Properties

Label 224.3.s.b.129.6
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: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 26 x^{14} - 16 x^{13} + 469 x^{12} + 144 x^{11} - 4526 x^{10} + 4440 x^{9} + 32608 x^{8} - 33728 x^{7} - 49760 x^{6} + 203528 x^{5} + 27401 x^{4} - 156928 x^{3} + 114964 x^{2} - 248608 x + 208849\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{20}\cdot 7 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 129.6
Root \(-1.90990 + 0.286185i\) of defining polynomial
Character \(\chi\) \(=\) 224.129
Dual form 224.3.s.b.33.6

$q$-expansion

\(f(q)\) \(=\) \(q+(2.20101 + 1.27075i) q^{3} +(3.56697 - 2.05939i) q^{5} +(6.98814 + 0.407289i) q^{7} +(-1.27038 - 2.20036i) q^{9} +O(q^{10})\) \(q+(2.20101 + 1.27075i) q^{3} +(3.56697 - 2.05939i) q^{5} +(6.98814 + 0.407289i) q^{7} +(-1.27038 - 2.20036i) q^{9} +(1.63392 - 2.83003i) q^{11} +5.88759i q^{13} +10.4679 q^{15} +(-12.0204 - 6.93999i) q^{17} +(13.7058 - 7.91304i) q^{19} +(14.8634 + 9.77664i) q^{21} +(18.2518 + 31.6131i) q^{23} +(-4.01784 + 6.95910i) q^{25} -29.3309i q^{27} -28.4655 q^{29} +(36.2014 + 20.9009i) q^{31} +(7.19253 - 4.15261i) q^{33} +(25.7652 - 12.9385i) q^{35} +(-7.14285 - 12.3718i) q^{37} +(-7.48167 + 12.9586i) q^{39} +21.3515i q^{41} -55.3992 q^{43} +(-9.06280 - 5.23241i) q^{45} +(-29.3178 + 16.9266i) q^{47} +(48.6682 + 5.69238i) q^{49} +(-17.6380 - 30.5499i) q^{51} +(42.4271 - 73.4859i) q^{53} -13.4595i q^{55} +40.2220 q^{57} +(-58.5062 - 33.7786i) q^{59} +(-25.6135 + 14.7879i) q^{61} +(-7.98140 - 15.8938i) q^{63} +(12.1248 + 21.0008i) q^{65} +(-27.4789 + 47.5949i) q^{67} +92.7741i q^{69} -83.8102 q^{71} +(-108.784 - 62.8065i) q^{73} +(-17.6866 + 10.2113i) q^{75} +(12.5707 - 19.1112i) q^{77} +(35.1955 + 60.9604i) q^{79} +(25.8389 - 44.7542i) q^{81} -27.1264i q^{83} -57.1685 q^{85} +(-62.6527 - 36.1726i) q^{87} +(-126.553 + 73.0654i) q^{89} +(-2.39795 + 41.1433i) q^{91} +(53.1196 + 92.0059i) q^{93} +(32.5920 - 56.4511i) q^{95} -11.3574i q^{97} -8.30278 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 40q^{9} + O(q^{10}) \) \( 16q + 40q^{9} - 48q^{17} - 136q^{21} + 80q^{25} - 16q^{29} - 264q^{33} + 72q^{37} + 312q^{45} + 128q^{49} + 40q^{53} + 368q^{57} + 216q^{61} - 168q^{65} - 312q^{73} + 64q^{77} - 384q^{81} - 1072q^{85} + 24q^{89} - 168q^{93} + O(q^{100}) \)

Character values

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

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

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
\(3\) 2.20101 + 1.27075i 0.733669 + 0.423584i 0.819763 0.572703i \(-0.194105\pi\)
−0.0860939 + 0.996287i \(0.527439\pi\)
\(4\) 0 0
\(5\) 3.56697 2.05939i 0.713393 0.411878i −0.0989230 0.995095i \(-0.531540\pi\)
0.812316 + 0.583217i \(0.198206\pi\)
\(6\) 0 0
\(7\) 6.98814 + 0.407289i 0.998306 + 0.0581841i
\(8\) 0 0
\(9\) −1.27038 2.20036i −0.141153 0.244485i
\(10\) 0 0
\(11\) 1.63392 2.83003i 0.148538 0.257275i −0.782149 0.623091i \(-0.785877\pi\)
0.930687 + 0.365816i \(0.119210\pi\)
\(12\) 0 0
\(13\) 5.88759i 0.452892i 0.974024 + 0.226446i \(0.0727107\pi\)
−0.974024 + 0.226446i \(0.927289\pi\)
\(14\) 0 0
\(15\) 10.4679 0.697859
\(16\) 0 0
\(17\) −12.0204 6.93999i −0.707083 0.408234i 0.102897 0.994692i \(-0.467189\pi\)
−0.809980 + 0.586458i \(0.800522\pi\)
\(18\) 0 0
\(19\) 13.7058 7.91304i 0.721357 0.416476i −0.0938951 0.995582i \(-0.529932\pi\)
0.815252 + 0.579107i \(0.196598\pi\)
\(20\) 0 0
\(21\) 14.8634 + 9.77664i 0.707780 + 0.465554i
\(22\) 0 0
\(23\) 18.2518 + 31.6131i 0.793557 + 1.37448i 0.923751 + 0.382993i \(0.125106\pi\)
−0.130194 + 0.991488i \(0.541560\pi\)
\(24\) 0 0
\(25\) −4.01784 + 6.95910i −0.160713 + 0.278364i
\(26\) 0 0
\(27\) 29.3309i 1.08633i
\(28\) 0 0
\(29\) −28.4655 −0.981568 −0.490784 0.871281i \(-0.663290\pi\)
−0.490784 + 0.871281i \(0.663290\pi\)
\(30\) 0 0
\(31\) 36.2014 + 20.9009i 1.16779 + 0.674222i 0.953158 0.302474i \(-0.0978126\pi\)
0.214629 + 0.976696i \(0.431146\pi\)
\(32\) 0 0
\(33\) 7.19253 4.15261i 0.217955 0.125837i
\(34\) 0 0
\(35\) 25.7652 12.9385i 0.736149 0.369672i
\(36\) 0 0
\(37\) −7.14285 12.3718i −0.193050 0.334372i 0.753210 0.657781i \(-0.228505\pi\)
−0.946260 + 0.323408i \(0.895171\pi\)
\(38\) 0 0
\(39\) −7.48167 + 12.9586i −0.191838 + 0.332273i
\(40\) 0 0
\(41\) 21.3515i 0.520769i 0.965505 + 0.260385i \(0.0838493\pi\)
−0.965505 + 0.260385i \(0.916151\pi\)
\(42\) 0 0
\(43\) −55.3992 −1.28835 −0.644177 0.764877i \(-0.722800\pi\)
−0.644177 + 0.764877i \(0.722800\pi\)
\(44\) 0 0
\(45\) −9.06280 5.23241i −0.201395 0.116276i
\(46\) 0 0
\(47\) −29.3178 + 16.9266i −0.623783 + 0.360141i −0.778340 0.627843i \(-0.783938\pi\)
0.154558 + 0.987984i \(0.450605\pi\)
\(48\) 0 0
\(49\) 48.6682 + 5.69238i 0.993229 + 0.116171i
\(50\) 0 0
\(51\) −17.6380 30.5499i −0.345843 0.599018i
\(52\) 0 0
\(53\) 42.4271 73.4859i 0.800512 1.38653i −0.118768 0.992922i \(-0.537894\pi\)
0.919280 0.393605i \(-0.128772\pi\)
\(54\) 0 0
\(55\) 13.4595i 0.244718i
\(56\) 0 0
\(57\) 40.2220 0.705649
\(58\) 0 0
\(59\) −58.5062 33.7786i −0.991631 0.572518i −0.0858695 0.996306i \(-0.527367\pi\)
−0.905761 + 0.423788i \(0.860700\pi\)
\(60\) 0 0
\(61\) −25.6135 + 14.7879i −0.419893 + 0.242425i −0.695032 0.718979i \(-0.744610\pi\)
0.275139 + 0.961405i \(0.411276\pi\)
\(62\) 0 0
\(63\) −7.98140 15.8938i −0.126689 0.252283i
\(64\) 0 0
\(65\) 12.1248 + 21.0008i 0.186536 + 0.323090i
\(66\) 0 0
\(67\) −27.4789 + 47.5949i −0.410133 + 0.710371i −0.994904 0.100827i \(-0.967851\pi\)
0.584771 + 0.811198i \(0.301184\pi\)
\(68\) 0 0
\(69\) 92.7741i 1.34455i
\(70\) 0 0
\(71\) −83.8102 −1.18043 −0.590213 0.807248i \(-0.700956\pi\)
−0.590213 + 0.807248i \(0.700956\pi\)
\(72\) 0 0
\(73\) −108.784 62.8065i −1.49019 0.860363i −0.490255 0.871579i \(-0.663096\pi\)
−0.999937 + 0.0112159i \(0.996430\pi\)
\(74\) 0 0
\(75\) −17.6866 + 10.2113i −0.235821 + 0.136151i
\(76\) 0 0
\(77\) 12.5707 19.1112i 0.163256 0.248197i
\(78\) 0 0
\(79\) 35.1955 + 60.9604i 0.445512 + 0.771650i 0.998088 0.0618128i \(-0.0196882\pi\)
−0.552575 + 0.833463i \(0.686355\pi\)
\(80\) 0 0
\(81\) 25.8389 44.7542i 0.318998 0.552521i
\(82\) 0 0
\(83\) 27.1264i 0.326824i −0.986558 0.163412i \(-0.947750\pi\)
0.986558 0.163412i \(-0.0522500\pi\)
\(84\) 0 0
\(85\) −57.1685 −0.672571
\(86\) 0 0
\(87\) −62.6527 36.1726i −0.720146 0.415777i
\(88\) 0 0
\(89\) −126.553 + 73.0654i −1.42194 + 0.820959i −0.996465 0.0840094i \(-0.973227\pi\)
−0.425478 + 0.904969i \(0.639894\pi\)
\(90\) 0 0
\(91\) −2.39795 + 41.1433i −0.0263511 + 0.452125i
\(92\) 0 0
\(93\) 53.1196 + 92.0059i 0.571179 + 0.989311i
\(94\) 0 0
\(95\) 32.5920 56.4511i 0.343074 0.594222i
\(96\) 0 0
\(97\) 11.3574i 0.117086i −0.998285 0.0585431i \(-0.981354\pi\)
0.998285 0.0585431i \(-0.0186455\pi\)
\(98\) 0 0
\(99\) −8.30278 −0.0838664
\(100\) 0 0
\(101\) −36.2851 20.9492i −0.359258 0.207418i 0.309497 0.950900i \(-0.399839\pi\)
−0.668755 + 0.743482i \(0.733173\pi\)
\(102\) 0 0
\(103\) −84.1601 + 48.5899i −0.817089 + 0.471746i −0.849412 0.527731i \(-0.823043\pi\)
0.0323227 + 0.999477i \(0.489710\pi\)
\(104\) 0 0
\(105\) 73.1511 + 4.26345i 0.696677 + 0.0406043i
\(106\) 0 0
\(107\) −41.7218 72.2643i −0.389924 0.675368i 0.602515 0.798107i \(-0.294165\pi\)
−0.992439 + 0.122740i \(0.960832\pi\)
\(108\) 0 0
\(109\) 80.9965 140.290i 0.743088 1.28707i −0.207995 0.978130i \(-0.566694\pi\)
0.951083 0.308936i \(-0.0999728\pi\)
\(110\) 0 0
\(111\) 36.3072i 0.327092i
\(112\) 0 0
\(113\) 27.2503 0.241153 0.120576 0.992704i \(-0.461526\pi\)
0.120576 + 0.992704i \(0.461526\pi\)
\(114\) 0 0
\(115\) 130.207 + 75.1751i 1.13224 + 0.653697i
\(116\) 0 0
\(117\) 12.9548 7.47948i 0.110725 0.0639271i
\(118\) 0 0
\(119\) −81.1737 53.3934i −0.682132 0.448684i
\(120\) 0 0
\(121\) 55.1606 + 95.5410i 0.455873 + 0.789595i
\(122\) 0 0
\(123\) −27.1325 + 46.9949i −0.220589 + 0.382072i
\(124\) 0 0
\(125\) 136.067i 1.08853i
\(126\) 0 0
\(127\) 232.457 1.83037 0.915183 0.403038i \(-0.132046\pi\)
0.915183 + 0.403038i \(0.132046\pi\)
\(128\) 0 0
\(129\) −121.934 70.3986i −0.945225 0.545726i
\(130\) 0 0
\(131\) 152.509 88.0512i 1.16419 0.672146i 0.211887 0.977294i \(-0.432039\pi\)
0.952305 + 0.305148i \(0.0987058\pi\)
\(132\) 0 0
\(133\) 99.0008 49.7152i 0.744367 0.373798i
\(134\) 0 0
\(135\) −60.4037 104.622i −0.447435 0.774980i
\(136\) 0 0
\(137\) 132.462 229.432i 0.966879 1.67468i 0.262400 0.964959i \(-0.415486\pi\)
0.704479 0.709725i \(-0.251181\pi\)
\(138\) 0 0
\(139\) 267.680i 1.92576i 0.269935 + 0.962878i \(0.412998\pi\)
−0.269935 + 0.962878i \(0.587002\pi\)
\(140\) 0 0
\(141\) −86.0382 −0.610200
\(142\) 0 0
\(143\) 16.6621 + 9.61984i 0.116518 + 0.0672716i
\(144\) 0 0
\(145\) −101.535 + 58.6215i −0.700244 + 0.404286i
\(146\) 0 0
\(147\) 99.8855 + 74.3742i 0.679493 + 0.505947i
\(148\) 0 0
\(149\) 0.972701 + 1.68477i 0.00652820 + 0.0113072i 0.869271 0.494336i \(-0.164589\pi\)
−0.862743 + 0.505643i \(0.831255\pi\)
\(150\) 0 0
\(151\) 50.1524 86.8665i 0.332135 0.575275i −0.650795 0.759253i \(-0.725564\pi\)
0.982930 + 0.183978i \(0.0588977\pi\)
\(152\) 0 0
\(153\) 35.2656i 0.230494i
\(154\) 0 0
\(155\) 172.172 1.11079
\(156\) 0 0
\(157\) −117.153 67.6386i −0.746200 0.430819i 0.0781191 0.996944i \(-0.475109\pi\)
−0.824319 + 0.566125i \(0.808442\pi\)
\(158\) 0 0
\(159\) 186.765 107.829i 1.17462 0.678168i
\(160\) 0 0
\(161\) 114.671 + 228.350i 0.712240 + 1.41832i
\(162\) 0 0
\(163\) 127.353 + 220.582i 0.781307 + 1.35326i 0.931180 + 0.364559i \(0.118780\pi\)
−0.149873 + 0.988705i \(0.547886\pi\)
\(164\) 0 0
\(165\) 17.1037 29.6244i 0.103659 0.179542i
\(166\) 0 0
\(167\) 50.9246i 0.304938i −0.988308 0.152469i \(-0.951278\pi\)
0.988308 0.152469i \(-0.0487224\pi\)
\(168\) 0 0
\(169\) 134.336 0.794889
\(170\) 0 0
\(171\) −34.8231 20.1051i −0.203644 0.117574i
\(172\) 0 0
\(173\) 60.9855 35.2100i 0.352517 0.203526i −0.313276 0.949662i \(-0.601427\pi\)
0.665793 + 0.746136i \(0.268093\pi\)
\(174\) 0 0
\(175\) −30.9116 + 46.9947i −0.176638 + 0.268541i
\(176\) 0 0
\(177\) −85.8484 148.694i −0.485019 0.840078i
\(178\) 0 0
\(179\) 73.7202 127.687i 0.411845 0.713336i −0.583247 0.812295i \(-0.698218\pi\)
0.995092 + 0.0989591i \(0.0315513\pi\)
\(180\) 0 0
\(181\) 294.491i 1.62702i 0.581550 + 0.813511i \(0.302447\pi\)
−0.581550 + 0.813511i \(0.697553\pi\)
\(182\) 0 0
\(183\) −75.1672 −0.410750
\(184\) 0 0
\(185\) −50.9566 29.4198i −0.275441 0.159026i
\(186\) 0 0
\(187\) −39.2807 + 22.6787i −0.210057 + 0.121277i
\(188\) 0 0
\(189\) 11.9461 204.968i 0.0632071 1.08449i
\(190\) 0 0
\(191\) −56.2595 97.4444i −0.294553 0.510180i 0.680328 0.732908i \(-0.261837\pi\)
−0.974881 + 0.222728i \(0.928504\pi\)
\(192\) 0 0
\(193\) −63.7435 + 110.407i −0.330277 + 0.572057i −0.982566 0.185914i \(-0.940475\pi\)
0.652289 + 0.757970i \(0.273809\pi\)
\(194\) 0 0
\(195\) 61.6307i 0.316055i
\(196\) 0 0
\(197\) −293.140 −1.48802 −0.744011 0.668167i \(-0.767079\pi\)
−0.744011 + 0.668167i \(0.767079\pi\)
\(198\) 0 0
\(199\) 8.43677 + 4.87097i 0.0423958 + 0.0244772i 0.521048 0.853527i \(-0.325541\pi\)
−0.478652 + 0.878005i \(0.658875\pi\)
\(200\) 0 0
\(201\) −120.963 + 69.8378i −0.601804 + 0.347452i
\(202\) 0 0
\(203\) −198.921 11.5937i −0.979905 0.0571117i
\(204\) 0 0
\(205\) 43.9711 + 76.1602i 0.214493 + 0.371513i
\(206\) 0 0
\(207\) 46.3734 80.3211i 0.224026 0.388025i
\(208\) 0 0
\(209\) 51.7170i 0.247450i
\(210\) 0 0
\(211\) 139.516 0.661214 0.330607 0.943769i \(-0.392747\pi\)
0.330607 + 0.943769i \(0.392747\pi\)
\(212\) 0 0
\(213\) −184.467 106.502i −0.866042 0.500009i
\(214\) 0 0
\(215\) −197.607 + 114.088i −0.919102 + 0.530644i
\(216\) 0 0
\(217\) 244.468 + 160.803i 1.12658 + 0.741026i
\(218\) 0 0
\(219\) −159.623 276.475i −0.728872 1.26244i
\(220\) 0 0
\(221\) 40.8598 70.7713i 0.184886 0.320232i
\(222\) 0 0
\(223\) 273.426i 1.22612i 0.790035 + 0.613062i \(0.210062\pi\)
−0.790035 + 0.613062i \(0.789938\pi\)
\(224\) 0 0
\(225\) 20.4167 0.0907409
\(226\) 0 0
\(227\) −58.4952 33.7722i −0.257688 0.148776i 0.365591 0.930775i \(-0.380867\pi\)
−0.623279 + 0.781999i \(0.714200\pi\)
\(228\) 0 0
\(229\) 166.765 96.2816i 0.728230 0.420444i −0.0895442 0.995983i \(-0.528541\pi\)
0.817774 + 0.575539i \(0.195208\pi\)
\(230\) 0 0
\(231\) 51.9537 26.0896i 0.224908 0.112942i
\(232\) 0 0
\(233\) −40.7024 70.4987i −0.174689 0.302569i 0.765365 0.643597i \(-0.222559\pi\)
−0.940053 + 0.341027i \(0.889225\pi\)
\(234\) 0 0
\(235\) −69.7170 + 120.753i −0.296668 + 0.513844i
\(236\) 0 0
\(237\) 178.899i 0.754848i
\(238\) 0 0
\(239\) −22.6152 −0.0946244 −0.0473122 0.998880i \(-0.515066\pi\)
−0.0473122 + 0.998880i \(0.515066\pi\)
\(240\) 0 0
\(241\) −81.5504 47.0832i −0.338384 0.195366i 0.321173 0.947020i \(-0.395923\pi\)
−0.659557 + 0.751655i \(0.729256\pi\)
\(242\) 0 0
\(243\) −114.869 + 66.3194i −0.472710 + 0.272919i
\(244\) 0 0
\(245\) 185.321 79.9223i 0.756411 0.326213i
\(246\) 0 0
\(247\) 46.5887 + 80.6941i 0.188618 + 0.326697i
\(248\) 0 0
\(249\) 34.4710 59.7054i 0.138438 0.239781i
\(250\) 0 0
\(251\) 316.694i 1.26173i −0.775892 0.630865i \(-0.782700\pi\)
0.775892 0.630865i \(-0.217300\pi\)
\(252\) 0 0
\(253\) 119.288 0.471493
\(254\) 0 0
\(255\) −125.828 72.6470i −0.493444 0.284890i
\(256\) 0 0
\(257\) 40.7550 23.5299i 0.158580 0.0915560i −0.418610 0.908166i \(-0.637483\pi\)
0.577190 + 0.816610i \(0.304149\pi\)
\(258\) 0 0
\(259\) −44.8764 89.3649i −0.173268 0.345038i
\(260\) 0 0
\(261\) 36.1619 + 62.6343i 0.138551 + 0.239978i
\(262\) 0 0
\(263\) −203.252 + 352.043i −0.772822 + 1.33857i 0.163189 + 0.986595i \(0.447822\pi\)
−0.936011 + 0.351972i \(0.885511\pi\)
\(264\) 0 0
\(265\) 349.496i 1.31885i
\(266\) 0 0
\(267\) −371.392 −1.39098
\(268\) 0 0
\(269\) 287.957 + 166.252i 1.07047 + 0.618038i 0.928311 0.371806i \(-0.121261\pi\)
0.142162 + 0.989843i \(0.454595\pi\)
\(270\) 0 0
\(271\) 61.7686 35.6621i 0.227928 0.131595i −0.381688 0.924291i \(-0.624657\pi\)
0.609616 + 0.792697i \(0.291324\pi\)
\(272\) 0 0
\(273\) −57.5609 + 87.5096i −0.210846 + 0.320548i
\(274\) 0 0
\(275\) 13.1296 + 22.7412i 0.0477441 + 0.0826952i
\(276\) 0 0
\(277\) 14.8574 25.7337i 0.0536367 0.0929015i −0.837960 0.545731i \(-0.816252\pi\)
0.891597 + 0.452829i \(0.149585\pi\)
\(278\) 0 0
\(279\) 106.208i 0.380674i
\(280\) 0 0
\(281\) 9.06447 0.0322579 0.0161289 0.999870i \(-0.494866\pi\)
0.0161289 + 0.999870i \(0.494866\pi\)
\(282\) 0 0
\(283\) −159.988 92.3689i −0.565327 0.326392i 0.189954 0.981793i \(-0.439166\pi\)
−0.755281 + 0.655401i \(0.772500\pi\)
\(284\) 0 0
\(285\) 143.471 82.8328i 0.503406 0.290641i
\(286\) 0 0
\(287\) −8.69624 + 149.208i −0.0303005 + 0.519887i
\(288\) 0 0
\(289\) −48.1732 83.4384i −0.166689 0.288714i
\(290\) 0 0
\(291\) 14.4324 24.9976i 0.0495959 0.0859026i
\(292\) 0 0
\(293\) 300.389i 1.02522i 0.858622 + 0.512609i \(0.171321\pi\)
−0.858622 + 0.512609i \(0.828679\pi\)
\(294\) 0 0
\(295\) −278.253 −0.943230
\(296\) 0 0
\(297\) −83.0072 47.9242i −0.279486 0.161361i
\(298\) 0 0
\(299\) −186.125 + 107.459i −0.622491 + 0.359395i
\(300\) 0 0
\(301\) −387.137 22.5635i −1.28617 0.0749617i
\(302\) 0 0
\(303\) −53.2425 92.2187i −0.175718 0.304352i
\(304\) 0 0
\(305\) −60.9083 + 105.496i −0.199699 + 0.345889i
\(306\) 0 0
\(307\) 390.385i 1.27161i −0.771848 0.635807i \(-0.780667\pi\)
0.771848 0.635807i \(-0.219333\pi\)
\(308\) 0 0
\(309\) −246.983 −0.799297
\(310\) 0 0
\(311\) 83.2050 + 48.0384i 0.267540 + 0.154464i 0.627769 0.778400i \(-0.283968\pi\)
−0.360229 + 0.932864i \(0.617301\pi\)
\(312\) 0 0
\(313\) −419.921 + 242.442i −1.34160 + 0.774574i −0.987042 0.160460i \(-0.948702\pi\)
−0.354559 + 0.935034i \(0.615369\pi\)
\(314\) 0 0
\(315\) −61.2010 40.2560i −0.194289 0.127797i
\(316\) 0 0
\(317\) −33.9714 58.8401i −0.107165 0.185616i 0.807456 0.589928i \(-0.200844\pi\)
−0.914621 + 0.404313i \(0.867511\pi\)
\(318\) 0 0
\(319\) −46.5102 + 80.5581i −0.145800 + 0.252533i
\(320\) 0 0
\(321\) 212.072i 0.660662i
\(322\) 0 0
\(323\) −219.665 −0.680079
\(324\) 0 0
\(325\) −40.9723 23.6554i −0.126069 0.0727858i
\(326\) 0 0
\(327\) 356.548 205.853i 1.09036 0.629520i
\(328\) 0 0
\(329\) −211.771 + 106.345i −0.643680 + 0.323237i
\(330\) 0 0
\(331\) 132.634 + 229.729i 0.400707 + 0.694046i 0.993811 0.111080i \(-0.0354311\pi\)
−0.593104 + 0.805126i \(0.702098\pi\)
\(332\) 0 0
\(333\) −18.1483 + 31.4337i −0.0544993 + 0.0943955i
\(334\) 0 0
\(335\) 226.359i 0.675699i
\(336\) 0 0
\(337\) 549.980 1.63199 0.815993 0.578061i \(-0.196191\pi\)
0.815993 + 0.578061i \(0.196191\pi\)
\(338\) 0 0
\(339\) 59.9780 + 34.6283i 0.176926 + 0.102148i
\(340\) 0 0
\(341\) 118.300 68.3006i 0.346921 0.200295i
\(342\) 0 0
\(343\) 337.782 + 59.6012i 0.984787 + 0.173764i
\(344\) 0 0
\(345\) 191.058 + 330.922i 0.553791 + 0.959194i
\(346\) 0 0
\(347\) 339.375 587.815i 0.978026 1.69399i 0.308463 0.951236i \(-0.400185\pi\)
0.669563 0.742755i \(-0.266481\pi\)
\(348\) 0 0
\(349\) 170.081i 0.487339i −0.969858 0.243669i \(-0.921649\pi\)
0.969858 0.243669i \(-0.0783511\pi\)
\(350\) 0 0
\(351\) 172.688 0.491990
\(352\) 0 0
\(353\) 204.423 + 118.024i 0.579102 + 0.334345i 0.760776 0.649014i \(-0.224818\pi\)
−0.181675 + 0.983359i \(0.558152\pi\)
\(354\) 0 0
\(355\) −298.948 + 172.598i −0.842108 + 0.486191i
\(356\) 0 0
\(357\) −110.814 220.671i −0.310404 0.618126i
\(358\) 0 0
\(359\) 229.058 + 396.740i 0.638044 + 1.10512i 0.985861 + 0.167562i \(0.0535895\pi\)
−0.347818 + 0.937562i \(0.613077\pi\)
\(360\) 0 0
\(361\) −55.2677 + 95.7266i −0.153096 + 0.265170i
\(362\) 0 0
\(363\) 280.382i 0.772402i
\(364\) 0 0
\(365\) −517.372 −1.41746
\(366\) 0 0
\(367\) 356.315 + 205.718i 0.970885 + 0.560541i 0.899506 0.436909i \(-0.143927\pi\)
0.0713791 + 0.997449i \(0.477260\pi\)
\(368\) 0 0
\(369\) 46.9811 27.1245i 0.127320 0.0735082i
\(370\) 0 0
\(371\) 326.417 496.250i 0.879829 1.33760i
\(372\) 0 0
\(373\) −7.89853 13.6807i −0.0211757 0.0366774i 0.855243 0.518227i \(-0.173408\pi\)
−0.876419 + 0.481549i \(0.840074\pi\)
\(374\) 0 0
\(375\) −172.907 + 299.483i −0.461085 + 0.798623i
\(376\) 0 0
\(377\) 167.593i 0.444544i
\(378\) 0 0
\(379\) 455.384 1.20154 0.600770 0.799422i \(-0.294861\pi\)
0.600770 + 0.799422i \(0.294861\pi\)
\(380\) 0 0
\(381\) 511.639 + 295.395i 1.34288 + 0.775314i
\(382\) 0 0
\(383\) −158.732 + 91.6439i −0.414443 + 0.239279i −0.692697 0.721229i \(-0.743578\pi\)
0.278254 + 0.960508i \(0.410244\pi\)
\(384\) 0 0
\(385\) 5.48190 94.0568i 0.0142387 0.244303i
\(386\) 0 0
\(387\) 70.3780 + 121.898i 0.181855 + 0.314982i
\(388\) 0 0
\(389\) 92.7471 160.643i 0.238424 0.412963i −0.721838 0.692062i \(-0.756702\pi\)
0.960262 + 0.279099i \(0.0900357\pi\)
\(390\) 0 0
\(391\) 506.669i 1.29583i
\(392\) 0 0
\(393\) 447.565 1.13884
\(394\) 0 0
\(395\) 251.082 + 144.962i 0.635651 + 0.366993i
\(396\) 0 0
\(397\) −39.5520 + 22.8353i −0.0996271 + 0.0575197i −0.548986 0.835832i \(-0.684986\pi\)
0.449359 + 0.893351i \(0.351653\pi\)
\(398\) 0 0
\(399\) 281.077 + 16.3820i 0.704454 + 0.0410576i
\(400\) 0 0
\(401\) −19.2312 33.3094i −0.0479580 0.0830657i 0.841050 0.540958i \(-0.181938\pi\)
−0.889008 + 0.457892i \(0.848605\pi\)
\(402\) 0 0
\(403\) −123.056 + 213.139i −0.305349 + 0.528881i
\(404\) 0 0
\(405\) 212.849i 0.525553i
\(406\) 0 0
\(407\) −46.6833 −0.114701
\(408\) 0 0
\(409\) −145.264 83.8684i −0.355169 0.205057i 0.311790 0.950151i \(-0.399071\pi\)
−0.666960 + 0.745094i \(0.732405\pi\)
\(410\) 0 0
\(411\) 583.102 336.654i 1.41874 0.819109i
\(412\) 0 0
\(413\) −395.092 259.878i −0.956640 0.629246i
\(414\) 0 0
\(415\) −55.8639 96.7590i −0.134612 0.233154i
\(416\) 0 0
\(417\) −340.155 + 589.166i −0.815720 + 1.41287i
\(418\) 0 0
\(419\) 300.318i 0.716751i −0.933578 0.358375i \(-0.883331\pi\)
0.933578 0.358375i \(-0.116669\pi\)
\(420\) 0 0
\(421\) 280.567 0.666430 0.333215 0.942851i \(-0.391867\pi\)
0.333215 + 0.942851i \(0.391867\pi\)
\(422\) 0 0
\(423\) 74.4894 + 43.0065i 0.176098 + 0.101670i
\(424\) 0 0
\(425\) 96.5920 55.7674i 0.227275 0.131218i
\(426\) 0 0
\(427\) −185.014 + 92.9082i −0.433287 + 0.217584i
\(428\) 0 0
\(429\) 24.4489 + 42.3467i 0.0569904 + 0.0987102i
\(430\) 0 0
\(431\) 112.382 194.651i 0.260747 0.451627i −0.705693 0.708517i \(-0.749364\pi\)
0.966441 + 0.256890i \(0.0826977\pi\)
\(432\) 0 0
\(433\) 731.236i 1.68877i −0.535739 0.844383i \(-0.679967\pi\)
0.535739 0.844383i \(-0.320033\pi\)
\(434\) 0 0
\(435\) −297.973 −0.684996
\(436\) 0 0
\(437\) 500.311 + 288.854i 1.14488 + 0.660994i
\(438\) 0 0
\(439\) 259.322 149.720i 0.590711 0.341047i −0.174668 0.984627i \(-0.555885\pi\)
0.765379 + 0.643580i \(0.222552\pi\)
\(440\) 0 0
\(441\) −49.3018 114.319i −0.111795 0.259227i
\(442\) 0 0
\(443\) 198.077 + 343.080i 0.447127 + 0.774447i 0.998198 0.0600116i \(-0.0191138\pi\)
−0.551070 + 0.834459i \(0.685780\pi\)
\(444\) 0 0
\(445\) −300.940 + 521.243i −0.676270 + 1.17133i
\(446\) 0 0
\(447\) 4.94425i 0.0110610i
\(448\) 0 0
\(449\) 128.183 0.285486 0.142743 0.989760i \(-0.454408\pi\)
0.142743 + 0.989760i \(0.454408\pi\)
\(450\) 0 0
\(451\) 60.4254 + 34.8866i 0.133981 + 0.0773540i
\(452\) 0 0
\(453\) 220.772 127.463i 0.487354 0.281374i
\(454\) 0 0
\(455\) 76.1767 + 151.695i 0.167421 + 0.333396i
\(456\) 0 0
\(457\) −202.574 350.868i −0.443268 0.767763i 0.554661 0.832076i \(-0.312848\pi\)
−0.997930 + 0.0643128i \(0.979514\pi\)
\(458\) 0 0
\(459\) −203.556 + 352.569i −0.443477 + 0.768124i
\(460\) 0 0
\(461\) 312.620i 0.678134i −0.940762 0.339067i \(-0.889889\pi\)
0.940762 0.339067i \(-0.110111\pi\)
\(462\) 0 0
\(463\) −246.396 −0.532173 −0.266087 0.963949i \(-0.585731\pi\)
−0.266087 + 0.963949i \(0.585731\pi\)
\(464\) 0 0
\(465\) 378.952 + 218.788i 0.814950 + 0.470512i
\(466\) 0 0
\(467\) −18.8539 + 10.8853i −0.0403723 + 0.0233090i −0.520050 0.854136i \(-0.674087\pi\)
0.479678 + 0.877445i \(0.340753\pi\)
\(468\) 0 0
\(469\) −211.411 + 321.408i −0.450770 + 0.685304i
\(470\) 0 0
\(471\) −171.904 297.746i −0.364976 0.632157i
\(472\) 0 0
\(473\) −90.5177 + 156.781i −0.191369 + 0.331461i
\(474\) 0 0
\(475\) 127.173i 0.267733i
\(476\) 0 0
\(477\) −215.594 −0.451979
\(478\) 0 0
\(479\) −452.490 261.245i −0.944656 0.545397i −0.0532389 0.998582i \(-0.516954\pi\)
−0.891417 + 0.453185i \(0.850288\pi\)
\(480\) 0 0
\(481\) 72.8400 42.0542i 0.151435 0.0874308i
\(482\) 0 0
\(483\) −37.7858 + 648.318i −0.0782316 + 1.34227i
\(484\) 0 0
\(485\) −23.3892 40.5113i −0.0482252 0.0835285i
\(486\) 0 0
\(487\) 409.067 708.525i 0.839974 1.45488i −0.0499421 0.998752i \(-0.515904\pi\)
0.889916 0.456125i \(-0.150763\pi\)
\(488\) 0 0
\(489\) 647.337i 1.32380i
\(490\) 0 0
\(491\) 762.002 1.55194 0.775969 0.630771i \(-0.217261\pi\)
0.775969 + 0.630771i \(0.217261\pi\)
\(492\) 0 0
\(493\) 342.167 + 197.550i 0.694050 + 0.400710i
\(494\) 0 0
\(495\) −29.6157 + 17.0986i −0.0598297 + 0.0345427i
\(496\) 0 0
\(497\) −585.678 34.1350i −1.17843 0.0686820i
\(498\) 0 0
\(499\) −25.4935 44.1560i −0.0510891 0.0884889i 0.839350 0.543592i \(-0.182936\pi\)
−0.890439 + 0.455103i \(0.849603\pi\)
\(500\) 0 0
\(501\) 64.7126 112.086i 0.129167 0.223724i
\(502\) 0 0
\(503\) 305.233i 0.606825i 0.952859 + 0.303413i \(0.0981260\pi\)
−0.952859 + 0.303413i \(0.901874\pi\)
\(504\) 0 0
\(505\) −172.570 −0.341723
\(506\) 0 0
\(507\) 295.675 + 170.708i 0.583185 + 0.336702i
\(508\) 0 0
\(509\) 156.536 90.3761i 0.307536 0.177556i −0.338287 0.941043i \(-0.609848\pi\)
0.645823 + 0.763487i \(0.276514\pi\)
\(510\) 0 0
\(511\) −734.618 483.207i −1.43761 0.945611i
\(512\) 0 0
\(513\) −232.096 402.003i −0.452429 0.783631i
\(514\) 0 0
\(515\) −200.131 + 346.637i −0.388604 + 0.673081i
\(516\) 0 0
\(517\) 110.627i 0.213978i
\(518\) 0 0
\(519\) 178.973 0.344841
\(520\) 0 0
\(521\) −312.767 180.576i −0.600321 0.346595i 0.168847 0.985642i \(-0.445996\pi\)
−0.769168 + 0.639047i \(0.779329\pi\)
\(522\) 0 0
\(523\) −566.506 + 327.072i −1.08318 + 0.625377i −0.931754 0.363091i \(-0.881721\pi\)
−0.151431 + 0.988468i \(0.548388\pi\)
\(524\) 0 0
\(525\) −127.755 + 64.1548i −0.243343 + 0.122200i
\(526\) 0 0
\(527\) −290.103 502.474i −0.550481 0.953461i
\(528\) 0 0
\(529\) −401.757 + 695.864i −0.759465 + 1.31543i
\(530\) 0 0
\(531\) 171.646i 0.323251i
\(532\) 0 0
\(533\) −125.709 −0.235852
\(534\) 0 0
\(535\) −297.641 171.843i −0.556338 0.321202i
\(536\) 0 0
\(537\) 324.517 187.360i 0.604315 0.348902i
\(538\) 0 0
\(539\) 95.6295 128.432i 0.177420 0.238277i
\(540\) 0 0
\(541\) −301.642 522.459i −0.557564 0.965729i −0.997699 0.0677973i \(-0.978403\pi\)
0.440135 0.897931i \(-0.354930\pi\)
\(542\) 0 0
\(543\) −374.225 + 648.177i −0.689180 + 1.19370i
\(544\) 0 0
\(545\) 667.214i 1.22424i
\(546\) 0 0
\(547\) −686.167 −1.25442 −0.627209 0.778851i \(-0.715803\pi\)
−0.627209 + 0.778851i \(0.715803\pi\)
\(548\) 0 0
\(549\) 65.0776 + 37.5726i 0.118538 + 0.0684382i
\(550\) 0 0
\(551\) −390.142 + 225.248i −0.708061 + 0.408799i
\(552\) 0 0
\(553\) 221.123 + 440.334i 0.399860 + 0.796265i
\(554\) 0 0
\(555\) −74.7706 129.506i −0.134722 0.233345i
\(556\) 0 0
\(557\) −392.661 + 680.108i −0.704956 + 1.22102i 0.261751 + 0.965135i \(0.415700\pi\)
−0.966707 + 0.255885i \(0.917633\pi\)
\(558\) 0 0
\(559\) 326.168i 0.583485i
\(560\) 0 0
\(561\) −115.276 −0.205483
\(562\) 0 0
\(563\) −393.226 227.029i −0.698447 0.403249i 0.108321 0.994116i \(-0.465452\pi\)
−0.806769 + 0.590867i \(0.798786\pi\)
\(564\) 0 0
\(565\) 97.2007 56.1189i 0.172037 0.0993254i
\(566\) 0 0
\(567\) 198.794 302.225i 0.350606 0.533025i
\(568\) 0 0
\(569\) 35.7137 + 61.8580i 0.0627658 + 0.108713i 0.895701 0.444657i \(-0.146675\pi\)
−0.832935 + 0.553371i \(0.813341\pi\)
\(570\) 0 0
\(571\) 359.033 621.864i 0.628780 1.08908i −0.359017 0.933331i \(-0.616888\pi\)
0.987797 0.155748i \(-0.0497787\pi\)
\(572\) 0 0
\(573\) 285.968i 0.499071i
\(574\) 0 0
\(575\) −293.331 −0.510141
\(576\) 0 0
\(577\) 786.338 + 453.993i 1.36280 + 0.786815i 0.989996 0.141093i \(-0.0450617\pi\)
0.372808 + 0.927909i \(0.378395\pi\)
\(578\) 0 0
\(579\) −280.600 + 162.004i −0.484628 + 0.279800i
\(580\) 0 0
\(581\) 11.0483 189.563i 0.0190160 0.326271i
\(582\) 0 0
\(583\) −138.645 240.140i −0.237813 0.411904i
\(584\) 0 0
\(585\) 30.8063 53.3581i 0.0526603 0.0912104i
\(586\) 0 0
\(587\) 862.870i 1.46997i 0.678086 + 0.734983i \(0.262810\pi\)
−0.678086 + 0.734983i \(0.737190\pi\)
\(588\) 0 0
\(589\) 661.557 1.12319
\(590\) 0 0
\(591\) −645.204 372.509i −1.09172 0.630302i
\(592\) 0 0
\(593\) 470.127 271.428i 0.792794 0.457720i −0.0481510 0.998840i \(-0.515333\pi\)
0.840945 + 0.541120i \(0.182000\pi\)
\(594\) 0 0
\(595\) −399.502 23.2841i −0.671431 0.0391329i
\(596\) 0 0
\(597\) 12.3796 + 21.4421i 0.0207363 + 0.0359164i
\(598\) 0 0
\(599\) 39.3074 68.0824i 0.0656216 0.113660i −0.831348 0.555752i \(-0.812430\pi\)
0.896970 + 0.442092i \(0.145764\pi\)
\(600\) 0 0
\(601\) 851.603i 1.41698i −0.705722 0.708489i \(-0.749377\pi\)
0.705722 0.708489i \(-0.250623\pi\)
\(602\) 0 0
\(603\) 139.635 0.231566
\(604\) 0 0
\(605\) 393.512 + 227.194i 0.650433 + 0.375528i
\(606\) 0 0
\(607\) −202.282 + 116.788i −0.333249 + 0.192401i −0.657282 0.753644i \(-0.728294\pi\)
0.324034 + 0.946045i \(0.394961\pi\)
\(608\) 0 0
\(609\) −423.093 278.297i −0.694734 0.456973i
\(610\) 0 0
\(611\) −99.6571 172.611i −0.163105 0.282506i
\(612\) 0 0
\(613\) −40.5620 + 70.2555i −0.0661697 + 0.114609i −0.897212 0.441600i \(-0.854411\pi\)
0.831043 + 0.556209i \(0.187745\pi\)
\(614\) 0 0
\(615\) 223.505i 0.363424i
\(616\) 0 0
\(617\) 47.2962 0.0766552 0.0383276 0.999265i \(-0.487797\pi\)
0.0383276 + 0.999265i \(0.487797\pi\)
\(618\) 0 0
\(619\) −569.331 328.703i −0.919759 0.531023i −0.0362006 0.999345i \(-0.511526\pi\)
−0.883558 + 0.468322i \(0.844859\pi\)
\(620\) 0 0
\(621\) 927.239 535.342i 1.49314 0.862064i
\(622\) 0 0
\(623\) −914.129 + 459.048i −1.46730 + 0.736834i
\(624\) 0 0
\(625\) 179.768 + 311.367i 0.287629 + 0.498188i
\(626\) 0 0
\(627\) 65.7194 113.829i 0.104816 0.181546i
\(628\) 0 0
\(629\) 198.285i 0.315239i
\(630\) 0 0
\(631\) 270.276 0.428330 0.214165 0.976797i \(-0.431297\pi\)
0.214165 + 0.976797i \(0.431297\pi\)
\(632\) 0 0
\(633\) 307.076 + 177.290i 0.485112 + 0.280079i
\(634\) 0 0
\(635\) 829.165 478.718i 1.30577 0.753887i
\(636\) 0 0
\(637\) −33.5144 + 286.539i −0.0526129 + 0.449825i
\(638\) 0 0
\(639\) 106.471 + 184.413i 0.166621 + 0.288596i
\(640\) 0 0
\(641\) −122.305 + 211.838i −0.190803 + 0.330481i −0.945517 0.325574i \(-0.894443\pi\)
0.754713 + 0.656055i \(0.227776\pi\)
\(642\) 0 0
\(643\) 358.233i 0.557128i 0.960418 + 0.278564i \(0.0898584\pi\)
−0.960418 + 0.278564i \(0.910142\pi\)
\(644\) 0 0
\(645\) −579.913 −0.899089
\(646\) 0 0
\(647\) 1024.30 + 591.377i 1.58315 + 0.914030i 0.994397 + 0.105715i \(0.0337130\pi\)
0.588750 + 0.808315i \(0.299620\pi\)
\(648\) 0 0
\(649\) −191.189 + 110.383i −0.294590 + 0.170081i
\(650\) 0 0
\(651\) 333.735 + 664.585i 0.512649 + 1.02087i
\(652\) 0 0
\(653\) −107.647 186.451i −0.164850 0.285529i 0.771752 0.635924i \(-0.219381\pi\)
−0.936602 + 0.350395i \(0.886047\pi\)
\(654\) 0 0
\(655\) 362.663 628.151i 0.553684 0.959009i
\(656\) 0 0
\(657\) 319.152i 0.485772i
\(658\) 0 0
\(659\) 254.983 0.386925 0.193462 0.981108i \(-0.438028\pi\)
0.193462 + 0.981108i \(0.438028\pi\)
\(660\) 0 0
\(661\) −1077.04 621.830i −1.62941 0.940741i −0.984269 0.176679i \(-0.943465\pi\)
−0.645142 0.764062i \(-0.723202\pi\)
\(662\) 0 0
\(663\) 179.865 103.845i 0.271290 0.156630i
\(664\) 0 0
\(665\) 250.750 381.214i 0.377067 0.573253i
\(666\) 0 0
\(667\) −519.546 899.881i −0.778930 1.34915i
\(668\) 0 0
\(669\) −347.456 + 601.812i −0.519367 + 0.899569i
\(670\) 0 0
\(671\) 96.6491i 0.144037i
\(672\) 0 0
\(673\) −63.0354 −0.0936633 −0.0468317 0.998903i \(-0.514912\pi\)
−0.0468317 + 0.998903i \(0.514912\pi\)
\(674\) 0 0
\(675\) 204.116 + 117.847i 0.302395 + 0.174588i
\(676\) 0 0
\(677\) −855.162 + 493.728i −1.26316 + 0.729288i −0.973685 0.227896i \(-0.926815\pi\)
−0.289479 + 0.957184i \(0.593482\pi\)
\(678\) 0 0
\(679\) 4.62573 79.3669i 0.00681256 0.116888i
\(680\) 0 0
\(681\) −85.8322 148.666i −0.126038 0.218305i
\(682\) 0 0
\(683\) −467.447 + 809.642i −0.684403 + 1.18542i 0.289221 + 0.957262i \(0.406604\pi\)
−0.973624 + 0.228159i \(0.926730\pi\)
\(684\) 0 0
\(685\) 1091.17i 1.59294i
\(686\) 0 0
\(687\) 489.400 0.712373
\(688\) 0 0
\(689\) 432.655 + 249.794i 0.627947 + 0.362545i
\(690\) 0 0
\(691\) 842.192 486.240i 1.21880 0.703676i 0.254140 0.967167i \(-0.418207\pi\)
0.964662 + 0.263492i \(0.0848741\pi\)
\(692\) 0 0
\(693\) −58.0210 3.38163i −0.0837243 0.00487969i
\(694\) 0 0
\(695\) 551.258 + 954.806i 0.793176 + 1.37382i
\(696\) 0 0
\(697\) 148.179 256.654i 0.212596 0.368227i
\(698\) 0 0
\(699\) 206.891i 0.295981i
\(700\) 0 0
\(701\) 695.549 0.992224 0.496112 0.868259i \(-0.334761\pi\)
0.496112 + 0.868259i \(0.334761\pi\)
\(702\) 0 0
\(703\) −195.797 113.043i −0.278516 0.160801i
\(704\) 0 0
\(705\) −306.895 + 177.186i −0.435312 + 0.251328i
\(706\) 0 0
\(707\) −245.033 161.175i −0.346581 0.227970i
\(708\) 0 0
\(709\) 78.6320 + 136.195i 0.110905 + 0.192094i 0.916136 0.400869i \(-0.131292\pi\)
−0.805230 + 0.592962i \(0.797958\pi\)
\(710\) 0 0
\(711\) 89.4232 154.886i 0.125771 0.217842i
\(712\) 0 0
\(713\) 1525.91i 2.14013i
\(714\) 0 0
\(715\) 79.2440 0.110831
\(716\) 0 0
\(717\) −49.7763 28.7384i −0.0694230 0.0400814i
\(718\) 0 0
\(719\) −183.553 + 105.975i −0.255290 + 0.147392i −0.622184 0.782871i \(-0.713754\pi\)
0.366894 + 0.930263i \(0.380421\pi\)
\(720\) 0 0
\(721\) −607.913 + 305.275i −0.843153 + 0.423406i
\(722\) 0 0
\(723\) −119.662 207.261i −0.165508 0.286668i
\(724\) 0 0
\(725\) 114.370 198.094i 0.157751 0.273233i
\(726\) 0 0
\(727\) 271.507i 0.373462i −0.982411 0.186731i \(-0.940211\pi\)
0.982411 0.186731i \(-0.0597893\pi\)
\(728\) 0 0
\(729\) −802.202 −1.10041
\(730\) 0 0
\(731\) 665.921 + 384.470i 0.910972 + 0.525950i
\(732\) 0 0
\(733\) −442.045 + 255.215i −0.603062 + 0.348178i −0.770245 0.637748i \(-0.779866\pi\)
0.167183 + 0.985926i \(0.446533\pi\)
\(734\) 0 0
\(735\) 509.454 + 59.5872i 0.693134 + 0.0810711i
\(736\) 0 0
\(737\) 89.7965 + 155.532i 0.121841 + 0.211034i
\(738\) 0 0
\(739\) −187.084 + 324.039i −0.253158 + 0.438483i −0.964394 0.264471i \(-0.914803\pi\)
0.711235 + 0.702954i \(0.248136\pi\)
\(740\) 0 0
\(741\) 236.811i 0.319583i
\(742\) 0 0
\(743\) 792.307 1.06636 0.533181 0.846001i \(-0.320996\pi\)
0.533181 + 0.846001i \(0.320996\pi\)
\(744\) 0 0
\(745\) 6.93919 + 4.00634i 0.00931434 + 0.00537764i
\(746\) 0 0
\(747\) −59.6879 + 34.4608i −0.0799035 + 0.0461323i
\(748\) 0 0
\(749\) −262.126 521.986i −0.349967 0.696911i
\(750\) 0 0
\(751\) −13.1482 22.7733i −0.0175076 0.0303240i 0.857139 0.515085i \(-0.172240\pi\)
−0.874646 + 0.484761i \(0.838906\pi\)
\(752\) 0 0
\(753\) 402.440 697.046i 0.534449 0.925692i
\(754\) 0 0
\(755\) 413.133i 0.547196i
\(756\) 0 0
\(757\) 1287.30 1.70053 0.850264 0.526356i \(-0.176442\pi\)
0.850264 + 0.526356i \(0.176442\pi\)
\(758\) 0 0
\(759\) 262.553 + 151.585i 0.345920 + 0.199717i
\(760\) 0 0
\(761\) 839.569 484.726i 1.10324 0.636959i 0.166174 0.986097i \(-0.446859\pi\)
0.937071 + 0.349138i \(0.113525\pi\)
\(762\) 0 0
\(763\) 623.154 947.378i 0.816715 1.24165i
\(764\) 0 0
\(765\) 72.6257 + 125.791i 0.0949355 + 0.164433i
\(766\) 0 0
\(767\) 198.875 344.461i 0.259289 0.449102i
\(768\) 0 0
\(769\) 499.204i 0.649160i −0.945858 0.324580i \(-0.894777\pi\)
0.945858 0.324580i \(-0.105223\pi\)
\(770\) 0 0
\(771\) 119.603 0.155127
\(772\) 0 0
\(773\) −125.870 72.6713i −0.162834 0.0940120i 0.416369 0.909196i \(-0.363303\pi\)
−0.579202 + 0.815184i \(0.696636\pi\)
\(774\) 0 0
\(775\) −290.902 + 167.953i −0.375358 + 0.216713i
\(776\) 0 0
\(777\) 14.7875 253.720i 0.0190315 0.326537i
\(778\) 0 0
\(779\) 168.955 + 292.639i 0.216888 + 0.375660i
\(780\) 0 0
\(781\) −136.939 + 237.185i −0.175338 + 0.303694i
\(782\) 0 0
\(783\) 834.918i 1.06631i
\(784\) 0 0
\(785\) −557.176 −0.709779
\(786\) 0 0
\(787\) −333.132 192.334i −0.423294 0.244389i 0.273192 0.961960i \(-0.411921\pi\)
−0.696486 + 0.717571i \(0.745254\pi\)
\(788\) 0 0
\(789\) −894.719 + 516.566i −1.13399 + 0.654710i
\(790\) 0 0
\(791\) 190.429 + 11.0987i 0.240744 + 0.0140313i
\(792\)