Properties

Label 304.3.r.a.65.1
Level $304$
Weight $3$
Character 304.65
Analytic conductor $8.283$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 304 = 2^{4} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 304.r (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.28340003655\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\sqrt{-2}, \sqrt{-3})\)
Defining polynomial: \(x^{4} - 2 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 38)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 65.1
Root \(-1.22474 + 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 304.65
Dual form 304.3.r.a.145.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.72474 - 1.57313i) q^{3} +(0.500000 - 0.866025i) q^{5} -6.89898 q^{7} +(0.449490 + 0.778539i) q^{9} +O(q^{10})\) \(q+(-2.72474 - 1.57313i) q^{3} +(0.500000 - 0.866025i) q^{5} -6.89898 q^{7} +(0.449490 + 0.778539i) q^{9} +14.8990 q^{11} +(-14.8485 + 8.57277i) q^{13} +(-2.72474 + 1.57313i) q^{15} +(1.05051 - 1.81954i) q^{17} +(-11.3485 + 15.2385i) q^{19} +(18.7980 + 10.8530i) q^{21} +(13.5227 + 23.4220i) q^{23} +(12.0000 + 20.7846i) q^{25} +25.4880i q^{27} +(-5.54541 + 3.20164i) q^{29} -31.1769i q^{31} +(-40.5959 - 23.4381i) q^{33} +(-3.44949 + 5.97469i) q^{35} +28.9199i q^{37} +53.9444 q^{39} +(55.9393 + 32.2966i) q^{41} +(-37.6691 + 65.2449i) q^{43} +0.898979 q^{45} +(-5.77015 - 9.99420i) q^{47} -1.40408 q^{49} +(-5.72474 + 3.30518i) q^{51} +(-69.2878 + 40.0033i) q^{53} +(7.44949 - 12.9029i) q^{55} +(54.8939 - 23.6684i) q^{57} +(-50.9166 - 29.3967i) q^{59} +(-1.09592 - 1.89819i) q^{61} +(-3.10102 - 5.37113i) q^{63} +17.1455i q^{65} +(51.6589 - 29.8253i) q^{67} -85.0920i q^{69} +(-87.5227 - 50.5313i) q^{71} +(63.6918 - 110.317i) q^{73} -75.5103i q^{75} -102.788 q^{77} +(5.78036 + 3.33729i) q^{79} +(44.1413 - 76.4550i) q^{81} +1.30306 q^{83} +(-1.05051 - 1.81954i) q^{85} +20.1464 q^{87} +(5.84847 - 3.37662i) q^{89} +(102.439 - 59.1433i) q^{91} +(-49.0454 + 84.9491i) q^{93} +(7.52270 + 17.4473i) q^{95} +(-114.152 - 65.9054i) q^{97} +(6.69694 + 11.5994i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 6 q^{3} + 2 q^{5} - 8 q^{7} - 8 q^{9} + O(q^{10}) \) \( 4 q - 6 q^{3} + 2 q^{5} - 8 q^{7} - 8 q^{9} + 40 q^{11} - 30 q^{13} - 6 q^{15} + 14 q^{17} - 16 q^{19} + 36 q^{21} + 10 q^{23} + 48 q^{25} + 66 q^{29} - 84 q^{33} - 4 q^{35} + 108 q^{39} + 18 q^{41} - 38 q^{43} - 16 q^{45} + 70 q^{47} - 84 q^{49} - 18 q^{51} - 42 q^{53} + 20 q^{55} + 102 q^{57} - 42 q^{59} + 74 q^{61} - 32 q^{63} - 102 q^{67} - 306 q^{71} + 98 q^{73} - 176 q^{77} + 126 q^{79} + 10 q^{81} + 64 q^{83} - 14 q^{85} + 12 q^{87} - 6 q^{89} + 204 q^{91} - 108 q^{93} - 14 q^{95} - 486 q^{97} - 32 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/304\mathbb{Z}\right)^\times\).

\(n\) \(97\) \(191\) \(229\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(1\) \(1\)

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
\(3\) −2.72474 1.57313i −0.908248 0.524377i −0.0283812 0.999597i \(-0.509035\pi\)
−0.879867 + 0.475220i \(0.842369\pi\)
\(4\) 0 0
\(5\) 0.500000 0.866025i 0.100000 0.173205i −0.811684 0.584096i \(-0.801449\pi\)
0.911684 + 0.410891i \(0.134782\pi\)
\(6\) 0 0
\(7\) −6.89898 −0.985568 −0.492784 0.870152i \(-0.664021\pi\)
−0.492784 + 0.870152i \(0.664021\pi\)
\(8\) 0 0
\(9\) 0.449490 + 0.778539i 0.0499433 + 0.0865043i
\(10\) 0 0
\(11\) 14.8990 1.35445 0.677226 0.735775i \(-0.263182\pi\)
0.677226 + 0.735775i \(0.263182\pi\)
\(12\) 0 0
\(13\) −14.8485 + 8.57277i −1.14219 + 0.659444i −0.946972 0.321316i \(-0.895875\pi\)
−0.195218 + 0.980760i \(0.562541\pi\)
\(14\) 0 0
\(15\) −2.72474 + 1.57313i −0.181650 + 0.104875i
\(16\) 0 0
\(17\) 1.05051 1.81954i 0.0617947 0.107032i −0.833473 0.552560i \(-0.813651\pi\)
0.895268 + 0.445529i \(0.146984\pi\)
\(18\) 0 0
\(19\) −11.3485 + 15.2385i −0.597288 + 0.802027i
\(20\) 0 0
\(21\) 18.7980 + 10.8530i 0.895141 + 0.516810i
\(22\) 0 0
\(23\) 13.5227 + 23.4220i 0.587944 + 1.01835i 0.994501 + 0.104723i \(0.0333957\pi\)
−0.406558 + 0.913625i \(0.633271\pi\)
\(24\) 0 0
\(25\) 12.0000 + 20.7846i 0.480000 + 0.831384i
\(26\) 0 0
\(27\) 25.4880i 0.943998i
\(28\) 0 0
\(29\) −5.54541 + 3.20164i −0.191221 + 0.110401i −0.592554 0.805531i \(-0.701880\pi\)
0.401333 + 0.915932i \(0.368547\pi\)
\(30\) 0 0
\(31\) 31.1769i 1.00571i −0.864372 0.502853i \(-0.832284\pi\)
0.864372 0.502853i \(-0.167716\pi\)
\(32\) 0 0
\(33\) −40.5959 23.4381i −1.23018 0.710244i
\(34\) 0 0
\(35\) −3.44949 + 5.97469i −0.0985568 + 0.170705i
\(36\) 0 0
\(37\) 28.9199i 0.781620i 0.920471 + 0.390810i \(0.127805\pi\)
−0.920471 + 0.390810i \(0.872195\pi\)
\(38\) 0 0
\(39\) 53.9444 1.38319
\(40\) 0 0
\(41\) 55.9393 + 32.2966i 1.36437 + 0.787721i 0.990202 0.139639i \(-0.0445942\pi\)
0.374170 + 0.927360i \(0.377928\pi\)
\(42\) 0 0
\(43\) −37.6691 + 65.2449i −0.876026 + 1.51732i −0.0203609 + 0.999793i \(0.506482\pi\)
−0.855665 + 0.517529i \(0.826852\pi\)
\(44\) 0 0
\(45\) 0.898979 0.0199773
\(46\) 0 0
\(47\) −5.77015 9.99420i −0.122769 0.212642i 0.798090 0.602539i \(-0.205844\pi\)
−0.920859 + 0.389896i \(0.872511\pi\)
\(48\) 0 0
\(49\) −1.40408 −0.0286547
\(50\) 0 0
\(51\) −5.72474 + 3.30518i −0.112250 + 0.0648075i
\(52\) 0 0
\(53\) −69.2878 + 40.0033i −1.30732 + 0.754779i −0.981647 0.190705i \(-0.938923\pi\)
−0.325669 + 0.945484i \(0.605589\pi\)
\(54\) 0 0
\(55\) 7.44949 12.9029i 0.135445 0.234598i
\(56\) 0 0
\(57\) 54.8939 23.6684i 0.963050 0.415235i
\(58\) 0 0
\(59\) −50.9166 29.3967i −0.862993 0.498249i 0.00202049 0.999998i \(-0.499357\pi\)
−0.865013 + 0.501749i \(0.832690\pi\)
\(60\) 0 0
\(61\) −1.09592 1.89819i −0.0179659 0.0311178i 0.856903 0.515478i \(-0.172386\pi\)
−0.874869 + 0.484360i \(0.839052\pi\)
\(62\) 0 0
\(63\) −3.10102 5.37113i −0.0492225 0.0852560i
\(64\) 0 0
\(65\) 17.1455i 0.263777i
\(66\) 0 0
\(67\) 51.6589 29.8253i 0.771029 0.445154i −0.0622127 0.998063i \(-0.519816\pi\)
0.833241 + 0.552909i \(0.186482\pi\)
\(68\) 0 0
\(69\) 85.0920i 1.23322i
\(70\) 0 0
\(71\) −87.5227 50.5313i −1.23271 0.711708i −0.265119 0.964216i \(-0.585411\pi\)
−0.967595 + 0.252508i \(0.918745\pi\)
\(72\) 0 0
\(73\) 63.6918 110.317i 0.872491 1.51120i 0.0130791 0.999914i \(-0.495837\pi\)
0.859412 0.511284i \(-0.170830\pi\)
\(74\) 0 0
\(75\) 75.5103i 1.00680i
\(76\) 0 0
\(77\) −102.788 −1.33491
\(78\) 0 0
\(79\) 5.78036 + 3.33729i 0.0731691 + 0.0422442i 0.536138 0.844130i \(-0.319883\pi\)
−0.462969 + 0.886374i \(0.653216\pi\)
\(80\) 0 0
\(81\) 44.1413 76.4550i 0.544955 0.943889i
\(82\) 0 0
\(83\) 1.30306 0.0156995 0.00784977 0.999969i \(-0.497501\pi\)
0.00784977 + 0.999969i \(0.497501\pi\)
\(84\) 0 0
\(85\) −1.05051 1.81954i −0.0123589 0.0214063i
\(86\) 0 0
\(87\) 20.1464 0.231568
\(88\) 0 0
\(89\) 5.84847 3.37662i 0.0657131 0.0379395i −0.466783 0.884372i \(-0.654587\pi\)
0.532497 + 0.846432i \(0.321254\pi\)
\(90\) 0 0
\(91\) 102.439 59.1433i 1.12571 0.649927i
\(92\) 0 0
\(93\) −49.0454 + 84.9491i −0.527370 + 0.913432i
\(94\) 0 0
\(95\) 7.52270 + 17.4473i 0.0791864 + 0.183656i
\(96\) 0 0
\(97\) −114.152 65.9054i −1.17682 0.679437i −0.221543 0.975151i \(-0.571109\pi\)
−0.955277 + 0.295713i \(0.904443\pi\)
\(98\) 0 0
\(99\) 6.69694 + 11.5994i 0.0676458 + 0.117166i
\(100\) 0 0
\(101\) −3.24235 5.61591i −0.0321024 0.0556031i 0.849528 0.527544i \(-0.176887\pi\)
−0.881630 + 0.471941i \(0.843554\pi\)
\(102\) 0 0
\(103\) 80.0243i 0.776935i 0.921462 + 0.388467i \(0.126995\pi\)
−0.921462 + 0.388467i \(0.873005\pi\)
\(104\) 0 0
\(105\) 18.7980 10.8530i 0.179028 0.103362i
\(106\) 0 0
\(107\) 80.0243i 0.747890i 0.927451 + 0.373945i \(0.121995\pi\)
−0.927451 + 0.373945i \(0.878005\pi\)
\(108\) 0 0
\(109\) −14.2423 8.22282i −0.130664 0.0754387i 0.433243 0.901277i \(-0.357369\pi\)
−0.563907 + 0.825838i \(0.690702\pi\)
\(110\) 0 0
\(111\) 45.4949 78.7995i 0.409864 0.709905i
\(112\) 0 0
\(113\) 132.843i 1.17560i 0.809006 + 0.587801i \(0.200006\pi\)
−0.809006 + 0.587801i \(0.799994\pi\)
\(114\) 0 0
\(115\) 27.0454 0.235177
\(116\) 0 0
\(117\) −13.3485 7.70674i −0.114089 0.0658696i
\(118\) 0 0
\(119\) −7.24745 + 12.5529i −0.0609029 + 0.105487i
\(120\) 0 0
\(121\) 100.980 0.834542
\(122\) 0 0
\(123\) −101.614 176.000i −0.826126 1.43089i
\(124\) 0 0
\(125\) 49.0000 0.392000
\(126\) 0 0
\(127\) −108.826 + 62.8306i −0.856896 + 0.494729i −0.862972 0.505253i \(-0.831399\pi\)
0.00607575 + 0.999982i \(0.498066\pi\)
\(128\) 0 0
\(129\) 205.278 118.517i 1.59130 0.918737i
\(130\) 0 0
\(131\) 53.6237 92.8790i 0.409341 0.709000i −0.585475 0.810691i \(-0.699092\pi\)
0.994816 + 0.101691i \(0.0324252\pi\)
\(132\) 0 0
\(133\) 78.2929 105.130i 0.588668 0.790452i
\(134\) 0 0
\(135\) 22.0732 + 12.7440i 0.163505 + 0.0943998i
\(136\) 0 0
\(137\) 1.05051 + 1.81954i 0.00766796 + 0.0132813i 0.869834 0.493345i \(-0.164226\pi\)
−0.862166 + 0.506626i \(0.830893\pi\)
\(138\) 0 0
\(139\) −15.8712 27.4897i −0.114181 0.197767i 0.803271 0.595614i \(-0.203091\pi\)
−0.917452 + 0.397846i \(0.869758\pi\)
\(140\) 0 0
\(141\) 36.3089i 0.257510i
\(142\) 0 0
\(143\) −221.227 + 127.725i −1.54704 + 0.893185i
\(144\) 0 0
\(145\) 6.40329i 0.0441606i
\(146\) 0 0
\(147\) 3.82577 + 2.20881i 0.0260256 + 0.0150259i
\(148\) 0 0
\(149\) −94.8383 + 164.265i −0.636498 + 1.10245i 0.349697 + 0.936863i \(0.386284\pi\)
−0.986196 + 0.165585i \(0.947049\pi\)
\(150\) 0 0
\(151\) 16.2707i 0.107753i 0.998548 + 0.0538764i \(0.0171577\pi\)
−0.998548 + 0.0538764i \(0.982842\pi\)
\(152\) 0 0
\(153\) 1.88877 0.0123449
\(154\) 0 0
\(155\) −27.0000 15.5885i −0.174194 0.100571i
\(156\) 0 0
\(157\) −135.076 + 233.958i −0.860354 + 1.49018i 0.0112344 + 0.999937i \(0.496424\pi\)
−0.871588 + 0.490239i \(0.836909\pi\)
\(158\) 0 0
\(159\) 251.722 1.58316
\(160\) 0 0
\(161\) −93.2929 161.588i −0.579459 1.00365i
\(162\) 0 0
\(163\) 156.697 0.961331 0.480665 0.876904i \(-0.340395\pi\)
0.480665 + 0.876904i \(0.340395\pi\)
\(164\) 0 0
\(165\) −40.5959 + 23.4381i −0.246036 + 0.142049i
\(166\) 0 0
\(167\) 78.0834 45.0815i 0.467565 0.269949i −0.247655 0.968848i \(-0.579660\pi\)
0.715220 + 0.698899i \(0.246326\pi\)
\(168\) 0 0
\(169\) 62.4847 108.227i 0.369732 0.640394i
\(170\) 0 0
\(171\) −16.9648 1.98567i −0.0992093 0.0116121i
\(172\) 0 0
\(173\) −263.379 152.062i −1.52242 0.878969i −0.999649 0.0264959i \(-0.991565\pi\)
−0.522771 0.852473i \(-0.675102\pi\)
\(174\) 0 0
\(175\) −82.7878 143.393i −0.473073 0.819386i
\(176\) 0 0
\(177\) 92.4898 + 160.197i 0.522541 + 0.905068i
\(178\) 0 0
\(179\) 315.198i 1.76088i 0.474156 + 0.880441i \(0.342753\pi\)
−0.474156 + 0.880441i \(0.657247\pi\)
\(180\) 0 0
\(181\) −27.8939 + 16.1045i −0.154110 + 0.0889753i −0.575072 0.818103i \(-0.695026\pi\)
0.420962 + 0.907078i \(0.361693\pi\)
\(182\) 0 0
\(183\) 6.89610i 0.0376836i
\(184\) 0 0
\(185\) 25.0454 + 14.4600i 0.135381 + 0.0781620i
\(186\) 0 0
\(187\) 15.6515 27.1092i 0.0836980 0.144969i
\(188\) 0 0
\(189\) 175.841i 0.930375i
\(190\) 0 0
\(191\) −280.252 −1.46729 −0.733644 0.679534i \(-0.762182\pi\)
−0.733644 + 0.679534i \(0.762182\pi\)
\(192\) 0 0
\(193\) 42.0153 + 24.2575i 0.217696 + 0.125687i 0.604883 0.796314i \(-0.293220\pi\)
−0.387187 + 0.922001i \(0.626553\pi\)
\(194\) 0 0
\(195\) 26.9722 46.7172i 0.138319 0.239575i
\(196\) 0 0
\(197\) 251.909 1.27873 0.639363 0.768905i \(-0.279198\pi\)
0.639363 + 0.768905i \(0.279198\pi\)
\(198\) 0 0
\(199\) 129.694 + 224.637i 0.651729 + 1.12883i 0.982703 + 0.185188i \(0.0592895\pi\)
−0.330974 + 0.943640i \(0.607377\pi\)
\(200\) 0 0
\(201\) −187.677 −0.933714
\(202\) 0 0
\(203\) 38.2577 22.0881i 0.188461 0.108808i
\(204\) 0 0
\(205\) 55.9393 32.2966i 0.272875 0.157544i
\(206\) 0 0
\(207\) −12.1566 + 21.0559i −0.0587277 + 0.101719i
\(208\) 0 0
\(209\) −169.081 + 227.038i −0.808998 + 1.08631i
\(210\) 0 0
\(211\) −60.2503 34.7855i −0.285546 0.164860i 0.350385 0.936606i \(-0.386051\pi\)
−0.635932 + 0.771745i \(0.719384\pi\)
\(212\) 0 0
\(213\) 158.985 + 275.370i 0.746407 + 1.29281i
\(214\) 0 0
\(215\) 37.6691 + 65.2449i 0.175205 + 0.303464i
\(216\) 0 0
\(217\) 215.089i 0.991193i
\(218\) 0 0
\(219\) −347.088 + 200.391i −1.58488 + 0.915029i
\(220\) 0 0
\(221\) 36.0231i 0.163001i
\(222\) 0 0
\(223\) 5.47730 + 3.16232i 0.0245619 + 0.0141808i 0.512231 0.858848i \(-0.328819\pi\)
−0.487669 + 0.873029i \(0.662153\pi\)
\(224\) 0 0
\(225\) −10.7878 + 18.6849i −0.0479456 + 0.0830442i
\(226\) 0 0
\(227\) 55.7402i 0.245552i 0.992434 + 0.122776i \(0.0391796\pi\)
−0.992434 + 0.122776i \(0.960820\pi\)
\(228\) 0 0
\(229\) −132.313 −0.577787 −0.288894 0.957361i \(-0.593287\pi\)
−0.288894 + 0.957361i \(0.593287\pi\)
\(230\) 0 0
\(231\) 280.070 + 161.699i 1.21243 + 0.699994i
\(232\) 0 0
\(233\) 111.859 193.745i 0.480080 0.831523i −0.519659 0.854374i \(-0.673941\pi\)
0.999739 + 0.0228507i \(0.00727424\pi\)
\(234\) 0 0
\(235\) −11.5403 −0.0491077
\(236\) 0 0
\(237\) −10.5000 18.1865i −0.0443038 0.0767364i
\(238\) 0 0
\(239\) 71.3235 0.298425 0.149212 0.988805i \(-0.452326\pi\)
0.149212 + 0.988805i \(0.452326\pi\)
\(240\) 0 0
\(241\) 120.727 69.7018i 0.500942 0.289219i −0.228160 0.973624i \(-0.573271\pi\)
0.729103 + 0.684405i \(0.239938\pi\)
\(242\) 0 0
\(243\) −41.8888 + 24.1845i −0.172382 + 0.0995247i
\(244\) 0 0
\(245\) −0.702041 + 1.21597i −0.00286547 + 0.00496315i
\(246\) 0 0
\(247\) 37.8712 323.556i 0.153325 1.30994i
\(248\) 0 0
\(249\) −3.55051 2.04989i −0.0142591 0.00823248i
\(250\) 0 0
\(251\) 120.038 + 207.912i 0.478239 + 0.828334i 0.999689 0.0249476i \(-0.00794190\pi\)
−0.521450 + 0.853282i \(0.674609\pi\)
\(252\) 0 0
\(253\) 201.474 + 348.964i 0.796342 + 1.37930i
\(254\) 0 0
\(255\) 6.61037i 0.0259230i
\(256\) 0 0
\(257\) 8.37857 4.83737i 0.0326014 0.0188224i −0.483611 0.875283i \(-0.660675\pi\)
0.516212 + 0.856461i \(0.327342\pi\)
\(258\) 0 0
\(259\) 199.518i 0.770340i
\(260\) 0 0
\(261\) −4.98521 2.87821i −0.0191004 0.0110276i
\(262\) 0 0
\(263\) −56.9620 + 98.6611i −0.216586 + 0.375137i −0.953762 0.300563i \(-0.902825\pi\)
0.737176 + 0.675700i \(0.236159\pi\)
\(264\) 0 0
\(265\) 80.0066i 0.301912i
\(266\) 0 0
\(267\) −21.2474 −0.0795785
\(268\) 0 0
\(269\) −348.090 200.970i −1.29402 0.747100i −0.314652 0.949207i \(-0.601888\pi\)
−0.979364 + 0.202106i \(0.935221\pi\)
\(270\) 0 0
\(271\) 199.492 345.530i 0.736133 1.27502i −0.218091 0.975928i \(-0.569983\pi\)
0.954224 0.299092i \(-0.0966836\pi\)
\(272\) 0 0
\(273\) −372.161 −1.36323
\(274\) 0 0
\(275\) 178.788 + 309.669i 0.650137 + 1.12607i
\(276\) 0 0
\(277\) 529.444 1.91135 0.955675 0.294424i \(-0.0951278\pi\)
0.955675 + 0.294424i \(0.0951278\pi\)
\(278\) 0 0
\(279\) 24.2724 14.0137i 0.0869980 0.0502283i
\(280\) 0 0
\(281\) 47.4092 27.3717i 0.168716 0.0974082i −0.413264 0.910611i \(-0.635611\pi\)
0.581980 + 0.813203i \(0.302278\pi\)
\(282\) 0 0
\(283\) −74.4671 + 128.981i −0.263135 + 0.455762i −0.967073 0.254498i \(-0.918090\pi\)
0.703939 + 0.710261i \(0.251423\pi\)
\(284\) 0 0
\(285\) 6.94949 59.3737i 0.0243842 0.208329i
\(286\) 0 0
\(287\) −385.924 222.813i −1.34468 0.776353i
\(288\) 0 0
\(289\) 142.293 + 246.458i 0.492363 + 0.852797i
\(290\) 0 0
\(291\) 207.356 + 359.151i 0.712563 + 1.23420i
\(292\) 0 0
\(293\) 145.685i 0.497218i 0.968604 + 0.248609i \(0.0799734\pi\)
−0.968604 + 0.248609i \(0.920027\pi\)
\(294\) 0 0
\(295\) −50.9166 + 29.3967i −0.172599 + 0.0996498i
\(296\) 0 0
\(297\) 379.744i 1.27860i
\(298\) 0 0
\(299\) −401.583 231.854i −1.34309 0.775431i
\(300\) 0 0
\(301\) 259.879 450.123i 0.863384 1.49542i
\(302\) 0 0
\(303\) 20.4026i 0.0673352i
\(304\) 0 0
\(305\) −2.19184 −0.00718635
\(306\) 0 0
\(307\) −98.0380 56.6023i −0.319342 0.184372i 0.331757 0.943365i \(-0.392359\pi\)
−0.651099 + 0.758993i \(0.725692\pi\)
\(308\) 0 0
\(309\) 125.889 218.046i 0.407407 0.705650i
\(310\) 0 0
\(311\) 105.666 0.339763 0.169882 0.985464i \(-0.445661\pi\)
0.169882 + 0.985464i \(0.445661\pi\)
\(312\) 0 0
\(313\) −124.121 214.984i −0.396552 0.686849i 0.596746 0.802431i \(-0.296460\pi\)
−0.993298 + 0.115582i \(0.963127\pi\)
\(314\) 0 0
\(315\) −6.20204 −0.0196890
\(316\) 0 0
\(317\) −196.061 + 113.196i −0.618488 + 0.357084i −0.776280 0.630388i \(-0.782896\pi\)
0.157792 + 0.987472i \(0.449562\pi\)
\(318\) 0 0
\(319\) −82.6209 + 47.7012i −0.259000 + 0.149534i
\(320\) 0 0
\(321\) 125.889 218.046i 0.392177 0.679270i
\(322\) 0 0
\(323\) 15.8054 + 36.6572i 0.0489330 + 0.113490i
\(324\) 0 0
\(325\) −356.363 205.746i −1.09650 0.633066i
\(326\) 0 0
\(327\) 25.8712 + 44.8102i 0.0791167 + 0.137034i
\(328\) 0 0
\(329\) 39.8082 + 68.9498i 0.120997 + 0.209574i
\(330\) 0 0
\(331\) 293.328i 0.886188i −0.896475 0.443094i \(-0.853881\pi\)
0.896475 0.443094i \(-0.146119\pi\)
\(332\) 0 0
\(333\) −22.5153 + 12.9992i −0.0676135 + 0.0390367i
\(334\) 0 0
\(335\) 59.6506i 0.178061i
\(336\) 0 0
\(337\) −399.393 230.590i −1.18514 0.684243i −0.227945 0.973674i \(-0.573201\pi\)
−0.957199 + 0.289431i \(0.906534\pi\)
\(338\) 0 0
\(339\) 208.980 361.963i 0.616459 1.06774i
\(340\) 0 0
\(341\) 464.504i 1.36218i
\(342\) 0 0
\(343\) 347.737 1.01381
\(344\) 0 0
\(345\) −73.6918 42.5460i −0.213600 0.123322i
\(346\) 0 0
\(347\) 152.129 263.495i 0.438412 0.759351i −0.559156 0.829063i \(-0.688875\pi\)
0.997567 + 0.0697116i \(0.0222079\pi\)
\(348\) 0 0
\(349\) 50.4337 0.144509 0.0722545 0.997386i \(-0.476981\pi\)
0.0722545 + 0.997386i \(0.476981\pi\)
\(350\) 0 0
\(351\) −218.502 378.457i −0.622514 1.07823i
\(352\) 0 0
\(353\) −316.817 −0.897500 −0.448750 0.893657i \(-0.648131\pi\)
−0.448750 + 0.893657i \(0.648131\pi\)
\(354\) 0 0
\(355\) −87.5227 + 50.5313i −0.246543 + 0.142342i
\(356\) 0 0
\(357\) 39.4949 22.8024i 0.110630 0.0638722i
\(358\) 0 0
\(359\) 74.7043 129.392i 0.208090 0.360423i −0.743023 0.669266i \(-0.766609\pi\)
0.951113 + 0.308844i \(0.0999420\pi\)
\(360\) 0 0
\(361\) −103.424 345.868i −0.286494 0.958082i
\(362\) 0 0
\(363\) −275.144 158.854i −0.757971 0.437615i
\(364\) 0 0
\(365\) −63.6918 110.317i −0.174498 0.302240i
\(366\) 0 0
\(367\) 117.038 + 202.716i 0.318905 + 0.552359i 0.980260 0.197714i \(-0.0633517\pi\)
−0.661355 + 0.750073i \(0.730018\pi\)
\(368\) 0 0
\(369\) 58.0679i 0.157366i
\(370\) 0 0
\(371\) 478.015 275.982i 1.28845 0.743887i
\(372\) 0 0
\(373\) 639.738i 1.71512i −0.514387 0.857558i \(-0.671981\pi\)
0.514387 0.857558i \(-0.328019\pi\)
\(374\) 0 0
\(375\) −133.512 77.0835i −0.356033 0.205556i
\(376\) 0 0
\(377\) 54.8939 95.0790i 0.145607 0.252199i
\(378\) 0 0
\(379\) 108.366i 0.285927i −0.989728 0.142963i \(-0.954337\pi\)
0.989728 0.142963i \(-0.0456631\pi\)
\(380\) 0 0
\(381\) 395.363 1.03770
\(382\) 0 0
\(383\) −215.552 124.449i −0.562800 0.324933i 0.191469 0.981499i \(-0.438675\pi\)
−0.754268 + 0.656566i \(0.772008\pi\)
\(384\) 0 0
\(385\) −51.3939 + 89.0168i −0.133491 + 0.231212i
\(386\) 0 0
\(387\) −67.7276 −0.175007
\(388\) 0 0
\(389\) 335.560 + 581.207i 0.862623 + 1.49411i 0.869389 + 0.494129i \(0.164513\pi\)
−0.00676592 + 0.999977i \(0.502154\pi\)
\(390\) 0 0
\(391\) 56.8230 0.145327
\(392\) 0 0
\(393\) −292.222 + 168.714i −0.743567 + 0.429299i
\(394\) 0 0
\(395\) 5.78036 3.33729i 0.0146338 0.00844884i
\(396\) 0 0
\(397\) 46.6816 80.8550i 0.117586 0.203665i −0.801225 0.598364i \(-0.795818\pi\)
0.918811 + 0.394699i \(0.129151\pi\)
\(398\) 0 0
\(399\) −378.712 + 163.288i −0.949152 + 0.409243i
\(400\) 0 0
\(401\) 242.484 + 139.998i 0.604699 + 0.349123i 0.770888 0.636971i \(-0.219813\pi\)
−0.166189 + 0.986094i \(0.553146\pi\)
\(402\) 0 0
\(403\) 267.272 + 462.929i 0.663207 + 1.14871i
\(404\) 0 0
\(405\) −44.1413 76.4550i −0.108991 0.188778i
\(406\) 0 0
\(407\) 430.878i 1.05867i
\(408\) 0 0
\(409\) −555.833 + 320.910i −1.35900 + 0.784621i −0.989490 0.144604i \(-0.953809\pi\)
−0.369514 + 0.929225i \(0.620476\pi\)
\(410\) 0 0
\(411\) 6.61037i 0.0160836i
\(412\) 0 0
\(413\) 351.272 + 202.807i 0.850539 + 0.491059i
\(414\) 0 0
\(415\) 0.651531 1.12848i 0.00156995 0.00271924i
\(416\) 0 0
\(417\) 99.8698i 0.239496i
\(418\) 0 0
\(419\) −668.879 −1.59637 −0.798184 0.602413i \(-0.794206\pi\)
−0.798184 + 0.602413i \(0.794206\pi\)
\(420\) 0 0
\(421\) 433.711 + 250.403i 1.03019 + 0.594782i 0.917040 0.398795i \(-0.130572\pi\)
0.113153 + 0.993578i \(0.463905\pi\)
\(422\) 0 0
\(423\) 5.18725 8.98458i 0.0122630 0.0212401i
\(424\) 0 0
\(425\) 50.4245 0.118646
\(426\) 0 0
\(427\) 7.56072 + 13.0955i 0.0177066 + 0.0306687i
\(428\) 0 0
\(429\) 803.716 1.87346
\(430\) 0 0
\(431\) −120.553 + 69.6015i −0.279706 + 0.161488i −0.633290 0.773914i \(-0.718296\pi\)
0.353584 + 0.935403i \(0.384963\pi\)
\(432\) 0 0
\(433\) 180.349 104.125i 0.416510 0.240472i −0.277073 0.960849i \(-0.589364\pi\)
0.693583 + 0.720377i \(0.256031\pi\)
\(434\) 0 0
\(435\) 10.0732 17.4473i 0.0231568 0.0401088i
\(436\) 0 0
\(437\) −510.379 59.7381i −1.16791 0.136700i
\(438\) 0 0
\(439\) −65.6748 37.9173i −0.149601 0.0863721i 0.423331 0.905975i \(-0.360861\pi\)
−0.572932 + 0.819603i \(0.694194\pi\)
\(440\) 0 0
\(441\) −0.631120 1.09313i −0.00143111 0.00247876i
\(442\) 0 0
\(443\) −227.628 394.264i −0.513834 0.889986i −0.999871 0.0160481i \(-0.994892\pi\)
0.486038 0.873938i \(-0.338442\pi\)
\(444\) 0 0
\(445\) 6.75323i 0.0151758i
\(446\) 0 0
\(447\) 516.820 298.386i 1.15620 0.667531i
\(448\) 0 0
\(449\) 8.44993i 0.0188194i 0.999956 + 0.00940972i \(0.00299525\pi\)
−0.999956 + 0.00940972i \(0.997005\pi\)
\(450\) 0 0
\(451\) 833.438 + 481.186i 1.84798 + 1.06693i
\(452\) 0 0
\(453\) 25.5959 44.3334i 0.0565031 0.0978663i
\(454\) 0 0
\(455\) 118.287i 0.259971i
\(456\) 0 0
\(457\) 208.424 0.456071 0.228036 0.973653i \(-0.426770\pi\)
0.228036 + 0.973653i \(0.426770\pi\)
\(458\) 0 0
\(459\) 46.3763 + 26.7754i 0.101038 + 0.0583341i
\(460\) 0 0
\(461\) 308.808 534.871i 0.669865 1.16024i −0.308077 0.951361i \(-0.599685\pi\)
0.977942 0.208878i \(-0.0669813\pi\)
\(462\) 0 0
\(463\) −640.958 −1.38436 −0.692179 0.721725i \(-0.743349\pi\)
−0.692179 + 0.721725i \(0.743349\pi\)
\(464\) 0 0
\(465\) 49.0454 + 84.9491i 0.105474 + 0.182686i
\(466\) 0 0
\(467\) −164.111 −0.351416 −0.175708 0.984442i \(-0.556221\pi\)
−0.175708 + 0.984442i \(0.556221\pi\)
\(468\) 0 0
\(469\) −356.394 + 205.764i −0.759902 + 0.438729i
\(470\) 0 0
\(471\) 736.093 424.983i 1.56283 0.902300i
\(472\) 0 0
\(473\) −561.232 + 972.082i −1.18654 + 2.05514i
\(474\) 0 0
\(475\) −452.908 53.0114i −0.953491 0.111603i
\(476\) 0 0
\(477\) −62.2883 35.9621i −0.130583 0.0753923i
\(478\) 0 0
\(479\) 401.401 + 695.247i 0.837998 + 1.45146i 0.891566 + 0.452892i \(0.149608\pi\)
−0.0535671 + 0.998564i \(0.517059\pi\)
\(480\) 0 0
\(481\) −247.924 429.417i −0.515434 0.892759i
\(482\) 0 0
\(483\) 587.048i 1.21542i
\(484\) 0 0
\(485\) −114.152 + 65.9054i −0.235364 + 0.135887i
\(486\) 0 0
\(487\) 454.391i 0.933041i 0.884510 + 0.466521i \(0.154493\pi\)
−0.884510 + 0.466521i \(0.845507\pi\)
\(488\) 0 0
\(489\) −426.959 246.505i −0.873127 0.504100i
\(490\) 0 0
\(491\) 259.826 450.031i 0.529177 0.916561i −0.470244 0.882536i \(-0.655834\pi\)
0.999421 0.0340247i \(-0.0108325\pi\)
\(492\) 0 0
\(493\) 13.4534i 0.0272889i
\(494\) 0 0
\(495\) 13.3939 0.0270583
\(496\) 0 0
\(497\) 603.817 + 348.614i 1.21492 + 0.701437i
\(498\) 0 0
\(499\) 221.543 383.724i 0.443974 0.768986i −0.554006 0.832513i \(-0.686902\pi\)
0.997980 + 0.0635269i \(0.0202349\pi\)
\(500\) 0 0
\(501\) −283.677 −0.566221
\(502\) 0 0
\(503\) −120.841 209.302i −0.240240 0.416107i 0.720543 0.693410i \(-0.243893\pi\)
−0.960782 + 0.277303i \(0.910559\pi\)
\(504\) 0 0
\(505\) −6.48469 −0.0128410
\(506\) 0 0
\(507\) −340.510 + 196.593i −0.671617 + 0.387758i
\(508\) 0 0
\(509\) 357.485 206.394i 0.702329 0.405490i −0.105886 0.994378i \(-0.533768\pi\)
0.808214 + 0.588889i \(0.200434\pi\)
\(510\) 0 0
\(511\) −439.409 + 761.078i −0.859900 + 1.48939i
\(512\) 0 0
\(513\) −388.398 289.249i −0.757112 0.563839i
\(514\) 0 0
\(515\) 69.3031 + 40.0121i 0.134569 + 0.0776935i
\(516\) 0 0
\(517\) −85.9694 148.903i −0.166285 0.288014i
\(518\) 0 0
\(519\) 478.426 + 828.659i 0.921823 + 1.59664i
\(520\) 0 0
\(521\) 888.839i 1.70602i 0.521891 + 0.853012i \(0.325227\pi\)
−0.521891 + 0.853012i \(0.674773\pi\)
\(522\) 0 0
\(523\) −132.856 + 76.7047i −0.254027 + 0.146663i −0.621607 0.783329i \(-0.713520\pi\)
0.367580 + 0.929992i \(0.380187\pi\)
\(524\) 0 0
\(525\) 520.944i 0.992275i
\(526\) 0 0
\(527\) −56.7276 32.7517i −0.107642 0.0621474i
\(528\) 0 0
\(529\) −101.227 + 175.330i −0.191355 + 0.331437i
\(530\) 0 0
\(531\) 52.8541i 0.0995368i
\(532\) 0 0
\(533\) −1107.48 −2.07783
\(534\) 0 0
\(535\) 69.3031 + 40.0121i 0.129538 + 0.0747890i
\(536\) 0 0
\(537\) 495.848 858.834i 0.923367 1.59932i
\(538\) 0 0
\(539\) −20.9194 −0.0388115
\(540\) 0 0
\(541\) 446.424 + 773.229i 0.825183 + 1.42926i 0.901779 + 0.432197i \(0.142261\pi\)
−0.0765964 + 0.997062i \(0.524405\pi\)
\(542\) 0 0
\(543\) 101.338 0.186627
\(544\) 0 0
\(545\) −14.2423 + 8.22282i −0.0261327 + 0.0150877i
\(546\) 0 0
\(547\) 748.841 432.343i 1.36900 0.790390i 0.378196 0.925726i \(-0.376545\pi\)
0.990800 + 0.135336i \(0.0432113\pi\)
\(548\) 0 0
\(549\) 0.985208 1.70643i 0.00179455 0.00310825i
\(550\) 0 0
\(551\) 14.1436 120.838i 0.0256690 0.219306i
\(552\) 0 0
\(553\) −39.8786 23.0239i −0.0721131 0.0416345i
\(554\) 0 0
\(555\) −45.4949 78.7995i −0.0819728 0.141981i
\(556\) 0 0
\(557\) −374.853 649.265i −0.672986 1.16565i −0.977053 0.212995i \(-0.931678\pi\)
0.304068 0.952650i \(-0.401655\pi\)
\(558\) 0 0
\(559\) 1291.71i 2.31076i
\(560\) 0 0
\(561\) −85.2929 + 49.2439i −0.152037 + 0.0877787i
\(562\) 0 0
\(563\) 162.777i 0.289125i 0.989496 + 0.144563i \(0.0461775\pi\)
−0.989496 + 0.144563i \(0.953823\pi\)
\(564\) 0 0
\(565\) 115.045 + 66.4215i 0.203620 + 0.117560i
\(566\) 0 0
\(567\) −304.530 + 527.462i −0.537090 + 0.930267i
\(568\) 0 0
\(569\) 296.076i 0.520345i −0.965562 0.260173i \(-0.916221\pi\)
0.965562 0.260173i \(-0.0837795\pi\)
\(570\) 0 0
\(571\) −274.758 −0.481188 −0.240594 0.970626i \(-0.577342\pi\)
−0.240594 + 0.970626i \(0.577342\pi\)
\(572\) 0 0
\(573\) 763.615 + 440.873i 1.33266 + 0.769413i
\(574\) 0 0
\(575\) −324.545 + 562.128i −0.564426 + 0.977614i
\(576\) 0 0
\(577\) 524.595 0.909177 0.454588 0.890702i \(-0.349786\pi\)
0.454588 + 0.890702i \(0.349786\pi\)
\(578\) 0 0
\(579\) −76.3207 132.191i −0.131815 0.228310i
\(580\) 0 0
\(581\) −8.98979 −0.0154730
\(582\) 0 0
\(583\) −1032.32 + 596.008i −1.77070 + 1.02231i
\(584\) 0 0
\(585\) −13.3485 + 7.70674i −0.0228179 + 0.0131739i
\(586\) 0 0
\(587\) −375.568 + 650.503i −0.639809 + 1.10818i 0.345665 + 0.938358i \(0.387653\pi\)
−0.985474 + 0.169824i \(0.945680\pi\)
\(588\) 0 0
\(589\) 475.090 + 353.810i 0.806604 + 0.600697i
\(590\) 0 0
\(591\) −686.388 396.286i −1.16140 0.670535i
\(592\) 0 0
\(593\) 285.030 + 493.687i 0.480658 + 0.832524i 0.999754 0.0221922i \(-0.00706458\pi\)
−0.519096 + 0.854716i \(0.673731\pi\)
\(594\) 0 0
\(595\) 7.24745 + 12.5529i 0.0121806 + 0.0210974i
\(596\) 0 0
\(597\) 816.104i 1.36701i
\(598\) 0 0
\(599\) 341.447 197.134i 0.570028 0.329106i −0.187133 0.982335i \(-0.559919\pi\)
0.757160 + 0.653229i \(0.226586\pi\)
\(600\) 0 0
\(601\) 241.665i 0.402105i 0.979580 + 0.201053i \(0.0644362\pi\)
−0.979580 + 0.201053i \(0.935564\pi\)
\(602\) 0 0
\(603\) 46.4403 + 26.8123i 0.0770154 + 0.0444649i
\(604\) 0 0
\(605\) 50.4898 87.4509i 0.0834542 0.144547i
\(606\) 0 0
\(607\) 369.224i 0.608276i −0.952628 0.304138i \(-0.901632\pi\)
0.952628 0.304138i \(-0.0983685\pi\)
\(608\) 0 0
\(609\) −138.990 −0.228226
\(610\) 0 0
\(611\) 171.356 + 98.9324i 0.280451 + 0.161919i
\(612\) 0 0
\(613\) −190.171 + 329.386i −0.310230 + 0.537334i −0.978412 0.206664i \(-0.933739\pi\)
0.668182 + 0.743998i \(0.267073\pi\)
\(614\) 0 0
\(615\) −203.227 −0.330450
\(616\) 0 0
\(617\) −277.869 481.283i −0.450355 0.780037i 0.548053 0.836444i \(-0.315369\pi\)
−0.998408 + 0.0564062i \(0.982036\pi\)
\(618\) 0 0
\(619\) 624.152 1.00832 0.504162 0.863609i \(-0.331802\pi\)
0.504162 + 0.863609i \(0.331802\pi\)
\(620\) 0 0
\(621\) −596.979 + 344.666i −0.961319 + 0.555018i
\(622\) 0 0
\(623\) −40.3485 + 23.2952i −0.0647648 + 0.0373920i
\(624\) 0 0
\(625\) −275.500 + 477.180i −0.440800 + 0.763488i
\(626\) 0 0
\(627\) 817.863 352.635i 1.30441 0.562417i
\(628\) 0 0
\(629\) 52.6209 + 30.3807i 0.0836581 + 0.0483000i
\(630\) 0 0
\(631\) 42.7247 + 74.0014i 0.0677096 + 0.117276i 0.897893 0.440214i \(-0.145098\pi\)
−0.830183 + 0.557491i \(0.811764\pi\)
\(632\) 0 0
\(633\) 109.444 + 189.563i 0.172898 + 0.299468i
\(634\) 0 0
\(635\) 125.661i 0.197892i
\(636\) 0 0
\(637\) 20.8485 12.0369i 0.0327292 0.0188962i
\(638\) 0 0
\(639\) 90.8531i 0.142180i
\(640\) 0 0
\(641\) 599.893 + 346.348i 0.935870 + 0.540325i 0.888663 0.458560i \(-0.151635\pi\)
0.0472069 + 0.998885i \(0.484968\pi\)
\(642\) 0 0
\(643\) −252.123 + 436.690i −0.392105 + 0.679145i −0.992727 0.120388i \(-0.961586\pi\)
0.600622 + 0.799533i \(0.294920\pi\)
\(644\) 0 0
\(645\) 237.034i 0.367495i
\(646\) 0 0
\(647\) 797.868 1.23318 0.616591 0.787284i \(-0.288513\pi\)
0.616591 + 0.787284i \(0.288513\pi\)
\(648\) 0 0
\(649\) −758.605 437.981i −1.16888 0.674855i
\(650\) 0 0
\(651\) 338.363 586.062i 0.519759 0.900249i
\(652\) 0 0
\(653\) −651.383 −0.997523 −0.498762 0.866739i \(-0.666212\pi\)
−0.498762 + 0.866739i \(0.666212\pi\)
\(654\) 0 0
\(655\) −53.6237 92.8790i −0.0818683 0.141800i
\(656\) 0 0
\(657\) 114.515 0.174300
\(658\) 0 0
\(659\) 395.082 228.101i 0.599518 0.346132i −0.169334 0.985559i \(-0.554162\pi\)
0.768852 + 0.639427i \(0.220828\pi\)
\(660\) 0 0
\(661\) 495.696 286.190i 0.749919 0.432966i −0.0757457 0.997127i \(-0.524134\pi\)
0.825665 + 0.564161i \(0.190800\pi\)
\(662\) 0 0
\(663\) 56.6691 98.1538i 0.0854738 0.148045i
\(664\) 0 0
\(665\) −51.8990 120.369i −0.0780436 0.181006i
\(666\) 0 0
\(667\) −149.978 86.5897i −0.224854 0.129820i
\(668\) 0 0
\(669\) −9.94949 17.2330i −0.0148722 0.0257594i
\(670\) 0 0
\(671\) −16.3281 28.2810i −0.0243339 0.0421476i
\(672\) 0 0
\(673\) 914.574i 1.35895i 0.733698 + 0.679476i \(0.237793\pi\)
−0.733698 + 0.679476i \(0.762207\pi\)
\(674\) 0 0
\(675\) −529.757 + 305.855i −0.784825 + 0.453119i
\(676\) 0 0
\(677\) 272.492i 0.402500i 0.979540 + 0.201250i \(0.0645003\pi\)
−0.979540 + 0.201250i \(0.935500\pi\)
\(678\) 0 0
\(679\) 787.529 + 454.680i 1.15984 + 0.669632i
\(680\) 0 0
\(681\) 87.6867 151.878i 0.128762 0.223022i
\(682\) 0 0
\(683\) 164.842i 0.241350i 0.992692 + 0.120675i \(0.0385058\pi\)
−0.992692 + 0.120675i \(0.961494\pi\)
\(684\) 0 0
\(685\) 2.10102 0.00306718
\(686\) 0 0
\(687\) 360.520 + 208.146i 0.524774 + 0.302979i
\(688\) 0 0
\(689\) 685.878 1187.98i 0.995469 1.72420i
\(690\) 0 0
\(691\) −1040.21 −1.50537 −0.752685 0.658380i \(-0.771242\pi\)
−0.752685 + 0.658380i \(0.771242\pi\)
\(692\) 0 0
\(693\) −46.2020 80.0243i −0.0666696 0.115475i
\(694\) 0 0
\(695\) −31.7423 −0.0456724
\(696\) 0 0
\(697\) 117.530 67.8557i 0.168622 0.0973540i
\(698\) 0 0
\(699\) −609.573 + 351.937i −0.872064 + 0.503486i
\(700\) 0 0
\(701\) 37.8179 65.5024i 0.0539484 0.0934414i −0.837790 0.545993i \(-0.816153\pi\)
0.891738 + 0.452551i \(0.149486\pi\)
\(702\) 0 0
\(703\) −440.697 328.197i −0.626880 0.466852i
\(704\) 0 0
\(705\) 31.4444 + 18.1544i 0.0446020 + 0.0257510i
\(706\) 0 0
\(707\) 22.3689 + 38.7440i 0.0316392 + 0.0548006i
\(708\) 0 0
\(709\) 451.379 + 781.811i 0.636641 + 1.10269i 0.986165 + 0.165767i \(0.0530101\pi\)
−0.349524 + 0.936928i \(0.613657\pi\)
\(710\) 0 0
\(711\) 6.00031i 0.00843926i
\(712\) 0 0
\(713\) 730.226 421.596i 1.02416 0.591299i
\(714\) 0 0
\(715\) 255.451i 0.357274i
\(716\) 0 0
\(717\) −194.338 112.201i −0.271044 0.156487i
\(718\) 0 0
\(719\) 586.734 1016.25i 0.816042 1.41343i −0.0925359 0.995709i \(-0.529497\pi\)
0.908578 0.417716i \(-0.137169\pi\)
\(720\) 0 0
\(721\) 552.086i 0.765722i
\(722\) 0 0
\(723\) −438.601 −0.606640
\(724\) 0 0
\(725\) −133.090 76.8394i −0.183572 0.105985i
\(726\) 0 0
\(727\) 288.552 499.787i 0.396908 0.687465i −0.596434 0.802662i \(-0.703416\pi\)
0.993343 + 0.115197i \(0.0367498\pi\)
\(728\) 0 0
\(729\) −642.362 −0.881155
\(730\) 0 0
\(731\) 79.1436 + 137.081i 0.108268 + 0.187525i
\(732\) 0 0
\(733\) −812.332 −1.10823 −0.554114 0.832441i \(-0.686943\pi\)
−0.554114 + 0.832441i \(0.686943\pi\)
\(734\) 0 0
\(735\) 3.82577 2.20881i 0.00520512 0.00300518i
\(736\) 0 0
\(737\) 769.665 444.366i 1.04432 0.602940i
\(738\) 0 0
\(739\) −380.931 + 659.792i −0.515469 + 0.892818i 0.484370 + 0.874863i \(0.339049\pi\)
−0.999839 + 0.0179548i \(0.994285\pi\)
\(740\) 0 0
\(741\) −612.186 + 822.032i −0.826162 + 1.10936i
\(742\) 0 0
\(743\) 118.810 + 68.5950i 0.159906 + 0.0923216i 0.577817 0.816166i \(-0.303905\pi\)
−0.417912 + 0.908488i \(0.637238\pi\)
\(744\) 0 0
\(745\) 94.8383 + 164.265i 0.127300 + 0.220490i
\(746\) 0 0
\(747\) 0.585713 + 1.01448i 0.000784087 + 0.00135808i
\(748\) 0 0
\(749\) 552.086i 0.737097i
\(750\) 0 0
\(751\) −95.0686 + 54.8879i −0.126589 + 0.0730864i −0.561957 0.827166i \(-0.689952\pi\)
0.435368 + 0.900253i \(0.356618\pi\)
\(752\) 0 0
\(753\) 755.343i 1.00311i
\(754\) 0 0
\(755\) 14.0908 + 8.13534i 0.0186633 + 0.0107753i
\(756\) 0 0
\(757\) −133.257 + 230.808i −0.176033 + 0.304898i −0.940518 0.339743i \(-0.889660\pi\)
0.764485 + 0.644641i \(0.222993\pi\)
\(758\) 0 0
\(759\) 1267.78i 1.67033i
\(760\) 0 0
\(761\) 1227.85 1.61346 0.806732 0.590918i \(-0.201234\pi\)
0.806732 + 0.590918i \(0.201234\pi\)
\(762\) 0 0
\(763\) 98.2577 + 56.7291i 0.128778 + 0.0743500i
\(764\) 0 0
\(765\) 0.944387 1.63573i 0.00123449 0.00213820i
\(766\) 0 0
\(767\) 1008.04 1.31427
\(768\) 0 0
\(769\) −334.115 578.705i −0.434480 0.752542i 0.562773 0.826612i \(-0.309735\pi\)
−0.997253 + 0.0740698i \(0.976401\pi\)
\(770\) 0 0
\(771\) −30.4393 −0.0394803
\(772\) 0 0
\(773\) −492.591 + 284.397i −0.637246 + 0.367914i −0.783553 0.621325i \(-0.786595\pi\)
0.146307 + 0.989239i \(0.453261\pi\)
\(774\) 0 0
\(775\) 648.000 374.123i 0.836129 0.482739i
\(776\) 0 0
\(777\) −313.868 + 543.636i −0.403949 + 0.699660i
\(778\) 0 0
\(779\) −1126.98 + 485.915i −1.44670 + 0.623768i
\(780\) 0 0
\(781\) −1304.00 752.864i −1.66965 0.963975i
\(782\) 0 0
\(783\) −81.6033 141.341i −0.104219 0.180512i
\(784\) 0 0
\(785\) 135.076 + 233.958i 0.172071 + 0.298035i
\(786\) 0 0
\(787\) 460.132i 0.584665i 0.956317 + 0.292333i \(0.0944315\pi\)
−0.956317 + 0.292333i \(0.905569\pi\)
\(788\) 0 0
\(789\) 310.414 179.217i 0.393427 0.227145i
\(790\) 0 0
\(791\) 916.481i 1.15864i
\(792\) 0 0