Properties

Label 912.3.be.f.673.3
Level $912$
Weight $3$
Character 912.673
Analytic conductor $24.850$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 912.be (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(24.8502001097\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{6})\)
Coefficient field: 6.0.92607408.1
Defining polynomial: \( x^{6} - 3x^{5} + 20x^{4} - 35x^{3} + 94x^{2} - 77x + 43 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 57)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 673.3
Root \(0.500000 - 0.630453i\) of defining polynomial
Character \(\chi\) \(=\) 912.673
Dual form 912.3.be.f.145.3

$q$-expansion

\(f(q)\) \(=\) \(q+(1.50000 + 0.866025i) q^{3} +(2.88028 - 4.98878i) q^{5} -1.94451 q^{7} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\) \(q+(1.50000 + 0.866025i) q^{3} +(2.88028 - 4.98878i) q^{5} -1.94451 q^{7} +(1.50000 + 2.59808i) q^{9} -8.46561 q^{11} +(-16.7415 + 9.66573i) q^{13} +(8.64083 - 4.98878i) q^{15} +(12.5365 - 21.7138i) q^{17} +(-17.8181 - 6.59651i) q^{19} +(-2.91676 - 1.68399i) q^{21} +(-15.6408 - 27.0907i) q^{23} +(-4.09198 - 7.08751i) q^{25} +5.19615i q^{27} +(13.7071 - 7.91383i) q^{29} -14.4237i q^{31} +(-12.6984 - 7.33143i) q^{33} +(-5.60071 + 9.70072i) q^{35} -41.6423i q^{37} -33.4831 q^{39} +(1.53439 + 0.885881i) q^{41} +(-14.4358 + 25.0035i) q^{43} +17.2817 q^{45} +(-1.70506 - 2.95325i) q^{47} -45.2189 q^{49} +(37.6094 - 21.7138i) q^{51} +(-80.0952 + 46.2430i) q^{53} +(-24.3833 + 42.2331i) q^{55} +(-21.0145 - 25.3257i) q^{57} +(-4.27292 - 2.46697i) q^{59} +(7.45989 + 12.9209i) q^{61} +(-2.91676 - 5.05197i) q^{63} +111.360i q^{65} +(70.4113 - 40.6520i) q^{67} -54.1814i q^{69} +(-52.9948 - 30.5966i) q^{71} +(-38.8299 + 67.2553i) q^{73} -14.1750i q^{75} +16.4614 q^{77} +(-84.0207 - 48.5094i) q^{79} +(-4.50000 + 7.79423i) q^{81} +102.323 q^{83} +(-72.2171 - 125.084i) q^{85} +27.4143 q^{87} +(103.596 - 59.8111i) q^{89} +(32.5540 - 18.7951i) q^{91} +(12.4913 - 21.6355i) q^{93} +(-84.2297 + 69.8911i) q^{95} +(-42.1438 - 24.3318i) q^{97} +(-12.6984 - 21.9943i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 9 q^{3} + 4 q^{5} + 22 q^{7} + 9 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 9 q^{3} + 4 q^{5} + 22 q^{7} + 9 q^{9} + 36 q^{11} - 3 q^{13} + 12 q^{15} + 38 q^{17} + 10 q^{19} + 33 q^{21} - 54 q^{23} - 21 q^{25} - 102 q^{29} + 54 q^{33} + 24 q^{35} - 6 q^{39} + 96 q^{41} - 107 q^{43} + 24 q^{45} + 50 q^{47} - 48 q^{49} + 114 q^{51} - 90 q^{53} - 148 q^{55} - 3 q^{57} + 27 q^{61} + 33 q^{63} + 39 q^{67} - 84 q^{71} - 77 q^{73} + 260 q^{77} - 9 q^{79} - 27 q^{81} + 348 q^{83} + 68 q^{85} - 204 q^{87} - 72 q^{89} + 393 q^{91} + 129 q^{93} - 104 q^{95} - 228 q^{97} + 54 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/912\mathbb{Z}\right)^\times\).

\(n\) \(97\) \(229\) \(305\) \(799\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(1\) \(1\) \(1\)

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
\(3\) 1.50000 + 0.866025i 0.500000 + 0.288675i
\(4\) 0 0
\(5\) 2.88028 4.98878i 0.576055 0.997757i −0.419871 0.907584i \(-0.637925\pi\)
0.995926 0.0901730i \(-0.0287420\pi\)
\(6\) 0 0
\(7\) −1.94451 −0.277787 −0.138893 0.990307i \(-0.544354\pi\)
−0.138893 + 0.990307i \(0.544354\pi\)
\(8\) 0 0
\(9\) 1.50000 + 2.59808i 0.166667 + 0.288675i
\(10\) 0 0
\(11\) −8.46561 −0.769601 −0.384800 0.923000i \(-0.625730\pi\)
−0.384800 + 0.923000i \(0.625730\pi\)
\(12\) 0 0
\(13\) −16.7415 + 9.66573i −1.28781 + 0.743518i −0.978263 0.207366i \(-0.933511\pi\)
−0.309547 + 0.950884i \(0.600178\pi\)
\(14\) 0 0
\(15\) 8.64083 4.98878i 0.576055 0.332586i
\(16\) 0 0
\(17\) 12.5365 21.7138i 0.737440 1.27728i −0.216204 0.976348i \(-0.569368\pi\)
0.953644 0.300936i \(-0.0972990\pi\)
\(18\) 0 0
\(19\) −17.8181 6.59651i −0.937797 0.347185i
\(20\) 0 0
\(21\) −2.91676 1.68399i −0.138893 0.0801901i
\(22\) 0 0
\(23\) −15.6408 27.0907i −0.680036 1.17786i −0.974969 0.222339i \(-0.928631\pi\)
0.294933 0.955518i \(-0.404703\pi\)
\(24\) 0 0
\(25\) −4.09198 7.08751i −0.163679 0.283500i
\(26\) 0 0
\(27\) 5.19615i 0.192450i
\(28\) 0 0
\(29\) 13.7071 7.91383i 0.472660 0.272891i −0.244692 0.969601i \(-0.578687\pi\)
0.717353 + 0.696710i \(0.245354\pi\)
\(30\) 0 0
\(31\) 14.4237i 0.465280i −0.972563 0.232640i \(-0.925264\pi\)
0.972563 0.232640i \(-0.0747363\pi\)
\(32\) 0 0
\(33\) −12.6984 7.33143i −0.384800 0.222165i
\(34\) 0 0
\(35\) −5.60071 + 9.70072i −0.160020 + 0.277163i
\(36\) 0 0
\(37\) 41.6423i 1.12547i −0.826638 0.562734i \(-0.809749\pi\)
0.826638 0.562734i \(-0.190251\pi\)
\(38\) 0 0
\(39\) −33.4831 −0.858541
\(40\) 0 0
\(41\) 1.53439 + 0.885881i 0.0374242 + 0.0216069i 0.518595 0.855020i \(-0.326455\pi\)
−0.481171 + 0.876627i \(0.659788\pi\)
\(42\) 0 0
\(43\) −14.4358 + 25.0035i −0.335716 + 0.581476i −0.983622 0.180243i \(-0.942311\pi\)
0.647906 + 0.761720i \(0.275645\pi\)
\(44\) 0 0
\(45\) 17.2817 0.384037
\(46\) 0 0
\(47\) −1.70506 2.95325i −0.0362778 0.0628350i 0.847316 0.531088i \(-0.178217\pi\)
−0.883594 + 0.468253i \(0.844883\pi\)
\(48\) 0 0
\(49\) −45.2189 −0.922835
\(50\) 0 0
\(51\) 37.6094 21.7138i 0.737440 0.425761i
\(52\) 0 0
\(53\) −80.0952 + 46.2430i −1.51123 + 0.872510i −0.511317 + 0.859392i \(0.670842\pi\)
−0.999914 + 0.0131174i \(0.995824\pi\)
\(54\) 0 0
\(55\) −24.3833 + 42.2331i −0.443333 + 0.767874i
\(56\) 0 0
\(57\) −21.0145 25.3257i −0.368675 0.444311i
\(58\) 0 0
\(59\) −4.27292 2.46697i −0.0724224 0.0418131i 0.463352 0.886175i \(-0.346647\pi\)
−0.535774 + 0.844361i \(0.679980\pi\)
\(60\) 0 0
\(61\) 7.45989 + 12.9209i 0.122293 + 0.211818i 0.920672 0.390338i \(-0.127642\pi\)
−0.798378 + 0.602156i \(0.794309\pi\)
\(62\) 0 0
\(63\) −2.91676 5.05197i −0.0462978 0.0801901i
\(64\) 0 0
\(65\) 111.360i 1.71323i
\(66\) 0 0
\(67\) 70.4113 40.6520i 1.05091 0.606746i 0.128009 0.991773i \(-0.459141\pi\)
0.922905 + 0.385027i \(0.125808\pi\)
\(68\) 0 0
\(69\) 54.1814i 0.785238i
\(70\) 0 0
\(71\) −52.9948 30.5966i −0.746406 0.430938i 0.0779878 0.996954i \(-0.475150\pi\)
−0.824394 + 0.566017i \(0.808484\pi\)
\(72\) 0 0
\(73\) −38.8299 + 67.2553i −0.531916 + 0.921306i 0.467390 + 0.884051i \(0.345195\pi\)
−0.999306 + 0.0372545i \(0.988139\pi\)
\(74\) 0 0
\(75\) 14.1750i 0.189000i
\(76\) 0 0
\(77\) 16.4614 0.213785
\(78\) 0 0
\(79\) −84.0207 48.5094i −1.06355 0.614043i −0.137140 0.990552i \(-0.543791\pi\)
−0.926413 + 0.376509i \(0.877125\pi\)
\(80\) 0 0
\(81\) −4.50000 + 7.79423i −0.0555556 + 0.0962250i
\(82\) 0 0
\(83\) 102.323 1.23280 0.616401 0.787432i \(-0.288590\pi\)
0.616401 + 0.787432i \(0.288590\pi\)
\(84\) 0 0
\(85\) −72.2171 125.084i −0.849612 1.47157i
\(86\) 0 0
\(87\) 27.4143 0.315107
\(88\) 0 0
\(89\) 103.596 59.8111i 1.16400 0.672034i 0.211739 0.977326i \(-0.432087\pi\)
0.952259 + 0.305292i \(0.0987540\pi\)
\(90\) 0 0
\(91\) 32.5540 18.7951i 0.357737 0.206539i
\(92\) 0 0
\(93\) 12.4913 21.6355i 0.134315 0.232640i
\(94\) 0 0
\(95\) −84.2297 + 69.8911i −0.886629 + 0.735695i
\(96\) 0 0
\(97\) −42.1438 24.3318i −0.434473 0.250843i 0.266778 0.963758i \(-0.414041\pi\)
−0.701250 + 0.712915i \(0.747374\pi\)
\(98\) 0 0
\(99\) −12.6984 21.9943i −0.128267 0.222165i
\(100\) 0 0
\(101\) −81.5540 141.256i −0.807465 1.39857i −0.914614 0.404327i \(-0.867506\pi\)
0.107149 0.994243i \(-0.465828\pi\)
\(102\) 0 0
\(103\) 18.2732i 0.177410i −0.996058 0.0887050i \(-0.971727\pi\)
0.996058 0.0887050i \(-0.0282728\pi\)
\(104\) 0 0
\(105\) −16.8021 + 9.70072i −0.160020 + 0.0923878i
\(106\) 0 0
\(107\) 55.4789i 0.518494i −0.965811 0.259247i \(-0.916526\pi\)
0.965811 0.259247i \(-0.0834744\pi\)
\(108\) 0 0
\(109\) 96.4369 + 55.6779i 0.884743 + 0.510806i 0.872219 0.489115i \(-0.162680\pi\)
0.0125234 + 0.999922i \(0.496014\pi\)
\(110\) 0 0
\(111\) 36.0633 62.4635i 0.324895 0.562734i
\(112\) 0 0
\(113\) 110.968i 0.982019i −0.871154 0.491010i \(-0.836628\pi\)
0.871154 0.491010i \(-0.163372\pi\)
\(114\) 0 0
\(115\) −180.200 −1.56695
\(116\) 0 0
\(117\) −50.2246 28.9972i −0.429270 0.247839i
\(118\) 0 0
\(119\) −24.3773 + 42.2227i −0.204851 + 0.354812i
\(120\) 0 0
\(121\) −49.3335 −0.407715
\(122\) 0 0
\(123\) 1.53439 + 2.65764i 0.0124747 + 0.0216069i
\(124\) 0 0
\(125\) 96.8697 0.774958
\(126\) 0 0
\(127\) 209.627 121.028i 1.65061 0.952979i 0.673785 0.738927i \(-0.264667\pi\)
0.976822 0.214052i \(-0.0686661\pi\)
\(128\) 0 0
\(129\) −43.3073 + 25.0035i −0.335716 + 0.193825i
\(130\) 0 0
\(131\) −78.7288 + 136.362i −0.600983 + 1.04093i 0.391689 + 0.920098i \(0.371891\pi\)
−0.992672 + 0.120836i \(0.961443\pi\)
\(132\) 0 0
\(133\) 34.6475 + 12.8270i 0.260507 + 0.0964433i
\(134\) 0 0
\(135\) 25.9225 + 14.9664i 0.192018 + 0.110862i
\(136\) 0 0
\(137\) 121.173 + 209.877i 0.884473 + 1.53195i 0.846317 + 0.532680i \(0.178815\pi\)
0.0381558 + 0.999272i \(0.487852\pi\)
\(138\) 0 0
\(139\) 65.0431 + 112.658i 0.467936 + 0.810489i 0.999329 0.0366365i \(-0.0116644\pi\)
−0.531392 + 0.847126i \(0.678331\pi\)
\(140\) 0 0
\(141\) 5.90649i 0.0418900i
\(142\) 0 0
\(143\) 141.727 81.8263i 0.991100 0.572212i
\(144\) 0 0
\(145\) 91.1760i 0.628800i
\(146\) 0 0
\(147\) −67.8283 39.1607i −0.461417 0.266399i
\(148\) 0 0
\(149\) −102.368 + 177.306i −0.687030 + 1.18997i 0.285764 + 0.958300i \(0.407753\pi\)
−0.972794 + 0.231672i \(0.925581\pi\)
\(150\) 0 0
\(151\) 234.305i 1.55169i −0.630924 0.775845i \(-0.717324\pi\)
0.630924 0.775845i \(-0.282676\pi\)
\(152\) 0 0
\(153\) 75.2189 0.491627
\(154\) 0 0
\(155\) −71.9566 41.5441i −0.464236 0.268027i
\(156\) 0 0
\(157\) 44.2955 76.7220i 0.282137 0.488675i −0.689774 0.724025i \(-0.742290\pi\)
0.971911 + 0.235349i \(0.0756234\pi\)
\(158\) 0 0
\(159\) −160.190 −1.00749
\(160\) 0 0
\(161\) 30.4137 + 52.6780i 0.188905 + 0.327193i
\(162\) 0 0
\(163\) −115.918 −0.711153 −0.355576 0.934647i \(-0.615715\pi\)
−0.355576 + 0.934647i \(0.615715\pi\)
\(164\) 0 0
\(165\) −73.1499 + 42.2331i −0.443333 + 0.255958i
\(166\) 0 0
\(167\) −78.0426 + 45.0579i −0.467321 + 0.269808i −0.715118 0.699004i \(-0.753627\pi\)
0.247797 + 0.968812i \(0.420293\pi\)
\(168\) 0 0
\(169\) 102.353 177.280i 0.605638 1.04900i
\(170\) 0 0
\(171\) −9.58896 56.1876i −0.0560758 0.328583i
\(172\) 0 0
\(173\) −38.5739 22.2707i −0.222971 0.128732i 0.384354 0.923186i \(-0.374424\pi\)
−0.607325 + 0.794454i \(0.707757\pi\)
\(174\) 0 0
\(175\) 7.95687 + 13.7817i 0.0454678 + 0.0787526i
\(176\) 0 0
\(177\) −4.27292 7.40091i −0.0241408 0.0418131i
\(178\) 0 0
\(179\) 229.632i 1.28286i 0.767181 + 0.641431i \(0.221659\pi\)
−0.767181 + 0.641431i \(0.778341\pi\)
\(180\) 0 0
\(181\) 157.070 90.6845i 0.867791 0.501019i 0.00117734 0.999999i \(-0.499625\pi\)
0.866613 + 0.498980i \(0.166292\pi\)
\(182\) 0 0
\(183\) 25.8418i 0.141212i
\(184\) 0 0
\(185\) −207.745 119.941i −1.12294 0.648332i
\(186\) 0 0
\(187\) −106.129 + 183.821i −0.567535 + 0.982999i
\(188\) 0 0
\(189\) 10.1039i 0.0534600i
\(190\) 0 0
\(191\) 278.704 1.45918 0.729592 0.683882i \(-0.239710\pi\)
0.729592 + 0.683882i \(0.239710\pi\)
\(192\) 0 0
\(193\) −167.512 96.7133i −0.867939 0.501105i −0.00127645 0.999999i \(-0.500406\pi\)
−0.866663 + 0.498894i \(0.833740\pi\)
\(194\) 0 0
\(195\) −96.4405 + 167.040i −0.494567 + 0.856615i
\(196\) 0 0
\(197\) −96.9300 −0.492030 −0.246015 0.969266i \(-0.579121\pi\)
−0.246015 + 0.969266i \(0.579121\pi\)
\(198\) 0 0
\(199\) −172.893 299.460i −0.868811 1.50482i −0.863213 0.504840i \(-0.831551\pi\)
−0.00559823 0.999984i \(-0.501782\pi\)
\(200\) 0 0
\(201\) 140.823 0.700610
\(202\) 0 0
\(203\) −26.6536 + 15.3885i −0.131299 + 0.0758053i
\(204\) 0 0
\(205\) 8.83894 5.10316i 0.0431168 0.0248935i
\(206\) 0 0
\(207\) 46.9225 81.2721i 0.226679 0.392619i
\(208\) 0 0
\(209\) 150.841 + 55.8435i 0.721729 + 0.267194i
\(210\) 0 0
\(211\) 11.1758 + 6.45233i 0.0529657 + 0.0305798i 0.526249 0.850330i \(-0.323598\pi\)
−0.473283 + 0.880910i \(0.656931\pi\)
\(212\) 0 0
\(213\) −52.9948 91.7897i −0.248802 0.430938i
\(214\) 0 0
\(215\) 83.1580 + 144.034i 0.386781 + 0.669925i
\(216\) 0 0
\(217\) 28.0469i 0.129248i
\(218\) 0 0
\(219\) −116.490 + 67.2553i −0.531916 + 0.307102i
\(220\) 0 0
\(221\) 484.697i 2.19320i
\(222\) 0 0
\(223\) 80.3821 + 46.4086i 0.360458 + 0.208110i 0.669282 0.743009i \(-0.266602\pi\)
−0.308824 + 0.951119i \(0.599935\pi\)
\(224\) 0 0
\(225\) 12.2759 21.2625i 0.0545597 0.0945002i
\(226\) 0 0
\(227\) 280.870i 1.23731i 0.785662 + 0.618656i \(0.212323\pi\)
−0.785662 + 0.618656i \(0.787677\pi\)
\(228\) 0 0
\(229\) 137.541 0.600615 0.300308 0.953842i \(-0.402911\pi\)
0.300308 + 0.953842i \(0.402911\pi\)
\(230\) 0 0
\(231\) 24.6921 + 14.2560i 0.106892 + 0.0617143i
\(232\) 0 0
\(233\) −183.683 + 318.148i −0.788339 + 1.36544i 0.138645 + 0.990342i \(0.455725\pi\)
−0.926984 + 0.375101i \(0.877608\pi\)
\(234\) 0 0
\(235\) −19.6441 −0.0835921
\(236\) 0 0
\(237\) −84.0207 145.528i −0.354518 0.614043i
\(238\) 0 0
\(239\) 196.388 0.821707 0.410854 0.911701i \(-0.365231\pi\)
0.410854 + 0.911701i \(0.365231\pi\)
\(240\) 0 0
\(241\) −118.225 + 68.2572i −0.490560 + 0.283225i −0.724807 0.688952i \(-0.758071\pi\)
0.234247 + 0.972177i \(0.424738\pi\)
\(242\) 0 0
\(243\) −13.5000 + 7.79423i −0.0555556 + 0.0320750i
\(244\) 0 0
\(245\) −130.243 + 225.587i −0.531604 + 0.920765i
\(246\) 0 0
\(247\) 362.063 61.7896i 1.46584 0.250160i
\(248\) 0 0
\(249\) 153.484 + 88.6140i 0.616401 + 0.355879i
\(250\) 0 0
\(251\) 23.3322 + 40.4126i 0.0929571 + 0.161006i 0.908754 0.417332i \(-0.137035\pi\)
−0.815797 + 0.578338i \(0.803701\pi\)
\(252\) 0 0
\(253\) 132.409 + 229.339i 0.523356 + 0.906480i
\(254\) 0 0
\(255\) 250.167i 0.981048i
\(256\) 0 0
\(257\) 4.73878 2.73593i 0.0184388 0.0106457i −0.490752 0.871299i \(-0.663278\pi\)
0.509191 + 0.860653i \(0.329945\pi\)
\(258\) 0 0
\(259\) 80.9737i 0.312640i
\(260\) 0 0
\(261\) 41.1214 + 23.7415i 0.157553 + 0.0909635i
\(262\) 0 0
\(263\) −37.1071 + 64.2713i −0.141091 + 0.244378i −0.927908 0.372809i \(-0.878394\pi\)
0.786816 + 0.617187i \(0.211728\pi\)
\(264\) 0 0
\(265\) 532.770i 2.01045i
\(266\) 0 0
\(267\) 207.192 0.775998
\(268\) 0 0
\(269\) −64.2197 37.0772i −0.238735 0.137834i 0.375860 0.926676i \(-0.377347\pi\)
−0.614595 + 0.788843i \(0.710681\pi\)
\(270\) 0 0
\(271\) −48.0380 + 83.2043i −0.177262 + 0.307027i −0.940942 0.338568i \(-0.890057\pi\)
0.763680 + 0.645595i \(0.223391\pi\)
\(272\) 0 0
\(273\) 65.1080 0.238491
\(274\) 0 0
\(275\) 34.6411 + 60.0001i 0.125968 + 0.218182i
\(276\) 0 0
\(277\) 123.007 0.444068 0.222034 0.975039i \(-0.428730\pi\)
0.222034 + 0.975039i \(0.428730\pi\)
\(278\) 0 0
\(279\) 37.4738 21.6355i 0.134315 0.0775466i
\(280\) 0 0
\(281\) 352.110 203.291i 1.25306 0.723454i 0.281344 0.959607i \(-0.409220\pi\)
0.971716 + 0.236153i \(0.0758866\pi\)
\(282\) 0 0
\(283\) 92.7689 160.680i 0.327805 0.567776i −0.654271 0.756260i \(-0.727024\pi\)
0.982076 + 0.188485i \(0.0603576\pi\)
\(284\) 0 0
\(285\) −186.872 + 31.8915i −0.655691 + 0.111900i
\(286\) 0 0
\(287\) −2.98363 1.72260i −0.0103959 0.00600209i
\(288\) 0 0
\(289\) −169.827 294.149i −0.587636 1.01782i
\(290\) 0 0
\(291\) −42.1438 72.9953i −0.144824 0.250843i
\(292\) 0 0
\(293\) 360.407i 1.23006i −0.788505 0.615028i \(-0.789145\pi\)
0.788505 0.615028i \(-0.210855\pi\)
\(294\) 0 0
\(295\) −24.6144 + 14.2111i −0.0834385 + 0.0481733i
\(296\) 0 0
\(297\) 43.9886i 0.148110i
\(298\) 0 0
\(299\) 523.703 + 302.360i 1.75152 + 1.01124i
\(300\) 0 0
\(301\) 28.0704 48.6194i 0.0932573 0.161526i
\(302\) 0 0
\(303\) 282.511i 0.932380i
\(304\) 0 0
\(305\) 85.9461 0.281791
\(306\) 0 0
\(307\) 233.152 + 134.610i 0.759453 + 0.438470i 0.829099 0.559101i \(-0.188854\pi\)
−0.0696463 + 0.997572i \(0.522187\pi\)
\(308\) 0 0
\(309\) 15.8251 27.4098i 0.0512139 0.0887050i
\(310\) 0 0
\(311\) −53.4530 −0.171874 −0.0859372 0.996301i \(-0.527388\pi\)
−0.0859372 + 0.996301i \(0.527388\pi\)
\(312\) 0 0
\(313\) −119.760 207.430i −0.382618 0.662715i 0.608817 0.793310i \(-0.291644\pi\)
−0.991436 + 0.130596i \(0.958311\pi\)
\(314\) 0 0
\(315\) −33.6043 −0.106680
\(316\) 0 0
\(317\) 391.754 226.179i 1.23582 0.713499i 0.267580 0.963536i \(-0.413776\pi\)
0.968236 + 0.250036i \(0.0804426\pi\)
\(318\) 0 0
\(319\) −116.039 + 66.9954i −0.363760 + 0.210017i
\(320\) 0 0
\(321\) 48.0461 83.2184i 0.149676 0.259247i
\(322\) 0 0
\(323\) −366.612 + 304.203i −1.13502 + 0.941805i
\(324\) 0 0
\(325\) 137.012 + 79.1039i 0.421575 + 0.243397i
\(326\) 0 0
\(327\) 96.4369 + 167.034i 0.294914 + 0.510806i
\(328\) 0 0
\(329\) 3.31549 + 5.74260i 0.0100775 + 0.0174547i
\(330\) 0 0
\(331\) 95.4707i 0.288431i 0.989546 + 0.144216i \(0.0460659\pi\)
−0.989546 + 0.144216i \(0.953934\pi\)
\(332\) 0 0
\(333\) 108.190 62.4635i 0.324895 0.187578i
\(334\) 0 0
\(335\) 468.356i 1.39808i
\(336\) 0 0
\(337\) −82.2367 47.4794i −0.244026 0.140888i 0.373000 0.927831i \(-0.378329\pi\)
−0.617026 + 0.786943i \(0.711663\pi\)
\(338\) 0 0
\(339\) 96.1013 166.452i 0.283485 0.491010i
\(340\) 0 0
\(341\) 122.105i 0.358080i
\(342\) 0 0
\(343\) 183.209 0.534138
\(344\) 0 0
\(345\) −270.299 156.057i −0.783476 0.452340i
\(346\) 0 0
\(347\) −115.221 + 199.568i −0.332048 + 0.575124i −0.982913 0.184069i \(-0.941073\pi\)
0.650865 + 0.759193i \(0.274406\pi\)
\(348\) 0 0
\(349\) −209.160 −0.599312 −0.299656 0.954047i \(-0.596872\pi\)
−0.299656 + 0.954047i \(0.596872\pi\)
\(350\) 0 0
\(351\) −50.2246 86.9916i −0.143090 0.247839i
\(352\) 0 0
\(353\) 326.125 0.923866 0.461933 0.886915i \(-0.347156\pi\)
0.461933 + 0.886915i \(0.347156\pi\)
\(354\) 0 0
\(355\) −305.279 + 176.253i −0.859942 + 0.496488i
\(356\) 0 0
\(357\) −73.1318 + 42.2227i −0.204851 + 0.118271i
\(358\) 0 0
\(359\) 268.735 465.463i 0.748566 1.29655i −0.199945 0.979807i \(-0.564076\pi\)
0.948510 0.316747i \(-0.102590\pi\)
\(360\) 0 0
\(361\) 273.972 + 235.075i 0.758925 + 0.651178i
\(362\) 0 0
\(363\) −74.0002 42.7240i −0.203857 0.117697i
\(364\) 0 0
\(365\) 223.682 + 387.428i 0.612826 + 1.06145i
\(366\) 0 0
\(367\) 181.274 + 313.976i 0.493935 + 0.855520i 0.999976 0.00698970i \(-0.00222491\pi\)
−0.506041 + 0.862509i \(0.668892\pi\)
\(368\) 0 0
\(369\) 5.31529i 0.0144046i
\(370\) 0 0
\(371\) 155.746 89.9198i 0.419800 0.242371i
\(372\) 0 0
\(373\) 336.486i 0.902108i 0.892497 + 0.451054i \(0.148952\pi\)
−0.892497 + 0.451054i \(0.851048\pi\)
\(374\) 0 0
\(375\) 145.305 + 83.8916i 0.387479 + 0.223711i
\(376\) 0 0
\(377\) −152.986 + 264.979i −0.405798 + 0.702863i
\(378\) 0 0
\(379\) 336.744i 0.888507i −0.895901 0.444253i \(-0.853469\pi\)
0.895901 0.444253i \(-0.146531\pi\)
\(380\) 0 0
\(381\) 419.254 1.10041
\(382\) 0 0
\(383\) 193.755 + 111.865i 0.505888 + 0.292075i 0.731142 0.682226i \(-0.238988\pi\)
−0.225254 + 0.974300i \(0.572321\pi\)
\(384\) 0 0
\(385\) 47.4134 82.1225i 0.123152 0.213305i
\(386\) 0 0
\(387\) −86.6146 −0.223810
\(388\) 0 0
\(389\) 100.458 + 173.998i 0.258246 + 0.447295i 0.965772 0.259392i \(-0.0835221\pi\)
−0.707526 + 0.706687i \(0.750189\pi\)
\(390\) 0 0
\(391\) −784.324 −2.00594
\(392\) 0 0
\(393\) −236.186 + 136.362i −0.600983 + 0.346978i
\(394\) 0 0
\(395\) −484.006 + 279.441i −1.22533 + 0.707445i
\(396\) 0 0
\(397\) −53.1506 + 92.0595i −0.133880 + 0.231888i −0.925169 0.379555i \(-0.876077\pi\)
0.791289 + 0.611443i \(0.209410\pi\)
\(398\) 0 0
\(399\) 40.8627 + 49.2460i 0.102413 + 0.123424i
\(400\) 0 0
\(401\) 185.008 + 106.815i 0.461368 + 0.266371i 0.712619 0.701551i \(-0.247509\pi\)
−0.251252 + 0.967922i \(0.580842\pi\)
\(402\) 0 0
\(403\) 139.415 + 241.474i 0.345944 + 0.599192i
\(404\) 0 0
\(405\) 25.9225 + 44.8991i 0.0640061 + 0.110862i
\(406\) 0 0
\(407\) 352.528i 0.866161i
\(408\) 0 0
\(409\) −46.6112 + 26.9110i −0.113964 + 0.0657970i −0.555898 0.831250i \(-0.687626\pi\)
0.441935 + 0.897047i \(0.354292\pi\)
\(410\) 0 0
\(411\) 419.755i 1.02130i
\(412\) 0 0
\(413\) 8.30872 + 4.79704i 0.0201180 + 0.0116151i
\(414\) 0 0
\(415\) 294.717 510.465i 0.710162 1.23004i
\(416\) 0 0
\(417\) 225.316i 0.540326i
\(418\) 0 0
\(419\) 808.890 1.93052 0.965262 0.261282i \(-0.0841454\pi\)
0.965262 + 0.261282i \(0.0841454\pi\)
\(420\) 0 0
\(421\) −309.086 178.451i −0.734171 0.423874i 0.0857753 0.996315i \(-0.472663\pi\)
−0.819946 + 0.572441i \(0.805997\pi\)
\(422\) 0 0
\(423\) 5.11517 8.85974i 0.0120926 0.0209450i
\(424\) 0 0
\(425\) −205.196 −0.482814
\(426\) 0 0
\(427\) −14.5058 25.1248i −0.0339714 0.0588402i
\(428\) 0 0
\(429\) 283.455 0.660733
\(430\) 0 0
\(431\) 36.3673 20.9967i 0.0843789 0.0487162i −0.457217 0.889355i \(-0.651154\pi\)
0.541596 + 0.840639i \(0.317820\pi\)
\(432\) 0 0
\(433\) 533.602 308.075i 1.23234 0.711491i 0.264821 0.964298i \(-0.414687\pi\)
0.967517 + 0.252807i \(0.0813538\pi\)
\(434\) 0 0
\(435\) 78.9607 136.764i 0.181519 0.314400i
\(436\) 0 0
\(437\) 99.9862 + 585.881i 0.228801 + 1.34069i
\(438\) 0 0
\(439\) 408.012 + 235.566i 0.929413 + 0.536597i 0.886626 0.462487i \(-0.153043\pi\)
0.0427870 + 0.999084i \(0.486376\pi\)
\(440\) 0 0
\(441\) −67.8283 117.482i −0.153806 0.266399i
\(442\) 0 0
\(443\) −52.2697 90.5338i −0.117990 0.204365i 0.800981 0.598690i \(-0.204312\pi\)
−0.918971 + 0.394325i \(0.870979\pi\)
\(444\) 0 0
\(445\) 689.089i 1.54852i
\(446\) 0 0
\(447\) −307.103 + 177.306i −0.687030 + 0.396657i
\(448\) 0 0
\(449\) 713.259i 1.58855i −0.607559 0.794275i \(-0.707851\pi\)
0.607559 0.794275i \(-0.292149\pi\)
\(450\) 0 0
\(451\) −12.9896 7.49952i −0.0288017 0.0166287i
\(452\) 0 0
\(453\) 202.914 351.458i 0.447934 0.775845i
\(454\) 0 0
\(455\) 216.540i 0.475912i
\(456\) 0 0
\(457\) −5.29457 −0.0115855 −0.00579275 0.999983i \(-0.501844\pi\)
−0.00579275 + 0.999983i \(0.501844\pi\)
\(458\) 0 0
\(459\) 112.828 + 65.1415i 0.245813 + 0.141920i
\(460\) 0 0
\(461\) −93.4120 + 161.794i −0.202629 + 0.350964i −0.949375 0.314146i \(-0.898282\pi\)
0.746746 + 0.665110i \(0.231615\pi\)
\(462\) 0 0
\(463\) −718.582 −1.55201 −0.776007 0.630725i \(-0.782758\pi\)
−0.776007 + 0.630725i \(0.782758\pi\)
\(464\) 0 0
\(465\) −71.9566 124.632i −0.154745 0.268027i
\(466\) 0 0
\(467\) −864.548 −1.85128 −0.925641 0.378404i \(-0.876473\pi\)
−0.925641 + 0.378404i \(0.876473\pi\)
\(468\) 0 0
\(469\) −136.915 + 79.0480i −0.291930 + 0.168546i
\(470\) 0 0
\(471\) 132.886 76.7220i 0.282137 0.162892i
\(472\) 0 0
\(473\) 122.208 211.670i 0.258367 0.447505i
\(474\) 0 0
\(475\) 26.1585 + 153.279i 0.0550706 + 0.322693i
\(476\) 0 0
\(477\) −240.286 138.729i −0.503744 0.290837i
\(478\) 0 0
\(479\) −63.1395 109.361i −0.131815 0.228311i 0.792561 0.609793i \(-0.208747\pi\)
−0.924376 + 0.381482i \(0.875414\pi\)
\(480\) 0 0
\(481\) 402.504 + 697.157i 0.836806 + 1.44939i
\(482\) 0 0
\(483\) 105.356i 0.218129i
\(484\) 0 0
\(485\) −242.772 + 140.164i −0.500560 + 0.288999i
\(486\) 0 0
\(487\) 12.1199i 0.0248868i 0.999923 + 0.0124434i \(0.00396097\pi\)
−0.999923 + 0.0124434i \(0.996039\pi\)
\(488\) 0 0
\(489\) −173.877 100.388i −0.355576 0.205292i
\(490\) 0 0
\(491\) −246.271 + 426.554i −0.501570 + 0.868745i 0.498428 + 0.866931i \(0.333911\pi\)
−0.999998 + 0.00181372i \(0.999423\pi\)
\(492\) 0 0
\(493\) 396.846i 0.804962i
\(494\) 0 0
\(495\) −146.300 −0.295555
\(496\) 0 0
\(497\) 103.049 + 59.4952i 0.207342 + 0.119709i
\(498\) 0 0
\(499\) −173.134 + 299.877i −0.346962 + 0.600956i −0.985708 0.168462i \(-0.946120\pi\)
0.638746 + 0.769417i \(0.279453\pi\)
\(500\) 0 0
\(501\) −156.085 −0.311547
\(502\) 0 0
\(503\) −166.249 287.952i −0.330516 0.572470i 0.652098 0.758135i \(-0.273889\pi\)
−0.982613 + 0.185665i \(0.940556\pi\)
\(504\) 0 0
\(505\) −939.592 −1.86058
\(506\) 0 0
\(507\) 307.058 177.280i 0.605638 0.349665i
\(508\) 0 0
\(509\) −461.493 + 266.443i −0.906666 + 0.523464i −0.879357 0.476163i \(-0.842027\pi\)
−0.0273090 + 0.999627i \(0.508694\pi\)
\(510\) 0 0
\(511\) 75.5049 130.778i 0.147759 0.255926i
\(512\) 0 0
\(513\) 34.2765 92.5858i 0.0668158 0.180479i
\(514\) 0 0
\(515\) −91.1612 52.6319i −0.177012 0.102198i
\(516\) 0 0
\(517\) 14.4343 + 25.0010i 0.0279194 + 0.0483579i
\(518\) 0 0
\(519\) −38.5739 66.8120i −0.0743235 0.128732i
\(520\) 0 0
\(521\) 74.3056i 0.142621i 0.997454 + 0.0713106i \(0.0227181\pi\)
−0.997454 + 0.0713106i \(0.977282\pi\)
\(522\) 0 0
\(523\) −25.3191 + 14.6180i −0.0484113 + 0.0279503i −0.524010 0.851712i \(-0.675565\pi\)
0.475599 + 0.879662i \(0.342231\pi\)
\(524\) 0 0
\(525\) 27.5634i 0.0525017i
\(526\) 0 0
\(527\) −313.193 180.822i −0.594294 0.343116i
\(528\) 0 0
\(529\) −224.771 + 389.315i −0.424898 + 0.735945i
\(530\) 0 0
\(531\) 14.8018i 0.0278754i
\(532\) 0 0
\(533\) −34.2508 −0.0642603
\(534\) 0 0
\(535\) −276.772 159.795i −0.517331 0.298681i
\(536\) 0 0
\(537\) −198.867 + 344.448i −0.370330 + 0.641431i
\(538\) 0 0
\(539\) 382.805 0.710214
\(540\) 0 0
\(541\) 109.055 + 188.889i 0.201580 + 0.349147i 0.949038 0.315163i \(-0.102059\pi\)
−0.747458 + 0.664310i \(0.768726\pi\)
\(542\) 0 0
\(543\) 314.140 0.578527
\(544\) 0 0
\(545\) 555.530 320.735i 1.01932 0.588505i
\(546\) 0 0
\(547\) 465.237 268.605i 0.850525 0.491051i −0.0103027 0.999947i \(-0.503279\pi\)
0.860828 + 0.508896i \(0.169946\pi\)
\(548\) 0 0
\(549\) −22.3797 + 38.7627i −0.0407644 + 0.0706060i
\(550\) 0 0
\(551\) −296.440 + 50.5903i −0.538003 + 0.0918154i
\(552\) 0 0
\(553\) 163.379 + 94.3268i 0.295441 + 0.170573i
\(554\) 0 0
\(555\) −207.745 359.824i −0.374315 0.648332i
\(556\) 0 0
\(557\) −158.164 273.947i −0.283956 0.491826i 0.688399 0.725332i \(-0.258314\pi\)
−0.972355 + 0.233505i \(0.924980\pi\)
\(558\) 0 0
\(559\) 558.129i 0.998442i
\(560\) 0 0
\(561\) −318.387 + 183.821i −0.567535 + 0.327666i
\(562\) 0 0
\(563\) 595.272i 1.05732i −0.848833 0.528661i \(-0.822694\pi\)
0.848833 0.528661i \(-0.177306\pi\)
\(564\) 0 0
\(565\) −553.596 319.619i −0.979816 0.565697i
\(566\) 0 0
\(567\) 8.75028 15.1559i 0.0154326 0.0267300i
\(568\) 0 0
\(569\) 536.213i 0.942377i −0.882032 0.471189i \(-0.843825\pi\)
0.882032 0.471189i \(-0.156175\pi\)
\(570\) 0 0
\(571\) 84.5912 0.148146 0.0740729 0.997253i \(-0.476400\pi\)
0.0740729 + 0.997253i \(0.476400\pi\)
\(572\) 0 0
\(573\) 418.056 + 241.365i 0.729592 + 0.421230i
\(574\) 0 0
\(575\) −128.004 + 221.709i −0.222615 + 0.385581i
\(576\) 0 0
\(577\) −850.008 −1.47315 −0.736575 0.676356i \(-0.763558\pi\)
−0.736575 + 0.676356i \(0.763558\pi\)
\(578\) 0 0
\(579\) −167.512 290.140i −0.289313 0.501105i
\(580\) 0 0
\(581\) −198.967 −0.342456
\(582\) 0 0
\(583\) 678.055 391.475i 1.16304 0.671484i
\(584\) 0 0
\(585\) −289.322 + 167.040i −0.494567 + 0.285538i
\(586\) 0 0
\(587\) −229.370 + 397.281i −0.390750 + 0.676798i −0.992549 0.121849i \(-0.961117\pi\)
0.601799 + 0.798648i \(0.294451\pi\)
\(588\) 0 0
\(589\) −95.1459 + 257.003i −0.161538 + 0.436338i
\(590\) 0 0
\(591\) −145.395 83.9438i −0.246015 0.142037i
\(592\) 0 0
\(593\) −51.3293 88.9049i −0.0865586 0.149924i 0.819496 0.573085i \(-0.194254\pi\)
−0.906054 + 0.423161i \(0.860920\pi\)
\(594\) 0 0
\(595\) 140.426 + 243.226i 0.236011 + 0.408783i
\(596\) 0 0
\(597\) 598.920i 1.00322i
\(598\) 0 0
\(599\) −322.250 + 186.051i −0.537980 + 0.310603i −0.744260 0.667890i \(-0.767198\pi\)
0.206280 + 0.978493i \(0.433864\pi\)
\(600\) 0 0
\(601\) 850.837i 1.41570i −0.706362 0.707851i \(-0.749665\pi\)
0.706362 0.707851i \(-0.250335\pi\)
\(602\) 0 0
\(603\) 211.234 + 121.956i 0.350305 + 0.202249i
\(604\) 0 0
\(605\) −142.094 + 246.114i −0.234866 + 0.406800i
\(606\) 0 0
\(607\) 314.498i 0.518119i −0.965861 0.259060i \(-0.916587\pi\)
0.965861 0.259060i \(-0.0834126\pi\)
\(608\) 0 0
\(609\) −53.3073 −0.0875324
\(610\) 0 0
\(611\) 57.0906 + 32.9613i 0.0934379 + 0.0539464i
\(612\) 0 0
\(613\) 146.198 253.222i 0.238495 0.413086i −0.721787 0.692115i \(-0.756679\pi\)
0.960283 + 0.279029i \(0.0900125\pi\)
\(614\) 0 0
\(615\) 17.6779 0.0287445
\(616\) 0 0
\(617\) −438.183 758.955i −0.710183 1.23007i −0.964788 0.263028i \(-0.915279\pi\)
0.254605 0.967045i \(-0.418055\pi\)
\(618\) 0 0
\(619\) 166.847 0.269542 0.134771 0.990877i \(-0.456970\pi\)
0.134771 + 0.990877i \(0.456970\pi\)
\(620\) 0 0
\(621\) 140.767 81.2721i 0.226679 0.130873i
\(622\) 0 0
\(623\) −201.443 + 116.303i −0.323343 + 0.186682i
\(624\) 0 0
\(625\) 381.311 660.450i 0.610097 1.05672i
\(626\) 0 0
\(627\) 177.900 + 214.398i 0.283732 + 0.341942i
\(628\) 0 0
\(629\) −904.214 522.048i −1.43754 0.829965i
\(630\) 0 0
\(631\) −464.592 804.698i −0.736280 1.27527i −0.954160 0.299298i \(-0.903248\pi\)
0.217880 0.975976i \(-0.430086\pi\)
\(632\) 0 0
\(633\) 11.1758 + 19.3570i 0.0176552 + 0.0305798i
\(634\) 0 0
\(635\) 1394.38i 2.19587i
\(636\) 0 0
\(637\) 757.034 437.074i 1.18844 0.686144i
\(638\) 0 0
\(639\) 183.579i 0.287292i
\(640\) 0 0
\(641\) 425.692 + 245.773i 0.664106 + 0.383422i 0.793840 0.608127i \(-0.208079\pi\)
−0.129734 + 0.991549i \(0.541412\pi\)
\(642\) 0 0
\(643\) −175.770 + 304.442i −0.273359 + 0.473472i −0.969720 0.244220i \(-0.921468\pi\)
0.696361 + 0.717692i \(0.254801\pi\)
\(644\) 0 0
\(645\) 288.068i 0.446617i
\(646\) 0 0
\(647\) −767.027 −1.18551 −0.592757 0.805381i \(-0.701961\pi\)
−0.592757 + 0.805381i \(0.701961\pi\)
\(648\) 0 0
\(649\) 36.1729 + 20.8844i 0.0557363 + 0.0321794i
\(650\) 0 0
\(651\) −24.2893 + 42.0704i −0.0373108 + 0.0646242i
\(652\) 0 0
\(653\) −254.877 −0.390317 −0.195159 0.980772i \(-0.562522\pi\)
−0.195159 + 0.980772i \(0.562522\pi\)
\(654\) 0 0
\(655\) 453.521 + 785.522i 0.692399 + 1.19927i
\(656\) 0 0
\(657\) −232.979 −0.354611
\(658\) 0 0
\(659\) 427.502 246.818i 0.648713 0.374535i −0.139250 0.990257i \(-0.544469\pi\)
0.787963 + 0.615723i \(0.211136\pi\)
\(660\) 0 0
\(661\) −1110.75 + 641.292i −1.68041 + 0.970185i −0.719021 + 0.694988i \(0.755410\pi\)
−0.961388 + 0.275197i \(0.911257\pi\)
\(662\) 0 0
\(663\) −419.760 + 727.046i −0.633122 + 1.09660i
\(664\) 0 0
\(665\) 163.785 135.904i 0.246294 0.204366i
\(666\) 0 0
\(667\) −428.782 247.558i −0.642852 0.371151i
\(668\) 0 0
\(669\) 80.3821 + 139.226i 0.120153 + 0.208110i
\(670\) 0 0
\(671\) −63.1525 109.383i −0.0941169 0.163015i
\(672\) 0 0
\(673\) 337.649i 0.501707i 0.968025 + 0.250853i \(0.0807112\pi\)
−0.968025 + 0.250853i \(0.919289\pi\)
\(674\) 0 0
\(675\) 36.8278 21.2625i 0.0545597 0.0315001i
\(676\) 0 0
\(677\) 394.197i 0.582270i 0.956682 + 0.291135i \(0.0940329\pi\)
−0.956682 + 0.291135i \(0.905967\pi\)
\(678\) 0 0
\(679\) 81.9489 + 47.3132i 0.120691 + 0.0696808i
\(680\) 0 0
\(681\) −243.240 + 421.305i −0.357181 + 0.618656i
\(682\) 0 0
\(683\) 612.782i 0.897192i −0.893735 0.448596i \(-0.851924\pi\)
0.893735 0.448596i \(-0.148076\pi\)
\(684\) 0 0
\(685\) 1396.04 2.03802
\(686\) 0 0
\(687\) 206.311 + 119.114i 0.300308 + 0.173383i
\(688\) 0 0
\(689\) 893.945 1548.36i 1.29745 2.24725i
\(690\) 0 0
\(691\) −254.757 −0.368678 −0.184339 0.982863i \(-0.559014\pi\)
−0.184339 + 0.982863i \(0.559014\pi\)
\(692\) 0 0
\(693\) 24.6921 + 42.7680i 0.0356308 + 0.0617143i
\(694\) 0 0
\(695\) 749.369 1.07823
\(696\) 0 0
\(697\) 38.4717 22.2117i 0.0551962 0.0318675i
\(698\) 0 0
\(699\) −551.049 + 318.148i −0.788339 + 0.455148i
\(700\) 0 0
\(701\) −3.62864 + 6.28499i −0.00517638 + 0.00896576i −0.868602 0.495510i \(-0.834981\pi\)
0.863426 + 0.504476i \(0.168314\pi\)
\(702\) 0 0
\(703\) −274.694 + 741.989i −0.390746 + 1.05546i
\(704\) 0 0
\(705\) −29.4662 17.0123i −0.0417960 0.0241310i
\(706\) 0 0
\(707\) 158.582 + 274.672i 0.224303 + 0.388504i
\(708\) 0 0
\(709\) −522.280 904.615i −0.736643 1.27590i −0.953999 0.299810i \(-0.903077\pi\)
0.217356 0.976092i \(-0.430257\pi\)
\(710\) 0 0
\(711\) 291.056i 0.409362i
\(712\) 0 0
\(713\) −390.747 + 225.598i −0.548033 + 0.316407i
\(714\) 0 0
\(715\) 942.729i 1.31850i
\(716\) 0 0
\(717\) 294.582 + 170.077i 0.410854 + 0.237207i
\(718\) 0 0
\(719\) 658.810 1141.09i 0.916286 1.58705i 0.111279 0.993789i \(-0.464505\pi\)
0.805007 0.593265i \(-0.202161\pi\)
\(720\) 0 0
\(721\) 35.5324i 0.0492821i
\(722\) 0 0
\(723\) −236.450 −0.327040
\(724\) 0 0
\(725\) −112.179 64.7664i −0.154729 0.0893330i
\(726\) 0 0
\(727\) 88.8280 153.855i 0.122184 0.211630i −0.798444 0.602068i \(-0.794343\pi\)
0.920629 + 0.390439i \(0.127677\pi\)
\(728\) 0 0
\(729\) −27.0000 −0.0370370
\(730\) 0 0
\(731\) 361.948 + 626.912i 0.495140 + 0.857608i
\(732\) 0 0
\(733\) 321.795 0.439011 0.219505 0.975611i \(-0.429556\pi\)
0.219505 + 0.975611i \(0.429556\pi\)
\(734\) 0 0
\(735\) −390.729 + 225.587i −0.531604 + 0.306922i
\(736\) 0 0
\(737\) −596.074 + 344.144i −0.808785 + 0.466952i
\(738\) 0 0
\(739\) −85.7034 + 148.443i −0.115972 + 0.200870i −0.918168 0.396191i \(-0.870332\pi\)
0.802196 + 0.597061i \(0.203665\pi\)
\(740\) 0 0
\(741\) 596.606 + 220.872i 0.805136 + 0.298072i
\(742\) 0 0
\(743\) 257.044 + 148.405i 0.345955 + 0.199737i 0.662902 0.748706i \(-0.269325\pi\)
−0.316947 + 0.948443i \(0.602658\pi\)
\(744\) 0 0
\(745\) 589.693 + 1021.38i 0.791535 + 1.37098i
\(746\) 0 0
\(747\) 153.484 + 265.842i 0.205467 + 0.355879i
\(748\) 0 0
\(749\) 107.879i 0.144031i
\(750\) 0 0
\(751\) 117.403 67.7829i 0.156329 0.0902568i −0.419795 0.907619i \(-0.637898\pi\)
0.576124 + 0.817362i \(0.304565\pi\)
\(752\) 0 0
\(753\) 80.8252i 0.107338i
\(754\) 0 0
\(755\) −1168.90 674.864i −1.54821 0.893859i
\(756\) 0 0
\(757\) 4.71078 8.15931i 0.00622296 0.0107785i −0.862897 0.505380i \(-0.831352\pi\)
0.869120 + 0.494601i \(0.164686\pi\)
\(758\) 0 0
\(759\) 458.679i 0.604320i
\(760\) 0 0
\(761\) −501.946 −0.659587 −0.329794 0.944053i \(-0.606979\pi\)
−0.329794 + 0.944053i \(0.606979\pi\)
\(762\) 0 0
\(763\) −187.522 108.266i −0.245770 0.141895i
\(764\) 0 0
\(765\) 216.651 375.251i 0.283204 0.490524i
\(766\) 0 0
\(767\) 95.3803 0.124355
\(768\) 0 0
\(769\) 722.257 + 1250.99i 0.939216 + 1.62677i 0.766937 + 0.641722i \(0.221780\pi\)
0.172279 + 0.985048i \(0.444887\pi\)
\(770\) 0 0
\(771\) 9.47756 0.0122926
\(772\) 0 0
\(773\) −572.771 + 330.690i −0.740972 + 0.427800i −0.822423 0.568877i \(-0.807378\pi\)
0.0814506 + 0.996677i \(0.474045\pi\)
\(774\) 0 0
\(775\) −102.228 + 59.0213i −0.131907 + 0.0761565i
\(776\) 0 0
\(777\) −70.1253 + 121.461i −0.0902514 + 0.156320i
\(778\) 0 0
\(779\) −21.4963 25.9064i −0.0275947 0.0332559i
\(780\) 0 0
\(781\) 448.633 + 259.019i 0.574435 + 0.331650i
\(782\) 0 0
\(783\) 41.1214 + 71.2244i 0.0525178 + 0.0909635i
\(784\) 0 0
\(785\) −255.166 441.961i −0.325053 0.563008i
\(786\) 0 0
\(787\) 1319.00i 1.67598i 0.545686 + 0.837990i \(0.316269\pi\)
−0.545686 + 0.837990i \(0.683731\pi\)
\(788\) 0 0
\(789\) −111.321 + 64.2713i −0.141091 + 0.0814592i
\(790\) 0 0
\(791\) 215.778i 0.272792i
\(792\) 0 0