Properties

Label 224.3.s.a.129.2
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 129.2
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.33.2

$q$-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 −0.137233 0.990539i \(-0.543821\pi\)
−0.926448 + 0.376422i \(0.877154\pi\)
\(4\) 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 −0.914486 0.404618i \(-0.867404\pi\)
0.807653 + 0.589659i \(0.200738\pi\)
\(12\) 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 −0.824308 0.566142i \(-0.808436\pi\)
0.0781390 + 0.996942i \(0.475102\pi\)
\(20\) 0 0
\(21\) −15.4021 + 20.6893i −0.733435 + 0.985205i
\(22\) 0 0
\(23\) 8.83413 + 15.3012i 0.384093 + 0.665268i 0.991643 0.129013i \(-0.0411810\pi\)
−0.607550 + 0.794281i \(0.707848\pi\)
\(24\) 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 0.597502 0.801867i \(-0.296160\pi\)
−0.395686 + 0.918386i \(0.629493\pi\)
\(32\) 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 \(-0.703162\pi\)
−0.595793 + 0.803138i \(0.703162\pi\)
\(44\) 0 0
\(45\) −12.0805 6.97466i −0.268455 0.154992i
\(46\) 0 0
\(47\) −27.1609 + 15.6814i −0.577892 + 0.333646i −0.760295 0.649578i \(-0.774946\pi\)
0.182403 + 0.983224i \(0.441612\pi\)
\(48\) 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 −0.387695 0.921788i \(-0.626728\pi\)
−0.992139 + 0.125141i \(0.960062\pi\)
\(60\) 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 −0.944008 0.329922i \(-0.892977\pi\)
0.757725 + 0.652574i \(0.226311\pi\)
\(68\) 0 0
\(69\) 65.1022i 0.943510i
\(70\) 0 0
\(71\) 50.8890 0.716746 0.358373 0.933579i \(-0.383332\pi\)
0.358373 + 0.933579i \(0.383332\pi\)
\(72\) 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 \(0.0928814\pi\)
−0.229733 + 0.973254i \(0.573785\pi\)
\(80\) 0 0
\(81\) 50.6220 87.6799i 0.624963 1.08247i
\(82\) 0 0
\(83\) 154.132i 1.85701i 0.371318 + 0.928506i \(0.378906\pi\)
−0.371318 + 0.928506i \(0.621094\pi\)
\(84\) 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 −0.916371 0.400330i \(-0.868895\pi\)
−0.111489 + 0.993766i \(0.535562\pi\)
\(104\) 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 \(-0.986897\pi\)
0.463937 0.885868i \(-0.346436\pi\)
\(108\) 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 \(-0.717082\pi\)
−0.630334 + 0.776324i \(0.717082\pi\)
\(128\) 0 0
\(129\) 163.503 + 94.3987i 1.26747 + 0.731773i
\(130\) 0 0
\(131\) 53.3272 30.7885i 0.407078 0.235027i −0.282455 0.959280i \(-0.591149\pi\)
0.689534 + 0.724254i \(0.257816\pi\)
\(132\) 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 \(-0.892568\pi\)
0.943583 0.331136i \(-0.107432\pi\)
\(140\) 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 \(-0.558097\pi\)
0.942394 0.334506i \(-0.108570\pi\)
\(152\) 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 0.949832 0.312761i \(-0.101254\pi\)
−0.745775 + 0.666198i \(0.767920\pi\)
\(164\) 0 0
\(165\) −13.1969 + 22.8577i −0.0799813 + 0.138532i
\(166\) 0 0
\(167\) 164.292i 0.983786i 0.870656 + 0.491893i \(0.163695\pi\)
−0.870656 + 0.491893i \(0.836305\pi\)
\(168\) 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 −0.686794 0.726853i \(-0.740982\pi\)
0.972870 + 0.231354i \(0.0743157\pi\)
\(180\) 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 \(0.165406\pi\)
−0.00396184 + 0.999992i \(0.501261\pi\)
\(192\) 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 −0.0847227 0.996405i \(-0.527000\pi\)
−0.905273 + 0.424830i \(0.860334\pi\)
\(200\) 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 \(-0.296908\pi\)
0.595617 + 0.803269i \(0.296908\pi\)
\(212\) 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 \(-0.921928\pi\)
0.970072 0.242818i \(-0.0780718\pi\)
\(224\) 0 0
\(225\) −71.9118 −0.319608
\(226\) 0 0
\(227\) −245.045 141.477i −1.07949 0.623245i −0.148733 0.988877i \(-0.547519\pi\)
−0.930759 + 0.365632i \(0.880853\pi\)
\(228\) 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 \(-0.488314\pi\)
0.0367052 + 0.999326i \(0.488314\pi\)
\(240\) 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 \(-0.856063\pi\)
0.899492 0.436937i \(-0.143937\pi\)
\(252\) 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 −0.768089 0.640343i \(-0.778792\pi\)
0.938598 + 0.345013i \(0.112125\pi\)
\(264\) 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 −0.358062 0.933698i \(-0.616562\pi\)
0.629575 + 0.776939i \(0.283229\pi\)
\(272\) 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 0.819547 0.573012i \(-0.194225\pi\)
−0.0864689 + 0.996255i \(0.527558\pi\)
\(284\) 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 \(0.131757\pi\)
−0.915549 + 0.402208i \(0.868243\pi\)
\(308\) 0 0
\(309\) 450.446 1.45775
\(310\) 0 0
\(311\) 294.487 + 170.022i 0.946905 + 0.546696i 0.892118 0.451802i \(-0.149219\pi\)
0.0547867 + 0.998498i \(0.482552\pi\)
\(312\) 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 0.913861 0.406027i \(-0.133086\pi\)
−0.808560 + 0.588413i \(0.799753\pi\)
\(332\) 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 \(0.470956\pi\)
−0.907982 + 0.419010i \(0.862377\pi\)
\(348\) 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 0.687192 0.726476i \(-0.258843\pi\)
−0.972743 + 0.231888i \(0.925510\pi\)
\(360\) 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 0.501989 0.864874i \(-0.332602\pi\)
−0.498008 + 0.867172i \(0.665935\pi\)
\(368\) 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 \(-0.274484\pi\)
0.650680 + 0.759352i \(0.274484\pi\)
\(380\) 0 0
\(381\) 510.902 + 294.969i 1.34095 + 0.774197i
\(382\) 0 0
\(383\) 496.266 286.519i 1.29573 0.748092i 0.316069 0.948736i \(-0.397637\pi\)
0.979664 + 0.200645i \(0.0643036\pi\)
\(384\) 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 \(-0.907902\pi\)
0.958434 0.285313i \(-0.0920977\pi\)
\(420\) 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 \(0.410882\pi\)
−0.970470 + 0.241223i \(0.922451\pi\)
\(432\) 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 −0.798202 0.602390i \(-0.794215\pi\)
0.122584 + 0.992458i \(0.460882\pi\)
\(440\) 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 \(0.0642421\pi\)
−0.316252 + 0.948675i \(0.602425\pi\)
\(444\) 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 \(-0.524892\pi\)
−0.0781210 + 0.996944i \(0.524892\pi\)
\(464\) 0 0
\(465\) 70.2572 + 40.5630i 0.151091 + 0.0872323i
\(466\) 0 0
\(467\) 453.684 261.935i 0.971487 0.560888i 0.0717975 0.997419i \(-0.477126\pi\)
0.899689 + 0.436531i \(0.143793\pi\)
\(468\) 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 \(0.0137617\pi\)
0.536963 + 0.843606i \(0.319572\pi\)
\(480\) 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 −0.995616 0.0935398i \(-0.970182\pi\)
0.578816 + 0.815458i \(0.303515\pi\)
\(488\) 0 0
\(489\) 245.116i 0.501260i
\(490\) 0 0
\(491\) −661.455 −1.34716 −0.673580 0.739115i \(-0.735244\pi\)
−0.673580 + 0.739115i \(0.735244\pi\)
\(492\) 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 0.720680 0.693268i \(-0.243830\pi\)
−0.960728 + 0.277493i \(0.910496\pi\)
\(500\) 0 0
\(501\) 302.684 524.263i 0.604159 1.04643i
\(502\) 0 0
\(503\) 578.149i 1.14940i 0.818364 + 0.574701i \(0.194882\pi\)
−0.818364 + 0.574701i \(0.805118\pi\)
\(504\) 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 −0.589078 0.808076i \(-0.700509\pi\)
0.405275 + 0.914195i \(0.367176\pi\)
\(524\) 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 \(-0.288657\pi\)
0.616236 + 0.787562i \(0.288657\pi\)
\(548\) 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 0.747550 0.664205i \(-0.231230\pi\)
−0.201444 + 0.979500i \(0.564563\pi\)
\(564\) 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 −0.998488 0.0549695i \(-0.982494\pi\)
0.546849 + 0.837231i \(0.315827\pi\)
\(572\) 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 \(0.0249371\pi\)
−0.996933 + 0.0782621i \(0.975063\pi\)
\(588\) 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 −0.771636 0.636064i \(-0.780561\pi\)
0.936666 + 0.350225i \(0.113895\pi\)
\(600\) 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 −0.953538 0.301274i \(-0.902588\pi\)
−0.215858 + 0.976425i \(0.569255\pi\)
\(608\) 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 0.0679258 0.997690i \(-0.478362\pi\)
−0.830062 + 0.557671i \(0.811695\pi\)
\(620\) 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 \(-0.395261\pi\)
0.323142 + 0.946350i \(0.395261\pi\)
\(632\) 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 \(-0.741653\pi\)
0.688324 0.725403i \(-0.258347\pi\)
\(644\) 0 0
\(645\) −575.397 −0.892089
\(646\) 0 0
\(647\) 420.287 + 242.653i 0.649594 + 0.375043i 0.788301 0.615290i \(-0.210961\pi\)
−0.138707 + 0.990333i \(0.544295\pi\)
\(648\) 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 \(-0.456206\pi\)
0.137148 + 0.990551i \(0.456206\pi\)
\(660\) 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 \(0.472720\pi\)
−0.905646 + 0.424034i \(0.860614\pi\)
\(684\) 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 −0.207710 0.978190i \(-0.566601\pi\)
0.743283 + 0.668978i \(0.233268\pi\)
\(692\) 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 0.0430100 0.999075i \(-0.486305\pi\)
0.886729 + 0.462290i \(0.152972\pi\)
\(720\) 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 \(-0.769323\pi\)
0.748703 0.662905i \(-0.230677\pi\)
\(728\) 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 \(0.450062\pi\)
−0.933511 + 0.358549i \(0.883271\pi\)
\(740\) 0 0
\(741\) 1526.54i 2.06011i
\(742\) 0 0
\(743\) −232.652 −0.313126 −0.156563 0.987668i \(-0.550041\pi\)
−0.156563 + 0.987668i \(0.550041\pi\)
\(744\) 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 0.998791 0.0491513i \(-0.0156516\pi\)
−0.541962 + 0.840403i \(0.682318\pi\)
\(752\) 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 0.154535 0.987987i \(-0.450612\pi\)
−0.778355 + 0.627825i \(0.783945\pi\)
\(788\) 0 0
\(789\) −286.198 + 165.236i −0.362735 + 0.209425i
\(790\) 0 0
\(791\) −100.001 +