Properties

Label 8001.2.a.z.1.9
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 1.9
Character \(\chi\) = 8001.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.56027 q^{2}\) \(+0.434445 q^{4}\) \(+1.69832 q^{5}\) \(-1.00000 q^{7}\) \(+2.44269 q^{8}\) \(+O(q^{10})\) \(q\)\(-1.56027 q^{2}\) \(+0.434445 q^{4}\) \(+1.69832 q^{5}\) \(-1.00000 q^{7}\) \(+2.44269 q^{8}\) \(-2.64985 q^{10}\) \(+1.57750 q^{11}\) \(+5.37691 q^{13}\) \(+1.56027 q^{14}\) \(-4.68015 q^{16}\) \(-7.38180 q^{17}\) \(-0.683565 q^{19}\) \(+0.737828 q^{20}\) \(-2.46133 q^{22}\) \(+8.53565 q^{23}\) \(-2.11570 q^{25}\) \(-8.38943 q^{26}\) \(-0.434445 q^{28}\) \(-5.81934 q^{29}\) \(+7.97047 q^{31}\) \(+2.41692 q^{32}\) \(+11.5176 q^{34}\) \(-1.69832 q^{35}\) \(-11.4098 q^{37}\) \(+1.06655 q^{38}\) \(+4.14848 q^{40}\) \(-5.44263 q^{41}\) \(+4.36687 q^{43}\) \(+0.685336 q^{44}\) \(-13.3179 q^{46}\) \(+3.11843 q^{47}\) \(+1.00000 q^{49}\) \(+3.30106 q^{50}\) \(+2.33597 q^{52}\) \(-7.03105 q^{53}\) \(+2.67911 q^{55}\) \(-2.44269 q^{56}\) \(+9.07974 q^{58}\) \(+5.82826 q^{59}\) \(-6.57944 q^{61}\) \(-12.4361 q^{62}\) \(+5.58925 q^{64}\) \(+9.13173 q^{65}\) \(-6.68183 q^{67}\) \(-3.20698 q^{68}\) \(+2.64985 q^{70}\) \(-4.90031 q^{71}\) \(-7.91813 q^{73}\) \(+17.8024 q^{74}\) \(-0.296971 q^{76}\) \(-1.57750 q^{77}\) \(-15.7765 q^{79}\) \(-7.94841 q^{80}\) \(+8.49197 q^{82}\) \(-6.39375 q^{83}\) \(-12.5367 q^{85}\) \(-6.81350 q^{86}\) \(+3.85334 q^{88}\) \(-2.66271 q^{89}\) \(-5.37691 q^{91}\) \(+3.70827 q^{92}\) \(-4.86560 q^{94}\) \(-1.16092 q^{95}\) \(+5.37034 q^{97}\) \(-1.56027 q^{98}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(32q \) \(\mathstrut +\mathstrut 30q^{4} \) \(\mathstrut -\mathstrut 32q^{7} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(32q \) \(\mathstrut +\mathstrut 30q^{4} \) \(\mathstrut -\mathstrut 32q^{7} \) \(\mathstrut -\mathstrut 16q^{10} \) \(\mathstrut -\mathstrut 14q^{13} \) \(\mathstrut +\mathstrut 18q^{16} \) \(\mathstrut -\mathstrut 30q^{19} \) \(\mathstrut -\mathstrut 10q^{22} \) \(\mathstrut +\mathstrut 36q^{25} \) \(\mathstrut -\mathstrut 30q^{28} \) \(\mathstrut -\mathstrut 58q^{31} \) \(\mathstrut -\mathstrut 34q^{34} \) \(\mathstrut +\mathstrut 8q^{37} \) \(\mathstrut -\mathstrut 34q^{40} \) \(\mathstrut +\mathstrut 6q^{43} \) \(\mathstrut -\mathstrut 36q^{46} \) \(\mathstrut +\mathstrut 32q^{49} \) \(\mathstrut -\mathstrut 56q^{52} \) \(\mathstrut -\mathstrut 88q^{55} \) \(\mathstrut -\mathstrut 22q^{58} \) \(\mathstrut -\mathstrut 46q^{61} \) \(\mathstrut +\mathstrut 20q^{64} \) \(\mathstrut -\mathstrut 8q^{67} \) \(\mathstrut +\mathstrut 16q^{70} \) \(\mathstrut -\mathstrut 60q^{73} \) \(\mathstrut -\mathstrut 128q^{76} \) \(\mathstrut -\mathstrut 74q^{79} \) \(\mathstrut -\mathstrut 52q^{82} \) \(\mathstrut -\mathstrut 16q^{85} \) \(\mathstrut -\mathstrut 64q^{88} \) \(\mathstrut +\mathstrut 14q^{91} \) \(\mathstrut -\mathstrut 58q^{94} \) \(\mathstrut -\mathstrut 44q^{97} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.56027 −1.10328 −0.551639 0.834083i \(-0.685997\pi\)
−0.551639 + 0.834083i \(0.685997\pi\)
\(3\) 0 0
\(4\) 0.434445 0.217222
\(5\) 1.69832 0.759514 0.379757 0.925086i \(-0.376008\pi\)
0.379757 + 0.925086i \(0.376008\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 2.44269 0.863621
\(9\) 0 0
\(10\) −2.64985 −0.837955
\(11\) 1.57750 0.475634 0.237817 0.971310i \(-0.423568\pi\)
0.237817 + 0.971310i \(0.423568\pi\)
\(12\) 0 0
\(13\) 5.37691 1.49129 0.745643 0.666346i \(-0.232143\pi\)
0.745643 + 0.666346i \(0.232143\pi\)
\(14\) 1.56027 0.417000
\(15\) 0 0
\(16\) −4.68015 −1.17004
\(17\) −7.38180 −1.79035 −0.895174 0.445717i \(-0.852949\pi\)
−0.895174 + 0.445717i \(0.852949\pi\)
\(18\) 0 0
\(19\) −0.683565 −0.156821 −0.0784103 0.996921i \(-0.524984\pi\)
−0.0784103 + 0.996921i \(0.524984\pi\)
\(20\) 0.737828 0.164983
\(21\) 0 0
\(22\) −2.46133 −0.524757
\(23\) 8.53565 1.77981 0.889903 0.456149i \(-0.150772\pi\)
0.889903 + 0.456149i \(0.150772\pi\)
\(24\) 0 0
\(25\) −2.11570 −0.423139
\(26\) −8.38943 −1.64530
\(27\) 0 0
\(28\) −0.434445 −0.0821023
\(29\) −5.81934 −1.08062 −0.540312 0.841465i \(-0.681694\pi\)
−0.540312 + 0.841465i \(0.681694\pi\)
\(30\) 0 0
\(31\) 7.97047 1.43154 0.715770 0.698336i \(-0.246076\pi\)
0.715770 + 0.698336i \(0.246076\pi\)
\(32\) 2.41692 0.427254
\(33\) 0 0
\(34\) 11.5176 1.97525
\(35\) −1.69832 −0.287069
\(36\) 0 0
\(37\) −11.4098 −1.87576 −0.937881 0.346956i \(-0.887215\pi\)
−0.937881 + 0.346956i \(0.887215\pi\)
\(38\) 1.06655 0.173017
\(39\) 0 0
\(40\) 4.14848 0.655932
\(41\) −5.44263 −0.849995 −0.424998 0.905194i \(-0.639725\pi\)
−0.424998 + 0.905194i \(0.639725\pi\)
\(42\) 0 0
\(43\) 4.36687 0.665942 0.332971 0.942937i \(-0.391949\pi\)
0.332971 + 0.942937i \(0.391949\pi\)
\(44\) 0.685336 0.103318
\(45\) 0 0
\(46\) −13.3179 −1.96362
\(47\) 3.11843 0.454870 0.227435 0.973793i \(-0.426966\pi\)
0.227435 + 0.973793i \(0.426966\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 3.30106 0.466840
\(51\) 0 0
\(52\) 2.33597 0.323941
\(53\) −7.03105 −0.965789 −0.482894 0.875679i \(-0.660415\pi\)
−0.482894 + 0.875679i \(0.660415\pi\)
\(54\) 0 0
\(55\) 2.67911 0.361250
\(56\) −2.44269 −0.326418
\(57\) 0 0
\(58\) 9.07974 1.19223
\(59\) 5.82826 0.758775 0.379388 0.925238i \(-0.376135\pi\)
0.379388 + 0.925238i \(0.376135\pi\)
\(60\) 0 0
\(61\) −6.57944 −0.842411 −0.421206 0.906965i \(-0.638393\pi\)
−0.421206 + 0.906965i \(0.638393\pi\)
\(62\) −12.4361 −1.57939
\(63\) 0 0
\(64\) 5.58925 0.698656
\(65\) 9.13173 1.13265
\(66\) 0 0
\(67\) −6.68183 −0.816316 −0.408158 0.912911i \(-0.633829\pi\)
−0.408158 + 0.912911i \(0.633829\pi\)
\(68\) −3.20698 −0.388904
\(69\) 0 0
\(70\) 2.64985 0.316717
\(71\) −4.90031 −0.581559 −0.290780 0.956790i \(-0.593915\pi\)
−0.290780 + 0.956790i \(0.593915\pi\)
\(72\) 0 0
\(73\) −7.91813 −0.926747 −0.463373 0.886163i \(-0.653361\pi\)
−0.463373 + 0.886163i \(0.653361\pi\)
\(74\) 17.8024 2.06949
\(75\) 0 0
\(76\) −0.296971 −0.0340650
\(77\) −1.57750 −0.179773
\(78\) 0 0
\(79\) −15.7765 −1.77499 −0.887496 0.460815i \(-0.847557\pi\)
−0.887496 + 0.460815i \(0.847557\pi\)
\(80\) −7.94841 −0.888659
\(81\) 0 0
\(82\) 8.49197 0.937781
\(83\) −6.39375 −0.701806 −0.350903 0.936412i \(-0.614125\pi\)
−0.350903 + 0.936412i \(0.614125\pi\)
\(84\) 0 0
\(85\) −12.5367 −1.35979
\(86\) −6.81350 −0.734719
\(87\) 0 0
\(88\) 3.85334 0.410768
\(89\) −2.66271 −0.282247 −0.141123 0.989992i \(-0.545071\pi\)
−0.141123 + 0.989992i \(0.545071\pi\)
\(90\) 0 0
\(91\) −5.37691 −0.563653
\(92\) 3.70827 0.386614
\(93\) 0 0
\(94\) −4.86560 −0.501848
\(95\) −1.16092 −0.119107
\(96\) 0 0
\(97\) 5.37034 0.545276 0.272638 0.962117i \(-0.412104\pi\)
0.272638 + 0.962117i \(0.412104\pi\)
\(98\) −1.56027 −0.157611
\(99\) 0 0
\(100\) −0.919153 −0.0919153
\(101\) 18.9810 1.88868 0.944342 0.328965i \(-0.106700\pi\)
0.944342 + 0.328965i \(0.106700\pi\)
\(102\) 0 0
\(103\) −6.36094 −0.626762 −0.313381 0.949627i \(-0.601462\pi\)
−0.313381 + 0.949627i \(0.601462\pi\)
\(104\) 13.1341 1.28791
\(105\) 0 0
\(106\) 10.9703 1.06553
\(107\) −1.79748 −0.173769 −0.0868844 0.996218i \(-0.527691\pi\)
−0.0868844 + 0.996218i \(0.527691\pi\)
\(108\) 0 0
\(109\) −16.5252 −1.58283 −0.791413 0.611281i \(-0.790654\pi\)
−0.791413 + 0.611281i \(0.790654\pi\)
\(110\) −4.18013 −0.398560
\(111\) 0 0
\(112\) 4.68015 0.442232
\(113\) 14.5665 1.37030 0.685151 0.728401i \(-0.259736\pi\)
0.685151 + 0.728401i \(0.259736\pi\)
\(114\) 0 0
\(115\) 14.4963 1.35179
\(116\) −2.52818 −0.234736
\(117\) 0 0
\(118\) −9.09367 −0.837140
\(119\) 7.38180 0.676688
\(120\) 0 0
\(121\) −8.51150 −0.773772
\(122\) 10.2657 0.929414
\(123\) 0 0
\(124\) 3.46273 0.310962
\(125\) −12.0848 −1.08089
\(126\) 0 0
\(127\) −1.00000 −0.0887357
\(128\) −13.5546 −1.19807
\(129\) 0 0
\(130\) −14.2480 −1.24963
\(131\) −13.0083 −1.13654 −0.568271 0.822841i \(-0.692388\pi\)
−0.568271 + 0.822841i \(0.692388\pi\)
\(132\) 0 0
\(133\) 0.683565 0.0592726
\(134\) 10.4255 0.900624
\(135\) 0 0
\(136\) −18.0314 −1.54618
\(137\) −11.0957 −0.947969 −0.473984 0.880533i \(-0.657185\pi\)
−0.473984 + 0.880533i \(0.657185\pi\)
\(138\) 0 0
\(139\) −4.43688 −0.376331 −0.188165 0.982137i \(-0.560254\pi\)
−0.188165 + 0.982137i \(0.560254\pi\)
\(140\) −0.737828 −0.0623578
\(141\) 0 0
\(142\) 7.64580 0.641622
\(143\) 8.48207 0.709306
\(144\) 0 0
\(145\) −9.88312 −0.820748
\(146\) 12.3544 1.02246
\(147\) 0 0
\(148\) −4.95694 −0.407458
\(149\) −0.577502 −0.0473108 −0.0236554 0.999720i \(-0.507530\pi\)
−0.0236554 + 0.999720i \(0.507530\pi\)
\(150\) 0 0
\(151\) −7.20366 −0.586225 −0.293113 0.956078i \(-0.594691\pi\)
−0.293113 + 0.956078i \(0.594691\pi\)
\(152\) −1.66974 −0.135434
\(153\) 0 0
\(154\) 2.46133 0.198339
\(155\) 13.5364 1.08727
\(156\) 0 0
\(157\) −4.25760 −0.339793 −0.169897 0.985462i \(-0.554343\pi\)
−0.169897 + 0.985462i \(0.554343\pi\)
\(158\) 24.6156 1.95831
\(159\) 0 0
\(160\) 4.10471 0.324506
\(161\) −8.53565 −0.672704
\(162\) 0 0
\(163\) −13.2923 −1.04113 −0.520567 0.853821i \(-0.674279\pi\)
−0.520567 + 0.853821i \(0.674279\pi\)
\(164\) −2.36452 −0.184638
\(165\) 0 0
\(166\) 9.97598 0.774287
\(167\) 7.11696 0.550727 0.275363 0.961340i \(-0.411202\pi\)
0.275363 + 0.961340i \(0.411202\pi\)
\(168\) 0 0
\(169\) 15.9111 1.22393
\(170\) 19.5606 1.50023
\(171\) 0 0
\(172\) 1.89716 0.144657
\(173\) 13.8378 1.05207 0.526035 0.850463i \(-0.323678\pi\)
0.526035 + 0.850463i \(0.323678\pi\)
\(174\) 0 0
\(175\) 2.11570 0.159932
\(176\) −7.38293 −0.556509
\(177\) 0 0
\(178\) 4.15455 0.311397
\(179\) 17.3579 1.29739 0.648697 0.761047i \(-0.275314\pi\)
0.648697 + 0.761047i \(0.275314\pi\)
\(180\) 0 0
\(181\) 20.9700 1.55869 0.779345 0.626595i \(-0.215552\pi\)
0.779345 + 0.626595i \(0.215552\pi\)
\(182\) 8.38943 0.621866
\(183\) 0 0
\(184\) 20.8500 1.53708
\(185\) −19.3776 −1.42467
\(186\) 0 0
\(187\) −11.6448 −0.851551
\(188\) 1.35479 0.0988080
\(189\) 0 0
\(190\) 1.81134 0.131409
\(191\) 12.2635 0.887358 0.443679 0.896186i \(-0.353673\pi\)
0.443679 + 0.896186i \(0.353673\pi\)
\(192\) 0 0
\(193\) −17.6311 −1.26912 −0.634558 0.772875i \(-0.718818\pi\)
−0.634558 + 0.772875i \(0.718818\pi\)
\(194\) −8.37919 −0.601591
\(195\) 0 0
\(196\) 0.434445 0.0310318
\(197\) 19.0024 1.35387 0.676933 0.736044i \(-0.263309\pi\)
0.676933 + 0.736044i \(0.263309\pi\)
\(198\) 0 0
\(199\) 8.01293 0.568021 0.284011 0.958821i \(-0.408335\pi\)
0.284011 + 0.958821i \(0.408335\pi\)
\(200\) −5.16799 −0.365432
\(201\) 0 0
\(202\) −29.6156 −2.08374
\(203\) 5.81934 0.408437
\(204\) 0 0
\(205\) −9.24334 −0.645583
\(206\) 9.92479 0.691493
\(207\) 0 0
\(208\) −25.1647 −1.74486
\(209\) −1.07832 −0.0745892
\(210\) 0 0
\(211\) 4.07668 0.280650 0.140325 0.990105i \(-0.455185\pi\)
0.140325 + 0.990105i \(0.455185\pi\)
\(212\) −3.05460 −0.209791
\(213\) 0 0
\(214\) 2.80455 0.191715
\(215\) 7.41636 0.505792
\(216\) 0 0
\(217\) −7.97047 −0.541071
\(218\) 25.7838 1.74630
\(219\) 0 0
\(220\) 1.16392 0.0784717
\(221\) −39.6912 −2.66992
\(222\) 0 0
\(223\) 5.02212 0.336306 0.168153 0.985761i \(-0.446220\pi\)
0.168153 + 0.985761i \(0.446220\pi\)
\(224\) −2.41692 −0.161487
\(225\) 0 0
\(226\) −22.7277 −1.51183
\(227\) −5.67133 −0.376420 −0.188210 0.982129i \(-0.560268\pi\)
−0.188210 + 0.982129i \(0.560268\pi\)
\(228\) 0 0
\(229\) 11.8322 0.781892 0.390946 0.920414i \(-0.372148\pi\)
0.390946 + 0.920414i \(0.372148\pi\)
\(230\) −22.6182 −1.49140
\(231\) 0 0
\(232\) −14.2148 −0.933250
\(233\) −22.7974 −1.49351 −0.746755 0.665099i \(-0.768389\pi\)
−0.746755 + 0.665099i \(0.768389\pi\)
\(234\) 0 0
\(235\) 5.29611 0.345480
\(236\) 2.53206 0.164823
\(237\) 0 0
\(238\) −11.5176 −0.746575
\(239\) 10.1782 0.658374 0.329187 0.944265i \(-0.393225\pi\)
0.329187 + 0.944265i \(0.393225\pi\)
\(240\) 0 0
\(241\) −26.7920 −1.72583 −0.862913 0.505353i \(-0.831362\pi\)
−0.862913 + 0.505353i \(0.831362\pi\)
\(242\) 13.2802 0.853686
\(243\) 0 0
\(244\) −2.85840 −0.182991
\(245\) 1.69832 0.108502
\(246\) 0 0
\(247\) −3.67547 −0.233864
\(248\) 19.4694 1.23631
\(249\) 0 0
\(250\) 18.8555 1.19253
\(251\) 20.6400 1.30279 0.651393 0.758741i \(-0.274185\pi\)
0.651393 + 0.758741i \(0.274185\pi\)
\(252\) 0 0
\(253\) 13.4650 0.846537
\(254\) 1.56027 0.0979001
\(255\) 0 0
\(256\) 9.97031 0.623144
\(257\) 12.6267 0.787632 0.393816 0.919189i \(-0.371155\pi\)
0.393816 + 0.919189i \(0.371155\pi\)
\(258\) 0 0
\(259\) 11.4098 0.708972
\(260\) 3.96723 0.246037
\(261\) 0 0
\(262\) 20.2965 1.25392
\(263\) −1.56670 −0.0966067 −0.0483034 0.998833i \(-0.515381\pi\)
−0.0483034 + 0.998833i \(0.515381\pi\)
\(264\) 0 0
\(265\) −11.9410 −0.733530
\(266\) −1.06655 −0.0653942
\(267\) 0 0
\(268\) −2.90289 −0.177322
\(269\) −21.7358 −1.32526 −0.662629 0.748948i \(-0.730559\pi\)
−0.662629 + 0.748948i \(0.730559\pi\)
\(270\) 0 0
\(271\) −15.5957 −0.947370 −0.473685 0.880694i \(-0.657076\pi\)
−0.473685 + 0.880694i \(0.657076\pi\)
\(272\) 34.5479 2.09477
\(273\) 0 0
\(274\) 17.3123 1.04587
\(275\) −3.33751 −0.201259
\(276\) 0 0
\(277\) 9.01303 0.541541 0.270770 0.962644i \(-0.412722\pi\)
0.270770 + 0.962644i \(0.412722\pi\)
\(278\) 6.92273 0.415198
\(279\) 0 0
\(280\) −4.14848 −0.247919
\(281\) −5.00890 −0.298806 −0.149403 0.988776i \(-0.547735\pi\)
−0.149403 + 0.988776i \(0.547735\pi\)
\(282\) 0 0
\(283\) 1.98588 0.118048 0.0590242 0.998257i \(-0.481201\pi\)
0.0590242 + 0.998257i \(0.481201\pi\)
\(284\) −2.12891 −0.126328
\(285\) 0 0
\(286\) −13.2343 −0.782562
\(287\) 5.44263 0.321268
\(288\) 0 0
\(289\) 37.4909 2.20535
\(290\) 15.4203 0.905514
\(291\) 0 0
\(292\) −3.43999 −0.201310
\(293\) 13.9204 0.813239 0.406620 0.913598i \(-0.366707\pi\)
0.406620 + 0.913598i \(0.366707\pi\)
\(294\) 0 0
\(295\) 9.89828 0.576300
\(296\) −27.8707 −1.61995
\(297\) 0 0
\(298\) 0.901059 0.0521970
\(299\) 45.8954 2.65420
\(300\) 0 0
\(301\) −4.36687 −0.251702
\(302\) 11.2397 0.646770
\(303\) 0 0
\(304\) 3.19919 0.183486
\(305\) −11.1740 −0.639823
\(306\) 0 0
\(307\) −28.6836 −1.63706 −0.818529 0.574465i \(-0.805210\pi\)
−0.818529 + 0.574465i \(0.805210\pi\)
\(308\) −0.685336 −0.0390507
\(309\) 0 0
\(310\) −21.1205 −1.19957
\(311\) −10.1277 −0.574288 −0.287144 0.957887i \(-0.592706\pi\)
−0.287144 + 0.957887i \(0.592706\pi\)
\(312\) 0 0
\(313\) −4.26249 −0.240930 −0.120465 0.992718i \(-0.538439\pi\)
−0.120465 + 0.992718i \(0.538439\pi\)
\(314\) 6.64300 0.374886
\(315\) 0 0
\(316\) −6.85401 −0.385568
\(317\) −10.8781 −0.610973 −0.305487 0.952196i \(-0.598819\pi\)
−0.305487 + 0.952196i \(0.598819\pi\)
\(318\) 0 0
\(319\) −9.18000 −0.513981
\(320\) 9.49236 0.530639
\(321\) 0 0
\(322\) 13.3179 0.742179
\(323\) 5.04594 0.280764
\(324\) 0 0
\(325\) −11.3759 −0.631021
\(326\) 20.7396 1.14866
\(327\) 0 0
\(328\) −13.2946 −0.734074
\(329\) −3.11843 −0.171925
\(330\) 0 0
\(331\) −14.9176 −0.819946 −0.409973 0.912098i \(-0.634462\pi\)
−0.409973 + 0.912098i \(0.634462\pi\)
\(332\) −2.77773 −0.152448
\(333\) 0 0
\(334\) −11.1044 −0.607605
\(335\) −11.3479 −0.620003
\(336\) 0 0
\(337\) 9.00961 0.490785 0.245392 0.969424i \(-0.421083\pi\)
0.245392 + 0.969424i \(0.421083\pi\)
\(338\) −24.8257 −1.35034
\(339\) 0 0
\(340\) −5.44649 −0.295378
\(341\) 12.5734 0.680889
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 10.6669 0.575122
\(345\) 0 0
\(346\) −21.5907 −1.16073
\(347\) 2.34030 0.125634 0.0628169 0.998025i \(-0.479992\pi\)
0.0628169 + 0.998025i \(0.479992\pi\)
\(348\) 0 0
\(349\) −16.1455 −0.864249 −0.432125 0.901814i \(-0.642236\pi\)
−0.432125 + 0.901814i \(0.642236\pi\)
\(350\) −3.30106 −0.176449
\(351\) 0 0
\(352\) 3.81268 0.203217
\(353\) −15.4517 −0.822412 −0.411206 0.911542i \(-0.634892\pi\)
−0.411206 + 0.911542i \(0.634892\pi\)
\(354\) 0 0
\(355\) −8.32231 −0.441702
\(356\) −1.15680 −0.0613103
\(357\) 0 0
\(358\) −27.0831 −1.43139
\(359\) 22.3811 1.18123 0.590616 0.806953i \(-0.298885\pi\)
0.590616 + 0.806953i \(0.298885\pi\)
\(360\) 0 0
\(361\) −18.5327 −0.975407
\(362\) −32.7189 −1.71967
\(363\) 0 0
\(364\) −2.33597 −0.122438
\(365\) −13.4475 −0.703877
\(366\) 0 0
\(367\) −23.4592 −1.22456 −0.612280 0.790641i \(-0.709747\pi\)
−0.612280 + 0.790641i \(0.709747\pi\)
\(368\) −39.9481 −2.08244
\(369\) 0 0
\(370\) 30.2343 1.57180
\(371\) 7.03105 0.365034
\(372\) 0 0
\(373\) 26.8125 1.38830 0.694150 0.719830i \(-0.255780\pi\)
0.694150 + 0.719830i \(0.255780\pi\)
\(374\) 18.1690 0.939497
\(375\) 0 0
\(376\) 7.61737 0.392836
\(377\) −31.2900 −1.61152
\(378\) 0 0
\(379\) 19.2840 0.990551 0.495275 0.868736i \(-0.335067\pi\)
0.495275 + 0.868736i \(0.335067\pi\)
\(380\) −0.504354 −0.0258728
\(381\) 0 0
\(382\) −19.1344 −0.979002
\(383\) 28.5258 1.45760 0.728799 0.684727i \(-0.240079\pi\)
0.728799 + 0.684727i \(0.240079\pi\)
\(384\) 0 0
\(385\) −2.67911 −0.136540
\(386\) 27.5093 1.40019
\(387\) 0 0
\(388\) 2.33312 0.118446
\(389\) 27.3537 1.38689 0.693443 0.720511i \(-0.256093\pi\)
0.693443 + 0.720511i \(0.256093\pi\)
\(390\) 0 0
\(391\) −63.0084 −3.18647
\(392\) 2.44269 0.123374
\(393\) 0 0
\(394\) −29.6489 −1.49369
\(395\) −26.7936 −1.34813
\(396\) 0 0
\(397\) −16.9610 −0.851250 −0.425625 0.904900i \(-0.639946\pi\)
−0.425625 + 0.904900i \(0.639946\pi\)
\(398\) −12.5023 −0.626685
\(399\) 0 0
\(400\) 9.90177 0.495088
\(401\) −17.7166 −0.884723 −0.442362 0.896837i \(-0.645859\pi\)
−0.442362 + 0.896837i \(0.645859\pi\)
\(402\) 0 0
\(403\) 42.8565 2.13483
\(404\) 8.24621 0.410264
\(405\) 0 0
\(406\) −9.07974 −0.450620
\(407\) −17.9990 −0.892177
\(408\) 0 0
\(409\) −1.61511 −0.0798619 −0.0399310 0.999202i \(-0.512714\pi\)
−0.0399310 + 0.999202i \(0.512714\pi\)
\(410\) 14.4221 0.712257
\(411\) 0 0
\(412\) −2.76348 −0.136147
\(413\) −5.82826 −0.286790
\(414\) 0 0
\(415\) −10.8587 −0.533031
\(416\) 12.9955 0.637158
\(417\) 0 0
\(418\) 1.68248 0.0822927
\(419\) −15.8383 −0.773753 −0.386876 0.922132i \(-0.626446\pi\)
−0.386876 + 0.922132i \(0.626446\pi\)
\(420\) 0 0
\(421\) −15.1541 −0.738564 −0.369282 0.929317i \(-0.620396\pi\)
−0.369282 + 0.929317i \(0.620396\pi\)
\(422\) −6.36072 −0.309635
\(423\) 0 0
\(424\) −17.1747 −0.834076
\(425\) 15.6176 0.757567
\(426\) 0 0
\(427\) 6.57944 0.318401
\(428\) −0.780905 −0.0377465
\(429\) 0 0
\(430\) −11.5715 −0.558029
\(431\) 28.5503 1.37522 0.687610 0.726080i \(-0.258660\pi\)
0.687610 + 0.726080i \(0.258660\pi\)
\(432\) 0 0
\(433\) 32.9912 1.58546 0.792729 0.609575i \(-0.208660\pi\)
0.792729 + 0.609575i \(0.208660\pi\)
\(434\) 12.4361 0.596952
\(435\) 0 0
\(436\) −7.17928 −0.343825
\(437\) −5.83468 −0.279110
\(438\) 0 0
\(439\) −20.1904 −0.963636 −0.481818 0.876271i \(-0.660023\pi\)
−0.481818 + 0.876271i \(0.660023\pi\)
\(440\) 6.54422 0.311984
\(441\) 0 0
\(442\) 61.9290 2.94566
\(443\) −40.8990 −1.94317 −0.971584 0.236694i \(-0.923936\pi\)
−0.971584 + 0.236694i \(0.923936\pi\)
\(444\) 0 0
\(445\) −4.52215 −0.214370
\(446\) −7.83587 −0.371039
\(447\) 0 0
\(448\) −5.58925 −0.264067
\(449\) 18.4836 0.872293 0.436146 0.899876i \(-0.356343\pi\)
0.436146 + 0.899876i \(0.356343\pi\)
\(450\) 0 0
\(451\) −8.58574 −0.404287
\(452\) 6.32835 0.297660
\(453\) 0 0
\(454\) 8.84882 0.415296
\(455\) −9.13173 −0.428102
\(456\) 0 0
\(457\) 4.17547 0.195320 0.0976601 0.995220i \(-0.468864\pi\)
0.0976601 + 0.995220i \(0.468864\pi\)
\(458\) −18.4614 −0.862645
\(459\) 0 0
\(460\) 6.29784 0.293638
\(461\) −27.4411 −1.27806 −0.639029 0.769182i \(-0.720664\pi\)
−0.639029 + 0.769182i \(0.720664\pi\)
\(462\) 0 0
\(463\) −28.4925 −1.32416 −0.662078 0.749435i \(-0.730325\pi\)
−0.662078 + 0.749435i \(0.730325\pi\)
\(464\) 27.2354 1.26437
\(465\) 0 0
\(466\) 35.5702 1.64776
\(467\) 31.9965 1.48062 0.740311 0.672265i \(-0.234678\pi\)
0.740311 + 0.672265i \(0.234678\pi\)
\(468\) 0 0
\(469\) 6.68183 0.308538
\(470\) −8.26336 −0.381161
\(471\) 0 0
\(472\) 14.2366 0.655295
\(473\) 6.88874 0.316745
\(474\) 0 0
\(475\) 1.44622 0.0663570
\(476\) 3.20698 0.146992
\(477\) 0 0
\(478\) −15.8808 −0.726369
\(479\) −0.125524 −0.00573535 −0.00286767 0.999996i \(-0.500913\pi\)
−0.00286767 + 0.999996i \(0.500913\pi\)
\(480\) 0 0
\(481\) −61.3495 −2.79730
\(482\) 41.8028 1.90406
\(483\) 0 0
\(484\) −3.69777 −0.168081
\(485\) 9.12058 0.414144
\(486\) 0 0
\(487\) 23.4115 1.06088 0.530439 0.847723i \(-0.322027\pi\)
0.530439 + 0.847723i \(0.322027\pi\)
\(488\) −16.0715 −0.727524
\(489\) 0 0
\(490\) −2.64985 −0.119708
\(491\) −20.9037 −0.943369 −0.471685 0.881767i \(-0.656354\pi\)
−0.471685 + 0.881767i \(0.656354\pi\)
\(492\) 0 0
\(493\) 42.9572 1.93469
\(494\) 5.73472 0.258017
\(495\) 0 0
\(496\) −37.3030 −1.67495
\(497\) 4.90031 0.219809
\(498\) 0 0
\(499\) 5.86107 0.262377 0.131189 0.991357i \(-0.458121\pi\)
0.131189 + 0.991357i \(0.458121\pi\)
\(500\) −5.25016 −0.234794
\(501\) 0 0
\(502\) −32.2040 −1.43733
\(503\) −30.4405 −1.35728 −0.678638 0.734473i \(-0.737429\pi\)
−0.678638 + 0.734473i \(0.737429\pi\)
\(504\) 0 0
\(505\) 32.2360 1.43448
\(506\) −21.0090 −0.933965
\(507\) 0 0
\(508\) −0.434445 −0.0192754
\(509\) 10.0065 0.443531 0.221766 0.975100i \(-0.428818\pi\)
0.221766 + 0.975100i \(0.428818\pi\)
\(510\) 0 0
\(511\) 7.91813 0.350277
\(512\) 11.5528 0.510565
\(513\) 0 0
\(514\) −19.7011 −0.868977
\(515\) −10.8029 −0.476034
\(516\) 0 0
\(517\) 4.91933 0.216352
\(518\) −17.8024 −0.782193
\(519\) 0 0
\(520\) 22.3060 0.978182
\(521\) −9.37377 −0.410672 −0.205336 0.978692i \(-0.565829\pi\)
−0.205336 + 0.978692i \(0.565829\pi\)
\(522\) 0 0
\(523\) 42.7780 1.87055 0.935277 0.353918i \(-0.115151\pi\)
0.935277 + 0.353918i \(0.115151\pi\)
\(524\) −5.65140 −0.246882
\(525\) 0 0
\(526\) 2.44447 0.106584
\(527\) −58.8364 −2.56295
\(528\) 0 0
\(529\) 49.8574 2.16771
\(530\) 18.6312 0.809287
\(531\) 0 0
\(532\) 0.296971 0.0128753
\(533\) −29.2645 −1.26759
\(534\) 0 0
\(535\) −3.05270 −0.131980
\(536\) −16.3217 −0.704988
\(537\) 0 0
\(538\) 33.9138 1.46213
\(539\) 1.57750 0.0679477
\(540\) 0 0
\(541\) 31.6416 1.36038 0.680189 0.733037i \(-0.261898\pi\)
0.680189 + 0.733037i \(0.261898\pi\)
\(542\) 24.3335 1.04521
\(543\) 0 0
\(544\) −17.8412 −0.764934
\(545\) −28.0651 −1.20218
\(546\) 0 0
\(547\) −23.6839 −1.01265 −0.506326 0.862342i \(-0.668997\pi\)
−0.506326 + 0.862342i \(0.668997\pi\)
\(548\) −4.82046 −0.205920
\(549\) 0 0
\(550\) 5.20742 0.222045
\(551\) 3.97790 0.169464
\(552\) 0 0
\(553\) 15.7765 0.670884
\(554\) −14.0628 −0.597470
\(555\) 0 0
\(556\) −1.92758 −0.0817475
\(557\) −20.7846 −0.880671 −0.440336 0.897833i \(-0.645141\pi\)
−0.440336 + 0.897833i \(0.645141\pi\)
\(558\) 0 0
\(559\) 23.4803 0.993109
\(560\) 7.94841 0.335881
\(561\) 0 0
\(562\) 7.81523 0.329666
\(563\) −12.9904 −0.547479 −0.273739 0.961804i \(-0.588261\pi\)
−0.273739 + 0.961804i \(0.588261\pi\)
\(564\) 0 0
\(565\) 24.7387 1.04076
\(566\) −3.09851 −0.130240
\(567\) 0 0
\(568\) −11.9699 −0.502247
\(569\) −29.1174 −1.22067 −0.610333 0.792145i \(-0.708964\pi\)
−0.610333 + 0.792145i \(0.708964\pi\)
\(570\) 0 0
\(571\) −21.9240 −0.917491 −0.458745 0.888568i \(-0.651701\pi\)
−0.458745 + 0.888568i \(0.651701\pi\)
\(572\) 3.68499 0.154077
\(573\) 0 0
\(574\) −8.49197 −0.354448
\(575\) −18.0588 −0.753106
\(576\) 0 0
\(577\) 15.9248 0.662958 0.331479 0.943463i \(-0.392452\pi\)
0.331479 + 0.943463i \(0.392452\pi\)
\(578\) −58.4960 −2.43311
\(579\) 0 0
\(580\) −4.29367 −0.178285
\(581\) 6.39375 0.265258
\(582\) 0 0
\(583\) −11.0915 −0.459362
\(584\) −19.3415 −0.800358
\(585\) 0 0
\(586\) −21.7196 −0.897229
\(587\) −1.21000 −0.0499420 −0.0249710 0.999688i \(-0.507949\pi\)
−0.0249710 + 0.999688i \(0.507949\pi\)
\(588\) 0 0
\(589\) −5.44834 −0.224495
\(590\) −15.4440 −0.635819
\(591\) 0 0
\(592\) 53.3996 2.19471
\(593\) 18.1805 0.746585 0.373292 0.927714i \(-0.378229\pi\)
0.373292 + 0.927714i \(0.378229\pi\)
\(594\) 0 0
\(595\) 12.5367 0.513954
\(596\) −0.250893 −0.0102770
\(597\) 0 0
\(598\) −71.6093 −2.92832
\(599\) 3.41903 0.139698 0.0698489 0.997558i \(-0.477748\pi\)
0.0698489 + 0.997558i \(0.477748\pi\)
\(600\) 0 0
\(601\) 20.4048 0.832328 0.416164 0.909290i \(-0.363374\pi\)
0.416164 + 0.909290i \(0.363374\pi\)
\(602\) 6.81350 0.277698
\(603\) 0 0
\(604\) −3.12959 −0.127341
\(605\) −14.4553 −0.587691
\(606\) 0 0
\(607\) 10.0628 0.408435 0.204217 0.978926i \(-0.434535\pi\)
0.204217 + 0.978926i \(0.434535\pi\)
\(608\) −1.65212 −0.0670023
\(609\) 0 0
\(610\) 17.4345 0.705902
\(611\) 16.7675 0.678341
\(612\) 0 0
\(613\) 0.173649 0.00701361 0.00350680 0.999994i \(-0.498884\pi\)
0.00350680 + 0.999994i \(0.498884\pi\)
\(614\) 44.7542 1.80613
\(615\) 0 0
\(616\) −3.85334 −0.155256
\(617\) 19.8820 0.800421 0.400210 0.916423i \(-0.368937\pi\)
0.400210 + 0.916423i \(0.368937\pi\)
\(618\) 0 0
\(619\) −41.5677 −1.67075 −0.835373 0.549684i \(-0.814748\pi\)
−0.835373 + 0.549684i \(0.814748\pi\)
\(620\) 5.88084 0.236180
\(621\) 0 0
\(622\) 15.8019 0.633599
\(623\) 2.66271 0.106679
\(624\) 0 0
\(625\) −9.94535 −0.397814
\(626\) 6.65064 0.265813
\(627\) 0 0
\(628\) −1.84969 −0.0738107
\(629\) 84.2250 3.35827
\(630\) 0 0
\(631\) 21.7909 0.867483 0.433742 0.901037i \(-0.357193\pi\)
0.433742 + 0.901037i \(0.357193\pi\)
\(632\) −38.5370 −1.53292
\(633\) 0 0
\(634\) 16.9727 0.674073
\(635\) −1.69832 −0.0673959
\(636\) 0 0
\(637\) 5.37691 0.213041
\(638\) 14.3233 0.567064
\(639\) 0 0
\(640\) −23.0201 −0.909948
\(641\) −14.0620 −0.555415 −0.277707 0.960666i \(-0.589575\pi\)
−0.277707 + 0.960666i \(0.589575\pi\)
\(642\) 0 0
\(643\) −3.13529 −0.123644 −0.0618219 0.998087i \(-0.519691\pi\)
−0.0618219 + 0.998087i \(0.519691\pi\)
\(644\) −3.70827 −0.146126
\(645\) 0 0
\(646\) −7.87303 −0.309760
\(647\) −31.1920 −1.22628 −0.613142 0.789973i \(-0.710094\pi\)
−0.613142 + 0.789973i \(0.710094\pi\)
\(648\) 0 0
\(649\) 9.19408 0.360899
\(650\) 17.7495 0.696192
\(651\) 0 0
\(652\) −5.77477 −0.226157
\(653\) −1.25769 −0.0492171 −0.0246085 0.999697i \(-0.507834\pi\)
−0.0246085 + 0.999697i \(0.507834\pi\)
\(654\) 0 0
\(655\) −22.0923 −0.863219
\(656\) 25.4723 0.994526
\(657\) 0 0
\(658\) 4.86560 0.189681
\(659\) −25.2125 −0.982140 −0.491070 0.871120i \(-0.663394\pi\)
−0.491070 + 0.871120i \(0.663394\pi\)
\(660\) 0 0
\(661\) 42.0623 1.63603 0.818017 0.575193i \(-0.195073\pi\)
0.818017 + 0.575193i \(0.195073\pi\)
\(662\) 23.2755 0.904628
\(663\) 0 0
\(664\) −15.6180 −0.606094
\(665\) 1.16092 0.0450184
\(666\) 0 0
\(667\) −49.6719 −1.92330
\(668\) 3.09193 0.119630
\(669\) 0 0
\(670\) 17.7058 0.684036
\(671\) −10.3791 −0.400679
\(672\) 0 0
\(673\) −25.1327 −0.968793 −0.484396 0.874849i \(-0.660961\pi\)
−0.484396 + 0.874849i \(0.660961\pi\)
\(674\) −14.0574 −0.541472
\(675\) 0 0
\(676\) 6.91250 0.265865
\(677\) 18.1849 0.698903 0.349452 0.936954i \(-0.386368\pi\)
0.349452 + 0.936954i \(0.386368\pi\)
\(678\) 0 0
\(679\) −5.37034 −0.206095
\(680\) −30.6232 −1.17435
\(681\) 0 0
\(682\) −19.6179 −0.751210
\(683\) 1.19845 0.0458573 0.0229286 0.999737i \(-0.492701\pi\)
0.0229286 + 0.999737i \(0.492701\pi\)
\(684\) 0 0
\(685\) −18.8441 −0.719995
\(686\) 1.56027 0.0595714
\(687\) 0 0
\(688\) −20.4376 −0.779176
\(689\) −37.8053 −1.44027
\(690\) 0 0
\(691\) −35.3781 −1.34585 −0.672924 0.739712i \(-0.734962\pi\)
−0.672924 + 0.739712i \(0.734962\pi\)
\(692\) 6.01177 0.228533
\(693\) 0 0
\(694\) −3.65150 −0.138609
\(695\) −7.53525 −0.285828
\(696\) 0 0
\(697\) 40.1763 1.52179
\(698\) 25.1914 0.953507
\(699\) 0 0
\(700\) 0.919153 0.0347407
\(701\) −21.6244 −0.816740 −0.408370 0.912816i \(-0.633903\pi\)
−0.408370 + 0.912816i \(0.633903\pi\)
\(702\) 0 0
\(703\) 7.79936 0.294158
\(704\) 8.81704 0.332305
\(705\) 0 0
\(706\) 24.1089 0.907349
\(707\) −18.9810 −0.713855
\(708\) 0 0
\(709\) −20.0892 −0.754467 −0.377233 0.926118i \(-0.623125\pi\)
−0.377233 + 0.926118i \(0.623125\pi\)
\(710\) 12.9850 0.487320
\(711\) 0 0
\(712\) −6.50418 −0.243754
\(713\) 68.0332 2.54786
\(714\) 0 0
\(715\) 14.4053 0.538728
\(716\) 7.54107 0.281823
\(717\) 0 0
\(718\) −34.9206 −1.30323
\(719\) −1.69180 −0.0630936 −0.0315468 0.999502i \(-0.510043\pi\)
−0.0315468 + 0.999502i \(0.510043\pi\)
\(720\) 0 0
\(721\) 6.36094 0.236894
\(722\) 28.9161 1.07615
\(723\) 0 0
\(724\) 9.11032 0.338582
\(725\) 12.3119 0.457254
\(726\) 0 0
\(727\) −19.4327 −0.720718 −0.360359 0.932814i \(-0.617346\pi\)
−0.360359 + 0.932814i \(0.617346\pi\)
\(728\) −13.1341 −0.486783
\(729\) 0 0
\(730\) 20.9818 0.776572
\(731\) −32.2354 −1.19227
\(732\) 0 0
\(733\) 1.18340 0.0437098 0.0218549 0.999761i \(-0.493043\pi\)
0.0218549 + 0.999761i \(0.493043\pi\)
\(734\) 36.6027 1.35103
\(735\) 0 0
\(736\) 20.6300 0.760430
\(737\) −10.5406 −0.388268
\(738\) 0 0
\(739\) −13.1398 −0.483355 −0.241677 0.970357i \(-0.577698\pi\)
−0.241677 + 0.970357i \(0.577698\pi\)
\(740\) −8.41848 −0.309470
\(741\) 0 0
\(742\) −10.9703 −0.402734
\(743\) −49.1903 −1.80462 −0.902308 0.431091i \(-0.858129\pi\)
−0.902308 + 0.431091i \(0.858129\pi\)
\(744\) 0 0
\(745\) −0.980785 −0.0359332
\(746\) −41.8348 −1.53168
\(747\) 0 0
\(748\) −5.05901 −0.184976
\(749\) 1.79748 0.0656785
\(750\) 0 0
\(751\) 3.63243 0.132549 0.0662746 0.997801i \(-0.478889\pi\)
0.0662746 + 0.997801i \(0.478889\pi\)
\(752\) −14.5947 −0.532215
\(753\) 0 0
\(754\) 48.8209 1.77795
\(755\) −12.2341 −0.445246
\(756\) 0 0
\(757\) −46.0208 −1.67265 −0.836327 0.548231i \(-0.815301\pi\)
−0.836327 + 0.548231i \(0.815301\pi\)
\(758\) −30.0882 −1.09285
\(759\) 0 0
\(760\) −2.83576 −0.102864
\(761\) −6.59912 −0.239218 −0.119609 0.992821i \(-0.538164\pi\)
−0.119609 + 0.992821i \(0.538164\pi\)
\(762\) 0 0
\(763\) 16.5252 0.598252
\(764\) 5.32782 0.192754
\(765\) 0 0
\(766\) −44.5079 −1.60814
\(767\) 31.3380 1.13155
\(768\) 0 0
\(769\) 18.9717 0.684138 0.342069 0.939675i \(-0.388872\pi\)
0.342069 + 0.939675i \(0.388872\pi\)
\(770\) 4.18013 0.150641
\(771\) 0 0
\(772\) −7.65975 −0.275681
\(773\) −21.5176 −0.773934 −0.386967 0.922094i \(-0.626477\pi\)
−0.386967 + 0.922094i \(0.626477\pi\)
\(774\) 0 0
\(775\) −16.8631 −0.605741
\(776\) 13.1181 0.470912
\(777\) 0 0
\(778\) −42.6792 −1.53012
\(779\) 3.72039 0.133297
\(780\) 0 0
\(781\) −7.73023 −0.276609
\(782\) 98.3102 3.51557
\(783\) 0 0
\(784\) −4.68015 −0.167148
\(785\) −7.23078 −0.258078
\(786\) 0 0
\(787\) −19.9237 −0.710205 −0.355102 0.934827i \(-0.615554\pi\)
−0.355102 + 0.934827i \(0.615554\pi\)
\(788\) 8.25550 0.294090
\(789\) 0 0
\(790\) 41.8052 1.48736
\(791\) −14.5665 −0.517926
\(792\) 0 0
\(793\) −35.3770 −1.25628
\(794\) 26.4638 0.939166
\(795\) 0 0
\(796\) 3.48117 0.123387
\(797\) −8.77923 −0.310976 −0.155488 0.987838i \(-0.549695\pi\)
−0.155488 + 0.987838i \(0.549695\pi\)
\(798\) 0 0
\(799\) −23.0196 −0.814376
\(800\) −5.11346 −0.180788
\(801\) 0 0
\(802\) 27.6426 0.976096
\(803\) −12.4908 −0.440792
\(804\) 0 0
\(805\) −14.4963 −0.510928
\(806\) −66.8677 −2.35532
\(807\) 0 0
\(808\) 46.3648 1.63111
\(809\) 10.0995 0.355080 0.177540 0.984114i \(-0.443186\pi\)
0.177540 + 0.984114i \(0.443186\pi\)
\(810\) 0 0
\(811\) −17.2459 −0.605584 −0.302792 0.953057i \(-0.597919\pi\)
−0.302792 + 0.953057i \(0.597919\pi\)
\(812\) 2.52818 0.0887217
\(813\) 0 0
\(814\) 28.0833 0.984319
\(815\) −22.5746 −0.790755
\(816\) 0 0
\(817\) −2.98504 −0.104433
\(818\) 2.52000 0.0881099
\(819\) 0 0
\(820\) −4.01572 −0.140235
\(821\) 2.22336 0.0775958 0.0387979 0.999247i \(-0.487647\pi\)
0.0387979 + 0.999247i \(0.487647\pi\)
\(822\) 0 0
\(823\) −49.5127 −1.72590 −0.862951 0.505287i \(-0.831387\pi\)
−0.862951 + 0.505287i \(0.831387\pi\)
\(824\) −15.5378 −0.541285
\(825\) 0 0
\(826\) 9.09367 0.316409
\(827\) 33.2176 1.15509 0.577544 0.816360i \(-0.304011\pi\)
0.577544 + 0.816360i \(0.304011\pi\)
\(828\) 0 0
\(829\) −56.8197 −1.97343 −0.986715 0.162464i \(-0.948056\pi\)
−0.986715 + 0.162464i \(0.948056\pi\)
\(830\) 16.9425 0.588081
\(831\) 0 0
\(832\) 30.0529 1.04190
\(833\) −7.38180 −0.255764
\(834\) 0 0
\(835\) 12.0869 0.418285
\(836\) −0.468472 −0.0162025
\(837\) 0 0
\(838\) 24.7121 0.853664
\(839\) 11.2187 0.387312 0.193656 0.981070i \(-0.437965\pi\)
0.193656 + 0.981070i \(0.437965\pi\)
\(840\) 0 0
\(841\) 4.86469 0.167748
\(842\) 23.6445 0.814842
\(843\) 0 0
\(844\) 1.77109 0.0609635
\(845\) 27.0222 0.929593
\(846\) 0 0
\(847\) 8.51150 0.292458
\(848\) 32.9063 1.13001
\(849\) 0 0
\(850\) −24.3677 −0.835807
\(851\) −97.3903 −3.33850
\(852\) 0 0
\(853\) −15.1859 −0.519956 −0.259978 0.965614i \(-0.583715\pi\)
−0.259978 + 0.965614i \(0.583715\pi\)
\(854\) −10.2657 −0.351285
\(855\) 0 0
\(856\) −4.39068 −0.150071
\(857\) 7.84113 0.267848 0.133924 0.990992i \(-0.457242\pi\)
0.133924 + 0.990992i \(0.457242\pi\)
\(858\) 0 0
\(859\) 5.04032 0.171973 0.0859867 0.996296i \(-0.472596\pi\)
0.0859867 + 0.996296i \(0.472596\pi\)
\(860\) 3.22200 0.109869
\(861\) 0 0
\(862\) −44.5462 −1.51725
\(863\) −22.2053 −0.755876 −0.377938 0.925831i \(-0.623367\pi\)
−0.377938 + 0.925831i \(0.623367\pi\)
\(864\) 0 0
\(865\) 23.5011 0.799061
\(866\) −51.4752 −1.74920
\(867\) 0 0
\(868\) −3.46273 −0.117533
\(869\) −24.8874 −0.844247
\(870\) 0 0
\(871\) −35.9276 −1.21736
\(872\) −40.3659 −1.36696
\(873\) 0 0
\(874\) 9.10368 0.307936
\(875\) 12.0848 0.408539
\(876\) 0 0
\(877\) 41.0971 1.38775 0.693875 0.720095i \(-0.255902\pi\)
0.693875 + 0.720095i \(0.255902\pi\)
\(878\) 31.5025 1.06316
\(879\) 0 0
\(880\) −12.5386 −0.422676
\(881\) −41.5727 −1.40062 −0.700309 0.713840i \(-0.746954\pi\)
−0.700309 + 0.713840i \(0.746954\pi\)
\(882\) 0 0
\(883\) 29.2046 0.982812 0.491406 0.870931i \(-0.336483\pi\)
0.491406 + 0.870931i \(0.336483\pi\)
\(884\) −17.2436 −0.579966
\(885\) 0 0
\(886\) 63.8135 2.14385
\(887\) −24.1854 −0.812067 −0.406033 0.913858i \(-0.633088\pi\)
−0.406033 + 0.913858i \(0.633088\pi\)
\(888\) 0 0
\(889\) 1.00000 0.0335389
\(890\) 7.05577 0.236510
\(891\) 0 0
\(892\) 2.18183 0.0730532
\(893\) −2.13165 −0.0713330
\(894\) 0 0
\(895\) 29.4794 0.985388
\(896\) 13.5546 0.452827
\(897\) 0 0
\(898\) −28.8393 −0.962381
\(899\) −46.3829 −1.54696
\(900\) 0 0
\(901\) 51.9018 1.72910
\(902\) 13.3961 0.446041
\(903\) 0 0
\(904\) 35.5815 1.18342
\(905\) 35.6139 1.18385
\(906\) 0 0
\(907\) −49.8040 −1.65371 −0.826857 0.562412i \(-0.809874\pi\)
−0.826857 + 0.562412i \(0.809874\pi\)
\(908\) −2.46388 −0.0817668
\(909\) 0 0
\(910\) 14.2480 0.472316
\(911\) 54.6229 1.80974 0.904869 0.425690i \(-0.139969\pi\)
0.904869 + 0.425690i \(0.139969\pi\)
\(912\) 0 0
\(913\) −10.0861 −0.333803
\(914\) −6.51486 −0.215492
\(915\) 0 0
\(916\) 5.14043 0.169845
\(917\) 13.0083 0.429573
\(918\) 0 0
\(919\) −27.0540 −0.892428 −0.446214 0.894926i \(-0.647228\pi\)
−0.446214 + 0.894926i \(0.647228\pi\)
\(920\) 35.4100 1.16743
\(921\) 0 0
\(922\) 42.8155 1.41005
\(923\) −26.3485 −0.867271
\(924\) 0 0
\(925\) 24.1397 0.793709
\(926\) 44.4559 1.46091
\(927\) 0 0
\(928\) −14.0649 −0.461701
\(929\) 17.5180 0.574748 0.287374 0.957818i \(-0.407218\pi\)
0.287374 + 0.957818i \(0.407218\pi\)
\(930\) 0 0
\(931\) −0.683565 −0.0224030
\(932\) −9.90423 −0.324424
\(933\) 0 0
\(934\) −49.9232 −1.63354
\(935\) −19.7766 −0.646764
\(936\) 0 0
\(937\) −52.0412 −1.70011 −0.850056 0.526692i \(-0.823432\pi\)
−0.850056 + 0.526692i \(0.823432\pi\)
\(938\) −10.4255 −0.340404
\(939\) 0 0
\(940\) 2.30087 0.0750460
\(941\) −10.3014 −0.335816 −0.167908 0.985803i \(-0.553701\pi\)
−0.167908 + 0.985803i \(0.553701\pi\)
\(942\) 0 0
\(943\) −46.4564 −1.51283
\(944\) −27.2771 −0.887795
\(945\) 0 0
\(946\) −10.7483 −0.349457
\(947\) −31.0642 −1.00945 −0.504726 0.863280i \(-0.668406\pi\)
−0.504726 + 0.863280i \(0.668406\pi\)
\(948\) 0 0
\(949\) −42.5750 −1.38204
\(950\) −2.25649 −0.0732102
\(951\) 0 0
\(952\) 18.0314 0.584402
\(953\) 28.8878 0.935768 0.467884 0.883790i \(-0.345016\pi\)
0.467884 + 0.883790i \(0.345016\pi\)
\(954\) 0 0
\(955\) 20.8274 0.673960
\(956\) 4.42187 0.143013
\(957\) 0 0
\(958\) 0.195852 0.00632768
\(959\) 11.0957 0.358299
\(960\) 0 0
\(961\) 32.5285 1.04931
\(962\) 95.7219 3.08620
\(963\) 0 0
\(964\) −11.6396 −0.374888
\(965\) −29.9434 −0.963911
\(966\) 0 0
\(967\) 33.6661 1.08263 0.541315 0.840820i \(-0.317927\pi\)
0.541315 + 0.840820i \(0.317927\pi\)
\(968\) −20.7909 −0.668246
\(969\) 0 0
\(970\) −14.2306 −0.456916
\(971\) −4.51372 −0.144852 −0.0724260 0.997374i \(-0.523074\pi\)
−0.0724260 + 0.997374i \(0.523074\pi\)
\(972\) 0 0
\(973\) 4.43688 0.142240
\(974\) −36.5283 −1.17044
\(975\) 0 0
\(976\) 30.7928 0.985652
\(977\) −49.7681 −1.59222 −0.796111 0.605151i \(-0.793113\pi\)
−0.796111 + 0.605151i \(0.793113\pi\)
\(978\) 0 0
\(979\) −4.20043 −0.134246
\(980\) 0.737828 0.0235690
\(981\) 0 0
\(982\) 32.6154 1.04080
\(983\) 28.8892 0.921422 0.460711 0.887550i \(-0.347594\pi\)
0.460711 + 0.887550i \(0.347594\pi\)
\(984\) 0 0
\(985\) 32.2723 1.02828
\(986\) −67.0248 −2.13450
\(987\) 0 0
\(988\) −1.59679 −0.0508006
\(989\) 37.2741 1.18525
\(990\) 0 0
\(991\) −16.6458 −0.528770 −0.264385 0.964417i \(-0.585169\pi\)
−0.264385 + 0.964417i \(0.585169\pi\)
\(992\) 19.2640 0.611632
\(993\) 0 0
\(994\) −7.64580 −0.242510
\(995\) 13.6085 0.431420
\(996\) 0 0
\(997\) 9.55174 0.302507 0.151253 0.988495i \(-0.451669\pi\)
0.151253 + 0.988495i \(0.451669\pi\)
\(998\) −9.14485 −0.289475
\(999\) 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 \(a_p\))