Properties

Label 230.6.a.a.1.1
Level $230$
Weight $6$
Character 230.1
Self dual yes
Analytic conductor $36.888$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 230 = 2 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 230.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(36.8882785570\)
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 \(\chi\) \(=\) 230.1

$q$-expansion

\(f(q)\) \(=\) \(q-4.00000 q^{2} +8.00000 q^{3} +16.0000 q^{4} -25.0000 q^{5} -32.0000 q^{6} +199.000 q^{7} -64.0000 q^{8} -179.000 q^{9} +O(q^{10})\) \(q-4.00000 q^{2} +8.00000 q^{3} +16.0000 q^{4} -25.0000 q^{5} -32.0000 q^{6} +199.000 q^{7} -64.0000 q^{8} -179.000 q^{9} +100.000 q^{10} +150.000 q^{11} +128.000 q^{12} -1202.00 q^{13} -796.000 q^{14} -200.000 q^{15} +256.000 q^{16} +735.000 q^{17} +716.000 q^{18} -22.0000 q^{19} -400.000 q^{20} +1592.00 q^{21} -600.000 q^{22} -529.000 q^{23} -512.000 q^{24} +625.000 q^{25} +4808.00 q^{26} -3376.00 q^{27} +3184.00 q^{28} -5525.00 q^{29} +800.000 q^{30} -95.0000 q^{31} -1024.00 q^{32} +1200.00 q^{33} -2940.00 q^{34} -4975.00 q^{35} -2864.00 q^{36} -397.000 q^{37} +88.0000 q^{38} -9616.00 q^{39} +1600.00 q^{40} +20633.0 q^{41} -6368.00 q^{42} -11384.0 q^{43} +2400.00 q^{44} +4475.00 q^{45} +2116.00 q^{46} +1992.00 q^{47} +2048.00 q^{48} +22794.0 q^{49} -2500.00 q^{50} +5880.00 q^{51} -19232.0 q^{52} -7349.00 q^{53} +13504.0 q^{54} -3750.00 q^{55} -12736.0 q^{56} -176.000 q^{57} +22100.0 q^{58} -23827.0 q^{59} -3200.00 q^{60} -44016.0 q^{61} +380.000 q^{62} -35621.0 q^{63} +4096.00 q^{64} +30050.0 q^{65} -4800.00 q^{66} -37713.0 q^{67} +11760.0 q^{68} -4232.00 q^{69} +19900.0 q^{70} -50057.0 q^{71} +11456.0 q^{72} -16698.0 q^{73} +1588.00 q^{74} +5000.00 q^{75} -352.000 q^{76} +29850.0 q^{77} +38464.0 q^{78} -31004.0 q^{79} -6400.00 q^{80} +16489.0 q^{81} -82532.0 q^{82} -70077.0 q^{83} +25472.0 q^{84} -18375.0 q^{85} +45536.0 q^{86} -44200.0 q^{87} -9600.00 q^{88} +7676.00 q^{89} -17900.0 q^{90} -239198. q^{91} -8464.00 q^{92} -760.000 q^{93} -7968.00 q^{94} +550.000 q^{95} -8192.00 q^{96} -150094. q^{97} -91176.0 q^{98} -26850.0 q^{99} +O(q^{100})\)

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
\(3\) 8.00000 0.513200 0.256600 0.966518i \(-0.417398\pi\)
0.256600 + 0.966518i \(0.417398\pi\)
\(4\) 16.0000 0.500000
\(5\) −25.0000 −0.447214
\(6\) −32.0000 −0.362887
\(7\) 199.000 1.53500 0.767499 0.641050i \(-0.221501\pi\)
0.767499 + 0.641050i \(0.221501\pi\)
\(8\) −64.0000 −0.353553
\(9\) −179.000 −0.736626
\(10\) 100.000 0.316228
\(11\) 150.000 0.373774 0.186887 0.982381i \(-0.440160\pi\)
0.186887 + 0.982381i \(0.440160\pi\)
\(12\) 128.000 0.256600
\(13\) −1202.00 −1.97263 −0.986316 0.164866i \(-0.947281\pi\)
−0.986316 + 0.164866i \(0.947281\pi\)
\(14\) −796.000 −1.08541
\(15\) −200.000 −0.229510
\(16\) 256.000 0.250000
\(17\) 735.000 0.616829 0.308415 0.951252i \(-0.400202\pi\)
0.308415 + 0.951252i \(0.400202\pi\)
\(18\) 716.000 0.520873
\(19\) −22.0000 −0.0139810 −0.00699051 0.999976i \(-0.502225\pi\)
−0.00699051 + 0.999976i \(0.502225\pi\)
\(20\) −400.000 −0.223607
\(21\) 1592.00 0.787762
\(22\) −600.000 −0.264298
\(23\) −529.000 −0.208514
\(24\) −512.000 −0.181444
\(25\) 625.000 0.200000
\(26\) 4808.00 1.39486
\(27\) −3376.00 −0.891237
\(28\) 3184.00 0.767499
\(29\) −5525.00 −1.21994 −0.609968 0.792426i \(-0.708818\pi\)
−0.609968 + 0.792426i \(0.708818\pi\)
\(30\) 800.000 0.162288
\(31\) −95.0000 −0.0177549 −0.00887747 0.999961i \(-0.502826\pi\)
−0.00887747 + 0.999961i \(0.502826\pi\)
\(32\) −1024.00 −0.176777
\(33\) 1200.00 0.191821
\(34\) −2940.00 −0.436164
\(35\) −4975.00 −0.686472
\(36\) −2864.00 −0.368313
\(37\) −397.000 −0.0476745 −0.0238373 0.999716i \(-0.507588\pi\)
−0.0238373 + 0.999716i \(0.507588\pi\)
\(38\) 88.0000 0.00988607
\(39\) −9616.00 −1.01236
\(40\) 1600.00 0.158114
\(41\) 20633.0 1.91691 0.958457 0.285236i \(-0.0920721\pi\)
0.958457 + 0.285236i \(0.0920721\pi\)
\(42\) −6368.00 −0.557032
\(43\) −11384.0 −0.938910 −0.469455 0.882957i \(-0.655550\pi\)
−0.469455 + 0.882957i \(0.655550\pi\)
\(44\) 2400.00 0.186887
\(45\) 4475.00 0.329429
\(46\) 2116.00 0.147442
\(47\) 1992.00 0.131536 0.0657680 0.997835i \(-0.479050\pi\)
0.0657680 + 0.997835i \(0.479050\pi\)
\(48\) 2048.00 0.128300
\(49\) 22794.0 1.35622
\(50\) −2500.00 −0.141421
\(51\) 5880.00 0.316557
\(52\) −19232.0 −0.986316
\(53\) −7349.00 −0.359367 −0.179684 0.983724i \(-0.557507\pi\)
−0.179684 + 0.983724i \(0.557507\pi\)
\(54\) 13504.0 0.630199
\(55\) −3750.00 −0.167157
\(56\) −12736.0 −0.542704
\(57\) −176.000 −0.00717506
\(58\) 22100.0 0.862625
\(59\) −23827.0 −0.891126 −0.445563 0.895250i \(-0.646997\pi\)
−0.445563 + 0.895250i \(0.646997\pi\)
\(60\) −3200.00 −0.114755
\(61\) −44016.0 −1.51456 −0.757279 0.653091i \(-0.773472\pi\)
−0.757279 + 0.653091i \(0.773472\pi\)
\(62\) 380.000 0.0125546
\(63\) −35621.0 −1.13072
\(64\) 4096.00 0.125000
\(65\) 30050.0 0.882188
\(66\) −4800.00 −0.135638
\(67\) −37713.0 −1.02637 −0.513185 0.858278i \(-0.671535\pi\)
−0.513185 + 0.858278i \(0.671535\pi\)
\(68\) 11760.0 0.308415
\(69\) −4232.00 −0.107010
\(70\) 19900.0 0.485409
\(71\) −50057.0 −1.17847 −0.589236 0.807961i \(-0.700571\pi\)
−0.589236 + 0.807961i \(0.700571\pi\)
\(72\) 11456.0 0.260436
\(73\) −16698.0 −0.366739 −0.183370 0.983044i \(-0.558701\pi\)
−0.183370 + 0.983044i \(0.558701\pi\)
\(74\) 1588.00 0.0337110
\(75\) 5000.00 0.102640
\(76\) −352.000 −0.00699051
\(77\) 29850.0 0.573743
\(78\) 38464.0 0.715843
\(79\) −31004.0 −0.558920 −0.279460 0.960157i \(-0.590156\pi\)
−0.279460 + 0.960157i \(0.590156\pi\)
\(80\) −6400.00 −0.111803
\(81\) 16489.0 0.279243
\(82\) −82532.0 −1.35546
\(83\) −70077.0 −1.11656 −0.558278 0.829654i \(-0.688538\pi\)
−0.558278 + 0.829654i \(0.688538\pi\)
\(84\) 25472.0 0.393881
\(85\) −18375.0 −0.275854
\(86\) 45536.0 0.663909
\(87\) −44200.0 −0.626072
\(88\) −9600.00 −0.132149
\(89\) 7676.00 0.102721 0.0513606 0.998680i \(-0.483644\pi\)
0.0513606 + 0.998680i \(0.483644\pi\)
\(90\) −17900.0 −0.232941
\(91\) −239198. −3.02799
\(92\) −8464.00 −0.104257
\(93\) −760.000 −0.00911184
\(94\) −7968.00 −0.0930100
\(95\) 550.000 0.00625250
\(96\) −8192.00 −0.0907218
\(97\) −150094. −1.61970 −0.809849 0.586639i \(-0.800451\pi\)
−0.809849 + 0.586639i \(0.800451\pi\)
\(98\) −91176.0 −0.958993
\(99\) −26850.0 −0.275332
\(100\) 10000.0 0.100000
\(101\) −95545.0 −0.931976 −0.465988 0.884791i \(-0.654301\pi\)
−0.465988 + 0.884791i \(0.654301\pi\)
\(102\) −23520.0 −0.223840
\(103\) −67960.0 −0.631190 −0.315595 0.948894i \(-0.602204\pi\)
−0.315595 + 0.948894i \(0.602204\pi\)
\(104\) 76928.0 0.697431
\(105\) −39800.0 −0.352298
\(106\) 29396.0 0.254111
\(107\) 160011. 1.35111 0.675555 0.737310i \(-0.263904\pi\)
0.675555 + 0.737310i \(0.263904\pi\)
\(108\) −54016.0 −0.445618
\(109\) −119442. −0.962921 −0.481461 0.876468i \(-0.659894\pi\)
−0.481461 + 0.876468i \(0.659894\pi\)
\(110\) 15000.0 0.118198
\(111\) −3176.00 −0.0244666
\(112\) 50944.0 0.383750
\(113\) 206491. 1.52127 0.760633 0.649182i \(-0.224889\pi\)
0.760633 + 0.649182i \(0.224889\pi\)
\(114\) 704.000 0.00507353
\(115\) 13225.0 0.0932505
\(116\) −88400.0 −0.609968
\(117\) 215158. 1.45309
\(118\) 95308.0 0.630122
\(119\) 146265. 0.946832
\(120\) 12800.0 0.0811441
\(121\) −138551. −0.860293
\(122\) 176064. 1.07095
\(123\) 165064. 0.983761
\(124\) −1520.00 −0.00887747
\(125\) −15625.0 −0.0894427
\(126\) 142484. 0.799539
\(127\) 310260. 1.70693 0.853467 0.521148i \(-0.174496\pi\)
0.853467 + 0.521148i \(0.174496\pi\)
\(128\) −16384.0 −0.0883883
\(129\) −91072.0 −0.481849
\(130\) −120200. −0.623801
\(131\) −16060.0 −0.0817650 −0.0408825 0.999164i \(-0.513017\pi\)
−0.0408825 + 0.999164i \(0.513017\pi\)
\(132\) 19200.0 0.0959106
\(133\) −4378.00 −0.0214608
\(134\) 150852. 0.725753
\(135\) 84400.0 0.398573
\(136\) −47040.0 −0.218082
\(137\) 175094. 0.797021 0.398511 0.917164i \(-0.369527\pi\)
0.398511 + 0.917164i \(0.369527\pi\)
\(138\) 16928.0 0.0756672
\(139\) 69059.0 0.303168 0.151584 0.988444i \(-0.451563\pi\)
0.151584 + 0.988444i \(0.451563\pi\)
\(140\) −79600.0 −0.343236
\(141\) 15936.0 0.0675043
\(142\) 200228. 0.833305
\(143\) −180300. −0.737319
\(144\) −45824.0 −0.184156
\(145\) 138125. 0.545572
\(146\) 66792.0 0.259324
\(147\) 182352. 0.696013
\(148\) −6352.00 −0.0238373
\(149\) −150080. −0.553805 −0.276903 0.960898i \(-0.589308\pi\)
−0.276903 + 0.960898i \(0.589308\pi\)
\(150\) −20000.0 −0.0725775
\(151\) −462052. −1.64911 −0.824553 0.565785i \(-0.808573\pi\)
−0.824553 + 0.565785i \(0.808573\pi\)
\(152\) 1408.00 0.00494303
\(153\) −131565. −0.454372
\(154\) −119400. −0.405698
\(155\) 2375.00 0.00794025
\(156\) −153856. −0.506178
\(157\) −211807. −0.685790 −0.342895 0.939374i \(-0.611408\pi\)
−0.342895 + 0.939374i \(0.611408\pi\)
\(158\) 124016. 0.395216
\(159\) −58792.0 −0.184427
\(160\) 25600.0 0.0790569
\(161\) −105271. −0.320069
\(162\) −65956.0 −0.197454
\(163\) −119454. −0.352153 −0.176077 0.984376i \(-0.556341\pi\)
−0.176077 + 0.984376i \(0.556341\pi\)
\(164\) 330128. 0.958457
\(165\) −30000.0 −0.0857850
\(166\) 280308. 0.789524
\(167\) 311784. 0.865093 0.432546 0.901612i \(-0.357615\pi\)
0.432546 + 0.901612i \(0.357615\pi\)
\(168\) −101888. −0.278516
\(169\) 1.07351e6 2.89128
\(170\) 73500.0 0.195059
\(171\) 3938.00 0.0102988
\(172\) −182144. −0.469455
\(173\) 485184. 1.23251 0.616256 0.787546i \(-0.288649\pi\)
0.616256 + 0.787546i \(0.288649\pi\)
\(174\) 176800. 0.442700
\(175\) 124375. 0.307000
\(176\) 38400.0 0.0934436
\(177\) −190616. −0.457326
\(178\) −30704.0 −0.0726348
\(179\) −260664. −0.608063 −0.304031 0.952662i \(-0.598333\pi\)
−0.304031 + 0.952662i \(0.598333\pi\)
\(180\) 71600.0 0.164714
\(181\) 111496. 0.252966 0.126483 0.991969i \(-0.459631\pi\)
0.126483 + 0.991969i \(0.459631\pi\)
\(182\) 956792. 2.14111
\(183\) −352128. −0.777272
\(184\) 33856.0 0.0737210
\(185\) 9925.00 0.0213207
\(186\) 3040.00 0.00644305
\(187\) 110250. 0.230555
\(188\) 31872.0 0.0657680
\(189\) −671824. −1.36805
\(190\) −2200.00 −0.00442118
\(191\) 282032. 0.559390 0.279695 0.960089i \(-0.409767\pi\)
0.279695 + 0.960089i \(0.409767\pi\)
\(192\) 32768.0 0.0641500
\(193\) −107808. −0.208333 −0.104166 0.994560i \(-0.533217\pi\)
−0.104166 + 0.994560i \(0.533217\pi\)
\(194\) 600376. 1.14530
\(195\) 240400. 0.452739
\(196\) 364704. 0.678110
\(197\) 417830. 0.767068 0.383534 0.923527i \(-0.374707\pi\)
0.383534 + 0.923527i \(0.374707\pi\)
\(198\) 107400. 0.194689
\(199\) −322018. −0.576431 −0.288216 0.957566i \(-0.593062\pi\)
−0.288216 + 0.957566i \(0.593062\pi\)
\(200\) −40000.0 −0.0707107
\(201\) −301704. −0.526733
\(202\) 382180. 0.659006
\(203\) −1.09948e6 −1.87260
\(204\) 94080.0 0.158278
\(205\) −515825. −0.857270
\(206\) 271840. 0.446319
\(207\) 94691.0 0.153597
\(208\) −307712. −0.493158
\(209\) −3300.00 −0.00522575
\(210\) 159200. 0.249112
\(211\) 1.02228e6 1.58075 0.790377 0.612621i \(-0.209885\pi\)
0.790377 + 0.612621i \(0.209885\pi\)
\(212\) −117584. −0.179684
\(213\) −400456. −0.604792
\(214\) −640044. −0.955378
\(215\) 284600. 0.419893
\(216\) 216064. 0.315100
\(217\) −18905.0 −0.0272538
\(218\) 477768. 0.680888
\(219\) −133584. −0.188211
\(220\) −60000.0 −0.0835785
\(221\) −883470. −1.21678
\(222\) 12704.0 0.0173005
\(223\) 1.07323e6 1.44521 0.722607 0.691259i \(-0.242944\pi\)
0.722607 + 0.691259i \(0.242944\pi\)
\(224\) −203776. −0.271352
\(225\) −111875. −0.147325
\(226\) −825964. −1.07570
\(227\) −532220. −0.685530 −0.342765 0.939421i \(-0.611363\pi\)
−0.342765 + 0.939421i \(0.611363\pi\)
\(228\) −2816.00 −0.00358753
\(229\) 176824. 0.222819 0.111410 0.993775i \(-0.464463\pi\)
0.111410 + 0.993775i \(0.464463\pi\)
\(230\) −52900.0 −0.0659380
\(231\) 238800. 0.294445
\(232\) 353600. 0.431313
\(233\) −442996. −0.534577 −0.267288 0.963617i \(-0.586128\pi\)
−0.267288 + 0.963617i \(0.586128\pi\)
\(234\) −860632. −1.02749
\(235\) −49800.0 −0.0588247
\(236\) −381232. −0.445563
\(237\) −248032. −0.286838
\(238\) −585060. −0.669511
\(239\) −1.30607e6 −1.47901 −0.739507 0.673149i \(-0.764941\pi\)
−0.739507 + 0.673149i \(0.764941\pi\)
\(240\) −51200.0 −0.0573775
\(241\) 1.60981e6 1.78538 0.892691 0.450670i \(-0.148815\pi\)
0.892691 + 0.450670i \(0.148815\pi\)
\(242\) 554204. 0.608319
\(243\) 952280. 1.03454
\(244\) −704256. −0.757279
\(245\) −569850. −0.606520
\(246\) −660256. −0.695624
\(247\) 26444.0 0.0275794
\(248\) 6080.00 0.00627732
\(249\) −560616. −0.573016
\(250\) 62500.0 0.0632456
\(251\) −1.13818e6 −1.14032 −0.570161 0.821533i \(-0.693119\pi\)
−0.570161 + 0.821533i \(0.693119\pi\)
\(252\) −569936. −0.565360
\(253\) −79350.0 −0.0779373
\(254\) −1.24104e6 −1.20698
\(255\) −147000. −0.141569
\(256\) 65536.0 0.0625000
\(257\) 216048. 0.204041 0.102020 0.994782i \(-0.467469\pi\)
0.102020 + 0.994782i \(0.467469\pi\)
\(258\) 364288. 0.340718
\(259\) −79003.0 −0.0731803
\(260\) 480800. 0.441094
\(261\) 988975. 0.898636
\(262\) 64240.0 0.0578166
\(263\) 1.59769e6 1.42431 0.712154 0.702023i \(-0.247720\pi\)
0.712154 + 0.702023i \(0.247720\pi\)
\(264\) −76800.0 −0.0678190
\(265\) 183725. 0.160714
\(266\) 17512.0 0.0151751
\(267\) 61408.0 0.0527165
\(268\) −603408. −0.513185
\(269\) 1.79855e6 1.51545 0.757723 0.652576i \(-0.226312\pi\)
0.757723 + 0.652576i \(0.226312\pi\)
\(270\) −337600. −0.281834
\(271\) −579025. −0.478932 −0.239466 0.970905i \(-0.576972\pi\)
−0.239466 + 0.970905i \(0.576972\pi\)
\(272\) 188160. 0.154207
\(273\) −1.91358e6 −1.55396
\(274\) −700376. −0.563579
\(275\) 93750.0 0.0747549
\(276\) −67712.0 −0.0535048
\(277\) −781034. −0.611604 −0.305802 0.952095i \(-0.598925\pi\)
−0.305802 + 0.952095i \(0.598925\pi\)
\(278\) −276236. −0.214372
\(279\) 17005.0 0.0130787
\(280\) 318400. 0.242705
\(281\) −261022. −0.197202 −0.0986010 0.995127i \(-0.531437\pi\)
−0.0986010 + 0.995127i \(0.531437\pi\)
\(282\) −63744.0 −0.0477328
\(283\) −190871. −0.141669 −0.0708343 0.997488i \(-0.522566\pi\)
−0.0708343 + 0.997488i \(0.522566\pi\)
\(284\) −800912. −0.589236
\(285\) 4400.00 0.00320878
\(286\) 721200. 0.521364
\(287\) 4.10597e6 2.94246
\(288\) 183296. 0.130218
\(289\) −879632. −0.619522
\(290\) −552500. −0.385778
\(291\) −1.20075e6 −0.831229
\(292\) −267168. −0.183370
\(293\) −769679. −0.523770 −0.261885 0.965099i \(-0.584344\pi\)
−0.261885 + 0.965099i \(0.584344\pi\)
\(294\) −729408. −0.492155
\(295\) 595675. 0.398524
\(296\) 25408.0 0.0168555
\(297\) −506400. −0.333121
\(298\) 600320. 0.391600
\(299\) 635858. 0.411322
\(300\) 80000.0 0.0513200
\(301\) −2.26542e6 −1.44122
\(302\) 1.84821e6 1.16609
\(303\) −764360. −0.478290
\(304\) −5632.00 −0.00349525
\(305\) 1.10040e6 0.677331
\(306\) 526260. 0.321290
\(307\) 551346. 0.333871 0.166935 0.985968i \(-0.446613\pi\)
0.166935 + 0.985968i \(0.446613\pi\)
\(308\) 477600. 0.286872
\(309\) −543680. −0.323927
\(310\) −9500.00 −0.00561461
\(311\) −3.25890e6 −1.91060 −0.955299 0.295640i \(-0.904467\pi\)
−0.955299 + 0.295640i \(0.904467\pi\)
\(312\) 615424. 0.357922
\(313\) 267129. 0.154120 0.0770602 0.997026i \(-0.475447\pi\)
0.0770602 + 0.997026i \(0.475447\pi\)
\(314\) 847228. 0.484927
\(315\) 890525. 0.505673
\(316\) −496064. −0.279460
\(317\) 2.41748e6 1.35119 0.675593 0.737274i \(-0.263887\pi\)
0.675593 + 0.737274i \(0.263887\pi\)
\(318\) 235168. 0.130410
\(319\) −828750. −0.455981
\(320\) −102400. −0.0559017
\(321\) 1.28009e6 0.693389
\(322\) 421084. 0.226323
\(323\) −16170.0 −0.00862390
\(324\) 263824. 0.139621
\(325\) −751250. −0.394526
\(326\) 477816. 0.249010
\(327\) −955536. −0.494171
\(328\) −1.32051e6 −0.677732
\(329\) 396408. 0.201908
\(330\) 120000. 0.0606592
\(331\) −1.62316e6 −0.814310 −0.407155 0.913359i \(-0.633479\pi\)
−0.407155 + 0.913359i \(0.633479\pi\)
\(332\) −1.12123e6 −0.558278
\(333\) 71063.0 0.0351183
\(334\) −1.24714e6 −0.611713
\(335\) 942825. 0.459007
\(336\) 407552. 0.196940
\(337\) −1.78809e6 −0.857657 −0.428829 0.903386i \(-0.641074\pi\)
−0.428829 + 0.903386i \(0.641074\pi\)
\(338\) −4.29404e6 −2.04444
\(339\) 1.65193e6 0.780714
\(340\) −294000. −0.137927
\(341\) −14250.0 −0.00663634
\(342\) −15752.0 −0.00728233
\(343\) 1.19141e6 0.546798
\(344\) 728576. 0.331955
\(345\) 105800. 0.0478562
\(346\) −1.94074e6 −0.871518
\(347\) −1.35799e6 −0.605442 −0.302721 0.953079i \(-0.597895\pi\)
−0.302721 + 0.953079i \(0.597895\pi\)
\(348\) −707200. −0.313036
\(349\) −2.82446e6 −1.24128 −0.620642 0.784094i \(-0.713128\pi\)
−0.620642 + 0.784094i \(0.713128\pi\)
\(350\) −497500. −0.217082
\(351\) 4.05795e6 1.75808
\(352\) −153600. −0.0660746
\(353\) 1.29972e6 0.555153 0.277577 0.960703i \(-0.410469\pi\)
0.277577 + 0.960703i \(0.410469\pi\)
\(354\) 762464. 0.323379
\(355\) 1.25142e6 0.527028
\(356\) 122816. 0.0513606
\(357\) 1.17012e6 0.485915
\(358\) 1.04266e6 0.429965
\(359\) 345284. 0.141397 0.0706985 0.997498i \(-0.477477\pi\)
0.0706985 + 0.997498i \(0.477477\pi\)
\(360\) −286400. −0.116471
\(361\) −2.47562e6 −0.999805
\(362\) −445984. −0.178874
\(363\) −1.10841e6 −0.441502
\(364\) −3.82717e6 −1.51399
\(365\) 417450. 0.164011
\(366\) 1.40851e6 0.549614
\(367\) 4.83833e6 1.87513 0.937563 0.347815i \(-0.113076\pi\)
0.937563 + 0.347815i \(0.113076\pi\)
\(368\) −135424. −0.0521286
\(369\) −3.69331e6 −1.41205
\(370\) −39700.0 −0.0150760
\(371\) −1.46245e6 −0.551628
\(372\) −12160.0 −0.00455592
\(373\) 303566. 0.112975 0.0564873 0.998403i \(-0.482010\pi\)
0.0564873 + 0.998403i \(0.482010\pi\)
\(374\) −441000. −0.163027
\(375\) −125000. −0.0459020
\(376\) −127488. −0.0465050
\(377\) 6.64105e6 2.40649
\(378\) 2.68730e6 0.967355
\(379\) −2.00528e6 −0.717097 −0.358548 0.933511i \(-0.616728\pi\)
−0.358548 + 0.933511i \(0.616728\pi\)
\(380\) 8800.00 0.00312625
\(381\) 2.48208e6 0.875998
\(382\) −1.12813e6 −0.395549
\(383\) −187083. −0.0651684 −0.0325842 0.999469i \(-0.510374\pi\)
−0.0325842 + 0.999469i \(0.510374\pi\)
\(384\) −131072. −0.0453609
\(385\) −746250. −0.256586
\(386\) 431232. 0.147314
\(387\) 2.03774e6 0.691625
\(388\) −2.40150e6 −0.809849
\(389\) 4.76936e6 1.59803 0.799017 0.601308i \(-0.205353\pi\)
0.799017 + 0.601308i \(0.205353\pi\)
\(390\) −961600. −0.320135
\(391\) −388815. −0.128618
\(392\) −1.45882e6 −0.479496
\(393\) −128480. −0.0419618
\(394\) −1.67132e6 −0.542399
\(395\) 775100. 0.249957
\(396\) −429600. −0.137666
\(397\) 2.60752e6 0.830333 0.415166 0.909746i \(-0.363723\pi\)
0.415166 + 0.909746i \(0.363723\pi\)
\(398\) 1.28807e6 0.407598
\(399\) −35024.0 −0.0110137
\(400\) 160000. 0.0500000
\(401\) −123598. −0.0383840 −0.0191920 0.999816i \(-0.506109\pi\)
−0.0191920 + 0.999816i \(0.506109\pi\)
\(402\) 1.20682e6 0.372457
\(403\) 114190. 0.0350240
\(404\) −1.52872e6 −0.465988
\(405\) −412225. −0.124881
\(406\) 4.39790e6 1.32413
\(407\) −59550.0 −0.0178195
\(408\) −376320. −0.111920
\(409\) −6.66194e6 −1.96921 −0.984606 0.174790i \(-0.944075\pi\)
−0.984606 + 0.174790i \(0.944075\pi\)
\(410\) 2.06330e6 0.606182
\(411\) 1.40075e6 0.409031
\(412\) −1.08736e6 −0.315595
\(413\) −4.74157e6 −1.36788
\(414\) −378764. −0.108610
\(415\) 1.75193e6 0.499339
\(416\) 1.23085e6 0.348715
\(417\) 552472. 0.155586
\(418\) 13200.0 0.00369516
\(419\) −2.35766e6 −0.656064 −0.328032 0.944667i \(-0.606385\pi\)
−0.328032 + 0.944667i \(0.606385\pi\)
\(420\) −636800. −0.176149
\(421\) 3.37575e6 0.928250 0.464125 0.885770i \(-0.346369\pi\)
0.464125 + 0.885770i \(0.346369\pi\)
\(422\) −4.08912e6 −1.11776
\(423\) −356568. −0.0968928
\(424\) 470336. 0.127056
\(425\) 459375. 0.123366
\(426\) 1.60182e6 0.427652
\(427\) −8.75918e6 −2.32484
\(428\) 2.56018e6 0.675555
\(429\) −1.44240e6 −0.378392
\(430\) −1.13840e6 −0.296909
\(431\) 2.04311e6 0.529783 0.264892 0.964278i \(-0.414664\pi\)
0.264892 + 0.964278i \(0.414664\pi\)
\(432\) −864256. −0.222809
\(433\) −546629. −0.140111 −0.0700556 0.997543i \(-0.522318\pi\)
−0.0700556 + 0.997543i \(0.522318\pi\)
\(434\) 75620.0 0.0192714
\(435\) 1.10500e6 0.279988
\(436\) −1.91107e6 −0.481461
\(437\) 11638.0 0.00291524
\(438\) 534336. 0.133085
\(439\) 2.47243e6 0.612298 0.306149 0.951984i \(-0.400959\pi\)
0.306149 + 0.951984i \(0.400959\pi\)
\(440\) 240000. 0.0590989
\(441\) −4.08013e6 −0.999027
\(442\) 3.53388e6 0.860392
\(443\) 3.68550e6 0.892252 0.446126 0.894970i \(-0.352803\pi\)
0.446126 + 0.894970i \(0.352803\pi\)
\(444\) −50816.0 −0.0122333
\(445\) −191900. −0.0459383
\(446\) −4.29294e6 −1.02192
\(447\) −1.20064e6 −0.284213
\(448\) 815104. 0.191875
\(449\) 908395. 0.212647 0.106323 0.994332i \(-0.466092\pi\)
0.106323 + 0.994332i \(0.466092\pi\)
\(450\) 447500. 0.104175
\(451\) 3.09495e6 0.716494
\(452\) 3.30386e6 0.760633
\(453\) −3.69642e6 −0.846321
\(454\) 2.12888e6 0.484743
\(455\) 5.97995e6 1.35416
\(456\) 11264.0 0.00253677
\(457\) 406629. 0.0910768 0.0455384 0.998963i \(-0.485500\pi\)
0.0455384 + 0.998963i \(0.485500\pi\)
\(458\) −707296. −0.157557
\(459\) −2.48136e6 −0.549741
\(460\) 211600. 0.0466252
\(461\) 6.75710e6 1.48084 0.740420 0.672144i \(-0.234627\pi\)
0.740420 + 0.672144i \(0.234627\pi\)
\(462\) −955200. −0.208204
\(463\) 1.21891e6 0.264253 0.132127 0.991233i \(-0.457819\pi\)
0.132127 + 0.991233i \(0.457819\pi\)
\(464\) −1.41440e6 −0.304984
\(465\) 19000.0 0.00407494
\(466\) 1.77198e6 0.378003
\(467\) 5.80503e6 1.23172 0.615860 0.787856i \(-0.288809\pi\)
0.615860 + 0.787856i \(0.288809\pi\)
\(468\) 3.44253e6 0.726546
\(469\) −7.50489e6 −1.57548
\(470\) 199200. 0.0415953
\(471\) −1.69446e6 −0.351948
\(472\) 1.52493e6 0.315061
\(473\) −1.70760e6 −0.350940
\(474\) 992128. 0.202825
\(475\) −13750.0 −0.00279620
\(476\) 2.34024e6 0.473416
\(477\) 1.31547e6 0.264719
\(478\) 5.22428e6 1.04582
\(479\) 4.27965e6 0.852255 0.426128 0.904663i \(-0.359877\pi\)
0.426128 + 0.904663i \(0.359877\pi\)
\(480\) 204800. 0.0405720
\(481\) 477194. 0.0940443
\(482\) −6.43922e6 −1.26246
\(483\) −842168. −0.164260
\(484\) −2.21682e6 −0.430146
\(485\) 3.75235e6 0.724351
\(486\) −3.80912e6 −0.731533
\(487\) −2.75263e6 −0.525927 −0.262963 0.964806i \(-0.584700\pi\)
−0.262963 + 0.964806i \(0.584700\pi\)
\(488\) 2.81702e6 0.535477
\(489\) −955632. −0.180725
\(490\) 2.27940e6 0.428875
\(491\) 9.21380e6 1.72479 0.862393 0.506240i \(-0.168965\pi\)
0.862393 + 0.506240i \(0.168965\pi\)
\(492\) 2.64102e6 0.491880
\(493\) −4.06088e6 −0.752493
\(494\) −105776. −0.0195016
\(495\) 671250. 0.123132
\(496\) −24320.0 −0.00443874
\(497\) −9.96134e6 −1.80895
\(498\) 2.24246e6 0.405184
\(499\) 7.86448e6 1.41390 0.706950 0.707264i \(-0.250071\pi\)
0.706950 + 0.707264i \(0.250071\pi\)
\(500\) −250000. −0.0447214
\(501\) 2.49427e6 0.443966
\(502\) 4.55273e6 0.806329
\(503\) −3.72163e6 −0.655863 −0.327932 0.944701i \(-0.606352\pi\)
−0.327932 + 0.944701i \(0.606352\pi\)
\(504\) 2.27974e6 0.399770
\(505\) 2.38862e6 0.416792
\(506\) 317400. 0.0551100
\(507\) 8.58809e6 1.48380
\(508\) 4.96416e6 0.853467
\(509\) 1.86151e6 0.318471 0.159236 0.987241i \(-0.449097\pi\)
0.159236 + 0.987241i \(0.449097\pi\)
\(510\) 588000. 0.100104
\(511\) −3.32290e6 −0.562944
\(512\) −262144. −0.0441942
\(513\) 74272.0 0.0124604
\(514\) −864192. −0.144279
\(515\) 1.69900e6 0.282277
\(516\) −1.45715e6 −0.240924
\(517\) 298800. 0.0491648
\(518\) 316012. 0.0517463
\(519\) 3.88147e6 0.632526
\(520\) −1.92320e6 −0.311901
\(521\) 6.78131e6 1.09451 0.547254 0.836966i \(-0.315673\pi\)
0.547254 + 0.836966i \(0.315673\pi\)
\(522\) −3.95590e6 −0.635432
\(523\) 6.13011e6 0.979973 0.489986 0.871730i \(-0.337002\pi\)
0.489986 + 0.871730i \(0.337002\pi\)
\(524\) −256960. −0.0408825
\(525\) 995000. 0.157552
\(526\) −6.39077e6 −1.00714
\(527\) −69825.0 −0.0109518
\(528\) 307200. 0.0479553
\(529\) 279841. 0.0434783
\(530\) −734900. −0.113642
\(531\) 4.26503e6 0.656426
\(532\) −70048.0 −0.0107304
\(533\) −2.48009e7 −3.78137
\(534\) −245632. −0.0372762
\(535\) −4.00028e6 −0.604234
\(536\) 2.41363e6 0.362877
\(537\) −2.08531e6 −0.312058
\(538\) −7.19418e6 −1.07158
\(539\) 3.41910e6 0.506921
\(540\) 1.35040e6 0.199287
\(541\) −1.00495e7 −1.47622 −0.738108 0.674683i \(-0.764280\pi\)
−0.738108 + 0.674683i \(0.764280\pi\)
\(542\) 2.31610e6 0.338656
\(543\) 891968. 0.129822
\(544\) −752640. −0.109041
\(545\) 2.98605e6 0.430632
\(546\) 7.65434e6 1.09882
\(547\) 2.25410e6 0.322111 0.161056 0.986945i \(-0.448510\pi\)
0.161056 + 0.986945i \(0.448510\pi\)
\(548\) 2.80150e6 0.398511
\(549\) 7.87886e6 1.11566
\(550\) −375000. −0.0528597
\(551\) 121550. 0.0170560
\(552\) 270848. 0.0378336
\(553\) −6.16980e6 −0.857942
\(554\) 3.12414e6 0.432470
\(555\) 79400.0 0.0109418
\(556\) 1.10494e6 0.151584
\(557\) 3.99580e6 0.545715 0.272858 0.962054i \(-0.412031\pi\)
0.272858 + 0.962054i \(0.412031\pi\)
\(558\) −68020.0 −0.00924807
\(559\) 1.36836e7 1.85212
\(560\) −1.27360e6 −0.171618
\(561\) 882000. 0.118321
\(562\) 1.04409e6 0.139443
\(563\) −9.21380e6 −1.22509 −0.612544 0.790436i \(-0.709854\pi\)
−0.612544 + 0.790436i \(0.709854\pi\)
\(564\) 254976. 0.0337522
\(565\) −5.16228e6 −0.680331
\(566\) 763484. 0.100175
\(567\) 3.28131e6 0.428637
\(568\) 3.20365e6 0.416652
\(569\) 2.92226e6 0.378388 0.189194 0.981940i \(-0.439412\pi\)
0.189194 + 0.981940i \(0.439412\pi\)
\(570\) −17600.0 −0.00226895
\(571\) −1.44280e7 −1.85189 −0.925946 0.377656i \(-0.876730\pi\)
−0.925946 + 0.377656i \(0.876730\pi\)
\(572\) −2.88480e6 −0.368660
\(573\) 2.25626e6 0.287079
\(574\) −1.64239e7 −2.08063
\(575\) −330625. −0.0417029
\(576\) −733184. −0.0920782
\(577\) −5.78445e6 −0.723307 −0.361654 0.932313i \(-0.617788\pi\)
−0.361654 + 0.932313i \(0.617788\pi\)
\(578\) 3.51853e6 0.438068
\(579\) −862464. −0.106916
\(580\) 2.21000e6 0.272786
\(581\) −1.39453e7 −1.71391
\(582\) 4.80301e6 0.587768
\(583\) −1.10235e6 −0.134322
\(584\) 1.06867e6 0.129662
\(585\) −5.37895e6 −0.649842
\(586\) 3.07872e6 0.370361
\(587\) −9.12050e6 −1.09250 −0.546252 0.837621i \(-0.683946\pi\)
−0.546252 + 0.837621i \(0.683946\pi\)
\(588\) 2.91763e6 0.348006
\(589\) 2090.00 0.000248232 0
\(590\) −2.38270e6 −0.281799
\(591\) 3.34264e6 0.393660
\(592\) −101632. −0.0119186
\(593\) −6.63750e6 −0.775118 −0.387559 0.921845i \(-0.626682\pi\)
−0.387559 + 0.921845i \(0.626682\pi\)
\(594\) 2.02560e6 0.235552
\(595\) −3.65662e6 −0.423436
\(596\) −2.40128e6 −0.276903
\(597\) −2.57614e6 −0.295825
\(598\) −2.54343e6 −0.290849
\(599\) −1.32534e7 −1.50925 −0.754624 0.656158i \(-0.772181\pi\)
−0.754624 + 0.656158i \(0.772181\pi\)
\(600\) −320000. −0.0362887
\(601\) −4.34856e6 −0.491089 −0.245544 0.969385i \(-0.578967\pi\)
−0.245544 + 0.969385i \(0.578967\pi\)
\(602\) 9.06166e6 1.01910
\(603\) 6.75063e6 0.756051
\(604\) −7.39283e6 −0.824553
\(605\) 3.46377e6 0.384735
\(606\) 3.05744e6 0.338202
\(607\) 1.45424e7 1.60201 0.801004 0.598659i \(-0.204300\pi\)
0.801004 + 0.598659i \(0.204300\pi\)
\(608\) 22528.0 0.00247152
\(609\) −8.79580e6 −0.961019
\(610\) −4.40160e6 −0.478945
\(611\) −2.39438e6 −0.259472
\(612\) −2.10504e6 −0.227186
\(613\) −1.53349e7 −1.64828 −0.824138 0.566389i \(-0.808340\pi\)
−0.824138 + 0.566389i \(0.808340\pi\)
\(614\) −2.20538e6 −0.236082
\(615\) −4.12660e6 −0.439951
\(616\) −1.91040e6 −0.202849
\(617\) 1.67548e7 1.77185 0.885923 0.463833i \(-0.153526\pi\)
0.885923 + 0.463833i \(0.153526\pi\)
\(618\) 2.17472e6 0.229051
\(619\) 1.36050e7 1.42716 0.713578 0.700576i \(-0.247074\pi\)
0.713578 + 0.700576i \(0.247074\pi\)
\(620\) 38000.0 0.00397013
\(621\) 1.78590e6 0.185836
\(622\) 1.30356e7 1.35100
\(623\) 1.52752e6 0.157677
\(624\) −2.46170e6 −0.253089
\(625\) 390625. 0.0400000
\(626\) −1.06852e6 −0.108980
\(627\) −26400.0 −0.00268185
\(628\) −3.38891e6 −0.342895
\(629\) −291795. −0.0294070
\(630\) −3.56210e6 −0.357565
\(631\) −1.35464e7 −1.35441 −0.677204 0.735796i \(-0.736808\pi\)
−0.677204 + 0.735796i \(0.736808\pi\)
\(632\) 1.98426e6 0.197608
\(633\) 8.17825e6 0.811243
\(634\) −9.66994e6 −0.955433
\(635\) −7.75650e6 −0.763364
\(636\) −940672. −0.0922137
\(637\) −2.73984e7 −2.67532
\(638\) 3.31500e6 0.322427
\(639\) 8.96020e6 0.868092
\(640\) 409600. 0.0395285
\(641\) 4.50097e6 0.432674 0.216337 0.976319i \(-0.430589\pi\)
0.216337 + 0.976319i \(0.430589\pi\)
\(642\) −5.12035e6 −0.490300
\(643\) 620123. 0.0591494 0.0295747 0.999563i \(-0.490585\pi\)
0.0295747 + 0.999563i \(0.490585\pi\)
\(644\) −1.68434e6 −0.160035
\(645\) 2.27680e6 0.215489
\(646\) 64680.0 0.00609802
\(647\) −1.56341e7 −1.46829 −0.734144 0.678994i \(-0.762416\pi\)
−0.734144 + 0.678994i \(0.762416\pi\)
\(648\) −1.05530e6 −0.0987272
\(649\) −3.57405e6 −0.333080
\(650\) 3.00500e6 0.278972
\(651\) −151240. −0.0139867
\(652\) −1.91126e6 −0.176077
\(653\) 2.46330e6 0.226065 0.113033 0.993591i \(-0.463944\pi\)
0.113033 + 0.993591i \(0.463944\pi\)
\(654\) 3.82214e6 0.349432
\(655\) 401500. 0.0365664
\(656\) 5.28205e6 0.479229
\(657\) 2.98894e6 0.270149
\(658\) −1.58563e6 −0.142770
\(659\) 1.28537e7 1.15296 0.576479 0.817112i \(-0.304426\pi\)
0.576479 + 0.817112i \(0.304426\pi\)
\(660\) −480000. −0.0428925
\(661\) 1.57203e7 1.39945 0.699724 0.714414i \(-0.253307\pi\)
0.699724 + 0.714414i \(0.253307\pi\)
\(662\) 6.49262e6 0.575804
\(663\) −7.06776e6 −0.624450
\(664\) 4.48493e6 0.394762
\(665\) 109450. 0.00959758
\(666\) −284252. −0.0248324
\(667\) 2.92272e6 0.254374
\(668\) 4.98854e6 0.432546
\(669\) 8.58587e6 0.741684
\(670\) −3.77130e6 −0.324567
\(671\) −6.60240e6 −0.566103
\(672\) −1.63021e6 −0.139258
\(673\) 1.43198e7 1.21870 0.609352 0.792900i \(-0.291430\pi\)
0.609352 + 0.792900i \(0.291430\pi\)
\(674\) 7.15234e6 0.606455
\(675\) −2.11000e6 −0.178247
\(676\) 1.71762e7 1.44564
\(677\) −1.79363e7 −1.50405 −0.752023 0.659136i \(-0.770922\pi\)
−0.752023 + 0.659136i \(0.770922\pi\)
\(678\) −6.60771e6 −0.552048
\(679\) −2.98687e7 −2.48623
\(680\) 1.17600e6 0.0975293
\(681\) −4.25776e6 −0.351814
\(682\) 57000.0 0.00469260
\(683\) 2.00563e7 1.64513 0.822564 0.568673i \(-0.192543\pi\)
0.822564 + 0.568673i \(0.192543\pi\)
\(684\) 63008.0 0.00514939
\(685\) −4.37735e6 −0.356439
\(686\) −4.76565e6 −0.386645
\(687\) 1.41459e6 0.114351
\(688\) −2.91430e6 −0.234727
\(689\) 8.83350e6 0.708899
\(690\) −423200. −0.0338394
\(691\) −7.25847e6 −0.578296 −0.289148 0.957284i \(-0.593372\pi\)
−0.289148 + 0.957284i \(0.593372\pi\)
\(692\) 7.76294e6 0.616256
\(693\) −5.34315e6 −0.422634
\(694\) 5.43195e6 0.428112
\(695\) −1.72648e6 −0.135581
\(696\) 2.82880e6 0.221350
\(697\) 1.51653e7 1.18241
\(698\) 1.12978e7 0.877721
\(699\) −3.54397e6 −0.274345
\(700\) 1.99000e6 0.153500
\(701\) −9.82493e6 −0.755152 −0.377576 0.925979i \(-0.623242\pi\)
−0.377576 + 0.925979i \(0.623242\pi\)
\(702\) −1.62318e7 −1.24315
\(703\) 8734.00 0.000666538 0
\(704\) 614400. 0.0467218
\(705\) −398400. −0.0301888
\(706\) −5.19888e6 −0.392553
\(707\) −1.90135e7 −1.43058
\(708\) −3.04986e6 −0.228663
\(709\) −1.39769e7 −1.04423 −0.522115 0.852875i \(-0.674857\pi\)
−0.522115 + 0.852875i \(0.674857\pi\)
\(710\) −5.00570e6 −0.372665
\(711\) 5.54972e6 0.411715
\(712\) −491264. −0.0363174
\(713\) 50255.0 0.00370216
\(714\) −4.68048e6 −0.343593
\(715\) 4.50750e6 0.329739
\(716\) −4.17062e6 −0.304031
\(717\) −1.04486e7 −0.759030
\(718\) −1.38114e6 −0.0999828
\(719\) −1.24469e7 −0.897925 −0.448963 0.893551i \(-0.648206\pi\)
−0.448963 + 0.893551i \(0.648206\pi\)
\(720\) 1.14560e6 0.0823572
\(721\) −1.35240e7 −0.968876
\(722\) 9.90246e6 0.706969
\(723\) 1.28784e7 0.916258
\(724\) 1.78394e6 0.126483
\(725\) −3.45312e6 −0.243987
\(726\) 4.43363e6 0.312189
\(727\) −1.24819e7 −0.875881 −0.437940 0.899004i \(-0.644292\pi\)
−0.437940 + 0.899004i \(0.644292\pi\)
\(728\) 1.53087e7 1.07056
\(729\) 3.61141e6 0.251686
\(730\) −1.66980e6 −0.115973
\(731\) −8.36724e6 −0.579147
\(732\) −5.63405e6 −0.388636
\(733\) −8.20260e6 −0.563886 −0.281943 0.959431i \(-0.590979\pi\)
−0.281943 + 0.959431i \(0.590979\pi\)
\(734\) −1.93533e7 −1.32591
\(735\) −4.55880e6 −0.311266
\(736\) 541696. 0.0368605
\(737\) −5.65695e6 −0.383631
\(738\) 1.47732e7 0.998469
\(739\) 1.56128e7 1.05164 0.525822 0.850594i \(-0.323758\pi\)
0.525822 + 0.850594i \(0.323758\pi\)
\(740\) 158800. 0.0106603
\(741\) 211552. 0.0141538
\(742\) 5.84980e6 0.390060
\(743\) −2.14835e7 −1.42769 −0.713843 0.700306i \(-0.753047\pi\)
−0.713843 + 0.700306i \(0.753047\pi\)
\(744\) 48640.0 0.00322152
\(745\) 3.75200e6 0.247669
\(746\) −1.21426e6 −0.0798851
\(747\) 1.25438e7 0.822483
\(748\) 1.76400e6 0.115278
\(749\) 3.18422e7 2.07395
\(750\) 500000. 0.0324576
\(751\) −1.39025e7 −0.899481 −0.449741 0.893159i \(-0.648484\pi\)
−0.449741 + 0.893159i \(0.648484\pi\)
\(752\) 509952. 0.0328840
\(753\) −9.10546e6 −0.585213
\(754\) −2.65642e7 −1.70164
\(755\) 1.15513e7 0.737502
\(756\) −1.07492e7 −0.684023
\(757\) −2.59152e7 −1.64367 −0.821835 0.569725i \(-0.807050\pi\)
−0.821835 + 0.569725i \(0.807050\pi\)
\(758\) 8.02114e6 0.507064
\(759\) −634800. −0.0399975
\(760\) −35200.0 −0.00221059
\(761\) −2.77075e7 −1.73434 −0.867172 0.498009i \(-0.834065\pi\)
−0.867172 + 0.498009i \(0.834065\pi\)
\(762\) −9.92832e6 −0.619424
\(763\) −2.37690e7 −1.47808
\(764\) 4.51251e6 0.279695
\(765\) 3.28912e6 0.203201
\(766\) 748332. 0.0460811
\(767\) 2.86401e7 1.75786
\(768\) 524288. 0.0320750
\(769\) 2.60919e7 1.59107 0.795535 0.605907i \(-0.207190\pi\)
0.795535 + 0.605907i \(0.207190\pi\)
\(770\) 2.98500e6 0.181434
\(771\) 1.72838e6 0.104714
\(772\) −1.72493e6 −0.104166
\(773\) −1.63038e7 −0.981388 −0.490694 0.871332i \(-0.663257\pi\)
−0.490694 + 0.871332i \(0.663257\pi\)
\(774\) −8.15094e6 −0.489053
\(775\) −59375.0 −0.00355099
\(776\) 9.60602e6 0.572650
\(777\) −632024. −0.0375561
\(778\) −1.90774e7 −1.12998
\(779\) −453926. −0.0268004
\(780\) 3.84640e6 0.226370
\(781\) −7.50855e6 −0.440482
\(782\) 1.55526e6 0.0909465
\(783\) 1.86524e7 1.08725
\(784\) 5.83526e6 0.339055
\(785\) 5.29518e6 0.306695
\(786\) 513920. 0.0296715
\(787\) 7.36100e6 0.423643 0.211822 0.977308i \(-0.432060\pi\)
0.211822 + 0.977308i \(0.432060\pi\)
\(788\) 6.68528e6 0.383534
\(789\) 1.27815e7 0.730955
\(790\) −3.10040e6 −0.176746
\(791\) 4.10917e7 2.33514
\(792\) 1.71840e6 0.0973445
\(793\) 5.29072e7 2.98767
\(794\) −1.04301e7 −0.587134
\(795\) 1.46980e6 0.0824784
\(796\) −5.15229e6 −0.288216
\(797\) 1.10916e7 0.618515 0.309257 0.950978i \(-0.399920\pi\)
0.309257 + 0.950978i \(0.399920\pi\)
\(798\) 140096. 0.00778787
\(799\) 1.46412e6 0.0811353
\(800\) −640000. −0.0353553
\(801\) −1.37400e6 −0.0756670
\(802\) 494392. 0.0271416
\(803\) −2.50470e6 −0.137078
\(804\) −4.82726e6 −0.263367
\(805\) 2.63178e6 0.143139
\(806\) −456760. −0.0247657
\(807\) 1.43884e7 0.777728
\(808\) 6.11488e6 0.329503
\(809\) 2.30394e6 0.123765 0.0618827 0.998083i \(-0.480290\pi\)
0.0618827 + 0.998083i \(0.480290\pi\)
\(810\) 1.64890e6 0.0883043
\(811\) 1.76030e7 0.939798 0.469899 0.882720i \(-0.344290\pi\)
0.469899 + 0.882720i \(0.344290\pi\)
\(812\) −1.75916e7 −0.936301
\(813\) −4.63220e6 −0.245788
\(814\) 238200. 0.0126003
\(815\) 2.98635e6 0.157488
\(816\) 1.50528e6 0.0791392
\(817\) 250448. 0.0131269
\(818\) 2.66478e7 1.39244
\(819\) 4.28164e7 2.23049
\(820\) −8.25320e6 −0.428635
\(821\) 9.04137e6 0.468141 0.234070 0.972220i \(-0.424795\pi\)
0.234070 + 0.972220i \(0.424795\pi\)
\(822\) −5.60301e6 −0.289229
\(823\) 8.44386e6 0.434552 0.217276 0.976110i \(-0.430283\pi\)
0.217276 + 0.976110i \(0.430283\pi\)
\(824\) 4.34944e6 0.223159
\(825\) 750000. 0.0383642
\(826\) 1.89663e7 0.967236
\(827\) 3.10957e6 0.158102 0.0790508 0.996871i \(-0.474811\pi\)
0.0790508 + 0.996871i \(0.474811\pi\)
\(828\) 1.51506e6 0.0767985
\(829\) −1.21126e6 −0.0612142 −0.0306071 0.999531i \(-0.509744\pi\)
−0.0306071 + 0.999531i \(0.509744\pi\)
\(830\) −7.00770e6 −0.353086
\(831\) −6.24827e6 −0.313875
\(832\) −4.92339e6 −0.246579
\(833\) 1.67536e7 0.836557
\(834\) −2.20989e6 −0.110016
\(835\) −7.79460e6 −0.386881
\(836\) −52800.0 −0.00261287
\(837\) 320720. 0.0158239
\(838\) 9.43065e6 0.463908
\(839\) −6.71229e6 −0.329204 −0.164602 0.986360i \(-0.552634\pi\)
−0.164602 + 0.986360i \(0.552634\pi\)
\(840\) 2.54720e6 0.124556
\(841\) 1.00145e7 0.488245
\(842\) −1.35030e7 −0.656372
\(843\) −2.08818e6 −0.101204
\(844\) 1.63565e7 0.790377
\(845\) −2.68378e7 −1.29302
\(846\) 1.42627e6 0.0685135
\(847\) −2.75716e7 −1.32055
\(848\) −1.88134e6 −0.0898418
\(849\) −1.52697e6 −0.0727044
\(850\) −1.83750e6 −0.0872328
\(851\) 210013. 0.00994082
\(852\) −6.40730e6 −0.302396
\(853\) 2.18153e7 1.02657 0.513286 0.858218i \(-0.328428\pi\)
0.513286 + 0.858218i \(0.328428\pi\)
\(854\) 3.50367e7 1.64391
\(855\) −98450.0 −0.00460575
\(856\) −1.02407e7 −0.477689
\(857\) −3.81073e7 −1.77238 −0.886188 0.463326i \(-0.846656\pi\)
−0.886188 + 0.463326i \(0.846656\pi\)
\(858\) 5.76960e6 0.267564
\(859\) 3.05903e7 1.41449 0.707245 0.706968i \(-0.249938\pi\)
0.707245 + 0.706968i \(0.249938\pi\)
\(860\) 4.55360e6 0.209947
\(861\) 3.28477e7 1.51007
\(862\) −8.17243e6 −0.374613
\(863\) −3.43749e7 −1.57114 −0.785570 0.618773i \(-0.787630\pi\)
−0.785570 + 0.618773i \(0.787630\pi\)
\(864\) 3.45702e6 0.157550
\(865\) −1.21296e7 −0.551196
\(866\) 2.18652e6 0.0990736
\(867\) −7.03706e6 −0.317939
\(868\) −302480. −0.0136269
\(869\) −4.65060e6 −0.208910
\(870\) −4.42000e6 −0.197981
\(871\) 4.53310e7 2.02465
\(872\) 7.64429e6 0.340444
\(873\) 2.68668e7 1.19311
\(874\) −46552.0 −0.00206139
\(875\) −3.10938e6 −0.137294
\(876\) −2.13734e6 −0.0941053
\(877\) −8.01422e6 −0.351854 −0.175927 0.984403i \(-0.556292\pi\)
−0.175927 + 0.984403i \(0.556292\pi\)
\(878\) −9.88973e6 −0.432960
\(879\) −6.15743e6 −0.268799
\(880\) −960000. −0.0417892
\(881\) −3.28421e7 −1.42558 −0.712788 0.701379i \(-0.752568\pi\)
−0.712788 + 0.701379i \(0.752568\pi\)
\(882\) 1.63205e7 0.706419
\(883\) 1.01380e6 0.0437573 0.0218787 0.999761i \(-0.493035\pi\)
0.0218787 + 0.999761i \(0.493035\pi\)
\(884\) −1.41355e7 −0.608389
\(885\) 4.76540e6 0.204523
\(886\) −1.47420e7 −0.630917
\(887\) 2.40446e7 1.02615 0.513073 0.858345i \(-0.328507\pi\)
0.513073 + 0.858345i \(0.328507\pi\)
\(888\) 203264. 0.00865024
\(889\) 6.17417e7 2.62014
\(890\) 767600. 0.0324833
\(891\) 2.47335e6 0.104374
\(892\) 1.71717e7 0.722607
\(893\) −43824.0 −0.00183901
\(894\) 4.80256e6 0.200969
\(895\) 6.51660e6 0.271934
\(896\) −3.26042e6 −0.135676
\(897\) 5.08686e6 0.211091
\(898\) −3.63358e6 −0.150364
\(899\) 524875. 0.0216599
\(900\) −1.79000e6 −0.0736626
\(901\) −5.40152e6 −0.221668
\(902\) −1.23798e7 −0.506637
\(903\) −1.81233e7 −0.739637
\(904\) −1.32154e7 −0.537849
\(905\) −2.78740e6 −0.113130
\(906\) 1.47857e7 0.598440
\(907\) 2.95798e7 1.19392 0.596962 0.802269i \(-0.296374\pi\)
0.596962 + 0.802269i \(0.296374\pi\)
\(908\) −8.51552e6 −0.342765
\(909\) 1.71026e7 0.686517
\(910\) −2.39198e7 −0.957534
\(911\) −1.68654e7 −0.673286 −0.336643 0.941632i \(-0.609292\pi\)
−0.336643 + 0.941632i \(0.609292\pi\)
\(912\) −45056.0 −0.00179376
\(913\) −1.05116e7 −0.417340
\(914\) −1.62652e6 −0.0644010
\(915\) 8.80320e6 0.347606
\(916\) 2.82918e6 0.111410
\(917\) −3.19594e6 −0.125509
\(918\) 9.92544e6 0.388726
\(919\) −4.24814e7 −1.65924 −0.829621 0.558327i \(-0.811443\pi\)
−0.829621 + 0.558327i \(0.811443\pi\)
\(920\) −846400. −0.0329690
\(921\) 4.41077e6 0.171343
\(922\) −2.70284e7 −1.04711
\(923\) 6.01685e7 2.32469
\(924\) 3.82080e6 0.147223
\(925\) −248125. −0.00953490
\(926\) −4.87566e6 −0.186855
\(927\) 1.21648e7 0.464951
\(928\) 5.65760e6 0.215656
\(929\) −1.06802e7 −0.406013 −0.203007 0.979177i \(-0.565071\pi\)
−0.203007 + 0.979177i \(0.565071\pi\)
\(930\) −76000.0 −0.00288142
\(931\) −501468. −0.0189613
\(932\) −7.08794e6 −0.267288
\(933\) −2.60712e7 −0.980520
\(934\) −2.32201e7 −0.870958
\(935\) −2.75625e6 −0.103107
\(936\) −1.37701e7 −0.513745
\(937\) −4.02213e7 −1.49661 −0.748303 0.663357i \(-0.769131\pi\)
−0.748303 + 0.663357i \(0.769131\pi\)
\(938\) 3.00195e7 1.11403
\(939\) 2.13703e6 0.0790946
\(940\) −796800. −0.0294123
\(941\) 1.05763e7 0.389366 0.194683 0.980866i \(-0.437632\pi\)
0.194683 + 0.980866i \(0.437632\pi\)
\(942\) 6.77782e6 0.248865
\(943\) −1.09149e7 −0.399704
\(944\) −6.09971e6 −0.222782
\(945\) 1.67956e7 0.611809
\(946\) 6.83040e6 0.248152
\(947\) 2.90132e7 1.05129 0.525643 0.850705i \(-0.323825\pi\)
0.525643 + 0.850705i \(0.323825\pi\)
\(948\) −3.96851e6 −0.143419
\(949\) 2.00710e7 0.723441
\(950\) 55000.0 0.00197721
\(951\) 1.93399e7 0.693429
\(952\) −9.36096e6 −0.334756
\(953\) 5.07650e7 1.81064 0.905320 0.424731i \(-0.139631\pi\)
0.905320 + 0.424731i \(0.139631\pi\)
\(954\) −5.26188e6 −0.187185
\(955\) −7.05080e6 −0.250167
\(956\) −2.08971e7 −0.739507
\(957\) −6.63000e6 −0.234010
\(958\) −1.71186e7 −0.602635
\(959\) 3.48437e7 1.22343
\(960\) −819200. −0.0286888
\(961\) −2.86201e7 −0.999685
\(962\) −1.90878e6 −0.0664993
\(963\) −2.86420e7 −0.995261
\(964\) 2.57569e7 0.892691
\(965\) 2.69520e6 0.0931693
\(966\) 3.36867e6 0.116149
\(967\) −2.26844e7 −0.780118 −0.390059 0.920790i \(-0.627545\pi\)
−0.390059 + 0.920790i \(0.627545\pi\)
\(968\) 8.86726e6 0.304159
\(969\) −129360. −0.00442579
\(970\) −1.50094e7 −0.512193
\(971\) 1.31840e7 0.448743 0.224372 0.974504i \(-0.427967\pi\)
0.224372 + 0.974504i \(0.427967\pi\)
\(972\) 1.52365e7 0.517272
\(973\) 1.37427e7 0.465362
\(974\) 1.10105e7 0.371886
\(975\) −6.01000e6 −0.202471
\(976\) −1.12681e7 −0.378640
\(977\) 2.68752e7 0.900772 0.450386 0.892834i \(-0.351286\pi\)
0.450386 + 0.892834i \(0.351286\pi\)
\(978\) 3.82253e6 0.127792
\(979\) 1.15140e6 0.0383945
\(980\) −9.11760e6 −0.303260
\(981\) 2.13801e7 0.709312
\(982\) −3.68552e7 −1.21961
\(983\) −1.10144e7 −0.363560 −0.181780 0.983339i \(-0.558186\pi\)
−0.181780 + 0.983339i \(0.558186\pi\)
\(984\) −1.05641e7 −0.347812
\(985\) −1.04458e7 −0.343043
\(986\) 1.62435e7 0.532093
\(987\) 3.17126e6 0.103619
\(988\) 423104. 0.0137897
\(989\) 6.02214e6 0.195776
\(990\) −2.68500e6 −0.0870675
\(991\) −3.37092e7 −1.09035 −0.545173 0.838323i \(-0.683536\pi\)
−0.545173 + 0.838323i \(0.683536\pi\)
\(992\) 97280.0 0.00313866
\(993\) −1.29852e7 −0.417904
\(994\) 3.98454e7 1.27912
\(995\) 8.05045e6 0.257788
\(996\) −8.96986e6 −0.286508
\(997\) 2.01824e7 0.643034 0.321517 0.946904i \(-0.395807\pi\)
0.321517 + 0.946904i \(0.395807\pi\)
\(998\) −3.14579e7 −0.999778
\(999\) 1.34027e6 0.0424893
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 230.6.a.a.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
230.6.a.a.1.1 1 1.1 even 1 trivial