Properties

Label 8001.2.a.z.1.4
Level 8001
Weight 2
Character 8001.1
Self dual Yes
Analytic conductor 63.888
Analytic rank 1
Dimension 32
CM No

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Newspace parameters

Level: \( N \) = \( 8001 = 3^{2} \cdot 7 \cdot 127 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8001.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.8883066572\)
Analytic rank: \(1\)
Dimension: \(32\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Character \(\chi\) = 8001.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.41110 q^{2}\) \(+3.81340 q^{4}\) \(-2.91376 q^{5}\) \(-1.00000 q^{7}\) \(-4.37229 q^{8}\) \(+O(q^{10})\) \(q\)\(-2.41110 q^{2}\) \(+3.81340 q^{4}\) \(-2.91376 q^{5}\) \(-1.00000 q^{7}\) \(-4.37229 q^{8}\) \(+7.02536 q^{10}\) \(+4.84187 q^{11}\) \(-5.92231 q^{13}\) \(+2.41110 q^{14}\) \(+2.91522 q^{16}\) \(+7.70060 q^{17}\) \(-7.16283 q^{19}\) \(-11.1113 q^{20}\) \(-11.6742 q^{22}\) \(-6.74473 q^{23}\) \(+3.48998 q^{25}\) \(+14.2793 q^{26}\) \(-3.81340 q^{28}\) \(+1.16404 q^{29}\) \(-3.19532 q^{31}\) \(+1.71568 q^{32}\) \(-18.5669 q^{34}\) \(+2.91376 q^{35}\) \(+6.23173 q^{37}\) \(+17.2703 q^{38}\) \(+12.7398 q^{40}\) \(-1.69054 q^{41}\) \(+10.5590 q^{43}\) \(+18.4640 q^{44}\) \(+16.2622 q^{46}\) \(+4.01302 q^{47}\) \(+1.00000 q^{49}\) \(-8.41468 q^{50}\) \(-22.5841 q^{52}\) \(+4.73182 q^{53}\) \(-14.1080 q^{55}\) \(+4.37229 q^{56}\) \(-2.80661 q^{58}\) \(+1.42000 q^{59}\) \(+5.30923 q^{61}\) \(+7.70423 q^{62}\) \(-9.96713 q^{64}\) \(+17.2562 q^{65}\) \(+0.727254 q^{67}\) \(+29.3655 q^{68}\) \(-7.02536 q^{70}\) \(-6.03872 q^{71}\) \(-7.68043 q^{73}\) \(-15.0253 q^{74}\) \(-27.3148 q^{76}\) \(-4.84187 q^{77}\) \(-4.20331 q^{79}\) \(-8.49425 q^{80}\) \(+4.07607 q^{82}\) \(-14.0855 q^{83}\) \(-22.4377 q^{85}\) \(-25.4588 q^{86}\) \(-21.1701 q^{88}\) \(+13.2348 q^{89}\) \(+5.92231 q^{91}\) \(-25.7204 q^{92}\) \(-9.67580 q^{94}\) \(+20.8708 q^{95}\) \(-0.0256030 q^{97}\) \(-2.41110 q^{98}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(32q \) \(\mathstrut +\mathstrut 30q^{4} \) \(\mathstrut -\mathstrut 32q^{7} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(32q \) \(\mathstrut +\mathstrut 30q^{4} \) \(\mathstrut -\mathstrut 32q^{7} \) \(\mathstrut -\mathstrut 16q^{10} \) \(\mathstrut -\mathstrut 14q^{13} \) \(\mathstrut +\mathstrut 18q^{16} \) \(\mathstrut -\mathstrut 30q^{19} \) \(\mathstrut -\mathstrut 10q^{22} \) \(\mathstrut +\mathstrut 36q^{25} \) \(\mathstrut -\mathstrut 30q^{28} \) \(\mathstrut -\mathstrut 58q^{31} \) \(\mathstrut -\mathstrut 34q^{34} \) \(\mathstrut +\mathstrut 8q^{37} \) \(\mathstrut -\mathstrut 34q^{40} \) \(\mathstrut +\mathstrut 6q^{43} \) \(\mathstrut -\mathstrut 36q^{46} \) \(\mathstrut +\mathstrut 32q^{49} \) \(\mathstrut -\mathstrut 56q^{52} \) \(\mathstrut -\mathstrut 88q^{55} \) \(\mathstrut -\mathstrut 22q^{58} \) \(\mathstrut -\mathstrut 46q^{61} \) \(\mathstrut +\mathstrut 20q^{64} \) \(\mathstrut -\mathstrut 8q^{67} \) \(\mathstrut +\mathstrut 16q^{70} \) \(\mathstrut -\mathstrut 60q^{73} \) \(\mathstrut -\mathstrut 128q^{76} \) \(\mathstrut -\mathstrut 74q^{79} \) \(\mathstrut -\mathstrut 52q^{82} \) \(\mathstrut -\mathstrut 16q^{85} \) \(\mathstrut -\mathstrut 64q^{88} \) \(\mathstrut +\mathstrut 14q^{91} \) \(\mathstrut -\mathstrut 58q^{94} \) \(\mathstrut -\mathstrut 44q^{97} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.41110 −1.70490 −0.852452 0.522805i \(-0.824886\pi\)
−0.852452 + 0.522805i \(0.824886\pi\)
\(3\) 0 0
\(4\) 3.81340 1.90670
\(5\) −2.91376 −1.30307 −0.651536 0.758618i \(-0.725875\pi\)
−0.651536 + 0.758618i \(0.725875\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) −4.37229 −1.54584
\(9\) 0 0
\(10\) 7.02536 2.22161
\(11\) 4.84187 1.45988 0.729940 0.683512i \(-0.239548\pi\)
0.729940 + 0.683512i \(0.239548\pi\)
\(12\) 0 0
\(13\) −5.92231 −1.64255 −0.821277 0.570530i \(-0.806738\pi\)
−0.821277 + 0.570530i \(0.806738\pi\)
\(14\) 2.41110 0.644393
\(15\) 0 0
\(16\) 2.91522 0.728806
\(17\) 7.70060 1.86767 0.933835 0.357705i \(-0.116441\pi\)
0.933835 + 0.357705i \(0.116441\pi\)
\(18\) 0 0
\(19\) −7.16283 −1.64327 −0.821633 0.570016i \(-0.806937\pi\)
−0.821633 + 0.570016i \(0.806937\pi\)
\(20\) −11.1113 −2.48457
\(21\) 0 0
\(22\) −11.6742 −2.48896
\(23\) −6.74473 −1.40637 −0.703187 0.711005i \(-0.748240\pi\)
−0.703187 + 0.711005i \(0.748240\pi\)
\(24\) 0 0
\(25\) 3.48998 0.697995
\(26\) 14.2793 2.80040
\(27\) 0 0
\(28\) −3.81340 −0.720665
\(29\) 1.16404 0.216156 0.108078 0.994142i \(-0.465530\pi\)
0.108078 + 0.994142i \(0.465530\pi\)
\(30\) 0 0
\(31\) −3.19532 −0.573896 −0.286948 0.957946i \(-0.592641\pi\)
−0.286948 + 0.957946i \(0.592641\pi\)
\(32\) 1.71568 0.303293
\(33\) 0 0
\(34\) −18.5669 −3.18420
\(35\) 2.91376 0.492515
\(36\) 0 0
\(37\) 6.23173 1.02449 0.512245 0.858840i \(-0.328814\pi\)
0.512245 + 0.858840i \(0.328814\pi\)
\(38\) 17.2703 2.80161
\(39\) 0 0
\(40\) 12.7398 2.01434
\(41\) −1.69054 −0.264019 −0.132009 0.991248i \(-0.542143\pi\)
−0.132009 + 0.991248i \(0.542143\pi\)
\(42\) 0 0
\(43\) 10.5590 1.61023 0.805115 0.593119i \(-0.202104\pi\)
0.805115 + 0.593119i \(0.202104\pi\)
\(44\) 18.4640 2.78355
\(45\) 0 0
\(46\) 16.2622 2.39773
\(47\) 4.01302 0.585359 0.292680 0.956211i \(-0.405453\pi\)
0.292680 + 0.956211i \(0.405453\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) −8.41468 −1.19002
\(51\) 0 0
\(52\) −22.5841 −3.13186
\(53\) 4.73182 0.649965 0.324982 0.945720i \(-0.394642\pi\)
0.324982 + 0.945720i \(0.394642\pi\)
\(54\) 0 0
\(55\) −14.1080 −1.90233
\(56\) 4.37229 0.584272
\(57\) 0 0
\(58\) −2.80661 −0.368526
\(59\) 1.42000 0.184868 0.0924338 0.995719i \(-0.470535\pi\)
0.0924338 + 0.995719i \(0.470535\pi\)
\(60\) 0 0
\(61\) 5.30923 0.679777 0.339888 0.940466i \(-0.389611\pi\)
0.339888 + 0.940466i \(0.389611\pi\)
\(62\) 7.70423 0.978439
\(63\) 0 0
\(64\) −9.96713 −1.24589
\(65\) 17.2562 2.14036
\(66\) 0 0
\(67\) 0.727254 0.0888482 0.0444241 0.999013i \(-0.485855\pi\)
0.0444241 + 0.999013i \(0.485855\pi\)
\(68\) 29.3655 3.56109
\(69\) 0 0
\(70\) −7.02536 −0.839691
\(71\) −6.03872 −0.716664 −0.358332 0.933594i \(-0.616654\pi\)
−0.358332 + 0.933594i \(0.616654\pi\)
\(72\) 0 0
\(73\) −7.68043 −0.898926 −0.449463 0.893299i \(-0.648385\pi\)
−0.449463 + 0.893299i \(0.648385\pi\)
\(74\) −15.0253 −1.74666
\(75\) 0 0
\(76\) −27.3148 −3.13322
\(77\) −4.84187 −0.551782
\(78\) 0 0
\(79\) −4.20331 −0.472909 −0.236455 0.971643i \(-0.575985\pi\)
−0.236455 + 0.971643i \(0.575985\pi\)
\(80\) −8.49425 −0.949686
\(81\) 0 0
\(82\) 4.07607 0.450127
\(83\) −14.0855 −1.54608 −0.773040 0.634358i \(-0.781265\pi\)
−0.773040 + 0.634358i \(0.781265\pi\)
\(84\) 0 0
\(85\) −22.4377 −2.43371
\(86\) −25.4588 −2.74529
\(87\) 0 0
\(88\) −21.1701 −2.25674
\(89\) 13.2348 1.40289 0.701444 0.712725i \(-0.252539\pi\)
0.701444 + 0.712725i \(0.252539\pi\)
\(90\) 0 0
\(91\) 5.92231 0.620827
\(92\) −25.7204 −2.68153
\(93\) 0 0
\(94\) −9.67580 −0.997982
\(95\) 20.8708 2.14129
\(96\) 0 0
\(97\) −0.0256030 −0.00259960 −0.00129980 0.999999i \(-0.500414\pi\)
−0.00129980 + 0.999999i \(0.500414\pi\)
\(98\) −2.41110 −0.243558
\(99\) 0 0
\(100\) 13.3087 1.33087
\(101\) −8.54546 −0.850305 −0.425152 0.905122i \(-0.639780\pi\)
−0.425152 + 0.905122i \(0.639780\pi\)
\(102\) 0 0
\(103\) −12.8304 −1.26421 −0.632107 0.774881i \(-0.717810\pi\)
−0.632107 + 0.774881i \(0.717810\pi\)
\(104\) 25.8941 2.53912
\(105\) 0 0
\(106\) −11.4089 −1.10813
\(107\) 14.8632 1.43688 0.718441 0.695587i \(-0.244856\pi\)
0.718441 + 0.695587i \(0.244856\pi\)
\(108\) 0 0
\(109\) 2.94497 0.282077 0.141039 0.990004i \(-0.454956\pi\)
0.141039 + 0.990004i \(0.454956\pi\)
\(110\) 34.0159 3.24329
\(111\) 0 0
\(112\) −2.91522 −0.275463
\(113\) 10.5406 0.991577 0.495789 0.868443i \(-0.334879\pi\)
0.495789 + 0.868443i \(0.334879\pi\)
\(114\) 0 0
\(115\) 19.6525 1.83260
\(116\) 4.43894 0.412145
\(117\) 0 0
\(118\) −3.42375 −0.315182
\(119\) −7.70060 −0.705913
\(120\) 0 0
\(121\) 12.4437 1.13125
\(122\) −12.8011 −1.15895
\(123\) 0 0
\(124\) −12.1850 −1.09425
\(125\) 4.39984 0.393534
\(126\) 0 0
\(127\) −1.00000 −0.0887357
\(128\) 20.6004 1.82083
\(129\) 0 0
\(130\) −41.6064 −3.64912
\(131\) −19.9073 −1.73931 −0.869655 0.493659i \(-0.835659\pi\)
−0.869655 + 0.493659i \(0.835659\pi\)
\(132\) 0 0
\(133\) 7.16283 0.621096
\(134\) −1.75348 −0.151478
\(135\) 0 0
\(136\) −33.6692 −2.88711
\(137\) −1.07424 −0.0917787 −0.0458894 0.998947i \(-0.514612\pi\)
−0.0458894 + 0.998947i \(0.514612\pi\)
\(138\) 0 0
\(139\) −5.35399 −0.454120 −0.227060 0.973881i \(-0.572911\pi\)
−0.227060 + 0.973881i \(0.572911\pi\)
\(140\) 11.1113 0.939078
\(141\) 0 0
\(142\) 14.5600 1.22184
\(143\) −28.6751 −2.39793
\(144\) 0 0
\(145\) −3.39172 −0.281667
\(146\) 18.5183 1.53258
\(147\) 0 0
\(148\) 23.7641 1.95339
\(149\) 3.75043 0.307247 0.153623 0.988129i \(-0.450906\pi\)
0.153623 + 0.988129i \(0.450906\pi\)
\(150\) 0 0
\(151\) −3.64734 −0.296817 −0.148408 0.988926i \(-0.547415\pi\)
−0.148408 + 0.988926i \(0.547415\pi\)
\(152\) 31.3180 2.54022
\(153\) 0 0
\(154\) 11.6742 0.940737
\(155\) 9.31038 0.747828
\(156\) 0 0
\(157\) 17.4878 1.39568 0.697841 0.716253i \(-0.254144\pi\)
0.697841 + 0.716253i \(0.254144\pi\)
\(158\) 10.1346 0.806265
\(159\) 0 0
\(160\) −4.99909 −0.395213
\(161\) 6.74473 0.531559
\(162\) 0 0
\(163\) −5.22206 −0.409023 −0.204512 0.978864i \(-0.565561\pi\)
−0.204512 + 0.978864i \(0.565561\pi\)
\(164\) −6.44672 −0.503405
\(165\) 0 0
\(166\) 33.9614 2.63592
\(167\) −10.5060 −0.812979 −0.406489 0.913655i \(-0.633247\pi\)
−0.406489 + 0.913655i \(0.633247\pi\)
\(168\) 0 0
\(169\) 22.0738 1.69798
\(170\) 54.0994 4.14924
\(171\) 0 0
\(172\) 40.2656 3.07023
\(173\) 1.45272 0.110448 0.0552240 0.998474i \(-0.482413\pi\)
0.0552240 + 0.998474i \(0.482413\pi\)
\(174\) 0 0
\(175\) −3.48998 −0.263817
\(176\) 14.1151 1.06397
\(177\) 0 0
\(178\) −31.9105 −2.39179
\(179\) 15.7102 1.17423 0.587117 0.809502i \(-0.300263\pi\)
0.587117 + 0.809502i \(0.300263\pi\)
\(180\) 0 0
\(181\) 17.3252 1.28777 0.643886 0.765121i \(-0.277321\pi\)
0.643886 + 0.765121i \(0.277321\pi\)
\(182\) −14.2793 −1.05845
\(183\) 0 0
\(184\) 29.4899 2.17403
\(185\) −18.1577 −1.33498
\(186\) 0 0
\(187\) 37.2853 2.72657
\(188\) 15.3033 1.11611
\(189\) 0 0
\(190\) −50.3215 −3.65070
\(191\) −10.6002 −0.767002 −0.383501 0.923541i \(-0.625282\pi\)
−0.383501 + 0.923541i \(0.625282\pi\)
\(192\) 0 0
\(193\) 25.0481 1.80300 0.901500 0.432779i \(-0.142467\pi\)
0.901500 + 0.432779i \(0.142467\pi\)
\(194\) 0.0617315 0.00443206
\(195\) 0 0
\(196\) 3.81340 0.272386
\(197\) 14.5870 1.03928 0.519641 0.854385i \(-0.326066\pi\)
0.519641 + 0.854385i \(0.326066\pi\)
\(198\) 0 0
\(199\) 19.8687 1.40846 0.704228 0.709974i \(-0.251293\pi\)
0.704228 + 0.709974i \(0.251293\pi\)
\(200\) −15.2592 −1.07899
\(201\) 0 0
\(202\) 20.6039 1.44969
\(203\) −1.16404 −0.0816994
\(204\) 0 0
\(205\) 4.92584 0.344035
\(206\) 30.9353 2.15537
\(207\) 0 0
\(208\) −17.2649 −1.19710
\(209\) −34.6815 −2.39897
\(210\) 0 0
\(211\) −16.8972 −1.16325 −0.581624 0.813458i \(-0.697582\pi\)
−0.581624 + 0.813458i \(0.697582\pi\)
\(212\) 18.0443 1.23929
\(213\) 0 0
\(214\) −35.8367 −2.44975
\(215\) −30.7663 −2.09824
\(216\) 0 0
\(217\) 3.19532 0.216912
\(218\) −7.10062 −0.480914
\(219\) 0 0
\(220\) −53.7996 −3.62717
\(221\) −45.6053 −3.06775
\(222\) 0 0
\(223\) −3.68685 −0.246890 −0.123445 0.992351i \(-0.539394\pi\)
−0.123445 + 0.992351i \(0.539394\pi\)
\(224\) −1.71568 −0.114634
\(225\) 0 0
\(226\) −25.4145 −1.69054
\(227\) 23.4616 1.55720 0.778602 0.627518i \(-0.215929\pi\)
0.778602 + 0.627518i \(0.215929\pi\)
\(228\) 0 0
\(229\) −25.9869 −1.71726 −0.858631 0.512595i \(-0.828684\pi\)
−0.858631 + 0.512595i \(0.828684\pi\)
\(230\) −47.3841 −3.12442
\(231\) 0 0
\(232\) −5.08951 −0.334143
\(233\) −24.6677 −1.61604 −0.808018 0.589158i \(-0.799459\pi\)
−0.808018 + 0.589158i \(0.799459\pi\)
\(234\) 0 0
\(235\) −11.6930 −0.762765
\(236\) 5.41501 0.352487
\(237\) 0 0
\(238\) 18.5669 1.20351
\(239\) 20.9419 1.35462 0.677310 0.735698i \(-0.263146\pi\)
0.677310 + 0.735698i \(0.263146\pi\)
\(240\) 0 0
\(241\) −2.75038 −0.177167 −0.0885837 0.996069i \(-0.528234\pi\)
−0.0885837 + 0.996069i \(0.528234\pi\)
\(242\) −30.0031 −1.92867
\(243\) 0 0
\(244\) 20.2462 1.29613
\(245\) −2.91376 −0.186153
\(246\) 0 0
\(247\) 42.4205 2.69915
\(248\) 13.9709 0.887151
\(249\) 0 0
\(250\) −10.6085 −0.670937
\(251\) 12.4711 0.787171 0.393586 0.919288i \(-0.371234\pi\)
0.393586 + 0.919288i \(0.371234\pi\)
\(252\) 0 0
\(253\) −32.6571 −2.05314
\(254\) 2.41110 0.151286
\(255\) 0 0
\(256\) −29.7353 −1.85846
\(257\) 27.8640 1.73811 0.869053 0.494718i \(-0.164729\pi\)
0.869053 + 0.494718i \(0.164729\pi\)
\(258\) 0 0
\(259\) −6.23173 −0.387221
\(260\) 65.8047 4.08103
\(261\) 0 0
\(262\) 47.9985 2.96536
\(263\) −9.19650 −0.567081 −0.283540 0.958960i \(-0.591509\pi\)
−0.283540 + 0.958960i \(0.591509\pi\)
\(264\) 0 0
\(265\) −13.7874 −0.846951
\(266\) −17.2703 −1.05891
\(267\) 0 0
\(268\) 2.77331 0.169407
\(269\) −16.8197 −1.02552 −0.512759 0.858533i \(-0.671376\pi\)
−0.512759 + 0.858533i \(0.671376\pi\)
\(270\) 0 0
\(271\) −2.27897 −0.138438 −0.0692188 0.997602i \(-0.522051\pi\)
−0.0692188 + 0.997602i \(0.522051\pi\)
\(272\) 22.4490 1.36117
\(273\) 0 0
\(274\) 2.59011 0.156474
\(275\) 16.8980 1.01899
\(276\) 0 0
\(277\) 2.00040 0.120192 0.0600961 0.998193i \(-0.480859\pi\)
0.0600961 + 0.998193i \(0.480859\pi\)
\(278\) 12.9090 0.774231
\(279\) 0 0
\(280\) −12.7398 −0.761348
\(281\) 14.6564 0.874325 0.437162 0.899383i \(-0.355984\pi\)
0.437162 + 0.899383i \(0.355984\pi\)
\(282\) 0 0
\(283\) −21.9212 −1.30308 −0.651539 0.758615i \(-0.725876\pi\)
−0.651539 + 0.758615i \(0.725876\pi\)
\(284\) −23.0281 −1.36646
\(285\) 0 0
\(286\) 69.1385 4.08824
\(287\) 1.69054 0.0997897
\(288\) 0 0
\(289\) 42.2992 2.48819
\(290\) 8.17778 0.480216
\(291\) 0 0
\(292\) −29.2885 −1.71398
\(293\) 15.8863 0.928089 0.464044 0.885812i \(-0.346398\pi\)
0.464044 + 0.885812i \(0.346398\pi\)
\(294\) 0 0
\(295\) −4.13752 −0.240896
\(296\) −27.2469 −1.58369
\(297\) 0 0
\(298\) −9.04265 −0.523827
\(299\) 39.9444 2.31004
\(300\) 0 0
\(301\) −10.5590 −0.608610
\(302\) 8.79411 0.506044
\(303\) 0 0
\(304\) −20.8813 −1.19762
\(305\) −15.4698 −0.885798
\(306\) 0 0
\(307\) −16.9610 −0.968014 −0.484007 0.875064i \(-0.660819\pi\)
−0.484007 + 0.875064i \(0.660819\pi\)
\(308\) −18.4640 −1.05208
\(309\) 0 0
\(310\) −22.4483 −1.27498
\(311\) 10.4649 0.593408 0.296704 0.954969i \(-0.404112\pi\)
0.296704 + 0.954969i \(0.404112\pi\)
\(312\) 0 0
\(313\) 12.9768 0.733494 0.366747 0.930321i \(-0.380471\pi\)
0.366747 + 0.930321i \(0.380471\pi\)
\(314\) −42.1649 −2.37950
\(315\) 0 0
\(316\) −16.0289 −0.901696
\(317\) −33.4039 −1.87615 −0.938076 0.346430i \(-0.887394\pi\)
−0.938076 + 0.346430i \(0.887394\pi\)
\(318\) 0 0
\(319\) 5.63612 0.315562
\(320\) 29.0418 1.62349
\(321\) 0 0
\(322\) −16.2622 −0.906258
\(323\) −55.1581 −3.06908
\(324\) 0 0
\(325\) −20.6687 −1.14649
\(326\) 12.5909 0.697346
\(327\) 0 0
\(328\) 7.39155 0.408130
\(329\) −4.01302 −0.221245
\(330\) 0 0
\(331\) −16.8998 −0.928896 −0.464448 0.885600i \(-0.653747\pi\)
−0.464448 + 0.885600i \(0.653747\pi\)
\(332\) −53.7135 −2.94791
\(333\) 0 0
\(334\) 25.3310 1.38605
\(335\) −2.11904 −0.115776
\(336\) 0 0
\(337\) 21.1038 1.14960 0.574799 0.818295i \(-0.305080\pi\)
0.574799 + 0.818295i \(0.305080\pi\)
\(338\) −53.2221 −2.89490
\(339\) 0 0
\(340\) −85.5638 −4.64035
\(341\) −15.4713 −0.837819
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) −46.1669 −2.48915
\(345\) 0 0
\(346\) −3.50264 −0.188303
\(347\) −14.5910 −0.783287 −0.391644 0.920117i \(-0.628093\pi\)
−0.391644 + 0.920117i \(0.628093\pi\)
\(348\) 0 0
\(349\) 2.54477 0.136218 0.0681091 0.997678i \(-0.478303\pi\)
0.0681091 + 0.997678i \(0.478303\pi\)
\(350\) 8.41468 0.449784
\(351\) 0 0
\(352\) 8.30712 0.442771
\(353\) 34.5501 1.83892 0.919458 0.393188i \(-0.128628\pi\)
0.919458 + 0.393188i \(0.128628\pi\)
\(354\) 0 0
\(355\) 17.5954 0.933864
\(356\) 50.4697 2.67489
\(357\) 0 0
\(358\) −37.8788 −2.00196
\(359\) 11.9986 0.633260 0.316630 0.948549i \(-0.397449\pi\)
0.316630 + 0.948549i \(0.397449\pi\)
\(360\) 0 0
\(361\) 32.3062 1.70033
\(362\) −41.7728 −2.19553
\(363\) 0 0
\(364\) 22.5841 1.18373
\(365\) 22.3789 1.17136
\(366\) 0 0
\(367\) −3.64367 −0.190198 −0.0950989 0.995468i \(-0.530317\pi\)
−0.0950989 + 0.995468i \(0.530317\pi\)
\(368\) −19.6624 −1.02497
\(369\) 0 0
\(370\) 43.7801 2.27602
\(371\) −4.73182 −0.245664
\(372\) 0 0
\(373\) 20.2311 1.04753 0.523765 0.851863i \(-0.324527\pi\)
0.523765 + 0.851863i \(0.324527\pi\)
\(374\) −89.8986 −4.64854
\(375\) 0 0
\(376\) −17.5461 −0.904871
\(377\) −6.89379 −0.355048
\(378\) 0 0
\(379\) −19.3071 −0.991739 −0.495870 0.868397i \(-0.665151\pi\)
−0.495870 + 0.868397i \(0.665151\pi\)
\(380\) 79.5886 4.08281
\(381\) 0 0
\(382\) 25.5581 1.30767
\(383\) −17.7304 −0.905981 −0.452991 0.891515i \(-0.649643\pi\)
−0.452991 + 0.891515i \(0.649643\pi\)
\(384\) 0 0
\(385\) 14.1080 0.719012
\(386\) −60.3934 −3.07394
\(387\) 0 0
\(388\) −0.0976347 −0.00495665
\(389\) −31.0388 −1.57373 −0.786865 0.617125i \(-0.788297\pi\)
−0.786865 + 0.617125i \(0.788297\pi\)
\(390\) 0 0
\(391\) −51.9384 −2.62664
\(392\) −4.37229 −0.220834
\(393\) 0 0
\(394\) −35.1708 −1.77188
\(395\) 12.2474 0.616234
\(396\) 0 0
\(397\) −6.66235 −0.334374 −0.167187 0.985925i \(-0.553468\pi\)
−0.167187 + 0.985925i \(0.553468\pi\)
\(398\) −47.9054 −2.40128
\(399\) 0 0
\(400\) 10.1741 0.508703
\(401\) −28.5013 −1.42329 −0.711643 0.702541i \(-0.752049\pi\)
−0.711643 + 0.702541i \(0.752049\pi\)
\(402\) 0 0
\(403\) 18.9237 0.942655
\(404\) −32.5873 −1.62128
\(405\) 0 0
\(406\) 2.80661 0.139290
\(407\) 30.1732 1.49563
\(408\) 0 0
\(409\) −26.0751 −1.28933 −0.644665 0.764465i \(-0.723003\pi\)
−0.644665 + 0.764465i \(0.723003\pi\)
\(410\) −11.8767 −0.586547
\(411\) 0 0
\(412\) −48.9274 −2.41048
\(413\) −1.42000 −0.0698734
\(414\) 0 0
\(415\) 41.0416 2.01465
\(416\) −10.1608 −0.498175
\(417\) 0 0
\(418\) 83.6206 4.09002
\(419\) −15.1006 −0.737714 −0.368857 0.929486i \(-0.620251\pi\)
−0.368857 + 0.929486i \(0.620251\pi\)
\(420\) 0 0
\(421\) −7.28830 −0.355210 −0.177605 0.984102i \(-0.556835\pi\)
−0.177605 + 0.984102i \(0.556835\pi\)
\(422\) 40.7407 1.98323
\(423\) 0 0
\(424\) −20.6889 −1.00474
\(425\) 26.8749 1.30362
\(426\) 0 0
\(427\) −5.30923 −0.256931
\(428\) 56.6795 2.73971
\(429\) 0 0
\(430\) 74.1806 3.57731
\(431\) −18.7701 −0.904123 −0.452062 0.891987i \(-0.649311\pi\)
−0.452062 + 0.891987i \(0.649311\pi\)
\(432\) 0 0
\(433\) −31.2440 −1.50149 −0.750747 0.660590i \(-0.770306\pi\)
−0.750747 + 0.660590i \(0.770306\pi\)
\(434\) −7.70423 −0.369815
\(435\) 0 0
\(436\) 11.2304 0.537836
\(437\) 48.3114 2.31105
\(438\) 0 0
\(439\) −13.7246 −0.655039 −0.327520 0.944844i \(-0.606213\pi\)
−0.327520 + 0.944844i \(0.606213\pi\)
\(440\) 61.6844 2.94069
\(441\) 0 0
\(442\) 109.959 5.23022
\(443\) 30.9731 1.47158 0.735789 0.677211i \(-0.236811\pi\)
0.735789 + 0.677211i \(0.236811\pi\)
\(444\) 0 0
\(445\) −38.5630 −1.82806
\(446\) 8.88936 0.420923
\(447\) 0 0
\(448\) 9.96713 0.470903
\(449\) −18.9463 −0.894130 −0.447065 0.894502i \(-0.647531\pi\)
−0.447065 + 0.894502i \(0.647531\pi\)
\(450\) 0 0
\(451\) −8.18540 −0.385435
\(452\) 40.1956 1.89064
\(453\) 0 0
\(454\) −56.5684 −2.65488
\(455\) −17.2562 −0.808982
\(456\) 0 0
\(457\) −6.49341 −0.303749 −0.151874 0.988400i \(-0.548531\pi\)
−0.151874 + 0.988400i \(0.548531\pi\)
\(458\) 62.6570 2.92777
\(459\) 0 0
\(460\) 74.9429 3.49423
\(461\) 28.4651 1.32575 0.662876 0.748729i \(-0.269336\pi\)
0.662876 + 0.748729i \(0.269336\pi\)
\(462\) 0 0
\(463\) −4.49350 −0.208831 −0.104415 0.994534i \(-0.533297\pi\)
−0.104415 + 0.994534i \(0.533297\pi\)
\(464\) 3.39343 0.157536
\(465\) 0 0
\(466\) 59.4763 2.75519
\(467\) −1.30117 −0.0602111 −0.0301055 0.999547i \(-0.509584\pi\)
−0.0301055 + 0.999547i \(0.509584\pi\)
\(468\) 0 0
\(469\) −0.727254 −0.0335815
\(470\) 28.1929 1.30044
\(471\) 0 0
\(472\) −6.20863 −0.285775
\(473\) 51.1252 2.35074
\(474\) 0 0
\(475\) −24.9981 −1.14699
\(476\) −29.3655 −1.34596
\(477\) 0 0
\(478\) −50.4930 −2.30950
\(479\) 24.2021 1.10582 0.552910 0.833241i \(-0.313517\pi\)
0.552910 + 0.833241i \(0.313517\pi\)
\(480\) 0 0
\(481\) −36.9062 −1.68278
\(482\) 6.63143 0.302054
\(483\) 0 0
\(484\) 47.4529 2.15695
\(485\) 0.0746010 0.00338746
\(486\) 0 0
\(487\) −16.8759 −0.764722 −0.382361 0.924013i \(-0.624889\pi\)
−0.382361 + 0.924013i \(0.624889\pi\)
\(488\) −23.2135 −1.05082
\(489\) 0 0
\(490\) 7.02536 0.317373
\(491\) 5.48154 0.247379 0.123689 0.992321i \(-0.460527\pi\)
0.123689 + 0.992321i \(0.460527\pi\)
\(492\) 0 0
\(493\) 8.96378 0.403709
\(494\) −102.280 −4.60180
\(495\) 0 0
\(496\) −9.31507 −0.418259
\(497\) 6.03872 0.270874
\(498\) 0 0
\(499\) −18.1726 −0.813517 −0.406759 0.913536i \(-0.633341\pi\)
−0.406759 + 0.913536i \(0.633341\pi\)
\(500\) 16.7784 0.750351
\(501\) 0 0
\(502\) −30.0692 −1.34205
\(503\) 12.4515 0.555183 0.277592 0.960699i \(-0.410464\pi\)
0.277592 + 0.960699i \(0.410464\pi\)
\(504\) 0 0
\(505\) 24.8994 1.10801
\(506\) 78.7396 3.50040
\(507\) 0 0
\(508\) −3.81340 −0.169192
\(509\) −20.7279 −0.918749 −0.459375 0.888243i \(-0.651926\pi\)
−0.459375 + 0.888243i \(0.651926\pi\)
\(510\) 0 0
\(511\) 7.68043 0.339762
\(512\) 30.4940 1.34766
\(513\) 0 0
\(514\) −67.1828 −2.96331
\(515\) 37.3846 1.64736
\(516\) 0 0
\(517\) 19.4305 0.854554
\(518\) 15.0253 0.660174
\(519\) 0 0
\(520\) −75.4490 −3.30866
\(521\) −31.8644 −1.39600 −0.698002 0.716096i \(-0.745927\pi\)
−0.698002 + 0.716096i \(0.745927\pi\)
\(522\) 0 0
\(523\) 31.9579 1.39742 0.698710 0.715405i \(-0.253758\pi\)
0.698710 + 0.715405i \(0.253758\pi\)
\(524\) −75.9146 −3.31634
\(525\) 0 0
\(526\) 22.1737 0.966819
\(527\) −24.6059 −1.07185
\(528\) 0 0
\(529\) 22.4914 0.977886
\(530\) 33.2427 1.44397
\(531\) 0 0
\(532\) 27.3148 1.18424
\(533\) 10.0119 0.433665
\(534\) 0 0
\(535\) −43.3078 −1.87236
\(536\) −3.17977 −0.137345
\(537\) 0 0
\(538\) 40.5541 1.74841
\(539\) 4.84187 0.208554
\(540\) 0 0
\(541\) −43.1995 −1.85729 −0.928646 0.370967i \(-0.879026\pi\)
−0.928646 + 0.370967i \(0.879026\pi\)
\(542\) 5.49482 0.236023
\(543\) 0 0
\(544\) 13.2118 0.566451
\(545\) −8.58093 −0.367567
\(546\) 0 0
\(547\) 6.00358 0.256695 0.128347 0.991729i \(-0.459033\pi\)
0.128347 + 0.991729i \(0.459033\pi\)
\(548\) −4.09652 −0.174995
\(549\) 0 0
\(550\) −40.7428 −1.73728
\(551\) −8.33781 −0.355203
\(552\) 0 0
\(553\) 4.20331 0.178743
\(554\) −4.82316 −0.204916
\(555\) 0 0
\(556\) −20.4169 −0.865870
\(557\) 11.8692 0.502914 0.251457 0.967868i \(-0.419090\pi\)
0.251457 + 0.967868i \(0.419090\pi\)
\(558\) 0 0
\(559\) −62.5336 −2.64489
\(560\) 8.49425 0.358948
\(561\) 0 0
\(562\) −35.3379 −1.49064
\(563\) 24.3997 1.02832 0.514162 0.857693i \(-0.328103\pi\)
0.514162 + 0.857693i \(0.328103\pi\)
\(564\) 0 0
\(565\) −30.7128 −1.29210
\(566\) 52.8541 2.22162
\(567\) 0 0
\(568\) 26.4030 1.10785
\(569\) −6.37571 −0.267284 −0.133642 0.991030i \(-0.542667\pi\)
−0.133642 + 0.991030i \(0.542667\pi\)
\(570\) 0 0
\(571\) 4.76600 0.199451 0.0997255 0.995015i \(-0.468204\pi\)
0.0997255 + 0.995015i \(0.468204\pi\)
\(572\) −109.350 −4.57213
\(573\) 0 0
\(574\) −4.07607 −0.170132
\(575\) −23.5389 −0.981642
\(576\) 0 0
\(577\) 10.7666 0.448220 0.224110 0.974564i \(-0.428053\pi\)
0.224110 + 0.974564i \(0.428053\pi\)
\(578\) −101.988 −4.24212
\(579\) 0 0
\(580\) −12.9340 −0.537055
\(581\) 14.0855 0.584363
\(582\) 0 0
\(583\) 22.9108 0.948870
\(584\) 33.5810 1.38959
\(585\) 0 0
\(586\) −38.3035 −1.58230
\(587\) 0.0116818 0.000482159 0 0.000241079 1.00000i \(-0.499923\pi\)
0.000241079 1.00000i \(0.499923\pi\)
\(588\) 0 0
\(589\) 22.8875 0.943065
\(590\) 9.97597 0.410704
\(591\) 0 0
\(592\) 18.1669 0.746654
\(593\) −37.5294 −1.54115 −0.770573 0.637351i \(-0.780030\pi\)
−0.770573 + 0.637351i \(0.780030\pi\)
\(594\) 0 0
\(595\) 22.4377 0.919855
\(596\) 14.3019 0.585828
\(597\) 0 0
\(598\) −96.3099 −3.93840
\(599\) −28.8340 −1.17812 −0.589062 0.808088i \(-0.700503\pi\)
−0.589062 + 0.808088i \(0.700503\pi\)
\(600\) 0 0
\(601\) 32.9469 1.34393 0.671966 0.740582i \(-0.265450\pi\)
0.671966 + 0.740582i \(0.265450\pi\)
\(602\) 25.4588 1.03762
\(603\) 0 0
\(604\) −13.9088 −0.565940
\(605\) −36.2580 −1.47410
\(606\) 0 0
\(607\) −37.9893 −1.54194 −0.770970 0.636872i \(-0.780228\pi\)
−0.770970 + 0.636872i \(0.780228\pi\)
\(608\) −12.2892 −0.498391
\(609\) 0 0
\(610\) 37.2992 1.51020
\(611\) −23.7664 −0.961484
\(612\) 0 0
\(613\) −17.9743 −0.725975 −0.362987 0.931794i \(-0.618243\pi\)
−0.362987 + 0.931794i \(0.618243\pi\)
\(614\) 40.8946 1.65037
\(615\) 0 0
\(616\) 21.1701 0.852966
\(617\) 25.2975 1.01844 0.509220 0.860637i \(-0.329934\pi\)
0.509220 + 0.860637i \(0.329934\pi\)
\(618\) 0 0
\(619\) 20.1324 0.809190 0.404595 0.914496i \(-0.367412\pi\)
0.404595 + 0.914496i \(0.367412\pi\)
\(620\) 35.5042 1.42588
\(621\) 0 0
\(622\) −25.2318 −1.01170
\(623\) −13.2348 −0.530242
\(624\) 0 0
\(625\) −30.2699 −1.21080
\(626\) −31.2884 −1.25054
\(627\) 0 0
\(628\) 66.6882 2.66115
\(629\) 47.9880 1.91341
\(630\) 0 0
\(631\) −11.4163 −0.454476 −0.227238 0.973839i \(-0.572969\pi\)
−0.227238 + 0.973839i \(0.572969\pi\)
\(632\) 18.3781 0.731041
\(633\) 0 0
\(634\) 80.5402 3.19866
\(635\) 2.91376 0.115629
\(636\) 0 0
\(637\) −5.92231 −0.234651
\(638\) −13.5892 −0.538003
\(639\) 0 0
\(640\) −60.0245 −2.37268
\(641\) 19.5013 0.770256 0.385128 0.922863i \(-0.374157\pi\)
0.385128 + 0.922863i \(0.374157\pi\)
\(642\) 0 0
\(643\) −49.5234 −1.95301 −0.976506 0.215492i \(-0.930864\pi\)
−0.976506 + 0.215492i \(0.930864\pi\)
\(644\) 25.7204 1.01352
\(645\) 0 0
\(646\) 132.992 5.23249
\(647\) 13.2292 0.520095 0.260047 0.965596i \(-0.416262\pi\)
0.260047 + 0.965596i \(0.416262\pi\)
\(648\) 0 0
\(649\) 6.87544 0.269884
\(650\) 49.8344 1.95466
\(651\) 0 0
\(652\) −19.9138 −0.779885
\(653\) 5.45442 0.213448 0.106724 0.994289i \(-0.465964\pi\)
0.106724 + 0.994289i \(0.465964\pi\)
\(654\) 0 0
\(655\) 58.0051 2.26645
\(656\) −4.92832 −0.192418
\(657\) 0 0
\(658\) 9.67580 0.377202
\(659\) 12.0550 0.469596 0.234798 0.972044i \(-0.424557\pi\)
0.234798 + 0.972044i \(0.424557\pi\)
\(660\) 0 0
\(661\) −1.99457 −0.0775799 −0.0387900 0.999247i \(-0.512350\pi\)
−0.0387900 + 0.999247i \(0.512350\pi\)
\(662\) 40.7471 1.58368
\(663\) 0 0
\(664\) 61.5857 2.38999
\(665\) −20.8708 −0.809333
\(666\) 0 0
\(667\) −7.85112 −0.303997
\(668\) −40.0636 −1.55011
\(669\) 0 0
\(670\) 5.10922 0.197386
\(671\) 25.7066 0.992392
\(672\) 0 0
\(673\) −10.7995 −0.416289 −0.208144 0.978098i \(-0.566742\pi\)
−0.208144 + 0.978098i \(0.566742\pi\)
\(674\) −50.8834 −1.95995
\(675\) 0 0
\(676\) 84.1762 3.23754
\(677\) −15.9165 −0.611722 −0.305861 0.952076i \(-0.598944\pi\)
−0.305861 + 0.952076i \(0.598944\pi\)
\(678\) 0 0
\(679\) 0.0256030 0.000982555 0
\(680\) 98.1040 3.76212
\(681\) 0 0
\(682\) 37.3029 1.42840
\(683\) −2.33667 −0.0894101 −0.0447050 0.999000i \(-0.514235\pi\)
−0.0447050 + 0.999000i \(0.514235\pi\)
\(684\) 0 0
\(685\) 3.13008 0.119594
\(686\) 2.41110 0.0920562
\(687\) 0 0
\(688\) 30.7818 1.17355
\(689\) −28.0233 −1.06760
\(690\) 0 0
\(691\) −13.2180 −0.502837 −0.251419 0.967878i \(-0.580897\pi\)
−0.251419 + 0.967878i \(0.580897\pi\)
\(692\) 5.53979 0.210591
\(693\) 0 0
\(694\) 35.1804 1.33543
\(695\) 15.6002 0.591750
\(696\) 0 0
\(697\) −13.0182 −0.493100
\(698\) −6.13568 −0.232239
\(699\) 0 0
\(700\) −13.3087 −0.503021
\(701\) −11.0311 −0.416639 −0.208320 0.978061i \(-0.566799\pi\)
−0.208320 + 0.978061i \(0.566799\pi\)
\(702\) 0 0
\(703\) −44.6368 −1.68351
\(704\) −48.2596 −1.81885
\(705\) 0 0
\(706\) −83.3037 −3.13518
\(707\) 8.54546 0.321385
\(708\) 0 0
\(709\) −44.7628 −1.68110 −0.840550 0.541733i \(-0.817768\pi\)
−0.840550 + 0.541733i \(0.817768\pi\)
\(710\) −42.4242 −1.59215
\(711\) 0 0
\(712\) −57.8665 −2.16864
\(713\) 21.5516 0.807112
\(714\) 0 0
\(715\) 83.5522 3.12467
\(716\) 59.9092 2.23891
\(717\) 0 0
\(718\) −28.9297 −1.07965
\(719\) −22.5152 −0.839674 −0.419837 0.907599i \(-0.637913\pi\)
−0.419837 + 0.907599i \(0.637913\pi\)
\(720\) 0 0
\(721\) 12.8304 0.477828
\(722\) −77.8934 −2.89889
\(723\) 0 0
\(724\) 66.0680 2.45540
\(725\) 4.06246 0.150876
\(726\) 0 0
\(727\) 45.2526 1.67832 0.839162 0.543881i \(-0.183046\pi\)
0.839162 + 0.543881i \(0.183046\pi\)
\(728\) −25.8941 −0.959698
\(729\) 0 0
\(730\) −53.9577 −1.99707
\(731\) 81.3105 3.00738
\(732\) 0 0
\(733\) −0.823994 −0.0304349 −0.0152175 0.999884i \(-0.504844\pi\)
−0.0152175 + 0.999884i \(0.504844\pi\)
\(734\) 8.78524 0.324269
\(735\) 0 0
\(736\) −11.5718 −0.426543
\(737\) 3.52127 0.129708
\(738\) 0 0
\(739\) −33.7283 −1.24071 −0.620357 0.784320i \(-0.713012\pi\)
−0.620357 + 0.784320i \(0.713012\pi\)
\(740\) −69.2427 −2.54541
\(741\) 0 0
\(742\) 11.4089 0.418833
\(743\) 42.3307 1.55296 0.776481 0.630141i \(-0.217003\pi\)
0.776481 + 0.630141i \(0.217003\pi\)
\(744\) 0 0
\(745\) −10.9278 −0.400365
\(746\) −48.7793 −1.78594
\(747\) 0 0
\(748\) 142.184 5.19875
\(749\) −14.8632 −0.543091
\(750\) 0 0
\(751\) 24.1432 0.880997 0.440498 0.897753i \(-0.354802\pi\)
0.440498 + 0.897753i \(0.354802\pi\)
\(752\) 11.6989 0.426613
\(753\) 0 0
\(754\) 16.6216 0.605324
\(755\) 10.6275 0.386773
\(756\) 0 0
\(757\) −34.4792 −1.25317 −0.626585 0.779353i \(-0.715548\pi\)
−0.626585 + 0.779353i \(0.715548\pi\)
\(758\) 46.5513 1.69082
\(759\) 0 0
\(760\) −91.2530 −3.31009
\(761\) 21.9434 0.795447 0.397724 0.917505i \(-0.369800\pi\)
0.397724 + 0.917505i \(0.369800\pi\)
\(762\) 0 0
\(763\) −2.94497 −0.106615
\(764\) −40.4227 −1.46244
\(765\) 0 0
\(766\) 42.7498 1.54461
\(767\) −8.40966 −0.303655
\(768\) 0 0
\(769\) −28.9123 −1.04260 −0.521302 0.853372i \(-0.674554\pi\)
−0.521302 + 0.853372i \(0.674554\pi\)
\(770\) −34.0159 −1.22585
\(771\) 0 0
\(772\) 95.5184 3.43778
\(773\) −37.5638 −1.35108 −0.675538 0.737325i \(-0.736089\pi\)
−0.675538 + 0.737325i \(0.736089\pi\)
\(774\) 0 0
\(775\) −11.1516 −0.400577
\(776\) 0.111944 0.00401855
\(777\) 0 0
\(778\) 74.8377 2.68306
\(779\) 12.1091 0.433853
\(780\) 0 0
\(781\) −29.2387 −1.04624
\(782\) 125.229 4.47817
\(783\) 0 0
\(784\) 2.91522 0.104115
\(785\) −50.9553 −1.81867
\(786\) 0 0
\(787\) −6.93126 −0.247073 −0.123536 0.992340i \(-0.539424\pi\)
−0.123536 + 0.992340i \(0.539424\pi\)
\(788\) 55.6261 1.98160
\(789\) 0 0
\(790\) −29.5297 −1.05062
\(791\) −10.5406 −0.374781
\(792\) 0 0
\(793\) −31.4429 −1.11657
\(794\) 16.0636 0.570075
\(795\) 0 0
\(796\) 75.7674 2.68550
\(797\) −19.9833 −0.707847 −0.353923 0.935274i \(-0.615153\pi\)
−0.353923 + 0.935274i \(0.615153\pi\)
\(798\) 0 0
\(799\) 30.9027 1.09326
\(800\) 5.98770 0.211697
\(801\) 0 0
\(802\) 68.7194 2.42657
\(803\) −37.1876 −1.31232
\(804\) 0 0
\(805\) −19.6525 −0.692660
\(806\) −45.6269 −1.60714
\(807\) 0 0
\(808\) 37.3632 1.31443
\(809\) −36.8912 −1.29702 −0.648512 0.761204i \(-0.724609\pi\)
−0.648512 + 0.761204i \(0.724609\pi\)
\(810\) 0 0
\(811\) −50.0117 −1.75615 −0.878075 0.478524i \(-0.841172\pi\)
−0.878075 + 0.478524i \(0.841172\pi\)
\(812\) −4.43894 −0.155776
\(813\) 0 0
\(814\) −72.7506 −2.54991
\(815\) 15.2158 0.532987
\(816\) 0 0
\(817\) −75.6323 −2.64604
\(818\) 62.8696 2.19818
\(819\) 0 0
\(820\) 18.7842 0.655972
\(821\) −41.7480 −1.45702 −0.728508 0.685037i \(-0.759786\pi\)
−0.728508 + 0.685037i \(0.759786\pi\)
\(822\) 0 0
\(823\) 32.5077 1.13315 0.566574 0.824011i \(-0.308269\pi\)
0.566574 + 0.824011i \(0.308269\pi\)
\(824\) 56.0981 1.95427
\(825\) 0 0
\(826\) 3.42375 0.119128
\(827\) 41.7566 1.45202 0.726010 0.687685i \(-0.241373\pi\)
0.726010 + 0.687685i \(0.241373\pi\)
\(828\) 0 0
\(829\) 40.4492 1.40486 0.702430 0.711753i \(-0.252098\pi\)
0.702430 + 0.711753i \(0.252098\pi\)
\(830\) −98.9553 −3.43479
\(831\) 0 0
\(832\) 59.0285 2.04644
\(833\) 7.70060 0.266810
\(834\) 0 0
\(835\) 30.6119 1.05937
\(836\) −132.255 −4.57412
\(837\) 0 0
\(838\) 36.4091 1.25773
\(839\) −28.2930 −0.976782 −0.488391 0.872625i \(-0.662416\pi\)
−0.488391 + 0.872625i \(0.662416\pi\)
\(840\) 0 0
\(841\) −27.6450 −0.953276
\(842\) 17.5728 0.605600
\(843\) 0 0
\(844\) −64.4356 −2.21797
\(845\) −64.3176 −2.21259
\(846\) 0 0
\(847\) −12.4437 −0.427571
\(848\) 13.7943 0.473698
\(849\) 0 0
\(850\) −64.7981 −2.22256
\(851\) −42.0313 −1.44081
\(852\) 0 0
\(853\) −10.1811 −0.348594 −0.174297 0.984693i \(-0.555765\pi\)
−0.174297 + 0.984693i \(0.555765\pi\)
\(854\) 12.8011 0.438044
\(855\) 0 0
\(856\) −64.9864 −2.22119
\(857\) −36.0529 −1.23154 −0.615772 0.787925i \(-0.711156\pi\)
−0.615772 + 0.787925i \(0.711156\pi\)
\(858\) 0 0
\(859\) 27.2611 0.930138 0.465069 0.885274i \(-0.346029\pi\)
0.465069 + 0.885274i \(0.346029\pi\)
\(860\) −117.324 −4.00072
\(861\) 0 0
\(862\) 45.2566 1.54144
\(863\) −47.4525 −1.61530 −0.807651 0.589661i \(-0.799261\pi\)
−0.807651 + 0.589661i \(0.799261\pi\)
\(864\) 0 0
\(865\) −4.23286 −0.143922
\(866\) 75.3325 2.55990
\(867\) 0 0
\(868\) 12.1850 0.413587
\(869\) −20.3519 −0.690390
\(870\) 0 0
\(871\) −4.30703 −0.145938
\(872\) −12.8763 −0.436045
\(873\) 0 0
\(874\) −116.484 −3.94011
\(875\) −4.39984 −0.148742
\(876\) 0 0
\(877\) 11.7097 0.395410 0.197705 0.980262i \(-0.436651\pi\)
0.197705 + 0.980262i \(0.436651\pi\)
\(878\) 33.0914 1.11678
\(879\) 0 0
\(880\) −41.1281 −1.38643
\(881\) −34.8353 −1.17363 −0.586815 0.809721i \(-0.699618\pi\)
−0.586815 + 0.809721i \(0.699618\pi\)
\(882\) 0 0
\(883\) −30.0139 −1.01005 −0.505025 0.863105i \(-0.668517\pi\)
−0.505025 + 0.863105i \(0.668517\pi\)
\(884\) −173.911 −5.84927
\(885\) 0 0
\(886\) −74.6793 −2.50890
\(887\) 17.5113 0.587971 0.293986 0.955810i \(-0.405018\pi\)
0.293986 + 0.955810i \(0.405018\pi\)
\(888\) 0 0
\(889\) 1.00000 0.0335389
\(890\) 92.9793 3.11667
\(891\) 0 0
\(892\) −14.0594 −0.470745
\(893\) −28.7446 −0.961902
\(894\) 0 0
\(895\) −45.7756 −1.53011
\(896\) −20.6004 −0.688210
\(897\) 0 0
\(898\) 45.6813 1.52441
\(899\) −3.71947 −0.124051
\(900\) 0 0
\(901\) 36.4378 1.21392
\(902\) 19.7358 0.657131
\(903\) 0 0
\(904\) −46.0866 −1.53282
\(905\) −50.4814 −1.67806
\(906\) 0 0
\(907\) 5.82321 0.193356 0.0966782 0.995316i \(-0.469178\pi\)
0.0966782 + 0.995316i \(0.469178\pi\)
\(908\) 89.4687 2.96912
\(909\) 0 0
\(910\) 41.6064 1.37924
\(911\) 6.00000 0.198789 0.0993944 0.995048i \(-0.468309\pi\)
0.0993944 + 0.995048i \(0.468309\pi\)
\(912\) 0 0
\(913\) −68.1999 −2.25709
\(914\) 15.6563 0.517863
\(915\) 0 0
\(916\) −99.0984 −3.27430
\(917\) 19.9073 0.657398
\(918\) 0 0
\(919\) −56.7463 −1.87189 −0.935944 0.352148i \(-0.885451\pi\)
−0.935944 + 0.352148i \(0.885451\pi\)
\(920\) −85.9264 −2.83291
\(921\) 0 0
\(922\) −68.6322 −2.26028
\(923\) 35.7632 1.17716
\(924\) 0 0
\(925\) 21.7486 0.715089
\(926\) 10.8343 0.356037
\(927\) 0 0
\(928\) 1.99712 0.0655587
\(929\) −17.9985 −0.590512 −0.295256 0.955418i \(-0.595405\pi\)
−0.295256 + 0.955418i \(0.595405\pi\)
\(930\) 0 0
\(931\) −7.16283 −0.234752
\(932\) −94.0679 −3.08130
\(933\) 0 0
\(934\) 3.13726 0.102654
\(935\) −108.640 −3.55292
\(936\) 0 0
\(937\) −52.5134 −1.71554 −0.857768 0.514036i \(-0.828150\pi\)
−0.857768 + 0.514036i \(0.828150\pi\)
\(938\) 1.75348 0.0572532
\(939\) 0 0
\(940\) −44.5900 −1.45436
\(941\) −10.8023 −0.352144 −0.176072 0.984377i \(-0.556339\pi\)
−0.176072 + 0.984377i \(0.556339\pi\)
\(942\) 0 0
\(943\) 11.4023 0.371309
\(944\) 4.13960 0.134733
\(945\) 0 0
\(946\) −123.268 −4.00779
\(947\) 9.48649 0.308269 0.154135 0.988050i \(-0.450741\pi\)
0.154135 + 0.988050i \(0.450741\pi\)
\(948\) 0 0
\(949\) 45.4859 1.47653
\(950\) 60.2730 1.95551
\(951\) 0 0
\(952\) 33.6692 1.09123
\(953\) 43.7726 1.41793 0.708966 0.705242i \(-0.249162\pi\)
0.708966 + 0.705242i \(0.249162\pi\)
\(954\) 0 0
\(955\) 30.8863 0.999458
\(956\) 79.8599 2.58285
\(957\) 0 0
\(958\) −58.3536 −1.88532
\(959\) 1.07424 0.0346891
\(960\) 0 0
\(961\) −20.7899 −0.670643
\(962\) 88.9846 2.86898
\(963\) 0 0
\(964\) −10.4883 −0.337805
\(965\) −72.9840 −2.34944
\(966\) 0 0
\(967\) −16.9435 −0.544865 −0.272432 0.962175i \(-0.587828\pi\)
−0.272432 + 0.962175i \(0.587828\pi\)
\(968\) −54.4076 −1.74873
\(969\) 0 0
\(970\) −0.179871 −0.00577529
\(971\) −32.4646 −1.04184 −0.520919 0.853606i \(-0.674411\pi\)
−0.520919 + 0.853606i \(0.674411\pi\)
\(972\) 0 0
\(973\) 5.35399 0.171641
\(974\) 40.6896 1.30378
\(975\) 0 0
\(976\) 15.4776 0.495425
\(977\) −30.0860 −0.962535 −0.481268 0.876574i \(-0.659823\pi\)
−0.481268 + 0.876574i \(0.659823\pi\)
\(978\) 0 0
\(979\) 64.0813 2.04805
\(980\) −11.1113 −0.354938
\(981\) 0 0
\(982\) −13.2165 −0.421757
\(983\) −36.4707 −1.16323 −0.581617 0.813462i \(-0.697580\pi\)
−0.581617 + 0.813462i \(0.697580\pi\)
\(984\) 0 0
\(985\) −42.5030 −1.35426
\(986\) −21.6126 −0.688285
\(987\) 0 0
\(988\) 161.767 5.14648
\(989\) −71.2175 −2.26458
\(990\) 0 0
\(991\) 36.7882 1.16862 0.584308 0.811532i \(-0.301366\pi\)
0.584308 + 0.811532i \(0.301366\pi\)
\(992\) −5.48216 −0.174059
\(993\) 0 0
\(994\) −14.5600 −0.461814
\(995\) −57.8926 −1.83532
\(996\) 0 0
\(997\) −6.17533 −0.195575 −0.0977873 0.995207i \(-0.531176\pi\)
−0.0977873 + 0.995207i \(0.531176\pi\)
\(998\) 43.8159 1.38697
\(999\) 0 0
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 \(a_p\))