Properties

Label 136.3.p.a.59.1
Level $136$
Weight $3$
Character 136.59
Analytic conductor $3.706$
Analytic rank $0$
Dimension $4$
CM discriminant -8
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 136 = 2^{3} \cdot 17 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 136.p (of order \(8\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.70573159530\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{8})\)
Defining polynomial: \( x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{U}(1)[D_{8}]$

Embedding invariants

Embedding label 59.1
Root \(-0.707107 - 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 136.59
Dual form 136.3.p.a.83.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.41421 + 1.41421i) q^{2} +(1.53553 - 3.70711i) q^{3} -4.00000i q^{4} +(3.07107 + 7.41421i) q^{6} +(5.65685 + 5.65685i) q^{8} +(-5.02082 - 5.02082i) q^{9} +O(q^{10})\) \(q+(-1.41421 + 1.41421i) q^{2} +(1.53553 - 3.70711i) q^{3} -4.00000i q^{4} +(3.07107 + 7.41421i) q^{6} +(5.65685 + 5.65685i) q^{8} +(-5.02082 - 5.02082i) q^{9} +(-8.05025 - 19.4350i) q^{11} +(-14.8284 - 6.14214i) q^{12} -16.0000 q^{16} +(-12.7071 - 11.2929i) q^{17} +14.2010 q^{18} +(12.0000 - 12.0000i) q^{19} +(38.8701 + 16.1005i) q^{22} +(29.6569 - 12.2843i) q^{24} +(17.6777 + 17.6777i) q^{25} +(7.04163 - 2.91674i) q^{27} +(22.6274 - 22.6274i) q^{32} -84.4092 q^{33} +(33.9411 - 2.00000i) q^{34} +(-20.0833 + 20.0833i) q^{36} +33.9411i q^{38} +(-41.6777 + 17.2635i) q^{41} +(49.4264 + 49.4264i) q^{43} +(-77.7401 + 32.2010i) q^{44} +(-24.5685 + 59.3137i) q^{48} +(34.6482 - 34.6482i) q^{49} -50.0000 q^{50} +(-61.3762 + 29.7660i) q^{51} +(-5.83348 + 14.0833i) q^{54} +(-26.0589 - 62.9117i) q^{57} +(83.4264 + 83.4264i) q^{59} +64.0000i q^{64} +(119.373 - 119.373i) q^{66} +40.1594 q^{67} +(-45.1716 + 50.8284i) q^{68} -56.8040i q^{72} +(-21.2340 - 8.79542i) q^{73} +(92.6777 - 38.3883i) q^{75} +(-48.0000 - 48.0000i) q^{76} -94.4874i q^{81} +(34.5269 - 83.3553i) q^{82} +(104.456 - 104.456i) q^{83} -139.799 q^{86} +(64.4020 - 155.480i) q^{88} +175.238i q^{89} +(-49.1371 - 118.627i) q^{96} +(140.234 + 58.0868i) q^{97} +98.0000i q^{98} +(-57.1609 + 137.999i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 8 q^{3} - 16 q^{6} + 28 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 8 q^{3} - 16 q^{6} + 28 q^{9} - 52 q^{11} - 48 q^{12} - 64 q^{16} - 48 q^{17} + 136 q^{18} + 48 q^{19} + 48 q^{22} + 96 q^{24} - 68 q^{27} + 64 q^{33} + 112 q^{36} - 96 q^{41} + 28 q^{43} - 96 q^{44} + 128 q^{48} - 200 q^{50} - 56 q^{51} - 408 q^{54} - 240 q^{57} + 164 q^{59} + 568 q^{66} + 336 q^{67} - 192 q^{68} + 48 q^{73} + 300 q^{75} - 192 q^{76} + 8 q^{82} + 316 q^{83} - 480 q^{86} + 416 q^{88} + 256 q^{96} + 428 q^{97} - 1080 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/136\mathbb{Z}\right)^\times\).

\(n\) \(69\) \(103\) \(105\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{5}{8}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.41421 + 1.41421i −0.707107 + 0.707107i
\(3\) 1.53553 3.70711i 0.511845 1.23570i −0.430964 0.902369i \(-0.641827\pi\)
0.942809 0.333333i \(-0.108173\pi\)
\(4\) 4.00000i 1.00000i
\(5\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(6\) 3.07107 + 7.41421i 0.511845 + 1.23570i
\(7\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(8\) 5.65685 + 5.65685i 0.707107 + 0.707107i
\(9\) −5.02082 5.02082i −0.557868 0.557868i
\(10\) 0 0
\(11\) −8.05025 19.4350i −0.731841 1.76682i −0.636364 0.771389i \(-0.719562\pi\)
−0.0954775 0.995432i \(-0.530438\pi\)
\(12\) −14.8284 6.14214i −1.23570 0.511845i
\(13\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −16.0000 −1.00000
\(17\) −12.7071 11.2929i −0.747477 0.664288i
\(18\) 14.2010 0.788945
\(19\) 12.0000 12.0000i 0.631579 0.631579i −0.316885 0.948464i \(-0.602637\pi\)
0.948464 + 0.316885i \(0.102637\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 38.8701 + 16.1005i 1.76682 + 0.731841i
\(23\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(24\) 29.6569 12.2843i 1.23570 0.511845i
\(25\) 17.6777 + 17.6777i 0.707107 + 0.707107i
\(26\) 0 0
\(27\) 7.04163 2.91674i 0.260801 0.108027i
\(28\) 0 0
\(29\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(30\) 0 0
\(31\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(32\) 22.6274 22.6274i 0.707107 0.707107i
\(33\) −84.4092 −2.55785
\(34\) 33.9411 2.00000i 0.998268 0.0588235i
\(35\) 0 0
\(36\) −20.0833 + 20.0833i −0.557868 + 0.557868i
\(37\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(38\) 33.9411i 0.893188i
\(39\) 0 0
\(40\) 0 0
\(41\) −41.6777 + 17.2635i −1.01653 + 0.421060i −0.827832 0.560976i \(-0.810426\pi\)
−0.188696 + 0.982036i \(0.560426\pi\)
\(42\) 0 0
\(43\) 49.4264 + 49.4264i 1.14945 + 1.14945i 0.986661 + 0.162791i \(0.0520495\pi\)
0.162791 + 0.986661i \(0.447950\pi\)
\(44\) −77.7401 + 32.2010i −1.76682 + 0.731841i
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(48\) −24.5685 + 59.3137i −0.511845 + 1.23570i
\(49\) 34.6482 34.6482i 0.707107 0.707107i
\(50\) −50.0000 −1.00000
\(51\) −61.3762 + 29.7660i −1.20345 + 0.583647i
\(52\) 0 0
\(53\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(54\) −5.83348 + 14.0833i −0.108027 + 0.260801i
\(55\) 0 0
\(56\) 0 0
\(57\) −26.0589 62.9117i −0.457173 1.10371i
\(58\) 0 0
\(59\) 83.4264 + 83.4264i 1.41401 + 1.41401i 0.719092 + 0.694915i \(0.244558\pi\)
0.694915 + 0.719092i \(0.255442\pi\)
\(60\) 0 0
\(61\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 64.0000i 1.00000i
\(65\) 0 0
\(66\) 119.373 119.373i 1.80868 1.80868i
\(67\) 40.1594 0.599394 0.299697 0.954034i \(-0.403114\pi\)
0.299697 + 0.954034i \(0.403114\pi\)
\(68\) −45.1716 + 50.8284i −0.664288 + 0.747477i
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(72\) 56.8040i 0.788945i
\(73\) −21.2340 8.79542i −0.290877 0.120485i 0.232473 0.972603i \(-0.425318\pi\)
−0.523350 + 0.852118i \(0.675318\pi\)
\(74\) 0 0
\(75\) 92.6777 38.3883i 1.23570 0.511845i
\(76\) −48.0000 48.0000i −0.631579 0.631579i
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(80\) 0 0
\(81\) 94.4874i 1.16651i
\(82\) 34.5269 83.3553i 0.421060 1.01653i
\(83\) 104.456 104.456i 1.25850 1.25850i 0.306697 0.951807i \(-0.400776\pi\)
0.951807 0.306697i \(-0.0992238\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −139.799 −1.62557
\(87\) 0 0
\(88\) 64.4020 155.480i 0.731841 1.76682i
\(89\) 175.238i 1.96896i 0.175492 + 0.984481i \(0.443848\pi\)
−0.175492 + 0.984481i \(0.556152\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) −49.1371 118.627i −0.511845 1.23570i
\(97\) 140.234 + 58.0868i 1.44571 + 0.598833i 0.961175 0.275938i \(-0.0889884\pi\)
0.484536 + 0.874771i \(0.338988\pi\)
\(98\) 98.0000i 1.00000i
\(99\) −57.1609 + 137.999i −0.577382 + 1.39392i
\(100\) 70.7107 70.7107i 0.707107 0.707107i
\(101\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(102\) 44.7035 128.894i 0.438270 1.26367i
\(103\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −193.933 80.3295i −1.81245 0.750743i −0.980678 0.195631i \(-0.937325\pi\)
−0.831776 0.555112i \(-0.812675\pi\)
\(108\) −11.6670 28.1665i −0.108027 0.260801i
\(109\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −4.82486 11.6482i −0.0426978 0.103082i 0.901092 0.433628i \(-0.142767\pi\)
−0.943790 + 0.330547i \(0.892767\pi\)
\(114\) 125.823 + 52.1177i 1.10371 + 0.457173i
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) −235.966 −1.99971
\(119\) 0 0
\(120\) 0 0
\(121\) −227.354 + 227.354i −1.87896 + 1.87896i
\(122\) 0 0
\(123\) 181.012i 1.47164i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(128\) −90.5097 90.5097i −0.707107 0.707107i
\(129\) 259.125 107.333i 2.00872 0.832039i
\(130\) 0 0
\(131\) −195.359 80.9203i −1.49129 0.617712i −0.519692 0.854354i \(-0.673953\pi\)
−0.971597 + 0.236641i \(0.923953\pi\)
\(132\) 337.637i 2.55785i
\(133\) 0 0
\(134\) −56.7939 + 56.7939i −0.423835 + 0.423835i
\(135\) 0 0
\(136\) −8.00000 135.765i −0.0588235 0.998268i
\(137\) 135.765 0.990982 0.495491 0.868613i \(-0.334988\pi\)
0.495491 + 0.868613i \(0.334988\pi\)
\(138\) 0 0
\(139\) 45.4939 109.832i 0.327294 0.790158i −0.671497 0.741007i \(-0.734348\pi\)
0.998791 0.0491511i \(-0.0156516\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 80.3330 + 80.3330i 0.557868 + 0.557868i
\(145\) 0 0
\(146\) 42.4680 17.5908i 0.290877 0.120485i
\(147\) −75.2412 181.648i −0.511845 1.23570i
\(148\) 0 0
\(149\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(150\) −76.7767 + 185.355i −0.511845 + 1.23570i
\(151\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(152\) 135.765 0.893188
\(153\) 7.10051 + 120.500i 0.0464085 + 0.787579i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 133.625 + 133.625i 0.824848 + 0.824848i
\(163\) 256.844 106.388i 1.57573 0.652689i 0.588001 0.808860i \(-0.299915\pi\)
0.987730 + 0.156171i \(0.0499150\pi\)
\(164\) 69.0538 + 166.711i 0.421060 + 1.01653i
\(165\) 0 0
\(166\) 295.446i 1.77979i
\(167\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(168\) 0 0
\(169\) −169.000 −1.00000
\(170\) 0 0
\(171\) −120.500 −0.704676
\(172\) 197.706 197.706i 1.14945 1.14945i
\(173\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 128.804 + 310.960i 0.731841 + 1.76682i
\(177\) 437.375 181.167i 2.47104 1.02354i
\(178\) −247.823 247.823i −1.39227 1.39227i
\(179\) −252.000 252.000i −1.40782 1.40782i −0.771066 0.636755i \(-0.780276\pi\)
−0.636755 0.771066i \(-0.719724\pi\)
\(180\) 0 0
\(181\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −117.182 + 337.874i −0.626643 + 1.80681i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(192\) 237.255 + 98.2742i 1.23570 + 0.511845i
\(193\) −89.3244 215.648i −0.462821 1.11735i −0.967234 0.253886i \(-0.918291\pi\)
0.504413 0.863462i \(-0.331709\pi\)
\(194\) −280.468 + 116.174i −1.44571 + 0.598833i
\(195\) 0 0
\(196\) −138.593 138.593i −0.707107 0.707107i
\(197\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(198\) −114.322 275.997i −0.577382 1.39392i
\(199\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(200\) 200.000i 1.00000i
\(201\) 61.6661 148.875i 0.306796 0.740672i
\(202\) 0 0
\(203\) 0 0
\(204\) 119.064 + 245.505i 0.583647 + 1.20345i
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −329.823 136.617i −1.57810 0.653671i
\(210\) 0 0
\(211\) −384.094 + 159.097i −1.82035 + 0.754014i −0.844507 + 0.535545i \(0.820106\pi\)
−0.975844 + 0.218469i \(0.929894\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 387.865 160.659i 1.81245 0.750743i
\(215\) 0 0
\(216\) 56.3330 + 23.3339i 0.260801 + 0.108027i
\(217\) 0 0
\(218\) 0 0
\(219\) −65.2111 + 65.2111i −0.297768 + 0.297768i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(224\) 0 0
\(225\) 177.513i 0.788945i
\(226\) 23.2965 + 9.64971i 0.103082 + 0.0426978i
\(227\) 145.258 + 350.685i 0.639905 + 1.54487i 0.826805 + 0.562488i \(0.190156\pi\)
−0.186900 + 0.982379i \(0.559844\pi\)
\(228\) −251.647 + 104.235i −1.10371 + 0.457173i
\(229\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 430.442 + 178.295i 1.84739 + 0.765215i 0.931330 + 0.364175i \(0.118649\pi\)
0.916061 + 0.401039i \(0.131351\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 333.706 333.706i 1.41401 1.41401i
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(240\) 0 0
\(241\) −184.411 + 445.207i −0.765189 + 1.84733i −0.362700 + 0.931906i \(0.618145\pi\)
−0.402490 + 0.915425i \(0.631855\pi\)
\(242\) 643.054i 2.65725i
\(243\) −286.900 118.838i −1.18066 0.489045i
\(244\) 0 0
\(245\) 0 0
\(246\) −255.990 255.990i −1.04061 1.04061i
\(247\) 0 0
\(248\) 0 0
\(249\) −226.833 547.624i −0.910978 2.19930i
\(250\) 0 0
\(251\) 461.512i 1.83869i −0.393450 0.919346i \(-0.628718\pi\)
0.393450 0.919346i \(-0.371282\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 256.000 1.00000
\(257\) −23.2944 + 23.2944i −0.0906396 + 0.0906396i −0.750973 0.660333i \(-0.770415\pi\)
0.660333 + 0.750973i \(0.270415\pi\)
\(258\) −214.666 + 518.250i −0.832039 + 2.00872i
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 390.718 161.841i 1.49129 0.617712i
\(263\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(264\) −477.490 477.490i −1.80868 1.80868i
\(265\) 0 0
\(266\) 0 0
\(267\) 649.624 + 269.083i 2.43305 + 1.00780i
\(268\) 160.638i 0.599394i
\(269\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(270\) 0 0
\(271\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(272\) 203.314 + 180.686i 0.747477 + 0.664288i
\(273\) 0 0
\(274\) −192.000 + 192.000i −0.700730 + 0.700730i
\(275\) 201.256 485.876i 0.731841 1.76682i
\(276\) 0 0
\(277\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(278\) 90.9878 + 219.664i 0.327294 + 0.790158i
\(279\) 0 0
\(280\) 0 0
\(281\) 360.000 + 360.000i 1.28114 + 1.28114i 0.940020 + 0.341118i \(0.110806\pi\)
0.341118 + 0.940020i \(0.389194\pi\)
\(282\) 0 0
\(283\) 185.991 + 449.023i 0.657213 + 1.58665i 0.802090 + 0.597204i \(0.203722\pi\)
−0.144876 + 0.989450i \(0.546278\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) −227.216 −0.788945
\(289\) 33.9411 + 287.000i 0.117443 + 0.993080i
\(290\) 0 0
\(291\) 430.668 430.668i 1.47996 1.47996i
\(292\) −35.1817 + 84.9361i −0.120485 + 0.290877i
\(293\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(294\) 363.296 + 150.482i 1.23570 + 0.511845i
\(295\) 0 0
\(296\) 0 0
\(297\) −113.374 113.374i −0.381730 0.381730i
\(298\) 0 0
\(299\) 0 0
\(300\) −153.553 370.711i −0.511845 1.23570i
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) −192.000 + 192.000i −0.631579 + 0.631579i
\(305\) 0 0
\(306\) −180.454 160.370i −0.589718 0.524087i
\(307\) −542.000 −1.76547 −0.882736 0.469869i \(-0.844301\pi\)
−0.882736 + 0.469869i \(0.844301\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(312\) 0 0
\(313\) 328.969 136.263i 1.05102 0.435347i 0.210764 0.977537i \(-0.432405\pi\)
0.840256 + 0.542191i \(0.182405\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) −595.580 + 595.580i −1.85539 + 1.85539i
\(322\) 0 0
\(323\) −288.000 + 16.9706i −0.891641 + 0.0525404i
\(324\) −377.949 −1.16651
\(325\) 0 0
\(326\) −212.777 + 513.688i −0.652689 + 1.57573i
\(327\) 0 0
\(328\) −333.421 138.108i −1.01653 0.421060i
\(329\) 0 0
\(330\) 0 0
\(331\) 337.926 + 337.926i 1.02092 + 1.02092i 0.999776 + 0.0211480i \(0.00673213\pi\)
0.0211480 + 0.999776i \(0.493268\pi\)
\(332\) −417.823 417.823i −1.25850 1.25850i
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 99.4106 239.999i 0.294987 0.712162i −0.705009 0.709199i \(-0.749057\pi\)
0.999996 0.00296297i \(-0.000943144\pi\)
\(338\) 239.002 239.002i 0.707107 0.707107i
\(339\) −50.5900 −0.149233
\(340\) 0 0
\(341\) 0 0
\(342\) 170.412 170.412i 0.498281 0.498281i
\(343\) 0 0
\(344\) 559.196i 1.62557i
\(345\) 0 0
\(346\) 0 0
\(347\) 420.947 174.362i 1.21310 0.502484i 0.317892 0.948127i \(-0.397025\pi\)
0.895211 + 0.445643i \(0.147025\pi\)
\(348\) 0 0
\(349\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −621.921 257.608i −1.76682 0.731841i
\(353\) 342.821i 0.971165i 0.874191 + 0.485583i \(0.161392\pi\)
−0.874191 + 0.485583i \(0.838608\pi\)
\(354\) −362.333 + 874.749i −1.02354 + 2.47104i
\(355\) 0 0
\(356\) 700.950 1.96896
\(357\) 0 0
\(358\) 712.764 1.99096
\(359\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(360\) 0 0
\(361\) 73.0000i 0.202216i
\(362\) 0 0
\(363\) 493.715 + 1191.93i 1.36010 + 3.28357i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(368\) 0 0
\(369\) 295.933 + 122.579i 0.801985 + 0.332193i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(374\) −312.105 643.546i −0.834505 1.72071i
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 32.6827 + 13.5376i 0.0862341 + 0.0357193i 0.425383 0.905013i \(-0.360139\pi\)
−0.339149 + 0.940733i \(0.610139\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(384\) −474.510 + 196.548i −1.23570 + 0.511845i
\(385\) 0 0
\(386\) 431.296 + 178.649i 1.11735 + 0.462821i
\(387\) 496.322i 1.28249i
\(388\) 232.347 560.936i 0.598833 1.44571i
\(389\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 392.000 1.00000
\(393\) −599.960 + 599.960i −1.52662 + 1.52662i
\(394\) 0 0
\(395\) 0 0
\(396\) 551.994 + 228.643i 1.39392 + 0.577382i
\(397\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −282.843 282.843i −0.707107 0.707107i
\(401\) −569.822 + 236.028i −1.42100 + 0.588598i −0.955112 0.296244i \(-0.904266\pi\)
−0.465890 + 0.884843i \(0.654266\pi\)
\(402\) 123.332 + 297.750i 0.306796 + 0.740672i
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) −515.578 178.814i −1.26367 0.438270i
\(409\) −764.174 −1.86840 −0.934198 0.356756i \(-0.883883\pi\)
−0.934198 + 0.356756i \(0.883883\pi\)
\(410\) 0 0
\(411\) 208.471 503.294i 0.507229 1.22456i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −337.302 337.302i −0.808877 0.808877i
\(418\) 659.647 273.235i 1.57810 0.653671i
\(419\) 84.8005 + 204.726i 0.202388 + 0.488607i 0.992187 0.124758i \(-0.0398154\pi\)
−0.789799 + 0.613365i \(0.789815\pi\)
\(420\) 0 0
\(421\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(422\) 318.194 768.188i 0.754014 1.82035i
\(423\) 0 0
\(424\) 0 0
\(425\) −25.0000 424.264i −0.0588235 0.998268i
\(426\) 0 0
\(427\) 0 0
\(428\) −321.318 + 775.730i −0.750743 + 1.81245i
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(432\) −112.666 + 46.6678i −0.260801 + 0.108027i
\(433\) −456.000 456.000i −1.05312 1.05312i −0.998508 0.0546100i \(-0.982608\pi\)
−0.0546100 0.998508i \(-0.517392\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 184.445i 0.421107i
\(439\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(440\) 0 0
\(441\) −347.925 −0.788945
\(442\) 0 0
\(443\) −536.840 −1.21183 −0.605914 0.795530i \(-0.707192\pi\)
−0.605914 + 0.795530i \(0.707192\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 823.177 340.971i 1.83336 0.759401i 0.868992 0.494827i \(-0.164769\pi\)
0.964365 0.264574i \(-0.0852315\pi\)
\(450\) 251.041 + 251.041i 0.557868 + 0.557868i
\(451\) 671.032 + 671.032i 1.48787 + 1.48787i
\(452\) −46.5929 + 19.2994i −0.103082 + 0.0426978i
\(453\) 0 0
\(454\) −701.370 290.517i −1.54487 0.639905i
\(455\) 0 0
\(456\) 208.471 503.294i 0.457173 1.10371i
\(457\) 624.000 624.000i 1.36543 1.36543i 0.498587 0.866840i \(-0.333852\pi\)
0.866840 0.498587i \(-0.166148\pi\)
\(458\) 0 0
\(459\) −122.417 42.4571i −0.266704 0.0924991i
\(460\) 0 0
\(461\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(462\) 0 0
\(463\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) −860.884 + 356.590i −1.84739 + 0.765215i
\(467\) −660.000 660.000i −1.41328 1.41328i −0.732379 0.680898i \(-0.761590\pi\)
−0.680898 0.732379i \(-0.738410\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 943.862i 1.99971i
\(473\) 562.709 1358.50i 1.18966 2.87209i
\(474\) 0 0
\(475\) 424.264 0.893188
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) −368.821 890.413i −0.765189 1.84733i
\(483\) 0 0
\(484\) 909.415 + 909.415i 1.87896 + 1.87896i
\(485\) 0 0
\(486\) 573.800 237.676i 1.18066 0.489045i
\(487\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(488\) 0 0
\(489\) 1115.51i 2.28121i
\(490\) 0 0
\(491\) 420.000 420.000i 0.855397 0.855397i −0.135395 0.990792i \(-0.543230\pi\)
0.990792 + 0.135395i \(0.0432302\pi\)
\(492\) 724.049 1.47164
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 1095.25 + 453.667i 2.19930 + 0.910978i
\(499\) −92.5498 223.435i −0.185471 0.447766i 0.803607 0.595160i \(-0.202911\pi\)
−0.989078 + 0.147394i \(0.952911\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 652.676 + 652.676i 1.30015 + 1.30015i
\(503\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −259.505 + 626.501i −0.511845 + 1.23570i
\(508\) 0 0
\(509\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −362.039 + 362.039i −0.707107 + 0.707107i
\(513\) 49.4987 119.500i 0.0964887 0.232944i
\(514\) 65.8864i 0.128184i
\(515\) 0 0
\(516\) −429.332 1036.50i −0.832039 2.00872i
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 243.325 + 587.439i 0.467035 + 1.12752i 0.965451 + 0.260584i \(0.0839152\pi\)
−0.498416 + 0.866938i \(0.666085\pi\)
\(522\) 0 0
\(523\) 402.572i 0.769735i 0.922972 + 0.384868i \(0.125753\pi\)
−0.922972 + 0.384868i \(0.874247\pi\)
\(524\) −323.681 + 781.436i −0.617712 + 1.49129i
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 1350.55 2.55785
\(529\) −374.059 + 374.059i −0.707107 + 0.707107i
\(530\) 0 0
\(531\) 837.737i 1.57766i
\(532\) 0 0
\(533\) 0 0
\(534\) −1299.25 + 538.167i −2.43305 + 1.00780i
\(535\) 0 0
\(536\) 227.176 + 227.176i 0.423835 + 0.423835i
\(537\) −1321.15 + 547.236i −2.46023 + 1.01906i
\(538\) 0 0
\(539\) −952.316 394.462i −1.76682 0.731841i
\(540\) 0 0
\(541\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) −543.058 + 32.0000i −0.998268 + 0.0588235i
\(545\) 0 0
\(546\) 0 0
\(547\) 418.493 1010.33i 0.765070 1.84704i 0.356785 0.934186i \(-0.383873\pi\)
0.408284 0.912855i \(-0.366127\pi\)
\(548\) 543.058i 0.990982i
\(549\) 0 0
\(550\) 402.513 + 971.751i 0.731841 + 1.76682i
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) −439.328 181.976i −0.790158 0.327294i
\(557\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 1072.60 + 953.224i 1.91194 + 1.69915i
\(562\) −1018.23 −1.81180
\(563\) −438.543 + 438.543i −0.778940 + 0.778940i −0.979651 0.200710i \(-0.935675\pi\)
0.200710 + 0.979651i \(0.435675\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −898.046 371.983i −1.58665 0.657213i
\(567\) 0 0
\(568\) 0 0
\(569\) 788.176 + 788.176i 1.38519 + 1.38519i 0.835107 + 0.550088i \(0.185406\pi\)
0.550088 + 0.835107i \(0.314594\pi\)
\(570\) 0 0
\(571\) −564.052 + 233.638i −0.987832 + 0.409174i −0.817321 0.576182i \(-0.804542\pi\)
−0.170511 + 0.985356i \(0.554542\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 321.332 321.332i 0.557868 0.557868i
\(577\) 2.00000 0.00346620 0.00173310 0.999998i \(-0.499448\pi\)
0.00173310 + 0.999998i \(0.499448\pi\)
\(578\) −453.879 357.879i −0.785258 0.619168i
\(579\) −936.592 −1.61760
\(580\) 0 0
\(581\) 0 0
\(582\) 1218.11i 2.09298i
\(583\) 0 0
\(584\) −70.3633 169.872i −0.120485 0.290877i
\(585\) 0 0
\(586\) 0 0
\(587\) 804.688 + 804.688i 1.37085 + 1.37085i 0.859189 + 0.511659i \(0.170969\pi\)
0.511659 + 0.859189i \(0.329031\pi\)
\(588\) −726.593 + 300.965i −1.23570 + 0.511845i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −838.294 + 838.294i −1.41365 + 1.41365i −0.686836 + 0.726813i \(0.741001\pi\)
−0.726813 + 0.686836i \(0.758999\pi\)
\(594\) 320.670 0.539848
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(600\) 741.421 + 307.107i 1.23570 + 0.511845i
\(601\) −208.825 504.148i −0.347462 0.838848i −0.996918 0.0784489i \(-0.975003\pi\)
0.649456 0.760399i \(-0.274997\pi\)
\(602\) 0 0
\(603\) −201.633 201.633i −0.334383 0.334383i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(608\) 543.058i 0.893188i
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 481.998 28.4020i 0.787579 0.0464085i
\(613\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(614\) 766.504 766.504i 1.24838 1.24838i
\(615\) 0 0
\(616\) 0 0
\(617\) 1132.06 + 468.913i 1.83478 + 0.759989i 0.962674 + 0.270665i \(0.0872434\pi\)
0.872102 + 0.489324i \(0.162757\pi\)
\(618\) 0 0
\(619\) −89.6970 + 37.1537i −0.144906 + 0.0600222i −0.453958 0.891023i \(-0.649988\pi\)
0.309052 + 0.951045i \(0.399988\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 625.000i 1.00000i
\(626\) −272.527 + 657.938i −0.435347 + 1.05102i
\(627\) −1012.91 + 1012.91i −1.61549 + 1.61549i
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(632\) 0 0
\(633\) 1668.18i 2.63535i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 843.557 + 349.413i 1.31600 + 0.545106i 0.926630 0.375975i \(-0.122692\pi\)
0.389372 + 0.921081i \(0.372692\pi\)
\(642\) 1684.55i 2.62392i
\(643\) −27.7862 + 67.0818i −0.0432133 + 0.104326i −0.944012 0.329910i \(-0.892982\pi\)
0.900799 + 0.434236i \(0.142982\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 383.294 431.294i 0.593334 0.667637i
\(647\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(648\) 534.501 534.501i 0.824848 0.824848i
\(649\) 949.791 2293.00i 1.46347 3.53313i
\(650\) 0 0
\(651\) 0 0
\(652\) −425.553 1027.38i −0.652689 1.57573i
\(653\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 666.843 276.215i 1.01653 0.421060i
\(657\) 62.4519 + 150.772i 0.0950562 + 0.229486i
\(658\) 0 0
\(659\) 994.000i 1.50835i −0.656676 0.754173i \(-0.728038\pi\)
0.656676 0.754173i \(-0.271962\pi\)
\(660\) 0 0
\(661\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(662\) −955.799 −1.44381
\(663\) 0 0
\(664\) 1181.78 1.77979
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −5.96908 + 2.47248i −0.00886937 + 0.00367381i −0.387114 0.922032i \(-0.626528\pi\)
0.378244 + 0.925706i \(0.376528\pi\)
\(674\) 198.821 + 479.997i 0.294987 + 0.712162i
\(675\) 176.041 + 72.9185i 0.260801 + 0.108027i
\(676\) 676.000i 1.00000i
\(677\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(678\) 71.5450 71.5450i 0.105524 0.105524i
\(679\) 0 0
\(680\) 0 0
\(681\) 1523.08 2.23653
\(682\) 0 0
\(683\) −520.286 + 1256.08i −0.761765 + 1.83906i −0.291362 + 0.956613i \(0.594108\pi\)
−0.470404 + 0.882451i \(0.655892\pi\)
\(684\) 481.998i 0.704676i
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) −790.823 790.823i −1.14945 1.14945i
\(689\) 0 0
\(690\) 0 0
\(691\) −306.508 739.976i −0.443572 1.07088i −0.974686 0.223577i \(-0.928227\pi\)
0.531114 0.847300i \(-0.321773\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) −348.724 + 841.894i −0.502484 + 1.21310i
\(695\) 0 0
\(696\) 0 0
\(697\) 724.557 + 251.293i 1.03954 + 0.360535i
\(698\) 0 0
\(699\) 1321.92 1321.92i 1.89115 1.89115i
\(700\) 0 0
\(701\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 1243.84 515.216i 1.76682 0.731841i
\(705\) 0 0
\(706\) −484.823 484.823i −0.686717 0.686717i
\(707\) 0 0
\(708\) −724.666 1749.50i −1.02354 2.47104i
\(709\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −991.294 + 991.294i −1.39227 + 1.39227i
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) −1008.00 + 1008.00i −1.40782 + 1.40782i
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −103.238 103.238i −0.142988 0.142988i
\(723\) 1367.26 + 1367.26i 1.89109 + 1.89109i
\(724\) 0 0
\(725\) 0 0
\(726\) −2383.87 987.431i −3.28357 1.36010i
\(727\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(728\) 0 0
\(729\) −279.776 + 279.776i −0.383780 + 0.383780i
\(730\) 0 0
\(731\) −69.8995 1186.23i −0.0956217 1.62275i
\(732\) 0 0
\(733\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −323.293 780.499i −0.438661 1.05902i
\(738\) −591.865 + 245.159i −0.801985 + 0.332193i
\(739\) 227.688 + 227.688i 0.308103 + 0.308103i 0.844173 0.536070i \(-0.180092\pi\)
−0.536070 + 0.844173i \(0.680092\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −1048.91 −1.40416
\(748\) 1351.49 + 468.729i 1.80681 + 0.626643i
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(752\) 0 0
\(753\) −1710.87 708.667i −2.27208 0.941125i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(758\) −65.3654 + 27.0753i −0.0862341 + 0.0357193i
\(759\) 0 0
\(760\) 0 0
\(761\) 610.940i 0.802812i 0.915900 + 0.401406i \(0.131478\pi\)
−0.915900 + 0.401406i \(0.868522\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 393.097 949.019i 0.511845 1.23570i
\(769\) 1120.06i 1.45651i −0.685306 0.728256i \(-0.740331\pi\)
0.685306 0.728256i \(-0.259669\pi\)
\(770\) 0 0
\(771\) 50.5854 + 122.124i 0.0656102 + 0.158397i
\(772\) −862.593 + 357.298i −1.11735 + 0.462821i
\(773\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(774\) 701.905 + 701.905i 0.906854 + 0.906854i
\(775\) 0 0
\(776\) 464.695 + 1121.87i 0.598833 + 1.44571i
\(777\) 0 0
\(778\) 0 0
\(779\) −292.971 + 707.294i −0.376085 + 0.907951i
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) −554.372 + 554.372i −0.707107 + 0.707107i
\(785\) 0 0
\(786\) 1696.94i 2.15896i
\(787\) −1240.39 513.787i −1.57610 0.652842i −0.588310 0.808635i \(-0.700207\pi\)
−0.987790 + 0.155794i \(0.950207\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) −1103.99 + 457.287i −1.39392 + 0.577382i
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0