Properties

Label 224.2.i.c.65.1
Level $224$
Weight $2$
Character 224.65
Analytic conductor $1.789$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 224 = 2^{5} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 224.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.78864900528\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{7})\)
Defining polynomial: \( x^{4} + 7x^{2} + 49 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 65.1
Root \(-1.32288 - 2.29129i\) of defining polynomial
Character \(\chi\) \(=\) 224.65
Dual form 224.2.i.c.193.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.32288 - 2.29129i) q^{3} +(1.50000 - 2.59808i) q^{5} -2.64575 q^{7} +(-2.00000 + 3.46410i) q^{9} +O(q^{10})\) \(q+(-1.32288 - 2.29129i) q^{3} +(1.50000 - 2.59808i) q^{5} -2.64575 q^{7} +(-2.00000 + 3.46410i) q^{9} +(1.32288 + 2.29129i) q^{11} -4.00000 q^{13} -7.93725 q^{15} +(-0.500000 - 0.866025i) q^{17} +(3.96863 - 6.87386i) q^{19} +(3.50000 + 6.06218i) q^{21} +(1.32288 - 2.29129i) q^{23} +(-2.00000 - 3.46410i) q^{25} +2.64575 q^{27} -4.00000 q^{29} +(1.32288 + 2.29129i) q^{31} +(3.50000 - 6.06218i) q^{33} +(-3.96863 + 6.87386i) q^{35} +(2.50000 - 4.33013i) q^{37} +(5.29150 + 9.16515i) q^{39} +8.00000 q^{41} +10.5830 q^{43} +(6.00000 + 10.3923i) q^{45} +(-1.32288 + 2.29129i) q^{47} +7.00000 q^{49} +(-1.32288 + 2.29129i) q^{51} +(-3.50000 - 6.06218i) q^{53} +7.93725 q^{55} -21.0000 q^{57} +(-1.32288 - 2.29129i) q^{59} +(2.50000 - 4.33013i) q^{61} +(5.29150 - 9.16515i) q^{63} +(-6.00000 + 10.3923i) q^{65} +(-1.32288 - 2.29129i) q^{67} -7.00000 q^{69} +(4.50000 + 7.79423i) q^{73} +(-5.29150 + 9.16515i) q^{75} +(-3.50000 - 6.06218i) q^{77} +(1.32288 - 2.29129i) q^{79} +(2.50000 + 4.33013i) q^{81} -10.5830 q^{83} -3.00000 q^{85} +(5.29150 + 9.16515i) q^{87} +(4.50000 - 7.79423i) q^{89} +10.5830 q^{91} +(3.50000 - 6.06218i) q^{93} +(-11.9059 - 20.6216i) q^{95} -8.00000 q^{97} -10.5830 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 6 q^{5} - 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 6 q^{5} - 8 q^{9} - 16 q^{13} - 2 q^{17} + 14 q^{21} - 8 q^{25} - 16 q^{29} + 14 q^{33} + 10 q^{37} + 32 q^{41} + 24 q^{45} + 28 q^{49} - 14 q^{53} - 84 q^{57} + 10 q^{61} - 24 q^{65} - 28 q^{69} + 18 q^{73} - 14 q^{77} + 10 q^{81} - 12 q^{85} + 18 q^{89} + 14 q^{93} - 32 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(127\) \(129\) \(197\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.32288 2.29129i −0.763763 1.32288i −0.940898 0.338689i \(-0.890016\pi\)
0.177136 0.984186i \(-0.443317\pi\)
\(4\) 0 0
\(5\) 1.50000 2.59808i 0.670820 1.16190i −0.306851 0.951757i \(-0.599275\pi\)
0.977672 0.210138i \(-0.0673912\pi\)
\(6\) 0 0
\(7\) −2.64575 −1.00000
\(8\) 0 0
\(9\) −2.00000 + 3.46410i −0.666667 + 1.15470i
\(10\) 0 0
\(11\) 1.32288 + 2.29129i 0.398862 + 0.690849i 0.993586 0.113081i \(-0.0360719\pi\)
−0.594724 + 0.803930i \(0.702739\pi\)
\(12\) 0 0
\(13\) −4.00000 −1.10940 −0.554700 0.832050i \(-0.687167\pi\)
−0.554700 + 0.832050i \(0.687167\pi\)
\(14\) 0 0
\(15\) −7.93725 −2.04939
\(16\) 0 0
\(17\) −0.500000 0.866025i −0.121268 0.210042i 0.799000 0.601331i \(-0.205363\pi\)
−0.920268 + 0.391289i \(0.872029\pi\)
\(18\) 0 0
\(19\) 3.96863 6.87386i 0.910465 1.57697i 0.0970575 0.995279i \(-0.469057\pi\)
0.813408 0.581694i \(-0.197610\pi\)
\(20\) 0 0
\(21\) 3.50000 + 6.06218i 0.763763 + 1.32288i
\(22\) 0 0
\(23\) 1.32288 2.29129i 0.275839 0.477767i −0.694508 0.719485i \(-0.744378\pi\)
0.970346 + 0.241719i \(0.0777111\pi\)
\(24\) 0 0
\(25\) −2.00000 3.46410i −0.400000 0.692820i
\(26\) 0 0
\(27\) 2.64575 0.509175
\(28\) 0 0
\(29\) −4.00000 −0.742781 −0.371391 0.928477i \(-0.621119\pi\)
−0.371391 + 0.928477i \(0.621119\pi\)
\(30\) 0 0
\(31\) 1.32288 + 2.29129i 0.237595 + 0.411527i 0.960024 0.279918i \(-0.0903074\pi\)
−0.722428 + 0.691446i \(0.756974\pi\)
\(32\) 0 0
\(33\) 3.50000 6.06218i 0.609272 1.05529i
\(34\) 0 0
\(35\) −3.96863 + 6.87386i −0.670820 + 1.16190i
\(36\) 0 0
\(37\) 2.50000 4.33013i 0.410997 0.711868i −0.584002 0.811752i \(-0.698514\pi\)
0.994999 + 0.0998840i \(0.0318472\pi\)
\(38\) 0 0
\(39\) 5.29150 + 9.16515i 0.847319 + 1.46760i
\(40\) 0 0
\(41\) 8.00000 1.24939 0.624695 0.780869i \(-0.285223\pi\)
0.624695 + 0.780869i \(0.285223\pi\)
\(42\) 0 0
\(43\) 10.5830 1.61389 0.806947 0.590624i \(-0.201119\pi\)
0.806947 + 0.590624i \(0.201119\pi\)
\(44\) 0 0
\(45\) 6.00000 + 10.3923i 0.894427 + 1.54919i
\(46\) 0 0
\(47\) −1.32288 + 2.29129i −0.192961 + 0.334219i −0.946230 0.323494i \(-0.895142\pi\)
0.753269 + 0.657713i \(0.228476\pi\)
\(48\) 0 0
\(49\) 7.00000 1.00000
\(50\) 0 0
\(51\) −1.32288 + 2.29129i −0.185240 + 0.320844i
\(52\) 0 0
\(53\) −3.50000 6.06218i −0.480762 0.832704i 0.518994 0.854778i \(-0.326307\pi\)
−0.999756 + 0.0220735i \(0.992973\pi\)
\(54\) 0 0
\(55\) 7.93725 1.07026
\(56\) 0 0
\(57\) −21.0000 −2.78152
\(58\) 0 0
\(59\) −1.32288 2.29129i −0.172224 0.298300i 0.766973 0.641679i \(-0.221762\pi\)
−0.939197 + 0.343379i \(0.888429\pi\)
\(60\) 0 0
\(61\) 2.50000 4.33013i 0.320092 0.554416i −0.660415 0.750901i \(-0.729619\pi\)
0.980507 + 0.196485i \(0.0629528\pi\)
\(62\) 0 0
\(63\) 5.29150 9.16515i 0.666667 1.15470i
\(64\) 0 0
\(65\) −6.00000 + 10.3923i −0.744208 + 1.28901i
\(66\) 0 0
\(67\) −1.32288 2.29129i −0.161615 0.279925i 0.773833 0.633390i \(-0.218337\pi\)
−0.935448 + 0.353464i \(0.885004\pi\)
\(68\) 0 0
\(69\) −7.00000 −0.842701
\(70\) 0 0
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 0 0
\(73\) 4.50000 + 7.79423i 0.526685 + 0.912245i 0.999517 + 0.0310925i \(0.00989865\pi\)
−0.472831 + 0.881153i \(0.656768\pi\)
\(74\) 0 0
\(75\) −5.29150 + 9.16515i −0.611010 + 1.05830i
\(76\) 0 0
\(77\) −3.50000 6.06218i −0.398862 0.690849i
\(78\) 0 0
\(79\) 1.32288 2.29129i 0.148835 0.257790i −0.781962 0.623326i \(-0.785781\pi\)
0.930797 + 0.365536i \(0.119114\pi\)
\(80\) 0 0
\(81\) 2.50000 + 4.33013i 0.277778 + 0.481125i
\(82\) 0 0
\(83\) −10.5830 −1.16164 −0.580818 0.814034i \(-0.697267\pi\)
−0.580818 + 0.814034i \(0.697267\pi\)
\(84\) 0 0
\(85\) −3.00000 −0.325396
\(86\) 0 0
\(87\) 5.29150 + 9.16515i 0.567309 + 0.982607i
\(88\) 0 0
\(89\) 4.50000 7.79423i 0.476999 0.826187i −0.522654 0.852545i \(-0.675058\pi\)
0.999653 + 0.0263586i \(0.00839118\pi\)
\(90\) 0 0
\(91\) 10.5830 1.10940
\(92\) 0 0
\(93\) 3.50000 6.06218i 0.362933 0.628619i
\(94\) 0 0
\(95\) −11.9059 20.6216i −1.22152 2.11573i
\(96\) 0 0
\(97\) −8.00000 −0.812277 −0.406138 0.913812i \(-0.633125\pi\)
−0.406138 + 0.913812i \(0.633125\pi\)
\(98\) 0 0
\(99\) −10.5830 −1.06363
\(100\) 0 0
\(101\) 7.50000 + 12.9904i 0.746278 + 1.29259i 0.949595 + 0.313478i \(0.101494\pi\)
−0.203317 + 0.979113i \(0.565172\pi\)
\(102\) 0 0
\(103\) 1.32288 2.29129i 0.130347 0.225767i −0.793463 0.608618i \(-0.791724\pi\)
0.923810 + 0.382851i \(0.125058\pi\)
\(104\) 0 0
\(105\) 21.0000 2.04939
\(106\) 0 0
\(107\) −6.61438 + 11.4564i −0.639436 + 1.10754i 0.346121 + 0.938190i \(0.387499\pi\)
−0.985557 + 0.169346i \(0.945835\pi\)
\(108\) 0 0
\(109\) −0.500000 0.866025i −0.0478913 0.0829502i 0.841086 0.540901i \(-0.181917\pi\)
−0.888977 + 0.457951i \(0.848583\pi\)
\(110\) 0 0
\(111\) −13.2288 −1.25562
\(112\) 0 0
\(113\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(114\) 0 0
\(115\) −3.96863 6.87386i −0.370076 0.640991i
\(116\) 0 0
\(117\) 8.00000 13.8564i 0.739600 1.28103i
\(118\) 0 0
\(119\) 1.32288 + 2.29129i 0.121268 + 0.210042i
\(120\) 0 0
\(121\) 2.00000 3.46410i 0.181818 0.314918i
\(122\) 0 0
\(123\) −10.5830 18.3303i −0.954237 1.65279i
\(124\) 0 0
\(125\) 3.00000 0.268328
\(126\) 0 0
\(127\) 21.1660 1.87818 0.939090 0.343672i \(-0.111671\pi\)
0.939090 + 0.343672i \(0.111671\pi\)
\(128\) 0 0
\(129\) −14.0000 24.2487i −1.23263 2.13498i
\(130\) 0 0
\(131\) −3.96863 + 6.87386i −0.346741 + 0.600572i −0.985668 0.168694i \(-0.946045\pi\)
0.638928 + 0.769267i \(0.279378\pi\)
\(132\) 0 0
\(133\) −10.5000 + 18.1865i −0.910465 + 1.57697i
\(134\) 0 0
\(135\) 3.96863 6.87386i 0.341565 0.591608i
\(136\) 0 0
\(137\) −0.500000 0.866025i −0.0427179 0.0739895i 0.843876 0.536538i \(-0.180268\pi\)
−0.886594 + 0.462549i \(0.846935\pi\)
\(138\) 0 0
\(139\) −10.5830 −0.897639 −0.448819 0.893622i \(-0.648155\pi\)
−0.448819 + 0.893622i \(0.648155\pi\)
\(140\) 0 0
\(141\) 7.00000 0.589506
\(142\) 0 0
\(143\) −5.29150 9.16515i −0.442498 0.766428i
\(144\) 0 0
\(145\) −6.00000 + 10.3923i −0.498273 + 0.863034i
\(146\) 0 0
\(147\) −9.26013 16.0390i −0.763763 1.32288i
\(148\) 0 0
\(149\) −10.5000 + 18.1865i −0.860194 + 1.48990i 0.0115483 + 0.999933i \(0.496324\pi\)
−0.871742 + 0.489966i \(0.837009\pi\)
\(150\) 0 0
\(151\) 1.32288 + 2.29129i 0.107654 + 0.186462i 0.914819 0.403863i \(-0.132333\pi\)
−0.807165 + 0.590325i \(0.798999\pi\)
\(152\) 0 0
\(153\) 4.00000 0.323381
\(154\) 0 0
\(155\) 7.93725 0.637536
\(156\) 0 0
\(157\) 4.50000 + 7.79423i 0.359139 + 0.622047i 0.987817 0.155618i \(-0.0497370\pi\)
−0.628678 + 0.777666i \(0.716404\pi\)
\(158\) 0 0
\(159\) −9.26013 + 16.0390i −0.734376 + 1.27198i
\(160\) 0 0
\(161\) −3.50000 + 6.06218i −0.275839 + 0.477767i
\(162\) 0 0
\(163\) 6.61438 11.4564i 0.518078 0.897338i −0.481701 0.876335i \(-0.659981\pi\)
0.999779 0.0210021i \(-0.00668568\pi\)
\(164\) 0 0
\(165\) −10.5000 18.1865i −0.817424 1.41582i
\(166\) 0 0
\(167\) 5.29150 0.409469 0.204734 0.978818i \(-0.434367\pi\)
0.204734 + 0.978818i \(0.434367\pi\)
\(168\) 0 0
\(169\) 3.00000 0.230769
\(170\) 0 0
\(171\) 15.8745 + 27.4955i 1.21395 + 2.10263i
\(172\) 0 0
\(173\) −1.50000 + 2.59808i −0.114043 + 0.197528i −0.917397 0.397974i \(-0.869713\pi\)
0.803354 + 0.595502i \(0.203047\pi\)
\(174\) 0 0
\(175\) 5.29150 + 9.16515i 0.400000 + 0.692820i
\(176\) 0 0
\(177\) −3.50000 + 6.06218i −0.263076 + 0.455661i
\(178\) 0 0
\(179\) 11.9059 + 20.6216i 0.889887 + 1.54133i 0.840007 + 0.542575i \(0.182551\pi\)
0.0498798 + 0.998755i \(0.484116\pi\)
\(180\) 0 0
\(181\) −6.00000 −0.445976 −0.222988 0.974821i \(-0.571581\pi\)
−0.222988 + 0.974821i \(0.571581\pi\)
\(182\) 0 0
\(183\) −13.2288 −0.977898
\(184\) 0 0
\(185\) −7.50000 12.9904i −0.551411 0.955072i
\(186\) 0 0
\(187\) 1.32288 2.29129i 0.0967382 0.167556i
\(188\) 0 0
\(189\) −7.00000 −0.509175
\(190\) 0 0
\(191\) −11.9059 + 20.6216i −0.861479 + 1.49213i 0.00902170 + 0.999959i \(0.497128\pi\)
−0.870501 + 0.492167i \(0.836205\pi\)
\(192\) 0 0
\(193\) 3.50000 + 6.06218i 0.251936 + 0.436365i 0.964059 0.265689i \(-0.0855996\pi\)
−0.712123 + 0.702055i \(0.752266\pi\)
\(194\) 0 0
\(195\) 31.7490 2.27359
\(196\) 0 0
\(197\) 12.0000 0.854965 0.427482 0.904024i \(-0.359401\pi\)
0.427482 + 0.904024i \(0.359401\pi\)
\(198\) 0 0
\(199\) −9.26013 16.0390i −0.656433 1.13698i −0.981532 0.191296i \(-0.938731\pi\)
0.325099 0.945680i \(-0.394602\pi\)
\(200\) 0 0
\(201\) −3.50000 + 6.06218i −0.246871 + 0.427593i
\(202\) 0 0
\(203\) 10.5830 0.742781
\(204\) 0 0
\(205\) 12.0000 20.7846i 0.838116 1.45166i
\(206\) 0 0
\(207\) 5.29150 + 9.16515i 0.367785 + 0.637022i
\(208\) 0 0
\(209\) 21.0000 1.45260
\(210\) 0 0
\(211\) −10.5830 −0.728564 −0.364282 0.931289i \(-0.618686\pi\)
−0.364282 + 0.931289i \(0.618686\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 15.8745 27.4955i 1.08263 1.87517i
\(216\) 0 0
\(217\) −3.50000 6.06218i −0.237595 0.411527i
\(218\) 0 0
\(219\) 11.9059 20.6216i 0.804525 1.39348i
\(220\) 0 0
\(221\) 2.00000 + 3.46410i 0.134535 + 0.233021i
\(222\) 0 0
\(223\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(224\) 0 0
\(225\) 16.0000 1.06667
\(226\) 0 0
\(227\) 1.32288 + 2.29129i 0.0878023 + 0.152078i 0.906582 0.422030i \(-0.138682\pi\)
−0.818780 + 0.574108i \(0.805349\pi\)
\(228\) 0 0
\(229\) 5.50000 9.52628i 0.363450 0.629514i −0.625076 0.780564i \(-0.714932\pi\)
0.988526 + 0.151050i \(0.0482653\pi\)
\(230\) 0 0
\(231\) −9.26013 + 16.0390i −0.609272 + 1.05529i
\(232\) 0 0
\(233\) −4.50000 + 7.79423i −0.294805 + 0.510617i −0.974939 0.222470i \(-0.928588\pi\)
0.680135 + 0.733087i \(0.261921\pi\)
\(234\) 0 0
\(235\) 3.96863 + 6.87386i 0.258885 + 0.448401i
\(236\) 0 0
\(237\) −7.00000 −0.454699
\(238\) 0 0
\(239\) 15.8745 1.02684 0.513418 0.858138i \(-0.328379\pi\)
0.513418 + 0.858138i \(0.328379\pi\)
\(240\) 0 0
\(241\) 0.500000 + 0.866025i 0.0322078 + 0.0557856i 0.881680 0.471848i \(-0.156413\pi\)
−0.849472 + 0.527633i \(0.823079\pi\)
\(242\) 0 0
\(243\) 10.5830 18.3303i 0.678900 1.17589i
\(244\) 0 0
\(245\) 10.5000 18.1865i 0.670820 1.16190i
\(246\) 0 0
\(247\) −15.8745 + 27.4955i −1.01007 + 1.74949i
\(248\) 0 0
\(249\) 14.0000 + 24.2487i 0.887214 + 1.53670i
\(250\) 0 0
\(251\) 5.29150 0.333997 0.166998 0.985957i \(-0.446593\pi\)
0.166998 + 0.985957i \(0.446593\pi\)
\(252\) 0 0
\(253\) 7.00000 0.440086
\(254\) 0 0
\(255\) 3.96863 + 6.87386i 0.248525 + 0.430458i
\(256\) 0 0
\(257\) −8.50000 + 14.7224i −0.530215 + 0.918360i 0.469163 + 0.883112i \(0.344556\pi\)
−0.999379 + 0.0352486i \(0.988778\pi\)
\(258\) 0 0
\(259\) −6.61438 + 11.4564i −0.410997 + 0.711868i
\(260\) 0 0
\(261\) 8.00000 13.8564i 0.495188 0.857690i
\(262\) 0 0
\(263\) 9.26013 + 16.0390i 0.571004 + 0.989008i 0.996463 + 0.0840304i \(0.0267793\pi\)
−0.425459 + 0.904978i \(0.639887\pi\)
\(264\) 0 0
\(265\) −21.0000 −1.29002
\(266\) 0 0
\(267\) −23.8118 −1.45726
\(268\) 0 0
\(269\) −7.50000 12.9904i −0.457283 0.792038i 0.541533 0.840679i \(-0.317844\pi\)
−0.998816 + 0.0486418i \(0.984511\pi\)
\(270\) 0 0
\(271\) 1.32288 2.29129i 0.0803590 0.139186i −0.823045 0.567976i \(-0.807727\pi\)
0.903404 + 0.428790i \(0.141060\pi\)
\(272\) 0 0
\(273\) −14.0000 24.2487i −0.847319 1.46760i
\(274\) 0 0
\(275\) 5.29150 9.16515i 0.319090 0.552679i
\(276\) 0 0
\(277\) 12.5000 + 21.6506i 0.751052 + 1.30086i 0.947313 + 0.320309i \(0.103787\pi\)
−0.196261 + 0.980552i \(0.562880\pi\)
\(278\) 0 0
\(279\) −10.5830 −0.633588
\(280\) 0 0
\(281\) −24.0000 −1.43172 −0.715860 0.698244i \(-0.753965\pi\)
−0.715860 + 0.698244i \(0.753965\pi\)
\(282\) 0 0
\(283\) −9.26013 16.0390i −0.550458 0.953420i −0.998241 0.0592787i \(-0.981120\pi\)
0.447784 0.894142i \(-0.352213\pi\)
\(284\) 0 0
\(285\) −31.5000 + 54.5596i −1.86590 + 3.23183i
\(286\) 0 0
\(287\) −21.1660 −1.24939
\(288\) 0 0
\(289\) 8.00000 13.8564i 0.470588 0.815083i
\(290\) 0 0
\(291\) 10.5830 + 18.3303i 0.620387 + 1.07454i
\(292\) 0 0
\(293\) −10.0000 −0.584206 −0.292103 0.956387i \(-0.594355\pi\)
−0.292103 + 0.956387i \(0.594355\pi\)
\(294\) 0 0
\(295\) −7.93725 −0.462125
\(296\) 0 0
\(297\) 3.50000 + 6.06218i 0.203091 + 0.351763i
\(298\) 0 0
\(299\) −5.29150 + 9.16515i −0.306015 + 0.530034i
\(300\) 0 0
\(301\) −28.0000 −1.61389
\(302\) 0 0
\(303\) 19.8431 34.3693i 1.13996 1.97447i
\(304\) 0 0
\(305\) −7.50000 12.9904i −0.429449 0.743827i
\(306\) 0 0
\(307\) 10.5830 0.604004 0.302002 0.953307i \(-0.402345\pi\)
0.302002 + 0.953307i \(0.402345\pi\)
\(308\) 0 0
\(309\) −7.00000 −0.398216
\(310\) 0 0
\(311\) −11.9059 20.6216i −0.675121 1.16934i −0.976434 0.215818i \(-0.930758\pi\)
0.301313 0.953525i \(-0.402575\pi\)
\(312\) 0 0
\(313\) 8.50000 14.7224i 0.480448 0.832161i −0.519300 0.854592i \(-0.673807\pi\)
0.999748 + 0.0224310i \(0.00714060\pi\)
\(314\) 0 0
\(315\) −15.8745 27.4955i −0.894427 1.54919i
\(316\) 0 0
\(317\) 6.50000 11.2583i 0.365076 0.632331i −0.623712 0.781654i \(-0.714376\pi\)
0.988788 + 0.149323i \(0.0477095\pi\)
\(318\) 0 0
\(319\) −5.29150 9.16515i −0.296267 0.513150i
\(320\) 0 0
\(321\) 35.0000 1.95351
\(322\) 0 0
\(323\) −7.93725 −0.441641
\(324\) 0 0
\(325\) 8.00000 + 13.8564i 0.443760 + 0.768615i
\(326\) 0 0
\(327\) −1.32288 + 2.29129i −0.0731552 + 0.126709i
\(328\) 0 0
\(329\) 3.50000 6.06218i 0.192961 0.334219i
\(330\) 0 0
\(331\) −3.96863 + 6.87386i −0.218135 + 0.377822i −0.954238 0.299048i \(-0.903331\pi\)
0.736102 + 0.676870i \(0.236664\pi\)
\(332\) 0 0
\(333\) 10.0000 + 17.3205i 0.547997 + 0.949158i
\(334\) 0 0
\(335\) −7.93725 −0.433659
\(336\) 0 0
\(337\) 24.0000 1.30736 0.653682 0.756770i \(-0.273224\pi\)
0.653682 + 0.756770i \(0.273224\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −3.50000 + 6.06218i −0.189536 + 0.328285i
\(342\) 0 0
\(343\) −18.5203 −1.00000
\(344\) 0 0
\(345\) −10.5000 + 18.1865i −0.565301 + 0.979130i
\(346\) 0 0
\(347\) −11.9059 20.6216i −0.639141 1.10702i −0.985622 0.168968i \(-0.945957\pi\)
0.346480 0.938057i \(-0.387377\pi\)
\(348\) 0 0
\(349\) 20.0000 1.07058 0.535288 0.844670i \(-0.320203\pi\)
0.535288 + 0.844670i \(0.320203\pi\)
\(350\) 0 0
\(351\) −10.5830 −0.564879
\(352\) 0 0
\(353\) −4.50000 7.79423i −0.239511 0.414845i 0.721063 0.692869i \(-0.243654\pi\)
−0.960574 + 0.278024i \(0.910320\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 3.50000 6.06218i 0.185240 0.320844i
\(358\) 0 0
\(359\) 9.26013 16.0390i 0.488731 0.846507i −0.511185 0.859471i \(-0.670793\pi\)
0.999916 + 0.0129639i \(0.00412664\pi\)
\(360\) 0 0
\(361\) −22.0000 38.1051i −1.15789 2.00553i
\(362\) 0 0
\(363\) −10.5830 −0.555464
\(364\) 0 0
\(365\) 27.0000 1.41324
\(366\) 0 0
\(367\) 9.26013 + 16.0390i 0.483375 + 0.837230i 0.999818 0.0190919i \(-0.00607750\pi\)
−0.516443 + 0.856322i \(0.672744\pi\)
\(368\) 0 0
\(369\) −16.0000 + 27.7128i −0.832927 + 1.44267i
\(370\) 0 0
\(371\) 9.26013 + 16.0390i 0.480762 + 0.832704i
\(372\) 0 0
\(373\) 10.5000 18.1865i 0.543669 0.941663i −0.455020 0.890481i \(-0.650368\pi\)
0.998689 0.0511818i \(-0.0162988\pi\)
\(374\) 0 0
\(375\) −3.96863 6.87386i −0.204939 0.354965i
\(376\) 0 0
\(377\) 16.0000 0.824042
\(378\) 0 0
\(379\) −5.29150 −0.271806 −0.135903 0.990722i \(-0.543394\pi\)
−0.135903 + 0.990722i \(0.543394\pi\)
\(380\) 0 0
\(381\) −28.0000 48.4974i −1.43448 2.48460i
\(382\) 0 0
\(383\) 9.26013 16.0390i 0.473171 0.819555i −0.526358 0.850263i \(-0.676443\pi\)
0.999528 + 0.0307077i \(0.00977611\pi\)
\(384\) 0 0
\(385\) −21.0000 −1.07026
\(386\) 0 0
\(387\) −21.1660 + 36.6606i −1.07593 + 1.86356i
\(388\) 0 0
\(389\) 7.50000 + 12.9904i 0.380265 + 0.658638i 0.991100 0.133120i \(-0.0424994\pi\)
−0.610835 + 0.791758i \(0.709166\pi\)
\(390\) 0 0
\(391\) −2.64575 −0.133801
\(392\) 0 0
\(393\) 21.0000 1.05931
\(394\) 0 0
\(395\) −3.96863 6.87386i −0.199683 0.345862i
\(396\) 0 0
\(397\) −2.50000 + 4.33013i −0.125471 + 0.217323i −0.921917 0.387387i \(-0.873378\pi\)
0.796446 + 0.604710i \(0.206711\pi\)
\(398\) 0 0
\(399\) 55.5608 2.78152
\(400\) 0 0
\(401\) 11.5000 19.9186i 0.574283 0.994687i −0.421837 0.906672i \(-0.638614\pi\)
0.996119 0.0880147i \(-0.0280523\pi\)
\(402\) 0 0
\(403\) −5.29150 9.16515i −0.263589 0.456549i
\(404\) 0 0
\(405\) 15.0000 0.745356
\(406\) 0 0
\(407\) 13.2288 0.655725
\(408\) 0 0
\(409\) 11.5000 + 19.9186i 0.568638 + 0.984911i 0.996701 + 0.0811615i \(0.0258630\pi\)
−0.428063 + 0.903749i \(0.640804\pi\)
\(410\) 0 0
\(411\) −1.32288 + 2.29129i −0.0652526 + 0.113021i
\(412\) 0 0
\(413\) 3.50000 + 6.06218i 0.172224 + 0.298300i
\(414\) 0 0
\(415\) −15.8745 + 27.4955i −0.779249 + 1.34970i
\(416\) 0 0
\(417\) 14.0000 + 24.2487i 0.685583 + 1.18746i
\(418\) 0 0
\(419\) −31.7490 −1.55104 −0.775520 0.631322i \(-0.782512\pi\)
−0.775520 + 0.631322i \(0.782512\pi\)
\(420\) 0 0
\(421\) −12.0000 −0.584844 −0.292422 0.956289i \(-0.594461\pi\)
−0.292422 + 0.956289i \(0.594461\pi\)
\(422\) 0 0
\(423\) −5.29150 9.16515i −0.257282 0.445625i
\(424\) 0 0
\(425\) −2.00000 + 3.46410i −0.0970143 + 0.168034i
\(426\) 0 0
\(427\) −6.61438 + 11.4564i −0.320092 + 0.554416i
\(428\) 0 0
\(429\) −14.0000 + 24.2487i −0.675926 + 1.17074i
\(430\) 0 0
\(431\) 1.32288 + 2.29129i 0.0637207 + 0.110367i 0.896126 0.443800i \(-0.146370\pi\)
−0.832405 + 0.554168i \(0.813037\pi\)
\(432\) 0 0
\(433\) −32.0000 −1.53782 −0.768911 0.639356i \(-0.779201\pi\)
−0.768911 + 0.639356i \(0.779201\pi\)
\(434\) 0 0
\(435\) 31.7490 1.52225
\(436\) 0 0
\(437\) −10.5000 18.1865i −0.502283 0.869980i
\(438\) 0 0
\(439\) −11.9059 + 20.6216i −0.568237 + 0.984215i 0.428504 + 0.903540i \(0.359041\pi\)
−0.996740 + 0.0806748i \(0.974292\pi\)
\(440\) 0 0
\(441\) −14.0000 + 24.2487i −0.666667 + 1.15470i
\(442\) 0 0
\(443\) 3.96863 6.87386i 0.188555 0.326587i −0.756214 0.654325i \(-0.772953\pi\)
0.944769 + 0.327738i \(0.106286\pi\)
\(444\) 0 0
\(445\) −13.5000 23.3827i −0.639961 1.10845i
\(446\) 0 0
\(447\) 55.5608 2.62793
\(448\) 0 0
\(449\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(450\) 0 0
\(451\) 10.5830 + 18.3303i 0.498334 + 0.863140i
\(452\) 0 0
\(453\) 3.50000 6.06218i 0.164444 0.284826i
\(454\) 0 0
\(455\) 15.8745 27.4955i 0.744208 1.28901i
\(456\) 0 0
\(457\) −3.50000 + 6.06218i −0.163723 + 0.283577i −0.936201 0.351465i \(-0.885684\pi\)
0.772478 + 0.635042i \(0.219017\pi\)
\(458\) 0 0
\(459\) −1.32288 2.29129i −0.0617465 0.106948i
\(460\) 0 0
\(461\) −20.0000 −0.931493 −0.465746 0.884918i \(-0.654214\pi\)
−0.465746 + 0.884918i \(0.654214\pi\)
\(462\) 0 0
\(463\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(464\) 0 0
\(465\) −10.5000 18.1865i −0.486926 0.843380i
\(466\) 0 0
\(467\) −3.96863 + 6.87386i −0.183646 + 0.318084i −0.943119 0.332454i \(-0.892123\pi\)
0.759473 + 0.650538i \(0.225457\pi\)
\(468\) 0 0
\(469\) 3.50000 + 6.06218i 0.161615 + 0.279925i
\(470\) 0 0
\(471\) 11.9059 20.6216i 0.548594 0.950193i
\(472\) 0 0
\(473\) 14.0000 + 24.2487i 0.643721 + 1.11496i
\(474\) 0 0
\(475\) −31.7490 −1.45674
\(476\) 0 0
\(477\) 28.0000 1.28203
\(478\) 0 0
\(479\) 19.8431 + 34.3693i 0.906656 + 1.57037i 0.818679 + 0.574252i \(0.194707\pi\)
0.0879772 + 0.996122i \(0.471960\pi\)
\(480\) 0 0
\(481\) −10.0000 + 17.3205i −0.455961 + 0.789747i
\(482\) 0 0
\(483\) 18.5203 0.842701
\(484\) 0 0
\(485\) −12.0000 + 20.7846i −0.544892 + 0.943781i
\(486\) 0 0
\(487\) −11.9059 20.6216i −0.539507 0.934453i −0.998931 0.0462362i \(-0.985277\pi\)
0.459424 0.888217i \(-0.348056\pi\)
\(488\) 0 0
\(489\) −35.0000 −1.58275
\(490\) 0 0
\(491\) 37.0405 1.67162 0.835808 0.549022i \(-0.185000\pi\)
0.835808 + 0.549022i \(0.185000\pi\)
\(492\) 0 0
\(493\) 2.00000 + 3.46410i 0.0900755 + 0.156015i
\(494\) 0 0
\(495\) −15.8745 + 27.4955i −0.713506 + 1.23583i
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 6.61438 11.4564i 0.296100 0.512861i −0.679140 0.734009i \(-0.737647\pi\)
0.975240 + 0.221148i \(0.0709804\pi\)
\(500\) 0 0
\(501\) −7.00000 12.1244i −0.312737 0.541676i
\(502\) 0 0
\(503\) 21.1660 0.943746 0.471873 0.881667i \(-0.343578\pi\)
0.471873 + 0.881667i \(0.343578\pi\)
\(504\) 0 0
\(505\) 45.0000 2.00247
\(506\) 0 0
\(507\) −3.96863 6.87386i −0.176253 0.305279i
\(508\) 0 0
\(509\) 9.50000 16.4545i 0.421080 0.729332i −0.574965 0.818178i \(-0.694984\pi\)
0.996045 + 0.0888457i \(0.0283178\pi\)
\(510\) 0 0
\(511\) −11.9059 20.6216i −0.526685 0.912245i
\(512\) 0 0
\(513\) 10.5000 18.1865i 0.463586 0.802955i
\(514\) 0 0
\(515\) −3.96863 6.87386i −0.174879 0.302899i
\(516\) 0 0
\(517\) −7.00000 −0.307860
\(518\) 0 0
\(519\) 7.93725 0.348407
\(520\) 0 0
\(521\) −11.5000 19.9186i −0.503824 0.872649i −0.999990 0.00442139i \(-0.998593\pi\)
0.496166 0.868228i \(-0.334741\pi\)
\(522\) 0 0
\(523\) −17.1974 + 29.7867i −0.751989 + 1.30248i 0.194868 + 0.980829i \(0.437572\pi\)
−0.946857 + 0.321654i \(0.895761\pi\)
\(524\) 0 0
\(525\) 14.0000 24.2487i 0.611010 1.05830i
\(526\) 0 0
\(527\) 1.32288 2.29129i 0.0576254 0.0998101i
\(528\) 0 0
\(529\) 8.00000 + 13.8564i 0.347826 + 0.602452i
\(530\) 0 0
\(531\) 10.5830 0.459263
\(532\) 0 0
\(533\) −32.0000 −1.38607
\(534\) 0 0
\(535\) 19.8431 + 34.3693i 0.857894 + 1.48592i
\(536\) 0 0
\(537\) 31.5000 54.5596i 1.35933 2.35442i
\(538\) 0 0
\(539\) 9.26013 + 16.0390i 0.398862 + 0.690849i
\(540\) 0 0
\(541\) −10.5000 + 18.1865i −0.451430 + 0.781900i −0.998475 0.0552031i \(-0.982419\pi\)
0.547045 + 0.837103i \(0.315753\pi\)
\(542\) 0 0
\(543\) 7.93725 + 13.7477i 0.340620 + 0.589971i
\(544\) 0 0
\(545\) −3.00000 −0.128506
\(546\) 0 0
\(547\) 26.4575 1.13124 0.565621 0.824665i \(-0.308637\pi\)
0.565621 + 0.824665i \(0.308637\pi\)
\(548\) 0 0
\(549\) 10.0000 + 17.3205i 0.426790 + 0.739221i
\(550\) 0 0
\(551\) −15.8745 + 27.4955i −0.676277 + 1.17135i
\(552\) 0 0
\(553\) −3.50000 + 6.06218i −0.148835 + 0.257790i
\(554\) 0 0
\(555\) −19.8431 + 34.3693i −0.842294 + 1.45890i
\(556\) 0 0
\(557\) 19.5000 + 33.7750i 0.826242 + 1.43109i 0.900967 + 0.433888i \(0.142859\pi\)
−0.0747252 + 0.997204i \(0.523808\pi\)
\(558\) 0 0
\(559\) −42.3320 −1.79045
\(560\) 0 0
\(561\) −7.00000 −0.295540
\(562\) 0 0
\(563\) −1.32288 2.29129i −0.0557526 0.0965663i 0.836802 0.547505i \(-0.184422\pi\)
−0.892555 + 0.450939i \(0.851089\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −6.61438 11.4564i −0.277778 0.481125i
\(568\) 0 0
\(569\) 16.5000 28.5788i 0.691716 1.19809i −0.279559 0.960128i \(-0.590188\pi\)
0.971275 0.237959i \(-0.0764783\pi\)
\(570\) 0 0
\(571\) 1.32288 + 2.29129i 0.0553606 + 0.0958874i 0.892378 0.451290i \(-0.149036\pi\)
−0.837017 + 0.547177i \(0.815702\pi\)
\(572\) 0 0
\(573\) 63.0000 2.63186
\(574\) 0 0
\(575\) −10.5830 −0.441342
\(576\) 0 0
\(577\) 20.5000 + 35.5070i 0.853426 + 1.47818i 0.878097 + 0.478482i \(0.158813\pi\)
−0.0246713 + 0.999696i \(0.507854\pi\)
\(578\) 0 0
\(579\) 9.26013 16.0390i 0.384838 0.666559i
\(580\) 0 0
\(581\) 28.0000 1.16164
\(582\) 0 0
\(583\) 9.26013 16.0390i 0.383515 0.664268i
\(584\) 0 0
\(585\) −24.0000 41.5692i −0.992278 1.71868i
\(586\) 0 0
\(587\) 31.7490 1.31042 0.655211 0.755446i \(-0.272580\pi\)
0.655211 + 0.755446i \(0.272580\pi\)
\(588\) 0 0
\(589\) 21.0000 0.865290
\(590\) 0 0
\(591\) −15.8745 27.4955i −0.652990 1.13101i
\(592\) 0 0
\(593\) −16.5000 + 28.5788i −0.677574 + 1.17359i 0.298136 + 0.954524i \(0.403635\pi\)
−0.975709 + 0.219069i \(0.929698\pi\)
\(594\) 0 0
\(595\) 7.93725 0.325396
\(596\) 0 0
\(597\) −24.5000 + 42.4352i −1.00272 + 1.73676i
\(598\) 0 0
\(599\) −11.9059 20.6216i −0.486461 0.842575i 0.513418 0.858139i \(-0.328379\pi\)
−0.999879 + 0.0155634i \(0.995046\pi\)
\(600\) 0 0
\(601\) 8.00000 0.326327 0.163163 0.986599i \(-0.447830\pi\)
0.163163 + 0.986599i \(0.447830\pi\)
\(602\) 0 0
\(603\) 10.5830 0.430973
\(604\) 0 0
\(605\) −6.00000 10.3923i −0.243935 0.422507i
\(606\) 0 0
\(607\) 19.8431 34.3693i 0.805408 1.39501i −0.110607 0.993864i \(-0.535280\pi\)
0.916015 0.401143i \(-0.131387\pi\)
\(608\) 0 0
\(609\) −14.0000 24.2487i −0.567309 0.982607i
\(610\) 0 0
\(611\) 5.29150 9.16515i 0.214071 0.370782i
\(612\) 0 0
\(613\) −20.5000 35.5070i −0.827987 1.43412i −0.899615 0.436684i \(-0.856153\pi\)
0.0716275 0.997431i \(-0.477181\pi\)
\(614\) 0 0
\(615\) −63.4980 −2.56049
\(616\) 0 0
\(617\) −32.0000 −1.28827 −0.644136 0.764911i \(-0.722783\pi\)
−0.644136 + 0.764911i \(0.722783\pi\)
\(618\) 0 0
\(619\) −22.4889 38.9519i −0.903905 1.56561i −0.822381 0.568937i \(-0.807355\pi\)
−0.0815238 0.996671i \(-0.525979\pi\)
\(620\) 0 0
\(621\) 3.50000 6.06218i 0.140450 0.243267i
\(622\) 0 0
\(623\) −11.9059 + 20.6216i −0.476999 + 0.826187i
\(624\) 0 0
\(625\) 14.5000 25.1147i 0.580000 1.00459i
\(626\) 0 0
\(627\) −27.7804 48.1170i −1.10944 1.92161i
\(628\) 0 0
\(629\) −5.00000 −0.199363
\(630\) 0 0
\(631\) −42.3320 −1.68521 −0.842606 0.538531i \(-0.818979\pi\)
−0.842606 + 0.538531i \(0.818979\pi\)
\(632\) 0 0
\(633\) 14.0000 + 24.2487i 0.556450 + 0.963800i
\(634\) 0 0
\(635\) 31.7490 54.9909i 1.25992 2.18225i
\(636\) 0 0
\(637\) −28.0000 −1.10940
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 0.500000 + 0.866025i 0.0197488 + 0.0342059i 0.875731 0.482800i \(-0.160380\pi\)
−0.855982 + 0.517005i \(0.827047\pi\)
\(642\) 0 0
\(643\) −10.5830 −0.417353 −0.208676 0.977985i \(-0.566916\pi\)
−0.208676 + 0.977985i \(0.566916\pi\)
\(644\) 0 0
\(645\) −84.0000 −3.30750
\(646\) 0 0
\(647\) 19.8431 + 34.3693i 0.780114 + 1.35120i 0.931875 + 0.362780i \(0.118172\pi\)
−0.151761 + 0.988417i \(0.548494\pi\)
\(648\) 0 0
\(649\) 3.50000 6.06218i 0.137387 0.237961i
\(650\) 0 0
\(651\) −9.26013 + 16.0390i −0.362933 + 0.628619i
\(652\) 0 0
\(653\) −9.50000 + 16.4545i −0.371764 + 0.643914i −0.989837 0.142207i \(-0.954580\pi\)
0.618073 + 0.786121i \(0.287914\pi\)
\(654\) 0 0
\(655\) 11.9059 + 20.6216i 0.465201 + 0.805752i
\(656\) 0 0
\(657\) −36.0000 −1.40449
\(658\) 0 0
\(659\) −31.7490 −1.23677 −0.618383 0.785877i \(-0.712212\pi\)
−0.618383 + 0.785877i \(0.712212\pi\)
\(660\) 0 0
\(661\) 16.5000 + 28.5788i 0.641776 + 1.11159i 0.985036 + 0.172348i \(0.0551353\pi\)
−0.343261 + 0.939240i \(0.611531\pi\)
\(662\) 0 0
\(663\) 5.29150 9.16515i 0.205505 0.355945i
\(664\) 0 0
\(665\) 31.5000 + 54.5596i 1.22152 + 2.11573i
\(666\) 0 0
\(667\) −5.29150 + 9.16515i −0.204888 + 0.354876i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 13.2288 0.510690
\(672\) 0 0
\(673\) −24.0000 −0.925132 −0.462566 0.886585i \(-0.653071\pi\)
−0.462566 + 0.886585i \(0.653071\pi\)
\(674\) 0 0
\(675\) −5.29150 9.16515i −0.203670 0.352767i
\(676\) 0 0
\(677\) 1.50000 2.59808i 0.0576497 0.0998522i −0.835760 0.549095i \(-0.814973\pi\)
0.893410 + 0.449242i \(0.148306\pi\)
\(678\) 0 0
\(679\) 21.1660 0.812277
\(680\) 0 0
\(681\) 3.50000 6.06218i 0.134120 0.232303i
\(682\) 0 0
\(683\) 11.9059 + 20.6216i 0.455566 + 0.789063i 0.998721 0.0505694i \(-0.0161036\pi\)
−0.543155 + 0.839633i \(0.682770\pi\)
\(684\) 0 0
\(685\) −3.00000 −0.114624
\(686\) 0 0
\(687\) −29.1033 −1.11036
\(688\) 0 0
\(689\) 14.0000 + 24.2487i 0.533358 + 0.923802i
\(690\) 0 0
\(691\) −14.5516 + 25.2042i −0.553570 + 0.958812i 0.444443 + 0.895807i \(0.353402\pi\)
−0.998013 + 0.0630046i \(0.979932\pi\)
\(692\) 0 0
\(693\) 28.0000 1.06363
\(694\) 0 0
\(695\) −15.8745 + 27.4955i −0.602154 + 1.04296i
\(696\) 0 0
\(697\) −4.00000 6.92820i −0.151511 0.262424i
\(698\) 0 0
\(699\) 23.8118 0.900644
\(700\) 0 0
\(701\) −18.0000 −0.679851 −0.339925 0.940452i \(-0.610402\pi\)
−0.339925 + 0.940452i \(0.610402\pi\)
\(702\) 0 0
\(703\) −19.8431 34.3693i −0.748398 1.29626i
\(704\) 0 0
\(705\) 10.5000 18.1865i 0.395453 0.684944i
\(706\) 0 0
\(707\) −19.8431 34.3693i −0.746278 1.29259i
\(708\) 0 0
\(709\) 18.5000 32.0429i 0.694782 1.20340i −0.275472 0.961309i \(-0.588834\pi\)
0.970254 0.242089i \(-0.0778325\pi\)
\(710\) 0 0
\(711\) 5.29150 + 9.16515i 0.198447 + 0.343720i
\(712\) 0 0
\(713\) 7.00000 0.262152
\(714\) 0 0
\(715\) −31.7490 −1.18735
\(716\) 0 0
\(717\) −21.0000 36.3731i −0.784259 1.35838i
\(718\) 0 0
\(719\) −19.8431 + 34.3693i −0.740024 + 1.28176i 0.212460 + 0.977170i \(0.431853\pi\)
−0.952484 + 0.304589i \(0.901481\pi\)
\(720\) 0 0
\(721\) −3.50000 + 6.06218i −0.130347 + 0.225767i
\(722\) 0 0
\(723\) 1.32288 2.29129i 0.0491983 0.0852139i
\(724\) 0 0
\(725\) 8.00000 + 13.8564i 0.297113 + 0.514614i
\(726\) 0 0
\(727\) 42.3320 1.57001 0.785004 0.619491i \(-0.212661\pi\)
0.785004 + 0.619491i \(0.212661\pi\)
\(728\) 0 0
\(729\) −41.0000 −1.51852
\(730\) 0 0
\(731\) −5.29150 9.16515i −0.195713 0.338985i
\(732\) 0 0
\(733\) −5.50000 + 9.52628i −0.203147 + 0.351861i −0.949541 0.313644i \(-0.898450\pi\)
0.746394 + 0.665505i \(0.231784\pi\)
\(734\) 0 0
\(735\) −55.5608 −2.04939
\(736\) 0 0
\(737\) 3.50000 6.06218i 0.128924 0.223303i
\(738\) 0 0
\(739\) 22.4889 + 38.9519i 0.827267 + 1.43287i 0.900174 + 0.435530i \(0.143439\pi\)
−0.0729072 + 0.997339i \(0.523228\pi\)
\(740\) 0 0
\(741\) 84.0000 3.08582
\(742\) 0 0
\(743\) −21.1660 −0.776506 −0.388253 0.921553i \(-0.626921\pi\)
−0.388253 + 0.921553i \(0.626921\pi\)
\(744\) 0 0
\(745\) 31.5000 + 54.5596i 1.15407 + 1.99891i
\(746\) 0 0
\(747\) 21.1660 36.6606i 0.774424 1.34134i
\(748\) 0 0
\(749\) 17.5000 30.3109i 0.639436 1.10754i
\(750\) 0 0
\(751\) 19.8431 34.3693i 0.724086 1.25415i −0.235263 0.971932i \(-0.575595\pi\)
0.959349 0.282222i \(-0.0910716\pi\)
\(752\) 0 0
\(753\) −7.00000 12.1244i −0.255094 0.441836i
\(754\) 0 0
\(755\) 7.93725 0.288866
\(756\) 0 0
\(757\) 4.00000 0.145382 0.0726912 0.997354i \(-0.476841\pi\)
0.0726912 + 0.997354i \(0.476841\pi\)
\(758\) 0 0
\(759\) −9.26013 16.0390i −0.336121 0.582179i
\(760\) 0 0
\(761\) −4.50000 + 7.79423i −0.163125 + 0.282541i −0.935988 0.352032i \(-0.885491\pi\)
0.772863 + 0.634573i \(0.218824\pi\)
\(762\) 0 0
\(763\) 1.32288 + 2.29129i 0.0478913 + 0.0829502i
\(764\) 0 0
\(765\) 6.00000 10.3923i 0.216930 0.375735i
\(766\) 0 0
\(767\) 5.29150 + 9.16515i 0.191065 + 0.330934i
\(768\) 0 0
\(769\) −24.0000 −0.865462 −0.432731 0.901523i \(-0.642450\pi\)
−0.432731 + 0.901523i \(0.642450\pi\)
\(770\) 0 0
\(771\) 44.9778 1.61983
\(772\) 0 0
\(773\) −16.5000 28.5788i −0.593464 1.02791i −0.993762 0.111524i \(-0.964427\pi\)
0.400298 0.916385i \(-0.368907\pi\)
\(774\) 0 0
\(775\) 5.29150 9.16515i 0.190076 0.329222i
\(776\) 0 0
\(777\) 35.0000 1.25562
\(778\) 0 0
\(779\) 31.7490 54.9909i 1.13753 1.97025i
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) −10.5830 −0.378206
\(784\) 0 0
\(785\) 27.0000 0.963671
\(786\) 0 0
\(787\) 9.26013 + 16.0390i 0.330088 + 0.571729i 0.982529 0.186111i \(-0.0595882\pi\)
−0.652441 + 0.757840i \(0.726255\pi\)
\(788\) 0 0
\(789\) 24.5000 42.4352i 0.872223 1.51073i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −10.0000 + 17.3205i −0.355110 + 0.615069i
\(794\) 0 0
\(795\) 27.7804 + 48.1170i 0.985269 + 1.70654i
\(796\) 0