Properties

Label 224.3.n.a.17.7
Level 224
Weight 3
Character 224.17
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 17.7
Character \(\chi\) \(=\) 224.17
Dual form 224.3.n.a.145.7

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.126628 + 0.219326i) q^{3} +(-1.78589 - 3.09325i) q^{5} +(-2.89466 - 6.37346i) q^{7} +(4.46793 + 7.73868i) q^{9} +O(q^{10})\) \(q+(-0.126628 + 0.219326i) q^{3} +(-1.78589 - 3.09325i) q^{5} +(-2.89466 - 6.37346i) q^{7} +(4.46793 + 7.73868i) q^{9} +(-6.82675 - 3.94142i) q^{11} -18.1529 q^{13} +0.904575 q^{15} +(-8.26180 - 4.76995i) q^{17} +(-12.4094 - 21.4938i) q^{19} +(1.76441 + 0.172184i) q^{21} +(-2.14949 - 3.72303i) q^{23} +(6.12120 - 10.6022i) q^{25} -4.54237 q^{27} -28.3630i q^{29} +(28.2372 + 16.3027i) q^{31} +(1.72891 - 0.998189i) q^{33} +(-14.5452 + 20.3362i) q^{35} +(-25.9006 + 14.9537i) q^{37} +(2.29867 - 3.98141i) q^{39} -45.2606i q^{41} +24.9109i q^{43} +(15.9585 - 27.6409i) q^{45} +(-44.0432 + 25.4284i) q^{47} +(-32.2419 + 36.8979i) q^{49} +(2.09235 - 1.20802i) q^{51} +(54.3930 + 31.4038i) q^{53} +28.1558i q^{55} +6.28554 q^{57} +(37.0048 - 64.0942i) q^{59} +(25.2994 + 43.8198i) q^{61} +(36.3890 - 50.8770i) q^{63} +(32.4191 + 56.1515i) q^{65} +(108.673 + 62.7422i) q^{67} +1.08875 q^{69} +5.33822 q^{71} +(-23.6569 - 13.6583i) q^{73} +(1.55023 + 2.68508i) q^{75} +(-5.35941 + 54.9191i) q^{77} +(-51.5380 - 89.2664i) q^{79} +(-39.6362 + 68.6519i) q^{81} -51.5695 q^{83} +34.0744i q^{85} +(6.22075 + 3.59155i) q^{87} +(133.222 - 76.9158i) q^{89} +(52.5464 + 115.697i) q^{91} +(-7.15123 + 4.12877i) q^{93} +(-44.3238 + 76.7711i) q^{95} +47.0436i q^{97} -70.4400i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28q + 4q^{7} - 32q^{9} + O(q^{10}) \) \( 28q + 4q^{7} - 32q^{9} - 28q^{15} - 6q^{17} - 30q^{23} - 32q^{25} + 6q^{31} - 6q^{33} + 20q^{39} + 294q^{47} - 20q^{49} + 124q^{57} - 432q^{63} - 52q^{65} + 136q^{71} + 234q^{73} + 162q^{79} - 18q^{81} - 48q^{87} - 150q^{89} - 290q^{95} + O(q^{100}) \)

Character values

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

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

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −0.126628 + 0.219326i −0.0422093 + 0.0731087i −0.886358 0.463000i \(-0.846773\pi\)
0.844149 + 0.536109i \(0.180106\pi\)
\(4\) 0 0
\(5\) −1.78589 3.09325i −0.357178 0.618650i 0.630310 0.776343i \(-0.282928\pi\)
−0.987488 + 0.157693i \(0.949594\pi\)
\(6\) 0 0
\(7\) −2.89466 6.37346i −0.413522 0.910494i
\(8\) 0 0
\(9\) 4.46793 + 7.73868i 0.496437 + 0.859854i
\(10\) 0 0
\(11\) −6.82675 3.94142i −0.620613 0.358311i 0.156494 0.987679i \(-0.449981\pi\)
−0.777108 + 0.629368i \(0.783314\pi\)
\(12\) 0 0
\(13\) −18.1529 −1.39638 −0.698189 0.715914i \(-0.746010\pi\)
−0.698189 + 0.715914i \(0.746010\pi\)
\(14\) 0 0
\(15\) 0.904575 0.0603050
\(16\) 0 0
\(17\) −8.26180 4.76995i −0.485988 0.280585i 0.236920 0.971529i \(-0.423862\pi\)
−0.722909 + 0.690944i \(0.757195\pi\)
\(18\) 0 0
\(19\) −12.4094 21.4938i −0.653129 1.13125i −0.982359 0.187003i \(-0.940123\pi\)
0.329231 0.944250i \(1.60679\pi\)
\(20\) 0 0
\(21\) 1.76441 + 0.172184i 0.0840196 + 0.00819925i
\(22\) 0 0
\(23\) −2.14949 3.72303i −0.0934563 0.161871i 0.815507 0.578747i \(-0.196458\pi\)
−0.908963 + 0.416876i \(0.863125\pi\)
\(24\) 0 0
\(25\) 6.12120 10.6022i 0.244848 0.424089i
\(26\) 0 0
\(27\) −4.54237 −0.168236
\(28\) 0 0
\(29\) 28.3630i 0.978035i −0.872274 0.489017i \(-0.837356\pi\)
0.872274 0.489017i \(-0.162644\pi\)
\(30\) 0 0
\(31\) 28.2372 + 16.3027i 0.910876 + 0.525895i 0.880713 0.473650i \(-0.157064\pi\)
0.0301634 + 0.999545i \(0.490397\pi\)
\(32\) 0 0
\(33\) 1.72891 0.998189i 0.0523914 0.0302482i
\(34\) 0 0
\(35\) −14.5452 + 20.3362i −0.415576 + 0.581034i
\(36\) 0 0
\(37\) −25.9006 + 14.9537i −0.700017 + 0.404155i −0.807354 0.590068i \(-0.799101\pi\)
0.107337 + 0.994223i \(0.465768\pi\)
\(38\) 0 0
\(39\) 2.29867 3.98141i 0.0589402 0.102087i
\(40\) 0 0
\(41\) 45.2606i 1.10392i −0.833872 0.551958i \(-0.813881\pi\)
0.833872 0.551958i \(-0.186119\pi\)
\(42\) 0 0
\(43\) 24.9109i 0.579323i 0.957129 + 0.289661i \(0.0935427\pi\)
−0.957129 + 0.289661i \(0.906457\pi\)
\(44\) 0 0
\(45\) 15.9585 27.6409i 0.354632 0.614242i
\(46\) 0 0
\(47\) −44.0432 + 25.4284i −0.937090 + 0.541029i −0.889047 0.457816i \(-0.848632\pi\)
−0.0480430 + 0.998845i \(0.515298\pi\)
\(48\) 0 0
\(49\) −32.2419 + 36.8979i −0.657998 + 0.753019i
\(50\) 0 0
\(51\) 2.09235 1.20802i 0.0410265 0.0236867i
\(52\) 0 0
\(53\) 54.3930 + 31.4038i 1.02628 + 0.592525i 0.915918 0.401366i \(-0.131465\pi\)
0.110365 + 0.993891i \(0.464798\pi\)
\(54\) 0 0
\(55\) 28.1558i 0.511924i
\(56\) 0 0
\(57\) 6.28554 0.110273
\(58\) 0 0
\(59\) 37.0048 64.0942i 0.627200 1.08634i −0.360912 0.932600i \(-0.617534\pi\)
0.988111 0.153741i \(-0.0491323\pi\)
\(60\) 0 0
\(61\) 25.2994 + 43.8198i 0.414743 + 0.718357i 0.995401 0.0957908i \(-0.0305380\pi\)
−0.580658 + 0.814148i \(0.697205\pi\)
\(62\) 0 0
\(63\) 36.3890 50.8770i 0.577604 0.807571i
\(64\) 0 0
\(65\) 32.4191 + 56.1515i 0.498755 + 0.863869i
\(66\) 0 0
\(67\) 108.673 + 62.7422i 1.62198 + 0.936451i 0.986389 + 0.164426i \(0.0525772\pi\)
0.635592 + 0.772025i \(0.280756\pi\)
\(68\) 0 0
\(69\) 1.08875 0.0157789
\(70\) 0 0
\(71\) 5.33822 0.0751863 0.0375931 0.999293i \(-0.488031\pi\)
0.0375931 + 0.999293i \(0.488031\pi\)
\(72\) 0 0
\(73\) −23.6569 13.6583i −0.324067 0.187100i 0.329137 0.944282i \(-0.393242\pi\)
−0.653204 + 0.757182i \(0.726576\pi\)
\(74\) 0 0
\(75\) 1.55023 + 2.68508i 0.0206697 + 0.0358010i
\(76\) 0 0
\(77\) −5.35941 + 54.9191i −0.0696027 + 0.713234i
\(78\) 0 0
\(79\) −51.5380 89.2664i −0.652380 1.12995i −0.982544 0.186031i \(-0.940437\pi\)
0.330164 0.943924i \(-0.392896\pi\)
\(80\) 0 0
\(81\) −39.6362 + 68.6519i −0.489336 + 0.847554i
\(82\) 0 0
\(83\) −51.5695 −0.621319 −0.310660 0.950521i \(-0.600550\pi\)
−0.310660 + 0.950521i \(0.600550\pi\)
\(84\) 0 0
\(85\) 34.0744i 0.400876i
\(86\) 0 0
\(87\) 6.22075 + 3.59155i 0.0715029 + 0.0412822i
\(88\) 0 0
\(89\) 133.222 76.9158i 1.49688 0.864222i 0.496883 0.867818i \(-0.334478\pi\)
0.999994 + 0.00359545i \(0.00114447\pi\)
\(90\) 0 0
\(91\) 52.5464 + 115.697i 0.577433 + 1.27139i
\(92\) 0 0
\(93\) −7.15123 + 4.12877i −0.0768950 + 0.0443953i
\(94\) 0 0
\(95\) −44.3238 + 76.7711i −0.466566 + 0.808117i
\(96\) 0 0
\(97\) 47.0436i 0.484986i 0.970153 + 0.242493i \(0.0779651\pi\)
−0.970153 + 0.242493i \(0.922035\pi\)
\(98\) 0 0
\(99\) 70.4400i 0.711516i
\(100\) 0 0
\(101\) 74.6727 129.337i 0.739333 1.28056i −0.213462 0.976951i \(-0.568474\pi\)
0.952796 0.303612i \(-0.0981926\pi\)
\(102\) 0 0
\(103\) 17.1847 9.92160i 0.166842 0.0963262i −0.414254 0.910161i \(-0.635957\pi\)
0.581096 + 0.813835i \(0.302624\pi\)
\(104\) 0 0
\(105\) −2.61843 5.76527i −0.0249375 0.0549073i
\(106\) 0 0
\(107\) 7.91877 4.57190i 0.0740072 0.0427281i −0.462540 0.886599i \(-0.653062\pi\)
0.536547 + 0.843870i \(0.319728\pi\)
\(108\) 0 0
\(109\) 103.229 + 59.5992i 0.947053 + 0.546781i 0.892164 0.451711i \(-0.149186\pi\)
0.0548888 + 0.998492i \(0.482520\pi\)
\(110\) 0 0
\(111\) 7.57425i 0.0682365i
\(112\) 0 0
\(113\) −124.011 −1.09744 −0.548720 0.836006i \(-0.684885\pi\)
−0.548720 + 0.836006i \(0.684885\pi\)
\(114\) 0 0
\(115\) −7.67752 + 13.2979i −0.0667611 + 0.115634i
\(116\) 0 0
\(117\) −81.1059 140.480i −0.693213 1.20068i
\(118\) 0 0
\(119\) −6.48601 + 66.4636i −0.0545043 + 0.558518i
\(120\) 0 0
\(121\) −29.4303 50.9749i −0.243226 0.421280i
\(122\) 0 0
\(123\) 9.92683 + 5.73126i 0.0807059 + 0.0465956i
\(124\) 0 0
\(125\) −133.022 −1.06417
\(126\) 0 0
\(127\) 57.6144 0.453656 0.226828 0.973935i \(-0.427164\pi\)
0.226828 + 0.973935i \(0.427164\pi\)
\(128\) 0 0
\(129\) −5.46361 3.15441i −0.0423535 0.0244528i
\(130\) 0 0
\(131\) −62.1497 107.646i −0.474425 0.821728i 0.525146 0.851012i \(-0.324011\pi\)
−0.999571 + 0.0292837i \(0.990677\pi\)
\(132\) 0 0
\(133\) −101.069 + 141.308i −0.759915 + 1.06247i
\(134\) 0 0
\(135\) 8.11216 + 14.0507i 0.0600901 + 0.104079i
\(136\) 0 0
\(137\) 84.7404 146.775i 0.618543 1.07135i −0.371208 0.928550i \(-0.621056\pi\)
0.989752 0.142799i \(-0.0456102\pi\)
\(138\) 0 0
\(139\) −266.497 −1.91725 −0.958624 0.284677i \(-0.908114\pi\)
−0.958624 + 0.284677i \(0.908114\pi\)
\(140\) 0 0
\(141\) 12.8798i 0.0913459i
\(142\) 0 0
\(143\) 123.925 + 71.5483i 0.866610 + 0.500338i
\(144\) 0 0
\(145\) −87.7339 + 50.6532i −0.605061 + 0.349332i
\(146\) 0 0
\(147\) −4.00996 11.7438i −0.0272786 0.0798899i
\(148\) 0 0
\(149\) −26.6902 + 15.4096i −0.179129 + 0.103420i −0.586883 0.809672i \(-0.699645\pi\)
0.407754 + 0.913092i \(0.366312\pi\)
\(150\) 0 0
\(151\) 11.7448 20.3425i 0.0777800 0.134719i −0.824512 0.565845i \(-0.808550\pi\)
0.902292 + 0.431126i \(0.141884\pi\)
\(152\) 0 0
\(153\) 85.2473i 0.557172i
\(154\) 0 0
\(155\) 116.460i 0.751352i
\(156\) 0 0
\(157\) 63.8147 110.530i 0.406463 0.704015i −0.588028 0.808841i \(-0.700095\pi\)
0.994491 + 0.104826i \(0.0334287\pi\)
\(158\) 0 0
\(159\) −13.7754 + 7.95320i −0.0866374 + 0.0500202i
\(160\) 0 0
\(161\) −17.5065 + 24.4766i −0.108736 + 0.152029i
\(162\) 0 0
\(163\) −138.291 + 79.8421i −0.848409 + 0.489829i −0.860114 0.510103i \(-0.829607\pi\)
0.0117050 + 0.999931i \(0.496274\pi\)
\(164\) 0 0
\(165\) −6.17530 3.56531i −0.0374261 0.0216080i
\(166\) 0 0
\(167\) 142.792i 0.855042i −0.904005 0.427521i \(-0.859387\pi\)
0.904005 0.427521i \(-0.140613\pi\)
\(168\) 0 0
\(169\) 160.528 0.949869
\(170\) 0 0
\(171\) 110.889 192.066i 0.648474 1.12319i
\(172\) 0 0
\(173\) −97.8898 169.550i −0.565837 0.980059i −0.996971 0.0777710i \(-0.975220\pi\)
0.431134 0.902288i \(1.64189\pi\)
\(174\) 0 0
\(175\) −85.2916 8.32338i −0.487380 0.0475622i
\(176\) 0 0
\(177\) 9.37168 + 16.2322i 0.0529474 + 0.0917075i
\(178\) 0 0
\(179\) 129.477 + 74.7535i 0.723334 + 0.417617i 0.815979 0.578082i \(-0.196199\pi\)
−0.0926444 + 0.995699i \(0.529532\pi\)
\(180\) 0 0
\(181\) −91.2994 −0.504417 −0.252208 0.967673i \(-0.581157\pi\)
−0.252208 + 0.967673i \(0.581157\pi\)
\(182\) 0 0
\(183\) −12.8144 −0.0700242
\(184\) 0 0
\(185\) 92.5114 + 53.4115i 0.500062 + 0.288711i
\(186\) 0 0
\(187\) 37.6008 + 65.1265i 0.201074 + 0.348270i
\(188\) 0 0
\(189\) 13.1486 + 28.9506i 0.0695693 + 0.153178i
\(190\) 0 0
\(191\) 13.9140 + 24.0997i 0.0728480 + 0.126176i 0.900148 0.435583i \(-0.143458\pi\)
−0.827300 + 0.561760i \(0.810125\pi\)
\(192\) 0 0
\(193\) −121.192 + 209.911i −0.627938 + 1.08762i 0.360027 + 0.932942i \(0.382767\pi\)
−0.987965 + 0.154678i \(0.950566\pi\)
\(194\) 0 0
\(195\) −16.4207 −0.0842085
\(196\) 0 0
\(197\) 94.7050i 0.480736i −0.970682 0.240368i \(-0.922732\pi\)
0.970682 0.240368i \(-0.0772682\pi\)
\(198\) 0 0
\(199\) −267.738 154.579i −1.34542 0.776778i −0.357823 0.933790i \(-0.616481\pi\)
−0.987597 + 0.157011i \(0.949814\pi\)
\(200\) 0 0
\(201\) −27.5220 + 15.8899i −0.136926 + 0.0790540i
\(202\) 0 0
\(203\) −180.770 + 82.1012i −0.890494 + 0.404439i
\(204\) 0 0
\(205\) −140.002 + 80.8304i −0.682938 + 0.394295i
\(206\) 0 0
\(207\) 19.2076 33.2685i 0.0927903 0.160717i
\(208\) 0 0
\(209\) 195.644i 0.936094i
\(210\) 0 0
\(211\) 125.864i 0.596514i 0.954486 + 0.298257i \(0.0964052\pi\)
−0.954486 + 0.298257i \(0.903595\pi\)
\(212\) 0 0
\(213\) −0.675969 + 1.17081i −0.00317356 + 0.00549677i
\(214\) 0 0
\(215\) 77.0556 44.4881i 0.358398 0.206921i
\(216\) 0 0
\(217\) 22.1679 227.159i 0.102156 1.04682i
\(218\) 0 0
\(219\) 5.99125 3.45905i 0.0273573 0.0157947i
\(220\) 0 0
\(221\) 149.976 + 86.5885i 0.678623 + 0.391803i
\(222\) 0 0
\(223\) 8.94619i 0.0401174i 0.999799 + 0.0200587i \(0.00638532\pi\)
−0.999799 + 0.0200587i \(0.993615\pi\)
\(224\) 0 0
\(225\) 109.396 0.486206
\(226\) 0 0
\(227\) 136.347 236.160i 0.600647 1.04035i −0.392076 0.919933i \(-0.628243\pi\)
0.992723 0.120419i \(-0.0384237\pi\)
\(228\) 0 0
\(229\) 165.611 + 286.846i 0.723191 + 1.25260i 0.959714 + 0.280978i \(0.0906588\pi\)
−0.236523 + 0.971626i \(0.576008\pi\)
\(230\) 0 0
\(231\) −11.3665 8.12975i −0.0492058 0.0351937i
\(232\) 0 0
\(233\) −79.1185 137.037i −0.339564 0.588143i 0.644786 0.764363i \(-0.276946\pi\)
−0.984351 + 0.176220i \(0.943613\pi\)
\(234\) 0 0
\(235\) 157.313 + 90.8245i 0.669416 + 0.386487i
\(236\) 0 0
\(237\) 26.1046 0.110146
\(238\) 0 0
\(239\) −48.9981 −0.205013 −0.102507 0.994732i \(-0.532686\pi\)
−0.102507 + 0.994732i \(0.532686\pi\)
\(240\) 0 0
\(241\) 170.914 + 98.6771i 0.709186 + 0.409449i 0.810759 0.585379i \(-0.199054\pi\)
−0.101574 + 0.994828i \(0.532388\pi\)
\(242\) 0 0
\(243\) −30.4787 52.7907i −0.125427 0.217246i
\(244\) 0 0
\(245\) 171.715 + 33.8367i 0.700878 + 0.138109i
\(246\) 0 0
\(247\) 225.267 + 390.175i 0.912014 + 1.57965i
\(248\) 0 0
\(249\) 6.53014 11.3105i 0.0262255 0.0454239i
\(250\) 0 0
\(251\) 315.497 1.25696 0.628480 0.777826i \(-0.283677\pi\)
0.628480 + 0.777826i \(0.283677\pi\)
\(252\) 0 0
\(253\) 33.8883i 0.133946i
\(254\) 0 0
\(255\) −7.47341 4.31478i −0.0293075 0.0169207i
\(256\) 0 0
\(257\) −329.533 + 190.256i −1.28223 + 0.740296i −0.977256 0.212065i \(-0.931981\pi\)
−0.304974 + 0.952361i \(0.598648\pi\)
\(258\) 0 0
\(259\) 170.281 + 121.791i 0.657454 + 0.470234i
\(260\) 0 0
\(261\) 219.492 126.724i 0.840967 0.485532i
\(262\) 0 0
\(263\) 98.1636 170.024i 0.373246 0.646480i −0.616817 0.787106i \(-0.711578\pi\)
0.990063 + 0.140626i \(0.0449116\pi\)
\(264\) 0 0
\(265\) 224.335i 0.846547i
\(266\) 0 0
\(267\) 38.9588i 0.145913i
\(268\) 0 0
\(269\) −51.1557 + 88.6043i −0.190170 + 0.329384i −0.945306 0.326184i \(-0.894237\pi\)
0.755137 + 0.655568i \(0.227571\pi\)
\(270\) 0 0
\(271\) 221.981 128.161i 0.819118 0.472918i −0.0309944 0.999520i \(-0.509867\pi\)
0.850112 + 0.526602i \(0.176534\pi\)
\(272\) 0 0
\(273\) −32.0292 3.12564i −0.117323 0.0114492i
\(274\) 0 0
\(275\) −83.5757 + 48.2525i −0.303912 + 0.175464i
\(276\) 0 0
\(277\) 170.372 + 98.3646i 0.615063 + 0.355107i 0.774944 0.632029i \(-0.217778\pi\)
−0.159881 + 0.987136i \(0.551111\pi\)
\(278\) 0 0
\(279\) 291.358i 1.04429i
\(280\) 0 0
\(281\) −70.2923 −0.250151 −0.125075 0.992147i \(-0.539917\pi\)
−0.125075 + 0.992147i \(0.539917\pi\)
\(282\) 0 0
\(283\) −148.495 + 257.201i −0.524718 + 0.908838i 0.474868 + 0.880057i \(0.342496\pi\)
−0.999586 + 0.0287807i \(0.990838\pi\)
\(284\) 0 0
\(285\) −11.2253 19.4427i −0.0393869 0.0682201i
\(286\) 0 0
\(287\) −288.466 + 131.014i −1.00511 + 0.456494i
\(288\) 0 0
\(289\) −98.9951 171.465i −0.342544 0.593303i
\(290\) 0 0
\(291\) −10.3179 5.95704i −0.0354567 0.0204709i
\(292\) 0 0
\(293\) −135.561 −0.462665 −0.231333 0.972875i \(-0.574309\pi\)
−0.231333 + 0.972875i \(0.574309\pi\)
\(294\) 0 0
\(295\) −264.346 −0.896087
\(296\) 0 0
\(297\) 31.0096 + 17.9034i 0.104409 + 0.0602808i
\(298\) 0 0
\(299\) 39.0196 + 67.5839i 0.130500 + 0.226033i
\(300\) 0 0
\(301\) 158.768 72.1084i 0.527470 0.239563i
\(302\) 0 0
\(303\) 18.9113 + 32.7553i 0.0624136 + 0.108103i
\(304\) 0 0
\(305\) 90.3637 156.515i 0.296274 0.513162i
\(306\) 0 0
\(307\) 76.2052 0.248225 0.124113 0.992268i \(-0.460392\pi\)
0.124113 + 0.992268i \(0.460392\pi\)
\(308\) 0 0
\(309\) 5.02541i 0.0162635i
\(310\) 0 0
\(311\) 171.554 + 99.0468i 0.551621 + 0.318479i 0.749776 0.661692i \(-0.230161\pi\)
−0.198154 + 0.980171i \(0.563495\pi\)
\(312\) 0 0
\(313\) −47.9693 + 27.6951i −0.153257 + 0.0884827i −0.574667 0.818387i \(-0.694868\pi\)
0.421411 + 0.906870i \(0.361535\pi\)
\(314\) 0 0
\(315\) −222.362 21.6997i −0.705912 0.0688881i
\(316\) 0 0
\(317\) 259.080 149.580i 0.817289 0.471862i −0.0321920 0.999482i \(-0.510249\pi\)
0.849481 + 0.527620i \(0.176915\pi\)
\(318\) 0 0
\(319\) −111.791 + 193.627i −0.350441 + 0.606981i
\(320\) 0 0
\(321\) 2.31572i 0.00721409i
\(322\) 0 0
\(323\) 236.770i 0.733034i
\(324\) 0 0
\(325\) −111.117 + 192.461i −0.341900 + 0.592188i
\(326\) 0 0
\(327\) −26.1433 + 15.0938i −0.0799490 + 0.0461586i
\(328\) 0 0
\(329\) 289.557 + 207.101i 0.880111 + 0.629487i
\(330\) 0 0
\(331\) 325.087 187.689i 0.982135 0.567036i 0.0792209 0.996857i \(-0.474757\pi\)
0.902914 + 0.429821i \(0.141423\pi\)
\(332\) 0 0
\(333\) −231.445 133.625i −0.695029 0.401275i
\(334\) 0 0
\(335\) 448.203i 1.33792i
\(336\) 0 0
\(337\) −4.99043 −0.0148084 −0.00740419 0.999973i \(-0.502357\pi\)
−0.00740419 + 0.999973i \(0.502357\pi\)
\(338\) 0 0
\(339\) 15.7032 27.1988i 0.0463222 0.0802324i
\(340\) 0 0
\(341\) −128.512 222.589i −0.376868 0.652755i
\(342\) 0 0
\(343\) 328.497 + 98.6856i 0.957717 + 0.287713i
\(344\) 0 0
\(345\) −1.94438 3.36776i −0.00563588 0.00976163i
\(346\) 0 0
\(347\) −320.772 185.198i −0.924414 0.533711i −0.0393734 0.999225i \(-0.512536\pi\)
−0.885041 + 0.465514i \(0.845870\pi\)
\(348\) 0 0
\(349\) −25.6801 −0.0735821 −0.0367910 0.999323i \(-0.511714\pi\)
−0.0367910 + 0.999323i \(0.511714\pi\)
\(350\) 0 0
\(351\) 82.4571 0.234921
\(352\) 0 0
\(353\) −229.938 132.755i −0.651383 0.376076i 0.137603 0.990487i \(-0.456060\pi\)
−0.788986 + 0.614411i \(0.789394\pi\)
\(354\) 0 0
\(355\) −9.53348 16.5125i −0.0268549 0.0465140i
\(356\) 0 0
\(357\) −13.7559 9.83871i −0.0385319 0.0275594i
\(358\) 0 0
\(359\) −275.228 476.709i −0.766651 1.32788i −0.939369 0.342908i \(-0.888588\pi\)
0.172718 0.984971i \(-0.444745\pi\)
\(360\) 0 0
\(361\) −127.489 + 220.817i −0.353155 + 0.611682i
\(362\) 0 0
\(363\) 14.9068 0.0410656
\(364\) 0 0
\(365\) 97.5689i 0.267312i
\(366\) 0 0
\(367\) −180.099 103.980i −0.490732 0.283324i 0.234146 0.972201i \(-0.424771\pi\)
−0.724878 + 0.688877i \(0.758104\pi\)
\(368\) 0 0
\(369\) 350.257 202.221i 0.949207 0.548025i
\(370\) 0 0
\(371\) 42.7018 437.575i 0.115099 1.17945i
\(372\) 0 0
\(373\) −393.539 + 227.210i −1.05507 + 0.609142i −0.924063 0.382240i \(-0.875153\pi\)
−0.131002 + 0.991382i \(0.541820\pi\)
\(374\) 0 0
\(375\) 16.8443 29.1751i 0.0449180 0.0778003i
\(376\) 0 0
\(377\) 514.871i 1.36570i
\(378\) 0 0
\(379\) 373.244i 0.984813i −0.870365 0.492406i \(-0.836117\pi\)
0.870365 0.492406i \(-0.163883\pi\)
\(380\) 0 0
\(381\) −7.29559 + 12.6363i −0.0191485 + 0.0331662i
\(382\) 0 0
\(383\) 270.298 156.056i 0.705738 0.407458i −0.103743 0.994604i \(-0.533082\pi\)
0.809481 + 0.587146i \(0.199749\pi\)
\(384\) 0 0
\(385\) 179.450 81.5014i 0.466103 0.211692i
\(386\) 0 0
\(387\) −192.777 + 111.300i −0.498133 + 0.287597i
\(388\) 0 0
\(389\) −439.628 253.819i −1.13015 0.652492i −0.186177 0.982516i \(-0.559610\pi\)
−0.943973 + 0.330024i \(0.892943\pi\)
\(390\) 0 0
\(391\) 41.0120i 0.104890i
\(392\) 0 0
\(393\) 31.4796 0.0801007
\(394\) 0 0
\(395\) −184.082 + 318.840i −0.466031 + 0.807190i
\(396\) 0 0
\(397\) 95.6487 + 165.668i 0.240929 + 0.417301i 0.960979 0.276621i \(-0.0892146\pi\)
−0.720050 + 0.693922i \(0.755881\pi\)
\(398\) 0 0
\(399\) −18.1945 40.0606i −0.0456002 0.100402i
\(400\) 0 0
\(401\) 61.2011 + 106.004i 0.152621 + 0.264348i 0.932190 0.361968i \(-0.117895\pi\)
−0.779569 + 0.626316i \(0.784562\pi\)
\(402\) 0 0
\(403\) −512.587 295.942i −1.27193 0.734347i
\(404\) 0 0
\(405\) 283.143 0.699120
\(406\) 0 0
\(407\) 235.756 0.579254
\(408\) 0 0
\(409\) −4.57744 2.64279i −0.0111918 0.00646158i 0.494394 0.869238i \(-0.335390\pi\)
−0.505585 + 0.862777i \(0.668723\pi\)
\(410\) 0 0
\(411\) 21.4610 + 37.1716i 0.0522166 + 0.0904418i
\(412\) 0 0
\(413\) −515.617 50.3178i −1.24847 0.121835i
\(414\) 0 0
\(415\) 92.0975 + 159.517i 0.221922 + 0.384379i
\(416\) 0 0
\(417\) 33.7460 58.4498i 0.0809257 0.140167i
\(418\) 0 0
\(419\) −34.7160 −0.0828545 −0.0414272 0.999142i \(-0.513190\pi\)
−0.0414272 + 0.999142i \(0.513190\pi\)
\(420\) 0 0
\(421\) 394.337i 0.936669i −0.883551 0.468334i \(-0.844854\pi\)
0.883551 0.468334i \(-0.155146\pi\)
\(422\) 0 0
\(423\) −393.564 227.224i −0.930412 0.537173i
\(424\) 0 0
\(425\) −101.144 + 58.3956i −0.237986 + 0.137401i
\(426\) 0 0
\(427\) 206.050 288.088i 0.482554 0.674678i
\(428\) 0 0
\(429\) −31.3848 + 18.1200i −0.0731581 + 0.0422378i
\(430\) 0 0
\(431\) −215.872 + 373.901i −0.500862 + 0.867519i 0.499137 + 0.866523i \(0.333650\pi\)
−1.00000 0.000995912i \(0.999683\pi\)
\(432\) 0 0
\(433\) 318.535i 0.735647i −0.929896 0.367823i \(-0.880103\pi\)
0.929896 0.367823i \(-0.119897\pi\)
\(434\) 0 0
\(435\) 25.6565i 0.0589803i
\(436\) 0 0
\(437\) −53.3481 + 92.4016i −0.122078 + 0.211445i
\(438\) 0 0
\(439\) −532.799 + 307.612i −1.21366 + 0.700710i −0.963556 0.267508i \(-0.913800\pi\)
−0.250109 + 0.968218i \(0.580467\pi\)
\(440\) 0 0
\(441\) −429.596 84.6525i −0.974141 0.191956i
\(442\) 0 0
\(443\) −86.4553 + 49.9150i −0.195159 + 0.112675i −0.594395 0.804173i \(-0.702609\pi\)
0.399237 + 0.916848i \(0.369275\pi\)
\(444\) 0 0
\(445\) −475.840 274.726i −1.06930 0.617362i
\(446\) 0 0
\(447\) 7.80515i 0.0174612i
\(448\) 0 0
\(449\) −75.3168 −0.167743 −0.0838717 0.996477i \(-0.526729\pi\)
−0.0838717 + 0.996477i \(0.526729\pi\)
\(450\) 0 0
\(451\) −178.391 + 308.983i −0.395546 + 0.685105i
\(452\) 0 0
\(453\) 2.97443 + 5.15187i 0.00656608 + 0.0113728i
\(454\) 0 0
\(455\) 264.037 369.161i 0.580301 0.811343i
\(456\) 0 0
\(457\) 104.447 + 180.907i 0.228549 + 0.395858i 0.957378 0.288837i \(-0.0932687\pi\)
−0.728830 + 0.684695i \(0.759935\pi\)
\(458\) 0 0
\(459\) 37.5281 + 21.6669i 0.0817606 + 0.0472045i
\(460\) 0 0
\(461\) 751.461 1.63007 0.815034 0.579413i \(-0.196718\pi\)
0.815034 + 0.579413i \(0.196718\pi\)
\(462\) 0 0
\(463\) 3.56075 0.00769060 0.00384530 0.999993i \(-0.498776\pi\)
0.00384530 + 0.999993i \(0.498776\pi\)
\(464\) 0 0
\(465\) 25.5426 + 14.7470i 0.0549304 + 0.0317141i
\(466\) 0 0
\(467\) 206.945 + 358.440i 0.443138 + 0.767537i 0.997920 0.0644583i \(-0.0205320\pi\)
−0.554783 + 0.831995i \(0.687199\pi\)
\(468\) 0 0
\(469\) 85.3146 874.238i 0.181908 1.86405i
\(470\) 0 0
\(471\) 16.1615 + 27.9925i 0.0343131 + 0.0594320i
\(472\) 0 0
\(473\) 98.1843 170.060i 0.207578 0.359535i
\(474\) 0 0
\(475\) −303.843 −0.639669
\(476\) 0 0
\(477\) 561.240i 1.17660i
\(478\) 0 0
\(479\) 785.798 + 453.681i 1.64050 + 0.947142i 0.980657 + 0.195737i \(0.0627098\pi\)
0.659841 + 0.751405i \(0.270624\pi\)
\(480\) 0 0
\(481\) 470.172 271.454i 0.977488 0.564353i
\(482\) 0 0
\(483\) −3.15154 6.93907i −0.00652494 0.0143666i
\(484\) 0 0
\(485\) 145.518 84.0147i 0.300037 0.173226i
\(486\) 0 0
\(487\) 421.452 729.977i 0.865405 1.49893i −0.00123943 0.999999i \(-0.500395\pi\)
0.866644 0.498926i \(-0.166272\pi\)
\(488\) 0 0
\(489\) 40.4410i 0.0827014i
\(490\) 0 0
\(491\) 144.126i 0.293535i 0.989171 + 0.146768i \(0.0468870\pi\)
−0.989171 + 0.146768i \(0.953113\pi\)
\(492\) 0 0
\(493\) −135.290 + 234.329i −0.274422 + 0.475313i
\(494\) 0 0
\(495\) −217.889 + 125.798i −0.440179 + 0.254138i
\(496\) 0 0
\(497\) −15.4523 34.0229i −0.0310912 0.0684566i
\(498\) 0 0
\(499\) 330.101 190.584i 0.661526 0.381932i −0.131332 0.991338i \(-0.541926\pi\)
0.792858 + 0.609406i \(0.208592\pi\)
\(500\) 0 0
\(501\) 31.3180 + 18.0815i 0.0625110 + 0.0360908i
\(502\) 0 0
\(503\) 936.429i 1.86169i 0.365418 + 0.930843i \(0.380926\pi\)
−0.365418 + 0.930843i \(0.619074\pi\)
\(504\) 0 0
\(505\) −533.429 −1.05629
\(506\) 0 0
\(507\) −20.3273 + 35.2080i −0.0400933 + 0.0694437i
\(508\) 0 0
\(509\) 167.592 + 290.278i 0.329258 + 0.570291i 0.982365 0.186975i \(-0.0598682\pi\)
−0.653107 + 0.757265i \(0.726535\pi\)
\(510\) 0 0
\(511\) −18.5721 + 190.312i −0.0363446 + 0.372431i
\(512\) 0 0
\(513\) 56.3682 + 97.6327i 0.109880 + 0.190317i
\(514\) 0 0
\(515\) −61.3800 35.4378i −0.119185 0.0688112i
\(516\) 0 0
\(517\) 400.896 0.775427
\(518\) 0 0
\(519\) 49.5824 0.0955345
\(520\) 0 0
\(521\) −421.675 243.454i −0.809357 0.467283i 0.0373754 0.999301i \(-0.488100\pi\)
−0.846733 + 0.532019i \(0.821434\pi\)
\(522\) 0 0
\(523\) 86.3132 + 149.499i 0.165035 + 0.285849i 0.936668 0.350220i \(-0.113893\pi\)
−0.771633 + 0.636068i \(0.780560\pi\)
\(524\) 0 0
\(525\) 12.6258 17.6527i 0.0240492 0.0336242i
\(526\) 0 0
\(527\) −155.527 269.380i −0.295117 0.511157i
\(528\) 0 0
\(529\) 255.259 442.122i 0.482532 0.835770i
\(530\) 0 0
\(531\) 661.339 1.24546
\(532\) 0 0
\(533\) 821.611i 1.54148i
\(534\) 0 0
\(535\) −28.2841 16.3298i −0.0528675 0.0305230i
\(536\) 0 0
\(537\) −32.7908 + 18.9318i −0.0610629 + 0.0352547i
\(538\) 0 0
\(539\) 365.538 124.814i 0.678178 0.231566i
\(540\) 0 0
\(541\) 500.736 289.100i 0.925574 0.534381i 0.0401652 0.999193i \(-0.487212\pi\)
0.885409 + 0.464812i \(0.153878\pi\)
\(542\) 0 0
\(543\) 11.5611 20.0244i 0.0212911 0.0368773i
\(544\) 0 0
\(545\) 425.750i 0.781193i
\(546\) 0 0
\(547\) 454.579i 0.831040i −0.909584 0.415520i \(-0.863600\pi\)
0.909584 0.415520i \(-0.136400\pi\)
\(548\) 0 0
\(549\) −226.071 + 391.567i −0.411788 + 0.713237i
\(550\) 0 0
\(551\) −609.629 + 351.969i −1.10640 + 0.638783i
\(552\) 0 0
\(553\) −419.751 + 586.871i −0.759043 + 1.06125i
\(554\) 0 0
\(555\) −23.4291 + 13.5268i −0.0422145 + 0.0243726i
\(556\) 0 0
\(557\) 25.2401 + 14.5724i 0.0453143 + 0.0261622i 0.522486 0.852648i \(-0.325005\pi\)
−0.477172 + 0.878810i \(0.658338\pi\)
\(558\) 0 0
\(559\) 452.205i 0.808953i
\(560\) 0 0
\(561\) −19.0453 −0.0339488
\(562\) 0 0
\(563\) −514.005 + 890.283i −0.912975 + 1.58132i −0.103136 + 0.994667i \(0.532888\pi\)
−0.809839 + 0.586652i \(0.800446\pi\)
\(564\) 0 0
\(565\) 221.469 + 383.596i 0.391981 + 0.678931i
\(566\) 0 0
\(567\) 552.283 + 53.8959i 0.974044 + 0.0950544i
\(568\) 0 0
\(569\) 409.852 + 709.885i 0.720303 + 1.24760i 0.960878 + 0.276971i \(0.0893305\pi\)
−0.240576 + 0.970630i \(0.577336\pi\)
\(570\) 0 0
\(571\) −140.820 81.3023i −0.246620 0.142386i 0.371596 0.928395i \(-0.378811\pi\)
−0.618215 + 0.786009i \(0.712144\pi\)
\(572\) 0 0
\(573\) −7.04760 −0.0122995
\(574\) 0 0
\(575\) −52.6299 −0.0915303
\(576\) 0 0
\(577\) 131.878 + 76.1400i 0.228559 + 0.131958i 0.609907 0.792473i \(-0.291207\pi\)
−0.381348 + 0.924431i \(0.624540\pi\)
\(578\) 0 0
\(579\) −30.6926 53.1611i −0.0530097 0.0918154i
\(580\) 0 0
\(581\) 149.276 + 328.676i 0.256930 + 0.565708i
\(582\) 0 0
\(583\) −247.551 428.772i −0.424617 0.735457i
\(584\) 0 0
\(585\) −289.692 + 501.762i −0.495201 + 0.857713i
\(586\) 0 0
\(587\) 894.404 1.52369 0.761843 0.647761i \(-0.224295\pi\)
0.761843 + 0.647761i \(0.224295\pi\)
\(588\) 0 0
\(589\) 809.232i 1.37391i
\(590\) 0 0
\(591\) 20.7713 + 11.9923i 0.0351460 + 0.0202916i
\(592\) 0 0
\(593\) 164.729 95.1064i 0.277789 0.160382i −0.354633 0.935006i \(-0.615394\pi\)
0.632422 + 0.774624i \(0.282061\pi\)
\(594\) 0 0
\(595\) 217.172 98.6338i 0.364995 0.165771i
\(596\) 0 0
\(597\) 67.8064 39.1480i 0.113579 0.0655746i
\(598\) 0 0
\(599\) −146.832 + 254.320i −0.245128 + 0.424574i −0.962168 0.272458i \(-0.912163\pi\)
0.717040 + 0.697033i \(0.245497\pi\)
\(600\) 0 0
\(601\) 597.574i 0.994299i 0.867665 + 0.497150i \(0.165620\pi\)
−0.867665 + 0.497150i \(0.834380\pi\)
\(602\) 0 0
\(603\) 1121.31i 1.85956i
\(604\) 0 0
\(605\) −105.119 + 182.071i −0.173750 + 0.300944i
\(606\) 0 0
\(607\) 10.6620 6.15569i 0.0175650 0.0101412i −0.491192 0.871051i \(-0.663439\pi\)
0.508757 + 0.860910i \(0.330105\pi\)
\(608\) 0 0
\(609\) 4.88366 50.0440i 0.00801915 0.0821740i
\(610\) 0 0
\(611\) 799.512 461.599i 1.30853 0.755481i
\(612\) 0 0
\(613\) −118.897 68.6451i −0.193959 0.111982i 0.399876 0.916569i \(-0.369053\pi\)
−0.593835 + 0.804587i \(0.702387\pi\)
\(614\) 0 0
\(615\) 40.9416i 0.0665717i
\(616\) 0 0
\(617\) 290.516 0.470853 0.235427 0.971892i \(-0.424351\pi\)
0.235427 + 0.971892i \(0.424351\pi\)
\(618\) 0 0
\(619\) 51.1586 88.6092i 0.0826471 0.143149i −0.821739 0.569864i \(-0.806996\pi\)
0.904386 + 0.426715i \(0.140329\pi\)
\(620\) 0 0
\(621\) 9.76379 + 16.9114i 0.0157227 + 0.0272325i
\(622\) 0 0
\(623\) −875.851 626.440i −1.40586 1.00552i
\(624\) 0 0
\(625\) 84.5320 + 146.414i 0.135251 + 0.234262i
\(626\) 0 0
\(627\) −42.9098 24.7740i −0.0684366 0.0395119i
\(628\) 0 0
\(629\) 285.315 0.453600
\(630\) 0 0
\(631\) 562.739 0.891820 0.445910 0.895078i \(-0.352880\pi\)
0.445910 + 0.895078i \(0.352880\pi\)
\(632\) 0 0
\(633\) −27.6054 15.9380i −0.0436104 0.0251785i
\(634\) 0 0
\(635\) −102.893 178.216i −0.162036 0.280655i
\(636\) 0 0
\(637\) 585.284 669.805i 0.918814 1.05150i
\(638\) 0 0
\(639\) 23.8508 + 41.3108i 0.0373252 + 0.0646492i
\(640\) 0 0
\(641\) 376.275 651.727i 0.587012 1.01673i −0.407610 0.913156i \(-0.633638\pi\)
0.994621 0.103578i \(-0.0330291\pi\)
\(642\) 0 0
\(643\) −253.143 −0.393690 −0.196845 0.980435i \(-0.563070\pi\)
−0.196845 + 0.980435i \(0.563070\pi\)
\(644\) 0 0
\(645\) 22.5337i 0.0349360i
\(646\) 0 0
\(647\) −485.492 280.299i −0.750374 0.433229i 0.0754551 0.997149i \(-0.475959\pi\)
−0.825829 + 0.563921i \(0.809292\pi\)
\(648\) 0 0
\(649\) −505.244 + 291.703i −0.778497 + 0.449465i
\(650\) 0 0
\(651\) 47.0149 + 33.6267i 0.0722195 + 0.0516539i
\(652\) 0 0
\(653\) −602.396 + 347.793i −0.922505 + 0.532609i −0.884433 0.466666i \(-0.845455\pi\)
−0.0380717 + 0.999275i \(0.512122\pi\)
\(654\) 0 0
\(655\) −221.985 + 384.489i −0.338908 + 0.587007i
\(656\) 0 0
\(657\) 244.097i 0.371533i
\(658\) 0 0
\(659\) 323.387i 0.490724i 0.969432 + 0.245362i \(0.0789068\pi\)
−0.969432 + 0.245362i \(0.921093\pi\)
\(660\) 0 0
\(661\) −15.5168 + 26.8758i −0.0234747 + 0.0406593i −0.877524 0.479533i \(-0.840806\pi\)
0.854049 + 0.520192i \(0.174140\pi\)
\(662\) 0 0
\(663\) −37.9822 + 21.9291i −0.0572884 + 0.0330755i
\(664\) 0 0
\(665\) 617.600 + 60.2699i 0.928721 + 0.0906315i
\(666\) 0 0
\(667\) −105.596 + 60.9661i −0.158315 + 0.0914035i
\(668\) 0 0
\(669\) −1.96213 1.13284i −0.00293293 0.00169333i
\(670\) 0 0
\(671\) 398.862i 0.594429i
\(672\) 0 0
\(673\) 1011.75 1.50334 0.751670 0.659539i \(-0.229249\pi\)
0.751670 + 0.659539i \(0.229249\pi\)
\(674\) 0 0
\(675\) −27.8047 + 48.1592i −0.0411922 + 0.0713469i
\(676\) 0 0
\(677\) 34.7377 + 60.1674i 0.0513112 + 0.0888736i 0.890540 0.454905i \(-0.150327\pi\)
−0.839229 + 0.543778i \(0.816993\pi\)
\(678\) 0 0
\(679\) 299.831 136.175i 0.441577 0.200553i
\(680\) 0 0
\(681\) 34.5307 + 59.8089i 0.0507058 + 0.0878251i
\(682\) 0 0
\(683\) −824.530 476.042i −1.20722 0.696987i −0.245067 0.969506i \(-0.578810\pi\)
−0.962150 + 0.272519i \(0.912143\pi\)
\(684\) 0 0
\(685\) −605.348 −0.883720
\(686\) 0 0
\(687\) −83.8839 −0.122102
\(688\) 0 0
\(689\) −987.391 570.070i −1.43308 0.827388i
\(690\) 0 0
\(691\) −34.0754 59.0204i −0.0493132 0.0854130i 0.840315 0.542098i \(-0.182370\pi\)
−0.889628 + 0.456685i \(0.849037\pi\)
\(692\) 0 0
\(693\) −448.947 + 203.900i −0.647831 + 0.294228i
\(694\) 0 0
\(695\) 475.935 + 824.343i 0.684798 + 1.18611i
\(696\) 0 0
\(697\) −215.891 + 373.934i −0.309743 + 0.536490i
\(698\) 0 0
\(699\) 40.0745 0.0573311
\(700\) 0 0
\(701\) 1.67276i 0.00238625i 0.999999 + 0.00119312i \(0.000379783\pi\)
−0.999999 + 0.00119312i \(0.999620\pi\)
\(702\) 0 0
\(703\) 642.825 + 371.135i 0.914403 + 0.527931i
\(704\) 0 0
\(705\) −39.8404 + 23.0019i −0.0565112 + 0.0326267i
\(706\) 0 0
\(707\) −1040.47 101.537i −1.47168 0.143617i
\(708\) 0 0
\(709\) −45.7969 + 26.4408i −0.0645936 + 0.0372931i −0.531949 0.846776i \(-0.678540\pi\)
0.467355 + 0.884070i \(0.345207\pi\)
\(710\) 0 0
\(711\) 460.536 797.673i 0.647731 1.12190i
\(712\) 0 0
\(713\) 140.171i 0.196593i
\(714\) 0 0
\(715\) 511.109i 0.714838i
\(716\) 0 0
\(717\) 6.20454 10.7466i 0.00865347 0.0149882i
\(718\) 0 0
\(719\) 824.178 475.840i 1.14628 0.661808i 0.198305 0.980140i \(-0.436456\pi\)
0.947979 + 0.318333i \(0.103123\pi\)
\(720\) 0 0
\(721\) −112.979 80.8064i −0.156697 0.112075i
\(722\) 0 0
\(723\) −43.2849 + 24.9906i −0.0598685 + 0.0345651i
\(724\) 0 0
\(725\) −300.711 173.615i −0.414774 0.239470i
\(726\) 0 0
\(727\) 1061.98i 1.46078i 0.683032 + 0.730388i \(0.260661\pi\)
−0.683032 + 0.730388i \(0.739339\pi\)
\(728\) 0 0
\(729\) −698.013 −0.957494
\(730\) 0 0
\(731\) 118.824 205.809i 0.162550 0.281544i
\(732\) 0 0
\(733\) 0.148102 + 0.256519i 0.000202048 + 0.000349958i 0.866126 0.499825i \(-0.166602\pi\)
−0.865924 + 0.500175i \(0.833269\pi\)
\(734\) 0 0
\(735\) −29.1652 + 33.3769i −0.0396806 + 0.0454108i
\(736\) 0 0
\(737\) −494.588 856.651i −0.671082 1.16235i
\(738\) 0 0
\(739\) 176.276 + 101.773i 0.238533 + 0.137717i 0.614502 0.788915i \(-0.289357\pi\)
−0.375969 + 0.926632i \(0.622690\pi\)
\(740\) 0 0
\(741\) −114.101 −0.153982
\(742\) 0 0
\(743\) −1142.13 −1.53718 −0.768592 0.639739i \(-0.779042\pi\)
−0.768592 + 0.639739i \(0.779042\pi\)
\(744\) 0 0
\(745\) 95.3315 + 55.0397i 0.127962 + 0.0738788i
\(746\) 0 0
\(747\) −230.409 399.080i −0.308446 0.534244i
\(748\) 0 0
\(749\) −52.0610 37.2358i −0.0695073 0.0497141i
\(750\) 0 0
\(751\) −396.068 686.010i −0.527387 0.913462i −0.999490 0.0319185i \(-0.989838\pi\)
0.472103 0.881543i \(-0.343495\pi\)
\(752\) 0 0
\(753\) −39.9508 + 69.1967i −0.0530554 + 0.0918947i
\(754\) 0 0
\(755\) −83.8995 −0.111125
\(756\) 0 0
\(757\) 1179.34i 1.55792i −0.627076 0.778958i \(-0.715748\pi\)
0.627076 0.778958i \(-0.284252\pi\)
\(758\) 0 0
\(759\) −7.43259 4.29121i −0.00979260 0.00565376i
\(760\) 0 0
\(761\) 197.869 114.240i 0.260011 0.150118i −0.364328 0.931271i \(-0.618701\pi\)
0.624340 + 0.781153i \(0.285368\pi\)
\(762\) 0 0
\(763\) 81.0408 830.443i 0.106213 1.08839i
\(764\) 0 0
\(765\) −263.691 + 152.242i −0.344694 + 0.199009i
\(766\) 0 0
\(767\) −671.744 + 1163.49i −0.875807 + 1.51694i
\(768\) 0 0
\(769\) 83.4232i 0.108483i −0.998528 0.0542414i \(-0.982726\pi\)
0.998528 0.0542414i \(-0.0172740\pi\)
\(770\) 0 0
\(771\) 96.3670i 0.124990i
\(772\) 0 0
\(773\) 285.318 494.186i 0.369105 0.639309i −0.620321 0.784348i \(-0.712998\pi\)
0.989426 + 0.145039i \(0.0463309\pi\)
\(774\) 0 0
\(775\) 345.691 199.585i 0.446052 0.257528i
\(776\) 0 0
\(777\) −48.2742 + 21.9249i −0.0621289 + 0.0282173i
\(778\) 0 0
\(779\) −972.822 + 561.659i −1.24881 + 0.721000i
\(780\) 0 0
\(781\) −36.4427 21.0402i −0.0466616 0.0269401i
\(782\) 0 0
\(783\) 128.835i 0.164540i
\(784\) 0 0
\(785\) −455.864 −0.580718
\(786\) 0 0
\(787\) 382.719 662.888i 0.486301 0.842298i −0.513575 0.858045i \(-0.671679\pi\)