Properties

Label 224.3.s.a.129.7
Level 224
Weight 3
Character 224.129
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: \( 2^{20} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 129.7
Root \(-0.707107 + 2.60548i\) of \(x^{16} + 36 x^{14} + 522 x^{12} + 3644 x^{10} + 12219 x^{8} + 15156 x^{6} + 15478 x^{4} - 10992 x^{2} + 11025\)
Character \(\chi\) \(=\) 224.129
Dual form 224.3.s.a.33.7

$q$-expansion

\(f(q)\) \(=\) \(q+(3.19104 + 1.84235i) q^{3} +(-2.63938 + 1.52385i) q^{5} +(-0.812549 + 6.95268i) q^{7} +(2.28850 + 3.96380i) q^{9} +O(q^{10})\) \(q+(3.19104 + 1.84235i) q^{3} +(-2.63938 + 1.52385i) q^{5} +(-0.812549 + 6.95268i) q^{7} +(2.28850 + 3.96380i) q^{9} +(1.17516 - 2.03544i) q^{11} +25.3073i q^{13} -11.2298 q^{15} +(3.08674 + 1.78213i) q^{17} +(14.1772 - 8.18522i) q^{19} +(-15.4021 + 20.6893i) q^{21} +(-8.83413 - 15.3012i) q^{23} +(-7.85577 + 13.6066i) q^{25} -16.2974i q^{27} +36.1220 q^{29} +(-6.25629 - 3.61207i) q^{31} +(7.50000 - 4.33013i) q^{33} +(-8.45020 - 19.5890i) q^{35} +(-18.4021 - 31.8734i) q^{37} +(-46.6249 + 80.7567i) q^{39} +53.7118i q^{41} +51.2382 q^{43} +(-12.0805 - 6.97466i) q^{45} +(27.1609 - 15.6814i) q^{47} +(-47.6795 - 11.2988i) q^{49} +(6.56661 + 11.3737i) q^{51} +(35.1137 - 60.8187i) q^{53} +7.16309i q^{55} +60.3201 q^{57} +(81.4102 + 47.0022i) q^{59} +(-1.89609 + 1.09471i) q^{61} +(-29.4186 + 12.6904i) q^{63} +(-38.5645 - 66.7957i) q^{65} +(12.4810 - 21.6177i) q^{67} -65.1022i q^{69} -50.8890 q^{71} +(-68.9008 - 39.7799i) q^{73} +(-50.1362 + 28.9461i) q^{75} +(13.1969 + 9.82444i) q^{77} +(-57.5117 - 99.6132i) q^{79} +(50.6220 - 87.6799i) q^{81} -154.132i q^{83} -10.8628 q^{85} +(115.267 + 66.5493i) q^{87} +(98.7274 - 57.0003i) q^{89} +(-175.954 - 20.5634i) q^{91} +(-13.3094 - 23.0525i) q^{93} +(-24.9461 + 43.2079i) q^{95} +53.9940i q^{97} +10.7575 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 8q^{9} + O(q^{10}) \) \( 16q + 8q^{9} + 48q^{17} + 56q^{21} + 16q^{25} + 112q^{29} + 120q^{33} + 8q^{37} - 72q^{45} - 128q^{49} - 24q^{53} - 528q^{57} - 360q^{61} - 8q^{65} + 72q^{73} + 32q^{81} + 720q^{85} + 408q^{89} - 232q^{93} + O(q^{100}) \)

Character values

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

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

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
\(3\) 3.19104 + 1.84235i 1.06368 + 0.614116i 0.926448 0.376422i \(-0.122846\pi\)
0.137233 + 0.990539i \(0.456179\pi\)
\(4\) 0 0
\(5\) −2.63938 + 1.52385i −0.527877 + 0.304770i −0.740151 0.672440i \(-0.765246\pi\)
0.212275 + 0.977210i \(0.431913\pi\)
\(6\) 0 0
\(7\) −0.812549 + 6.95268i −0.116078 + 0.993240i
\(8\) 0 0
\(9\) 2.28850 + 3.96380i 0.254278 + 0.440422i
\(10\) 0 0
\(11\) 1.17516 2.03544i 0.106833 0.185040i −0.807653 0.589659i \(-0.799262\pi\)
0.914486 + 0.404618i \(0.132596\pi\)
\(12\) 0 0
\(13\) 25.3073i 1.94672i 0.229292 + 0.973358i \(0.426359\pi\)
−0.229292 + 0.973358i \(0.573641\pi\)
\(14\) 0 0
\(15\) −11.2298 −0.748656
\(16\) 0 0
\(17\) 3.08674 + 1.78213i 0.181573 + 0.104831i 0.588031 0.808838i \(-0.299903\pi\)
−0.406459 + 0.913669i \(0.633236\pi\)
\(18\) 0 0
\(19\) 14.1772 8.18522i 0.746169 0.430801i −0.0781390 0.996942i \(-0.524898\pi\)
0.824308 + 0.566142i \(0.191564\pi\)
\(20\) 0 0
\(21\) −15.4021 + 20.6893i −0.733435 + 0.985205i
\(22\) 0 0
\(23\) −8.83413 15.3012i −0.384093 0.665268i 0.607550 0.794281i \(-0.292152\pi\)
−0.991643 + 0.129013i \(0.958819\pi\)
\(24\) 0 0
\(25\) −7.85577 + 13.6066i −0.314231 + 0.544264i
\(26\) 0 0
\(27\) 16.2974i 0.603608i
\(28\) 0 0
\(29\) 36.1220 1.24559 0.622793 0.782387i \(-0.285998\pi\)
0.622793 + 0.782387i \(0.285998\pi\)
\(30\) 0 0
\(31\) −6.25629 3.61207i −0.201816 0.116518i 0.395686 0.918386i \(-0.370507\pi\)
−0.597502 + 0.801867i \(0.703840\pi\)
\(32\) 0 0
\(33\) 7.50000 4.33013i 0.227273 0.131216i
\(34\) 0 0
\(35\) −8.45020 19.5890i −0.241434 0.559685i
\(36\) 0 0
\(37\) −18.4021 31.8734i −0.497355 0.861445i 0.502640 0.864496i \(-0.332362\pi\)
−0.999995 + 0.00305120i \(0.999029\pi\)
\(38\) 0 0
\(39\) −46.6249 + 80.7567i −1.19551 + 2.07068i
\(40\) 0 0
\(41\) 53.7118i 1.31004i 0.755610 + 0.655022i \(0.227341\pi\)
−0.755610 + 0.655022i \(0.772659\pi\)
\(42\) 0 0
\(43\) 51.2382 1.19159 0.595793 0.803138i \(-0.296838\pi\)
0.595793 + 0.803138i \(0.296838\pi\)
\(44\) 0 0
\(45\) −12.0805 6.97466i −0.268455 0.154992i
\(46\) 0 0
\(47\) 27.1609 15.6814i 0.577892 0.333646i −0.182403 0.983224i \(-0.558388\pi\)
0.760295 + 0.649578i \(0.225054\pi\)
\(48\) 0 0
\(49\) −47.6795 11.2988i −0.973052 0.230588i
\(50\) 0 0
\(51\) 6.56661 + 11.3737i 0.128757 + 0.223014i
\(52\) 0 0
\(53\) 35.1137 60.8187i 0.662522 1.14752i −0.317428 0.948282i \(-0.602819\pi\)
0.979951 0.199240i \(-0.0638474\pi\)
\(54\) 0 0
\(55\) 7.16309i 0.130238i
\(56\) 0 0
\(57\) 60.3201 1.05825
\(58\) 0 0
\(59\) 81.4102 + 47.0022i 1.37983 + 0.796647i 0.992139 0.125141i \(-0.0399382\pi\)
0.387695 + 0.921788i \(0.373272\pi\)
\(60\) 0 0
\(61\) −1.89609 + 1.09471i −0.0310835 + 0.0179461i −0.515461 0.856913i \(-0.672379\pi\)
0.484378 + 0.874859i \(0.339046\pi\)
\(62\) 0 0
\(63\) −29.4186 + 12.6904i −0.466961 + 0.201435i
\(64\) 0 0
\(65\) −38.5645 66.7957i −0.593300 1.02763i
\(66\) 0 0
\(67\) 12.4810 21.6177i 0.186283 0.322652i −0.757725 0.652574i \(-0.773689\pi\)
0.944008 + 0.329922i \(0.107023\pi\)
\(68\) 0 0
\(69\) 65.1022i 0.943510i
\(70\) 0 0
\(71\) −50.8890 −0.716746 −0.358373 0.933579i \(-0.616668\pi\)
−0.358373 + 0.933579i \(0.616668\pi\)
\(72\) 0 0
\(73\) −68.9008 39.7799i −0.943847 0.544930i −0.0526830 0.998611i \(-0.516777\pi\)
−0.891164 + 0.453681i \(0.850111\pi\)
\(74\) 0 0
\(75\) −50.1362 + 28.9461i −0.668483 + 0.385949i
\(76\) 0 0
\(77\) 13.1969 + 9.82444i 0.171389 + 0.127590i
\(78\) 0 0
\(79\) −57.5117 99.6132i −0.727996 1.26093i −0.957729 0.287672i \(-0.907119\pi\)
0.229733 0.973254i \(-0.426215\pi\)
\(80\) 0 0
\(81\) 50.6220 87.6799i 0.624963 1.08247i
\(82\) 0 0
\(83\) 154.132i 1.85701i −0.371318 0.928506i \(-0.621094\pi\)
0.371318 0.928506i \(-0.378906\pi\)
\(84\) 0 0
\(85\) −10.8628 −0.127797
\(86\) 0 0
\(87\) 115.267 + 66.5493i 1.32491 + 0.764935i
\(88\) 0 0
\(89\) 98.7274 57.0003i 1.10930 0.640453i 0.170649 0.985332i \(-0.445414\pi\)
0.938647 + 0.344879i \(0.112080\pi\)
\(90\) 0 0
\(91\) −175.954 20.5634i −1.93356 0.225972i
\(92\) 0 0
\(93\) −13.3094 23.0525i −0.143112 0.247877i
\(94\) 0 0
\(95\) −24.9461 + 43.2079i −0.262590 + 0.454820i
\(96\) 0 0
\(97\) 53.9940i 0.556640i 0.960488 + 0.278320i \(0.0897775\pi\)
−0.960488 + 0.278320i \(0.910222\pi\)
\(98\) 0 0
\(99\) 10.7575 0.108661
\(100\) 0 0
\(101\) 18.0305 + 10.4099i 0.178519 + 0.103068i 0.586597 0.809879i \(-0.300467\pi\)
−0.408077 + 0.912947i \(0.633801\pi\)
\(102\) 0 0
\(103\) 105.870 61.1238i 1.02786 0.593435i 0.111489 0.993766i \(-0.464438\pi\)
0.916371 + 0.400330i \(0.131105\pi\)
\(104\) 0 0
\(105\) 9.12480 78.0775i 0.0869029 0.743596i
\(106\) 0 0
\(107\) 57.2681 + 99.1912i 0.535216 + 0.927021i 0.999153 + 0.0411525i \(0.0131030\pi\)
−0.463937 + 0.885868i \(0.653564\pi\)
\(108\) 0 0
\(109\) −82.9057 + 143.597i −0.760603 + 1.31740i 0.181938 + 0.983310i \(0.441763\pi\)
−0.942540 + 0.334092i \(0.891570\pi\)
\(110\) 0 0
\(111\) 135.613i 1.22174i
\(112\) 0 0
\(113\) −123.071 −1.08912 −0.544560 0.838722i \(-0.683303\pi\)
−0.544560 + 0.838722i \(0.683303\pi\)
\(114\) 0 0
\(115\) 46.6333 + 26.9238i 0.405507 + 0.234120i
\(116\) 0 0
\(117\) −100.313 + 57.9158i −0.857377 + 0.495007i
\(118\) 0 0
\(119\) −14.8987 + 20.0130i −0.125199 + 0.168177i
\(120\) 0 0
\(121\) 57.7380 + 100.005i 0.477173 + 0.826489i
\(122\) 0 0
\(123\) −98.9559 + 171.397i −0.804520 + 1.39347i
\(124\) 0 0
\(125\) 124.076i 0.992612i
\(126\) 0 0
\(127\) 160.105 1.26067 0.630334 0.776324i \(-0.282918\pi\)
0.630334 + 0.776324i \(0.282918\pi\)
\(128\) 0 0
\(129\) 163.503 + 94.3987i 1.26747 + 0.731773i
\(130\) 0 0
\(131\) −53.3272 + 30.7885i −0.407078 + 0.235027i −0.689534 0.724254i \(-0.742184\pi\)
0.282455 + 0.959280i \(0.408851\pi\)
\(132\) 0 0
\(133\) 45.3895 + 105.221i 0.341275 + 0.791132i
\(134\) 0 0
\(135\) 24.8348 + 43.0151i 0.183961 + 0.318630i
\(136\) 0 0
\(137\) −47.5511 + 82.3609i −0.347088 + 0.601174i −0.985731 0.168329i \(-0.946163\pi\)
0.638643 + 0.769503i \(0.279496\pi\)
\(138\) 0 0
\(139\) 92.0558i 0.662272i 0.943583 + 0.331136i \(0.107432\pi\)
−0.943583 + 0.331136i \(0.892568\pi\)
\(140\) 0 0
\(141\) 115.562 0.819590
\(142\) 0 0
\(143\) 51.5116 + 29.7402i 0.360221 + 0.207974i
\(144\) 0 0
\(145\) −95.3398 + 55.0445i −0.657516 + 0.379617i
\(146\) 0 0
\(147\) −131.331 123.897i −0.893409 0.842838i
\(148\) 0 0
\(149\) 88.7225 + 153.672i 0.595453 + 1.03136i 0.993483 + 0.113983i \(0.0363608\pi\)
−0.398030 + 0.917373i \(0.630306\pi\)
\(150\) 0 0
\(151\) −114.894 + 199.002i −0.760888 + 1.31790i 0.181506 + 0.983390i \(0.441903\pi\)
−0.942394 + 0.334506i \(0.891430\pi\)
\(152\) 0 0
\(153\) 16.3136i 0.106625i
\(154\) 0 0
\(155\) 22.0170 0.142045
\(156\) 0 0
\(157\) −42.9871 24.8186i −0.273803 0.158080i 0.356812 0.934176i \(-0.383864\pi\)
−0.630615 + 0.776096i \(0.717197\pi\)
\(158\) 0 0
\(159\) 224.099 129.383i 1.40942 0.813732i
\(160\) 0 0
\(161\) 113.562 48.9879i 0.705356 0.304273i
\(162\) 0 0
\(163\) −33.2613 57.6103i −0.204057 0.353438i 0.745775 0.666198i \(-0.232080\pi\)
−0.949832 + 0.312761i \(0.898746\pi\)
\(164\) 0 0
\(165\) −13.1969 + 22.8577i −0.0799813 + 0.138532i
\(166\) 0 0
\(167\) 164.292i 0.983786i −0.870656 0.491893i \(-0.836305\pi\)
0.870656 0.491893i \(-0.163695\pi\)
\(168\) 0 0
\(169\) −471.460 −2.78970
\(170\) 0 0
\(171\) 64.8891 + 37.4638i 0.379469 + 0.219086i
\(172\) 0 0
\(173\) −33.4995 + 19.3409i −0.193639 + 0.111797i −0.593685 0.804698i \(-0.702327\pi\)
0.400046 + 0.916495i \(0.368994\pi\)
\(174\) 0 0
\(175\) −88.2191 65.6747i −0.504109 0.375284i
\(176\) 0 0
\(177\) 173.189 + 299.972i 0.978468 + 1.69476i
\(178\) 0 0
\(179\) −51.2076 + 88.6942i −0.286076 + 0.495498i −0.972870 0.231354i \(-0.925684\pi\)
0.686794 + 0.726853i \(0.259018\pi\)
\(180\) 0 0
\(181\) 44.5843i 0.246322i −0.992387 0.123161i \(-0.960697\pi\)
0.992387 0.123161i \(-0.0393032\pi\)
\(182\) 0 0
\(183\) −8.06735 −0.0440839
\(184\) 0 0
\(185\) 97.1406 + 56.0842i 0.525084 + 0.303158i
\(186\) 0 0
\(187\) 7.25485 4.18859i 0.0387960 0.0223989i
\(188\) 0 0
\(189\) 113.311 + 13.2424i 0.599527 + 0.0700659i
\(190\) 0 0
\(191\) −165.031 285.842i −0.864038 1.49656i −0.868000 0.496565i \(-0.834594\pi\)
0.00396184 0.999992i \(-0.498739\pi\)
\(192\) 0 0
\(193\) −69.6777 + 120.685i −0.361024 + 0.625312i −0.988130 0.153622i \(-0.950906\pi\)
0.627105 + 0.778934i \(0.284240\pi\)
\(194\) 0 0
\(195\) 284.197i 1.45742i
\(196\) 0 0
\(197\) 174.724 0.886925 0.443462 0.896293i \(-0.353750\pi\)
0.443462 + 0.896293i \(0.353750\pi\)
\(198\) 0 0
\(199\) 197.009 + 113.743i 0.989996 + 0.571574i 0.905273 0.424830i \(-0.139666\pi\)
0.0847227 + 0.996405i \(0.473000\pi\)
\(200\) 0 0
\(201\) 79.6546 45.9886i 0.396291 0.228799i
\(202\) 0 0
\(203\) −29.3509 + 251.145i −0.144586 + 1.23717i
\(204\) 0 0
\(205\) −81.8487 141.766i −0.399262 0.691542i
\(206\) 0 0
\(207\) 40.4338 70.0335i 0.195333 0.338326i
\(208\) 0 0
\(209\) 38.4759i 0.184095i
\(210\) 0 0
\(211\) −251.350 −1.19123 −0.595617 0.803269i \(-0.703092\pi\)
−0.595617 + 0.803269i \(0.703092\pi\)
\(212\) 0 0
\(213\) −162.389 93.7552i −0.762389 0.440165i
\(214\) 0 0
\(215\) −135.237 + 78.0793i −0.629011 + 0.363160i
\(216\) 0 0
\(217\) 30.1971 40.5630i 0.139157 0.186926i
\(218\) 0 0
\(219\) −146.577 253.879i −0.669301 1.15926i
\(220\) 0 0
\(221\) −45.1009 + 78.1170i −0.204076 + 0.353471i
\(222\) 0 0
\(223\) 108.297i 0.485636i 0.970072 + 0.242818i \(0.0780718\pi\)
−0.970072 + 0.242818i \(0.921928\pi\)
\(224\) 0 0
\(225\) −71.9118 −0.319608
\(226\) 0 0
\(227\) 245.045 + 141.477i 1.07949 + 0.623245i 0.930759 0.365632i \(-0.119147\pi\)
0.148733 + 0.988877i \(0.452481\pi\)
\(228\) 0 0
\(229\) −153.011 + 88.3412i −0.668172 + 0.385769i −0.795384 0.606106i \(-0.792731\pi\)
0.127212 + 0.991876i \(0.459397\pi\)
\(230\) 0 0
\(231\) 24.0119 + 55.6635i 0.103947 + 0.240968i
\(232\) 0 0
\(233\) −177.693 307.773i −0.762630 1.32091i −0.941491 0.337039i \(-0.890575\pi\)
0.178861 0.983874i \(-0.442759\pi\)
\(234\) 0 0
\(235\) −47.7921 + 82.7783i −0.203370 + 0.352248i
\(236\) 0 0
\(237\) 423.826i 1.78830i
\(238\) 0 0
\(239\) −17.5451 −0.0734104 −0.0367052 0.999326i \(-0.511686\pi\)
−0.0367052 + 0.999326i \(0.511686\pi\)
\(240\) 0 0
\(241\) 104.909 + 60.5693i 0.435308 + 0.251325i 0.701605 0.712566i \(-0.252467\pi\)
−0.266298 + 0.963891i \(0.585800\pi\)
\(242\) 0 0
\(243\) 196.048 113.189i 0.806783 0.465797i
\(244\) 0 0
\(245\) 143.062 42.8346i 0.583927 0.174835i
\(246\) 0 0
\(247\) 207.146 + 358.787i 0.838647 + 1.45258i
\(248\) 0 0
\(249\) 283.965 491.842i 1.14042 1.97527i
\(250\) 0 0
\(251\) 219.342i 0.873874i 0.899492 + 0.436937i \(0.143937\pi\)
−0.899492 + 0.436937i \(0.856063\pi\)
\(252\) 0 0
\(253\) −41.5262 −0.164135
\(254\) 0 0
\(255\) −34.6636 20.0130i −0.135936 0.0784825i
\(256\) 0 0
\(257\) 417.447 241.013i 1.62431 0.937794i 0.638558 0.769574i \(-0.279531\pi\)
0.985749 0.168220i \(-0.0538019\pi\)
\(258\) 0 0
\(259\) 236.559 102.045i 0.913353 0.393998i
\(260\) 0 0
\(261\) 82.6652 + 143.180i 0.316725 + 0.548584i
\(262\) 0 0
\(263\) −44.8439 + 77.6720i −0.170509 + 0.295331i −0.938598 0.345013i \(-0.887875\pi\)
0.768089 + 0.640343i \(0.221208\pi\)
\(264\) 0 0
\(265\) 214.032i 0.807667i
\(266\) 0 0
\(267\) 420.058 1.57325
\(268\) 0 0
\(269\) −32.9768 19.0392i −0.122590 0.0707776i 0.437451 0.899242i \(-0.355881\pi\)
−0.560041 + 0.828465i \(0.689215\pi\)
\(270\) 0 0
\(271\) −73.5803 + 42.4816i −0.271514 + 0.156759i −0.629575 0.776939i \(-0.716771\pi\)
0.358062 + 0.933698i \(0.383438\pi\)
\(272\) 0 0
\(273\) −523.590 389.787i −1.91791 1.42779i
\(274\) 0 0
\(275\) 18.4636 + 31.9800i 0.0671405 + 0.116291i
\(276\) 0 0
\(277\) −31.2523 + 54.1306i −0.112824 + 0.195417i −0.916908 0.399099i \(-0.869323\pi\)
0.804084 + 0.594516i \(0.202656\pi\)
\(278\) 0 0
\(279\) 33.0649i 0.118512i
\(280\) 0 0
\(281\) 58.6599 0.208754 0.104377 0.994538i \(-0.466715\pi\)
0.104377 + 0.994538i \(0.466715\pi\)
\(282\) 0 0
\(283\) −207.461 119.778i −0.733078 0.423243i 0.0864689 0.996255i \(-0.472442\pi\)
−0.819547 + 0.573012i \(0.805775\pi\)
\(284\) 0 0
\(285\) −159.208 + 91.9187i −0.558624 + 0.322522i
\(286\) 0 0
\(287\) −373.441 43.6435i −1.30119 0.152068i
\(288\) 0 0
\(289\) −138.148 239.279i −0.478021 0.827956i
\(290\) 0 0
\(291\) −99.4759 + 172.297i −0.341842 + 0.592087i
\(292\) 0 0
\(293\) 196.503i 0.670658i −0.942101 0.335329i \(-0.891152\pi\)
0.942101 0.335329i \(-0.108848\pi\)
\(294\) 0 0
\(295\) −286.497 −0.971176
\(296\) 0 0
\(297\) −33.1725 19.1521i −0.111692 0.0644853i
\(298\) 0 0
\(299\) 387.231 223.568i 1.29509 0.747719i
\(300\) 0 0
\(301\) −41.6336 + 356.243i −0.138318 + 1.18353i
\(302\) 0 0
\(303\) 38.3573 + 66.4368i 0.126592 + 0.219263i
\(304\) 0 0
\(305\) 3.33634 5.77871i 0.0109388 0.0189466i
\(306\) 0 0
\(307\) 246.955i 0.804415i −0.915549 0.402208i \(-0.868243\pi\)
0.915549 0.402208i \(-0.131757\pi\)
\(308\) 0 0
\(309\) 450.446 1.45775
\(310\) 0 0
\(311\) −294.487 170.022i −0.946905 0.546696i −0.0547867 0.998498i \(-0.517448\pi\)
−0.892118 + 0.451802i \(0.850781\pi\)
\(312\) 0 0
\(313\) 98.2049 56.6987i 0.313754 0.181146i −0.334851 0.942271i \(-0.608686\pi\)
0.648605 + 0.761125i \(0.275353\pi\)
\(314\) 0 0
\(315\) 58.3086 78.3244i 0.185107 0.248649i
\(316\) 0 0
\(317\) −121.155 209.847i −0.382192 0.661976i 0.609183 0.793030i \(-0.291497\pi\)
−0.991375 + 0.131053i \(0.958164\pi\)
\(318\) 0 0
\(319\) 42.4493 73.5243i 0.133070 0.230484i
\(320\) 0 0
\(321\) 422.031i 1.31474i
\(322\) 0 0
\(323\) 58.3484 0.180645
\(324\) 0 0
\(325\) −344.346 198.808i −1.05953 0.611718i
\(326\) 0 0
\(327\) −529.111 + 305.482i −1.61808 + 0.934197i
\(328\) 0 0
\(329\) 86.9579 + 201.583i 0.264310 + 0.612715i
\(330\) 0 0
\(331\) −34.8544 60.3697i −0.105300 0.182386i 0.808560 0.588413i \(-0.200247\pi\)
−0.913861 + 0.406027i \(0.866914\pi\)
\(332\) 0 0
\(333\) 84.2267 145.885i 0.252933 0.438093i
\(334\) 0 0
\(335\) 76.0764i 0.227094i
\(336\) 0 0
\(337\) 165.816 0.492037 0.246019 0.969265i \(-0.420878\pi\)
0.246019 + 0.969265i \(0.420878\pi\)
\(338\) 0 0
\(339\) −392.723 226.739i −1.15848 0.668846i
\(340\) 0 0
\(341\) −14.7043 + 8.48956i −0.0431212 + 0.0248961i
\(342\) 0 0
\(343\) 117.299 322.320i 0.341979 0.939708i
\(344\) 0 0
\(345\) 99.2059 + 171.830i 0.287553 + 0.498057i
\(346\) 0 0
\(347\) 283.452 490.953i 0.816864 1.41485i −0.0911175 0.995840i \(-0.529044\pi\)
0.907982 0.419010i \(-0.137623\pi\)
\(348\) 0 0
\(349\) 245.773i 0.704219i 0.935959 + 0.352110i \(0.114536\pi\)
−0.935959 + 0.352110i \(0.885464\pi\)
\(350\) 0 0
\(351\) 412.443 1.17505
\(352\) 0 0
\(353\) −137.837 79.5801i −0.390472 0.225439i 0.291892 0.956451i \(-0.405715\pi\)
−0.682365 + 0.731012i \(0.739048\pi\)
\(354\) 0 0
\(355\) 134.315 77.5471i 0.378353 0.218442i
\(356\) 0 0
\(357\) −84.4134 + 36.4138i −0.236452 + 0.102000i
\(358\) 0 0
\(359\) 102.513 + 177.557i 0.285550 + 0.494588i 0.972743 0.231888i \(-0.0744902\pi\)
−0.687192 + 0.726476i \(0.741157\pi\)
\(360\) 0 0
\(361\) −46.5044 + 80.5480i −0.128821 + 0.223125i
\(362\) 0 0
\(363\) 425.494i 1.17216i
\(364\) 0 0
\(365\) 242.474 0.664313
\(366\) 0 0
\(367\) −1.46112 0.843577i −0.00398125 0.00229858i 0.498008 0.867172i \(-0.334065\pi\)
−0.501989 + 0.864874i \(0.667398\pi\)
\(368\) 0 0
\(369\) −212.903 + 122.920i −0.576973 + 0.333115i
\(370\) 0 0
\(371\) 394.321 + 293.552i 1.06286 + 0.791246i
\(372\) 0 0
\(373\) −231.702 401.320i −0.621186 1.07593i −0.989265 0.146131i \(-0.953318\pi\)
0.368079 0.929795i \(-0.380016\pi\)
\(374\) 0 0
\(375\) 228.592 395.933i 0.609579 1.05582i
\(376\) 0 0
\(377\) 914.150i 2.42480i
\(378\) 0 0
\(379\) −493.215 −1.30136 −0.650680 0.759352i \(-0.725516\pi\)
−0.650680 + 0.759352i \(0.725516\pi\)
\(380\) 0 0
\(381\) 510.902 + 294.969i 1.34095 + 0.774197i
\(382\) 0 0
\(383\) −496.266 + 286.519i −1.29573 + 0.748092i −0.979664 0.200645i \(-0.935696\pi\)
−0.316069 + 0.948736i \(0.602363\pi\)
\(384\) 0 0
\(385\) −49.8027 5.82036i −0.129358 0.0151178i
\(386\) 0 0
\(387\) 117.259 + 203.098i 0.302994 + 0.524801i
\(388\) 0 0
\(389\) 23.2756 40.3146i 0.0598346 0.103637i −0.834556 0.550922i \(-0.814276\pi\)
0.894391 + 0.447286i \(0.147609\pi\)
\(390\) 0 0
\(391\) 62.9742i 0.161059i
\(392\) 0 0
\(393\) −226.893 −0.577335
\(394\) 0 0
\(395\) 303.591 + 175.278i 0.768584 + 0.443742i
\(396\) 0 0
\(397\) 180.743 104.352i 0.455273 0.262852i −0.254782 0.966999i \(-0.582004\pi\)
0.710055 + 0.704147i \(0.248670\pi\)
\(398\) 0 0
\(399\) −49.0131 + 419.386i −0.122840 + 1.05109i
\(400\) 0 0
\(401\) 110.595 + 191.556i 0.275798 + 0.477696i 0.970336 0.241760i \(-0.0777246\pi\)
−0.694538 + 0.719456i \(0.744391\pi\)
\(402\) 0 0
\(403\) 91.4118 158.330i 0.226828 0.392878i
\(404\) 0 0
\(405\) 308.561i 0.761880i
\(406\) 0 0
\(407\) −86.5022 −0.212536
\(408\) 0 0
\(409\) 83.5098 + 48.2144i 0.204181 + 0.117884i 0.598604 0.801045i \(-0.295722\pi\)
−0.394423 + 0.918929i \(0.629056\pi\)
\(410\) 0 0
\(411\) −303.475 + 175.211i −0.738382 + 0.426305i
\(412\) 0 0
\(413\) −392.941 + 527.827i −0.951431 + 1.27803i
\(414\) 0 0
\(415\) 234.874 + 406.813i 0.565961 + 0.980273i
\(416\) 0 0
\(417\) −169.599 + 293.754i −0.406712 + 0.704446i
\(418\) 0 0
\(419\) 239.093i 0.570627i 0.958434 + 0.285313i \(0.0920977\pi\)
−0.958434 + 0.285313i \(0.907902\pi\)
\(420\) 0 0
\(421\) 508.228 1.20719 0.603596 0.797290i \(-0.293734\pi\)
0.603596 + 0.797290i \(0.293734\pi\)
\(422\) 0 0
\(423\) 124.316 + 71.7737i 0.293890 + 0.169678i
\(424\) 0 0
\(425\) −48.4974 + 28.0000i −0.114112 + 0.0658823i
\(426\) 0 0
\(427\) −6.07049 14.0724i −0.0142166 0.0329565i
\(428\) 0 0
\(429\) 109.584 + 189.805i 0.255440 + 0.442435i
\(430\) 0 0
\(431\) 299.174 518.185i 0.694140 1.20229i −0.276329 0.961063i \(-0.589118\pi\)
0.970470 0.241223i \(-0.0775486\pi\)
\(432\) 0 0
\(433\) 283.405i 0.654516i −0.944935 0.327258i \(-0.893875\pi\)
0.944935 0.327258i \(-0.106125\pi\)
\(434\) 0 0
\(435\) −405.644 −0.932516
\(436\) 0 0
\(437\) −250.487 144.619i −0.573196 0.330935i
\(438\) 0 0
\(439\) 296.596 171.240i 0.675618 0.390068i −0.122584 0.992458i \(-0.539118\pi\)
0.798202 + 0.602390i \(0.205785\pi\)
\(440\) 0 0
\(441\) −64.3285 214.849i −0.145870 0.487187i
\(442\) 0 0
\(443\) −293.909 509.065i −0.663451 1.14913i −0.979703 0.200455i \(-0.935758\pi\)
0.316252 0.948675i \(-0.397575\pi\)
\(444\) 0 0
\(445\) −173.720 + 300.891i −0.390381 + 0.676160i
\(446\) 0 0
\(447\) 653.831i 1.46271i
\(448\) 0 0
\(449\) −265.522 −0.591364 −0.295682 0.955286i \(-0.595547\pi\)
−0.295682 + 0.955286i \(0.595547\pi\)
\(450\) 0 0
\(451\) 109.327 + 63.1202i 0.242411 + 0.139956i
\(452\) 0 0
\(453\) −733.264 + 423.350i −1.61868 + 0.934547i
\(454\) 0 0
\(455\) 495.745 213.852i 1.08955 0.470004i
\(456\) 0 0
\(457\) 198.296 + 343.458i 0.433907 + 0.751550i 0.997206 0.0747039i \(-0.0238012\pi\)
−0.563298 + 0.826254i \(0.690468\pi\)
\(458\) 0 0
\(459\) 29.0441 50.3058i 0.0632769 0.109599i
\(460\) 0 0
\(461\) 143.388i 0.311037i −0.987833 0.155519i \(-0.950295\pi\)
0.987833 0.155519i \(-0.0497049\pi\)
\(462\) 0 0
\(463\) 72.3400 0.156242 0.0781210 0.996944i \(-0.475108\pi\)
0.0781210 + 0.996944i \(0.475108\pi\)
\(464\) 0 0
\(465\) 70.2572 + 40.5630i 0.151091 + 0.0872323i
\(466\) 0 0
\(467\) −453.684 + 261.935i −0.971487 + 0.560888i −0.899689 0.436531i \(-0.856207\pi\)
−0.0717975 + 0.997419i \(0.522874\pi\)
\(468\) 0 0
\(469\) 140.159 + 104.342i 0.298847 + 0.222477i
\(470\) 0 0
\(471\) −91.4491 158.394i −0.194159 0.336294i
\(472\) 0 0
\(473\) 60.2134 104.293i 0.127301 0.220492i
\(474\) 0 0
\(475\) 257.205i 0.541484i
\(476\) 0 0
\(477\) 321.431 0.673859
\(478\) 0 0
\(479\) −735.758 424.790i −1.53603 0.886826i −0.999066 0.0432203i \(-0.986238\pi\)
−0.536963 0.843606i \(-0.680428\pi\)
\(480\) 0 0
\(481\) 806.631 465.709i 1.67699 0.968209i
\(482\) 0 0
\(483\) 452.635 + 52.8987i 0.937132 + 0.109521i
\(484\) 0 0
\(485\) −82.2788 142.511i −0.169647 0.293837i
\(486\) 0 0
\(487\) 202.982 351.574i 0.416800 0.721919i −0.578816 0.815458i \(-0.696485\pi\)
0.995616 + 0.0935398i \(0.0298182\pi\)
\(488\) 0 0
\(489\) 245.116i 0.501260i
\(490\) 0 0
\(491\) 661.455 1.34716 0.673580 0.739115i \(-0.264756\pi\)
0.673580 + 0.739115i \(0.264756\pi\)
\(492\) 0 0
\(493\) 111.499 + 64.3740i 0.226165 + 0.130576i
\(494\) 0 0
\(495\) −28.3931 + 16.3927i −0.0573597 + 0.0331167i
\(496\) 0 0
\(497\) 41.3498 353.815i 0.0831987 0.711901i
\(498\) 0 0
\(499\) 119.784 + 207.472i 0.240048 + 0.415775i 0.960728 0.277493i \(-0.0895035\pi\)
−0.720680 + 0.693268i \(0.756170\pi\)
\(500\) 0 0
\(501\) 302.684 524.263i 0.604159 1.04643i
\(502\) 0 0
\(503\) 578.149i 1.14940i −0.818364 0.574701i \(-0.805118\pi\)
0.818364 0.574701i \(-0.194882\pi\)
\(504\) 0 0
\(505\) −63.4524 −0.125648
\(506\) 0 0
\(507\) −1504.45 868.593i −2.96735 1.71320i
\(508\) 0 0
\(509\) 260.924 150.644i 0.512621 0.295962i −0.221290 0.975208i \(-0.571027\pi\)
0.733910 + 0.679247i \(0.237693\pi\)
\(510\) 0 0
\(511\) 332.562 446.722i 0.650807 0.874212i
\(512\) 0 0
\(513\) −133.398 231.052i −0.260035 0.450393i
\(514\) 0 0
\(515\) −186.287 + 322.659i −0.361722 + 0.626521i
\(516\) 0 0
\(517\) 73.7127i 0.142578i
\(518\) 0 0
\(519\) −142.531 −0.274626
\(520\) 0 0
\(521\) −114.812 66.2868i −0.220369 0.127230i 0.385752 0.922602i \(-0.373942\pi\)
−0.606121 + 0.795372i \(0.707275\pi\)
\(522\) 0 0
\(523\) 96.1291 55.5001i 0.183803 0.106119i −0.405275 0.914195i \(-0.632824\pi\)
0.589078 + 0.808076i \(0.299491\pi\)
\(524\) 0 0
\(525\) −160.515 372.101i −0.305743 0.708764i
\(526\) 0 0
\(527\) −12.8744 22.2990i −0.0244295 0.0423132i
\(528\) 0 0
\(529\) 108.416 187.783i 0.204946 0.354976i
\(530\) 0 0
\(531\) 430.258i 0.810279i
\(532\) 0 0
\(533\) −1359.30 −2.55028
\(534\) 0 0
\(535\) −302.305 174.536i −0.565056 0.326235i
\(536\) 0 0
\(537\) −326.811 + 188.685i −0.608587 + 0.351368i
\(538\) 0 0
\(539\) −79.0294 + 83.7711i −0.146622 + 0.155419i
\(540\) 0 0
\(541\) −42.8522 74.2221i −0.0792092 0.137194i 0.823700 0.567026i \(-0.191906\pi\)
−0.902909 + 0.429832i \(0.858573\pi\)
\(542\) 0 0
\(543\) 82.1399 142.271i 0.151271 0.262008i
\(544\) 0 0
\(545\) 505.343i 0.927235i
\(546\) 0 0
\(547\) −674.162 −1.23247 −0.616236 0.787562i \(-0.711343\pi\)
−0.616236 + 0.787562i \(0.711343\pi\)
\(548\) 0 0
\(549\) −8.67842 5.01049i −0.0158077 0.00912657i
\(550\) 0 0
\(551\) 512.109 295.666i 0.929418 0.536600i
\(552\) 0 0
\(553\) 739.310 318.920i 1.33691 0.576708i
\(554\) 0 0
\(555\) 206.653 + 357.934i 0.372348 + 0.644926i
\(556\) 0 0
\(557\) −381.745 + 661.202i −0.685359 + 1.18708i 0.287964 + 0.957641i \(0.407022\pi\)
−0.973324 + 0.229436i \(0.926312\pi\)
\(558\) 0 0
\(559\) 1296.70i 2.31968i
\(560\) 0 0
\(561\) 30.8674 0.0550221
\(562\) 0 0
\(563\) −307.458 177.511i −0.546107 0.315295i 0.201444 0.979500i \(-0.435437\pi\)
−0.747550 + 0.664205i \(0.768770\pi\)
\(564\) 0 0
\(565\) 324.830 187.541i 0.574921 0.331931i
\(566\) 0 0
\(567\) 568.478 + 423.203i 1.00261 + 0.746390i
\(568\) 0 0
\(569\) −263.535 456.455i −0.463154 0.802206i 0.535962 0.844242i \(-0.319949\pi\)
−0.999116 + 0.0420357i \(0.986616\pi\)
\(570\) 0 0
\(571\) 257.886 446.671i 0.451639 0.782262i −0.546849 0.837231i \(-0.684173\pi\)
0.998488 + 0.0549695i \(0.0175062\pi\)
\(572\) 0 0
\(573\) 1216.18i 2.12248i
\(574\) 0 0
\(575\) 277.596 0.482775
\(576\) 0 0
\(577\) 182.029 + 105.095i 0.315476 + 0.182140i 0.649374 0.760469i \(-0.275031\pi\)
−0.333898 + 0.942609i \(0.608364\pi\)
\(578\) 0 0
\(579\) −444.689 + 256.741i −0.768029 + 0.443422i
\(580\) 0 0
\(581\) 1071.63 + 125.240i 1.84446 + 0.215559i
\(582\) 0 0
\(583\) −82.5287 142.944i −0.141559 0.245187i
\(584\) 0 0
\(585\) 176.510 305.724i 0.301726 0.522605i
\(586\) 0 0
\(587\) 91.8797i 0.156524i −0.996933 0.0782621i \(-0.975063\pi\)
0.996933 0.0782621i \(-0.0249371\pi\)
\(588\) 0 0
\(589\) −118.262 −0.200785
\(590\) 0 0
\(591\) 557.552 + 321.903i 0.943405 + 0.544675i
\(592\) 0 0
\(593\) −388.734 + 224.436i −0.655538 + 0.378475i −0.790575 0.612366i \(-0.790218\pi\)
0.135037 + 0.990841i \(0.456885\pi\)
\(594\) 0 0
\(595\) 8.82654 75.5254i 0.0148345 0.126933i
\(596\) 0 0
\(597\) 419.110 + 725.919i 0.702026 + 1.21595i
\(598\) 0 0
\(599\) −98.8525 + 171.218i −0.165029 + 0.285839i −0.936666 0.350225i \(-0.886105\pi\)
0.771636 + 0.636064i \(0.219439\pi\)
\(600\) 0 0
\(601\) 232.075i 0.386148i −0.981184 0.193074i \(-0.938154\pi\)
0.981184 0.193074i \(-0.0618458\pi\)
\(602\) 0 0
\(603\) 114.251 0.189471
\(604\) 0 0
\(605\) −304.785 175.968i −0.503777 0.290856i
\(606\) 0 0
\(607\) 709.823 409.816i 1.16940 0.675151i 0.215858 0.976425i \(-0.430745\pi\)
0.953538 + 0.301274i \(0.0974119\pi\)
\(608\) 0 0
\(609\) −556.356 + 747.339i −0.913557 + 1.22716i
\(610\) 0 0
\(611\) 396.853 + 687.370i 0.649514 + 1.12499i
\(612\) 0 0
\(613\) 405.695 702.684i 0.661819 1.14630i −0.318319 0.947984i \(-0.603118\pi\)
0.980137 0.198320i \(-0.0635485\pi\)
\(614\) 0 0
\(615\) 603.175i 0.980773i
\(616\) 0 0
\(617\) 248.808 0.403255 0.201627 0.979462i \(-0.435377\pi\)
0.201627 + 0.979462i \(0.435377\pi\)
\(618\) 0 0
\(619\) 471.762 + 272.372i 0.762136 + 0.440020i 0.830062 0.557671i \(-0.188305\pi\)
−0.0679258 + 0.997690i \(0.521638\pi\)
\(620\) 0 0
\(621\) −249.369 + 143.973i −0.401561 + 0.231841i
\(622\) 0 0
\(623\) 316.084 + 732.735i 0.507358 + 1.17614i
\(624\) 0 0
\(625\) −7.32049 12.6795i −0.0117128 0.0202871i
\(626\) 0 0
\(627\) 70.8861 122.778i 0.113056 0.195819i
\(628\) 0 0
\(629\) 131.180i 0.208553i
\(630\) 0 0
\(631\) −407.805 −0.646284 −0.323142 0.946350i \(-0.604739\pi\)
−0.323142 + 0.946350i \(0.604739\pi\)
\(632\) 0 0
\(633\) −802.069 463.075i −1.26709 0.731556i
\(634\) 0 0
\(635\) −422.578 + 243.976i −0.665478 + 0.384214i
\(636\) 0 0
\(637\) 285.942 1206.64i 0.448888 1.89425i
\(638\) 0 0
\(639\) −116.459 201.714i −0.182253 0.315671i
\(640\) 0 0
\(641\) −322.840 + 559.175i −0.503650 + 0.872347i 0.496341 + 0.868128i \(0.334677\pi\)
−0.999991 + 0.00421968i \(0.998657\pi\)
\(642\) 0 0
\(643\) 932.869i 1.45081i 0.688324 + 0.725403i \(0.258347\pi\)
−0.688324 + 0.725403i \(0.741653\pi\)
\(644\) 0 0
\(645\) −575.397 −0.892089
\(646\) 0 0
\(647\) −420.287 242.653i −0.649594 0.375043i 0.138707 0.990333i \(-0.455705\pi\)
−0.788301 + 0.615290i \(0.789039\pi\)
\(648\) 0 0
\(649\) 191.341 110.471i 0.294824 0.170217i
\(650\) 0 0
\(651\) 171.092 73.8046i 0.262813 0.113371i
\(652\) 0 0
\(653\) 180.587 + 312.786i 0.276550 + 0.478998i 0.970525 0.241001i \(-0.0774757\pi\)
−0.693975 + 0.719999i \(0.744142\pi\)
\(654\) 0 0
\(655\) 93.8340 162.525i 0.143258 0.248130i
\(656\) 0 0
\(657\) 364.146i 0.554255i
\(658\) 0 0
\(659\) −180.761 −0.274296 −0.137148 0.990551i \(-0.543794\pi\)
−0.137148 + 0.990551i \(0.543794\pi\)
\(660\) 0 0
\(661\) 510.800 + 294.910i 0.772768 + 0.446158i 0.833861 0.551974i \(-0.186125\pi\)
−0.0610929 + 0.998132i \(0.519459\pi\)
\(662\) 0 0
\(663\) −287.838 + 166.183i −0.434144 + 0.250653i
\(664\) 0 0
\(665\) −280.141 208.551i −0.421264 0.313610i
\(666\) 0 0
\(667\) −319.106 552.708i −0.478420 0.828648i
\(668\) 0 0
\(669\) −199.521 + 345.580i −0.298237 + 0.516562i
\(670\) 0 0
\(671\) 5.14585i 0.00766893i
\(672\) 0 0
\(673\) −416.772 −0.619276 −0.309638 0.950855i \(-0.600208\pi\)
−0.309638 + 0.950855i \(0.600208\pi\)
\(674\) 0 0
\(675\) 221.752 + 128.029i 0.328522 + 0.189672i
\(676\) 0 0
\(677\) 398.113 229.851i 0.588055 0.339514i −0.176273 0.984341i \(-0.556404\pi\)
0.764328 + 0.644827i \(0.223071\pi\)
\(678\) 0 0
\(679\) −375.403 43.8728i −0.552877 0.0646139i
\(680\) 0 0
\(681\) 521.299 + 902.916i 0.765490 + 1.32587i
\(682\) 0 0
\(683\) 560.093 970.109i 0.820048 1.42036i −0.0855985 0.996330i \(-0.527280\pi\)
0.905646 0.424034i \(-0.139386\pi\)
\(684\) 0 0
\(685\) 289.843i 0.423128i
\(686\) 0 0
\(687\) −651.021 −0.947629
\(688\) 0 0
\(689\) 1539.16 + 888.633i 2.23390 + 1.28974i
\(690\) 0 0
\(691\) −370.080 + 213.666i −0.535572 + 0.309213i −0.743283 0.668978i \(-0.766732\pi\)
0.207710 + 0.978190i \(0.433399\pi\)
\(692\) 0 0
\(693\) −8.74097 + 74.7932i −0.0126132 + 0.107927i
\(694\) 0 0
\(695\) −140.279 242.971i −0.201840 0.349598i
\(696\) 0 0
\(697\) −95.7214 + 165.794i −0.137333 + 0.237868i
\(698\) 0 0
\(699\) 1309.49i 1.87337i
\(700\) 0 0
\(701\) −99.9460 −0.142576 −0.0712882 0.997456i \(-0.522711\pi\)
−0.0712882 + 0.997456i \(0.522711\pi\)
\(702\) 0 0
\(703\) −521.782 301.251i −0.742222 0.428522i
\(704\) 0 0
\(705\) −305.013 + 176.099i −0.432643 + 0.249786i
\(706\) 0 0
\(707\) −87.0272 + 116.901i −0.123094 + 0.165349i
\(708\) 0 0
\(709\) −19.5862 33.9244i −0.0276252 0.0478482i 0.851882 0.523733i \(-0.175461\pi\)
−0.879507 + 0.475885i \(0.842128\pi\)
\(710\) 0 0
\(711\) 263.231 455.930i 0.370227 0.641251i
\(712\) 0 0
\(713\) 127.638i 0.179015i
\(714\) 0 0
\(715\) −181.279 −0.253536
\(716\) 0 0
\(717\) −55.9871 32.3242i −0.0780853 0.0450825i
\(718\) 0 0
\(719\) −668.482 + 385.948i −0.929739 + 0.536785i −0.886729 0.462290i \(-0.847028\pi\)
−0.0430100 + 0.999075i \(0.513695\pi\)
\(720\) 0 0
\(721\) 338.950 + 785.744i 0.470111 + 1.08980i
\(722\) 0 0
\(723\) 223.180 + 386.559i 0.308686 + 0.534659i
\(724\) 0 0
\(725\) −283.766 + 491.497i −0.391401 + 0.677927i
\(726\) 0 0
\(727\) 963.864i 1.32581i 0.748703 + 0.662905i \(0.230677\pi\)
−0.748703 + 0.662905i \(0.769323\pi\)
\(728\) 0 0
\(729\) −77.0650 −0.105713
\(730\) 0 0
\(731\) 158.159 + 91.3131i 0.216360 + 0.124915i
\(732\) 0 0
\(733\) −82.3471 + 47.5431i −0.112343 + 0.0648610i −0.555118 0.831771i \(-0.687327\pi\)
0.442776 + 0.896632i \(0.353994\pi\)
\(734\) 0 0
\(735\) 535.434 + 126.884i 0.728481 + 0.172631i
\(736\) 0 0
\(737\) −29.3344 50.8086i −0.0398024 0.0689398i
\(738\) 0 0
\(739\) 574.401 994.892i 0.777268 1.34627i −0.156243 0.987719i \(-0.549938\pi\)
0.933511 0.358549i \(-0.116729\pi\)
\(740\) 0 0
\(741\) 1526.54i 2.06011i
\(742\) 0 0
\(743\) 232.652 0.313126 0.156563 0.987668i \(-0.449959\pi\)
0.156563 + 0.987668i \(0.449959\pi\)
\(744\) 0 0
\(745\) −468.346 270.399i −0.628652 0.362952i
\(746\) 0 0
\(747\) 610.949 352.731i 0.817869 0.472197i
\(748\) 0 0
\(749\) −736.178 + 317.569i −0.982881 + 0.423990i
\(750\) 0 0
\(751\) −343.079 594.230i −0.456829 0.791252i 0.541962 0.840403i \(-0.317682\pi\)
−0.998791 + 0.0491513i \(0.984348\pi\)
\(752\) 0 0
\(753\) −404.105 + 699.931i −0.536660 + 0.929523i
\(754\) 0 0
\(755\) 700.325i 0.927582i
\(756\) 0 0
\(757\) 657.058 0.867976 0.433988 0.900919i \(-0.357106\pi\)
0.433988 + 0.900919i \(0.357106\pi\)
\(758\) 0 0
\(759\) −132.512 76.5058i −0.174588 0.100798i
\(760\) 0 0
\(761\) −1063.63 + 614.086i −1.39767 + 0.806946i −0.994148 0.108024i \(-0.965548\pi\)
−0.403523 + 0.914970i \(0.632214\pi\)
\(762\) 0 0
\(763\) −931.018 693.096i −1.22021 0.908383i
\(764\) 0 0
\(765\) −24.8595 43.0579i −0.0324961 0.0562848i
\(766\) 0 0
\(767\) −1189.50 + 2060.27i −1.55085 + 2.68614i
\(768\) 0 0
\(769\) 499.279i 0.649257i −0.945842 0.324629i \(-0.894761\pi\)
0.945842 0.324629i \(-0.105239\pi\)
\(770\) 0 0
\(771\) 1776.12 2.30366
\(772\) 0 0
\(773\) −277.318 160.110i −0.358756 0.207128i 0.309779 0.950809i \(-0.399745\pi\)
−0.668535 + 0.743681i \(0.733078\pi\)
\(774\) 0 0
\(775\) 98.2960 56.7512i 0.126834 0.0732274i
\(776\) 0 0
\(777\) 942.872 + 110.192i 1.21348 + 0.141817i
\(778\) 0 0
\(779\) 439.643 + 761.484i 0.564368 + 0.977514i
\(780\) 0 0
\(781\) −59.8029 + 103.582i −0.0765722 + 0.132627i
\(782\) 0 0
\(783\) 588.695i 0.751845i
\(784\) 0 0
\(785\) 151.279 0.192712
\(786\) 0 0
\(787\) 490.946 + 283.448i 0.623820 + 0.360162i 0.778355 0.627825i \(-0.216055\pi\)
−0.154535 + 0.987987i \(0.549388\pi\)
\(788\) 0 0
\(789\) −286.198 + 165.236i −0.362735 + 0.209425i
\(790\) 0 0
\(791\) 100.001