Properties

Label 1764.2.e.h.1079.16
Level $1764$
Weight $2$
Character 1764.1079
Analytic conductor $14.086$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1764.e (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(14.0856109166\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
Defining polynomial: \(x^{16} + x^{12} - 10 x^{10} + 4 x^{8} - 40 x^{6} + 16 x^{4} + 256\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{10} \)
Twist minimal: no (minimal twist has level 252)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1079.16
Root \(-1.41135 - 0.0900240i\) of defining polynomial
Character \(\chi\) \(=\) 1764.1079
Dual form 1764.2.e.h.1079.15

$q$-expansion

\(f(q)\) \(=\) \(q+(1.41135 + 0.0900240i) q^{2} +(1.98379 + 0.254110i) q^{4} +2.48866i q^{5} +(2.77694 + 0.537226i) q^{8} +O(q^{10})\) \(q+(1.41135 + 0.0900240i) q^{2} +(1.98379 + 0.254110i) q^{4} +2.48866i q^{5} +(2.77694 + 0.537226i) q^{8} +(-0.224040 + 3.51237i) q^{10} -4.60787 q^{11} -5.22221 q^{13} +(3.87086 + 1.00820i) q^{16} +5.61101i q^{17} +3.19355i q^{19} +(-0.632394 + 4.93699i) q^{20} +(-6.50329 - 0.414819i) q^{22} -0.718731 q^{23} -1.19345 q^{25} +(-7.37034 - 0.470124i) q^{26} +4.53656i q^{29} +1.17715i q^{31} +(5.37235 + 1.77139i) q^{32} +(-0.505125 + 7.91907i) q^{34} +2.71296 q^{37} +(-0.287496 + 4.50721i) q^{38} +(-1.33697 + 6.91087i) q^{40} +3.83670i q^{41} -11.1773i q^{43} +(-9.14105 - 1.17091i) q^{44} +(-1.01438 - 0.0647031i) q^{46} +5.41810 q^{47} +(-1.68437 - 0.107439i) q^{50} +(-10.3598 - 1.32702i) q^{52} +2.06823i q^{53} -11.4674i q^{55} +(-0.408399 + 6.40265i) q^{58} -4.11641 q^{59} +1.01025 q^{61} +(-0.105972 + 1.66136i) q^{62} +(7.42278 + 2.98369i) q^{64} -12.9963i q^{65} +12.6446i q^{67} +(-1.42581 + 11.1311i) q^{68} +7.31012 q^{71} -9.63787 q^{73} +(3.82892 + 0.244231i) q^{74} +(-0.811513 + 6.33534i) q^{76} -8.83951i q^{79} +(-2.50908 + 9.63326i) q^{80} +(-0.345395 + 5.41491i) q^{82} +13.7657 q^{83} -13.9639 q^{85} +(1.00623 - 15.7751i) q^{86} +(-12.7958 - 2.47547i) q^{88} -8.52595i q^{89} +(-1.42581 - 0.182637i) q^{92} +(7.64682 + 0.487759i) q^{94} -7.94768 q^{95} +10.7232 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + O(q^{10}) \) \( 16q - 8q^{13} - 4q^{16} - 16q^{22} - 24q^{25} + 8q^{34} - 8q^{37} - 52q^{40} + 24q^{46} - 52q^{52} + 12q^{58} - 16q^{61} + 60q^{64} - 8q^{73} - 36q^{76} + 68q^{82} - 16q^{85} - 44q^{88} + 60q^{94} + 88q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(883\) \(1081\)
\(\chi(n)\) \(-1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.41135 + 0.0900240i 0.997972 + 0.0636566i
\(3\) 0 0
\(4\) 1.98379 + 0.254110i 0.991896 + 0.127055i
\(5\) 2.48866i 1.11296i 0.830859 + 0.556482i \(0.187849\pi\)
−0.830859 + 0.556482i \(0.812151\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 2.77694 + 0.537226i 0.981796 + 0.189938i
\(9\) 0 0
\(10\) −0.224040 + 3.51237i −0.0708475 + 1.11071i
\(11\) −4.60787 −1.38932 −0.694662 0.719336i \(-0.744446\pi\)
−0.694662 + 0.719336i \(0.744446\pi\)
\(12\) 0 0
\(13\) −5.22221 −1.44838 −0.724190 0.689600i \(-0.757786\pi\)
−0.724190 + 0.689600i \(0.757786\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 3.87086 + 1.00820i 0.967714 + 0.252051i
\(17\) 5.61101i 1.36087i 0.732809 + 0.680435i \(0.238209\pi\)
−0.732809 + 0.680435i \(0.761791\pi\)
\(18\) 0 0
\(19\) 3.19355i 0.732651i 0.930487 + 0.366326i \(0.119384\pi\)
−0.930487 + 0.366326i \(0.880616\pi\)
\(20\) −0.632394 + 4.93699i −0.141408 + 1.10394i
\(21\) 0 0
\(22\) −6.50329 0.414819i −1.38651 0.0884397i
\(23\) −0.718731 −0.149866 −0.0749329 0.997189i \(-0.523874\pi\)
−0.0749329 + 0.997189i \(0.523874\pi\)
\(24\) 0 0
\(25\) −1.19345 −0.238691
\(26\) −7.37034 0.470124i −1.44544 0.0921989i
\(27\) 0 0
\(28\) 0 0
\(29\) 4.53656i 0.842418i 0.906964 + 0.421209i \(0.138394\pi\)
−0.906964 + 0.421209i \(0.861606\pi\)
\(30\) 0 0
\(31\) 1.17715i 0.211422i 0.994397 + 0.105711i \(0.0337119\pi\)
−0.994397 + 0.105711i \(0.966288\pi\)
\(32\) 5.37235 + 1.77139i 0.949707 + 0.313141i
\(33\) 0 0
\(34\) −0.505125 + 7.91907i −0.0866283 + 1.35811i
\(35\) 0 0
\(36\) 0 0
\(37\) 2.71296 0.446007 0.223004 0.974818i \(-0.428414\pi\)
0.223004 + 0.974818i \(0.428414\pi\)
\(38\) −0.287496 + 4.50721i −0.0466381 + 0.731165i
\(39\) 0 0
\(40\) −1.33697 + 6.91087i −0.211394 + 1.09270i
\(41\) 3.83670i 0.599192i 0.954066 + 0.299596i \(0.0968519\pi\)
−0.954066 + 0.299596i \(0.903148\pi\)
\(42\) 0 0
\(43\) 11.1773i 1.70453i −0.523113 0.852263i \(-0.675229\pi\)
0.523113 0.852263i \(-0.324771\pi\)
\(44\) −9.14105 1.17091i −1.37807 0.176521i
\(45\) 0 0
\(46\) −1.01438 0.0647031i −0.149562 0.00953995i
\(47\) 5.41810 0.790312 0.395156 0.918614i \(-0.370691\pi\)
0.395156 + 0.918614i \(0.370691\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −1.68437 0.107439i −0.238206 0.0151942i
\(51\) 0 0
\(52\) −10.3598 1.32702i −1.43664 0.184024i
\(53\) 2.06823i 0.284093i 0.989860 + 0.142046i \(0.0453682\pi\)
−0.989860 + 0.142046i \(0.954632\pi\)
\(54\) 0 0
\(55\) 11.4674i 1.54627i
\(56\) 0 0
\(57\) 0 0
\(58\) −0.408399 + 6.40265i −0.0536254 + 0.840709i
\(59\) −4.11641 −0.535912 −0.267956 0.963431i \(-0.586348\pi\)
−0.267956 + 0.963431i \(0.586348\pi\)
\(60\) 0 0
\(61\) 1.01025 0.129349 0.0646747 0.997906i \(-0.479399\pi\)
0.0646747 + 0.997906i \(0.479399\pi\)
\(62\) −0.105972 + 1.66136i −0.0134584 + 0.210993i
\(63\) 0 0
\(64\) 7.42278 + 2.98369i 0.927847 + 0.372961i
\(65\) 12.9963i 1.61200i
\(66\) 0 0
\(67\) 12.6446i 1.54478i 0.635147 + 0.772391i \(0.280940\pi\)
−0.635147 + 0.772391i \(0.719060\pi\)
\(68\) −1.42581 + 11.1311i −0.172905 + 1.34984i
\(69\) 0 0
\(70\) 0 0
\(71\) 7.31012 0.867552 0.433776 0.901021i \(-0.357181\pi\)
0.433776 + 0.901021i \(0.357181\pi\)
\(72\) 0 0
\(73\) −9.63787 −1.12803 −0.564014 0.825765i \(-0.690744\pi\)
−0.564014 + 0.825765i \(0.690744\pi\)
\(74\) 3.82892 + 0.244231i 0.445103 + 0.0283913i
\(75\) 0 0
\(76\) −0.811513 + 6.33534i −0.0930870 + 0.726714i
\(77\) 0 0
\(78\) 0 0
\(79\) 8.83951i 0.994522i −0.867601 0.497261i \(-0.834339\pi\)
0.867601 0.497261i \(-0.165661\pi\)
\(80\) −2.50908 + 9.63326i −0.280523 + 1.07703i
\(81\) 0 0
\(82\) −0.345395 + 5.41491i −0.0381425 + 0.597977i
\(83\) 13.7657 1.51099 0.755493 0.655157i \(-0.227397\pi\)
0.755493 + 0.655157i \(0.227397\pi\)
\(84\) 0 0
\(85\) −13.9639 −1.51460
\(86\) 1.00623 15.7751i 0.108504 1.70107i
\(87\) 0 0
\(88\) −12.7958 2.47547i −1.36403 0.263886i
\(89\) 8.52595i 0.903749i −0.892082 0.451874i \(-0.850756\pi\)
0.892082 0.451874i \(-0.149244\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −1.42581 0.182637i −0.148651 0.0190412i
\(93\) 0 0
\(94\) 7.64682 + 0.487759i 0.788709 + 0.0503085i
\(95\) −7.94768 −0.815415
\(96\) 0 0
\(97\) 10.7232 1.08878 0.544388 0.838833i \(-0.316762\pi\)
0.544388 + 0.838833i \(0.316762\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −2.36756 0.303268i −0.236756 0.0303268i
\(101\) 3.83670i 0.381766i 0.981613 + 0.190883i \(0.0611351\pi\)
−0.981613 + 0.190883i \(0.938865\pi\)
\(102\) 0 0
\(103\) 16.6774i 1.64327i −0.570012 0.821636i \(-0.693061\pi\)
0.570012 0.821636i \(-0.306939\pi\)
\(104\) −14.5018 2.80550i −1.42201 0.275102i
\(105\) 0 0
\(106\) −0.186190 + 2.91898i −0.0180844 + 0.283517i
\(107\) 5.73689 0.554606 0.277303 0.960783i \(-0.410559\pi\)
0.277303 + 0.960783i \(0.410559\pi\)
\(108\) 0 0
\(109\) −2.82705 −0.270782 −0.135391 0.990792i \(-0.543229\pi\)
−0.135391 + 0.990792i \(0.543229\pi\)
\(110\) 1.03235 16.1845i 0.0984302 1.54313i
\(111\) 0 0
\(112\) 0 0
\(113\) 5.59651i 0.526476i −0.964731 0.263238i \(-0.915210\pi\)
0.964731 0.263238i \(-0.0847904\pi\)
\(114\) 0 0
\(115\) 1.78868i 0.166795i
\(116\) −1.15278 + 8.99958i −0.107033 + 0.835590i
\(117\) 0 0
\(118\) −5.80968 0.370576i −0.534825 0.0341143i
\(119\) 0 0
\(120\) 0 0
\(121\) 10.2325 0.930224
\(122\) 1.42581 + 0.0909468i 0.129087 + 0.00823394i
\(123\) 0 0
\(124\) −0.299125 + 2.33522i −0.0268622 + 0.209709i
\(125\) 9.47322i 0.847311i
\(126\) 0 0
\(127\) 15.2266i 1.35114i 0.737294 + 0.675572i \(0.236103\pi\)
−0.737294 + 0.675572i \(0.763897\pi\)
\(128\) 10.2075 + 4.87924i 0.902224 + 0.431268i
\(129\) 0 0
\(130\) 1.16998 18.3423i 0.102614 1.60873i
\(131\) −4.15332 −0.362877 −0.181438 0.983402i \(-0.558075\pi\)
−0.181438 + 0.983402i \(0.558075\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −1.13832 + 17.8459i −0.0983356 + 1.54165i
\(135\) 0 0
\(136\) −3.01438 + 15.5814i −0.258481 + 1.33610i
\(137\) 16.3317i 1.39531i 0.716433 + 0.697656i \(0.245774\pi\)
−0.716433 + 0.697656i \(0.754226\pi\)
\(138\) 0 0
\(139\) 10.2903i 0.872811i −0.899750 0.436406i \(-0.856251\pi\)
0.899750 0.436406i \(-0.143749\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 10.3171 + 0.658086i 0.865792 + 0.0552254i
\(143\) 24.0633 2.01227
\(144\) 0 0
\(145\) −11.2900 −0.937581
\(146\) −13.6024 0.867640i −1.12574 0.0718064i
\(147\) 0 0
\(148\) 5.38194 + 0.689389i 0.442393 + 0.0566674i
\(149\) 5.65685i 0.463428i 0.972784 + 0.231714i \(0.0744333\pi\)
−0.972784 + 0.231714i \(0.925567\pi\)
\(150\) 0 0
\(151\) 12.1625i 0.989767i 0.868959 + 0.494884i \(0.164789\pi\)
−0.868959 + 0.494884i \(0.835211\pi\)
\(152\) −1.71566 + 8.86830i −0.139158 + 0.719314i
\(153\) 0 0
\(154\) 0 0
\(155\) −2.92953 −0.235305
\(156\) 0 0
\(157\) −7.03901 −0.561774 −0.280887 0.959741i \(-0.590629\pi\)
−0.280887 + 0.959741i \(0.590629\pi\)
\(158\) 0.795768 12.4756i 0.0633079 0.992505i
\(159\) 0 0
\(160\) −4.40840 + 13.3700i −0.348515 + 1.05699i
\(161\) 0 0
\(162\) 0 0
\(163\) 1.78868i 0.140100i −0.997543 0.0700502i \(-0.977684\pi\)
0.997543 0.0700502i \(-0.0223159\pi\)
\(164\) −0.974943 + 7.61121i −0.0761303 + 0.594336i
\(165\) 0 0
\(166\) 19.4282 + 1.23925i 1.50792 + 0.0961842i
\(167\) 8.26973 0.639931 0.319965 0.947429i \(-0.396329\pi\)
0.319965 + 0.947429i \(0.396329\pi\)
\(168\) 0 0
\(169\) 14.2715 1.09781
\(170\) −19.7079 1.25709i −1.51153 0.0964143i
\(171\) 0 0
\(172\) 2.84027 22.1735i 0.216569 1.69071i
\(173\) 19.3472i 1.47094i 0.677557 + 0.735470i \(0.263039\pi\)
−0.677557 + 0.735470i \(0.736961\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −17.8364 4.64566i −1.34447 0.350180i
\(177\) 0 0
\(178\) 0.767540 12.0331i 0.0575296 0.901916i
\(179\) 12.0538 0.900941 0.450470 0.892791i \(-0.351256\pi\)
0.450470 + 0.892791i \(0.351256\pi\)
\(180\) 0 0
\(181\) −20.7992 −1.54599 −0.772997 0.634410i \(-0.781243\pi\)
−0.772997 + 0.634410i \(0.781243\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −1.99587 0.386121i −0.147138 0.0284652i
\(185\) 6.75164i 0.496390i
\(186\) 0 0
\(187\) 25.8548i 1.89069i
\(188\) 10.7484 + 1.37679i 0.783907 + 0.100413i
\(189\) 0 0
\(190\) −11.2169 0.715482i −0.813761 0.0519065i
\(191\) 10.6163 0.768169 0.384084 0.923298i \(-0.374517\pi\)
0.384084 + 0.923298i \(0.374517\pi\)
\(192\) 0 0
\(193\) 12.9927 0.935233 0.467617 0.883931i \(-0.345113\pi\)
0.467617 + 0.883931i \(0.345113\pi\)
\(194\) 15.1341 + 0.965346i 1.08657 + 0.0693078i
\(195\) 0 0
\(196\) 0 0
\(197\) 3.18852i 0.227173i 0.993528 + 0.113586i \(0.0362339\pi\)
−0.993528 + 0.113586i \(0.963766\pi\)
\(198\) 0 0
\(199\) 14.0495i 0.995940i −0.867194 0.497970i \(-0.834079\pi\)
0.867194 0.497970i \(-0.165921\pi\)
\(200\) −3.31415 0.641153i −0.234345 0.0453364i
\(201\) 0 0
\(202\) −0.345395 + 5.41491i −0.0243019 + 0.380992i
\(203\) 0 0
\(204\) 0 0
\(205\) −9.54826 −0.666879
\(206\) 1.50137 23.5376i 0.104605 1.63994i
\(207\) 0 0
\(208\) −20.2144 5.26504i −1.40162 0.365065i
\(209\) 14.7155i 1.01789i
\(210\) 0 0
\(211\) 9.12962i 0.628509i −0.949339 0.314255i \(-0.898245\pi\)
0.949339 0.314255i \(-0.101755\pi\)
\(212\) −0.525557 + 4.10293i −0.0360954 + 0.281790i
\(213\) 0 0
\(214\) 8.09673 + 0.516457i 0.553481 + 0.0353043i
\(215\) 27.8166 1.89708
\(216\) 0 0
\(217\) 0 0
\(218\) −3.98994 0.254502i −0.270233 0.0172371i
\(219\) 0 0
\(220\) 2.91399 22.7490i 0.196461 1.53374i
\(221\) 29.3019i 1.97106i
\(222\) 0 0
\(223\) 23.8384i 1.59634i −0.602434 0.798168i \(-0.705802\pi\)
0.602434 0.798168i \(-0.294198\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0.503820 7.89861i 0.0335136 0.525408i
\(227\) −10.0124 −0.664544 −0.332272 0.943184i \(-0.607815\pi\)
−0.332272 + 0.943184i \(0.607815\pi\)
\(228\) 0 0
\(229\) 5.33630 0.352633 0.176316 0.984334i \(-0.443582\pi\)
0.176316 + 0.984334i \(0.443582\pi\)
\(230\) 0.161024 2.52445i 0.0106176 0.166457i
\(231\) 0 0
\(232\) −2.43716 + 12.5977i −0.160007 + 0.827082i
\(233\) 8.76818i 0.574423i 0.957867 + 0.287211i \(0.0927282\pi\)
−0.957867 + 0.287211i \(0.907272\pi\)
\(234\) 0 0
\(235\) 13.4838i 0.879589i
\(236\) −8.16611 1.04602i −0.531568 0.0680902i
\(237\) 0 0
\(238\) 0 0
\(239\) 13.1385 0.849860 0.424930 0.905226i \(-0.360299\pi\)
0.424930 + 0.905226i \(0.360299\pi\)
\(240\) 0 0
\(241\) 22.0638 1.42125 0.710627 0.703569i \(-0.248412\pi\)
0.710627 + 0.703569i \(0.248412\pi\)
\(242\) 14.4415 + 0.921167i 0.928337 + 0.0592149i
\(243\) 0 0
\(244\) 2.00413 + 0.256715i 0.128301 + 0.0164345i
\(245\) 0 0
\(246\) 0 0
\(247\) 16.6774i 1.06116i
\(248\) −0.632394 + 3.26887i −0.0401571 + 0.207573i
\(249\) 0 0
\(250\) −0.852817 + 13.3700i −0.0539369 + 0.845592i
\(251\) 26.5149 1.67361 0.836804 0.547503i \(-0.184421\pi\)
0.836804 + 0.547503i \(0.184421\pi\)
\(252\) 0 0
\(253\) 3.31182 0.208212
\(254\) −1.37076 + 21.4900i −0.0860092 + 1.34840i
\(255\) 0 0
\(256\) 13.9671 + 7.80521i 0.872941 + 0.487826i
\(257\) 16.9392i 1.05664i −0.849046 0.528320i \(-0.822822\pi\)
0.849046 0.528320i \(-0.177178\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 3.30250 25.7820i 0.204812 1.59893i
\(261\) 0 0
\(262\) −5.86176 0.373898i −0.362141 0.0230995i
\(263\) −13.9594 −0.860772 −0.430386 0.902645i \(-0.641623\pi\)
−0.430386 + 0.902645i \(0.641623\pi\)
\(264\) 0 0
\(265\) −5.14712 −0.316185
\(266\) 0 0
\(267\) 0 0
\(268\) −3.21312 + 25.0842i −0.196272 + 1.53226i
\(269\) 15.5402i 0.947500i −0.880659 0.473750i \(-0.842900\pi\)
0.880659 0.473750i \(-0.157100\pi\)
\(270\) 0 0
\(271\) 0.227723i 0.0138332i 0.999976 + 0.00691658i \(0.00220163\pi\)
−0.999976 + 0.00691658i \(0.997798\pi\)
\(272\) −5.65703 + 21.7194i −0.343008 + 1.31693i
\(273\) 0 0
\(274\) −1.47025 + 23.0497i −0.0888208 + 1.39248i
\(275\) 5.49927 0.331619
\(276\) 0 0
\(277\) −18.1028 −1.08769 −0.543846 0.839185i \(-0.683032\pi\)
−0.543846 + 0.839185i \(0.683032\pi\)
\(278\) 0.926373 14.5232i 0.0555602 0.871041i
\(279\) 0 0
\(280\) 0 0
\(281\) 16.5594i 0.987854i 0.869503 + 0.493927i \(0.164439\pi\)
−0.869503 + 0.493927i \(0.835561\pi\)
\(282\) 0 0
\(283\) 3.19355i 0.189837i −0.995485 0.0949185i \(-0.969741\pi\)
0.995485 0.0949185i \(-0.0302590\pi\)
\(284\) 14.5018 + 1.85757i 0.860521 + 0.110227i
\(285\) 0 0
\(286\) 33.9616 + 2.16627i 2.00819 + 0.128094i
\(287\) 0 0
\(288\) 0 0
\(289\) −14.4834 −0.851966
\(290\) −15.9341 1.01637i −0.935680 0.0596832i
\(291\) 0 0
\(292\) −19.1195 2.44908i −1.11889 0.143321i
\(293\) 3.17751i 0.185632i −0.995683 0.0928160i \(-0.970413\pi\)
0.995683 0.0928160i \(-0.0295868\pi\)
\(294\) 0 0
\(295\) 10.2444i 0.596451i
\(296\) 7.53371 + 1.45747i 0.437888 + 0.0847137i
\(297\) 0 0
\(298\) −0.509253 + 7.98377i −0.0295002 + 0.462488i
\(299\) 3.75337 0.217063
\(300\) 0 0
\(301\) 0 0
\(302\) −1.09491 + 17.1654i −0.0630052 + 0.987760i
\(303\) 0 0
\(304\) −3.21975 + 12.3618i −0.184665 + 0.708997i
\(305\) 2.51418i 0.143961i
\(306\) 0 0
\(307\) 10.8559i 0.619579i 0.950805 + 0.309790i \(0.100259\pi\)
−0.950805 + 0.309790i \(0.899741\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −4.13458 0.263728i −0.234828 0.0149787i
\(311\) −18.6821 −1.05936 −0.529681 0.848197i \(-0.677688\pi\)
−0.529681 + 0.848197i \(0.677688\pi\)
\(312\) 0 0
\(313\) 15.8313 0.894839 0.447420 0.894324i \(-0.352343\pi\)
0.447420 + 0.894324i \(0.352343\pi\)
\(314\) −9.93447 0.633680i −0.560635 0.0357606i
\(315\) 0 0
\(316\) 2.24621 17.5357i 0.126359 0.986462i
\(317\) 6.13829i 0.344761i −0.985030 0.172380i \(-0.944854\pi\)
0.985030 0.172380i \(-0.0551458\pi\)
\(318\) 0 0
\(319\) 20.9039i 1.17039i
\(320\) −7.42539 + 18.4728i −0.415092 + 1.03266i
\(321\) 0 0
\(322\) 0 0
\(323\) −17.9191 −0.997043
\(324\) 0 0
\(325\) 6.23246 0.345715
\(326\) 0.161024 2.52445i 0.00891831 0.139816i
\(327\) 0 0
\(328\) −2.06117 + 10.6543i −0.113809 + 0.588284i
\(329\) 0 0
\(330\) 0 0
\(331\) 0.388432i 0.0213501i −0.999943 0.0106751i \(-0.996602\pi\)
0.999943 0.0106751i \(-0.00339804\pi\)
\(332\) 27.3084 + 3.49801i 1.49874 + 0.191978i
\(333\) 0 0
\(334\) 11.6714 + 0.744474i 0.638633 + 0.0407358i
\(335\) −31.4681 −1.71929
\(336\) 0 0
\(337\) 6.10384 0.332497 0.166249 0.986084i \(-0.446835\pi\)
0.166249 + 0.986084i \(0.446835\pi\)
\(338\) 20.1420 + 1.28477i 1.09558 + 0.0698825i
\(339\) 0 0
\(340\) −27.7015 3.54837i −1.50233 0.192437i
\(341\) 5.42415i 0.293734i
\(342\) 0 0
\(343\) 0 0
\(344\) 6.00475 31.0388i 0.323754 1.67350i
\(345\) 0 0
\(346\) −1.74171 + 27.3056i −0.0936351 + 1.46796i
\(347\) −29.0268 −1.55824 −0.779120 0.626874i \(-0.784334\pi\)
−0.779120 + 0.626874i \(0.784334\pi\)
\(348\) 0 0
\(349\) 27.2889 1.46074 0.730371 0.683050i \(-0.239347\pi\)
0.730371 + 0.683050i \(0.239347\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −24.7551 8.16234i −1.31945 0.435054i
\(353\) 30.2811i 1.61170i −0.592118 0.805851i \(-0.701708\pi\)
0.592118 0.805851i \(-0.298292\pi\)
\(354\) 0 0
\(355\) 18.1924i 0.965554i
\(356\) 2.16653 16.9137i 0.114826 0.896424i
\(357\) 0 0
\(358\) 17.0120 + 1.08513i 0.899113 + 0.0573508i
\(359\) −20.7780 −1.09662 −0.548312 0.836274i \(-0.684729\pi\)
−0.548312 + 0.836274i \(0.684729\pi\)
\(360\) 0 0
\(361\) 8.80122 0.463222
\(362\) −29.3549 1.87243i −1.54286 0.0984127i
\(363\) 0 0
\(364\) 0 0
\(365\) 23.9854i 1.25545i
\(366\) 0 0
\(367\) 20.4825i 1.06918i 0.845112 + 0.534589i \(0.179533\pi\)
−0.845112 + 0.534589i \(0.820467\pi\)
\(368\) −2.78211 0.724626i −0.145027 0.0377738i
\(369\) 0 0
\(370\) −0.607810 + 9.52889i −0.0315985 + 0.495384i
\(371\) 0 0
\(372\) 0 0
\(373\) −23.9599 −1.24060 −0.620299 0.784365i \(-0.712989\pi\)
−0.620299 + 0.784365i \(0.712989\pi\)
\(374\) 2.32755 36.4900i 0.120355 1.88686i
\(375\) 0 0
\(376\) 15.0457 + 2.91074i 0.775925 + 0.150110i
\(377\) 23.6909i 1.22014i
\(378\) 0 0
\(379\) 3.00154i 0.154179i 0.997024 + 0.0770894i \(0.0245627\pi\)
−0.997024 + 0.0770894i \(0.975437\pi\)
\(380\) −15.7665 2.01958i −0.808807 0.103603i
\(381\) 0 0
\(382\) 14.9833 + 0.955722i 0.766611 + 0.0488990i
\(383\) −28.6815 −1.46555 −0.732777 0.680469i \(-0.761776\pi\)
−0.732777 + 0.680469i \(0.761776\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 18.3372 + 1.16965i 0.933337 + 0.0595338i
\(387\) 0 0
\(388\) 21.2726 + 2.72487i 1.07995 + 0.138334i
\(389\) 12.0942i 0.613202i −0.951838 0.306601i \(-0.900808\pi\)
0.951838 0.306601i \(-0.0991918\pi\)
\(390\) 0 0
\(391\) 4.03281i 0.203948i
\(392\) 0 0
\(393\) 0 0
\(394\) −0.287044 + 4.50011i −0.0144610 + 0.226712i
\(395\) 21.9986 1.10687
\(396\) 0 0
\(397\) −5.25829 −0.263906 −0.131953 0.991256i \(-0.542125\pi\)
−0.131953 + 0.991256i \(0.542125\pi\)
\(398\) 1.26479 19.8286i 0.0633981 0.993920i
\(399\) 0 0
\(400\) −4.61968 1.20324i −0.230984 0.0601621i
\(401\) 18.5470i 0.926193i 0.886308 + 0.463096i \(0.153262\pi\)
−0.886308 + 0.463096i \(0.846738\pi\)
\(402\) 0 0
\(403\) 6.14732i 0.306220i
\(404\) −0.974943 + 7.61121i −0.0485052 + 0.378672i
\(405\) 0 0
\(406\) 0 0
\(407\) −12.5009 −0.619649
\(408\) 0 0
\(409\) 17.5224 0.866429 0.433214 0.901291i \(-0.357379\pi\)
0.433214 + 0.901291i \(0.357379\pi\)
\(410\) −13.4759 0.859573i −0.665527 0.0424513i
\(411\) 0 0
\(412\) 4.23789 33.0845i 0.208786 1.62996i
\(413\) 0 0
\(414\) 0 0
\(415\) 34.2583i 1.68167i
\(416\) −28.0555 9.25058i −1.37554 0.453547i
\(417\) 0 0
\(418\) 1.32475 20.7686i 0.0647954 1.01583i
\(419\) −26.9149 −1.31488 −0.657439 0.753508i \(-0.728360\pi\)
−0.657439 + 0.753508i \(0.728360\pi\)
\(420\) 0 0
\(421\) −4.71296 −0.229695 −0.114848 0.993383i \(-0.536638\pi\)
−0.114848 + 0.993383i \(0.536638\pi\)
\(422\) 0.821885 12.8850i 0.0400087 0.627234i
\(423\) 0 0
\(424\) −1.11110 + 5.74334i −0.0539600 + 0.278921i
\(425\) 6.69647i 0.324827i
\(426\) 0 0
\(427\) 0 0
\(428\) 11.3808 + 1.45780i 0.550111 + 0.0704654i
\(429\) 0 0
\(430\) 39.2589 + 2.50416i 1.89323 + 0.120761i
\(431\) −3.82093 −0.184048 −0.0920239 0.995757i \(-0.529334\pi\)
−0.0920239 + 0.995757i \(0.529334\pi\)
\(432\) 0 0
\(433\) 34.7992 1.67234 0.836172 0.548467i \(-0.184788\pi\)
0.836172 + 0.548467i \(0.184788\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −5.60828 0.718381i −0.268588 0.0344042i
\(437\) 2.29531i 0.109799i
\(438\) 0 0
\(439\) 35.4814i 1.69343i 0.532044 + 0.846717i \(0.321424\pi\)
−0.532044 + 0.846717i \(0.678576\pi\)
\(440\) 6.16060 31.8444i 0.293695 1.51812i
\(441\) 0 0
\(442\) 2.63787 41.3550i 0.125471 1.96706i
\(443\) 10.9584 0.520648 0.260324 0.965521i \(-0.416171\pi\)
0.260324 + 0.965521i \(0.416171\pi\)
\(444\) 0 0
\(445\) 21.2182 1.00584
\(446\) 2.14603 33.6442i 0.101617 1.59310i
\(447\) 0 0
\(448\) 0 0
\(449\) 27.1675i 1.28211i −0.767494 0.641056i \(-0.778497\pi\)
0.767494 0.641056i \(-0.221503\pi\)
\(450\) 0 0
\(451\) 17.6790i 0.832472i
\(452\) 1.42213 11.1023i 0.0668913 0.522209i
\(453\) 0 0
\(454\) −14.1309 0.901354i −0.663197 0.0423026i
\(455\) 0 0
\(456\) 0 0
\(457\) 38.5614 1.80383 0.901914 0.431916i \(-0.142162\pi\)
0.901914 + 0.431916i \(0.142162\pi\)
\(458\) 7.53136 + 0.480395i 0.351918 + 0.0224474i
\(459\) 0 0
\(460\) 0.454522 3.54837i 0.0211922 0.165444i
\(461\) 13.5543i 0.631287i 0.948878 + 0.315643i \(0.102220\pi\)
−0.948878 + 0.315643i \(0.897780\pi\)
\(462\) 0 0
\(463\) 17.7564i 0.825212i −0.910910 0.412606i \(-0.864619\pi\)
0.910910 0.412606i \(-0.135381\pi\)
\(464\) −4.57377 + 17.5604i −0.212332 + 0.815219i
\(465\) 0 0
\(466\) −0.789347 + 12.3749i −0.0365658 + 0.573258i
\(467\) 10.7993 0.499732 0.249866 0.968280i \(-0.419613\pi\)
0.249866 + 0.968280i \(0.419613\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −1.21387 + 19.0304i −0.0559916 + 0.877805i
\(471\) 0 0
\(472\) −11.4310 2.21144i −0.526156 0.101790i
\(473\) 51.5037i 2.36814i
\(474\) 0 0
\(475\) 3.81135i 0.174877i
\(476\) 0 0
\(477\) 0 0
\(478\) 18.5430 + 1.18278i 0.848136 + 0.0540992i
\(479\) −18.9672 −0.866634 −0.433317 0.901242i \(-0.642657\pi\)
−0.433317 + 0.901242i \(0.642657\pi\)
\(480\) 0 0
\(481\) −14.1676 −0.645988
\(482\) 31.1396 + 1.98627i 1.41837 + 0.0904721i
\(483\) 0 0
\(484\) 20.2991 + 2.60017i 0.922685 + 0.118190i
\(485\) 26.6865i 1.21177i
\(486\) 0 0
\(487\) 14.5316i 0.658489i 0.944245 + 0.329245i \(0.106794\pi\)
−0.944245 + 0.329245i \(0.893206\pi\)
\(488\) 2.80541 + 0.542733i 0.126995 + 0.0245684i
\(489\) 0 0
\(490\) 0 0
\(491\) 26.0025 1.17348 0.586738 0.809777i \(-0.300412\pi\)
0.586738 + 0.809777i \(0.300412\pi\)
\(492\) 0 0
\(493\) −25.4547 −1.14642
\(494\) 1.50137 23.5376i 0.0675497 1.05901i
\(495\) 0 0
\(496\) −1.18680 + 4.55657i −0.0532891 + 0.204596i
\(497\) 0 0
\(498\) 0 0
\(499\) 2.74273i 0.122781i 0.998114 + 0.0613907i \(0.0195536\pi\)
−0.998114 + 0.0613907i \(0.980446\pi\)
\(500\) −2.40724 + 18.7929i −0.107655 + 0.840444i
\(501\) 0 0
\(502\) 37.4217 + 2.38698i 1.67021 + 0.106536i
\(503\) 21.5337 0.960139 0.480070 0.877230i \(-0.340611\pi\)
0.480070 + 0.877230i \(0.340611\pi\)
\(504\) 0 0
\(505\) −9.54826 −0.424892
\(506\) 4.67412 + 0.298143i 0.207790 + 0.0132541i
\(507\) 0 0
\(508\) −3.86923 + 30.2064i −0.171669 + 1.34019i
\(509\) 13.1345i 0.582177i 0.956696 + 0.291089i \(0.0940175\pi\)
−0.956696 + 0.291089i \(0.905983\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 19.0097 + 12.2732i 0.840117 + 0.542405i
\(513\) 0 0
\(514\) 1.52494 23.9071i 0.0672620 1.05450i
\(515\) 41.5045 1.82890
\(516\) 0 0
\(517\) −24.9659 −1.09800
\(518\) 0 0
\(519\) 0 0
\(520\) 6.98196 36.0900i 0.306179 1.58265i
\(521\) 7.27913i 0.318905i −0.987206 0.159452i \(-0.949027\pi\)
0.987206 0.159452i \(-0.0509728\pi\)
\(522\) 0 0
\(523\) 2.79029i 0.122011i 0.998137 + 0.0610055i \(0.0194307\pi\)
−0.998137 + 0.0610055i \(0.980569\pi\)
\(524\) −8.23931 1.05540i −0.359936 0.0461053i
\(525\) 0 0
\(526\) −19.7015 1.25668i −0.859027 0.0547938i
\(527\) −6.60499 −0.287718
\(528\) 0 0
\(529\) −22.4834 −0.977540
\(530\) −7.26437 0.463365i −0.315544 0.0201273i
\(531\) 0 0
\(532\) 0 0
\(533\) 20.0360i 0.867858i
\(534\) 0 0
\(535\) 14.2772i 0.617257i
\(536\) −6.79300 + 35.1133i −0.293413 + 1.51666i
\(537\) 0 0
\(538\) 1.39899 21.9325i 0.0603146 0.945578i
\(539\) 0 0
\(540\) 0 0
\(541\) 0.607118 0.0261020 0.0130510 0.999915i \(-0.495846\pi\)
0.0130510 + 0.999915i \(0.495846\pi\)
\(542\) −0.0205005 + 0.321395i −0.000880572 + 0.0138051i
\(543\) 0 0
\(544\) −9.93929 + 30.1443i −0.426144 + 1.29243i
\(545\) 7.03558i 0.301371i
\(546\) 0 0
\(547\) 11.1295i 0.475865i 0.971282 + 0.237933i \(0.0764697\pi\)
−0.971282 + 0.237933i \(0.923530\pi\)
\(548\) −4.15005 + 32.3987i −0.177281 + 1.38400i
\(549\) 0 0
\(550\) 7.76138 + 0.495067i 0.330946 + 0.0211097i
\(551\) −14.4877 −0.617198
\(552\) 0 0
\(553\) 0 0
\(554\) −25.5493 1.62969i −1.08549 0.0692387i
\(555\) 0 0
\(556\) 2.61487 20.4138i 0.110895 0.865738i
\(557\) 29.6533i 1.25645i −0.778031 0.628225i \(-0.783782\pi\)
0.778031 0.628225i \(-0.216218\pi\)
\(558\) 0 0
\(559\) 58.3703i 2.46880i
\(560\) 0 0
\(561\) 0 0
\(562\) −1.49075 + 23.3711i −0.0628834 + 0.985850i
\(563\) −32.8348 −1.38382 −0.691910 0.721983i \(-0.743231\pi\)
−0.691910 + 0.721983i \(0.743231\pi\)
\(564\) 0 0
\(565\) 13.9278 0.585949
\(566\) 0.287496 4.50721i 0.0120844 0.189452i
\(567\) 0 0
\(568\) 20.2998 + 3.92718i 0.851759 + 0.164781i
\(569\) 9.16895i 0.384382i 0.981358 + 0.192191i \(0.0615594\pi\)
−0.981358 + 0.192191i \(0.938441\pi\)
\(570\) 0 0
\(571\) 24.4499i 1.02320i −0.859224 0.511599i \(-0.829053\pi\)
0.859224 0.511599i \(-0.170947\pi\)
\(572\) 47.7365 + 6.11471i 1.99596 + 0.255669i
\(573\) 0 0
\(574\) 0 0
\(575\) 0.857772 0.0357716
\(576\) 0 0
\(577\) 12.0185 0.500337 0.250168 0.968202i \(-0.419514\pi\)
0.250168 + 0.968202i \(0.419514\pi\)
\(578\) −20.4411 1.30386i −0.850238 0.0542333i
\(579\) 0 0
\(580\) −22.3969 2.86889i −0.929983 0.119124i
\(581\) 0 0
\(582\) 0 0
\(583\) 9.53012i 0.394697i
\(584\) −26.7638 5.17771i −1.10749 0.214255i
\(585\) 0 0
\(586\) 0.286052 4.48456i 0.0118167 0.185256i
\(587\) −18.8618 −0.778510 −0.389255 0.921130i \(-0.627267\pi\)
−0.389255 + 0.921130i \(0.627267\pi\)
\(588\) 0 0
\(589\) −3.75929 −0.154899
\(590\) 0.922240 14.4584i 0.0379680 0.595241i
\(591\) 0 0
\(592\) 10.5015 + 2.73521i 0.431608 + 0.112416i
\(593\) 8.83457i 0.362792i 0.983410 + 0.181396i \(0.0580616\pi\)
−0.983410 + 0.181396i \(0.941938\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −1.43746 + 11.2220i −0.0588808 + 0.459672i
\(597\) 0 0
\(598\) 5.29729 + 0.337893i 0.216622 + 0.0138175i
\(599\) 27.8030 1.13600 0.568000 0.823028i \(-0.307717\pi\)
0.568000 + 0.823028i \(0.307717\pi\)
\(600\) 0 0
\(601\) 12.1977 0.497556 0.248778 0.968561i \(-0.419971\pi\)
0.248778 + 0.968561i \(0.419971\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −3.09060 + 24.1278i −0.125755 + 0.981746i
\(605\) 25.4652i 1.03531i
\(606\) 0 0
\(607\) 10.5180i 0.426913i 0.976953 + 0.213457i \(0.0684722\pi\)
−0.976953 + 0.213457i \(0.931528\pi\)
\(608\) −5.65703 + 17.1569i −0.229423 + 0.695804i
\(609\) 0 0
\(610\) −0.226336 + 3.54837i −0.00916408 + 0.143669i
\(611\) −28.2945 −1.14467
\(612\) 0 0
\(613\) 39.4103 1.59177 0.795884 0.605449i \(-0.207006\pi\)
0.795884 + 0.605449i \(0.207006\pi\)
\(614\) −0.977292 + 15.3214i −0.0394403 + 0.618323i
\(615\) 0 0
\(616\) 0 0
\(617\) 35.9618i 1.44777i 0.689922 + 0.723884i \(0.257645\pi\)
−0.689922 + 0.723884i \(0.742355\pi\)
\(618\) 0 0
\(619\) 24.4499i 0.982726i 0.870955 + 0.491363i \(0.163501\pi\)
−0.870955 + 0.491363i \(0.836499\pi\)
\(620\) −5.81157 0.744422i −0.233398 0.0298967i
\(621\) 0 0
\(622\) −26.3668 1.68183i −1.05721 0.0674354i
\(623\) 0 0
\(624\) 0 0
\(625\) −29.5429 −1.18172
\(626\) 22.3435 + 1.42520i 0.893024 + 0.0569624i
\(627\) 0 0
\(628\) −13.9639 1.78868i −0.557221 0.0713762i
\(629\) 15.2224i 0.606958i
\(630\) 0 0
\(631\) 5.08034i 0.202245i −0.994874 0.101123i \(-0.967757\pi\)
0.994874 0.101123i \(-0.0322434\pi\)
\(632\) 4.74881 24.5468i 0.188897 0.976418i
\(633\) 0 0
\(634\) 0.552594 8.66325i 0.0219463 0.344062i
\(635\) −37.8939 −1.50377
\(636\) 0 0
\(637\) 0 0
\(638\) 1.88185 29.5026i 0.0745031 1.16802i
\(639\) 0 0
\(640\) −12.1428 + 25.4030i −0.479986 + 1.00414i
\(641\) 26.7077i 1.05489i −0.849589 0.527445i \(-0.823150\pi\)
0.849589 0.527445i \(-0.176850\pi\)
\(642\) 0 0
\(643\) 24.3919i 0.961924i 0.876741 + 0.480962i \(0.159713\pi\)
−0.876741 + 0.480962i \(0.840287\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −25.2900 1.61314i −0.995021 0.0634683i
\(647\) 4.83841 0.190218 0.0951088 0.995467i \(-0.469680\pi\)
0.0951088 + 0.995467i \(0.469680\pi\)
\(648\) 0 0
\(649\) 18.9679 0.744555
\(650\) 8.79615 + 0.561071i 0.345014 + 0.0220070i
\(651\) 0 0
\(652\) 0.454522 3.54837i 0.0178004 0.138965i
\(653\) 22.5851i 0.883821i −0.897059 0.441911i \(-0.854301\pi\)
0.897059 0.441911i \(-0.145699\pi\)
\(654\) 0 0
\(655\) 10.3362i 0.403869i
\(656\) −3.86817 + 14.8513i −0.151027 + 0.579846i
\(657\) 0 0
\(658\) 0 0
\(659\) −13.4237 −0.522911 −0.261456 0.965215i \(-0.584203\pi\)
−0.261456 + 0.965215i \(0.584203\pi\)
\(660\) 0 0
\(661\) 14.2037 0.552460 0.276230 0.961092i \(-0.410915\pi\)
0.276230 + 0.961092i \(0.410915\pi\)
\(662\) 0.0349682 0.548211i 0.00135908 0.0213068i
\(663\) 0 0
\(664\) 38.2266 + 7.39531i 1.48348 + 0.286994i
\(665\) 0 0
\(666\) 0 0
\(667\) 3.26057i 0.126250i
\(668\) 16.4054 + 2.10142i 0.634745 + 0.0813064i
\(669\) 0 0
\(670\) −44.4124 2.83289i −1.71580 0.109444i
\(671\) −4.65510 −0.179708
\(672\) 0 0
\(673\) 11.3016 0.435643 0.217822 0.975989i \(-0.430105\pi\)
0.217822 + 0.975989i \(0.430105\pi\)
\(674\) 8.61463 + 0.549492i 0.331823 + 0.0211657i
\(675\) 0 0
\(676\) 28.3116 + 3.62652i 1.08891 + 0.139482i
\(677\) 3.17751i 0.122122i −0.998134 0.0610608i \(-0.980552\pi\)
0.998134 0.0610608i \(-0.0194484\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −38.7770 7.50178i −1.48703 0.287680i
\(681\) 0 0
\(682\) 0.488303 7.65534i 0.0186981 0.293138i
\(683\) 6.26524 0.239733 0.119866 0.992790i \(-0.461753\pi\)
0.119866 + 0.992790i \(0.461753\pi\)
\(684\) 0 0
\(685\) −40.6441 −1.55293
\(686\) 0 0
\(687\) 0 0
\(688\) 11.2690 43.2658i 0.429627 1.64949i
\(689\) 10.8007i 0.411474i
\(690\) 0 0
\(691\) 16.1301i 0.613619i −0.951771 0.306809i \(-0.900739\pi\)
0.951771 0.306809i \(-0.0992614\pi\)
\(692\) −4.91632 + 38.3808i −0.186890 + 1.45902i
\(693\) 0 0
\(694\) −40.9669 2.61311i −1.55508 0.0991923i
\(695\) 25.6091 0.971408
\(696\) 0 0
\(697\) −21.5278 −0.815422
\(698\) 38.5141 + 2.45666i 1.45778 + 0.0929859i
\(699\) 0 0
\(700\) 0 0
\(701\) 50.8903i 1.92210i 0.276373 + 0.961050i \(0.410867\pi\)
−0.276373 + 0.961050i \(0.589133\pi\)
\(702\) 0 0
\(703\) 8.66397i 0.326768i
\(704\) −34.2032 13.7484i −1.28908 0.518164i
\(705\) 0 0
\(706\) 2.72603 42.7371i 0.102595 1.60843i
\(707\) 0 0
\(708\) 0 0
\(709\) 21.3743 0.802727 0.401364 0.915919i \(-0.368536\pi\)
0.401364 + 0.915919i \(0.368536\pi\)
\(710\) −1.63776 + 25.6758i −0.0614639 + 0.963596i
\(711\) 0 0
\(712\) 4.58036 23.6760i 0.171656 0.887297i
\(713\) 0.846054i 0.0316850i
\(714\) 0 0
\(715\) 59.8854i 2.23959i
\(716\) 23.9122 + 3.06298i 0.893639 + 0.114469i
\(717\) 0 0
\(718\) −29.3250 1.87052i −1.09440 0.0698073i
\(719\) −24.3853 −0.909418 −0.454709 0.890640i \(-0.650257\pi\)
−0.454709 + 0.890640i \(0.650257\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 12.4216 + 0.792321i 0.462283 + 0.0294871i
\(723\) 0 0
\(724\) −41.2613 5.28529i −1.53346 0.196426i
\(725\) 5.41417i 0.201077i
\(726\) 0 0
\(727\) 37.0825i 1.37531i 0.726037 + 0.687656i \(0.241360\pi\)
−0.726037 + 0.687656i \(0.758640\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 2.15926 33.8517i 0.0799180 1.25291i
\(731\) 62.7161 2.31964
\(732\) 0 0
\(733\) −45.1262 −1.66678 −0.833388 0.552689i \(-0.813602\pi\)
−0.833388 + 0.552689i \(0.813602\pi\)
\(734\) −1.84392 + 28.9079i −0.0680602 + 1.06701i
\(735\) 0 0
\(736\) −3.86128 1.27315i −0.142329 0.0469291i
\(737\) 58.2646i 2.14621i
\(738\) 0 0
\(739\) 43.0456i 1.58346i −0.610872 0.791729i \(-0.709181\pi\)
0.610872 0.791729i \(-0.290819\pi\)
\(740\) −1.71566 + 13.3938i −0.0630689 + 0.492367i
\(741\) 0 0
\(742\) 0 0
\(743\) 7.52770 0.276165 0.138082 0.990421i \(-0.455906\pi\)
0.138082 + 0.990421i \(0.455906\pi\)
\(744\) 0 0
\(745\) −14.0780 −0.515779
\(746\) −33.8158 2.15697i −1.23808 0.0789723i
\(747\) 0 0
\(748\) 6.56996 51.2905i 0.240222 1.87537i
\(749\) 0 0
\(750\) 0 0
\(751\) 44.0306i 1.60670i 0.595509 + 0.803349i \(0.296950\pi\)
−0.595509 + 0.803349i \(0.703050\pi\)
\(752\) 20.9727 + 5.46254i 0.764796 + 0.199198i
\(753\) 0 0
\(754\) 2.13275 33.4360i 0.0776700 1.21767i
\(755\) −30.2683 −1.10158
\(756\) 0 0
\(757\) 7.64185 0.277748 0.138874 0.990310i \(-0.455652\pi\)
0.138874 + 0.990310i \(0.455652\pi\)
\(758\) −0.270211 + 4.23621i −0.00981449 + 0.153866i
\(759\) 0 0
\(760\) −22.0702 4.26970i −0.800571 0.154878i
\(761\) 17.4602i 0.632932i −0.948604 0.316466i \(-0.897504\pi\)
0.948604 0.316466i \(-0.102496\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 21.0605 + 2.69771i 0.761943 + 0.0975996i
\(765\) 0 0
\(766\) −40.4794 2.58202i −1.46258 0.0932922i
\(767\) 21.4968 0.776204
\(768\) 0 0
\(769\) −3.13489 −0.113047 −0.0565235 0.998401i \(-0.518002\pi\)
−0.0565235 + 0.998401i \(0.518002\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 25.7748 + 3.30157i 0.927654 + 0.118826i
\(773\) 19.0221i 0.684179i 0.939667 + 0.342090i \(0.111135\pi\)
−0.939667 + 0.342090i \(0.888865\pi\)
\(774\) 0 0
\(775\) 1.40487i 0.0504645i
\(776\) 29.7777 + 5.76078i 1.06896 + 0.206800i
\(777\) 0 0
\(778\) 1.08877 17.0692i 0.0390344 0.611959i
\(779\) −12.2527 −0.438999
\(780\) 0 0
\(781\) −33.6841 −1.20531
\(782\) 0.363050 5.69169i 0.0129826 0.203534i
\(783\) 0 0
\(784\) 0 0
\(785\) 17.5177i 0.625235i
\(786\) 0 0
\(787\) 4.59842i 0.163916i −0.996636 0.0819581i \(-0.973883\pi\)
0.996636 0.0819581i \(-0.0261174\pi\)
\(788\) −0.810235 + 6.32536i −0.0288634 + 0.225332i
\(789\) 0 0
\(790\) 31.0476 + 1.98040i 1.10462 + 0.0704594i
\(791\) 0 0
\(792\) 0 0
\(793\) −5.27574