Properties

Label 490.6.a.k.1.1
Level $490$
Weight $6$
Character 490.1
Self dual yes
Analytic conductor $78.588$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 490.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(78.5880717084\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 10)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 490.1

$q$-expansion

\(f(q)\) \(=\) \(q+4.00000 q^{2} -6.00000 q^{3} +16.0000 q^{4} +25.0000 q^{5} -24.0000 q^{6} +64.0000 q^{8} -207.000 q^{9} +O(q^{10})\) \(q+4.00000 q^{2} -6.00000 q^{3} +16.0000 q^{4} +25.0000 q^{5} -24.0000 q^{6} +64.0000 q^{8} -207.000 q^{9} +100.000 q^{10} +192.000 q^{11} -96.0000 q^{12} -1106.00 q^{13} -150.000 q^{15} +256.000 q^{16} -762.000 q^{17} -828.000 q^{18} +2740.00 q^{19} +400.000 q^{20} +768.000 q^{22} +1566.00 q^{23} -384.000 q^{24} +625.000 q^{25} -4424.00 q^{26} +2700.00 q^{27} +5910.00 q^{29} -600.000 q^{30} +6868.00 q^{31} +1024.00 q^{32} -1152.00 q^{33} -3048.00 q^{34} -3312.00 q^{36} -5518.00 q^{37} +10960.0 q^{38} +6636.00 q^{39} +1600.00 q^{40} +378.000 q^{41} -2434.00 q^{43} +3072.00 q^{44} -5175.00 q^{45} +6264.00 q^{46} -13122.0 q^{47} -1536.00 q^{48} +2500.00 q^{50} +4572.00 q^{51} -17696.0 q^{52} -9174.00 q^{53} +10800.0 q^{54} +4800.00 q^{55} -16440.0 q^{57} +23640.0 q^{58} +34980.0 q^{59} -2400.00 q^{60} +9838.00 q^{61} +27472.0 q^{62} +4096.00 q^{64} -27650.0 q^{65} -4608.00 q^{66} +33722.0 q^{67} -12192.0 q^{68} -9396.00 q^{69} +70212.0 q^{71} -13248.0 q^{72} -21986.0 q^{73} -22072.0 q^{74} -3750.00 q^{75} +43840.0 q^{76} +26544.0 q^{78} +4520.00 q^{79} +6400.00 q^{80} +34101.0 q^{81} +1512.00 q^{82} +109074. q^{83} -19050.0 q^{85} -9736.00 q^{86} -35460.0 q^{87} +12288.0 q^{88} -38490.0 q^{89} -20700.0 q^{90} +25056.0 q^{92} -41208.0 q^{93} -52488.0 q^{94} +68500.0 q^{95} -6144.00 q^{96} +1918.00 q^{97} -39744.0 q^{99} +O(q^{100})\)

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
\(3\) −6.00000 −0.384900 −0.192450 0.981307i \(-0.561643\pi\)
−0.192450 + 0.981307i \(0.561643\pi\)
\(4\) 16.0000 0.500000
\(5\) 25.0000 0.447214
\(6\) −24.0000 −0.272166
\(7\) 0 0
\(8\) 64.0000 0.353553
\(9\) −207.000 −0.851852
\(10\) 100.000 0.316228
\(11\) 192.000 0.478431 0.239216 0.970966i \(-0.423110\pi\)
0.239216 + 0.970966i \(0.423110\pi\)
\(12\) −96.0000 −0.192450
\(13\) −1106.00 −1.81508 −0.907542 0.419961i \(-0.862044\pi\)
−0.907542 + 0.419961i \(0.862044\pi\)
\(14\) 0 0
\(15\) −150.000 −0.172133
\(16\) 256.000 0.250000
\(17\) −762.000 −0.639488 −0.319744 0.947504i \(-0.603597\pi\)
−0.319744 + 0.947504i \(0.603597\pi\)
\(18\) −828.000 −0.602350
\(19\) 2740.00 1.74127 0.870636 0.491928i \(-0.163708\pi\)
0.870636 + 0.491928i \(0.163708\pi\)
\(20\) 400.000 0.223607
\(21\) 0 0
\(22\) 768.000 0.338302
\(23\) 1566.00 0.617266 0.308633 0.951181i \(-0.400129\pi\)
0.308633 + 0.951181i \(0.400129\pi\)
\(24\) −384.000 −0.136083
\(25\) 625.000 0.200000
\(26\) −4424.00 −1.28346
\(27\) 2700.00 0.712778
\(28\) 0 0
\(29\) 5910.00 1.30495 0.652473 0.757812i \(-0.273732\pi\)
0.652473 + 0.757812i \(0.273732\pi\)
\(30\) −600.000 −0.121716
\(31\) 6868.00 1.28359 0.641795 0.766877i \(-0.278190\pi\)
0.641795 + 0.766877i \(0.278190\pi\)
\(32\) 1024.00 0.176777
\(33\) −1152.00 −0.184148
\(34\) −3048.00 −0.452187
\(35\) 0 0
\(36\) −3312.00 −0.425926
\(37\) −5518.00 −0.662640 −0.331320 0.943519i \(-0.607494\pi\)
−0.331320 + 0.943519i \(0.607494\pi\)
\(38\) 10960.0 1.23127
\(39\) 6636.00 0.698626
\(40\) 1600.00 0.158114
\(41\) 378.000 0.0351182 0.0175591 0.999846i \(-0.494410\pi\)
0.0175591 + 0.999846i \(0.494410\pi\)
\(42\) 0 0
\(43\) −2434.00 −0.200747 −0.100374 0.994950i \(-0.532004\pi\)
−0.100374 + 0.994950i \(0.532004\pi\)
\(44\) 3072.00 0.239216
\(45\) −5175.00 −0.380960
\(46\) 6264.00 0.436473
\(47\) −13122.0 −0.866474 −0.433237 0.901280i \(-0.642629\pi\)
−0.433237 + 0.901280i \(0.642629\pi\)
\(48\) −1536.00 −0.0962250
\(49\) 0 0
\(50\) 2500.00 0.141421
\(51\) 4572.00 0.246139
\(52\) −17696.0 −0.907542
\(53\) −9174.00 −0.448610 −0.224305 0.974519i \(-0.572011\pi\)
−0.224305 + 0.974519i \(0.572011\pi\)
\(54\) 10800.0 0.504010
\(55\) 4800.00 0.213961
\(56\) 0 0
\(57\) −16440.0 −0.670216
\(58\) 23640.0 0.922736
\(59\) 34980.0 1.30825 0.654124 0.756388i \(-0.273038\pi\)
0.654124 + 0.756388i \(0.273038\pi\)
\(60\) −2400.00 −0.0860663
\(61\) 9838.00 0.338518 0.169259 0.985572i \(-0.445863\pi\)
0.169259 + 0.985572i \(0.445863\pi\)
\(62\) 27472.0 0.907635
\(63\) 0 0
\(64\) 4096.00 0.125000
\(65\) −27650.0 −0.811730
\(66\) −4608.00 −0.130212
\(67\) 33722.0 0.917754 0.458877 0.888500i \(-0.348252\pi\)
0.458877 + 0.888500i \(0.348252\pi\)
\(68\) −12192.0 −0.319744
\(69\) −9396.00 −0.237586
\(70\) 0 0
\(71\) 70212.0 1.65297 0.826486 0.562957i \(-0.190336\pi\)
0.826486 + 0.562957i \(0.190336\pi\)
\(72\) −13248.0 −0.301175
\(73\) −21986.0 −0.482880 −0.241440 0.970416i \(-0.577620\pi\)
−0.241440 + 0.970416i \(0.577620\pi\)
\(74\) −22072.0 −0.468557
\(75\) −3750.00 −0.0769800
\(76\) 43840.0 0.870636
\(77\) 0 0
\(78\) 26544.0 0.494003
\(79\) 4520.00 0.0814837 0.0407418 0.999170i \(-0.487028\pi\)
0.0407418 + 0.999170i \(0.487028\pi\)
\(80\) 6400.00 0.111803
\(81\) 34101.0 0.577503
\(82\) 1512.00 0.0248323
\(83\) 109074. 1.73790 0.868952 0.494896i \(-0.164794\pi\)
0.868952 + 0.494896i \(0.164794\pi\)
\(84\) 0 0
\(85\) −19050.0 −0.285988
\(86\) −9736.00 −0.141950
\(87\) −35460.0 −0.502274
\(88\) 12288.0 0.169151
\(89\) −38490.0 −0.515078 −0.257539 0.966268i \(-0.582912\pi\)
−0.257539 + 0.966268i \(0.582912\pi\)
\(90\) −20700.0 −0.269379
\(91\) 0 0
\(92\) 25056.0 0.308633
\(93\) −41208.0 −0.494054
\(94\) −52488.0 −0.612689
\(95\) 68500.0 0.778720
\(96\) −6144.00 −0.0680414
\(97\) 1918.00 0.0206976 0.0103488 0.999946i \(-0.496706\pi\)
0.0103488 + 0.999946i \(0.496706\pi\)
\(98\) 0 0
\(99\) −39744.0 −0.407553
\(100\) 10000.0 0.100000
\(101\) −77622.0 −0.757149 −0.378575 0.925571i \(-0.623586\pi\)
−0.378575 + 0.925571i \(0.623586\pi\)
\(102\) 18288.0 0.174047
\(103\) 46714.0 0.433864 0.216932 0.976187i \(-0.430395\pi\)
0.216932 + 0.976187i \(0.430395\pi\)
\(104\) −70784.0 −0.641729
\(105\) 0 0
\(106\) −36696.0 −0.317215
\(107\) −1038.00 −0.00876472 −0.00438236 0.999990i \(-0.501395\pi\)
−0.00438236 + 0.999990i \(0.501395\pi\)
\(108\) 43200.0 0.356389
\(109\) 206930. 1.66823 0.834117 0.551587i \(-0.185977\pi\)
0.834117 + 0.551587i \(0.185977\pi\)
\(110\) 19200.0 0.151293
\(111\) 33108.0 0.255050
\(112\) 0 0
\(113\) 139386. 1.02689 0.513444 0.858123i \(-0.328369\pi\)
0.513444 + 0.858123i \(0.328369\pi\)
\(114\) −65760.0 −0.473914
\(115\) 39150.0 0.276050
\(116\) 94560.0 0.652473
\(117\) 228942. 1.54618
\(118\) 139920. 0.925070
\(119\) 0 0
\(120\) −9600.00 −0.0608581
\(121\) −124187. −0.771104
\(122\) 39352.0 0.239369
\(123\) −2268.00 −0.0135170
\(124\) 109888. 0.641795
\(125\) 15625.0 0.0894427
\(126\) 0 0
\(127\) 299882. 1.64984 0.824919 0.565252i \(-0.191221\pi\)
0.824919 + 0.565252i \(0.191221\pi\)
\(128\) 16384.0 0.0883883
\(129\) 14604.0 0.0772676
\(130\) −110600. −0.573980
\(131\) −7872.00 −0.0400781 −0.0200390 0.999799i \(-0.506379\pi\)
−0.0200390 + 0.999799i \(0.506379\pi\)
\(132\) −18432.0 −0.0920741
\(133\) 0 0
\(134\) 134888. 0.648950
\(135\) 67500.0 0.318764
\(136\) −48768.0 −0.226093
\(137\) −164238. −0.747605 −0.373803 0.927508i \(-0.621946\pi\)
−0.373803 + 0.927508i \(0.621946\pi\)
\(138\) −37584.0 −0.167998
\(139\) 282100. 1.23841 0.619207 0.785228i \(-0.287454\pi\)
0.619207 + 0.785228i \(0.287454\pi\)
\(140\) 0 0
\(141\) 78732.0 0.333506
\(142\) 280848. 1.16883
\(143\) −212352. −0.868393
\(144\) −52992.0 −0.212963
\(145\) 147750. 0.583590
\(146\) −87944.0 −0.341448
\(147\) 0 0
\(148\) −88288.0 −0.331320
\(149\) −388950. −1.43525 −0.717626 0.696429i \(-0.754771\pi\)
−0.717626 + 0.696429i \(0.754771\pi\)
\(150\) −15000.0 −0.0544331
\(151\) −97948.0 −0.349585 −0.174793 0.984605i \(-0.555926\pi\)
−0.174793 + 0.984605i \(0.555926\pi\)
\(152\) 175360. 0.615633
\(153\) 157734. 0.544749
\(154\) 0 0
\(155\) 171700. 0.574039
\(156\) 106176. 0.349313
\(157\) 3718.00 0.0120382 0.00601908 0.999982i \(-0.498084\pi\)
0.00601908 + 0.999982i \(0.498084\pi\)
\(158\) 18080.0 0.0576177
\(159\) 55044.0 0.172670
\(160\) 25600.0 0.0790569
\(161\) 0 0
\(162\) 136404. 0.408357
\(163\) −43234.0 −0.127455 −0.0637274 0.997967i \(-0.520299\pi\)
−0.0637274 + 0.997967i \(0.520299\pi\)
\(164\) 6048.00 0.0175591
\(165\) −28800.0 −0.0823536
\(166\) 436296. 1.22888
\(167\) −186522. −0.517534 −0.258767 0.965940i \(-0.583316\pi\)
−0.258767 + 0.965940i \(0.583316\pi\)
\(168\) 0 0
\(169\) 851943. 2.29453
\(170\) −76200.0 −0.202224
\(171\) −567180. −1.48331
\(172\) −38944.0 −0.100374
\(173\) 374454. 0.951225 0.475612 0.879655i \(-0.342226\pi\)
0.475612 + 0.879655i \(0.342226\pi\)
\(174\) −141840. −0.355161
\(175\) 0 0
\(176\) 49152.0 0.119608
\(177\) −209880. −0.503545
\(178\) −153960. −0.364215
\(179\) 272100. 0.634740 0.317370 0.948302i \(-0.397200\pi\)
0.317370 + 0.948302i \(0.397200\pi\)
\(180\) −82800.0 −0.190480
\(181\) 75418.0 0.171111 0.0855556 0.996333i \(-0.472733\pi\)
0.0855556 + 0.996333i \(0.472733\pi\)
\(182\) 0 0
\(183\) −59028.0 −0.130296
\(184\) 100224. 0.218236
\(185\) −137950. −0.296341
\(186\) −164832. −0.349349
\(187\) −146304. −0.305951
\(188\) −209952. −0.433237
\(189\) 0 0
\(190\) 274000. 0.550638
\(191\) −356988. −0.708060 −0.354030 0.935234i \(-0.615189\pi\)
−0.354030 + 0.935234i \(0.615189\pi\)
\(192\) −24576.0 −0.0481125
\(193\) −438694. −0.847751 −0.423876 0.905720i \(-0.639331\pi\)
−0.423876 + 0.905720i \(0.639331\pi\)
\(194\) 7672.00 0.0146354
\(195\) 165900. 0.312435
\(196\) 0 0
\(197\) −156798. −0.287856 −0.143928 0.989588i \(-0.545973\pi\)
−0.143928 + 0.989588i \(0.545973\pi\)
\(198\) −158976. −0.288183
\(199\) 162520. 0.290920 0.145460 0.989364i \(-0.453534\pi\)
0.145460 + 0.989364i \(0.453534\pi\)
\(200\) 40000.0 0.0707107
\(201\) −202332. −0.353244
\(202\) −310488. −0.535385
\(203\) 0 0
\(204\) 73152.0 0.123070
\(205\) 9450.00 0.0157053
\(206\) 186856. 0.306788
\(207\) −324162. −0.525819
\(208\) −283136. −0.453771
\(209\) 526080. 0.833079
\(210\) 0 0
\(211\) −181648. −0.280882 −0.140441 0.990089i \(-0.544852\pi\)
−0.140441 + 0.990089i \(0.544852\pi\)
\(212\) −146784. −0.224305
\(213\) −421272. −0.636229
\(214\) −4152.00 −0.00619759
\(215\) −60850.0 −0.0897769
\(216\) 172800. 0.252005
\(217\) 0 0
\(218\) 827720. 1.17962
\(219\) 131916. 0.185861
\(220\) 76800.0 0.106980
\(221\) 842772. 1.16073
\(222\) 132432. 0.180348
\(223\) 288274. 0.388189 0.194095 0.980983i \(-0.437823\pi\)
0.194095 + 0.980983i \(0.437823\pi\)
\(224\) 0 0
\(225\) −129375. −0.170370
\(226\) 557544. 0.726119
\(227\) −1.12552e6 −1.44974 −0.724869 0.688887i \(-0.758100\pi\)
−0.724869 + 0.688887i \(0.758100\pi\)
\(228\) −263040. −0.335108
\(229\) 415810. 0.523970 0.261985 0.965072i \(-0.415623\pi\)
0.261985 + 0.965072i \(0.415623\pi\)
\(230\) 156600. 0.195197
\(231\) 0 0
\(232\) 378240. 0.461368
\(233\) 770586. 0.929889 0.464945 0.885340i \(-0.346074\pi\)
0.464945 + 0.885340i \(0.346074\pi\)
\(234\) 915768. 1.09332
\(235\) −328050. −0.387499
\(236\) 559680. 0.654124
\(237\) −27120.0 −0.0313631
\(238\) 0 0
\(239\) −595320. −0.674149 −0.337074 0.941478i \(-0.609437\pi\)
−0.337074 + 0.941478i \(0.609437\pi\)
\(240\) −38400.0 −0.0430331
\(241\) −273902. −0.303775 −0.151888 0.988398i \(-0.548535\pi\)
−0.151888 + 0.988398i \(0.548535\pi\)
\(242\) −496748. −0.545253
\(243\) −860706. −0.935059
\(244\) 157408. 0.169259
\(245\) 0 0
\(246\) −9072.00 −0.00955796
\(247\) −3.03044e6 −3.16055
\(248\) 439552. 0.453817
\(249\) −654444. −0.668920
\(250\) 62500.0 0.0632456
\(251\) −850752. −0.852351 −0.426176 0.904640i \(-0.640139\pi\)
−0.426176 + 0.904640i \(0.640139\pi\)
\(252\) 0 0
\(253\) 300672. 0.295319
\(254\) 1.19953e6 1.16661
\(255\) 114300. 0.110077
\(256\) 65536.0 0.0625000
\(257\) −825402. −0.779530 −0.389765 0.920914i \(-0.627444\pi\)
−0.389765 + 0.920914i \(0.627444\pi\)
\(258\) 58416.0 0.0546365
\(259\) 0 0
\(260\) −442400. −0.405865
\(261\) −1.22337e6 −1.11162
\(262\) −31488.0 −0.0283395
\(263\) 1.36465e6 1.21655 0.608276 0.793726i \(-0.291861\pi\)
0.608276 + 0.793726i \(0.291861\pi\)
\(264\) −73728.0 −0.0651062
\(265\) −229350. −0.200625
\(266\) 0 0
\(267\) 230940. 0.198254
\(268\) 539552. 0.458877
\(269\) 113310. 0.0954745 0.0477373 0.998860i \(-0.484799\pi\)
0.0477373 + 0.998860i \(0.484799\pi\)
\(270\) 270000. 0.225400
\(271\) 849628. 0.702758 0.351379 0.936233i \(-0.385713\pi\)
0.351379 + 0.936233i \(0.385713\pi\)
\(272\) −195072. −0.159872
\(273\) 0 0
\(274\) −656952. −0.528637
\(275\) 120000. 0.0956862
\(276\) −150336. −0.118793
\(277\) 438602. 0.343456 0.171728 0.985144i \(-0.445065\pi\)
0.171728 + 0.985144i \(0.445065\pi\)
\(278\) 1.12840e6 0.875691
\(279\) −1.42168e6 −1.09343
\(280\) 0 0
\(281\) −1.45670e6 −1.10053 −0.550267 0.834989i \(-0.685474\pi\)
−0.550267 + 0.834989i \(0.685474\pi\)
\(282\) 314928. 0.235824
\(283\) 120394. 0.0893591 0.0446795 0.999001i \(-0.485773\pi\)
0.0446795 + 0.999001i \(0.485773\pi\)
\(284\) 1.12339e6 0.826486
\(285\) −411000. −0.299730
\(286\) −849408. −0.614047
\(287\) 0 0
\(288\) −211968. −0.150588
\(289\) −839213. −0.591055
\(290\) 591000. 0.412660
\(291\) −11508.0 −0.00796650
\(292\) −351776. −0.241440
\(293\) 2.64209e6 1.79796 0.898978 0.437993i \(-0.144311\pi\)
0.898978 + 0.437993i \(0.144311\pi\)
\(294\) 0 0
\(295\) 874500. 0.585066
\(296\) −353152. −0.234278
\(297\) 518400. 0.341015
\(298\) −1.55580e6 −1.01488
\(299\) −1.73200e6 −1.12039
\(300\) −60000.0 −0.0384900
\(301\) 0 0
\(302\) −391792. −0.247194
\(303\) 465732. 0.291427
\(304\) 701440. 0.435318
\(305\) 245950. 0.151390
\(306\) 630936. 0.385196
\(307\) 1.44756e6 0.876577 0.438288 0.898834i \(-0.355585\pi\)
0.438288 + 0.898834i \(0.355585\pi\)
\(308\) 0 0
\(309\) −280284. −0.166994
\(310\) 686800. 0.405907
\(311\) 928068. 0.544100 0.272050 0.962283i \(-0.412298\pi\)
0.272050 + 0.962283i \(0.412298\pi\)
\(312\) 424704. 0.247002
\(313\) −2.29563e6 −1.32446 −0.662232 0.749299i \(-0.730391\pi\)
−0.662232 + 0.749299i \(0.730391\pi\)
\(314\) 14872.0 0.00851227
\(315\) 0 0
\(316\) 72320.0 0.0407418
\(317\) 2.73652e6 1.52950 0.764752 0.644324i \(-0.222861\pi\)
0.764752 + 0.644324i \(0.222861\pi\)
\(318\) 220176. 0.122096
\(319\) 1.13472e6 0.624327
\(320\) 102400. 0.0559017
\(321\) 6228.00 0.00337354
\(322\) 0 0
\(323\) −2.08788e6 −1.11352
\(324\) 545616. 0.288752
\(325\) −691250. −0.363017
\(326\) −172936. −0.0901242
\(327\) −1.24158e6 −0.642104
\(328\) 24192.0 0.0124162
\(329\) 0 0
\(330\) −115200. −0.0582328
\(331\) 3.81879e6 1.91583 0.957913 0.287059i \(-0.0926776\pi\)
0.957913 + 0.287059i \(0.0926776\pi\)
\(332\) 1.74518e6 0.868952
\(333\) 1.14223e6 0.564471
\(334\) −746088. −0.365952
\(335\) 843050. 0.410432
\(336\) 0 0
\(337\) −2.21088e6 −1.06045 −0.530225 0.847857i \(-0.677892\pi\)
−0.530225 + 0.847857i \(0.677892\pi\)
\(338\) 3.40777e6 1.62248
\(339\) −836316. −0.395249
\(340\) −304800. −0.142994
\(341\) 1.31866e6 0.614109
\(342\) −2.26872e6 −1.04886
\(343\) 0 0
\(344\) −155776. −0.0709748
\(345\) −234900. −0.106252
\(346\) 1.49782e6 0.672618
\(347\) −2.32724e6 −1.03757 −0.518785 0.854905i \(-0.673615\pi\)
−0.518785 + 0.854905i \(0.673615\pi\)
\(348\) −567360. −0.251137
\(349\) 311290. 0.136805 0.0684024 0.997658i \(-0.478210\pi\)
0.0684024 + 0.997658i \(0.478210\pi\)
\(350\) 0 0
\(351\) −2.98620e6 −1.29375
\(352\) 196608. 0.0845755
\(353\) 3.08657e6 1.31838 0.659189 0.751977i \(-0.270900\pi\)
0.659189 + 0.751977i \(0.270900\pi\)
\(354\) −839520. −0.356060
\(355\) 1.75530e6 0.739232
\(356\) −615840. −0.257539
\(357\) 0 0
\(358\) 1.08840e6 0.448829
\(359\) −3.53076e6 −1.44588 −0.722940 0.690911i \(-0.757210\pi\)
−0.722940 + 0.690911i \(0.757210\pi\)
\(360\) −331200. −0.134690
\(361\) 5.03150e6 2.03203
\(362\) 301672. 0.120994
\(363\) 745122. 0.296798
\(364\) 0 0
\(365\) −549650. −0.215950
\(366\) −236112. −0.0921330
\(367\) −35762.0 −0.0138598 −0.00692989 0.999976i \(-0.502206\pi\)
−0.00692989 + 0.999976i \(0.502206\pi\)
\(368\) 400896. 0.154316
\(369\) −78246.0 −0.0299155
\(370\) −551800. −0.209545
\(371\) 0 0
\(372\) −659328. −0.247027
\(373\) −1.71525e6 −0.638346 −0.319173 0.947696i \(-0.603405\pi\)
−0.319173 + 0.947696i \(0.603405\pi\)
\(374\) −585216. −0.216340
\(375\) −93750.0 −0.0344265
\(376\) −839808. −0.306345
\(377\) −6.53646e6 −2.36859
\(378\) 0 0
\(379\) −3.10174e6 −1.10919 −0.554597 0.832119i \(-0.687127\pi\)
−0.554597 + 0.832119i \(0.687127\pi\)
\(380\) 1.09600e6 0.389360
\(381\) −1.79929e6 −0.635023
\(382\) −1.42795e6 −0.500674
\(383\) −5.31949e6 −1.85299 −0.926494 0.376309i \(-0.877193\pi\)
−0.926494 + 0.376309i \(0.877193\pi\)
\(384\) −98304.0 −0.0340207
\(385\) 0 0
\(386\) −1.75478e6 −0.599451
\(387\) 503838. 0.171007
\(388\) 30688.0 0.0103488
\(389\) 1.16145e6 0.389158 0.194579 0.980887i \(-0.437666\pi\)
0.194579 + 0.980887i \(0.437666\pi\)
\(390\) 663600. 0.220925
\(391\) −1.19329e6 −0.394734
\(392\) 0 0
\(393\) 47232.0 0.0154261
\(394\) −627192. −0.203545
\(395\) 113000. 0.0364406
\(396\) −635904. −0.203776
\(397\) −628562. −0.200157 −0.100079 0.994980i \(-0.531909\pi\)
−0.100079 + 0.994980i \(0.531909\pi\)
\(398\) 650080. 0.205712
\(399\) 0 0
\(400\) 160000. 0.0500000
\(401\) −2.72432e6 −0.846052 −0.423026 0.906118i \(-0.639032\pi\)
−0.423026 + 0.906118i \(0.639032\pi\)
\(402\) −809328. −0.249781
\(403\) −7.59601e6 −2.32982
\(404\) −1.24195e6 −0.378575
\(405\) 852525. 0.258267
\(406\) 0 0
\(407\) −1.05946e6 −0.317027
\(408\) 292608. 0.0870233
\(409\) −1.78019e6 −0.526209 −0.263104 0.964767i \(-0.584746\pi\)
−0.263104 + 0.964767i \(0.584746\pi\)
\(410\) 37800.0 0.0111053
\(411\) 985428. 0.287753
\(412\) 747424. 0.216932
\(413\) 0 0
\(414\) −1.29665e6 −0.371810
\(415\) 2.72685e6 0.777215
\(416\) −1.13254e6 −0.320865
\(417\) −1.69260e6 −0.476666
\(418\) 2.10432e6 0.589076
\(419\) −650580. −0.181036 −0.0905181 0.995895i \(-0.528852\pi\)
−0.0905181 + 0.995895i \(0.528852\pi\)
\(420\) 0 0
\(421\) −3.54060e6 −0.973579 −0.486790 0.873519i \(-0.661832\pi\)
−0.486790 + 0.873519i \(0.661832\pi\)
\(422\) −726592. −0.198614
\(423\) 2.71625e6 0.738107
\(424\) −587136. −0.158608
\(425\) −476250. −0.127898
\(426\) −1.68509e6 −0.449882
\(427\) 0 0
\(428\) −16608.0 −0.00438236
\(429\) 1.27411e6 0.334245
\(430\) −243400. −0.0634818
\(431\) −548748. −0.142292 −0.0711459 0.997466i \(-0.522666\pi\)
−0.0711459 + 0.997466i \(0.522666\pi\)
\(432\) 691200. 0.178195
\(433\) 1.49241e6 0.382534 0.191267 0.981538i \(-0.438740\pi\)
0.191267 + 0.981538i \(0.438740\pi\)
\(434\) 0 0
\(435\) −886500. −0.224624
\(436\) 3.31088e6 0.834117
\(437\) 4.29084e6 1.07483
\(438\) 527664. 0.131423
\(439\) −4.86212e6 −1.20411 −0.602053 0.798456i \(-0.705650\pi\)
−0.602053 + 0.798456i \(0.705650\pi\)
\(440\) 307200. 0.0756466
\(441\) 0 0
\(442\) 3.37109e6 0.820757
\(443\) −1.86155e6 −0.450678 −0.225339 0.974280i \(-0.572349\pi\)
−0.225339 + 0.974280i \(0.572349\pi\)
\(444\) 529728. 0.127525
\(445\) −962250. −0.230350
\(446\) 1.15310e6 0.274491
\(447\) 2.33370e6 0.552429
\(448\) 0 0
\(449\) 3.73719e6 0.874841 0.437421 0.899257i \(-0.355892\pi\)
0.437421 + 0.899257i \(0.355892\pi\)
\(450\) −517500. −0.120470
\(451\) 72576.0 0.0168016
\(452\) 2.23018e6 0.513444
\(453\) 587688. 0.134555
\(454\) −4.50209e6 −1.02512
\(455\) 0 0
\(456\) −1.05216e6 −0.236957
\(457\) −6.48276e6 −1.45201 −0.726005 0.687690i \(-0.758625\pi\)
−0.726005 + 0.687690i \(0.758625\pi\)
\(458\) 1.66324e6 0.370503
\(459\) −2.05740e6 −0.455813
\(460\) 626400. 0.138025
\(461\) −1.50910e6 −0.330724 −0.165362 0.986233i \(-0.552879\pi\)
−0.165362 + 0.986233i \(0.552879\pi\)
\(462\) 0 0
\(463\) 8.68401e6 1.88264 0.941321 0.337513i \(-0.109586\pi\)
0.941321 + 0.337513i \(0.109586\pi\)
\(464\) 1.51296e6 0.326236
\(465\) −1.03020e6 −0.220948
\(466\) 3.08234e6 0.657531
\(467\) −6.96412e6 −1.47766 −0.738829 0.673893i \(-0.764621\pi\)
−0.738829 + 0.673893i \(0.764621\pi\)
\(468\) 3.66307e6 0.773091
\(469\) 0 0
\(470\) −1.31220e6 −0.274003
\(471\) −22308.0 −0.00463349
\(472\) 2.23872e6 0.462535
\(473\) −467328. −0.0960437
\(474\) −108480. −0.0221771
\(475\) 1.71250e6 0.348254
\(476\) 0 0
\(477\) 1.89902e6 0.382149
\(478\) −2.38128e6 −0.476695
\(479\) 5.51052e6 1.09737 0.548686 0.836029i \(-0.315128\pi\)
0.548686 + 0.836029i \(0.315128\pi\)
\(480\) −153600. −0.0304290
\(481\) 6.10291e6 1.20275
\(482\) −1.09561e6 −0.214802
\(483\) 0 0
\(484\) −1.98699e6 −0.385552
\(485\) 47950.0 0.00925623
\(486\) −3.44282e6 −0.661187
\(487\) 5.51808e6 1.05430 0.527152 0.849771i \(-0.323260\pi\)
0.527152 + 0.849771i \(0.323260\pi\)
\(488\) 629632. 0.119684
\(489\) 259404. 0.0490574
\(490\) 0 0
\(491\) −1.51277e6 −0.283184 −0.141592 0.989925i \(-0.545222\pi\)
−0.141592 + 0.989925i \(0.545222\pi\)
\(492\) −36288.0 −0.00675850
\(493\) −4.50342e6 −0.834498
\(494\) −1.21218e7 −2.23485
\(495\) −993600. −0.182263
\(496\) 1.75821e6 0.320897
\(497\) 0 0
\(498\) −2.61778e6 −0.472998
\(499\) −1.93042e6 −0.347057 −0.173528 0.984829i \(-0.555517\pi\)
−0.173528 + 0.984829i \(0.555517\pi\)
\(500\) 250000. 0.0447214
\(501\) 1.11913e6 0.199199
\(502\) −3.40301e6 −0.602703
\(503\) −6.73105e6 −1.18621 −0.593106 0.805124i \(-0.702099\pi\)
−0.593106 + 0.805124i \(0.702099\pi\)
\(504\) 0 0
\(505\) −1.94055e6 −0.338607
\(506\) 1.20269e6 0.208822
\(507\) −5.11166e6 −0.883165
\(508\) 4.79811e6 0.824919
\(509\) 556650. 0.0952331 0.0476165 0.998866i \(-0.484837\pi\)
0.0476165 + 0.998866i \(0.484837\pi\)
\(510\) 457200. 0.0778360
\(511\) 0 0
\(512\) 262144. 0.0441942
\(513\) 7.39800e6 1.24114
\(514\) −3.30161e6 −0.551211
\(515\) 1.16785e6 0.194030
\(516\) 233664. 0.0386338
\(517\) −2.51942e6 −0.414548
\(518\) 0 0
\(519\) −2.24672e6 −0.366127
\(520\) −1.76960e6 −0.286990
\(521\) −1.01110e7 −1.63192 −0.815962 0.578106i \(-0.803792\pi\)
−0.815962 + 0.578106i \(0.803792\pi\)
\(522\) −4.89348e6 −0.786034
\(523\) 7.03719e6 1.12498 0.562491 0.826804i \(-0.309843\pi\)
0.562491 + 0.826804i \(0.309843\pi\)
\(524\) −125952. −0.0200390
\(525\) 0 0
\(526\) 5.45858e6 0.860232
\(527\) −5.23342e6 −0.820840
\(528\) −294912. −0.0460371
\(529\) −3.98399e6 −0.618983
\(530\) −917400. −0.141863
\(531\) −7.24086e6 −1.11443
\(532\) 0 0
\(533\) −418068. −0.0637425
\(534\) 923760. 0.140186
\(535\) −25950.0 −0.00391970
\(536\) 2.15821e6 0.324475
\(537\) −1.63260e6 −0.244312
\(538\) 453240. 0.0675107
\(539\) 0 0
\(540\) 1.08000e6 0.159382
\(541\) −4.23114e6 −0.621533 −0.310766 0.950486i \(-0.600586\pi\)
−0.310766 + 0.950486i \(0.600586\pi\)
\(542\) 3.39851e6 0.496925
\(543\) −452508. −0.0658608
\(544\) −780288. −0.113047
\(545\) 5.17325e6 0.746057
\(546\) 0 0
\(547\) 4.44024e6 0.634510 0.317255 0.948340i \(-0.397239\pi\)
0.317255 + 0.948340i \(0.397239\pi\)
\(548\) −2.62781e6 −0.373803
\(549\) −2.03647e6 −0.288367
\(550\) 480000. 0.0676604
\(551\) 1.61934e7 2.27227
\(552\) −601344. −0.0839992
\(553\) 0 0
\(554\) 1.75441e6 0.242860
\(555\) 827700. 0.114062
\(556\) 4.51360e6 0.619207
\(557\) −9.01448e6 −1.23113 −0.615563 0.788088i \(-0.711071\pi\)
−0.615563 + 0.788088i \(0.711071\pi\)
\(558\) −5.68670e6 −0.773170
\(559\) 2.69200e6 0.364373
\(560\) 0 0
\(561\) 877824. 0.117761
\(562\) −5.82679e6 −0.778196
\(563\) 9.81287e6 1.30474 0.652372 0.757899i \(-0.273774\pi\)
0.652372 + 0.757899i \(0.273774\pi\)
\(564\) 1.25971e6 0.166753
\(565\) 3.48465e6 0.459238
\(566\) 481576. 0.0631864
\(567\) 0 0
\(568\) 4.49357e6 0.584414
\(569\) 1.33152e7 1.72412 0.862061 0.506804i \(-0.169173\pi\)
0.862061 + 0.506804i \(0.169173\pi\)
\(570\) −1.64400e6 −0.211941
\(571\) 9.95895e6 1.27827 0.639136 0.769094i \(-0.279292\pi\)
0.639136 + 0.769094i \(0.279292\pi\)
\(572\) −3.39763e6 −0.434196
\(573\) 2.14193e6 0.272533
\(574\) 0 0
\(575\) 978750. 0.123453
\(576\) −847872. −0.106481
\(577\) −4.50372e6 −0.563160 −0.281580 0.959538i \(-0.590859\pi\)
−0.281580 + 0.959538i \(0.590859\pi\)
\(578\) −3.35685e6 −0.417939
\(579\) 2.63216e6 0.326300
\(580\) 2.36400e6 0.291795
\(581\) 0 0
\(582\) −46032.0 −0.00563316
\(583\) −1.76141e6 −0.214629
\(584\) −1.40710e6 −0.170724
\(585\) 5.72355e6 0.691474
\(586\) 1.05684e7 1.27135
\(587\) −625842. −0.0749669 −0.0374834 0.999297i \(-0.511934\pi\)
−0.0374834 + 0.999297i \(0.511934\pi\)
\(588\) 0 0
\(589\) 1.88183e7 2.23508
\(590\) 3.49800e6 0.413704
\(591\) 940788. 0.110796
\(592\) −1.41261e6 −0.165660
\(593\) 2.50385e6 0.292397 0.146198 0.989255i \(-0.453296\pi\)
0.146198 + 0.989255i \(0.453296\pi\)
\(594\) 2.07360e6 0.241134
\(595\) 0 0
\(596\) −6.22320e6 −0.717626
\(597\) −975120. −0.111975
\(598\) −6.92798e6 −0.792235
\(599\) −756480. −0.0861451 −0.0430725 0.999072i \(-0.513715\pi\)
−0.0430725 + 0.999072i \(0.513715\pi\)
\(600\) −240000. −0.0272166
\(601\) 1.38565e7 1.56483 0.782413 0.622760i \(-0.213989\pi\)
0.782413 + 0.622760i \(0.213989\pi\)
\(602\) 0 0
\(603\) −6.98045e6 −0.781791
\(604\) −1.56717e6 −0.174793
\(605\) −3.10468e6 −0.344848
\(606\) 1.86293e6 0.206070
\(607\) −1.13772e7 −1.25333 −0.626663 0.779291i \(-0.715580\pi\)
−0.626663 + 0.779291i \(0.715580\pi\)
\(608\) 2.80576e6 0.307816
\(609\) 0 0
\(610\) 983800. 0.107049
\(611\) 1.45129e7 1.57272
\(612\) 2.52374e6 0.272375
\(613\) −7.00161e6 −0.752570 −0.376285 0.926504i \(-0.622799\pi\)
−0.376285 + 0.926504i \(0.622799\pi\)
\(614\) 5.79023e6 0.619833
\(615\) −56700.0 −0.00604499
\(616\) 0 0
\(617\) 7.90300e6 0.835755 0.417878 0.908503i \(-0.362774\pi\)
0.417878 + 0.908503i \(0.362774\pi\)
\(618\) −1.12114e6 −0.118083
\(619\) −4.02362e6 −0.422076 −0.211038 0.977478i \(-0.567684\pi\)
−0.211038 + 0.977478i \(0.567684\pi\)
\(620\) 2.74720e6 0.287019
\(621\) 4.22820e6 0.439974
\(622\) 3.71227e6 0.384737
\(623\) 0 0
\(624\) 1.69882e6 0.174657
\(625\) 390625. 0.0400000
\(626\) −9.18250e6 −0.936538
\(627\) −3.15648e6 −0.320652
\(628\) 59488.0 0.00601908
\(629\) 4.20472e6 0.423750
\(630\) 0 0
\(631\) −1.00227e7 −1.00210 −0.501049 0.865419i \(-0.667052\pi\)
−0.501049 + 0.865419i \(0.667052\pi\)
\(632\) 289280. 0.0288088
\(633\) 1.08989e6 0.108112
\(634\) 1.09461e7 1.08152
\(635\) 7.49705e6 0.737830
\(636\) 880704. 0.0863351
\(637\) 0 0
\(638\) 4.53888e6 0.441466
\(639\) −1.45339e7 −1.40809
\(640\) 409600. 0.0395285
\(641\) 6.37390e6 0.612718 0.306359 0.951916i \(-0.400889\pi\)
0.306359 + 0.951916i \(0.400889\pi\)
\(642\) 24912.0 0.00238545
\(643\) −5.00457e6 −0.477352 −0.238676 0.971099i \(-0.576713\pi\)
−0.238676 + 0.971099i \(0.576713\pi\)
\(644\) 0 0
\(645\) 365100. 0.0345551
\(646\) −8.35152e6 −0.787380
\(647\) 8.71928e6 0.818879 0.409440 0.912337i \(-0.365724\pi\)
0.409440 + 0.912337i \(0.365724\pi\)
\(648\) 2.18246e6 0.204178
\(649\) 6.71616e6 0.625906
\(650\) −2.76500e6 −0.256692
\(651\) 0 0
\(652\) −691744. −0.0637274
\(653\) −1.58477e6 −0.145440 −0.0727201 0.997352i \(-0.523168\pi\)
−0.0727201 + 0.997352i \(0.523168\pi\)
\(654\) −4.96632e6 −0.454036
\(655\) −196800. −0.0179235
\(656\) 96768.0 0.00877955
\(657\) 4.55110e6 0.411342
\(658\) 0 0
\(659\) 1.26410e7 1.13388 0.566940 0.823759i \(-0.308127\pi\)
0.566940 + 0.823759i \(0.308127\pi\)
\(660\) −460800. −0.0411768
\(661\) 3.61572e6 0.321878 0.160939 0.986964i \(-0.448548\pi\)
0.160939 + 0.986964i \(0.448548\pi\)
\(662\) 1.52752e7 1.35469
\(663\) −5.05663e6 −0.446763
\(664\) 6.98074e6 0.614442
\(665\) 0 0
\(666\) 4.56890e6 0.399141
\(667\) 9.25506e6 0.805498
\(668\) −2.98435e6 −0.258767
\(669\) −1.72964e6 −0.149414
\(670\) 3.37220e6 0.290219
\(671\) 1.88890e6 0.161958
\(672\) 0 0
\(673\) 1.11313e7 0.947349 0.473675 0.880700i \(-0.342927\pi\)
0.473675 + 0.880700i \(0.342927\pi\)
\(674\) −8.84351e6 −0.749851
\(675\) 1.68750e6 0.142556
\(676\) 1.36311e7 1.14727
\(677\) 235518. 0.0197493 0.00987467 0.999951i \(-0.496857\pi\)
0.00987467 + 0.999951i \(0.496857\pi\)
\(678\) −3.34526e6 −0.279483
\(679\) 0 0
\(680\) −1.21920e6 −0.101112
\(681\) 6.75313e6 0.558004
\(682\) 5.27462e6 0.434241
\(683\) 2.05830e7 1.68833 0.844164 0.536084i \(-0.180097\pi\)
0.844164 + 0.536084i \(0.180097\pi\)
\(684\) −9.07488e6 −0.741653
\(685\) −4.10595e6 −0.334339
\(686\) 0 0
\(687\) −2.49486e6 −0.201676
\(688\) −623104. −0.0501868
\(689\) 1.01464e7 0.814265
\(690\) −939600. −0.0751312
\(691\) 9.54825e6 0.760727 0.380363 0.924837i \(-0.375799\pi\)
0.380363 + 0.924837i \(0.375799\pi\)
\(692\) 5.99126e6 0.475612
\(693\) 0 0
\(694\) −9.30895e6 −0.733672
\(695\) 7.05250e6 0.553836
\(696\) −2.26944e6 −0.177581
\(697\) −288036. −0.0224577
\(698\) 1.24516e6 0.0967357
\(699\) −4.62352e6 −0.357915
\(700\) 0 0
\(701\) 1.29304e6 0.0993843 0.0496921 0.998765i \(-0.484176\pi\)
0.0496921 + 0.998765i \(0.484176\pi\)
\(702\) −1.19448e7 −0.914821
\(703\) −1.51193e7 −1.15384
\(704\) 786432. 0.0598039
\(705\) 1.96830e6 0.149148
\(706\) 1.23463e7 0.932234
\(707\) 0 0
\(708\) −3.35808e6 −0.251772
\(709\) −2.12720e7 −1.58926 −0.794628 0.607097i \(-0.792334\pi\)
−0.794628 + 0.607097i \(0.792334\pi\)
\(710\) 7.02120e6 0.522716
\(711\) −935640. −0.0694120
\(712\) −2.46336e6 −0.182108
\(713\) 1.07553e7 0.792316
\(714\) 0 0
\(715\) −5.30880e6 −0.388357
\(716\) 4.35360e6 0.317370
\(717\) 3.57192e6 0.259480
\(718\) −1.41230e7 −1.02239
\(719\) −8.31732e6 −0.600014 −0.300007 0.953937i \(-0.596989\pi\)
−0.300007 + 0.953937i \(0.596989\pi\)
\(720\) −1.32480e6 −0.0952399
\(721\) 0 0
\(722\) 2.01260e7 1.43686
\(723\) 1.64341e6 0.116923
\(724\) 1.20669e6 0.0855556
\(725\) 3.69375e6 0.260989
\(726\) 2.98049e6 0.209868
\(727\) 4.36740e6 0.306469 0.153235 0.988190i \(-0.451031\pi\)
0.153235 + 0.988190i \(0.451031\pi\)
\(728\) 0 0
\(729\) −3.12231e6 −0.217599
\(730\) −2.19860e6 −0.152700
\(731\) 1.85471e6 0.128375
\(732\) −944448. −0.0651479
\(733\) 4.05645e6 0.278860 0.139430 0.990232i \(-0.455473\pi\)
0.139430 + 0.990232i \(0.455473\pi\)
\(734\) −143048. −0.00980035
\(735\) 0 0
\(736\) 1.60358e6 0.109118
\(737\) 6.47462e6 0.439082
\(738\) −312984. −0.0211535
\(739\) 768260. 0.0517484 0.0258742 0.999665i \(-0.491763\pi\)
0.0258742 + 0.999665i \(0.491763\pi\)
\(740\) −2.20720e6 −0.148171
\(741\) 1.81826e7 1.21650
\(742\) 0 0
\(743\) 6.18781e6 0.411211 0.205605 0.978635i \(-0.434084\pi\)
0.205605 + 0.978635i \(0.434084\pi\)
\(744\) −2.63731e6 −0.174674
\(745\) −9.72375e6 −0.641864
\(746\) −6.86102e6 −0.451379
\(747\) −2.25783e7 −1.48044
\(748\) −2.34086e6 −0.152976
\(749\) 0 0
\(750\) −375000. −0.0243432
\(751\) 1.81698e7 1.17557 0.587787 0.809016i \(-0.299999\pi\)
0.587787 + 0.809016i \(0.299999\pi\)
\(752\) −3.35923e6 −0.216618
\(753\) 5.10451e6 0.328070
\(754\) −2.61458e7 −1.67484
\(755\) −2.44870e6 −0.156339
\(756\) 0 0
\(757\) 1.93494e7 1.22724 0.613618 0.789603i \(-0.289714\pi\)
0.613618 + 0.789603i \(0.289714\pi\)
\(758\) −1.24070e7 −0.784318
\(759\) −1.80403e6 −0.113668
\(760\) 4.38400e6 0.275319
\(761\) 3.01992e7 1.89031 0.945155 0.326621i \(-0.105910\pi\)
0.945155 + 0.326621i \(0.105910\pi\)
\(762\) −7.19717e6 −0.449029
\(763\) 0 0
\(764\) −5.71181e6 −0.354030
\(765\) 3.94335e6 0.243619
\(766\) −2.12779e7 −1.31026
\(767\) −3.86879e7 −2.37458
\(768\) −393216. −0.0240563
\(769\) −2.15854e7 −1.31627 −0.658134 0.752901i \(-0.728654\pi\)
−0.658134 + 0.752901i \(0.728654\pi\)
\(770\) 0 0
\(771\) 4.95241e6 0.300041
\(772\) −7.01910e6 −0.423876
\(773\) −3.90895e6 −0.235294 −0.117647 0.993055i \(-0.537535\pi\)
−0.117647 + 0.993055i \(0.537535\pi\)
\(774\) 2.01535e6 0.120920
\(775\) 4.29250e6 0.256718
\(776\) 122752. 0.00731769
\(777\) 0 0
\(778\) 4.64580e6 0.275177
\(779\) 1.03572e6 0.0611503
\(780\) 2.65440e6 0.156218
\(781\) 1.34807e7 0.790833
\(782\) −4.77317e6 −0.279119
\(783\) 1.59570e7 0.930137
\(784\) 0 0
\(785\) 92950.0 0.00538363
\(786\) 188928. 0.0109079
\(787\) 2.65082e7 1.52561 0.762806 0.646628i \(-0.223821\pi\)
0.762806 + 0.646628i \(0.223821\pi\)
\(788\) −2.50877e6 −0.143928
\(789\) −8.18788e6 −0.468251
\(790\) 452000. 0.0257674
\(791\) 0 0
\(792\) −2.54362e6 −0.144092
\(793\) −1.08808e7 −0.614439
\(794\) −2.51425e6 −0.141533
\(795\) 1.37610e6 0.0772204
\(796\) 2.60032e6 0.145460
\(797\) −1.07940e7 −0.601919 −0.300960 0.953637i \(-0.597307\pi\)
−0.300960 + 0.953637i \(0.597307\pi\)
\(798\) 0 0
\(799\) 9.99896e6 0.554100
\(800\) 640000. 0.0353553
\(801\) 7.96743e6 0.438770
\(802\) −1.08973e7 −0.598249
\(803\) −4.22131e6 −0.231025
\(804\) −3.23731e6 −0.176622
\(805\) 0 0
\(806\) −3.03840e7 −1.64743
\(807\) −679860. −0.0367482
\(808\) −4.96781e6 −0.267693
\(809\) −1.11446e7 −0.598675 −0.299338 0.954147i \(-0.596766\pi\)
−0.299338 + 0.954147i \(0.596766\pi\)
\(810\) 3.41010e6 0.182623
\(811\) 1.14866e7 0.613253 0.306626 0.951830i \(-0.400800\pi\)
0.306626 + 0.951830i \(0.400800\pi\)
\(812\) 0 0
\(813\) −5.09777e6 −0.270492
\(814\) −4.23782e6 −0.224172
\(815\) −1.08085e6 −0.0569995
\(816\) 1.17043e6 0.0615348
\(817\) −6.66916e6 −0.349555
\(818\) −7.12076e6 −0.372086
\(819\) 0 0
\(820\) 151200. 0.00785267
\(821\) 3.04347e7 1.57584 0.787918 0.615781i \(-0.211159\pi\)
0.787918 + 0.615781i \(0.211159\pi\)
\(822\) 3.94171e6 0.203472
\(823\) 4.09773e6 0.210884 0.105442 0.994425i \(-0.466374\pi\)
0.105442 + 0.994425i \(0.466374\pi\)
\(824\) 2.98970e6 0.153394
\(825\) −720000. −0.0368297
\(826\) 0 0
\(827\) −1.70652e7 −0.867654 −0.433827 0.900996i \(-0.642837\pi\)
−0.433827 + 0.900996i \(0.642837\pi\)
\(828\) −5.18659e6 −0.262909
\(829\) 2.47617e7 1.25139 0.625697 0.780066i \(-0.284815\pi\)
0.625697 + 0.780066i \(0.284815\pi\)
\(830\) 1.09074e7 0.549574
\(831\) −2.63161e6 −0.132196
\(832\) −4.53018e6 −0.226886
\(833\) 0 0
\(834\) −6.77040e6 −0.337054
\(835\) −4.66305e6 −0.231448
\(836\) 8.41728e6 0.416539
\(837\) 1.85436e7 0.914914
\(838\) −2.60232e6 −0.128012
\(839\) −3.16529e7 −1.55242 −0.776208 0.630476i \(-0.782860\pi\)
−0.776208 + 0.630476i \(0.782860\pi\)
\(840\) 0 0
\(841\) 1.44170e7 0.702884
\(842\) −1.41624e7 −0.688425
\(843\) 8.74019e6 0.423596
\(844\) −2.90637e6 −0.140441
\(845\) 2.12986e7 1.02615
\(846\) 1.08650e7 0.521921
\(847\) 0 0
\(848\) −2.34854e6 −0.112153
\(849\) −722364. −0.0343943
\(850\) −1.90500e6 −0.0904373
\(851\) −8.64119e6 −0.409025
\(852\) −6.74035e6 −0.318115
\(853\) −2.82671e7 −1.33017 −0.665087 0.746765i \(-0.731606\pi\)
−0.665087 + 0.746765i \(0.731606\pi\)
\(854\) 0 0
\(855\) −1.41795e7 −0.663354
\(856\) −66432.0 −0.00309880
\(857\) −2.60870e7 −1.21331 −0.606655 0.794966i \(-0.707489\pi\)
−0.606655 + 0.794966i \(0.707489\pi\)
\(858\) 5.09645e6 0.236347
\(859\) 3.38111e7 1.56342 0.781710 0.623642i \(-0.214348\pi\)
0.781710 + 0.623642i \(0.214348\pi\)
\(860\) −973600. −0.0448884
\(861\) 0 0
\(862\) −2.19499e6 −0.100615
\(863\) 2.22817e7 1.01841 0.509204 0.860646i \(-0.329940\pi\)
0.509204 + 0.860646i \(0.329940\pi\)
\(864\) 2.76480e6 0.126003
\(865\) 9.36135e6 0.425401
\(866\) 5.96966e6 0.270492
\(867\) 5.03528e6 0.227497
\(868\) 0 0
\(869\) 867840. 0.0389843
\(870\) −3.54600e6 −0.158833
\(871\) −3.72965e7 −1.66580
\(872\) 1.32435e7 0.589810
\(873\) −397026. −0.0176313
\(874\) 1.71634e7 0.760018
\(875\) 0 0
\(876\) 2.11066e6 0.0929303
\(877\) −3.46748e7 −1.52235 −0.761177 0.648545i \(-0.775378\pi\)
−0.761177 + 0.648545i \(0.775378\pi\)
\(878\) −1.94485e7 −0.851431
\(879\) −1.58526e7 −0.692034
\(880\) 1.22880e6 0.0534902
\(881\) −1.42603e7 −0.618998 −0.309499 0.950900i \(-0.600161\pi\)
−0.309499 + 0.950900i \(0.600161\pi\)
\(882\) 0 0
\(883\) −3.75177e7 −1.61933 −0.809663 0.586895i \(-0.800350\pi\)
−0.809663 + 0.586895i \(0.800350\pi\)
\(884\) 1.34844e7 0.580363
\(885\) −5.24700e6 −0.225192
\(886\) −7.44622e6 −0.318677
\(887\) −4.07657e7 −1.73975 −0.869873 0.493275i \(-0.835800\pi\)
−0.869873 + 0.493275i \(0.835800\pi\)
\(888\) 2.11891e6 0.0901738
\(889\) 0 0
\(890\) −3.84900e6 −0.162882
\(891\) 6.54739e6 0.276296
\(892\) 4.61238e6 0.194095
\(893\) −3.59543e7 −1.50877
\(894\) 9.33480e6 0.390626
\(895\) 6.80250e6 0.283864
\(896\) 0 0
\(897\) 1.03920e7 0.431238
\(898\) 1.49488e7 0.618606
\(899\) 4.05899e7 1.67501
\(900\) −2.07000e6 −0.0851852
\(901\) 6.99059e6 0.286881
\(902\) 290304. 0.0118806
\(903\) 0 0
\(904\) 8.92070e6 0.363060
\(905\) 1.88545e6 0.0765233
\(906\) 2.35075e6 0.0951451
\(907\) −3.57116e7 −1.44142 −0.720712 0.693235i \(-0.756185\pi\)
−0.720712 + 0.693235i \(0.756185\pi\)
\(908\) −1.80084e7 −0.724869
\(909\) 1.60678e7 0.644979
\(910\) 0 0
\(911\) −2.11389e7 −0.843893 −0.421947 0.906621i \(-0.638653\pi\)
−0.421947 + 0.906621i \(0.638653\pi\)
\(912\) −4.20864e6 −0.167554
\(913\) 2.09422e7 0.831468
\(914\) −2.59310e7 −1.02673
\(915\) −1.47570e6 −0.0582700
\(916\) 6.65296e6 0.261985
\(917\) 0 0
\(918\) −8.22960e6 −0.322309
\(919\) 1.85996e7 0.726465 0.363233 0.931698i \(-0.381673\pi\)
0.363233 + 0.931698i \(0.381673\pi\)
\(920\) 2.50560e6 0.0975983
\(921\) −8.68535e6 −0.337395
\(922\) −6.03641e6 −0.233857
\(923\) −7.76545e7 −3.00028
\(924\) 0 0
\(925\) −3.44875e6 −0.132528
\(926\) 3.47360e7 1.33123
\(927\) −9.66980e6 −0.369588
\(928\) 6.05184e6 0.230684
\(929\) −4.45110e7 −1.69211 −0.846055 0.533096i \(-0.821028\pi\)
−0.846055 + 0.533096i \(0.821028\pi\)
\(930\) −4.12080e6 −0.156234
\(931\) 0 0
\(932\) 1.23294e7 0.464945
\(933\) −5.56841e6 −0.209424
\(934\) −2.78565e7 −1.04486
\(935\) −3.65760e6 −0.136826
\(936\) 1.46523e7 0.546658
\(937\) 2.19419e7 0.816441 0.408221 0.912883i \(-0.366149\pi\)
0.408221 + 0.912883i \(0.366149\pi\)
\(938\) 0 0
\(939\) 1.37738e7 0.509787
\(940\) −5.24880e6 −0.193749
\(941\) 7.77722e6 0.286319 0.143160 0.989700i \(-0.454274\pi\)
0.143160 + 0.989700i \(0.454274\pi\)
\(942\) −89232.0 −0.00327637
\(943\) 591948. 0.0216773
\(944\) 8.95488e6 0.327062
\(945\) 0 0
\(946\) −1.86931e6 −0.0679132
\(947\) 3.17199e7 1.14936 0.574681 0.818378i \(-0.305126\pi\)
0.574681 + 0.818378i \(0.305126\pi\)
\(948\) −433920. −0.0156815
\(949\) 2.43165e7 0.876468
\(950\) 6.85000e6 0.246253
\(951\) −1.64191e7 −0.588707
\(952\) 0 0
\(953\) −5.60285e6 −0.199838 −0.0999188 0.994996i \(-0.531858\pi\)
−0.0999188 + 0.994996i \(0.531858\pi\)
\(954\) 7.59607e6 0.270220
\(955\) −8.92470e6 −0.316654
\(956\) −9.52512e6 −0.337074
\(957\) −6.80832e6 −0.240304
\(958\) 2.20421e7 0.775959
\(959\) 0 0
\(960\) −614400. −0.0215166
\(961\) 1.85403e7 0.647601
\(962\) 2.44116e7 0.850470
\(963\) 214866. 0.00746624
\(964\) −4.38243e6 −0.151888
\(965\) −1.09673e7 −0.379126
\(966\) 0 0
\(967\) −2.03532e7 −0.699949 −0.349975 0.936759i \(-0.613810\pi\)
−0.349975 + 0.936759i \(0.613810\pi\)
\(968\) −7.94797e6 −0.272626
\(969\) 1.25273e7 0.428595
\(970\) 191800. 0.00654514
\(971\) 2.34306e7 0.797510 0.398755 0.917057i \(-0.369442\pi\)
0.398755 + 0.917057i \(0.369442\pi\)
\(972\) −1.37713e7 −0.467530
\(973\) 0 0
\(974\) 2.20723e7 0.745505
\(975\) 4.14750e6 0.139725
\(976\) 2.51853e6 0.0846296
\(977\) −4.30412e7 −1.44261 −0.721303 0.692619i \(-0.756457\pi\)
−0.721303 + 0.692619i \(0.756457\pi\)
\(978\) 1.03762e6 0.0346888
\(979\) −7.39008e6 −0.246429
\(980\) 0 0
\(981\) −4.28345e7 −1.42109
\(982\) −6.05107e6 −0.200241
\(983\) 4.75003e7 1.56788 0.783940 0.620837i \(-0.213207\pi\)
0.783940 + 0.620837i \(0.213207\pi\)
\(984\) −145152. −0.00477898
\(985\) −3.91995e6 −0.128733
\(986\) −1.80137e7 −0.590079
\(987\) 0 0
\(988\) −4.84870e7 −1.58028
\(989\) −3.81164e6 −0.123914
\(990\) −3.97440e6 −0.128879
\(991\) 2.09231e7 0.676770 0.338385 0.941008i \(-0.390119\pi\)
0.338385 + 0.941008i \(0.390119\pi\)
\(992\) 7.03283e6 0.226909
\(993\) −2.29128e7 −0.737402
\(994\) 0 0
\(995\) 4.06300e6 0.130104
\(996\) −1.04711e7 −0.334460
\(997\) −2.96332e7 −0.944148 −0.472074 0.881559i \(-0.656495\pi\)
−0.472074 + 0.881559i \(0.656495\pi\)
\(998\) −7.72168e6 −0.245406
\(999\) −1.48986e7 −0.472315
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 490.6.a.k.1.1 1
7.6 odd 2 10.6.a.c.1.1 1
21.20 even 2 90.6.a.b.1.1 1
28.27 even 2 80.6.a.c.1.1 1
35.13 even 4 50.6.b.b.49.1 2
35.27 even 4 50.6.b.b.49.2 2
35.34 odd 2 50.6.a.b.1.1 1
56.13 odd 2 320.6.a.f.1.1 1
56.27 even 2 320.6.a.k.1.1 1
84.83 odd 2 720.6.a.v.1.1 1
105.62 odd 4 450.6.c.f.199.1 2
105.83 odd 4 450.6.c.f.199.2 2
105.104 even 2 450.6.a.u.1.1 1
140.27 odd 4 400.6.c.i.49.2 2
140.83 odd 4 400.6.c.i.49.1 2
140.139 even 2 400.6.a.i.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
10.6.a.c.1.1 1 7.6 odd 2
50.6.a.b.1.1 1 35.34 odd 2
50.6.b.b.49.1 2 35.13 even 4
50.6.b.b.49.2 2 35.27 even 4
80.6.a.c.1.1 1 28.27 even 2
90.6.a.b.1.1 1 21.20 even 2
320.6.a.f.1.1 1 56.13 odd 2
320.6.a.k.1.1 1 56.27 even 2
400.6.a.i.1.1 1 140.139 even 2
400.6.c.i.49.1 2 140.83 odd 4
400.6.c.i.49.2 2 140.27 odd 4
450.6.a.u.1.1 1 105.104 even 2
450.6.c.f.199.1 2 105.62 odd 4
450.6.c.f.199.2 2 105.83 odd 4
490.6.a.k.1.1 1 1.1 even 1 trivial
720.6.a.v.1.1 1 84.83 odd 2