Properties

Label 128.3.h.a.79.7
Level $128$
Weight $3$
Character 128.79
Analytic conductor $3.488$
Analytic rank $0$
Dimension $28$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 128 = 2^{7} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 128.h (of order \(8\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.48774738381\)
Analytic rank: \(0\)
Dimension: \(28\)
Relative dimension: \(7\) over \(\Q(\zeta_{8})\)
Twist minimal: no (minimal twist has level 32)
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 79.7
Character \(\chi\) \(=\) 128.79
Dual form 128.3.h.a.47.7

$q$-expansion

\(f(q)\) \(=\) \(q+(1.73217 + 4.18183i) q^{3} +(-1.85856 + 4.48696i) q^{5} +(5.27676 - 5.27676i) q^{7} +(-8.12333 + 8.12333i) q^{9} +O(q^{10})\) \(q+(1.73217 + 4.18183i) q^{3} +(-1.85856 + 4.48696i) q^{5} +(5.27676 - 5.27676i) q^{7} +(-8.12333 + 8.12333i) q^{9} +(-6.20050 + 14.9693i) q^{11} +(-4.22532 - 10.2008i) q^{13} -21.9830 q^{15} +2.84356i q^{17} +(12.4276 - 5.14768i) q^{19} +(31.2068 + 12.9263i) q^{21} +(1.43918 + 1.43918i) q^{23} +(0.999126 + 0.999126i) q^{25} +(-10.4049 - 4.30987i) q^{27} +(36.9596 - 15.3092i) q^{29} -4.73823i q^{31} -73.3396 q^{33} +(13.8694 + 33.4838i) q^{35} +(-6.68390 + 16.1364i) q^{37} +(35.3392 - 35.3392i) q^{39} +(40.4523 - 40.4523i) q^{41} +(24.5000 - 59.1482i) q^{43} +(-21.3514 - 51.5467i) q^{45} +16.5262 q^{47} -6.68842i q^{49} +(-11.8913 + 4.92553i) q^{51} +(-46.9950 - 19.4659i) q^{53} +(-55.6428 - 55.6428i) q^{55} +(43.0535 + 43.0535i) q^{57} +(-50.0578 - 20.7346i) q^{59} +(-54.3116 + 22.4966i) q^{61} +85.7298i q^{63} +53.6237 q^{65} +(25.5017 + 61.5665i) q^{67} +(-3.52550 + 8.51131i) q^{69} +(-7.12641 + 7.12641i) q^{71} +(55.3669 - 55.3669i) q^{73} +(-2.44752 + 5.90883i) q^{75} +(46.2711 + 111.708i) q^{77} -11.0986 q^{79} +52.4160i q^{81} +(29.9476 - 12.4047i) q^{83} +(-12.7589 - 5.28492i) q^{85} +(128.041 + 128.041i) q^{87} +(16.7667 + 16.7667i) q^{89} +(-76.1234 - 31.5313i) q^{91} +(19.8145 - 8.20743i) q^{93} +65.3294i q^{95} -67.8301 q^{97} +(-71.2322 - 171.970i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28q + 4q^{3} - 4q^{5} + 4q^{7} - 4q^{9} + O(q^{10}) \) \( 28q + 4q^{3} - 4q^{5} + 4q^{7} - 4q^{9} + 4q^{11} - 4q^{13} + 8q^{15} + 4q^{19} - 4q^{21} + 68q^{23} - 4q^{25} + 100q^{27} - 4q^{29} - 8q^{33} - 92q^{35} - 4q^{37} - 188q^{39} - 4q^{41} - 92q^{43} - 40q^{45} + 8q^{47} - 224q^{51} - 164q^{53} - 252q^{55} - 4q^{57} - 124q^{59} - 68q^{61} - 8q^{65} + 164q^{67} + 188q^{69} + 260q^{71} - 4q^{73} + 488q^{75} + 220q^{77} + 520q^{79} + 484q^{83} + 96q^{85} + 452q^{87} - 4q^{89} + 196q^{91} + 32q^{93} - 8q^{97} - 216q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/128\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(127\)
\(\chi(n)\) \(e\left(\frac{5}{8}\right)\) \(-1\)

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
\(3\) 1.73217 + 4.18183i 0.577390 + 1.39394i 0.895147 + 0.445771i \(0.147071\pi\)
−0.317756 + 0.948172i \(0.602929\pi\)
\(4\) 0 0
\(5\) −1.85856 + 4.48696i −0.371712 + 0.897391i 0.621749 + 0.783217i \(0.286422\pi\)
−0.993461 + 0.114175i \(0.963578\pi\)
\(6\) 0 0
\(7\) 5.27676 5.27676i 0.753823 0.753823i −0.221367 0.975190i \(-0.571052\pi\)
0.975190 + 0.221367i \(0.0710520\pi\)
\(8\) 0 0
\(9\) −8.12333 + 8.12333i −0.902593 + 0.902593i
\(10\) 0 0
\(11\) −6.20050 + 14.9693i −0.563682 + 1.36085i 0.343120 + 0.939292i \(0.388516\pi\)
−0.906802 + 0.421557i \(0.861484\pi\)
\(12\) 0 0
\(13\) −4.22532 10.2008i −0.325025 0.784680i −0.998947 0.0458772i \(-0.985392\pi\)
0.673922 0.738802i \(-0.264608\pi\)
\(14\) 0 0
\(15\) −21.9830 −1.46554
\(16\) 0 0
\(17\) 2.84356i 0.167268i 0.996497 + 0.0836341i \(0.0266527\pi\)
−0.996497 + 0.0836341i \(0.973347\pi\)
\(18\) 0 0
\(19\) 12.4276 5.14768i 0.654084 0.270931i −0.0308626 0.999524i \(-0.509825\pi\)
0.684947 + 0.728593i \(0.259825\pi\)
\(20\) 0 0
\(21\) 31.2068 + 12.9263i 1.48604 + 0.615537i
\(22\) 0 0
\(23\) 1.43918 + 1.43918i 0.0625730 + 0.0625730i 0.737701 0.675128i \(-0.235912\pi\)
−0.675128 + 0.737701i \(0.735912\pi\)
\(24\) 0 0
\(25\) 0.999126 + 0.999126i 0.0399650 + 0.0399650i
\(26\) 0 0
\(27\) −10.4049 4.30987i −0.385368 0.159625i
\(28\) 0 0
\(29\) 36.9596 15.3092i 1.27447 0.527902i 0.360148 0.932895i \(-0.382726\pi\)
0.914320 + 0.404993i \(0.132726\pi\)
\(30\) 0 0
\(31\) 4.73823i 0.152846i −0.997075 0.0764231i \(-0.975650\pi\)
0.997075 0.0764231i \(-0.0243500\pi\)
\(32\) 0 0
\(33\) −73.3396 −2.22241
\(34\) 0 0
\(35\) 13.8694 + 33.4838i 0.396269 + 0.956679i
\(36\) 0 0
\(37\) −6.68390 + 16.1364i −0.180646 + 0.436118i −0.988100 0.153812i \(-0.950845\pi\)
0.807454 + 0.589930i \(0.200845\pi\)
\(38\) 0 0
\(39\) 35.3392 35.3392i 0.906133 0.906133i
\(40\) 0 0
\(41\) 40.4523 40.4523i 0.986641 0.986641i −0.0132711 0.999912i \(-0.504224\pi\)
0.999912 + 0.0132711i \(0.00422444\pi\)
\(42\) 0 0
\(43\) 24.5000 59.1482i 0.569767 1.37554i −0.331984 0.943285i \(-0.607718\pi\)
0.901751 0.432255i \(-0.142282\pi\)
\(44\) 0 0
\(45\) −21.3514 51.5467i −0.474475 1.14548i
\(46\) 0 0
\(47\) 16.5262 0.351622 0.175811 0.984424i \(-0.443745\pi\)
0.175811 + 0.984424i \(0.443745\pi\)
\(48\) 0 0
\(49\) 6.68842i 0.136498i
\(50\) 0 0
\(51\) −11.8913 + 4.92553i −0.233162 + 0.0965790i
\(52\) 0 0
\(53\) −46.9950 19.4659i −0.886697 0.367282i −0.107607 0.994194i \(-0.534319\pi\)
−0.779090 + 0.626912i \(0.784319\pi\)
\(54\) 0 0
\(55\) −55.6428 55.6428i −1.01169 1.01169i
\(56\) 0 0
\(57\) 43.0535 + 43.0535i 0.755324 + 0.755324i
\(58\) 0 0
\(59\) −50.0578 20.7346i −0.848437 0.351434i −0.0842623 0.996444i \(-0.526853\pi\)
−0.764174 + 0.645010i \(0.776853\pi\)
\(60\) 0 0
\(61\) −54.3116 + 22.4966i −0.890353 + 0.368796i −0.780503 0.625152i \(-0.785037\pi\)
−0.109850 + 0.993948i \(0.535037\pi\)
\(62\) 0 0
\(63\) 85.7298i 1.36079i
\(64\) 0 0
\(65\) 53.6237 0.824980
\(66\) 0 0
\(67\) 25.5017 + 61.5665i 0.380622 + 0.918904i 0.991846 + 0.127445i \(0.0406778\pi\)
−0.611223 + 0.791458i \(0.709322\pi\)
\(68\) 0 0
\(69\) −3.52550 + 8.51131i −0.0510942 + 0.123352i
\(70\) 0 0
\(71\) −7.12641 + 7.12641i −0.100372 + 0.100372i −0.755510 0.655138i \(-0.772611\pi\)
0.655138 + 0.755510i \(0.272611\pi\)
\(72\) 0 0
\(73\) 55.3669 55.3669i 0.758451 0.758451i −0.217590 0.976040i \(-0.569819\pi\)
0.976040 + 0.217590i \(0.0698194\pi\)
\(74\) 0 0
\(75\) −2.44752 + 5.90883i −0.0326336 + 0.0787844i
\(76\) 0 0
\(77\) 46.2711 + 111.708i 0.600923 + 1.45076i
\(78\) 0 0
\(79\) −11.0986 −0.140489 −0.0702446 0.997530i \(-0.522378\pi\)
−0.0702446 + 0.997530i \(0.522378\pi\)
\(80\) 0 0
\(81\) 52.4160i 0.647112i
\(82\) 0 0
\(83\) 29.9476 12.4047i 0.360814 0.149454i −0.194909 0.980821i \(-0.562441\pi\)
0.555724 + 0.831367i \(0.312441\pi\)
\(84\) 0 0
\(85\) −12.7589 5.28492i −0.150105 0.0621755i
\(86\) 0 0
\(87\) 128.041 + 128.041i 1.47173 + 1.47173i
\(88\) 0 0
\(89\) 16.7667 + 16.7667i 0.188390 + 0.188390i 0.795000 0.606610i \(-0.207471\pi\)
−0.606610 + 0.795000i \(0.707471\pi\)
\(90\) 0 0
\(91\) −76.1234 31.5313i −0.836521 0.346498i
\(92\) 0 0
\(93\) 19.8145 8.20743i 0.213059 0.0882520i
\(94\) 0 0
\(95\) 65.3294i 0.687678i
\(96\) 0 0
\(97\) −67.8301 −0.699280 −0.349640 0.936884i \(-0.613696\pi\)
−0.349640 + 0.936884i \(0.613696\pi\)
\(98\) 0 0
\(99\) −71.2322 171.970i −0.719517 1.73707i
\(100\) 0 0
\(101\) −45.6943 + 110.316i −0.452419 + 1.09224i 0.518981 + 0.854786i \(0.326311\pi\)
−0.971400 + 0.237450i \(0.923689\pi\)
\(102\) 0 0
\(103\) −61.7093 + 61.7093i −0.599120 + 0.599120i −0.940078 0.340959i \(-0.889248\pi\)
0.340959 + 0.940078i \(0.389248\pi\)
\(104\) 0 0
\(105\) −115.999 + 115.999i −1.10475 + 1.10475i
\(106\) 0 0
\(107\) −7.13652 + 17.2291i −0.0666965 + 0.161020i −0.953713 0.300718i \(-0.902774\pi\)
0.887017 + 0.461737i \(0.152774\pi\)
\(108\) 0 0
\(109\) −75.1681 181.472i −0.689616 1.66488i −0.745554 0.666445i \(-0.767815\pi\)
0.0559384 0.998434i \(-0.482185\pi\)
\(110\) 0 0
\(111\) −79.0572 −0.712227
\(112\) 0 0
\(113\) 156.784i 1.38747i −0.720232 0.693734i \(-0.755965\pi\)
0.720232 0.693734i \(-0.244035\pi\)
\(114\) 0 0
\(115\) −9.13234 + 3.78274i −0.0794116 + 0.0328934i
\(116\) 0 0
\(117\) 117.189 + 48.5411i 1.00161 + 0.414881i
\(118\) 0 0
\(119\) 15.0048 + 15.0048i 0.126091 + 0.126091i
\(120\) 0 0
\(121\) −100.075 100.075i −0.827066 0.827066i
\(122\) 0 0
\(123\) 239.235 + 99.0943i 1.94500 + 0.805645i
\(124\) 0 0
\(125\) −118.514 + 49.0901i −0.948111 + 0.392720i
\(126\) 0 0
\(127\) 192.971i 1.51946i −0.650240 0.759729i \(-0.725332\pi\)
0.650240 0.759729i \(-0.274668\pi\)
\(128\) 0 0
\(129\) 289.786 2.24640
\(130\) 0 0
\(131\) −18.2599 44.0834i −0.139389 0.336515i 0.838734 0.544541i \(-0.183296\pi\)
−0.978123 + 0.208026i \(0.933296\pi\)
\(132\) 0 0
\(133\) 38.4144 92.7406i 0.288830 0.697297i
\(134\) 0 0
\(135\) 38.6764 38.6764i 0.286492 0.286492i
\(136\) 0 0
\(137\) −27.8671 + 27.8671i −0.203409 + 0.203409i −0.801459 0.598050i \(-0.795943\pi\)
0.598050 + 0.801459i \(0.295943\pi\)
\(138\) 0 0
\(139\) −33.3447 + 80.5013i −0.239890 + 0.579146i −0.997271 0.0738274i \(-0.976479\pi\)
0.757381 + 0.652973i \(0.226479\pi\)
\(140\) 0 0
\(141\) 28.6263 + 69.1099i 0.203023 + 0.490141i
\(142\) 0 0
\(143\) 178.899 1.25104
\(144\) 0 0
\(145\) 194.289i 1.33992i
\(146\) 0 0
\(147\) 27.9698 11.5855i 0.190271 0.0788128i
\(148\) 0 0
\(149\) −125.860 52.1327i −0.844695 0.349884i −0.0819919 0.996633i \(-0.526128\pi\)
−0.762703 + 0.646749i \(0.776128\pi\)
\(150\) 0 0
\(151\) −106.254 106.254i −0.703672 0.703672i 0.261525 0.965197i \(-0.415775\pi\)
−0.965197 + 0.261525i \(0.915775\pi\)
\(152\) 0 0
\(153\) −23.0992 23.0992i −0.150975 0.150975i
\(154\) 0 0
\(155\) 21.2603 + 8.80629i 0.137163 + 0.0568147i
\(156\) 0 0
\(157\) 209.345 86.7136i 1.33341 0.552316i 0.401783 0.915735i \(-0.368391\pi\)
0.931626 + 0.363419i \(0.118391\pi\)
\(158\) 0 0
\(159\) 230.243i 1.44807i
\(160\) 0 0
\(161\) 15.1884 0.0943380
\(162\) 0 0
\(163\) 0.176018 + 0.424946i 0.00107987 + 0.00260703i 0.924419 0.381380i \(-0.124551\pi\)
−0.923339 + 0.383987i \(0.874551\pi\)
\(164\) 0 0
\(165\) 136.306 329.072i 0.826096 1.99437i
\(166\) 0 0
\(167\) −96.7499 + 96.7499i −0.579341 + 0.579341i −0.934722 0.355381i \(-0.884351\pi\)
0.355381 + 0.934722i \(0.384351\pi\)
\(168\) 0 0
\(169\) 33.2974 33.2974i 0.197026 0.197026i
\(170\) 0 0
\(171\) −59.1372 + 142.770i −0.345832 + 0.834912i
\(172\) 0 0
\(173\) 102.242 + 246.834i 0.590994 + 1.42678i 0.882544 + 0.470229i \(0.155829\pi\)
−0.291551 + 0.956555i \(0.594171\pi\)
\(174\) 0 0
\(175\) 10.5443 0.0602531
\(176\) 0 0
\(177\) 245.249i 1.38559i
\(178\) 0 0
\(179\) −269.771 + 111.743i −1.50710 + 0.624262i −0.974957 0.222393i \(-0.928613\pi\)
−0.532144 + 0.846654i \(0.678613\pi\)
\(180\) 0 0
\(181\) −33.2079 13.7552i −0.183469 0.0759954i 0.289058 0.957312i \(-0.406658\pi\)
−0.472527 + 0.881316i \(0.656658\pi\)
\(182\) 0 0
\(183\) −188.154 188.154i −1.02816 1.02816i
\(184\) 0 0
\(185\) −59.9808 59.9808i −0.324220 0.324220i
\(186\) 0 0
\(187\) −42.5662 17.6315i −0.227627 0.0942861i
\(188\) 0 0
\(189\) −77.6465 + 32.1622i −0.410828 + 0.170171i
\(190\) 0 0
\(191\) 47.7299i 0.249895i −0.992163 0.124947i \(-0.960124\pi\)
0.992163 0.124947i \(-0.0398762\pi\)
\(192\) 0 0
\(193\) −302.171 −1.56565 −0.782827 0.622240i \(-0.786223\pi\)
−0.782827 + 0.622240i \(0.786223\pi\)
\(194\) 0 0
\(195\) 92.8855 + 224.245i 0.476336 + 1.14998i
\(196\) 0 0
\(197\) 18.2996 44.1791i 0.0928913 0.224259i −0.870604 0.491984i \(-0.836272\pi\)
0.963495 + 0.267725i \(0.0862718\pi\)
\(198\) 0 0
\(199\) 94.2590 94.2590i 0.473663 0.473663i −0.429435 0.903098i \(-0.641287\pi\)
0.903098 + 0.429435i \(0.141287\pi\)
\(200\) 0 0
\(201\) −213.288 + 213.288i −1.06113 + 1.06113i
\(202\) 0 0
\(203\) 114.244 275.810i 0.562779 1.35867i
\(204\) 0 0
\(205\) 106.325 + 256.691i 0.518657 + 1.25215i
\(206\) 0 0
\(207\) −23.3819 −0.112956
\(208\) 0 0
\(209\) 217.951i 1.04283i
\(210\) 0 0
\(211\) 267.734 110.899i 1.26888 0.525589i 0.356259 0.934387i \(-0.384052\pi\)
0.912625 + 0.408799i \(0.134052\pi\)
\(212\) 0 0
\(213\) −42.1456 17.4573i −0.197867 0.0819591i
\(214\) 0 0
\(215\) 219.861 + 219.861i 1.02261 + 1.02261i
\(216\) 0 0
\(217\) −25.0025 25.0025i −0.115219 0.115219i
\(218\) 0 0
\(219\) 327.440 + 135.630i 1.49516 + 0.619316i
\(220\) 0 0
\(221\) 29.0067 12.0150i 0.131252 0.0543663i
\(222\) 0 0
\(223\) 408.363i 1.83123i 0.402061 + 0.915613i \(0.368294\pi\)
−0.402061 + 0.915613i \(0.631706\pi\)
\(224\) 0 0
\(225\) −16.2325 −0.0721443
\(226\) 0 0
\(227\) −82.5132 199.204i −0.363494 0.877553i −0.994784 0.102005i \(-0.967474\pi\)
0.631290 0.775547i \(-0.282526\pi\)
\(228\) 0 0
\(229\) 22.6069 54.5778i 0.0987200 0.238331i −0.866802 0.498652i \(-0.833828\pi\)
0.965522 + 0.260321i \(0.0838284\pi\)
\(230\) 0 0
\(231\) −386.995 + 386.995i −1.67531 + 1.67531i
\(232\) 0 0
\(233\) 58.2826 58.2826i 0.250140 0.250140i −0.570888 0.821028i \(-0.693401\pi\)
0.821028 + 0.570888i \(0.193401\pi\)
\(234\) 0 0
\(235\) −30.7150 + 74.1525i −0.130702 + 0.315543i
\(236\) 0 0
\(237\) −19.2248 46.4127i −0.0811171 0.195834i
\(238\) 0 0
\(239\) 367.366 1.53710 0.768548 0.639792i \(-0.220979\pi\)
0.768548 + 0.639792i \(0.220979\pi\)
\(240\) 0 0
\(241\) 312.345i 1.29604i 0.761624 + 0.648020i \(0.224403\pi\)
−0.761624 + 0.648020i \(0.775597\pi\)
\(242\) 0 0
\(243\) −312.839 + 129.582i −1.28741 + 0.533261i
\(244\) 0 0
\(245\) 30.0106 + 12.4308i 0.122492 + 0.0507380i
\(246\) 0 0
\(247\) −105.021 105.021i −0.425187 0.425187i
\(248\) 0 0
\(249\) 103.749 + 103.749i 0.416661 + 0.416661i
\(250\) 0 0
\(251\) −223.120 92.4192i −0.888923 0.368204i −0.108972 0.994045i \(-0.534756\pi\)
−0.779951 + 0.625841i \(0.784756\pi\)
\(252\) 0 0
\(253\) −30.4672 + 12.6199i −0.120424 + 0.0498811i
\(254\) 0 0
\(255\) 62.5101i 0.245138i
\(256\) 0 0
\(257\) 178.176 0.693293 0.346646 0.937996i \(-0.387320\pi\)
0.346646 + 0.937996i \(0.387320\pi\)
\(258\) 0 0
\(259\) 49.8784 + 120.417i 0.192581 + 0.464931i
\(260\) 0 0
\(261\) −175.874 + 424.596i −0.673845 + 1.62681i
\(262\) 0 0
\(263\) 147.164 147.164i 0.559558 0.559558i −0.369623 0.929182i \(-0.620513\pi\)
0.929182 + 0.369623i \(0.120513\pi\)
\(264\) 0 0
\(265\) 174.686 174.686i 0.659191 0.659191i
\(266\) 0 0
\(267\) −41.0728 + 99.1585i −0.153831 + 0.371380i
\(268\) 0 0
\(269\) −138.119 333.450i −0.513455 1.23959i −0.941861 0.336004i \(-0.890924\pi\)
0.428405 0.903587i \(-0.359076\pi\)
\(270\) 0 0
\(271\) −218.643 −0.806801 −0.403400 0.915024i \(-0.632172\pi\)
−0.403400 + 0.915024i \(0.632172\pi\)
\(272\) 0 0
\(273\) 372.953i 1.36613i
\(274\) 0 0
\(275\) −21.1513 + 8.76117i −0.0769139 + 0.0318588i
\(276\) 0 0
\(277\) 256.038 + 106.054i 0.924323 + 0.382867i 0.793522 0.608541i \(-0.208245\pi\)
0.130801 + 0.991409i \(0.458245\pi\)
\(278\) 0 0
\(279\) 38.4903 + 38.4903i 0.137958 + 0.137958i
\(280\) 0 0
\(281\) −49.4126 49.4126i −0.175845 0.175845i 0.613697 0.789542i \(-0.289682\pi\)
−0.789542 + 0.613697i \(0.789682\pi\)
\(282\) 0 0
\(283\) −118.290 48.9975i −0.417987 0.173136i 0.163770 0.986499i \(-0.447635\pi\)
−0.581757 + 0.813363i \(0.697635\pi\)
\(284\) 0 0
\(285\) −273.196 + 113.162i −0.958584 + 0.397058i
\(286\) 0 0
\(287\) 426.914i 1.48751i
\(288\) 0 0
\(289\) 280.914 0.972021
\(290\) 0 0
\(291\) −117.493 283.654i −0.403757 0.974757i
\(292\) 0 0
\(293\) −100.203 + 241.910i −0.341988 + 0.825633i 0.655526 + 0.755172i \(0.272447\pi\)
−0.997515 + 0.0704605i \(0.977553\pi\)
\(294\) 0 0
\(295\) 186.071 186.071i 0.630748 0.630748i
\(296\) 0 0
\(297\) 129.032 129.032i 0.434450 0.434450i
\(298\) 0 0
\(299\) 8.59983 20.7618i 0.0287620 0.0694376i
\(300\) 0 0
\(301\) −182.830 441.392i −0.607410 1.46642i
\(302\) 0 0
\(303\) −540.472 −1.78374
\(304\) 0 0
\(305\) 285.505i 0.936081i
\(306\) 0 0
\(307\) 371.163 153.741i 1.20900 0.500784i 0.315103 0.949058i \(-0.397961\pi\)
0.893896 + 0.448274i \(0.147961\pi\)
\(308\) 0 0
\(309\) −364.949 151.167i −1.18107 0.489213i
\(310\) 0 0
\(311\) 312.733 + 312.733i 1.00557 + 1.00557i 0.999984 + 0.00558671i \(0.00177831\pi\)
0.00558671 + 0.999984i \(0.498222\pi\)
\(312\) 0 0
\(313\) 358.245 + 358.245i 1.14455 + 1.14455i 0.987607 + 0.156946i \(0.0501649\pi\)
0.156946 + 0.987607i \(0.449835\pi\)
\(314\) 0 0
\(315\) −384.666 159.334i −1.22116 0.505822i
\(316\) 0 0
\(317\) 164.720 68.2292i 0.519621 0.215234i −0.107429 0.994213i \(-0.534262\pi\)
0.627051 + 0.778979i \(0.284262\pi\)
\(318\) 0 0
\(319\) 648.185i 2.03193i
\(320\) 0 0
\(321\) −84.4108 −0.262962
\(322\) 0 0
\(323\) 14.6377 + 35.3386i 0.0453181 + 0.109407i
\(324\) 0 0
\(325\) 5.97029 14.4135i 0.0183701 0.0443494i
\(326\) 0 0
\(327\) 628.681 628.681i 1.92257 1.92257i
\(328\) 0 0
\(329\) 87.2050 87.2050i 0.265061 0.265061i
\(330\) 0 0
\(331\) −21.3130 + 51.4542i −0.0643898 + 0.155451i −0.952799 0.303601i \(-0.901811\pi\)
0.888409 + 0.459052i \(0.151811\pi\)
\(332\) 0 0
\(333\) −76.7855 185.377i −0.230587 0.556687i
\(334\) 0 0
\(335\) −323.643 −0.966098
\(336\) 0 0
\(337\) 173.028i 0.513437i −0.966486 0.256718i \(-0.917359\pi\)
0.966486 0.256718i \(-0.0826413\pi\)
\(338\) 0 0
\(339\) 655.643 271.576i 1.93405 0.801110i
\(340\) 0 0
\(341\) 70.9282 + 29.3794i 0.208001 + 0.0861567i
\(342\) 0 0
\(343\) 223.268 + 223.268i 0.650927 + 0.650927i
\(344\) 0 0
\(345\) −31.6375 31.6375i −0.0917030 0.0917030i
\(346\) 0 0
\(347\) −48.9563 20.2784i −0.141085 0.0584391i 0.311024 0.950402i \(-0.399328\pi\)
−0.452109 + 0.891963i \(0.649328\pi\)
\(348\) 0 0
\(349\) −222.227 + 92.0495i −0.636754 + 0.263752i −0.677620 0.735412i \(-0.736988\pi\)
0.0408656 + 0.999165i \(0.486988\pi\)
\(350\) 0 0
\(351\) 124.350i 0.354273i
\(352\) 0 0
\(353\) −75.1997 −0.213030 −0.106515 0.994311i \(-0.533969\pi\)
−0.106515 + 0.994311i \(0.533969\pi\)
\(354\) 0 0
\(355\) −18.7310 45.2208i −0.0527635 0.127382i
\(356\) 0 0
\(357\) −36.7566 + 88.7383i −0.102960 + 0.248567i
\(358\) 0 0
\(359\) −369.532 + 369.532i −1.02934 + 1.02934i −0.0297806 + 0.999556i \(0.509481\pi\)
−0.999556 + 0.0297806i \(0.990519\pi\)
\(360\) 0 0
\(361\) −127.319 + 127.319i −0.352684 + 0.352684i
\(362\) 0 0
\(363\) 245.150 591.844i 0.675343 1.63042i
\(364\) 0 0
\(365\) 145.526 + 351.332i 0.398702 + 0.962552i
\(366\) 0 0
\(367\) 482.888 1.31577 0.657885 0.753118i \(-0.271451\pi\)
0.657885 + 0.753118i \(0.271451\pi\)
\(368\) 0 0
\(369\) 657.215i 1.78107i
\(370\) 0 0
\(371\) −350.698 + 145.264i −0.945278 + 0.391547i
\(372\) 0 0
\(373\) 459.056 + 190.147i 1.23071 + 0.509778i 0.900801 0.434233i \(-0.142980\pi\)
0.329913 + 0.944011i \(0.392980\pi\)
\(374\) 0 0
\(375\) −410.573 410.573i −1.09486 1.09486i
\(376\) 0 0
\(377\) −312.332 312.332i −0.828468 0.828468i
\(378\) 0 0
\(379\) −209.167 86.6398i −0.551891 0.228601i 0.0892693 0.996008i \(-0.471547\pi\)
−0.641161 + 0.767407i \(0.721547\pi\)
\(380\) 0 0
\(381\) 806.973 334.259i 2.11804 0.877320i
\(382\) 0 0
\(383\) 243.083i 0.634682i 0.948312 + 0.317341i \(0.102790\pi\)
−0.948312 + 0.317341i \(0.897210\pi\)
\(384\) 0 0
\(385\) −587.227 −1.52527
\(386\) 0 0
\(387\) 281.459 + 679.503i 0.727285 + 1.75582i
\(388\) 0 0
\(389\) 100.024 241.479i 0.257131 0.620768i −0.741616 0.670825i \(-0.765940\pi\)
0.998746 + 0.0500566i \(0.0159402\pi\)
\(390\) 0 0
\(391\) −4.09239 + 4.09239i −0.0104665 + 0.0104665i
\(392\) 0 0
\(393\) 152.720 152.720i 0.388601 0.388601i
\(394\) 0 0
\(395\) 20.6275 49.7992i 0.0522215 0.126074i
\(396\) 0 0
\(397\) −177.617 428.806i −0.447399 1.08012i −0.973293 0.229566i \(-0.926269\pi\)
0.525894 0.850550i \(-0.323731\pi\)
\(398\) 0 0
\(399\) 454.366 1.13876
\(400\) 0 0
\(401\) 539.233i 1.34472i −0.740224 0.672360i \(-0.765281\pi\)
0.740224 0.672360i \(-0.234719\pi\)
\(402\) 0 0
\(403\) −48.3339 + 20.0206i −0.119935 + 0.0496788i
\(404\) 0 0
\(405\) −235.188 97.4183i −0.580712 0.240539i
\(406\) 0 0
\(407\) −200.107 200.107i −0.491664 0.491664i
\(408\) 0 0
\(409\) 177.821 + 177.821i 0.434769 + 0.434769i 0.890247 0.455478i \(-0.150532\pi\)
−0.455478 + 0.890247i \(0.650532\pi\)
\(410\) 0 0
\(411\) −164.806 68.2648i −0.400988 0.166094i
\(412\) 0 0
\(413\) −373.554 + 154.731i −0.904490 + 0.374652i
\(414\) 0 0
\(415\) 157.428i 0.379345i
\(416\) 0 0
\(417\) −394.402 −0.945807
\(418\) 0 0
\(419\) −55.0604 132.927i −0.131409 0.317249i 0.844456 0.535625i \(-0.179924\pi\)
−0.975865 + 0.218376i \(0.929924\pi\)
\(420\) 0 0
\(421\) −292.384 + 705.877i −0.694498 + 1.67667i 0.0410159 + 0.999158i \(0.486941\pi\)
−0.735514 + 0.677509i \(0.763059\pi\)
\(422\) 0 0
\(423\) −134.248 + 134.248i −0.317371 + 0.317371i
\(424\) 0 0
\(425\) −2.84107 + 2.84107i −0.00668488 + 0.00668488i
\(426\) 0 0
\(427\) −167.880 + 405.298i −0.393162 + 0.949176i
\(428\) 0 0
\(429\) 309.883 + 748.125i 0.722339 + 1.74388i
\(430\) 0 0
\(431\) −810.711 −1.88100 −0.940500 0.339794i \(-0.889643\pi\)
−0.940500 + 0.339794i \(0.889643\pi\)
\(432\) 0 0
\(433\) 753.072i 1.73920i 0.493759 + 0.869599i \(0.335622\pi\)
−0.493759 + 0.869599i \(0.664378\pi\)
\(434\) 0 0
\(435\) −812.484 + 336.542i −1.86778 + 0.773659i
\(436\) 0 0
\(437\) 25.2940 + 10.4771i 0.0578810 + 0.0239751i
\(438\) 0 0
\(439\) −504.938 504.938i −1.15020 1.15020i −0.986512 0.163689i \(-0.947661\pi\)
−0.163689 0.986512i \(-0.552339\pi\)
\(440\) 0 0
\(441\) 54.3323 + 54.3323i 0.123202 + 0.123202i
\(442\) 0 0
\(443\) 697.291 + 288.827i 1.57402 + 0.651981i 0.987452 0.157919i \(-0.0504784\pi\)
0.586569 + 0.809899i \(0.300478\pi\)
\(444\) 0 0
\(445\) −106.394 + 44.0697i −0.239087 + 0.0990330i
\(446\) 0 0
\(447\) 616.626i 1.37948i
\(448\) 0 0
\(449\) −294.056 −0.654913 −0.327457 0.944866i \(-0.606192\pi\)
−0.327457 + 0.944866i \(0.606192\pi\)
\(450\) 0 0
\(451\) 354.719 + 856.368i 0.786517 + 1.89882i
\(452\) 0 0
\(453\) 260.287 628.389i 0.574585 1.38717i
\(454\) 0 0
\(455\) 282.960 282.960i 0.621889 0.621889i
\(456\) 0 0
\(457\) 175.139 175.139i 0.383237 0.383237i −0.489030 0.872267i \(-0.662649\pi\)
0.872267 + 0.489030i \(0.162649\pi\)
\(458\) 0 0
\(459\) 12.2554 29.5871i 0.0267001 0.0644598i
\(460\) 0 0
\(461\) −107.290 259.020i −0.232732 0.561866i 0.763765 0.645495i \(-0.223349\pi\)
−0.996497 + 0.0836293i \(0.973349\pi\)
\(462\) 0 0
\(463\) −53.7059 −0.115996 −0.0579978 0.998317i \(-0.518472\pi\)
−0.0579978 + 0.998317i \(0.518472\pi\)
\(464\) 0 0
\(465\) 104.161i 0.224002i
\(466\) 0 0
\(467\) −101.550 + 42.0634i −0.217452 + 0.0900716i −0.488750 0.872424i \(-0.662547\pi\)
0.271298 + 0.962495i \(0.412547\pi\)
\(468\) 0 0
\(469\) 459.438 + 190.306i 0.979613 + 0.405769i
\(470\) 0 0
\(471\) 725.243 + 725.243i 1.53979 + 1.53979i
\(472\) 0 0
\(473\) 733.498 + 733.498i 1.55074 + 1.55074i
\(474\) 0 0
\(475\) 17.5599 + 7.27355i 0.0369682 + 0.0153127i
\(476\) 0 0
\(477\) 539.884 223.627i 1.13183 0.468820i
\(478\) 0 0
\(479\) 40.7997i 0.0851769i −0.999093 0.0425884i \(-0.986440\pi\)
0.999093 0.0425884i \(-0.0135604\pi\)
\(480\) 0 0
\(481\) 192.846 0.400927
\(482\) 0 0
\(483\) 26.3089 + 63.5154i 0.0544698 + 0.131502i
\(484\) 0 0
\(485\) 126.066 304.351i 0.259931 0.627528i
\(486\) 0 0
\(487\) 143.660 143.660i 0.294989 0.294989i −0.544058 0.839047i \(-0.683113\pi\)
0.839047 + 0.544058i \(0.183113\pi\)
\(488\) 0 0
\(489\) −1.47216 + 1.47216i −0.00301055 + 0.00301055i
\(490\) 0 0
\(491\) −182.575 + 440.775i −0.371843 + 0.897709i 0.621595 + 0.783339i \(0.286485\pi\)
−0.993438 + 0.114370i \(0.963515\pi\)
\(492\) 0 0
\(493\) 43.5325 + 105.097i 0.0883012 + 0.213178i
\(494\) 0 0
\(495\) 904.010 1.82628
\(496\) 0 0
\(497\) 75.2087i 0.151325i
\(498\) 0 0
\(499\) 409.850 169.766i 0.821343 0.340211i 0.0678733 0.997694i \(-0.478379\pi\)
0.753470 + 0.657482i \(0.228379\pi\)
\(500\) 0 0
\(501\) −572.179 237.004i −1.14207 0.473063i
\(502\) 0 0
\(503\) −453.715 453.715i −0.902019 0.902019i 0.0935920 0.995611i \(-0.470165\pi\)
−0.995611 + 0.0935920i \(0.970165\pi\)
\(504\) 0 0
\(505\) −410.057 410.057i −0.811993 0.811993i
\(506\) 0 0
\(507\) 196.921 + 81.5673i 0.388404 + 0.160882i
\(508\) 0 0
\(509\) −71.5029 + 29.6175i −0.140477 + 0.0581876i −0.451815 0.892112i \(-0.649223\pi\)
0.311337 + 0.950299i \(0.399223\pi\)
\(510\) 0 0
\(511\) 584.316i 1.14348i
\(512\) 0 0
\(513\) −151.494 −0.295310
\(514\) 0 0
\(515\) −162.197 391.578i −0.314945 0.760345i
\(516\) 0 0
\(517\) −102.471 + 247.387i −0.198203 + 0.478504i
\(518\) 0 0
\(519\) −855.117 + 855.117i −1.64762 + 1.64762i
\(520\) 0 0
\(521\) −565.729 + 565.729i −1.08585 + 1.08585i −0.0899020 + 0.995951i \(0.528655\pi\)
−0.995951 + 0.0899020i \(0.971345\pi\)
\(522\) 0 0
\(523\) 1.50925 3.64366i 0.00288576 0.00696685i −0.922430 0.386164i \(-0.873800\pi\)
0.925316 + 0.379197i \(0.123800\pi\)
\(524\) 0 0
\(525\) 18.2645 + 44.0945i 0.0347896 + 0.0839895i
\(526\) 0 0
\(527\) 13.4734 0.0255663
\(528\) 0 0
\(529\) 524.858i 0.992169i
\(530\) 0 0
\(531\) 575.070 238.202i 1.08299 0.448591i
\(532\) 0 0
\(533\) −583.571 241.723i −1.09488 0.453514i
\(534\) 0 0
\(535\) −64.0426 64.0426i −0.119706 0.119706i
\(536\) 0 0
\(537\) −934.579 934.579i −1.74037 1.74037i
\(538\) 0 0
\(539\) 100.121 + 41.4716i 0.185754 + 0.0769417i
\(540\) 0 0
\(541\) −746.681 + 309.286i −1.38019 + 0.571692i −0.944531 0.328421i \(-0.893483\pi\)
−0.435656 + 0.900113i \(0.643483\pi\)
\(542\) 0 0
\(543\) 162.696i 0.299625i
\(544\) 0 0
\(545\) 953.961 1.75039
\(546\) 0 0
\(547\) −298.176 719.861i −0.545112 1.31602i −0.921076 0.389383i \(-0.872688\pi\)
0.375964 0.926634i \(-0.377312\pi\)
\(548\) 0 0
\(549\) 258.444 623.938i 0.470754 1.13650i
\(550\) 0 0
\(551\) 380.512 380.512i 0.690585 0.690585i
\(552\) 0 0
\(553\) −58.5649 + 58.5649i −0.105904 + 0.105904i
\(554\) 0 0
\(555\) 146.932 354.726i 0.264743 0.639147i
\(556\) 0 0
\(557\) 83.4142 + 201.380i 0.149756 + 0.361544i 0.980900 0.194515i \(-0.0623132\pi\)
−0.831143 + 0.556058i \(0.812313\pi\)
\(558\) 0 0
\(559\) −706.882 −1.26455
\(560\) 0 0
\(561\) 208.545i 0.371739i
\(562\) 0 0
\(563\) 19.5811 8.11076i 0.0347800 0.0144063i −0.365226 0.930919i \(-0.619008\pi\)
0.400006 + 0.916513i \(0.369008\pi\)
\(564\) 0 0
\(565\) 703.482 + 291.392i 1.24510 + 0.515738i
\(566\) 0 0
\(567\) 276.587 + 276.587i 0.487808 + 0.487808i
\(568\) 0 0
\(569\) −366.760 366.760i −0.644569 0.644569i 0.307106 0.951675i \(-0.400639\pi\)
−0.951675 + 0.307106i \(0.900639\pi\)
\(570\) 0 0
\(571\) 121.285 + 50.2378i 0.212408 + 0.0879822i 0.486350 0.873764i \(-0.338328\pi\)
−0.273943 + 0.961746i \(0.588328\pi\)
\(572\) 0 0
\(573\) 199.599 82.6764i 0.348339 0.144287i
\(574\) 0 0
\(575\) 2.87584i 0.00500147i
\(576\) 0 0
\(577\) 464.948 0.805802 0.402901 0.915244i \(-0.368002\pi\)
0.402901 + 0.915244i \(0.368002\pi\)
\(578\) 0 0
\(579\) −523.412 1263.63i −0.903993 2.18243i
\(580\) 0 0
\(581\) 92.5696 223.483i 0.159328 0.384652i
\(582\) 0 0
\(583\) 582.785 582.785i 0.999631 0.999631i
\(584\) 0 0
\(585\) −435.603 + 435.603i −0.744621 + 0.744621i
\(586\) 0 0
\(587\) −159.551 + 385.190i −0.271807 + 0.656201i −0.999561 0.0296380i \(-0.990565\pi\)
0.727753 + 0.685839i \(0.240565\pi\)
\(588\) 0 0
\(589\) −24.3909 58.8849i −0.0414107 0.0999743i
\(590\) 0 0
\(591\) 216.448 0.366239
\(592\) 0 0
\(593\) 470.422i 0.793292i −0.917972 0.396646i \(-0.870174\pi\)
0.917972 0.396646i \(-0.129826\pi\)
\(594\) 0 0
\(595\) −95.2131 + 39.4385i −0.160022 + 0.0662833i
\(596\) 0 0
\(597\) 557.448 + 230.903i 0.933749 + 0.386771i
\(598\) 0 0
\(599\) 506.817 + 506.817i 0.846105 + 0.846105i 0.989645 0.143540i \(-0.0458485\pi\)
−0.143540 + 0.989645i \(0.545849\pi\)
\(600\) 0 0
\(601\) −261.398 261.398i −0.434939 0.434939i 0.455366 0.890305i \(-0.349509\pi\)
−0.890305 + 0.455366i \(0.849509\pi\)
\(602\) 0 0
\(603\) −707.285 292.967i −1.17294 0.485849i
\(604\) 0 0
\(605\) 635.027 263.037i 1.04963 0.434772i
\(606\) 0 0
\(607\) 812.089i 1.33787i 0.743319 + 0.668937i \(0.233250\pi\)
−0.743319 + 0.668937i \(0.766750\pi\)
\(608\) 0 0
\(609\) 1351.28 2.21885
\(610\) 0 0
\(611\) −69.8287 168.581i −0.114286 0.275911i
\(612\) 0 0
\(613\) 105.168 253.898i 0.171563 0.414190i −0.814588 0.580040i \(-0.803037\pi\)
0.986151 + 0.165850i \(0.0530369\pi\)
\(614\) 0 0
\(615\) −889.264 + 889.264i −1.44596 + 1.44596i
\(616\) 0 0
\(617\) −508.739 + 508.739i −0.824536 + 0.824536i −0.986755 0.162218i \(-0.948135\pi\)
0.162218 + 0.986755i \(0.448135\pi\)
\(618\) 0 0
\(619\) 6.64960 16.0536i 0.0107425 0.0259347i −0.918417 0.395613i \(-0.870532\pi\)
0.929160 + 0.369678i \(0.120532\pi\)
\(620\) 0 0
\(621\) −8.77191 21.1773i −0.0141255 0.0341019i
\(622\) 0 0
\(623\) 176.948 0.284026
\(624\) 0 0
\(625\) 587.679i 0.940287i
\(626\) 0 0
\(627\) −911.435 + 377.529i −1.45364 + 0.602119i
\(628\) 0 0
\(629\) −45.8847 19.0061i −0.0729487 0.0302163i
\(630\) 0 0
\(631\) 177.518 + 177.518i 0.281329 + 0.281329i 0.833639 0.552310i \(-0.186254\pi\)
−0.552310 + 0.833639i \(0.686254\pi\)
\(632\) 0 0
\(633\) 927.524 + 927.524i 1.46528 + 1.46528i
\(634\) 0 0
\(635\) 865.853 + 358.648i 1.36355 + 0.564800i
\(636\) 0 0
\(637\) −68.2274 + 28.2607i −0.107107 + 0.0443654i
\(638\) 0 0
\(639\) 115.780i 0.181190i
\(640\) 0 0
\(641\) 334.058 0.521151 0.260575 0.965454i \(-0.416088\pi\)
0.260575 + 0.965454i \(0.416088\pi\)
\(642\) 0 0
\(643\) 19.9758 + 48.2257i 0.0310665 + 0.0750011i 0.938651 0.344867i \(-0.112076\pi\)
−0.907585 + 0.419869i \(0.862076\pi\)
\(644\) 0 0
\(645\) −538.584 + 1300.26i −0.835015 + 2.01590i
\(646\) 0 0
\(647\) −443.581 + 443.581i −0.685596 + 0.685596i −0.961255 0.275659i \(-0.911104\pi\)
0.275659 + 0.961255i \(0.411104\pi\)
\(648\) 0 0
\(649\) 620.767 620.767i 0.956497 0.956497i
\(650\) 0 0
\(651\) 61.2477 147.865i 0.0940825 0.227135i
\(652\) 0 0
\(653\) −14.0746 33.9792i −0.0215538 0.0520355i 0.912736 0.408549i \(-0.133965\pi\)
−0.934290 + 0.356514i \(0.883965\pi\)
\(654\) 0 0
\(655\) 231.737 0.353798
\(656\) 0 0
\(657\) 899.528i 1.36914i
\(658\) 0 0
\(659\) 845.778 350.333i 1.28343 0.531613i 0.366407 0.930455i \(-0.380588\pi\)
0.917020 + 0.398842i \(0.130588\pi\)
\(660\) 0 0
\(661\) −1022.39 423.490i −1.54674 0.640680i −0.564017 0.825763i \(-0.690745\pi\)
−0.982723 + 0.185083i \(0.940745\pi\)
\(662\) 0 0
\(663\) 100.489 + 100.489i 0.151567 + 0.151567i
\(664\) 0 0
\(665\) 344.727 + 344.727i 0.518387 + 0.518387i
\(666\) 0 0
\(667\) 75.2241 + 31.1588i 0.112780 + 0.0467149i
\(668\) 0 0
\(669\) −1707.71 + 707.355i −2.55263 + 1.05733i
\(670\) 0 0
\(671\) 952.498i 1.41952i
\(672\) 0 0
\(673\) −441.074 −0.655385 −0.327693 0.944784i \(-0.606271\pi\)
−0.327693 + 0.944784i \(0.606271\pi\)
\(674\) 0 0
\(675\) −6.08974 14.7019i −0.00902184 0.0217807i
\(676\) 0 0
\(677\) −3.12869 + 7.55333i −0.00462140 + 0.0111571i −0.926173 0.377098i \(-0.876922\pi\)
0.921552 + 0.388255i \(0.126922\pi\)
\(678\) 0 0
\(679\) −357.923 + 357.923i −0.527133 + 0.527133i
\(680\) 0 0
\(681\) 690.112 690.112i 1.01338 1.01338i
\(682\) 0 0
\(683\) 198.853 480.073i 0.291146 0.702889i −0.708851 0.705358i \(-0.750786\pi\)
0.999997 + 0.00246964i \(0.000786112\pi\)
\(684\) 0 0
\(685\) −73.2458 176.831i −0.106928 0.258147i
\(686\) 0 0
\(687\) 267.394 0.389220
\(688\) 0 0
\(689\) 561.638i 0.815149i
\(690\) 0 0
\(691\) −260.304 + 107.822i −0.376707 + 0.156037i −0.563000 0.826457i \(-0.690353\pi\)
0.186293 + 0.982494i \(0.440353\pi\)
\(692\) 0 0
\(693\) −1283.32 531.568i −1.85183 0.767053i
\(694\) 0 0
\(695\) −299.233 299.233i −0.430551 0.430551i
\(696\) 0 0
\(697\) 115.028 + 115.028i 0.165034 + 0.165034i
\(698\) 0 0
\(699\) 344.683 + 142.772i 0.493109 + 0.204252i
\(700\) 0 0
\(701\) −487.328 + 201.858i −0.695189 + 0.287957i −0.702160 0.712019i \(-0.747781\pi\)
0.00697111 + 0.999976i \(0.497781\pi\)
\(702\) 0 0
\(703\) 234.943i 0.334200i
\(704\) 0 0
\(705\) −363.297 −0.515315
\(706\) 0 0
\(707\) 340.992 + 823.228i 0.482309 + 1.16440i
\(708\) 0 0
\(709\) 260.932 629.945i 0.368028 0.888498i −0.626046 0.779786i \(-0.715328\pi\)
0.994073 0.108711i \(-0.0346724\pi\)
\(710\) 0 0
\(711\) 90.1580 90.1580i 0.126805 0.126805i
\(712\) 0 0
\(713\) 6.81917 6.81917i 0.00956405 0.00956405i
\(714\) 0 0
\(715\) −332.494 + 802.712i −0.465027 + 1.12267i
\(716\) 0 0
\(717\) 636.341 + 1536.26i 0.887505 + 2.14263i
\(718\) 0 0
\(719\) 349.854 0.486585 0.243292 0.969953i \(-0.421773\pi\)
0.243292 + 0.969953i \(0.421773\pi\)
\(720\) 0 0
\(721\) 651.251i 0.903261i
\(722\) 0 0
\(723\) −1306.18 + 541.036i −1.80661 + 0.748321i
\(724\) 0 0
\(725\) 52.2230 + 21.6315i 0.0720318 + 0.0298365i
\(726\) 0 0
\(727\) 58.3736 + 58.3736i 0.0802938 + 0.0802938i 0.746113 0.665819i \(-0.231918\pi\)
−0.665819 + 0.746113i \(0.731918\pi\)
\(728\) 0 0
\(729\) −750.210 750.210i −1.02909 1.02909i
\(730\) 0 0
\(731\) 168.191 + 69.6672i 0.230084 + 0.0953040i
\(732\) 0 0
\(733\) 327.632 135.710i 0.446975 0.185143i −0.147831 0.989013i \(-0.547229\pi\)
0.594805 + 0.803870i \(0.297229\pi\)
\(734\) 0 0
\(735\) 147.032i 0.200043i
\(736\) 0 0
\(737\) −1079.73 −1.46504
\(738\) 0 0
\(739\) −328.523 793.126i −0.444551 1.07324i −0.974334 0.225108i \(-0.927726\pi\)
0.529783 0.848134i \(-0.322274\pi\)
\(740\) 0 0
\(741\) 257.266 621.096i 0.347188 0.838186i
\(742\) 0 0
\(743\) −79.8532 + 79.8532i −0.107474 + 0.107474i −0.758799 0.651325i \(-0.774214\pi\)
0.651325 + 0.758799i \(0.274214\pi\)
\(744\) 0 0
\(745\) 467.835 467.835i 0.627966 0.627966i
\(746\) 0 0
\(747\) −142.507 + 344.042i −0.190772 + 0.460565i
\(748\) 0 0
\(749\) 53.2561 + 128.572i 0.0711029 + 0.171658i
\(750\) 0 0
\(751\) 729.615 0.971524 0.485762 0.874091i \(-0.338542\pi\)
0.485762 + 0.874091i \(0.338542\pi\)
\(752\) 0 0
\(753\) 1093.13i 1.45171i
\(754\) 0 0
\(755\) 674.239 279.279i 0.893032 0.369906i
\(756\) 0 0
\(757\) 565.974 + 234.434i 0.747654 + 0.309688i 0.723784 0.690027i \(-0.242401\pi\)
0.0238700 + 0.999715i \(0.492401\pi\)
\(758\) 0 0
\(759\) −105.549 105.549i −0.139063 0.139063i
\(760\) 0 0
\(761\) 186.563 + 186.563i 0.245155 + 0.245155i 0.818979 0.573824i \(-0.194541\pi\)
−0.573824 + 0.818979i \(0.694541\pi\)
\(762\) 0 0
\(763\) −1354.23 560.940i −1.77487 0.735176i
\(764\) 0 0
\(765\) 146.576 60.7139i 0.191603 0.0793645i
\(766\) 0 0
\(767\) 598.241i 0.779976i
\(768\) 0 0
\(769\) 134.178 0.174484 0.0872420 0.996187i \(-0.472195\pi\)
0.0872420 + 0.996187i \(0.472195\pi\)
\(770\) 0 0
\(771\) 308.632 + 745.103i 0.400301 + 0.966411i
\(772\) 0 0
\(773\) −155.016 + 374.241i −0.200538 + 0.484141i −0.991872 0.127243i \(-0.959387\pi\)
0.791334 + 0.611384i \(0.209387\pi\)
\(774\) 0 0
\(775\) 4.73409 4.73409i 0.00610851 0.00610851i
\(776\) 0 0
\(777\) −417.166 + 417.166i −0.536893 + 0.536893i
\(778\) 0 0
\(779\) 294.489 710.960i 0.378035 0.912657i
\(780\) 0 0
\(781\) −62.4903 150.865i −0.0800132 0.193169i
\(782\) 0 0
\(783\) −450.543 −0.575406
\(784\) 0 0
\(785\) 1100.49i 1.40189i
\(786\) 0 0
\(787\) −464.245 + 192.297i −0.589892 + 0.244341i −0.657604 0.753364i \(-0.728430\pi\)
0.0677120 + 0.997705i \(0.478430\pi\)
\(788\) 0 0
\(789\) 870.327 + 360.501i 1.10308 + 0.456909i
\(790\) 0 0
\(791\) −827.311 827.311i −1.04590 1.04590i
\(792\) 0 0
\(793\) 458.968 + 458.968i 0.578774 + 0.578774i
\(794\) 0 0
\(795\) 1033.09 + 427.921i 1.29949 + 0.538265i
\(796\) 0 0
\(797\) 1426.93 591.055i 1.79038 0.741600i 0.800564 0.599247i \(-0.204533\pi\)
0.989816