Properties

Label 700.2.g.f.251.2
Level $700$
Weight $2$
Character 700.251
Analytic conductor $5.590$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 700.g (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.58952814149\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \(x^{4} - x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 140)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 251.2
Root \(-0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 700.251
Dual form 700.2.g.f.251.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.366025 + 1.36603i) q^{2} +1.73205 q^{3} +(-1.73205 - 1.00000i) q^{4} +(-0.633975 + 2.36603i) q^{6} +(1.73205 + 2.00000i) q^{7} +(2.00000 - 2.00000i) q^{8} +O(q^{10})\) \(q+(-0.366025 + 1.36603i) q^{2} +1.73205 q^{3} +(-1.73205 - 1.00000i) q^{4} +(-0.633975 + 2.36603i) q^{6} +(1.73205 + 2.00000i) q^{7} +(2.00000 - 2.00000i) q^{8} -0.267949i q^{11} +(-3.00000 - 1.73205i) q^{12} +0.464102i q^{13} +(-3.36603 + 1.63397i) q^{14} +(2.00000 + 3.46410i) q^{16} +6.46410i q^{17} +6.00000 q^{19} +(3.00000 + 3.46410i) q^{21} +(0.366025 + 0.0980762i) q^{22} +1.46410i q^{23} +(3.46410 - 3.46410i) q^{24} +(-0.633975 - 0.169873i) q^{26} -5.19615 q^{27} +(-1.00000 - 5.19615i) q^{28} +7.92820 q^{29} -6.00000 q^{31} +(-5.46410 + 1.46410i) q^{32} -0.464102i q^{33} +(-8.83013 - 2.36603i) q^{34} +9.46410 q^{37} +(-2.19615 + 8.19615i) q^{38} +0.803848i q^{39} -3.46410i q^{41} +(-5.83013 + 2.83013i) q^{42} +2.00000i q^{43} +(-0.267949 + 0.464102i) q^{44} +(-2.00000 - 0.535898i) q^{46} -1.73205 q^{47} +(3.46410 + 6.00000i) q^{48} +(-1.00000 + 6.92820i) q^{49} +11.1962i q^{51} +(0.464102 - 0.803848i) q^{52} -2.00000 q^{53} +(1.90192 - 7.09808i) q^{54} +(7.46410 + 0.535898i) q^{56} +10.3923 q^{57} +(-2.90192 + 10.8301i) q^{58} -3.46410 q^{59} +9.46410i q^{61} +(2.19615 - 8.19615i) q^{62} -8.00000i q^{64} +(0.633975 + 0.169873i) q^{66} -3.46410i q^{67} +(6.46410 - 11.1962i) q^{68} +2.53590i q^{69} -7.46410i q^{71} -12.9282i q^{73} +(-3.46410 + 12.9282i) q^{74} +(-10.3923 - 6.00000i) q^{76} +(0.535898 - 0.464102i) q^{77} +(-1.09808 - 0.294229i) q^{78} -14.6603i q^{79} -9.00000 q^{81} +(4.73205 + 1.26795i) q^{82} -15.4641 q^{83} +(-1.73205 - 9.00000i) q^{84} +(-2.73205 - 0.732051i) q^{86} +13.7321 q^{87} +(-0.535898 - 0.535898i) q^{88} +2.53590i q^{89} +(-0.928203 + 0.803848i) q^{91} +(1.46410 - 2.53590i) q^{92} -10.3923 q^{93} +(0.633975 - 2.36603i) q^{94} +(-9.46410 + 2.53590i) q^{96} +13.3923i q^{97} +(-9.09808 - 3.90192i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{2} - 6 q^{6} + 8 q^{8} + O(q^{10}) \) \( 4 q + 2 q^{2} - 6 q^{6} + 8 q^{8} - 12 q^{12} - 10 q^{14} + 8 q^{16} + 24 q^{19} + 12 q^{21} - 2 q^{22} - 6 q^{26} - 4 q^{28} + 4 q^{29} - 24 q^{31} - 8 q^{32} - 18 q^{34} + 24 q^{37} + 12 q^{38} - 6 q^{42} - 8 q^{44} - 8 q^{46} - 4 q^{49} - 12 q^{52} - 8 q^{53} + 18 q^{54} + 16 q^{56} - 22 q^{58} - 12 q^{62} + 6 q^{66} + 12 q^{68} + 16 q^{77} + 6 q^{78} - 36 q^{81} + 12 q^{82} - 48 q^{83} - 4 q^{86} + 48 q^{87} - 16 q^{88} + 24 q^{91} - 8 q^{92} + 6 q^{94} - 24 q^{96} - 26 q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/700\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(351\) \(477\)
\(\chi(n)\) \(-1\) \(-1\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.366025 + 1.36603i −0.258819 + 0.965926i
\(3\) 1.73205 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(4\) −1.73205 1.00000i −0.866025 0.500000i
\(5\) 0 0
\(6\) −0.633975 + 2.36603i −0.258819 + 0.965926i
\(7\) 1.73205 + 2.00000i 0.654654 + 0.755929i
\(8\) 2.00000 2.00000i 0.707107 0.707107i
\(9\) 0 0
\(10\) 0 0
\(11\) 0.267949i 0.0807897i −0.999184 0.0403949i \(-0.987138\pi\)
0.999184 0.0403949i \(-0.0128616\pi\)
\(12\) −3.00000 1.73205i −0.866025 0.500000i
\(13\) 0.464102i 0.128719i 0.997927 + 0.0643593i \(0.0205004\pi\)
−0.997927 + 0.0643593i \(0.979500\pi\)
\(14\) −3.36603 + 1.63397i −0.899608 + 0.436698i
\(15\) 0 0
\(16\) 2.00000 + 3.46410i 0.500000 + 0.866025i
\(17\) 6.46410i 1.56777i 0.620903 + 0.783887i \(0.286766\pi\)
−0.620903 + 0.783887i \(0.713234\pi\)
\(18\) 0 0
\(19\) 6.00000 1.37649 0.688247 0.725476i \(-0.258380\pi\)
0.688247 + 0.725476i \(0.258380\pi\)
\(20\) 0 0
\(21\) 3.00000 + 3.46410i 0.654654 + 0.755929i
\(22\) 0.366025 + 0.0980762i 0.0780369 + 0.0209099i
\(23\) 1.46410i 0.305286i 0.988281 + 0.152643i \(0.0487785\pi\)
−0.988281 + 0.152643i \(0.951221\pi\)
\(24\) 3.46410 3.46410i 0.707107 0.707107i
\(25\) 0 0
\(26\) −0.633975 0.169873i −0.124333 0.0333148i
\(27\) −5.19615 −1.00000
\(28\) −1.00000 5.19615i −0.188982 0.981981i
\(29\) 7.92820 1.47223 0.736115 0.676856i \(-0.236658\pi\)
0.736115 + 0.676856i \(0.236658\pi\)
\(30\) 0 0
\(31\) −6.00000 −1.07763 −0.538816 0.842424i \(-0.681128\pi\)
−0.538816 + 0.842424i \(0.681128\pi\)
\(32\) −5.46410 + 1.46410i −0.965926 + 0.258819i
\(33\) 0.464102i 0.0807897i
\(34\) −8.83013 2.36603i −1.51435 0.405770i
\(35\) 0 0
\(36\) 0 0
\(37\) 9.46410 1.55589 0.777944 0.628333i \(-0.216263\pi\)
0.777944 + 0.628333i \(0.216263\pi\)
\(38\) −2.19615 + 8.19615i −0.356263 + 1.32959i
\(39\) 0.803848i 0.128719i
\(40\) 0 0
\(41\) 3.46410i 0.541002i −0.962720 0.270501i \(-0.912811\pi\)
0.962720 0.270501i \(-0.0871893\pi\)
\(42\) −5.83013 + 2.83013i −0.899608 + 0.436698i
\(43\) 2.00000i 0.304997i 0.988304 + 0.152499i \(0.0487319\pi\)
−0.988304 + 0.152499i \(0.951268\pi\)
\(44\) −0.267949 + 0.464102i −0.0403949 + 0.0699660i
\(45\) 0 0
\(46\) −2.00000 0.535898i −0.294884 0.0790139i
\(47\) −1.73205 −0.252646 −0.126323 0.991989i \(-0.540318\pi\)
−0.126323 + 0.991989i \(0.540318\pi\)
\(48\) 3.46410 + 6.00000i 0.500000 + 0.866025i
\(49\) −1.00000 + 6.92820i −0.142857 + 0.989743i
\(50\) 0 0
\(51\) 11.1962i 1.56777i
\(52\) 0.464102 0.803848i 0.0643593 0.111474i
\(53\) −2.00000 −0.274721 −0.137361 0.990521i \(-0.543862\pi\)
−0.137361 + 0.990521i \(0.543862\pi\)
\(54\) 1.90192 7.09808i 0.258819 0.965926i
\(55\) 0 0
\(56\) 7.46410 + 0.535898i 0.997433 + 0.0716124i
\(57\) 10.3923 1.37649
\(58\) −2.90192 + 10.8301i −0.381041 + 1.42207i
\(59\) −3.46410 −0.450988 −0.225494 0.974245i \(-0.572400\pi\)
−0.225494 + 0.974245i \(0.572400\pi\)
\(60\) 0 0
\(61\) 9.46410i 1.21175i 0.795558 + 0.605877i \(0.207178\pi\)
−0.795558 + 0.605877i \(0.792822\pi\)
\(62\) 2.19615 8.19615i 0.278912 1.04091i
\(63\) 0 0
\(64\) 8.00000i 1.00000i
\(65\) 0 0
\(66\) 0.633975 + 0.169873i 0.0780369 + 0.0209099i
\(67\) 3.46410i 0.423207i −0.977356 0.211604i \(-0.932131\pi\)
0.977356 0.211604i \(-0.0678686\pi\)
\(68\) 6.46410 11.1962i 0.783887 1.35773i
\(69\) 2.53590i 0.305286i
\(70\) 0 0
\(71\) 7.46410i 0.885826i −0.896565 0.442913i \(-0.853945\pi\)
0.896565 0.442913i \(-0.146055\pi\)
\(72\) 0 0
\(73\) 12.9282i 1.51313i −0.653917 0.756566i \(-0.726876\pi\)
0.653917 0.756566i \(-0.273124\pi\)
\(74\) −3.46410 + 12.9282i −0.402694 + 1.50287i
\(75\) 0 0
\(76\) −10.3923 6.00000i −1.19208 0.688247i
\(77\) 0.535898 0.464102i 0.0610713 0.0528893i
\(78\) −1.09808 0.294229i −0.124333 0.0333148i
\(79\) 14.6603i 1.64941i −0.565565 0.824704i \(-0.691342\pi\)
0.565565 0.824704i \(-0.308658\pi\)
\(80\) 0 0
\(81\) −9.00000 −1.00000
\(82\) 4.73205 + 1.26795i 0.522568 + 0.140022i
\(83\) −15.4641 −1.69741 −0.848703 0.528870i \(-0.822616\pi\)
−0.848703 + 0.528870i \(0.822616\pi\)
\(84\) −1.73205 9.00000i −0.188982 0.981981i
\(85\) 0 0
\(86\) −2.73205 0.732051i −0.294605 0.0789391i
\(87\) 13.7321 1.47223
\(88\) −0.535898 0.535898i −0.0571270 0.0571270i
\(89\) 2.53590i 0.268805i 0.990927 + 0.134402i \(0.0429115\pi\)
−0.990927 + 0.134402i \(0.957089\pi\)
\(90\) 0 0
\(91\) −0.928203 + 0.803848i −0.0973021 + 0.0842661i
\(92\) 1.46410 2.53590i 0.152643 0.264386i
\(93\) −10.3923 −1.07763
\(94\) 0.633975 2.36603i 0.0653895 0.244037i
\(95\) 0 0
\(96\) −9.46410 + 2.53590i −0.965926 + 0.258819i
\(97\) 13.3923i 1.35978i 0.733313 + 0.679891i \(0.237973\pi\)
−0.733313 + 0.679891i \(0.762027\pi\)
\(98\) −9.09808 3.90192i −0.919044 0.394154i
\(99\) 0 0
\(100\) 0 0
\(101\) 15.4641i 1.53874i −0.638806 0.769368i \(-0.720571\pi\)
0.638806 0.769368i \(-0.279429\pi\)
\(102\) −15.2942 4.09808i −1.51435 0.405770i
\(103\) 6.80385 0.670403 0.335202 0.942146i \(-0.391196\pi\)
0.335202 + 0.942146i \(0.391196\pi\)
\(104\) 0.928203 + 0.928203i 0.0910178 + 0.0910178i
\(105\) 0 0
\(106\) 0.732051 2.73205i 0.0711031 0.265360i
\(107\) 2.39230i 0.231273i −0.993292 0.115636i \(-0.963109\pi\)
0.993292 0.115636i \(-0.0368907\pi\)
\(108\) 9.00000 + 5.19615i 0.866025 + 0.500000i
\(109\) 2.07180 0.198442 0.0992211 0.995065i \(-0.468365\pi\)
0.0992211 + 0.995065i \(0.468365\pi\)
\(110\) 0 0
\(111\) 16.3923 1.55589
\(112\) −3.46410 + 10.0000i −0.327327 + 0.944911i
\(113\) −5.46410 −0.514019 −0.257010 0.966409i \(-0.582737\pi\)
−0.257010 + 0.966409i \(0.582737\pi\)
\(114\) −3.80385 + 14.1962i −0.356263 + 1.32959i
\(115\) 0 0
\(116\) −13.7321 7.92820i −1.27499 0.736115i
\(117\) 0 0
\(118\) 1.26795 4.73205i 0.116724 0.435621i
\(119\) −12.9282 + 11.1962i −1.18513 + 1.02635i
\(120\) 0 0
\(121\) 10.9282 0.993473
\(122\) −12.9282 3.46410i −1.17046 0.313625i
\(123\) 6.00000i 0.541002i
\(124\) 10.3923 + 6.00000i 0.933257 + 0.538816i
\(125\) 0 0
\(126\) 0 0
\(127\) 15.4641i 1.37222i −0.727499 0.686109i \(-0.759317\pi\)
0.727499 0.686109i \(-0.240683\pi\)
\(128\) 10.9282 + 2.92820i 0.965926 + 0.258819i
\(129\) 3.46410i 0.304997i
\(130\) 0 0
\(131\) 2.53590 0.221562 0.110781 0.993845i \(-0.464665\pi\)
0.110781 + 0.993845i \(0.464665\pi\)
\(132\) −0.464102 + 0.803848i −0.0403949 + 0.0699660i
\(133\) 10.3923 + 12.0000i 0.901127 + 1.04053i
\(134\) 4.73205 + 1.26795i 0.408787 + 0.109534i
\(135\) 0 0
\(136\) 12.9282 + 12.9282i 1.10858 + 1.10858i
\(137\) −20.3923 −1.74223 −0.871116 0.491077i \(-0.836603\pi\)
−0.871116 + 0.491077i \(0.836603\pi\)
\(138\) −3.46410 0.928203i −0.294884 0.0790139i
\(139\) 6.92820 0.587643 0.293821 0.955860i \(-0.405073\pi\)
0.293821 + 0.955860i \(0.405073\pi\)
\(140\) 0 0
\(141\) −3.00000 −0.252646
\(142\) 10.1962 + 2.73205i 0.855642 + 0.229269i
\(143\) 0.124356 0.0103991
\(144\) 0 0
\(145\) 0 0
\(146\) 17.6603 + 4.73205i 1.46157 + 0.391627i
\(147\) −1.73205 + 12.0000i −0.142857 + 0.989743i
\(148\) −16.3923 9.46410i −1.34744 0.777944i
\(149\) 3.07180 0.251651 0.125826 0.992052i \(-0.459842\pi\)
0.125826 + 0.992052i \(0.459842\pi\)
\(150\) 0 0
\(151\) 15.1962i 1.23665i −0.785924 0.618323i \(-0.787812\pi\)
0.785924 0.618323i \(-0.212188\pi\)
\(152\) 12.0000 12.0000i 0.973329 0.973329i
\(153\) 0 0
\(154\) 0.437822 + 0.901924i 0.0352807 + 0.0726791i
\(155\) 0 0
\(156\) 0.803848 1.39230i 0.0643593 0.111474i
\(157\) 7.85641i 0.627009i −0.949587 0.313505i \(-0.898497\pi\)
0.949587 0.313505i \(-0.101503\pi\)
\(158\) 20.0263 + 5.36603i 1.59321 + 0.426898i
\(159\) −3.46410 −0.274721
\(160\) 0 0
\(161\) −2.92820 + 2.53590i −0.230775 + 0.199857i
\(162\) 3.29423 12.2942i 0.258819 0.965926i
\(163\) 20.7846i 1.62798i −0.580881 0.813988i \(-0.697292\pi\)
0.580881 0.813988i \(-0.302708\pi\)
\(164\) −3.46410 + 6.00000i −0.270501 + 0.468521i
\(165\) 0 0
\(166\) 5.66025 21.1244i 0.439321 1.63957i
\(167\) 5.19615 0.402090 0.201045 0.979582i \(-0.435566\pi\)
0.201045 + 0.979582i \(0.435566\pi\)
\(168\) 12.9282 + 0.928203i 0.997433 + 0.0716124i
\(169\) 12.7846 0.983432
\(170\) 0 0
\(171\) 0 0
\(172\) 2.00000 3.46410i 0.152499 0.264135i
\(173\) 14.3205i 1.08877i 0.838836 + 0.544384i \(0.183237\pi\)
−0.838836 + 0.544384i \(0.816763\pi\)
\(174\) −5.02628 + 18.7583i −0.381041 + 1.42207i
\(175\) 0 0
\(176\) 0.928203 0.535898i 0.0699660 0.0403949i
\(177\) −6.00000 −0.450988
\(178\) −3.46410 0.928203i −0.259645 0.0695718i
\(179\) 6.39230i 0.477783i 0.971046 + 0.238892i \(0.0767841\pi\)
−0.971046 + 0.238892i \(0.923216\pi\)
\(180\) 0 0
\(181\) 0.928203i 0.0689928i −0.999405 0.0344964i \(-0.989017\pi\)
0.999405 0.0344964i \(-0.0109827\pi\)
\(182\) −0.758330 1.56218i −0.0562112 0.115796i
\(183\) 16.3923i 1.21175i
\(184\) 2.92820 + 2.92820i 0.215870 + 0.215870i
\(185\) 0 0
\(186\) 3.80385 14.1962i 0.278912 1.04091i
\(187\) 1.73205 0.126660
\(188\) 3.00000 + 1.73205i 0.218797 + 0.126323i
\(189\) −9.00000 10.3923i −0.654654 0.755929i
\(190\) 0 0
\(191\) 7.19615i 0.520695i −0.965515 0.260348i \(-0.916163\pi\)
0.965515 0.260348i \(-0.0838372\pi\)
\(192\) 13.8564i 1.00000i
\(193\) 9.46410 0.681241 0.340620 0.940201i \(-0.389363\pi\)
0.340620 + 0.940201i \(0.389363\pi\)
\(194\) −18.2942 4.90192i −1.31345 0.351938i
\(195\) 0 0
\(196\) 8.66025 11.0000i 0.618590 0.785714i
\(197\) 13.3205 0.949047 0.474523 0.880243i \(-0.342620\pi\)
0.474523 + 0.880243i \(0.342620\pi\)
\(198\) 0 0
\(199\) 3.46410 0.245564 0.122782 0.992434i \(-0.460818\pi\)
0.122782 + 0.992434i \(0.460818\pi\)
\(200\) 0 0
\(201\) 6.00000i 0.423207i
\(202\) 21.1244 + 5.66025i 1.48630 + 0.398254i
\(203\) 13.7321 + 15.8564i 0.963801 + 1.11290i
\(204\) 11.1962 19.3923i 0.783887 1.35773i
\(205\) 0 0
\(206\) −2.49038 + 9.29423i −0.173513 + 0.647560i
\(207\) 0 0
\(208\) −1.60770 + 0.928203i −0.111474 + 0.0643593i
\(209\) 1.60770i 0.111207i
\(210\) 0 0
\(211\) 3.19615i 0.220032i −0.993930 0.110016i \(-0.964910\pi\)
0.993930 0.110016i \(-0.0350902\pi\)
\(212\) 3.46410 + 2.00000i 0.237915 + 0.137361i
\(213\) 12.9282i 0.885826i
\(214\) 3.26795 + 0.875644i 0.223392 + 0.0598578i
\(215\) 0 0
\(216\) −10.3923 + 10.3923i −0.707107 + 0.707107i
\(217\) −10.3923 12.0000i −0.705476 0.814613i
\(218\) −0.758330 + 2.83013i −0.0513606 + 0.191680i
\(219\) 22.3923i 1.51313i
\(220\) 0 0
\(221\) −3.00000 −0.201802
\(222\) −6.00000 + 22.3923i −0.402694 + 1.50287i
\(223\) 13.7321 0.919566 0.459783 0.888031i \(-0.347927\pi\)
0.459783 + 0.888031i \(0.347927\pi\)
\(224\) −12.3923 8.39230i −0.827996 0.560734i
\(225\) 0 0
\(226\) 2.00000 7.46410i 0.133038 0.496505i
\(227\) −20.6603 −1.37127 −0.685635 0.727946i \(-0.740475\pi\)
−0.685635 + 0.727946i \(0.740475\pi\)
\(228\) −18.0000 10.3923i −1.19208 0.688247i
\(229\) 8.53590i 0.564068i −0.959404 0.282034i \(-0.908991\pi\)
0.959404 0.282034i \(-0.0910091\pi\)
\(230\) 0 0
\(231\) 0.928203 0.803848i 0.0610713 0.0528893i
\(232\) 15.8564 15.8564i 1.04102 1.04102i
\(233\) 9.07180 0.594313 0.297157 0.954829i \(-0.403962\pi\)
0.297157 + 0.954829i \(0.403962\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 6.00000 + 3.46410i 0.390567 + 0.225494i
\(237\) 25.3923i 1.64941i
\(238\) −10.5622 21.7583i −0.684644 1.41038i
\(239\) 23.9808i 1.55119i 0.631233 + 0.775593i \(0.282549\pi\)
−0.631233 + 0.775593i \(0.717451\pi\)
\(240\) 0 0
\(241\) 16.3923i 1.05592i 0.849269 + 0.527961i \(0.177043\pi\)
−0.849269 + 0.527961i \(0.822957\pi\)
\(242\) −4.00000 + 14.9282i −0.257130 + 0.959621i
\(243\) 0 0
\(244\) 9.46410 16.3923i 0.605877 1.04941i
\(245\) 0 0
\(246\) 8.19615 + 2.19615i 0.522568 + 0.140022i
\(247\) 2.78461i 0.177180i
\(248\) −12.0000 + 12.0000i −0.762001 + 0.762001i
\(249\) −26.7846 −1.69741
\(250\) 0 0
\(251\) −25.8564 −1.63204 −0.816021 0.578022i \(-0.803825\pi\)
−0.816021 + 0.578022i \(0.803825\pi\)
\(252\) 0 0
\(253\) 0.392305 0.0246640
\(254\) 21.1244 + 5.66025i 1.32546 + 0.355156i
\(255\) 0 0
\(256\) −8.00000 + 13.8564i −0.500000 + 0.866025i
\(257\) 6.00000i 0.374270i −0.982334 0.187135i \(-0.940080\pi\)
0.982334 0.187135i \(-0.0599201\pi\)
\(258\) −4.73205 1.26795i −0.294605 0.0789391i
\(259\) 16.3923 + 18.9282i 1.01857 + 1.17614i
\(260\) 0 0
\(261\) 0 0
\(262\) −0.928203 + 3.46410i −0.0573446 + 0.214013i
\(263\) 11.4641i 0.706907i −0.935452 0.353453i \(-0.885007\pi\)
0.935452 0.353453i \(-0.114993\pi\)
\(264\) −0.928203 0.928203i −0.0571270 0.0571270i
\(265\) 0 0
\(266\) −20.1962 + 9.80385i −1.23831 + 0.601112i
\(267\) 4.39230i 0.268805i
\(268\) −3.46410 + 6.00000i −0.211604 + 0.366508i
\(269\) 12.0000i 0.731653i −0.930683 0.365826i \(-0.880786\pi\)
0.930683 0.365826i \(-0.119214\pi\)
\(270\) 0 0
\(271\) 9.46410 0.574903 0.287452 0.957795i \(-0.407192\pi\)
0.287452 + 0.957795i \(0.407192\pi\)
\(272\) −22.3923 + 12.9282i −1.35773 + 0.783887i
\(273\) −1.60770 + 1.39230i −0.0973021 + 0.0842661i
\(274\) 7.46410 27.8564i 0.450923 1.68287i
\(275\) 0 0
\(276\) 2.53590 4.39230i 0.152643 0.264386i
\(277\) −16.7846 −1.00849 −0.504245 0.863561i \(-0.668229\pi\)
−0.504245 + 0.863561i \(0.668229\pi\)
\(278\) −2.53590 + 9.46410i −0.152093 + 0.567619i
\(279\) 0 0
\(280\) 0 0
\(281\) −7.92820 −0.472957 −0.236478 0.971637i \(-0.575993\pi\)
−0.236478 + 0.971637i \(0.575993\pi\)
\(282\) 1.09808 4.09808i 0.0653895 0.244037i
\(283\) −12.1244 −0.720718 −0.360359 0.932814i \(-0.617346\pi\)
−0.360359 + 0.932814i \(0.617346\pi\)
\(284\) −7.46410 + 12.9282i −0.442913 + 0.767148i
\(285\) 0 0
\(286\) −0.0455173 + 0.169873i −0.00269150 + 0.0100448i
\(287\) 6.92820 6.00000i 0.408959 0.354169i
\(288\) 0 0
\(289\) −24.7846 −1.45792
\(290\) 0 0
\(291\) 23.1962i 1.35978i
\(292\) −12.9282 + 22.3923i −0.756566 + 1.31041i
\(293\) 20.3205i 1.18714i −0.804784 0.593568i \(-0.797719\pi\)
0.804784 0.593568i \(-0.202281\pi\)
\(294\) −15.7583 6.75833i −0.919044 0.394154i
\(295\) 0 0
\(296\) 18.9282 18.9282i 1.10018 1.10018i
\(297\) 1.39230i 0.0807897i
\(298\) −1.12436 + 4.19615i −0.0651322 + 0.243077i
\(299\) −0.679492 −0.0392960
\(300\) 0 0
\(301\) −4.00000 + 3.46410i −0.230556 + 0.199667i
\(302\) 20.7583 + 5.56218i 1.19451 + 0.320067i
\(303\) 26.7846i 1.53874i
\(304\) 12.0000 + 20.7846i 0.688247 + 1.19208i
\(305\) 0 0
\(306\) 0 0
\(307\) −1.73205 −0.0988534 −0.0494267 0.998778i \(-0.515739\pi\)
−0.0494267 + 0.998778i \(0.515739\pi\)
\(308\) −1.39230 + 0.267949i −0.0793339 + 0.0152678i
\(309\) 11.7846 0.670403
\(310\) 0 0
\(311\) 7.85641 0.445496 0.222748 0.974876i \(-0.428497\pi\)
0.222748 + 0.974876i \(0.428497\pi\)
\(312\) 1.60770 + 1.60770i 0.0910178 + 0.0910178i
\(313\) 17.5359i 0.991188i 0.868554 + 0.495594i \(0.165050\pi\)
−0.868554 + 0.495594i \(0.834950\pi\)
\(314\) 10.7321 + 2.87564i 0.605645 + 0.162282i
\(315\) 0 0
\(316\) −14.6603 + 25.3923i −0.824704 + 1.42843i
\(317\) 3.07180 0.172529 0.0862646 0.996272i \(-0.472507\pi\)
0.0862646 + 0.996272i \(0.472507\pi\)
\(318\) 1.26795 4.73205i 0.0711031 0.265360i
\(319\) 2.12436i 0.118941i
\(320\) 0 0
\(321\) 4.14359i 0.231273i
\(322\) −2.39230 4.92820i −0.133318 0.274638i
\(323\) 38.7846i 2.15803i
\(324\) 15.5885 + 9.00000i 0.866025 + 0.500000i
\(325\) 0 0
\(326\) 28.3923 + 7.60770i 1.57250 + 0.421351i
\(327\) 3.58846 0.198442
\(328\) −6.92820 6.92820i −0.382546 0.382546i
\(329\) −3.00000 3.46410i −0.165395 0.190982i
\(330\) 0 0
\(331\) 26.3923i 1.45065i 0.688405 + 0.725326i \(0.258311\pi\)
−0.688405 + 0.725326i \(0.741689\pi\)
\(332\) 26.7846 + 15.4641i 1.47000 + 0.848703i
\(333\) 0 0
\(334\) −1.90192 + 7.09808i −0.104069 + 0.388389i
\(335\) 0 0
\(336\) −6.00000 + 17.3205i −0.327327 + 0.944911i
\(337\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(338\) −4.67949 + 17.4641i −0.254531 + 0.949922i
\(339\) −9.46410 −0.514019
\(340\) 0 0
\(341\) 1.60770i 0.0870616i
\(342\) 0 0
\(343\) −15.5885 + 10.0000i −0.841698 + 0.539949i
\(344\) 4.00000 + 4.00000i 0.215666 + 0.215666i
\(345\) 0 0
\(346\) −19.5622 5.24167i −1.05167 0.281794i
\(347\) 34.2487i 1.83857i 0.393596 + 0.919284i \(0.371231\pi\)
−0.393596 + 0.919284i \(0.628769\pi\)
\(348\) −23.7846 13.7321i −1.27499 0.736115i
\(349\) 5.32051i 0.284800i −0.989809 0.142400i \(-0.954518\pi\)
0.989809 0.142400i \(-0.0454820\pi\)
\(350\) 0 0
\(351\) 2.41154i 0.128719i
\(352\) 0.392305 + 1.46410i 0.0209099 + 0.0780369i
\(353\) 7.39230i 0.393453i 0.980458 + 0.196726i \(0.0630311\pi\)
−0.980458 + 0.196726i \(0.936969\pi\)
\(354\) 2.19615 8.19615i 0.116724 0.435621i
\(355\) 0 0
\(356\) 2.53590 4.39230i 0.134402 0.232792i
\(357\) −22.3923 + 19.3923i −1.18513 + 1.02635i
\(358\) −8.73205 2.33975i −0.461503 0.123659i
\(359\) 25.3205i 1.33637i −0.743997 0.668183i \(-0.767072\pi\)
0.743997 0.668183i \(-0.232928\pi\)
\(360\) 0 0
\(361\) 17.0000 0.894737
\(362\) 1.26795 + 0.339746i 0.0666419 + 0.0178567i
\(363\) 18.9282 0.993473
\(364\) 2.41154 0.464102i 0.126399 0.0243255i
\(365\) 0 0
\(366\) −22.3923 6.00000i −1.17046 0.313625i
\(367\) −11.8756 −0.619904 −0.309952 0.950752i \(-0.600313\pi\)
−0.309952 + 0.950752i \(0.600313\pi\)
\(368\) −5.07180 + 2.92820i −0.264386 + 0.152643i
\(369\) 0 0
\(370\) 0 0
\(371\) −3.46410 4.00000i −0.179847 0.207670i
\(372\) 18.0000 + 10.3923i 0.933257 + 0.538816i
\(373\) 3.60770 0.186799 0.0933997 0.995629i \(-0.470227\pi\)
0.0933997 + 0.995629i \(0.470227\pi\)
\(374\) −0.633975 + 2.36603i −0.0327820 + 0.122344i
\(375\) 0 0
\(376\) −3.46410 + 3.46410i −0.178647 + 0.178647i
\(377\) 3.67949i 0.189503i
\(378\) 17.4904 8.49038i 0.899608 0.436698i
\(379\) 5.60770i 0.288048i −0.989574 0.144024i \(-0.953996\pi\)
0.989574 0.144024i \(-0.0460042\pi\)
\(380\) 0 0
\(381\) 26.7846i 1.37222i
\(382\) 9.83013 + 2.63397i 0.502953 + 0.134766i
\(383\) −27.4641 −1.40335 −0.701675 0.712497i \(-0.747564\pi\)
−0.701675 + 0.712497i \(0.747564\pi\)
\(384\) 18.9282 + 5.07180i 0.965926 + 0.258819i
\(385\) 0 0
\(386\) −3.46410 + 12.9282i −0.176318 + 0.658028i
\(387\) 0 0
\(388\) 13.3923 23.1962i 0.679891 1.17761i
\(389\) −20.8564 −1.05746 −0.528731 0.848790i \(-0.677332\pi\)
−0.528731 + 0.848790i \(0.677332\pi\)
\(390\) 0 0
\(391\) −9.46410 −0.478620
\(392\) 11.8564 + 15.8564i 0.598839 + 0.800869i
\(393\) 4.39230 0.221562
\(394\) −4.87564 + 18.1962i −0.245631 + 0.916709i
\(395\) 0 0
\(396\) 0 0
\(397\) 12.4641i 0.625555i −0.949826 0.312778i \(-0.898741\pi\)
0.949826 0.312778i \(-0.101259\pi\)
\(398\) −1.26795 + 4.73205i −0.0635566 + 0.237196i
\(399\) 18.0000 + 20.7846i 0.901127 + 1.04053i
\(400\) 0 0
\(401\) −10.0718 −0.502962 −0.251481 0.967862i \(-0.580918\pi\)
−0.251481 + 0.967862i \(0.580918\pi\)
\(402\) 8.19615 + 2.19615i 0.408787 + 0.109534i
\(403\) 2.78461i 0.138711i
\(404\) −15.4641 + 26.7846i −0.769368 + 1.33258i
\(405\) 0 0
\(406\) −26.6865 + 12.9545i −1.32443 + 0.642920i
\(407\) 2.53590i 0.125700i
\(408\) 22.3923 + 22.3923i 1.10858 + 1.10858i
\(409\) 4.14359i 0.204888i 0.994739 + 0.102444i \(0.0326662\pi\)
−0.994739 + 0.102444i \(0.967334\pi\)
\(410\) 0 0
\(411\) −35.3205 −1.74223
\(412\) −11.7846 6.80385i −0.580586 0.335202i
\(413\) −6.00000 6.92820i −0.295241 0.340915i
\(414\) 0 0
\(415\) 0 0
\(416\) −0.679492 2.53590i −0.0333148 0.124333i
\(417\) 12.0000 0.587643
\(418\) 2.19615 + 0.588457i 0.107417 + 0.0287824i
\(419\) −24.2487 −1.18463 −0.592314 0.805708i \(-0.701785\pi\)
−0.592314 + 0.805708i \(0.701785\pi\)
\(420\) 0 0
\(421\) 19.0000 0.926003 0.463002 0.886357i \(-0.346772\pi\)
0.463002 + 0.886357i \(0.346772\pi\)
\(422\) 4.36603 + 1.16987i 0.212535 + 0.0569485i
\(423\) 0 0
\(424\) −4.00000 + 4.00000i −0.194257 + 0.194257i
\(425\) 0 0
\(426\) 17.6603 + 4.73205i 0.855642 + 0.229269i
\(427\) −18.9282 + 16.3923i −0.916000 + 0.793279i
\(428\) −2.39230 + 4.14359i −0.115636 + 0.200288i
\(429\) 0.215390 0.0103991
\(430\) 0 0
\(431\) 13.5885i 0.654533i 0.944932 + 0.327266i \(0.106127\pi\)
−0.944932 + 0.327266i \(0.893873\pi\)
\(432\) −10.3923 18.0000i −0.500000 0.866025i
\(433\) 31.8564i 1.53092i 0.643483 + 0.765461i \(0.277489\pi\)
−0.643483 + 0.765461i \(0.722511\pi\)
\(434\) 20.1962 9.80385i 0.969446 0.470600i
\(435\) 0 0
\(436\) −3.58846 2.07180i −0.171856 0.0992211i
\(437\) 8.78461i 0.420225i
\(438\) 30.5885 + 8.19615i 1.46157 + 0.391627i
\(439\) −39.7128 −1.89539 −0.947695 0.319179i \(-0.896593\pi\)
−0.947695 + 0.319179i \(0.896593\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 1.09808 4.09808i 0.0522302 0.194926i
\(443\) 26.0000i 1.23530i −0.786454 0.617649i \(-0.788085\pi\)
0.786454 0.617649i \(-0.211915\pi\)
\(444\) −28.3923 16.3923i −1.34744 0.777944i
\(445\) 0 0
\(446\) −5.02628 + 18.7583i −0.238001 + 0.888233i
\(447\) 5.32051 0.251651
\(448\) 16.0000 13.8564i 0.755929 0.654654i
\(449\) 11.9282 0.562927 0.281463 0.959572i \(-0.409180\pi\)
0.281463 + 0.959572i \(0.409180\pi\)
\(450\) 0 0
\(451\) −0.928203 −0.0437074
\(452\) 9.46410 + 5.46410i 0.445154 + 0.257010i
\(453\) 26.3205i 1.23665i
\(454\) 7.56218 28.2224i 0.354911 1.32454i
\(455\) 0 0
\(456\) 20.7846 20.7846i 0.973329 0.973329i
\(457\) −20.5359 −0.960629 −0.480314 0.877096i \(-0.659477\pi\)
−0.480314 + 0.877096i \(0.659477\pi\)
\(458\) 11.6603 + 3.12436i 0.544848 + 0.145992i
\(459\) 33.5885i 1.56777i
\(460\) 0 0
\(461\) 27.7128i 1.29071i 0.763881 + 0.645357i \(0.223291\pi\)
−0.763881 + 0.645357i \(0.776709\pi\)
\(462\) 0.758330 + 1.56218i 0.0352807 + 0.0726791i
\(463\) 16.3923i 0.761815i −0.924613 0.380908i \(-0.875612\pi\)
0.924613 0.380908i \(-0.124388\pi\)
\(464\) 15.8564 + 27.4641i 0.736115 + 1.27499i
\(465\) 0 0
\(466\) −3.32051 + 12.3923i −0.153820 + 0.574062i
\(467\) −22.5167 −1.04195 −0.520973 0.853573i \(-0.674431\pi\)
−0.520973 + 0.853573i \(0.674431\pi\)
\(468\) 0 0
\(469\) 6.92820 6.00000i 0.319915 0.277054i
\(470\) 0 0
\(471\) 13.6077i 0.627009i
\(472\) −6.92820 + 6.92820i −0.318896 + 0.318896i
\(473\) 0.535898 0.0246406
\(474\) 34.6865 + 9.29423i 1.59321 + 0.426898i
\(475\) 0 0
\(476\) 33.5885 6.46410i 1.53952 0.296282i
\(477\) 0 0
\(478\) −32.7583 8.77757i −1.49833 0.401477i
\(479\) 25.1769 1.15036 0.575181 0.818026i \(-0.304932\pi\)
0.575181 + 0.818026i \(0.304932\pi\)
\(480\) 0 0
\(481\) 4.39230i 0.200272i
\(482\) −22.3923 6.00000i −1.01994 0.273293i
\(483\) −5.07180 + 4.39230i −0.230775 + 0.199857i
\(484\) −18.9282 10.9282i −0.860373 0.496737i
\(485\) 0 0
\(486\) 0 0
\(487\) 12.7846i 0.579326i −0.957129 0.289663i \(-0.906457\pi\)
0.957129 0.289663i \(-0.0935432\pi\)
\(488\) 18.9282 + 18.9282i 0.856840 + 0.856840i
\(489\) 36.0000i 1.62798i
\(490\) 0 0
\(491\) 9.87564i 0.445682i 0.974855 + 0.222841i \(0.0715330\pi\)
−0.974855 + 0.222841i \(0.928467\pi\)
\(492\) −6.00000 + 10.3923i −0.270501 + 0.468521i
\(493\) 51.2487i 2.30813i
\(494\) −3.80385 1.01924i −0.171143 0.0458577i
\(495\) 0 0
\(496\) −12.0000 20.7846i −0.538816 0.933257i
\(497\) 14.9282 12.9282i 0.669621 0.579909i
\(498\) 9.80385 36.5885i 0.439321 1.63957i
\(499\) 25.5885i 1.14550i −0.819731 0.572748i \(-0.805877\pi\)
0.819731 0.572748i \(-0.194123\pi\)
\(500\) 0 0
\(501\) 9.00000 0.402090
\(502\) 9.46410 35.3205i 0.422404 1.57643i
\(503\) 15.5885 0.695055 0.347527 0.937670i \(-0.387021\pi\)
0.347527 + 0.937670i \(0.387021\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) −0.143594 + 0.535898i −0.00638351 + 0.0238236i
\(507\) 22.1436 0.983432
\(508\) −15.4641 + 26.7846i −0.686109 + 1.18837i
\(509\) 25.8564i 1.14607i 0.819533 + 0.573033i \(0.194233\pi\)
−0.819533 + 0.573033i \(0.805767\pi\)
\(510\) 0 0
\(511\) 25.8564 22.3923i 1.14382 0.990577i
\(512\) −16.0000 16.0000i −0.707107 0.707107i
\(513\) −31.1769 −1.37649
\(514\) 8.19615 + 2.19615i 0.361517 + 0.0968681i
\(515\) 0 0
\(516\) 3.46410 6.00000i 0.152499 0.264135i
\(517\) 0.464102i 0.0204112i
\(518\) −31.8564 + 15.4641i −1.39969 + 0.679454i
\(519\) 24.8038i 1.08877i
\(520\) 0 0
\(521\) 13.6077i 0.596164i 0.954540 + 0.298082i \(0.0963469\pi\)
−0.954540 + 0.298082i \(0.903653\pi\)
\(522\) 0 0
\(523\) 24.2487 1.06032 0.530161 0.847897i \(-0.322131\pi\)
0.530161 + 0.847897i \(0.322131\pi\)
\(524\) −4.39230 2.53590i −0.191879 0.110781i
\(525\) 0 0
\(526\) 15.6603 + 4.19615i 0.682820 + 0.182961i
\(527\) 38.7846i 1.68948i
\(528\) 1.60770 0.928203i 0.0699660 0.0403949i
\(529\) 20.8564 0.906800
\(530\) 0 0
\(531\) 0 0
\(532\) −6.00000 31.1769i −0.260133 1.35169i
\(533\) 1.60770 0.0696370
\(534\) −6.00000 1.60770i −0.259645 0.0695718i
\(535\) 0 0
\(536\) −6.92820 6.92820i −0.299253 0.299253i
\(537\) 11.0718i 0.477783i
\(538\) 16.3923 + 4.39230i 0.706722 + 0.189366i
\(539\) 1.85641 + 0.267949i 0.0799611 + 0.0115414i
\(540\) 0 0
\(541\) 7.78461 0.334687 0.167343 0.985899i \(-0.446481\pi\)
0.167343 + 0.985899i \(0.446481\pi\)
\(542\) −3.46410 + 12.9282i −0.148796 + 0.555314i
\(543\) 1.60770i 0.0689928i
\(544\) −9.46410 35.3205i −0.405770 1.51435i
\(545\) 0 0
\(546\) −1.31347 2.70577i −0.0562112 0.115796i
\(547\) 21.4641i 0.917739i 0.888504 + 0.458869i \(0.151745\pi\)
−0.888504 + 0.458869i \(0.848255\pi\)
\(548\) 35.3205 + 20.3923i 1.50882 + 0.871116i
\(549\) 0 0
\(550\) 0 0
\(551\) 47.5692 2.02652
\(552\) 5.07180 + 5.07180i 0.215870 + 0.215870i
\(553\) 29.3205 25.3923i 1.24683 1.07979i
\(554\) 6.14359 22.9282i 0.261016 0.974126i
\(555\) 0 0
\(556\) −12.0000 6.92820i −0.508913 0.293821i
\(557\) 21.8564 0.926086 0.463043 0.886336i \(-0.346758\pi\)
0.463043 + 0.886336i \(0.346758\pi\)
\(558\) 0 0
\(559\) −0.928203 −0.0392588
\(560\) 0 0
\(561\) 3.00000 0.126660
\(562\) 2.90192 10.8301i 0.122410 0.456841i
\(563\) −19.1769 −0.808211 −0.404105 0.914712i \(-0.632417\pi\)
−0.404105 + 0.914712i \(0.632417\pi\)
\(564\) 5.19615 + 3.00000i 0.218797 + 0.126323i
\(565\) 0 0
\(566\) 4.43782 16.5622i 0.186536 0.696160i
\(567\) −15.5885 18.0000i −0.654654 0.755929i
\(568\) −14.9282 14.9282i −0.626373 0.626373i
\(569\) 7.07180 0.296465 0.148233 0.988953i \(-0.452642\pi\)
0.148233 + 0.988953i \(0.452642\pi\)
\(570\) 0 0
\(571\) 6.67949i 0.279528i 0.990185 + 0.139764i \(0.0446344\pi\)
−0.990185 + 0.139764i \(0.955366\pi\)
\(572\) −0.215390 0.124356i −0.00900592 0.00519957i
\(573\) 12.4641i 0.520695i
\(574\) 5.66025 + 11.6603i 0.236254 + 0.486690i
\(575\) 0 0
\(576\) 0 0
\(577\) 19.3923i 0.807312i −0.914911 0.403656i \(-0.867739\pi\)
0.914911 0.403656i \(-0.132261\pi\)
\(578\) 9.07180 33.8564i 0.377337 1.40824i
\(579\) 16.3923 0.681241
\(580\) 0 0
\(581\) −26.7846 30.9282i −1.11121 1.28312i
\(582\) −31.6865 8.49038i −1.31345 0.351938i
\(583\) 0.535898i 0.0221946i
\(584\) −25.8564 25.8564i −1.06995 1.06995i
\(585\) 0 0
\(586\) 27.7583 + 7.43782i 1.14669 + 0.307254i
\(587\) 20.5359 0.847607 0.423804 0.905754i \(-0.360695\pi\)
0.423804 + 0.905754i \(0.360695\pi\)
\(588\) 15.0000 19.0526i 0.618590 0.785714i
\(589\) −36.0000 −1.48335
\(590\) 0 0
\(591\) 23.0718 0.949047
\(592\) 18.9282 + 32.7846i 0.777944 + 1.34744i
\(593\) 30.4641i 1.25101i −0.780220 0.625505i \(-0.784893\pi\)
0.780220 0.625505i \(-0.215107\pi\)
\(594\) −1.90192 0.509619i −0.0780369 0.0209099i
\(595\) 0 0
\(596\) −5.32051 3.07180i −0.217937 0.125826i
\(597\) 6.00000 0.245564
\(598\) 0.248711 0.928203i 0.0101706 0.0379571i
\(599\) 10.1244i 0.413670i 0.978376 + 0.206835i \(0.0663163\pi\)
−0.978376 + 0.206835i \(0.933684\pi\)
\(600\) 0 0
\(601\) 14.7846i 0.603077i −0.953454 0.301538i \(-0.902500\pi\)
0.953454 0.301538i \(-0.0975001\pi\)
\(602\) −3.26795 6.73205i −0.133192 0.274378i
\(603\) 0 0
\(604\) −15.1962 + 26.3205i −0.618323 + 1.07097i
\(605\) 0 0
\(606\) 36.5885 + 9.80385i 1.48630 + 0.398254i
\(607\) 29.1962 1.18504 0.592518 0.805557i \(-0.298134\pi\)
0.592518 + 0.805557i \(0.298134\pi\)
\(608\) −32.7846 + 8.78461i −1.32959 + 0.356263i
\(609\) 23.7846 + 27.4641i 0.963801 + 1.11290i
\(610\) 0 0
\(611\) 0.803848i 0.0325202i
\(612\) 0 0
\(613\) 10.0000 0.403896 0.201948 0.979396i \(-0.435273\pi\)
0.201948 + 0.979396i \(0.435273\pi\)
\(614\) 0.633975 2.36603i 0.0255851 0.0954850i
\(615\) 0 0
\(616\) 0.143594 2.00000i 0.00578555 0.0805823i
\(617\) 22.9282 0.923055 0.461527 0.887126i \(-0.347302\pi\)
0.461527 + 0.887126i \(0.347302\pi\)
\(618\) −4.31347 + 16.0981i −0.173513 + 0.647560i
\(619\) 0.679492 0.0273111 0.0136555 0.999907i \(-0.495653\pi\)
0.0136555 + 0.999907i \(0.495653\pi\)
\(620\) 0 0
\(621\) 7.60770i 0.305286i
\(622\) −2.87564 + 10.7321i −0.115303 + 0.430316i
\(623\) −5.07180 + 4.39230i −0.203197 + 0.175974i
\(624\) −2.78461 + 1.60770i −0.111474 + 0.0643593i
\(625\) 0 0
\(626\) −23.9545 6.41858i −0.957414 0.256538i
\(627\) 2.78461i 0.111207i
\(628\) −7.85641 + 13.6077i −0.313505 + 0.543006i
\(629\) 61.1769i 2.43928i
\(630\) 0 0
\(631\) 38.9090i 1.54894i −0.632610 0.774471i \(-0.718016\pi\)
0.632610 0.774471i \(-0.281984\pi\)
\(632\) −29.3205 29.3205i −1.16631 1.16631i
\(633\) 5.53590i 0.220032i
\(634\) −1.12436 + 4.19615i −0.0446539 + 0.166651i
\(635\) 0 0
\(636\) 6.00000 + 3.46410i 0.237915 + 0.137361i
\(637\) −3.21539 0.464102i −0.127398 0.0183884i
\(638\) 2.90192 + 0.777568i 0.114888 + 0.0307842i
\(639\) 0 0
\(640\) 0 0
\(641\) 8.92820 0.352643 0.176321 0.984333i \(-0.443580\pi\)
0.176321 + 0.984333i \(0.443580\pi\)
\(642\) 5.66025 + 1.51666i 0.223392 + 0.0598578i
\(643\) −7.05256 −0.278126 −0.139063 0.990284i \(-0.544409\pi\)
−0.139063 + 0.990284i \(0.544409\pi\)
\(644\) 7.60770 1.46410i 0.299785 0.0576937i
\(645\) 0 0
\(646\) −52.9808 14.1962i −2.08450 0.558540i
\(647\) 10.3923 0.408564 0.204282 0.978912i \(-0.434514\pi\)
0.204282 + 0.978912i \(0.434514\pi\)
\(648\) −18.0000 + 18.0000i −0.707107 + 0.707107i
\(649\) 0.928203i 0.0364352i
\(650\) 0 0
\(651\) −18.0000 20.7846i −0.705476 0.814613i
\(652\) −20.7846 + 36.0000i −0.813988 + 1.40987i
\(653\) −17.6077 −0.689042 −0.344521 0.938779i \(-0.611959\pi\)
−0.344521 + 0.938779i \(0.611959\pi\)
\(654\) −1.31347 + 4.90192i −0.0513606 + 0.191680i
\(655\) 0 0
\(656\) 12.0000 6.92820i 0.468521 0.270501i
\(657\) 0 0
\(658\) 5.83013 2.83013i 0.227282 0.110330i
\(659\) 31.1962i 1.21523i 0.794232 + 0.607615i \(0.207874\pi\)
−0.794232 + 0.607615i \(0.792126\pi\)
\(660\) 0 0
\(661\) 39.7128i 1.54465i 0.635228 + 0.772325i \(0.280906\pi\)
−0.635228 + 0.772325i \(0.719094\pi\)
\(662\) −36.0526 9.66025i −1.40122 0.375456i
\(663\) −5.19615 −0.201802
\(664\) −30.9282 + 30.9282i −1.20025 + 1.20025i
\(665\) 0 0
\(666\) 0 0
\(667\) 11.6077i 0.449452i
\(668\) −9.00000 5.19615i −0.348220 0.201045i
\(669\) 23.7846 0.919566
\(670\) 0 0
\(671\) 2.53590 0.0978973
\(672\) −21.4641 14.5359i −0.827996 0.560734i
\(673\) 13.1769 0.507933 0.253966 0.967213i \(-0.418265\pi\)
0.253966 + 0.967213i \(0.418265\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) −22.1436 12.7846i −0.851677 0.491716i
\(677\) 25.3923i 0.975906i 0.872870 + 0.487953i \(0.162256\pi\)
−0.872870 + 0.487953i \(0.837744\pi\)
\(678\) 3.46410 12.9282i 0.133038 0.496505i
\(679\) −26.7846 + 23.1962i −1.02790 + 0.890187i
\(680\) 0 0
\(681\) −35.7846 −1.37127
\(682\) −2.19615 0.588457i −0.0840950 0.0225332i
\(683\) 7.32051i 0.280111i 0.990144 + 0.140056i \(0.0447282\pi\)
−0.990144 + 0.140056i \(0.955272\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −7.95448 24.9545i −0.303704 0.952767i
\(687\) 14.7846i 0.564068i
\(688\) −6.92820 + 4.00000i −0.264135 + 0.152499i
\(689\) 0.928203i 0.0353617i
\(690\) 0 0
\(691\) −22.6410 −0.861305 −0.430652 0.902518i \(-0.641717\pi\)
−0.430652 + 0.902518i \(0.641717\pi\)
\(692\) 14.3205 24.8038i 0.544384 0.942901i
\(693\) 0 0
\(694\) −46.7846 12.5359i −1.77592 0.475856i
\(695\) 0 0
\(696\) 27.4641 27.4641i 1.04102 1.04102i
\(697\) 22.3923 0.848169
\(698\) 7.26795 + 1.94744i 0.275096 + 0.0737117i
\(699\) 15.7128 0.594313
\(700\) 0 0
\(701\) −37.7846 −1.42711 −0.713553 0.700602i \(-0.752915\pi\)
−0.713553 + 0.700602i \(0.752915\pi\)
\(702\) 3.29423 + 0.882686i 0.124333 + 0.0333148i
\(703\) 56.7846 2.14167
\(704\) −2.14359 −0.0807897
\(705\) 0 0
\(706\) −10.0981 2.70577i −0.380046 0.101833i
\(707\) 30.9282 26.7846i 1.16317 1.00734i
\(708\) 10.3923 + 6.00000i 0.390567 + 0.225494i
\(709\) 21.0000 0.788672 0.394336 0.918966i \(-0.370975\pi\)
0.394336 + 0.918966i \(0.370975\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 5.07180 + 5.07180i 0.190074 + 0.190074i
\(713\) 8.78461i 0.328986i
\(714\) −18.2942 37.6865i −0.684644 1.41038i
\(715\) 0 0
\(716\) 6.39230 11.0718i 0.238892 0.413772i
\(717\) 41.5359i 1.55119i
\(718\) 34.5885 + 9.26795i 1.29083 + 0.345877i
\(719\) 38.5359 1.43715 0.718573 0.695451i \(-0.244795\pi\)
0.718573 + 0.695451i \(0.244795\pi\)
\(720\) 0 0
\(721\) 11.7846 + 13.6077i 0.438882 + 0.506777i
\(722\) −6.22243 + 23.2224i −0.231575 + 0.864249i
\(723\) 28.3923i 1.05592i
\(724\) −0.928203 + 1.60770i −0.0344964 + 0.0597495i
\(725\) 0 0
\(726\) −6.92820 + 25.8564i −0.257130 + 0.959621i
\(727\) 13.6077 0.504681 0.252341 0.967638i \(-0.418800\pi\)
0.252341 + 0.967638i \(0.418800\pi\)
\(728\) −0.248711 + 3.46410i −0.00921785 + 0.128388i
\(729\) 27.0000 1.00000
\(730\) 0 0
\(731\) −12.9282 −0.478167
\(732\) 16.3923 28.3923i 0.605877 1.04941i
\(733\) 11.5359i 0.426088i −0.977043 0.213044i \(-0.931662\pi\)
0.977043 0.213044i \(-0.0683378\pi\)
\(734\) 4.34679 16.2224i 0.160443 0.598781i
\(735\) 0 0
\(736\) −2.14359 8.00000i −0.0790139 0.294884i
\(737\) −0.928203 −0.0341908
\(738\) 0 0
\(739\) 4.26795i 0.156999i 0.996914 + 0.0784995i \(0.0250129\pi\)
−0.996914 + 0.0784995i \(0.974987\pi\)
\(740\) 0 0
\(741\) 4.82309i 0.177180i
\(742\) 6.73205 3.26795i 0.247141 0.119970i
\(743\) 30.3923i 1.11499i 0.830182 + 0.557493i \(0.188237\pi\)
−0.830182 + 0.557493i \(0.811763\pi\)
\(744\) −20.7846 + 20.7846i −0.762001 + 0.762001i
\(745\) 0 0
\(746\) −1.32051 + 4.92820i −0.0483472 + 0.180434i
\(747\) 0 0
\(748\) −3.00000 1.73205i −0.109691 0.0633300i
\(749\) 4.78461 4.14359i 0.174826 0.151404i
\(750\) 0 0
\(751\) 25.5885i 0.933736i 0.884327 + 0.466868i \(0.154618\pi\)
−0.884327 + 0.466868i \(0.845382\pi\)
\(752\) −3.46410 6.00000i −0.126323 0.218797i
\(753\) −44.7846 −1.63204
\(754\) −5.02628 1.34679i −0.183046 0.0490471i
\(755\) 0 0
\(756\) 5.19615 + 27.0000i 0.188982 + 0.981981i
\(757\) −37.8564 −1.37591 −0.687957 0.725751i \(-0.741492\pi\)
−0.687957 + 0.725751i \(0.741492\pi\)
\(758\) 7.66025 + 2.05256i 0.278233 + 0.0745523i
\(759\) 0.679492 0.0246640
\(760\) 0 0
\(761\) 42.2487i 1.53151i −0.643130 0.765757i \(-0.722364\pi\)
0.643130 0.765757i \(-0.277636\pi\)
\(762\) 36.5885 + 9.80385i 1.32546 + 0.355156i
\(763\) 3.58846 + 4.14359i 0.129911 + 0.150008i
\(764\) −7.19615 + 12.4641i −0.260348 + 0.450935i
\(765\) 0 0
\(766\) 10.0526 37.5167i 0.363214 1.35553i
\(767\) 1.60770i 0.0580505i
\(768\) −13.8564 + 24.0000i −0.500000 + 0.866025i
\(769\) 18.0000i 0.649097i 0.945869 + 0.324548i \(0.105212\pi\)
−0.945869 + 0.324548i \(0.894788\pi\)
\(770\) 0 0
\(771\) 10.3923i 0.374270i
\(772\) −16.3923 9.46410i −0.589972 0.340620i
\(773\) 5.53590i 0.199112i 0.995032 + 0.0995562i \(0.0317423\pi\)
−0.995032 + 0.0995562i \(0.968258\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 26.7846 + 26.7846i 0.961511 + 0.961511i
\(777\) 28.3923 + 32.7846i 1.01857 + 1.17614i
\(778\) 7.63397 28.4904i 0.273691 1.02143i
\(779\) 20.7846i 0.744686i
\(780\) 0 0
\(781\) −2.00000 −0.0715656
\(782\) 3.46410 12.9282i 0.123876 0.462312i
\(783\) −41.1962 −1.47223
\(784\) −26.0000 + 10.3923i −0.928571 + 0.371154i
\(785\) 0 0
\(786\) −1.60770 + 6.00000i −0.0573446 + 0.214013i
\(787\) −32.6603 −1.16421 −0.582106 0.813113i \(-0.697771\pi\)
−0.582106 + 0.813113i \(0.697771\pi\)
\(788\)