Properties

Label 966.6.a.a.1.1
Level $966$
Weight $6$
Character 966.1
Self dual yes
Analytic conductor $154.931$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 966.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(154.930769939\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 966.1

$q$-expansion

\(f(q)\) \(=\) \(q-4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} -54.0000 q^{5} +36.0000 q^{6} +49.0000 q^{7} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})\) \(q-4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} -54.0000 q^{5} +36.0000 q^{6} +49.0000 q^{7} -64.0000 q^{8} +81.0000 q^{9} +216.000 q^{10} +564.000 q^{11} -144.000 q^{12} +476.000 q^{13} -196.000 q^{14} +486.000 q^{15} +256.000 q^{16} -1308.00 q^{17} -324.000 q^{18} +14.0000 q^{19} -864.000 q^{20} -441.000 q^{21} -2256.00 q^{22} +529.000 q^{23} +576.000 q^{24} -209.000 q^{25} -1904.00 q^{26} -729.000 q^{27} +784.000 q^{28} -6702.00 q^{29} -1944.00 q^{30} -10258.0 q^{31} -1024.00 q^{32} -5076.00 q^{33} +5232.00 q^{34} -2646.00 q^{35} +1296.00 q^{36} +14078.0 q^{37} -56.0000 q^{38} -4284.00 q^{39} +3456.00 q^{40} -2826.00 q^{41} +1764.00 q^{42} +14216.0 q^{43} +9024.00 q^{44} -4374.00 q^{45} -2116.00 q^{46} -9990.00 q^{47} -2304.00 q^{48} +2401.00 q^{49} +836.000 q^{50} +11772.0 q^{51} +7616.00 q^{52} +16698.0 q^{53} +2916.00 q^{54} -30456.0 q^{55} -3136.00 q^{56} -126.000 q^{57} +26808.0 q^{58} +19044.0 q^{59} +7776.00 q^{60} +5678.00 q^{61} +41032.0 q^{62} +3969.00 q^{63} +4096.00 q^{64} -25704.0 q^{65} +20304.0 q^{66} -39736.0 q^{67} -20928.0 q^{68} -4761.00 q^{69} +10584.0 q^{70} +60108.0 q^{71} -5184.00 q^{72} -7714.00 q^{73} -56312.0 q^{74} +1881.00 q^{75} +224.000 q^{76} +27636.0 q^{77} +17136.0 q^{78} +106472. q^{79} -13824.0 q^{80} +6561.00 q^{81} +11304.0 q^{82} -7662.00 q^{83} -7056.00 q^{84} +70632.0 q^{85} -56864.0 q^{86} +60318.0 q^{87} -36096.0 q^{88} -76536.0 q^{89} +17496.0 q^{90} +23324.0 q^{91} +8464.00 q^{92} +92322.0 q^{93} +39960.0 q^{94} -756.000 q^{95} +9216.00 q^{96} -19048.0 q^{97} -9604.00 q^{98} +45684.0 q^{99} +O(q^{100})\)

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
\(3\) −9.00000 −0.577350
\(4\) 16.0000 0.500000
\(5\) −54.0000 −0.965981 −0.482991 0.875625i \(-0.660450\pi\)
−0.482991 + 0.875625i \(0.660450\pi\)
\(6\) 36.0000 0.408248
\(7\) 49.0000 0.377964
\(8\) −64.0000 −0.353553
\(9\) 81.0000 0.333333
\(10\) 216.000 0.683052
\(11\) 564.000 1.40539 0.702696 0.711490i \(-0.251979\pi\)
0.702696 + 0.711490i \(0.251979\pi\)
\(12\) −144.000 −0.288675
\(13\) 476.000 0.781175 0.390588 0.920566i \(-0.372272\pi\)
0.390588 + 0.920566i \(0.372272\pi\)
\(14\) −196.000 −0.267261
\(15\) 486.000 0.557710
\(16\) 256.000 0.250000
\(17\) −1308.00 −1.09770 −0.548852 0.835919i \(-0.684935\pi\)
−0.548852 + 0.835919i \(0.684935\pi\)
\(18\) −324.000 −0.235702
\(19\) 14.0000 0.00889701 0.00444850 0.999990i \(-0.498584\pi\)
0.00444850 + 0.999990i \(0.498584\pi\)
\(20\) −864.000 −0.482991
\(21\) −441.000 −0.218218
\(22\) −2256.00 −0.993762
\(23\) 529.000 0.208514
\(24\) 576.000 0.204124
\(25\) −209.000 −0.0668800
\(26\) −1904.00 −0.552374
\(27\) −729.000 −0.192450
\(28\) 784.000 0.188982
\(29\) −6702.00 −1.47982 −0.739911 0.672705i \(-0.765132\pi\)
−0.739911 + 0.672705i \(0.765132\pi\)
\(30\) −1944.00 −0.394360
\(31\) −10258.0 −1.91716 −0.958580 0.284823i \(-0.908065\pi\)
−0.958580 + 0.284823i \(0.908065\pi\)
\(32\) −1024.00 −0.176777
\(33\) −5076.00 −0.811403
\(34\) 5232.00 0.776194
\(35\) −2646.00 −0.365107
\(36\) 1296.00 0.166667
\(37\) 14078.0 1.69058 0.845292 0.534305i \(-0.179427\pi\)
0.845292 + 0.534305i \(0.179427\pi\)
\(38\) −56.0000 −0.00629114
\(39\) −4284.00 −0.451012
\(40\) 3456.00 0.341526
\(41\) −2826.00 −0.262550 −0.131275 0.991346i \(-0.541907\pi\)
−0.131275 + 0.991346i \(0.541907\pi\)
\(42\) 1764.00 0.154303
\(43\) 14216.0 1.17248 0.586241 0.810137i \(-0.300607\pi\)
0.586241 + 0.810137i \(0.300607\pi\)
\(44\) 9024.00 0.702696
\(45\) −4374.00 −0.321994
\(46\) −2116.00 −0.147442
\(47\) −9990.00 −0.659661 −0.329831 0.944040i \(-0.606992\pi\)
−0.329831 + 0.944040i \(0.606992\pi\)
\(48\) −2304.00 −0.144338
\(49\) 2401.00 0.142857
\(50\) 836.000 0.0472913
\(51\) 11772.0 0.633760
\(52\) 7616.00 0.390588
\(53\) 16698.0 0.816535 0.408267 0.912862i \(-0.366133\pi\)
0.408267 + 0.912862i \(0.366133\pi\)
\(54\) 2916.00 0.136083
\(55\) −30456.0 −1.35758
\(56\) −3136.00 −0.133631
\(57\) −126.000 −0.00513669
\(58\) 26808.0 1.04639
\(59\) 19044.0 0.712243 0.356121 0.934440i \(-0.384099\pi\)
0.356121 + 0.934440i \(0.384099\pi\)
\(60\) 7776.00 0.278855
\(61\) 5678.00 0.195376 0.0976879 0.995217i \(-0.468855\pi\)
0.0976879 + 0.995217i \(0.468855\pi\)
\(62\) 41032.0 1.35564
\(63\) 3969.00 0.125988
\(64\) 4096.00 0.125000
\(65\) −25704.0 −0.754601
\(66\) 20304.0 0.573749
\(67\) −39736.0 −1.08143 −0.540713 0.841207i \(-0.681846\pi\)
−0.540713 + 0.841207i \(0.681846\pi\)
\(68\) −20928.0 −0.548852
\(69\) −4761.00 −0.120386
\(70\) 10584.0 0.258169
\(71\) 60108.0 1.41510 0.707549 0.706664i \(-0.249801\pi\)
0.707549 + 0.706664i \(0.249801\pi\)
\(72\) −5184.00 −0.117851
\(73\) −7714.00 −0.169423 −0.0847115 0.996406i \(-0.526997\pi\)
−0.0847115 + 0.996406i \(0.526997\pi\)
\(74\) −56312.0 −1.19542
\(75\) 1881.00 0.0386132
\(76\) 224.000 0.00444850
\(77\) 27636.0 0.531188
\(78\) 17136.0 0.318914
\(79\) 106472. 1.91941 0.959705 0.281010i \(-0.0906694\pi\)
0.959705 + 0.281010i \(0.0906694\pi\)
\(80\) −13824.0 −0.241495
\(81\) 6561.00 0.111111
\(82\) 11304.0 0.185651
\(83\) −7662.00 −0.122081 −0.0610403 0.998135i \(-0.519442\pi\)
−0.0610403 + 0.998135i \(0.519442\pi\)
\(84\) −7056.00 −0.109109
\(85\) 70632.0 1.06036
\(86\) −56864.0 −0.829070
\(87\) 60318.0 0.854376
\(88\) −36096.0 −0.496881
\(89\) −76536.0 −1.02421 −0.512107 0.858922i \(-0.671135\pi\)
−0.512107 + 0.858922i \(0.671135\pi\)
\(90\) 17496.0 0.227684
\(91\) 23324.0 0.295257
\(92\) 8464.00 0.104257
\(93\) 92322.0 1.10687
\(94\) 39960.0 0.466451
\(95\) −756.000 −0.00859434
\(96\) 9216.00 0.102062
\(97\) −19048.0 −0.205551 −0.102776 0.994705i \(-0.532772\pi\)
−0.102776 + 0.994705i \(0.532772\pi\)
\(98\) −9604.00 −0.101015
\(99\) 45684.0 0.468464
\(100\) −3344.00 −0.0334400
\(101\) 67176.0 0.655256 0.327628 0.944807i \(-0.393751\pi\)
0.327628 + 0.944807i \(0.393751\pi\)
\(102\) −47088.0 −0.448136
\(103\) −6052.00 −0.0562090 −0.0281045 0.999605i \(-0.508947\pi\)
−0.0281045 + 0.999605i \(0.508947\pi\)
\(104\) −30464.0 −0.276187
\(105\) 23814.0 0.210794
\(106\) −66792.0 −0.577377
\(107\) −182748. −1.54310 −0.771548 0.636171i \(-0.780517\pi\)
−0.771548 + 0.636171i \(0.780517\pi\)
\(108\) −11664.0 −0.0962250
\(109\) 136274. 1.09862 0.549309 0.835619i \(-0.314891\pi\)
0.549309 + 0.835619i \(0.314891\pi\)
\(110\) 121824. 0.959956
\(111\) −126702. −0.976059
\(112\) 12544.0 0.0944911
\(113\) −233886. −1.72309 −0.861545 0.507681i \(-0.830503\pi\)
−0.861545 + 0.507681i \(0.830503\pi\)
\(114\) 504.000 0.00363219
\(115\) −28566.0 −0.201421
\(116\) −107232. −0.739911
\(117\) 38556.0 0.260392
\(118\) −76176.0 −0.503632
\(119\) −64092.0 −0.414893
\(120\) −31104.0 −0.197180
\(121\) 157045. 0.975126
\(122\) −22712.0 −0.138152
\(123\) 25434.0 0.151583
\(124\) −164128. −0.958580
\(125\) 180036. 1.03059
\(126\) −15876.0 −0.0890871
\(127\) −183124. −1.00748 −0.503739 0.863856i \(-0.668043\pi\)
−0.503739 + 0.863856i \(0.668043\pi\)
\(128\) −16384.0 −0.0883883
\(129\) −127944. −0.676933
\(130\) 102816. 0.533583
\(131\) −227148. −1.15646 −0.578230 0.815874i \(-0.696256\pi\)
−0.578230 + 0.815874i \(0.696256\pi\)
\(132\) −81216.0 −0.405702
\(133\) 686.000 0.00336275
\(134\) 158944. 0.764684
\(135\) 39366.0 0.185903
\(136\) 83712.0 0.388097
\(137\) 319902. 1.45618 0.728091 0.685481i \(-0.240408\pi\)
0.728091 + 0.685481i \(0.240408\pi\)
\(138\) 19044.0 0.0851257
\(139\) 126944. 0.557282 0.278641 0.960395i \(-0.410116\pi\)
0.278641 + 0.960395i \(0.410116\pi\)
\(140\) −42336.0 −0.182553
\(141\) 89910.0 0.380855
\(142\) −240432. −1.00063
\(143\) 268464. 1.09786
\(144\) 20736.0 0.0833333
\(145\) 361908. 1.42948
\(146\) 30856.0 0.119800
\(147\) −21609.0 −0.0824786
\(148\) 225248. 0.845292
\(149\) 129990. 0.479672 0.239836 0.970813i \(-0.422906\pi\)
0.239836 + 0.970813i \(0.422906\pi\)
\(150\) −7524.00 −0.0273036
\(151\) −326932. −1.16685 −0.583425 0.812167i \(-0.698288\pi\)
−0.583425 + 0.812167i \(0.698288\pi\)
\(152\) −896.000 −0.00314557
\(153\) −105948. −0.365901
\(154\) −110544. −0.375607
\(155\) 553932. 1.85194
\(156\) −68544.0 −0.225506
\(157\) 469394. 1.51981 0.759903 0.650036i \(-0.225246\pi\)
0.759903 + 0.650036i \(0.225246\pi\)
\(158\) −425888. −1.35723
\(159\) −150282. −0.471427
\(160\) 55296.0 0.170763
\(161\) 25921.0 0.0788110
\(162\) −26244.0 −0.0785674
\(163\) 113348. 0.334153 0.167076 0.985944i \(-0.446567\pi\)
0.167076 + 0.985944i \(0.446567\pi\)
\(164\) −45216.0 −0.131275
\(165\) 274104. 0.783800
\(166\) 30648.0 0.0863241
\(167\) −220386. −0.611495 −0.305747 0.952113i \(-0.598906\pi\)
−0.305747 + 0.952113i \(0.598906\pi\)
\(168\) 28224.0 0.0771517
\(169\) −144717. −0.389765
\(170\) −282528. −0.749789
\(171\) 1134.00 0.00296567
\(172\) 227456. 0.586241
\(173\) −647784. −1.64556 −0.822782 0.568357i \(-0.807579\pi\)
−0.822782 + 0.568357i \(0.807579\pi\)
\(174\) −241272. −0.604135
\(175\) −10241.0 −0.0252783
\(176\) 144384. 0.351348
\(177\) −171396. −0.411214
\(178\) 306144. 0.724229
\(179\) 402348. 0.938576 0.469288 0.883045i \(-0.344511\pi\)
0.469288 + 0.883045i \(0.344511\pi\)
\(180\) −69984.0 −0.160997
\(181\) 338150. 0.767208 0.383604 0.923498i \(-0.374683\pi\)
0.383604 + 0.923498i \(0.374683\pi\)
\(182\) −93296.0 −0.208778
\(183\) −51102.0 −0.112800
\(184\) −33856.0 −0.0737210
\(185\) −760212. −1.63307
\(186\) −369288. −0.782677
\(187\) −737712. −1.54270
\(188\) −159840. −0.329831
\(189\) −35721.0 −0.0727393
\(190\) 3024.00 0.00607712
\(191\) 34992.0 0.0694041 0.0347021 0.999398i \(-0.488952\pi\)
0.0347021 + 0.999398i \(0.488952\pi\)
\(192\) −36864.0 −0.0721688
\(193\) 733766. 1.41796 0.708981 0.705228i \(-0.249155\pi\)
0.708981 + 0.705228i \(0.249155\pi\)
\(194\) 76192.0 0.145347
\(195\) 231336. 0.435669
\(196\) 38416.0 0.0714286
\(197\) −191970. −0.352426 −0.176213 0.984352i \(-0.556385\pi\)
−0.176213 + 0.984352i \(0.556385\pi\)
\(198\) −182736. −0.331254
\(199\) 295412. 0.528805 0.264402 0.964412i \(-0.414825\pi\)
0.264402 + 0.964412i \(0.414825\pi\)
\(200\) 13376.0 0.0236457
\(201\) 357624. 0.624362
\(202\) −268704. −0.463336
\(203\) −328398. −0.559320
\(204\) 188352. 0.316880
\(205\) 152604. 0.253619
\(206\) 24208.0 0.0397458
\(207\) 42849.0 0.0695048
\(208\) 121856. 0.195294
\(209\) 7896.00 0.0125038
\(210\) −95256.0 −0.149054
\(211\) −605956. −0.936990 −0.468495 0.883466i \(-0.655204\pi\)
−0.468495 + 0.883466i \(0.655204\pi\)
\(212\) 267168. 0.408267
\(213\) −540972. −0.817007
\(214\) 730992. 1.09113
\(215\) −767664. −1.13260
\(216\) 46656.0 0.0680414
\(217\) −502642. −0.724619
\(218\) −545096. −0.776840
\(219\) 69426.0 0.0978164
\(220\) −487296. −0.678791
\(221\) −622608. −0.857500
\(222\) 506808. 0.690178
\(223\) −702694. −0.946246 −0.473123 0.880996i \(-0.656873\pi\)
−0.473123 + 0.880996i \(0.656873\pi\)
\(224\) −50176.0 −0.0668153
\(225\) −16929.0 −0.0222933
\(226\) 935544. 1.21841
\(227\) 268398. 0.345712 0.172856 0.984947i \(-0.444700\pi\)
0.172856 + 0.984947i \(0.444700\pi\)
\(228\) −2016.00 −0.00256835
\(229\) 275966. 0.347750 0.173875 0.984768i \(-0.444371\pi\)
0.173875 + 0.984768i \(0.444371\pi\)
\(230\) 114264. 0.142426
\(231\) −248724. −0.306682
\(232\) 428928. 0.523196
\(233\) 492054. 0.593776 0.296888 0.954912i \(-0.404051\pi\)
0.296888 + 0.954912i \(0.404051\pi\)
\(234\) −154224. −0.184125
\(235\) 539460. 0.637220
\(236\) 304704. 0.356121
\(237\) −958248. −1.10817
\(238\) 256368. 0.293374
\(239\) −476556. −0.539659 −0.269829 0.962908i \(-0.586967\pi\)
−0.269829 + 0.962908i \(0.586967\pi\)
\(240\) 124416. 0.139427
\(241\) 910508. 1.00981 0.504907 0.863174i \(-0.331527\pi\)
0.504907 + 0.863174i \(0.331527\pi\)
\(242\) −628180. −0.689518
\(243\) −59049.0 −0.0641500
\(244\) 90848.0 0.0976879
\(245\) −129654. −0.137997
\(246\) −101736. −0.107186
\(247\) 6664.00 0.00695012
\(248\) 656512. 0.677819
\(249\) 68958.0 0.0704833
\(250\) −720144. −0.728734
\(251\) −1.05776e6 −1.05975 −0.529873 0.848077i \(-0.677761\pi\)
−0.529873 + 0.848077i \(0.677761\pi\)
\(252\) 63504.0 0.0629941
\(253\) 298356. 0.293044
\(254\) 732496. 0.712395
\(255\) −635688. −0.612200
\(256\) 65536.0 0.0625000
\(257\) −1.99438e6 −1.88354 −0.941771 0.336254i \(-0.890840\pi\)
−0.941771 + 0.336254i \(0.890840\pi\)
\(258\) 511776. 0.478664
\(259\) 689822. 0.638981
\(260\) −411264. −0.377300
\(261\) −542862. −0.493274
\(262\) 908592. 0.817741
\(263\) −2.05939e6 −1.83590 −0.917951 0.396693i \(-0.870158\pi\)
−0.917951 + 0.396693i \(0.870158\pi\)
\(264\) 324864. 0.286874
\(265\) −901692. −0.788758
\(266\) −2744.00 −0.00237783
\(267\) 688824. 0.591330
\(268\) −635776. −0.540713
\(269\) 610872. 0.514718 0.257359 0.966316i \(-0.417148\pi\)
0.257359 + 0.966316i \(0.417148\pi\)
\(270\) −157464. −0.131453
\(271\) −1.83771e6 −1.52004 −0.760019 0.649900i \(-0.774811\pi\)
−0.760019 + 0.649900i \(0.774811\pi\)
\(272\) −334848. −0.274426
\(273\) −209916. −0.170466
\(274\) −1.27961e6 −1.02968
\(275\) −117876. −0.0939926
\(276\) −76176.0 −0.0601929
\(277\) −1.15727e6 −0.906220 −0.453110 0.891455i \(-0.649686\pi\)
−0.453110 + 0.891455i \(0.649686\pi\)
\(278\) −507776. −0.394058
\(279\) −830898. −0.639053
\(280\) 169344. 0.129085
\(281\) −1.33204e6 −1.00636 −0.503179 0.864182i \(-0.667836\pi\)
−0.503179 + 0.864182i \(0.667836\pi\)
\(282\) −359640. −0.269305
\(283\) 1.93125e6 1.43341 0.716707 0.697375i \(-0.245649\pi\)
0.716707 + 0.697375i \(0.245649\pi\)
\(284\) 961728. 0.707549
\(285\) 6804.00 0.00496195
\(286\) −1.07386e6 −0.776302
\(287\) −138474. −0.0992347
\(288\) −82944.0 −0.0589256
\(289\) 291007. 0.204955
\(290\) −1.44763e6 −1.01080
\(291\) 171432. 0.118675
\(292\) −123424. −0.0847115
\(293\) 1.47079e6 1.00088 0.500438 0.865772i \(-0.333172\pi\)
0.500438 + 0.865772i \(0.333172\pi\)
\(294\) 86436.0 0.0583212
\(295\) −1.02838e6 −0.688013
\(296\) −900992. −0.597712
\(297\) −411156. −0.270468
\(298\) −519960. −0.339179
\(299\) 251804. 0.162886
\(300\) 30096.0 0.0193066
\(301\) 696584. 0.443157
\(302\) 1.30773e6 0.825088
\(303\) −604584. −0.378312
\(304\) 3584.00 0.00222425
\(305\) −306612. −0.188729
\(306\) 423792. 0.258731
\(307\) 1.66333e6 1.00724 0.503619 0.863926i \(-0.332002\pi\)
0.503619 + 0.863926i \(0.332002\pi\)
\(308\) 442176. 0.265594
\(309\) 54468.0 0.0324523
\(310\) −2.21573e6 −1.30952
\(311\) 1.45701e6 0.854204 0.427102 0.904203i \(-0.359535\pi\)
0.427102 + 0.904203i \(0.359535\pi\)
\(312\) 274176. 0.159457
\(313\) 740588. 0.427283 0.213642 0.976912i \(-0.431468\pi\)
0.213642 + 0.976912i \(0.431468\pi\)
\(314\) −1.87758e6 −1.07467
\(315\) −214326. −0.121702
\(316\) 1.70355e6 0.959705
\(317\) −566826. −0.316812 −0.158406 0.987374i \(-0.550635\pi\)
−0.158406 + 0.987374i \(0.550635\pi\)
\(318\) 601128. 0.333349
\(319\) −3.77993e6 −2.07973
\(320\) −221184. −0.120748
\(321\) 1.64473e6 0.890907
\(322\) −103684. −0.0557278
\(323\) −18312.0 −0.00976629
\(324\) 104976. 0.0555556
\(325\) −99484.0 −0.0522450
\(326\) −453392. −0.236282
\(327\) −1.22647e6 −0.634287
\(328\) 180864. 0.0928255
\(329\) −489510. −0.249328
\(330\) −1.09642e6 −0.554231
\(331\) −2.83750e6 −1.42353 −0.711764 0.702419i \(-0.752103\pi\)
−0.711764 + 0.702419i \(0.752103\pi\)
\(332\) −122592. −0.0610403
\(333\) 1.14032e6 0.563528
\(334\) 881544. 0.432392
\(335\) 2.14574e6 1.04464
\(336\) −112896. −0.0545545
\(337\) 1.24573e6 0.597517 0.298759 0.954329i \(-0.403427\pi\)
0.298759 + 0.954329i \(0.403427\pi\)
\(338\) 578868. 0.275605
\(339\) 2.10497e6 0.994827
\(340\) 1.13011e6 0.530181
\(341\) −5.78551e6 −2.69436
\(342\) −4536.00 −0.00209705
\(343\) 117649. 0.0539949
\(344\) −909824. −0.414535
\(345\) 257094. 0.116290
\(346\) 2.59114e6 1.16359
\(347\) 3.13938e6 1.39965 0.699826 0.714313i \(-0.253261\pi\)
0.699826 + 0.714313i \(0.253261\pi\)
\(348\) 965088. 0.427188
\(349\) −2.87018e6 −1.26138 −0.630689 0.776036i \(-0.717227\pi\)
−0.630689 + 0.776036i \(0.717227\pi\)
\(350\) 40964.0 0.0178744
\(351\) −347004. −0.150337
\(352\) −577536. −0.248441
\(353\) −4.37219e6 −1.86751 −0.933754 0.357914i \(-0.883488\pi\)
−0.933754 + 0.357914i \(0.883488\pi\)
\(354\) 685584. 0.290772
\(355\) −3.24583e6 −1.36696
\(356\) −1.22458e6 −0.512107
\(357\) 576828. 0.239539
\(358\) −1.60939e6 −0.663673
\(359\) −597504. −0.244684 −0.122342 0.992488i \(-0.539040\pi\)
−0.122342 + 0.992488i \(0.539040\pi\)
\(360\) 279936. 0.113842
\(361\) −2.47590e6 −0.999921
\(362\) −1.35260e6 −0.542498
\(363\) −1.41340e6 −0.562989
\(364\) 373184. 0.147628
\(365\) 416556. 0.163660
\(366\) 204408. 0.0797618
\(367\) −879460. −0.340840 −0.170420 0.985371i \(-0.554512\pi\)
−0.170420 + 0.985371i \(0.554512\pi\)
\(368\) 135424. 0.0521286
\(369\) −228906. −0.0875168
\(370\) 3.04085e6 1.15476
\(371\) 818202. 0.308621
\(372\) 1.47715e6 0.553437
\(373\) −671626. −0.249951 −0.124976 0.992160i \(-0.539885\pi\)
−0.124976 + 0.992160i \(0.539885\pi\)
\(374\) 2.95085e6 1.09086
\(375\) −1.62032e6 −0.595009
\(376\) 639360. 0.233225
\(377\) −3.19015e6 −1.15600
\(378\) 142884. 0.0514344
\(379\) −1.46187e6 −0.522769 −0.261385 0.965235i \(-0.584179\pi\)
−0.261385 + 0.965235i \(0.584179\pi\)
\(380\) −12096.0 −0.00429717
\(381\) 1.64812e6 0.581668
\(382\) −139968. −0.0490761
\(383\) −2.94245e6 −1.02497 −0.512486 0.858696i \(-0.671275\pi\)
−0.512486 + 0.858696i \(0.671275\pi\)
\(384\) 147456. 0.0510310
\(385\) −1.49234e6 −0.513118
\(386\) −2.93506e6 −1.00265
\(387\) 1.15150e6 0.390827
\(388\) −304768. −0.102776
\(389\) 3.19939e6 1.07199 0.535997 0.844220i \(-0.319936\pi\)
0.535997 + 0.844220i \(0.319936\pi\)
\(390\) −925344. −0.308065
\(391\) −691932. −0.228887
\(392\) −153664. −0.0505076
\(393\) 2.04433e6 0.667683
\(394\) 767880. 0.249203
\(395\) −5.74949e6 −1.85411
\(396\) 730944. 0.234232
\(397\) −634420. −0.202023 −0.101011 0.994885i \(-0.532208\pi\)
−0.101011 + 0.994885i \(0.532208\pi\)
\(398\) −1.18165e6 −0.373922
\(399\) −6174.00 −0.00194149
\(400\) −53504.0 −0.0167200
\(401\) −147642. −0.0458510 −0.0229255 0.999737i \(-0.507298\pi\)
−0.0229255 + 0.999737i \(0.507298\pi\)
\(402\) −1.43050e6 −0.441491
\(403\) −4.88281e6 −1.49764
\(404\) 1.07482e6 0.327628
\(405\) −354294. −0.107331
\(406\) 1.31359e6 0.395499
\(407\) 7.93999e6 2.37593
\(408\) −753408. −0.224068
\(409\) −5.10744e6 −1.50971 −0.754857 0.655889i \(-0.772294\pi\)
−0.754857 + 0.655889i \(0.772294\pi\)
\(410\) −610416. −0.179335
\(411\) −2.87912e6 −0.840727
\(412\) −96832.0 −0.0281045
\(413\) 933156. 0.269203
\(414\) −171396. −0.0491473
\(415\) 413748. 0.117928
\(416\) −487424. −0.138094
\(417\) −1.14250e6 −0.321747
\(418\) −31584.0 −0.00884151
\(419\) −2.26352e6 −0.629867 −0.314934 0.949114i \(-0.601982\pi\)
−0.314934 + 0.949114i \(0.601982\pi\)
\(420\) 381024. 0.105397
\(421\) −3.67663e6 −1.01098 −0.505492 0.862831i \(-0.668689\pi\)
−0.505492 + 0.862831i \(0.668689\pi\)
\(422\) 2.42382e6 0.662552
\(423\) −809190. −0.219887
\(424\) −1.06867e6 −0.288689
\(425\) 273372. 0.0734145
\(426\) 2.16389e6 0.577711
\(427\) 278222. 0.0738451
\(428\) −2.92397e6 −0.771548
\(429\) −2.41618e6 −0.633848
\(430\) 3.07066e6 0.800866
\(431\) 2.62430e6 0.680489 0.340244 0.940337i \(-0.389490\pi\)
0.340244 + 0.940337i \(0.389490\pi\)
\(432\) −186624. −0.0481125
\(433\) 3.02994e6 0.776629 0.388315 0.921527i \(-0.373057\pi\)
0.388315 + 0.921527i \(0.373057\pi\)
\(434\) 2.01057e6 0.512383
\(435\) −3.25717e6 −0.825311
\(436\) 2.18038e6 0.549309
\(437\) 7406.00 0.00185515
\(438\) −277704. −0.0691667
\(439\) 2.80942e6 0.695753 0.347876 0.937540i \(-0.386903\pi\)
0.347876 + 0.937540i \(0.386903\pi\)
\(440\) 1.94918e6 0.479978
\(441\) 194481. 0.0476190
\(442\) 2.49043e6 0.606344
\(443\) −3.10168e6 −0.750909 −0.375454 0.926841i \(-0.622513\pi\)
−0.375454 + 0.926841i \(0.622513\pi\)
\(444\) −2.02723e6 −0.488029
\(445\) 4.13294e6 0.989372
\(446\) 2.81078e6 0.669097
\(447\) −1.16991e6 −0.276939
\(448\) 200704. 0.0472456
\(449\) −5.66786e6 −1.32679 −0.663396 0.748268i \(-0.730886\pi\)
−0.663396 + 0.748268i \(0.730886\pi\)
\(450\) 67716.0 0.0157638
\(451\) −1.59386e6 −0.368986
\(452\) −3.74218e6 −0.861545
\(453\) 2.94239e6 0.673681
\(454\) −1.07359e6 −0.244455
\(455\) −1.25950e6 −0.285212
\(456\) 8064.00 0.00181609
\(457\) 6.09312e6 1.36474 0.682369 0.731008i \(-0.260950\pi\)
0.682369 + 0.731008i \(0.260950\pi\)
\(458\) −1.10386e6 −0.245896
\(459\) 953532. 0.211253
\(460\) −457056. −0.100711
\(461\) −5.71469e6 −1.25239 −0.626196 0.779666i \(-0.715389\pi\)
−0.626196 + 0.779666i \(0.715389\pi\)
\(462\) 994896. 0.216857
\(463\) −1.42574e6 −0.309091 −0.154546 0.987986i \(-0.549391\pi\)
−0.154546 + 0.987986i \(0.549391\pi\)
\(464\) −1.71571e6 −0.369955
\(465\) −4.98539e6 −1.06922
\(466\) −1.96822e6 −0.419863
\(467\) 6.52861e6 1.38525 0.692625 0.721298i \(-0.256454\pi\)
0.692625 + 0.721298i \(0.256454\pi\)
\(468\) 616896. 0.130196
\(469\) −1.94706e6 −0.408741
\(470\) −2.15784e6 −0.450583
\(471\) −4.22455e6 −0.877461
\(472\) −1.21882e6 −0.251816
\(473\) 8.01782e6 1.64780
\(474\) 3.83299e6 0.783596
\(475\) −2926.00 −0.000595032 0
\(476\) −1.02547e6 −0.207447
\(477\) 1.35254e6 0.272178
\(478\) 1.90622e6 0.381596
\(479\) −3.68276e6 −0.733390 −0.366695 0.930341i \(-0.619511\pi\)
−0.366695 + 0.930341i \(0.619511\pi\)
\(480\) −497664. −0.0985901
\(481\) 6.70113e6 1.32064
\(482\) −3.64203e6 −0.714046
\(483\) −233289. −0.0455016
\(484\) 2.51272e6 0.487563
\(485\) 1.02859e6 0.198559
\(486\) 236196. 0.0453609
\(487\) 1.12249e6 0.214466 0.107233 0.994234i \(-0.465801\pi\)
0.107233 + 0.994234i \(0.465801\pi\)
\(488\) −363392. −0.0690758
\(489\) −1.02013e6 −0.192923
\(490\) 518616. 0.0975789
\(491\) −8.07479e6 −1.51157 −0.755783 0.654822i \(-0.772744\pi\)
−0.755783 + 0.654822i \(0.772744\pi\)
\(492\) 406944. 0.0757917
\(493\) 8.76622e6 1.62441
\(494\) −26656.0 −0.00491448
\(495\) −2.46694e6 −0.452527
\(496\) −2.62605e6 −0.479290
\(497\) 2.94529e6 0.534857
\(498\) −275832. −0.0498392
\(499\) 1.98616e6 0.357079 0.178539 0.983933i \(-0.442863\pi\)
0.178539 + 0.983933i \(0.442863\pi\)
\(500\) 2.88058e6 0.515293
\(501\) 1.98347e6 0.353047
\(502\) 4.23103e6 0.749354
\(503\) −1.85566e6 −0.327022 −0.163511 0.986541i \(-0.552282\pi\)
−0.163511 + 0.986541i \(0.552282\pi\)
\(504\) −254016. −0.0445435
\(505\) −3.62750e6 −0.632965
\(506\) −1.19342e6 −0.207214
\(507\) 1.30245e6 0.225031
\(508\) −2.92998e6 −0.503739
\(509\) −827808. −0.141623 −0.0708117 0.997490i \(-0.522559\pi\)
−0.0708117 + 0.997490i \(0.522559\pi\)
\(510\) 2.54275e6 0.432891
\(511\) −377986. −0.0640359
\(512\) −262144. −0.0441942
\(513\) −10206.0 −0.00171223
\(514\) 7.97753e6 1.33187
\(515\) 326808. 0.0542968
\(516\) −2.04710e6 −0.338466
\(517\) −5.63436e6 −0.927082
\(518\) −2.75929e6 −0.451827
\(519\) 5.83006e6 0.950067
\(520\) 1.64506e6 0.266792
\(521\) −9.85788e6 −1.59107 −0.795535 0.605908i \(-0.792810\pi\)
−0.795535 + 0.605908i \(0.792810\pi\)
\(522\) 2.17145e6 0.348797
\(523\) −9.92288e6 −1.58629 −0.793147 0.609030i \(-0.791559\pi\)
−0.793147 + 0.609030i \(0.791559\pi\)
\(524\) −3.63437e6 −0.578230
\(525\) 92169.0 0.0145944
\(526\) 8.23757e6 1.29818
\(527\) 1.34175e7 2.10448
\(528\) −1.29946e6 −0.202851
\(529\) 279841. 0.0434783
\(530\) 3.60677e6 0.557736
\(531\) 1.54256e6 0.237414
\(532\) 10976.0 0.00168138
\(533\) −1.34518e6 −0.205098
\(534\) −2.75530e6 −0.418134
\(535\) 9.86839e6 1.49060
\(536\) 2.54310e6 0.382342
\(537\) −3.62113e6 −0.541887
\(538\) −2.44349e6 −0.363961
\(539\) 1.35416e6 0.200770
\(540\) 629856. 0.0929516
\(541\) 5.71216e6 0.839087 0.419544 0.907735i \(-0.362190\pi\)
0.419544 + 0.907735i \(0.362190\pi\)
\(542\) 7.35086e6 1.07483
\(543\) −3.04335e6 −0.442948
\(544\) 1.33939e6 0.194049
\(545\) −7.35880e6 −1.06124
\(546\) 839664. 0.120538
\(547\) 3.60165e6 0.514675 0.257338 0.966322i \(-0.417155\pi\)
0.257338 + 0.966322i \(0.417155\pi\)
\(548\) 5.11843e6 0.728091
\(549\) 459918. 0.0651253
\(550\) 471504. 0.0664628
\(551\) −93828.0 −0.0131660
\(552\) 304704. 0.0425628
\(553\) 5.21713e6 0.725469
\(554\) 4.62906e6 0.640794
\(555\) 6.84191e6 0.942855
\(556\) 2.03110e6 0.278641
\(557\) 1.12908e7 1.54201 0.771003 0.636832i \(-0.219755\pi\)
0.771003 + 0.636832i \(0.219755\pi\)
\(558\) 3.32359e6 0.451879
\(559\) 6.76682e6 0.915914
\(560\) −677376. −0.0912767
\(561\) 6.63941e6 0.890681
\(562\) 5.32817e6 0.711602
\(563\) −5.01085e6 −0.666254 −0.333127 0.942882i \(-0.608104\pi\)
−0.333127 + 0.942882i \(0.608104\pi\)
\(564\) 1.43856e6 0.190428
\(565\) 1.26298e7 1.66447
\(566\) −7.72498e6 −1.01358
\(567\) 321489. 0.0419961
\(568\) −3.84691e6 −0.500313
\(569\) −2.99546e6 −0.387867 −0.193933 0.981015i \(-0.562125\pi\)
−0.193933 + 0.981015i \(0.562125\pi\)
\(570\) −27216.0 −0.00350863
\(571\) 2.00434e6 0.257266 0.128633 0.991692i \(-0.458941\pi\)
0.128633 + 0.991692i \(0.458941\pi\)
\(572\) 4.29542e6 0.548929
\(573\) −314928. −0.0400705
\(574\) 553896. 0.0701695
\(575\) −110561. −0.0139454
\(576\) 331776. 0.0416667
\(577\) 9.02687e6 1.12875 0.564375 0.825519i \(-0.309117\pi\)
0.564375 + 0.825519i \(0.309117\pi\)
\(578\) −1.16403e6 −0.144925
\(579\) −6.60389e6 −0.818660
\(580\) 5.79053e6 0.714740
\(581\) −375438. −0.0461422
\(582\) −685728. −0.0839159
\(583\) 9.41767e6 1.14755
\(584\) 493696. 0.0599001
\(585\) −2.08202e6 −0.251534
\(586\) −5.88314e6 −0.707726
\(587\) 5.29598e6 0.634383 0.317191 0.948362i \(-0.397260\pi\)
0.317191 + 0.948362i \(0.397260\pi\)
\(588\) −345744. −0.0412393
\(589\) −143612. −0.0170570
\(590\) 4.11350e6 0.486499
\(591\) 1.72773e6 0.203473
\(592\) 3.60397e6 0.422646
\(593\) 1.05619e7 1.23340 0.616701 0.787197i \(-0.288469\pi\)
0.616701 + 0.787197i \(0.288469\pi\)
\(594\) 1.64462e6 0.191250
\(595\) 3.46097e6 0.400779
\(596\) 2.07984e6 0.239836
\(597\) −2.65871e6 −0.305306
\(598\) −1.00722e6 −0.115178
\(599\) −1.35753e7 −1.54590 −0.772952 0.634464i \(-0.781221\pi\)
−0.772952 + 0.634464i \(0.781221\pi\)
\(600\) −120384. −0.0136518
\(601\) −1.51018e7 −1.70547 −0.852733 0.522347i \(-0.825057\pi\)
−0.852733 + 0.522347i \(0.825057\pi\)
\(602\) −2.78634e6 −0.313359
\(603\) −3.21862e6 −0.360476
\(604\) −5.23091e6 −0.583425
\(605\) −8.48043e6 −0.941953
\(606\) 2.41834e6 0.267507
\(607\) 3.43828e6 0.378764 0.189382 0.981903i \(-0.439351\pi\)
0.189382 + 0.981903i \(0.439351\pi\)
\(608\) −14336.0 −0.00157278
\(609\) 2.95558e6 0.322924
\(610\) 1.22645e6 0.133452
\(611\) −4.75524e6 −0.515311
\(612\) −1.69517e6 −0.182951
\(613\) −6.27036e6 −0.673971 −0.336985 0.941510i \(-0.609407\pi\)
−0.336985 + 0.941510i \(0.609407\pi\)
\(614\) −6.65331e6 −0.712225
\(615\) −1.37344e6 −0.146427
\(616\) −1.76870e6 −0.187803
\(617\) 1.14567e7 1.21157 0.605783 0.795630i \(-0.292860\pi\)
0.605783 + 0.795630i \(0.292860\pi\)
\(618\) −217872. −0.0229472
\(619\) −820462. −0.0860660 −0.0430330 0.999074i \(-0.513702\pi\)
−0.0430330 + 0.999074i \(0.513702\pi\)
\(620\) 8.86291e6 0.925971
\(621\) −385641. −0.0401286
\(622\) −5.82804e6 −0.604013
\(623\) −3.75026e6 −0.387117
\(624\) −1.09670e6 −0.112753
\(625\) −9.06882e6 −0.928647
\(626\) −2.96235e6 −0.302135
\(627\) −71064.0 −0.00721906
\(628\) 7.51030e6 0.759903
\(629\) −1.84140e7 −1.85576
\(630\) 857304. 0.0860565
\(631\) −8.69085e6 −0.868938 −0.434469 0.900687i \(-0.643064\pi\)
−0.434469 + 0.900687i \(0.643064\pi\)
\(632\) −6.81421e6 −0.678614
\(633\) 5.45360e6 0.540971
\(634\) 2.26730e6 0.224020
\(635\) 9.88870e6 0.973206
\(636\) −2.40451e6 −0.235713
\(637\) 1.14288e6 0.111596
\(638\) 1.51197e7 1.47059
\(639\) 4.86875e6 0.471699
\(640\) 884736. 0.0853815
\(641\) −7.07488e6 −0.680102 −0.340051 0.940407i \(-0.610444\pi\)
−0.340051 + 0.940407i \(0.610444\pi\)
\(642\) −6.57893e6 −0.629967
\(643\) −6.96165e6 −0.664026 −0.332013 0.943275i \(-0.607728\pi\)
−0.332013 + 0.943275i \(0.607728\pi\)
\(644\) 414736. 0.0394055
\(645\) 6.90898e6 0.653905
\(646\) 73248.0 0.00690581
\(647\) 1.56651e6 0.147120 0.0735601 0.997291i \(-0.476564\pi\)
0.0735601 + 0.997291i \(0.476564\pi\)
\(648\) −419904. −0.0392837
\(649\) 1.07408e7 1.00098
\(650\) 397936. 0.0369428
\(651\) 4.52378e6 0.418359
\(652\) 1.81357e6 0.167076
\(653\) 608610. 0.0558542 0.0279271 0.999610i \(-0.491109\pi\)
0.0279271 + 0.999610i \(0.491109\pi\)
\(654\) 4.90586e6 0.448509
\(655\) 1.22660e7 1.11712
\(656\) −723456. −0.0656376
\(657\) −624834. −0.0564743
\(658\) 1.95804e6 0.176302
\(659\) 1.62441e7 1.45707 0.728536 0.685007i \(-0.240201\pi\)
0.728536 + 0.685007i \(0.240201\pi\)
\(660\) 4.38566e6 0.391900
\(661\) −6.58633e6 −0.586327 −0.293163 0.956062i \(-0.594708\pi\)
−0.293163 + 0.956062i \(0.594708\pi\)
\(662\) 1.13500e7 1.00659
\(663\) 5.60347e6 0.495078
\(664\) 490368. 0.0431620
\(665\) −37044.0 −0.00324836
\(666\) −4.56127e6 −0.398474
\(667\) −3.54536e6 −0.308564
\(668\) −3.52618e6 −0.305747
\(669\) 6.32425e6 0.546315
\(670\) −8.58298e6 −0.738671
\(671\) 3.20239e6 0.274580
\(672\) 451584. 0.0385758
\(673\) 1.96029e6 0.166833 0.0834165 0.996515i \(-0.473417\pi\)
0.0834165 + 0.996515i \(0.473417\pi\)
\(674\) −4.98294e6 −0.422509
\(675\) 152361. 0.0128711
\(676\) −2.31547e6 −0.194882
\(677\) −1.79225e7 −1.50289 −0.751443 0.659798i \(-0.770642\pi\)
−0.751443 + 0.659798i \(0.770642\pi\)
\(678\) −8.41990e6 −0.703449
\(679\) −933352. −0.0776911
\(680\) −4.52045e6 −0.374895
\(681\) −2.41558e6 −0.199597
\(682\) 2.31420e7 1.90520
\(683\) −2.47564e6 −0.203065 −0.101532 0.994832i \(-0.532375\pi\)
−0.101532 + 0.994832i \(0.532375\pi\)
\(684\) 18144.0 0.00148283
\(685\) −1.72747e7 −1.40664
\(686\) −470596. −0.0381802
\(687\) −2.48369e6 −0.200773
\(688\) 3.63930e6 0.293121
\(689\) 7.94825e6 0.637857
\(690\) −1.02838e6 −0.0822298
\(691\) 6.03663e6 0.480950 0.240475 0.970655i \(-0.422697\pi\)
0.240475 + 0.970655i \(0.422697\pi\)
\(692\) −1.03645e7 −0.822782
\(693\) 2.23852e6 0.177063
\(694\) −1.25575e7 −0.989704
\(695\) −6.85498e6 −0.538324
\(696\) −3.86035e6 −0.302067
\(697\) 3.69641e6 0.288203
\(698\) 1.14807e7 0.891928
\(699\) −4.42849e6 −0.342817
\(700\) −163856. −0.0126391
\(701\) −1.37988e7 −1.06059 −0.530294 0.847814i \(-0.677919\pi\)
−0.530294 + 0.847814i \(0.677919\pi\)
\(702\) 1.38802e6 0.106305
\(703\) 197092. 0.0150411
\(704\) 2.31014e6 0.175674
\(705\) −4.85514e6 −0.367899
\(706\) 1.74888e7 1.32053
\(707\) 3.29162e6 0.247663
\(708\) −2.74234e6 −0.205607
\(709\) −1.06221e7 −0.793587 −0.396794 0.917908i \(-0.629877\pi\)
−0.396794 + 0.917908i \(0.629877\pi\)
\(710\) 1.29833e7 0.966585
\(711\) 8.62423e6 0.639803
\(712\) 4.89830e6 0.362114
\(713\) −5.42648e6 −0.399756
\(714\) −2.30731e6 −0.169379
\(715\) −1.44971e7 −1.06051
\(716\) 6.43757e6 0.469288
\(717\) 4.28900e6 0.311572
\(718\) 2.39002e6 0.173017
\(719\) −1.38913e7 −1.00212 −0.501061 0.865412i \(-0.667057\pi\)
−0.501061 + 0.865412i \(0.667057\pi\)
\(720\) −1.11974e6 −0.0804984
\(721\) −296548. −0.0212450
\(722\) 9.90361e6 0.707051
\(723\) −8.19457e6 −0.583016
\(724\) 5.41040e6 0.383604
\(725\) 1.40072e6 0.0989705
\(726\) 5.65362e6 0.398093
\(727\) −1.68319e7 −1.18113 −0.590566 0.806989i \(-0.701095\pi\)
−0.590566 + 0.806989i \(0.701095\pi\)
\(728\) −1.49274e6 −0.104389
\(729\) 531441. 0.0370370
\(730\) −1.66622e6 −0.115725
\(731\) −1.85945e7 −1.28704
\(732\) −817632. −0.0564001
\(733\) −1.36596e7 −0.939025 −0.469513 0.882926i \(-0.655570\pi\)
−0.469513 + 0.882926i \(0.655570\pi\)
\(734\) 3.51784e6 0.241010
\(735\) 1.16689e6 0.0796728
\(736\) −541696. −0.0368605
\(737\) −2.24111e7 −1.51983
\(738\) 915624. 0.0618837
\(739\) 375596. 0.0252994 0.0126497 0.999920i \(-0.495973\pi\)
0.0126497 + 0.999920i \(0.495973\pi\)
\(740\) −1.21634e7 −0.816536
\(741\) −59976.0 −0.00401266
\(742\) −3.27281e6 −0.218228
\(743\) −2.07706e7 −1.38031 −0.690156 0.723661i \(-0.742458\pi\)
−0.690156 + 0.723661i \(0.742458\pi\)
\(744\) −5.90861e6 −0.391339
\(745\) −7.01946e6 −0.463354
\(746\) 2.68650e6 0.176742
\(747\) −620622. −0.0406936
\(748\) −1.18034e7 −0.771352
\(749\) −8.95465e6 −0.583236
\(750\) 6.48130e6 0.420735
\(751\) 2.52927e7 1.63642 0.818210 0.574919i \(-0.194967\pi\)
0.818210 + 0.574919i \(0.194967\pi\)
\(752\) −2.55744e6 −0.164915
\(753\) 9.51982e6 0.611845
\(754\) 1.27606e7 0.817416
\(755\) 1.76543e7 1.12716
\(756\) −571536. −0.0363696
\(757\) 2.10396e7 1.33444 0.667219 0.744862i \(-0.267485\pi\)
0.667219 + 0.744862i \(0.267485\pi\)
\(758\) 5.84747e6 0.369654
\(759\) −2.68520e6 −0.169189
\(760\) 48384.0 0.00303856
\(761\) 1.55777e7 0.975082 0.487541 0.873100i \(-0.337894\pi\)
0.487541 + 0.873100i \(0.337894\pi\)
\(762\) −6.59246e6 −0.411302
\(763\) 6.67743e6 0.415239
\(764\) 559872. 0.0347021
\(765\) 5.72119e6 0.353454
\(766\) 1.17698e7 0.724764
\(767\) 9.06494e6 0.556387
\(768\) −589824. −0.0360844
\(769\) 1.22003e7 0.743970 0.371985 0.928239i \(-0.378677\pi\)
0.371985 + 0.928239i \(0.378677\pi\)
\(770\) 5.96938e6 0.362829
\(771\) 1.79494e7 1.08746
\(772\) 1.17403e7 0.708981
\(773\) 2.20997e7 1.33027 0.665133 0.746725i \(-0.268375\pi\)
0.665133 + 0.746725i \(0.268375\pi\)
\(774\) −4.60598e6 −0.276357
\(775\) 2.14392e6 0.128220
\(776\) 1.21907e6 0.0726733
\(777\) −6.20840e6 −0.368916
\(778\) −1.27975e7 −0.758015
\(779\) −39564.0 −0.00233591
\(780\) 3.70138e6 0.217835
\(781\) 3.39009e7 1.98877
\(782\) 2.76773e6 0.161848
\(783\) 4.88576e6 0.284792
\(784\) 614656. 0.0357143
\(785\) −2.53473e7 −1.46811
\(786\) −8.17733e6 −0.472123
\(787\) 1.21476e7 0.699122 0.349561 0.936914i \(-0.386331\pi\)
0.349561 + 0.936914i \(0.386331\pi\)
\(788\) −3.07152e6 −0.176213
\(789\) 1.85345e7 1.05996
\(790\) 2.29980e7 1.31106
\(791\) −1.14604e7 −0.651267
\(792\) −2.92378e6 −0.165627
\(793\) 2.70273e6 0.152623
\(794\) 2.53768e6 0.142852
\(795\) 8.11523e6 0.455389
\(796\) 4.72659e6 0.264402
\(797\) 1.80768e7 1.00803 0.504016 0.863694i \(-0.331855\pi\)
0.504016 + 0.863694i \(0.331855\pi\)
\(798\) 24696.0 0.00137284
\(799\) 1.30669e7 0.724113
\(800\) 214016. 0.0118228
\(801\) −6.19942e6 −0.341405
\(802\) 590568. 0.0324216
\(803\) −4.35070e6 −0.238106
\(804\) 5.72198e6 0.312181
\(805\) −1.39973e6 −0.0761300
\(806\) 1.95312e7 1.05899
\(807\) −5.49785e6 −0.297173
\(808\) −4.29926e6 −0.231668
\(809\) −3.50042e7 −1.88039 −0.940197 0.340630i \(-0.889359\pi\)
−0.940197 + 0.340630i \(0.889359\pi\)
\(810\) 1.41718e6 0.0758947
\(811\) 9.45753e6 0.504924 0.252462 0.967607i \(-0.418760\pi\)
0.252462 + 0.967607i \(0.418760\pi\)
\(812\) −5.25437e6 −0.279660
\(813\) 1.65394e7 0.877595
\(814\) −3.17600e7 −1.68004
\(815\) −6.12079e6 −0.322785
\(816\) 3.01363e6 0.158440
\(817\) 199024. 0.0104316
\(818\) 2.04298e7 1.06753
\(819\) 1.88924e6 0.0984189
\(820\) 2.44166e6 0.126809
\(821\) −3.41482e7 −1.76812 −0.884058 0.467378i \(-0.845199\pi\)
−0.884058 + 0.467378i \(0.845199\pi\)
\(822\) 1.15165e7 0.594484
\(823\) 9.87880e6 0.508399 0.254200 0.967152i \(-0.418188\pi\)
0.254200 + 0.967152i \(0.418188\pi\)
\(824\) 387328. 0.0198729
\(825\) 1.06088e6 0.0542667
\(826\) −3.73262e6 −0.190355
\(827\) −2.42903e7 −1.23501 −0.617503 0.786569i \(-0.711856\pi\)
−0.617503 + 0.786569i \(0.711856\pi\)
\(828\) 685584. 0.0347524
\(829\) −8.88732e6 −0.449143 −0.224572 0.974458i \(-0.572098\pi\)
−0.224572 + 0.974458i \(0.572098\pi\)
\(830\) −1.65499e6 −0.0833874
\(831\) 1.04154e7 0.523207
\(832\) 1.94970e6 0.0976469
\(833\) −3.14051e6 −0.156815
\(834\) 4.56998e6 0.227510
\(835\) 1.19008e7 0.590693
\(836\) 126336. 0.00625189
\(837\) 7.47808e6 0.368958
\(838\) 9.05407e6 0.445383
\(839\) −1.77347e7 −0.869797 −0.434898 0.900479i \(-0.643216\pi\)
−0.434898 + 0.900479i \(0.643216\pi\)
\(840\) −1.52410e6 −0.0745271
\(841\) 2.44057e7 1.18987
\(842\) 1.47065e7 0.714874
\(843\) 1.19884e7 0.581021
\(844\) −9.69530e6 −0.468495
\(845\) 7.81472e6 0.376506
\(846\) 3.23676e6 0.155484
\(847\) 7.69520e6 0.368563
\(848\) 4.27469e6 0.204134
\(849\) −1.73812e7 −0.827582
\(850\) −1.09349e6 −0.0519119
\(851\) 7.44726e6 0.352511
\(852\) −8.65555e6 −0.408504
\(853\) −9.61944e6 −0.452665 −0.226333 0.974050i \(-0.572674\pi\)
−0.226333 + 0.974050i \(0.572674\pi\)
\(854\) −1.11289e6 −0.0522164
\(855\) −61236.0 −0.00286478
\(856\) 1.16959e7 0.545567
\(857\) −1.39472e7 −0.648687 −0.324344 0.945939i \(-0.605143\pi\)
−0.324344 + 0.945939i \(0.605143\pi\)
\(858\) 9.66470e6 0.448198
\(859\) 6.76628e6 0.312872 0.156436 0.987688i \(-0.449999\pi\)
0.156436 + 0.987688i \(0.449999\pi\)
\(860\) −1.22826e7 −0.566298
\(861\) 1.24627e6 0.0572932
\(862\) −1.04972e7 −0.481178
\(863\) −3.07028e7 −1.40330 −0.701650 0.712522i \(-0.747553\pi\)
−0.701650 + 0.712522i \(0.747553\pi\)
\(864\) 746496. 0.0340207
\(865\) 3.49803e7 1.58958
\(866\) −1.21197e7 −0.549160
\(867\) −2.61906e6 −0.118331
\(868\) −8.04227e6 −0.362309
\(869\) 6.00502e7 2.69752
\(870\) 1.30287e7 0.583583
\(871\) −1.89143e7 −0.844784
\(872\) −8.72154e6 −0.388420
\(873\) −1.54289e6 −0.0685171
\(874\) −29624.0 −0.00131179
\(875\) 8.82176e6 0.389525
\(876\) 1.11082e6 0.0489082
\(877\) −6.06173e6 −0.266132 −0.133066 0.991107i \(-0.542482\pi\)
−0.133066 + 0.991107i \(0.542482\pi\)
\(878\) −1.12377e7 −0.491972
\(879\) −1.32371e7 −0.577856
\(880\) −7.79674e6 −0.339396
\(881\) 5.92432e6 0.257157 0.128579 0.991699i \(-0.458959\pi\)
0.128579 + 0.991699i \(0.458959\pi\)
\(882\) −777924. −0.0336718
\(883\) 4.36075e7 1.88217 0.941087 0.338166i \(-0.109806\pi\)
0.941087 + 0.338166i \(0.109806\pi\)
\(884\) −9.96173e6 −0.428750
\(885\) 9.25538e6 0.397225
\(886\) 1.24067e7 0.530973
\(887\) −9.69254e6 −0.413646 −0.206823 0.978378i \(-0.566312\pi\)
−0.206823 + 0.978378i \(0.566312\pi\)
\(888\) 8.10893e6 0.345089
\(889\) −8.97308e6 −0.380791
\(890\) −1.65318e7 −0.699591
\(891\) 3.70040e6 0.156155
\(892\) −1.12431e7 −0.473123
\(893\) −139860. −0.00586901
\(894\) 4.67964e6 0.195825
\(895\) −2.17268e7 −0.906647
\(896\) −802816. −0.0334077
\(897\) −2.26624e6 −0.0940425
\(898\) 2.26714e7 0.938184
\(899\) 6.87491e7 2.83706
\(900\) −270864. −0.0111467
\(901\) −2.18410e7 −0.896314
\(902\) 6.37546e6 0.260913
\(903\) −6.26926e6 −0.255857
\(904\) 1.49687e7 0.609205
\(905\) −1.82601e7 −0.741108
\(906\) −1.17696e7 −0.476365
\(907\) −4.13096e6 −0.166737 −0.0833686 0.996519i \(-0.526568\pi\)
−0.0833686 + 0.996519i \(0.526568\pi\)
\(908\) 4.29437e6 0.172856
\(909\) 5.44126e6 0.218419
\(910\) 5.03798e6 0.201676
\(911\) 3.79068e7 1.51329 0.756644 0.653827i \(-0.226838\pi\)
0.756644 + 0.653827i \(0.226838\pi\)
\(912\) −32256.0 −0.00128417
\(913\) −4.32137e6 −0.171571
\(914\) −2.43725e7 −0.965016
\(915\) 2.75951e6 0.108963
\(916\) 4.41546e6 0.173875
\(917\) −1.11303e7 −0.437101
\(918\) −3.81413e6 −0.149379
\(919\) −4.32179e7 −1.68801 −0.844004 0.536337i \(-0.819808\pi\)
−0.844004 + 0.536337i \(0.819808\pi\)
\(920\) 1.82822e6 0.0712131
\(921\) −1.49700e7 −0.581529
\(922\) 2.28588e7 0.885575
\(923\) 2.86114e7 1.10544
\(924\) −3.97958e6 −0.153341
\(925\) −2.94230e6 −0.113066
\(926\) 5.70294e6 0.218560
\(927\) −490212. −0.0187363
\(928\) 6.86285e6 0.261598
\(929\) −3.08783e7 −1.17385 −0.586927 0.809640i \(-0.699662\pi\)
−0.586927 + 0.809640i \(0.699662\pi\)
\(930\) 1.99416e7 0.756052
\(931\) 33614.0 0.00127100
\(932\) 7.87286e6 0.296888
\(933\) −1.31131e7 −0.493175
\(934\) −2.61144e7 −0.979520
\(935\) 3.98364e7 1.49022
\(936\) −2.46758e6 −0.0920624
\(937\) 8.44029e6 0.314057 0.157029 0.987594i \(-0.449809\pi\)
0.157029 + 0.987594i \(0.449809\pi\)
\(938\) 7.78826e6 0.289023
\(939\) −6.66529e6 −0.246692
\(940\) 8.63136e6 0.318610
\(941\) −2.11969e7 −0.780367 −0.390183 0.920737i \(-0.627588\pi\)
−0.390183 + 0.920737i \(0.627588\pi\)
\(942\) 1.68982e7 0.620459
\(943\) −1.49495e6 −0.0547455
\(944\) 4.87526e6 0.178061
\(945\) 1.92893e6 0.0702648
\(946\) −3.20713e7 −1.16517
\(947\) 6.75954e6 0.244930 0.122465 0.992473i \(-0.460920\pi\)
0.122465 + 0.992473i \(0.460920\pi\)
\(948\) −1.53320e7 −0.554086
\(949\) −3.67186e6 −0.132349
\(950\) 11704.0 0.000420751 0
\(951\) 5.10143e6 0.182911
\(952\) 4.10189e6 0.146687
\(953\) −2.24168e7 −0.799543 −0.399771 0.916615i \(-0.630911\pi\)
−0.399771 + 0.916615i \(0.630911\pi\)
\(954\) −5.41015e6 −0.192459
\(955\) −1.88957e6 −0.0670431
\(956\) −7.62490e6 −0.269829
\(957\) 3.40194e7 1.20073
\(958\) 1.47311e7 0.518585
\(959\) 1.56752e7 0.550385
\(960\) 1.99066e6 0.0697137
\(961\) 7.65974e7 2.67550
\(962\) −2.68045e7 −0.933835
\(963\) −1.48026e7 −0.514366
\(964\) 1.45681e7 0.504907
\(965\) −3.96234e7 −1.36972
\(966\) 933156. 0.0321745
\(967\) −3.40977e7 −1.17263 −0.586313 0.810085i \(-0.699421\pi\)
−0.586313 + 0.810085i \(0.699421\pi\)
\(968\) −1.00509e7 −0.344759
\(969\) 164808. 0.00563857
\(970\) −4.11437e6 −0.140402
\(971\) 5.25978e7 1.79027 0.895137 0.445791i \(-0.147078\pi\)
0.895137 + 0.445791i \(0.147078\pi\)
\(972\) −944784. −0.0320750
\(973\) 6.22026e6 0.210633
\(974\) −4.48995e6 −0.151651
\(975\) 895356. 0.0301637
\(976\) 1.45357e6 0.0488440
\(977\) 1.10581e6 0.0370632 0.0185316 0.999828i \(-0.494101\pi\)
0.0185316 + 0.999828i \(0.494101\pi\)
\(978\) 4.08053e6 0.136417
\(979\) −4.31663e7 −1.43942
\(980\) −2.07446e6 −0.0689987
\(981\) 1.10382e7 0.366206
\(982\) 3.22992e7 1.06884
\(983\) 1.47662e7 0.487399 0.243700 0.969851i \(-0.421639\pi\)
0.243700 + 0.969851i \(0.421639\pi\)
\(984\) −1.62778e6 −0.0535929
\(985\) 1.03664e7 0.340437
\(986\) −3.50649e7 −1.14863
\(987\) 4.40559e6 0.143950
\(988\) 106624. 0.00347506
\(989\) 7.52026e6 0.244479
\(990\) 9.86774e6 0.319985
\(991\) 3.14816e7 1.01829 0.509147 0.860680i \(-0.329961\pi\)
0.509147 + 0.860680i \(0.329961\pi\)
\(992\) 1.05042e7 0.338909
\(993\) 2.55375e7 0.821874
\(994\) −1.17812e7 −0.378201
\(995\) −1.59522e7 −0.510816
\(996\) 1.10333e6 0.0352417
\(997\) −5.60269e7 −1.78509 −0.892543 0.450963i \(-0.851081\pi\)
−0.892543 + 0.450963i \(0.851081\pi\)
\(998\) −7.94466e6 −0.252493
\(999\) −1.02629e7 −0.325353
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 966.6.a.a.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
966.6.a.a.1.1 1 1.1 even 1 trivial