Properties

Label 1008.2.r.f.337.2
Level $1008$
Weight $2$
Character 1008.337
Analytic conductor $8.049$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1008.r (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.04892052375\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{-11})\)
Defining polynomial: \(x^{4} - x^{3} - 2 x^{2} - 3 x + 9\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 337.2
Root \(1.68614 - 0.396143i\) of defining polynomial
Character \(\chi\) \(=\) 1008.337
Dual form 1008.2.r.f.673.2

$q$-expansion

\(f(q)\) \(=\) \(q+(1.68614 + 0.396143i) q^{3} +(-2.18614 + 3.78651i) q^{5} +(0.500000 + 0.866025i) q^{7} +(2.68614 + 1.33591i) q^{9} +O(q^{10})\) \(q+(1.68614 + 0.396143i) q^{3} +(-2.18614 + 3.78651i) q^{5} +(0.500000 + 0.866025i) q^{7} +(2.68614 + 1.33591i) q^{9} +(-0.686141 - 1.18843i) q^{11} +(-1.00000 + 1.73205i) q^{13} +(-5.18614 + 5.51856i) q^{15} +1.37228 q^{17} -5.00000 q^{19} +(0.500000 + 1.65831i) q^{21} +(-0.813859 + 1.40965i) q^{23} +(-7.05842 - 12.2255i) q^{25} +(4.00000 + 3.31662i) q^{27} +(4.37228 + 7.57301i) q^{29} +(1.00000 - 1.73205i) q^{31} +(-0.686141 - 2.27567i) q^{33} -4.37228 q^{35} +2.00000 q^{37} +(-2.37228 + 2.52434i) q^{39} +(-2.31386 + 4.00772i) q^{41} +(-4.05842 - 7.02939i) q^{43} +(-10.9307 + 7.25061i) q^{45} +(-0.500000 + 0.866025i) q^{49} +(2.31386 + 0.543620i) q^{51} -8.74456 q^{53} +6.00000 q^{55} +(-8.43070 - 1.98072i) q^{57} +(-5.05842 + 8.76144i) q^{59} +(-1.55842 - 2.69927i) q^{61} +(0.186141 + 2.99422i) q^{63} +(-4.37228 - 7.57301i) q^{65} +(-1.05842 + 1.83324i) q^{67} +(-1.93070 + 2.05446i) q^{69} +7.11684 q^{71} +12.1168 q^{73} +(-7.05842 - 23.4101i) q^{75} +(0.686141 - 1.18843i) q^{77} +(-2.55842 - 4.43132i) q^{79} +(5.43070 + 7.17687i) q^{81} +(8.74456 + 15.1460i) q^{83} +(-3.00000 + 5.19615i) q^{85} +(4.37228 + 14.5012i) q^{87} +14.7446 q^{89} -2.00000 q^{91} +(2.37228 - 2.52434i) q^{93} +(10.9307 - 18.9325i) q^{95} +(4.05842 + 7.02939i) q^{97} +(-0.255437 - 4.10891i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + q^{3} - 3 q^{5} + 2 q^{7} + 5 q^{9} + O(q^{10}) \) \( 4 q + q^{3} - 3 q^{5} + 2 q^{7} + 5 q^{9} + 3 q^{11} - 4 q^{13} - 15 q^{15} - 6 q^{17} - 20 q^{19} + 2 q^{21} - 9 q^{23} - 11 q^{25} + 16 q^{27} + 6 q^{29} + 4 q^{31} + 3 q^{33} - 6 q^{35} + 8 q^{37} + 2 q^{39} - 15 q^{41} + q^{43} - 15 q^{45} - 2 q^{49} + 15 q^{51} - 12 q^{53} + 24 q^{55} - 5 q^{57} - 3 q^{59} + 11 q^{61} - 5 q^{63} - 6 q^{65} + 13 q^{67} + 21 q^{69} - 6 q^{71} + 14 q^{73} - 11 q^{75} - 3 q^{77} + 7 q^{79} - 7 q^{81} + 12 q^{83} - 12 q^{85} + 6 q^{87} + 36 q^{89} - 8 q^{91} - 2 q^{93} + 15 q^{95} - q^{97} - 24 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(577\) \(757\) \(785\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.68614 + 0.396143i 0.973494 + 0.228714i
\(4\) 0 0
\(5\) −2.18614 + 3.78651i −0.977672 + 1.69338i −0.306851 + 0.951757i \(0.599275\pi\)
−0.670820 + 0.741620i \(0.734058\pi\)
\(6\) 0 0
\(7\) 0.500000 + 0.866025i 0.188982 + 0.327327i
\(8\) 0 0
\(9\) 2.68614 + 1.33591i 0.895380 + 0.445302i
\(10\) 0 0
\(11\) −0.686141 1.18843i −0.206879 0.358325i 0.743851 0.668346i \(-0.232997\pi\)
−0.950730 + 0.310021i \(0.899664\pi\)
\(12\) 0 0
\(13\) −1.00000 + 1.73205i −0.277350 + 0.480384i −0.970725 0.240192i \(-0.922790\pi\)
0.693375 + 0.720577i \(0.256123\pi\)
\(14\) 0 0
\(15\) −5.18614 + 5.51856i −1.33906 + 1.42489i
\(16\) 0 0
\(17\) 1.37228 0.332827 0.166414 0.986056i \(-0.446781\pi\)
0.166414 + 0.986056i \(0.446781\pi\)
\(18\) 0 0
\(19\) −5.00000 −1.14708 −0.573539 0.819178i \(-0.694430\pi\)
−0.573539 + 0.819178i \(0.694430\pi\)
\(20\) 0 0
\(21\) 0.500000 + 1.65831i 0.109109 + 0.361873i
\(22\) 0 0
\(23\) −0.813859 + 1.40965i −0.169701 + 0.293931i −0.938315 0.345782i \(-0.887614\pi\)
0.768613 + 0.639713i \(0.220947\pi\)
\(24\) 0 0
\(25\) −7.05842 12.2255i −1.41168 2.44511i
\(26\) 0 0
\(27\) 4.00000 + 3.31662i 0.769800 + 0.638285i
\(28\) 0 0
\(29\) 4.37228 + 7.57301i 0.811912 + 1.40627i 0.911524 + 0.411247i \(0.134907\pi\)
−0.0996117 + 0.995026i \(0.531760\pi\)
\(30\) 0 0
\(31\) 1.00000 1.73205i 0.179605 0.311086i −0.762140 0.647412i \(-0.775851\pi\)
0.941745 + 0.336327i \(0.109185\pi\)
\(32\) 0 0
\(33\) −0.686141 2.27567i −0.119442 0.396143i
\(34\) 0 0
\(35\) −4.37228 −0.739050
\(36\) 0 0
\(37\) 2.00000 0.328798 0.164399 0.986394i \(-0.447432\pi\)
0.164399 + 0.986394i \(0.447432\pi\)
\(38\) 0 0
\(39\) −2.37228 + 2.52434i −0.379869 + 0.404218i
\(40\) 0 0
\(41\) −2.31386 + 4.00772i −0.361364 + 0.625901i −0.988186 0.153262i \(-0.951022\pi\)
0.626821 + 0.779163i \(0.284356\pi\)
\(42\) 0 0
\(43\) −4.05842 7.02939i −0.618904 1.07197i −0.989686 0.143253i \(-0.954244\pi\)
0.370783 0.928720i \(-0.379090\pi\)
\(44\) 0 0
\(45\) −10.9307 + 7.25061i −1.62945 + 1.08086i
\(46\) 0 0
\(47\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(48\) 0 0
\(49\) −0.500000 + 0.866025i −0.0714286 + 0.123718i
\(50\) 0 0
\(51\) 2.31386 + 0.543620i 0.324005 + 0.0761221i
\(52\) 0 0
\(53\) −8.74456 −1.20116 −0.600579 0.799565i \(-0.705063\pi\)
−0.600579 + 0.799565i \(0.705063\pi\)
\(54\) 0 0
\(55\) 6.00000 0.809040
\(56\) 0 0
\(57\) −8.43070 1.98072i −1.11667 0.262352i
\(58\) 0 0
\(59\) −5.05842 + 8.76144i −0.658550 + 1.14064i 0.322441 + 0.946590i \(0.395497\pi\)
−0.980991 + 0.194053i \(0.937837\pi\)
\(60\) 0 0
\(61\) −1.55842 2.69927i −0.199535 0.345606i 0.748842 0.662748i \(-0.230610\pi\)
−0.948378 + 0.317142i \(0.897277\pi\)
\(62\) 0 0
\(63\) 0.186141 + 2.99422i 0.0234515 + 0.377236i
\(64\) 0 0
\(65\) −4.37228 7.57301i −0.542315 0.939317i
\(66\) 0 0
\(67\) −1.05842 + 1.83324i −0.129307 + 0.223966i −0.923408 0.383819i \(-0.874609\pi\)
0.794101 + 0.607785i \(0.207942\pi\)
\(68\) 0 0
\(69\) −1.93070 + 2.05446i −0.232429 + 0.247327i
\(70\) 0 0
\(71\) 7.11684 0.844614 0.422307 0.906453i \(-0.361220\pi\)
0.422307 + 0.906453i \(0.361220\pi\)
\(72\) 0 0
\(73\) 12.1168 1.41817 0.709085 0.705123i \(-0.249108\pi\)
0.709085 + 0.705123i \(0.249108\pi\)
\(74\) 0 0
\(75\) −7.05842 23.4101i −0.815036 2.70317i
\(76\) 0 0
\(77\) 0.686141 1.18843i 0.0781930 0.135434i
\(78\) 0 0
\(79\) −2.55842 4.43132i −0.287845 0.498562i 0.685450 0.728120i \(-0.259605\pi\)
−0.973295 + 0.229557i \(0.926272\pi\)
\(80\) 0 0
\(81\) 5.43070 + 7.17687i 0.603411 + 0.797430i
\(82\) 0 0
\(83\) 8.74456 + 15.1460i 0.959840 + 1.66249i 0.722881 + 0.690973i \(0.242818\pi\)
0.236960 + 0.971519i \(0.423849\pi\)
\(84\) 0 0
\(85\) −3.00000 + 5.19615i −0.325396 + 0.563602i
\(86\) 0 0
\(87\) 4.37228 + 14.5012i 0.468758 + 1.55469i
\(88\) 0 0
\(89\) 14.7446 1.56292 0.781460 0.623955i \(-0.214475\pi\)
0.781460 + 0.623955i \(0.214475\pi\)
\(90\) 0 0
\(91\) −2.00000 −0.209657
\(92\) 0 0
\(93\) 2.37228 2.52434i 0.245994 0.261762i
\(94\) 0 0
\(95\) 10.9307 18.9325i 1.12147 1.94244i
\(96\) 0 0
\(97\) 4.05842 + 7.02939i 0.412070 + 0.713727i 0.995116 0.0987127i \(-0.0314725\pi\)
−0.583046 + 0.812439i \(0.698139\pi\)
\(98\) 0 0
\(99\) −0.255437 4.10891i −0.0256724 0.412961i
\(100\) 0 0
\(101\) −0.813859 1.40965i −0.0809820 0.140265i 0.822690 0.568490i \(-0.192472\pi\)
−0.903672 + 0.428225i \(0.859139\pi\)
\(102\) 0 0
\(103\) −5.00000 + 8.66025i −0.492665 + 0.853320i −0.999964 0.00844953i \(-0.997310\pi\)
0.507300 + 0.861770i \(0.330644\pi\)
\(104\) 0 0
\(105\) −7.37228 1.73205i −0.719461 0.169031i
\(106\) 0 0
\(107\) 7.37228 0.712705 0.356353 0.934352i \(-0.384020\pi\)
0.356353 + 0.934352i \(0.384020\pi\)
\(108\) 0 0
\(109\) 14.0000 1.34096 0.670478 0.741929i \(-0.266089\pi\)
0.670478 + 0.741929i \(0.266089\pi\)
\(110\) 0 0
\(111\) 3.37228 + 0.792287i 0.320083 + 0.0752006i
\(112\) 0 0
\(113\) 2.18614 3.78651i 0.205655 0.356205i −0.744686 0.667415i \(-0.767401\pi\)
0.950341 + 0.311210i \(0.100734\pi\)
\(114\) 0 0
\(115\) −3.55842 6.16337i −0.331825 0.574737i
\(116\) 0 0
\(117\) −5.00000 + 3.31662i −0.462250 + 0.306622i
\(118\) 0 0
\(119\) 0.686141 + 1.18843i 0.0628984 + 0.108943i
\(120\) 0 0
\(121\) 4.55842 7.89542i 0.414402 0.717765i
\(122\) 0 0
\(123\) −5.48913 + 5.84096i −0.494938 + 0.526662i
\(124\) 0 0
\(125\) 39.8614 3.56531
\(126\) 0 0
\(127\) −3.11684 −0.276575 −0.138288 0.990392i \(-0.544160\pi\)
−0.138288 + 0.990392i \(0.544160\pi\)
\(128\) 0 0
\(129\) −4.05842 13.4603i −0.357324 1.18511i
\(130\) 0 0
\(131\) −0.813859 + 1.40965i −0.0711072 + 0.123161i −0.899387 0.437154i \(-0.855987\pi\)
0.828280 + 0.560315i \(0.189320\pi\)
\(132\) 0 0
\(133\) −2.50000 4.33013i −0.216777 0.375470i
\(134\) 0 0
\(135\) −21.3030 + 7.89542i −1.83347 + 0.679529i
\(136\) 0 0
\(137\) −5.31386 9.20387i −0.453994 0.786340i 0.544636 0.838672i \(-0.316668\pi\)
−0.998630 + 0.0523324i \(0.983334\pi\)
\(138\) 0 0
\(139\) 6.61684 11.4607i 0.561233 0.972085i −0.436156 0.899871i \(-0.643660\pi\)
0.997389 0.0722136i \(-0.0230063\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 2.74456 0.229512
\(144\) 0 0
\(145\) −38.2337 −3.17513
\(146\) 0 0
\(147\) −1.18614 + 1.26217i −0.0978312 + 0.104102i
\(148\) 0 0
\(149\) −1.62772 + 2.81929i −0.133348 + 0.230965i −0.924965 0.380052i \(-0.875906\pi\)
0.791617 + 0.611017i \(0.209239\pi\)
\(150\) 0 0
\(151\) 4.55842 + 7.89542i 0.370959 + 0.642520i 0.989713 0.143065i \(-0.0456957\pi\)
−0.618754 + 0.785585i \(0.712362\pi\)
\(152\) 0 0
\(153\) 3.68614 + 1.83324i 0.298007 + 0.148209i
\(154\) 0 0
\(155\) 4.37228 + 7.57301i 0.351190 + 0.608279i
\(156\) 0 0
\(157\) −4.55842 + 7.89542i −0.363802 + 0.630123i −0.988583 0.150677i \(-0.951855\pi\)
0.624781 + 0.780800i \(0.285188\pi\)
\(158\) 0 0
\(159\) −14.7446 3.46410i −1.16932 0.274721i
\(160\) 0 0
\(161\) −1.62772 −0.128282
\(162\) 0 0
\(163\) 18.2337 1.42817 0.714086 0.700058i \(-0.246842\pi\)
0.714086 + 0.700058i \(0.246842\pi\)
\(164\) 0 0
\(165\) 10.1168 + 2.37686i 0.787595 + 0.185038i
\(166\) 0 0
\(167\) −2.74456 + 4.75372i −0.212381 + 0.367854i −0.952459 0.304666i \(-0.901455\pi\)
0.740078 + 0.672521i \(0.234788\pi\)
\(168\) 0 0
\(169\) 4.50000 + 7.79423i 0.346154 + 0.599556i
\(170\) 0 0
\(171\) −13.4307 6.67954i −1.02707 0.510797i
\(172\) 0 0
\(173\) 3.00000 + 5.19615i 0.228086 + 0.395056i 0.957241 0.289292i \(-0.0934200\pi\)
−0.729155 + 0.684349i \(0.760087\pi\)
\(174\) 0 0
\(175\) 7.05842 12.2255i 0.533567 0.924164i
\(176\) 0 0
\(177\) −12.0000 + 12.7692i −0.901975 + 0.959789i
\(178\) 0 0
\(179\) −3.25544 −0.243323 −0.121661 0.992572i \(-0.538822\pi\)
−0.121661 + 0.992572i \(0.538822\pi\)
\(180\) 0 0
\(181\) 0.883156 0.0656445 0.0328222 0.999461i \(-0.489550\pi\)
0.0328222 + 0.999461i \(0.489550\pi\)
\(182\) 0 0
\(183\) −1.55842 5.16870i −0.115202 0.382081i
\(184\) 0 0
\(185\) −4.37228 + 7.57301i −0.321457 + 0.556779i
\(186\) 0 0
\(187\) −0.941578 1.63086i −0.0688550 0.119260i
\(188\) 0 0
\(189\) −0.872281 + 5.12241i −0.0634491 + 0.372601i
\(190\) 0 0
\(191\) −9.55842 16.5557i −0.691623 1.19793i −0.971306 0.237834i \(-0.923563\pi\)
0.279683 0.960092i \(-0.409771\pi\)
\(192\) 0 0
\(193\) 3.50000 6.06218i 0.251936 0.436365i −0.712123 0.702055i \(-0.752266\pi\)
0.964059 + 0.265689i \(0.0855996\pi\)
\(194\) 0 0
\(195\) −4.37228 14.5012i −0.313106 1.03845i
\(196\) 0 0
\(197\) −6.00000 −0.427482 −0.213741 0.976890i \(-0.568565\pi\)
−0.213741 + 0.976890i \(0.568565\pi\)
\(198\) 0 0
\(199\) 10.0000 0.708881 0.354441 0.935079i \(-0.384671\pi\)
0.354441 + 0.935079i \(0.384671\pi\)
\(200\) 0 0
\(201\) −2.51087 + 2.67181i −0.177103 + 0.188455i
\(202\) 0 0
\(203\) −4.37228 + 7.57301i −0.306874 + 0.531521i
\(204\) 0 0
\(205\) −10.1168 17.5229i −0.706591 1.22385i
\(206\) 0 0
\(207\) −4.06930 + 2.69927i −0.282836 + 0.187612i
\(208\) 0 0
\(209\) 3.43070 + 5.94215i 0.237307 + 0.411027i
\(210\) 0 0
\(211\) −8.00000 + 13.8564i −0.550743 + 0.953914i 0.447478 + 0.894295i \(0.352322\pi\)
−0.998221 + 0.0596196i \(0.981011\pi\)
\(212\) 0 0
\(213\) 12.0000 + 2.81929i 0.822226 + 0.193175i
\(214\) 0 0
\(215\) 35.4891 2.42034
\(216\) 0 0
\(217\) 2.00000 0.135769
\(218\) 0 0
\(219\) 20.4307 + 4.80001i 1.38058 + 0.324355i
\(220\) 0 0
\(221\) −1.37228 + 2.37686i −0.0923096 + 0.159885i
\(222\) 0 0
\(223\) −2.00000 3.46410i −0.133930 0.231973i 0.791258 0.611482i \(-0.209426\pi\)
−0.925188 + 0.379509i \(0.876093\pi\)
\(224\) 0 0
\(225\) −2.62772 42.2689i −0.175181 2.81793i
\(226\) 0 0
\(227\) −6.12772 10.6135i −0.406711 0.704444i 0.587808 0.809000i \(-0.299991\pi\)
−0.994519 + 0.104556i \(0.966658\pi\)
\(228\) 0 0
\(229\) 1.44158 2.49689i 0.0952622 0.164999i −0.814456 0.580226i \(-0.802964\pi\)
0.909718 + 0.415227i \(0.136298\pi\)
\(230\) 0 0
\(231\) 1.62772 1.73205i 0.107096 0.113961i
\(232\) 0 0
\(233\) −0.255437 −0.0167343 −0.00836713 0.999965i \(-0.502663\pi\)
−0.00836713 + 0.999965i \(0.502663\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −2.55842 8.48533i −0.166187 0.551181i
\(238\) 0 0
\(239\) 4.93070 8.54023i 0.318941 0.552421i −0.661327 0.750098i \(-0.730006\pi\)
0.980267 + 0.197677i \(0.0633396\pi\)
\(240\) 0 0
\(241\) −9.05842 15.6896i −0.583504 1.01066i −0.995060 0.0992745i \(-0.968348\pi\)
0.411556 0.911385i \(-0.364986\pi\)
\(242\) 0 0
\(243\) 6.31386 + 14.2525i 0.405034 + 0.914302i
\(244\) 0 0
\(245\) −2.18614 3.78651i −0.139667 0.241911i
\(246\) 0 0
\(247\) 5.00000 8.66025i 0.318142 0.551039i
\(248\) 0 0
\(249\) 8.74456 + 29.0024i 0.554164 + 1.83795i
\(250\) 0 0
\(251\) 9.00000 0.568075 0.284037 0.958813i \(-0.408326\pi\)
0.284037 + 0.958813i \(0.408326\pi\)
\(252\) 0 0
\(253\) 2.23369 0.140431
\(254\) 0 0
\(255\) −7.11684 + 7.57301i −0.445674 + 0.474240i
\(256\) 0 0
\(257\) 3.43070 5.94215i 0.214001 0.370661i −0.738962 0.673747i \(-0.764684\pi\)
0.952963 + 0.303086i \(0.0980170\pi\)
\(258\) 0 0
\(259\) 1.00000 + 1.73205i 0.0621370 + 0.107624i
\(260\) 0 0
\(261\) 1.62772 + 26.1831i 0.100753 + 1.62070i
\(262\) 0 0
\(263\) 3.81386 + 6.60580i 0.235173 + 0.407331i 0.959323 0.282311i \(-0.0911011\pi\)
−0.724150 + 0.689642i \(0.757768\pi\)
\(264\) 0 0
\(265\) 19.1168 33.1113i 1.17434 2.03401i
\(266\) 0 0
\(267\) 24.8614 + 5.84096i 1.52149 + 0.357461i
\(268\) 0 0
\(269\) −1.62772 −0.0992438 −0.0496219 0.998768i \(-0.515802\pi\)
−0.0496219 + 0.998768i \(0.515802\pi\)
\(270\) 0 0
\(271\) −16.2337 −0.986126 −0.493063 0.869994i \(-0.664123\pi\)
−0.493063 + 0.869994i \(0.664123\pi\)
\(272\) 0 0
\(273\) −3.37228 0.792287i −0.204100 0.0479514i
\(274\) 0 0
\(275\) −9.68614 + 16.7769i −0.584096 + 1.01168i
\(276\) 0 0
\(277\) 6.11684 + 10.5947i 0.367526 + 0.636573i 0.989178 0.146720i \(-0.0468717\pi\)
−0.621652 + 0.783293i \(0.713538\pi\)
\(278\) 0 0
\(279\) 5.00000 3.31662i 0.299342 0.198561i
\(280\) 0 0
\(281\) −8.18614 14.1788i −0.488344 0.845837i 0.511566 0.859244i \(-0.329066\pi\)
−0.999910 + 0.0134071i \(0.995732\pi\)
\(282\) 0 0
\(283\) 13.5584 23.4839i 0.805965 1.39597i −0.109673 0.993968i \(-0.534981\pi\)
0.915638 0.402004i \(-0.131686\pi\)
\(284\) 0 0
\(285\) 25.9307 27.5928i 1.53600 1.63446i
\(286\) 0 0
\(287\) −4.62772 −0.273166
\(288\) 0 0
\(289\) −15.1168 −0.889226
\(290\) 0 0
\(291\) 4.05842 + 13.4603i 0.237909 + 0.789055i
\(292\) 0 0
\(293\) 5.18614 8.98266i 0.302978 0.524773i −0.673831 0.738885i \(-0.735353\pi\)
0.976809 + 0.214113i \(0.0686859\pi\)
\(294\) 0 0
\(295\) −22.1168 38.3075i −1.28769 2.23035i
\(296\) 0 0
\(297\) 1.19702 7.02939i 0.0694579 0.407887i
\(298\) 0 0
\(299\) −1.62772 2.81929i −0.0941334 0.163044i
\(300\) 0 0
\(301\) 4.05842 7.02939i 0.233924 0.405167i
\(302\) 0 0
\(303\) −0.813859 2.69927i −0.0467550 0.155069i
\(304\) 0 0
\(305\) 13.6277 0.780321
\(306\) 0 0
\(307\) 13.0000 0.741949 0.370975 0.928643i \(-0.379024\pi\)
0.370975 + 0.928643i \(0.379024\pi\)
\(308\) 0 0
\(309\) −11.8614 + 12.6217i −0.674772 + 0.718023i
\(310\) 0 0
\(311\) 4.11684 7.13058i 0.233445 0.404338i −0.725375 0.688354i \(-0.758334\pi\)
0.958820 + 0.284016i \(0.0916668\pi\)
\(312\) 0 0
\(313\) 10.0584 + 17.4217i 0.568536 + 0.984733i 0.996711 + 0.0810370i \(0.0258232\pi\)
−0.428175 + 0.903696i \(0.640843\pi\)
\(314\) 0 0
\(315\) −11.7446 5.84096i −0.661731 0.329101i
\(316\) 0 0
\(317\) 3.00000 + 5.19615i 0.168497 + 0.291845i 0.937892 0.346929i \(-0.112775\pi\)
−0.769395 + 0.638774i \(0.779442\pi\)
\(318\) 0 0
\(319\) 6.00000 10.3923i 0.335936 0.581857i
\(320\) 0 0
\(321\) 12.4307 + 2.92048i 0.693814 + 0.163005i
\(322\) 0 0
\(323\) −6.86141 −0.381779
\(324\) 0 0
\(325\) 28.2337 1.56612
\(326\) 0 0
\(327\) 23.6060 + 5.54601i 1.30541 + 0.306695i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 11.1168 + 19.2549i 0.611037 + 1.05835i 0.991066 + 0.133373i \(0.0425807\pi\)
−0.380029 + 0.924975i \(0.624086\pi\)
\(332\) 0 0
\(333\) 5.37228 + 2.67181i 0.294399 + 0.146415i
\(334\) 0 0
\(335\) −4.62772 8.01544i −0.252839 0.437930i
\(336\) 0 0
\(337\) 4.05842 7.02939i 0.221076 0.382915i −0.734059 0.679086i \(-0.762376\pi\)
0.955135 + 0.296171i \(0.0957097\pi\)
\(338\) 0 0
\(339\) 5.18614 5.51856i 0.281672 0.299727i
\(340\) 0 0
\(341\) −2.74456 −0.148626
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) −3.55842 11.8020i −0.191579 0.635396i
\(346\) 0 0
\(347\) −5.05842 + 8.76144i −0.271550 + 0.470339i −0.969259 0.246043i \(-0.920870\pi\)
0.697709 + 0.716382i \(0.254203\pi\)
\(348\) 0 0
\(349\) 11.0000 + 19.0526i 0.588817 + 1.01986i 0.994388 + 0.105797i \(0.0337393\pi\)
−0.405571 + 0.914063i \(0.632927\pi\)
\(350\) 0 0
\(351\) −9.74456 + 3.61158i −0.520126 + 0.192772i
\(352\) 0 0
\(353\) 6.68614 + 11.5807i 0.355867 + 0.616380i 0.987266 0.159078i \(-0.0508522\pi\)
−0.631399 + 0.775458i \(0.717519\pi\)
\(354\) 0 0
\(355\) −15.5584 + 26.9480i −0.825755 + 1.43025i
\(356\) 0 0
\(357\) 0.686141 + 2.27567i 0.0363144 + 0.120441i
\(358\) 0 0
\(359\) −21.8614 −1.15380 −0.576900 0.816814i \(-0.695738\pi\)
−0.576900 + 0.816814i \(0.695738\pi\)
\(360\) 0 0
\(361\) 6.00000 0.315789
\(362\) 0 0
\(363\) 10.8139 11.5070i 0.567580 0.603961i
\(364\) 0 0
\(365\) −26.4891 + 45.8805i −1.38650 + 2.40150i
\(366\) 0 0
\(367\) −6.11684 10.5947i −0.319297 0.553038i 0.661045 0.750346i \(-0.270113\pi\)
−0.980341 + 0.197308i \(0.936780\pi\)
\(368\) 0 0
\(369\) −11.5693 + 7.67420i −0.602274 + 0.399503i
\(370\) 0 0
\(371\) −4.37228 7.57301i −0.226998 0.393171i
\(372\) 0 0
\(373\) 5.00000 8.66025i 0.258890 0.448411i −0.707055 0.707159i \(-0.749977\pi\)
0.965945 + 0.258748i \(0.0833099\pi\)
\(374\) 0 0
\(375\) 67.2119 + 15.7908i 3.47081 + 0.815435i
\(376\) 0 0
\(377\) −17.4891 −0.900736
\(378\) 0 0
\(379\) 8.11684 0.416934 0.208467 0.978029i \(-0.433153\pi\)
0.208467 + 0.978029i \(0.433153\pi\)
\(380\) 0 0
\(381\) −5.25544 1.23472i −0.269244 0.0632565i
\(382\) 0 0
\(383\) −16.3723 + 28.3576i −0.836584 + 1.44901i 0.0561493 + 0.998422i \(0.482118\pi\)
−0.892734 + 0.450584i \(0.851216\pi\)
\(384\) 0 0
\(385\) 3.00000 + 5.19615i 0.152894 + 0.264820i
\(386\) 0 0
\(387\) −1.51087 24.3036i −0.0768021 1.23542i
\(388\) 0 0
\(389\) −5.48913 9.50744i −0.278310 0.482047i 0.692655 0.721269i \(-0.256441\pi\)
−0.970965 + 0.239222i \(0.923107\pi\)
\(390\) 0 0
\(391\) −1.11684 + 1.93443i −0.0564812 + 0.0978284i
\(392\) 0 0
\(393\) −1.93070 + 2.05446i −0.0973911 + 0.103634i
\(394\) 0 0
\(395\) 22.3723 1.12567
\(396\) 0 0
\(397\) −22.0000 −1.10415 −0.552074 0.833795i \(-0.686163\pi\)
−0.552074 + 0.833795i \(0.686163\pi\)
\(398\) 0 0
\(399\) −2.50000 8.29156i −0.125157 0.415097i
\(400\) 0 0
\(401\) 5.87228 10.1711i 0.293248 0.507920i −0.681328 0.731978i \(-0.738597\pi\)
0.974576 + 0.224058i \(0.0719306\pi\)
\(402\) 0 0
\(403\) 2.00000 + 3.46410i 0.0996271 + 0.172559i
\(404\) 0 0
\(405\) −39.0475 + 4.87375i −1.94029 + 0.242178i
\(406\) 0 0
\(407\) −1.37228 2.37686i −0.0680215 0.117817i
\(408\) 0 0
\(409\) 11.1753 19.3561i 0.552581 0.957099i −0.445506 0.895279i \(-0.646976\pi\)
0.998087 0.0618200i \(-0.0196905\pi\)
\(410\) 0 0
\(411\) −5.31386 17.6241i −0.262113 0.869332i
\(412\) 0 0
\(413\) −10.1168 −0.497817
\(414\) 0 0
\(415\) −76.4674 −3.75364
\(416\) 0 0
\(417\) 15.6970 16.7031i 0.768686 0.817957i
\(418\) 0 0
\(419\) −6.30298 + 10.9171i −0.307921 + 0.533335i −0.977907 0.209039i \(-0.932967\pi\)
0.669986 + 0.742373i \(0.266300\pi\)
\(420\) 0 0
\(421\) −17.1168 29.6472i −0.834224 1.44492i −0.894661 0.446746i \(-0.852583\pi\)
0.0604368 0.998172i \(-0.480751\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −9.68614 16.7769i −0.469847 0.813799i
\(426\) 0 0
\(427\) 1.55842 2.69927i 0.0754173 0.130627i
\(428\) 0 0
\(429\) 4.62772 + 1.08724i 0.223428 + 0.0524925i
\(430\) 0 0
\(431\) 6.51087 0.313618 0.156809 0.987629i \(-0.449879\pi\)
0.156809 + 0.987629i \(0.449879\pi\)
\(432\) 0 0
\(433\) −20.1168 −0.966754 −0.483377 0.875412i \(-0.660590\pi\)
−0.483377 + 0.875412i \(0.660590\pi\)
\(434\) 0 0
\(435\) −64.4674 15.1460i −3.09097 0.726196i
\(436\) 0 0
\(437\) 4.06930 7.04823i 0.194661 0.337162i
\(438\) 0 0
\(439\) 4.00000 + 6.92820i 0.190910 + 0.330665i 0.945552 0.325471i \(-0.105523\pi\)
−0.754642 + 0.656136i \(0.772190\pi\)
\(440\) 0 0
\(441\) −2.50000 + 1.65831i −0.119048 + 0.0789673i
\(442\) 0 0
\(443\) −20.0584 34.7422i −0.953004 1.65065i −0.738870 0.673848i \(-0.764640\pi\)
−0.214134 0.976804i \(-0.568693\pi\)
\(444\) 0 0
\(445\) −32.2337 + 55.8304i −1.52802 + 2.64661i
\(446\) 0 0
\(447\) −3.86141 + 4.10891i −0.182638 + 0.194345i
\(448\) 0 0
\(449\) 33.0000 1.55737 0.778683 0.627417i \(-0.215888\pi\)
0.778683 + 0.627417i \(0.215888\pi\)
\(450\) 0 0
\(451\) 6.35053 0.299035
\(452\) 0 0
\(453\) 4.55842 + 15.1186i 0.214173 + 0.710333i
\(454\) 0 0
\(455\) 4.37228 7.57301i 0.204976 0.355028i
\(456\) 0 0
\(457\) 17.7337 + 30.7156i 0.829547 + 1.43682i 0.898394 + 0.439190i \(0.144735\pi\)
−0.0688472 + 0.997627i \(0.521932\pi\)
\(458\) 0 0
\(459\) 5.48913 + 4.55134i 0.256210 + 0.212438i
\(460\) 0 0
\(461\) −1.06930 1.85208i −0.0498021 0.0862598i 0.840050 0.542509i \(-0.182526\pi\)
−0.889852 + 0.456250i \(0.849192\pi\)
\(462\) 0 0
\(463\) −11.5584 + 20.0198i −0.537165 + 0.930398i 0.461890 + 0.886937i \(0.347172\pi\)
−0.999055 + 0.0434604i \(0.986162\pi\)
\(464\) 0 0
\(465\) 4.37228 + 14.5012i 0.202760 + 0.672478i
\(466\) 0 0
\(467\) −33.0951 −1.53146 −0.765729 0.643163i \(-0.777622\pi\)
−0.765729 + 0.643163i \(0.777622\pi\)
\(468\) 0 0
\(469\) −2.11684 −0.0977468
\(470\) 0 0
\(471\) −10.8139 + 11.5070i −0.498276 + 0.530214i
\(472\) 0 0
\(473\) −5.56930 + 9.64630i −0.256077 + 0.443538i
\(474\) 0 0
\(475\) 35.2921 + 61.1277i 1.61931 + 2.80473i
\(476\) 0 0
\(477\) −23.4891 11.6819i −1.07549 0.534879i
\(478\) 0 0
\(479\) 16.3723 + 28.3576i 0.748069 + 1.29569i 0.948747 + 0.316036i \(0.102352\pi\)
−0.200679 + 0.979657i \(0.564315\pi\)
\(480\) 0 0
\(481\) −2.00000 + 3.46410i −0.0911922 + 0.157949i
\(482\) 0 0
\(483\) −2.74456 0.644810i −0.124882 0.0293399i
\(484\) 0 0
\(485\) −35.4891 −1.61148
\(486\) 0 0
\(487\) −35.3505 −1.60189 −0.800943 0.598741i \(-0.795668\pi\)
−0.800943 + 0.598741i \(0.795668\pi\)
\(488\) 0 0
\(489\) 30.7446 + 7.22316i 1.39032 + 0.326642i
\(490\) 0 0
\(491\) −12.6861 + 21.9730i −0.572518 + 0.991629i 0.423789 + 0.905761i \(0.360700\pi\)
−0.996306 + 0.0858685i \(0.972634\pi\)
\(492\) 0 0
\(493\) 6.00000 + 10.3923i 0.270226 + 0.468046i
\(494\) 0 0
\(495\) 16.1168 + 8.01544i 0.724398 + 0.360267i
\(496\) 0 0
\(497\) 3.55842 + 6.16337i 0.159617 + 0.276465i
\(498\) 0 0
\(499\) 9.05842 15.6896i 0.405511 0.702365i −0.588870 0.808228i \(-0.700427\pi\)
0.994381 + 0.105863i \(0.0337604\pi\)
\(500\) 0 0
\(501\) −6.51087 + 6.92820i −0.290884 + 0.309529i
\(502\) 0 0
\(503\) 32.2337 1.43723 0.718615 0.695409i \(-0.244777\pi\)
0.718615 + 0.695409i \(0.244777\pi\)
\(504\) 0 0
\(505\) 7.11684 0.316695
\(506\) 0 0
\(507\) 4.50000 + 14.9248i 0.199852 + 0.662834i
\(508\) 0 0
\(509\) 14.4891 25.0959i 0.642219 1.11236i −0.342717 0.939439i \(-0.611347\pi\)
0.984936 0.172918i \(-0.0553194\pi\)
\(510\) 0 0
\(511\) 6.05842 + 10.4935i 0.268009 + 0.464205i
\(512\) 0 0
\(513\) −20.0000 16.5831i −0.883022 0.732163i
\(514\) 0 0
\(515\) −21.8614 37.8651i −0.963329 1.66853i
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 3.00000 + 9.94987i 0.131685 + 0.436751i
\(520\) 0 0
\(521\) −24.8614 −1.08920 −0.544599 0.838697i \(-0.683318\pi\)
−0.544599 + 0.838697i \(0.683318\pi\)
\(522\) 0 0
\(523\) 35.1168 1.53555 0.767776 0.640718i \(-0.221363\pi\)
0.767776 + 0.640718i \(0.221363\pi\)
\(524\) 0 0
\(525\) 16.7446 17.8178i 0.730793 0.777634i
\(526\) 0 0
\(527\) 1.37228 2.37686i 0.0597775 0.103538i
\(528\) 0 0
\(529\) 10.1753 + 17.6241i 0.442403 + 0.766264i
\(530\) 0 0
\(531\) −25.2921 + 16.7769i −1.09758 + 0.728055i
\(532\) 0 0
\(533\) −4.62772 8.01544i −0.200449 0.347187i
\(534\) 0 0
\(535\) −16.1168 + 27.9152i −0.696792 + 1.20688i
\(536\) 0 0
\(537\) −5.48913 1.28962i −0.236873 0.0556512i
\(538\) 0 0
\(539\) 1.37228 0.0591083
\(540\) 0 0
\(541\) −6.23369 −0.268007 −0.134004 0.990981i \(-0.542783\pi\)
−0.134004 + 0.990981i \(0.542783\pi\)
\(542\) 0 0
\(543\) 1.48913 + 0.349857i 0.0639045 + 0.0150138i
\(544\) 0 0
\(545\) −30.6060 + 53.0111i −1.31102 + 2.27075i
\(546\) 0 0
\(547\) 9.05842 + 15.6896i 0.387310 + 0.670841i 0.992087 0.125554i \(-0.0400709\pi\)
−0.604777 + 0.796395i \(0.706738\pi\)
\(548\) 0 0
\(549\) −0.580171 9.33252i −0.0247611 0.398302i
\(550\) 0 0
\(551\) −21.8614 37.8651i −0.931327 1.61311i
\(552\) 0 0
\(553\) 2.55842 4.43132i 0.108795 0.188439i
\(554\) 0 0
\(555\) −10.3723 + 11.0371i −0.440279 + 0.468499i
\(556\) 0 0
\(557\) 29.4891 1.24949 0.624747 0.780827i \(-0.285202\pi\)
0.624747 + 0.780827i \(0.285202\pi\)
\(558\) 0 0
\(559\) 16.2337 0.686612
\(560\) 0 0
\(561\) −0.941578 3.12286i −0.0397535 0.131847i
\(562\) 0 0
\(563\) 1.50000 2.59808i 0.0632175 0.109496i −0.832684 0.553748i \(-0.813197\pi\)
0.895902 + 0.444252i \(0.146530\pi\)
\(564\) 0 0
\(565\) 9.55842 + 16.5557i 0.402126 + 0.696502i
\(566\) 0 0
\(567\) −3.50000 + 8.29156i −0.146986 + 0.348213i
\(568\) 0 0
\(569\) −8.05842 13.9576i −0.337827 0.585133i 0.646197 0.763171i \(-0.276358\pi\)
−0.984024 + 0.178038i \(0.943025\pi\)
\(570\) 0 0
\(571\) −11.1753 + 19.3561i −0.467670 + 0.810029i −0.999318 0.0369371i \(-0.988240\pi\)
0.531647 + 0.846966i \(0.321573\pi\)
\(572\) 0 0
\(573\) −9.55842 31.7017i −0.399309 1.32436i
\(574\) 0 0
\(575\) 22.9783 0.958259
\(576\) 0 0
\(577\) 9.88316 0.411441 0.205721 0.978611i \(-0.434046\pi\)
0.205721 + 0.978611i \(0.434046\pi\)
\(578\) 0 0
\(579\) 8.30298 8.83518i 0.345060 0.367178i
\(580\) 0 0
\(581\) −8.74456 + 15.1460i −0.362786 + 0.628363i
\(582\) 0 0
\(583\) 6.00000 + 10.3923i 0.248495 + 0.430405i
\(584\) 0 0
\(585\) −1.62772 26.1831i −0.0672979 1.08254i
\(586\) 0 0
\(587\) 7.24456 + 12.5480i 0.299015 + 0.517909i 0.975911 0.218170i \(-0.0700086\pi\)
−0.676896 + 0.736079i \(0.736675\pi\)
\(588\) 0 0
\(589\) −5.00000 + 8.66025i −0.206021 + 0.356840i
\(590\) 0 0
\(591\) −10.1168 2.37686i −0.416151 0.0977710i
\(592\) 0 0
\(593\) 14.7446 0.605487 0.302743 0.953072i \(-0.402098\pi\)
0.302743 + 0.953072i \(0.402098\pi\)
\(594\) 0 0
\(595\) −6.00000 −0.245976
\(596\) 0 0
\(597\) 16.8614 + 3.96143i 0.690091 + 0.162131i
\(598\) 0 0
\(599\) 12.0000 20.7846i 0.490307 0.849236i −0.509631 0.860393i \(-0.670218\pi\)
0.999938 + 0.0111569i \(0.00355143\pi\)
\(600\) 0 0
\(601\) −12.0584 20.8858i −0.491873 0.851950i 0.508083 0.861308i \(-0.330354\pi\)
−0.999956 + 0.00935863i \(0.997021\pi\)
\(602\) 0 0
\(603\) −5.29211 + 3.51039i −0.215511 + 0.142954i
\(604\) 0 0
\(605\) 19.9307 + 34.5210i 0.810298 + 1.40348i
\(606\) 0 0
\(607\) 11.1168 19.2549i 0.451219 0.781534i −0.547243 0.836974i \(-0.684323\pi\)
0.998462 + 0.0554398i \(0.0176561\pi\)
\(608\) 0 0
\(609\) −10.3723 + 11.0371i −0.420306 + 0.447246i
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) −36.2337 −1.46346 −0.731732 0.681592i \(-0.761288\pi\)
−0.731732 + 0.681592i \(0.761288\pi\)
\(614\) 0 0
\(615\) −10.1168 33.5538i −0.407951 1.35302i
\(616\) 0 0
\(617\) −9.43070 + 16.3345i −0.379666 + 0.657600i −0.991014 0.133762i \(-0.957294\pi\)
0.611348 + 0.791362i \(0.290628\pi\)
\(618\) 0 0
\(619\) 22.7337 + 39.3759i 0.913744 + 1.58265i 0.808730 + 0.588180i \(0.200156\pi\)
0.105014 + 0.994471i \(0.466511\pi\)
\(620\) 0 0
\(621\) −7.93070 + 2.93932i −0.318248 + 0.117951i
\(622\) 0 0
\(623\) 7.37228 + 12.7692i 0.295364 + 0.511586i
\(624\) 0 0
\(625\) −51.8505 + 89.8078i −2.07402 + 3.59231i
\(626\) 0 0
\(627\) 3.43070 + 11.3784i 0.137009 + 0.454408i
\(628\) 0 0
\(629\) 2.74456 0.109433
\(630\) 0 0
\(631\) 37.3505 1.48690 0.743451 0.668791i \(-0.233188\pi\)
0.743451 + 0.668791i \(0.233188\pi\)
\(632\) 0 0
\(633\) −18.9783 + 20.1947i −0.754318 + 0.802667i
\(634\) 0 0
\(635\) 6.81386 11.8020i 0.270400 0.468346i
\(636\) 0 0
\(637\) −1.00000 1.73205i −0.0396214 0.0686264i
\(638\) 0 0
\(639\) 19.1168 + 9.50744i 0.756251 + 0.376109i
\(640\) 0 0
\(641\) −17.1060 29.6284i −0.675645 1.17025i −0.976280 0.216512i \(-0.930532\pi\)
0.300635 0.953739i \(-0.402802\pi\)
\(642\) 0 0
\(643\) 13.1753 22.8202i 0.519582 0.899942i −0.480159 0.877181i \(-0.659421\pi\)
0.999741 0.0227606i \(-0.00724556\pi\)
\(644\) 0 0
\(645\) 59.8397 + 14.0588i 2.35618 + 0.553564i
\(646\) 0 0
\(647\) −5.48913 −0.215800 −0.107900 0.994162i \(-0.534413\pi\)
−0.107900 + 0.994162i \(0.534413\pi\)
\(648\) 0 0
\(649\) 13.8832 0.544962
\(650\) 0 0
\(651\) 3.37228 + 0.792287i 0.132170 + 0.0310522i
\(652\) 0 0
\(653\) 13.3723 23.1615i 0.523298 0.906378i −0.476335 0.879264i \(-0.658035\pi\)
0.999632 0.0271143i \(-0.00863179\pi\)
\(654\) 0 0
\(655\) −3.55842 6.16337i −0.139039 0.240823i
\(656\) 0 0
\(657\) 32.5475 + 16.1870i 1.26980 + 0.631514i
\(658\) 0 0
\(659\) −10.3723 17.9653i −0.404047 0.699829i 0.590163 0.807284i \(-0.299063\pi\)
−0.994210 + 0.107454i \(0.965730\pi\)
\(660\) 0 0
\(661\) −13.5584 + 23.4839i −0.527361 + 0.913417i 0.472130 + 0.881529i \(0.343485\pi\)
−0.999491 + 0.0318879i \(0.989848\pi\)
\(662\) 0 0
\(663\) −3.25544 + 3.46410i −0.126431 + 0.134535i
\(664\) 0 0
\(665\) 21.8614 0.847749
\(666\) 0 0
\(667\) −14.2337 −0.551131
\(668\) 0 0
\(669\) −2.00000 6.63325i −0.0773245 0.256456i
\(670\) 0 0
\(671\) −2.13859 + 3.70415i −0.0825595 + 0.142997i
\(672\) 0 0
\(673\) 1.44158 + 2.49689i 0.0555687 + 0.0962479i 0.892472 0.451103i \(-0.148969\pi\)
−0.836903 + 0.547351i \(0.815636\pi\)
\(674\) 0 0
\(675\) 12.3139 72.3123i 0.473961 2.78330i
\(676\) 0 0
\(677\) −17.2337 29.8496i −0.662344 1.14721i −0.979998 0.199007i \(-0.936228\pi\)
0.317654 0.948207i \(-0.397105\pi\)
\(678\) 0 0
\(679\) −4.05842 + 7.02939i −0.155748 + 0.269763i
\(680\) 0 0
\(681\) −6.12772 20.3233i −0.234815 0.778792i
\(682\) 0 0
\(683\) −29.8397 −1.14178 −0.570891 0.821026i \(-0.693402\pi\)
−0.570891 + 0.821026i \(0.693402\pi\)
\(684\) 0 0
\(685\) 46.4674 1.77543
\(686\) 0 0
\(687\) 3.41983 3.63903i 0.130475 0.138838i
\(688\) 0 0
\(689\) 8.74456 15.1460i 0.333141 0.577018i
\(690\) 0 0
\(691\) −11.5584 20.0198i −0.439703 0.761588i 0.557963 0.829866i \(-0.311583\pi\)
−0.997666 + 0.0682775i \(0.978250\pi\)
\(692\) 0 0
\(693\) 3.43070 2.27567i 0.130322 0.0864456i
\(694\) 0 0
\(695\) 28.9307 + 50.1094i 1.09740 + 1.90076i
\(696\) 0 0
\(697\) −3.17527 + 5.49972i −0.120272 + 0.208317i
\(698\) 0 0
\(699\) −0.430703 0.101190i −0.0162907 0.00382735i
\(700\) 0 0
\(701\) −38.2337 −1.44407 −0.722033 0.691858i \(-0.756792\pi\)
−0.722033 + 0.691858i \(0.756792\pi\)
\(702\) 0 0
\(703\) −10.0000 −0.377157
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0.813859 1.40965i 0.0306083 0.0530152i
\(708\) 0 0
\(709\) −22.0000 38.1051i −0.826227 1.43107i −0.900978 0.433865i \(-0.857149\pi\)
0.0747503 0.997202i \(-0.476184\pi\)
\(710\) 0 0
\(711\) −0.952453 15.3210i −0.0357198 0.574581i
\(712\) 0 0
\(713\) 1.62772 + 2.81929i 0.0609585 + 0.105583i
\(714\) 0 0
\(715\) −6.00000 + 10.3923i −0.224387 + 0.388650i
\(716\) 0 0
\(717\) 11.6970 12.4468i 0.436833 0.464833i
\(718\) 0 0
\(719\) −2.74456 −0.102355 −0.0511775 0.998690i \(-0.516297\pi\)
−0.0511775 + 0.998690i \(0.516297\pi\)
\(720\) 0 0
\(721\) −10.0000 −0.372419
\(722\) 0 0
\(723\) −9.05842 30.0434i −0.336886 1.11733i
\(724\) 0 0
\(725\) 61.7228 106.907i 2.29233 3.97043i
\(726\) 0 0
\(727\) −18.1168 31.3793i −0.671917 1.16379i −0.977360 0.211583i \(-0.932138\pi\)
0.305443 0.952210i \(-0.401195\pi\)
\(728\) 0 0
\(729\) 5.00000 + 26.5330i 0.185185 + 0.982704i
\(730\) 0 0
\(731\) −5.56930 9.64630i −0.205988 0.356781i
\(732\) 0 0
\(733\) 20.5584 35.6082i 0.759343 1.31522i −0.183844 0.982956i \(-0.558854\pi\)
0.943186 0.332265i \(-0.107813\pi\)
\(734\) 0 0
\(735\) −2.18614 7.25061i −0.0806370 0.267443i
\(736\) 0 0
\(737\) 2.90491 0.107004
\(738\) 0 0
\(739\) 8.11684 0.298583 0.149291 0.988793i \(-0.452301\pi\)
0.149291 + 0.988793i \(0.452301\pi\)
\(740\) 0 0
\(741\) 11.8614 12.6217i 0.435740 0.463669i
\(742\) 0 0
\(743\) −6.86141 + 11.8843i −0.251721 + 0.435993i −0.964000 0.265904i \(-0.914330\pi\)
0.712279 + 0.701896i \(0.247663\pi\)
\(744\) 0 0
\(745\) −7.11684 12.3267i −0.260741 0.451617i
\(746\) 0 0
\(747\) 3.25544 + 52.3663i 0.119110 + 1.91598i
\(748\) 0 0
\(749\) 3.68614 + 6.38458i 0.134689 + 0.233288i
\(750\) 0 0
\(751\) −8.55842 + 14.8236i −0.312301 + 0.540922i −0.978860 0.204531i \(-0.934433\pi\)
0.666559 + 0.745452i \(0.267766\pi\)
\(752\) 0 0
\(753\) 15.1753 + 3.56529i 0.553017 + 0.129926i
\(754\) 0 0
\(755\) −39.8614 −1.45071
\(756\) 0 0
\(757\) 46.2337 1.68039 0.840196 0.542283i \(-0.182440\pi\)
0.840196 + 0.542283i \(0.182440\pi\)
\(758\) 0 0
\(759\) 3.76631 + 0.884861i 0.136708 + 0.0321184i
\(760\) 0 0
\(761\) −17.7446 + 30.7345i −0.643240 + 1.11412i 0.341465 + 0.939894i \(0.389077\pi\)
−0.984705 + 0.174230i \(0.944256\pi\)
\(762\) 0 0
\(763\) 7.00000 + 12.1244i 0.253417 + 0.438931i
\(764\) 0 0
\(765\) −15.0000 + 9.94987i −0.542326 + 0.359738i
\(766\) 0 0
\(767\) −10.1168 17.5229i −0.365298 0.632715i
\(768\) 0 0
\(769\) 5.00000 8.66025i 0.180305 0.312297i −0.761680 0.647954i \(-0.775625\pi\)
0.941984 + 0.335657i \(0.108958\pi\)
\(770\) 0 0
\(771\) 8.13859 8.66025i 0.293104 0.311891i
\(772\) 0 0
\(773\) −39.8614 −1.43372 −0.716858 0.697220i \(-0.754420\pi\)
−0.716858 + 0.697220i \(0.754420\pi\)
\(774\) 0 0
\(775\) −28.2337 −1.01418
\(776\) 0 0
\(777\) 1.00000 + 3.31662i 0.0358748 + 0.118983i
\(778\) 0 0
\(779\) 11.5693 20.0386i 0.414513 0.717958i
\(780\) 0 0
\(781\) −4.88316 8.45787i −0.174733 0.302647i
\(782\) 0 0
\(783\) −7.62772 + 44.7933i −0.272592 + 1.60078i
\(784\) 0 0
\(785\) −19.9307 34.5210i −0.711357 1.23211i
\(786\) 0 0
\(787\) −2.00000 + 3.46410i −0.0712923 + 0.123482i −0.899468 0.436987i \(-0.856046\pi\)
0.828176 + 0.560469i \(0.189379\pi\)
\(788\) 0 0
\(789\) 3.81386 + 12.6491i 0.135777 + 0.450321i
\(790\) 0 0
\(791\) 4.37228 0.155460
\(792\) 0 0
\(793\) 6.23369 0.221365
\(794\) 0 0
\(795\) 45.3505 48.2574i 1.60842 1.71151i