.23490
$796$	27885.3	1.24167
$797$	−8333.55	−0.370376	−0.185188	−	0.982703i	$-0.559289\pi$
$797$	−8333.55	−0.370376	−0.185188	+	0.982703i	$0.559289\pi$
$798$	−61275.2	−2.71820
$799$	13016.0	0.576310
$800$	9076.96	0.401149
$801$	−27871.8	−1.22946
$802$	32178.1	1.41677
$803$	10587.2	0.465271
$804$	−77964.5	−3.41989
$805$	−82267.6	−3.60193
$806$	11738.2	0.512976
$807$	23825.0	1.03925
$808$	16423.8	0.715085
$809$	−19773.7	−0.859340	−0.429670	−	0.902986i	$-0.641370\pi$
$809$	−19773.7	−0.859340	−0.429670	+	0.902986i	$0.641370\pi$
$810$	−38488.8	−1.66958
$811$	−28019.5	−1.21319	−0.606596	−	0.795011i	$-0.707465\pi$
$811$	−28019.5	−1.21319	−0.606596	+	0.795011i	$0.707465\pi$
$812$	−35458.9	−1.53247
$813$	−8176.17	−0.352707
$814$	1621.97	0.0698402
$815$	−10542.7	−0.453122
$816$	11766.5	0.504792
$817$	26137.7	1.11927
$818$	25007.4	1.06890
$819$	85391.2	3.64323
$820$	−11289.3	−0.480782
$821$	−746.823	−0.0317470	−0.0158735	−	0.999874i	$-0.505053\pi$
$821$	−746.823	−0.0317470	−0.0158735	+	0.999874i	$0.505053\pi$
$822$	54227.6	2.30098
$823$	26234.5	1.11115	0.555575	−	0.831466i	$-0.312498\pi$
$823$	26234.5	1.11115	0.555575	+	0.831466i	$0.312498\pi$
$824$	15012.5	0.634692
$825$	2621.33	0.110622
$826$	−4670.46	−0.196738
$827$	10284.2	0.432428	0.216214	−	0.976346i	$-0.430629\pi$
$827$	10284.2	0.432428	0.216214	+	0.976346i	$0.430629\pi$
$828$	−61349.1	−2.57491
$829$	3824.90	0.160246	0.0801231	−	0.996785i	$-0.474469\pi$
$829$	3824.90	0.160246	0.0801231	+	0.996785i	$0.474469\pi$
$830$	−13250.6	−0.554138
$831$	55048.9	2.29798
$832$	71519.9	2.98018
$833$	48770.5	2.02857
$834$	−10731.9	−0.445580
$835$	5039.37	0.208856
$836$	−5620.59	−0.232527
$837$	−360.878	−0.0149030
$838$	43125.2	1.77773
$839$	−7662.34	−0.315296	−0.157648	−	0.987495i	$-0.550391\pi$
$839$	−7662.34	−0.315296	−0.157648	+	0.987495i	$0.550391\pi$
$840$	47555.6	1.95336
$841$	−15896.0	−0.651770
$842$	32866.3	1.34519
$843$	−38746.3	−1.58303
$844$	−44745.1	−1.82487
$845$	−71010.1	−2.89091
$846$	−27146.8	−1.10322
$847$	42422.8	1.72097
$848$	19874.6	0.804831
$849$	−11304.9	−0.456990
$850$	−10351.3	−0.417702
$851$	−7752.59	−0.312286
$852$	23464.2	0.943511
$853$	−2815.22	−0.113003	−0.0565013	−	0.998403i	$-0.517995\pi$
$853$	−2815.22	−0.113003	−0.0565013	+	0.998403i	$0.517995\pi$
$854$	100221.	4.01581
$855$	−20166.8	−0.806656
$856$	7598.31	0.303393
$857$	−8530.58	−0.340022	−0.170011	−	0.985442i	$-0.554380\pi$
$857$	−8530.58	−0.340022	−0.170011	+	0.985442i	$0.554380\pi$
$858$	25974.8	1.03352
$859$	−25315.5	−1.00553	−0.502767	−	0.864422i	$-0.667685\pi$
$859$	−25315.5	−1.00553	−0.502767	+	0.864422i	$0.667685\pi$
$860$	−68923.6	−2.73288
$861$	19676.1	0.778816
$862$	−37819.6	−1.49436
$863$	−42760.7	−1.68666	−0.843332	−	0.537393i	$-0.819409\pi$
$863$	−42760.7	−1.68666	−0.843332	+	0.537393i	$0.819409\pi$
$864$	−2765.24	−0.108883
$865$	1426.55	0.0560743
$866$	−19097.4	−0.749370
$867$	9530.32	0.373318
$868$	−11673.5	−0.456480
$869$	−6909.98	−0.269741
$870$	−38700.8	−1.50814
$871$	−81152.3	−3.15699
$872$	20277.2	0.787469
$873$	25370.3	0.983566
$874$	45823.1	1.77344
$875$	−37365.3	−1.44363
$876$	99389.4	3.83340
$877$	14525.1	0.559266	0.279633	−	0.960107i	$-0.409787\pi$
$877$	14525.1	0.559266	0.279633	+	0.960107i	$0.409787\pi$
$878$	−5042.58	−0.193825
$879$	26009.7	0.998048
$880$	−3018.61	−0.115633
$881$	17562.4	0.671613	0.335807	−	0.941931i	$-0.390991\pi$
$881$	17562.4	0.671613	0.335807	+	0.941931i	$0.390991\pi$
$882$	−101718.	−3.88326
$883$	41816.8	1.59371	0.796855	−	0.604170i	$-0.206495\pi$
$883$	41816.8	1.59371	0.796855	+	0.604170i	$0.206495\pi$
$884$	−60135.0	−2.28796
$885$	−2988.51	−0.113512
$886$	50188.5	1.90307
$887$	−20970.3	−0.793813	−0.396907	−	0.917859i	$-0.629916\pi$
$887$	−20970.3	−0.793813	−0.396907	+	0.917859i	$0.629916\pi$
$888$	4481.47	0.169356
$889$	16597.3	0.626160
$890$	−54896.0	−2.06755
$891$	6153.23	0.231359
$892$	39175.0	1.47049
$893$	11887.7	0.445471
$894$	−8383.64	−0.313636
$895$	−25084.6	−0.936855
$896$	−58196.3	−2.16987
$897$	−124153.	−4.62134
$898$	−43700.3	−1.62394
$899$	2796.00	0.103728
$900$	12657.2	0.468786
$901$	−45777.7	−1.69265
$902$	3078.47	0.113638
$903$	120127.	4.42698
$904$	−22497.6	−0.827720
$905$	−1229.22	−0.0451497
$906$	104171.	3.81993
$907$	−28887.2	−1.05753	−0.528766	−	0.848767i	$-0.677345\pi$
$907$	−28887.2	−1.05753	−0.528766	+	0.848767i	$0.677345\pi$
$908$	−65152.0	−2.38122
$909$	−32009.7	−1.16798
$910$	168186.	6.12671
$911$	34851.6	1.26749	0.633746	−	0.773541i	$-0.281516\pi$
$911$	34851.6	1.26749	0.633746	+	0.773541i	$0.281516\pi$
$912$	10746.5	0.390189
$913$	2118.38	0.0767887
$914$	−62224.3	−2.25186
$915$	64129.2	2.31699
$916$	37875.1	1.36619
$917$	79623.9	2.86741
$918$	3153.45	0.113376
$919$	35797.4	1.28493	0.642464	−	0.766316i	$-0.277912\pi$
$919$	35797.4	1.28493	0.642464	+	0.766316i	$0.277912\pi$
$920$	−35563.3	−1.27444
$921$	−40076.2	−1.43383
$922$	−61722.8	−2.20470
$923$	24423.7	0.870980
$924$	−25831.7	−0.919699
$925$	1599.47	0.0568544
$926$	2888.24	0.102498
$927$	−29259.1	−1.03667
$928$	21424.4	0.757855
$929$	9570.96	0.338012	0.169006	−	0.985615i	$-0.445944\pi$
$929$	9570.96	0.338012	0.169006	+	0.985615i	$0.445944\pi$
$930$	−12740.8	−0.449233
$931$	44542.8	1.56802
$932$	−34381.4	−1.20837
$933$	−20980.7	−0.736204
$934$	−31665.8	−1.10935
$935$	6952.84	0.243190
$936$	36913.6	1.28906
$937$	16673.1	0.581310	0.290655	−	0.956828i	$-0.406127\pi$
$937$	16673.1	0.581310	0.290655	+	0.956828i	$0.406127\pi$
$938$	137658.	4.79178
$939$	−22611.1	−0.785822
$940$	−31347.0	−1.08769
$941$	253.566	0.00878429	0.00439215	−	0.999990i	$-0.498602\pi$
$941$	253.566	0.00878429	0.00439215	+	0.999990i	$0.498602\pi$
$942$	38398.6	1.32813
$943$	−14714.3	−0.508127
$944$	819.110	0.0282413
$945$	−5170.71	−0.177993
$946$	18794.7	0.645948
$947$	−12494.5	−0.428740	−0.214370	−	0.976753i	$-0.568770\pi$
$947$	−12494.5	−0.428740	−0.214370	+	0.976753i	$0.568770\pi$
$948$	−64869.1	−2.22242
$949$	103453.	3.53871
$950$	−9453.98	−0.322871
$951$	31909.0	1.08804
$952$	30022.3	1.02209
$953$	1087.63	0.0369693	0.0184847	−	0.999829i	$-0.494116\pi$
$953$	1087.63	0.0369693	0.0184847	+	0.999829i	$0.494116\pi$
$954$	95476.2	3.24021
$955$	−22618.4	−0.766404
$956$	35377.9	1.19687
$957$	6187.12	0.208988
$958$	23541.9	0.793951
$959$	−56134.0	−1.89016
$960$	−77628.9	−2.60985
$961$	−28870.5	−0.969102
$962$	15849.2	0.531184
$963$	−14808.9	−0.495546
$964$	−1299.49	−0.0434168
$965$	−28733.3	−0.958504
$966$	210599.	7.01440
$967$	−17696.9	−0.588514	−0.294257	−	0.955726i	$-0.595072\pi$
$967$	−17696.9	−0.588514	−0.294257	+	0.955726i	$0.595072\pi$
$968$	18338.8	0.608918
$969$	−24752.7	−0.820611
$970$	49969.1	1.65403
$971$	−16328.8	−0.539666	−0.269833	−	0.962907i	$-0.586968\pi$
$971$	−16328.8	−0.539666	−0.269833	+	0.962907i	$0.586968\pi$
$972$	61405.7	2.02633
$973$	11109.2	0.366026
$974$	−83342.4	−2.74175
$975$	25614.5	0.841355
$976$	−17576.9	−0.576458
$977$	519.660	0.0170168	0.00850838	−	0.999964i	$-0.497292\pi$
$977$	519.660	0.0170168	0.00850838	+	0.999964i	$0.497292\pi$
$978$	26988.5	0.882410
$979$	8776.25	0.286507
$980$	−117457.	−3.82858
$981$	−39519.8	−1.28621
$982$	−2658.82	−0.0864015
$983$	−8932.98	−0.289845	−0.144923	−	0.989443i	$-0.546293\pi$
$983$	−8932.98	−0.289845	−0.144923	+	0.989443i	$0.546293\pi$
$984$	8505.75	0.275562
$985$	−4316.08	−0.139616
$986$	−24432.2	−0.789126
$987$	54634.6	1.76194
$988$	−54922.1	−1.76853
$989$	−89833.6	−2.88832
$990$	−14501.2	−0.465534
$991$	34629.6	1.11004	0.555018	−	0.831838i	$-0.312711\pi$
$991$	34629.6	1.11004	0.555018	+	0.831838i	$0.312711\pi$
$992$	7053.16	0.225744
$993$	26348.1	0.842027
$994$	−41429.6	−1.32200
$995$	−31504.7	−1.00378
$996$	19886.8	0.632667
$997$	−1299.62	−0.0412834	−0.0206417	−	0.999787i	$-0.506571\pi$
$997$	−1299.62	−0.0412834	−0.0206417	+	0.999787i	$0.506571\pi$
$998$	−4462.59	−0.141544
$999$	−487.269	−0.0154319

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	547.4.a.a.1.10	✓	65

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
547.4.a.a.1.10	✓	65	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:	\( N \)	\(=\)	\( 547 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	547.a (trivial)

\(f(q)\)	\(=\)	\(q-4.39733 q^{2} -7.45622 q^{3} +11.3366 q^{4} -12.8080 q^{5} +32.7875 q^{6} -33.9402 q^{7} -14.6719 q^{8} +28.5953 q^{9} +O(q^{10})\)	\(q-4.39733 q^{2} -7.45622 q^{3} +11.3366 q^{4} -12.8080 q^{5} +32.7875 q^{6} -33.9402 q^{7} -14.6719 q^{8} +28.5953 q^{9} +56.3210 q^{10} -9.00407 q^{11} -84.5279 q^{12} -87.9841 q^{13} +149.246 q^{14} +95.4993 q^{15} -26.1750 q^{16} +60.2896 q^{17} -125.743 q^{18} +55.0633 q^{19} -145.199 q^{20} +253.066 q^{21} +39.5939 q^{22} -189.249 q^{23} +109.397 q^{24} +39.0448 q^{25} +386.896 q^{26} -11.8947 q^{27} -384.765 q^{28} +92.1574 q^{29} -419.942 q^{30} +30.3394 q^{31} +232.476 q^{32} +67.1364 q^{33} -265.113 q^{34} +434.706 q^{35} +324.172 q^{36} +40.9651 q^{37} -242.132 q^{38} +656.029 q^{39} +187.918 q^{40} +77.7511 q^{41} -1112.81 q^{42} +474.686 q^{43} -102.075 q^{44} -366.248 q^{45} +832.190 q^{46} +215.891 q^{47} +195.167 q^{48} +808.938 q^{49} -171.693 q^{50} -449.532 q^{51} -997.436 q^{52} -759.297 q^{53} +52.3051 q^{54} +115.324 q^{55} +497.969 q^{56} -410.564 q^{57} -405.247 q^{58} -31.2936 q^{59} +1082.63 q^{60} +671.515 q^{61} -133.412 q^{62} -970.530 q^{63} -812.874 q^{64} +1126.90 q^{65} -295.221 q^{66} +922.352 q^{67} +683.476 q^{68} +1411.08 q^{69} -1911.55 q^{70} -277.592 q^{71} -419.548 q^{72} -1175.82 q^{73} -180.137 q^{74} -291.127 q^{75} +624.228 q^{76} +305.600 q^{77} -2884.78 q^{78} +767.428 q^{79} +335.249 q^{80} -683.383 q^{81} -341.897 q^{82} -235.269 q^{83} +2868.89 q^{84} -772.188 q^{85} -2087.35 q^{86} -687.146 q^{87} +132.107 q^{88} -974.698 q^{89} +1610.52 q^{90} +2986.20 q^{91} -2145.43 q^{92} -226.217 q^{93} -949.344 q^{94} -705.250 q^{95} -1733.39 q^{96} +887.219 q^{97} -3557.17 q^{98} -257.474 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 65 q - 12 q^{2} - 35 q^{3} + 234 q^{4} - 151 q^{5} - 60 q^{6} - 74 q^{7} - 144 q^{8} + 468 q^{9}+O(q^{10}) \) 65 * q - 12 * q^2 - 35 * q^3 + 234 * q^4 - 151 * q^5 - 60 * q^6 - 74 * q^7 - 144 * q^8 + 468 * q^9	\( 65 q - 12 q^{2} - 35 q^{3} + 234 q^{4} - 151 q^{5} - 60 q^{6} - 74 q^{7} - 144 q^{8} + 468 q^{9} - 60 q^{10} - 191 q^{11} - 483 q^{12} - 333 q^{13} - 377 q^{14} - 166 q^{15} + 818 q^{16} - 858 q^{17} - 279 q^{18} - 185 q^{19} - 1188 q^{20} - 406 q^{21} - 356 q^{22} - 836 q^{23} - 505 q^{24} + 1156 q^{25} - 696 q^{26} - 1094 q^{27} - 1096 q^{28} - 1209 q^{29} - 1054 q^{30} - 286 q^{31} - 1484 q^{32} - 1296 q^{33} - 763 q^{34} - 1374 q^{35} + 296 q^{36} - 1705 q^{37} - 2535 q^{38} - 622 q^{39} - 888 q^{40} - 1348 q^{41} - 1716 q^{42} - 973 q^{43} - 2568 q^{44} - 4529 q^{45} - 322 q^{46} - 2498 q^{47} - 5358 q^{48} + 2081 q^{49} - 2002 q^{50} - 1108 q^{51} - 3290 q^{52} - 5947 q^{53} - 2783 q^{54} - 1344 q^{55} - 5111 q^{56} - 3134 q^{57} - 1676 q^{58} - 1625 q^{59} - 2902 q^{60} - 3103 q^{61} - 5242 q^{62} - 3106 q^{63} + 1722 q^{64} - 3160 q^{65} - 3672 q^{66} - 2395 q^{67} - 8447 q^{68} - 4944 q^{69} - 597 q^{70} - 2654 q^{71} - 3929 q^{72} - 2116 q^{73} - 3969 q^{74} - 3759 q^{75} - 1844 q^{76} - 9938 q^{77} - 3935 q^{78} - 1206 q^{79} - 11619 q^{80} + 1889 q^{81} - 7674 q^{82} - 4337 q^{83} - 1873 q^{84} - 2624 q^{85} - 3543 q^{86} - 3066 q^{87} - 3689 q^{88} - 5774 q^{89} - 3149 q^{90} - 3148 q^{91} - 8942 q^{92} - 7118 q^{93} - 5137 q^{94} - 2742 q^{95} - 6558 q^{96} - 6378 q^{97} - 7250 q^{98} - 3941 q^{99}+O(q^{100}) \) 65 * q - 12 * q^2 - 35 * q^3 + 234 * q^4 - 151 * q^5 - 60 * q^6 - 74 * q^7 - 144 * q^8 + 468 * q^9 - 60 * q^10 - 191 * q^11 - 483 * q^12 - 333 * q^13 - 377 * q^14 - 166 * q^15 + 818 * q^16 - 858 * q^17 - 279 * q^18 - 185 * q^19 - 1188 * q^20 - 406 * q^21 - 356 * q^22 - 836 * q^23 - 505 * q^24 + 1156 * q^25 - 696 * q^26 - 1094 * q^27 - 1096 * q^28 - 1209 * q^29 - 1054 * q^30 - 286 * q^31 - 1484 * q^32 - 1296 * q^33 - 763 * q^34 - 1374 * q^35 + 296 * q^36 - 1705 * q^37 - 2535 * q^38 - 622 * q^39 - 888 * q^40 - 1348 * q^41 - 1716 * q^42 - 973 * q^43 - 2568 * q^44 - 4529 * q^45 - 322 * q^46 - 2498 * q^47 - 5358 * q^48 + 2081 * q^49 - 2002 * q^50 - 1108 * q^51 - 3290 * q^52 - 5947 * q^53 - 2783 * q^54 - 1344 * q^55 - 5111 * q^56 - 3134 * q^57 - 1676 * q^58 - 1625 * q^59 - 2902 * q^60 - 3103 * q^61 - 5242 * q^62 - 3106 * q^63 + 1722 * q^64 - 3160 * q^65 - 3672 * q^66 - 2395 * q^67 - 8447 * q^68 - 4944 * q^69 - 597 * q^70 - 2654 * q^71 - 3929 * q^72 - 2116 * q^73 - 3969 * q^74 - 3759 * q^75 - 1844 * q^76 - 9938 * q^77 - 3935 * q^78 - 1206 * q^79 - 11619 * q^80 + 1889 * q^81 - 7674 * q^82 - 4337 * q^83 - 1873 * q^84 - 2624 * q^85 - 3543 * q^86 - 3066 * q^87 - 3689 * q^88 - 5774 * q^89 - 3149 * q^90 - 3148 * q^91 - 8942 * q^92 - 7118 * q^93 - 5137 * q^94 - 2742 * q^95 - 6558 * q^96 - 6378 * q^97 - 7250 * q^98 - 3941 * q^99

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