Properties

Label 224.3.s.b.129.3
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: \( 2^{20}\cdot 7 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 129.3
Root \(1.20279 - 1.51093i\) of \(x^{16} - 26 x^{14} - 16 x^{13} + 469 x^{12} + 144 x^{11} - 4526 x^{10} + 4440 x^{9} + 32608 x^{8} - 33728 x^{7} - 49760 x^{6} + 203528 x^{5} + 27401 x^{4} - 156928 x^{3} + 114964 x^{2} - 248608 x + 208849\)
Character \(\chi\) \(=\) 224.129
Dual form 224.3.s.b.33.3

$q$-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 0.0860939 0.996287i \(-0.472561\pi\)
−0.819763 + 0.572703i \(0.805895\pi\)
\(4\) 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 −0.930687 0.365816i \(-0.880790\pi\)
0.782149 + 0.623091i \(0.214123\pi\)
\(12\) 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 −0.815252 0.579107i \(-0.803402\pi\)
0.0938951 + 0.995582i \(0.470068\pi\)
\(20\) 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 \(-0.874894\pi\)
0.130194 0.991488i \(-0.458440\pi\)
\(24\) 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 −0.214629 0.976696i \(-0.568854\pi\)
−0.953158 + 0.302474i \(0.902187\pi\)
\(32\) 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 \(-0.277200\pi\)
0.644177 + 0.764877i \(0.277200\pi\)
\(44\) 0 0
\(45\) −9.06280 5.23241i −0.201395 0.116276i
\(46\) 0 0
\(47\) 29.3178 16.9266i 0.623783 0.360141i −0.154558 0.987984i \(-0.549395\pi\)
0.778340 + 0.627843i \(0.216062\pi\)
\(48\) 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 0.905761 0.423788i \(-0.139300\pi\)
0.0858695 + 0.996306i \(0.472633\pi\)
\(60\) 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 −0.584771 0.811198i \(-0.698816\pi\)
0.994904 + 0.100827i \(0.0321489\pi\)
\(68\) 0 0
\(69\) 92.7741i 1.34455i
\(70\) 0 0
\(71\) 83.8102 1.18043 0.590213 0.807248i \(-0.299044\pi\)
0.590213 + 0.807248i \(0.299044\pi\)
\(72\) 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 0.552575 0.833463i \(-0.313645\pi\)
−0.998088 + 0.0618128i \(0.980312\pi\)
\(80\) 0 0
\(81\) 25.8389 44.7542i 0.318998 0.552521i
\(82\) 0 0
\(83\) 27.1264i 0.326824i 0.986558 + 0.163412i \(0.0522500\pi\)
−0.986558 + 0.163412i \(0.947750\pi\)
\(84\) 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 −0.0323227 0.999477i \(-0.510290\pi\)
0.849412 + 0.527731i \(0.176957\pi\)
\(104\) 0 0
\(105\) 73.1511 + 4.26345i 0.696677 + 0.0406043i
\(106\) 0 0
\(107\) 41.7218 + 72.2643i 0.389924 + 0.675368i 0.992439 0.122740i \(-0.0391680\pi\)
−0.602515 + 0.798107i \(0.705835\pi\)
\(108\) 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 \(-0.867954\pi\)
−0.915183 + 0.403038i \(0.867954\pi\)
\(128\) 0 0
\(129\) −121.934 70.3986i −0.945225 0.545726i
\(130\) 0 0
\(131\) −152.509 + 88.0512i −1.16419 + 0.672146i −0.952305 0.305148i \(-0.901294\pi\)
−0.211887 + 0.977294i \(0.567961\pi\)
\(132\) 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 \(-0.587002\pi\)
0.269935 0.962878i \(-0.412998\pi\)
\(140\) 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 −0.982930 0.183978i \(-0.941102\pi\)
0.650795 + 0.759253i \(0.274436\pi\)
\(152\) 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 \(-0.881220\pi\)
0.149873 0.988705i \(-0.452114\pi\)
\(164\) 0 0
\(165\) 17.1037 29.6244i 0.103659 0.179542i
\(166\) 0 0
\(167\) 50.9246i 0.304938i 0.988308 + 0.152469i \(0.0487224\pi\)
−0.988308 + 0.152469i \(0.951278\pi\)
\(168\) 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 −0.995092 0.0989591i \(-0.968449\pi\)
0.583247 + 0.812295i \(0.301782\pi\)
\(180\) 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 0.974881 0.222728i \(-0.0714961\pi\)
−0.680328 + 0.732908i \(0.738163\pi\)
\(192\) 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 0.478652 0.878005i \(-0.341125\pi\)
−0.521048 + 0.853527i \(0.674459\pi\)
\(200\) 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 \(-0.607253\pi\)
−0.330607 + 0.943769i \(0.607253\pi\)
\(212\) 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 \(-0.789938\pi\)
0.790035 0.613062i \(-0.210062\pi\)
\(224\) 0 0
\(225\) 20.4167 0.0907409
\(226\) 0 0
\(227\) 58.4952 + 33.7722i 0.257688 + 0.148776i 0.623279 0.781999i \(-0.285800\pi\)
−0.365591 + 0.930775i \(0.619133\pi\)
\(228\) 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 \(-0.484934\pi\)
0.0473122 + 0.998880i \(0.484934\pi\)
\(240\) 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 \(0.217300\pi\)
−0.775892 + 0.630865i \(0.782700\pi\)
\(252\) 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 \(-0.552178\pi\)
0.936011 0.351972i \(-0.114489\pi\)
\(264\) 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 −0.609616 0.792697i \(-0.708676\pi\)
0.381688 + 0.924291i \(0.375343\pi\)
\(272\) 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 0.755281 0.655401i \(-0.227500\pi\)
−0.189954 + 0.981793i \(0.560834\pi\)
\(284\) 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 \(0.219333\pi\)
−0.771848 + 0.635807i \(0.780667\pi\)
\(308\) 0 0
\(309\) −246.983 −0.799297
\(310\) 0 0
\(311\) −83.2050 48.0384i −0.267540 0.154464i 0.360229 0.932864i \(-0.382699\pi\)
−0.627769 + 0.778400i \(0.716032\pi\)
\(312\) 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 0.593104 0.805126i \(-0.297902\pi\)
−0.993811 + 0.111080i \(0.964569\pi\)
\(332\) 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 \(0.599815\pi\)
−0.669563 + 0.742755i \(0.733519\pi\)
\(348\) 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 \(-0.946410\pi\)
0.347818 0.937562i \(-0.386923\pi\)
\(360\) 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 −0.0713791 0.997449i \(-0.522740\pi\)
−0.899506 + 0.436909i \(0.856073\pi\)
\(368\) 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 \(-0.705139\pi\)
−0.600770 + 0.799422i \(0.705139\pi\)
\(380\) 0 0
\(381\) 511.639 + 295.395i 1.34288 + 0.775314i
\(382\) 0 0
\(383\) 158.732 91.6439i 0.414443 0.239279i −0.278254 0.960508i \(-0.589756\pi\)
0.692697 + 0.721229i \(0.256422\pi\)
\(384\) 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 \(0.116669\pi\)
−0.933578 + 0.358375i \(0.883331\pi\)
\(420\) 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 −0.966441 0.256890i \(-0.917302\pi\)
0.705693 + 0.708517i \(0.250636\pi\)
\(432\) 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 −0.765379 0.643580i \(-0.777448\pi\)
0.174668 + 0.984627i \(0.444115\pi\)
\(440\) 0 0
\(441\) −49.3018 114.319i −0.111795 0.259227i
\(442\) 0 0
\(443\) −198.077 343.080i −0.447127 0.774447i 0.551070 0.834459i \(-0.314220\pi\)
−0.998198 + 0.0600116i \(0.980886\pi\)
\(444\) 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 \(-0.414269\pi\)
0.266087 + 0.963949i \(0.414269\pi\)
\(464\) 0 0
\(465\) 378.952 + 218.788i 0.814950 + 0.470512i
\(466\) 0 0
\(467\) 18.8539 10.8853i 0.0403723 0.0233090i −0.479678 0.877445i \(-0.659247\pi\)
0.520050 + 0.854136i \(0.325913\pi\)
\(468\) 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 0.891417 0.453185i \(-0.149712\pi\)
0.0532389 + 0.998582i \(0.483046\pi\)
\(480\) 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 \(0.484096\pi\)
−0.889916 + 0.456125i \(0.849237\pi\)
\(488\) 0 0
\(489\) 647.337i 1.32380i
\(490\) 0 0
\(491\) −762.002 −1.55194 −0.775969 0.630771i \(-0.782739\pi\)
−0.775969 + 0.630771i \(0.782739\pi\)
\(492\) 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 0.890439 0.455103i \(-0.150397\pi\)
−0.839350 + 0.543592i \(0.817064\pi\)
\(500\) 0 0
\(501\) 64.7126 112.086i 0.129167 0.223724i
\(502\) 0 0
\(503\) 305.233i 0.606825i −0.952859 0.303413i \(-0.901874\pi\)
0.952859 0.303413i \(-0.0981260\pi\)
\(504\) 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 0.151431 0.988468i \(-0.451612\pi\)
0.931754 + 0.363091i \(0.118279\pi\)
\(524\) 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 \(-0.284197\pi\)
0.627209 + 0.778851i \(0.284197\pi\)
\(548\) 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 0.806769 0.590867i \(-0.201214\pi\)
−0.108321 + 0.994116i \(0.534548\pi\)
\(564\) 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 \(0.383112\pi\)
−0.987797 + 0.155748i \(0.950221\pi\)
\(572\) 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 \(-0.737190\pi\)
0.678086 0.734983i \(-0.262810\pi\)
\(588\) 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 −0.896970 0.442092i \(-0.854236\pi\)
0.831348 + 0.555752i \(0.187570\pi\)
\(600\) 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 −0.324034 0.946045i \(-0.605039\pi\)
0.657282 + 0.753644i \(0.271706\pi\)
\(608\) 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 0.883558 0.468322i \(-0.155141\pi\)
0.0362006 + 0.999345i \(0.488474\pi\)
\(620\) 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 \(-0.568703\pi\)
−0.214165 + 0.976797i \(0.568703\pi\)
\(632\) 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 \(-0.910142\pi\)
0.960418 0.278564i \(-0.0898584\pi\)
\(644\) 0 0
\(645\) −579.913 −0.899089
\(646\) 0 0
\(647\) −1024.30 591.377i −1.58315 0.914030i −0.994397 0.105715i \(-0.966287\pi\)
−0.588750 0.808315i \(-0.700380\pi\)
\(648\) 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 \(-0.561972\pi\)
−0.193462 + 0.981108i \(0.561972\pi\)
\(660\) 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 \(-0.593396\pi\)
0.973624 0.228159i \(-0.0732705\pi\)
\(684\) 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 −0.964662 0.263492i \(-0.915126\pi\)
−0.254140 + 0.967167i \(0.581793\pi\)
\(692\) 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 −0.366894 0.930263i \(-0.619579\pi\)
0.622184 + 0.782871i \(0.286246\pi\)
\(720\) 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 \(0.0597893\pi\)
−0.982411 + 0.186731i \(0.940211\pi\)
\(728\) 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 −0.711235 0.702954i \(-0.751864\pi\)
0.964394 + 0.264471i \(0.0851973\pi\)
\(740\) 0 0
\(741\) 236.811i 0.319583i
\(742\) 0 0
\(743\) −792.307 −1.06636 −0.533181 0.846001i \(-0.679004\pi\)
−0.533181 + 0.846001i \(0.679004\pi\)
\(744\) 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 0.874646 0.484761i \(-0.161094\pi\)
−0.857139 + 0.515085i \(0.827760\pi\)
\(752\) 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 0.696486 0.717571i \(-0.254746\pi\)
−0.273192 + 0.961960i \(0.588079\pi\)
\(788\) 0 0
\(789\) −894.719 + 516.566i −1.13399 + 0.654710i
\(790\) 0 0