Properties

Label 128.3.h.a.47.7
Level $128$
Weight $3$
Character 128.47
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 47.7
Character \(\chi\) \(=\) 128.47
Dual form 128.3.h.a.79.7

$q$-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 \(\left(\mathbb{Z}/128\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(127\)
\(\chi(n)\) \(e\left(\frac{3}{8}\right)\) \(-1\)

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 −0.317756 0.948172i \(-0.602929\pi\)
0.895147 0.445771i \(-0.147071\pi\)
\(4\) 0 0
\(5\) −1.85856 4.48696i −0.371712 0.897391i −0.993461 0.114175i \(-0.963578\pi\)
0.621749 0.783217i \(-0.286422\pi\)
\(6\) 0 0
\(7\) 5.27676 + 5.27676i 0.753823 + 0.753823i 0.975190 0.221367i \(-0.0710520\pi\)
−0.221367 + 0.975190i \(0.571052\pi\)
\(8\) 0 0
\(9\) −8.12333 8.12333i −0.902593 0.902593i
\(10\) 0 0
\(11\) −6.20050 14.9693i −0.563682 1.36085i −0.906802 0.421557i \(-0.861484\pi\)
0.343120 0.939292i \(-0.388516\pi\)
\(12\) 0 0
\(13\) −4.22532 + 10.2008i −0.325025 + 0.784680i 0.673922 + 0.738802i \(0.264608\pi\)
−0.998947 + 0.0458772i \(0.985392\pi\)
\(14\) 0 0
\(15\) −21.9830 −1.46554
\(16\) 0 0
\(17\) 2.84356i 0.167268i −0.996497 0.0836341i \(-0.973347\pi\)
0.996497 0.0836341i \(-0.0266527\pi\)
\(18\) 0 0
\(19\) 12.4276 + 5.14768i 0.654084 + 0.270931i 0.684947 0.728593i \(-0.259825\pi\)
−0.0308626 + 0.999524i \(0.509825\pi\)
\(20\) 0 0
\(21\) 31.2068 12.9263i 1.48604 0.615537i
\(22\) 0 0
\(23\) 1.43918 1.43918i 0.0625730 0.0625730i −0.675128 0.737701i \(-0.735912\pi\)
0.737701 + 0.675128i \(0.235912\pi\)
\(24\) 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 0.914320 0.404993i \(-0.132726\pi\)
0.360148 + 0.932895i \(0.382726\pi\)
\(30\) 0 0
\(31\) 4.73823i 0.152846i 0.997075 + 0.0764231i \(0.0243500\pi\)
−0.997075 + 0.0764231i \(0.975650\pi\)
\(32\) 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 0.807454 0.589930i \(-0.200845\pi\)
−0.988100 + 0.153812i \(0.950845\pi\)
\(38\) 0 0
\(39\) 35.3392 + 35.3392i 0.906133 + 0.906133i
\(40\) 0 0
\(41\) 40.4523 + 40.4523i 0.986641 + 0.986641i 0.999912 0.0132711i \(-0.00422444\pi\)
−0.0132711 + 0.999912i \(0.504224\pi\)
\(42\) 0 0
\(43\) 24.5000 + 59.1482i 0.569767 + 1.37554i 0.901751 + 0.432255i \(0.142282\pi\)
−0.331984 + 0.943285i \(0.607718\pi\)
\(44\) 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 −0.779090 0.626912i \(-0.784319\pi\)
−0.107607 + 0.994194i \(0.534319\pi\)
\(54\) 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 −0.764174 0.645010i \(-0.776853\pi\)
−0.0842623 + 0.996444i \(0.526853\pi\)
\(60\) 0 0
\(61\) −54.3116 22.4966i −0.890353 0.368796i −0.109850 0.993948i \(-0.535037\pi\)
−0.780503 + 0.625152i \(0.785037\pi\)
\(62\) 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 −0.611223 0.791458i \(-0.709322\pi\)
0.991846 0.127445i \(-0.0406778\pi\)
\(68\) 0 0
\(69\) −3.52550 8.51131i −0.0510942 0.123352i
\(70\) 0 0
\(71\) −7.12641 7.12641i −0.100372 0.100372i 0.655138 0.755510i \(-0.272611\pi\)
−0.755510 + 0.655138i \(0.772611\pi\)
\(72\) 0 0
\(73\) 55.3669 + 55.3669i 0.758451 + 0.758451i 0.976040 0.217590i \(-0.0698194\pi\)
−0.217590 + 0.976040i \(0.569819\pi\)
\(74\) 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 0.555724 0.831367i \(-0.312441\pi\)
−0.194909 + 0.980821i \(0.562441\pi\)
\(84\) 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 −0.606610 0.795000i \(-0.707471\pi\)
0.795000 + 0.606610i \(0.207471\pi\)
\(90\) 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 −0.971400 0.237450i \(-0.923689\pi\)
0.518981 0.854786i \(-0.326311\pi\)
\(102\) 0 0
\(103\) −61.7093 61.7093i −0.599120 0.599120i 0.340959 0.940078i \(-0.389248\pi\)
−0.940078 + 0.340959i \(0.889248\pi\)
\(104\) 0 0
\(105\) −115.999 115.999i −1.10475 1.10475i
\(106\) 0 0
\(107\) −7.13652 17.2291i −0.0666965 0.161020i 0.887017 0.461737i \(-0.152774\pi\)
−0.953713 + 0.300718i \(0.902774\pi\)
\(108\) 0 0
\(109\) −75.1681 + 181.472i −0.689616 + 1.66488i 0.0559384 + 0.998434i \(0.482185\pi\)
−0.745554 + 0.666445i \(0.767815\pi\)
\(110\) 0 0
\(111\) −79.0572 −0.712227
\(112\) 0 0
\(113\) 156.784i 1.38747i 0.720232 + 0.693734i \(0.244035\pi\)
−0.720232 + 0.693734i \(0.755965\pi\)
\(114\) 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 \(0.274668\pi\)
−0.650240 + 0.759729i \(0.725332\pi\)
\(128\) 0 0
\(129\) 289.786 2.24640
\(130\) 0 0
\(131\) −18.2599 + 44.0834i −0.139389 + 0.336515i −0.978123 0.208026i \(-0.933296\pi\)
0.838734 + 0.544541i \(0.183296\pi\)
\(132\) 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 0.598050 0.801459i \(-0.295943\pi\)
−0.801459 + 0.598050i \(0.795943\pi\)
\(138\) 0 0
\(139\) −33.3447 80.5013i −0.239890 0.579146i 0.757381 0.652973i \(-0.226479\pi\)
−0.997271 + 0.0738274i \(0.976479\pi\)
\(140\) 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 −0.762703 0.646749i \(-0.776128\pi\)
−0.0819919 + 0.996633i \(0.526128\pi\)
\(150\) 0 0
\(151\) −106.254 + 106.254i −0.703672 + 0.703672i −0.965197 0.261525i \(-0.915775\pi\)
0.261525 + 0.965197i \(0.415775\pi\)
\(152\) 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 0.931626 0.363419i \(-0.118391\pi\)
0.401783 + 0.915735i \(0.368391\pi\)
\(158\) 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 −0.923339 0.383987i \(-0.874551\pi\)
0.924419 + 0.381380i \(0.124551\pi\)
\(164\) 0 0
\(165\) 136.306 + 329.072i 0.826096 + 1.99437i
\(166\) 0 0
\(167\) −96.7499 96.7499i −0.579341 0.579341i 0.355381 0.934722i \(-0.384351\pi\)
−0.934722 + 0.355381i \(0.884351\pi\)
\(168\) 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 −0.291551 0.956555i \(-0.594171\pi\)
0.882544 0.470229i \(-0.155829\pi\)
\(174\) 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 −0.532144 0.846654i \(-0.678613\pi\)
−0.974957 + 0.222393i \(0.928613\pi\)
\(180\) 0 0
\(181\) −33.2079 + 13.7552i −0.183469 + 0.0759954i −0.472527 0.881316i \(-0.656658\pi\)
0.289058 + 0.957312i \(0.406658\pi\)
\(182\) 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 \(0.0398762\pi\)
−0.992163 + 0.124947i \(0.960124\pi\)
\(192\) 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 0.963495 0.267725i \(-0.0862718\pi\)
−0.870604 + 0.491984i \(0.836272\pi\)
\(198\) 0 0
\(199\) 94.2590 + 94.2590i 0.473663 + 0.473663i 0.903098 0.429435i \(-0.141287\pi\)
−0.429435 + 0.903098i \(0.641287\pi\)
\(200\) 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 0.912625 0.408799i \(-0.134052\pi\)
0.356259 + 0.934387i \(0.384052\pi\)
\(212\) 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 \(-0.631706\pi\)
0.402061 0.915613i \(-0.368294\pi\)
\(224\) 0 0
\(225\) −16.2325 −0.0721443
\(226\) 0 0
\(227\) −82.5132 + 199.204i −0.363494 + 0.877553i 0.631290 + 0.775547i \(0.282526\pi\)
−0.994784 + 0.102005i \(0.967474\pi\)
\(228\) 0 0
\(229\) 22.6069 + 54.5778i 0.0987200 + 0.238331i 0.965522 0.260321i \(-0.0838284\pi\)
−0.866802 + 0.498652i \(0.833828\pi\)
\(230\) 0 0
\(231\) −386.995 386.995i −1.67531 1.67531i
\(232\) 0 0
\(233\) 58.2826 + 58.2826i 0.250140 + 0.250140i 0.821028 0.570888i \(-0.193401\pi\)
−0.570888 + 0.821028i \(0.693401\pi\)
\(234\) 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 \(-0.775597\pi\)
0.761624 0.648020i \(-0.224403\pi\)
\(242\) 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 −0.779951 0.625841i \(-0.784756\pi\)
−0.108972 + 0.994045i \(0.534756\pi\)
\(252\) 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 0.929182 0.369623i \(-0.120513\pi\)
−0.369623 + 0.929182i \(0.620513\pi\)
\(264\) 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 0.428405 + 0.903587i \(0.359076\pi\)
−0.941861 + 0.336004i \(0.890924\pi\)
\(270\) 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 0.130801 0.991409i \(-0.458245\pi\)
0.793522 + 0.608541i \(0.208245\pi\)
\(278\) 0 0
\(279\) 38.4903 38.4903i 0.137958 0.137958i
\(280\) 0 0
\(281\) −49.4126 + 49.4126i −0.175845 + 0.175845i −0.789542 0.613697i \(-0.789682\pi\)
0.613697 + 0.789542i \(0.289682\pi\)
\(282\) 0 0
\(283\) −118.290 + 48.9975i −0.417987 + 0.173136i −0.581757 0.813363i \(-0.697635\pi\)
0.163770 + 0.986499i \(0.447635\pi\)
\(284\) 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 −0.997515 0.0704605i \(-0.977553\pi\)
0.655526 0.755172i \(-0.272447\pi\)
\(294\) 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 0.893896 0.448274i \(-0.147961\pi\)
0.315103 + 0.949058i \(0.397961\pi\)
\(308\) 0 0
\(309\) −364.949 + 151.167i −1.18107 + 0.489213i
\(310\) 0 0
\(311\) 312.733 312.733i 1.00557 1.00557i 0.00558671 0.999984i \(-0.498222\pi\)
0.999984 0.00558671i \(-0.00177831\pi\)
\(312\) 0 0
\(313\) 358.245 358.245i 1.14455 1.14455i 0.156946 0.987607i \(-0.449835\pi\)
0.987607 0.156946i \(-0.0501649\pi\)
\(314\) 0 0
\(315\) −384.666 + 159.334i −1.22116 + 0.505822i
\(316\) 0 0
\(317\) 164.720 + 68.2292i 0.519621 + 0.215234i 0.627051 0.778979i \(-0.284262\pi\)
−0.107429 + 0.994213i \(0.534262\pi\)
\(318\) 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 0.888409 0.459052i \(-0.151811\pi\)
−0.952799 + 0.303601i \(0.901811\pi\)
\(332\) 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 \(0.0826413\pi\)
−0.966486 + 0.256718i \(0.917359\pi\)
\(338\) 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 −0.452109 0.891963i \(-0.649328\pi\)
0.311024 + 0.950402i \(0.399328\pi\)
\(348\) 0 0
\(349\) −222.227 92.0495i −0.636754 0.263752i 0.0408656 0.999165i \(-0.486988\pi\)
−0.677620 + 0.735412i \(0.736988\pi\)
\(350\) 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 −0.999556 0.0297806i \(-0.990519\pi\)
−0.0297806 0.999556i \(-0.509481\pi\)
\(360\) 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 0.329913 0.944011i \(-0.392980\pi\)
0.900801 + 0.434233i \(0.142980\pi\)
\(374\) 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 −0.641161 0.767407i \(-0.721547\pi\)
0.0892693 + 0.996008i \(0.471547\pi\)
\(380\) 0 0
\(381\) 806.973 + 334.259i 2.11804 + 0.877320i
\(382\) 0 0
\(383\) 243.083i 0.634682i −0.948312 0.317341i \(-0.897210\pi\)
0.948312 0.317341i \(-0.102790\pi\)
\(384\) 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 0.998746 0.0500566i \(-0.0159402\pi\)
−0.741616 + 0.670825i \(0.765940\pi\)
\(390\) 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 0.525894 + 0.850550i \(0.323731\pi\)
−0.973293 + 0.229566i \(0.926269\pi\)
\(398\) 0 0
\(399\) 454.366 1.13876
\(400\) 0 0
\(401\) 539.233i 1.34472i 0.740224 + 0.672360i \(0.234719\pi\)
−0.740224 + 0.672360i \(0.765281\pi\)
\(402\) 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 −0.455478 0.890247i \(-0.650532\pi\)
0.890247 + 0.455478i \(0.150532\pi\)
\(410\) 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 −0.975865 0.218376i \(-0.929924\pi\)
0.844456 + 0.535625i \(0.179924\pi\)
\(420\) 0 0
\(421\) −292.384 705.877i −0.694498 1.67667i −0.735514 0.677509i \(-0.763059\pi\)
0.0410159 0.999158i \(-0.486941\pi\)
\(422\) 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 \(-0.664378\pi\)
0.493759 0.869599i \(-0.335622\pi\)
\(434\) 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 −0.163689 + 0.986512i \(0.552339\pi\)
−0.986512 + 0.163689i \(0.947661\pi\)
\(440\) 0 0
\(441\) 54.3323 54.3323i 0.123202 0.123202i
\(442\) 0 0
\(443\) 697.291 288.827i 1.57402 0.651981i 0.586569 0.809899i \(-0.300478\pi\)
0.987452 + 0.157919i \(0.0504784\pi\)
\(444\) 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 0.872267 0.489030i \(-0.162649\pi\)
−0.489030 + 0.872267i \(0.662649\pi\)
\(458\) 0 0
\(459\) 12.2554 + 29.5871i 0.0267001 + 0.0644598i
\(460\) 0 0
\(461\) −107.290 + 259.020i −0.232732 + 0.561866i −0.996497 0.0836293i \(-0.973349\pi\)
0.763765 + 0.645495i \(0.223349\pi\)
\(462\) 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 0.271298 0.962495i \(-0.412547\pi\)
−0.488750 + 0.872424i \(0.662547\pi\)
\(468\) 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 \(0.0135604\pi\)
−0.999093 + 0.0425884i \(0.986440\pi\)
\(480\) 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 0.839047 0.544058i \(-0.183113\pi\)
−0.544058 + 0.839047i \(0.683113\pi\)
\(488\) 0 0
\(489\) −1.47216 1.47216i −0.00301055 0.00301055i
\(490\) 0 0
\(491\) −182.575 440.775i −0.371843 0.897709i −0.993438 0.114370i \(-0.963515\pi\)
0.621595 0.783339i \(-0.286485\pi\)
\(492\) 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 0.753470 0.657482i \(-0.228379\pi\)
0.0678733 + 0.997694i \(0.478379\pi\)
\(500\) 0 0
\(501\) −572.179 + 237.004i −1.14207 + 0.473063i
\(502\) 0 0
\(503\) −453.715 + 453.715i −0.902019 + 0.902019i −0.995611 0.0935920i \(-0.970165\pi\)
0.0935920 + 0.995611i \(0.470165\pi\)
\(504\) 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 0.311337 0.950299i \(-0.399223\pi\)
−0.451815 + 0.892112i \(0.649223\pi\)
\(510\) 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 −0.995951 0.0899020i \(-0.971345\pi\)
−0.0899020 0.995951i \(-0.528655\pi\)
\(522\) 0 0
\(523\) 1.50925 + 3.64366i 0.00288576 + 0.00696685i 0.925316 0.379197i \(-0.123800\pi\)
−0.922430 + 0.386164i \(0.873800\pi\)
\(524\) 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 −0.435656 0.900113i \(-0.643483\pi\)
−0.944531 + 0.328421i \(0.893483\pi\)
\(542\) 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 0.375964 + 0.926634i \(0.377312\pi\)
−0.921076 + 0.389383i \(0.872688\pi\)
\(548\) 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 −0.831143 0.556058i \(-0.812313\pi\)
0.980900 + 0.194515i \(0.0623132\pi\)
\(558\) 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 0.400006 0.916513i \(-0.369008\pi\)
−0.365226 + 0.930919i \(0.619008\pi\)
\(564\) 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 −0.951675 0.307106i \(-0.900639\pi\)
0.307106 + 0.951675i \(0.400639\pi\)
\(570\) 0 0
\(571\) 121.285 50.2378i 0.212408 0.0879822i −0.273943 0.961746i \(-0.588328\pi\)
0.486350 + 0.873764i \(0.338328\pi\)
\(572\) 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 0.727753 0.685839i \(-0.240565\pi\)
−0.999561 + 0.0296380i \(0.990565\pi\)
\(588\) 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 \(0.129826\pi\)
−0.917972 + 0.396646i \(0.870174\pi\)
\(594\) 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 −0.143540 0.989645i \(-0.545849\pi\)
0.989645 + 0.143540i \(0.0458485\pi\)
\(600\) 0 0
\(601\) −261.398 + 261.398i −0.434939 + 0.434939i −0.890305 0.455366i \(-0.849509\pi\)
0.455366 + 0.890305i \(0.349509\pi\)
\(602\) 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 \(-0.766750\pi\)
0.743319 0.668937i \(-0.233250\pi\)
\(608\) 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 0.986151 0.165850i \(-0.0530369\pi\)
−0.814588 + 0.580040i \(0.803037\pi\)
\(614\) 0 0
\(615\) −889.264 889.264i −1.44596 1.44596i
\(616\) 0 0
\(617\) −508.739 508.739i −0.824536 0.824536i 0.162218 0.986755i \(-0.448135\pi\)
−0.986755 + 0.162218i \(0.948135\pi\)
\(618\) 0 0
\(619\) 6.64960 + 16.0536i 0.0107425 + 0.0259347i 0.929160 0.369678i \(-0.120532\pi\)
−0.918417 + 0.395613i \(0.870532\pi\)
\(620\) 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 −0.552310 0.833639i \(-0.686254\pi\)
0.833639 + 0.552310i \(0.186254\pi\)
\(632\) 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 −0.907585 0.419869i \(-0.862076\pi\)
0.938651 + 0.344867i \(0.112076\pi\)
\(644\) 0 0
\(645\) −538.584 1300.26i −0.835015 2.01590i
\(646\) 0 0
\(647\) −443.581 443.581i −0.685596 0.685596i 0.275659 0.961255i \(-0.411104\pi\)
−0.961255 + 0.275659i \(0.911104\pi\)
\(648\) 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 −0.934290 0.356514i \(-0.883965\pi\)
0.912736 + 0.408549i \(0.133965\pi\)
\(654\) 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 0.917020 0.398842i \(-0.130588\pi\)
0.366407 + 0.930455i \(0.380588\pi\)
\(660\) 0 0
\(661\) −1022.39 + 423.490i −1.54674 + 0.640680i −0.982723 0.185083i \(-0.940745\pi\)
−0.564017 + 0.825763i \(0.690745\pi\)
\(662\) 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 0.921552 0.388255i \(-0.126922\pi\)
−0.926173 + 0.377098i \(0.876922\pi\)
\(678\) 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 0.999997 0.00246964i \(-0.000786112\pi\)
−0.708851 + 0.705358i \(0.750786\pi\)
\(684\) 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 0.186293 0.982494i \(-0.440353\pi\)
−0.563000 + 0.826457i \(0.690353\pi\)
\(692\) 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 0.00697111 0.999976i \(-0.497781\pi\)
−0.702160 + 0.712019i \(0.747781\pi\)
\(702\) 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 0.994073 + 0.108711i \(0.0346724\pi\)
−0.626046 + 0.779786i \(0.715328\pi\)
\(710\) 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 −0.665819 0.746113i \(-0.731918\pi\)
0.746113 + 0.665819i \(0.231918\pi\)
\(728\) 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 0.594805 0.803870i \(-0.297229\pi\)
−0.147831 + 0.989013i \(0.547229\pi\)
\(734\) 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 0.529783 + 0.848134i \(0.322274\pi\)
−0.974334 + 0.225108i \(0.927726\pi\)
\(740\) 0 0
\(741\) 257.266 + 621.096i 0.347188 + 0.838186i
\(742\) 0 0
\(743\) −79.8532 79.8532i −0.107474 0.107474i 0.651325 0.758799i \(-0.274214\pi\)
−0.758799 + 0.651325i \(0.774214\pi\)
\(744\) 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 0.0238700 0.999715i \(-0.492401\pi\)
0.723784 + 0.690027i \(0.242401\pi\)
\(758\) 0 0
\(759\) −105.549 + 105.549i −0.139063 + 0.139063i
\(760\) 0 0
\(761\) 186.563 186.563i 0.245155 0.245155i −0.573824 0.818979i \(-0.694541\pi\)
0.818979 + 0.573824i \(0.194541\pi\)
\(762\) 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 0.791334 0.611384i \(-0.209387\pi\)
−0.991872 + 0.127243i \(0.959387\pi\)
\(774\) 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 0.0677120 0.997705i \(-0.478430\pi\)
−0.657604 + 0.753364i \(0.728430\pi\)
\(788\) 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 0.989816 + 0.142353i \(0.0454669\pi\)
0.800564