Properties

Label 120.2.r.b.17.1
Level $120$
Weight $2$
Character 120.17
Analytic conductor $0.958$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 120 = 2^{3} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 120.r (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.958204824255\)
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: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 17.1
Root \(0.707107 - 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 120.17
Dual form 120.2.r.b.113.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.41421 - 1.00000i) q^{3} +(-1.00000 - 2.00000i) q^{5} +(-2.41421 - 2.41421i) q^{7} +(1.00000 + 2.82843i) q^{9} +O(q^{10})\) \(q+(-1.41421 - 1.00000i) q^{3} +(-1.00000 - 2.00000i) q^{5} +(-2.41421 - 2.41421i) q^{7} +(1.00000 + 2.82843i) q^{9} -0.828427i q^{11} +(3.82843 - 3.82843i) q^{13} +(-0.585786 + 3.82843i) q^{15} +(-1.82843 + 1.82843i) q^{17} -0.828427i q^{19} +(1.00000 + 5.82843i) q^{21} +(4.41421 + 4.41421i) q^{23} +(-3.00000 + 4.00000i) q^{25} +(1.41421 - 5.00000i) q^{27} +3.65685 q^{29} +5.65685 q^{31} +(-0.828427 + 1.17157i) q^{33} +(-2.41421 + 7.24264i) q^{35} +(-5.82843 - 5.82843i) q^{37} +(-9.24264 + 1.58579i) q^{39} -5.65685i q^{41} +(-0.414214 + 0.414214i) q^{43} +(4.65685 - 4.82843i) q^{45} +(3.58579 - 3.58579i) q^{47} +4.65685i q^{49} +(4.41421 - 0.757359i) q^{51} +(-3.00000 - 3.00000i) q^{53} +(-1.65685 + 0.828427i) q^{55} +(-0.828427 + 1.17157i) q^{57} -4.00000 q^{59} +0.343146 q^{61} +(4.41421 - 9.24264i) q^{63} +(-11.4853 - 3.82843i) q^{65} +(10.0711 + 10.0711i) q^{67} +(-1.82843 - 10.6569i) q^{69} -10.4853i q^{71} +(-4.65685 + 4.65685i) q^{73} +(8.24264 - 2.65685i) q^{75} +(-2.00000 + 2.00000i) q^{77} +0.828427i q^{79} +(-7.00000 + 5.65685i) q^{81} +(3.24264 + 3.24264i) q^{83} +(5.48528 + 1.82843i) q^{85} +(-5.17157 - 3.65685i) q^{87} +15.6569 q^{89} -18.4853 q^{91} +(-8.00000 - 5.65685i) q^{93} +(-1.65685 + 0.828427i) q^{95} +(1.00000 + 1.00000i) q^{97} +(2.34315 - 0.828427i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 4 q^{5} - 4 q^{7} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 4 q^{5} - 4 q^{7} + 4 q^{9} + 4 q^{13} - 8 q^{15} + 4 q^{17} + 4 q^{21} + 12 q^{23} - 12 q^{25} - 8 q^{29} + 8 q^{33} - 4 q^{35} - 12 q^{37} - 20 q^{39} + 4 q^{43} - 4 q^{45} + 20 q^{47} + 12 q^{51} - 12 q^{53} + 16 q^{55} + 8 q^{57} - 16 q^{59} + 24 q^{61} + 12 q^{63} - 12 q^{65} + 12 q^{67} + 4 q^{69} + 4 q^{73} + 16 q^{75} - 8 q^{77} - 28 q^{81} - 4 q^{83} - 12 q^{85} - 32 q^{87} + 40 q^{89} - 40 q^{91} - 32 q^{93} + 16 q^{95} + 4 q^{97} + 32 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/120\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(41\) \(61\) \(97\)
\(\chi(n)\) \(1\) \(-1\) \(1\) \(e\left(\frac{1}{4}\right)\)

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
\(3\) −1.41421 1.00000i −0.816497 0.577350i
\(4\) 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 \(-0.473237\pi\)
−0.996467 + 0.0839804i \(0.973237\pi\)
\(8\) 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
\(15\) −0.585786 + 3.82843i −0.151249 + 0.988496i
\(16\) 0 0
\(17\) −1.82843 + 1.82843i −0.443459 + 0.443459i −0.893173 0.449714i \(-0.851526\pi\)
0.449714 + 0.893173i \(0.351526\pi\)
\(18\) 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 0.997059 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
\(27\) 1.41421 5.00000i 0.272166 0.962250i
\(28\) 0 0
\(29\) 3.65685 0.679061 0.339530 0.940595i \(-0.389732\pi\)
0.339530 + 0.940595i \(0.389732\pi\)
\(30\) 0 0
\(31\) 5.65685 1.01600 0.508001 0.861357i \(-0.330385\pi\)
0.508001 + 0.861357i \(0.330385\pi\)
\(32\) 0 0
\(33\) −0.828427 + 1.17157i −0.144211 + 0.203945i
\(34\) 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 \(-0.854366\pi\)
0.897150 0.441726i \(-0.145634\pi\)
\(42\) 0 0
\(43\) −0.414214 + 0.414214i −0.0631670 + 0.0631670i −0.737985 0.674818i \(-0.764222\pi\)
0.674818 + 0.737985i \(0.264222\pi\)
\(44\) 0 0
\(45\) 4.65685 4.82843i 0.694203 0.719779i
\(46\) 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 0.470381 0.882463i \(-0.344116\pi\)
−0.882463 + 0.470381i \(0.844116\pi\)
\(54\) 0 0
\(55\) −1.65685 + 0.828427i −0.223410 + 0.111705i
\(56\) 0 0
\(57\) −0.828427 + 1.17157i −0.109728 + 0.155179i
\(58\) 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
\(63\) 4.41421 9.24264i 0.556139 1.16446i
\(64\) 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 \(0.0858863\pi\)
0.266558 + 0.963819i \(0.414114\pi\)
\(68\) 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
\(75\) 8.24264 2.65685i 0.951778 0.306787i
\(76\) 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 0.862309 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
\(87\) −5.17157 3.65685i −0.554451 0.392056i
\(88\) 0 0
\(89\) 15.6569 1.65962 0.829812 0.558044i \(-0.188448\pi\)
0.829812 + 0.558044i \(0.188448\pi\)
\(90\) 0 0
\(91\) −18.4853 −1.93778
\(92\) 0 0
\(93\) −8.00000 5.65685i −0.829561 0.586588i
\(94\) 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 \(0.159525\pi\)
−0.877024 + 0.480446i \(0.840475\pi\)
\(102\) 0 0
\(103\) −5.58579 + 5.58579i −0.550384 + 0.550384i −0.926552 0.376168i \(-0.877242\pi\)
0.376168 + 0.926552i \(0.377242\pi\)
\(104\) 0 0
\(105\) 10.6569 7.82843i 1.04000 0.763976i
\(106\) 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 0.994739 0.102439i \(-0.0326647\pi\)
−0.102439 + 0.994739i \(0.532665\pi\)
\(114\) 0 0
\(115\) 4.41421 13.2426i 0.411628 1.23488i
\(116\) 0 0
\(117\) 14.6569 + 7.00000i 1.35503 + 0.647150i
\(118\) 0 0
\(119\) 8.82843 0.809301
\(120\) 0 0
\(121\) 10.3137 0.937610
\(122\) 0 0
\(123\) −5.65685 + 8.00000i −0.510061 + 0.721336i
\(124\) 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 \(-0.136017\pi\)
−0.414425 + 0.910083i \(0.636017\pi\)
\(128\) 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
\(135\) −11.4142 + 2.17157i −0.982379 + 0.186899i
\(136\) 0 0
\(137\) −9.82843 + 9.82843i −0.839699 + 0.839699i −0.988819 0.149120i \(-0.952356\pi\)
0.149120 + 0.988819i \(0.452356\pi\)
\(138\) 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
\(147\) 4.65685 6.58579i 0.384091 0.543187i
\(148\) 0 0
\(149\) −13.3137 −1.09070 −0.545351 0.838208i \(-0.683604\pi\)
−0.545351 + 0.838208i \(0.683604\pi\)
\(150\) 0 0
\(151\) −13.6569 −1.11138 −0.555690 0.831390i \(-0.687546\pi\)
−0.555690 + 0.831390i \(0.687546\pi\)
\(152\) 0 0
\(153\) −7.00000 3.34315i −0.565916 0.270277i
\(154\) 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 −0.723143 0.690699i \(-0.757303\pi\)
0.690699 + 0.723143i \(0.257303\pi\)
\(164\) 0 0
\(165\) 3.17157 + 0.485281i 0.246907 + 0.0377791i
\(166\) 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 0.681696 0.731636i \(-0.261243\pi\)
−0.731636 + 0.681696i \(0.761243\pi\)
\(174\) 0 0
\(175\) 16.8995 2.41421i 1.27748 0.182497i
\(176\) 0 0
\(177\) 5.65685 + 4.00000i 0.425195 + 0.300658i
\(178\) 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
\(183\) −0.485281 0.343146i −0.0358730 0.0253661i
\(184\) 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
\(195\) 12.4142 + 16.8995i 0.889000 + 1.21020i
\(196\) 0 0
\(197\) 14.6569 14.6569i 1.04426 1.04426i 0.0452834 0.998974i \(-0.485581\pi\)
0.998974 0.0452834i \(-0.0144191\pi\)
\(198\) 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
\(207\) −8.07107 + 16.8995i −0.560978 + 1.17460i
\(208\) 0 0
\(209\) −0.686292 −0.0474718
\(210\) 0 0
\(211\) 20.9706 1.44367 0.721837 0.692064i \(-0.243298\pi\)
0.721837 + 0.692064i \(0.243298\pi\)
\(212\) 0 0
\(213\) −10.4853 + 14.8284i −0.718440 + 1.01603i
\(214\) 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 \(-0.835205\pi\)
0.494899 + 0.868951i \(0.335205\pi\)
\(224\) 0 0
\(225\) −14.3137 4.48528i −0.954247 0.299019i
\(226\) 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 0.978960 0.204054i \(-0.0654117\pi\)
−0.204054 + 0.978960i \(0.565412\pi\)
\(234\) 0 0
\(235\) −10.7574 3.58579i −0.701733 0.233911i
\(236\) 0 0
\(237\) 0.828427 1.17157i 0.0538121 0.0761018i
\(238\) 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
\(243\) 15.5563 1.00000i 0.997940 0.0641500i
\(244\) 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
\(255\) −5.92893 8.07107i −0.371284 0.505430i
\(256\) 0 0
\(257\) 9.48528 9.48528i 0.591676 0.591676i −0.346408 0.938084i \(-0.612599\pi\)
0.938084 + 0.346408i \(0.112599\pi\)
\(258\) 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
\(267\) −22.1421 15.6569i −1.35508 0.958184i
\(268\) 0 0
\(269\) −16.6274 −1.01379 −0.506896 0.862007i \(-0.669207\pi\)
−0.506896 + 0.862007i \(0.669207\pi\)
\(270\) 0 0
\(271\) 10.3431 0.628301 0.314151 0.949373i \(-0.398280\pi\)
0.314151 + 0.949373i \(0.398280\pi\)
\(272\) 0 0
\(273\) 26.1421 + 18.4853i 1.58219 + 1.11878i
\(274\) 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 \(0.0539665\pi\)
−0.985662 + 0.168730i \(0.946033\pi\)
\(282\) 0 0
\(283\) 5.24264 5.24264i 0.311643 0.311643i −0.533903 0.845546i \(-0.679275\pi\)
0.845546 + 0.533903i \(0.179275\pi\)
\(284\) 0 0
\(285\) 3.17157 + 0.485281i 0.187868 + 0.0287456i
\(286\) 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 \(-0.491550\pi\)
−0.999648 + 0.0265438i \(0.991550\pi\)
\(294\) 0 0
\(295\) 4.00000 + 8.00000i 0.232889 + 0.465778i
\(296\) 0 0
\(297\) −4.14214 1.17157i −0.240351 0.0679816i
\(298\) 0 0
\(299\) 33.7990 1.95465
\(300\) 0 0
\(301\) 2.00000 0.115278
\(302\) 0 0
\(303\) 9.65685 13.6569i 0.554772 0.784566i
\(304\) 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 \(-0.339818\pi\)
−0.876031 + 0.482256i \(0.839818\pi\)
\(308\) 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
\(315\) −22.8995 + 0.414214i −1.29024 + 0.0233383i
\(316\) 0 0
\(317\) −4.65685 + 4.65685i −0.261555 + 0.261555i −0.825686 0.564131i \(-0.809211\pi\)
0.564131 + 0.825686i \(0.309211\pi\)
\(318\) 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
\(327\) 4.00000 5.65685i 0.221201 0.312825i
\(328\) 0 0
\(329\) −17.3137 −0.954536
\(330\) 0 0
\(331\) −9.65685 −0.530789 −0.265394 0.964140i \(-0.585502\pi\)
−0.265394 + 0.964140i \(0.585502\pi\)
\(332\) 0 0
\(333\) 10.6569 22.3137i 0.583992 1.22278i
\(334\) 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
\(345\) −19.4853 + 14.3137i −1.04905 + 0.770624i
\(346\) 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 0.162509 0.986707i \(-0.448041\pi\)
−0.986707 + 0.162509i \(0.948041\pi\)
\(354\) 0 0
\(355\) −20.9706 + 10.4853i −1.11300 + 0.556501i
\(356\) 0 0
\(357\) −12.4853 8.82843i −0.660791 0.467250i
\(358\) 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
\(363\) −14.5858 10.3137i −0.765555 0.541329i
\(364\) 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 \(-0.306186\pi\)
−0.820286 + 0.571954i \(0.806186\pi\)
\(368\) 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
\(375\) −13.5563 13.8284i −0.700047 0.714097i
\(376\) 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 0.949153 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
\(387\) −1.58579 0.757359i −0.0806101 0.0384987i
\(388\) 0 0
\(389\) −6.68629 −0.339008 −0.169504 0.985529i \(-0.554217\pi\)
−0.169504 + 0.985529i \(0.554217\pi\)
\(390\) 0 0
\(391\) −16.1421 −0.816343
\(392\) 0 0
\(393\) −8.82843 + 12.4853i −0.445335 + 0.629799i
\(394\) 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 \(-0.869183\pi\)
0.916733 0.399501i \(-0.130817\pi\)
\(402\) 0 0
\(403\) 21.6569 21.6569i 1.07880 1.07880i
\(404\) 0 0
\(405\) 18.3137 + 8.34315i 0.910015 + 0.414574i
\(406\) 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
\(417\) −8.82843 + 12.4853i −0.432330 + 0.611407i
\(418\) 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
\(423\) 13.7279 + 6.55635i 0.667474 + 0.318781i
\(424\) 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
\(435\) −2.14214 + 14.0000i −0.102708 + 0.671249i
\(436\) 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 0.705416 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
\(447\) 18.8284 + 13.3137i 0.890554 + 0.629717i
\(448\) 0 0
\(449\) −1.31371 −0.0619977 −0.0309989 0.999519i \(-0.509869\pi\)
−0.0309989 + 0.999519i \(0.509869\pi\)
\(450\) 0 0
\(451\) −4.68629 −0.220669
\(452\) 0 0
\(453\) 19.3137 + 13.6569i 0.907437 + 0.641655i
\(454\) 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 \(0.235704\pi\)
−0.738141 + 0.674647i \(0.764296\pi\)
\(462\) 0 0
\(463\) −21.5858 + 21.5858i −1.00318 + 1.00318i −0.00318163 + 0.999995i \(0.501013\pi\)
−0.999995 + 0.00318163i \(0.998987\pi\)
\(464\) 0 0
\(465\) −3.31371 + 21.6569i −0.153670 + 1.00431i
\(466\) 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
\(477\) 5.48528 11.4853i 0.251154 0.525875i
\(478\) 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
\(483\) −21.3137 + 30.1421i −0.969807 + 1.37151i
\(484\) 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 \(-0.0955452\pi\)
−0.295677 + 0.955288i \(0.595545\pi\)
\(488\) 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
\(495\) −4.00000 3.85786i −0.179787 0.173398i
\(496\) 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 0.562464 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
\(507\) −16.3137 + 23.0711i −0.724517 + 1.02462i
\(508\) 0 0
\(509\) 3.65685 0.162087 0.0810436 0.996711i \(-0.474175\pi\)
0.0810436 + 0.996711i \(0.474175\pi\)
\(510\) 0 0
\(511\) 22.4853 0.994690
\(512\) 0 0
\(513\) −4.14214 1.17157i −0.182880 0.0517262i
\(514\) 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 0.195536 0.980696i \(-0.437355\pi\)
0.980696 0.195536i \(-0.0626448\pi\)
\(524\) 0 0
\(525\) −26.3137 13.4853i −1.14842 0.588546i
\(526\) 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
\(537\) 16.9706 + 12.0000i 0.732334 + 0.517838i
\(538\) 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
\(543\) 7.51472 + 5.31371i 0.322487 + 0.228033i
\(544\) 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 \(-0.0922623\pi\)
−0.285809 + 0.958287i \(0.592262\pi\)
\(548\) 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
\(555\) 25.7279 18.8995i 1.09209 0.802239i
\(556\) 0 0
\(557\) 15.6274 15.6274i 0.662155 0.662155i −0.293733 0.955888i \(-0.594898\pi\)
0.955888 + 0.293733i \(0.0948976\pi\)
\(558\) 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
\(567\) 30.5563 + 3.24264i 1.28325 + 0.136178i
\(568\) 0 0
\(569\) 45.3137 1.89965 0.949825 0.312783i \(-0.101261\pi\)
0.949825 + 0.312783i \(0.101261\pi\)
\(570\) 0 0
\(571\) −4.97056 −0.208012 −0.104006 0.994577i \(-0.533166\pi\)
−0.104006 + 0.994577i \(0.533166\pi\)
\(572\) 0 0
\(573\) 4.14214 5.85786i 0.173040 0.244716i
\(574\) 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
\(585\) −0.656854 36.3137i −0.0271576 1.50139i
\(586\) 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 0.313638 0.949543i \(-0.398452\pi\)
−0.949543 + 0.313638i \(0.898452\pi\)
\(594\) 0 0
\(595\) −8.82843 17.6569i −0.361930 0.723860i
\(596\) 0 0
\(597\) −18.4853 + 26.1421i −0.756552 + 1.06993i
\(598\) 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
\(603\) −18.4142 + 38.5563i −0.749885 + 1.57014i
\(604\) 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 \(-0.852788\pi\)
−0.446170 0.894948i \(-0.647212\pi\)
\(608\) 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
\(615\) 21.6569 + 3.31371i 0.873289 + 0.133622i
\(616\) 0 0
\(617\) −12.1716 + 12.1716i −0.490009 + 0.490009i −0.908309 0.418300i \(-0.862626\pi\)
0.418300 + 0.908309i \(0.362626\pi\)
\(618\) 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
\(627\) 0.970563 + 0.686292i 0.0387605 + 0.0274078i
\(628\) 0 0
\(629\) 21.3137 0.849833
\(630\) 0 0
\(631\) 31.5980 1.25790 0.628948 0.777447i \(-0.283486\pi\)
0.628948 + 0.777447i \(0.283486\pi\)
\(632\) 0 0
\(633\) −29.6569 20.9706i −1.17875 0.833505i
\(634\) 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 −0.141873 + 0.989885i \(0.545312\pi\)
−0.989885 + 0.141873i \(0.954688\pi\)
\(644\) 0 0
\(645\) −1.34315 1.82843i −0.0528863 0.0719942i
\(646\) 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 \(0.0140541\pi\)
0.0441379 + 0.999025i \(0.485946\pi\)
\(654\) 0 0
\(655\) −17.6569 + 8.82843i −0.689910 + 0.344955i
\(656\) 0 0
\(657\) −17.8284 8.51472i −0.695553 0.332191i
\(658\) 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
\(663\) 14.0000 19.7990i 0.543715 0.768929i
\(664\) 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
\(675\) 15.7574 + 20.6569i 0.606501 + 0.795083i
\(676\) 0 0
\(677\) −35.2843 + 35.2843i −1.35608 + 1.35608i −0.477397 + 0.878688i \(0.658420\pi\)
−0.878688 + 0.477397i \(0.841580\pi\)
\(678\) 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
\(687\) 14.3431 20.2843i 0.547225 0.773893i
\(688\) 0 0
\(689\) −22.9706 −0.875109
\(690\) 0 0
\(691\) −33.6569 −1.28037 −0.640184 0.768222i \(-0.721142\pi\)
−0.640184 + 0.768222i \(0.721142\pi\)
\(692\) 0 0
\(693\) −7.65685 3.65685i −0.290860 0.138912i
\(694\) 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
\(705\) 11.6274 + 15.8284i 0.437914 + 0.596133i
\(706\) 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
\(717\) −22.6274 16.0000i −0.845036 0.597531i
\(718\) 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
\(723\) 0.485281 + 0.343146i 0.0180478 + 0.0127617i
\(724\) 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 \(-0.358589\pi\)
−0.902931 + 0.429786i \(0.858589\pi\)
\(728\) 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
\(735\) −17.8284 2.72792i −0.657611 0.100621i
\(736\) 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 0.858202 + 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
\(747\) −5.92893 + 12.4142i −0.216928 + 0.454212i
\(748\) 0 0
\(749\) 46.2843 1.69119
\(750\) 0 0
\(751\) −12.2843 −0.448259 −0.224130 0.974559i \(-0.571954\pi\)
−0.224130 + 0.974559i \(0.571954\pi\)
\(752\) 0 0
\(753\) 26.4853 37.4558i 0.965177 1.36497i
\(754\) 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 \(0.0738526\pi\)
−0.973205 + 0.229939i \(0.926147\pi\)
\(762\) 0 0
\(763\) 9.65685 9.65685i 0.349602 0.349602i
\(764\) 0 0
\(765\) 0.313708 + 17.3431i 0.0113422 + 0.627043i
\(766\) 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 0.872290 0.488989i \(-0.162634\pi\)
−0.488989 + 0.872290i \(0.662634\pi\)
\(774\) 0 0
\(775\) −16.9706 + 22.6274i −0.609601 + 0.812801i
\(776\) 0 0
\(777\) 28.1421 39.7990i 1.00959 1.42778i
\(778\) 0 0
\(779\) −4.68629 −0.167904
\(780\) 0 0
\(781\) −8.68629 −0.310820
\(782\) 0 0
\(783\) 5.17157 18.2843i 0.184817 0.653427i
\(784\) 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 \(-0.494736\pi\)
−0.999863 + 0.0165362i \(0.994736\pi\)
\(788\) 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