Properties

Label 700.2.c.c.699.2
Level $700$
Weight $2$
Character 700.699
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.c (of order \(2\), degree \(1\), not 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: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 140)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 699.2
Root \(0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 700.699
Dual form 700.2.c.c.699.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.36603 + 0.366025i) q^{2} -1.73205i q^{3} +(1.73205 - 1.00000i) q^{4} +(0.633975 + 2.36603i) q^{6} +(-2.00000 + 1.73205i) q^{7} +(-2.00000 + 2.00000i) q^{8} +O(q^{10})\) \(q+(-1.36603 + 0.366025i) q^{2} -1.73205i q^{3} +(1.73205 - 1.00000i) q^{4} +(0.633975 + 2.36603i) q^{6} +(-2.00000 + 1.73205i) q^{7} +(-2.00000 + 2.00000i) q^{8} +0.267949i q^{11} +(-1.73205 - 3.00000i) q^{12} -0.464102 q^{13} +(2.09808 - 3.09808i) q^{14} +(2.00000 - 3.46410i) q^{16} +6.46410 q^{17} +6.00000 q^{19} +(3.00000 + 3.46410i) q^{21} +(-0.0980762 - 0.366025i) q^{22} +1.46410 q^{23} +(3.46410 + 3.46410i) q^{24} +(0.633975 - 0.169873i) q^{26} -5.19615i q^{27} +(-1.73205 + 5.00000i) q^{28} -7.92820 q^{29} +6.00000 q^{31} +(-1.46410 + 5.46410i) q^{32} +0.464102 q^{33} +(-8.83013 + 2.36603i) q^{34} -9.46410i q^{37} +(-8.19615 + 2.19615i) q^{38} +0.803848i q^{39} -3.46410i q^{41} +(-5.36603 - 3.63397i) q^{42} +2.00000 q^{43} +(0.267949 + 0.464102i) q^{44} +(-2.00000 + 0.535898i) q^{46} -1.73205i q^{47} +(-6.00000 - 3.46410i) q^{48} +(1.00000 - 6.92820i) q^{49} -11.1962i q^{51} +(-0.803848 + 0.464102i) q^{52} -2.00000i q^{53} +(1.90192 + 7.09808i) q^{54} +(0.535898 - 7.46410i) q^{56} -10.3923i q^{57} +(10.8301 - 2.90192i) q^{58} -3.46410 q^{59} +9.46410i q^{61} +(-8.19615 + 2.19615i) q^{62} -8.00000i q^{64} +(-0.633975 + 0.169873i) q^{66} +3.46410 q^{67} +(11.1962 - 6.46410i) q^{68} -2.53590i q^{69} +7.46410i q^{71} +12.9282 q^{73} +(3.46410 + 12.9282i) q^{74} +(10.3923 - 6.00000i) q^{76} +(-0.464102 - 0.535898i) q^{77} +(-0.294229 - 1.09808i) q^{78} -14.6603i q^{79} -9.00000 q^{81} +(1.26795 + 4.73205i) q^{82} +15.4641i q^{83} +(8.66025 + 3.00000i) q^{84} +(-2.73205 + 0.732051i) q^{86} +13.7321i q^{87} +(-0.535898 - 0.535898i) q^{88} -2.53590i q^{89} +(0.928203 - 0.803848i) q^{91} +(2.53590 - 1.46410i) q^{92} -10.3923i q^{93} +(0.633975 + 2.36603i) q^{94} +(9.46410 + 2.53590i) q^{96} +13.3923 q^{97} +(1.16987 + 9.83013i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 2q^{2} + 6q^{6} - 8q^{7} - 8q^{8} + O(q^{10}) \) \( 4q - 2q^{2} + 6q^{6} - 8q^{7} - 8q^{8} + 12q^{13} - 2q^{14} + 8q^{16} + 12q^{17} + 24q^{19} + 12q^{21} + 10q^{22} - 8q^{23} + 6q^{26} - 4q^{29} + 24q^{31} + 8q^{32} - 12q^{33} - 18q^{34} - 12q^{38} - 18q^{42} + 8q^{43} + 8q^{44} - 8q^{46} - 24q^{48} + 4q^{49} - 24q^{52} + 18q^{54} + 16q^{56} + 26q^{58} - 12q^{62} - 6q^{66} + 24q^{68} + 24q^{73} + 12q^{77} + 30q^{78} - 36q^{81} + 12q^{82} - 4q^{86} - 16q^{88} - 24q^{91} + 24q^{92} + 6q^{94} + 24q^{96} + 12q^{97} + 22q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.36603 + 0.366025i −0.965926 + 0.258819i
\(3\) 1.73205i 1.00000i −0.866025 0.500000i \(-0.833333\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(4\) 1.73205 1.00000i 0.866025 0.500000i
\(5\) 0 0
\(6\) 0.633975 + 2.36603i 0.258819 + 0.965926i
\(7\) −2.00000 + 1.73205i −0.755929 + 0.654654i
\(8\) −2.00000 + 2.00000i −0.707107 + 0.707107i
\(9\) 0 0
\(10\) 0 0
\(11\) 0.267949i 0.0807897i 0.999184 + 0.0403949i \(0.0128616\pi\)
−0.999184 + 0.0403949i \(0.987138\pi\)
\(12\) −1.73205 3.00000i −0.500000 0.866025i
\(13\) −0.464102 −0.128719 −0.0643593 0.997927i \(-0.520500\pi\)
−0.0643593 + 0.997927i \(0.520500\pi\)
\(14\) 2.09808 3.09808i 0.560734 0.827996i
\(15\) 0 0
\(16\) 2.00000 3.46410i 0.500000 0.866025i
\(17\) 6.46410 1.56777 0.783887 0.620903i \(-0.213234\pi\)
0.783887 + 0.620903i \(0.213234\pi\)
\(18\) 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
\(22\) −0.0980762 0.366025i −0.0209099 0.0780369i
\(23\) 1.46410 0.305286 0.152643 0.988281i \(-0.451221\pi\)
0.152643 + 0.988281i \(0.451221\pi\)
\(24\) 3.46410 + 3.46410i 0.707107 + 0.707107i
\(25\) 0 0
\(26\) 0.633975 0.169873i 0.124333 0.0333148i
\(27\) 5.19615i 1.00000i
\(28\) −1.73205 + 5.00000i −0.327327 + 0.944911i
\(29\) −7.92820 −1.47223 −0.736115 0.676856i \(-0.763342\pi\)
−0.736115 + 0.676856i \(0.763342\pi\)
\(30\) 0 0
\(31\) 6.00000 1.07763 0.538816 0.842424i \(-0.318872\pi\)
0.538816 + 0.842424i \(0.318872\pi\)
\(32\) −1.46410 + 5.46410i −0.258819 + 0.965926i
\(33\) 0.464102 0.0807897
\(34\) −8.83013 + 2.36603i −1.51435 + 0.405770i
\(35\) 0 0
\(36\) 0 0
\(37\) 9.46410i 1.55589i −0.628333 0.777944i \(-0.716263\pi\)
0.628333 0.777944i \(-0.283737\pi\)
\(38\) −8.19615 + 2.19615i −1.32959 + 0.356263i
\(39\) 0.803848i 0.128719i
\(40\) 0 0
\(41\) 3.46410i 0.541002i −0.962720 0.270501i \(-0.912811\pi\)
0.962720 0.270501i \(-0.0871893\pi\)
\(42\) −5.36603 3.63397i −0.827996 0.560734i
\(43\) 2.00000 0.304997 0.152499 0.988304i \(-0.451268\pi\)
0.152499 + 0.988304i \(0.451268\pi\)
\(44\) 0.267949 + 0.464102i 0.0403949 + 0.0699660i
\(45\) 0 0
\(46\) −2.00000 + 0.535898i −0.294884 + 0.0790139i
\(47\) 1.73205i 0.252646i −0.991989 0.126323i \(-0.959682\pi\)
0.991989 0.126323i \(-0.0403175\pi\)
\(48\) −6.00000 3.46410i −0.866025 0.500000i
\(49\) 1.00000 6.92820i 0.142857 0.989743i
\(50\) 0 0
\(51\) 11.1962i 1.56777i
\(52\) −0.803848 + 0.464102i −0.111474 + 0.0643593i
\(53\) 2.00000i 0.274721i −0.990521 0.137361i \(-0.956138\pi\)
0.990521 0.137361i \(-0.0438619\pi\)
\(54\) 1.90192 + 7.09808i 0.258819 + 0.965926i
\(55\) 0 0
\(56\) 0.535898 7.46410i 0.0716124 0.997433i
\(57\) 10.3923i 1.37649i
\(58\) 10.8301 2.90192i 1.42207 0.381041i
\(59\) −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 \(0.792822\pi\)
\(62\) −8.19615 + 2.19615i −1.04091 + 0.278912i
\(63\) 0 0
\(64\) 8.00000i 1.00000i
\(65\) 0 0
\(66\) −0.633975 + 0.169873i −0.0780369 + 0.0209099i
\(67\) 3.46410 0.423207 0.211604 0.977356i \(-0.432131\pi\)
0.211604 + 0.977356i \(0.432131\pi\)
\(68\) 11.1962 6.46410i 1.35773 0.783887i
\(69\) 2.53590i 0.305286i
\(70\) 0 0
\(71\) 7.46410i 0.885826i 0.896565 + 0.442913i \(0.146055\pi\)
−0.896565 + 0.442913i \(0.853945\pi\)
\(72\) 0 0
\(73\) 12.9282 1.51313 0.756566 0.653917i \(-0.226876\pi\)
0.756566 + 0.653917i \(0.226876\pi\)
\(74\) 3.46410 + 12.9282i 0.402694 + 1.50287i
\(75\) 0 0
\(76\) 10.3923 6.00000i 1.19208 0.688247i
\(77\) −0.464102 0.535898i −0.0528893 0.0610713i
\(78\) −0.294229 1.09808i −0.0333148 0.124333i
\(79\) 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
\(82\) 1.26795 + 4.73205i 0.140022 + 0.522568i
\(83\) 15.4641i 1.69741i 0.528870 + 0.848703i \(0.322616\pi\)
−0.528870 + 0.848703i \(0.677384\pi\)
\(84\) 8.66025 + 3.00000i 0.944911 + 0.327327i
\(85\) 0 0
\(86\) −2.73205 + 0.732051i −0.294605 + 0.0789391i
\(87\) 13.7321i 1.47223i
\(88\) −0.535898 0.535898i −0.0571270 0.0571270i
\(89\) 2.53590i 0.268805i −0.990927 0.134402i \(-0.957089\pi\)
0.990927 0.134402i \(-0.0429115\pi\)
\(90\) 0 0
\(91\) 0.928203 0.803848i 0.0973021 0.0842661i
\(92\) 2.53590 1.46410i 0.264386 0.152643i
\(93\) 10.3923i 1.07763i
\(94\) 0.633975 + 2.36603i 0.0653895 + 0.244037i
\(95\) 0 0
\(96\) 9.46410 + 2.53590i 0.965926 + 0.258819i
\(97\) 13.3923 1.35978 0.679891 0.733313i \(-0.262027\pi\)
0.679891 + 0.733313i \(0.262027\pi\)
\(98\) 1.16987 + 9.83013i 0.118175 + 0.992993i
\(99\) 0 0
\(100\) 0 0
\(101\) 15.4641i 1.53874i −0.638806 0.769368i \(-0.720571\pi\)
0.638806 0.769368i \(-0.279429\pi\)
\(102\) 4.09808 + 15.2942i 0.405770 + 1.51435i
\(103\) 6.80385i 0.670403i −0.942146 0.335202i \(-0.891196\pi\)
0.942146 0.335202i \(-0.108804\pi\)
\(104\) 0.928203 0.928203i 0.0910178 0.0910178i
\(105\) 0 0
\(106\) 0.732051 + 2.73205i 0.0711031 + 0.265360i
\(107\) 2.39230 0.231273 0.115636 0.993292i \(-0.463109\pi\)
0.115636 + 0.993292i \(0.463109\pi\)
\(108\) −5.19615 9.00000i −0.500000 0.866025i
\(109\) −2.07180 −0.198442 −0.0992211 0.995065i \(-0.531635\pi\)
−0.0992211 + 0.995065i \(0.531635\pi\)
\(110\) 0 0
\(111\) −16.3923 −1.55589
\(112\) 2.00000 + 10.3923i 0.188982 + 0.981981i
\(113\) 5.46410i 0.514019i −0.966409 0.257010i \(-0.917263\pi\)
0.966409 0.257010i \(-0.0827372\pi\)
\(114\) 3.80385 + 14.1962i 0.356263 + 1.32959i
\(115\) 0 0
\(116\) −13.7321 + 7.92820i −1.27499 + 0.736115i
\(117\) 0 0
\(118\) 4.73205 1.26795i 0.435621 0.116724i
\(119\) −12.9282 + 11.1962i −1.18513 + 1.02635i
\(120\) 0 0
\(121\) 10.9282 0.993473
\(122\) −3.46410 12.9282i −0.313625 1.17046i
\(123\) −6.00000 −0.541002
\(124\) 10.3923 6.00000i 0.933257 0.538816i
\(125\) 0 0
\(126\) 0 0
\(127\) 15.4641 1.37222 0.686109 0.727499i \(-0.259317\pi\)
0.686109 + 0.727499i \(0.259317\pi\)
\(128\) 2.92820 + 10.9282i 0.258819 + 0.965926i
\(129\) 3.46410i 0.304997i
\(130\) 0 0
\(131\) −2.53590 −0.221562 −0.110781 0.993845i \(-0.535335\pi\)
−0.110781 + 0.993845i \(0.535335\pi\)
\(132\) 0.803848 0.464102i 0.0699660 0.0403949i
\(133\) −12.0000 + 10.3923i −1.04053 + 0.901127i
\(134\) −4.73205 + 1.26795i −0.408787 + 0.109534i
\(135\) 0 0
\(136\) −12.9282 + 12.9282i −1.10858 + 1.10858i
\(137\) 20.3923i 1.74223i 0.491077 + 0.871116i \(0.336603\pi\)
−0.491077 + 0.871116i \(0.663397\pi\)
\(138\) 0.928203 + 3.46410i 0.0790139 + 0.294884i
\(139\) 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
\(142\) −2.73205 10.1962i −0.229269 0.855642i
\(143\) 0.124356i 0.0103991i
\(144\) 0 0
\(145\) 0 0
\(146\) −17.6603 + 4.73205i −1.46157 + 0.391627i
\(147\) −12.0000 1.73205i −0.989743 0.142857i
\(148\) −9.46410 16.3923i −0.777944 1.34744i
\(149\) −3.07180 −0.251651 −0.125826 0.992052i \(-0.540158\pi\)
−0.125826 + 0.992052i \(0.540158\pi\)
\(150\) 0 0
\(151\) 15.1962i 1.23665i 0.785924 + 0.618323i \(0.212188\pi\)
−0.785924 + 0.618323i \(0.787812\pi\)
\(152\) −12.0000 + 12.0000i −0.973329 + 0.973329i
\(153\) 0 0
\(154\) 0.830127 + 0.562178i 0.0668935 + 0.0453016i
\(155\) 0 0
\(156\) 0.803848 + 1.39230i 0.0643593 + 0.111474i
\(157\) −7.85641 −0.627009 −0.313505 0.949587i \(-0.601503\pi\)
−0.313505 + 0.949587i \(0.601503\pi\)
\(158\) 5.36603 + 20.0263i 0.426898 + 1.59321i
\(159\) −3.46410 −0.274721
\(160\) 0 0
\(161\) −2.92820 + 2.53590i −0.230775 + 0.199857i
\(162\) 12.2942 3.29423i 0.965926 0.258819i
\(163\) −20.7846 −1.62798 −0.813988 0.580881i \(-0.802708\pi\)
−0.813988 + 0.580881i \(0.802708\pi\)
\(164\) −3.46410 6.00000i −0.270501 0.468521i
\(165\) 0 0
\(166\) −5.66025 21.1244i −0.439321 1.63957i
\(167\) 5.19615i 0.402090i 0.979582 + 0.201045i \(0.0644338\pi\)
−0.979582 + 0.201045i \(0.935566\pi\)
\(168\) −12.9282 0.928203i −0.997433 0.0716124i
\(169\) −12.7846 −0.983432
\(170\) 0 0
\(171\) 0 0
\(172\) 3.46410 2.00000i 0.264135 0.152499i
\(173\) −14.3205 −1.08877 −0.544384 0.838836i \(-0.683237\pi\)
−0.544384 + 0.838836i \(0.683237\pi\)
\(174\) −5.02628 18.7583i −0.381041 1.42207i
\(175\) 0 0
\(176\) 0.928203 + 0.535898i 0.0699660 + 0.0403949i
\(177\) 6.00000i 0.450988i
\(178\) 0.928203 + 3.46410i 0.0695718 + 0.259645i
\(179\) 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 \(-0.0109827\pi\)
\(182\) −0.973721 + 1.43782i −0.0721770 + 0.106578i
\(183\) 16.3923 1.21175
\(184\) −2.92820 + 2.92820i −0.215870 + 0.215870i
\(185\) 0 0
\(186\) 3.80385 + 14.1962i 0.278912 + 1.04091i
\(187\) 1.73205i 0.126660i
\(188\) −1.73205 3.00000i −0.126323 0.218797i
\(189\) 9.00000 + 10.3923i 0.654654 + 0.755929i
\(190\) 0 0
\(191\) 7.19615i 0.520695i 0.965515 + 0.260348i \(0.0838372\pi\)
−0.965515 + 0.260348i \(0.916163\pi\)
\(192\) −13.8564 −1.00000
\(193\) 9.46410i 0.681241i 0.940201 + 0.340620i \(0.110637\pi\)
−0.940201 + 0.340620i \(0.889363\pi\)
\(194\) −18.2942 + 4.90192i −1.31345 + 0.351938i
\(195\) 0 0
\(196\) −5.19615 13.0000i −0.371154 0.928571i
\(197\) 13.3205i 0.949047i −0.880243 0.474523i \(-0.842620\pi\)
0.880243 0.474523i \(-0.157380\pi\)
\(198\) 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
\(202\) 5.66025 + 21.1244i 0.398254 + 1.48630i
\(203\) 15.8564 13.7321i 1.11290 0.963801i
\(204\) −11.1962 19.3923i −0.783887 1.35773i
\(205\) 0 0
\(206\) 2.49038 + 9.29423i 0.173513 + 0.647560i
\(207\) 0 0
\(208\) −0.928203 + 1.60770i −0.0643593 + 0.111474i
\(209\) 1.60770i 0.111207i
\(210\) 0 0
\(211\) 3.19615i 0.220032i 0.993930 + 0.110016i \(0.0350902\pi\)
−0.993930 + 0.110016i \(0.964910\pi\)
\(212\) −2.00000 3.46410i −0.137361 0.237915i
\(213\) 12.9282 0.885826
\(214\) −3.26795 + 0.875644i −0.223392 + 0.0598578i
\(215\) 0 0
\(216\) 10.3923 + 10.3923i 0.707107 + 0.707107i
\(217\) −12.0000 + 10.3923i −0.814613 + 0.705476i
\(218\) 2.83013 0.758330i 0.191680 0.0513606i
\(219\) 22.3923i 1.51313i
\(220\) 0 0
\(221\) −3.00000 −0.201802
\(222\) 22.3923 6.00000i 1.50287 0.402694i
\(223\) 13.7321i 0.919566i −0.888031 0.459783i \(-0.847927\pi\)
0.888031 0.459783i \(-0.152073\pi\)
\(224\) −6.53590 13.4641i −0.436698 0.899608i
\(225\) 0 0
\(226\) 2.00000 + 7.46410i 0.133038 + 0.496505i
\(227\) 20.6603i 1.37127i −0.727946 0.685635i \(-0.759525\pi\)
0.727946 0.685635i \(-0.240475\pi\)
\(228\) −10.3923 18.0000i −0.688247 1.19208i
\(229\) 8.53590i 0.564068i 0.959404 + 0.282034i \(0.0910091\pi\)
−0.959404 + 0.282034i \(0.908991\pi\)
\(230\) 0 0
\(231\) −0.928203 + 0.803848i −0.0610713 + 0.0528893i
\(232\) 15.8564 15.8564i 1.04102 1.04102i
\(233\) 9.07180i 0.594313i 0.954829 + 0.297157i \(0.0960383\pi\)
−0.954829 + 0.297157i \(0.903962\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −6.00000 + 3.46410i −0.390567 + 0.225494i
\(237\) −25.3923 −1.64941
\(238\) 13.5622 20.0263i 0.879105 1.29811i
\(239\) 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 \(0.822957\pi\)
\(242\) −14.9282 + 4.00000i −0.959621 + 0.257130i
\(243\) 0 0
\(244\) 9.46410 + 16.3923i 0.605877 + 1.04941i
\(245\) 0 0
\(246\) 8.19615 2.19615i 0.522568 0.140022i
\(247\) −2.78461 −0.177180
\(248\) −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 \(-0.196175\pi\)
0.816021 + 0.578022i \(0.196175\pi\)
\(252\) 0 0
\(253\) 0.392305i 0.0246640i
\(254\) −21.1244 + 5.66025i −1.32546 + 0.355156i
\(255\) 0 0
\(256\) −8.00000 13.8564i −0.500000 0.866025i
\(257\) −6.00000 −0.374270 −0.187135 0.982334i \(-0.559920\pi\)
−0.187135 + 0.982334i \(0.559920\pi\)
\(258\) 1.26795 + 4.73205i 0.0789391 + 0.294605i
\(259\) 16.3923 + 18.9282i 1.01857 + 1.17614i
\(260\) 0 0
\(261\) 0 0
\(262\) 3.46410 0.928203i 0.214013 0.0573446i
\(263\) −11.4641 −0.706907 −0.353453 0.935452i \(-0.614993\pi\)
−0.353453 + 0.935452i \(0.614993\pi\)
\(264\) −0.928203 + 0.928203i −0.0571270 + 0.0571270i
\(265\) 0 0
\(266\) 12.5885 18.5885i 0.771848 1.13973i
\(267\) −4.39230 −0.268805
\(268\) 6.00000 3.46410i 0.366508 0.211604i
\(269\) 12.0000i 0.731653i 0.930683 + 0.365826i \(0.119214\pi\)
−0.930683 + 0.365826i \(0.880786\pi\)
\(270\) 0 0
\(271\) −9.46410 −0.574903 −0.287452 0.957795i \(-0.592808\pi\)
−0.287452 + 0.957795i \(0.592808\pi\)
\(272\) 12.9282 22.3923i 0.783887 1.35773i
\(273\) −1.39230 1.60770i −0.0842661 0.0973021i
\(274\) −7.46410 27.8564i −0.450923 1.68287i
\(275\) 0 0
\(276\) −2.53590 4.39230i −0.152643 0.264386i
\(277\) 16.7846i 1.00849i 0.863561 + 0.504245i \(0.168229\pi\)
−0.863561 + 0.504245i \(0.831771\pi\)
\(278\) −9.46410 + 2.53590i −0.567619 + 0.152093i
\(279\) 0 0
\(280\) 0 0
\(281\) −7.92820 −0.472957 −0.236478 0.971637i \(-0.575993\pi\)
−0.236478 + 0.971637i \(0.575993\pi\)
\(282\) 4.09808 1.09808i 0.244037 0.0653895i
\(283\) 12.1244i 0.720718i 0.932814 + 0.360359i \(0.117346\pi\)
−0.932814 + 0.360359i \(0.882654\pi\)
\(284\) 7.46410 + 12.9282i 0.442913 + 0.767148i
\(285\) 0 0
\(286\) 0.0455173 + 0.169873i 0.00269150 + 0.0100448i
\(287\) 6.00000 + 6.92820i 0.354169 + 0.408959i
\(288\) 0 0
\(289\) 24.7846 1.45792
\(290\) 0 0
\(291\) 23.1962i 1.35978i
\(292\) 22.3923 12.9282i 1.31041 0.756566i
\(293\) 20.3205 1.18714 0.593568 0.804784i \(-0.297719\pi\)
0.593568 + 0.804784i \(0.297719\pi\)
\(294\) 17.0263 2.02628i 0.992993 0.118175i
\(295\) 0 0
\(296\) 18.9282 + 18.9282i 1.10018 + 1.10018i
\(297\) 1.39230 0.0807897
\(298\) 4.19615 1.12436i 0.243077 0.0651322i
\(299\) −0.679492 −0.0392960
\(300\) 0 0
\(301\) −4.00000 + 3.46410i −0.230556 + 0.199667i
\(302\) −5.56218 20.7583i −0.320067 1.19451i
\(303\) −26.7846 −1.53874
\(304\) 12.0000 20.7846i 0.688247 1.19208i
\(305\) 0 0
\(306\) 0 0
\(307\) 1.73205i 0.0988534i −0.998778 0.0494267i \(-0.984261\pi\)
0.998778 0.0494267i \(-0.0157394\pi\)
\(308\) −1.33975 0.464102i −0.0763391 0.0264446i
\(309\) −11.7846 −0.670403
\(310\) 0 0
\(311\) −7.85641 −0.445496 −0.222748 0.974876i \(-0.571503\pi\)
−0.222748 + 0.974876i \(0.571503\pi\)
\(312\) −1.60770 1.60770i −0.0910178 0.0910178i
\(313\) −17.5359 −0.991188 −0.495594 0.868554i \(-0.665050\pi\)
−0.495594 + 0.868554i \(0.665050\pi\)
\(314\) 10.7321 2.87564i 0.605645 0.162282i
\(315\) 0 0
\(316\) −14.6603 25.3923i −0.824704 1.42843i
\(317\) 3.07180i 0.172529i −0.996272 0.0862646i \(-0.972507\pi\)
0.996272 0.0862646i \(-0.0274931\pi\)
\(318\) 4.73205 1.26795i 0.265360 0.0711031i
\(319\) 2.12436i 0.118941i
\(320\) 0 0
\(321\) 4.14359i 0.231273i
\(322\) 3.07180 4.53590i 0.171185 0.252776i
\(323\) 38.7846 2.15803
\(324\) −15.5885 + 9.00000i −0.866025 + 0.500000i
\(325\) 0 0
\(326\) 28.3923 7.60770i 1.57250 0.421351i
\(327\) 3.58846i 0.198442i
\(328\) 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 \(-0.741689\pi\)
0.688405 0.725326i \(-0.258311\pi\)
\(332\) 15.4641 + 26.7846i 0.848703 + 1.47000i
\(333\) 0 0
\(334\) −1.90192 7.09808i −0.104069 0.388389i
\(335\) 0 0
\(336\) 18.0000 3.46410i 0.981981 0.188982i
\(337\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(338\) 17.4641 4.67949i 0.949922 0.254531i
\(339\) −9.46410 −0.514019
\(340\) 0 0
\(341\) 1.60770i 0.0870616i
\(342\) 0 0
\(343\) 10.0000 + 15.5885i 0.539949 + 0.841698i
\(344\) −4.00000 + 4.00000i −0.215666 + 0.215666i
\(345\) 0 0
\(346\) 19.5622 5.24167i 1.05167 0.281794i
\(347\) −34.2487 −1.83857 −0.919284 0.393596i \(-0.871231\pi\)
−0.919284 + 0.393596i \(0.871231\pi\)
\(348\) 13.7321 + 23.7846i 0.736115 + 1.27499i
\(349\) 5.32051i 0.284800i 0.989809 + 0.142400i \(0.0454820\pi\)
−0.989809 + 0.142400i \(0.954518\pi\)
\(350\) 0 0
\(351\) 2.41154i 0.128719i
\(352\) −1.46410 0.392305i −0.0780369 0.0209099i
\(353\) −7.39230 −0.393453 −0.196726 0.980458i \(-0.563031\pi\)
−0.196726 + 0.980458i \(0.563031\pi\)
\(354\) −2.19615 8.19615i −0.116724 0.435621i
\(355\) 0 0
\(356\) −2.53590 4.39230i −0.134402 0.232792i
\(357\) 19.3923 + 22.3923i 1.02635 + 1.18513i
\(358\) −2.33975 8.73205i −0.123659 0.461503i
\(359\) 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
\(362\) 0.339746 + 1.26795i 0.0178567 + 0.0666419i
\(363\) 18.9282i 0.993473i
\(364\) 0.803848 2.32051i 0.0421331 0.121628i
\(365\) 0 0
\(366\) −22.3923 + 6.00000i −1.17046 + 0.313625i
\(367\) 11.8756i 0.619904i −0.950752 0.309952i \(-0.899687\pi\)
0.950752 0.309952i \(-0.100313\pi\)
\(368\) 2.92820 5.07180i 0.152643 0.264386i
\(369\) 0 0
\(370\) 0 0
\(371\) 3.46410 + 4.00000i 0.179847 + 0.207670i
\(372\) −10.3923 18.0000i −0.538816 0.933257i
\(373\) 3.60770i 0.186799i 0.995629 + 0.0933997i \(0.0297734\pi\)
−0.995629 + 0.0933997i \(0.970227\pi\)
\(374\) −0.633975 2.36603i −0.0327820 0.122344i
\(375\) 0 0
\(376\) 3.46410 + 3.46410i 0.178647 + 0.178647i
\(377\) 3.67949 0.189503
\(378\) −16.0981 10.9019i −0.827996 0.560734i
\(379\) 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
\(382\) −2.63397 9.83013i −0.134766 0.502953i
\(383\) 27.4641i 1.40335i 0.712497 + 0.701675i \(0.247564\pi\)
−0.712497 + 0.701675i \(0.752436\pi\)
\(384\) 18.9282 5.07180i 0.965926 0.258819i
\(385\) 0 0
\(386\) −3.46410 12.9282i −0.176318 0.658028i
\(387\) 0 0
\(388\) 23.1962 13.3923i 1.17761 0.679891i
\(389\) 20.8564 1.05746 0.528731 0.848790i \(-0.322668\pi\)
0.528731 + 0.848790i \(0.322668\pi\)
\(390\) 0 0
\(391\) 9.46410 0.478620
\(392\) 11.8564 + 15.8564i 0.598839 + 0.800869i
\(393\) 4.39230i 0.221562i
\(394\) 4.87564 + 18.1962i 0.245631 + 0.916709i
\(395\) 0 0
\(396\) 0 0
\(397\) −12.4641 −0.625555 −0.312778 0.949826i \(-0.601259\pi\)
−0.312778 + 0.949826i \(0.601259\pi\)
\(398\) −4.73205 + 1.26795i −0.237196 + 0.0635566i
\(399\) 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 \(0.580918\pi\)
\(402\) 2.19615 + 8.19615i 0.109534 + 0.408787i
\(403\) −2.78461 −0.138711
\(404\) −15.4641 26.7846i −0.769368 1.33258i
\(405\) 0 0
\(406\) −16.6340 + 24.5622i −0.825530 + 1.21900i
\(407\) 2.53590 0.125700
\(408\) 22.3923 + 22.3923i 1.10858 + 1.10858i
\(409\) 4.14359i 0.204888i −0.994739 0.102444i \(-0.967334\pi\)
0.994739 0.102444i \(-0.0326662\pi\)
\(410\) 0 0
\(411\) 35.3205 1.74223
\(412\) −6.80385 11.7846i −0.335202 0.580586i
\(413\) 6.92820 6.00000i 0.340915 0.295241i
\(414\) 0 0
\(415\) 0 0
\(416\) 0.679492 2.53590i 0.0333148 0.124333i
\(417\) 12.0000i 0.587643i
\(418\) −0.588457 2.19615i −0.0287824 0.107417i
\(419\) −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 \(0.346772\pi\)
\(422\) −1.16987 4.36603i −0.0569485 0.212535i
\(423\) 0 0
\(424\) 4.00000 + 4.00000i 0.194257 + 0.194257i
\(425\) 0 0
\(426\) −17.6603 + 4.73205i −0.855642 + 0.229269i
\(427\) −16.3923 18.9282i −0.793279 0.916000i
\(428\) 4.14359 2.39230i 0.200288 0.115636i
\(429\) −0.215390 −0.0103991
\(430\) 0 0
\(431\) 13.5885i 0.654533i −0.944932 0.327266i \(-0.893873\pi\)
0.944932 0.327266i \(-0.106127\pi\)
\(432\) −18.0000 10.3923i −0.866025 0.500000i
\(433\) −31.8564 −1.53092 −0.765461 0.643483i \(-0.777489\pi\)
−0.765461 + 0.643483i \(0.777489\pi\)
\(434\) 12.5885 18.5885i 0.604265 0.892275i
\(435\) 0 0
\(436\) −3.58846 + 2.07180i −0.171856 + 0.0992211i
\(437\) 8.78461 0.420225
\(438\) 8.19615 + 30.5885i 0.391627 + 1.46157i
\(439\) −39.7128 −1.89539 −0.947695 0.319179i \(-0.896593\pi\)
−0.947695 + 0.319179i \(0.896593\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 4.09808 1.09808i 0.194926 0.0522302i
\(443\) −26.0000 −1.23530 −0.617649 0.786454i \(-0.711915\pi\)
−0.617649 + 0.786454i \(0.711915\pi\)
\(444\) −28.3923 + 16.3923i −1.34744 + 0.777944i
\(445\) 0 0
\(446\) 5.02628 + 18.7583i 0.238001 + 0.888233i
\(447\) 5.32051i 0.251651i
\(448\) 13.8564 + 16.0000i 0.654654 + 0.755929i
\(449\) −11.9282 −0.562927 −0.281463 0.959572i \(-0.590820\pi\)
−0.281463 + 0.959572i \(0.590820\pi\)
\(450\) 0 0
\(451\) 0.928203 0.0437074
\(452\) −5.46410 9.46410i −0.257010 0.445154i
\(453\) 26.3205 1.23665
\(454\) 7.56218 + 28.2224i 0.354911 + 1.32454i
\(455\) 0 0
\(456\) 20.7846 + 20.7846i 0.973329 + 0.973329i
\(457\) 20.5359i 0.960629i 0.877096 + 0.480314i \(0.159477\pi\)
−0.877096 + 0.480314i \(0.840523\pi\)
\(458\) −3.12436 11.6603i −0.145992 0.544848i
\(459\) 33.5885i 1.56777i
\(460\) 0 0
\(461\) 27.7128i 1.29071i 0.763881 + 0.645357i \(0.223291\pi\)
−0.763881 + 0.645357i \(0.776709\pi\)
\(462\) 0.973721 1.43782i 0.0453016 0.0668935i
\(463\) −16.3923 −0.761815 −0.380908 0.924613i \(-0.624388\pi\)
−0.380908 + 0.924613i \(0.624388\pi\)
\(464\) −15.8564 + 27.4641i −0.736115 + 1.27499i
\(465\) 0 0
\(466\) −3.32051 12.3923i −0.153820 0.574062i
\(467\) 22.5167i 1.04195i −0.853573 0.520973i \(-0.825569\pi\)
0.853573 0.520973i \(-0.174431\pi\)
\(468\) 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
\(473\) 0.535898i 0.0246406i
\(474\) 34.6865 9.29423i 1.59321 0.426898i
\(475\) 0 0
\(476\) −11.1962 + 32.3205i −0.513175 + 1.48141i
\(477\) 0 0
\(478\) −8.77757 32.7583i −0.401477 1.49833i
\(479\) 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
\(482\) −6.00000 22.3923i −0.273293 1.01994i
\(483\) 4.39230 + 5.07180i 0.199857 + 0.230775i
\(484\) 18.9282 10.9282i 0.860373 0.496737i
\(485\) 0 0
\(486\) 0 0
\(487\) 12.7846 0.579326 0.289663 0.957129i \(-0.406457\pi\)
0.289663 + 0.957129i \(0.406457\pi\)
\(488\) −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 \(-0.928467\pi\)
0.974855 0.222841i \(-0.0715330\pi\)
\(492\) −10.3923 + 6.00000i −0.468521 + 0.270501i
\(493\) −51.2487 −2.30813
\(494\) 3.80385 1.01924i 0.171143 0.0458577i
\(495\) 0 0
\(496\) 12.0000 20.7846i 0.538816 0.933257i
\(497\) −12.9282 14.9282i −0.579909 0.669621i
\(498\) −36.5885 + 9.80385i −1.63957 + 0.439321i
\(499\) 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
\(502\) −35.3205 + 9.46410i −1.57643 + 0.422404i
\(503\) 15.5885i 0.695055i −0.937670 0.347527i \(-0.887021\pi\)
0.937670 0.347527i \(-0.112979\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) −0.143594 0.535898i −0.00638351 0.0238236i
\(507\) 22.1436i 0.983432i
\(508\) 26.7846 15.4641i 1.18837 0.686109i
\(509\) 25.8564i 1.14607i −0.819533 0.573033i \(-0.805767\pi\)
0.819533 0.573033i \(-0.194233\pi\)
\(510\) 0 0
\(511\) −25.8564 + 22.3923i −1.14382 + 0.990577i
\(512\) 16.0000 + 16.0000i 0.707107 + 0.707107i
\(513\) 31.1769i 1.37649i
\(514\) 8.19615 2.19615i 0.361517 0.0968681i
\(515\) 0 0
\(516\) −3.46410 6.00000i −0.152499 0.264135i
\(517\) 0.464102 0.0204112
\(518\) −29.3205 19.8564i −1.28827 0.872440i
\(519\) 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
\(523\) 24.2487i 1.06032i −0.847897 0.530161i \(-0.822131\pi\)
0.847897 0.530161i \(-0.177869\pi\)
\(524\) −4.39230 + 2.53590i −0.191879 + 0.110781i
\(525\) 0 0
\(526\) 15.6603 4.19615i 0.682820 0.182961i
\(527\) 38.7846 1.68948
\(528\) 0.928203 1.60770i 0.0403949 0.0699660i
\(529\) −20.8564 −0.906800
\(530\) 0 0
\(531\) 0 0
\(532\) −10.3923 + 30.0000i −0.450564 + 1.30066i
\(533\) 1.60770i 0.0696370i
\(534\) 6.00000 1.60770i 0.259645 0.0695718i
\(535\) 0 0
\(536\) −6.92820 + 6.92820i −0.299253 + 0.299253i
\(537\) 11.0718 0.477783
\(538\) −4.39230 16.3923i −0.189366 0.706722i
\(539\) 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 \(0.446481\pi\)
\(542\) 12.9282 3.46410i 0.555314 0.148796i
\(543\) −1.60770 −0.0689928
\(544\) −9.46410 + 35.3205i −0.405770 + 1.51435i
\(545\) 0 0
\(546\) 2.49038 + 1.68653i 0.106578 + 0.0721770i
\(547\) −21.4641 −0.917739 −0.458869 0.888504i \(-0.651745\pi\)
−0.458869 + 0.888504i \(0.651745\pi\)
\(548\) 20.3923 + 35.3205i 0.871116 + 1.50882i
\(549\) 0 0
\(550\) 0 0
\(551\) −47.5692 −2.02652
\(552\) 5.07180 + 5.07180i 0.215870 + 0.215870i
\(553\) 25.3923 + 29.3205i 1.07979 + 1.24683i
\(554\) −6.14359 22.9282i −0.261016 0.974126i
\(555\) 0 0
\(556\) 12.0000 6.92820i 0.508913 0.293821i
\(557\) 21.8564i 0.926086i −0.886336 0.463043i \(-0.846758\pi\)
0.886336 0.463043i \(-0.153242\pi\)
\(558\) 0 0
\(559\) −0.928203 −0.0392588
\(560\) 0 0
\(561\) 3.00000 0.126660
\(562\) 10.8301 2.90192i 0.456841 0.122410i
\(563\) 19.1769i 0.808211i 0.914712 + 0.404105i \(0.132417\pi\)
−0.914712 + 0.404105i \(0.867583\pi\)
\(564\) −5.19615 + 3.00000i −0.218797 + 0.126323i
\(565\) 0 0
\(566\) −4.43782 16.5622i −0.186536 0.696160i
\(567\) 18.0000 15.5885i 0.755929 0.654654i
\(568\) −14.9282 14.9282i −0.626373 0.626373i
\(569\) −7.07180 −0.296465 −0.148233 0.988953i \(-0.547358\pi\)
−0.148233 + 0.988953i \(0.547358\pi\)
\(570\) 0 0
\(571\) 6.67949i 0.279528i −0.990185 0.139764i \(-0.955366\pi\)
0.990185 0.139764i \(-0.0446344\pi\)
\(572\) −0.124356 0.215390i −0.00519957 0.00900592i
\(573\) 12.4641 0.520695
\(574\) −10.7321 7.26795i −0.447947 0.303358i
\(575\) 0 0
\(576\) 0 0
\(577\) −19.3923 −0.807312 −0.403656 0.914911i \(-0.632261\pi\)
−0.403656 + 0.914911i \(0.632261\pi\)
\(578\) −33.8564 + 9.07180i −1.40824 + 0.377337i
\(579\) 16.3923 0.681241
\(580\) 0 0
\(581\) −26.7846 30.9282i −1.11121 1.28312i
\(582\) 8.49038 + 31.6865i 0.351938 + 1.31345i
\(583\) 0.535898 0.0221946
\(584\) −25.8564 + 25.8564i −1.06995 + 1.06995i
\(585\) 0 0
\(586\) −27.7583 + 7.43782i −1.14669 + 0.307254i
\(587\) 20.5359i 0.847607i 0.905754 + 0.423804i \(0.139305\pi\)
−0.905754 + 0.423804i \(0.860695\pi\)
\(588\) −22.5167 + 9.00000i −0.928571 + 0.371154i
\(589\) 36.0000 1.48335
\(590\) 0 0
\(591\) −23.0718 −0.949047
\(592\) −32.7846 18.9282i −1.34744 0.777944i
\(593\) 30.4641 1.25101 0.625505 0.780220i \(-0.284893\pi\)
0.625505 + 0.780220i \(0.284893\pi\)
\(594\) −1.90192 + 0.509619i −0.0780369 + 0.0209099i
\(595\) 0 0
\(596\) −5.32051 + 3.07180i −0.217937 + 0.125826i
\(597\) 6.00000i 0.245564i
\(598\) 0.928203 0.248711i 0.0379571 0.0101706i
\(599\) 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 \(-0.0975001\pi\)
\(602\) 4.19615 6.19615i 0.171022 0.252536i
\(603\) 0 0
\(604\) 15.1962 + 26.3205i 0.618323 + 1.07097i
\(605\) 0 0
\(606\) 36.5885 9.80385i 1.48630 0.398254i
\(607\) 29.1962i 1.18504i 0.805557 + 0.592518i \(0.201866\pi\)
−0.805557 + 0.592518i \(0.798134\pi\)
\(608\) −8.78461 + 32.7846i −0.356263 + 1.32959i
\(609\) −23.7846 27.4641i −0.963801 1.11290i
\(610\) 0 0
\(611\) 0.803848i 0.0325202i
\(612\) 0 0
\(613\) 10.0000i 0.403896i 0.979396 + 0.201948i \(0.0647272\pi\)
−0.979396 + 0.201948i \(0.935273\pi\)
\(614\) 0.633975 + 2.36603i 0.0255851 + 0.0954850i
\(615\) 0 0
\(616\) 2.00000 + 0.143594i 0.0805823 + 0.00578555i
\(617\) 22.9282i 0.923055i −0.887126 0.461527i \(-0.847302\pi\)
0.887126 0.461527i \(-0.152698\pi\)
\(618\) 16.0981 4.31347i 0.647560 0.173513i
\(619\) 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
\(622\) 10.7321 2.87564i 0.430316 0.115303i
\(623\) 4.39230 + 5.07180i 0.175974 + 0.203197i
\(624\) 2.78461 + 1.60770i 0.111474 + 0.0643593i
\(625\) 0 0
\(626\) 23.9545 6.41858i 0.957414 0.256538i
\(627\) 2.78461 0.111207
\(628\) −13.6077 + 7.85641i −0.543006 + 0.313505i
\(629\) 61.1769i 2.43928i
\(630\) 0 0
\(631\) 38.9090i 1.54894i 0.632610 + 0.774471i \(0.281984\pi\)
−0.632610 + 0.774471i \(0.718016\pi\)
\(632\) 29.3205 + 29.3205i 1.16631 + 1.16631i
\(633\) 5.53590 0.220032
\(634\) 1.12436 + 4.19615i 0.0446539 + 0.166651i
\(635\) 0 0
\(636\) −6.00000 + 3.46410i −0.237915 + 0.137361i
\(637\) −0.464102 + 3.21539i −0.0183884 + 0.127398i
\(638\) 0.777568 + 2.90192i 0.0307842 + 0.114888i
\(639\) 0 0
\(640\) 0 0
\(641\) 8.92820 0.352643 0.176321 0.984333i \(-0.443580\pi\)
0.176321 + 0.984333i \(0.443580\pi\)
\(642\) 1.51666 + 5.66025i 0.0598578 + 0.223392i
\(643\) 7.05256i 0.278126i 0.990284 + 0.139063i \(0.0444090\pi\)
−0.990284 + 0.139063i \(0.955591\pi\)
\(644\) −2.53590 + 7.32051i −0.0999284 + 0.288468i
\(645\) 0 0
\(646\) −52.9808 + 14.1962i −2.08450 + 0.558540i
\(647\) 10.3923i 0.408564i 0.978912 + 0.204282i \(0.0654859\pi\)
−0.978912 + 0.204282i \(0.934514\pi\)
\(648\) 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
\(652\) −36.0000 + 20.7846i −1.40987 + 0.813988i
\(653\) 17.6077i 0.689042i −0.938779 0.344521i \(-0.888041\pi\)
0.938779 0.344521i \(-0.111959\pi\)
\(654\) −1.31347 4.90192i −0.0513606 0.191680i
\(655\) 0 0
\(656\) −12.0000 6.92820i −0.468521 0.270501i
\(657\) 0 0
\(658\) −5.36603 3.63397i −0.209189 0.141667i
\(659\) 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 \(0.719094\pi\)
\(662\) 9.66025 + 36.0526i 0.375456 + 1.40122i
\(663\) 5.19615i 0.201802i
\(664\) −30.9282 30.9282i −1.20025 1.20025i
\(665\) 0 0
\(666\) 0 0
\(667\) −11.6077 −0.449452
\(668\) 5.19615 + 9.00000i 0.201045 + 0.348220i
\(669\) −23.7846 −0.919566
\(670\) 0 0
\(671\) −2.53590 −0.0978973
\(672\) −23.3205 + 11.3205i −0.899608 + 0.436698i
\(673\) 13.1769i 0.507933i 0.967213 + 0.253966i \(0.0817353\pi\)
−0.967213 + 0.253966i \(0.918265\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) −22.1436 + 12.7846i −0.851677 + 0.491716i
\(677\) 25.3923 0.975906 0.487953 0.872870i \(-0.337744\pi\)
0.487953 + 0.872870i \(0.337744\pi\)
\(678\) 12.9282 3.46410i 0.496505 0.133038i
\(679\) −26.7846 + 23.1962i −1.02790 + 0.890187i
\(680\) 0 0
\(681\) −35.7846 −1.37127
\(682\) −0.588457 2.19615i −0.0225332 0.0840950i
\(683\) 7.32051 0.280111 0.140056 0.990144i \(-0.455272\pi\)
0.140056 + 0.990144i \(0.455272\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −19.3660 17.6340i −0.739398 0.673268i
\(687\) 14.7846 0.564068
\(688\) 4.00000 6.92820i 0.152499 0.264135i
\(689\) 0.928203i 0.0353617i
\(690\) 0 0
\(691\) 22.6410 0.861305 0.430652 0.902518i \(-0.358283\pi\)
0.430652 + 0.902518i \(0.358283\pi\)
\(692\) −24.8038 + 14.3205i −0.942901 + 0.544384i
\(693\) 0 0
\(694\) 46.7846 12.5359i 1.77592 0.475856i
\(695\) 0 0
\(696\) −27.4641 27.4641i −1.04102 1.04102i
\(697\) 22.3923i 0.848169i
\(698\) −1.94744 7.26795i −0.0737117 0.275096i
\(699\) 15.7128 0.594313
\(700\) 0 0
\(701\) −37.7846 −1.42711 −0.713553 0.700602i \(-0.752915\pi\)
−0.713553 + 0.700602i \(0.752915\pi\)
\(702\) −0.882686 3.29423i −0.0333148 0.124333i
\(703\) 56.7846i 2.14167i
\(704\) 2.14359 0.0807897
\(705\) 0 0
\(706\) 10.0981 2.70577i 0.380046 0.101833i
\(707\) 26.7846 + 30.9282i 1.00734 + 1.16317i
\(708\) 6.00000 + 10.3923i 0.225494 + 0.390567i
\(709\) −21.0000 −0.788672 −0.394336 0.918966i \(-0.629025\pi\)
−0.394336 + 0.918966i \(0.629025\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 5.07180 + 5.07180i 0.190074 + 0.190074i
\(713\) 8.78461 0.328986
\(714\) −34.6865 23.4904i −1.29811 0.879105i
\(715\) 0 0
\(716\) 6.39230 + 11.0718i 0.238892 + 0.413772i
\(717\) 41.5359 1.55119
\(718\) 9.26795 + 34.5885i 0.345877 + 1.29083i
\(719\) 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
\(722\) −23.2224 + 6.22243i −0.864249 + 0.231575i
\(723\) 28.3923 1.05592
\(724\) −0.928203 1.60770i −0.0344964 0.0597495i
\(725\) 0 0
\(726\) 6.92820 + 25.8564i 0.257130 + 0.959621i
\(727\) 13.6077i 0.504681i 0.967638 + 0.252341i \(0.0812004\pi\)
−0.967638 + 0.252341i \(0.918800\pi\)
\(728\) −0.248711 + 3.46410i −0.00921785 + 0.128388i
\(729\) −27.0000 −1.00000
\(730\) 0 0
\(731\) 12.9282 0.478167
\(732\) 28.3923 16.3923i 1.04941 0.605877i
\(733\) 11.5359 0.426088 0.213044 0.977043i \(-0.431662\pi\)
0.213044 + 0.977043i \(0.431662\pi\)
\(734\) 4.34679 + 16.2224i 0.160443 + 0.598781i
\(735\) 0 0
\(736\) −2.14359 + 8.00000i −0.0790139 + 0.294884i
\(737\) 0.928203i 0.0341908i
\(738\) 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
\(742\) −6.19615 4.19615i −0.227468 0.154046i
\(743\) 30.3923 1.11499 0.557493 0.830182i \(-0.311763\pi\)
0.557493 + 0.830182i \(0.311763\pi\)
\(744\) 20.7846 + 20.7846i 0.762001 + 0.762001i
\(745\) 0 0
\(746\) −1.32051 4.92820i −0.0483472 0.180434i
\(747\) 0 0
\(748\) 1.73205 + 3.00000i 0.0633300 + 0.109691i
\(749\) −4.78461 + 4.14359i −0.174826 + 0.151404i
\(750\) 0 0
\(751\) 25.5885i 0.933736i −0.884327 0.466868i \(-0.845382\pi\)
0.884327 0.466868i \(-0.154618\pi\)
\(752\) −6.00000 3.46410i −0.218797 0.126323i
\(753\) 44.7846i 1.63204i
\(754\) −5.02628 + 1.34679i −0.183046 + 0.0490471i
\(755\) 0 0
\(756\) 25.9808 + 9.00000i 0.944911 + 0.327327i
\(757\) 37.8564i 1.37591i 0.725751 + 0.687957i \(0.241492\pi\)
−0.725751 + 0.687957i \(0.758508\pi\)
\(758\) 2.05256 + 7.66025i 0.0745523 + 0.278233i
\(759\) 0.679492 0.0246640
\(760\) 0 0
\(761\) 42.2487i 1.53151i −0.643130 0.765757i \(-0.722364\pi\)
0.643130 0.765757i \(-0.277636\pi\)
\(762\) 9.80385 + 36.5885i 0.355156 + 1.32546i
\(763\) 4.14359 3.58846i 0.150008 0.129911i
\(764\) 7.19615 + 12.4641i 0.260348 + 0.450935i
\(765\) 0 0
\(766\) −10.0526 37.5167i −0.363214 1.35553i
\(767\) 1.60770 0.0580505
\(768\) −24.0000 + 13.8564i −0.866025 + 0.500000i
\(769\) 18.0000i 0.649097i −0.945869 0.324548i \(-0.894788\pi\)
0.945869 0.324548i \(-0.105212\pi\)
\(770\) 0 0
\(771\) 10.3923i 0.374270i
\(772\) 9.46410 + 16.3923i 0.340620 + 0.589972i
\(773\) −5.53590 −0.199112 −0.0995562 0.995032i \(-0.531742\pi\)
−0.0995562 + 0.995032i \(0.531742\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) −26.7846 + 26.7846i −0.961511 + 0.961511i
\(777\) 32.7846 28.3923i 1.17614 1.01857i
\(778\) −28.4904 + 7.63397i −1.02143 + 0.273691i
\(779\) 20.7846i 0.744686i
\(780\) 0 0
\(781\) −2.00000 −0.0715656
\(782\) −12.9282 + 3.46410i −0.462312 + 0.123876i
\(783\) 41.1962i 1.47223i
\(784\) −22.0000 17.3205i −0.785714 0.618590i
\(785\) 0 0
\(786\) −1.60770 6.00000i −0.0573446 0.214013i
\(787\) 32.6603i 1.16421i −0.813113 0.582106i \(-0.802229\pi\)
0.813113 0.582106i \(-0.197771\pi\)