Properties

Label 240.2.v.a.17.1
Level $240$
Weight $2$
Character 240.17
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: \( x^{4} + 1 \) Copy content Toggle raw display
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 17.1
Root \(-0.707107 - 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 240.17
Dual form 240.2.v.a.113.2

$q$-expansion

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

Character values

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

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

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 0.996467 0.0839804i \(-0.0267633\pi\)
−0.0839804 + 0.996467i \(0.526763\pi\)
\(8\) 0 0
\(9\) −1.00000 + 2.82843i −0.333333 + 0.942809i
\(10\) 0 0
\(11\) 0.828427i 0.249780i −0.992171 0.124890i \(-0.960142\pi\)
0.992171 0.124890i \(-0.0398578\pi\)
\(12\) 0 0
\(13\) 3.82843 3.82843i 1.06181 1.06181i 0.0638555 0.997959i \(-0.479660\pi\)
0.997959 0.0638555i \(-0.0203397\pi\)
\(14\) 0 0
\(15\) 1.82843 3.41421i 0.472098 0.881546i
\(16\) 0 0
\(17\) 1.82843 1.82843i 0.443459 0.443459i −0.449714 0.893173i \(-0.648474\pi\)
0.893173 + 0.449714i \(0.148474\pi\)
\(18\) 0 0
\(19\) 0.828427i 0.190054i 0.995475 + 0.0950271i \(0.0302938\pi\)
−0.995475 + 0.0950271i \(0.969706\pi\)
\(20\) 0 0
\(21\) 1.00000 5.82843i 0.218218 1.27187i
\(22\) 0 0
\(23\) 4.41421 + 4.41421i 0.920427 + 0.920427i 0.997059 0.0766323i \(-0.0244167\pi\)
−0.0766323 + 0.997059i \(0.524417\pi\)
\(24\) 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 0.0409727 0.999160i \(-0.486954\pi\)
−0.999160 + 0.0409727i \(0.986954\pi\)
\(38\) 0 0
\(39\) −9.24264 1.58579i −1.48001 0.253929i
\(40\) 0 0
\(41\) 5.65685i 0.883452i 0.897150 + 0.441726i \(0.145634\pi\)
−0.897150 + 0.441726i \(0.854366\pi\)
\(42\) 0 0
\(43\) 0.414214 0.414214i 0.0631670 0.0631670i −0.674818 0.737985i \(-0.735778\pi\)
0.737985 + 0.674818i \(0.235778\pi\)
\(44\) 0 0
\(45\) −6.65685 + 0.828427i −0.992345 + 0.123495i
\(46\) 0 0
\(47\) 3.58579 3.58579i 0.523041 0.523041i −0.395448 0.918488i \(-0.629411\pi\)
0.918488 + 0.395448i \(0.129411\pi\)
\(48\) 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 0.882463 0.470381i \(-0.155884\pi\)
−0.470381 + 0.882463i \(0.655884\pi\)
\(54\) 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 −0.963819 0.266558i \(-0.914114\pi\)
−0.266558 0.963819i \(-0.585886\pi\)
\(68\) 0 0
\(69\) 1.82843 10.6569i 0.220117 1.28293i
\(70\) 0 0
\(71\) 10.4853i 1.24437i −0.782869 0.622187i \(-0.786244\pi\)
0.782869 0.622187i \(-0.213756\pi\)
\(72\) 0 0
\(73\) −4.65685 + 4.65685i −0.545044 + 0.545044i −0.925003 0.379960i \(-0.875938\pi\)
0.379960 + 0.925003i \(0.375938\pi\)
\(74\) 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 \(-0.985161\pi\)
0.998914 0.0466027i \(-0.0148395\pi\)
\(80\) 0 0
\(81\) −7.00000 5.65685i −0.777778 0.628539i
\(82\) 0 0
\(83\) 3.24264 + 3.24264i 0.355926 + 0.355926i 0.862309 0.506383i \(-0.169018\pi\)
−0.506383 + 0.862309i \(0.669018\pi\)
\(84\) 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 0.756049 0.654515i \(-0.227127\pi\)
−0.654515 + 0.756049i \(0.727127\pi\)
\(98\) 0 0
\(99\) 2.34315 + 0.828427i 0.235495 + 0.0832601i
\(100\) 0 0
\(101\) 9.65685i 0.960893i −0.877024 0.480446i \(-0.840475\pi\)
0.877024 0.480446i \(-0.159525\pi\)
\(102\) 0 0
\(103\) 5.58579 5.58579i 0.550384 0.550384i −0.376168 0.926552i \(-0.622758\pi\)
0.926552 + 0.376168i \(0.122758\pi\)
\(104\) 0 0
\(105\) 12.6569 3.82843i 1.23518 0.373616i
\(106\) 0 0
\(107\) −9.58579 + 9.58579i −0.926693 + 0.926693i −0.997491 0.0707977i \(-0.977446\pi\)
0.0707977 + 0.997491i \(0.477446\pi\)
\(108\) 0 0
\(109\) 4.00000i 0.383131i 0.981480 + 0.191565i \(0.0613564\pi\)
−0.981480 + 0.191565i \(0.938644\pi\)
\(110\) 0 0
\(111\) −2.41421 + 14.0711i −0.229147 + 1.33557i
\(112\) 0 0
\(113\) −9.48528 9.48528i −0.892300 0.892300i 0.102439 0.994739i \(-0.467335\pi\)
−0.994739 + 0.102439i \(0.967335\pi\)
\(114\) 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 0.414425 0.910083i \(-0.363983\pi\)
−0.910083 + 0.414425i \(0.863983\pi\)
\(128\) 0 0
\(129\) −1.00000 0.171573i −0.0880451 0.0151061i
\(130\) 0 0
\(131\) 8.82843i 0.771343i −0.922636 0.385672i \(-0.873970\pi\)
0.922636 0.385672i \(-0.126030\pi\)
\(132\) 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 −0.149120 0.988819i \(-0.547644\pi\)
0.988819 + 0.149120i \(0.0476440\pi\)
\(138\) 0 0
\(139\) 8.82843i 0.748817i 0.927264 + 0.374409i \(0.122154\pi\)
−0.927264 + 0.374409i \(0.877846\pi\)
\(140\) 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 0.891262 0.453489i \(-0.149821\pi\)
−0.453489 + 0.891262i \(0.649821\pi\)
\(158\) 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 −0.690699 0.723143i \(-0.742697\pi\)
0.723143 + 0.690699i \(0.242697\pi\)
\(164\) 0 0
\(165\) −2.82843 1.51472i −0.220193 0.117921i
\(166\) 0 0
\(167\) 9.24264 9.24264i 0.715217 0.715217i −0.252405 0.967622i \(-0.581221\pi\)
0.967622 + 0.252405i \(0.0812214\pi\)
\(168\) 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 0.731636 0.681696i \(-0.238757\pi\)
−0.681696 + 0.731636i \(0.738757\pi\)
\(174\) 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 \(0.0478814\pi\)
−0.988708 + 0.149857i \(0.952119\pi\)
\(192\) 0 0
\(193\) 14.6569 14.6569i 1.05502 1.05502i 0.0566281 0.998395i \(-0.481965\pi\)
0.998395 0.0566281i \(-0.0180349\pi\)
\(194\) 0 0
\(195\) −6.07107 20.0711i −0.434758 1.43732i
\(196\) 0 0
\(197\) −14.6569 + 14.6569i −1.04426 + 1.04426i −0.0452834 + 0.998974i \(0.514419\pi\)
−0.998974 + 0.0452834i \(0.985581\pi\)
\(198\) 0 0
\(199\) 18.4853i 1.31039i 0.755461 + 0.655193i \(0.227413\pi\)
−0.755461 + 0.655193i \(0.772587\pi\)
\(200\) 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 −0.494899 0.868951i \(-0.664795\pi\)
0.868951 + 0.494899i \(0.164795\pi\)
\(224\) 0 0
\(225\) −8.31371 12.4853i −0.554247 0.832352i
\(226\) 0 0
\(227\) −4.89949 + 4.89949i −0.325191 + 0.325191i −0.850754 0.525563i \(-0.823855\pi\)
0.525563 + 0.850754i \(0.323855\pi\)
\(228\) 0 0
\(229\) 14.3431i 0.947822i 0.880573 + 0.473911i \(0.157158\pi\)
−0.880573 + 0.473911i \(0.842842\pi\)
\(230\) 0 0
\(231\) −4.82843 0.828427i −0.317687 0.0545065i
\(232\) 0 0
\(233\) −11.8284 11.8284i −0.774906 0.774906i 0.204054 0.978960i \(-0.434588\pi\)
−0.978960 + 0.204054i \(0.934588\pi\)
\(234\) 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 \(0.315035\pi\)
−0.548930 + 0.835868i \(0.684965\pi\)
\(252\) 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 −0.938084 0.346408i \(-0.887401\pi\)
0.346408 + 0.938084i \(0.387401\pi\)
\(258\) 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 0.461631 0.887072i \(-0.347264\pi\)
−0.887072 + 0.461631i \(0.847264\pi\)
\(264\) 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 0.417633 0.908616i \(-0.362860\pi\)
−0.908616 + 0.417633i \(0.862860\pi\)
\(278\) 0 0
\(279\) 5.65685 16.0000i 0.338667 0.957895i
\(280\) 0 0
\(281\) 5.65685i 0.337460i −0.985662 0.168730i \(-0.946033\pi\)
0.985662 0.168730i \(-0.0539665\pi\)
\(282\) 0 0
\(283\) −5.24264 + 5.24264i −0.311643 + 0.311643i −0.845546 0.533903i \(-0.820725\pi\)
0.533903 + 0.845546i \(0.320725\pi\)
\(284\) 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 0.999648 0.0265438i \(-0.00845016\pi\)
−0.0265438 + 0.999648i \(0.508450\pi\)
\(294\) 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 0.876031 0.482256i \(-0.160182\pi\)
−0.482256 + 0.876031i \(0.660182\pi\)
\(308\) 0 0
\(309\) −13.4853 2.31371i −0.767151 0.131622i
\(310\) 0 0
\(311\) 5.51472i 0.312711i 0.987701 + 0.156356i \(0.0499746\pi\)
−0.987701 + 0.156356i \(0.950025\pi\)
\(312\) 0 0
\(313\) −2.31371 + 2.31371i −0.130779 + 0.130779i −0.769466 0.638688i \(-0.779478\pi\)
0.638688 + 0.769466i \(0.279478\pi\)
\(314\) 0 0
\(315\) −18.0711 14.0711i −1.01819 0.792815i
\(316\) 0 0
\(317\) 4.65685 4.65685i 0.261555 0.261555i −0.564131 0.825686i \(-0.690789\pi\)
0.825686 + 0.564131i \(0.190789\pi\)
\(318\) 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 0.733819 0.679345i \(-0.237736\pi\)
−0.679345 + 0.733819i \(0.737736\pi\)
\(338\) 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 −0.304503 0.952511i \(-0.598490\pi\)
0.952511 + 0.304503i \(0.0984902\pi\)
\(348\) 0 0
\(349\) 9.65685i 0.516920i −0.966022 0.258460i \(-0.916785\pi\)
0.966022 0.258460i \(-0.0832149\pi\)
\(350\) 0 0
\(351\) 13.7279 24.5563i 0.732742 1.31072i
\(352\) 0 0
\(353\) 15.4853 + 15.4853i 0.824198 + 0.824198i 0.986707 0.162509i \(-0.0519586\pi\)
−0.162509 + 0.986707i \(0.551959\pi\)
\(354\) 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 0.820286 0.571954i \(-0.193814\pi\)
−0.571954 + 0.820286i \(0.693814\pi\)
\(368\) 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 −0.693656 0.720307i \(-0.744001\pi\)
0.720307 + 0.693656i \(0.244001\pi\)
\(374\) 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 \(-0.722573\pi\)
0.643631 0.765336i \(-0.277427\pi\)
\(380\) 0 0
\(381\) −2.31371 + 13.4853i −0.118535 + 0.690872i
\(382\) 0 0
\(383\) 12.4142 + 12.4142i 0.634337 + 0.634337i 0.949153 0.314816i \(-0.101943\pi\)
−0.314816 + 0.949153i \(0.601943\pi\)
\(384\) 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 0.875719 0.482821i \(-0.160388\pi\)
−0.482821 + 0.875719i \(0.660388\pi\)
\(398\) 0 0
\(399\) 4.82843 + 0.828427i 0.241724 + 0.0414732i
\(400\) 0 0
\(401\) 16.0000i 0.799002i 0.916733 + 0.399501i \(0.130817\pi\)
−0.916733 + 0.399501i \(0.869183\pi\)
\(402\) 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 \(0.179851\pi\)
−0.844579 + 0.535431i \(0.820149\pi\)
\(410\) 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 \(0.161219\pi\)
−0.874455 + 0.485106i \(0.838781\pi\)
\(432\) 0 0
\(433\) −15.0000 + 15.0000i −0.720854 + 0.720854i −0.968779 0.247925i \(-0.920251\pi\)
0.247925 + 0.968779i \(0.420251\pi\)
\(434\) 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 \(0.106811\pi\)
−0.944227 + 0.329295i \(0.893189\pi\)
\(440\) 0 0
\(441\) −13.1716 4.65685i −0.627218 0.221755i
\(442\) 0 0
\(443\) −0.0710678 0.0710678i −0.00337653 0.00337653i 0.705416 0.708793i \(-0.250760\pi\)
−0.708793 + 0.705416i \(0.750760\pi\)
\(444\) 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 0.730109 0.683331i \(-0.239469\pi\)
−0.683331 + 0.730109i \(0.739469\pi\)
\(458\) 0 0
\(459\) 6.55635 11.7279i 0.306024 0.547413i
\(460\) 0 0
\(461\) 28.9706i 1.34929i −0.738141 0.674647i \(-0.764296\pi\)
0.738141 0.674647i \(-0.235704\pi\)
\(462\) 0 0
\(463\) 21.5858 21.5858i 1.00318 1.00318i 0.00318163 0.999995i \(-0.498987\pi\)
0.999995 0.00318163i \(-0.00101275\pi\)
\(464\) 0 0
\(465\) −10.3431 + 19.3137i −0.479652 + 0.895652i
\(466\) 0 0
\(467\) 23.3848 23.3848i 1.08212 1.08212i 0.0858066 0.996312i \(-0.472653\pi\)
0.996312 0.0858066i \(-0.0273467\pi\)
\(468\) 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 0.295677 0.955288i \(-0.404455\pi\)
−0.955288 + 0.295677i \(0.904455\pi\)
\(488\) 0 0
\(489\) −1.00000 0.171573i −0.0452216 0.00775879i
\(490\) 0 0
\(491\) 21.5147i 0.970946i −0.874252 0.485473i \(-0.838647\pi\)
0.874252 0.485473i \(-0.161353\pi\)
\(492\) 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 \(0.283892\pi\)
−0.627955 + 0.778249i \(0.716108\pi\)
\(500\) 0 0
\(501\) −22.3137 3.82843i −0.996903 0.171042i
\(502\) 0 0
\(503\) −5.92893 5.92893i −0.264358 0.264358i 0.562464 0.826822i \(-0.309854\pi\)
−0.826822 + 0.562464i \(0.809854\pi\)
\(504\) 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 \(-0.823792\pi\)
0.850652 0.525730i \(-0.176208\pi\)
\(522\) 0 0
\(523\) −26.8995 + 26.8995i −1.17623 + 1.17623i −0.195536 + 0.980696i \(0.562645\pi\)
−0.980696 + 0.195536i \(0.937355\pi\)
\(524\) 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 0.285809 0.958287i \(-0.407738\pi\)
−0.958287 + 0.285809i \(0.907738\pi\)
\(548\) 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 −0.955888 0.293733i \(-0.905102\pi\)
0.293733 + 0.955888i \(0.405102\pi\)
\(558\) 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 0.676031 0.736873i \(-0.263699\pi\)
−0.736873 + 0.676031i \(0.763699\pi\)
\(564\) 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 0.942991 0.332818i \(-0.108000\pi\)
−0.332818 + 0.942991i \(0.608000\pi\)
\(578\) 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 −0.890564 0.454857i \(-0.849690\pi\)
0.454857 + 0.890564i \(0.349690\pi\)
\(588\) 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 0.949543 0.313638i \(-0.101548\pi\)
−0.313638 + 0.949543i \(0.601548\pi\)
\(594\) 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 0.894948 + 0.446170i \(0.147212\pi\)
0.446170 + 0.894948i \(0.352788\pi\)
\(608\) 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 −0.489113 0.872220i \(-0.662680\pi\)
0.872220 + 0.489113i \(0.162680\pi\)
\(614\) 0 0
\(615\) 19.3137 + 10.3431i 0.778804 + 0.417076i
\(616\) 0 0
\(617\) 12.1716 12.1716i 0.490009 0.490009i −0.418300 0.908309i \(-0.637374\pi\)
0.908309 + 0.418300i \(0.137374\pi\)
\(618\) 0 0
\(619\) 20.1421i 0.809581i 0.914410 + 0.404790i \(0.132656\pi\)
−0.914410 + 0.404790i \(0.867344\pi\)
\(620\) 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 \(-0.868805\pi\)
0.916257 0.400590i \(-0.131195\pi\)
\(642\) 0 0
\(643\) 28.6985 28.6985i 1.13176 1.13176i 0.141873 0.989885i \(-0.454688\pi\)
0.989885 0.141873i \(-0.0453124\pi\)
\(644\) 0 0
\(645\) −0.656854 2.17157i −0.0258636 0.0855056i
\(646\) 0 0
\(647\) 26.2132 26.2132i 1.03055 1.03055i 0.0310289 0.999518i \(-0.490122\pi\)
0.999518 0.0310289i \(-0.00987838\pi\)
\(648\) 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 −0.999025 0.0441379i \(-0.985946\pi\)
−0.0441379 0.999025i \(-0.514054\pi\)
\(654\) 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 −0.774576 0.632480i \(-0.782037\pi\)
0.632480 + 0.774576i \(0.282037\pi\)
\(674\) 0 0
\(675\) −9.34315 + 24.2426i −0.359618 + 0.933100i
\(676\) 0 0
\(677\) 35.2843 35.2843i 1.35608 1.35608i 0.477397 0.878688i \(-0.341580\pi\)
0.878688 0.477397i \(-0.158420\pi\)
\(678\) 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 0.991696 0.128602i \(-0.0410488\pi\)
−0.128602 + 0.991696i \(0.541049\pi\)
\(684\) 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 \(-0.975932\pi\)
0.997143 0.0755390i \(-0.0240677\pi\)
\(702\) 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 \(0.207319\pi\)
−0.795289 + 0.606231i \(0.792681\pi\)
\(710\) 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 0.902931 0.429786i \(-0.141411\pi\)
−0.429786 + 0.902931i \(0.641411\pi\)
\(728\) 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 −0.795665 0.605736i \(-0.792879\pi\)
0.605736 + 0.795665i \(0.292879\pi\)
\(734\) 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 \(-0.665650\pi\)
0.497233 0.867617i \(-0.334350\pi\)
\(740\) 0 0
\(741\) 1.31371 7.65685i 0.0482603 0.281282i
\(742\) 0 0
\(743\) 37.3848 + 37.3848i 1.37151 + 1.37151i 0.858202 + 0.513313i \(0.171582\pi\)
0.513313 + 0.858202i \(0.328418\pi\)
\(744\) 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 0.919199 0.393793i \(-0.128837\pi\)
−0.393793 + 0.919199i \(0.628837\pi\)
\(758\) 0 0
\(759\) −8.82843 1.51472i −0.320452 0.0549808i
\(760\) 0 0
\(761\) 12.6863i 0.459878i −0.973205 0.229939i \(-0.926147\pi\)
0.973205 0.229939i \(-0.0738526\pi\)
\(762\) 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 \(-0.643229\pi\)
0.434936 0.900462i \(-0.356771\pi\)
\(770\) 0 0
\(771\) 22.8995 + 3.92893i 0.824705 + 0.141497i
\(772\) 0 0
\(773\) −10.6569 10.6569i −0.383300 0.383300i 0.488989 0.872290i \(-0.337366\pi\)
−0.872290 + 0.488989i \(0.837366\pi\)
\(774\) 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 0.999863 0.0165362i \(-0.00526387\pi\)
−0.0165362 + 0.999863i \(0.505264\pi\)
\(788\) 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