Properties

Label 10.6.a.b.1.1
Level 10
Weight 6
Character 10.1
Self dual Yes
Analytic conductor 1.604
Analytic rank 0
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 10 = 2 \cdot 5 \)
Weight: \( k \) = \( 6 \)
Character orbit: \([\chi]\) = 10.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(1.60383819813\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(0\)
Character \(\chi\) = 10.1

$q$-expansion

\(f(q)\) \(=\) \(q-4.00000 q^{2} +24.0000 q^{3} +16.0000 q^{4} +25.0000 q^{5} -96.0000 q^{6} -172.000 q^{7} -64.0000 q^{8} +333.000 q^{9} +O(q^{10})\) \(q-4.00000 q^{2} +24.0000 q^{3} +16.0000 q^{4} +25.0000 q^{5} -96.0000 q^{6} -172.000 q^{7} -64.0000 q^{8} +333.000 q^{9} -100.000 q^{10} +132.000 q^{11} +384.000 q^{12} -946.000 q^{13} +688.000 q^{14} +600.000 q^{15} +256.000 q^{16} -222.000 q^{17} -1332.00 q^{18} +500.000 q^{19} +400.000 q^{20} -4128.00 q^{21} -528.000 q^{22} +3564.00 q^{23} -1536.00 q^{24} +625.000 q^{25} +3784.00 q^{26} +2160.00 q^{27} -2752.00 q^{28} +2190.00 q^{29} -2400.00 q^{30} +2312.00 q^{31} -1024.00 q^{32} +3168.00 q^{33} +888.000 q^{34} -4300.00 q^{35} +5328.00 q^{36} -11242.0 q^{37} -2000.00 q^{38} -22704.0 q^{39} -1600.00 q^{40} +1242.00 q^{41} +16512.0 q^{42} +20624.0 q^{43} +2112.00 q^{44} +8325.00 q^{45} -14256.0 q^{46} +6588.00 q^{47} +6144.00 q^{48} +12777.0 q^{49} -2500.00 q^{50} -5328.00 q^{51} -15136.0 q^{52} -21066.0 q^{53} -8640.00 q^{54} +3300.00 q^{55} +11008.0 q^{56} +12000.0 q^{57} -8760.00 q^{58} +7980.00 q^{59} +9600.00 q^{60} +16622.0 q^{61} -9248.00 q^{62} -57276.0 q^{63} +4096.00 q^{64} -23650.0 q^{65} -12672.0 q^{66} +1808.00 q^{67} -3552.00 q^{68} +85536.0 q^{69} +17200.0 q^{70} -24528.0 q^{71} -21312.0 q^{72} +20474.0 q^{73} +44968.0 q^{74} +15000.0 q^{75} +8000.00 q^{76} -22704.0 q^{77} +90816.0 q^{78} -46240.0 q^{79} +6400.00 q^{80} -29079.0 q^{81} -4968.00 q^{82} -51576.0 q^{83} -66048.0 q^{84} -5550.00 q^{85} -82496.0 q^{86} +52560.0 q^{87} -8448.00 q^{88} -110310. q^{89} -33300.0 q^{90} +162712. q^{91} +57024.0 q^{92} +55488.0 q^{93} -26352.0 q^{94} +12500.0 q^{95} -24576.0 q^{96} -78382.0 q^{97} -51108.0 q^{98} +43956.0 q^{99} +O(q^{100})\)

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
\(3\) 24.0000 1.53960 0.769800 0.638285i \(-0.220356\pi\)
0.769800 + 0.638285i \(0.220356\pi\)
\(4\) 16.0000 0.500000
\(5\) 25.0000 0.447214
\(6\) −96.0000 −1.08866
\(7\) −172.000 −1.32673 −0.663366 0.748295i \(-0.730873\pi\)
−0.663366 + 0.748295i \(0.730873\pi\)
\(8\) −64.0000 −0.353553
\(9\) 333.000 1.37037
\(10\) −100.000 −0.316228
\(11\) 132.000 0.328921 0.164461 0.986384i \(-0.447412\pi\)
0.164461 + 0.986384i \(0.447412\pi\)
\(12\) 384.000 0.769800
\(13\) −946.000 −1.55250 −0.776252 0.630423i \(-0.782882\pi\)
−0.776252 + 0.630423i \(0.782882\pi\)
\(14\) 688.000 0.938142
\(15\) 600.000 0.688530
\(16\) 256.000 0.250000
\(17\) −222.000 −0.186308 −0.0931538 0.995652i \(-0.529695\pi\)
−0.0931538 + 0.995652i \(0.529695\pi\)
\(18\) −1332.00 −0.968998
\(19\) 500.000 0.317750 0.158875 0.987299i \(-0.449213\pi\)
0.158875 + 0.987299i \(0.449213\pi\)
\(20\) 400.000 0.223607
\(21\) −4128.00 −2.04264
\(22\) −528.000 −0.232583
\(23\) 3564.00 1.40481 0.702406 0.711777i \(-0.252109\pi\)
0.702406 + 0.711777i \(0.252109\pi\)
\(24\) −1536.00 −0.544331
\(25\) 625.000 0.200000
\(26\) 3784.00 1.09779
\(27\) 2160.00 0.570222
\(28\) −2752.00 −0.663366
\(29\) 2190.00 0.483559 0.241779 0.970331i \(-0.422269\pi\)
0.241779 + 0.970331i \(0.422269\pi\)
\(30\) −2400.00 −0.486864
\(31\) 2312.00 0.432099 0.216050 0.976382i \(-0.430683\pi\)
0.216050 + 0.976382i \(0.430683\pi\)
\(32\) −1024.00 −0.176777
\(33\) 3168.00 0.506408
\(34\) 888.000 0.131739
\(35\) −4300.00 −0.593333
\(36\) 5328.00 0.685185
\(37\) −11242.0 −1.35002 −0.675009 0.737810i \(-0.735860\pi\)
−0.675009 + 0.737810i \(0.735860\pi\)
\(38\) −2000.00 −0.224683
\(39\) −22704.0 −2.39024
\(40\) −1600.00 −0.158114
\(41\) 1242.00 0.115388 0.0576942 0.998334i \(-0.481625\pi\)
0.0576942 + 0.998334i \(0.481625\pi\)
\(42\) 16512.0 1.44436
\(43\) 20624.0 1.70099 0.850495 0.525983i \(-0.176303\pi\)
0.850495 + 0.525983i \(0.176303\pi\)
\(44\) 2112.00 0.164461
\(45\) 8325.00 0.612848
\(46\) −14256.0 −0.993352
\(47\) 6588.00 0.435020 0.217510 0.976058i \(-0.430207\pi\)
0.217510 + 0.976058i \(0.430207\pi\)
\(48\) 6144.00 0.384900
\(49\) 12777.0 0.760219
\(50\) −2500.00 −0.141421
\(51\) −5328.00 −0.286839
\(52\) −15136.0 −0.776252
\(53\) −21066.0 −1.03013 −0.515065 0.857151i \(-0.672232\pi\)
−0.515065 + 0.857151i \(0.672232\pi\)
\(54\) −8640.00 −0.403208
\(55\) 3300.00 0.147098
\(56\) 11008.0 0.469071
\(57\) 12000.0 0.489209
\(58\) −8760.00 −0.341928
\(59\) 7980.00 0.298451 0.149225 0.988803i \(-0.452322\pi\)
0.149225 + 0.988803i \(0.452322\pi\)
\(60\) 9600.00 0.344265
\(61\) 16622.0 0.571951 0.285975 0.958237i \(-0.407682\pi\)
0.285975 + 0.958237i \(0.407682\pi\)
\(62\) −9248.00 −0.305540
\(63\) −57276.0 −1.81811
\(64\) 4096.00 0.125000
\(65\) −23650.0 −0.694301
\(66\) −12672.0 −0.358084
\(67\) 1808.00 0.0492052 0.0246026 0.999697i \(-0.492168\pi\)
0.0246026 + 0.999697i \(0.492168\pi\)
\(68\) −3552.00 −0.0931538
\(69\) 85536.0 2.16285
\(70\) 17200.0 0.419550
\(71\) −24528.0 −0.577452 −0.288726 0.957412i \(-0.593232\pi\)
−0.288726 + 0.957412i \(0.593232\pi\)
\(72\) −21312.0 −0.484499
\(73\) 20474.0 0.449672 0.224836 0.974397i \(-0.427815\pi\)
0.224836 + 0.974397i \(0.427815\pi\)
\(74\) 44968.0 0.954606
\(75\) 15000.0 0.307920
\(76\) 8000.00 0.158875
\(77\) −22704.0 −0.436391
\(78\) 90816.0 1.69015
\(79\) −46240.0 −0.833585 −0.416793 0.909002i \(-0.636846\pi\)
−0.416793 + 0.909002i \(0.636846\pi\)
\(80\) 6400.00 0.111803
\(81\) −29079.0 −0.492455
\(82\) −4968.00 −0.0815919
\(83\) −51576.0 −0.821774 −0.410887 0.911686i \(-0.634781\pi\)
−0.410887 + 0.911686i \(0.634781\pi\)
\(84\) −66048.0 −1.02132
\(85\) −5550.00 −0.0833193
\(86\) −82496.0 −1.20278
\(87\) 52560.0 0.744487
\(88\) −8448.00 −0.116291
\(89\) −110310. −1.47618 −0.738091 0.674701i \(-0.764272\pi\)
−0.738091 + 0.674701i \(0.764272\pi\)
\(90\) −33300.0 −0.433349
\(91\) 162712. 2.05976
\(92\) 57024.0 0.702406
\(93\) 55488.0 0.665260
\(94\) −26352.0 −0.307605
\(95\) 12500.0 0.142102
\(96\) −24576.0 −0.272166
\(97\) −78382.0 −0.845838 −0.422919 0.906168i \(-0.638994\pi\)
−0.422919 + 0.906168i \(0.638994\pi\)
\(98\) −51108.0 −0.537556
\(99\) 43956.0 0.450744
\(100\) 10000.0 0.100000
\(101\) 141942. 1.38455 0.692273 0.721636i \(-0.256609\pi\)
0.692273 + 0.721636i \(0.256609\pi\)
\(102\) 21312.0 0.202826
\(103\) −436.000 −0.00404943 −0.00202471 0.999998i \(-0.500644\pi\)
−0.00202471 + 0.999998i \(0.500644\pi\)
\(104\) 60544.0 0.548893
\(105\) −103200. −0.913496
\(106\) 84264.0 0.728413
\(107\) 232968. 1.96715 0.983574 0.180508i \(-0.0577742\pi\)
0.983574 + 0.180508i \(0.0577742\pi\)
\(108\) 34560.0 0.285111
\(109\) −174850. −1.40961 −0.704806 0.709400i \(-0.748966\pi\)
−0.704806 + 0.709400i \(0.748966\pi\)
\(110\) −13200.0 −0.104014
\(111\) −269808. −2.07849
\(112\) −44032.0 −0.331683
\(113\) 182994. 1.34816 0.674079 0.738659i \(-0.264541\pi\)
0.674079 + 0.738659i \(0.264541\pi\)
\(114\) −48000.0 −0.345923
\(115\) 89100.0 0.628251
\(116\) 35040.0 0.241779
\(117\) −315018. −2.12751
\(118\) −31920.0 −0.211037
\(119\) 38184.0 0.247180
\(120\) −38400.0 −0.243432
\(121\) −143627. −0.891811
\(122\) −66488.0 −0.404430
\(123\) 29808.0 0.177652
\(124\) 36992.0 0.216050
\(125\) 15625.0 0.0894427
\(126\) 229104. 1.28560
\(127\) −122452. −0.673685 −0.336842 0.941561i \(-0.609359\pi\)
−0.336842 + 0.941561i \(0.609359\pi\)
\(128\) −16384.0 −0.0883883
\(129\) 494976. 2.61885
\(130\) 94600.0 0.490945
\(131\) −241908. −1.23161 −0.615803 0.787900i \(-0.711168\pi\)
−0.615803 + 0.787900i \(0.711168\pi\)
\(132\) 50688.0 0.253204
\(133\) −86000.0 −0.421570
\(134\) −7232.00 −0.0347934
\(135\) 54000.0 0.255011
\(136\) 14208.0 0.0658697
\(137\) 277098. 1.26134 0.630670 0.776051i \(-0.282780\pi\)
0.630670 + 0.776051i \(0.282780\pi\)
\(138\) −342144. −1.52937
\(139\) −193540. −0.849638 −0.424819 0.905278i \(-0.639662\pi\)
−0.424819 + 0.905278i \(0.639662\pi\)
\(140\) −68800.0 −0.296666
\(141\) 158112. 0.669757
\(142\) 98112.0 0.408321
\(143\) −124872. −0.510652
\(144\) 85248.0 0.342593
\(145\) 54750.0 0.216254
\(146\) −81896.0 −0.317966
\(147\) 306648. 1.17043
\(148\) −179872. −0.675009
\(149\) 140550. 0.518639 0.259320 0.965792i \(-0.416502\pi\)
0.259320 + 0.965792i \(0.416502\pi\)
\(150\) −60000.0 −0.217732
\(151\) 433952. 1.54881 0.774407 0.632688i \(-0.218048\pi\)
0.774407 + 0.632688i \(0.218048\pi\)
\(152\) −32000.0 −0.112342
\(153\) −73926.0 −0.255310
\(154\) 90816.0 0.308575
\(155\) 57800.0 0.193241
\(156\) −363264. −1.19512
\(157\) −555922. −1.79997 −0.899984 0.435923i \(-0.856422\pi\)
−0.899984 + 0.435923i \(0.856422\pi\)
\(158\) 184960. 0.589434
\(159\) −505584. −1.58599
\(160\) −25600.0 −0.0790569
\(161\) −613008. −1.86381
\(162\) 116316. 0.348219
\(163\) −66616.0 −0.196386 −0.0981928 0.995167i \(-0.531306\pi\)
−0.0981928 + 0.995167i \(0.531306\pi\)
\(164\) 19872.0 0.0576942
\(165\) 79200.0 0.226472
\(166\) 206304. 0.581082
\(167\) −205692. −0.570724 −0.285362 0.958420i \(-0.592114\pi\)
−0.285362 + 0.958420i \(0.592114\pi\)
\(168\) 264192. 0.722182
\(169\) 523623. 1.41027
\(170\) 22200.0 0.0589156
\(171\) 166500. 0.435436
\(172\) 329984. 0.850495
\(173\) 433854. 1.10212 0.551059 0.834466i \(-0.314224\pi\)
0.551059 + 0.834466i \(0.314224\pi\)
\(174\) −210240. −0.526432
\(175\) −107500. −0.265346
\(176\) 33792.0 0.0822304
\(177\) 191520. 0.459495
\(178\) 441240. 1.04382
\(179\) −489180. −1.14113 −0.570566 0.821252i \(-0.693276\pi\)
−0.570566 + 0.821252i \(0.693276\pi\)
\(180\) 133200. 0.306424
\(181\) 719462. 1.63234 0.816172 0.577810i \(-0.196092\pi\)
0.816172 + 0.577810i \(0.196092\pi\)
\(182\) −650848. −1.45647
\(183\) 398928. 0.880576
\(184\) −228096. −0.496676
\(185\) −281050. −0.603746
\(186\) −221952. −0.470410
\(187\) −29304.0 −0.0612806
\(188\) 105408. 0.217510
\(189\) −371520. −0.756533
\(190\) −50000.0 −0.100481
\(191\) −185928. −0.368775 −0.184387 0.982854i \(-0.559030\pi\)
−0.184387 + 0.982854i \(0.559030\pi\)
\(192\) 98304.0 0.192450
\(193\) −591406. −1.14286 −0.571429 0.820651i \(-0.693611\pi\)
−0.571429 + 0.820651i \(0.693611\pi\)
\(194\) 313528. 0.598098
\(195\) −567600. −1.06895
\(196\) 204432. 0.380109
\(197\) 449478. 0.825169 0.412584 0.910919i \(-0.364626\pi\)
0.412584 + 0.910919i \(0.364626\pi\)
\(198\) −175824. −0.318724
\(199\) 157160. 0.281326 0.140663 0.990058i \(-0.455077\pi\)
0.140663 + 0.990058i \(0.455077\pi\)
\(200\) −40000.0 −0.0707107
\(201\) 43392.0 0.0757564
\(202\) −567768. −0.979022
\(203\) −376680. −0.641553
\(204\) −85248.0 −0.143420
\(205\) 31050.0 0.0516032
\(206\) 1744.00 0.00286338
\(207\) 1.18681e6 1.92511
\(208\) −242176. −0.388126
\(209\) 66000.0 0.104515
\(210\) 412800. 0.645939
\(211\) 253052. 0.391294 0.195647 0.980674i \(-0.437319\pi\)
0.195647 + 0.980674i \(0.437319\pi\)
\(212\) −337056. −0.515065
\(213\) −588672. −0.889046
\(214\) −931872. −1.39098
\(215\) 515600. 0.760706
\(216\) −138240. −0.201604
\(217\) −397664. −0.573280
\(218\) 699400. 0.996746
\(219\) 491376. 0.692315
\(220\) 52800.0 0.0735491
\(221\) 210012. 0.289243
\(222\) 1.07923e6 1.46971
\(223\) 1.07344e6 1.44550 0.722749 0.691111i \(-0.242878\pi\)
0.722749 + 0.691111i \(0.242878\pi\)
\(224\) 176128. 0.234535
\(225\) 208125. 0.274074
\(226\) −731976. −0.953292
\(227\) −626832. −0.807396 −0.403698 0.914892i \(-0.632275\pi\)
−0.403698 + 0.914892i \(0.632275\pi\)
\(228\) 192000. 0.244604
\(229\) −116650. −0.146993 −0.0734964 0.997295i \(-0.523416\pi\)
−0.0734964 + 0.997295i \(0.523416\pi\)
\(230\) −356400. −0.444240
\(231\) −544896. −0.671868
\(232\) −140160. −0.170964
\(233\) −743046. −0.896656 −0.448328 0.893869i \(-0.647980\pi\)
−0.448328 + 0.893869i \(0.647980\pi\)
\(234\) 1.26007e6 1.50437
\(235\) 164700. 0.194547
\(236\) 127680. 0.149225
\(237\) −1.10976e6 −1.28339
\(238\) −152736. −0.174783
\(239\) 978720. 1.10832 0.554158 0.832411i \(-0.313040\pi\)
0.554158 + 0.832411i \(0.313040\pi\)
\(240\) 153600. 0.172133
\(241\) −1.13280e6 −1.25635 −0.628174 0.778073i \(-0.716197\pi\)
−0.628174 + 0.778073i \(0.716197\pi\)
\(242\) 574508. 0.630605
\(243\) −1.22278e6 −1.32841
\(244\) 265952. 0.285975
\(245\) 319425. 0.339980
\(246\) −119232. −0.125619
\(247\) −473000. −0.493309
\(248\) −147968. −0.152770
\(249\) −1.23782e6 −1.26520
\(250\) −62500.0 −0.0632456
\(251\) 905652. 0.907355 0.453677 0.891166i \(-0.350112\pi\)
0.453677 + 0.891166i \(0.350112\pi\)
\(252\) −916416. −0.909057
\(253\) 470448. 0.462073
\(254\) 489808. 0.476367
\(255\) −133200. −0.128278
\(256\) 65536.0 0.0625000
\(257\) 1.93994e6 1.83212 0.916062 0.401036i \(-0.131350\pi\)
0.916062 + 0.401036i \(0.131350\pi\)
\(258\) −1.97990e6 −1.85180
\(259\) 1.93362e6 1.79111
\(260\) −378400. −0.347150
\(261\) 729270. 0.662654
\(262\) 967632. 0.870877
\(263\) −805476. −0.718064 −0.359032 0.933325i \(-0.616893\pi\)
−0.359032 + 0.933325i \(0.616893\pi\)
\(264\) −202752. −0.179042
\(265\) −526650. −0.460689
\(266\) 344000. 0.298095
\(267\) −2.64744e6 −2.27273
\(268\) 28928.0 0.0246026
\(269\) −858690. −0.723529 −0.361764 0.932270i \(-0.617825\pi\)
−0.361764 + 0.932270i \(0.617825\pi\)
\(270\) −216000. −0.180320
\(271\) −383608. −0.317296 −0.158648 0.987335i \(-0.550713\pi\)
−0.158648 + 0.987335i \(0.550713\pi\)
\(272\) −56832.0 −0.0465769
\(273\) 3.90509e6 3.17120
\(274\) −1.10839e6 −0.891902
\(275\) 82500.0 0.0657843
\(276\) 1.36858e6 1.08142
\(277\) 2.01076e6 1.57456 0.787282 0.616593i \(-0.211488\pi\)
0.787282 + 0.616593i \(0.211488\pi\)
\(278\) 774160. 0.600785
\(279\) 769896. 0.592136
\(280\) 275200. 0.209775
\(281\) 202602. 0.153066 0.0765329 0.997067i \(-0.475615\pi\)
0.0765329 + 0.997067i \(0.475615\pi\)
\(282\) −632448. −0.473589
\(283\) −221536. −0.164429 −0.0822145 0.996615i \(-0.526199\pi\)
−0.0822145 + 0.996615i \(0.526199\pi\)
\(284\) −392448. −0.288726
\(285\) 300000. 0.218781
\(286\) 499488. 0.361085
\(287\) −213624. −0.153089
\(288\) −340992. −0.242250
\(289\) −1.37057e6 −0.965289
\(290\) −219000. −0.152915
\(291\) −1.88117e6 −1.30225
\(292\) 327584. 0.224836
\(293\) −322506. −0.219467 −0.109733 0.993961i \(-0.535000\pi\)
−0.109733 + 0.993961i \(0.535000\pi\)
\(294\) −1.22659e6 −0.827622
\(295\) 199500. 0.133471
\(296\) 719488. 0.477303
\(297\) 285120. 0.187558
\(298\) −562200. −0.366733
\(299\) −3.37154e6 −2.18098
\(300\) 240000. 0.153960
\(301\) −3.54733e6 −2.25676
\(302\) −1.73581e6 −1.09518
\(303\) 3.40661e6 2.13165
\(304\) 128000. 0.0794376
\(305\) 415550. 0.255784
\(306\) 295704. 0.180532
\(307\) 1.44301e6 0.873822 0.436911 0.899505i \(-0.356073\pi\)
0.436911 + 0.899505i \(0.356073\pi\)
\(308\) −363264. −0.218195
\(309\) −10464.0 −0.00623450
\(310\) −231200. −0.136642
\(311\) 171312. 0.100435 0.0502177 0.998738i \(-0.484008\pi\)
0.0502177 + 0.998738i \(0.484008\pi\)
\(312\) 1.45306e6 0.845076
\(313\) −1.02689e6 −0.592463 −0.296232 0.955116i \(-0.595730\pi\)
−0.296232 + 0.955116i \(0.595730\pi\)
\(314\) 2.22369e6 1.27277
\(315\) −1.43190e6 −0.813086
\(316\) −739840. −0.416793
\(317\) 752958. 0.420845 0.210423 0.977610i \(-0.432516\pi\)
0.210423 + 0.977610i \(0.432516\pi\)
\(318\) 2.02234e6 1.12146
\(319\) 289080. 0.159053
\(320\) 102400. 0.0559017
\(321\) 5.59123e6 3.02862
\(322\) 2.45203e6 1.31791
\(323\) −111000. −0.0591993
\(324\) −465264. −0.246228
\(325\) −591250. −0.310501
\(326\) 266464. 0.138866
\(327\) −4.19640e6 −2.17024
\(328\) −79488.0 −0.0407959
\(329\) −1.13314e6 −0.577155
\(330\) −316800. −0.160140
\(331\) 1.99413e6 1.00042 0.500212 0.865903i \(-0.333255\pi\)
0.500212 + 0.865903i \(0.333255\pi\)
\(332\) −825216. −0.410887
\(333\) −3.74359e6 −1.85002
\(334\) 822768. 0.403563
\(335\) 45200.0 0.0220053
\(336\) −1.05677e6 −0.510660
\(337\) −987022. −0.473426 −0.236713 0.971580i \(-0.576070\pi\)
−0.236713 + 0.971580i \(0.576070\pi\)
\(338\) −2.09449e6 −0.997211
\(339\) 4.39186e6 2.07562
\(340\) −88800.0 −0.0416597
\(341\) 305184. 0.142127
\(342\) −666000. −0.307899
\(343\) 693160. 0.318125
\(344\) −1.31994e6 −0.601391
\(345\) 2.13840e6 0.967256
\(346\) −1.73542e6 −0.779316
\(347\) 2.20601e6 0.983520 0.491760 0.870731i \(-0.336354\pi\)
0.491760 + 0.870731i \(0.336354\pi\)
\(348\) 840960. 0.372244
\(349\) 2.74187e6 1.20499 0.602495 0.798123i \(-0.294173\pi\)
0.602495 + 0.798123i \(0.294173\pi\)
\(350\) 430000. 0.187628
\(351\) −2.04336e6 −0.885273
\(352\) −135168. −0.0581456
\(353\) −2.38957e6 −1.02066 −0.510331 0.859978i \(-0.670477\pi\)
−0.510331 + 0.859978i \(0.670477\pi\)
\(354\) −766080. −0.324912
\(355\) −613200. −0.258245
\(356\) −1.76496e6 −0.738091
\(357\) 916416. 0.380559
\(358\) 1.95672e6 0.806903
\(359\) −279480. −0.114450 −0.0572248 0.998361i \(-0.518225\pi\)
−0.0572248 + 0.998361i \(0.518225\pi\)
\(360\) −532800. −0.216675
\(361\) −2.22610e6 −0.899035
\(362\) −2.87785e6 −1.15424
\(363\) −3.44705e6 −1.37303
\(364\) 2.60339e6 1.02988
\(365\) 511850. 0.201099
\(366\) −1.59571e6 −0.622661
\(367\) −2.47637e6 −0.959734 −0.479867 0.877341i \(-0.659315\pi\)
−0.479867 + 0.877341i \(0.659315\pi\)
\(368\) 912384. 0.351203
\(369\) 413586. 0.158125
\(370\) 1.12420e6 0.426913
\(371\) 3.62335e6 1.36671
\(372\) 887808. 0.332630
\(373\) 2.74525e6 1.02167 0.510835 0.859679i \(-0.329336\pi\)
0.510835 + 0.859679i \(0.329336\pi\)
\(374\) 117216. 0.0433319
\(375\) 375000. 0.137706
\(376\) −421632. −0.153803
\(377\) −2.07174e6 −0.750727
\(378\) 1.48608e6 0.534949
\(379\) −1.18906e6 −0.425212 −0.212606 0.977138i \(-0.568195\pi\)
−0.212606 + 0.977138i \(0.568195\pi\)
\(380\) 200000. 0.0710511
\(381\) −2.93885e6 −1.03721
\(382\) 743712. 0.260763
\(383\) 3.25760e6 1.13475 0.567377 0.823458i \(-0.307958\pi\)
0.567377 + 0.823458i \(0.307958\pi\)
\(384\) −393216. −0.136083
\(385\) −567600. −0.195160
\(386\) 2.36562e6 0.808123
\(387\) 6.86779e6 2.33099
\(388\) −1.25411e6 −0.422919
\(389\) 1.98351e6 0.664600 0.332300 0.943174i \(-0.392175\pi\)
0.332300 + 0.943174i \(0.392175\pi\)
\(390\) 2.27040e6 0.755859
\(391\) −791208. −0.261727
\(392\) −817728. −0.268778
\(393\) −5.80579e6 −1.89618
\(394\) −1.79791e6 −0.583483
\(395\) −1.15600e6 −0.372791
\(396\) 703296. 0.225372
\(397\) 4.97416e6 1.58396 0.791978 0.610549i \(-0.209051\pi\)
0.791978 + 0.610549i \(0.209051\pi\)
\(398\) −628640. −0.198927
\(399\) −2.06400e6 −0.649049
\(400\) 160000. 0.0500000
\(401\) −1.34264e6 −0.416963 −0.208482 0.978026i \(-0.566852\pi\)
−0.208482 + 0.978026i \(0.566852\pi\)
\(402\) −173568. −0.0535679
\(403\) −2.18715e6 −0.670836
\(404\) 2.27107e6 0.692273
\(405\) −726975. −0.220233
\(406\) 1.50672e6 0.453646
\(407\) −1.48394e6 −0.444050
\(408\) 340992. 0.101413
\(409\) −1.09423e6 −0.323445 −0.161722 0.986836i \(-0.551705\pi\)
−0.161722 + 0.986836i \(0.551705\pi\)
\(410\) −124200. −0.0364890
\(411\) 6.65035e6 1.94196
\(412\) −6976.00 −0.00202471
\(413\) −1.37256e6 −0.395964
\(414\) −4.74725e6 −1.36126
\(415\) −1.28940e6 −0.367509
\(416\) 968704. 0.274447
\(417\) −4.64496e6 −1.30810
\(418\) −264000. −0.0739032
\(419\) −954060. −0.265485 −0.132743 0.991151i \(-0.542378\pi\)
−0.132743 + 0.991151i \(0.542378\pi\)
\(420\) −1.65120e6 −0.456748
\(421\) −1.59390e6 −0.438284 −0.219142 0.975693i \(-0.570326\pi\)
−0.219142 + 0.975693i \(0.570326\pi\)
\(422\) −1.01221e6 −0.276687
\(423\) 2.19380e6 0.596138
\(424\) 1.34822e6 0.364206
\(425\) −138750. −0.0372615
\(426\) 2.35469e6 0.628651
\(427\) −2.85898e6 −0.758826
\(428\) 3.72749e6 0.983574
\(429\) −2.99693e6 −0.786200
\(430\) −2.06240e6 −0.537900
\(431\) −2.64665e6 −0.686283 −0.343141 0.939284i \(-0.611491\pi\)
−0.343141 + 0.939284i \(0.611491\pi\)
\(432\) 552960. 0.142556
\(433\) 3.72355e6 0.954416 0.477208 0.878790i \(-0.341649\pi\)
0.477208 + 0.878790i \(0.341649\pi\)
\(434\) 1.59066e6 0.405370
\(435\) 1.31400e6 0.332945
\(436\) −2.79760e6 −0.704806
\(437\) 1.78200e6 0.446379
\(438\) −1.96550e6 −0.489541
\(439\) −2.58340e6 −0.639780 −0.319890 0.947455i \(-0.603646\pi\)
−0.319890 + 0.947455i \(0.603646\pi\)
\(440\) −211200. −0.0520071
\(441\) 4.25474e6 1.04178
\(442\) −840048. −0.204526
\(443\) 7.56206e6 1.83076 0.915379 0.402593i \(-0.131891\pi\)
0.915379 + 0.402593i \(0.131891\pi\)
\(444\) −4.31693e6 −1.03924
\(445\) −2.75775e6 −0.660169
\(446\) −4.29378e6 −1.02212
\(447\) 3.37320e6 0.798497
\(448\) −704512. −0.165842
\(449\) 4.30773e6 1.00840 0.504200 0.863587i \(-0.331788\pi\)
0.504200 + 0.863587i \(0.331788\pi\)
\(450\) −832500. −0.193800
\(451\) 163944. 0.0379537
\(452\) 2.92790e6 0.674079
\(453\) 1.04148e7 2.38456
\(454\) 2.50733e6 0.570915
\(455\) 4.06780e6 0.921152
\(456\) −768000. −0.172961
\(457\) −2.24354e6 −0.502509 −0.251254 0.967921i \(-0.580843\pi\)
−0.251254 + 0.967921i \(0.580843\pi\)
\(458\) 466600. 0.103940
\(459\) −479520. −0.106237
\(460\) 1.42560e6 0.314125
\(461\) 1.65670e6 0.363071 0.181536 0.983384i \(-0.441893\pi\)
0.181536 + 0.983384i \(0.441893\pi\)
\(462\) 2.17958e6 0.475082
\(463\) −2.89160e6 −0.626881 −0.313441 0.949608i \(-0.601482\pi\)
−0.313441 + 0.949608i \(0.601482\pi\)
\(464\) 560640. 0.120890
\(465\) 1.38720e6 0.297514
\(466\) 2.97218e6 0.634032
\(467\) −6.52699e6 −1.38491 −0.692454 0.721462i \(-0.743470\pi\)
−0.692454 + 0.721462i \(0.743470\pi\)
\(468\) −5.04029e6 −1.06375
\(469\) −310976. −0.0652822
\(470\) −658800. −0.137565
\(471\) −1.33421e7 −2.77123
\(472\) −510720. −0.105518
\(473\) 2.72237e6 0.559492
\(474\) 4.43904e6 0.907493
\(475\) 312500. 0.0635501
\(476\) 610944. 0.123590
\(477\) −7.01498e6 −1.41166
\(478\) −3.91488e6 −0.783698
\(479\) −5.96232e6 −1.18734 −0.593672 0.804707i \(-0.702322\pi\)
−0.593672 + 0.804707i \(0.702322\pi\)
\(480\) −614400. −0.121716
\(481\) 1.06349e7 2.09591
\(482\) 4.53119e6 0.888372
\(483\) −1.47122e7 −2.86952
\(484\) −2.29803e6 −0.445905
\(485\) −1.95955e6 −0.378270
\(486\) 4.89110e6 0.939326
\(487\) 2.99191e6 0.571644 0.285822 0.958283i \(-0.407733\pi\)
0.285822 + 0.958283i \(0.407733\pi\)
\(488\) −1.06381e6 −0.202215
\(489\) −1.59878e6 −0.302355
\(490\) −1.27770e6 −0.240402
\(491\) −1.20419e6 −0.225419 −0.112710 0.993628i \(-0.535953\pi\)
−0.112710 + 0.993628i \(0.535953\pi\)
\(492\) 476928. 0.0888260
\(493\) −486180. −0.0900907
\(494\) 1.89200e6 0.348822
\(495\) 1.09890e6 0.201579
\(496\) 591872. 0.108025
\(497\) 4.21882e6 0.766125
\(498\) 4.95130e6 0.894634
\(499\) 9.20546e6 1.65499 0.827493 0.561477i \(-0.189767\pi\)
0.827493 + 0.561477i \(0.189767\pi\)
\(500\) 250000. 0.0447214
\(501\) −4.93661e6 −0.878687
\(502\) −3.62261e6 −0.641597
\(503\) −3.35956e6 −0.592055 −0.296027 0.955179i \(-0.595662\pi\)
−0.296027 + 0.955179i \(0.595662\pi\)
\(504\) 3.66566e6 0.642801
\(505\) 3.54855e6 0.619188
\(506\) −1.88179e6 −0.326735
\(507\) 1.25670e7 2.17125
\(508\) −1.95923e6 −0.336842
\(509\) −2.53701e6 −0.434038 −0.217019 0.976167i \(-0.569633\pi\)
−0.217019 + 0.976167i \(0.569633\pi\)
\(510\) 532800. 0.0907066
\(511\) −3.52153e6 −0.596594
\(512\) −262144. −0.0441942
\(513\) 1.08000e6 0.181188
\(514\) −7.75975e6 −1.29551
\(515\) −10900.0 −0.00181096
\(516\) 7.91962e6 1.30942
\(517\) 869616. 0.143087
\(518\) −7.73450e6 −1.26651
\(519\) 1.04125e7 1.69682
\(520\) 1.51360e6 0.245472
\(521\) −9.31580e6 −1.50358 −0.751789 0.659404i \(-0.770809\pi\)
−0.751789 + 0.659404i \(0.770809\pi\)
\(522\) −2.91708e6 −0.468567
\(523\) −5.02802e6 −0.803790 −0.401895 0.915686i \(-0.631648\pi\)
−0.401895 + 0.915686i \(0.631648\pi\)
\(524\) −3.87053e6 −0.615803
\(525\) −2.58000e6 −0.408528
\(526\) 3.22190e6 0.507748
\(527\) −513264. −0.0805034
\(528\) 811008. 0.126602
\(529\) 6.26575e6 0.973496
\(530\) 2.10660e6 0.325756
\(531\) 2.65734e6 0.408988
\(532\) −1.37600e6 −0.210785
\(533\) −1.17493e6 −0.179141
\(534\) 1.05898e7 1.60706
\(535\) 5.82420e6 0.879735
\(536\) −115712. −0.0173967
\(537\) −1.17403e7 −1.75689
\(538\) 3.43476e6 0.511612
\(539\) 1.68656e6 0.250052
\(540\) 864000. 0.127506
\(541\) 134222. 0.0197165 0.00985827 0.999951i \(-0.496862\pi\)
0.00985827 + 0.999951i \(0.496862\pi\)
\(542\) 1.53443e6 0.224362
\(543\) 1.72671e7 2.51316
\(544\) 227328. 0.0329348
\(545\) −4.37125e6 −0.630397
\(546\) −1.56204e7 −2.24238
\(547\) 605648. 0.0865470 0.0432735 0.999063i \(-0.486221\pi\)
0.0432735 + 0.999063i \(0.486221\pi\)
\(548\) 4.43357e6 0.630670
\(549\) 5.53513e6 0.783784
\(550\) −330000. −0.0465165
\(551\) 1.09500e6 0.153651
\(552\) −5.47430e6 −0.764683
\(553\) 7.95328e6 1.10594
\(554\) −8.04303e6 −1.11339
\(555\) −6.74520e6 −0.929528
\(556\) −3.09664e6 −0.424819
\(557\) −7.06240e6 −0.964527 −0.482264 0.876026i \(-0.660185\pi\)
−0.482264 + 0.876026i \(0.660185\pi\)
\(558\) −3.07958e6 −0.418703
\(559\) −1.95103e7 −2.64079
\(560\) −1.10080e6 −0.148333
\(561\) −703296. −0.0943476
\(562\) −810408. −0.108234
\(563\) −1.03029e7 −1.36990 −0.684952 0.728588i \(-0.740177\pi\)
−0.684952 + 0.728588i \(0.740177\pi\)
\(564\) 2.52979e6 0.334878
\(565\) 4.57485e6 0.602915
\(566\) 886144. 0.116269
\(567\) 5.00159e6 0.653357
\(568\) 1.56979e6 0.204160
\(569\) 1.04769e6 0.135660 0.0678300 0.997697i \(-0.478392\pi\)
0.0678300 + 0.997697i \(0.478392\pi\)
\(570\) −1.20000e6 −0.154701
\(571\) 1.40765e7 1.80677 0.903385 0.428830i \(-0.141074\pi\)
0.903385 + 0.428830i \(0.141074\pi\)
\(572\) −1.99795e6 −0.255326
\(573\) −4.46227e6 −0.567766
\(574\) 854496. 0.108251
\(575\) 2.22750e6 0.280962
\(576\) 1.36397e6 0.171296
\(577\) 1.62682e6 0.203423 0.101711 0.994814i \(-0.467568\pi\)
0.101711 + 0.994814i \(0.467568\pi\)
\(578\) 5.48229e6 0.682563
\(579\) −1.41937e7 −1.75955
\(580\) 876000. 0.108127
\(581\) 8.87107e6 1.09027
\(582\) 7.52467e6 0.920831
\(583\) −2.78071e6 −0.338832
\(584\) −1.31034e6 −0.158983
\(585\) −7.87545e6 −0.951449
\(586\) 1.29002e6 0.155186
\(587\) 6.96089e6 0.833814 0.416907 0.908949i \(-0.363114\pi\)
0.416907 + 0.908949i \(0.363114\pi\)
\(588\) 4.90637e6 0.585217
\(589\) 1.15600e6 0.137300
\(590\) −798000. −0.0943785
\(591\) 1.07875e7 1.27043
\(592\) −2.87795e6 −0.337504
\(593\) −1.13639e7 −1.32706 −0.663529 0.748150i \(-0.730942\pi\)
−0.663529 + 0.748150i \(0.730942\pi\)
\(594\) −1.14048e6 −0.132624
\(595\) 954600. 0.110542
\(596\) 2.24880e6 0.259320
\(597\) 3.77184e6 0.433129
\(598\) 1.34862e7 1.54218
\(599\) 1.48688e7 1.69321 0.846603 0.532224i \(-0.178644\pi\)
0.846603 + 0.532224i \(0.178644\pi\)
\(600\) −960000. −0.108866
\(601\) −1.23612e6 −0.139596 −0.0697981 0.997561i \(-0.522236\pi\)
−0.0697981 + 0.997561i \(0.522236\pi\)
\(602\) 1.41893e7 1.59577
\(603\) 602064. 0.0674294
\(604\) 6.94323e6 0.774407
\(605\) −3.59068e6 −0.398830
\(606\) −1.36264e7 −1.50730
\(607\) −1.24498e7 −1.37149 −0.685743 0.727844i \(-0.740522\pi\)
−0.685743 + 0.727844i \(0.740522\pi\)
\(608\) −512000. −0.0561709
\(609\) −9.04032e6 −0.987735
\(610\) −1.66220e6 −0.180867
\(611\) −6.23225e6 −0.675370
\(612\) −1.18282e6 −0.127655
\(613\) −8.73491e6 −0.938873 −0.469437 0.882966i \(-0.655543\pi\)
−0.469437 + 0.882966i \(0.655543\pi\)
\(614\) −5.77203e6 −0.617885
\(615\) 745200. 0.0794484
\(616\) 1.45306e6 0.154287
\(617\) 1.25495e7 1.32713 0.663565 0.748119i \(-0.269043\pi\)
0.663565 + 0.748119i \(0.269043\pi\)
\(618\) 41856.0 0.00440846
\(619\) −1.46658e7 −1.53843 −0.769216 0.638988i \(-0.779353\pi\)
−0.769216 + 0.638988i \(0.779353\pi\)
\(620\) 924800. 0.0966203
\(621\) 7.69824e6 0.801055
\(622\) −685248. −0.0710186
\(623\) 1.89733e7 1.95850
\(624\) −5.81222e6 −0.597559
\(625\) 390625. 0.0400000
\(626\) 4.10754e6 0.418935
\(627\) 1.58400e6 0.160911
\(628\) −8.89475e6 −0.899984
\(629\) 2.49572e6 0.251519
\(630\) 5.72760e6 0.574938
\(631\) −196288. −0.0196255 −0.00981274 0.999952i \(-0.503124\pi\)
−0.00981274 + 0.999952i \(0.503124\pi\)
\(632\) 2.95936e6 0.294717
\(633\) 6.07325e6 0.602437
\(634\) −3.01183e6 −0.297583
\(635\) −3.06130e6 −0.301281
\(636\) −8.08934e6 −0.792995
\(637\) −1.20870e7 −1.18024
\(638\) −1.15632e6 −0.112467
\(639\) −8.16782e6 −0.791324
\(640\) −409600. −0.0395285
\(641\) −1.11596e7 −1.07276 −0.536381 0.843976i \(-0.680209\pi\)
−0.536381 + 0.843976i \(0.680209\pi\)
\(642\) −2.23649e7 −2.14156
\(643\) −2.25158e6 −0.214763 −0.107381 0.994218i \(-0.534247\pi\)
−0.107381 + 0.994218i \(0.534247\pi\)
\(644\) −9.80813e6 −0.931905
\(645\) 1.23744e7 1.17118
\(646\) 444000. 0.0418602
\(647\) 8.05319e6 0.756323 0.378161 0.925740i \(-0.376556\pi\)
0.378161 + 0.925740i \(0.376556\pi\)
\(648\) 1.86106e6 0.174109
\(649\) 1.05336e6 0.0981669
\(650\) 2.36500e6 0.219557
\(651\) −9.54394e6 −0.882623
\(652\) −1.06586e6 −0.0981928
\(653\) −416466. −0.0382205 −0.0191103 0.999817i \(-0.506083\pi\)
−0.0191103 + 0.999817i \(0.506083\pi\)
\(654\) 1.67856e7 1.53459
\(655\) −6.04770e6 −0.550791
\(656\) 317952. 0.0288471
\(657\) 6.81784e6 0.616217
\(658\) 4.53254e6 0.408110
\(659\) 1.31721e7 1.18152 0.590761 0.806847i \(-0.298828\pi\)
0.590761 + 0.806847i \(0.298828\pi\)
\(660\) 1.26720e6 0.113236
\(661\) −1.69494e6 −0.150886 −0.0754432 0.997150i \(-0.524037\pi\)
−0.0754432 + 0.997150i \(0.524037\pi\)
\(662\) −7.97653e6 −0.707406
\(663\) 5.04029e6 0.445319
\(664\) 3.30086e6 0.290541
\(665\) −2.15000e6 −0.188532
\(666\) 1.49743e7 1.30816
\(667\) 7.80516e6 0.679309
\(668\) −3.29107e6 −0.285362
\(669\) 2.57627e7 2.22549
\(670\) −180800. −0.0155601
\(671\) 2.19410e6 0.188127
\(672\) 4.22707e6 0.361091
\(673\) −8.91605e6 −0.758813 −0.379406 0.925230i \(-0.623872\pi\)
−0.379406 + 0.925230i \(0.623872\pi\)
\(674\) 3.94809e6 0.334763
\(675\) 1.35000e6 0.114044
\(676\) 8.37797e6 0.705134
\(677\) −1.42894e7 −1.19824 −0.599118 0.800661i \(-0.704482\pi\)
−0.599118 + 0.800661i \(0.704482\pi\)
\(678\) −1.75674e7 −1.46769
\(679\) 1.34817e7 1.12220
\(680\) 355200. 0.0294578
\(681\) −1.50440e7 −1.24307
\(682\) −1.22074e6 −0.100499
\(683\) −5.33314e6 −0.437452 −0.218726 0.975786i \(-0.570190\pi\)
−0.218726 + 0.975786i \(0.570190\pi\)
\(684\) 2.66400e6 0.217718
\(685\) 6.92745e6 0.564088
\(686\) −2.77264e6 −0.224949
\(687\) −2.79960e6 −0.226310
\(688\) 5.27974e6 0.425248
\(689\) 1.99284e7 1.59928
\(690\) −8.55360e6 −0.683953
\(691\) 698252. 0.0556310 0.0278155 0.999613i \(-0.491145\pi\)
0.0278155 + 0.999613i \(0.491145\pi\)
\(692\) 6.94166e6 0.551059
\(693\) −7.56043e6 −0.598017
\(694\) −8.82403e6 −0.695454
\(695\) −4.83850e6 −0.379969
\(696\) −3.36384e6 −0.263216
\(697\) −275724. −0.0214977
\(698\) −1.09675e7 −0.852056
\(699\) −1.78331e7 −1.38049
\(700\) −1.72000e6 −0.132673
\(701\) 1.79880e7 1.38257 0.691285 0.722582i \(-0.257045\pi\)
0.691285 + 0.722582i \(0.257045\pi\)
\(702\) 8.17344e6 0.625982
\(703\) −5.62100e6 −0.428968
\(704\) 540672. 0.0411152
\(705\) 3.95280e6 0.299524
\(706\) 9.55826e6 0.721718
\(707\) −2.44140e7 −1.83692
\(708\) 3.06432e6 0.229748
\(709\) −1.39464e7 −1.04195 −0.520975 0.853572i \(-0.674432\pi\)
−0.520975 + 0.853572i \(0.674432\pi\)
\(710\) 2.45280e6 0.182607
\(711\) −1.53979e7 −1.14232
\(712\) 7.05984e6 0.521909
\(713\) 8.23997e6 0.607018
\(714\) −3.66566e6 −0.269096
\(715\) −3.12180e6 −0.228370
\(716\) −7.82688e6 −0.570566
\(717\) 2.34893e7 1.70636
\(718\) 1.11792e6 0.0809282
\(719\) 6.22272e6 0.448909 0.224454 0.974485i \(-0.427940\pi\)
0.224454 + 0.974485i \(0.427940\pi\)
\(720\) 2.13120e6 0.153212
\(721\) 74992.0 0.00537250
\(722\) 8.90440e6 0.635714
\(723\) −2.71872e7 −1.93427
\(724\) 1.15114e7 0.816172
\(725\) 1.36875e6 0.0967117
\(726\) 1.37882e7 0.970880
\(727\) −7.76729e6 −0.545047 −0.272523 0.962149i \(-0.587858\pi\)
−0.272523 + 0.962149i \(0.587858\pi\)
\(728\) −1.04136e7 −0.728234
\(729\) −2.22804e7 −1.55276
\(730\) −2.04740e6 −0.142199
\(731\) −4.57853e6 −0.316907
\(732\) 6.38285e6 0.440288
\(733\) 2.42083e7 1.66420 0.832099 0.554627i \(-0.187139\pi\)
0.832099 + 0.554627i \(0.187139\pi\)
\(734\) 9.90549e6 0.678634
\(735\) 7.66620e6 0.523434
\(736\) −3.64954e6 −0.248338
\(737\) 238656. 0.0161847
\(738\) −1.65434e6 −0.111811
\(739\) 1.26850e7 0.854434 0.427217 0.904149i \(-0.359494\pi\)
0.427217 + 0.904149i \(0.359494\pi\)
\(740\) −4.49680e6 −0.301873
\(741\) −1.13520e7 −0.759498
\(742\) −1.44934e7 −0.966409
\(743\) 1.97632e7 1.31337 0.656684 0.754166i \(-0.271959\pi\)
0.656684 + 0.754166i \(0.271959\pi\)
\(744\) −3.55123e6 −0.235205
\(745\) 3.51375e6 0.231942
\(746\) −1.09810e7 −0.722429
\(747\) −1.71748e7 −1.12613
\(748\) −468864. −0.0306403
\(749\) −4.00705e7 −2.60988
\(750\) −1.50000e6 −0.0973729
\(751\) −9.01761e6 −0.583434 −0.291717 0.956505i \(-0.594226\pi\)
−0.291717 + 0.956505i \(0.594226\pi\)
\(752\) 1.68653e6 0.108755
\(753\) 2.17356e7 1.39696
\(754\) 8.28696e6 0.530844
\(755\) 1.08488e7 0.692651
\(756\) −5.94432e6 −0.378266
\(757\) −1.12556e6 −0.0713887 −0.0356944 0.999363i \(-0.511364\pi\)
−0.0356944 + 0.999363i \(0.511364\pi\)
\(758\) 4.75624e6 0.300670
\(759\) 1.12908e7 0.711407
\(760\) −800000. −0.0502407
\(761\) 2.25747e7 1.41306 0.706529 0.707684i \(-0.250260\pi\)
0.706529 + 0.707684i \(0.250260\pi\)
\(762\) 1.17554e7 0.733415
\(763\) 3.00742e7 1.87018
\(764\) −2.97485e6 −0.184387
\(765\) −1.84815e6 −0.114178
\(766\) −1.30304e7 −0.802392
\(767\) −7.54908e6 −0.463346
\(768\) 1.57286e6 0.0962250
\(769\) −632350. −0.0385604 −0.0192802 0.999814i \(-0.506137\pi\)
−0.0192802 + 0.999814i \(0.506137\pi\)
\(770\) 2.27040e6 0.137999
\(771\) 4.65585e7 2.82074
\(772\) −9.46250e6 −0.571429
\(773\) −1.25867e7 −0.757643 −0.378822 0.925470i \(-0.623671\pi\)
−0.378822 + 0.925470i \(0.623671\pi\)
\(774\) −2.74712e7 −1.64826
\(775\) 1.44500e6 0.0864199
\(776\) 5.01645e6 0.299049
\(777\) 4.64070e7 2.75760
\(778\) −7.93404e6 −0.469943
\(779\) 621000. 0.0366647
\(780\) −9.08160e6 −0.534473
\(781\) −3.23770e6 −0.189937
\(782\) 3.16483e6 0.185069
\(783\) 4.73040e6 0.275736
\(784\) 3.27091e6 0.190055
\(785\) −1.38981e7 −0.804970
\(786\) 2.32232e7 1.34080
\(787\) 2.15792e7 1.24194 0.620968 0.783836i \(-0.286740\pi\)
0.620968 + 0.783836i \(0.286740\pi\)
\(788\) 7.19165e6 0.412584
\(789\) −1.93314e7 −1.10553
\(790\) 4.62400e6 0.263603
\(791\) −3.14750e7 −1.78864
\(792\) −2.81318e6 −0.159362
\(793\) −1.57244e7 −0.887956
\(794\) −1.98966e7 −1.12003
\(795\) −1.26396e7 −0.709276
\(796\) 2.51456e6 0.140663
\(797\) −3.09760e7 −1.72735 −0.863673 0.504052i \(-0.831842\pi\)
−0.863673 + 0.504052i \(0.831842\pi\)
\(798\) 8.25600e6 0.458947
\(799\) −1.46254e6 −0.0810475
\(800\) −640000. −0.0353553
\(801\) −3.67332e7 −2.02292
\(802\) 5.37055e6 0.294838
\(803\) 2.70257e6 0.147907
\(804\) 694272. 0.0378782
\(805\) −1.53252e7 −0.833521
\(806\) 8.74861e6 0.474353
\(807\) −2.06086e7 −1.11395
\(808\) −9.08429e6 −0.489511
\(809\) 4.24929e6 0.228268 0.114134 0.993465i \(-0.463591\pi\)
0.114134 + 0.993465i \(0.463591\pi\)
\(810\) 2.90790e6 0.155728
\(811\) 3.42333e6 0.182767 0.0913833 0.995816i \(-0.470871\pi\)
0.0913833 + 0.995816i \(0.470871\pi\)
\(812\) −6.02688e6 −0.320776
\(813\) −9.20659e6 −0.488509
\(814\) 5.93578e6 0.313990
\(815\) −1.66540e6 −0.0878263
\(816\) −1.36397e6 −0.0717098
\(817\) 1.03120e7 0.540490
\(818\) 4.37692e6 0.228710
\(819\) 5.41831e7 2.82263
\(820\) 496800. 0.0258016
\(821\) 3.10571e7 1.60806 0.804030 0.594588i \(-0.202685\pi\)
0.804030 + 0.594588i \(0.202685\pi\)
\(822\) −2.66014e7 −1.37317
\(823\) −3.11904e7 −1.60517 −0.802584 0.596538i \(-0.796542\pi\)
−0.802584 + 0.596538i \(0.796542\pi\)
\(824\) 27904.0 0.00143169
\(825\) 1.98000e6 0.101282
\(826\) 5.49024e6 0.279989
\(827\) −8.28487e6 −0.421233 −0.210616 0.977569i \(-0.567547\pi\)
−0.210616 + 0.977569i \(0.567547\pi\)
\(828\) 1.89890e7 0.962556
\(829\) −1.81689e7 −0.918208 −0.459104 0.888383i \(-0.651829\pi\)
−0.459104 + 0.888383i \(0.651829\pi\)
\(830\) 5.15760e6 0.259868
\(831\) 4.82582e7 2.42420
\(832\) −3.87482e6 −0.194063
\(833\) −2.83649e6 −0.141635
\(834\) 1.85798e7 0.924968
\(835\) −5.14230e6 −0.255236
\(836\) 1.05600e6 0.0522575
\(837\) 4.99392e6 0.246393
\(838\) 3.81624e6 0.187727
\(839\) −1.02743e7 −0.503902 −0.251951 0.967740i \(-0.581072\pi\)
−0.251951 + 0.967740i \(0.581072\pi\)
\(840\) 6.60480e6 0.322969
\(841\) −1.57150e7 −0.766171
\(842\) 6.37559e6 0.309913
\(843\) 4.86245e6 0.235660
\(844\) 4.04883e6 0.195647
\(845\) 1.30906e7 0.630691
\(846\) −8.77522e6 −0.421533
\(847\) 2.47038e7 1.18319
\(848\) −5.39290e6 −0.257533
\(849\) −5.31686e6 −0.253155
\(850\) 555000. 0.0263479
\(851\) −4.00665e7 −1.89652
\(852\) −9.41875e6 −0.444523
\(853\) 6.28597e6 0.295801 0.147901 0.989002i \(-0.452748\pi\)
0.147901 + 0.989002i \(0.452748\pi\)
\(854\) 1.14359e7 0.536571
\(855\) 4.16250e6 0.194733
\(856\) −1.49100e7 −0.695492
\(857\) 1.54050e7 0.716490 0.358245 0.933628i \(-0.383375\pi\)
0.358245 + 0.933628i \(0.383375\pi\)
\(858\) 1.19877e7 0.555927
\(859\) 1.43526e7 0.663664 0.331832 0.943338i \(-0.392333\pi\)
0.331832 + 0.943338i \(0.392333\pi\)
\(860\) 8.24960e6 0.380353
\(861\) −5.12698e6 −0.235697
\(862\) 1.05866e7 0.485275
\(863\) 1.33278e7 0.609158 0.304579 0.952487i \(-0.401484\pi\)
0.304579 + 0.952487i \(0.401484\pi\)
\(864\) −2.21184e6 −0.100802
\(865\) 1.08464e7 0.492882
\(866\) −1.48942e7 −0.674874
\(867\) −3.28938e7 −1.48616
\(868\) −6.36262e6 −0.286640
\(869\) −6.10368e6 −0.274184
\(870\) −5.25600e6 −0.235428
\(871\) −1.71037e6 −0.0763913
\(872\) 1.11904e7 0.498373
\(873\) −2.61012e7 −1.15911
\(874\) −7.12800e6 −0.315638
\(875\) −2.68750e6 −0.118667
\(876\) 7.86202e6 0.346157
\(877\) 3.24846e7 1.42620 0.713098 0.701065i \(-0.247292\pi\)
0.713098 + 0.701065i \(0.247292\pi\)
\(878\) 1.03336e7 0.452392
\(879\) −7.74014e6 −0.337891
\(880\) 844800. 0.0367745
\(881\) 1.54600e7 0.671073 0.335537 0.942027i \(-0.391082\pi\)
0.335537 + 0.942027i \(0.391082\pi\)
\(882\) −1.70190e7 −0.736651
\(883\) −1.69478e6 −0.0731494 −0.0365747 0.999331i \(-0.511645\pi\)
−0.0365747 + 0.999331i \(0.511645\pi\)
\(884\) 3.36019e6 0.144622
\(885\) 4.78800e6 0.205492
\(886\) −3.02483e7 −1.29454
\(887\) −2.87257e6 −0.122592 −0.0612960 0.998120i \(-0.519523\pi\)
−0.0612960 + 0.998120i \(0.519523\pi\)
\(888\) 1.72677e7 0.734856
\(889\) 2.10617e7 0.893799
\(890\) 1.10310e7 0.466810
\(891\) −3.83843e6 −0.161979
\(892\) 1.71751e7 0.722749
\(893\) 3.29400e6 0.138228
\(894\) −1.34928e7 −0.564623
\(895\) −1.22295e7 −0.510330
\(896\) 2.81805e6 0.117268
\(897\) −8.09171e7 −3.35783
\(898\) −1.72309e7 −0.713046
\(899\) 5.06328e6 0.208945
\(900\) 3.33000e6 0.137037
\(901\) 4.67665e6 0.191921
\(902\) −655776. −0.0268373
\(903\) −8.51359e7 −3.47451
\(904\) −1.17116e7 −0.476646
\(905\) 1.79865e7 0.730006
\(906\) −4.16594e7 −1.68614
\(907\) 3.95422e7 1.59603 0.798017 0.602635i \(-0.205882\pi\)
0.798017 + 0.602635i \(0.205882\pi\)
\(908\) −1.00293e7 −0.403698
\(909\) 4.72667e7 1.89734
\(910\) −1.62712e7 −0.651353
\(911\) 1.13178e7 0.451819 0.225909 0.974148i \(-0.427465\pi\)
0.225909 + 0.974148i \(0.427465\pi\)
\(912\) 3.07200e6 0.122302
\(913\) −6.80803e6 −0.270299
\(914\) 8.97417e6 0.355327
\(915\) 9.97320e6 0.393806
\(916\) −1.86640e6 −0.0734964
\(917\) 4.16082e7 1.63401
\(918\) 1.91808e6 0.0751208
\(919\) 8.51348e6 0.332520 0.166260 0.986082i \(-0.446831\pi\)
0.166260 + 0.986082i \(0.446831\pi\)
\(920\) −5.70240e6 −0.222120
\(921\) 3.46322e7 1.34534
\(922\) −6.62681e6 −0.256730
\(923\) 2.32035e7 0.896497
\(924\) −8.71834e6 −0.335934
\(925\) −7.02625e6 −0.270003
\(926\) 1.15664e7 0.443272
\(927\) −145188. −0.00554921
\(928\) −2.24256e6 −0.0854819
\(929\) −7.54587e6 −0.286860 −0.143430 0.989660i \(-0.545813\pi\)
−0.143430 + 0.989660i \(0.545813\pi\)
\(930\) −5.54880e6 −0.210374
\(931\) 6.38850e6 0.241560
\(932\) −1.18887e7 −0.448328
\(933\) 4.11149e6 0.154630
\(934\) 2.61080e7 0.979278
\(935\) −732600. −0.0274055
\(936\) 2.01612e7 0.752187
\(937\) −1.84500e7 −0.686512 −0.343256 0.939242i \(-0.611530\pi\)
−0.343256 + 0.939242i \(0.611530\pi\)
\(938\) 1.24390e6 0.0461615
\(939\) −2.46453e7 −0.912157
\(940\) 2.63520e6 0.0972734
\(941\) 6.75046e6 0.248519 0.124259 0.992250i \(-0.460344\pi\)
0.124259 + 0.992250i \(0.460344\pi\)
\(942\) 5.33685e7 1.95956
\(943\) 4.42649e6 0.162099
\(944\) 2.04288e6 0.0746127
\(945\) −9.28800e6 −0.338332
\(946\) −1.08895e7 −0.395621
\(947\) 6.45677e6 0.233959 0.116980 0.993134i \(-0.462679\pi\)
0.116980 + 0.993134i \(0.462679\pi\)
\(948\) −1.77562e7 −0.641694
\(949\) −1.93684e7 −0.698117
\(950\) −1.25000e6 −0.0449367
\(951\) 1.80710e7 0.647934
\(952\) −2.44378e6 −0.0873915
\(953\) −3.96648e7 −1.41473 −0.707364 0.706849i \(-0.750116\pi\)
−0.707364 + 0.706849i \(0.750116\pi\)
\(954\) 2.80599e7 0.998195
\(955\) −4.64820e6 −0.164921
\(956\) 1.56595e7 0.554158
\(957\) 6.93792e6 0.244878
\(958\) 2.38493e7 0.839579
\(959\) −4.76609e7 −1.67346
\(960\) 2.45760e6 0.0860663
\(961\) −2.32838e7 −0.813290
\(962\) −4.25397e7 −1.48203
\(963\) 7.75783e7 2.69572
\(964\) −1.81248e7 −0.628174
\(965\) −1.47851e7 −0.511102
\(966\) 5.88488e7 2.02906
\(967\) −3.43015e7 −1.17963 −0.589816 0.807538i \(-0.700800\pi\)
−0.589816 + 0.807538i \(0.700800\pi\)
\(968\) 9.19213e6 0.315303
\(969\) −2.66400e6 −0.0911433
\(970\) 7.83820e6 0.267477
\(971\) −5.77115e6 −0.196433 −0.0982164 0.995165i \(-0.531314\pi\)
−0.0982164 + 0.995165i \(0.531314\pi\)
\(972\) −1.95644e7 −0.664204
\(973\) 3.32889e7 1.12724
\(974\) −1.19676e7 −0.404214
\(975\) −1.41900e7 −0.478047
\(976\) 4.25523e6 0.142988
\(977\) 7.08746e6 0.237549 0.118775 0.992921i \(-0.462103\pi\)
0.118775 + 0.992921i \(0.462103\pi\)
\(978\) 6.39514e6 0.213798
\(979\) −1.45609e7 −0.485548
\(980\) 5.11080e6 0.169990
\(981\) −5.82251e7 −1.93169
\(982\) 4.81675e6 0.159395
\(983\) 4.59362e7 1.51625 0.758126 0.652108i \(-0.226115\pi\)
0.758126 + 0.652108i \(0.226115\pi\)
\(984\) −1.90771e6 −0.0628095
\(985\) 1.12369e7 0.369027
\(986\) 1.94472e6 0.0637037
\(987\) −2.71953e7 −0.888588
\(988\) −7.56800e6 −0.246654
\(989\) 7.35039e7 2.38957
\(990\) −4.39560e6 −0.142538
\(991\) −4.50298e7 −1.45652 −0.728260 0.685301i \(-0.759671\pi\)
−0.728260 + 0.685301i \(0.759671\pi\)
\(992\) −2.36749e6 −0.0763851
\(993\) 4.78592e7 1.54025
\(994\) −1.68753e7 −0.541732
\(995\) 3.92900e6 0.125813
\(996\) −1.98052e7 −0.632602
\(997\) −2.37364e7 −0.756271 −0.378136 0.925750i \(-0.623435\pi\)
−0.378136 + 0.925750i \(0.623435\pi\)
\(998\) −3.68218e7 −1.17025
\(999\) −2.42827e7 −0.769810
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 \(a_p\))