Properties

Label 240.2.v.a.113.2
Level $240$
Weight $2$
Character 240.113
Analytic conductor $1.916$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 240.v (of order \(4\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.91640964851\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(i)\)
Coefficient field: \(\Q(\zeta_{8})\)
Defining polynomial: \(x^{4} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 120)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 113.2
Root \(-0.707107 + 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 240.113
Dual form 240.2.v.a.17.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 + 1.41421i) q^{3} +(1.00000 - 2.00000i) q^{5} +(2.41421 - 2.41421i) q^{7} +(-1.00000 - 2.82843i) q^{9} +O(q^{10})\) \(q+(-1.00000 + 1.41421i) q^{3} +(1.00000 - 2.00000i) q^{5} +(2.41421 - 2.41421i) q^{7} +(-1.00000 - 2.82843i) q^{9} +0.828427i q^{11} +(3.82843 + 3.82843i) q^{13} +(1.82843 + 3.41421i) q^{15} +(1.82843 + 1.82843i) q^{17} -0.828427i q^{19} +(1.00000 + 5.82843i) q^{21} +(4.41421 - 4.41421i) q^{23} +(-3.00000 - 4.00000i) q^{25} +(5.00000 + 1.41421i) q^{27} -3.65685 q^{29} -5.65685 q^{31} +(-1.17157 - 0.828427i) q^{33} +(-2.41421 - 7.24264i) q^{35} +(-5.82843 + 5.82843i) q^{37} +(-9.24264 + 1.58579i) q^{39} -5.65685i q^{41} +(0.414214 + 0.414214i) q^{43} +(-6.65685 - 0.828427i) q^{45} +(3.58579 + 3.58579i) q^{47} -4.65685i q^{49} +(-4.41421 + 0.757359i) q^{51} +(3.00000 - 3.00000i) q^{53} +(1.65685 + 0.828427i) q^{55} +(1.17157 + 0.828427i) q^{57} -4.00000 q^{59} +0.343146 q^{61} +(-9.24264 - 4.41421i) q^{63} +(11.4853 - 3.82843i) q^{65} +(-10.0711 + 10.0711i) q^{67} +(1.82843 + 10.6569i) q^{69} +10.4853i q^{71} +(-4.65685 - 4.65685i) q^{73} +(8.65685 - 0.242641i) q^{75} +(2.00000 + 2.00000i) q^{77} +0.828427i q^{79} +(-7.00000 + 5.65685i) q^{81} +(3.24264 - 3.24264i) q^{83} +(5.48528 - 1.82843i) q^{85} +(3.65685 - 5.17157i) q^{87} -15.6569 q^{89} +18.4853 q^{91} +(5.65685 - 8.00000i) q^{93} +(-1.65685 - 0.828427i) q^{95} +(1.00000 - 1.00000i) q^{97} +(2.34315 - 0.828427i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 4 q^{3} + 4 q^{5} + 4 q^{7} - 4 q^{9} + O(q^{10}) \) \( 4 q - 4 q^{3} + 4 q^{5} + 4 q^{7} - 4 q^{9} + 4 q^{13} - 4 q^{15} - 4 q^{17} + 4 q^{21} + 12 q^{23} - 12 q^{25} + 20 q^{27} + 8 q^{29} - 16 q^{33} - 4 q^{35} - 12 q^{37} - 20 q^{39} - 4 q^{43} - 4 q^{45} + 20 q^{47} - 12 q^{51} + 12 q^{53} - 16 q^{55} + 16 q^{57} - 16 q^{59} + 24 q^{61} - 20 q^{63} + 12 q^{65} - 12 q^{67} - 4 q^{69} + 4 q^{73} + 12 q^{75} + 8 q^{77} - 28 q^{81} - 4 q^{83} - 12 q^{85} - 8 q^{87} - 40 q^{89} + 40 q^{91} + 16 q^{95} + 4 q^{97} + 32 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/240\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(97\) \(161\) \(181\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{4}\right)\) \(-1\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.00000 + 1.41421i −0.577350 + 0.816497i
\(4\) 0 0
\(5\) 1.00000 2.00000i 0.447214 0.894427i
\(6\) 0 0
\(7\) 2.41421 2.41421i 0.912487 0.912487i −0.0839804 0.996467i \(-0.526763\pi\)
0.996467 + 0.0839804i \(0.0267633\pi\)
\(8\) 0 0
\(9\) −1.00000 2.82843i −0.333333 0.942809i
\(10\) 0 0
\(11\) 0.828427i 0.249780i 0.992171 + 0.124890i \(0.0398578\pi\)
−0.992171 + 0.124890i \(0.960142\pi\)
\(12\) 0 0
\(13\) 3.82843 + 3.82843i 1.06181 + 1.06181i 0.997959 + 0.0638555i \(0.0203397\pi\)
0.0638555 + 0.997959i \(0.479660\pi\)
\(14\) 0 0
\(15\) 1.82843 + 3.41421i 0.472098 + 0.881546i
\(16\) 0 0
\(17\) 1.82843 + 1.82843i 0.443459 + 0.443459i 0.893173 0.449714i \(-0.148474\pi\)
−0.449714 + 0.893173i \(0.648474\pi\)
\(18\) 0 0
\(19\) 0.828427i 0.190054i −0.995475 0.0950271i \(-0.969706\pi\)
0.995475 0.0950271i \(-0.0302938\pi\)
\(20\) 0 0
\(21\) 1.00000 + 5.82843i 0.218218 + 1.27187i
\(22\) 0 0
\(23\) 4.41421 4.41421i 0.920427 0.920427i −0.0766323 0.997059i \(-0.524417\pi\)
0.997059 + 0.0766323i \(0.0244167\pi\)
\(24\) 0 0
\(25\) −3.00000 4.00000i −0.600000 0.800000i
\(26\) 0 0
\(27\) 5.00000 + 1.41421i 0.962250 + 0.272166i
\(28\) 0 0
\(29\) −3.65685 −0.679061 −0.339530 0.940595i \(-0.610268\pi\)
−0.339530 + 0.940595i \(0.610268\pi\)
\(30\) 0 0
\(31\) −5.65685 −1.01600 −0.508001 0.861357i \(-0.669615\pi\)
−0.508001 + 0.861357i \(0.669615\pi\)
\(32\) 0 0
\(33\) −1.17157 0.828427i −0.203945 0.144211i
\(34\) 0 0
\(35\) −2.41421 7.24264i −0.408077 1.22423i
\(36\) 0 0
\(37\) −5.82843 + 5.82843i −0.958188 + 0.958188i −0.999160 0.0409727i \(-0.986954\pi\)
0.0409727 + 0.999160i \(0.486954\pi\)
\(38\) 0 0
\(39\) −9.24264 + 1.58579i −1.48001 + 0.253929i
\(40\) 0 0
\(41\) 5.65685i 0.883452i −0.897150 0.441726i \(-0.854366\pi\)
0.897150 0.441726i \(-0.145634\pi\)
\(42\) 0 0
\(43\) 0.414214 + 0.414214i 0.0631670 + 0.0631670i 0.737985 0.674818i \(-0.235778\pi\)
−0.674818 + 0.737985i \(0.735778\pi\)
\(44\) 0 0
\(45\) −6.65685 0.828427i −0.992345 0.123495i
\(46\) 0 0
\(47\) 3.58579 + 3.58579i 0.523041 + 0.523041i 0.918488 0.395448i \(-0.129411\pi\)
−0.395448 + 0.918488i \(0.629411\pi\)
\(48\) 0 0
\(49\) 4.65685i 0.665265i
\(50\) 0 0
\(51\) −4.41421 + 0.757359i −0.618114 + 0.106052i
\(52\) 0 0
\(53\) 3.00000 3.00000i 0.412082 0.412082i −0.470381 0.882463i \(-0.655884\pi\)
0.882463 + 0.470381i \(0.155884\pi\)
\(54\) 0 0
\(55\) 1.65685 + 0.828427i 0.223410 + 0.111705i
\(56\) 0 0
\(57\) 1.17157 + 0.828427i 0.155179 + 0.109728i
\(58\) 0 0
\(59\) −4.00000 −0.520756 −0.260378 0.965507i \(-0.583847\pi\)
−0.260378 + 0.965507i \(0.583847\pi\)
\(60\) 0 0
\(61\) 0.343146 0.0439353 0.0219677 0.999759i \(-0.493007\pi\)
0.0219677 + 0.999759i \(0.493007\pi\)
\(62\) 0 0
\(63\) −9.24264 4.41421i −1.16446 0.556139i
\(64\) 0 0
\(65\) 11.4853 3.82843i 1.42457 0.474858i
\(66\) 0 0
\(67\) −10.0711 + 10.0711i −1.23038 + 1.23038i −0.266558 + 0.963819i \(0.585886\pi\)
−0.963819 + 0.266558i \(0.914114\pi\)
\(68\) 0 0
\(69\) 1.82843 + 10.6569i 0.220117 + 1.28293i
\(70\) 0 0
\(71\) 10.4853i 1.24437i 0.782869 + 0.622187i \(0.213756\pi\)
−0.782869 + 0.622187i \(0.786244\pi\)
\(72\) 0 0
\(73\) −4.65685 4.65685i −0.545044 0.545044i 0.379960 0.925003i \(-0.375938\pi\)
−0.925003 + 0.379960i \(0.875938\pi\)
\(74\) 0 0
\(75\) 8.65685 0.242641i 0.999607 0.0280177i
\(76\) 0 0
\(77\) 2.00000 + 2.00000i 0.227921 + 0.227921i
\(78\) 0 0
\(79\) 0.828427i 0.0932053i 0.998914 + 0.0466027i \(0.0148395\pi\)
−0.998914 + 0.0466027i \(0.985161\pi\)
\(80\) 0 0
\(81\) −7.00000 + 5.65685i −0.777778 + 0.628539i
\(82\) 0 0
\(83\) 3.24264 3.24264i 0.355926 0.355926i −0.506383 0.862309i \(-0.669018\pi\)
0.862309 + 0.506383i \(0.169018\pi\)
\(84\) 0 0
\(85\) 5.48528 1.82843i 0.594962 0.198321i
\(86\) 0 0
\(87\) 3.65685 5.17157i 0.392056 0.554451i
\(88\) 0 0
\(89\) −15.6569 −1.65962 −0.829812 0.558044i \(-0.811552\pi\)
−0.829812 + 0.558044i \(0.811552\pi\)
\(90\) 0 0
\(91\) 18.4853 1.93778
\(92\) 0 0
\(93\) 5.65685 8.00000i 0.586588 0.829561i
\(94\) 0 0
\(95\) −1.65685 0.828427i −0.169990 0.0849948i
\(96\) 0 0
\(97\) 1.00000 1.00000i 0.101535 0.101535i −0.654515 0.756049i \(-0.727127\pi\)
0.756049 + 0.654515i \(0.227127\pi\)
\(98\) 0 0
\(99\) 2.34315 0.828427i 0.235495 0.0832601i
\(100\) 0 0
\(101\) 9.65685i 0.960893i 0.877024 + 0.480446i \(0.159525\pi\)
−0.877024 + 0.480446i \(0.840475\pi\)
\(102\) 0 0
\(103\) 5.58579 + 5.58579i 0.550384 + 0.550384i 0.926552 0.376168i \(-0.122758\pi\)
−0.376168 + 0.926552i \(0.622758\pi\)
\(104\) 0 0
\(105\) 12.6569 + 3.82843i 1.23518 + 0.373616i
\(106\) 0 0
\(107\) −9.58579 9.58579i −0.926693 0.926693i 0.0707977 0.997491i \(-0.477446\pi\)
−0.997491 + 0.0707977i \(0.977446\pi\)
\(108\) 0 0
\(109\) 4.00000i 0.383131i −0.981480 0.191565i \(-0.938644\pi\)
0.981480 0.191565i \(-0.0613564\pi\)
\(110\) 0 0
\(111\) −2.41421 14.0711i −0.229147 1.33557i
\(112\) 0 0
\(113\) −9.48528 + 9.48528i −0.892300 + 0.892300i −0.994739 0.102439i \(-0.967335\pi\)
0.102439 + 0.994739i \(0.467335\pi\)
\(114\) 0 0
\(115\) −4.41421 13.2426i −0.411628 1.23488i
\(116\) 0 0
\(117\) 7.00000 14.6569i 0.647150 1.35503i
\(118\) 0 0
\(119\) 8.82843 0.809301
\(120\) 0 0
\(121\) 10.3137 0.937610
\(122\) 0 0
\(123\) 8.00000 + 5.65685i 0.721336 + 0.510061i
\(124\) 0 0
\(125\) −11.0000 + 2.00000i −0.983870 + 0.178885i
\(126\) 0 0
\(127\) −5.58579 + 5.58579i −0.495658 + 0.495658i −0.910083 0.414425i \(-0.863983\pi\)
0.414425 + 0.910083i \(0.363983\pi\)
\(128\) 0 0
\(129\) −1.00000 + 0.171573i −0.0880451 + 0.0151061i
\(130\) 0 0
\(131\) 8.82843i 0.771343i 0.922636 + 0.385672i \(0.126030\pi\)
−0.922636 + 0.385672i \(0.873970\pi\)
\(132\) 0 0
\(133\) −2.00000 2.00000i −0.173422 0.173422i
\(134\) 0 0
\(135\) 7.82843 8.58579i 0.673764 0.738947i
\(136\) 0 0
\(137\) 9.82843 + 9.82843i 0.839699 + 0.839699i 0.988819 0.149120i \(-0.0476440\pi\)
−0.149120 + 0.988819i \(0.547644\pi\)
\(138\) 0 0
\(139\) 8.82843i 0.748817i −0.927264 0.374409i \(-0.877846\pi\)
0.927264 0.374409i \(-0.122154\pi\)
\(140\) 0 0
\(141\) −8.65685 + 1.48528i −0.729039 + 0.125083i
\(142\) 0 0
\(143\) −3.17157 + 3.17157i −0.265220 + 0.265220i
\(144\) 0 0
\(145\) −3.65685 + 7.31371i −0.303685 + 0.607370i
\(146\) 0 0
\(147\) 6.58579 + 4.65685i 0.543187 + 0.384091i
\(148\) 0 0
\(149\) 13.3137 1.09070 0.545351 0.838208i \(-0.316396\pi\)
0.545351 + 0.838208i \(0.316396\pi\)
\(150\) 0 0
\(151\) 13.6569 1.11138 0.555690 0.831390i \(-0.312454\pi\)
0.555690 + 0.831390i \(0.312454\pi\)
\(152\) 0 0
\(153\) 3.34315 7.00000i 0.270277 0.565916i
\(154\) 0 0
\(155\) −5.65685 + 11.3137i −0.454369 + 0.908739i
\(156\) 0 0
\(157\) 5.48528 5.48528i 0.437773 0.437773i −0.453489 0.891262i \(-0.649821\pi\)
0.891262 + 0.453489i \(0.149821\pi\)
\(158\) 0 0
\(159\) 1.24264 + 7.24264i 0.0985478 + 0.574379i
\(160\) 0 0
\(161\) 21.3137i 1.67976i
\(162\) 0 0
\(163\) 0.414214 + 0.414214i 0.0324437 + 0.0324437i 0.723143 0.690699i \(-0.242697\pi\)
−0.690699 + 0.723143i \(0.742697\pi\)
\(164\) 0 0
\(165\) −2.82843 + 1.51472i −0.220193 + 0.117921i
\(166\) 0 0
\(167\) 9.24264 + 9.24264i 0.715217 + 0.715217i 0.967622 0.252405i \(-0.0812214\pi\)
−0.252405 + 0.967622i \(0.581221\pi\)
\(168\) 0 0
\(169\) 16.3137i 1.25490i
\(170\) 0 0
\(171\) −2.34315 + 0.828427i −0.179185 + 0.0633514i
\(172\) 0 0
\(173\) 0.656854 0.656854i 0.0499397 0.0499397i −0.681696 0.731636i \(-0.738757\pi\)
0.731636 + 0.681696i \(0.238757\pi\)
\(174\) 0 0
\(175\) −16.8995 2.41421i −1.27748 0.182497i
\(176\) 0 0
\(177\) 4.00000 5.65685i 0.300658 0.425195i
\(178\) 0 0
\(179\) −12.0000 −0.896922 −0.448461 0.893802i \(-0.648028\pi\)
−0.448461 + 0.893802i \(0.648028\pi\)
\(180\) 0 0
\(181\) −5.31371 −0.394965 −0.197482 0.980306i \(-0.563277\pi\)
−0.197482 + 0.980306i \(0.563277\pi\)
\(182\) 0 0
\(183\) −0.343146 + 0.485281i −0.0253661 + 0.0358730i
\(184\) 0 0
\(185\) 5.82843 + 17.4853i 0.428514 + 1.28554i
\(186\) 0 0
\(187\) −1.51472 + 1.51472i −0.110767 + 0.110767i
\(188\) 0 0
\(189\) 15.4853 8.65685i 1.12639 0.629693i
\(190\) 0 0
\(191\) 4.14214i 0.299714i −0.988708 0.149857i \(-0.952119\pi\)
0.988708 0.149857i \(-0.0478814\pi\)
\(192\) 0 0
\(193\) 14.6569 + 14.6569i 1.05502 + 1.05502i 0.998395 + 0.0566281i \(0.0180349\pi\)
0.0566281 + 0.998395i \(0.481965\pi\)
\(194\) 0 0
\(195\) −6.07107 + 20.0711i −0.434758 + 1.43732i
\(196\) 0 0
\(197\) −14.6569 14.6569i −1.04426 1.04426i −0.998974 0.0452834i \(-0.985581\pi\)
−0.0452834 0.998974i \(-0.514419\pi\)
\(198\) 0 0
\(199\) 18.4853i 1.31039i −0.755461 0.655193i \(-0.772587\pi\)
0.755461 0.655193i \(-0.227413\pi\)
\(200\) 0 0
\(201\) −4.17157 24.3137i −0.294240 1.71496i
\(202\) 0 0
\(203\) −8.82843 + 8.82843i −0.619634 + 0.619634i
\(204\) 0 0
\(205\) −11.3137 5.65685i −0.790184 0.395092i
\(206\) 0 0
\(207\) −16.8995 8.07107i −1.17460 0.560978i
\(208\) 0 0
\(209\) 0.686292 0.0474718
\(210\) 0 0
\(211\) −20.9706 −1.44367 −0.721837 0.692064i \(-0.756702\pi\)
−0.721837 + 0.692064i \(0.756702\pi\)
\(212\) 0 0
\(213\) −14.8284 10.4853i −1.01603 0.718440i
\(214\) 0 0
\(215\) 1.24264 0.414214i 0.0847474 0.0282491i
\(216\) 0 0
\(217\) −13.6569 + 13.6569i −0.927088 + 0.927088i
\(218\) 0 0
\(219\) 11.2426 1.92893i 0.759707 0.130345i
\(220\) 0 0
\(221\) 14.0000i 0.941742i
\(222\) 0 0
\(223\) 5.58579 + 5.58579i 0.374052 + 0.374052i 0.868951 0.494899i \(-0.164795\pi\)
−0.494899 + 0.868951i \(0.664795\pi\)
\(224\) 0 0
\(225\) −8.31371 + 12.4853i −0.554247 + 0.832352i
\(226\) 0 0
\(227\) −4.89949 4.89949i −0.325191 0.325191i 0.525563 0.850754i \(-0.323855\pi\)
−0.850754 + 0.525563i \(0.823855\pi\)
\(228\) 0 0
\(229\) 14.3431i 0.947822i −0.880573 0.473911i \(-0.842842\pi\)
0.880573 0.473911i \(-0.157158\pi\)
\(230\) 0 0
\(231\) −4.82843 + 0.828427i −0.317687 + 0.0545065i
\(232\) 0 0
\(233\) −11.8284 + 11.8284i −0.774906 + 0.774906i −0.978960 0.204054i \(-0.934588\pi\)
0.204054 + 0.978960i \(0.434588\pi\)
\(234\) 0 0
\(235\) 10.7574 3.58579i 0.701733 0.233911i
\(236\) 0 0
\(237\) −1.17157 0.828427i −0.0761018 0.0538121i
\(238\) 0 0
\(239\) 16.0000 1.03495 0.517477 0.855697i \(-0.326871\pi\)
0.517477 + 0.855697i \(0.326871\pi\)
\(240\) 0 0
\(241\) −0.343146 −0.0221040 −0.0110520 0.999939i \(-0.503518\pi\)
−0.0110520 + 0.999939i \(0.503518\pi\)
\(242\) 0 0
\(243\) −1.00000 15.5563i −0.0641500 0.997940i
\(244\) 0 0
\(245\) −9.31371 4.65685i −0.595031 0.297516i
\(246\) 0 0
\(247\) 3.17157 3.17157i 0.201802 0.201802i
\(248\) 0 0
\(249\) 1.34315 + 7.82843i 0.0851184 + 0.496106i
\(250\) 0 0
\(251\) 26.4853i 1.67174i −0.548930 0.835868i \(-0.684965\pi\)
0.548930 0.835868i \(-0.315035\pi\)
\(252\) 0 0
\(253\) 3.65685 + 3.65685i 0.229904 + 0.229904i
\(254\) 0 0
\(255\) −2.89949 + 9.58579i −0.181573 + 0.600285i
\(256\) 0 0
\(257\) −9.48528 9.48528i −0.591676 0.591676i 0.346408 0.938084i \(-0.387401\pi\)
−0.938084 + 0.346408i \(0.887401\pi\)
\(258\) 0 0
\(259\) 28.1421i 1.74867i
\(260\) 0 0
\(261\) 3.65685 + 10.3431i 0.226354 + 0.640225i
\(262\) 0 0
\(263\) −6.89949 + 6.89949i −0.425441 + 0.425441i −0.887072 0.461631i \(-0.847264\pi\)
0.461631 + 0.887072i \(0.347264\pi\)
\(264\) 0 0
\(265\) −3.00000 9.00000i −0.184289 0.552866i
\(266\) 0 0
\(267\) 15.6569 22.1421i 0.958184 1.35508i
\(268\) 0 0
\(269\) 16.6274 1.01379 0.506896 0.862007i \(-0.330793\pi\)
0.506896 + 0.862007i \(0.330793\pi\)
\(270\) 0 0
\(271\) −10.3431 −0.628301 −0.314151 0.949373i \(-0.601720\pi\)
−0.314151 + 0.949373i \(0.601720\pi\)
\(272\) 0 0
\(273\) −18.4853 + 26.1421i −1.11878 + 1.58219i
\(274\) 0 0
\(275\) 3.31371 2.48528i 0.199824 0.149868i
\(276\) 0 0
\(277\) −8.17157 + 8.17157i −0.490982 + 0.490982i −0.908616 0.417633i \(-0.862860\pi\)
0.417633 + 0.908616i \(0.362860\pi\)
\(278\) 0 0
\(279\) 5.65685 + 16.0000i 0.338667 + 0.957895i
\(280\) 0 0
\(281\) 5.65685i 0.337460i 0.985662 + 0.168730i \(0.0539665\pi\)
−0.985662 + 0.168730i \(0.946033\pi\)
\(282\) 0 0
\(283\) −5.24264 5.24264i −0.311643 0.311643i 0.533903 0.845546i \(-0.320725\pi\)
−0.845546 + 0.533903i \(0.820725\pi\)
\(284\) 0 0
\(285\) 2.82843 1.51472i 0.167542 0.0897242i
\(286\) 0 0
\(287\) −13.6569 13.6569i −0.806139 0.806139i
\(288\) 0 0
\(289\) 10.3137i 0.606689i
\(290\) 0 0
\(291\) 0.414214 + 2.41421i 0.0242816 + 0.141524i
\(292\) 0 0
\(293\) 16.6569 16.6569i 0.973104 0.973104i −0.0265438 0.999648i \(-0.508450\pi\)
0.999648 + 0.0265438i \(0.00845016\pi\)
\(294\) 0 0
\(295\) −4.00000 + 8.00000i −0.232889 + 0.465778i
\(296\) 0 0
\(297\) −1.17157 + 4.14214i −0.0679816 + 0.240351i
\(298\) 0 0
\(299\) 33.7990 1.95465
\(300\) 0 0
\(301\) 2.00000 0.115278
\(302\) 0 0
\(303\) −13.6569 9.65685i −0.784566 0.554772i
\(304\) 0 0
\(305\) 0.343146 0.686292i 0.0196485 0.0392969i
\(306\) 0 0
\(307\) 6.89949 6.89949i 0.393775 0.393775i −0.482256 0.876031i \(-0.660182\pi\)
0.876031 + 0.482256i \(0.160182\pi\)
\(308\) 0 0
\(309\) −13.4853 + 2.31371i −0.767151 + 0.131622i
\(310\) 0 0
\(311\) 5.51472i 0.312711i −0.987701 0.156356i \(-0.950025\pi\)
0.987701 0.156356i \(-0.0499746\pi\)
\(312\) 0 0
\(313\) −2.31371 2.31371i −0.130779 0.130779i 0.638688 0.769466i \(-0.279478\pi\)
−0.769466 + 0.638688i \(0.779478\pi\)
\(314\) 0 0
\(315\) −18.0711 + 14.0711i −1.01819 + 0.792815i
\(316\) 0 0
\(317\) 4.65685 + 4.65685i 0.261555 + 0.261555i 0.825686 0.564131i \(-0.190789\pi\)
−0.564131 + 0.825686i \(0.690789\pi\)
\(318\) 0 0
\(319\) 3.02944i 0.169616i
\(320\) 0 0
\(321\) 23.1421 3.97056i 1.29167 0.221615i
\(322\) 0 0
\(323\) 1.51472 1.51472i 0.0842812 0.0842812i
\(324\) 0 0
\(325\) 3.82843 26.7990i 0.212363 1.48654i
\(326\) 0 0
\(327\) 5.65685 + 4.00000i 0.312825 + 0.221201i
\(328\) 0 0
\(329\) 17.3137 0.954536
\(330\) 0 0
\(331\) 9.65685 0.530789 0.265394 0.964140i \(-0.414498\pi\)
0.265394 + 0.964140i \(0.414498\pi\)
\(332\) 0 0
\(333\) 22.3137 + 10.6569i 1.22278 + 0.583992i
\(334\) 0 0
\(335\) 10.0711 + 30.2132i 0.550241 + 1.65072i
\(336\) 0 0
\(337\) 1.00000 1.00000i 0.0544735 0.0544735i −0.679345 0.733819i \(-0.737736\pi\)
0.733819 + 0.679345i \(0.237736\pi\)
\(338\) 0 0
\(339\) −3.92893 22.8995i −0.213390 1.24373i
\(340\) 0 0
\(341\) 4.68629i 0.253777i
\(342\) 0 0
\(343\) 5.65685 + 5.65685i 0.305441 + 0.305441i
\(344\) 0 0
\(345\) 23.1421 + 7.00000i 1.24593 + 0.376867i
\(346\) 0 0
\(347\) 12.0711 + 12.0711i 0.648009 + 0.648009i 0.952511 0.304503i \(-0.0984902\pi\)
−0.304503 + 0.952511i \(0.598490\pi\)
\(348\) 0 0
\(349\) 9.65685i 0.516920i 0.966022 + 0.258460i \(0.0832149\pi\)
−0.966022 + 0.258460i \(0.916785\pi\)
\(350\) 0 0
\(351\) 13.7279 + 24.5563i 0.732742 + 1.31072i
\(352\) 0 0
\(353\) 15.4853 15.4853i 0.824198 0.824198i −0.162509 0.986707i \(-0.551959\pi\)
0.986707 + 0.162509i \(0.0519586\pi\)
\(354\) 0 0
\(355\) 20.9706 + 10.4853i 1.11300 + 0.556501i
\(356\) 0 0
\(357\) −8.82843 + 12.4853i −0.467250 + 0.660791i
\(358\) 0 0
\(359\) −35.3137 −1.86379 −0.931893 0.362733i \(-0.881844\pi\)
−0.931893 + 0.362733i \(0.881844\pi\)
\(360\) 0 0
\(361\) 18.3137 0.963879
\(362\) 0 0
\(363\) −10.3137 + 14.5858i −0.541329 + 0.765555i
\(364\) 0 0
\(365\) −13.9706 + 4.65685i −0.731253 + 0.243751i
\(366\) 0 0
\(367\) 4.75736 4.75736i 0.248332 0.248332i −0.571954 0.820286i \(-0.693814\pi\)
0.820286 + 0.571954i \(0.193814\pi\)
\(368\) 0 0
\(369\) −16.0000 + 5.65685i −0.832927 + 0.294484i
\(370\) 0 0
\(371\) 14.4853i 0.752038i
\(372\) 0 0
\(373\) 0.514719 + 0.514719i 0.0266511 + 0.0266511i 0.720307 0.693656i \(-0.244001\pi\)
−0.693656 + 0.720307i \(0.744001\pi\)
\(374\) 0 0
\(375\) 8.17157 17.5563i 0.421978 0.906606i
\(376\) 0 0
\(377\) −14.0000 14.0000i −0.721037 0.721037i
\(378\) 0 0
\(379\) 29.7990i 1.53067i 0.643631 + 0.765336i \(0.277427\pi\)
−0.643631 + 0.765336i \(0.722573\pi\)
\(380\) 0 0
\(381\) −2.31371 13.4853i −0.118535 0.690872i
\(382\) 0 0
\(383\) 12.4142 12.4142i 0.634337 0.634337i −0.314816 0.949153i \(-0.601943\pi\)
0.949153 + 0.314816i \(0.101943\pi\)
\(384\) 0 0
\(385\) 6.00000 2.00000i 0.305788 0.101929i
\(386\) 0 0
\(387\) 0.757359 1.58579i 0.0384987 0.0806101i
\(388\) 0 0
\(389\) 6.68629 0.339008 0.169504 0.985529i \(-0.445783\pi\)
0.169504 + 0.985529i \(0.445783\pi\)
\(390\) 0 0
\(391\) 16.1421 0.816343
\(392\) 0 0
\(393\) −12.4853 8.82843i −0.629799 0.445335i
\(394\) 0 0
\(395\) 1.65685 + 0.828427i 0.0833654 + 0.0416827i
\(396\) 0 0
\(397\) 7.82843 7.82843i 0.392897 0.392897i −0.482821 0.875719i \(-0.660388\pi\)
0.875719 + 0.482821i \(0.160388\pi\)
\(398\) 0 0
\(399\) 4.82843 0.828427i 0.241724 0.0414732i
\(400\) 0 0
\(401\) 16.0000i 0.799002i −0.916733 0.399501i \(-0.869183\pi\)
0.916733 0.399501i \(-0.130817\pi\)
\(402\) 0 0
\(403\) −21.6569 21.6569i −1.07880 1.07880i
\(404\) 0 0
\(405\) 4.31371 + 19.6569i 0.214350 + 0.976757i
\(406\) 0 0
\(407\) −4.82843 4.82843i −0.239336 0.239336i
\(408\) 0 0
\(409\) 21.6569i 1.07086i −0.844579 0.535431i \(-0.820149\pi\)
0.844579 0.535431i \(-0.179851\pi\)
\(410\) 0 0
\(411\) −23.7279 + 4.07107i −1.17041 + 0.200811i
\(412\) 0 0
\(413\) −9.65685 + 9.65685i −0.475183 + 0.475183i
\(414\) 0 0
\(415\) −3.24264 9.72792i −0.159175 0.477525i
\(416\) 0 0
\(417\) 12.4853 + 8.82843i 0.611407 + 0.432330i
\(418\) 0 0
\(419\) −29.9411 −1.46272 −0.731360 0.681992i \(-0.761114\pi\)
−0.731360 + 0.681992i \(0.761114\pi\)
\(420\) 0 0
\(421\) 30.9706 1.50941 0.754706 0.656063i \(-0.227779\pi\)
0.754706 + 0.656063i \(0.227779\pi\)
\(422\) 0 0
\(423\) 6.55635 13.7279i 0.318781 0.667474i
\(424\) 0 0
\(425\) 1.82843 12.7990i 0.0886917 0.620842i
\(426\) 0 0
\(427\) 0.828427 0.828427i 0.0400904 0.0400904i
\(428\) 0 0
\(429\) −1.31371 7.65685i −0.0634264 0.369676i
\(430\) 0 0
\(431\) 20.1421i 0.970213i −0.874455 0.485106i \(-0.838781\pi\)
0.874455 0.485106i \(-0.161219\pi\)
\(432\) 0 0
\(433\) −15.0000 15.0000i −0.720854 0.720854i 0.247925 0.968779i \(-0.420251\pi\)
−0.968779 + 0.247925i \(0.920251\pi\)
\(434\) 0 0
\(435\) −6.68629 12.4853i −0.320583 0.598623i
\(436\) 0 0
\(437\) −3.65685 3.65685i −0.174931 0.174931i
\(438\) 0 0
\(439\) 13.7990i 0.658590i −0.944227 0.329295i \(-0.893189\pi\)
0.944227 0.329295i \(-0.106811\pi\)
\(440\) 0 0
\(441\) −13.1716 + 4.65685i −0.627218 + 0.221755i
\(442\) 0 0
\(443\) −0.0710678 + 0.0710678i −0.00337653 + 0.00337653i −0.708793 0.705416i \(-0.750760\pi\)
0.705416 + 0.708793i \(0.250760\pi\)
\(444\) 0 0
\(445\) −15.6569 + 31.3137i −0.742206 + 1.48441i
\(446\) 0 0
\(447\) −13.3137 + 18.8284i −0.629717 + 0.890554i
\(448\) 0 0
\(449\) 1.31371 0.0619977 0.0309989 0.999519i \(-0.490131\pi\)
0.0309989 + 0.999519i \(0.490131\pi\)
\(450\) 0 0
\(451\) 4.68629 0.220669
\(452\) 0 0
\(453\) −13.6569 + 19.3137i −0.641655 + 0.907437i
\(454\) 0 0
\(455\) 18.4853 36.9706i 0.866603 1.73321i
\(456\) 0 0
\(457\) 1.00000 1.00000i 0.0467780 0.0467780i −0.683331 0.730109i \(-0.739469\pi\)
0.730109 + 0.683331i \(0.239469\pi\)
\(458\) 0 0
\(459\) 6.55635 + 11.7279i 0.306024 + 0.547413i
\(460\) 0 0
\(461\) 28.9706i 1.34929i 0.738141 + 0.674647i \(0.235704\pi\)
−0.738141 + 0.674647i \(0.764296\pi\)
\(462\) 0 0
\(463\) 21.5858 + 21.5858i 1.00318 + 1.00318i 0.999995 + 0.00318163i \(0.00101275\pi\)
0.00318163 + 0.999995i \(0.498987\pi\)
\(464\) 0 0
\(465\) −10.3431 19.3137i −0.479652 0.895652i
\(466\) 0 0
\(467\) 23.3848 + 23.3848i 1.08212 + 1.08212i 0.996312 + 0.0858066i \(0.0273467\pi\)
0.0858066 + 0.996312i \(0.472653\pi\)
\(468\) 0 0
\(469\) 48.6274i 2.24541i
\(470\) 0 0
\(471\) 2.27208 + 13.2426i 0.104692 + 0.610189i
\(472\) 0 0
\(473\) −0.343146 + 0.343146i −0.0157779 + 0.0157779i
\(474\) 0 0
\(475\) −3.31371 + 2.48528i −0.152043 + 0.114033i
\(476\) 0 0
\(477\) −11.4853 5.48528i −0.525875 0.251154i
\(478\) 0 0
\(479\) 22.6274 1.03387 0.516937 0.856024i \(-0.327072\pi\)
0.516937 + 0.856024i \(0.327072\pi\)
\(480\) 0 0
\(481\) −44.6274 −2.03484
\(482\) 0 0
\(483\) 30.1421 + 21.3137i 1.37151 + 0.969807i
\(484\) 0 0
\(485\) −1.00000 3.00000i −0.0454077 0.136223i
\(486\) 0 0
\(487\) −14.5563 + 14.5563i −0.659611 + 0.659611i −0.955288 0.295677i \(-0.904455\pi\)
0.295677 + 0.955288i \(0.404455\pi\)
\(488\) 0 0
\(489\) −1.00000 + 0.171573i −0.0452216 + 0.00775879i
\(490\) 0 0
\(491\) 21.5147i 0.970946i 0.874252 + 0.485473i \(0.161353\pi\)
−0.874252 + 0.485473i \(0.838647\pi\)
\(492\) 0 0
\(493\) −6.68629 6.68629i −0.301135 0.301135i
\(494\) 0 0
\(495\) 0.686292 5.51472i 0.0308465 0.247868i
\(496\) 0 0
\(497\) 25.3137 + 25.3137i 1.13548 + 1.13548i
\(498\) 0 0
\(499\) 34.7696i 1.55650i −0.627955 0.778249i \(-0.716108\pi\)
0.627955 0.778249i \(-0.283892\pi\)
\(500\) 0 0
\(501\) −22.3137 + 3.82843i −0.996903 + 0.171042i
\(502\) 0 0
\(503\) −5.92893 + 5.92893i −0.264358 + 0.264358i −0.826822 0.562464i \(-0.809854\pi\)
0.562464 + 0.826822i \(0.309854\pi\)
\(504\) 0 0
\(505\) 19.3137 + 9.65685i 0.859449 + 0.429724i
\(506\) 0 0
\(507\) −23.0711 16.3137i −1.02462 0.724517i
\(508\) 0 0
\(509\) −3.65685 −0.162087 −0.0810436 0.996711i \(-0.525825\pi\)
−0.0810436 + 0.996711i \(0.525825\pi\)
\(510\) 0 0
\(511\) −22.4853 −0.994690
\(512\) 0 0
\(513\) 1.17157 4.14214i 0.0517262 0.182880i
\(514\) 0 0
\(515\) 16.7574 5.58579i 0.738417 0.246139i
\(516\) 0 0
\(517\) −2.97056 + 2.97056i −0.130645 + 0.130645i
\(518\) 0 0
\(519\) 0.272078 + 1.58579i 0.0119429 + 0.0696083i
\(520\) 0 0
\(521\) 24.0000i 1.05146i 0.850652 + 0.525730i \(0.176208\pi\)
−0.850652 + 0.525730i \(0.823792\pi\)
\(522\) 0 0
\(523\) −26.8995 26.8995i −1.17623 1.17623i −0.980696 0.195536i \(-0.937355\pi\)
−0.195536 0.980696i \(-0.562645\pi\)
\(524\) 0 0
\(525\) 20.3137 21.4853i 0.886563 0.937695i
\(526\) 0 0
\(527\) −10.3431 10.3431i −0.450555 0.450555i
\(528\) 0 0
\(529\) 15.9706i 0.694372i
\(530\) 0 0
\(531\) 4.00000 + 11.3137i 0.173585 + 0.490973i
\(532\) 0 0
\(533\) 21.6569 21.6569i 0.938062 0.938062i
\(534\) 0 0
\(535\) −28.7574 + 9.58579i −1.24329 + 0.414430i
\(536\) 0 0
\(537\) 12.0000 16.9706i 0.517838 0.732334i
\(538\) 0 0
\(539\) 3.85786 0.166170
\(540\) 0 0
\(541\) −29.3137 −1.26029 −0.630147 0.776476i \(-0.717006\pi\)
−0.630147 + 0.776476i \(0.717006\pi\)
\(542\) 0 0
\(543\) 5.31371 7.51472i 0.228033 0.322487i
\(544\) 0 0
\(545\) −8.00000 4.00000i −0.342682 0.171341i
\(546\) 0 0
\(547\) −15.7279 + 15.7279i −0.672477 + 0.672477i −0.958287 0.285809i \(-0.907738\pi\)
0.285809 + 0.958287i \(0.407738\pi\)
\(548\) 0 0
\(549\) −0.343146 0.970563i −0.0146451 0.0414226i
\(550\) 0 0
\(551\) 3.02944i 0.129058i
\(552\) 0 0
\(553\) 2.00000 + 2.00000i 0.0850487 + 0.0850487i
\(554\) 0 0
\(555\) −30.5563 9.24264i −1.29704 0.392328i
\(556\) 0 0
\(557\) −15.6274 15.6274i −0.662155 0.662155i 0.293733 0.955888i \(-0.405102\pi\)
−0.955888 + 0.293733i \(0.905102\pi\)
\(558\) 0 0
\(559\) 3.17157i 0.134143i
\(560\) 0 0
\(561\) −0.627417 3.65685i −0.0264896 0.154393i
\(562\) 0 0
\(563\) −1.44365 + 1.44365i −0.0608426 + 0.0608426i −0.736873 0.676031i \(-0.763699\pi\)
0.676031 + 0.736873i \(0.263699\pi\)
\(564\) 0 0
\(565\) 9.48528 + 28.4558i 0.399049 + 1.19715i
\(566\) 0 0
\(567\) −3.24264 + 30.5563i −0.136178 + 1.28325i
\(568\) 0 0
\(569\) −45.3137 −1.89965 −0.949825 0.312783i \(-0.898739\pi\)
−0.949825 + 0.312783i \(0.898739\pi\)
\(570\) 0 0
\(571\) 4.97056 0.208012 0.104006 0.994577i \(-0.466834\pi\)
0.104006 + 0.994577i \(0.466834\pi\)
\(572\) 0 0
\(573\) 5.85786 + 4.14214i 0.244716 + 0.173040i
\(574\) 0 0
\(575\) −30.8995 4.41421i −1.28860 0.184085i
\(576\) 0 0
\(577\) 14.6569 14.6569i 0.610173 0.610173i −0.332818 0.942991i \(-0.608000\pi\)
0.942991 + 0.332818i \(0.108000\pi\)
\(578\) 0 0
\(579\) −35.3848 + 6.07107i −1.47054 + 0.252305i
\(580\) 0 0
\(581\) 15.6569i 0.649556i
\(582\) 0 0
\(583\) 2.48528 + 2.48528i 0.102930 + 0.102930i
\(584\) 0 0
\(585\) −22.3137 28.6569i −0.922558 1.18482i
\(586\) 0 0
\(587\) −10.5563 10.5563i −0.435707 0.435707i 0.454857 0.890564i \(-0.349690\pi\)
−0.890564 + 0.454857i \(0.849690\pi\)
\(588\) 0 0
\(589\) 4.68629i 0.193095i
\(590\) 0 0
\(591\) 35.3848 6.07107i 1.45554 0.249730i
\(592\) 0 0
\(593\) 15.4853 15.4853i 0.635904 0.635904i −0.313638 0.949543i \(-0.601548\pi\)
0.949543 + 0.313638i \(0.101548\pi\)
\(594\) 0 0
\(595\) 8.82843 17.6569i 0.361930 0.723860i
\(596\) 0 0
\(597\) 26.1421 + 18.4853i 1.06993 + 0.756552i
\(598\) 0 0
\(599\) −41.9411 −1.71367 −0.856834 0.515592i \(-0.827572\pi\)
−0.856834 + 0.515592i \(0.827572\pi\)
\(600\) 0 0
\(601\) −14.9706 −0.610662 −0.305331 0.952246i \(-0.598767\pi\)
−0.305331 + 0.952246i \(0.598767\pi\)
\(602\) 0 0
\(603\) 38.5563 + 18.4142i 1.57014 + 0.749885i
\(604\) 0 0
\(605\) 10.3137 20.6274i 0.419312 0.838624i
\(606\) 0 0
\(607\) 33.0416 33.0416i 1.34112 1.34112i 0.446170 0.894948i \(-0.352788\pi\)
0.894948 0.446170i \(-0.147212\pi\)
\(608\) 0 0
\(609\) −3.65685 21.3137i −0.148183 0.863675i
\(610\) 0 0
\(611\) 27.4558i 1.11074i
\(612\) 0 0
\(613\) 9.48528 + 9.48528i 0.383107 + 0.383107i 0.872220 0.489113i \(-0.162680\pi\)
−0.489113 + 0.872220i \(0.662680\pi\)
\(614\) 0 0
\(615\) 19.3137 10.3431i 0.778804 0.417076i
\(616\) 0 0
\(617\) 12.1716 + 12.1716i 0.490009 + 0.490009i 0.908309 0.418300i \(-0.137374\pi\)
−0.418300 + 0.908309i \(0.637374\pi\)
\(618\) 0 0
\(619\) 20.1421i 0.809581i −0.914410 0.404790i \(-0.867344\pi\)
0.914410 0.404790i \(-0.132656\pi\)
\(620\) 0 0
\(621\) 28.3137 15.8284i 1.13619 0.635173i
\(622\) 0 0
\(623\) −37.7990 + 37.7990i −1.51438 + 1.51438i
\(624\) 0 0
\(625\) −7.00000 + 24.0000i −0.280000 + 0.960000i
\(626\) 0 0
\(627\) −0.686292 + 0.970563i −0.0274078 + 0.0387605i
\(628\) 0 0
\(629\) −21.3137 −0.849833
\(630\) 0 0
\(631\) −31.5980 −1.25790 −0.628948 0.777447i \(-0.716514\pi\)
−0.628948 + 0.777447i \(0.716514\pi\)
\(632\) 0 0
\(633\) 20.9706 29.6569i 0.833505 1.17875i
\(634\) 0 0
\(635\) 5.58579 + 16.7574i 0.221665 + 0.664996i
\(636\) 0 0
\(637\) 17.8284 17.8284i 0.706388 0.706388i
\(638\) 0 0
\(639\) 29.6569 10.4853i 1.17321 0.414791i
\(640\) 0 0
\(641\) 20.2843i 0.801181i 0.916257 + 0.400590i \(0.131195\pi\)
−0.916257 + 0.400590i \(0.868805\pi\)
\(642\) 0 0
\(643\) 28.6985 + 28.6985i 1.13176 + 1.13176i 0.989885 + 0.141873i \(0.0453124\pi\)
0.141873 + 0.989885i \(0.454688\pi\)
\(644\) 0 0
\(645\) −0.656854 + 2.17157i −0.0258636 + 0.0855056i
\(646\) 0 0
\(647\) 26.2132 + 26.2132i 1.03055 + 1.03055i 0.999518 + 0.0310289i \(0.00987838\pi\)
0.0310289 + 0.999518i \(0.490122\pi\)
\(648\) 0 0
\(649\) 3.31371i 0.130074i
\(650\) 0 0
\(651\) −5.65685 32.9706i −0.221710 1.29222i
\(652\) 0 0
\(653\) −26.6569 + 26.6569i −1.04316 + 1.04316i −0.0441379 + 0.999025i \(0.514054\pi\)
−0.999025 + 0.0441379i \(0.985946\pi\)
\(654\) 0 0
\(655\) 17.6569 + 8.82843i 0.689910 + 0.344955i
\(656\) 0 0
\(657\) −8.51472 + 17.8284i −0.332191 + 0.695553i
\(658\) 0 0
\(659\) 10.6274 0.413985 0.206993 0.978342i \(-0.433632\pi\)
0.206993 + 0.978342i \(0.433632\pi\)
\(660\) 0 0
\(661\) −7.65685 −0.297817 −0.148909 0.988851i \(-0.547576\pi\)
−0.148909 + 0.988851i \(0.547576\pi\)
\(662\) 0 0
\(663\) −19.7990 14.0000i −0.768929 0.543715i
\(664\) 0 0
\(665\) −6.00000 + 2.00000i −0.232670 + 0.0775567i
\(666\) 0 0
\(667\) −16.1421 + 16.1421i −0.625026 + 0.625026i
\(668\) 0 0
\(669\) −13.4853 + 2.31371i −0.521371 + 0.0894531i
\(670\) 0 0
\(671\) 0.284271i 0.0109742i
\(672\) 0 0
\(673\) −3.68629 3.68629i −0.142096 0.142096i 0.632480 0.774576i \(-0.282037\pi\)
−0.774576 + 0.632480i \(0.782037\pi\)
\(674\) 0 0
\(675\) −9.34315 24.2426i −0.359618 0.933100i
\(676\) 0 0
\(677\) 35.2843 + 35.2843i 1.35608 + 1.35608i 0.878688 + 0.477397i \(0.158420\pi\)
0.477397 + 0.878688i \(0.341580\pi\)
\(678\) 0 0
\(679\) 4.82843i 0.185298i
\(680\) 0 0
\(681\) 11.8284 2.02944i 0.453266 0.0777682i
\(682\) 0 0
\(683\) 22.5563 22.5563i 0.863095 0.863095i −0.128602 0.991696i \(-0.541049\pi\)
0.991696 + 0.128602i \(0.0410488\pi\)
\(684\) 0 0
\(685\) 29.4853 9.82843i 1.12657 0.375525i
\(686\) 0 0
\(687\) 20.2843 + 14.3431i 0.773893 + 0.547225i
\(688\) 0 0
\(689\) 22.9706 0.875109
\(690\) 0 0
\(691\) 33.6569 1.28037 0.640184 0.768222i \(-0.278858\pi\)
0.640184 + 0.768222i \(0.278858\pi\)
\(692\) 0 0
\(693\) 3.65685 7.65685i 0.138912 0.290860i
\(694\) 0 0
\(695\) −17.6569 8.82843i −0.669763 0.334881i
\(696\) 0 0
\(697\) 10.3431 10.3431i 0.391775 0.391775i
\(698\) 0 0
\(699\) −4.89949 28.5563i −0.185316 1.08010i
\(700\) 0 0
\(701\) 4.00000i 0.151078i 0.997143 + 0.0755390i \(0.0240677\pi\)
−0.997143 + 0.0755390i \(0.975932\pi\)
\(702\) 0 0
\(703\) 4.82843 + 4.82843i 0.182108 + 0.182108i
\(704\) 0 0
\(705\) −5.68629 + 18.7990i −0.214158 + 0.708011i
\(706\) 0 0
\(707\) 23.3137 + 23.3137i 0.876802 + 0.876802i
\(708\) 0 0
\(709\) 32.2843i 1.21246i −0.795289 0.606231i \(-0.792681\pi\)
0.795289 0.606231i \(-0.207319\pi\)
\(710\) 0 0
\(711\) 2.34315 0.828427i 0.0878748 0.0310684i
\(712\) 0 0
\(713\) −24.9706 + 24.9706i −0.935155 + 0.935155i
\(714\) 0 0
\(715\) 3.17157 + 9.51472i 0.118610 + 0.355830i
\(716\) 0 0
\(717\) −16.0000 + 22.6274i −0.597531 + 0.845036i
\(718\) 0 0
\(719\) −16.0000 −0.596699 −0.298350 0.954457i \(-0.596436\pi\)
−0.298350 + 0.954457i \(0.596436\pi\)
\(720\) 0 0
\(721\) 26.9706 1.00444
\(722\) 0 0
\(723\) 0.343146 0.485281i 0.0127617 0.0180478i
\(724\) 0 0
\(725\) 10.9706 + 14.6274i 0.407436 + 0.543249i
\(726\) 0 0
\(727\) 12.7574 12.7574i 0.473144 0.473144i −0.429786 0.902931i \(-0.641411\pi\)
0.902931 + 0.429786i \(0.141411\pi\)
\(728\) 0 0
\(729\) 23.0000 + 14.1421i 0.851852 + 0.523783i
\(730\) 0 0
\(731\) 1.51472i 0.0560239i
\(732\) 0 0
\(733\) −5.14214 5.14214i −0.189929 0.189929i 0.605736 0.795665i \(-0.292879\pi\)
−0.795665 + 0.605736i \(0.792879\pi\)
\(734\) 0 0
\(735\) 15.8995 8.51472i 0.586462 0.314070i
\(736\) 0 0
\(737\) −8.34315 8.34315i −0.307324 0.307324i
\(738\) 0 0
\(739\) 47.1716i 1.73523i 0.497233 + 0.867617i \(0.334350\pi\)
−0.497233 + 0.867617i \(0.665650\pi\)
\(740\) 0 0
\(741\) 1.31371 + 7.65685i 0.0482603 + 0.281282i
\(742\) 0 0
\(743\) 37.3848 37.3848i 1.37151 1.37151i 0.513313 0.858202i \(-0.328418\pi\)
0.858202 0.513313i \(-0.171582\pi\)
\(744\) 0 0
\(745\) 13.3137 26.6274i 0.487777 0.975553i
\(746\) 0 0
\(747\) −12.4142 5.92893i −0.454212 0.216928i
\(748\) 0 0
\(749\) −46.2843 −1.69119
\(750\) 0 0
\(751\) 12.2843 0.448259 0.224130 0.974559i \(-0.428046\pi\)
0.224130 + 0.974559i \(0.428046\pi\)
\(752\) 0 0
\(753\) 37.4558 + 26.4853i 1.36497 + 0.965177i
\(754\) 0 0
\(755\) 13.6569 27.3137i 0.497024 0.994048i
\(756\) 0 0
\(757\) 14.4558 14.4558i 0.525407 0.525407i −0.393793 0.919199i \(-0.628837\pi\)
0.919199 + 0.393793i \(0.128837\pi\)
\(758\) 0 0
\(759\) −8.82843 + 1.51472i −0.320452 + 0.0549808i
\(760\) 0 0
\(761\) 12.6863i 0.459878i 0.973205 + 0.229939i \(0.0738526\pi\)
−0.973205 + 0.229939i \(0.926147\pi\)
\(762\) 0 0
\(763\) −9.65685 9.65685i −0.349602 0.349602i
\(764\) 0 0
\(765\) −10.6569 13.6863i −0.385299 0.494829i
\(766\) 0 0
\(767\) −15.3137 15.3137i −0.552946 0.552946i
\(768\) 0 0
\(769\) 49.9411i 1.80092i 0.434936 + 0.900462i \(0.356771\pi\)
−0.434936 + 0.900462i \(0.643229\pi\)
\(770\) 0 0
\(771\) 22.8995 3.92893i 0.824705 0.141497i
\(772\) 0 0
\(773\) −10.6569 + 10.6569i −0.383300 + 0.383300i −0.872290 0.488989i \(-0.837366\pi\)
0.488989 + 0.872290i \(0.337366\pi\)
\(774\) 0 0
\(775\) 16.9706 + 22.6274i 0.609601 + 0.812801i
\(776\) 0 0
\(777\) −39.7990 28.1421i −1.42778 1.00959i
\(778\) 0 0
\(779\) −4.68629 −0.167904
\(780\) 0 0
\(781\) −8.68629 −0.310820
\(782\) 0 0
\(783\) −18.2843 5.17157i −0.653427 0.184817i
\(784\) 0 0
\(785\) −5.48528 16.4558i −0.195778 0.587334i
\(786\) 0 0
\(787\) 27.5858 27.5858i 0.983327 0.983327i −0.0165362 0.999863i \(-0.505264\pi\)
0.999863 + 0.0165362i \(0.00526387\pi\)
\(788\) 0 0
\(789\) −2.85786 16.6569i −0.101743 0.593000i
\(790\) 0 0
\(791\) 45.7990i 1.62842i
\(792\) 0 0
\(793\) 1.31371 + 1.31371i 0.0466512 + 0.0466512i
\(794\) 0 0