Properties

Label 224.3.o.d.79.2
Level 224
Weight 3
Character 224.79
Analytic conductor 6.104
Analytic rank 0
Dimension 12
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.o (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.10355792167\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{23}]\)
Coefficient ring index: \( 2^{6} \)
Twist minimal: no (minimal twist has level 56)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 79.2
Root \(0.121721 + 0.507075i\) of \(x^{12} - 3 x^{11} - 4 x^{10} + 3 x^{9} + 86 x^{8} - 163 x^{7} + 155 x^{6} - 166 x^{5} + 164 x^{4} - 116 x^{3} + 60 x^{2} - 20 x + 4\)
Character \(\chi\) \(=\) 224.79
Dual form 224.3.o.d.207.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.99052 - 3.44767i) q^{3} +(1.63031 + 0.941260i) q^{5} +(5.14749 - 4.74377i) q^{7} +(-3.42430 + 5.93106i) q^{9} +O(q^{10})\) \(q+(-1.99052 - 3.44767i) q^{3} +(1.63031 + 0.941260i) q^{5} +(5.14749 - 4.74377i) q^{7} +(-3.42430 + 5.93106i) q^{9} +(-3.93973 - 6.82381i) q^{11} -11.4863i q^{13} -7.49437i q^{15} +(1.44921 + 2.51011i) q^{17} +(-15.0223 + 26.0194i) q^{19} +(-26.6011 - 8.30431i) q^{21} +(-33.3838 - 19.2741i) q^{23} +(-10.7281 - 18.5815i) q^{25} -8.56478 q^{27} -27.8701i q^{29} +(19.4709 - 11.2416i) q^{31} +(-15.6842 + 27.1658i) q^{33} +(12.8571 - 2.88869i) q^{35} +(39.4520 + 22.7776i) q^{37} +(-39.6011 + 22.8637i) q^{39} -40.6313 q^{41} +47.2806 q^{43} +(-11.1653 + 6.44632i) q^{45} +(71.5172 + 41.2905i) q^{47} +(3.99327 - 48.8370i) q^{49} +(5.76936 - 9.99283i) q^{51} +(23.2823 - 13.4420i) q^{53} -14.8332i q^{55} +119.609 q^{57} +(-5.20555 - 9.01627i) q^{59} +(19.1932 + 11.0812i) q^{61} +(10.5091 + 46.7742i) q^{63} +(10.8116 - 18.7263i) q^{65} +(-29.6549 - 51.3639i) q^{67} +153.462i q^{69} -38.2541i q^{71} +(-6.98890 - 12.1051i) q^{73} +(-42.7087 + 73.9737i) q^{75} +(-52.6503 - 16.4363i) q^{77} +(44.3314 + 25.5948i) q^{79} +(47.8670 + 82.9081i) q^{81} +89.4458 q^{83} +5.45635i q^{85} +(-96.0871 + 55.4759i) q^{87} +(-52.6288 + 91.1558i) q^{89} +(-54.4885 - 59.1258i) q^{91} +(-77.5144 - 44.7530i) q^{93} +(-48.9821 + 28.2798i) q^{95} +55.3301 q^{97} +53.9633 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q + 6q^{3} - 40q^{9} + O(q^{10}) \) \( 12q + 6q^{3} - 40q^{9} - 30q^{11} + 30q^{17} - 78q^{19} - 92q^{25} - 156q^{27} - 78q^{33} + 222q^{35} - 232q^{41} + 200q^{43} + 372q^{49} - 10q^{51} + 332q^{57} + 110q^{59} - 32q^{65} - 434q^{67} + 102q^{73} + 60q^{75} - 82q^{81} + 536q^{83} + 214q^{89} + 8q^{91} - 152q^{97} - 504q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(127\) \(129\) \(197\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(-1\)

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
\(3\) −1.99052 3.44767i −0.663505 1.14922i −0.979688 0.200526i \(-0.935735\pi\)
0.316183 0.948698i \(-0.397599\pi\)
\(4\) 0 0
\(5\) 1.63031 + 0.941260i 0.326062 + 0.188252i 0.654091 0.756416i \(-0.273051\pi\)
−0.328029 + 0.944668i \(0.606384\pi\)
\(6\) 0 0
\(7\) 5.14749 4.74377i 0.735355 0.677682i
\(8\) 0 0
\(9\) −3.42430 + 5.93106i −0.380478 + 0.659007i
\(10\) 0 0
\(11\) −3.93973 6.82381i −0.358157 0.620346i 0.629496 0.777004i \(-0.283261\pi\)
−0.987653 + 0.156658i \(0.949928\pi\)
\(12\) 0 0
\(13\) 11.4863i 0.883564i −0.897122 0.441782i \(-0.854346\pi\)
0.897122 0.441782i \(-0.145654\pi\)
\(14\) 0 0
\(15\) 7.49437i 0.499625i
\(16\) 0 0
\(17\) 1.44921 + 2.51011i 0.0852478 + 0.147654i 0.905497 0.424353i \(-0.139498\pi\)
−0.820249 + 0.572007i \(0.806165\pi\)
\(18\) 0 0
\(19\) −15.0223 + 26.0194i −0.790649 + 1.36944i 0.134916 + 0.990857i \(0.456923\pi\)
−0.925566 + 0.378587i \(0.876410\pi\)
\(20\) 0 0
\(21\) −26.6011 8.30431i −1.26672 0.395443i
\(22\) 0 0
\(23\) −33.3838 19.2741i −1.45147 0.838006i −0.452904 0.891559i \(-0.649612\pi\)
−0.998565 + 0.0535530i \(0.982945\pi\)
\(24\) 0 0
\(25\) −10.7281 18.5815i −0.429122 0.743262i
\(26\) 0 0
\(27\) −8.56478 −0.317214
\(28\) 0 0
\(29\) 27.8701i 0.961039i −0.876984 0.480519i \(-0.840448\pi\)
0.876984 0.480519i \(-0.159552\pi\)
\(30\) 0 0
\(31\) 19.4709 11.2416i 0.628095 0.362631i −0.151919 0.988393i \(-0.548545\pi\)
0.780014 + 0.625762i \(0.215212\pi\)
\(32\) 0 0
\(33\) −15.6842 + 27.1658i −0.475278 + 0.823206i
\(34\) 0 0
\(35\) 12.8571 2.88869i 0.367346 0.0825341i
\(36\) 0 0
\(37\) 39.4520 + 22.7776i 1.06627 + 0.615611i 0.927160 0.374666i \(-0.122243\pi\)
0.139109 + 0.990277i \(0.455576\pi\)
\(38\) 0 0
\(39\) −39.6011 + 22.8637i −1.01541 + 0.586249i
\(40\) 0 0
\(41\) −40.6313 −0.991007 −0.495503 0.868606i \(-0.665016\pi\)
−0.495503 + 0.868606i \(0.665016\pi\)
\(42\) 0 0
\(43\) 47.2806 1.09955 0.549774 0.835313i \(-0.314714\pi\)
0.549774 + 0.835313i \(0.314714\pi\)
\(44\) 0 0
\(45\) −11.1653 + 6.44632i −0.248119 + 0.143251i
\(46\) 0 0
\(47\) 71.5172 + 41.2905i 1.52164 + 0.878520i 0.999673 + 0.0255554i \(0.00813541\pi\)
0.521968 + 0.852965i \(0.325198\pi\)
\(48\) 0 0
\(49\) 3.99327 48.8370i 0.0814954 0.996674i
\(50\) 0 0
\(51\) 5.76936 9.99283i 0.113125 0.195938i
\(52\) 0 0
\(53\) 23.2823 13.4420i 0.439288 0.253623i −0.264007 0.964521i \(-0.585044\pi\)
0.703296 + 0.710897i \(0.251711\pi\)
\(54\) 0 0
\(55\) 14.8332i 0.269695i
\(56\) 0 0
\(57\) 119.609 2.09840
\(58\) 0 0
\(59\) −5.20555 9.01627i −0.0882296 0.152818i 0.818533 0.574459i \(-0.194788\pi\)
−0.906763 + 0.421641i \(0.861454\pi\)
\(60\) 0 0
\(61\) 19.1932 + 11.0812i 0.314642 + 0.181659i 0.649002 0.760787i \(-0.275187\pi\)
−0.334360 + 0.942446i \(0.608520\pi\)
\(62\) 0 0
\(63\) 10.5091 + 46.7742i 0.166810 + 0.742447i
\(64\) 0 0
\(65\) 10.8116 18.7263i 0.166333 0.288097i
\(66\) 0 0
\(67\) −29.6549 51.3639i −0.442611 0.766625i 0.555271 0.831669i \(-0.312614\pi\)
−0.997882 + 0.0650444i \(0.979281\pi\)
\(68\) 0 0
\(69\) 153.462i 2.22409i
\(70\) 0 0
\(71\) 38.2541i 0.538791i −0.963030 0.269395i \(-0.913176\pi\)
0.963030 0.269395i \(-0.0868238\pi\)
\(72\) 0 0
\(73\) −6.98890 12.1051i −0.0957383 0.165824i 0.814178 0.580615i \(-0.197188\pi\)
−0.909917 + 0.414791i \(0.863855\pi\)
\(74\) 0 0
\(75\) −42.7087 + 73.9737i −0.569450 + 0.986316i
\(76\) 0 0
\(77\) −52.6503 16.4363i −0.683770 0.213459i
\(78\) 0 0
\(79\) 44.3314 + 25.5948i 0.561157 + 0.323984i 0.753610 0.657322i \(-0.228311\pi\)
−0.192453 + 0.981306i \(0.561644\pi\)
\(80\) 0 0
\(81\) 47.8670 + 82.9081i 0.590951 + 1.02356i
\(82\) 0 0
\(83\) 89.4458 1.07766 0.538830 0.842414i \(-0.318866\pi\)
0.538830 + 0.842414i \(0.318866\pi\)
\(84\) 0 0
\(85\) 5.45635i 0.0641923i
\(86\) 0 0
\(87\) −96.0871 + 55.4759i −1.10445 + 0.637654i
\(88\) 0 0
\(89\) −52.6288 + 91.1558i −0.591335 + 1.02422i 0.402718 + 0.915324i \(0.368066\pi\)
−0.994053 + 0.108898i \(0.965268\pi\)
\(90\) 0 0
\(91\) −54.4885 59.1258i −0.598775 0.649734i
\(92\) 0 0
\(93\) −77.5144 44.7530i −0.833488 0.481215i
\(94\) 0 0
\(95\) −48.9821 + 28.2798i −0.515601 + 0.297683i
\(96\) 0 0
\(97\) 55.3301 0.570413 0.285206 0.958466i \(-0.407938\pi\)
0.285206 + 0.958466i \(0.407938\pi\)
\(98\) 0 0
\(99\) 53.9633 0.545084
\(100\) 0 0
\(101\) −27.2216 + 15.7164i −0.269521 + 0.155608i −0.628670 0.777672i \(-0.716400\pi\)
0.359149 + 0.933280i \(0.383067\pi\)
\(102\) 0 0
\(103\) 69.2701 + 39.9931i 0.672525 + 0.388283i 0.797033 0.603936i \(-0.206402\pi\)
−0.124508 + 0.992219i \(0.539735\pi\)
\(104\) 0 0
\(105\) −35.5516 38.5772i −0.338586 0.367402i
\(106\) 0 0
\(107\) 24.3817 42.2303i 0.227866 0.394676i −0.729309 0.684184i \(-0.760158\pi\)
0.957175 + 0.289508i \(0.0934918\pi\)
\(108\) 0 0
\(109\) 99.6528 57.5346i 0.914246 0.527840i 0.0324509 0.999473i \(-0.489669\pi\)
0.881795 + 0.471633i \(0.156335\pi\)
\(110\) 0 0
\(111\) 181.357i 1.63384i
\(112\) 0 0
\(113\) −55.7570 −0.493425 −0.246712 0.969089i \(-0.579350\pi\)
−0.246712 + 0.969089i \(0.579350\pi\)
\(114\) 0 0
\(115\) −36.2840 62.8457i −0.315513 0.546484i
\(116\) 0 0
\(117\) 68.1262 + 39.3327i 0.582275 + 0.336177i
\(118\) 0 0
\(119\) 19.3672 + 6.04603i 0.162750 + 0.0508070i
\(120\) 0 0
\(121\) 29.4571 51.0212i 0.243447 0.421663i
\(122\) 0 0
\(123\) 80.8772 + 140.083i 0.657538 + 1.13889i
\(124\) 0 0
\(125\) 87.4546i 0.699637i
\(126\) 0 0
\(127\) 35.6964i 0.281074i 0.990075 + 0.140537i \(0.0448828\pi\)
−0.990075 + 0.140537i \(0.955117\pi\)
\(128\) 0 0
\(129\) −94.1127 163.008i −0.729556 1.26363i
\(130\) 0 0
\(131\) −60.6462 + 105.042i −0.462948 + 0.801849i −0.999106 0.0422680i \(-0.986542\pi\)
0.536158 + 0.844117i \(0.319875\pi\)
\(132\) 0 0
\(133\) 46.1030 + 205.197i 0.346639 + 1.54284i
\(134\) 0 0
\(135\) −13.9632 8.06168i −0.103431 0.0597162i
\(136\) 0 0
\(137\) 4.24835 + 7.35836i 0.0310099 + 0.0537107i 0.881114 0.472904i \(-0.156794\pi\)
−0.850104 + 0.526615i \(0.823461\pi\)
\(138\) 0 0
\(139\) 3.05942 0.0220102 0.0110051 0.999939i \(-0.496497\pi\)
0.0110051 + 0.999939i \(0.496497\pi\)
\(140\) 0 0
\(141\) 328.757i 2.33161i
\(142\) 0 0
\(143\) −78.3806 + 45.2530i −0.548116 + 0.316455i
\(144\) 0 0
\(145\) 26.2330 45.4370i 0.180918 0.313358i
\(146\) 0 0
\(147\) −176.323 + 83.4433i −1.19947 + 0.567642i
\(148\) 0 0
\(149\) −27.4740 15.8621i −0.184389 0.106457i 0.404964 0.914333i \(-0.367284\pi\)
−0.589353 + 0.807876i \(0.700617\pi\)
\(150\) 0 0
\(151\) 219.621 126.798i 1.45444 0.839723i 0.455713 0.890127i \(-0.349384\pi\)
0.998729 + 0.0504039i \(0.0160509\pi\)
\(152\) 0 0
\(153\) −19.8502 −0.129740
\(154\) 0 0
\(155\) 42.3249 0.273064
\(156\) 0 0
\(157\) 42.7187 24.6636i 0.272093 0.157093i −0.357745 0.933819i \(-0.616454\pi\)
0.629839 + 0.776726i \(0.283121\pi\)
\(158\) 0 0
\(159\) −92.6875 53.5132i −0.582940 0.336561i
\(160\) 0 0
\(161\) −263.275 + 59.1516i −1.63525 + 0.367402i
\(162\) 0 0
\(163\) 57.8597 100.216i 0.354967 0.614821i −0.632145 0.774850i \(-0.717825\pi\)
0.987112 + 0.160029i \(0.0511587\pi\)
\(164\) 0 0
\(165\) −51.1401 + 29.5258i −0.309940 + 0.178944i
\(166\) 0 0
\(167\) 32.3859i 0.193928i 0.995288 + 0.0969639i \(0.0309131\pi\)
−0.995288 + 0.0969639i \(0.969087\pi\)
\(168\) 0 0
\(169\) 37.0641 0.219314
\(170\) 0 0
\(171\) −102.882 178.197i −0.601649 1.04209i
\(172\) 0 0
\(173\) −179.479 103.622i −1.03745 0.598973i −0.118341 0.992973i \(-0.537758\pi\)
−0.919110 + 0.394000i \(0.871091\pi\)
\(174\) 0 0
\(175\) −143.369 44.7568i −0.819252 0.255753i
\(176\) 0 0
\(177\) −20.7234 + 35.8941i −0.117082 + 0.202791i
\(178\) 0 0
\(179\) 87.0837 + 150.833i 0.486501 + 0.842644i 0.999880 0.0155178i \(-0.00493966\pi\)
−0.513379 + 0.858162i \(0.671606\pi\)
\(180\) 0 0
\(181\) 204.244i 1.12842i −0.825632 0.564209i \(-0.809181\pi\)
0.825632 0.564209i \(-0.190819\pi\)
\(182\) 0 0
\(183\) 88.2291i 0.482126i
\(184\) 0 0
\(185\) 42.8793 + 74.2691i 0.231780 + 0.401455i
\(186\) 0 0
\(187\) 11.4190 19.7783i 0.0610642 0.105766i
\(188\) 0 0
\(189\) −44.0871 + 40.6293i −0.233265 + 0.214970i
\(190\) 0 0
\(191\) −258.518 149.255i −1.35350 0.781442i −0.364759 0.931102i \(-0.618849\pi\)
−0.988737 + 0.149660i \(0.952182\pi\)
\(192\) 0 0
\(193\) 165.381 + 286.448i 0.856896 + 1.48419i 0.874875 + 0.484349i \(0.160943\pi\)
−0.0179791 + 0.999838i \(0.505723\pi\)
\(194\) 0 0
\(195\) −86.0828 −0.441450
\(196\) 0 0
\(197\) 327.309i 1.66146i 0.556672 + 0.830732i \(0.312078\pi\)
−0.556672 + 0.830732i \(0.687922\pi\)
\(198\) 0 0
\(199\) 11.0295 6.36789i 0.0554246 0.0319994i −0.472032 0.881582i \(-0.656479\pi\)
0.527456 + 0.849582i \(0.323146\pi\)
\(200\) 0 0
\(201\) −118.057 + 204.481i −0.587349 + 1.01732i
\(202\) 0 0
\(203\) −132.210 143.461i −0.651278 0.706705i
\(204\) 0 0
\(205\) −66.2416 38.2446i −0.323130 0.186559i
\(206\) 0 0
\(207\) 228.632 132.001i 1.10450 0.637686i
\(208\) 0 0
\(209\) 236.736 1.13271
\(210\) 0 0
\(211\) −120.455 −0.570875 −0.285437 0.958397i \(-0.592139\pi\)
−0.285437 + 0.958397i \(0.592139\pi\)
\(212\) 0 0
\(213\) −131.888 + 76.1454i −0.619191 + 0.357490i
\(214\) 0 0
\(215\) 77.0820 + 44.5033i 0.358521 + 0.206992i
\(216\) 0 0
\(217\) 46.8991 150.231i 0.216125 0.692311i
\(218\) 0 0
\(219\) −27.8230 + 48.1909i −0.127046 + 0.220050i
\(220\) 0 0
\(221\) 28.8320 16.6461i 0.130461 0.0753219i
\(222\) 0 0
\(223\) 372.958i 1.67246i 0.548382 + 0.836228i \(0.315244\pi\)
−0.548382 + 0.836228i \(0.684756\pi\)
\(224\) 0 0
\(225\) 146.944 0.653086
\(226\) 0 0
\(227\) 36.7128 + 63.5885i 0.161730 + 0.280125i 0.935489 0.353355i \(-0.114959\pi\)
−0.773759 + 0.633480i \(0.781626\pi\)
\(228\) 0 0
\(229\) 367.587 + 212.226i 1.60518 + 0.926752i 0.990428 + 0.138034i \(0.0440783\pi\)
0.614755 + 0.788718i \(0.289255\pi\)
\(230\) 0 0
\(231\) 48.1342 + 214.238i 0.208373 + 0.927436i
\(232\) 0 0
\(233\) 41.7070 72.2386i 0.179000 0.310037i −0.762538 0.646943i \(-0.776047\pi\)
0.941538 + 0.336906i \(0.109380\pi\)
\(234\) 0 0
\(235\) 77.7301 + 134.632i 0.330766 + 0.572904i
\(236\) 0 0
\(237\) 203.787i 0.859861i
\(238\) 0 0
\(239\) 112.561i 0.470967i −0.971878 0.235484i \(-0.924333\pi\)
0.971878 0.235484i \(-0.0756674\pi\)
\(240\) 0 0
\(241\) −140.216 242.861i −0.581809 1.00772i −0.995265 0.0971992i \(-0.969012\pi\)
0.413455 0.910524i \(-0.364322\pi\)
\(242\) 0 0
\(243\) 152.019 263.304i 0.625591 1.08356i
\(244\) 0 0
\(245\) 52.4786 75.8608i 0.214198 0.309636i
\(246\) 0 0
\(247\) 298.868 + 172.552i 1.20999 + 0.698589i
\(248\) 0 0
\(249\) −178.043 308.380i −0.715033 1.23847i
\(250\) 0 0
\(251\) 32.9560 0.131299 0.0656493 0.997843i \(-0.479088\pi\)
0.0656493 + 0.997843i \(0.479088\pi\)
\(252\) 0 0
\(253\) 303.740i 1.20055i
\(254\) 0 0
\(255\) 18.8117 10.8609i 0.0737714 0.0425919i
\(256\) 0 0
\(257\) 112.109 194.179i 0.436223 0.755561i −0.561172 0.827700i \(-0.689649\pi\)
0.997395 + 0.0721390i \(0.0229825\pi\)
\(258\) 0 0
\(259\) 311.130 69.9036i 1.20127 0.269898i
\(260\) 0 0
\(261\) 165.300 + 95.4357i 0.633332 + 0.365654i
\(262\) 0 0
\(263\) −147.190 + 84.9804i −0.559659 + 0.323119i −0.753009 0.658011i \(-0.771398\pi\)
0.193350 + 0.981130i \(0.438065\pi\)
\(264\) 0 0
\(265\) 50.6098 0.190980
\(266\) 0 0
\(267\) 419.034 1.56942
\(268\) 0 0
\(269\) −93.9863 + 54.2630i −0.349391 + 0.201721i −0.664417 0.747362i \(-0.731320\pi\)
0.315026 + 0.949083i \(0.397987\pi\)
\(270\) 0 0
\(271\) 16.7690 + 9.68157i 0.0618781 + 0.0357253i 0.530620 0.847610i \(-0.321959\pi\)
−0.468742 + 0.883335i \(0.655293\pi\)
\(272\) 0 0
\(273\) −95.3861 + 305.549i −0.349400 + 1.11923i
\(274\) 0 0
\(275\) −84.5313 + 146.412i −0.307386 + 0.532409i
\(276\) 0 0
\(277\) −112.104 + 64.7231i −0.404707 + 0.233658i −0.688513 0.725224i \(-0.741736\pi\)
0.283806 + 0.958882i \(0.408403\pi\)
\(278\) 0 0
\(279\) 153.978i 0.551892i
\(280\) 0 0
\(281\) 83.3608 0.296658 0.148329 0.988938i \(-0.452611\pi\)
0.148329 + 0.988938i \(0.452611\pi\)
\(282\) 0 0
\(283\) 14.4646 + 25.0535i 0.0511118 + 0.0885282i 0.890449 0.455082i \(-0.150390\pi\)
−0.839338 + 0.543611i \(0.817057\pi\)
\(284\) 0 0
\(285\) 194.999 + 112.583i 0.684208 + 0.395028i
\(286\) 0 0
\(287\) −209.149 + 192.746i −0.728742 + 0.671587i
\(288\) 0 0
\(289\) 140.300 243.006i 0.485466 0.840851i
\(290\) 0 0
\(291\) −110.135 190.760i −0.378472 0.655533i
\(292\) 0 0
\(293\) 214.613i 0.732468i 0.930523 + 0.366234i \(0.119353\pi\)
−0.930523 + 0.366234i \(0.880647\pi\)
\(294\) 0 0
\(295\) 19.5991i 0.0664376i
\(296\) 0 0
\(297\) 33.7429 + 58.4444i 0.113612 + 0.196783i
\(298\) 0 0
\(299\) −221.389 + 383.457i −0.740432 + 1.28247i
\(300\) 0 0
\(301\) 243.376 224.288i 0.808559 0.745144i
\(302\) 0 0
\(303\) 108.370 + 62.5675i 0.357657 + 0.206493i
\(304\) 0 0
\(305\) 20.8606 + 36.1316i 0.0683953 + 0.118464i
\(306\) 0 0
\(307\) 120.542 0.392644 0.196322 0.980539i \(-0.437100\pi\)
0.196322 + 0.980539i \(0.437100\pi\)
\(308\) 0 0
\(309\) 318.427i 1.03051i
\(310\) 0 0
\(311\) 281.771 162.681i 0.906016 0.523089i 0.0268689 0.999639i \(-0.491446\pi\)
0.879147 + 0.476550i \(0.158113\pi\)
\(312\) 0 0
\(313\) −228.378 + 395.562i −0.729642 + 1.26378i 0.227392 + 0.973803i \(0.426980\pi\)
−0.957034 + 0.289974i \(0.906353\pi\)
\(314\) 0 0
\(315\) −26.8936 + 86.1482i −0.0853767 + 0.273486i
\(316\) 0 0
\(317\) −104.980 60.6102i −0.331167 0.191199i 0.325192 0.945648i \(-0.394571\pi\)
−0.656359 + 0.754449i \(0.727904\pi\)
\(318\) 0 0
\(319\) −190.180 + 109.801i −0.596177 + 0.344203i
\(320\) 0 0
\(321\) −194.128 −0.604761
\(322\) 0 0
\(323\) −87.0822 −0.269604
\(324\) 0 0
\(325\) −213.434 + 123.226i −0.656719 + 0.379157i
\(326\) 0 0
\(327\) −396.721 229.047i −1.21321 0.700449i
\(328\) 0 0
\(329\) 564.006 126.719i 1.71430 0.385164i
\(330\) 0 0
\(331\) 60.5842 104.935i 0.183034 0.317024i −0.759878 0.650065i \(-0.774742\pi\)
0.942912 + 0.333041i \(0.108075\pi\)
\(332\) 0 0
\(333\) −270.191 + 155.995i −0.811384 + 0.468453i
\(334\) 0 0
\(335\) 111.652i 0.333290i
\(336\) 0 0
\(337\) −464.021 −1.37692 −0.688459 0.725275i \(-0.741713\pi\)
−0.688459 + 0.725275i \(0.741713\pi\)
\(338\) 0 0
\(339\) 110.985 + 192.232i 0.327390 + 0.567056i
\(340\) 0 0
\(341\) −153.420 88.5773i −0.449913 0.259758i
\(342\) 0 0
\(343\) −211.116 270.331i −0.615499 0.788137i
\(344\) 0 0
\(345\) −144.448 + 250.190i −0.418688 + 0.725190i
\(346\) 0 0
\(347\) −185.593 321.457i −0.534851 0.926388i −0.999171 0.0407208i \(-0.987035\pi\)
0.464320 0.885667i \(-0.346299\pi\)
\(348\) 0 0
\(349\) 207.871i 0.595619i −0.954625 0.297809i \(-0.903744\pi\)
0.954625 0.297809i \(-0.0962560\pi\)
\(350\) 0 0
\(351\) 98.3779i 0.280279i
\(352\) 0 0
\(353\) 307.007 + 531.751i 0.869708 + 1.50638i 0.862296 + 0.506405i \(0.169026\pi\)
0.00741211 + 0.999973i \(0.497641\pi\)
\(354\) 0 0
\(355\) 36.0071 62.3661i 0.101428 0.175679i
\(356\) 0 0
\(357\) −17.7060 78.8065i −0.0495965 0.220746i
\(358\) 0 0
\(359\) −93.5930 54.0359i −0.260705 0.150518i 0.363951 0.931418i \(-0.381427\pi\)
−0.624656 + 0.780900i \(0.714761\pi\)
\(360\) 0 0
\(361\) −270.841 469.110i −0.750252 1.29947i
\(362\) 0 0
\(363\) −234.539 −0.646113
\(364\) 0 0
\(365\) 26.3135i 0.0720917i
\(366\) 0 0
\(367\) 393.881 227.407i 1.07325 0.619639i 0.144179 0.989552i \(-0.453946\pi\)
0.929067 + 0.369913i \(0.120612\pi\)
\(368\) 0 0
\(369\) 139.134 240.987i 0.377056 0.653081i
\(370\) 0 0
\(371\) 56.0794 179.639i 0.151157 0.484201i
\(372\) 0 0
\(373\) −235.344 135.876i −0.630949 0.364279i 0.150171 0.988660i \(-0.452018\pi\)
−0.781119 + 0.624382i \(0.785351\pi\)
\(374\) 0 0
\(375\) −301.515 + 174.080i −0.804039 + 0.464212i
\(376\) 0 0
\(377\) −320.126 −0.849140
\(378\) 0 0
\(379\) −268.351 −0.708051 −0.354026 0.935236i \(-0.615187\pi\)
−0.354026 + 0.935236i \(0.615187\pi\)
\(380\) 0 0
\(381\) 123.069 71.0541i 0.323017 0.186494i
\(382\) 0 0
\(383\) 283.718 + 163.805i 0.740779 + 0.427689i 0.822352 0.568979i \(-0.192661\pi\)
−0.0815738 + 0.996667i \(0.525995\pi\)
\(384\) 0 0
\(385\) −70.3655 76.3539i −0.182767 0.198322i
\(386\) 0 0
\(387\) −161.903 + 280.424i −0.418354 + 0.724610i
\(388\) 0 0
\(389\) 109.380 63.1506i 0.281183 0.162341i −0.352776 0.935708i \(-0.614762\pi\)
0.633959 + 0.773367i \(0.281429\pi\)
\(390\) 0 0
\(391\) 111.729i 0.285753i
\(392\) 0 0
\(393\) 482.869 1.22867
\(394\) 0 0
\(395\) 48.1826 + 83.4548i 0.121981 + 0.211278i
\(396\) 0 0
\(397\) 110.110 + 63.5720i 0.277355 + 0.160131i 0.632225 0.774784i \(-0.282142\pi\)
−0.354870 + 0.934916i \(0.615475\pi\)
\(398\) 0 0
\(399\) 615.685 567.396i 1.54307 1.42205i
\(400\) 0 0
\(401\) −30.0751 + 52.0916i −0.0750003 + 0.129904i −0.901086 0.433640i \(-0.857229\pi\)
0.826086 + 0.563544i \(0.190562\pi\)
\(402\) 0 0
\(403\) −129.124 223.650i −0.320408 0.554962i
\(404\) 0 0
\(405\) 180.221i 0.444991i
\(406\) 0 0
\(407\) 358.950i 0.881941i
\(408\) 0 0
\(409\) 34.8873 + 60.4267i 0.0852991 + 0.147742i 0.905519 0.424306i \(-0.139482\pi\)
−0.820220 + 0.572049i \(0.806149\pi\)
\(410\) 0 0
\(411\) 16.9128 29.2939i 0.0411504 0.0712746i
\(412\) 0 0
\(413\) −69.5666 21.7172i −0.168442 0.0525841i
\(414\) 0 0
\(415\) 145.824 + 84.1918i 0.351384 + 0.202872i
\(416\) 0 0
\(417\) −6.08982 10.5479i −0.0146039 0.0252947i
\(418\) 0 0
\(419\) −714.794 −1.70595 −0.852976 0.521950i \(-0.825205\pi\)
−0.852976 + 0.521950i \(0.825205\pi\)
\(420\) 0 0
\(421\) 303.440i 0.720759i −0.932806 0.360380i \(-0.882647\pi\)
0.932806 0.360380i \(-0.117353\pi\)
\(422\) 0 0
\(423\) −489.793 + 282.782i −1.15790 + 0.668515i
\(424\) 0 0
\(425\) 31.0945 53.8572i 0.0731635 0.126723i
\(426\) 0 0
\(427\) 151.363 34.0078i 0.354481 0.0796435i
\(428\) 0 0
\(429\) 312.035 + 180.154i 0.727355 + 0.419939i
\(430\) 0 0
\(431\) 373.685 215.747i 0.867019 0.500574i 0.000662591 1.00000i \(-0.499789\pi\)
0.866357 + 0.499426i \(0.166456\pi\)
\(432\) 0 0
\(433\) 194.875 0.450057 0.225029 0.974352i \(-0.427752\pi\)
0.225029 + 0.974352i \(0.427752\pi\)
\(434\) 0 0
\(435\) −208.869 −0.480159
\(436\) 0 0
\(437\) 1003.00 579.085i 2.29521 1.32514i
\(438\) 0 0
\(439\) −264.977 152.985i −0.603593 0.348485i 0.166861 0.985980i \(-0.446637\pi\)
−0.770454 + 0.637496i \(0.779970\pi\)
\(440\) 0 0
\(441\) 275.981 + 190.917i 0.625808 + 0.432918i
\(442\) 0 0
\(443\) 125.099 216.677i 0.282390 0.489113i −0.689583 0.724206i \(-0.742206\pi\)
0.971973 + 0.235093i \(0.0755396\pi\)
\(444\) 0 0
\(445\) −171.603 + 99.0748i −0.385624 + 0.222640i
\(446\) 0 0
\(447\) 126.295i 0.282539i
\(448\) 0 0
\(449\) −688.681 −1.53381 −0.766905 0.641761i \(-0.778204\pi\)
−0.766905 + 0.641761i \(0.778204\pi\)
\(450\) 0 0
\(451\) 160.076 + 277.260i 0.354936 + 0.614768i
\(452\) 0 0
\(453\) −874.317 504.787i −1.93006 1.11432i
\(454\) 0 0
\(455\) −33.1805 147.681i −0.0729242 0.324574i
\(456\) 0 0
\(457\) −402.259 + 696.733i −0.880217 + 1.52458i −0.0291166 + 0.999576i \(0.509269\pi\)
−0.851100 + 0.525004i \(0.824064\pi\)
\(458\) 0 0
\(459\) −12.4122 21.4985i −0.0270418 0.0468378i
\(460\) 0 0
\(461\) 693.657i 1.50468i 0.658776 + 0.752339i \(0.271074\pi\)
−0.658776 + 0.752339i \(0.728926\pi\)
\(462\) 0 0
\(463\) 321.194i 0.693724i 0.937916 + 0.346862i \(0.112753\pi\)
−0.937916 + 0.346862i \(0.887247\pi\)
\(464\) 0 0
\(465\) −84.2484 145.922i −0.181179 0.313812i
\(466\) 0 0
\(467\) 375.937 651.142i 0.805005 1.39431i −0.111283 0.993789i \(-0.535496\pi\)
0.916288 0.400521i \(-0.131171\pi\)
\(468\) 0 0
\(469\) −396.307 123.719i −0.845004 0.263792i
\(470\) 0 0
\(471\) −170.064 98.1867i −0.361071 0.208464i
\(472\) 0 0
\(473\) −186.273 322.634i −0.393811 0.682101i
\(474\) 0 0
\(475\) 644.642 1.35714
\(476\) 0 0
\(477\) 184.118i 0.385992i
\(478\) 0 0
\(479\) −625.392 + 361.070i −1.30562 + 0.753800i −0.981362 0.192169i \(-0.938448\pi\)
−0.324257 + 0.945969i \(0.605114\pi\)
\(480\) 0 0
\(481\) 261.631 453.158i 0.543932 0.942117i
\(482\) 0 0
\(483\) 727.988 + 789.943i 1.50722 + 1.63549i
\(484\) 0 0
\(485\) 90.2052 + 52.0800i 0.185990 + 0.107381i
\(486\) 0 0
\(487\) −41.4211 + 23.9145i −0.0850536 + 0.0491057i −0.541924 0.840428i \(-0.682304\pi\)
0.456870 + 0.889533i \(0.348970\pi\)
\(488\) 0 0
\(489\) −460.682 −0.942090
\(490\) 0 0
\(491\) −44.4724 −0.0905752 −0.0452876 0.998974i \(-0.514420\pi\)
−0.0452876 + 0.998974i \(0.514420\pi\)
\(492\) 0 0
\(493\) 69.9571 40.3898i 0.141901 0.0819265i
\(494\) 0 0
\(495\) 87.9769 + 50.7935i 0.177731 + 0.102613i
\(496\) 0 0
\(497\) −181.469 196.913i −0.365128 0.396203i
\(498\) 0 0
\(499\) −250.786 + 434.374i −0.502577 + 0.870489i 0.497418 + 0.867511i \(0.334281\pi\)
−0.999996 + 0.00297862i \(0.999052\pi\)
\(500\) 0 0
\(501\) 111.656 64.4647i 0.222867 0.128672i
\(502\) 0 0
\(503\) 462.733i 0.919946i −0.887933 0.459973i \(-0.847859\pi\)
0.887933 0.459973i \(-0.152141\pi\)
\(504\) 0 0
\(505\) −59.1729 −0.117174
\(506\) 0 0
\(507\) −73.7767 127.785i −0.145516 0.252041i
\(508\) 0 0
\(509\) −408.751 235.992i −0.803046 0.463639i 0.0414889 0.999139i \(-0.486790\pi\)
−0.844535 + 0.535500i \(0.820123\pi\)
\(510\) 0 0
\(511\) −93.3992 29.1573i −0.182777 0.0570592i
\(512\) 0 0
\(513\) 128.663 222.851i 0.250805 0.434407i
\(514\) 0 0
\(515\) 75.2878 + 130.402i 0.146190 + 0.253208i
\(516\) 0 0
\(517\) 650.693i 1.25859i
\(518\) 0 0
\(519\) 825.047i 1.58969i
\(520\) 0 0
\(521\) 45.3709 + 78.5848i 0.0870843 + 0.150834i 0.906277 0.422683i \(-0.138912\pi\)
−0.819193 + 0.573518i \(0.805578\pi\)
\(522\) 0 0
\(523\) −180.256 + 312.213i −0.344658 + 0.596965i −0.985292 0.170882i \(-0.945338\pi\)
0.640634 + 0.767847i \(0.278672\pi\)
\(524\) 0 0
\(525\) 131.072 + 583.379i 0.249660 + 1.11120i
\(526\) 0 0
\(527\) 56.4351 + 32.5828i 0.107087 + 0.0618270i
\(528\) 0 0
\(529\) 478.485 + 828.760i 0.904509 + 1.56665i
\(530\) 0 0
\(531\) 71.3014 0.134278
\(532\) 0 0
\(533\) 466.705i 0.875618i
\(534\) 0 0
\(535\) 79.4994 45.8990i 0.148597 0.0857925i
\(536\) 0 0
\(537\) 346.683 600.472i 0.645592 1.11820i
\(538\) 0 0
\(539\) −348.987 + 165.155i −0.647471 + 0.306410i
\(540\) 0 0
\(541\) 485.969 + 280.574i 0.898278 + 0.518621i 0.876641 0.481145i \(-0.159779\pi\)
0.0216371 + 0.999766i \(0.493112\pi\)
\(542\) 0 0
\(543\) −704.166 + 406.550i −1.29681 + 0.748712i
\(544\) 0 0
\(545\) 216.620 0.397468
\(546\) 0 0
\(547\) −1043.62 −1.90790 −0.953952 0.299960i \(-0.903027\pi\)
−0.953952 + 0.299960i \(0.903027\pi\)
\(548\) 0 0
\(549\) −131.447 + 75.8907i −0.239429 + 0.138234i
\(550\) 0 0
\(551\) 725.165 + 418.674i 1.31609 + 0.759845i
\(552\) 0 0
\(553\) 349.611 78.5494i 0.632208 0.142042i
\(554\) 0 0
\(555\) 170.704 295.667i 0.307574 0.532734i
\(556\) 0 0
\(557\) −42.1273 + 24.3222i −0.0756324 + 0.0436664i −0.537339 0.843366i \(-0.680571\pi\)
0.461707 + 0.887033i \(0.347237\pi\)
\(558\) 0 0
\(559\) 543.081i 0.971522i
\(560\) 0 0
\(561\) −90.9189 −0.162066
\(562\) 0 0
\(563\) 363.015 + 628.761i 0.644787 + 1.11680i 0.984351 + 0.176221i \(0.0563874\pi\)
−0.339563 + 0.940583i \(0.610279\pi\)
\(564\) 0 0
\(565\) −90.9012 52.4818i −0.160887 0.0928882i
\(566\) 0 0
\(567\) 639.692 + 199.698i 1.12820 + 0.352202i
\(568\) 0 0
\(569\) 240.696 416.898i 0.423016 0.732685i −0.573217 0.819404i \(-0.694305\pi\)
0.996233 + 0.0867185i \(0.0276381\pi\)
\(570\) 0 0
\(571\) 55.0633 + 95.3724i 0.0964331 + 0.167027i 0.910206 0.414156i \(-0.135923\pi\)
−0.813773 + 0.581183i \(0.802590\pi\)
\(572\) 0 0
\(573\) 1188.38i 2.07396i
\(574\) 0 0
\(575\) 827.097i 1.43843i
\(576\) 0 0
\(577\) 101.168 + 175.228i 0.175335 + 0.303688i 0.940277 0.340410i \(-0.110566\pi\)
−0.764942 + 0.644099i \(0.777233\pi\)
\(578\) 0 0
\(579\) 658.386 1140.36i 1.13711 1.96953i
\(580\) 0 0
\(581\) 460.421 424.310i 0.792463 0.730310i
\(582\) 0 0
\(583\) −183.452 105.916i −0.314669 0.181674i
\(584\) 0 0
\(585\) 74.0445 + 128.249i 0.126572 + 0.219229i
\(586\) 0 0
\(587\) 568.689 0.968805 0.484403 0.874845i \(-0.339037\pi\)
0.484403 + 0.874845i \(0.339037\pi\)
\(588\) 0 0
\(589\) 675.497i 1.14685i
\(590\) 0 0
\(591\) 1128.45 651.513i 1.90940 1.10239i
\(592\) 0 0
\(593\) 342.686 593.550i 0.577886 1.00093i −0.417835 0.908523i \(-0.637211\pi\)
0.995721 0.0924054i \(-0.0294556\pi\)
\(594\) 0 0
\(595\) 25.8837 + 28.0865i 0.0435019 + 0.0472042i
\(596\) 0 0
\(597\) −43.9088 25.3507i −0.0735491 0.0424636i
\(598\) 0 0
\(599\) 318.077 183.642i 0.531013 0.306580i −0.210416 0.977612i \(-0.567482\pi\)
0.741429 + 0.671032i \(0.234149\pi\)
\(600\) 0 0
\(601\) 412.344 0.686097 0.343049 0.939318i \(-0.388540\pi\)
0.343049 + 0.939318i \(0.388540\pi\)
\(602\) 0 0
\(603\) 406.190 0.673615
\(604\) 0 0
\(605\) 96.0484 55.4535i 0.158758 0.0916588i
\(606\) 0 0
\(607\) −1010.46 583.389i −1.66468 0.961102i −0.970436 0.241359i \(-0.922407\pi\)
−0.694241 0.719743i \(1.25574\pi\)
\(608\) 0 0
\(609\) −231.442 + 741.377i −0.380036 + 1.21737i
\(610\) 0 0
\(611\) 474.276 821.470i 0.776229 1.34447i
\(612\) 0 0
\(613\) 373.900 215.871i 0.609951 0.352155i −0.162995 0.986627i \(-0.552115\pi\)
0.772946 + 0.634471i \(0.218782\pi\)
\(614\) 0 0
\(615\) 304.506i 0.495131i
\(616\) 0 0
\(617\) −333.751 −0.540926 −0.270463 0.962730i \(-0.587177\pi\)
−0.270463 + 0.962730i \(0.587177\pi\)
\(618\) 0 0
\(619\) −488.158 845.514i −0.788624 1.36594i −0.926810 0.375530i \(-0.877461\pi\)
0.138187 0.990406i \(-0.455873\pi\)
\(620\) 0 0
\(621\) 285.925 + 165.079i 0.460426 + 0.265827i
\(622\) 0 0
\(623\) 161.516 + 718.883i 0.259255 + 1.15390i
\(624\) 0 0
\(625\) −185.884 + 321.961i −0.297414 + 0.515137i
\(626\) 0 0
\(627\) −471.226 816.187i −0.751556 1.30173i
\(628\) 0 0
\(629\) 132.038i 0.209918i
\(630\) 0 0
\(631\) 639.885i 1.01408i 0.861922 + 0.507040i \(0.169261\pi\)
−0.861922 + 0.507040i \(0.830739\pi\)
\(632\) 0 0
\(633\) 239.767 + 415.288i 0.378778 + 0.656063i
\(634\) 0 0
\(635\) −33.5995 + 58.1961i −0.0529127 + 0.0916474i
\(636\) 0 0
\(637\) −560.958 45.8681i −0.880625 0.0720064i
\(638\) 0 0
\(639\) 226.888 + 130.994i 0.355067 + 0.204998i
\(640\) 0 0
\(641\) −10.4295 18.0645i −0.0162707 0.0281817i 0.857775 0.514025i \(-0.171846\pi\)
−0.874046 + 0.485843i \(0.838513\pi\)
\(642\) 0 0
\(643\) 69.1348 0.107519 0.0537596 0.998554i \(-0.482880\pi\)
0.0537596 + 0.998554i \(0.482880\pi\)
\(644\) 0 0
\(645\) 354.338i 0.549362i
\(646\) 0 0
\(647\) 310.868 179.480i 0.480476 0.277403i −0.240139 0.970739i \(-0.577193\pi\)
0.720615 + 0.693336i \(0.243860\pi\)
\(648\) 0 0
\(649\) −41.0169 + 71.0433i −0.0632001 + 0.109466i
\(650\) 0 0
\(651\) −611.302 + 137.345i −0.939021 + 0.210976i
\(652\) 0 0
\(653\) −32.1227 18.5460i −0.0491925 0.0284013i 0.475202 0.879877i \(-0.342375\pi\)
−0.524395 + 0.851475i \(0.675708\pi\)
\(654\) 0 0
\(655\) −197.744 + 114.168i −0.301900 + 0.174302i
\(656\) 0 0
\(657\) 95.7284 0.145705
\(658\) 0 0
\(659\) −197.302 −0.299396 −0.149698 0.988732i \(-0.547830\pi\)
−0.149698 + 0.988732i \(0.547830\pi\)
\(660\) 0 0
\(661\) −938.626 + 541.916i −1.42001 + 0.819843i −0.996299 0.0859554i \(-0.972606\pi\)
−0.423710 + 0.905798i \(0.639272\pi\)
\(662\) 0 0
\(663\) −114.781 66.2688i −0.173124 0.0999530i
\(664\) 0 0
\(665\) −117.982 + 377.930i −0.177416 + 0.568316i
\(666\) 0 0
\(667\) −537.173 + 930.411i −0.805357 + 1.39492i
\(668\) 0 0
\(669\) 1285.84 742.378i 1.92203 1.10968i
\(670\) 0 0
\(671\) 174.628i 0.260250i
\(672\) 0 0
\(673\) −286.066 −0.425061 −0.212530 0.977154i \(-0.568170\pi\)
−0.212530 + 0.977154i \(0.568170\pi\)
\(674\) 0 0
\(675\) 91.8834 + 159.147i 0.136124 + 0.235773i
\(676\) 0 0
\(677\) −433.324 250.180i −0.640065 0.369542i 0.144575 0.989494i \(-0.453819\pi\)
−0.784640 + 0.619952i \(0.787152\pi\)
\(678\) 0 0
\(679\) 284.811 262.473i 0.419456 0.386558i
\(680\) 0 0
\(681\) 146.155 253.148i 0.214618 0.371729i
\(682\) 0 0
\(683\) 473.225 + 819.650i 0.692862 + 1.20007i 0.970896 + 0.239501i \(0.0769840\pi\)
−0.278034 + 0.960571i \(0.589683\pi\)
\(684\) 0 0
\(685\) 15.9952i 0.0233507i
\(686\) 0 0
\(687\) 1689.76i 2.45962i
\(688\) 0 0
\(689\) −154.400 267.428i −0.224092 0.388140i
\(690\) 0 0
\(691\) 151.632 262.634i 0.219439 0.380079i −0.735198 0.677853i \(-0.762911\pi\)
0.954636 + 0.297774i \(0.0962441\pi\)
\(692\) 0 0
\(693\) 277.775 255.989i 0.400830 0.369393i
\(694\) 0 0
\(695\) 4.98781 + 2.87971i 0.00717670 + 0.00414347i
\(696\) 0 0
\(697\) −58.8834 101.989i −0.0844812 0.146326i
\(698\) 0 0
\(699\) −332.074 −0.475069
\(700\) 0 0
\(701\) 390.864i 0.557580i 0.960352 + 0.278790i \(0.0899333\pi\)
−0.960352 + 0.278790i \(0.910067\pi\)
\(702\) 0 0
\(703\) −1185.32 + 684.345i −1.68609 + 0.973464i
\(704\) 0 0
\(705\) 309.446 535.976i 0.438930 0.760250i
\(706\) 0 0
\(707\) −65.5679 + 210.033i −0.0927411 + 0.297077i
\(708\) 0 0
\(709\) −832.393 480.582i −1.17404 0.677831i −0.219410 0.975633i \(-0.570413\pi\)
−0.954628 + 0.297801i \(0.903747\pi\)
\(710\) 0 0
\(711\) −303.608 + 175.288i −0.427016 + 0.246538i
\(712\) 0 0
\(713\) −866.685 −1.21555
\(714\) 0 0
\(715\) −170.379 −0.238293
\(716\) 0 0
\(717\) −388.074 + 224.055i −0.541247 + 0.312489i
\(718\) 0 0
\(719\) −454.773 262.563i −0.632507 0.365178i 0.149215 0.988805i \(-0.452325\pi\)
−0.781722 + 0.623627i \(0.785659\pi\)
\(720\) 0 0
\(721\) 546.285 122.737i 0.757677 0.170232i
\(722\) 0 0
\(723\) −558.204 + 966.838i −0.772067 + 1.33726i
\(724\) 0 0
\(725\) −517.870 + 298.992i −0.714304 + 0.412403i
\(726\) 0 0
\(727\) 108.633i 0.149426i −0.997205 0.0747131i \(-0.976196\pi\)
0.997205 0.0747131i \(-0.0238041\pi\)
\(728\) 0 0
\(729\) −348.775 −0.478429
\(730\) 0 0
\(731\) 68.5197 + 118.680i 0.0937341 + 0.162352i
\(732\) 0 0
\(733\) −34.8609 20.1270i −0.0475593 0.0274584i 0.476032 0.879428i \(-0.342075\pi\)
−0.523591 + 0.851970i \(0.675408\pi\)
\(734\) 0 0
\(735\) −366.003 29.9271i −0.497963 0.0407171i
\(736\) 0 0
\(737\) −233.665 + 404.719i −0.317049 + 0.549144i
\(738\) 0 0
\(739\) 498.602 + 863.603i 0.674698 + 1.16861i 0.976557 + 0.215258i \(0.0690594\pi\)
−0.301859 + 0.953352i \(0.597607\pi\)
\(740\) 0 0
\(741\) 1373.87i 1.85407i
\(742\) 0 0
\(743\) 476.575i 0.641420i −0.947177 0.320710i \(-0.896078\pi\)
0.947177 0.320710i \(-0.103922\pi\)
\(744\) 0 0
\(745\) −29.8607 51.7203i −0.0400815 0.0694232i
\(746\) 0 0
\(747\) −306.289 + 530.509i −0.410026 + 0.710186i
\(748\) 0 0
\(749\) −74.8265 333.041i −0.0999018 0.444648i
\(750\) 0 0
\(751\) −457.691 264.248i −0.609442 0.351862i 0.163305 0.986576i \(-0.447785\pi\)
−0.772747 + 0.634714i \(0.781118\pi\)
\(752\) 0 0
\(753\) −65.5993 113.621i −0.0871173 0.150892i
\(754\) 0 0
\(755\) 477.400 0.632318
\(756\) 0 0
\(757\) 455.964i 0.602331i −0.953572 0.301165i \(-0.902624\pi\)
0.953572 0.301165i \(-0.0973756\pi\)
\(758\) 0 0
\(759\) 1047.19 604.598i 1.37970 0.796572i
\(760\) 0 0
\(761\) −238.325 + 412.791i −0.313174 + 0.542433i −0.979048 0.203632i \(-0.934726\pi\)
0.665874 + 0.746064i \(0.268059\pi\)
\(762\) 0 0
\(763\) 240.031 768.888i 0.314588 1.00772i
\(764\) 0 0
\(765\) −32.3619 18.6842i −0.0423032 0.0244238i
\(766\) 0 0
\(767\) −103.564 + 59.7927i −0.135025 + 0.0779565i
\(768\) 0 0
\(769\) −568.246 −0.738941 −0.369471 0.929242i \(-0.620461\pi\)
−0.369471 + 0.929242i \(0.620461\pi\)
\(770\) 0 0
\(771\) −892.621 −1.15774
\(772\) 0 0
\(773\) 1036.66 598.515i 1.34108 0.774275i 0.354118 0.935201i \(-0.384781\pi\)
0.986967 + 0.160925i \(0.0514478\pi\)
\(774\) 0 0
\(775\) −417.771 241.200i −0.539059 0.311226i
\(776\) 0 0
\(777\) −860.314 933.531i −1.10723 1.20146i
\(778\) 0 0
\(779\) 610.377 1057.20i 0.783539 1.35713i
\(780\) 0 0
\(781\) −261.039 + 150.711i −0.334237 + 0.192972i
\(782\) 0 0
\(783\) 238.701i 0.304855i
\(784\) 0 0
\(785\) 92.8596 0.118292
\(786\) 0 0
\(787\) 226.134 + 391.676i 0.287337 + 0.497682i 0.973173 0.230074i \(-0.0738967\pi\)
−0.685836 + 0.727756i \(0.740563\pi\)
\(788\) 0 0
\(789\) 585.969 + 338.309i 0.742673 + 0.428783i
\(790\) 0 0
\(791\) −287.008 + 264.498i −0.362843 + 0.334385i
\(792\) 0 0
\(793\) 127.282 220.459i 0.160507 0.278007