Properties

Label 280.2.s.a.237.3
Level $280$
Weight $2$
Character 280.237
Analytic conductor $2.236$
Analytic rank $0$
Dimension $8$
CM discriminant -56
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 280.s (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.23581125660\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(i)\)
Coefficient field: 8.0.40282095616.8
Defining polynomial: \(x^{8} - 4 x^{6} + 8 x^{4} - 36 x^{2} + 81\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{U}(1)[D_{4}]$

Embedding invariants

Embedding label 237.3
Root \(1.03179 + 1.39119i\) of defining polynomial
Character \(\chi\) \(=\) 280.237
Dual form 280.2.s.a.13.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 - 1.00000i) q^{2} +(0.359404 - 0.359404i) q^{3} +2.00000i q^{4} +(-1.39119 + 1.75060i) q^{5} -0.718808 q^{6} +(-1.87083 - 1.87083i) q^{7} +(2.00000 - 2.00000i) q^{8} +2.74166i q^{9} +O(q^{10})\) \(q+(-1.00000 - 1.00000i) q^{2} +(0.359404 - 0.359404i) q^{3} +2.00000i q^{4} +(-1.39119 + 1.75060i) q^{5} -0.718808 q^{6} +(-1.87083 - 1.87083i) q^{7} +(2.00000 - 2.00000i) q^{8} +2.74166i q^{9} +(3.14179 - 0.359404i) q^{10} +(0.718808 + 0.718808i) q^{12} +(-4.48655 + 4.48655i) q^{13} +3.74166i q^{14} +(0.129171 + 1.12917i) q^{15} -4.00000 q^{16} +(2.74166 - 2.74166i) q^{18} +7.62834i q^{19} +(-3.50119 - 2.78238i) q^{20} -1.34477 q^{21} +(0.741657 - 0.741657i) q^{23} -1.43762i q^{24} +(-1.12917 - 4.87083i) q^{25} +8.97311 q^{26} +(2.06358 + 2.06358i) q^{27} +(3.74166 - 3.74166i) q^{28} +(1.00000 - 1.25834i) q^{30} +(4.00000 + 4.00000i) q^{32} +(5.87775 - 0.672384i) q^{35} -5.48331 q^{36} +(7.62834 - 7.62834i) q^{38} +3.22497i q^{39} +(0.718808 + 6.28357i) q^{40} +(1.34477 + 1.34477i) q^{42} +(-4.79953 - 3.81417i) q^{45} -1.48331 q^{46} +(-1.43762 + 1.43762i) q^{48} +7.00000i q^{49} +(-3.74166 + 6.00000i) q^{50} +(-8.97311 - 8.97311i) q^{52} -4.12715i q^{54} -7.48331 q^{56} +(2.74166 + 2.74166i) q^{57} -15.3495i q^{59} +(-2.25834 + 0.258343i) q^{60} -14.6307 q^{61} +(5.12917 - 5.12917i) q^{63} -8.00000i q^{64} +(-1.61249 - 14.0958i) q^{65} -0.533109i q^{69} +(-6.55013 - 5.20536i) q^{70} +7.22497 q^{71} +(5.48331 + 5.48331i) q^{72} +(-2.15642 - 1.34477i) q^{75} -15.2567 q^{76} +(3.22497 - 3.22497i) q^{78} +15.7417i q^{79} +(5.56477 - 7.00238i) q^{80} -6.74166 q^{81} +(5.83132 - 5.83132i) q^{83} -2.68953i q^{84} +(0.985363 + 8.61370i) q^{90} +16.7871 q^{91} +(1.48331 + 1.48331i) q^{92} +(-13.3541 - 10.6125i) q^{95} +2.87523 q^{96} +(7.00000 - 7.00000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 8q^{2} + 16q^{8} + O(q^{10}) \) \( 8q - 8q^{2} + 16q^{8} + 16q^{15} - 32q^{16} - 8q^{18} - 24q^{23} - 24q^{25} + 8q^{30} + 32q^{32} + 16q^{36} + 48q^{46} - 8q^{57} - 48q^{60} + 56q^{63} + 32q^{65} - 32q^{71} - 16q^{72} - 64q^{78} - 24q^{81} - 48q^{92} - 32q^{95} + 56q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/280\mathbb{Z}\right)^\times\).

\(n\) \(57\) \(71\) \(141\) \(241\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\) \(-1\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 1.00000i −0.707107 0.707107i
\(3\) 0.359404 0.359404i 0.207502 0.207502i −0.595703 0.803205i \(-0.703126\pi\)
0.803205 + 0.595703i \(0.203126\pi\)
\(4\) 2.00000i 1.00000i
\(5\) −1.39119 + 1.75060i −0.622160 + 0.782890i
\(6\) −0.718808 −0.293452
\(7\) −1.87083 1.87083i −0.707107 0.707107i
\(8\) 2.00000 2.00000i 0.707107 0.707107i
\(9\) 2.74166i 0.913886i
\(10\) 3.14179 0.359404i 0.993520 0.113654i
\(11\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(12\) 0.718808 + 0.718808i 0.207502 + 0.207502i
\(13\) −4.48655 + 4.48655i −1.24435 + 1.24435i −0.286166 + 0.958180i \(0.592381\pi\)
−0.958180 + 0.286166i \(0.907619\pi\)
\(14\) 3.74166i 1.00000i
\(15\) 0.129171 + 1.12917i 0.0333519 + 0.291551i
\(16\) −4.00000 −1.00000
\(17\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(18\) 2.74166 2.74166i 0.646215 0.646215i
\(19\) 7.62834i 1.75006i 0.484067 + 0.875031i \(0.339159\pi\)
−0.484067 + 0.875031i \(0.660841\pi\)
\(20\) −3.50119 2.78238i −0.782890 0.622160i
\(21\) −1.34477 −0.293452
\(22\) 0 0
\(23\) 0.741657 0.741657i 0.154646 0.154646i −0.625543 0.780189i \(-0.715123\pi\)
0.780189 + 0.625543i \(0.215123\pi\)
\(24\) 1.43762i 0.293452i
\(25\) −1.12917 4.87083i −0.225834 0.974166i
\(26\) 8.97311 1.75977
\(27\) 2.06358 + 2.06358i 0.397135 + 0.397135i
\(28\) 3.74166 3.74166i 0.707107 0.707107i
\(29\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(30\) 1.00000 1.25834i 0.182574 0.229741i
\(31\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(32\) 4.00000 + 4.00000i 0.707107 + 0.707107i
\(33\) 0 0
\(34\) 0 0
\(35\) 5.87775 0.672384i 0.993520 0.113654i
\(36\) −5.48331 −0.913886
\(37\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(38\) 7.62834 7.62834i 1.23748 1.23748i
\(39\) 3.22497i 0.516409i
\(40\) 0.718808 + 6.28357i 0.113654 + 0.993520i
\(41\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(42\) 1.34477 + 1.34477i 0.207502 + 0.207502i
\(43\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(44\) 0 0
\(45\) −4.79953 3.81417i −0.715472 0.568583i
\(46\) −1.48331 −0.218703
\(47\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(48\) −1.43762 + 1.43762i −0.207502 + 0.207502i
\(49\) 7.00000i 1.00000i
\(50\) −3.74166 + 6.00000i −0.529150 + 0.848528i
\(51\) 0 0
\(52\) −8.97311 8.97311i −1.24435 1.24435i
\(53\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(54\) 4.12715i 0.561634i
\(55\) 0 0
\(56\) −7.48331 −1.00000
\(57\) 2.74166 + 2.74166i 0.363141 + 0.363141i
\(58\) 0 0
\(59\) 15.3495i 1.99834i −0.0407464 0.999170i \(-0.512974\pi\)
0.0407464 0.999170i \(-0.487026\pi\)
\(60\) −2.25834 + 0.258343i −0.291551 + 0.0333519i
\(61\) −14.6307 −1.87327 −0.936636 0.350304i \(-0.886078\pi\)
−0.936636 + 0.350304i \(0.886078\pi\)
\(62\) 0 0
\(63\) 5.12917 5.12917i 0.646215 0.646215i
\(64\) 8.00000i 1.00000i
\(65\) −1.61249 14.0958i −0.200004 1.74837i
\(66\) 0 0
\(67\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(68\) 0 0
\(69\) 0.533109i 0.0641788i
\(70\) −6.55013 5.20536i −0.782890 0.622160i
\(71\) 7.22497 0.857446 0.428723 0.903436i \(-0.358964\pi\)
0.428723 + 0.903436i \(0.358964\pi\)
\(72\) 5.48331 + 5.48331i 0.646215 + 0.646215i
\(73\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(74\) 0 0
\(75\) −2.15642 1.34477i −0.249002 0.155280i
\(76\) −15.2567 −1.75006
\(77\) 0 0
\(78\) 3.22497 3.22497i 0.365156 0.365156i
\(79\) 15.7417i 1.77107i 0.464568 + 0.885537i \(0.346210\pi\)
−0.464568 + 0.885537i \(0.653790\pi\)
\(80\) 5.56477 7.00238i 0.622160 0.782890i
\(81\) −6.74166 −0.749073
\(82\) 0 0
\(83\) 5.83132 5.83132i 0.640071 0.640071i −0.310502 0.950573i \(-0.600497\pi\)
0.950573 + 0.310502i \(0.100497\pi\)
\(84\) 2.68953i 0.293452i
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(90\) 0.985363 + 8.61370i 0.103866 + 0.907964i
\(91\) 16.7871 1.75977
\(92\) 1.48331 + 1.48331i 0.154646 + 0.154646i
\(93\) 0 0
\(94\) 0 0
\(95\) −13.3541 10.6125i −1.37011 1.08882i
\(96\) 2.87523 0.293452
\(97\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(98\) 7.00000 7.00000i 0.707107 0.707107i
\(99\) 0 0
\(100\) 9.74166 2.25834i 0.974166 0.225834i
\(101\) 13.1931 1.31276 0.656382 0.754429i \(-0.272086\pi\)
0.656382 + 0.754429i \(0.272086\pi\)
\(102\) 0 0
\(103\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(104\) 17.9462i 1.75977i
\(105\) 1.87083 2.35414i 0.182574 0.229741i
\(106\) 0 0
\(107\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(108\) −4.12715 + 4.12715i −0.397135 + 0.397135i
\(109\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 7.48331 + 7.48331i 0.707107 + 0.707107i
\(113\) −11.2250 + 11.2250i −1.05596 + 1.05596i −0.0576178 + 0.998339i \(0.518350\pi\)
−0.998339 + 0.0576178i \(0.981650\pi\)
\(114\) 5.48331i 0.513559i
\(115\) 0.266555 + 2.33013i 0.0248564 + 0.217286i
\(116\) 0 0
\(117\) −12.3006 12.3006i −1.13719 1.13719i
\(118\) −15.3495 + 15.3495i −1.41304 + 1.41304i
\(119\) 0 0
\(120\) 2.51669 + 2.00000i 0.229741 + 0.182574i
\(121\) 11.0000 1.00000
\(122\) 14.6307 + 14.6307i 1.32460 + 1.32460i
\(123\) 0 0
\(124\) 0 0
\(125\) 10.0977 + 4.79953i 0.903170 + 0.429283i
\(126\) −10.2583 −0.913886
\(127\) −12.2250 12.2250i −1.08479 1.08479i −0.996055 0.0887357i \(-0.971717\pi\)
−0.0887357 0.996055i \(-0.528283\pi\)
\(128\) −8.00000 + 8.00000i −0.707107 + 0.707107i
\(129\) 0 0
\(130\) −12.4833 + 15.7083i −1.09486 + 1.37771i
\(131\) −4.93881 −0.431506 −0.215753 0.976448i \(-0.569221\pi\)
−0.215753 + 0.976448i \(0.569221\pi\)
\(132\) 0 0
\(133\) 14.2713 14.2713i 1.23748 1.23748i
\(134\) 0 0
\(135\) −6.48331 + 0.741657i −0.557995 + 0.0638317i
\(136\) 0 0
\(137\) 16.4833 + 16.4833i 1.40826 + 1.40826i 0.768922 + 0.639343i \(0.220793\pi\)
0.639343 + 0.768922i \(0.279207\pi\)
\(138\) −0.533109 + 0.533109i −0.0453813 + 0.0453813i
\(139\) 12.4743i 1.05806i 0.848604 + 0.529028i \(0.177443\pi\)
−0.848604 + 0.529028i \(0.822557\pi\)
\(140\) 1.34477 + 11.7555i 0.113654 + 0.993520i
\(141\) 0 0
\(142\) −7.22497 7.22497i −0.606306 0.606306i
\(143\) 0 0
\(144\) 10.9666i 0.913886i
\(145\) 0 0
\(146\) 0 0
\(147\) 2.51583 + 2.51583i 0.207502 + 0.207502i
\(148\) 0 0
\(149\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(150\) 0.811658 + 3.50119i 0.0662716 + 0.285871i
\(151\) 22.4499 1.82695 0.913475 0.406894i \(-0.133388\pi\)
0.913475 + 0.406894i \(0.133388\pi\)
\(152\) 15.2567 + 15.2567i 1.23748 + 1.23748i
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) −6.44994 −0.516409
\(157\) 16.4277 + 16.4277i 1.31108 + 1.31108i 0.920622 + 0.390455i \(0.127682\pi\)
0.390455 + 0.920622i \(0.372318\pi\)
\(158\) 15.7417 15.7417i 1.25234 1.25234i
\(159\) 0 0
\(160\) −12.5671 + 1.43762i −0.993520 + 0.113654i
\(161\) −2.77503 −0.218703
\(162\) 6.74166 + 6.74166i 0.529675 + 0.529675i
\(163\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) −11.6626 −0.905197
\(167\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(168\) −2.68953 + 2.68953i −0.207502 + 0.207502i
\(169\) 27.2583i 2.09680i
\(170\) 0 0
\(171\) −20.9143 −1.59936
\(172\) 0 0
\(173\) −13.5525 + 13.5525i −1.03038 + 1.03038i −0.0308546 + 0.999524i \(0.509823\pi\)
−0.999524 + 0.0308546i \(0.990177\pi\)
\(174\) 0 0
\(175\) −7.00000 + 11.2250i −0.529150 + 0.848528i
\(176\) 0 0
\(177\) −5.51669 5.51669i −0.414659 0.414659i
\(178\) 0 0
\(179\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(180\) 7.62834 9.59907i 0.568583 0.715472i
\(181\) 19.2910 1.43389 0.716944 0.697131i \(-0.245540\pi\)
0.716944 + 0.697131i \(0.245540\pi\)
\(182\) −16.7871 16.7871i −1.24435 1.24435i
\(183\) −5.25834 + 5.25834i −0.388708 + 0.388708i
\(184\) 2.96663i 0.218703i
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 7.72119i 0.561634i
\(190\) 2.74166 + 23.9666i 0.198901 + 1.73872i
\(191\) 27.2250 1.96993 0.984965 0.172754i \(-0.0552667\pi\)
0.984965 + 0.172754i \(0.0552667\pi\)
\(192\) −2.87523 2.87523i −0.207502 0.207502i
\(193\) −6.00000 + 6.00000i −0.431889 + 0.431889i −0.889271 0.457381i \(-0.848787\pi\)
0.457381 + 0.889271i \(0.348787\pi\)
\(194\) 0 0
\(195\) −5.64562 4.48655i −0.404291 0.321289i
\(196\) −14.0000 −1.00000
\(197\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(198\) 0 0
\(199\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(200\) −12.0000 7.48331i −0.848528 0.529150i
\(201\) 0 0
\(202\) −13.1931 13.1931i −0.928264 0.928264i
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 2.03337 + 2.03337i 0.141329 + 0.141329i
\(208\) 17.9462 17.9462i 1.24435 1.24435i
\(209\) 0 0
\(210\) −4.22497 + 0.483315i −0.291551 + 0.0333519i
\(211\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(212\) 0 0
\(213\) 2.59668 2.59668i 0.177922 0.177922i
\(214\) 0 0
\(215\) 0 0
\(216\) 8.25430 0.561634
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(224\) 14.9666i 1.00000i
\(225\) 13.3541 3.09580i 0.890276 0.206387i
\(226\) 22.4499 1.49335
\(227\) −21.0880 21.0880i −1.39966 1.39966i −0.801013 0.598647i \(-0.795705\pi\)
−0.598647 0.801013i \(-0.704295\pi\)
\(228\) −5.48331 + 5.48331i −0.363141 + 0.363141i
\(229\) 18.9436i 1.25183i −0.779893 0.625913i \(-0.784726\pi\)
0.779893 0.625913i \(-0.215274\pi\)
\(230\) 2.06358 2.59668i 0.136068 0.171220i
\(231\) 0 0
\(232\) 0 0
\(233\) −17.9666 + 17.9666i −1.17703 + 1.17703i −0.196537 + 0.980497i \(0.562969\pi\)
−0.980497 + 0.196537i \(0.937031\pi\)
\(234\) 24.6012i 1.60823i
\(235\) 0 0
\(236\) 30.6991 1.99834
\(237\) 5.65762 + 5.65762i 0.367502 + 0.367502i
\(238\) 0 0
\(239\) 7.48331i 0.484055i 0.970269 + 0.242028i \(0.0778125\pi\)
−0.970269 + 0.242028i \(0.922188\pi\)
\(240\) −0.516685 4.51669i −0.0333519 0.291551i
\(241\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(242\) −11.0000 11.0000i −0.707107 0.707107i
\(243\) −8.61370 + 8.61370i −0.552569 + 0.552569i
\(244\) 29.2615i 1.87327i
\(245\) −12.2542 9.73834i −0.782890 0.622160i
\(246\) 0 0
\(247\) −34.2250 34.2250i −2.17768 2.17768i
\(248\) 0 0
\(249\) 4.19160i 0.265632i
\(250\) −5.29821 14.8973i −0.335088 0.942187i
\(251\) −11.0367 −0.696629 −0.348315 0.937378i \(-0.613246\pi\)
−0.348315 + 0.937378i \(0.613246\pi\)
\(252\) 10.2583 + 10.2583i 0.646215 + 0.646215i
\(253\) 0 0
\(254\) 24.4499i 1.53413i
\(255\) 0 0
\(256\) 16.0000 1.00000
\(257\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 28.1916 3.22497i 1.74837 0.200004i
\(261\) 0 0
\(262\) 4.93881 + 4.93881i 0.305121 + 0.305121i
\(263\) −11.2250 + 11.2250i −0.692161 + 0.692161i −0.962707 0.270546i \(-0.912796\pi\)
0.270546 + 0.962707i \(0.412796\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −28.5426 −1.75006
\(267\) 0 0
\(268\) 0 0
\(269\) 31.8581i 1.94242i 0.238215 + 0.971212i \(0.423438\pi\)
−0.238215 + 0.971212i \(0.576562\pi\)
\(270\) 7.22497 + 5.74166i 0.439698 + 0.349426i
\(271\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(272\) 0 0
\(273\) 6.03337 6.03337i 0.365156 0.365156i
\(274\) 32.9666i 1.99159i
\(275\) 0 0
\(276\) 1.06622 0.0641788
\(277\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(278\) 12.4743 12.4743i 0.748159 0.748159i
\(279\) 0 0
\(280\) 10.4107 13.1003i 0.622160 0.782890i
\(281\) −14.9666 −0.892834 −0.446417 0.894825i \(-0.647300\pi\)
−0.446417 + 0.894825i \(0.647300\pi\)
\(282\) 0 0
\(283\) −18.3985 + 18.3985i −1.09368 + 1.09368i −0.0985428 + 0.995133i \(0.531418\pi\)
−0.995133 + 0.0985428i \(0.968582\pi\)
\(284\) 14.4499i 0.857446i
\(285\) −8.61370 + 0.985363i −0.510232 + 0.0583679i
\(286\) 0 0
\(287\) 0 0
\(288\) −10.9666 + 10.9666i −0.646215 + 0.646215i
\(289\) 17.0000i 1.00000i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 17.8654 17.8654i 1.04371 1.04371i 0.0447054 0.999000i \(-0.485765\pi\)
0.999000 0.0447054i \(-0.0142349\pi\)
\(294\) 5.03166i 0.293452i
\(295\) 26.8708 + 21.3541i 1.56448 + 1.24329i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 6.65497i 0.384867i
\(300\) 2.68953 4.31285i 0.155280 0.249002i
\(301\) 0 0
\(302\) −22.4499 22.4499i −1.29185 1.29185i
\(303\) 4.74166 4.74166i 0.272401 0.272401i
\(304\) 30.5134i 1.75006i
\(305\) 20.3541 25.6125i 1.16547 1.46657i
\(306\) 0 0
\(307\) −0.452253 0.452253i −0.0258115 0.0258115i 0.694083 0.719895i \(-0.255810\pi\)
−0.719895 + 0.694083i \(0.755810\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(312\) 6.44994 + 6.44994i 0.365156 + 0.365156i
\(313\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(314\) 32.8555i 1.85414i
\(315\) 1.84345 + 16.1148i 0.103866 + 0.907964i
\(316\) −31.4833 −1.77107
\(317\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 14.0048 + 11.1295i 0.782890 + 0.622160i
\(321\) 0 0
\(322\) 2.77503 + 2.77503i 0.154646 + 0.154646i
\(323\) 0 0
\(324\) 13.4833i 0.749073i
\(325\) 26.9193 + 16.7871i 1.49322 + 0.931184i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(332\) 11.6626 + 11.6626i 0.640071 + 0.640071i
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 5.37907 0.293452
\(337\) 18.0000 + 18.0000i 0.980522 + 0.980522i 0.999814 0.0192914i \(-0.00614103\pi\)
−0.0192914 + 0.999814i \(0.506141\pi\)
\(338\) −27.2583 + 27.2583i −1.48266 + 1.48266i
\(339\) 8.06860i 0.438226i
\(340\) 0 0
\(341\) 0 0
\(342\) 20.9143 + 20.9143i 1.13092 + 1.13092i
\(343\) 13.0958 13.0958i 0.707107 0.707107i
\(344\) 0 0
\(345\) 0.933259 + 0.741657i 0.0502450 + 0.0399295i
\(346\) 27.1050 1.45718
\(347\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(348\) 0 0
\(349\) 11.2224i 0.600720i 0.953826 + 0.300360i \(0.0971069\pi\)
−0.953826 + 0.300360i \(0.902893\pi\)
\(350\) 18.2250 4.22497i 0.974166 0.225834i
\(351\) −18.5167 −0.988348
\(352\) 0 0
\(353\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(354\) 11.0334i 0.586417i
\(355\) −10.0513 + 12.6480i −0.533469 + 0.671286i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 6.00000i 0.316668i −0.987386 0.158334i \(-0.949388\pi\)
0.987386 0.158334i \(-0.0506123\pi\)
\(360\) −17.2274 + 1.97073i −0.907964 + 0.103866i
\(361\) −39.1916 −2.06272
\(362\) −19.2910 19.2910i −1.01391 1.01391i
\(363\) 3.95345 3.95345i 0.207502 0.207502i
\(364\) 33.5743i 1.75977i
\(365\) 0 0
\(366\) 10.5167 0.549716
\(367\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(368\) −2.96663 + 2.96663i −0.154646 + 0.154646i
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(374\) 0 0
\(375\) 5.35414 1.90420i 0.276487 0.0983324i
\(376\) 0 0
\(377\) 0 0
\(378\) −7.72119 + 7.72119i −0.397135 + 0.397135i
\(379\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(380\) 21.2250 26.7083i 1.08882 1.37011i
\(381\) −8.78741 −0.450193
\(382\) −27.2250 27.2250i −1.39295 1.39295i
\(383\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(384\) 5.75047i 0.293452i
\(385\) 0 0
\(386\) 12.0000 0.610784
\(387\) 0 0
\(388\) 0 0
\(389\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(390\) 1.15907 + 10.1322i 0.0586917 + 0.513063i
\(391\) 0 0
\(392\) 14.0000 + 14.0000i 0.707107 + 0.707107i
\(393\) −1.77503 + 1.77503i −0.0895383 + 0.0895383i
\(394\) 0 0
\(395\) −27.5573 21.8997i −1.38656 1.10189i
\(396\) 0 0
\(397\) −18.5842 18.5842i −0.932713 0.932713i 0.0651619 0.997875i \(-0.479244\pi\)
−0.997875 + 0.0651619i \(0.979244\pi\)
\(398\) 0 0
\(399\) 10.2583i 0.513559i
\(400\) 4.51669 + 19.4833i 0.225834 + 0.974166i
\(401\) 37.2250 1.85893 0.929463 0.368915i \(-0.120271\pi\)
0.929463 + 0.368915i \(0.120271\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 26.3862i 1.31276i
\(405\) 9.37894 11.8019i 0.466043 0.586442i
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(410\) 0 0
\(411\) 11.8483 0.584436
\(412\) 0 0
\(413\) −28.7163 + 28.7163i −1.41304 + 1.41304i
\(414\) 4.06674i 0.199869i
\(415\) 2.09580 + 18.3208i 0.102879 + 0.899331i
\(416\) −35.8924 −1.75977
\(417\) 4.48331 + 4.48331i 0.219549 + 0.219549i
\(418\) 0 0
\(419\) 40.8312i 1.99474i −0.0725002 0.997368i \(-0.523098\pi\)
0.0725002 0.997368i \(-0.476902\pi\)
\(420\) 4.70829 + 3.74166i 0.229741 + 0.182574i
\(421\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) −5.19337 −0.251620
\(427\) 27.3716 + 27.3716i 1.32460 + 1.32460i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −18.0000 −0.867029 −0.433515 0.901146i \(-0.642727\pi\)
−0.433515 + 0.901146i \(0.642727\pi\)
\(432\) −8.25430 8.25430i −0.397135 0.397135i
\(433\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 5.65762 + 5.65762i 0.270640 + 0.270640i
\(438\) 0 0
\(439\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(440\) 0 0
\(441\) −19.1916 −0.913886
\(442\) 0 0
\(443\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) −14.9666 + 14.9666i −0.707107 + 0.707107i
\(449\) 29.9333i 1.41264i −0.707894 0.706319i \(-0.750354\pi\)
0.707894 0.706319i \(-0.249646\pi\)
\(450\) −16.4499 10.2583i −0.775458 0.483583i
\(451\) 0 0
\(452\) −22.4499 22.4499i −1.05596 1.05596i
\(453\) 8.06860 8.06860i 0.379096 0.379096i
\(454\) 42.1760i 1.97942i
\(455\) −23.3541 + 29.3875i −1.09486 + 1.37771i
\(456\) 10.9666 0.513559
\(457\) −3.74166 3.74166i −0.175027 0.175027i 0.614157 0.789184i \(-0.289496\pi\)
−0.789184 + 0.614157i \(0.789496\pi\)
\(458\) −18.9436 + 18.9436i −0.885175 + 0.885175i
\(459\) 0 0
\(460\) −4.66026 + 0.533109i −0.217286 + 0.0248564i
\(461\) −21.9805 −1.02373 −0.511867 0.859064i \(-0.671046\pi\)
−0.511867 + 0.859064i \(0.671046\pi\)
\(462\) 0 0
\(463\) 24.0000 24.0000i 1.11537 1.11537i 0.122963 0.992411i \(-0.460760\pi\)
0.992411 0.122963i \(-0.0392398\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 35.9333 1.66458
\(467\) 30.3397 + 30.3397i 1.40395 + 1.40395i 0.787003 + 0.616949i \(0.211632\pi\)
0.616949 + 0.787003i \(0.288368\pi\)
\(468\) 24.6012 24.6012i 1.13719 1.13719i
\(469\) 0 0
\(470\) 0 0
\(471\) 11.8084 0.544102
\(472\) −30.6991 30.6991i −1.41304 1.41304i
\(473\) 0 0
\(474\) 11.3152i 0.519726i
\(475\) 37.1563 8.61370i 1.70485 0.395224i
\(476\) 0 0
\(477\) 0 0
\(478\) 7.48331 7.48331i 0.342279 0.342279i
\(479\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(480\) −4.00000 + 5.03337i −0.182574 + 0.229741i
\(481\) 0 0
\(482\) 0 0
\(483\) −0.997356 + 0.997356i −0.0453813 + 0.0453813i
\(484\) 22.0000i 1.00000i
\(485\) 0 0
\(486\) 17.2274 0.781451
\(487\) 7.77503 + 7.77503i 0.352320 + 0.352320i 0.860972 0.508652i \(-0.169856\pi\)
−0.508652 + 0.860972i \(0.669856\pi\)
\(488\) −29.2615 + 29.2615i −1.32460 + 1.32460i
\(489\) 0 0
\(490\) 2.51583 + 21.9925i 0.113654 + 0.993520i
\(491\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 68.4499i 3.07971i
\(495\) 0 0
\(496\) 0 0
\(497\) −13.5167 13.5167i −0.606306 0.606306i
\(498\) −4.19160 + 4.19160i −0.187830 + 0.187830i
\(499\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(500\) −9.59907 + 20.1955i −0.429283 + 0.903170i
\(501\) 0 0
\(502\) 11.0367 + 11.0367i 0.492591 + 0.492591i
\(503\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(504\) 20.5167i 0.913886i
\(505\) −18.3541 + 23.0958i −0.816749 + 1.02775i
\(506\) 0 0
\(507\) −9.79676 9.79676i −0.435089 0.435089i
\(508\) 24.4499 24.4499i 1.08479 1.08479i
\(509\) 8.88026i 0.393611i 0.980443 + 0.196805i \(0.0630567\pi\)
−0.980443 + 0.196805i \(0.936943\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −16.0000 16.0000i −0.707107 0.707107i
\(513\) −15.7417 + 15.7417i −0.695011 + 0.695011i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 9.74166i 0.427611i
\(520\) −31.4166 24.9666i −1.37771 1.09486i
\(521\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(522\) 0 0
\(523\) 31.7773 31.7773i 1.38952 1.38952i 0.563209 0.826315i \(-0.309567\pi\)
0.826315 0.563209i \(-0.190433\pi\)
\(524\) 9.87762i 0.431506i
\(525\) 1.51847 + 6.55013i 0.0662716 + 0.285871i
\(526\) 22.4499 0.978864
\(527\) 0 0
\(528\) 0 0
\(529\) 21.8999i 0.952169i
\(530\) 0 0
\(531\) 42.0832 1.82625
\(532\) 28.5426 + 28.5426i 1.23748 + 1.23748i
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 31.8581 31.8581i 1.37350 1.37350i
\(539\) 0 0
\(540\) −1.48331 12.9666i −0.0638317 0.557995i
\(541\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(542\) 0 0
\(543\) 6.93326 6.93326i 0.297535 0.297535i
\(544\) 0 0
\(545\) 0 0
\(546\) −12.0667 −0.516409
\(547\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(548\) −32.9666 + 32.9666i −1.40826 + 1.40826i
\(549\) 40.1124i 1.71196i
\(550\) 0 0
\(551\) 0 0
\(552\) −1.06622 1.06622i −0.0453813 0.0453813i
\(553\) 29.4499 29.4499i 1.25234 1.25234i
\(554\) 0 0
\(555\) 0 0
\(556\) −24.9486 −1.05806
\(557\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) −23.5110 + 2.68953i −0.993520 + 0.113654i
\(561\) 0 0
\(562\) 14.9666 + 14.9666i 0.631329 + 0.631329i
\(563\) 28.1832 28.1832i 1.18778 1.18778i 0.210103 0.977679i \(-0.432620\pi\)
0.977679 0.210103i \(-0.0673798\pi\)
\(564\) 0 0
\(565\) −4.03430 35.2665i −0.169724 1.48367i
\(566\) 36.7969 1.54669
\(567\) 12.6125 + 12.6125i 0.529675 + 0.529675i
\(568\) 14.4499 14.4499i 0.606306 0.606306i
\(569\) 31.6749i 1.32788i −0.747785 0.663941i \(-0.768883\pi\)
0.747785 0.663941i \(-0.231117\pi\)
\(570\) 9.59907 + 7.62834i 0.402061 + 0.319516i
\(571\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(572\) 0 0
\(573\) 9.78477 9.78477i 0.408764 0.408764i
\(574\) 0 0
\(575\) −4.44994 2.77503i −0.185576 0.115727i
\(576\) 21.9333 0.913886
\(577\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(578\) 17.0000 17.0000i 0.707107 0.707107i
\(579\) 4.31285i 0.179236i
\(580\) 0 0
\(581\) −21.8188 −0.905197
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 38.6459 4.42088i 1.59781 0.182781i
\(586\) −35.7307 −1.47602
\(587\) −32.4961 32.4961i −1.34126 1.34126i −0.894810 0.446447i \(-0.852689\pi\)
−0.446447 0.894810i \(-0.647311\pi\)
\(588\) −5.03166 + 5.03166i −0.207502 + 0.207502i
\(589\) 0 0
\(590\) −5.51669 48.2250i −0.227118 1.98539i
\(591\) 0 0
\(592\) 0 0
\(593\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 6.65497 6.65497i 0.272142 0.272142i
\(599\) 41.6749i 1.70279i −0.524524 0.851395i \(-0.675757\pi\)
0.524524 0.851395i \(-0.324243\pi\)
\(600\) −7.00238 + 1.62332i −0.285871 + 0.0662716i
\(601\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 44.8999i 1.82695i
\(605\) −15.3031 + 19.2566i −0.622160 + 0.782890i
\(606\) −9.48331 −0.385233
\(607\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(608\) −30.5134 + 30.5134i −1.23748 + 1.23748i
\(609\) 0 0
\(610\) −45.9666 + 5.25834i −1.86113 + 0.212904i
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(614\) 0.904507i 0.0365029i
\(615\) 0 0
\(616\) 0 0
\(617\) 33.6749 + 33.6749i 1.35570 + 1.35570i 0.879143 + 0.476558i \(0.158116\pi\)
0.476558 + 0.879143i \(0.341884\pi\)
\(618\) 0 0
\(619\) 8.16145i 0.328036i −0.986457 0.164018i \(-0.947554\pi\)
0.986457 0.164018i \(-0.0524456\pi\)
\(620\) 0 0
\(621\) 3.06093 0.122831
\(622\) 0 0
\(623\) 0 0
\(624\) 12.8999i 0.516409i
\(625\) −22.4499 + 11.0000i −0.897998 + 0.440000i
\(626\) 0 0
\(627\) 0 0
\(628\) −32.8555 + 32.8555i −1.31108 + 1.31108i
\(629\) 0 0
\(630\) 14.2713 17.9582i 0.568583 0.715472i
\(631\) −50.1916 −1.99810 −0.999048 0.0436231i \(-0.986110\pi\)
−0.999048 + 0.0436231i \(0.986110\pi\)
\(632\) 31.4833 + 31.4833i 1.25234 + 1.25234i
\(633\) 0 0
\(634\) 0 0
\(635\) 38.4083 4.39371i 1.52419 0.174359i
\(636\) 0 0
\(637\) −31.4059 31.4059i −1.24435 1.24435i
\(638\) 0 0
\(639\) 19.8084i 0.783608i
\(640\) −2.87523 25.1343i −0.113654 0.993520i
\(641\) −22.7750 −0.899560 −0.449780 0.893140i \(-0.648498\pi\)
−0.449780 + 0.893140i \(0.648498\pi\)
\(642\) 0 0
\(643\) −27.4644 + 27.4644i −1.08309 + 1.08309i −0.0868719 + 0.996219i \(0.527687\pi\)
−0.996219 + 0.0868719i \(0.972313\pi\)
\(644\) 5.55006i 0.218703i
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(648\) −13.4833 + 13.4833i −0.529675 + 0.529675i
\(649\) 0 0
\(650\) −10.1322 43.7065i −0.397417 1.71431i
\(651\) 0 0
\(652\) 0 0
\(653\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(654\) 0 0
\(655\) 6.87083 8.64586i 0.268465 0.337822i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(660\) 0 0
\(661\) 26.4791 1.02992 0.514958 0.857215i \(-0.327807\pi\)
0.514958 + 0.857215i \(0.327807\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 23.3253i 0.905197i
\(665\) 5.12917 + 44.8375i 0.198901 + 1.73872i
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) −5.37907 5.37907i −0.207502 0.207502i
\(673\) 9.44994 9.44994i 0.364269 0.364269i −0.501113 0.865382i \(-0.667076\pi\)
0.865382 + 0.501113i \(0.167076\pi\)
\(674\) 36.0000i 1.38667i
\(675\) 7.72119 12.3815i 0.297189 0.476562i
\(676\) 54.5167 2.09680
\(677\) 20.0218 + 20.0218i 0.769500 + 0.769500i 0.978018 0.208519i \(-0.0668642\pi\)
−0.208519 + 0.978018i \(0.566864\pi\)
\(678\) 8.06860 8.06860i 0.309873 0.309873i
\(679\) 0 0
\(680\) 0 0
\(681\) −15.1582 −0.580865
\(682\) 0 0
\(683\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(684\) 41.8286i 1.59936i
\(685\) −51.7871 + 5.92417i −1.97868 + 0.226351i
\(686\) −26.1916 −1.00000
\(687\) −6.80840 6.80840i −0.259757 0.259757i
\(688\) 0 0
\(689\) 0 0
\(690\) −0.191602 1.67492i −0.00729415 0.0637630i
\(691\) 15.6969 0.597140 0.298570 0.954388i \(-0.403490\pi\)
0.298570 + 0.954388i \(0.403490\pi\)
\(692\) −27.1050 27.1050i −1.03038 1.03038i
\(693\) 0 0
\(694\) 0 0
\(695\) −21.8375 17.3541i −0.828342 0.658280i
\(696\) 0 0
\(697\) 0 0
\(698\) 11.2224 11.2224i 0.424773 0.424773i
\(699\) 12.9146i 0.488474i
\(700\) −22.4499 14.0000i −0.848528 0.529150i
\(701\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(702\) 18.5167 + 18.5167i 0.698867 + 0.698867i
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −24.6820 24.6820i −0.928264 0.928264i
\(708\) 11.0334 11.0334i 0.414659 0.414659i
\(709\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(710\) 22.6993 2.59668i 0.851891 0.0974518i
\(711\) −43.1582 −1.61856
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 2.68953 + 2.68953i 0.100442 + 0.100442i
\(718\) −6.00000 + 6.00000i −0.223918 + 0.223918i
\(719\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(720\) 19.1981 + 15.2567i 0.715472 + 0.568583i
\(721\) 0 0
\(722\) 39.1916 + 39.1916i 1.45856 + 1.45856i
\(723\) 0 0
\(724\) 38.5820i 1.43389i
\(725\) 0 0
\(726\) −7.90689 −0.293452
\(727\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(728\) 33.5743 33.5743i 1.24435 1.24435i
\(729\) 14.0334i 0.519754i
\(730\) 0 0
\(731\) 0 0
\(732\) −10.5167 10.5167i −0.388708 0.388708i
\(733\) −9.95847 + 9.95847i −0.367825 + 0.367825i −0.866683 0.498859i \(-0.833753\pi\)
0.498859 + 0.866683i \(0.333753\pi\)
\(734\) 0 0
\(735\) −7.90420 + 0.904199i −0.291551 + 0.0333519i
\(736\) 5.93326 0.218703
\(737\) 0 0
\(738\) 0 0
\(739\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(740\) 0 0
\(741\) −24.6012 −0.903747
\(742\) 0 0
\(743\) 30.7417 30.7417i 1.12780 1.12780i 0.137268 0.990534i \(-0.456168\pi\)
0.990534 0.137268i \(-0.0438322\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 15.9875 + 15.9875i 0.584952 + 0.584952i
\(748\) 0 0
\(749\) 0 0
\(750\) −7.25834 3.44994i −0.265037 0.125974i
\(751\) 22.4499 0.819210 0.409605 0.912263i \(-0.365667\pi\)
0.409605 + 0.912263i \(0.365667\pi\)
\(752\) 0 0
\(753\) −3.96663 + 3.96663i −0.144552 + 0.144552i
\(754\) 0 0
\(755\) −31.2322 + 39.3008i −1.13666 + 1.43030i
\(756\) 15.4424 0.561634
\(757\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) −47.9333 + 5.48331i −1.73872 + 0.198901i
\(761\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(762\) 8.78741 + 8.78741i 0.318334 + 0.318334i
\(763\) 0 0
\(764\) 54.4499i 1.96993i
\(765\) 0 0
\(766\) 0 0
\(767\) 68.8665 + 68.8665i 2.48663 + 2.48663i
\(768\) 5.75047 5.75047i 0.207502 0.207502i
\(769\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −12.0000 12.0000i −0.431889 0.431889i
\(773\) −25.1223 + 25.1223i −0.903587 + 0.903587i −0.995744 0.0921578i \(-0.970624\pi\)
0.0921578 + 0.995744i \(0.470624\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 8.97311 11.2912i 0.321289 0.404291i
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 28.0000i 1.00000i
\(785\) −51.6125 + 5.90420i −1.84213 + 0.210730i
\(786\) 3.55006 0.126626
\(787\) 33.9337 + 33.9337i 1.20961 + 1.20961i 0.971154 + 0.238451i \(0.0766398\pi\)
0.238451 + 0.971154i \(0.423360\pi\)
\(788\) 0 0
\(789\) 8.06860i 0.287250i
\(790\) 5.65762 + 49.4569i 0.201289 + 1.75960i
\(791\) 42.0000 1.49335
\(792\) 0 0
\(793\) 65.6415 65.6415i 2.33100 2.33100i
\(794\) 37.1683i 1.31906i
\(795\) 0 0
\(796\) 0 0
\(797\) 9.86562 + 9.86562i 0.349458 + 0.349458i