LMFDB - Embedded newform 177.6.a.a.1.7

Newspace parameters

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	177.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$28.3879361069$
Analytic rank:	$1$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
Defining polynomial:	$x^{11} - 5 x^{10} - 238 x^{9} + 1067 x^{8} + 20782 x^{7} - 79077 x^{6} - 813818 x^{5} + 2364885 x^{4} + 13849341 x^{3} - 23890558 x^{2} - 74443300 x - 14846072$
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$4.20625$ of defining polynomial
Character	$\chi$	$=$	177.1

$q$-expansion

$f(q)$	$=$	$q+3.20625 q^{2} +9.00000 q^{3} -21.7200 q^{4} +26.7258 q^{5} +28.8562 q^{6} +39.0273 q^{7} -172.240 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q+3.20625 q^{2} +9.00000 q^{3} -21.7200 q^{4} +26.7258 q^{5} +28.8562 q^{6} +39.0273 q^{7} -172.240 q^{8} +81.0000 q^{9} +85.6897 q^{10} -606.405 q^{11} -195.480 q^{12} -161.707 q^{13} +125.131 q^{14} +240.533 q^{15} +142.797 q^{16} -1651.20 q^{17} +259.706 q^{18} +882.094 q^{19} -580.485 q^{20} +351.246 q^{21} -1944.28 q^{22} +2923.63 q^{23} -1550.16 q^{24} -2410.73 q^{25} -518.474 q^{26} +729.000 q^{27} -847.672 q^{28} -7064.00 q^{29} +771.207 q^{30} -2253.17 q^{31} +5969.51 q^{32} -5457.64 q^{33} -5294.14 q^{34} +1043.04 q^{35} -1759.32 q^{36} -7561.88 q^{37} +2828.21 q^{38} -1455.37 q^{39} -4603.25 q^{40} -16708.0 q^{41} +1126.18 q^{42} -4502.50 q^{43} +13171.1 q^{44} +2164.79 q^{45} +9373.88 q^{46} +8408.79 q^{47} +1285.17 q^{48} -15283.9 q^{49} -7729.39 q^{50} -14860.8 q^{51} +3512.28 q^{52} +11049.2 q^{53} +2337.35 q^{54} -16206.7 q^{55} -6722.04 q^{56} +7938.85 q^{57} -22648.9 q^{58} +3481.00 q^{59} -5224.36 q^{60} +34738.9 q^{61} -7224.23 q^{62} +3161.21 q^{63} +14570.2 q^{64} -4321.76 q^{65} -17498.5 q^{66} -57227.0 q^{67} +35863.9 q^{68} +26312.7 q^{69} +3344.23 q^{70} +26.9044 q^{71} -13951.4 q^{72} +54481.3 q^{73} -24245.2 q^{74} -21696.6 q^{75} -19159.1 q^{76} -23666.3 q^{77} -4666.26 q^{78} +93190.6 q^{79} +3816.37 q^{80} +6561.00 q^{81} -53569.9 q^{82} -89600.1 q^{83} -7629.05 q^{84} -44129.6 q^{85} -14436.1 q^{86} -63576.0 q^{87} +104447. q^{88} -128157. q^{89} +6940.86 q^{90} -6311.00 q^{91} -63501.2 q^{92} -20278.6 q^{93} +26960.7 q^{94} +23574.7 q^{95} +53725.6 q^{96} -26665.5 q^{97} -49003.9 q^{98} -49118.8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11q - 6q^{2} + 99q^{3} + 150q^{4} - 192q^{5} - 54q^{6} - 371q^{7} - 621q^{8} + 891q^{9} + O(q^{10}) $	\( 11q - 6q^{2} + 99q^{3} + 150q^{4} - 192q^{5} - 54q^{6} - 371q^{7} - 621q^{8} + 891q^{9} - 399q^{10} - 698q^{11} + 1350q^{12} - 1556q^{13} - 1679q^{14} - 1728q^{15} - 2662q^{16} - 4793q^{17} - 486q^{18} - 3753q^{19} - 11023q^{20} - 3339q^{21} - 9534q^{22} - 7323q^{23} - 5589q^{24} + 7867q^{25} - 4844q^{26} + 8019q^{27} + 3650q^{28} - 15467q^{29} - 3591q^{30} - 5151q^{31} - 15368q^{32} - 6282q^{33} + 8452q^{34} - 23285q^{35} + 12150q^{36} + 8623q^{37} + 15205q^{38} - 14004q^{39} + 41530q^{40} - 6369q^{41} - 15111q^{42} - 20506q^{43} - 55632q^{44} - 15552q^{45} - 45191q^{46} - 47899q^{47} - 23958q^{48} - 10322q^{49} - 102147q^{50} - 43137q^{51} - 292q^{52} - 80048q^{53} - 4374q^{54} - 2114q^{55} - 108126q^{56} - 33777q^{57} - 58294q^{58} + 38291q^{59} - 99207q^{60} - 82527q^{61} - 67438q^{62} - 30051q^{63} - 51411q^{64} - 167646q^{65} - 85806q^{66} - 166976q^{67} - 136533q^{68} - 65907q^{69} + 76140q^{70} - 183560q^{71} - 50301q^{72} - 36809q^{73} - 116686q^{74} + 70803q^{75} + 55580q^{76} - 164885q^{77} - 43596q^{78} - 281518q^{79} - 32683q^{80} + 72171q^{81} + 178815q^{82} - 254691q^{83} + 32850q^{84} + 4763q^{85} + 349324q^{86} - 139203q^{87} + 251285q^{88} - 89687q^{89} - 32319q^{90} + 34897q^{91} - 20240q^{92} - 46359q^{93} + 96548q^{94} - 155113q^{95} - 138312q^{96} - 45828q^{97} + 465864q^{98} - 56538q^{99} + O(q^{100}) \)

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 $

$2$	3.20625	0.566790	0.283395	−	0.959003i	$-0.408539\pi$
$2$	3.20625	0.566790	0.283395	+	0.959003i	$0.408539\pi$
$3$	9.00000	0.577350
$3$	9.00000	0.577350
$4$	−21.7200	−0.678749
$5$	26.7258	0.478086	0.239043	−	0.971009i	$-0.423166\pi$
$5$	26.7258	0.478086	0.239043	+	0.971009i	$0.423166\pi$
$6$	28.8562	0.327236
$7$	39.0273	0.301039	0.150520	−	0.988607i	$-0.451905\pi$
$7$	39.0273	0.301039	0.150520	+	0.988607i	$0.451905\pi$
$8$	−172.240	−0.951498
$9$	81.0000	0.333333
$10$	85.6897	0.270974
$11$	−606.405	−1.51106	−0.755528	−	0.655116i	$-0.772620\pi$
$11$	−606.405	−1.51106	−0.755528	+	0.655116i	$0.772620\pi$
$12$	−195.480	−0.391876
$13$	−161.707	−0.265382	−0.132691	−	0.991157i	$-0.542362\pi$
$13$	−161.707	−0.265382	−0.132691	+	0.991157i	$0.542362\pi$
$14$	125.131	0.170626
$15$	240.533	0.276023
$16$	142.797	0.139450
$17$	−1651.20	−1.38572	−0.692861	−	0.721071i	$-0.743650\pi$
$17$	−1651.20	−1.38572	−0.692861	+	0.721071i	$0.743650\pi$
$18$	259.706	0.188930
$19$	882.094	0.560572	0.280286	−	0.959917i	$-0.409571\pi$
$19$	882.094	0.560572	0.280286	+	0.959917i	$0.409571\pi$
$20$	−580.485	−0.324501
$21$	351.246	0.173805
$22$	−1944.28	−0.856451
$23$	2923.63	1.15240	0.576199	−	0.817309i	$-0.304535\pi$
$23$	2923.63	1.15240	0.576199	+	0.817309i	$0.304535\pi$
$24$	−1550.16	−0.549348
$25$	−2410.73	−0.771433
$26$	−518.474	−0.150416
$27$	729.000	0.192450
$28$	−847.672	−0.204330
$29$	−7064.00	−1.55975	−0.779876	−	0.625934i	$-0.784718\pi$
$29$	−7064.00	−1.55975	−0.779876	+	0.625934i	$0.784718\pi$
$30$	771.207	0.156447
$31$	−2253.17	−0.421105	−0.210553	−	0.977583i	$-0.567526\pi$
$31$	−2253.17	−0.421105	−0.210553	+	0.977583i	$0.567526\pi$
$32$	5969.51	1.03054
$33$	−5457.64	−0.872409
$34$	−5294.14	−0.785413
$35$	1043.04	0.143923
$36$	−1759.32	−0.226250
$37$	−7561.88	−0.908082	−0.454041	−	0.890981i	$-0.650018\pi$
$37$	−7561.88	−0.908082	−0.454041	+	0.890981i	$0.650018\pi$
$38$	2828.21	0.317726
$39$	−1455.37	−0.153218
$40$	−4603.25	−0.454898
$41$	−16708.0	−1.55226	−0.776130	−	0.630574i	$-0.782820\pi$
$41$	−16708.0	−1.55226	−0.776130	+	0.630574i	$0.782820\pi$
$42$	1126.18	0.0985110
$43$	−4502.50	−0.371349	−0.185675	−	0.982611i	$-0.559447\pi$
$43$	−4502.50	−0.371349	−0.185675	+	0.982611i	$0.559447\pi$
$44$	13171.1	1.02563
$45$	2164.79	0.159362
$46$	9373.88	0.653168
$47$	8408.79	0.555251	0.277625	−	0.960689i	$-0.410453\pi$
$47$	8408.79	0.555251	0.277625	+	0.960689i	$0.410453\pi$
$48$	1285.17	0.0805116
$49$	−15283.9	−0.909375
$50$	−7729.39	−0.437241
$51$	−14860.8	−0.800047
$52$	3512.28	0.180128
$53$	11049.2	0.540307	0.270154	−	0.962817i	$-0.412925\pi$
$53$	11049.2	0.540307	0.270154	+	0.962817i	$0.412925\pi$
$54$	2337.35	0.109079
$55$	−16206.7	−0.722416
$56$	−6722.04	−0.286438
$57$	7938.85	0.323646
$58$	−22648.9	−0.884052
$59$	3481.00	0.130189
$59$	3481.00	0.130189
$60$	−5224.36	−0.187351
$61$	34738.9	1.19534	0.597670	−	0.801742i	$-0.296093\pi$
$61$	34738.9	1.19534	0.597670	+	0.801742i	$0.296093\pi$
$62$	−7224.23	−0.238678
$63$	3161.21	0.100346
$64$	14570.2	0.444648
$65$	−4321.76	−0.126875
$66$	−17498.5	−0.494472
$67$	−57227.0	−1.55745	−0.778724	−	0.627366i	$-0.784133\pi$
$67$	−57227.0	−1.55745	−0.778724	+	0.627366i	$0.784133\pi$
$68$	35863.9	0.940558
$69$	26312.7	0.665338
$70$	3344.23	0.0815740
$71$	26.9044	0.000633398 0	0.000316699	−	1.00000i	$-0.499899\pi$
$71$	26.9044	0.000633398 0	0.000316699		1.00000i	$0.499899\pi$
$72$	−13951.4	−0.317166
$73$	54481.3	1.19658	0.598288	−	0.801281i	$-0.295848\pi$
$73$	54481.3	1.19658	0.598288	+	0.801281i	$0.295848\pi$
$74$	−24245.2	−0.514692
$75$	−21696.6	−0.445387
$76$	−19159.1	−0.380488
$77$	−23666.3	−0.454887
$78$	−4666.26	−0.0868426
$79$	93190.6	1.67998	0.839990	−	0.542601i	$-0.182561\pi$
$79$	93190.6	1.67998	0.839990	+	0.542601i	$0.182561\pi$
$80$	3816.37	0.0666692
$81$	6561.00	0.111111
$82$	−53569.9	−0.879805
$83$	−89600.1	−1.42762	−0.713811	−	0.700339i	$-0.753032\pi$
$83$	−89600.1	−1.42762	−0.713811	+	0.700339i	$0.753032\pi$
$84$	−7629.05	−0.117970
$85$	−44129.6	−0.662495
$86$	−14436.1	−0.210477
$87$	−63576.0	−0.900524
$88$	104447.	1.43777
$89$	−128157.	−1.71502	−0.857508	−	0.514471i	$-0.827988\pi$
$89$	−128157.	−1.71502	−0.857508	+	0.514471i	$0.827988\pi$
$90$	6940.86	0.0903248
$91$	−6311.00	−0.0798904
$92$	−63501.2	−0.782190
$93$	−20278.6	−0.243125
$94$	26960.7	0.314710
$95$	23574.7	0.268002
$96$	53725.6	0.594981
$97$	−26665.5	−0.287753	−0.143877	−	0.989596i	$-0.545957\pi$
$97$	−26665.5	−0.287753	−0.143877	+	0.989596i	$0.545957\pi$
$98$	−49003.9	−0.515425
$99$	−49118.8	−0.503686
$100$	52361.0	0.523610
$101$	153961.	1.50178	0.750890	−	0.660427i	$-0.229625\pi$
$101$	153961.	1.50178	0.750890	+	0.660427i	$0.229625\pi$
$102$	−47647.3	−0.453459
$103$	−51991.3	−0.482878	−0.241439	−	0.970416i	$-0.577619\pi$
$103$	−51991.3	−0.482878	−0.241439	+	0.970416i	$0.577619\pi$
$104$	27852.4	0.252510
$105$	9387.33	0.0830939
$106$	35426.4	0.306241
$107$	215950.	1.82345	0.911725	−	0.410801i	$-0.134751\pi$
$107$	215950.	1.82345	0.911725	+	0.410801i	$0.134751\pi$
$108$	−15833.9	−0.130625
$109$	62561.7	0.504362	0.252181	−	0.967680i	$-0.418852\pi$
$109$	62561.7	0.504362	0.252181	+	0.967680i	$0.418852\pi$
$110$	−51962.6	−0.409458
$111$	−68056.9	−0.524282
$112$	5572.98	0.0419800
$113$	242539.	1.78684	0.893421	−	0.449220i	$-0.148298\pi$
$113$	242539.	1.78684	0.893421	+	0.449220i	$0.148298\pi$
$114$	25453.9	0.183439
$115$	78136.5	0.550946
$116$	153430.	1.05868
$117$	−13098.3	−0.0884606
$118$	11160.9	0.0737897
$119$	−64441.7	−0.417157
$120$	−41429.2	−0.262636
$121$	206675.	1.28329
$122$	111381.	0.677506
$123$	−150372.	−0.896197
$124$	48938.9	0.285825
$125$	−147947.	−0.846898
$126$	10135.6	0.0568753
$127$	4520.72	0.0248713	0.0124356	−	0.999923i	$-0.496042\pi$
$127$	4520.72	0.0248713	0.0124356	+	0.999923i	$0.496042\pi$
$128$	−144309.	−0.778515
$129$	−40522.5	−0.214399
$130$	−13856.6	−0.0719117
$131$	−201847.	−1.02765	−0.513823	−	0.857896i	$-0.671771\pi$
$131$	−201847.	−1.02765	−0.513823	+	0.857896i	$0.671771\pi$
$132$	118540.	0.592147
$133$	34425.8	0.168754
$134$	−183484.	−0.882746
$135$	19483.1	0.0920078
$136$	284401.	1.31851
$137$	128569.	0.585242	0.292621	−	0.956229i	$-0.405473\pi$
$137$	128569.	0.585242	0.292621	+	0.956229i	$0.405473\pi$
$138$	84364.9	0.377107
$139$	264506.	1.16118	0.580588	−	0.814198i	$-0.302823\pi$
$139$	264506.	1.16118	0.580588	+	0.814198i	$0.302823\pi$
$140$	−22654.7	−0.0976875
$141$	75679.1	0.320574
$142$	86.2620	0.000359003 0
$143$	98060.0	0.401007
$144$	11566.6	0.0464834
$145$	−188791.	−0.745697
$146$	174680.	0.678207
$147$	−137555.	−0.525028
$148$	164244.	0.616360
$149$	−310579.	−1.14606	−0.573028	−	0.819536i	$-0.694231\pi$
$149$	−310579.	−1.14606	−0.573028	+	0.819536i	$0.694231\pi$
$150$	−69564.5	−0.252441
$151$	150211.	0.536118	0.268059	−	0.963402i	$-0.413618\pi$
$151$	150211.	0.536118	0.268059	+	0.963402i	$0.413618\pi$
$152$	−151932.	−0.533383
$153$	−133747.	−0.461907
$154$	−75880.1	−0.257826
$155$	−60218.0	−0.201325
$156$	31610.5	0.103997
$157$	381735.	1.23598	0.617992	−	0.786185i	$-0.287947\pi$
$157$	381735.	1.23598	0.617992	+	0.786185i	$0.287947\pi$
$158$	298792.	0.952196
$159$	99442.7	0.311947
$160$	159540.	0.492686
$161$	114101.	0.346917
$162$	21036.2	0.0629766
$163$	−43367.4	−0.127848	−0.0639240	−	0.997955i	$-0.520362\pi$
$163$	−43367.4	−0.127848	−0.0639240	+	0.997955i	$0.520362\pi$
$164$	362897.	1.05359
$165$	−145860.	−0.417087
$166$	−287280.	−0.809161
$167$	227398.	0.630951	0.315475	−	0.948934i	$-0.397836\pi$
$167$	227398.	0.630951	0.315475	+	0.948934i	$0.397836\pi$
$168$	−60498.4	−0.165375
$169$	−345144.	−0.929572
$170$	−141490.	−0.375495
$171$	71449.7	0.186857
$172$	97794.2	0.252053
$173$	−196716.	−0.499716	−0.249858	−	0.968282i	$-0.580384\pi$
$173$	−196716.	−0.499716	−0.249858	+	0.968282i	$0.580384\pi$
$174$	−203840.	−0.510408
$175$	−94084.2	−0.232232
$176$	−86592.7	−0.210717
$177$	31329.0	0.0751646
$178$	−410904.	−0.972053
$179$	−51846.3	−0.120944	−0.0604722	−	0.998170i	$-0.519261\pi$
$179$	−51846.3	−0.120944	−0.0604722	+	0.998170i	$0.519261\pi$
$180$	−47019.3	−0.108167
$181$	692422.	1.57099	0.785496	−	0.618866i	$-0.212408\pi$
$181$	692422.	1.57099	0.785496	+	0.618866i	$0.212408\pi$
$182$	−20234.6	−0.0452810
$183$	312650.	0.690130
$184$	−503565.	−1.09651
$185$	−202098.	−0.434142
$186$	−65018.1	−0.137801
$187$	1.00129e6	2.09390
$188$	−182639.	−0.376876
$189$	28450.9	0.0579350
$190$	75586.4	0.151901
$191$	−964737.	−1.91349	−0.956743	−	0.290933i	$-0.906034\pi$
$191$	−964737.	−1.91349	−0.956743	+	0.290933i	$0.906034\pi$
$192$	131132.	0.256717
$193$	−305452.	−0.590268	−0.295134	−	0.955456i	$-0.595364\pi$
$193$	−305452.	−0.590268	−0.295134	+	0.955456i	$0.595364\pi$
$194$	−85496.1	−0.163096
$195$	−38895.9	−0.0732516
$196$	331965.	0.617238
$197$	−31988.0	−0.0587249	−0.0293624	−	0.999569i	$-0.509348\pi$
$197$	−31988.0	−0.0587249	−0.0293624	+	0.999569i	$0.509348\pi$
$198$	−157487.	−0.285484
$199$	428137.	0.766390	0.383195	−	0.923668i	$-0.374824\pi$
$199$	428137.	0.766390	0.383195	+	0.923668i	$0.374824\pi$
$200$	415223.	0.734017
$201$	−515043.	−0.899193
$202$	493636.	0.851193
$203$	−275689.	−0.469547
$204$	322775.	0.543032
$205$	−446535.	−0.742114
$206$	−166697.	−0.273691
$207$	236814.	0.384133
$208$	−23091.3	−0.0370075
$209$	−534906.	−0.847055
$210$	30098.1	0.0470968
$211$	−1.07522e6	−1.66261	−0.831306	−	0.555815i	$-0.812406\pi$
$211$	−1.07522e6	−1.66261	−0.831306	+	0.555815i	$0.812406\pi$
$212$	−239988.	−0.366733
$213$	242.139	0.000365693 0
$214$	692389.	1.03351
$215$	−120333.	−0.177537
$216$	−125563.	−0.183116
$217$	−87935.3	−0.126769
$218$	200588.	0.285867
$219$	490332.	0.690843
$220$	352009.	0.490339
$221$	267010.	0.367746
$222$	−218207.	−0.297157
$223$	541635.	0.729365	0.364682	−	0.931132i	$-0.381178\pi$
$223$	541635.	0.729365	0.364682	+	0.931132i	$0.381178\pi$
$224$	232974.	0.310232
$225$	−195269.	−0.257144
$226$	777641.	1.01276
$227$	−503824.	−0.648954	−0.324477	−	0.945894i	$-0.605188\pi$
$227$	−503824.	−0.648954	−0.324477	+	0.945894i	$0.605188\pi$
$228$	−172432.	−0.219675
$229$	236193.	0.297631	0.148815	−	0.988865i	$-0.452454\pi$
$229$	236193.	0.297631	0.148815	+	0.988865i	$0.452454\pi$
$230$	250525.	0.312271
$231$	−212997.	−0.262629
$232$	1.21670e6	1.48410
$233$	−1.35136e6	−1.63073	−0.815366	−	0.578946i	$-0.803464\pi$
$233$	−1.35136e6	−1.63073	−0.815366	+	0.578946i	$0.803464\pi$
$234$	−41996.4	−0.0501386
$235$	224732.	0.265458
$236$	−75607.3	−0.0883656
$237$	838715.	0.969937
$238$	−206616.	−0.236440
$239$	−1.00537e6	−1.13849	−0.569245	−	0.822168i	$-0.692765\pi$
$239$	−1.00537e6	−1.13849	−0.569245	+	0.822168i	$0.692765\pi$
$240$	34347.3	0.0384915
$241$	−968910.	−1.07458	−0.537292	−	0.843396i	$-0.680553\pi$
$241$	−968910.	−1.07458	−0.537292	+	0.843396i	$0.680553\pi$
$242$	662653.	0.727357
$243$	59049.0	0.0641500
$244$	−754528.	−0.811336
$245$	−408474.	−0.434760
$246$	−482129.	−0.507955
$247$	−142641.	−0.148766
$248$	388086.	0.400681
$249$	−806401.	−0.824238
$250$	−474355.	−0.480013
$251$	−1.74198e6	−1.74525	−0.872626	−	0.488390i	$-0.837584\pi$
$251$	−1.74198e6	−1.74525	−0.872626	+	0.488390i	$0.837584\pi$
$252$	−68661.4	−0.0681101
$253$	−1.77290e6	−1.74134
$254$	14494.5	0.0140968
$255$	−397166.	−0.382492
$256$	−928936.	−0.885902
$257$	−696669.	−0.657951	−0.328976	−	0.944338i	$-0.606703\pi$
$257$	−696669.	−0.657951	−0.328976	+	0.944338i	$0.606703\pi$
$258$	−129925.	−0.121519
$259$	−295120.	−0.273369
$260$	93868.6	0.0861166
$261$	−572184.	−0.519918
$262$	−647171.	−0.582459
$263$	−894241.	−0.797196	−0.398598	−	0.917126i	$-0.630503\pi$
$263$	−894241.	−0.797196	−0.398598	+	0.917126i	$0.630503\pi$
$264$	940021.	0.830095
$265$	295299.	0.258314
$266$	110377.	0.0956481
$267$	−1.15341e6	−0.990164
$268$	1.24297e6	1.05712
$269$	346103.	0.291625	0.145812	−	0.989312i	$-0.453420\pi$
$269$	346103.	0.291625	0.145812	+	0.989312i	$0.453420\pi$
$270$	62467.8	0.0521491
$271$	476055.	0.393762	0.196881	−	0.980427i	$-0.436919\pi$
$271$	476055.	0.393762	0.196881	+	0.980427i	$0.436919\pi$
$272$	−235786.	−0.193239
$273$	−56799.0	−0.0461247
$274$	412224.	0.331709
$275$	1.46188e6	1.16568
$276$	−571511.	−0.451598
$277$	−1.33986e6	−1.04920	−0.524600	−	0.851349i	$-0.675785\pi$
$277$	−1.33986e6	−1.04920	−0.524600	+	0.851349i	$0.675785\pi$
$278$	848071.	0.658143
$279$	−182507.	−0.140368
$280$	−179652.	−0.136942
$281$	767258.	0.579663	0.289831	−	0.957078i	$-0.406401\pi$
$281$	767258.	0.579663	0.289831	+	0.957078i	$0.406401\pi$
$282$	242646.	0.181698
$283$	391631.	0.290677	0.145339	−	0.989382i	$-0.453573\pi$
$283$	391631.	0.290677	0.145339	+	0.989382i	$0.453573\pi$
$284$	−584.362	−0.000429919 0
$285$	212172.	0.154731
$286$	314405.	0.227287
$287$	−652067.	−0.467291
$288$	483530.	0.343512
$289$	1.30659e6	0.920227
$290$	−605312.	−0.422653
$291$	−239989.	−0.166134
$292$	−1.18333e6	−0.812175
$293$	1.78575e6	1.21521	0.607606	−	0.794239i	$-0.292130\pi$
$293$	1.78575e6	1.21521	0.607606	+	0.794239i	$0.292130\pi$
$294$	−441035.	−0.297581
$295$	93032.7	0.0622415
$296$	1.30245e6	0.864039
$297$	−442069.	−0.290803
$298$	−995791.	−0.649573
$299$	−472772.	−0.305826
$300$	471249.	0.302306
$301$	−175720.	−0.111791
$302$	481615.	0.303866
$303$	1.38565e6	0.867053
$304$	125960.	0.0781718
$305$	928426.	0.571476
$306$	−428825.	−0.261804
$307$	−927343.	−0.561558	−0.280779	−	0.959772i	$-0.590593\pi$
$307$	−927343.	−0.561558	−0.280779	+	0.959772i	$0.590593\pi$
$308$	514032.	0.308755
$309$	−467922.	−0.278790
$310$	−193074.	−0.114109
$311$	766407.	0.449323	0.224661	−	0.974437i	$-0.427872\pi$
$311$	766407.	0.449323	0.224661	+	0.974437i	$0.427872\pi$
$312$	250671.	0.145787
$313$	226189.	0.130500	0.0652501	−	0.997869i	$-0.479215\pi$
$313$	226189.	0.130500	0.0652501	+	0.997869i	$0.479215\pi$
$314$	1.22394e6	0.700543
$315$	84486.0	0.0479743
$316$	−2.02410e6	−1.14029
$317$	1.08057e6	0.603955	0.301978	−	0.953315i	$-0.402353\pi$
$317$	1.08057e6	0.603955	0.301978	+	0.953315i	$0.402353\pi$
$318$	318838.	0.176808
$319$	4.28364e6	2.35687
$320$	389401.	0.212580
$321$	1.94355e6	1.05277
$322$	365837.	0.196629
$323$	−1.45651e6	−0.776797
$324$	−142505.	−0.0754166
$325$	389833.	0.204724
$326$	−139047.	−0.0724630
$327$	563055.	0.291193
$328$	2.87777e6	1.47697
$329$	328172.	0.167152
$330$	−467663.	−0.236401
$331$	−2.89963e6	−1.45470	−0.727350	−	0.686267i	$-0.759248\pi$
$331$	−2.89963e6	−1.45470	−0.727350	+	0.686267i	$0.759248\pi$
$332$	1.94611e6	0.968997
$333$	−612512.	−0.302694
$334$	729094.	0.357617
$335$	−1.52944e6	−0.744595
$336$	50156.8	0.0242371
$337$	−204495.	−0.0980863	−0.0490432	−	0.998797i	$-0.515617\pi$
$337$	−204495.	−0.0980863	−0.0490432	+	0.998797i	$0.515617\pi$
$338$	−1.10662e6	−0.526872
$339$	2.18285e6	1.03163
$340$	958494.	0.449668
$341$	1.36634e6	0.636314
$342$	229085.	0.105909
$343$	−1.25242e6	−0.574797
$344$	775509.	0.353338
$345$	703228.	0.318089
$346$	−630719.	−0.283234
$347$	1.14557e6	0.510739	0.255370	−	0.966843i	$-0.417803\pi$
$347$	1.14557e6	0.510739	0.255370	+	0.966843i	$0.417803\pi$
$348$	1.38087e6	0.611230
$349$	3.14511e6	1.38220	0.691101	−	0.722758i	$-0.257126\pi$
$349$	3.14511e6	1.38220	0.691101	+	0.722758i	$0.257126\pi$
$350$	−301657.	−0.131627
$351$	−117885.	−0.0510728
$352$	−3.61994e6	−1.55720
$353$	−2.35284e6	−1.00497	−0.502487	−	0.864584i	$-0.667582\pi$
$353$	−2.35284e6	−1.00497	−0.502487	+	0.864584i	$0.667582\pi$
$354$	100449.	0.0426025
$355$	719.042	0.000302819 0
$356$	2.78357e6	1.16407
$357$	−579975.	−0.240846
$358$	−166232.	−0.0685500
$359$	198560.	0.0813122	0.0406561	−	0.999173i	$-0.487055\pi$
$359$	198560.	0.0813122	0.0406561	+	0.999173i	$0.487055\pi$
$360$	−372863.	−0.151633
$361$	−1.69801e6	−0.685759
$362$	2.22007e6	0.890423
$363$	1.86008e6	0.740909
$364$	137075.	0.0542255
$365$	1.45606e6	0.572067
$366$	1.00243e6	0.391158
$367$	3.33716e6	1.29334	0.646669	−	0.762771i	$-0.276162\pi$
$367$	3.33716e6	1.29334	0.646669	+	0.762771i	$0.276162\pi$
$368$	417485.	0.160702
$369$	−1.35335e6	−0.517420
$370$	−647975.	−0.246067
$371$	431220.	0.162654
$372$	440450.	0.165021
$373$	3.49695e6	1.30142	0.650710	−	0.759326i	$-0.274471\pi$
$373$	3.49695e6	1.30142	0.650710	+	0.759326i	$0.274471\pi$
$374$	3.21039e6	1.18680
$375$	−1.33152e6	−0.488957
$376$	−1.44833e6	−0.528320
$377$	1.14230e6	0.413930
$378$	91220.6	0.0328370
$379$	−4.62014e6	−1.65218	−0.826089	−	0.563539i	$-0.809439\pi$
$379$	−4.62014e6	−1.65218	−0.826089	+	0.563539i	$0.809439\pi$
$380$	−512042.	−0.181906
$381$	40686.4	0.0143594
$382$	−3.09318e6	−1.08454
$383$	−3.77589e6	−1.31529	−0.657645	−	0.753328i	$-0.728447\pi$
$383$	−3.77589e6	−1.31529	−0.657645	+	0.753328i	$0.728447\pi$
$384$	−1.29878e6	−0.449476
$385$	−632502.	−0.217475
$386$	−979353.	−0.334558
$387$	−364703.	−0.123783
$388$	579174.	0.195312
$389$	1.44066e6	0.482710	0.241355	−	0.970437i	$-0.422408\pi$
$389$	1.44066e6	0.482710	0.241355	+	0.970437i	$0.422408\pi$
$390$	−124710.	−0.0415182
$391$	−4.82749e6	−1.59691
$392$	2.63249e6	0.865269
$393$	−1.81662e6	−0.593312
$394$	−102562.	−0.0332846
$395$	2.49060e6	0.803176
$396$	1.06686e6	0.341876
$397$	4.04765e6	1.28892	0.644461	−	0.764637i	$-0.277082\pi$
$397$	4.04765e6	1.28892	0.644461	+	0.764637i	$0.277082\pi$
$398$	1.37271e6	0.434382
$399$	309832.	0.0974302
$400$	−344245.	−0.107576
$401$	−187555.	−0.0582462	−0.0291231	−	0.999576i	$-0.509271\pi$
$401$	−187555.	−0.0582462	−0.0291231	+	0.999576i	$0.509271\pi$
$402$	−1.65135e6	−0.509653
$403$	364355.	0.111754
$404$	−3.34402e6	−1.01933
$405$	175348.	0.0531207
$406$	−883926.	−0.266134
$407$	4.58556e6	1.37216
$408$	2.55961e6	0.761243
$409$	−3.25079e6	−0.960906	−0.480453	−	0.877021i	$-0.659528\pi$
$409$	−3.25079e6	−0.960906	−0.480453	+	0.877021i	$0.659528\pi$
$410$	−1.43170e6	−0.420623
$411$	1.15712e6	0.337889
$412$	1.12925e6	0.327753
$413$	135854.	0.0391920
$414$	759284.	0.217723
$415$	−2.39464e6	−0.682526
$416$	−965313.	−0.273486
$417$	2.38055e6	0.670405
$418$	−1.71504e6	−0.480102
$419$	3.65412e6	1.01683	0.508414	−	0.861113i	$-0.330232\pi$
$419$	3.65412e6	1.01683	0.508414	+	0.861113i	$0.330232\pi$
$420$	−203893.	−0.0563999
$421$	−5.36572e6	−1.47544	−0.737722	−	0.675105i	$-0.764098\pi$
$421$	−5.36572e6	−1.47544	−0.737722	+	0.675105i	$0.764098\pi$
$422$	−3.44742e6	−0.942351
$423$	681112.	0.185084
$424$	−1.90311e6	−0.514101
$425$	3.98059e6	1.06899
$426$	776.358	0.000207271 0
$427$	1.35576e6	0.359844
$428$	−4.69043e6	−1.23767
$429$	882540.	0.231522
$430$	−385818.	−0.100626
$431$	−6.87518e6	−1.78275	−0.891377	−	0.453264i	$-0.850260\pi$
$431$	−6.87518e6	−1.78275	−0.891377	+	0.453264i	$0.850260\pi$
$432$	104099.	0.0268372
$433$	40489.0	0.0103781	0.00518904	−	0.999987i	$-0.498348\pi$
$433$	40489.0	0.0103781	0.00518904	+	0.999987i	$0.498348\pi$
$434$	−281942.	−0.0718515
$435$	−1.69912e6	−0.430528
$436$	−1.35884e6	−0.342335
$437$	2.57892e6	0.646002
$438$	1.57212e6	0.391563
$439$	−4.44389e6	−1.10053	−0.550265	−	0.834990i	$-0.685473\pi$
$439$	−4.44389e6	−1.10053	−0.550265	+	0.834990i	$0.685473\pi$
$440$	2.79143e6	0.687377
$441$	−1.23799e6	−0.303125
$442$	856101.	0.208434
$443$	−278084.	−0.0673236	−0.0336618	−	0.999433i	$-0.510717\pi$
$443$	−278084.	−0.0673236	−0.0336618	+	0.999433i	$0.510717\pi$
$444$	1.47819e6	0.355856
$445$	−3.42511e6	−0.819925
$446$	1.73662e6	0.413397
$447$	−2.79521e6	−0.661676
$448$	568636.	0.133856
$449$	1.07874e6	0.252523	0.126262	−	0.991997i	$-0.459702\pi$
$449$	1.07874e6	0.252523	0.126262	+	0.991997i	$0.459702\pi$
$450$	−626081.	−0.145747
$451$	1.01318e7	2.34555
$452$	−5.26795e6	−1.21282
$453$	1.35190e6	0.309528
$454$	−1.61538e6	−0.367821
$455$	−168667.	−0.0381945
$456$	−1.36738e6	−0.307949
$457$	−2.34460e6	−0.525144	−0.262572	−	0.964912i	$-0.584571\pi$
$457$	−2.34460e6	−0.525144	−0.262572	+	0.964912i	$0.584571\pi$
$458$	757292.	0.168694
$459$	−1.20372e6	−0.266682
$460$	−1.69712e6	−0.373954
$461$	−8.15879e6	−1.78802	−0.894012	−	0.448043i	$-0.852121\pi$
$461$	−8.15879e6	−1.78802	−0.894012	+	0.448043i	$0.852121\pi$
$462$	−682921.	−0.148856
$463$	5.42287e6	1.17565	0.587823	−	0.808990i	$-0.299985\pi$
$463$	5.42287e6	1.17565	0.587823	+	0.808990i	$0.299985\pi$
$464$	−1.00872e6	−0.217508
$465$	−541962.	−0.116235
$466$	−4.33281e6	−0.924282
$467$	8.21137e6	1.74230	0.871151	−	0.491015i	$-0.163374\pi$
$467$	8.21137e6	1.74230	0.871151	+	0.491015i	$0.163374\pi$
$468$	284495.	0.0600426
$469$	−2.23341e6	−0.468853
$470$	720547.	0.150459
$471$	3.43561e6	0.713595
$472$	−599566.	−0.123874
$473$	2.73034e6	0.561130
$474$	2.68913e6	0.549751
$475$	−2.12649e6	−0.432444
$476$	1.39967e6	0.283145
$477$	894985.	0.180102
$478$	−3.22345e6	−0.645285
$479$	−5.34027e6	−1.06347	−0.531734	−	0.846911i	$-0.678459\pi$
$479$	−5.34027e6	−1.06347	−0.531734	+	0.846911i	$0.678459\pi$
$480$	1.43586e6	0.284452
$481$	1.22281e6	0.240989
$482$	−3.10656e6	−0.609064
$483$	1.02691e6	0.200293
$484$	−4.48899e6	−0.871034
$485$	−712658.	−0.137571
$486$	189326.	0.0363596
$487$	2.52006e6	0.481492	0.240746	−	0.970588i	$-0.422608\pi$
$487$	2.52006e6	0.481492	0.240746	+	0.970588i	$0.422608\pi$
$488$	−5.98341e6	−1.13736
$489$	−390306.	−0.0738131
$490$	−1.30967e6	−0.246417
$491$	−8.33075e6	−1.55948	−0.779741	−	0.626102i	$-0.784649\pi$
$491$	−8.33075e6	−1.55948	−0.779741	+	0.626102i	$0.784649\pi$
$492$	3.26607e6	0.608293
$493$	1.16640e7	2.16138
$494$	−457343.	−0.0843188
$495$	−1.31274e6	−0.240805
$496$	−321746.	−0.0587232
$497$	1050.00	0.000190678 0
$498$	−2.58552e6	−0.467169
$499$	9.76824e6	1.75616	0.878082	−	0.478510i	$-0.158823\pi$
$499$	9.76824e6	1.75616	0.878082	+	0.478510i	$0.158823\pi$
$500$	3.21341e6	0.574832
$501$	2.04658e6	0.364280
$502$	−5.58521e6	−0.989190
$503$	2.49233e6	0.439223	0.219612	−	0.975587i	$-0.429521\pi$
$503$	2.49233e6	0.439223	0.219612	+	0.975587i	$0.429521\pi$
$504$	−544485.	−0.0954794
$505$	4.11473e6	0.717981
$506$	−5.68436e6	−0.986974
$507$	−3.10629e6	−0.536689
$508$	−98189.9	−0.0168814
$509$	−7.02509e6	−1.20187	−0.600935	−	0.799298i	$-0.705205\pi$
$509$	−7.02509e6	−1.20187	−0.600935	+	0.799298i	$0.705205\pi$
$510$	−1.27341e6	−0.216792
$511$	2.12626e6	0.360216
$512$	1.63948e6	0.276395
$513$	643047.	0.107882
$514$	−2.23369e6	−0.372920
$515$	−1.38951e6	−0.230858
$516$	880148.	0.145523
$517$	−5.09913e6	−0.839015
$518$	−946226.	−0.154942
$519$	−1.77044e6	−0.288511
$520$	744379.	0.120722
$521$	−5.27900e6	−0.852034	−0.426017	−	0.904715i	$-0.640084\pi$
$521$	−5.27900e6	−0.852034	−0.426017	+	0.904715i	$0.640084\pi$
$522$	−1.83456e6	−0.294684
$523$	−291703.	−0.0466322	−0.0233161	−	0.999728i	$-0.507422\pi$
$523$	−291703.	−0.0466322	−0.0233161	+	0.999728i	$0.507422\pi$
$524$	4.38411e6	0.697514
$525$	−846758.	−0.134079
$526$	−2.86716e6	−0.451843
$527$	3.72043e6	0.583535
$528$	−779334.	−0.121658
$529$	2.11127e6	0.328023
$530$	946802.	0.146410
$531$	281961.	0.0433963
$532$	−747727.	−0.114542
$533$	2.70180e6	0.411941
$534$	−3.69813e6	−0.561215
$535$	5.77145e6	0.871767
$536$	9.85674e6	1.48191
$537$	−466617.	−0.0698273
$538$	1.10969e6	0.165290
$539$	9.26821e6	1.37412
$540$	−423173.	−0.0624502
$541$	1.81999e6	0.267347	0.133673	−	0.991025i	$-0.457323\pi$
$541$	1.81999e6	0.267347	0.133673	+	0.991025i	$0.457323\pi$
$542$	1.52635e6	0.223180
$543$	6.23179e6	0.907013
$544$	−9.85682e6	−1.42804
$545$	1.67201e6	0.241128
$546$	−182112.	−0.0261430
$547$	−9.72974e6	−1.39038	−0.695189	−	0.718827i	$-0.744679\pi$
$547$	−9.72974e6	−1.39038	−0.695189	+	0.718827i	$0.744679\pi$
$548$	−2.79252e6	−0.397232
$549$	2.81385e6	0.398447
$550$	4.68714e6	0.660695
$551$	−6.23112e6	−0.874353
$552$	−4.53208e6	−0.633068
$553$	3.63698e6	0.505740
$554$	−4.29591e6	−0.594676
$555$	−1.81888e6	−0.250652
$556$	−5.74506e6	−0.788147
$557$	−3.95131e6	−0.539638	−0.269819	−	0.962911i	$-0.586964\pi$
$557$	−3.95131e6	−0.539638	−0.269819	+	0.962911i	$0.586964\pi$
$558$	−585163.	−0.0795594
$559$	728087.	0.0985494
$560$	148942.	0.0200701
$561$	9.01163e6	1.20892
$562$	2.46002e6	0.328547
$563$	−907456.	−0.120658	−0.0603288	−	0.998179i	$-0.519215\pi$
$563$	−907456.	−0.120658	−0.0603288	+	0.998179i	$0.519215\pi$
$564$	−1.64375e6	−0.217589
$565$	6.48207e6	0.854265
$566$	1.25567e6	0.164753
$567$	256058.	0.0334488
$568$	−4633.99	−0.000602677 0
$569$	−4.32375e6	−0.559861	−0.279931	−	0.960020i	$-0.590311\pi$
$569$	−4.32375e6	−0.559861	−0.279931	+	0.960020i	$0.590311\pi$
$570$	680277.	0.0876999
$571$	−1.76582e6	−0.226650	−0.113325	−	0.993558i	$-0.536150\pi$
$571$	−1.76582e6	−0.226650	−0.113325	+	0.993558i	$0.536150\pi$
$572$	−2.12986e6	−0.272183
$573$	−8.68263e6	−1.10475
$574$	−2.09069e6	−0.264856
$575$	−7.04808e6	−0.888999
$576$	1.18019e6	0.148216
$577$	4.97841e6	0.622516	0.311258	−	0.950325i	$-0.399250\pi$
$577$	4.97841e6	0.622516	0.311258	+	0.950325i	$0.399250\pi$
$578$	4.18925e6	0.521575
$579$	−2.74906e6	−0.340791
$580$	4.10054e6	0.506141
$581$	−3.49685e6	−0.429770
$582$	−769465.	−0.0941633
$583$	−6.70028e6	−0.816435
$584$	−9.38383e6	−1.13854
$585$	−350063.	−0.0422918
$586$	5.72556e6	0.688769
$587$	2.55026e6	0.305484	0.152742	−	0.988266i	$-0.451190\pi$
$587$	2.55026e6	0.305484	0.152742	+	0.988266i	$0.451190\pi$
$588$	2.98769e6	0.356362
$589$	−1.98751e6	−0.236060
$590$	298286.	0.0352779
$591$	−287892.	−0.0339048
$592$	−1.07981e6	−0.126632
$593$	5.95905e6	0.695889	0.347945	−	0.937515i	$-0.386880\pi$
$593$	5.95905e6	0.695889	0.347945	+	0.937515i	$0.386880\pi$
$594$	−1.41738e6	−0.164824
$595$	−1.72226e6	−0.199437
$596$	6.74576e6	0.777885
$597$	3.85323e6	0.442475
$598$	−1.51582e6	−0.173339
$599$	7.34100e6	0.835966	0.417983	−	0.908455i	$-0.362737\pi$
$599$	7.34100e6	0.835966	0.417983	+	0.908455i	$0.362737\pi$
$600$	3.73701e6	0.423785
$601$	5.04285e6	0.569495	0.284748	−	0.958603i	$-0.408090\pi$
$601$	5.04285e6	0.569495	0.284748	+	0.958603i	$0.408090\pi$
$602$	−563403.	−0.0633619
$603$	−4.63538e6	−0.519149
$604$	−3.26259e6	−0.363890
$605$	5.52358e6	0.613524
$606$	4.44272e6	0.491437
$607$	1.78269e7	1.96383	0.981916	−	0.189318i	$-0.0606277\pi$
$607$	1.78269e7	1.96383	0.981916	+	0.189318i	$0.0606277\pi$
$608$	5.26567e6	0.577690
$609$	−2.48120e6	−0.271093
$610$	2.97676e6	0.323906
$611$	−1.35976e6	−0.147353
$612$	2.90498e6	0.313519
$613$	1.10977e7	1.19284	0.596421	−	0.802672i	$-0.296589\pi$
$613$	1.10977e7	1.19284	0.596421	+	0.802672i	$0.296589\pi$
$614$	−2.97329e6	−0.318285
$615$	−4.01881e6	−0.428460
$616$	4.07628e6	0.432824
$617$	6.00790e6	0.635345	0.317673	−	0.948200i	$-0.397099\pi$
$617$	6.00790e6	0.635345	0.317673	+	0.948200i	$0.397099\pi$
$618$	−1.50027e6	−0.158015
$619$	1.79364e6	0.188151	0.0940757	−	0.995565i	$-0.470010\pi$
$619$	1.79364e6	0.188151	0.0940757	+	0.995565i	$0.470010\pi$
$620$	1.30793e6	0.136649
$621$	2.13133e6	0.221779
$622$	2.45729e6	0.254672
$623$	−5.00163e6	−0.516287
$624$	−207822.	−0.0213663
$625$	3.57952e6	0.366543
$626$	725218.	0.0739661
$627$	−4.81415e6	−0.489048
$628$	−8.29127e6	−0.838923
$629$	1.24861e7	1.25835
$630$	270883.	0.0271913
$631$	−1.00827e7	−1.00810	−0.504052	−	0.863673i	$-0.668158\pi$
$631$	−1.00827e7	−1.00810	−0.504052	+	0.863673i	$0.668158\pi$
$632$	−1.60511e7	−1.59850
$633$	−9.67697e6	−0.959909
$634$	3.46457e6	0.342316
$635$	120820.	0.0118906
$636$	−2.15989e6	−0.211734
$637$	2.47151e6	0.241332
$638$	1.37344e7	1.33585
$639$	2179.25	0.000211133 0
$640$	−3.85677e6	−0.372198
$641$	−5.75277e6	−0.553009	−0.276505	−	0.961013i	$-0.589176\pi$
$641$	−5.75277e6	−0.553009	−0.276505	+	0.961013i	$0.589176\pi$
$642$	6.23150e6	0.596699
$643$	−5.46072e6	−0.520862	−0.260431	−	0.965492i	$-0.583865\pi$
$643$	−5.46072e6	−0.520862	−0.260431	+	0.965492i	$0.583865\pi$
$644$	−2.47828e6	−0.235470
$645$	−1.08300e6	−0.102501
$646$	−4.66993e6	−0.440280
$647$	2.48477e6	0.233360	0.116680	−	0.993170i	$-0.462775\pi$
$647$	2.48477e6	0.233360	0.116680	+	0.993170i	$0.462775\pi$
$648$	−1.13006e6	−0.105722
$649$	−2.11089e6	−0.196723
$650$	1.24990e6	0.116036
$651$	−791417.	−0.0731902
$652$	941939.	0.0867768
$653$	−9.47172e6	−0.869253	−0.434626	−	0.900611i	$-0.643120\pi$
$653$	−9.47172e6	−0.869253	−0.434626	+	0.900611i	$0.643120\pi$
$654$	1.80529e6	0.165045
$655$	−5.39453e6	−0.491304
$656$	−2.38585e6	−0.216463
$657$	4.41298e6	0.398859
$658$	1.05220e6	0.0947402
$659$	9.34926e6	0.838617	0.419309	−	0.907844i	$-0.362273\pi$
$659$	9.34926e6	0.838617	0.419309	+	0.907844i	$0.362273\pi$
$660$	3.16808e6	0.283097
$661$	4.30563e6	0.383295	0.191647	−	0.981464i	$-0.438617\pi$
$661$	4.30563e6	0.383295	0.191647	+	0.981464i	$0.438617\pi$
$662$	−9.29694e6	−0.824509
$663$	2.40309e6	0.212318
$664$	1.54327e7	1.35838
$665$	920057.	0.0806790
$666$	−1.96386e6	−0.171564
$667$	−2.06525e7	−1.79746
$668$	−4.93908e6	−0.428258
$669$	4.87472e6	0.421099
$670$	−4.90376e6	−0.422029
$671$	−2.10658e7	−1.80623
$672$	2.09676e6	0.179113
$673$	1.43291e7	1.21950	0.609748	−	0.792595i	$-0.291271\pi$
$673$	1.43291e7	1.21950	0.609748	+	0.792595i	$0.291271\pi$
$674$	−655662.	−0.0555943
$675$	−1.75742e6	−0.148462
$676$	7.49652e6	0.630947
$677$	−6.86042e6	−0.575279	−0.287640	−	0.957739i	$-0.592871\pi$
$677$	−6.86042e6	−0.575279	−0.287640	+	0.957739i	$0.592871\pi$
$678$	6.99877e6	0.584719
$679$	−1.04068e6	−0.0866250
$680$	7.60086e6	0.630363
$681$	−4.53441e6	−0.374674
$682$	4.38081e6	0.360656
$683$	−2.00520e7	−1.64478	−0.822388	−	0.568927i	$-0.807359\pi$
$683$	−2.00520e7	−1.64478	−0.822388	+	0.568927i	$0.807359\pi$
$684$	−1.55189e6	−0.126829
$685$	3.43612e6	0.279796
$686$	−4.01557e6	−0.325789
$687$	2.12573e6	0.171837
$688$	−642943.	−0.0517847
$689$	−1.78674e6	−0.143388
$690$	2.25472e6	0.180290
$691$	1.21795e7	0.970365	0.485182	−	0.874413i	$-0.338753\pi$
$691$	1.21795e7	0.970365	0.485182	+	0.874413i	$0.338753\pi$
$692$	4.27266e6	0.339182
$693$	−1.91697e6	−0.151629
$694$	3.67299e6	0.289482
$695$	7.06914e6	0.555142
$696$	1.09503e7	0.856846
$697$	2.75881e7	2.15100
$698$	1.00840e7	0.783418
$699$	−1.21623e7	−0.941503
$700$	2.04351e6	0.157627
$701$	1.23445e7	0.948809	0.474404	−	0.880307i	$-0.342663\pi$
$701$	1.23445e7	0.948809	0.474404	+	0.880307i	$0.342663\pi$
$702$	−377967.	−0.0289475
$703$	−6.67029e6	−0.509045
$704$	−8.83544e6	−0.671888
$705$	2.02259e6	0.153262
$706$	−7.54378e6	−0.569609
$707$	6.00867e6	0.452095
$708$	−680465.	−0.0510179
$709$	2.21727e7	1.65654	0.828272	−	0.560327i	$-0.189324\pi$
$709$	2.21727e7	1.65654	0.828272	+	0.560327i	$0.189324\pi$
$710$	2305.42	0.000171635 0
$711$	7.54844e6	0.559994
$712$	2.20737e7	1.63183
$713$	−6.58745e6	−0.485281
$714$	−1.85954e6	−0.136509
$715$	2.62074e6	0.191716
$716$	1.12610e6	0.0820909
$717$	−9.04830e6	−0.657308
$718$	636632.	0.0460869
$719$	−2.40050e6	−0.173173	−0.0865864	−	0.996244i	$-0.527596\pi$
$719$	−2.40050e6	−0.173173	−0.0865864	+	0.996244i	$0.527596\pi$
$720$	309126.	0.0222231
$721$	−2.02908e6	−0.145365
$722$	−5.44423e6	−0.388681
$723$	−8.72019e6	−0.620412
$724$	−1.50394e7	−1.06631
$725$	1.70294e7	1.20325
$726$	5.96387e6	0.419940
$727$	−9.51466e6	−0.667663	−0.333831	−	0.942633i	$-0.608342\pi$
$727$	−9.51466e6	−0.667663	−0.333831	+	0.942633i	$0.608342\pi$
$728$	1.08700e6	0.0760155
$729$	531441.	0.0370370
$730$	4.66848e6	0.324242
$731$	7.43451e6	0.514587
$732$	−6.79075e6	−0.468425
$733$	1.04964e6	0.0721572	0.0360786	−	0.999349i	$-0.488513\pi$
$733$	1.04964e6	0.0721572	0.0360786	+	0.999349i	$0.488513\pi$
$734$	1.06998e7	0.733050
$735$	−3.67627e6	−0.251009
$736$	1.74526e7	1.18759
$737$	3.47027e7	2.35339
$738$	−4.33916e6	−0.293268
$739$	−2.68604e6	−0.180926	−0.0904629	−	0.995900i	$-0.528835\pi$
$739$	−2.68604e6	−0.180926	−0.0904629	+	0.995900i	$0.528835\pi$
$740$	4.38955e6	0.294674
$741$	−1.28377e6	−0.0858898
$742$	1.38260e6	0.0921905
$743$	−2.09335e7	−1.39114	−0.695569	−	0.718460i	$-0.744847\pi$
$743$	−2.09335e7	−1.39114	−0.695569	+	0.718460i	$0.744847\pi$
$744$	3.49277e6	0.231333
$745$	−8.30047e6	−0.547914
$746$	1.12121e7	0.737632
$747$	−7.25761e6	−0.475874
$748$	−2.17481e7	−1.42124
$749$	8.42794e6	0.548930
$750$	−4.26919e6	−0.277136
$751$	2.59501e7	1.67895	0.839477	−	0.543395i	$-0.182861\pi$
$751$	2.59501e7	1.67895	0.839477	+	0.543395i	$0.182861\pi$
$752$	1.20075e6	0.0774298
$753$	−1.56778e7	−1.00762
$754$	3.66250e6	0.234611
$755$	4.01452e6	0.256311
$756$	−617953.	−0.0393234
$757$	−8.97503e6	−0.569241	−0.284620	−	0.958640i	$-0.591868\pi$
$757$	−8.97503e6	−0.569241	−0.284620	+	0.958640i	$0.591868\pi$
$758$	−1.48133e7	−0.936438
$759$	−1.59561e7	−1.00536
$760$	−4.06050e6	−0.255003
$761$	1.20515e7	0.754361	0.377180	−	0.926140i	$-0.376894\pi$
$761$	1.20515e7	0.754361	0.377180	+	0.926140i	$0.376894\pi$
$762$	130451.	0.00813878
$763$	2.44161e6	0.151833
$764$	2.09541e7	1.29878
$765$	−3.57450e6	−0.220832
$766$	−1.21064e7	−0.745493
$767$	−562903.	−0.0345498
$768$	−8.36042e6	−0.511476
$769$	1.32176e7	0.806001	0.403001	−	0.915200i	$-0.367967\pi$
$769$	1.32176e7	0.806001	0.403001	+	0.915200i	$0.367967\pi$
$770$	−2.02796e6	−0.123263
$771$	−6.27002e6	−0.379868
$772$	6.63440e6	0.400644
$773$	−1.10628e7	−0.665914	−0.332957	−	0.942942i	$-0.608046\pi$
$773$	−1.10628e7	−0.665914	−0.332957	+	0.942942i	$0.608046\pi$
$774$	−1.16933e6	−0.0701590
$775$	5.43179e6	0.324855
$776$	4.59285e6	0.273797
$777$	−2.65608e6	−0.157829
$778$	4.61910e6	0.273595
$779$	−1.47380e7	−0.870152
$780$	844818.	0.0497195
$781$	−16314.9	−0.000957100 0
$782$	−1.54781e7	−0.905109
$783$	−5.14966e6	−0.300175
$784$	−2.18249e6	−0.126813
$785$	1.02022e7	0.590907
$786$	−5.82454e6	−0.336283
$787$	−1.33119e7	−0.766132	−0.383066	−	0.923721i	$-0.625132\pi$
$787$	−1.33119e7	−0.766132	−0.383066	+	0.923721i	$0.625132\pi$
$788$	694779.	0.0398595
$789$	−8.04817e6	−0.460261
$790$	7.98547e6	0.455232
$791$	9.46565e6	0.537910
$792$	8.46019e6	0.479256
$793$	−5.61753e6	−0.317221
$794$	1.29778e7	0.730548
$795$	2.65769e6	0.149137
$796$	−9.29912e6	−0.520186
$797$	1.61590e6	0.0901089	0.0450544	−	0.998985i	$-0.485654\pi$
$797$	1.61590e6	0.0901089	0.0450544	+	0.998985i	$0.485654\pi$
$798$	993397.	0.0552224
$799$	−1.38846e7	−0.769423
$800$	−1.43909e7	−0.794991
$801$	−1.03807e7	−0.571672
$802$	−601347.	−0.0330133
$803$	−3.30377e7	−1.80809
$804$	1.11867e7	0.610327
$805$	3.04945e6	0.165856
$806$	1.16821e6	0.0633408
$807$	3.11492e6	0.168370
$808$	−2.65181e7	−1.42894
$809$	−1.48836e7	−0.799535	−0.399768	−	0.916617i	$-0.630909\pi$
$809$	−1.48836e7	−0.799535	−0.399768	+	0.916617i	$0.630909\pi$
$810$	562210.	0.0301083
$811$	−3.19912e7	−1.70796	−0.853982	−	0.520303i	$-0.825819\pi$
$811$	−3.19912e7	−1.70796	−0.853982	+	0.520303i	$0.825819\pi$
$812$	5.98795e6	0.318705
$813$	4.28450e6	0.227339
$814$	1.47024e7	0.777728
$815$	−1.15903e6	−0.0611224
$816$	−2.12207e6	−0.111567
$817$	−3.97163e6	−0.208168
$818$	−1.04228e7	−0.544632
$819$	−511191.	−0.0266301
$820$	9.69873e6	0.503709
$821$	−2.95946e7	−1.53234	−0.766169	−	0.642640i	$-0.777839\pi$
$821$	−2.95946e7	−1.53234	−0.766169	+	0.642640i	$0.777839\pi$
$822$	3.71002e6	0.191512
$823$	1.71026e7	0.880163	0.440081	−	0.897958i	$-0.354950\pi$
$823$	1.71026e7	0.880163	0.440081	+	0.897958i	$0.354950\pi$
$824$	8.95496e6	0.459458
$825$	1.31569e7	0.673005
$826$	435581.	0.0222136
$827$	−2.24600e7	−1.14195	−0.570974	−	0.820968i	$-0.693434\pi$
$827$	−2.24600e7	−1.14195	−0.570974	+	0.820968i	$0.693434\pi$
$828$	−5.14360e6	−0.260730
$829$	−2.65000e7	−1.33924	−0.669622	−	0.742702i	$-0.733544\pi$
$829$	−2.65000e7	−1.33924	−0.669622	+	0.742702i	$0.733544\pi$
$830$	−7.67780e6	−0.386849
$831$	−1.20587e7	−0.605756
$832$	−2.35611e6	−0.118001
$833$	2.52367e7	1.26014
$834$	7.63263e6	0.379979
$835$	6.07740e6	0.301649
$836$	1.16182e7	0.574938
$837$	−1.64256e6	−0.0810417
$838$	1.17160e7	0.576328
$839$	3.38841e7	1.66185	0.830924	−	0.556386i	$-0.187813\pi$
$839$	3.38841e7	1.66185	0.830924	+	0.556386i	$0.187813\pi$
$840$	−1.61687e6	−0.0790636
$841$	2.93890e7	1.43283
$842$	−1.72038e7	−0.836266
$843$	6.90532e6	0.334669
$844$	2.33537e7	1.12850
$845$	−9.22426e6	−0.444416
$846$	2.18381e6	0.104903
$847$	8.06598e6	0.386321
$848$	1.57779e6	0.0753459
$849$	3.52468e6	0.167823
$850$	1.27627e7	0.605894
$851$	−2.21081e7	−1.04647
$852$	−5259.26	−0.000248214 0
$853$	−1.88452e6	−0.0886804	−0.0443402	−	0.999016i	$-0.514119\pi$
$853$	−1.88452e6	−0.0886804	−0.0443402	+	0.999016i	$0.514119\pi$
$854$	4.34691e6	0.203956
$855$	1.90955e6	0.0893339
$856$	−3.71951e7	−1.73501
$857$	1.95529e6	0.0909407	0.0454704	−	0.998966i	$-0.485521\pi$
$857$	1.95529e6	0.0909407	0.0454704	+	0.998966i	$0.485521\pi$
$858$	2.82964e6	0.131224
$859$	−1.15147e7	−0.532437	−0.266219	−	0.963913i	$-0.585774\pi$
$859$	−1.15147e7	−0.532437	−0.266219	+	0.963913i	$0.585774\pi$
$860$	2.61363e6	0.120503
$861$	−5.86860e6	−0.269791
$862$	−2.20435e7	−1.01045
$863$	2.60655e6	0.119135	0.0595674	−	0.998224i	$-0.481028\pi$
$863$	2.60655e6	0.119135	0.0595674	+	0.998224i	$0.481028\pi$
$864$	4.35177e6	0.198327
$865$	−5.25739e6	−0.238908
$866$	129818.	0.00588219
$867$	1.17593e7	0.531293
$868$	1.90995e6	0.0860445
$869$	−5.65112e7	−2.53855
$870$	−5.44781e6	−0.244019
$871$	9.25402e6	0.413319
$872$	−1.07756e7	−0.479899
$873$	−2.15990e6	−0.0959177
$874$	8.26865e6	0.366147
$875$	−5.77397e6	−0.254950
$876$	−1.06500e7	−0.468910
$877$	3.54109e7	1.55467	0.777335	−	0.629087i	$-0.216571\pi$
$877$	3.54109e7	1.55467	0.777335	+	0.629087i	$0.216571\pi$
$878$	−1.42482e7	−0.623769
$879$	1.60718e7	0.701602
$880$	−2.31426e6	−0.100741
$881$	1.78051e7	0.772867	0.386434	−	0.922317i	$-0.373707\pi$
$881$	1.78051e7	0.772867	0.386434	+	0.922317i	$0.373707\pi$
$882$	−3.96931e6	−0.171808
$883$	−3.70288e7	−1.59822	−0.799111	−	0.601183i	$-0.794696\pi$
$883$	−3.70288e7	−1.59822	−0.799111	+	0.601183i	$0.794696\pi$
$884$	−5.79946e6	−0.249607
$885$	837294.	0.0359352
$886$	−891607.	−0.0381583
$887$	−3.85936e7	−1.64705	−0.823524	−	0.567281i	$-0.807995\pi$
$887$	−3.85936e7	−1.64705	−0.823524	+	0.567281i	$0.807995\pi$
$888$	1.17221e7	0.498853
$889$	176431.	0.00748723
$890$	−1.09817e7	−0.464725
$891$	−3.97862e6	−0.167895
$892$	−1.17643e7	−0.495056
$893$	7.41735e6	0.311258
$894$	−8.96212e6	−0.375031
$895$	−1.38564e6	−0.0578218
$896$	−5.63197e6	−0.234364
$897$	−4.25495e6	−0.176569
$898$	3.45871e6	0.143128
$899$	1.59164e7	0.656820
$900$	4.24124e6	0.174537
$901$	−1.82444e7	−0.748716
$902$	3.24850e7	1.32943
$903$	−1.58148e6	−0.0645424
$904$	−4.17749e7	−1.70018
$905$	1.85056e7	0.751070
$906$	4.33453e6	0.175437
$907$	−9.11662e6	−0.367973	−0.183986	−	0.982929i	$-0.558900\pi$
$907$	−9.11662e6	−0.367973	−0.183986	+	0.982929i	$0.558900\pi$
$908$	1.09430e7	0.440477
$909$	1.24708e7	0.500593
$910$	−540787.	−0.0216483
$911$	−4.35218e7	−1.73745	−0.868723	−	0.495299i	$-0.835059\pi$
$911$	−4.35218e7	−1.73745	−0.868723	+	0.495299i	$0.835059\pi$
$912$	1.13364e6	0.0451325
$913$	5.43339e7	2.15722
$914$	−7.51737e6	−0.297646
$915$	8.35583e6	0.329942
$916$	−5.13010e6	−0.202017
$917$	−7.87753e6	−0.309362
$918$	−3.85943e6	−0.151153
$919$	2.99781e6	0.117089	0.0585444	−	0.998285i	$-0.481354\pi$
$919$	2.99781e6	0.117089	0.0585444	+	0.998285i	$0.481354\pi$
$920$	−1.34582e7	−0.524224
$921$	−8.34609e6	−0.324216
$922$	−2.61591e7	−1.01343
$923$	−4350.63	−0.000168092 0
$924$	4.62629e6	0.178260
$925$	1.82296e7	0.700525
$926$	1.73871e7	0.666344
$927$	−4.21130e6	−0.160959
$928$	−4.21686e7	−1.60738
$929$	2.19993e7	0.836313	0.418156	−	0.908375i	$-0.362676\pi$
$929$	2.19993e7	0.836313	0.418156	+	0.908375i	$0.362676\pi$
$930$	−1.73766e6	−0.0658807
$931$	−1.34818e7	−0.509770
$932$	2.93516e7	1.10686
$933$	6.89767e6	0.259417
$934$	2.63277e7	0.987519
$935$	2.67604e7	1.00107
$936$	2.25604e6	0.0841701
$937$	8.01794e6	0.298341	0.149171	−	0.988811i	$-0.452340\pi$
$937$	8.01794e6	0.298341	0.149171	+	0.988811i	$0.452340\pi$
$938$	−7.16087e6	−0.265741
$939$	2.03570e6	0.0753443
$940$	−4.88118e6	−0.180179
$941$	9.19445e6	0.338494	0.169247	−	0.985574i	$-0.445866\pi$
$941$	9.19445e6	0.338494	0.169247	+	0.985574i	$0.445866\pi$
$942$	1.10154e7	0.404459
$943$	−4.88479e7	−1.78882
$944$	497076.	0.0181549
$945$	760374.	0.0276980
$946$	8.75414e6	0.318043
$947$	−4.27420e6	−0.154874	−0.0774372	−	0.996997i	$-0.524674\pi$
$947$	−4.27420e6	−0.154874	−0.0774372	+	0.996997i	$0.524674\pi$
$948$	−1.82169e7	−0.658344
$949$	−8.81002e6	−0.317550
$950$	−6.81806e6	−0.245105
$951$	9.72513e6	0.348694
$952$	1.10994e7	0.396924
$953$	−5.03679e7	−1.79648	−0.898239	−	0.439507i	$-0.855153\pi$
$953$	−5.03679e7	−1.79648	−0.898239	+	0.439507i	$0.855153\pi$
$954$	2.86954e6	0.102080
$955$	−2.57834e7	−0.914812
$956$	2.18365e7	0.772750
$957$	3.85528e7	1.36074
$958$	−1.71222e7	−0.602763
$959$	5.01770e6	0.176181
$960$	3.50461e6	0.122733
$961$	−2.35524e7	−0.822670
$962$	3.92063e6	0.136590
$963$	1.74920e7	0.607817
$964$	2.10447e7	0.729374
$965$	−8.16345e6	−0.282199
$966$	3.29253e6	0.113524
$967$	−1.89781e6	−0.0652659	−0.0326329	−	0.999467i	$-0.510389\pi$
$967$	−1.89781e6	−0.0652659	−0.0326329	+	0.999467i	$0.510389\pi$
$968$	−3.55977e7	−1.22105
$969$	−1.31086e7	−0.448484
$970$	−2.28496e6	−0.0779738
$971$	2.68041e7	0.912331	0.456166	−	0.889895i	$-0.349222\pi$
$971$	2.68041e7	0.912331	0.456166	+	0.889895i	$0.349222\pi$
$972$	−1.28254e6	−0.0435418
$973$	1.03229e7	0.349560
$974$	8.07994e6	0.272905
$975$	3.50849e6	0.118198
$976$	4.96061e6	0.166690
$977$	4.27764e7	1.43373	0.716865	−	0.697212i	$-0.245576\pi$
$977$	4.27764e7	1.43373	0.716865	+	0.697212i	$0.245576\pi$
$978$	−1.25142e6	−0.0418365
$979$	7.77151e7	2.59148
$980$	8.87205e6	0.295093
$981$	5.06750e6	0.168121
$982$	−2.67104e7	−0.883898
$983$	−3.97908e7	−1.31340	−0.656702	−	0.754150i	$-0.728049\pi$
$983$	−3.97908e7	−1.31340	−0.656702	+	0.754150i	$0.728049\pi$
$984$	2.59000e7	0.852730
$985$	−854907.	−0.0280756
$986$	3.73978e7	1.22505
$987$	2.95355e6	0.0965054
$988$	3.09816e6	0.100975
$989$	−1.31636e7	−0.427943
$990$	−4.20897e6	−0.136486
$991$	2.18022e7	0.705207	0.352604	−	0.935773i	$-0.385296\pi$
$991$	2.18022e7	0.705207	0.352604	+	0.935773i	$0.385296\pi$
$992$	−1.34503e7	−0.433964
$993$	−2.60967e7	−0.839871
$994$	3366.57	0.000108074 0
$995$	1.14423e7	0.366400
$996$	1.75150e7	0.559451
$997$	−2.61869e7	−0.834346	−0.417173	−	0.908827i	$-0.636979\pi$
$997$	−2.61869e7	−0.834346	−0.417173	+	0.908827i	$0.636979\pi$
$998$	3.13194e7	0.995376
$999$	−5.51261e6	−0.174761

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.6.a.a.1.7	✓	11
3.2	odd	2		531.6.a.b.1.5		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.6.a.a.1.7	✓	11	1.1	even	1	trivial
531.6.a.b.1.5		11	3.2	odd	2

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:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	177.a (trivial)

\(f(q)\)	\(=\)	\(q+3.20625 q^{2} +9.00000 q^{3} -21.7200 q^{4} +26.7258 q^{5} +28.8562 q^{6} +39.0273 q^{7} -172.240 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q+3.20625 q^{2} +9.00000 q^{3} -21.7200 q^{4} +26.7258 q^{5} +28.8562 q^{6} +39.0273 q^{7} -172.240 q^{8} +81.0000 q^{9} +85.6897 q^{10} -606.405 q^{11} -195.480 q^{12} -161.707 q^{13} +125.131 q^{14} +240.533 q^{15} +142.797 q^{16} -1651.20 q^{17} +259.706 q^{18} +882.094 q^{19} -580.485 q^{20} +351.246 q^{21} -1944.28 q^{22} +2923.63 q^{23} -1550.16 q^{24} -2410.73 q^{25} -518.474 q^{26} +729.000 q^{27} -847.672 q^{28} -7064.00 q^{29} +771.207 q^{30} -2253.17 q^{31} +5969.51 q^{32} -5457.64 q^{33} -5294.14 q^{34} +1043.04 q^{35} -1759.32 q^{36} -7561.88 q^{37} +2828.21 q^{38} -1455.37 q^{39} -4603.25 q^{40} -16708.0 q^{41} +1126.18 q^{42} -4502.50 q^{43} +13171.1 q^{44} +2164.79 q^{45} +9373.88 q^{46} +8408.79 q^{47} +1285.17 q^{48} -15283.9 q^{49} -7729.39 q^{50} -14860.8 q^{51} +3512.28 q^{52} +11049.2 q^{53} +2337.35 q^{54} -16206.7 q^{55} -6722.04 q^{56} +7938.85 q^{57} -22648.9 q^{58} +3481.00 q^{59} -5224.36 q^{60} +34738.9 q^{61} -7224.23 q^{62} +3161.21 q^{63} +14570.2 q^{64} -4321.76 q^{65} -17498.5 q^{66} -57227.0 q^{67} +35863.9 q^{68} +26312.7 q^{69} +3344.23 q^{70} +26.9044 q^{71} -13951.4 q^{72} +54481.3 q^{73} -24245.2 q^{74} -21696.6 q^{75} -19159.1 q^{76} -23666.3 q^{77} -4666.26 q^{78} +93190.6 q^{79} +3816.37 q^{80} +6561.00 q^{81} -53569.9 q^{82} -89600.1 q^{83} -7629.05 q^{84} -44129.6 q^{85} -14436.1 q^{86} -63576.0 q^{87} +104447. q^{88} -128157. q^{89} +6940.86 q^{90} -6311.00 q^{91} -63501.2 q^{92} -20278.6 q^{93} +26960.7 q^{94} +23574.7 q^{95} +53725.6 q^{96} -26665.5 q^{97} -49003.9 q^{98} -49118.8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11q - 6q^{2} + 99q^{3} + 150q^{4} - 192q^{5} - 54q^{6} - 371q^{7} - 621q^{8} + 891q^{9} + O(q^{10}) \)	\( 11q - 6q^{2} + 99q^{3} + 150q^{4} - 192q^{5} - 54q^{6} - 371q^{7} - 621q^{8} + 891q^{9} - 399q^{10} - 698q^{11} + 1350q^{12} - 1556q^{13} - 1679q^{14} - 1728q^{15} - 2662q^{16} - 4793q^{17} - 486q^{18} - 3753q^{19} - 11023q^{20} - 3339q^{21} - 9534q^{22} - 7323q^{23} - 5589q^{24} + 7867q^{25} - 4844q^{26} + 8019q^{27} + 3650q^{28} - 15467q^{29} - 3591q^{30} - 5151q^{31} - 15368q^{32} - 6282q^{33} + 8452q^{34} - 23285q^{35} + 12150q^{36} + 8623q^{37} + 15205q^{38} - 14004q^{39} + 41530q^{40} - 6369q^{41} - 15111q^{42} - 20506q^{43} - 55632q^{44} - 15552q^{45} - 45191q^{46} - 47899q^{47} - 23958q^{48} - 10322q^{49} - 102147q^{50} - 43137q^{51} - 292q^{52} - 80048q^{53} - 4374q^{54} - 2114q^{55} - 108126q^{56} - 33777q^{57} - 58294q^{58} + 38291q^{59} - 99207q^{60} - 82527q^{61} - 67438q^{62} - 30051q^{63} - 51411q^{64} - 167646q^{65} - 85806q^{66} - 166976q^{67} - 136533q^{68} - 65907q^{69} + 76140q^{70} - 183560q^{71} - 50301q^{72} - 36809q^{73} - 116686q^{74} + 70803q^{75} + 55580q^{76} - 164885q^{77} - 43596q^{78} - 281518q^{79} - 32683q^{80} + 72171q^{81} + 178815q^{82} - 254691q^{83} + 32850q^{84} + 4763q^{85} + 349324q^{86} - 139203q^{87} + 251285q^{88} - 89687q^{89} - 32319q^{90} + 34897q^{91} - 20240q^{92} - 46359q^{93} + 96548q^{94} - 155113q^{95} - 138312q^{96} - 45828q^{97} + 465864q^{98} - 56538q^{99} + O(q^{100}) \)

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