Properties

Label 700.2.c.e.699.4
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 699.4
Root \(0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 700.699
Dual form 700.2.c.e.699.3

$q$-expansion

\(f(q)\) \(=\) \(q+(1.36603 + 0.366025i) q^{2} +1.73205i q^{3} +(1.73205 + 1.00000i) q^{4} +(-0.633975 + 2.36603i) q^{6} +(2.00000 - 1.73205i) q^{7} +(2.00000 + 2.00000i) q^{8} +O(q^{10})\) \(q+(1.36603 + 0.366025i) q^{2} +1.73205i q^{3} +(1.73205 + 1.00000i) q^{4} +(-0.633975 + 2.36603i) q^{6} +(2.00000 - 1.73205i) q^{7} +(2.00000 + 2.00000i) q^{8} -0.267949i q^{11} +(-1.73205 + 3.00000i) q^{12} -0.464102 q^{13} +(3.36603 - 1.63397i) q^{14} +(2.00000 + 3.46410i) q^{16} +6.46410 q^{17} -6.00000 q^{19} +(3.00000 + 3.46410i) q^{21} +(0.0980762 - 0.366025i) q^{22} -1.46410 q^{23} +(-3.46410 + 3.46410i) q^{24} +(-0.633975 - 0.169873i) q^{26} +5.19615i q^{27} +(5.19615 - 1.00000i) q^{28} -7.92820 q^{29} -6.00000 q^{31} +(1.46410 + 5.46410i) q^{32} +0.464102 q^{33} +(8.83013 + 2.36603i) q^{34} -9.46410i q^{37} +(-8.19615 - 2.19615i) q^{38} -0.803848i q^{39} -3.46410i q^{41} +(2.83013 + 5.83013i) q^{42} -2.00000 q^{43} +(0.267949 - 0.464102i) q^{44} +(-2.00000 - 0.535898i) q^{46} +1.73205i q^{47} +(-6.00000 + 3.46410i) q^{48} +(1.00000 - 6.92820i) q^{49} +11.1962i q^{51} +(-0.803848 - 0.464102i) q^{52} -2.00000i q^{53} +(-1.90192 + 7.09808i) q^{54} +(7.46410 + 0.535898i) q^{56} -10.3923i q^{57} +(-10.8301 - 2.90192i) q^{58} +3.46410 q^{59} +9.46410i q^{61} +(-8.19615 - 2.19615i) q^{62} +8.00000i q^{64} +(0.633975 + 0.169873i) q^{66} -3.46410 q^{67} +(11.1962 + 6.46410i) q^{68} -2.53590i q^{69} -7.46410i q^{71} +12.9282 q^{73} +(3.46410 - 12.9282i) q^{74} +(-10.3923 - 6.00000i) q^{76} +(-0.464102 - 0.535898i) q^{77} +(0.294229 - 1.09808i) q^{78} +14.6603i q^{79} -9.00000 q^{81} +(1.26795 - 4.73205i) q^{82} -15.4641i q^{83} +(1.73205 + 9.00000i) q^{84} +(-2.73205 - 0.732051i) q^{86} -13.7321i q^{87} +(0.535898 - 0.535898i) q^{88} -2.53590i q^{89} +(-0.928203 + 0.803848i) q^{91} +(-2.53590 - 1.46410i) q^{92} -10.3923i q^{93} +(-0.633975 + 2.36603i) q^{94} +(-9.46410 + 2.53590i) q^{96} +13.3923 q^{97} +(3.90192 - 9.09808i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{2} - 6 q^{6} + 8 q^{7} + 8 q^{8} + O(q^{10}) \) \( 4 q + 2 q^{2} - 6 q^{6} + 8 q^{7} + 8 q^{8} + 12 q^{13} + 10 q^{14} + 8 q^{16} + 12 q^{17} - 24 q^{19} + 12 q^{21} - 10 q^{22} + 8 q^{23} - 6 q^{26} - 4 q^{29} - 24 q^{31} - 8 q^{32} - 12 q^{33} + 18 q^{34} - 12 q^{38} - 6 q^{42} - 8 q^{43} + 8 q^{44} - 8 q^{46} - 24 q^{48} + 4 q^{49} - 24 q^{52} - 18 q^{54} + 16 q^{56} - 26 q^{58} - 12 q^{62} + 6 q^{66} + 24 q^{68} + 24 q^{73} + 12 q^{77} - 30 q^{78} - 36 q^{81} + 12 q^{82} - 4 q^{86} + 16 q^{88} + 24 q^{91} - 24 q^{92} - 6 q^{94} - 24 q^{96} + 12 q^{97} + 26 q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.36603 + 0.366025i 0.965926 + 0.258819i
\(3\) 1.73205i 1.00000i 0.866025 + 0.500000i \(0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(4\) 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 \(-0.987138\pi\)
0.999184 0.0403949i \(-0.0128616\pi\)
\(12\) −1.73205 + 3.00000i −0.500000 + 0.866025i
\(13\) −0.464102 −0.128719 −0.0643593 0.997927i \(-0.520500\pi\)
−0.0643593 + 0.997927i \(0.520500\pi\)
\(14\) 3.36603 1.63397i 0.899608 0.436698i
\(15\) 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 \(-0.741620\pi\)
−0.688247 + 0.725476i \(0.741620\pi\)
\(20\) 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 \(-0.548779\pi\)
−0.152643 + 0.988281i \(0.548779\pi\)
\(24\) −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
\(28\) 5.19615 1.00000i 0.981981 0.188982i
\(29\) −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 \(-0.681128\pi\)
−0.538816 + 0.842424i \(0.681128\pi\)
\(32\) 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 \(-0.0871893\pi\)
\(42\) 2.83013 + 5.83013i 0.436698 + 0.899608i
\(43\) −2.00000 −0.304997 −0.152499 0.988304i \(-0.548732\pi\)
−0.152499 + 0.988304i \(0.548732\pi\)
\(44\) 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 \(0.0403175\pi\)
−0.991989 + 0.126323i \(0.959682\pi\)
\(48\) −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
\(56\) 7.46410 + 0.535898i 0.997433 + 0.0716124i
\(57\) 10.3923i 1.37649i
\(58\) −10.8301 2.90192i −1.42207 0.381041i
\(59\) 3.46410 0.450988 0.225494 0.974245i \(-0.427600\pi\)
0.225494 + 0.974245i \(0.427600\pi\)
\(60\) 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 \(-0.567869\pi\)
−0.211604 + 0.977356i \(0.567869\pi\)
\(68\) 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 \(-0.853945\pi\)
0.896565 0.442913i \(-0.146055\pi\)
\(72\) 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 \(0.308658\pi\)
−0.565565 + 0.824704i \(0.691342\pi\)
\(80\) 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 \(-0.677384\pi\)
0.528870 0.848703i \(-0.322616\pi\)
\(84\) 1.73205 + 9.00000i 0.188982 + 0.981981i
\(85\) 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 \(0.262027\pi\)
\(98\) 3.90192 9.09808i 0.394154 0.919044i
\(99\) 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 \(0.108804\pi\)
−0.942146 + 0.335202i \(0.891196\pi\)
\(104\) −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 \(-0.536891\pi\)
−0.115636 + 0.993292i \(0.536891\pi\)
\(108\) −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
\(112\) 10.0000 + 3.46410i 0.944911 + 0.327327i
\(113\) 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 \(-0.740683\pi\)
−0.686109 + 0.727499i \(0.740683\pi\)
\(128\) −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 \(-0.464665\pi\)
0.110781 + 0.993845i \(0.464665\pi\)
\(132\) 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 \(-0.594927\pi\)
−0.293821 + 0.955860i \(0.594927\pi\)
\(140\) 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 \(-0.787812\pi\)
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
\(157\) −7.85641 −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 \(-0.197292\pi\)
0.813988 + 0.580881i \(0.197292\pi\)
\(164\) 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 \(-0.935566\pi\)
0.979582 0.201045i \(-0.0644338\pi\)
\(168\) −0.928203 + 12.9282i −0.0716124 + 0.997433i
\(169\) −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 \(-0.923216\pi\)
0.971046 0.238892i \(-0.0767841\pi\)
\(180\) 0 0
\(181\) 0.928203i 0.0689928i −0.999405 0.0344964i \(-0.989017\pi\)
0.999405 0.0344964i \(-0.0109827\pi\)
\(182\) −1.56218 + 0.758330i −0.115796 + 0.0562112i
\(183\) −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 \(-0.916163\pi\)
0.965515 0.260348i \(-0.0838372\pi\)
\(192\) −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
\(196\) 8.66025 11.0000i 0.618590 0.785714i
\(197\) 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 \(-0.539182\pi\)
−0.122782 + 0.992434i \(0.539182\pi\)
\(200\) 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 \(-0.964910\pi\)
0.993930 0.110016i \(-0.0350902\pi\)
\(212\) 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 \(0.152073\pi\)
−0.888031 + 0.459783i \(0.847927\pi\)
\(224\) 12.3923 + 8.39230i 0.827996 + 0.560734i
\(225\) 0 0
\(226\) 2.00000 7.46410i 0.133038 0.496505i
\(227\) 20.6603i 1.37127i 0.727946 + 0.685635i \(0.240475\pi\)
−0.727946 + 0.685635i \(0.759525\pi\)
\(228\) 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
\(238\) 21.7583 10.5622i 1.41038 0.684644i
\(239\) 23.9808i 1.55119i −0.631233 0.775593i \(-0.717451\pi\)
0.631233 0.775593i \(-0.282549\pi\)
\(240\) 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 \(-0.803825\pi\)
−0.816021 + 0.578022i \(0.803825\pi\)
\(252\) 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 \(-0.385007\pi\)
0.353453 + 0.935452i \(0.385007\pi\)
\(264\) 0.928203 + 0.928203i 0.0571270 + 0.0571270i
\(265\) 0 0
\(266\) −20.1962 + 9.80385i −1.23831 + 0.601112i
\(267\) 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 \(-0.407192\pi\)
0.287452 + 0.957795i \(0.407192\pi\)
\(272\) 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 \(-0.882654\pi\)
0.932814 0.360359i \(-0.117346\pi\)
\(284\) 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 \(0.297719\pi\)
\(294\) 15.7583 + 6.75833i 0.919044 + 0.394154i
\(295\) 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 \(0.0157394\pi\)
−0.998778 + 0.0494267i \(0.984261\pi\)
\(308\) −0.267949 1.39230i −0.0152678 0.0793339i
\(309\) −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
\(313\) −17.5359 −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
\(322\) −4.92820 + 2.39230i −0.274638 + 0.133318i
\(323\) −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 \(0.258311\pi\)
−0.688405 + 0.725326i \(0.741689\pi\)
\(332\) 15.4641 26.7846i 0.848703 1.47000i
\(333\) 0 0
\(334\) 1.90192 7.09808i 0.104069 0.388389i
\(335\) 0 0
\(336\) −6.00000 + 17.3205i −0.327327 + 0.944911i
\(337\) 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 \(-0.128769\pi\)
0.919284 + 0.393596i \(0.128769\pi\)
\(348\) 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 \(0.232928\pi\)
−0.743997 + 0.668183i \(0.767072\pi\)
\(360\) 0 0
\(361\) 17.0000 0.894737
\(362\) 0.339746 1.26795i 0.0178567 0.0666419i
\(363\) 18.9282i 0.993473i
\(364\) −2.41154 + 0.464102i −0.126399 + 0.0243255i
\(365\) 0 0
\(366\) −22.3923 6.00000i −1.17046 0.313625i
\(367\) 11.8756i 0.619904i 0.950752 + 0.309952i \(0.100313\pi\)
−0.950752 + 0.309952i \(0.899687\pi\)
\(368\) −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
\(378\) 8.49038 + 17.4904i 0.436698 + 0.899608i
\(379\) 5.60770i 0.288048i 0.989574 + 0.144024i \(0.0460042\pi\)
−0.989574 + 0.144024i \(0.953996\pi\)
\(380\) 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 \(-0.752436\pi\)
0.712497 0.701675i \(-0.247564\pi\)
\(384\) −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
\(392\) 15.8564 11.8564i 0.800869 0.598839i
\(393\) 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
\(406\) −26.6865 + 12.9545i −1.32443 + 0.642920i
\(407\) −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 \(-0.298215\pi\)
0.592314 + 0.805708i \(0.298215\pi\)
\(420\) 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 \(0.106127\pi\)
−0.944932 + 0.327266i \(0.893873\pi\)
\(432\) −18.0000 + 10.3923i −0.866025 + 0.500000i
\(433\) −31.8564 −1.53092 −0.765461 0.643483i \(-0.777489\pi\)
−0.765461 + 0.643483i \(0.777489\pi\)
\(434\) −20.1962 + 9.80385i −0.969446 + 0.470600i
\(435\) 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 \(-0.103407\pi\)
0.947695 + 0.319179i \(0.103407\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −4.09808 1.09808i −0.194926 0.0522302i
\(443\) 26.0000 1.23530 0.617649 0.786454i \(-0.288085\pi\)
0.617649 + 0.786454i \(0.288085\pi\)
\(444\) 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 \(0.776709\pi\)
\(462\) 1.56218 0.758330i 0.0726791 0.0352807i
\(463\) 16.3923 0.761815 0.380908 0.924613i \(-0.375612\pi\)
0.380908 + 0.924613i \(0.375612\pi\)
\(464\) −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 \(0.174431\pi\)
−0.853573 + 0.520973i \(0.825569\pi\)
\(468\) 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
\(476\) 33.5885 6.46410i 1.53952 0.296282i
\(477\) 0 0
\(478\) 8.77757 32.7583i 0.401477 1.49833i
\(479\) −25.1769 −1.15036 −0.575181 0.818026i \(-0.695068\pi\)
−0.575181 + 0.818026i \(0.695068\pi\)
\(480\) 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 \(-0.593543\pi\)
−0.289663 + 0.957129i \(0.593543\pi\)
\(488\) −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 \(0.928467\pi\)
\(492\) 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 \(0.194123\pi\)
−0.819731 + 0.572748i \(0.805877\pi\)
\(500\) 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 \(0.112979\pi\)
−0.937670 + 0.347527i \(0.887021\pi\)
\(504\) 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
\(518\) −15.4641 31.8564i −0.679454 1.39969i
\(519\) 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 \(0.177869\pi\)
−0.847897 + 0.530161i \(0.822131\pi\)
\(524\) 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
\(532\) −31.1769 + 6.00000i −1.35169 + 0.260133i
\(533\) 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
\(546\) −1.31347 2.70577i −0.0562112 0.115796i
\(547\) 21.4641 0.917739 0.458869 0.888504i \(-0.348255\pi\)
0.458869 + 0.888504i \(0.348255\pi\)
\(548\) −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 \(-0.867583\pi\)
0.914712 0.404105i \(-0.132417\pi\)
\(564\) −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 \(0.0446344\pi\)
−0.990185 + 0.139764i \(0.955366\pi\)
\(572\) −0.124356 + 0.215390i −0.00519957 + 0.00900592i
\(573\) 12.4641 0.520695
\(574\) −5.66025 11.6603i −0.236254 0.486690i
\(575\) 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 \(-0.860695\pi\)
0.905754 0.423804i \(-0.139305\pi\)
\(588\) 19.0526 + 15.0000i 0.785714 + 0.618590i
\(589\) 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 \(-0.933684\pi\)
0.978376 0.206835i \(-0.0663163\pi\)
\(600\) 0 0
\(601\) 14.7846i 0.603077i −0.953454 0.301538i \(-0.902500\pi\)
0.953454 0.301538i \(-0.0975001\pi\)
\(602\) −6.73205 + 3.26795i −0.274378 + 0.133192i
\(603\) 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 \(-0.798134\pi\)
0.805557 0.592518i \(-0.201866\pi\)
\(608\) −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
\(616\) 0.143594 2.00000i 0.00578555 0.0805823i
\(617\) 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 \(-0.504347\pi\)
−0.0136555 + 0.999907i \(0.504347\pi\)
\(620\) 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 \(-0.718016\pi\)
0.632610 0.774471i \(-0.281984\pi\)
\(632\) −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 \(-0.955591\pi\)
0.990284 0.139063i \(-0.0444090\pi\)
\(644\) −7.60770 + 1.46410i −0.299785 + 0.0576937i
\(645\) 0 0
\(646\) −52.9808 14.1962i −2.08450 0.558540i
\(647\) 10.3923i 0.408564i −0.978912 0.204282i \(-0.934514\pi\)
0.978912 0.204282i \(-0.0654859\pi\)
\(648\) −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
\(658\) 2.83013 + 5.83013i 0.110330 + 0.227282i
\(659\) 31.1962i 1.21523i −0.794232 0.607615i \(-0.792126\pi\)
0.794232 0.607615i \(-0.207874\pi\)
\(660\) 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
\(672\) −14.5359 + 21.4641i −0.560734 + 0.827996i
\(673\) 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 \(-0.544728\pi\)
−0.140056 + 0.990144i \(0.544728\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −7.95448 24.9545i −0.303704 0.952767i
\(687\) −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 \(-0.641717\pi\)
−0.430652 + 0.902518i \(0.641717\pi\)
\(692\) −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
\(714\) 18.2942 + 37.6865i 0.684644 + 1.41038i
\(715\) 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 \(-0.755205\pi\)
−0.718573 + 0.695451i \(0.755205\pi\)
\(720\) 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 \(-0.918800\pi\)
0.967638 0.252341i \(-0.0812004\pi\)
\(728\) −3.46410 0.248711i −0.128388 0.00921785i
\(729\) −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 \(-0.974987\pi\)
0.996914 0.0784995i \(-0.0250129\pi\)
\(740\) 0 0
\(741\) 4.82309i 0.177180i
\(742\) −3.26795 6.73205i −0.119970 0.247141i
\(743\) −30.3923 −1.11499 −0.557493 0.830182i \(-0.688237\pi\)
−0.557493 + 0.830182i \(0.688237\pi\)
\(744\) 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 \(0.154618\pi\)
−0.884327 + 0.466868i \(0.845382\pi\)
\(752\) −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
\(756\) 5.19615 + 27.0000i 0.188982 + 0.981981i
\(757\) 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
\(784\) 26.0000 10.3923i 0.928571 0.371154i
\(785\) 0 0
\(786\) −1.60770 + 6.00000i −0.0573446 + 0.214013i
\(787\) 32.6603i 1.16421i