Properties

Label 570.6.a.k.1.2
Level $570$
Weight $6$
Character 570.1
Self dual yes
Analytic conductor $91.419$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 570.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(91.4187772934\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\mathbb{Q}[x]/(x^{4} - \cdots)\)
Defining polynomial: \(x^{4} - x^{3} - 26355 x^{2} - 7203 x + 128450070\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-140.053\) of defining polynomial
Character \(\chi\) \(=\) 570.1

$q$-expansion

\(f(q)\) \(=\) \(q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} -25.0000 q^{5} -36.0000 q^{6} -34.2967 q^{7} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})\) \(q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} -25.0000 q^{5} -36.0000 q^{6} -34.2967 q^{7} -64.0000 q^{8} +81.0000 q^{9} +100.000 q^{10} +148.750 q^{11} +144.000 q^{12} +1140.54 q^{13} +137.187 q^{14} -225.000 q^{15} +256.000 q^{16} +1864.37 q^{17} -324.000 q^{18} -361.000 q^{19} -400.000 q^{20} -308.670 q^{21} -595.000 q^{22} +356.293 q^{23} -576.000 q^{24} +625.000 q^{25} -4562.17 q^{26} +729.000 q^{27} -548.747 q^{28} -5821.97 q^{29} +900.000 q^{30} -10419.4 q^{31} -1024.00 q^{32} +1338.75 q^{33} -7457.50 q^{34} +857.417 q^{35} +1296.00 q^{36} +6390.89 q^{37} +1444.00 q^{38} +10264.9 q^{39} +1600.00 q^{40} +3876.23 q^{41} +1234.68 q^{42} +23107.7 q^{43} +2380.00 q^{44} -2025.00 q^{45} -1425.17 q^{46} -24172.3 q^{47} +2304.00 q^{48} -15630.7 q^{49} -2500.00 q^{50} +16779.4 q^{51} +18248.7 q^{52} -24781.8 q^{53} -2916.00 q^{54} -3718.75 q^{55} +2194.99 q^{56} -3249.00 q^{57} +23287.9 q^{58} +29282.3 q^{59} -3600.00 q^{60} +559.719 q^{61} +41677.7 q^{62} -2778.03 q^{63} +4096.00 q^{64} -28513.6 q^{65} -5355.00 q^{66} +34672.3 q^{67} +29830.0 q^{68} +3206.64 q^{69} -3429.67 q^{70} +63980.4 q^{71} -5184.00 q^{72} +15833.5 q^{73} -25563.6 q^{74} +5625.00 q^{75} -5776.00 q^{76} -5101.63 q^{77} -41059.6 q^{78} +72369.2 q^{79} -6400.00 q^{80} +6561.00 q^{81} -15504.9 q^{82} -70180.7 q^{83} -4938.72 q^{84} -46609.3 q^{85} -92431.0 q^{86} -52397.7 q^{87} -9520.01 q^{88} +72450.1 q^{89} +8100.00 q^{90} -39116.8 q^{91} +5700.69 q^{92} -93774.8 q^{93} +96689.3 q^{94} +9025.00 q^{95} -9216.00 q^{96} +7227.34 q^{97} +62523.0 q^{98} +12048.8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 16q^{2} + 36q^{3} + 64q^{4} - 100q^{5} - 144q^{6} + 26q^{7} - 256q^{8} + 324q^{9} + O(q^{10}) \) \( 4q - 16q^{2} + 36q^{3} + 64q^{4} - 100q^{5} - 144q^{6} + 26q^{7} - 256q^{8} + 324q^{9} + 400q^{10} - 472q^{11} + 576q^{12} - 482q^{13} - 104q^{14} - 900q^{15} + 1024q^{16} + 1816q^{17} - 1296q^{18} - 1444q^{19} - 1600q^{20} + 234q^{21} + 1888q^{22} - 418q^{23} - 2304q^{24} + 2500q^{25} + 1928q^{26} + 2916q^{27} + 416q^{28} - 10396q^{29} + 3600q^{30} + 528q^{31} - 4096q^{32} - 4248q^{33} - 7264q^{34} - 650q^{35} + 5184q^{36} + 5774q^{37} + 5776q^{38} - 4338q^{39} + 6400q^{40} + 9620q^{41} - 936q^{42} + 21098q^{43} - 7552q^{44} - 8100q^{45} + 1672q^{46} - 18858q^{47} + 9216q^{48} + 2148q^{49} - 10000q^{50} + 16344q^{51} - 7712q^{52} + 822q^{53} - 11664q^{54} + 11800q^{55} - 1664q^{56} - 12996q^{57} + 41584q^{58} + 28672q^{59} - 14400q^{60} + 77748q^{61} - 2112q^{62} + 2106q^{63} + 16384q^{64} + 12050q^{65} + 16992q^{66} + 82400q^{67} + 29056q^{68} - 3762q^{69} + 2600q^{70} + 928q^{71} - 20736q^{72} + 121100q^{73} - 23096q^{74} + 22500q^{75} - 23104q^{76} - 120220q^{77} + 17352q^{78} + 144284q^{79} - 25600q^{80} + 26244q^{81} - 38480q^{82} - 6082q^{83} + 3744q^{84} - 45400q^{85} - 84392q^{86} - 93564q^{87} + 30208q^{88} + 43260q^{89} + 32400q^{90} + 135148q^{91} - 6688q^{92} + 4752q^{93} + 75432q^{94} + 36100q^{95} - 36864q^{96} - 6862q^{97} - 8592q^{98} - 38232q^{99} + O(q^{100}) \)

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 \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −4.00000 −0.707107
\(3\) 9.00000 0.577350
\(4\) 16.0000 0.500000
\(5\) −25.0000 −0.447214
\(6\) −36.0000 −0.408248
\(7\) −34.2967 −0.264549 −0.132275 0.991213i \(-0.542228\pi\)
−0.132275 + 0.991213i \(0.542228\pi\)
\(8\) −64.0000 −0.353553
\(9\) 81.0000 0.333333
\(10\) 100.000 0.316228
\(11\) 148.750 0.370660 0.185330 0.982676i \(-0.440665\pi\)
0.185330 + 0.982676i \(0.440665\pi\)
\(12\) 144.000 0.288675
\(13\) 1140.54 1.87177 0.935887 0.352300i \(-0.114600\pi\)
0.935887 + 0.352300i \(0.114600\pi\)
\(14\) 137.187 0.187065
\(15\) −225.000 −0.258199
\(16\) 256.000 0.250000
\(17\) 1864.37 1.56463 0.782313 0.622885i \(-0.214040\pi\)
0.782313 + 0.622885i \(0.214040\pi\)
\(18\) −324.000 −0.235702
\(19\) −361.000 −0.229416
\(20\) −400.000 −0.223607
\(21\) −308.670 −0.152738
\(22\) −595.000 −0.262096
\(23\) 356.293 0.140439 0.0702196 0.997532i \(-0.477630\pi\)
0.0702196 + 0.997532i \(0.477630\pi\)
\(24\) −576.000 −0.204124
\(25\) 625.000 0.200000
\(26\) −4562.17 −1.32354
\(27\) 729.000 0.192450
\(28\) −548.747 −0.132275
\(29\) −5821.97 −1.28551 −0.642754 0.766072i \(-0.722208\pi\)
−0.642754 + 0.766072i \(0.722208\pi\)
\(30\) 900.000 0.182574
\(31\) −10419.4 −1.94733 −0.973665 0.227983i \(-0.926787\pi\)
−0.973665 + 0.227983i \(0.926787\pi\)
\(32\) −1024.00 −0.176777
\(33\) 1338.75 0.214001
\(34\) −7457.50 −1.10636
\(35\) 857.417 0.118310
\(36\) 1296.00 0.166667
\(37\) 6390.89 0.767462 0.383731 0.923445i \(-0.374639\pi\)
0.383731 + 0.923445i \(0.374639\pi\)
\(38\) 1444.00 0.162221
\(39\) 10264.9 1.08067
\(40\) 1600.00 0.158114
\(41\) 3876.23 0.360122 0.180061 0.983655i \(-0.442370\pi\)
0.180061 + 0.983655i \(0.442370\pi\)
\(42\) 1234.68 0.108002
\(43\) 23107.7 1.90584 0.952920 0.303223i \(-0.0980626\pi\)
0.952920 + 0.303223i \(0.0980626\pi\)
\(44\) 2380.00 0.185330
\(45\) −2025.00 −0.149071
\(46\) −1425.17 −0.0993055
\(47\) −24172.3 −1.59615 −0.798075 0.602558i \(-0.794148\pi\)
−0.798075 + 0.602558i \(0.794148\pi\)
\(48\) 2304.00 0.144338
\(49\) −15630.7 −0.930014
\(50\) −2500.00 −0.141421
\(51\) 16779.4 0.903338
\(52\) 18248.7 0.935887
\(53\) −24781.8 −1.21184 −0.605918 0.795527i \(-0.707194\pi\)
−0.605918 + 0.795527i \(0.707194\pi\)
\(54\) −2916.00 −0.136083
\(55\) −3718.75 −0.165764
\(56\) 2194.99 0.0935323
\(57\) −3249.00 −0.132453
\(58\) 23287.9 0.908992
\(59\) 29282.3 1.09515 0.547576 0.836756i \(-0.315551\pi\)
0.547576 + 0.836756i \(0.315551\pi\)
\(60\) −3600.00 −0.129099
\(61\) 559.719 0.0192595 0.00962976 0.999954i \(-0.496935\pi\)
0.00962976 + 0.999954i \(0.496935\pi\)
\(62\) 41677.7 1.37697
\(63\) −2778.03 −0.0881831
\(64\) 4096.00 0.125000
\(65\) −28513.6 −0.837083
\(66\) −5355.00 −0.151321
\(67\) 34672.3 0.943618 0.471809 0.881701i \(-0.343601\pi\)
0.471809 + 0.881701i \(0.343601\pi\)
\(68\) 29830.0 0.782313
\(69\) 3206.64 0.0810826
\(70\) −3429.67 −0.0836579
\(71\) 63980.4 1.50626 0.753132 0.657869i \(-0.228542\pi\)
0.753132 + 0.657869i \(0.228542\pi\)
\(72\) −5184.00 −0.117851
\(73\) 15833.5 0.347752 0.173876 0.984768i \(-0.444371\pi\)
0.173876 + 0.984768i \(0.444371\pi\)
\(74\) −25563.6 −0.542678
\(75\) 5625.00 0.115470
\(76\) −5776.00 −0.114708
\(77\) −5101.63 −0.0980578
\(78\) −41059.6 −0.764149
\(79\) 72369.2 1.30463 0.652313 0.757950i \(-0.273799\pi\)
0.652313 + 0.757950i \(0.273799\pi\)
\(80\) −6400.00 −0.111803
\(81\) 6561.00 0.111111
\(82\) −15504.9 −0.254645
\(83\) −70180.7 −1.11821 −0.559104 0.829098i \(-0.688855\pi\)
−0.559104 + 0.829098i \(0.688855\pi\)
\(84\) −4938.72 −0.0763688
\(85\) −46609.3 −0.699722
\(86\) −92431.0 −1.34763
\(87\) −52397.7 −0.742189
\(88\) −9520.01 −0.131048
\(89\) 72450.1 0.969536 0.484768 0.874643i \(-0.338904\pi\)
0.484768 + 0.874643i \(0.338904\pi\)
\(90\) 8100.00 0.105409
\(91\) −39116.8 −0.495177
\(92\) 5700.69 0.0702196
\(93\) −93774.8 −1.12429
\(94\) 96689.3 1.12865
\(95\) 9025.00 0.102598
\(96\) −9216.00 −0.102062
\(97\) 7227.34 0.0779919 0.0389959 0.999239i \(-0.487584\pi\)
0.0389959 + 0.999239i \(0.487584\pi\)
\(98\) 62523.0 0.657619
\(99\) 12048.8 0.123553
\(100\) 10000.0 0.100000
\(101\) −57122.3 −0.557189 −0.278594 0.960409i \(-0.589869\pi\)
−0.278594 + 0.960409i \(0.589869\pi\)
\(102\) −67117.5 −0.638756
\(103\) 158486. 1.47197 0.735985 0.676998i \(-0.236719\pi\)
0.735985 + 0.676998i \(0.236719\pi\)
\(104\) −72994.8 −0.661772
\(105\) 7716.75 0.0683064
\(106\) 99127.3 0.856897
\(107\) 21702.8 0.183255 0.0916276 0.995793i \(-0.470793\pi\)
0.0916276 + 0.995793i \(0.470793\pi\)
\(108\) 11664.0 0.0962250
\(109\) −39796.2 −0.320831 −0.160415 0.987050i \(-0.551283\pi\)
−0.160415 + 0.987050i \(0.551283\pi\)
\(110\) 14875.0 0.117213
\(111\) 57518.0 0.443095
\(112\) −8779.95 −0.0661374
\(113\) 10111.2 0.0744913 0.0372456 0.999306i \(-0.488142\pi\)
0.0372456 + 0.999306i \(0.488142\pi\)
\(114\) 12996.0 0.0936586
\(115\) −8907.33 −0.0628063
\(116\) −93151.5 −0.642754
\(117\) 92384.0 0.623925
\(118\) −117129. −0.774390
\(119\) −63941.8 −0.413921
\(120\) 14400.0 0.0912871
\(121\) −138924. −0.862611
\(122\) −2238.88 −0.0136185
\(123\) 34886.0 0.207917
\(124\) −166711. −0.973665
\(125\) −15625.0 −0.0894427
\(126\) 11112.1 0.0623549
\(127\) −202642. −1.11486 −0.557431 0.830224i \(-0.688213\pi\)
−0.557431 + 0.830224i \(0.688213\pi\)
\(128\) −16384.0 −0.0883883
\(129\) 207970. 1.10034
\(130\) 114054. 0.591907
\(131\) 91463.8 0.465662 0.232831 0.972517i \(-0.425201\pi\)
0.232831 + 0.972517i \(0.425201\pi\)
\(132\) 21420.0 0.107000
\(133\) 12381.1 0.0606918
\(134\) −138689. −0.667239
\(135\) −18225.0 −0.0860663
\(136\) −119320. −0.553179
\(137\) 288820. 1.31470 0.657348 0.753587i \(-0.271678\pi\)
0.657348 + 0.753587i \(0.271678\pi\)
\(138\) −12826.6 −0.0573340
\(139\) 386148. 1.69518 0.847592 0.530649i \(-0.178052\pi\)
0.847592 + 0.530649i \(0.178052\pi\)
\(140\) 13718.7 0.0591550
\(141\) −217551. −0.921537
\(142\) −255922. −1.06509
\(143\) 169656. 0.693792
\(144\) 20736.0 0.0833333
\(145\) 145549. 0.574897
\(146\) −63334.0 −0.245898
\(147\) −140677. −0.536944
\(148\) 102254. 0.383731
\(149\) −8960.62 −0.0330653 −0.0165326 0.999863i \(-0.505263\pi\)
−0.0165326 + 0.999863i \(0.505263\pi\)
\(150\) −22500.0 −0.0816497
\(151\) 404681. 1.44434 0.722172 0.691714i \(-0.243144\pi\)
0.722172 + 0.691714i \(0.243144\pi\)
\(152\) 23104.0 0.0811107
\(153\) 151014. 0.521542
\(154\) 20406.5 0.0693374
\(155\) 260486. 0.870873
\(156\) 164238. 0.540335
\(157\) −426481. −1.38086 −0.690431 0.723398i \(-0.742579\pi\)
−0.690431 + 0.723398i \(0.742579\pi\)
\(158\) −289477. −0.922510
\(159\) −223037. −0.699654
\(160\) 25600.0 0.0790569
\(161\) −12219.7 −0.0371531
\(162\) −26244.0 −0.0785674
\(163\) 510951. 1.50630 0.753148 0.657851i \(-0.228534\pi\)
0.753148 + 0.657851i \(0.228534\pi\)
\(164\) 62019.6 0.180061
\(165\) −33468.8 −0.0957040
\(166\) 280723. 0.790692
\(167\) −398804. −1.10654 −0.553271 0.833001i \(-0.686621\pi\)
−0.553271 + 0.833001i \(0.686621\pi\)
\(168\) 19754.9 0.0540009
\(169\) 929547. 2.50354
\(170\) 186437. 0.494778
\(171\) −29241.0 −0.0764719
\(172\) 369724. 0.952920
\(173\) −619744. −1.57434 −0.787168 0.616739i \(-0.788453\pi\)
−0.787168 + 0.616739i \(0.788453\pi\)
\(174\) 209591. 0.524807
\(175\) −21435.4 −0.0529099
\(176\) 38080.0 0.0926650
\(177\) 263540. 0.632286
\(178\) −289800. −0.685565
\(179\) 21840.6 0.0509487 0.0254743 0.999675i \(-0.491890\pi\)
0.0254743 + 0.999675i \(0.491890\pi\)
\(180\) −32400.0 −0.0745356
\(181\) 22711.9 0.0515297 0.0257649 0.999668i \(-0.491798\pi\)
0.0257649 + 0.999668i \(0.491798\pi\)
\(182\) 156467. 0.350143
\(183\) 5037.47 0.0111195
\(184\) −22802.8 −0.0496527
\(185\) −159772. −0.343220
\(186\) 375099. 0.794994
\(187\) 277326. 0.579944
\(188\) −386757. −0.798075
\(189\) −25002.3 −0.0509126
\(190\) −36100.0 −0.0725476
\(191\) 153640. 0.304734 0.152367 0.988324i \(-0.451310\pi\)
0.152367 + 0.988324i \(0.451310\pi\)
\(192\) 36864.0 0.0721688
\(193\) 875318. 1.69150 0.845751 0.533578i \(-0.179153\pi\)
0.845751 + 0.533578i \(0.179153\pi\)
\(194\) −28909.4 −0.0551486
\(195\) −256622. −0.483290
\(196\) −250092. −0.465007
\(197\) 820414. 1.50615 0.753074 0.657936i \(-0.228570\pi\)
0.753074 + 0.657936i \(0.228570\pi\)
\(198\) −48195.0 −0.0873654
\(199\) 683129. 1.22284 0.611421 0.791306i \(-0.290598\pi\)
0.611421 + 0.791306i \(0.290598\pi\)
\(200\) −40000.0 −0.0707107
\(201\) 312051. 0.544798
\(202\) 228489. 0.393992
\(203\) 199674. 0.340081
\(204\) 268470. 0.451669
\(205\) −96905.7 −0.161051
\(206\) −633946. −1.04084
\(207\) 28859.8 0.0468130
\(208\) 291979. 0.467944
\(209\) −53698.8 −0.0850352
\(210\) −30867.0 −0.0482999
\(211\) −211031. −0.326318 −0.163159 0.986600i \(-0.552168\pi\)
−0.163159 + 0.986600i \(0.552168\pi\)
\(212\) −396509. −0.605918
\(213\) 575824. 0.869642
\(214\) −86811.2 −0.129581
\(215\) −577693. −0.852317
\(216\) −46656.0 −0.0680414
\(217\) 357352. 0.515165
\(218\) 159185. 0.226861
\(219\) 142502. 0.200775
\(220\) −59500.0 −0.0828821
\(221\) 2.12640e6 2.92863
\(222\) −230072. −0.313315
\(223\) 1.09637e6 1.47637 0.738184 0.674599i \(-0.235683\pi\)
0.738184 + 0.674599i \(0.235683\pi\)
\(224\) 35119.8 0.0467662
\(225\) 50625.0 0.0666667
\(226\) −40444.7 −0.0526733
\(227\) −957257. −1.23300 −0.616501 0.787354i \(-0.711451\pi\)
−0.616501 + 0.787354i \(0.711451\pi\)
\(228\) −51984.0 −0.0662266
\(229\) 531154. 0.669317 0.334659 0.942339i \(-0.391379\pi\)
0.334659 + 0.942339i \(0.391379\pi\)
\(230\) 35629.3 0.0444108
\(231\) −45914.7 −0.0566137
\(232\) 372606. 0.454496
\(233\) −18960.6 −0.0228803 −0.0114402 0.999935i \(-0.503642\pi\)
−0.0114402 + 0.999935i \(0.503642\pi\)
\(234\) −369536. −0.441181
\(235\) 604308. 0.713820
\(236\) 468516. 0.547576
\(237\) 651323. 0.753226
\(238\) 255767. 0.292686
\(239\) 465206. 0.526805 0.263403 0.964686i \(-0.415155\pi\)
0.263403 + 0.964686i \(0.415155\pi\)
\(240\) −57600.0 −0.0645497
\(241\) −1.41287e6 −1.56697 −0.783484 0.621412i \(-0.786559\pi\)
−0.783484 + 0.621412i \(0.786559\pi\)
\(242\) 555698. 0.609958
\(243\) 59049.0 0.0641500
\(244\) 8955.50 0.00962976
\(245\) 390768. 0.415915
\(246\) −139544. −0.147019
\(247\) −411736. −0.429415
\(248\) 666843. 0.688485
\(249\) −631626. −0.645598
\(250\) 62500.0 0.0632456
\(251\) 752819. 0.754234 0.377117 0.926166i \(-0.376915\pi\)
0.377117 + 0.926166i \(0.376915\pi\)
\(252\) −44448.5 −0.0440916
\(253\) 52998.7 0.0520551
\(254\) 810569. 0.788326
\(255\) −419484. −0.403985
\(256\) 65536.0 0.0625000
\(257\) 1.28310e6 1.21179 0.605895 0.795545i \(-0.292815\pi\)
0.605895 + 0.795545i \(0.292815\pi\)
\(258\) −831879. −0.778056
\(259\) −219186. −0.203032
\(260\) −456217. −0.418542
\(261\) −471580. −0.428503
\(262\) −365855. −0.329273
\(263\) −926179. −0.825669 −0.412834 0.910806i \(-0.635461\pi\)
−0.412834 + 0.910806i \(0.635461\pi\)
\(264\) −85680.1 −0.0756606
\(265\) 619546. 0.541949
\(266\) −49524.4 −0.0429156
\(267\) 652051. 0.559762
\(268\) 554757. 0.471809
\(269\) 388774. 0.327579 0.163790 0.986495i \(-0.447628\pi\)
0.163790 + 0.986495i \(0.447628\pi\)
\(270\) 72900.0 0.0608581
\(271\) −332637. −0.275136 −0.137568 0.990492i \(-0.543929\pi\)
−0.137568 + 0.990492i \(0.543929\pi\)
\(272\) 477280. 0.391157
\(273\) −352052. −0.285890
\(274\) −1.15528e6 −0.929631
\(275\) 92968.8 0.0741320
\(276\) 51306.2 0.0405413
\(277\) 1.13035e6 0.885146 0.442573 0.896733i \(-0.354066\pi\)
0.442573 + 0.896733i \(0.354066\pi\)
\(278\) −1.54459e6 −1.19868
\(279\) −843974. −0.649110
\(280\) −54874.7 −0.0418289
\(281\) −2.39691e6 −1.81087 −0.905434 0.424488i \(-0.860454\pi\)
−0.905434 + 0.424488i \(0.860454\pi\)
\(282\) 870203. 0.651625
\(283\) −496875. −0.368791 −0.184396 0.982852i \(-0.559033\pi\)
−0.184396 + 0.982852i \(0.559033\pi\)
\(284\) 1.02369e6 0.753132
\(285\) 81225.0 0.0592349
\(286\) −678624. −0.490585
\(287\) −132942. −0.0952700
\(288\) −82944.0 −0.0589256
\(289\) 2.05603e6 1.44806
\(290\) −582197. −0.406514
\(291\) 65046.1 0.0450286
\(292\) 253336. 0.173876
\(293\) −443119. −0.301544 −0.150772 0.988569i \(-0.548176\pi\)
−0.150772 + 0.988569i \(0.548176\pi\)
\(294\) 562707. 0.379676
\(295\) −732056. −0.489767
\(296\) −409017. −0.271339
\(297\) 108439. 0.0713335
\(298\) 35842.5 0.0233807
\(299\) 406368. 0.262870
\(300\) 90000.0 0.0577350
\(301\) −792518. −0.504189
\(302\) −1.61872e6 −1.02130
\(303\) −514101. −0.321693
\(304\) −92416.0 −0.0573539
\(305\) −13993.0 −0.00861312
\(306\) −604057. −0.368786
\(307\) 2.01345e6 1.21926 0.609629 0.792687i \(-0.291319\pi\)
0.609629 + 0.792687i \(0.291319\pi\)
\(308\) −81626.1 −0.0490289
\(309\) 1.42638e6 0.849843
\(310\) −1.04194e6 −0.615800
\(311\) −2.84464e6 −1.66773 −0.833867 0.551966i \(-0.813878\pi\)
−0.833867 + 0.551966i \(0.813878\pi\)
\(312\) −656953. −0.382074
\(313\) 83906.4 0.0484099 0.0242049 0.999707i \(-0.492295\pi\)
0.0242049 + 0.999707i \(0.492295\pi\)
\(314\) 1.70592e6 0.976417
\(315\) 69450.7 0.0394367
\(316\) 1.15791e6 0.652313
\(317\) 1.68748e6 0.943173 0.471586 0.881820i \(-0.343682\pi\)
0.471586 + 0.881820i \(0.343682\pi\)
\(318\) 892146. 0.494730
\(319\) −866019. −0.476487
\(320\) −102400. −0.0559017
\(321\) 195325. 0.105802
\(322\) 48878.7 0.0262712
\(323\) −673039. −0.358950
\(324\) 104976. 0.0555556
\(325\) 712840. 0.374355
\(326\) −2.04380e6 −1.06511
\(327\) −358166. −0.185232
\(328\) −248079. −0.127322
\(329\) 829030. 0.422260
\(330\) 133875. 0.0676729
\(331\) −375316. −0.188290 −0.0941449 0.995559i \(-0.530012\pi\)
−0.0941449 + 0.995559i \(0.530012\pi\)
\(332\) −1.12289e6 −0.559104
\(333\) 517662. 0.255821
\(334\) 1.59522e6 0.782444
\(335\) −866808. −0.421999
\(336\) −79019.5 −0.0381844
\(337\) −2.48793e6 −1.19334 −0.596669 0.802488i \(-0.703509\pi\)
−0.596669 + 0.802488i \(0.703509\pi\)
\(338\) −3.71819e6 −1.77027
\(339\) 91000.5 0.0430075
\(340\) −745750. −0.349861
\(341\) −1.54989e6 −0.721797
\(342\) 116964. 0.0540738
\(343\) 1.11251e6 0.510584
\(344\) −1.47890e6 −0.673816
\(345\) −80166.0 −0.0362612
\(346\) 2.47898e6 1.11322
\(347\) −498265. −0.222145 −0.111073 0.993812i \(-0.535429\pi\)
−0.111073 + 0.993812i \(0.535429\pi\)
\(348\) −838364. −0.371094
\(349\) 133574. 0.0587028 0.0293514 0.999569i \(-0.490656\pi\)
0.0293514 + 0.999569i \(0.490656\pi\)
\(350\) 85741.7 0.0374129
\(351\) 831456. 0.360223
\(352\) −152320. −0.0655240
\(353\) 281870. 0.120396 0.0601980 0.998186i \(-0.480827\pi\)
0.0601980 + 0.998186i \(0.480827\pi\)
\(354\) −1.05416e6 −0.447094
\(355\) −1.59951e6 −0.673622
\(356\) 1.15920e6 0.484768
\(357\) −575476. −0.238977
\(358\) −87362.6 −0.0360262
\(359\) 4.17309e6 1.70892 0.854460 0.519518i \(-0.173888\pi\)
0.854460 + 0.519518i \(0.173888\pi\)
\(360\) 129600. 0.0527046
\(361\) 130321. 0.0526316
\(362\) −90847.8 −0.0364370
\(363\) −1.25032e6 −0.498029
\(364\) −625870. −0.247588
\(365\) −395838. −0.155520
\(366\) −20149.9 −0.00786267
\(367\) 2.84118e6 1.10112 0.550558 0.834797i \(-0.314415\pi\)
0.550558 + 0.834797i \(0.314415\pi\)
\(368\) 91211.1 0.0351098
\(369\) 313974. 0.120041
\(370\) 639089. 0.242693
\(371\) 849934. 0.320590
\(372\) −1.50040e6 −0.562146
\(373\) −4.86188e6 −1.80939 −0.904695 0.426060i \(-0.859901\pi\)
−0.904695 + 0.426060i \(0.859901\pi\)
\(374\) −1.10930e6 −0.410083
\(375\) −140625. −0.0516398
\(376\) 1.54703e6 0.564324
\(377\) −6.64021e6 −2.40618
\(378\) 100009. 0.0360006
\(379\) 1.89991e6 0.679415 0.339708 0.940531i \(-0.389672\pi\)
0.339708 + 0.940531i \(0.389672\pi\)
\(380\) 144400. 0.0512989
\(381\) −1.82378e6 −0.643665
\(382\) −614559. −0.215479
\(383\) −3.09421e6 −1.07784 −0.538919 0.842358i \(-0.681167\pi\)
−0.538919 + 0.842358i \(0.681167\pi\)
\(384\) −147456. −0.0510310
\(385\) 127541. 0.0438528
\(386\) −3.50127e6 −1.19607
\(387\) 1.87173e6 0.635280
\(388\) 115637. 0.0389959
\(389\) −3.22237e6 −1.07970 −0.539848 0.841763i \(-0.681518\pi\)
−0.539848 + 0.841763i \(0.681518\pi\)
\(390\) 1.02649e6 0.341738
\(391\) 664264. 0.219735
\(392\) 1.00037e6 0.328809
\(393\) 823174. 0.268850
\(394\) −3.28166e6 −1.06501
\(395\) −1.80923e6 −0.583446
\(396\) 192780. 0.0617766
\(397\) −1.92728e6 −0.613717 −0.306859 0.951755i \(-0.599278\pi\)
−0.306859 + 0.951755i \(0.599278\pi\)
\(398\) −2.73252e6 −0.864680
\(399\) 111430. 0.0350404
\(400\) 160000. 0.0500000
\(401\) 480845. 0.149329 0.0746644 0.997209i \(-0.476211\pi\)
0.0746644 + 0.997209i \(0.476211\pi\)
\(402\) −1.24820e6 −0.385230
\(403\) −1.18838e7 −3.64496
\(404\) −913957. −0.278594
\(405\) −164025. −0.0496904
\(406\) −798697. −0.240473
\(407\) 950646. 0.284467
\(408\) −1.07388e6 −0.319378
\(409\) −3.36840e6 −0.995668 −0.497834 0.867272i \(-0.665871\pi\)
−0.497834 + 0.867272i \(0.665871\pi\)
\(410\) 387623. 0.113881
\(411\) 2.59938e6 0.759040
\(412\) 2.53578e6 0.735985
\(413\) −1.00428e6 −0.289722
\(414\) −115439. −0.0331018
\(415\) 1.75452e6 0.500078
\(416\) −1.16792e6 −0.330886
\(417\) 3.47533e6 0.978715
\(418\) 214795. 0.0601290
\(419\) −1.72677e6 −0.480507 −0.240254 0.970710i \(-0.577231\pi\)
−0.240254 + 0.970710i \(0.577231\pi\)
\(420\) 123468. 0.0341532
\(421\) 6.88025e6 1.89190 0.945951 0.324309i \(-0.105132\pi\)
0.945951 + 0.324309i \(0.105132\pi\)
\(422\) 844125. 0.230741
\(423\) −1.95796e6 −0.532050
\(424\) 1.58604e6 0.428449
\(425\) 1.16523e6 0.312925
\(426\) −2.30330e6 −0.614930
\(427\) −19196.5 −0.00509509
\(428\) 347245. 0.0916276
\(429\) 1.52690e6 0.400561
\(430\) 2.31077e6 0.602679
\(431\) 6.57589e6 1.70514 0.852572 0.522610i \(-0.175041\pi\)
0.852572 + 0.522610i \(0.175041\pi\)
\(432\) 186624. 0.0481125
\(433\) 6.40443e6 1.64158 0.820788 0.571233i \(-0.193535\pi\)
0.820788 + 0.571233i \(0.193535\pi\)
\(434\) −1.42941e6 −0.364277
\(435\) 1.30994e6 0.331917
\(436\) −636740. −0.160415
\(437\) −128622. −0.0322189
\(438\) −570006. −0.141969
\(439\) 4.61471e6 1.14283 0.571417 0.820660i \(-0.306394\pi\)
0.571417 + 0.820660i \(0.306394\pi\)
\(440\) 238000. 0.0586065
\(441\) −1.26609e6 −0.310005
\(442\) −8.50560e6 −2.07085
\(443\) 709966. 0.171881 0.0859405 0.996300i \(-0.472610\pi\)
0.0859405 + 0.996300i \(0.472610\pi\)
\(444\) 920288. 0.221547
\(445\) −1.81125e6 −0.433590
\(446\) −4.38548e6 −1.04395
\(447\) −80645.5 −0.0190902
\(448\) −140479. −0.0330687
\(449\) −7.60136e6 −1.77941 −0.889704 0.456539i \(-0.849089\pi\)
−0.889704 + 0.456539i \(0.849089\pi\)
\(450\) −202500. −0.0471405
\(451\) 576589. 0.133483
\(452\) 161779. 0.0372456
\(453\) 3.64213e6 0.833892
\(454\) 3.82903e6 0.871865
\(455\) 977921. 0.221450
\(456\) 207936. 0.0468293
\(457\) 5.76215e6 1.29061 0.645304 0.763926i \(-0.276731\pi\)
0.645304 + 0.763926i \(0.276731\pi\)
\(458\) −2.12462e6 −0.473279
\(459\) 1.35913e6 0.301113
\(460\) −142517. −0.0314031
\(461\) −1.22229e6 −0.267870 −0.133935 0.990990i \(-0.542761\pi\)
−0.133935 + 0.990990i \(0.542761\pi\)
\(462\) 183659. 0.0400319
\(463\) −1.41076e6 −0.305844 −0.152922 0.988238i \(-0.548868\pi\)
−0.152922 + 0.988238i \(0.548868\pi\)
\(464\) −1.49042e6 −0.321377
\(465\) 2.34437e6 0.502798
\(466\) 75842.3 0.0161788
\(467\) −7.26181e6 −1.54082 −0.770411 0.637547i \(-0.779949\pi\)
−0.770411 + 0.637547i \(0.779949\pi\)
\(468\) 1.47814e6 0.311962
\(469\) −1.18915e6 −0.249634
\(470\) −2.41723e6 −0.504747
\(471\) −3.83833e6 −0.797241
\(472\) −1.87406e6 −0.387195
\(473\) 3.43728e6 0.706418
\(474\) −2.60529e6 −0.532611
\(475\) −225625. −0.0458831
\(476\) −1.02307e6 −0.206961
\(477\) −2.00733e6 −0.403945
\(478\) −1.86082e6 −0.372508
\(479\) 2.58287e6 0.514355 0.257178 0.966364i \(-0.417207\pi\)
0.257178 + 0.966364i \(0.417207\pi\)
\(480\) 230400. 0.0456435
\(481\) 7.28909e6 1.43652
\(482\) 5.65149e6 1.10801
\(483\) −109977. −0.0214503
\(484\) −2.22279e6 −0.431306
\(485\) −180684. −0.0348790
\(486\) −236196. −0.0453609
\(487\) 5.60709e6 1.07131 0.535655 0.844437i \(-0.320065\pi\)
0.535655 + 0.844437i \(0.320065\pi\)
\(488\) −35822.0 −0.00680927
\(489\) 4.59856e6 0.869660
\(490\) −1.56307e6 −0.294096
\(491\) 1.79394e6 0.335818 0.167909 0.985802i \(-0.446298\pi\)
0.167909 + 0.985802i \(0.446298\pi\)
\(492\) 558177. 0.103958
\(493\) −1.08543e7 −2.01134
\(494\) 1.64695e6 0.303642
\(495\) −301219. −0.0552547
\(496\) −2.66737e6 −0.486833
\(497\) −2.19431e6 −0.398481
\(498\) 2.52651e6 0.456506
\(499\) 2.70944e6 0.487112 0.243556 0.969887i \(-0.421686\pi\)
0.243556 + 0.969887i \(0.421686\pi\)
\(500\) −250000. −0.0447214
\(501\) −3.58924e6 −0.638863
\(502\) −3.01128e6 −0.533324
\(503\) −9.67452e6 −1.70494 −0.852471 0.522775i \(-0.824897\pi\)
−0.852471 + 0.522775i \(0.824897\pi\)
\(504\) 177794. 0.0311774
\(505\) 1.42806e6 0.249182
\(506\) −211995. −0.0368085
\(507\) 8.36592e6 1.44542
\(508\) −3.24228e6 −0.557431
\(509\) 7.81169e6 1.33644 0.668222 0.743962i \(-0.267056\pi\)
0.668222 + 0.743962i \(0.267056\pi\)
\(510\) 1.67794e6 0.285660
\(511\) −543036. −0.0919977
\(512\) −262144. −0.0441942
\(513\) −263169. −0.0441511
\(514\) −5.13239e6 −0.856864
\(515\) −3.96216e6 −0.658285
\(516\) 3.32751e6 0.550168
\(517\) −3.59563e6 −0.591629
\(518\) 876745. 0.143565
\(519\) −5.57770e6 −0.908943
\(520\) 1.82487e6 0.295954
\(521\) −427731. −0.0690361 −0.0345180 0.999404i \(-0.510990\pi\)
−0.0345180 + 0.999404i \(0.510990\pi\)
\(522\) 1.88632e6 0.302997
\(523\) 1.04844e6 0.167606 0.0838032 0.996482i \(-0.473293\pi\)
0.0838032 + 0.996482i \(0.473293\pi\)
\(524\) 1.46342e6 0.232831
\(525\) −192919. −0.0305475
\(526\) 3.70472e6 0.583836
\(527\) −1.94257e7 −3.04684
\(528\) 342720. 0.0535001
\(529\) −6.30940e6 −0.980277
\(530\) −2.47818e6 −0.383216
\(531\) 2.37186e6 0.365051
\(532\) 198098. 0.0303459
\(533\) 4.42101e6 0.674067
\(534\) −2.60820e6 −0.395811
\(535\) −542570. −0.0819542
\(536\) −2.21903e6 −0.333619
\(537\) 196566. 0.0294152
\(538\) −1.55510e6 −0.231634
\(539\) −2.32507e6 −0.344719
\(540\) −291600. −0.0430331
\(541\) −4.43514e6 −0.651499 −0.325750 0.945456i \(-0.605617\pi\)
−0.325750 + 0.945456i \(0.605617\pi\)
\(542\) 1.33055e6 0.194550
\(543\) 204407. 0.0297507
\(544\) −1.90912e6 −0.276590
\(545\) 994906. 0.143480
\(546\) 1.40821e6 0.202155
\(547\) −6.31985e6 −0.903105 −0.451553 0.892244i \(-0.649130\pi\)
−0.451553 + 0.892244i \(0.649130\pi\)
\(548\) 4.62112e6 0.657348
\(549\) 45337.2 0.00641984
\(550\) −371875. −0.0524192
\(551\) 2.10173e6 0.294916
\(552\) −205225. −0.0286670
\(553\) −2.48202e6 −0.345138
\(554\) −4.52141e6 −0.625893
\(555\) −1.43795e6 −0.198158
\(556\) 6.17837e6 0.847592
\(557\) 7.35307e6 1.00422 0.502112 0.864803i \(-0.332557\pi\)
0.502112 + 0.864803i \(0.332557\pi\)
\(558\) 3.37589e6 0.458990
\(559\) 2.63554e7 3.56730
\(560\) 219499. 0.0295775
\(561\) 2.49593e6 0.334831
\(562\) 9.58765e6 1.28048
\(563\) −1.21188e7 −1.61134 −0.805670 0.592365i \(-0.798194\pi\)
−0.805670 + 0.592365i \(0.798194\pi\)
\(564\) −3.48081e6 −0.460769
\(565\) −252779. −0.0333135
\(566\) 1.98750e6 0.260775
\(567\) −225020. −0.0293944
\(568\) −4.09475e6 −0.532545
\(569\) −3.22312e6 −0.417346 −0.208673 0.977985i \(-0.566914\pi\)
−0.208673 + 0.977985i \(0.566914\pi\)
\(570\) −324900. −0.0418854
\(571\) −404549. −0.0519255 −0.0259627 0.999663i \(-0.508265\pi\)
−0.0259627 + 0.999663i \(0.508265\pi\)
\(572\) 2.71450e6 0.346896
\(573\) 1.38276e6 0.175938
\(574\) 531767. 0.0673661
\(575\) 222683. 0.0280878
\(576\) 331776. 0.0416667
\(577\) 2.00205e6 0.250343 0.125172 0.992135i \(-0.460052\pi\)
0.125172 + 0.992135i \(0.460052\pi\)
\(578\) −8.22413e6 −1.02393
\(579\) 7.87786e6 0.976589
\(580\) 2.32879e6 0.287449
\(581\) 2.40696e6 0.295821
\(582\) −260184. −0.0318400
\(583\) −3.68630e6 −0.449179
\(584\) −1.01334e6 −0.122949
\(585\) −2.30960e6 −0.279028
\(586\) 1.77247e6 0.213224
\(587\) 1.26153e7 1.51114 0.755569 0.655069i \(-0.227361\pi\)
0.755569 + 0.655069i \(0.227361\pi\)
\(588\) −2.25083e6 −0.268472
\(589\) 3.76141e6 0.446748
\(590\) 2.92823e6 0.346318
\(591\) 7.38372e6 0.869574
\(592\) 1.63607e6 0.191866
\(593\) 3.02364e6 0.353096 0.176548 0.984292i \(-0.443507\pi\)
0.176548 + 0.984292i \(0.443507\pi\)
\(594\) −433755. −0.0504404
\(595\) 1.59855e6 0.185111
\(596\) −143370. −0.0165326
\(597\) 6.14816e6 0.706008
\(598\) −1.62547e6 −0.185877
\(599\) 1.16163e6 0.132282 0.0661412 0.997810i \(-0.478931\pi\)
0.0661412 + 0.997810i \(0.478931\pi\)
\(600\) −360000. −0.0408248
\(601\) 1.41403e7 1.59688 0.798441 0.602073i \(-0.205658\pi\)
0.798441 + 0.602073i \(0.205658\pi\)
\(602\) 3.17007e6 0.356515
\(603\) 2.80846e6 0.314539
\(604\) 6.47490e6 0.722172
\(605\) 3.47311e6 0.385771
\(606\) 2.05640e6 0.227471
\(607\) 1.18789e7 1.30860 0.654299 0.756236i \(-0.272964\pi\)
0.654299 + 0.756236i \(0.272964\pi\)
\(608\) 369664. 0.0405554
\(609\) 1.79707e6 0.196346
\(610\) 55971.9 0.00609040
\(611\) −2.75696e7 −2.98763
\(612\) 2.41623e6 0.260771
\(613\) −1.37570e6 −0.147867 −0.0739335 0.997263i \(-0.523555\pi\)
−0.0739335 + 0.997263i \(0.523555\pi\)
\(614\) −8.05381e6 −0.862145
\(615\) −872151. −0.0929831
\(616\) 326504. 0.0346687
\(617\) 4.54793e6 0.480951 0.240475 0.970655i \(-0.422697\pi\)
0.240475 + 0.970655i \(0.422697\pi\)
\(618\) −5.70551e6 −0.600929
\(619\) 5.48774e6 0.575661 0.287830 0.957681i \(-0.407066\pi\)
0.287830 + 0.957681i \(0.407066\pi\)
\(620\) 4.16777e6 0.435436
\(621\) 259738. 0.0270275
\(622\) 1.13786e7 1.17927
\(623\) −2.48480e6 −0.256490
\(624\) 2.62781e6 0.270167
\(625\) 390625. 0.0400000
\(626\) −335625. −0.0342310
\(627\) −483289. −0.0490951
\(628\) −6.82369e6 −0.690431
\(629\) 1.19150e7 1.20079
\(630\) −277803. −0.0278860
\(631\) −1.28567e7 −1.28545 −0.642727 0.766095i \(-0.722197\pi\)
−0.642727 + 0.766095i \(0.722197\pi\)
\(632\) −4.63163e6 −0.461255
\(633\) −1.89928e6 −0.188400
\(634\) −6.74993e6 −0.666924
\(635\) 5.06606e6 0.498581
\(636\) −3.56858e6 −0.349827
\(637\) −1.78275e7 −1.74078
\(638\) 3.46408e6 0.336927
\(639\) 5.18241e6 0.502088
\(640\) 409600. 0.0395285
\(641\) 1.09210e6 0.104982 0.0524912 0.998621i \(-0.483284\pi\)
0.0524912 + 0.998621i \(0.483284\pi\)
\(642\) −781301. −0.0748136
\(643\) 1.47390e7 1.40586 0.702930 0.711259i \(-0.251875\pi\)
0.702930 + 0.711259i \(0.251875\pi\)
\(644\) −195515. −0.0185765
\(645\) −5.19924e6 −0.492086
\(646\) 2.69216e6 0.253816
\(647\) −6.54046e6 −0.614254 −0.307127 0.951669i \(-0.599368\pi\)
−0.307127 + 0.951669i \(0.599368\pi\)
\(648\) −419904. −0.0392837
\(649\) 4.35574e6 0.405929
\(650\) −2.85136e6 −0.264709
\(651\) 3.21616e6 0.297431
\(652\) 8.17522e6 0.753148
\(653\) −1.07827e7 −0.989568 −0.494784 0.869016i \(-0.664753\pi\)
−0.494784 + 0.869016i \(0.664753\pi\)
\(654\) 1.43266e6 0.130979
\(655\) −2.28659e6 −0.208250
\(656\) 992314. 0.0900305
\(657\) 1.28251e6 0.115917
\(658\) −3.31612e6 −0.298583
\(659\) 9.27679e6 0.832116 0.416058 0.909338i \(-0.363411\pi\)
0.416058 + 0.909338i \(0.363411\pi\)
\(660\) −535500. −0.0478520
\(661\) −5.45372e6 −0.485500 −0.242750 0.970089i \(-0.578050\pi\)
−0.242750 + 0.970089i \(0.578050\pi\)
\(662\) 1.50126e6 0.133141
\(663\) 1.91376e7 1.69084
\(664\) 4.49157e6 0.395346
\(665\) −309527. −0.0271422
\(666\) −2.07065e6 −0.180893
\(667\) −2.07433e6 −0.180536
\(668\) −6.38086e6 −0.553271
\(669\) 9.86733e6 0.852382
\(670\) 3.46723e6 0.298398
\(671\) 83258.3 0.00713873
\(672\) 316078. 0.0270005
\(673\) −1.02341e7 −0.870986 −0.435493 0.900192i \(-0.643426\pi\)
−0.435493 + 0.900192i \(0.643426\pi\)
\(674\) 9.95172e6 0.843817
\(675\) 455625. 0.0384900
\(676\) 1.48727e7 1.25177
\(677\) 1.53143e7 1.28418 0.642090 0.766629i \(-0.278068\pi\)
0.642090 + 0.766629i \(0.278068\pi\)
\(678\) −364002. −0.0304109
\(679\) −247874. −0.0206327
\(680\) 2.98300e6 0.247389
\(681\) −8.61532e6 −0.711875
\(682\) 6.19956e6 0.510388
\(683\) −1.28493e7 −1.05397 −0.526986 0.849874i \(-0.676678\pi\)
−0.526986 + 0.849874i \(0.676678\pi\)
\(684\) −467856. −0.0382360
\(685\) −7.22049e6 −0.587950
\(686\) −4.45003e6 −0.361037
\(687\) 4.78039e6 0.386431
\(688\) 5.91558e6 0.476460
\(689\) −2.82648e7 −2.26828
\(690\) 320664. 0.0256406
\(691\) −555664. −0.0442708 −0.0221354 0.999755i \(-0.507046\pi\)
−0.0221354 + 0.999755i \(0.507046\pi\)
\(692\) −9.91591e6 −0.787168
\(693\) −413232. −0.0326859
\(694\) 1.99306e6 0.157080
\(695\) −9.65370e6 −0.758109
\(696\) 3.35346e6 0.262403
\(697\) 7.22674e6 0.563456
\(698\) −534296. −0.0415091
\(699\) −170645. −0.0132099
\(700\) −342967. −0.0264549
\(701\) 1.18413e7 0.910132 0.455066 0.890458i \(-0.349616\pi\)
0.455066 + 0.890458i \(0.349616\pi\)
\(702\) −3.32583e6 −0.254716
\(703\) −2.30711e6 −0.176068
\(704\) 609280. 0.0463325
\(705\) 5.43877e6 0.412124
\(706\) −1.12748e6 −0.0851328
\(707\) 1.95911e6 0.147404
\(708\) 4.21664e6 0.316143
\(709\) −2.12821e7 −1.59000 −0.795002 0.606606i \(-0.792530\pi\)
−0.795002 + 0.606606i \(0.792530\pi\)
\(710\) 6.39804e6 0.476323
\(711\) 5.86190e6 0.434875
\(712\) −4.63681e6 −0.342783
\(713\) −3.71237e6 −0.273481
\(714\) 2.30190e6 0.168983
\(715\) −4.24140e6 −0.310273
\(716\) 349450. 0.0254743
\(717\) 4.18685e6 0.304151
\(718\) −1.66924e7 −1.20839
\(719\) 5.69123e6 0.410567 0.205284 0.978703i \(-0.434188\pi\)
0.205284 + 0.978703i \(0.434188\pi\)
\(720\) −518400. −0.0372678
\(721\) −5.43556e6 −0.389409
\(722\) −521284. −0.0372161
\(723\) −1.27158e7 −0.904690
\(724\) 363391. 0.0257649
\(725\) −3.63873e6 −0.257102
\(726\) 5.00128e6 0.352160
\(727\) −9.24730e6 −0.648902 −0.324451 0.945903i \(-0.605179\pi\)
−0.324451 + 0.945903i \(0.605179\pi\)
\(728\) 2.50348e6 0.175071
\(729\) 531441. 0.0370370
\(730\) 1.58335e6 0.109969
\(731\) 4.30815e7 2.98193
\(732\) 80599.5 0.00555974
\(733\) −9.96970e6 −0.685366 −0.342683 0.939451i \(-0.611336\pi\)
−0.342683 + 0.939451i \(0.611336\pi\)
\(734\) −1.13647e7 −0.778607
\(735\) 3.51692e6 0.240128
\(736\) −364844. −0.0248264
\(737\) 5.15751e6 0.349761
\(738\) −1.25590e6 −0.0848816
\(739\) −2.01922e7 −1.36011 −0.680053 0.733163i \(-0.738043\pi\)
−0.680053 + 0.733163i \(0.738043\pi\)
\(740\) −2.55636e6 −0.171610
\(741\) −3.70563e6 −0.247923
\(742\) −3.39974e6 −0.226692
\(743\) 2.26791e7 1.50714 0.753569 0.657369i \(-0.228331\pi\)
0.753569 + 0.657369i \(0.228331\pi\)
\(744\) 6.00159e6 0.397497
\(745\) 224015. 0.0147872
\(746\) 1.94475e7 1.27943
\(747\) −5.68464e6 −0.372736
\(748\) 4.43721e6 0.289972
\(749\) −744333. −0.0484800
\(750\) 562500. 0.0365148
\(751\) 8.27843e6 0.535609 0.267805 0.963473i \(-0.413702\pi\)
0.267805 + 0.963473i \(0.413702\pi\)
\(752\) −6.18811e6 −0.399037
\(753\) 6.77537e6 0.435457
\(754\) 2.65609e7 1.70143
\(755\) −1.01170e7 −0.645930
\(756\) −400036. −0.0254563
\(757\) −9.08003e6 −0.575901 −0.287950 0.957645i \(-0.592974\pi\)
−0.287950 + 0.957645i \(0.592974\pi\)
\(758\) −7.59965e6 −0.480419
\(759\) 476988. 0.0300541
\(760\) −577600. −0.0362738
\(761\) 1.22929e7 0.769471 0.384736 0.923027i \(-0.374293\pi\)
0.384736 + 0.923027i \(0.374293\pi\)
\(762\) 7.29512e6 0.455140
\(763\) 1.36488e6 0.0848755
\(764\) 2.45824e6 0.152367
\(765\) −3.77536e6 −0.233241
\(766\) 1.23769e7 0.762147
\(767\) 3.33977e7 2.04988
\(768\) 589824. 0.0360844
\(769\) −2.10319e7 −1.28252 −0.641258 0.767325i \(-0.721587\pi\)
−0.641258 + 0.767325i \(0.721587\pi\)
\(770\) −510163. −0.0310086
\(771\) 1.15479e7 0.699627
\(772\) 1.40051e7 0.845751
\(773\) −4.14872e6 −0.249727 −0.124864 0.992174i \(-0.539849\pi\)
−0.124864 + 0.992174i \(0.539849\pi\)
\(774\) −7.48691e6 −0.449211
\(775\) −6.51214e6 −0.389466
\(776\) −462550. −0.0275743
\(777\) −1.97268e6 −0.117220
\(778\) 1.28895e7 0.763460
\(779\) −1.39932e6 −0.0826176
\(780\) −4.10596e6 −0.241645
\(781\) 9.51709e6 0.558312
\(782\) −2.65706e6 −0.155376
\(783\) −4.24422e6 −0.247396
\(784\) −4.00147e6 −0.232503
\(785\) 1.06620e7 0.617540
\(786\) −3.29270e6 −0.190106
\(787\) −2.45443e7 −1.41258 −0.706290 0.707923i \(-0.749633\pi\)
−0.706290 + 0.707923i \(0.749633\pi\)
\(788\) 1.31266e7 0.753074
\(789\) −8.33561e6 −0.476700
\(790\) 7.23692e6 0.412559
\(791\) −346779. −0.0197066
\(792\) −771121. −0.0436827
\(793\) 638384. 0.0360495
\(794\) 7.70911e6 0.433963
\(795\) 5.57591e6 0.312895
\(796\) 1.09301e7 0.611421
\(797\) −2.69314e7 −1.50180 −0.750902 0.660414i \(-0.770381\pi\)
−0.750902 + 0.660414i \(0.770381\pi\)
\(798\) −445719. −0.0247773
\(799\) −4.50662e7 −2.49738
\(800\) −640000. −0.0353553
\(801\) 5.86846e6 0.323179
\(802\) −1.92338e6 −0.105591
\(803\) 2.35524e6 0.128898
\(804\) 4.99282e6 0.272399
\(805\) 305492. 0.0166154
\(806\) 4.75352e7 2.57738
\(807\) 3.49897e6 0.189128
\(808\) 3.65583e6 0.196996
\(809\) 1.07394e7 0.576913 0.288456 0.957493i \(-0.406858\pi\)
0.288456 + 0.957493i \(0.406858\pi\)
\(810\) 656100. 0.0351364
\(811\) 1.37435e7 0.733747 0.366873 0.930271i \(-0.380428\pi\)
0.366873 + 0.930271i \(0.380428\pi\)
\(812\) 3.19479e6 0.170040
\(813\) −2.99373e6 −0.158850
\(814\) −3.80258e6 −0.201149
\(815\) −1.27738e7 −0.673636
\(816\) 4.29552e6 0.225834
\(817\) −8.34189e6 −0.437230
\(818\) 1.34736e7 0.704044
\(819\) −3.16846e6 −0.165059
\(820\) −1.55049e6 −0.0805257
\(821\) −2.34142e7 −1.21233 −0.606165 0.795339i \(-0.707293\pi\)
−0.606165 + 0.795339i \(0.707293\pi\)
\(822\) −1.03975e7 −0.536723
\(823\) −3.26808e7 −1.68187 −0.840936 0.541134i \(-0.817995\pi\)
−0.840936 + 0.541134i \(0.817995\pi\)
\(824\) −1.01431e7 −0.520420
\(825\) 836719. 0.0428001
\(826\) 4.01713e6 0.204864
\(827\) −3.24011e6 −0.164739 −0.0823695 0.996602i \(-0.526249\pi\)
−0.0823695 + 0.996602i \(0.526249\pi\)
\(828\) 461756. 0.0234065
\(829\) 1.19172e7 0.602267 0.301133 0.953582i \(-0.402635\pi\)
0.301133 + 0.953582i \(0.402635\pi\)
\(830\) −7.01807e6 −0.353608
\(831\) 1.01732e7 0.511039
\(832\) 4.67167e6 0.233972
\(833\) −2.91415e7 −1.45512
\(834\) −1.39013e7 −0.692056
\(835\) 9.97010e6 0.494861
\(836\) −859181. −0.0425176
\(837\) −7.59576e6 −0.374764
\(838\) 6.90709e6 0.339770
\(839\) 7.70311e6 0.377800 0.188900 0.981996i \(-0.439508\pi\)
0.188900 + 0.981996i \(0.439508\pi\)
\(840\) −493872. −0.0241499
\(841\) 1.33842e7 0.652533
\(842\) −2.75210e7 −1.33778
\(843\) −2.15722e7 −1.04550
\(844\) −3.37650e6 −0.163159
\(845\) −2.32387e7 −1.11962
\(846\) 7.83183e6 0.376216
\(847\) 4.76464e6 0.228203
\(848\) −6.34415e6 −0.302959
\(849\) −4.47187e6 −0.212922
\(850\) −4.66093e6 −0.221272
\(851\) 2.27703e6 0.107782
\(852\) 9.21318e6 0.434821
\(853\) 1.45542e7 0.684884 0.342442 0.939539i \(-0.388746\pi\)
0.342442 + 0.939539i \(0.388746\pi\)
\(854\) 76786.0 0.00360278
\(855\) 731025. 0.0341993
\(856\) −1.38898e6 −0.0647905
\(857\) −8.43725e6 −0.392418 −0.196209 0.980562i \(-0.562863\pi\)
−0.196209 + 0.980562i \(0.562863\pi\)
\(858\) −6.10762e6 −0.283239
\(859\) 1.70266e7 0.787311 0.393655 0.919258i \(-0.371210\pi\)
0.393655 + 0.919258i \(0.371210\pi\)
\(860\) −9.24310e6 −0.426159
\(861\) −1.19648e6 −0.0550042
\(862\) −2.63035e7 −1.20572
\(863\) −2.31049e7 −1.05603 −0.528016 0.849235i \(-0.677064\pi\)
−0.528016 + 0.849235i \(0.677064\pi\)
\(864\) −746496. −0.0340207
\(865\) 1.54936e7 0.704064
\(866\) −2.56177e7 −1.16077
\(867\) 1.85043e7 0.836036
\(868\) 5.71763e6 0.257583
\(869\) 1.07649e7 0.483572
\(870\) −5.23977e6 −0.234701
\(871\) 3.95453e7 1.76624
\(872\) 2.54696e6 0.113431
\(873\) 585415. 0.0259973
\(874\) 514488. 0.0227822
\(875\) 535885. 0.0236620
\(876\) 2.28002e6 0.100387
\(877\) 4.19637e7 1.84236 0.921180 0.389138i \(-0.127227\pi\)
0.921180 + 0.389138i \(0.127227\pi\)
\(878\) −1.84588e7 −0.808105
\(879\) −3.98807e6 −0.174097
\(880\) −952001. −0.0414410
\(881\) −2.74856e7 −1.19307 −0.596533 0.802588i \(-0.703456\pi\)
−0.596533 + 0.802588i \(0.703456\pi\)
\(882\) 5.06436e6 0.219206
\(883\) −2.77312e7 −1.19692 −0.598462 0.801151i \(-0.704221\pi\)
−0.598462 + 0.801151i \(0.704221\pi\)
\(884\) 3.40224e7 1.46431
\(885\) −6.58851e6 −0.282767
\(886\) −2.83986e6 −0.121538
\(887\) 3.03743e6 0.129628 0.0648138 0.997897i \(-0.479355\pi\)
0.0648138 + 0.997897i \(0.479355\pi\)
\(888\) −3.68115e6 −0.156658
\(889\) 6.94996e6 0.294936
\(890\) 7.24501e6 0.306594
\(891\) 975949. 0.0411844
\(892\) 1.75419e7 0.738184
\(893\) 8.72621e6 0.366182
\(894\) 322582. 0.0134988
\(895\) −546016. −0.0227849
\(896\) 561917. 0.0233831
\(897\) 3.65731e6 0.151768
\(898\) 3.04054e7 1.25823
\(899\) 6.06616e7 2.50331
\(900\) 810000. 0.0333333
\(901\) −4.62026e7 −1.89607
\(902\) −2.30636e6 −0.0943866
\(903\) −7.13267e6 −0.291093
\(904\) −647115. −0.0263366
\(905\) −567798. −0.0230448
\(906\) −1.45685e7 −0.589651
\(907\) 4.35461e6 0.175765 0.0878823 0.996131i \(-0.471990\pi\)
0.0878823 + 0.996131i \(0.471990\pi\)
\(908\) −1.53161e7 −0.616501
\(909\) −4.62691e6 −0.185730
\(910\) −3.91168e6 −0.156589
\(911\) 9.94232e6 0.396910 0.198455 0.980110i \(-0.436408\pi\)
0.198455 + 0.980110i \(0.436408\pi\)
\(912\) −831744. −0.0331133
\(913\) −1.04394e7 −0.414475
\(914\) −2.30486e7 −0.912597
\(915\) −125937. −0.00497279
\(916\) 8.49847e6 0.334659
\(917\) −3.13690e6 −0.123191
\(918\) −5.43651e6 −0.212919
\(919\) −2.07729e7 −0.811350 −0.405675 0.914017i \(-0.632964\pi\)
−0.405675 + 0.914017i \(0.632964\pi\)
\(920\) 570069. 0.0222054
\(921\) 1.81211e7 0.703939
\(922\) 4.88918e6 0.189413
\(923\) 7.29725e7 2.81939
\(924\) −734635. −0.0283069
\(925\) 3.99431e6 0.153492
\(926\) 5.64304e6 0.216265
\(927\) 1.28374e7 0.490657
\(928\) 5.96170e6 0.227248
\(929\) −2.40385e7 −0.913837 −0.456918 0.889509i \(-0.651047\pi\)
−0.456918 + 0.889509i \(0.651047\pi\)
\(930\) −9.37748e6 −0.355532
\(931\) 5.64270e6 0.213360
\(932\) −303369. −0.0114402
\(933\) −2.56018e7 −0.962867
\(934\) 2.90472e7 1.08953
\(935\) −6.93314e6 −0.259359
\(936\) −5.91258e6 −0.220591
\(937\) −2.84683e7 −1.05928 −0.529642 0.848221i \(-0.677674\pi\)
−0.529642 + 0.848221i \(0.677674\pi\)
\(938\) 4.75658e6 0.176518
\(939\) 755157. 0.0279495
\(940\) 9.66893e6 0.356910
\(941\) 1.90770e7 0.702321 0.351161 0.936315i \(-0.385787\pi\)
0.351161 + 0.936315i \(0.385787\pi\)
\(942\) 1.53533e7 0.563734
\(943\) 1.38107e6 0.0505752
\(944\) 7.49626e6 0.273788
\(945\) 625057. 0.0227688
\(946\) −1.37491e7 −0.499513
\(947\) 1.04106e7 0.377224 0.188612 0.982052i \(-0.439601\pi\)
0.188612 + 0.982052i \(0.439601\pi\)
\(948\) 1.04212e7 0.376613
\(949\) 1.80588e7 0.650914
\(950\) 902500. 0.0324443
\(951\) 1.51873e7 0.544541
\(952\) 4.09228e6 0.146343
\(953\) 1.36160e7 0.485642 0.242821 0.970071i \(-0.421927\pi\)
0.242821 + 0.970071i \(0.421927\pi\)
\(954\) 8.02931e6 0.285632
\(955\) −3.84100e6 −0.136281
\(956\) 7.44329e6 0.263403
\(957\) −7.79417e6 −0.275100
\(958\) −1.03315e7 −0.363704
\(959\) −9.90555e6 −0.347802
\(960\) −921600. −0.0322749
\(961\) 7.99353e7 2.79209
\(962\) −2.91564e7 −1.01577
\(963\) 1.75793e6 0.0610850
\(964\) −2.26060e7 −0.783484
\(965\) −2.18829e7 −0.756463
\(966\) 439908. 0.0151677
\(967\) 1.92401e7 0.661670 0.330835 0.943689i \(-0.392670\pi\)
0.330835 + 0.943689i \(0.392670\pi\)
\(968\) 8.89116e6 0.304979
\(969\) −6.05735e6 −0.207240
\(970\) 722734. 0.0246632
\(971\) 2.73741e7 0.931732 0.465866 0.884855i \(-0.345743\pi\)
0.465866 + 0.884855i \(0.345743\pi\)
\(972\) 944784. 0.0320750
\(973\) −1.32436e7 −0.448460
\(974\) −2.24284e7 −0.757530
\(975\) 6.41556e6 0.216134
\(976\) 143288. 0.00481488
\(977\) −3.27651e7 −1.09819 −0.549093 0.835761i \(-0.685027\pi\)
−0.549093 + 0.835761i \(0.685027\pi\)
\(978\) −1.83942e7 −0.614943
\(979\) 1.07770e7 0.359368
\(980\) 6.25230e6 0.207957
\(981\) −3.22349e6 −0.106944
\(982\) −7.17576e6 −0.237459
\(983\) −3.39811e7 −1.12164 −0.560820 0.827938i \(-0.689514\pi\)
−0.560820 + 0.827938i \(0.689514\pi\)
\(984\) −2.23271e6 −0.0735096
\(985\) −2.05103e7 −0.673569
\(986\) 4.34173e7 1.42223
\(987\) 7.46127e6 0.243792
\(988\) −6.58778e6 −0.214707
\(989\) 8.23313e6 0.267654
\(990\) 1.20488e6 0.0390710
\(991\) −5.88603e7 −1.90388 −0.951938 0.306291i \(-0.900912\pi\)
−0.951938 + 0.306291i \(0.900912\pi\)
\(992\) 1.06695e7 0.344243
\(993\) −3.37784e6 −0.108709
\(994\) 8.77726e6 0.281769
\(995\) −1.70782e7 −0.546871
\(996\) −1.01060e7 −0.322799
\(997\) −5.35191e7 −1.70518 −0.852591 0.522579i \(-0.824970\pi\)
−0.852591 + 0.522579i \(0.824970\pi\)
\(998\) −1.08378e7 −0.344440
\(999\) 4.65896e6 0.147698
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 570.6.a.k.1.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
570.6.a.k.1.2 4 1.1 even 1 trivial