LMFDB - Embedded newform 547.4.a.a.1.3

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			1.3
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)

$f(q)$	$=$	$q-5.47859 q^{2} -7.38039 q^{3} +22.0150 q^{4} -19.6221 q^{5} +40.4341 q^{6} +27.6127 q^{7} -76.7823 q^{8} +27.4701 q^{9} +O(q^{10})$	\(q-5.47859 q^{2} -7.38039 q^{3} +22.0150 q^{4} -19.6221 q^{5} +40.4341 q^{6} +27.6127 q^{7} -76.7823 q^{8} +27.4701 q^{9} +107.502 q^{10} -17.4771 q^{11} -162.479 q^{12} -65.3229 q^{13} -151.279 q^{14} +144.819 q^{15} +244.539 q^{16} -59.8854 q^{17} -150.498 q^{18} -12.3029 q^{19} -431.980 q^{20} -203.793 q^{21} +95.7500 q^{22} +9.99135 q^{23} +566.683 q^{24} +260.027 q^{25} +357.878 q^{26} -3.46981 q^{27} +607.893 q^{28} -59.1875 q^{29} -793.403 q^{30} -29.1625 q^{31} -725.471 q^{32} +128.988 q^{33} +328.088 q^{34} -541.820 q^{35} +604.754 q^{36} +169.384 q^{37} +67.4024 q^{38} +482.109 q^{39} +1506.63 q^{40} +477.714 q^{41} +1116.50 q^{42} -459.527 q^{43} -384.758 q^{44} -539.022 q^{45} -54.7385 q^{46} +364.853 q^{47} -1804.79 q^{48} +419.462 q^{49} -1424.58 q^{50} +441.977 q^{51} -1438.08 q^{52} +636.584 q^{53} +19.0097 q^{54} +342.938 q^{55} -2120.17 q^{56} +90.8000 q^{57} +324.264 q^{58} +157.467 q^{59} +3188.18 q^{60} +720.921 q^{61} +159.769 q^{62} +758.525 q^{63} +2018.25 q^{64} +1281.77 q^{65} -706.673 q^{66} -1075.27 q^{67} -1318.37 q^{68} -73.7400 q^{69} +2968.41 q^{70} +657.312 q^{71} -2109.22 q^{72} -224.369 q^{73} -927.987 q^{74} -1919.10 q^{75} -270.847 q^{76} -482.591 q^{77} -2641.28 q^{78} +1035.67 q^{79} -4798.37 q^{80} -716.085 q^{81} -2617.20 q^{82} -170.097 q^{83} -4486.49 q^{84} +1175.08 q^{85} +2517.56 q^{86} +436.826 q^{87} +1341.93 q^{88} -589.633 q^{89} +2953.08 q^{90} -1803.74 q^{91} +219.959 q^{92} +215.231 q^{93} -1998.88 q^{94} +241.408 q^{95} +5354.26 q^{96} -167.597 q^{97} -2298.06 q^{98} -480.099 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−5.47859	−1.93697	−0.968487	−	0.249063i	$-0.919877\pi$
$2$	−5.47859	−1.93697	−0.968487	+	0.249063i	$0.919877\pi$
$3$	−7.38039	−1.42036	−0.710178	−	0.704022i	$-0.751386\pi$
$3$	−7.38039	−1.42036	−0.710178	+	0.704022i	$0.751386\pi$
$4$	22.0150	2.75187
$5$	−19.6221	−1.75505	−0.877527	−	0.479527i	$-0.840808\pi$
$5$	−19.6221	−1.75505	−0.877527	+	0.479527i	$0.840808\pi$
$6$	40.4341	2.75119
$7$	27.6127	1.49095	0.745473	−	0.666535i	$-0.232223\pi$
$7$	27.6127	1.49095	0.745473	+	0.666535i	$0.232223\pi$
$8$	−76.7823	−3.39333
$9$	27.4701	1.01741
$10$	107.502	3.39950
$11$	−17.4771	−0.479050	−0.239525	−	0.970890i	$-0.576992\pi$
$11$	−17.4771	−0.479050	−0.239525	+	0.970890i	$0.576992\pi$
$12$	−162.479	−3.90864
$13$	−65.3229	−1.39364	−0.696820	−	0.717246i	$-0.745402\pi$
$13$	−65.3229	−1.39364	−0.696820	+	0.717246i	$0.745402\pi$
$14$	−151.279	−2.88793
$15$	144.819	2.49280
$16$	244.539	3.82092
$17$	−59.8854	−0.854373	−0.427186	−	0.904164i	$-0.640495\pi$
$17$	−59.8854	−0.854373	−0.427186	+	0.904164i	$0.640495\pi$
$18$	−150.498	−1.97070
$19$	−12.3029	−0.148551	−0.0742756	−	0.997238i	$-0.523664\pi$
$19$	−12.3029	−0.148551	−0.0742756	+	0.997238i	$0.523664\pi$
$20$	−431.980	−4.82968
$21$	−203.793	−2.11768
$22$	95.7500	0.927908
$23$	9.99135	0.0905800	0.0452900	−	0.998974i	$-0.485579\pi$
$23$	9.99135	0.0905800	0.0452900	+	0.998974i	$0.485579\pi$
$24$	566.683	4.81974
$25$	260.027	2.08022
$26$	357.878	2.69945
$27$	−3.46981	−0.0247321
$28$	607.893	4.10289
$29$	−59.1875	−0.378994	−0.189497	−	0.981881i	$-0.560686\pi$
$29$	−59.1875	−0.378994	−0.189497	+	0.981881i	$0.560686\pi$
$30$	−793.403	−4.82850
$31$	−29.1625	−0.168959	−0.0844797	−	0.996425i	$-0.526923\pi$
$31$	−29.1625	−0.168959	−0.0844797	+	0.996425i	$0.526923\pi$
$32$	−725.471	−4.00770
$33$	128.988	0.680422
$34$	328.088	1.65490
$35$	−541.820	−2.61669
$36$	604.754	2.79979
$37$	169.384	0.752611	0.376306	−	0.926496i	$-0.377194\pi$
$37$	169.384	0.752611	0.376306	+	0.926496i	$0.377194\pi$
$38$	67.4024	0.287740
$39$	482.109	1.97947
$40$	1506.63	5.95548
$41$	477.714	1.81967	0.909835	−	0.414971i	$-0.136208\pi$
$41$	477.714	1.81967	0.909835	+	0.414971i	$0.136208\pi$
$42$	1116.50	4.10188
$43$	−459.527	−1.62970	−0.814852	−	0.579669i	$-0.803182\pi$
$43$	−459.527	−1.62970	−0.814852	+	0.579669i	$0.803182\pi$
$44$	−384.758	−1.31828
$45$	−539.022	−1.78561
$46$	−54.7385	−0.175451
$47$	364.853	1.13233	0.566163	−	0.824293i	$-0.308427\pi$
$47$	364.853	1.13233	0.566163	+	0.824293i	$0.308427\pi$
$48$	−1804.79	−5.42707
$49$	419.462	1.22292
$50$	−1424.58	−4.02933
$51$	441.977	1.21351
$52$	−1438.08	−3.83512
$53$	636.584	1.64984	0.824920	−	0.565250i	$-0.191220\pi$
$53$	636.584	1.64984	0.824920	+	0.565250i	$0.191220\pi$
$54$	19.0097	0.0479054
$55$	342.938	0.840759
$56$	−2120.17	−5.05927
$57$	90.8000	0.210996
$58$	324.264	0.734102
$59$	157.467	0.347465	0.173732	−	0.984793i	$-0.444417\pi$
$59$	157.467	0.347465	0.173732	+	0.984793i	$0.444417\pi$
$60$	3188.18	6.85987
$61$	720.921	1.51319	0.756594	−	0.653885i	$-0.226862\pi$
$61$	720.921	1.51319	0.756594	+	0.653885i	$0.226862\pi$
$62$	159.769	0.327270
$63$	758.525	1.51691
$64$	2018.25	3.94189
$65$	1281.77	2.44592
$66$	−706.673	−1.31796
$67$	−1075.27	−1.96068	−0.980338	−	0.197325i	$-0.936775\pi$
$67$	−1075.27	−1.96068	−0.980338	+	0.197325i	$0.936775\pi$
$68$	−1318.37	−2.35112
$69$	−73.7400	−0.128656
$70$	2968.41	5.06847
$71$	657.312	1.09871	0.549356	−	0.835588i	$-0.314873\pi$
$71$	657.312	1.09871	0.549356	+	0.835588i	$0.314873\pi$
$72$	−2109.22	−3.45242
$73$	−224.369	−0.359732	−0.179866	−	0.983691i	$-0.557566\pi$
$73$	−224.369	−0.359732	−0.179866	+	0.983691i	$0.557566\pi$
$74$	−927.987	−1.45779
$75$	−1919.10	−2.95465
$76$	−270.847	−0.408794
$77$	−482.591	−0.714238
$78$	−2641.28	−3.83418
$79$	1035.67	1.47497	0.737483	−	0.675366i	$-0.236014\pi$
$79$	1035.67	1.47497	0.737483	+	0.675366i	$0.236014\pi$
$80$	−4798.37	−6.70592
$81$	−716.085	−0.982284
$82$	−2617.20	−3.52465
$83$	−170.097	−0.224947	−0.112473	−	0.993655i	$-0.535877\pi$
$83$	−170.097	−0.224947	−0.112473	+	0.993655i	$0.535877\pi$
$84$	−4486.49	−5.82757
$85$	1175.08	1.49947
$86$	2517.56	3.15669
$87$	436.826	0.538307
$88$	1341.93	1.62557
$89$	−589.633	−0.702258	−0.351129	−	0.936327i	$-0.614202\pi$
$89$	−589.633	−0.702258	−0.351129	+	0.936327i	$0.614202\pi$
$90$	2953.08	3.45869
$91$	−1803.74	−2.07784
$92$	219.959	0.249264
$93$	215.231	0.239982
$94$	−1998.88	−2.19329
$95$	241.408	0.260715
$96$	5354.26	5.69236
$97$	−167.597	−0.175432	−0.0877162	−	0.996146i	$-0.527957\pi$
$97$	−167.597	−0.175432	−0.0877162	+	0.996146i	$0.527957\pi$
$98$	−2298.06	−2.36877
$99$	−480.099	−0.487392
$100$	5724.49	5.72449
$101$	−24.3432	−0.0239826	−0.0119913	−	0.999928i	$-0.503817\pi$
$101$	−24.3432	−0.0239826	−0.0119913	+	0.999928i	$0.503817\pi$
$102$	−2421.41	−2.35055
$103$	−1568.26	−1.50025	−0.750124	−	0.661297i	$-0.770006\pi$
$103$	−1568.26	−1.50025	−0.750124	+	0.661297i	$0.770006\pi$
$104$	5015.64	4.72908
$105$	3998.84	3.71664
$106$	−3487.58	−3.19570
$107$	93.3967	0.0843832	0.0421916	−	0.999110i	$-0.486566\pi$
$107$	93.3967	0.0843832	0.0421916	+	0.999110i	$0.486566\pi$
$108$	−76.3878	−0.0680594
$109$	1522.82	1.33816	0.669080	−	0.743190i	$-0.266688\pi$
$109$	1522.82	1.33816	0.669080	+	0.743190i	$0.266688\pi$
$110$	−1878.82	−1.62853
$111$	−1250.12	−1.06898
$112$	6752.39	5.69679
$113$	−94.2707	−0.0784800	−0.0392400	−	0.999230i	$-0.512494\pi$
$113$	−94.2707	−0.0784800	−0.0392400	+	0.999230i	$0.512494\pi$
$114$	−497.456	−0.408693
$115$	−196.051	−0.158973
$116$	−1303.01	−1.04294
$117$	−1794.43	−1.41791
$118$	−862.696	−0.673031
$119$	−1653.60	−1.27382
$120$	−11119.5	−8.45890
$121$	−1025.55	−0.770511
$122$	−3949.63	−2.93101
$123$	−3525.72	−2.58458
$124$	−642.011	−0.464954
$125$	−2649.52	−1.89584
$126$	−4155.65	−2.93821
$127$	2182.70	1.52506	0.762532	−	0.646950i	$-0.223956\pi$
$127$	2182.70	1.52506	0.762532	+	0.646950i	$0.223956\pi$
$128$	−5253.38	−3.62764
$129$	3391.49	2.31476
$130$	−7022.32	−4.73768
$131$	−1312.97	−0.875683	−0.437842	−	0.899052i	$-0.644257\pi$
$131$	−1312.97	−0.875683	−0.437842	+	0.899052i	$0.644257\pi$
$132$	2839.67	1.87243
$133$	−339.716	−0.221482
$134$	5890.97	3.79778
$135$	68.0850	0.0434061
$136$	4598.14	2.89917
$137$	416.714	0.259871	0.129935	−	0.991522i	$-0.458523\pi$
$137$	416.714	0.259871	0.129935	+	0.991522i	$0.458523\pi$
$138$	403.991	0.249203
$139$	−241.875	−0.147594	−0.0737971	−	0.997273i	$-0.523512\pi$
$139$	−241.875	−0.147594	−0.0737971	+	0.997273i	$0.523512\pi$
$140$	−11928.1	−7.20080
$141$	−2692.76	−1.60831
$142$	−3601.15	−2.12818
$143$	1141.66	0.667624
$144$	6717.52	3.88745
$145$	1161.38	0.665156
$146$	1229.23	0.696792
$147$	−3095.80	−1.73699
$148$	3728.99	2.07109
$149$	−368.680	−0.202708	−0.101354	−	0.994850i	$-0.532317\pi$
$149$	−368.680	−0.202708	−0.101354	+	0.994850i	$0.532317\pi$
$150$	10514.0	5.72308
$151$	−1663.40	−0.896458	−0.448229	−	0.893919i	$-0.647945\pi$
$151$	−1663.40	−0.896458	−0.448229	+	0.893919i	$0.647945\pi$
$152$	944.643	0.504083
$153$	−1645.06	−0.869250
$154$	2643.92	1.38346
$155$	572.230	0.296533
$156$	10613.6	5.44723
$157$	−380.465	−0.193404	−0.0967019	−	0.995313i	$-0.530829\pi$
$157$	−380.465	−0.193404	−0.0967019	+	0.995313i	$0.530829\pi$
$158$	−5674.03	−2.85697
$159$	−4698.24	−2.34336
$160$	14235.3	7.03373
$161$	275.888	0.135050
$162$	3923.14	1.90266
$163$	−1067.08	−0.512763	−0.256381	−	0.966576i	$-0.582530\pi$
$163$	−1067.08	−0.512763	−0.256381	+	0.966576i	$0.582530\pi$
$164$	10516.9	5.00750
$165$	−2531.02	−1.19418
$166$	931.893	0.435716
$167$	3691.27	1.71041	0.855207	−	0.518286i	$-0.173430\pi$
$167$	3691.27	1.71041	0.855207	+	0.518286i	$0.173430\pi$
$168$	15647.7	7.18597
$169$	2070.09	0.942234
$170$	−6437.77	−2.90444
$171$	−337.962	−0.151138
$172$	−10116.5	−4.48473
$173$	−4145.60	−1.82187	−0.910936	−	0.412548i	$-0.864639\pi$
$173$	−4145.60	−1.82187	−0.910936	+	0.412548i	$0.864639\pi$
$174$	−2393.19	−1.04269
$175$	7180.06	3.10149
$176$	−4273.84	−1.83041
$177$	−1162.17	−0.493524
$178$	3230.36	1.36026
$179$	3328.76	1.38996	0.694982	−	0.719027i	$-0.255412\pi$
$179$	3328.76	1.38996	0.694982	+	0.719027i	$0.255412\pi$
$180$	−11866.6	−4.91378
$181$	2355.11	0.967149	0.483575	−	0.875303i	$-0.339338\pi$
$181$	2355.11	0.967149	0.483575	+	0.875303i	$0.339338\pi$
$182$	9881.98	4.02473
$183$	−5320.67	−2.14927
$184$	−767.158	−0.307368
$185$	−3323.68	−1.32087
$186$	−1179.16	−0.464840
$187$	1046.62	0.409288
$188$	8032.23	3.11602
$189$	−95.8110	−0.0368742
$190$	−1322.58	−0.504999
$191$	1728.33	0.654750	0.327375	−	0.944894i	$-0.393836\pi$
$191$	1728.33	0.654750	0.327375	+	0.944894i	$0.393836\pi$
$192$	−14895.4	−5.59889
$193$	−610.508	−0.227696	−0.113848	−	0.993498i	$-0.536318\pi$
$193$	−610.508	−0.227696	−0.113848	+	0.993498i	$0.536318\pi$
$194$	918.198	0.339808
$195$	−9459.99	−3.47407
$196$	9234.45	3.36532
$197$	2842.12	1.02788	0.513941	−	0.857825i	$-0.328185\pi$
$197$	2842.12	1.02788	0.513941	+	0.857825i	$0.328185\pi$
$198$	2630.27	0.944065
$199$	1052.98	0.375095	0.187548	−	0.982255i	$-0.439946\pi$
$199$	1052.98	0.375095	0.187548	+	0.982255i	$0.439946\pi$
$200$	−19965.5	−7.05886
$201$	7935.92	2.78486
$202$	133.366	0.0464536
$203$	−1634.33	−0.565060
$204$	9730.12	3.33943
$205$	−9373.76	−3.19362
$206$	8591.88	2.90594
$207$	274.464	0.0921572
$208$	−15974.0	−5.32499
$209$	215.019	0.0711635
$210$	−21908.0	−7.19903
$211$	2520.45	0.822344	0.411172	−	0.911558i	$-0.365120\pi$
$211$	2520.45	0.822344	0.411172	+	0.911558i	$0.365120\pi$
$212$	14014.4	4.54015
$213$	−4851.22	−1.56056
$214$	−511.682	−0.163448
$215$	9016.89	2.86022
$216$	266.420	0.0839240
$217$	−805.256	−0.251909
$218$	−8342.89	−2.59198
$219$	1655.93	0.510948
$220$	7549.77	2.31366
$221$	3911.89	1.19069
$222$	6848.91	2.07058
$223$	−3327.38	−0.999183	−0.499592	−	0.866261i	$-0.666517\pi$
$223$	−3327.38	−0.999183	−0.499592	+	0.866261i	$0.666517\pi$
$224$	−20032.2	−5.97526
$225$	7142.98	2.11644
$226$	516.471	0.152014
$227$	3976.21	1.16260	0.581300	−	0.813689i	$-0.302544\pi$
$227$	3976.21	1.16260	0.581300	+	0.813689i	$0.302544\pi$
$228$	1998.96	0.580633
$229$	−3979.50	−1.14835	−0.574176	−	0.818732i	$-0.694677\pi$
$229$	−3979.50	−1.14835	−0.574176	+	0.818732i	$0.694677\pi$
$230$	1074.08	0.307926
$231$	3561.71	1.01447
$232$	4544.55	1.28605
$233$	1496.33	0.420721	0.210360	−	0.977624i	$-0.432536\pi$
$233$	1496.33	0.420721	0.210360	+	0.977624i	$0.432536\pi$
$234$	9830.95	2.74645
$235$	−7159.19	−1.98729
$236$	3466.63	0.956179
$237$	−7643.67	−2.09498
$238$	9059.39	2.46737
$239$	−5964.64	−1.61431	−0.807155	−	0.590339i	$-0.798994\pi$
$239$	−5964.64	−1.61431	−0.807155	+	0.590339i	$0.798994\pi$
$240$	35413.8	9.52480
$241$	−2761.22	−0.738031	−0.369016	−	0.929423i	$-0.620305\pi$
$241$	−2761.22	−0.738031	−0.369016	+	0.929423i	$0.620305\pi$
$242$	5618.57	1.49246
$243$	5378.67	1.41993
$244$	15871.0	4.16410
$245$	−8230.74	−2.14630
$246$	19316.0	5.00627
$247$	803.660	0.207027
$248$	2239.16	0.573335
$249$	1255.38	0.319505
$250$	14515.6	3.67219
$251$	−3420.79	−0.860234	−0.430117	−	0.902773i	$-0.641528\pi$
$251$	−3420.79	−0.860234	−0.430117	+	0.902773i	$0.641528\pi$
$252$	16698.9	4.17433
$253$	−174.620	−0.0433924
$254$	−11958.1	−2.95401
$255$	−8672.53	−2.12978
$256$	12635.2	3.08476
$257$	−7317.62	−1.77611	−0.888055	−	0.459737i	$-0.847944\pi$
$257$	−7317.62	−1.77611	−0.888055	+	0.459737i	$0.847944\pi$
$258$	−18580.6	−4.48363
$259$	4677.16	1.12210
$260$	28218.2	6.73084
$261$	−1625.89	−0.385594
$262$	7193.21	1.69618
$263$	−6340.49	−1.48658	−0.743291	−	0.668968i	$-0.766736\pi$
$263$	−6340.49	−1.48658	−0.743291	+	0.668968i	$0.766736\pi$
$264$	−9903.99	−2.30890
$265$	−12491.1	−2.89556
$266$	1861.16	0.429005
$267$	4351.72	0.997456
$268$	−23672.1	−5.39553
$269$	1453.72	0.329497	0.164748	−	0.986336i	$-0.447319\pi$
$269$	1453.72	0.329497	0.164748	+	0.986336i	$0.447319\pi$
$270$	−373.010	−0.0840766
$271$	127.091	0.0284880	0.0142440	−	0.999899i	$-0.495466\pi$
$271$	127.091	0.0284880	0.0142440	+	0.999899i	$0.495466\pi$
$272$	−14644.3	−3.26449
$273$	13312.3	2.95128
$274$	−2283.01	−0.503363
$275$	−4544.53	−0.996528
$276$	−1623.38	−0.354044
$277$	−4202.08	−0.911474	−0.455737	−	0.890114i	$-0.650624\pi$
$277$	−4202.08	−0.911474	−0.455737	+	0.890114i	$0.650624\pi$
$278$	1325.14	0.285886
$279$	−801.098	−0.171901
$280$	41602.1	8.87930
$281$	1191.51	0.252953	0.126476	−	0.991970i	$-0.459633\pi$
$281$	1191.51	0.252953	0.126476	+	0.991970i	$0.459633\pi$
$282$	14752.5	3.11525
$283$	5011.85	1.05273	0.526366	−	0.850258i	$-0.323554\pi$
$283$	5011.85	1.05273	0.526366	+	0.850258i	$0.323554\pi$
$284$	14470.7	3.02352
$285$	−1781.69	−0.370309
$286$	−6254.68	−1.29317
$287$	13191.0	2.71303
$288$	−19928.8	−4.07748
$289$	−1326.74	−0.270047
$290$	−6362.74	−1.28839
$291$	1236.93	0.249176
$292$	−4939.48	−0.989937
$293$	−4804.38	−0.957934	−0.478967	−	0.877833i	$-0.658989\pi$
$293$	−4804.38	−0.957934	−0.478967	+	0.877833i	$0.658989\pi$
$294$	16960.6	3.36450
$295$	−3089.83	−0.609820
$296$	−13005.7	−2.55386
$297$	60.6424	0.0118479
$298$	2019.85	0.392639
$299$	−652.664	−0.126236
$300$	−42248.9	−8.13081
$301$	−12688.8	−2.42980
$302$	9113.06	1.73642
$303$	179.662	0.0340638
$304$	−3008.53	−0.567602
$305$	−14146.0	−2.65573
$306$	9012.61	1.68371
$307$	8.76668	0.00162978	0.000814888	−	1.00000i	$-0.499741\pi$
$307$	8.76668	0.00162978	0.000814888		1.00000i	$0.499741\pi$
$308$	−10624.2	−1.96549
$309$	11574.4	2.13089
$310$	−3135.01	−0.574377
$311$	−5239.44	−0.955310	−0.477655	−	0.878548i	$-0.658513\pi$
$311$	−5239.44	−0.955310	−0.477655	+	0.878548i	$0.658513\pi$
$312$	−37017.4	−6.71698
$313$	−1740.50	−0.314310	−0.157155	−	0.987574i	$-0.550232\pi$
$313$	−1740.50	−0.314310	−0.157155	+	0.987574i	$0.550232\pi$
$314$	2084.41	0.374618
$315$	−14883.9	−2.66226
$316$	22800.3	4.05891
$317$	1879.73	0.333049	0.166524	−	0.986037i	$-0.446746\pi$
$317$	1879.73	0.333049	0.166524	+	0.986037i	$0.446746\pi$
$318$	25739.7	4.53903
$319$	1034.43	0.181557
$320$	−39602.3	−6.91823
$321$	−689.304	−0.119854
$322$	−1511.48	−0.261588
$323$	736.762	0.126918
$324$	−15764.6	−2.70312
$325$	−16985.7	−2.89907
$326$	5846.11	0.993208
$327$	−11239.0	−1.90066
$328$	−36680.0	−6.17474
$329$	10074.6	1.68824
$330$	13866.4	2.31309
$331$	−2957.76	−0.491158	−0.245579	−	0.969377i	$-0.578978\pi$
$331$	−2957.76	−0.491158	−0.245579	+	0.969377i	$0.578978\pi$
$332$	−3744.68	−0.619025
$333$	4653.01	0.765716
$334$	−20223.0	−3.31303
$335$	21099.1	3.44109
$336$	−49835.2	−8.09147
$337$	6640.87	1.07345	0.536723	−	0.843759i	$-0.319662\pi$
$337$	6640.87	1.07345	0.536723	+	0.843759i	$0.319662\pi$
$338$	−11341.2	−1.82508
$339$	695.755	0.111470
$340$	25869.3	4.12635
$341$	509.677	0.0809400
$342$	1851.55	0.292750
$343$	2111.33	0.332365
$344$	35283.5	5.53012
$345$	1446.93	0.225798
$346$	22712.0	3.52892
$347$	−6615.49	−1.02345	−0.511727	−	0.859148i	$-0.670994\pi$
$347$	−6615.49	−1.02345	−0.511727	+	0.859148i	$0.670994\pi$
$348$	9616.72	1.48135
$349$	−2782.72	−0.426807	−0.213403	−	0.976964i	$-0.568455\pi$
$349$	−2782.72	−0.426807	−0.213403	+	0.976964i	$0.568455\pi$
$350$	−39336.6	−6.00751
$351$	226.658	0.0344676
$352$	12679.1	1.91989
$353$	−7975.52	−1.20253	−0.601266	−	0.799049i	$-0.705337\pi$
$353$	−7975.52	−1.20253	−0.601266	+	0.799049i	$0.705337\pi$
$354$	6367.03	0.955944
$355$	−12897.9	−1.92830
$356$	−12980.7	−1.93252
$357$	12204.2	1.80928
$358$	−18236.9	−2.69232
$359$	5182.19	0.761854	0.380927	−	0.924605i	$-0.375605\pi$
$359$	5182.19	0.761854	0.380927	+	0.924605i	$0.375605\pi$
$360$	41387.3	6.05918
$361$	−6707.64	−0.977933
$362$	−12902.7	−1.87334
$363$	7568.96	1.09440
$364$	−39709.4	−5.71796
$365$	4402.60	0.631350
$366$	29149.8	4.16307
$367$	−3448.66	−0.490513	−0.245257	−	0.969458i	$-0.578872\pi$
$367$	−3448.66	−0.490513	−0.245257	+	0.969458i	$0.578872\pi$
$368$	2443.27	0.346099
$369$	13122.9	1.85135
$370$	18209.1	2.55850
$371$	17577.8	2.45982
$372$	4738.29	0.660401
$373$	2756.65	0.382665	0.191332	−	0.981525i	$-0.438719\pi$
$373$	2756.65	0.382665	0.191332	+	0.981525i	$0.438719\pi$
$374$	−5734.03	−0.792780
$375$	19554.5	2.69277
$376$	−28014.3	−3.84236
$377$	3866.30	0.528182
$378$	524.909	0.0714244
$379$	1870.16	0.253466	0.126733	−	0.991937i	$-0.459551\pi$
$379$	1870.16	0.253466	0.126733	+	0.991937i	$0.459551\pi$
$380$	5314.60	0.717455
$381$	−16109.2	−2.16614
$382$	−9468.79	−1.26823
$383$	−10799.1	−1.44075	−0.720376	−	0.693584i	$-0.756031\pi$
$383$	−10799.1	−1.44075	−0.720376	+	0.693584i	$0.756031\pi$
$384$	38772.0	5.15254
$385$	9469.45	1.25353
$386$	3344.72	0.441041
$387$	−12623.3	−1.65808
$388$	−3689.65	−0.482767
$389$	11287.6	1.47123	0.735613	−	0.677403i	$-0.236894\pi$
$389$	11287.6	1.47123	0.735613	+	0.677403i	$0.236894\pi$
$390$	51827.4	6.72919
$391$	−598.336	−0.0773891
$392$	−32207.3	−4.14978
$393$	9690.21	1.24378
$394$	−15570.8	−1.99098
$395$	−20322.1	−2.58865
$396$	−10569.4	−1.34124
$397$	9004.51	1.13835	0.569173	−	0.822218i	$-0.307263\pi$
$397$	9004.51	1.13835	0.569173	+	0.822218i	$0.307263\pi$
$398$	−5768.86	−0.726550
$399$	2507.24	0.314583
$400$	63586.7	7.94834
$401$	−2752.41	−0.342765	−0.171383	−	0.985205i	$-0.554823\pi$
$401$	−2752.41	−0.342765	−0.171383	+	0.985205i	$0.554823\pi$
$402$	−43477.7	−5.39420
$403$	1904.98	0.235469
$404$	−535.915	−0.0659969
$405$	14051.1	1.72396
$406$	8953.81	1.09451
$407$	−2960.35	−0.360538
$408$	−33936.0	−4.11785
$409$	2560.59	0.309567	0.154784	−	0.987948i	$-0.450532\pi$
$409$	2560.59	0.309567	0.154784	+	0.987948i	$0.450532\pi$
$410$	51355.0	6.18596
$411$	−3075.51	−0.369109
$412$	−34525.3	−4.12849
$413$	4348.09	0.518052
$414$	−1503.67	−0.178506
$415$	3337.66	0.394794
$416$	47389.9	5.58529
$417$	1785.13	0.209636
$418$	−1178.00	−0.137842
$419$	−5247.97	−0.611886	−0.305943	−	0.952050i	$-0.598972\pi$
$419$	−5247.97	−0.611886	−0.305943	+	0.952050i	$0.598972\pi$
$420$	88034.3	10.2277
$421$	12496.9	1.44670	0.723350	−	0.690481i	$-0.242601\pi$
$421$	12496.9	1.44670	0.723350	+	0.690481i	$0.242601\pi$
$422$	−13808.5	−1.59286
$423$	10022.6	1.15204
$424$	−48878.3	−5.59845
$425$	−15571.8	−1.77728
$426$	26577.9	3.02277
$427$	19906.6	2.25608
$428$	2056.13	0.232212
$429$	−8425.88	−0.948264
$430$	−49399.9	−5.54017
$431$	2671.24	0.298536	0.149268	−	0.988797i	$-0.452308\pi$
$431$	2671.24	0.298536	0.149268	+	0.988797i	$0.452308\pi$
$432$	−848.504	−0.0944992
$433$	5144.30	0.570946	0.285473	−	0.958387i	$-0.407849\pi$
$433$	5144.30	0.570946	0.285473	+	0.958387i	$0.407849\pi$
$434$	4411.67	0.487942
$435$	−8571.46	−0.944758
$436$	33524.8	3.68244
$437$	−122.922	−0.0134558
$438$	−9072.18	−0.989693
$439$	−7335.74	−0.797530	−0.398765	−	0.917053i	$-0.630561\pi$
$439$	−7335.74	−0.797530	−0.398765	+	0.917053i	$0.630561\pi$
$440$	−26331.6	−2.85297
$441$	11522.7	1.24422
$442$	−21431.6	−2.30633
$443$	2823.15	0.302781	0.151390	−	0.988474i	$-0.451625\pi$
$443$	2823.15	0.302781	0.151390	+	0.988474i	$0.451625\pi$
$444$	−27521.4	−2.94168
$445$	11569.8	1.23250
$446$	18229.4	1.93539
$447$	2721.00	0.287917
$448$	55729.3	5.87714
$449$	−9905.06	−1.04109	−0.520544	−	0.853835i	$-0.674271\pi$
$449$	−9905.06	−1.04109	−0.520544	+	0.853835i	$0.674271\pi$
$450$	−39133.5	−4.09949
$451$	−8349.08	−0.871713
$452$	−2075.37	−0.215967
$453$	12276.5	1.27329
$454$	−21784.0	−2.25193
$455$	35393.3	3.64673
$456$	−6971.83	−0.715978
$457$	5225.67	0.534894	0.267447	−	0.963573i	$-0.413820\pi$
$457$	5225.67	0.534894	0.267447	+	0.963573i	$0.413820\pi$
$458$	21802.0	2.22433
$459$	207.791	0.0211304
$460$	−4316.06	−0.437473
$461$	9005.11	0.909783	0.454891	−	0.890547i	$-0.349678\pi$
$461$	9005.11	0.909783	0.454891	+	0.890547i	$0.349678\pi$
$462$	−19513.2	−1.96501
$463$	11875.9	1.19205	0.596025	−	0.802966i	$-0.296746\pi$
$463$	11875.9	1.19205	0.596025	+	0.802966i	$0.296746\pi$
$464$	−14473.6	−1.44811
$465$	−4223.28	−0.421182
$466$	−8197.79	−0.814926
$467$	−10771.2	−1.06731	−0.533654	−	0.845703i	$-0.679182\pi$
$467$	−10771.2	−1.06731	−0.533654	+	0.845703i	$0.679182\pi$
$468$	−39504.3	−3.90190
$469$	−29691.2	−2.92326
$470$	39222.3	3.84934
$471$	2807.98	0.274702
$472$	−12090.7	−1.17906
$473$	8031.22	0.780710
$474$	41876.5	4.05792
$475$	−3199.08	−0.309019
$476$	−36403.9	−3.50540
$477$	17487.0	1.67857
$478$	32677.8	3.12688
$479$	−7469.77	−0.712532	−0.356266	−	0.934385i	$-0.615950\pi$
$479$	−7469.77	−0.712532	−0.356266	+	0.934385i	$0.615950\pi$
$480$	−105062.	−9.99040
$481$	−11064.7	−1.04887
$482$	15127.6	1.42955
$483$	−2036.16	−0.191819
$484$	−22577.4	−2.12035
$485$	3288.61	0.307893
$486$	−29467.5	−2.75036
$487$	2333.48	0.217125	0.108563	−	0.994090i	$-0.465375\pi$
$487$	2333.48	0.217125	0.108563	+	0.994090i	$0.465375\pi$
$488$	−55353.9	−5.13474
$489$	7875.48	0.728306
$490$	45092.8	4.15732
$491$	−9389.19	−0.862990	−0.431495	−	0.902115i	$-0.642014\pi$
$491$	−9389.19	−0.862990	−0.431495	+	0.902115i	$0.642014\pi$
$492$	−77618.6	−7.11243
$493$	3544.46	0.323802
$494$	−4402.92	−0.401006
$495$	9420.56	0.855399
$496$	−7131.37	−0.645580
$497$	18150.2	1.63812
$498$	−6877.73	−0.618873
$499$	9660.33	0.866645	0.433322	−	0.901239i	$-0.357341\pi$
$499$	9660.33	0.866645	0.433322	+	0.901239i	$0.357341\pi$
$500$	−58329.0	−5.21710
$501$	−27243.0	−2.42940
$502$	18741.1	1.66625
$503$	−20626.6	−1.82842	−0.914210	−	0.405241i	$-0.867188\pi$
$503$	−20626.6	−1.82842	−0.914210	+	0.405241i	$0.867188\pi$
$504$	−58241.3	−5.14737
$505$	477.665	0.0420907
$506$	956.672	0.0840499
$507$	−15278.0	−1.33831
$508$	48052.0	4.19678
$509$	−6328.89	−0.551126	−0.275563	−	0.961283i	$-0.588864\pi$
$509$	−6328.89	−0.551126	−0.275563	+	0.961283i	$0.588864\pi$
$510$	47513.2	4.12534
$511$	−6195.45	−0.536342
$512$	−27195.8	−2.34746
$513$	42.6887	0.00367398
$514$	40090.2	3.44028
$515$	30772.6	2.63302
$516$	74663.5	6.36992
$517$	−6376.59	−0.542441
$518$	−25624.3	−2.17348
$519$	30596.1	2.58771
$520$	−98417.5	−8.29979
$521$	−19477.9	−1.63790	−0.818949	−	0.573867i	$-0.805443\pi$
$521$	−19477.9	−1.63790	−0.818949	+	0.573867i	$0.805443\pi$
$522$	8907.57	0.746885
$523$	16695.1	1.39585	0.697923	−	0.716173i	$-0.254108\pi$
$523$	16695.1	1.39585	0.697923	+	0.716173i	$0.254108\pi$
$524$	−28904.9	−2.40977
$525$	−52991.6	−4.40523
$526$	34736.9	2.87947
$527$	1746.41	0.144354
$528$	31542.6	2.59984
$529$	−12067.2	−0.991795
$530$	68433.7	5.60862
$531$	4325.64	0.353515
$532$	−7478.83	−0.609490
$533$	−31205.7	−2.53597
$534$	−23841.3	−1.93205
$535$	−1832.64	−0.148097
$536$	82561.8	6.65322
$537$	−24567.6	−1.97424
$538$	−7964.32	−0.638227
$539$	−7331.00	−0.585841
$540$	1498.89	0.119448
$541$	8273.48	0.657494	0.328747	−	0.944418i	$-0.393374\pi$
$541$	8273.48	0.657494	0.328747	+	0.944418i	$0.393374\pi$
$542$	−696.281	−0.0551805
$543$	−17381.6	−1.37370
$544$	43445.1	3.42407
$545$	−29880.9	−2.34854
$546$	−72932.8	−5.71655
$547$	547.000	0.0427569
$547$	547.000	0.0427569
$548$	9173.95	0.715131
$549$	19803.8	1.53954
$550$	24897.6	1.93025
$551$	728.176	0.0563001
$552$	5661.93	0.436572
$553$	28597.7	2.19910
$554$	23021.5	1.76550
$555$	24530.0	1.87611
$556$	−5324.88	−0.406160
$557$	4214.08	0.320568	0.160284	−	0.987071i	$-0.448759\pi$
$557$	4214.08	0.320568	0.160284	+	0.987071i	$0.448759\pi$
$558$	4388.89	0.332969
$559$	30017.7	2.27122
$560$	−132496.	−9.99818
$561$	−7724.50	−0.581334
$562$	−6527.81	−0.489963
$563$	−9304.01	−0.696478	−0.348239	−	0.937406i	$-0.613220\pi$
$563$	−9304.01	−0.696478	−0.348239	+	0.937406i	$0.613220\pi$
$564$	−59281.0	−4.42585
$565$	1849.79	0.137737
$566$	−27457.9	−2.03912
$567$	−19773.1	−1.46453
$568$	−50469.9	−3.72829
$569$	−7030.88	−0.518014	−0.259007	−	0.965875i	$-0.583395\pi$
$569$	−7030.88	−0.518014	−0.259007	+	0.965875i	$0.583395\pi$
$570$	9761.14	0.717279
$571$	−8844.16	−0.648190	−0.324095	−	0.946025i	$-0.605060\pi$
$571$	−8844.16	−0.648190	−0.324095	+	0.946025i	$0.605060\pi$
$572$	25133.5	1.83721
$573$	−12755.7	−0.929979
$574$	−72268.1	−5.25507
$575$	2598.02	0.188426
$576$	55441.5	4.01053
$577$	17072.5	1.23178	0.615890	−	0.787832i	$-0.288797\pi$
$577$	17072.5	1.23178	0.615890	+	0.787832i	$0.288797\pi$
$578$	7268.67	0.523074
$579$	4505.79	0.323410
$580$	25567.8	1.83042
$581$	−4696.85	−0.335384
$582$	−6776.66	−0.482648
$583$	−11125.7	−0.790356
$584$	17227.6	1.22069
$585$	35210.5	2.48850
$586$	26321.2	1.85549
$587$	14465.9	1.01716	0.508580	−	0.861015i	$-0.330171\pi$
$587$	14465.9	1.01716	0.508580	+	0.861015i	$0.330171\pi$
$588$	−68153.8	−4.77996
$589$	358.783	0.0250991
$590$	16927.9	1.18121
$591$	−20976.0	−1.45996
$592$	41421.1	2.87567
$593$	−2401.75	−0.166321	−0.0831603	−	0.996536i	$-0.526501\pi$
$593$	−2401.75	−0.166321	−0.0831603	+	0.996536i	$0.526501\pi$
$594$	−332.235	−0.0229491
$595$	32447.1	2.23563
$596$	−8116.47	−0.557825
$597$	−7771.42	−0.532769
$598$	3575.68	0.244516
$599$	16093.6	1.09778	0.548888	−	0.835896i	$-0.315051\pi$
$599$	16093.6	1.09778	0.548888	+	0.835896i	$0.315051\pi$
$600$	147353.	10.0261
$601$	16714.9	1.13447	0.567234	−	0.823557i	$-0.308014\pi$
$601$	16714.9	1.13447	0.567234	+	0.823557i	$0.308014\pi$
$602$	69516.7	4.70646
$603$	−29537.9	−1.99482
$604$	−36619.6	−2.46694
$605$	20123.5	1.35229
$606$	−984.296	−0.0659807
$607$	11413.8	0.763218	0.381609	−	0.924324i	$-0.375370\pi$
$607$	11413.8	0.763218	0.381609	+	0.924324i	$0.375370\pi$
$608$	8925.38	0.595348
$609$	12062.0	0.802587
$610$	77500.1	5.14408
$611$	−23833.3	−1.57806
$612$	−36215.9	−2.39206
$613$	282.040	0.0185832	0.00929160	−	0.999957i	$-0.497042\pi$
$613$	282.040	0.0185832	0.00929160	+	0.999957i	$0.497042\pi$
$614$	−48.0291	−0.00315683
$615$	69182.0	4.53608
$616$	37054.4	2.42365
$617$	17047.3	1.11231	0.556157	−	0.831078i	$-0.312275\pi$
$617$	17047.3	1.11231	0.556157	+	0.831078i	$0.312275\pi$
$618$	−63411.4	−4.12748
$619$	−21825.9	−1.41722	−0.708608	−	0.705602i	$-0.750677\pi$
$619$	−21825.9	−1.41722	−0.708608	+	0.705602i	$0.750677\pi$
$620$	12597.6	0.816020
$621$	−34.6681	−0.00224023
$622$	28704.7	1.85041
$623$	−16281.4	−1.04703
$624$	117894.	7.56338
$625$	19485.7	1.24709
$626$	9535.49	0.608810
$627$	−1586.92	−0.101078
$628$	−8375.92	−0.532222
$629$	−10143.6	−0.643010
$630$	81542.6	5.15672
$631$	−21853.0	−1.37869	−0.689347	−	0.724431i	$-0.742102\pi$
$631$	−21853.0	−1.37869	−0.689347	+	0.724431i	$0.742102\pi$
$632$	−79521.3	−5.00504
$633$	−18601.9	−1.16802
$634$	−10298.3	−0.645107
$635$	−42829.2	−2.67657
$636$	−103431.	−6.44862
$637$	−27400.5	−1.70431
$638$	−5667.20	−0.351672
$639$	18056.5	1.11784
$640$	103082.	6.36670
$641$	8493.72	0.523373	0.261686	−	0.965153i	$-0.415721\pi$
$641$	8493.72	0.523373	0.261686	+	0.965153i	$0.415721\pi$
$642$	3776.42	0.232155
$643$	24742.2	1.51748	0.758738	−	0.651396i	$-0.225816\pi$
$643$	24742.2	1.51748	0.758738	+	0.651396i	$0.225816\pi$
$644$	6073.67	0.371640
$645$	−66548.2	−4.06253
$646$	−4036.42	−0.245837
$647$	6013.28	0.365388	0.182694	−	0.983170i	$-0.441518\pi$
$647$	6013.28	0.365388	0.182694	+	0.983170i	$0.441518\pi$
$648$	54982.6	3.33321
$649$	−2752.07	−0.166453
$650$	93057.9	5.61543
$651$	5943.10	0.357801
$652$	−23491.8	−1.41106
$653$	−3216.67	−0.192769	−0.0963845	−	0.995344i	$-0.530728\pi$
$653$	−3216.67	−0.192769	−0.0963845	+	0.995344i	$0.530728\pi$
$654$	61573.8	3.68154
$655$	25763.2	1.53687
$656$	116820.	6.95281
$657$	−6163.46	−0.365996
$658$	−55194.6	−3.27007
$659$	3189.22	0.188519	0.0942597	−	0.995548i	$-0.469952\pi$
$659$	3189.22	0.188519	0.0942597	+	0.995548i	$0.469952\pi$
$660$	−55720.2	−3.28622
$661$	−30948.1	−1.82109	−0.910545	−	0.413410i	$-0.864337\pi$
$661$	−30948.1	−1.82109	−0.910545	+	0.413410i	$0.864337\pi$
$662$	16204.4	0.951361
$663$	−28871.3	−1.69120
$664$	13060.4	0.763319
$665$	6665.94	0.388713
$666$	−25491.9	−1.48317
$667$	−591.362	−0.0343293
$668$	81263.2	4.70684
$669$	24557.4	1.41920
$670$	−115593.	−6.66531
$671$	−12599.6	−0.724893
$672$	147846.	8.48701
$673$	−230.729	−0.0132154	−0.00660768	−	0.999978i	$-0.502103\pi$
$673$	−230.729	−0.0132154	−0.00660768	+	0.999978i	$0.502103\pi$
$674$	−36382.6	−2.07924
$675$	−902.245	−0.0514481
$676$	45572.9	2.59290
$677$	−29339.5	−1.66559	−0.832797	−	0.553579i	$-0.813262\pi$
$677$	−29339.5	−1.66559	−0.832797	+	0.553579i	$0.813262\pi$
$678$	−3811.75	−0.215914
$679$	−4627.82	−0.261560
$680$	−90225.1	−5.08820
$681$	−29346.0	−1.65131
$682$	−2792.31	−0.156779
$683$	20031.4	1.12222	0.561112	−	0.827740i	$-0.310374\pi$
$683$	20031.4	1.12222	0.561112	+	0.827740i	$0.310374\pi$
$684$	−7440.21	−0.415912
$685$	−8176.82	−0.456088
$686$	−11567.1	−0.643783
$687$	29370.2	1.63107
$688$	−112372.	−6.22697
$689$	−41583.5	−2.29928
$690$	−7927.16	−0.437365
$691$	−11979.4	−0.659504	−0.329752	−	0.944068i	$-0.606965\pi$
$691$	−11979.4	−0.659504	−0.329752	+	0.944068i	$0.606965\pi$
$692$	−91265.1	−5.01356
$693$	−13256.8	−0.726675
$694$	36243.6	1.98240
$695$	4746.11	0.259036
$696$	−33540.5	−1.82665
$697$	−28608.1	−1.55468
$698$	15245.4	0.826714
$699$	−11043.5	−0.597574
$700$	158069.	8.53491
$701$	13962.1	0.752272	0.376136	−	0.926565i	$-0.377253\pi$
$701$	13962.1	0.752272	0.376136	+	0.926565i	$0.377253\pi$
$702$	−1241.77	−0.0667629
$703$	−2083.91	−0.111801
$704$	−35273.2	−1.88836
$705$	52837.6	2.82267
$706$	43694.6	2.32928
$707$	−672.182	−0.0357567
$708$	−25585.1	−1.35811
$709$	11468.5	0.607488	0.303744	−	0.952754i	$-0.401763\pi$
$709$	11468.5	0.607488	0.303744	+	0.952754i	$0.401763\pi$
$710$	70662.1	3.73507
$711$	28450.1	1.50065
$712$	45273.3	2.38299
$713$	−291.373	−0.0153043
$714$	−66861.8	−3.50454
$715$	−22401.7	−1.17172
$716$	73282.6	3.82500
$717$	44021.3	2.29290
$718$	−28391.1	−1.47569
$719$	−9420.79	−0.488646	−0.244323	−	0.969694i	$-0.578566\pi$
$719$	−9420.79	−0.488646	−0.244323	+	0.969694i	$0.578566\pi$
$720$	−131812.	−6.82269
$721$	−43304.0	−2.23679
$722$	36748.4	1.89423
$723$	20378.8	1.04827
$724$	51847.7	2.66147
$725$	−15390.3	−0.788390
$726$	−41467.2	−2.11983
$727$	29945.1	1.52765	0.763826	−	0.645422i	$-0.223319\pi$
$727$	29945.1	1.52765	0.763826	+	0.645422i	$0.223319\pi$
$728$	138496.	7.05081
$729$	−20362.4	−1.03452
$730$	−24120.1	−1.22291
$731$	27519.0	1.39237
$732$	−117134.	−5.91450
$733$	2875.67	0.144905	0.0724524	−	0.997372i	$-0.476917\pi$
$733$	2875.67	0.144905	0.0724524	+	0.997372i	$0.476917\pi$
$734$	18893.8	0.950112
$735$	60746.0	3.04850
$736$	−7248.43	−0.363017
$737$	18792.7	0.939263
$738$	−71894.9	−3.58603
$739$	6053.18	0.301312	0.150656	−	0.988586i	$-0.451861\pi$
$739$	6053.18	0.301312	0.150656	+	0.988586i	$0.451861\pi$
$740$	−73170.6	−3.63487
$741$	−5931.32	−0.294052
$742$	−96301.6	−4.76461
$743$	18335.7	0.905343	0.452672	−	0.891677i	$-0.350471\pi$
$743$	18335.7	0.905343	0.452672	+	0.891677i	$0.350471\pi$
$744$	−16525.9	−0.814339
$745$	7234.27	0.355763
$746$	−15102.6	−0.741212
$747$	−4672.59	−0.228864
$748$	23041.4	1.12631
$749$	2578.94	0.125811
$750$	−107131.	−5.21582
$751$	25022.6	1.21583	0.607914	−	0.794003i	$-0.292006\pi$
$751$	25022.6	1.21583	0.607914	+	0.794003i	$0.292006\pi$
$752$	89220.9	4.32653
$753$	25246.8	1.22184
$754$	−21181.9	−1.02307
$755$	32639.3	1.57333
$756$	−2109.27	−0.101473
$757$	−1956.86	−0.0939540	−0.0469770	−	0.998896i	$-0.514959\pi$
$757$	−1956.86	−0.0939540	−0.0469770	+	0.998896i	$0.514959\pi$
$758$	−10245.8	−0.490957
$759$	1288.76	0.0616326
$760$	−18535.9	−0.884693
$761$	−20096.3	−0.957279	−0.478639	−	0.878012i	$-0.658870\pi$
$761$	−20096.3	−0.957279	−0.478639	+	0.878012i	$0.658870\pi$
$762$	88255.5	4.19575
$763$	42049.1	1.99513
$764$	38049.0	1.80179
$765$	32279.5	1.52558
$766$	59163.8	2.79070
$767$	−10286.2	−0.484241
$768$	−93252.4	−4.38145
$769$	37342.6	1.75112	0.875559	−	0.483112i	$-0.160494\pi$
$769$	37342.6	1.75112	0.875559	+	0.483112i	$0.160494\pi$
$770$	−51879.3	−2.42805
$771$	54006.9	2.52271
$772$	−13440.3	−0.626590
$773$	23374.0	1.08759	0.543794	−	0.839219i	$-0.316987\pi$
$773$	23374.0	1.08759	0.543794	+	0.839219i	$0.316987\pi$
$774$	69157.8	3.21166
$775$	−7583.04	−0.351472
$776$	12868.5	0.595300
$777$	−34519.3	−1.59379
$778$	−61840.4	−2.84973
$779$	−5877.26	−0.270314
$780$	−208261.	−9.56019
$781$	−11487.9	−0.526339
$782$	3278.04	0.149901
$783$	205.369	0.00937331
$784$	102575.	4.67269
$785$	7465.52	0.339434
$786$	−53088.7	−2.40917
$787$	16052.5	0.727075	0.363538	−	0.931579i	$-0.381569\pi$
$787$	16052.5	0.727075	0.363538	+	0.931579i	$0.381569\pi$
$788$	62569.2	2.82860
$789$	46795.3	2.11148
$790$	111336.	5.01414
$791$	−2603.07	−0.117010
$792$	36863.1	1.65388
$793$	−47092.7	−2.10884
$794$	−49332.0	−2.20495
$795$	92189.3	4.11273
$796$	23181.4	1.03221
$797$	−32808.2	−1.45813	−0.729064	−	0.684446i	$-0.760044\pi$
$797$	−32808.2	−1.45813	−0.729064	+	0.684446i	$0.760044\pi$
$798$	−13736.1	−0.609340
$799$	−21849.4	−0.967429
$800$	−188642.	−8.33688
$801$	−16197.3	−0.714486
$802$	15079.3	0.663928
$803$	3921.33	0.172330
$804$	174709.	7.66357
$805$	−5413.51	−0.237020
$806$	−10436.6	−0.456097
$807$	−10729.0	−0.468003
$808$	1869.13	0.0813807
$809$	10949.7	0.475861	0.237930	−	0.971282i	$-0.423531\pi$
$809$	10949.7	0.475861	0.237930	+	0.971282i	$0.423531\pi$
$810$	−76980.2	−3.33927
$811$	−23829.9	−1.03179	−0.515894	−	0.856652i	$-0.672540\pi$
$811$	−23829.9	−1.03179	−0.515894	+	0.856652i	$0.672540\pi$
$812$	−35979.6	−1.55497
$813$	−937.983	−0.0404631
$814$	16218.6	0.698354
$815$	20938.4	0.899927
$816$	108081.	4.63674
$817$	5653.51	0.242094
$818$	−14028.4	−0.599624
$819$	−49549.1	−2.11402
$820$	−206363.	−8.78843
$821$	−343.463	−0.0146004	−0.00730020	−	0.999973i	$-0.502324\pi$
$821$	−343.463	−0.0146004	−0.00730020	+	0.999973i	$0.502324\pi$
$822$	16849.5	0.714955
$823$	−23288.5	−0.986375	−0.493188	−	0.869923i	$-0.664168\pi$
$823$	−23288.5	−0.986375	−0.493188	+	0.869923i	$0.664168\pi$
$824$	120415.	5.09084
$825$	33540.4	1.41543
$826$	−23821.4	−1.00345
$827$	7468.58	0.314036	0.157018	−	0.987596i	$-0.449812\pi$
$827$	7468.58	0.314036	0.157018	+	0.987596i	$0.449812\pi$
$828$	6042.31	0.253605
$829$	−6783.03	−0.284179	−0.142089	−	0.989854i	$-0.545382\pi$
$829$	−6783.03	−0.284179	−0.142089	+	0.989854i	$0.545382\pi$
$830$	−18285.7	−0.764706
$831$	31013.0	1.29462
$832$	−131838.	−5.49357
$833$	−25119.7	−1.04483
$834$	−9780.02	−0.406061
$835$	−72430.6	−3.00187
$836$	4733.63	0.195833
$837$	101.188	0.00417871
$838$	28751.5	1.18521
$839$	47295.9	1.94617	0.973084	−	0.230452i	$-0.0740205\pi$
$839$	47295.9	1.94617	0.973084	+	0.230452i	$0.0740205\pi$
$840$	−307040.	−12.6118
$841$	−20885.8	−0.856363
$842$	−68465.3	−2.80222
$843$	−8793.83	−0.359283
$844$	55487.5	2.26298
$845$	−40619.5	−1.65367
$846$	−54909.6	−2.23148
$847$	−28318.2	−1.14879
$848$	155670.	6.30391
$849$	−36989.4	−1.49526
$850$	85311.7	3.44255
$851$	1692.38	0.0681715
$852$	−106799.	−4.29447
$853$	−26720.2	−1.07255	−0.536274	−	0.844044i	$-0.680169\pi$
$853$	−26720.2	−1.07255	−0.536274	+	0.844044i	$0.680169\pi$
$854$	−109060.	−4.36997
$855$	6631.52	0.265255
$856$	−7171.21	−0.286340
$857$	−21197.8	−0.844927	−0.422463	−	0.906380i	$-0.638834\pi$
$857$	−21197.8	−0.844927	−0.422463	+	0.906380i	$0.638834\pi$
$858$	46161.9	1.83676
$859$	−41967.1	−1.66694	−0.833469	−	0.552566i	$-0.813649\pi$
$859$	−41967.1	−1.66694	−0.833469	+	0.552566i	$0.813649\pi$
$860$	198507.	7.87095
$861$	−97354.7	−3.85347
$862$	−14634.6	−0.578258
$863$	−6348.26	−0.250402	−0.125201	−	0.992131i	$-0.539958\pi$
$863$	−6348.26	−0.250402	−0.125201	+	0.992131i	$0.539958\pi$
$864$	2517.25	0.0991186
$865$	81345.3	3.19748
$866$	−28183.5	−1.10591
$867$	9791.86	0.383563
$868$	−17727.7	−0.693222
$869$	−18100.6	−0.706583
$870$	46959.5	1.82997
$871$	70239.9	2.73248
$872$	−116925.	−4.54082
$873$	−4603.92	−0.178487
$874$	673.441	0.0260635
$875$	−73160.4	−2.82660
$876$	36455.3	1.40606
$877$	−4695.70	−0.180801	−0.0904006	−	0.995905i	$-0.528815\pi$
$877$	−4695.70	−0.180801	−0.0904006	+	0.995905i	$0.528815\pi$
$878$	40189.5	1.54480
$879$	35458.2	1.36061
$880$	83861.7	3.21247
$881$	−14169.6	−0.541868	−0.270934	−	0.962598i	$-0.587332\pi$
$881$	−14169.6	−0.541868	−0.270934	+	0.962598i	$0.587332\pi$
$882$	−63128.1	−2.41002
$883$	32464.5	1.23728	0.618639	−	0.785675i	$-0.287684\pi$
$883$	32464.5	1.23728	0.618639	+	0.785675i	$0.287684\pi$
$884$	86120.1	3.27662
$885$	22804.2	0.866162
$886$	−15466.9	−0.586478
$887$	−5200.26	−0.196852	−0.0984259	−	0.995144i	$-0.531381\pi$
$887$	−5200.26	−0.196852	−0.0984259	+	0.995144i	$0.531381\pi$
$888$	95987.2	3.62739
$889$	60270.3	2.27379
$890$	−63386.4	−2.38732
$891$	12515.1	0.470563
$892$	−73252.2	−2.74962
$893$	−4488.75	−0.168208
$894$	−14907.2	−0.557688
$895$	−65317.4	−2.43946
$896$	−145060.	−5.40862
$897$	4816.92	0.179300
$898$	54265.8	2.01656
$899$	1726.05	0.0640346
$900$	157252.	5.82417
$901$	−38122.1	−1.40958
$902$	45741.2	1.68849
$903$	93648.3	3.45118
$904$	7238.32	0.266309
$905$	−46212.2	−1.69740
$906$	−67258.0	−2.46633
$907$	830.518	0.0304045	0.0152023	−	0.999884i	$-0.495161\pi$
$907$	830.518	0.0304045	0.0152023	+	0.999884i	$0.495161\pi$
$908$	87536.1	3.19932
$909$	−668.711	−0.0244002
$910$	−193905.	−7.06362
$911$	14415.5	0.524266	0.262133	−	0.965032i	$-0.415574\pi$
$911$	14415.5	0.524266	0.262133	+	0.965032i	$0.415574\pi$
$912$	22204.1	0.806198
$913$	2972.81	0.107761
$914$	−28629.3	−1.03608
$915$	104403.	3.77208
$916$	−87608.5	−3.16011
$917$	−36254.6	−1.30560
$918$	−1138.40	−0.0409291
$919$	47464.7	1.70372	0.851858	−	0.523773i	$-0.175476\pi$
$919$	47464.7	1.70372	0.851858	+	0.523773i	$0.175476\pi$
$920$	15053.3	0.539447
$921$	−64.7015	−0.00231486
$922$	−49335.3	−1.76223
$923$	−42937.6	−1.53121
$924$	78410.9	2.79170
$925$	44044.5	1.56559
$926$	−65063.1	−2.30897
$927$	−43080.4	−1.52637
$928$	42938.8	1.51889
$929$	−22045.4	−0.778563	−0.389281	−	0.921119i	$-0.627277\pi$
$929$	−22045.4	−0.778563	−0.389281	+	0.921119i	$0.627277\pi$
$930$	23137.6	0.815820
$931$	−5160.59	−0.181667
$932$	32941.7	1.15777
$933$	38669.1	1.35688
$934$	59011.2	2.06735
$935$	−20537.0	−0.718322
$936$	137780.	4.81143
$937$	−55138.9	−1.92242	−0.961212	−	0.275811i	$-0.911054\pi$
$937$	−55138.9	−1.92242	−0.961212	+	0.275811i	$0.911054\pi$
$938$	162666.	5.66229
$939$	12845.6	0.446432
$940$	−157609.	−5.46878
$941$	7613.94	0.263770	0.131885	−	0.991265i	$-0.457897\pi$
$941$	7613.94	0.263770	0.131885	+	0.991265i	$0.457897\pi$
$942$	−15383.8	−0.532092
$943$	4773.01	0.164826
$944$	38506.8	1.32764
$945$	1880.01	0.0647162
$946$	−43999.8	−1.51222
$947$	−42239.8	−1.44943	−0.724715	−	0.689049i	$-0.758029\pi$
$947$	−42239.8	−1.44943	−0.724715	+	0.689049i	$0.758029\pi$
$948$	−168275.	−5.76511
$949$	14656.5	0.501337
$950$	17526.5	0.598561
$951$	−13873.2	−0.473048
$952$	126967.	4.32251
$953$	48501.7	1.64861	0.824305	−	0.566146i	$-0.191566\pi$
$953$	48501.7	1.64861	0.824305	+	0.566146i	$0.191566\pi$
$954$	−95804.4	−3.25134
$955$	−33913.4	−1.14912
$956$	−131311.	−4.44237
$957$	−7634.47	−0.257876
$958$	40923.8	1.38016
$959$	11506.6	0.387454
$960$	292280.	9.82635
$961$	−28940.5	−0.971453
$962$	60618.9	2.03163
$963$	2565.62	0.0858525
$964$	−60788.1	−2.03097
$965$	11979.5	0.399619
$966$	11155.3	0.371549
$967$	21006.0	0.698561	0.349281	−	0.937018i	$-0.386426\pi$
$967$	21006.0	0.698561	0.349281	+	0.937018i	$0.386426\pi$
$968$	78744.0	2.61460
$969$	−5437.59	−0.180269
$970$	−18017.0	−0.596382
$971$	−9069.18	−0.299736	−0.149868	−	0.988706i	$-0.547885\pi$
$971$	−9069.18	−0.299736	−0.149868	+	0.988706i	$0.547885\pi$
$972$	118411.	3.90745
$973$	−6678.84	−0.220055
$974$	−12784.2	−0.420566
$975$	125361.	4.11772
$976$	176293.	5.78177
$977$	38950.3	1.27546	0.637732	−	0.770258i	$-0.279873\pi$
$977$	38950.3	1.27546	0.637732	+	0.770258i	$0.279873\pi$
$978$	−43146.5	−1.41071
$979$	10305.1	0.336417
$980$	−181199.	−5.90633
$981$	41832.0	1.36146
$982$	51439.5	1.67159
$983$	−8229.07	−0.267006	−0.133503	−	0.991048i	$-0.542623\pi$
$983$	−8229.07	−0.267006	−0.133503	+	0.991048i	$0.542623\pi$
$984$	270713.	8.77033
$985$	−55768.4	−1.80399
$986$	−19418.7	−0.627197
$987$	−74354.4	−2.39790
$988$	17692.5	0.569711
$989$	−4591.30	−0.147619
$990$	−51611.4	−1.65689
$991$	−16389.9	−0.525370	−0.262685	−	0.964882i	$-0.584608\pi$
$991$	−16389.9	−0.525370	−0.262685	+	0.964882i	$0.584608\pi$
$992$	21156.5	0.677138
$993$	21829.5	0.697620
$994$	−99437.4	−3.17300
$995$	−20661.7	−0.658313
$996$	27637.2	0.879236
$997$	3935.01	0.124998	0.0624990	−	0.998045i	$-0.480093\pi$
$997$	3935.01	0.124998	0.0624990	+	0.998045i	$0.480093\pi$
$998$	−52925.0	−1.67867
$999$	−587.732	−0.0186136

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	547.4.a.a.1.3	✓	65

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
547.4.a.a.1.3	✓	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)

\(f(q)\)	\(=\)	\(q-5.47859 q^{2} -7.38039 q^{3} +22.0150 q^{4} -19.6221 q^{5} +40.4341 q^{6} +27.6127 q^{7} -76.7823 q^{8} +27.4701 q^{9} +O(q^{10})\)	\(q-5.47859 q^{2} -7.38039 q^{3} +22.0150 q^{4} -19.6221 q^{5} +40.4341 q^{6} +27.6127 q^{7} -76.7823 q^{8} +27.4701 q^{9} +107.502 q^{10} -17.4771 q^{11} -162.479 q^{12} -65.3229 q^{13} -151.279 q^{14} +144.819 q^{15} +244.539 q^{16} -59.8854 q^{17} -150.498 q^{18} -12.3029 q^{19} -431.980 q^{20} -203.793 q^{21} +95.7500 q^{22} +9.99135 q^{23} +566.683 q^{24} +260.027 q^{25} +357.878 q^{26} -3.46981 q^{27} +607.893 q^{28} -59.1875 q^{29} -793.403 q^{30} -29.1625 q^{31} -725.471 q^{32} +128.988 q^{33} +328.088 q^{34} -541.820 q^{35} +604.754 q^{36} +169.384 q^{37} +67.4024 q^{38} +482.109 q^{39} +1506.63 q^{40} +477.714 q^{41} +1116.50 q^{42} -459.527 q^{43} -384.758 q^{44} -539.022 q^{45} -54.7385 q^{46} +364.853 q^{47} -1804.79 q^{48} +419.462 q^{49} -1424.58 q^{50} +441.977 q^{51} -1438.08 q^{52} +636.584 q^{53} +19.0097 q^{54} +342.938 q^{55} -2120.17 q^{56} +90.8000 q^{57} +324.264 q^{58} +157.467 q^{59} +3188.18 q^{60} +720.921 q^{61} +159.769 q^{62} +758.525 q^{63} +2018.25 q^{64} +1281.77 q^{65} -706.673 q^{66} -1075.27 q^{67} -1318.37 q^{68} -73.7400 q^{69} +2968.41 q^{70} +657.312 q^{71} -2109.22 q^{72} -224.369 q^{73} -927.987 q^{74} -1919.10 q^{75} -270.847 q^{76} -482.591 q^{77} -2641.28 q^{78} +1035.67 q^{79} -4798.37 q^{80} -716.085 q^{81} -2617.20 q^{82} -170.097 q^{83} -4486.49 q^{84} +1175.08 q^{85} +2517.56 q^{86} +436.826 q^{87} +1341.93 q^{88} -589.633 q^{89} +2953.08 q^{90} -1803.74 q^{91} +219.959 q^{92} +215.231 q^{93} -1998.88 q^{94} +241.408 q^{95} +5354.26 q^{96} -167.597 q^{97} -2298.06 q^{98} -480.099 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 65 q - 12 q^{2} - 35 q^{3} + 234 q^{4} - 151 q^{5} - 60 q^{6} - 74 q^{7} - 144 q^{8} + 468 q^{9}+O(q^{10}) \) 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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