Properties

Label 224.3.n.a.145.4
Level 224
Weight 3
Character 224.145
Analytic conductor 6.104
Analytic rank 0
Dimension 28
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 224 = 2^{5} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 224.n (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.10355792167\)
Analytic rank: \(0\)
Dimension: \(28\)
Relative dimension: \(14\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 56)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 145.4
Character \(\chi\) \(=\) 224.145
Dual form 224.3.n.a.17.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.70138 - 2.94687i) q^{3} +(-2.15858 + 3.73877i) q^{5} +(1.43197 - 6.85197i) q^{7} +(-1.28938 + 2.23327i) q^{9} +O(q^{10})\) \(q+(-1.70138 - 2.94687i) q^{3} +(-2.15858 + 3.73877i) q^{5} +(1.43197 - 6.85197i) q^{7} +(-1.28938 + 2.23327i) q^{9} +(-15.4899 + 8.94308i) q^{11} -3.25607 q^{13} +14.6903 q^{15} +(-13.6263 + 7.86717i) q^{17} +(0.778522 - 1.34844i) q^{19} +(-22.6282 + 7.43796i) q^{21} +(-20.7069 + 35.8655i) q^{23} +(3.18105 + 5.50975i) q^{25} -21.8499 q^{27} -3.74374i q^{29} +(0.0145172 - 0.00838150i) q^{31} +(52.7082 + 30.4311i) q^{33} +(22.5269 + 20.1443i) q^{35} +(1.16774 + 0.674194i) q^{37} +(5.53981 + 9.59523i) q^{39} -70.3018i q^{41} -13.0380i q^{43} +(-5.56646 - 9.64139i) q^{45} +(-30.9797 - 17.8862i) q^{47} +(-44.8989 - 19.6236i) q^{49} +(46.3671 + 26.7701i) q^{51} +(-39.7989 + 22.9779i) q^{53} -77.2174i q^{55} -5.29824 q^{57} +(-34.3509 - 59.4974i) q^{59} +(48.0386 - 83.2052i) q^{61} +(13.4559 + 12.0328i) q^{63} +(7.02849 - 12.1737i) q^{65} +(12.0808 - 6.97484i) q^{67} +140.921 q^{69} +75.7095 q^{71} +(-46.0282 + 26.5744i) q^{73} +(10.8244 - 18.7483i) q^{75} +(39.0967 + 118.942i) q^{77} +(-11.6744 + 20.2206i) q^{79} +(48.7794 + 84.4884i) q^{81} +102.487 q^{83} -67.9277i q^{85} +(-11.0323 + 6.36952i) q^{87} +(-76.6985 - 44.2819i) q^{89} +(-4.66259 + 22.3105i) q^{91} +(-0.0493984 - 0.0285202i) q^{93} +(3.36100 + 5.82143i) q^{95} +140.869i q^{97} -46.1241i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28q + 4q^{7} - 32q^{9} + O(q^{10}) \) \( 28q + 4q^{7} - 32q^{9} - 28q^{15} - 6q^{17} - 30q^{23} - 32q^{25} + 6q^{31} - 6q^{33} + 20q^{39} + 294q^{47} - 20q^{49} + 124q^{57} - 432q^{63} - 52q^{65} + 136q^{71} + 234q^{73} + 162q^{79} - 18q^{81} - 48q^{87} - 150q^{89} - 290q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/224\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(129\) \(197\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(-1\)

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
\(3\) −1.70138 2.94687i −0.567126 0.982291i −0.996848 0.0793303i \(-0.974722\pi\)
0.429722 0.902961i \(1.64139\pi\)
\(4\) 0 0
\(5\) −2.15858 + 3.73877i −0.431716 + 0.747754i −0.997021 0.0771275i \(-0.975425\pi\)
0.565305 + 0.824882i \(0.308758\pi\)
\(6\) 0 0
\(7\) 1.43197 6.85197i 0.204567 0.978853i
\(8\) 0 0
\(9\) −1.28938 + 2.23327i −0.143264 + 0.248141i
\(10\) 0 0
\(11\) −15.4899 + 8.94308i −1.40817 + 0.813007i −0.995212 0.0977432i \(-0.968838\pi\)
−0.412958 + 0.910750i \(0.635504\pi\)
\(12\) 0 0
\(13\) −3.25607 −0.250467 −0.125233 0.992127i \(-0.539968\pi\)
−0.125233 + 0.992127i \(0.539968\pi\)
\(14\) 0 0
\(15\) 14.6903 0.979350
\(16\) 0 0
\(17\) −13.6263 + 7.86717i −0.801550 + 0.462775i −0.844013 0.536323i \(-0.819813\pi\)
0.0424631 + 0.999098i \(0.486479\pi\)
\(18\) 0 0
\(19\) 0.778522 1.34844i 0.0409748 0.0709705i −0.844811 0.535065i \(-0.820287\pi\)
0.885786 + 0.464095i \(0.153620\pi\)
\(20\) 0 0
\(21\) −22.6282 + 7.43796i −1.07753 + 0.354188i
\(22\) 0 0
\(23\) −20.7069 + 35.8655i −0.900301 + 1.55937i −0.0731984 + 0.997317i \(0.523321\pi\)
−0.827103 + 0.562050i \(0.810013\pi\)
\(24\) 0 0
\(25\) 3.18105 + 5.50975i 0.127242 + 0.220390i
\(26\) 0 0
\(27\) −21.8499 −0.809257
\(28\) 0 0
\(29\) 3.74374i 0.129095i −0.997915 0.0645473i \(-0.979440\pi\)
0.997915 0.0645473i \(-0.0205603\pi\)
\(30\) 0 0
\(31\) 0.0145172 0.00838150i 0.000468296 0.000270371i −0.499766 0.866161i \(-0.666581\pi\)
0.500234 + 0.865890i \(0.333247\pi\)
\(32\) 0 0
\(33\) 52.7082 + 30.4311i 1.59722 + 0.922155i
\(34\) 0 0
\(35\) 22.5269 + 20.1443i 0.643626 + 0.575553i
\(36\) 0 0
\(37\) 1.16774 + 0.674194i 0.0315605 + 0.0182215i 0.515697 0.856771i \(-0.327533\pi\)
−0.484137 + 0.874992i \(0.660866\pi\)
\(38\) 0 0
\(39\) 5.53981 + 9.59523i 0.142046 + 0.246031i
\(40\) 0 0
\(41\) 70.3018i 1.71468i −0.514753 0.857339i \(-0.672116\pi\)
0.514753 0.857339i \(-0.327884\pi\)
\(42\) 0 0
\(43\) 13.0380i 0.303210i −0.988441 0.151605i \(-0.951556\pi\)
0.988441 0.151605i \(-0.0484442\pi\)
\(44\) 0 0
\(45\) −5.56646 9.64139i −0.123699 0.214253i
\(46\) 0 0
\(47\) −30.9797 17.8862i −0.659144 0.380557i 0.132807 0.991142i \(-0.457601\pi\)
−0.791951 + 0.610585i \(0.790934\pi\)
\(48\) 0 0
\(49\) −44.8989 19.6236i −0.916305 0.400482i
\(50\) 0 0
\(51\) 46.3671 + 26.7701i 0.909160 + 0.524904i
\(52\) 0 0
\(53\) −39.7989 + 22.9779i −0.750923 + 0.433546i −0.826027 0.563630i \(-0.809404\pi\)
0.0751042 + 0.997176i \(0.476071\pi\)
\(54\) 0 0
\(55\) 77.2174i 1.40395i
\(56\) 0 0
\(57\) −5.29824 −0.0929516
\(58\) 0 0
\(59\) −34.3509 59.4974i −0.582218 1.00843i −0.995216 0.0976993i \(-0.968852\pi\)
0.412998 0.910732i \(1.63552\pi\)
\(60\) 0 0
\(61\) 48.0386 83.2052i 0.787517 1.36402i −0.139966 0.990156i \(-0.544699\pi\)
0.927484 0.373864i \(-0.121967\pi\)
\(62\) 0 0
\(63\) 13.4559 + 12.0328i 0.213586 + 0.190996i
\(64\) 0 0
\(65\) 7.02849 12.1737i 0.108131 0.187288i
\(66\) 0 0
\(67\) 12.0808 6.97484i 0.180310 0.104102i −0.407128 0.913371i \(-0.633470\pi\)
0.587438 + 0.809269i \(0.300136\pi\)
\(68\) 0 0
\(69\) 140.921 2.04234
\(70\) 0 0
\(71\) 75.7095 1.06633 0.533166 0.846011i \(-0.321002\pi\)
0.533166 + 0.846011i \(0.321002\pi\)
\(72\) 0 0
\(73\) −46.0282 + 26.5744i −0.630523 + 0.364033i −0.780955 0.624588i \(-0.785267\pi\)
0.150432 + 0.988620i \(0.451934\pi\)
\(74\) 0 0
\(75\) 10.8244 18.7483i 0.144325 0.249978i
\(76\) 0 0
\(77\) 39.0967 + 118.942i 0.507749 + 1.54470i
\(78\) 0 0
\(79\) −11.6744 + 20.2206i −0.147777 + 0.255957i −0.930406 0.366532i \(-0.880545\pi\)
0.782628 + 0.622489i \(0.213878\pi\)
\(80\) 0 0
\(81\) 48.7794 + 84.4884i 0.602215 + 1.04307i
\(82\) 0 0
\(83\) 102.487 1.23479 0.617393 0.786655i \(-0.288189\pi\)
0.617393 + 0.786655i \(0.288189\pi\)
\(84\) 0 0
\(85\) 67.9277i 0.799150i
\(86\) 0 0
\(87\) −11.0323 + 6.36952i −0.126808 + 0.0732129i
\(88\) 0 0
\(89\) −76.6985 44.2819i −0.861781 0.497549i 0.00282755 0.999996i \(-0.499100\pi\)
−0.864608 + 0.502447i \(0.832433\pi\)
\(90\) 0 0
\(91\) −4.66259 + 22.3105i −0.0512373 + 0.245170i
\(92\) 0 0
\(93\) −0.0493984 0.0285202i −0.000531166 0.000306669i
\(94\) 0 0
\(95\) 3.36100 + 5.82143i 0.0353790 + 0.0612782i
\(96\) 0 0
\(97\) 140.869i 1.45226i 0.687558 + 0.726130i \(0.258683\pi\)
−0.687558 + 0.726130i \(0.741317\pi\)
\(98\) 0 0
\(99\) 46.1241i 0.465900i
\(100\) 0 0
\(101\) −17.6988 30.6553i −0.175236 0.303518i 0.765007 0.644022i \(-0.222735\pi\)
−0.940243 + 0.340504i \(0.889402\pi\)
\(102\) 0 0
\(103\) −87.1651 50.3248i −0.846263 0.488590i 0.0131250 0.999914i \(-0.495822\pi\)
−0.859388 + 0.511324i \(0.829155\pi\)
\(104\) 0 0
\(105\) 21.0360 100.657i 0.200343 0.958640i
\(106\) 0 0
\(107\) 92.6215 + 53.4751i 0.865622 + 0.499767i 0.865891 0.500233i \(-0.166752\pi\)
−0.000269099 1.00000i \(0.500086\pi\)
\(108\) 0 0
\(109\) −45.5799 + 26.3156i −0.418165 + 0.241427i −0.694292 0.719694i \(-0.744282\pi\)
0.276127 + 0.961121i \(0.410949\pi\)
\(110\) 0 0
\(111\) 4.58824i 0.0413355i
\(112\) 0 0
\(113\) 45.4346 0.402076 0.201038 0.979583i \(-0.435568\pi\)
0.201038 + 0.979583i \(0.435568\pi\)
\(114\) 0 0
\(115\) −89.3952 154.837i −0.777350 1.34641i
\(116\) 0 0
\(117\) 4.19831 7.27168i 0.0358830 0.0621511i
\(118\) 0 0
\(119\) 34.3931 + 104.633i 0.289018 + 0.879267i
\(120\) 0 0
\(121\) 99.4572 172.265i 0.821961 1.42368i
\(122\) 0 0
\(123\) −207.171 + 119.610i −1.68431 + 0.972439i
\(124\) 0 0
\(125\) −135.395 −1.08316
\(126\) 0 0
\(127\) −125.695 −0.989723 −0.494861 0.868972i \(-0.664781\pi\)
−0.494861 + 0.868972i \(0.664781\pi\)
\(128\) 0 0
\(129\) −38.4215 + 22.1827i −0.297841 + 0.171959i
\(130\) 0 0
\(131\) −56.6504 + 98.1214i −0.432446 + 0.749018i −0.997083 0.0763210i \(-0.975683\pi\)
0.564638 + 0.825339i \(0.309016\pi\)
\(132\) 0 0
\(133\) −8.12464 7.26533i −0.0610875 0.0546265i
\(134\) 0 0
\(135\) 47.1648 81.6919i 0.349369 0.605125i
\(136\) 0 0
\(137\) −39.1679 67.8408i −0.285897 0.495188i 0.686929 0.726724i \(-0.258958\pi\)
−0.972826 + 0.231536i \(0.925625\pi\)
\(138\) 0 0
\(139\) 149.038 1.07222 0.536109 0.844149i \(-0.319894\pi\)
0.536109 + 0.844149i \(0.319894\pi\)
\(140\) 0 0
\(141\) 121.725i 0.863295i
\(142\) 0 0
\(143\) 50.4361 29.1193i 0.352700 0.203631i
\(144\) 0 0
\(145\) 13.9970 + 8.08117i 0.0965310 + 0.0557322i
\(146\) 0 0
\(147\) 18.5617 + 165.699i 0.126270 + 1.12720i
\(148\) 0 0
\(149\) −73.8369 42.6298i −0.495550 0.286106i 0.231324 0.972877i \(-0.425694\pi\)
−0.726874 + 0.686771i \(0.759028\pi\)
\(150\) 0 0
\(151\) 65.9012 + 114.144i 0.436432 + 0.755922i 0.997411 0.0719076i \(-0.0229087\pi\)
−0.560979 + 0.827830i \(0.689575\pi\)
\(152\) 0 0
\(153\) 40.5751i 0.265197i
\(154\) 0 0
\(155\) 0.0723686i 0.000466894i
\(156\) 0 0
\(157\) −122.552 212.267i −0.780589 1.35202i −0.931599 0.363487i \(-0.881586\pi\)
0.151010 0.988532i \(1.54825\pi\)
\(158\) 0 0
\(159\) 135.426 + 78.1883i 0.851737 + 0.491750i
\(160\) 0 0
\(161\) 216.097 + 193.241i 1.34222 + 1.20026i
\(162\) 0 0
\(163\) −208.089 120.140i −1.27662 0.737057i −0.300395 0.953815i \(-0.597118\pi\)
−0.976225 + 0.216758i \(0.930452\pi\)
\(164\) 0 0
\(165\) −227.550 + 131.376i −1.37909 + 0.796219i
\(166\) 0 0
\(167\) 73.1965i 0.438302i 0.975691 + 0.219151i \(0.0703288\pi\)
−0.975691 + 0.219151i \(0.929671\pi\)
\(168\) 0 0
\(169\) −158.398 −0.937266
\(170\) 0 0
\(171\) 2.00762 + 3.47730i 0.0117405 + 0.0203351i
\(172\) 0 0
\(173\) 18.5246 32.0855i 0.107078 0.185465i −0.807507 0.589858i \(-0.799184\pi\)
0.914585 + 0.404393i \(0.132517\pi\)
\(174\) 0 0
\(175\) 42.3078 13.9067i 0.241759 0.0794668i
\(176\) 0 0
\(177\) −116.888 + 202.455i −0.660382 + 1.14382i
\(178\) 0 0
\(179\) −205.982 + 118.924i −1.15074 + 0.664379i −0.949067 0.315074i \(-0.897971\pi\)
−0.201672 + 0.979453i \(0.564637\pi\)
\(180\) 0 0
\(181\) 292.553 1.61631 0.808157 0.588966i \(-0.200465\pi\)
0.808157 + 0.588966i \(0.200465\pi\)
\(182\) 0 0
\(183\) −326.927 −1.78649
\(184\) 0 0
\(185\) −5.04132 + 2.91061i −0.0272504 + 0.0157330i
\(186\) 0 0
\(187\) 140.713 243.723i 0.752478 1.30333i
\(188\) 0 0
\(189\) −31.2884 + 149.715i −0.165547 + 0.792143i
\(190\) 0 0
\(191\) 70.6135 122.306i 0.369704 0.640346i −0.619815 0.784748i \(-0.712792\pi\)
0.989519 + 0.144402i \(0.0461257\pi\)
\(192\) 0 0
\(193\) 32.9799 + 57.1229i 0.170880 + 0.295973i 0.938728 0.344659i \(-0.112006\pi\)
−0.767848 + 0.640633i \(0.778672\pi\)
\(194\) 0 0
\(195\) −47.8325 −0.245295
\(196\) 0 0
\(197\) 199.421i 1.01229i 0.862448 + 0.506145i \(0.168930\pi\)
−0.862448 + 0.506145i \(0.831070\pi\)
\(198\) 0 0
\(199\) −58.6230 + 33.8460i −0.294588 + 0.170080i −0.640009 0.768367i \(-0.721069\pi\)
0.345421 + 0.938448i \(0.387736\pi\)
\(200\) 0 0
\(201\) −41.1079 23.7337i −0.204517 0.118078i
\(202\) 0 0
\(203\) −25.6520 5.36092i −0.126365 0.0264085i
\(204\) 0 0
\(205\) 262.842 + 151.752i 1.28216 + 0.740254i
\(206\) 0 0
\(207\) −53.3982 92.4884i −0.257962 0.446804i
\(208\) 0 0
\(209\) 27.8495i 0.133251i
\(210\) 0 0
\(211\) 62.1464i 0.294533i −0.989097 0.147266i \(-0.952953\pi\)
0.989097 0.147266i \(-0.0470475\pi\)
\(212\) 0 0
\(213\) −128.811 223.106i −0.604744 1.04745i
\(214\) 0 0
\(215\) 48.7463 + 28.1437i 0.226727 + 0.130901i
\(216\) 0 0
\(217\) −0.0366416 0.111473i −0.000168855 0.000513702i
\(218\) 0 0
\(219\) 156.623 + 90.4261i 0.715172 + 0.412905i
\(220\) 0 0
\(221\) 44.3683 25.6161i 0.200762 0.115910i
\(222\) 0 0
\(223\) 115.525i 0.518050i 0.965871 + 0.259025i \(0.0834012\pi\)
−0.965871 + 0.259025i \(0.916599\pi\)
\(224\) 0 0
\(225\) −16.4063 −0.0729171
\(226\) 0 0
\(227\) 28.2532 + 48.9360i 0.124463 + 0.215577i 0.921523 0.388324i \(-0.126946\pi\)
−0.797060 + 0.603901i \(0.793612\pi\)
\(228\) 0 0
\(229\) −59.1696 + 102.485i −0.258383 + 0.447532i −0.965809 0.259255i \(-0.916523\pi\)
0.707426 + 0.706787i \(0.249856\pi\)
\(230\) 0 0
\(231\) 283.990 317.579i 1.22939 1.37480i
\(232\) 0 0
\(233\) 12.3403 21.3740i 0.0529625 0.0917337i −0.838329 0.545165i \(-0.816467\pi\)
0.891291 + 0.453431i \(0.149800\pi\)
\(234\) 0 0
\(235\) 133.745 77.2175i 0.569126 0.328585i
\(236\) 0 0
\(237\) 79.4503 0.335233
\(238\) 0 0
\(239\) 251.189 1.05100 0.525499 0.850794i \(-0.323879\pi\)
0.525499 + 0.850794i \(0.323879\pi\)
\(240\) 0 0
\(241\) 97.3782 56.2213i 0.404059 0.233283i −0.284175 0.958772i \(-0.591720\pi\)
0.688234 + 0.725489i \(0.258386\pi\)
\(242\) 0 0
\(243\) 67.6598 117.190i 0.278436 0.482265i
\(244\) 0 0
\(245\) 170.286 125.508i 0.695046 0.512276i
\(246\) 0 0
\(247\) −2.53492 + 4.39061i −0.0102628 + 0.0177758i
\(248\) 0 0
\(249\) −174.370 302.017i −0.700280 1.21292i
\(250\) 0 0
\(251\) 121.248 0.483059 0.241529 0.970394i \(-0.422351\pi\)
0.241529 + 0.970394i \(0.422351\pi\)
\(252\) 0 0
\(253\) 740.735i 2.92781i
\(254\) 0 0
\(255\) −200.174 + 115.571i −0.784998 + 0.453219i
\(256\) 0 0
\(257\) −90.7377 52.3874i −0.353065 0.203842i 0.312969 0.949763i \(-0.398676\pi\)
−0.666034 + 0.745921i \(0.732010\pi\)
\(258\) 0 0
\(259\) 6.29172 7.03588i 0.0242924 0.0271656i
\(260\) 0 0
\(261\) 8.36079 + 4.82710i 0.0320337 + 0.0184946i
\(262\) 0 0
\(263\) −52.3392 90.6542i −0.199008 0.344693i 0.749199 0.662345i \(-0.230439\pi\)
−0.948207 + 0.317653i \(0.897105\pi\)
\(264\) 0 0
\(265\) 198.399i 0.748675i
\(266\) 0 0
\(267\) 301.361i 1.12869i
\(268\) 0 0
\(269\) 152.466 + 264.079i 0.566789 + 0.981707i 0.996881 + 0.0789222i \(0.0251479\pi\)
−0.430092 + 0.902785i \(0.641519\pi\)
\(270\) 0 0
\(271\) −88.8942 51.3231i −0.328023 0.189384i 0.326940 0.945045i \(-0.393982\pi\)
−0.654963 + 0.755661i \(0.727316\pi\)
\(272\) 0 0
\(273\) 73.6790 24.2185i 0.269886 0.0887125i
\(274\) 0 0
\(275\) −98.5482 56.8968i −0.358357 0.206898i
\(276\) 0 0
\(277\) −14.4235 + 8.32739i −0.0520703 + 0.0300628i −0.525809 0.850603i \(-0.676237\pi\)
0.473739 + 0.880665i \(0.342904\pi\)
\(278\) 0 0
\(279\) 0.0432277i 0.000154938i
\(280\) 0 0
\(281\) 75.8291 0.269855 0.134927 0.990856i \(-0.456920\pi\)
0.134927 + 0.990856i \(0.456920\pi\)
\(282\) 0 0
\(283\) 43.6656 + 75.6311i 0.154296 + 0.267248i 0.932802 0.360389i \(-0.117356\pi\)
−0.778507 + 0.627636i \(0.784023\pi\)
\(284\) 0 0
\(285\) 11.4367 19.8089i 0.0401287 0.0695050i
\(286\) 0 0
\(287\) −481.706 100.670i −1.67842 0.350767i
\(288\) 0 0
\(289\) −20.7152 + 35.8798i −0.0716789 + 0.124151i
\(290\) 0 0
\(291\) 415.124 239.672i 1.42654 0.823614i
\(292\) 0 0
\(293\) −27.5057 −0.0938760 −0.0469380 0.998898i \(-0.514946\pi\)
−0.0469380 + 0.998898i \(0.514946\pi\)
\(294\) 0 0
\(295\) 296.597 1.00541
\(296\) 0 0
\(297\) 338.452 195.406i 1.13957 0.657931i
\(298\) 0 0
\(299\) 67.4232 116.780i 0.225496 0.390570i
\(300\) 0 0
\(301\) −89.3363 18.6701i −0.296798 0.0620269i
\(302\) 0 0
\(303\) −60.2248 + 104.312i −0.198762 + 0.344266i
\(304\) 0 0
\(305\) 207.390 + 359.211i 0.679968 + 1.17774i
\(306\) 0 0
\(307\) 247.996 0.807805 0.403902 0.914802i \(-0.367654\pi\)
0.403902 + 0.914802i \(0.367654\pi\)
\(308\) 0 0
\(309\) 342.486i 1.10837i
\(310\) 0 0
\(311\) −378.484 + 218.518i −1.21699 + 0.702630i −0.964273 0.264910i \(-0.914658\pi\)
−0.252717 + 0.967540i \(0.581324\pi\)
\(312\) 0 0
\(313\) −71.7330 41.4151i −0.229179 0.132317i 0.381014 0.924569i \(-0.375575\pi\)
−0.610193 + 0.792253i \(0.708908\pi\)
\(314\) 0 0
\(315\) −74.0335 + 24.3350i −0.235027 + 0.0772540i
\(316\) 0 0
\(317\) 211.775 + 122.268i 0.668059 + 0.385704i 0.795341 0.606162i \(-0.207292\pi\)
−0.127282 + 0.991867i \(0.540625\pi\)
\(318\) 0 0
\(319\) 33.4806 + 57.9900i 0.104955 + 0.181787i
\(320\) 0 0
\(321\) 363.925i 1.13372i
\(322\) 0 0
\(323\) 24.4991i 0.0758485i
\(324\) 0 0
\(325\) −10.3577 17.9401i −0.0318699 0.0552004i
\(326\) 0 0
\(327\) 155.097 + 89.5456i 0.474304 + 0.273840i
\(328\) 0 0
\(329\) −166.917 + 186.660i −0.507348 + 0.567355i
\(330\) 0 0
\(331\) −66.2919 38.2736i −0.200278 0.115630i 0.396507 0.918032i \(-0.370222\pi\)
−0.596785 + 0.802401i \(0.703555\pi\)
\(332\) 0 0
\(333\) −3.01132 + 1.73858i −0.00904299 + 0.00522097i
\(334\) 0 0
\(335\) 60.2230i 0.179770i
\(336\) 0 0
\(337\) −38.2520 −0.113507 −0.0567537 0.998388i \(-0.518075\pi\)
−0.0567537 + 0.998388i \(0.518075\pi\)
\(338\) 0 0
\(339\) −77.3015 133.890i −0.228028 0.394956i
\(340\) 0 0
\(341\) −0.149913 + 0.259656i −0.000439627 + 0.000761456i
\(342\) 0 0
\(343\) −198.754 + 279.546i −0.579459 + 0.815002i
\(344\) 0 0
\(345\) −304.190 + 526.873i −0.881711 + 1.52717i
\(346\) 0 0
\(347\) −208.395 + 120.317i −0.600561 + 0.346734i −0.769262 0.638933i \(-0.779376\pi\)
0.168701 + 0.985667i \(0.446043\pi\)
\(348\) 0 0
\(349\) −430.367 −1.23314 −0.616572 0.787298i \(-0.711479\pi\)
−0.616572 + 0.787298i \(0.711479\pi\)
\(350\) 0 0
\(351\) 71.1449 0.202692
\(352\) 0 0
\(353\) −265.950 + 153.546i −0.753399 + 0.434975i −0.826921 0.562318i \(-0.809910\pi\)
0.0735214 + 0.997294i \(0.476576\pi\)
\(354\) 0 0
\(355\) −163.425 + 283.061i −0.460353 + 0.797354i
\(356\) 0 0
\(357\) 249.824 279.372i 0.699787 0.782555i
\(358\) 0 0
\(359\) 230.880 399.896i 0.643120 1.11392i −0.341613 0.939841i \(-0.610973\pi\)
0.984732 0.174075i \(-0.0556935\pi\)
\(360\) 0 0
\(361\) 179.288 + 310.536i 0.496642 + 0.860209i
\(362\) 0 0
\(363\) −676.858 −1.86462
\(364\) 0 0
\(365\) 229.452i 0.628635i
\(366\) 0 0
\(367\) 542.949 313.471i 1.47942 0.854146i 0.479695 0.877435i \(-0.340747\pi\)
0.999729 + 0.0232895i \(0.00741394\pi\)
\(368\) 0 0
\(369\) 157.003 + 90.6457i 0.425482 + 0.245652i
\(370\) 0 0
\(371\) 100.453 + 305.605i 0.270763 + 0.823732i
\(372\) 0 0
\(373\) −357.317 206.297i −0.957953 0.553075i −0.0624108 0.998051i \(-0.519879\pi\)
−0.895543 + 0.444976i \(0.853212\pi\)
\(374\) 0 0
\(375\) 230.359 + 398.993i 0.614290 + 1.06398i
\(376\) 0 0
\(377\) 12.1899i 0.0323339i
\(378\) 0 0
\(379\) 327.118i 0.863107i −0.902087 0.431554i \(-0.857966\pi\)
0.902087 0.431554i \(-0.142034\pi\)
\(380\) 0 0
\(381\) 213.854 + 370.407i 0.561298 + 0.972196i
\(382\) 0 0
\(383\) 215.523 + 124.432i 0.562724 + 0.324889i 0.754238 0.656601i \(-0.228006\pi\)
−0.191514 + 0.981490i \(0.561340\pi\)
\(384\) 0 0
\(385\) −529.091 110.573i −1.37426 0.287203i
\(386\) 0 0
\(387\) 29.1175 + 16.8110i 0.0752390 + 0.0434392i
\(388\) 0 0
\(389\) 326.728 188.637i 0.839918 0.484927i −0.0173181 0.999850i \(-0.505513\pi\)
0.857236 + 0.514923i \(0.172179\pi\)
\(390\) 0 0
\(391\) 651.620i 1.66655i
\(392\) 0 0
\(393\) 385.535 0.981005
\(394\) 0 0
\(395\) −50.4003 87.2958i −0.127596 0.221002i
\(396\) 0 0
\(397\) −335.874 + 581.752i −0.846031 + 1.46537i 0.0386913 + 0.999251i \(0.487681\pi\)
−0.884723 + 0.466118i \(0.845652\pi\)
\(398\) 0 0
\(399\) −7.58692 + 36.3034i −0.0190148 + 0.0909859i
\(400\) 0 0
\(401\) 235.200 407.378i 0.586534 1.01591i −0.408149 0.912915i \(-0.633826\pi\)
0.994682 0.102991i \(-0.0328411\pi\)
\(402\) 0 0
\(403\) −0.0472689 + 0.0272907i −0.000117293 + 6.77189e-5i
\(404\) 0 0
\(405\) −421.177 −1.03994
\(406\) 0 0
\(407\) −24.1175 −0.0592567
\(408\) 0 0
\(409\) −57.7400 + 33.3362i −0.141174 + 0.0815067i −0.568923 0.822391i \(-0.692640\pi\)
0.427750 + 0.903897i \(0.359307\pi\)
\(410\) 0 0
\(411\) −133.279 + 230.846i −0.324279 + 0.561669i
\(412\) 0 0
\(413\) −456.864 + 150.172i −1.10621 + 0.363614i
\(414\) 0 0
\(415\) −221.227 + 383.177i −0.533077 + 0.923317i
\(416\) 0 0
\(417\) −253.571 439.197i −0.608083 1.05323i
\(418\) 0 0
\(419\) −437.380 −1.04387 −0.521933 0.852986i \(-0.674789\pi\)
−0.521933 + 0.852986i \(0.674789\pi\)
\(420\) 0 0
\(421\) 703.800i 1.67173i 0.548933 + 0.835867i \(0.315034\pi\)
−0.548933 + 0.835867i \(0.684966\pi\)
\(422\) 0 0
\(423\) 79.8893 46.1241i 0.188864 0.109040i
\(424\) 0 0
\(425\) −86.6923 50.0518i −0.203982 0.117769i
\(426\) 0 0
\(427\) −501.330 448.306i −1.17407 1.04990i
\(428\) 0 0
\(429\) −171.622 99.0858i −0.400051 0.230969i
\(430\) 0 0
\(431\) −274.869 476.087i −0.637747 1.10461i −0.985926 0.167183i \(-0.946533\pi\)
0.348178 0.937428i \(-0.386800\pi\)
\(432\) 0 0
\(433\) 355.012i 0.819890i 0.912110 + 0.409945i \(0.134452\pi\)
−0.912110 + 0.409945i \(0.865548\pi\)
\(434\) 0 0
\(435\) 54.9965i 0.126429i
\(436\) 0 0
\(437\) 32.2416 + 55.8441i 0.0737794 + 0.127790i
\(438\) 0 0
\(439\) −477.032 275.415i −1.08663 0.627369i −0.153956 0.988078i \(-0.549201\pi\)
−0.932678 + 0.360709i \(0.882535\pi\)
\(440\) 0 0
\(441\) 101.717 74.9692i 0.230650 0.169998i
\(442\) 0 0
\(443\) −234.027 135.116i −0.528278 0.305001i 0.212037 0.977262i \(-0.431990\pi\)
−0.740315 + 0.672260i \(0.765324\pi\)
\(444\) 0 0
\(445\) 331.120 191.172i 0.744089 0.429600i
\(446\) 0 0
\(447\) 290.117i 0.649032i
\(448\) 0 0
\(449\) 455.397 1.01425 0.507124 0.861873i \(-0.330709\pi\)
0.507124 + 0.861873i \(0.330709\pi\)
\(450\) 0 0
\(451\) 628.714 + 1088.96i 1.39404 + 2.41456i
\(452\) 0 0
\(453\) 224.246 388.405i 0.495024 0.857406i
\(454\) 0 0
\(455\) −73.3492 65.5914i −0.161207 0.144157i
\(456\) 0 0
\(457\) 84.3172 146.042i 0.184501 0.319566i −0.758907 0.651199i \(-0.774266\pi\)
0.943408 + 0.331633i \(0.107600\pi\)
\(458\) 0 0
\(459\) 297.735 171.897i 0.648659 0.374504i
\(460\) 0 0
\(461\) −265.062 −0.574971 −0.287485 0.957785i \(-0.592819\pi\)
−0.287485 + 0.957785i \(0.592819\pi\)
\(462\) 0 0
\(463\) −97.4735 −0.210526 −0.105263 0.994444i \(-0.533568\pi\)
−0.105263 + 0.994444i \(0.533568\pi\)
\(464\) 0 0
\(465\) 0.213261 0.123126i 0.000458626 0.000264788i
\(466\) 0 0
\(467\) −37.0997 + 64.2586i −0.0794427 + 0.137599i −0.903010 0.429620i \(-0.858647\pi\)
0.823567 + 0.567219i \(0.191981\pi\)
\(468\) 0 0
\(469\) −30.4921 92.7648i −0.0650150 0.197793i
\(470\) 0 0
\(471\) −417.016 + 722.293i −0.885385 + 1.53353i
\(472\) 0 0
\(473\) 116.600 + 201.958i 0.246512 + 0.426972i
\(474\) 0 0
\(475\) 9.90608 0.0208549
\(476\) 0 0
\(477\) 118.509i 0.248447i
\(478\) 0 0
\(479\) 475.220 274.368i 0.992108 0.572794i 0.0862043 0.996277i \(-0.472526\pi\)
0.905904 + 0.423484i \(0.139193\pi\)
\(480\) 0 0
\(481\) −3.80224 2.19522i −0.00790486 0.00456387i
\(482\) 0 0
\(483\) 201.795 965.588i 0.417795 1.99915i
\(484\) 0 0
\(485\) −526.678 304.078i −1.08593 0.626964i
\(486\) 0 0
\(487\) 283.938 + 491.795i 0.583034 + 1.00985i 0.995117 + 0.0986990i \(0.0314681\pi\)
−0.412083 + 0.911146i \(0.635199\pi\)
\(488\) 0 0
\(489\) 817.617i 1.67202i
\(490\) 0 0
\(491\) 78.8005i 0.160490i 0.996775 + 0.0802449i \(0.0255702\pi\)
−0.996775 + 0.0802449i \(0.974430\pi\)
\(492\) 0 0
\(493\) 29.4527 + 51.0135i 0.0597417 + 0.103476i
\(494\) 0 0
\(495\) 172.447 + 99.5626i 0.348379 + 0.201136i
\(496\) 0 0
\(497\) 108.414 518.759i 0.218136 1.04378i
\(498\) 0 0
\(499\) 290.932 + 167.970i 0.583030 + 0.336612i 0.762337 0.647181i \(-0.224052\pi\)
−0.179307 + 0.983793i \(0.557385\pi\)
\(500\) 0 0
\(501\) 215.701 124.535i 0.430541 0.248573i
\(502\) 0 0
\(503\) 274.052i 0.544836i 0.962179 + 0.272418i \(0.0878233\pi\)
−0.962179 + 0.272418i \(0.912177\pi\)
\(504\) 0 0
\(505\) 152.817 0.302609
\(506\) 0 0
\(507\) 269.495 + 466.779i 0.531548 + 0.920669i
\(508\) 0 0
\(509\) 168.009 291.000i 0.330076 0.571709i −0.652450 0.757831i \(-0.726259\pi\)
0.982526 + 0.186123i \(0.0595923\pi\)
\(510\) 0 0
\(511\) 116.176 + 353.437i 0.227350 + 0.691658i
\(512\) 0 0
\(513\) −17.0106 + 29.4633i −0.0331591 + 0.0574333i
\(514\) 0 0
\(515\) 376.306 217.260i 0.730691 0.421865i
\(516\) 0 0
\(517\) 639.829 1.23758
\(518\) 0 0
\(519\) −126.069 −0.242908
\(520\) 0 0
\(521\) −547.572 + 316.141i −1.05100 + 0.606796i −0.922930 0.384969i \(-0.874212\pi\)
−0.128072 + 0.991765i \(0.540879\pi\)
\(522\) 0 0
\(523\) −389.623 + 674.847i −0.744977 + 1.29034i 0.205229 + 0.978714i \(0.434206\pi\)
−0.950206 + 0.311624i \(0.899127\pi\)
\(524\) 0 0
\(525\) −112.963 101.015i −0.215167 0.192410i
\(526\) 0 0
\(527\) −0.131877 + 0.228418i −0.000250242 + 0.000433431i
\(528\) 0 0
\(529\) −593.054 1027.20i −1.12109 1.94178i
\(530\) 0 0
\(531\) 177.165 0.333644
\(532\) 0 0
\(533\) 228.907i 0.429470i
\(534\) 0 0
\(535\) −399.862 + 230.861i −0.747406 + 0.431515i
\(536\) 0 0
\(537\) 700.908 + 404.669i 1.30523 + 0.753574i
\(538\) 0 0
\(539\) 870.974 97.5673i 1.61591 0.181015i
\(540\) 0 0
\(541\) 583.617 + 336.952i 1.07878 + 0.622831i 0.930566 0.366125i \(-0.119316\pi\)
0.148209 + 0.988956i \(0.452649\pi\)
\(542\) 0 0
\(543\) −497.743 862.117i −0.916655 1.58769i
\(544\) 0 0
\(545\) 227.217i 0.416913i
\(546\) 0 0
\(547\) 52.5329i 0.0960382i −0.998846 0.0480191i \(-0.984709\pi\)
0.998846 0.0480191i \(-0.0152908\pi\)
\(548\) 0 0
\(549\) 123.880 + 214.566i 0.225646 + 0.390831i
\(550\) 0 0
\(551\) −5.04821 2.91458i −0.00916190 0.00528963i
\(552\) 0 0
\(553\) 121.834 + 108.948i 0.220314 + 0.197012i
\(554\) 0 0
\(555\) 17.1544 + 9.90409i 0.0309088 + 0.0178452i
\(556\) 0 0
\(557\) 678.123 391.515i 1.21746 0.702899i 0.253083 0.967445i \(-0.418555\pi\)
0.964373 + 0.264546i \(0.0852220\pi\)
\(558\) 0 0
\(559\) 42.4528i 0.0759441i
\(560\) 0 0
\(561\) −957.628 −1.70700
\(562\) 0 0
\(563\) −446.202 772.844i −0.792543 1.37272i −0.924388 0.381454i \(-0.875423\pi\)
0.131845 0.991270i \(1.54209\pi\)
\(564\) 0 0
\(565\) −98.0743 + 169.870i −0.173583 + 0.300654i
\(566\) 0 0
\(567\) 648.763 213.250i 1.14420 0.376102i
\(568\) 0 0
\(569\) 148.722 257.593i 0.261373 0.452712i −0.705234 0.708975i \(-0.749158\pi\)
0.966607 + 0.256263i \(0.0824912\pi\)
\(570\) 0 0
\(571\) 218.885 126.373i 0.383335 0.221319i −0.295933 0.955209i \(-0.595631\pi\)
0.679268 + 0.733890i \(0.262297\pi\)
\(572\) 0 0
\(573\) −480.561 −0.838676
\(574\) 0 0
\(575\) −263.479 −0.458225
\(576\) 0 0
\(577\) 764.454 441.358i 1.32488 0.764918i 0.340375 0.940290i \(-0.389446\pi\)
0.984502 + 0.175371i \(0.0561126\pi\)
\(578\) 0 0
\(579\) 112.223 194.375i 0.193821 0.335709i
\(580\) 0 0
\(581\) 146.759 702.239i 0.252597 1.20867i
\(582\) 0 0
\(583\) 410.987 711.850i 0.704951 1.22101i
\(584\) 0 0
\(585\) 18.1248 + 31.3930i 0.0309825 + 0.0536633i
\(586\) 0 0
\(587\) 66.7814 0.113767 0.0568836 0.998381i \(-0.481884\pi\)
0.0568836 + 0.998381i \(0.481884\pi\)
\(588\) 0 0
\(589\) 0.0261007i 4.43136e-5i
\(590\) 0 0
\(591\) 587.670 339.291i 0.994365 0.574097i
\(592\) 0 0
\(593\) −311.911 180.082i −0.525989 0.303680i 0.213393 0.976967i \(-0.431549\pi\)
−0.739381 + 0.673287i \(0.764882\pi\)
\(594\) 0 0
\(595\) −465.439 97.2704i −0.782250 0.163480i
\(596\) 0 0
\(597\) 199.480 + 115.170i 0.334137 + 0.192914i
\(598\) 0 0
\(599\) −99.0219 171.511i −0.165312 0.286329i 0.771454 0.636285i \(-0.219530\pi\)
−0.936766 + 0.349956i \(0.886196\pi\)
\(600\) 0 0
\(601\) 373.907i 0.622141i 0.950387 + 0.311071i \(0.100688\pi\)
−0.950387 + 0.311071i \(0.899312\pi\)
\(602\) 0 0
\(603\) 35.9728i 0.0596565i
\(604\) 0 0
\(605\) 429.373 + 743.696i 0.709708 + 1.22925i
\(606\) 0 0
\(607\) −200.164 115.565i −0.329760 0.190387i 0.325975 0.945379i \(-0.394308\pi\)
−0.655735 + 0.754992i \(0.727641\pi\)
\(608\) 0 0
\(609\) 27.8458 + 84.7142i 0.0457238 + 0.139104i
\(610\) 0 0
\(611\) 100.872 + 58.2386i 0.165094 + 0.0953168i
\(612\) 0 0
\(613\) −444.718 + 256.758i −0.725479 + 0.418855i −0.816766 0.576969i \(-0.804235\pi\)
0.0912873 + 0.995825i \(0.470902\pi\)
\(614\) 0 0
\(615\) 1032.75i 1.67927i
\(616\) 0 0
\(617\) −1119.01 −1.81363 −0.906815 0.421529i \(-0.861493\pi\)
−0.906815 + 0.421529i \(0.861493\pi\)
\(618\) 0 0
\(619\) −64.1019 111.028i −0.103557 0.179366i 0.809591 0.586995i \(-0.199689\pi\)
−0.913148 + 0.407629i \(0.866356\pi\)
\(620\) 0 0
\(621\) 452.445 783.658i 0.728575 1.26193i
\(622\) 0 0
\(623\) −413.248 + 462.125i −0.663319 + 0.741774i
\(624\) 0 0
\(625\) 212.735 368.469i 0.340377 0.589550i
\(626\) 0 0
\(627\) 82.0690 47.3826i 0.130892 0.0755703i
\(628\) 0 0
\(629\) −21.2160 −0.0337297
\(630\) 0 0
\(631\) −313.995 −0.497615 −0.248808 0.968553i \(-0.580039\pi\)
−0.248808 + 0.968553i \(0.580039\pi\)
\(632\) 0 0
\(633\) −183.138 + 105.735i −0.289317 + 0.167037i
\(634\) 0 0
\(635\) 271.322 469.944i 0.427279 0.740070i
\(636\) 0 0
\(637\) 146.194 + 63.8959i 0.229504 + 0.100307i
\(638\) 0 0
\(639\) −97.6183 + 169.080i −0.152767 + 0.264601i
\(640\) 0 0
\(641\) 115.594 + 200.215i 0.180334 + 0.312348i 0.941994 0.335629i \(-0.108949\pi\)
−0.761660 + 0.647977i \(0.775615\pi\)
\(642\) 0 0
\(643\) −637.869 −0.992020 −0.496010 0.868317i \(-0.665202\pi\)
−0.496010 + 0.868317i \(0.665202\pi\)
\(644\) 0 0
\(645\) 191.532i 0.296949i
\(646\) 0 0
\(647\) 586.461 338.594i 0.906432 0.523329i 0.0271505 0.999631i \(-0.491357\pi\)
0.879281 + 0.476303i \(0.158023\pi\)
\(648\) 0 0
\(649\) 1064.18 + 614.405i 1.63972 + 0.946695i
\(650\) 0 0
\(651\) −0.266157 + 0.297636i −0.000408843 + 0.000457199i
\(652\) 0 0
\(653\) −916.022 528.865i −1.40279 0.809901i −0.408112 0.912932i \(-0.633813\pi\)
−0.994678 + 0.103031i \(0.967146\pi\)
\(654\) 0 0
\(655\) −244.569 423.606i −0.373388 0.646726i
\(656\) 0 0
\(657\) 137.058i 0.208612i
\(658\) 0 0
\(659\) 644.502i 0.978000i 0.872284 + 0.489000i \(0.162638\pi\)
−0.872284 + 0.489000i \(0.837362\pi\)
\(660\) 0 0
\(661\) 560.069 + 970.068i 0.847306 + 1.46758i 0.883604 + 0.468236i \(0.155110\pi\)
−0.0362979 + 0.999341i \(0.511557\pi\)
\(662\) 0 0
\(663\) −150.975 87.1652i −0.227714 0.131471i
\(664\) 0 0
\(665\) 44.7011 14.6934i 0.0672197 0.0220953i
\(666\) 0 0
\(667\) 134.271 + 77.5214i 0.201306 + 0.116224i
\(668\) 0 0
\(669\) 340.438 196.552i 0.508876 0.293800i
\(670\) 0 0
\(671\) 1718.45i 2.56103i
\(672\) 0 0
\(673\) −307.811 −0.457371 −0.228686 0.973500i \(-0.573443\pi\)
−0.228686 + 0.973500i \(0.573443\pi\)
\(674\) 0 0
\(675\) −69.5058 120.388i −0.102972 0.178352i
\(676\) 0 0
\(677\) −507.773 + 879.488i −0.750033 + 1.29910i 0.197773 + 0.980248i \(0.436629\pi\)
−0.947806 + 0.318848i \(0.896704\pi\)
\(678\) 0 0
\(679\) 965.231 + 201.720i 1.42155 + 0.297084i
\(680\) 0 0
\(681\) 96.1388 166.517i 0.141173 0.244519i
\(682\) 0 0
\(683\) 840.220 485.102i 1.23019 0.710251i 0.263121 0.964763i \(-0.415248\pi\)
0.967070 + 0.254512i \(0.0819147\pi\)
\(684\) 0 0
\(685\) 338.188 0.493706
\(686\) 0 0
\(687\) 402.680 0.586143
\(688\) 0 0
\(689\) 129.588 74.8177i 0.188081 0.108589i
\(690\) 0 0
\(691\) −274.581 + 475.588i −0.397367 + 0.688260i −0.993400 0.114700i \(-0.963409\pi\)
0.596033 + 0.802960i \(0.296743\pi\)
\(692\) 0 0
\(693\) −316.041 66.0483i −0.456047 0.0953078i
\(694\) 0 0
\(695\) −321.711 + 557.221i −0.462894 + 0.801756i
\(696\) 0 0
\(697\) 553.076 + 957.956i 0.793510 + 1.37440i
\(698\) 0 0
\(699\) −83.9818 −0.120146
\(700\) 0 0
\(701\) 452.665i 0.645742i 0.946443 + 0.322871i \(0.104648\pi\)
−0.946443 + 0.322871i \(0.895352\pi\)
\(702\) 0 0
\(703\) 1.81822 1.04975i 0.00258637 0.00149324i
\(704\) 0 0
\(705\) −455.100 262.752i −0.645533 0.372698i
\(706\) 0 0
\(707\) −235.393 + 77.3744i −0.332946 + 0.109440i
\(708\) 0 0
\(709\) −609.174 351.707i −0.859202 0.496060i 0.00454321 0.999990i \(-0.498554\pi\)
−0.863745 + 0.503929i \(0.831887\pi\)
\(710\) 0 0
\(711\) −30.1054 52.1442i −0.0423424 0.0733392i
\(712\) 0 0
\(713\) 0.694220i 0.000973661i
\(714\) 0 0
\(715\) 251.425i 0.351644i
\(716\) 0 0
\(717\) −427.367 740.221i −0.596049 1.03239i
\(718\) 0 0
\(719\) −54.1160 31.2439i −0.0752656 0.0434546i 0.461895 0.886935i \(-0.347170\pi\)
−0.537161 + 0.843480i \(0.680503\pi\)
\(720\) 0 0
\(721\) −469.642 + 525.189i −0.651376 + 0.728417i
\(722\) 0 0
\(723\) −331.354 191.307i −0.458305 0.264602i
\(724\) 0 0
\(725\) 20.6271 11.9090i 0.0284511 0.0164263i
\(726\) 0 0
\(727\) 889.995i 1.22420i 0.790779 + 0.612101i \(0.209676\pi\)
−0.790779 + 0.612101i \(0.790324\pi\)
\(728\) 0 0
\(729\) 417.569 0.572797
\(730\) 0 0
\(731\) 102.573 + 177.661i 0.140318 + 0.243038i
\(732\) 0 0
\(733\) −456.127 + 790.035i −0.622274 + 1.07781i 0.366787 + 0.930305i \(0.380458\pi\)
−0.989061 + 0.147505i \(0.952876\pi\)
\(734\) 0 0
\(735\) −659.577 288.276i −0.897383 0.392212i
\(736\) 0 0
\(737\) −124.753 + 216.079i −0.169271 + 0.293187i
\(738\) 0 0
\(739\) −1081.52 + 624.415i −1.46349 + 0.844946i −0.999171 0.0407224i \(-0.987034\pi\)
−0.464319 + 0.885668i \(0.653701\pi\)
\(740\) 0 0
\(741\) 17.2514 0.0232813
\(742\) 0 0
\(743\) 305.880 0.411682 0.205841 0.978585i \(-0.434007\pi\)
0.205841 + 0.978585i \(0.434007\pi\)
\(744\) 0 0
\(745\) 318.766 184.040i 0.427874 0.247033i
\(746\) 0 0
\(747\) −132.145 + 228.882i −0.176901 + 0.306401i
\(748\) 0 0
\(749\) 499.041 558.065i 0.666276 0.745080i
\(750\) 0 0
\(751\) 258.895 448.420i 0.344734 0.597097i −0.640571 0.767899i \(-0.721302\pi\)
0.985305 + 0.170802i \(0.0546358\pi\)
\(752\) 0 0
\(753\) −206.288 357.302i −0.273955 0.474504i
\(754\) 0 0
\(755\) −569.012 −0.753659
\(756\) 0 0
\(757\) 939.898i 1.24161i −0.783965 0.620804i \(-0.786806\pi\)
0.783965 0.620804i \(-0.213194\pi\)
\(758\) 0 0
\(759\) −2182.85 + 1260.27i −2.87596 + 1.66044i
\(760\) 0 0
\(761\) −976.757 563.931i −1.28352 0.741039i −0.306028 0.952022i \(-0.599000\pi\)
−0.977490 + 0.210983i \(0.932334\pi\)
\(762\) 0 0
\(763\) 115.044 + 349.995i 0.150779 + 0.458710i
\(764\) 0 0
\(765\) 151.701 + 87.5846i 0.198302 + 0.114490i
\(766\) 0 0
\(767\) 111.849 + 193.728i 0.145826 + 0.252579i
\(768\) 0 0
\(769\) 300.115i 0.390267i −0.980777 0.195133i \(-0.937486\pi\)
0.980777 0.195133i \(-0.0625139\pi\)
\(770\) 0 0
\(771\) 356.524i 0.462417i
\(772\) 0 0
\(773\) −375.120 649.727i −0.485278 0.840527i 0.514579 0.857443i \(-0.327948\pi\)
−0.999857 + 0.0169165i \(0.994615\pi\)
\(774\) 0 0
\(775\) 0.0923598 + 0.0533240i 0.000119174 + 6.88051e-5i
\(776\) 0 0
\(777\) −31.4385 6.57022i −0.0404613 0.00845588i
\(778\) 0 0
\(779\) −94.7977 54.7315i −0.121691 0.0702586i
\(780\) 0 0
\(781\) −1172.73 + 677.076i −1.50158 + 0.866935i
\(782\) 0 0
\(783\) 81.8005i 0.104471i
\(784\) 0 0
\(785\) 1058.16 1.34797
\(786\) 0 0
\(787\) 144.776 + 250.760i 0.183960 + 0.318627i 0.943225 0.332153i \(-0.107775\pi\)
−0.759266 +