Properties

Label 224.3.s.b.33.1
Level 224
Weight 3
Character 224.33
Analytic conductor 6.104
Analytic rank 0
Dimension 16
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.s (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.10355792167\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{20}\cdot 7 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 33.1
Root \(-3.16141 - 2.64174i\) of \(x^{16} - 26 x^{14} - 16 x^{13} + 469 x^{12} + 144 x^{11} - 4526 x^{10} + 4440 x^{9} + 32608 x^{8} - 33728 x^{7} - 49760 x^{6} + 203528 x^{5} + 27401 x^{4} - 156928 x^{3} + 114964 x^{2} - 248608 x + 208849\)
Character \(\chi\) \(=\) 224.33
Dual form 224.3.s.b.129.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-4.97091 + 2.86995i) q^{3} +(5.45949 + 3.15204i) q^{5} +(5.64993 + 4.13259i) q^{7} +(11.9733 - 20.7383i) q^{9} +O(q^{10})\) \(q+(-4.97091 + 2.86995i) q^{3} +(5.45949 + 3.15204i) q^{5} +(5.64993 + 4.13259i) q^{7} +(11.9733 - 20.7383i) q^{9} +(2.70557 + 4.68619i) q^{11} +15.9368i q^{13} -36.1848 q^{15} +(-17.7354 + 10.2395i) q^{17} +(-11.7669 - 6.79363i) q^{19} +(-39.9456 - 4.32768i) q^{21} +(2.35080 - 4.07170i) q^{23} +(7.37071 + 12.7664i) q^{25} +85.7918i q^{27} +1.76543 q^{29} +(11.9039 - 6.87274i) q^{31} +(-26.8983 - 15.5297i) q^{33} +(17.8197 + 40.3706i) q^{35} +(-5.23363 + 9.06491i) q^{37} +(-45.7380 - 79.2205i) q^{39} +11.2412i q^{41} -49.1704 q^{43} +(130.736 - 75.4805i) q^{45} +(9.02382 + 5.20991i) q^{47} +(14.8434 + 46.6977i) q^{49} +(58.7740 - 101.800i) q^{51} +(-16.0506 - 27.8005i) q^{53} +34.1123i q^{55} +77.9897 q^{57} +(57.2860 - 33.0741i) q^{59} +(-27.6804 - 15.9813i) q^{61} +(153.351 - 67.6894i) q^{63} +(-50.2335 + 87.0070i) q^{65} +(49.2688 + 85.3361i) q^{67} +26.9867i q^{69} -61.7537 q^{71} +(15.6253 - 9.02127i) q^{73} +(-73.2782 - 42.3072i) q^{75} +(-4.07980 + 37.6576i) q^{77} +(15.0018 - 25.9839i) q^{79} +(-138.459 - 239.818i) q^{81} -63.4583i q^{83} -129.102 q^{85} +(-8.77580 + 5.06671i) q^{87} +(119.129 + 68.7791i) q^{89} +(-65.8604 + 90.0420i) q^{91} +(-39.4489 + 68.3275i) q^{93} +(-42.8276 - 74.1796i) q^{95} +131.075i q^{97} +129.578 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 40q^{9} + O(q^{10}) \) \( 16q + 40q^{9} - 48q^{17} - 136q^{21} + 80q^{25} - 16q^{29} - 264q^{33} + 72q^{37} + 312q^{45} + 128q^{49} + 40q^{53} + 368q^{57} + 216q^{61} - 168q^{65} - 312q^{73} + 64q^{77} - 384q^{81} - 1072q^{85} + 24q^{89} - 168q^{93} + O(q^{100}) \)

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
\(3\) −4.97091 + 2.86995i −1.65697 + 0.956651i −0.682867 + 0.730543i \(0.739267\pi\)
−0.974102 + 0.226109i \(0.927400\pi\)
\(4\) 0 0
\(5\) 5.45949 + 3.15204i 1.09190 + 0.630408i 0.934081 0.357060i \(-0.116221\pi\)
0.157817 + 0.987468i \(0.449554\pi\)
\(6\) 0 0
\(7\) 5.64993 + 4.13259i 0.807133 + 0.590370i
\(8\) 0 0
\(9\) 11.9733 20.7383i 1.33036 2.30426i
\(10\) 0 0
\(11\) 2.70557 + 4.68619i 0.245961 + 0.426017i 0.962401 0.271631i \(-0.0875632\pi\)
−0.716440 + 0.697648i \(0.754230\pi\)
\(12\) 0 0
\(13\) 15.9368i 1.22591i 0.790118 + 0.612955i \(0.210019\pi\)
−0.790118 + 0.612955i \(0.789981\pi\)
\(14\) 0 0
\(15\) −36.1848 −2.41232
\(16\) 0 0
\(17\) −17.7354 + 10.2395i −1.04326 + 0.602326i −0.920755 0.390142i \(-0.872426\pi\)
−0.122505 + 0.992468i \(0.539093\pi\)
\(18\) 0 0
\(19\) −11.7669 6.79363i −0.619311 0.357560i 0.157289 0.987553i \(-0.449724\pi\)
−0.776601 + 0.629993i \(0.783058\pi\)
\(20\) 0 0
\(21\) −39.9456 4.32768i −1.90217 0.206080i
\(22\) 0 0
\(23\) 2.35080 4.07170i 0.102209 0.177030i −0.810386 0.585897i \(-0.800742\pi\)
0.912594 + 0.408866i \(0.134076\pi\)
\(24\) 0 0
\(25\) 7.37071 + 12.7664i 0.294828 + 0.510658i
\(26\) 0 0
\(27\) 85.7918i 3.17748i
\(28\) 0 0
\(29\) 1.76543 0.0608770 0.0304385 0.999537i \(-0.490310\pi\)
0.0304385 + 0.999537i \(0.490310\pi\)
\(30\) 0 0
\(31\) 11.9039 6.87274i 0.383998 0.221701i −0.295558 0.955325i \(-0.595506\pi\)
0.679556 + 0.733623i \(0.262172\pi\)
\(32\) 0 0
\(33\) −26.8983 15.5297i −0.815099 0.470598i
\(34\) 0 0
\(35\) 17.8197 + 40.3706i 0.509133 + 1.15345i
\(36\) 0 0
\(37\) −5.23363 + 9.06491i −0.141449 + 0.244998i −0.928043 0.372474i \(-0.878510\pi\)
0.786593 + 0.617472i \(0.211843\pi\)
\(38\) 0 0
\(39\) −45.7380 79.2205i −1.17277 2.03130i
\(40\) 0 0
\(41\) 11.2412i 0.274175i 0.990559 + 0.137088i \(0.0437742\pi\)
−0.990559 + 0.137088i \(0.956226\pi\)
\(42\) 0 0
\(43\) −49.1704 −1.14350 −0.571749 0.820428i \(-0.693735\pi\)
−0.571749 + 0.820428i \(0.693735\pi\)
\(44\) 0 0
\(45\) 130.736 75.4805i 2.90525 1.67734i
\(46\) 0 0
\(47\) 9.02382 + 5.20991i 0.191996 + 0.110849i 0.592917 0.805264i \(-0.297976\pi\)
−0.400921 + 0.916113i \(0.631310\pi\)
\(48\) 0 0
\(49\) 14.8434 + 46.6977i 0.302927 + 0.953014i
\(50\) 0 0
\(51\) 58.7740 101.800i 1.15243 1.99607i
\(52\) 0 0
\(53\) −16.0506 27.8005i −0.302842 0.524538i 0.673936 0.738789i \(-0.264602\pi\)
−0.976779 + 0.214251i \(0.931269\pi\)
\(54\) 0 0
\(55\) 34.1123i 0.620223i
\(56\) 0 0
\(57\) 77.9897 1.36824
\(58\) 0 0
\(59\) 57.2860 33.0741i 0.970950 0.560578i 0.0714242 0.997446i \(-0.477246\pi\)
0.899526 + 0.436868i \(0.143912\pi\)
\(60\) 0 0
\(61\) −27.6804 15.9813i −0.453778 0.261989i 0.255647 0.966770i \(-0.417712\pi\)
−0.709424 + 0.704782i \(0.751045\pi\)
\(62\) 0 0
\(63\) 153.351 67.6894i 2.43415 1.07444i
\(64\) 0 0
\(65\) −50.2335 + 87.0070i −0.772824 + 1.33857i
\(66\) 0 0
\(67\) 49.2688 + 85.3361i 0.735356 + 1.27367i 0.954567 + 0.297996i \(0.0963182\pi\)
−0.219211 + 0.975677i \(0.570348\pi\)
\(68\) 0 0
\(69\) 26.9867i 0.391112i
\(70\) 0 0
\(71\) −61.7537 −0.869770 −0.434885 0.900486i \(-0.643211\pi\)
−0.434885 + 0.900486i \(0.643211\pi\)
\(72\) 0 0
\(73\) 15.6253 9.02127i 0.214045 0.123579i −0.389145 0.921177i \(-0.627229\pi\)
0.603190 + 0.797598i \(0.293896\pi\)
\(74\) 0 0
\(75\) −73.2782 42.3072i −0.977043 0.564096i
\(76\) 0 0
\(77\) −4.07980 + 37.6576i −0.0529844 + 0.489060i
\(78\) 0 0
\(79\) 15.0018 25.9839i 0.189896 0.328910i −0.755319 0.655357i \(-0.772518\pi\)
0.945215 + 0.326447i \(0.105851\pi\)
\(80\) 0 0
\(81\) −138.459 239.818i −1.70937 2.96072i
\(82\) 0 0
\(83\) 63.4583i 0.764558i −0.924047 0.382279i \(-0.875139\pi\)
0.924047 0.382279i \(-0.124861\pi\)
\(84\) 0 0
\(85\) −129.102 −1.51884
\(86\) 0 0
\(87\) −8.77580 + 5.06671i −0.100871 + 0.0582381i
\(88\) 0 0
\(89\) 119.129 + 68.7791i 1.33853 + 0.772799i 0.986589 0.163224i \(-0.0521894\pi\)
0.351938 + 0.936023i \(0.385523\pi\)
\(90\) 0 0
\(91\) −65.8604 + 90.0420i −0.723741 + 0.989472i
\(92\) 0 0
\(93\) −39.4489 + 68.3275i −0.424182 + 0.734705i
\(94\) 0 0
\(95\) −42.8276 74.1796i −0.450817 0.780838i
\(96\) 0 0
\(97\) 131.075i 1.35129i 0.737228 + 0.675644i \(0.236134\pi\)
−0.737228 + 0.675644i \(0.763866\pi\)
\(98\) 0 0
\(99\) 129.578 1.30887
\(100\) 0 0
\(101\) −99.2877 + 57.3238i −0.983046 + 0.567562i −0.903188 0.429244i \(-0.858780\pi\)
−0.0798578 + 0.996806i \(0.525447\pi\)
\(102\) 0 0
\(103\) 173.736 + 100.307i 1.68676 + 0.973851i 0.956973 + 0.290176i \(0.0937137\pi\)
0.729786 + 0.683675i \(0.239620\pi\)
\(104\) 0 0
\(105\) −204.442 149.537i −1.94706 1.42416i
\(106\) 0 0
\(107\) 49.7054 86.0923i 0.464537 0.804601i −0.534644 0.845078i \(-0.679554\pi\)
0.999181 + 0.0404762i \(0.0128875\pi\)
\(108\) 0 0
\(109\) 7.59446 + 13.1540i 0.0696740 + 0.120679i 0.898758 0.438445i \(-0.144471\pi\)
−0.829084 + 0.559124i \(0.811137\pi\)
\(110\) 0 0
\(111\) 60.0811i 0.541271i
\(112\) 0 0
\(113\) 114.050 1.00929 0.504645 0.863327i \(-0.331623\pi\)
0.504645 + 0.863327i \(0.331623\pi\)
\(114\) 0 0
\(115\) 25.6683 14.8196i 0.223203 0.128866i
\(116\) 0 0
\(117\) 330.503 + 190.816i 2.82481 + 1.63091i
\(118\) 0 0
\(119\) −142.520 15.4405i −1.19764 0.129752i
\(120\) 0 0
\(121\) 45.8598 79.4315i 0.379006 0.656458i
\(122\) 0 0
\(123\) −32.2617 55.8789i −0.262290 0.454300i
\(124\) 0 0
\(125\) 64.6709i 0.517367i
\(126\) 0 0
\(127\) 27.7466 0.218477 0.109239 0.994016i \(-0.465159\pi\)
0.109239 + 0.994016i \(0.465159\pi\)
\(128\) 0 0
\(129\) 244.422 141.117i 1.89474 1.09393i
\(130\) 0 0
\(131\) −158.266 91.3750i −1.20814 0.697519i −0.245786 0.969324i \(-0.579046\pi\)
−0.962352 + 0.271805i \(0.912379\pi\)
\(132\) 0 0
\(133\) −38.4069 87.0114i −0.288774 0.654221i
\(134\) 0 0
\(135\) −270.419 + 468.380i −2.00311 + 3.46948i
\(136\) 0 0
\(137\) −50.5536 87.5614i −0.369004 0.639134i 0.620406 0.784281i \(-0.286968\pi\)
−0.989410 + 0.145147i \(0.953635\pi\)
\(138\) 0 0
\(139\) 88.5595i 0.637119i 0.947903 + 0.318559i \(0.103199\pi\)
−0.947903 + 0.318559i \(0.896801\pi\)
\(140\) 0 0
\(141\) −59.8088 −0.424176
\(142\) 0 0
\(143\) −74.6830 + 43.1182i −0.522258 + 0.301526i
\(144\) 0 0
\(145\) 9.63837 + 5.56472i 0.0664715 + 0.0383773i
\(146\) 0 0
\(147\) −207.805 189.530i −1.41364 1.28932i
\(148\) 0 0
\(149\) 63.5182 110.017i 0.426296 0.738367i −0.570244 0.821475i \(-0.693151\pi\)
0.996541 + 0.0831082i \(0.0264847\pi\)
\(150\) 0 0
\(151\) 145.693 + 252.347i 0.964852 + 1.67117i 0.710011 + 0.704190i \(0.248690\pi\)
0.254841 + 0.966983i \(0.417977\pi\)
\(152\) 0 0
\(153\) 490.403i 3.20525i
\(154\) 0 0
\(155\) 86.6526 0.559049
\(156\) 0 0
\(157\) 186.624 107.747i 1.18869 0.686289i 0.230679 0.973030i \(-0.425905\pi\)
0.958008 + 0.286741i \(0.0925719\pi\)
\(158\) 0 0
\(159\) 159.572 + 92.1292i 1.00360 + 0.579429i
\(160\) 0 0
\(161\) 30.1085 13.2899i 0.187009 0.0825462i
\(162\) 0 0
\(163\) −87.0084 + 150.703i −0.533794 + 0.924558i 0.465427 + 0.885086i \(0.345901\pi\)
−0.999221 + 0.0394714i \(0.987433\pi\)
\(164\) 0 0
\(165\) −97.9006 169.569i −0.593337 1.02769i
\(166\) 0 0
\(167\) 241.170i 1.44413i −0.691823 0.722067i \(-0.743192\pi\)
0.691823 0.722067i \(-0.256808\pi\)
\(168\) 0 0
\(169\) −84.9827 −0.502856
\(170\) 0 0
\(171\) −281.777 + 162.684i −1.64782 + 0.951369i
\(172\) 0 0
\(173\) −187.037 107.986i −1.08114 0.624197i −0.149937 0.988696i \(-0.547907\pi\)
−0.931204 + 0.364499i \(0.881240\pi\)
\(174\) 0 0
\(175\) −11.1145 + 102.590i −0.0635114 + 0.586227i
\(176\) 0 0
\(177\) −189.842 + 328.817i −1.07256 + 1.85772i
\(178\) 0 0
\(179\) 89.0372 + 154.217i 0.497414 + 0.861547i 0.999996 0.00298291i \(-0.000949492\pi\)
−0.502581 + 0.864530i \(0.667616\pi\)
\(180\) 0 0
\(181\) 172.429i 0.952648i −0.879270 0.476324i \(-0.841969\pi\)
0.879270 0.476324i \(-0.158031\pi\)
\(182\) 0 0
\(183\) 183.462 1.00253
\(184\) 0 0
\(185\) −57.1459 + 32.9932i −0.308897 + 0.178342i
\(186\) 0 0
\(187\) −95.9688 55.4076i −0.513202 0.296297i
\(188\) 0 0
\(189\) −354.543 + 484.718i −1.87589 + 2.56464i
\(190\) 0 0
\(191\) 69.6230 120.591i 0.364518 0.631364i −0.624181 0.781280i \(-0.714567\pi\)
0.988699 + 0.149916i \(0.0479004\pi\)
\(192\) 0 0
\(193\) 21.6165 + 37.4409i 0.112003 + 0.193994i 0.916578 0.399857i \(-0.130940\pi\)
−0.804575 + 0.593851i \(0.797607\pi\)
\(194\) 0 0
\(195\) 576.672i 2.95729i
\(196\) 0 0
\(197\) 205.910 1.04523 0.522614 0.852570i \(-0.324957\pi\)
0.522614 + 0.852570i \(0.324957\pi\)
\(198\) 0 0
\(199\) −260.927 + 150.646i −1.31119 + 0.757016i −0.982293 0.187350i \(-0.940010\pi\)
−0.328896 + 0.944366i \(0.606677\pi\)
\(200\) 0 0
\(201\) −489.822 282.799i −2.43692 1.40696i
\(202\) 0 0
\(203\) 9.97457 + 7.29581i 0.0491358 + 0.0359400i
\(204\) 0 0
\(205\) −35.4327 + 61.3712i −0.172842 + 0.299372i
\(206\) 0 0
\(207\) −56.2935 97.5032i −0.271949 0.471030i
\(208\) 0 0
\(209\) 73.5226i 0.351783i
\(210\) 0 0
\(211\) 310.102 1.46968 0.734839 0.678241i \(-0.237258\pi\)
0.734839 + 0.678241i \(0.237258\pi\)
\(212\) 0 0
\(213\) 306.972 177.230i 1.44118 0.832067i
\(214\) 0 0
\(215\) −268.446 154.987i −1.24858 0.720871i
\(216\) 0 0
\(217\) 95.6586 + 10.3636i 0.440823 + 0.0477585i
\(218\) 0 0
\(219\) −51.7812 + 89.6877i −0.236444 + 0.409533i
\(220\) 0 0
\(221\) −163.186 282.646i −0.738398 1.27894i
\(222\) 0 0
\(223\) 266.090i 1.19323i 0.802528 + 0.596614i \(0.203488\pi\)
−0.802528 + 0.596614i \(0.796512\pi\)
\(224\) 0 0
\(225\) 353.006 1.56892
\(226\) 0 0
\(227\) 264.188 152.529i 1.16382 0.671933i 0.211605 0.977355i \(-0.432131\pi\)
0.952217 + 0.305422i \(0.0987976\pi\)
\(228\) 0 0
\(229\) 171.968 + 99.2857i 0.750952 + 0.433562i 0.826038 0.563615i \(-0.190590\pi\)
−0.0750860 + 0.997177i \(0.523923\pi\)
\(230\) 0 0
\(231\) −87.7954 198.901i −0.380066 0.861045i
\(232\) 0 0
\(233\) 123.928 214.650i 0.531881 0.921246i −0.467426 0.884032i \(-0.654819\pi\)
0.999307 0.0372134i \(-0.0118481\pi\)
\(234\) 0 0
\(235\) 32.8437 + 56.8869i 0.139760 + 0.242072i
\(236\) 0 0
\(237\) 172.218i 0.726658i
\(238\) 0 0
\(239\) 120.884 0.505790 0.252895 0.967494i \(-0.418617\pi\)
0.252895 + 0.967494i \(0.418617\pi\)
\(240\) 0 0
\(241\) 125.956 72.7209i 0.522640 0.301746i −0.215374 0.976532i \(-0.569097\pi\)
0.738014 + 0.674785i \(0.235764\pi\)
\(242\) 0 0
\(243\) 707.854 + 408.680i 2.91298 + 1.68181i
\(244\) 0 0
\(245\) −66.1555 + 301.733i −0.270023 + 1.23156i
\(246\) 0 0
\(247\) 108.269 187.527i 0.438336 0.759220i
\(248\) 0 0
\(249\) 182.123 + 315.446i 0.731416 + 1.26685i
\(250\) 0 0
\(251\) 212.061i 0.844865i 0.906394 + 0.422432i \(0.138824\pi\)
−0.906394 + 0.422432i \(0.861176\pi\)
\(252\) 0 0
\(253\) 25.4410 0.100557
\(254\) 0 0
\(255\) 641.753 370.516i 2.51668 1.45300i
\(256\) 0 0
\(257\) 8.71846 + 5.03361i 0.0339240 + 0.0195860i 0.516866 0.856066i \(-0.327099\pi\)
−0.482942 + 0.875652i \(0.660432\pi\)
\(258\) 0 0
\(259\) −67.0312 + 29.5877i −0.258808 + 0.114238i
\(260\) 0 0
\(261\) 21.1380 36.6121i 0.0809886 0.140276i
\(262\) 0 0
\(263\) 0.0417642 + 0.0723377i 0.000158799 + 0.000275048i 0.866105 0.499862i \(-0.166616\pi\)
−0.865946 + 0.500138i \(0.833283\pi\)
\(264\) 0 0
\(265\) 202.369i 0.763657i
\(266\) 0 0
\(267\) −789.572 −2.95720
\(268\) 0 0
\(269\) −1.10371 + 0.637226i −0.00410301 + 0.00236887i −0.502050 0.864839i \(-0.667421\pi\)
0.497947 + 0.867207i \(0.334087\pi\)
\(270\) 0 0
\(271\) −309.749 178.834i −1.14298 0.659903i −0.195817 0.980641i \(-0.562736\pi\)
−0.947168 + 0.320738i \(0.896069\pi\)
\(272\) 0 0
\(273\) 68.9695 636.607i 0.252636 2.33189i
\(274\) 0 0
\(275\) −39.8840 + 69.0810i −0.145033 + 0.251204i
\(276\) 0 0
\(277\) 84.6074 + 146.544i 0.305442 + 0.529041i 0.977360 0.211585i \(-0.0678625\pi\)
−0.671918 + 0.740626i \(0.734529\pi\)
\(278\) 0 0
\(279\) 329.157i 1.17977i
\(280\) 0 0
\(281\) 246.835 0.878418 0.439209 0.898385i \(-0.355259\pi\)
0.439209 + 0.898385i \(0.355259\pi\)
\(282\) 0 0
\(283\) 198.888 114.828i 0.702783 0.405752i −0.105600 0.994409i \(-0.533676\pi\)
0.808383 + 0.588657i \(0.200343\pi\)
\(284\) 0 0
\(285\) 425.784 + 245.827i 1.49398 + 0.862549i
\(286\) 0 0
\(287\) −46.4552 + 63.5119i −0.161865 + 0.221296i
\(288\) 0 0
\(289\) 65.1965 112.924i 0.225593 0.390739i
\(290\) 0 0
\(291\) −376.179 651.561i −1.29271 2.23904i
\(292\) 0 0
\(293\) 228.171i 0.778740i 0.921081 + 0.389370i \(0.127307\pi\)
−0.921081 + 0.389370i \(0.872693\pi\)
\(294\) 0 0
\(295\) 417.004 1.41357
\(296\) 0 0
\(297\) −402.036 + 232.116i −1.35366 + 0.781535i
\(298\) 0 0
\(299\) 64.8900 + 37.4643i 0.217023 + 0.125299i
\(300\) 0 0
\(301\) −277.810 203.201i −0.922955 0.675087i
\(302\) 0 0
\(303\) 329.033 569.902i 1.08592 1.88087i
\(304\) 0 0
\(305\) −100.747 174.500i −0.330319 0.572130i
\(306\) 0 0
\(307\) 333.745i 1.08712i 0.839371 + 0.543559i \(0.182924\pi\)
−0.839371 + 0.543559i \(0.817076\pi\)
\(308\) 0 0
\(309\) −1151.50 −3.72654
\(310\) 0 0
\(311\) −215.654 + 124.508i −0.693421 + 0.400347i −0.804892 0.593421i \(-0.797777\pi\)
0.111471 + 0.993768i \(0.464444\pi\)
\(312\) 0 0
\(313\) −34.5147 19.9271i −0.110271 0.0636648i 0.443850 0.896101i \(-0.353612\pi\)
−0.554121 + 0.832436i \(0.686946\pi\)
\(314\) 0 0
\(315\) 1050.58 + 113.819i 3.33517 + 0.361330i
\(316\) 0 0
\(317\) 221.206 383.140i 0.697811 1.20864i −0.271413 0.962463i \(-0.587491\pi\)
0.969224 0.246181i \(-0.0791756\pi\)
\(318\) 0 0
\(319\) 4.77650 + 8.27315i 0.0149734 + 0.0259346i
\(320\) 0 0
\(321\) 570.609i 1.77760i
\(322\) 0 0
\(323\) 278.255 0.861470
\(324\) 0 0
\(325\) −203.457 + 117.466i −0.626021 + 0.361433i
\(326\) 0 0
\(327\) −75.5027 43.5915i −0.230895 0.133307i
\(328\) 0 0
\(329\) 29.4535 + 66.7274i 0.0895245 + 0.202819i
\(330\) 0 0
\(331\) 71.9641 124.646i 0.217414 0.376573i −0.736602 0.676326i \(-0.763571\pi\)
0.954017 + 0.299753i \(0.0969044\pi\)
\(332\) 0 0
\(333\) 125.327 + 217.073i 0.376359 + 0.651872i
\(334\) 0 0
\(335\) 621.189i 1.85430i
\(336\) 0 0
\(337\) −428.372 −1.27113 −0.635567 0.772046i \(-0.719234\pi\)
−0.635567 + 0.772046i \(0.719234\pi\)
\(338\) 0 0
\(339\) −566.930 + 327.317i −1.67236 + 0.965538i
\(340\) 0 0
\(341\) 64.4139 + 37.1894i 0.188897 + 0.109060i
\(342\) 0 0
\(343\) −109.118 + 325.180i −0.318129 + 0.948047i
\(344\) 0 0
\(345\) −85.0632 + 147.334i −0.246560 + 0.427054i
\(346\) 0 0
\(347\) 122.803 + 212.700i 0.353898 + 0.612969i 0.986929 0.161158i \(-0.0515228\pi\)
−0.633031 + 0.774126i \(0.718189\pi\)
\(348\) 0 0
\(349\) 675.578i 1.93575i −0.251428 0.967876i \(-0.580900\pi\)
0.251428 0.967876i \(-0.419100\pi\)
\(350\) 0 0
\(351\) −1367.25 −3.89530
\(352\) 0 0
\(353\) −492.343 + 284.254i −1.39474 + 0.805252i −0.993835 0.110868i \(-0.964637\pi\)
−0.400903 + 0.916121i \(0.631304\pi\)
\(354\) 0 0
\(355\) −337.144 194.650i −0.949701 0.548310i
\(356\) 0 0
\(357\) 752.765 332.272i 2.10859 0.930733i
\(358\) 0 0
\(359\) 336.956 583.625i 0.938596 1.62570i 0.170504 0.985357i \(-0.445460\pi\)
0.768092 0.640339i \(-0.221206\pi\)
\(360\) 0 0
\(361\) −88.1931 152.755i −0.244302 0.423144i
\(362\) 0 0
\(363\) 526.462i 1.45031i
\(364\) 0 0
\(365\) 113.742 0.311621
\(366\) 0 0
\(367\) 37.3366 21.5563i 0.101735 0.0587366i −0.448269 0.893899i \(-0.647959\pi\)
0.550004 + 0.835162i \(0.314626\pi\)
\(368\) 0 0
\(369\) 233.123 + 134.594i 0.631771 + 0.364753i
\(370\) 0 0
\(371\) 24.2032 223.402i 0.0652377 0.602161i
\(372\) 0 0
\(373\) −316.582 + 548.337i −0.848746 + 1.47007i 0.0335811 + 0.999436i \(0.489309\pi\)
−0.882328 + 0.470636i \(0.844025\pi\)
\(374\) 0 0
\(375\) 185.603 + 321.473i 0.494940 + 0.857261i
\(376\) 0 0
\(377\) 28.1354i 0.0746297i
\(378\) 0 0
\(379\) −611.641 −1.61383 −0.806914 0.590669i \(-0.798864\pi\)
−0.806914 + 0.590669i \(0.798864\pi\)
\(380\) 0 0
\(381\) −137.926 + 79.6316i −0.362010 + 0.209007i
\(382\) 0 0
\(383\) −555.198 320.544i −1.44960 0.836929i −0.451145 0.892450i \(-0.648984\pi\)
−0.998457 + 0.0555219i \(0.982318\pi\)
\(384\) 0 0
\(385\) −140.972 + 192.732i −0.366161 + 0.500602i
\(386\) 0 0
\(387\) −588.731 + 1019.71i −1.52127 + 2.63492i
\(388\) 0 0
\(389\) 177.180 + 306.884i 0.455475 + 0.788905i 0.998715 0.0506717i \(-0.0161362\pi\)
−0.543241 + 0.839577i \(0.682803\pi\)
\(390\) 0 0
\(391\) 96.2843i 0.246251i
\(392\) 0 0
\(393\) 1048.97 2.66913
\(394\) 0 0
\(395\) 163.805 94.5726i 0.414695 0.239424i
\(396\) 0 0
\(397\) 271.796 + 156.922i 0.684625 + 0.395268i 0.801595 0.597867i \(-0.203985\pi\)
−0.116970 + 0.993135i \(0.537318\pi\)
\(398\) 0 0
\(399\) 440.636 + 322.299i 1.10435 + 0.807768i
\(400\) 0 0
\(401\) −161.060 + 278.963i −0.401645 + 0.695669i −0.993925 0.110063i \(-0.964895\pi\)
0.592280 + 0.805732i \(0.298228\pi\)
\(402\) 0 0
\(403\) 109.530 + 189.711i 0.271786 + 0.470747i
\(404\) 0 0
\(405\) 1745.72i 4.31041i
\(406\) 0 0
\(407\) −56.6398 −0.139164
\(408\) 0 0
\(409\) 413.847 238.935i 1.01185 0.584192i 0.100117 0.994976i \(-0.468078\pi\)
0.911733 + 0.410784i \(0.134745\pi\)
\(410\) 0 0
\(411\) 502.594 + 290.173i 1.22286 + 0.706017i
\(412\) 0 0
\(413\) 460.344 + 49.8733i 1.11463 + 0.120759i
\(414\) 0 0
\(415\) 200.023 346.450i 0.481984 0.834820i
\(416\) 0 0
\(417\) −254.162 440.221i −0.609500 1.05569i
\(418\) 0 0
\(419\) 194.885i 0.465119i 0.972582 + 0.232560i \(0.0747101\pi\)
−0.972582 + 0.232560i \(0.925290\pi\)
\(420\) 0 0
\(421\) 290.331 0.689621 0.344811 0.938672i \(-0.387943\pi\)
0.344811 + 0.938672i \(0.387943\pi\)
\(422\) 0 0
\(423\) 216.089 124.759i 0.510850 0.294939i
\(424\) 0 0
\(425\) −261.445 150.945i −0.615165 0.355166i
\(426\) 0 0
\(427\) −90.3483 204.685i −0.211589 0.479356i
\(428\) 0 0
\(429\) 247.495 428.673i 0.576911 0.999239i
\(430\) 0 0
\(431\) −191.169 331.115i −0.443549 0.768249i 0.554401 0.832249i \(-0.312947\pi\)
−0.997950 + 0.0640009i \(0.979614\pi\)
\(432\) 0 0
\(433\) 295.254i 0.681879i 0.940085 + 0.340940i \(0.110745\pi\)
−0.940085 + 0.340940i \(0.889255\pi\)
\(434\) 0 0
\(435\) −63.8819 −0.146855
\(436\) 0 0
\(437\) −55.3233 + 31.9409i −0.126598 + 0.0730913i
\(438\) 0 0
\(439\) −42.5045 24.5400i −0.0968212 0.0558997i 0.450808 0.892621i \(-0.351136\pi\)
−0.547629 + 0.836721i \(0.684469\pi\)
\(440\) 0 0
\(441\) 1146.16 + 251.297i 2.59899 + 0.569835i
\(442\) 0 0
\(443\) 316.862 548.821i 0.715264 1.23887i −0.247594 0.968864i \(-0.579640\pi\)
0.962858 0.270010i \(-0.0870269\pi\)
\(444\) 0 0
\(445\) 433.589 + 750.998i 0.974357 + 1.68764i
\(446\) 0 0
\(447\) 729.177i 1.63127i
\(448\) 0 0
\(449\) −27.3296 −0.0608677 −0.0304339 0.999537i \(-0.509689\pi\)
−0.0304339 + 0.999537i \(0.509689\pi\)
\(450\) 0 0
\(451\) −52.6783 + 30.4138i −0.116803 + 0.0674364i
\(452\) 0 0
\(453\) −1448.45 836.263i −3.19746 1.84605i
\(454\) 0 0
\(455\) −643.380 + 283.989i −1.41402 + 0.624152i
\(456\) 0 0
\(457\) −169.555 + 293.677i −0.371017 + 0.642620i −0.989722 0.143003i \(-0.954324\pi\)
0.618705 + 0.785623i \(0.287658\pi\)
\(458\) 0 0
\(459\) −878.469 1521.55i −1.91388 3.31493i
\(460\) 0 0
\(461\) 580.237i 1.25865i 0.777143 + 0.629324i \(0.216668\pi\)
−0.777143 + 0.629324i \(0.783332\pi\)
\(462\) 0 0
\(463\) 433.685 0.936684 0.468342 0.883547i \(-0.344852\pi\)
0.468342 + 0.883547i \(0.344852\pi\)
\(464\) 0 0
\(465\) −430.742 + 248.689i −0.926327 + 0.534815i
\(466\) 0 0
\(467\) 86.6558 + 50.0308i 0.185558 + 0.107132i 0.589902 0.807475i \(-0.299167\pi\)
−0.404343 + 0.914607i \(0.632500\pi\)
\(468\) 0 0
\(469\) −74.2938 + 685.751i −0.158409 + 1.46216i
\(470\) 0 0
\(471\) −618.460 + 1071.20i −1.31308 + 2.27432i
\(472\) 0 0
\(473\) −133.034 230.422i −0.281256 0.487150i
\(474\) 0 0
\(475\) 200.296i 0.421675i
\(476\) 0 0
\(477\) −768.715 −1.61156
\(478\) 0 0
\(479\) −418.996 + 241.907i −0.874730 + 0.505026i −0.868917 0.494957i \(-0.835184\pi\)
−0.00581309 + 0.999983i \(0.501850\pi\)
\(480\) 0 0
\(481\) −144.466 83.4075i −0.300345 0.173404i
\(482\) 0 0
\(483\) −111.525 + 152.473i −0.230901 + 0.315679i
\(484\) 0 0
\(485\) −413.154 + 715.603i −0.851863 + 1.47547i
\(486\) 0 0
\(487\) 114.763 + 198.776i 0.235654 + 0.408164i 0.959462 0.281836i \(-0.0909436\pi\)
−0.723809 + 0.690001i \(0.757610\pi\)
\(488\) 0 0
\(489\) 998.840i 2.04262i
\(490\) 0 0
\(491\) −221.445 −0.451008 −0.225504 0.974242i \(-0.572403\pi\)
−0.225504 + 0.974242i \(0.572403\pi\)
\(492\) 0 0
\(493\) −31.3107 + 18.0772i −0.0635105 + 0.0366678i
\(494\) 0 0
\(495\) 707.431 + 408.436i 1.42915 + 0.825122i
\(496\) 0 0
\(497\) −348.904 255.203i −0.702020 0.513486i
\(498\) 0 0
\(499\) 256.703 444.622i 0.514435 0.891027i −0.485425 0.874278i \(-0.661335\pi\)
0.999860 0.0167486i \(-0.00533150\pi\)
\(500\) 0 0
\(501\) 692.148 + 1198.83i 1.38153 + 2.39288i
\(502\) 0 0
\(503\) 360.553i 0.716806i −0.933567 0.358403i \(-0.883321\pi\)
0.933567 0.358403i \(-0.116679\pi\)
\(504\) 0 0
\(505\) −722.747 −1.43118
\(506\) 0 0
\(507\) 422.441 243.896i 0.833217 0.481058i
\(508\) 0 0
\(509\) 163.560 + 94.4312i 0.321335 + 0.185523i 0.651988 0.758230i \(-0.273935\pi\)
−0.330652 + 0.943753i \(0.607269\pi\)
\(510\) 0 0
\(511\) 125.563 + 13.6034i 0.245720 + 0.0266212i
\(512\) 0 0
\(513\) 582.838 1009.51i 1.13614 1.96785i
\(514\) 0 0
\(515\) 632.341 + 1095.25i 1.22785 + 2.12669i
\(516\) 0 0
\(517\) 56.3831i 0.109058i
\(518\) 0 0
\(519\) 1239.66 2.38856
\(520\) 0 0
\(521\) −409.657 + 236.516i −0.786291 + 0.453965i −0.838655 0.544663i \(-0.816658\pi\)
0.0523644 + 0.998628i \(0.483324\pi\)
\(522\) 0 0
\(523\) −362.994 209.575i −0.694061 0.400716i 0.111071 0.993812i \(-0.464572\pi\)
−0.805131 + 0.593096i \(0.797905\pi\)
\(524\) 0 0
\(525\) −239.178 541.862i −0.455578 1.03212i
\(526\) 0 0
\(527\) −140.747 + 243.782i −0.267073 + 0.462584i
\(528\) 0 0
\(529\) 253.448 + 438.984i 0.479107 + 0.829837i
\(530\) 0 0
\(531\) 1584.02i 2.98309i
\(532\) 0 0
\(533\) −179.149 −0.336114
\(534\) 0 0
\(535\) 542.733 313.347i 1.01445 0.585695i
\(536\) 0 0
\(537\) −885.191 511.065i −1.64840 0.951705i
\(538\) 0 0
\(539\) −178.674 + 195.903i −0.331492 + 0.363456i
\(540\) 0 0
\(541\) 309.243 535.625i 0.571614 0.990065i −0.424786 0.905294i \(-0.639651\pi\)
0.996400 0.0847712i \(-0.0270159\pi\)
\(542\) 0 0
\(543\) 494.864 + 857.129i 0.911352 + 1.57851i
\(544\) 0 0
\(545\) 95.7522i 0.175692i
\(546\) 0 0
\(547\) −255.031 −0.466236 −0.233118 0.972448i \(-0.574893\pi\)
−0.233118 + 0.972448i \(0.574893\pi\)
\(548\) 0 0
\(549\) −662.851 + 382.697i −1.20738 + 0.697081i
\(550\) 0 0
\(551\) −20.7737 11.9937i −0.0377018 0.0217672i
\(552\) 0 0
\(553\) 192.140 84.8108i 0.347450 0.153365i
\(554\) 0 0
\(555\) 189.378 328.013i 0.341222 0.591014i
\(556\) 0 0
\(557\) −244.130 422.845i −0.438294 0.759148i 0.559264 0.828990i \(-0.311084\pi\)
−0.997558 + 0.0698419i \(0.977751\pi\)
\(558\) 0 0
\(559\) 783.621i 1.40183i
\(560\) 0 0
\(561\) 636.069 1.13381
\(562\) 0 0
\(563\) −42.5152 + 24.5462i −0.0755155 + 0.0435989i −0.537282 0.843402i \(-0.680549\pi\)
0.461767 + 0.887001i \(0.347216\pi\)
\(564\) 0 0
\(565\) 622.654 + 359.489i 1.10204 + 0.636264i
\(566\) 0 0
\(567\) 208.786 1927.15i 0.368230 3.39886i
\(568\) 0 0
\(569\) 304.056 526.641i 0.534370 0.925556i −0.464824 0.885403i \(-0.653882\pi\)
0.999194 0.0401523i \(-0.0127843\pi\)
\(570\) 0 0
\(571\) 150.396 + 260.494i 0.263391 + 0.456207i 0.967141 0.254241i \(-0.0818257\pi\)
−0.703750 + 0.710448i \(0.748492\pi\)
\(572\) 0 0
\(573\) 799.259i 1.39487i
\(574\) 0 0
\(575\) 69.3082 0.120536
\(576\) 0 0
\(577\) −150.719 + 87.0176i −0.261211 + 0.150810i −0.624887 0.780715i \(-0.714855\pi\)
0.363676 + 0.931526i \(0.381522\pi\)
\(578\) 0 0
\(579\) −214.907 124.077i −0.371170 0.214295i
\(580\) 0 0
\(581\) 262.247 358.535i 0.451372 0.617100i
\(582\) 0 0
\(583\) 86.8523 150.433i 0.148975 0.258032i
\(584\) 0 0
\(585\) 1202.92 + 2083.52i 2.05627 + 3.56157i
\(586\) 0 0
\(587\) 477.592i 0.813614i −0.913514 0.406807i \(-0.866642\pi\)
0.913514 0.406807i \(-0.133358\pi\)
\(588\) 0 0
\(589\) −186.764 −0.317086
\(590\) 0 0
\(591\) −1023.56 + 590.952i −1.73191 + 0.999918i
\(592\) 0 0
\(593\) 382.387 + 220.771i 0.644834 + 0.372295i 0.786474 0.617623i \(-0.211904\pi\)
−0.141640 + 0.989918i \(0.545238\pi\)
\(594\) 0 0
\(595\) −729.416 533.525i −1.22591 0.896680i
\(596\) 0 0
\(597\) 864.695 1497.70i 1.44840 2.50870i
\(598\) 0 0
\(599\) −146.046 252.959i −0.243816 0.422302i 0.717982 0.696062i \(-0.245066\pi\)
−0.961798 + 0.273759i \(0.911733\pi\)
\(600\) 0 0
\(601\) 614.010i 1.02165i −0.859685 0.510824i \(-0.829340\pi\)
0.859685 0.510824i \(-0.170660\pi\)
\(602\) 0 0
\(603\) 2359.64 3.91316
\(604\) 0 0
\(605\) 500.742 289.104i 0.827673 0.477857i
\(606\) 0 0
\(607\) −281.659 162.616i −0.464019 0.267901i 0.249714 0.968320i \(-0.419663\pi\)
−0.713732 + 0.700418i \(0.752997\pi\)
\(608\) 0 0
\(609\) −70.5213 7.64023i −0.115799 0.0125455i
\(610\) 0 0
\(611\) −83.0294 + 143.811i −0.135891 + 0.235370i
\(612\) 0 0
\(613\) −278.468 482.321i −0.454271 0.786820i 0.544375 0.838842i \(-0.316767\pi\)
−0.998646 + 0.0520217i \(0.983434\pi\)
\(614\) 0 0
\(615\) 406.761i 0.661399i
\(616\) 0 0
\(617\) 277.944 0.450476 0.225238 0.974304i \(-0.427684\pi\)
0.225238 + 0.974304i \(0.427684\pi\)
\(618\) 0 0
\(619\) 111.665 64.4696i 0.180395 0.104151i −0.407083 0.913391i \(-0.633454\pi\)
0.587478 + 0.809240i \(0.300121\pi\)
\(620\) 0 0
\(621\) 349.319 + 201.679i 0.562510 + 0.324765i
\(622\) 0 0
\(623\) 388.834 + 880.908i 0.624132 + 1.41398i
\(624\) 0 0
\(625\) 388.113 672.231i 0.620981 1.07557i
\(626\) 0 0
\(627\) 211.006 + 365.474i 0.336533 + 0.582893i
\(628\) 0 0
\(629\) 214.360i 0.340795i
\(630\) 0 0
\(631\) 279.339 0.442692 0.221346 0.975195i \(-0.428955\pi\)
0.221346 + 0.975195i \(0.428955\pi\)
\(632\) 0 0
\(633\) −1541.49 + 889.979i −2.43521 + 1.40597i
\(634\) 0 0
\(635\) 151.483 + 87.4585i 0.238555 + 0.137730i
\(636\) 0 0
\(637\) −744.213 + 236.557i −1.16831 + 0.371361i
\(638\) 0 0
\(639\) −739.394 + 1280.67i −1.15711 + 2.00417i
\(640\) 0 0
\(641\) 441.133 + 764.064i 0.688194 + 1.19199i 0.972421 + 0.233231i \(0.0749297\pi\)
−0.284227 + 0.958757i \(0.591737\pi\)
\(642\) 0 0
\(643\) 575.210i 0.894572i −0.894391 0.447286i \(-0.852391\pi\)
0.894391 0.447286i \(-0.147609\pi\)
\(644\) 0 0
\(645\) 1779.22 2.75849
\(646\) 0 0
\(647\) 406.207 234.524i 0.627832 0.362479i −0.152080 0.988368i \(-0.548597\pi\)
0.779912 + 0.625889i \(0.215264\pi\)
\(648\) 0 0
\(649\) 309.983 + 178.969i 0.477632 + 0.275761i
\(650\) 0 0
\(651\) −505.253 + 223.019i −0.776119 + 0.342580i
\(652\) 0 0
\(653\) −412.463 + 714.407i −0.631644 + 1.09404i 0.355572 + 0.934649i \(0.384286\pi\)
−0.987216 + 0.159390i \(0.949047\pi\)
\(654\) 0 0
\(655\) −576.035 997.722i −0.879443 1.52324i
\(656\) 0 0
\(657\) 432.056i 0.657620i
\(658\) 0 0
\(659\) 888.926 1.34890 0.674451 0.738320i \(-0.264381\pi\)
0.674451 + 0.738320i \(0.264381\pi\)
\(660\) 0 0
\(661\) −131.019 + 75.6439i −0.198214 + 0.114439i −0.595822 0.803117i \(-0.703174\pi\)
0.397608 + 0.917555i \(0.369840\pi\)
\(662\) 0 0
\(663\) 1622.36 + 936.672i 2.44700 + 1.41278i
\(664\) 0 0
\(665\) 64.5809 596.098i 0.0971141 0.896388i
\(666\) 0 0
\(667\) 4.15017 7.18831i 0.00622215 0.0107771i
\(668\) 0 0
\(669\) −763.666 1322.71i −1.14150 1.97714i
\(670\) 0 0
\(671\) 172.954i 0.257756i
\(672\) 0 0
\(673\) −904.158 −1.34347 −0.671737 0.740790i \(-0.734452\pi\)
−0.671737 + 0.740790i \(0.734452\pi\)
\(674\) 0 0
\(675\) −1095.26 + 632.347i −1.62260 + 0.936810i
\(676\) 0 0
\(677\) −762.576 440.273i −1.12640 0.650330i −0.183376 0.983043i \(-0.558703\pi\)
−0.943028 + 0.332713i \(0.892036\pi\)
\(678\) 0 0
\(679\) −541.679 + 740.564i −0.797760 + 1.09067i
\(680\) 0 0
\(681\) −875.501 + 1516.41i −1.28561 + 2.22674i
\(682\) 0 0
\(683\) 272.776 + 472.461i 0.399379 + 0.691744i 0.993649 0.112521i \(-0.0358926\pi\)
−0.594271 + 0.804265i \(0.702559\pi\)
\(684\) 0 0
\(685\) 637.388i 0.930493i
\(686\) 0 0
\(687\) −1139.78 −1.65907
\(688\) 0 0
\(689\) 443.052 255.796i 0.643037 0.371257i
\(690\) 0 0
\(691\) −815.732 470.963i −1.18051 0.681568i −0.224377 0.974502i \(-0.572035\pi\)
−0.956132 + 0.292935i \(0.905368\pi\)
\(692\) 0 0
\(693\) 732.107 + 535.493i 1.05643 + 0.772718i
\(694\) 0 0
\(695\) −279.143 + 483.490i −0.401645 + 0.695669i
\(696\) 0 0
\(697\) −115.105 199.367i −0.165143 0.286036i
\(698\) 0 0
\(699\) 1422.67i 2.03530i
\(700\) 0 0
\(701\) −304.580 −0.434494 −0.217247 0.976117i \(-0.569708\pi\)
−0.217247 + 0.976117i \(0.569708\pi\)
\(702\) 0 0
\(703\) 123.167 71.1107i 0.175203 0.101153i
\(704\) 0 0
\(705\) −326.526 188.520i −0.463157 0.267404i
\(706\) 0 0
\(707\) −797.864 86.4400i −1.12852 0.122263i
\(708\) 0 0
\(709\) 321.938 557.614i 0.454074 0.786479i −0.544561 0.838722i \(-0.683304\pi\)
0.998634 + 0.0522425i \(0.0166369\pi\)
\(710\) 0 0
\(711\) −359.242 622.225i −0.505262 0.875140i
\(712\) 0 0
\(713\) 64.6257i 0.0906391i
\(714\) 0 0
\(715\) −543.641 −0.760338
\(716\) 0 0
\(717\) −600.902 + 346.931i −0.838079 + 0.483865i
\(718\) 0 0
\(719\) 628.047 + 362.603i 0.873500 + 0.504316i 0.868510 0.495672i \(-0.165078\pi\)
0.00499056 + 0.999988i \(0.498411\pi\)
\(720\) 0 0
\(721\) 567.071 + 1284.71i 0.786506 + 1.78184i
\(722\) 0 0
\(723\) −417.411 + 722.977i −0.577332 + 0.999968i
\(724\) 0 0
\(725\) 13.0125 + 22.5383i 0.0179483 + 0.0310873i
\(726\) 0 0
\(727\) 1090.68i 1.50025i −0.661295 0.750126i \(-0.729993\pi\)
0.661295 0.750126i \(-0.270007\pi\)
\(728\) 0 0
\(729\) −2199.30 −3.01688
\(730\) 0 0
\(731\) 872.058 503.483i 1.19297 0.688759i
\(732\) 0 0
\(733\) −204.559 118.102i −0.279071 0.161122i 0.353932 0.935271i \(-0.384845\pi\)
−0.633003 + 0.774149i \(0.718178\pi\)
\(734\) 0 0
\(735\) −537.106 1689.75i −0.730757 2.29898i
\(736\) 0 0
\(737\) −266.601 + 461.766i −0.361738 + 0.626548i
\(738\) 0 0
\(739\) 0.140534 + 0.243412i 0.000190168 + 0.000329381i 0.866120 0.499835i \(-0.166606\pi\)
−0.865930 + 0.500165i \(0.833273\pi\)
\(740\) 0 0
\(741\) 1242.91i 1.67734i
\(742\) 0 0
\(743\) −172.285 −0.231878 −0.115939 0.993256i \(-0.536988\pi\)
−0.115939 + 0.993256i \(0.536988\pi\)
\(744\) 0 0
\(745\) 693.554 400.424i 0.930945 0.537481i
\(746\) 0 0
\(747\) −1316.02 759.804i −1.76174 1.01714i
\(748\) 0 0
\(749\) 636.617 281.003i 0.849955 0.375172i
\(750\) 0 0
\(751\) 25.4735 44.1215i 0.0339195 0.0587503i −0.848567 0.529087i \(-0.822534\pi\)
0.882487 + 0.470337i \(0.155868\pi\)
\(752\) 0 0
\(753\) −608.606 1054.14i −0.808241 1.39991i
\(754\) 0 0
\(755\) 1836.92i 2.43300i
\(756\) 0 0
\(757\) −472.598 −0.624304 −0.312152 0.950032i \(-0.601050\pi\)
−0.312152 + 0.950032i \(0.601050\pi\)
\(758\) 0 0
\(759\) −126.465 + 73.0145i −0.166620 + 0.0961982i
\(760\) 0 0
\(761\) −370.248 213.763i −0.486528 0.280897i 0.236605 0.971606i \(-0.423965\pi\)
−0.723133 + 0.690709i \(0.757299\pi\)
\(762\) 0 0
\(763\) −11.4519 + 105.704i −0.0150090 + 0.138537i
\(764\) 0 0
\(765\) −1545.77 + 2677.35i −2.02062 + 3.49981i
\(766\) 0 0
\(767\) 527.097 + 912.958i 0.687219 + 1.19030i
\(768\) 0 0
\(769\) 199.651i 0.259625i −0.991539 0.129812i \(-0.958563\pi\)
0.991539 0.129812i \(-0.0414375\pi\)
\(770\) 0 0
\(771\) −57.7849 −0.0749480
\(772\) 0 0
\(773\) −36.7213 + 21.2011i −0.0475049 + 0.0274270i −0.523564 0.851986i \(-0.675398\pi\)
0.476059 + 0.879413i \(0.342065\pi\)
\(774\) 0 0
\(775\) 175.481 + 101.314i 0.226427 + 0.130728i
\(776\) 0 0
\(777\) 248.291 339.454i 0.319550 0.436878i
\(778\) 0 0
\(779\) 76.3685 132.274i 0.0980340 0.169800i
\(780\) 0 0
\(781\) −167.079 289.389i −0.213929 0.370537i
\(782\) 0 0
\(783\) 151.460i 0.193435i
\(784\) 0 0
\(785\) 1358.50 1.73057
\(786\) 0 0
\(787\) 524.104 302.591i 0.665951 0.384487i −0.128589 0.991698i \(-0.541045\pi\)
0.794541 + 0.607211i \(0.207712\pi\)
\(788\) 0 0
\(789\) −0.415212 0.239723i −0.000526251 0.000303831i
\(790\) 0 0
\(791\) 644.373