Properties

Label 1040.2.da.b.641.1
Level $1040$
Weight $2$
Character 1040.641
Analytic conductor $8.304$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1040 = 2^{4} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1040.da (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.30444181021\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.22581504.2
Defining polynomial: \(x^{8} - 4 x^{7} + 5 x^{6} + 2 x^{5} - 11 x^{4} + 4 x^{3} + 20 x^{2} - 32 x + 16\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 65)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 641.1
Root \(1.20036 - 0.747754i\) of defining polynomial
Character \(\chi\) \(=\) 1040.641
Dual form 1040.2.da.b.881.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.41342 + 2.44811i) q^{3} -1.00000i q^{5} +(1.64996 - 0.952606i) q^{7} +(-2.49551 - 4.32235i) q^{9} +O(q^{10})\) \(q+(-1.41342 + 2.44811i) q^{3} -1.00000i q^{5} +(1.64996 - 0.952606i) q^{7} +(-2.49551 - 4.32235i) q^{9} +(-0.926118 - 0.534695i) q^{11} +(1.40072 + 3.32235i) q^{13} +(2.44811 + 1.41342i) q^{15} +(0.318632 + 0.551886i) q^{17} +(-4.96410 + 2.86603i) q^{19} +5.38573i q^{21} +(-1.90893 + 3.30636i) q^{23} -1.00000 q^{25} +5.62828 q^{27} +(-4.72756 + 8.18837i) q^{29} +1.46410i q^{31} +(2.61799 - 1.51150i) q^{33} +(-0.952606 - 1.64996i) q^{35} +(0.655970 + 0.378725i) q^{37} +(-10.1133 - 1.26675i) q^{39} +(-0.232051 - 0.133975i) q^{41} +(-0.318632 - 0.551886i) q^{43} +(-4.32235 + 2.49551i) q^{45} -9.44613i q^{47} +(-1.68508 + 2.91865i) q^{49} -1.80144 q^{51} -6.99102 q^{53} +(-0.534695 + 0.926118i) q^{55} -16.2036i q^{57} +(0.641756 - 0.370518i) q^{59} +(-2.09928 - 3.63606i) q^{61} +(-8.23499 - 4.75447i) q^{63} +(3.32235 - 1.40072i) q^{65} +(7.01029 + 4.04739i) q^{67} +(-5.39623 - 9.34654i) q^{69} +(-8.45663 + 4.88244i) q^{71} +3.71649i q^{73} +(1.41342 - 2.44811i) q^{75} -2.03741 q^{77} +9.31937 q^{79} +(-0.468594 + 0.811629i) q^{81} -5.11778i q^{83} +(0.551886 - 0.318632i) q^{85} +(-13.3640 - 23.1472i) q^{87} +(-10.8932 - 6.28917i) q^{89} +(5.47602 + 4.14741i) q^{91} +(-3.58429 - 2.06939i) q^{93} +(2.86603 + 4.96410i) q^{95} +(-3.65597 + 2.11078i) q^{97} +5.33734i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 2 q^{3} + 6 q^{7} - 4 q^{9} + O(q^{10}) \) \( 8 q - 2 q^{3} + 6 q^{7} - 4 q^{9} + 6 q^{15} - 2 q^{17} - 12 q^{19} + 10 q^{23} - 8 q^{25} + 4 q^{27} - 8 q^{29} + 42 q^{33} - 10 q^{35} + 6 q^{37} + 12 q^{41} + 2 q^{43} + 12 q^{49} + 8 q^{51} - 24 q^{53} + 12 q^{59} - 28 q^{61} + 24 q^{63} - 8 q^{65} - 6 q^{67} - 16 q^{69} + 2 q^{75} - 36 q^{77} + 16 q^{79} + 8 q^{81} + 18 q^{85} - 22 q^{87} + 24 q^{89} - 28 q^{91} + 16 q^{95} - 30 q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1040\mathbb{Z}\right)^\times\).

\(n\) \(261\) \(417\) \(561\) \(911\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(1\)

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
\(3\) −1.41342 + 2.44811i −0.816038 + 1.41342i 0.0925423 + 0.995709i \(0.470501\pi\)
−0.908580 + 0.417710i \(0.862833\pi\)
\(4\) 0 0
\(5\) 1.00000i 0.447214i
\(6\) 0 0
\(7\) 1.64996 0.952606i 0.623627 0.360051i −0.154653 0.987969i \(-0.549426\pi\)
0.778280 + 0.627918i \(0.216093\pi\)
\(8\) 0 0
\(9\) −2.49551 4.32235i −0.831836 1.44078i
\(10\) 0 0
\(11\) −0.926118 0.534695i −0.279235 0.161217i 0.353842 0.935305i \(-0.384875\pi\)
−0.633077 + 0.774089i \(0.718208\pi\)
\(12\) 0 0
\(13\) 1.40072 + 3.32235i 0.388490 + 0.921453i
\(14\) 0 0
\(15\) 2.44811 + 1.41342i 0.632100 + 0.364943i
\(16\) 0 0
\(17\) 0.318632 + 0.551886i 0.0772795 + 0.133852i 0.902075 0.431579i \(-0.142043\pi\)
−0.824796 + 0.565431i \(0.808710\pi\)
\(18\) 0 0
\(19\) −4.96410 + 2.86603i −1.13884 + 0.657511i −0.946144 0.323747i \(-0.895057\pi\)
−0.192699 + 0.981258i \(0.561724\pi\)
\(20\) 0 0
\(21\) 5.38573i 1.17526i
\(22\) 0 0
\(23\) −1.90893 + 3.30636i −0.398039 + 0.689423i −0.993484 0.113973i \(-0.963642\pi\)
0.595445 + 0.803396i \(0.296976\pi\)
\(24\) 0 0
\(25\) −1.00000 −0.200000
\(26\) 0 0
\(27\) 5.62828 1.08316
\(28\) 0 0
\(29\) −4.72756 + 8.18837i −0.877886 + 1.52054i −0.0242288 + 0.999706i \(0.507713\pi\)
−0.853657 + 0.520836i \(0.825620\pi\)
\(30\) 0 0
\(31\) 1.46410i 0.262960i 0.991319 + 0.131480i \(0.0419730\pi\)
−0.991319 + 0.131480i \(0.958027\pi\)
\(32\) 0 0
\(33\) 2.61799 1.51150i 0.455733 0.263118i
\(34\) 0 0
\(35\) −0.952606 1.64996i −0.161020 0.278895i
\(36\) 0 0
\(37\) 0.655970 + 0.378725i 0.107841 + 0.0622619i 0.552950 0.833214i \(-0.313502\pi\)
−0.445110 + 0.895476i \(0.646835\pi\)
\(38\) 0 0
\(39\) −10.1133 1.26675i −1.61942 0.202842i
\(40\) 0 0
\(41\) −0.232051 0.133975i −0.0362402 0.0209233i 0.481770 0.876297i \(-0.339994\pi\)
−0.518011 + 0.855374i \(0.673327\pi\)
\(42\) 0 0
\(43\) −0.318632 0.551886i −0.0485909 0.0841618i 0.840707 0.541490i \(-0.182140\pi\)
−0.889298 + 0.457328i \(0.848806\pi\)
\(44\) 0 0
\(45\) −4.32235 + 2.49551i −0.644337 + 0.372008i
\(46\) 0 0
\(47\) 9.44613i 1.37786i −0.724828 0.688930i \(-0.758081\pi\)
0.724828 0.688930i \(-0.241919\pi\)
\(48\) 0 0
\(49\) −1.68508 + 2.91865i −0.240726 + 0.416950i
\(50\) 0 0
\(51\) −1.80144 −0.252252
\(52\) 0 0
\(53\) −6.99102 −0.960290 −0.480145 0.877189i \(-0.659416\pi\)
−0.480145 + 0.877189i \(0.659416\pi\)
\(54\) 0 0
\(55\) −0.534695 + 0.926118i −0.0720982 + 0.124878i
\(56\) 0 0
\(57\) 16.2036i 2.14622i
\(58\) 0 0
\(59\) 0.641756 0.370518i 0.0835495 0.0482373i −0.457643 0.889136i \(-0.651306\pi\)
0.541193 + 0.840899i \(0.317973\pi\)
\(60\) 0 0
\(61\) −2.09928 3.63606i −0.268785 0.465550i 0.699763 0.714375i \(-0.253289\pi\)
−0.968548 + 0.248825i \(0.919956\pi\)
\(62\) 0 0
\(63\) −8.23499 4.75447i −1.03751 0.599007i
\(64\) 0 0
\(65\) 3.32235 1.40072i 0.412086 0.173738i
\(66\) 0 0
\(67\) 7.01029 + 4.04739i 0.856443 + 0.494468i 0.862820 0.505512i \(-0.168696\pi\)
−0.00637624 + 0.999980i \(0.502030\pi\)
\(68\) 0 0
\(69\) −5.39623 9.34654i −0.649629 1.12519i
\(70\) 0 0
\(71\) −8.45663 + 4.88244i −1.00362 + 0.579439i −0.909317 0.416105i \(-0.863395\pi\)
−0.0943010 + 0.995544i \(0.530062\pi\)
\(72\) 0 0
\(73\) 3.71649i 0.434982i 0.976062 + 0.217491i \(0.0697873\pi\)
−0.976062 + 0.217491i \(0.930213\pi\)
\(74\) 0 0
\(75\) 1.41342 2.44811i 0.163208 0.282684i
\(76\) 0 0
\(77\) −2.03741 −0.232185
\(78\) 0 0
\(79\) 9.31937 1.04851 0.524255 0.851561i \(-0.324344\pi\)
0.524255 + 0.851561i \(0.324344\pi\)
\(80\) 0 0
\(81\) −0.468594 + 0.811629i −0.0520660 + 0.0901809i
\(82\) 0 0
\(83\) 5.11778i 0.561749i −0.959744 0.280875i \(-0.909376\pi\)
0.959744 0.280875i \(-0.0906245\pi\)
\(84\) 0 0
\(85\) 0.551886 0.318632i 0.0598605 0.0345605i
\(86\) 0 0
\(87\) −13.3640 23.1472i −1.43278 2.48164i
\(88\) 0 0
\(89\) −10.8932 6.28917i −1.15467 0.666650i −0.204651 0.978835i \(-0.565606\pi\)
−0.950021 + 0.312185i \(0.898939\pi\)
\(90\) 0 0
\(91\) 5.47602 + 4.14741i 0.574043 + 0.434767i
\(92\) 0 0
\(93\) −3.58429 2.06939i −0.371673 0.214586i
\(94\) 0 0
\(95\) 2.86603 + 4.96410i 0.294048 + 0.509306i
\(96\) 0 0
\(97\) −3.65597 + 2.11078i −0.371208 + 0.214317i −0.673986 0.738744i \(-0.735419\pi\)
0.302778 + 0.953061i \(0.402086\pi\)
\(98\) 0 0
\(99\) 5.33734i 0.536423i
\(100\) 0 0
\(101\) −7.62379 + 13.2048i −0.758595 + 1.31393i 0.184972 + 0.982744i \(0.440781\pi\)
−0.943567 + 0.331181i \(0.892553\pi\)
\(102\) 0 0
\(103\) −13.5269 −1.33285 −0.666423 0.745574i \(-0.732176\pi\)
−0.666423 + 0.745574i \(0.732176\pi\)
\(104\) 0 0
\(105\) 5.38573 0.525593
\(106\) 0 0
\(107\) −3.68137 + 6.37632i −0.355891 + 0.616422i −0.987270 0.159053i \(-0.949156\pi\)
0.631379 + 0.775475i \(0.282489\pi\)
\(108\) 0 0
\(109\) 10.0760i 0.965103i 0.875868 + 0.482551i \(0.160290\pi\)
−0.875868 + 0.482551i \(0.839710\pi\)
\(110\) 0 0
\(111\) −1.85432 + 1.07059i −0.176004 + 0.101616i
\(112\) 0 0
\(113\) 3.34403 + 5.79203i 0.314580 + 0.544868i 0.979348 0.202181i \(-0.0648030\pi\)
−0.664768 + 0.747050i \(0.731470\pi\)
\(114\) 0 0
\(115\) 3.30636 + 1.90893i 0.308320 + 0.178008i
\(116\) 0 0
\(117\) 10.8648 14.3453i 1.00445 1.32623i
\(118\) 0 0
\(119\) 1.05146 + 0.607061i 0.0963872 + 0.0556492i
\(120\) 0 0
\(121\) −4.92820 8.53590i −0.448018 0.775991i
\(122\) 0 0
\(123\) 0.655970 0.378725i 0.0591468 0.0341484i
\(124\) 0 0
\(125\) 1.00000i 0.0894427i
\(126\) 0 0
\(127\) −0.744750 + 1.28994i −0.0660859 + 0.114464i −0.897175 0.441675i \(-0.854384\pi\)
0.831089 + 0.556139i \(0.187718\pi\)
\(128\) 0 0
\(129\) 1.80144 0.158608
\(130\) 0 0
\(131\) −4.12676 −0.360557 −0.180278 0.983616i \(-0.557700\pi\)
−0.180278 + 0.983616i \(0.557700\pi\)
\(132\) 0 0
\(133\) −5.46039 + 9.45767i −0.473476 + 0.820084i
\(134\) 0 0
\(135\) 5.62828i 0.484405i
\(136\) 0 0
\(137\) 17.4155 10.0548i 1.48790 0.859041i 0.487999 0.872844i \(-0.337727\pi\)
0.999905 + 0.0138029i \(0.00439372\pi\)
\(138\) 0 0
\(139\) 10.4126 + 18.0352i 0.883189 + 1.52973i 0.847776 + 0.530355i \(0.177941\pi\)
0.0354130 + 0.999373i \(0.488725\pi\)
\(140\) 0 0
\(141\) 23.1252 + 13.3513i 1.94749 + 1.12439i
\(142\) 0 0
\(143\) 0.479208 3.82584i 0.0400734 0.319933i
\(144\) 0 0
\(145\) 8.18837 + 4.72756i 0.680007 + 0.392602i
\(146\) 0 0
\(147\) −4.76346 8.25055i −0.392883 0.680494i
\(148\) 0 0
\(149\) 11.5768 6.68388i 0.948410 0.547565i 0.0558233 0.998441i \(-0.482222\pi\)
0.892587 + 0.450876i \(0.148888\pi\)
\(150\) 0 0
\(151\) 18.2984i 1.48910i 0.667567 + 0.744550i \(0.267336\pi\)
−0.667567 + 0.744550i \(0.732664\pi\)
\(152\) 0 0
\(153\) 1.59030 2.75447i 0.128568 0.222686i
\(154\) 0 0
\(155\) 1.46410 0.117599
\(156\) 0 0
\(157\) 2.42229 0.193320 0.0966599 0.995317i \(-0.469184\pi\)
0.0966599 + 0.995317i \(0.469184\pi\)
\(158\) 0 0
\(159\) 9.88124 17.1148i 0.783633 1.35729i
\(160\) 0 0
\(161\) 7.27382i 0.573258i
\(162\) 0 0
\(163\) 13.8416 7.99144i 1.08416 0.625938i 0.152142 0.988359i \(-0.451383\pi\)
0.932015 + 0.362421i \(0.118050\pi\)
\(164\) 0 0
\(165\) −1.51150 2.61799i −0.117670 0.203810i
\(166\) 0 0
\(167\) 12.4648 + 7.19658i 0.964558 + 0.556888i 0.897573 0.440866i \(-0.145329\pi\)
0.0669853 + 0.997754i \(0.478662\pi\)
\(168\) 0 0
\(169\) −9.07597 + 9.30735i −0.698151 + 0.715950i
\(170\) 0 0
\(171\) 24.7759 + 14.3044i 1.89466 + 1.09388i
\(172\) 0 0
\(173\) −12.1745 21.0868i −0.925608 1.60320i −0.790581 0.612358i \(-0.790221\pi\)
−0.135027 0.990842i \(-0.543112\pi\)
\(174\) 0 0
\(175\) −1.64996 + 0.952606i −0.124725 + 0.0720103i
\(176\) 0 0
\(177\) 2.09479i 0.157454i
\(178\) 0 0
\(179\) −1.89414 + 3.28075i −0.141575 + 0.245215i −0.928090 0.372356i \(-0.878550\pi\)
0.786515 + 0.617571i \(0.211883\pi\)
\(180\) 0 0
\(181\) 8.48794 0.630904 0.315452 0.948942i \(-0.397844\pi\)
0.315452 + 0.948942i \(0.397844\pi\)
\(182\) 0 0
\(183\) 11.8687 0.877356
\(184\) 0 0
\(185\) 0.378725 0.655970i 0.0278444 0.0482279i
\(186\) 0 0
\(187\) 0.681482i 0.0498349i
\(188\) 0 0
\(189\) 9.28645 5.36153i 0.675490 0.389994i
\(190\) 0 0
\(191\) −2.72155 4.71386i −0.196924 0.341083i 0.750605 0.660751i \(-0.229762\pi\)
−0.947530 + 0.319668i \(0.896429\pi\)
\(192\) 0 0
\(193\) 10.5288 + 6.07880i 0.757879 + 0.437562i 0.828534 0.559939i \(-0.189176\pi\)
−0.0706548 + 0.997501i \(0.522509\pi\)
\(194\) 0 0
\(195\) −1.26675 + 10.1133i −0.0907135 + 0.724227i
\(196\) 0 0
\(197\) 3.79172 + 2.18915i 0.270149 + 0.155970i 0.628955 0.777442i \(-0.283483\pi\)
−0.358807 + 0.933412i \(0.616816\pi\)
\(198\) 0 0
\(199\) −10.4186 18.0456i −0.738558 1.27922i −0.953144 0.302516i \(-0.902174\pi\)
0.214586 0.976705i \(-0.431160\pi\)
\(200\) 0 0
\(201\) −19.8170 + 11.4413i −1.39778 + 0.807009i
\(202\) 0 0
\(203\) 18.0140i 1.26434i
\(204\) 0 0
\(205\) −0.133975 + 0.232051i −0.00935719 + 0.0162071i
\(206\) 0 0
\(207\) 19.0550 1.32441
\(208\) 0 0
\(209\) 6.12979 0.424007
\(210\) 0 0
\(211\) −5.32684 + 9.22635i −0.366715 + 0.635168i −0.989050 0.147583i \(-0.952851\pi\)
0.622335 + 0.782751i \(0.286184\pi\)
\(212\) 0 0
\(213\) 27.6037i 1.89138i
\(214\) 0 0
\(215\) −0.551886 + 0.318632i −0.0376383 + 0.0217305i
\(216\) 0 0
\(217\) 1.39471 + 2.41571i 0.0946792 + 0.163989i
\(218\) 0 0
\(219\) −9.09839 5.25296i −0.614812 0.354962i
\(220\) 0 0
\(221\) −1.38724 + 1.83164i −0.0933161 + 0.123210i
\(222\) 0 0
\(223\) 18.4804 + 10.6697i 1.23754 + 0.714494i 0.968591 0.248661i \(-0.0799905\pi\)
0.268949 + 0.963155i \(0.413324\pi\)
\(224\) 0 0
\(225\) 2.49551 + 4.32235i 0.166367 + 0.288156i
\(226\) 0 0
\(227\) −13.5842 + 7.84283i −0.901613 + 0.520547i −0.877723 0.479168i \(-0.840938\pi\)
−0.0238900 + 0.999715i \(0.507605\pi\)
\(228\) 0 0
\(229\) 7.62085i 0.503600i 0.967779 + 0.251800i \(0.0810225\pi\)
−0.967779 + 0.251800i \(0.918977\pi\)
\(230\) 0 0
\(231\) 2.87972 4.98782i 0.189472 0.328175i
\(232\) 0 0
\(233\) 19.0550 1.24833 0.624166 0.781292i \(-0.285439\pi\)
0.624166 + 0.781292i \(0.285439\pi\)
\(234\) 0 0
\(235\) −9.44613 −0.616198
\(236\) 0 0
\(237\) −13.1722 + 22.8149i −0.855625 + 1.48199i
\(238\) 0 0
\(239\) 12.7535i 0.824954i −0.910968 0.412477i \(-0.864664\pi\)
0.910968 0.412477i \(-0.135336\pi\)
\(240\) 0 0
\(241\) −22.4550 + 12.9644i −1.44646 + 0.835111i −0.998268 0.0588285i \(-0.981263\pi\)
−0.448187 + 0.893940i \(0.647930\pi\)
\(242\) 0 0
\(243\) 7.11778 + 12.3284i 0.456606 + 0.790864i
\(244\) 0 0
\(245\) 2.91865 + 1.68508i 0.186466 + 0.107656i
\(246\) 0 0
\(247\) −16.4752 12.4780i −1.04829 0.793954i
\(248\) 0 0
\(249\) 12.5289 + 7.23357i 0.793987 + 0.458409i
\(250\) 0 0
\(251\) −3.80593 6.59207i −0.240228 0.416088i 0.720551 0.693402i \(-0.243889\pi\)
−0.960779 + 0.277314i \(0.910556\pi\)
\(252\) 0 0
\(253\) 3.53578 2.04139i 0.222293 0.128341i
\(254\) 0 0
\(255\) 1.80144i 0.112811i
\(256\) 0 0
\(257\) 0.167891 0.290796i 0.0104728 0.0181394i −0.860742 0.509042i \(-0.830000\pi\)
0.871214 + 0.490903i \(0.163333\pi\)
\(258\) 0 0
\(259\) 1.44310 0.0896700
\(260\) 0 0
\(261\) 47.1906 2.92103
\(262\) 0 0
\(263\) −2.68795 + 4.65566i −0.165746 + 0.287080i −0.936920 0.349544i \(-0.886336\pi\)
0.771174 + 0.636624i \(0.219670\pi\)
\(264\) 0 0
\(265\) 6.99102i 0.429455i
\(266\) 0 0
\(267\) 30.7932 17.7785i 1.88451 1.08802i
\(268\) 0 0
\(269\) 0.655192 + 1.13483i 0.0399478 + 0.0691916i 0.885308 0.465005i \(-0.153948\pi\)
−0.845360 + 0.534197i \(0.820614\pi\)
\(270\) 0 0
\(271\) 10.0851 + 5.82266i 0.612629 + 0.353701i 0.773994 0.633194i \(-0.218256\pi\)
−0.161365 + 0.986895i \(0.551590\pi\)
\(272\) 0 0
\(273\) −17.8933 + 7.54390i −1.08295 + 0.456577i
\(274\) 0 0
\(275\) 0.926118 + 0.534695i 0.0558470 + 0.0322433i
\(276\) 0 0
\(277\) −10.1581 17.5943i −0.610338 1.05714i −0.991183 0.132498i \(-0.957700\pi\)
0.380845 0.924639i \(-0.375633\pi\)
\(278\) 0 0
\(279\) 6.32835 3.65368i 0.378869 0.218740i
\(280\) 0 0
\(281\) 11.8744i 0.708366i 0.935176 + 0.354183i \(0.115241\pi\)
−0.935176 + 0.354183i \(0.884759\pi\)
\(282\) 0 0
\(283\) 11.3261 19.6173i 0.673264 1.16613i −0.303709 0.952765i \(-0.598225\pi\)
0.976973 0.213363i \(-0.0684418\pi\)
\(284\) 0 0
\(285\) −16.2036 −0.959817
\(286\) 0 0
\(287\) −0.510500 −0.0301339
\(288\) 0 0
\(289\) 8.29695 14.3707i 0.488056 0.845337i
\(290\) 0 0
\(291\) 11.9336i 0.699562i
\(292\) 0 0
\(293\) −16.1191 + 9.30636i −0.941687 + 0.543683i −0.890489 0.455005i \(-0.849637\pi\)
−0.0511983 + 0.998689i \(0.516304\pi\)
\(294\) 0 0
\(295\) −0.370518 0.641756i −0.0215724 0.0373645i
\(296\) 0 0
\(297\) −5.21245 3.00941i −0.302457 0.174624i
\(298\) 0 0
\(299\) −13.6587 1.71083i −0.789905 0.0989400i
\(300\) 0 0
\(301\) −1.05146 0.607061i −0.0606052 0.0349904i
\(302\) 0 0
\(303\) −21.5512 37.3278i −1.23808 2.14443i
\(304\) 0 0
\(305\) −3.63606 + 2.09928i −0.208200 + 0.120204i
\(306\) 0 0
\(307\) 3.14776i 0.179652i 0.995957 + 0.0898262i \(0.0286311\pi\)
−0.995957 + 0.0898262i \(0.971369\pi\)
\(308\) 0 0
\(309\) 19.1192 33.1154i 1.08765 1.88387i
\(310\) 0 0
\(311\) −3.18059 −0.180355 −0.0901774 0.995926i \(-0.528743\pi\)
−0.0901774 + 0.995926i \(0.528743\pi\)
\(312\) 0 0
\(313\) 35.3533 1.99829 0.999144 0.0413596i \(-0.0131689\pi\)
0.999144 + 0.0413596i \(0.0131689\pi\)
\(314\) 0 0
\(315\) −4.75447 + 8.23499i −0.267884 + 0.463989i
\(316\) 0 0
\(317\) 13.6357i 0.765858i −0.923778 0.382929i \(-0.874915\pi\)
0.923778 0.382929i \(-0.125085\pi\)
\(318\) 0 0
\(319\) 8.75656 5.05560i 0.490273 0.283059i
\(320\) 0 0
\(321\) −10.4066 18.0248i −0.580842 1.00605i
\(322\) 0 0
\(323\) −3.16344 1.82641i −0.176018 0.101624i
\(324\) 0 0
\(325\) −1.40072 3.32235i −0.0776980 0.184291i
\(326\) 0 0
\(327\) −24.6671 14.2416i −1.36409 0.787560i
\(328\) 0 0
\(329\) −8.99844 15.5858i −0.496100 0.859271i
\(330\) 0 0
\(331\) 24.9380 14.3980i 1.37072 0.791383i 0.379698 0.925110i \(-0.376028\pi\)
0.991018 + 0.133727i \(0.0426945\pi\)
\(332\) 0 0
\(333\) 3.78044i 0.207167i
\(334\) 0 0
\(335\) 4.04739 7.01029i 0.221133 0.383013i
\(336\) 0 0
\(337\) −11.7493 −0.640026 −0.320013 0.947413i \(-0.603687\pi\)
−0.320013 + 0.947413i \(0.603687\pi\)
\(338\) 0 0
\(339\) −18.9061 −1.02684
\(340\) 0 0
\(341\) 0.782847 1.35593i 0.0423936 0.0734278i
\(342\) 0 0
\(343\) 19.7574i 1.06680i
\(344\) 0 0
\(345\) −9.34654 + 5.39623i −0.503201 + 0.290523i
\(346\) 0 0
\(347\) 0.949887 + 1.64525i 0.0509926 + 0.0883218i 0.890395 0.455189i \(-0.150428\pi\)
−0.839402 + 0.543510i \(0.817095\pi\)
\(348\) 0 0
\(349\) −8.89329 5.13454i −0.476047 0.274846i 0.242721 0.970096i \(-0.421960\pi\)
−0.718768 + 0.695250i \(0.755293\pi\)
\(350\) 0 0
\(351\) 7.88364 + 18.6991i 0.420798 + 0.998084i
\(352\) 0 0
\(353\) −0.693330 0.400294i −0.0369022 0.0213055i 0.481435 0.876482i \(-0.340116\pi\)
−0.518338 + 0.855176i \(0.673449\pi\)
\(354\) 0 0
\(355\) 4.88244 + 8.45663i 0.259133 + 0.448831i
\(356\) 0 0
\(357\) −2.97231 + 1.71606i −0.157311 + 0.0908237i
\(358\) 0 0
\(359\) 8.13272i 0.429228i 0.976699 + 0.214614i \(0.0688494\pi\)
−0.976699 + 0.214614i \(0.931151\pi\)
\(360\) 0 0
\(361\) 6.92820 12.0000i 0.364642 0.631579i
\(362\) 0 0
\(363\) 27.8625 1.46240
\(364\) 0 0
\(365\) 3.71649 0.194530
\(366\) 0 0
\(367\) −10.2632 + 17.7765i −0.535737 + 0.927924i 0.463390 + 0.886154i \(0.346633\pi\)
−0.999127 + 0.0417696i \(0.986700\pi\)
\(368\) 0 0
\(369\) 1.33734i 0.0696191i
\(370\) 0 0
\(371\) −11.5349 + 6.65968i −0.598863 + 0.345754i
\(372\) 0 0
\(373\) 8.90292 + 15.4203i 0.460976 + 0.798433i 0.999010 0.0444897i \(-0.0141662\pi\)
−0.538034 + 0.842923i \(0.680833\pi\)
\(374\) 0 0
\(375\) −2.44811 1.41342i −0.126420 0.0729887i
\(376\) 0 0
\(377\) −33.8266 4.23697i −1.74216 0.218215i
\(378\) 0 0
\(379\) 1.77150 + 1.02277i 0.0909956 + 0.0525363i 0.544807 0.838561i \(-0.316603\pi\)
−0.453812 + 0.891098i \(0.649936\pi\)
\(380\) 0 0
\(381\) −2.10529 3.64647i −0.107857 0.186814i
\(382\) 0 0
\(383\) 6.84611 3.95261i 0.349820 0.201969i −0.314786 0.949163i \(-0.601933\pi\)
0.664606 + 0.747194i \(0.268599\pi\)
\(384\) 0 0
\(385\) 2.03741i 0.103836i
\(386\) 0 0
\(387\) −1.59030 + 2.75447i −0.0808393 + 0.140018i
\(388\) 0 0
\(389\) 9.21171 0.467052 0.233526 0.972351i \(-0.424974\pi\)
0.233526 + 0.972351i \(0.424974\pi\)
\(390\) 0 0
\(391\) −2.43298 −0.123041
\(392\) 0 0
\(393\) 5.83285 10.1028i 0.294228 0.509618i
\(394\) 0 0
\(395\) 9.31937i 0.468908i
\(396\) 0 0
\(397\) 5.50305 3.17719i 0.276190 0.159458i −0.355507 0.934674i \(-0.615692\pi\)
0.631697 + 0.775215i \(0.282359\pi\)
\(398\) 0 0
\(399\) −15.4356 26.7353i −0.772748 1.33844i
\(400\) 0 0
\(401\) 3.61063 + 2.08460i 0.180306 + 0.104100i 0.587437 0.809270i \(-0.300137\pi\)
−0.407130 + 0.913370i \(0.633470\pi\)
\(402\) 0 0
\(403\) −4.86425 + 2.05080i −0.242306 + 0.102157i
\(404\) 0 0
\(405\) 0.811629 + 0.468594i 0.0403301 + 0.0232846i
\(406\) 0 0
\(407\) −0.405004 0.701487i −0.0200753 0.0347714i
\(408\) 0 0
\(409\) 8.80580 5.08403i 0.435419 0.251389i −0.266234 0.963909i \(-0.585779\pi\)
0.701652 + 0.712519i \(0.252446\pi\)
\(410\) 0 0
\(411\) 56.8467i 2.80404i
\(412\) 0 0
\(413\) 0.705915 1.22268i 0.0347358 0.0601642i
\(414\) 0 0
\(415\) −5.11778 −0.251222
\(416\) 0 0
\(417\) −58.8697 −2.88286
\(418\) 0 0
\(419\) 14.2954 24.7604i 0.698378 1.20963i −0.270651 0.962677i \(-0.587239\pi\)
0.969029 0.246948i \(-0.0794277\pi\)
\(420\) 0 0
\(421\) 2.01797i 0.0983498i 0.998790 + 0.0491749i \(0.0156592\pi\)
−0.998790 + 0.0491749i \(0.984341\pi\)
\(422\) 0 0
\(423\) −40.8295 + 23.5729i −1.98520 + 1.14615i
\(424\) 0 0
\(425\) −0.318632 0.551886i −0.0154559 0.0267704i
\(426\) 0 0
\(427\) −6.92747 3.99957i −0.335244 0.193553i
\(428\) 0 0
\(429\) 8.68878 + 6.58068i 0.419498 + 0.317718i
\(430\) 0 0
\(431\) −17.8508 10.3061i −0.859842 0.496430i 0.00411765 0.999992i \(-0.498689\pi\)
−0.863959 + 0.503562i \(0.832023\pi\)
\(432\) 0 0
\(433\) 14.7178 + 25.4920i 0.707292 + 1.22507i 0.965858 + 0.259072i \(0.0834168\pi\)
−0.258566 + 0.965994i \(0.583250\pi\)
\(434\) 0 0
\(435\) −23.1472 + 13.3640i −1.10982 + 0.640757i
\(436\) 0 0
\(437\) 21.8841i 1.04686i
\(438\) 0 0
\(439\) −8.47602 + 14.6809i −0.404538 + 0.700681i −0.994268 0.106920i \(-0.965901\pi\)
0.589729 + 0.807601i \(0.299235\pi\)
\(440\) 0 0
\(441\) 16.8205 0.800978
\(442\) 0 0
\(443\) 24.1399 1.14692 0.573461 0.819233i \(-0.305600\pi\)
0.573461 + 0.819233i \(0.305600\pi\)
\(444\) 0 0
\(445\) −6.28917 + 10.8932i −0.298135 + 0.516385i
\(446\) 0 0
\(447\) 37.7885i 1.78733i
\(448\) 0 0
\(449\) 18.0679 10.4315i 0.852676 0.492293i −0.00887706 0.999961i \(-0.502826\pi\)
0.861553 + 0.507668i \(0.169492\pi\)
\(450\) 0 0
\(451\) 0.143271 + 0.248153i 0.00674637 + 0.0116851i
\(452\) 0 0
\(453\) −44.7965 25.8633i −2.10472 1.21516i
\(454\) 0 0
\(455\) 4.14741 5.47602i 0.194434 0.256720i
\(456\) 0 0
\(457\) 26.4708 + 15.2830i 1.23825 + 0.714906i 0.968737 0.248089i \(-0.0798027\pi\)
0.269517 + 0.962996i \(0.413136\pi\)
\(458\) 0 0
\(459\) 1.79335 + 3.10617i 0.0837063 + 0.144984i
\(460\) 0 0
\(461\) 4.05146 2.33911i 0.188695 0.108943i −0.402676 0.915342i \(-0.631920\pi\)
0.591372 + 0.806399i \(0.298587\pi\)
\(462\) 0 0
\(463\) 14.0011i 0.650688i −0.945596 0.325344i \(-0.894520\pi\)
0.945596 0.325344i \(-0.105480\pi\)
\(464\) 0 0
\(465\) −2.06939 + 3.58429i −0.0959656 + 0.166217i
\(466\) 0 0
\(467\) −6.98506 −0.323230 −0.161615 0.986854i \(-0.551670\pi\)
−0.161615 + 0.986854i \(0.551670\pi\)
\(468\) 0 0
\(469\) 15.4223 0.712135
\(470\) 0 0
\(471\) −3.42371 + 5.93004i −0.157756 + 0.273242i
\(472\) 0 0
\(473\) 0.681482i 0.0313346i
\(474\) 0 0
\(475\) 4.96410 2.86603i 0.227769 0.131502i
\(476\) 0 0
\(477\) 17.4461 + 30.2176i 0.798804 + 1.38357i
\(478\) 0 0
\(479\) 14.1065 + 8.14438i 0.644542 + 0.372126i 0.786362 0.617766i \(-0.211962\pi\)
−0.141820 + 0.989892i \(0.545296\pi\)
\(480\) 0 0
\(481\) −0.339423 + 2.70985i −0.0154764 + 0.123558i
\(482\) 0 0
\(483\) −17.8071 10.2810i −0.810253 0.467800i
\(484\) 0 0
\(485\) 2.11078 + 3.65597i 0.0958454 + 0.166009i
\(486\) 0 0
\(487\) −17.3559 + 10.0204i −0.786471 + 0.454069i −0.838719 0.544565i \(-0.816695\pi\)
0.0522474 + 0.998634i \(0.483362\pi\)
\(488\) 0 0
\(489\) 45.1810i 2.04316i
\(490\) 0 0
\(491\) 7.89916 13.6818i 0.356484 0.617449i −0.630887 0.775875i \(-0.717309\pi\)
0.987371 + 0.158426i \(0.0506420\pi\)
\(492\) 0 0
\(493\) −6.02540 −0.271370
\(494\) 0 0
\(495\) 5.33734 0.239896
\(496\) 0 0
\(497\) −9.30208 + 16.1117i −0.417255 + 0.722708i
\(498\) 0 0
\(499\) 1.24651i 0.0558016i −0.999611 0.0279008i \(-0.991118\pi\)
0.999611 0.0279008i \(-0.00888226\pi\)
\(500\) 0 0
\(501\) −35.2361 + 20.3436i −1.57423 + 0.908883i
\(502\) 0 0
\(503\) −3.82672 6.62808i −0.170625 0.295532i 0.768013 0.640434i \(-0.221245\pi\)
−0.938639 + 0.344902i \(0.887912\pi\)
\(504\) 0 0
\(505\) 13.2048 + 7.62379i 0.587605 + 0.339254i
\(506\) 0 0
\(507\) −9.95732 35.3742i −0.442220 1.57102i
\(508\) 0 0
\(509\) −22.2777 12.8621i −0.987444 0.570101i −0.0829345 0.996555i \(-0.526429\pi\)
−0.904509 + 0.426454i \(0.859763\pi\)
\(510\) 0 0
\(511\) 3.54035 + 6.13207i 0.156616 + 0.271267i
\(512\) 0 0
\(513\) −27.9393 + 16.1308i −1.23355 + 0.712192i
\(514\) 0 0
\(515\) 13.5269i 0.596067i
\(516\) 0 0
\(517\) −5.05080 + 8.74824i −0.222134 + 0.384747i
\(518\) 0 0
\(519\) 68.8305 3.02132
\(520\) 0 0
\(521\) −30.1519 −1.32098 −0.660490 0.750835i \(-0.729651\pi\)
−0.660490 + 0.750835i \(0.729651\pi\)
\(522\) 0 0
\(523\) 1.96876 3.41000i 0.0860880 0.149109i −0.819766 0.572698i \(-0.805897\pi\)
0.905854 + 0.423589i \(0.139230\pi\)
\(524\) 0 0
\(525\) 5.38573i 0.235052i
\(526\) 0 0
\(527\) −0.808017 + 0.466509i −0.0351978 + 0.0203215i
\(528\) 0 0
\(529\) 4.21200 + 7.29539i 0.183130 + 0.317191i
\(530\) 0 0
\(531\) −3.20301 1.84926i −0.138999 0.0802510i
\(532\) 0 0
\(533\) 0.120072 0.958614i 0.00520088 0.0415222i
\(534\) 0 0
\(535\) 6.37632 + 3.68137i 0.275672 + 0.159159i
\(536\) 0 0
\(537\) −5.35444 9.27415i −0.231061 0.400209i
\(538\) 0 0
\(539\) 3.12117 1.80201i 0.134438 0.0776180i
\(540\) 0 0
\(541\) 15.8881i 0.683083i 0.939867 + 0.341541i \(0.110949\pi\)
−0.939867 + 0.341541i \(0.889051\pi\)
\(542\) 0 0
\(543\) −11.9970 + 20.7795i −0.514842 + 0.891732i
\(544\) 0 0
\(545\) 10.0760 0.431607
\(546\) 0 0
\(547\) 6.56107 0.280531 0.140266 0.990114i \(-0.455204\pi\)
0.140266 + 0.990114i \(0.455204\pi\)
\(548\) 0 0
\(549\) −10.4775 + 18.1476i −0.447170 + 0.774522i
\(550\) 0 0
\(551\) 54.1972i 2.30888i
\(552\) 0 0
\(553\) 15.3766 8.87769i 0.653880 0.377518i
\(554\) 0 0
\(555\) 1.07059 + 1.85432i 0.0454441 + 0.0787116i
\(556\) 0 0
\(557\) 6.79835 + 3.92503i 0.288055 + 0.166309i 0.637065 0.770810i \(-0.280148\pi\)
−0.349009 + 0.937119i \(0.613482\pi\)
\(558\) 0 0
\(559\) 1.38724 1.83164i 0.0586741 0.0774702i
\(560\) 0 0
\(561\) 1.66835 + 0.963220i 0.0704377 + 0.0406672i
\(562\) 0 0
\(563\) 7.77976 + 13.4749i 0.327878 + 0.567901i 0.982091 0.188410i \(-0.0603333\pi\)
−0.654213 + 0.756310i \(0.727000\pi\)
\(564\) 0 0
\(565\) 5.79203 3.34403i 0.243673 0.140684i
\(566\) 0 0
\(567\) 1.78554i 0.0749857i
\(568\) 0 0
\(569\) 1.73957 3.01303i 0.0729267 0.126313i −0.827256 0.561825i \(-0.810099\pi\)
0.900183 + 0.435512i \(0.143433\pi\)
\(570\) 0 0
\(571\) −21.5118 −0.900240 −0.450120 0.892968i \(-0.648619\pi\)
−0.450120 + 0.892968i \(0.648619\pi\)
\(572\) 0 0
\(573\) 15.3868 0.642791
\(574\) 0 0
\(575\) 1.90893 3.30636i 0.0796078 0.137885i
\(576\) 0 0
\(577\) 9.97608i 0.415310i 0.978202 + 0.207655i \(0.0665831\pi\)
−0.978202 + 0.207655i \(0.933417\pi\)
\(578\) 0 0
\(579\) −29.7632 + 17.1838i −1.23692 + 0.714134i
\(580\) 0 0
\(581\) −4.87523 8.44414i −0.202259 0.350322i
\(582\) 0 0
\(583\) 6.47451 + 3.73806i 0.268147 + 0.154815i
\(584\) 0 0
\(585\) −14.3453 10.8648i −0.593107 0.449205i
\(586\) 0 0
\(587\) −20.8341 12.0286i −0.859915 0.496472i 0.00406862 0.999992i \(-0.498705\pi\)
−0.863984 + 0.503519i \(0.832038\pi\)
\(588\) 0 0
\(589\) −4.19615 7.26795i −0.172899 0.299471i
\(590\) 0 0
\(591\) −10.7186 + 6.18837i −0.440903 + 0.254556i
\(592\) 0 0
\(593\) 0.940219i 0.0386102i −0.999814 0.0193051i \(-0.993855\pi\)
0.999814 0.0193051i \(-0.00614538\pi\)
\(594\) 0 0
\(595\) 0.607061 1.05146i 0.0248871 0.0431057i
\(596\) 0 0
\(597\) 58.9037 2.41077
\(598\) 0 0
\(599\) 11.4270 0.466896 0.233448 0.972369i \(-0.424999\pi\)
0.233448 + 0.972369i \(0.424999\pi\)
\(600\) 0 0
\(601\) 18.0215 31.2142i 0.735114 1.27325i −0.219560 0.975599i \(-0.570462\pi\)
0.954674 0.297655i \(-0.0962045\pi\)
\(602\) 0 0
\(603\) 40.4012i 1.64526i
\(604\) 0 0
\(605\) −8.53590 + 4.92820i −0.347034 + 0.200360i
\(606\) 0 0
\(607\) 19.9454 + 34.5464i 0.809557 + 1.40219i 0.913171 + 0.407576i \(0.133626\pi\)
−0.103614 + 0.994618i \(0.533041\pi\)
\(608\) 0 0
\(609\) −44.1003 25.4613i −1.78704 1.03175i
\(610\) 0 0
\(611\) 31.3833 13.2314i 1.26963 0.535285i
\(612\) 0 0
\(613\) 0.299187 + 0.172736i 0.0120841 + 0.00697673i 0.506030 0.862516i \(-0.331113\pi\)
−0.493946 + 0.869493i \(0.664446\pi\)
\(614\) 0 0
\(615\) −0.378725 0.655970i −0.0152716 0.0264513i
\(616\) 0 0
\(617\) 33.5022 19.3425i 1.34875 0.778700i 0.360676 0.932691i \(-0.382546\pi\)
0.988072 + 0.153991i \(0.0492128\pi\)
\(618\) 0 0
\(619\) 14.8971i 0.598764i 0.954133 + 0.299382i \(0.0967805\pi\)
−0.954133 + 0.299382i \(0.903219\pi\)
\(620\) 0 0
\(621\) −10.7440 + 18.6091i −0.431141 + 0.746758i
\(622\) 0 0
\(623\) −23.9644 −0.960113
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) −8.66397 + 15.0064i −0.346006 + 0.599299i
\(628\) 0 0
\(629\) 0.482694i 0.0192463i
\(630\) 0 0
\(631\) −33.6408 + 19.4225i −1.33922 + 0.773198i −0.986691 0.162604i \(-0.948011\pi\)
−0.352526 + 0.935802i \(0.614677\pi\)
\(632\) 0 0
\(633\) −15.0581 26.0814i −0.598506 1.03664i
\(634\) 0 0
\(635\) 1.28994 + 0.744750i 0.0511899 + 0.0295545i
\(636\) 0 0
\(637\) −12.0571 1.51022i −0.477719 0.0598370i
\(638\) 0 0
\(639\) 42.2072 + 24.3683i 1.66969 + 0.963996i
\(640\) 0 0
\(641\) 18.5908 + 32.2003i 0.734293 + 1.27183i 0.955033 + 0.296501i \(0.0958197\pi\)
−0.220739 + 0.975333i \(0.570847\pi\)
\(642\) 0 0
\(643\) −7.88410 + 4.55189i −0.310918 + 0.179509i −0.647337 0.762204i \(-0.724118\pi\)
0.336419 + 0.941712i \(0.390784\pi\)
\(644\) 0 0
\(645\) 1.80144i 0.0709316i
\(646\) 0 0
\(647\) 9.56118 16.5605i 0.375889 0.651059i −0.614571 0.788862i \(-0.710671\pi\)
0.990460 + 0.137803i \(0.0440041\pi\)
\(648\) 0 0
\(649\) −0.792455 −0.0311066
\(650\) 0 0
\(651\) −7.88525 −0.309047
\(652\) 0 0
\(653\) −17.3162 + 29.9926i −0.677636 + 1.17370i 0.298055 + 0.954549i \(0.403662\pi\)
−0.975691 + 0.219152i \(0.929671\pi\)
\(654\) 0 0
\(655\) 4.12676i 0.161246i
\(656\) 0 0
\(657\) 16.0640 9.27453i 0.626714 0.361834i
\(658\) 0 0
\(659\) −3.34926 5.80109i −0.130469 0.225978i 0.793389 0.608715i \(-0.208315\pi\)
−0.923857 + 0.382737i \(0.874982\pi\)
\(660\) 0 0
\(661\) 5.22004 + 3.01379i 0.203036 + 0.117223i 0.598071 0.801443i \(-0.295934\pi\)
−0.395035 + 0.918666i \(0.629268\pi\)
\(662\) 0 0
\(663\) −2.52331 5.98501i −0.0979974 0.232438i
\(664\) 0 0
\(665\) 9.45767 + 5.46039i 0.366753 + 0.211745i
\(666\) 0 0
\(667\) −18.0491 31.2620i −0.698865 1.21047i
\(668\) 0 0
\(669\) −52.2411 + 30.1614i −2.01976 + 1.16611i
\(670\) 0 0
\(671\) 4.48990i 0.173330i
\(672\) 0 0
\(673\) 11.6784 20.2276i 0.450169 0.779715i −0.548227 0.836329i \(-0.684697\pi\)
0.998396 + 0.0566140i \(0.0180304\pi\)
\(674\) 0 0
\(675\) −5.62828 −0.216633
\(676\) 0 0
\(677\) −45.4042 −1.74503 −0.872513 0.488590i \(-0.837511\pi\)
−0.872513 + 0.488590i \(0.837511\pi\)
\(678\) 0 0
\(679\) −4.02148 + 6.96540i −0.154330 + 0.267308i
\(680\) 0 0
\(681\) 44.3408i 1.69914i
\(682\) 0 0
\(683\) −22.0817 + 12.7489i −0.844934 + 0.487823i −0.858938 0.512079i \(-0.828875\pi\)
0.0140045 + 0.999902i \(0.495542\pi\)
\(684\) 0 0
\(685\) −10.0548 17.4155i −0.384175 0.665411i
\(686\) 0 0
\(687\) −18.6567 10.7715i −0.711798 0.410957i
\(688\) 0 0
\(689\) −9.79246 23.2266i −0.373063 0.884862i
\(690\) 0 0
\(691\) −5.71257 3.29815i −0.217316 0.125468i 0.387391 0.921916i \(-0.373376\pi\)
−0.604707 + 0.796448i \(0.706710\pi\)
\(692\) 0 0
\(693\) 5.08438 + 8.80641i 0.193140 + 0.334528i
\(694\) 0 0
\(695\) 18.0352 10.4126i 0.684115 0.394974i
\(696\) 0 0
\(697\) 0.170754i 0.00646778i
\(698\) 0 0
\(699\) −26.9327 + 46.6487i −1.01869 + 1.76442i
\(700\) 0 0
\(701\) −29.2474 −1.10466 −0.552329 0.833626i \(-0.686261\pi\)
−0.552329 + 0.833626i \(0.686261\pi\)
\(702\) 0 0
\(703\) −4.34174 −0.163752
\(704\) 0 0
\(705\) 13.3513 23.1252i 0.502841 0.870946i
\(706\) 0 0
\(707\) 29.0499i 1.09253i
\(708\) 0 0
\(709\) −9.46865 + 5.46673i −0.355603 + 0.205307i −0.667150 0.744923i \(-0.732486\pi\)
0.311548 + 0.950231i \(0.399153\pi\)
\(710\) 0 0
\(711\) −23.2566 40.2815i −0.872189 1.51068i
\(712\) 0 0
\(713\) −4.84084 2.79486i −0.181291 0.104668i
\(714\) 0 0
\(715\) −3.82584 0.479208i −0.143078 0.0179214i
\(716\) 0 0
\(717\) 31.2220 + 18.0260i 1.16601 + 0.673194i
\(718\) 0 0
\(719\) −8.02989 13.9082i −0.299464 0.518688i 0.676549 0.736398i \(-0.263475\pi\)
−0.976014 + 0.217710i \(0.930141\pi\)
\(720\) 0 0
\(721\) −22.3189 + 12.8858i −0.831199 + 0.479893i
\(722\) 0 0
\(723\) 73.2966i 2.72593i
\(724\) 0 0
\(725\) 4.72756 8.18837i 0.175577 0.304108i
\(726\) 0 0
\(727\) 51.3754 1.90541 0.952704 0.303900i \(-0.0982889\pi\)
0.952704 + 0.303900i \(0.0982889\pi\)
\(728\) 0 0
\(729\) −43.0532 −1.59456
\(730\) 0 0
\(731\) 0.203052 0.351697i 0.00751016 0.0130080i
\(732\) 0 0
\(733\) 9.82358i 0.362842i −0.983406 0.181421i \(-0.941930\pi\)
0.983406 0.181421i \(-0.0580697\pi\)
\(734\) 0 0
\(735\) −8.25055 + 4.76346i −0.304326 + 0.175703i
\(736\) 0 0
\(737\) −4.32824 7.49673i −0.159433 0.276146i
\(738\) 0 0
\(739\) −42.5082 24.5421i −1.56369 0.902797i −0.996879 0.0789487i \(-0.974844\pi\)
−0.566811 0.823848i \(-0.691823\pi\)
\(740\) 0 0
\(741\) 53.8339 22.6967i 1.97764 0.833783i
\(742\) 0 0
\(743\) 35.3663 + 20.4188i 1.29746 + 0.749091i 0.979966 0.199167i \(-0.0638237\pi\)
0.317499 + 0.948259i \(0.397157\pi\)
\(744\) 0 0
\(745\) −6.68388 11.5768i −0.244878 0.424142i
\(746\) 0 0
\(747\) −22.1208 + 12.7715i −0.809358 + 0.467283i
\(748\) 0 0
\(749\) 14.0276i 0.512557i
\(750\) 0 0
\(751\) 1.36340 2.36148i 0.0497512 0.0861716i −0.840077 0.542467i \(-0.817490\pi\)
0.889829 + 0.456295i \(0.150824\pi\)
\(752\) 0 0
\(753\) 21.5175 0.784142
\(754\) 0 0
\(755\) 18.2984 0.665946
\(756\) 0 0
\(757\) −7.40301 + 12.8224i −0.269067 + 0.466038i −0.968621 0.248542i \(-0.920049\pi\)
0.699554 + 0.714580i \(0.253382\pi\)
\(758\) 0 0
\(759\) 11.5413i 0.418924i
\(760\) 0 0
\(761\) 9.84575 5.68445i 0.356908 0.206061i −0.310815 0.950470i \(-0.600602\pi\)
0.667724 + 0.744409i \(0.267269\pi\)
\(762\) 0 0
\(763\) 9.59843 + 16.6250i 0.347486 + 0.601864i
\(764\) 0 0
\(765\) −2.75447 1.59030i −0.0995882 0.0574972i
\(766\) 0 0
\(767\) 2.12991 + 1.61314i 0.0769065 + 0.0582472i
\(768\) 0 0
\(769\) 18.2352 + 10.5281i 0.657579 + 0.379654i 0.791354 0.611358i \(-0.209377\pi\)
−0.133775 + 0.991012i \(0.542710\pi\)
\(770\) 0 0
\(771\) 0.474602 + 0.822034i 0.0170924 + 0.0296048i
\(772\) 0 0
\(773\) 12.1961 7.04144i 0.438664 0.253263i −0.264367 0.964422i \(-0.585163\pi\)
0.703031 + 0.711159i \(0.251830\pi\)
\(774\) 0 0
\(775\) 1.46410i 0.0525921i
\(776\) 0 0
\(777\) −2.03971 + 3.53288i −0.0731741 + 0.126741i
\(778\) 0 0
\(779\) 1.53590 0.0550293
\(780\) 0 0
\(781\) 10.4425 0.373660
\(782\) 0 0
\(783\) −26.6080 + 46.0864i −0.950893 + 1.64699i
\(784\) 0 0
\(785\) 2.42229i 0.0864552i
\(786\) 0 0
\(787\) 28.5998 16.5121i 1.01947 0.588593i 0.105522 0.994417i \(-0.466349\pi\)
0.913951 + 0.405823i \(0.133015\pi\)
\(788\) 0 0
\(789\) −7.59839 13.1608i −0.270510 0.468537i
\(790\) 0 0
\(791\) 11.0350 + 6.37109i 0.392361 + 0.226530i
\(792\) 0 0
\(793\) 9.13974 12.0676i 0.324562 0.428534i
\(794\) 0 0
\(795\) −17.1148 9.88124i −0.606999 0.350451i
\(796\) 0 0